LMFDB - Embedded newform 280.2.bv.e.213.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(117,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 3, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("280.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bv (of order $12$, degree $4$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			213.9
Character	$\chi$	$=$	280.213
Dual form			280.2.bv.e.117.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16877 + 0.796228i) q^{2} +(-2.48518 + 0.665902i) q^{3} +(0.732043 - 1.86121i) q^{4} +(-2.21132 - 0.331769i) q^{5} +(2.37439 - 2.75706i) q^{6} +(-2.18569 - 1.49090i) q^{7} +(0.626360 + 2.75820i) q^{8} +(3.13462 - 1.80978i) q^{9} +O(q^{10})$	\(q+(-1.16877 + 0.796228i) q^{2} +(-2.48518 + 0.665902i) q^{3} +(0.732043 - 1.86121i) q^{4} +(-2.21132 - 0.331769i) q^{5} +(2.37439 - 2.75706i) q^{6} +(-2.18569 - 1.49090i) q^{7} +(0.626360 + 2.75820i) q^{8} +(3.13462 - 1.80978i) q^{9} +(2.84868 - 1.37295i) q^{10} +(1.96732 + 1.13583i) q^{11} +(-0.579873 + 5.11292i) q^{12} +(-0.266469 - 0.266469i) q^{13} +(3.74166 + 0.00220981i) q^{14} +(5.71645 - 0.648016i) q^{15} +(-2.92823 - 2.72498i) q^{16} +(5.62393 - 1.50693i) q^{17} +(-2.22266 + 4.61108i) q^{18} +(-2.59772 + 1.49979i) q^{19} +(-2.23627 + 3.87287i) q^{20} +(6.42462 + 2.24969i) q^{21} +(-3.20372 + 0.238908i) q^{22} +(-1.99687 + 7.45242i) q^{23} +(-3.39331 - 6.43753i) q^{24} +(4.77986 + 1.46729i) q^{25} +(0.523611 + 0.0992708i) q^{26} +(-1.12713 + 1.12713i) q^{27} +(-4.37489 + 2.97663i) q^{28} +8.88892 q^{29} +(-6.16525 + 5.30898i) q^{30} +(-1.92658 - 1.11231i) q^{31} +(5.59212 + 0.853332i) q^{32} +(-5.64549 - 1.51270i) q^{33} +(-5.37322 + 6.23918i) q^{34} +(4.33862 + 4.02199i) q^{35} +(-1.07370 - 7.15903i) q^{36} +(0.654604 - 2.44302i) q^{37} +(1.84196 - 3.82129i) q^{38} +(0.839667 + 0.484782i) q^{39} +(-0.469996 - 6.30707i) q^{40} -0.631279i q^{41} +(-9.30017 + 2.48609i) q^{42} +(7.46831 - 7.46831i) q^{43} +(3.55418 - 2.83012i) q^{44} +(-7.53208 + 2.96202i) q^{45} +(-3.59995 - 10.3001i) q^{46} +(1.07540 - 4.01346i) q^{47} +(9.09174 + 4.82214i) q^{48} +(2.55445 + 6.51727i) q^{49} +(-6.75485 + 2.09093i) q^{50} +(-12.9730 + 7.48998i) q^{51} +(-0.691023 + 0.300889i) q^{52} +(-0.645780 - 2.41008i) q^{53} +(0.419905 - 2.21482i) q^{54} +(-3.97353 - 3.16438i) q^{55} +(2.74317 - 6.96240i) q^{56} +(5.45708 - 5.45708i) q^{57} +(-10.3891 + 7.07760i) q^{58} +(1.38162 + 0.797678i) q^{59} +(2.97859 - 11.1139i) q^{60} +(-3.61096 - 6.25437i) q^{61} +(3.13738 - 0.233961i) q^{62} +(-9.54949 - 0.717797i) q^{63} +(-7.21535 + 3.45525i) q^{64} +(0.500842 + 0.677654i) q^{65} +(7.80273 - 2.72709i) q^{66} +(3.68507 - 0.987412i) q^{67} +(1.31225 - 11.5705i) q^{68} -19.8503i q^{69} +(-8.27326 - 1.24625i) q^{70} -7.81014 q^{71} +(6.95513 + 7.51235i) q^{72} +(0.809910 + 3.02262i) q^{73} +(1.18012 + 3.37654i) q^{74} +(-12.8559 - 0.463573i) q^{75} +(0.889793 + 5.93282i) q^{76} +(-2.60653 - 5.41563i) q^{77} +(-1.36737 + 0.101968i) q^{78} +(14.7923 - 8.54036i) q^{79} +(5.57118 + 6.99728i) q^{80} +(-3.37875 + 5.85217i) q^{81} +(0.502642 + 0.737820i) q^{82} +(8.50310 + 8.50310i) q^{83} +(8.89026 - 10.3107i) q^{84} +(-12.9363 + 1.46645i) q^{85} +(-2.78226 + 14.6752i) q^{86} +(-22.0906 + 5.91915i) q^{87} +(-1.90060 + 6.13769i) q^{88} +(3.06855 + 5.31488i) q^{89} +(6.44482 - 9.45916i) q^{90} +(0.185140 + 0.979696i) q^{91} +(12.4088 + 9.17210i) q^{92} +(5.52859 + 1.48138i) q^{93} +(1.93873 + 5.54707i) q^{94} +(6.24197 - 2.45468i) q^{95} +(-14.4657 + 1.60312i) q^{96} +(7.08893 + 7.08893i) q^{97} +(-8.17480 - 5.58325i) q^{98} +8.22239 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} + 12 q^{7} + 4 q^{8}+O(q^{10}) $ 160 * q - 2 * q^2 + 12 * q^7 + 4 * q^8	$ 160 q - 2 q^{2} + 12 q^{7} + 4 q^{8} - 6 q^{10} + 6 q^{12} - 8 q^{15} + 4 q^{16} - 12 q^{17} - 28 q^{18} - 24 q^{22} - 16 q^{23} + 20 q^{25} - 12 q^{26} - 46 q^{28} + 32 q^{30} + 48 q^{31} + 18 q^{32} - 12 q^{33} - 32 q^{36} - 48 q^{38} + 54 q^{40} + 6 q^{42} - 64 q^{46} - 132 q^{47} - 12 q^{50} - 20 q^{56} - 88 q^{57} + 6 q^{58} + 34 q^{60} - 32 q^{63} - 28 q^{65} - 180 q^{66} + 60 q^{68} - 108 q^{70} - 160 q^{71} + 52 q^{72} + 84 q^{73} + 48 q^{78} - 48 q^{80} + 16 q^{81} - 90 q^{82} - 84 q^{86} - 12 q^{87} + 44 q^{88} + 36 q^{92} - 20 q^{95} - 48 q^{96} - 94 q^{98}+O(q^{100}) $ 160 * q - 2 * q^2 + 12 * q^7 + 4 * q^8 - 6 * q^10 + 6 * q^12 - 8 * q^15 + 4 * q^16 - 12 * q^17 - 28 * q^18 - 24 * q^22 - 16 * q^23 + 20 * q^25 - 12 * q^26 - 46 * q^28 + 32 * q^30 + 48 * q^31 + 18 * q^32 - 12 * q^33 - 32 * q^36 - 48 * q^38 + 54 * q^40 + 6 * q^42 - 64 * q^46 - 132 * q^47 - 12 * q^50 - 20 * q^56 - 88 * q^57 + 6 * q^58 + 34 * q^60 - 32 * q^63 - 28 * q^65 - 180 * q^66 + 60 * q^68 - 108 * q^70 - 160 * q^71 + 52 * q^72 + 84 * q^73 + 48 * q^78 - 48 * q^80 + 16 * q^81 - 90 * q^82 - 84 * q^86 - 12 * q^87 + 44 * q^88 + 36 * q^92 - 20 * q^95 - 48 * q^96 - 94 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.16877	+	0.796228i	−0.826445	+	0.563018i
$2$	−1.16877	+	0.796228i	−0.826445	+	0.563018i
$3$	−2.48518	+	0.665902i	−1.43482	+	0.384459i	−0.890716	−	0.454559i	$-0.849797\pi$
$3$	−2.48518	+	0.665902i	−1.43482	+	0.384459i	−0.544103	+	0.839018i	$0.683130\pi$
$4$	0.732043	−	1.86121i	0.366021	−	0.930606i
$5$	−2.21132	−	0.331769i	−0.988932	−	0.148372i
$5$	−2.21132	−	0.331769i	−0.988932	−	0.148372i
$6$	2.37439	−	2.75706i	0.969342	−	1.12556i
$7$	−2.18569	−	1.49090i	−0.826112	−	0.563506i
$7$	−2.18569	−	1.49090i	−0.826112	−	0.563506i
$8$	0.626360	+	2.75820i	0.221452	+	0.975171i
$9$	3.13462	−	1.80978i	1.04487	−	0.603258i
$10$	2.84868	−	1.37295i	0.900833	−	0.434165i
$11$	1.96732	+	1.13583i	0.593168	+	0.342466i	0.766349	−	0.642424i	$-0.222071\pi$
$11$	1.96732	+	1.13583i	0.593168	+	0.342466i	−0.173181	+	0.984890i	$0.555405\pi$
$12$	−0.579873	+	5.11292i	−0.167395	+	1.47597i
$13$	−0.266469	−	0.266469i	−0.0739053	−	0.0739053i	0.669188	−	0.743093i	$-0.266642\pi$
$13$	−0.266469	−	0.266469i	−0.0739053	−	0.0739053i	−0.743093	+	0.669188i	$0.766642\pi$
$14$	3.74166	+	0.00220981i	1.00000	+	0.000590596i
$15$	5.71645	−	0.648016i	1.47598	−	0.167317i
$16$	−2.92823	−	2.72498i	−0.732057	−	0.681244i
$17$	5.62393	−	1.50693i	1.36400	−	0.365484i	0.498719	−	0.866764i	$-0.333804\pi$
$17$	5.62393	−	1.50693i	1.36400	−	0.365484i	0.865285	+	0.501280i	$0.167137\pi$
$18$	−2.22266	+	4.61108i	−0.523885	+	1.08684i
$19$	−2.59772	+	1.49979i	−0.595957	+	0.344076i	−0.767450	−	0.641109i	$-0.778474\pi$
$19$	−2.59772	+	1.49979i	−0.595957	+	0.344076i	0.171492	+	0.985185i	$0.445141\pi$
$20$	−2.23627	+	3.87287i	−0.500046	+	0.865999i
$21$	6.42462	+	2.24969i	1.40197	+	0.490924i
$22$	−3.20372	+	0.238908i	−0.683035	+	0.0509353i
$23$	−1.99687	+	7.45242i	−0.416376	+	1.55394i	0.365686	+	0.930738i	$0.380834\pi$
$23$	−1.99687	+	7.45242i	−0.416376	+	1.55394i	−0.782063	+	0.623200i	$0.785832\pi$
$24$	−3.39331	−	6.43753i	−0.692657	−	1.31406i
$25$	4.77986	+	1.46729i	0.955972	+	0.293459i
$26$	0.523611	+	0.0992708i	0.102689	+	0.0194686i
$27$	−1.12713	+	1.12713i	−0.216917	+	0.216917i
$28$	−4.37489	+	2.97663i	−0.826777	+	0.562530i
$29$	8.88892			1.65063			0.825315	−	0.564672i	$-0.190997\pi$
$29$	8.88892			1.65063			0.825315	+	0.564672i	$0.190997\pi$
$30$	−6.16525	+	5.30898i	−1.12561	+	0.969282i
$31$	−1.92658	−	1.11231i	−0.346024	−	0.199777i	0.316909	−	0.948456i	$-0.397355\pi$
$31$	−1.92658	−	1.11231i	−0.346024	−	0.199777i	−0.662933	+	0.748679i	$0.730688\pi$
$32$	5.59212	+	0.853332i	0.988557	+	0.150849i
$33$	−5.64549	−	1.51270i	−0.982753	−	0.263328i
$34$	−5.37322	+	6.23918i	−0.921500	+	1.07001i
$35$	4.33862	+	4.02199i	0.733360	+	0.679841i
$36$	−1.07370	−	7.15903i	−0.178950	−	1.19317i
$37$	0.654604	−	2.44302i	0.107616	−	0.401630i	−0.891013	−	0.453979i	$-0.850004\pi$
$37$	0.654604	−	2.44302i	0.107616	−	0.401630i	0.998629	+	0.0523492i	$0.0166709\pi$
$38$	1.84196	−	3.82129i	0.298805	−	0.619894i
$39$	0.839667	+	0.484782i	0.134454	+	0.0776272i
$40$	−0.469996	−	6.30707i	−0.0743129	−	0.997235i
$41$		−	0.631279i		−	0.0985893i	−0.998784	−	0.0492946i	$-0.984303\pi$
$41$		−	0.631279i		−	0.0985893i	0.998784	−	0.0492946i	$-0.0156973\pi$
$42$	−9.30017	+	2.48609i	−1.43505	+	0.383611i
$43$	7.46831	−	7.46831i	1.13891	−	1.13891i	0.150261	−	0.988646i	$-0.451989\pi$
$43$	7.46831	−	7.46831i	1.13891	−	1.13891i	0.988646	−	0.150261i	$-0.0480113\pi$
$44$	3.55418	−	2.83012i	0.535813	−	0.426656i
$45$	−7.53208	+	2.96202i	−1.12282	+	0.441552i
$46$	−3.59995	−	10.3001i	−0.530783	−	1.51867i
$47$	1.07540	−	4.01346i	0.156864	−	0.585423i	−0.842075	−	0.539360i	$-0.818666\pi$
$47$	1.07540	−	4.01346i	0.156864	−	0.585423i	0.998939	−	0.0460623i	$-0.0146673\pi$
$48$	9.09174	+	4.82214i	1.31228	+	0.696016i
$49$	2.55445	+	6.51727i	0.364922	+	0.931038i
$50$	−6.75485	+	2.09093i	−0.955280	+	0.295702i
$51$	−12.9730	+	7.48998i	−1.81659	+	1.04881i
$52$	−0.691023	+	0.300889i	−0.0958276	+	0.0417258i
$53$	−0.645780	−	2.41008i	−0.0887047	−	0.331050i	0.907285	−	0.420516i	$-0.138151\pi$
$53$	−0.645780	−	2.41008i	−0.0887047	−	0.331050i	−0.995990	+	0.0894653i	$0.971484\pi$
$54$	0.419905	−	2.21482i	0.0571418	−	0.301398i
$55$	−3.97353	−	3.16438i	−0.535791	−	0.426685i
$56$	2.74317	−	6.96240i	0.366571	−	0.930390i
$57$	5.45708	−	5.45708i	0.722808	−	0.722808i
$58$	−10.3891	+	7.07760i	−1.36415	+	0.929335i
$59$	1.38162	+	0.797678i	0.179871	+	0.103849i	0.587232	−	0.809418i	$-0.300218\pi$
$59$	1.38162	+	0.797678i	0.179871	+	0.103849i	−0.407361	+	0.913267i	$0.633551\pi$
$60$	2.97859	−	11.1139i	0.384535	−	1.43480i
$61$	−3.61096	−	6.25437i	−0.462337	−	0.800791i	0.536740	−	0.843748i	$-0.319656\pi$
$61$	−3.61096	−	6.25437i	−0.462337	−	0.800791i	−0.999077	+	0.0429569i	$0.986322\pi$
$62$	3.13738	−	0.233961i	0.398448	−	0.0297131i
$63$	−9.54949	−	0.717797i	−1.20312	−	0.0904339i
$64$	−7.21535	+	3.45525i	−0.901918	+	0.431907i
$65$	0.500842	+	0.677654i	0.0621218	+	0.0840527i
$66$	7.80273	−	2.72709i	0.960450	−	0.335682i
$67$	3.68507	−	0.987412i	0.450203	−	0.120632i	−0.0265912	−	0.999646i	$-0.508465\pi$
$67$	3.68507	−	0.987412i	0.450203	−	0.120632i	0.476794	+	0.879015i	$0.341799\pi$
$68$	1.31225	−	11.5705i	0.159133	−	1.40313i
$69$		−	19.8503i		−	2.38970i
$70$	−8.27326	−	1.24625i	−0.988844	−	0.148956i
$71$	−7.81014			−0.926893			−0.463447	−	0.886125i	$-0.653387\pi$
$71$	−7.81014			−0.926893			−0.463447	+	0.886125i	$0.653387\pi$
$72$	6.95513	+	7.51235i	0.819670	+	0.885339i
$73$	0.809910	+	3.02262i	0.0947928	+	0.353771i	0.996988	−	0.0775566i	$-0.0247118\pi$
$73$	0.809910	+	3.02262i	0.0947928	+	0.353771i	−0.902195	+	0.431328i	$0.858045\pi$
$74$	1.18012	+	3.37654i	0.137186	+	0.392514i
$75$	−12.8559	−	0.463573i	−1.48447	−	0.0535288i
$76$	0.889793	+	5.93282i	0.102066	+	0.680541i
$77$	−2.60653	−	5.41563i	−0.297042	−	0.617169i
$78$	−1.36737	+	0.101968i	−0.154825	+	0.0115456i
$79$	14.7923	−	8.54036i	1.66427	−	0.960865i	0.693626	−	0.720335i	$-0.256012\pi$
$79$	14.7923	−	8.54036i	1.66427	−	0.960865i	0.970642	−	0.240530i	$-0.0773212\pi$
$80$	5.57118	+	6.99728i	0.622877	+	0.782320i
$81$	−3.37875	+	5.85217i	−0.375417	+	0.650241i
$82$	0.502642	+	0.737820i	0.0555075	+	0.0814786i
$83$	8.50310	+	8.50310i	0.933336	+	0.933336i	0.997913	−	0.0645764i	$-0.0205696\pi$
$83$	8.50310	+	8.50310i	0.933336	+	0.933336i	−0.0645764	+	0.997913i	$0.520570\pi$
$84$	8.89026	−	10.3107i	0.970007	−	1.12499i
$85$	−12.9363	+	1.46645i	−1.40313	+	0.159059i
$86$	−2.78226	+	14.6752i	−0.300018	+	1.58247i
$87$	−22.0906	+	5.91915i	−2.36836	+	0.634599i
$88$	−1.90060	+	6.13769i	−0.202605	+	0.654280i
$89$	3.06855	+	5.31488i	0.325265	+	0.563376i	0.981566	−	0.191123i	$-0.0612130\pi$
$89$	3.06855	+	5.31488i	0.325265	+	0.563376i	−0.656301	+	0.754500i	$0.727880\pi$
$90$	6.44482	−	9.45916i	0.679343	−	0.997083i
$91$	0.185140	+	0.979696i	0.0194080	+	0.102700i
$92$	12.4088	+	9.17210i	1.29370	+	0.956257i
$93$	5.52859	+	1.48138i	0.573288	+	0.153612i
$94$	1.93873	+	5.54707i	0.199965	+	0.572137i
$95$	6.24197	−	2.45468i	0.640412	−	0.251845i
$96$	−14.4657	+	1.60312i	−1.47640	+	0.163618i
$97$	7.08893	+	7.08893i	0.719772	+	0.719772i	0.968558	−	0.248787i	$-0.0800318\pi$
$97$	7.08893	+	7.08893i	0.719772	+	0.719772i	−0.248787	+	0.968558i	$0.580032\pi$
$98$	−8.17480	−	5.58325i	−0.825779	−	0.563994i
$99$	8.22239			0.826381
$100$	6.23001	−	7.82221i	0.623001	−	0.782221i
$101$	−0.992304	+	1.71872i	−0.0987380	+	0.171019i	−0.911163	−	0.412047i	$-0.864814\pi$
$101$	−0.992304	+	1.71872i	−0.0987380	+	0.171019i	0.812425	+	0.583066i	$0.198147\pi$
$102$	9.19874	−	19.0835i	0.910811	−	1.88955i
$103$	9.25736	+	2.48050i	0.912154	+	0.244411i	0.684229	−	0.729267i	$-0.260139\pi$
$103$	9.25736	+	2.48050i	0.912154	+	0.244411i	0.227926	+	0.973679i	$0.426806\pi$
$104$	0.568070	−	0.901881i	0.0557038	−	0.0884367i
$105$	−13.4605	−	7.10628i	−1.31361	−	0.693502i
$106$	2.67374	+	2.30264i	0.259697	+	0.223652i
$107$	−0.0651921	+	0.243300i	−0.00630236	+	0.0235207i	−0.969005	−	0.247040i	$-0.920542\pi$
$107$	−0.0651921	+	0.243300i	−0.00630236	+	0.0235207i	0.962703	+	0.270560i	$0.0872089\pi$
$108$	1.27273	+	2.92295i	0.122468	+	0.281261i
$109$	−6.40394	+	11.0919i	−0.613386	+	1.06242i	0.377280	+	0.926099i	$0.376860\pi$
$109$	−6.40394	+	11.0919i	−0.613386	+	1.06242i	−0.990665	+	0.136316i	$0.956474\pi$
$110$	7.16370	+	0.534593i	0.683032	+	0.0509714i
$111$			6.50724i			0.617640i
$112$	2.33753	+	10.3216i	0.220876	+	0.975302i
$113$	−10.0319	−	10.0319i	−0.943721	−	0.943721i	0.0547780	−	0.998499i	$-0.482555\pi$
$113$	−10.0319	−	10.0319i	−0.943721	−	0.943721i	−0.998499	+	0.0547780i	$0.982555\pi$
$114$	−2.03299	+	10.7231i	−0.190407	+	1.00432i
$115$	6.88820	−	15.8172i	0.642328	−	1.47496i
$116$	6.50707	−	16.5442i	0.604166	−	1.53609i
$117$	−1.31753	−	0.353031i	−0.121806	−	0.0326377i
$118$	−2.24993	+	0.167782i	−0.207123	+	0.0154456i
$119$	−14.5388	−	5.09103i	−1.33277	−	0.466694i
$120$	5.36792	+	15.3612i	0.490021	+	1.40228i
$121$	−2.91978	−	5.05720i	−0.265434	−	0.459746i
$122$	9.20029	+	4.43477i	0.832955	+	0.401505i
$123$	0.420370	+	1.56884i	0.0379035	+	0.141458i
$124$	−3.48059	+	2.77152i	−0.312566	+	0.248890i
$125$	−10.0830	−	4.83046i	−0.901850	−	0.432050i
$126$	11.7327	−	6.76463i	1.04523	−	0.602641i
$127$	1.73859	−	1.73859i	0.154275	−	0.154275i	−0.625749	−	0.780024i	$-0.715207\pi$
$127$	1.73859	−	1.73859i	0.154275	−	0.154275i	0.780024	+	0.625749i	$0.215207\pi$
$128$	5.68190	−	9.78345i	0.502214	−	0.864743i
$129$	−13.5869	+	23.5333i	−1.19626	+	2.07199i
$130$	−1.12494	−	0.393237i	−0.0986634	−	0.0344892i
$131$	9.62714	+	16.6747i	0.841127	+	1.45687i	0.888943	+	0.458018i	$0.151441\pi$
$131$	9.62714	+	16.6747i	0.841127	+	1.45687i	−0.0478159	+	0.998856i	$0.515226\pi$
$132$	−6.94820	+	9.40009i	−0.604764	+	0.818173i
$133$	7.91383	+	0.594851i	0.686216	+	0.0515801i
$134$	−3.52079	+	4.08821i	−0.304150	+	0.353168i
$135$	2.86640	−	2.11851i	0.246701	−	0.182332i
$136$	7.67902	+	14.5681i	0.658470	+	1.24920i
$137$	2.58733	+	9.65606i	0.221051	+	0.824973i	0.983948	+	0.178453i	$0.0571094\pi$
$137$	2.58733	+	9.65606i	0.221051	+	0.824973i	−0.762898	+	0.646519i	$0.776224\pi$
$138$	15.8054	+	23.2005i	1.34544	+	1.97496i
$139$			0.593011i			0.0502985i	0.999684	+	0.0251493i	$0.00800610\pi$
$139$			0.593011i			0.0502985i	−0.999684	+	0.0251493i	$0.991994\pi$
$140$	10.6618	−	5.13082i	0.901089	−	0.433633i
$141$			10.6903i			0.900284i
$142$	9.12825	−	6.21865i	0.766026	−	0.521858i
$143$	−0.221565	−	0.826893i	−0.0185282	−	0.0691483i
$144$	−14.1105	−	3.24234i	−1.17587	−	0.270195i
$145$	−19.6562	−	2.94907i	−1.63236	−	0.244907i
$146$	−3.35329	−	2.88788i	−0.277521	−	0.239002i
$147$	−10.6881	−	14.4956i	−0.881543	−	1.19557i
$148$	−4.06778	−	3.00675i	−0.334369	−	0.247153i
$149$	8.73650	+	15.1321i	0.715722	+	1.23967i	0.962680	+	0.270641i	$0.0872356\pi$
$149$	8.73650	+	15.1321i	0.715722	+	1.23967i	−0.246958	+	0.969026i	$0.579431\pi$
$150$	15.3947	−	9.69441i	1.25697	−	0.791545i
$151$	5.11662	−	8.86224i	0.416385	−	0.721199i	−0.579188	−	0.815194i	$-0.696630\pi$
$151$	5.11662	−	8.86224i	0.416385	−	0.721199i	0.995573	+	0.0939947i	$0.0299637\pi$
$152$	−5.76384	−	6.22562i	−0.467509	−	0.504964i
$153$	14.9017	−	14.9017i	1.20473	−	1.20473i
$154$	7.35851	+	4.25424i	0.592966	+	0.342816i
$155$	3.89125	+	3.09886i	0.312553	+	0.248906i
$156$	1.51695	−	1.20792i	0.121454	−	0.0967108i
$157$	3.01367	+	11.2472i	0.240517	+	0.897621i	0.975584	+	0.219627i	$0.0704839\pi$
$157$	3.01367	+	11.2472i	0.240517	+	0.897621i	−0.735067	+	0.677994i	$0.762849\pi$
$158$	−10.4888	+	21.7598i	−0.834441	+	1.73111i
$159$	3.20976	+	5.55947i	0.254550	+	0.440894i
$160$	−12.0829	−	3.74228i	−0.955233	−	0.295853i
$161$	15.4753	−	13.3115i	1.21963	−	1.04910i
$162$	−0.710679	−	9.53009i	−0.0558362	−	0.748755i
$163$	−16.6963	−	4.47376i	−1.30775	−	0.350412i	−0.463378	−	0.886161i	$-0.653363\pi$
$163$	−16.6963	−	4.47376i	−1.30775	−	0.350412i	−0.844377	+	0.535749i	$0.820029\pi$
$164$	−1.17495	−	0.462123i	−0.0917478	−	0.0360858i
$165$	11.9821	+	5.21807i	0.932806	+	0.406226i
$166$	−16.7086	−	3.16776i	−1.29684	−	0.245866i
$167$	−0.291949	−	0.291949i	−0.0225917	−	0.0225917i	0.695721	−	0.718312i	$-0.255085\pi$
$167$	−0.291949	−	0.291949i	−0.0225917	−	0.0225917i	−0.718312	+	0.695721i	$0.755085\pi$
$168$	−2.18098	+	19.1295i	−0.168267	+	1.47587i
$169$		−	12.8580i		−	0.989076i
$170$	13.9519	−	12.0142i	1.07006	−	0.921443i
$171$	−5.42858	+	9.40257i	−0.415134	+	0.719032i
$172$	−8.43300	−	19.3672i	−0.643010	−	1.47674i
$173$	2.34863	−	8.76520i	0.178563	−	0.666406i	−0.817354	−	0.576135i	$-0.804560\pi$
$173$	2.34863	−	8.76520i	0.178563	−	0.666406i	0.995917	−	0.0902708i	$-0.0287732\pi$
$174$	21.1058	−	24.5072i	1.60003	−	1.85789i
$175$	−8.25969	−	10.3333i	−0.624374	−	0.781126i
$176$	−2.66564	−	8.68686i	−0.200930	−	0.654796i
$177$	−3.96475	−	1.06235i	−0.298009	−	0.0798512i
$178$	−7.81828	−	3.76861i	−0.586005	−	0.282469i
$179$	5.02822	−	8.70913i	0.375827	−	0.650951i	−0.614624	−	0.788821i	$-0.710692\pi$
$179$	5.02822	−	8.70913i	0.375827	−	0.650951i	0.990450	+	0.137869i	$0.0440254\pi$
$180$	−0.000855305		16.1871i	−6.37507e−5		1.20652i
$181$	15.6839			1.16578			0.582888	−	0.812553i	$-0.301923\pi$
$181$	15.6839			1.16578			0.582888	+	0.812553i	$0.301923\pi$
$182$	−0.996447	−	0.997625i	−0.0738616	−	0.0739489i
$183$	13.1387	+	13.1387i	0.971241	+	0.971241i
$184$	−21.8060	−	0.839870i	−1.60756	−	0.0619160i
$185$	−2.25806	+	5.18511i	−0.166016	+	0.381217i
$186$	−7.64117	+	2.67063i	−0.560277	+	0.195820i
$187$	12.7757	+	3.42323i	0.934249	+	0.250331i
$188$	−6.68266	−	4.93957i	−0.487383	−	0.360256i
$189$	4.14401	−	0.783122i	0.301432	−	0.0569638i
$190$	−5.34093	+	7.83898i	−0.387472	+	0.568699i
$191$	5.25829	+	9.10763i	0.380477	+	0.659005i	0.991130	−	0.132893i	$-0.0424267\pi$
$191$	5.25829	+	9.10763i	0.380477	+	0.659005i	−0.610654	+	0.791898i	$0.709093\pi$
$192$	15.6306	−	13.3916i	1.12804	−	0.966459i
$193$	10.2673	−	2.75110i	0.739054	−	0.198029i	0.130396	−	0.991462i	$-0.458375\pi$
$193$	10.2673	−	2.75110i	0.739054	−	0.198029i	0.608657	+	0.793433i	$0.291708\pi$
$194$	−13.9297	−	2.64092i	−1.00010	−	0.189607i
$195$	−1.69593	−	1.35058i	−0.121448	−	0.0967172i
$196$	14.0000	+	0.0165367i	0.999999	+	0.00118119i
$197$	−1.31944	−	1.31944i	−0.0940062	−	0.0940062i	0.658540	−	0.752546i	$-0.271174\pi$
$197$	−1.31944	−	1.31944i	−0.0940062	−	0.0940062i	−0.752546	+	0.658540i	$0.771174\pi$
$198$	−9.61008	+	6.54690i	−0.682958	+	0.465268i
$199$	−0.660921	+	1.14475i	−0.0468514	+	0.0811491i	−0.888500	−	0.458876i	$-0.848252\pi$
$199$	−0.660921	+	1.14475i	−0.0468514	+	0.0811491i	0.841649	+	0.540025i	$0.181585\pi$
$200$	−1.05318	+	14.1029i	−0.0744710	+	0.997223i
$201$	−8.50055	+	4.90780i	−0.599583	+	0.346169i
$202$	−0.208719	−	2.79889i	−0.0146854	−	0.196929i
$203$	−19.4284	−	13.2525i	−1.36361	−	0.930140i
$204$	4.44364	+	29.6285i	0.311117	+	2.07441i
$205$	−0.209439	+	1.39596i	−0.0146278	+	0.0974980i
$206$	−12.7948	+	4.47183i	−0.891453	+	0.311567i
$207$	7.22778	+	26.9744i	0.502365	+	1.87485i
$208$	0.0541603	+	1.50640i	0.00375534	+	0.104450i
$209$	−6.81404			−0.471337
$210$	21.3904	−	2.41202i	1.47608	−	0.166445i
$211$			6.65971i			0.458473i	0.973371	+	0.229237i	$0.0736229\pi$
$211$			6.65971i			0.458473i	−0.973371	+	0.229237i	$0.926377\pi$
$212$	−4.95842	−	0.562350i	−0.340545	−	0.0386224i
$213$	19.4096	−	5.20079i	1.32992	−	0.356352i
$214$	−0.117528	−	0.336270i	−0.00803404	−	0.0229869i
$215$	−18.9926	+	14.0371i	−1.29528	+	0.957320i
$216$	−3.81486	−	2.40287i	−0.259568	−	0.163495i
$217$	2.55256	+	5.30350i	0.173279	+	0.360025i
$218$	−1.34699	−	18.0629i	−0.0912296	−	1.22337i
$219$	−4.02554	−	6.97245i	−0.272021	−	0.471154i
$220$	−8.79837	+	5.07912i	−0.593186	+	0.342434i
$221$	−1.90015	−	1.09705i	−0.127818	−	0.0737959i
$222$	−5.18125	−	7.60546i	−0.347742	−	0.510445i
$223$	2.20733	−	2.20733i	0.147814	−	0.147814i	−0.629327	−	0.777141i	$-0.716669\pi$
$223$	2.20733	−	2.20733i	0.147814	−	0.147814i	0.777141	+	0.629327i	$0.216669\pi$
$224$	−10.9504	−	10.2024i	−0.731654	−	0.681676i
$225$	17.6385	−	4.05106i	1.17590	−	0.270070i
$226$	19.7126	+	3.73729i	1.31126	+	0.248601i
$227$	−5.79069	−	21.6111i	−0.384341	−	1.43438i	−0.839203	−	0.543819i	$-0.816978\pi$
$227$	−5.79069	−	21.6111i	−0.384341	−	1.43438i	0.454861	−	0.890562i	$-0.349689\pi$
$228$	−6.16197	−	14.1516i	−0.408087	−	0.937213i
$229$	8.05287	−	4.64933i	0.532149	−	0.307236i	−0.209742	−	0.977757i	$-0.567262\pi$
$229$	8.05287	−	4.64933i	0.532149	−	0.307236i	0.741891	+	0.670520i	$0.233929\pi$
$230$	4.54336	+	23.9712i	0.299580	+	1.58061i
$231$	10.0840	+	11.7231i	0.663477	+	0.771326i
$232$	5.56766	+	24.5174i	0.365535	+	1.60965i
$233$	−4.26849	+	15.9302i	−0.279638	+	1.04362i	0.673031	+	0.739614i	$0.264992\pi$
$233$	−4.26849	+	15.9302i	−0.279638	+	1.04362i	−0.952669	+	0.304009i	$0.901675\pi$
$234$	1.82098	−	0.636442i	0.119041	−	0.0416055i
$235$	−3.70960	+	8.51824i	−0.241987	+	0.555669i
$236$	2.49605	−	1.98755i	0.162479	−	0.129379i
$237$	−31.0746	+	31.0746i	−2.01851	+	2.01851i
$238$	21.0462	−	5.62598i	1.36422	−	0.364678i
$239$		−	12.4926i		−	0.808078i	−0.914742	−	0.404039i	$-0.867606\pi$
$239$		−	12.4926i		−	0.808078i	0.914742	−	0.404039i	$-0.132394\pi$
$240$	−18.5049	−	13.6797i	−1.19449	−	0.883018i
$241$	−15.5296	−	8.96602i	−1.00035	−	0.577552i	−0.0919978	−	0.995759i	$-0.529325\pi$
$241$	−15.5296	−	8.96602i	−1.00035	−	0.577552i	−0.908352	+	0.418207i	$0.862659\pi$
$242$	7.43923	+	3.58590i	0.478212	+	0.230510i
$243$	5.73752	−	21.4127i	0.368062	−	1.37363i
$244$	−14.2841	+	2.14230i	−0.914446	+	0.137147i
$245$	−3.48648	−	15.2592i	−0.222743	−	0.974877i
$246$	−1.74047	−	1.49891i	−0.110968	−	0.0955667i
$247$	1.09186	+	0.292563i	0.0694734	+	0.0186153i
$248$	1.86125	−	6.01060i	0.118189	−	0.381674i
$249$	−26.7940	−	15.4695i	−1.69800	−	0.980340i
$250$	15.6308	−	2.38266i	0.988581	−	0.150692i
$251$	15.7482			0.994015			0.497007	−	0.867746i	$-0.334432\pi$
$251$	15.7482			0.994015			0.497007	+	0.867746i	$0.334432\pi$
$252$	−8.32661	+	17.2482i	−0.524527	+	1.08653i
$253$	−12.3932	+	12.3932i	−0.779152	+	0.779152i
$254$	−0.647698	+	3.41633i	−0.0406402	+	0.214360i
$255$	31.1724	−	12.2587i	1.95209	−	0.767668i
$256$	1.14902	+	15.9587i	0.0718139	+	0.997418i
$257$	7.30733	−	27.2713i	0.455818	−	1.70114i	−0.229852	−	0.973226i	$-0.573824\pi$
$257$	7.30733	−	27.2713i	0.455818	−	1.70114i	0.685671	−	0.727912i	$-0.259509\pi$
$258$	−2.85785	−	38.3233i	−0.177922	−	2.38590i
$259$	−5.07305	+	4.36372i	−0.315224	+	0.271149i
$260$	1.62790	−	0.436101i	0.100958	−	0.0270459i
$261$	27.8634	−	16.0869i	1.72470	−	0.995757i
$262$	−24.5288	−	11.8235i	−1.51539	−	0.730456i
$263$	−1.15767	+	0.310196i	−0.0713848	+	0.0191275i	−0.294335	−	0.955702i	$-0.595098\pi$
$263$	−1.15767	+	0.310196i	−0.0713848	+	0.0191275i	0.222950	+	0.974830i	$0.428431\pi$
$264$	0.636233	−	16.5189i	0.0391574	−	1.01667i
$265$	0.628434	+	5.54371i	0.0386044	+	0.340547i
$266$	−9.72308	+	5.60597i	−0.596160	+	0.343724i
$267$	−11.1651	−	11.1651i	−0.683292	−	0.683292i
$268$	0.859847	−	7.58153i	0.0525235	−	0.463116i
$269$	−12.5767	−	7.26116i	−0.766814	−	0.442721i	0.0649226	−	0.997890i	$-0.479320\pi$
$269$	−12.5767	−	7.26116i	−0.766814	−	0.442721i	−0.831737	+	0.555170i	$0.812653\pi$
$270$	−1.66335	+	4.75835i	−0.101228	+	0.289584i
$271$	22.1123	−	12.7665i	1.34323	−	0.775512i	0.355947	−	0.934506i	$-0.384158\pi$
$271$	22.1123	−	12.7665i	1.34323	−	0.775512i	0.987280	+	0.158994i	$0.0508251\pi$
$272$	−20.5745	−	10.9125i	−1.24751	−	0.661664i
$273$	−1.11249	−	2.31144i	−0.0673309	−	0.139895i
$274$	−10.7124	−	9.22560i	−0.647161	−	0.557339i
$275$	7.73690	+	8.31574i	0.466552	+	0.501458i
$276$	−36.9457	−	14.5313i	−2.22387	−	0.874682i
$277$	−2.27883	+	0.610610i	−0.136922	+	0.0366880i	−0.326629	−	0.945153i	$-0.605913\pi$
$277$	−2.27883	+	0.610610i	−0.136922	+	0.0366880i	0.189707	+	0.981841i	$0.439246\pi$
$278$	−0.472171	−	0.693093i	−0.0283190	−	0.0415689i
$279$	−8.05214			−0.482069
$280$	−8.37592	+	14.4860i	−0.500557	+	0.865704i
$281$	−1.71589			−0.102361			−0.0511807	−	0.998689i	$-0.516298\pi$
$281$	−1.71589			−0.102361			−0.0511807	+	0.998689i	$0.516298\pi$
$282$	−8.51190	−	12.4945i	−0.506876	−	0.744035i
$283$	0.278331	−	0.0745786i	0.0165451	−	0.00443324i	−0.250537	−	0.968107i	$-0.580607\pi$
$283$	0.278331	−	0.0745786i	0.0165451	−	0.00443324i	0.267082	+	0.963674i	$0.413941\pi$
$284$	−5.71736	+	14.5363i	−0.339263	+	0.862573i
$285$	−13.8778	+	10.2569i	−0.822052	+	0.607564i
$286$	0.917354	+	0.790031i	0.0542443	+	0.0467155i
$287$	−0.941172	+	1.37978i	−0.0555556	+	0.0814458i
$288$	19.0735	−	7.44561i	1.12392	−	0.438737i
$289$	14.6354	−	8.44973i	0.860904	−	0.497043i
$290$	25.3217	−	12.2041i	1.48694	−	0.716647i
$291$	−22.3378	−	12.8967i	−1.30947	−	0.756020i
$292$	6.21864	+	0.705276i	0.363918	+	0.0412732i
$293$	0.120381	+	0.120381i	0.00703275	+	0.00703275i	0.710614	−	0.703582i	$-0.248417\pi$
$293$	0.120381	+	0.120381i	0.00703275	+	0.00703275i	−0.703582	+	0.710614i	$0.748417\pi$
$294$	24.0337	+	8.43178i	1.40168	+	0.491752i
$295$	−2.79055	−	2.22230i	−0.162472	−	0.129387i
$296$	7.14835	+	0.275322i	0.415489	+	0.0160028i
$297$	−3.49766	+	0.937196i	−0.202955	+	0.0543817i
$298$	−22.2595	−	10.7296i	−1.28946	−	0.621552i
$299$	2.51795	−	1.45374i	0.145617	−	0.0840718i
$300$	−10.2739	+	23.5882i	−0.593162	+	1.36186i
$301$	−27.4579	+	5.18891i	−1.58265	+	0.299084i
$302$	1.07622	+	14.4319i	0.0619294	+	0.830463i
$303$	1.32156	−	4.93211i	0.0759214	−	0.283342i
$304$	11.6936	+	2.68698i	0.670674	+	0.154109i
$305$	5.90999	+	15.0284i	0.338405	+	0.860525i
$306$	−5.55150	+	29.2818i	−0.317358	+	1.67393i
$307$	−6.77266	+	6.77266i	−0.386536	+	0.386536i	−0.873450	−	0.486914i	$-0.838123\pi$
$307$	−6.77266	+	6.77266i	−0.386536	+	0.386536i	0.486914	+	0.873450i	$0.338123\pi$
$308$	−11.9877	+	0.886832i	−0.683065	+	0.0505319i
$309$	−24.6580			−1.40274
$310$	−7.01537	−	0.523524i	−0.398446	−	0.0297341i
$311$	−2.69965	−	1.55864i	−0.153083	−	0.0883824i	0.421502	−	0.906828i	$-0.361503\pi$
$311$	−2.69965	−	1.55864i	−0.153083	−	0.0883824i	−0.574585	+	0.818445i	$0.694836\pi$
$312$	−0.811192	+	2.61962i	−0.0459247	+	0.148307i
$313$	18.2884	+	4.90038i	1.03372	+	0.276986i	0.735510	−	0.677513i	$-0.236942\pi$
$313$	18.2884	+	4.90038i	1.03372	+	0.276986i	0.298214	+	0.954499i	$0.403609\pi$
$314$	−12.4776	−	10.7458i	−0.704151	−	0.606419i
$315$	20.8788	+	4.75550i	1.17639	+	0.267942i
$316$	−5.06680	−	33.7836i	−0.285030	−	1.90048i
$317$	−7.05051	+	26.3129i	−0.395996	+	1.47788i	0.424081	+	0.905624i	$0.360597\pi$
$317$	−7.05051	+	26.3129i	−0.395996	+	1.47788i	−0.820077	+	0.572253i	$0.806070\pi$
$318$	−8.17807	−	3.94203i	−0.458603	−	0.221058i
$319$	17.4873	+	10.0963i	0.979101	+	0.565284i
$320$	17.1018	−	5.24684i	0.956018	−	0.293307i
$321$		−	0.648057i		−	0.0361710i
$322$	−7.48807	+	27.8800i	−0.417294	+	1.55369i
$323$	−12.3493	+	12.3493i	−0.687134	+	0.687134i
$324$	8.41875	+	10.5726i	0.467708	+	0.587368i
$325$	−0.882696	−	1.66467i	−0.0489632	−	0.0923395i
$326$	23.0762	−	8.06526i	1.27808	−	0.446694i
$327$	8.52879	−	31.8299i	0.471643	−	1.76020i
$328$	1.74120	−	0.395408i	0.0961414	−	0.0218328i
$329$	−8.33414	+	7.16884i	−0.459476	+	0.395231i
$330$	−18.1591	+	3.44177i	−0.999625	+	0.189463i
$331$	9.65242	−	5.57282i	0.530545	−	0.306310i	−0.210694	−	0.977552i	$-0.567572\pi$
$331$	9.65242	−	5.57282i	0.530545	−	0.306310i	0.741238	+	0.671242i	$0.234239\pi$
$332$	22.0507	−	9.60144i	1.21019	−	0.526948i
$333$	−2.36937	−	8.84262i	−0.129841	−	0.484573i
$334$	0.573678	+	0.108763i	0.0313903	+	0.00595124i
$335$	−8.47646	+	0.960890i	−0.463119	+	0.0524990i
$336$	−12.6824	−	24.0945i	−0.691880	−	1.31447i
$337$	−4.45046	+	4.45046i	−0.242432	+	0.242432i	−0.817856	−	0.575424i	$-0.804837\pi$
$337$	−4.45046	+	4.45046i	−0.242432	+	0.242432i	0.575424	+	0.817856i	$0.304837\pi$
$338$	10.2379	+	15.0280i	0.556868	+	0.817417i
$339$	31.6113	+	18.2508i	1.71689	+	0.991247i
$340$	−6.74052	+	25.1506i	−0.365556	+	1.36398i
$341$	−2.52680	−	4.37654i	−0.136834	−	0.237003i
$342$	−1.14183	−	15.3118i	−0.0617433	−	0.827968i
$343$	4.13334	−	18.0531i	0.223179	−	0.974777i
$344$	25.2770	+	15.9213i	1.36284	+	0.858417i
$345$	−6.58573	+	43.8954i	−0.354564	+	2.36325i
$346$	4.23409	+	12.1145i	0.227626	+	0.651282i
$347$	15.5564	−	4.16832i	0.835110	−	0.223767i	0.184168	−	0.982895i	$-0.441041\pi$
$347$	15.5564	−	4.16832i	0.835110	−	0.223767i	0.650942	+	0.759128i	$0.274374\pi$
$348$	−5.15444	+	45.4483i	−0.276307	+	2.43629i
$349$		−	4.57660i		−	0.244980i	−0.992470	−	0.122490i	$-0.960912\pi$
$349$		−	4.57660i		−	0.244980i	0.992470	−	0.122490i	$-0.0390879\pi$
$350$	17.8813	+	5.50067i	0.955798	+	0.294023i
$351$	0.600693			0.0320626
$352$	10.0322	+	8.03048i	0.534720	+	0.428026i
$353$	9.57675	+	35.7409i	0.509719	+	1.90230i	0.423175	+	0.906048i	$0.360916\pi$
$353$	9.57675	+	35.7409i	0.509719	+	1.90230i	0.0865441	+	0.996248i	$0.472418\pi$
$354$	5.47975	−	1.91520i	0.291245	−	0.101792i
$355$	17.2707	+	2.59116i	0.916634	+	0.137525i
$356$	12.1384	−	1.82050i	0.643336	−	0.0964863i
$357$	39.5218	+	2.97069i	2.09171	+	0.157226i
$358$	1.05762	+	14.1826i	0.0558972	+	0.749572i
$359$	25.1771	−	14.5360i	1.32880	−	0.767181i	0.343683	−	0.939086i	$-0.388325\pi$
$359$	25.1771	−	14.5360i	1.32880	−	0.767181i	0.985114	+	0.171905i	$0.0549921\pi$
$360$	−12.8876	−	18.9197i	−0.679238	−	0.997155i
$361$	−5.00124	+	8.66241i	−0.263223	+	0.455916i
$362$	−18.3309	+	12.4880i	−0.963449	+	0.656353i
$363$	10.6238	+	10.6238i	0.557604	+	0.557604i
$364$	1.95895	+	0.372594i	0.102677	+	0.0195293i
$365$	−0.788155	−	6.95269i	−0.0412539	−	0.363920i
$366$	−25.8175	−	4.89471i	−1.34950	−	0.255851i
$367$	−5.44702	+	1.45952i	−0.284332	+	0.0761865i	−0.398166	−	0.917313i	$-0.630353\pi$
$367$	−5.44702	+	1.45952i	−0.284332	+	0.0761865i	0.113834	+	0.993500i	$0.463687\pi$
$368$	26.1550	−	16.3810i	1.36342	−	0.853917i
$369$	−1.14247	−	1.97882i	−0.0594748	−	0.103013i
$370$	−1.48938	−	7.85813i	−0.0774293	−	0.408524i
$371$	−2.18171	+	6.23048i	−0.113269	+	0.323470i
$372$	6.80433	−	9.20545i	0.352788	−	0.477280i
$373$	−1.84065	−	0.493201i	−0.0953054	−	0.0255370i	0.210851	−	0.977518i	$-0.432376\pi$
$373$	−1.84065	−	0.493201i	−0.0953054	−	0.0255370i	−0.306157	+	0.951981i	$0.599043\pi$
$374$	−17.6575	+	6.17138i	−0.913047	+	0.319114i
$375$	28.2747	+	5.29029i	1.46010	+	0.273190i
$376$	11.7435	+	0.452307i	0.605625	+	0.0233259i
$377$	−2.36862	−	2.36862i	−0.121990	−	0.121990i
$378$	−4.21984	+	4.21486i	−0.217045	+	0.216789i
$379$	−1.51131			−0.0776310			−0.0388155	−	0.999246i	$-0.512358\pi$
$379$	−1.51131			−0.0776310			−0.0388155	+	0.999246i	$0.512358\pi$
$380$	0.000708807	−	13.4146i	3.63610e−5	−	0.688152i
$381$	−3.16298	+	5.47845i	−0.162045	+	0.280669i
$382$	−13.3975	−	6.45792i	−0.685474	−	0.330416i
$383$	−11.9124	−	3.19192i	−0.608696	−	0.163100i	−0.0587121	−	0.998275i	$-0.518699\pi$
$383$	−11.9124	−	3.19192i	−0.608696	−	0.163100i	−0.549984	+	0.835175i	$0.685366\pi$
$384$	−7.60574	+	28.0972i	−0.388129	+	1.43383i
$385$	3.96713	+	12.8405i	0.202184	+	0.654410i
$386$	−9.80955	+	11.3905i	−0.499293	+	0.579760i
$387$	9.89438	−	36.9263i	0.502959	−	1.87707i
$388$	18.3834	−	8.00461i	0.933276	−	0.406372i
$389$	−1.32471	+	2.29447i	−0.0671656	+	0.116334i	−0.897653	−	0.440704i	$-0.854729\pi$
$389$	−1.32471	+	2.29447i	−0.0671656	+	0.116334i	0.830487	+	0.557038i	$0.188062\pi$
$390$	3.05753	+	0.228169i	0.154824	+	0.0115538i
$391$			44.9211i			2.27176i
$392$	−16.3759	+	11.1279i	−0.827109	+	0.562041i
$393$	−35.0289	−	35.0289i	−1.76697	−	1.76697i
$394$	2.59270	+	0.491546i	0.130618	+	0.0247637i
$395$	−35.5440	+	13.9778i	−1.78841	+	0.703300i
$396$	6.01914	−	15.3036i	0.302473	−	0.769036i
$397$	27.1100	+	7.26411i	1.36061	+	0.364575i	0.864042	−	0.503420i	$-0.167925\pi$
$397$	27.1100	+	7.26411i	1.36061	+	0.364575i	0.496572	+	0.867995i	$0.334592\pi$
$398$	−0.139017	−	1.86419i	−0.00696827	−	0.0934434i
$399$	−20.0634	+	3.79153i	−1.00443	+	0.189814i
$400$	−9.99817	−	17.3216i	−0.499908	−	0.866078i
$401$	−12.5972	−	21.8191i	−0.629076	−	1.08959i	−0.987737	−	0.156124i	$-0.950100\pi$
$401$	−12.5972	−	21.8191i	−0.629076	−	1.08959i	0.358661	−	0.933468i	$-0.383233\pi$
$402$	6.02746	−	12.5045i	0.300622	−	0.623666i
$403$	0.216978	+	0.809771i	0.0108084	+	0.0403376i
$404$	2.47250	+	3.10507i	0.123011	+	0.154483i
$405$	9.41307	−	11.8200i	0.467739	−	0.587343i
$406$	33.2593	+	0.0196428i	1.65063	+	0.000974855i
$407$	4.06267	−	4.06267i	0.201379	−	0.201379i
$408$	−28.7847	−	31.0908i	−1.42505	−	1.53922i
$409$	14.2361	−	24.6576i	0.703929	−	1.21924i	−0.263147	−	0.964756i	$-0.584760\pi$
$409$	14.2361	−	24.6576i	0.703929	−	1.21924i	0.967077	−	0.254486i	$-0.0819062\pi$
$410$	−0.866716	−	1.79832i	−0.0428040	−	0.0888125i
$411$	−12.8600	−	22.2741i	−0.634336	−	1.09870i
$412$	11.3935	−	15.4141i	0.561319	−	0.759397i
$413$	−1.83053	−	3.80333i	−0.0900745	−	0.187149i
$414$	−29.9254	−	25.7719i	−1.47075	−	1.26662i
$415$	−15.9820	−	21.6241i	−0.784525	−	1.06149i
$416$	−1.26274	−	1.71751i	−0.0619110	−	0.0842081i
$417$	−0.394887	−	1.47374i	−0.0193377	−	0.0721693i
$418$	7.96404	−	5.42553i	0.389534	−	0.265371i
$419$			29.7916i			1.45542i	0.685887	+	0.727708i	$0.259415\pi$
$419$			29.7916i			1.45542i	−0.685887	+	0.727708i	$0.740585\pi$
$420$	−23.0800	+	19.8508i	−1.12619	+	0.968618i
$421$			7.57624i			0.369243i	0.982810	+	0.184622i	$0.0591060\pi$
$421$			7.57624i			0.369243i	−0.982810	+	0.184622i	$0.940894\pi$
$422$	−5.30264	−	7.78366i	−0.258129	−	0.378903i
$423$	−3.89247	−	14.5269i	−0.189259	−	0.706322i
$424$	6.24300	−	3.29077i	0.303187	−	0.159814i
$425$	29.0927	+	1.04906i	1.41120	+	0.0508868i
$426$	−18.5443	+	21.5330i	−0.898477	+	1.04328i
$427$	−1.43219	+	19.0537i	−0.0693085	+	0.922072i
$428$	0.405110	+	0.299443i	0.0195817	+	0.0144741i
$429$	1.10126	+	1.90744i	0.0531693	+	0.0920920i
$430$	11.0212	−	31.5285i	0.531491	−	1.52044i
$431$	−7.38841	+	12.7971i	−0.355887	+	0.616415i	−0.987269	−	0.159057i	$-0.949155\pi$
$431$	−7.38841	+	12.7971i	−0.355887	+	0.616415i	0.631382	+	0.775472i	$0.282488\pi$
$432$	6.37192	−	0.229092i	0.306569	−	0.0110222i
$433$	9.44547	−	9.44547i	0.453920	−	0.453920i	−0.442733	−	0.896653i	$-0.645991\pi$
$433$	9.44547	−	9.44547i	0.453920	−	0.453920i	0.896653	+	0.442733i	$0.145991\pi$
$434$	−7.20615	−	4.16615i	−0.345906	−	0.199981i
$435$	50.8131	−	5.76016i	2.43630	−	0.276178i
$436$	15.9565	+	20.0389i	0.764178	+	0.959687i
$437$	−5.98979	−	22.3542i	−0.286530	−	1.06935i
$438$	10.2566	+	4.94393i	0.490079	+	0.236230i
$439$	8.29191	+	14.3620i	0.395751	+	0.685461i	0.993197	−	0.116448i	$-0.0371510\pi$
$439$	8.29191	+	14.3620i	0.395751	+	0.685461i	−0.597446	+	0.801909i	$0.703818\pi$
$440$	6.23913	−	12.9418i	0.297439	−	0.616978i
$441$	19.8020	+	15.8062i	0.942954	+	0.752675i
$442$	3.09435	−	0.230752i	0.147183	−	0.0109758i
$443$	10.6247	+	2.84689i	0.504797	+	0.135260i	0.502225	−	0.864737i	$-0.332515\pi$
$443$	10.6247	+	2.84689i	0.504797	+	0.135260i	0.00257156	+	0.999997i	$0.499181\pi$
$444$	12.1114	+	4.76358i	0.574780	+	0.226069i
$445$	−5.02222	−	12.7709i	−0.238076	−	0.605401i
$446$	−0.822321	+	4.33739i	−0.0389380	+	0.205381i
$447$	−31.7883	−	31.7883i	−1.50353	−	1.50353i
$448$	20.9219	+	3.20523i	0.988468	+	0.151433i
$449$			3.01286i			0.142186i	0.997470	+	0.0710929i	$0.0226487\pi$
$449$			3.01286i			0.142186i	−0.997470	+	0.0710929i	$0.977351\pi$
$450$	−17.3898	+	18.7790i	−0.819763	+	0.885252i
$451$	0.717026	−	1.24193i	0.0337634	−	0.0584800i
$452$	−26.0152	+	11.3277i	−1.22365	+	0.532810i
$453$	−6.81434	+	25.4315i	−0.320165	+	1.19487i
$454$	23.9754	+	20.6477i	1.12522	+	0.969046i
$455$	−0.0843709	−	2.22784i	−0.00395537	−	0.104443i
$456$	18.4698	+	11.6336i	0.864929	+	0.544795i
$457$	−24.8395	−	6.65571i	−1.16194	−	0.311341i	−0.374200	−	0.927348i	$-0.622083\pi$
$457$	−24.8395	−	6.65571i	−1.16194	−	0.311341i	−0.787741	+	0.616007i	$0.788749\pi$
$458$	−5.71003	+	11.8459i	−0.266812	+	0.553523i
$459$	−4.64042	+	8.03744i	−0.216596	+	0.375156i
$460$	−24.3967	−	24.3993i	−1.13750	−	1.13762i
$461$	10.5558			0.491634			0.245817	−	0.969316i	$-0.420944\pi$
$461$	10.5558			0.491634			0.245817	+	0.969316i	$0.420944\pi$
$462$	−21.1201	−	5.67249i	−0.982598	−	0.263908i
$463$	25.8053	+	25.8053i	1.19928	+	1.19928i	0.974384	+	0.224892i	$0.0722029\pi$
$463$	25.8053	+	25.8053i	1.19928	+	1.19928i	0.224892	+	0.974384i	$0.427797\pi$
$464$	−26.0288	−	24.2221i	−1.20835	−	1.12448i
$465$	−11.7340	−	5.11002i	−0.544151	−	0.236972i
$466$	−7.69520	−	22.0174i	−0.356473	−	1.01994i
$467$	−3.91552	−	1.04916i	−0.181189	−	0.0485494i	0.167084	−	0.985943i	$-0.446565\pi$
$467$	−3.91552	−	1.04916i	−0.181189	−	0.0485494i	−0.348273	+	0.937393i	$0.613232\pi$
$468$	−1.62155	+	2.19377i	−0.0749564	+	0.101407i
$469$	−9.52654	−	3.33589i	−0.439895	−	0.154037i
$470$	−2.44680	−	12.9095i	−0.112862	−	0.595473i
$471$	−14.9790	−	25.9444i	−0.690197	−	1.19546i
$472$	−1.33477	+	4.31042i	−0.0614376	+	0.198403i
$473$	23.1753	−	6.20980i	1.06560	−	0.285527i
$474$	11.5766	−	61.0615i	0.531730	−	2.80465i
$475$	−14.6174	+	3.35718i	−0.670690	+	0.154038i
$476$	−20.1185	+	23.3330i	−0.922132	+	1.06947i
$477$	−6.38599	−	6.38599i	−0.292394	−	0.292394i
$478$	9.94693	+	14.6009i	0.454962	+	0.667831i
$479$	−17.1560	+	29.7150i	−0.783876	+	1.35771i	0.145792	+	0.989315i	$0.453427\pi$
$479$	−17.1560	+	29.7150i	−0.783876	+	1.35771i	−0.929668	+	0.368398i	$0.879906\pi$
$480$	32.5201	+	1.25425i	1.48433	+	0.0572483i
$481$	−0.825421	+	0.476557i	−0.0376359	+	0.0217291i
$482$	25.2895	−	1.88589i	1.15191	−	0.0859000i
$483$	−29.5948	+	43.3866i	−1.34661	+	1.97416i
$484$	−11.5499	+	1.73224i	−0.524997	+	0.0787381i
$485$	−13.3240	−	18.0278i	−0.605011	−	0.818599i
$486$	10.3436	+	29.5949i	0.469193	+	1.34245i
$487$	−0.0731692	−	0.273071i	−0.00331561	−	0.0123740i	0.964248	−	0.265001i	$-0.0853722\pi$
$487$	−0.0731692	−	0.273071i	−0.00331561	−	0.0123740i	−0.967564	+	0.252627i	$0.918706\pi$
$488$	14.9891	−	13.8773i	0.678523	−	0.628194i
$489$	44.4724			2.01111
$490$	16.2247	+	15.0585i	0.732958	+	0.680274i
$491$		−	15.6289i		−	0.705322i	−0.935751	−	0.352661i	$-0.885277\pi$
$491$		−	15.6289i		−	0.705322i	0.935751	−	0.352661i	$-0.114723\pi$
$492$	3.22768	+	0.366062i	0.145515	+	0.0165033i
$493$	49.9907	−	13.3950i	2.25147	−	0.603279i
$494$	−1.50908	+	0.527431i	−0.0678967	+	0.0237302i
$495$	−18.1823	−	2.72793i	−0.817235	−	0.122612i
$496$	2.61044	+	8.50699i	0.117212	+	0.381975i
$497$	17.0705	+	11.6441i	0.765718	+	0.522310i
$498$	43.6332	−	3.25382i	1.95525	−	0.145807i
$499$	−12.4829	−	21.6210i	−0.558810	−	0.967887i	−0.997596	−	0.0692957i	$-0.977925\pi$
$499$	−12.4829	−	21.6210i	−0.558810	−	0.967887i	0.438786	−	0.898591i	$-0.355409\pi$
$500$	−16.3717	+	15.2305i	−0.732165	+	0.681128i
$501$	0.919954	+	0.531136i	0.0411005	+	0.0237294i
$502$	−18.4060	+	12.5391i	−0.821498	+	0.559648i
$503$	−18.6017	+	18.6017i	−0.829408	+	0.829408i	−0.987435	−	0.158027i	$-0.949487\pi$
$503$	−18.6017	+	18.6017i	−0.829408	+	0.829408i	0.158027	+	0.987435i	$0.449487\pi$
$504$	−4.00159	−	26.7890i	−0.178245	−	1.19328i
$505$	2.76452	−	3.47142i	0.123020	−	0.154476i
$506$	4.61697	−	24.3525i	0.205249	−	1.08260i
$507$	8.56216	+	31.9544i	0.380259	+	1.41915i
$508$	−1.96317	−	4.50862i	−0.0871014	−	0.200037i
$509$	−10.6639	+	6.15682i	−0.472670	+	0.272896i	−0.717357	−	0.696706i	$-0.754648\pi$
$509$	−10.6639	+	6.15682i	−0.472670	+	0.272896i	0.244687	+	0.969602i	$0.421315\pi$
$510$	−26.6727	+	39.1479i	−1.18109	+	1.73350i
$511$	2.73621	−	7.81400i	0.121043	−	0.345671i
$512$	−14.0497	−	17.7371i	−0.620915	−	0.783878i
$513$	1.23751	−	4.61845i	0.0546374	−	0.203909i
$514$	13.1736	+	37.6922i	0.581062	+	1.66253i
$515$	−19.6480	−	8.55648i	−0.865795	−	0.377044i
$516$	33.8542	+	42.5156i	1.49035	+	1.87164i
$517$	6.67426	−	6.67426i	0.293534	−	0.293534i
$518$	2.45470	−	9.13948i	0.107853	−	0.401566i
$519$			23.3471i			1.02482i
$520$	−1.55540	+	1.80588i	−0.0682088	+	0.0791930i
$521$	−18.9164	−	10.9214i	−0.828744	−	0.478475i	0.0246787	−	0.999695i	$-0.492144\pi$
$521$	−18.9164	−	10.9214i	−0.828744	−	0.478475i	−0.853422	+	0.521220i	$0.825477\pi$
$522$	−19.7570	+	40.9875i	−0.864741	+	1.79398i
$523$	3.72547	−	13.9037i	0.162904	−	0.607965i	−0.835395	−	0.549651i	$-0.814761\pi$
$523$	3.72547	−	13.9037i	0.162904	−	0.607965i	0.998298	−	0.0583140i	$-0.0185725\pi$
$524$	38.0826	−	5.71156i	1.66365	−	0.249511i
$525$	27.4078	+	20.1800i	1.19617	+	0.880729i
$526$	1.10606	−	1.28431i	0.0482265	−	0.0559988i
$527$	−12.5111	−	3.35235i	−0.544994	−	0.146031i
$528$	12.4092	+	19.8134i	0.540041	+	0.862266i
$529$	−31.6325	−	18.2631i	−1.37533	−	0.794046i
$530$	−5.14855	−	5.97894i	−0.223639	−	0.259709i
$531$	5.77447			0.250591
$532$	6.90041	−	14.2939i	0.299171	−	0.619718i
$533$	−0.168216	+	0.168216i	−0.00728626	+	0.00728626i
$534$	21.9394	+	4.15946i	0.949409	+	0.179997i
$535$	0.224880	−	0.516385i	0.00972241	−	0.0223253i
$536$	5.03166	+	9.54569i	0.217335	+	0.412311i
$537$	−6.69661	+	24.9921i	−0.288980	+	1.07849i
$538$	20.4808	−	1.52729i	0.882989	−	0.0658464i
$539$	−2.37709	+	15.7229i	−0.102389	+	0.677235i
$540$	−1.84466	−	6.88582i	−0.0793816	−	0.296319i
$541$	2.53435	−	1.46321i	0.108960	−	0.0629082i	−0.444530	−	0.895764i	$-0.646629\pi$
$541$	2.53435	−	1.46321i	0.108960	−	0.0629082i	0.553490	+	0.832856i	$0.313296\pi$
$542$	−15.6791	+	32.5276i	−0.673475	+	1.39718i
$543$	−38.9773	+	10.4439i	−1.67268	+	0.448193i
$544$	32.7356	−	3.62785i	1.40353	−	0.155543i
$545$	17.8411	−	22.4032i	0.764229	−	0.959647i
$546$	3.14067	+	1.81574i	0.134408	+	0.0777066i
$547$	−26.4813	−	26.4813i	−1.13226	−	1.13226i	−0.989801	−	0.142456i	$-0.954500\pi$
$547$	−26.4813	−	26.4813i	−1.13226	−	1.13226i	−0.142456	−	0.989801i	$-0.545500\pi$
$548$	19.8660	+	2.25307i	0.848634	+	0.0962464i
$549$	−22.6380	−	13.0701i	−0.966167	−	0.557817i
$550$	−15.6639	−	3.55885i	−0.667910	−	0.151750i
$551$	−23.0909	+	13.3315i	−0.983705	+	0.567942i
$552$	54.7512	−	12.4335i	2.33037	−	0.529203i
$553$	−45.0642	−	3.38730i	−1.91632	−	0.144042i
$554$	2.17724	−	2.52813i	0.0925021	−	0.107410i
$555$	2.15890	−	14.3896i	0.0916403	−	0.610804i
$556$	1.10372	+	0.434109i	0.0468081	+	0.0184103i
$557$	−19.8817	+	5.32729i	−0.842415	+	0.225725i	−0.654123	−	0.756388i	$-0.726962\pi$
$557$	−19.8817	+	5.32729i	−0.842415	+	0.225725i	−0.188293	+	0.982113i	$0.560295\pi$
$558$	9.41109	−	6.41134i	0.398403	−	0.271413i
$559$	−3.98015			−0.168342
$560$	−1.74463	−	23.5999i	−0.0737239	−	0.997279i
$561$	−34.0294			−1.43672
$562$	2.00548	−	1.36624i	0.0845960	−	0.0576313i
$563$	−38.1670	+	10.2268i	−1.60855	+	0.431009i	−0.947610	−	0.319430i	$-0.896508\pi$
$563$	−38.1670	+	10.2268i	−1.60855	+	0.431009i	−0.660939	+	0.750440i	$0.729842\pi$
$564$	19.8969	+	7.82574i	0.837810	+	0.329523i
$565$	18.8554	+	25.5120i	0.793254	+	1.07330i
$566$	−0.265923	+	0.308780i	−0.0111776	+	0.0129790i
$567$	16.1099	−	7.75364i	0.676551	−	0.325622i
$568$	−4.89196	−	21.5419i	−0.205262	−	0.903880i
$569$	−9.87826	+	5.70321i	−0.414118	+	0.239091i	−0.692558	−	0.721363i	$-0.743516\pi$
$569$	−9.87826	+	5.70321i	−0.414118	+	0.239091i	0.278440	+	0.960454i	$0.410183\pi$
$570$	8.05320	−	23.0378i	0.337311	−	0.964948i
$571$	−26.6881	−	15.4084i	−1.11686	−	0.644822i	−0.176266	−	0.984343i	$-0.556402\pi$
$571$	−26.6881	−	15.4084i	−1.11686	−	0.644822i	−0.940599	+	0.339521i	$0.889735\pi$
$572$	−1.70122	−	0.192941i	−0.0711315	−	0.00806726i
$573$	−19.1326	−	19.1326i	−0.799275	−	0.799275i
$574$	0.00139500	−	2.36203i	5.82264e−5	−	0.0985892i
$575$	−20.4797	+	32.6915i	−0.854061	+	1.36333i
$576$	−16.3642	+	23.8891i	−0.681840	+	0.995378i
$577$	23.9843	−	6.42658i	0.998480	−	0.267542i	0.277672	−	0.960676i	$-0.410437\pi$
$577$	23.9843	−	6.42658i	0.998480	−	0.267542i	0.720809	+	0.693134i	$0.243771\pi$
$578$	−10.3775	+	21.5289i	−0.431645	+	0.895483i
$579$	−23.6840	+	13.6740i	−0.984275	+	0.568272i
$580$	−19.8780	+	34.4256i	−0.825391	+	1.42944i
$581$	−5.90787	−	31.2624i	−0.245100	−	1.29698i
$582$	36.3765	−	2.71267i	1.50785	−	0.112444i
$583$	1.46699	−	5.47489i	0.0607566	−	0.226747i
$584$	−7.82971	+	4.12715i	−0.323996	+	0.170782i
$585$	2.79635	+	1.21778i	0.115615	+	0.0503490i
$586$	−0.236549	−	0.0448470i	−0.00977174	−	0.00185261i
$587$	5.46663	−	5.46663i	0.225632	−	0.225632i	−0.585233	−	0.810865i	$-0.698997\pi$
$587$	5.46663	−	5.46663i	0.225632	−	0.225632i	0.810865	+	0.585233i	$0.198997\pi$
$588$	−34.8035	+	9.28153i	−1.43527	+	0.382764i
$589$	6.67295			0.274954
$590$	5.03097	+	0.375437i	0.207122	+	0.0154565i
$591$	4.15766	+	2.40043i	0.171023	+	0.0987404i
$592$	−8.57399	+	5.36993i	−0.352389	+	0.220703i
$593$	−23.2200	−	6.22177i	−0.953530	−	0.255497i	−0.251670	−	0.967813i	$-0.580980\pi$
$593$	−23.2200	−	6.22177i	−0.953530	−	0.255497i	−0.701859	+	0.712316i	$0.747647\pi$
$594$	3.34174	−	3.88030i	0.137113	−	0.159211i
$595$	30.4609	+	16.0814i	1.24878	+	0.659274i
$596$	34.5595	−	5.18317i	1.41561	−	0.212311i
$597$	0.880217	−	3.28502i	0.0360249	−	0.134447i
$598$	−1.78539	+	3.70394i	−0.0730101	+	0.151465i
$599$	−25.8564	−	14.9282i	−1.05647	−	0.609951i	−0.132013	−	0.991248i	$-0.542144\pi$
$599$	−25.8564	−	14.9282i	−1.05647	−	0.609951i	−0.924452	+	0.381297i	$0.875477\pi$
$600$	−6.77379	−	35.7495i	−0.276539	−	1.45947i
$601$			13.8947i			0.566775i	0.959005	+	0.283388i	$0.0914583\pi$
$601$			13.8947i			0.566775i	−0.959005	+	0.283388i	$0.908542\pi$
$602$	27.9604	−	27.9274i	1.13958	−	1.13823i
$603$	9.76432	−	9.76432i	0.397634	−	0.397634i
$604$	−12.7489	−	16.0107i	−0.518747	−	0.651465i
$605$	4.77874	+	12.1518i	0.194283	+	0.494040i
$606$	2.38249	+	6.81676i	0.0967821	+	0.276912i
$607$	−3.35624	+	12.5256i	−0.136225	+	0.508400i	0.863764	+	0.503896i	$0.168100\pi$
$607$	−3.35624	+	12.5256i	−0.136225	+	0.508400i	−0.999990	+	0.00450428i	$0.998566\pi$
$608$	−15.8066	+	6.17031i	−0.641041	+	0.250239i
$609$	57.1079	+	19.9973i	2.31413	+	0.810333i
$610$	−18.8735	−	12.8591i	−0.764164	−	0.520648i
$611$	−1.35602	+	0.782901i	−0.0548589	+	0.0316728i
$612$	−16.8266	−	38.6439i	−0.680173	−	1.56209i
$613$	6.87935	+	25.6741i	0.277854	+	1.03697i	0.953904	+	0.300111i	$0.0970236\pi$
$613$	6.87935	+	25.6741i	0.277854	+	1.03697i	−0.676050	+	0.736856i	$0.736310\pi$
$614$	2.52310	−	13.3083i	0.101824	−	0.537078i
$615$	−0.409079	−	3.60868i	−0.0164957	−	0.145516i
$616$	13.3048	−	10.5815i	0.536065	−	0.426340i
$617$	−4.15023	+	4.15023i	−0.167082	+	0.167082i	−0.785695	−	0.618614i	$-0.787695\pi$
$617$	−4.15023	+	4.15023i	−0.167082	+	0.167082i	0.618614	+	0.785695i	$0.287695\pi$
$618$	28.8195	−	19.6334i	1.15929	−	0.789770i
$619$	−13.0671	−	7.54430i	−0.525212	−	0.303231i	0.213853	−	0.976866i	$-0.431399\pi$
$619$	−13.0671	−	7.54430i	−0.525212	−	0.303231i	−0.739064	+	0.673635i	$0.764732\pi$
$620$	8.61619	−	4.97395i	0.346035	−	0.199759i
$621$	−6.14914	−	10.6506i	−0.246757	−	0.427395i
$622$	4.39630	−	0.327841i	0.176275	−	0.0131452i
$623$	1.21705	−	16.1916i	0.0487603	−	0.648701i
$624$	−1.13772	−	3.70762i	−0.0455451	−	0.148424i
$625$	20.6941	+	14.0269i	0.827764	+	0.561077i
$626$	−25.2768	+	8.83436i	−1.01026	+	0.353092i
$627$	16.9341	−	4.53749i	0.676284	−	0.181210i
$628$	23.1395	+	2.62433i	0.923366	+	0.104722i
$629$		−	14.7258i		−	0.587156i
$630$	−28.1890	+	11.0662i	−1.12308	+	0.440888i
$631$	18.0603			0.718967			0.359484	−	0.933151i	$-0.382953\pi$
$631$	18.0603			0.718967			0.359484	+	0.933151i	$0.382953\pi$
$632$	32.8214	+	35.4509i	1.30556	+	1.41016i
$633$	−4.43471	−	16.5506i	−0.176264	−	0.657826i
$634$	−12.7106	−	36.3675i	−0.504803	−	1.44434i
$635$	−4.42139	+	3.26777i	−0.175458	+	0.129678i
$636$	12.6970	−	1.90428i	0.503470	−	0.0755095i
$637$	1.05597	−	2.41733i	0.0418390	−	0.0957783i
$638$	−28.4776	+	2.12363i	−1.12744	+	0.0840754i
$639$	−24.4818	+	14.1346i	−0.968487	+	0.559156i
$640$	−15.8103	+	19.7493i	−0.624959	+	0.780658i
$641$	9.32370	−	16.1491i	0.368264	−	0.637852i	−0.621030	−	0.783787i	$-0.713286\pi$
$641$	9.32370	−	16.1491i	0.368264	−	0.637852i	0.989294	+	0.145935i	$0.0466190\pi$
$642$	0.516001	+	0.757429i	0.0203649	+	0.0298933i
$643$	−20.2835	−	20.2835i	−0.799901	−	0.799901i	0.183178	−	0.983080i	$-0.441361\pi$
$643$	−20.2835	−	20.2835i	−0.799901	−	0.799901i	−0.983080	+	0.183178i	$0.941361\pi$
$644$	−13.4470	−	38.5475i	−0.529886	−	1.51898i
$645$	37.8527	−	47.5318i	1.49045	−	1.87156i
$646$	4.60063	−	24.2664i	0.181009	−	0.954747i
$647$	8.96115	−	2.40113i	0.352299	−	0.0943982i	−0.0783295	−	0.996928i	$-0.524959\pi$
$647$	8.96115	−	2.40113i	0.352299	−	0.0943982i	0.430628	+	0.902529i	$0.358292\pi$
$648$	−18.2578	−	5.65371i	−0.717233	−	0.222099i
$649$	1.81205	+	3.13857i	0.0711293	+	0.123200i
$650$	2.35713	+	1.24279i	0.0924542	+	0.0487463i
$651$	−9.87518	−	11.4804i	−0.387039	−	0.449952i
$652$	−20.5490	+	27.8004i	−0.804762	+	1.08875i
$653$	−31.6406	−	8.47808i	−1.23819	−	0.331773i	−0.420428	−	0.907326i	$-0.638120\pi$
$653$	−31.6406	−	8.47808i	−1.23819	−	0.331773i	−0.817765	+	0.575553i	$0.804787\pi$
$654$	15.3756	+	43.9926i	0.601235	+	1.72025i
$655$	−15.7565	−	40.0670i	−0.615658	−	1.56555i
$656$	−1.72022	+	1.84853i	−0.0671633	+	0.0721729i
$657$	8.00903	+	8.00903i	0.312462	+	0.312462i
$658$	4.03266	−	15.0146i	0.157209	−	0.585330i
$659$	43.2371			1.68428			0.842138	−	0.539261i	$-0.181296\pi$
$659$	43.2371			1.68428			0.842138	+	0.539261i	$0.181296\pi$
$660$	18.4834	−	18.4814i	0.719463	−	0.719387i
$661$	3.72730	−	6.45587i	0.144975	−	0.251104i	−0.784389	−	0.620270i	$-0.787023\pi$
$661$	3.72730	−	6.45587i	0.144975	−	0.251104i	0.929364	+	0.369166i	$0.120356\pi$
$662$	−6.84421	+	14.1989i	−0.266008	+	0.551855i
$663$	5.45276	+	1.46106i	0.211768	+	0.0567430i
$664$	−18.1273	+	28.7793i	−0.703474	+	1.11685i
$665$	−17.3027	−	3.94097i	−0.670968	−	0.152824i
$666$	9.80999	+	8.44842i	0.380129	+	0.327370i
$667$	−17.7500	+	66.2440i	−0.687283	+	2.56498i
$668$	−0.757097	+	0.329660i	−0.0292930	+	0.0127549i
$669$	−4.01574	+	6.95547i	−0.155258	+	0.268914i
$670$	9.14194	−	7.87225i	0.353184	−	0.304132i
$671$		−	16.4058i		−	0.633338i
$672$	34.0075	+	18.0629i	1.31187	+	0.696791i
$673$	30.9386	+	30.9386i	1.19259	+	1.19259i	0.976336	+	0.216258i	$0.0693853\pi$
$673$	30.9386	+	30.9386i	1.19259	+	1.19259i	0.216258	+	0.976336i	$0.430615\pi$
$674$	1.65798	−	8.74514i	0.0638630	−	0.336850i
$675$	−7.04138	+	3.73371i	−0.271023	+	0.143710i
$676$	−23.9315	−	9.41260i	−0.920441	−	0.362023i
$677$	10.6938	+	2.86539i	0.410995	+	0.110126i	0.458392	−	0.888750i	$-0.348426\pi$
$677$	10.6938	+	2.86539i	0.410995	+	0.110126i	−0.0473963	+	0.998876i	$0.515092\pi$
$678$	−51.4781	+	3.83883i	−1.97701	+	0.147429i
$679$	−4.92532	−	26.0630i	−0.189016	−	1.00021i
$680$	−12.1475	−	34.7623i	−0.465836	−	1.33307i
$681$	28.7818	+	49.8515i	1.10292	+	1.91032i
$682$	6.43796	+	3.10326i	0.246522	+	0.118830i
$683$	10.1568	+	37.9058i	0.388640	+	1.45043i	0.832348	+	0.554254i	$0.186996\pi$
$683$	10.1568	+	37.9058i	0.388640	+	1.45043i	−0.443707	+	0.896172i	$0.646337\pi$
$684$	13.5262	+	16.9868i	0.517188	+	0.649507i
$685$	−2.51784	−	22.2110i	−0.0962016	−	0.848639i
$686$	9.54349	+	24.3910i	0.364372	+	0.931253i
$687$	−16.9169	+	16.9169i	−0.645418	+	0.645418i
$688$	−42.2199	+	1.51795i	−1.60962	+	0.0578712i
$689$	−0.470132	+	0.814293i	−0.0179106	+	0.0310221i
$690$	−27.2536	−	56.5474i	−1.03753	−	2.15272i
$691$	−2.80628	−	4.86061i	−0.106756	−	0.184906i	0.807698	−	0.589596i	$-0.200713\pi$
$691$	−2.80628	−	4.86061i	−0.106756	−	0.184906i	−0.914454	+	0.404689i	$0.867380\pi$
$692$	−14.5946	−	10.7878i	−0.554804	−	0.410091i
$693$	−17.9716	−	12.2587i	−0.682684	−	0.465671i
$694$	−14.8629	+	17.2582i	−0.564187	+	0.655113i
$695$	0.196743	−	1.31134i	0.00746287	−	0.0497418i
$696$	−30.1629	−	57.2227i	−1.14332	−	2.16902i
$697$	−0.951293	−	3.55027i	−0.0360328	−	0.134476i
$698$	3.64401	+	5.34898i	0.137928	+	0.202462i
$699$		−	42.4318i		−	1.60492i
$700$	−25.2790	+	7.80861i	−0.955455	+	0.295138i
$701$		−	17.1666i		−	0.648373i	−0.945993	−	0.324187i	$-0.894909\pi$
$701$		−	17.1666i		−	0.648373i	0.945993	−	0.324187i	$-0.105091\pi$
$702$	−0.702072	+	0.478289i	−0.0264980	+	0.0180518i
$703$	1.96354	+	7.32804i	0.0740564	+	0.276382i
$704$	−18.1194	−	1.39783i	−0.682902	−	0.0526828i
$705$	3.54670	−	23.6396i	0.133577	−	0.890319i
$706$	−39.6509	−	34.1476i	−1.49228	−	1.28516i
$707$	4.73130	−	2.27716i	0.177939	−	0.0856416i
$708$	−4.87963	+	6.60156i	−0.183388	+	0.248102i
$709$	−6.21802	−	10.7699i	−0.233522	−	0.404473i	0.725320	−	0.688412i	$-0.241692\pi$
$709$	−6.21802	−	10.7699i	−0.233522	−	0.404473i	−0.958842	+	0.283939i	$0.908359\pi$
$710$	−22.2486	+	10.7229i	−0.834976	+	0.402425i
$711$	30.9123	−	53.5416i	1.15930	−	2.00797i
$712$	−12.7375	+	11.7927i	−0.477358	+	0.441950i
$713$	12.1366	−	12.1366i	0.454517	−	0.454517i
$714$	−48.5572	+	27.9963i	−1.81721	+	1.04773i
$715$	0.215614	+	1.90203i	0.00806350	+	0.0711320i
$716$	−12.5287	−	15.7340i	−0.468219	−	0.588009i
$717$	8.31883	+	31.0463i	0.310673	+	1.15945i
$718$	−17.8522	+	37.0359i	−0.666240	+	1.38217i
$719$	7.58211	+	13.1326i	0.282765	+	0.489763i	0.972065	−	0.234713i	$-0.0754150\pi$
$719$	7.58211	+	13.1326i	0.282765	+	0.489763i	−0.689300	+	0.724476i	$0.742082\pi$
$720$	30.1271	+	11.8513i	1.12277	+	0.441670i
$721$	−16.5355	−	19.2234i	−0.615815	−	0.715915i
$722$	−1.05195	−	14.1065i	−0.0391495	−	0.524989i
$723$	44.5644	+	11.9410i	1.65737	+	0.444090i
$724$	11.4813	−	29.1911i	0.426699	−	1.08488i
$725$	42.4878	+	13.0427i	1.57796	+	0.484392i
$726$	−20.8757	−	3.95780i	−0.774770	−	0.146888i
$727$	20.4327	+	20.4327i	0.757806	+	0.757806i	0.975923	−	0.218117i	$-0.0699913\pi$
$727$	20.4327	+	20.4327i	0.757806	+	0.757806i	−0.218117	+	0.975923i	$0.569991\pi$
$728$	−2.58623	+	1.12430i	−0.0958522	+	0.0416692i
$729$			36.7626i			1.36158i
$730$	6.45709	+	7.49854i	0.238988	+	0.277533i
$731$	30.7471	−	53.2555i	1.13722	−	1.96973i
$732$	34.0720	−	14.8358i	1.25934	−	0.548348i
$733$	−5.61754	+	20.9650i	−0.207489	+	0.774358i	0.781188	+	0.624296i	$0.214614\pi$
$733$	−5.61754	+	20.9650i	−0.207489	+	0.774358i	−0.988677	+	0.150062i	$0.952053\pi$
$734$	5.20419	−	6.04291i	0.192090	−	0.223048i
$735$	18.8257	+	35.6003i	0.694397	+	1.31314i
$736$	−17.5261	+	39.9709i	−0.646022	+	1.47335i
$737$	8.37124	+	2.24307i	0.308358	+	0.0826244i
$738$	2.91088	+	1.40312i	0.107151	+	0.0516495i
$739$	8.04625	−	13.9365i	0.295986	−	0.512663i	−0.679228	−	0.733928i	$-0.737685\pi$
$739$	8.04625	−	13.9365i	0.295986	−	0.512663i	0.975214	+	0.221265i	$0.0710184\pi$
$740$	7.99760	+	7.99845i	0.293998	+	0.294029i
$741$	−2.90829			−0.106839
$742$	−2.41096	−	9.01913i	−0.0885092	−	0.331103i
$743$	−5.05372	−	5.05372i	−0.185403	−	0.185403i	0.608302	−	0.793705i	$-0.291851\pi$
$743$	−5.05372	−	5.05372i	−0.185403	−	0.185403i	−0.793705	+	0.608302i	$0.791851\pi$
$744$	−0.623059	+	16.1768i	−0.0228424	+	0.593072i
$745$	−14.2988	−	36.3603i	−0.523869	−	1.33214i
$746$	2.54400	−	0.889140i	0.0931424	−	0.0325537i
$747$	42.0427	+	11.2653i	1.53826	+	0.412176i
$748$	15.7237	−	21.2723i	0.574915	−	0.777792i
$749$	0.505225	−	0.434583i	0.0184605	−	0.0158793i
$750$	−37.2588	+	16.3299i	−1.36050	+	0.596285i
$751$	−7.22663	−	12.5169i	−0.263704	−	0.456748i	0.703520	−	0.710676i	$-0.251611\pi$
$751$	−7.22663	−	12.5169i	−0.263704	−	0.456748i	−0.967223	+	0.253928i	$0.918277\pi$
$752$	−14.0856	+	8.82187i	−0.513649	+	0.321700i
$753$	−39.1370	+	10.4867i	−1.42623	+	0.382158i
$754$	4.65434	+	0.882410i	0.169501	+	0.0321355i
$755$	−14.2547	+	17.8997i	−0.518781	+	0.651437i
$756$	1.57603	−	8.28616i	0.0573198	−	0.301365i
$757$	2.97568	+	2.97568i	0.108153	+	0.108153i	0.759112	−	0.650960i	$-0.225633\pi$
$757$	2.97568	+	2.97568i	0.108153	+	0.108153i	−0.650960	+	0.759112i	$0.725633\pi$
$758$	1.76638	−	1.20335i	0.0641577	−	0.0437077i
$759$	22.5466	−	39.0519i	0.818391	−	1.41749i
$760$	10.6802	+	15.6791i	0.387412	+	0.568740i
$761$	34.7136	−	20.0419i	1.25837	−	0.726519i	0.285610	−	0.958346i	$-0.407804\pi$
$761$	34.7136	−	20.0419i	1.25837	−	0.726519i	0.972757	+	0.231827i	$0.0744704\pi$
$762$	−0.665295	−	8.92150i	−0.0241011	−	0.323192i
$763$	30.5339	−	14.6959i	1.10540	−	0.532027i
$764$	20.8005	−	3.11963i	0.752537	−	0.112864i
$765$	−37.8963	+	28.0085i	−1.37015	+	1.01265i
$766$	16.4644	−	5.75437i	0.594881	−	0.207914i
$767$	−0.155602	−	0.580716i	−0.00561847	−	0.0209684i
$768$	−13.4825	−	38.8951i	−0.486506	−	1.40351i
$769$	−53.2226			−1.91926			−0.959629	−	0.281270i	$-0.909244\pi$
$769$	−53.2226			−1.91926			−0.959629	+	0.281270i	$0.909244\pi$
$770$	−14.8606	−	11.8488i	−0.535538	−	0.427001i
$771$			72.6401i			2.61607i
$772$	2.39568	−	21.1235i	0.0862226	−	0.760251i
$773$	−4.66524	+	1.25005i	−0.167797	+	0.0449611i	−0.341739	−	0.939795i	$-0.611016\pi$
$773$	−4.66524	+	1.25005i	−0.167797	+	0.0449611i	0.173942	+	0.984756i	$0.444349\pi$
$774$	17.8375	+	51.0365i	0.641156	+	1.83447i
$775$	−7.57669	−	8.14355i	−0.272163	−	0.292525i
$776$	−15.1125	+	23.9929i	−0.542506	+	0.861296i
$777$	9.70163	−	14.2228i	0.348044	−	0.510240i
$778$	−0.278637	−	3.73648i	−0.00998962	−	0.133959i
$779$	0.946788	+	1.63989i	0.0339222	+	0.0587550i
$780$	−3.75522	+	2.16781i	−0.134458	+	0.0776201i
$781$	−15.3650	−	8.87100i	−0.549804	−	0.317429i
$782$	−35.7674	−	52.5024i	−1.27904	−	1.87748i
$783$	−10.0190	+	10.0190i	−0.358050	+	0.358050i
$784$	10.2794	−	26.0449i	0.367120	−	0.930173i
$785$	−2.93272	−	25.8709i	−0.104673	−	0.923372i
$786$	68.8317	+	13.0497i	2.45514	+	0.465468i
$787$	3.26436	+	12.1828i	0.116362	+	0.434269i	0.999385	−	0.0350606i	$-0.0111624\pi$
$787$	3.26436	+	12.1828i	0.116362	+	0.434269i	−0.883023	+	0.469329i	$0.844496\pi$
$788$	−3.42164	+	1.48987i	−0.121891	+	0.0530745i
$789$	2.67045	−	1.54179i	0.0950707	−	0.0548891i
$790$	30.4132	−	44.6379i	1.08205	−	1.58815i
$791$	6.97005	+	36.8831i	0.247827	+	1.31141i
$792$	5.15018	+	22.6790i	0.183004	+	0.805863i
$793$	−0.704387	+	2.62881i	−0.0250135	+	0.0933517i
$794$	−37.4693	+	13.0957i	−1.32973	+	0.464749i
$795$	−5.25334	−	13.3587i	−0.186317	−	0.473783i
$796$	1.64680	+	2.06812i	0.0583692	+	0.0733025i
$797$	32.1191	−	32.1191i	1.13772	−	1.13772i	0.148856	−	0.988859i	$-0.452441\pi$
$797$	32.1191	−	32.1191i	1.13772	−	1.13772i	0.988859	−	0.148856i	$-0.0475592\pi$
$798$	20.4306	−	20.4065i	0.723235	−	0.722381i
$799$		−	24.1920i		−	0.855850i
$800$	25.4775	+	12.2841i	0.900764	+	0.434308i
$801$	19.2375	+	11.1068i	0.679723	+	0.392438i
$802$	32.0962	+	15.4712i	1.13336	+	0.546306i
$803$	−1.83984	+	6.86638i	−0.0649266	+	0.242309i
$804$	2.91168	+	19.4141i	0.102687	+	0.684681i
$805$	−38.6372	+	24.3018i	−1.36178	+	0.856526i
$806$	−0.898359	−	0.773672i	−0.0316433	−	0.0272514i
$807$	36.0906	+	9.67044i	1.27045	+	0.340416i
$808$	−5.36212	−	1.66044i	−0.188639	−	0.0584139i
$809$	15.1482	+	8.74583i	0.532583	+	0.307487i	0.742068	−	0.670325i	$-0.233845\pi$
$809$	15.1482	+	8.74583i	0.532583	+	0.307487i	−0.209485	+	0.977812i	$0.567179\pi$
$810$	−1.59025	+	21.3099i	−0.0558758	+	0.748752i
$811$	18.9966			0.667061			0.333531	−	0.942739i	$-0.391760\pi$
$811$	18.9966			0.667061			0.333531	+	0.942739i	$0.391760\pi$
$812$	−38.8881	+	26.4590i	−1.36470	+	0.928529i
$813$	−46.4518	+	46.4518i	−1.62914	+	1.62914i
$814$	−1.51351	+	7.98313i	−0.0530486	+	0.279808i
$815$	35.4366	+	15.4322i	1.24129	+	0.540567i
$816$	58.3980	+	13.4188i	2.04434	+	0.469752i
$817$	−8.19964	+	30.6015i	−0.286869	+	1.07061i
$818$	2.99439	+	40.1543i	0.104696	+	1.40396i
$819$	2.35337	+	2.73592i	0.0822336	+	0.0956006i
$820$	2.44486	+	1.41171i	0.0853782	+	0.0492991i
$821$	3.22323	−	1.86093i	0.112492	−	0.0649470i	−0.442699	−	0.896670i	$-0.645979\pi$
$821$	3.22323	−	1.86093i	0.112492	−	0.0649470i	0.555190	+	0.831723i	$0.312645\pi$
$822$	32.7656	+	15.7939i	1.14283	+	0.550874i
$823$	−26.4188	+	7.07889i	−0.920901	+	0.246755i	−0.687971	−	0.725739i	$-0.741498\pi$
$823$	−26.4188	+	7.07889i	−0.920901	+	0.246755i	−0.232931	+	0.972493i	$0.574832\pi$
$824$	−1.04328	+	27.0873i	−0.0363444	+	0.943632i
$825$	−24.7651	−	15.5141i	−0.862209	−	0.540132i
$826$	5.16778	+	2.98769i	0.179810	+	0.103955i
$827$	−17.6105	−	17.6105i	−0.612375	−	0.612375i	0.331189	−	0.943564i	$-0.392550\pi$
$827$	−17.6105	−	17.6105i	−0.612375	−	0.612375i	−0.943564	+	0.331189i	$0.892550\pi$
$828$	55.4962	+	6.29401i	1.92863	+	0.218732i
$829$	−14.8575	−	8.57799i	−0.516023	−	0.297926i	0.219283	−	0.975661i	$-0.429628\pi$
$829$	−14.8575	−	8.57799i	−0.516023	−	0.297926i	−0.735306	+	0.677735i	$0.762961\pi$
$830$	35.8970	+	12.5483i	1.24600	+	0.435558i
$831$	5.25670	−	3.03496i	0.182353	−	0.105281i
$832$	2.84339	+	1.00195i	0.0985767	+	0.0347363i
$833$	24.1871	+	32.8033i	0.838034	+	1.13657i
$834$	1.63496	+	1.40804i	0.0566142	+	0.0487564i
$835$	0.548732	+	0.742451i	0.0189896	+	0.0256936i
$836$	−4.98817	+	12.6824i	−0.172519	+	0.438629i
$837$	3.42524	−	0.917791i	0.118394	−	0.0317235i
$838$	−23.7209	−	34.8195i	−0.819426	−	1.20282i
$839$	52.5145			1.81300			0.906501	−	0.422204i	$-0.138743\pi$
$839$	52.5145			1.81300			0.906501	+	0.422204i	$0.138743\pi$
$840$	11.1694	−	41.5779i	0.385382	−	1.43457i
$841$	50.0128			1.72458
$842$	−6.03241	−	8.85487i	−0.207891	−	0.305159i
$843$	4.26429	−	1.14261i	0.146870	−	0.0393537i
$844$	12.3951	+	4.87519i	0.426658	+	0.167811i
$845$	−4.26588	+	28.4331i	−0.146751	+	0.978129i
$846$	16.1161	+	13.8793i	0.554084	+	0.477180i
$847$	−1.15805	+	15.4066i	−0.0397910	+	0.529375i
$848$	−4.67643	+	8.81700i	−0.160589	+	0.302777i
$849$	−0.642041	+	0.370682i	−0.0220348	+	0.0127218i
$850$	−34.8380	+	21.9383i	−1.19493	+	0.752478i
$851$	16.8992	+	9.75678i	0.579298	+	0.334458i
$852$	4.52889	−	39.9326i	0.155157	−	1.36807i
$853$	28.5671	+	28.5671i	0.978117	+	0.978117i	0.999766	−	0.0216483i	$-0.00689139\pi$
$853$	28.5671	+	28.5671i	0.978117	+	0.978117i	−0.0216483	+	0.999766i	$0.506891\pi$
$854$	−13.4972	−	23.4097i	−0.461864	−	0.801064i
$855$	15.1238	−	18.9910i	0.517223	−	0.649480i
$856$	−0.711905	−	0.0274193i	−0.0243324	−	0.000937174i
$857$	42.1111	−	11.2836i	1.43849	−	0.385442i	0.546484	−	0.837470i	$-0.315966\pi$
$857$	42.1111	−	11.2836i	1.43849	−	0.385442i	0.892004	+	0.452028i	$0.149299\pi$
$858$	−2.80587	−	1.35250i	−0.0957909	−	0.0461736i
$859$	−43.7008	+	25.2307i	−1.49105	+	0.860859i	−0.999948	−	0.0102418i	$-0.996740\pi$
$859$	−43.7008	+	25.2307i	−1.49105	+	0.860859i	−0.491104	+	0.871101i	$0.663407\pi$
$860$	12.2226	+	45.6250i	0.416787	+	1.55580i
$861$	1.42019	−	4.05573i	0.0483998	−	0.138219i
$862$	−1.55406	−	20.8397i	−0.0529315	−	0.709804i
$863$	3.86849	−	14.4374i	0.131685	−	0.491455i	−0.868305	−	0.496031i	$-0.834790\pi$
$863$	3.86849	−	14.4374i	0.131685	−	0.491455i	0.999990	+	0.00457643i	$0.00145673\pi$
$864$	−7.26490	+	5.34126i	−0.247157	+	0.181713i
$865$	−8.10159	+	18.6035i	−0.275462	+	0.632536i
$866$	−3.51883	+	18.5603i	−0.119575	+	0.630705i
$867$	−30.7448	+	30.7448i	−1.04415	+	1.04415i
$868$	11.7395	−	0.868469i	0.398465	−	0.0294778i
$869$	38.8016			1.31625
$870$	−54.8023	+	47.1911i	−1.85797	+	1.59993i
$871$	−1.24507	−	0.718843i	−0.0421877	−	0.0243571i
$872$	−34.6050	−	10.7158i	−1.17187	−	0.362882i
$873$	35.0505	+	9.39175i	1.18628	+	0.317863i
$874$	24.7997	+	21.3576i	0.838862	+	0.722433i
$875$	14.8365	+	25.5906i	0.501566	+	0.865119i
$876$	−15.9241	+	2.38826i	−0.538025	+	0.0806920i
$877$	7.90879	−	29.5160i	0.267061	−	0.996685i	−0.693916	−	0.720056i	$-0.744116\pi$
$877$	7.90879	−	29.5160i	0.267061	−	0.996685i	0.960977	−	0.276629i	$-0.0892173\pi$
$878$	−21.1268	−	10.1836i	−0.712993	−	0.343681i
$879$	−0.379331	−	0.219007i	−0.0127945	−	0.00738693i
$880$	3.01254	+	20.0938i	0.101553	+	0.677361i
$881$			20.6792i			0.696700i	0.937364	+	0.348350i	$0.113258\pi$
$881$			20.6792i			0.696700i	−0.937364	+	0.348350i	$0.886742\pi$
$882$	−35.7293	−	2.70685i	−1.20307	−	0.0911445i
$883$	9.13918	−	9.13918i	0.307558	−	0.307558i	−0.536404	−	0.843962i	$-0.680218\pi$
$883$	9.13918	−	9.13918i	0.307558	−	0.307558i	0.843962	+	0.536404i	$0.180218\pi$
$884$	−3.43285	+	2.73350i	−0.115459	+	0.0919376i
$885$	8.41487	+	3.66458i	0.282863	+	0.123183i
$886$	−14.6847	+	5.13236i	−0.493341	+	0.172425i
$887$	−7.10509	+	26.5165i	−0.238565	+	0.890338i	0.737944	+	0.674862i	$0.235797\pi$
$887$	−7.10509	+	26.5165i	−0.238565	+	0.890338i	−0.976509	+	0.215476i	$0.930870\pi$
$888$	−17.9483	+	4.07588i	−0.602305	+	0.136777i
$889$	−6.39208	+	1.20796i	−0.214384	+	0.0405136i
$890$	16.0384	+	10.9275i	0.537608	+	0.366289i
$891$	−13.2942	+	7.67538i	−0.445371	+	0.257135i
$892$	−2.49245	−	5.72416i	−0.0834533	−	0.191659i
$893$	3.22576	+	12.0387i	0.107946	+	0.402860i
$894$	62.4638	+	11.8424i	2.08910	+	0.396071i
$895$	−14.0084	+	17.5905i	−0.468250	+	0.587984i
$896$	−27.0050	+	12.9124i	−0.902173	+	0.431374i
$897$	−5.28950	+	5.28950i	−0.176611	+	0.176611i
$898$	−2.39893	−	3.52134i	−0.0800532	−	0.117509i
$899$	−17.1252	−	9.88725i	−0.571158	−	0.329758i
$900$	5.37228	−	35.7946i	0.179076	−	1.19315i
$901$	−7.26365	−	12.5810i	−0.241987	−	0.419134i
$902$	0.150818	+	2.02244i	0.00502168	+	0.0673399i
$903$	64.7825	−	31.1796i	2.15583	−	1.03759i
$904$	21.3864	−	33.9535i	0.711301	−	1.12928i
$905$	−34.6821	−	5.20343i	−1.15287	−	0.172968i
$906$	−12.2848	−	35.1493i	−0.408136	−	1.16776i
$907$	30.8577	−	8.26829i	1.02461	−	0.274544i	0.292889	−	0.956146i	$-0.405383\pi$
$907$	30.8577	−	8.26829i	1.02461	−	0.274544i	0.731723	+	0.681602i	$0.238717\pi$
$908$	−44.4619	−	5.04258i	−1.47552	−	0.167344i
$909$			7.18339i			0.238258i
$910$	1.87248	+	2.53666i	0.0620722	+	0.0840894i
$911$	−16.1539			−0.535203			−0.267601	−	0.963530i	$-0.586231\pi$
$911$	−16.1539			−0.535203			−0.267601	+	0.963530i	$0.586231\pi$
$912$	−30.8500	+	1.10916i	−1.02155	+	0.0367280i
$913$	7.07020	+	26.3864i	0.233990	+	0.873261i
$914$	34.3311	−	11.9989i	1.13557	−	0.396887i
$915$	−24.6948	−	33.4129i	−0.816386	−	1.10460i
$916$	−2.75834	−	18.3916i	−0.0911382	−	0.607676i
$917$	3.81834	−	50.7987i	0.126093	−	1.67752i
$918$	−0.976055	−	13.0887i	−0.0322146	−	0.431993i
$919$	−25.7389	+	14.8604i	−0.849049	+	0.490199i	−0.860330	−	0.509738i	$-0.829742\pi$
$919$	−25.7389	+	14.8604i	−0.849049	+	0.490199i	0.0112810	+	0.999936i	$0.496409\pi$
$920$	47.9415	+	9.09179i	1.58058	+	0.299747i
$921$	12.3214	−	21.3412i	0.406003	−	0.703217i
$922$	−12.3373	+	8.40485i	−0.406308	+	0.276799i
$923$	2.08116	+	2.08116i	0.0685023	+	0.0685023i
$924$	29.2012	−	10.1866i	0.960648	−	0.335115i
$925$	6.71354	−	10.7168i	0.220740	−	0.352366i
$926$	−50.7074	−	9.61356i	−1.66635	−	0.315921i
$927$	33.5075	−	8.97830i	1.10053	−	0.294886i
$928$	49.7079	+	7.58519i	1.63174	+	0.248996i
$929$	−16.8503	−	29.1857i	−0.552842	−	0.957550i	−0.998068	−	0.0621321i	$-0.980210\pi$
$929$	−16.8503	−	29.1857i	−0.552842	−	0.957550i	0.445226	−	0.895418i	$-0.353123\pi$
$930$	17.7831	−	3.37050i	0.583130	−	0.110523i
$931$	−16.4103	−	13.0989i	−0.537826	−	0.429298i
$932$	26.5248	+	19.6062i	0.868848	+	0.642221i
$933$	7.74701	+	2.07580i	0.253626	+	0.0679588i
$934$	5.41171	−	1.89142i	0.177077	−	0.0618891i
$935$	−27.1154	−	11.8084i	−0.886767	−	0.386177i
$936$	0.148482	−	3.85514i	0.00485330	−	0.126009i
$937$	−31.2144	−	31.2144i	−1.01973	−	1.01973i	−0.999801	−	0.0199291i	$-0.993656\pi$
$937$	−31.2144	−	31.2144i	−1.01973	−	1.01973i	−0.0199291	−	0.999801i	$-0.506344\pi$
$938$	13.7905	−	3.68641i	0.450274	−	0.120366i
$939$	−48.7133			−1.58970
$940$	13.1387	+	13.1401i	0.428537	+	0.428582i
$941$	−13.6064	+	23.5670i	−0.443557	+	0.768264i	−0.997950	−	0.0639913i	$-0.979617\pi$
$941$	−13.6064	+	23.5670i	−0.443557	+	0.768264i	0.554393	+	0.832255i	$0.312950\pi$
$942$	38.1647	+	18.3963i	1.24347	+	0.599385i
$943$	4.70456	+	1.26058i	0.153202	+	0.0410502i
$944$	−1.87204	−	6.10066i	−0.0609297	−	0.198560i
$945$	−9.42353	+	0.356879i	−0.306548	+	0.0116093i
$946$	−22.1421	+	25.7106i	−0.719903	+	0.835924i
$947$	0.549516	−	2.05082i	0.0178569	−	0.0666427i	−0.956422	−	0.291986i	$-0.905684\pi$
$947$	0.549516	−	2.05082i	0.0178569	−	0.0666427i	0.974279	+	0.225344i	$0.0723505\pi$
$948$	35.0885	+	80.5843i	1.13962	+	2.61726i
$949$	0.589620	−	1.02125i	0.0191399	−	0.0331512i
$950$	14.4112	−	15.5625i	0.467562	−	0.504915i
$951$		−	70.0871i		−	2.27273i
$952$	4.93554	−	43.2898i	0.159962	−	1.40303i
$953$	−17.1127	−	17.1127i	−0.554335	−	0.554335i	0.373354	−	0.927689i	$-0.378208\pi$
$953$	−17.1127	−	17.1127i	−0.554335	−	0.554335i	−0.927689	+	0.373354i	$0.878208\pi$
$954$	12.5484	+	2.37904i	0.406271	+	0.0770244i
$955$	−8.60613	−	21.8844i	−0.278488	−	0.708163i
$956$	−23.2513	−	9.14510i	−0.752002	−	0.295774i
$957$	−50.1823	−	13.4463i	−1.62216	−	0.434657i
$958$	−3.60855	−	48.3900i	−0.116587	−	1.56341i
$959$	8.74109	−	24.9626i	0.282264	−	0.806083i
$960$	−39.0071	+	24.4275i	−1.25895	+	0.788393i
$961$	−13.0255	−	22.5609i	−0.420178	−	0.727770i
$962$	0.585278	−	1.21421i	0.0188701	−	0.0391476i
$963$	0.235966	+	0.880637i	0.00760390	+	0.0283781i
$964$	−28.0560	+	22.3404i	−0.903623	+	0.719535i
$965$	−23.6169	+	2.67721i	−0.760256	+	0.0861824i
$966$	0.0438654	−	74.2732i	0.00141135	−	2.38970i
$967$	−19.0419	+	19.0419i	−0.612346	+	0.612346i	−0.943557	−	0.331211i	$-0.892543\pi$
$967$	−19.0419	+	19.0419i	−0.612346	+	0.612346i	0.331211	+	0.943557i	$0.392543\pi$
$968$	12.1200	−	11.2210i	0.389550	−	0.360656i
$969$	22.4668	−	38.9137i	0.721739	−	1.25009i
$970$	29.9269	+	10.4614i	0.960894	+	0.335894i
$971$	−0.879367	−	1.52311i	−0.0282202	−	0.0488788i	0.851570	−	0.524240i	$-0.175651\pi$
$971$	−0.879367	−	1.52311i	−0.0282202	−	0.0488788i	−0.879791	+	0.475361i	$0.842317\pi$
$972$	−35.6535	−	26.3538i	−1.14359	−	0.845297i
$973$	0.884118	−	1.29614i	0.0283435	−	0.0415522i
$974$	0.302945	+	0.260898i	0.00970697	+	0.00835970i
$975$	3.30217	+	3.54923i	0.105754	+	0.113666i
$976$	−6.46929	+	28.1540i	−0.207077	+	0.901188i
$977$	−3.57319	−	13.3353i	−0.114317	−	0.426635i	0.884918	−	0.465746i	$-0.154214\pi$
$977$	−3.57319	−	13.3353i	−0.114317	−	0.426635i	−0.999235	+	0.0391110i	$0.987547\pi$
$978$	−51.9780	+	35.4102i	−1.66207	+	1.13229i
$979$			13.9414i			0.445569i
$980$	−30.9530	−	4.68133i	−0.988756	−	0.149540i
$981$			46.3587i			1.48012i
$982$	12.4442	+	18.2666i	0.397109	+	0.582910i
$983$	−1.70329	−	6.35678i	−0.0543266	−	0.202750i	0.933428	−	0.358765i	$-0.116802\pi$
$983$	−1.70329	−	6.35678i	−0.0543266	−	0.202750i	−0.987755	+	0.156015i	$0.950135\pi$
$984$	−4.06388	+	2.14213i	−0.129552	+	0.0682885i
$985$	2.47995	+	3.35545i	0.0790179	+	0.106914i
$986$	−47.7621	+	55.4596i	−1.52106	+	1.76619i
$987$	15.9381	−	23.3656i	0.507315	−	0.743735i
$988$	1.34381	−	1.81802i	0.0427523	−	0.0578388i
$989$	40.7438	+	70.5703i	1.29558	+	2.24400i
$990$	23.4230	−	11.2889i	0.744432	−	0.358786i
$991$	0.497114	−	0.861026i	0.0157913	−	0.0273514i	−0.858022	−	0.513613i	$-0.828307\pi$
$991$	0.497114	−	0.861026i	0.0157913	−	0.0273514i	0.873813	+	0.486262i	$0.161640\pi$
$992$	−9.82450	−	7.86420i	−0.311928	−	0.249688i
$993$	−20.2770	+	20.2770i	−0.643473	+	0.643473i
$994$	−29.2229	−	0.0172589i	−0.926893	−	0.000547419i
$995$	1.84130	−	2.31213i	0.0583731	−	0.0732995i
$996$	−48.4064	+	38.5449i	−1.53381	+	1.22134i
$997$	2.13419	+	7.96490i	0.0675904	+	0.252251i	0.991451	−	0.130478i	$-0.0416511\pi$
$997$	2.13419	+	7.96490i	0.0675904	+	0.252251i	−0.923861	+	0.382729i	$0.874984\pi$
$998$	31.8048	+	15.3307i	1.00676	+	0.485285i
$999$	2.01578	+	3.49144i	0.0637765	+	0.110464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bv.e.213.9	yes	160
5.2	odd	4	inner	280.2.bv.e.157.13	yes	160
7.5	odd	6	inner	280.2.bv.e.173.34	yes	160
8.5	even	2	inner	280.2.bv.e.213.15	yes	160
35.12	even	12	inner	280.2.bv.e.117.15	yes	160
40.37	odd	4	inner	280.2.bv.e.157.34	yes	160
56.5	odd	6	inner	280.2.bv.e.173.13	yes	160
280.117	even	12	inner	280.2.bv.e.117.9	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bv.e.117.9	✓	160	280.117	even	12	inner
280.2.bv.e.117.15	yes	160	35.12	even	12	inner
280.2.bv.e.157.13	yes	160	5.2	odd	4	inner
280.2.bv.e.157.34	yes	160	40.37	odd	4	inner
280.2.bv.e.173.13	yes	160	56.5	odd	6	inner
280.2.bv.e.173.34	yes	160	7.5	odd	6	inner
280.2.bv.e.213.9	yes	160	1.1	even	1	trivial
280.2.bv.e.213.15	yes	160	8.5	even	2	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16877 + 0.796228i) q^{2} +(-2.48518 + 0.665902i) q^{3} +(0.732043 - 1.86121i) q^{4} +(-2.21132 - 0.331769i) q^{5} +(2.37439 - 2.75706i) q^{6} +(-2.18569 - 1.49090i) q^{7} +(0.626360 + 2.75820i) q^{8} +(3.13462 - 1.80978i) q^{9} +O(q^{10})\)	\(q+(-1.16877 + 0.796228i) q^{2} +(-2.48518 + 0.665902i) q^{3} +(0.732043 - 1.86121i) q^{4} +(-2.21132 - 0.331769i) q^{5} +(2.37439 - 2.75706i) q^{6} +(-2.18569 - 1.49090i) q^{7} +(0.626360 + 2.75820i) q^{8} +(3.13462 - 1.80978i) q^{9} +(2.84868 - 1.37295i) q^{10} +(1.96732 + 1.13583i) q^{11} +(-0.579873 + 5.11292i) q^{12} +(-0.266469 - 0.266469i) q^{13} +(3.74166 + 0.00220981i) q^{14} +(5.71645 - 0.648016i) q^{15} +(-2.92823 - 2.72498i) q^{16} +(5.62393 - 1.50693i) q^{17} +(-2.22266 + 4.61108i) q^{18} +(-2.59772 + 1.49979i) q^{19} +(-2.23627 + 3.87287i) q^{20} +(6.42462 + 2.24969i) q^{21} +(-3.20372 + 0.238908i) q^{22} +(-1.99687 + 7.45242i) q^{23} +(-3.39331 - 6.43753i) q^{24} +(4.77986 + 1.46729i) q^{25} +(0.523611 + 0.0992708i) q^{26} +(-1.12713 + 1.12713i) q^{27} +(-4.37489 + 2.97663i) q^{28} +8.88892 q^{29} +(-6.16525 + 5.30898i) q^{30} +(-1.92658 - 1.11231i) q^{31} +(5.59212 + 0.853332i) q^{32} +(-5.64549 - 1.51270i) q^{33} +(-5.37322 + 6.23918i) q^{34} +(4.33862 + 4.02199i) q^{35} +(-1.07370 - 7.15903i) q^{36} +(0.654604 - 2.44302i) q^{37} +(1.84196 - 3.82129i) q^{38} +(0.839667 + 0.484782i) q^{39} +(-0.469996 - 6.30707i) q^{40} -0.631279i q^{41} +(-9.30017 + 2.48609i) q^{42} +(7.46831 - 7.46831i) q^{43} +(3.55418 - 2.83012i) q^{44} +(-7.53208 + 2.96202i) q^{45} +(-3.59995 - 10.3001i) q^{46} +(1.07540 - 4.01346i) q^{47} +(9.09174 + 4.82214i) q^{48} +(2.55445 + 6.51727i) q^{49} +(-6.75485 + 2.09093i) q^{50} +(-12.9730 + 7.48998i) q^{51} +(-0.691023 + 0.300889i) q^{52} +(-0.645780 - 2.41008i) q^{53} +(0.419905 - 2.21482i) q^{54} +(-3.97353 - 3.16438i) q^{55} +(2.74317 - 6.96240i) q^{56} +(5.45708 - 5.45708i) q^{57} +(-10.3891 + 7.07760i) q^{58} +(1.38162 + 0.797678i) q^{59} +(2.97859 - 11.1139i) q^{60} +(-3.61096 - 6.25437i) q^{61} +(3.13738 - 0.233961i) q^{62} +(-9.54949 - 0.717797i) q^{63} +(-7.21535 + 3.45525i) q^{64} +(0.500842 + 0.677654i) q^{65} +(7.80273 - 2.72709i) q^{66} +(3.68507 - 0.987412i) q^{67} +(1.31225 - 11.5705i) q^{68} -19.8503i q^{69} +(-8.27326 - 1.24625i) q^{70} -7.81014 q^{71} +(6.95513 + 7.51235i) q^{72} +(0.809910 + 3.02262i) q^{73} +(1.18012 + 3.37654i) q^{74} +(-12.8559 - 0.463573i) q^{75} +(0.889793 + 5.93282i) q^{76} +(-2.60653 - 5.41563i) q^{77} +(-1.36737 + 0.101968i) q^{78} +(14.7923 - 8.54036i) q^{79} +(5.57118 + 6.99728i) q^{80} +(-3.37875 + 5.85217i) q^{81} +(0.502642 + 0.737820i) q^{82} +(8.50310 + 8.50310i) q^{83} +(8.89026 - 10.3107i) q^{84} +(-12.9363 + 1.46645i) q^{85} +(-2.78226 + 14.6752i) q^{86} +(-22.0906 + 5.91915i) q^{87} +(-1.90060 + 6.13769i) q^{88} +(3.06855 + 5.31488i) q^{89} +(6.44482 - 9.45916i) q^{90} +(0.185140 + 0.979696i) q^{91} +(12.4088 + 9.17210i) q^{92} +(5.52859 + 1.48138i) q^{93} +(1.93873 + 5.54707i) q^{94} +(6.24197 - 2.45468i) q^{95} +(-14.4657 + 1.60312i) q^{96} +(7.08893 + 7.08893i) q^{97} +(-8.17480 - 5.58325i) q^{98} +8.22239 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} + 12 q^{7} + 4 q^{8}+O(q^{10}) \) 160 * q - 2 * q^2 + 12 * q^7 + 4 * q^8	\( 160 q - 2 q^{2} + 12 q^{7} + 4 q^{8} - 6 q^{10} + 6 q^{12} - 8 q^{15} + 4 q^{16} - 12 q^{17} - 28 q^{18} - 24 q^{22} - 16 q^{23} + 20 q^{25} - 12 q^{26} - 46 q^{28} + 32 q^{30} + 48 q^{31} + 18 q^{32} - 12 q^{33} - 32 q^{36} - 48 q^{38} + 54 q^{40} + 6 q^{42} - 64 q^{46} - 132 q^{47} - 12 q^{50} - 20 q^{56} - 88 q^{57} + 6 q^{58} + 34 q^{60} - 32 q^{63} - 28 q^{65} - 180 q^{66} + 60 q^{68} - 108 q^{70} - 160 q^{71} + 52 q^{72} + 84 q^{73} + 48 q^{78} - 48 q^{80} + 16 q^{81} - 90 q^{82} - 84 q^{86} - 12 q^{87} + 44 q^{88} + 36 q^{92} - 20 q^{95} - 48 q^{96} - 94 q^{98}+O(q^{100}) \) 160 * q - 2 * q^2 + 12 * q^7 + 4 * q^8 - 6 * q^10 + 6 * q^12 - 8 * q^15 + 4 * q^16 - 12 * q^17 - 28 * q^18 - 24 * q^22 - 16 * q^23 + 20 * q^25 - 12 * q^26 - 46 * q^28 + 32 * q^30 + 48 * q^31 + 18 * q^32 - 12 * q^33 - 32 * q^36 - 48 * q^38 + 54 * q^40 + 6 * q^42 - 64 * q^46 - 132 * q^47 - 12 * q^50 - 20 * q^56 - 88 * q^57 + 6 * q^58 + 34 * q^60 - 32 * q^63 - 28 * q^65 - 180 * q^66 + 60 * q^68 - 108 * q^70 - 160 * q^71 + 52 * q^72 + 84 * q^73 + 48 * q^78 - 48 * q^80 + 16 * q^81 - 90 * q^82 - 84 * q^86 - 12 * q^87 + 44 * q^88 + 36 * q^92 - 20 * q^95 - 48 * q^96 - 94 * q^98

Introduction

L-functions

Modular forms

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