LMFDB - Embedded newform 29.9.f.a.15.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,9,Mod(2,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	29.f (of order $28$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.8139796918$
Analytic rank:	$0$
Dimension:	$228$
Relative dimension:	$19$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			15.8
Character	$\chi$	$=$	29.15
Dual form			29.9.f.a.2.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.51607 + 0.621512i) q^{2} +(67.5754 - 42.4604i) q^{3} +(-219.541 + 50.1088i) q^{4} +(264.780 + 211.155i) q^{5} +(-346.361 + 276.213i) q^{6} +(606.153 - 2655.73i) q^{7} +(2521.16 - 882.193i) q^{8} +(-83.1675 + 172.699i) q^{9} +O(q^{10})$	\(q+(-5.51607 + 0.621512i) q^{2} +(67.5754 - 42.4604i) q^{3} +(-219.541 + 50.1088i) q^{4} +(264.780 + 211.155i) q^{5} +(-346.361 + 276.213i) q^{6} +(606.153 - 2655.73i) q^{7} +(2521.16 - 882.193i) q^{8} +(-83.1675 + 172.699i) q^{9} +(-1591.78 - 1000.18i) q^{10} +(-1969.45 - 689.141i) q^{11} +(-12707.9 + 12707.9i) q^{12} +(-14575.2 - 30265.7i) q^{13} +(-1693.01 + 15025.9i) q^{14} +(26858.3 + 3026.21i) q^{15} +(38580.3 - 18579.3i) q^{16} +(-83330.5 - 83330.5i) q^{17} +(351.423 - 1004.31i) q^{18} +(97302.1 - 154855. i) q^{19} +(-68710.7 - 33089.4i) q^{20} +(-71802.4 - 205199. i) q^{21} +(11291.9 + 2577.31i) q^{22} +(-175466. - 220028. i) q^{23} +(132910. - 166664. i) q^{24} +(-61400.2 - 269012. i) q^{25} +(99208.2 + 157889. i) q^{26} +(60339.7 + 535529. i) q^{27} +613415. i q^{28} +(389422. + 590421. i) q^{29} -150033. q^{30} +(-407677. + 45934.1i) q^{31} +(-780245. + 490261. i) q^{32} +(-162348. + 37054.8i) q^{33} +(511447. + 407866. i) q^{34} +(721268. - 575192. i) q^{35} +(9604.93 - 42081.9i) q^{36} +(2.81148e6 - 983781. i) q^{37} +(-440481. + 914667. i) q^{38} +(-2.27002e6 - 1.42635e6i) q^{39} +(853833. + 298769. i) q^{40} +(-355267. + 355267. i) q^{41} +(523601. + 1.08727e6i) q^{42} +(-457817. + 4.06324e6i) q^{43} +(466907. + 52607.8i) q^{44} +(-58487.4 + 28166.0i) q^{45} +(1.10463e6 + 1.10463e6i) q^{46} +(-1.42653e6 + 4.07679e6i) q^{47} +(1.81819e6 - 2.89364e6i) q^{48} +(-1.49157e6 - 718303. i) q^{49} +(505882. + 1.44573e6i) q^{50} +(-9.16934e6 - 2.09284e6i) q^{51} +(4.71643e6 + 5.91421e6i) q^{52} +(4.24635e6 - 5.32475e6i) q^{53} +(-665675. - 2.91651e6i) q^{54} +(-375956. - 598330. i) q^{55} +(-814656. - 7.23027e6i) q^{56} -1.45959e7i q^{57} +(-2.51503e6 - 3.01477e6i) q^{58} +4.96718e6 q^{59} +(-6.04814e6 + 681462. i) q^{60} +(-4.06782e6 + 2.55598e6i) q^{61} +(2.22022e6 - 506751. i) q^{62} +(408230. + 325553. i) q^{63} +(-4.57136e6 + 3.64554e6i) q^{64} +(2.53153e6 - 1.10914e7i) q^{65} +(872490. - 305298. i) q^{66} +(8.71514e6 - 1.80972e7i) q^{67} +(2.24700e7 + 1.41189e7i) q^{68} +(-2.11997e7 - 7.41809e6i) q^{69} +(-3.62107e6 + 3.62107e6i) q^{70} +(2.78678e6 + 5.78682e6i) q^{71} +(-57324.9 + 508773. i) q^{72} +(2.53184e6 + 285270. i) q^{73} +(-1.48969e7 + 7.17397e6i) q^{74} +(-1.55715e7 - 1.55715e7i) q^{75} +(-1.36022e7 + 3.88728e7i) q^{76} +(-3.02396e6 + 4.81261e6i) q^{77} +(1.34081e7 + 6.45698e6i) q^{78} +(-1.94140e7 - 5.54822e7i) q^{79} +(1.41384e7 + 3.22700e6i) q^{80} +(2.60322e7 + 3.26433e7i) q^{81} +(1.73888e6 - 2.18048e6i) q^{82} +(1.60187e7 + 7.01826e7i) q^{83} +(2.60458e7 + 4.14517e7i) q^{84} +(-4.46860e6 - 3.96599e7i) q^{85} -2.26976e7i q^{86} +(5.13849e7 + 2.33629e7i) q^{87} -5.57326e6 q^{88} +(-867477. + 97741.2i) q^{89} +(305115. - 191716. i) q^{90} +(-8.92123e7 + 2.03621e7i) q^{91} +(4.95473e7 + 3.95127e7i) q^{92} +(-2.55985e7 + 2.04141e7i) q^{93} +(5.33506e6 - 2.33744e7i) q^{94} +(5.84622e7 - 2.04568e7i) q^{95} +(-3.19087e7 + 6.62591e7i) q^{96} +(-4.90325e7 - 3.08091e7i) q^{97} +(8.67405e6 + 3.03518e6i) q^{98} +(282808. - 282808. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9}+O(q^{10}) $ 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9} - 15884 q^{10} + 8376 q^{11} - 5036 q^{12} - 14 q^{13} - 12742 q^{14} + 35516 q^{15} + 245898 q^{16} - 76248 q^{17} + 465008 q^{18} + 164474 q^{19} - 907274 q^{20} - 628270 q^{21} + 1214962 q^{22} + 173408 q^{23} + 1858618 q^{24} + 43976 q^{25} - 4604204 q^{26} - 1727586 q^{27} + 1079922 q^{29} + 8909208 q^{30} + 3657848 q^{31} + 1160364 q^{32} - 4279184 q^{33} - 8655374 q^{34} - 8269058 q^{35} - 3366854 q^{36} - 5622890 q^{37} + 15536626 q^{38} + 16110008 q^{39} - 23544696 q^{40} - 9561672 q^{41} - 14 q^{42} + 5181008 q^{43} + 51041750 q^{44} - 35245194 q^{45} - 43159224 q^{46} - 12806808 q^{47} + 83954488 q^{48} + 10429400 q^{49} + 80809398 q^{50} + 18760882 q^{51} - 93050550 q^{52} - 30960322 q^{53} - 106220916 q^{54} - 126174004 q^{55} - 40136268 q^{56} + 159368354 q^{58} + 11188020 q^{59} + 255893612 q^{60} + 139657128 q^{61} + 102501616 q^{62} + 9797746 q^{63} - 135941792 q^{64} - 14207858 q^{65} - 447597656 q^{66} - 148930894 q^{67} - 167094904 q^{68} + 66986722 q^{69} + 586255934 q^{70} - 15272096 q^{71} + 41230600 q^{72} - 219415072 q^{73} - 347464696 q^{74} + 391507416 q^{75} + 271512490 q^{76} + 240416780 q^{77} + 141747906 q^{78} + 112667220 q^{79} - 375642638 q^{80} - 358099268 q^{81} - 262154910 q^{82} - 109463350 q^{83} - 694921012 q^{84} - 356627386 q^{85} + 199703522 q^{87} + 251202768 q^{88} + 839849154 q^{89} + 675826020 q^{90} + 533256766 q^{91} + 742339570 q^{92} + 78998570 q^{93} - 209116610 q^{94} - 633414122 q^{95} - 431412576 q^{96} - 402046736 q^{97} - 2192087384 q^{98} - 1966368188 q^{99}+O(q^{100}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9 - 15884 * q^10 + 8376 * q^11 - 5036 * q^12 - 14 * q^13 - 12742 * q^14 + 35516 * q^15 + 245898 * q^16 - 76248 * q^17 + 465008 * q^18 + 164474 * q^19 - 907274 * q^20 - 628270 * q^21 + 1214962 * q^22 + 173408 * q^23 + 1858618 * q^24 + 43976 * q^25 - 4604204 * q^26 - 1727586 * q^27 + 1079922 * q^29 + 8909208 * q^30 + 3657848 * q^31 + 1160364 * q^32 - 4279184 * q^33 - 8655374 * q^34 - 8269058 * q^35 - 3366854 * q^36 - 5622890 * q^37 + 15536626 * q^38 + 16110008 * q^39 - 23544696 * q^40 - 9561672 * q^41 - 14 * q^42 + 5181008 * q^43 + 51041750 * q^44 - 35245194 * q^45 - 43159224 * q^46 - 12806808 * q^47 + 83954488 * q^48 + 10429400 * q^49 + 80809398 * q^50 + 18760882 * q^51 - 93050550 * q^52 - 30960322 * q^53 - 106220916 * q^54 - 126174004 * q^55 - 40136268 * q^56 + 159368354 * q^58 + 11188020 * q^59 + 255893612 * q^60 + 139657128 * q^61 + 102501616 * q^62 + 9797746 * q^63 - 135941792 * q^64 - 14207858 * q^65 - 447597656 * q^66 - 148930894 * q^67 - 167094904 * q^68 + 66986722 * q^69 + 586255934 * q^70 - 15272096 * q^71 + 41230600 * q^72 - 219415072 * q^73 - 347464696 * q^74 + 391507416 * q^75 + 271512490 * q^76 + 240416780 * q^77 + 141747906 * q^78 + 112667220 * q^79 - 375642638 * q^80 - 358099268 * q^81 - 262154910 * q^82 - 109463350 * q^83 - 694921012 * q^84 - 356627386 * q^85 + 199703522 * q^87 + 251202768 * q^88 + 839849154 * q^89 + 675826020 * q^90 + 533256766 * q^91 + 742339570 * q^92 + 78998570 * q^93 - 209116610 * q^94 - 633414122 * q^95 - 431412576 * q^96 - 402046736 * q^97 - 2192087384 * q^98 - 1966368188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{27}{28}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−5.51607	+	0.621512i	−0.344754	+	0.0388445i	−0.282644	−	0.959225i	$-0.591212\pi$
$2$	−5.51607	+	0.621512i	−0.344754	+	0.0388445i	−0.0621101	+	0.998069i	$0.519783\pi$
$3$	67.5754	−	42.4604i	0.834264	−	0.524203i	−0.0458594	−	0.998948i	$-0.514603\pi$
$3$	67.5754	−	42.4604i	0.834264	−	0.524203i	0.880123	+	0.474745i	$0.157460\pi$
$4$	−219.541	+	50.1088i	−0.857581	+	0.195737i
$5$	264.780	+	211.155i	0.423648	+	0.337848i	0.811994	−	0.583666i	$-0.198382\pi$
$5$	264.780	+	211.155i	0.423648	+	0.337848i	−0.388346	+	0.921514i	$0.626953\pi$
$6$	−346.361	+	276.213i	−0.267254	+	0.213128i
$7$	606.153	−	2655.73i	0.252459	−	1.10609i	−0.676655	−	0.736300i	$-0.736571\pi$
$7$	606.153	−	2655.73i	0.252459	−	1.10609i	0.929114	−	0.369793i	$-0.120572\pi$
$8$	2521.16	−	882.193i	0.615518	−	0.215379i
$9$	−83.1675	+	172.699i	−0.0126760	+	0.0263221i
$10$	−1591.78	−	1000.18i	−0.159178	−	0.100018i
$11$	−1969.45	−	689.141i	−0.134516	−	0.0470692i	0.262181	−	0.965019i	$-0.415558\pi$
$11$	−1969.45	−	689.141i	−0.134516	−	0.0470692i	−0.396698	+	0.917949i	$0.629844\pi$
$12$	−12707.9	+	12707.9i	−0.612843	+	0.612843i
$13$	−14575.2	−	30265.7i	−0.510318	−	1.05969i	−0.983864	−	0.178917i	$-0.942741\pi$
$13$	−14575.2	−	30265.7i	−0.510318	−	1.05969i	0.473546	−	0.880769i	$-0.342974\pi$
$14$	−1693.01	+	15025.9i	−0.0440705	+	0.391137i
$15$	26858.3	+	3026.21i	0.530535	+	0.0597770i
$16$	38580.3	−	18579.3i	0.588688	−	0.283497i
$17$	−83330.5	−	83330.5i	−0.997719	−	0.997719i	0.00227856	−	0.999997i	$-0.499275\pi$
$17$	−83330.5	−	83330.5i	−0.997719	−	0.997719i	−0.999997	+	0.00227856i	$0.999275\pi$
$18$	351.423	−	1004.31i	0.00334765	−	0.00956704i
$19$	97302.1	−	154855.i	0.746634	−	1.18826i	−0.229966	−	0.973199i	$-0.573861\pi$
$19$	97302.1	−	154855.i	0.746634	−	1.18826i	0.976600	−	0.215063i	$-0.0689957\pi$
$20$	−68710.7	−	33089.4i	−0.429442	−	0.206808i
$21$	−71802.4	−	205199.i	−0.369200	−	1.05511i
$22$	11291.9	+	2577.31i	0.0482034	+	0.0110021i
$23$	−175466.	−	220028.i	−0.627022	−	0.786260i	0.362292	−	0.932065i	$-0.381994\pi$
$23$	−175466.	−	220028.i	−0.627022	−	0.786260i	−0.989313	+	0.145805i	$0.953423\pi$
$24$	132910.	−	166664.i	0.400602	−	0.502339i
$25$	−61400.2	−	269012.i	−0.157185	−	0.688671i
$26$	99208.2	+	157889.i	0.217097	+	0.345508i
$27$	60339.7	+	535529.i	0.113540	+	1.00769i
$28$			613415.i			0.997980i
$29$	389422.	+	590421.i	0.550591	+	0.834775i
$29$	389422.	+	590421.i	0.550591	+	0.834775i
$30$	−150033.			−0.185226
$31$	−407677.	+	45934.1i	−0.441437	+	0.0497380i	−0.329886	−	0.944021i	$-0.607010\pi$
$31$	−407677.	+	45934.1i	−0.441437	+	0.0497380i	−0.111551	+	0.993759i	$0.535582\pi$
$32$	−780245.	+	490261.i	−0.744100	+	0.467549i
$33$	−162348.	+	37054.8i	−0.136896	+	0.0312456i
$34$	511447.	+	407866.i	0.382724	+	0.305212i
$35$	721268.	−	575192.i	0.480645	−	0.383302i
$36$	9604.93	−	42081.9i	0.00571853	−	0.0250545i
$37$	2.81148e6	−	983781.i	1.50013	−	0.524918i	0.549566	−	0.835450i	$-0.314793\pi$
$37$	2.81148e6	−	983781.i	1.50013	−	0.524918i	0.950563	+	0.310532i	$0.100507\pi$
$38$	−440481.	+	914667.i	−0.211248	+	0.438661i
$39$	−2.27002e6	−	1.42635e6i	−0.981230	−	0.616548i
$40$	853833.	+	298769.i	0.333529	+	0.116707i
$41$	−355267.	+	355267.i	−0.125724	+	0.125724i	−0.767169	−	0.641445i	$-0.778335\pi$
$41$	−355267.	+	355267.i	−0.125724	+	0.125724i	0.641445	+	0.767169i	$0.278335\pi$
$42$	523601.	+	1.08727e6i	0.168269	+	0.349413i
$43$	−457817.	+	4.06324e6i	−0.133912	+	1.18850i	0.729494	+	0.683987i	$0.239756\pi$
$43$	−457817.	+	4.06324e6i	−0.133912	+	1.18850i	−0.863406	+	0.504511i	$0.831673\pi$
$44$	466907.	+	52607.8i	0.124572	+	0.0140359i
$45$	−58487.4	+	28166.0i	−0.0142630	+	0.00686872i
$46$	1.10463e6	+	1.10463e6i	0.246710	+	0.246710i
$47$	−1.42653e6	+	4.07679e6i	−0.292341	+	0.835462i	0.700244	+	0.713904i	$0.253075\pi$
$47$	−1.42653e6	+	4.07679e6i	−0.292341	+	0.835462i	−0.992584	+	0.121558i	$0.961211\pi$
$48$	1.81819e6	−	2.89364e6i	0.342511	−	0.545103i
$49$	−1.49157e6	−	718303.i	−0.258738	−	0.124602i
$50$	505882.	+	1.44573e6i	0.0809411	+	0.231316i
$51$	−9.16934e6	−	2.09284e6i	−1.35537	−	0.309354i
$52$	4.71643e6	+	5.91421e6i	0.645059	+	0.808879i
$53$	4.24635e6	−	5.32475e6i	0.538161	−	0.674832i	−0.436193	−	0.899853i	$-0.643674\pi$
$53$	4.24635e6	−	5.32475e6i	0.538161	−	0.674832i	0.974354	+	0.225021i	$0.0722451\pi$
$54$	−665675.	−	2.91651e6i	−0.0782866	−	0.342996i
$55$	−375956.	−	598330.i	−0.0410853	−	0.0653868i
$56$	−814656.	−	7.23027e6i	−0.0828366	−	0.735195i
$57$		−	1.45959e7i		−	1.38271i
$58$	−2.51503e6	−	3.01477e6i	−0.222245	−	0.266405i
$59$	4.96718e6			0.409922			0.204961	−	0.978770i	$-0.434293\pi$
$59$	4.96718e6			0.409922			0.204961	+	0.978770i	$0.434293\pi$
$60$	−6.04814e6	+	681462.i	−0.466678	+	0.0525819i
$61$	−4.06782e6	+	2.55598e6i	−0.293794	+	0.184603i	−0.670861	−	0.741583i	$-0.734075\pi$
$61$	−4.06782e6	+	2.55598e6i	−0.293794	+	0.184603i	0.377068	+	0.926186i	$0.376932\pi$
$62$	2.22022e6	−	506751.i	0.150255	−	0.0342948i
$63$	408230.	+	325553.i	0.0259145	+	0.0206661i
$64$	−4.57136e6	+	3.64554e6i	−0.272474	+	0.217291i
$65$	2.53153e6	−	1.10914e7i	0.141818	−	0.621344i
$66$	872490.	−	305298.i	0.0459817	−	0.0160897i
$67$	8.71514e6	−	1.80972e7i	0.432489	−	0.898073i	−0.564852	−	0.825192i	$-0.691067\pi$
$67$	8.71514e6	−	1.80972e7i	0.432489	−	0.898073i	0.997341	−	0.0728802i	$-0.0232191\pi$
$68$	2.24700e7	+	1.41189e7i	1.05092	+	0.660334i
$69$	−2.11997e7	−	7.41809e6i	−0.935261	−	0.327262i
$70$	−3.62107e6	+	3.62107e6i	−0.150815	+	0.150815i
$71$	2.78678e6	+	5.78682e6i	0.109665	+	0.227723i	0.948578	−	0.316544i	$-0.102522\pi$
$71$	2.78678e6	+	5.78682e6i	0.109665	+	0.227723i	−0.838912	+	0.544266i	$0.816808\pi$
$72$	−57324.9	+	508773.i	−0.00213311	+	0.0189319i
$73$	2.53184e6	+	285270.i	0.0891547	+	0.0100453i	0.156429	−	0.987689i	$-0.450002\pi$
$73$	2.53184e6	+	285270.i	0.0891547	+	0.0100453i	−0.0672744	+	0.997735i	$0.521430\pi$
$74$	−1.48969e7	+	7.17397e6i	−0.496786	+	0.239239i
$75$	−1.55715e7	−	1.55715e7i	−0.492136	−	0.492136i
$76$	−1.36022e7	+	3.88728e7i	−0.407712	+	1.16518i
$77$	−3.02396e6	+	4.81261e6i	−0.0860227	+	0.136904i
$78$	1.34081e7	+	6.45698e6i	0.362233	+	0.174442i
$79$	−1.94140e7	−	5.54822e7i	−0.498434	−	1.42444i	−0.868617	−	0.495484i	$-0.834991\pi$
$79$	−1.94140e7	−	5.54822e7i	−0.498434	−	1.42444i	0.370183	−	0.928959i	$-0.379295\pi$
$80$	1.41384e7	+	3.22700e6i	0.345176	+	0.0787841i
$81$	2.60322e7	+	3.26433e7i	0.604742	+	0.758323i
$82$	1.73888e6	−	2.18048e6i	0.0384603	−	0.0482277i
$83$	1.60187e7	+	7.01826e7i	0.337533	+	1.47883i	0.804181	+	0.594384i	$0.202604\pi$
$83$	1.60187e7	+	7.01826e7i	0.337533	+	1.47883i	−0.466649	+	0.884443i	$0.654539\pi$
$84$	2.60458e7	+	4.14517e7i	0.523144	+	0.832579i
$85$	−4.46860e6	−	3.96599e7i	−0.0856043	−	0.759759i
$86$		−	2.26976e7i		−	0.414941i
$87$	5.13849e7	+	2.33629e7i	0.896930	+	0.407802i
$88$	−5.57326e6			−0.0929349
$89$	−867477.	+	97741.2i	−0.0138260	+	0.00155782i	−0.118875	−	0.992909i	$-0.537929\pi$
$89$	−867477.	+	97741.2i	−0.0138260	+	0.00155782i	0.105049	+	0.994467i	$0.466500\pi$
$90$	305115.	−	191716.i	0.00465043	−	0.00292206i
$91$	−8.92123e7	+	2.03621e7i	−1.30095	+	0.296932i
$92$	4.95473e7	+	3.95127e7i	0.691622	+	0.551551i
$93$	−2.55985e7	+	2.04141e7i	−0.342202	+	0.272897i
$94$	5.33506e6	−	2.33744e7i	0.0683326	−	0.299385i
$95$	5.84622e7	−	2.04568e7i	0.717762	−	0.251156i
$96$	−3.19087e7	+	6.62591e7i	−0.375685	+	0.780118i
$97$	−4.90325e7	−	3.08091e7i	−0.553856	−	0.348011i	0.225845	−	0.974163i	$-0.427486\pi$
$97$	−4.90325e7	−	3.08091e7i	−0.553856	−	0.348011i	−0.779701	+	0.626153i	$0.784629\pi$
$98$	8.67405e6	+	3.03518e6i	0.0940411	+	0.0329064i
$99$	282808.	−	282808.i	0.00294409	−	0.00294409i
$100$	2.69597e7	+	5.59824e7i	0.269597	+	0.559824i
$101$	8.48654e6	−	7.53201e7i	0.0815540	−	0.723811i	−0.884689	−	0.466181i	$-0.845630\pi$
$101$	8.48654e6	−	7.53201e7i	0.0815540	−	0.723811i	0.966243	−	0.257631i	$-0.0829418\pi$
$102$	5.18794e7	+	5.84540e6i	0.479285	+	0.0540025i
$103$	−1.32350e8	+	6.37366e7i	−1.17592	+	0.566291i	−0.916719	−	0.399533i	$-0.869172\pi$
$103$	−1.32350e8	+	6.37366e7i	−1.17592	+	0.566291i	−0.259197	+	0.965824i	$0.583458\pi$
$104$	−6.34466e7	−	6.34466e7i	−0.542344	−	0.542344i
$105$	2.43171e7	−	6.94941e7i	0.200057	−	0.571730i
$106$	−2.01137e7	+	3.20108e7i	−0.159320	+	0.253556i
$107$	1.09864e8	+	5.29075e7i	0.838144	+	0.403629i	0.803163	−	0.595759i	$-0.203149\pi$
$107$	1.09864e8	+	5.29075e7i	0.838144	+	0.403629i	0.0349806	+	0.999388i	$0.488863\pi$
$108$	−4.00817e7	−	1.14547e8i	−0.294613	−	0.841955i
$109$	6.41220e6	+	1.46354e6i	0.0454257	+	0.0103681i	0.245173	−	0.969479i	$-0.421155\pi$
$109$	6.41220e6	+	1.46354e6i	0.0454257	+	0.0103681i	−0.199748	+	0.979847i	$0.564012\pi$
$110$	2.44567e6	+	3.06677e6i	0.0167042	+	0.0209464i
$111$	1.48215e8	−	1.85856e8i	0.976340	−	1.22429i
$112$	−2.59560e7	−	1.13721e8i	−0.164955	−	0.722715i
$113$	−1.35158e7	−	2.15102e7i	−0.0828947	−	0.131926i	0.802704	−	0.596378i	$-0.203394\pi$
$113$	−1.35158e7	−	2.15102e7i	−0.0828947	−	0.131926i	−0.885598	+	0.464452i	$0.846251\pi$
$114$	9.07152e6	+	8.05120e7i	0.0537107	+	0.476696i
$115$		−	9.53096e7i		−	0.544936i
$116$	−1.15079e8	−	1.10108e8i	−0.635573	−	0.608116i
$117$	6.43904e6			0.0343620
$118$	−2.73993e7	+	3.08716e6i	−0.141322	+	0.0159232i
$119$	−2.71814e8	+	1.70792e8i	−1.35545	+	0.851687i
$120$	7.03840e7	−	1.60647e7i	0.339429	−	0.0774724i
$121$	−1.64189e8	−	1.30936e8i	−0.765952	−	0.610827i
$122$	2.08498e7	−	1.66272e7i	0.0941158	−	0.0750548i
$123$	−8.92252e6	+	3.90921e7i	−0.0389823	+	0.170792i
$124$	8.72000e7	−	3.05126e7i	0.368833	−	0.129060i
$125$	9.79448e7	−	2.03385e8i	0.401182	−	0.833063i
$126$	−2.45416e6	−	1.54205e6i	−0.00973690	−	0.00611810i
$127$	3.17861e8	+	1.11224e8i	1.22186	+	0.427548i	0.862695	−	0.505725i	$-0.168775\pi$
$127$	3.17861e8	+	1.11224e8i	1.22186	+	0.427548i	0.359168	+	0.933273i	$0.383061\pi$
$128$	1.89757e8	−	1.89757e8i	0.706901	−	0.706901i
$129$	1.41590e8	+	2.94014e8i	0.511296	+	1.06172i
$130$	−7.07070e6	+	6.27542e7i	−0.0247565	+	0.219720i
$131$	−1.24633e8	−	1.40428e7i	−0.423204	−	0.0476836i	−0.102205	−	0.994763i	$-0.532590\pi$
$131$	−1.24633e8	−	1.40428e7i	−0.423204	−	0.0476836i	−0.320998	+	0.947080i	$0.604018\pi$
$132$	3.37852e7	−	1.62701e7i	0.111283	−	0.0535912i
$133$	−3.52274e8	−	3.52274e8i	−1.12583	−	1.12583i
$134$	−3.68257e7	+	1.05242e8i	−0.114217	+	0.326414i
$135$	−9.71030e7	+	1.54539e8i	−0.292346	+	0.465266i
$136$	−2.83603e8	−	1.36576e8i	−0.829002	−	0.399226i
$137$	1.43398e8	+	4.09809e8i	0.407063	+	1.16332i	0.946894	+	0.321546i	$0.104202\pi$
$137$	1.43398e8	+	4.09809e8i	0.407063	+	1.16332i	−0.539831	+	0.841774i	$0.681512\pi$
$138$	1.21549e8	+	2.77428e7i	0.335148	+	0.0764952i
$139$	2.58933e8	+	3.24692e8i	0.693631	+	0.869786i	0.996530	−	0.0832365i	$-0.0265257\pi$
$139$	2.58933e8	+	3.24692e8i	0.693631	+	0.869786i	−0.302898	+	0.953023i	$0.597954\pi$
$140$	−1.29526e8	+	1.62420e8i	−0.337166	+	0.422792i
$141$	7.67038e7	+	3.36061e8i	0.194062	+	0.850241i
$142$	−1.89687e7	−	3.01885e7i	−0.0466534	−	0.0742485i
$143$	7.84780e6	+	6.96512e7i	0.0187674	+	0.166565i
$144$			8.20797e6i			0.0190891i
$145$	−2.15590e7	+	2.38560e8i	−0.0487704	+	0.539667i
$146$	−1.41431e7			−0.0311267
$147$	−1.31293e8	+	1.47932e7i	−0.281172	+	0.0316805i
$148$	−5.67939e8	+	3.56860e8i	−1.18374	+	0.743791i
$149$	8.94474e8	−	2.04158e8i	1.81477	−	0.414210i	0.826005	−	0.563663i	$-0.190608\pi$
$149$	8.94474e8	−	2.04158e8i	1.81477	−	0.414210i	0.988769	+	0.149453i	$0.0477511\pi$
$150$	9.55713e7	+	7.62156e7i	0.188783	+	0.150549i
$151$	−3.70406e8	+	2.95389e8i	−0.712475	+	0.568180i	−0.911244	−	0.411866i	$-0.864877\pi$
$151$	−3.70406e8	+	2.95389e8i	−0.712475	+	0.568180i	0.198769	+	0.980046i	$0.436306\pi$
$152$	1.08702e8	−	4.76255e8i	0.203640	−	0.892206i
$153$	2.13215e7	−	7.46071e6i	0.0389092	−	0.0136149i
$154$	1.36893e7	−	2.84261e7i	0.0243387	−	0.0505399i
$155$	−1.17644e8	−	7.39205e7i	−0.203818	−	0.128067i
$156$	5.69834e8	+	1.99394e8i	0.962166	+	0.336676i
$157$	3.27791e8	−	3.27791e8i	0.539509	−	0.539509i	−0.383876	−	0.923385i	$-0.625411\pi$
$157$	3.27791e8	−	3.27791e8i	0.539509	−	0.539509i	0.923385	+	0.383876i	$0.125411\pi$
$158$	1.41572e8	+	2.93977e8i	0.227169	+	0.471721i
$159$	6.08573e7	−	5.40123e8i	0.0952191	−	0.845093i
$160$	−3.10114e8	−	3.49415e7i	−0.473197	−	0.0533165i
$161$	−6.90694e8	+	3.32621e8i	−1.02797	+	0.495046i
$162$	−1.63883e8	−	1.63883e8i	−0.237944	−	0.237944i
$163$	1.43808e8	−	4.10980e8i	0.203720	−	0.582198i	−0.796014	−	0.605279i	$-0.793062\pi$
$163$	1.43808e8	−	4.10980e8i	0.203720	−	0.582198i	0.999734	+	0.0230806i	$0.00734744\pi$
$164$	6.01937e7	−	9.57977e7i	0.0832100	−	0.132428i
$165$	−5.08107e7	−	2.44691e7i	−0.0685519	−	0.0330129i
$166$	−1.31980e8	−	3.77176e8i	−0.173810	−	0.496720i
$167$	1.17207e9	+	2.67517e8i	1.50691	+	0.343942i	0.894669	−	0.446730i	$-0.147412\pi$
$167$	1.17207e9	+	2.67517e8i	1.50691	+	0.343942i	0.612240	+	0.790672i	$0.290269\pi$
$168$	−3.62051e8	−	4.53998e8i	−0.454499	−	0.569923i
$169$	−1.94976e8	+	2.44492e8i	−0.239020	+	0.299722i
$170$	4.92982e7	+	2.15989e8i	0.0590249	+	0.258605i
$171$	1.86510e7	+	2.96829e7i	0.0218131	+	0.0347154i
$172$	−1.03094e8	−	9.14987e8i	−0.117793	−	1.04544i
$173$			8.93266e8i			0.997232i	0.866823	+	0.498616i	$0.166158\pi$
$173$			8.93266e8i			0.997232i	−0.866823	+	0.498616i	$0.833842\pi$
$174$	−2.97963e8	−	9.69348e7i	−0.325061	−	0.105751i
$175$	−7.51641e8			−0.801416
$176$	−8.87857e7	+	1.00037e7i	−0.0925321	+	0.0104259i
$177$	3.35659e8	−	2.10908e8i	0.341983	−	0.214882i
$178$	4.72432e6	−	1.07829e6i	0.00470608	−	0.00107413i
$179$	−6.14730e8	−	4.90231e8i	−0.598787	−	0.477517i	0.276570	−	0.960994i	$-0.410802\pi$
$179$	−6.14730e8	−	4.90231e8i	−0.598787	−	0.477517i	−0.875357	+	0.483477i	$0.839374\pi$
$180$	1.14290e7	−	9.11433e6i	0.0108873	−	0.00868230i
$181$	−8.86308e7	+	3.88317e8i	−0.0825791	+	0.361803i	−0.999287	−	0.0377552i	$-0.987979\pi$
$181$	−8.86308e7	+	3.88317e8i	−0.0825791	+	0.361803i	0.916708	+	0.399558i	$0.130836\pi$
$182$	4.79446e8	−	1.67765e8i	0.436972	−	0.152903i
$183$	−1.66356e8	+	3.45443e8i	−0.148332	+	0.308015i
$184$	−6.36486e8	−	3.99931e8i	−0.555287	−	0.348910i
$185$	9.52155e8	+	3.33173e8i	0.812869	+	0.284435i
$186$	1.28516e8	−	1.28516e8i	0.107375	−	0.107375i
$187$	1.06689e8	+	2.21542e8i	0.0872474	+	0.181171i
$188$	1.08899e8	−	9.66503e8i	0.0871749	−	0.773698i
$189$	1.45880e9	+	1.64367e8i	1.14327	+	0.128815i
$190$	−3.09767e8	+	1.49176e8i	−0.237695	+	0.114468i
$191$	−1.74479e9	−	1.74479e9i	−1.31102	−	1.31102i	−0.920664	−	0.390355i	$-0.872352\pi$
$191$	−1.74479e9	−	1.74479e9i	−1.31102	−	1.31102i	−0.390355	−	0.920664i	$-0.627648\pi$
$192$	−1.54120e8	+	4.40451e8i	−0.113411	+	0.324110i
$193$	−1.22591e9	+	1.95103e9i	−0.883548	+	1.40616i	0.0300544	+	0.999548i	$0.490432\pi$
$193$	−1.22591e9	+	1.95103e9i	−0.883548	+	1.40616i	−0.913602	+	0.406610i	$0.866711\pi$
$194$	2.89615e8	+	1.39471e8i	0.204462	+	0.0984639i
$195$	−2.99875e8	−	8.56994e8i	−0.207397	−	0.592706i
$196$	3.63454e8	+	8.29561e7i	0.246278	+	0.0562113i
$197$	8.17253e8	+	1.02480e9i	0.542615	+	0.680418i	0.975238	−	0.221157i	$-0.0709834\pi$
$197$	8.17253e8	+	1.02480e9i	0.542615	+	0.680418i	−0.432623	+	0.901575i	$0.642412\pi$
$198$	−1.38422e6	+	1.73576e6i	−0.000900627	+	0.00112935i
$199$	−4.95307e8	−	2.17008e9i	−0.315836	−	1.38377i	−0.844781	−	0.535113i	$-0.820269\pi$
$199$	−4.95307e8	−	2.17008e9i	−0.315836	−	1.38377i	0.528944	−	0.848657i	$-0.322588\pi$
$200$	−3.92120e8	−	6.24056e8i	−0.245075	−	0.390035i
$201$	−1.79485e8	−	1.59297e9i	−0.109962	−	0.975941i
$202$			4.20745e8i			0.252705i
$203$	1.80405e9	−	6.76316e8i	1.06234	−	0.398259i
$204$	2.11791e9			1.22289
$205$	−1.69084e8	+	1.90512e7i	−0.0957387	+	0.0107872i
$206$	6.90441e8	−	4.33833e8i	0.383405	−	0.240909i
$207$	5.25917e7	−	1.20037e7i	0.0286442	−	0.00653784i
$208$	−1.12463e9	−	8.96862e8i	−0.600836	−	0.479151i
$209$	−2.98349e8	+	2.37925e8i	−0.156365	+	0.124697i
$210$	−9.09431e7	+	3.98448e8i	−0.0467619	+	0.204877i
$211$	9.94512e7	−	3.47995e7i	0.0501742	−	0.0175567i	−0.305075	−	0.952328i	$-0.598682\pi$
$211$	9.94512e7	−	3.47995e7i	0.0501742	−	0.0175567i	0.355249	+	0.934772i	$0.384396\pi$
$212$	−6.65430e8	+	1.38178e9i	−0.329427	+	0.684061i
$213$	4.34029e8	+	2.72718e8i	0.210863	+	0.132494i
$214$	−6.38897e8	−	2.23560e8i	−0.304632	−	0.106595i
$215$	−9.79194e8	+	9.79194e8i	−0.458263	+	0.458263i
$216$	6.24567e8	+	1.29693e9i	0.286922	+	0.595799i
$217$	−1.25126e8	+	1.11052e9i	−0.0564297	+	0.500828i
$218$	−3.62797e7	−	4.08775e6i	−0.0160634	−	0.00180991i
$219$	1.83203e8	−	8.82257e7i	0.0796443	−	0.0383547i
$220$	1.12519e8	+	1.12519e8i	0.0480326	+	0.0480326i
$221$	−1.30750e9	+	3.73661e9i	−0.548115	+	1.56642i
$222$	−7.02054e8	+	1.11731e9i	−0.289040	+	0.460005i
$223$	−1.06045e9	−	5.10686e8i	−0.428816	−	0.206507i	0.207011	−	0.978339i	$-0.433627\pi$
$223$	−1.06045e9	−	5.10686e8i	−0.428816	−	0.206507i	−0.635827	+	0.771832i	$0.719341\pi$
$224$	8.29052e8	+	2.36929e9i	0.329298	+	0.941081i
$225$	5.15646e7	+	1.17693e7i	0.0201197	+	0.00459219i
$226$	8.79227e7	+	1.10252e8i	0.0337029	+	0.0422621i
$227$	1.11344e9	−	1.39621e9i	0.419337	−	0.525831i	−0.526630	−	0.850094i	$-0.676545\pi$
$227$	1.11344e9	−	1.39621e9i	0.419337	−	0.525831i	0.945967	+	0.324263i	$0.105116\pi$
$228$	7.31383e8	+	3.20440e9i	0.270648	+	1.18579i
$229$	1.08168e9	+	1.72149e9i	0.393330	+	0.625981i	0.983417	−	0.181358i	$-0.0580494\pi$
$229$	1.08168e9	+	1.72149e9i	0.393330	+	0.625981i	−0.590087	+	0.807340i	$0.700907\pi$
$230$	5.92360e7	+	5.25734e8i	0.0211677	+	0.187869i
$231$			4.53612e8i			0.159308i
$232$	1.50266e9	+	1.14500e9i	0.518692	+	0.395234i
$233$	1.87181e9			0.635093			0.317547	−	0.948243i	$-0.397141\pi$
$233$	1.87181e9			0.635093			0.317547	+	0.948243i	$0.397141\pi$
$234$	−3.55182e7	+	4.00194e6i	−0.0118464	+	0.00133477i
$235$	−1.23855e9	+	7.78233e8i	−0.406109	+	0.255175i
$236$	−1.09050e9	+	2.48899e8i	−0.351542	+	0.0802371i
$237$	−3.66771e9	−	2.92490e9i	−1.16252	−	0.927080i
$238$	1.39320e9	−	1.11104e9i	0.434215	−	0.346275i
$239$	5.89235e8	−	2.58161e9i	0.180591	−	0.791222i	−0.800758	−	0.598988i	$-0.795570\pi$
$239$	5.89235e8	−	2.58161e9i	0.180591	−	0.791222i	0.981349	−	0.192234i	$-0.0615732\pi$
$240$	1.09243e9	−	3.82257e8i	0.329266	−	0.115215i
$241$	1.95577e9	−	4.06120e9i	0.579762	−	1.20389i	−0.380498	−	0.924782i	$-0.624247\pi$
$241$	1.95577e9	−	4.06120e9i	0.579762	−	1.20389i	0.960260	−	0.279107i	$-0.0900384\pi$
$242$	9.87054e8	+	6.20207e8i	0.287793	+	0.180832i
$243$	−1.92240e8	−	6.72676e7i	−0.0551338	−	0.0192922i
$244$	7.64975e8	−	7.64975e8i	0.215818	−	0.215818i
$245$	−2.43265e8	−	5.05145e8i	−0.0675174	−	0.140201i
$246$	2.49210e7	−	2.21180e8i	0.00680496	−	0.0603957i
$247$	−6.10500e9	−	6.87869e8i	−1.64021	−	0.184807i
$248$	−9.87296e8	+	4.75457e8i	−0.261000	+	0.125691i
$249$	4.06246e9	+	4.06246e9i	1.05680	+	1.05680i
$250$	−4.13864e8	+	1.18276e9i	−0.105949	+	0.302786i
$251$	2.18654e9	−	3.47985e9i	0.550886	−	0.876730i	−0.448973	−	0.893545i	$-0.648210\pi$
$251$	2.18654e9	−	3.47985e9i	0.550886	−	0.876730i	0.999859	+	0.0168155i	$0.00535280\pi$
$252$	−1.05936e8	−	5.10162e7i	−0.0262689	−	0.0126504i
$253$	1.93942e8	+	5.54255e8i	0.0473359	+	0.135278i
$254$	−1.82247e9	−	4.15967e8i	−0.437850	−	0.0999365i
$255$	−1.98594e9	−	2.49029e9i	−0.469684	−	0.588966i
$256$	4.48127e6	−	5.61933e6i	0.00104338	−	0.00130835i
$257$	−1.00319e9	−	4.39526e9i	−0.229959	−	1.00752i	−0.949672	−	0.313245i	$-0.898584\pi$
$257$	−1.00319e9	−	4.39526e9i	−0.229959	−	1.00752i	0.719714	−	0.694271i	$-0.244273\pi$
$258$	−9.63751e8	−	1.53380e9i	−0.217513	−	0.346171i
$259$	−9.08467e8	−	8.06286e9i	−0.201888	−	1.79180i
$260$			2.56186e9i			0.560612i
$261$	−1.34352e8	+	1.81491e7i	−0.0289523	+	0.00391105i
$262$	6.96215e8			0.147754
$263$	−4.58801e9	+	5.16945e8i	−0.958962	+	0.108049i	−0.577549	−	0.816356i	$-0.695991\pi$
$263$	−4.58801e9	+	5.16945e8i	−0.958962	+	0.108049i	−0.381413	+	0.924405i	$0.624562\pi$
$264$	−3.76615e8	+	2.36643e8i	−0.0775322	+	0.0487167i
$265$	2.24869e9	−	5.13250e8i	0.455981	−	0.104075i
$266$	2.16211e9	+	1.72423e9i	0.431868	+	0.344404i
$267$	−5.44700e7	+	4.34383e7i	−0.0107180	+	0.00854729i
$268$	−1.00650e9	+	4.40977e9i	−0.195108	+	0.854825i
$269$	8.54960e9	−	2.99163e9i	1.63281	−	0.571346i	0.650650	−	0.759377i	$-0.274496\pi$
$269$	8.54960e9	−	2.99163e9i	1.63281	−	0.571346i	0.982163	+	0.188031i	$0.0602106\pi$
$270$	4.39579e8	−	9.12796e8i	0.0827146	−	0.171759i
$271$	5.17055e9	+	3.24887e9i	0.958649	+	0.602359i	0.917901	−	0.396811i	$-0.129883\pi$
$271$	5.17055e9	+	3.24887e9i	0.958649	+	0.602359i	0.0407482	+	0.999169i	$0.487026\pi$
$272$	−4.76313e9	−	1.66669e9i	−0.870196	−	0.304495i
$273$	−5.16397e9	+	5.16397e9i	−0.929679	+	0.929679i
$274$	−1.04570e9	−	2.17141e9i	−0.185525	−	0.385247i
$275$	−6.44624e7	+	5.72119e8i	−0.0112713	+	0.100036i
$276$	5.02591e9	+	5.66284e8i	0.866120	+	0.0975883i
$277$	−3.26116e9	+	1.57049e9i	−0.553928	+	0.266758i	−0.689838	−	0.723963i	$-0.742318\pi$
$277$	−3.26116e9	+	1.57049e9i	−0.553928	+	0.266758i	0.135910	+	0.990721i	$0.456604\pi$
$278$	−1.63009e9	−	1.63009e9i	−0.272919	−	0.272919i
$279$	2.59727e7	−	7.42256e7i	0.00428647	−	0.0122500i
$280$	1.31100e9	−	2.08645e9i	0.213291	−	0.339450i
$281$	−6.75334e9	−	3.25224e9i	−1.08316	−	0.521624i	−0.194836	−	0.980836i	$-0.562417\pi$
$281$	−6.75334e9	−	3.25224e9i	−1.08316	−	0.521624i	−0.888327	+	0.459212i	$0.848132\pi$
$282$	−6.31970e8	−	1.80607e9i	−0.0999309	−	0.285586i
$283$	−2.49700e9	−	5.69924e8i	−0.389290	−	0.0888528i	0.0233961	−	0.999726i	$-0.492552\pi$
$283$	−2.49700e9	−	5.69924e8i	−0.389290	−	0.0888528i	−0.412686	+	0.910873i	$0.635409\pi$
$284$	−9.01783e8	−	1.13080e9i	−0.138621	−	0.173825i
$285$	3.08200e9	−	3.86470e9i	0.467146	−	0.585783i
$286$	−8.65780e7	−	3.79323e8i	−0.0129403	−	0.0566950i
$287$	7.28148e8	+	1.15884e9i	0.107323	+	0.170803i
$288$	−1.97765e7	−	1.75521e8i	−0.00287462	−	0.0255129i
$289$			6.91218e9i			0.990886i
$290$	−2.93470e7	−	1.32931e9i	−0.00414927	−	0.187947i
$291$	−4.62156e9			−0.644490
$292$	−5.70136e8	+	6.42389e7i	−0.0784237	+	0.00883623i
$293$	4.09926e9	−	2.57574e9i	0.556205	−	0.349487i	−0.224414	−	0.974494i	$-0.572047\pi$
$293$	4.09926e9	−	2.57574e9i	0.556205	−	0.349487i	0.780619	+	0.625007i	$0.214904\pi$
$294$	7.15027e8	−	1.63200e8i	0.0957047	−	0.0218440i
$295$	1.31521e9	+	1.04884e9i	0.173663	+	0.138491i
$296$	6.22032e9	−	4.96054e9i	0.810301	−	0.646193i
$297$	2.50219e8	−	1.09628e9i	0.0321584	−	0.140895i
$298$	−4.80709e9	+	1.68207e9i	−0.609561	+	0.213295i
$299$	−4.10184e9	+	8.51756e9i	−0.513209	+	1.06569i
$300$	4.19885e9	+	2.63831e9i	0.518376	+	0.325718i
$301$	1.05134e10	+	3.67878e9i	1.28078	+	0.448165i
$302$	1.85959e9	−	1.85959e9i	0.223558	−	0.223558i
$303$	−2.62464e9	−	5.45013e9i	−0.311386	−	0.646601i
$304$	8.76840e8	−	7.78217e9i	0.102666	−	0.911184i
$305$	−1.61679e9	−	1.82168e8i	−0.186833	−	0.0210510i
$306$	−1.12974e8	+	5.44054e7i	−0.0128852	+	0.00620520i
$307$	9.84095e9	+	9.84095e9i	1.10786	+	1.10786i	0.993432	+	0.114425i	$0.0365024\pi$
$307$	9.84095e9	+	9.84095e9i	1.10786	+	1.10786i	0.114425	+	0.993432i	$0.463498\pi$
$308$	4.22729e8	−	1.20809e9i	0.0469742	−	0.134245i
$309$	−6.23734e9	+	9.92667e9i	−0.684173	+	1.08885i
$310$	6.94874e8	+	3.34634e8i	0.0752418	+	0.0362345i
$311$	1.54184e9	+	4.40631e9i	0.164815	+	0.471014i	0.996438	−	0.0843263i	$-0.0268738\pi$
$311$	1.54184e9	+	4.40631e9i	0.164815	+	0.471014i	−0.831623	+	0.555340i	$0.812588\pi$
$312$	−6.98140e9	−	1.59346e9i	−0.736757	−	0.168160i
$313$	8.19996e8	+	1.02824e9i	0.0854347	+	0.107132i	0.822712	−	0.568459i	$-0.192460\pi$
$313$	8.19996e8	+	1.02824e9i	0.0854347	+	0.107132i	−0.737277	+	0.675591i	$0.763889\pi$
$314$	−1.60439e9	+	2.01185e9i	−0.165041	+	0.206955i
$315$	3.93491e7	+	1.72400e8i	0.00399662	+	0.0175103i
$316$	7.04232e9	+	1.12078e10i	0.706264	+	1.12401i
$317$	2.21459e9	+	1.96551e10i	0.219309	+	1.94642i	0.310459	+	0.950587i	$0.399517\pi$
$317$	2.21459e9	+	1.96551e10i	0.219309	+	1.94642i	−0.0911498	+	0.995837i	$0.529054\pi$
$318$			3.01718e9i			0.295048i
$319$	−3.60066e8	−	1.43117e9i	−0.0347711	−	0.138207i
$320$	−1.98018e9			−0.188845
$321$	9.67054e9	−	1.08961e9i	0.910816	−	0.102624i
$322$	3.60319e9	−	2.26403e9i	0.335169	−	0.210600i
$323$	−2.10124e10	+	4.79595e9i	−1.93048	+	0.440620i
$324$	−7.35084e9	−	5.86210e9i	−0.667048	−	0.531953i
$325$	−7.24691e9	+	5.77922e9i	−0.649560	+	0.518007i
$326$	−5.37827e8	+	2.35637e9i	−0.0476181	+	0.208629i
$327$	4.95450e8	−	1.73365e8i	0.0433320	−	0.0151625i
$328$	−5.82272e8	+	1.20910e9i	−0.0503073	+	0.104464i
$329$	9.96215e9	+	6.25963e9i	0.850295	+	0.534276i
$330$	2.95483e8	+	1.03394e8i	0.0249159	+	0.00871846i
$331$	8.53241e9	−	8.53241e9i	0.710820	−	0.710820i	−0.255886	−	0.966707i	$-0.582367\pi$
$331$	8.53241e9	−	8.53241e9i	0.710820	−	0.710820i	0.966707	+	0.255886i	$0.0823673\pi$
$332$	−7.03353e9	−	1.46053e10i	−0.578923	−	1.20215i
$333$	−6.39261e7	+	5.67360e8i	−0.00519878	+	0.0461404i
$334$	−6.63147e9	−	7.47187e8i	−0.532873	−	0.0600404i
$335$	6.12890e9	−	2.95152e9i	0.486635	−	0.234351i
$336$	−6.58261e9	−	6.58261e9i	−0.516465	−	0.516465i
$337$	7.17434e9	−	2.05031e10i	0.556240	−	1.58964i	−0.230972	−	0.972961i	$-0.574190\pi$
$337$	7.17434e9	−	2.05031e10i	0.556240	−	1.58964i	0.787212	−	0.616683i	$-0.211524\pi$
$338$	9.23547e8	−	1.46982e9i	0.0707607	−	0.112615i
$339$	−1.82667e9	−	8.79676e8i	−0.138312	−	0.0666076i
$340$	2.96835e9	+	8.48305e9i	0.222126	+	0.634799i
$341$	8.34554e8	+	1.90482e8i	0.0617216	+	0.0140875i
$342$	−1.21329e8	−	1.52141e8i	−0.00886868	−	0.0111210i
$343$	6.97921e9	−	8.75166e9i	0.504232	−	0.632286i
$344$	2.43033e9	+	1.06480e10i	0.173553	+	0.760384i
$345$	−4.04689e9	−	6.44058e9i	−0.285657	−	0.454620i
$346$	−5.55175e8	−	4.92732e9i	−0.0387370	−	0.343800i
$347$		−	4.28877e9i		−	0.295812i	−0.989001	−	0.147906i	$-0.952747\pi$
$347$		−	4.28877e9i		−	0.295812i	0.989001	−	0.147906i	$-0.0472533\pi$
$348$	−1.24518e10	−	2.55427e9i	−0.849012	−	0.174160i
$349$	−1.26894e9			−0.0855340			−0.0427670	−	0.999085i	$-0.513617\pi$
$349$	−1.26894e9			−0.0855340			−0.0427670	+	0.999085i	$0.513617\pi$
$350$	4.14610e9	−	4.67153e8i	0.276292	−	0.0311306i
$351$	1.53287e10	−	9.63167e9i	1.00990	−	0.634560i
$352$	1.87451e9	−	4.27846e8i	0.122101	−	0.0278687i
$353$	−4.03529e9	−	3.21804e9i	−0.259882	−	0.207249i	0.484877	−	0.874582i	$-0.338864\pi$
$353$	−4.03529e9	−	3.21804e9i	−0.259882	−	0.207249i	−0.744759	+	0.667333i	$0.767436\pi$
$354$	−1.72043e9	+	1.37200e9i	−0.109553	+	0.0873658i
$355$	−4.84031e8	+	2.12068e9i	−0.0304761	+	0.133525i
$356$	1.85549e8	−	6.49264e7i	0.0115520	−	0.00404223i
$357$	−1.11160e10	+	2.30827e10i	−0.684348	+	1.42106i
$358$	3.69558e9	+	2.32209e9i	0.224983	+	0.141366i
$359$	2.82671e9	+	9.89109e8i	0.170178	+	0.0595479i	0.414023	−	0.910266i	$-0.364123\pi$
$359$	2.82671e9	+	9.89109e8i	0.170178	+	0.0595479i	−0.243845	+	0.969814i	$0.578409\pi$
$360$	−1.22608e8	+	1.22608e8i	−0.00729979	+	0.00729979i
$361$	−7.14361e9	−	1.48339e10i	−0.420619	−	0.873425i
$362$	2.47550e8	−	2.19707e9i	0.0144155	−	0.127941i
$363$	−1.66547e10	−	1.87654e9i	−0.959203	−	0.108076i
$364$	1.85654e10	−	8.94063e9i	1.05755	−	0.509287i
$365$	6.10144e8	+	6.10144e8i	0.0343764	+	0.0343764i
$366$	7.02936e8	−	2.00888e9i	0.0391734	−	0.111951i
$367$	6.16364e9	−	9.80938e9i	0.339761	−	0.540726i	−0.632520	−	0.774544i	$-0.717979\pi$
$367$	6.16364e9	−	9.80938e9i	0.339761	−	0.540726i	0.972280	+	0.233818i	$0.0751221\pi$
$368$	−1.08575e10	−	5.22869e9i	−0.592023	−	0.285103i
$369$	−3.18077e7	−	9.09011e7i	−0.00171564	−	0.00490302i
$370$	−5.45922e9	−	1.24603e9i	−0.291289	−	0.0664848i
$371$	−1.15672e10	−	1.45048e10i	−0.610564	−	0.765623i
$372$	4.59699e9	−	5.76445e9i	0.240050	−	0.301013i
$373$	8.23928e9	+	3.60987e10i	0.425651	+	1.86490i	0.497467	+	0.867483i	$0.334263\pi$
$373$	8.23928e9	+	3.60987e10i	0.425651	+	1.86490i	−0.0718159	+	0.997418i	$0.522879\pi$
$374$	−7.26194e8	−	1.15573e9i	−0.0371164	−	0.0590705i
$375$	−2.01713e9	−	1.79026e10i	−0.102002	−	0.905295i
$376$			1.15367e10i			0.577206i
$377$	1.21936e10	−	2.03916e10i	0.603623	−	1.00945i
$378$	−8.14898e9			−0.399150
$379$	−2.22819e9	+	2.51056e8i	−0.107993	+	0.0121679i	−0.165795	−	0.986160i	$-0.553019\pi$
$379$	−2.22819e9	+	2.51056e8i	−0.107993	+	0.0121679i	0.0578027	+	0.998328i	$0.481591\pi$
$380$	−1.18098e10	+	7.42057e9i	−0.566379	+	0.355879i
$381$	2.62022e10	−	5.98048e9i	1.24348	−	0.283816i
$382$	1.07088e10	+	8.53996e9i	0.502905	+	0.401054i
$383$	−3.25196e10	+	2.59335e10i	−1.51130	+	1.20522i	−0.595644	+	0.803249i	$0.703103\pi$
$383$	−3.25196e10	+	2.59335e10i	−1.51130	+	1.20522i	−0.915653	+	0.401970i	$0.868326\pi$
$384$	4.76574e9	−	2.08801e10i	0.219182	−	0.960301i
$385$	−1.81689e9	+	6.35757e8i	−0.0826962	+	0.0289367i
$386$	5.54963e9	−	1.15239e10i	0.249985	−	0.519100i
$387$	−6.63642e8	−	4.16994e8i	−0.0295863	−	0.0185903i
$388$	1.23084e10	+	4.30691e9i	0.543095	+	0.190037i
$389$	−6.70607e9	+	6.70607e9i	−0.292867	+	0.292867i	−0.838212	−	0.545345i	$-0.816399\pi$
$389$	−6.70607e9	+	6.70607e9i	−0.292867	+	0.292867i	0.545345	+	0.838212i	$0.316399\pi$
$390$	2.18676e9	+	4.54086e9i	0.0945243	+	0.196282i
$391$	−3.71333e9	+	3.29567e10i	−0.158875	+	1.41006i
$392$	−4.39418e9	−	4.95105e8i	−0.186094	−	0.0209678i
$393$	−9.01842e9	+	4.34304e9i	−0.378060	+	0.182064i
$394$	−5.14495e9	−	5.14495e9i	−0.213499	−	0.213499i
$395$	6.57488e9	−	1.87899e10i	0.270085	−	0.771857i
$396$	−4.79168e7	+	7.62592e7i	−0.00194853	+	0.00310107i
$397$	2.26377e10	+	1.09018e10i	0.911320	+	0.438868i	0.829964	−	0.557817i	$-0.188361\pi$
$397$	2.26377e10	+	1.09018e10i	0.911320	+	0.438868i	0.0813554	+	0.996685i	$0.474075\pi$
$398$	4.08088e9	+	1.16625e10i	0.162638	+	0.464792i
$399$	−3.87628e10	−	8.84735e9i	−1.52941	−	0.349077i
$400$	−7.36688e9	−	9.23778e9i	−0.287769	−	0.360851i
$401$	2.10046e10	−	2.63390e10i	0.812340	−	1.01864i	−0.187001	−	0.982360i	$-0.559877\pi$
$401$	2.10046e10	−	2.63390e10i	0.812340	−	1.01864i	0.999342	−	0.0362826i	$-0.0115517\pi$
$402$	1.98010e9	+	8.67539e9i	0.0758199	+	0.332188i
$403$	7.33219e9	+	1.16691e10i	0.277980	+	0.442403i
$404$	1.91106e9	+	1.69611e10i	0.0717378	+	0.636690i
$405$			1.41401e10i			0.525573i
$406$	−9.53091e9	+	4.85184e9i	−0.350776	+	0.178567i
$407$	−6.21504e9			−0.226499
$408$	−2.49637e10	+	2.81273e9i	−0.900882	+	0.101505i
$409$	−1.24847e9	+	7.84463e8i	−0.0446153	+	0.0280336i	−0.554155	−	0.832413i	$-0.686959\pi$
$409$	−1.24847e9	+	7.84463e8i	−0.0446153	+	0.0280336i	0.509540	+	0.860447i	$0.329816\pi$
$410$	9.20839e8	−	2.10176e8i	0.0325873	−	0.00743784i
$411$	2.70909e10	+	2.16042e10i	0.949413	+	0.757132i
$412$	2.58625e10	−	2.06247e10i	0.897599	−	0.715811i
$413$	3.01087e9	−	1.31915e10i	0.103488	−	0.453412i
$414$	−2.82639e8	+	9.88997e7i	−0.00962124	+	0.00336662i
$415$	−1.05780e10	+	2.19654e10i	−0.356624	+	0.740537i
$416$	2.62103e10	+	1.64690e10i	0.875183	+	0.549914i
$417$	3.12841e10	+	1.09468e10i	1.03462	+	0.362028i
$418$	1.49784e9	−	1.49784e9i	0.0490637	−	0.0490637i
$419$	−2.23880e10	−	4.64892e10i	−0.726372	−	1.50833i	−0.856118	−	0.516780i	$-0.827130\pi$
$419$	−2.23880e10	−	4.64892e10i	−0.726372	−	1.50833i	0.129746	−	0.991547i	$-0.458584\pi$
$420$	−1.85632e9	+	1.64753e10i	−0.0596562	+	0.529464i
$421$	1.74652e10	+	1.96786e9i	0.555963	+	0.0626420i	0.385476	−	0.922718i	$-0.374037\pi$
$421$	1.74652e10	+	1.96786e9i	0.555963	+	0.0626420i	0.170487	+	0.985360i	$0.445466\pi$
$422$	−5.26951e8	+	2.53766e8i	−0.0166158	+	0.00800173i
$423$	−5.85417e8	−	5.85417e8i	−0.0182854	−	0.0182854i
$424$	6.00827e9	−	1.71707e10i	0.185903	−	0.531280i
$425$	−1.73004e10	+	2.75334e10i	−0.530274	+	0.843926i
$426$	−2.56363e9	−	1.23458e9i	−0.0778425	−	0.0374870i
$427$	4.32227e9	+	1.23523e10i	0.130017	+	0.371568i
$428$	−2.67707e10	−	6.11023e9i	−0.797782	−	0.182088i
$429$	3.48774e9	+	4.37348e9i	0.102971	+	0.129121i
$430$	4.79272e9	−	6.00988e9i	0.140187	−	0.175789i
$431$	2.83808e9	+	1.24345e10i	0.0822462	+	0.360344i	0.999258	−	0.0385159i	$-0.0122630\pi$
$431$	2.83808e9	+	1.24345e10i	0.0822462	+	0.360344i	−0.917012	+	0.398860i	$0.869406\pi$
$432$	1.22777e10	+	1.95398e10i	0.352518	+	0.561029i
$433$	−3.05329e9	−	2.70987e10i	−0.0868592	−	0.770897i	−0.959341	−	0.282250i	$-0.908919\pi$
$433$	−3.05329e9	−	2.70987e10i	−0.0868592	−	0.770897i	0.872482	−	0.488647i	$-0.162509\pi$
$434$		−	6.20348e9i		−	0.174854i
$435$	8.67251e9	+	1.70362e10i	0.242208	+	0.475790i
$436$	−1.48108e9			−0.0409856
$437$	−5.11458e10	+	5.76274e9i	−1.40244	+	0.158017i
$438$	−9.55724e8	+	6.00521e8i	−0.0259679	+	0.0163167i
$439$	−7.59813e9	+	1.73422e9i	−0.204573	+	0.0466925i	−0.323579	−	0.946201i	$-0.604886\pi$
$439$	−7.59813e9	+	1.73422e9i	−0.204573	+	0.0466925i	0.119006	+	0.992893i	$0.462029\pi$
$440$	−1.47569e9	−	1.17682e9i	−0.0393717	−	0.0313979i
$441$	2.48101e8	−	1.97854e8i	0.00655955	−	0.00523106i
$442$	4.88989e9	−	2.14240e10i	0.128118	−	0.561322i
$443$	1.23477e10	−	4.32064e9i	0.320605	−	0.112185i	−0.165178	−	0.986264i	$-0.552820\pi$
$443$	1.23477e10	−	4.32064e9i	0.320605	−	0.112185i	0.485784	+	0.874079i	$0.338534\pi$
$444$	−2.32263e10	+	4.82299e10i	−0.597652	+	1.24104i
$445$	−2.50329e8	−	1.57292e8i	−0.00638369	−	0.00401114i
$446$	6.16692e9	+	2.15790e9i	0.155858	+	0.0545370i
$447$	5.17758e10	−	5.17758e10i	1.29687	−	1.29687i
$448$	6.91062e9	+	1.43501e10i	0.171556	+	0.356239i
$449$	−4.90078e9	+	4.34957e10i	−0.120581	+	1.07019i	0.777049	+	0.629440i	$0.216716\pi$
$449$	−4.90078e9	+	4.34957e10i	−0.120581	+	1.07019i	−0.897630	+	0.440749i	$0.854713\pi$
$450$	−2.91749e8	−	3.28722e7i	−0.00711474	−	0.000801639i
$451$	9.44511e8	−	4.54852e8i	0.0228297	−	0.0109942i
$452$	4.04511e9	+	4.04511e9i	0.0969119	+	0.0969119i
$453$	−1.24880e10	+	3.56886e10i	−0.296551	+	0.847493i
$454$	−5.27404e9	+	8.39359e9i	−0.124142	+	0.197572i
$455$	−2.79212e10	−	1.34461e10i	−0.651461	−	0.313727i
$456$	−1.28764e10	−	3.67986e10i	−0.297807	−	0.851084i
$457$	−5.40855e10	−	1.23447e10i	−1.23998	−	0.283018i	−0.448263	−	0.893902i	$-0.647957\pi$
$457$	−5.40855e10	−	1.23447e10i	−1.23998	−	0.283018i	−0.791720	+	0.610884i	$0.790814\pi$
$458$	−7.03655e9	−	8.82355e9i	−0.159918	−	0.200531i
$459$	3.95978e10	−	4.96541e10i	0.892114	−	1.11868i
$460$	4.77585e9	+	2.09243e10i	0.106664	+	0.467327i
$461$	2.02046e10	+	3.21554e10i	0.447349	+	0.711952i	0.991934	−	0.126754i	$-0.0404558\pi$
$461$	2.02046e10	+	3.21554e10i	0.447349	+	0.711952i	−0.544585	+	0.838706i	$0.683313\pi$
$462$	−2.81925e8	−	2.50216e9i	−0.00618822	−	0.0549220i
$463$		−	8.66867e9i		−	0.188638i	−0.995542	−	0.0943189i	$-0.969933\pi$
$463$		−	8.66867e9i		−	0.188638i	0.995542	−	0.0943189i	$-0.0300673\pi$
$464$	2.59936e10	+	1.55434e10i	0.560783	+	0.335331i
$465$	−1.10885e10			−0.237171
$466$	−1.03250e10	+	1.16335e9i	−0.218951	+	0.0246699i
$467$	5.92302e10	−	3.72168e10i	1.24530	−	0.782477i	0.262110	−	0.965038i	$-0.415582\pi$
$467$	5.92302e10	−	3.72168e10i	1.24530	−	0.782477i	0.983194	+	0.182562i	$0.0584389\pi$
$468$	−1.41363e9	+	3.22652e8i	−0.0294682	+	0.00672592i
$469$	−4.27785e10	−	3.41147e10i	−0.884166	−	0.705099i
$470$	6.34825e9	−	5.06256e9i	0.130096	−	0.103748i
$471$	8.23246e9	−	3.60688e10i	0.167281	−	0.732905i
$472$	1.25231e10	−	4.38201e9i	0.252315	−	0.0882887i
$473$	3.70179e9	−	7.68685e9i	0.0739550	−	0.153569i
$474$	2.20492e10	+	1.38544e10i	0.436796	+	0.274457i
$475$	−4.76323e10	−	1.66673e10i	−0.935680	−	0.327409i
$476$	5.11161e10	−	5.11161e10i	0.995704	−	0.995704i
$477$	5.66422e8	+	1.17619e9i	0.0109412	+	0.0227197i
$478$	−1.64576e9	+	1.46065e10i	−0.0315250	+	0.279792i
$479$	−1.76259e10	−	1.98596e9i	−0.334818	−	0.0377250i	−0.0570450	−	0.998372i	$-0.518168\pi$
$479$	−1.76259e10	−	1.98596e9i	−0.334818	−	0.0377250i	−0.277773	+	0.960647i	$0.589596\pi$
$480$	−2.24397e10	+	1.08064e10i	−0.422720	+	0.203571i
$481$	−7.07527e10	−	7.07527e10i	−1.32179	−	1.32179i
$482$	−8.26408e9	+	2.36174e10i	−0.153111	+	0.437566i
$483$	−3.25507e10	+	5.18041e10i	−0.598097	+	0.951866i
$484$	4.26072e10	+	2.05185e10i	0.776428	+	0.373908i
$485$	−6.47731e9	−	1.85111e10i	−0.117065	−	0.334553i
$486$	1.10222e9	+	2.51574e8i	0.0197570	+	0.00450941i
$487$	−2.38887e10	−	2.99554e10i	−0.424694	−	0.532549i	0.522744	−	0.852490i	$-0.324908\pi$
$487$	−2.38887e10	−	2.99554e10i	−0.424694	−	0.532549i	−0.947438	+	0.319941i	$0.896337\pi$
$488$	−8.00076e9	+	1.00326e10i	−0.141076	+	0.176903i
$489$	−7.73250e9	−	3.38783e10i	−0.135234	−	0.592497i
$490$	1.65582e9	+	2.63522e9i	0.0287230	+	0.0457123i
$491$	−8.23931e9	−	7.31259e10i	−0.141764	−	1.25819i	−0.840106	−	0.542423i	$-0.817507\pi$
$491$	−8.23931e9	−	7.31259e10i	−0.141764	−	1.25819i	0.698342	−	0.715764i	$-0.253921\pi$
$492$		−	9.02941e9i		−	0.154099i
$493$	1.67493e10	−	8.16508e10i	0.283536	−	1.38221i
$494$	3.41031e10			0.572646
$495$	1.34598e8	−	1.51656e7i	0.00224192	−	0.000252603i
$496$	−1.48748e10	+	9.34649e9i	−0.245768	+	0.154426i
$497$	1.70574e10	−	3.89325e9i	0.279569	−	0.0638097i
$498$	−2.49336e10	−	1.98839e10i	−0.405386	−	0.323284i
$499$	−1.88799e10	+	1.50562e10i	−0.304508	+	0.242837i	−0.763807	−	0.645445i	$-0.776672\pi$
$499$	−1.88799e10	+	1.50562e10i	−0.304508	+	0.242837i	0.459299	+	0.888282i	$0.348101\pi$
$500$	−1.13115e10	+	4.95591e10i	−0.180985	+	0.792946i
$501$	9.05618e10	−	3.16889e10i	1.43745	−	0.502987i
$502$	−9.89831e9	+	2.05541e10i	−0.155864	+	0.323655i
$503$	8.56166e10	+	5.37965e10i	1.33748	+	0.840392i	0.995071	−	0.0991605i	$-0.0316157\pi$
$503$	8.56166e10	+	5.37965e10i	1.33748	+	0.840392i	0.342405	+	0.939553i	$0.388759\pi$
$504$	1.31641e9	+	4.60633e8i	0.0204019	+	0.00713893i
$505$	1.81513e10	−	1.81513e10i	0.279088	−	0.279088i
$506$	−1.41427e9	−	2.93677e9i	−0.0215740	−	0.0447990i
$507$	−2.79434e9	+	2.48004e10i	−0.0422909	+	0.375342i
$508$	−7.53568e10	−	8.49067e9i	−1.13153	−	0.127493i
$509$	3.56438e9	−	1.71651e9i	0.0531022	−	0.0255727i	−0.407144	−	0.913364i	$-0.633475\pi$
$509$	3.56438e9	−	1.71651e9i	0.0531022	−	0.0255727i	0.460246	+	0.887791i	$0.347761\pi$
$510$	1.25023e10	+	1.25023e10i	0.184804	+	0.184804i
$511$	2.29228e9	−	6.55096e9i	0.0336189	−	0.0960774i
$512$	−3.65715e10	+	5.82033e10i	−0.532186	+	0.846969i
$513$	8.88008e10	+	4.27642e10i	1.28218	+	0.617463i
$514$	8.26536e9	+	2.36210e10i	0.118416	+	0.338413i
$515$	−4.85020e10	−	1.10703e10i	−0.689495	−	0.157373i
$516$	−4.58174e10	−	5.74532e10i	−0.646296	−	0.810429i
$517$	5.61896e9	−	7.04595e9i	0.0786491	−	0.0986229i
$518$	1.00223e10	+	4.39107e10i	0.139203	+	0.609889i
$519$	3.79285e10	+	6.03628e10i	0.522752	+	0.831955i
$520$	−3.40232e9	−	3.01965e10i	−0.0465331	−	0.412993i
$521$			1.31773e11i			1.78844i	0.447623	+	0.894222i	$0.352271\pi$
$521$			1.31773e11i			1.78844i	−0.447623	+	0.894222i	$0.647729\pi$
$522$	7.29817e8	−	1.83613e8i	0.00982952	−	0.00247299i
$523$	−1.22419e11			−1.63623			−0.818113	−	0.575057i	$-0.804980\pi$
$523$	−1.22419e11			−1.63623			−0.818113	+	0.575057i	$0.804980\pi$
$524$	2.80658e10	−	3.16226e9i	0.372265	−	0.0419442i
$525$	−5.07924e10	+	3.19150e10i	−0.668593	+	0.420105i
$526$	2.49865e10	−	5.70300e9i	0.326409	−	0.0745008i
$527$	3.77996e10	+	3.01442e10i	0.490055	+	0.390806i
$528$	−5.57496e9	+	4.44588e9i	−0.0717309	+	0.0572035i
$529$	−1.97978e8	+	8.67398e8i	−0.00252810	+	0.0110763i
$530$	−1.20850e10	+	4.22871e9i	−0.153159	+	0.0535926i
$531$	−4.13108e8	+	8.57827e8i	−0.00519619	+	0.0107900i
$532$	9.49906e10	+	5.96865e10i	1.18586	+	0.745126i
$533$	1.59305e10	+	5.57432e9i	0.197388	+	0.0690690i
$534$	2.73463e8	−	2.73463e8i	0.00336305	−	0.00336305i
$535$	1.79180e10	+	3.72071e10i	0.218713	+	0.454162i
$536$	6.00708e9	−	5.33143e10i	0.0727787	−	0.645929i
$537$	−6.23561e10	−	7.02584e9i	−0.749862	−	0.0844892i
$538$	−4.53008e10	+	2.18157e10i	−0.540726	+	0.260400i
$539$	2.44257e9	+	2.44257e9i	0.0289395	+	0.0289395i
$540$	1.35743e10	−	3.87932e10i	0.159641	−	0.456227i
$541$	−8.65826e10	+	1.37795e11i	−1.01074	+	1.60859i	−0.240702	+	0.970599i	$0.577378\pi$
$541$	−8.65826e10	+	1.37795e11i	−1.01074	+	1.60859i	−0.770043	+	0.637992i	$0.779765\pi$
$542$	−3.05403e10	−	1.47074e10i	−0.353897	−	0.170428i
$543$	1.04988e10	+	3.00040e10i	0.120765	+	0.345127i
$544$	1.05872e11	+	2.41646e10i	1.20889	+	0.275920i
$545$	1.38879e9	+	1.74149e9i	0.0157416	+	0.0197394i
$546$	2.52753e10	−	3.16943e10i	0.284398	−	0.356624i
$547$	3.87586e10	+	1.69813e11i	0.432931	+	1.89680i	0.442353	+	0.896841i	$0.354144\pi$
$547$	3.87586e10	+	1.69813e11i	0.432931	+	1.89680i	−0.00942184	+	0.999956i	$0.502999\pi$
$548$	−5.20168e10	−	8.27843e10i	−0.576795	−	0.917964i
$549$	−1.03105e8	−	9.15083e8i	−0.00113499	−	0.0100733i
$550$		−	3.19591e9i		−	0.0349256i
$551$	1.29321e11	−	2.85501e9i	1.40302	−	0.0309743i
$552$	−5.99920e10			−0.646156
$553$	−1.59113e11	+	1.79278e10i	−1.70140	+	0.191702i
$554$	1.70127e10	−	1.06898e10i	0.180607	−	0.113483i
$555$	7.84889e10	−	1.79146e10i	0.827249	−	0.188814i
$556$	−7.31164e10	−	5.83084e10i	−0.765095	−	0.610143i
$557$	1.46445e11	−	1.16786e11i	1.52144	−	1.21331i	0.616803	−	0.787118i	$-0.288428\pi$
$557$	1.46445e11	−	1.16786e11i	1.52144	−	1.21331i	0.904635	−	0.426188i	$-0.140144\pi$
$558$	−9.71349e7	+	4.25576e8i	−0.00100193	+	0.00438975i
$559$	1.29649e11	−	4.53663e10i	1.32777	−	0.464607i
$560$	1.71401e10	−	3.55917e10i	0.174285	−	0.361907i
$561$	1.66163e10	+	1.04407e10i	0.167758	+	0.105409i
$562$	3.92732e10	+	1.37423e10i	0.393687	+	0.137757i
$563$	−1.50054e10	+	1.50054e10i	−0.149353	+	0.149353i	−0.777829	−	0.628476i	$-0.783679\pi$
$563$	−1.50054e10	+	1.50054e10i	−0.149353	+	0.149353i	0.628476	+	0.777829i	$0.283679\pi$
$564$	−3.36792e10	−	6.99357e10i	−0.332848	−	0.691166i
$565$	9.63286e8	−	8.54940e9i	0.00945282	−	0.0838961i
$566$	1.41278e10	+	1.59183e9i	0.137661	+	0.0155106i
$567$	1.02471e11	−	4.93476e10i	0.991448	−	0.477456i
$568$	1.21310e10	+	1.21310e10i	0.116548	+	0.116548i
$569$	1.36102e9	−	3.88958e9i	0.0129842	−	0.0371068i	−0.937209	−	0.348769i	$-0.886600\pi$
$569$	1.36102e9	−	3.88958e9i	0.0129842	−	0.0371068i	0.950193	+	0.311662i	$0.100886\pi$
$570$	−1.45986e10	+	2.32335e10i	−0.138296	+	0.220097i
$571$	−1.76512e11	−	8.50038e10i	−1.66047	−	0.799639i	−0.998755	−	0.0498820i	$-0.984115\pi$
$571$	−1.76512e11	−	8.50038e10i	−1.66047	−	0.799639i	−0.661713	−	0.749757i	$-0.730170\pi$
$572$	−5.21305e9	−	1.48980e10i	−0.0486976	−	0.139170i
$573$	−1.91989e11	−	4.38203e10i	−1.78098	−	0.406496i
$574$	−4.73674e9	−	5.93969e9i	−0.0436347	−	0.0547162i
$575$	−4.84164e10	+	6.07123e10i	−0.442916	+	0.555399i
$576$	−2.49393e8	−	1.09266e9i	−0.00226566	−	0.00992649i
$577$	−8.93323e10	−	1.42172e11i	−0.805945	−	1.28265i	−0.955821	−	0.293949i	$-0.905030\pi$
$577$	−8.93323e10	−	1.42172e11i	−0.805945	−	1.28265i	0.149876	−	0.988705i	$-0.452112\pi$
$578$	−4.29600e9	−	3.81280e10i	−0.0384904	−	0.341612i
$579$			1.83894e11i			1.63626i
$580$	−7.22087e9	−	5.34540e10i	−0.0638084	−	0.472355i
$581$	1.96096e11			1.72093
$582$	2.54928e10	−	2.87235e9i	0.222191	−	0.0250349i
$583$	−1.20325e10	+	7.56050e9i	−0.104155	+	0.0654450i
$584$	6.63484e9	−	1.51436e9i	0.0570399	−	0.0130190i
$585$	1.70493e9	+	1.35964e9i	0.0145574	+	0.0116091i
$586$	−2.10110e10	+	1.67557e10i	−0.178178	+	0.142093i
$587$	−1.64109e10	+	7.19011e10i	−0.138223	+	0.605596i	0.857602	+	0.514314i	$0.171953\pi$
$587$	−1.64109e10	+	7.19011e10i	−0.138223	+	0.605596i	−0.995825	+	0.0912816i	$0.970904\pi$
$588$	2.80829e10	−	9.82664e9i	0.234927	−	0.0822045i
$589$	−3.25546e10	+	6.76004e10i	−0.270490	+	0.561679i
$590$	−7.90665e9	−	4.96808e9i	−0.0652506	−	0.0409997i
$591$	9.87398e10	+	3.45505e10i	0.809361	+	0.283208i
$592$	9.01899e10	−	9.01899e10i	0.734296	−	0.734296i
$593$	−2.59921e9	−	5.39732e9i	−0.0210195	−	0.0436475i	0.890195	−	0.455580i	$-0.150568\pi$
$593$	−2.59921e9	−	5.39732e9i	−0.0210195	−	0.0436475i	−0.911214	+	0.411933i	$0.864854\pi$
$594$	−6.98874e8	+	6.20268e9i	−0.00561375	+	0.0498234i
$595$	−1.08035e11	−	1.21726e10i	−0.861976	−	0.0971213i
$596$	−1.86143e11	+	8.96419e10i	−1.47524	+	0.710438i
$597$	−1.25613e11	−	1.25613e11i	−0.988866	−	0.988866i
$598$	1.73323e10	−	4.95328e10i	0.135535	−	0.387336i
$599$	−5.57164e10	+	8.86721e10i	−0.432789	+	0.688779i	−0.989917	−	0.141647i	$-0.954760\pi$
$599$	−5.57164e10	+	8.86721e10i	−0.432789	+	0.688779i	0.557129	+	0.830426i	$0.311903\pi$
$600$	−5.29954e10	−	2.55212e10i	−0.408915	−	0.196923i
$601$	−3.86682e9	−	1.10507e10i	−0.0296385	−	0.0847019i	0.928114	−	0.372297i	$-0.121430\pi$
$601$	−3.86682e9	−	1.10507e10i	−0.0296385	−	0.0847019i	−0.957752	+	0.287595i	$0.907144\pi$
$602$	−6.02788e10	−	1.37582e10i	−0.458964	−	0.104755i
$603$	2.40055e9	+	3.01019e9i	0.0181569	+	0.0227680i
$604$	6.65176e10	−	8.34104e10i	0.499791	−	0.626718i
$605$	−1.58261e10	−	6.93385e10i	−0.118128	−	0.517551i
$606$	1.78650e10	+	2.84320e10i	0.132469	+	0.210823i
$607$	4.48303e9	+	3.97879e10i	0.0330230	+	0.293087i	0.999359	+	0.0358033i	$0.0113990\pi$
$607$	4.48303e9	+	3.97879e10i	0.0330230	+	0.293087i	−0.966336	+	0.257284i	$0.917172\pi$
$608$			1.68529e11i			1.23327i
$609$	9.31925e10	−	1.22303e11i	0.677504	−	0.889135i
$610$	9.03152e9			0.0652291
$611$	1.44179e11	−	1.62450e10i	1.03451	−	0.116562i
$612$	−4.30709e9	+	2.70632e9i	−0.0307028	+	0.0192919i
$613$	2.50589e11	−	5.71953e10i	1.77468	−	0.405059i	0.795158	−	0.606402i	$-0.207388\pi$
$613$	2.50589e11	−	5.71953e10i	1.77468	−	0.405059i	0.979521	+	0.201344i	$0.0645308\pi$
$614$	−6.03996e10	−	4.81671e10i	−0.424972	−	0.338904i
$615$	−1.06170e10	+	8.46678e9i	−0.0742167	+	0.0591858i
$616$	−3.37825e9	+	1.48011e10i	−0.0234622	+	0.102795i
$617$	8.99665e10	−	3.14806e10i	0.620783	−	0.217222i	−0.00151845	−	0.999999i	$-0.500483\pi$
$617$	8.99665e10	−	3.14806e10i	0.620783	−	0.217222i	0.622302	+	0.782777i	$0.286198\pi$
$618$	2.82361e10	−	5.86328e10i	0.193575	−	0.401964i
$619$	2.87347e9	+	1.80552e9i	0.0195724	+	0.0122982i	0.541783	−	0.840519i	$-0.317750\pi$
$619$	2.87347e9	+	1.80552e9i	0.0195724	+	0.0122982i	−0.522210	+	0.852817i	$0.674892\pi$
$620$	2.95317e10	+	1.03336e10i	0.199858	+	0.0699333i
$621$	1.07244e11	−	1.07244e11i	0.721117	−	0.721117i
$622$	−1.12434e10	−	2.33472e10i	−0.0751169	−	0.155982i
$623$	−2.66250e8	+	2.36303e9i	−0.00176741	+	0.0156862i
$624$	−1.14078e11	−	1.28535e10i	−0.752428	−	0.0847783i
$625$	−2.82316e10	+	1.35956e10i	−0.185019	+	0.0891003i
$626$	−5.16222e9	−	5.16222e9i	−0.0336155	−	0.0336155i
$627$	−1.00586e10	+	2.87459e10i	−0.0650832	+	0.185997i
$628$	−5.55384e10	+	8.83888e10i	−0.357071	+	0.568275i
$629$	−3.16261e11	−	1.52303e11i	−2.02043	−	0.972987i
$630$	−3.24201e8	−	9.26512e8i	−0.00205803	−	0.00588151i
$631$	−8.14427e10	−	1.85888e10i	−0.513730	−	0.117256i	−0.0422063	−	0.999109i	$-0.513439\pi$
$631$	−8.14427e10	−	1.85888e10i	−0.513730	−	0.117256i	−0.471524	+	0.881853i	$0.656296\pi$
$632$	−9.78919e10	−	1.22753e11i	−0.613590	−	0.769418i
$633$	5.24285e9	−	6.57433e9i	0.0326552	−	0.0409483i
$634$	−2.44317e10	−	1.07042e11i	−0.151216	−	0.662519i
$635$	6.06777e10	+	9.65680e10i	0.373193	+	0.593934i
$636$	1.37043e10	+	1.21629e11i	0.0837581	+	0.743374i
$637$			5.56129e10i			0.337767i
$638$	2.87564e9	+	7.67065e9i	0.0173561	+	0.0462967i
$639$	−1.23115e9			−0.00738426
$640$	9.03121e10	−	1.01757e10i	0.538302	−	0.0606521i
$641$	1.79312e11	−	1.12669e11i	1.06213	−	0.667381i	0.116687	−	0.993169i	$-0.462772\pi$
$641$	1.79312e11	−	1.12669e11i	1.06213	−	0.667381i	0.945443	+	0.325788i	$0.105630\pi$
$642$	−5.26662e10	+	1.20207e10i	−0.310021	+	0.0707603i
$643$	2.40550e10	+	1.91832e10i	0.140722	+	0.112222i	0.691321	−	0.722548i	$-0.257029\pi$
$643$	2.40550e10	+	1.91832e10i	0.140722	+	0.112222i	−0.550599	+	0.834770i	$0.685601\pi$
$644$	1.34968e11	−	1.07634e11i	0.784672	−	0.625755i
$645$	−2.45924e10	+	1.07746e11i	−0.142090	+	0.622535i
$646$	1.12925e11	−	3.95142e10i	0.648426	−	0.226894i
$647$	−1.21591e11	+	2.52487e11i	−0.693881	+	1.44086i	0.194102	+	0.980981i	$0.437821\pi$
$647$	−1.21591e11	+	2.52487e11i	−0.693881	+	1.44086i	−0.887983	+	0.459877i	$0.847894\pi$
$648$	9.44290e10	+	5.93337e10i	0.535557	+	0.336513i
$649$	−9.78261e9	−	3.42308e9i	−0.0551412	−	0.0192947i
$650$	3.63826e10	−	3.63826e10i	0.203817	−	0.203817i
$651$	3.86978e10	+	8.03568e10i	0.215458	+	0.447403i
$652$	−1.09781e10	+	9.74330e10i	−0.0607485	+	0.539158i
$653$	−8.82646e10	−	9.94503e9i	−0.485438	−	0.0546957i	−0.134146	−	0.990962i	$-0.542829\pi$
$653$	−8.82646e10	−	9.94503e9i	−0.485438	−	0.0546957i	−0.351292	+	0.936266i	$0.614258\pi$
$654$	−2.62518e9	+	1.26422e9i	−0.0143499	+	0.00691055i
$655$	−3.00352e10	−	3.00352e10i	−0.163180	−	0.163180i
$656$	−7.10570e9	+	2.03069e10i	−0.0383700	+	0.109655i
$657$	−2.59832e8	+	4.13521e8i	−0.00139454	+	0.00221940i
$658$	−5.88423e10	−	2.83370e10i	−0.313896	−	0.151164i
$659$	2.86174e10	+	8.17839e10i	0.151736	+	0.433637i	0.994511	−	0.104629i	$-0.0333655\pi$
$659$	2.86174e10	+	8.17839e10i	0.151736	+	0.433637i	−0.842775	+	0.538266i	$0.819080\pi$
$660$	1.23811e10	+	2.82592e9i	0.0652507	+	0.0148930i
$661$	9.72707e10	+	1.21974e11i	0.509537	+	0.638940i	0.968351	−	0.249593i	$-0.0802968\pi$
$661$	9.72707e10	+	1.21974e11i	0.509537	+	0.638940i	−0.458813	+	0.888533i	$0.651725\pi$
$662$	−4.17624e10	+	5.23684e10i	−0.217447	+	0.272670i
$663$	7.03035e10	+	3.08020e11i	0.363850	+	1.59413i
$664$	1.02300e11	+	1.62810e11i	0.526266	+	0.837547i
$665$	−1.88907e10	−	1.67660e11i	−0.0965966	−	0.857318i
$666$		−	3.16932e9i		−	0.0161090i
$667$	6.15784e10	−	1.89283e11i	0.311118	−	0.956330i
$668$	−2.70722e11			−1.35962
$669$	−9.33444e10	+	1.05174e10i	−0.465998	+	0.0525053i
$670$	−3.19730e10	+	2.00900e10i	−0.158666	+	0.0996966i
$671$	9.77280e9	−	2.23058e9i	0.0482091	−	0.0110034i
$672$	1.56625e11	+	1.24904e11i	0.768039	+	0.612490i
$673$	−2.95214e11	+	2.35425e11i	−1.43905	+	1.14761i	−0.475620	+	0.879651i	$0.657776\pi$
$673$	−2.95214e11	+	2.35425e11i	−1.43905	+	1.14761i	−0.963432	+	0.267955i	$0.913652\pi$
$674$	−2.68312e10	+	1.17555e11i	−0.130017	+	0.569643i
$675$	1.40359e11	−	4.91137e10i	0.676122	−	0.236585i
$676$	3.05540e10	−	6.34461e10i	0.146313	−	0.303821i
$677$	1.57250e11	+	9.88067e10i	0.748576	+	0.470362i	0.851518	−	0.524326i	$-0.175683\pi$
$677$	1.57250e11	+	9.88067e10i	0.748576	+	0.470362i	−0.102942	+	0.994687i	$0.532825\pi$
$678$	1.06227e10	+	3.71706e9i	0.0502710	+	0.0175906i
$679$	−1.11542e11	+	1.11542e11i	−0.524758	+	0.524758i
$680$	−4.62537e10	−	9.60469e10i	−0.216327	−	0.449208i
$681$	1.59575e10	−	1.41626e11i	0.0741951	−	0.658500i
$682$	−4.72184e9	−	5.32024e8i	−0.0218260	−	0.00245920i
$683$	1.43079e11	−	6.89033e10i	0.657497	−	0.316634i	−0.0752206	−	0.997167i	$-0.523966\pi$
$683$	1.43079e11	−	6.89033e10i	0.657497	−	0.316634i	0.732717	+	0.680533i	$0.238252\pi$
$684$	−5.58204e9	−	5.58204e9i	−0.0255017	−	0.0255017i
$685$	−4.85642e10	+	1.38788e11i	−0.220574	+	0.630364i
$686$	−3.30586e10	+	5.26124e10i	−0.149275	+	0.237570i
$687$	1.46190e11	+	7.04014e10i	0.656282	+	0.316049i
$688$	5.78293e10	+	1.65267e11i	0.258104	+	0.737618i
$689$	−2.23048e11	−	5.09094e10i	−0.989743	−	0.225902i
$690$	2.63258e10	+	3.30115e10i	0.116141	+	0.145636i
$691$	1.90628e10	−	2.39040e10i	0.0836133	−	0.104848i	−0.738265	−	0.674510i	$-0.764355\pi$
$691$	1.90628e10	−	2.39040e10i	0.0836133	−	0.104848i	0.821879	+	0.569663i	$0.192926\pi$
$692$	−4.47605e10	−	1.96108e11i	−0.195196	−	0.855208i
$693$	−5.79638e8	−	9.22488e8i	−0.00251318	−	0.00399970i
$694$	2.66552e9	+	2.36572e10i	0.0114906	+	0.101982i
$695$			1.40647e11i			0.602825i
$696$	1.50160e11	+	1.35702e10i	0.639908	+	0.0578294i
$697$	5.92092e10			0.250875
$698$	6.99955e9	−	7.88660e8i	0.0294882	−	0.00332252i
$699$	1.26488e11	−	7.94777e10i	0.529835	−	0.332918i
$700$	1.65016e11	−	3.76638e10i	0.687280	−	0.156867i
$701$	−1.97529e11	−	1.57524e11i	−0.818010	−	0.652341i	0.122363	−	0.992485i	$-0.460953\pi$
$701$	−1.97529e11	−	1.57524e11i	−0.818010	−	0.652341i	−0.940373	+	0.340144i	$0.889524\pi$
$702$	−7.85680e10	+	6.26559e10i	−0.323517	+	0.257996i
$703$	1.21220e11	−	5.31098e11i	0.496308	−	2.17447i
$704$	1.15154e10	−	4.02940e9i	0.0468800	−	0.0164040i
$705$	−5.06514e10	+	1.05179e11i	−0.205038	+	0.425767i
$706$	2.42590e10	+	1.52429e10i	0.0976459	+	0.0613550i
$707$	−1.94886e11	−	6.81935e10i	−0.780014	−	0.272939i
$708$	−6.31224e10	+	6.31224e10i	−0.251218	+	0.251218i
$709$	−1.91782e11	−	3.98239e11i	−0.758965	−	1.57601i	−0.816283	−	0.577652i	$-0.803969\pi$
$709$	−1.91782e11	−	3.98239e11i	−0.758965	−	1.57601i	0.0573179	−	0.998356i	$-0.481745\pi$
$710$	1.35192e9	−	1.19986e10i	0.00532008	−	0.0472170i
$711$	1.11963e10	+	1.26152e9i	0.0438125	+	0.00493648i
$712$	−2.10082e9	+	1.01170e9i	−0.00817466	+	0.00393671i
$713$	8.16403e10	+	8.16403e10i	0.315898	+	0.315898i
$714$	4.69707e10	−	1.34234e11i	0.180731	−	0.516501i
$715$	−1.26293e10	+	2.00993e10i	−0.0483230	+	0.0769055i
$716$	1.59523e11	+	7.68224e10i	0.606977	+	0.292305i
$717$	−6.97983e10	−	1.99472e11i	−0.264100	−	0.754754i
$718$	−1.62071e10	−	3.69916e9i	−0.0609827	−	0.0139189i
$719$	−1.15510e10	−	1.44845e10i	−0.0432219	−	0.0541985i	0.759751	−	0.650214i	$-0.225321\pi$
$719$	−1.15510e10	−	1.44845e10i	−0.0432219	−	0.0541985i	−0.802973	+	0.596016i	$0.796750\pi$
$720$	−1.73315e9	+	2.17331e9i	−0.00644922	+	0.00808707i
$721$	8.90425e10	+	3.90121e11i	0.329501	+	1.44364i
$722$	4.86241e10	+	7.73848e10i	0.178938	+	0.284778i
$723$	−4.02783e10	−	3.57480e11i	−0.147407	−	1.30827i
$724$		−	8.96926e10i		−	0.326439i
$725$	1.34920e11	−	1.41011e11i	0.488341	−	0.510390i
$726$	9.30348e10			0.334888
$727$	5.05089e8	−	5.69099e7i	0.00180813	−	0.000203728i	−0.111060	−	0.993814i	$-0.535425\pi$
$727$	5.05089e8	−	5.69099e7i	0.00180813	−	0.000203728i	0.112868	+	0.993610i	$0.463996\pi$
$728$	−2.06955e11	+	1.30039e11i	−0.736803	+	0.462964i
$729$	−2.82916e11	+	6.45737e10i	−1.00172	+	0.228637i
$730$	−3.74481e9	−	2.98638e9i	−0.0131868	−	0.0105161i
$731$	3.76742e11	−	3.00441e11i	1.31939	−	1.05218i
$732$	1.92123e10	−	8.41747e10i	0.0669168	−	0.293182i
$733$	−1.30386e11	+	4.56241e10i	−0.451664	+	0.158044i	−0.546518	−	0.837447i	$-0.684047\pi$
$733$	−1.30386e11	+	4.56241e10i	−0.451664	+	0.158044i	0.0948546	+	0.995491i	$0.469761\pi$
$734$	−2.79024e10	+	5.79400e10i	−0.0961297	+	0.199615i
$735$	−3.78874e10	−	2.38062e10i	−0.129821	−	0.0815721i
$736$	2.44778e11	+	8.56515e10i	0.834182	+	0.291893i
$737$	−2.96355e10	+	2.96355e10i	−0.100448	+	0.100448i
$738$	2.31949e8	+	4.81648e8i	0.000781929	+	0.00162369i
$739$	−1.07825e10	+	9.56971e10i	−0.0361527	+	0.320864i	0.962600	+	0.270928i	$0.0873304\pi$
$739$	−1.07825e10	+	9.56971e10i	−0.0361527	+	0.320864i	−0.998752	+	0.0499363i	$0.984098\pi$
$740$	−2.25732e11	−	2.54339e10i	−0.752776	−	0.0848175i
$741$	−4.41755e11	+	2.12738e11i	−1.46524	+	0.705622i
$742$	7.28201e10	+	7.28201e10i	0.240235	+	0.240235i
$743$	−1.03066e11	+	2.94547e11i	−0.338191	+	0.966494i	0.641699	+	0.766956i	$0.278230\pi$
$743$	−1.03066e11	+	2.94547e11i	−0.338191	+	0.966494i	−0.979890	+	0.199538i	$0.936056\pi$
$744$	−4.65288e10	+	7.40502e10i	−0.151855	+	0.241677i
$745$	2.79948e11	+	1.34816e11i	0.908766	+	0.437638i
$746$	−6.78842e10	−	1.94002e11i	−0.219186	−	0.626398i
$747$	−1.34527e10	−	3.07050e9i	−0.0432044	−	0.00986112i
$748$	−3.45237e10	−	4.32914e10i	−0.110284	−	0.138291i
$749$	2.07102e11	−	2.59698e11i	0.658047	−	0.825165i
$750$	2.22533e10	+	9.74981e10i	0.0703314	+	0.308142i
$751$	−1.48578e11	−	2.36461e11i	−0.467084	−	0.743360i	0.527244	−	0.849714i	$-0.323225\pi$
$751$	−1.48578e11	−	2.36461e11i	−0.467084	−	0.743360i	−0.994328	+	0.106353i	$0.966083\pi$
$752$	2.07079e10	+	1.83787e11i	0.0647536	+	0.574704i
$753$		−	3.27993e11i		−	1.02020i
$754$	−5.45870e10	+	1.20060e11i	−0.168890	+	0.371461i
$755$	−1.60449e11			−0.493797
$756$	−3.28502e11	+	3.70132e10i	−1.00566	+	0.113310i
$757$	1.46491e10	−	9.20462e9i	0.0446094	−	0.0280299i	−0.509543	−	0.860445i	$-0.670185\pi$
$757$	1.46491e10	−	9.20462e9i	0.0446094	−	0.0280299i	0.554152	+	0.832415i	$0.313043\pi$
$758$	1.21348e10	−	2.76969e9i	0.0367583	−	0.00838985i
$759$	3.66396e10	+	2.92191e10i	0.110404	+	0.0880441i
$760$	1.29346e11	−	1.03150e11i	0.387702	−	0.309182i
$761$	−2.76800e10	+	1.21274e11i	−0.0825331	+	0.361601i	−0.999283	−	0.0378605i	$-0.987946\pi$
$761$	−2.76800e10	+	1.21274e11i	−0.0825331	+	0.361601i	0.916750	+	0.399462i	$0.130803\pi$
$762$	−1.40816e11	+	4.92737e10i	−0.417670	+	0.146149i
$763$	7.77355e9	−	1.61419e10i	0.0229362	−	0.0476275i
$764$	4.70481e11	+	2.95623e11i	1.38092	+	0.867690i
$765$	7.22087e9	+	2.52669e9i	0.0210836	+	0.00737746i
$766$	1.63262e11	−	1.63262e11i	0.474210	−	0.474210i
$767$	−7.23975e10	−	1.50335e11i	−0.209191	−	0.434389i
$768$	6.42241e7	−	5.70005e8i	0.000184609	−	0.00163845i
$769$	3.96661e11	+	4.46930e10i	1.13426	+	0.127801i	0.659071	−	0.752081i	$-0.270950\pi$
$769$	3.96661e11	+	4.46930e10i	1.13426	+	0.127801i	0.475193	+	0.879882i	$0.342378\pi$
$770$	9.62696e9	−	4.63610e9i	0.0273858	−	0.0131883i
$771$	−2.54415e11	−	2.54415e11i	−0.719989	−	0.719989i
$772$	1.71374e11	−	4.89759e11i	0.482476	−	1.37884i
$773$	2.87121e11	−	4.56951e11i	0.804170	−	1.27983i	−0.152398	−	0.988319i	$-0.548700\pi$
$773$	2.87121e11	−	4.56951e11i	0.804170	−	1.27983i	0.956568	−	0.291510i	$-0.0941575\pi$
$774$	3.91986e9	+	1.88771e9i	0.0109221	+	0.00525982i
$775$	3.73883e10	+	1.06850e11i	0.103640	+	0.296187i
$776$	−1.50798e11	−	3.44188e10i	−0.415863	−	0.0949179i
$777$	−4.03743e11	−	5.06277e11i	−1.10770	−	1.38901i
$778$	3.28232e10	−	4.11590e10i	0.0895907	−	0.112343i
$779$	2.04468e10	+	8.95833e10i	0.0555234	+	0.243264i
$780$	1.08778e11	+	1.73119e11i	0.293874	+	0.467698i
$781$	−1.50050e9	−	1.33173e10i	−0.00403304	−	0.0357943i
$782$		−	1.84099e11i		−	0.492295i
$783$	−2.92690e11	+	2.44173e11i	−0.778683	+	0.649607i
$784$	−7.08908e10			−0.187640
$785$	1.56007e11	−	1.75778e10i	0.410834	−	0.0462899i
$786$	4.70470e10	−	2.95616e10i	0.123265	−	0.0774528i
$787$	−3.74989e11	+	8.55888e10i	−0.977506	+	0.223109i	−0.681292	−	0.732012i	$-0.738581\pi$
$787$	−3.74989e11	+	8.55888e10i	−0.977506	+	0.223109i	−0.296214	+	0.955121i	$0.595724\pi$
$788$	−2.30772e11	−	1.84035e11i	−0.598520	−	0.477303i
$789$	−2.88087e11	+	2.29742e11i	−0.743388	+	0.592832i
$790$	−2.45893e10	+	1.07733e11i	−0.0631304	+	0.276592i
$791$	−6.53180e10	+	2.28557e10i	−0.166850	+	0.0583834i
$792$	4.63515e8	−	9.62498e8i	0.00117805	−	0.00244624i
$793$	1.36648e11	+	8.58615e10i	0.345549	+	0.217123i
$794$	−1.31647e11	−	4.60652e10i	−0.331229	−	0.115902i
$795$	1.30164e11	−	1.30164e11i	0.325852	−	0.325852i
$796$	2.17480e11	+	4.51602e11i	0.541711	+	1.12487i
$797$	−8.62134e10	+	7.65165e11i	−0.213669	+	1.89636i	0.190510	+	0.981685i	$0.438986\pi$
$797$	−8.62134e10	+	7.65165e11i	−0.213669	+	1.89636i	−0.404179	+	0.914680i	$0.632443\pi$
$798$	2.19317e11	+	2.47111e10i	0.540829	+	0.0609368i
$799$	4.58594e11	−	2.20847e11i	1.12523	−	0.541882i
$800$	1.79793e11	+	1.79793e11i	0.438948	+	0.438948i
$801$	5.52661e7	−	1.57941e8i	0.000134255	−	0.000383677i
$802$	−9.94931e10	+	1.58342e11i	−0.240489	+	0.382736i
$803$	−4.78974e9	−	2.30662e9i	−0.0115199	−	0.00554770i
$804$	1.19226e11	+	3.40728e11i	0.285330	+	0.815425i
$805$	−2.53116e11	−	5.77722e10i	−0.602750	−	0.137574i
$806$	−4.76974e10	−	5.98106e10i	−0.113020	−	0.141722i
$807$	4.50716e11	−	5.65180e11i	1.06270	−	1.33258i
$808$	−4.50509e10	−	1.97381e11i	−0.105696	−	0.463084i
$809$	1.24394e11	+	1.97971e11i	0.290405	+	0.462176i	0.959782	−	0.280746i	$-0.0905819\pi$
$809$	1.24394e11	+	1.97971e11i	0.290405	+	0.462176i	−0.669377	+	0.742923i	$0.733439\pi$
$810$	−8.78825e9	−	7.79979e10i	−0.0204156	−	0.181193i
$811$			1.71911e11i			0.397394i	0.980061	+	0.198697i	$0.0636710\pi$
$811$			1.71911e11i			0.397394i	−0.980061	+	0.198697i	$0.936329\pi$
$812$	−3.62173e11	+	2.38877e11i	−0.833089	+	0.549479i
$813$	4.87350e11			1.11552
$814$	3.42826e10	−	3.86272e9i	0.0780865	−	0.00879824i
$815$	1.24858e11	−	7.84536e10i	0.283000	−	0.177821i
$816$	−3.92639e11	+	8.96172e10i	−0.885590	+	0.202130i
$817$	5.84668e11	+	4.66257e11i	1.31226	+	1.04650i
$818$	6.39907e9	−	5.10309e9i	0.0142924	−	0.0113978i
$819$	3.90304e9	−	1.71004e10i	0.00867497	−	0.0380075i
$820$	3.61662e10	−	1.26551e10i	0.0799923	−	0.0279905i
$821$	−1.39178e11	+	2.89005e11i	−0.306335	+	0.636111i	−0.996130	−	0.0878938i	$-0.971986\pi$
$821$	−1.39178e11	+	2.89005e11i	−0.306335	+	0.636111i	0.689795	+	0.724005i	$0.257701\pi$
$822$	−1.62862e11	−	1.02333e11i	−0.356725	−	0.224145i
$823$	4.58782e11	+	1.60535e11i	1.00002	+	0.349921i	0.780139	−	0.625607i	$-0.215148\pi$
$823$	4.58782e11	+	1.60535e11i	1.00002	+	0.349921i	0.219878	+	0.975527i	$0.429434\pi$
$824$	−2.77449e11	+	2.77449e11i	−0.601830	+	0.601830i
$825$	1.99364e10	+	4.13983e10i	0.0430358	+	0.0893648i
$826$	−8.40950e9	+	7.46364e10i	−0.0180655	+	0.160336i
$827$	−3.99636e11	−	4.50281e10i	−0.854363	−	0.0962635i	−0.326090	−	0.945339i	$-0.605731\pi$
$827$	−3.99636e11	−	4.50281e10i	−0.854363	−	0.0962635i	−0.528272	+	0.849075i	$0.677160\pi$
$828$	−1.09445e10	+	5.27061e9i	−0.0232850	+	0.0112135i
$829$	1.68790e11	+	1.68790e11i	0.357378	+	0.357378i	0.862845	−	0.505468i	$-0.168680\pi$
$829$	1.68790e11	+	1.68790e11i	0.357378	+	0.357378i	−0.505468	+	0.862845i	$0.668680\pi$
$830$	4.46971e10	−	1.27737e11i	0.0941818	−	0.269156i
$831$	−1.53691e11	+	2.44597e11i	−0.322287	+	0.512917i
$832$	1.76963e11	+	8.52210e10i	0.369309	+	0.177850i
$833$	6.44369e10	+	1.84150e11i	0.133830	+	0.382465i
$834$	−1.79369e11	−	4.09397e10i	−0.370751	−	0.0846215i
$835$	2.53853e11	+	3.18321e11i	0.522199	+	0.654816i
$836$	5.35776e10	−	6.71842e10i	0.109688	−	0.137544i
$837$	−4.91981e10	−	2.15551e11i	−0.100241	−	0.439186i
$838$	1.52387e11	+	2.42523e11i	0.309010	+	0.491787i
$839$	2.06626e10	+	1.83386e11i	0.0417001	+	0.370099i	0.997180	+	0.0750433i	$0.0239095\pi$
$839$	2.06626e10	+	1.83386e11i	0.0417001	+	0.370099i	−0.955480	+	0.295055i	$0.904662\pi$
$840$		−	1.96658e11i		−	0.394998i
$841$	−1.96947e11	+	4.59846e11i	−0.393699	+	0.919239i
$842$	−9.75624e10			−0.194104
$843$	−5.94451e11	+	6.69786e10i	−1.17708	+	0.132625i
$844$	−2.00898e10	+	1.26233e10i	−0.0395919	+	0.0248773i
$845$	−1.03252e11	+	2.35665e10i	−0.202521	+	0.0462241i
$846$	3.59304e9	+	2.86535e9i	0.00701424	+	0.00559367i
$847$	−4.47254e11	+	3.56673e11i	−0.869002	+	0.693006i
$848$	6.48951e10	−	2.84324e11i	0.125496	−	0.549833i
$849$	−1.92935e11	+	6.75109e10i	−0.371347	+	0.129940i
$850$	7.83178e10	−	1.62628e11i	0.150032	−	0.311545i
$851$	−7.09780e11	−	4.45984e11i	−1.35334	−	0.850357i
$852$	−1.08953e11	−	3.81242e10i	−0.206766	−	0.0723506i
$853$	3.83427e11	−	3.83427e11i	0.724247	−	0.724247i	−0.245220	−	0.969467i	$-0.578860\pi$
$853$	3.83427e11	−	3.83427e11i	0.724247	−	0.724247i	0.969467	+	0.245220i	$0.0788602\pi$
$854$	−3.15191e10	−	6.54500e10i	−0.0592573	−	0.123049i
$855$	−1.32928e9	+	1.17977e10i	−0.00248744	+	0.0220767i
$856$	3.23658e11	+	3.64676e10i	0.602826	+	0.0679222i
$857$	7.18696e11	−	3.46106e11i	1.33236	−	0.641631i	0.374063	−	0.927403i	$-0.377964\pi$
$857$	7.18696e11	−	3.46106e11i	1.33236	−	0.641631i	0.958297	+	0.285773i	$0.0922502\pi$
$858$	−2.19568e10	−	2.19568e10i	−0.0405153	−	0.0405153i
$859$	5.68419e10	−	1.62445e11i	0.104399	−	0.298355i	−0.879821	−	0.475305i	$-0.842338\pi$
$859$	5.68419e10	−	1.62445e11i	0.104399	−	0.298355i	0.984220	+	0.176951i	$0.0566233\pi$
$860$	1.65907e11	−	2.64039e11i	0.303299	−	0.482697i
$861$	9.84097e10	+	4.73916e10i	0.179071	+	0.0862360i
$862$	−2.33832e10	−	6.68254e10i	−0.0423521	−	0.121035i
$863$	5.58824e11	+	1.27548e11i	1.00747	+	0.229948i	0.694251	−	0.719733i	$-0.255736\pi$
$863$	5.58824e11	+	1.27548e11i	1.00747	+	0.229948i	0.313218	+	0.949681i	$0.398593\pi$
$864$	−3.09629e11	−	3.88262e11i	−0.555631	−	0.696739i
$865$	−1.88618e11	+	2.36519e11i	−0.336913	+	0.422476i
$866$	3.36843e10	+	1.47580e11i	0.0598901	+	0.262396i
$867$	2.93494e11	+	4.67093e11i	0.519425	+	0.826660i
$868$	−2.81767e10	−	2.50075e11i	−0.0496376	−	0.440546i
$869$			1.22648e11i			0.215071i
$870$	−5.84263e10	−	8.85827e10i	−0.101984	−	0.154622i
$871$	−6.74748e11			−1.17238
$872$	1.74573e10	−	1.96697e9i	0.0301934	−	0.00340198i
$873$	9.39862e9	−	5.90555e9i	0.0161811	−	0.0101672i
$874$	2.78542e11	−	6.35754e10i	0.477359	−	0.108954i
$875$	−4.80765e11	−	3.83397e11i	−0.820163	−	0.654059i
$876$	−3.57996e10	+	2.85492e10i	−0.0607941	+	0.0484816i
$877$	3.88427e10	−	1.70181e11i	0.0656615	−	0.287682i	−0.931428	−	0.363927i	$-0.881436\pi$
$877$	3.88427e10	−	1.70181e11i	0.0656615	−	0.287682i	0.997089	+	0.0762448i	$0.0242931\pi$
$878$	4.08339e10	−	1.42884e10i	0.0687137	−	0.0240440i
$879$	1.67642e11	−	3.48113e11i	0.280820	−	0.583129i
$880$	−2.56210e10	−	1.60988e10i	−0.0427234	−	0.0268449i
$881$	−2.60977e11	−	9.13197e10i	−0.433210	−	0.151587i	0.104860	−	0.994487i	$-0.466561\pi$
$881$	−2.60977e11	−	9.13197e10i	−0.433210	−	0.151587i	−0.538070	+	0.842900i	$0.680846\pi$
$882$	−1.24557e9	+	1.24557e9i	−0.00205823	+	0.00205823i
$883$	−1.80848e11	−	3.75535e11i	−0.297489	−	0.617743i	0.697626	−	0.716462i	$-0.254240\pi$
$883$	−1.80848e11	−	3.75535e11i	−0.297489	−	0.617743i	−0.995115	+	0.0987190i	$0.968525\pi$
$884$	9.98120e10	−	8.85856e11i	0.163446	−	1.45062i
$885$	1.33410e11	+	1.50317e10i	0.217478	+	0.0245039i
$886$	−6.54253e10	+	3.15072e10i	−0.106172	+	0.0511298i
$887$	3.94697e11	+	3.94697e11i	0.637631	+	0.637631i	0.949971	−	0.312340i	$-0.101113\pi$
$887$	3.94697e11	+	3.94697e11i	0.637631	+	0.637631i	−0.312340	+	0.949971i	$0.601113\pi$
$888$	2.09714e11	−	5.99328e11i	0.337268	−	0.963857i
$889$	4.88054e11	−	7.76734e11i	0.781378	−	1.24356i
$890$	1.47859e9	+	7.12052e8i	0.00235661	+	0.00113488i
$891$	−2.87733e10	−	8.22292e10i	−0.0456539	−	0.130471i
$892$	2.58402e11	+	5.89786e10i	0.408166	+	0.0931612i
$893$	4.92508e11	+	6.17586e11i	0.774476	+	0.971162i
$894$	−2.53419e11	+	3.17778e11i	−0.396725	+	0.497478i
$895$	−5.92536e10	−	2.59607e11i	−0.0923469	−	0.404598i
$896$	−3.88922e11	−	6.18966e11i	−0.603435	−	0.960361i
$897$	8.44757e10	+	7.49743e11i	0.130486	+	1.15809i
$898$		−	2.42971e11i		−	0.373636i
$899$	−1.85879e11	−	2.22813e11i	−0.284571	−	0.341116i
$900$	−1.19103e10			−0.0181532
$901$	−7.97564e11	+	8.98639e10i	−1.21023	+	0.136360i
$902$	−4.92729e9	+	3.09602e9i	−0.00744358	+	0.00467711i
$903$	8.66646e11	−	1.97806e11i	1.30344	−	0.297502i
$904$	−5.30516e10	−	4.23073e10i	−0.0794374	−	0.0633492i
$905$	−1.05463e11	+	8.41037e10i	−0.157219	+	0.125378i
$906$	4.67036e10	−	2.04622e11i	0.0693167	−	0.303696i
$907$	−7.85521e11	+	2.74866e11i	−1.16072	+	0.406154i	−0.840830	−	0.541299i	$-0.817933\pi$
$907$	−7.85521e11	+	2.74866e11i	−1.16072	+	0.406154i	−0.319893	+	0.947454i	$0.603647\pi$
$908$	−1.74483e11	+	3.62318e11i	−0.256690	+	0.533023i
$909$	1.23019e10	+	7.72981e9i	0.0180184	+	0.0113217i
$910$	1.62372e11	+	5.68165e10i	0.236781	+	0.0828531i
$911$	−1.50950e11	+	1.50950e11i	−0.219160	+	0.219160i	−0.808144	−	0.588985i	$-0.799528\pi$
$911$	−1.50950e11	+	1.50950e11i	−0.219160	+	0.219160i	0.588985	+	0.808144i	$0.299528\pi$
$912$	−2.71181e11	−	5.63114e11i	−0.391995	−	0.813986i
$913$	1.68176e10	−	1.49260e11i	0.0242037	−	0.214814i
$914$	3.06011e11	+	3.44792e10i	0.438483	+	0.0494052i
$915$	−1.16990e11	+	5.63393e10i	−0.166903	+	0.0803761i
$916$	−3.23735e11	−	3.23735e11i	−0.459841	−	0.459841i
$917$	−1.12841e11	+	3.22481e11i	−0.159584	+	0.456065i
$918$	−1.87564e11	+	2.98506e11i	−0.264106	+	0.420322i
$919$	−1.72890e11	−	8.32596e10i	−0.242387	−	0.116727i	0.308747	−	0.951144i	$-0.400090\pi$
$919$	−1.72890e11	−	8.32596e10i	−0.242387	−	0.116727i	−0.551134	+	0.834417i	$0.685805\pi$
$920$	−8.40814e10	−	2.40291e11i	−0.117368	−	0.335418i
$921$	1.08286e12	+	2.47155e11i	1.50499	+	0.343503i
$922$	−1.31435e11	−	1.64814e11i	−0.181881	−	0.228071i
$923$	1.34524e11	−	1.68688e11i	0.185350	−	0.232422i
$924$	−2.27299e10	−	9.95864e10i	−0.0311825	−	0.136619i
$925$	−4.37275e11	−	6.95918e11i	−0.597293	−	0.950586i
$926$	5.38768e9	+	4.78170e10i	0.00732753	+	0.0650337i
$927$		−	2.81576e10i		−	0.0381309i
$928$	−5.93305e11	−	2.69754e11i	−0.799993	−	0.363728i
$929$	3.63778e10			0.0488397			0.0244199	−	0.999702i	$-0.492226\pi$
$929$	3.63778e10			0.0488397			0.0244199	+	0.999702i	$0.492226\pi$
$930$	6.11650e10	−	6.89165e9i	0.0817658	−	0.00921279i
$931$	−2.56366e11	+	1.61086e11i	−0.341242	+	0.214416i
$932$	−4.10938e11	+	9.37939e10i	−0.544644	+	0.124311i
$933$	2.91284e11	+	2.32291e11i	0.384406	+	0.306553i
$934$	−3.03587e11	+	2.42103e11i	−0.398929	+	0.318135i
$935$	−1.85306e10	+	8.11877e10i	−0.0242461	+	0.106229i
$936$	1.62339e10	−	5.68048e9i	0.0211504	−	0.00740085i
$937$	−1.23788e11	+	2.57049e11i	−0.160591	+	0.333471i	−0.965702	−	0.259654i	$-0.916392\pi$
$937$	−1.23788e11	+	2.57049e11i	−0.160591	+	0.333471i	0.805111	+	0.593124i	$0.202106\pi$
$938$	2.57172e11	+	1.61592e11i	0.332209	+	0.208741i
$939$	9.90711e10	+	3.46665e10i	0.127434	+	0.0445910i
$940$	2.32916e11	−	2.32916e11i	0.298324	−	0.298324i
$941$	−5.01852e10	−	1.04211e11i	−0.0640055	−	0.132909i	0.866512	−	0.499156i	$-0.166357\pi$
$941$	−5.01852e10	−	1.04211e11i	−0.0640055	−	0.132909i	−0.930517	+	0.366247i	$0.880642\pi$
$942$	−2.29937e10	+	2.04074e11i	−0.0292015	+	0.259170i
$943$	1.40506e11	+	1.58312e10i	0.177684	+	0.0200202i
$944$	1.91635e11	−	9.22865e10i	0.241316	−	0.116212i
$945$	3.51553e11	+	3.51553e11i	0.440823	+	0.440823i
$946$	−1.56419e10	+	4.47019e10i	−0.0195310	+	0.0558163i
$947$	3.45041e11	−	5.49130e11i	0.429014	−	0.682772i	−0.560346	−	0.828258i	$-0.689332\pi$
$947$	3.45041e11	−	5.49130e11i	0.429014	−	0.682772i	0.989360	+	0.145487i	$0.0464748\pi$
$948$	9.51774e11	+	4.58350e11i	1.17842	+	0.567498i
$949$	−2.82681e10	−	8.07857e10i	−0.0348524	−	0.0996023i
$950$	2.73102e11	+	6.23338e10i	0.335298	+	0.0765295i
$951$	9.84214e11	+	1.23417e12i	1.20328	+	1.50887i
$952$	−5.34616e11	+	6.70388e11i	−0.650870	+	0.816165i
$953$	8.29721e10	+	3.63524e11i	0.100591	+	0.440719i	0.999994	+	0.00359728i	$0.00114505\pi$
$953$	8.29721e10	+	3.63524e11i	0.100591	+	0.440719i	−0.899402	+	0.437122i	$0.855998\pi$
$954$	−3.85543e9	−	6.13589e9i	−0.00465457	−	0.00740771i
$955$	−9.35642e10	−	8.30406e11i	−0.112485	−	0.998336i
$956$			5.96294e11i			0.713886i
$957$	−8.50997e10	−	8.14234e10i	−0.101457	−	0.0970737i
$958$	9.84600e10			0.116895
$959$	1.17526e12	−	1.32420e11i	1.38951	−	0.156560i
$960$	−1.33811e11	+	8.40793e10i	−0.157546	+	0.0989929i
$961$	−6.67417e11	+	1.52334e11i	−0.782535	+	0.178608i
$962$	4.34250e11	+	3.46303e11i	0.507037	+	0.404349i
$963$	−1.82742e10	+	1.45732e10i	−0.0212487	+	0.0169453i
$964$	−2.25870e11	+	9.89601e11i	−0.261547	+	1.14591i
$965$	−7.36566e11	+	2.57736e11i	−0.849381	+	0.297211i
$966$	1.47355e11	−	3.05986e11i	0.169222	−	0.351393i
$967$	−9.26311e11	−	5.82040e11i	−1.05938	−	0.665651i	−0.114616	−	0.993410i	$-0.536564\pi$
$967$	−9.26311e11	−	5.82040e11i	−1.05938	−	0.665651i	−0.944761	+	0.327759i	$0.893707\pi$
$968$	−5.29457e11	−	1.85265e11i	−0.603017	−	0.211005i
$969$	−1.21628e12	+	1.21628e12i	−1.37956	+	1.37956i
$970$	4.72342e10	+	9.80827e10i	0.0533543	+	0.110791i
$971$	−1.21255e10	+	1.07617e11i	−0.0136403	+	0.121061i	−0.998687	−	0.0512262i	$-0.983687\pi$
$971$	−1.21255e10	+	1.07617e11i	−0.0136403	+	0.121061i	0.985047	+	0.172287i	$0.0551156\pi$
$972$	4.55752e10	+	5.13509e9i	0.0510580	+	0.00575285i
$973$	1.01925e12	−	4.90844e11i	1.13718	−	0.547636i
$974$	1.50389e11	+	1.50389e11i	0.167102	+	0.167102i
$975$	−2.44325e11	+	6.98240e11i	−0.270364	+	0.772656i
$976$	−1.09449e11	+	1.74187e11i	−0.120618	+	0.191963i
$977$	−9.68069e11	−	4.66198e11i	−1.06250	−	0.511672i	−0.180817	−	0.983517i	$-0.557874\pi$
$977$	−9.68069e11	−	4.66198e11i	−1.06250	−	0.511672i	−0.881682	+	0.471845i	$0.843588\pi$
$978$	6.37088e10	+	1.82069e11i	0.0696376	+	0.199013i
$979$	1.77581e9	+	4.05317e8i	0.00193315	+	0.000441229i
$980$	7.87189e10	+	9.87103e10i	0.0853443	+	0.107018i
$981$	−7.86040e8	+	9.85663e8i	−0.000848728	+	0.00106427i
$982$	9.08971e10	+	3.98246e11i	0.0977472	+	0.428258i
$983$	2.66311e10	+	4.23831e10i	0.0285216	+	0.0453919i	0.860681	−	0.509145i	$-0.170038\pi$
$983$	2.66311e10	+	4.23831e10i	0.0285216	+	0.0453919i	−0.832159	+	0.554537i	$0.812895\pi$
$984$	1.19917e10	+	1.06429e11i	0.0127908	+	0.113522i
$985$			4.43915e11i			0.471579i
$986$	−4.16432e10	+	4.60801e11i	−0.0440592	+	0.487535i
$987$	9.38983e11			0.989439
$988$	1.37477e12	−	1.54899e11i	1.44278	−	0.162563i
$989$	9.74357e11	−	6.12229e11i	1.01843	−	0.639924i
$990$	−7.33029e8	+	1.67309e8i	−0.000763098	+	0.000174172i
$991$	−7.39054e11	−	5.89376e11i	−0.766270	−	0.611080i	0.160358	−	0.987059i	$-0.448735\pi$
$991$	−7.39054e11	−	5.89376e11i	−0.766270	−	0.611080i	−0.926628	+	0.375979i	$0.877306\pi$
$992$	2.95568e11	−	2.35708e11i	0.305218	−	0.243404i
$993$	2.14291e11	−	9.38871e11i	0.220398	−	0.965626i
$994$	−9.16703e10	+	3.20768e10i	−0.0939038	+	0.0328584i
$995$	3.27076e11	−	6.79181e11i	0.333700	−	0.692936i
$996$	−1.09544e12	−	6.88310e11i	−1.11314	−	0.699434i
$997$	6.96505e11	+	2.43718e11i	0.704926	+	0.246664i	0.658851	−	0.752274i	$-0.271043\pi$
$997$	6.96505e11	+	2.43718e11i	0.704926	+	0.246664i	0.0460755	+	0.998938i	$0.485329\pi$
$998$	9.47853e10	−	9.47853e10i	0.0955474	−	0.0955474i
$999$	6.96488e11	+	1.44627e12i	0.699281	+	1.45207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.f.a.15.8	yes	228
29.2	odd	28	inner	29.9.f.a.2.8	✓	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.f.a.2.8	✓	228	29.2	odd	28	inner
29.9.f.a.15.8	yes	228	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	29.f (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.51607 + 0.621512i) q^{2} +(67.5754 - 42.4604i) q^{3} +(-219.541 + 50.1088i) q^{4} +(264.780 + 211.155i) q^{5} +(-346.361 + 276.213i) q^{6} +(606.153 - 2655.73i) q^{7} +(2521.16 - 882.193i) q^{8} +(-83.1675 + 172.699i) q^{9} +O(q^{10})\)	\(q+(-5.51607 + 0.621512i) q^{2} +(67.5754 - 42.4604i) q^{3} +(-219.541 + 50.1088i) q^{4} +(264.780 + 211.155i) q^{5} +(-346.361 + 276.213i) q^{6} +(606.153 - 2655.73i) q^{7} +(2521.16 - 882.193i) q^{8} +(-83.1675 + 172.699i) q^{9} +(-1591.78 - 1000.18i) q^{10} +(-1969.45 - 689.141i) q^{11} +(-12707.9 + 12707.9i) q^{12} +(-14575.2 - 30265.7i) q^{13} +(-1693.01 + 15025.9i) q^{14} +(26858.3 + 3026.21i) q^{15} +(38580.3 - 18579.3i) q^{16} +(-83330.5 - 83330.5i) q^{17} +(351.423 - 1004.31i) q^{18} +(97302.1 - 154855. i) q^{19} +(-68710.7 - 33089.4i) q^{20} +(-71802.4 - 205199. i) q^{21} +(11291.9 + 2577.31i) q^{22} +(-175466. - 220028. i) q^{23} +(132910. - 166664. i) q^{24} +(-61400.2 - 269012. i) q^{25} +(99208.2 + 157889. i) q^{26} +(60339.7 + 535529. i) q^{27} +613415. i q^{28} +(389422. + 590421. i) q^{29} -150033. q^{30} +(-407677. + 45934.1i) q^{31} +(-780245. + 490261. i) q^{32} +(-162348. + 37054.8i) q^{33} +(511447. + 407866. i) q^{34} +(721268. - 575192. i) q^{35} +(9604.93 - 42081.9i) q^{36} +(2.81148e6 - 983781. i) q^{37} +(-440481. + 914667. i) q^{38} +(-2.27002e6 - 1.42635e6i) q^{39} +(853833. + 298769. i) q^{40} +(-355267. + 355267. i) q^{41} +(523601. + 1.08727e6i) q^{42} +(-457817. + 4.06324e6i) q^{43} +(466907. + 52607.8i) q^{44} +(-58487.4 + 28166.0i) q^{45} +(1.10463e6 + 1.10463e6i) q^{46} +(-1.42653e6 + 4.07679e6i) q^{47} +(1.81819e6 - 2.89364e6i) q^{48} +(-1.49157e6 - 718303. i) q^{49} +(505882. + 1.44573e6i) q^{50} +(-9.16934e6 - 2.09284e6i) q^{51} +(4.71643e6 + 5.91421e6i) q^{52} +(4.24635e6 - 5.32475e6i) q^{53} +(-665675. - 2.91651e6i) q^{54} +(-375956. - 598330. i) q^{55} +(-814656. - 7.23027e6i) q^{56} -1.45959e7i q^{57} +(-2.51503e6 - 3.01477e6i) q^{58} +4.96718e6 q^{59} +(-6.04814e6 + 681462. i) q^{60} +(-4.06782e6 + 2.55598e6i) q^{61} +(2.22022e6 - 506751. i) q^{62} +(408230. + 325553. i) q^{63} +(-4.57136e6 + 3.64554e6i) q^{64} +(2.53153e6 - 1.10914e7i) q^{65} +(872490. - 305298. i) q^{66} +(8.71514e6 - 1.80972e7i) q^{67} +(2.24700e7 + 1.41189e7i) q^{68} +(-2.11997e7 - 7.41809e6i) q^{69} +(-3.62107e6 + 3.62107e6i) q^{70} +(2.78678e6 + 5.78682e6i) q^{71} +(-57324.9 + 508773. i) q^{72} +(2.53184e6 + 285270. i) q^{73} +(-1.48969e7 + 7.17397e6i) q^{74} +(-1.55715e7 - 1.55715e7i) q^{75} +(-1.36022e7 + 3.88728e7i) q^{76} +(-3.02396e6 + 4.81261e6i) q^{77} +(1.34081e7 + 6.45698e6i) q^{78} +(-1.94140e7 - 5.54822e7i) q^{79} +(1.41384e7 + 3.22700e6i) q^{80} +(2.60322e7 + 3.26433e7i) q^{81} +(1.73888e6 - 2.18048e6i) q^{82} +(1.60187e7 + 7.01826e7i) q^{83} +(2.60458e7 + 4.14517e7i) q^{84} +(-4.46860e6 - 3.96599e7i) q^{85} -2.26976e7i q^{86} +(5.13849e7 + 2.33629e7i) q^{87} -5.57326e6 q^{88} +(-867477. + 97741.2i) q^{89} +(305115. - 191716. i) q^{90} +(-8.92123e7 + 2.03621e7i) q^{91} +(4.95473e7 + 3.95127e7i) q^{92} +(-2.55985e7 + 2.04141e7i) q^{93} +(5.33506e6 - 2.33744e7i) q^{94} +(5.84622e7 - 2.04568e7i) q^{95} +(-3.19087e7 + 6.62591e7i) q^{96} +(-4.90325e7 - 3.08091e7i) q^{97} +(8.67405e6 + 3.03518e6i) q^{98} +(282808. - 282808. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9}+O(q^{10}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9	\( 228 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 14 q^{5} - 14 q^{6} - 10 q^{7} + 3664 q^{8} - 14 q^{9} - 15884 q^{10} + 8376 q^{11} - 5036 q^{12} - 14 q^{13} - 12742 q^{14} + 35516 q^{15} + 245898 q^{16} - 76248 q^{17} + 465008 q^{18} + 164474 q^{19} - 907274 q^{20} - 628270 q^{21} + 1214962 q^{22} + 173408 q^{23} + 1858618 q^{24} + 43976 q^{25} - 4604204 q^{26} - 1727586 q^{27} + 1079922 q^{29} + 8909208 q^{30} + 3657848 q^{31} + 1160364 q^{32} - 4279184 q^{33} - 8655374 q^{34} - 8269058 q^{35} - 3366854 q^{36} - 5622890 q^{37} + 15536626 q^{38} + 16110008 q^{39} - 23544696 q^{40} - 9561672 q^{41} - 14 q^{42} + 5181008 q^{43} + 51041750 q^{44} - 35245194 q^{45} - 43159224 q^{46} - 12806808 q^{47} + 83954488 q^{48} + 10429400 q^{49} + 80809398 q^{50} + 18760882 q^{51} - 93050550 q^{52} - 30960322 q^{53} - 106220916 q^{54} - 126174004 q^{55} - 40136268 q^{56} + 159368354 q^{58} + 11188020 q^{59} + 255893612 q^{60} + 139657128 q^{61} + 102501616 q^{62} + 9797746 q^{63} - 135941792 q^{64} - 14207858 q^{65} - 447597656 q^{66} - 148930894 q^{67} - 167094904 q^{68} + 66986722 q^{69} + 586255934 q^{70} - 15272096 q^{71} + 41230600 q^{72} - 219415072 q^{73} - 347464696 q^{74} + 391507416 q^{75} + 271512490 q^{76} + 240416780 q^{77} + 141747906 q^{78} + 112667220 q^{79} - 375642638 q^{80} - 358099268 q^{81} - 262154910 q^{82} - 109463350 q^{83} - 694921012 q^{84} - 356627386 q^{85} + 199703522 q^{87} + 251202768 q^{88} + 839849154 q^{89} + 675826020 q^{90} + 533256766 q^{91} + 742339570 q^{92} + 78998570 q^{93} - 209116610 q^{94} - 633414122 q^{95} - 431412576 q^{96} - 402046736 q^{97} - 2192087384 q^{98} - 1966368188 q^{99}+O(q^{100}) \) 228 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 14 * q^5 - 14 * q^6 - 10 * q^7 + 3664 * q^8 - 14 * q^9 - 15884 * q^10 + 8376 * q^11 - 5036 * q^12 - 14 * q^13 - 12742 * q^14 + 35516 * q^15 + 245898 * q^16 - 76248 * q^17 + 465008 * q^18 + 164474 * q^19 - 907274 * q^20 - 628270 * q^21 + 1214962 * q^22 + 173408 * q^23 + 1858618 * q^24 + 43976 * q^25 - 4604204 * q^26 - 1727586 * q^27 + 1079922 * q^29 + 8909208 * q^30 + 3657848 * q^31 + 1160364 * q^32 - 4279184 * q^33 - 8655374 * q^34 - 8269058 * q^35 - 3366854 * q^36 - 5622890 * q^37 + 15536626 * q^38 + 16110008 * q^39 - 23544696 * q^40 - 9561672 * q^41 - 14 * q^42 + 5181008 * q^43 + 51041750 * q^44 - 35245194 * q^45 - 43159224 * q^46 - 12806808 * q^47 + 83954488 * q^48 + 10429400 * q^49 + 80809398 * q^50 + 18760882 * q^51 - 93050550 * q^52 - 30960322 * q^53 - 106220916 * q^54 - 126174004 * q^55 - 40136268 * q^56 + 159368354 * q^58 + 11188020 * q^59 + 255893612 * q^60 + 139657128 * q^61 + 102501616 * q^62 + 9797746 * q^63 - 135941792 * q^64 - 14207858 * q^65 - 447597656 * q^66 - 148930894 * q^67 - 167094904 * q^68 + 66986722 * q^69 + 586255934 * q^70 - 15272096 * q^71 + 41230600 * q^72 - 219415072 * q^73 - 347464696 * q^74 + 391507416 * q^75 + 271512490 * q^76 + 240416780 * q^77 + 141747906 * q^78 + 112667220 * q^79 - 375642638 * q^80 - 358099268 * q^81 - 262154910 * q^82 - 109463350 * q^83 - 694921012 * q^84 - 356627386 * q^85 + 199703522 * q^87 + 251202768 * q^88 + 839849154 * q^89 + 675826020 * q^90 + 533256766 * q^91 + 742339570 * q^92 + 78998570 * q^93 - 209116610 * q^94 - 633414122 * q^95 - 431412576 * q^96 - 402046736 * q^97 - 2192087384 * q^98 - 1966368188 * q^99

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