LMFDB - Embedded newform 29.9.f.a.3.1

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			3.1
Character	$\chi$	$=$	29.3
Dual form			29.9.f.a.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-25.9849 - 16.3274i) q^{2} +(93.5645 - 32.7396i) q^{3} +(297.558 + 617.886i) q^{4} +(-652.275 + 148.877i) q^{5} +(-2965.82 - 676.929i) q^{6} +(2496.53 + 1202.27i) q^{7} +(1476.82 - 13107.1i) q^{8} +(2552.84 - 2035.82i) q^{9} +O(q^{10})$	\(q+(-25.9849 - 16.3274i) q^{2} +(93.5645 - 32.7396i) q^{3} +(297.558 + 617.886i) q^{4} +(-652.275 + 148.877i) q^{5} +(-2965.82 - 676.929i) q^{6} +(2496.53 + 1202.27i) q^{7} +(1476.82 - 13107.1i) q^{8} +(2552.84 - 2035.82i) q^{9} +(19380.1 + 6781.39i) q^{10} +(-2854.15 - 25331.3i) q^{11} +(48070.2 + 48070.2i) q^{12} +(-18661.6 - 14882.1i) q^{13} +(-45242.3 - 72002.8i) q^{14} +(-56155.6 + 35284.9i) q^{15} +(-142918. + 179213. i) q^{16} +(-33455.0 + 33455.0i) q^{17} +(-99575.0 + 11219.4i) q^{18} +(44702.5 - 127752. i) q^{19} +(-286079. - 358731. i) q^{20} +(272949. + 30753.9i) q^{21} +(-339429. + 704832. i) q^{22} +(36794.7 - 161208. i) q^{23} +(-290945. - 1.27471e6i) q^{24} +(51356.7 - 24732.1i) q^{25} +(241933. + 691405. i) q^{26} +(-173817. + 276627. i) q^{27} +1.90032e6i q^{28} +(-549688. - 445072. i) q^{29} +2.03531e6 q^{30} +(-222378. - 139729. i) q^{31} +(3.45262e6 - 1.20812e6i) q^{32} +(-1.09638e6 - 2.27666e6i) q^{33} +(1.41556e6 - 323092. i) q^{34} +(-1.80742e6 - 412531. i) q^{35} +(2.01752e6 + 971587. i) q^{36} +(271984. - 2.41392e6i) q^{37} +(-3.24746e6 + 2.58976e6i) q^{38} +(-2.23329e6 - 781463. i) q^{39} +(988065. + 8.76932e6i) q^{40} +(2.01161e6 + 2.01161e6i) q^{41} +(-6.59042e6 - 5.25569e6i) q^{42} +(-1.11166e6 - 1.76919e6i) q^{43} +(1.48026e7 - 9.30106e6i) q^{44} +(-1.36206e6 + 1.70797e6i) q^{45} +(-3.58822e6 + 3.58822e6i) q^{46} +(-2.74566e6 + 309362. i) q^{47} +(-7.50465e6 + 2.14471e7i) q^{48} +(1.19294e6 + 1.49590e6i) q^{49} +(-1.73831e6 - 195861. i) q^{50} +(-2.03490e6 + 4.22551e6i) q^{51} +(3.64254e6 - 1.59590e7i) q^{52} +(-1.91644e6 - 8.39647e6i) q^{53} +(9.03322e6 - 4.35017e6i) q^{54} +(5.63294e6 + 1.60980e7i) q^{55} +(1.94452e7 - 3.09469e7i) q^{56} -1.34166e7i q^{57} +(7.01672e6 + 2.05402e7i) q^{58} -1.05938e7 q^{59} +(-3.85116e7 - 2.41984e7i) q^{60} +(1.66630e7 - 5.83062e6i) q^{61} +(3.49706e6 + 7.26172e6i) q^{62} +(8.82085e6 - 2.01330e6i) q^{63} +(-5.22320e7 - 1.19216e7i) q^{64} +(1.43881e7 + 6.92893e6i) q^{65} +(-8.68259e6 + 7.70601e7i) q^{66} +(-7.31557e6 + 5.83397e6i) q^{67} +(-3.06262e7 - 1.07166e7i) q^{68} +(-1.83522e6 - 1.62880e7i) q^{69} +(4.02300e7 + 4.02300e7i) q^{70} +(-1.93567e7 - 1.54364e7i) q^{71} +(-2.29137e7 - 3.64669e7i) q^{72} +(-1.33793e7 + 8.40679e6i) q^{73} +(-4.64806e7 + 5.82848e7i) q^{74} +(3.99544e6 - 3.99544e6i) q^{75} +(9.22380e7 - 1.03927e7i) q^{76} +(2.33295e7 - 6.66718e7i) q^{77} +(4.52727e7 + 5.67702e7i) q^{78} +(-1.81723e7 - 2.04753e6i) q^{79} +(6.65408e7 - 1.38173e8i) q^{80} +(-1.19734e7 + 5.24591e7i) q^{81} +(-1.94272e7 - 8.51160e7i) q^{82} +(4.22464e7 - 2.03448e7i) q^{83} +(6.22157e7 + 1.77802e8i) q^{84} +(1.68412e7 - 2.68025e7i) q^{85} +6.41229e7i q^{86} +(-6.60028e7 - 2.36464e7i) q^{87} -3.36236e8 q^{88} +(1.01204e8 + 6.35910e7i) q^{89} +(6.32799e7 - 2.21426e7i) q^{90} +(-2.86970e7 - 5.95898e7i) q^{91} +(1.10557e8 - 2.52339e7i) q^{92} +(-2.53814e7 - 5.79314e6i) q^{93} +(7.63969e7 + 3.67908e7i) q^{94} +(-1.01389e7 + 8.99849e7i) q^{95} +(2.83489e8 - 2.26075e8i) q^{96} +(9.20721e7 + 3.22174e7i) q^{97} +(-6.57429e6 - 5.83485e7i) q^{98} +(-5.88561e7 - 5.88561e7i) 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 $\left(\mathbb{Z}/29\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{28}\right)$

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 $

$2$	−25.9849	−	16.3274i	−1.62406	−	1.02046i	−0.962766	−	0.270335i	$-0.912866\pi$
$2$	−25.9849	−	16.3274i	−1.62406	−	1.02046i	−0.661292	−	0.750129i	$-0.729992\pi$
$3$	93.5645	−	32.7396i	1.15512	−	0.404193i	0.316328	−	0.948650i	$-0.397550\pi$
$3$	93.5645	−	32.7396i	1.15512	−	0.404193i	0.838789	+	0.544457i	$0.183264\pi$
$4$	297.558	+	617.886i	1.16234	+	2.41362i
$5$	−652.275	+	148.877i	−1.04364	+	0.238204i	−0.709783	−	0.704420i	$-0.751207\pi$
$5$	−652.275	+	148.877i	−1.04364	+	0.238204i	−0.333856	+	0.942624i	$0.608350\pi$
$6$	−2965.82	−	676.929i	−2.28844	−	0.522322i
$7$	2496.53	+	1202.27i	1.03979	+	0.500736i	0.874255	−	0.485468i	$-0.161351\pi$
$7$	2496.53	+	1202.27i	1.03979	+	0.500736i	0.165535	+	0.986204i	$0.447065\pi$
$8$	1476.82	−	13107.1i	0.360552	−	3.19998i
$9$	2552.84	−	2035.82i	0.389093	−	0.310291i
$10$	19380.1	+	6781.39i	1.93801	+	0.678139i
$11$	−2854.15	−	25331.3i	−0.194942	−	1.73016i	−0.586450	−	0.809985i	$-0.699475\pi$
$11$	−2854.15	−	25331.3i	−0.194942	−	1.73016i	0.391508	−	0.920175i	$-0.371954\pi$
$12$	48070.2	+	48070.2i	2.31820	+	2.31820i
$13$	−18661.6	−	14882.1i	−0.653393	−	0.521064i	0.239751	−	0.970834i	$-0.422934\pi$
$13$	−18661.6	−	14882.1i	−0.653393	−	0.521064i	−0.893144	+	0.449771i	$0.851506\pi$
$14$	−45242.3	−	72002.8i	−1.17770	−	1.87429i
$15$	−56155.6	+	35284.9i	−1.10925	+	0.696985i
$16$	−142918.	+	179213.i	−2.18075	+	2.73457i
$17$	−33455.0	+	33455.0i	−0.400558	+	0.400558i	−0.878430	−	0.477872i	$-0.841408\pi$
$17$	−33455.0	+	33455.0i	−0.400558	+	0.400558i	0.477872	+	0.878430i	$0.341408\pi$
$18$	−99575.0	+	11219.4i	−0.948550	+	0.106876i
$19$	44702.5	−	127752.i	0.343019	−	0.980291i	−0.635134	−	0.772402i	$-0.719055\pi$
$19$	44702.5	−	127752.i	0.343019	−	0.980291i	0.978152	−	0.207889i	$-0.0666592\pi$
$20$	−286079.	−	358731.i	−1.78799	−	2.24207i
$21$	272949.	+	30753.9i	1.40347	+	0.158133i
$22$	−339429.	+	704832.i	−1.44897	+	3.00881i
$23$	36794.7	−	161208.i	0.131484	−	0.576071i	−0.865665	−	0.500623i	$-0.833104\pi$
$23$	36794.7	−	161208.i	0.131484	−	0.576071i	0.997150	−	0.0754476i	$-0.0240386\pi$
$24$	−290945.	−	1.27471e6i	−0.876932	−	3.84209i
$25$	51356.7	−	24732.1i	0.131473	−	0.0633141i
$26$	241933.	+	691405.i	0.529422	+	1.51300i
$27$	−173817.	+	276627.i	−0.327067	+	0.520523i
$28$			1.90032e6i			3.09167i
$29$	−549688.	−	445072.i	−0.777185	−	0.629272i
$29$	−549688.	−	445072.i	−0.777185	−	0.629272i
$30$	2.03531e6			2.51273
$31$	−222378.	−	139729.i	−0.240794	−	0.151301i	0.406229	−	0.913771i	$-0.366843\pi$
$31$	−222378.	−	139729.i	−0.240794	−	0.151301i	−0.647023	+	0.762470i	$0.723986\pi$
$32$	3.45262e6	−	1.20812e6i	3.29268	−	1.15216i
$33$	−1.09638e6	−	2.27666e6i	−0.924500	−	1.91974i
$34$	1.41556e6	−	323092.i	1.05928	−	0.241775i
$35$	−1.80742e6	−	412531.i	−1.20444	−	0.274906i
$36$	2.01752e6	+	971587.i	1.20118	+	0.578458i
$37$	271984.	−	2.41392e6i	0.145123	−	1.28800i	−0.684226	−	0.729270i	$-0.739860\pi$
$37$	271984.	−	2.41392e6i	0.145123	−	1.28800i	0.829349	−	0.558731i	$-0.188712\pi$
$38$	−3.24746e6	+	2.58976e6i	−1.55743	+	1.24201i
$39$	−2.23329e6	−	781463.i	−0.965356	−	0.337793i
$40$	988065.	+	8.76932e6i	0.385963	+	3.42551i
$41$	2.01161e6	+	2.01161e6i	0.711883	+	0.711883i	0.966929	−	0.255046i	$-0.0820907\pi$
$41$	2.01161e6	+	2.01161e6i	0.711883	+	0.711883i	−0.255046	+	0.966929i	$0.582091\pi$
$42$	−6.59042e6	−	5.25569e6i	−2.11795	−	1.68901i
$43$	−1.11166e6	−	1.76919e6i	−0.325160	−	0.517490i	0.643641	−	0.765327i	$-0.277423\pi$
$43$	−1.11166e6	−	1.76919e6i	−0.325160	−	0.517490i	−0.968802	+	0.247838i	$0.920280\pi$
$44$	1.48026e7	−	9.30106e6i	3.94935	−	2.48154i
$45$	−1.36206e6	+	1.70797e6i	−0.332160	+	0.416516i
$46$	−3.58822e6	+	3.58822e6i	−0.801397	+	0.801397i
$47$	−2.74566e6	+	309362.i	−0.562673	+	0.0633980i	−0.388720	−	0.921356i	$-0.627083\pi$
$47$	−2.74566e6	+	309362.i	−0.562673	+	0.0633980i	−0.173953	+	0.984754i	$0.555654\pi$
$48$	−7.50465e6	+	2.14471e7i	−1.41373	+	4.04020i
$49$	1.19294e6	+	1.49590e6i	0.206935	+	0.259488i
$50$	−1.73831e6	−	195861.i	−0.278130	−	0.0313377i
$51$	−2.03490e6	+	4.22551e6i	−0.300789	+	0.624594i
$52$	3.64254e6	−	1.59590e7i	0.498185	−	2.18269i
$53$	−1.91644e6	−	8.39647e6i	−0.242880	−	1.06413i	−0.938381	−	0.345602i	$-0.887675\pi$
$53$	−1.91644e6	−	8.39647e6i	−0.242880	−	1.06413i	0.695501	−	0.718525i	$-0.255182\pi$
$54$	9.03322e6	−	4.35017e6i	1.06235	−	0.511601i
$55$	5.63294e6	+	1.60980e7i	0.615580	+	1.75923i
$56$	1.94452e7	−	3.09469e7i	1.97725	−	3.14677i
$57$		−	1.34166e7i		−	1.27100i
$58$	7.01672e6	+	2.05402e7i	0.620044	+	1.81506i
$59$	−1.05938e7			−0.874264			−0.437132	−	0.899397i	$-0.644006\pi$
$59$	−1.05938e7			−0.874264			−0.437132	+	0.899397i	$0.644006\pi$
$60$	−3.85116e7	−	2.41984e7i	−2.97157	−	1.86716i
$61$	1.66630e7	−	5.83062e6i	1.20346	−	0.421110i	0.347269	−	0.937765i	$-0.387109\pi$
$61$	1.66630e7	−	5.83062e6i	1.20346	−	0.421110i	0.856193	+	0.516656i	$0.172823\pi$
$62$	3.49706e6	+	7.26172e6i	0.236666	+	0.491442i
$63$	8.82085e6	−	2.01330e6i	0.559949	−	0.127805i
$64$	−5.22320e7	−	1.19216e7i	−3.11327	−	0.710584i
$65$	1.43881e7	+	6.92893e6i	0.806026	+	0.388162i
$66$	−8.68259e6	+	7.70601e7i	−0.457587	+	4.06119i
$67$	−7.31557e6	+	5.83397e6i	−0.363035	+	0.289511i	−0.787971	−	0.615713i	$-0.788868\pi$
$67$	−7.31557e6	+	5.83397e6i	−0.363035	+	0.289511i	0.424936	+	0.905224i	$0.360297\pi$
$68$	−3.06262e7	−	1.07166e7i	−1.43238	−	0.501210i
$69$	−1.83522e6	−	1.62880e7i	−0.0809639	−	0.718574i
$70$	4.02300e7	+	4.02300e7i	1.67555	+	1.67555i
$71$	−1.93567e7	−	1.54364e7i	−0.761724	−	0.607454i	0.163646	−	0.986519i	$-0.447674\pi$
$71$	−1.93567e7	−	1.54364e7i	−0.761724	−	0.607454i	−0.925370	+	0.379065i	$0.876246\pi$
$72$	−2.29137e7	−	3.64669e7i	−0.852639	−	1.35697i
$73$	−1.33793e7	+	8.40679e6i	−0.471132	+	0.296032i	−0.746594	−	0.665280i	$-0.768312\pi$
$73$	−1.33793e7	+	8.40679e6i	−0.471132	+	0.296032i	0.275462	+	0.961312i	$0.411169\pi$
$74$	−4.64806e7	+	5.82848e7i	−1.55005	+	1.94370i
$75$	3.99544e6	−	3.99544e6i	0.126276	−	0.126276i
$76$	9.22380e7	−	1.03927e7i	2.76475	−	0.311512i
$77$	2.33295e7	−	6.66718e7i	0.663655	−	1.89662i
$78$	4.52727e7	+	5.67702e7i	1.22309	+	1.53371i
$79$	−1.81723e7	−	2.04753e6i	−0.466554	−	0.0525680i	−0.124441	−	0.992227i	$-0.539714\pi$
$79$	−1.81723e7	−	2.04753e6i	−0.466554	−	0.0525680i	−0.342113	+	0.939659i	$0.611142\pi$
$80$	6.65408e7	−	1.38173e8i	1.62453	−	3.37337i
$81$	−1.19734e7	+	5.24591e7i	−0.278150	+	1.21865i
$82$	−1.94272e7	−	8.51160e7i	−0.429689	−	1.88259i
$83$	4.22464e7	−	2.03448e7i	0.890178	−	0.428687i	0.0678467	−	0.997696i	$-0.478387\pi$
$83$	4.22464e7	−	2.03448e7i	0.890178	−	0.428687i	0.822332	+	0.569008i	$0.192673\pi$
$84$	6.22157e7	+	1.77802e8i	1.24963	+	3.57125i
$85$	1.68412e7	−	2.68025e7i	0.322624	−	0.513452i
$86$			6.41229e7i			1.17225i
$87$	−6.60028e7	−	2.36464e7i	−1.15209	−	0.412751i
$88$	−3.36236e8			−5.60677
$89$	1.01204e8	+	6.35910e7i	1.61302	+	1.01353i	0.968524	+	0.248919i	$0.0800754\pi$
$89$	1.01204e8	+	6.35910e7i	1.61302	+	1.01353i	0.644496	+	0.764608i	$0.277067\pi$
$90$	6.32799e7	−	2.21426e7i	0.964486	−	0.337488i
$91$	−2.86970e7	−	5.95898e7i	−0.418476	−	0.868974i
$92$	1.10557e8	−	2.52339e7i	1.54324	−	0.352235i
$93$	−2.53814e7	−	5.79314e6i	−0.339300	−	0.0774429i
$94$	7.63969e7	+	3.67908e7i	0.978508	+	0.471225i
$95$	−1.01389e7	+	8.99849e7i	−0.124479	+	1.10478i
$96$	2.83489e8	−	2.26075e8i	3.33773	−	2.66175i
$97$	9.20721e7	+	3.22174e7i	1.04002	+	0.363918i	0.795645	−	0.605763i	$-0.207132\pi$
$97$	9.20721e7	+	3.22174e7i	1.04002	+	0.363918i	0.244373	+	0.969681i	$0.421418\pi$
$98$	−6.57429e6	−	5.83485e7i	−0.0712762	−	0.632594i
$99$	−5.88561e7	−	5.88561e7i	−0.612704	−	0.612704i
$100$	3.05632e7	+	2.43733e7i	0.305632	+	0.243733i
$101$	2.83966e7	+	4.51929e7i	0.272886	+	0.434295i	0.954849	−	0.297091i	$-0.0960165\pi$
$101$	2.83966e7	+	4.51929e7i	0.272886	+	0.434295i	−0.681963	+	0.731386i	$0.738874\pi$
$102$	1.21868e8	−	7.65749e7i	1.12587	−	0.707434i
$103$	−8.35085e6	+	1.04716e7i	−0.0741962	+	0.0930391i	−0.817544	−	0.575866i	$-0.804665\pi$
$103$	−8.35085e6	+	1.04716e7i	−0.0741962	+	0.0930391i	0.743348	+	0.668905i	$0.233237\pi$
$104$	−2.22621e8	+	2.22621e8i	−1.90298	+	1.90298i
$105$	−1.82616e8	+	2.05759e7i	−1.50239	+	0.169278i
$106$	−8.72941e7	+	2.49472e8i	−0.691451	+	1.97605i
$107$	7.21720e7	+	9.05009e7i	0.550597	+	0.690427i	0.976788	−	0.214206i	$-0.0687165\pi$
$107$	7.21720e7	+	9.05009e7i	0.550597	+	0.690427i	−0.426191	+	0.904633i	$0.640145\pi$
$108$	−2.22645e8	−	2.50860e7i	−1.63650	−	0.184390i
$109$	7.33549e7	−	1.52323e8i	0.519665	−	1.07909i	−0.461717	−	0.887027i	$-0.652766\pi$
$109$	7.33549e7	−	1.52323e8i	0.519665	−	1.07909i	0.981382	−	0.192068i	$-0.0615193\pi$
$110$	1.16468e8	−	5.10278e8i	0.795489	−	3.48526i
$111$	−5.35829e7	−	2.34762e8i	−0.352967	−	1.54645i
$112$	−5.72261e8	+	2.75586e8i	−3.63682	+	1.75140i
$113$	−1.63515e7	−	4.67298e7i	−0.100287	−	0.286603i	0.882798	−	0.469752i	$-0.155657\pi$
$113$	−1.63515e7	−	4.67298e7i	−0.100287	−	0.286603i	−0.983085	+	0.183149i	$0.941371\pi$
$114$	−2.19059e8	+	3.48631e8i	−1.29701	+	2.06417i
$115$			1.10630e8i			0.632530i
$116$	1.11440e8	−	4.72079e8i	0.615472	−	2.60725i
$117$	−7.79372e7			−0.415912
$118$	2.75279e8	+	1.72969e8i	1.41986	+	0.892155i
$119$	−1.23743e8	+	4.32997e7i	−0.617070	+	0.215922i
$120$	3.79552e8	+	7.88148e8i	1.83040	+	3.80087i
$121$	−4.24543e8	+	9.68991e7i	−1.98052	+	0.452041i
$122$	−5.28185e8	−	1.20555e8i	−2.38422	−	0.544183i
$123$	2.54075e8	+	1.22356e8i	1.11005	+	0.534570i
$124$	2.01664e7	−	1.78982e8i	0.0852986	−	0.757046i
$125$	1.74513e8	−	1.39169e8i	0.714805	−	0.570038i
$126$	−2.62081e8	−	9.17062e7i	−1.03981	−	0.363845i
$127$	−1.13399e7	−	1.00644e8i	−0.0435908	−	0.386879i	−0.996498	−	0.0836169i	$-0.973353\pi$
$127$	−1.13399e7	−	1.00644e8i	−0.0435908	−	0.386879i	0.952907	−	0.303262i	$-0.0980758\pi$
$128$	5.00448e8	+	5.00448e8i	1.86431	+	1.86431i
$129$	−1.61935e8	−	1.29139e8i	−0.584764	−	0.466334i
$130$	−2.60741e8	−	4.14968e8i	−0.912928	−	1.45292i
$131$	7.07820e7	−	4.44752e7i	0.240346	−	0.151020i	−0.406473	−	0.913663i	$-0.633242\pi$
$131$	7.07820e7	−	4.44752e7i	0.240346	−	0.151020i	0.646819	+	0.762643i	$0.276099\pi$
$132$	1.08048e9	−	1.35488e9i	3.55894	−	4.46277i
$133$	2.65194e8	−	2.65194e8i	0.847534	−	0.847534i
$134$	2.85348e8	−	3.21510e7i	0.885026	−	0.0997184i
$135$	7.21925e7	−	2.06314e8i	0.217349	−	0.621147i
$136$	3.89092e8	+	4.87906e8i	1.13736	+	1.42620i
$137$	−1.86241e8	−	2.09843e7i	−0.528680	−	0.0595679i	−0.156410	−	0.987692i	$-0.549992\pi$
$137$	−1.86241e8	−	2.09843e7i	−0.528680	−	0.0595679i	−0.372270	+	0.928124i	$0.621421\pi$
$138$	−2.18253e8	+	4.53207e8i	−0.601789	+	1.24963i
$139$	−9.04173e7	+	3.96144e8i	−0.242210	+	1.06119i	0.696790	+	0.717275i	$0.254611\pi$
$139$	−9.04173e7	+	3.96144e8i	−0.242210	+	1.06119i	−0.939000	+	0.343917i	$0.888246\pi$
$140$	−2.82914e8	−	1.23953e9i	−0.736449	−	3.22659i
$141$	−2.46768e8	+	1.18837e8i	−0.624328	+	0.300660i
$142$	2.50945e8	+	7.17159e8i	0.617199	+	1.76385i
$143$	−3.23720e8	+	5.15197e8i	−0.774149	+	1.23205i
$144$			7.48457e8i			1.74067i
$145$	4.24809e8	+	2.08473e8i	0.960996	+	0.471605i
$146$	4.84922e8			1.06724
$147$	1.60592e8	+	1.00907e8i	0.343918	+	0.216098i
$148$	1.57246e9	−	5.50227e8i	3.27742	−	1.14682i
$149$	3.70239e8	+	7.68809e8i	0.751168	+	1.55982i	0.826680	+	0.562672i	$0.190227\pi$
$149$	3.70239e8	+	7.68809e8i	0.751168	+	1.55982i	−0.0755121	+	0.997145i	$0.524059\pi$
$150$	−1.69057e8	+	3.85861e7i	−0.333939	+	0.0762194i
$151$	1.91075e8	+	4.36116e7i	0.367533	+	0.0838870i	0.402299	−	0.915508i	$-0.368211\pi$
$151$	1.91075e8	+	4.36116e7i	0.367533	+	0.0838870i	−0.0347657	+	0.999395i	$0.511068\pi$
$152$	−1.60845e9	−	7.74590e8i	−3.01324	−	1.45110i
$153$	−1.72968e7	+	1.53514e8i	−0.0315646	+	0.280144i
$154$	−1.69479e9	+	1.35155e9i	−3.01324	+	2.40298i
$155$	1.65854e8	+	5.80349e7i	0.287342	+	0.100545i
$156$	−1.81680e8	−	1.61245e9i	−0.306766	−	2.72263i
$157$	−3.44280e8	−	3.44280e8i	−0.566648	−	0.566648i	0.364540	−	0.931188i	$-0.381226\pi$
$157$	−3.44280e8	−	3.44280e8i	−0.566648	−	0.566648i	−0.931188	+	0.364540i	$0.881226\pi$
$158$	4.38775e8	+	3.49912e8i	0.704067	+	0.561475i
$159$	−4.54208e8	−	7.22869e8i	−0.710668	−	1.13102i
$160$	−2.07219e9	+	1.30205e9i	−3.16192	+	1.98676i
$161$	2.85675e8	−	3.58225e8i	0.425175	−	0.533153i
$162$	1.16765e9	−	1.16765e9i	1.69532	−	1.69532i
$163$	3.85862e8	−	4.34762e7i	0.546615	−	0.0615888i	0.165661	−	0.986183i	$-0.447024\pi$
$163$	3.85862e8	−	4.34762e7i	0.546615	−	0.0615888i	0.380954	+	0.924594i	$0.375596\pi$
$164$	−6.44374e8	+	1.84152e9i	−0.890764	+	2.54566i
$165$	1.05409e9	+	1.32178e9i	1.42213	+	1.78330i
$166$	−1.42995e9	−	1.61116e8i	−1.88316	−	0.212181i
$167$	−1.40555e8	+	2.91865e8i	−0.180709	+	0.375246i	−0.971571	−	0.236748i	$-0.923918\pi$
$167$	−1.40555e8	+	2.91865e8i	−0.180709	+	0.375246i	0.790862	+	0.611995i	$0.209633\pi$
$168$	8.06192e8	−	3.53216e9i	1.01205	−	4.43408i
$169$	−5.47402e7	−	2.39832e8i	−0.0671057	−	0.294009i
$170$	−8.75232e8	+	4.21490e8i	−1.04792	+	0.504651i
$171$	−1.45963e8	−	4.17138e8i	−0.170710	−	0.487860i
$172$	7.62377e8	−	1.21332e9i	0.871076	−	1.38631i
$173$		−	8.52851e8i		−	0.952114i	−0.879414	−	0.476057i	$-0.842066\pi$
$173$		−	8.52851e8i		−	0.952114i	0.879414	−	0.476057i	$-0.157934\pi$
$174$	1.32899e9	+	1.69211e9i	1.44986	+	1.84599i
$175$	1.57948e8			0.168408
$176$	4.94760e9	+	3.10879e9i	5.15637	+	3.23996i
$177$	−9.91201e8	+	3.46836e8i	−1.00988	+	0.353372i
$178$	−1.59151e9	−	3.30481e9i	−1.58537	−	3.29206i
$179$	−1.86024e8	+	4.24588e7i	−0.181199	+	0.0413576i	−0.312158	−	0.950030i	$-0.601052\pi$
$179$	−1.86024e8	+	4.24588e7i	−0.181199	+	0.0413576i	0.130958	+	0.991388i	$0.458195\pi$
$180$	−1.46063e9	−	3.33378e8i	−1.39139	−	0.317576i
$181$	9.72994e8	+	4.68569e8i	0.906558	+	0.436575i	0.828253	−	0.560354i	$-0.189335\pi$
$181$	9.72994e8	+	4.68569e8i	0.906558	+	0.436575i	0.0783050	+	0.996929i	$0.475049\pi$
$182$	−2.27260e8	+	2.01698e9i	−0.207127	+	1.83830i
$183$	1.36817e9	−	1.09108e9i	1.21993	−	0.972862i
$184$	−2.05864e9	−	7.20349e8i	−1.79601	−	0.628451i
$185$	1.81970e8	+	1.61503e9i	0.155351	+	1.37878i
$186$	5.64947e8	+	5.64947e8i	0.472015	+	0.472015i
$187$	9.42943e8	+	7.51972e8i	0.771115	+	0.614944i
$188$	−1.00814e9	−	1.60445e9i	−0.807033	−	1.28439i
$189$	−7.66519e8	+	4.81636e8i	−0.600725	+	0.377461i
$190$	1.73268e9	−	2.17271e9i	1.32955	−	1.66720i
$191$	−4.36923e8	+	4.36923e8i	−0.328300	+	0.328300i	−0.851940	−	0.523640i	$-0.824574\pi$
$191$	−4.36923e8	+	4.36923e8i	−0.328300	+	0.328300i	0.523640	+	0.851940i	$0.324574\pi$
$192$	−5.27738e9	+	5.94617e8i	−3.88341	+	0.437555i
$193$	−1.37551e8	+	3.93098e8i	−0.0991367	+	0.283316i	−0.982761	−	0.184880i	$-0.940810\pi$
$193$	−1.37551e8	+	3.93098e8i	−0.0991367	+	0.283316i	0.883624	+	0.468196i	$0.155096\pi$
$194$	−1.86646e9	−	2.34047e9i	−1.31769	−	1.65233i
$195$	1.57306e9	+	1.77242e8i	1.08795	+	0.122582i
$196$	−5.69326e8	+	1.18222e9i	−0.385777	+	0.801075i
$197$	−4.78435e8	+	2.09616e9i	−0.317657	+	1.39175i	0.523993	+	0.851722i	$0.324442\pi$
$197$	−4.78435e8	+	2.09616e9i	−0.317657	+	1.39175i	−0.841650	+	0.540023i	$0.818415\pi$
$198$	5.68404e8	+	2.49034e9i	0.369825	+	1.62031i
$199$	2.22232e9	−	1.07021e9i	1.41708	−	0.682429i	0.440533	−	0.897737i	$-0.354790\pi$
$199$	2.22232e9	−	1.07021e9i	1.41708	−	0.682429i	0.976546	+	0.215307i	$0.0690753\pi$
$200$	−2.48322e8	−	7.09664e8i	−0.155201	−	0.443540i
$201$	−4.93475e8	+	7.85361e8i	−0.302330	+	0.481155i
$202$		−	1.63798e9i		−	0.983791i
$203$	−8.37219e8	−	1.77201e9i	−0.493009	−	1.04348i
$204$	−3.21638e9			−1.85715
$205$	−1.61161e9	−	1.01264e9i	−0.912522	−	0.573376i
$206$	3.87971e8	−	1.35757e8i	0.215442	−	0.0753864i
$207$	−2.34260e8	−	4.86446e8i	−0.127590	−	0.264943i
$208$	5.33413e9	−	1.21748e9i	2.84977	−	0.650442i
$209$	−3.36372e9	−	7.67747e8i	−1.76293	−	0.402377i
$210$	5.08122e9	+	2.44699e9i	2.61271	+	1.25821i
$211$	−4.29613e7	+	3.81292e8i	−0.0216744	+	0.192366i	−0.999884	−	0.0152559i	$-0.995144\pi$
$211$	−4.29613e7	+	3.81292e8i	−0.0216744	+	0.192366i	0.978209	+	0.207622i	$0.0665723\pi$
$212$	4.61781e9	−	3.68258e9i	2.28609	−	1.82309i
$213$	−2.31648e9	−	8.10572e8i	−1.12541	−	0.393798i
$214$	−3.97740e8	−	3.53004e9i	−0.189646	−	1.68316i
$215$	9.88500e8	+	9.88500e8i	0.462618	+	0.462618i
$216$	3.36910e9	+	2.68677e9i	1.54774	+	1.23428i
$217$	−3.87182e8	−	6.16197e8i	−0.174613	−	0.277895i
$218$	−4.39316e9	+	2.76041e9i	−1.94514	+	1.22221i
$219$	−9.76595e8	+	1.22461e9i	−0.424559	+	0.532380i
$220$	−8.27061e9	+	8.27061e9i	−3.53059	+	3.53059i
$221$	1.12220e9	−	1.26442e8i	0.470438	−	0.0530056i
$222$	−2.44071e9	+	6.97515e9i	−1.00486	+	2.87172i
$223$	1.88761e9	+	2.36699e9i	0.763296	+	0.957143i	0.999895	−	0.0144641i	$-0.00460422\pi$
$223$	1.88761e9	+	2.36699e9i	0.763296	+	0.957143i	−0.236599	+	0.971607i	$0.576033\pi$
$224$	1.00721e10	+	1.13485e9i	4.00062	+	0.450761i
$225$	8.07552e7	−	1.67690e8i	0.0315094	−	0.0654300i
$226$	−3.38085e8	+	1.48125e9i	−0.129596	+	0.567799i
$227$	−7.70844e8	−	3.37729e9i	−0.290311	−	1.27193i	−0.884094	−	0.467309i	$-0.845224\pi$
$227$	−7.70844e8	−	3.37729e9i	−0.290311	−	1.27193i	0.593784	−	0.804625i	$-0.297634\pi$
$228$	8.28995e9	−	3.99223e9i	3.06770	−	1.47733i
$229$	−8.47424e8	−	2.42180e9i	−0.308148	−	0.880635i	−0.988961	−	0.148178i	$-0.952659\pi$
$229$	−8.47424e8	−	2.42180e9i	−0.308148	−	0.880635i	0.680813	−	0.732457i	$-0.261627\pi$
$230$	1.80630e9	−	2.87471e9i	0.645474	−	1.02727i
$231$		−	7.00192e9i		−	2.45906i
$232$	−6.64542e9	+	6.54754e9i	−2.29388	+	2.26009i
$233$	1.05383e9			0.357559			0.178780	−	0.983889i	$-0.442785\pi$
$233$	1.05383e9			0.357559			0.178780	+	0.983889i	$0.442785\pi$
$234$	2.02519e9	+	1.27251e9i	0.675465	+	0.424423i
$235$	1.74487e9	−	6.10556e8i	0.572126	−	0.200195i
$236$	−3.15226e9	−	6.54574e9i	−1.01619	−	2.11014i
$237$	−1.76732e9	+	4.03379e8i	−0.560172	+	0.127856i
$238$	3.92244e9	+	8.95270e8i	1.22250	+	0.279027i
$239$	−5.47404e9	−	2.63616e9i	−1.67771	−	0.807941i	−0.997166	−	0.0752301i	$-0.976031\pi$
$239$	−5.47404e9	−	2.63616e9i	−1.67771	−	0.807941i	−0.680540	−	0.732711i	$-0.738255\pi$
$240$	1.70211e9	−	1.51066e10i	0.513030	−	4.55327i
$241$	−1.16279e9	+	9.27296e8i	−0.344694	+	0.274885i	−0.780499	−	0.625157i	$-0.785035\pi$
$241$	−1.16279e9	+	9.27296e8i	−0.344694	+	0.274885i	0.435805	+	0.900041i	$0.356464\pi$
$242$	1.26138e10	+	4.41377e9i	3.67778	+	1.28691i
$243$	3.57206e8	+	3.17029e9i	0.102446	+	0.909231i
$244$	8.56085e9	+	8.56085e9i	2.41522	+	2.41522i
$245$	−1.00083e9	−	7.98135e8i	−0.277777	−	0.221520i
$246$	−4.60436e9	−	7.32780e9i	−1.25727	−	2.00093i
$247$	−2.73544e9	+	1.71879e9i	−0.734920	+	0.461781i
$248$	−2.15986e9	+	2.70838e9i	−0.570979	+	0.715984i
$249$	3.28668e9	−	3.28668e9i	0.854988	−	0.854988i
$250$	−6.80698e9	+	7.66963e8i	−1.74259	+	0.196342i
$251$	7.08377e8	−	2.02442e9i	0.178472	−	0.510043i	−0.819543	−	0.573017i	$-0.805773\pi$
$251$	7.08377e8	−	2.02442e9i	0.178472	−	0.510043i	0.998015	+	0.0629742i	$0.0200586\pi$
$252$	3.86870e9	+	4.85120e9i	0.959319	+	1.20295i
$253$	−4.18863e9	−	4.71945e8i	−1.02233	−	0.115188i
$254$	−1.34860e9	+	2.80039e9i	−0.324002	+	0.672797i
$255$	6.98229e8	−	3.05914e9i	0.165134	−	0.723500i
$256$	−1.78115e9	−	7.80373e9i	−0.414706	−	1.81695i
$257$	1.12922e9	−	5.43806e8i	0.258850	−	0.124655i	−0.299959	−	0.953952i	$-0.596973\pi$
$257$	1.12922e9	−	5.43806e8i	0.258850	−	0.124655i	0.558809	+	0.829297i	$0.311259\pi$
$258$	2.09936e9	+	5.99963e9i	0.473815	+	1.35408i
$259$	3.58120e9	−	5.69944e9i	0.795846	−	1.26658i
$260$			1.09519e10i			2.39661i
$261$	−2.30935e9	−	1.71319e7i	−0.497655	−	0.00369184i
$262$	−2.56543e9			−0.544446
$263$	−7.83440e9	−	4.92268e9i	−1.63750	−	1.02891i	−0.954373	−	0.298617i	$-0.903475\pi$
$263$	−7.83440e9	−	4.92268e9i	−1.63750	−	1.02891i	−0.683132	−	0.730295i	$-0.739382\pi$
$264$	−3.14597e10	+	1.10082e10i	−6.47648	+	2.26622i
$265$	2.50009e9	+	5.19149e9i	0.506958	+	1.05271i
$266$	−1.12210e10	+	2.56112e9i	−2.24132	+	0.511567i
$267$	1.15511e10	+	2.63646e9i	2.27289	+	0.518772i
$268$	−5.78153e9	−	2.78424e9i	−1.12074	−	0.539718i
$269$	−7.89968e7	+	7.01116e8i	−0.0150869	+	0.133900i	−0.998998	−	0.0447601i	$-0.985748\pi$
$269$	−7.89968e7	+	7.01116e8i	−0.0150869	+	0.133900i	0.983911	+	0.178660i	$0.0571762\pi$
$270$	−5.24450e9	+	4.18235e9i	−0.986845	+	0.786983i
$271$	4.00371e9	+	1.40096e9i	0.742311	+	0.259746i	0.674828	−	0.737975i	$-0.264218\pi$
$271$	4.00371e9	+	1.40096e9i	0.742311	+	0.259746i	0.0674824	+	0.997720i	$0.478503\pi$
$272$	−1.21426e9	−	1.07769e10i	−0.221839	−	1.96887i
$273$	−4.63597e9	−	4.63597e9i	−0.834622	−	0.834622i
$274$	4.49684e9	+	3.58611e9i	0.797820	+	0.636240i
$275$	−7.73075e8	−	1.23034e9i	−0.135173	−	0.215127i
$276$	9.51804e9	−	5.98058e9i	1.64025	−	1.03064i
$277$	−3.19110e9	+	4.00151e9i	−0.542027	+	0.679681i	−0.975122	−	0.221668i	$-0.928850\pi$
$277$	−3.19110e9	+	4.00151e9i	−0.542027	+	0.679681i	0.433095	+	0.901348i	$0.357421\pi$
$278$	8.81749e9	−	8.81749e9i	1.47627	−	1.47627i
$279$	−8.52159e8	+	9.60153e7i	−0.140638	+	0.0158461i
$280$	−8.07633e9	+	2.30808e10i	−1.31396	+	3.75508i
$281$	7.72546e9	+	9.68742e9i	1.23908	+	1.55376i	0.707407	+	0.706807i	$0.249865\pi$
$281$	7.72546e9	+	9.68742e9i	1.23908	+	1.55376i	0.531673	+	0.846950i	$0.321564\pi$
$282$	8.35256e9	+	9.41108e8i	1.32076	+	0.148814i
$283$	3.77058e8	−	7.82969e8i	0.0587845	−	0.122067i	−0.869507	−	0.493921i	$-0.835563\pi$
$283$	3.77058e8	−	7.82969e8i	0.0587845	−	0.122067i	0.928291	+	0.371853i	$0.121278\pi$
$284$	3.77822e9	−	1.65534e10i	0.580782	−	2.54457i
$285$	1.99744e9	+	8.75134e9i	0.302756	+	1.32646i
$286$	1.68237e10	−	8.10185e9i	2.51453	−	1.21093i
$287$	2.60356e9	+	7.44055e9i	0.383743	+	1.09667i
$288$	6.35446e9	−	1.01131e10i	0.923652	−	1.46998i
$289$			4.73728e9i			0.679107i
$290$	−7.63480e9	−	1.23532e10i	−1.07946	−	1.74658i
$291$	9.66947e9			1.34844
$292$	−9.17556e9	−	5.76539e9i	−1.26212	−	0.793043i
$293$	−9.42350e9	+	3.29743e9i	−1.27862	+	0.447409i	−0.882293	−	0.470700i	$-0.844001\pi$
$293$	−9.42350e9	+	3.29743e9i	−1.27862	+	0.447409i	−0.396328	+	0.918109i	$0.629716\pi$
$294$	−2.52543e9	−	5.24411e9i	−0.338023	−	0.701911i
$295$	6.91005e9	−	1.57717e9i	0.912417	−	0.208253i
$296$	−3.12379e10	−	7.12986e9i	−4.06926	−	0.928782i
$297$	7.50342e9	+	3.61346e9i	0.964348	+	0.464405i
$298$	2.93203e9	−	2.60225e10i	0.371795	−	3.29977i
$299$	−3.08576e9	+	2.46081e9i	−0.386080	+	0.307889i
$300$	3.65760e9	+	1.27985e9i	0.451556	+	0.158006i
$301$	−6.48249e8	−	5.75337e9i	−0.0789725	−	0.700900i
$302$	−4.25301e9	−	4.25301e9i	−0.511291	−	0.511291i
$303$	4.13652e9	+	3.29876e9i	0.490754	+	0.391364i
$304$	1.65061e10	+	2.62694e10i	1.93264	+	3.07578i
$305$	−1.00008e10	+	6.28390e9i	−1.15567	+	0.726156i
$306$	2.95594e9	−	3.70663e9i	0.337139	−	0.422759i
$307$	4.75823e9	−	4.75823e9i	0.535664	−	0.535664i	−0.386589	−	0.922252i	$-0.626347\pi$
$307$	4.75823e9	−	4.75823e9i	0.535664	−	0.535664i	0.922252	+	0.386589i	$0.126347\pi$
$308$	4.81374e10	−	5.42379e9i	5.34909	−	0.602698i
$309$	−4.38506e8	+	1.25318e9i	−0.0480996	+	0.137461i
$310$	−3.36215e9	−	4.21600e9i	−0.364058	−	0.456514i
$311$	−8.66961e9	−	9.76831e8i	−0.926740	−	0.104419i	−0.364324	−	0.931272i	$-0.618700\pi$
$311$	−8.66961e9	−	9.76831e8i	−0.926740	−	0.104419i	−0.562417	+	0.826854i	$0.690128\pi$
$312$	−1.35409e10	+	2.81180e10i	−1.42899	+	2.96733i
$313$	1.22095e9	−	5.34935e9i	0.127210	−	0.557344i	−0.870647	−	0.491909i	$-0.836299\pi$
$313$	1.22095e9	−	5.34935e9i	0.127210	−	0.557344i	0.997857	−	0.0654352i	$-0.0208436\pi$
$314$	3.32489e9	+	1.45673e10i	0.342026	+	1.49851i
$315$	−5.45388e9	+	2.62645e9i	−0.553941	+	0.266764i
$316$	−4.14218e9	−	1.18377e10i	−0.415413	−	1.18718i
$317$	8.00459e9	−	1.27392e10i	0.792688	−	1.26156i	−0.168511	−	0.985700i	$-0.553896\pi$
$317$	8.00459e9	−	1.27392e10i	0.792688	−	1.26156i	0.961199	−	0.275856i	$-0.0889613\pi$
$318$			2.61997e10i			2.56206i
$319$	−9.70536e9	+	1.51946e10i	−0.937236	+	1.46733i
$320$	3.58445e10			3.41840
$321$	9.71571e9	+	6.10478e9i	0.915070	+	0.574977i
$322$	−1.32721e10	+	4.64411e9i	−1.23457	+	0.431996i
$323$	2.77844e9	+	5.76948e9i	0.255264	+	0.530062i
$324$	−3.59765e10	+	8.21140e9i	−3.26467	+	0.745139i
$325$	−1.32646e9	−	3.02756e8i	−0.118894	−	0.0271368i
$326$	−1.07365e10	−	5.17041e9i	−0.950584	−	0.457777i
$327$	1.87642e9	−	1.66536e10i	0.164111	−	1.45653i
$328$	2.93372e10	−	2.33957e10i	2.53468	−	2.02134i
$329$	−7.22658e9	−	2.52869e9i	−0.616807	−	0.215830i
$330$	−5.80908e9	−	5.15570e10i	−0.489837	−	4.34742i
$331$	−1.81170e9	−	1.81170e9i	−0.150929	−	0.150929i	0.627604	−	0.778533i	$-0.284036\pi$
$331$	−1.81170e9	−	1.81170e9i	−0.150929	−	0.150929i	−0.778533	+	0.627604i	$0.784036\pi$
$332$	2.51415e10	+	2.00497e10i	2.06937	+	1.65027i
$333$	−4.21998e9	−	6.71606e9i	−0.343189	−	0.546183i
$334$	8.41772e9	−	5.28920e9i	0.676408	−	0.425015i
$335$	3.90321e9	−	4.89447e9i	0.309915	−	0.388621i
$336$	−4.45207e10	+	4.45207e10i	−3.49305	+	3.49305i
$337$	9.75625e9	−	1.09927e9i	0.756421	−	0.0852282i	0.274673	−	0.961538i	$-0.411431\pi$
$337$	9.75625e9	−	1.09927e9i	0.756421	−	0.0852282i	0.481748	+	0.876310i	$0.340002\pi$
$338$	−2.49342e9	+	7.12580e9i	−0.191042	+	0.545967i
$339$	−3.05984e9	−	3.83691e9i	−0.231686	−	0.290525i
$340$	2.15721e10	+	2.43059e9i	1.61427	+	0.181885i
$341$	−2.90482e9	+	6.03193e9i	−0.214834	+	0.446107i
$342$	−3.01795e9	+	1.32225e10i	−0.220601	+	0.966516i
$343$	−2.37479e9	−	1.04046e10i	−0.171573	−	0.751711i
$344$	−2.48308e10	+	1.19579e10i	−1.77320	+	0.853927i
$345$	3.62198e9	+	1.03510e10i	0.255664	+	0.730646i
$346$	−1.39249e10	+	2.21613e10i	−0.971597	+	1.54629i
$347$		−	2.78724e9i		−	0.192246i	−0.995369	−	0.0961228i	$-0.969356\pi$
$347$		−	2.78724e9i		−	0.192246i	0.995369	−	0.0961228i	$-0.0306442\pi$
$348$	−5.02889e9	−	4.78184e10i	−0.342890	−	3.26045i
$349$	−1.67223e10			−1.12718			−0.563591	−	0.826054i	$-0.690580\pi$
$349$	−1.67223e10			−1.12718			−0.563591	+	0.826054i	$0.690580\pi$
$350$	−4.10428e9	−	2.57889e9i	−0.273504	−	0.171854i
$351$	7.36048e9	−	2.57555e9i	0.484929	−	0.169684i
$352$	−4.04576e10	−	8.40111e10i	−2.63530	−	5.47225i
$353$	2.10075e9	−	4.79483e8i	0.135293	−	0.0308798i	−0.154338	−	0.988018i	$-0.549324\pi$
$353$	2.10075e9	−	4.79483e8i	0.135293	−	0.0308798i	0.289631	+	0.957138i	$0.406467\pi$
$354$	3.14192e10	+	7.17124e9i	2.00070	+	0.456647i
$355$	1.49240e10	+	7.18702e9i	0.939663	+	0.452518i
$356$	−9.17775e9	+	8.14548e10i	−0.571395	+	5.07127i
$357$	−1.01604e10	+	8.10263e9i	−0.625514	+	0.498831i
$358$	5.52706e9	+	1.93400e9i	0.336482	+	0.117740i
$359$	2.03393e9	+	1.80517e10i	0.122450	+	1.08677i	0.893207	+	0.449645i	$0.148450\pi$
$359$	2.03393e9	+	1.80517e10i	0.122450	+	1.08677i	−0.770757	+	0.637129i	$0.780122\pi$
$360$	2.03751e10	+	2.03751e10i	1.21308	+	1.21308i
$361$	−1.04410e9	−	8.32639e8i	−0.0614769	−	0.0490262i
$362$	−1.76327e10	−	2.80622e10i	−1.02679	−	1.63413i
$363$	−3.65497e10	+	2.29657e10i	−2.10502	+	1.32267i
$364$	2.82807e10	−	3.54629e10i	1.61096	−	2.02008i
$365$	7.47541e9	−	7.47541e9i	0.421176	−	0.421176i
$366$	−5.33663e10	+	6.01293e9i	−2.97401	+	0.335090i
$367$	3.64656e9	−	1.04213e10i	0.201011	−	0.574456i	−0.798614	−	0.601844i	$-0.794433\pi$
$367$	3.64656e9	−	1.04213e10i	0.201011	−	0.574456i	0.999625	+	0.0273875i	$0.00871880\pi$
$368$	2.36320e10	+	2.96336e10i	1.28857	+	1.61582i
$369$	9.23059e9	+	1.04004e9i	0.497879	+	0.0560975i
$370$	2.16408e10	−	4.49376e10i	1.15469	−	2.39775i
$371$	5.31035e9	−	2.32662e10i	0.280303	−	1.22809i
$372$	−3.97294e9	−	1.74066e10i	−0.207463	−	0.908954i
$373$	2.83402e9	−	1.36479e9i	0.146409	−	0.0705069i	−0.359245	−	0.933243i	$-0.616966\pi$
$373$	2.83402e9	−	1.36479e9i	0.146409	−	0.0705069i	0.505654	+	0.862737i	$0.331251\pi$
$374$	−1.22246e10	−	3.49358e10i	−0.624808	−	1.78560i
$375$	1.17719e10	−	1.87348e10i	0.595278	−	0.947380i
$376$			3.64446e10i			1.82340i
$377$	3.63442e9	+	1.64863e10i	0.179916	+	0.816125i
$378$	2.77818e10			1.36080
$379$	−1.28303e10	−	8.06182e9i	−0.621842	−	0.390729i	0.183943	−	0.982937i	$-0.441114\pi$
$379$	−1.28303e10	−	8.06182e9i	−0.621842	−	0.390729i	−0.805786	+	0.592207i	$0.798257\pi$
$380$	−5.86173e10	+	2.05111e10i	−2.81120	+	0.983680i
$381$	−4.35608e9	−	9.04549e9i	−0.206726	−	0.429272i
$382$	1.84872e10	−	4.21959e9i	0.868197	−	0.198160i
$383$	1.22761e10	+	2.80193e9i	0.570512	+	0.130216i	0.498039	−	0.867155i	$-0.334054\pi$
$383$	1.22761e10	+	2.80193e9i	0.570512	+	0.130216i	0.0724730	+	0.997370i	$0.476911\pi$
$384$	6.32087e10	+	3.04397e10i	2.90705	+	1.39996i
$385$	−5.29130e9	+	4.69616e10i	−0.240835	+	2.13747i
$386$	9.99253e9	−	7.96878e9i	0.450118	−	0.358957i
$387$	−6.43965e9	−	2.25333e9i	−0.287090	−	0.100457i
$388$	7.49011e9	+	6.64766e10i	0.330492	+	2.93320i
$389$	−5.35554e9	−	5.35554e9i	−0.233886	−	0.233886i	0.580426	−	0.814313i	$-0.302886\pi$
$389$	−5.35554e9	−	5.35554e9i	−0.233886	−	0.233886i	−0.814313	+	0.580426i	$0.802886\pi$
$390$	−3.79820e10	−	3.02897e10i	−1.64180	−	1.30929i
$391$	4.16225e9	+	6.62419e9i	0.178083	+	0.283417i
$392$	2.13687e10	−	1.34269e10i	0.904970	−	0.568630i
$393$	5.16658e9	−	6.47868e9i	0.216587	−	0.271592i
$394$	4.66570e10	−	4.66570e10i	1.93612	−	1.93612i
$395$	1.21582e10	−	1.36990e9i	0.499436	−	0.0562729i
$396$	1.88532e10	−	5.38794e10i	0.766664	−	2.19100i
$397$	−3.57667e9	−	4.48500e9i	−0.143985	−	0.180551i	0.704610	−	0.709595i	$-0.251122\pi$
$397$	−3.57667e9	−	4.48500e9i	−0.143985	−	0.180551i	−0.848594	+	0.529044i	$0.822551\pi$
$398$	−7.52206e10	−	8.47533e9i	−2.99781	−	0.337772i
$399$	1.61304e10	−	3.34951e10i	0.636434	−	1.32157i
$400$	−2.90747e9	+	1.27384e10i	−0.113573	+	0.497595i
$401$	−6.18390e7	−	2.70934e8i	−0.00239158	−	0.0104782i	0.973718	−	0.227757i	$-0.0731391\pi$
$401$	−6.18390e7	−	2.70934e8i	−0.00239158	−	0.0104782i	−0.976110	+	0.217279i	$0.930282\pi$
$402$	2.56458e10	−	1.23504e10i	0.982003	−	0.472908i
$403$	2.07045e9	+	5.91702e9i	0.0784956	+	0.224328i
$404$	−1.94744e10	+	3.09934e10i	−0.731037	+	1.16344i
$405$		−	3.60003e10i		−	1.33809i
$406$	−7.17728e9	+	5.97152e10i	−0.264153	+	2.19776i
$407$	−6.19240e10			−2.25674
$408$	5.23791e10	+	3.29120e10i	1.89024	+	1.18772i
$409$	6.02136e9	−	2.10697e9i	0.215180	−	0.0752947i	−0.220536	−	0.975379i	$-0.570781\pi$
$409$	6.02136e9	−	2.10697e9i	0.215180	−	0.0752947i	0.435716	+	0.900084i	$0.356495\pi$
$410$	2.53437e10	+	5.26267e10i	0.896880	+	1.86239i
$411$	−1.81126e10	+	4.13407e9i	−0.634764	+	0.144881i
$412$	−8.95513e9	−	2.04395e9i	−0.310801	−	0.0709384i
$413$	−2.64477e10	−	1.27365e10i	−0.909050	−	0.437776i
$414$	−1.85517e9	+	1.64651e10i	−0.0631514	+	0.560484i
$415$	−2.45274e10	+	1.95599e10i	−0.826910	+	0.659439i
$416$	−8.24107e10	−	2.88368e10i	−2.75176	−	0.962882i
$417$	4.50976e9	+	4.00252e10i	0.149145	+	1.32370i
$418$	7.48707e10	+	7.48707e10i	2.45249	+	2.45249i
$419$	−8.79944e9	−	7.01732e9i	−0.285495	−	0.227675i	0.470262	−	0.882527i	$-0.344160\pi$
$419$	−8.79944e9	−	7.01732e9i	−0.285495	−	0.227675i	−0.755757	+	0.654852i	$0.772731\pi$
$420$	−6.70524e10	−	1.06713e11i	−2.15485	−	3.42943i
$421$	9.89266e9	−	6.21597e9i	0.314909	−	0.197870i	−0.365298	−	0.930891i	$-0.619033\pi$
$421$	9.89266e9	−	6.21597e9i	0.314909	−	0.197870i	0.680207	+	0.733020i	$0.261890\pi$
$422$	7.34186e9	−	9.20640e9i	0.231503	−	0.290295i
$423$	−6.37943e9	+	6.37943e9i	−0.199260	+	0.199260i
$424$	−1.12884e11	+	1.27190e10i	−3.49276	+	0.393540i
$425$	−8.90726e8	+	2.54555e9i	−0.0273016	+	0.0780236i
$426$	4.69591e10	+	5.88848e10i	1.42587	+	1.78799i
$427$	4.86096e10	+	5.47698e9i	1.46221	+	0.164752i
$428$	−3.44438e10	+	7.15233e10i	−1.02645	+	2.13144i
$429$	−1.34213e10	+	5.88026e10i	−0.396247	+	1.73607i
$430$	−9.54646e9	−	4.18258e10i	−0.279234	−	1.22340i
$431$	1.74026e10	−	8.38066e9i	0.504320	−	0.242867i	−0.164384	−	0.986396i	$-0.552564\pi$
$431$	1.74026e10	−	8.38066e9i	0.504320	−	0.242867i	0.668704	+	0.743529i	$0.266849\pi$
$432$	−2.47338e10	−	7.06852e10i	−0.710160	−	2.02952i
$433$	3.36180e10	−	5.35028e10i	0.956359	−	1.52204i	0.106974	−	0.994262i	$-0.465884\pi$
$433$	3.36180e10	−	5.35028e10i	0.956359	−	1.52204i	0.849385	−	0.527774i	$-0.176973\pi$
$434$			2.23335e10i			0.629504i
$435$	4.65724e10	+	5.59762e9i	1.30068	+	0.156331i
$436$	1.15946e11			3.20854
$437$	−1.89499e10	−	1.19070e10i	−0.519615	−	0.326496i
$438$	4.53715e10	−	1.58762e10i	1.23278	−	0.431369i
$439$	1.67800e10	+	3.48440e10i	0.451787	+	0.938146i	0.995124	+	0.0986312i	$0.0314464\pi$
$439$	1.67800e10	+	3.48440e10i	0.451787	+	0.938146i	−0.543337	+	0.839515i	$0.682839\pi$
$440$	2.19318e11	−	5.00579e10i	5.85145	−	1.33555i
$441$	6.09077e9	+	1.39018e9i	0.161034	+	0.0367550i
$442$	−3.12248e10	−	1.50371e10i	−0.818109	−	0.393980i
$443$	−1.01664e9	+	9.02297e9i	−0.0263970	+	0.234280i	0.973585	+	0.228324i	$0.0733244\pi$
$443$	−1.01664e9	+	9.02297e9i	−0.0263970	+	0.234280i	−0.999982	+	0.00595602i	$0.998104\pi$
$444$	1.29112e11	−	1.02963e11i	3.32227	−	2.64942i
$445$	−7.54804e10	−	2.64117e10i	−1.92484	−	0.673530i
$446$	−1.04026e10	−	9.23259e10i	−0.262908	−	2.33337i
$447$	5.98118e10	+	5.98118e10i	1.49815	+	1.49815i
$448$	−1.16066e11	−	9.25596e10i	−2.88133	−	2.29779i
$449$	4.18120e9	+	6.65435e9i	0.102876	+	0.163727i	0.894196	−	0.447676i	$-0.147748\pi$
$449$	4.18120e9	+	6.65435e9i	0.102876	+	0.163727i	−0.791319	+	0.611403i	$0.790605\pi$
$450$	−4.83636e9	+	3.03889e9i	−0.117942	+	0.0741079i
$451$	4.52152e10	−	5.66981e10i	1.09290	−	1.37045i
$452$	2.40082e10	−	2.40082e10i	0.575182	−	0.575182i
$453$	1.93057e10	−	2.17523e9i	0.458450	−	0.0516549i
$454$	−3.51120e10	+	1.00344e11i	−0.826481	+	2.36195i
$455$	2.75899e10	+	3.45966e10i	0.643731	+	0.807213i
$456$	−1.75854e11	−	1.98140e10i	−4.06717	−	0.458260i
$457$	1.45440e10	−	3.02010e10i	0.333441	−	0.692398i	−0.665079	−	0.746773i	$-0.731602\pi$
$457$	1.45440e10	−	3.02010e10i	0.333441	−	0.692398i	0.998521	+	0.0543745i	$0.0173165\pi$
$458$	−1.75215e10	+	7.67665e10i	−0.398206	+	1.74466i
$459$	−3.43954e9	−	1.50696e10i	−0.0774907	−	0.339509i
$460$	−6.83566e10	+	3.29188e10i	−1.52668	+	0.735212i
$461$	1.22166e10	+	3.49131e10i	0.270487	+	0.773008i	0.996365	+	0.0851846i	$0.0271480\pi$
$461$	1.22166e10	+	3.49131e10i	0.270487	+	0.773008i	−0.725878	+	0.687824i	$0.758566\pi$
$462$	−1.14323e11	+	1.81944e11i	−2.50938	+	3.99366i
$463$		−	5.00789e10i		−	1.08976i	−0.838514	−	0.544880i	$-0.816575\pi$
$463$		−	5.00789e10i		−	1.08976i	0.838514	−	0.544880i	$-0.183425\pi$
$464$	1.58323e11	−	3.49026e10i	3.41564	−	0.752983i
$465$	1.74181e10			0.372554
$466$	−2.73838e10	−	1.72064e10i	−0.580697	−	0.364876i
$467$	−1.83459e10	+	6.41952e9i	−0.385720	+	0.134969i	−0.516171	−	0.856485i	$-0.672643\pi$
$467$	−1.83459e10	+	6.41952e9i	−0.385720	+	0.134969i	0.130451	+	0.991455i	$0.458358\pi$
$468$	−2.31908e10	−	4.81563e10i	−0.483429	−	1.00385i
$469$	−2.52775e10	+	5.76944e9i	−0.522449	+	0.119245i
$470$	−5.53091e10	−	1.26239e10i	−1.13346	−	0.258704i
$471$	−4.34840e10	−	2.09408e10i	−0.883581	−	0.425510i
$472$	−1.56451e10	+	1.38854e11i	−0.315217	+	2.79763i
$473$	−4.16431e10	+	3.32093e10i	−0.831953	+	0.663460i
$474$	5.25098e10	+	1.83740e10i	1.04022	+	0.363990i
$475$	−8.63811e8	−	7.66653e9i	−0.0169685	−	0.150600i
$476$	−6.35751e10	−	6.35751e10i	−1.23839	−	1.23839i
$477$	−2.19861e10	−	1.75333e10i	−0.424692	−	0.338681i
$478$	9.92008e10	+	1.57877e11i	1.90022	+	3.02418i
$479$	4.70300e10	−	2.95509e10i	0.893373	−	0.561344i	−0.00528853	−	0.999986i	$-0.501683\pi$
$479$	4.70300e10	−	2.95509e10i	0.893373	−	0.561344i	0.898662	+	0.438642i	$0.144541\pi$
$480$	−1.51255e11	+	1.89668e11i	−2.84935	+	3.57297i
$481$	−4.09999e10	+	4.09999e10i	−0.765953	+	0.765953i
$482$	4.53554e10	−	5.11033e9i	0.840313	−	0.0946806i
$483$	1.50009e10	−	4.28700e10i	0.275631	−	0.787707i
$484$	−1.86199e11	−	2.33486e11i	−3.39309	−	4.25480i
$485$	−6.48527e10	−	7.30715e9i	−1.17209	−	0.132063i
$486$	4.24807e10	−	8.82121e10i	0.761459	−	1.58119i
$487$	2.09707e10	−	9.18788e10i	0.372819	−	1.63343i	−0.346005	−	0.938233i	$-0.612462\pi$
$487$	2.09707e10	−	9.18788e10i	0.372819	−	1.63343i	0.718824	−	0.695193i	$-0.244681\pi$
$488$	−5.18145e10	−	2.27014e11i	−0.913634	−	4.00289i
$489$	3.46796e10	−	1.67008e10i	0.606511	−	0.292080i
$490$	1.29750e10	+	3.70805e10i	0.225073	+	0.643222i
$491$	−2.52384e10	+	4.01666e10i	−0.434245	+	0.691097i	−0.990128	−	0.140163i	$-0.955237\pi$
$491$	−2.52384e10	+	4.01666e10i	−0.434245	+	0.691097i	0.555883	+	0.831260i	$0.312380\pi$
$492$			1.93397e11i			3.30057i
$493$	3.32797e10	−	3.49991e9i	0.563368	−	0.0592474i
$494$	9.91438e10			1.66478
$495$	4.71527e10	+	2.96280e10i	0.785390	+	0.493494i
$496$	5.68231e10	−	1.98833e10i	0.938854	−	0.328519i
$497$	−2.97659e10	−	6.18095e10i	−0.487858	−	1.01305i
$498$	−1.39067e11	+	3.17412e10i	−2.26103	+	0.516066i
$499$	−3.16402e10	−	7.22167e9i	−0.510314	−	0.116476i	−0.0403922	−	0.999184i	$-0.512861\pi$
$499$	−3.16402e10	−	7.22167e9i	−0.510314	−	0.116476i	−0.469922	+	0.882708i	$0.655718\pi$
$500$	1.37918e11	+	6.64180e10i	2.20670	+	1.06269i
$501$	−3.59539e9	+	3.19100e10i	−0.0570683	+	0.506495i
$502$	−5.14607e10	+	4.10386e10i	−0.810329	+	0.646216i
$503$	1.96783e10	+	6.88572e9i	0.307408	+	0.107567i	0.479574	−	0.877501i	$-0.340791\pi$
$503$	1.96783e10	+	6.88572e9i	0.307408	+	0.107567i	−0.172167	+	0.985068i	$0.555077\pi$
$504$	−1.33618e10	−	1.18589e11i	−0.207082	−	1.83791i
$505$	−2.52506e10	−	2.52506e10i	−0.388245	−	0.388245i
$506$	1.01136e11	+	8.06529e10i	1.54277	+	1.23032i
$507$	−1.29738e10	−	2.06476e10i	−0.196352	−	0.312492i
$508$	5.88125e10	−	3.69543e10i	0.883110	−	0.554895i
$509$	−6.38058e9	+	8.00100e9i	−0.0950581	+	0.119199i	−0.827086	−	0.562076i	$-0.810003\pi$
$509$	−6.38058e9	+	8.00100e9i	−0.0950581	+	0.119199i	0.732027	+	0.681275i	$0.238574\pi$
$510$	−6.80913e10	+	6.80913e10i	−1.00649	+	1.00649i
$511$	−4.35091e10	+	4.90230e9i	−0.638112	+	0.0718980i
$512$	−2.12912e10	+	6.08468e10i	−0.309828	+	0.885437i
$513$	2.75698e10	+	3.45714e10i	0.398074	+	0.499170i
$514$	−3.82218e10	−	4.30656e9i	−0.547593	−	0.0616989i
$515$	3.88806e9	−	8.07363e9i	0.0552718	−	0.114773i
$516$	3.16079e10	−	1.38483e11i	0.445858	−	1.95343i
$517$	1.56731e10	+	6.86682e10i	0.219377	+	0.961155i
$518$	−1.86114e11	+	8.96279e10i	−2.58500	+	1.24487i
$519$	−2.79220e10	−	7.97966e10i	−0.384838	−	1.09980i
$520$	1.12067e11	−	1.78354e11i	1.53273	−	2.43932i
$521$		−	6.84661e10i		−	0.929234i	−0.885512	−	0.464617i	$-0.846192\pi$
$521$		−	6.84661e10i		−	0.929234i	0.885512	−	0.464617i	$-0.153808\pi$
$522$	5.97286e10	+	3.81509e10i	0.804453	+	0.513834i
$523$	−1.43102e11			−1.91266			−0.956329	−	0.292291i	$-0.905582\pi$
$523$	−1.43102e11			−1.91266			−0.956329	+	0.292291i	$0.905582\pi$
$524$	4.85423e10	+	3.05012e10i	0.643866	+	0.404568i
$525$	1.47784e10	−	5.17117e9i	0.194531	−	0.0680694i
$526$	1.23202e11	+	2.55831e11i	1.60944	+	3.34203i
$527$	1.21143e10	−	2.76501e9i	0.157057	−	0.0358471i
$528$	5.64701e11	+	1.28889e11i	7.26579	+	1.65837i
$529$	4.59215e10	+	2.21146e10i	0.586400	+	0.282395i
$530$	1.97990e10	−	1.75721e11i	0.250922	−	2.22699i
$531$	−2.70442e10	+	2.15670e10i	−0.340170	+	0.271276i
$532$	2.42770e11	+	8.49489e10i	3.03074	+	1.06050i
$533$	−7.60281e9	−	6.74768e10i	−0.0942031	−	0.836075i
$534$	−2.57108e11	−	2.57108e11i	−3.16191	−	3.16191i
$535$	−6.05495e10	−	4.82866e10i	−0.739087	−	0.589402i
$536$	6.56629e10	+	1.04502e11i	0.795537	+	1.26609i
$537$	−1.60152e10	+	1.00630e10i	−0.192590	+	0.121012i
$538$	1.35001e10	−	1.69286e10i	0.161142	−	0.202066i
$539$	3.44882e10	−	3.44882e10i	0.408616	−	0.408616i
$540$	1.48960e11	−	1.67838e10i	1.75184	−	0.197385i
$541$	2.39054e10	−	6.83177e10i	0.279066	−	0.797524i	−0.715981	−	0.698119i	$-0.754020\pi$
$541$	2.39054e10	−	6.83177e10i	0.279066	−	0.797524i	0.995047	−	0.0994048i	$-0.0316939\pi$
$542$	−8.11622e10	−	1.01774e11i	−0.940495	−	1.17934i
$543$	1.06378e11	+	1.19860e10i	1.22364	+	0.137871i
$544$	−7.50896e10	+	1.55925e11i	−0.857402	+	1.78041i
$545$	−2.51701e10	+	1.10277e11i	−0.285298	+	1.24997i
$546$	4.47719e10	+	1.96159e11i	0.503773	+	2.20718i
$547$	−1.25797e11	+	6.05807e10i	−1.40515	+	0.676682i	−0.974198	−	0.225695i	$-0.927535\pi$
$547$	−1.25797e11	+	6.05807e10i	−1.40515	+	0.676682i	−0.430947	+	0.902377i	$0.641821\pi$
$548$	−4.24516e10	−	1.21320e11i	−0.470730	−	1.34527i
$549$	3.06677e10	−	4.88074e10i	0.337592	−	0.537275i
$550$			4.45926e10i			0.487318i
$551$	−8.14316e10	+	5.03281e10i	−0.883459	+	0.546015i
$552$	−2.16199e11			−2.32862
$553$	−4.29061e10	−	2.69597e10i	−0.458795	−	0.288280i
$554$	1.48255e11	−	5.18766e10i	1.57387	−	0.550722i
$555$	6.99016e10	+	1.45152e11i	0.736741	+	1.52986i
$556$	−2.71676e11	+	6.20083e10i	−2.84284	+	0.648859i
$557$	1.07021e10	+	2.44268e9i	0.111185	+	0.0253773i	0.277752	−	0.960653i	$-0.410411\pi$
$557$	1.07021e10	+	2.44268e9i	0.111185	+	0.0253773i	−0.166566	+	0.986030i	$0.553268\pi$
$558$	2.37110e10	+	1.14186e10i	0.244575	+	0.117781i
$559$	−5.58404e9	+	4.95597e10i	−0.0571875	+	0.507554i
$560$	3.32243e11	−	2.64955e11i	3.37834	−	2.69414i
$561$	1.12845e11	+	3.94863e10i	1.13928	+	0.398653i
$562$	−4.25750e10	−	3.77864e11i	−0.426786	−	3.78783i
$563$	7.42542e9	+	7.42542e9i	0.0739073	+	0.0739073i	0.743094	−	0.669187i	$-0.233357\pi$
$563$	7.42542e9	+	7.42542e9i	0.0739073	+	0.0739073i	−0.669187	+	0.743094i	$0.733357\pi$
$564$	−1.46856e11	−	1.17114e11i	−1.45136	−	1.15742i
$565$	1.76227e10	+	2.80463e10i	0.172933	+	0.275221i
$566$	−2.25817e10	+	1.41890e10i	−0.220035	+	0.138257i
$567$	−9.29620e10	+	1.16571e11i	−0.899442	+	1.12786i
$568$	−2.30914e11	+	2.30914e11i	−2.21849	+	2.21849i
$569$	2.04517e11	−	2.30436e10i	1.95111	−	0.219837i	0.954246	−	0.299024i	$-0.0966610\pi$
$569$	2.04517e11	−	2.30436e10i	1.95111	−	0.219837i	0.996860	+	0.0791871i	$0.0252324\pi$
$570$	9.09835e10	−	2.60016e11i	0.861912	−	2.46320i
$571$	−4.45585e10	−	5.58745e10i	−0.419166	−	0.525617i	0.526754	−	0.850018i	$-0.323409\pi$
$571$	−4.45585e10	−	5.58745e10i	−0.419166	−	0.525617i	−0.945920	+	0.324401i	$0.894837\pi$
$572$	−4.14658e11	−	4.67207e10i	−3.87352	−	0.436441i
$573$	−2.65758e10	+	5.51852e10i	−0.246529	+	0.511922i
$574$	5.38316e10	−	2.35852e11i	0.495895	−	2.17266i
$575$	−2.09736e9	−	9.18913e9i	−0.0191867	−	0.0840626i
$576$	−1.57610e11	+	7.59011e10i	−1.43184	+	0.689538i
$577$	−2.94046e9	−	8.40335e9i	−0.0265285	−	0.0758140i	0.929858	−	0.367920i	$-0.119930\pi$
$577$	−2.94046e9	−	8.40335e9i	−0.0265285	−	0.0758140i	−0.956386	+	0.292106i	$0.905644\pi$
$578$	7.73476e10	−	1.23098e11i	0.693004	−	1.10291i
$579$			4.12834e10i			0.367334i
$580$	−2.40742e9	+	3.24516e11i	−0.0212735	+	2.86764i
$581$	1.29929e11			1.14026
$582$	−2.51260e11	−	1.57877e11i	−2.18994	−	1.37603i
$583$	−2.07224e11	+	7.25107e10i	−1.79376	+	0.627665i
$584$	9.04301e10	+	1.87780e11i	0.777430	+	1.61435i
$585$	5.08365e10	−	1.16031e10i	0.434062	−	0.0990718i
$586$	2.98708e11	+	6.81780e10i	2.53312	+	0.578168i
$587$	5.37991e10	+	2.59083e10i	0.453130	+	0.218216i	0.646506	−	0.762909i	$-0.276230\pi$
$587$	5.37991e10	+	2.59083e10i	0.453130	+	0.218216i	−0.193376	+	0.981125i	$0.561944\pi$
$588$	−1.45633e10	+	1.29253e11i	−0.121829	+	1.08126i
$589$	−2.77916e10	+	2.21631e10i	−0.230915	+	0.184149i
$590$	−2.05308e11	−	7.18405e10i	−1.69433	−	0.592873i
$591$	2.38630e10	+	2.11790e11i	0.195603	+	1.73602i
$592$	3.93735e11	+	3.93735e11i	3.20566	+	3.20566i
$593$	−1.42508e11	−	1.13646e11i	−1.15245	−	0.919045i	−0.154822	−	0.987942i	$-0.549480\pi$
$593$	−1.42508e11	−	1.13646e11i	−1.15245	−	0.919045i	−0.997624	+	0.0688975i	$0.978052\pi$
$594$	−1.35978e11	−	2.16407e11i	−1.09225	−	1.73830i
$595$	7.42683e10	−	4.66659e10i	0.592565	−	0.372333i
$596$	−3.64869e11	+	4.57531e11i	−2.89169	+	3.62606i
$597$	1.72892e11	−	1.72892e11i	1.36106	−	1.36106i
$598$	1.20362e11	−	1.35615e10i	0.941206	−	0.106048i
$599$	−6.31240e10	+	1.80398e11i	−0.490328	+	1.40128i	0.387308	+	0.921950i	$0.373405\pi$
$599$	−6.31240e10	+	1.80398e11i	−0.490328	+	1.40128i	−0.877636	+	0.479327i	$0.840881\pi$
$600$	−4.64683e10	−	5.82694e10i	−0.358552	−	0.449609i
$601$	1.27799e11	+	1.43995e10i	0.979559	+	0.110370i	0.587199	−	0.809442i	$-0.300230\pi$
$601$	1.27799e11	+	1.43995e10i	0.979559	+	0.110370i	0.392359	+	0.919812i	$0.371659\pi$
$602$	−7.70929e10	+	1.60085e11i	−0.586987	+	1.21889i
$603$	−6.79854e9	+	2.97864e10i	−0.0514217	+	0.225293i
$604$	2.99089e10	+	1.31040e11i	0.224726	+	0.984588i
$605$	2.62492e11	−	1.26410e11i	1.95927	−	0.943536i
$606$	−5.36268e10	−	1.53257e11i	−0.397641	−	1.13639i
$607$	−8.84855e10	+	1.40824e11i	−0.651805	+	1.03734i	0.343368	+	0.939201i	$0.388432\pi$
$607$	−8.84855e10	+	1.40824e11i	−0.651805	+	1.03734i	−0.995173	+	0.0981402i	$0.968711\pi$
$608$		−	4.95087e11i		−	3.62299i
$609$	−1.36349e11	−	1.38387e11i	−0.991249	−	1.00607i
$610$	3.62469e11			2.61789
$611$	5.58423e10	+	3.50880e10i	0.400681	+	0.251764i
$612$	−1.00001e11	+	3.49917e10i	−0.712848	+	0.249436i
$613$	−9.09385e10	−	1.88836e11i	−0.644030	−	1.33734i	−0.925856	−	0.377876i	$-0.876654\pi$
$613$	−9.09385e10	−	1.88836e11i	−0.644030	−	1.33734i	0.281826	−	0.959466i	$-0.409060\pi$
$614$	−2.01332e11	+	4.59527e10i	−1.41657	+	0.323324i
$615$	−1.83943e11	−	4.19837e10i	−1.28582	−	0.293481i
$616$	−8.39423e11	−	4.04245e11i	−5.82986	−	2.80751i
$617$	2.61656e10	−	2.32226e11i	0.180547	−	1.60240i	−0.497555	−	0.867433i	$-0.665769\pi$
$617$	2.61656e10	−	2.32226e11i	0.180547	−	1.60240i	0.678102	−	0.734968i	$-0.262803\pi$
$618$	3.18557e10	−	2.54041e10i	0.218390	−	0.174160i
$619$	1.03749e11	+	3.63035e10i	0.706681	+	0.247278i	0.659604	−	0.751613i	$-0.270724\pi$
$619$	1.03749e11	+	3.63035e10i	0.706681	+	0.247278i	0.0470764	+	0.998891i	$0.485010\pi$
$620$	1.34923e10	+	1.19748e11i	0.0913103	+	0.810401i
$621$	3.81991e10	+	3.81991e10i	0.256854	+	0.256854i
$622$	2.09330e11	+	1.66935e11i	1.39853	+	1.11529i
$623$	1.76207e11	+	2.80432e11i	1.16969	+	1.86155i
$624$	4.59226e11	−	2.88551e11i	3.02892	−	1.90320i
$625$	−1.06994e11	+	1.34166e11i	−0.701196	+	0.879271i
$626$	−1.19067e11	+	1.19067e11i	−0.775346	+	0.775346i
$627$	−3.39861e11	+	3.82931e10i	−2.19903	+	0.247771i
$628$	1.10282e11	−	3.15169e11i	0.709035	−	2.02631i
$629$	7.16585e10	+	8.98570e10i	0.457789	+	0.574049i
$630$	1.84602e11	+	2.07996e10i	1.17185	+	0.132036i
$631$	1.18480e11	−	2.46026e11i	0.747356	−	1.55190i	−0.0841933	−	0.996449i	$-0.526831\pi$
$631$	1.18480e11	−	2.46026e11i	0.747356	−	1.55190i	0.831549	−	0.555451i	$-0.187454\pi$
$632$	−5.36744e10	+	2.35163e11i	−0.336433	+	1.47401i
$633$	8.46371e9	+	3.70819e10i	0.0527164	+	0.230966i
$634$	−4.15998e11	+	2.00334e11i	−2.57474	+	1.23993i
$635$	2.23804e10	+	6.39596e10i	0.137649	+	0.393379i
$636$	3.11497e11	−	4.95744e11i	1.90382	−	3.02991i
$637$		−	4.56693e10i		−	0.277374i
$638$	5.00282e11	−	2.36367e11i	3.01948	−	1.42661i
$639$	−8.08403e10			−0.484869
$640$	−4.00935e11	−	2.51924e11i	−2.38976	−	1.50159i
$641$	3.08998e11	−	1.08123e11i	1.83030	−	0.640451i	0.834281	−	0.551339i	$-0.185883\pi$
$641$	3.08998e11	−	1.08123e11i	1.83030	−	0.640451i	0.996022	−	0.0891120i	$-0.0284029\pi$
$642$	−1.52787e11	−	3.17265e11i	−0.899384	−	1.86759i
$643$	3.02645e11	−	6.90766e10i	1.77047	−	0.404099i	0.792007	−	0.610513i	$-0.209037\pi$
$643$	3.02645e11	−	6.90766e10i	1.77047	−	0.404099i	0.978465	+	0.206414i	$0.0661794\pi$
$644$	3.06347e11	+	6.99216e10i	1.78102	+	0.406507i
$645$	1.24852e11	+	6.01254e10i	0.721366	+	0.347391i
$646$	2.20033e10	−	1.95284e11i	0.126345	−	1.12134i
$647$	4.53325e10	−	3.61515e10i	0.258698	−	0.206305i	−0.485549	−	0.874210i	$-0.661380\pi$
$647$	4.53325e10	−	3.61515e10i	0.258698	−	0.206305i	0.744247	+	0.667905i	$0.232809\pi$
$648$	6.69906e11	+	2.34410e11i	3.79939	+	1.32946i
$649$	3.02362e10	+	2.68354e11i	0.170431	+	1.51262i
$650$	2.95248e10	+	2.95248e10i	0.165399	+	0.165399i
$651$	−5.64006e10	−	4.49780e10i	−0.314022	−	0.250424i
$652$	1.41680e11	+	2.25482e11i	0.784002	+	1.24773i
$653$	−6.90844e10	+	4.34086e10i	−0.379951	+	0.238739i	−0.708443	−	0.705768i	$-0.750602\pi$
$653$	−6.90844e10	+	4.34086e10i	−0.379951	+	0.238739i	0.328493	+	0.944507i	$0.393459\pi$
$654$	−3.20669e11	+	4.02107e11i	−1.75286	+	2.19801i
$655$	−3.95479e10	+	3.95479e10i	−0.214861	+	0.214861i
$656$	−6.48002e11	+	7.30123e10i	−3.49914	+	0.394258i
$657$	−1.70405e10	+	4.86991e10i	−0.0914581	+	0.261372i
$658$	1.46495e11	+	1.83699e11i	0.781483	+	0.979949i
$659$	2.23154e10	+	2.51434e9i	0.118321	+	0.0133316i	0.170927	−	0.985284i	$-0.445324\pi$
$659$	2.23154e10	+	2.51434e9i	0.118321	+	0.0133316i	−0.0526051	+	0.998615i	$0.516752\pi$
$660$	−5.03059e11	+	1.04461e12i	−2.65120	+	5.50528i
$661$	9.50290e9	−	4.16349e10i	0.0497795	−	0.218098i	−0.943920	−	0.330174i	$-0.892893\pi$
$661$	9.50290e9	−	4.16349e10i	0.0497795	−	0.218098i	0.993700	+	0.112076i	$0.0357499\pi$
$662$	1.74965e10	+	7.66572e10i	0.0911002	+	0.399136i
$663$	1.00859e11	−	4.85710e10i	0.521987	−	0.251375i
$664$	−2.04272e11	−	5.83775e11i	−1.05084	−	3.00312i
$665$	−1.33498e11	+	2.12461e11i	−0.682634	+	1.08641i
$666$			2.43418e11i			1.23724i
$667$	−9.19749e10	+	7.22379e10i	−0.464693	+	0.364974i
$668$	−2.22163e11			−1.11575
$669$	2.54108e11	+	1.59667e11i	1.26857	+	0.797094i
$670$	−1.81339e11	+	6.34532e10i	−0.899894	+	0.314887i
$671$	−1.95256e11	−	4.05452e11i	−0.963193	−	2.00009i
$672$	9.79543e11	−	2.23574e11i	4.80338	−	1.09634i
$673$	−2.43550e11	−	5.55887e10i	−1.18721	−	0.270973i	−0.417086	−	0.908867i	$-0.636949\pi$
$673$	−2.43550e11	−	5.55887e10i	−1.18721	−	0.270973i	−0.770124	+	0.637894i	$0.779806\pi$
$674$	−2.71464e11	−	1.30730e11i	−1.31544	−	0.633484i
$675$	−2.08507e9	+	1.85055e10i	−0.0100440	+	0.0891428i
$676$	1.31901e11	−	1.05187e11i	0.631626	−	0.503705i
$677$	−1.02906e11	−	3.60083e10i	−0.489875	−	0.171415i	0.0740273	−	0.997256i	$-0.476415\pi$
$677$	−1.02906e11	−	3.60083e10i	−0.489875	−	0.171415i	−0.563902	+	0.825842i	$0.690701\pi$
$678$	1.68628e10	+	1.49661e11i	0.0798013	+	0.708256i
$679$	1.91127e11	+	1.91127e11i	0.899173	+	0.899173i
$680$	−3.26433e11	−	2.60322e11i	−1.52672	−	1.21752i
$681$	−1.82695e11	−	2.90757e11i	−0.849450	−	1.35189i
$682$	1.73967e11	−	1.09311e11i	0.804138	−	0.505273i
$683$	−1.91531e11	+	2.40173e11i	−0.880150	+	1.10367i	0.113763	+	0.993508i	$0.463709\pi$
$683$	−1.91531e11	+	2.40173e11i	−0.880150	+	1.10367i	−0.993913	+	0.110165i	$0.964862\pi$
$684$	2.14311e11	−	2.14311e11i	0.979084	−	0.979084i
$685$	1.24604e11	−	1.40395e10i	0.565941	−	0.0637662i
$686$	−1.08172e11	+	3.09138e11i	−0.488449	+	1.39591i
$687$	−1.58578e11	−	1.98850e11i	−0.711893	−	0.892686i
$688$	4.75939e11	+	5.36254e10i	2.12421	+	0.239341i
$689$	−8.91934e10	+	1.85212e11i	−0.395782	+	0.821849i
$690$	7.48886e10	−	3.28109e11i	0.330384	−	1.44751i
$691$	1.85439e10	+	8.12463e10i	0.0813373	+	0.356362i	0.999176	−	0.0405919i	$-0.0129244\pi$
$691$	1.85439e10	+	8.12463e10i	0.0813373	+	0.356362i	−0.917838	+	0.396954i	$0.870067\pi$
$692$	5.26964e11	−	2.53773e11i	2.29804	−	1.10668i
$693$	−7.61755e10	−	2.17697e11i	−0.330280	−	0.943886i
$694$	−4.55084e10	+	7.24263e10i	−0.196180	+	0.312218i
$695$		−	2.71856e11i		−	1.16520i
$696$	−4.07411e11	+	8.30186e11i	−1.73618	+	3.53784i
$697$	−1.34597e11			−0.570301
$698$	4.34527e11	+	2.73032e11i	1.83061	+	1.15025i
$699$	9.86014e10	−	3.45021e10i	0.413023	−	0.144523i
$700$	4.69988e10	+	9.75940e10i	0.195747	+	0.406472i
$701$	3.83681e11	−	8.75728e10i	1.58891	−	0.362658i	0.665476	−	0.746419i	$-0.268229\pi$
$701$	3.83681e11	−	8.75728e10i	1.58891	−	0.362658i	0.923432	+	0.383762i	$0.125372\pi$
$702$	−2.33314e11	−	5.32523e10i	−0.960709	−	0.219276i
$703$	−2.96226e11	−	1.42655e11i	−1.21284	−	0.584071i
$704$	−1.52912e11	+	1.35713e12i	−0.622516	+	5.52498i
$705$	1.43268e11	−	1.14253e11i	0.579955	−	0.462498i
$706$	−6.24166e10	−	2.18405e10i	−0.251236	−	0.0879112i
$707$	1.65591e10	+	1.46966e11i	0.0662764	+	0.588219i
$708$	−5.09245e11	−	5.09245e11i	−2.02672	−	2.02672i
$709$	2.18717e10	+	1.74421e10i	0.0865559	+	0.0690260i	0.665812	−	0.746120i	$-0.268085\pi$
$709$	2.18717e10	+	1.74421e10i	0.0865559	+	0.0690260i	−0.579256	+	0.815146i	$0.696657\pi$
$710$	−2.70454e11	−	4.30425e11i	−1.06429	−	1.69381i
$711$	−5.05594e10	+	3.17685e10i	−0.197844	+	0.124314i
$712$	9.82957e11	−	1.23259e12i	3.82485	−	4.79621i
$713$	−3.07079e10	+	3.07079e10i	−0.118821	+	0.118821i
$714$	3.96312e11	−	4.46536e10i	1.52491	−	0.171816i
$715$	1.34453e11	−	3.84244e11i	0.514453	−	1.47022i
$716$	−8.15876e10	−	1.02308e11i	−0.310436	−	0.389274i
$717$	−5.98482e11	−	6.74328e10i	−2.26451	−	0.255149i
$718$	2.41885e11	−	5.02280e11i	0.910148	−	1.88994i
$719$	8.28768e8	−	3.63107e9i	0.00310111	−	0.0135869i	−0.973354	−	0.229309i	$-0.926353\pi$
$719$	8.28768e8	−	3.63107e9i	0.00310111	−	0.0135869i	0.976455	+	0.215722i	$0.0692105\pi$
$720$	−1.11428e11	−	4.88199e11i	−0.414635	−	1.81663i
$721$	−3.34379e10	+	1.61028e10i	−0.123736	+	0.0595883i
$722$	1.35359e10	+	3.86835e10i	0.0498126	+	0.142356i
$723$	−7.84368e10	+	1.24831e11i	−0.287056	+	0.456847i
$724$			7.40625e11i			2.69553i
$725$	−3.92377e10	−	9.26252e9i	−0.142021	−	0.0335257i
$726$	1.32471e12			4.76842
$727$	−3.67879e11	−	2.31154e11i	−1.31694	−	0.827490i	−0.323997	−	0.946058i	$-0.605027\pi$
$727$	−3.67879e11	−	2.31154e11i	−1.31694	−	0.827490i	−0.992946	+	0.118568i	$0.962170\pi$
$728$	−8.23432e11	+	2.88131e11i	−2.93158	+	1.02581i
$729$	−1.59602e10	−	3.31417e10i	−0.0565104	−	0.117345i
$730$	−3.16302e11	+	7.21939e10i	−1.11381	+	0.254220i
$731$	9.63790e10	+	2.19979e10i	0.337530	+	0.0770391i
$732$	1.08127e12	+	5.20713e11i	3.76609	+	1.81365i
$733$	5.78359e9	−	5.13308e10i	0.0200346	−	0.177812i	−0.979710	−	0.200422i	$-0.935769\pi$
$733$	5.78359e9	−	5.13308e10i	0.0200346	−	0.177812i	0.999744	+	0.0226093i	$0.00719737\pi$
$734$	−2.64908e11	+	2.11257e11i	−0.912665	+	0.727826i
$735$	−1.19773e11	−	4.19103e10i	−0.410402	−	0.143606i
$736$	−6.77213e10	−	6.01043e11i	−0.230788	−	2.04830i
$737$	1.68662e11	+	1.68662e11i	0.571671	+	0.571671i
$738$	−2.22875e11	−	1.77737e11i	−0.751340	−	0.599173i
$739$	8.06529e10	+	1.28358e11i	0.270422	+	0.430375i	0.954135	−	0.299377i	$-0.0967787\pi$
$739$	8.06529e10	+	1.28358e11i	0.270422	+	0.430375i	−0.683713	+	0.729751i	$0.739636\pi$
$740$	−9.43758e11	+	5.93003e11i	−3.14727	+	1.97756i
$741$	−1.99668e11	+	2.50375e11i	−0.662270	+	0.830460i
$742$	−5.17865e11	+	5.17865e11i	−1.70845	+	1.70845i
$743$	3.09465e11	−	3.48683e10i	1.01544	−	0.114413i	0.411475	−	0.911421i	$-0.365014\pi$
$743$	3.09465e11	−	3.48683e10i	1.01544	−	0.114413i	0.603969	+	0.797008i	$0.293585\pi$
$744$	−1.13415e11	+	3.24122e11i	−0.370151	+	1.05783i
$745$	−3.55956e11	−	4.46355e11i	−1.15550	−	1.44896i
$746$	−9.59255e10	−	1.08082e10i	−0.309727	−	0.0348978i
$747$	6.64298e10	−	1.37943e11i	0.213344	−	0.443014i
$748$	−1.84052e11	+	8.06386e11i	−0.587943	+	2.57595i
$749$	7.13737e10	+	3.12709e11i	0.226783	+	0.993602i
$750$	−6.11782e11	+	2.94619e11i	−1.93353	+	0.931141i
$751$	2.66020e10	+	7.60240e10i	0.0836284	+	0.238996i	0.978103	−	0.208123i	$-0.0667355\pi$
$751$	2.66020e10	+	7.60240e10i	0.0836284	+	0.238996i	−0.894474	+	0.447120i	$0.852450\pi$
$752$	3.36962e11	−	5.36272e11i	1.05368	−	1.67693i
$753$		−	2.12606e11i		−	0.661297i
$754$	1.74738e11	−	4.87735e11i	0.540631	−	1.50903i
$755$	−1.31126e11			−0.403554
$756$	−5.25680e11	−	3.30306e11i	−1.60929	−	1.01118i
$757$	1.51861e11	−	5.31384e10i	0.462447	−	0.161817i	−0.0889922	−	0.996032i	$-0.528365\pi$
$757$	1.51861e11	−	5.31384e10i	0.462447	−	0.161817i	0.551439	+	0.834215i	$0.314079\pi$
$758$	2.01766e11	+	4.18972e11i	0.611183	+	1.26913i
$759$	−4.07358e11	+	9.29768e10i	−1.22747	+	0.280161i
$760$	1.16447e12	+	2.65783e11i	3.49039	+	0.796659i
$761$	5.18429e11	+	2.49662e11i	1.54579	+	0.744414i	0.995869	−	0.0908012i	$-0.0289428\pi$
$761$	5.18429e11	+	2.49662e11i	1.54579	+	0.744414i	0.549923	+	0.835215i	$0.314657\pi$
$762$	−3.44971e10	+	3.06170e11i	−0.102320	+	0.908119i
$763$	3.66266e11	−	2.92087e11i	1.08068	−	0.861816i
$764$	−3.99978e11	−	1.39958e11i	−1.17399	−	0.410795i
$765$	−1.15724e10	−	1.02708e11i	−0.0337893	−	0.299888i
$766$	−2.73245e11	−	2.73245e11i	−0.793664	−	0.793664i
$767$	1.97696e11	+	1.57658e11i	0.571238	+	0.455547i
$768$	−4.22144e11	−	6.71838e11i	−1.21343	−	1.93117i
$769$	−1.33574e11	+	8.39303e10i	−0.381960	+	0.240001i	−0.709302	−	0.704905i	$-0.750990\pi$
$769$	−1.33574e11	+	8.39303e10i	−0.381960	+	0.240001i	0.327342	+	0.944906i	$0.393847\pi$
$770$	9.04255e11	−	1.13390e12i	2.57234	−	3.22561i
$771$	8.78513e10	−	8.78513e10i	0.248617	−	0.248617i
$772$	−2.83819e11	+	3.19787e10i	−0.799047	+	0.0900310i
$773$	−7.76639e10	+	2.21951e11i	−0.217521	+	0.621640i	−0.999999	−	0.00103814i	$-0.999670\pi$
$773$	−7.76639e10	+	2.21951e11i	−0.217521	+	0.621640i	0.782478	+	0.622678i	$0.213955\pi$
$774$	1.30543e11	+	1.63695e11i	0.363738	+	0.456113i
$775$	−1.48764e10	−	1.67617e9i	−0.0412374	−	0.00464634i
$776$	5.58252e11	−	1.15922e12i	1.53951	−	3.19683i
$777$	1.48475e11	−	6.50513e11i	0.407352	−	1.78473i
$778$	5.17212e10	+	2.26606e11i	0.141173	+	0.618518i
$779$	3.46912e11	−	1.67064e11i	0.942041	−	0.453663i
$780$	3.58562e11	+	1.02471e12i	0.968694	+	2.76837i
$781$	−3.35778e11	+	5.34387e11i	−0.902501	+	1.43632i
$782$		−	2.40088e11i		−	0.642012i
$783$	2.18664e11	−	7.46978e10i	0.581742	−	0.198729i
$784$	−4.38577e11			−1.16086
$785$	2.75821e11	+	1.73310e11i	0.726354	+	0.456399i
$786$	−2.40033e11	+	8.39913e10i	−0.628899	+	0.220061i
$787$	9.39001e9	+	1.94986e10i	0.0244775	+	0.0508281i	0.912849	−	0.408297i	$-0.133877\pi$
$787$	9.39001e9	+	1.94986e10i	0.0244775	+	0.0508281i	−0.888372	+	0.459125i	$0.848163\pi$
$788$	−1.43755e12	+	3.28111e11i	−3.72836	+	0.850974i
$789$	−8.94188e11	−	2.04093e11i	−2.30739	−	0.526647i
$790$	−3.38296e11	−	1.62915e11i	−0.868537	−	0.418265i
$791$	1.53597e10	−	1.36322e11i	0.0392354	−	0.348224i
$792$	−8.58355e11	+	6.84515e11i	−2.18155	+	1.73973i
$793$	−3.97728e11	−	1.39171e11i	−1.00576	−	0.351930i
$794$	1.97110e10	+	1.74940e11i	0.0495938	+	0.440157i
$795$	4.03887e11	+	4.03887e11i	1.01109	+	1.01109i
$796$	1.32254e12	+	1.05469e12i	3.29424	+	2.62707i
$797$	−2.21572e11	−	3.52630e11i	−0.549138	−	0.873949i	0.450686	−	0.892682i	$-0.351179\pi$
$797$	−2.21572e11	−	3.52630e11i	−0.549138	−	0.873949i	−0.999825	+	0.0187338i	$0.994036\pi$
$798$	−9.66036e11	+	6.07000e11i	−2.38222	+	1.49685i
$799$	8.15064e10	−	1.02206e11i	0.199988	−	0.250778i
$800$	1.47436e11	−	1.47436e11i	0.359951	−	0.359951i
$801$	3.87818e11	−	4.36966e10i	0.942103	−	0.106150i
$802$	−2.81678e9	+	8.04988e9i	−0.00680855	+	0.0194577i
$803$	2.51141e11	+	3.14921e11i	0.604026	+	0.757425i
$804$	−6.32101e11	−	7.12207e10i	−1.51273	−	0.170444i
$805$	−1.33007e11	+	2.76191e11i	−0.316731	+	0.657698i
$806$	4.28090e10	−	1.87559e11i	0.101437	−	0.444423i
$807$	1.55630e10	+	6.81859e10i	0.0366943	+	0.160768i
$808$	6.34287e11	−	3.05456e11i	1.48813	−	0.716645i
$809$	−1.92868e11	−	5.51185e11i	−0.450263	−	1.28678i	−0.915759	−	0.401728i	$-0.868410\pi$
$809$	−1.92868e11	−	5.51185e11i	−0.450263	−	1.28678i	0.465496	−	0.885050i	$-0.345876\pi$
$810$	−5.87792e11	+	9.35465e11i	−1.36547	+	2.17314i
$811$			3.89074e11i			0.899391i	0.893182	+	0.449696i	$0.148468\pi$
$811$			3.89074e11i			0.899391i	−0.893182	+	0.449696i	$0.851532\pi$
$812$	8.45779e11	−	1.04458e12i	1.94551	−	2.40280i
$813$	4.20472e11			0.962444
$814$	1.60909e12	+	1.01106e12i	3.66508	+	2.30292i
$815$	−2.45216e11	+	8.58046e10i	−0.555799	+	0.194482i
$816$	−4.66443e11	−	9.68579e11i	−1.05205	−	2.18461i
$817$	−2.75713e11	+	6.29297e10i	−0.618827	+	0.141243i
$818$	−1.90866e11	−	4.35639e10i	−0.426300	−	0.0973002i
$819$	−1.94573e11	−	9.37014e10i	−0.432461	−	0.208262i
$820$	1.46149e11	−	1.29711e12i	0.323251	−	2.86893i
$821$	4.17206e11	−	3.32711e11i	0.918287	−	0.732309i	−0.0455054	−	0.998964i	$-0.514490\pi$
$821$	4.17206e11	−	3.32711e11i	0.918287	−	0.732309i	0.963792	+	0.266655i	$0.0859184\pi$
$822$	5.38152e11	+	1.88308e11i	1.17874	+	0.412459i
$823$	−6.64561e10	−	5.89815e11i	−0.144856	−	1.28563i	−0.830222	−	0.557432i	$-0.811787\pi$
$823$	−6.64561e10	−	5.89815e11i	−0.144856	−	1.28563i	0.685367	−	0.728198i	$-0.259642\pi$
$824$	1.24920e11	+	1.24920e11i	0.270972	+	0.270972i
$825$	−1.12613e11	−	8.98061e10i	−0.243094	−	0.193861i
$826$	4.79287e11	+	7.62781e11i	1.02962	+	1.63863i
$827$	4.47284e11	−	2.81047e11i	0.956228	−	0.600838i	0.0390168	−	0.999239i	$-0.487577\pi$
$827$	4.47284e11	−	2.81047e11i	0.956228	−	0.600838i	0.917212	+	0.398400i	$0.130435\pi$
$828$	2.30862e11	−	2.89492e11i	0.491169	−	0.615906i
$829$	−3.48367e11	+	3.48367e11i	−0.737596	+	0.737596i	−0.972112	−	0.234516i	$-0.924649\pi$
$829$	−3.48367e11	+	3.48367e11i	−0.737596	+	0.737596i	0.234516	+	0.972112i	$0.424649\pi$
$830$	9.56705e11	−	1.07795e11i	2.01588	−	0.227136i
$831$	−1.67566e11	+	4.78875e11i	−0.351383	+	1.00419i
$832$	7.97313e11	+	9.99798e11i	1.66393	+	2.08650i
$833$	−8.99551e10	−	1.01355e10i	−0.186830	−	0.0210507i
$834$	5.36323e11	−	1.11369e12i	1.10857	−	2.30196i
$835$	4.82283e10	−	2.11302e11i	0.0992100	−	0.434668i
$836$	−5.26522e11	−	2.30684e12i	−1.07793	−	4.72273i
$837$	7.73060e10	−	3.72286e10i	0.157511	−	0.0758534i
$838$	1.14078e11	+	3.26017e11i	0.231327	+	0.661095i
$839$	2.36546e11	−	3.76460e11i	0.477383	−	0.759751i	−0.518036	−	0.855359i	$-0.673337\pi$
$839$	2.36546e11	−	3.76460e11i	0.477383	−	0.759751i	0.995419	+	0.0956078i	$0.0304795\pi$
$840$			2.42396e12i			4.86865i
$841$	1.04067e11	+	4.89302e11i	0.208032	+	0.978122i
$842$	−3.58551e11			−0.713349
$843$	1.03999e12	+	6.53470e11i	2.05930	+	1.29394i
$844$	−2.48378e11	+	8.69113e10i	−0.489490	+	0.171280i
$845$	7.14113e10	+	1.48287e11i	0.140068	+	0.290855i
$846$	2.69929e11	−	6.16094e10i	0.526947	−	0.120272i
$847$	−1.17638e12	−	2.68502e11i	−2.28568	−	0.521692i
$848$	1.77865e12	+	8.56553e11i	3.43960	+	1.65642i
$849$	9.64513e9	−	8.56029e10i	0.0185642	−	0.164762i
$850$	6.47077e10	−	5.16027e10i	0.123960	−	0.0988545i
$851$	−3.79136e11	−	1.32666e11i	−0.722898	−	0.252953i
$852$	−1.88447e11	−	1.67251e12i	−0.357627	−	3.17403i
$853$	2.06382e11	+	2.06382e11i	0.389830	+	0.389830i	0.874627	−	0.484797i	$-0.161107\pi$
$853$	2.06382e11	+	2.06382e11i	0.389830	+	0.389830i	−0.484797	+	0.874627i	$0.661107\pi$
$854$	−1.17369e12	−	9.35988e11i	−2.20659	−	1.75970i
$855$	1.57310e11	+	2.50358e11i	0.294369	+	0.468486i
$856$	1.29279e12	−	8.12315e11i	2.40787	−	1.51297i
$857$	4.75784e10	−	5.96615e10i	0.0882037	−	0.110604i	−0.735771	−	0.677230i	$-0.763180\pi$
$857$	4.75784e10	−	5.96615e10i	0.0882037	−	0.110604i	0.823975	+	0.566626i	$0.191752\pi$
$858$	1.30885e12	−	1.30885e12i	2.41512	−	2.41512i
$859$	−4.84866e11	+	5.46312e10i	−0.890530	+	0.100339i	−0.545360	−	0.838202i	$-0.683607\pi$
$859$	−4.84866e11	+	5.46312e10i	−0.890530	+	0.100339i	−0.345170	+	0.938540i	$0.612179\pi$
$860$	−3.16644e11	+	9.04916e11i	−0.578865	+	1.65430i
$861$	4.87202e11	+	6.10932e11i	0.886536	+	1.11168i
$862$	−5.89041e11	−	6.63690e10i	−1.06688	−	0.120209i
$863$	1.34889e11	−	2.80099e11i	0.243182	−	0.504973i	−0.743276	−	0.668985i	$-0.766729\pi$
$863$	1.34889e11	−	2.80099e11i	0.243182	−	0.504973i	0.986458	+	0.164012i	$0.0524434\pi$
$864$	−2.65922e11	+	1.16508e12i	−0.477199	+	2.09075i
$865$	1.26970e11	+	5.56293e11i	0.226797	+	0.993663i
$866$	−1.74712e12	+	8.41371e11i	−3.10636	+	1.49595i
$867$	1.55097e11	+	4.43242e11i	0.274490	+	0.784448i
$868$	2.65530e11	−	4.22589e11i	0.467773	−	0.744456i
$869$			4.66172e11i			0.817460i
$870$	−1.11879e12	−	9.05860e11i	−1.95285	−	1.58119i
$871$	2.23342e11			0.388058
$872$	−1.88819e12	−	1.18643e12i	−3.26572	−	2.05199i
$873$	3.00634e11	−	1.05196e11i	0.517584	−	0.181111i
$874$	2.98002e11	+	6.18807e11i	0.510708	+	1.06050i
$875$	6.02996e11	−	1.37630e11i	1.02868	−	0.234791i
$876$	−1.04726e12	−	2.39031e11i	−1.77844	−	0.405918i
$877$	9.21647e11	+	4.43842e11i	1.55800	+	0.750291i	0.996991	−	0.0775215i	$-0.0247006\pi$
$877$	9.21647e11	+	4.43842e11i	1.55800	+	0.750291i	0.561005	+	0.827813i	$0.310415\pi$
$878$	1.32886e11	−	1.17939e12i	0.223615	−	1.98464i
$879$	−7.73749e11	+	6.17044e11i	−1.29612	+	1.03362i
$880$	−3.69002e12	−	1.29120e12i	−6.15316	−	2.15309i
$881$	9.24430e10	+	8.20454e11i	0.153451	+	1.36192i	0.800438	+	0.599416i	$0.204600\pi$
$881$	9.24430e10	+	8.20454e11i	0.153451	+	1.36192i	−0.646987	+	0.762501i	$0.723971\pi$
$882$	−1.35570e11	−	1.35570e11i	−0.224021	−	0.224021i
$883$	−6.35527e11	−	5.06816e11i	−1.04542	−	0.833695i	−0.0590531	−	0.998255i	$-0.518808\pi$
$883$	−6.35527e11	−	5.06816e11i	−1.04542	−	0.833695i	−0.986367	+	0.164560i	$0.947380\pi$
$884$	4.12047e11	+	6.55769e11i	0.674742	+	1.07385i
$885$	5.94899e11	−	3.73800e11i	0.969774	−	0.609349i
$886$	1.73739e11	−	2.17862e11i	0.281944	−	0.353547i
$887$	−3.21343e11	+	3.21343e11i	−0.519127	+	0.519127i	−0.917307	−	0.398180i	$-0.869642\pi$
$887$	−3.21343e11	+	3.21343e11i	−0.519127	+	0.519127i	0.398180	+	0.917307i	$0.369642\pi$
$888$	−3.15619e12	+	3.55617e11i	−5.07588	+	0.571914i
$889$	9.26911e10	−	2.64896e11i	0.148399	−	0.424100i
$890$	1.53012e12	+	1.91871e12i	2.43874	+	3.05808i
$891$	1.36303e12	+	1.53577e11i	2.16269	+	0.243677i
$892$	−9.00855e11	+	1.87064e12i	−1.42297	+	2.95483i
$893$	−8.32163e10	+	3.64594e11i	−0.130859	+	0.573329i
$894$	−5.77633e11	−	2.53078e12i	−0.904278	−	3.96190i
$895$	1.15018e11	−	5.53896e10i	0.179255	−	0.0863248i
$896$	6.47713e11	+	1.85106e12i	1.00496	+	2.87202i
$897$	−2.08152e11	+	3.31272e11i	−0.321522	+	0.511699i
$898$		−	2.41181e11i		−	0.370884i
$899$	6.00488e10	+	1.75782e11i	0.0919318	+	0.269113i
$900$	1.27643e11			0.194547
$901$	3.45019e11	+	2.16790e11i	0.523532	+	0.328957i
$902$	−2.10065e12	+	7.35048e11i	−3.17342	+	1.11043i
$903$	−2.49016e11	−	5.17087e11i	−0.374521	−	0.777702i
$904$	−6.36643e11	+	1.45310e11i	−0.953283	+	0.217581i
$905$	−7.04418e11	−	1.60779e11i	−1.05011	−	0.239682i
$906$	−5.37173e11	−	2.58689e11i	−0.797262	−	0.383941i
$907$	−5.12105e10	+	4.54506e11i	−0.0756711	+	0.671600i	0.897420	+	0.441178i	$0.145439\pi$
$907$	−5.12105e10	+	4.54506e11i	−0.0756711	+	0.671600i	−0.973091	+	0.230422i	$0.925989\pi$
$908$	1.85741e12	−	1.48123e12i	2.73252	−	2.17911i
$909$	1.64497e11	+	5.75599e10i	0.240936	+	0.0843071i
$910$	−1.52048e11	−	1.34946e12i	−0.221725	−	1.96786i
$911$	3.52857e11	+	3.52857e11i	0.512300	+	0.512300i	0.915231	−	0.402930i	$-0.132008\pi$
$911$	3.52857e11	+	3.52857e11i	0.512300	+	0.512300i	−0.402930	+	0.915231i	$0.632008\pi$
$912$	2.40444e12	+	1.91748e12i	3.47564	+	2.77173i
$913$	−6.35937e11	−	1.01209e12i	−0.915231	−	1.45658i
$914$	−8.71029e11	+	5.47304e11i	−1.24810	+	0.784230i
$915$	−7.29985e11	+	9.15372e11i	−1.04143	+	1.30591i
$916$	1.24424e12	−	1.24424e12i	1.76734	−	1.76734i
$917$	2.30181e11	−	2.59351e10i	0.325530	−	0.0366785i
$918$	−1.56672e11	+	4.47741e11i	−0.220607	+	0.630459i
$919$	−3.55009e11	−	4.45168e11i	−0.497711	−	0.624110i	0.468000	−	0.883729i	$-0.344975\pi$
$919$	−3.55009e11	−	4.45168e11i	−0.497711	−	0.624110i	−0.965711	+	0.259618i	$0.916403\pi$
$920$	1.45004e12	+	1.63380e11i	2.02409	+	0.228060i
$921$	2.89419e11	−	6.00985e11i	0.402243	−	0.835266i
$922$	2.52592e11	−	1.10668e12i	0.349540	−	1.53143i
$923$	1.31499e11	+	5.76136e11i	0.181183	+	0.793813i
$924$	4.32638e12	−	2.08348e12i	5.93522	−	2.85825i
$925$	−4.57331e10	−	1.30698e11i	−0.0624689	−	0.178526i
$926$	−8.17660e11	+	1.30130e12i	−1.11206	+	1.76984i
$927$			4.37332e10i			0.0592233i
$928$	−2.43557e12	−	8.72575e11i	−3.28404	−	1.17655i
$929$	−8.09891e11			−1.08734			−0.543668	−	0.839300i	$-0.682965\pi$
$929$	−8.09891e11			−1.08734			−0.543668	+	0.839300i	$0.682965\pi$
$930$	−4.52608e11	−	2.84393e11i	−0.605049	−	0.380177i
$931$	2.44432e11	−	8.55306e10i	0.325357	−	0.113847i
$932$	3.13577e11	+	6.51148e11i	0.415604	+	0.863011i
$933$	−8.43149e11	+	1.92443e11i	−1.11270	+	0.253966i
$934$	5.81532e11	+	1.32731e11i	0.764164	+	0.174415i
$935$	−7.27010e11	−	3.50109e11i	−0.951248	−	0.458097i
$936$	−1.15099e11	+	1.02153e12i	−0.149958	+	1.33091i
$937$	−4.47805e11	+	3.57113e11i	−0.580939	+	0.463284i	−0.869332	−	0.494229i	$-0.835451\pi$
$937$	−4.47805e11	+	3.57113e11i	−0.580939	+	0.463284i	0.288393	+	0.957512i	$0.406879\pi$
$938$	7.51035e11	+	2.62799e11i	0.970173	+	0.339478i
$939$	−6.08978e10	−	5.40483e11i	−0.0783320	−	0.695215i
$940$	8.96453e11	+	8.96453e11i	1.14820	+	1.14820i
$941$	−1.04278e12	−	8.31587e11i	−1.32994	−	1.06059i	−0.992881	−	0.119113i	$-0.961995\pi$
$941$	−1.04278e12	−	8.31587e11i	−1.32994	−	1.06059i	−0.337063	−	0.941482i	$-0.609434\pi$
$942$	7.88020e11	+	1.25413e12i	1.00077	+	1.59271i
$943$	3.98305e11	−	2.50271e11i	0.503696	−	0.316493i
$944$	1.51404e12	−	1.89854e12i	1.90655	−	2.39074i
$945$	4.28276e11	−	4.28276e11i	0.537028	−	0.537028i
$946$	1.62432e12	−	1.83016e11i	2.02818	−	0.228521i
$947$	4.22452e11	−	1.20730e12i	0.525264	−	1.50112i	−0.309711	−	0.950831i	$-0.600232\pi$
$947$	4.22452e11	−	1.20730e12i	0.525264	−	1.50112i	0.834975	−	0.550288i	$-0.185482\pi$
$948$	−7.75122e11	−	9.71972e11i	−0.959702	−	1.20343i
$949$	3.74790e11	+	4.22287e10i	0.462086	+	0.0520646i
$950$	−1.02729e11	+	2.13318e11i	−0.126124	+	0.261899i
$951$	3.31868e11	−	1.45401e12i	0.405736	−	1.77764i
$952$	3.84788e11	+	1.68587e12i	0.468462	+	2.05246i
$953$	−7.00869e11	+	3.37521e11i	−0.849699	+	0.409193i	−0.807466	−	0.589914i	$-0.799161\pi$
$953$	−7.00869e11	+	3.37521e11i	−0.849699	+	0.409193i	−0.0422331	+	0.999108i	$0.513447\pi$
$954$	2.85033e11	+	8.14578e11i	0.344114	+	0.983420i
$955$	2.19946e11	−	3.50042e11i	0.264425	−	0.420829i
$956$		−	4.16674e12i		−	4.98844i
$957$	−4.10612e11	+	1.73943e12i	−0.489535	+	2.07376i
$958$	−1.70456e12			−2.02372
$959$	−4.39728e11	−	2.76299e11i	−0.519888	−	0.326667i
$960$	3.35377e12	−	1.17354e12i	3.94865	−	1.38169i
$961$	−3.40128e11	−	7.06283e11i	−0.398794	−	0.828104i
$962$	1.73480e12	−	3.95957e11i	2.02558	−	0.462325i
$963$	3.68487e11	+	8.41048e10i	0.428467	+	0.0977947i
$964$	−9.18961e11	−	4.42548e11i	−1.06412	−	0.512451i
$965$	3.11976e10	−	2.76886e11i	0.0359759	−	0.319295i
$966$	−1.08975e12	+	8.69049e11i	−1.25147	+	0.998012i
$967$	7.37171e11	+	2.57947e11i	0.843068	+	0.295002i	0.717047	−	0.697025i	$-0.245493\pi$
$967$	7.37171e11	+	2.57947e11i	0.843068	+	0.295002i	0.126021	+	0.992028i	$0.459779\pi$
$968$	6.43097e11	+	5.70764e12i	0.732445	+	6.50063i
$969$	4.48854e11	+	4.48854e11i	0.509108	+	0.509108i
$970$	1.56589e12	+	1.24875e12i	1.76878	+	1.41055i
$971$	5.82442e11	+	9.26951e11i	0.655203	+	1.04275i	0.994767	+	0.102167i	$0.0325775\pi$
$971$	5.82442e11	+	9.26951e11i	0.655203	+	1.04275i	−0.339564	+	0.940583i	$0.610280\pi$
$972$	−1.85259e12	+	1.16406e12i	−2.07546	+	1.30410i
$973$	−7.02001e11	+	8.80281e11i	−0.783224	+	0.982132i
$974$	−2.04507e12	+	2.04507e12i	−2.27233	+	2.27233i
$975$	−1.34022e11	+	1.51006e10i	−0.148305	+	0.0167100i
$976$	−1.33651e12	+	3.81952e12i	−1.47290	+	4.20929i
$977$	6.02017e11	+	7.54905e11i	0.660740	+	0.828542i	0.993424	−	0.114497i	$-0.0365256\pi$
$977$	6.02017e11	+	7.54905e11i	0.660740	+	0.828542i	−0.332684	+	0.943038i	$0.607954\pi$
$978$	−1.17383e12	−	1.32259e11i	−1.28307	−	0.144567i
$979$	1.32199e12	−	2.74514e12i	1.43912	−	2.98836i
$980$	1.95351e11	−	8.55890e11i	0.211793	−	0.927927i
$981$	−1.22839e11	−	5.38193e11i	−0.132636	−	0.581115i
$982$	1.31163e12	−	6.31650e11i	1.41048	−	0.679251i
$983$	−2.58295e11	−	7.38165e11i	−0.276632	−	0.790568i	−0.995443	−	0.0953623i	$-0.969599\pi$
$983$	−2.58295e11	−	7.38165e11i	−0.276632	−	0.790568i	0.718811	−	0.695206i	$-0.244687\pi$
$984$	1.97896e12	−	3.14950e12i	2.11085	−	3.35939i
$985$		−	1.43850e12i		−	1.52815i
$986$	−9.21916e11	−	4.52427e11i	−0.975402	−	0.478675i
$987$	−7.58939e11			−0.799721
$988$	−1.87597e12	−	1.17875e12i	−1.96878	−	1.23707i
$989$	−3.26112e11	+	1.14111e11i	−0.340864	+	0.119274i
$990$	−7.41511e11	−	1.53976e12i	−0.771928	−	1.60292i
$991$	−1.16081e12	+	2.64947e11i	−1.20356	+	0.274704i	−0.776849	−	0.629687i	$-0.783183\pi$
$991$	−1.16081e12	+	2.64947e11i	−1.20356	+	0.274704i	−0.426706	+	0.904390i	$0.640326\pi$
$992$	−9.36598e11	−	2.13772e11i	−0.967178	−	0.220752i
$993$	−2.28825e11	−	1.10196e11i	−0.235346	−	0.113337i
$994$	−2.35725e11	+	2.09212e12i	−0.241468	+	2.14309i
$995$	−1.29023e12	+	1.02893e12i	−1.31636	+	1.04976i
$996$	3.00877e12	+	1.05281e12i	3.05740	+	1.06983i
$997$	2.18372e10	+	1.93811e11i	0.0221013	+	0.196154i	0.999911	−	0.0133408i	$-0.00424663\pi$
$997$	2.18372e10	+	1.93811e11i	0.0221013	+	0.196154i	−0.977810	+	0.209495i	$0.932818\pi$
$998$	7.04258e11	+	7.04258e11i	0.709920	+	0.709920i
$999$	6.20482e11	+	4.94818e11i	0.622970	+	0.496802i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.9.f.a.3.1	✓	228
29.10	odd	28	inner	29.9.f.a.10.1	yes	228

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.9.f.a.3.1	✓	228	1.1	even	1	trivial
29.9.f.a.10.1	yes	228	29.10	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)

\(f(q)\)	\(=\)	\(q+(-25.9849 - 16.3274i) q^{2} +(93.5645 - 32.7396i) q^{3} +(297.558 + 617.886i) q^{4} +(-652.275 + 148.877i) q^{5} +(-2965.82 - 676.929i) q^{6} +(2496.53 + 1202.27i) q^{7} +(1476.82 - 13107.1i) q^{8} +(2552.84 - 2035.82i) q^{9} +O(q^{10})\)	\(q+(-25.9849 - 16.3274i) q^{2} +(93.5645 - 32.7396i) q^{3} +(297.558 + 617.886i) q^{4} +(-652.275 + 148.877i) q^{5} +(-2965.82 - 676.929i) q^{6} +(2496.53 + 1202.27i) q^{7} +(1476.82 - 13107.1i) q^{8} +(2552.84 - 2035.82i) q^{9} +(19380.1 + 6781.39i) q^{10} +(-2854.15 - 25331.3i) q^{11} +(48070.2 + 48070.2i) q^{12} +(-18661.6 - 14882.1i) q^{13} +(-45242.3 - 72002.8i) q^{14} +(-56155.6 + 35284.9i) q^{15} +(-142918. + 179213. i) q^{16} +(-33455.0 + 33455.0i) q^{17} +(-99575.0 + 11219.4i) q^{18} +(44702.5 - 127752. i) q^{19} +(-286079. - 358731. i) q^{20} +(272949. + 30753.9i) q^{21} +(-339429. + 704832. i) q^{22} +(36794.7 - 161208. i) q^{23} +(-290945. - 1.27471e6i) q^{24} +(51356.7 - 24732.1i) q^{25} +(241933. + 691405. i) q^{26} +(-173817. + 276627. i) q^{27} +1.90032e6i q^{28} +(-549688. - 445072. i) q^{29} +2.03531e6 q^{30} +(-222378. - 139729. i) q^{31} +(3.45262e6 - 1.20812e6i) q^{32} +(-1.09638e6 - 2.27666e6i) q^{33} +(1.41556e6 - 323092. i) q^{34} +(-1.80742e6 - 412531. i) q^{35} +(2.01752e6 + 971587. i) q^{36} +(271984. - 2.41392e6i) q^{37} +(-3.24746e6 + 2.58976e6i) q^{38} +(-2.23329e6 - 781463. i) q^{39} +(988065. + 8.76932e6i) q^{40} +(2.01161e6 + 2.01161e6i) q^{41} +(-6.59042e6 - 5.25569e6i) q^{42} +(-1.11166e6 - 1.76919e6i) q^{43} +(1.48026e7 - 9.30106e6i) q^{44} +(-1.36206e6 + 1.70797e6i) q^{45} +(-3.58822e6 + 3.58822e6i) q^{46} +(-2.74566e6 + 309362. i) q^{47} +(-7.50465e6 + 2.14471e7i) q^{48} +(1.19294e6 + 1.49590e6i) q^{49} +(-1.73831e6 - 195861. i) q^{50} +(-2.03490e6 + 4.22551e6i) q^{51} +(3.64254e6 - 1.59590e7i) q^{52} +(-1.91644e6 - 8.39647e6i) q^{53} +(9.03322e6 - 4.35017e6i) q^{54} +(5.63294e6 + 1.60980e7i) q^{55} +(1.94452e7 - 3.09469e7i) q^{56} -1.34166e7i q^{57} +(7.01672e6 + 2.05402e7i) q^{58} -1.05938e7 q^{59} +(-3.85116e7 - 2.41984e7i) q^{60} +(1.66630e7 - 5.83062e6i) q^{61} +(3.49706e6 + 7.26172e6i) q^{62} +(8.82085e6 - 2.01330e6i) q^{63} +(-5.22320e7 - 1.19216e7i) q^{64} +(1.43881e7 + 6.92893e6i) q^{65} +(-8.68259e6 + 7.70601e7i) q^{66} +(-7.31557e6 + 5.83397e6i) q^{67} +(-3.06262e7 - 1.07166e7i) q^{68} +(-1.83522e6 - 1.62880e7i) q^{69} +(4.02300e7 + 4.02300e7i) q^{70} +(-1.93567e7 - 1.54364e7i) q^{71} +(-2.29137e7 - 3.64669e7i) q^{72} +(-1.33793e7 + 8.40679e6i) q^{73} +(-4.64806e7 + 5.82848e7i) q^{74} +(3.99544e6 - 3.99544e6i) q^{75} +(9.22380e7 - 1.03927e7i) q^{76} +(2.33295e7 - 6.66718e7i) q^{77} +(4.52727e7 + 5.67702e7i) q^{78} +(-1.81723e7 - 2.04753e6i) q^{79} +(6.65408e7 - 1.38173e8i) q^{80} +(-1.19734e7 + 5.24591e7i) q^{81} +(-1.94272e7 - 8.51160e7i) q^{82} +(4.22464e7 - 2.03448e7i) q^{83} +(6.22157e7 + 1.77802e8i) q^{84} +(1.68412e7 - 2.68025e7i) q^{85} +6.41229e7i q^{86} +(-6.60028e7 - 2.36464e7i) q^{87} -3.36236e8 q^{88} +(1.01204e8 + 6.35910e7i) q^{89} +(6.32799e7 - 2.21426e7i) q^{90} +(-2.86970e7 - 5.95898e7i) q^{91} +(1.10557e8 - 2.52339e7i) q^{92} +(-2.53814e7 - 5.79314e6i) q^{93} +(7.63969e7 + 3.67908e7i) q^{94} +(-1.01389e7 + 8.99849e7i) q^{95} +(2.83489e8 - 2.26075e8i) q^{96} +(9.20721e7 + 3.22174e7i) q^{97} +(-6.57429e6 - 5.83485e7i) q^{98} +(-5.88561e7 - 5.88561e7i) 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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