LMFDB - Embedded newform 552.2.t.a.451.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.t (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			451.3
Character	$\chi$	$=$	552.451
Dual form			552.2.t.a.235.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32437 - 0.496025i) q^{2} +(0.654861 + 0.755750i) q^{3} +(1.50792 + 1.31384i) q^{4} +(-0.392396 - 2.72917i) q^{5} +(-0.492408 - 1.32572i) q^{6} +(-0.907403 + 1.98694i) q^{7} +(-1.34534 - 2.48798i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-1.32437 - 0.496025i) q^{2} +(0.654861 + 0.755750i) q^{3} +(1.50792 + 1.31384i) q^{4} +(-0.392396 - 2.72917i) q^{5} +(-0.492408 - 1.32572i) q^{6} +(-0.907403 + 1.98694i) q^{7} +(-1.34534 - 2.48798i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.834061 + 3.80908i) q^{10} +(-0.950246 + 3.23624i) q^{11} +(-0.00545963 + 1.99999i) q^{12} +(-4.51920 + 2.06385i) q^{13} +(2.18731 - 2.18135i) q^{14} +(1.80561 - 2.08378i) q^{15} +(0.547635 + 3.96233i) q^{16} +(-1.30480 + 2.03030i) q^{17} +(0.679454 - 1.24030i) q^{18} +(2.69557 + 4.19438i) q^{19} +(2.99400 - 4.63092i) q^{20} +(-2.09585 + 0.615397i) q^{21} +(2.86373 - 3.81464i) q^{22} +(4.18970 - 2.33376i) q^{23} +(0.999277 - 2.64602i) q^{24} +(-2.49695 + 0.733171i) q^{25} +(7.00882 - 0.491666i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(-3.97881 + 1.80395i) q^{28} +(-2.47606 + 3.85282i) q^{29} +(-3.42490 + 1.86407i) q^{30} +(1.92486 + 1.66790i) q^{31} +(1.24015 - 5.51924i) q^{32} +(-3.06807 + 1.40114i) q^{33} +(2.73511 - 2.04166i) q^{34} +(5.77875 + 1.69679i) q^{35} +(-1.51507 + 1.30559i) q^{36} +(0.432813 - 3.01028i) q^{37} +(-1.48941 - 6.89199i) q^{38} +(-4.51920 - 2.06385i) q^{39} +(-6.26222 + 4.64795i) q^{40} +(0.605627 + 4.21223i) q^{41} +(3.08093 + 0.224580i) q^{42} +(-7.38230 + 6.39680i) q^{43} +(-5.68480 + 3.63151i) q^{44} +2.75724 q^{45} +(-6.70632 + 1.01257i) q^{46} +2.58881i q^{47} +(-2.63591 + 3.00865i) q^{48} +(1.45949 + 1.68435i) q^{49} +(3.67056 + 0.267560i) q^{50} +(-2.38886 + 0.343466i) q^{51} +(-9.52616 - 2.82540i) q^{52} +(-0.154143 + 0.337526i) q^{53} +(1.38230 - 0.298726i) q^{54} +(9.20513 + 1.32350i) q^{55} +(6.16423 - 0.415511i) q^{56} +(-1.40468 + 4.78391i) q^{57} +(5.19032 - 3.87438i) q^{58} +(-3.80405 - 8.32970i) q^{59} +(5.46047 - 0.769889i) q^{60} +(0.0167960 - 0.0193837i) q^{61} +(-1.72191 - 3.16370i) q^{62} +(-1.83757 - 1.18094i) q^{63} +(-4.38010 + 6.69438i) q^{64} +(7.40592 + 11.5238i) q^{65} +(4.75826 - 0.333790i) q^{66} +(-1.24726 - 4.24779i) q^{67} +(-4.63502 + 1.34723i) q^{68} +(4.50741 + 1.63808i) q^{69} +(-6.81156 - 5.11359i) q^{70} +(2.62218 + 8.93032i) q^{71} +(2.65412 - 0.977574i) q^{72} +(-1.85893 + 1.19466i) q^{73} +(-2.06638 + 3.77204i) q^{74} +(-2.18925 - 1.40694i) q^{75} +(-1.44607 + 9.86634i) q^{76} +(-5.56794 - 4.82465i) q^{77} +(4.96138 + 4.97494i) q^{78} +(1.14713 + 2.51186i) q^{79} +(10.5990 - 3.04939i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(1.28730 - 5.87896i) q^{82} +(9.68626 + 1.39267i) q^{83} +(-3.96890 - 1.82565i) q^{84} +(6.05304 + 2.76433i) q^{85} +(12.9499 - 4.80993i) q^{86} +(-4.53325 + 0.651782i) q^{87} +(9.33011 - 1.98966i) q^{88} +(-9.02948 + 7.82409i) q^{89} +(-3.65161 - 1.36766i) q^{90} -10.8521i q^{91} +(9.38391 + 1.98549i) q^{92} +2.54696i q^{93} +(1.28411 - 3.42854i) q^{94} +(10.3895 - 9.00253i) q^{95} +(4.98329 - 2.67710i) q^{96} +(17.0750 - 2.45501i) q^{97} +(-1.09743 - 2.95464i) q^{98} +(-3.06807 - 1.40114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{21}{22}\right)$	$1$	$-1$	$-1$

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 $

$2$	−1.32437	−	0.496025i	−0.936472	−	0.350743i
$2$	−1.32437	−	0.496025i	−0.936472	−	0.350743i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	1.50792	+	1.31384i	0.753959	+	0.656921i
$5$	−0.392396	−	2.72917i	−0.175485	−	1.22052i	−0.867054	−	0.498214i	$-0.833990\pi$
$5$	−0.392396	−	2.72917i	−0.175485	−	1.22052i	0.691569	−	0.722310i	$-0.256920\pi$
$6$	−0.492408	−	1.32572i	−0.201025	−	0.541223i
$7$	−0.907403	+	1.98694i	−0.342966	+	0.750991i	−0.999996	−	0.00287367i	$-0.999085\pi$
$7$	−0.907403	+	1.98694i	−0.342966	+	0.750991i	0.657030	+	0.753865i	$0.271813\pi$
$8$	−1.34534	−	2.48798i	−0.475651	−	0.879634i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	−0.834061	+	3.80908i	−0.263753	+	1.20454i
$11$	−0.950246	+	3.23624i	−0.286510	+	0.975763i	0.682940	+	0.730474i	$0.260701\pi$
$11$	−0.950246	+	3.23624i	−0.286510	+	0.975763i	−0.969450	+	0.245289i	$0.921117\pi$
$12$	−0.00545963	+	1.99999i	−0.00157606	+	0.577348i
$13$	−4.51920	+	2.06385i	−1.25340	+	0.572409i	−0.927793	−	0.373096i	$-0.878296\pi$
$13$	−4.51920	+	2.06385i	−1.25340	+	0.572409i	−0.325608	+	0.945505i	$0.605569\pi$
$14$	2.18731	−	2.18135i	0.584583	−	0.582989i
$15$	1.80561	−	2.08378i	0.466206	−	0.538030i
$16$	0.547635	+	3.96233i	0.136909	+	0.990584i
$17$	−1.30480	+	2.03030i	−0.316459	+	0.492420i	−0.962647	−	0.270758i	$-0.912726\pi$
$17$	−1.30480	+	2.03030i	−0.316459	+	0.492420i	0.646188	+	0.763178i	$0.276362\pi$
$18$	0.679454	−	1.24030i	0.160149	−	0.292341i
$19$	2.69557	+	4.19438i	0.618405	+	0.962258i	0.999292	+	0.0376357i	$0.0119826\pi$
$19$	2.69557	+	4.19438i	0.618405	+	0.962258i	−0.380886	+	0.924622i	$0.624381\pi$
$20$	2.99400	−	4.63092i	0.669480	−	1.03550i
$21$	−2.09585	+	0.615397i	−0.457352	+	0.134291i
$22$	2.86373	−	3.81464i	0.610550	−	0.813283i
$23$	4.18970	−	2.33376i	0.873612	−	0.486622i
$23$	4.18970	−	2.33376i	0.873612	−	0.486622i
$24$	0.999277	−	2.64602i	0.203977	−	0.540117i
$25$	−2.49695	+	0.733171i	−0.499390	+	0.146634i
$26$	7.00882	−	0.491666i	1.37454	−	0.0964237i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	−3.97881	+	1.80395i	−0.751924	+	0.340915i
$29$	−2.47606	+	3.85282i	−0.459793	+	0.715452i	−0.991303	−	0.131600i	$-0.957988\pi$
$29$	−2.47606	+	3.85282i	−0.459793	+	0.715452i	0.531510	+	0.847052i	$0.321625\pi$
$30$	−3.42490	+	1.86407i	−0.625299	+	0.340332i
$31$	1.92486	+	1.66790i	0.345716	+	0.299564i	0.810359	−	0.585934i	$-0.199272\pi$
$31$	1.92486	+	1.66790i	0.345716	+	0.299564i	−0.464643	+	0.885498i	$0.653817\pi$
$32$	1.24015	−	5.51924i	0.219229	−	0.975673i
$33$	−3.06807	+	1.40114i	−0.534082	+	0.243907i
$34$	2.73511	−	2.04166i	0.469068	−	0.350142i
$35$	5.77875	+	1.69679i	0.976788	+	0.286811i
$36$	−1.51507	+	1.30559i	−0.252511	+	0.217598i
$37$	0.432813	−	3.01028i	0.0711540	−	0.494887i	−0.922817	−	0.385240i	$-0.874119\pi$
$37$	0.432813	−	3.01028i	0.0711540	−	0.494887i	0.993971	−	0.109647i	$-0.0349721\pi$
$38$	−1.48941	−	6.89199i	−0.241614	−	1.11803i
$39$	−4.51920	−	2.06385i	−0.723651	−	0.330480i
$40$	−6.26222	+	4.64795i	−0.990145	+	0.734906i
$41$	0.605627	+	4.21223i	0.0945830	+	0.657839i	0.980864	+	0.194692i	$0.0623707\pi$
$41$	0.605627	+	4.21223i	0.0945830	+	0.657839i	−0.886281	+	0.463147i	$0.846720\pi$
$42$	3.08093	+	0.224580i	0.475398	+	0.0346534i
$43$	−7.38230	+	6.39680i	−1.12579	+	0.975503i	−0.999863	−	0.0165368i	$-0.994736\pi$
$43$	−7.38230	+	6.39680i	−1.12579	+	0.975503i	−0.125927	+	0.992040i	$0.540190\pi$
$44$	−5.68480	+	3.63151i	−0.857016	+	0.547471i
$45$	2.75724			0.411025
$46$	−6.70632	+	1.01257i	−0.988793	+	0.149295i
$47$			2.58881i			0.377617i	0.982014	+	0.188808i	$0.0604625\pi$
$47$			2.58881i			0.377617i	−0.982014	+	0.188808i	$0.939538\pi$
$48$	−2.63591	+	3.00865i	−0.380461	+	0.434262i
$49$	1.45949	+	1.68435i	0.208499	+	0.240621i
$50$	3.67056	+	0.267560i	0.519096	+	0.0378387i
$51$	−2.38886	+	0.343466i	−0.334507	+	0.0480949i
$52$	−9.52616	−	2.82540i	−1.32104	−	0.391813i
$53$	−0.154143	+	0.337526i	−0.0211732	+	0.0463628i	−0.919923	−	0.392099i	$-0.871749\pi$
$53$	−0.154143	+	0.337526i	−0.0211732	+	0.0463628i	0.898750	+	0.438462i	$0.144476\pi$
$54$	1.38230	−	0.298726i	0.188108	−	0.0406515i
$55$	9.20513	+	1.32350i	1.24122	+	0.178460i
$56$	6.16423	−	0.415511i	0.823729	−	0.0555251i
$57$	−1.40468	+	4.78391i	−0.186055	+	0.633644i
$58$	5.19032	−	3.87438i	0.681522	−	0.508731i
$59$	−3.80405	−	8.32970i	−0.495245	−	1.08443i	−0.977986	−	0.208671i	$-0.933086\pi$
$59$	−3.80405	−	8.32970i	−0.495245	−	1.08443i	0.482741	−	0.875763i	$-0.339641\pi$
$60$	5.46047	−	0.769889i	0.704944	−	0.0993922i
$61$	0.0167960	−	0.0193837i	0.00215051	−	0.00248182i	−0.754673	−	0.656101i	$-0.772205\pi$
$61$	0.0167960	−	0.0193837i	0.00215051	−	0.00248182i	0.756824	+	0.653619i	$0.226750\pi$
$62$	−1.72191	−	3.16370i	−0.218683	−	0.401791i
$63$	−1.83757	−	1.18094i	−0.231513	−	0.148784i
$64$	−4.38010	+	6.69438i	−0.547512	+	0.836798i
$65$	7.40592	+	11.5238i	0.918591	+	1.42936i
$66$	4.75826	−	0.333790i	0.585701	−	0.0410867i
$67$	−1.24726	−	4.24779i	−0.152378	−	0.518950i	0.847553	−	0.530710i	$-0.178075\pi$
$67$	−1.24726	−	4.24779i	−0.152378	−	0.518950i	−0.999931	+	0.0117600i	$0.996257\pi$
$68$	−4.63502	+	1.34723i	−0.562079	+	0.163376i
$69$	4.50741	+	1.63808i	0.542628	+	0.197201i
$70$	−6.81156	−	5.11359i	−0.814137	−	0.611191i
$71$	2.62218	+	8.93032i	0.311195	+	1.05983i	0.955482	+	0.295050i	$0.0953363\pi$
$71$	2.62218	+	8.93032i	0.311195	+	1.05983i	−0.644286	+	0.764784i	$0.722846\pi$
$72$	2.65412	−	0.977574i	0.312791	−	0.115208i
$73$	−1.85893	+	1.19466i	−0.217572	+	0.139825i	−0.644887	−	0.764278i	$-0.723096\pi$
$73$	−1.85893	+	1.19466i	−0.217572	+	0.139825i	0.427316	+	0.904102i	$0.359459\pi$
$74$	−2.06638	+	3.77204i	−0.240212	+	0.438491i
$75$	−2.18925	−	1.40694i	−0.252793	−	0.162460i
$76$	−1.44607	+	9.86634i	−0.165875	+	1.13175i
$77$	−5.56794	−	4.82465i	−0.634526	−	0.549820i
$78$	4.96138	+	4.97494i	0.561765	+	0.563301i
$79$	1.14713	+	2.51186i	0.129062	+	0.282606i	0.963121	−	0.269069i	$-0.0867160\pi$
$79$	1.14713	+	2.51186i	0.129062	+	0.282606i	−0.834059	+	0.551675i	$0.813989\pi$
$80$	10.5990	−	3.04939i	1.18501	−	0.340933i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	1.28730	−	5.87896i	0.142158	−	0.649222i
$83$	9.68626	+	1.39267i	1.06321	+	0.152866i	0.651651	−	0.758519i	$-0.274077\pi$
$83$	9.68626	+	1.39267i	1.06321	+	0.152866i	0.411554	+	0.911385i	$0.364986\pi$
$84$	−3.96890	−	1.82565i	−0.433043	−	0.199194i
$85$	6.05304	+	2.76433i	0.656544	+	0.299834i
$86$	12.9499	−	4.80993i	1.39642	−	0.518668i
$87$	−4.53325	+	0.651782i	−0.486015	+	0.0698784i
$88$	9.33011	−	1.98966i	0.994593	−	0.212099i
$89$	−9.02948	+	7.82409i	−0.957123	+	0.829352i	−0.985401	−	0.170249i	$-0.945543\pi$
$89$	−9.02948	+	7.82409i	−0.957123	+	0.829352i	0.0282785	+	0.999600i	$0.490997\pi$
$90$	−3.65161	−	1.36766i	−0.384913	−	0.144164i
$91$		−	10.8521i		−	1.13761i
$92$	9.38391	+	1.98549i	0.978341	+	0.207001i
$93$			2.54696i			0.264107i
$94$	1.28411	−	3.42854i	0.132446	−	0.353627i
$95$	10.3895	−	9.00253i	1.06594	−	0.923640i
$96$	4.98329	−	2.67710i	0.508605	−	0.273230i
$97$	17.0750	−	2.45501i	1.73370	−	0.249268i	0.798149	−	0.602460i	$-0.205813\pi$
$97$	17.0750	−	2.45501i	1.73370	−	0.249268i	0.935551	+	0.353192i	$0.114904\pi$
$98$	−1.09743	−	2.95464i	−0.110858	−	0.298464i
$99$	−3.06807	−	1.40114i	−0.308352	−	0.140820i
$100$	−4.72847	−	2.17504i	−0.472847	−	0.217504i
$101$	−17.6356	−	2.53562i	−1.75481	−	0.252304i	−0.811533	−	0.584307i	$-0.801367\pi$
$101$	−17.6356	−	2.53562i	−1.75481	−	0.252304i	−0.943278	+	0.332003i	$0.892276\pi$
$102$	3.33410	+	0.730057i	0.330125	+	0.0722864i
$103$	−10.3332	−	3.03411i	−1.01816	−	0.298960i	−0.270275	−	0.962783i	$-0.587115\pi$
$103$	−10.3332	−	3.03411i	−1.01816	−	0.298960i	−0.747889	+	0.663823i	$0.768933\pi$
$104$	11.2147	+	8.46710i	1.09969	+	0.830267i
$105$	2.50193	+	5.47845i	0.244163	+	0.534642i
$106$	0.371564	−	0.370551i	0.0360895	−	0.0359911i
$107$	−7.93319	−	6.87415i	−0.766931	−	0.664549i	0.180836	−	0.983513i	$-0.442120\pi$
$107$	−7.93319	−	6.87415i	−0.766931	−	0.664549i	−0.947767	+	0.318964i	$0.896665\pi$
$108$	−1.97886	−	0.290033i	−0.190416	−	0.0279084i
$109$	1.97350	+	1.26829i	0.189027	+	0.121480i	0.631731	−	0.775187i	$-0.282345\pi$
$109$	1.97350	+	1.26829i	0.189027	+	0.121480i	−0.442705	+	0.896668i	$0.645981\pi$
$110$	−11.5345	−	6.31878i	−1.09977	−	0.602472i
$111$	2.55845	−	1.64422i	0.242837	−	0.156062i
$112$	−8.36983	−	2.50732i	−0.790874	−	0.236919i
$113$	−0.258681	−	0.880985i	−0.0243346	−	0.0828761i	0.946430	−	0.322908i	$-0.104660\pi$
$113$	−0.258681	−	0.880985i	−0.0243346	−	0.0828761i	−0.970765	+	0.240032i	$0.922842\pi$
$114$	4.23326	−	5.63892i	0.396481	−	0.528133i
$115$	−8.01325	−	10.5187i	−0.747240	−	0.980870i
$116$	−8.79570	+	2.55659i	−0.816660	+	0.237374i
$117$	−1.39969	−	4.76692i	−0.129402	−	0.440702i
$118$	0.906229	+	12.9185i	0.0834252	+	1.18925i
$119$	−2.85010	−	4.43484i	−0.261268	−	0.406542i
$120$	−7.61357	−	1.68891i	−0.695021	−	0.154176i
$121$	−0.316491	−	0.203397i	−0.0287719	−	0.0184906i
$122$	−0.0318590	+	0.0173399i	−0.00288437	+	0.00156988i
$123$	−2.78679	+	3.21612i	−0.251276	+	0.289988i
$124$	0.711174	+	5.04403i	0.0638653	+	0.452967i
$125$	−2.74625	−	6.01344i	−0.245632	−	0.537859i
$126$	1.84786	+	2.47548i	0.164620	+	0.220533i
$127$	0.636009	−	2.16605i	0.0564367	−	0.192206i	−0.926450	−	0.376419i	$-0.877155\pi$
$127$	0.636009	−	2.16605i	0.0564367	−	0.192206i	0.982886	+	0.184213i	$0.0589736\pi$
$128$	9.12146	−	6.69321i	0.806230	−	0.591602i
$129$	−9.66876	−	1.39016i	−0.851287	−	0.122397i
$130$	−4.09208	−	18.9354i	−0.358899	−	1.66074i
$131$	7.65667	−	16.7658i	0.668966	−	1.46483i	−0.204959	−	0.978771i	$-0.565706\pi$
$131$	7.65667	−	16.7658i	0.668966	−	1.46483i	0.873925	−	0.486061i	$-0.161567\pi$
$132$	−6.46727	−	1.91815i	−0.562903	−	0.166954i
$133$	−10.7799	+	1.54992i	−0.934739	+	0.134395i
$134$	−0.455170	+	6.24433i	−0.0393207	+	0.539428i
$135$	1.80561	+	2.08378i	0.155402	+	0.179343i
$136$	6.80675	+	0.514851i	0.583674	+	0.0441481i
$137$		−	23.0051i		−	1.96546i	−0.185049	−	0.982729i	$-0.559244\pi$
$137$		−	23.0051i		−	1.96546i	0.185049	−	0.982729i	$-0.440756\pi$
$138$	−5.15695	−	4.40521i	−0.438989	−	0.374996i
$139$	10.1011			0.856765			0.428382	−	0.903598i	$-0.359084\pi$
$139$	10.1011			0.856765			0.428382	+	0.903598i	$0.359084\pi$
$140$	6.48456	+	10.1510i	0.548046	+	0.857916i
$141$	−1.95649	+	1.69531i	−0.164766	+	0.142771i
$142$	0.956925	−	13.1277i	0.0803034	−	1.10165i
$143$	−2.38476	−	16.5864i	−0.199424	−	1.38702i
$144$	−3.99994	−	0.0218385i	−0.333328	−	0.00181987i
$145$	11.4866	+	5.24577i	0.953912	+	0.435637i
$146$	3.05450	−	0.660100i	0.252792	−	0.0546303i
$147$	−0.317178	+	2.20602i	−0.0261604	+	0.181950i
$148$	4.60768	−	3.97061i	0.378749	−	0.326382i
$149$	−13.9319	−	4.09077i	−1.14134	−	0.335129i	−0.344187	−	0.938901i	$-0.611845\pi$
$149$	−13.9319	−	4.09077i	−1.14134	−	0.335129i	−0.797157	+	0.603772i	$0.793664\pi$
$150$	2.20150	+	2.94924i	0.179752	+	0.240804i
$151$	7.70596	−	3.51920i	0.627102	−	0.286388i	−0.0764041	−	0.997077i	$-0.524344\pi$
$151$	7.70596	−	3.51920i	0.627102	−	0.286388i	0.703506	+	0.710689i	$0.251617\pi$
$152$	6.80908	−	12.3494i	0.552289	−	1.00167i
$153$	−1.82394	−	1.58046i	−0.147457	−	0.127772i
$154$	4.98088	+	9.15147i	0.401370	+	0.737446i
$155$	3.79669	−	5.90776i	0.304957	−	0.474523i
$156$	−4.10301	−	9.04964i	−0.328504	−	0.724551i
$157$	−18.9352	+	12.1689i	−1.51120	+	0.971188i	−0.517920	+	0.855429i	$0.673293\pi$
$157$	−18.9352	+	12.1689i	−1.51120	+	0.971188i	−0.993277	+	0.115758i	$0.963070\pi$
$158$	−0.273278	−	3.89564i	−0.0217408	−	0.309921i
$159$	−0.356028	+	0.104539i	−0.0282348	+	0.00829049i
$160$	−15.5496	−	1.21884i	−1.22930	−	0.0963582i
$161$	0.835283	+	10.4423i	0.0658295	+	0.822970i
$162$	1.13098	+	0.849051i	0.0888581	+	0.0667078i
$163$	21.1907	−	6.22215i	1.65978	−	0.487356i	0.688491	−	0.725245i	$-0.258273\pi$
$163$	21.1907	−	6.22215i	1.65978	−	0.487356i	0.971292	+	0.237888i	$0.0764553\pi$
$164$	−4.62097	+	7.14739i	−0.360837	+	0.558117i
$165$	5.02785	+	7.82348i	0.391417	+	0.609057i
$166$	−12.1374	−	6.64904i	−0.942045	−	0.516066i
$167$	−6.56497	+	10.2153i	−0.508013	+	0.790484i	−0.996631	−	0.0820141i	$-0.973865\pi$
$167$	−6.56497	+	10.2153i	−0.508013	+	0.790484i	0.488618	+	0.872498i	$0.337501\pi$
$168$	4.35073	+	4.38651i	0.335666	+	0.338427i
$169$	7.65051	−	8.82916i	0.588501	−	0.679166i
$170$	−6.64529	−	6.66346i	−0.509671	−	0.511064i
$171$	−4.53531	+	2.07121i	−0.346824	+	0.158389i
$172$	−19.5363	−	0.0533307i	−1.48963	−	0.00406643i
$173$	−2.79857	+	9.53105i	−0.212771	+	0.724632i	0.782070	+	0.623190i	$0.214164\pi$
$173$	−2.79857	+	9.53105i	−0.212771	+	0.724632i	−0.994841	+	0.101442i	$0.967654\pi$
$174$	6.32700	+	1.38540i	0.479649	+	0.105027i
$175$	0.808977	−	5.62656i	0.0611529	−	0.425328i
$176$	−13.3435	−	1.99291i	−1.00580	−	0.150222i
$177$	3.80405	−	8.32970i	0.285930	−	0.626098i
$178$	15.8393	−	5.88315i	1.18721	−	0.440961i
$179$	2.50722	+	17.4381i	0.187399	+	1.30339i	0.838711	+	0.544577i	$0.183310\pi$
$179$	2.50722	+	17.4381i	0.187399	+	1.30339i	−0.651312	+	0.758810i	$0.725781\pi$
$180$	4.15769	+	3.62258i	0.309896	+	0.270011i
$181$	11.4622	+	13.2281i	0.851981	+	0.983238i	0.999983	−	0.00574885i	$-0.00182993\pi$
$181$	11.4622	+	13.2281i	0.851981	+	0.983238i	−0.148003	+	0.988987i	$0.547284\pi$
$182$	−5.38292	+	14.3722i	−0.399008	+	1.06534i
$183$	0.0256483			0.00189597
$184$	−11.4429	−	7.28418i	−0.843584	−	0.536997i
$185$	−8.38541			−0.616507
$186$	1.26336	−	3.37312i	0.0926337	−	0.247329i
$187$	−5.33066	−	6.15191i	−0.389817	−	0.449873i
$188$	−3.40129	+	3.90371i	−0.248064	+	0.284708i
$189$	−0.310862	−	2.16210i	−0.0226119	−	0.157269i
$190$	−18.2250	+	6.76925i	−1.32218	+	0.491093i
$191$	1.62204	−	3.55177i	0.117366	−	0.256997i	−0.841827	−	0.539748i	$-0.818520\pi$
$191$	1.62204	−	3.55177i	0.117366	−	0.256997i	0.959193	+	0.282751i	$0.0912470\pi$
$192$	−7.92763	+	1.07363i	−0.572127	+	0.0774827i
$193$	2.61107	−	18.1604i	0.187949	−	1.30721i	−0.649360	−	0.760481i	$-0.724963\pi$
$193$	2.61107	−	18.1604i	0.187949	−	1.30721i	0.837308	−	0.546731i	$-0.184128\pi$
$194$	−23.8313	−	5.21827i	−1.71099	−	0.374650i
$195$	−3.85929	+	13.1435i	−0.276369	+	0.941228i
$196$	−0.0121679	+	4.45740i	−0.000869138	+	0.318386i
$197$	12.0302	−	5.49401i	0.857116	−	0.391432i	0.0621365	−	0.998068i	$-0.480209\pi$
$197$	12.0302	−	5.49401i	0.857116	−	0.391432i	0.794980	+	0.606636i	$0.207481\pi$
$198$	3.36826	+	3.37746i	0.239372	+	0.240026i
$199$	7.98063	−	9.21014i	0.565732	−	0.652890i	−0.398743	−	0.917063i	$-0.630554\pi$
$199$	7.98063	−	9.21014i	0.565732	−	0.652890i	0.964475	+	0.264173i	$0.0850990\pi$
$200$	5.18337	+	5.22600i	0.366520	+	0.369534i
$201$	2.39348	−	3.72433i	0.168823	−	0.262694i
$202$	22.0984	+	12.1058i	1.55484	+	0.851763i
$203$	−5.40853	−	8.41584i	−0.379604	−	0.590676i
$204$	−4.05346	−	2.62067i	−0.283799	−	0.183483i
$205$	11.2583	−	3.30572i	0.786310	−	0.230882i
$206$	12.1800	+	9.14384i	0.848624	+	0.637081i
$207$	1.71375	+	4.47918i	0.119114	+	0.311325i
$208$	−10.6525	−	16.7763i	−0.738620	−	1.16323i
$209$	−16.1355	+	4.73780i	−1.11611	+	0.327721i
$210$	−0.596028	−	8.49653i	−0.0411299	−	0.586316i
$211$	−14.8519	+	9.54476i	−1.02245	+	0.657088i	−0.940586	−	0.339556i	$-0.889723\pi$
$211$	−14.8519	+	9.54476i	−1.02245	+	0.657088i	−0.0818630	+	0.996644i	$0.526087\pi$
$212$	−0.675892	+	0.306442i	−0.0464204	+	0.0210465i
$213$	−5.03193	+	7.82983i	−0.344782	+	0.536491i
$214$	7.09674	+	13.0390i	0.485123	+	0.891327i
$215$	20.3548	+	17.6375i	1.38818	+	1.20287i
$216$	2.47688	+	1.36567i	0.168530	+	0.0929224i
$217$	−5.06064	+	2.31112i	−0.343539	+	0.156889i
$218$	−1.98454	−	2.65859i	−0.134410	−	0.180062i
$219$	−2.12021	−	0.622549i	−0.143270	−	0.0420680i
$220$	12.1417	+	14.0898i	0.818595	+	0.949936i
$221$	1.70639	−	11.8682i	0.114785	−	0.798344i
$222$	−4.20391	+	0.908497i	−0.282148	+	0.0609743i
$223$	16.5088	+	7.53930i	1.10551	+	0.504869i	0.882673	−	0.469987i	$-0.155742\pi$
$223$	16.5088	+	7.53930i	1.10551	+	0.504869i	0.222835	+	0.974856i	$0.428469\pi$
$224$	9.84107	+	7.47227i	0.657534	+	0.499262i
$225$	−0.370355	−	2.57588i	−0.0246903	−	0.171725i
$226$	−0.0944016	+	1.29506i	−0.00627950	+	0.0861463i
$227$	−6.16514	+	5.34213i	−0.409195	+	0.354569i	−0.835004	−	0.550244i	$-0.814535\pi$
$227$	−6.16514	+	5.34213i	−0.409195	+	0.354569i	0.425809	+	0.904813i	$0.359989\pi$
$228$	−8.40345	+	5.36821i	−0.556532	+	0.355519i
$229$	11.6320			0.768664			0.384332	−	0.923195i	$-0.374432\pi$
$229$	11.6320			0.768664			0.384332	+	0.923195i	$0.374432\pi$
$230$	5.39500	+	17.9054i	0.355736	+	1.18065i
$231$		−	7.36744i		−	0.484742i
$232$	12.9169	+	0.977013i	0.848037	+	0.0641441i
$233$	16.7544	+	19.3357i	1.09762	+	1.26672i	0.961135	+	0.276079i	$0.0890352\pi$
$233$	16.7544	+	19.3357i	1.09762	+	1.26672i	0.136485	+	0.990642i	$0.456419\pi$
$234$	−0.510797	+	7.00745i	−0.0333919	+	0.458091i
$235$	7.06531	−	1.01584i	0.460890	−	0.0662660i
$236$	5.20772	−	17.5584i	0.338994	−	1.14296i
$237$	−1.14713	+	2.51186i	−0.0745140	+	0.163163i
$238$	1.57480	+	7.28710i	0.102079	+	0.472353i
$239$	27.1701	+	3.90647i	1.75749	+	0.252689i	0.944247	−	0.329238i	$-0.106792\pi$
$239$	27.1701	+	3.90647i	1.75749	+	0.252689i	0.813241	+	0.581927i	$0.197701\pi$
$240$	9.24545	+	6.01327i	0.596791	+	0.388155i
$241$	5.48439	−	18.6781i	0.353281	−	1.20316i	−0.570840	−	0.821062i	$-0.693382\pi$
$241$	5.48439	−	18.6781i	0.353281	−	1.20316i	0.924120	−	0.382102i	$-0.124800\pi$
$242$	0.318262	+	0.426360i	0.0204587	+	0.0274075i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	0.0507941	−	0.00716162i	0.00325176	−	0.000458476i
$245$	4.02417	−	4.64414i	0.257095	−	0.296703i
$246$	5.28602	−	2.87702i	0.337024	−	0.183432i
$247$	−20.8384	−	13.3920i	−1.32591	−	0.852114i
$248$	1.56011	−	7.03293i	0.0990669	−	0.446591i
$249$	5.29064	+	8.23239i	0.335281	+	0.521707i
$250$	0.654233	+	9.32624i	0.0413773	+	0.589843i
$251$	−5.69632	−	19.3999i	−0.359549	−	1.22451i	−0.918537	−	0.395335i	$-0.870629\pi$
$251$	−5.69632	−	19.3999i	−0.359549	−	1.22451i	0.558988	−	0.829175i	$-0.311190\pi$
$252$	−1.21935	−	4.19504i	−0.0768116	−	0.264263i
$253$	3.57136	+	15.7765i	0.224529	+	0.991861i
$254$	−1.91673	+	2.55318i	−0.120266	+	0.160200i
$255$	1.87476	+	6.38483i	0.117402	+	0.399834i
$256$	−15.4002	+	4.33982i	−0.962512	+	0.271239i
$257$	−9.50241	+	6.10683i	−0.592744	+	0.380934i	−0.802351	−	0.596852i	$-0.796418\pi$
$257$	−9.50241	+	6.10683i	−0.592744	+	0.380934i	0.209607	+	0.977786i	$0.432782\pi$
$258$	12.1155	+	6.63703i	0.754276	+	0.413203i
$259$	5.58849	+	3.59151i	0.347252	+	0.223165i
$260$	−3.97299	+	27.1072i	−0.246394	+	1.68112i
$261$	−3.46123	−	2.99917i	−0.214245	−	0.185644i
$262$	−18.4565	+	18.4062i	−1.14025	+	1.13714i
$263$	7.41287	+	16.2319i	0.457097	+	1.00090i	0.988140	+	0.153558i	$0.0490731\pi$
$263$	7.41287	+	16.2319i	0.457097	+	1.00090i	−0.531043	+	0.847345i	$0.678200\pi$
$264$	7.61361	+	5.74827i	0.468585	+	0.353782i
$265$	0.981653	+	0.288239i	0.0603025	+	0.0177064i
$266$	15.0454	+	3.29445i	0.922495	+	0.201996i
$267$	−11.8261	−	1.70034i	−0.723746	−	0.104059i
$268$	3.70016	−	8.04403i	0.226023	−	0.491367i
$269$	21.1920	+	9.67805i	1.29210	+	0.590081i	0.938488	−	0.345312i	$-0.112227\pi$
$269$	21.1920	+	9.67805i	1.29210	+	0.590081i	0.353609	+	0.935393i	$0.384954\pi$
$270$	−1.35769	−	3.65533i	−0.0826261	−	0.222456i
$271$	16.1312	−	2.31932i	0.979900	−	0.140888i	0.366293	−	0.930500i	$-0.380627\pi$
$271$	16.1312	−	2.31932i	0.979900	−	0.140888i	0.613607	+	0.789611i	$0.289718\pi$
$272$	−8.75928	−	4.05817i	−0.531109	−	0.246063i
$273$	8.20147	−	7.10662i	0.496376	−	0.430112i
$274$	−11.4111	+	30.4673i	−0.689370	+	1.84060i
$275$		−	8.77742i		−	0.529298i
$276$	4.64463	+	8.39211i	0.279574	+	0.505145i
$277$		−	22.0485i		−	1.32477i	−0.749165	−	0.662384i	$-0.769545\pi$
$277$		−	22.0485i		−	1.32477i	0.749165	−	0.662384i	$-0.230455\pi$
$278$	−13.3776	−	5.01040i	−0.802336	−	0.300504i
$279$	−1.92486	+	1.66790i	−0.115239	+	0.0998548i
$280$	−3.55282	−	16.6602i	−0.212322	−	0.995637i
$281$	−4.89254	+	0.703441i	−0.291865	+	0.0419638i	−0.286692	−	0.958023i	$-0.592556\pi$
$281$	−4.89254	+	0.703441i	−0.291865	+	0.0419638i	−0.00517264	+	0.999987i	$0.501647\pi$
$282$	3.43204	−	1.27475i	0.204375	−	0.0759103i
$283$	20.8075	+	9.50246i	1.23688	+	0.564863i	0.923073	−	0.384625i	$-0.125669\pi$
$283$	20.8075	+	9.50246i	1.23688	+	0.564863i	0.313804	+	0.949488i	$0.398397\pi$
$284$	−7.77901	+	16.9113i	−0.461599	+	1.00350i
$285$	13.6073	+	1.95644i	0.806028	+	0.115889i
$286$	−5.06895	+	23.1494i	−0.299733	+	1.36885i
$287$	−8.91897	−	2.61884i	−0.526470	−	0.154586i
$288$	5.28657	+	2.01299i	0.311514	+	0.118617i
$289$	4.64242	+	10.1655i	0.273084	+	0.597970i
$290$	−12.6105	−	12.6450i	−0.740515	−	0.742540i
$291$	13.0371	+	11.2967i	0.764248	+	0.662225i
$292$	−4.37272	−	0.640890i	−0.255894	−	0.0375053i
$293$	−16.1936	−	10.4070i	−0.946041	−	0.607984i	−0.0259394	−	0.999664i	$-0.508258\pi$
$293$	−16.1936	−	10.4070i	−0.946041	−	0.607984i	−0.920102	+	0.391680i	$0.871894\pi$
$294$	1.51430	−	2.76427i	0.0883160	−	0.161215i
$295$	−21.2405	+	13.6504i	−1.23667	+	0.794759i
$296$	−8.07180	+	2.97303i	−0.469164	+	0.172804i
$297$	−0.950246	−	3.23624i	−0.0551388	−	0.187786i
$298$	16.4219	+	12.3283i	0.951292	+	0.714157i
$299$	−14.1176	+	19.1936i	−0.816440	+	1.11000i
$300$	−1.45270	−	4.99788i	−0.0838719	−	0.288553i
$301$	−6.01131	−	20.4726i	−0.346486	−	1.18002i
$302$	−11.9512	+	0.838370i	−0.687712	+	0.0482428i
$303$	−9.63259	−	14.9886i	−0.553378	−	0.861073i
$304$	−15.1434	+	12.9777i	−0.868532	+	0.744324i
$305$	−0.0594921	−	0.0382332i	−0.00340651	−	0.00218923i
$306$	1.63163	+	2.99783i	0.0932742	+	0.171375i
$307$	−4.49701	+	5.18983i	−0.256658	+	0.296199i	−0.869425	−	0.494064i	$-0.835511\pi$
$307$	−4.49701	+	5.18983i	−0.256658	+	0.296199i	0.612767	+	0.790263i	$0.290056\pi$
$308$	−2.05717	−	14.5906i	−0.117218	−	0.831375i
$309$	−4.47380	−	9.79626i	−0.254506	−	0.557290i
$310$	−7.95863	+	5.94082i	−0.452020	+	0.337416i
$311$	−7.82965	+	26.6653i	−0.443979	+	1.51205i	0.368816	+	0.929503i	$0.379763\pi$
$311$	−7.82965	+	26.6653i	−0.443979	+	1.51205i	−0.812795	+	0.582550i	$0.802055\pi$
$312$	0.945063	+	14.0203i	0.0535037	+	0.793742i
$313$	−12.3792	−	1.77986i	−0.699714	−	0.100604i	−0.216728	−	0.976232i	$-0.569539\pi$
$313$	−12.3792	−	1.77986i	−0.699714	−	0.100604i	−0.482986	+	0.875628i	$0.660448\pi$
$314$	31.1134	−	6.72384i	1.75583	−	0.379448i
$315$	−2.50193	+	5.47845i	−0.140968	+	0.308676i
$316$	−1.57041	+	5.29483i	−0.0883427	+	0.297857i
$317$	−15.4180	+	2.21678i	−0.865963	+	0.124507i	−0.560958	−	0.827844i	$-0.689567\pi$
$317$	−15.4180	+	2.21678i	−0.865963	+	0.124507i	−0.305005	+	0.952351i	$0.598658\pi$
$318$	0.523367	+	0.0381500i	0.0293490	+	0.00213935i
$319$	−10.1158	−	11.6743i	−0.566376	−	0.653633i
$320$	19.9889	+	9.32720i	1.11741	+	0.521406i
$321$		−	10.4971i		−	0.585892i
$322$	4.07343	−	14.2438i	0.227003	−	0.793777i
$323$	−12.0330			−0.669535
$324$	−1.07668	−	1.68545i	−0.0598158	−	0.0936362i
$325$	9.77106	−	8.46668i	0.542001	−	0.469647i
$326$	−31.1507	−	2.27068i	−1.72528	−	0.125761i
$327$	0.333856	+	2.32202i	0.0184623	+	0.128408i
$328$	9.66516	−	7.17368i	0.533669	−	0.396100i
$329$	−5.14380	−	2.34909i	−0.283587	−	0.129510i
$330$	−2.77809	−	12.8551i	−0.152929	−	0.707652i
$331$	3.72906	−	25.9362i	0.204968	−	1.42558i	−0.584302	−	0.811536i	$-0.698632\pi$
$331$	3.72906	−	25.9362i	0.204968	−	1.42558i	0.789270	−	0.614046i	$-0.210459\pi$
$332$	12.7763	+	14.8263i	0.701192	+	0.813697i
$333$	2.91804	+	0.856815i	0.159908	+	0.0469532i
$334$	13.7615	−	10.2725i	0.752996	−	0.562084i
$335$	−11.1035	+	5.07082i	−0.606651	+	0.277048i
$336$	−3.58617	−	7.96744i	−0.195641	−	0.434659i
$337$	−24.0421	−	20.8326i	−1.30965	−	1.13482i	−0.981763	−	0.190107i	$-0.939117\pi$
$337$	−24.0421	−	20.8326i	−1.30965	−	1.13482i	−0.327891	−	0.944715i	$-0.606338\pi$
$338$	−14.5116	+	7.89824i	−0.789327	+	0.429608i
$339$	0.496404	−	0.772420i	0.0269610	−	0.0419521i
$340$	5.49559	+	12.1211i	0.298040	+	0.657360i
$341$	−7.22683	+	4.64440i	−0.391355	+	0.251508i
$342$	7.03380	−	0.493419i	0.380345	−	0.0266810i
$343$	−19.3420	+	5.67931i	−1.04437	+	0.306654i
$344$	25.8468	+	9.76112i	1.39357	+	0.526284i
$345$	2.70191	−	12.9443i	0.145466	−	0.696896i
$346$	8.43398	−	11.2345i	0.453414	−	0.603970i
$347$	8.78664	−	2.57999i	0.471692	−	0.138501i	−0.0372432	−	0.999306i	$-0.511858\pi$
$347$	8.78664	−	2.57999i	0.471692	−	0.138501i	0.508935	+	0.860805i	$0.330039\pi$
$348$	−7.69210	−	4.97314i	−0.412340	−	0.266588i
$349$	15.5077	+	24.1304i	0.830107	+	1.29167i	0.954130	+	0.299392i	$0.0967839\pi$
$349$	15.5077	+	24.1304i	0.830107	+	1.29167i	−0.124023	+	0.992279i	$0.539580\pi$
$350$	−3.86230	+	7.05038i	−0.206449	+	0.376859i
$351$	2.68599	−	4.17949i	0.143368	−	0.223084i
$352$	16.6831	+	9.25805i	0.889215	+	0.493455i
$353$	−14.8566	+	17.1455i	−0.790738	+	0.912561i	−0.997835	−	0.0657598i	$-0.979053\pi$
$353$	−14.8566	+	17.1455i	−0.790738	+	0.912561i	0.207097	+	0.978320i	$0.433598\pi$
$354$	−9.16971	+	9.14471i	−0.487364	+	0.486036i
$355$	23.3435	−	10.6606i	1.23894	−	0.565806i
$356$	−23.8953	−	0.0652301i	−1.26645	−	0.00345719i
$357$	1.48521	−	5.05817i	0.0786058	−	0.267707i
$358$	5.32925	−	24.3382i	0.281660	−	1.28631i
$359$	0.787732	−	5.47880i	0.0415749	−	0.289160i	−0.958418	−	0.285368i	$-0.907884\pi$
$359$	0.787732	−	5.47880i	0.0415749	−	0.289160i	0.999993	−	0.00379141i	$-0.00120685\pi$
$360$	−3.70944	−	6.85996i	−0.195504	−	0.361551i
$361$	−2.43389	+	5.32948i	−0.128099	+	0.280499i
$362$	−8.61877	−	23.2045i	−0.452992	−	1.21960i
$363$	−0.0535408	−	0.372385i	−0.00281016	−	0.0195451i
$364$	14.2580	−	16.3641i	0.747320	−	0.857711i
$365$	3.98988	+	4.60457i	0.208840	+	0.241014i
$366$	−0.0339678	−	0.0127222i	−0.00177553	−	0.000664999i
$367$	−37.3121			−1.94768			−0.973838	−	0.227241i	$-0.927029\pi$
$367$	−37.3121			−1.94768			−0.973838	+	0.227241i	$0.927029\pi$
$368$	11.5416	+	15.3229i	0.601645	+	0.798763i
$369$	−4.25554			−0.221535
$370$	11.1054	+	4.15937i	0.577342	+	0.216235i
$371$	−0.530773	−	0.612545i	−0.0275564	−	0.0318017i
$372$	−3.34630	+	3.84061i	−0.173498	+	0.199126i
$373$	0.752811	+	5.23591i	0.0389791	+	0.271105i	0.999985	−	0.00542137i	$-0.00172569\pi$
$373$	0.752811	+	5.23591i	0.0389791	+	0.271105i	−0.961006	+	0.276527i	$0.910817\pi$
$374$	4.00827	+	10.7916i	0.207263	+	0.558018i
$375$	2.74625	−	6.01344i	0.141816	−	0.310533i
$376$	6.44091	−	3.48284i	0.332164	−	0.179614i
$377$	3.23816	−	22.5219i	0.166774	−	1.15994i
$378$	−0.660756	+	3.01761i	−0.0339856	+	0.155209i
$379$	−8.66036	+	29.4945i	−0.444853	+	1.51503i	0.366469	+	0.930430i	$0.380567\pi$
$379$	−8.66036	+	29.4945i	−0.444853	+	1.51503i	−0.811322	+	0.584600i	$0.801252\pi$
$380$	27.4944	+	0.0750549i	1.41043	+	0.00385024i
$381$	2.05349	−	0.937796i	0.105203	−	0.0480448i
$382$	−3.90994	+	3.89929i	−0.200050	+	0.199505i
$383$	4.61548	−	5.32654i	0.235840	−	0.272174i	−0.625476	−	0.780243i	$-0.715095\pi$
$383$	4.61548	−	5.32654i	0.235840	−	0.272174i	0.861316	+	0.508070i	$0.169641\pi$
$384$	11.0317	+	2.51042i	0.562958	+	0.128109i
$385$	−10.9825	+	17.0891i	−0.559718	+	0.870939i
$386$	−12.4660	+	22.7559i	−0.634504	+	1.15825i
$387$	−5.28108	−	8.21752i	−0.268452	−	0.417720i
$388$	28.9731	+	18.7319i	1.47089	+	0.950966i
$389$	−6.40765	+	1.88146i	−0.324881	+	0.0953936i	−0.440106	−	0.897946i	$-0.645059\pi$
$389$	−6.40765	+	1.88146i	−0.324881	+	0.0953936i	0.115225	+	0.993339i	$0.463241\pi$
$390$	11.6307	−	15.4926i	0.588941	−	0.784499i
$391$	−0.728465	+	11.5514i	−0.0368401	+	0.584181i
$392$	2.22710	−	5.89722i	0.112485	−	0.297854i
$393$	17.6848	−	5.19272i	0.892078	−	0.261938i
$394$	−18.6576	+	1.30883i	−0.939957	+	0.0659377i
$395$	6.40518	−	4.11636i	0.322279	−	0.207116i
$396$	−2.78552	−	6.14376i	−0.139977	−	0.308735i
$397$	17.0168	−	26.4786i	0.854046	−	1.32892i	−0.0889215	−	0.996039i	$-0.528342\pi$
$397$	17.0168	−	26.4786i	0.854046	−	1.32892i	0.942968	−	0.332884i	$-0.108022\pi$
$398$	−15.1378	+	8.23905i	−0.758788	+	0.412986i
$399$	−8.23071	−	7.13195i	−0.412051	−	0.357044i
$400$	−4.27248	−	9.49224i	−0.213624	−	0.474612i
$401$	−1.30839	+	0.597522i	−0.0653379	+	0.0298388i	−0.447816	−	0.894126i	$-0.647798\pi$
$401$	−1.30839	+	0.597522i	−0.0653379	+	0.0298388i	0.382478	+	0.923965i	$0.375071\pi$
$402$	−5.01722	+	3.74517i	−0.250236	+	0.186792i
$403$	−12.1411	−	3.56496i	−0.604794	−	0.177583i
$404$	−23.2617	−	26.9940i	−1.15731	−	1.34300i
$405$	−0.392396	+	2.72917i	−0.0194983	+	0.135614i
$406$	2.98843	+	13.8285i	0.148314	+	0.686295i
$407$	9.33071	+	4.26119i	0.462506	+	0.211219i
$408$	4.06837	+	5.48135i	0.201415	+	0.271367i
$409$	−0.328734	−	2.28639i	−0.0162548	−	0.113055i	0.980079	−	0.198610i	$-0.0636427\pi$
$409$	−0.328734	−	2.28639i	−0.0162548	−	0.113055i	−0.996333	+	0.0855551i	$0.972734\pi$
$410$	−16.5498	−	1.20637i	−0.817337	−	0.0595785i
$411$	17.3861	−	15.0651i	0.857593	−	0.743109i
$412$	−11.5953	−	18.1514i	−0.571261	−	0.894257i
$413$	20.0024			0.984252
$414$	−0.0478524	−	6.78216i	−0.00235182	−	0.333325i
$415$		−	26.9820i		−	1.32449i
$416$	5.78642	+	27.5020i	0.283703	+	1.34840i
$417$	6.61482	+	7.63391i	0.323929	+	0.373834i
$418$	23.7194	+	1.72899i	1.16016	+	0.0845677i
$419$	−16.7002	+	2.40112i	−0.815857	+	0.117303i	−0.537596	−	0.843203i	$-0.680667\pi$
$419$	−16.7002	+	2.40112i	−0.815857	+	0.117303i	−0.278262	+	0.960505i	$0.589758\pi$
$420$	−3.42513	+	11.5482i	−0.167129	+	0.563494i
$421$	−1.71577	+	3.75700i	−0.0836213	+	0.183105i	−0.946824	−	0.321753i	$-0.895728\pi$
$421$	−1.71577	+	3.75700i	−0.0836213	+	0.183105i	0.863202	+	0.504858i	$0.168455\pi$
$422$	24.4039	−	5.27387i	1.18796	−	0.256728i
$423$	−2.56246	−	0.368426i	−0.124591	−	0.0179135i
$424$	1.04713	−	0.0705841i	0.0508534	−	0.00342787i
$425$	1.76945	−	6.02620i	0.0858310	−	0.292313i
$426$	10.5479	−	7.87364i	0.511049	−	0.381479i
$427$	0.0232733	+	0.0509614i	0.00112627	+	0.00246620i
$428$	−2.93105	−	20.7886i	−0.141678	−	1.00486i
$429$	10.9735	−	12.6641i	0.529804	−	0.611426i
$430$	−18.2086	−	33.4551i	−0.878097	−	1.61335i
$431$	6.79544	+	4.36717i	0.327325	+	0.210359i	0.693973	−	0.720001i	$-0.255858\pi$
$431$	6.79544	+	4.36717i	0.327325	+	0.210359i	−0.366649	+	0.930360i	$0.619495\pi$
$432$	−2.60290	−	3.03725i	−0.125232	−	0.146130i
$433$	−1.91656	−	2.98222i	−0.0921039	−	0.143317i	0.792144	−	0.610334i	$-0.208965\pi$
$433$	−1.91656	−	2.98222i	−0.0921039	−	0.143317i	−0.884248	+	0.467018i	$0.845328\pi$
$434$	7.84854	−	0.550573i	0.376742	−	0.0264283i
$435$	3.55765	+	12.1163i	0.170576	+	0.580930i
$436$	1.30954	+	4.50534i	0.0627155	+	0.215767i
$437$	21.0823	+	11.2824i	1.00850	+	0.539710i
$438$	2.49914	+	1.87616i	0.119414	+	0.0896465i
$439$	5.26906	+	17.9448i	0.251478	+	0.856457i	0.984370	+	0.176112i	$0.0563519\pi$
$439$	5.26906	+	17.9448i	0.251478	+	0.856457i	−0.732892	+	0.680345i	$0.761830\pi$
$440$	−9.09124	−	24.6828i	−0.433408	−	1.17670i
$441$	−1.87491	+	1.20493i	−0.0892814	+	0.0573776i
$442$	−8.14684	+	14.8715i	−0.387506	+	0.707367i
$443$	30.4302	+	19.5563i	1.44578	+	0.929148i	0.999412	+	0.0343008i	$0.0109204\pi$
$443$	30.4302	+	19.5563i	1.44578	+	0.929148i	0.446372	+	0.894848i	$0.352716\pi$
$444$	6.01817	+	0.882057i	0.285610	+	0.0418606i
$445$	24.8964	+	21.5729i	1.18020	+	1.02265i
$446$	−18.1240	−	18.1736i	−0.858199	−	0.860544i
$447$	−6.03184	−	13.2079i	−0.285296	−	0.624712i
$448$	−9.32679	−	14.7775i	−0.440650	−	0.698170i
$449$	0.744198	+	0.218516i	0.0351209	+	0.0103124i	0.299246	−	0.954176i	$-0.403265\pi$
$449$	0.744198	+	0.218516i	0.0351209	+	0.0103124i	−0.264125	+	0.964488i	$0.585083\pi$
$450$	−0.787211	+	3.59512i	−0.0371095	+	0.169476i
$451$	−14.2073	−	2.04270i	−0.668994	−	0.0961868i
$452$	0.767407	−	1.66832i	0.0360958	−	0.0784711i
$453$	7.70596	+	3.51920i	0.362058	+	0.165346i
$454$	10.8148	−	4.01689i	0.507562	−	0.188522i
$455$	−29.6173	+	4.25832i	−1.38848	+	0.199633i
$456$	13.7921	−	2.94118i	0.645872	−	0.137734i
$457$	28.4967	−	24.6925i	1.33302	−	1.15507i	0.357808	−	0.933795i	$-0.383524\pi$
$457$	28.4967	−	24.6925i	1.33302	−	1.15507i	0.975212	−	0.221273i	$-0.0710213\pi$
$458$	−15.4051	−	5.76977i	−0.719833	−	0.269603i
$459$		−	2.41342i		−	0.112649i
$460$	1.73653	−	26.3894i	0.0809661	−	1.23041i
$461$			8.78009i			0.408929i	0.978874	+	0.204465i	$0.0655454\pi$
$461$			8.78009i			0.408929i	−0.978874	+	0.204465i	$0.934455\pi$
$462$	−3.65444	+	9.75723i	−0.170020	+	0.453947i
$463$	−11.1596	+	9.66987i	−0.518631	+	0.449397i	−0.874420	−	0.485170i	$-0.838758\pi$
$463$	−11.1596	+	9.66987i	−0.518631	+	0.449397i	0.355788	+	0.934567i	$0.384212\pi$
$464$	−16.6222	−	7.70104i	−0.771664	−	0.357512i
$465$	6.95109	−	0.999416i	0.322349	−	0.0463468i
$466$	−12.5981	−	33.9182i	−0.583597	−	1.57123i
$467$	15.4030	+	7.03431i	0.712766	+	0.325509i	0.738588	−	0.674157i	$-0.235493\pi$
$467$	15.4030	+	7.03431i	0.712766	+	0.325509i	−0.0258221	+	0.999667i	$0.508220\pi$
$468$	4.15236	−	9.02710i	0.191943	−	0.417278i
$469$	9.57186	+	1.37623i	0.441987	+	0.0635482i
$470$	−9.86098	−	2.15922i	−0.454853	−	0.0995976i
$471$	−21.5966	−	6.34134i	−0.995120	−	0.292194i
$472$	−15.6064	+	20.6707i	−0.718342	+	0.951446i
$473$	−13.6866	−	29.9694i	−0.629309	−	1.37800i
$474$	2.76517	−	2.75763i	0.127008	−	0.126662i
$475$	−9.80589	−	8.49686i	−0.449925	−	0.389862i
$476$	1.52897	−	10.4320i	0.0700801	−	0.478148i
$477$	−0.312154	−	0.200609i	−0.0142925	−	0.00918526i
$478$	−34.0456	−	18.6507i	−1.55721	−	0.853062i
$479$	16.8671	−	10.8398i	0.770678	−	0.495285i	−0.0952500	−	0.995453i	$-0.530365\pi$
$479$	16.8671	−	10.8398i	0.770678	−	0.495285i	0.865928	+	0.500169i	$0.166729\pi$
$480$	−9.26168	−	12.5498i	−0.422736	−	0.572816i
$481$	4.25680	+	14.4973i	0.194093	+	0.661021i
$482$	−16.5282	+	22.0164i	−0.752838	+	1.00282i
$483$	−7.34478	+	7.46953i	−0.334199	+	0.339875i
$484$	−0.210012	−	0.722525i	−0.00954599	−	0.0328421i
$485$	−13.4003	−	45.6372i	−0.608476	−	2.07228i
$486$	0.0989634	+	1.41075i	0.00448907	+	0.0639928i
$487$	6.88509	+	10.7134i	0.311993	+	0.485471i	0.961470	−	0.274911i	$-0.0886483\pi$
$487$	6.88509	+	10.7134i	0.311993	+	0.485471i	−0.649476	+	0.760382i	$0.725012\pi$
$488$	−0.0708226	−	0.0157105i	−0.00320599	−	0.000711181i
$489$	18.5793	+	11.9402i	0.840187	+	0.539955i
$490$	−7.63311	+	4.15448i	−0.344829	+	0.187680i
$491$	2.57074	−	2.96679i	0.116016	−	0.133889i	−0.694771	−	0.719231i	$-0.744494\pi$
$491$	2.57074	−	2.96679i	0.116016	−	0.133889i	0.810787	+	0.585342i	$0.199040\pi$
$492$	−8.42773	+	1.18825i	−0.379951	+	0.0535705i
$493$	−4.59164	−	10.0543i	−0.206797	−	0.452823i
$494$	20.9550	+	28.0724i	0.942809	+	1.26304i
$495$	−2.62005	+	8.92308i	−0.117763	+	0.401063i
$496$	−5.55467	+	8.54035i	−0.249412	+	0.383473i
$497$	−20.1233	−	2.89330i	−0.902655	−	0.129782i
$498$	−2.92329	−	13.5270i	−0.130996	−	0.606161i
$499$	−1.75763	+	3.84868i	−0.0786825	+	0.172291i	−0.944885	−	0.327403i	$-0.893827\pi$
$499$	−1.75763	+	3.84868i	−0.0786825	+	0.172291i	0.866202	+	0.499693i	$0.166554\pi$
$500$	3.75960	−	12.6759i	0.168135	−	0.566884i
$501$	−12.0194	+	1.72812i	−0.536985	+	0.0772068i
$502$	−2.07879	+	28.5182i	−0.0927808	+	1.27283i
$503$	8.41784	+	9.71471i	0.375333	+	0.433157i	0.911718	−	0.410816i	$-0.134756\pi$
$503$	8.41784	+	9.71471i	0.375333	+	0.433157i	−0.536385	+	0.843973i	$0.680211\pi$
$504$	−0.465979	+	6.16062i	−0.0207563	+	0.274416i
$505$			49.1257i			2.18606i
$506$	3.09574	−	22.6654i	0.137622	−	1.00760i
$507$	11.6827			0.518845
$508$	3.80490	−	2.43061i	0.168815	−	0.107841i
$509$	−2.73073	+	2.36619i	−0.121037	+	0.104880i	−0.713276	−	0.700883i	$-0.752790\pi$
$509$	−2.73073	+	2.36619i	−0.121037	+	0.104880i	0.592239	+	0.805762i	$0.298244\pi$
$510$	0.684164	−	9.38582i	0.0302953	−	0.415611i
$511$	−0.686918	−	4.77762i	−0.0303875	−	0.211349i
$512$	22.5482	+	1.89134i	0.996501	+	0.0835864i
$513$	−4.53531	−	2.07121i	−0.200239	−	0.0914460i
$514$	15.6139	−	3.37428i	0.688698	−	0.148833i
$515$	−4.22590	+	29.3918i	−0.186215	+	1.29516i
$516$	−12.7532	−	14.7995i	−0.561430	−	0.651510i
$517$	−8.37801	−	2.46000i	−0.368464	−	0.108191i
$518$	−5.61976	−	7.52852i	−0.246918	−	0.330784i
$519$	−9.03576	+	4.12649i	−0.396626	+	0.181133i
$520$	18.7076	−	33.9293i	0.820381	−	1.48790i
$521$	8.53535	+	7.39592i	0.373940	+	0.324021i	0.821474	−	0.570246i	$-0.193152\pi$
$521$	8.53535	+	7.39592i	0.373940	+	0.324021i	−0.447534	+	0.894267i	$0.647698\pi$
$522$	3.09629	+	5.68887i	0.135521	+	0.248995i
$523$	−20.9444	+	32.5901i	−0.915834	+	1.42506i	−0.0106974	+	0.999943i	$0.503405\pi$
$523$	−20.9444	+	32.5901i	−0.915834	+	1.42506i	−0.905136	+	0.425122i	$0.860231\pi$
$524$	33.5732	−	15.2217i	1.46665	−	0.664965i
$525$	4.78204	−	3.07323i	0.208705	−	0.134127i
$526$	−1.76595	−	25.1741i	−0.0769991	−	1.09764i
$527$	−5.89790	+	1.73178i	−0.256916	+	0.0754375i
$528$	−7.23196	−	11.3894i	−0.314731	−	0.495660i
$529$	12.1071	−	19.5555i	0.526397	−	0.850239i
$530$	−1.15710	−	0.868661i	−0.0502612	−	0.0377322i
$531$	8.78629	−	2.57989i	0.381292	−	0.111958i
$532$	−18.2916	−	11.8260i	−0.793042	−	0.512721i
$533$	−11.4303	−	17.7860i	−0.495103	−	0.770396i
$534$	14.8187	+	8.11792i	0.641269	+	0.351297i
$535$	−15.6478	+	24.3485i	−0.676513	+	1.05268i
$536$	−8.89042	+	8.81791i	−0.384008	+	0.380876i
$537$	−11.5370	+	13.3144i	−0.497857	+	0.574558i
$538$	−23.2655	−	23.3291i	−1.00305	−	1.00579i
$539$	−6.83782	+	3.12273i	−0.294526	+	0.134505i
$540$	−0.0150535	+	5.51446i	−0.000647800	+	0.237304i
$541$	−8.45359	+	28.7903i	−0.363448	+	1.23779i	0.551485	+	0.834185i	$0.314061\pi$
$541$	−8.45359	+	28.7903i	−0.363448	+	1.23779i	−0.914933	+	0.403606i	$0.867757\pi$
$542$	−22.5141	−	4.92984i	−0.967064	−	0.211755i
$543$	−2.49098	+	17.3251i	−0.106898	+	0.743493i
$544$	9.58759	+	9.71935i	0.411064	+	0.416714i
$545$	2.68699	−	5.88369i	0.115098	−	0.252029i
$546$	−14.3869	+	5.34366i	−0.615700	+	0.228688i
$547$	0.434797	+	3.02408i	0.0185906	+	0.129300i	0.997003	−	0.0773609i	$-0.0246494\pi$
$547$	0.434797	+	3.02408i	0.0185906	+	0.129300i	−0.978413	+	0.206661i	$0.933740\pi$
$548$	30.2251	−	34.6898i	1.29115	−	1.48188i
$549$	0.0167960	+	0.0193837i	0.000716837	+	0.000827274i
$550$	−4.35382	+	11.6246i	−0.185648	+	0.495673i
$551$	−22.8346			−0.972787
$552$	−1.98851	−	13.4181i	−0.0846367	−	0.571113i
$553$	−6.03181			−0.256499
$554$	−10.9366	+	29.2004i	−0.464653	+	1.24061i
$555$	−5.49127	−	6.33727i	−0.233092	−	0.269002i
$556$	15.2316	+	13.2713i	0.645965	+	0.562827i
$557$	−5.29513	−	36.8285i	−0.224362	−	1.56047i	−0.721261	−	0.692664i	$-0.756437\pi$
$557$	−5.29513	−	36.8285i	−0.224362	−	1.56047i	0.496899	−	0.867809i	$-0.334472\pi$
$558$	3.37656	−	1.25414i	0.142941	−	0.0530921i
$559$	20.1601	−	44.1444i	0.852680	−	1.86711i
$560$	−3.55862	+	23.8266i	−0.150379	+	1.00686i
$561$	1.15846	−	8.05729i	0.0489104	−	0.340179i
$562$	6.82847	+	1.49521i	0.288041	+	0.0630715i
$563$	2.51955	−	8.58080i	0.106186	−	0.361638i	−0.889208	−	0.457503i	$-0.848744\pi$
$563$	2.51955	−	8.58080i	0.106186	−	0.361638i	0.995394	+	0.0958657i	$0.0305619\pi$
$564$	−5.17760	−	0.0141340i	−0.218016	−	0.000595147i
$565$	−2.30286	+	1.05168i	−0.0968819	+	0.0442445i
$566$	−22.8434	−	22.9058i	−0.960179	−	0.962803i
$567$	1.43043	−	1.65081i	0.0600725	−	0.0693273i
$568$	18.6907	−	18.5383i	0.784246	−	0.777849i
$569$	0.665868	−	1.03611i	0.0279147	−	0.0434361i	−0.827016	−	0.562179i	$-0.809963\pi$
$569$	0.665868	−	1.03611i	0.0279147	−	0.0434361i	0.854930	+	0.518743i	$0.173600\pi$
$570$	−17.0507	−	9.34062i	−0.714175	−	0.391235i
$571$	15.6679	+	24.3797i	0.655681	+	1.02026i	0.996776	+	0.0802309i	$0.0255658\pi$
$571$	15.6679	+	24.3797i	0.655681	+	1.02026i	−0.341095	+	0.940029i	$0.610798\pi$
$572$	18.1959	−	28.1441i	0.760808	−	1.17676i
$573$	3.74645	−	1.10006i	0.156510	−	0.0459556i
$574$	10.5130	+	7.89235i	0.438805	+	0.329421i
$575$	−8.75042	+	8.89904i	−0.364918	+	0.371116i
$576$	−6.00289	−	5.28822i	−0.250120	−	0.220343i
$577$	−2.49360	+	0.732188i	−0.103810	+	0.0304814i	−0.333225	−	0.942847i	$-0.608137\pi$
$577$	−2.49360	+	0.732188i	−0.103810	+	0.0304814i	0.229415	+	0.973329i	$0.426319\pi$
$578$	−1.10595	−	15.7656i	−0.0460016	−	0.655764i
$579$	15.4346	−	9.91920i	0.641439	−	0.412228i
$580$	10.4288	+	23.0018i	0.433031	+	0.955098i
$581$	−11.5565	+	17.9823i	−0.479444	+	0.746030i
$582$	−11.6625	−	21.4278i	−0.483426	−	0.888209i
$583$	−0.945842	−	0.819577i	−0.0391728	−	0.0339434i
$584$	5.47320	+	3.01775i	0.226483	+	0.124876i
$585$	−12.4605	+	5.69053i	−0.515179	+	0.235274i
$586$	16.2842	+	21.8152i	0.672695	+	0.901176i
$587$	45.4086	+	13.3332i	1.87421	+	0.550318i	0.997609	+	0.0691044i	$0.0220142\pi$
$587$	45.4086	+	13.3332i	1.87421	+	0.550318i	0.876603	+	0.481214i	$0.159804\pi$
$588$	−3.37665	+	2.90978i	−0.139251	+	0.119997i
$589$	−1.80723	+	12.5696i	−0.0744656	+	0.517920i
$590$	34.9013	−	7.54243i	1.43686	−	0.310517i
$591$	12.0302	+	5.49401i	0.494856	+	0.225993i
$592$	12.1648	+	0.0664159i	0.499968	+	0.00272967i
$593$	4.04937	+	28.1640i	0.166288	+	1.15656i	0.886475	+	0.462776i	$0.153147\pi$
$593$	4.04937	+	28.1640i	0.166288	+	1.15656i	−0.720187	+	0.693779i	$0.755944\pi$
$594$	−0.346778	+	4.75733i	−0.0142285	+	0.195196i
$595$	−10.9851	+	9.51864i	−0.450345	+	0.390226i
$596$	−15.6335	−	24.4728i	−0.640373	−	1.00245i
$597$	12.1868			0.498771
$598$	28.2174	−	18.4168i	1.15390	−	0.753120i
$599$		−	1.14403i		−	0.0467438i	−0.999727	−	0.0233719i	$-0.992560\pi$
$599$		−	1.14403i		−	0.0467438i	0.999727	−	0.0233719i	$-0.00744019\pi$
$600$	−0.555157	+	7.33963i	−0.0226642	+	0.299639i
$601$	−8.76245	−	10.1124i	−0.357428	−	0.412494i	0.548348	−	0.836250i	$-0.315257\pi$
$601$	−8.76245	−	10.1124i	−0.357428	−	0.412494i	−0.905776	+	0.423756i	$0.860711\pi$
$602$	−2.19374	+	30.0951i	−0.0894100	+	1.22659i
$603$	4.38206	−	0.630045i	0.178451	−	0.0256574i
$604$	16.2436	+	4.81776i	0.660944	+	0.196032i
$605$	−0.430915	+	0.943572i	−0.0175192	+	0.0383616i
$606$	5.32240	+	24.6285i	0.216208	+	1.00046i
$607$	26.7598	+	3.84747i	1.08615	+	0.156164i	0.662055	−	0.749456i	$-0.269685\pi$
$607$	26.7598	+	3.84747i	1.08615	+	0.156164i	0.424091	+	0.905620i	$0.360594\pi$
$608$	26.4927	−	9.67584i	1.07442	−	0.392407i
$609$	2.81843	−	9.59869i	0.114209	−	0.388959i
$610$	0.0598249	+	0.0801445i	0.00242224	+	0.00324496i
$611$	−5.34291	−	11.6993i	−0.216151	−	0.473305i
$612$	−0.673887	−	4.77957i	−0.0272403	−	0.193203i
$613$	15.2641	−	17.6157i	0.616510	−	0.711491i	−0.358530	−	0.933518i	$-0.616722\pi$
$613$	15.2641	−	17.6157i	0.616510	−	0.711491i	0.975040	+	0.222027i	$0.0712674\pi$
$614$	8.53000	−	4.64263i	0.344243	−	0.187361i
$615$	9.87088	+	6.34363i	0.398032	+	0.255800i
$616$	−4.51283	+	20.3438i	−0.181827	+	0.819673i
$617$	−9.29257	−	14.4595i	−0.374105	−	0.582118i	0.602246	−	0.798311i	$-0.294273\pi$
$617$	−9.29257	−	14.4595i	−0.374105	−	0.582118i	−0.976351	+	0.216192i	$0.930636\pi$
$618$	1.06578	+	15.1930i	0.0428721	+	0.611152i
$619$	6.71549	+	22.8709i	0.269918	+	0.919258i	0.977199	+	0.212325i	$0.0681035\pi$
$619$	6.71549	+	22.8709i	0.269918	+	0.919258i	−0.707281	+	0.706933i	$0.750078\pi$
$620$	13.4870	−	3.92017i	0.541650	−	0.157438i
$621$	−2.26287	+	4.22840i	−0.0908060	+	0.169680i
$622$	23.5960	−	31.4311i	0.946115	−	1.26027i
$623$	−7.35258	−	25.0406i	−0.294575	−	1.00323i
$624$	5.70279	−	19.0368i	0.228294	−	0.762083i
$625$	−26.2804	+	16.8894i	−1.05121	+	0.675574i
$626$	15.5118	+	8.49759i	0.619976	+	0.339632i
$627$	−14.1471	−	9.09178i	−0.564980	−	0.363091i
$628$	−44.5409	−	6.52816i	−1.77737	−	0.260502i
$629$	5.54704	+	4.80654i	0.221175	+	0.191649i
$630$	6.03093	−	6.01449i	0.240278	−	0.239623i
$631$	3.15377	+	6.90580i	0.125550	+	0.274916i	0.961961	−	0.273187i	$-0.0880777\pi$
$631$	3.15377	+	6.90580i	0.125550	+	0.274916i	−0.836411	+	0.548102i	$0.815350\pi$
$632$	4.70618	−	6.23335i	0.187202	−	0.247949i
$633$	−16.9394	−	4.97385i	−0.673280	−	0.197693i
$634$	21.5188	+	4.71189i	0.854620	+	0.187133i
$635$	−6.16109	−	0.885831i	−0.244495	−	0.0351531i
$636$	−0.674209	−	0.310128i	−0.0267341	−	0.0122974i
$637$	−10.0720	−	4.59972i	−0.399066	−	0.182248i
$638$	7.60635	+	20.4787i	0.301138	+	0.810761i
$639$	−9.21260	+	1.32457i	−0.364445	+	0.0523993i
$640$	−21.8462	−	22.2676i	−0.863545	−	0.880206i
$641$	28.3790	−	24.5906i	1.12090	−	0.971269i	0.121133	−	0.992636i	$-0.461347\pi$
$641$	28.3790	−	24.5906i	1.12090	−	0.971269i	0.999772	+	0.0213671i	$0.00680187\pi$
$642$	−5.20683	+	13.9021i	−0.205497	+	0.548671i
$643$			20.9338i			0.825548i	0.910833	+	0.412774i	$0.135440\pi$
$643$			20.9338i			0.825548i	−0.910833	+	0.412774i	$0.864560\pi$
$644$	−12.4600	+	16.8436i	−0.490994	+	0.663731i
$645$			26.9332i			1.06049i
$646$	15.9362	+	5.96868i	0.627001	+	0.234835i
$647$	1.05449	−	0.913717i	0.0414561	−	0.0359219i	−0.633886	−	0.773426i	$-0.718541\pi$
$647$	1.05449	−	0.913717i	0.0414561	−	0.0359219i	0.675342	+	0.737504i	$0.263996\pi$
$648$	0.589903	+	2.76623i	0.0231736	+	0.108668i
$649$	30.5717	−	4.39554i	1.20004	−	0.172540i
$650$	−17.1402	+	6.36633i	−0.672294	+	0.249708i
$651$	−5.06064	−	2.31112i	−0.198342	−	0.0905799i
$652$	40.1288	+	18.4587i	1.57156	+	0.722900i
$653$	−19.6266	−	2.82189i	−0.768050	−	0.110429i	−0.252858	−	0.967504i	$-0.581370\pi$
$653$	−19.6266	−	2.82189i	−0.768050	−	0.110429i	−0.515192	+	0.857075i	$0.672280\pi$
$654$	0.709631	−	3.24082i	0.0277488	−	0.126726i
$655$	−48.7611	−	14.3176i	−1.90525	−	0.559433i
$656$	−16.3586	+	4.70646i	−0.638695	+	0.183756i
$657$	−0.917949	−	2.01003i	−0.0358126	−	0.0784187i
$658$	5.64709	+	5.66252i	0.220146	+	0.220748i
$659$	13.8116	+	11.9678i	0.538022	+	0.466199i	0.880981	−	0.473152i	$-0.156884\pi$
$659$	13.8116	+	11.9678i	0.538022	+	0.466199i	−0.342959	+	0.939350i	$0.611429\pi$
$660$	−2.69724	+	18.4030i	−0.104990	+	0.716335i
$661$	6.18889	+	3.97736i	0.240720	+	0.154701i	0.655439	−	0.755248i	$-0.272484\pi$
$661$	6.18889	+	3.97736i	0.240720	+	0.154701i	−0.414719	+	0.909950i	$0.636120\pi$
$662$	−17.8037	+	32.4994i	−0.691959	+	1.26313i
$663$	10.0869	−	6.48244i	0.391741	−	0.251757i
$664$	−9.56641	−	25.9729i	−0.371249	−	1.00794i
$665$	8.46000	+	28.8121i	0.328065	+	1.11729i
$666$	−3.43957	−	2.58216i	−0.133281	−	0.100057i
$667$	−1.38238	+	21.9207i	−0.0535260	+	0.848773i
$668$	−23.3207	+	6.77849i	−0.902307	+	0.262268i
$669$	5.11312	+	17.4137i	0.197685	+	0.673252i
$670$	17.2205	−	1.20801i	0.665284	−	0.0466695i
$671$	0.0467698	+	0.0727752i	0.00180553	+	0.00280946i
$672$	0.797365	+	12.3307i	0.0307590	+	0.475666i
$673$	−24.3614	−	15.6562i	−0.939065	−	0.603500i	−0.0209353	−	0.999781i	$-0.506664\pi$
$673$	−24.3614	−	15.6562i	−0.939065	−	0.603500i	−0.918129	+	0.396281i	$0.870301\pi$
$674$	21.5071	+	39.5155i	0.828424	+	1.52208i
$675$	1.70419	−	1.96674i	0.0655942	−	0.0756997i
$676$	23.1365	−	3.26208i	0.889864	−	0.125465i
$677$	13.5024	+	29.5662i	0.518940	+	1.13632i	0.969839	+	0.243745i	$0.0783760\pi$
$677$	13.5024	+	29.5662i	0.518940	+	1.13632i	−0.450900	+	0.892575i	$0.648897\pi$
$678$	−1.04056	+	0.776742i	−0.0399626	+	0.0298306i
$679$	−10.6159	+	36.1545i	−0.407402	+	1.38748i
$680$	−1.26582	−	18.7788i	−0.0485421	−	0.720135i
$681$	−8.07462	−	1.16096i	−0.309420	−	0.0444879i
$682$	11.8747	−	2.56622i	0.454707	−	0.0982657i
$683$	−3.67115	+	8.03869i	−0.140472	+	0.307592i	−0.966772	−	0.255638i	$-0.917714\pi$
$683$	−3.67115	+	8.03869i	−0.140472	+	0.307592i	0.826300	+	0.563230i	$0.190442\pi$
$684$	−9.56012	−	2.83547i	−0.365540	−	0.108417i
$685$	−62.7849	+	9.02711i	−2.39889	+	0.344908i
$686$	28.4330	+	2.07258i	1.08558	+	0.0791315i
$687$	7.61734	+	8.79088i	0.290620	+	0.335393i
$688$	−29.3891	−	25.7480i	−1.12045	−	0.981635i
$689$		−	1.84348i		−	0.0702309i
$690$	−9.99901	+	15.8028i	−0.380656	+	0.601602i
$691$	−31.8081			−1.21004			−0.605018	−	0.796212i	$-0.706834\pi$
$691$	−31.8081			−1.21004			−0.605018	+	0.796212i	$0.706834\pi$
$692$	−16.7423	+	10.6952i	−0.636447	+	0.406569i
$693$	5.56794	−	4.82465i	0.211509	−	0.183273i
$694$	−12.9165	−	0.941529i	−0.490304	−	0.0357400i
$695$	−3.96363	−	27.5677i	−0.150349	−	1.04570i
$696$	7.72040	+	10.4018i	0.292641	+	0.394278i
$697$	−9.34230	−	4.26649i	−0.353865	−	0.161605i
$698$	−8.56863	−	39.6498i	−0.324327	−	1.50077i
$699$	−3.64109	+	25.3243i	−0.137719	+	0.957854i
$700$	8.61229	−	7.42152i	0.325514	−	0.280507i
$701$	12.6911	+	3.72646i	0.479338	+	0.140746i	0.512471	−	0.858705i	$-0.328730\pi$
$701$	12.6911	+	3.72646i	0.479338	+	0.140746i	−0.0331329	+	0.999451i	$0.510548\pi$
$702$	−5.63038	+	4.20287i	−0.212505	+	0.158627i
$703$	13.7929	−	6.29902i	0.520211	−	0.237572i
$704$	−17.5025	−	20.5363i	−0.659649	−	0.773993i
$705$	5.39451	+	4.67437i	0.203169	+	0.176047i
$706$	28.1803	−	15.3377i	1.06058	−	0.577242i
$707$	21.0407	−	32.7400i	0.791319	−	1.23132i
$708$	16.6801	−	7.56259i	0.626877	−	0.284219i
$709$	18.6010	−	11.9541i	0.698575	−	0.448947i	−0.142550	−	0.989788i	$-0.545530\pi$
$709$	18.6010	−	11.9541i	0.698575	−	0.448947i	0.841125	+	0.540841i	$0.181894\pi$
$710$	−36.2033	+	2.53965i	−1.35869	+	0.0953115i
$711$	−2.64955	+	0.777977i	−0.0993658	+	0.0291764i
$712$	31.6139	+	11.9391i	1.18478	+	0.447436i
$713$	11.9571	+	2.49585i	0.447796	+	0.0934702i
$714$	−4.47595	+	5.96219i	−0.167508	+	0.223129i
$715$	−44.3313	+	13.0169i	−1.65790	+	0.486803i
$716$	−19.1303	+	29.5894i	−0.714932	+	1.10581i
$717$	14.8403	+	23.0920i	0.554222	+	0.862386i
$718$	−3.76087	+	6.86522i	−0.140354	+	0.256208i
$719$	−6.55278	+	10.1963i	−0.244378	+	0.380259i	−0.941675	−	0.336523i	$-0.890749\pi$
$719$	−6.55278	+	10.1963i	−0.244378	+	0.380259i	0.697298	+	0.716782i	$0.254386\pi$
$720$	1.50996	+	10.9251i	0.0562729	+	0.407155i
$721$	15.4050	−	17.7783i	0.573712	−	0.662099i
$722$	5.86693	−	5.85093i	0.218344	−	0.217749i
$723$	17.7075	−	8.08674i	0.658549	−	0.300749i
$724$	−0.0955616	+	35.0065i	−0.00355152	+	1.30101i
$725$	3.35782	−	11.4357i	0.124706	−	0.424711i
$726$	−0.113804	+	0.519733i	−0.00422367	+	0.0192891i
$727$	3.84676	−	26.7548i	0.142668	−	0.992281i	−0.785165	−	0.619286i	$-0.787422\pi$
$727$	3.84676	−	26.7548i	0.142668	−	0.992281i	0.927834	−	0.372994i	$-0.121669\pi$
$728$	−26.9998	+	14.5998i	−1.00068	+	0.541105i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−3.00010	−	8.07724i	−0.111039	−	0.298952i
$731$	−3.35504	−	23.3348i	−0.124091	−	0.863069i
$732$	0.0386755	+	0.0336978i	0.00142949	+	0.00124551i
$733$	−28.0536	−	32.3756i	−1.03618	−	1.19582i	−0.980327	−	0.197381i	$-0.936756\pi$
$733$	−28.0536	−	32.3756i	−1.03618	−	1.19582i	−0.0558566	−	0.998439i	$-0.517789\pi$
$734$	49.4151	+	18.5077i	1.82394	+	0.683133i
$735$	6.14508			0.226665
$736$	−7.68474	−	26.0182i	−0.283263	−	0.959042i
$737$	14.9321			0.550030
$738$	5.63592	+	2.11086i	0.207461	+	0.0777016i
$739$	−32.6293	−	37.6563i	−1.20029	−	1.38521i	−0.902563	−	0.430557i	$-0.858317\pi$
$739$	−32.6293	−	37.6563i	−1.20029	−	1.38521i	−0.297727	−	0.954651i	$-0.596228\pi$
$740$	−12.6445	−	11.0171i	−0.464821	−	0.404997i
$741$	−3.52523	−	24.5185i	−0.129503	−	0.900710i
$742$	0.399103	+	1.07451i	0.0146515	+	0.0394466i
$743$	1.95866	−	4.28887i	0.0718563	−	0.157343i	−0.870295	−	0.492530i	$-0.836072\pi$
$743$	1.95866	−	4.28887i	0.0718563	−	0.157343i	0.942152	+	0.335187i	$0.108799\pi$
$744$	6.33679	−	3.42654i	0.232318	−	0.125623i
$745$	−5.69760	+	39.6277i	−0.208744	+	1.45185i
$746$	1.60014	−	7.30770i	0.0585854	−	0.267554i
$747$	−2.75700	+	9.38947i	−0.100873	+	0.343543i
$748$	0.0444422	−	16.2802i	0.00162497	−	0.595264i
$749$	20.8571	−	9.52512i	0.762102	−	0.348040i
$750$	−6.61987	+	6.60182i	−0.241724	+	0.241065i
$751$	18.6769	−	21.5543i	0.681528	−	0.786526i	−0.304605	−	0.952479i	$-0.598525\pi$
$751$	18.6769	−	21.5543i	0.681528	−	0.786526i	0.986134	+	0.165953i	$0.0530700\pi$
$752$	−10.2577	+	1.41772i	−0.374061	+	0.0516990i
$753$	10.9312	−	17.0092i	0.398354	−	0.619850i
$754$	−15.4600	+	28.2212i	−0.563018	+	1.02775i
$755$	−12.6283	−	19.6500i	−0.459590	−	0.715136i
$756$	2.37190	−	3.66869i	0.0862651	−	0.133429i
$757$	−7.16049	+	2.10251i	−0.260252	+	0.0764170i	−0.409256	−	0.912420i	$-0.634212\pi$
$757$	−7.16049	+	2.10251i	−0.260252	+	0.0764170i	0.149003	+	0.988837i	$0.452393\pi$
$758$	26.0995	−	34.7659i	0.947978	−	1.26275i
$759$	−9.58435	+	13.0305i	−0.347890	+	0.472976i
$760$	−36.3755	−	13.7373i	−1.31948	−	0.498304i
$761$	10.9017	−	3.20103i	0.395187	−	0.116037i	−0.0781005	−	0.996945i	$-0.524885\pi$
$761$	10.9017	−	3.20103i	0.395187	−	0.116037i	0.473287	+	0.880908i	$0.343067\pi$
$762$	−3.18475	+	0.223409i	−0.115371	+	0.00809326i
$763$	−4.31077	+	2.77036i	−0.156060	+	0.100294i
$764$	7.11236	−	3.22467i	0.257316	−	0.116664i
$765$	−3.59763	+	5.59802i	−0.130073	+	0.202397i
$766$	−8.75470	+	4.76493i	−0.316320	+	0.172164i
$767$	34.3825	+	29.7926i	1.24148	+	1.07575i
$768$	−13.3648	−	8.79671i	−0.482261	−	0.317424i
$769$	4.02722	−	1.83917i	0.145225	−	0.0663221i	−0.341477	−	0.939890i	$-0.610927\pi$
$769$	4.02722	−	1.83917i	0.145225	−	0.0663221i	0.486702	+	0.873568i	$0.338200\pi$
$770$	23.0215	−	17.1847i	0.829636	−	0.619293i
$771$	−10.8380	−	3.18232i	−0.390321	−	0.114609i
$772$	27.7972	−	23.9538i	1.00044	−	0.862117i
$773$	−6.48266	+	45.0879i	−0.233165	+	1.62170i	0.451105	+	0.892471i	$0.351030\pi$
$773$	−6.48266	+	45.0879i	−0.233165	+	1.62170i	−0.684270	+	0.729228i	$0.739879\pi$
$774$	2.91801	+	13.5026i	0.104886	+	0.485341i
$775$	−6.02915	−	2.75342i	−0.216573	−	0.0989057i
$776$	−29.0797	−	39.1793i	−1.04390	−	1.40646i
$777$	0.945405	+	6.57544i	0.0339162	+	0.235893i
$778$	9.41936	+	0.686609i	0.337700	+	0.0246161i
$779$	−16.0352	+	13.8946i	−0.574520	+	0.497824i
$780$	−23.0880	+	14.7489i	−0.826684	+	0.528094i
$781$	−31.3924			−1.12331
$782$	6.69455	−	14.9370i	0.239397	−	0.534147i
$783$		−	4.57986i		−	0.163671i
$784$	−5.87467	+	6.70541i	−0.209810	+	0.239479i
$785$	40.6413	+	46.9025i	1.45055	+	1.67402i
$786$	−25.9969	−	1.89500i	−0.927279	−	0.0675926i
$787$	−0.865471	+	0.124436i	−0.0308507	+	0.00443566i	−0.157723	−	0.987483i	$-0.550415\pi$
$787$	−0.865471	+	0.124436i	−0.0308507	+	0.00443566i	0.126872	+	0.991919i	$0.459506\pi$
$788$	25.3588	+	7.52128i	0.903371	+	0.267934i
$789$	−7.41287	+	16.2319i	−0.263905	+	0.577872i
$790$	−10.5246	+	2.27446i	−0.374450	+	0.0809215i
$791$	1.98519	+	0.285427i	0.0705851	+	0.0101486i
$792$	0.641599	+	9.51830i	0.0227982	+	0.338218i
$793$	−0.0358997	+	0.122263i	−0.00127484	+	0.00434169i
$794$	−35.6705	+	26.6267i	−1.26590	+	0.944948i
$795$	0.425009	+	0.930641i	0.0150735	+	0.0330064i
$796$	24.1348	−	3.40284i	0.855436	−	0.120611i
$797$	11.8244	−	13.6461i	0.418843	−	0.483371i	−0.506641	−	0.862157i	$-0.669113\pi$
$797$	11.8244	−	13.6461i	0.418843	−	0.483371i	0.925484	+	0.378786i	$0.123658\pi$
$798$	7.36289	+	13.5280i	0.260643	+	0.478885i
$799$	−5.25606	−	3.37787i	−0.185946	−	0.119500i
$800$	0.949965	+	14.6905i	0.0335863	+	0.519388i
$801$	−6.45942	−	10.0511i	−0.228232	−	0.355137i
$802$	2.02918	−	0.142346i	0.0716529	−	0.00502643i
$803$	−2.09977	−	7.15117i	−0.0740994	−	0.252359i
$804$	8.50236	−	2.47133i	0.299855	−	0.0871570i
$805$	28.1711	−	6.37716i	0.992902	−	0.224765i
$806$	14.3111	+	10.7436i	0.504086	+	0.378429i
$807$	6.56361	+	22.3536i	0.231050	+	0.786884i
$808$	17.4174	+	47.2884i	0.612743	+	1.66360i
$809$	−14.2158	+	9.13597i	−0.499802	+	0.321203i	−0.766137	−	0.642677i	$-0.777824\pi$
$809$	−14.2158	+	9.13597i	−0.499802	+	0.321203i	0.266335	+	0.963881i	$0.414187\pi$
$810$	1.87342	−	3.41980i	0.0658251	−	0.120160i
$811$	−0.520703	−	0.334635i	−0.0182843	−	0.0117506i	0.531467	−	0.847079i	$-0.321641\pi$
$811$	−0.520703	−	0.334635i	−0.0182843	−	0.0117506i	−0.549751	+	0.835329i	$0.685277\pi$
$812$	2.90146	−	19.7963i	0.101821	−	0.694716i
$813$	12.3165	+	10.6723i	0.431959	+	0.374294i
$814$	−10.2437	−	10.2717i	−0.359040	−	0.360022i
$815$	−25.2965	−	55.3915i	−0.886097	−	1.94028i
$816$	−2.66915	−	9.27736i	−0.0934389	−	0.324773i
$817$	−46.7301	−	13.7212i	−1.63488	−	0.480044i
$818$	−0.698743	+	3.19109i	−0.0244310	+	0.111574i
$819$	10.7416	+	1.54442i	0.375343	+	0.0539662i
$820$	21.3197	+	9.80681i	0.744517	+	0.342469i
$821$	43.7710	+	19.9895i	1.52762	+	0.697639i	0.989407	−	0.145171i	$-0.0463732\pi$
$821$	43.7710	+	19.9895i	1.52762	+	0.697639i	0.538211	+	0.842810i	$0.319100\pi$
$822$	−30.4983	+	11.3279i	−1.06375	+	0.395106i
$823$	−1.13687	+	0.163458i	−0.0396289	+	0.00569778i	−0.162101	−	0.986774i	$-0.551827\pi$
$823$	−1.13687	+	0.163458i	−0.0396289	+	0.00569778i	0.122472	+	0.992472i	$0.460918\pi$
$824$	6.35295	+	29.7908i	0.221316	+	1.03781i
$825$	6.63353	−	5.74799i	0.230950	−	0.200119i
$826$	−26.4906	−	9.92168i	−0.921725	−	0.345219i
$827$			6.85368i			0.238326i	0.992875	+	0.119163i	$0.0380211\pi$
$827$			6.85368i			0.238326i	−0.992875	+	0.119163i	$0.961979\pi$
$828$	−3.30075	+	9.00583i	−0.114709	+	0.312974i
$829$		−	13.4626i		−	0.467575i	−0.972288	−	0.233788i	$-0.924888\pi$
$829$		−	13.4626i		−	0.467575i	0.972288	−	0.233788i	$-0.0751120\pi$
$830$	−13.3837	+	35.7341i	−0.464556	+	1.24035i
$831$	16.6632	−	14.4387i	0.578039	−	0.500873i
$832$	5.97833	−	39.2931i	0.207261	−	1.36224i
$833$	−5.32407	+	0.765485i	−0.184468	+	0.0265225i
$834$	−4.97386	−	13.3912i	−0.172231	−	0.463701i
$835$	30.4554	+	13.9085i	1.05395	+	0.481324i
$836$	−30.5557	−	14.0553i	−1.05679	−	0.486111i
$837$	−2.52103	−	0.362470i	−0.0871397	−	0.0125288i
$838$	23.3083	+	5.10373i	0.805171	+	0.176305i
$839$	23.5070	+	6.90227i	0.811551	+	0.238293i	0.661074	−	0.750321i	$-0.270101\pi$
$839$	23.5070	+	6.90227i	0.811551	+	0.238293i	0.150477	+	0.988614i	$0.451919\pi$
$840$	10.2643	−	13.5952i	0.354153	−	0.469077i
$841$	3.33365	+	7.29968i	0.114953	+	0.251713i
$842$	4.13588	−	4.12460i	0.142532	−	0.142143i
$843$	−3.73556	−	3.23688i	−0.128659	−	0.111484i
$844$	−34.9358	−	5.12039i	−1.20254	−	0.176251i
$845$	−27.0983	−	17.4150i	−0.932211	−	0.599096i
$846$	3.21090	+	1.75898i	0.110393	+	0.0604749i
$847$	0.691321	−	0.444285i	0.0237541	−	0.0152658i
$848$	−1.42181	−	0.425926i	−0.0488250	−	0.0146263i
$849$	6.44452	+	21.9480i	0.221175	+	0.753255i
$850$	−5.33256	+	7.10323i	−0.182905	+	0.243639i
$851$	−5.21191	−	13.6222i	−0.178662	−	0.466964i
$852$	−17.8749	+	5.19558i	−0.612384	+	0.177998i
$853$	−10.0955	−	34.3821i	−0.345663	−	1.17722i	−0.930568	−	0.366118i	$-0.880687\pi$
$853$	−10.0955	−	34.3821i	−0.345663	−	1.17722i	0.584906	−	0.811101i	$-0.301132\pi$
$854$	−0.00554435	−	0.0790360i	−0.000189724	−	0.00270456i
$855$	7.43232	+	11.5649i	0.254180	+	0.395512i
$856$	−6.42988	+	28.9857i	−0.219769	+	0.990712i
$857$	−39.8931	−	25.6378i	−1.36272	−	0.875769i	−0.364266	−	0.931295i	$-0.618680\pi$
$857$	−39.8931	−	25.6378i	−1.36272	−	0.875769i	−0.998457	+	0.0555258i	$0.982317\pi$
$858$	−20.8146	+	11.3288i	−0.710600	+	0.386759i
$859$	4.31449	−	4.97919i	0.147208	−	0.169888i	−0.677356	−	0.735655i	$-0.736875\pi$
$859$	4.31449	−	4.97919i	0.147208	−	0.169888i	0.824565	+	0.565767i	$0.191420\pi$
$860$	7.52041	+	53.3389i	0.256444	+	1.81884i
$861$	−3.86149	−	8.45548i	−0.131599	−	0.288162i
$862$	−6.83346	−	9.15446i	−0.232749	−	0.311802i
$863$	−4.63949	+	15.8007i	−0.157930	+	0.537861i	−0.999999	−	0.00150951i	$-0.999520\pi$
$863$	−4.63949	+	15.8007i	−0.157930	+	0.537861i	0.842069	+	0.539370i	$0.181338\pi$
$864$	1.94065	+	5.31356i	0.0660223	+	0.180771i
$865$	27.1100	+	3.89784i	0.921769	+	0.132530i
$866$	1.05898	+	4.90023i	0.0359855	+	0.166517i
$867$	−4.64242	+	10.1655i	−0.157665	+	0.345238i
$868$	−10.6675	−	3.16391i	−0.362078	−	0.107390i
$869$	−9.21904	+	1.32550i	−0.312734	+	0.0449644i
$870$	1.29831	−	17.8111i	0.0440169	−	0.603853i
$871$	14.4034	+	16.6225i	0.488042	+	0.563230i
$872$	0.500446	−	6.61631i	0.0169473	−	0.224056i
$873$			17.2505i			0.583843i
$874$	−22.3244	−	25.3994i	−0.755135	−	0.859149i
$875$	14.4403			0.488171
$876$	−2.37917	−	3.72437i	−0.0803846	−	0.125835i
$877$	36.1655	−	31.3376i	1.22122	−	1.05820i	0.224739	−	0.974419i	$-0.427847\pi$
$877$	36.1655	−	31.3376i	1.22122	−	1.05820i	0.996485	−	0.0837772i	$-0.0266984\pi$
$878$	1.92286	−	26.3791i	0.0648935	−	0.890252i
$879$	−2.73947	−	19.0535i	−0.0924001	−	0.642657i
$880$	−0.203093	+	37.1986i	−0.00684627	+	1.25396i
$881$	−4.72642	−	2.15848i	−0.159237	−	0.0727211i	0.334202	−	0.942501i	$-0.391533\pi$
$881$	−4.72642	−	2.15848i	−0.159237	−	0.0727211i	−0.493439	+	0.869780i	$0.664260\pi$
$882$	3.08075	−	0.665774i	0.103734	−	0.0224178i
$883$	−3.72807	+	25.9293i	−0.125459	+	0.872590i	0.825748	+	0.564039i	$0.190753\pi$
$883$	−3.72807	+	25.9293i	−0.125459	+	0.872590i	−0.951208	+	0.308551i	$0.900156\pi$
$884$	18.1661	−	15.6544i	0.610992	−	0.526514i
$885$	−24.2259	−	7.11336i	−0.814344	−	0.239113i
$886$	−30.6005	−	40.9940i	−1.02804	−	1.37722i
$887$	−48.7549	+	22.2656i	−1.63703	+	0.747607i	−0.999735	−	0.0230131i	$-0.992674\pi$
$887$	−48.7549	+	22.2656i	−1.63703	+	0.747607i	−0.637295	+	0.770620i	$0.719947\pi$
$888$	−7.53277	−	4.15334i	−0.252783	−	0.139377i
$889$	3.72668	+	3.22919i	0.124989	+	0.108303i
$890$	−22.2714	−	40.9197i	−0.746540	−	1.37163i
$891$	1.82351	−	2.83743i	0.0610898	−	0.0950576i
$892$	14.9884	+	33.0586i	0.501849	+	1.10688i
$893$	−10.8585	+	6.97831i	−0.363365	+	0.233520i
$894$	1.43695	+	20.4841i	0.0480589	+	0.685091i
$895$	46.6078	−	13.6853i	1.55793	−	0.457449i
$896$	5.02214	+	24.1972i	0.167778	+	0.808371i
$897$	−23.7506	+	1.89982i	−0.793010	+	0.0634330i
$898$	−0.877205	−	0.658538i	−0.0292727	−	0.0219757i
$899$	−11.1922	+	3.28633i	−0.373281	+	0.109605i
$900$	2.82583	−	4.37080i	0.0941943	−	0.145693i
$901$	−0.484155	−	0.753360i	−0.0161295	−	0.0250980i
$902$	17.8025	+	9.75245i	0.592757	+	0.324721i
$903$	11.5356	−	17.9498i	0.383881	−	0.597331i
$904$	−1.84386	+	1.82882i	−0.0613258	+	0.0608257i
$905$	31.6041	−	36.4731i	1.05056	−	1.21241i
$906$	−8.45995	−	8.48307i	−0.281063	−	0.281831i
$907$	39.2807	−	17.9389i	1.30429	−	0.595651i	0.362544	−	0.931967i	$-0.381908\pi$
$907$	39.2807	−	17.9389i	1.30429	−	0.595651i	0.941749	+	0.336316i	$0.109181\pi$
$908$	−16.3152	−	0.0445378i	−0.541440	−	0.00147804i
$909$	5.01963	−	17.0953i	0.166490	−	0.567014i
$910$	41.3365	+	9.05131i	1.37029	+	0.300048i
$911$	6.58341	−	45.7886i	0.218118	−	1.51704i	−0.526858	−	0.849953i	$-0.676630\pi$
$911$	6.58341	−	45.7886i	0.218118	−	1.51704i	0.744976	−	0.667091i	$-0.232461\pi$
$912$	−19.7247	−	2.94599i	−0.653150	−	0.0975514i
$913$	−13.7114	+	30.0237i	−0.453780	+	0.993639i
$914$	−49.9883	+	18.5670i	−1.65347	+	0.614142i
$915$	−0.0100643	−	0.0699985i	−0.000332714	−	0.00231408i
$916$	17.5401	+	15.2826i	0.579542	+	0.504952i
$917$	26.3648	+	30.4266i	0.870642	+	1.00477i
$918$	−1.19712	+	3.19627i	−0.0395108	+	0.105493i
$919$	3.77685			0.124587			0.0622934	−	0.998058i	$-0.480159\pi$
$919$	3.77685			0.124587			0.0622934	+	0.998058i	$0.480159\pi$
$920$	−15.3896	+	34.0880i	−0.507381	+	1.12385i
$921$	−6.86713			−0.226280
$922$	4.35514	−	11.6281i	0.143429	−	0.382951i
$923$	−30.2810	−	34.9461i	−0.996711	−	1.15027i
$924$	9.67966	−	11.1095i	0.318438	−	0.365476i
$925$	1.12634	+	7.83384i	0.0370337	+	0.257575i
$926$	19.5760	−	7.27104i	0.643306	−	0.238941i
$927$	4.47380	−	9.79626i	0.146939	−	0.321751i
$928$	18.1940	+	18.4440i	0.597247	+	0.605455i
$929$	−2.63688	+	18.3399i	−0.0865134	+	0.601714i	0.899734	+	0.436439i	$0.143760\pi$
$929$	−2.63688	+	18.3399i	−0.0865134	+	0.601714i	−0.986247	+	0.165275i	$0.947149\pi$
$930$	−9.70156	−	2.12432i	−0.318127	−	0.0696592i
$931$	−3.13063	+	10.6619i	−0.102602	+	0.349431i
$932$	−0.139683	+	51.1693i	−0.00457548	+	1.67611i
$933$	−25.2797	+	11.5448i	−0.827619	+	0.377961i
$934$	−16.9101	−	16.9563i	−0.553315	−	0.554828i
$935$	−14.6979	+	16.9623i	−0.480673	+	0.554726i
$936$	−9.97693	+	9.89556i	−0.326106	+	0.323446i
$937$	−11.8726	+	18.4741i	−0.387861	+	0.603524i	−0.979200	−	0.202900i	$-0.934963\pi$
$937$	−11.8726	+	18.4741i	−0.387861	+	0.603524i	0.591338	+	0.806424i	$0.298600\pi$
$938$	−11.9940	−	6.57051i	−0.391620	−	0.214535i
$939$	−6.76152	−	10.5211i	−0.220654	−	0.343344i
$940$	11.9886	+	7.75091i	0.391024	+	0.252807i
$941$	43.6758	−	12.8244i	1.42379	−	0.418063i	0.523006	−	0.852329i	$-0.324811\pi$
$941$	43.6758	−	12.8244i	1.42379	−	0.418063i	0.900784	+	0.434266i	$0.142992\pi$
$942$	25.4565	+	19.1108i	0.829417	+	0.622662i
$943$	12.3677	+	16.2346i	0.402748	+	0.528670i
$944$	30.9218	−	19.6345i	1.00642	−	0.639050i
$945$	−5.77875	+	1.69679i	−0.187983	+	0.0551967i
$946$	3.26052	+	46.4795i	0.106009	+	1.51118i
$947$	39.4963	−	25.3828i	1.28346	−	0.824829i	0.292148	−	0.956373i	$-0.405630\pi$
$947$	39.4963	−	25.3828i	1.28346	−	0.824829i	0.991310	+	0.131544i	$0.0419935\pi$
$948$	−5.02997	+	2.28053i	−0.163366	+	0.0740683i
$949$	5.93528	−	9.23548i	0.192667	−	0.299796i
$950$	8.77199	+	16.1170i	0.284601	+	0.522903i
$951$	−11.7720	−	10.2005i	−0.381733	−	0.330774i
$952$	−7.19944	+	13.0574i	−0.233335	+	0.423192i
$953$	5.24830	−	2.39682i	0.170009	−	0.0776406i	−0.328593	−	0.944472i	$-0.606574\pi$
$953$	5.24830	−	2.39682i	0.170009	−	0.0776406i	0.498602	+	0.866831i	$0.333847\pi$
$954$	0.313901	+	0.420517i	0.0101629	+	0.0136147i
$955$	−10.3299	−	3.03312i	−0.334267	−	0.0981495i
$956$	35.8378	+	41.5879i	1.15908	+	1.34505i
$957$	2.19837	−	15.2900i	0.0710633	−	0.494256i
$958$	−27.7151	+	5.98945i	−0.895436	+	0.193510i
$959$	45.7097	+	20.8749i	1.47604	+	0.674086i
$960$	6.04090	+	21.2146i	0.194969	+	0.684698i
$961$	−3.48856	−	24.2635i	−0.112534	−	0.782693i
$962$	1.55345	−	21.3113i	0.0500854	−	0.687104i
$963$	7.93319	−	6.87415i	0.255644	−	0.221516i
$964$	32.8101	−	20.9594i	1.05674	−	0.675058i
$965$	−50.5874			−1.62847
$966$	13.4323	−	6.24923i	0.432177	−	0.201066i
$967$			36.6375i			1.17818i	0.808066	+	0.589092i	$0.200514\pi$
$967$			36.6375i			1.17818i	−0.808066	+	0.589092i	$0.799486\pi$
$968$	−0.0802570	+	1.06106i	−0.00257956	+	0.0341038i
$969$	−7.87995	−	9.09395i	−0.253141	−	0.292140i
$970$	−4.89024	+	67.0875i	−0.157016	+	2.15405i
$971$	23.0277	−	3.31088i	0.738994	−	0.106251i	0.237470	−	0.971395i	$-0.423682\pi$
$971$	23.0277	−	3.31088i	0.738994	−	0.106251i	0.501524	+	0.865144i	$0.332773\pi$
$972$	0.568701	−	1.91744i	0.0182411	−	0.0615019i
$973$	−9.16577	+	20.0702i	−0.293841	+	0.643422i
$974$	−3.80430	−	17.6037i	−0.121898	−	0.564059i
$975$	12.7974	+	1.83998i	0.409844	+	0.0589267i
$976$	0.0860026	+	0.0559363i	0.00275288	+	0.00179048i
$977$	2.22761	−	7.58654i	0.0712676	−	0.242715i	−0.916154	−	0.400827i	$-0.868723\pi$
$977$	2.22761	−	7.58654i	0.0712676	−	0.242715i	0.987421	+	0.158112i	$0.0505409\pi$
$978$	−18.6833	−	25.0291i	−0.597426	−	0.800342i
$979$	−16.7404	−	36.6564i	−0.535025	−	1.17154i
$980$	12.1698	−	1.71586i	0.388750	−	0.0548110i
$981$	−1.53624	+	1.77291i	−0.0490483	+	0.0566048i
$982$	−4.87621	+	2.65398i	−0.155606	+	0.0846919i
$983$	−11.8631	−	7.62395i	−0.378374	−	0.243166i	0.337605	−	0.941288i	$-0.390383\pi$
$983$	−11.8631	−	7.62395i	−0.378374	−	0.243166i	−0.715979	+	0.698122i	$0.754019\pi$
$984$	11.7508	+	2.60668i	0.374603	+	0.0830978i
$985$	−19.7147	−	30.6767i	−0.628163	−	0.977440i
$986$	1.09386	+	15.5932i	0.0348355	+	0.496588i
$987$	−1.59314	−	5.42575i	−0.0507103	−	0.172704i
$988$	−13.8276	−	47.5724i	−0.439914	−	1.51348i
$989$	−16.0010	+	44.0292i	−0.508803	+	1.40005i
$990$	7.89600	−	10.5179i	0.250951	−	0.334280i
$991$	−1.41250	−	4.81052i	−0.0448694	−	0.152811i	0.934011	−	0.357244i	$-0.116283\pi$
$991$	−1.41250	−	4.81052i	−0.0448694	−	0.152811i	−0.978881	+	0.204432i	$0.934465\pi$
$992$	11.5927	−	8.55534i	0.368068	−	0.271632i
$993$	22.0433	−	14.1664i	0.699522	−	0.449556i
$994$	25.2156	+	13.8135i	0.799791	+	0.438137i
$995$	−28.2676	−	18.1665i	−0.896145	−	0.575917i
$996$	−2.83822	+	19.3648i	−0.0899325	+	0.613598i
$997$	35.7696	+	30.9945i	1.13283	+	0.981606i	0.999955	−	0.00952626i	$-0.00303235\pi$
$997$	35.7696	+	30.9945i	1.13283	+	0.981606i	0.132879	+	0.991132i	$0.457578\pi$
$998$	4.23680	−	4.22525i	0.134114	−	0.133748i
$999$	1.26337	+	2.76640i	0.0399714	+	0.0875251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.451.3	yes	240
8.3	odd	2	inner	552.2.t.a.451.7	yes	240
23.5	odd	22	inner	552.2.t.a.235.7	yes	240
184.51	even	22	inner	552.2.t.a.235.3	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.235.3	✓	240	184.51	even	22	inner
552.2.t.a.235.7	yes	240	23.5	odd	22	inner
552.2.t.a.451.3	yes	240	1.1	even	1	trivial
552.2.t.a.451.7	yes	240	8.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32437 - 0.496025i) q^{2} +(0.654861 + 0.755750i) q^{3} +(1.50792 + 1.31384i) q^{4} +(-0.392396 - 2.72917i) q^{5} +(-0.492408 - 1.32572i) q^{6} +(-0.907403 + 1.98694i) q^{7} +(-1.34534 - 2.48798i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-1.32437 - 0.496025i) q^{2} +(0.654861 + 0.755750i) q^{3} +(1.50792 + 1.31384i) q^{4} +(-0.392396 - 2.72917i) q^{5} +(-0.492408 - 1.32572i) q^{6} +(-0.907403 + 1.98694i) q^{7} +(-1.34534 - 2.48798i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(-0.834061 + 3.80908i) q^{10} +(-0.950246 + 3.23624i) q^{11} +(-0.00545963 + 1.99999i) q^{12} +(-4.51920 + 2.06385i) q^{13} +(2.18731 - 2.18135i) q^{14} +(1.80561 - 2.08378i) q^{15} +(0.547635 + 3.96233i) q^{16} +(-1.30480 + 2.03030i) q^{17} +(0.679454 - 1.24030i) q^{18} +(2.69557 + 4.19438i) q^{19} +(2.99400 - 4.63092i) q^{20} +(-2.09585 + 0.615397i) q^{21} +(2.86373 - 3.81464i) q^{22} +(4.18970 - 2.33376i) q^{23} +(0.999277 - 2.64602i) q^{24} +(-2.49695 + 0.733171i) q^{25} +(7.00882 - 0.491666i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(-3.97881 + 1.80395i) q^{28} +(-2.47606 + 3.85282i) q^{29} +(-3.42490 + 1.86407i) q^{30} +(1.92486 + 1.66790i) q^{31} +(1.24015 - 5.51924i) q^{32} +(-3.06807 + 1.40114i) q^{33} +(2.73511 - 2.04166i) q^{34} +(5.77875 + 1.69679i) q^{35} +(-1.51507 + 1.30559i) q^{36} +(0.432813 - 3.01028i) q^{37} +(-1.48941 - 6.89199i) q^{38} +(-4.51920 - 2.06385i) q^{39} +(-6.26222 + 4.64795i) q^{40} +(0.605627 + 4.21223i) q^{41} +(3.08093 + 0.224580i) q^{42} +(-7.38230 + 6.39680i) q^{43} +(-5.68480 + 3.63151i) q^{44} +2.75724 q^{45} +(-6.70632 + 1.01257i) q^{46} +2.58881i q^{47} +(-2.63591 + 3.00865i) q^{48} +(1.45949 + 1.68435i) q^{49} +(3.67056 + 0.267560i) q^{50} +(-2.38886 + 0.343466i) q^{51} +(-9.52616 - 2.82540i) q^{52} +(-0.154143 + 0.337526i) q^{53} +(1.38230 - 0.298726i) q^{54} +(9.20513 + 1.32350i) q^{55} +(6.16423 - 0.415511i) q^{56} +(-1.40468 + 4.78391i) q^{57} +(5.19032 - 3.87438i) q^{58} +(-3.80405 - 8.32970i) q^{59} +(5.46047 - 0.769889i) q^{60} +(0.0167960 - 0.0193837i) q^{61} +(-1.72191 - 3.16370i) q^{62} +(-1.83757 - 1.18094i) q^{63} +(-4.38010 + 6.69438i) q^{64} +(7.40592 + 11.5238i) q^{65} +(4.75826 - 0.333790i) q^{66} +(-1.24726 - 4.24779i) q^{67} +(-4.63502 + 1.34723i) q^{68} +(4.50741 + 1.63808i) q^{69} +(-6.81156 - 5.11359i) q^{70} +(2.62218 + 8.93032i) q^{71} +(2.65412 - 0.977574i) q^{72} +(-1.85893 + 1.19466i) q^{73} +(-2.06638 + 3.77204i) q^{74} +(-2.18925 - 1.40694i) q^{75} +(-1.44607 + 9.86634i) q^{76} +(-5.56794 - 4.82465i) q^{77} +(4.96138 + 4.97494i) q^{78} +(1.14713 + 2.51186i) q^{79} +(10.5990 - 3.04939i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(1.28730 - 5.87896i) q^{82} +(9.68626 + 1.39267i) q^{83} +(-3.96890 - 1.82565i) q^{84} +(6.05304 + 2.76433i) q^{85} +(12.9499 - 4.80993i) q^{86} +(-4.53325 + 0.651782i) q^{87} +(9.33011 - 1.98966i) q^{88} +(-9.02948 + 7.82409i) q^{89} +(-3.65161 - 1.36766i) q^{90} -10.8521i q^{91} +(9.38391 + 1.98549i) q^{92} +2.54696i q^{93} +(1.28411 - 3.42854i) q^{94} +(10.3895 - 9.00253i) q^{95} +(4.98329 - 2.67710i) q^{96} +(17.0750 - 2.45501i) q^{97} +(-1.09743 - 2.95464i) q^{98} +(-3.06807 - 1.40114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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