LMFDB - Embedded newform 416.2.bd.a.83.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(83,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 7, 6]))

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

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

chi := DirichletCharacter("416.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bd (of order $8$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			83.18
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.798622 + 1.16713i) q^{2} +(-1.28933 - 0.534060i) q^{3} +(-0.724407 - 1.86420i) q^{4} +(-0.341082 + 0.823446i) q^{5} +(1.65301 - 1.07832i) q^{6} +0.829877i q^{7} +(2.75430 + 0.643308i) q^{8} +(-0.744158 - 0.744158i) q^{9} +O(q^{10})$	\(q+(-0.798622 + 1.16713i) q^{2} +(-1.28933 - 0.534060i) q^{3} +(-0.724407 - 1.86420i) q^{4} +(-0.341082 + 0.823446i) q^{5} +(1.65301 - 1.07832i) q^{6} +0.829877i q^{7} +(2.75430 + 0.643308i) q^{8} +(-0.744158 - 0.744158i) q^{9} +(-0.688676 - 1.05571i) q^{10} +(2.33339 + 0.966524i) q^{11} +(-0.0615900 + 2.79045i) q^{12} +(0.852274 - 3.50337i) q^{13} +(-0.968579 - 0.662758i) q^{14} +(0.879538 - 0.879538i) q^{15} +(-2.95047 + 2.70088i) q^{16} -2.23714 q^{17} +(1.46283 - 0.274232i) q^{18} +(1.60629 + 3.87793i) q^{19} +(1.78215 + 0.0393350i) q^{20} +(0.443204 - 1.06999i) q^{21} +(-2.99156 + 1.95150i) q^{22} +(6.05432 + 6.05432i) q^{23} +(-3.20764 - 2.30040i) q^{24} +(2.97381 + 2.97381i) q^{25} +(3.40826 + 3.79259i) q^{26} +(2.16422 + 5.22489i) q^{27} +(1.54706 - 0.601169i) q^{28} +(-4.05013 + 9.77788i) q^{29} +(0.324121 + 1.72896i) q^{30} +(0.778167 + 0.778167i) q^{31} +(-0.795980 - 5.60057i) q^{32} +(-2.49234 - 2.49234i) q^{33} +(1.78663 - 2.61104i) q^{34} +(-0.683359 - 0.283056i) q^{35} +(-0.848184 + 1.92633i) q^{36} +(-8.68611 - 3.59791i) q^{37} +(-5.80888 - 1.22224i) q^{38} +(-2.96988 + 4.06185i) q^{39} +(-1.46917 + 2.04859i) q^{40} +10.1839 q^{41} +(0.894869 + 1.37180i) q^{42} +(0.0881390 + 0.212786i) q^{43} +(0.111464 - 5.05007i) q^{44} +(0.866592 - 0.358954i) q^{45} +(-11.9013 + 2.23110i) q^{46} +(5.95825 + 5.95825i) q^{47} +(5.24657 - 1.90661i) q^{48} +6.31130 q^{49} +(-5.84578 + 1.09589i) q^{50} +(2.88442 + 1.19476i) q^{51} +(-7.14838 + 0.949061i) q^{52} +(-2.97291 - 7.17724i) q^{53} +(-7.82655 - 1.64677i) q^{54} +(-1.59176 + 1.59176i) q^{55} +(-0.533866 + 2.28573i) q^{56} -5.85780i q^{57} +(-8.17758 - 12.5359i) q^{58} +(2.74340 - 6.62316i) q^{59} +(-2.27678 - 1.00249i) q^{60} +(-0.566092 + 1.36667i) q^{61} +(-1.52969 + 0.286765i) q^{62} +(0.617560 - 0.617560i) q^{63} +(7.17231 + 3.54372i) q^{64} +(2.59414 + 1.89674i) q^{65} +(4.89934 - 0.918462i) q^{66} +(-12.4932 + 5.17487i) q^{67} +(1.62060 + 4.17047i) q^{68} +(-4.57267 - 11.0394i) q^{69} +(0.876110 - 0.571517i) q^{70} +7.77796 q^{71} +(-1.57091 - 2.52835i) q^{72} -0.109606i q^{73} +(11.1362 - 7.26450i) q^{74} +(-2.24604 - 5.42242i) q^{75} +(6.06562 - 5.80364i) q^{76} +(-0.802096 + 1.93643i) q^{77} +(-2.36892 - 6.71013i) q^{78} -1.79121 q^{79} +(-1.21767 - 3.35077i) q^{80} -4.73526i q^{81} +(-8.13306 + 11.8860i) q^{82} +(0.736523 + 1.77812i) q^{83} +(-2.31573 - 0.0511121i) q^{84} +(0.763048 - 1.84216i) q^{85} +(-0.318740 - 0.0670657i) q^{86} +(10.4439 - 10.4439i) q^{87} +(5.80509 + 4.16318i) q^{88} +5.10185 q^{89} +(-0.273131 + 1.29810i) q^{90} +(2.90737 + 0.707283i) q^{91} +(6.90065 - 15.6722i) q^{92} +(-0.587730 - 1.41890i) q^{93} +(-11.7125 + 2.19569i) q^{94} -3.74114 q^{95} +(-1.96476 + 7.64611i) q^{96} +(-0.0376467 + 0.0376467i) q^{97} +(-5.04034 + 7.36614i) q^{98} +(-1.01717 - 2.45566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	$ 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) $ 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.798622	+	1.16713i	−0.564711	+	0.825289i
$2$	−0.798622	+	1.16713i	−0.564711	+	0.825289i
$3$	−1.28933	−	0.534060i	−0.744397	−	0.308339i	−0.0219441	−	0.999759i	$-0.506986\pi$
$3$	−1.28933	−	0.534060i	−0.744397	−	0.308339i	−0.722453	+	0.691420i	$0.756986\pi$
$4$	−0.724407	−	1.86420i	−0.362204	−	0.932099i
$5$	−0.341082	+	0.823446i	−0.152537	+	0.368256i	−0.981614	−	0.190878i	$-0.938866\pi$
$5$	−0.341082	+	0.823446i	−0.152537	+	0.368256i	0.829077	+	0.559134i	$0.188866\pi$
$6$	1.65301	−	1.07832i	0.674838	−	0.440220i
$7$			0.829877i			0.313664i	0.987625	+	0.156832i	$0.0501281\pi$
$7$			0.829877i			0.313664i	−0.987625	+	0.156832i	$0.949872\pi$
$8$	2.75430	+	0.643308i	0.973791	+	0.227444i
$9$	−0.744158	−	0.744158i	−0.248053	−	0.248053i
$10$	−0.688676	−	1.05571i	−0.217779	−	0.333845i
$11$	2.33339	+	0.966524i	0.703545	+	0.291418i	0.705630	−	0.708580i	$-0.250664\pi$
$11$	2.33339	+	0.966524i	0.703545	+	0.291418i	−0.00208563	+	0.999998i	$0.500664\pi$
$12$	−0.0615900	+	2.79045i	−0.0177795	+	0.805534i
$13$	0.852274	−	3.50337i	0.236378	−	0.971661i
$13$	0.852274	−	3.50337i	0.236378	−	0.971661i
$14$	−0.968579	−	0.662758i	−0.258864	−	0.177129i
$15$	0.879538	−	0.879538i	0.227096	−	0.227096i
$16$	−2.95047	+	2.70088i	−0.737617	+	0.675219i
$17$	−2.23714			−0.542586			−0.271293	−	0.962497i	$-0.587451\pi$
$17$	−2.23714			−0.542586			−0.271293	+	0.962497i	$0.587451\pi$
$18$	1.46283	−	0.274232i	0.344793	−	0.0646371i
$19$	1.60629	+	3.87793i	0.368508	+	0.889658i	0.993995	+	0.109423i	$0.0349003\pi$
$19$	1.60629	+	3.87793i	0.368508	+	0.889658i	−0.625487	+	0.780235i	$0.715100\pi$
$20$	1.78215	+	0.0393350i	0.398500	+	0.00879558i
$21$	0.443204	−	1.06999i	0.0967150	−	0.233491i
$22$	−2.99156	+	1.95150i	−0.637803	+	0.416061i
$23$	6.05432	+	6.05432i	1.26241	+	1.26241i	0.949920	+	0.312492i	$0.101164\pi$
$23$	6.05432	+	6.05432i	1.26241	+	1.26241i	0.312492	+	0.949920i	$0.398836\pi$
$24$	−3.20764	−	2.30040i	−0.654758	−	0.469567i
$25$	2.97381	+	2.97381i	0.594762	+	0.594762i
$26$	3.40826	+	3.79259i	0.668416	+	0.743788i
$27$	2.16422	+	5.22489i	0.416505	+	1.00553i
$28$	1.54706	−	0.601169i	0.292366	−	0.113610i
$29$	−4.05013	+	9.77788i	−0.752090	+	1.81571i	−0.204708	+	0.978823i	$0.565624\pi$
$29$	−4.05013	+	9.77788i	−0.752090	+	1.81571i	−0.547382	+	0.836883i	$0.684376\pi$
$30$	0.324121	+	1.72896i	0.0591762	+	0.315663i
$31$	0.778167	+	0.778167i	0.139763	+	0.139763i	0.773527	−	0.633764i	$-0.218491\pi$
$31$	0.778167	+	0.778167i	0.139763	+	0.139763i	−0.633764	+	0.773527i	$0.718491\pi$
$32$	−0.795980	−	5.60057i	−0.140711	−	0.990051i
$33$	−2.49234	−	2.49234i	−0.433861	−	0.433861i
$34$	1.78663	−	2.61104i	0.306404	−	0.447790i
$35$	−0.683359	−	0.283056i	−0.115509	−	0.0478453i
$36$	−0.848184	+	1.92633i	−0.141364	+	0.321055i
$37$	−8.68611	−	3.59791i	−1.42799	−	0.591492i	−0.471134	−	0.882062i	$-0.656155\pi$
$37$	−8.68611	−	3.59791i	−1.42799	−	0.591492i	−0.956854	+	0.290570i	$0.906155\pi$
$38$	−5.80888	−	1.22224i	−0.942325	−	0.198273i
$39$	−2.96988	+	4.06185i	−0.475561	+	0.650417i
$40$	−1.46917	+	2.04859i	−0.232296	+	0.323911i
$41$	10.1839			1.59045			0.795227	−	0.606311i	$-0.207352\pi$
$41$	10.1839			1.59045			0.795227	+	0.606311i	$0.207352\pi$
$42$	0.894869	+	1.37180i	0.138081	+	0.211673i
$43$	0.0881390	+	0.212786i	0.0134411	+	0.0324496i	0.930458	−	0.366400i	$-0.119410\pi$
$43$	0.0881390	+	0.212786i	0.0134411	+	0.0324496i	−0.917017	+	0.398849i	$0.869410\pi$
$44$	0.111464	−	5.05007i	0.0168038	−	0.761326i
$45$	0.866592	−	0.358954i	0.129184	−	0.0535097i
$46$	−11.9013	+	2.23110i	−1.75475	+	0.328957i
$47$	5.95825	+	5.95825i	0.869100	+	0.869100i	0.992373	−	0.123273i	$-0.0393391\pi$
$47$	5.95825	+	5.95825i	0.869100	+	0.869100i	−0.123273	+	0.992373i	$0.539339\pi$
$48$	5.24657	−	1.90661i	0.757277	−	0.275195i
$49$	6.31130			0.901615
$50$	−5.84578	+	1.09589i	−0.826719	+	0.154982i
$51$	2.88442	+	1.19476i	0.403899	+	0.167301i
$52$	−7.14838	+	0.949061i	−0.991301	+	0.131611i
$53$	−2.97291	−	7.17724i	−0.408360	−	0.985869i	−0.985569	−	0.169273i	$-0.945858\pi$
$53$	−2.97291	−	7.17724i	−0.408360	−	0.985869i	0.577209	−	0.816597i	$-0.304142\pi$
$54$	−7.82655	−	1.64677i	−1.06506	−	0.224098i
$55$	−1.59176	+	1.59176i	−0.214633	+	0.214633i
$56$	−0.533866	+	2.28573i	−0.0713409	+	0.305443i
$57$		−	5.85780i		−	0.775884i
$58$	−8.17758	−	12.5359i	−1.07377	−	1.64604i
$59$	2.74340	−	6.62316i	0.357161	−	0.862262i	−0.638536	−	0.769592i	$-0.720460\pi$
$59$	2.74340	−	6.62316i	0.357161	−	0.862262i	0.995697	−	0.0926704i	$-0.0295403\pi$
$60$	−2.27678	−	1.00249i	−0.293931	−	0.129421i
$61$	−0.566092	+	1.36667i	−0.0724806	+	0.174984i	−0.955968	−	0.293472i	$-0.905189\pi$
$61$	−0.566092	+	1.36667i	−0.0724806	+	0.174984i	0.883487	+	0.468455i	$0.155189\pi$
$62$	−1.52969	+	0.286765i	−0.194270	+	0.0364192i
$63$	0.617560	−	0.617560i	0.0778052	−	0.0778052i
$64$	7.17231	+	3.54372i	0.896539	+	0.442965i
$65$	2.59414	+	1.89674i	0.321764	+	0.235262i
$66$	4.89934	−	0.918462i	0.603067	−	0.113055i
$67$	−12.4932	+	5.17487i	−1.52629	+	0.632211i	−0.978840	−	0.204625i	$-0.934402\pi$
$67$	−12.4932	+	5.17487i	−1.52629	+	0.632211i	−0.547453	+	0.836836i	$0.684402\pi$
$68$	1.62060	+	4.17047i	0.196526	+	0.505743i
$69$	−4.57267	−	11.0394i	−0.550485	−	1.32899i
$70$	0.876110	−	0.571517i	0.104715	−	0.0683093i
$71$	7.77796			0.923074			0.461537	−	0.887121i	$-0.347298\pi$
$71$	7.77796			0.923074			0.461537	+	0.887121i	$0.347298\pi$
$72$	−1.57091	−	2.52835i	−0.185133	−	0.297969i
$73$		−	0.109606i		−	0.0128284i	−0.999979	−	0.00641419i	$-0.997958\pi$
$73$		−	0.109606i		−	0.0128284i	0.999979	−	0.00641419i	$-0.00204171\pi$
$74$	11.1362	−	7.26450i	1.29455	−	0.844481i
$75$	−2.24604	−	5.42242i	−0.259351	−	0.626128i
$76$	6.06562	−	5.80364i	0.695774	−	0.665723i
$77$	−0.802096	+	1.93643i	−0.0914073	+	0.220677i
$78$	−2.36892	−	6.71013i	−0.268228	−	0.759773i
$79$	−1.79121			−0.201527			−0.100764	−	0.994910i	$-0.532129\pi$
$79$	−1.79121			−0.201527			−0.100764	+	0.994910i	$0.532129\pi$
$80$	−1.21767	−	3.35077i	−0.136140	−	0.374628i
$81$		−	4.73526i		−	0.526141i
$82$	−8.13306	+	11.8860i	−0.898147	+	1.31258i
$83$	0.736523	+	1.77812i	0.0808440	+	0.195175i	0.959133	−	0.282955i	$-0.0913148\pi$
$83$	0.736523	+	1.77812i	0.0808440	+	0.195175i	−0.878289	+	0.478130i	$0.841315\pi$
$84$	−2.31573	−	0.0511121i	−0.252667	−	0.00557679i
$85$	0.763048	−	1.84216i	0.0827642	−	0.199810i
$86$	−0.318740	−	0.0670657i	−0.0343706	−	0.00723188i
$87$	10.4439	−	10.4439i	1.11971	−	1.11971i
$88$	5.80509	+	4.16318i	0.618825	+	0.443797i
$89$	5.10185			0.540795			0.270398	−	0.962749i	$-0.412845\pi$
$89$	5.10185			0.540795			0.270398	+	0.962749i	$0.412845\pi$
$90$	−0.273131	+	1.29810i	−0.0287906	+	0.136832i
$91$	2.90737	+	0.707283i	0.304775	+	0.0741434i
$92$	6.90065	−	15.6722i	0.719443	−	1.63394i
$93$	−0.587730	−	1.41890i	−0.0609447	−	0.147134i
$94$	−11.7125	+	2.19569i	−1.20805	+	0.226468i
$95$	−3.74114			−0.383833
$96$	−1.96476	+	7.64611i	−0.200527	+	0.780378i
$97$	−0.0376467	+	0.0376467i	−0.00382244	+	0.00382244i	−0.709015	−	0.705193i	$-0.750860\pi$
$97$	−0.0376467	+	0.0376467i	−0.00382244	+	0.00382244i	0.705193	+	0.709015i	$0.250860\pi$
$98$	−5.04034	+	7.36614i	−0.509152	+	0.744093i
$99$	−1.01717	−	2.45566i	−0.102229	−	0.246803i
$100$	3.38952	−	7.69802i	0.338952	−	0.769802i
$101$	5.45788	+	13.1765i	0.543079	+	1.31111i	0.922540	+	0.385902i	$0.126110\pi$
$101$	5.45788	+	13.1765i	0.543079	+	1.31111i	−0.379461	+	0.925208i	$0.623890\pi$
$102$	−3.69801	+	2.41234i	−0.366158	+	0.238857i
$103$	−6.30366	+	6.30366i	−0.621118	+	0.621118i	−0.945817	−	0.324699i	$-0.894737\pi$
$103$	−6.30366	+	6.30366i	−0.621118	+	0.621118i	0.324699	+	0.945817i	$0.394737\pi$
$104$	4.60116	−	9.10106i	0.451181	−	0.892432i
$105$	0.729909	+	0.729909i	0.0712318	+	0.0712318i
$106$	10.7510	+	2.26211i	1.04423	+	0.219716i
$107$	1.87203	−	0.775420i	0.180976	−	0.0749627i	−0.290356	−	0.956919i	$-0.593774\pi$
$107$	1.87203	−	0.775420i	0.180976	−	0.0749627i	0.471331	+	0.881956i	$0.343774\pi$
$108$	8.17246	−	7.81949i	0.786395	−	0.752431i
$109$	12.4324	−	5.14966i	1.19081	−	0.493248i	0.302789	−	0.953058i	$-0.402082\pi$
$109$	12.4324	−	5.14966i	1.19081	−	0.493248i	0.888017	+	0.459810i	$0.152082\pi$
$110$	−0.586584	−	3.12901i	−0.0559286	−	0.298339i
$111$	9.27780	+	9.27780i	0.880610	+	0.880610i
$112$	−2.24140	−	2.44853i	−0.211792	−	0.231364i
$113$		−	20.6945i		−	1.94677i	−0.229172	−	0.973386i	$-0.573602\pi$
$113$		−	20.6945i		−	1.94677i	0.229172	−	0.973386i	$-0.426398\pi$
$114$	6.83684	+	4.67816i	0.640329	+	0.438150i
$115$	−7.05042	+	2.92038i	−0.657455	+	0.272327i
$116$	21.1618	+	0.467078i	1.96483	+	0.0433671i
$117$	−3.24129	+	1.97284i	−0.299657	+	0.182389i
$118$	5.53918	+	8.49132i	0.509923	+	0.781689i
$119$		−	1.85655i		−	0.170190i
$120$	2.98832	−	1.85670i	0.272795	−	0.169492i
$121$	−3.26761	−	3.26761i	−0.297056	−	0.297056i
$122$	−1.14299	−	1.75216i	−0.103482	−	0.158633i
$123$	−13.1304	−	5.43880i	−1.18393	−	0.490400i
$124$	0.886947	−	2.01437i	0.0796502	−	0.180896i
$125$	−7.58031	+	3.13987i	−0.678004	+	0.280838i
$126$	0.227579	+	1.21397i	0.0202743	+	0.108149i
$127$	5.33063			0.473017			0.236508	−	0.971629i	$-0.423997\pi$
$127$	5.33063			0.473017			0.236508	+	0.971629i	$0.423997\pi$
$128$	−9.86396	+	5.54096i	−0.871859	+	0.489756i
$129$		−	0.321424i		−	0.0282998i
$130$	−4.28549	+	1.51294i	−0.375862	+	0.132693i
$131$	−11.8671	−	4.91551i	−1.03683	−	0.429470i	−0.201658	−	0.979456i	$-0.564633\pi$
$131$	−11.8671	−	4.91551i	−1.03683	−	0.429470i	−0.835174	+	0.549986i	$0.814633\pi$
$132$	−2.84075	+	6.45169i	−0.247256	+	0.561548i
$133$	−3.21820	+	1.33302i	−0.279054	+	0.115588i
$134$	3.93760	−	18.7141i	0.340157	−	1.61665i
$135$	−5.04059			−0.433825
$136$	−6.16174	−	1.43917i	−0.528365	−	0.123408i
$137$			6.07190i			0.518758i	0.965776	+	0.259379i	$0.0835178\pi$
$137$			6.07190i			0.518758i	−0.965776	+	0.259379i	$0.916482\pi$
$138$	16.5363	+	3.47938i	1.40766	+	0.296185i
$139$	19.0052	−	7.87221i	1.61200	−	0.667712i	0.618953	−	0.785428i	$-0.287557\pi$
$139$	19.0052	−	7.87221i	1.61200	−	0.667712i	0.993047	+	0.117716i	$0.0375572\pi$
$140$	−0.0326432	+	1.47896i	−0.00275886	+	0.124995i
$141$	−4.50011	−	10.8642i	−0.378978	−	0.914933i
$142$	−6.21164	+	9.07792i	−0.521270	+	0.761802i
$143$	5.37479	−	7.35101i	0.449462	−	0.614722i
$144$	4.20549	+	0.185735i	0.350458	+	0.0154779i
$145$	−6.67012	−	6.67012i	−0.553923	−	0.553923i
$146$	0.127925	+	0.0875335i	0.0105871	+	0.00724433i
$147$	−8.13738	−	3.37061i	−0.671160	−	0.278003i
$148$	−0.414925	+	18.7990i	−0.0341067	+	1.54527i
$149$	−0.560642	−	0.232226i	−0.0459296	−	0.0190247i	0.359600	−	0.933106i	$-0.382913\pi$
$149$	−0.560642	−	0.232226i	−0.0459296	−	0.0190247i	−0.405530	+	0.914082i	$0.632913\pi$
$150$	8.12244	+	1.70903i	0.663194	+	0.139542i
$151$	−21.8946			−1.78175			−0.890877	−	0.454244i	$-0.849909\pi$
$151$	−21.8946			−1.78175			−0.890877	+	0.454244i	$0.849909\pi$
$152$	1.92950	+	11.7143i	0.156503	+	0.950156i
$153$	1.66478	+	1.66478i	0.134590	+	0.134590i
$154$	−1.61950	−	2.48263i	−0.130503	−	0.200056i
$155$	−0.906197	+	0.375359i	−0.0727875	+	0.0301496i
$156$	9.72350	+	2.59400i	0.778503	+	0.207686i
$157$	−6.14895	+	14.8449i	−0.490740	+	1.18475i	0.463604	+	0.886042i	$0.346556\pi$
$157$	−6.14895	+	14.8449i	−0.490740	+	1.18475i	−0.954344	+	0.298709i	$0.903444\pi$
$158$	1.43050	−	2.09059i	0.113805	−	0.166318i
$159$			10.8416i			0.859792i
$160$	4.88326	+	1.25481i	0.386056	+	0.0992014i
$161$	−5.02434	+	5.02434i	−0.395973	+	0.395973i
$162$	5.52669	+	3.78168i	0.434218	+	0.297117i
$163$	−3.23712	−	7.81511i	−0.253551	−	0.612127i	0.744935	−	0.667138i	$-0.232481\pi$
$163$	−3.23712	−	7.81511i	−0.253551	−	0.612127i	−0.998486	+	0.0550109i	$0.982481\pi$
$164$	−7.37727	−	18.9848i	−0.576068	−	1.48246i
$165$	2.90240	−	1.20221i	0.225952	−	0.0935923i
$166$	−2.66351	−	0.560427i	−0.206729	−	0.0434975i
$167$			5.20162i			0.402513i	0.979539	+	0.201257i	$0.0645025\pi$
$167$			5.20162i			0.402513i	−0.979539	+	0.201257i	$0.935497\pi$
$168$	1.90905	−	2.66195i	0.147286	−	0.205374i
$169$	−11.5473	−	5.97167i	−0.888251	−	0.459359i
$170$	1.54066	+	2.36177i	0.118163	+	0.181139i
$171$	1.69046	−	4.08112i	0.129272	−	0.312091i
$172$	0.332828	−	0.318453i	0.0253779	−	0.0242818i
$173$	−4.66094	+	11.2525i	−0.354364	+	0.855511i	0.641706	+	0.766950i	$0.278227\pi$
$173$	−4.66094	+	11.2525i	−0.354364	+	0.855511i	−0.996071	+	0.0885608i	$0.971773\pi$
$174$	3.84873	+	20.5302i	0.291771	+	1.55639i
$175$	−2.46790	+	2.46790i	−0.186555	+	0.186555i
$176$	−9.49507	+	3.45051i	−0.715718	+	0.260092i
$177$	−7.07433	+	7.07433i	−0.531739	+	0.531739i
$178$	−4.07445	+	5.95455i	−0.305393	+	0.446312i
$179$	15.2058	+	6.29843i	1.13653	+	0.470767i	0.869997	−	0.493058i	$-0.164121\pi$
$179$	15.2058	+	6.29843i	1.13653	+	0.470767i	0.266536	+	0.963825i	$0.414121\pi$
$180$	−1.29693	−	1.35547i	−0.0966673	−	0.101031i
$181$	−11.0913	+	4.59417i	−0.824411	+	0.341482i	−0.754688	−	0.656084i	$-0.772212\pi$
$181$	−11.0913	+	4.59417i	−0.824411	+	0.341482i	−0.0697233	+	0.997566i	$0.522212\pi$
$182$	−3.14738	+	2.82844i	−0.233300	+	0.209658i
$183$	1.45976	−	1.45976i	0.107909	−	0.107909i
$184$	12.7806	+	20.5702i	0.942198	+	1.51645i
$185$	5.92536	−	5.92536i	0.435641	−	0.435641i
$186$	2.12543	+	0.447208i	0.155844	+	0.0327909i
$187$	−5.22012	−	2.16225i	−0.381733	−	0.158119i
$188$	6.79116	−	15.4236i	0.495296	−	1.12488i
$189$	−4.33602	+	1.79604i	−0.315399	+	0.130643i
$190$	2.98775	−	4.36641i	0.216754	−	0.316773i
$191$			19.8925i			1.43937i	0.694301	+	0.719684i	$0.255714\pi$
$191$			19.8925i			1.43937i	−0.694301	+	0.719684i	$0.744286\pi$
$192$	−7.35494	−	8.39948i	−0.530797	−	0.606180i
$193$	−6.02037	−	6.02037i	−0.433356	−	0.433356i	0.456412	−	0.889768i	$-0.349134\pi$
$193$	−6.02037	−	6.02037i	−0.433356	−	0.433356i	−0.889768	+	0.456412i	$0.849134\pi$
$194$	−0.0138733	−	0.0740042i	−0.000996045	−	0.00531319i
$195$	−2.33174	−	3.83096i	−0.166980	−	0.274341i
$196$	−4.57195	−	11.7655i	−0.326568	−	0.840394i
$197$	6.66483	−	16.0903i	0.474849	−	1.14639i	−0.487145	−	0.873321i	$-0.661962\pi$
$197$	6.66483	−	16.0903i	0.474849	−	1.14639i	0.961995	−	0.273067i	$-0.0880381\pi$
$198$	3.67842	+	0.773971i	0.261414	+	0.0550037i
$199$	−1.80087	+	1.80087i	−0.127660	+	0.127660i	−0.768050	−	0.640390i	$-0.778773\pi$
$199$	−1.80087	+	1.80087i	−0.127660	+	0.127660i	0.640390	+	0.768050i	$0.278773\pi$
$200$	6.27768	+	10.1038i	0.443899	+	0.714449i
$201$	18.8717			1.33110
$202$	−19.7375	−	4.15295i	−1.38873	−	0.292200i
$203$	−8.11444	−	3.36111i	−0.569522	−	0.235904i
$204$	0.137785	−	6.24262i	0.00964690	−	0.437071i
$205$	−3.47354	+	8.38587i	−0.242603	+	0.585694i
$206$	−2.32298	−	12.3915i	−0.161850	−	0.863354i
$207$		−	9.01073i		−	0.626289i
$208$	6.94757	+	12.6385i	0.481728	+	0.876321i
$209$			10.6013i			0.733304i
$210$	−1.43482	+	0.268981i	−0.0990122	+	0.0185615i
$211$	−1.02245	+	2.46842i	−0.0703886	+	0.169933i	−0.955158	−	0.296095i	$-0.904315\pi$
$211$	−1.02245	+	2.46842i	−0.0703886	+	0.169933i	0.884770	+	0.466028i	$0.154315\pi$
$212$	−11.2262	+	10.7413i	−0.771018	+	0.737718i
$213$	−10.0284	−	4.15389i	−0.687134	−	0.284620i
$214$	−0.590023	+	2.80418i	−0.0403332	+	0.191690i
$215$	−0.205281			−0.0140000
$216$	2.59970	+	15.7832i	0.176887	+	1.07391i
$217$	−0.645783	+	0.645783i	−0.0438386	+	0.0438386i
$218$	−3.91842	+	18.6229i	−0.265389	+	1.26130i
$219$	−0.0585360	+	0.141318i	−0.00395550	+	0.00954942i
$220$	4.12044	+	1.81427i	0.277800	+	0.122318i
$221$	−1.90665	+	7.83753i	−0.128255	+	0.527209i
$222$	−18.2379	+	3.41899i	−1.22405	+	0.229468i
$223$	−7.29274	−	7.29274i	−0.488358	−	0.488358i	0.419430	−	0.907788i	$-0.362230\pi$
$223$	−7.29274	−	7.29274i	−0.488358	−	0.488358i	−0.907788	+	0.419430i	$0.862230\pi$
$224$	4.64779	−	0.660566i	0.310543	−	0.0441359i
$225$		−	4.42597i		−	0.295064i
$226$	24.1532	+	16.5270i	1.60665	+	1.09936i
$227$	−8.31242	+	3.44312i	−0.551715	+	0.228528i	−0.641084	−	0.767471i	$-0.721515\pi$
$227$	−8.31242	+	3.44312i	−0.551715	+	0.228528i	0.0893692	+	0.995999i	$0.471515\pi$
$228$	−10.9201	+	4.24343i	−0.723201	+	0.281028i
$229$	5.19562	+	2.15210i	0.343337	+	0.142215i	0.547687	−	0.836683i	$-0.315508\pi$
$229$	5.19562	+	2.15210i	0.343337	+	0.142215i	−0.204351	+	0.978898i	$0.565508\pi$
$230$	2.22214	−	10.5611i	0.146524	−	0.696376i
$231$	2.06834	−	2.06834i	0.136087	−	0.136087i
$232$	−17.4454	+	24.3257i	−1.14535	+	1.59706i
$233$	3.79321	−	3.79321i	0.248501	−	0.248501i	−0.571854	−	0.820355i	$-0.693776\pi$
$233$	3.79321	−	3.79321i	0.248501	−	0.248501i	0.820355	+	0.571854i	$0.193776\pi$
$234$	0.285998	−	5.35857i	0.0186962	−	0.350301i
$235$	−6.93855	+	2.87404i	−0.452621	+	0.187482i
$236$	−14.3342	−	0.316381i	−0.933079	−	0.0205946i
$237$	2.30947	+	0.956615i	0.150016	+	0.0621388i
$238$	2.16684	+	1.48268i	0.140456	+	0.0961079i
$239$	−3.82332	+	3.82332i	−0.247310	+	0.247310i	−0.819866	−	0.572556i	$-0.805952\pi$
$239$	−3.82332	+	3.82332i	−0.247310	+	0.247310i	0.572556	+	0.819866i	$0.305952\pi$
$240$	−0.219525	+	4.97057i	−0.0141703	+	0.320849i
$241$	16.0420	−	16.0420i	1.03336	−	1.03336i	0.0339314	−	0.999424i	$-0.489197\pi$
$241$	16.0420	−	16.0420i	1.03336	−	1.03336i	0.999424	−	0.0339314i	$-0.0108028\pi$
$242$	6.42333	−	1.20416i	0.412907	−	0.0774063i
$243$	3.96375	−	9.56935i	0.254275	−	0.613874i
$244$	2.95782	+	0.0652841i	0.189355	+	0.00417939i
$245$	−2.15267	+	5.19701i	−0.137529	+	0.332025i
$246$	16.8340	−	10.9814i	1.07330	−	0.700150i
$247$	14.9548	−	2.32238i	0.951553	−	0.147769i
$248$	1.64270	+	2.64390i	0.104312	+	0.167888i
$249$		−	2.68594i		−	0.170215i
$250$	2.38915	−	11.3548i	0.151103	−	0.718141i
$251$	7.98132	−	3.30597i	0.503776	−	0.208671i	−0.116298	−	0.993214i	$-0.537103\pi$
$251$	7.98132	−	3.30597i	0.503776	−	0.208671i	0.620074	+	0.784543i	$0.287103\pi$
$252$	−1.59862	−	0.703889i	−0.100703	−	0.0443408i
$253$	8.27547	+	19.9787i	0.520274	+	1.25605i
$254$	−4.25716	+	6.22156i	−0.267118	+	0.390376i
$255$	−1.96765	+	1.96765i	−0.123219	+	0.123219i
$256$	1.41053	−	15.9377i	0.0881579	−	0.996107i
$257$			25.6188i			1.59806i	0.601294	+	0.799028i	$0.294652\pi$
$257$			25.6188i			1.59806i	−0.601294	+	0.799028i	$0.705348\pi$
$258$	0.375146	+	0.256696i	0.0233555	+	0.0159812i
$259$	2.98582	−	7.20841i	0.185530	−	0.447909i
$260$	1.65668	−	6.21001i	0.102743	−	0.385128i
$261$	10.2902	−	4.26235i	0.636948	−	0.263833i
$262$	15.2144	−	9.92486i	0.939947	−	0.613160i
$263$	−9.41630	−	9.41630i	−0.580634	−	0.580634i	0.354444	−	0.935077i	$-0.384670\pi$
$263$	−9.41630	−	9.41630i	−0.580634	−	0.580634i	−0.935077	+	0.354444i	$0.884670\pi$
$264$	−5.26131	−	8.46800i	−0.323811	−	0.521169i
$265$	6.92407			0.425342
$266$	1.01431	−	4.82066i	0.0621913	−	0.295574i
$267$	−6.57799	−	2.72469i	−0.402566	−	0.166748i
$268$	18.6972	+	19.5412i	1.14211	+	1.19367i
$269$	−1.36161	−	0.563998i	−0.0830190	−	0.0343876i	0.340788	−	0.940140i	$-0.389306\pi$
$269$	−1.36161	−	0.563998i	−0.0830190	−	0.0343876i	−0.423806	+	0.905753i	$0.639306\pi$
$270$	4.02553	−	5.88305i	0.244986	−	0.358031i
$271$	17.1691	+	17.1691i	1.04295	+	1.04295i	0.999035	+	0.0439147i	$0.0139830\pi$
$271$	17.1691	+	17.1691i	1.04295	+	1.04295i	0.0439147	+	0.999035i	$0.486017\pi$
$272$	6.60060	−	6.04223i	0.400220	−	0.366364i
$273$	−3.37084	−	2.46463i	−0.204013	−	0.149166i
$274$	−7.08673	−	4.84915i	−0.428125	−	0.292948i
$275$	4.06481	+	9.81332i	0.245117	+	0.591766i
$276$	−17.2672	+	16.5214i	−1.03936	+	0.994471i
$277$	−2.78714	+	1.15447i	−0.167463	+	0.0693654i	−0.464840	−	0.885395i	$-0.653888\pi$
$277$	−2.78714	+	1.15447i	−0.167463	+	0.0693654i	0.297377	+	0.954760i	$0.403888\pi$
$278$	−5.99003	+	28.4686i	−0.359258	+	1.70743i
$279$		−	1.15816i		−	0.0693371i
$280$	−1.70008	−	1.21923i	−0.101599	−	0.0728630i
$281$	−7.47748			−0.446069			−0.223035	−	0.974811i	$-0.571596\pi$
$281$	−7.47748			−0.446069			−0.223035	+	0.974811i	$0.571596\pi$
$282$	16.2739	+	3.42417i	0.969097	+	0.203906i
$283$	18.1443	−	7.51563i	1.07857	−	0.446758i	0.228562	−	0.973529i	$-0.426598\pi$
$283$	18.1443	−	7.51563i	1.07857	−	0.446758i	0.850007	+	0.526772i	$0.176598\pi$
$284$	−5.63441	−	14.4997i	−0.334341	−	0.860396i
$285$	4.82358	+	1.99799i	0.285724	+	0.118351i
$286$	4.28720	+	12.1438i	0.253507	+	0.718076i
$287$			8.45137i			0.498868i
$288$	−3.57537	+	4.76004i	−0.210681	+	0.280488i
$289$	−11.9952			−0.705601
$290$	13.1118	−	2.45803i	0.769953	−	0.144340i
$291$	0.0686447	−	0.0284336i	0.00402402	−	0.00166681i
$292$	−0.204327	+	0.0793992i	−0.0119573	+	0.00464649i
$293$	−23.3719	−	9.68096i	−1.36540	−	0.565568i	−0.424864	−	0.905257i	$-0.639678\pi$
$293$	−23.3719	−	9.68096i	−1.36540	−	0.565568i	−0.940538	+	0.339690i	$0.889678\pi$
$294$	10.4326	−	6.80557i	0.608444	−	0.396909i
$295$	4.51809	+	4.51809i	0.263053	+	0.263053i
$296$	−21.6096	−	15.4975i	−1.25603	−	0.900776i
$297$			14.2835i			0.828813i
$298$	0.718780	−	0.468885i	0.0416378	−	0.0271618i
$299$	26.3705	−	16.0506i	1.52504	−	0.928230i
$300$	−8.48142	+	8.11511i	−0.489675	+	0.468526i
$301$	−0.176587	+	0.0731446i	−0.0101783	+	0.00421598i
$302$	17.4855	−	25.5539i	1.00618	−	1.47046i
$303$		−	19.9037i		−	1.14344i
$304$	−15.2131	−	7.10331i	−0.872532	−	0.407403i
$305$	−0.932292	−	0.932292i	−0.0533829	−	0.0533829i
$306$	−3.27256	+	0.613495i	−0.187080	+	0.0350712i
$307$	−7.65544	+	3.17099i	−0.436919	+	0.180978i	−0.590291	−	0.807191i	$-0.700987\pi$
$307$	−7.65544	+	3.17099i	−0.436919	+	0.180978i	0.153372	+	0.988169i	$0.450987\pi$
$308$	4.19093	+	0.0925010i	0.238801	+	0.00527074i
$309$	11.4941	−	4.76100i	0.653874	−	0.270844i
$310$	0.285614	−	1.35742i	0.0162218	−	0.0770965i
$311$	−2.94510	−	2.94510i	−0.167001	−	0.167001i	0.618659	−	0.785660i	$-0.287676\pi$
$311$	−2.94510	−	2.94510i	−0.167001	−	0.167001i	−0.785660	+	0.618659i	$0.787676\pi$
$312$	−10.7929	+	9.27701i	−0.611030	+	0.525207i
$313$	3.74367	−	3.74367i	0.211605	−	0.211605i	−0.593344	−	0.804949i	$-0.702193\pi$
$313$	3.74367	−	3.74367i	0.211605	−	0.211605i	0.804949	+	0.593344i	$0.202193\pi$
$314$	−12.4153	−	19.0321i	−0.700636	−	1.07404i
$315$	0.297888	+	0.719165i	0.0167841	+	0.0405204i
$316$	1.29757	+	3.33918i	0.0729939	+	0.187843i
$317$	−0.912543	−	2.20307i	−0.0512535	−	0.123737i	0.896179	−	0.443693i	$-0.146332\pi$
$317$	−0.912543	−	2.20307i	−0.0512535	−	0.123737i	−0.947432	+	0.319956i	$0.896332\pi$
$318$	−12.6536	−	8.65831i	−0.709577	−	0.485534i
$319$	−18.9011	+	18.9011i	−1.05826	+	1.05826i
$320$	−5.36441	+	4.69731i	−0.299880	+	0.262587i
$321$	−2.82779			−0.157832
$322$	−1.85154	−	9.87663i	−0.103182	−	0.550403i
$323$	−3.59349	−	8.67546i	−0.199947	−	0.482715i
$324$	−8.82747	+	3.43026i	−0.490415	+	0.190570i
$325$	12.9529	−	7.88386i	0.718496	−	0.437318i
$326$	11.7065	+	2.46315i	0.648364	+	0.136422i
$327$	−18.7797			−1.03852
$328$	28.0494	+	6.55137i	1.54877	+	0.361739i
$329$	−4.94461	+	4.94461i	−0.272605	+	0.272605i
$330$	−0.914775	+	4.34761i	−0.0503567	+	0.239328i
$331$	2.04707	−	4.94206i	0.112517	−	0.271640i	−0.857583	−	0.514346i	$-0.828035\pi$
$331$	2.04707	−	4.94206i	0.112517	−	0.271640i	0.970100	+	0.242705i	$0.0780348\pi$
$332$	2.78123	−	2.66111i	0.152640	−	0.146047i
$333$	3.78643	+	9.14125i	0.207495	+	0.500937i
$334$	−6.07099	−	4.15412i	−0.332190	−	0.227304i
$335$		−	12.0526i		−	0.658502i
$336$	1.58225	+	4.35401i	0.0863188	+	0.237531i
$337$	2.89843			0.157888			0.0789438	−	0.996879i	$-0.474845\pi$
$337$	2.89843			0.157888			0.0789438	+	0.996879i	$0.474845\pi$
$338$	16.1916	−	8.70810i	0.880709	−	0.473658i
$339$	−11.0521	+	26.6821i	−0.600267	+	1.44917i
$340$	−3.98691	−	0.0879979i	−0.216221	−	0.00477235i
$341$	1.06365	+	2.56789i	0.0576001	+	0.139059i
$342$	3.41319	+	5.23226i	0.184564	+	0.282928i
$343$			11.0467i			0.596468i
$344$	0.105874	+	0.642778i	0.00570834	+	0.0346563i
$345$	10.6500			0.573377
$346$	−9.41085	−	14.4264i	−0.505931	−	0.775569i
$347$	−10.8694	−	26.2411i	−0.583502	−	1.40870i	−0.889619	−	0.456704i	$-0.849030\pi$
$347$	−10.8694	−	26.2411i	−0.583502	−	1.40870i	0.306117	−	0.951994i	$-0.400970\pi$
$348$	−27.0352	−	11.9039i	−1.44924	−	0.638116i
$349$	12.9761	−	5.37487i	0.694594	−	0.287710i	−0.00731850	−	0.999973i	$-0.502330\pi$
$349$	12.9761	−	5.37487i	0.694594	−	0.287710i	0.701913	+	0.712263i	$0.252330\pi$
$350$	−0.909452	−	4.85128i	−0.0486123	−	0.259312i
$351$	20.1493	−	3.12904i	1.07549	−	0.167016i
$352$	3.55575	−	13.8377i	0.189522	−	0.737551i
$353$	6.18989	−	6.18989i	0.329455	−	0.329455i	−0.522924	−	0.852379i	$-0.675159\pi$
$353$	6.18989	−	6.18989i	0.329455	−	0.329455i	0.852379	+	0.522924i	$0.175159\pi$
$354$	−2.60698	−	13.9064i	−0.138560	−	0.739117i
$355$	−2.65292	+	6.40472i	−0.140803	+	0.339927i
$356$	−3.69582	−	9.51086i	−0.195878	−	0.504075i
$357$	−0.991508	+	2.39371i	−0.0524762	+	0.126689i
$358$	−19.4948	+	12.7171i	−1.03033	+	0.672120i
$359$		−	16.6589i		−	0.879226i	−0.898187	−	0.439613i	$-0.855116\pi$
$359$		−	16.6589i		−	0.879226i	0.898187	−	0.439613i	$-0.144884\pi$
$360$	2.61777	−	0.431181i	0.137969	−	0.0227253i
$361$	0.976874	−	0.976874i	0.0514144	−	0.0514144i
$362$	3.49574	−	16.6141i	0.183732	−	0.873216i
$363$	2.46794	+	5.95815i	0.129534	+	0.312722i
$364$	−0.787604	−	5.93227i	−0.0412817	−	0.310936i
$365$	0.0902544	+	0.0373846i	0.00472413	+	0.00195680i
$366$	0.537942	+	2.86954i	0.0281187	+	0.149993i
$367$	13.1908			0.688552			0.344276	−	0.938869i	$-0.388124\pi$
$367$	13.1908			0.688552			0.344276	+	0.938869i	$0.388124\pi$
$368$	−34.2150	−	1.51110i	−1.78358	−	0.0787718i
$369$	−7.57841	−	7.57841i	−0.394516	−	0.394516i
$370$	2.18357	+	11.6478i	0.113519	+	0.605541i
$371$	5.95622	−	2.46715i	0.309232	−	0.128088i
$372$	−2.21936	+	2.12351i	−0.115069	+	0.110099i
$373$	−5.15365	−	12.4420i	−0.266846	−	0.644223i	0.732486	−	0.680782i	$-0.238360\pi$
$373$	−5.15365	−	12.4420i	−0.266846	−	0.644223i	−0.999331	+	0.0365598i	$0.988360\pi$
$374$	6.69254	−	4.36577i	0.346063	−	0.225749i
$375$	11.4504			0.591298
$376$	12.5778	+	20.2438i	0.648651	+	1.04399i
$377$	30.8037	+	22.5225i	1.58647	+	1.15997i
$378$	1.36662	−	6.49508i	0.0702914	−	0.334071i
$379$	−11.7367	−	4.86151i	−0.602875	−	0.249719i	0.0603036	−	0.998180i	$-0.480793\pi$
$379$	−11.7367	−	4.86151i	−0.602875	−	0.249719i	−0.663179	+	0.748461i	$0.730793\pi$
$380$	2.71011	+	6.97422i	0.139026	+	0.357770i
$381$	−6.87296	−	2.84687i	−0.352112	−	0.145850i
$382$	−23.2172	−	15.8866i	−1.18790	−	0.812827i
$383$	21.2202	+	21.2202i	1.08430	+	1.08430i	0.996103	+	0.0881968i	$0.0281105\pi$
$383$	21.2202	+	21.2202i	1.08430	+	1.08430i	0.0881968	+	0.996103i	$0.471890\pi$
$384$	15.6771	−	1.87620i	0.800021	−	0.0957446i
$385$	−1.32096	−	1.32096i	−0.0673226	−	0.0673226i
$386$	11.8346	−	2.21859i	0.602365	−	0.112923i
$387$	0.0927573	−	0.223936i	0.00471512	−	0.0113833i
$388$	0.0974524	+	0.0429093i	0.00494739	+	0.00217839i
$389$	12.2318	+	29.5302i	0.620177	+	1.49724i	0.851496	+	0.524361i	$0.175696\pi$
$389$	12.2318	+	29.5302i	0.620177	+	1.49724i	−0.231319	+	0.972878i	$0.574304\pi$
$390$	6.33343	+	0.338028i	0.320705	+	0.0171167i
$391$	−13.5443	−	13.5443i	−0.684967	−	0.684967i
$392$	17.3832	+	4.06011i	0.877985	+	0.205067i
$393$	12.6755	+	12.6755i	0.639393	+	0.639393i
$394$	13.4569	+	20.6288i	0.677949	+	1.03927i
$395$	0.610951	−	1.47497i	0.0307403	−	0.0742136i
$396$	−3.84099	+	3.67510i	−0.193017	+	0.184681i
$397$	−0.632732	−	1.52755i	−0.0317559	−	0.0766656i	0.907206	−	0.420687i	$-0.138211\pi$
$397$	−0.632732	−	1.52755i	−0.0317559	−	0.0766656i	−0.938962	+	0.344021i	$0.888211\pi$
$398$	−0.663643	−	3.54006i	−0.0332654	−	0.177447i
$399$	4.86125			0.243367
$400$	−16.8060	−	0.742236i	−0.840301	−	0.0371118i
$401$	−0.453877	+	0.453877i	−0.0226655	+	0.0226655i	−0.718349	−	0.695683i	$-0.755102\pi$
$401$	−0.453877	+	0.453877i	−0.0226655	+	0.0226655i	0.695683	+	0.718349i	$0.255102\pi$
$402$	−15.0713	+	22.0258i	−0.751689	+	1.09855i
$403$	3.38942	−	2.06300i	0.168839	−	0.102765i
$404$	20.6099	−	19.7197i	1.02538	−	0.981092i
$405$	3.89923	+	1.61512i	0.193754	+	0.0802557i
$406$	10.4032	−	6.78639i	0.516304	−	0.336803i
$407$	−16.7907	−	16.7907i	−0.832282	−	0.832282i
$408$	7.17594	+	5.14631i	0.355262	+	0.254780i
$409$		−	26.5907i		−	1.31483i	−0.753531	−	0.657413i	$-0.771651\pi$
$409$		−	26.5907i		−	1.31483i	0.753531	−	0.657413i	$-0.228349\pi$
$410$	−7.01339	−	10.7512i	−0.346367	−	0.530965i
$411$	3.24276	−	7.82871i	0.159953	−	0.386162i
$412$	16.3177	+	7.18486i	0.803915	+	0.353973i
$413$	5.49641	+	2.27669i	0.270461	+	0.112028i
$414$	10.5167	+	7.19617i	0.516870	+	0.353672i
$415$	−1.71540			−0.0842059
$416$	−20.2993	−	1.98461i	−0.995255	−	0.0973034i
$417$	−28.7083			−1.40585
$418$	−12.3731	−	8.46639i	−0.605188	−	0.414105i
$419$	−24.2779	−	10.0562i	−1.18605	−	0.491279i	−0.299585	−	0.954069i	$-0.596848\pi$
$419$	−24.2779	−	10.0562i	−1.18605	−	0.491279i	−0.886468	+	0.462790i	$0.846848\pi$
$420$	0.831943	−	1.88945i	0.0405947	−	0.0921955i
$421$	8.86234	−	21.3956i	0.431924	−	1.04276i	−0.546742	−	0.837301i	$-0.684132\pi$
$421$	8.86234	−	21.3956i	0.431924	−	1.04276i	0.978666	−	0.205456i	$-0.0658677\pi$
$422$	−2.06443	−	3.16467i	−0.100495	−	0.154054i
$423$		−	8.86775i		−	0.431165i
$424$	−3.57110	−	21.6807i	−0.173428	−	1.05291i
$425$	−6.65282	−	6.65282i	−0.322709	−	0.322709i
$426$	12.8570	−	8.38709i	0.622925	−	0.406356i
$427$	−1.13417	−	0.469787i	−0.0548861	−	0.0227346i
$428$	−2.80165	−	2.92811i	−0.135423	−	0.141536i
$429$	−10.8558	+	6.60745i	−0.524122	+	0.319011i
$430$	0.163942	−	0.239590i	0.00790597	−	0.0115541i
$431$	−5.29119	+	5.29119i	−0.254867	+	0.254867i	−0.822963	−	0.568095i	$-0.807680\pi$
$431$	−5.29119	+	5.29119i	−0.254867	+	0.254867i	0.568095	+	0.822963i	$0.307680\pi$
$432$	−20.4973	−	9.57059i	−0.986175	−	0.460465i
$433$	8.11000			0.389742			0.194871	−	0.980829i	$-0.437571\pi$
$433$	8.11000			0.389742			0.194871	+	0.980829i	$0.437571\pi$
$434$	−0.237980	−	1.26945i	−0.0114234	−	0.0609357i
$435$	5.03777	+	12.1623i	0.241543	+	0.583136i
$436$	−18.6061	−	19.4460i	−0.891070	−	0.931293i
$437$	−13.7532	+	33.2032i	−0.657905	+	1.58832i
$438$	−0.118190	−	0.181179i	−0.00564732	−	0.00865709i
$439$	−12.9581	−	12.9581i	−0.618456	−	0.618456i	0.326679	−	0.945135i	$-0.394070\pi$
$439$	−12.9581	−	12.9581i	−0.618456	−	0.618456i	−0.945135	+	0.326679i	$0.894070\pi$
$440$	−5.40817	+	3.36019i	−0.257824	+	0.160191i
$441$	−4.69661	−	4.69661i	−0.223648	−	0.223648i
$442$	−7.62476	−	8.48454i	−0.362673	−	0.403569i
$443$	9.52286	+	22.9902i	0.452445	+	1.09230i	0.971390	+	0.237491i	$0.0763249\pi$
$443$	9.52286	+	22.9902i	0.452445	+	1.09230i	−0.518945	+	0.854808i	$0.673675\pi$
$444$	10.5748	−	24.0166i	0.501856	−	1.13978i
$445$	−1.74015	+	4.20110i	−0.0824911	+	0.199151i
$446$	14.3358	−	2.68747i	0.678818	−	0.127256i
$447$	0.598833	+	0.598833i	0.0283238	+	0.0283238i
$448$	−2.94085	+	5.95214i	−0.138942	+	0.281212i
$449$	11.1013	+	11.1013i	0.523902	+	0.523902i	0.918748	−	0.394845i	$-0.129202\pi$
$449$	11.1013	+	11.1013i	0.523902	+	0.523902i	−0.394845	+	0.918748i	$0.629202\pi$
$450$	5.16570	+	3.53467i	0.243513	+	0.166626i
$451$	23.7630	+	9.84296i	1.11896	+	0.463487i
$452$	−38.5786	+	14.9912i	−1.81458	+	0.705128i
$453$	28.2294	+	11.6930i	1.32633	+	0.549385i
$454$	2.61990	−	12.4515i	0.122958	−	0.584376i
$455$	−1.57406	+	2.15282i	−0.0737931	+	0.100926i
$456$	3.76837	−	16.1341i	0.176470	−	0.755549i
$457$	10.9893			0.514058			0.257029	−	0.966404i	$-0.417256\pi$
$457$	10.9893			0.514058			0.257029	+	0.966404i	$0.417256\pi$
$458$	−6.66113	+	4.34528i	−0.311254	+	0.203042i
$459$	−4.84166	−	11.6888i	−0.225989	−	0.545587i
$460$	10.5515	+	11.0278i	0.491968	+	0.514175i
$461$	−11.7052	+	4.84845i	−0.545165	+	0.225815i	−0.638231	−	0.769845i	$-0.720333\pi$
$461$	−11.7052	+	4.84845i	−0.545165	+	0.225815i	0.0930653	+	0.995660i	$0.470333\pi$
$462$	0.762210	+	4.06585i	0.0354612	+	0.189160i
$463$	−23.9065	−	23.9065i	−1.11103	−	1.11103i	−0.993012	−	0.118017i	$-0.962346\pi$
$463$	−23.9065	−	23.9065i	−1.11103	−	1.11103i	−0.118017	−	0.993012i	$-0.537654\pi$
$464$	−14.4591	−	39.7882i	−0.671245	−	1.84712i
$465$	1.36885			0.0634791
$466$	1.39785	+	7.45653i	0.0647541	+	0.345417i
$467$	−23.0434	−	9.54488i	−1.06632	−	0.441684i	−0.220629	−	0.975358i	$-0.570811\pi$
$467$	−23.0434	−	9.54488i	−1.06632	−	0.441684i	−0.845691	+	0.533674i	$0.820811\pi$
$468$	6.02577	+	4.61327i	0.278541	+	0.213248i
$469$	−4.29451	−	10.3679i	−0.198302	−	0.478743i
$470$	2.18688	−	10.3935i	0.100873	−	0.479416i
$471$	15.8561	−	15.8561i	0.730611	−	0.730611i
$472$	11.8169	−	16.4773i	0.543916	−	0.758429i
$473$			0.581703i			0.0267467i
$474$	−2.96089	+	1.93149i	−0.135998	+	0.0887164i
$475$	−6.75541	+	16.3090i	−0.309960	+	0.748309i
$476$	−3.46098	+	1.34490i	−0.158634	+	0.0616433i
$477$	−3.12868	+	7.55331i	−0.143253	+	0.345842i
$478$	−1.40894	−	7.51572i	−0.0644436	−	0.343761i
$479$	18.0000	−	18.0000i	0.822443	−	0.822443i	−0.164015	−	0.986458i	$-0.552445\pi$
$479$	18.0000	−	18.0000i	0.822443	−	0.822443i	0.986458	+	0.164015i	$0.0524446\pi$
$480$	−5.62601	−	4.22582i	−0.256791	−	0.192882i
$481$	−20.0078	+	27.3643i	−0.912275	+	1.24770i
$482$	5.91169	+	31.5346i	0.269270	+	1.43636i
$483$	9.16135	−	3.79476i	0.416856	−	0.172667i
$484$	−3.72440	+	8.45856i	−0.169291	+	0.384480i
$485$	−0.0181594	−	0.0438406i	−0.000824574	−	0.00199070i
$486$	8.00318	+	12.2685i	0.363032	+	0.556511i
$487$	0.103787			0.00470306			0.00235153	−	0.999997i	$-0.499251\pi$
$487$	0.103787			0.00470306			0.00235153	+	0.999997i	$0.499251\pi$
$488$	−2.43837	+	3.40004i	−0.110380	+	0.153912i
$489$			11.8051i			0.533845i
$490$	−4.34645	−	6.66291i	−0.196352	−	0.301000i
$491$	1.07977	+	2.60680i	0.0487294	+	0.117643i	0.946370	−	0.323085i	$-0.104720\pi$
$491$	1.07977	+	2.60680i	0.0487294	+	0.117643i	−0.897640	+	0.440729i	$0.854720\pi$
$492$	−0.627225	+	28.4176i	−0.0282775	+	1.28116i
$493$	9.06069	−	21.8745i	0.408073	−	0.985176i
$494$	−9.23272	+	19.3090i	−0.415400	+	0.868753i
$495$	2.36904			0.106480
$496$	−4.39769	−	0.194224i	−0.197462	−	0.00872090i
$497$			6.45475i			0.289535i
$498$	3.13486	+	2.14505i	0.140476	+	0.0961221i
$499$	−11.6254	−	28.0661i	−0.520423	−	1.25641i	−0.937641	−	0.347606i	$-0.886995\pi$
$499$	−11.6254	−	28.0661i	−0.520423	−	1.25641i	0.417217	−	0.908807i	$-0.363005\pi$
$500$	11.3446	+	11.8567i	0.507344	+	0.530246i
$501$	2.77797	−	6.70662i	0.124111	−	0.299630i
$502$	−2.51554	+	11.9555i	−0.112274	+	0.533600i
$503$	−19.1706	+	19.1706i	−0.854777	+	0.854777i	−0.990717	−	0.135940i	$-0.956594\pi$
$503$	−19.1706	+	19.1706i	−0.854777	+	0.854777i	0.135940	+	0.990717i	$0.456594\pi$
$504$	2.09822	−	1.30366i	0.0934623	−	0.0580697i
$505$	−12.7117			−0.565664
$506$	−29.9269	−	6.29687i	−1.33041	−	0.279930i
$507$	11.6990	+	13.8664i	0.519573	+	0.615829i
$508$	−3.86155	−	9.93735i	−0.171328	−	0.440899i
$509$	7.30830	+	17.6438i	0.323935	+	0.782048i	0.999018	+	0.0443062i	$0.0141077\pi$
$509$	7.30830	+	17.6438i	0.323935	+	0.782048i	−0.675083	+	0.737742i	$0.735892\pi$
$510$	−0.725104	−	3.86792i	−0.0321082	−	0.171274i
$511$	0.0909593			0.00402380
$512$	17.4750	+	14.3745i	0.772292	+	0.635268i
$513$	−16.7854	+	16.7854i	−0.741093	+	0.741093i
$514$	−29.9006	−	20.4597i	−1.31886	−	0.902439i
$515$	−3.04066	−	7.34079i	−0.133987	−	0.323474i
$516$	−0.599199	+	0.232842i	−0.0263782	+	0.0102503i
$517$	8.14415	+	19.6617i	0.358180	+	0.864722i
$518$	6.02864	+	9.24164i	0.264883	+	0.406054i
$519$	12.0190	−	12.0190i	0.527576	−	0.527576i
$520$	5.92485	+	6.89302i	0.259822	+	0.302279i
$521$	16.1305	+	16.1305i	0.706691	+	0.706691i	0.965838	−	0.259147i	$-0.0834413\pi$
$521$	16.1305	+	16.1305i	0.706691	+	0.706691i	−0.259147	+	0.965838i	$0.583441\pi$
$522$	−3.24325	+	15.4141i	−0.141953	+	0.674656i
$523$	−16.9456	+	7.01910i	−0.740980	+	0.306924i	−0.721055	−	0.692878i	$-0.756343\pi$
$523$	−16.9456	+	7.01910i	−0.740980	+	0.306924i	−0.0199246	+	0.999801i	$0.506343\pi$
$524$	−0.566877	+	25.6834i	−0.0247641	+	1.12199i
$525$	4.49995	−	1.86394i	0.196394	−	0.0813490i
$526$	18.5101	−	3.47003i	0.807081	−	0.151301i
$527$	−1.74087	−	1.74087i	−0.0758333	−	0.0758333i
$528$	14.0851	+	0.622067i	0.612975	+	0.0270720i
$529$			50.3095i			2.18737i
$530$	−5.52971	+	8.08132i	−0.240195	+	0.351030i
$531$	−6.97020	+	2.88715i	−0.302481	+	0.125292i
$532$	4.81631	+	5.03372i	0.208814	+	0.218239i
$533$	8.67946	−	35.6779i	0.375949	−	1.54538i
$534$	8.43341	−	5.50140i	0.364949	−	0.238069i
$535$			1.80600i			0.0780800i
$536$	−37.7392	+	6.21614i	−1.63008	+	0.268496i
$537$	−16.2416	−	16.2416i	−0.700876	−	0.700876i
$538$	1.74567	−	1.13876i	0.0752614	−	0.0490956i
$539$	14.7268	+	6.10002i	0.634326	+	0.262747i
$540$	3.65144	+	9.39667i	0.157133	+	0.404368i
$541$	−0.792975	+	0.328461i	−0.0340926	+	0.0141216i	−0.399665	−	0.916661i	$-0.630873\pi$
$541$	−0.792975	+	0.328461i	−0.0340926	+	0.0141216i	0.365572	+	0.930783i	$0.380873\pi$
$542$	−33.7503	+	6.32705i	−1.44970	+	0.271770i
$543$	16.7540			0.718982
$544$	1.78072	+	12.5293i	0.0763476	+	0.537187i
$545$			11.9938i			0.513760i
$546$	5.56858	−	1.96592i	0.238313	−	0.0841334i
$547$	37.9355	+	15.7134i	1.62201	+	0.671857i	0.994302	−	0.106596i	$-0.0339951\pi$
$547$	37.9355	+	15.7134i	1.62201	+	0.671857i	0.627703	+	0.778453i	$0.283995\pi$
$548$	11.3192	−	4.39853i	0.483534	−	0.187896i
$549$	1.43828	−	0.595754i	0.0613842	−	0.0254262i
$550$	−14.6997	−	3.09295i	−0.626798	−	0.131884i
$551$	−44.4236			−1.89251
$552$	−5.49276	−	33.3474i	−0.233787	−	1.41936i
$553$		−	1.48649i		−	0.0632119i
$554$	0.878446	−	4.17495i	0.0373216	−	0.177377i
$555$	−10.8043	+	4.47527i	−0.458615	+	0.189965i
$556$	−28.4429	−	29.7268i	−1.20625	−	1.26070i
$557$	−9.25938	−	22.3541i	−0.392333	−	0.947175i	−0.989431	−	0.145007i	$-0.953680\pi$
$557$	−9.25938	−	22.3541i	−0.392333	−	0.947175i	0.597098	−	0.802168i	$-0.296320\pi$
$558$	1.35173	+	0.924930i	0.0572231	+	0.0391554i
$559$	0.820589	−	0.127432i	0.0347072	−	0.00538978i
$560$	2.78073	−	1.01052i	0.117507	−	0.0427022i
$561$	5.57571	+	5.57571i	0.235407	+	0.235407i
$562$	5.97168	−	8.72723i	0.251900	−	0.368136i
$563$	29.2302	+	12.1076i	1.23191	+	0.510272i	0.901176	−	0.433453i	$-0.142705\pi$
$563$	29.2302	+	12.1076i	1.23191	+	0.510272i	0.330730	+	0.943725i	$0.392705\pi$
$564$	−16.9932	+	16.2592i	−0.715541	+	0.684637i
$565$	17.0408	+	7.05852i	0.716910	+	0.296954i
$566$	−5.71870	+	27.1790i	−0.240375	+	1.14242i
$567$	3.92969			0.165031
$568$	21.4228	+	5.00362i	0.898881	+	0.209947i
$569$	8.76654	+	8.76654i	0.367513	+	0.367513i	0.866569	−	0.499057i	$-0.166320\pi$
$569$	8.76654	+	8.76654i	0.367513	+	0.367513i	−0.499057	+	0.866569i	$0.666320\pi$
$570$	−6.18414	+	4.03413i	−0.259025	+	0.168971i
$571$	11.9915	−	4.96705i	0.501829	−	0.207864i	−0.117385	−	0.993086i	$-0.537451\pi$
$571$	11.9915	−	4.96705i	0.501829	−	0.207864i	0.619214	+	0.785222i	$0.287451\pi$
$572$	−17.5973	−	4.69454i	−0.735779	−	0.196289i
$573$	10.6238	−	25.6480i	0.443814	−	1.07146i
$574$	−9.86389	−	6.74944i	−0.411711	−	0.281716i
$575$			36.0088i			1.50167i
$576$	−2.70024	−	7.97442i	−0.112510	−	0.332267i
$577$	6.50897	−	6.50897i	0.270972	−	0.270972i	−0.558519	−	0.829491i	$-0.688630\pi$
$577$	6.50897	−	6.50897i	0.270972	−	0.270972i	0.829491	+	0.558519i	$0.188630\pi$
$578$	9.57964	−	14.0000i	0.398460	−	0.582325i
$579$	4.54703	+	10.9775i	0.188968	+	0.456210i
$580$	−7.60254	+	17.2663i	−0.315678	+	0.716944i
$581$	−1.47563	+	0.611224i	−0.0612193	+	0.0253578i
$582$	−0.0216353	+	0.102825i	−0.000896813	+	0.00426225i
$583$		−	19.6207i		−	0.812607i
$584$	0.0705102	−	0.301887i	0.00291773	−	0.0124922i
$585$	−0.518977	−	3.34192i	−0.0214570	−	0.138172i
$586$	29.9643	−	19.5467i	1.23781	−	0.807468i
$587$	3.38471	−	8.17142i	0.139702	−	0.337271i	−0.838508	−	0.544890i	$-0.816571\pi$
$587$	3.38471	−	8.17142i	0.139702	−	0.337271i	0.978210	+	0.207619i	$0.0665715\pi$
$588$	−0.388713	+	17.6114i	−0.0160303	+	0.726281i
$589$	−1.76771	+	4.26764i	−0.0728374	+	0.175845i
$590$	−8.88146	+	1.66497i	−0.365644	+	0.0685459i
$591$	−17.1864	+	17.1864i	−0.706953	+	0.706953i
$592$	35.3456	−	12.8446i	1.45270	−	0.527910i
$593$	8.99288	−	8.99288i	0.369293	−	0.369293i	−0.497926	−	0.867219i	$-0.665905\pi$
$593$	8.99288	−	8.99288i	0.369293	−	0.369293i	0.867219	+	0.497926i	$0.165905\pi$
$594$	−16.6708	−	11.4071i	−0.684011	−	0.468040i
$595$	1.52877	+	0.633236i	0.0626733	+	0.0259602i
$596$	−0.0267812	+	1.21337i	−0.00109700	+	0.0497018i
$597$	3.28369	−	1.36015i	0.134392	−	0.0556671i
$598$	−2.32682	+	43.5963i	−0.0951507	+	1.78278i
$599$	12.4096	−	12.4096i	0.507042	−	0.507042i	−0.406575	−	0.913617i	$-0.633277\pi$
$599$	12.4096	−	12.4096i	0.507042	−	0.507042i	0.913617	+	0.406575i	$0.133277\pi$
$600$	−2.69798	−	16.3799i	−0.110145	−	0.668705i
$601$	4.04864	−	4.04864i	0.165147	−	0.165147i	−0.619695	−	0.784843i	$-0.712744\pi$
$601$	4.04864	−	4.04864i	0.165147	−	0.165147i	0.784843	+	0.619695i	$0.212744\pi$
$602$	0.0556563	−	0.264515i	0.00226838	−	0.0107808i
$603$	13.1479	+	5.44603i	0.535423	+	0.221779i
$604$	15.8606	+	40.8158i	0.645358	+	1.66077i
$605$	3.80523	−	1.57618i	0.154704	−	0.0640807i
$606$	23.2303	+	15.8955i	0.943668	+	0.645712i
$607$		−	3.67342i		−	0.149099i	−0.997217	−	0.0745497i	$-0.976248\pi$
$607$		−	3.67342i		−	0.149099i	0.997217	−	0.0745497i	$-0.0237519\pi$
$608$	20.4400	−	12.0829i	0.828953	−	0.490026i
$609$	8.66719	+	8.66719i	0.351212	+	0.351212i
$610$	1.83266	−	0.343562i	0.0742022	−	0.0139104i
$611$	25.9520	−	15.7959i	1.04991	−	0.639034i
$612$	1.89750	−	4.30947i	0.0767021	−	0.174200i
$613$	8.32980	−	20.1099i	0.336437	−	0.812232i	−0.661615	−	0.749844i	$-0.730129\pi$
$613$	8.32980	−	20.1099i	0.336437	−	0.812232i	0.998052	−	0.0623875i	$-0.0198715\pi$
$614$	2.41283	−	11.4673i	0.0973739	−	0.462785i
$615$	8.95711	−	8.95711i	0.361185	−	0.361185i
$616$	−3.45493	+	4.81751i	−0.139203	+	0.194103i
$617$	−12.1373			−0.488628			−0.244314	−	0.969696i	$-0.578563\pi$
$617$	−12.1373			−0.488628			−0.244314	+	0.969696i	$0.578563\pi$
$618$	−3.62268	+	17.2174i	−0.145726	+	0.692584i
$619$	2.80738	+	1.16286i	0.112838	+	0.0467391i	0.438388	−	0.898786i	$-0.355549\pi$
$619$	2.80738	+	1.16286i	0.112838	+	0.0467391i	−0.325550	+	0.945525i	$0.605549\pi$
$620$	1.35620	+	1.41742i	0.0544663	+	0.0569249i
$621$	−18.5303	+	44.7361i	−0.743595	+	1.79520i
$622$	5.78934	−	1.08531i	0.232132	−	0.0435169i
$623$			4.23391i			0.169628i
$624$	−2.20804	−	20.0056i	−0.0883924	−	0.800867i
$625$			13.7151i			0.548603i
$626$	1.37959	+	7.35914i	0.0551396	+	0.294131i
$627$	5.66170	−	13.6686i	0.226107	−	0.545870i
$628$	32.1282	+	0.709123i	1.28205	+	0.0282971i
$629$	19.4320	+	8.04901i	0.774806	+	0.320935i
$630$	−1.07726	−	0.226665i	−0.0429192	−	0.00903057i
$631$	13.0300			0.518718			0.259359	−	0.965781i	$-0.416489\pi$
$631$	13.0300			0.518718			0.259359	+	0.965781i	$0.416489\pi$
$632$	−4.93353	−	1.15230i	−0.196245	−	0.0458361i
$633$	2.63657	−	2.63657i	0.104794	−	0.104794i
$634$	3.30006	+	0.694361i	0.131062	+	0.0275766i
$635$	−1.81818	+	4.38948i	−0.0721524	+	0.174191i
$636$	20.2108	−	7.85371i	0.801411	−	0.311420i
$637$	5.37896	−	22.1109i	0.213122	−	0.876064i
$638$	−6.96530	−	37.1549i	−0.275759	−	1.47098i
$639$	−5.78803	−	5.78803i	−0.228971	−	0.228971i
$640$	−1.19826	−	10.0124i	−0.0473652	−	0.395773i
$641$		−	20.0675i		−	0.792619i	−0.918117	−	0.396309i	$-0.870291\pi$
$641$		−	20.0675i		−	0.792619i	0.918117	−	0.396309i	$-0.129709\pi$
$642$	2.25834	−	3.30041i	0.0891294	−	0.130257i
$643$	−35.6943	+	14.7851i	−1.40765	+	0.583066i	−0.951724	−	0.306954i	$-0.900690\pi$
$643$	−35.6943	+	14.7851i	−1.40765	+	0.583066i	−0.455921	+	0.890020i	$0.650690\pi$
$644$	13.0060	+	5.72670i	0.512509	+	0.225663i
$645$	0.264675	+	0.109632i	0.0104216	+	0.00431676i
$646$	12.9953	+	2.73432i	0.511292	+	0.107580i
$647$	15.4064	−	15.4064i	0.605688	−	0.605688i	−0.336128	−	0.941816i	$-0.609118\pi$
$647$	15.4064	−	15.4064i	0.605688	−	0.605688i	0.941816	+	0.336128i	$0.109118\pi$
$648$	3.04623	−	13.0423i	0.119667	−	0.512351i
$649$	12.8029	−	12.8029i	0.502557	−	0.502557i
$650$	−1.14291	+	21.4140i	−0.0448285	+	0.839925i
$651$	1.17752	−	0.487743i	0.0461505	−	0.0191162i
$652$	−12.2239	+	11.6960i	−0.478725	+	0.458049i
$653$	−4.44571	−	1.84147i	−0.173974	−	0.0720624i	0.293996	−	0.955807i	$-0.405015\pi$
$653$	−4.44571	−	1.84147i	−0.173974	−	0.0720624i	−0.467970	+	0.883744i	$0.655015\pi$
$654$	14.9979	−	21.9185i	0.586464	−	0.857080i
$655$	8.09531	−	8.09531i	0.316310	−	0.316310i
$656$	−30.0472	+	27.5054i	−1.17315	+	1.07391i
$657$	−0.0815640	+	0.0815640i	−0.00318211	+	0.00318211i
$658$	−1.82216	−	9.71991i	−0.0710350	−	0.378921i
$659$	−15.6050	+	37.6738i	−0.607885	+	1.46756i	0.257411	+	0.966302i	$0.417131\pi$
$659$	−15.6050	+	37.6738i	−0.607885	+	1.46756i	−0.865296	+	0.501262i	$0.832869\pi$
$660$	−4.34369	−	4.53976i	−0.169078	−	0.176710i
$661$	16.4803	−	39.7869i	0.641009	−	1.54753i	−0.184312	−	0.982868i	$-0.559006\pi$
$661$	16.4803	−	39.7869i	0.641009	−	1.54753i	0.825321	−	0.564664i	$-0.190994\pi$
$662$	4.13322	+	6.33604i	0.160642	+	0.246257i
$663$	6.64402	−	9.08693i	0.258032	−	0.352907i
$664$	0.884723	+	5.37130i	0.0343339	+	0.208447i
$665$		−	3.10469i		−	0.120395i
$666$	−13.6930	−	2.88112i	−0.530593	−	0.111641i
$667$	−83.7191	+	34.6776i	−3.24162	+	1.34272i
$668$	9.69685	−	3.76809i	0.375182	−	0.145792i
$669$	5.50802	+	13.2975i	0.212952	+	0.514113i
$670$	14.0670	+	9.62544i	0.543455	+	0.371863i
$671$	−2.64183	+	2.64183i	−0.101987	+	0.101987i
$672$	−6.34533	−	1.63051i	−0.244777	−	0.0628981i
$673$		−	39.5769i		−	1.52558i	−0.646648	−	0.762788i	$-0.723830\pi$
$673$		−	39.5769i		−	1.52558i	0.646648	−	0.762788i	$-0.276170\pi$
$674$	−2.31475	+	3.38286i	−0.0891608	+	0.130303i
$675$	−9.10185	+	21.9738i	−0.350331	+	0.845773i
$676$	−2.76746	+	25.8523i	−0.106441	+	0.994319i
$677$	−18.1490	+	7.51754i	−0.697521	+	0.288923i	−0.703130	−	0.711062i	$-0.748215\pi$
$677$	−18.1490	+	7.51754i	−0.697521	+	0.288923i	0.00560877	+	0.999984i	$0.498215\pi$
$678$	−22.3152	−	34.2082i	−0.857008	−	1.31376i
$679$	−0.0312421	−	0.0312421i	−0.00119896	−	0.00119896i
$680$	3.28674	−	4.58298i	0.126041	−	0.175749i
$681$	12.5563			0.481159
$682$	−3.84653	−	0.809343i	−0.147291	−	0.0309913i
$683$	20.1952	+	8.36511i	0.772746	+	0.320082i	0.733984	−	0.679167i	$-0.237659\pi$
$683$	20.1952	+	8.36511i	0.772746	+	0.320082i	0.0387620	+	0.999248i	$0.487659\pi$
$684$	−8.83260	−	0.194951i	−0.337723	−	0.00745412i
$685$	−4.99988	−	2.07102i	−0.191036	−	0.0791296i
$686$	−12.8930	−	8.82217i	−0.492259	−	0.336832i
$687$	−5.54955	−	5.54955i	−0.211728	−	0.211728i
$688$	−0.834762	−	0.389767i	−0.0318250	−	0.0148597i
$689$	−27.6783	+	4.29824i	−1.05446	+	0.163750i
$690$	−8.50532	+	12.4300i	−0.323792	+	0.473202i
$691$	11.8233	+	28.5439i	0.449778	+	1.08586i	0.972405	+	0.233298i	$0.0749519\pi$
$691$	11.8233	+	28.5439i	0.449778	+	1.08586i	−0.522627	+	0.852561i	$0.675048\pi$
$692$	24.3533	+	0.537518i	0.925773	+	0.0204334i
$693$	2.03790	−	0.844124i	0.0774133	−	0.0320656i
$694$	39.3075	+	8.27064i	1.49209	+	0.313949i
$695$			18.3348i			0.695479i
$696$	35.4844	−	22.0470i	1.34503	−	0.835691i
$697$	−22.7827			−0.862958
$698$	−4.08979	+	19.4373i	−0.154801	+	0.735714i
$699$	−6.91651	+	2.86491i	−0.261607	+	0.108361i
$700$	6.38841	+	2.81288i	0.241459	+	0.106317i
$701$	−3.43432	−	1.42254i	−0.129712	−	0.0537286i	0.316883	−	0.948465i	$-0.397364\pi$
$701$	−3.43432	−	1.42254i	−0.129712	−	0.0537286i	−0.446596	+	0.894736i	$0.647364\pi$
$702$	−12.4396	+	26.0158i	−0.469504	+	0.981904i
$703$		−	39.4634i		−	1.48839i
$704$	13.3107	+	15.2011i	0.501667	+	0.572913i
$705$	10.4810			0.394738
$706$	2.28106	+	12.1678i	0.0858487	+	0.457942i
$707$	−10.9349	+	4.52937i	−0.411248	+	0.170345i
$708$	18.3126	+	8.06325i	0.688231	+	0.303036i
$709$	−12.8333	−	5.31574i	−0.481966	−	0.199637i	0.128453	−	0.991716i	$-0.458999\pi$
$709$	−12.8333	−	5.31574i	−0.481966	−	0.199637i	−0.610419	+	0.792079i	$0.708999\pi$
$710$	−5.35649	−	8.21127i	−0.201026	−	0.308163i
$711$	1.33295	+	1.33295i	0.0499893	+	0.0499893i
$712$	14.0520	+	3.28206i	0.526622	+	0.123000i
$713$			9.42254i			0.352877i
$714$	−2.00195	−	3.06889i	−0.0749209	−	0.114850i
$715$	4.21991	+	6.93314i	0.157816	+	0.259285i
$716$	0.726362	−	32.9092i	0.0271454	−	1.22987i
$717$	6.97142	−	2.88766i	0.260352	−	0.107842i
$718$	19.4432	+	13.3042i	0.725615	+	0.496508i
$719$			19.4222i			0.724324i	0.932115	+	0.362162i	$0.117961\pi$
$719$			19.4222i			0.724324i	−0.932115	+	0.362162i	$0.882039\pi$
$720$	−1.58736	+	3.39964i	−0.0591575	+	0.126697i
$721$	−5.23127	−	5.23127i	−0.194823	−	0.194823i
$722$	0.359991	+	1.92030i	0.0133975	+	0.0714660i
$723$	−29.2509	+	12.1161i	−1.08785	+	0.450603i
$724$	16.5991	+	17.3484i	0.616900	+	0.644747i
$725$	−41.1218	+	17.0332i	−1.52723	+	0.632598i
$726$	−8.92491	−	1.87788i	−0.331235	−	0.0696946i
$727$	4.53442	+	4.53442i	0.168172	+	0.168172i	0.786175	−	0.618003i	$-0.212058\pi$
$727$	4.53442	+	4.53442i	0.168172	+	0.168172i	−0.618003	+	0.786175i	$0.712058\pi$
$728$	7.55276	+	3.81840i	0.279924	+	0.141519i
$729$	−20.2662	+	20.2662i	−0.750601	+	0.750601i
$730$	−0.115712	+	0.0754829i	−0.00428269	+	0.00279375i
$731$	−0.197179	−	0.476033i	−0.00729293	−	0.0176067i
$732$	−3.77875	−	1.66382i	−0.139667	−	0.0614967i
$733$	−17.7693	−	42.8989i	−0.656324	−	1.58451i	−0.803439	−	0.595387i	$-0.796999\pi$
$733$	−17.7693	−	42.8989i	−0.656324	−	1.58451i	0.147115	−	0.989119i	$-0.453001\pi$
$734$	−10.5344	+	15.3954i	−0.388832	+	0.568254i
$735$	5.55103	−	5.55103i	0.204753	−	0.204753i
$736$	29.0885	−	38.7268i	1.07222	−	1.42749i
$737$	−34.1533			−1.25805
$738$	14.8973	−	2.79274i	0.548378	−	0.102802i
$739$	18.8383	+	45.4796i	0.692977	+	1.67300i	0.738694	+	0.674041i	$0.235443\pi$
$739$	18.8383	+	45.4796i	0.692977	+	1.67300i	−0.0457165	+	0.998954i	$0.514557\pi$
$740$	−15.3384	−	6.75367i	−0.563851	−	0.248270i
$741$	−20.5221	−	4.99245i	−0.753897	−	0.183402i
$742$	−1.87727	+	8.92204i	−0.0689169	+	0.327538i
$743$	−24.2181			−0.888477			−0.444238	−	0.895909i	$-0.646526\pi$
$743$	−24.2181			−0.888477			−0.444238	+	0.895909i	$0.646526\pi$
$744$	−0.705990	−	4.28618i	−0.0258828	−	0.157139i
$745$	0.382450	−	0.382450i	0.0140119	−	0.0140119i
$746$	18.6373	+	3.92145i	0.682360	+	0.143575i
$747$	0.775116	−	1.87129i	0.0283600	−	0.0684671i
$748$	−0.249359	+	11.2977i	−0.00911748	+	0.413084i
$749$	0.643503	+	1.55355i	0.0235131	+	0.0567656i
$750$	−9.14456	+	13.3642i	−0.333912	+	0.487991i
$751$		−	38.3104i		−	1.39796i	−0.715139	−	0.698982i	$-0.753637\pi$
$751$		−	38.3104i		−	1.39796i	0.715139	−	0.698982i	$-0.246363\pi$
$752$	−33.6721	−	1.48713i	−1.22790	−	0.0542299i
$753$	−12.0562			−0.439351
$754$	−50.8874	+	17.9651i	−1.85321	+	0.654251i
$755$	7.46785	−	18.0290i	0.271783	−	0.656142i
$756$	6.48922	+	6.78214i	0.236011	+	0.246664i
$757$	2.34752	+	5.66742i	0.0853221	+	0.205986i	0.960782	−	0.277305i	$-0.0894413\pi$
$757$	2.34752	+	5.66742i	0.0853221	+	0.205986i	−0.875460	+	0.483291i	$0.839441\pi$
$758$	15.0472	−	9.81583i	0.546540	−	0.356527i
$759$		−	30.1789i		−	1.09542i
$760$	−10.3042	−	2.40670i	−0.373773	−	0.0873003i
$761$	−23.7237			−0.859984			−0.429992	−	0.902833i	$-0.641484\pi$
$761$	−23.7237			−0.859984			−0.429992	+	0.902833i	$0.641484\pi$
$762$	8.81158	−	5.74810i	0.319210	−	0.208232i
$763$	4.27359	+	10.3173i	0.154714	+	0.373513i
$764$	37.0835	−	14.4103i	1.34163	−	0.521345i
$765$	−1.93869	+	0.803030i	−0.0700933	+	0.0290336i
$766$	−41.7137	+	7.81991i	−1.50718	+	0.282545i
$767$	−20.8653	−	15.2559i	−0.753402	−	0.550859i
$768$	−10.3303	+	19.7957i	−0.372763	+	0.714317i
$769$	34.0861	−	34.0861i

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bd (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.798622 + 1.16713i) q^{2} +(-1.28933 - 0.534060i) q^{3} +(-0.724407 - 1.86420i) q^{4} +(-0.341082 + 0.823446i) q^{5} +(1.65301 - 1.07832i) q^{6} +0.829877i q^{7} +(2.75430 + 0.643308i) q^{8} +(-0.744158 - 0.744158i) q^{9} +O(q^{10})\)	\(q+(-0.798622 + 1.16713i) q^{2} +(-1.28933 - 0.534060i) q^{3} +(-0.724407 - 1.86420i) q^{4} +(-0.341082 + 0.823446i) q^{5} +(1.65301 - 1.07832i) q^{6} +0.829877i q^{7} +(2.75430 + 0.643308i) q^{8} +(-0.744158 - 0.744158i) q^{9} +(-0.688676 - 1.05571i) q^{10} +(2.33339 + 0.966524i) q^{11} +(-0.0615900 + 2.79045i) q^{12} +(0.852274 - 3.50337i) q^{13} +(-0.968579 - 0.662758i) q^{14} +(0.879538 - 0.879538i) q^{15} +(-2.95047 + 2.70088i) q^{16} -2.23714 q^{17} +(1.46283 - 0.274232i) q^{18} +(1.60629 + 3.87793i) q^{19} +(1.78215 + 0.0393350i) q^{20} +(0.443204 - 1.06999i) q^{21} +(-2.99156 + 1.95150i) q^{22} +(6.05432 + 6.05432i) q^{23} +(-3.20764 - 2.30040i) q^{24} +(2.97381 + 2.97381i) q^{25} +(3.40826 + 3.79259i) q^{26} +(2.16422 + 5.22489i) q^{27} +(1.54706 - 0.601169i) q^{28} +(-4.05013 + 9.77788i) q^{29} +(0.324121 + 1.72896i) q^{30} +(0.778167 + 0.778167i) q^{31} +(-0.795980 - 5.60057i) q^{32} +(-2.49234 - 2.49234i) q^{33} +(1.78663 - 2.61104i) q^{34} +(-0.683359 - 0.283056i) q^{35} +(-0.848184 + 1.92633i) q^{36} +(-8.68611 - 3.59791i) q^{37} +(-5.80888 - 1.22224i) q^{38} +(-2.96988 + 4.06185i) q^{39} +(-1.46917 + 2.04859i) q^{40} +10.1839 q^{41} +(0.894869 + 1.37180i) q^{42} +(0.0881390 + 0.212786i) q^{43} +(0.111464 - 5.05007i) q^{44} +(0.866592 - 0.358954i) q^{45} +(-11.9013 + 2.23110i) q^{46} +(5.95825 + 5.95825i) q^{47} +(5.24657 - 1.90661i) q^{48} +6.31130 q^{49} +(-5.84578 + 1.09589i) q^{50} +(2.88442 + 1.19476i) q^{51} +(-7.14838 + 0.949061i) q^{52} +(-2.97291 - 7.17724i) q^{53} +(-7.82655 - 1.64677i) q^{54} +(-1.59176 + 1.59176i) q^{55} +(-0.533866 + 2.28573i) q^{56} -5.85780i q^{57} +(-8.17758 - 12.5359i) q^{58} +(2.74340 - 6.62316i) q^{59} +(-2.27678 - 1.00249i) q^{60} +(-0.566092 + 1.36667i) q^{61} +(-1.52969 + 0.286765i) q^{62} +(0.617560 - 0.617560i) q^{63} +(7.17231 + 3.54372i) q^{64} +(2.59414 + 1.89674i) q^{65} +(4.89934 - 0.918462i) q^{66} +(-12.4932 + 5.17487i) q^{67} +(1.62060 + 4.17047i) q^{68} +(-4.57267 - 11.0394i) q^{69} +(0.876110 - 0.571517i) q^{70} +7.77796 q^{71} +(-1.57091 - 2.52835i) q^{72} -0.109606i q^{73} +(11.1362 - 7.26450i) q^{74} +(-2.24604 - 5.42242i) q^{75} +(6.06562 - 5.80364i) q^{76} +(-0.802096 + 1.93643i) q^{77} +(-2.36892 - 6.71013i) q^{78} -1.79121 q^{79} +(-1.21767 - 3.35077i) q^{80} -4.73526i q^{81} +(-8.13306 + 11.8860i) q^{82} +(0.736523 + 1.77812i) q^{83} +(-2.31573 - 0.0511121i) q^{84} +(0.763048 - 1.84216i) q^{85} +(-0.318740 - 0.0670657i) q^{86} +(10.4439 - 10.4439i) q^{87} +(5.80509 + 4.16318i) q^{88} +5.10185 q^{89} +(-0.273131 + 1.29810i) q^{90} +(2.90737 + 0.707283i) q^{91} +(6.90065 - 15.6722i) q^{92} +(-0.587730 - 1.41890i) q^{93} +(-11.7125 + 2.19569i) q^{94} -3.74114 q^{95} +(-1.96476 + 7.64611i) q^{96} +(-0.0376467 + 0.0376467i) q^{97} +(-5.04034 + 7.36614i) q^{98} +(-1.01717 - 2.45566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9	\( 216 q - 4 q^{2} - 8 q^{3} - 4 q^{5} + 8 q^{6} - 4 q^{8} - 8 q^{9} - 4 q^{11} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{15} - 8 q^{16} - 12 q^{18} - 4 q^{19} - 20 q^{20} + 8 q^{21} - 24 q^{22} - 36 q^{24} - 4 q^{26} - 8 q^{27} + 56 q^{28} - 8 q^{29} - 16 q^{30} - 44 q^{32} - 8 q^{33} + 8 q^{34} - 8 q^{35} - 4 q^{37} - 28 q^{39} - 8 q^{40} - 8 q^{41} - 48 q^{42} - 32 q^{43} + 12 q^{44} - 36 q^{45} - 48 q^{46} - 8 q^{47} - 8 q^{48} - 168 q^{49} + 76 q^{50} - 4 q^{52} - 8 q^{53} - 28 q^{54} - 40 q^{55} + 56 q^{56} + 32 q^{58} + 52 q^{59} - 36 q^{60} - 8 q^{61} + 72 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} - 4 q^{67} - 64 q^{68} + 20 q^{70} + 56 q^{71} + 8 q^{72} - 8 q^{74} - 68 q^{76} + 56 q^{77} - 48 q^{78} - 16 q^{79} + 28 q^{80} - 88 q^{82} + 36 q^{83} + 100 q^{84} - 24 q^{85} + 96 q^{86} - 8 q^{87} + 64 q^{88} - 8 q^{89} - 64 q^{90} + 72 q^{91} - 8 q^{92} - 40 q^{93} - 56 q^{94} + 36 q^{96} - 8 q^{97} + 52 q^{98} - 44 q^{99}+O(q^{100}) \) 216 * q - 4 * q^2 - 8 * q^3 - 4 * q^5 + 8 * q^6 - 4 * q^8 - 8 * q^9 - 4 * q^11 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^15 - 8 * q^16 - 12 * q^18 - 4 * q^19 - 20 * q^20 + 8 * q^21 - 24 * q^22 - 36 * q^24 - 4 * q^26 - 8 * q^27 + 56 * q^28 - 8 * q^29 - 16 * q^30 - 44 * q^32 - 8 * q^33 + 8 * q^34 - 8 * q^35 - 4 * q^37 - 28 * q^39 - 8 * q^40 - 8 * q^41 - 48 * q^42 - 32 * q^43 + 12 * q^44 - 36 * q^45 - 48 * q^46 - 8 * q^47 - 8 * q^48 - 168 * q^49 + 76 * q^50 - 4 * q^52 - 8 * q^53 - 28 * q^54 - 40 * q^55 + 56 * q^56 + 32 * q^58 + 52 * q^59 - 36 * q^60 - 8 * q^61 + 72 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 - 4 * q^67 - 64 * q^68 + 20 * q^70 + 56 * q^71 + 8 * q^72 - 8 * q^74 - 68 * q^76 + 56 * q^77 - 48 * q^78 - 16 * q^79 + 28 * q^80 - 88 * q^82 + 36 * q^83 + 100 * q^84 - 24 * q^85 + 96 * q^86 - 8 * q^87 + 64 * q^88 - 8 * q^89 - 64 * q^90 + 72 * q^91 - 8 * q^92 - 40 * q^93 - 56 * q^94 + 36 * q^96 - 8 * q^97 + 52 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more