LMFDB - Embedded newform 29.9.f.a.2.19

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			2.19
Character	$\chi$	$=$	29.2
Dual form			29.9.f.a.15.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(29.9840 + 3.37838i) q^{2} +(11.3862 + 7.15440i) q^{3} +(638.043 + 145.629i) q^{4} +(-500.927 + 399.476i) q^{5} +(317.232 + 252.984i) q^{6} +(838.383 + 3673.20i) q^{7} +(11348.1 + 3970.86i) q^{8} +(-2768.25 - 5748.33i) q^{9} +O(q^{10})$	\(q+(29.9840 + 3.37838i) q^{2} +(11.3862 + 7.15440i) q^{3} +(638.043 + 145.629i) q^{4} +(-500.927 + 399.476i) q^{5} +(317.232 + 252.984i) q^{6} +(838.383 + 3673.20i) q^{7} +(11348.1 + 3970.86i) q^{8} +(-2768.25 - 5748.33i) q^{9} +(-16369.4 + 10285.5i) q^{10} +(13317.0 - 4659.83i) q^{11} +(6222.97 + 6222.97i) q^{12} +(14877.4 - 30893.2i) q^{13} +(12728.6 + 112969. i) q^{14} +(-8561.64 + 964.666i) q^{15} +(175897. + 84707.6i) q^{16} +(-13167.6 + 13167.6i) q^{17} +(-63583.1 - 181710. i) q^{18} +(-122185. - 194457. i) q^{19} +(-377788. + 181933. i) q^{20} +(-16733.5 + 47821.7i) q^{21} +(415040. - 94730.2i) q^{22} +(-132959. + 166725. i) q^{23} +(100802. + 126401. i) q^{24} +(4424.54 - 19385.2i) q^{25} +(550451. - 876038. i) q^{26} +(19484.5 - 172930. i) q^{27} +2.46575e6i q^{28} +(703196. - 75909.6i) q^{29} -259971. q^{30} +(-941790. - 106114. i) q^{31} +(2.38185e6 + 1.49661e6i) q^{32} +(184968. + 42217.8i) q^{33} +(-439302. + 350332. i) q^{34} +(-1.88732e6 - 1.50509e6i) q^{35} +(-929139. - 4.07082e6i) q^{36} +(1.65611e6 + 579499. i) q^{37} +(-3.00665e6 - 6.24337e6i) q^{38} +(390418. - 245316. i) q^{39} +(-7.27082e6 + 2.54417e6i) q^{40} +(-775813. - 775813. i) q^{41} +(-663298. + 1.37735e6i) q^{42} +(-216287. - 1.91960e6i) q^{43} +(9.17545e6 - 1.03383e6i) q^{44} +(3.68301e6 + 1.77365e6i) q^{45} +(-4.54989e6 + 4.54989e6i) q^{46} +(-973692. - 2.78265e6i) q^{47} +(1.39676e6 + 2.22293e6i) q^{48} +(-7.59558e6 + 3.65784e6i) q^{49} +(198156. - 566297. i) q^{50} +(-244135. + 55722.1i) q^{51} +(1.39913e7 - 1.75446e7i) q^{52} +(-5.05866e6 - 6.34336e6i) q^{53} +(1.16844e6 - 5.11929e6i) q^{54} +(-4.80937e6 + 7.65407e6i) q^{55} +(-5.07172e6 + 4.50128e7i) q^{56} -3.08828e6i q^{57} +(2.13410e7 + 99591.1i) q^{58} +8.50967e6 q^{59} +(-5.60318e6 - 631327. i) q^{60} +(1.53473e7 + 9.64333e6i) q^{61} +(-2.78801e7 - 6.36345e6i) q^{62} +(1.87939e7 - 1.49876e7i) q^{63} +(2.72859e7 + 2.17597e7i) q^{64} +(4.88860e6 + 2.14184e7i) q^{65} +(5.40345e6 + 1.89075e6i) q^{66} +(9.88877e6 + 2.05342e7i) q^{67} +(-1.03191e7 + 6.48391e6i) q^{68} +(-2.70671e6 + 947118. i) q^{69} +(-5.15046e7 - 5.15046e7i) q^{70} +(-1.23497e7 + 2.56444e7i) q^{71} +(-8.58848e6 - 7.62248e7i) q^{72} +(-1.06709e7 + 1.20232e6i) q^{73} +(4.76991e7 + 2.29707e7i) q^{74} +(189068. - 189068. i) q^{75} +(-4.96409e7 - 1.41865e8i) q^{76} +(2.82813e7 + 4.50094e7i) q^{77} +(1.25351e7 - 6.03657e6i) q^{78} +(-7.58821e6 + 2.16859e7i) q^{79} +(-1.21950e8 + 2.78343e7i) q^{80} +(-2.46404e7 + 3.08981e7i) q^{81} +(-2.06410e7 - 2.58829e7i) q^{82} +(6.00911e6 - 2.63276e7i) q^{83} +(-1.76410e7 + 2.80754e7i) q^{84} +(1.33587e6 - 1.18561e7i) q^{85} -5.82879e7i q^{86} +(8.54979e6 + 4.16662e6i) q^{87} +1.69626e8 q^{88} +(7.87249e6 + 887017. i) q^{89} +(1.04439e8 + 6.56235e7i) q^{90} +(1.25950e8 + 2.87472e7i) q^{91} +(-1.09113e8 + 8.70150e7i) q^{92} +(-9.96419e6 - 7.94617e6i) q^{93} +(-1.97943e7 - 8.67245e7i) q^{94} +(1.38887e8 + 4.85986e7i) q^{95} +(1.64127e7 + 3.40814e7i) q^{96} +(-7.23040e7 + 4.54316e7i) q^{97} +(-2.40103e8 + 8.40157e7i) q^{98} +(-6.36512e7 - 6.36512e7i) 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 $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{28}\right)$

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 $

$2$	29.9840	+	3.37838i	1.87400	+	0.211149i	0.974283	−	0.225329i	$-0.0723458\pi$
$2$	29.9840	+	3.37838i	1.87400	+	0.211149i	0.899715	+	0.436478i	$0.143774\pi$
$3$	11.3862	+	7.15440i	0.140570	+	0.0883259i	0.600481	−	0.799639i	$-0.294976\pi$
$3$	11.3862	+	7.15440i	0.140570	+	0.0883259i	−0.459911	+	0.887965i	$0.652119\pi$
$4$	638.043	+	145.629i	2.49235	+	0.568864i
$5$	−500.927	+	399.476i	−0.801483	+	0.639161i	−0.936099	−	0.351736i	$-0.885591\pi$
$5$	−500.927	+	399.476i	−0.801483	+	0.639161i	0.134616	+	0.990898i	$0.457020\pi$
$6$	317.232	+	252.984i	0.244778	+	0.195204i
$7$	838.383	+	3673.20i	0.349181	+	1.52986i	0.779045	+	0.626968i	$0.215704\pi$
$7$	838.383	+	3673.20i	0.349181	+	1.52986i	−0.429864	+	0.902893i	$0.641439\pi$
$8$	11348.1	+	3970.86i	2.77052	+	0.969448i
$9$	−2768.25	−	5748.33i	−0.421925	−	0.876137i
$10$	−16369.4	+	10285.5i	−1.63694	+	1.02855i
$11$	13317.0	−	4659.83i	0.909572	−	0.318273i	0.165373	−	0.986231i	$-0.447117\pi$
$11$	13317.0	−	4659.83i	0.909572	−	0.318273i	0.744199	+	0.667958i	$0.232831\pi$
$12$	6222.97	+	6222.97i	0.300105	+	0.300105i
$13$	14877.4	−	30893.2i	0.520898	−	1.08166i	−0.460141	−	0.887846i	$-0.652201\pi$
$13$	14877.4	−	30893.2i	0.520898	−	1.08166i	0.981039	−	0.193810i	$-0.0620846\pi$
$14$	12728.6	+	112969.i	0.331336	+	2.94069i
$15$	−8561.64	+	964.666i	−0.169119	+	0.0190551i
$16$	175897.	+	84707.6i	2.68398	+	1.29253i
$17$	−13167.6	+	13167.6i	−0.157656	+	0.157656i	−0.781527	−	0.623871i	$-0.785559\pi$
$17$	−13167.6	+	13167.6i	−0.157656	+	0.157656i	0.623871	+	0.781527i	$0.285559\pi$
$18$	−63583.1	−	181710.i	−0.605692	−	1.73097i
$19$	−122185.	−	194457.i	−0.937572	−	1.49214i	−0.869190	−	0.494478i	$-0.835359\pi$
$19$	−122185.	−	194457.i	−0.937572	−	1.49214i	−0.0683813	−	0.997659i	$-0.521783\pi$
$20$	−377788.	+	181933.i	−2.36118	+	1.13708i
$21$	−16733.5	+	47821.7i	−0.0860421	+	0.245894i
$22$	415040.	−	94730.2i	1.77174	−	0.404388i
$23$	−132959.	+	166725.i	−0.475122	+	0.595785i	−0.960417	−	0.278566i	$-0.910141\pi$
$23$	−132959.	+	166725.i	−0.475122	+	0.595785i	0.485295	+	0.874351i	$0.338712\pi$
$24$	100802.	+	126401.i	0.303825	+	0.380984i
$25$	4424.54	−	19385.2i	0.0113268	−	0.0496261i
$26$	550451.	−	876038.i	1.20455	−	1.91703i
$27$	19484.5	−	172930.i	0.0366635	−	0.325398i
$28$			2.46575e6i			4.01159i
$29$	703196.	−	75909.6i	0.994224	−	0.107326i
$29$	703196.	−	75909.6i	0.994224	−	0.107326i
$30$	−259971.			−0.320952
$31$	−941790.	−	106114.i	−1.01978	−	0.114902i	−0.413790	−	0.910373i	$-0.635795\pi$
$31$	−941790.	−	106114.i	−1.01978	−	0.114902i	−0.605992	+	0.795471i	$0.707224\pi$
$32$	2.38185e6	+	1.49661e6i	2.27151	+	1.42728i
$33$	184968.	+	42217.8i	0.155970	+	0.0355992i
$34$	−439302.	+	350332.i	−0.328736	+	0.262158i
$35$	−1.88732e6	−	1.50509e6i	−1.25769	−	1.00297i
$36$	−929139.	−	4.07082e6i	−0.553185	−	2.42366i
$37$	1.65611e6	+	579499.i	0.883656	+	0.309205i	0.733688	−	0.679486i	$-0.237797\pi$
$37$	1.65611e6	+	579499.i	0.883656	+	0.309205i	0.149968	+	0.988691i	$0.452083\pi$
$38$	−3.00665e6	−	6.24337e6i	−1.44194	−	2.99423i
$39$	390418.	−	245316.i	0.168761	−	0.106039i
$40$	−7.27082e6	+	2.54417e6i	−2.84016	+	0.993816i
$41$	−775813.	−	775813.i	−0.274550	−	0.274550i	0.556379	−	0.830929i	$-0.312190\pi$
$41$	−775813.	−	775813.i	−0.274550	−	0.274550i	−0.830929	+	0.556379i	$0.812190\pi$
$42$	−663298.	+	1.37735e6i	−0.213163	+	0.442637i
$43$	−216287.	−	1.91960e6i	−0.0632640	−	0.561483i	−0.984862	−	0.173338i	$-0.944545\pi$
$43$	−216287.	−	1.91960e6i	−0.0632640	−	0.561483i	0.921598	−	0.388145i	$-0.126884\pi$
$44$	9.17545e6	−	1.03383e6i	2.44803	−	0.275827i
$45$	3.68301e6	+	1.77365e6i	0.898159	+	0.432531i
$46$	−4.54989e6	+	4.54989e6i	−1.01618	+	1.01618i
$47$	−973692.	−	2.78265e6i	−0.199540	−	0.570253i	0.800018	−	0.599976i	$-0.204823\pi$
$47$	−973692.	−	2.78265e6i	−0.199540	−	0.570253i	−0.999558	+	0.0297229i	$0.990538\pi$
$48$	1.39676e6	+	2.22293e6i	0.263122	+	0.418756i
$49$	−7.59558e6	+	3.65784e6i	−1.31758	+	0.634513i
$50$	198156.	−	566297.i	0.0317049	−	0.0906075i
$51$	−244135.	+	55722.1i	−0.0360868	+	0.00823658i
$52$	1.39913e7	−	1.75446e7i	1.91358	−	2.39955i
$53$	−5.05866e6	−	6.34336e6i	−0.641109	−	0.803925i	0.350032	−	0.936738i	$-0.386171\pi$
$53$	−5.05866e6	−	6.34336e6i	−0.641109	−	0.803925i	−0.991141	+	0.132812i	$0.957599\pi$
$54$	1.16844e6	−	5.11929e6i	0.137415	−	0.602053i
$55$	−4.80937e6	+	7.65407e6i	−0.525579	+	0.836454i
$56$	−5.07172e6	+	4.50128e7i	−0.515708	+	4.57703i
$57$		−	3.08828e6i		−	0.292561i
$58$	2.13410e7	+	99591.1i	1.88583	+	0.00880053i
$59$	8.50967e6			0.702271			0.351136	−	0.936325i	$-0.385796\pi$
$59$	8.50967e6			0.702271			0.351136	+	0.936325i	$0.385796\pi$
$60$	−5.60318e6	−	631327.i	−0.432344	−	0.0487135i
$61$	1.53473e7	+	9.64333e6i	1.10844	+	0.696478i	0.956448	−	0.291903i	$-0.0942886\pi$
$61$	1.53473e7	+	9.64333e6i	1.10844	+	0.696478i	0.151991	+	0.988382i	$0.451431\pi$
$62$	−2.78801e7	−	6.36345e6i	−1.88681	−	0.430651i
$63$	1.87939e7	−	1.49876e7i	1.19304	−	0.951417i
$64$	2.72859e7	+	2.17597e7i	1.62636	+	1.29698i
$65$	4.88860e6	+	2.14184e7i	0.273862	+	1.19987i
$66$	5.40345e6	+	1.89075e6i	0.284771	+	0.0996457i
$67$	9.88877e6	+	2.05342e7i	0.490731	+	1.01901i	0.988432	+	0.151664i	$0.0484632\pi$
$67$	9.88877e6	+	2.05342e7i	0.490731	+	1.01901i	−0.497701	+	0.867348i	$0.665822\pi$
$68$	−1.03191e7	+	6.48391e6i	−0.482620	+	0.303250i
$69$	−2.70671e6	+	947118.i	−0.119411	+	0.0417838i
$70$	−5.15046e7	−	5.15046e7i	−2.14513	−	2.14513i
$71$	−1.23497e7	+	2.56444e7i	−0.485984	+	1.00916i	0.503430	+	0.864036i	$0.332071\pi$
$71$	−1.23497e7	+	2.56444e7i	−0.485984	+	1.00916i	−0.989414	+	0.145120i	$0.953643\pi$
$72$	−8.58848e6	−	7.62248e7i	−0.319585	−	2.83639i
$73$	−1.06709e7	+	1.20232e6i	−0.375759	+	0.0423379i	−0.297825	−	0.954621i	$-0.596261\pi$
$73$	−1.06709e7	+	1.20232e6i	−0.375759	+	0.0423379i	−0.0779346	+	0.996958i	$0.524833\pi$
$74$	4.76991e7	+	2.29707e7i	1.59068	+	0.766031i
$75$	189068.	−	189068.i	0.00597548	−	0.00597548i
$76$	−4.96409e7	−	1.41865e8i	−1.48794	−	4.25229i
$77$	2.82813e7	+	4.50094e7i	0.804518	+	1.28038i
$78$	1.25351e7	−	6.03657e6i	0.338648	−	0.163084i
$79$	−7.58821e6	+	2.16859e7i	−0.194819	+	0.556761i	−0.999308	−	0.0372075i	$-0.988154\pi$
$79$	−7.58821e6	+	2.16859e7i	−0.194819	+	0.556761i	0.804489	+	0.593968i	$0.202439\pi$
$80$	−1.21950e8	+	2.78343e7i	−2.97730	+	0.679549i
$81$	−2.46404e7	+	3.08981e7i	−0.572411	+	0.717780i
$82$	−2.06410e7	−	2.58829e7i	−0.456535	−	0.572477i
$83$	6.00911e6	−	2.63276e7i	0.126619	−	0.554753i	−0.871328	−	0.490701i	$-0.836741\pi$
$83$	6.00911e6	−	2.63276e7i	0.126619	−	0.554753i	0.997947	−	0.0640514i	$-0.0204022\pi$
$84$	−1.76410e7	+	2.80754e7i	−0.354328	+	0.563909i
$85$	1.33587e6	−	1.18561e7i	0.0255910	−	0.227126i
$86$		−	5.82879e7i		−	1.06558i
$87$	8.54979e6	+	4.16662e6i	0.149238	+	0.0727289i
$88$	1.69626e8			2.82854
$89$	7.87249e6	+	887017.i	0.125474	+	0.0141375i	0.174478	−	0.984661i	$-0.444176\pi$
$89$	7.87249e6	+	887017.i	0.125474	+	0.0141375i	−0.0490043	+	0.998799i	$0.515605\pi$
$90$	1.04439e8	+	6.56235e7i	1.59182	+	1.00021i
$91$	1.25950e8	+	2.87472e7i	1.83667	+	0.419208i
$92$	−1.09113e8	+	8.70150e7i	−1.52309	+	1.21463i
$93$	−9.96419e6	−	7.94617e6i	−0.133202	−	0.106225i
$94$	−1.97943e7	−	8.67245e7i	−0.253530	−	1.11079i
$95$	1.38887e8	+	4.85986e7i	1.70516	+	0.596663i
$96$	1.64127e7	+	3.40814e7i	0.193240	+	0.401266i
$97$	−7.23040e7	+	4.54316e7i	−0.816724	+	0.513182i	−0.874430	−	0.485152i	$-0.838764\pi$
$97$	−7.23040e7	+	4.54316e7i	−0.816724	+	0.513182i	0.0577056	+	0.998334i	$0.481622\pi$
$98$	−2.40103e8	+	8.40157e7i	−2.60312	+	0.910870i
$99$	−6.36512e7	−	6.36512e7i	−0.662622	−	0.662622i
$100$	5.64610e6	−	1.17242e7i	0.0564610	−	0.117242i
$101$	2.82347e6	+	2.50590e7i	0.0271330	+	0.240812i	0.999957	+	0.00926648i	$0.00294966\pi$
$101$	2.82347e6	+	2.50590e7i	0.0271330	+	0.240812i	−0.972824	+	0.231546i	$0.925622\pi$
$102$	−7.50837e6	+	845991.i	−0.0693658	+	0.00781565i
$103$	−8.97954e7	−	4.32432e7i	−0.797821	−	0.384210i	−0.00987209	−	0.999951i	$-0.503142\pi$
$103$	−8.97954e7	−	4.32432e7i	−0.797821	−	0.384210i	−0.787949	+	0.615741i	$0.788857\pi$
$104$	2.91502e8	−	2.91502e8i	2.49177	−	2.49177i
$105$	−1.07213e7	−	3.06398e7i	−0.0882048	−	0.252075i
$106$	−1.30248e8	−	2.07289e8i	−1.03169	−	1.64192i
$107$	−1.50885e8	+	7.26624e7i	−1.15109	+	0.554338i	−0.909362	−	0.416005i	$-0.863430\pi$
$107$	−1.50885e8	+	7.26624e7i	−1.15109	+	0.554338i	−0.241732	+	0.970343i	$0.577715\pi$
$108$	3.76155e7	−	1.07499e8i	0.276485	−	0.790150i
$109$	1.57186e8	−	3.58768e7i	1.11355	−	0.254160i	0.374110	−	0.927384i	$-0.377948\pi$
$109$	1.57186e8	−	3.58768e7i	1.11355	−	0.254160i	0.739439	+	0.673224i	$0.235091\pi$
$110$	−1.70062e8	+	2.13252e8i	−1.16155	+	1.45654i
$111$	1.47108e7	+	1.84468e7i	0.0969046	+	0.121515i
$112$	−1.63678e8	+	7.17122e8i	−1.04021	+	4.55744i
$113$	7.94589e7	−	1.26458e8i	0.487336	−	0.775591i	−0.509032	−	0.860748i	$-0.669996\pi$
$113$	7.94589e7	−	1.26458e8i	0.487336	−	0.775591i	0.996368	+	0.0851571i	$0.0271392\pi$
$114$	1.04334e7	−	9.25988e7i	0.0617740	−	0.548259i
$115$		−	1.36631e8i		−	0.781191i
$116$	4.59724e8	+	5.39722e7i	2.53901	+	0.298083i
$117$	−2.18769e8			−1.16746
$118$	2.55154e8	+	2.87489e7i	1.31605	+	0.148284i
$119$	−5.94067e7	−	3.73277e7i	−0.296243	−	0.186142i
$120$	−1.00989e8	−	2.30500e7i	−0.487021	−	0.111159i
$121$	−1.19630e7	+	9.54016e6i	−0.0558082	+	0.0445055i
$122$	4.27593e8	+	3.40994e8i	1.93015	+	1.53924i
$123$	−3.28306e6	−	1.43840e7i	−0.0143436	−	0.0628434i
$124$	−5.85449e8	−	2.04857e8i	−2.47629	−	0.866493i
$125$	−1.03064e8	−	2.14014e8i	−0.422149	−	0.876601i
$126$	6.14150e8	−	3.85896e8i	2.43664	−	1.53104i
$127$	−3.81607e8	+	1.33530e8i	−1.46690	+	0.513292i	−0.941339	−	0.337463i	$-0.890431\pi$
$127$	−3.81607e8	+	1.33530e8i	−1.46690	+	0.513292i	−0.525564	+	0.850754i	$0.676146\pi$
$128$	2.35415e8	+	2.35415e8i	0.876990	+	0.876990i
$129$	1.12709e7	−	2.34043e7i	0.0407005	−	0.0845155i
$130$	7.42203e7	+	6.58723e8i	0.259866	+	2.30637i
$131$	−2.28425e8	+	2.57373e7i	−0.775637	+	0.0873933i	−0.490904	−	0.871214i	$-0.663333\pi$
$131$	−2.28425e8	+	2.57373e7i	−0.775637	+	0.0873933i	−0.284733	+	0.958607i	$0.591905\pi$
$132$	1.11870e8	+	5.38735e7i	0.368482	+	0.177452i
$133$	6.11840e8	−	6.11840e8i	1.95538	−	1.95538i
$134$	2.27132e8	+	6.49106e8i	0.704465	+	2.01324i
$135$	5.93209e7	+	9.44087e7i	0.178596	+	0.284235i
$136$	−2.01714e8	+	9.71401e7i	−0.589630	+	0.283951i
$137$	4.39480e7	−	1.25596e8i	0.124755	−	0.356529i	−0.864519	−	0.502600i	$-0.832377\pi$
$137$	4.39480e7	−	1.25596e8i	0.124755	−	0.356529i	0.989274	+	0.146071i	$0.0466628\pi$
$138$	−8.43575e7	+	1.92541e7i	−0.232599	+	0.0530892i
$139$	−3.28100e8	+	4.11424e8i	−0.878914	+	1.10212i	0.115152	+	0.993348i	$0.463264\pi$
$139$	−3.28100e8	+	4.11424e8i	−0.878914	+	1.10212i	−0.994066	+	0.108776i	$0.965307\pi$
$140$	−9.85008e8	−	1.23516e9i	−2.56406	−	3.21522i
$141$	8.82159e6	−	3.86499e7i	0.0223188	−	0.0977850i
$142$	−4.56928e8	+	7.27197e8i	−1.12381	+	1.78854i
$143$	5.41655e7	−	4.80732e8i	0.129532	−	1.14963i
$144$		−	1.24561e9i		−	2.89688i
$145$	−3.21926e8	+	3.18935e8i	−0.728255	+	0.721489i
$146$	−3.24018e8			−0.713112
$147$	−1.12654e8	−	1.26931e7i	−0.241256	−	0.0271830i
$148$	9.72279e8	+	6.10924e8i	2.02649	+	1.27333i
$149$	4.24310e8	+	9.68459e7i	0.860871	+	0.196488i	0.630094	−	0.776519i	$-0.283016\pi$
$149$	4.24310e8	+	9.68459e7i	0.860871	+	0.196488i	0.230776	+	0.973007i	$0.425873\pi$
$150$	6.30775e6	−	5.03026e6i	0.0124598	−	0.00993632i
$151$	6.95546e8	+	5.54679e8i	1.33788	+	1.06693i	0.991675	+	0.128768i	$0.0411022\pi$
$151$	6.95546e8	+	5.54679e8i	1.33788	+	1.06693i	0.346208	+	0.938158i	$0.387469\pi$
$152$	−6.14406e8	−	2.69189e9i	−1.15102	−	5.04293i
$153$	1.12143e8	+	3.92405e7i	0.204647	+	0.0716093i
$154$	6.95926e8	+	1.44510e9i	1.23731	+	2.56931i
$155$	5.14158e8	−	3.23067e8i	0.890778	−	0.559713i
$156$	2.84829e8	−	9.96659e7i	0.480934	−	0.168286i
$157$	−3.54436e8	−	3.54436e8i	−0.583364	−	0.583364i	0.352462	−	0.935826i	$-0.385344\pi$
$157$	−3.54436e8	−	3.54436e8i	−0.583364	−	0.583364i	−0.935826	+	0.352462i	$0.885344\pi$
$158$	−3.00788e8	+	6.24592e8i	−0.482650	+	1.00223i
$159$	−1.22158e7	−	1.08418e8i	−0.0191132	−	0.169634i
$160$	−1.79099e9	+	2.01797e8i	−2.73284	+	0.307917i
$161$	−7.23884e8	−	3.48604e8i	−1.07737	−	0.518835i
$162$	−8.43202e8	+	8.43202e8i	−1.22425	+	1.22425i
$163$	−2.24264e8	−	6.40910e8i	−0.317694	−	0.907918i	−0.986396	−	0.164387i	$-0.947435\pi$
$163$	−2.24264e8	−	6.40910e8i	−0.317694	−	0.907918i	0.668702	−	0.743531i	$-0.266850\pi$
$164$	−3.82021e8	−	6.07983e8i	−0.528095	−	0.840458i
$165$	−1.09521e8	+	5.27423e7i	−0.147761	+	0.0711580i
$166$	2.69122e8	−	7.69105e8i	0.354418	−	1.01287i
$167$	1.00010e9	−	2.28266e8i	1.28581	−	0.293478i	0.475623	−	0.879649i	$-0.342223\pi$
$167$	1.00010e9	−	2.28266e8i	1.28581	−	0.293478i	0.810187	+	0.586171i	$0.199365\pi$
$168$	−3.79787e8	+	4.76238e8i	−0.476763	+	0.597842i
$169$	−2.24453e8	−	2.81455e8i	−0.275155	−	0.345034i
$170$	8.01091e7	−	3.50981e8i	0.0959150	−	0.420231i
$171$	−7.79563e8	+	1.24067e9i	−0.911731	+	1.45101i
$172$	1.41549e8	−	1.25628e9i	0.161731	−	1.43540i
$173$			8.23260e8i			0.919079i	0.888157	+	0.459539i	$0.151986\pi$
$173$			8.23260e8i			0.919079i	−0.888157	+	0.459539i	$0.848014\pi$
$174$	2.42280e8	+	1.53816e8i	0.264314	+	0.167805i
$175$	7.49151e7			0.0798762
$176$	2.73715e9	+	3.08403e8i	2.85265	+	0.321416i
$177$	9.68925e7	+	6.08816e7i	0.0987182	+	0.0620287i
$178$	2.33052e8	+	5.31926e7i	0.232152	+	0.0529872i
$179$	−1.74582e8	+	1.39224e8i	−0.170054	+	0.135613i	−0.704819	−	0.709388i	$-0.748972\pi$
$179$	−1.74582e8	+	1.39224e8i	−0.170054	+	0.135613i	0.534765	+	0.845001i	$0.320400\pi$
$180$	2.09163e9	+	1.66802e9i	1.99248	+	1.58895i
$181$	3.58451e8	+	1.57048e9i	0.333977	+	1.46325i	0.811357	+	0.584550i	$0.198729\pi$
$181$	3.58451e8	+	1.57048e9i	0.333977	+	1.46325i	−0.477381	+	0.878697i	$0.658414\pi$
$182$	3.67935e9	+	1.28746e9i	3.35340	+	1.17341i
$183$	1.05754e8	+	2.19601e8i	0.0942961	+	0.195808i
$184$	−2.17087e9	+	1.36405e9i	−1.89392	+	1.19003i
$185$	−1.06109e9	+	3.71291e8i	−0.905867	+	0.316977i
$186$	−2.71921e8	−	2.71921e8i	−0.227191	−	0.227191i
$187$	−1.13995e8	+	2.36712e8i	−0.0932219	+	0.193577i
$188$	−2.16022e8	−	1.91725e9i	−0.172929	−	1.53478i
$189$	6.51540e8	−	7.34109e7i	0.510615	−	0.0575325i
$190$	4.00019e9	+	1.92639e9i	3.06949	+	1.47819i
$191$	1.13852e9	−	1.13852e9i	0.855476	−	0.855476i	−0.135325	−	0.990801i	$-0.543208\pi$
$191$	1.13852e9	−	1.13852e9i	0.855476	−	0.855476i	0.990801	+	0.135325i	$0.0432079\pi$
$192$	1.55003e8	+	4.42974e8i	0.114061	+	0.325967i
$193$	−8.20787e8	−	1.30628e9i	−0.591564	−	0.941468i	−0.999594	−	0.0284996i	$-0.990927\pi$
$193$	−8.20787e8	−	1.30628e9i	−0.591564	−	0.941468i	0.408030	−	0.912968i	$-0.366216\pi$
$194$	−2.32145e9	+	1.11795e9i	−1.63890	+	0.789251i
$195$	−9.75732e7	+	2.78848e8i	−0.0674826	+	0.192854i
$196$	−5.37899e9	+	1.22772e9i	−3.64483	+	0.831908i
$197$	7.00307e8	−	8.78157e8i	0.464968	−	0.583052i	−0.492963	−	0.870050i	$-0.664086\pi$
$197$	7.00307e8	−	8.78157e8i	0.464968	−	0.583052i	0.957931	+	0.286999i	$0.0926575\pi$
$198$	−1.69348e9	−	2.12355e9i	−1.10184	−	1.38166i
$199$	2.90899e8	−	1.27451e9i	0.185494	−	0.812702i	−0.793460	−	0.608622i	$-0.791723\pi$
$199$	2.90899e8	−	1.27451e9i	0.185494	−	0.812702i	0.978954	−	0.204080i	$-0.0654203\pi$
$200$	1.27186e8	−	2.02415e8i	0.0794912	−	0.126510i
$201$	−3.43150e7	+	3.04554e8i	−0.0210233	+	0.186587i
$202$			7.60907e8i			0.457010i
$203$	8.68378e8	+	2.51933e9i	0.511358	+	1.48355i
$204$	−1.63883e8			−0.0946267
$205$	6.98544e8	+	7.87070e7i	0.395529	+	0.0445654i
$206$	−2.54633e9	−	1.59997e9i	−1.41399	−	0.888468i
$207$	1.32645e9	+	3.02755e8i	0.722455	+	0.164896i
$208$	5.23377e9	−	4.17379e9i	2.79616	−	2.22986i
$209$	−2.53328e9	−	2.02023e9i	−1.32770	−	1.05880i
$210$	−2.17955e8	−	9.54925e8i	−0.112070	−	0.491012i
$211$	−2.31343e9	−	8.09504e8i	−1.16715	−	0.408403i	−0.323987	−	0.946062i	$-0.605023\pi$
$211$	−2.31343e9	−	8.09504e8i	−1.16715	−	0.408403i	−0.843163	+	0.537658i	$0.819309\pi$
$212$	−2.30386e9	−	4.78402e9i	−1.14055	−	2.36837i
$213$	−3.24085e8	+	2.03636e8i	−0.157449	+	0.0989320i
$214$	−4.76961e9	+	1.66896e9i	−2.27420	+	0.795775i
$215$	8.75178e8	+	8.75178e8i	0.409584	+	0.409584i
$216$	9.07791e8	−	1.88505e9i	0.417033	−	0.865979i
$217$	−3.99802e8	−	3.54834e9i	−0.180304	−	1.60025i
$218$	4.83428e9	−	5.44692e8i	2.14045	−	0.241171i
$219$	−1.30103e8	−	6.26541e7i	−0.0565600	−	0.0272378i
$220$	−4.18324e9	+	4.18324e9i	−1.78576	+	1.78576i
$221$	2.10890e8	+	6.02688e8i	0.0884069	+	0.252653i
$222$	3.78768e8	+	6.02806e8i	0.155941	+	0.248179i
$223$	−4.02085e8	+	1.93634e8i	−0.162592	+	0.0783000i	−0.513410	−	0.858144i	$-0.671618\pi$
$223$	−4.02085e8	+	1.93634e8i	−0.162592	+	0.0783000i	0.350818	+	0.936444i	$0.385904\pi$
$224$	−3.50046e9	+	1.00037e10i	−1.39038	+	3.97347i
$225$	−1.23681e8	+	2.82293e7i	−0.0482583	+	0.0110147i
$226$	2.80971e9	−	3.52327e9i	1.07703	−	1.35055i
$227$	1.62288e9	+	2.03503e9i	0.611200	+	0.766421i	0.987077	−	0.160249i	$-0.0512297\pi$
$227$	1.62288e9	+	2.03503e9i	0.611200	+	0.766421i	−0.375876	+	0.926670i	$0.622658\pi$
$228$	4.49743e8	−	1.97045e9i	0.166428	−	0.729167i
$229$	1.93323e7	−	3.07671e7i	0.00702977	−	0.0111878i	−0.843191	−	0.537614i	$-0.819326\pi$
$229$	1.93323e7	−	3.07671e7i	0.00702977	−	0.0111878i	0.850221	+	0.526427i	$0.176468\pi$
$230$	4.61591e8	−	4.09673e9i	0.164948	−	1.46395i
$231$			7.14820e8i			0.251043i
$232$	8.28134e9	+	1.93086e9i	2.85857	+	0.666500i
$233$	2.12438e8			0.0720791			0.0360396	−	0.999350i	$-0.488526\pi$
$233$	2.12438e8			0.0720791			0.0360396	+	0.999350i	$0.488526\pi$
$234$	−6.55955e9	−	7.39084e8i	−2.18782	−	0.246508i
$235$	1.59935e9	+	1.00494e9i	0.524412	+	0.329510i
$236$	5.42954e9	+	1.23926e9i	1.75031	+	0.399497i
$237$	−2.41550e8	+	1.92630e8i	−0.0765621	+	0.0610562i
$238$	−1.65514e9	−	1.31993e9i	−0.515854	−	0.411380i
$239$	−3.28637e7	−	1.43985e8i	−0.0100722	−	0.0441293i	0.969642	−	0.244529i	$-0.0786332\pi$
$239$	−3.28637e7	−	1.43985e8i	−0.0100722	−	0.0441293i	−0.979714	+	0.200399i	$0.935776\pi$
$240$	−1.58768e9	−	5.55554e8i	−0.478540	−	0.167449i
$241$	1.28370e9	+	2.66564e9i	0.380537	+	0.790193i	0.999987	+	0.00515644i	$0.00164135\pi$
$241$	1.28370e9	+	2.66564e9i	0.380537	+	0.790193i	−0.619450	+	0.785036i	$0.712644\pi$
$242$	−3.90928e8	+	2.45636e8i	−0.113982	+	0.0716194i
$243$	−1.57932e9	+	5.52626e8i	−0.452943	+	0.158492i
$244$	8.38787e9	+	8.38787e9i	2.36642	+	2.36642i
$245$	2.34361e9	−	4.86656e9i	0.650461	−	1.35070i
$246$	−4.98443e7	−	4.42381e8i	−0.0136105	−	0.120797i
$247$	−7.82518e9	+	8.81686e8i	−2.10236	+	0.236879i
$248$	−1.02661e10	−	4.94391e9i	−2.71394	−	1.30696i
$249$	2.56779e8	−	2.56779e8i	0.0667978	−	0.0667978i
$250$	−2.36724e9	−	6.76517e9i	−0.606012	−	1.73188i
$251$	9.47049e8	+	1.50722e9i	0.238604	+	0.379736i	0.944464	−	0.328615i	$-0.106582\pi$
$251$	9.47049e8	+	1.50722e9i	0.238604	+	0.379736i	−0.705860	+	0.708352i	$0.749439\pi$
$252$	1.41740e10	−	6.82582e9i	3.51471	−	1.69259i
$253$	−9.93706e8	+	2.83985e9i	−0.242536	+	0.693128i
$254$	−1.18932e10	+	2.71455e9i	−2.85735	+	0.652172i
$255$	1.00034e8	−	1.25439e8i	0.0236585	−	0.0296668i
$256$	6.92861e8	+	8.68821e8i	0.161319	+	0.202288i
$257$	8.37719e8	−	3.67029e9i	0.192029	−	0.841332i	−0.783488	−	0.621407i	$-0.786561\pi$
$257$	8.37719e8	−	3.67029e9i	0.192029	−	0.841332i	0.975517	−	0.219925i	$-0.0705814\pi$
$258$	4.17015e8	−	6.63676e8i	0.0941180	−	0.149788i
$259$	−7.40157e8	+	6.56907e9i	−0.164484	+	1.45984i
$260$			1.43778e10i			3.14628i
$261$	−2.38298e9	−	3.83207e9i	−0.513520	−	0.825793i
$262$	−6.93604e9			−1.47200
$263$	5.34358e9	+	6.02076e8i	1.11689	+	0.125843i	0.651055	−	0.759031i	$-0.274327\pi$
$263$	5.34358e9	+	6.02076e8i	1.11689	+	0.125843i	0.465831	+	0.884874i	$0.345755\pi$
$264$	1.93139e9	+	1.21357e9i	0.397608	+	0.249833i
$265$	5.06804e9	+	1.15675e9i	1.02768	+	0.234560i
$266$	2.04124e10	−	1.62784e10i	4.07725	−	3.25150i
$267$	8.32914e7	+	6.64227e7i	0.0163891	+	0.0130699i
$268$	3.31908e9	+	1.45418e10i	0.643395	+	2.81890i
$269$	−8.91755e9	−	3.12039e9i	−1.70309	−	0.595935i	−0.709066	−	0.705142i	$-0.750883\pi$
$269$	−8.91755e9	−	3.12039e9i	−1.70309	−	0.595935i	−0.994019	+	0.109207i	$0.965169\pi$
$270$	1.45973e9	+	3.03116e9i	0.274673	+	0.570365i
$271$	−1.37170e9	+	8.61894e8i	−0.254320	+	0.159800i	−0.653158	−	0.757221i	$-0.726556\pi$
$271$	−1.37170e9	+	8.61894e8i	−0.254320	+	0.159800i	0.398838	+	0.917021i	$0.369414\pi$
$272$	−3.43154e9	+	1.20075e9i	−0.626921	+	0.219369i
$273$	1.22841e9	+	1.22841e9i	0.221154	+	0.221154i
$274$	1.74205e9	−	3.61740e9i	0.309071	−	0.641792i
$275$	−3.14100e7	−	2.78771e8i	−0.00549208	−	0.0487435i
$276$	−1.86492e9	+	2.10126e8i	−0.321384	+	0.0362113i
$277$	5.48857e9	+	2.64315e9i	0.932266	+	0.448956i	0.837435	−	0.546538i	$-0.184054\pi$
$277$	5.48857e9	+	2.64315e9i	0.932266	+	0.448956i	0.0948315	+	0.995493i	$0.469769\pi$
$278$	−1.12277e10	+	1.12277e10i	−1.87980	+	1.87980i
$279$	1.99713e9	+	5.70747e9i	0.329602	+	0.941948i
$280$	−1.54410e10	−	2.45741e10i	−2.51213	−	3.99803i
$281$	7.73664e9	−	3.72577e9i	1.24087	−	0.597572i	0.305822	−	0.952089i	$-0.401069\pi$
$281$	7.73664e9	−	3.72577e9i	1.24087	−	0.597572i	0.935050	+	0.354516i	$0.115354\pi$
$282$	3.95080e8	−	1.12907e9i	0.0624725	−	0.178536i
$283$	5.69400e9	−	1.29962e9i	0.887711	−	0.202614i	0.245734	−	0.969337i	$-0.420971\pi$
$283$	5.69400e9	−	1.29962e9i	0.887711	−	0.202614i	0.641978	+	0.766723i	$0.278114\pi$
$284$	−1.16142e10	+	1.45637e10i	−1.78532	+	2.23872i
$285$	1.23369e9	+	1.54700e9i	0.186994	+	0.234483i
$286$	3.24819e9	−	1.42313e10i	0.485487	−	2.12706i
$287$	2.19928e9	−	3.50014e9i	0.324156	−	0.515891i
$288$	2.00948e9	−	1.78347e10i	0.292089	−	2.59236i
$289$			6.62899e9i			0.950289i
$290$	−1.07301e10	+	8.47534e9i	−1.51709	+	1.19830i
$291$	−1.14830e9			−0.160134
$292$	−6.98359e9	−	7.86861e8i	−0.960610	−	0.108235i
$293$	−8.19440e9	−	5.14888e9i	−1.11185	−	0.698622i	−0.154628	−	0.987973i	$-0.549418\pi$
$293$	−8.19440e9	−	5.14888e9i	−1.11185	−	0.698622i	−0.957223	+	0.289351i	$0.906561\pi$
$294$	−3.33494e9	−	7.61177e8i	−0.446373	−	0.101882i
$295$	−4.26272e9	+	3.39941e9i	−0.562859	+	0.448865i
$296$	1.64926e10	+	1.31524e10i	2.14843	+	1.71332i
$297$	−5.46348e8	−	2.39371e9i	−0.0702172	−	0.307642i
$298$	1.23953e10	+	4.33730e9i	1.57178	+	0.549990i
$299$	3.17259e9	+	6.58795e9i	0.396944	+	0.824262i
$300$	1.48167e8	−	9.30997e7i	0.0182923	−	0.0114938i
$301$	6.86974e9	−	2.40383e9i	0.836901	−	0.292844i
$302$	1.89813e10	+	1.89813e10i	2.28191	+	2.28191i
$303$	−1.47134e8	+	3.05526e8i	−0.0174559	+	0.0362475i
$304$	−5.02007e9	−	4.45544e10i	−0.587781	−	5.21670i
$305$	−1.15401e10	+	1.30026e9i	−1.33356	+	0.150256i
$306$	3.22992e9	+	1.55545e9i	0.368389	+	0.177407i
$307$	−3.99987e9	+	3.99987e9i	−0.450291	+	0.450291i	−0.895451	−	0.445160i	$-0.853147\pi$
$307$	−3.99987e9	+	3.99987e9i	−0.450291	+	0.450291i	0.445160	+	0.895451i	$0.353147\pi$
$308$	1.14900e10	+	3.28365e10i	1.27678	+	3.64883i
$309$	−7.13046e8	−	1.13481e9i	−0.0782138	−	0.124477i
$310$	1.65079e10	−	7.94980e9i	1.78750	−	0.860814i
$311$	−2.35308e9	+	6.72471e9i	−0.251533	+	0.718839i	0.747007	+	0.664816i	$0.231490\pi$
$311$	−2.35308e9	+	6.72471e9i	−0.251533	+	0.718839i	−0.998540	+	0.0540230i	$0.982796\pi$
$312$	5.40461e9	−	1.23357e9i	0.570356	−	0.130180i
$313$	2.20007e9	−	2.75881e9i	0.229224	−	0.287438i	−0.653897	−	0.756584i	$-0.726867\pi$
$313$	2.20007e9	−	2.75881e9i	0.229224	−	0.287438i	0.883120	+	0.469146i	$0.155438\pi$
$314$	−9.42998e9	−	1.18248e10i	−0.970046	−	1.21640i
$315$	−3.42717e9	+	1.50154e10i	−0.348092	+	1.52509i
$316$	−7.99970e9	+	1.27314e10i	−0.802279	+	1.27682i
$317$	1.61630e9	−	1.43451e10i	0.160061	−	1.42058i	−0.614917	−	0.788592i	$-0.710811\pi$
$317$	1.61630e9	−	1.43451e10i	0.160061	−	1.42058i	0.774978	−	0.631988i	$-0.217761\pi$
$318$		−	3.29208e9i		−	0.321930i
$319$	9.01076e9	−	4.28767e9i	0.870159	−	0.414055i
$320$	−2.23607e10			−2.13248
$321$	−2.23786e9	−	2.52146e8i	−0.210772	−	0.0237482i
$322$	−2.05272e10	−	1.28981e10i	−1.90944	−	1.19978i
$323$	4.16942e9	+	9.51642e8i	0.383058	+	0.0874306i
$324$	−2.02213e10	+	1.61259e10i	−1.83497	+	1.46334i
$325$	−5.33045e8	−	4.25089e8i	−0.0477782	−	0.0381019i
$326$	−4.55909e9	−	1.99747e10i	−0.403652	−	1.76852i
$327$	2.04643e9	+	7.16076e8i	0.178980	+	0.0626279i
$328$	−5.72333e9	−	1.18846e10i	−0.494486	−	1.02681i
$329$	9.40490e9	−	5.90949e9i	0.802732	−	0.504390i
$330$	−3.46204e9	+	1.21142e9i	−0.291929	+	0.102150i
$331$	4.52766e9	+	4.52766e9i	0.377192	+	0.377192i	0.870088	−	0.492896i	$-0.164062\pi$
$331$	4.52766e9	+	4.52766e9i	0.377192	+	0.377192i	−0.492896	+	0.870088i	$0.664062\pi$
$332$	7.66814e9	−	1.59231e10i	0.631157	−	1.31061i
$333$	−1.25338e9	−	1.11241e10i	−0.101931	−	0.904665i
$334$	3.07581e10	−	3.46560e9i	2.47157	−	0.278479i
$335$	−1.31565e10	−	6.33583e9i	−1.04463	−	0.503065i
$336$	−6.99424e9	+	6.99424e9i	−0.548762	+	0.548762i
$337$	−1.61347e9	−	4.61103e9i	−0.125095	−	0.357502i	0.864255	−	0.503053i	$-0.167790\pi$
$337$	−1.61347e9	−	4.61103e9i	−0.125095	−	0.357502i	−0.989351	+	0.145552i	$0.953504\pi$
$338$	−5.77912e9	−	9.19741e9i	−0.442787	−	0.704691i
$339$	1.80946e9	−	8.71391e8i	0.137010	−	0.0659803i
$340$	2.57894e9	−	7.37019e9i	0.192986	−	0.551522i
$341$	−1.30363e10	+	2.97546e9i	−0.964135	+	0.220057i
$342$	−2.75658e10	+	3.45665e10i	−2.01496	+	2.52668i
$343$	−6.26189e9	−	7.85216e9i	−0.452407	−	0.567300i
$344$	5.16803e9	−	2.26426e10i	0.369055	−	1.61693i
$345$	9.77512e8	−	1.55570e9i	0.0689994	−	0.109812i
$346$	−2.78129e9	+	2.46846e10i	−0.194062	+	1.72235i
$347$			9.90412e8i			0.0683122i	0.999417	+	0.0341561i	$0.0108743\pi$
$347$			9.90412e8i			0.0683122i	−0.999417	+	0.0341561i	$0.989126\pi$
$348$	4.84835e9	+	3.90358e9i	0.330580	+	0.266162i
$349$	−2.25843e10			−1.52231			−0.761157	−	0.648568i	$-0.775368\pi$
$349$	−2.25843e10			−1.52231			−0.761157	+	0.648568i	$0.775368\pi$
$350$	2.24625e9	+	2.53092e8i	0.149688	+	0.0168658i
$351$	−5.05247e9	−	3.17468e9i	−0.332870	−	0.209156i
$352$	3.86932e10	+	8.83146e9i	2.52037	+	0.575257i
$353$	1.83705e10	−	1.46500e10i	1.18310	−	0.943492i	0.183881	−	0.982949i	$-0.441134\pi$
$353$	1.83705e10	−	1.46500e10i	1.18310	−	0.943492i	0.999221	+	0.0394563i	$0.0125626\pi$
$354$	2.69954e9	+	2.15281e9i	0.171900	+	0.137086i
$355$	−4.05802e9	−	1.77793e10i	−0.255506	−	1.11944i
$356$	4.89381e9	+	1.71242e9i	0.304682	+	0.106613i
$357$	−4.09357e8	−	8.50038e8i	−0.0252017	−	0.0523318i
$358$	−5.70500e9	+	3.58469e9i	−0.347315	+	0.218232i
$359$	1.24855e10	−	4.36887e9i	0.751672	−	0.263021i	0.0728687	−	0.997342i	$-0.476785\pi$
$359$	1.24855e10	−	4.36887e9i	0.751672	−	0.263021i	0.678803	+	0.734320i	$0.262499\pi$
$360$	3.47522e10	+	3.47522e10i	2.06906	+	2.06906i
$361$	−1.55153e10	+	3.22178e10i	−0.913548	+	1.89700i
$362$	5.44212e9	+	4.83001e10i	0.316908	+	2.81264i
$363$	−2.04466e8	+	2.30378e7i	−0.0117759	+	0.00132683i
$364$	7.61749e10	+	3.66839e10i	4.33916	+	2.08963i
$365$	4.86504e9	−	4.86504e9i	0.274104	−	0.274104i
$366$	2.42904e9	+	6.94179e9i	0.135366	+	0.386854i
$367$	4.31738e9	+	6.87107e9i	0.237989	+	0.378757i	0.944269	−	0.329176i	$-0.106771\pi$
$367$	4.31738e9	+	6.87107e9i	0.237989	+	0.378757i	−0.706280	+	0.707933i	$0.749628\pi$
$368$	−3.75099e10	+	1.80638e10i	−2.04529	+	0.984960i
$369$	−2.31199e9	+	6.60728e9i	−0.124704	+	0.356383i
$370$	−3.30700e10	+	7.54801e9i	−1.76452	+	0.402740i
$371$	1.90593e10	−	2.38996e10i	1.00603	−	1.26152i
$372$	−5.20038e9	−	6.52107e9i	−0.271559	−	0.340524i
$373$	1.82305e9	−	7.98728e9i	0.0941808	−	0.412633i	−0.905757	−	0.423798i	$-0.860697\pi$
$373$	1.82305e9	−	7.98728e9i	0.0941808	−	0.412633i	0.999938	+	0.0111648i	$0.00355393\pi$
$374$	−4.21771e9	+	6.71245e9i	−0.215571	+	0.343080i
$375$	3.57641e8	−	3.17415e9i	0.0180852	−	0.160510i
$376$		−	3.54441e10i		−	1.77334i
$377$	8.11661e9	−	2.28533e10i	0.401800	−	1.13131i
$378$	1.97838e10			0.969040
$379$	−1.69144e10	−	1.90580e9i	−0.819785	−	0.0923676i	−0.307897	−	0.951420i	$-0.599625\pi$
$379$	−1.69144e10	−	1.90580e9i	−0.819785	−	0.0923676i	−0.511888	+	0.859052i	$0.671054\pi$
$380$	8.15383e10	+	5.12339e10i	3.91045	+	2.45710i
$381$	−5.30037e9	−	1.20977e9i	−0.251539	−	0.0574122i
$382$	3.79838e10	−	3.02910e10i	1.78379	−	1.42253i
$383$	1.40882e10	+	1.12349e10i	0.654725	+	0.522126i	0.893565	−	0.448933i	$-0.148196\pi$
$383$	1.40882e10	+	1.12349e10i	0.654725	+	0.522126i	−0.238840	+	0.971059i	$0.576767\pi$
$384$	9.96221e8	+	4.36473e9i	0.0458174	+	0.200739i
$385$	−3.21470e10	−	1.12487e10i	−1.46318	−	0.511989i
$386$	−2.01974e10	−	4.19402e10i	−0.909799	−	1.88922i
$387$	−1.04358e10	+	6.55723e9i	−0.465244	+	0.292332i
$388$	−5.27492e10	+	1.84578e10i	−2.32750	+	0.814427i
$389$	−1.59696e10	−	1.59696e10i	−0.697423	−	0.697423i	0.266431	−	0.963854i	$-0.414156\pi$
$389$	−1.59696e10	−	1.59696e10i	−0.697423	−	0.697423i	−0.963854	+	0.266431i	$0.914156\pi$
$390$	−3.86768e9	+	8.03133e9i	−0.167183	+	0.347160i
$391$	−4.44620e8	−	3.94612e9i	−0.0190231	−	0.168835i
$392$	−1.00720e11	+	1.13484e10i	−4.26551	+	0.480608i
$393$	−2.78502e9	−	1.34119e9i	−0.116750	−	0.0562240i
$394$	2.39647e10	−	2.39647e10i	0.994460	−	0.994460i
$395$	−4.86184e9	−	1.38943e10i	−0.199716	−	0.570755i
$396$	−3.13427e10	−	4.98817e10i	−1.27455	−	2.02843i
$397$	−1.93059e10	+	9.29725e9i	−0.777193	+	0.374276i	−0.780048	−	0.625720i	$-0.784805\pi$
$397$	−1.93059e10	+	9.29725e9i	−0.777193	+	0.374276i	0.00285533	+	0.999996i	$0.499091\pi$
$398$	1.30281e10	−	3.72321e10i	0.519216	−	1.48384i
$399$	1.13439e10	−	2.58916e9i	0.447578	−	0.102157i
$400$	2.42034e9	−	3.03501e9i	0.0945444	−	0.118555i
$401$	7.54360e8	+	9.45937e8i	0.0291743	+	0.0365835i	0.796205	−	0.605027i	$-0.206838\pi$
$401$	7.54360e8	+	9.45937e8i	0.0291743	+	0.0365835i	−0.767030	+	0.641611i	$0.778266\pi$
$402$	−2.05780e9	+	9.01582e9i	−0.0787951	+	0.345224i
$403$	−1.72896e10	+	2.75162e10i	−0.655487	+	1.04320i
$404$	−1.84782e9	+	1.63999e10i	−0.0693642	+	0.615624i
$405$		−	2.53209e10i		−	0.941152i
$406$	1.75262e10	+	7.84733e10i	0.645034	+	2.88814i
$407$	2.47549e10			0.902160
$408$	−2.99172e9	−	3.37086e8i	−0.107964	−	0.0121647i
$409$	3.43187e10	+	2.15639e10i	1.22642	+	0.770608i	0.980085	−	0.198577i	$-0.0636321\pi$
$409$	3.43187e10	+	2.15639e10i	1.22642	+	0.770608i	0.246331	+	0.969186i	$0.420775\pi$
$410$	2.06792e10	+	4.71990e9i	0.731810	+	0.167031i
$411$	1.39897e9	−	1.11564e9i	0.0490275	−	0.0390981i
$412$	−5.09959e10	−	4.06678e10i	−1.76989	−	1.41144i
$413$	7.13437e9	+	3.12577e10i	0.245220	+	1.07438i
$414$	3.87495e10	+	1.35590e10i	1.31906	+	0.461560i
$415$	7.50713e9	+	1.55887e10i	0.253094	+	0.525554i
$416$	8.16708e10	−	5.13172e10i	2.72705	−	1.71352i
$417$	−6.67929e9	+	2.33718e9i	−0.220895	+	0.0772945i
$418$	−6.91328e10	−	6.91328e10i	−2.26453	−	2.26453i
$419$	1.15507e10	−	2.39853e10i	0.374759	−	0.778195i	−0.625239	−	0.780434i	$-0.714998\pi$
$419$	1.15507e10	−	2.39853e10i	0.374759	−	0.778195i	0.999997	+	0.00223875i	$0.000712618\pi$
$420$	−2.37862e9	−	2.11109e10i	−0.0764414	−	0.678436i
$421$	3.62514e10	−	4.08455e9i	1.15397	−	0.130022i	0.485830	−	0.874053i	$-0.338517\pi$
$421$	3.62514e10	−	4.08455e9i	1.15397	−	0.130022i	0.668145	+	0.744031i	$0.267089\pi$
$422$	−6.66310e10	−	3.20878e10i	−2.10100	−	1.01179i
$423$	−1.33002e10	+	1.33002e10i	−0.415429	+	0.415429i
$424$	−3.22174e10	−	9.20721e10i	−0.996844	−	2.84882i
$425$	1.96996e8	+	3.13517e8i	0.00603811	+	0.00960960i
$426$	−1.04053e10	+	5.01094e9i	−0.315949	+	0.152153i
$427$	−2.25550e10	+	6.44584e10i	−0.678470	+	1.93895i
$428$	−1.06853e11	+	2.43885e10i	−3.18428	+	0.726791i
$429$	4.05608e9	−	5.08617e9i	0.119751	−	0.150163i
$430$	2.32846e10	+	2.91980e10i	0.681075	+	0.854042i
$431$	−7.74683e9	+	3.39411e10i	−0.224499	+	0.983595i	0.729546	+	0.683932i	$0.239731\pi$
$431$	−7.74683e9	+	3.39411e10i	−0.224499	+	0.983595i	−0.954045	+	0.299663i	$0.903126\pi$
$432$	1.80757e10	−	2.87673e10i	0.518992	−	0.825971i
$433$	1.35600e8	−	1.20348e9i	0.00385752	−	0.0342364i	−0.991636	−	0.129066i	$-0.958802\pi$
$433$	1.35600e8	−	1.20348e9i	0.00385752	−	0.0342364i	0.995494	+	0.0948297i	$0.0302306\pi$
$434$		−	1.07744e11i		−	3.03693i
$435$	−5.94728e9	+	1.32826e9i	−0.166097	+	0.0370959i
$436$	1.05516e11			2.91994
$437$	4.86664e10	+	5.48339e9i	1.33445	+	0.150357i
$438$	−3.68932e9	−	2.31815e9i	−0.100242	−	0.0629862i
$439$	5.74899e9	+	1.31217e9i	0.154787	+	0.0353290i	0.299212	−	0.954187i	$-0.403276\pi$
$439$	5.74899e9	+	1.31217e9i	0.154787	+	0.0353290i	−0.144425	+	0.989516i	$0.546133\pi$
$440$	−8.49704e10	+	6.77616e10i	−2.26703	+	1.80789i
$441$	4.20530e10	+	3.35361e10i	1.11184	+	0.886663i
$442$	4.28720e9	+	1.87834e10i	0.112327	+	0.492137i
$443$	2.86163e10	+	1.00133e10i	0.743016	+	0.259992i	0.675128	−	0.737701i	$-0.264088\pi$
$443$	2.86163e10	+	1.00133e10i	0.743016	+	0.259992i	0.0678876	+	0.997693i	$0.478374\pi$
$444$	6.69974e9	+	1.39121e10i	0.172396	+	0.357983i
$445$	−4.29789e9	+	2.70054e9i	−0.109601	+	0.0688669i
$446$	−1.27103e10	+	4.44751e9i	−0.321229	+	0.112403i
$447$	4.13838e9	+	4.13838e9i	0.103658	+	0.103658i
$448$	−5.70518e10	+	1.18469e11i	−1.41631	+	2.94099i
$449$	−1.10035e9	−	9.76586e9i	−0.0270735	−	0.240284i	−0.999960	−	0.00899896i	$-0.997136\pi$
$449$	−1.10035e9	−	9.76586e9i	−0.0270735	−	0.240284i	0.972886	−	0.231285i	$-0.0742931\pi$
$450$	−3.80381e9	+	4.28587e8i	−0.0927617	+	0.0104517i
$451$	−1.39467e10	−	6.71637e9i	−0.337105	−	0.162341i
$452$	6.91141e10	−	6.91141e10i	1.65582	−	1.65582i
$453$	3.95120e9	+	1.12919e10i	0.0938288	+	0.268147i
$454$	4.17853e10	+	6.65010e10i	0.983559	+	1.56532i
$455$	−7.45754e10	+	3.59136e10i	−1.74000	+	0.837941i
$456$	1.22631e10	−	3.50460e10i	0.283623	−	0.810548i
$457$	3.69024e10	−	8.42274e9i	0.846038	−	0.193103i	0.222536	−	0.974924i	$-0.428566\pi$
$457$	3.69024e10	−	8.42274e9i	0.846038	−	0.193103i	0.623502	+	0.781822i	$0.285709\pi$
$458$	6.83601e8	−	8.57209e8i	0.0155361	−	0.0194816i
$459$	2.02050e9	+	2.53363e9i	0.0455207	+	0.0570812i
$460$	1.98974e10	−	8.71763e10i	0.444391	−	1.94701i
$461$	1.02174e10	−	1.62608e10i	0.226222	−	0.360030i	−0.714256	−	0.699884i	$-0.753235\pi$
$461$	1.02174e10	−	1.62608e10i	0.226222	−	0.360030i	0.940478	+	0.339854i	$0.110378\pi$
$462$	−2.41493e9	+	2.14331e10i	−0.0530075	+	0.470454i
$463$		−	1.62167e10i		−	0.352889i	−0.984311	−	0.176445i	$-0.943540\pi$
$463$		−	1.62167e10i		−	0.352889i	0.984311	−	0.176445i	$-0.0564596\pi$
$464$	1.30120e11	+	4.62137e10i	2.80720	+	0.997008i
$465$	8.16563e9			0.174654
$466$	6.36975e9	+	7.17698e8i	0.135076	+	0.0152194i
$467$	3.20363e10	+	2.01298e10i	0.673558	+	0.423225i	0.824917	−	0.565254i	$-0.191222\pi$
$467$	3.20363e10	+	2.01298e10i	0.673558	+	0.423225i	−0.151359	+	0.988479i	$0.548365\pi$
$468$	−1.39584e11	−	3.18591e10i	−2.90972	−	0.664125i
$469$	−6.71357e10	+	5.35390e10i	−1.38759	+	1.10657i
$470$	4.45598e10	+	3.55353e10i	0.913171	+	0.728229i
$471$	−1.49989e9	−	6.57144e9i	−0.0304772	−	0.133530i
$472$	9.65684e10	+	3.37907e10i	1.94566	+	0.680816i
$473$	−1.18253e10	−	2.45555e10i	−0.236248	−	0.490574i
$474$	−7.89340e9	+	4.95975e9i	−0.156369	+	0.0982532i
$475$	−4.31020e9	+	1.50820e9i	−0.0846686	+	0.0296268i
$476$	−3.24680e10	−	3.24680e10i	−0.632452	−	0.632452i
$477$	−2.24601e10	+	4.66389e10i	−0.433849	+	0.900896i
$478$	−4.98947e8	−	4.42828e9i	−0.00955747	−	0.0848249i
$479$	5.69806e10	−	6.42017e9i	1.08239	−	0.121956i	0.447293	−	0.894387i	$-0.352388\pi$
$479$	5.69806e10	−	6.42017e9i	1.08239	−	0.121956i	0.635099	+	0.772431i	$0.280959\pi$
$480$	−2.18363e10	−	1.05158e10i	−0.411352	−	0.198097i
$481$	4.25412e10	−	4.25412e10i	0.794748	−	0.794748i
$482$	2.94850e10	+	8.42632e10i	0.546277	+	1.56117i
$483$	−5.74821e9	−	9.14822e9i	−0.105619	−	0.168092i
$484$	−9.02222e9	+	4.34487e9i	−0.164411	+	0.0791763i
$485$	1.80702e10	−	5.16416e10i	0.326585	−	0.933325i
$486$	−4.92211e10	+	1.12344e10i	−0.882280	+	0.201375i
$487$	−5.93192e10	+	7.43839e10i	−1.05458	+	1.32240i	−0.110067	+	0.993924i	$0.535106\pi$
$487$	−5.93192e10	+	7.43839e10i	−1.05458	+	1.32240i	−0.944512	+	0.328476i	$0.893465\pi$
$488$	1.35870e11	+	1.70375e11i	2.39576	+	3.00419i
$489$	2.03182e9	−	8.90198e9i	0.0355344	−	0.155686i
$490$	8.67119e10	−	1.38001e11i	1.50416	−	2.39386i
$491$	5.26449e9	−	4.67237e10i	0.0905796	−	0.803916i	−0.863497	−	0.504354i	$-0.831731\pi$
$491$	5.26449e9	−	4.67237e10i	0.0905796	−	0.803916i	0.954077	−	0.299562i	$-0.0968407\pi$
$492$		−	9.65572e9i		−	0.164787i
$493$	−8.25985e9	+	1.02589e10i	−0.139825	+	0.173666i
$494$	−2.37609e11			−3.98983
$495$	5.73117e10	+	6.45748e9i	0.954603	+	0.107558i
$496$	−1.56669e11	−	9.84419e10i	−2.58855	−	1.62650i
$497$	−1.04551e11	−	2.38630e10i	−1.71357	−	0.391110i
$498$	8.56675e9	−	6.83175e9i	0.139283	−	0.111075i
$499$	−4.14198e10	−	3.30311e10i	−0.668044	−	0.532748i	0.229702	−	0.973261i	$-0.426225\pi$
$499$	−4.14198e10	−	3.30311e10i	−0.668044	−	0.532748i	−0.897746	+	0.440514i	$0.854796\pi$
$500$	−3.45924e10	−	1.51559e11i	−0.553478	−	2.42495i
$501$	1.30204e10	+	4.55603e9i	0.206668	+	0.0723162i
$502$	2.33043e10	+	4.83919e10i	0.366962	+	0.762005i
$503$	2.72053e10	−	1.70942e10i	0.424993	−	0.267041i	−0.302509	−	0.953147i	$-0.597824\pi$
$503$	2.72053e10	−	1.70942e10i	0.424993	−	0.267041i	0.727502	+	0.686106i	$0.240681\pi$
$504$	2.72788e11	−	9.54528e10i	4.22770	−	1.47933i
$505$	−1.14248e10	−	1.14248e10i	−0.175664	−	0.175664i
$506$	−3.93893e10	+	8.17928e10i	−0.600865	+	1.24771i
$507$	−5.42014e8	−	4.81051e9i	−0.00820312	−	0.0728047i
$508$	−2.62927e11	+	2.96248e10i	−3.94804	+	0.444837i
$509$	4.85608e10	+	2.33857e10i	0.723461	+	0.348400i	0.759109	−	0.650964i	$-0.225635\pi$
$509$	4.85608e10	+	2.33857e10i	0.723461	+	0.348400i	−0.0356478	+	0.999364i	$0.511349\pi$
$510$	3.42319e9	−	3.42319e9i	0.0506000	−	0.0506000i
$511$	−1.33627e10	−	3.81883e10i	−0.195979	−	0.560076i
$512$	−2.75053e10	−	4.37744e10i	−0.400254	−	0.637001i
$513$	−3.60081e10	+	1.73406e10i	−0.519913	+	0.250377i
$514$	3.75178e10	−	1.07220e11i	0.537507	−	1.53611i
$515$	6.22555e10	−	1.42094e10i	0.885012	−	0.201998i
$516$	1.05997e10	−	1.32916e10i	0.149518	−	0.187490i
$517$	−2.59334e10	−	3.25195e10i	−0.362992	−	0.455178i
$518$	−4.43857e10	+	1.94466e11i	−0.616487	+	2.70100i
$519$	−5.88993e9	+	9.37378e9i	−0.0811785	+	0.129195i
$520$	−2.95732e10	+	2.62469e11i	−0.404468	+	3.58976i
$521$			9.72560e10i			1.31997i	0.751277	+	0.659987i	$0.229438\pi$
$521$			9.72560e10i			1.31997i	−0.751277	+	0.659987i	$0.770562\pi$
$522$	−5.85049e10	−	1.22951e11i	−0.787971	−	1.65596i
$523$	1.06142e11			1.41867			0.709334	−	0.704873i	$-0.248996\pi$
$523$	1.06142e11			1.41867			0.709334	+	0.704873i	$0.248996\pi$
$524$	−1.49493e11	−	1.68438e10i	−1.98288	−	0.223417i
$525$	8.52995e8	+	5.35972e8i	0.0112282	+	0.00705513i
$526$	1.58188e11	+	3.61053e10i	2.06647	+	0.471658i
$527$	1.37984e10	−	1.10038e10i	0.178890	−	0.142660i
$528$	2.89592e10	+	2.30942e10i	0.372607	+	0.297144i
$529$	7.30664e9	+	3.20125e10i	0.0933028	+	0.408786i
$530$	1.48052e11	+	5.18056e10i	1.87634	+	0.656558i
$531$	−2.35569e10	−	4.89165e10i	−0.296306	−	0.615286i
$532$	4.79482e11	−	3.01278e11i	5.98585	−	3.76116i
$533$	−3.55094e10	+	1.24253e10i	−0.439981	+	0.153956i
$534$	2.27300e9	+	2.27300e9i	0.0279534	+	0.0279534i
$535$	4.65555e10	−	9.66734e10i	0.568271	−	1.18003i
$536$	3.06798e10	+	2.72291e11i	0.371701	+	3.29894i
$537$	−2.98388e9	+	3.36202e8i	−0.0358826	+	0.00404300i
$538$	−2.56842e11	−	1.23688e11i	−3.06575	−	1.47639i
$539$	−8.41057e10	+	8.41057e10i	−0.996485	+	0.996485i
$540$	2.41006e10	+	6.88757e10i	0.283435	+	0.810011i
$541$	1.82021e10	+	2.89684e10i	0.212487	+	0.338171i	0.935913	−	0.352231i	$-0.114577\pi$
$541$	1.82021e10	+	2.89684e10i	0.212487	+	0.338171i	−0.723426	+	0.690401i	$0.757434\pi$
$542$	−4.40407e10	+	2.12089e10i	−0.510337	+	0.245765i
$543$	−7.15444e9	+	2.04462e10i	−0.0822956	+	0.235187i
$544$	−5.10701e10	+	1.16564e10i	−0.583137	+	0.133097i
$545$	−6.44070e10	+	8.07639e10i	−0.730041	+	0.915442i
$546$	3.26827e10	+	4.09828e10i	0.367745	+	0.461138i
$547$	3.47135e10	−	1.52090e11i	0.387748	−	1.69883i	−0.284639	−	0.958635i	$-0.591874\pi$
$547$	3.47135e10	−	1.52090e11i	0.387748	−	1.69883i	0.672387	−	0.740200i	$-0.265269\pi$
$548$	4.63312e10	−	7.37357e10i	0.513749	−	0.817627i
$549$	1.29480e10	−	1.14916e11i	0.142532	−	1.26501i
$550$		−	8.46478e9i		−	0.0925049i
$551$	−1.00681e11	−	1.27466e11i	−1.09230	−	1.38289i
$552$	−3.44768e10			−0.371339
$553$	−8.60183e10	−	9.69193e9i	−0.919793	−	0.103636i
$554$	1.55639e11	+	9.77947e10i	1.65227	+	1.03819i
$555$	−1.47381e10	−	3.36387e9i	−0.155335	−	0.0354542i
$556$	−2.69257e11	+	2.14725e11i	−2.81752	+	2.24690i
$557$	−3.11096e10	−	2.48091e10i	−0.323201	−	0.257745i	0.448425	−	0.893820i	$-0.351985\pi$
$557$	−3.11096e10	−	2.48091e10i	−0.323201	−	0.257745i	−0.771627	+	0.636076i	$0.780557\pi$
$558$	4.05999e10	+	1.77880e11i	0.418782	+	1.83480i
$559$	−6.25203e10	−	2.18768e10i	−0.640286	−	0.224046i
$560$	−2.04482e11	−	4.24611e11i	−2.07923	−	4.31757i
$561$	−2.99150e9	+	1.87968e9i	−0.0302021	+	0.0189772i
$562$	2.44562e11	−	8.55760e10i	2.45157	−	0.857841i
$563$	5.34763e10	+	5.34763e10i	0.532265	+	0.532265i	0.921246	−	0.388981i	$-0.127173\pi$
$563$	5.34763e10	+	5.34763e10i	0.532265	+	0.532265i	−0.388981	+	0.921246i	$0.627173\pi$
$564$	1.12571e10	−	2.33756e10i	0.111253	−	0.231019i
$565$	1.07139e10	+	9.50881e10i	0.105136	+	0.933109i
$566$	1.75119e11	−	1.97312e10i	1.70635	−	0.192260i
$567$	−1.34153e11	−	6.46046e10i	−1.29798	−	0.625074i
$568$	−2.41975e11	+	2.41975e11i	−2.32476	+	2.32476i
$569$	−1.55736e10	−	4.45069e10i	−0.148573	−	0.424599i	0.845411	−	0.534116i	$-0.179355\pi$
$569$	−1.55736e10	−	4.45069e10i	−0.148573	−	0.424599i	−0.993985	+	0.109517i	$0.965070\pi$
$570$	3.17646e10	+	5.05531e10i	0.300915	+	0.478904i
$571$	4.25971e10	−	2.05137e10i	0.400715	−	0.192974i	−0.222662	−	0.974896i	$-0.571475\pi$
$571$	4.25971e10	−	2.05137e10i	0.400715	−	0.192974i	0.623377	+	0.781922i	$0.285760\pi$
$572$	1.04568e11	−	2.98839e11i	0.976824	−	2.79160i
$573$	2.11088e10	−	4.81795e9i	0.195815	−	0.0446935i
$574$	7.77681e10	−	9.75181e10i	0.716397	−	0.898333i
$575$	2.64371e9	+	3.31511e9i	0.0241848	+	0.0303268i
$576$	4.95482e10	−	2.17085e11i	0.450130	−	1.97215i
$577$	−2.97401e10	+	4.73312e10i	−0.268312	+	0.427016i	−0.953519	−	0.301332i	$-0.902569\pi$
$577$	−2.97401e10	+	4.73312e10i	−0.268312	+	0.427016i	0.685207	+	0.728348i	$0.259712\pi$
$578$	−2.23952e10	+	1.98763e11i	−0.200652	+	1.78084i
$579$		−	2.07457e10i		−	0.184592i
$580$	−2.51849e11	+	1.56612e11i	−2.22550	+	1.38393i
$581$	1.01744e11			0.892907
$582$	−3.44306e10	−	3.87940e9i	−0.300091	−	0.0338121i
$583$	−9.69254e10	−	6.09022e10i	−0.839003	−	0.527180i
$584$	−1.25868e11	−	2.87286e10i	−1.08209	−	0.246981i
$585$	1.09587e11	−	8.73928e10i	0.935699	−	0.746195i
$586$	−2.28306e11	−	1.82068e11i	−1.93609	−	1.54398i
$587$	2.21190e9	+	9.69097e9i	0.0186300	+	0.0816234i	0.983388	−	0.181514i	$-0.0580998\pi$
$587$	2.21190e9	+	9.69097e9i	0.0186300	+	0.0816234i	−0.964758	+	0.263138i	$0.915243\pi$
$588$	−7.00297e10	−	2.45044e10i	−0.585832	−	0.204991i
$589$	9.44382e10	+	1.96103e11i	0.784669	+	1.62938i
$590$	−1.39298e11	+	8.75267e10i	−1.14957	+	0.722324i
$591$	1.42565e10	−	4.98856e9i	0.116859	−	0.0408908i
$592$	2.42218e11	+	2.42218e11i	1.97205	+	1.97205i
$593$	−2.65554e10	+	5.51429e10i	−0.214751	+	0.445934i	−0.980319	−	0.197420i	$-0.936744\pi$
$593$	−2.65554e10	+	5.51429e10i	−0.214751	+	0.445934i	0.765568	+	0.643355i	$0.222458\pi$
$594$	−8.29482e9	−	7.36186e10i	−0.0666287	−	0.591346i
$595$	4.46699e10	−	5.03309e9i	0.356408	−	0.0401575i
$596$	2.56624e11	+	1.23584e11i	2.03382	+	0.979436i
$597$	1.24306e10	−	1.24306e10i	0.0978575	−	0.0978575i
$598$	7.28702e10	+	2.08251e11i	0.569830	+	1.62848i
$599$	−4.73253e10	−	7.53178e10i	−0.367609	−	0.585046i	0.610785	−	0.791797i	$-0.290854\pi$
$599$	−4.73253e10	−	7.53178e10i	−0.367609	−	0.585046i	−0.978394	+	0.206750i	$0.933711\pi$
$600$	2.89632e9	−	1.39479e9i	0.0223481	−	0.0107623i
$601$	3.69274e10	−	1.05532e11i	0.283042	−	0.808887i	−0.711322	−	0.702866i	$-0.751903\pi$
$601$	3.69274e10	−	1.05532e11i	0.283042	−	0.808887i	0.994364	−	0.106021i	$-0.0338109\pi$
$602$	2.14103e11	−	4.88676e10i	1.63018	−	0.372079i
$603$	9.06631e10	−	1.13688e11i	0.685743	−	0.859894i
$604$	3.63011e11	+	4.55201e11i	2.72754	+	3.42023i
$605$	2.18152e9	−	9.55784e9i	0.0162831	−	0.0713409i
$606$	−5.44383e9	+	8.66381e9i	−0.0403658	+	0.0642419i
$607$	−1.34315e10	+	1.19208e11i	−0.0989396	+	0.878114i	0.841986	+	0.539500i	$0.181387\pi$
$607$	−1.34315e10	+	1.19208e11i	−0.0989396	+	0.878114i	−0.940925	+	0.338614i	$0.890042\pi$
$608$		−	6.46031e11i		−	4.72758i
$609$	−8.13683e9	+	3.48983e10i	−0.0591543	+	0.253708i
$610$	−3.50412e11			−2.53081
$611$	−1.00451e11	−	1.13181e10i	−0.720758	−	0.0812099i
$612$	6.58375e10	+	4.13684e10i	0.469318	+	0.294892i
$613$	9.97740e10	+	2.27728e10i	0.706603	+	0.161277i	0.560697	−	0.828021i	$-0.310533\pi$
$613$	9.97740e10	+	2.27728e10i	0.706603	+	0.161277i	0.145906	+	0.989299i	$0.453390\pi$
$614$	−1.33445e11	+	1.06419e11i	−0.938922	+	0.748765i
$615$	7.39063e9	+	5.89383e9i	0.0516632	+	0.0412000i
$616$	1.42212e11	+	6.23071e11i	0.987672	+	4.32727i
$617$	−7.14279e10	−	2.49937e10i	−0.492864	−	0.172461i	0.0723918	−	0.997376i	$-0.476937\pi$
$617$	−7.14279e10	−	2.49937e10i	−0.492864	−	0.172461i	−0.565256	+	0.824916i	$0.691223\pi$
$618$	−1.75461e10	−	3.64349e10i	−0.120289	−	0.249784i
$619$	−2.88148e10	+	1.81056e10i	−0.196270	+	0.123325i	−0.626582	−	0.779356i	$-0.715546\pi$
$619$	−2.88148e10	+	1.81056e10i	−0.196270	+	0.123325i	0.430312	+	0.902680i	$0.358404\pi$
$620$	3.75103e11	−	1.31254e11i	2.53854	−	0.888272i
$621$	2.62411e10	+	2.62411e10i	0.176447	+	0.176447i
$622$	−9.32732e10	+	1.93684e11i	−0.623154	+	1.29399i
$623$	3.34198e9	+	2.96609e10i	0.0221846	+	0.196894i
$624$	8.94535e10	−	1.00790e10i	0.590010	−	0.0664781i
$625$	1.44119e11	+	6.94039e10i	0.944496	+	0.454845i
$626$	7.52872e10	−	7.52872e10i	0.490257	−	0.490257i
$627$	−1.43909e10	−	4.11267e10i	−0.0931144	−	0.266106i
$628$	−1.74529e11	−	2.77762e11i	−1.12209	−	1.78580i
$629$	−2.94376e10	+	1.41764e10i	−0.188062	+	0.0905658i
$630$	−1.53488e11	+	4.38644e11i	−0.974344	+	2.78452i
$631$	−1.44233e11	+	3.29203e10i	−0.909804	+	0.207657i	−0.651715	−	0.758464i	$-0.725950\pi$
$631$	−1.44233e11	+	3.29203e10i	−0.909804	+	0.207657i	−0.258090	+	0.966121i	$0.583093\pi$
$632$	−1.72223e11	+	2.15961e11i	−1.07950	+	1.35365i
$633$	−2.05496e10	−	2.57684e10i	−0.127994	−	0.160499i
$634$	9.69262e10	−	4.24662e11i	0.599908	−	2.62837i
$635$	1.37815e11	−	2.19332e11i	0.847622	−	1.34898i
$636$	7.99464e9	−	7.09544e10i	0.0488619	−	0.433662i
$637$			2.89071e11i			1.75568i
$638$	2.84664e11	−	9.81195e10i	1.71810	−	0.592206i
$639$	1.81599e11			1.08921
$640$	−2.11968e11	−	2.38831e10i	−1.26343	−	0.142354i
$641$	−9.35981e10	−	5.88116e10i	−0.554415	−	0.348362i	0.225504	−	0.974242i	$-0.427597\pi$
$641$	−9.35981e10	−	5.88116e10i	−0.554415	−	0.348362i	−0.779919	+	0.625880i	$0.784740\pi$
$642$	−6.62479e10	−	1.51207e10i	−0.389971	−	0.0890083i
$643$	−1.61743e11	+	1.28986e11i	−0.946196	+	0.754566i	−0.969482	−	0.245163i	$-0.921159\pi$
$643$	−1.61743e11	+	1.28986e11i	−0.946196	+	0.754566i	0.0232858	+	0.999729i	$0.492587\pi$
$644$	−4.11102e11	−	3.27843e11i	−2.39005	−	1.90600i
$645$	3.70354e9	+	1.62263e10i	0.0213983	+	0.0937520i
$646$	1.21801e11	+	4.26199e10i	0.699390	+	0.244727i
$647$	−5.48384e10	−	1.13873e11i	−0.312945	−	0.649836i	0.683869	−	0.729605i	$-0.260296\pi$
$647$	−5.48384e10	−	1.13873e11i	−0.312945	−	0.649836i	−0.996813	+	0.0797689i	$0.974582\pi$
$648$	−4.02313e11	+	2.52790e11i	−2.28173	+	1.43371i
$649$	1.13324e11	−	3.96537e10i	0.638766	−	0.223514i
$650$	−1.45467e10	−	1.45467e10i	−0.0814911	−	0.0814911i
$651$	2.08340e10	−	4.32624e10i	0.115998	−	0.240872i
$652$	−4.97549e10	−	4.41587e11i	−0.275325	−	2.44358i
$653$	1.32861e11	−	1.49698e10i	0.730708	−	0.0823310i	0.261232	−	0.965276i	$-0.415871\pi$
$653$	1.32861e11	−	1.49698e10i	0.730708	−	0.0823310i	0.469476	+	0.882945i	$0.344443\pi$
$654$	5.89408e10	+	2.83844e10i	0.322185	+	0.155156i
$655$	1.04143e11	−	1.04143e11i	0.565802	−	0.565802i
$656$	−7.07460e10	−	2.02180e11i	−0.382020	−	1.09175i
$657$	3.64511e10	+	5.80116e10i	0.195636	+	0.311353i
$658$	3.01961e11	−	1.45417e11i	1.61082	−	0.775730i
$659$	−1.06375e11	+	3.04001e11i	−0.564022	+	1.61188i	0.209287	+	0.977854i	$0.432886\pi$
$659$	−1.06375e11	+	3.04001e11i	−0.564022	+	1.61188i	−0.773310	+	0.634029i	$0.781400\pi$
$660$	−7.75596e10	+	1.77025e10i	−0.408752	+	0.0932950i
$661$	7.11068e10	−	8.91651e10i	0.372482	−	0.467078i	−0.559896	−	0.828563i	$-0.689159\pi$
$661$	7.11068e10	−	8.91651e10i	0.372482	−	0.467078i	0.932378	+	0.361485i	$0.117730\pi$
$662$	1.20461e11	+	1.51053e11i	0.627213	+	0.786500i
$663$	−1.91065e9	+	8.37109e9i	−0.00988841	+	0.0433240i
$664$	1.72735e11	−	2.74906e11i	0.888604	−	1.41421i
$665$	−6.20718e10	+	5.50902e11i	−0.317401	+	2.81701i
$666$		−	3.37779e11i		−	1.71686i
$667$	−8.08400e10	+	1.27333e11i	−0.408435	+	0.643336i
$668$	6.71348e11			3.37165
$669$	−5.96354e9	−	6.71929e8i	−0.0297714	−	0.00335443i
$670$	−3.73079e11	−	2.34421e11i	−1.85140	−	1.16331i
$671$	2.49317e11	+	5.69049e10i	1.22988	+	0.280711i
$672$	−1.11427e11	+	8.88605e10i	−0.546406	+	0.435744i
$673$	−1.11711e11	−	8.90867e10i	−0.544549	−	0.434263i	0.312186	−	0.950021i	$-0.398939\pi$
$673$	−1.11711e11	−	8.90867e10i	−0.544549	−	0.434263i	−0.856734	+	0.515758i	$0.827510\pi$
$674$	−3.28003e10	−	1.43708e11i	−0.158942	−	0.696371i
$675$	−3.26607e9	−	1.14285e9i	−0.0157329	−	0.00550519i
$676$	−1.02222e11	−	2.12267e11i	−0.489507	−	1.01647i
$677$	−2.65301e11	+	1.66699e11i	−1.26294	+	0.793559i	−0.985906	−	0.167300i	$-0.946495\pi$
$677$	−2.65301e11	+	1.66699e11i	−1.26294	+	0.793559i	−0.277036	+	0.960859i	$0.589352\pi$
$678$	5.71987e10	−	2.00147e10i	0.270687	−	0.0947175i
$679$	−2.27498e11	−	2.27498e11i	−1.07028	−	1.07028i
$680$	6.22386e10	−	1.29240e11i	0.291088	−	0.604450i
$681$	3.91898e9	+	3.47819e10i	0.0182215	+	0.161720i
$682$	−4.00933e11	+	4.51743e10i	−1.85325	+	0.208811i
$683$	5.48919e10	+	2.64346e10i	0.252247	+	0.121476i	0.555735	−	0.831360i	$-0.312437\pi$
$683$	5.48919e10	+	2.64346e10i	0.252247	+	0.121476i	−0.303488	+	0.952835i	$0.598151\pi$
$684$	−6.78072e11	+	6.78072e11i	−3.09778	+	3.09778i
$685$	2.81579e10	+	8.04707e10i	0.127891	+	0.365490i
$686$	−1.61229e11	−	2.56594e11i	−0.728024	−	1.15864i
$687$	4.40241e8	−	2.12009e8i	0.00197635	−	0.000951759i
$688$	1.24560e11	−	3.55973e11i	0.555938	−	1.58878i
$689$	−2.71226e11	+	6.19056e10i	−1.20352	+	0.274696i
$690$	3.45654e10	−	4.33437e10i	0.152491	−	0.191218i
$691$	−3.84944e9	−	4.82705e9i	−0.0168844	−	0.0211724i	0.773318	−	0.634019i	$-0.218596\pi$
$691$	−3.84944e9	−	4.82705e9i	−0.0168844	−	0.0211724i	−0.790202	+	0.612846i	$0.790024\pi$
$692$	−1.19891e11	+	5.25275e11i	−0.522831	+	2.29067i
$693$	1.80439e11	−	2.87168e11i	0.782345	−	1.24509i
$694$	−3.34599e9	+	2.96965e10i	−0.0144240	+	0.128017i
$695$		−	3.37161e11i		−	1.44510i
$696$	8.04785e10	+	8.12331e10i	0.342959	+	0.346175i
$697$	2.04312e10			0.0865690
$698$	−6.77165e11	−	7.62982e10i	−2.85281	−	0.321435i
$699$	2.41886e9	+	1.51987e9i	0.0101322	+	0.00636645i
$700$	4.77990e10	+	1.09098e10i	0.199080	+	0.0454386i
$701$	2.62363e11	−	2.09227e11i	1.08650	−	0.866455i	0.0948606	−	0.995491i	$-0.469759\pi$
$701$	2.62363e11	−	2.09227e11i	1.08650	−	0.866455i	0.991640	+	0.129035i	$0.0411880\pi$
$702$	−1.40768e11	−	1.12259e11i	−0.579635	−	0.462244i
$703$	−8.96652e10	−	3.92849e11i	−0.367115	−	1.60844i
$704$	4.64764e11	+	1.62628e11i	1.89209	+	0.662071i
$705$	1.10207e10	+	2.28848e10i	0.0446123	+	0.0926383i
$706$	6.00314e11	−	3.77202e11i	2.41635	−	1.51829i
$707$	−8.96795e10	+	3.13802e10i	−0.358935	+	0.125597i
$708$	5.29554e10	+	5.29554e10i	0.210755	+	0.210755i
$709$	−1.28036e11	+	2.65869e11i	−0.506694	+	1.05216i	0.478079	+	0.878317i	$0.341333\pi$
$709$	−1.28036e11	+	2.65869e11i	−0.506694	+	1.05216i	−0.984773	+	0.173845i	$0.944381\pi$
$710$	−6.16101e10	−	5.46805e11i	−0.242448	−	2.15178i
$711$	1.45664e11	−	1.64124e10i	0.569998	−	0.0642233i
$712$	8.58154e10	+	4.13265e10i	0.333922	+	0.160808i
$713$	1.42911e11	−	1.42911e11i	0.552978	−	0.552978i
$714$	−9.40238e9	−	2.68705e10i	−0.0361780	−	0.103391i
$715$	1.64908e11	+	2.62449e11i	0.630982	+	1.00420i
$716$	−1.31666e11	+	6.34068e10i	−0.500980	+	0.241259i
$717$	6.55938e8	−	1.87456e9i	0.00248191	−	0.00709289i
$718$	3.89125e11	−	8.88152e10i	1.46417	−	0.334187i
$719$	1.31127e11	−	1.64428e11i	0.490654	−	0.615261i	−0.473439	−	0.880827i	$-0.656987\pi$
$719$	1.31127e11	−	1.64428e11i	0.490654	−	0.615261i	0.964093	+	0.265566i	$0.0855589\pi$
$720$	4.97590e11	+	6.23958e11i	1.85158	+	2.32180i
$721$	8.35578e10	−	3.66091e11i	0.309205	−	1.35471i
$722$	−5.74054e11	+	9.13602e11i	−2.11254	+	3.36208i
$723$	−4.45458e9	+	3.95355e10i	−0.0163025	+	0.144689i
$724$			1.05423e12i			3.83692i
$725$	1.63980e9	−	1.39675e10i	0.00593524	−	0.0505551i
$726$	−6.20855e9			−0.0223482
$727$	5.20785e10	+	5.86784e9i	0.186432	+	0.0210059i	0.204687	−	0.978827i	$-0.434382\pi$
$727$	5.20785e10	+	5.86784e9i	0.186432	+	0.0210059i	−0.0182546	+	0.999833i	$0.505811\pi$
$728$	1.31513e12	+	8.26354e11i	4.68214	+	2.94198i
$729$	2.30855e11	+	5.26911e10i	0.817388	+	0.186564i
$730$	1.62309e11	−	1.29437e11i	0.571547	−	0.455793i
$731$	2.81245e10	+	2.24285e10i	0.0984953	+	0.0785474i
$732$	3.54955e10	+	1.55516e11i	0.123631	+	0.541664i
$733$	−4.48159e11	−	1.56818e11i	−1.55245	−	0.543224i	−0.588311	−	0.808635i	$-0.700207\pi$
$733$	−4.48159e11	−	1.56818e11i	−1.55245	−	0.543224i	−0.964135	+	0.265411i	$0.914492\pi$
$734$	1.06239e11	+	2.20608e11i	0.366016	+	0.760040i
$735$	6.15021e10	−	3.86443e10i	0.210737	−	0.132415i
$736$	−5.66211e11	+	1.98126e11i	−1.92960	+	0.675196i
$737$	2.27375e11	+	2.27375e11i	0.770679	+	0.770679i
$738$	−9.16444e10	+	1.90302e11i	−0.308945	+	0.641530i
$739$	1.51961e10	+	1.34869e11i	0.0509510	+	0.452203i	0.993123	+	0.117074i	$0.0373514\pi$
$739$	1.51961e10	+	1.34869e11i	0.0509510	+	0.452203i	−0.942172	+	0.335129i	$0.891220\pi$
$740$	−7.31090e11	+	8.23741e10i	−2.43806	+	0.274703i
$741$	−9.54067e10	−	4.59455e10i	−0.316451	−	0.152395i
$742$	6.52215e11	−	6.52215e11i	2.15167	−	2.15167i
$743$	1.62652e11	+	4.64833e11i	0.533709	+	1.52525i	0.823017	+	0.568016i	$0.192289\pi$
$743$	1.62652e11	+	4.64833e11i	0.533709	+	1.52525i	−0.289308	+	0.957236i	$0.593425\pi$
$744$	−8.15211e10	−	1.29740e11i	−0.266059	−	0.423431i
$745$	−2.51236e11	+	1.20989e11i	−0.815561	+	0.392753i
$746$	8.16462e10	−	2.33331e11i	0.263621	−	0.753387i
$747$	−1.67975e11	+	3.83391e10i	−0.539463	+	0.123129i
$748$	−1.07206e11	+	1.34432e11i	−0.342461	+	0.429433i
$749$	−3.93403e11	−	4.93311e11i	−1.25000	−	1.56745i
$750$	2.14470e10	−	9.39655e10i	0.0677831	−	0.296977i
$751$	2.10239e10	−	3.34594e10i	0.0660927	−	0.105186i	−0.812043	−	0.583598i	$-0.801645\pi$
$751$	2.10239e10	−	3.34594e10i	0.0660927	−	0.105186i	0.878136	+	0.478412i	$0.158787\pi$
$752$	6.44421e10	−	5.71940e11i	0.201511	−	1.78846i
$753$			2.39370e10i			0.0744544i
$754$	3.20575e11	−	6.57811e11i	0.991847	−	2.03524i
$755$	−5.69999e11			−1.75423
$756$	4.26401e11	+	4.80439e10i	1.30536	+	0.147079i
$757$	−4.54685e11	−	2.85698e11i	−1.38461	−	0.870008i	−0.385988	−	0.922504i	$-0.626139\pi$
$757$	−4.54685e11	−	2.85698e11i	−1.38461	−	0.870008i	−0.998621	+	0.0524963i	$0.983282\pi$
$758$	−5.00723e11	−	1.14287e11i	−1.51677	−	0.346193i
$759$	−3.16319e10	+	2.52256e10i	−0.0953144	+	0.0760107i
$760$	1.38312e12	+	1.10300e12i	4.14577	+	3.30614i
$761$	8.21451e10	+	3.59901e11i	0.244931	+	1.07311i	0.936463	+	0.350766i	$0.114079\pi$
$761$	8.21451e10	+	3.59901e11i	0.244931	+	1.07311i	−0.691533	+	0.722345i	$0.743064\pi$
$762$	−1.54839e11	−	5.41805e10i	−0.459262	−	0.160703i
$763$	2.63565e11	+	5.47298e11i	0.777660	+	1.61483i
$764$	8.92228e11	−	5.60624e11i	2.61880	−	1.64550i
$765$	−7.18511e10	+	2.51418e10i	−0.209791	+	0.0734092i
$766$	3.84463e11	+	3.84463e11i	1.11671	+	1.11671i
$767$	1.26602e11	−	2.62891e11i	0.365812	−	0.759616i
$768$	1.67314e9	+	1.48495e10i	0.00480936	+	0.0426843i
$769$	3.34885e11	−	3.77324e10i	0.957613	−	0.107897i	0.380696	−	0.924700i	$-0.375684\pi$
$769$	3.34885e11	−	3.77324e10i	0.957613	−	0.107897i	0.576917	+	0.816803i	$0.304256\pi$
$770$	−9.25892e11	−	4.45886e11i	−2.63389	−	1.26841i
$771$	3.57971e10	−	3.57971e10i	0.101305	−	0.101305i
$772$	−3.33466e11	−	9.52990e11i	−0.938819	−	2.68299i
$773$	−1.56249e11	−	2.48669e11i	−0.437622	−	0.696471i	0.552988	−	0.833189i	$-0.313487\pi$
$773$	−1.56249e11	−	2.48669e11i	−0.437622	−	0.696471i	−0.990610	+	0.136718i	$0.956345\pi$
$774$	−3.35058e11	+	1.61356e11i	−0.933591	+	0.449594i
$775$	−6.22404e9	+	1.77873e10i	−0.0172530	+	0.0493063i
$776$	−1.00091e12	+	2.28452e11i	−2.76026	+	0.630011i
$777$	−5.54253e10	+	6.95011e10i	−0.152063	+	0.190681i
$778$	−4.24881e11	−	5.32784e11i	−1.15971	−	1.45423i
$779$	−5.60691e10	+	2.45655e11i	−0.152256	+	0.667077i
$780$	−1.02864e11	+	1.63708e11i	−0.277898	+	0.442273i
$781$	−4.49626e10	+	3.99054e11i	−0.120850	+	1.07258i
$782$		−	1.19822e11i		−	0.320413i
$783$	5.74382e8	−	1.23082e11i	0.00152811	−	0.327453i
$784$	−1.64589e12			−4.35648
$785$	3.19135e11	+	3.59579e10i	0.840420	+	0.0946926i
$786$	−7.89749e10	−	4.96232e10i	−0.206918	−	0.130015i
$787$	−2.78678e11	−	6.36065e10i	−0.726447	−	0.165807i	−0.156723	−	0.987643i	$-0.550093\pi$
$787$	−2.78678e11	−	6.36065e10i	−0.726447	−	0.165807i	−0.569724	+	0.821836i	$0.692950\pi$
$788$	5.74711e11	−	4.58317e11i	1.49054	−	1.18867i
$789$	5.65353e10	+	4.50854e10i	0.145885	+	0.116340i
$790$	−9.88369e10	−	4.33033e11i	−0.253753	−	1.11176i
$791$	5.31122e11	+	1.85848e11i	1.35671	+	0.474735i
$792$	−4.69568e11	−	9.75068e11i	−1.19343	−	2.47819i
$793$	5.26240e11	−	3.30659e11i	1.33073	−	0.836156i
$794$	−6.10278e11	+	2.13545e11i	−1.53549	+	0.537289i
$795$	4.94297e10	+	4.94297e10i	0.123743	+	0.123743i
$796$	3.71212e11	−	7.70830e11i	0.924634	−	1.92002i
$797$	2.70264e10	+	2.39866e11i	0.0669815	+	0.594478i	0.981706	+	0.190401i	$0.0609787\pi$
$797$	2.70264e10	+	2.39866e11i	0.0669815	+	0.594478i	−0.914725	+	0.404077i	$0.867593\pi$
$798$	3.48881e11	−	3.93094e10i	0.860331	−	0.0969360i
$799$	4.94620e10	+	2.38197e10i	0.121363	+	0.0584452i
$800$	3.95508e10	−	3.95508e10i	0.0965595	−	0.0965595i
$801$	−1.66942e10	−	4.77092e10i	−0.0405541	−	0.115897i
$802$	1.94230e10	+	3.09115e10i	0.0469481	+	0.0747174i
$803$	−1.36502e11	+	6.57360e10i	−0.328305	+	0.158103i
$804$	−6.62465e10	+	1.89322e11i	−0.158540	+	0.453081i
$805$	5.01872e11	−	1.14549e11i	1.19511	−	0.272777i
$806$	−6.11370e11	+	7.66633e11i	−1.44865	+	1.81655i
$807$	−7.92122e10	−	9.93289e10i	−0.186766	−	0.234197i
$808$	−6.74648e10	+	2.95583e11i	−0.158282	+	0.693480i
$809$	−5.35353e10	+	8.52009e10i	−0.124982	+	0.198907i	−0.903354	−	0.428896i	$-0.858903\pi$
$809$	−5.35353e10	+	8.52009e10i	−0.124982	+	0.198907i	0.778372	+	0.627803i	$0.216046\pi$
$810$	8.55438e10	−	7.59222e11i	0.198723	−	1.76372i
$811$		−	1.14511e11i		−	0.264707i	−0.991203	−	0.132354i	$-0.957747\pi$
$811$		−	1.14511e11i		−	0.264707i	0.991203	−	0.132354i	$-0.0422534\pi$
$812$	1.87174e11	+	1.73390e12i	0.430548	+	3.98842i
$813$	−2.17847e10			−0.0498642
$814$	7.42250e11	+	8.36315e10i	1.69065	+	0.190490i
$815$	3.68368e11	+	2.31461e11i	0.834932	+	0.524623i
$816$	−4.76626e10	−	1.08787e10i	−0.107502	−	0.0245367i
$817$	−3.46852e11	+	2.76605e11i	−0.778496	+	0.620830i
$818$	9.56160e11	+	7.62512e11i	2.13559	+	1.70307i
$819$	−1.83412e11	−	8.03580e11i	−0.407654	−	1.78605i
$820$	4.34239e11	+	1.51947e11i	0.960447	+	0.336075i
$821$	3.23006e11	+	6.70728e11i	0.710948	+	1.47630i	0.872079	+	0.489365i	$0.162771\pi$
$821$	3.23006e11	+	6.70728e11i	0.710948	+	1.47630i	−0.161131	+	0.986933i	$0.551514\pi$
$822$	4.57156e10	−	2.87250e10i	0.100133	−	0.0629177i
$823$	−3.06450e11	+	1.07231e11i	−0.667975	+	0.233735i	−0.642899	−	0.765951i	$-0.722269\pi$
$823$	−3.06450e11	+	1.07231e11i	−0.667975	+	0.233735i	−0.0250761	+	0.999686i	$0.507983\pi$
$824$	−8.47292e11	−	8.47292e11i	−1.83791	−	1.83791i
$825$	1.63680e9	−	3.39885e9i	0.00353330	−	0.00733696i
$826$	1.08316e11	+	9.61332e11i	0.232687	+	2.06516i
$827$	2.04016e11	−	2.29871e10i	0.436156	−	0.0491430i	0.108843	−	0.994059i	$-0.465285\pi$
$827$	2.04016e11	−	2.29871e10i	0.436156	−	0.0491430i	0.327313	+	0.944916i	$0.393857\pi$
$828$	8.02245e11	+	3.86341e11i	1.70681	+	0.821957i
$829$	−6.25998e10	+	6.25998e10i	−0.132542	+	0.132542i	−0.770266	−	0.637723i	$-0.779876\pi$
$829$	−6.25998e10	+	6.25998e10i	−0.132542	+	0.132542i	0.637723	+	0.770266i	$0.279876\pi$
$830$	1.72429e11	+	4.92773e11i	0.363327	+	1.03833i
$831$	4.35835e10	+	6.93628e10i	0.0913941	+	0.145453i
$832$	1.07817e12	−	5.19219e11i	2.25006	−	1.08357i
$833$	5.18506e10	−	1.48181e11i	0.107690	−	0.307759i
$834$	−2.08167e11	+	4.75128e10i	−0.430277	+	0.0982080i
$835$	−4.09790e11	+	5.13860e11i	−0.842976	+	1.05706i
$836$	−1.32214e12	−	1.65791e12i	−2.70677	−	3.39419i
$837$	−3.67006e10	+	1.60796e11i	−0.0747776	+	0.327622i
$838$	4.27367e11	−	6.80151e11i	0.866612	−	1.37921i
$839$	2.78097e10	−	2.46818e11i	0.0561239	−	0.498114i	−0.933933	−	0.357448i	$-0.883647\pi$
$839$	2.78097e10	−	2.46818e11i	0.0561239	−	0.498114i	0.990057	−	0.140666i	$-0.0449244\pi$
$840$		−	3.90276e11i		−	0.783889i
$841$	4.88722e11	−	1.06759e11i	0.976962	−	0.213412i
$842$	1.10076e12			2.19000
$843$	1.14746e11	+	1.29288e10i	0.227210	+	0.0256005i
$844$	−1.35818e12	−	8.53401e11i	−2.67663	−	1.68184i
$845$	2.24869e11	+	5.13248e10i	0.441064	+	0.100670i
$846$	−4.43726e11	+	3.53859e11i	−0.866230	+	0.690795i
$847$	−4.50724e10	−	3.59441e10i	−0.0875744	−	0.0698383i
$848$	−3.52473e11	−	1.54428e12i	−0.681620	−	2.98637i
$849$	7.41308e10	+	2.59395e10i	0.142682	+	0.0499264i
$850$	4.84754e9	+	1.00660e10i	0.00928636	+	0.0192833i
$851$	−3.16812e11	+	1.99066e11i	−0.604064	+	0.379559i
$852$	−2.36436e11	+	8.27324e10i	−0.448698	+	0.157006i
$853$	−3.13472e11	−	3.13472e11i	−0.592111	−	0.592111i	0.346091	−	0.938201i	$-0.387509\pi$
$853$	−3.13472e11	−	3.13472e11i	−0.592111	−	0.592111i	−0.938201	+	0.346091i	$0.887509\pi$
$854$	−8.94052e11	+	1.85652e12i	−1.68086	+	3.49034i
$855$	−1.05113e11	−	9.32900e11i	−0.196694	−	1.74570i
$856$	−2.00078e12	+	2.25434e11i	−3.72654	+	0.419880i
$857$	−3.49480e11	−	1.68301e11i	−0.647887	−	0.312006i	0.0809248	−	0.996720i	$-0.474213\pi$
$857$	−3.49480e11	−	1.68301e11i	−0.647887	−	0.312006i	−0.728811	+	0.684714i	$0.759927\pi$
$858$	1.38800e11	−	1.38800e11i	0.256119	−	0.256119i
$859$	3.25988e11	+	9.31620e11i	0.598727	+	1.71106i	0.698088	+	0.716012i	$0.254034\pi$
$859$	3.25988e11	+	9.31620e11i	0.598727	+	1.71106i	−0.0993609	+	0.995051i	$0.531680\pi$
$860$	4.30950e11	+	6.85852e11i	0.787830	+	1.25382i
$861$	5.00828e10	−	2.41186e10i	0.0911331	−	0.0438874i
$862$	−3.46946e11	+	9.91516e11i	−0.628396	+	1.79585i
$863$	−1.01673e12	+	2.32063e11i	−1.83301	+	0.418372i	−0.992377	−	0.123238i	$-0.960672\pi$
$863$	−1.01673e12	+	2.32063e11i	−1.83301	+	0.418372i	−0.840630	+	0.541610i	$0.817815\pi$
$864$	3.05218e11	−	3.82732e11i	0.547716	−	0.686814i
$865$	−3.28873e11	−	4.12393e11i	−0.587440	−	0.736626i
$866$	8.13164e9	−	3.56271e10i	0.0144580	−	0.0633444i
$867$	−4.74264e10	+	7.54787e10i	−0.0839351	+	0.133582i
$868$	2.61651e11	−	2.32222e12i	0.460939	−	4.09095i
$869$			3.24151e11i			0.568419i
$870$	−1.82810e11	+	1.97343e10i	−0.319098	+	0.0344465i
$871$	7.81487e11			1.35784
$872$	1.92622e12	+	2.17033e11i	3.33151	+	0.375371i
$873$	4.61312e11	+	2.89862e11i	0.794214	+	0.499038i
$874$	1.44069e12	+	3.28827e11i	2.46902	+	0.563537i
$875$	6.99708e11	−	5.57999e11i	1.19367	−	0.951921i
$876$	−7.38867e10	−	5.89227e10i	−0.125473	−	0.100061i
$877$	4.44652e10	+	1.94815e11i	0.0751661	+	0.329324i	0.998505	−	0.0546620i	$-0.0174081\pi$
$877$	4.44652e10	+	1.94815e11i	0.0751661	+	0.329324i	−0.923339	+	0.383986i	$0.874551\pi$
$878$	1.67944e11	+	5.87663e10i	0.282610	+	0.0988895i
$879$	−5.64656e10	−	1.17252e11i	−0.0945863	−	0.196410i
$880$	−1.49431e12	+	9.38939e11i	−2.49179	+	1.56569i
$881$	4.27789e11	−	1.49690e11i	0.710111	−	0.248478i	0.0490343	−	0.998797i	$-0.484386\pi$
$881$	4.27789e11	−	1.49690e11i	0.710111	−	0.248478i	0.661076	+	0.750319i	$0.270100\pi$
$882$	1.14762e12	+	1.14762e12i	1.89637	+	1.89637i
$883$	−5.04018e10	+	1.04660e11i	−0.0829093	+	0.172163i	−0.938302	−	0.345817i	$-0.887602\pi$
$883$	−5.04018e10	+	1.04660e11i	−0.0829093	+	0.172163i	0.855393	+	0.517980i	$0.173316\pi$
$884$	4.67877e10	+	4.15253e11i	0.0766166	+	0.679991i
$885$	−7.28568e10	+	8.20899e9i	−0.118767	+	0.0133819i
$886$	8.24200e11	+	3.96914e11i	1.33751	+	0.644112i
$887$	8.30744e11	−	8.30744e11i	1.34206	−	1.34206i	0.448056	−	0.894005i	$-0.352116\pi$
$887$	8.30744e11	−	8.30744e11i	1.34206	−	1.34206i	0.894005	−	0.448056i	$-0.147884\pi$
$888$	9.36897e10	+	2.67750e11i	0.150675	+	0.430603i
$889$	−8.10415e11	−	1.28977e12i	−1.29748	−	2.06493i
$890$	−1.37991e11	+	6.64530e10i	−0.219933	+	0.105914i
$891$	−1.84157e11	+	5.26291e11i	−0.292199	+	0.835056i
$892$	−2.84746e11	+	6.49914e10i	−0.449778	+	0.102659i
$893$	−4.22135e11	+	5.29340e11i	−0.663812	+	0.832394i
$894$	1.10104e11	+	1.38066e11i	0.172367	+	0.216141i
$895$	3.18359e10	−	1.39482e11i	0.0496164	−	0.217384i
$896$	−6.67358e11	+	1.06209e12i	−1.03544	+	1.64790i
$897$	−1.10092e10	+	9.77094e10i	−0.0170054	+	0.150927i
$898$		−	2.96537e11i		−	0.456009i
$899$	−6.70318e11	−	3.12814e9i	−1.02622	−	0.00478902i
$900$	−8.30247e10			−0.126543
$901$	1.50137e11	+	1.69164e10i	0.227819	+	0.0256690i
$902$	−3.95487e11	−	2.48501e11i	−0.597456	−	0.375406i
$903$	9.54179e10	+	2.17785e10i	0.143509	+	0.0327550i
$904$	1.40385e12	−	1.11953e12i	2.10207	−	1.67635i
$905$	−8.06926e11	−	6.43502e11i	−1.20293	−	0.959303i
$906$	8.03243e10	+	3.51924e11i	0.119216	+	0.522319i
$907$	−2.89992e11	−	1.01473e11i	−0.428506	−	0.149941i	0.107405	−	0.994215i	$-0.465746\pi$
$907$	−2.89992e11	−	1.01473e11i	−0.428506	−	0.149941i	−0.535911	+	0.844275i	$0.680032\pi$
$908$	7.39109e11	+	1.53477e12i	1.08734	+	2.25788i
$909$	1.36231e11	−	8.55999e10i	0.199536	−	0.125377i
$910$	−2.35740e12	+	8.24888e11i	−3.43769	+	1.20290i
$911$	−7.82193e11	−	7.82193e11i	−1.13564	−	1.13564i	−0.989223	−	0.146416i	$-0.953226\pi$
$911$	−7.82193e11	−	7.82193e11i	−1.13564	−	1.13564i	−0.146416	−	0.989223i	$-0.546774\pi$
$912$	2.61600e11	−	5.43219e11i	0.378146	−	0.785228i
$913$	−4.26588e10	−	3.78608e11i	−0.0613940	−	0.544887i
$914$	1.13494e12	−	1.27877e11i	1.62625	−	0.183234i
$915$	−1.40700e11	−	6.77578e10i	−0.200729	−	0.0966662i
$916$	1.68154e10	−	1.68154e10i	0.0238850	−	0.0238850i
$917$	−2.86046e11	−	8.17472e11i	−0.404537	−	1.15610i
$918$	5.20231e10	+	8.27944e10i	0.0732531	+	0.116582i
$919$	−9.26072e11	+	4.45973e11i	−1.29832	+	0.625239i	−0.950034	−	0.312148i	$-0.898952\pi$
$919$	−9.26072e11	+	4.45973e11i	−1.29832	+	0.625239i	−0.348289	+	0.937387i	$0.613237\pi$
$920$	5.42542e11	−	1.55050e12i	0.757325	−	2.16431i
$921$	−7.41599e10	+	1.69265e10i	−0.103070	+	0.0235250i
$922$	3.61292e11	−	4.53046e11i	0.499959	−	0.626929i
$923$	6.08505e11	+	7.63041e11i	0.838412	+	1.05134i
$924$	−1.04099e11	+	4.56086e11i	−0.142809	+	0.625689i
$925$	1.85613e10	−	2.95401e10i	0.0253536	−	0.0403501i
$926$	5.47862e10	−	4.86241e11i	0.0745121	−	0.661313i
$927$			6.35882e11i			0.861108i
$928$	1.78851e12	+	8.71608e11i	2.41157	+	1.17525i
$929$	−4.71521e11			−0.633051			−0.316525	−	0.948584i	$-0.602516\pi$
$929$	−4.71521e11			−0.633051			−0.316525	+	0.948584i	$0.602516\pi$
$930$	2.44838e11	+	2.75866e10i	0.327301	+	0.0368779i
$931$	1.63936e12	+	1.03008e12i	2.18210	+	1.37111i
$932$	1.35545e11	+	3.09372e10i	0.179647	+	0.0410032i
$933$	−7.49037e10	+	5.97337e10i	−0.0988501	+	0.0788303i
$934$	8.92570e11	+	7.11801e11i	1.17288	+	0.935343i
$935$	−3.74579e10	−	1.64114e11i	−0.0490113	−	0.214733i
$936$	−2.48260e12	−	8.68700e11i	−3.23447	−	1.13179i
$937$	−3.23457e11	−	6.71665e11i	−0.419621	−	0.871353i	−0.998437	−	0.0558942i	$-0.982199\pi$
$937$	−3.23457e11	−	6.71665e11i	−0.419621	−	0.871353i	0.578815	−	0.815459i	$-0.303515\pi$
$938$	−2.19387e12	+	1.37850e12i	−2.83400	+	1.78072i
$939$	4.47880e10	−	1.56720e10i	0.0576102	−	0.0201587i
$940$	8.74106e11	+	8.74106e11i	1.11957	+	1.11957i
$941$	5.72600e11	−	1.18902e12i	0.730286	−	1.51646i	−0.121515	−	0.992590i	$-0.538775\pi$
$941$	5.72600e11	−	1.18902e12i	0.730286	−	1.51646i	0.851801	−	0.523866i	$-0.175511\pi$
$942$	−2.27718e10	−	2.02105e11i	−0.0289197	−	0.256669i
$943$	2.32499e11	−	2.61963e10i	0.294018	−	0.0331278i
$944$	1.49683e12	+	7.20834e11i	1.88488	+	0.907710i
$945$	−2.97048e11	+	2.97048e11i	−0.372477	+	0.372477i
$946$	−2.71612e11	−	7.76223e11i	−0.339144	−	0.969219i
$947$	−6.93361e11	−	1.10348e12i	−0.862104	−	1.37203i	−0.927363	−	0.374163i	$-0.877930\pi$
$947$	−6.93361e11	−	1.10348e12i	−0.862104	−	1.37203i	0.0652589	−	0.997868i	$-0.479213\pi$
$948$	−1.82172e11	+	8.77293e10i	−0.225552	+	0.108620i
$949$	−1.21611e11	+	3.47545e11i	−0.149937	+	0.428496i
$950$	−1.34332e11	+	3.06604e10i	−0.164925	+	0.0376429i
$951$	1.21034e11	−	1.51772e11i	0.147974	−	0.185553i
$952$	−5.25928e11	−	6.59493e11i	−0.640293	−	0.802901i
$953$	2.14933e11	−	9.41681e11i	0.260574	−	1.14165i	−0.660058	−	0.751215i	$-0.729468\pi$
$953$	2.14933e11	−	9.41681e11i	0.260574	−	1.14165i	0.920631	−	0.390433i	$-0.127675\pi$
$954$	−8.31007e11	+	1.32254e12i	−1.00325	+	1.59667i
$955$	−1.15504e11	+	1.02513e12i	−0.138862	+	1.23244i
$956$		−	9.66548e10i		−	0.115716i
$957$	1.33274e11	+	1.56465e10i	0.158890	+	0.0186539i
$958$	1.73019e12			2.05415
$959$	4.98185e11	+	5.61320e10i	0.589001	+	0.0663645i
$960$	−2.54603e11	−	1.59977e11i	−0.299763	−	0.188354i
$961$	4.42004e10	+	1.00885e10i	0.0518242	+	0.0118285i
$962$	1.41927e12	−	1.13183e12i	1.65717	−	1.32155i
$963$	8.35375e11	+	6.66189e11i	0.971351	+	0.774627i
$964$	4.30863e11	+	1.88774e12i	0.498921	+	2.18591i
$965$	9.32980e11	+	3.26464e11i	1.07588	+	0.376466i
$966$	−1.41448e11	−	2.93719e11i	−0.162438	−	0.337306i
$967$	−3.42410e11	+	2.15150e11i	−0.391598	+	0.246057i	−0.713411	−	0.700746i	$-0.752851\pi$
$967$	−3.42410e11	+	2.15150e11i	−0.391598	+	0.246057i	0.321813	+	0.946803i	$0.395708\pi$
$968$	−1.73639e11	+	6.07590e10i	−0.197764	+	0.0692005i
$969$	4.06652e10	+	4.06652e10i	0.0461241	+	0.0461241i
$970$	7.16281e11	−	1.48737e12i	0.809089	−	1.68009i
$971$	−5.75973e10	−	5.11190e11i	−0.0647925	−	0.575050i	−0.983603	−	0.180350i	$-0.942277\pi$
$971$	−5.75973e10	−	5.11190e11i	−0.0647925	−	0.575050i	0.918810	−	0.394700i	$-0.129151\pi$
$972$	−1.08815e12	+	1.22605e11i	−1.21906	+	0.137355i
$973$	−1.78631e12	−	8.60243e11i	−1.99300	−	0.959776i
$974$	−2.02992e12	+	2.02992e12i	−2.25550	+	2.25550i
$975$	−3.02808e9	−	8.65375e9i	−0.00335080	−	0.00957603i
$976$	1.88268e12	+	2.99626e12i	2.07480	+	3.30203i
$977$	−1.19909e12	+	5.77451e11i	−1.31605	+	0.633778i	−0.954399	−	0.298535i	$-0.903502\pi$
$977$	−1.19909e12	+	5.77451e11i	−1.31605	+	0.633778i	−0.361654	+	0.932312i	$0.617788\pi$
$978$	9.09962e10	−	2.60052e11i	0.0994644	−	0.284253i
$979$	1.08972e11	−	2.48721e10i	0.118627	−	0.0270758i
$980$	2.20404e12	−	2.76378e12i	2.38954	−	2.99639i
$981$	−6.41364e11	−	8.04245e11i	−0.692514	−	0.868385i
$982$	3.15701e11	−	1.38317e12i	0.339492	−	1.48741i
$983$	5.82219e10	−	9.26596e10i	0.0623551	−	0.0992376i	−0.814092	−	0.580737i	$-0.802765\pi$
$983$	5.82219e10	−	9.26596e10i	0.0623551	−	0.0992376i	0.876447	+	0.481499i	$0.159907\pi$
$984$	1.98605e10	−	1.76267e11i	0.0211841	−	0.188014i
$985$			7.19648e11i			0.764496i
$986$	−2.82322e11	+	2.79699e11i	−0.298701	+	0.295926i
$987$	1.49365e11			0.157391
$988$	−5.12120e12	−	5.77021e11i	−5.37457	−	0.605569i
$989$	3.48803e11	+	2.19167e11i	0.364581	+	0.229082i
$990$	1.69662e12	+	3.87242e11i	1.76621	+	0.403126i
$991$	3.28172e11	−	2.61709e11i	0.340257	−	0.271346i	−0.438421	−	0.898770i	$-0.644462\pi$
$991$	3.28172e11	−	2.61709e11i	0.340257	−	0.271346i	0.778678	+	0.627424i	$0.215891\pi$
$992$	−2.08439e12	−	1.66224e12i	−2.15244	−	1.71652i
$993$	1.91600e10	+	8.39454e10i	0.0197060	+	0.0863376i
$994$	−3.05422e12	−	1.06872e12i	−3.12863	−	1.09476i
$995$	3.63417e11	+	7.54644e11i	0.370778	+	0.769928i
$996$	2.01230e11	−	1.26442e11i	0.204483	−	0.128485i
$997$	1.42797e12	−	4.99668e11i	1.44523	−	0.505709i	0.510134	−	0.860095i	$-0.329596\pi$
$997$	1.42797e12	−	4.99668e11i	1.44523	−	0.505709i	0.935099	+	0.354386i	$0.115310\pi$
$998$	−1.13034e12	−	1.13034e12i	−1.13942	−	1.13942i
$999$	1.32481e11	−	2.75100e11i	0.133012	−	0.276203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.f.a.2.19	✓	228
29.15	odd	28	inner	29.9.f.a.15.19	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.f.a.2.19	✓	228	1.1	even	1	trivial
29.9.f.a.15.19	yes	228	29.15	odd	28	inner

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)

\(f(q)\)	\(=\)	\(q+(29.9840 + 3.37838i) q^{2} +(11.3862 + 7.15440i) q^{3} +(638.043 + 145.629i) q^{4} +(-500.927 + 399.476i) q^{5} +(317.232 + 252.984i) q^{6} +(838.383 + 3673.20i) q^{7} +(11348.1 + 3970.86i) q^{8} +(-2768.25 - 5748.33i) q^{9} +O(q^{10})\)	\(q+(29.9840 + 3.37838i) q^{2} +(11.3862 + 7.15440i) q^{3} +(638.043 + 145.629i) q^{4} +(-500.927 + 399.476i) q^{5} +(317.232 + 252.984i) q^{6} +(838.383 + 3673.20i) q^{7} +(11348.1 + 3970.86i) q^{8} +(-2768.25 - 5748.33i) q^{9} +(-16369.4 + 10285.5i) q^{10} +(13317.0 - 4659.83i) q^{11} +(6222.97 + 6222.97i) q^{12} +(14877.4 - 30893.2i) q^{13} +(12728.6 + 112969. i) q^{14} +(-8561.64 + 964.666i) q^{15} +(175897. + 84707.6i) q^{16} +(-13167.6 + 13167.6i) q^{17} +(-63583.1 - 181710. i) q^{18} +(-122185. - 194457. i) q^{19} +(-377788. + 181933. i) q^{20} +(-16733.5 + 47821.7i) q^{21} +(415040. - 94730.2i) q^{22} +(-132959. + 166725. i) q^{23} +(100802. + 126401. i) q^{24} +(4424.54 - 19385.2i) q^{25} +(550451. - 876038. i) q^{26} +(19484.5 - 172930. i) q^{27} +2.46575e6i q^{28} +(703196. - 75909.6i) q^{29} -259971. q^{30} +(-941790. - 106114. i) q^{31} +(2.38185e6 + 1.49661e6i) q^{32} +(184968. + 42217.8i) q^{33} +(-439302. + 350332. i) q^{34} +(-1.88732e6 - 1.50509e6i) q^{35} +(-929139. - 4.07082e6i) q^{36} +(1.65611e6 + 579499. i) q^{37} +(-3.00665e6 - 6.24337e6i) q^{38} +(390418. - 245316. i) q^{39} +(-7.27082e6 + 2.54417e6i) q^{40} +(-775813. - 775813. i) q^{41} +(-663298. + 1.37735e6i) q^{42} +(-216287. - 1.91960e6i) q^{43} +(9.17545e6 - 1.03383e6i) q^{44} +(3.68301e6 + 1.77365e6i) q^{45} +(-4.54989e6 + 4.54989e6i) q^{46} +(-973692. - 2.78265e6i) q^{47} +(1.39676e6 + 2.22293e6i) q^{48} +(-7.59558e6 + 3.65784e6i) q^{49} +(198156. - 566297. i) q^{50} +(-244135. + 55722.1i) q^{51} +(1.39913e7 - 1.75446e7i) q^{52} +(-5.05866e6 - 6.34336e6i) q^{53} +(1.16844e6 - 5.11929e6i) q^{54} +(-4.80937e6 + 7.65407e6i) q^{55} +(-5.07172e6 + 4.50128e7i) q^{56} -3.08828e6i q^{57} +(2.13410e7 + 99591.1i) q^{58} +8.50967e6 q^{59} +(-5.60318e6 - 631327. i) q^{60} +(1.53473e7 + 9.64333e6i) q^{61} +(-2.78801e7 - 6.36345e6i) q^{62} +(1.87939e7 - 1.49876e7i) q^{63} +(2.72859e7 + 2.17597e7i) q^{64} +(4.88860e6 + 2.14184e7i) q^{65} +(5.40345e6 + 1.89075e6i) q^{66} +(9.88877e6 + 2.05342e7i) q^{67} +(-1.03191e7 + 6.48391e6i) q^{68} +(-2.70671e6 + 947118. i) q^{69} +(-5.15046e7 - 5.15046e7i) q^{70} +(-1.23497e7 + 2.56444e7i) q^{71} +(-8.58848e6 - 7.62248e7i) q^{72} +(-1.06709e7 + 1.20232e6i) q^{73} +(4.76991e7 + 2.29707e7i) q^{74} +(189068. - 189068. i) q^{75} +(-4.96409e7 - 1.41865e8i) q^{76} +(2.82813e7 + 4.50094e7i) q^{77} +(1.25351e7 - 6.03657e6i) q^{78} +(-7.58821e6 + 2.16859e7i) q^{79} +(-1.21950e8 + 2.78343e7i) q^{80} +(-2.46404e7 + 3.08981e7i) q^{81} +(-2.06410e7 - 2.58829e7i) q^{82} +(6.00911e6 - 2.63276e7i) q^{83} +(-1.76410e7 + 2.80754e7i) q^{84} +(1.33587e6 - 1.18561e7i) q^{85} -5.82879e7i q^{86} +(8.54979e6 + 4.16662e6i) q^{87} +1.69626e8 q^{88} +(7.87249e6 + 887017. i) q^{89} +(1.04439e8 + 6.56235e7i) q^{90} +(1.25950e8 + 2.87472e7i) q^{91} +(-1.09113e8 + 8.70150e7i) q^{92} +(-9.96419e6 - 7.94617e6i) q^{93} +(-1.97943e7 - 8.67245e7i) q^{94} +(1.38887e8 + 4.85986e7i) q^{95} +(1.64127e7 + 3.40814e7i) q^{96} +(-7.23040e7 + 4.54316e7i) q^{97} +(-2.40103e8 + 8.40157e7i) q^{98} +(-6.36512e7 - 6.36512e7i) 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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