LMFDB - Embedded newform 690.2.w.a.217.2

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			217.2
Character	$\chi$	$=$	690.217
Dual form			690.2.w.a.283.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0713392 + 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.84002 + 1.27057i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.09069 - 1.14160i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.0713392 + 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.84002 + 1.27057i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.09069 - 1.14160i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-1.13606 - 1.92597i) q^{10} +(-2.30969 - 2.00135i) q^{11} +(0.997452 - 0.0713392i) q^{12} +(-1.43513 + 2.62824i) q^{13} +(0.989548 + 2.16681i) q^{14} +(1.52789 - 1.63265i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-4.68542 - 3.50746i) q^{17} +(0.349464 + 0.936950i) q^{18} +(0.140830 - 0.979493i) q^{19} +(2.00211 - 0.995772i) q^{20} +(-1.80025 + 1.55992i) q^{21} +(2.16103 - 2.16103i) q^{22} +(1.37563 - 4.59431i) q^{23} +1.00000i q^{24} +(1.77132 - 4.67573i) q^{25} +(-2.51916 - 1.61897i) q^{26} +(-0.800541 + 0.599278i) q^{27} +(-2.23188 + 0.832448i) q^{28} +(-0.861813 + 0.123910i) q^{29} +(1.51950 + 1.64047i) q^{30} +(8.81840 - 5.66724i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(2.68232 + 1.46466i) q^{33} +(3.83278 - 4.42326i) q^{34} +(-2.39643 + 4.75693i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(6.88519 + 2.56804i) q^{37} +(0.966951 + 0.210347i) q^{38} +(0.843658 - 2.87323i) q^{39} +(0.850406 + 2.06804i) q^{40} +(4.85958 - 10.6410i) q^{41} +(-1.42752 - 1.90695i) q^{42} +(0.899167 + 4.13340i) q^{43} +(2.00135 + 2.30969i) q^{44} +(-1.14593 + 1.92012i) q^{45} +(4.48446 + 1.69988i) q^{46} +(-0.0353404 - 0.0353404i) q^{47} +(-0.997452 - 0.0713392i) q^{48} +(-0.716751 + 1.11529i) q^{49} +(4.53745 + 2.10037i) q^{50} +(5.32390 + 2.43135i) q^{51} +(1.79456 - 2.39725i) q^{52} +(1.69886 + 3.11123i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(6.79272 + 0.747917i) q^{55} +(-0.671107 - 2.28558i) q^{56} +(0.0705948 + 0.987044i) q^{57} +(-0.0621132 - 0.868457i) q^{58} +(-2.30687 - 7.85647i) q^{59} +(-1.74469 + 1.39859i) q^{60} +(-5.80221 - 9.02841i) q^{61} +(5.02371 + 9.20023i) q^{62} +(1.42752 - 1.90695i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-0.698693 - 6.65943i) q^{65} +(-1.65228 + 2.57100i) q^{66} +(-1.56730 - 0.112095i) q^{67} +(4.13856 + 4.13856i) q^{68} +(-0.367603 + 4.78172i) q^{69} +(-4.57386 - 2.72968i) q^{70} +(1.17691 + 1.35823i) q^{71} +(-0.212565 - 0.977147i) q^{72} +(-9.16298 - 12.2403i) q^{73} +(-3.05268 + 6.68444i) q^{74} +(-0.736947 + 4.94539i) q^{75} +(-0.278793 + 0.949481i) q^{76} +(-7.11360 - 1.54747i) q^{77} +(2.80573 + 1.04648i) q^{78} +(-16.0559 + 4.71444i) q^{79} +(-2.12344 + 0.700707i) q^{80} +(0.654861 - 0.755750i) q^{81} +(10.2672 + 5.60631i) q^{82} +(-1.97579 + 5.29729i) q^{83} +(2.00392 - 1.28784i) q^{84} +(13.0777 + 0.500652i) q^{85} +(-4.18702 + 0.602002i) q^{86} +(0.815779 - 0.304270i) q^{87} +(-2.44658 + 1.83148i) q^{88} +(-5.50859 - 3.54016i) q^{89} +(-1.83348 - 1.27999i) q^{90} +7.13319i q^{91} +(-2.01547 + 4.35177i) q^{92} +(-7.41221 + 7.41221i) q^{93} +(0.0377715 - 0.0327292i) q^{94} +(0.985382 + 1.98122i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-0.873842 - 2.34286i) q^{97} +(-1.06131 - 0.794489i) q^{98} +(-2.93236 - 0.861018i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.0713392	+	0.997452i	−0.0504444	+	0.705305i
$2$	−0.0713392	+	0.997452i	−0.0504444	+	0.705305i
$3$	−0.977147	+	0.212565i	−0.564156	+	0.122725i
$3$	−0.977147	+	0.212565i	−0.564156	+	0.122725i
$4$	−0.989821	−	0.142315i	−0.494911	−	0.0711574i
$5$	−1.84002	+	1.27057i	−0.822881	+	0.568214i
$5$	−1.84002	+	1.27057i	−0.822881	+	0.568214i
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	2.09069	−	1.14160i	0.790208	−	0.431486i	−0.0328385	−	0.999461i	$-0.510455\pi$
$7$	2.09069	−	1.14160i	0.790208	−	0.431486i	0.823046	+	0.567975i	$0.192273\pi$
$8$	0.212565	−	0.977147i	0.0751532	−	0.345474i
$9$	0.909632	−	0.415415i	0.303211	−	0.138472i
$10$	−1.13606	−	1.92597i	−0.359255	−	0.609045i
$11$	−2.30969	−	2.00135i	−0.696397	−	0.603431i	0.233016	−	0.972473i	$-0.425141\pi$
$11$	−2.30969	−	2.00135i	−0.696397	−	0.603431i	−0.929413	+	0.369042i	$0.879686\pi$
$12$	0.997452	−	0.0713392i	0.287940	−	0.0205938i
$13$	−1.43513	+	2.62824i	−0.398033	+	0.728942i	−0.997440	−	0.0715014i	$-0.977221\pi$
$13$	−1.43513	+	2.62824i	−0.398033	+	0.728942i	0.599408	+	0.800444i	$0.295403\pi$
$14$	0.989548	+	2.16681i	0.264468	+	0.579103i
$15$	1.52789	−	1.63265i	0.394499	−	0.421549i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−4.68542	−	3.50746i	−1.13638	−	0.850684i	−0.146031	−	0.989280i	$-0.546650\pi$
$17$	−4.68542	−	3.50746i	−1.13638	−	0.850684i	−0.990349	+	0.138596i	$0.955741\pi$
$18$	0.349464	+	0.936950i	0.0823695	+	0.220841i
$19$	0.140830	−	0.979493i	0.0323086	−	0.224711i	−0.967270	−	0.253751i	$-0.918336\pi$
$19$	0.140830	−	0.979493i	0.0323086	−	0.224711i	0.999578	+	0.0290394i	$0.00924484\pi$
$20$	2.00211	−	0.995772i	0.447685	−	0.222661i
$21$	−1.80025	+	1.55992i	−0.392846	+	0.340403i
$22$	2.16103	−	2.16103i	0.460732	−	0.460732i
$23$	1.37563	−	4.59431i	0.286839	−	0.957979i
$23$	1.37563	−	4.59431i	0.286839	−	0.957979i
$24$			1.00000i			0.204124i
$25$	1.77132	−	4.67573i	0.354265	−	0.935145i
$26$	−2.51916	−	1.61897i	−0.494048	−	0.317506i
$27$	−0.800541	+	0.599278i	−0.154064	+	0.115331i
$28$	−2.23188	+	0.832448i	−0.421786	+	0.157318i
$29$	−0.861813	+	0.123910i	−0.160035	+	0.0230095i	−0.221866	−	0.975077i	$-0.571215\pi$
$29$	−0.861813	+	0.123910i	−0.160035	+	0.0230095i	0.0618317	+	0.998087i	$0.480306\pi$
$30$	1.51950	+	1.64047i	0.277421	+	0.299507i
$31$	8.81840	−	5.66724i	1.58383	−	1.01787i	0.609490	−	0.792794i	$-0.291374\pi$
$31$	8.81840	−	5.66724i	1.58383	−	1.01787i	0.974342	−	0.225073i	$-0.0722620\pi$
$32$	−0.349464	+	0.936950i	−0.0617771	+	0.165631i
$33$	2.68232	+	1.46466i	0.466932	+	0.254964i
$34$	3.83278	−	4.42326i	0.657316	−	0.758583i
$35$	−2.39643	+	4.75693i	−0.405070	+	0.804069i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	6.88519	+	2.56804i	1.13192	+	0.422183i	0.844465	−	0.535611i	$-0.179919\pi$
$37$	6.88519	+	2.56804i	1.13192	+	0.422183i	0.287453	+	0.957795i	$0.407192\pi$
$38$	0.966951	+	0.210347i	0.156860	+	0.0341228i
$39$	0.843658	−	2.87323i	0.135093	−	0.460086i
$40$	0.850406	+	2.06804i	0.134461	+	0.326987i
$41$	4.85958	−	10.6410i	0.758938	−	1.66184i	0.00933471	−	0.999956i	$-0.497029\pi$
$41$	4.85958	−	10.6410i	0.758938	−	1.66184i	0.749604	−	0.661887i	$-0.230244\pi$
$42$	−1.42752	−	1.90695i	−0.220271	−	0.294248i
$43$	0.899167	+	4.13340i	0.137122	+	0.630338i	0.993485	+	0.113964i	$0.0363549\pi$
$43$	0.899167	+	4.13340i	0.137122	+	0.630338i	−0.856363	+	0.516374i	$0.827281\pi$
$44$	2.00135	+	2.30969i	0.301716	+	0.348198i
$45$	−1.14593	+	1.92012i	−0.170825	+	0.286234i
$46$	4.48446	+	1.69988i	0.661198	+	0.250633i
$47$	−0.0353404	−	0.0353404i	−0.00515493	−	0.00515493i	0.704525	−	0.709680i	$-0.251160\pi$
$47$	−0.0353404	−	0.0353404i	−0.00515493	−	0.00515493i	−0.709680	+	0.704525i	$0.751160\pi$
$48$	−0.997452	−	0.0713392i	−0.143970	−	0.0102969i
$49$	−0.716751	+	1.11529i	−0.102393	+	0.159327i
$50$	4.53745	+	2.10037i	0.641692	+	0.297038i
$51$	5.32390	+	2.43135i	0.745496	+	0.340456i
$52$	1.79456	−	2.39725i	0.248860	−	0.332438i
$53$	1.69886	+	3.11123i	0.233356	+	0.427360i	0.967949	−	0.251149i	$-0.0808083\pi$
$53$	1.69886	+	3.11123i	0.233356	+	0.427360i	−0.734592	+	0.678509i	$0.762626\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	6.79272	+	0.747917i	0.915930	+	0.100849i
$56$	−0.671107	−	2.28558i	−0.0896804	−	0.305423i
$57$	0.0705948	+	0.987044i	0.00935051	+	0.130737i
$58$	−0.0621132	−	0.868457i	−0.00815587	−	0.114034i
$59$	−2.30687	−	7.85647i	−0.300329	−	1.02283i	−0.962004	−	0.273035i	$-0.911972\pi$
$59$	−2.30687	−	7.85647i	−0.300329	−	1.02283i	0.661675	−	0.749790i	$-0.269846\pi$
$60$	−1.74469	+	1.39859i	−0.225238	+	0.180558i
$61$	−5.80221	−	9.02841i	−0.742896	−	1.15597i	−0.982710	−	0.185151i	$-0.940723\pi$
$61$	−5.80221	−	9.02841i	−0.742896	−	1.15597i	0.239814	−	0.970819i	$-0.422914\pi$
$62$	5.02371	+	9.20023i	0.638011	+	1.16843i
$63$	1.42752	−	1.90695i	0.179851	−	0.240252i
$64$	−0.909632	−	0.415415i	−0.113704	−	0.0519269i
$65$	−0.698693	−	6.65943i	−0.0866622	−	0.826000i
$66$	−1.65228	+	2.57100i	−0.203382	+	0.316468i
$67$	−1.56730	−	0.112095i	−0.191476	−	0.0136946i	−0.0247280	−	0.999694i	$-0.507872\pi$
$67$	−1.56730	−	0.112095i	−0.191476	−	0.0136946i	−0.166748	+	0.986000i	$0.553327\pi$
$68$	4.13856	+	4.13856i	0.501874	+	0.501874i
$69$	−0.367603	+	4.78172i	−0.0442542	+	0.575652i
$70$	−4.57386	−	2.72968i	−0.546680	−	0.326259i
$71$	1.17691	+	1.35823i	0.139674	+	0.161192i	0.821277	−	0.570530i	$-0.193262\pi$
$71$	1.17691	+	1.35823i	0.139674	+	0.161192i	−0.681603	+	0.731722i	$0.738717\pi$
$72$	−0.212565	−	0.977147i	−0.0250511	−	0.115158i
$73$	−9.16298	−	12.2403i	−1.07245	−	1.43262i	−0.893667	−	0.448730i	$-0.851876\pi$
$73$	−9.16298	−	12.2403i	−1.07245	−	1.43262i	−0.178778	−	0.983889i	$-0.557214\pi$
$74$	−3.05268	+	6.68444i	−0.354867	+	0.777050i
$75$	−0.736947	+	4.94539i	−0.0850953	+	0.571045i
$76$	−0.278793	+	0.949481i	−0.0319797	+	0.108913i
$77$	−7.11360	−	1.54747i	−0.810670	−	0.176350i
$78$	2.80573	+	1.04648i	0.317686	+	0.118491i
$79$	−16.0559	+	4.71444i	−1.80643	+	0.530416i	−0.998284	−	0.0585643i	$-0.981348\pi$
$79$	−16.0559	+	4.71444i	−1.80643	+	0.530416i	−0.808147	+	0.588980i	$0.799530\pi$
$80$	−2.12344	+	0.700707i	−0.237408	+	0.0783414i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	10.2672	+	5.60631i	1.13382	+	0.619114i
$83$	−1.97579	+	5.29729i	−0.216871	+	0.581453i	−0.999139	−	0.0414887i	$-0.986790\pi$
$83$	−1.97579	+	5.29729i	−0.216871	+	0.581453i	0.782268	+	0.622942i	$0.214063\pi$
$84$	2.00392	−	1.28784i	0.218646	−	0.140515i
$85$	13.0777	+	0.500652i	1.41848	+	0.0543033i
$86$	−4.18702	+	0.602002i	−0.451498	+	0.0649156i
$87$	0.815779	−	0.304270i	0.0874607	−	0.0326211i
$88$	−2.44658	+	1.83148i	−0.260806	+	0.195237i
$89$	−5.50859	−	3.54016i	−0.583910	−	0.375256i	0.215084	−	0.976596i	$-0.430998\pi$
$89$	−5.50859	−	3.54016i	−0.583910	−	0.375256i	−0.798994	+	0.601340i	$0.794634\pi$
$90$	−1.83348	−	1.27999i	−0.193265	−	0.134922i
$91$			7.13319i			0.747761i
$92$	−2.01547	+	4.35177i	−0.210127	+	0.453703i
$93$	−7.41221	+	7.41221i	−0.768611	+	0.768611i
$94$	0.0377715	−	0.0327292i	0.00389583	−	0.00337576i
$95$	0.985382	+	1.98122i	0.101098	+	0.203269i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	−0.873842	−	2.34286i	−0.0887252	−	0.237881i	0.885007	−	0.465578i	$-0.154153\pi$
$97$	−0.873842	−	2.34286i	−0.0887252	−	0.237881i	−0.973732	+	0.227696i	$0.926881\pi$
$98$	−1.06131	−	0.794489i	−0.107209	−	0.0802555i
$99$	−2.93236	−	0.861018i	−0.294713	−	0.0865356i
$100$	−2.41872	+	4.37605i	−0.241872	+	0.437605i
$101$	−2.18984	−	4.79507i	−0.217897	−	0.477127i	0.768843	−	0.639438i	$-0.220833\pi$
$101$	−2.18984	−	4.79507i	−0.217897	−	0.477127i	−0.986740	+	0.162310i	$0.948105\pi$
$102$	−2.80495	+	5.13689i	−0.277732	+	0.508628i
$103$	7.89456	−	0.564630i	0.777874	−	0.0556346i	0.323245	−	0.946315i	$-0.395226\pi$
$103$	7.89456	−	0.564630i	0.777874	−	0.0556346i	0.454629	+	0.890681i	$0.349772\pi$
$104$	2.26312	+	1.96100i	0.221917	+	0.192292i
$105$	1.33050	−	5.15762i	0.129844	−	0.503332i
$106$	−3.22450	+	1.47258i	−0.313191	+	0.143029i
$107$	−0.0676639	+	0.311046i	−0.00654132	+	0.0300700i	−0.980302	−	0.197505i	$-0.936716\pi$
$107$	−0.0676639	+	0.311046i	−0.00654132	+	0.0300700i	0.973761	+	0.227575i	$0.0730797\pi$
$108$	0.877679	−	0.479249i	0.0844547	−	0.0461158i
$109$	−1.84890	−	12.8594i	−0.177093	−	1.23171i	−0.863447	−	0.504440i	$-0.831699\pi$
$109$	−1.84890	−	12.8594i	−0.177093	−	1.23171i	0.686354	−	0.727268i	$-0.259210\pi$
$110$	−1.23060	+	6.72205i	−0.117333	+	0.640923i
$111$	−7.27371	−	1.04580i	−0.690390	−	0.0992632i
$112$	2.32763	−	0.506345i	0.219941	−	0.0478451i
$113$	−1.14678	+	16.0340i	−0.107880	+	1.50835i	0.598845	+	0.800865i	$0.295626\pi$
$113$	−1.14678	+	16.0340i	−0.107880	+	1.50835i	−0.706725	+	0.707488i	$0.749828\pi$
$114$	−0.989566			−0.0926813
$115$	3.30619	+	10.2014i	0.308303	+	0.951288i
$116$	0.870675			0.0808401
$117$	−0.213628	+	2.98690i	−0.0197499	+	0.276139i
$118$	8.00102	−	1.74052i	0.736554	−	0.160228i
$119$	−13.7999	−	1.98413i	−1.26503	−	0.181884i
$120$	−1.27057	−	1.84002i	−0.115986	−	0.167970i
$121$	−0.236232	−	1.64303i	−0.0214756	−	0.149366i
$122$	9.41933	−	5.14334i	0.852786	−	0.465656i
$123$	−2.48662	+	11.4308i	−0.224211	+	1.03068i
$124$	−9.53518	+	4.35457i	−0.856284	+	0.391052i
$125$	2.68155	+	10.8540i	0.239845	+	0.970811i
$126$	1.80025	+	1.55992i	0.160379	+	0.138969i
$127$	2.29512	−	0.164150i	0.203659	−	0.0145660i	0.0308630	−	0.999524i	$-0.490174\pi$
$127$	2.29512	−	0.164150i	0.203659	−	0.0145660i	0.172796	+	0.984958i	$0.444720\pi$
$128$	0.479249	−	0.877679i	0.0423600	−	0.0775766i
$129$	−1.75724	−	3.84781i	−0.154716	−	0.338781i
$130$	6.69230	−	0.221835i	0.586954	−	0.0194562i
$131$	1.85547	+	0.544815i	0.162113	+	0.0476007i	0.361782	−	0.932263i	$-0.382168\pi$
$131$	1.85547	+	0.544815i	0.162113	+	0.0476007i	−0.199669	+	0.979863i	$0.563987\pi$
$132$	−2.44658	−	1.83148i	−0.212947	−	0.159410i
$133$	−0.823762	−	2.20859i	−0.0714292	−	0.191509i
$134$	0.223619	−	1.55531i	0.0193178	−	0.134358i
$135$	0.711587	−	2.11982i	0.0612437	−	0.182445i
$136$	−4.42326	+	3.83278i	−0.379291	+	0.328658i
$137$	−9.28084	+	9.28084i	−0.792915	+	0.792915i	−0.981967	−	0.189052i	$-0.939459\pi$
$137$	−9.28084	+	9.28084i	−0.792915	+	0.792915i	0.189052	+	0.981967i	$0.439459\pi$
$138$	−4.74331	−	0.707790i	−0.403778	−	0.0602511i
$139$		−	15.4238i		−	1.30823i	−0.756396	−	0.654114i	$-0.773041\pi$
$139$		−	15.4238i		−	1.30823i	0.756396	−	0.654114i	$-0.226959\pi$
$140$	3.04902	−	4.36747i	0.257689	−	0.369118i
$141$	0.0420449	+	0.0270206i	0.00354082	+	0.00227555i
$142$	−1.43873	+	1.07702i	−0.120736	+	0.0903815i
$143$	8.57473	−	3.19821i	0.717055	−	0.267448i
$144$	0.989821	−	0.142315i	0.0824851	−	0.0118596i
$145$	1.42831	−	1.32299i	0.118615	−	0.109868i
$146$	12.8628	−	8.26642i	1.06453	−	0.684134i
$147$	0.463300	−	1.24216i	0.0382123	−	0.102451i
$148$	−6.44963	−	3.52177i	−0.530157	−	0.289487i
$149$	10.9813	−	12.6731i	0.899622	−	1.03822i	−0.0994450	−	0.995043i	$-0.531707\pi$
$149$	10.9813	−	12.6731i	0.899622	−	1.03822i	0.999067	−	0.0431766i	$-0.0137478\pi$
$150$	−4.88022	−	1.08787i	−0.398468	−	0.0888241i
$151$	4.85383	−	1.42521i	0.394999	−	0.115982i	−0.0781999	−	0.996938i	$-0.524917\pi$
$151$	4.85383	−	1.42521i	0.394999	−	0.115982i	0.473199	+	0.880955i	$0.343099\pi$
$152$	−0.927173	−	0.345818i	−0.0752037	−	0.0280495i
$153$	−5.71906	−	1.24410i	−0.462358	−	0.100580i
$154$	2.05100	−	6.98508i	0.165275	−	0.562874i
$155$	−9.02540	+	21.6322i	−0.724938	+	1.73754i
$156$	−1.24397	+	2.72392i	−0.0995976	+	0.218088i
$157$	3.99841	+	5.34125i	0.319108	+	0.426278i	0.931200	−	0.364508i	$-0.118763\pi$
$157$	3.99841	+	5.34125i	0.319108	+	0.426278i	−0.612092	+	0.790786i	$0.709672\pi$
$158$	−3.55701	−	16.3513i	−0.282981	−	1.30084i
$159$	−2.32137	−	2.67901i	−0.184097	−	0.212459i
$160$	−0.547437	−	2.16802i	−0.0432787	−	0.171397i
$161$	−2.36886	−	11.1757i	−0.186692	−	0.880769i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−1.49555	−	0.106964i	−0.117140	−	0.00837804i	0.0126460	−	0.999920i	$-0.495975\pi$
$163$	−1.49555	−	0.106964i	−0.117140	−	0.00837804i	−0.129786	+	0.991542i	$0.541429\pi$
$164$	−6.32448	+	9.84109i	−0.493859	+	0.768460i
$165$	−6.79646	+	0.713071i	−0.529104	+	0.0555125i
$166$	−5.14284	−	2.34866i	−0.399162	−	0.182291i
$167$	−5.34938	+	7.14593i	−0.413947	+	0.552969i	−0.958254	−	0.285917i	$-0.907702\pi$
$167$	−5.34938	+	7.14593i	−0.413947	+	0.552969i	0.544307	+	0.838886i	$0.316793\pi$
$168$	1.14160	+	2.09069i	0.0880767	+	0.161300i
$169$	2.18028	+	3.39258i	0.167714	+	0.260968i
$170$	−1.43233	+	13.0087i	−0.109855	+	0.997719i
$171$	−0.278793	−	0.949481i	−0.0213198	−	0.0726086i
$172$	−0.301770	−	4.21930i	−0.0230098	−	0.321718i
$173$	0.483609	+	6.76174i	0.0367681	+	0.514086i	0.982147	+	0.188113i	$0.0602371\pi$
$173$	0.483609	+	6.76174i	0.0367681	+	0.514086i	−0.945379	+	0.325973i	$0.894308\pi$
$174$	0.245298	+	0.835407i	0.0185960	+	0.0633320i
$175$	−1.63454	−	11.7977i	−0.123559	−	0.891819i
$176$	−1.65228	−	2.57100i	−0.124545	−	0.193796i
$177$	3.92416	+	7.18657i	0.294958	+	0.540175i
$178$	3.92412	−	5.24201i	0.294125	−	0.392905i
$179$	−2.12122	−	0.968731i	−0.158548	−	0.0724063i	0.334561	−	0.942374i	$-0.391412\pi$
$179$	−2.12122	−	0.968731i	−0.158548	−	0.0724063i	−0.493108	+	0.869968i	$0.664139\pi$
$180$	1.40752	−	1.73749i	0.104911	−	0.129505i
$181$	10.8796	−	16.9290i	0.808677	−	1.25833i	−0.154108	−	0.988054i	$-0.549250\pi$
$181$	10.8796	−	16.9290i	0.808677	−	1.25833i	0.962784	−	0.270271i	$-0.0871134\pi$
$182$	−7.11501	−	0.508876i	−0.527400	−	0.0377204i
$183$	7.58873	+	7.58873i	0.560975	+	0.560975i
$184$	−4.19690	−	2.32078i	−0.309400	−	0.171090i
$185$	−15.9317	+	4.02284i	−1.17132	+	0.295765i
$186$	−6.86455	−	7.92211i	−0.503333	−	0.580877i
$187$	3.80217	+	17.4783i	0.278042	+	1.27814i
$188$	0.0299512	+	0.0400101i	0.00218442	+	0.00291804i
$189$	−0.989548	+	2.16681i	−0.0719790	+	0.157612i
$190$	−2.04647	+	0.841532i	−0.148466	+	0.0610512i
$191$	−6.89390	+	23.4785i	−0.498825	+	1.69884i	0.196806	+	0.980443i	$0.436943\pi$
$191$	−6.89390	+	23.4785i	−0.498825	+	1.69884i	−0.695631	+	0.718400i	$0.744875\pi$
$192$	0.977147	+	0.212565i	0.0705195	+	0.0153406i
$193$	−14.7034	−	5.48408i	−1.05837	−	0.394752i	−0.240798	−	0.970575i	$-0.577409\pi$
$193$	−14.7034	−	5.48408i	−1.05837	−	0.394752i	−0.817575	+	0.575823i	$0.804682\pi$
$194$	2.39923	−	0.704478i	0.172255	−	0.0505786i
$195$	2.09829	+	6.35872i	0.150262	+	0.455357i
$196$	0.868178	−	1.00193i	0.0620127	−	0.0715665i
$197$	−23.8625	−	13.0299i	−1.70013	−	0.928343i	−0.969333	−	0.245752i	$-0.920965\pi$
$197$	−23.8625	−	13.0299i	−1.70013	−	0.928343i	−0.730800	−	0.682591i	$-0.760853\pi$
$198$	1.06802	−	2.86346i	0.0759006	−	0.203497i
$199$	−10.9459	+	7.03451i	−0.775935	+	0.498663i	−0.867682	−	0.497119i	$-0.834391\pi$
$199$	−10.9459	+	7.03451i	−0.775935	+	0.498663i	0.0917475	+	0.995782i	$0.470755\pi$
$200$	−4.19235	−	2.72474i	−0.296444	−	0.192668i
$201$	1.55531	−	0.223619i	0.109703	−	0.0157729i
$202$	4.93907	−	1.84218i	0.347512	−	0.129615i
$203$	−1.66033	+	1.24291i	−0.116532	+	0.0872350i
$204$	−4.92370	−	3.16427i	−0.344728	−	0.221543i
$205$	4.57838	+	25.7540i	0.319768	+	1.79874i
$206$			7.91472i			0.551445i
$207$	−0.657226	−	4.75058i	−0.0456804	−	0.330188i
$208$	−2.11745	+	2.11745i	−0.146819	+	0.146819i
$209$	−2.28559	+	1.98047i	−0.158097	+	0.136992i
$210$	5.04956	+	1.69505i	0.348453	+	0.116970i
$211$	−3.64083	+	25.3225i	−0.250645	+	1.74328i	0.343712	+	0.939075i	$0.388315\pi$
$211$	−3.64083	+	25.3225i	−0.250645	+	1.74328i	−0.594358	+	0.804201i	$0.702594\pi$
$212$	−1.23879	−	3.32133i	−0.0850807	−	0.228110i
$213$	−1.43873	−	1.07702i	−0.0985802	−	0.0737962i
$214$	−0.305427	−	0.0896813i	−0.0208785	−	0.00613049i
$215$	−6.90625	−	6.46308i	−0.471002	−	0.440779i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	11.9668	−	21.9156i	0.812360	−	1.48773i
$218$	12.9585	−	0.926813i	0.877663	−	0.0627717i
$219$	11.5554	+	10.0128i	0.780844	+	0.676605i
$220$	−6.61714	−	1.70701i	−0.446127	−	0.115087i
$221$	15.9426	−	7.28074i	1.07242	−	0.489756i
$222$	1.56204	−	7.18057i	0.104837	−	0.481929i
$223$	2.39280	−	1.30657i	0.160234	−	0.0874942i	−0.397131	−	0.917762i	$-0.629994\pi$
$223$	2.39280	−	1.30657i	0.160234	−	0.0874942i	0.557365	+	0.830268i	$0.311812\pi$
$224$	0.339004	+	2.35782i	0.0226506	+	0.157539i
$225$	−0.331114	−	4.98902i	−0.0220743	−	0.332602i
$226$	−15.9113	−	2.28771i	−1.05841	−	0.152176i
$227$	17.0861	−	3.71685i	1.13404	−	0.246696i	0.393905	−	0.919151i	$-0.371124\pi$
$227$	17.0861	−	3.71685i	1.13404	−	0.246696i	0.740138	+	0.672456i	$0.234760\pi$
$228$	0.0705948	−	0.987044i	0.00467526	−	0.0653686i
$229$	−7.47461			−0.493936			−0.246968	−	0.969024i	$-0.579434\pi$
$229$	−7.47461			−0.493936			−0.246968	+	0.969024i	$0.579434\pi$
$230$	−10.4113	+	2.57000i	−0.686501	+	0.169461i
$231$	7.27997			0.478987
$232$	−0.0621132	+	0.868457i	−0.00407793	+	0.0570170i
$233$	12.0633	−	2.62421i	0.790292	−	0.171917i	0.200736	−	0.979645i	$-0.435667\pi$
$233$	12.0633	−	2.62421i	0.790292	−	0.171917i	0.589555	+	0.807728i	$0.299303\pi$
$234$	−2.96405	−	0.426167i	−0.193766	−	0.0278594i
$235$	0.109929	+	0.0201246i	0.00717099	+	0.00131279i
$236$	1.16530	+	8.10481i	0.0758542	+	0.527578i
$237$	14.6869	−	8.01963i	0.954014	−	0.520931i
$238$	2.96354	−	13.6232i	0.192098	−	0.883060i
$239$	8.48816	−	3.87641i	0.549053	−	0.250744i	−0.121518	−	0.992589i	$-0.538776\pi$
$239$	8.48816	−	3.87641i	0.549053	−	0.250744i	0.670571	+	0.741845i	$0.266049\pi$
$240$	1.92597	−	1.13606i	0.124321	−	0.0733326i
$241$	−19.3040	−	16.7270i	−1.24348	−	1.07748i	−0.994031	−	0.109096i	$-0.965204\pi$
$241$	−19.3040	−	16.7270i	−1.24348	−	1.07748i	−0.249451	−	0.968387i	$-0.580250\pi$
$242$	1.65570	−	0.118418i	0.106432	−	0.00761218i
$243$	−0.479249	+	0.877679i	−0.0307438	+	0.0563031i
$244$	4.45827	+	9.76225i	0.285412	+	0.624964i
$245$	−0.0982111	−	2.96283i	−0.00627448	−	0.189288i
$246$	−11.2243	−	3.29574i	−0.715633	−	0.210129i
$247$	2.37223	+	1.77583i	0.150942	+	0.112993i
$248$	−3.66324	−	9.82153i	−0.232616	−	0.623668i
$249$	0.804614	−	5.59621i	0.0509904	−	0.354646i
$250$	−11.0176	+	1.90041i	−0.696817	+	0.120192i
$251$	10.2649	−	8.89460i	0.647916	−	0.561422i	−0.267687	−	0.963506i	$-0.586259\pi$
$251$	10.2649	−	8.89460i	0.647916	−	0.561422i	0.915603	+	0.402083i	$0.131714\pi$
$252$	−1.68438	+	1.68438i	−0.106106	+	0.106106i
$253$	−12.3721	+	7.85828i	−0.777828	+	0.494046i
$254$			2.30098i			0.144376i
$255$	−12.8853	+	2.29065i	−0.806906	+	0.143446i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	3.46838	−	2.59639i	0.216351	−	0.161959i	−0.485605	−	0.874178i	$-0.661401\pi$
$257$	3.46838	−	2.59639i	0.216351	−	0.161959i	0.701957	+	0.712219i	$0.252310\pi$
$258$	3.96337	−	1.47826i	0.246749	−	0.0920324i
$259$	17.3265	−	2.49117i	1.07662	−	0.154794i
$260$	−0.256154	+	6.69108i	−0.0158860	+	0.414963i
$261$	−0.732458	+	0.470722i	−0.0453380	+	0.0291370i
$262$	−0.675795	+	1.81188i	−0.0417507	+	0.111938i
$263$	−0.985805	−	0.538290i	−0.0607873	−	0.0331924i	0.448568	−	0.893749i	$-0.351934\pi$
$263$	−0.985805	−	0.538290i	−0.0607873	−	0.0331924i	−0.509355	+	0.860556i	$0.670116\pi$
$264$	2.00135	−	2.30969i	0.123175	−	0.142151i
$265$	−7.07895	−	3.56620i	−0.434857	−	0.219070i
$266$	2.26173	−	0.664104i	0.138676	−	0.0407188i
$267$	6.13522	+	2.28832i	0.375469	+	0.140043i
$268$	1.53539	+	0.334004i	0.0937889	+	0.0204025i
$269$	1.00766	−	3.43177i	0.0614381	−	0.209239i	−0.923053	−	0.384672i	$-0.874314\pi$
$269$	1.00766	−	3.43177i	0.0614381	−	0.209239i	0.984491	+	0.175433i	$0.0561326\pi$
$270$	2.06366	+	0.861001i	0.125590	+	0.0523988i
$271$	−1.58384	+	3.46812i	−0.0962113	+	0.210673i	−0.951618	−	0.307284i	$-0.900580\pi$
$271$	−1.58384	+	3.46812i	−0.0962113	+	0.210673i	0.855407	+	0.517957i	$0.173307\pi$
$272$	−3.50746	−	4.68542i	−0.212671	−	0.284095i
$273$	−1.51627	−	6.97017i	−0.0917687	−	0.421854i
$274$	−8.59510	−	9.91928i	−0.519249	−	0.599246i
$275$	−13.4490	+	7.25441i	−0.811005	+	0.437458i
$276$	1.04437	−	4.68074i	0.0628638	−	0.281747i
$277$	−14.2261	−	14.2261i	−0.854763	−	0.854763i	0.135952	−	0.990715i	$-0.456591\pi$
$277$	−14.2261	−	14.2261i	−0.854763	−	0.854763i	−0.990715	+	0.135952i	$0.956591\pi$
$278$	15.3845	+	1.10032i	0.922701	+	0.0659929i
$279$	5.66724	−	8.81840i	0.339289	−	0.527944i
$280$	4.13883	+	3.35282i	0.247342	+	0.200369i
$281$	22.0443	+	10.0673i	1.31505	+	0.600564i	0.944581	−	0.328280i	$-0.106469\pi$
$281$	22.0443	+	10.0673i	1.31505	+	0.600564i	0.370472	+	0.928844i	$0.379196\pi$
$282$	−0.0299512	+	0.0400101i	−0.00178357	+	0.00238257i
$283$	3.64119	+	6.66835i	0.216446	+	0.396392i	0.963231	−	0.268674i	$-0.0865853\pi$
$283$	3.64119	+	6.66835i	0.216446	+	0.396392i	−0.746785	+	0.665066i	$0.768404\pi$
$284$	−0.971638	−	1.51190i	−0.0576561	−	0.0897147i
$285$	−1.38400	−	1.72648i	−0.0819811	−	0.102268i
$286$	2.57835	+	8.78104i	0.152461	+	0.519234i
$287$	−1.98792	−	27.7948i	−0.117343	−	1.64067i
$288$	0.0713392	+	0.997452i	0.00420370	+	0.0587754i
$289$	4.86141	+	16.5564i	0.285965	+	0.973907i
$290$	1.21772	+	1.51906i	0.0715070	+	0.0892020i
$291$	1.35188	+	2.10357i	0.0792488	+	0.123314i
$292$	7.32774	+	13.4197i	0.428823	+	0.785331i
$293$	−9.80777	+	13.1016i	−0.572976	+	0.765406i	−0.989627	−	0.143660i	$-0.954113\pi$
$293$	−9.80777	+	13.1016i	−0.572976	+	0.765406i	0.416651	+	0.909066i	$0.363204\pi$
$294$	1.20594	+	0.550734i	0.0703318	+	0.0321195i
$295$	14.2268	+	11.5250i	0.828319	+	0.671012i
$296$	3.97291	−	6.18196i	0.230920	−	0.359319i
$297$	3.04837	+	0.218023i	0.176884	+	0.0126510i
$298$	11.8574	+	11.8574i	0.686881	+	0.686881i
$299$	10.1007	+	10.2089i	0.584140	+	0.590396i
$300$	1.43325	−	4.79018i	0.0827486	−	0.276561i
$301$	6.59860	+	7.61519i	0.380337	+	0.438932i
$302$	1.07531	+	4.94314i	0.0618774	+	0.284446i
$303$	3.15906	+	4.22001i	0.181483	+	0.242433i
$304$	0.411080	−	0.900141i	0.0235771	−	0.0516266i
$305$	22.1473	+	9.24034i	1.26815	+	0.529100i
$306$	1.64893	−	5.61573i	0.0942629	−	0.321030i
$307$	21.6590	+	4.71162i	1.23614	+	0.268906i	0.782711	−	0.622385i	$-0.213836\pi$
$307$	21.6590	+	4.71162i	1.23614	+	0.268906i	0.453431	+	0.891291i	$0.350200\pi$
$308$	6.82097	+	2.54409i	0.388661	+	0.144963i
$309$	−7.59412	+	2.22983i	−0.432014	+	0.126851i
$310$	−20.9332	−	10.5456i	−1.18893	−	0.598951i
$311$	14.4431	−	16.6682i	0.818991	−	0.945166i	−0.180269	−	0.983617i	$-0.557697\pi$
$311$	14.4431	−	16.6682i	0.818991	−	0.945166i	0.999260	+	0.0384513i	$0.0122424\pi$
$312$	−2.62824	−	1.43513i	−0.148795	−	0.0812481i
$313$	−4.18943	+	11.2323i	−0.236800	+	0.634887i	−0.999936	−	0.0113524i	$-0.996386\pi$
$313$	−4.18943	+	11.2323i	−0.236800	+	0.634887i	0.763135	+	0.646239i	$0.223659\pi$
$314$	−5.61288	+	3.60718i	−0.316753	+	0.203565i
$315$	−0.203763	+	5.32257i	−0.0114808	+	0.299893i
$316$	16.5634	−	2.38146i	0.931765	−	0.133968i
$317$	13.4293	−	5.00887i	0.754265	−	0.281326i	0.0572276	−	0.998361i	$-0.481774\pi$
$317$	13.4293	−	5.00887i	0.754265	−	0.281326i	0.697037	+	0.717035i	$0.254501\pi$
$318$	2.83779	−	2.12434i	0.159135	−	0.119127i
$319$	2.23851	+	1.43860i	0.125332	+	0.0805461i
$320$	2.20155	−	0.391377i	0.123070	−	0.0218786i
$321$		−	0.318321i		−	0.0177669i
$322$	11.3162	−	1.56556i	0.630628	−	0.0872452i
$323$	−4.09538	+	4.09538i	−0.227873	+	0.227873i
$324$	−0.755750	+	0.654861i	−0.0419861	+	0.0363812i
$325$	9.74685	+	11.3657i	0.540658	+	0.630457i
$326$	0.213382	−	1.48411i	0.0118181	−	0.0821970i
$327$	4.54011	+	12.1725i	0.251069	+	0.673141i
$328$	−9.36483	−	7.01043i	−0.517086	−	0.387086i
$329$	−0.114231	−	0.0335412i	−0.00629774	−	0.00184918i
$330$	−0.226400	−	6.83002i	−0.0124629	−	0.375980i
$331$	9.97279	+	21.8374i	0.548154	+	1.20029i	0.957639	+	0.287973i	$0.0929813\pi$
$331$	9.97279	+	21.8374i	0.548154	+	1.20029i	−0.409484	+	0.912317i	$0.634291\pi$
$332$	2.70956	−	4.96219i	0.148706	−	0.272335i
$333$	7.32979	−	0.524237i	0.401670	−	0.0287280i
$334$	−6.74610	−	5.84553i	−0.369130	−	0.319853i
$335$	3.02628	−	1.78510i	0.165343	−	0.0975302i
$336$	−2.16681	+	0.989548i	−0.118209	+	0.0539842i
$337$	5.74003	−	26.3865i	0.312679	−	1.43736i	−0.505712	−	0.862702i	$-0.668770\pi$
$337$	5.74003	−	26.3865i	0.312679	−	1.43736i	0.818391	−	0.574661i	$-0.194866\pi$
$338$	−3.53948	+	1.93270i	−0.192522	+	0.105125i
$339$	−2.28771	−	15.9113i	−0.124251	−	0.864186i
$340$	−12.8733	−	2.35671i	−0.698155	−	0.127810i
$341$	−31.7099	−	4.55920i	−1.71719	−	0.246894i
$342$	0.966951	−	0.210347i	0.0522867	−	0.0113743i
$343$	−1.41483	+	19.7820i	−0.0763939	+	1.06813i
$344$	4.23008			0.228070
$345$	−5.39910	−	9.26551i	−0.290678	−	0.498838i
$346$	−6.77901			−0.364442
$347$	−0.683812	+	9.56095i	−0.0367090	+	0.513259i	0.945519	+	0.325567i	$0.105555\pi$
$347$	−0.683812	+	9.56095i	−0.0367090	+	0.513259i	−0.982228	+	0.187692i	$0.939899\pi$
$348$	−0.850777	+	0.185075i	−0.0456065	+	0.00992108i
$349$	−33.0329	−	4.74942i	−1.76821	−	0.254230i	−0.820112	−	0.572204i	$-0.806089\pi$
$349$	−33.0329	−	4.74942i	−1.76821	−	0.254230i	−0.948100	+	0.317973i	$0.896998\pi$
$350$	11.8842	−	0.788736i	0.635237	−	0.0421597i
$351$	−0.426167	−	2.96405i	−0.0227471	−	0.158209i
$352$	2.68232	−	1.46466i	0.142968	−	0.0780666i
$353$	4.46864	−	20.5420i	0.237842	−	1.09334i	−0.690998	−	0.722857i	$-0.742829\pi$
$353$	4.46864	−	20.5420i	0.237842	−	1.09334i	0.928839	−	0.370483i	$-0.120808\pi$
$354$	−7.44820	+	3.40148i	−0.395867	+	0.180787i
$355$	−3.89126	−	1.00382i	−0.206527	−	0.0532773i
$356$	4.94871	+	4.28808i	0.262281	+	0.227268i
$357$	13.9063	−	0.994597i	0.735998	−	0.0526396i
$358$	1.11759	−	2.04671i	0.0590664	−	0.108172i
$359$	−5.64290	−	12.3562i	−0.297821	−	0.652136i	0.700272	−	0.713877i	$-0.253062\pi$
$359$	−5.64290	−	12.3562i	−0.297821	−	0.652136i	−0.998092	+	0.0617401i	$0.980335\pi$
$360$	1.63265	+	1.52789i	0.0860484	+	0.0805268i
$361$	17.2908	+	5.07703i	0.910042	+	0.267212i
$362$	16.1098	+	12.0596i	0.846710	+	0.633839i
$363$	0.580085	+	1.55527i	0.0304465	+	0.0816303i
$364$	1.01516	−	7.06058i	0.0532088	−	0.370075i
$365$	32.4122	+	10.8802i	1.69653	+	0.569496i
$366$	−8.11077	+	7.02803i	−0.423957	+	0.367361i
$367$	−1.65343	+	1.65343i	−0.0863081	+	0.0863081i	−0.748943	−	0.662635i	$-0.769438\pi$
$367$	−1.65343	+	1.65343i	−0.0863081	+	0.0863081i	0.662635	+	0.748943i	$0.269438\pi$
$368$	2.61427	−	4.02064i	0.136278	−	0.209591i
$369$		−	11.6981i		−	0.608980i
$370$	−2.87604	−	16.1781i	−0.149518	−	0.841060i
$371$	7.10359	+	4.56520i	0.368800	+	0.237013i
$372$	8.39164	−	6.28190i	0.435086	−	0.325701i
$373$	−2.15276	+	0.802939i	−0.111466	+	0.0415746i	−0.404578	−	0.914503i	$-0.632582\pi$
$373$	−2.15276	+	0.802939i	−0.111466	+	0.0415746i	0.293112	+	0.956078i	$0.405309\pi$
$374$	−17.7050	+	2.54560i	−0.915505	+	0.131630i
$375$	−4.92745	−	10.0359i	−0.254453	−	0.518254i
$376$	−0.0420449	+	0.0270206i	−0.00216830	+	0.00139348i
$377$	0.911146	−	2.44288i	0.0469264	−	0.125815i
$378$	−2.09069	−	1.14160i	−0.107534	−	0.0587178i
$379$	−13.1910	+	15.2232i	−0.677575	+	0.781964i	−0.985542	−	0.169434i	$-0.945806\pi$
$379$	−13.1910	+	15.2232i	−0.677575	+	0.781964i	0.307966	+	0.951397i	$0.400352\pi$
$380$	−0.693395	−	2.10129i	−0.0355704	−	0.107794i
$381$	−2.20778	+	0.648262i	−0.113108	+	0.0332114i
$382$	−22.9268	−	8.55127i	−1.17304	−	0.437521i
$383$	−6.18803	−	1.34612i	−0.316194	−	0.0687837i	0.0516678	−	0.998664i	$-0.483546\pi$
$383$	−6.18803	−	1.34612i	−0.316194	−	0.0687837i	−0.367861	+	0.929881i	$0.619910\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	15.0553	−	6.19093i	0.767289	−	0.315519i
$386$	6.51903	−	14.2747i	0.331810	−	0.726562i
$387$	2.53499	+	3.38635i	0.128861	+	0.172138i
$388$	0.531524	+	2.44337i	0.0269840	+	0.124044i
$389$	19.4911	+	22.4940i	0.988240	+	1.14049i	0.990082	+	0.140491i	$0.0448682\pi$
$389$	19.4911	+	22.4940i	0.988240	+	1.14049i	−0.00184194	+	0.999998i	$0.500586\pi$
$390$	−6.49221	+	1.63932i	−0.328746	+	0.0830100i
$391$	−22.5597	+	16.7013i	−1.14089	+	0.844619i
$392$	0.937442	+	0.937442i	0.0473480	+	0.0473480i
$393$	−1.92888	−	0.137956i	−0.0972989	−	0.00695895i
$394$	14.6990	−	22.8722i	0.740527	−	1.15228i
$395$	23.5531	−	29.0747i	1.18509	−	1.46291i
$396$	2.77998	+	1.26957i	0.139699	+	0.0637984i
$397$	−2.38727	+	3.18902i	−0.119814	+	0.160052i	−0.856438	−	0.516250i	$-0.827328\pi$
$397$	−2.38727	+	3.18902i	−0.119814	+	0.160052i	0.736625	+	0.676302i	$0.236419\pi$
$398$	−6.23571	−	11.4199i	−0.312568	−	0.572425i
$399$	1.27441	+	1.98301i	0.0638001	+	0.0992749i
$400$	3.01688	−	3.98729i	0.150844	−	0.199364i
$401$	0.475169	+	1.61828i	0.0237288	+	0.0808128i	0.970506	−	0.241076i	$-0.0775004\pi$
$401$	0.475169	+	1.61828i	0.0237288	+	0.0808128i	−0.946777	+	0.321889i	$0.895682\pi$
$402$	0.112095	+	1.56730i	0.00559080	+	0.0781696i
$403$	2.23934	+	31.3101i	0.111550	+	1.55967i
$404$	1.48514	+	5.05791i	0.0738883	+	0.251640i
$405$	−0.244725	+	2.22264i	−0.0121605	+	0.110444i
$406$	−1.12129	−	1.74477i	−0.0556489	−	0.0865913i
$407$	−10.7631	−	19.7111i	−0.533505	−	0.977042i
$408$	3.50746	−	4.68542i	0.173645	−	0.231963i
$409$	15.8686	+	7.24695i	0.784652	+	0.358338i	0.767116	−	0.641508i	$-0.221691\pi$
$409$	15.8686	+	7.24695i	0.784652	+	0.358338i	0.0175352	+	0.999846i	$0.494418\pi$
$410$	−26.0150	+	2.72944i	−1.28479	+	0.134797i
$411$	7.09596	−	11.0415i	0.350018	−	0.544638i
$412$	−7.89456	−	0.564630i	−0.388937	−	0.0278173i
$413$	−13.7919	−	13.7919i	−0.678657	−	0.678657i
$414$	4.78537	−	0.316649i	0.235188	−	0.0155624i
$415$	−3.09508	−	12.2575i	−0.151931	−	0.601696i
$416$	−1.96100	−	2.26312i	−0.0961460	−	0.110958i
$417$	3.27856	+	15.0713i	0.160552	+	0.738045i
$418$	−1.81237	−	2.42105i	−0.0886461	−	0.118417i
$419$	6.73249	−	14.7421i	0.328903	−	0.720198i	−0.670868	−	0.741577i	$-0.734078\pi$
$419$	6.73249	−	14.7421i	0.328903	−	0.720198i	0.999771	+	0.0213786i	$0.00680555\pi$
$420$	−2.05096	+	4.91577i	−0.100077	+	0.239865i
$421$	5.16776	−	17.5998i	0.251861	−	0.857761i	−0.732375	−	0.680902i	$-0.761588\pi$
$421$	5.16776	−	17.5998i	0.251861	−	0.857761i	0.984236	−	0.176859i	$-0.0565937\pi$
$422$	−24.9983	−	5.43805i	−1.21690	−	0.264720i
$423$	−0.0468277	−	0.0174658i	−0.00227684	−	0.000849218i
$424$	3.40125	−	0.998696i	0.165179	−	0.0485010i
$425$	−24.6993	+	15.6949i	−1.19809	+	0.761313i
$426$	1.17691	−	1.35823i	0.0570217	−	0.0658065i
$427$	−22.4375	−	12.2518i	−1.08583	−	0.592906i
$428$	0.111242	−	0.298251i	0.00537707	−	0.0144165i
$429$	−7.69894	+	4.94781i	−0.371709	+	0.238883i
$430$	6.93930	−	6.42758i	0.334643	−	0.309965i
$431$	26.0053	−	3.73900i	1.25263	−	0.180101i	0.516113	−	0.856520i	$-0.327378\pi$
$431$	26.0053	−	3.73900i	1.25263	−	0.180101i	0.736517	+	0.676419i	$0.236469\pi$
$432$	−0.936950	+	0.349464i	−0.0450790	+	0.0168136i
$433$	−0.366211	+	0.274142i	−0.0175990	+	0.0131744i	−0.608041	−	0.793906i	$-0.708044\pi$
$433$	−0.366211	+	0.274142i	−0.0175990	+	0.0131744i	0.590442	+	0.807080i	$0.298953\pi$
$434$	21.0060	+	13.4998i	1.00832	+	0.648010i
$435$	−1.11445	+	1.59636i	−0.0534339	+	0.0765397i
$436$			12.9916i			0.622187i
$437$	−4.30636	−	1.99444i	−0.206001	−	0.0954068i
$438$	−10.8117	+	10.8117i	−0.516603	+	0.516603i
$439$	15.1838	−	13.1569i	0.724686	−	0.627944i	−0.212344	−	0.977195i	$-0.568110\pi$
$439$	15.1838	−	13.1569i	0.724686	−	0.627944i	0.937029	+	0.349252i	$0.113564\pi$
$440$	2.17472	−	6.47850i	0.103676	−	0.308850i
$441$	−0.188673	+	1.31225i	−0.00898443	+	0.0624881i
$442$	6.12486	+	16.4214i	0.291330	+	0.781086i
$443$	−20.8407	−	15.6011i	−0.990169	−	0.741232i	−0.0241520	−	0.999708i	$-0.507689\pi$
$443$	−20.8407	−	15.6011i	−0.990169	−	0.741232i	−0.966017	+	0.258477i	$0.916779\pi$
$444$	7.05084	+	2.07031i	0.334618	+	0.0982528i
$445$	14.6339	−	0.485081i	0.693714	−	0.0229951i
$446$	1.13254	+	2.47991i	0.0536272	+	0.117427i
$447$	−8.03648	+	14.7177i	−0.380112	+	0.696124i
$448$	−2.37600	+	0.169935i	−0.112255	+	0.00802867i
$449$	9.10205	+	7.88697i	0.429552	+	0.372209i	0.842636	−	0.538484i	$-0.181003\pi$
$449$	9.10205	+	7.88697i	0.429552	+	0.372209i	−0.413084	+	0.910693i	$0.635548\pi$
$450$	4.99993	+	0.0256427i	0.235699	+	0.00120881i
$451$	−32.5205	+	14.8516i	−1.53133	+	0.699335i
$452$	3.41698	−	15.7076i	0.160721	−	0.738824i
$453$	−4.43996	+	2.42440i	−0.208607	+	0.113908i
$454$	2.48847	+	17.3077i	0.116790	+	0.812290i
$455$	−9.06319	−	13.1252i	−0.424889	−	0.615318i
$456$	0.979493	+	0.140830i	0.0458690	+	0.00659496i
$457$	−17.5707	+	3.82228i	−0.821925	+	0.178799i	−0.603814	−	0.797125i	$-0.706353\pi$
$457$	−17.5707	+	3.82228i	−0.821925	+	0.178799i	−0.218111	+	0.975924i	$0.569989\pi$
$458$	0.533232	−	7.45556i	0.0249163	−	0.348376i
$459$	5.85281			0.273186
$460$	−1.82072	−	10.5681i	−0.0848915	−	0.492741i
$461$	−7.90378			−0.368116			−0.184058	−	0.982915i	$-0.558923\pi$
$461$	−7.90378			−0.368116			−0.184058	+	0.982915i	$0.558923\pi$
$462$	−0.519347	+	7.26142i	−0.0241622	+	0.337832i
$463$	40.7957	−	8.87457i	1.89594	−	0.412436i	0.896413	−	0.443221i	$-0.146164\pi$
$463$	40.7957	−	8.87457i	1.89594	−	0.412436i	0.999526	+	0.0307845i	$0.00980055\pi$
$464$	−0.861813	−	0.123910i	−0.0400087	−	0.00575238i
$465$	4.22089	−	23.0563i	0.195739	−	1.06921i
$466$	1.75694	+	12.2198i	0.0813885	+	0.566069i
$467$	−5.13554	+	2.80422i	−0.237645	+	0.129764i	−0.593659	−	0.804717i	$-0.702317\pi$
$467$	−5.13554	+	2.80422i	−0.237645	+	0.129764i	0.356014	+	0.934480i	$0.384135\pi$
$468$	0.636534	−	2.92610i	0.0294238	−	0.135259i
$469$	−3.40470	+	1.55488i	−0.157215	+	0.0717975i
$470$	−0.0279156	+	0.108213i	−0.00128765	+	0.00499152i
$471$	−5.04240	−	4.36926i	−0.232341	−	0.201325i
$472$	−8.16729	+	0.584136i	−0.375930	+	0.0268870i
$473$	6.19562	−	11.3464i	0.284875	−	0.521709i
$474$	6.95145	+	15.2215i	0.319291	+	0.699149i
$475$	−4.33039	−	2.39348i	−0.198692	−	0.109820i
$476$	13.3771	+	3.92786i	0.613137	+	0.180033i
$477$	2.83779	+	2.12434i	0.129933	+	0.0972669i
$478$	3.26100	+	8.74307i	0.149154	+	0.399899i
$479$	−5.57649	+	38.7854i	−0.254797	+	1.77215i	0.313758	+	0.949503i	$0.398412\pi$
$479$	−5.57649	+	38.7854i	−0.254797	+	1.77215i	−0.568554	+	0.822646i	$0.692497\pi$
$480$	0.995772	+	2.00211i	0.0454506	+	0.0913833i
$481$	−16.6305	+	14.4104i	−0.758287	+	0.657060i
$482$	18.0616	−	18.0616i	0.822682	−	0.822682i
$483$	4.69029	+	10.4168i	0.213416	+	0.473979i
$484$			1.65993i			0.0754512i
$485$	4.58464	+	3.20063i	0.208178	+	0.145333i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	28.2241	−	21.1283i	1.27896	−	0.957416i	0.278962	−	0.960302i	$-0.410010\pi$
$487$	28.2241	−	21.1283i	1.27896	−	0.957416i	0.999996	+	0.00288615i	$0.000918693\pi$
$488$	−10.0554	+	3.75048i	−0.455188	+	0.169776i
$489$	1.48411	−	0.213382i	0.0671136	−	0.00964948i
$490$	2.96228	+	0.113405i	0.133822	+	0.00512310i
$491$	27.9911	−	17.9888i	1.26322	−	0.811824i	0.274501	−	0.961587i	$-0.411487\pi$
$491$	27.9911	−	17.9888i	1.26322	−	0.811824i	0.988722	+	0.149763i	$0.0478510\pi$
$492$	4.08808	−	10.9606i	0.184305	−	0.494140i
$493$	4.47256	+	2.44220i	0.201434	+	0.109991i
$494$	−1.94054	+	2.23950i	−0.0873090	+	0.100760i
$495$	6.48957	−	2.14147i	0.291684	−	0.0962518i
$496$	10.0578	−	2.95325i	0.451610	−	0.132605i
$497$	4.01113	+	1.49607i	0.179924	+	0.0671081i
$498$	5.52456	+	1.20179i	0.247561	+	0.0538537i
$499$	3.04235	−	10.3613i	0.136194	−	0.463834i	−0.862946	−	0.505296i	$-0.831383\pi$
$499$	3.04235	−	10.3613i	0.136194	−	0.463834i	0.999140	+	0.0414617i	$0.0132014\pi$
$500$	−1.10957	−	11.1251i	−0.0496216	−	0.497532i
$501$	3.70815	−	8.11971i	0.165668	−	0.362762i
$502$	8.13965	+	10.8733i	0.363290	+	0.485299i
$503$	−8.74451	−	40.1978i	−0.389898	−	1.79233i	−0.584437	−	0.811439i	$-0.698685\pi$
$503$	−8.74451	−	40.1978i	−0.389898	−	1.79233i	0.194539	−	0.980895i	$-0.437679\pi$
$504$	−1.55992	−	1.80025i	−0.0694845	−	0.0801894i
$505$	10.1218	+	6.04068i	0.450414	+	0.268807i
$506$	−6.95564	−	12.9012i	−0.309216	−	0.573528i
$507$	−2.85160	−	2.85160i	−0.126644	−	0.126644i
$508$	−2.29512	−	0.164150i	−0.101829	−	0.00728299i
$509$	−2.23246	+	3.47378i	−0.0989522	+	0.153973i	−0.887200	−	0.461386i	$-0.847352\pi$
$509$	−2.23246	+	3.47378i	−0.0989522	+	0.153973i	0.788247	+	0.615358i	$0.210989\pi$
$510$	−1.36559	−	13.0158i	−0.0604696	−	0.576351i
$511$	−33.1306	−	15.1302i	−1.46561	−	0.669322i
$512$	−0.599278	+	0.800541i	−0.0264846	+	0.0353793i
$513$	0.474248	+	0.868521i	0.0209386	+	0.0383461i
$514$	2.34235	+	3.64476i	0.103317	+	0.160764i
$515$	−13.8087	+	11.0695i	−0.608485	+	0.487780i
$516$	1.19175	+	4.05873i	0.0524639	+	0.178676i
$517$	0.0108966	+	0.152354i	0.000479231	+	0.00670052i
$518$	1.24877	+	17.4601i	0.0548677	+	0.767151i
$519$	−1.90987	−	6.50441i	−0.0838339	−	0.285512i
$520$	−6.65576	−	0.732837i	−0.291874	−	0.0321370i
$521$	1.95337	+	3.03951i	0.0855789	+	0.133163i	0.881404	−	0.472363i	$-0.156599\pi$
$521$	1.95337	+	3.03951i	0.0855789	+	0.133163i	−0.795825	+	0.605527i	$0.792963\pi$
$522$	−0.417270	−	0.764173i	−0.0182634	−	0.0334470i
$523$	2.46720	−	3.29580i	0.107883	−	0.144115i	−0.743350	−	0.668903i	$-0.766764\pi$
$523$	2.46720	−	3.29580i	0.107883	−	0.144115i	0.851233	+	0.524787i	$0.175855\pi$
$524$	−1.75905	−	0.803331i	−0.0768444	−	0.0350937i
$525$	4.10495	+	11.1806i	0.179155	+	0.487961i
$526$	0.607245	−	0.944892i	0.0264771	−	0.0411992i
$527$	−61.1955	−	4.37679i	−2.66572	−	0.190656i
$528$	2.16103	+	2.16103i	0.0940466	+	0.0940466i
$529$	−19.2153	−	12.6401i	−0.835447	−	0.549571i
$530$	4.06212	−	6.80651i	0.176447	−	0.295656i
$531$	−5.36210	−	6.18819i	−0.232695	−	0.268545i
$532$	0.501062	+	2.30334i	0.0217238	+	0.0998627i
$533$	20.9930	+	28.0433i	0.909306	+	1.21469i
$534$	−2.72017	+	5.95634i	−0.117713	+	0.257756i
$535$	−0.270702	−	0.658302i	−0.0117035	−	0.0284609i
$536$	−0.442686	+	1.50765i	−0.0191211	+	0.0651206i
$537$	2.27867	+	0.495693i	0.0983317	+	0.0213908i
$538$	3.35115	+	1.24991i	0.144478	+	0.0538876i
$539$	3.88756	−	1.14149i	0.167449	−	0.0491674i
$540$	−1.00603	+	1.99698i	−0.0432925	+	0.0859361i
$541$	−22.2650	+	25.6951i	−0.957246	+	1.10472i	0.0371827	+	0.999308i	$0.488162\pi$
$541$	−22.2650	+	25.6951i	−0.957246	+	1.10472i	−0.994429	+	0.105412i	$0.966384\pi$
$542$	−3.34630	−	1.82722i	−0.143736	−	0.0784856i
$543$	−7.03247	+	18.8548i	−0.301792	+	0.809136i
$544$	4.92370	−	3.16427i	0.211102	−	0.135667i
$545$	19.7407	+	21.3124i	0.845600	+	0.912921i
$546$	7.06058	−	1.01516i	0.302165	−	0.0434448i
$547$	26.2069	−	9.77465i	1.12052	−	0.417934i	0.280159	−	0.959954i	$-0.409613\pi$
$547$	26.2069	−	9.77465i	1.12052	−	0.417934i	0.840366	+	0.542020i	$0.182340\pi$
$548$	10.5072	−	7.86557i	0.448844	−	0.336001i
$549$	−9.02841	−	5.80221i	−0.385323	−	0.247632i
$550$	−6.27649	−	13.9322i	−0.267630	−	0.594073i
$551$			0.861590i			0.0367050i
$552$	4.59431	+	1.37563i	0.195547	+	0.0585507i
$553$	−28.1859	+	28.1859i	−1.19859	+	1.19859i
$554$	15.2047	−	13.1750i	0.645987	−	0.559751i
$555$	14.7125	−	7.31744i	0.624512	−	0.310608i
$556$	−2.19503	+	15.2668i	−0.0930902	+	0.647457i
$557$	−3.08456	−	8.27004i	−0.130697	−	0.350413i	0.855074	−	0.518506i	$-0.173512\pi$
$557$	−3.08456	−	8.27004i	−0.130697	−	0.350413i	−0.985771	+	0.168093i	$0.946239\pi$
$558$	8.39164	+	6.28190i	0.355246	+	0.265934i
$559$	−12.1540	−	3.56873i	−0.514059	−	0.150941i
$560$	−3.63954	+	3.88909i	−0.153798	+	0.164344i
$561$	−7.43056	−	16.2707i	−0.313719	−	0.686948i
$562$	−11.6143	+	21.2699i	−0.489918	+	0.897218i
$563$	−11.1477	+	0.797301i	−0.469820	+	0.0336022i	−0.304243	−	0.952595i	$-0.598403\pi$
$563$	−11.1477	+	0.797301i	−0.469820	+	0.0336022i	−0.165578	+	0.986197i	$0.552949\pi$
$564$	−0.0377715	−	0.0327292i	−0.00159047	−	0.00137815i
$565$	−18.2622	−	30.9599i	−0.768296	−	1.30249i
$566$	−6.91112	+	3.15620i	−0.290496	+	0.132665i
$567$	0.506345	−	2.32763i	0.0212645	−	0.0977514i
$568$	1.57736	−	0.861305i	0.0661847	−	0.0361396i
$569$	3.39980	+	23.6461i	0.142527	+	0.991296i	0.928048	+	0.372461i	$0.121486\pi$
$569$	3.39980	+	23.6461i	0.142527	+	0.991296i	−0.785521	+	0.618835i	$0.787605\pi$
$570$	1.82082	−	1.25731i	0.0762657	−	0.0526629i
$571$	−13.3304	−	1.91663i	−0.557861	−	0.0802083i	−0.142383	−	0.989812i	$-0.545477\pi$
$571$	−13.3304	−	1.91663i	−0.557861	−	0.0802083i	−0.415478	+	0.909603i	$0.636386\pi$
$572$	−8.94261	+	1.94535i	−0.373909	+	0.0813390i
$573$	1.74565	−	24.4073i	0.0729254	−	1.01963i
$574$	27.8658			1.16309
$575$	−19.0450	−	14.5701i	−0.794232	−	0.607614i
$576$	−1.00000			−0.0416667
$577$	−2.91740	+	40.7905i	−0.121453	+	1.69813i	0.462721	+	0.886504i	$0.346873\pi$
$577$	−2.91740	+	40.7905i	−0.121453	+	1.69813i	−0.584174	+	0.811628i	$0.698581\pi$
$578$	−16.8611	+	3.66790i	−0.701327	+	0.152564i
$579$	15.5331	+	2.23332i	0.645533	+	0.0928136i
$580$	−1.60206	+	1.10625i	−0.0665218	+	0.0459345i
$581$	1.91665	+	13.3306i	0.0795159	+	0.553045i
$582$	−2.19465	+	1.19837i	−0.0909713	+	0.0496741i
$583$	2.30284	−	10.5860i	0.0953739	−	0.438427i
$584$	−13.9083	+	6.35171i	−0.575530	+	0.262836i
$585$	−3.40198	−	5.76738i	−0.140655	−	0.238452i
$586$	−12.3686	−	10.7174i	−0.510941	−	0.442733i
$587$	−30.8709	+	2.20793i	−1.27418	+	0.0911309i	−0.691980	−	0.721917i	$-0.743261\pi$
$587$	−30.8709	+	2.20793i	−1.27418	+	0.0911309i	−0.582197	+	0.813048i	$0.697807\pi$
$588$	−0.635361	+	1.16358i	−0.0262019	+	0.0479851i
$589$	−4.30913	−	9.43568i	−0.177555	−	0.388791i
$590$	−12.5106	+	13.3684i	−0.515052	+	0.550369i
$591$	26.0869	+	7.65980i	1.07307	+	0.315082i
$592$	5.88279	+	4.40380i	0.241781	+	0.180995i
$593$	5.40387	+	14.4883i	0.221910	+	0.594965i	0.999425	−	0.0338998i	$-0.0107927\pi$
$593$	5.40387	+	14.4883i	0.221910	+	0.594965i	−0.777515	+	0.628865i	$0.783520\pi$
$594$	−0.434936	+	3.02505i	−0.0178456	+	0.124119i
$595$	27.9130	−	13.8829i	1.14432	−	0.569142i
$596$	−12.6731	+	10.9813i	−0.519110	+	0.449811i
$597$	9.20047	−	9.20047i	0.376550	−	0.376550i
$598$	−10.9035	+	9.34670i	−0.445876	+	0.382215i
$599$		−	38.4324i		−	1.57031i	−0.619302	−	0.785153i	$-0.712584\pi$
$599$		−	38.4324i		−	1.57031i	0.619302	−	0.785153i	$-0.287416\pi$
$600$	4.67573	+	1.77132i	0.190886	+	0.0723140i
$601$	11.2250	+	7.21388i	0.457878	+	0.294260i	0.749175	−	0.662372i	$-0.230450\pi$
$601$	11.2250	+	7.21388i	0.457878	+	0.294260i	−0.291297	+	0.956633i	$0.594087\pi$
$602$	−8.06652	+	6.03852i	−0.328767	+	0.246112i
$603$	−1.47223	+	0.549113i	−0.0599538	+	0.0223616i
$604$	−5.00726	+	0.719935i	−0.203742	+	0.0292937i
$605$	2.52225	+	2.72305i	0.102544	+	0.110708i
$606$	−4.43462	+	2.84996i	−0.180144	+	0.115772i
$607$	0.989308	−	2.65244i	0.0401548	−	0.107659i	−0.915325	−	0.402717i	$-0.868066\pi$
$607$	0.989308	−	2.65244i	0.0401548	−	0.107659i	0.955480	+	0.295057i	$0.0953388\pi$
$608$	0.868521	+	0.474248i	0.0352232	+	0.0192333i
$609$	1.35819	−	1.56743i	0.0550365	−	0.0635155i
$610$	−10.7968	+	21.4317i	−0.437148	+	0.867745i
$611$	0.143601	−	0.0421651i	0.00580947	−	0.00170582i
$612$	5.48379	+	2.04535i	0.221669	+	0.0826783i
$613$	30.1580	+	6.56048i	1.21807	+	0.264975i	0.775262	−	0.631640i	$-0.217618\pi$
$613$	30.1580	+	6.56048i	1.21807	+	0.264975i	0.442810	+	0.896615i	$0.353982\pi$
$614$	−6.24475	+	21.2677i	−0.252018	+	0.858293i
$615$	−9.94816	−	24.1922i	−0.401148	−	0.975526i
$616$	−3.02421	+	6.62209i	−0.121849	+	0.266812i
$617$	2.78168	+	3.71589i	0.111986	+	0.149596i	0.853032	−	0.521858i	$-0.174761\pi$
$617$	2.78168	+	3.71589i	0.111986	+	0.149596i	−0.741046	+	0.671454i	$0.765670\pi$
$618$	−1.68240	−	7.73385i	−0.0676759	−	0.311101i
$619$	−1.35712	−	1.56620i	−0.0545471	−	0.0629507i	0.727820	−	0.685768i	$-0.240533\pi$
$619$	−1.35712	−	1.56620i	−0.0545471	−	0.0629507i	−0.782367	+	0.622817i	$0.785988\pi$
$620$	12.0121	−	20.1275i	0.482418	−	0.808342i
$621$	1.65202	+	4.50232i	0.0662931	+	0.180672i
$622$	15.5954	+	15.5954i	0.625317	+	0.625317i
$623$	−15.5582	−	1.11275i	−0.623328	−	0.0445813i
$624$	1.61897	−	2.51916i	0.0648105	−	0.100847i
$625$	−18.7248	−	16.5644i	−0.748993	−	0.662578i
$626$	−10.9048	−	4.98006i	−0.435844	−	0.199043i
$627$	1.81237	−	2.42105i	0.0723793	−	0.0966874i
$628$	−3.19757	−	5.85592i	−0.127597	−	0.233677i
$629$	−23.2527	−	36.1818i	−0.927144	−	1.44266i
$630$	−5.29447	−	0.582952i	−0.210937	−	0.0232254i
$631$	7.47503	+	25.4576i	0.297576	+	1.01345i	0.963561	+	0.267487i	$0.0861933\pi$
$631$	7.47503	+	25.4576i	0.297576	+	1.01345i	−0.665985	+	0.745965i	$0.731989\pi$
$632$	1.19377	+	16.6911i	0.0474857	+	0.663937i
$633$	−1.82507	−	25.5178i	−0.0725399	−	1.01424i
$634$	4.03807	+	13.7524i	0.160372	+	0.546178i
$635$	−4.01450	+	3.21814i	−0.159310	+	0.127708i
$636$	1.91648	+	2.98211i	0.0759935	+	0.118248i
$637$	−1.90261	−	3.48437i	−0.0753842	−	0.138056i
$638$	−1.59463	+	2.13017i	−0.0631319	+	0.0843344i
$639$	1.63479	+	0.746583i	0.0646712	+	0.0295344i
$640$	0.233323	+	2.22386i	0.00922290	+	0.0879058i
$641$	14.1565	−	22.0280i	0.559150	−	0.870054i	−0.440466	−	0.897769i	$-0.645187\pi$
$641$	14.1565	−	22.0280i	0.559150	−	0.870054i	0.999616	+	0.0277154i	$0.00882322\pi$
$642$	0.317510	+	0.0227087i	0.0125311	+	0.000896243i
$643$	9.15728	+	9.15728i	0.361128	+	0.361128i	0.864228	−	0.503100i	$-0.167807\pi$
$643$	9.15728	+	9.15728i	0.361128	+	0.361128i	−0.503100	+	0.864228i	$0.667807\pi$
$644$	0.754280	+	11.3991i	0.0297228	+	0.449187i
$645$	8.12224	+	4.84735i	0.319813	+	0.190864i
$646$	−3.79278	−	4.37711i	−0.149225	−	0.172215i
$647$	3.61054	+	16.5974i	0.141945	+	0.652511i	0.992044	+	0.125889i	$0.0401782\pi$
$647$	3.61054	+	16.5974i	0.141945	+	0.652511i	−0.850099	+	0.526622i	$0.823458\pi$
$648$	−0.599278	−	0.800541i	−0.0235419	−	0.0314482i
$649$	−10.3954	+	22.7628i	−0.408057	+	0.893520i
$650$	−12.0321	+	8.91119i	−0.471938	+	0.349526i
$651$	−7.03484	+	23.9585i	−0.275717	+	0.939007i
$652$	1.46510	+	0.318713i	0.0573778	+	0.0124818i
$653$	8.33944	+	3.11045i	0.326347	+	0.121721i	0.507298	−	0.861771i	$-0.330645\pi$
$653$	8.33944	+	3.11045i	0.326347	+	0.121721i	−0.180950	+	0.983492i	$0.557917\pi$
$654$	−12.4654	+	3.66017i	−0.487435	+	0.143124i
$655$	−4.10632	+	1.35503i	−0.160447	+	0.0529453i
$656$	7.66064	−	8.84085i	0.299098	−	0.345177i
$657$	−13.4197	−	7.32774i	−0.523554	−	0.285882i
$658$	0.0416048	−	0.111547i	0.00162192	−	0.00434855i
$659$	−31.7122	+	20.3802i	−1.23533	+	0.793898i	−0.984712	−	0.174188i	$-0.944270\pi$
$659$	−31.7122	+	20.3802i	−1.23533	+	0.793898i	−0.250618	+	0.968086i	$0.580634\pi$
$660$	6.82876	+	0.261425i	0.265809	+	0.0101759i
$661$	2.00630	−	0.288462i	0.0780359	−	0.0112199i	−0.103186	−	0.994662i	$-0.532904\pi$
$661$	2.00630	−	0.288462i	0.0780359	−	0.0112199i	0.181222	+	0.983442i	$0.441995\pi$
$662$	−22.4932	+	8.38952i	−0.874222	+	0.326068i
$663$	−14.0306	+	10.5032i	−0.544905	+	0.407911i
$664$	4.75625	+	3.05665i	0.184578	+	0.118621i
$665$	4.32190	+	3.01720i	0.167596	+	0.117002i
$666$			7.34851i			0.284749i
$667$	−0.616255	+	4.12989i	−0.0238615	+	0.159910i
$668$	6.31190	−	6.31190i	0.244215	−	0.244215i
$669$	−2.06039	+	1.78533i	−0.0796591	+	0.0690250i
$670$	1.56466	+	3.14591i	0.0604479	+	0.121537i
$671$	−4.66777	+	32.4651i	−0.180197	+	1.25330i
$672$	−0.832448	−	2.23188i	−0.0321124	−	0.0860966i
$673$	−12.3112	−	9.21603i	−0.474561	−	0.355252i	0.335068	−	0.942194i	$-0.391241\pi$
$673$	−12.3112	−	9.21603i	−0.474561	−	0.355252i	−0.809629	+	0.586942i	$0.800332\pi$
$674$	25.9098	+	7.60779i	0.998007	+	0.293041i
$675$	1.38404	+	4.80463i	0.0532717	+	0.184930i
$676$	−1.67527	−	3.66834i	−0.0644336	−	0.141090i
$677$	−22.7167	+	41.6026i	−0.873074	+	1.59892i	−0.0743399	+	0.997233i	$0.523685\pi$
$677$	−22.7167	+	41.6026i	−0.873074	+	1.59892i	−0.798735	+	0.601684i	$0.794497\pi$
$678$	16.0340	−	1.14678i	0.615782	−	0.0440416i
$679$	−4.50156	−	3.90062i	−0.172754	−	0.149692i
$680$	3.26908	−	12.6724i	0.125363	−	0.485965i
$681$	−15.9055	+	7.26381i	−0.609501	+	0.278350i
$682$	6.80974	−	31.3039i	0.260758	−	1.19869i
$683$	22.9321	−	12.5219i	0.877474	−	0.479137i	0.0236627	−	0.999720i	$-0.492467\pi$
$683$	22.9321	−	12.5219i	0.877474	−	0.479137i	0.853811	+	0.520583i	$0.174285\pi$
$684$	0.140830	+	0.979493i	0.00538476	+	0.0374519i
$685$	5.28498	−	28.8688i	0.201929	−	1.10302i
$686$	−19.6306	−	2.82246i	−0.749501	−	0.107762i
$687$	7.30379	−	1.58884i	0.278657	−	0.0606181i
$688$	−0.301770	+	4.21930i	−0.0115049	+	0.160859i
$689$	−10.6151			−0.404404
$690$	9.62707	−	4.72435i	0.366496	−	0.179853i
$691$	−12.7217			−0.483956			−0.241978	−	0.970282i	$-0.577796\pi$
$691$	−12.7217			−0.483956			−0.241978	+	0.970282i	$0.577796\pi$
$692$	0.483609	−	6.76174i	0.0183841	−	0.257043i
$693$	−7.11360	+	1.54747i	−0.270223	+	0.0587835i
$694$	−9.48780	−	1.36414i	−0.360152	−	0.0517821i
$695$	19.5969	+	28.3800i	0.743355	+	1.07652i
$696$	−0.123910	−	0.861813i	−0.00469680	−	0.0326669i
$697$	−60.0920	+	32.8127i	−2.27615	+	1.24287i
$698$	7.09386	−	32.6099i	0.268506	−	1.23430i
$699$	−11.2298	+	5.12847i	−0.424749	+	0.193977i
$700$	−0.0610827	+	11.9102i	−0.00230871	+	0.450163i
$701$	−21.9835	−	19.0488i	−0.830304	−	0.719462i	0.132056	−	0.991242i	$-0.457842\pi$
$701$	−21.9835	−	19.0488i	−0.830304	−	0.719462i	−0.962359	+	0.271780i	$0.912388\pi$
$702$	2.98690	−	0.213628i	0.112733	−	0.00806285i
$703$	3.48502	−	6.38234i	0.131440	−	0.240714i
$704$	1.26957	+	2.77998i	0.0478488	+	0.104774i
$705$	−0.111695	+	0.00370243i	−0.00420667	+	0.000139442i
$706$	20.1709	+	5.92270i	0.759140	+	0.222904i
$707$	−10.0523	−	7.52509i	−0.378057	−	0.283010i
$708$	−2.86146	−	7.67188i	−0.107540	−	0.288327i
$709$	−2.11887	+	14.7370i	−0.0795757	+	0.553461i	0.910563	+	0.413370i	$0.135649\pi$
$709$	−2.11887	+	14.7370i	−0.0795757	+	0.553461i	−0.990139	+	0.140091i	$0.955261\pi$
$710$	1.27886	−	3.80974i	0.0479949	−	0.142977i
$711$	−12.6465	+	10.9583i	−0.474282	+	0.410967i
$712$	−4.63019	+	4.63019i	−0.173524	+	0.173524i
$713$	−13.9062	−	48.3105i	−0.520791	−	1.80924i
$714$			13.9418i			0.521759i
$715$	−11.7141	+	16.7795i	−0.438083	+	0.627519i
$716$	1.96177	+	1.26075i	0.0733147	+	0.0471165i
$717$	−7.47018	+	5.59211i	−0.278979	+	0.208841i
$718$	12.7273	−	4.74704i	0.474979	−	0.177158i
$719$	27.9988	−	4.02562i	1.04418	−	0.150130i	0.401182	−	0.915999i	$-0.368600\pi$
$719$	27.9988	−	4.02562i	1.04418	−	0.150130i	0.642997	+	0.765868i	$0.277691\pi$
$720$	−1.64047	+	1.51950i	−0.0611366	+	0.0566282i
$721$	15.8605	−	10.1929i	0.590676	−	0.379604i
$722$	−6.29761	+	16.8845i	−0.234373	+	0.628378i
$723$	22.4185	+	12.2414i	0.833752	+	0.455263i
$724$	−13.1781	+	15.2084i	−0.489762	+	0.565215i
$725$	−0.947180	+	4.24909i	−0.0351774	+	0.157807i
$726$	−1.59269	+	0.467655i	−0.0591102	+	0.0173563i
$727$	−16.9967	−	6.33943i	−0.630372	−	0.235116i	0.0139118	−	0.999903i	$-0.495572\pi$
$727$	−16.9967	−	6.33943i	−0.630372	−	0.235116i	−0.644284	+	0.764787i	$0.722844\pi$
$728$	6.97017	+	1.51627i	0.258332	+	0.0561966i
$729$	0.281733	−	0.959493i	0.0104345	−	0.0355368i
$730$	−13.1647	+	31.5534i	−0.487249	+	1.16784i
$731$	10.2848	−	22.5205i	0.380396	−	0.832951i
$732$	−6.43150	−	8.59148i	−0.237715	−	0.317550i
$733$	−3.27953	−	15.0758i	−0.121132	−	0.556836i	−0.997209	−	0.0746640i	$-0.976212\pi$
$733$	−3.27953	−	15.0758i	−0.121132	−	0.556836i	0.876076	−	0.482172i	$-0.160152\pi$
$734$	−1.53126	−	1.76717i	−0.0565198	−	0.0652273i
$735$	0.725761	+	2.87424i	0.0267701	+	0.106018i
$736$	3.82390	+	2.89444i	0.140951	+	0.106691i
$737$	3.39562	+	3.39562i	0.125079	+	0.125079i
$738$	11.6683	+	0.834535i	0.429517	+	0.0307196i
$739$	−11.6563	+	18.1376i	−0.428785	+	0.667203i	−0.986673	−	0.162713i	$-0.947975\pi$
$739$	−11.6563	+	18.1376i	−0.428785	+	0.667203i	0.557888	+	0.829916i	$0.311612\pi$
$740$	16.3421	−	1.71458i	0.600747	−	0.0630291i
$741$	−2.69550	−	1.23099i	−0.0990217	−	0.0452217i
$742$	−5.06033	+	6.75981i	−0.185771	+	0.248160i
$743$	0.986645	+	1.80691i	0.0361965	+	0.0662890i	0.895151	−	0.445763i	$-0.147067\pi$
$743$	0.986645	+	1.80691i	0.0361965	+	0.0662890i	−0.858955	+	0.512052i	$0.828886\pi$
$744$	5.66724	+	8.81840i	0.207771	+	0.323298i
$745$	−4.10377	+	37.2711i	−0.150350	+	1.36551i
$746$	−0.647317	−	2.20456i	−0.0236999	−	0.0807146i
$747$	0.403335	+	5.63936i	0.0147572	+	0.206333i
$748$	−1.27605	−	17.8415i	−0.0466570	−	0.652350i
$749$	0.213627	+	0.727547i	0.00780577	+	0.0265840i
$750$	10.3619	−	4.19894i	0.378363	−	0.153324i
$751$	15.7964	+	24.5796i	0.576417	+	0.896922i	0.999960	−	0.00895363i	$-0.00285007\pi$
$751$	15.7964	+	24.5796i	0.576417	+	0.896922i	−0.423543	+	0.905876i	$0.639214\pi$
$752$	−0.0239523	−	0.0438654i	−0.000873451	−	0.00159961i
$753$	−8.13965	+	10.8733i	−0.296625	+	0.396245i
$754$	2.37165	+	1.08310i	0.0863705	+	0.0394441i
$755$	−7.12031	+	8.78954i	−0.259135	+	0.319884i
$756$	1.28784	−	2.00392i	0.0468384	−	0.0728820i
$757$	−41.5928	−	2.97478i	−1.51172	−	0.108120i	−0.709310	−	0.704897i	$-0.750993\pi$
$757$	−41.5928	−	2.97478i	−1.51172	−	0.108120i	−0.802407	+	0.596777i	$0.796448\pi$
$758$	−14.2434	−	14.2434i	−0.517343	−	0.517343i
$759$	10.4190	−	10.3086i	0.378185	−	0.374178i
$760$	2.14540	−	0.541724i	0.0778218	−	0.0196504i
$761$	20.3856	+	23.5262i	0.738977	+	0.852825i	0.993452	−	0.114254i	$-0.0364479\pi$
$761$	20.3856	+	23.5262i	0.738977	+	0.852825i	−0.254474	+	0.967080i	$0.581902\pi$
$762$	−0.489109	−	2.24840i	−0.0177185	−	0.0814509i
$763$	−18.5458	−	24.7743i	−0.671404	−	0.896891i
$764$	10.1651	−	22.2584i	0.367759	−	0.805280i
$765$	12.1039	−	4.97726i	0.437617	−	0.179953i
$766$	1.78414	−	6.07623i	0.0644637	−	0.219543i
$767$	23.9593	+	5.21203i	0.865121	+	0.188196i
$768$	−0.936950	−	0.349464i	−0.0338093	−	0.0126102i
$769$	44.0075	−	12.9218i	1.58695	−	0.465971i	0.635074	−	0.772452i	$-0.280970\pi$
$769$	44.0075	−	12.9218i	1.58695	−	0.465971i	0.951877	+	0.306481i	$0.0991515\pi$
$770$	5.10112	+	15.4586i	0.183832	+	0.557089i
$771$	−2.83721	+	3.27432i	−0.102180	+	0.117922i
$772$	13.7733	+	7.52077i	0.495710	+	0.270678i
$773$	12.8250	−	34.3851i	0.461282	−	1.23675i	−0.473269	−	0.880918i	$-0.656926\pi$
$773$	12.8250	−	34.3851i	0.461282	−	1.23675i	0.934551	−	0.355828i	$-0.115801\pi$
$774$	−3.55857	+	2.28695i	−0.127910	+	0.0822028i
$775$	−10.8782	−	51.2709i	−0.390757	−	1.84171i
$776$	−2.47507	+	0.355861i	−0.0888498	+	0.0127747i
$777$	−16.4010	+	6.11725i	−0.588382	+	0.219455i
$778$	−23.8271	+	17.8368i	−0.854244	+	0.639479i
$779$	−9.73840	−	6.25849i	−0.348915	−	0.224234i
$780$	−1.17199	−	6.59262i	−0.0419640	−	0.236054i
$781$		−	5.49251i		−	0.196538i
$782$	−15.0493	−	23.6937i	−0.538163	−	0.847285i
$783$	0.615660	−	0.615660i	0.0220019	−	0.0220019i
$784$	−1.00193	+	0.868178i	−0.0357832	+	0.0310063i
$785$	−14.1436	−	4.74775i	−0.504805	−	0.169454i
$786$	0.275209	−	1.91412i	0.00981637	−	0.0682744i
$787$	0.808211	+	2.16690i	0.0288096	+	0.0772415i	0.950558	−	0.310546i	$-0.100512\pi$
$787$	0.808211	+	2.16690i	0.0288096	+	0.0772415i	−0.921749	+	0.387788i	$0.873239\pi$
$788$	21.7653	+	16.2933i	0.775356	+	0.580424i
$789$	1.07770	+	0.316441i	0.0383671	+	0.0112656i
$790$	27.3204	+	25.5673i	0.972016	+	0.909644i
$791$	15.9069	+	34.8314i	0.565586	+	1.23846i
$792$	−1.46466	+	2.68232i	−0.0520444	+	0.0953122i
$793$	32.0557	−	2.29267i	1.13833	−	0.0814151i
$794$	−3.01059	−	2.60869i	−0.106842	−	0.0925788i
$795$	7.67523	+	1.97996i	0.272212	+	0.0702220i
$796$	11.8356	−	5.40514i	0.419502	−	0.191580i
$797$	0.704718	−	3.23954i	0.0249624	−	0.114750i	−0.962980	−	0.269574i	$-0.913117\pi$
$797$	0.704718	−	3.23954i	0.0249624	−	0.114750i	0.987942	+	0.154823i	$0.0494809\pi$
$798$	−2.06888	+	1.12969i	−0.0732375	+	0.0399907i
$799$	0.0416295	+	0.289539i	0.00147275	+	0.0102432i
$800$	3.76191	+	3.29364i	0.133003	+	0.116448i
$801$	−6.48143	−	0.931889i	−0.229010	−	0.0329267i
$802$	−1.64805	+	0.358511i	−0.0581947	+	0.0126595i
$803$	−3.33359	+	46.6096i	−0.117640	+	1.64482i
$804$	−1.57130			−0.0554155
$805$	18.5582	+	17.5537i	0.654091	+	0.618686i
$806$	−31.3901			−1.10567
$807$	−0.255156	+	3.56754i	−0.00898190	+	0.125583i
$808$	−5.15097	+	1.12053i	−0.181211	+	0.0394199i
$809$	48.1040	+	6.91631i	1.69125	+	0.243165i	0.919592	−	0.392876i	$-0.128520\pi$
$809$	48.1040	+	6.91631i	1.69125	+	0.243165i	0.771656	+	0.636040i	$0.219429\pi$
$810$	−2.19951	−	0.402663i	−0.0772831	−	0.0141481i
$811$	−3.62846	−	25.2365i	−0.127412	−	0.886173i	−0.948817	−	0.315827i	$-0.897718\pi$
$811$	−3.62846	−	25.2365i	−0.127412	−	0.886173i	0.821405	−	0.570346i	$-0.193191\pi$
$812$	1.82031	−	0.993967i	0.0638805	−	0.0348814i
$813$	0.810440	−	3.72553i	0.0284234	−	0.130660i
$814$	20.4287	−	9.32946i	0.716025	−	0.326998i
$815$	2.88774	−	1.70338i	0.101153	−	0.0596667i
$816$	4.42326	+	3.83278i	0.154845	+	0.134174i
$817$	4.17527	−	0.298621i	0.146074	−	0.0104474i
$818$	−8.36053	+	15.3112i	−0.292319	+	0.535343i
$819$	2.96323	+	6.48858i	0.103544	+	0.226729i
$820$	−0.866597	−	26.1434i	−0.0302629	−	0.912969i
$821$	−21.2118	−	6.22835i	−0.740297	−	0.217371i	−0.110224	−	0.993907i	$-0.535157\pi$
$821$	−21.2118	−	6.22835i	−0.740297	−	0.217371i	−0.630073	+	0.776536i	$0.716975\pi$
$822$	10.5072	+	7.86557i	0.366480	+	0.274343i
$823$	−10.1783	−	27.2892i	−0.354795	−	0.951241i	−0.984652	−	0.174530i	$-0.944159\pi$
$823$	−10.1783	−	27.2892i	−0.354795	−	0.951241i	0.629857	−	0.776711i	$-0.283113\pi$
$824$	1.12638	−	7.83416i	0.0392394	−	0.272916i
$825$	11.5996	−	9.94742i	0.403846	−	0.346325i
$826$	14.7407	−	12.7729i	0.512895	−	0.444426i
$827$	7.76695	−	7.76695i	0.270083	−	0.270083i	−0.559050	−	0.829134i	$-0.688834\pi$
$827$	7.76695	−	7.76695i	0.270083	−	0.270083i	0.829134	+	0.559050i	$0.188834\pi$
$828$	−0.0255419	+	4.79576i	−0.000887644	+	0.166664i
$829$			2.87165i			0.0997365i	0.998756	+	0.0498683i	$0.0158801\pi$
$829$			2.87165i			0.0997365i	−0.998756	+	0.0498683i	$0.984120\pi$
$830$	12.4470	−	2.21275i	0.432043	−	0.0768057i
$831$	16.9250	+	10.8770i	0.587120	+	0.377319i
$832$	2.39725	−	1.79456i	0.0831096	−	0.0622151i
$833$	7.27010	−	2.71161i	0.251894	−	0.0939516i
$834$	−15.2668	+	2.19503i	−0.528646	+	0.0760078i
$835$	0.763566	−	19.9454i	0.0264243	−	0.690238i
$836$	2.54417	−	1.63504i	0.0879921	−	0.0565491i
$837$	−3.66324	+	9.82153i	−0.126620	+	0.339482i
$838$	14.2242	+	7.76702i	0.491368	+	0.268307i
$839$	7.09333	−	8.18614i	0.244889	−	0.282617i	−0.619977	−	0.784620i	$-0.712858\pi$
$839$	7.09333	−	8.18614i	0.244889	−	0.282617i	0.864866	+	0.502003i	$0.167403\pi$
$840$	−4.75693	−	2.39643i	−0.164130	−	0.0826845i
$841$	−27.0979	+	7.95667i	−0.934411	+	0.274368i
$842$	17.1863	+	6.41015i	0.592278	+	0.220908i
$843$	−23.6805	−	5.15137i	−0.815599	−	0.177423i
$844$	7.20755	−	24.5467i	0.248094	−	0.844931i
$845$	−8.32225	−	3.47222i	−0.286294	−	0.119448i
$846$	0.0207620	−	0.0454624i	0.000713811	−	0.00156303i
$847$	−2.36958	−	3.16539i	−0.0814197	−	0.108764i
$848$	0.753509	+	3.46383i	0.0258756	+	0.118948i
$849$	−4.97544	−	5.74196i	−0.170757	−	0.197064i
$850$	−13.8929	−	25.7560i	−0.476521	−	0.883425i
$851$	21.2698	−	28.1000i	0.729121	−	0.963255i
$852$	1.27081	+	1.27081i	0.0435372	+	0.0435372i
$853$	14.9195	+	1.06706i	0.510832	+	0.0365355i	0.324377	−	0.945928i	$-0.394845\pi$
$853$	14.9195	+	1.06706i	0.510832	+	0.0365355i	0.186456	+	0.982463i	$0.440300\pi$
$854$	13.8213	−	21.5063i	0.472954	−	0.735931i
$855$	1.71936	+	1.39284i	0.0588009	+	0.0476340i
$856$	0.289555	+	0.132235i	0.00989678	+	0.00451971i
$857$	−17.7953	+	23.7717i	−0.607875	+	0.812026i	−0.993879	−	0.110471i	$-0.964764\pi$
$857$	−17.7953	+	23.7717i	−0.607875	+	0.812026i	0.386004	+	0.922497i	$0.373855\pi$
$858$	−4.38597	−	8.03230i	−0.149734	−	0.274218i
$859$	24.2957	+	37.8048i	0.828957	+	1.28988i	0.954625	+	0.297810i	$0.0962562\pi$
$859$	24.2957	+	37.8048i	0.828957	+	1.28988i	−0.125668	+	0.992072i	$0.540107\pi$
$860$	5.91616	+	7.38016i	0.201739	+	0.251661i
$861$	7.85069	+	26.7370i	0.267551	+	0.911194i
$862$	1.87427	+	26.2058i	0.0638380	+	0.892572i
$863$	1.70043	+	23.7751i	0.0578832	+	0.809313i	0.940624	+	0.339452i	$0.110241\pi$
$863$	1.70043	+	23.7751i	0.0578832	+	0.809313i	−0.882740	+	0.469861i	$0.844304\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	−9.48109	−	11.8273i	−0.322367	−	0.402139i
$866$	−0.247318	−	0.384835i	−0.00840421	−	0.0130772i
$867$	−8.26963	−	15.1447i	−0.280851	−	0.514341i
$868$	−14.9639	+	19.9895i	−0.507909	+	0.678487i
$869$	46.5194	+	21.2447i	1.57806	+	0.720677i
$870$	−1.51279	−	1.22550i	−0.0512884	−	0.0415482i
$871$	2.54388	−	3.95836i	0.0861962	−	0.134124i
$872$	−12.9585	−	0.926813i	−0.438831	−	0.0313858i
$873$	−1.76813	−	1.76813i	−0.0598423	−	0.0598423i
$874$	2.29657	−	4.15311i	0.0776825	−	0.140481i
$875$	17.9973	+	19.6311i	0.608419	+	0.663652i
$876$	−10.0128	−	11.5554i	−0.338303	−	0.390422i
$877$	−3.49415	−	16.0623i	−0.117989	−	0.542387i	−0.997754	−	0.0669787i	$-0.978664\pi$
$877$	−3.49415	−	16.0623i	−0.117989	−	0.542387i	0.879765	−	0.475408i	$-0.157700\pi$
$878$	12.0402	+	16.0838i	0.406335	+	0.542801i
$879$	6.79867	−	14.8870i	0.229314	−	0.502127i
$880$	6.30685	+	2.63135i	0.212604	+	0.0887028i
$881$	−10.4790	+	35.6881i	−0.353045	+	1.20236i	0.571280	+	0.820756i	$0.306447\pi$
$881$	−10.4790	+	35.6881i	−0.353045	+	1.20236i	−0.924325	+	0.381606i	$0.875371\pi$
$882$	−1.29545	−	0.281807i	−0.0436199	−	0.00948894i
$883$	5.72983	+	2.13711i	0.192824	+	0.0719196i	0.444021	−	0.896016i	$-0.353552\pi$
$883$	5.72983	+	2.13711i	0.192824	+	0.0719196i	−0.251197	+	0.967936i	$0.580824\pi$
$884$	−16.8165	+	4.93777i	−0.565600	+	0.166075i
$885$	−16.3515	−	8.23750i	−0.549651	−	0.276900i
$886$	17.0481	−	19.6746i	0.572743	−	0.660981i
$887$	25.5584	+	13.9559i	0.858167	+	0.468595i	0.847156	−	0.531345i	$-0.178313\pi$
$887$	25.5584	+	13.9559i	0.858167	+	0.468595i	0.0110112	+	0.999939i	$0.496495\pi$
$888$	−2.56804	+	6.88519i	−0.0861778	+	0.231052i
$889$	4.61099	−	2.96331i	0.154648	−	0.0993861i
$890$	−0.560126	+	14.6312i	−0.0187755	+	0.490440i
$891$	−3.02505	+	0.434936i	−0.101343	+	0.0145709i
$892$	−2.55439	+	0.952738i	−0.0855273	+	0.0319000i
$893$	−0.0395927	+	0.0296387i	−0.00132492	+	0.000991821i
$894$	−14.1069	−	9.06595i	−0.471805	−	0.303211i
$895$	5.13392	−	0.912675i	0.171608	−	0.0305074i
$896$		−	2.38207i		−	0.0795794i
$897$	−12.0400	−	7.82853i	−0.402002	−	0.261387i
$898$	−8.51621	+	8.51621i	−0.284189	+	0.284189i
$899$	−6.89758	+	5.97679i	−0.230047	+	0.199337i
$900$	−0.382269	+	4.98537i	−0.0127423	+	0.166179i
$901$	2.95264	−	20.5361i	0.0983668	−	0.684156i
$902$	−12.4938	−	33.4971i	−0.415998	−	1.11533i
$903$	−8.06652	−	6.03852i	−0.268437	−	0.200949i
$904$	15.4238	+	4.52884i	0.512989	+	0.150627i
$905$	1.49075	+	44.9730i	0.0495544	+	1.49495i
$906$	−2.10148	−	4.60160i	−0.0698170	−	0.152878i
$907$	−14.9378	+	27.3566i	−0.496002	+	0.908361i	0.503025	+	0.864272i	$0.332220\pi$
$907$	−14.9378	+	27.3566i	−0.496002	+	0.908361i	−0.999028	+	0.0440889i	$0.985962\pi$
$908$	−17.4411	+	1.24741i	−0.578804	+	0.0413969i
$909$	−3.98389	−	3.45206i	−0.132137	−	0.114498i
$910$	13.7383	−	8.10375i	0.455420	−	0.268637i
$911$	−27.4247	+	12.5245i	−0.908622	+	0.414954i	−0.814204	−	0.580579i	$-0.802826\pi$
$911$	−27.4247	+	12.5245i	−0.908622	+	0.414954i	−0.0944177	+	0.995533i	$0.530099\pi$
$912$	−0.210347	+	0.966951i	−0.00696530	+	0.0320189i
$913$	15.1652	−	8.28083i	0.501895	−	0.274055i
$914$	−2.55906	−	17.7987i	−0.0846462	−	0.588727i
$915$	−23.6054	−	4.32141i	−0.780370	−	0.142861i
$916$	7.39853	+	1.06375i	0.244454	+	0.0351472i
$917$	4.50118	−	0.979172i	0.148642	−	0.0323351i
$918$	−0.417535	+	5.83790i	−0.0137807	+	0.192679i
$919$	−2.56840			−0.0847237			−0.0423619	−	0.999102i	$-0.513488\pi$
$919$	−2.56840			−0.0847237			−0.0423619	+	0.999102i	$0.513488\pi$
$920$	10.6711	−	1.06216i	0.351815	−	0.0350184i
$921$	−22.1655			−0.730379
$922$	0.563849	−	7.88364i	0.0185694	−	0.259634i
$923$	−5.25878	+	1.14398i	−0.173095	+	0.0376545i
$924$	−7.20587	−	1.03605i	−0.237056	−	0.0340835i
$925$	24.2034	−	27.6444i	0.795801	−	0.908943i
$926$	5.94162	+	41.3249i	0.195254	+	1.35802i
$927$	6.94659	−	3.79312i	0.228156	−	0.124582i
$928$	0.185075	−	0.850777i	0.00607539	−	0.0279281i
$929$	49.3484	−	22.5367i	1.61907	−	0.739405i	0.620089	−	0.784532i	$-0.287097\pi$
$929$	49.3484	−	22.5367i	1.61907	−	0.739405i	0.998981	+	0.0451271i	$0.0143693\pi$
$930$	22.6964	+	5.85495i	0.744246	+	0.191992i
$931$	0.991476	+	0.859119i	0.0324943	+	0.0281565i
$932$	−12.3140	+	0.880712i	−0.403357	+	0.0288487i
$933$	−10.5699	+	19.3574i	−0.346044	+	0.633731i
$934$	−2.43071	−	5.32251i	−0.0795352	−	0.174158i
$935$	−29.2034	−	27.3295i	−0.955054	−	0.893769i
$936$	2.87323	+	0.843658i	0.0939146	+	0.0275758i
$937$	−11.1389	−	8.33847i	−0.363892	−	0.272406i	0.401649	−	0.915794i	$-0.368437\pi$
$937$	−11.1389	−	8.33847i	−0.363892	−	0.272406i	−0.765540	+	0.643388i	$0.777528\pi$
$938$	−1.30803	−	3.50695i	−0.0427085	−	0.114506i
$939$	1.70609	−	11.8661i	0.0556762	−	0.387236i
$940$	−0.105946	−	0.0355643i	−0.00345559	−	0.00115998i
$941$	0.476928	−	0.413260i	0.0155474	−	0.0134719i	−0.647052	−	0.762446i	$-0.723999\pi$
$941$	0.476928	−	0.413260i	0.0155474	−	0.0134719i	0.662600	+	0.748974i	$0.269453\pi$
$942$	4.71785	−	4.71785i	0.153716	−	0.153716i
$943$	−42.2030	−	36.9644i	−1.37432	−	1.20373i
$944$		−	8.18815i		−	0.266502i
$945$	−0.932287	−	5.24425i	−0.0303273	−	0.170595i
$946$	10.8755	+	6.98927i	0.353594	+	0.227241i
$947$	22.8164	−	17.0801i	0.741433	−	0.555029i	−0.160433	−	0.987047i	$-0.551289\pi$
$947$	22.8164	−	17.0801i	0.741433	−	0.555029i	0.901865	+	0.432017i	$0.142198\pi$
$948$	−15.6787	+	5.84784i	−0.509220	+	0.189929i
$949$	45.3205	−	6.51610i	1.47117	−	0.211522i
$950$	2.69631	−	4.14860i	0.0874798	−	0.134599i
$951$	−12.0577	+	7.74901i	−0.390997	+	0.251279i
$952$	−4.87216	+	13.0628i	−0.157908	+	0.423367i
$953$	−8.67129	−	4.73488i	−0.280891	−	0.153378i	0.332628	−	0.943058i	$-0.392065\pi$
$953$	−8.67129	−	4.73488i	−0.280891	−	0.153378i	−0.613519	+	0.789680i	$0.710246\pi$
$954$	−2.32137	+	2.67901i	−0.0751573	+	0.0867361i
$955$	−17.1460	−	51.9599i	−0.554833	−	1.68138i
$956$	−8.95343	+	2.62896i	−0.289575	+	0.0850268i
$957$	−2.49315	−	0.929895i	−0.0805919	−	0.0300592i
$958$	−38.2887	−	8.32920i	−1.23705	−	0.269104i
$959$	−8.80833	+	29.9984i	−0.284436	+	0.968700i
$960$	−2.06804	+	0.850406i	−0.0667459	+	0.0274467i
$961$	32.7687	−	71.7534i	1.05705	−	2.31463i
$962$	−13.1873	−	17.6162i	−0.425176	−	0.567969i
$963$	0.0676639	+	0.311046i	0.00218044	+	0.0100233i
$964$	16.7270	+	19.3040i	0.538742	+	0.621741i
$965$	34.0223	−	8.59082i	1.09522	−	0.276548i
$966$	−10.7248	+	3.93522i	−0.345066	+	0.126614i
$967$	−1.44519	−	1.44519i	−0.0464742	−	0.0464742i	0.683488	−	0.729962i	$-0.260462\pi$
$967$	−1.44519	−	1.44519i	−0.0464742	−	0.0464742i	−0.729962	+	0.683488i	$0.760462\pi$
$968$	−1.65570	−	0.118418i	−0.0532161	−	0.00380609i
$969$	3.13125	−	4.87232i	0.100590	−	0.156522i
$970$	−3.51954	+	4.34463i	−0.113006	+	0.139498i
$971$	−21.7763	−	9.94492i	−0.698836	−	0.319148i	0.0341259	−	0.999418i	$-0.489135\pi$
$971$	−21.7763	−	9.94492i	−0.698836	−	0.319148i	−0.732962	+	0.680270i	$0.761863\pi$
$972$	0.599278	−	0.800541i	0.0192218	−	0.0256774i
$973$	−17.6079	−	32.2464i	−0.564482	−	1.03377i
$974$	19.0610	+	29.6595i	0.610754	+	0.950352i
$975$	−11.9401	−	9.03414i	−0.382388	−	0.289324i
$976$	−3.02358	−	10.2974i	−0.0967824	−	0.329611i
$977$	0.306628	+	4.28722i	0.00980990	+	0.137160i	0.999997	−	0.00259022i	$-0.000824493\pi$
$977$	0.306628	+	4.28722i	0.00980990	+	0.137160i	−0.990187	+	0.139751i	$0.955370\pi$
$978$	0.106964	+	1.49555i	0.00342032	+	0.0478223i
$979$	5.63801	+	19.2013i	0.180192	+	0.613676i
$980$	−0.324443	+	2.94665i	−0.0103639	+	0.0941271i
$981$	−7.02381	−	10.9293i	−0.224253	−	0.348944i
$982$	15.9461	+	29.2031i	0.508861	+	0.931910i
$983$	13.8612	−	18.5164i	0.442103	−	0.590580i	−0.523039	−	0.852309i	$-0.675202\pi$
$983$	13.8612	−	18.5164i	0.442103	−	0.590580i	0.965142	+	0.261729i	$0.0842925\pi$
$984$	10.6410	+	4.85958i	0.339222	+	0.154918i
$985$	60.4628	−	6.34363i	1.92650	−	0.202125i
$986$	−2.75505	+	4.28694i	−0.0877386	+	0.136524i
$987$	0.118750	+	0.00849316i	0.00377985	+	0.000270340i
$988$	−2.09536	−	2.09536i	−0.0666623	−	0.0666623i
$989$	20.2270	+	1.55499i	0.643183	+	0.0494457i
$990$	1.67305	+	6.62580i	0.0531730	+	0.210582i
$991$	−27.5618	−	31.8080i	−0.875528	−	1.01041i	−0.999835	−	0.0181695i	$-0.994216\pi$
$991$	−27.5618	−	31.8080i	−0.875528	−	1.01041i	0.124307	−	0.992244i	$-0.460329\pi$
$992$	2.22821	+	10.2429i	0.0707456	+	0.325212i
$993$	−14.3867	−	19.2184i	−0.456550	−	0.609879i
$994$	−1.77841	+	3.89418i	−0.0564078	+	0.123516i
$995$	11.2028	−	26.8511i	0.355154	−	0.851237i
$996$	−1.59285	+	5.42474i	−0.0504713	+	0.171890i
$997$	18.4396	+	4.01130i	0.583989	+	0.127039i	0.494847	−	0.868980i	$-0.335224\pi$
$997$	18.4396	+	4.01130i	0.583989	+	0.127039i	0.0891418	+	0.996019i	$0.471588\pi$
$998$	10.1178	+	3.77376i	0.320275	+	0.119456i
$999$	−7.05084	+	2.07031i	−0.223079	+	0.0655019i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.217.2	yes	240
5.3	odd	4	inner	690.2.w.a.493.10	yes	240
23.7	odd	22	inner	690.2.w.a.7.10	✓	240
115.53	even	44	inner	690.2.w.a.283.2	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.10	✓	240	23.7	odd	22	inner
690.2.w.a.217.2	yes	240	1.1	even	1	trivial
690.2.w.a.283.2	yes	240	115.53	even	44	inner
690.2.w.a.493.10	yes	240	5.3	odd	4	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)

\(f(q)\)	\(=\)	\(q+(-0.0713392 + 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.84002 + 1.27057i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.09069 - 1.14160i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.0713392 + 0.997452i) q^{2} +(-0.977147 + 0.212565i) q^{3} +(-0.989821 - 0.142315i) q^{4} +(-1.84002 + 1.27057i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(2.09069 - 1.14160i) q^{7} +(0.212565 - 0.977147i) q^{8} +(0.909632 - 0.415415i) q^{9} +(-1.13606 - 1.92597i) q^{10} +(-2.30969 - 2.00135i) q^{11} +(0.997452 - 0.0713392i) q^{12} +(-1.43513 + 2.62824i) q^{13} +(0.989548 + 2.16681i) q^{14} +(1.52789 - 1.63265i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-4.68542 - 3.50746i) q^{17} +(0.349464 + 0.936950i) q^{18} +(0.140830 - 0.979493i) q^{19} +(2.00211 - 0.995772i) q^{20} +(-1.80025 + 1.55992i) q^{21} +(2.16103 - 2.16103i) q^{22} +(1.37563 - 4.59431i) q^{23} +1.00000i q^{24} +(1.77132 - 4.67573i) q^{25} +(-2.51916 - 1.61897i) q^{26} +(-0.800541 + 0.599278i) q^{27} +(-2.23188 + 0.832448i) q^{28} +(-0.861813 + 0.123910i) q^{29} +(1.51950 + 1.64047i) q^{30} +(8.81840 - 5.66724i) q^{31} +(-0.349464 + 0.936950i) q^{32} +(2.68232 + 1.46466i) q^{33} +(3.83278 - 4.42326i) q^{34} +(-2.39643 + 4.75693i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(6.88519 + 2.56804i) q^{37} +(0.966951 + 0.210347i) q^{38} +(0.843658 - 2.87323i) q^{39} +(0.850406 + 2.06804i) q^{40} +(4.85958 - 10.6410i) q^{41} +(-1.42752 - 1.90695i) q^{42} +(0.899167 + 4.13340i) q^{43} +(2.00135 + 2.30969i) q^{44} +(-1.14593 + 1.92012i) q^{45} +(4.48446 + 1.69988i) q^{46} +(-0.0353404 - 0.0353404i) q^{47} +(-0.997452 - 0.0713392i) q^{48} +(-0.716751 + 1.11529i) q^{49} +(4.53745 + 2.10037i) q^{50} +(5.32390 + 2.43135i) q^{51} +(1.79456 - 2.39725i) q^{52} +(1.69886 + 3.11123i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(6.79272 + 0.747917i) q^{55} +(-0.671107 - 2.28558i) q^{56} +(0.0705948 + 0.987044i) q^{57} +(-0.0621132 - 0.868457i) q^{58} +(-2.30687 - 7.85647i) q^{59} +(-1.74469 + 1.39859i) q^{60} +(-5.80221 - 9.02841i) q^{61} +(5.02371 + 9.20023i) q^{62} +(1.42752 - 1.90695i) q^{63} +(-0.909632 - 0.415415i) q^{64} +(-0.698693 - 6.65943i) q^{65} +(-1.65228 + 2.57100i) q^{66} +(-1.56730 - 0.112095i) q^{67} +(4.13856 + 4.13856i) q^{68} +(-0.367603 + 4.78172i) q^{69} +(-4.57386 - 2.72968i) q^{70} +(1.17691 + 1.35823i) q^{71} +(-0.212565 - 0.977147i) q^{72} +(-9.16298 - 12.2403i) q^{73} +(-3.05268 + 6.68444i) q^{74} +(-0.736947 + 4.94539i) q^{75} +(-0.278793 + 0.949481i) q^{76} +(-7.11360 - 1.54747i) q^{77} +(2.80573 + 1.04648i) q^{78} +(-16.0559 + 4.71444i) q^{79} +(-2.12344 + 0.700707i) q^{80} +(0.654861 - 0.755750i) q^{81} +(10.2672 + 5.60631i) q^{82} +(-1.97579 + 5.29729i) q^{83} +(2.00392 - 1.28784i) q^{84} +(13.0777 + 0.500652i) q^{85} +(-4.18702 + 0.602002i) q^{86} +(0.815779 - 0.304270i) q^{87} +(-2.44658 + 1.83148i) q^{88} +(-5.50859 - 3.54016i) q^{89} +(-1.83348 - 1.27999i) q^{90} +7.13319i q^{91} +(-2.01547 + 4.35177i) q^{92} +(-7.41221 + 7.41221i) q^{93} +(0.0377715 - 0.0327292i) q^{94} +(0.985382 + 1.98122i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-0.873842 - 2.34286i) q^{97} +(-1.06131 - 0.794489i) q^{98} +(-2.93236 - 0.861018i) 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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