LMFDB - Embedded newform 690.2.w.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	690.37
Dual form			690.2.w.a.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877679 - 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-2.15875 - 0.582912i) q^{5} +(0.841254 + 0.540641i) q^{6} +(0.0886059 + 0.237562i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})$	\(q+(-0.877679 - 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-2.15875 - 0.582912i) q^{5} +(0.841254 + 0.540641i) q^{6} +(0.0886059 + 0.237562i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(1.61533 + 1.54619i) q^{10} +(0.594895 - 2.02602i) q^{11} +(-0.479249 - 0.877679i) q^{12} +(-0.382567 - 0.142690i) q^{13} +(0.0360836 - 0.250967i) q^{14} +(2.11167 + 0.735431i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(-7.97727 + 1.73535i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(3.05348 - 1.96235i) q^{19} +(-0.676733 - 2.13120i) q^{20} +(-0.0714327 - 0.243277i) q^{21} +(-1.49310 + 1.49310i) q^{22} +(2.70000 + 3.96358i) q^{23} +1.00000i q^{24} +(4.32043 + 2.51673i) q^{25} +(0.267387 + 0.308581i) q^{26} +(-0.977147 - 0.212565i) q^{27} +(-0.151946 + 0.202976i) q^{28} +(1.60703 - 2.50059i) q^{29} +(-1.50091 - 1.65749i) q^{30} +(-3.97959 + 4.59270i) q^{31} +(0.800541 - 0.599278i) q^{32} +(-0.737914 + 1.97842i) q^{33} +(7.83314 + 2.30002i) q^{34} +(-0.0528006 - 0.564486i) q^{35} +(0.415415 + 0.909632i) q^{36} +(5.63502 + 7.52751i) q^{37} +(-3.62043 + 0.258938i) q^{38} +(0.371412 + 0.169618i) q^{39} +(-0.427424 + 2.19484i) q^{40} +(1.69304 + 11.7754i) q^{41} +(-0.0538955 + 0.247754i) q^{42} +(-0.646245 + 9.03569i) q^{43} +(2.02602 - 0.594895i) q^{44} +(-2.05382 - 0.884202i) q^{45} +(-0.470191 - 4.77273i) q^{46} +(-2.48616 - 2.48616i) q^{47} +(0.479249 - 0.877679i) q^{48} +(5.24166 - 4.54193i) q^{49} +(-2.58581 - 4.27944i) q^{50} +(8.08074 - 1.16183i) q^{51} +(-0.0867927 - 0.398980i) q^{52} +(7.18696 - 2.68060i) q^{53} +(0.755750 + 0.654861i) q^{54} +(-2.46523 + 4.02692i) q^{55} +(0.230635 - 0.105328i) q^{56} +(-3.18569 + 1.73952i) q^{57} +(-2.60887 + 1.42455i) q^{58} +(3.05706 - 1.39611i) q^{59} +(0.522970 + 2.17405i) q^{60} +(0.0803523 + 0.0696257i) q^{61} +(5.69385 - 2.12370i) q^{62} +(0.0538955 + 0.247754i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(0.742691 + 0.531035i) q^{65} +(1.59581 - 1.38278i) q^{66} +(-6.97786 + 12.7790i) q^{67} +(-5.77270 - 5.77270i) q^{68} +(-2.41036 - 4.14610i) q^{69} +(-0.224188 + 0.520742i) q^{70} +(-7.61707 + 2.23657i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(1.35911 - 6.24771i) q^{73} +(-1.33819 - 9.30732i) q^{74} +(-4.12988 - 2.81853i) q^{75} +(3.30167 + 1.50782i) q^{76} +(0.534017 - 0.0381936i) q^{77} +(-0.244691 - 0.326870i) q^{78} +(6.13266 + 13.4287i) q^{79} +(1.42701 - 1.72152i) q^{80} +(0.959493 + 0.281733i) q^{81} +(4.15738 - 11.1464i) q^{82} +(-1.45447 + 1.08880i) q^{83} +(0.166039 - 0.191619i) q^{84} +(18.2325 + 0.903861i) q^{85} +(4.89754 - 7.62072i) q^{86} +(-1.78133 + 2.37958i) q^{87} +(-2.06330 - 0.448844i) q^{88} +(9.72027 + 11.2178i) q^{89} +(1.37884 + 1.76034i) q^{90} -0.103526i q^{91} +(-1.87465 + 4.41426i) q^{92} +(4.29709 - 4.29709i) q^{93} +(0.990561 + 3.37354i) q^{94} +(-7.73559 + 2.45632i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(-10.3179 - 7.72389i) q^{97} +(-6.77721 + 1.47429i) q^{98} +(0.877173 - 1.92074i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{21}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.877679	−	0.479249i	−0.620613	−	0.338880i
$2$	−0.877679	−	0.479249i	−0.620613	−	0.338880i
$3$	−0.997452	−	0.0713392i	−0.575879	−	0.0411877i
$3$	−0.997452	−	0.0713392i	−0.575879	−	0.0411877i
$4$	0.540641	+	0.841254i	0.270320	+	0.420627i
$5$	−2.15875	−	0.582912i	−0.965424	−	0.260686i
$5$	−2.15875	−	0.582912i	−0.965424	−	0.260686i
$6$	0.841254	+	0.540641i	0.343440	+	0.220716i
$7$	0.0886059	+	0.237562i	0.0334899	+	0.0897899i	0.952618	−	0.304168i	$-0.0983784\pi$
$7$	0.0886059	+	0.237562i	0.0334899	+	0.0897899i	−0.919129	+	0.393958i	$0.871106\pi$
$8$	−0.0713392	−	0.997452i	−0.0252222	−	0.352653i
$9$	0.989821	+	0.142315i	0.329940	+	0.0474383i
$10$	1.61533	+	1.54619i	0.510813	+	0.488948i
$11$	0.594895	−	2.02602i	0.179367	−	0.610869i	−0.819897	−	0.572512i	$-0.805969\pi$
$11$	0.594895	−	2.02602i	0.179367	−	0.610869i	0.999264	−	0.0383579i	$-0.0122127\pi$
$12$	−0.479249	−	0.877679i	−0.138347	−	0.253364i
$13$	−0.382567	−	0.142690i	−0.106105	−	0.0395751i	0.295851	−	0.955234i	$-0.404397\pi$
$13$	−0.382567	−	0.142690i	−0.106105	−	0.0395751i	−0.401956	+	0.915659i	$0.631670\pi$
$14$	0.0360836	−	0.250967i	0.00964376	−	0.0670738i
$15$	2.11167	+	0.735431i	0.545230	+	0.189887i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	−7.97727	+	1.73535i	−1.93477	+	0.420884i	−0.937415	+	0.348214i	$0.886788\pi$
$17$	−7.97727	+	1.73535i	−1.93477	+	0.420884i	−0.997356	+	0.0726700i	$0.976848\pi$
$18$	−0.800541	−	0.599278i	−0.188689	−	0.141251i
$19$	3.05348	−	1.96235i	0.700516	−	0.450194i	−0.141294	−	0.989968i	$-0.545126\pi$
$19$	3.05348	−	1.96235i	0.700516	−	0.450194i	0.841810	+	0.539773i	$0.181490\pi$
$20$	−0.676733	−	2.13120i	−0.151322	−	0.476552i
$21$	−0.0714327	−	0.243277i	−0.0155879	−	0.0530875i
$22$	−1.49310	+	1.49310i	−0.318329	+	0.318329i
$23$	2.70000	+	3.96358i	0.562989	+	0.826464i
$23$	2.70000	+	3.96358i	0.562989	+	0.826464i
$24$			1.00000i			0.204124i
$25$	4.32043	+	2.51673i	0.864085	+	0.503346i
$26$	0.267387	+	0.308581i	0.0524388	+	0.0605176i
$27$	−0.977147	−	0.212565i	−0.188052	−	0.0409082i
$28$	−0.151946	+	0.202976i	−0.0287150	+	0.0383588i
$29$	1.60703	−	2.50059i	0.298419	−	0.464348i	−0.659371	−	0.751817i	$-0.729177\pi$
$29$	1.60703	−	2.50059i	0.298419	−	0.464348i	0.957790	+	0.287469i	$0.0928138\pi$
$30$	−1.50091	−	1.65749i	−0.274028	−	0.302614i
$31$	−3.97959	+	4.59270i	−0.714756	+	0.824873i	−0.990666	−	0.136311i	$-0.956475\pi$
$31$	−3.97959	+	4.59270i	−0.714756	+	0.824873i	0.275910	+	0.961184i	$0.411021\pi$
$32$	0.800541	−	0.599278i	0.141517	−	0.105938i
$33$	−0.737914	+	1.97842i	−0.128454	+	0.344399i
$34$	7.83314	+	2.30002i	1.34337	+	0.394450i
$35$	−0.0528006	−	0.564486i	−0.00892493	−	0.0954156i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	5.63502	+	7.52751i	0.926392	+	1.23752i	0.971138	+	0.238517i	$0.0766612\pi$
$37$	5.63502	+	7.52751i	0.926392	+	1.23752i	−0.0447460	+	0.998998i	$0.514248\pi$
$38$	−3.62043	+	0.258938i	−0.587311	+	0.0420053i
$39$	0.371412	+	0.169618i	0.0594736	+	0.0271607i
$40$	−0.427424	+	2.19484i	−0.0675816	+	0.347034i
$41$	1.69304	+	11.7754i	0.264409	+	1.83900i	0.498625	+	0.866818i	$0.333839\pi$
$41$	1.69304	+	11.7754i	0.264409	+	1.83900i	−0.234216	+	0.972185i	$0.575252\pi$
$42$	−0.0538955	+	0.247754i	−0.00831625	+	0.0382292i
$43$	−0.646245	+	9.03569i	−0.0985515	+	1.37793i	0.672000	+	0.740552i	$0.265436\pi$
$43$	−0.646245	+	9.03569i	−0.0985515	+	1.37793i	−0.770551	+	0.637378i	$0.780019\pi$
$44$	2.02602	−	0.594895i	0.305435	−	0.0896837i
$45$	−2.05382	−	0.884202i	−0.306166	−	0.131809i
$46$	−0.470191	−	4.77273i	−0.0693258	−	0.703700i
$47$	−2.48616	−	2.48616i	−0.362644	−	0.362644i	0.502142	−	0.864785i	$-0.332546\pi$
$47$	−2.48616	−	2.48616i	−0.362644	−	0.362644i	−0.864785	+	0.502142i	$0.832546\pi$
$48$	0.479249	−	0.877679i	0.0691736	−	0.126682i
$49$	5.24166	−	4.54193i	0.748809	−	0.648847i
$50$	−2.58581	−	4.27944i	−0.365688	−	0.605204i
$51$	8.08074	−	1.16183i	1.13153	−	0.162689i
$52$	−0.0867927	−	0.398980i	−0.0120360	−	0.0553285i
$53$	7.18696	−	2.68060i	0.987205	−	0.368209i	0.196566	−	0.980491i	$-0.437021\pi$
$53$	7.18696	−	2.68060i	0.987205	−	0.368209i	0.790639	+	0.612282i	$0.209748\pi$
$54$	0.755750	+	0.654861i	0.102844	+	0.0891153i
$55$	−2.46523	+	4.02692i	−0.332411	+	0.542989i
$56$	0.230635	−	0.105328i	0.0308199	−	0.0140750i
$57$	−3.18569	+	1.73952i	−0.421955	+	0.230405i
$58$	−2.60887	+	1.42455i	−0.342561	+	0.187052i
$59$	3.05706	−	1.39611i	0.397996	−	0.181759i	−0.206355	−	0.978477i	$-0.566160\pi$
$59$	3.05706	−	1.39611i	0.397996	−	0.181759i	0.604350	+	0.796719i	$0.293433\pi$
$60$	0.522970	+	2.17405i	0.0675151	+	0.280669i
$61$	0.0803523	+	0.0696257i	0.0102881	+	0.00891466i	0.659990	−	0.751275i	$-0.270561\pi$
$61$	0.0803523	+	0.0696257i	0.0102881	+	0.00891466i	−0.649702	+	0.760189i	$0.725106\pi$
$62$	5.69385	−	2.12370i	0.723120	−	0.269710i
$63$	0.0538955	+	0.247754i	0.00679019	+	0.0312140i
$64$	−0.989821	+	0.142315i	−0.123728	+	0.0177894i
$65$	0.742691	+	0.531035i	0.0921195	+	0.0658668i
$66$	1.59581	−	1.38278i	0.196430	−	0.170208i
$67$	−6.97786	+	12.7790i	−0.852482	+	1.56120i	−0.0250166	+	0.999687i	$0.507964\pi$
$67$	−6.97786	+	12.7790i	−0.852482	+	1.56120i	−0.827465	+	0.561517i	$0.810218\pi$
$68$	−5.77270	−	5.77270i	−0.700043	−	0.700043i
$69$	−2.41036	−	4.14610i	−0.290174	−	0.499132i
$70$	−0.224188	+	0.520742i	−0.0267955	+	0.0622406i
$71$	−7.61707	+	2.23657i	−0.903980	+	0.265432i	−0.700505	−	0.713648i	$-0.747042\pi$
$71$	−7.61707	+	2.23657i	−0.903980	+	0.265432i	−0.203475	+	0.979080i	$0.565224\pi$
$72$	0.0713392	−	0.997452i	0.00840740	−	0.117551i
$73$	1.35911	−	6.24771i	0.159071	−	0.731239i	−0.826631	−	0.562744i	$-0.809746\pi$
$73$	1.35911	−	6.24771i	0.159071	−	0.731239i	0.985703	−	0.168495i	$-0.0538907\pi$
$74$	−1.33819	−	9.30732i	−0.155561	−	1.08195i
$75$	−4.12988	−	2.81853i	−0.476877	−	0.325456i
$76$	3.30167	+	1.50782i	0.378728	+	0.172959i
$77$	0.534017	−	0.0381936i	0.0608569	−	0.00435257i
$78$	−0.244691	−	0.326870i	−0.0277059	−	0.0370107i
$79$	6.13266	+	13.4287i	0.689978	+	1.51084i	0.851714	+	0.524008i	$0.175564\pi$
$79$	6.13266	+	13.4287i	0.689978	+	1.51084i	−0.161735	+	0.986834i	$0.551709\pi$
$80$	1.42701	−	1.72152i	0.159545	−	0.192472i
$81$	0.959493	+	0.281733i	0.106610	+	0.0313036i
$82$	4.15738	−	11.1464i	0.459106	−	1.23091i
$83$	−1.45447	+	1.08880i	−0.159649	+	0.119512i	−0.676115	−	0.736796i	$-0.736338\pi$
$83$	−1.45447	+	1.08880i	−0.159649	+	0.119512i	0.516467	+	0.856307i	$0.327247\pi$
$84$	0.166039	−	0.191619i	0.0181163	−	0.0209073i
$85$	18.2325	+	0.903861i	1.97759	+	0.0980375i
$86$	4.89754	−	7.62072i	0.528115	−	0.821764i
$87$	−1.78133	+	2.37958i	−0.190979	+	0.255117i
$88$	−2.06330	−	0.448844i	−0.219949	−	0.0478469i
$89$	9.72027	+	11.2178i	1.03035	+	1.18908i	0.981733	+	0.190265i	$0.0609348\pi$
$89$	9.72027	+	11.2178i	1.03035	+	1.18908i	0.0486133	+	0.998818i	$0.484520\pi$
$90$	1.37884	+	1.76034i	0.145343	+	0.185556i
$91$		−	0.103526i		−	0.0108525i
$92$	−1.87465	+	4.41426i	−0.195446	+	0.460218i
$93$	4.29709	−	4.29709i	0.445588	−	0.445588i
$94$	0.990561	+	3.37354i	0.102169	+	0.347954i
$95$	−7.73559	+	2.45632i	−0.793654	+	0.252013i
$96$	−0.841254	+	0.540641i	−0.0858601	+	0.0551789i
$97$	−10.3179	−	7.72389i	−1.04762	−	0.784242i	−0.0706294	−	0.997503i	$-0.522501\pi$
$97$	−10.3179	−	7.72389i	−1.04762	−	0.784242i	−0.976995	+	0.213261i	$0.931592\pi$
$98$	−6.77721	+	1.47429i	−0.684602	+	0.148926i
$99$	0.877173	−	1.92074i	0.0881592	−	0.193042i
$100$	0.218593	+	4.99522i	0.0218593	+	0.499522i
$101$	0.529176	−	3.68050i	0.0526549	−	0.366223i	−0.946409	−	0.322970i	$-0.895319\pi$
$101$	0.529176	−	3.68050i	0.0526549	−	0.366223i	0.999064	−	0.0432531i	$-0.0137722\pi$
$102$	−7.64910	−	2.85297i	−0.757374	−	0.282486i
$103$	−6.31658	−	11.5680i	−0.622391	−	1.13982i	−0.978669	−	0.205444i	$-0.934136\pi$
$103$	−6.31658	−	11.5680i	−0.622391	−	1.13982i	0.356278	−	0.934380i	$-0.384046\pi$
$104$	−0.115034	+	0.391771i	−0.0112801	+	0.0384163i
$105$	0.0123961	+	0.566815i	0.00120973	+	0.0553155i
$106$	−7.59252	−	1.09164i	−0.737451	−	0.106029i
$107$	1.38753	+	19.4002i	0.134137	+	1.87549i	0.406994	+	0.913431i	$0.366577\pi$
$107$	1.38753	+	19.4002i	0.134137	+	1.87549i	−0.272856	+	0.962055i	$0.587968\pi$
$108$	−0.349464	−	0.936950i	−0.0336272	−	0.0901580i
$109$	8.34335	+	5.36195i	0.799148	+	0.513581i	0.875338	−	0.483512i	$-0.160639\pi$
$109$	8.34335	+	5.36195i	0.799148	+	0.513581i	−0.0761896	+	0.997093i	$0.524275\pi$
$110$	4.09357	−	2.35288i	0.390307	−	0.224338i
$111$	−5.08366	−	7.91033i	−0.482520	−	0.750815i
$112$	−0.252902	−	0.0180879i	−0.0238970	−	0.00170915i
$113$	−7.39815	−	4.03970i	−0.695960	−	0.380023i	0.0919919	−	0.995760i	$-0.470677\pi$
$113$	−7.39815	−	4.03970i	−0.695960	−	0.380023i	−0.787952	+	0.615737i	$0.788858\pi$
$114$	3.62968			0.339951
$115$	−3.51821	−	10.1303i	−0.328075	−	0.944652i
$116$	2.97246			0.275986
$117$	−0.358366	−	0.195682i	−0.0331309	−	0.0180909i
$118$	−3.35221	−	0.239755i	−0.308596	−	0.0220712i
$119$	−1.11908	−	1.74133i	−0.102586	−	0.159627i
$120$	0.582912	−	2.15875i	0.0532124	−	0.197066i
$121$	5.50291	+	3.53651i	0.500265	+	0.321501i
$122$	−0.0371555	−	0.0996178i	−0.00336390	−	0.00901897i
$123$	−0.848683	−	11.8661i	−0.0765232	−	1.06993i
$124$	−6.01515	−	0.864848i	−0.540177	−	0.0776657i
$125$	−7.85970	−	7.95142i	−0.702993	−	0.711197i
$126$	0.0714327	−	0.243277i	0.00636373	−	0.0216729i
$127$	−3.46160	−	6.33944i	−0.307167	−	0.562535i	0.677806	−	0.735241i	$-0.262931\pi$
$127$	−3.46160	−	6.33944i	−0.307167	−	0.562535i	−0.984973	+	0.172706i	$0.944749\pi$
$128$	0.936950	+	0.349464i	0.0828154	+	0.0308886i
$129$	1.28920	−	8.96657i	0.113508	−	0.789462i
$130$	−0.397346	−	0.822012i	−0.0348496	−	0.0720953i
$131$	0.674741	−	1.47748i	0.0589524	−	0.129088i	−0.877863	−	0.478912i	$-0.841031\pi$
$131$	0.674741	−	1.47748i	0.0589524	−	0.129088i	0.936815	+	0.349824i	$0.113759\pi$
$132$	−2.06330	+	0.448844i	−0.179587	+	0.0390668i
$133$	0.736736	+	0.551514i	0.0638831	+	0.0478223i
$134$	12.2487	−	7.87173i	1.05812	−	0.680014i
$135$	1.98551	+	1.02847i	0.170886	+	0.0885163i
$136$	2.30002	+	7.83314i	0.197225	+	0.671686i
$137$	4.74965	−	4.74965i	0.405790	−	0.405790i	−0.474478	−	0.880268i	$-0.657363\pi$
$137$	4.74965	−	4.74965i	0.405790	−	0.405790i	0.880268	+	0.474478i	$0.157363\pi$
$138$	0.128510	+	4.79411i	0.0109395	+	0.408102i
$139$		−	1.10890i		−	0.0940555i	−0.998894	−	0.0470277i	$-0.985025\pi$
$139$		−	1.10890i		−	0.0940555i	0.998894	−	0.0470277i	$-0.0149749\pi$
$140$	0.446330	−	0.349603i	0.0377218	−	0.0295468i
$141$	2.30246	+	2.65719i	0.193903	+	0.223775i
$142$	7.75722	+	1.68748i	0.650971	+	0.141610i
$143$	−0.516680	+	0.690204i	−0.0432070	+	0.0577178i
$144$	−0.540641	+	0.841254i	−0.0450534	+	0.0701045i
$145$	−4.92681	+	4.46140i	−0.409150	+	0.370499i
$146$	−4.18707	+	4.83213i	−0.346524	+	0.399910i
$147$	−5.55232	+	4.15642i	−0.457948	+	0.342816i
$148$	−3.28602	+	8.81016i	−0.270109	+	0.724191i
$149$	−13.4814	−	3.95849i	−1.10444	−	0.324292i	−0.321824	−	0.946800i	$-0.604296\pi$
$149$	−13.4814	−	3.95849i	−1.10444	−	0.324292i	−0.782614	+	0.622507i	$0.786114\pi$
$150$	2.27393	+	4.45300i	0.185665	+	0.363586i
$151$	−4.65696	−	10.1973i	−0.378978	−	0.829845i	−0.998976	−	0.0452423i	$-0.985594\pi$
$151$	−4.65696	−	10.1973i	−0.378978	−	0.829845i	0.619998	−	0.784603i	$-0.287133\pi$
$152$	−2.17519	−	2.90571i	−0.176431	−	0.235684i
$153$	−8.14303	+	0.582401i	−0.658325	+	0.0470844i
$154$	−0.487000	−	0.222405i	−0.0392436	−	0.0179219i
$155$	11.2681	−	7.59474i	0.905076	−	0.610024i
$156$	0.0581087	+	0.404155i	0.00465242	+	0.0323583i
$157$	0.459072	−	2.11032i	0.0366380	−	0.168422i	−0.955192	−	0.295985i	$-0.904352\pi$
$157$	0.459072	−	2.11032i	0.0366380	−	0.168422i	0.991830	+	0.127563i	$0.0407156\pi$
$158$	1.05316	−	14.7251i	0.0837850	−	1.17147i
$159$	−7.35988	+	2.16106i	−0.583677	+	0.171383i
$160$	−2.07750	+	0.827047i	−0.164241	+	0.0653838i
$161$	−0.702359	+	0.992614i	−0.0553537	+	0.0782289i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	0.0317034	−	0.0580604i	0.00248320	−	0.00454764i	−0.876434	−	0.481521i	$-0.840084\pi$
$163$	0.0317034	−	0.0580604i	0.00248320	−	0.00454764i	0.878918	+	0.476974i	$0.158266\pi$
$164$	−8.99074	+	7.79052i	−0.702059	+	0.608337i
$165$	2.74622	−	3.84079i	0.213793	−	0.299005i
$166$	1.79837	−	0.258566i	0.139580	−	0.0200686i
$167$	−0.170189	−	0.782348i	−0.0131697	−	0.0605399i	0.970093	−	0.242733i	$-0.0780440\pi$
$167$	−0.170189	−	0.782348i	−0.0131697	−	0.0605399i	−0.983263	+	0.182193i	$0.941680\pi$
$168$	−0.237562	+	0.0886059i	−0.0183283	+	0.00683609i
$169$	−9.69875	−	8.40401i	−0.746058	−	0.646463i
$170$	−15.5691	−	9.53121i	−1.19410	−	0.731010i
$171$	3.30167	−	1.50782i	0.252485	−	0.115306i
$172$	−7.95069	+	4.34141i	−0.606235	+	0.331029i
$173$	0.152275	−	0.0831486i	0.0115773	−	0.00632167i	−0.473450	−	0.880821i	$-0.656992\pi$
$173$	0.152275	−	0.0831486i	0.0115773	−	0.00632167i	0.485027	+	0.874499i	$0.338810\pi$
$174$	2.70384	−	1.23480i	0.204978	−	0.0936103i
$175$	−0.215063	+	1.24936i	−0.0162572	+	0.0944431i
$176$	1.59581	+	1.38278i	0.120289	+	0.104231i
$177$	−3.14887	+	1.17447i	−0.236684	+	0.0882785i
$178$	−3.15516	−	14.5040i	−0.236489	−	1.08712i
$179$	4.32502	−	0.621844i	0.323267	−	0.0464788i	0.0212291	−	0.999775i	$-0.493242\pi$
$179$	4.32502	−	0.621844i	0.323267	−	0.0464788i	0.302038	+	0.953296i	$0.402333\pi$
$180$	−0.366542	−	2.20582i	−0.0273205	−	0.164412i
$181$	−8.61336	+	7.46352i	−0.640226	+	0.554759i	−0.913327	−	0.407226i	$-0.866496\pi$
$181$	−8.61336	+	7.46352i	−0.640226	+	0.554759i	0.273101	+	0.961985i	$0.411951\pi$
$182$	−0.0496149	+	0.0908629i	−0.00367770	+	0.00673520i
$183$	−0.0751806	−	0.0751806i	−0.00555751	−	0.00555751i
$184$	3.76087	−	2.97588i	0.277255	−	0.219385i
$185$	−7.77674	−	19.5348i	−0.571758	−	1.43622i
$186$	−5.83085	+	1.71209i	−0.427538	+	0.125537i
$187$	−1.22977	+	17.1945i	−0.0899300	+	1.25739i
$188$	0.747371	−	3.43561i	0.0545077	−	0.250568i
$189$	−0.0360836	−	0.250967i	−0.00262470	−	0.0182552i
$190$	7.96655	+	1.55141i	0.577954	+	0.112551i
$191$	−21.8098	−	9.96021i	−1.57810	−	0.720696i	−0.582366	−	0.812927i	$-0.697873\pi$
$191$	−21.8098	−	9.96021i	−1.57810	−	0.720696i	−0.995738	+	0.0922309i	$0.970600\pi$
$192$	0.997452	−	0.0713392i	0.0719849	−	0.00514846i
$193$	0.796788	+	1.06438i	0.0573540	+	0.0766160i	0.828301	−	0.560283i	$-0.189308\pi$
$193$	0.796788	+	1.06438i	0.0573540	+	0.0766160i	−0.770947	+	0.636899i	$0.780217\pi$
$194$	5.35414	+	11.7239i	0.384405	+	0.841730i
$195$	−0.702915	−	0.582665i	−0.0503368	−	0.0417255i
$196$	6.65477	+	1.95402i	0.475341	+	0.139573i
$197$	−4.12353	+	11.0556i	−0.293789	+	0.787679i	0.703262	+	0.710931i	$0.251726\pi$
$197$	−4.12353	+	11.0556i	−0.293789	+	0.787679i	−0.997051	+	0.0767476i	$0.975546\pi$
$198$	−1.69039	+	1.26541i	−0.120131	+	0.0899287i
$199$	−11.3806	+	13.1339i	−0.806749	+	0.931038i	−0.998731	−	0.0503601i	$-0.983963\pi$
$199$	−11.3806	+	13.1339i	−0.806749	+	0.931038i	0.191982	+	0.981398i	$0.438509\pi$
$200$	2.20210	−	4.48896i	0.155712	−	0.317417i
$201$	7.87173	−	12.2487i	0.555229	−	0.863953i
$202$	−2.22832	+	2.97669i	−0.156784	+	0.209439i
$203$	0.736438	+	0.160202i	0.0516878	+	0.0112440i
$204$	5.34618	+	6.16982i	0.374307	+	0.431973i
$205$	3.20915	−	26.4070i	0.224137	−	1.84434i
$206$			13.1802i			0.918306i
$207$	2.10844	+	4.30749i	0.146547	+	0.299391i
$208$	0.288719	−	0.288719i	0.0200191	−	0.0200191i
$209$	−2.15928	−	7.35382i	−0.149360	−	0.508674i
$210$	0.260766	−	0.503422i	0.0179945	−	0.0347394i
$211$	−3.24223	+	2.08365i	−0.223204	+	0.143445i	−0.647464	−	0.762096i	$-0.724171\pi$
$211$	−3.24223	+	2.08365i	−0.223204	+	0.143445i	0.424260	+	0.905540i	$0.360534\pi$
$212$	6.14063	+	4.59682i	0.421740	+	0.315711i
$213$	7.75722	−	1.68748i	0.531516	−	0.115624i
$214$	8.07971	−	17.6921i	0.552318	−	1.20941i
$215$	6.66210	−	19.1291i	0.454351	−	1.30459i
$216$	−0.142315	+	0.989821i	−0.00968330	+	0.0673488i
$217$	−1.44366	−	0.538459i	−0.0980023	−	0.0365530i
$218$	−4.75308	−	8.70461i	−0.321919	−	0.589551i
$219$	−1.80135	+	6.13483i	−0.121724	+	0.414554i
$220$	−4.72046	+	0.103235i	−0.318253	+	0.00696011i
$221$	3.29945	+	0.474390i	0.221945	+	0.0319109i
$222$	0.670804	+	9.37907i	0.0450214	+	0.629482i
$223$	−5.66409	−	15.1860i	−0.379296	−	1.01693i	−0.976628	−	0.214937i	$-0.931045\pi$
$223$	−5.66409	−	15.1860i	−0.379296	−	1.01693i	0.597332	−	0.801994i	$-0.296227\pi$
$224$	0.213298	+	0.137078i	0.0142516	+	0.00915893i
$225$	3.91828	+	3.10597i	0.261219	+	0.207065i
$226$	4.55718	+	7.09112i	0.303139	+	0.471694i
$227$	20.1384	+	1.44033i	1.33664	+	0.0955981i	0.721276	−	0.692648i	$-0.243556\pi$
$227$	20.1384	+	1.44033i	1.33664	+	0.0955981i	0.615360	+	0.788246i	$0.289011\pi$
$228$	−3.18569	−	1.73952i	−0.210978	−	0.115203i
$229$	3.15741			0.208648			0.104324	−	0.994543i	$-0.466732\pi$
$229$	3.15741			0.208648			0.104324	+	0.994543i	$0.466732\pi$
$230$	−1.76706	+	10.5772i	−0.116516	+	0.697441i
$231$	−0.535381			−0.0352255
$232$	−2.60887	−	1.42455i	−0.171280	−	0.0935262i
$233$	23.2549	+	1.66323i	1.52348	+	0.108962i	0.807796	−	0.589462i	$-0.200660\pi$
$233$	23.2549	+	1.66323i	1.52348	+	0.108962i	0.715685	+	0.698423i	$0.246115\pi$
$234$	0.220749	+	0.343493i	0.0144308	+	0.0224548i
$235$	3.91779	+	6.81622i	0.255568	+	0.444641i
$236$	2.82726	+	1.81697i	0.184039	+	0.118275i
$237$	−5.15905	−	13.8319i	−0.335116	−	0.898481i
$238$	0.147667	+	2.06465i	0.00957181	+	0.133831i
$239$	−8.14124	−	1.17053i	−0.526613	−	0.0757156i	−0.126120	−	0.992015i	$-0.540252\pi$
$239$	−8.14124	−	1.17053i	−0.526613	−	0.0757156i	−0.400494	+	0.916300i	$0.631161\pi$
$240$	−1.54619	+	1.61533i	−0.0998061	+	0.104269i
$241$	3.39311	−	11.5559i	0.218569	−	0.744378i	−0.775081	−	0.631862i	$-0.782291\pi$
$241$	3.39311	−	11.5559i	0.218569	−	0.744378i	0.993650	−	0.112516i	$-0.0358910\pi$
$242$	−3.13492	−	5.74118i	−0.201520	−	0.369057i
$243$	−0.936950	−	0.349464i	−0.0601054	−	0.0224181i
$244$	−0.0151311	+	0.105239i	−0.000968670	+	0.00673725i
$245$	−13.9630	+	6.74947i	−0.892063	+	0.431208i
$246$	−4.94196	+	10.8214i	−0.315088	+	0.689947i
$247$	−1.44817	+	0.315030i	−0.0921447	+	0.0200448i
$248$	4.86490	+	3.64182i	0.308921	+	0.231256i
$249$	1.52844	−	0.982268i	0.0968609	−	0.0622487i
$250$	3.08758	+	10.7455i	0.195276	+	0.679608i
$251$	7.79498	+	26.5473i	0.492015	+	1.67565i	0.713637	+	0.700516i	$0.247047\pi$
$251$	7.79498	+	26.5473i	0.492015	+	1.67565i	−0.221622	+	0.975133i	$0.571135\pi$
$252$	−0.179285	+	0.179285i	−0.0112939	+	0.0112939i
$253$	9.63654	−	3.11235i	0.605844	−	0.195672i
$254$			7.22296i			0.453209i
$255$	−18.1216	−	2.20225i	−1.13482	−	0.137910i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	10.8460	+	2.35940i	0.676555	+	0.147176i	0.537699	−	0.843137i	$-0.319294\pi$
$257$	10.8460	+	2.35940i	0.676555	+	0.147176i	0.138856	+	0.990313i	$0.455657\pi$
$258$	−5.42872	+	7.25192i	−0.337977	+	0.451485i
$259$	−1.28895	+	2.00565i	−0.0800915	+	0.124625i
$260$	−0.0452062	+	0.911891i	−0.00280357	+	0.0565531i
$261$	1.94655	−	2.24644i	0.120488	−	0.139051i
$262$	−1.30029	+	0.973382i	−0.0803319	+	0.0601357i
$263$	−9.81307	+	26.3098i	−0.605100	+	1.62233i	0.166366	+	0.986064i	$0.446797\pi$
$263$	−9.81307	+	26.3098i	−0.605100	+	1.62233i	−0.771466	+	0.636271i	$0.780476\pi$
$264$	2.02602	+	0.594895i	0.124693	+	0.0366132i
$265$	−17.0774	+	1.59738i	−1.04906	+	0.0981262i
$266$	−0.382305	−	0.837132i	−0.0234406	−	0.0513278i
$267$	−8.89523	−	11.8826i	−0.544379	−	0.727206i
$268$	−14.5229	+	1.03870i	−0.887127	+	0.0634486i
$269$	10.4022	+	4.75051i	0.634231	+	0.289644i	0.706469	−	0.707744i	$-0.250287\pi$
$269$	10.4022	+	4.75051i	0.634231	+	0.289644i	−0.0722382	+	0.997387i	$0.523014\pi$
$270$	−1.24975	−	1.85422i	−0.0760574	−	0.112844i
$271$	1.93386	+	13.4503i	0.117474	+	0.817047i	0.960322	+	0.278895i	$0.0899683\pi$
$271$	1.93386	+	13.4503i	0.117474	+	0.817047i	−0.842848	+	0.538152i	$0.819123\pi$
$272$	1.73535	−	7.97727i	0.105221	−	0.483693i
$273$	−0.00738548	+	0.103263i	−0.000446990	+	0.00624973i
$274$	−6.44493	+	1.89240i	−0.389352	+	0.114324i
$275$	7.66915	−	7.25610i	0.462467	−	0.437559i
$276$	2.18478	−	4.26928i	0.131508	−	0.256980i
$277$	8.64431	+	8.64431i	0.519387	+	0.519387i	0.917386	−	0.397999i	$-0.130295\pi$
$277$	8.64431	+	8.64431i	0.519387	+	0.519387i	−0.397999	+	0.917386i	$0.630295\pi$
$278$	−0.531438	+	0.973256i	−0.0318735	+	0.0583720i
$279$	−4.59270	+	3.97959i	−0.274958	+	0.238252i
$280$	−0.559281	+	0.0929361i	−0.0334235	+	0.00555399i
$281$	−2.27478	+	0.327063i	−0.135702	+	0.0195110i	−0.209831	−	0.977738i	$-0.567291\pi$
$281$	−2.27478	+	0.327063i	−0.135702	+	0.0195110i	0.0741292	+	0.997249i	$0.476382\pi$
$282$	−0.747371	−	3.43561i	−0.0445053	−	0.204588i
$283$	18.4459	−	6.87998i	1.09650	−	0.408972i	0.264857	−	0.964288i	$-0.414675\pi$
$283$	18.4459	−	6.87998i	1.09650	−	0.408972i	0.831640	+	0.555315i	$0.187402\pi$
$284$	−5.99962	−	5.19870i	−0.356012	−	0.308486i
$285$	7.89111	−	1.89821i	0.467429	−	0.112440i
$286$	0.784259	−	0.358159i	0.0463742	−	0.0211784i
$287$	−2.64736	+	1.44557i	−0.156269	+	0.0853292i
$288$	0.877679	−	0.479249i	0.0517177	−	0.0282400i
$289$	45.1616	−	20.6246i	2.65656	−	1.21321i
$290$	6.46228	−	1.55451i	0.379478	−	0.0912838i
$291$	9.74060	+	8.44028i	0.571004	+	0.494778i
$292$	5.99069	−	2.23441i	0.350579	−	0.130759i
$293$	4.99320	+	22.9534i	0.291706	+	1.34095i	0.856683	+	0.515844i	$0.172521\pi$
$293$	4.99320	+	22.9534i	0.291706	+	1.34095i	−0.564977	+	0.825107i	$0.691115\pi$
$294$	6.86512	−	0.987055i	0.400382	−	0.0575662i
$295$	−7.41326	+	1.23186i	−0.431616	+	0.0717219i
$296$	7.10633	−	6.15767i	0.413047	−	0.357908i
$297$	−1.01196	+	1.85327i	−0.0587200	+	0.107538i
$298$	9.93522	+	9.93522i	0.575532	+	0.575532i
$299$	−0.467367	−	1.90160i	−0.0270285	−	0.109972i
$300$	0.138319	−	4.99809i	0.00798587	−	0.288565i
$301$	−2.20379	+	0.647092i	−0.127025	+	0.0372978i
$302$	−0.799739	+	11.1818i	−0.0460198	+	0.643441i
$303$	−0.790391	+	3.63337i	−0.0454068	+	0.208732i
$304$	0.516557	+	3.59273i	0.0296266	+	0.206057i
$305$	−0.132875	−	0.197143i	−0.00760841	−	0.0112884i
$306$	7.42609	+	3.39138i	0.424521	+	0.193872i
$307$	−10.6519	+	0.761836i	−0.607934	+	0.0434803i	−0.371913	−	0.928268i	$-0.621298\pi$
$307$	−10.6519	+	0.761836i	−0.607934	+	0.0434803i	−0.236021	+	0.971748i	$0.575843\pi$
$308$	0.320842	+	0.428595i	0.0182817	+	0.0244214i
$309$	5.47524	+	11.9891i	0.311475	+	0.682036i
$310$	−13.5295	+	1.26552i	−0.768427	+	0.0718766i
$311$	−9.66958	−	2.83924i	−0.548311	−	0.160999i	−0.00416856	−	0.999991i	$-0.501327\pi$
$311$	−9.66958	−	2.83924i	−0.548311	−	0.160999i	−0.544143	+	0.838993i	$0.683145\pi$
$312$	0.142690	−	0.382567i	0.00807823	−	0.0216586i
$313$	15.4665	−	11.5781i	0.874220	−	0.654433i	−0.0649485	−	0.997889i	$-0.520688\pi$
$313$	15.4665	−	11.5781i	0.874220	−	0.654433i	0.939169	+	0.343455i	$0.111597\pi$
$314$	−1.41429	+	1.63217i	−0.0798129	+	0.0921089i
$315$	0.0280716	−	0.566255i	0.00158166	−	0.0319049i
$316$	−7.98134	+	12.4192i	−0.448985	+	0.698635i
$317$	11.0333	−	14.7387i	0.619690	−	0.827809i	−0.375392	−	0.926866i	$-0.622492\pi$
$317$	11.0333	−	14.7387i	0.619690	−	0.827809i	0.995082	+	0.0990573i	$0.0315827\pi$
$318$	7.49530	+	1.63050i	0.420316	+	0.0914341i
$319$	−4.11025	−	4.74348i	−0.230130	−	0.265584i
$320$	2.21974	+	0.269757i	0.124087	+	0.0150799i
$321$		−	19.4497i		−	1.08558i
$322$	1.09216	−	0.534591i	0.0608634	−	0.0297916i
$323$	−20.9531	+	20.9531i	−1.16586	+	1.16586i
$324$	0.281733	+	0.959493i	0.0156518	+	0.0533052i
$325$	−1.29374	−	1.57930i	−0.0717637	−	0.0876037i
$326$	−0.0556507	+	0.0357646i	−0.00308221	+	0.00198082i
$327$	−7.93958	−	5.94349i	−0.439060	−	0.328676i
$328$	11.6246	−	2.52877i	0.641860	−	0.139628i
$329$	0.370328	−	0.810905i	0.0204168	−	0.0447066i
$330$	−4.25099	+	2.05486i	−0.234010	+	0.113116i
$331$	−1.08146	+	7.52169i	−0.0594422	+	0.413429i	0.938275	+	0.345891i	$0.112423\pi$
$331$	−1.08146	+	7.52169i	−0.0594422	+	0.413429i	−0.997717	+	0.0675379i	$0.978486\pi$
$332$	−1.70231	−	0.634927i	−0.0934261	−	0.0348461i
$333$	4.50639	+	8.25284i	0.246949	+	0.452253i
$334$	−0.225568	+	0.768213i	−0.0123425	+	0.0420348i
$335$	22.5125	−	23.5192i	1.22999	−	1.28499i
$336$	0.250967	+	0.0360836i	0.0136914	+	0.00196852i
$337$	−0.660640	−	9.23696i	−0.0359874	−	0.503169i	−0.983196	−	0.182552i	$-0.941564\pi$
$337$	−0.660640	−	9.23696i	−0.0359874	−	0.503169i	0.947209	−	0.320617i	$-0.103890\pi$
$338$	4.48477	+	12.0241i	0.243939	+	0.654027i
$339$	7.09112	+	4.55718i	0.385137	+	0.247512i
$340$	9.09686	+	15.8268i	0.493346	+	0.858330i
$341$	6.93748	+	10.7949i	0.375686	+	0.584578i
$342$	−3.62043	−	0.258938i	−0.195770	−	0.0140018i
$343$	3.10117	+	1.69336i	0.167447	+	0.0914331i
$344$	9.05877			0.488416
$345$	2.78656	+	10.3554i	0.150024	+	0.557518i
$346$	−0.173498			−0.00932730
$347$	16.9213	+	9.23972i	0.908382	+	0.496014i	0.864279	−	0.503013i	$-0.167775\pi$
$347$	16.9213	+	9.23972i	0.908382	+	0.496014i	0.0441029	+	0.999027i	$0.485957\pi$
$348$	−2.96489	−	0.212053i	−0.158935	−	0.0113672i
$349$	−9.31235	−	14.4903i	−0.498478	−	0.775648i	0.497286	−	0.867587i	$-0.334330\pi$
$349$	−9.31235	−	14.4903i	−0.498478	−	0.775648i	−0.995765	+	0.0919390i	$0.970694\pi$
$350$	0.787513	−	0.993472i	0.0420943	−	0.0531033i
$351$	0.343493	+	0.220749i	0.0183343	+	0.0117827i
$352$	−0.737914	−	1.97842i	−0.0393309	−	0.105450i
$353$	1.68852	+	23.6086i	0.0898708	+	1.25656i	0.819646	+	0.572870i	$0.194170\pi$
$353$	1.68852	+	23.6086i	0.0898708	+	1.25656i	−0.729775	+	0.683687i	$0.760375\pi$
$354$	3.32656	+	0.478287i	0.176805	+	0.0254207i
$355$	17.7471	−	0.388124i	0.941918	−	0.0205995i
$356$	−4.18183	+	14.2420i	−0.221636	+	0.754824i
$357$	0.992009	+	1.81673i	0.0525027	+	0.0961514i
$358$	−4.09400	−	1.52698i	−0.216375	−	0.0807036i
$359$	−2.66411	+	18.5293i	−0.140606	+	0.977938i	0.790311	+	0.612706i	$0.209919\pi$
$359$	−2.66411	+	18.5293i	−0.140606	+	0.977938i	−0.930917	+	0.365231i	$0.880990\pi$
$360$	−0.735431	+	2.11167i	−0.0387606	+	0.111295i
$361$	−2.41997	+	5.29900i	−0.127367	+	0.278895i
$362$	11.1367	−	2.42263i	0.585330	−	0.127331i
$363$	−5.23660	−	3.92007i	−0.274850	−	0.205750i
$364$	0.0870919	−	0.0559706i	0.00456486	−	0.00293365i
$365$	−6.57584	+	12.6950i	−0.344195	+	0.664488i
$366$	0.0299542	+	0.102015i	0.00156573	+	0.00533239i
$367$	−13.9579	+	13.9579i	−0.728594	+	0.728594i	−0.970340	−	0.241745i	$-0.922280\pi$
$367$	−13.9579	+	13.9579i	−0.728594	+	0.728594i	0.241745	+	0.970340i	$0.422280\pi$
$368$	−4.72702	+	0.809475i	−0.246413	+	0.0421968i
$369$			11.8965i			0.619305i
$370$	−2.53653	+	20.8722i	−0.131868	+	1.08510i
$371$	1.27361	+	1.46983i	0.0661228	+	0.0763098i
$372$	5.93813	+	1.29176i	0.307878	+	0.0669747i
$373$	12.2188	−	16.3224i	0.632667	−	0.845144i	−0.363592	−	0.931558i	$-0.618450\pi$
$373$	12.2188	−	16.3224i	0.632667	−	0.845144i	0.996259	+	0.0864140i	$0.0275408\pi$
$374$	9.31979	−	14.5019i	0.481915	−	0.749874i
$375$	7.27243	+	8.49187i	0.375546	+	0.438518i
$376$	−2.30246	+	2.65719i	−0.118741	+	0.137034i
$377$	−0.971607	+	0.727336i	−0.0500403	+	0.0374597i
$378$	−0.0886059	+	0.237562i	−0.00455740	+	0.0122189i
$379$	−13.9048	−	4.08283i	−0.714243	−	0.209721i	−0.0956305	−	0.995417i	$-0.530487\pi$
$379$	−13.9048	−	4.08283i	−0.714243	−	0.209721i	−0.618613	+	0.785696i	$0.712305\pi$
$380$	−6.24856	−	5.17960i	−0.320545	−	0.265708i
$381$	3.00053	+	6.57024i	0.153722	+	0.336604i
$382$	14.3686	+	19.1942i	0.735162	+	0.982061i
$383$	−0.209665	+	0.0149956i	−0.0107134	+	0.000766237i	−0.0766949	−	0.997055i	$-0.524437\pi$
$383$	−0.209665	+	0.0149956i	−0.0107134	+	0.000766237i	0.0659815	+	0.997821i	$0.478982\pi$
$384$	−0.909632	−	0.415415i	−0.0464195	−	0.0211991i
$385$	−1.17507	−	0.228835i	−0.0598873	−	0.0116625i
$386$	−0.189219	−	1.31605i	−0.00963099	−	0.0669850i
$387$	−1.92558	+	8.85175i	−0.0978827	+	0.449960i
$388$	0.919467	−	12.8558i	0.0466789	−	0.652656i
$389$	9.71689	−	2.85314i	0.492666	−	0.144660i	−0.0259566	−	0.999663i	$-0.508263\pi$
$389$	9.71689	−	2.85314i	0.492666	−	0.144660i	0.518623	+	0.855003i	$0.326445\pi$
$390$	0.337692	+	0.848264i	0.0170997	+	0.0429535i
$391$	−28.4168	−	26.9331i	−1.43710	−	1.36207i
$392$	−4.90429	−	4.90429i	−0.247704	−	0.247704i
$393$	−0.778424	+	1.42558i	−0.0392663	+	0.0719109i
$394$	8.91752	−	7.72707i	0.449258	−	0.389284i
$395$	−5.41117	−	32.5640i	−0.272265	−	1.63847i
$396$	2.09007	−	0.300506i	0.105030	−	0.0151010i
$397$	−5.87300	−	26.9978i	−0.294758	−	1.35498i	−0.851527	−	0.524311i	$-0.824323\pi$
$397$	−5.87300	−	26.9978i	−0.294758	−	1.35498i	0.556769	−	0.830667i	$-0.312041\pi$
$398$	16.2829	−	6.07322i	0.816189	−	0.304423i
$399$	−0.695514	−	0.602667i	−0.0348193	−	0.0301711i
$400$	−4.08407	+	2.88451i	−0.204203	+	0.144226i
$401$	−16.1258	+	7.36441i	−0.805284	+	0.367761i	−0.775144	−	0.631785i	$-0.782323\pi$
$401$	−16.1258	+	7.36441i	−0.805284	+	0.367761i	−0.0301403	+	0.999546i	$0.509595\pi$
$402$	−12.7790	+	6.97786i	−0.637359	+	0.348024i
$403$	2.17779	−	1.18916i	0.108484	−	0.0592365i
$404$	3.38232	−	1.54466i	0.168277	−	0.0768495i
$405$	−1.90708	−	1.16749i	−0.0947637	−	0.0580131i
$406$	−0.569579	−	0.493543i	−0.0282677	−	0.0244941i
$407$	18.6032	−	6.93862i	0.922125	−	0.343935i
$408$	−1.73535	−	7.97727i	−0.0859125	−	0.394934i
$409$	−28.6192	+	4.11482i	−1.41513	+	0.203465i	−0.807084	−	0.590437i	$-0.798955\pi$
$409$	−28.6192	+	4.11482i	−1.41513	+	0.203465i	−0.608046	+	0.793902i	$0.708046\pi$
$410$	−15.4721	+	21.6389i	−0.764114	+	1.06867i
$411$	−5.07638	+	4.39871i	−0.250399	+	0.216972i
$412$	6.31658	−	11.5680i	0.311196	−	0.569912i
$413$	0.602537	+	0.602537i	0.0296489	+	0.0296489i
$414$	0.213825	−	4.79106i	0.0105089	−	0.235468i
$415$	3.77452	−	1.50263i	0.185284	−	0.0737611i
$416$	−0.391771	+	0.115034i	−0.0192082	+	0.00564003i
$417$	−0.0791079	+	1.10607i	−0.00387393	+	0.0541646i
$418$	−1.62916	+	7.48912i	−0.0796848	+	0.366305i
$419$	−0.813929	−	5.66100i	−0.0397630	−	0.276558i	0.960233	−	0.279198i	$-0.0900687\pi$
$419$	−0.813929	−	5.66100i	−0.0397630	−	0.276558i	−0.999997	+	0.00264027i	$0.999160\pi$
$420$	−0.470133	+	0.316871i	−0.0229401	+	0.0154617i
$421$	−0.433236	−	0.197852i	−0.0211146	−	0.00964273i	0.404830	−	0.914392i	$-0.367331\pi$
$421$	−0.433236	−	0.197852i	−0.0211146	−	0.00964273i	−0.425944	+	0.904749i	$0.640058\pi$
$422$	3.84422	−	0.274944i	0.187134	−	0.0133841i
$423$	−2.10704	−	2.81467i	−0.102448	−	0.136854i
$424$	−3.18648	−	6.97742i	−0.154749	−	0.338854i
$425$	−38.8326	−	12.5792i	−1.88366	−	0.610179i
$426$	−7.61707	−	2.23657i	−0.369048	−	0.108362i
$427$	−0.00942070	+	0.0252579i	−0.000455900	+	0.00122231i
$428$	−15.5703	+	11.6558i	−0.752619	+	0.563404i
$429$	0.564602	−	0.651586i	0.0272593	−	0.0314589i
$430$	−15.0148	+	13.5964i	−0.724078	+	0.655678i
$431$	2.40989	−	3.74986i	0.116080	−	0.180625i	−0.778352	−	0.627829i	$-0.783944\pi$
$431$	2.40989	−	3.74986i	0.116080	−	0.180625i	0.894432	+	0.447204i	$0.147580\pi$
$432$	0.599278	−	0.800541i	0.0288328	−	0.0385161i
$433$	−0.136438	−	0.0296803i	−0.00655680	−	0.00142635i	0.209286	−	0.977855i	$-0.432886\pi$
$433$	−0.136438	−	0.0296803i	−0.00655680	−	0.00142635i	−0.215842	+	0.976428i	$0.569250\pi$
$434$	1.00902	+	1.16447i	0.0484344	+	0.0558963i
$435$	5.23253	−	4.09856i	0.250881	−	0.196511i
$436$			9.91776i			0.474975i
$437$	16.0223	+	6.80437i	0.766453	+	0.325497i
$438$	4.52112	−	4.52112i	0.216027	−	0.216027i
$439$	1.78191	+	6.06862i	0.0850458	+	0.289639i	0.991024	−	0.133685i	$-0.0426811\pi$
$439$	1.78191	+	6.06862i	0.0850458	+	0.289639i	−0.905978	+	0.423325i	$0.860863\pi$
$440$	4.19252	+	2.17167i	0.199871	+	0.103530i
$441$	5.83469	−	3.74973i	0.277843	−	0.178559i
$442$	−2.66851	−	1.99762i	−0.126928	−	0.0950171i
$443$	20.3444	−	4.42564i	0.966589	−	0.210269i	0.298550	−	0.954394i	$-0.403497\pi$
$443$	20.3444	−	4.42564i	0.966589	−	0.210269i	0.668040	+	0.744125i	$0.267134\pi$
$444$	3.90616	−	8.55330i	0.185378	−	0.405921i
$445$	−14.4447	−	29.8825i	−0.684743	−	1.41657i
$446$	−2.30663	+	16.0430i	−0.109222	+	0.759656i
$447$	13.1646	+	4.91016i	0.622666	+	0.232242i
$448$	−0.121513	−	0.222534i	−0.00574093	−	0.0105137i
$449$	−4.80712	+	16.3716i	−0.226862	+	0.772622i	0.764857	+	0.644200i	$0.222809\pi$
$449$	−4.80712	+	16.3716i	−0.226862	+	0.772622i	−0.991720	+	0.128422i	$0.959009\pi$
$450$	−1.95046	−	4.60388i	−0.0919456	−	0.217029i
$451$	24.8644	+	3.57496i	1.17082	+	0.168338i
$452$	−0.601334	−	8.40775i	−0.0282844	−	0.395467i
$453$	3.91762	+	10.5036i	0.184066	+	0.493500i
$454$	−16.9848	−	10.9155i	−0.797137	−	0.512289i
$455$	−0.0603468	+	0.223488i	−0.00282910	+	0.0104773i
$456$	1.96235	+	3.05348i	0.0918956	+	0.142992i
$457$	−9.70539	−	0.694143i	−0.453999	−	0.0324707i	−0.157532	−	0.987514i	$-0.550354\pi$
$457$	−9.70539	−	0.694143i	−0.453999	−	0.0324707i	−0.296467	+	0.955043i	$0.595808\pi$
$458$	−2.77119	−	1.51319i	−0.129489	−	0.0707066i
$459$	8.16384			0.381055
$460$	6.62003	−	8.43654i	0.308660	−	0.393356i
$461$	−12.3875			−0.576942			−0.288471	−	0.957489i	$-0.593147\pi$
$461$	−12.3875			−0.576942			−0.288471	+	0.957489i	$0.593147\pi$
$462$	0.469893	+	0.256581i	0.0218614	+	0.0119372i
$463$	−17.1405	−	1.22591i	−0.796584	−	0.0569728i	−0.332887	−	0.942967i	$-0.608023\pi$
$463$	−17.1405	−	1.22591i	−0.796584	−	0.0569728i	−0.463697	+	0.885994i	$0.653477\pi$
$464$	1.60703	+	2.50059i	0.0746046	+	0.116087i
$465$	−11.7812	+	6.77153i	−0.546340	+	0.314022i
$466$	−19.6133	−	12.6047i	−0.908567	−	0.583901i
$467$	4.92576	+	13.2065i	0.227937	+	0.611122i	0.999693	−	0.0247969i	$-0.00789390\pi$
$467$	4.92576	+	13.2065i	0.227937	+	0.611122i	−0.771756	+	0.635919i	$0.780621\pi$
$468$	−0.0291286	−	0.407270i	−0.00134647	−	0.0188261i
$469$	−3.65408	−	0.525378i	−0.168730	−	0.0242597i
$470$	−0.171897	−	7.86005i	−0.00792902	−	0.362557i
$471$	−0.608451	+	2.07219i	−0.0280360	+	0.0954817i
$472$	−1.61065	−	2.94968i	−0.0741360	−	0.135770i
$473$	17.9221	+	6.68459i	0.824058	+	0.307358i
$474$	−2.10096	+	14.6125i	−0.0965001	+	0.671173i
$475$	18.1310	−	0.793421i	0.831909	−	0.0364046i
$476$	0.859877	−	1.88287i	0.0394124	−	0.0863011i
$477$	7.49530	−	1.63050i	0.343186	−	0.0746556i
$478$	6.58442	+	4.92904i	0.301164	+	0.225449i
$479$	−9.86782	+	6.34167i	−0.450872	+	0.289758i	−0.746303	−	0.665606i	$-0.768173\pi$
$479$	−9.86782	+	6.34167i	−0.450872	+	0.289758i	0.295431	+	0.955364i	$0.404537\pi$
$480$	2.13120	−	0.676733i	0.0972757	−	0.0308885i
$481$	−1.08167	−	3.68384i	−0.0493200	−	0.167968i
$482$	−8.51619	+	8.51619i	−0.387902	+	0.387902i
$483$	0.771382	−	0.939979i	0.0350991	−	0.0427705i
$484$			6.54132i			0.297333i
$485$	17.7715	+	22.6884i	0.806960	+	1.03023i
$486$	0.654861	+	0.755750i	0.0297051	+	0.0342815i
$487$	−22.6069	−	4.91784i	−1.02442	−	0.222848i	−0.331188	−	0.943565i	$-0.607449\pi$
$487$	−22.6069	−	4.91784i	−1.02442	−	0.222848i	−0.693230	+	0.720717i	$0.743813\pi$
$488$	0.0637160	−	0.0851147i	0.00288429	−	0.00385296i
$489$	−0.0357646	+	0.0556507i	−0.00161733	+	0.00251661i
$490$	15.4897	+	0.767889i	0.699754	+	0.0346897i
$491$	10.0043	−	11.5456i	0.451488	−	0.521045i	−0.483682	−	0.875244i	$-0.660701\pi$
$491$	10.0043	−	11.5456i	0.451488	−	0.521045i	0.935170	+	0.354199i	$0.115246\pi$
$492$	9.52360	−	7.12928i	0.429357	−	0.321413i
$493$	−8.48033	+	22.7367i	−0.381935	+	1.02401i
$494$	1.42200	+	0.417538i	0.0639790	+	0.0187859i
$495$	−3.01322	+	3.63509i	−0.135434	+	0.163385i
$496$	−2.52448	−	5.52784i	−0.113353	−	0.248207i
$497$	−1.20624	−	1.61135i	−0.0541073	−	0.0722789i
$498$	−1.81223	+	0.129613i	−0.0812079	+	0.00580811i
$499$	9.60267	+	4.38539i	0.429875	+	0.196317i	0.618589	−	0.785715i	$-0.287705\pi$
$499$	9.60267	+	4.38539i	0.429875	+	0.196317i	−0.188714	+	0.982032i	$0.560432\pi$
$500$	2.43989	−	10.9109i	0.109115	−	0.487949i
$501$	0.113944	+	0.792496i	0.00509063	+	0.0354061i
$502$	5.88126	−	27.0357i	0.262493	−	1.20666i
$503$	−2.57580	+	36.0143i	−0.114849	+	1.60580i	0.534405	+	0.845229i	$0.320536\pi$
$503$	−2.57580	+	36.0143i	−0.114849	+	1.60580i	−0.649254	+	0.760572i	$0.724919\pi$
$504$	0.243277	−	0.0714327i	0.0108364	−	0.00318187i
$505$	−3.28777	+	7.63682i	−0.146304	+	0.339834i
$506$	−9.94938	−	1.88665i	−0.442304	−	0.0838719i
$507$	9.07450	+	9.07450i	0.403013	+	0.403013i
$508$	3.46160	−	6.33944i	0.153584	−	0.281267i
$509$	−17.4626	+	15.1315i	−0.774018	+	0.670691i	−0.949491	−	0.313794i	$-0.898400\pi$
$509$	−17.4626	+	15.1315i	−0.774018	+	0.670691i	0.175473	+	0.984484i	$0.443855\pi$
$510$	14.8495	+	10.6176i	0.657547	+	0.470156i
$511$	1.60464	−	0.230712i	0.0709851	−	0.0102061i
$512$	0.212565	+	0.977147i	0.00939415	+	0.0431842i
$513$	−3.40083	+	1.26844i	−0.150150	+	0.0560031i
$514$	−8.38857	−	7.26874i	−0.370004	−	0.320610i
$515$	6.89283	+	28.6544i	0.303734	+	1.26266i
$516$	8.24015	−	3.76315i	0.362752	−	0.165663i
$517$	−6.51602	+	3.55802i	−0.286574	+	0.156481i
$518$	2.09249	−	1.14259i	0.0919387	−	0.0502024i
$519$	−0.157819	+	0.0720736i	−0.00692749	+	0.00316368i
$520$	0.476699	−	0.778682i	0.0209046	−	0.0341475i
$521$	14.2826	+	12.3760i	0.625733	+	0.542200i	0.908976	−	0.416847i	$-0.136865\pi$
$521$	14.2826	+	12.3760i	0.625733	+	0.542200i	−0.283244	+	0.959048i	$0.591411\pi$
$522$	−2.78505	+	1.03877i	−0.121898	+	0.0454657i
$523$	−3.26036	−	14.9876i	−0.142566	−	0.655364i	−0.991848	−	0.127425i	$-0.959329\pi$
$523$	−3.26036	−	14.9876i	−0.142566	−	0.655364i	0.849283	−	0.527939i	$-0.177035\pi$
$524$	1.60773	−	0.231156i	0.0702338	−	0.0100981i
$525$	0.303643	−	1.23084i	0.0132521	−	0.0537182i
$526$	21.2217	−	18.3887i	0.925310	−	0.801785i
$527$	23.7764	−	43.5431i	1.03571	−	1.89677i
$528$	−1.49310	−	1.49310i	−0.0649787	−	0.0649787i
$529$	−8.41999	+	21.4034i	−0.366087	+	0.930581i
$530$	15.7540	+	6.78236i	0.684312	+	0.294607i
$531$	3.22463	−	0.946838i	0.139937	−	0.0410893i
$532$	−0.0656533	+	0.917952i	−0.00284643	+	0.0397983i
$533$	1.03252	−	4.74644i	0.0447236	−	0.205591i
$534$	2.11242	+	14.6922i	0.0914132	+	0.635793i
$535$	8.31327	−	42.6890i	0.359414	−	1.84561i
$536$	13.2442	+	6.04844i	0.572064	+	0.261253i
$537$	−4.35837	+	0.311716i	−0.188077	+	0.0134516i
$538$	−6.85308	−	9.15465i	−0.295457	−	0.394685i
$539$	−6.08382	−	13.3217i	−0.262049	−	0.573807i
$540$	0.208247	+	2.22635i	0.00896153	+	0.0958068i
$541$	36.4224	+	10.6946i	1.56592	+	0.459796i	0.945811	−	0.324718i	$-0.105269\pi$
$541$	36.4224	+	10.6946i	1.56592	+	0.459796i	0.620111	+	0.784514i	$0.287087\pi$
$542$	4.74873	−	12.7318i	0.203975	−	0.546879i
$543$	9.12386	−	6.83004i	0.391542	−	0.293105i
$544$	−5.34618	+	6.16982i	−0.229215	+	0.264529i
$545$	−14.8857	−	16.4386i	−0.637633	−	0.704150i
$546$	0.0559706	−	0.0870919i	0.00239532	−	0.00372719i
$547$	−17.0958	+	22.8373i	−0.730964	+	0.976454i	0.268947	+	0.963155i	$0.413324\pi$
$547$	−17.0958	+	22.8373i	−0.730964	+	0.976454i	−0.999912	+	0.0132991i	$0.995767\pi$
$548$	6.56351	+	1.42780i	0.280379	+	0.0609928i
$549$	0.0696257	+	0.0803523i	0.00297155	+	0.00342935i
$550$	−10.2085	+	2.69310i	−0.435293	+	0.114834i
$551$		−	10.7891i		−	0.459630i
$552$	−3.96358	+	2.70000i	−0.168701	+	0.114920i
$553$	−2.64674	+	2.64674i	−0.112551	+	0.112551i
$554$	−3.44415	−	11.7297i	−0.146328	−	0.498348i
$555$	6.36334	+	20.0398i	0.270109	+	0.850641i
$556$	0.932864	−	0.599515i	0.0395622	−	0.0254251i
$557$	−21.2940	−	15.9405i	−0.902254	−	0.675419i	0.0439349	−	0.999034i	$-0.486011\pi$
$557$	−21.2940	−	15.9405i	−0.902254	−	0.675419i	−0.946189	+	0.323616i	$0.895101\pi$
$558$	5.93813	−	1.29176i	0.251381	−	0.0546846i
$559$	1.53653	−	3.36454i	0.0649885	−	0.142305i
$560$	0.535409	+	0.186467i	0.0226252	+	0.00787967i
$561$	2.45328	−	17.0629i	0.103578	−	0.720398i
$562$	2.15327	+	0.803127i	0.0908301	+	0.0338779i
$563$	−21.8622	−	40.0376i	−0.921380	−	1.68738i	−0.702570	−	0.711615i	$-0.747964\pi$
$563$	−21.8622	−	40.0376i	−0.921380	−	1.68738i	−0.218811	−	0.975767i	$-0.570218\pi$
$564$	−0.990561	+	3.37354i	−0.0417101	+	0.142052i
$565$	13.6160	+	13.0332i	0.572829	+	0.548310i
$566$	−19.4868	−	2.80178i	−0.819093	−	0.117768i
$567$	0.0180879	+	0.252902i	0.000759620	+	0.0106209i
$568$	2.77427	+	7.43811i	0.116406	+	0.312096i
$569$	−33.8362	−	21.7452i	−1.41849	−	0.911606i	−0.999994	−	0.00338602i	$-0.998922\pi$
$569$	−33.8362	−	21.7452i	−1.41849	−	0.911606i	−0.418493	−	0.908220i	$-0.637441\pi$
$570$	−7.83558	−	2.11578i	−0.328196	−	0.0886205i
$571$	−15.4109	−	23.9799i	−0.644927	−	1.00353i	−0.997698	−	0.0678167i	$-0.978397\pi$
$571$	−15.4109	−	23.9799i	−0.644927	−	1.00353i	0.352770	−	0.935710i	$-0.385240\pi$
$572$	−0.859975	−	0.0615066i	−0.0359574	−	0.00257172i
$573$	21.0437	+	11.4907i	0.879113	+	0.480032i
$574$	3.01632			0.125899
$575$	1.68989	+	23.9195i	0.0704734	+	0.997514i
$576$	−1.00000			−0.0416667
$577$	30.3993	+	16.5993i	1.26554	+	0.691037i	0.964879	−	0.262694i	$-0.0846110\pi$
$577$	30.3993	+	16.5993i	1.26554	+	0.691037i	0.300661	+	0.953731i	$0.402793\pi$
$578$	−49.5217	−	3.54186i	−2.05983	−	0.147322i
$579$	−0.718825	−	1.11851i	−0.0298734	−	0.0464839i
$580$	−6.41681	−	1.73268i	−0.266443	−	0.0719458i
$581$	−0.387532	−	0.249052i	−0.0160776	−	0.0103324i
$582$	−4.50413	−	12.0760i	−0.186702	−	0.500568i
$583$	−1.15547	−	16.1556i	−0.0478549	−	0.669098i
$584$	−6.32875	−	0.909936i	−0.261885	−	0.0376534i
$585$	0.659557	+	0.631326i	0.0272693	+	0.0261021i
$586$	6.61795	−	22.5387i	0.273385	−	0.931064i
$587$	−16.3211	−	29.8898i	−0.673642	−	1.23368i	−0.961182	−	0.275915i	$-0.911019\pi$
$587$	−16.3211	−	29.8898i	−0.673642	−	1.23368i	0.287540	−	0.957769i	$-0.407163\pi$
$588$	−6.49841	−	2.42378i	−0.267990	−	0.0999551i
$589$	−3.13912	+	21.8331i	−0.129345	+	0.899616i
$590$	7.09683	+	2.47161i	0.292172	+	0.101755i
$591$	4.90172	−	10.7333i	0.201630	−	0.441507i
$592$	−9.18814	+	1.99876i	−0.377630	+	0.0821484i
$593$	19.9336	+	14.9221i	0.818576	+	0.612778i	0.924321	−	0.381615i	$-0.124632\pi$
$593$	19.9336	+	14.9221i	0.818576	+	0.612778i	−0.105745	+	0.994393i	$0.533723\pi$
$594$	1.77636	−	1.14159i	0.0728847	−	0.0468402i
$595$	1.40078	+	4.41143i	0.0574266	+	0.180851i
$596$	−3.95849	−	13.4814i	−0.162146	−	0.552219i
$597$	12.2886	−	12.2886i	0.502938	−	0.502938i
$598$	−0.501141	+	1.89298i	−0.0204932	+	0.0774096i
$599$		−	29.9967i		−	1.22563i	−0.790226	−	0.612815i	$-0.790037\pi$
$599$		−	29.9967i		−	1.22563i	0.790226	−	0.612815i	$-0.209963\pi$
$600$	−2.51673	+	4.32043i	−0.102745	+	0.176381i
$601$	14.1270	+	16.3035i	0.576253	+	0.665032i	0.966795	−	0.255554i	$-0.0822577\pi$
$601$	14.1270	+	16.3035i	0.576253	+	0.665032i	−0.390542	+	0.920585i	$0.627712\pi$
$602$	2.24434	+	0.488227i	0.0914726	+	0.0198986i
$603$	−8.72548	+	11.6559i	−0.355329	+	0.474664i
$604$	6.06078	−	9.43076i	0.246610	−	0.383732i
$605$	−9.81795	−	10.8422i	−0.399156	−	0.440796i
$606$	2.43500	−	2.81014i	0.0989150	−	0.114154i
$607$	−9.85289	+	7.37578i	−0.399916	+	0.299374i	−0.780240	−	0.625480i	$-0.784903\pi$
$607$	−9.85289	+	7.37578i	−0.399916	+	0.299374i	0.380324	+	0.924853i	$0.375812\pi$
$608$	1.26844	−	3.40083i	0.0514421	−	0.137922i
$609$	−0.723132	−	0.212331i	−0.0293028	−	0.00860408i
$610$	0.0221411	+	0.236709i	0.000896467	+	0.00958405i
$611$	0.596372	+	1.30587i	0.0241266	+	0.0528299i
$612$	−4.89240	−	6.53549i	−0.197764	−	0.264181i
$613$	−41.1696	+	2.94451i	−1.66283	+	0.118928i	−0.870825	−	0.491593i	$-0.836415\pi$
$613$	−41.1696	+	2.94451i	−1.66283	+	0.118928i	−0.792001	+	0.610520i	$0.790960\pi$
$614$	9.71403	+	4.43625i	0.392026	+	0.179032i
$615$	−5.08482	+	26.1108i	−0.205040	+	1.05289i
$616$	−0.0761927	−	0.529932i	−0.00306989	−	0.0213516i
$617$	0.754797	−	3.46974i	0.0303870	−	0.139687i	−0.959454	−	0.281865i	$-0.909047\pi$
$617$	0.754797	−	3.46974i	0.0303870	−	0.139687i	0.989841	+	0.142178i	$0.0454106\pi$
$618$	0.940262	−	13.1466i	0.0378229	−	0.528833i
$619$	−1.36483	+	0.400751i	−0.0548572	+	0.0161075i	−0.309046	−	0.951047i	$-0.600010\pi$
$619$	−1.36483	+	0.400751i	−0.0548572	+	0.0161075i	0.254189	+	0.967155i	$0.418192\pi$
$620$	12.4811	+	5.37330i	0.501253	+	0.215797i
$621$	−1.79578	−	4.44693i	−0.0720620	−	0.178449i
$622$	7.12608	+	7.12608i	0.285730	+	0.285730i
$623$	−1.80364	+	3.30312i	−0.0722614	+	0.132337i
$624$	−0.308581	+	0.267387i	−0.0123531	+	0.0107040i
$625$	12.3322	+	21.7467i	0.493287	+	0.869867i
$626$	−19.1235	+	2.74954i	−0.764327	+	0.109894i
$627$	1.62916	+	7.48912i	0.0650623	+	0.299087i
$628$	2.02351	−	0.754730i	0.0807468	−	0.0301170i
$629$	−58.0149	−	50.2702i	−2.31321	−	2.00441i
$630$	−0.296015	+	0.483537i	−0.0117935	+	0.0192646i
$631$	−5.23484	+	2.39067i	−0.208396	+	0.0951712i	−0.516878	−	0.856059i	$-0.672906\pi$
$631$	−5.23484	+	2.39067i	−0.208396	+	0.0951712i	0.308483	+	0.951230i	$0.400179\pi$
$632$	12.9569	−	7.07503i	0.515399	−	0.281429i
$633$	3.38261	−	1.84705i	0.134447	−	0.0734135i
$634$	−16.7472	+	7.64818i	−0.665116	+	0.303748i
$635$	3.77739	+	15.7031i	0.149901	+	0.623158i
$636$	−5.79705	−	5.02317i	−0.229868	−	0.199182i
$637$	−2.65337	+	0.989657i	−0.105130	+	0.0392116i
$638$	1.33417	+	6.13308i	0.0528203	+	0.242811i
$639$	−7.85784	+	1.12979i	−0.310851	+	0.0446937i
$640$	−1.81894	−	1.30057i	−0.0718997	−	0.0514094i
$641$	5.76082	−	4.99178i	0.227539	−	0.197163i	−0.533629	−	0.845719i	$-0.679172\pi$
$641$	5.76082	−	4.99178i	0.227539	−	0.197163i	0.761167	+	0.648555i	$0.224627\pi$
$642$	−9.32126	+	17.0706i	−0.367881	+	0.673724i
$643$	−13.9165	−	13.9165i	−0.548813	−	0.548813i	0.377285	−	0.926097i	$-0.376858\pi$
$643$	−13.9165	−	13.9165i	−0.548813	−	0.548813i	−0.926097	+	0.377285i	$0.876858\pi$
$644$	−1.21476	−	0.0542149i	−0.0478684	−	0.00213637i
$645$	−8.00978	+	18.6051i	−0.315385	+	0.732575i
$646$	28.4318	−	8.34833i	1.11863	−	0.328460i
$647$	−2.15873	+	30.1830i	−0.0848685	+	1.18662i	0.759373	+	0.650655i	$0.225506\pi$
$647$	−2.15873	+	30.1830i	−0.0848685	+	1.18662i	−0.844242	+	0.535962i	$0.819949\pi$
$648$	0.212565	−	0.977147i	0.00835035	−	0.0383860i
$649$	−1.00993	−	7.02423i	−0.0396433	−	0.275725i
$650$	0.378611	+	2.00614i	0.0148503	+	0.0786873i
$651$	1.40157	+	0.640077i	0.0549320	+	0.0250866i
$652$	0.0659836	−	0.00471924i	0.00258412	−	0.000184820i
$653$	−6.89326	−	9.20832i	−0.269754	−	0.360349i	0.645125	−	0.764077i	$-0.276805\pi$
$653$	−6.89326	−	9.20832i	−0.269754	−	0.360349i	−0.914879	+	0.403728i	$0.867714\pi$
$654$	4.11999	+	9.02151i	0.161104	+	0.352769i
$655$	−2.31784	+	2.79619i	−0.0905655	+	0.109256i
$656$	−11.4146	−	3.35162i	−0.445664	−	0.130859i
$657$	2.23441	−	5.99069i	0.0871728	−	0.233719i
$658$	−0.713654	+	0.534235i	−0.0278211	+	0.0208266i
$659$	3.45998	−	3.99303i	0.134782	−	0.155546i	−0.684346	−	0.729157i	$-0.739912\pi$
$659$	3.45998	−	3.99303i	0.134782	−	0.155546i	0.819128	+	0.573611i	$0.194458\pi$
$660$	4.71580	+	0.233782i	0.183562	+	0.00909994i
$661$	9.26257	−	14.4128i	0.360272	−	0.560594i	−0.613048	−	0.790046i	$-0.710057\pi$
$661$	9.26257	−	14.4128i	0.360272	−	0.560594i	0.973320	+	0.229451i	$0.0736932\pi$
$662$	4.55393	−	6.08334i	0.176994	−	0.236436i
$663$	−3.25720	−	0.708561i	−0.126499	−	0.0275182i
$664$	1.18979	+	1.37309i	0.0461728	+	0.0532862i
$665$	−1.26895	−	1.62003i	−0.0492076	−	0.0628222i
$666$		−	9.40303i		−	0.364360i
$667$	14.2503	−	0.381991i	0.551774	−	0.0147908i
$668$	0.566142	−	0.566142i	0.0219047	−	0.0219047i
$669$	4.56630	+	15.5514i	0.176544	+	0.601252i
$670$	−31.0303	+	9.85323i	−1.19881	+	0.380663i
$671$	0.188865	−	0.121376i	0.00729104	−	0.00468566i
$672$	−0.202976	−	0.151946i	−0.00782995	−	0.00586143i
$673$	16.4631	−	3.58133i	0.634606	−	0.138050i	0.116257	−	0.993219i	$-0.462910\pi$
$673$	16.4631	−	3.58133i	0.634606	−	0.138050i	0.518349	+	0.855169i	$0.326547\pi$
$674$	−3.84697	+	8.42370i	−0.148180	+	0.324469i
$675$	−3.68672	−	3.37759i	−0.141902	−	0.130003i
$676$	1.82637	−	12.7027i	0.0702449	−	0.488564i
$677$	6.71074	+	2.50298i	0.257915	+	0.0961973i	0.475096	−	0.879934i	$-0.342413\pi$
$677$	6.71074	+	2.50298i	0.257915	+	0.0961973i	−0.217181	+	0.976131i	$0.569686\pi$
$678$	−4.03970	−	7.39815i	−0.155144	−	0.284124i
$679$	0.920672	−	3.13552i	0.0353321	−	0.120330i
$680$	−0.399134	−	18.2505i	−0.0153061	−	0.699876i
$681$	−19.9844	−	2.87332i	−0.765803	−	0.110106i
$682$	−0.915421	−	12.7993i	−0.0350533	−	0.490109i
$683$	2.95459	+	7.92156i	0.113054	+	0.303110i	0.981138	−	0.193307i	$-0.0619213\pi$
$683$	2.95459	+	7.92156i	0.113054	+	0.303110i	−0.868084	+	0.496417i	$0.834649\pi$
$684$	3.05348	+	1.96235i	0.116753	+	0.0750324i
$685$	−13.0219	+	7.48469i	−0.497543	+	0.285975i
$686$	−1.91028	−	2.97246i	−0.0729350	−	0.113489i
$687$	−3.14937	−	0.225247i	−0.120156	−	0.00859372i
$688$	−7.95069	−	4.34141i	−0.303117	−	0.165515i
$689$	−3.13199			−0.119319
$690$	2.51712	−	10.4242i	0.0958253	−	0.396843i
$691$	−17.5692			−0.668365			−0.334182	−	0.942508i	$-0.608460\pi$
$691$	−17.5692			−0.668365			−0.334182	+	0.942508i	$0.608460\pi$
$692$	0.152275	+	0.0831486i	0.00578864	+	0.00316084i
$693$	0.534017	+	0.0381936i	0.0202856	+	0.00145086i
$694$	−10.4233	−	16.2190i	−0.395664	−	0.615665i
$695$	−0.646390	+	2.39384i	−0.0245190	+	0.0908034i
$696$	2.50059	+	1.60703i	0.0947847	+	0.0609144i
$697$	−33.9402	−	90.9972i	−1.28558	−	3.44676i
$698$	1.22879	+	17.1808i	0.0465105	+	0.650301i
$699$	−23.0770	−	3.31798i	−0.872854	−	0.125497i
$700$	−1.16730	+	0.494535i	−0.0441199	+	0.0186917i
$701$	−3.18331	+	10.8413i	−0.120232	+	0.409472i	−0.997511	−	0.0705081i	$-0.977538\pi$
$701$	−3.18331	+	10.8413i	−0.120232	+	0.409472i	0.877279	+	0.479980i	$0.159356\pi$
$702$	−0.195682	−	0.358366i	−0.00738556	−	0.0135256i
$703$	31.9781	+	11.9272i	1.20608	+	0.449843i
$704$	−0.300506	+	2.09007i	−0.0113257	+	0.0787723i
$705$	−3.42155	−	7.07834i	−0.128863	−	0.266586i
$706$	9.83241	−	21.5300i	0.370048	−	0.810291i
$707$	0.921233	−	0.200402i	0.0346465	−	0.00753689i
$708$	−2.69043	−	2.01403i	−0.101113	−	0.0756920i
$709$	−20.9351	+	13.4542i	−0.786233	+	0.505281i	−0.871097	−	0.491111i	$-0.836591\pi$
$709$	−20.9351	+	13.4542i	−0.786233	+	0.505281i	0.0848637	+	0.996393i	$0.472955\pi$
$710$	−15.7623	−	8.16463i	−0.591547	−	0.306413i
$711$	4.15914	+	14.1647i	0.155980	+	0.531219i
$712$	10.4958	−	10.4958i	0.393345	−	0.393345i
$713$	−28.9484	−	3.37317i	−1.08413	−	0.126326i
$714$		−	2.06992i		−	0.0774649i
$715$	1.51771	−	1.18880i	0.0567593	−	0.0444586i
$716$	2.86141	+	3.30225i	0.106936	+	0.123411i
$717$	8.03700	+	1.74834i	0.300147	+	0.0652930i
$718$	11.2184	−	14.9860i	0.418666	−	0.559272i
$719$	2.54283	−	3.95672i	0.0948315	−	0.147561i	−0.790596	−	0.612338i	$-0.790229\pi$
$719$	2.54283	−	3.95672i	0.0948315	−	0.147561i	0.885428	+	0.464777i	$0.153866\pi$
$720$	1.65749	−	1.50091i	0.0617709	−	0.0559357i
$721$	2.18842	−	2.52557i	0.0815009	−	0.0940570i
$722$	4.66350	−	3.49105i	0.173558	−	0.129924i
$723$	−4.20885	+	11.2844i	−0.156529	+	0.419670i
$724$	−10.9355	−	3.21094i	−0.406413	−	0.119334i
$725$	13.2364	−	6.75916i	0.491587	−	0.251029i
$726$	2.71736	+	5.95020i	0.100851	+	0.220833i
$727$	−6.70530	−	8.95723i	−0.248686	−	0.332205i	0.658777	−	0.752339i	$-0.271074\pi$
$727$	−6.70530	−	8.95723i	−0.248686	−	0.332205i	−0.907462	+	0.420133i	$0.861983\pi$
$728$	−0.103263	+	0.00738548i	−0.00382716	+	0.000273724i
$729$	0.909632	+	0.415415i	0.0336901	+	0.0153857i
$730$	11.8555	−	7.99068i	0.438794	−	0.295748i
$731$	−10.5248	−	73.2016i	−0.389274	−	2.70746i
$732$	0.0226002	−	0.103892i	0.000835329	−	0.00383994i
$733$	0.573690	−	8.02123i	0.0211897	−	0.296271i	−0.975796	−	0.218684i	$-0.929824\pi$
$733$	0.573690	−	8.02123i	0.0211897	−	0.296271i	0.996986	−	0.0775874i	$-0.0247217\pi$
$734$	18.9398	−	5.56123i	0.699081	−	0.205269i
$735$	14.4089	−	5.73616i	0.531481	−	0.211581i
$736$	4.53675	+	1.55496i	0.167227	+	0.0573167i
$737$	21.7395	+	21.7395i	0.800784	+	0.800784i
$738$	5.70136	−	10.4413i	0.209870	−	0.384348i
$739$	0.839920	−	0.727795i	0.0308969	−	0.0267724i	−0.639275	−	0.768978i	$-0.720766\pi$
$739$	0.839920	−	0.727795i	0.0308969	−	0.0267724i	0.670172	+	0.742205i	$0.266220\pi$
$740$	12.2293	−	17.1035i	0.449557	−	0.628737i
$741$	1.46695	−	0.210916i	0.0538898	−	0.00774819i
$742$	−0.413411	−	1.90042i	−0.0151768	−	0.0697665i
$743$	21.1388	−	7.88436i	0.775507	−	0.289249i	0.0696199	−	0.997574i	$-0.477821\pi$
$743$	21.1388	−	7.88436i	0.775507	−	0.289249i	0.705887	+	0.708324i	$0.250549\pi$
$744$	−4.59270	−	3.97959i	−0.168376	−	0.145899i
$745$	26.7955	+	16.4039i	0.981712	+	0.600991i
$746$	−18.5467	+	8.47001i	−0.679044	+	0.310109i
$747$	−1.59462	+	0.870728i	−0.0583440	+	0.0318583i
$748$	−15.1298	+	8.26149i	−0.553200	+	0.302070i
$749$	−4.48579	+	2.04859i	−0.163907	+	0.0748540i
$750$	−2.31314	−	10.9384i	−0.0844638	−	0.399415i
$751$	−6.64458	−	5.75756i	−0.242464	−	0.210096i	0.525148	−	0.851011i	$-0.324010\pi$
$751$	−6.64458	−	5.75756i	−0.242464	−	0.210096i	−0.767612	+	0.640914i	$0.778555\pi$
$752$	3.29428	−	1.22870i	0.120130	−	0.0448062i
$753$	−5.88126	−	27.0357i	−0.214325	−	0.985236i
$754$	1.20133	−	0.172726i	0.0437500	−	0.00629030i
$755$	4.10908	+	24.7281i	0.149545	+	0.899947i
$756$	0.191619	−	0.166039i	0.00696911	−	0.00603876i
$757$	0.238405	−	0.436606i	0.00866497	−	0.0158687i	−0.873311	−	0.487164i	$-0.838031\pi$
$757$	0.238405	−	0.436606i	0.00866497	−	0.0158687i	0.881976	+	0.471295i	$0.156213\pi$
$758$	10.2473	+	10.2473i	0.372198	+	0.372198i
$759$	−9.83402	+	2.41696i	−0.356952	+	0.0877302i
$760$	3.00191	+	7.54065i	0.108891	+	0.273528i
$761$	−6.79030	+	1.99381i	−0.246148	+	0.0722756i	−0.402479	−	0.915429i	$-0.631851\pi$
$761$	−6.79030	+	1.99381i	−0.246148	+	0.0722756i	0.156331	+	0.987705i	$0.450033\pi$
$762$	0.515280	−	7.20456i	0.0186666	−	0.260994i
$763$	−0.534522	+	2.45716i	−0.0193510	+	0.0889552i
$764$	−3.41222	−	23.7325i	−0.123450	−	0.858611i
$765$	17.9183	+	3.48942i	0.647837	+	0.126160i
$766$	0.191205	+	0.0873206i	0.00690854	+	0.00315502i
$767$	−1.36874	+	0.0978944i	−0.0494224	+	0.00353476i
$768$	0.599278	+	0.800541i	0.0216246	+	0.0288870i
$769$	13.0524	+	28.5807i	0.470681	+	1.03065i	0.984922	+	0.173001i	$0.0553464\pi$
$769$	13.0524	+	28.5807i	0.470681	+	1.03065i	−0.514241	+	0.857646i	$0.671926\pi$
$770$	0.921669	+	0.763996i	0.0332146	+	0.0275325i
$771$	−10.6501	−	3.12714i	−0.383552	−	0.112621i
$772$	−0.464641	+	1.24575i	−0.0167228	+	0.0448355i
$773$	−2.05858	+	1.54104i	−0.0740421	+	0.0554272i	−0.635658	−	0.771971i	$-0.719271\pi$
$773$	−2.05858	+	1.54104i	−0.0740421	+	0.0554272i	0.561615	+	0.827398i	$0.310180\pi$
$774$	5.93223	−	6.84616i	0.213230	−	0.246080i
$775$	−28.7521	+	9.82685i	−1.03281	+	0.352991i
$776$	−6.96814	+	10.8426i	−0.250142	+	0.389228i
$777$	1.42875	−	1.90858i	0.0512561	−	0.0684701i
$778$	−9.89568	−	2.15267i	−0.354777	−	0.0771770i
$779$	28.2771	+	32.6335i	1.01313	+	1.16922i
$780$	0.110145	−	0.906342i	0.00394381	−	0.0324523i
$781$			16.7629i			0.599824i
$782$	12.0332	+	37.2574i	0.430306	+	1.33232i
$783$	−2.10185	+	2.10185i	−0.0751139	+	0.0751139i
$784$	1.95402	+	6.65477i	0.0697863	+	0.237670i
$785$	−2.22116	+	4.28806i	−0.0792765	+	0.153048i
$786$	1.36641	−	0.878140i	0.0487383	−	0.0313222i
$787$	39.9379	+	29.8972i	1.42363	+	1.06572i	0.986033	+	0.166550i	$0.0532626\pi$
$787$	39.9379	+	29.8972i	1.42363	+	1.06572i	0.437601	+	0.899169i	$0.355828\pi$
$788$	−11.5299	+	2.50818i	−0.410736	+	0.0893501i
$789$	11.6650	−	25.5428i	0.415285	−	0.909346i
$790$	−10.8570	+	31.1740i	−0.386274	+	1.10912i
$791$	0.304157	−	2.11546i	0.0108146	−	0.0752171i
$792$	−1.97842	−	0.737914i	−0.0703002	−	0.0262206i
$793$	−0.0208052	−	0.0381019i	−0.000738816	−	0.00135304i
$794$	−7.78404	+	26.5100i	−0.276245	+	0.940804i
$795$	17.1479	−	0.375019i	0.608173	−	0.0133006i
$796$	−17.2018	−	2.47324i	−0.609701	−	0.0876617i
$797$	2.07134	+	28.9611i	0.0733707	+	1.02586i	0.892148	+	0.451744i	$0.149198\pi$
$797$	2.07134	+	28.9611i	0.0733707	+	1.02586i	−0.818777	+	0.574112i	$0.805347\pi$
$798$	0.321611	+	0.862272i	0.0113849	+	0.0305241i
$799$	24.1471	+	15.5184i	0.854263	+	0.549002i
$800$	4.96690	−	0.574390i	0.175606	−	0.0203078i
$801$	8.02487	+	12.4869i	0.283545	+	0.441204i
$802$	17.6827	+	1.26469i	0.624397	+	0.0446577i
$803$	−11.8495	−	6.47031i	−0.418159	−	0.228332i
$804$	14.5600			0.513492
$805$	2.09483	−	1.73339i	0.0738330	−	0.0610941i
$806$	−2.48131			−0.0874003
$807$	−10.0368	−	5.48049i	−0.353311	−	0.192922i
$808$	−3.70887	−	0.265264i	−0.130478	−	0.00933194i
$809$	−13.3051	−	20.7031i	−0.467781	−	0.727882i	0.524565	−	0.851371i	$-0.324228\pi$
$809$	−13.3051	−	20.7031i	−0.467781	−	0.727882i	−0.992346	+	0.123489i	$0.960592\pi$
$810$	1.11429	+	1.93865i	0.0391521	+	0.0681172i
$811$	7.30145	+	4.69236i	0.256389	+	0.164771i	0.662521	−	0.749043i	$-0.269486\pi$
$811$	7.30145	+	4.69236i	0.256389	+	0.164771i	−0.406132	+	0.913814i	$0.633123\pi$
$812$	0.263378	+	0.706142i	0.00924274	+	0.0247807i
$813$	−0.969400	−	13.5540i	−0.0339983	−	0.475359i
$814$	−19.6529	−	2.82567i	−0.688835	−	0.0990396i
$815$	−0.102284	+	0.106858i	−0.00358285	+	0.00374306i
$816$	−2.30002	+	7.83314i	−0.0805167	+	0.274215i
$817$	15.7579	+	28.8585i	0.551299	+	1.00963i
$818$	27.0905	+	10.1042i	0.947198	+	0.353287i
$819$	0.0147333	−	0.102473i	0.000514824	−	0.00358068i
$820$	23.9500	−	11.5770i	0.836369	−	0.404286i
$821$	19.0358	−	41.6826i	0.664354	−	1.45473i	−0.214054	−	0.976822i	$-0.568667\pi$
$821$	19.0358	−	41.6826i	0.664354	−	1.45473i	0.878408	−	0.477911i	$-0.158606\pi$
$822$	6.56351	−	1.42780i	0.228929	−	0.0498004i
$823$	35.3523	+	26.4644i	1.23230	+	0.922492i	0.998757	−	0.0498536i	$-0.0158755\pi$
$823$	35.3523	+	26.4644i	1.23230	+	0.922492i	0.233548	+	0.972345i	$0.424966\pi$
$824$	−11.0879	+	7.12574i	−0.386264	+	0.248237i
$825$	−8.16726	+	6.69050i	−0.284347	+	0.232933i
$826$	−0.240069	−	0.817599i	−0.00835306	−	0.0284479i
$827$	37.0602	−	37.0602i	1.28871	−	1.28871i	0.353139	−	0.935571i	$-0.385114\pi$
$827$	37.0602	−	37.0602i	1.28871	−	1.28871i	0.935571	−	0.353139i	$-0.114886\pi$
$828$	−2.48378	+	4.10254i	−0.0863174	+	0.142573i
$829$			8.73544i			0.303394i	0.988427	+	0.151697i	$0.0484739\pi$
$829$			8.73544i			0.303394i	−0.988427	+	0.151697i	$0.951526\pi$
$830$	−4.03295	−	0.490110i	−0.139986	−	0.0170120i
$831$	−8.00561	−	9.23897i	−0.277712	−	0.320496i
$832$	0.398980	+	0.0867927i	0.0138321	+	0.00300900i
$833$	−33.9323	+	45.3283i	−1.17568	+	1.57053i
$834$	0.599515	−	0.932864i	0.0207595	−	0.0323024i
$835$	−0.0886436	+	1.78810i	−0.00306764	+	0.0618798i
$836$	5.01903	−	5.79227i	0.173587	−	0.200330i
$837$	4.86490	−	3.64182i	0.168155	−	0.125880i
$838$	−1.99866	+	5.35862i	−0.0690426	+	0.185110i
$839$	−17.2029	−	5.05124i	−0.593911	−	0.174388i	−0.0290555	−	0.999578i	$-0.509250\pi$
$839$	−17.2029	−	5.05124i	−0.593911	−	0.174388i	−0.564856	+	0.825190i	$0.691068\pi$
$840$	0.564486	−	0.0528006i	0.0194766	−	0.00182179i
$841$	8.37663	+	18.3423i	0.288849	+	0.632492i
$842$	0.285422	+	0.381279i	0.00983628	+	0.0131397i
$843$	2.29231	−	0.163949i	0.0789514	−	0.00564672i
$844$	−3.50576	−	1.60103i	−0.120673	−	0.0551096i
$845$	16.0384	+	23.7957i	0.551738	+	0.818597i
$846$	0.500373	+	3.48017i	0.0172032	+	0.119651i
$847$	−0.352548	+	1.62064i	−0.0121137	+	0.0556857i
$848$	−0.547214	+	7.65105i	−0.0187914	+	0.262738i
$849$	−18.8898	+	5.54653i	−0.648295	+	0.190356i
$850$	28.0540	+	29.6509i	0.962244	+	1.01702i
$851$	−14.6214	+	42.6592i	−0.501213	+	1.46234i
$852$	5.61347	+	5.61347i	0.192314	+	0.192314i
$853$	14.3534	−	26.2862i	0.491449	−	0.900023i	−0.507807	−	0.861471i	$-0.669544\pi$
$853$	14.3534	−	26.2862i	0.491449	−	0.900023i	0.999257	−	0.0385517i	$-0.0122744\pi$
$854$	0.0203732	−	0.0176534i	0.000697155	−	0.000604089i
$855$	−8.00642	+	1.33043i	−0.273814	+	0.0454998i
$856$	19.2518	−	2.76799i	0.658012	−	0.0946078i
$857$	−6.66406	−	30.6342i	−0.227640	−	1.04644i	−0.939081	−	0.343697i	$-0.888321\pi$
$857$	−6.66406	−	30.6342i	−0.227640	−	1.04644i	0.711441	−	0.702746i	$-0.248043\pi$
$858$	−0.807812	+	0.301298i	−0.0275782	+	0.0102861i
$859$	−0.401097	−	0.347553i	−0.0136853	−	0.0118584i	0.647991	−	0.761648i	$-0.275609\pi$
$859$	−0.401097	−	0.347553i	−0.0136853	−	0.0118584i	−0.661677	+	0.749789i	$0.730155\pi$
$860$	19.6942	−	4.73747i	0.671568	−	0.161546i
$861$	2.74374	−	1.25302i	0.0935065	−	0.0427030i
$862$	−3.91223	+	2.13624i	−0.133251	+	0.0727606i
$863$	43.3245	−	23.6570i	1.47478	−	0.805293i	0.477478	−	0.878644i	$-0.341551\pi$
$863$	43.3245	−	23.6570i	1.47478	−	0.805293i	0.997306	+	0.0733503i	$0.0233691\pi$
$864$	−0.909632	+	0.415415i	−0.0309463	+	0.0141327i
$865$	−0.377193	+	0.0907341i	−0.0128250	+	0.00308505i
$866$	0.105525	+	0.0914377i	0.00358588	+	0.00310718i
$867$	−46.5179	+	17.3503i	−1.57983	+	0.589246i
$868$	−0.327523	−	1.50560i	−0.0111169	−	0.0511034i
$869$	30.8551	−	4.43629i	1.04669	−	0.150491i
$870$	−6.55672	+	1.08953i	−0.222293	+	0.0369386i
$871$	4.49293	−	3.89315i	0.152237	−	0.131914i
$872$	4.75308	−	8.70461i	0.160959	−	0.294775i
$873$	−9.11366	−	9.11366i	−0.308451	−	0.308451i
$874$	−10.8015	−	13.6507i	−0.365366	−	0.461743i
$875$	1.19254	−	2.57171i	0.0403151	−	0.0869395i
$876$	−6.13483	+	1.80135i	−0.207277	+	0.0608619i
$877$	0.0679735	−	0.950393i	0.00229530	−	0.0320925i	−0.996175	−	0.0873762i	$-0.972152\pi$
$877$	0.0679735	−	0.950393i	0.00229530	−	0.0320925i	0.998471	+	0.0552837i	$0.0176063\pi$
$878$	1.34444	−	6.18028i	0.0453725	−	0.208574i
$879$	−3.34300	−	23.2511i	−0.112757	−	0.784240i
$880$	−2.63892	−	3.91529i	−0.0889579	−	0.131984i
$881$	48.5684	+	22.1804i	1.63631	+	0.747278i	0.999714	−	0.0239200i	$-0.00761468\pi$
$881$	48.5684	+	22.1804i	1.63631	+	0.747278i	0.636596	+	0.771198i	$0.280342\pi$
$882$	−6.91804	+	0.494788i	−0.232943	+	0.0166604i
$883$	9.54446	+	12.7499i	0.321197	+	0.429069i	0.931858	−	0.362823i	$-0.118187\pi$
$883$	9.54446	+	12.7499i	0.321197	+	0.429069i	−0.610661	+	0.791892i	$0.709096\pi$
$884$	1.38474	+	3.03215i	0.0465737	+	0.101982i
$885$	7.48225	−	0.699870i	0.251513	−	0.0235259i
$886$	−19.9768	−	5.86572i	−0.671134	−	0.197063i
$887$	−8.13160	+	21.8017i	−0.273032	+	0.732028i	0.725985	+	0.687710i	$0.241384\pi$
$887$	−8.13160	+	21.8017i	−0.273032	+	0.732028i	−0.999017	+	0.0443177i	$0.985889\pi$
$888$	−7.52751	+	5.63502i	−0.252607	+	0.189099i
$889$	1.19929	−	1.38405i	0.0402229	−	0.0464197i
$890$	−1.64337	+	33.1498i	−0.0550860	+	1.11118i
$891$	1.14159	−	1.77636i	0.0382448	−	0.0595101i
$892$	9.71306	−	12.9751i	0.325217	−	0.434439i
$893$	−12.4702	−	2.71272i	−0.417298	−	0.0907776i
$894$	−9.20114	−	10.6187i	−0.307732	−	0.355142i
$895$	−9.69914	−	1.17870i	−0.324206	−	0.0393997i
$896$			0.253548i			0.00847044i
$897$	0.330517	+	1.93009i	0.0110357	+	0.0644440i
$898$	12.0652	−	12.0652i	0.402620	−	0.402620i
$899$	5.08912	+	17.3320i	0.169732	+	0.578053i
$900$	−0.494526	+	4.97548i	−0.0164842	+	0.165849i
$901$	−52.6806	+	33.8557i	−1.75504	+	1.12790i
$902$	−20.1096	−	15.0539i	−0.669578	−	0.501239i
$903$	2.24434	−	0.488227i	0.0746870	−	0.0162472i
$904$	−3.50163	+	7.66749i	−0.116462	+	0.255017i
$905$	22.9447	−	11.0911i	0.762708	−	0.368679i
$906$	1.59540	−	11.0963i	0.0530037	−	0.368649i
$907$	−30.3805	−	11.3313i	−1.00877	−	0.376251i	−0.209877	−	0.977728i	$-0.567306\pi$
$907$	−30.3805	−	11.3313i	−1.00877	−	0.376251i	−0.798890	+	0.601477i	$0.794579\pi$
$908$	9.67598	+	17.7202i	0.321109	+	0.588067i
$909$	1.04758	−	3.56772i	0.0347460	−	0.118334i
$910$	0.160071	−	0.167229i	0.00530631	−	0.00554360i
$911$	−23.0214	−	3.30998i	−0.762733	−	0.109664i	−0.250039	−	0.968236i	$-0.580443\pi$
$911$	−23.0214	−	3.30998i	−0.762733	−	0.109664i	−0.512694	+	0.858571i	$0.671353\pi$
$912$	−0.258938	−	3.62043i	−0.00857430	−	0.119884i
$913$	1.34069	+	3.59452i	0.0443702	+	0.118961i
$914$	8.18555	+	5.26053i	0.270754	+	0.174003i
$915$	0.118473	+	0.206120i	0.00391658	+	0.00681412i
$916$	1.70703	+	2.65618i	0.0564017	+	0.0877628i
$917$	0.410778	+	0.0293794i	0.0135651	+	0.000970194i
$918$	−7.16523	−	3.91251i	−0.236488	−	0.129132i
$919$	46.9056			1.54727			0.773637	−	0.633629i	$-0.218436\pi$
$919$	46.9056			1.54727			0.773637	+	0.633629i	$0.218436\pi$
$920$	−9.85346	+	4.23193i	−0.324859	+	0.139523i
$921$	10.6791			0.351887
$922$	10.8722	+	5.93668i	0.358058	+	0.195514i
$923$	3.23317	+	0.231241i	0.106421	+	0.00761139i
$924$	−0.289449	−	0.450391i	−0.00952217	−	0.0148168i
$925$	5.40101	+	46.7039i	0.177584	+	1.53561i
$926$	14.4563	+	9.29050i	0.475064	+	0.305305i
$927$	−4.60600	−	12.3492i	−0.151281	−	0.405599i
$928$	−0.212053	−	2.96489i	−0.00696098	−	0.0973272i
$929$	−36.9796	−	5.31687i	−1.21326	−	0.174441i	−0.494177	−	0.869362i	$-0.664530\pi$
$929$	−36.9796	−	5.31687i	−1.21326	−	0.174441i	−0.719086	+	0.694921i	$0.755439\pi$
$930$	13.5854	−	0.297108i	0.445481	−	0.00974255i
$931$	7.09245	−	24.1547i	0.232446	−	0.791637i
$932$	11.1734	+	20.4625i	0.365996	+	0.670272i
$933$	9.44239	+	3.52183i	0.309130	+	0.115300i
$934$	2.00595	−	13.9517i	0.0656367	−	0.456514i
$935$	12.6777	−	36.4018i	0.414604	−	1.19047i
$936$	−0.169618	+	0.371412i	−0.00554415	+	0.0121400i
$937$	−46.2033	+	10.0509i	−1.50940	+	0.328349i	−0.889719	−	0.456509i	$-0.849100\pi$
$937$	−46.2033	+	10.0509i	−1.50940	+	0.328349i	−0.619676	+	0.784858i	$0.712736\pi$
$938$	2.95532	+	2.21233i	0.0964947	+	0.0722351i
$939$	−16.2531	+	10.4452i	−0.530400	+	0.340867i
$940$	−3.61605	+	6.98098i	−0.117943	+	0.227694i
$941$	7.24847	+	24.6860i	0.236294	+	0.804742i	0.989195	+	0.146608i	$0.0468357\pi$
$941$	7.24847	+	24.6860i	0.236294	+	0.804742i	−0.752901	+	0.658134i	$0.771346\pi$
$942$	1.52712	−	1.52712i	0.0497563	−	0.0497563i
$943$	−42.1014	+	38.5040i	−1.37101	+	1.25386i
$944$			3.36077i			0.109384i
$945$	−0.0683963	+	0.562810i	−0.00222493	+	0.0183082i
$946$	−12.5263	−	14.4561i	−0.407264	−	0.470007i
$947$	16.7782	+	3.64988i	0.545219	+	0.118605i	0.476735	−	0.879047i	$-0.341820\pi$
$947$	16.7782	+	3.64988i	0.545219	+	0.118605i	0.0684838	+	0.997652i	$0.478184\pi$
$948$	8.84698	−	11.8182i	0.287336	−	0.383837i
$949$	−1.41143	+	2.19623i	−0.0458171	+	0.0712928i
$950$	−16.2935	−	7.99291i	−0.528630	−	0.259324i
$951$	−12.0566	+	13.9141i	−0.390962	+	0.451194i
$952$	−1.65706	+	1.24046i	−0.0537056	+	0.0402035i
$953$	17.2864	−	46.3467i	0.559962	−	1.50132i	−0.280722	−	0.959789i	$-0.590574\pi$
$953$	17.2864	−	46.3467i	0.559962	−	1.50132i	0.840683	−	0.541527i	$-0.182154\pi$
$954$	−7.35988	−	2.16106i	−0.238285	−	0.0699668i
$955$	41.2761	+	34.2149i	1.33566	+	1.10717i
$956$	−3.41677	−	7.48169i	−0.110506	−	0.241975i
$957$	3.76138	+	5.02461i	0.121588	+	0.162423i
$958$	11.7000	−	0.836802i	0.378010	−	0.0270358i
$959$	1.54918	+	0.707487i	0.0500257	+	0.0228460i
$960$	−2.19484	−	0.427424i	−0.0708381	−	0.0137950i
$961$	−0.843931	−	5.86967i	−0.0272236	−	0.189344i
$962$	−0.816114	+	3.75162i	−0.0263126	+	0.120957i
$963$	−1.38753	+	19.4002i	−0.0447125	+	0.625162i
$964$	11.5559	−	3.39311i	0.372189	−	0.109285i
$965$	−1.09962	−	2.76220i	−0.0353982	−	0.0889183i
$966$	−1.12751	+	0.455315i	−0.0362770	+	0.0146495i
$967$	15.4172	+	15.4172i	0.495785	+	0.495785i	0.910123	−	0.414338i	$-0.135987\pi$
$967$	15.4172	+	15.4172i	0.495785	+	0.495785i	−0.414338	+	0.910123i	$0.635987\pi$
$968$	3.13492	−	5.74118i	0.100760	−	0.184529i
$969$	22.3944	−	19.4049i	0.719413	−	0.623375i
$970$	−4.72424	−	28.4301i	−0.151686	−	0.912835i
$971$	22.3708	−	3.21643i	0.717912	−	0.103220i	0.226329	−	0.974051i	$-0.427328\pi$
$971$	22.3708	−	3.21643i	0.717912	−	0.103220i	0.491583	+	0.870831i	$0.336419\pi$
$972$	−0.212565	−	0.977147i	−0.00681803	−	0.0313420i
$973$	0.263432	−	0.0982549i	0.00844523	−	0.00314991i
$974$	17.4848	+	15.1506i	0.560248	+	0.485457i
$975$	1.17778	+	1.66757i	0.0377190	+	0.0534049i
$976$	−0.0967133	+	0.0441675i	−0.00309572	+	0.00141377i
$977$	−42.9151	+	23.4334i	−1.37298	+	0.749702i	−0.985096	−	0.172008i	$-0.944974\pi$
$977$	−42.9151	+	23.4334i	−1.37298	+	0.749702i	−0.387880	+	0.921710i	$0.626793\pi$
$978$	0.0580604	−	0.0317034i	0.00185657	−	0.00101376i
$979$	28.5100	−	13.0201i	0.911185	−	0.416124i
$980$	−13.2270	−	8.09739i	−0.422520	−	0.258661i
$981$	7.49534	+	6.49475i	0.239308	+	0.207361i
$982$	−14.3138	+	5.33877i	−0.456771	+	0.170367i
$983$	−2.43619	−	11.1990i	−0.0777025	−	0.357193i	0.921836	−	0.387581i	$-0.126689\pi$
$983$	−2.43619	−	11.1990i	−0.0777025	−	0.357193i	−0.999538	+	0.0303883i	$0.990326\pi$
$984$	−11.7754	+	1.69304i	−0.375385	+	0.0539722i
$985$	15.3461	−	21.4626i	0.488968	−	0.683857i
$986$	18.3395	−	15.8913i	0.584050	−	0.506082i
$987$	−0.427233	+	0.782420i	−0.0135990	+	0.0249047i
$988$	−1.04796	−	1.04796i	−0.0333400	−	0.0333400i
$989$	−37.5586	+	21.8349i	−1.19429	+	0.694310i
$990$	4.38675	−	1.74636i	0.139420	−	0.0555029i
$991$	−0.135497	+	0.0397855i	−0.00430420	+	0.00126383i	−0.283884	−	0.958859i	$-0.591623\pi$
$991$	−0.135497	+	0.0397855i	−0.00430420	+	0.00126383i	0.279580	+	0.960122i	$0.409805\pi$
$992$	−0.433529	+	6.06152i	−0.0137646	+	0.192454i
$993$	1.61529	−	7.42537i	0.0512597	−	0.235637i
$994$	0.286455	+	1.99234i	0.00908580	+	0.0631931i
$995$	32.2238	−	21.7190i	1.02156	−	0.688538i
$996$	1.65267	+	0.754750i	0.0523669	+	0.0239152i
$997$	−35.0064	+	2.50371i	−1.10866	+	0.0792932i	−0.613640	−	0.789586i	$-0.710295\pi$
$997$	−35.0064	+	2.50371i	−1.10866	+	0.0792932i	−0.495024	+	0.868879i	$0.664841\pi$
$998$	−6.32637	−	8.45104i	−0.200258	−	0.267513i
$999$	−3.90616	−	8.55330i	−0.123585	−	0.270614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.37.1	✓	240
5.3	odd	4	inner	690.2.w.a.313.1	yes	240
23.5	odd	22	inner	690.2.w.a.97.1	yes	240
115.28	even	44	inner	690.2.w.a.373.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.37.1	✓	240	1.1	even	1	trivial
690.2.w.a.97.1	yes	240	23.5	odd	22	inner
690.2.w.a.313.1	yes	240	5.3	odd	4	inner
690.2.w.a.373.1	yes	240	115.28	even	44	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.877679 - 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-2.15875 - 0.582912i) q^{5} +(0.841254 + 0.540641i) q^{6} +(0.0886059 + 0.237562i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})\)	\(q+(-0.877679 - 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-2.15875 - 0.582912i) q^{5} +(0.841254 + 0.540641i) q^{6} +(0.0886059 + 0.237562i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(1.61533 + 1.54619i) q^{10} +(0.594895 - 2.02602i) q^{11} +(-0.479249 - 0.877679i) q^{12} +(-0.382567 - 0.142690i) q^{13} +(0.0360836 - 0.250967i) q^{14} +(2.11167 + 0.735431i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(-7.97727 + 1.73535i) q^{17} +(-0.800541 - 0.599278i) q^{18} +(3.05348 - 1.96235i) q^{19} +(-0.676733 - 2.13120i) q^{20} +(-0.0714327 - 0.243277i) q^{21} +(-1.49310 + 1.49310i) q^{22} +(2.70000 + 3.96358i) q^{23} +1.00000i q^{24} +(4.32043 + 2.51673i) q^{25} +(0.267387 + 0.308581i) q^{26} +(-0.977147 - 0.212565i) q^{27} +(-0.151946 + 0.202976i) q^{28} +(1.60703 - 2.50059i) q^{29} +(-1.50091 - 1.65749i) q^{30} +(-3.97959 + 4.59270i) q^{31} +(0.800541 - 0.599278i) q^{32} +(-0.737914 + 1.97842i) q^{33} +(7.83314 + 2.30002i) q^{34} +(-0.0528006 - 0.564486i) q^{35} +(0.415415 + 0.909632i) q^{36} +(5.63502 + 7.52751i) q^{37} +(-3.62043 + 0.258938i) q^{38} +(0.371412 + 0.169618i) q^{39} +(-0.427424 + 2.19484i) q^{40} +(1.69304 + 11.7754i) q^{41} +(-0.0538955 + 0.247754i) q^{42} +(-0.646245 + 9.03569i) q^{43} +(2.02602 - 0.594895i) q^{44} +(-2.05382 - 0.884202i) q^{45} +(-0.470191 - 4.77273i) q^{46} +(-2.48616 - 2.48616i) q^{47} +(0.479249 - 0.877679i) q^{48} +(5.24166 - 4.54193i) q^{49} +(-2.58581 - 4.27944i) q^{50} +(8.08074 - 1.16183i) q^{51} +(-0.0867927 - 0.398980i) q^{52} +(7.18696 - 2.68060i) q^{53} +(0.755750 + 0.654861i) q^{54} +(-2.46523 + 4.02692i) q^{55} +(0.230635 - 0.105328i) q^{56} +(-3.18569 + 1.73952i) q^{57} +(-2.60887 + 1.42455i) q^{58} +(3.05706 - 1.39611i) q^{59} +(0.522970 + 2.17405i) q^{60} +(0.0803523 + 0.0696257i) q^{61} +(5.69385 - 2.12370i) q^{62} +(0.0538955 + 0.247754i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(0.742691 + 0.531035i) q^{65} +(1.59581 - 1.38278i) q^{66} +(-6.97786 + 12.7790i) q^{67} +(-5.77270 - 5.77270i) q^{68} +(-2.41036 - 4.14610i) q^{69} +(-0.224188 + 0.520742i) q^{70} +(-7.61707 + 2.23657i) q^{71} +(0.0713392 - 0.997452i) q^{72} +(1.35911 - 6.24771i) q^{73} +(-1.33819 - 9.30732i) q^{74} +(-4.12988 - 2.81853i) q^{75} +(3.30167 + 1.50782i) q^{76} +(0.534017 - 0.0381936i) q^{77} +(-0.244691 - 0.326870i) q^{78} +(6.13266 + 13.4287i) q^{79} +(1.42701 - 1.72152i) q^{80} +(0.959493 + 0.281733i) q^{81} +(4.15738 - 11.1464i) q^{82} +(-1.45447 + 1.08880i) q^{83} +(0.166039 - 0.191619i) q^{84} +(18.2325 + 0.903861i) q^{85} +(4.89754 - 7.62072i) q^{86} +(-1.78133 + 2.37958i) q^{87} +(-2.06330 - 0.448844i) q^{88} +(9.72027 + 11.2178i) q^{89} +(1.37884 + 1.76034i) q^{90} -0.103526i q^{91} +(-1.87465 + 4.41426i) q^{92} +(4.29709 - 4.29709i) q^{93} +(0.990561 + 3.37354i) q^{94} +(-7.73559 + 2.45632i) q^{95} +(-0.841254 + 0.540641i) q^{96} +(-10.3179 - 7.72389i) q^{97} +(-6.77721 + 1.47429i) q^{98} +(0.877173 - 1.92074i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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