LMFDB - Embedded newform 900.2.bj.f.487.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			487.12
Character	$\chi$	$=$	900.487
Dual form			900.2.bj.f.523.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.448691 - 1.34115i) q^{2} +(-1.59735 + 1.20352i) q^{4} +(-2.23534 - 0.0568795i) q^{5} +(2.47703 - 2.47703i) q^{7} +(2.33082 + 1.60227i) q^{8} +(0.926696 + 3.02345i) q^{10} +(-2.07978 + 2.86258i) q^{11} +(-0.541843 + 3.42106i) q^{13} +(-4.43349 - 2.21064i) q^{14} +(1.10307 - 3.84490i) q^{16} +(3.90086 - 1.98759i) q^{17} +(-1.81409 + 5.58320i) q^{19} +(3.63909 - 2.59943i) q^{20} +(4.77232 + 1.50488i) q^{22} +(-0.0122038 - 0.0770517i) q^{23} +(4.99353 + 0.254291i) q^{25} +(4.83127 - 0.808310i) q^{26} +(-0.975529 + 6.93786i) q^{28} +(0.807803 - 0.262471i) q^{29} +(-0.000123334 - 4.00736e-5i) q^{31} +(-5.65151 + 0.245797i) q^{32} +(-4.41593 - 4.33981i) q^{34} +(-5.67791 + 5.39613i) q^{35} +(5.10375 + 0.808354i) q^{37} +(8.30186 - 0.0721695i) q^{38} +(-5.11905 - 3.71421i) q^{40} +(4.23098 - 3.07399i) q^{41} +(-4.57632 - 4.57632i) q^{43} +(-0.123028 - 7.07561i) q^{44} +(-0.0978619 + 0.0509395i) q^{46} +(11.5502 + 5.88510i) q^{47} -5.27138i q^{49} +(-1.89951 - 6.81116i) q^{50} +(-3.25181 - 6.11676i) q^{52} +(9.59125 + 4.88699i) q^{53} +(4.81186 - 6.28055i) q^{55} +(9.74240 - 1.80463i) q^{56} +(-0.714467 - 0.965614i) q^{58} +(7.12122 - 5.17387i) q^{59} +(8.17083 + 5.93646i) q^{61} +(1.59424e-6 + 0.000183390i) q^{62} +(2.86543 + 7.46922i) q^{64} +(1.40579 - 7.61643i) q^{65} +(-4.18342 - 8.21042i) q^{67} +(-3.83894 + 7.86965i) q^{68} +(9.78463 + 5.19372i) q^{70} +(1.99288 - 0.647527i) q^{71} +(12.5935 - 1.99462i) q^{73} +(-1.20589 - 7.20758i) q^{74} +(-3.82176 - 11.1016i) q^{76} +(1.93900 + 12.2424i) q^{77} +(0.609102 + 1.87462i) q^{79} +(-2.68443 + 8.53193i) q^{80} +(-6.02107 - 4.29510i) q^{82} +(-14.4825 + 7.37922i) q^{83} +(-8.83282 + 4.22106i) q^{85} +(-4.08417 + 8.19088i) q^{86} +(-9.43424 + 3.33977i) q^{88} +(3.49423 - 4.80940i) q^{89} +(7.13192 + 9.81624i) q^{91} +(0.112227 + 0.108391i) q^{92} +(2.71033 - 18.1311i) q^{94} +(4.37269 - 12.3772i) q^{95} +(-1.72335 + 3.38227i) q^{97} +(-7.06970 + 2.36522i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58}+ \cdots - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{20}\right)$

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 $

$2$	−0.448691	−	1.34115i	−0.317273	−	0.948334i
$2$	−0.448691	−	1.34115i	−0.317273	−	0.948334i
$3$		0			0
$3$		0			0
$4$	−1.59735	+	1.20352i	−0.798676	+	0.601761i
$5$	−2.23534	−	0.0568795i	−0.999676	−	0.0254373i
$5$	−2.23534	−	0.0568795i	−0.999676	−	0.0254373i
$6$		0			0
$7$	2.47703	−	2.47703i	0.936230	−	0.936230i	−0.0618548	−	0.998085i	$-0.519702\pi$
$7$	2.47703	−	2.47703i	0.936230	−	0.936230i	0.998085	+	0.0618548i	$0.0197016\pi$
$8$	2.33082	+	1.60227i	0.824069	+	0.566490i
$9$		0			0
$10$	0.926696	+	3.02345i	0.293047	+	0.956098i
$11$	−2.07978	+	2.86258i	−0.627079	+	0.863100i	−0.997844	−	0.0656267i	$-0.979095\pi$
$11$	−2.07978	+	2.86258i	−0.627079	+	0.863100i	0.370766	+	0.928726i	$0.379095\pi$
$12$		0			0
$13$	−0.541843	+	3.42106i	−0.150280	+	0.948832i	0.791150	+	0.611623i	$0.209483\pi$
$13$	−0.541843	+	3.42106i	−0.150280	+	0.948832i	−0.941430	+	0.337209i	$0.890517\pi$
$14$	−4.43349	−	2.21064i	−1.18490	−	0.590819i
$15$		0			0
$16$	1.10307	−	3.84490i	0.275767	−	0.961225i
$17$	3.90086	−	1.98759i	0.946097	−	0.482061i	0.0883256	−	0.996092i	$-0.471848\pi$
$17$	3.90086	−	1.98759i	0.946097	−	0.482061i	0.857772	+	0.514031i	$0.171848\pi$
$18$		0			0
$19$	−1.81409	+	5.58320i	−0.416181	+	1.28087i	0.495009	+	0.868888i	$0.335165\pi$
$19$	−1.81409	+	5.58320i	−0.416181	+	1.28087i	−0.911190	+	0.411986i	$0.864835\pi$
$20$	3.63909	−	2.59943i	0.813725	−	0.581250i
$21$		0			0
$22$	4.77232	+	1.50488i	1.01746	+	0.320842i
$23$	−0.0122038	−	0.0770517i	−0.00254466	−	0.0160664i	0.986383	−	0.164462i	$-0.0525889\pi$
$23$	−0.0122038	−	0.0770517i	−0.00254466	−	0.0160664i	−0.988928	+	0.148396i	$0.952589\pi$
$24$		0			0
$25$	4.99353	+	0.254291i	0.998706	+	0.0508581i
$26$	4.83127	−	0.808310i	0.947489	−	0.158523i
$27$		0			0
$28$	−0.975529	+	6.93786i	−0.184358	+	1.31113i
$29$	0.807803	−	0.262471i	0.150005	−	0.0487397i	−0.233052	−	0.972464i	$-0.574871\pi$
$29$	0.807803	−	0.262471i	0.150005	−	0.0487397i	0.383057	+	0.923725i	$0.374871\pi$
$30$		0			0
$31$	−0.000123334	0	4.00736e-5i	−2.21514e−5	0	7.19743e-6i	0.309006	−	0.951060i	$-0.400004\pi$
$31$	−0.000123334	0	4.00736e-5i	−2.21514e−5	0	7.19743e-6i	−0.309028	+	0.951053i	$0.600004\pi$
$32$	−5.65151	+	0.245797i	−0.999056	+	0.0434511i
$33$		0			0
$34$	−4.41593	−	4.33981i	−0.757325	−	0.744272i
$35$	−5.67791	+	5.39613i	−0.959743	+	0.912112i
$36$		0			0
$37$	5.10375	+	0.808354i	0.839051	+	0.132893i	0.561147	−	0.827716i	$-0.310360\pi$
$37$	5.10375	+	0.808354i	0.839051	+	0.132893i	0.277904	+	0.960609i	$0.410360\pi$
$38$	8.30186	−	0.0721695i	1.34674	−	0.0117074i
$39$		0			0
$40$	−5.11905	−	3.71421i	−0.809392	−	0.587268i
$41$	4.23098	−	3.07399i	0.660768	−	0.480076i	−0.206154	−	0.978520i	$-0.566095\pi$
$41$	4.23098	−	3.07399i	0.660768	−	0.480076i	0.866922	+	0.498443i	$0.166095\pi$
$42$		0			0
$43$	−4.57632	−	4.57632i	−0.697883	−	0.697883i	0.266071	−	0.963954i	$-0.414275\pi$
$43$	−4.57632	−	4.57632i	−0.697883	−	0.697883i	−0.963954	+	0.266071i	$0.914275\pi$
$44$	−0.123028	−	7.07561i	−0.0185472	−	1.06669i
$45$		0			0
$46$	−0.0978619	+	0.0509395i	−0.0144289	+	0.00751062i
$47$	11.5502	+	5.88510i	1.68476	+	0.858430i	0.990307	+	0.138896i	$0.0443555\pi$
$47$	11.5502	+	5.88510i	1.68476	+	0.858430i	0.694457	+	0.719534i	$0.255644\pi$
$48$		0			0
$49$		−	5.27138i		−	0.753054i
$50$	−1.89951	−	6.81116i	−0.268632	−	0.963243i
$51$		0			0
$52$	−3.25181	−	6.11676i	−0.450945	−	0.848242i
$53$	9.59125	+	4.88699i	1.31746	+	0.671279i	0.964431	−	0.264333i	$-0.0851519\pi$
$53$	9.59125	+	4.88699i	1.31746	+	0.671279i	0.353029	+	0.935613i	$0.385152\pi$
$54$		0			0
$55$	4.81186	−	6.28055i	0.648831	−	0.846869i
$56$	9.74240	−	1.80463i	1.30188	−	0.241154i
$57$		0			0
$58$	−0.714467	−	0.965614i	−0.0938141	−	0.126791i
$59$	7.12122	−	5.17387i	0.927104	−	0.673580i	−0.0181782	−	0.999835i	$-0.505787\pi$
$59$	7.12122	−	5.17387i	0.927104	−	0.673580i	0.945282	+	0.326254i	$0.105787\pi$
$60$		0			0
$61$	8.17083	+	5.93646i	1.04617	+	0.760085i	0.971480	−	0.237122i	$-0.0762040\pi$
$61$	8.17083	+	5.93646i	1.04617	+	0.760085i	0.0746877	+	0.997207i	$0.476204\pi$
$62$	1.59424e−6	0	0.000183390i	2.02468e−7	0	2.32905e-5i
$63$		0			0
$64$	2.86543	+	7.46922i	0.358179	+	0.933653i
$65$	1.40579	−	7.61643i	0.174367	−	0.944702i
$66$		0			0
$67$	−4.18342	−	8.21042i	−0.511086	−	1.00306i	−0.991993	−	0.126291i	$-0.959693\pi$
$67$	−4.18342	−	8.21042i	−0.511086	−	1.00306i	0.480907	−	0.876771i	$-0.340307\pi$
$68$	−3.83894	+	7.86965i	−0.465540	+	0.954335i
$69$		0			0
$70$	9.78463	+	5.19372i	1.16949	+	0.620769i
$71$	1.99288	−	0.647527i	0.236512	−	0.0768473i	−0.188363	−	0.982099i	$-0.560318\pi$
$71$	1.99288	−	0.647527i	0.236512	−	0.0768473i	0.424875	+	0.905252i	$0.360318\pi$
$72$		0			0
$73$	12.5935	−	1.99462i	1.47396	−	0.233453i	0.632834	−	0.774288i	$-0.281892\pi$
$73$	12.5935	−	1.99462i	1.47396	−	0.233453i	0.841129	+	0.540835i	$0.181892\pi$
$74$	−1.20589	−	7.20758i	−0.140181	−	0.837864i
$75$		0			0
$76$	−3.82176	−	11.1016i	−0.438386	−	1.27344i
$77$	1.93900	+	12.2424i	0.220970	+	1.39515i
$78$		0			0
$79$	0.609102	+	1.87462i	0.0685293	+	0.210911i	0.979456	−	0.201656i	$-0.0646322\pi$
$79$	0.609102	+	1.87462i	0.0685293	+	0.210911i	−0.910927	+	0.412567i	$0.864632\pi$
$80$	−2.68443	+	8.53193i	−0.300129	+	0.953899i
$81$		0			0
$82$	−6.02107	−	4.29510i	−0.664916	−	0.474314i
$83$	−14.4825	+	7.37922i	−1.58966	+	0.809974i	−0.589667	+	0.807647i	$0.700741\pi$
$83$	−14.4825	+	7.37922i	−1.58966	+	0.809974i	−0.999997	+	0.00232773i	$0.999259\pi$
$84$		0			0
$85$	−8.83282	+	4.22106i	−0.958053	+	0.457838i
$86$	−4.08417	+	8.19088i	−0.440407	+	0.883245i
$87$		0			0
$88$	−9.43424	+	3.33977i	−1.00569	+	0.356020i
$89$	3.49423	−	4.80940i	0.370388	−	0.509795i	−0.582618	−	0.812746i	$-0.697972\pi$
$89$	3.49423	−	4.80940i	0.370388	−	0.509795i	0.953006	+	0.302951i	$0.0979718\pi$
$90$		0			0
$91$	7.13192	+	9.81624i	0.747628	+	1.02902i
$92$	0.112227	+	0.108391i	0.0117005	+	0.0113006i
$93$		0			0
$94$	2.71033	−	18.1311i	0.279549	−	1.87008i
$95$	4.37269	−	12.3772i	0.448628	−	1.26987i
$96$		0			0
$97$	−1.72335	+	3.38227i	−0.174980	+	0.343417i	−0.961795	−	0.273772i	$-0.911729\pi$
$97$	−1.72335	+	3.38227i	−0.174980	+	0.343417i	0.786815	+	0.617189i	$0.211729\pi$
$98$	−7.06970	+	2.36522i	−0.714147	+	0.238924i
$99$		0			0
$100$	−8.28247	+	5.60363i	−0.828247	+	0.560363i
$101$	−5.57248			−0.554482			−0.277241	−	0.960800i	$-0.589420\pi$
$101$	−5.57248			−0.554482			−0.277241	+	0.960800i	$0.589420\pi$
$102$		0			0
$103$	−7.38093	+	14.4859i	−0.727265	+	1.42734i	0.169818	+	0.985475i	$0.445682\pi$
$103$	−7.38093	+	14.4859i	−0.727265	+	1.42734i	−0.897083	+	0.441862i	$0.854318\pi$
$104$	−6.74442	+	7.10569i	−0.661344	+	0.696771i
$105$		0			0
$106$	2.25066	−	15.0560i	0.218603	−	1.46237i
$107$	0.755111	−	0.755111i	0.0729993	−	0.0729993i	−0.669664	−	0.742664i	$-0.733562\pi$
$107$	0.755111	−	0.755111i	0.0729993	−	0.0729993i	0.742664	+	0.669664i	$0.233562\pi$
$108$		0			0
$109$	−4.88498	−	6.72359i	−0.467896	−	0.644003i	0.508227	−	0.861223i	$-0.330301\pi$
$109$	−4.88498	−	6.72359i	−0.467896	−	0.644003i	−0.976123	+	0.217220i	$0.930301\pi$
$110$	−10.5822	−	3.63538i	−1.00897	−	0.346620i
$111$		0			0
$112$	−6.79160	−	12.2563i	−0.641746	−	1.15811i
$113$	−2.07827	+	13.1217i	−0.195508	+	1.23439i	0.673350	+	0.739324i	$0.264855\pi$
$113$	−2.07827	+	13.1217i	−0.195508	+	1.23439i	−0.868858	+	0.495062i	$0.835145\pi$
$114$		0			0
$115$	0.0228970	+	0.172931i	0.00213516	+	0.0161259i
$116$	−0.974456	+	1.39147i	−0.0904760	+	0.129195i
$117$		0			0
$118$	−10.1342	−	7.22913i	−0.932924	−	0.665496i
$119$	4.73924	−	14.5859i	0.434445	−	1.33708i
$120$		0			0
$121$	−0.469662	−	1.44547i	−0.0426965	−	0.131406i
$122$	4.29548	−	13.6219i	0.388895	−	1.23327i
$123$		0			0
$124$	0.000245237	0	8.44235e-5i	2.20230e−5	0	7.58145e-6i
$125$	−11.1478	−	0.852457i	−0.997089	−	0.0762460i
$126$		0			0
$127$	−13.9231	+	2.20521i	−1.23548	+	0.195680i	−0.739800	−	0.672827i	$-0.765080\pi$
$127$	−13.9231	+	2.20521i	−1.23548	+	0.195680i	−0.495677	+	0.868507i	$0.665080\pi$
$128$	8.73163	−	7.19434i	0.771775	−	0.635896i
$129$		0			0
$130$	−10.8455	+	1.53205i	−0.951215	+	0.134370i
$131$	−9.73405	−	3.16278i	−0.850468	−	0.276334i	−0.148826	−	0.988863i	$-0.547549\pi$
$131$	−9.73405	−	3.16278i	−0.850468	−	0.276334i	−0.701642	+	0.712530i	$0.747549\pi$
$132$		0			0
$133$	9.33620	+	18.3233i	0.809551	+	1.58883i
$134$	−9.13432	+	9.29453i	−0.789085	+	0.802925i
$135$		0			0
$136$	12.2769	+	1.61754i	1.05273	+	0.138703i
$137$	−2.60954	−	0.413311i	−0.222948	−	0.0353115i	0.0439608	−	0.999033i	$-0.486002\pi$
$137$	−2.60954	−	0.413311i	−0.222948	−	0.0353115i	−0.266909	+	0.963722i	$0.586002\pi$
$138$		0			0
$139$	5.28116	+	3.83699i	0.447942	+	0.325449i	0.788783	−	0.614672i	$-0.210712\pi$
$139$	5.28116	+	3.83699i	0.447942	+	0.325449i	−0.340841	+	0.940121i	$0.610712\pi$
$140$	2.57527	−	15.4530i	0.217650	−	1.30602i
$141$		0			0
$142$	−1.76262	−	2.38221i	−0.147916	−	0.199911i
$143$	−8.66614	−	8.66614i	−0.724699	−	0.724699i
$144$		0			0
$145$	−1.82065	+	0.540766i	−0.151197	+	0.0449082i
$146$	−8.32569	−	15.9948i	−0.689039	−	1.32374i
$147$		0			0
$148$	−9.12536	+	4.85125i	−0.750100	+	0.398770i
$149$		−	1.66225i		−	0.136177i	−0.997679	−	0.0680885i	$-0.978310\pi$
$149$		−	1.66225i		−	0.136177i	0.997679	−	0.0680885i	$-0.0216900\pi$
$150$		0			0
$151$			14.2155i			1.15684i	0.815738	+	0.578422i	$0.196331\pi$
$151$			14.2155i			1.15684i	−0.815738	+	0.578422i	$0.803669\pi$
$152$	−13.1741	+	10.1068i	−1.06856	+	0.819766i
$153$		0			0
$154$	15.5488	−	8.09355i	1.25296	−	0.652197i
$155$	0.000273414	0	9.65935e-5i	2.19612e−5	0	7.75858e-6i
$156$		0			0
$157$	−10.3354	−	10.3354i	−0.824857	−	0.824857i	0.161943	−	0.986800i	$-0.448224\pi$
$157$	−10.3354	−	10.3354i	−0.824857	−	0.824857i	−0.986800	+	0.161943i	$0.948224\pi$
$158$	2.24085	−	1.65802i	0.178272	−	0.131905i
$159$		0			0
$160$	12.6471	−	0.227985i	0.999838	−	0.0180238i
$161$	−0.221089	−	0.160630i	−0.0174242	−	0.0126594i
$162$		0			0
$163$	23.5826	+	3.73511i	1.84713	+	0.292556i	0.979012	−	0.203804i	$-0.0653305\pi$
$163$	23.5826	+	3.73511i	1.84713	+	0.292556i	0.868117	+	0.496360i	$0.165331\pi$
$164$	−3.05875	+	10.0023i	−0.238848	+	0.781050i
$165$		0			0
$166$	16.3948	+	16.1122i	1.27248	+	1.25055i
$167$	3.90289	+	7.65985i	0.302015	+	0.592737i	0.991280	−	0.131772i	$-0.0420667\pi$
$167$	3.90289	+	7.65985i	0.302015	+	0.592737i	−0.689266	+	0.724509i	$0.742067\pi$
$168$		0			0
$169$	0.953668	+	0.309865i	0.0733591	+	0.0238358i
$170$	9.62427	+	9.95215i	0.738148	+	0.763295i
$171$		0			0
$172$	12.8177	+	1.80229i	0.977341	+	0.137423i
$173$	24.3562	−	3.85764i	1.85176	−	0.293291i	0.871413	−	0.490551i	$-0.163204\pi$
$173$	24.3562	−	3.85764i	1.85176	−	0.293291i	0.980351	+	0.197260i	$0.0632043\pi$
$174$		0			0
$175$	12.9990	−	11.7392i	0.982634	−	0.887404i
$176$	8.71218	+	11.1542i	0.656705	+	0.840778i
$177$		0			0
$178$	−8.01794	−	2.52834i	−0.600970	−	0.189507i
$179$	2.88996	+	8.89439i	0.216006	+	0.664798i	0.999081	+	0.0428703i	$0.0136502\pi$
$179$	2.88996	+	8.89439i	0.216006	+	0.664798i	−0.783075	+	0.621928i	$0.786350\pi$
$180$		0			0
$181$	−1.13761	+	3.50121i	−0.0845580	+	0.260243i	−0.984392	−	0.175990i	$-0.943687\pi$
$181$	−1.13761	+	3.50121i	−0.0845580	+	0.260243i	0.899834	+	0.436233i	$0.143687\pi$
$182$	9.96500	−	13.9694i	0.738655	−	1.03548i
$183$		0			0
$184$	0.0950131	−	0.199147i	0.00700446	−	0.0146813i
$185$	−11.3627	−	2.09725i	−0.835399	−	0.154193i
$186$		0			0
$187$	−2.42332	+	15.3003i	−0.177211	+	1.11887i
$188$	−25.5325	+	4.50030i	−1.86215	+	0.328218i
$189$		0			0
$190$	−18.5616	−	0.310882i	−1.34660	−	0.0225538i
$191$	−0.778612	−	1.07167i	−0.0563384	−	0.0775431i	0.779918	−	0.625881i	$-0.215261\pi$
$191$	−0.778612	−	1.07167i	−0.0563384	−	0.0775431i	−0.836257	+	0.548338i	$0.815261\pi$
$192$		0			0
$193$	−8.28171	+	8.28171i	−0.596131	+	0.596131i	−0.939281	−	0.343150i	$-0.888506\pi$
$193$	−8.28171	+	8.28171i	−0.596131	+	0.596131i	0.343150	+	0.939281i	$0.388506\pi$
$194$	5.30937	+	0.793674i	0.381191	+	0.0569824i
$195$		0			0
$196$	6.34423	+	8.42025i	0.453159	+	0.601447i
$197$	−7.57112	+	14.8592i	−0.539420	+	1.05867i	0.447016	+	0.894526i	$0.352487\pi$
$197$	−7.57112	+	14.8592i	−0.539420	+	1.05867i	−0.986436	+	0.164146i	$0.947513\pi$
$198$		0			0
$199$	−18.7284			−1.32762			−0.663811	−	0.747900i	$-0.731062\pi$
$199$	−18.7284			−1.32762			−0.663811	+	0.747900i	$0.731062\pi$
$200$	11.2316	+	8.59371i	0.794192	+	0.607667i
$201$		0			0
$202$	2.50032	+	7.47351i	0.175922	+	0.525835i
$203$	1.35080	−	2.65110i	0.0948079	−	0.186071i
$204$		0			0
$205$	−9.63254	+	6.63076i	−0.672766	+	0.463113i
$206$	22.7395	+	3.39922i	1.58433	+	0.236835i
$207$		0			0
$208$	12.5559	+	5.85699i	0.870598	+	0.406109i
$209$	−12.2094	−	16.8048i	−0.844544	−	1.16241i
$210$		0			0
$211$	9.53944	−	13.1299i	0.656722	−	0.903901i	−0.342645	−	0.939465i	$-0.611323\pi$
$211$	9.53944	−	13.1299i	0.656722	−	0.903901i	0.999367	+	0.0355641i	$0.0113228\pi$
$212$	−21.2022	+	3.73705i	−1.45617	+	0.256662i
$213$		0			0
$214$	−1.35153	−	0.673903i	−0.0923884	−	0.0460671i
$215$	9.96936	+	10.4900i	0.679905	+	0.715409i
$216$		0			0
$217$	−0.000404766	0	0.000206238i	−2.74773e−5	0	1.40004e-5i
$218$	−6.82548	+	9.56829i	−0.462280	+	0.648046i
$219$		0			0
$220$	−0.127447	+	15.8234i	−0.00859245	+	1.06682i
$221$	4.68600	+	14.4220i	0.315215	+	0.970131i
$222$		0			0
$223$	−2.09027	−	13.1975i	−0.139975	−	0.883768i	−0.953315	−	0.301979i	$-0.902353\pi$
$223$	−2.09027	−	13.1975i	−0.139975	−	0.883768i	0.813340	−	0.581789i	$-0.197647\pi$
$224$	−13.3901	+	14.6078i	−0.894666	+	0.976026i
$225$		0			0
$226$	18.5306	−	3.10032i	1.23264	−	0.206230i
$227$	−21.8851	+	3.46626i	−1.45256	+	0.230064i	−0.832298	−	0.554328i	$-0.812975\pi$
$227$	−21.8851	+	3.46626i	−1.45256	+	0.230064i	−0.620266	+	0.784392i	$0.712975\pi$
$228$		0			0
$229$	21.0179	−	6.82911i	1.38890	−	0.451281i	0.483314	−	0.875447i	$-0.339433\pi$
$229$	21.0179	−	6.82911i	1.38890	−	0.451281i	0.905584	+	0.424166i	$0.139433\pi$
$230$	0.221652	−	0.108301i	0.0146153	−	0.00714115i
$231$		0			0
$232$	2.30339	+	0.682549i	0.151225	+	0.0448116i
$233$	−6.93889	−	13.6183i	−0.454582	−	0.892167i	−0.998590	−	0.0530874i	$-0.983094\pi$
$233$	−6.93889	−	13.6183i	−0.454582	−	0.892167i	0.544008	−	0.839080i	$-0.316906\pi$
$234$		0			0
$235$	−25.4838	−	13.8122i	−1.66238	−	0.901008i
$236$	−5.14823	+	16.8350i	−0.335121	+	1.09587i
$237$		0			0
$238$	−21.6883	+	0.188540i	−1.40584	+	0.0122212i
$239$	1.66547	+	1.21003i	0.107730	+	0.0782704i	0.640346	−	0.768087i	$-0.278791\pi$
$239$	1.66547	+	1.21003i	0.107730	+	0.0782704i	−0.532616	+	0.846357i	$0.678791\pi$
$240$		0			0
$241$	16.0774	−	11.6809i	1.03564	−	0.752434i	0.0662080	−	0.997806i	$-0.478910\pi$
$241$	16.0774	−	11.6809i	1.03564	−	0.752434i	0.969429	+	0.245371i	$0.0789099\pi$
$242$	−1.72786	+	1.27846i	−0.111071	+	0.0821823i
$243$		0			0
$244$	−20.1964	+	0.351167i	−1.29294	+	0.0224812i
$245$	−0.299834	+	11.7834i	−0.0191557	+	0.752811i
$246$		0			0
$247$	−18.1175	−	9.23133i	−1.15279	−	0.587376i
$248$	−0.000223260	0	0.000291019i	−1.41770e−5	0	1.84797e-5i
$249$		0			0
$250$	3.85865	+	15.3333i	0.244042	+	0.969765i
$251$		−	25.9642i		−	1.63885i	−0.573188	−	0.819424i	$-0.694293\pi$
$251$		−	25.9642i		−	1.63885i	0.573188	−	0.819424i	$-0.305707\pi$
$252$		0			0
$253$	0.245948	+	0.125317i	0.0154626	+	0.00787859i
$254$	9.20469	+	17.6835i	0.577554	+	1.10956i
$255$		0			0
$256$	−13.5665	−	8.48237i	−0.847905	−	0.530148i
$257$	5.28943	+	5.28943i	0.329946	+	0.329946i	0.852566	−	0.522620i	$-0.175045\pi$
$257$	5.28943	+	5.28943i	0.329946	+	0.329946i	−0.522620	+	0.852566i	$0.675045\pi$
$258$		0			0
$259$	14.6445	−	10.6398i	0.909963	−	0.661127i
$260$	6.92100	+	13.8580i	0.429222	+	0.859438i
$261$		0			0
$262$	0.125824	+	14.4739i	0.00777345	+	0.894201i
$263$	13.9709	+	2.21277i	0.861481	+	0.136445i	0.571515	−	0.820592i	$-0.306356\pi$
$263$	13.9709	+	2.21277i	0.861481	+	0.136445i	0.289966	+	0.957037i	$0.406356\pi$
$264$		0			0
$265$	−21.1618	−	11.4696i	−1.29996	−	0.704575i
$266$	20.3852	−	20.7427i	1.24990	−	1.27182i
$267$		0			0
$268$	16.5638	+	8.08010i	1.01180	+	0.493570i
$269$	−9.22474	−	2.99730i	−0.562443	−	0.182749i	0.0139774	−	0.999902i	$-0.495551\pi$
$269$	−9.22474	−	2.99730i	−0.562443	−	0.182749i	−0.576420	+	0.817154i	$0.695551\pi$
$270$		0			0
$271$	−11.2200	+	3.64559i	−0.681564	+	0.221454i	−0.629280	−	0.777179i	$-0.716650\pi$
$271$	−11.2200	+	3.64559i	−0.681564	+	0.221454i	−0.0522842	+	0.998632i	$0.516650\pi$
$272$	−3.33916	−	17.1908i	−0.202466	−	1.04235i
$273$		0			0
$274$	0.616568	+	3.68523i	0.0372483	+	0.222633i
$275$	−11.1134	+	13.7655i	−0.670163	+	0.830091i
$276$		0			0
$277$	3.91891	+	24.7430i	0.235464	+	1.48666i	0.768106	+	0.640322i	$0.221199\pi$
$277$	3.91891	+	24.7430i	0.235464	+	1.48666i	−0.532642	+	0.846341i	$0.678801\pi$
$278$	2.77635	−	8.80444i	0.166515	−	0.528055i
$279$		0			0
$280$	−21.8803	+	3.47982i	−1.30760	+	0.207959i
$281$	−4.75790	+	14.6433i	−0.283832	+	0.873546i	0.702914	+	0.711275i	$0.251882\pi$
$281$	−4.75790	+	14.6433i	−0.283832	+	0.873546i	−0.986746	+	0.162271i	$0.948118\pi$
$282$		0			0
$283$	13.9254	−	7.09534i	0.827778	−	0.421774i	0.0118519	−	0.999930i	$-0.496227\pi$
$283$	13.9254	−	7.09534i	0.827778	−	0.421774i	0.815927	+	0.578156i	$0.196227\pi$
$284$	−2.40402	+	3.43281i	−0.142652	+	0.203700i
$285$		0			0
$286$	−7.73415	+	15.5110i	−0.457330	+	0.917184i
$287$	2.86591	−	18.0946i	0.169169	−	1.06809i
$288$		0			0
$289$	1.27385	−	1.75330i	0.0749323	−	0.103135i
$290$	1.54216	+	2.19912i	0.0905585	+	0.129137i
$291$		0			0
$292$	−17.7157	+	18.3427i	−1.03674	+	1.07343i
$293$	−12.3367	+	12.3367i	−0.720717	+	0.720717i	−0.968751	−	0.248035i	$-0.920215\pi$
$293$	−12.3367	+	12.3367i	−0.720717	+	0.720717i	0.248035	+	0.968751i	$0.420215\pi$
$294$		0			0
$295$	−16.2127	+	11.1603i	−0.943938	+	0.649779i
$296$	10.6007	+	10.0617i	0.616154	+	0.584826i
$297$		0			0
$298$	−2.22933	+	0.745839i	−0.129141	+	0.0432053i
$299$	0.270211			0.0156267
$300$		0			0
$301$	−22.6714			−1.30676
$302$	19.0651	−	6.37838i	1.09707	−	0.367035i
$303$		0			0
$304$	19.4658	+	13.1336i	1.11644	+	0.753266i
$305$	−17.9270	−	13.7348i	−1.02649	−	0.786451i
$306$		0			0
$307$	21.4864	−	21.4864i	1.22629	−	1.22629i	0.260937	−	0.965356i	$-0.415969\pi$
$307$	21.4864	−	21.4864i	1.22629	−	1.22629i	0.965356	−	0.260937i	$-0.0840315\pi$
$308$	−17.8313	−	17.2218i	−1.01603	−	0.981302i
$309$		0			0
$310$	6.86744e−6	0	0.000410030i	3.90044e−7	0	2.32881e-5i
$311$	−7.60468	+	10.4670i	−0.431222	+	0.593526i	−0.968233	−	0.250049i	$-0.919553\pi$
$311$	−7.60468	+	10.4670i	−0.431222	+	0.593526i	0.537011	+	0.843575i	$0.319553\pi$
$312$		0			0
$313$	0.282072	−	1.78093i	0.0159436	−	0.100664i	−0.978433	−	0.206563i	$-0.933772\pi$
$313$	0.282072	−	1.78093i	0.0159436	−	0.100664i	0.994377	+	0.105899i	$0.0337721\pi$
$314$	−9.22392	+	18.4988i	−0.520536	+	1.04395i
$315$		0			0
$316$	−3.22910	−	2.26136i	−0.181651	−	0.127212i
$317$	−0.555856	+	0.283223i	−0.0312200	+	0.0159074i	−0.469531	−	0.882916i	$-0.655577\pi$
$317$	−0.555856	+	0.283223i	−0.0312200	+	0.0159074i	0.438311	+	0.898823i	$0.355577\pi$
$318$		0			0
$319$	−0.928712	+	2.85828i	−0.0519979	+	0.160033i
$320$	−5.98039	−	16.8593i	−0.334314	−	0.942462i
$321$		0			0
$322$	−0.116228	+	0.368586i	−0.00647715	+	0.0205405i
$323$	4.02058	+	25.3849i	0.223711	+	1.41246i
$324$		0			0
$325$	−3.57565	+	16.9454i	−0.198341	+	0.939961i
$326$	−5.57196	−	33.3036i	−0.308602	−	1.84452i
$327$		0			0
$328$	14.7870	−	0.385716i	0.816477	−	0.0212976i
$329$	43.1877	−	14.0325i	2.38102	−	0.773639i
$330$		0			0
$331$	−10.1209	−	3.28849i	−0.556297	−	0.180752i	0.0173575	−	0.999849i	$-0.494475\pi$
$331$	−10.1209	−	3.28849i	−0.556297	−	0.180752i	−0.573654	+	0.819098i	$0.694475\pi$
$332$	14.2526	−	29.2173i	0.782216	−	1.60351i
$333$		0			0
$334$	8.52179	−	8.67126i	0.466292	−	0.474470i
$335$	8.88438	+	18.5911i	0.485405	+	1.01574i
$336$		0			0
$337$	−16.9393	−	2.68292i	−0.922741	−	0.146148i	−0.323052	−	0.946381i	$-0.604709\pi$
$337$	−16.9393	−	2.68292i	−0.922741	−	0.146148i	−0.599689	+	0.800233i	$0.704709\pi$
$338$	−0.0123273	−	1.41804i	−0.000670516	−	0.0771314i
$339$		0			0
$340$	9.02897	−	17.3730i	0.489665	−	0.942184i
$341$	0.000371222	0	0.000269708i	2.01028e−5	0	1.46055e-5i
$342$		0			0
$343$	4.28185	+	4.28185i	0.231198	+	0.231198i
$344$	−3.33406	−	17.9991i	−0.179760	−	0.970447i
$345$		0			0
$346$	−16.1021	−	30.9343i	−0.865652	−	1.66304i
$347$	4.15803	+	2.11862i	0.223215	+	0.113734i	0.562022	−	0.827122i	$-0.310023\pi$
$347$	4.15803	+	2.11862i	0.223215	+	0.113734i	−0.338807	+	0.940856i	$0.610023\pi$
$348$		0			0
$349$		−	27.0365i		−	1.44723i	−0.690203	−	0.723616i	$-0.742479\pi$
$349$		−	27.0365i		−	1.44723i	0.690203	−	0.723616i	$-0.257521\pi$
$350$	−21.5766	−	12.1663i	−1.15332	−	0.650316i
$351$		0			0
$352$	11.0503	−	16.6891i	0.588984	−	0.889532i
$353$	10.5828	+	5.39221i	0.563266	+	0.286998i	0.712348	−	0.701826i	$-0.247632\pi$
$353$	10.5828	+	5.39221i	0.563266	+	0.286998i	−0.149082	+	0.988825i	$0.547632\pi$
$354$		0			0
$355$	−4.49161	+	1.33409i	−0.238390	+	0.0708062i
$356$	0.206699	+	11.8877i	0.0109550	+	0.630046i
$357$		0			0
$358$	10.6320	−	7.86670i	0.561918	−	0.415768i
$359$	−12.3154	+	8.94766i	−0.649981	+	0.472239i	−0.863265	−	0.504751i	$-0.831584\pi$
$359$	−12.3154	+	8.94766i	−0.649981	+	0.472239i	0.213283	+	0.976990i	$0.431584\pi$
$360$		0			0
$361$	−12.5099	−	9.08895i	−0.658414	−	0.478366i
$362$	5.20608	−	0.0452573i	0.273625	−	0.00237867i
$363$		0			0
$364$	−23.2063	−	7.09657i	−1.21634	−	0.371962i
$365$	−28.2643	+	3.74235i	−1.47942	+	0.195884i
$366$		0			0
$367$	10.8842	+	21.3614i	0.568149	+	1.11505i	0.979097	+	0.203396i	$0.0651977\pi$
$367$	10.8842	+	21.3614i	0.568149	+	1.11505i	−0.410948	+	0.911659i	$0.634802\pi$
$368$	−0.309717	−	0.0380709i	−0.0161451	−	0.00198458i
$369$		0			0
$370$	2.28561	+	16.1800i	0.118823	+	0.841159i
$371$	35.8631	−	11.6526i	1.86192	−	0.604974i
$372$		0			0
$373$	21.4232	−	3.39311i	1.10925	−	0.175689i	0.425185	−	0.905106i	$-0.360209\pi$
$373$	21.4232	−	3.39311i	1.10925	−	0.175689i	0.684068	+	0.729418i	$0.260209\pi$
$374$	21.6072	−	3.61506i	1.11728	−	0.186930i
$375$		0			0
$376$	17.4918	+	32.2236i	0.902070	+	1.66181i
$377$	0.460227	+	2.90576i	0.0237029	+	0.149654i
$378$		0			0
$379$	−1.83578	−	5.64994i	−0.0942976	−	0.290218i	0.892772	−	0.450508i	$-0.148757\pi$
$379$	−1.83578	−	5.64994i	−0.0942976	−	0.290218i	−0.987070	+	0.160290i	$0.948757\pi$
$380$	7.91150	+	25.0334i	0.405851	+	1.28418i
$381$		0			0
$382$	−1.08791	+	1.52508i	−0.0556622	+	0.0780299i
$383$	−4.12547	+	2.10203i	−0.210802	+	0.107409i	−0.556204	−	0.831046i	$-0.687743\pi$
$383$	−4.12547	+	2.10203i	−0.210802	+	0.107409i	0.345402	+	0.938455i	$0.387743\pi$
$384$		0			0
$385$	−3.63800	−	27.4763i	−0.185410	−	1.40032i
$386$	14.8229	+	7.39106i	0.754467	+	0.376195i
$387$		0			0
$388$	−1.31784	−	7.47676i	−0.0669030	−	0.379575i
$389$	5.61572	−	7.72937i	0.284728	−	0.391895i	−0.642565	−	0.766231i	$-0.722130\pi$
$389$	5.61572	−	7.72937i	0.284728	−	0.391895i	0.927293	+	0.374337i	$0.122130\pi$
$390$		0			0
$391$	−0.200752	−	0.276312i	−0.0101525	−	0.0139737i
$392$	8.44620	−	12.2866i	0.426597	−	0.620569i
$393$		0			0
$394$	23.3254	+	3.48681i	1.17512	+	0.175663i
$395$	−1.25492	−	4.22507i	−0.0631421	−	0.212586i
$396$		0			0
$397$	9.59631	−	18.8338i	0.481625	−	0.945242i	−0.514517	−	0.857480i	$-0.672029\pi$
$397$	9.59631	−	18.8338i	0.481625	−	0.945242i	0.996142	−	0.0877616i	$-0.0279714\pi$
$398$	8.40328	+	25.1176i	0.421218	+	1.25903i
$399$		0			0
$400$	6.48592	−	18.9191i	0.324296	−	0.945956i
$401$	−16.7730			−0.837604			−0.418802	−	0.908078i	$-0.637550\pi$
$401$	−16.7730			−0.837604			−0.418802	+	0.908078i	$0.637550\pi$
$402$		0			0
$403$	0.000203922	0	0.000400219i	1.01581e−5	0	1.99363e-5i
$404$	8.90121	−	6.70660i	0.442852	−	0.333666i
$405$		0			0
$406$	−4.16162	−	0.622101i	−0.206537	−	0.0308743i
$407$	−12.9287	+	12.9287i	−0.640851	+	0.640851i
$408$		0			0
$409$	−6.44004	−	8.86395i	−0.318439	−	0.438294i	0.619551	−	0.784957i	$-0.287315\pi$
$409$	−6.44004	−	8.86395i	−0.318439	−	0.438294i	−0.937990	+	0.346663i	$0.887315\pi$
$410$	13.2149	+	9.94349i	0.652636	+	0.491074i
$411$		0			0
$412$	−5.64415	−	32.0222i	−0.278067	−	1.57762i
$413$	4.82365	−	30.4553i	0.237356	−	1.49861i
$414$		0			0
$415$	32.7932	−	15.6713i	1.60975	−	0.769275i
$416$	2.22135	−	19.4674i	0.108910	−	0.954465i
$417$		0			0
$418$	−17.0595	+	23.9148i	−0.834407	+	1.16971i
$419$	−5.83515	+	17.9587i	−0.285066	+	0.877342i	0.701313	+	0.712853i	$0.252597\pi$
$419$	−5.83515	+	17.9587i	−0.285066	+	0.877342i	−0.986379	+	0.164489i	$0.947403\pi$
$420$		0			0
$421$	4.18623	+	12.8839i	0.204024	+	0.627922i	0.999752	+	0.0222675i	$0.00708854\pi$
$421$	4.18623	+	12.8839i	0.204024	+	0.627922i	−0.795728	+	0.605654i	$0.792911\pi$
$422$	−21.8894	−	6.90252i	−1.06556	−	0.336009i
$423$		0			0
$424$	14.5252	+	26.7585i	0.705405	+	1.29951i
$425$	19.9845	−	8.93312i	0.969390	−	0.433320i
$426$		0			0
$427$	34.9442	−	5.53462i	1.69107	−	0.267839i
$428$	−0.297385	+	2.11497i	−0.0143746	+	0.102231i
$429$		0			0
$430$	9.59541	−	18.0771i	0.462732	−	0.871757i
$431$	8.92558	+	2.90010i	0.429930	+	0.139693i	0.515985	−	0.856598i	$-0.327426\pi$
$431$	8.92558	+	2.90010i	0.429930	+	0.139693i	−0.0860549	+	0.996290i	$0.527426\pi$
$432$		0			0
$433$	−13.2636	−	26.0312i	−0.637406	−	1.25098i	−0.953254	−	0.302170i	$-0.902289\pi$
$433$	−13.2636	−	26.0312i	−0.637406	−	1.25098i	0.315848	−	0.948810i	$-0.397711\pi$
$434$	0.000458211	0	0.000450313i	2.19948e−5	0	2.16157e-5i
$435$		0			0
$436$	15.8950	+	4.86077i	0.761233	+	0.232788i
$437$	0.452334	+	0.0716426i	0.0216380	+	0.00342713i
$438$		0			0
$439$	8.37262	+	6.08307i	0.399603	+	0.290329i	0.769379	−	0.638792i	$-0.220566\pi$
$439$	8.37262	+	6.08307i	0.399603	+	0.290329i	−0.369776	+	0.929121i	$0.620566\pi$
$440$	21.2787	−	6.92891i	1.01442	−	0.330323i
$441$		0			0
$442$	17.2395	−	12.7557i	0.820000	−	0.606725i
$443$	1.22412	+	1.22412i	0.0581596	+	0.0581596i	0.735588	−	0.677429i	$-0.236906\pi$
$443$	1.22412	+	1.22412i	0.0581596	+	0.0581596i	−0.677429	+	0.735588i	$0.736906\pi$
$444$		0			0
$445$	−8.08437	+	10.5519i	−0.383236	+	0.500208i
$446$	−16.7619	+	8.72495i	−0.793697	+	0.413138i
$447$		0			0
$448$	25.5993	+	11.4037i	1.20945	+	0.538776i
$449$		−	36.0614i		−	1.70184i	−0.525292	−	0.850922i	$-0.676044\pi$
$449$		−	36.0614i		−	1.70184i	0.525292	−	0.850922i	$-0.323956\pi$
$450$		0			0
$451$			18.5047i			0.871354i
$452$	−12.4725	−	23.4612i	−0.586658	−	1.10352i
$453$		0			0
$454$	14.4684	+	27.7958i	0.679036	+	1.30452i
$455$	−15.3840	−	22.3483i	−0.721211	−	1.04771i
$456$		0			0
$457$	−2.22184	−	2.22184i	−0.103933	−	0.103933i	0.653228	−	0.757161i	$-0.273414\pi$
$457$	−2.22184	−	2.22184i	−0.103933	−	0.103933i	−0.757161	+	0.653228i	$0.773414\pi$
$458$	−18.5894	−	25.1239i	−0.868624	−	1.17396i
$459$		0			0
$460$	−0.244701	−	0.248675i	−0.0114092	−	0.0115945i
$461$	−21.0778	−	15.3139i	−0.981692	−	0.713241i	−0.0236057	−	0.999721i	$-0.507515\pi$
$461$	−21.0778	−	15.3139i	−0.981692	−	0.713241i	−0.958086	+	0.286481i	$0.907515\pi$
$462$		0			0
$463$	−25.1759	−	3.98747i	−1.17002	−	0.185314i	−0.458970	−	0.888452i	$-0.651782\pi$
$463$	−25.1759	−	3.98747i	−1.17002	−	0.185314i	−0.711053	+	0.703138i	$0.751782\pi$
$464$	−0.118113	−	3.39544i	−0.00548328	−	0.157630i
$465$		0			0
$466$	−15.1508	+	15.4165i	−0.701847	+	0.714156i
$467$	−17.3078	−	33.9686i	−0.800911	−	1.57188i	−0.820209	−	0.572063i	$-0.806143\pi$
$467$	−17.3078	−	33.9686i	−0.800911	−	1.57188i	0.0192980	−	0.999814i	$-0.493857\pi$
$468$		0			0
$469$	−30.6999	−	9.97502i	−1.41759	−	0.460603i
$470$	−7.08981	+	40.3750i	−0.327028	+	1.86236i
$471$		0			0
$472$	24.8882	−	0.649204i	1.14557	−	0.0298820i
$473$	22.6179	−	3.58232i	1.03997	−	0.164715i
$474$		0			0
$475$	−10.4785	+	27.4186i	−0.480785	+	1.25805i
$476$	9.98419	+	29.0026i	0.457625	+	1.32933i
$477$		0			0
$478$	0.875550	−	2.77656i	0.0400467	−	0.126997i
$479$	−2.02143	−	6.22131i	−0.0923613	−	0.284259i	0.894196	−	0.447676i	$-0.147748\pi$
$479$	−2.02143	−	6.22131i	−0.0923613	−	0.284259i	−0.986557	+	0.163417i	$0.947748\pi$
$480$		0			0
$481$	−5.53086	+	17.0222i	−0.252186	+	0.776147i
$482$	−22.8796	−	16.3210i	−1.04214	−	0.743403i
$483$		0			0
$484$	2.48987	+	1.74368i	0.113176	+	0.0792580i
$485$	4.04466	−	7.46251i	0.183659	−	0.338855i
$486$		0			0
$487$	−1.93534	+	12.2192i	−0.0876986	+	0.553707i	0.904244	+	0.427017i	$0.140435\pi$
$487$	−1.93534	+	12.2192i	−0.0876986	+	0.553707i	−0.991942	+	0.126690i	$0.959565\pi$
$488$	9.53290	+	26.9287i	0.431534	+	1.21901i
$489$		0			0
$490$	15.9377	−	4.88497i	0.719994	−	0.220680i
$491$	−1.51867	−	2.09027i	−0.0685365	−	0.0943323i	0.773373	−	0.633952i	$-0.218568\pi$
$491$	−1.51867	−	2.09027i	−0.0685365	−	0.0943323i	−0.841909	+	0.539619i	$0.818568\pi$
$492$		0			0
$493$	2.62944	−	2.62944i	0.118424	−	0.118424i
$494$	−4.25141	+	28.4403i	−0.191280	+	1.27959i
$495$		0			0
$496$	−0.000290125	0	0.000430002i	−1.30270e−5	0	1.93077e-5i
$497$	3.33249	−	6.54038i	0.149483	−	0.293376i
$498$		0			0
$499$	−1.41851			−0.0635014			−0.0317507	−	0.999496i	$-0.510108\pi$
$499$	−1.41851			−0.0635014			−0.0317507	+	0.999496i	$0.510108\pi$
$500$	18.8329	−	12.0549i	0.842233	−	0.539114i
$501$		0			0
$502$	−34.8219	+	11.6499i	−1.55418	+	0.519962i
$503$	5.08096	−	9.97194i	0.226549	−	0.444627i	−0.749552	−	0.661945i	$-0.769731\pi$
$503$	5.08096	−	9.97194i	0.226549	−	0.444627i	0.976101	+	0.217319i	$0.0697310\pi$
$504$		0			0
$505$	12.4564	+	0.316960i	0.554303	+	0.0141045i
$506$	0.0577134	−	0.386080i	0.00256567	−	0.0171634i
$507$		0			0
$508$	19.5861	−	20.2793i	0.868993	−	0.899747i
$509$	6.17501	+	8.49917i	0.273702	+	0.376719i	0.923635	−	0.383273i	$-0.125203\pi$
$509$	6.17501	+	8.49917i	0.273702	+	0.376719i	−0.649933	+	0.759992i	$0.725203\pi$
$510$		0			0
$511$	26.2539	−	36.1353i	1.16140	−	1.59853i
$512$	−5.28894	+	22.0006i	−0.233740	+	0.972299i
$513$		0			0
$514$	4.72059	−	9.46723i	0.208216	−	0.417582i
$515$	17.3229	−	31.9611i	0.763337	−	1.40838i
$516$		0			0
$517$	−40.8684	+	20.8235i	−1.79739	+	0.915816i
$518$	−20.8404	−	14.8664i	−0.915676	−	0.653192i
$519$		0			0
$520$	15.4803	−	15.5001i	0.678854	−	0.679722i
$521$	−5.86783	−	18.0593i	−0.257074	−	0.791193i	−0.993414	−	0.114581i	$-0.963447\pi$
$521$	−5.86783	−	18.0593i	−0.257074	−	0.791193i	0.736340	−	0.676612i	$-0.236553\pi$
$522$		0			0
$523$	−0.798016	−	5.03848i	−0.0348948	−	0.220317i	0.964079	−	0.265617i	$-0.0855757\pi$
$523$	−0.798016	−	5.03848i	−0.0348948	−	0.220317i	−0.998973	+	0.0452999i	$0.985576\pi$
$524$	19.3552	−	6.66307i	0.845535	−	0.291077i
$525$		0			0
$526$	−3.30096	−	19.7298i	−0.143929	−	0.860262i
$527$	−0.000560758	0	8.88153e-5i	−2.44270e−5	0	3.86886e-6i
$528$		0			0
$529$	21.8685	−	7.10551i	0.950805	−	0.308935i
$530$	−5.88737	+	33.5274i	−0.255731	+	1.45634i
$531$		0			0
$532$	−36.9657	−	18.0325i	−1.60267	−	0.781807i
$533$	8.22377	+	16.1401i	0.356211	+	0.699104i
$534$		0			0
$535$	−1.73088	+	1.64498i	−0.0748326	+	0.0711188i
$536$	3.40456	−	25.8400i	0.147054	−	1.11612i
$537$		0			0
$538$	0.119241	+	13.7166i	0.00514084	+	0.591365i
$539$	15.0897	+	10.9633i	0.649961	+	0.472224i
$540$		0			0
$541$	3.67152	−	2.66752i	0.157851	−	0.114685i	−0.506056	−	0.862501i	$-0.668897\pi$
$541$	3.67152	−	2.66752i	0.157851	−	0.114685i	0.663907	+	0.747815i	$0.268897\pi$
$542$	9.92357	+	13.4119i	0.426254	+	0.576090i
$543$		0			0
$544$	−21.5572	+	12.1917i	−0.924258	+	0.522714i
$545$	10.5372	+	15.3074i	0.451363	+	0.655697i
$546$		0			0
$547$	−10.6451	−	5.42393i	−0.455150	−	0.231910i	0.211358	−	0.977409i	$-0.432212\pi$
$547$	−10.6451	−	5.42393i	−0.455150	−	0.231910i	−0.666507	+	0.745498i	$0.732212\pi$
$548$	4.66579	−	2.48044i	0.199313	−	0.105959i
$549$		0			0
$550$	23.4480	+	8.72824i	0.999828	+	0.372173i
$551$			4.98627i			0.212422i
$552$		0			0
$553$	6.15226	+	3.13474i	0.261621	+	0.133302i
$554$	31.4256	−	16.3578i	1.33515	−	0.694976i
$555$		0			0
$556$	−13.0538	+	0.226975i	−0.553603	+	0.00962587i
$557$	−10.4828	−	10.4828i	−0.444172	−	0.444172i	0.449239	−	0.893412i	$-0.351695\pi$
$557$	−10.4828	−	10.4828i	−0.444172	−	0.444172i	−0.893412	+	0.449239i	$0.851695\pi$
$558$		0			0
$559$	18.1355	−	13.1762i	0.767051	−	0.557295i
$560$	14.4844	+	27.7833i	0.612079	+	1.17406i
$561$		0			0
$562$	21.7737	−	0.189282i	0.918466	−	0.00798439i
$563$	8.04485	+	1.27418i	0.339050	+	0.0537002i	0.323638	−	0.946181i	$-0.395094\pi$
$563$	8.04485	+	1.27418i	0.339050	+	0.0537002i	0.0154120	+	0.999881i	$0.495094\pi$
$564$		0			0
$565$	5.39201	−	29.2133i	0.226844	−	1.22901i
$566$	−15.7641	−	15.4924i	−0.662614	−	0.651193i
$567$		0			0
$568$	5.68256	+	1.68388i	0.238435	+	0.0706539i
$569$	−25.0837	−	8.15020i	−1.05157	−	0.341674i	−0.268283	−	0.963340i	$-0.586456\pi$
$569$	−25.0837	−	8.15020i	−1.05157	−	0.341674i	−0.783283	+	0.621666i	$0.786456\pi$
$570$		0			0
$571$	−32.3724	+	10.5184i	−1.35474	+	0.440182i	−0.894284	−	0.447500i	$-0.852314\pi$
$571$	−32.3724	+	10.5184i	−1.35474	+	0.440182i	−0.460457	+	0.887682i	$0.652314\pi$
$572$	24.2728	+	3.41298i	1.01490	+	0.142704i
$573$		0			0
$574$	−25.5535	+	4.27530i	−1.06658	+	0.178448i
$575$	−0.0413464	−	0.387863i	−0.00172427	−	0.0161750i
$576$		0			0
$577$	1.79773	+	11.3504i	0.0748405	+	0.472524i	0.996435	+	0.0843691i	$0.0268875\pi$
$577$	1.79773	+	11.3504i	0.0748405	+	0.472524i	−0.921594	+	0.388155i	$0.873113\pi$
$578$	−2.92300	−	0.921727i	−0.121581	−	0.0383388i
$579$		0			0
$580$	2.25739	−	3.05498i	0.0937330	−	0.126851i
$581$	−17.5951	+	54.1523i	−0.729969	+	2.24661i
$582$		0			0
$583$	−33.9371	+	17.2918i	−1.40553	+	0.716154i
$584$	32.5492	+	15.5292i	1.34689	+	0.642603i
$585$		0			0
$586$	22.0807	+	11.0099i	0.912144	+	0.454817i
$587$	4.04749	−	25.5549i	0.167058	−	1.05476i	−0.751574	−	0.659649i	$-0.770705\pi$
$587$	4.04749	−	25.5549i	0.167058	−	1.05476i	0.918632	−	0.395114i	$-0.129295\pi$
$588$		0			0
$589$	0.000447478	0	0.000615901i	1.84380e−5	0	2.53777e-5i
$590$	22.2421	+	16.7360i	0.915694	+	0.689011i
$591$		0			0
$592$	8.73782	−	18.7317i	0.359122	−	0.769869i
$593$	20.9734	−	20.9734i	0.861274	−	0.861274i	−0.130212	−	0.991486i	$-0.541566\pi$
$593$	20.9734	−	20.9734i	0.861274	−	0.861274i	0.991486	+	0.130212i	$0.0415658\pi$
$594$		0			0
$595$	−11.4235	+	32.3349i	−0.468316	+	1.32560i
$596$	2.00056	+	2.65520i	0.0819461	+	0.108761i
$597$		0			0
$598$	−0.121241	−	0.362393i	−0.00495793	−	0.0148193i
$599$	−3.33851			−0.136408			−0.0682039	−	0.997671i	$-0.521727\pi$
$599$	−3.33851			−0.136408			−0.0682039	+	0.997671i	$0.521727\pi$
$600$		0			0
$601$	−10.9587			−0.447013			−0.223506	−	0.974702i	$-0.571750\pi$
$601$	−10.9587			−0.447013			−0.223506	+	0.974702i	$0.571750\pi$
$602$	10.1725	+	30.4057i	0.414599	+	1.23924i
$603$		0			0
$604$	−17.1087	−	22.7072i	−0.696143	−	0.923943i
$605$	0.967638	+	3.25784i	0.0393401	+	0.132450i
$606$		0			0
$607$	−5.16417	+	5.16417i	−0.209607	+	0.209607i	−0.804101	−	0.594493i	$-0.797353\pi$
$607$	−5.16417	+	5.16417i	−0.209607	+	0.209607i	0.594493	+	0.804101i	$0.297353\pi$
$608$	8.88003	−	31.9994i	0.360133	−	1.29775i
$609$		0			0
$610$	−10.3767	+	30.2054i	−0.420140	+	1.22298i
$611$	−26.3917	+	36.3250i	−1.06769	+	1.46955i
$612$		0			0
$613$	2.23054	−	14.0831i	0.0900905	−	0.568809i	−0.900810	−	0.434213i	$-0.857026\pi$
$613$	2.23054	−	14.0831i	0.0900905	−	0.568809i	0.990901	−	0.134596i	$-0.0429736\pi$
$614$	−38.4572	−	19.1757i	−1.55200	−	0.773866i
$615$		0			0
$616$	−15.0962	+	31.6416i	−0.608243	+	1.27488i
$617$	−5.96590	+	3.03978i	−0.240178	+	0.122377i	−0.569937	−	0.821688i	$-0.693032\pi$
$617$	−5.96590	+	3.03978i	−0.240178	+	0.122377i	0.329759	+	0.944065i	$0.393032\pi$
$618$		0			0
$619$	3.98349	−	12.2599i	0.160110	−	0.492768i	−0.838533	−	0.544851i	$-0.816586\pi$
$619$	3.98349	−	12.2599i	0.160110	−	0.492768i	0.998643	+	0.0520830i	$0.0165860\pi$
$620$	−0.000552992	0	0.000174767i	−2.22087e−5	0	7.01879e-6i
$621$		0			0
$622$	17.4499	+	5.50257i	0.699676	+	0.220633i
$623$	−3.25771	−	20.5684i	−0.130517	−	0.824054i
$624$		0			0
$625$	24.8707	+	2.53962i	0.994827	+	0.101585i
$626$	−2.51506	+	0.420789i	−0.100522	+	0.0168181i
$627$		0			0
$628$	28.9483	+	4.07040i	1.15516	+	0.162427i
$629$	21.5157	−	6.99087i	0.857886	−	0.278744i
$630$		0			0
$631$	−6.89142	−	2.23916i	−0.274343	−	0.0891394i	0.168614	−	0.985682i	$-0.446071\pi$
$631$	−6.89142	−	2.23916i	−0.274343	−	0.0891394i	−0.442957	+	0.896543i	$0.646071\pi$
$632$	−1.58395	+	5.34535i	−0.0630063	+	0.212627i
$633$		0			0
$634$	0.629251	+	0.618405i	0.0249908	+	0.0245600i
$635$	31.2484	−	4.13745i	1.24005	−	0.164190i
$636$		0			0
$637$	18.0337	+	2.85626i	0.714522	+	0.113169i
$638$	4.25008	−	0.0369467i	0.168262	−	0.00146273i
$639$		0			0
$640$	−19.9274	+	15.5852i	−0.787700	+	0.616059i
$641$	−32.0344	+	23.2743i	−1.26528	+	0.919281i	−0.999004	−	0.0446150i	$-0.985794\pi$
$641$	−32.0344	+	23.2743i	−1.26528	+	0.919281i	−0.266278	+	0.963896i	$0.585794\pi$
$642$		0			0
$643$	8.11866	+	8.11866i	0.320169	+	0.320169i	0.848832	−	0.528663i	$-0.177306\pi$
$643$	8.11866	+	8.11866i	0.320169	+	0.320169i	−0.528663	+	0.848832i	$0.677306\pi$
$644$	0.546479	−	0.00950198i	0.0215343	−	0.000374431i
$645$		0			0
$646$	32.2409	−	16.7822i	1.26850	−	0.660286i
$647$	27.6446	+	14.0856i	1.08682	+	0.553763i	0.903194	−	0.429233i	$-0.141216\pi$
$647$	27.6446	+	14.0856i	1.08682	+	0.553763i	0.183628	+	0.982996i	$0.441216\pi$
$648$		0			0
$649$			31.1456i			1.22257i
$650$	24.3306	−	2.80777i	0.954325	−	0.110130i
$651$		0			0
$652$	−42.1649	+	22.4158i	−1.65131	+	0.877872i
$653$	14.2708	+	7.27133i	0.558459	+	0.284549i	0.710351	−	0.703848i	$-0.248536\pi$
$653$	14.2708	+	7.27133i	0.558459	+	0.284549i	−0.151891	+	0.988397i	$0.548536\pi$
$654$		0			0
$655$	21.5791	+	7.62358i	0.843164	+	0.297878i
$656$	−7.15211	−	19.6585i	−0.279243	−	0.767536i
$657$		0			0
$658$	−38.1977	−	51.6248i	−1.48910	−	2.01254i
$659$	11.4410	−	8.31238i	0.445679	−	0.323804i	−0.342209	−	0.939624i	$-0.611175\pi$
$659$	11.4410	−	8.31238i	0.445679	−	0.323804i	0.787887	+	0.615820i	$0.211175\pi$
$660$		0			0
$661$	−30.5608	−	22.2037i	−1.18868	−	0.863623i	−0.195552	−	0.980693i	$-0.562650\pi$
$661$	−30.5608	−	22.2037i	−1.18868	−	0.863623i	−0.993124	+	0.117070i	$0.962650\pi$
$662$	0.130825	+	15.0492i	0.00508466	+	0.584903i
$663$		0			0
$664$	−45.5797	−	6.00537i	−1.76883	−	0.233053i
$665$	−19.8274	−	41.4900i	−0.768874	−	1.60891i
$666$		0			0
$667$	−0.0300821	−	0.0590394i	−0.00116478	−	0.00228602i
$668$	−15.4531	−	7.53826i	−0.597898	−	0.291664i
$669$		0			0
$670$	20.9470	−	20.2569i	0.809254	−	0.782593i
$671$	−33.9871	+	11.0431i	−1.31206	+	0.426314i
$672$		0			0
$673$	6.11086	−	0.967866i	0.235556	−	0.0373085i	−0.0375400	−	0.999295i	$-0.511952\pi$
$673$	6.11086	−	0.967866i	0.235556	−	0.0373085i	0.273096	+	0.961987i	$0.411952\pi$
$674$	4.00232	+	23.9219i	0.154163	+	0.921435i
$675$		0			0
$676$	−1.89627	+	0.652796i	−0.0729336	+	0.0251075i
$677$	4.28502	+	27.0545i	0.164687	+	1.03979i	0.922127	+	0.386886i	$0.126449\pi$
$677$	4.28502	+	27.0545i	0.164687	+	1.03979i	−0.757441	+	0.652904i	$0.773551\pi$
$678$		0			0
$679$	4.10919	+	12.6468i	0.157696	+	0.485339i
$680$	−27.3510	−	4.31406i	−1.04886	−	0.165437i
$681$		0			0
$682$	−0.000528283	0	0.000376847i	−2.02290e−5	0	1.44302e-5i
$683$	38.8244	−	19.7820i	1.48558	−	0.756939i	0.492052	−	0.870566i	$-0.336247\pi$
$683$	38.8244	−	19.7820i	1.48558	−	0.756939i	0.993523	+	0.113627i	$0.0362469\pi$
$684$		0			0
$685$	5.80972	+	1.07232i	0.221978	+	0.0409713i
$686$	3.82136	−	7.66381i	0.145900	−	0.292606i
$687$		0			0
$688$	−22.6435	+	12.5475i	−0.863275	+	0.478369i
$689$	−21.9156	+	30.1643i	−0.834919	+	1.14917i
$690$		0			0
$691$	−24.1230	−	33.2025i	−0.917682	−	1.26308i	−0.964474	−	0.264176i	$-0.914900\pi$
$691$	−24.1230	−	33.2025i	−0.917682	−	1.26308i	0.0467925	−	0.998905i	$-0.485100\pi$
$692$	−34.2626	+	35.4752i	−1.30247	+	1.34856i
$693$		0			0
$694$	0.975713	−	6.52715i	0.0370376	−	0.247767i
$695$	−11.5870	−	8.87738i	−0.439519	−	0.336738i
$696$		0			0
$697$	10.3946	−	20.4006i	0.393725	−	0.772729i
$698$	−36.2600	+	12.1311i	−1.37246	+	0.459167i
$699$		0			0
$700$	−6.63556	+	34.3963i	−0.250801	+	1.30006i
$701$	17.6319			0.665949			0.332974	−	0.942936i	$-0.391948\pi$
$701$	17.6319			0.665949			0.332974	+	0.942936i	$0.391948\pi$
$702$		0			0
$703$	−13.7719	+	27.0288i	−0.519416	+	1.01941i
$704$	−27.3407	−	7.33185i	−1.03044	−	0.276329i
$705$		0			0
$706$	2.48333	−	16.6125i	0.0934615	−	0.625222i
$707$	−13.8032	+	13.8032i	−0.519123	+	0.519123i
$708$		0			0
$709$	4.19370	+	5.77214i	0.157498	+	0.216777i	0.880472	−	0.474098i	$-0.157226\pi$
$709$	4.19370	+	5.77214i	0.157498	+	0.216777i	−0.722974	+	0.690875i	$0.757226\pi$
$710$	3.80456	+	5.42531i	0.142783	+	0.203608i
$711$		0			0
$712$	15.8504	−	5.61112i	0.594019	−	0.210285i
$713$	−1.58260e−6	0	9.99213e-6i	−5.92688e−8	0	3.74208e-7i
$714$		0			0
$715$	18.8789	+	19.8647i	0.706030	+	0.742899i
$716$	−15.3209	−	10.7293i	−0.572568	−	0.400974i
$717$		0			0
$718$	17.5259	+	12.5020i	0.654062	+	0.466571i
$719$	−4.73921	+	14.5858i	−0.176743	+	0.543958i	−0.999709	−	0.0241324i	$-0.992318\pi$
$719$	−4.73921	+	14.5858i	−0.176743	+	0.543958i	0.822966	+	0.568091i	$0.192318\pi$
$720$		0			0
$721$	17.5992	+	54.1648i	0.655429	+	2.01720i
$722$	−6.57655	+	20.8557i	−0.244754	+	0.776169i
$723$		0			0
$724$	−2.39662	−	6.96181i	−0.0890696	−	0.258734i
$725$	4.10053	−	1.10524i	0.152290	−	0.0410476i
$726$		0			0
$727$	2.15735	−	0.341691i	0.0800117	−	0.0126726i	−0.116300	−	0.993214i	$-0.537103\pi$
$727$	2.15735	−	0.341691i	0.0800117	−	0.0126726i	0.196312	+	0.980541i	$0.437103\pi$
$728$	0.894895	+	34.3072i	0.0331670	+	1.27151i
$729$		0			0
$730$	17.7010	+	36.2275i	0.655144	+	1.34084i
$731$	−26.9474	−	8.75575i	−0.996687	−	0.323843i
$732$		0			0
$733$	6.40810	+	12.5766i	0.236689	+	0.464528i	0.978546	−	0.206031i	$-0.0660546\pi$
$733$	6.40810	+	12.5766i	0.236689	+	0.464528i	−0.741857	+	0.670558i	$0.766055\pi$
$734$	23.7651	−	24.1819i	0.877186	−	0.892571i
$735$		0			0
$736$	0.0879088	+	0.432459i	0.00324036	+	0.0159406i
$737$	32.2036	+	5.10055i	1.18623	+	0.187881i
$738$		0			0
$739$	−14.6312	−	10.6302i	−0.538218	−	0.391039i	0.285205	−	0.958467i	$-0.407938\pi$
$739$	−14.6312	−	10.6302i	−0.538218	−	0.391039i	−0.823423	+	0.567428i	$0.807938\pi$
$740$	20.6743	−	10.3252i	0.760001	−	0.379561i
$741$		0			0
$742$	−31.7193	−	42.8692i	−1.16445	−	1.57378i
$743$	−9.25021	−	9.25021i	−0.339357	−	0.339357i	0.516768	−	0.856125i	$-0.327135\pi$
$743$	−9.25021	−	9.25021i	−0.339357	−	0.339357i	−0.856125	+	0.516768i	$0.827135\pi$
$744$		0			0
$745$	−0.0945482	+	3.71571i	−0.00346398	+	0.136133i
$746$	−14.1631	−	27.2093i	−0.518547	−	0.996202i
$747$		0			0
$748$	−14.5433	−	27.3564i	−0.531756	−	1.00025i
$749$		−	3.74087i		−	0.136688i
$750$		0			0
$751$		−	25.6382i		−	0.935550i	−0.883848	−	0.467775i	$-0.845056\pi$
$751$		−	25.6382i		−	0.935550i	0.883848	−	0.467775i	$-0.154944\pi$
$752$	35.3682	−	37.9175i	1.28975	−	1.38271i
$753$		0			0
$754$	3.69055	−	1.92102i	0.134402	−	0.0699595i
$755$	0.808572	−	31.7766i	0.0294270	−	1.15647i
$756$		0			0
$757$	24.1240	+	24.1240i	0.876803	+	0.876803i	0.993202	−	0.116400i	$-0.0371353\pi$
$757$	24.1240	+	24.1240i	0.876803	+	0.876803i	−0.116400	+	0.993202i	$0.537135\pi$
$758$	−6.75371	+	4.99713i	−0.245306	+	0.181504i
$759$		0			0
$760$	30.0236	−	21.8427i	1.08907	−	0.792319i
$761$	−10.8763	−	7.90212i	−0.394267	−	0.286452i	0.372935	−	0.927858i	$-0.378352\pi$
$761$	−10.8763	−	7.90212i	−0.394267	−	0.286452i	−0.767202	+	0.641406i	$0.778352\pi$
$762$		0			0
$763$	−28.7548	−	4.55431i	−1.04099	−	0.164877i
$764$	2.53349	+	0.774753i	0.0916586	+	0.0280296i
$765$		0			0
$766$	4.67020	+	4.58970i	0.168741	+	0.165833i
$767$	13.8415	+	27.1656i	0.499789	+	0.980891i
$768$		0			0
$769$	37.1381	+	12.0669i	1.33924	+	0.435144i	0.889058	−	0.457795i	$-0.151361\pi$
$769$	37.1381	+	12.0669i	1.33924	+	0.435144i	0.450178	+	0.892939i	$0.351361\pi$
$770$	−35.2174	+	17.2075i	−1.26915	+	0.620114i
$771$		0			0
$772$	3.26158	−	23.1960i	0.117387	−	0.834844i
$773$	19.5920	−	3.10306i	0.704674	−	0.111609i	0.206195	−	0.978511i	$-0.433892\pi$
$773$	19.5920	−	3.10306i	0.704674	−	0.111609i	0.498479	+	0.866902i	$0.333892\pi$
$774$		0			0
$775$	−0.000605681	0	0.000231471i	−2.17567e−5	0	8.31470e-6i
$776$	−9.43614	+	5.12217i	−0.338738	+	0.183875i
$777$		0			0
$778$	−12.8860	−	4.06340i	−0.461984	−	0.145680i
$779$	9.48730	+	29.1989i	0.339918	+	1.04616i
$780$		0			0
$781$	−2.29117	+	7.05150i	−0.0819845	+	0.252322i
$782$	−0.280499	+	0.393217i	−0.0100306	+	0.0140614i
$783$		0			0
$784$	−20.2679	−	5.81469i	−0.723854	−	0.207667i
$785$	22.5154	+	23.6911i	0.803608	+	0.845573i
$786$		0			0
$787$	−2.45311	+	15.4883i	−0.0874439	+	0.552099i	0.904606	+	0.426250i	$0.140166\pi$
$787$	−2.45311	+	15.4883i	−0.0874439	+	0.552099i	−0.992049	+	0.125849i	$0.959834\pi$
$788$	−5.78959	−	32.8473i	−0.206246	−	1.17014i
$789$		0			0
$790$	−5.10337	+	3.57879i	−0.181570	+	0.127328i
$791$	27.3549	+	37.6508i	0.972629	+	1.33871i
$792$		0			0
$793$	−24.7363	+	24.7363i	−0.878411	+	0.878411i
$794$	−29.5647	−	4.41949i	−1.04921	−	0.156842i
$795$		0			0
$796$	29.9159	−	22.5401i	1.06034	−	0.798912i
$797$	−8.18837	+	16.0706i	−0.290047	+	0.569249i	−0.989347	−	0.145580i	$-0.953495\pi$
$797$	−8.18837	+	16.0706i	−0.290047	+	0.569249i	0.699300	+	0.714829i	$0.253495\pi$
$798$		0			0
$799$	56.7527			2.00777
$800$	−28.2835	−	0.209734i	−0.999973	−	0.00741522i
$801$		0			0
$802$	7.52590	+	22.4951i	0.265749	+	0.794328i
$803$	−20.4821	+	40.1984i	−0.722797	+	1.41857i
$804$		0			0
$805$	0.485073	+	0.371639i	0.0170966	+	0.0130986i
$806$	−0.000628251	0	9.39144e-5i	−2.21292e−5	0	3.30799e-6i
$807$		0			0
$808$	−12.9884	−	8.92864i	−0.456932	−	0.314108i
$809$	19.5336	+	26.8857i	0.686765	+	0.945251i	0.999990	−	0.00442775i	$-0.00140940\pi$
$809$	19.5336	+	26.8857i	0.686765	+	0.945251i	−0.313225	+	0.949679i	$0.601409\pi$
$810$		0			0
$811$	−6.93113	+	9.53989i	−0.243385	+	0.334991i	−0.913181	−	0.407555i	$-0.866382\pi$
$811$	−6.93113	+	9.53989i	−0.243385	+	0.334991i	0.669796	+	0.742545i	$0.266382\pi$
$812$	1.03295	+	5.86047i	0.0362495	+	0.205662i
$813$		0			0
$814$	23.1402	+	11.5383i	0.811065	+	0.404416i
$815$	−52.5027	−	9.69062i	−1.83909	−	0.339448i
$816$		0			0
$817$	33.8524	−	17.2487i	1.18435	−	0.603454i
$818$	−8.99827	+	12.6142i	−0.314617	+	0.441046i
$819$		0			0
$820$	7.40629	−	22.1846i	0.258639	−	0.774721i
$821$	10.4922	+	32.2916i	0.366180	+	1.12699i	0.949239	+	0.314556i	$0.101856\pi$
$821$	10.4922	+	32.2916i	0.366180	+	1.12699i	−0.583059	+	0.812430i	$0.698144\pi$
$822$		0			0
$823$	−1.35624	−	8.56297i	−0.0472756	−	0.298486i	0.952710	−	0.303881i	$-0.0982827\pi$
$823$	−1.35624	−	8.56297i	−0.0472756	−	0.298486i	−0.999985	+	0.00539505i	$0.998283\pi$
$824$	−40.4140	+	21.9377i	−1.40789	+	0.764237i
$825$		0			0
$826$	−43.0094	+	7.19582i	−1.49649	+	0.250375i
$827$	−6.75206	+	1.06942i	−0.234792	+	0.0371874i	−0.272722	−	0.962093i	$-0.587924\pi$
$827$	−6.75206	+	1.06942i	−0.234792	+	0.0371874i	0.0379294	+	0.999280i	$0.487924\pi$
$828$		0			0
$829$	−1.59946	+	0.519697i	−0.0555516	+	0.0180498i	−0.336661	−	0.941626i	$-0.609298\pi$
$829$	−1.59946	+	0.519697i	−0.0555516	+	0.0180498i	0.281109	+	0.959676i	$0.409298\pi$
$830$	−35.7316	−	36.9489i	−1.24026	−	1.28251i
$831$		0			0
$832$	−27.1053	+	5.75568i	−0.939707	+	0.199542i
$833$	−10.4773	−	20.5629i	−0.363018	−	0.712463i
$834$		0			0
$835$	−8.28861	−	17.3444i	−0.286839	−	0.600228i
$836$	39.7277	+	12.1489i	1.37401	+	0.420179i
$837$		0			0
$838$	26.7035	−	0.232138i	0.922457	−	0.00801908i
$839$	−32.2588	−	23.4374i	−1.11370	−	0.809148i	−0.130455	−	0.991454i	$-0.541644\pi$
$839$	−32.2588	−	23.4374i	−1.11370	−	0.809148i	−0.983242	+	0.182307i	$0.941644\pi$
$840$		0			0
$841$	−22.8778	+	16.6217i	−0.788891	+	0.573163i
$842$	15.4009	−	11.3952i	0.530748	−	0.392706i
$843$		0			0
$844$	0.564300	+	32.4540i	0.0194240	+	1.11711i
$845$	−2.11415	−	0.746900i	−0.0727290	−	0.0256941i
$846$		0			0
$847$	−4.74385	−	2.41711i	−0.163000	−	0.0830529i
$848$	29.3698	−	31.4867i	1.00856	−	1.08126i
$849$		0			0
$850$	−20.9475	−	22.7939i	−0.718493	−	0.781825i
$851$		−	0.403117i		−	0.0138187i
$852$		0			0
$853$	−11.5438	−	5.88186i	−0.395252	−	0.201391i	0.245056	−	0.969509i	$-0.421194\pi$
$853$	−11.5438	−	5.88186i	−0.395252	−	0.201391i	−0.640309	+	0.768118i	$0.721194\pi$
$854$	−23.1019	−	44.3820i	−0.790531	−	1.51872i
$855$		0			0
$856$	2.96992	−	0.550132i	0.101510	−	0.0188031i
$857$	11.9042	+	11.9042i	0.406640	+	0.406640i	0.880565	−	0.473925i	$-0.157163\pi$
$857$	11.9042	+	11.9042i	0.406640	+	0.406640i	−0.473925	+	0.880565i	$0.657163\pi$
$858$		0			0
$859$	−28.2976	+	20.5594i	−0.965502	+	0.701478i	−0.954422	−	0.298460i	$-0.903527\pi$
$859$	−28.2976	+	20.5594i	−0.965502	+	0.701478i	−0.0110802	+	0.999939i	$0.503527\pi$
$860$	−28.5495	−	4.75781i	−0.973529	−	0.162240i
$861$		0			0
$862$	−0.115374	−	13.2718i	−0.00392965	−	0.452038i
$863$	27.6579	+	4.38058i	0.941485	+	0.149117i	0.608266	−	0.793733i	$-0.291865\pi$
$863$	27.6579	+	4.38058i	0.941485	+	0.149117i	0.333219	+	0.942850i	$0.391865\pi$
$864$		0			0
$865$	−54.6638	+	7.23778i	−1.85863	+	0.246092i
$866$	−28.9604	+	29.4684i	−0.984116	+	1.00138i
$867$		0			0
$868$	0.000398341	0	0.000816580i	1.35206e−5	0	2.77165e-5i
$869$	−6.63305	−	2.15521i	−0.225011	−	0.0731105i
$870$		0			0
$871$	30.3551	−	9.86297i	1.02854	−	0.334194i
$872$	−0.612954	−	23.4985i	−0.0207573	−	0.795761i
$873$		0			0
$874$	−0.106875	−	0.638791i	−0.00361510	−	0.0216074i
$875$	−29.7250	+	25.5019i	−1.00489	+	0.862121i
$876$		0			0
$877$	−0.453223	−	2.86154i	−0.0153043	−	0.0966273i	0.978854	−	0.204561i	$-0.0655766\pi$
$877$	−0.453223	−	2.86154i	−0.0153043	−	0.0966273i	−0.994158	+	0.107934i	$0.965577\pi$
$878$	4.40156	−	13.9583i	0.148546	−	0.471071i
$879$		0			0
$880$	−18.8403	−	25.4290i	−0.635106	−	0.857211i
$881$	13.8508	−	42.6283i	0.466645	−	1.43619i	−0.390257	−	0.920706i	$-0.627614\pi$
$881$	13.8508	−	42.6283i	0.466645	−	1.43619i	0.856902	−	0.515479i	$-0.172386\pi$
$882$		0			0
$883$	24.6083	−	12.5385i	0.828134	−	0.421955i	0.0120772	−	0.999927i	$-0.496156\pi$
$883$	24.6083	−	12.5385i	0.828134	−	0.421955i	0.816057	+	0.577972i	$0.196156\pi$
$884$	−24.8424	−	17.3974i	−0.835542	−	0.585137i
$885$		0			0
$886$	1.09247	−	2.19097i	0.0367023	−	0.0736072i
$887$	5.07182	−	32.0222i	0.170295	−	1.07520i	−0.743414	−	0.668831i	$-0.766795\pi$
$887$	5.07182	−	32.0222i	0.170295	−	1.07520i	0.913709	−	0.406369i	$-0.133205\pi$
$888$		0			0
$889$	−29.0257	+	39.9504i	−0.973489	+	1.33989i
$890$	17.7790	+	6.10778i	0.595955	+	0.204733i
$891$		0			0
$892$	19.2223	+	18.5653i	0.643612	+	0.621612i
$893$	−53.8107	+	53.8107i	−1.80071	+	1.80071i
$894$		0			0
$895$	−5.95415	−	20.0464i	−0.199025	−	0.670077i
$896$	3.80791	−	39.4492i	0.127213	−	1.31790i
$897$		0			0
$898$	−48.3637	+	16.1805i	−1.61392	+	0.539949i
$899$	−0.000110148	0		−3.67363e−6	0
$900$		0			0
$901$	47.1274			1.57004
$902$	24.8176	−	8.30292i	0.826335	−	0.276457i
$903$		0			0
$904$	−25.8686	+	27.2543i	−0.860378	+	0.906466i
$905$	2.74210	−	7.76170i	0.0911506	−	0.258008i
$906$		0			0
$907$	11.7557	−	11.7557i	0.390343	−	0.390343i	−0.484467	−	0.874810i	$-0.660986\pi$
$907$	11.7557	−	11.7557i	0.390343	−	0.390343i	0.874810	+	0.484467i	$0.160986\pi$
$908$	30.7865	−	31.8760i	1.02169	−	1.05784i
$909$		0			0
$910$	−23.0698	+	30.6597i	−0.764756	+	1.01636i
$911$	−9.75815	+	13.4309i	−0.323302	+	0.444987i	−0.939472	−	0.342626i	$-0.888684\pi$
$911$	−9.75815	+	13.4309i	−0.323302	+	0.444987i	0.616170	+	0.787613i	$0.288684\pi$
$912$		0			0
$913$	8.99696	−	56.8046i	0.297756	−	1.87996i
$914$	−1.98290	+	3.97674i	−0.0655884	+	0.131539i
$915$		0			0
$916$	−25.3539	+	36.2040i	−0.837717	+	1.19621i
$917$	−31.9459	+	16.2772i	−1.05495	+	0.537522i
$918$		0			0
$919$	6.92595	−	21.3159i	0.228466	−	0.703146i	−0.769455	−	0.638701i	$-0.779472\pi$
$919$	6.92595	−	21.3159i	0.228466	−	0.703146i	0.997921	−	0.0644452i	$-0.0205278\pi$
$920$	−0.223714	+	0.439758i	−0.00737564	+	0.0144984i
$921$		0			0
$922$	−11.0808	+	35.1397i	−0.364927	+	1.15726i
$923$	1.13540	+	7.16863i	0.0373721	+	0.235958i
$924$		0			0
$925$	25.2802	+	5.33438i	0.831207	+	0.175393i
$926$	5.94842	+	35.5537i	0.195477	+	1.16837i
$927$		0			0
$928$	−4.50079	+	1.68191i	−0.147746	+	0.0552115i
$929$	−8.61163	+	2.79809i	−0.282539	+	0.0918023i	−0.446858	−	0.894605i	$-0.647457\pi$
$929$	−8.61163	+	2.79809i	−0.282539	+	0.0918023i	0.164320	+	0.986407i	$0.447457\pi$
$930$		0			0
$931$	29.4312	+	9.56277i	0.964568	+	0.313407i
$932$	27.4738	+	13.4022i	0.899936	+	0.439003i
$933$		0			0
$934$	−37.7910	+	38.4538i	−1.23656	+	1.25825i
$935$	6.28724	−	34.0635i	0.205615	−	1.11400i
$936$		0			0
$937$	50.3586	+	7.97602i	1.64514	+	0.260565i	0.909164	−	0.416438i	$-0.136722\pi$
$937$	50.3586	+	7.97602i	1.64514	+	0.260565i	0.735980	+	0.677004i	$0.236722\pi$
$938$	0.396833	+	45.6489i	0.0129571	+	1.49049i
$939$		0			0
$940$	57.3300	−	8.60744i	1.86990	−	0.280744i
$941$	25.8577	−	18.7867i	0.842937	−	0.612429i	−0.0802527	−	0.996775i	$-0.525573\pi$
$941$	25.8577	−	18.7867i	0.842937	−	0.612429i	0.923189	+	0.384345i	$0.125573\pi$
$942$		0			0
$943$	−0.288490	−	0.288490i	−0.00939452	−	0.00939452i
$944$	−12.0378	−	33.0875i	−0.391797	−	1.07691i
$945$		0			0
$946$	−14.9528	−	28.7265i	−0.486159	−	0.933980i
$947$	−2.86881	−	1.46173i	−0.0932239	−	0.0474999i	0.406757	−	0.913536i	$-0.366660\pi$
$947$	−2.86881	−	1.46173i	−0.0932239	−	0.0474999i	−0.499981	+	0.866036i	$0.666660\pi$
$948$		0			0
$949$			44.1640i			1.43363i
$950$	41.4739	+	1.75070i	1.34559	+	0.0568003i
$951$		0			0
$952$	34.4169	−	26.4035i	1.11546	−	0.855741i
$953$	−28.9987	−	14.7756i	−0.939360	−	0.478628i	−0.0838869	−	0.996475i	$-0.526733\pi$
$953$	−28.9987	−	14.7756i	−0.939360	−	0.478628i	−0.855473	+	0.517848i	$0.826733\pi$
$954$		0			0
$955$	1.67951	+	2.43983i	0.0543477	+	0.0789511i
$956$	−4.11663	+	0.0715787i	−0.133141	+	0.00231502i
$957$		0			0
$958$	−7.43670	+	5.50248i	−0.240269	+	0.177777i
$959$	−7.48771	+	5.44014i	−0.241791	+	0.175671i
$960$		0			0
$961$	−25.0795	−	18.2213i	−0.809017	−	0.587785i
$962$	25.3110	−	0.220033i	0.816059	−	0.00709414i
$963$		0			0
$964$	−11.6230	+	38.0081i	−0.374353	+	1.22416i
$965$	18.9835	−	18.0414i	0.611102	−	0.580774i
$966$		0			0
$967$	−6.18287	−	12.1346i	−0.198828	−	0.390221i	0.769968	−	0.638083i	$-0.220272\pi$
$967$	−6.18287	−	12.1346i	−0.198828	−	0.390221i	−0.968796	+	0.247861i	$0.920272\pi$
$968$	1.22134	−	4.12166i	0.0392555	−	0.132475i
$969$		0			0
$970$	−11.8231	−	2.07613i	−0.379618	−	0.0666605i
$971$	21.7239	−	7.05851i	0.697152	−	0.226518i	0.0610628	−	0.998134i	$-0.480551\pi$
$971$	21.7239	−	7.05851i	0.697152	−	0.226518i	0.636089	+	0.771616i	$0.280551\pi$
$972$		0			0
$973$	22.5859	−	3.57726i	0.724072	−	0.114682i
$974$	17.2562	−	2.88710i	0.552924	−	0.0925085i
$975$		0			0
$976$	31.8380	−	24.8677i	1.01911	−	0.795996i
$977$	−1.60253	−	10.1180i	−0.0512695	−	0.323703i	−0.999972	−	0.00753150i	$-0.997603\pi$
$977$	−1.60253	−	10.1180i	−0.0512695	−	0.323703i	0.948702	−	0.316171i	$-0.102397\pi$
$978$		0			0
$979$	6.50003	+	20.0050i	0.207742	+	0.639363i
$980$	−13.7026	−	19.1830i	−0.437713	−	0.612779i
$981$		0			0
$982$	−2.12194	+	2.97464i	−0.0677139	+	0.0949246i
$983$	31.8803	−	16.2438i	1.01682	−	0.518097i	0.135583	−	0.990766i	$-0.456709\pi$
$983$	31.8803	−	16.2438i	1.01682	−	0.518097i	0.881240	+	0.472669i	$0.156709\pi$
$984$		0			0
$985$	17.7692	−	32.7847i	0.566175	−	1.04461i
$986$	−4.70628	−	2.34666i	−0.149878	−	0.0747329i
$987$		0			0
$988$	40.0502	−	7.05914i	1.27417	−	0.224581i
$989$	−0.296765	+	0.408462i	−0.00943657	+	0.0129883i
$990$		0			0
$991$	−17.5929	−	24.2146i	−0.558858	−	0.769202i	0.432323	−	0.901719i	$-0.357694\pi$
$991$	−17.5929	−	24.2146i	−0.558858	−	0.769202i	−0.991181	+	0.132517i	$0.957694\pi$
$992$	0.000706873	0	0.000196161i	2.24432e−5	0	6.22813e-6i
$993$		0			0
$994$	−10.2669	−	1.53475i	−0.325645	−	0.0486792i
$995$	41.8645	+	1.06526i	1.32719	+	0.0337711i
$996$		0			0
$997$	−18.8432	+	36.9818i	−0.596769	+	1.17123i	0.373144	+	0.927773i	$0.378280\pi$
$997$	−18.8432	+	36.9818i	−0.596769	+	1.17123i	−0.969913	+	0.243452i	$0.921720\pi$
$998$	0.636475	+	1.90244i	0.0201473	+	0.0602206i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.487.12		240
3.2	odd	2		300.2.w.a.187.19	yes	240
4.3	odd	2	inner	900.2.bj.f.487.15		240
12.11	even	2		300.2.w.a.187.16	✓	240
25.23	odd	20	inner	900.2.bj.f.523.15		240
75.23	even	20		300.2.w.a.223.16	yes	240
100.23	even	20	inner	900.2.bj.f.523.12		240
300.23	odd	20		300.2.w.a.223.19	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.16	✓	240	12.11	even	2
300.2.w.a.187.19	yes	240	3.2	odd	2
300.2.w.a.223.16	yes	240	75.23	even	20
300.2.w.a.223.19	yes	240	300.23	odd	20
900.2.bj.f.487.12		240	1.1	even	1	trivial
900.2.bj.f.487.15		240	4.3	odd	2	inner
900.2.bj.f.523.12		240	100.23	even	20	inner
900.2.bj.f.523.15		240	25.23	odd	20	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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.448691 - 1.34115i) q^{2} +(-1.59735 + 1.20352i) q^{4} +(-2.23534 - 0.0568795i) q^{5} +(2.47703 - 2.47703i) q^{7} +(2.33082 + 1.60227i) q^{8} +(0.926696 + 3.02345i) q^{10} +(-2.07978 + 2.86258i) q^{11} +(-0.541843 + 3.42106i) q^{13} +(-4.43349 - 2.21064i) q^{14} +(1.10307 - 3.84490i) q^{16} +(3.90086 - 1.98759i) q^{17} +(-1.81409 + 5.58320i) q^{19} +(3.63909 - 2.59943i) q^{20} +(4.77232 + 1.50488i) q^{22} +(-0.0122038 - 0.0770517i) q^{23} +(4.99353 + 0.254291i) q^{25} +(4.83127 - 0.808310i) q^{26} +(-0.975529 + 6.93786i) q^{28} +(0.807803 - 0.262471i) q^{29} +(-0.000123334 - 4.00736e-5i) q^{31} +(-5.65151 + 0.245797i) q^{32} +(-4.41593 - 4.33981i) q^{34} +(-5.67791 + 5.39613i) q^{35} +(5.10375 + 0.808354i) q^{37} +(8.30186 - 0.0721695i) q^{38} +(-5.11905 - 3.71421i) q^{40} +(4.23098 - 3.07399i) q^{41} +(-4.57632 - 4.57632i) q^{43} +(-0.123028 - 7.07561i) q^{44} +(-0.0978619 + 0.0509395i) q^{46} +(11.5502 + 5.88510i) q^{47} -5.27138i q^{49} +(-1.89951 - 6.81116i) q^{50} +(-3.25181 - 6.11676i) q^{52} +(9.59125 + 4.88699i) q^{53} +(4.81186 - 6.28055i) q^{55} +(9.74240 - 1.80463i) q^{56} +(-0.714467 - 0.965614i) q^{58} +(7.12122 - 5.17387i) q^{59} +(8.17083 + 5.93646i) q^{61} +(1.59424e-6 + 0.000183390i) q^{62} +(2.86543 + 7.46922i) q^{64} +(1.40579 - 7.61643i) q^{65} +(-4.18342 - 8.21042i) q^{67} +(-3.83894 + 7.86965i) q^{68} +(9.78463 + 5.19372i) q^{70} +(1.99288 - 0.647527i) q^{71} +(12.5935 - 1.99462i) q^{73} +(-1.20589 - 7.20758i) q^{74} +(-3.82176 - 11.1016i) q^{76} +(1.93900 + 12.2424i) q^{77} +(0.609102 + 1.87462i) q^{79} +(-2.68443 + 8.53193i) q^{80} +(-6.02107 - 4.29510i) q^{82} +(-14.4825 + 7.37922i) q^{83} +(-8.83282 + 4.22106i) q^{85} +(-4.08417 + 8.19088i) q^{86} +(-9.43424 + 3.33977i) q^{88} +(3.49423 - 4.80940i) q^{89} +(7.13192 + 9.81624i) q^{91} +(0.112227 + 0.108391i) q^{92} +(2.71033 - 18.1311i) q^{94} +(4.37269 - 12.3772i) q^{95} +(-1.72335 + 3.38227i) q^{97} +(-7.06970 + 2.36522i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58}+ \cdots - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Introduction

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