LMFDB - Embedded newform 416.2.bd.a.83.6

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			83.6
Character	$\chi$	$=$	416.83
Dual form			416.2.bd.a.411.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32811 + 0.485919i) q^{2} +(-1.25935 - 0.521639i) q^{3} +(1.52777 - 1.29071i) q^{4} +(0.194227 - 0.468906i) q^{5} +(1.92603 + 0.0808542i) q^{6} +2.08466i q^{7} +(-1.40186 + 2.45658i) q^{8} +(-0.807469 - 0.807469i) q^{9} +O(q^{10})$	\(q+(-1.32811 + 0.485919i) q^{2} +(-1.25935 - 0.521639i) q^{3} +(1.52777 - 1.29071i) q^{4} +(0.194227 - 0.468906i) q^{5} +(1.92603 + 0.0808542i) q^{6} +2.08466i q^{7} +(-1.40186 + 2.45658i) q^{8} +(-0.807469 - 0.807469i) q^{9} +(-0.0301053 + 0.717139i) q^{10} +(2.71337 + 1.12391i) q^{11} +(-2.59727 + 0.828511i) q^{12} +(-3.41200 + 1.16545i) q^{13} +(-1.01298 - 2.76867i) q^{14} +(-0.489200 + 0.489200i) q^{15} +(0.668134 - 3.94380i) q^{16} +5.31344 q^{17} +(1.46477 + 0.680045i) q^{18} +(0.106653 + 0.257484i) q^{19} +(-0.308488 - 0.967070i) q^{20} +(1.08744 - 2.62532i) q^{21} +(-4.14979 - 0.174207i) q^{22} +(-1.46125 - 1.46125i) q^{23} +(3.04688 - 2.36242i) q^{24} +(3.35339 + 3.35339i) q^{25} +(3.96520 - 3.20580i) q^{26} +(2.16060 + 5.21614i) q^{27} +(2.69070 + 3.18488i) q^{28} +(3.35321 - 8.09536i) q^{29} +(0.412001 - 0.887424i) q^{30} +(7.22717 + 7.22717i) q^{31} +(1.02901 + 5.56248i) q^{32} +(-2.83080 - 2.83080i) q^{33} +(-7.05685 + 2.58190i) q^{34} +(0.977512 + 0.404899i) q^{35} +(-2.27583 - 0.191415i) q^{36} +(1.06725 + 0.442071i) q^{37} +(-0.266764 - 0.290142i) q^{38} +(4.90484 + 0.312127i) q^{39} +(0.879625 + 1.13448i) q^{40} -0.681081 q^{41} +(-0.168554 + 4.01513i) q^{42} +(3.85652 + 9.31046i) q^{43} +(5.59604 - 1.78510i) q^{44} +(-0.535460 + 0.221795i) q^{45} +(2.65076 + 1.23066i) q^{46} +(7.28593 + 7.28593i) q^{47} +(-2.89866 + 4.61810i) q^{48} +2.65418 q^{49} +(-6.08315 - 2.82420i) q^{50} +(-6.69148 - 2.77170i) q^{51} +(-3.70848 + 6.18443i) q^{52} +(-3.33170 - 8.04345i) q^{53} +(-5.40413 - 5.87774i) q^{54} +(1.05402 - 1.05402i) q^{55} +(-5.12114 - 2.92241i) q^{56} -0.379896i q^{57} +(-0.519748 + 12.3809i) q^{58} +(-0.127334 + 0.307412i) q^{59} +(-0.115967 + 1.37880i) q^{60} +(-1.36541 + 3.29640i) q^{61} +(-13.1103 - 6.08667i) q^{62} +(1.68330 - 1.68330i) q^{63} +(-4.06956 - 6.88758i) q^{64} +(-0.116218 + 1.82627i) q^{65} +(5.13516 + 2.38408i) q^{66} +(3.87328 - 1.60437i) q^{67} +(8.11770 - 6.85812i) q^{68} +(1.07798 + 2.60247i) q^{69} +(-1.49499 - 0.0627594i) q^{70} +3.99453 q^{71} +(3.11557 - 0.851650i) q^{72} +1.56592i q^{73} +(-1.63224 - 0.0685211i) q^{74} +(-2.47382 - 5.97234i) q^{75} +(0.495278 + 0.255716i) q^{76} +(-2.34298 + 5.65646i) q^{77} +(-6.66584 + 1.96881i) q^{78} -7.51320 q^{79} +(-1.71950 - 1.07929i) q^{80} -4.27018i q^{81} +(0.904552 - 0.330950i) q^{82} +(-6.09398 - 14.7122i) q^{83} +(-1.72717 - 5.41444i) q^{84} +(1.03202 - 2.49151i) q^{85} +(-9.64602 - 10.4914i) q^{86} +(-8.44571 + 8.44571i) q^{87} +(-6.56476 + 5.09003i) q^{88} +6.02327 q^{89} +(0.603377 - 0.554759i) q^{90} +(-2.42957 - 7.11287i) q^{91} +(-4.11850 - 0.346397i) q^{92} +(-5.33155 - 12.8715i) q^{93} +(-13.2169 - 6.13616i) q^{94} +0.141451 q^{95} +(1.60572 - 7.54187i) q^{96} +(7.41089 - 7.41089i) q^{97} +(-3.52505 + 1.28972i) q^{98} +(-1.28344 - 3.09849i) 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 $

$2$	−1.32811	+	0.485919i	−0.939117	+	0.343597i
$2$	−1.32811	+	0.485919i	−0.939117	+	0.343597i
$3$	−1.25935	−	0.521639i	−0.727085	−	0.301169i	−0.0117315	−	0.999931i	$-0.503734\pi$
$3$	−1.25935	−	0.521639i	−0.727085	−	0.301169i	−0.715354	+	0.698763i	$0.753734\pi$
$4$	1.52777	−	1.29071i	0.763883	−	0.645355i
$5$	0.194227	−	0.468906i	0.0868611	−	0.209701i	−0.874480	−	0.485062i	$-0.838797\pi$
$5$	0.194227	−	0.468906i	0.0868611	−	0.209701i	0.961341	+	0.275360i	$0.0887972\pi$
$6$	1.92603	+	0.0808542i	0.786299	+	0.0330086i
$7$			2.08466i			0.787929i	0.919126	+	0.393964i	$0.128897\pi$
$7$			2.08466i			0.787929i	−0.919126	+	0.393964i	$0.871103\pi$
$8$	−1.40186	+	2.45658i	−0.495634	+	0.868532i
$9$	−0.807469	−	0.807469i	−0.269156	−	0.269156i
$10$	−0.0301053	+	0.717139i	−0.00952012	+	0.226779i
$11$	2.71337	+	1.12391i	0.818112	+	0.338873i	0.752185	−	0.658951i	$-0.229000\pi$
$11$	2.71337	+	1.12391i	0.818112	+	0.338873i	0.0659264	+	0.997824i	$0.479000\pi$
$12$	−2.59727	+	0.828511i	−0.749768	+	0.239171i
$13$	−3.41200	+	1.16545i	−0.946318	+	0.323237i
$13$	−3.41200	+	1.16545i	−0.946318	+	0.323237i
$14$	−1.01298	−	2.76867i	−0.270730	−	0.739957i
$15$	−0.489200	+	0.489200i	−0.126311	+	0.126311i
$16$	0.668134	−	3.94380i	0.167034	−	0.985951i
$17$	5.31344			1.28870			0.644350	−	0.764731i	$-0.277128\pi$
$17$	5.31344			1.28870			0.644350	+	0.764731i	$0.277128\pi$
$18$	1.46477	+	0.680045i	0.345251	+	0.160288i
$19$	0.106653	+	0.257484i	0.0244679	+	0.0590708i	0.935641	−	0.352952i	$-0.114822\pi$
$19$	0.106653	+	0.257484i	0.0244679	+	0.0590708i	−0.911173	+	0.412023i	$0.864822\pi$
$20$	−0.308488	−	0.967070i	−0.0689801	−	0.216243i
$21$	1.08744	−	2.62532i	0.237299	−	0.572891i
$22$	−4.14979	−	0.174207i	−0.884739	−	0.0371411i
$23$	−1.46125	−	1.46125i	−0.304692	−	0.304692i	0.538154	−	0.842846i	$-0.319122\pi$
$23$	−1.46125	−	1.46125i	−0.304692	−	0.304692i	−0.842846	+	0.538154i	$0.819122\pi$
$24$	3.04688	−	2.36242i	0.621942	−	0.482227i
$25$	3.35339	+	3.35339i	0.670677	+	0.670677i
$26$	3.96520	−	3.20580i	0.777641	−	0.628709i
$27$	2.16060	+	5.21614i	0.415807	+	1.00385i
$28$	2.69070	+	3.18488i	0.508494	+	0.601885i
$29$	3.35321	−	8.09536i	0.622675	−	1.50327i	−0.225876	−	0.974156i	$-0.572524\pi$
$29$	3.35321	−	8.09536i	0.622675	−	1.50327i	0.848551	−	0.529114i	$-0.177476\pi$
$30$	0.412001	−	0.887424i	0.0752207	−	0.162021i
$31$	7.22717	+	7.22717i	1.29804	+	1.29804i	0.929687	+	0.368350i	$0.120077\pi$
$31$	7.22717	+	7.22717i	1.29804	+	1.29804i	0.368350	+	0.929687i	$0.379923\pi$
$32$	1.02901	+	5.56248i	0.181905	+	0.983316i
$33$	−2.83080	−	2.83080i	−0.492779	−	0.492779i
$34$	−7.05685	+	2.58190i	−1.21024	+	0.442793i
$35$	0.977512	+	0.404899i	0.165230	+	0.0684404i
$36$	−2.27583	−	0.191415i	−0.379305	−	0.0319025i
$37$	1.06725	+	0.442071i	0.175455	+	0.0726760i	0.468682	−	0.883367i	$-0.344729\pi$
$37$	1.06725	+	0.442071i	0.175455	+	0.0726760i	−0.293227	+	0.956043i	$0.594729\pi$
$38$	−0.266764	−	0.290142i	−0.0432748	−	0.0470673i
$39$	4.90484	+	0.312127i	0.785403	+	0.0499804i
$40$	0.879625	+	1.13448i	0.139081	+	0.179377i
$41$	−0.681081			−0.106367			−0.0531835	−	0.998585i	$-0.516937\pi$
$41$	−0.681081			−0.106367			−0.0531835	+	0.998585i	$0.516937\pi$
$42$	−0.168554	+	4.01513i	−0.0260084	+	0.619547i
$43$	3.85652	+	9.31046i	0.588113	+	1.41983i	0.885304	+	0.465013i	$0.153950\pi$
$43$	3.85652	+	9.31046i	0.588113	+	1.41983i	−0.297190	+	0.954818i	$0.596050\pi$
$44$	5.59604	−	1.78510i	0.843635	−	0.269113i
$45$	−0.535460	+	0.221795i	−0.0798217	+	0.0330632i
$46$	2.65076	+	1.23066i	0.390833	+	0.181450i
$47$	7.28593	+	7.28593i	1.06276	+	1.06276i	0.997894	+	0.0648684i	$0.0206627\pi$
$47$	7.28593	+	7.28593i	1.06276	+	1.06276i	0.0648684	+	0.997894i	$0.479337\pi$
$48$	−2.89866	+	4.61810i	−0.418385	+	0.666565i
$49$	2.65418			0.379169
$50$	−6.08315	−	2.82420i	−0.860287	−	0.399402i
$51$	−6.69148	−	2.77170i	−0.936994	−	0.388116i
$52$	−3.70848	+	6.18443i	−0.514273	+	0.857626i
$53$	−3.33170	−	8.04345i	−0.457645	−	1.10485i	−0.969348	−	0.245690i	$-0.920985\pi$
$53$	−3.33170	−	8.04345i	−0.457645	−	1.10485i	0.511704	−	0.859162i	$-0.329015\pi$
$54$	−5.40413	−	5.87774i	−0.735409	−	0.799860i
$55$	1.05402	−	1.05402i	0.142124	−	0.142124i
$56$	−5.12114	−	2.92241i	−0.684341	−	0.390524i
$57$		−	0.379896i		−	0.0503185i
$58$	−0.519748	+	12.3809i	−0.0682462	+	1.62570i
$59$	−0.127334	+	0.307412i	−0.0165775	+	0.0400216i	−0.931952	−	0.362583i	$-0.881895\pi$
$59$	−0.127334	+	0.307412i	−0.0165775	+	0.0400216i	0.915374	+	0.402604i	$0.131895\pi$
$60$	−0.115967	+	1.37880i	−0.0149713	+	0.178002i
$61$	−1.36541	+	3.29640i	−0.174823	+	0.422060i	−0.986867	−	0.161536i	$-0.948355\pi$
$61$	−1.36541	+	3.29640i	−0.174823	+	0.422060i	0.812044	+	0.583597i	$0.198355\pi$
$62$	−13.1103	−	6.08667i	−1.66501	−	0.773008i
$63$	1.68330	−	1.68330i	0.212076	−	0.212076i
$64$	−4.06956	−	6.88758i	−0.508695	−	0.860947i
$65$	−0.116218	+	1.82627i	−0.0144150	+	0.226521i
$66$	5.13516	+	2.38408i	0.632095	+	0.293460i
$67$	3.87328	−	1.60437i	0.473197	−	0.196005i	−0.133323	−	0.991073i	$-0.542565\pi$
$67$	3.87328	−	1.60437i	0.473197	−	0.196005i	0.606520	+	0.795068i	$0.292565\pi$
$68$	8.11770	−	6.85812i	0.984415	−	0.831669i
$69$	1.07798	+	2.60247i	0.129773	+	0.313301i
$70$	−1.49499	−	0.0627594i	−0.178686	−	0.00750118i
$71$	3.99453			0.474064			0.237032	−	0.971502i	$-0.423825\pi$
$71$	3.99453			0.474064			0.237032	+	0.971502i	$0.423825\pi$
$72$	3.11557	−	0.851650i	0.367174	−	0.100368i
$73$			1.56592i			0.183277i	0.995792	+	0.0916384i	$0.0292104\pi$
$73$			1.56592i			0.183277i	−0.995792	+	0.0916384i	$0.970790\pi$
$74$	−1.63224	−	0.0685211i	−0.189744	−	0.00796541i
$75$	−2.47382	−	5.97234i	−0.285652	−	0.689626i
$76$	0.495278	+	0.255716i	0.0568123	+	0.0293327i
$77$	−2.34298	+	5.65646i	−0.267008	+	0.644614i
$78$	−6.66584	+	1.96881i	−0.754758	+	0.222924i
$79$	−7.51320			−0.845301			−0.422650	−	0.906293i	$-0.638900\pi$
$79$	−7.51320			−0.845301			−0.422650	+	0.906293i	$0.638900\pi$
$80$	−1.71950	−	1.07929i	−0.192247	−	0.120668i
$81$		−	4.27018i		−	0.474465i
$82$	0.904552	−	0.330950i	0.0998911	−	0.0365473i
$83$	−6.09398	−	14.7122i	−0.668901	−	1.61487i	−0.783451	−	0.621453i	$-0.786543\pi$
$83$	−6.09398	−	14.7122i	−0.668901	−	1.61487i	0.114550	−	0.993418i	$-0.463457\pi$
$84$	−1.72717	−	5.41444i	−0.188449	−	0.590764i
$85$	1.03202	−	2.49151i	0.111938	−	0.270242i
$86$	−9.64602	−	10.4914i	−1.04016	−	1.13131i
$87$	−8.44571	+	8.44571i	−0.905475	+	0.905475i
$88$	−6.56476	+	5.09003i	−0.699806	+	0.542599i
$89$	6.02327			0.638466			0.319233	−	0.947676i	$-0.396575\pi$
$89$	6.02327			0.638466			0.319233	+	0.947676i	$0.396575\pi$
$90$	0.603377	−	0.554759i	0.0636015	−	0.0584767i
$91$	−2.42957	−	7.11287i	−0.254688	−	0.745631i
$92$	−4.11850	−	0.346397i	−0.429383	−	0.0361144i
$93$	−5.33155	−	12.8715i	−0.552856	−	1.33471i
$94$	−13.2169	−	6.13616i	−1.36322	−	0.632897i
$95$	0.141451			0.0145125
$96$	1.60572	−	7.54187i	0.163883	−	0.769739i
$97$	7.41089	−	7.41089i	0.752462	−	0.752462i	−0.222476	−	0.974938i	$-0.571414\pi$
$97$	7.41089	−	7.41089i	0.752462	−	0.752462i	0.974938	+	0.222476i	$0.0714140\pi$
$98$	−3.52505	+	1.28972i	−0.356084	+	0.130281i
$99$	−1.28344	−	3.09849i	−0.128990	−	0.311410i
$100$	9.45143	+	0.794937i	0.945143	+	0.0794937i
$101$	−4.89562	−	11.8191i	−0.487133	−	1.17604i	−0.956156	−	0.292857i	$-0.905394\pi$
$101$	−4.89562	−	11.8191i	−0.487133	−	1.17604i	0.469023	−	0.883186i	$-0.344606\pi$
$102$	10.2339	+	0.429614i	1.01330	+	0.0425381i
$103$	−7.36565	+	7.36565i	−0.725759	+	0.725759i	−0.969772	−	0.244013i	$-0.921536\pi$
$103$	−7.36565	+	7.36565i	−0.725759	+	0.725759i	0.244013	+	0.969772i	$0.421536\pi$
$104$	1.92014	−	10.0156i	0.188285	−	0.982114i
$105$	−1.01982	−	1.01982i	−0.0995239	−	0.0995239i
$106$	8.33334	+	9.06366i	0.809406	+	0.880341i
$107$	3.76342	−	1.55886i	0.363824	−	0.150701i	−0.193280	−	0.981144i	$-0.561913\pi$
$107$	3.76342	−	1.55886i	0.363824	−	0.150701i	0.557104	+	0.830443i	$0.311913\pi$
$108$	10.0334	+	5.18033i	0.965465	+	0.498478i
$109$	−15.3079	+	6.34074i	−1.46623	+	0.607332i	−0.965996	−	0.258558i	$-0.916753\pi$
$109$	−15.3079	+	6.34074i	−1.46623	+	0.607332i	−0.500234	+	0.865890i	$0.666753\pi$
$110$	−0.887690	+	1.91203i	−0.0846379	+	0.182305i
$111$	−1.11344	−	1.11344i	−0.105683	−	0.105683i
$112$	8.22150	+	1.39284i	0.776859	+	0.131611i
$113$			18.0993i			1.70264i	0.524645	+	0.851321i	$0.324198\pi$
$113$			18.0993i			1.70264i	−0.524645	+	0.851321i	$0.675802\pi$
$114$	0.184599	+	0.504545i	0.0172893	+	0.0472550i
$115$	−0.969005	+	0.401375i	−0.0903601	+	0.0374284i
$116$	−5.32585	−	16.6958i	−0.494492	−	1.55017i
$117$	3.69615	+	1.81402i	0.341709	+	0.167706i
$118$	0.0197368	−	0.470152i	0.00181692	−	0.0432810i
$119$			11.0767i			1.01540i
$120$	−0.515966	−	1.88755i	−0.0471011	−	0.172309i
$121$	−1.67898	−	1.67898i	−0.152635	−	0.152635i
$122$	0.211639	−	5.04147i	0.0191609	−	0.456433i
$123$	0.857719	+	0.355279i	0.0773379	+	0.0320344i
$124$	20.3696	+	1.71324i	1.82924	+	0.153853i
$125$	4.56827	−	1.89224i	0.408599	−	0.169247i
$126$	−1.41767	+	3.05356i	−0.126296	+	0.272033i
$127$	−17.6544			−1.56657			−0.783286	−	0.621662i	$-0.786458\pi$
$127$	−17.6544			−1.56657			−0.783286	+	0.621662i	$0.786458\pi$
$128$	8.75163	+	7.17000i	0.773542	+	0.633745i
$129$		−	13.7368i		−	1.20946i
$130$	−0.733069	−	2.48196i	−0.0642944	−	0.217683i
$131$	17.9384	+	7.43031i	1.56728	+	0.649189i	0.986335	−	0.164752i	$-0.0526825\pi$
$131$	17.9384	+	7.43031i	1.56728	+	0.649189i	0.580947	+	0.813942i	$0.302683\pi$
$132$	−7.97854	−	0.671056i	−0.694443	−	0.0584079i
$133$	−0.536767	+	0.222336i	−0.0465436	+	0.0192790i
$134$	−4.36456	+	4.01288i	−0.377041	+	0.346660i
$135$	2.86553			0.246625
$136$	−7.44872	+	13.0529i	−0.638723	+	1.11928i
$137$			16.4259i			1.40336i	0.712491	+	0.701681i	$0.247567\pi$
$137$			16.4259i			1.40336i	−0.712491	+	0.701681i	$0.752433\pi$
$138$	−2.69627	−	2.93256i	−0.229521	−	0.249636i
$139$	−8.79037	+	3.64109i	−0.745589	+	0.308833i	−0.722940	−	0.690910i	$-0.757210\pi$
$139$	−8.79037	+	3.64109i	−0.745589	+	0.308833i	−0.0226486	+	0.999743i	$0.507210\pi$
$140$	2.01602	−	0.643094i	0.170384	−	0.0543514i
$141$	−5.37490	−	12.9762i	−0.452648	−	1.09279i
$142$	−5.30519	+	1.94102i	−0.445202	+	0.162887i
$143$	−10.5679	−	0.672504i	−0.883730	−	0.0562376i
$144$	−3.72400	+	2.64500i	−0.310333	+	0.220417i
$145$	−3.14468	−	3.14468i	−0.261151	−	0.261151i
$146$	−0.760909	−	2.07971i	−0.0629733	−	0.172118i
$147$	−3.34254	−	1.38452i	−0.275688	−	0.114194i
$148$	2.20110	−	0.702134i	0.180929	−	0.0577151i
$149$	−0.103430	−	0.0428422i	−0.00847334	−	0.00350977i	0.378443	−	0.925625i	$-0.376460\pi$
$149$	−0.103430	−	0.0428422i	−0.00847334	−	0.00350977i	−0.386916	+	0.922115i	$0.626460\pi$
$150$	6.18759	+	6.72986i	0.505214	+	0.549491i
$151$	−3.18762			−0.259405			−0.129702	−	0.991553i	$-0.541402\pi$
$151$	−3.18762			−0.259405			−0.129702	+	0.991553i	$0.541402\pi$
$152$	−0.782042	−	0.0989550i	−0.0634320	−	0.00802631i
$153$	−4.29044	−	4.29044i	−0.346862	−	0.346862i
$154$	0.363163	−	8.65092i	0.0292645	−	0.697111i
$155$	4.79258	−	1.98515i	0.384949	−	0.159451i
$156$	7.89631	−	5.85387i	0.632211	−	0.468684i
$157$	−0.833628	+	2.01256i	−0.0665307	+	0.160619i	−0.953648	−	0.300925i	$-0.902705\pi$
$157$	−0.833628	+	2.01256i	−0.0665307	+	0.160619i	0.887117	+	0.461545i	$0.152705\pi$
$158$	9.97837	−	3.65081i	0.793837	−	0.290443i
$159$			11.8674i			0.941150i
$160$	2.80814	+	0.597875i	0.222003	+	0.0472661i
$161$	3.04622	−	3.04622i	0.240075	−	0.240075i
$162$	2.07496	+	5.67128i	0.163025	+	0.445578i
$163$	−3.29362	−	7.95149i	−0.257976	−	0.622809i	0.740828	−	0.671694i	$-0.234433\pi$
$163$	−3.29362	−	7.95149i	−0.257976	−	0.622809i	−0.998804	+	0.0488852i	$0.984433\pi$
$164$	−1.04053	+	0.879079i	−0.0812519	+	0.0686445i
$165$	−1.87720	+	0.777561i	−0.146140	+	0.0605331i
$166$	15.2424	+	16.5782i	1.18304	+	1.28672i
$167$		−	14.0874i		−	1.09012i	−0.838397	−	0.545060i	$-0.816507\pi$
$167$		−	14.0874i		−	1.09012i	0.838397	−	0.545060i	$-0.183493\pi$
$168$	4.92485	+	6.35172i	0.379961	+	0.490046i
$169$	10.2835	−	7.95301i	0.791036	−	0.611770i
$170$	−0.159963	+	3.81048i	−0.0122686	+	0.292250i
$171$	0.121791	−	0.294029i	0.00931359	−	0.0224850i
$172$	17.9090	+	9.24655i	1.36555	+	0.705043i
$173$	−6.07124	+	14.6573i	−0.461588	+	1.11437i	0.506158	+	0.862441i	$0.331065\pi$
$173$	−6.07124	+	14.6573i	−0.461588	+	1.11437i	−0.967745	+	0.251930i	$0.918935\pi$
$174$	7.11292	−	15.3208i	0.539229	−	1.16147i
$175$	−6.99068	+	6.99068i	−0.528446	+	0.528446i
$176$	6.24540	−	9.95008i	0.470764	−	0.750015i
$177$	0.320716	−	0.320716i	0.0241065	−	0.0241065i
$178$	−7.99959	+	2.92682i	−0.599594	+	0.219375i
$179$	−22.4299	−	9.29077i	−1.67649	−	0.694425i	−0.677340	−	0.735670i	$-0.736867\pi$
$179$	−22.4299	−	9.29077i	−1.67649	−	0.694425i	−0.999149	+	0.0412454i	$0.986867\pi$
$180$	−0.531785	+	1.02997i	−0.0396369	+	0.0767698i
$181$	10.9956	−	4.55455i	0.817300	−	0.338537i	0.0654375	−	0.997857i	$-0.479156\pi$
$181$	10.9956	−	4.55455i	0.817300	−	0.338537i	0.751863	+	0.659320i	$0.229156\pi$
$182$	6.68301	+	8.26611i	0.495378	+	0.612725i
$183$	3.43906	−	3.43906i	0.254223	−	0.254223i
$184$	5.63815	−	1.54120i	0.415650	−	0.113619i
$185$	0.414580	−	0.414580i	0.0304805	−	0.0304805i
$186$	13.3354	+	14.5041i	0.977799	+	1.06349i
$187$	14.4173	+	5.97186i	1.05430	+	0.436706i
$188$	20.5352	+	1.72717i	1.49768	+	0.125967i
$189$	−10.8739	+	4.50411i	−0.790959	+	0.327626i
$190$	−0.187862	+	0.0687336i	−0.0136290	+	0.00498646i
$191$			2.39853i			0.173552i	0.996228	+	0.0867759i	$0.0276564\pi$
$191$			2.39853i			0.173552i	−0.996228	+	0.0867759i	$0.972344\pi$
$192$	1.53216	+	10.7967i	0.110574	+	0.779185i
$193$	4.90919	+	4.90919i	0.353371	+	0.353371i	0.861362	−	0.507991i	$-0.169612\pi$
$193$	4.90919	+	4.90919i	0.353371	+	0.353371i	−0.507991	+	0.861362i	$0.669612\pi$
$194$	−6.24140	+	13.4436i	−0.448107	+	0.965193i
$195$	1.09901	−	2.23929i	0.0787019	−	0.160359i
$196$	4.05496	−	3.42578i	0.289640	−	0.244698i
$197$	−5.13706	+	12.4020i	−0.366000	+	0.883603i	0.628397	+	0.777893i	$0.283712\pi$
$197$	−5.13706	+	12.4020i	−0.366000	+	0.883603i	−0.994397	+	0.105710i	$0.966288\pi$
$198$	3.21016	+	3.49150i	0.228136	+	0.248130i
$199$	6.31126	−	6.31126i	0.447393	−	0.447393i	−0.447094	−	0.894487i	$-0.647541\pi$
$199$	6.31126	−	6.31126i	0.447393	−	0.447393i	0.894487	+	0.447094i	$0.147541\pi$
$200$	−12.9388	+	3.53687i	−0.914914	+	0.250094i
$201$	−5.71471			−0.403085
$202$	12.2451	+	13.3182i	0.861559	+	0.937065i
$203$	16.8761	+	6.99031i	1.18447	+	0.490623i
$204$	−13.8005	+	4.40225i	−0.966226	+	0.308219i
$205$	−0.132285	+	0.319363i	−0.00923916	+	0.0223053i
$206$	6.20330	−	13.3615i	0.432204	−	0.930941i
$207$			2.35983i			0.164020i
$208$	2.31662	+	14.2349i	0.160629	+	0.987015i
$209$			0.818518i			0.0566181i
$210$	1.84998	+	0.858883i	0.127661	+	0.0592686i
$211$	0.785392	−	1.89610i	0.0540686	−	0.130533i	−0.894537	−	0.446994i	$-0.852495\pi$
$211$	0.785392	−	1.89610i	0.0540686	−	0.130533i	0.948606	+	0.316461i	$0.102495\pi$
$212$	−15.4718	−	7.98823i	−1.06261	−	0.548634i
$213$	−5.03051	−	2.08370i	−0.344685	−	0.142773i
$214$	−4.24077	+	3.89906i	−0.289893	+	0.266534i
$215$	5.11477			0.348825
$216$	−15.8427	−	2.00464i	−1.07796	−	0.136399i
$217$	−15.0662	+	15.0662i	−1.02276	+	1.02276i
$218$	17.2495	−	15.8596i	1.16828	−	1.07415i
$219$	0.816844	−	1.97204i	0.0551972	−	0.133258i
$220$	0.249861	−	2.97073i	0.0168456	−	0.200287i
$221$	−18.1295	+	6.19254i	−1.21952	+	0.416555i
$222$	2.01982	+	0.937734i	0.135561	+	0.0629366i
$223$	0.908648	+	0.908648i	0.0608476	+	0.0608476i	0.736876	−	0.676028i	$-0.236300\pi$
$223$	0.908648	+	0.908648i	0.0608476	+	0.0608476i	−0.676028	+	0.736876i	$0.736300\pi$
$224$	−11.5959	+	2.14514i	−0.774783	+	0.143328i
$225$		−	5.41551i		−	0.361034i
$226$	−8.79481	−	24.0380i	−0.585022	−	1.59898i
$227$	5.81035	−	2.40673i	0.385647	−	0.159740i	−0.181433	−	0.983403i	$-0.558073\pi$
$227$	5.81035	−	2.40673i	0.385647	−	0.159740i	0.567079	+	0.823663i	$0.308073\pi$
$228$	−0.490336	−	0.580392i	−0.0324733	−	0.0384374i
$229$	19.7265	+	8.17099i	1.30356	+	0.539954i	0.923000	−	0.384800i	$-0.125730\pi$
$229$	19.7265	+	8.17099i	1.30356	+	0.539954i	0.380565	+	0.924754i	$0.375730\pi$
$230$	1.09191	−	1.00393i	0.0719985	−	0.0661971i
$231$	5.90127	−	5.90127i	0.388275	−	0.388275i
$232$	15.1861	+	19.5860i	0.997019	+	1.28588i
$233$	5.78713	−	5.78713i	0.379127	−	0.379127i	−0.491660	−	0.870787i	$-0.663610\pi$
$233$	5.78713	−	5.78713i	0.379127	−	0.379127i	0.870787	+	0.491660i	$0.163610\pi$
$234$	−5.79037	−	0.613195i	−0.378528	−	0.0400858i
$235$	4.83155	−	2.00129i	0.315175	−	0.130550i
$236$	0.202243	+	0.634005i	0.0131649	+	0.0412702i
$237$	9.46173	+	3.91918i	0.614606	+	0.254578i
$238$	−5.38240	−	14.7112i	−0.348889	−	0.953583i
$239$	−9.44526	+	9.44526i	−0.610963	+	0.610963i	−0.943197	−	0.332234i	$-0.892198\pi$
$239$	−9.44526	+	9.44526i	−0.610963	+	0.610963i	0.332234	+	0.943197i	$0.392198\pi$
$240$	1.60246	+	2.25616i	0.103438	+	0.145634i
$241$	13.6672	−	13.6672i	0.880385	−	0.880385i	−0.113189	−	0.993573i	$-0.536107\pi$
$241$	13.6672	−	13.6672i	0.880385	−	0.880385i	0.993573	+	0.113189i	$0.0361065\pi$
$242$	3.04572	+	1.41403i	0.195787	+	0.0908971i
$243$	4.25429	−	10.2708i	0.272913	−	0.658870i
$244$	2.16866	+	6.79847i	0.138834	+	0.435228i
$245$	0.515514	−	1.24456i	0.0329350	−	0.0795121i
$246$	−1.31178	−	0.0550683i	−0.0836363	−	0.00351102i
$247$	−0.663984	−	0.754235i	−0.0422483	−	0.0479908i
$248$	−27.8856	+	7.62260i	−1.77074	+	0.484036i
$249$			21.7066i			1.37560i
$250$	−5.14771	+	4.73292i	−0.325570	+	0.299336i
$251$	3.08730	−	1.27880i	0.194868	−	0.0807172i	−0.283115	−	0.959086i	$-0.591368\pi$
$251$	3.08730	−	1.27880i	0.194868	−	0.0807172i	0.477984	+	0.878369i	$0.341368\pi$
$252$	0.399035	−	4.74434i	0.0251369	−	0.298866i
$253$	−2.32259	−	5.60724i	−0.146020	−	0.352524i
$254$	23.4470	−	8.57859i	1.47119	−	0.538269i
$255$	−2.59934	+	2.59934i	−0.162777	+	0.162777i
$256$	−15.1072	−	5.26998i	−0.944200	−	0.329374i
$257$		−	10.5251i		−	0.656539i	−0.944584	−	0.328270i	$-0.893535\pi$
$257$		−	10.5251i		−	0.656539i	0.944584	−	0.328270i	$-0.106465\pi$
$258$	6.67498	+	18.2440i	0.415566	+	1.13582i
$259$	−0.921569	+	2.22486i	−0.0572635	+	0.138246i
$260$	2.17963	+	2.94011i	0.135175	+	0.182338i
$261$	−9.24436	+	3.82914i	−0.572212	+	0.237018i
$262$	−27.4347	−	1.15170i	−1.69492	−	0.0711522i
$263$	−7.49375	−	7.49375i	−0.462085	−	0.462085i	0.437254	−	0.899338i	$-0.355951\pi$
$263$	−7.49375	−	7.49375i	−0.462085	−	0.462085i	−0.899338	+	0.437254i	$0.855951\pi$
$264$	10.9225	−	2.98569i	0.672232	−	0.183756i
$265$	−4.41873			−0.271440
$266$	0.604849	−	0.556112i	0.0370857	−	0.0340974i
$267$	−7.58540	−	3.14198i	−0.464219	−	0.192286i
$268$	3.84670	−	7.45038i	0.234974	−	0.455105i
$269$	2.02867	+	0.840302i	0.123690	+	0.0512341i	0.443670	−	0.896190i	$-0.353676\pi$
$269$	2.02867	+	0.840302i	0.123690	+	0.0512341i	−0.319980	+	0.947424i	$0.603676\pi$
$270$	−3.80574	+	1.39241i	−0.231610	+	0.0847396i
$271$	1.06697	+	1.06697i	0.0648136	+	0.0648136i	0.738771	−	0.673957i	$-0.235407\pi$
$271$	1.06697	+	1.06697i	0.0648136	+	0.0648136i	−0.673957	+	0.738771i	$0.735407\pi$
$272$	3.55009	−	20.9552i	0.215256	−	1.27059i
$273$	−0.650680	+	10.2249i	−0.0393810	+	0.618841i
$274$	−7.98167	−	21.8155i	−0.482190	−	1.31792i
$275$	5.33006	+	12.8679i	0.321414	+	0.775963i
$276$	5.00593	+	2.58461i	0.301322	+	0.155575i
$277$	15.2732	−	6.32636i	0.917676	−	0.380114i	0.126686	−	0.991943i	$-0.459566\pi$
$277$	15.2732	−	6.32636i	0.917676	−	0.380114i	0.790990	+	0.611829i	$0.209566\pi$
$278$	9.90532	−	9.10718i	0.594082	−	0.546212i
$279$		−	11.6714i		−	0.698750i
$280$	−2.36500	+	1.83372i	−0.141336	+	0.109586i
$281$	11.4982			0.685923			0.342961	−	0.939350i	$-0.388570\pi$
$281$	11.4982			0.685923			0.342961	+	0.939350i	$0.388570\pi$
$282$	13.4438	+	14.6220i	0.800568	+	0.870729i
$283$	−2.97701	+	1.23312i	−0.176965	+	0.0733014i	−0.469407	−	0.882982i	$-0.655532\pi$
$283$	−2.97701	+	1.23312i	−0.176965	+	0.0733014i	0.292442	+	0.956283i	$0.405532\pi$
$284$	6.10271	−	5.15578i	0.362129	−	0.305940i
$285$	−0.178136	−	0.0737862i	−0.0105518	−	0.00437072i
$286$	14.3621	−	4.24197i	0.849250	−	0.250833i
$287$		−	1.41982i		−	0.0838096i
$288$	3.66063	−	5.32242i	0.215705	−	0.313627i
$289$	11.2327			0.660746
$290$	5.70455	+	2.64843i	0.334983	+	0.155521i
$291$	−13.1987	+	5.46708i	−0.773722	+	0.320486i
$292$	2.02115	+	2.39235i	0.118279	+	0.140002i
$293$	−10.4946	−	4.34699i	−0.613099	−	0.253954i	0.0544537	−	0.998516i	$-0.482658\pi$
$293$	−10.4946	−	4.34699i	−0.613099	−	0.253954i	−0.667553	+	0.744562i	$0.732658\pi$
$294$	5.11203	+	0.214602i	0.298140	+	0.0125158i
$295$	0.119416	+	0.119416i	0.00695265	+	0.00695265i
$296$	−2.58213	+	2.00207i	−0.150083	+	0.116368i
$297$			16.5816i			0.962164i
$298$	0.158185	+	0.00664055i	0.00916340	+	0.000384677i
$299$	6.68880	+	3.28277i	0.386823	+	0.189848i
$300$	−11.4880	−	5.93134i	−0.663259	−	0.342446i
$301$	−19.4092	+	8.03954i	−1.11873	+	0.463391i
$302$	4.23352	−	1.54893i	0.243612	−	0.0891306i
$303$			17.4381i			1.00179i
$304$	1.08672	−	0.248586i	0.0623279	−	0.0142574i
$305$	1.28050	+	1.28050i	0.0733213	+	0.0733213i
$306$	7.78300	+	3.61338i	0.444925	+	0.206563i
$307$	−11.2705	+	4.66838i	−0.643239	+	0.266438i	−0.680366	−	0.732872i	$-0.738179\pi$
$307$	−11.2705	+	4.66838i	−0.643239	+	0.266438i	0.0371271	+	0.999311i	$0.488179\pi$
$308$	3.72132	+	11.6659i	0.212042	+	0.664724i
$309$	13.1181	−	5.43370i	0.746264	−	0.309113i
$310$	−5.40046	+	4.96531i	−0.306725	+	0.282010i
$311$	−0.866663	−	0.866663i	−0.0491440	−	0.0491440i	0.682108	−	0.731252i	$-0.261064\pi$
$311$	−0.866663	−	0.866663i	−0.0491440	−	0.0491440i	−0.731252	+	0.682108i	$0.761064\pi$
$312$	−7.64268	+	11.6116i	−0.432681	+	0.657375i
$313$	22.4794	−	22.4794i	1.27061	−	1.27061i	0.324841	−	0.945769i	$-0.394689\pi$
$313$	22.4794	−	22.4794i	1.27061	−	1.27061i	0.945769	−	0.324841i	$-0.105311\pi$
$314$	0.129212	−	3.07798i	0.00729188	−	0.173700i
$315$	−0.462368	−	1.11625i	−0.0260515	−	0.0628938i
$316$	−11.4784	+	9.69736i	−0.645711	+	0.545519i
$317$	−10.5362	−	25.4365i	−0.591769	−	1.42866i	−0.881792	−	0.471638i	$-0.843663\pi$
$317$	−10.5362	−	25.4365i	−0.591769	−	1.42866i	0.290023	−	0.957020i	$-0.406337\pi$
$318$	−5.76662	−	15.7613i	−0.323376	−	0.883850i
$319$	18.1970	−	18.1970i	1.01884	−	1.01884i
$320$	−4.02005	+	0.570485i	−0.224727	+	0.0318911i
$321$	−5.55262			−0.309917
$322$	−2.56550	+	5.52593i	−0.142970	+	0.307948i
$323$	0.566696	+	1.36813i	0.0315318	+	0.0761245i
$324$	−5.51157	−	6.52384i	−0.306198	−	0.362435i
$325$	−15.3499	−	7.53355i	−0.851461	−	0.417886i
$326$	8.23808	+	8.96005i	0.456265	+	0.496251i
$327$	22.5855			1.24898
$328$	0.954783	−	1.67313i	0.0527191	−	0.0923831i
$329$	−15.1887	+	15.1887i	−0.837381	+	0.837381i
$330$	2.11530	−	1.94486i	0.116443	−	0.107061i
$331$	1.40066	−	3.38150i	0.0769874	−	0.185864i	−0.880700	−	0.473675i	$-0.842927\pi$
$331$	1.40066	−	3.38150i	0.0769874	−	0.185864i	0.957687	+	0.287810i	$0.0929273\pi$
$332$	−28.2993	−	14.6112i	−1.55313	−	0.801893i
$333$	−0.504816	−	1.21873i	−0.0276637	−	0.0667862i
$334$	6.84536	+	18.7097i	0.374561	+	1.02375i
$335$		−	2.12782i		−	0.116255i
$336$	−9.62718	−	6.04272i	−0.525206	−	0.329658i
$337$	−24.6026			−1.34019			−0.670095	−	0.742276i	$-0.733747\pi$
$337$	−24.6026			−1.34019			−0.670095	+	0.742276i	$0.733747\pi$
$338$	−9.79308	+	15.5594i	−0.532673	+	0.846321i
$339$	9.44132	−	22.7934i	0.512782	−	1.23797i
$340$	−1.63914	−	5.13847i	−0.0888946	−	0.278673i
$341$	11.4873	+	27.7327i	0.622070	+	1.50181i
$342$	−0.0188776	+	0.449685i	−0.00102079	+	0.0243162i
$343$			20.1257i			1.08669i
$344$	−28.2782	−	3.57815i	−1.52466	−	0.192921i
$345$	1.42969			0.0769718
$346$	0.941043	−	22.4166i	0.0505908	−	1.20513i
$347$	−7.64871	−	18.4656i	−0.410604	−	0.991287i	−0.984976	−	0.172692i	$-0.944753\pi$
$347$	−7.64871	−	18.4656i	−0.410604	−	0.991287i	0.574371	−	0.818595i	$-0.305247\pi$
$348$	−2.00210	+	23.8040i	−0.107324	+	1.27603i
$349$	−18.3498	+	7.60073i	−0.982242	+	0.406858i	−0.815256	−	0.579101i	$-0.803404\pi$
$349$	−18.3498	+	7.60073i	−0.982242	+	0.406858i	−0.166986	+	0.985959i	$0.553404\pi$
$350$	5.88750	−	12.6813i	0.314700	−	0.677845i
$351$	−13.4511	−	15.2794i	−0.717966	−	0.815554i
$352$	−3.45966	+	16.2496i	−0.184400	+	0.866105i
$353$	16.0310	−	16.0310i	0.853244	−	0.853244i	−0.137287	−	0.990531i	$-0.543838\pi$
$353$	16.0310	−	16.0310i	0.853244	−	0.853244i	0.990531	+	0.137287i	$0.0438383\pi$
$354$	−0.270105	+	0.581789i	−0.0143559	+	0.0309218i
$355$	0.775848	−	1.87306i	0.0411777	−	0.0994118i
$356$	9.20215	−	7.77430i	0.487713	−	0.412037i
$357$	5.77806	−	13.9495i	0.305807	−	0.738285i
$358$	34.3040	+	1.44007i	1.81302	+	0.0761101i
$359$			5.90681i			0.311750i	0.987777	+	0.155875i	$0.0498196\pi$
$359$			5.90681i			0.311750i	−0.987777	+	0.155875i	$0.950180\pi$
$360$	0.205786	−	1.62633i	0.0108459	−	0.0857149i
$361$	13.3801	−	13.3801i	0.704216	−	0.704216i
$362$	−12.3903	+	11.3919i	−0.651221	+	0.598747i
$363$	1.23860	+	2.99024i	0.0650096	+	0.156947i
$364$	−12.8925	−	7.73093i	−0.675748	−	0.405211i
$365$	0.734269	+	0.304144i	0.0384334	+	0.0159196i
$366$	−2.89635	+	6.23856i	−0.151395	+	0.326095i
$367$	11.6274			0.606944			0.303472	−	0.952840i	$-0.401854\pi$
$367$	11.6274			0.606944			0.303472	+	0.952840i	$0.401854\pi$
$368$	−6.73920	+	4.78658i	−0.351305	+	0.249518i
$369$	0.549952	+	0.549952i	0.0286294	+	0.0286294i
$370$	−0.349156	+	0.752061i	−0.0181518	+	0.0390978i
$371$	16.7679	−	6.94548i	0.870545	−	0.360591i
$372$	−24.7587	−	12.7831i	−1.28368	−	0.662775i
$373$	−1.32770	−	3.20536i	−0.0687459	−	0.165967i	0.885772	−	0.464120i	$-0.153629\pi$
$373$	−1.32770	−	3.20536i	−0.0687459	−	0.165967i	−0.954518	+	0.298153i	$0.903629\pi$
$374$	−22.0497	−	0.925639i	−1.14016	−	0.0478637i
$375$	−6.74012			−0.348058
$376$	−28.1123	+	7.68458i	−1.44978	+	0.396302i
$377$	−2.00642	+	31.5293i	−0.103336	+	1.62384i
$378$	12.2531	−	11.2658i	0.630232	−	0.579450i
$379$	6.67458	+	2.76470i	0.342850	+	0.142013i	0.547463	−	0.836830i	$-0.315594\pi$
$379$	6.67458	+	2.76470i	0.342850	+	0.142013i	−0.204613	+	0.978843i	$0.565594\pi$
$380$	0.216103	−	0.182572i	0.0110859	−	0.00936574i
$381$	22.2330	+	9.20921i	1.13903	+	0.471802i
$382$	−1.16549	−	3.18552i	−0.0596318	−	0.162985i
$383$	−16.7020	−	16.7020i	−0.853433	−	0.853433i	0.137121	−	0.990554i	$-0.456215\pi$
$383$	−16.7020	−	16.7020i	−0.853433	−	0.853433i	−0.990554	+	0.137121i	$0.956215\pi$
$384$	−7.28120	−	13.5947i	−0.371567	−	0.693753i
$385$	2.19728	+	2.19728i	0.111984	+	0.111984i
$386$	−8.90542	−	4.13448i	−0.453274	−	0.210440i
$387$	4.40389	−	10.6319i	0.223862	−	0.540451i
$388$	1.75679	−	20.8874i	0.0891875	−	1.06040i
$389$	13.2343	+	31.9504i	0.671005	+	1.61995i	0.779905	+	0.625898i	$0.215267\pi$
$389$	13.2343	+	31.9504i	0.671005	+	1.61995i	−0.108900	+	0.994053i	$0.534733\pi$
$390$	−0.371500	+	3.50805i	−0.0188116	+	0.177637i
$391$	−7.76428	−	7.76428i	−0.392656	−	0.392656i
$392$	−3.72080	+	6.52020i	−0.187929	+	0.329320i
$393$	−18.7147	−	18.7147i	−0.944032	−	0.944032i
$394$	0.796245	−	18.9674i	0.0401143	−	0.955564i
$395$	−1.45927	+	3.52299i	−0.0734238	+	0.177261i
$396$	−5.96004	−	3.07722i	−0.299503	−	0.154636i
$397$	10.3137	+	24.8994i	0.517628	+	1.24966i	0.939357	+	0.342942i	$0.111423\pi$
$397$	10.3137	+	24.8994i	0.517628	+	1.24966i	−0.421729	+	0.906722i	$0.638577\pi$
$398$	−5.31530	+	11.4488i	−0.266432	+	0.573877i
$399$	0.791956			0.0396474
$400$	15.4656	−	10.9846i	0.773280	−	0.549229i
$401$	−9.05462	+	9.05462i	−0.452166	+	0.452166i	−0.896073	−	0.443907i	$-0.853592\pi$
$401$	−9.05462	+	9.05462i	−0.452166	+	0.452166i	0.443907	+	0.896073i	$0.353592\pi$
$402$	7.58978	−	2.77689i	0.378544	−	0.138499i
$403$	−33.0820	−	16.2362i	−1.64793	−	0.808782i
$404$	−22.7344	−	11.7380i	−1.13108	−	0.583985i
$405$	−2.00232	−	0.829386i	−0.0994959	−	0.0412125i
$406$	−25.8101	−	1.08350i	−1.28093	−	0.0537731i
$407$	2.39900	+	2.39900i	0.118914	+	0.118914i
$408$	16.1894	−	12.5526i	0.801497	−	0.621446i
$409$		−	7.42900i		−	0.367341i	−0.982988	−	0.183670i	$-0.941202\pi$
$409$		−	7.42900i		−	0.367341i	0.982988	−	0.183670i	$-0.0587979\pi$
$410$	0.0205041	−	0.488430i	0.00101263	−	0.0241218i
$411$	8.56841	−	20.6860i	0.422648	−	1.02036i
$412$	−1.74607	+	20.7599i	−0.0860225	+	1.02277i
$413$	−0.640850	−	0.265449i	−0.0315342	−	0.0130619i
$414$	−1.14669	−	3.13412i	−0.0563566	−	0.154034i
$415$	−8.08225			−0.396742
$416$	−9.99376	−	17.7799i	−0.489984	−	0.871731i
$417$	12.9695			0.635118
$418$	−0.397733	−	1.08708i	−0.0194538	−	0.0531710i
$419$	−1.63004	−	0.675186i	−0.0796329	−	0.0329850i	0.342511	−	0.939514i	$-0.388722\pi$
$419$	−1.63004	−	0.675186i	−0.0796329	−	0.0329850i	−0.422144	+	0.906529i	$0.638722\pi$
$420$	−2.87433	−	0.241753i	−0.140253	−	0.0117963i
$421$	1.15708	−	2.79343i	0.0563924	−	0.136143i	−0.893172	−	0.449715i	$-0.851526\pi$
$421$	1.15708	−	2.79343i	0.0563924	−	0.136143i	0.949565	+	0.313572i	$0.101526\pi$
$422$	−0.121736	+	2.89988i	−0.00592601	+	0.141164i
$423$		−	11.7663i		−	0.572099i
$424$	24.4300	+	3.09122i	1.18642	+	0.150123i
$425$	17.8180	+	17.8180i	0.864301	+	0.864301i
$426$	7.69359	+	0.322975i	0.372756	+	0.0156482i
$427$	−6.87188	−	2.84643i	−0.332554	−	0.137748i
$428$	3.73759	−	7.23906i	0.180663	−	0.349913i
$429$	12.9578	+	6.35954i	0.625610	+	0.307041i
$430$	−6.79299	+	2.48537i	−0.327587	+	0.119855i
$431$	−18.5498	+	18.5498i	−0.893511	+	0.893511i	−0.994852	−	0.101340i	$-0.967687\pi$
$431$	−18.5498	+	18.5498i	−0.893511	+	0.893511i	0.101340	+	0.994852i	$0.467687\pi$
$432$	22.0150	−	5.03588i	1.05920	−	0.242289i
$433$	−22.6751			−1.08969			−0.544847	−	0.838535i	$-0.683412\pi$
$433$	−22.6751			−1.08969			−0.544847	+	0.838535i	$0.683412\pi$
$434$	12.6887	−	27.3306i	0.609075	−	1.31191i
$435$	2.31986	+	5.60063i	0.111229	+	0.268530i
$436$	−15.2028	+	29.4452i	−0.728083	+	1.41017i
$437$	0.220401	−	0.532095i	0.0105432	−	0.0254536i
$438$	−0.126611	+	3.01600i	−0.00604971	+	0.144110i
$439$	−16.0097	−	16.0097i	−0.764100	−	0.764100i	0.212961	−	0.977061i	$-0.431689\pi$
$439$	−16.0097	−	16.0097i	−0.764100	−	0.764100i	−0.977061	+	0.212961i	$0.931689\pi$
$440$	1.11169	+	4.06688i	0.0529978	+	0.193881i
$441$	−2.14317	−	2.14317i	−0.102056	−	0.102056i
$442$	21.0689	−	17.0338i	1.00214	−	0.810217i
$443$	2.72198	+	6.57145i	0.129325	+	0.312219i	0.975258	−	0.221071i	$-0.0709553\pi$
$443$	2.72198	+	6.57145i	0.129325	+	0.312219i	−0.845932	+	0.533290i	$0.820955\pi$
$444$	−3.13821	−	0.263947i	−0.148933	−	0.0125264i
$445$	1.16988	−	2.82435i	0.0554579	−	0.133887i
$446$	−1.64832	−	0.765257i	−0.0780500	−	0.0362360i
$447$	0.107907	+	0.107907i	0.00510380	+	0.00510380i
$448$	14.3583	−	8.48365i	0.678365	−	0.400815i
$449$	−19.3195	−	19.3195i	−0.911744	−	0.911744i	0.0846659	−	0.996409i	$-0.473018\pi$
$449$	−19.3195	−	19.3195i	−0.911744	−	0.911744i	−0.996409	+	0.0846659i	$0.973018\pi$
$450$	2.63150	+	7.19241i	0.124050	+	0.339053i
$451$	−1.84803	−	0.765477i	−0.0870201	−	0.0360449i
$452$	23.3610	+	27.6515i	1.09881	+	1.30062i
$453$	4.01432	+	1.66279i	0.188609	+	0.0781246i
$454$	−6.54733	+	6.01976i	−0.307281	+	0.282521i
$455$	−3.80716	−	0.242275i	−0.178482	−	0.0113580i
$456$	0.933245	+	0.532563i	0.0437032	+	0.0249395i
$457$	−3.56967			−0.166982			−0.0834911	−	0.996509i	$-0.526607\pi$
$457$	−3.56967			−0.166982			−0.0834911	+	0.996509i	$0.526607\pi$
$458$	−30.1695	−	1.26650i	−1.40973	−	0.0591799i
$459$	11.4802	+	27.7157i	0.535850	+	1.29366i
$460$	−0.962353	+	1.86391i	−0.0448699	+	0.0869053i
$461$	−1.61875	+	0.670507i	−0.0753925	+	0.0312286i	−0.420061	−	0.907496i	$-0.637991\pi$
$461$	−1.61875	+	0.670507i	−0.0753925	+	0.0312286i	0.344668	+	0.938724i	$0.387991\pi$
$462$	−4.97001	+	10.7051i	−0.231226	+	0.498045i
$463$	8.52614	+	8.52614i	0.396243	+	0.396243i	0.876906	−	0.480663i	$-0.159604\pi$
$463$	8.52614	+	8.52614i	0.396243	+	0.396243i	−0.480663	+	0.876906i	$0.659604\pi$
$464$	−29.6861	−	18.6332i	−1.37814	−	0.865024i
$465$	−7.07106			−0.327912
$466$	−4.87388	+	10.4980i	−0.225778	+	0.486312i
$467$	−0.549711	−	0.227698i	−0.0254376	−	0.0105366i	0.369928	−	0.929060i	$-0.379382\pi$
$467$	−0.549711	−	0.227698i	−0.0254376	−	0.0105366i	−0.395366	+	0.918524i	$0.629382\pi$
$468$	7.98822	−	1.99926i	0.369256	−	0.0924157i
$469$	3.34456	+	8.07449i	0.154438	+	0.372845i
$470$	−5.44437	+	5.00568i	−0.251130	+	0.230895i
$471$	2.09966	−	2.09966i	0.0967470	−	0.0967470i
$472$	−0.576676	−	0.743756i	−0.0265437	−	0.0342341i
$473$			29.5971i			1.36088i
$474$	−14.4707	−	0.607473i	−0.664659	−	0.0279022i
$475$	−0.505793	+	1.22109i	−0.0232074	+	0.0560275i
$476$	14.2969	+	16.9227i	0.655296	+	0.775649i
$477$	−3.80459	+	9.18509i	−0.174200	+	0.420556i
$478$	7.95474	−	17.1340i	0.363841	−	0.783691i
$479$	8.30563	−	8.30563i	0.379494	−	0.379494i	−0.491426	−	0.870920i	$-0.663524\pi$
$479$	8.30563	−	8.30563i	0.379494	−	0.379494i	0.870920	+	0.491426i	$0.163524\pi$
$480$	−3.22455	−	2.21777i	−0.147180	−	0.101227i
$481$	−4.15668	−	0.264517i	−0.189528	−	0.0120609i
$482$	−11.5105	+	24.7928i	−0.524287	+	1.12928i
$483$	−5.42527	+	2.24722i	−0.246858	+	0.102252i
$484$	−4.73217	−	0.398011i	−0.215098	−	0.0180914i
$485$	−2.03562	−	4.91441i	−0.0924325	−	0.223152i
$486$	−0.659416	+	15.7080i	−0.0299117	+	0.712528i
$487$	35.9242			1.62788			0.813940	−	0.580948i	$-0.197318\pi$
$487$	35.9242			1.62788			0.813940	+	0.580948i	$0.197318\pi$
$488$	−6.18374	−	7.97534i	−0.279925	−	0.361027i
$489$			11.7318i			0.530530i
$490$	−0.0799048	+	1.90342i	−0.00360973	+	0.0859876i
$491$	2.43257	+	5.87275i	0.109781	+	0.265034i	0.969217	−	0.246210i	$-0.0791851\pi$
$491$	2.43257	+	5.87275i	0.109781	+	0.265034i	−0.859436	+	0.511243i	$0.829185\pi$
$492$	1.76895	−	0.564284i	0.0797506	−	0.0254399i
$493$	17.8171	−	43.0142i	0.802441	−	1.93726i
$494$	1.24834	+	0.679066i	0.0561656	+	0.0305526i
$495$	−1.70218			−0.0765073
$496$	33.3312	−	23.6738i	1.49662	−	1.06299i
$497$			8.32726i			0.373528i
$498$	−10.5477	−	28.8288i	−0.472652	−	1.29185i
$499$	10.1255	+	24.4450i	0.453278	+	1.09431i	0.971068	+	0.238803i	$0.0767549\pi$
$499$	10.1255	+	24.4450i	0.453278	+	1.09431i	−0.517790	+	0.855508i	$0.673245\pi$
$500$	4.53692	−	8.78722i	0.202897	−	0.392976i
$501$	−7.34856	+	17.7410i	−0.328310	+	0.792609i
$502$	−3.47888	+	3.19857i	−0.155270	+	0.142759i
$503$	27.1661	−	27.1661i	1.21128	−	1.21128i	0.240669	−	0.970607i	$-0.422633\pi$
$503$	27.1661	−	27.1661i	1.21128	−	1.21128i	0.970607	−	0.240669i	$-0.0773667\pi$
$504$	1.77540	+	6.49492i	0.0790828	+	0.289307i
$505$	−6.49291			−0.288931
$506$	5.80933	+	6.31845i	0.258256	+	0.280889i
$507$	−17.0991	+	4.65135i	−0.759396	+	0.206574i
$508$	−26.9717	+	22.7867i	−1.19668	+	1.01099i
$509$	3.08613	+	7.45057i	0.136790	+	0.330241i	0.977399	−	0.211402i	$-0.0678028\pi$
$509$	3.08613	+	7.45057i	0.136790	+	0.330241i	−0.840609	+	0.541642i	$0.817803\pi$
$510$	2.18914	−	4.71528i	0.0969369	−	0.208796i
$511$	−3.26441			−0.144409
$512$	22.6248	−	0.341742i	0.999886	−	0.0151030i
$513$	−1.11264	+	1.11264i	−0.0491241	+	0.0491241i
$514$	5.11436	+	13.9785i	0.225585	+	0.616567i
$515$	2.02319	+	4.88441i	0.0891523	+	0.215233i
$516$	−17.7303	−	20.9866i	−0.780531	−	0.923885i
$517$	11.5807	+	27.9582i	0.509317	+	1.22960i
$518$	0.142843	−	3.40268i	0.00627618	−	0.149505i
$519$	15.2916	−	15.2916i	0.671227	−	0.671227i
$520$	−4.32345	−	2.84568i	−0.189596	−	0.124791i
$521$	18.4517	+	18.4517i	0.808386	+	0.808386i	0.984389	−	0.176004i	$-0.0563171\pi$
$521$	18.4517	+	18.4517i	0.808386	+	0.808386i	−0.176004	+	0.984389i	$0.556317\pi$
$522$	10.4169	−	9.57754i	0.455935	−	0.419198i
$523$	−24.4761	+	10.1383i	−1.07026	+	0.443318i	−0.847084	−	0.531459i	$-0.821644\pi$
$523$	−24.4761	+	10.1383i	−1.07026	+	0.443318i	−0.223180	+	0.974777i	$0.571644\pi$
$524$	36.9960	−	11.8014i	1.61618	−	0.515549i
$525$	12.4503	−	5.15709i	0.543376	−	0.225074i
$526$	13.5939	+	6.31119i	0.592722	+	0.275181i
$527$	38.4011	+	38.4011i	1.67278	+	1.67278i
$528$	−13.0555	+	9.27277i	−0.568167	+	0.403545i
$529$		−	18.7295i		−	0.814326i
$530$	5.86857	−	2.14715i	0.254914	−	0.0932660i
$531$	0.351044	−	0.145407i	0.0152340	−	0.00631014i
$532$	−0.533082	+	1.03249i	−0.0231120	+	0.0447640i
$533$	2.32385	−	0.793765i	0.100657	−	0.0343818i
$534$	11.6010	+	0.487007i	0.502025	+	0.0210749i
$535$		−	2.06746i		−	0.0893843i
$536$	−1.48856	+	11.7641i	−0.0642961	+	0.508133i
$537$	23.4006	+	23.4006i	1.00981	+	1.00981i
$538$	−3.10262	−	0.130247i	−0.133763	−	0.00561534i
$539$	7.20177	+	2.98307i	0.310202	+	0.128490i
$540$	4.37785	−	3.69856i	0.188393	−	0.159161i
$541$	22.4171	−	9.28547i	0.963786	−	0.399213i	0.155391	−	0.987853i	$-0.450336\pi$
$541$	22.4171	−	9.28547i	0.963786	−	0.399213i	0.808396	+	0.588640i	$0.200336\pi$
$542$	−1.93551	−	0.898593i	−0.0831374	−	0.0385979i
$543$	−16.2232			−0.696203
$544$	5.46760	+	29.5559i	0.234421	+	1.26720i
$545$			8.40951i			0.360224i
$546$	−4.10431	−	13.8960i	−0.175648	−	0.594696i
$547$	−7.53430	−	3.12081i	−0.322143	−	0.133436i	0.215751	−	0.976448i	$-0.430780\pi$
$547$	−7.53430	−	3.12081i	−0.322143	−	0.133436i	−0.537894	+	0.843012i	$0.680780\pi$
$548$	21.2011	+	25.0950i	0.905667	+	1.07200i
$549$	3.76427	−	1.55921i	0.160655	−	0.0665455i
$550$	−13.3317	−	14.5000i	−0.568464	−	0.618284i
$551$	2.44205			0.104035
$552$	−7.90435	−	1.00017i	−0.336431	−	0.0425700i
$553$		−	15.6625i		−	0.666037i
$554$	−17.2104	+	15.8236i	−0.731200	+	0.672282i
$555$	−0.738361	+	0.305839i	−0.0313417	+	0.0129822i
$556$	−8.73003	+	16.9085i	−0.370236	+	0.717082i
$557$	−1.13162	−	2.73198i	−0.0479484	−	0.115758i	0.898091	−	0.439811i	$-0.144954\pi$
$557$	−1.13162	−	2.73198i	−0.0479484	−	0.115758i	−0.946039	+	0.324053i	$0.894954\pi$
$558$	5.67137	+	15.5010i	0.240088	+	0.656208i
$559$	−24.0093	−	27.2727i	−1.01548	−	1.15351i
$560$	2.24995	−	3.58459i	0.0950777	−	0.151477i
$561$	−15.0413	−	15.0413i	−0.635044	−	0.635044i
$562$	−15.2708	+	5.58717i	−0.644162	+	0.235681i
$563$	25.8867	+	10.7226i	1.09100	+	0.451905i	0.854354	−	0.519692i	$-0.173953\pi$
$563$	25.8867	+	10.7226i	1.09100	+	0.451905i	0.236642	+	0.971597i	$0.423953\pi$
$564$	−24.9600	−	12.8871i	−1.05101	−	0.542644i
$565$	8.48689	+	3.51539i	0.357046	+	0.147893i
$566$	3.35461	−	3.08431i	0.141005	−	0.129643i
$567$	8.90189			0.373844
$568$	−5.59979	+	9.81288i	−0.234962	+	0.411739i
$569$	9.17870	+	9.17870i	0.384791	+	0.384791i	0.872825	−	0.488034i	$-0.162286\pi$
$569$	9.17870	+	9.17870i	0.384791	+	0.384791i	−0.488034	+	0.872825i	$0.662286\pi$
$570$	0.272438	+	0.0114369i	0.0114112	+	0.000479038i
$571$	21.5955	−	8.94513i	0.903742	−	0.374342i	0.118084	−	0.993004i	$-0.462325\pi$
$571$	21.5955	−	8.94513i	0.903742	−	0.374342i	0.785658	+	0.618661i	$0.212325\pi$
$572$	−17.0132	+	12.6126i	−0.711360	+	0.527361i
$573$	1.25117	−	3.02059i	0.0522683	−	0.126187i
$574$	0.689920	+	1.88569i	0.0287967	+	0.0787071i
$575$		−	9.80027i		−	0.408700i
$576$	−2.27547	+	8.84755i	−0.0948110	+	0.368648i
$577$	−27.3036	+	27.3036i	−1.13667	+	1.13667i	−0.147622	+	0.989044i	$0.547162\pi$
$577$	−27.3036	+	27.3036i	−1.13667	+	1.13667i	−0.989044	+	0.147622i	$0.952838\pi$
$578$	−14.9183	+	5.45818i	−0.620518	+	0.227030i
$579$	−3.62155	−	8.74320i	−0.150507	−	0.363355i
$580$	−8.86320	−	0.745463i	−0.368024	−	0.0309537i
$581$	30.6699	−	12.7039i	1.27240	−	0.527047i
$582$	14.8728	−	13.6744i	0.616498	−	0.566822i
$583$		−	25.5694i		−	1.05898i
$584$	−3.84680	−	2.19520i	−0.159182	−	0.0908381i
$585$	1.56850	−	1.38081i	0.0648494	−	0.0570897i
$586$	16.0503	+	0.673785i	0.663030	+	0.0278338i
$587$	−0.786805	+	1.89952i	−0.0324749	+	0.0784014i	−0.939285	−	0.343138i	$-0.888510\pi$
$587$	−0.786805	+	1.89952i	−0.0324749	+	0.0784014i	0.906810	+	0.421540i	$0.138510\pi$
$588$	−6.89363	+	2.19902i	−0.284289	+	0.0906860i
$589$	−1.09008	+	2.63168i	−0.0449158	+	0.108436i
$590$	−0.216624	−	0.100571i	−0.00891826	−	0.00414044i
$591$	12.9387	−	12.9387i	0.532227	−	0.532227i
$592$	2.45651	−	3.91368i	0.100962	−	0.160851i
$593$	25.2611	−	25.2611i	1.03735	−	1.03735i	0.0380735	−	0.999275i	$-0.487878\pi$
$593$	25.2611	−	25.2611i	1.03735	−	1.03735i	0.999275	−	0.0380735i	$-0.0121221\pi$
$594$	−8.05733	−	22.0223i	−0.330596	−	0.903585i
$595$	5.19395	+	2.15141i	0.212931	+	0.0881991i
$596$	−0.213314	+	0.0680456i	−0.00873768	+	0.00278726i
$597$	−11.2403	+	4.65587i	−0.460034	+	0.190552i
$598$	−10.4786	−	1.10968i	−0.428503	−	0.0453782i
$599$	6.64216	−	6.64216i	0.271391	−	0.271391i	−0.558269	−	0.829660i	$-0.688534\pi$
$599$	6.64216	−	6.64216i	0.271391	−	0.271391i	0.829660	+	0.558269i	$0.188534\pi$
$600$	18.1395	+	2.29526i	0.740541	+	0.0937037i
$601$	27.3596	−	27.3596i	1.11602	−	1.11602i	0.123704	−	0.992319i	$-0.460523\pi$
$601$	27.3596	−	27.3596i	1.11602	−	1.11602i	0.992319	−	0.123704i	$-0.0394773\pi$
$602$	21.8710	−	20.1087i	0.891395	−	0.819569i
$603$	−4.42304	−	1.83208i	−0.180120	−	0.0746081i
$604$	−4.86994	+	4.11429i	−0.198155	+	0.167408i
$605$	−1.11339	+	0.461181i	−0.0452657	+	0.0187497i
$606$	−8.47350	−	23.1597i	−0.344212	−	0.940801i
$607$			18.2383i			0.740269i	0.928978	+	0.370135i	$0.120688\pi$
$607$			18.2383i			0.740269i	−0.928978	+	0.370135i	$0.879312\pi$
$608$	−1.32250	+	0.858210i	−0.0536344	+	0.0348050i
$609$	−17.6065	−	17.6065i	−0.713450	−	0.713450i
$610$	−2.32287	−	1.07843i	−0.0940502	−	0.0436643i
$611$	−33.3510	−	16.3682i	−1.34924	−	0.662187i
$612$	−12.0925	−	1.01707i	−0.488811	−	0.0411127i
$613$	8.29495	−	20.0258i	0.335030	−	0.808834i	−0.663148	−	0.748489i	$-0.730780\pi$
$613$	8.29495	−	20.0258i	0.335030	−	0.808834i	0.998178	−	0.0603453i	$-0.0192202\pi$
$614$	12.7000	−	11.6767i	0.512530	−	0.471232i
$615$	0.333185	−	0.333185i	0.0134353	−	0.0134353i
$616$	−10.6110	−	13.6853i	−0.427529	−	0.551397i
$617$	−46.9045			−1.88830			−0.944151	−	0.329512i	$-0.893116\pi$
$617$	−46.9045			−1.88830			−0.944151	+	0.329512i	$0.893116\pi$
$618$	−14.7820	+	13.5909i	−0.594619	+	0.546707i
$619$	−17.6988	−	7.33109i	−0.711376	−	0.294661i	−0.00250190	−	0.999997i	$-0.500796\pi$
$619$	−17.6988	−	7.33109i	−0.711376	−	0.294661i	−0.708874	+	0.705335i	$0.750796\pi$
$620$	4.75968	−	9.21867i	0.191153	−	0.370231i
$621$	4.46491	−	10.7793i	0.179171	−	0.432557i
$622$	1.57215	+	0.729898i	0.0630377	+	0.0292663i
$623$			12.5565i			0.503066i
$624$	4.50806	−	19.1352i	0.180467	−	0.766020i
$625$			21.2024i			0.848096i
$626$	−18.9320	+	40.7783i	−0.756674	+	1.62983i
$627$	0.426971	−	1.03080i	0.0170516	−	0.0411661i
$628$	1.32404	+	4.15068i	0.0528349	+	0.165630i
$629$	5.67079	+	2.34892i	0.226109	+	0.0936575i
$630$	1.15649	+	1.25784i	0.0460755	+	0.0501135i
$631$	−11.2410			−0.447498			−0.223749	−	0.974647i	$-0.571830\pi$
$631$	−11.2410			−0.447498			−0.223749	+	0.974647i	$0.571830\pi$
$632$	10.5325	−	18.4568i	0.418960	−	0.734171i
$633$	−1.97816	+	1.97816i	−0.0786250	+	0.0786250i
$634$	26.3533	+	28.6628i	1.04662	+	1.13835i
$635$	−3.42896	+	8.27824i	−0.136074	+	0.328512i
$636$	15.3174	+	18.1307i	0.607376	+	0.718928i
$637$	−9.05606	+	3.09331i	−0.358814	+	0.122561i
$638$	−15.3254	+	33.0099i	−0.606738	+	1.30687i
$639$	−3.22546	−	3.22546i	−0.127597	−	0.127597i
$640$	5.06187	−	2.71109i	0.200088	−	0.107165i
$641$			11.2701i			0.445143i	0.974916	+	0.222572i	$0.0714451\pi$
$641$			11.2701i			0.445143i	−0.974916	+	0.222572i	$0.928555\pi$
$642$	7.37450	−	2.69812i	0.291048	−	0.106486i
$643$	−24.8174	+	10.2797i	−0.978703	+	0.405392i	−0.813945	−	0.580942i	$-0.802684\pi$
$643$	−24.8174	+	10.2797i	−0.978703	+	0.405392i	−0.164758	+	0.986334i	$0.552684\pi$
$644$	0.722121	−	8.58568i	0.0284556	−	0.338323i
$645$	−6.44128	−	2.66807i	−0.253625	−	0.105055i
$646$	−1.41743	−	1.54166i	−0.0557682	−	0.0606556i
$647$	−6.63607	+	6.63607i	−0.260891	+	0.260891i	−0.825416	−	0.564525i	$-0.809059\pi$
$647$	−6.63607	+	6.63607i	−0.260891	+	0.260891i	0.564525	+	0.825416i	$0.309059\pi$
$648$	10.4900	+	5.98622i	0.412088	+	0.235161i
$649$	−0.691010	+	0.691010i	−0.0271245	+	0.0271245i
$650$	24.0471	+	2.54657i	0.943206	+	0.0998848i
$651$	26.8327	−	11.1145i	1.05166	−	0.435611i
$652$	−15.2949	−	7.89691i	−0.598996	−	0.309267i
$653$	−19.7892	−	8.19697i	−0.774413	−	0.320772i	−0.0397544	−	0.999209i	$-0.512658\pi$
$653$	−19.7892	−	8.19697i	−0.774413	−	0.320772i	−0.734658	+	0.678437i	$0.762658\pi$
$654$	−29.9961	+	10.9747i	−1.17294	+	0.429147i
$655$	6.96824	−	6.96824i	0.272272	−	0.272272i
$656$	−0.455054	+	2.68605i	−0.0177669	+	0.104873i
$657$	1.26443	−	1.26443i	0.0493301	−	0.0493301i
$658$	12.7918	−	27.5528i	0.498678	−	1.07412i
$659$	4.29124	−	10.3600i	0.167163	−	0.403567i	−0.817993	−	0.575228i	$-0.804913\pi$
$659$	4.29124	−	10.3600i	0.167163	−	0.403567i	0.985156	+	0.171661i	$0.0549134\pi$
$660$	−1.86431	+	3.61085i	−0.0725683	+	0.140552i
$661$	−6.03274	+	14.5643i	−0.234647	+	0.566487i	−0.996713	−	0.0810117i	$-0.974185\pi$
$661$	−6.03274	+	14.5643i	−0.234647	+	0.566487i	0.762067	+	0.647499i	$0.224185\pi$
$662$	−0.217103	+	5.17162i	−0.00843795	+	0.201001i
$663$	26.0616	+	1.65847i	1.01215	+	0.0644097i
$664$	44.6845	+	5.65412i	1.73410	+	0.219422i
$665$			0.294877i			0.0114348i
$666$	1.26266	+	1.37332i	0.0489270	+	0.0532149i
$667$	−16.7292	+	6.92947i	−0.647758	+	0.268310i
$668$	−18.1828	−	21.5223i	−0.703514	−	0.832723i
$669$	−0.670318	−	1.61829i	−0.0259160	−	0.0625667i
$670$	1.03395	+	2.82598i	0.0399449	+	0.109177i
$671$	−7.40974	+	7.40974i	−0.286050	+	0.286050i
$672$	15.7223	+	3.34739i	0.606499	+	0.129128i
$673$		−	12.3717i		−	0.476895i	−0.971155	−	0.238447i	$-0.923362\pi$
$673$		−	12.3717i		−	0.476895i	0.971155	−	0.238447i	$-0.0766384\pi$
$674$	32.6750	−	11.9549i	1.25860	−	0.460485i
$675$	−10.2464	+	24.7370i	−0.394385	+	0.952129i
$676$	5.44569	−	25.4233i	0.209450	−	0.977819i
$677$	−2.54875	+	1.05573i	−0.0979565	+	0.0405749i	−0.431124	−	0.902293i	$-0.641883\pi$
$677$	−2.54875	+	1.05573i	−0.0979565	+	0.0405749i	0.333167	+	0.942868i	$0.391883\pi$
$678$	−1.46341	+	34.8599i	−0.0562018	+	1.33879i
$679$	15.4492	+	15.4492i	0.592886	+	0.592886i
$680$	4.67384	+	6.02798i	0.179234	+	0.231163i
$681$	−8.57270			−0.328507
$682$	−28.7322	−	31.2503i	−1.10021	−	1.19663i
$683$	−16.9478	−	7.02001i	−0.648490	−	0.268613i	0.0340962	−	0.999419i	$-0.489145\pi$
$683$	−16.9478	−	7.02001i	−0.648490	−	0.268613i	−0.682586	+	0.730805i	$0.739145\pi$
$684$	−0.193439	−	0.606405i	−0.00739632	−	0.0231865i
$685$	7.70222	+	3.19037i	0.294287	+	0.121898i
$686$	−9.77947	−	26.7292i	−0.373382	−	1.02053i
$687$	−20.5802	−	20.5802i	−0.785185	−	0.785185i
$688$	39.2953	−	8.98872i	1.49812	−	0.342692i
$689$	20.7420	+	23.5613i	0.790207	+	0.897614i
$690$	−1.89879	+	0.694712i	−0.0722855	+	0.0264472i
$691$	15.4250	+	37.2393i	0.586795	+	1.41665i	0.886550	+	0.462632i	$0.153095\pi$
$691$	15.4250	+	37.2393i	0.586795	+	1.41665i	−0.299756	+	0.954016i	$0.596905\pi$
$692$	9.64285	+	30.2291i	0.366566	+	1.14914i
$693$	6.45931	−	2.67553i	0.245369	−	0.101635i
$694$	19.1312	+	20.8078i	0.726209	+	0.789852i
$695$			4.82906i			0.183177i
$696$	−8.90782	−	32.5873i	−0.337650	−	1.23522i
$697$	−3.61889			−0.137075
$698$	20.6772	−	19.0111i	0.782645	−	0.719582i
$699$	−10.3068	+	4.26922i	−0.389839	+	0.161477i
$700$	−1.65718	+	19.7031i	−0.0626354	+	0.744705i
$701$	−40.7324	−	16.8719i	−1.53844	−	0.637244i	−0.557263	−	0.830336i	$-0.688148\pi$
$701$	−40.7324	−	16.8719i	−1.53844	−	0.637244i	−0.981181	+	0.193092i	$0.938148\pi$
$702$	25.2891	+	13.7566i	0.954476	+	0.519210i
$703$			0.321949i			0.0121425i
$704$	−3.30116	−	23.2624i	−0.124417	−	0.876734i
$705$	−7.12855			−0.268477
$706$	−13.5012	+	29.0807i	−0.508125	+	1.09447i
$707$	24.6388	−	10.2057i	0.926638	−	0.383826i
$708$	0.0760275	−	0.903931i	0.00285729	−	0.0339718i
$709$	−31.7641	−	13.1571i	−1.19293	−	0.494126i	−0.304219	−	0.952602i	$-0.598395\pi$
$709$	−31.7641	−	13.1571i	−1.19293	−	0.494126i	−0.888707	+	0.458476i	$0.848395\pi$
$710$	−0.120257	+	2.86464i	−0.00451315	+	0.107508i
$711$	6.06668	+	6.06668i	0.227518	+	0.227518i
$712$	−8.44381	+	14.7966i	−0.316445	+	0.554528i
$713$		−	21.1214i		−	0.791003i
$714$	−0.895601	+	21.3341i	−0.0335170	+	0.798410i
$715$	−2.36791	+	4.82473i	−0.0885549	+	0.180435i
$716$	−46.2593	+	14.7564i	−1.72879	+	0.551472i
$717$	16.8219	−	6.96786i	0.628225	−	0.260219i
$718$	−2.87023	−	7.84491i	−0.107116	−	0.292769i
$719$		−	42.7587i		−	1.59463i	−0.603564	−	0.797315i	$-0.706253\pi$
$719$		−	42.7587i		−	1.59463i	0.603564	−	0.797315i	$-0.293747\pi$
$720$	0.516956	+	2.25994i	0.0192658	+	0.0842230i
$721$	−15.3549	−	15.3549i	−0.571846	−	0.571846i
$722$	−11.2686	+	24.2719i	−0.419375	+	0.903308i
$723$	−24.3412	+	10.0825i	−0.905259	+	0.374970i
$724$	10.9202	−	21.1505i	0.405845	−	0.786051i
$725$	38.3914	−	15.9023i	1.42582	−	0.590595i
$726$	−3.09802	−	3.36952i	−0.114978	−	0.125055i
$727$	−13.0837	−	13.0837i	−0.485249	−	0.485249i	0.421554	−	0.906803i	$-0.361485\pi$
$727$	−13.0837	−	13.0837i	−0.485249	−	0.485249i	−0.906803	+	0.421554i	$0.861485\pi$
$728$	20.8792	+	4.00285i	0.773836	+	0.148355i
$729$	−19.7737	+	19.7737i	−0.732359	+	0.732359i
$730$	−1.12298	−	0.0471424i	−0.0415634	−	0.00174482i
$731$	20.4914	+	49.4706i	0.757902	+	1.82974i
$732$	0.815247	−	9.69291i	0.0301324	−	0.358260i
$733$	−6.51107	−	15.7191i	−0.240492	−	0.580599i	0.756840	−	0.653600i	$-0.226742\pi$
$733$	−6.51107	−	15.7191i	−0.240492	−	0.580599i	−0.997332	+	0.0730013i	$0.976742\pi$
$734$	−15.4425	+	5.64996i	−0.569992	+	0.208544i
$735$	−1.29842	+	1.29842i	−0.0478931	+	0.0478931i
$736$	6.62453	−	9.63182i	0.244183	−	0.355033i
$737$	12.3128			0.453549
$738$	−0.997631	−	0.463166i	−0.0367233	−	0.0170494i
$739$	16.3901	+	39.5691i	0.602918	+	1.45557i	0.870563	+	0.492056i	$0.163755\pi$
$739$	16.3901	+	39.5691i	0.602918	+	1.45557i	−0.267645	+	0.963518i	$0.586245\pi$
$740$	0.0982783	−	1.16848i	0.00361278	−	0.0429543i
$741$	0.442749	+	1.29621i	0.0162648	+	0.0476173i
$742$	−18.8947	+	17.3722i	−0.693646	+	0.637754i
$743$	−16.5640			−0.607673			−0.303837	−	0.952724i	$-0.598268\pi$
$743$	−16.5640			−0.607673			−0.303837	+	0.952724i	$0.598268\pi$
$744$	39.0939	+	4.94671i	1.43325	+	0.181355i
$745$	−0.0401780	+	0.0401780i	−0.00147201	+	0.00147201i
$746$	3.32088	+	3.61192i	0.121586	+	0.132242i
$747$	−6.95893	+	16.8003i	−0.254614	+	0.614692i
$748$	29.7343	−	9.48501i	1.08719	−	0.346806i
$749$	3.24970	+	7.84546i	0.118741	+	0.286667i
$750$	8.95163	−	3.27515i	0.326867	−	0.119592i
$751$		−	10.5081i		−	0.383446i	−0.981449	−	0.191723i	$-0.938593\pi$
$751$		−	10.5081i		−	0.383446i	0.981449	−	0.191723i	$-0.0614075\pi$
$752$	33.6023	−	23.8663i	1.22535	−	0.870315i
$753$	−4.55506			−0.165995
$754$	−12.6559	−	42.8495i	−0.460902	−	1.56048i
$755$	−0.619123	+	1.49470i	−0.0225322	+	0.0543975i
$756$	−10.7992	+	20.9163i	−0.392765	+	0.760717i
$757$	−15.9231	−	38.4417i	−0.578735	−	1.39719i	−0.893949	−	0.448169i	$-0.852076\pi$
$757$	−15.9231	−	38.4417i	−0.578735	−	1.39719i	0.315214	−	0.949020i	$-0.397924\pi$
$758$	−10.2080	−	0.428529i	−0.370772	−	0.0155649i
$759$			8.27302i			0.300292i
$760$	−0.198295	+	0.347485i	−0.00719290	+	0.0126046i
$761$	−27.8286			−1.00879			−0.504394	−	0.863474i	$-0.668284\pi$
$761$	−27.8286			−1.00879			−0.504394	+	0.863474i	$0.668284\pi$
$762$	−34.0028	−	1.42743i	−1.23179	−	0.0517103i
$763$	−13.2183	−	31.9118i	−0.478535	−	1.15528i
$764$	3.09581	+	3.66440i	0.112003	+	0.132573i
$765$	−2.84514	+	1.17849i	−0.102866	+	0.0426086i
$766$	30.2980	+	14.0663i	1.09471	+	0.508237i
$767$	0.0761915	−	1.19729i	0.00275112	−	0.0432316i
$768$	16.2762	+	14.5172i	0.587316	+	0.523846i
$769$	6.33433	&

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)

\(f(q)\)	\(=\)	\(q+(-1.32811 + 0.485919i) q^{2} +(-1.25935 - 0.521639i) q^{3} +(1.52777 - 1.29071i) q^{4} +(0.194227 - 0.468906i) q^{5} +(1.92603 + 0.0808542i) q^{6} +2.08466i q^{7} +(-1.40186 + 2.45658i) q^{8} +(-0.807469 - 0.807469i) q^{9} +O(q^{10})\)	\(q+(-1.32811 + 0.485919i) q^{2} +(-1.25935 - 0.521639i) q^{3} +(1.52777 - 1.29071i) q^{4} +(0.194227 - 0.468906i) q^{5} +(1.92603 + 0.0808542i) q^{6} +2.08466i q^{7} +(-1.40186 + 2.45658i) q^{8} +(-0.807469 - 0.807469i) q^{9} +(-0.0301053 + 0.717139i) q^{10} +(2.71337 + 1.12391i) q^{11} +(-2.59727 + 0.828511i) q^{12} +(-3.41200 + 1.16545i) q^{13} +(-1.01298 - 2.76867i) q^{14} +(-0.489200 + 0.489200i) q^{15} +(0.668134 - 3.94380i) q^{16} +5.31344 q^{17} +(1.46477 + 0.680045i) q^{18} +(0.106653 + 0.257484i) q^{19} +(-0.308488 - 0.967070i) q^{20} +(1.08744 - 2.62532i) q^{21} +(-4.14979 - 0.174207i) q^{22} +(-1.46125 - 1.46125i) q^{23} +(3.04688 - 2.36242i) q^{24} +(3.35339 + 3.35339i) q^{25} +(3.96520 - 3.20580i) q^{26} +(2.16060 + 5.21614i) q^{27} +(2.69070 + 3.18488i) q^{28} +(3.35321 - 8.09536i) q^{29} +(0.412001 - 0.887424i) q^{30} +(7.22717 + 7.22717i) q^{31} +(1.02901 + 5.56248i) q^{32} +(-2.83080 - 2.83080i) q^{33} +(-7.05685 + 2.58190i) q^{34} +(0.977512 + 0.404899i) q^{35} +(-2.27583 - 0.191415i) q^{36} +(1.06725 + 0.442071i) q^{37} +(-0.266764 - 0.290142i) q^{38} +(4.90484 + 0.312127i) q^{39} +(0.879625 + 1.13448i) q^{40} -0.681081 q^{41} +(-0.168554 + 4.01513i) q^{42} +(3.85652 + 9.31046i) q^{43} +(5.59604 - 1.78510i) q^{44} +(-0.535460 + 0.221795i) q^{45} +(2.65076 + 1.23066i) q^{46} +(7.28593 + 7.28593i) q^{47} +(-2.89866 + 4.61810i) q^{48} +2.65418 q^{49} +(-6.08315 - 2.82420i) q^{50} +(-6.69148 - 2.77170i) q^{51} +(-3.70848 + 6.18443i) q^{52} +(-3.33170 - 8.04345i) q^{53} +(-5.40413 - 5.87774i) q^{54} +(1.05402 - 1.05402i) q^{55} +(-5.12114 - 2.92241i) q^{56} -0.379896i q^{57} +(-0.519748 + 12.3809i) q^{58} +(-0.127334 + 0.307412i) q^{59} +(-0.115967 + 1.37880i) q^{60} +(-1.36541 + 3.29640i) q^{61} +(-13.1103 - 6.08667i) q^{62} +(1.68330 - 1.68330i) q^{63} +(-4.06956 - 6.88758i) q^{64} +(-0.116218 + 1.82627i) q^{65} +(5.13516 + 2.38408i) q^{66} +(3.87328 - 1.60437i) q^{67} +(8.11770 - 6.85812i) q^{68} +(1.07798 + 2.60247i) q^{69} +(-1.49499 - 0.0627594i) q^{70} +3.99453 q^{71} +(3.11557 - 0.851650i) q^{72} +1.56592i q^{73} +(-1.63224 - 0.0685211i) q^{74} +(-2.47382 - 5.97234i) q^{75} +(0.495278 + 0.255716i) q^{76} +(-2.34298 + 5.65646i) q^{77} +(-6.66584 + 1.96881i) q^{78} -7.51320 q^{79} +(-1.71950 - 1.07929i) q^{80} -4.27018i q^{81} +(0.904552 - 0.330950i) q^{82} +(-6.09398 - 14.7122i) q^{83} +(-1.72717 - 5.41444i) q^{84} +(1.03202 - 2.49151i) q^{85} +(-9.64602 - 10.4914i) q^{86} +(-8.44571 + 8.44571i) q^{87} +(-6.56476 + 5.09003i) q^{88} +6.02327 q^{89} +(0.603377 - 0.554759i) q^{90} +(-2.42957 - 7.11287i) q^{91} +(-4.11850 - 0.346397i) q^{92} +(-5.33155 - 12.8715i) q^{93} +(-13.2169 - 6.13616i) q^{94} +0.141451 q^{95} +(1.60572 - 7.54187i) q^{96} +(7.41089 - 7.41089i) q^{97} +(-3.52505 + 1.28972i) q^{98} +(-1.28344 - 3.09849i) 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