LMFDB - Embedded newform 900.2.bj.f.523.15

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			523.15
Character	$\chi$	$=$	900.523
Dual form			900.2.bj.f.487.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0122935 + 1.41416i) q^{2} +(-1.99970 + 0.0347701i) q^{4} +(-2.23534 + 0.0568795i) q^{5} +(-2.47703 - 2.47703i) q^{7} +(-0.0737538 - 2.82747i) q^{8} +O(q^{10})$	\(q+(0.0122935 + 1.41416i) q^{2} +(-1.99970 + 0.0347701i) q^{4} +(-2.23534 + 0.0568795i) q^{5} +(-2.47703 - 2.47703i) q^{7} +(-0.0737538 - 2.82747i) q^{8} +(-0.107917 - 3.16044i) q^{10} +(2.07978 + 2.86258i) q^{11} +(-0.541843 - 3.42106i) q^{13} +(3.47247 - 3.53337i) q^{14} +(3.99758 - 0.139059i) q^{16} +(3.90086 + 1.98759i) q^{17} +(1.81409 + 5.58320i) q^{19} +(4.46804 - 0.191465i) q^{20} +(-4.02258 + 2.97634i) q^{22} +(0.0122038 - 0.0770517i) q^{23} +(4.99353 - 0.254291i) q^{25} +(4.83127 - 0.808310i) q^{26} +(5.03944 + 4.86719i) q^{28} +(0.807803 + 0.262471i) q^{29} +(0.000123334 - 4.00736e-5i) q^{31} +(0.245797 + 5.65151i) q^{32} +(-2.76281 + 5.54087i) q^{34} +(5.67791 + 5.39613i) q^{35} +(5.10375 - 0.808354i) q^{37} +(-7.87324 + 2.63405i) q^{38} +(0.325690 + 6.31616i) q^{40} +(4.23098 + 3.07399i) q^{41} +(4.57632 - 4.57632i) q^{43} +(-4.25847 - 5.65198i) q^{44} +(0.109113 + 0.0163109i) q^{46} +(-11.5502 + 5.88510i) q^{47} +5.27138i q^{49} +(0.420996 + 7.05852i) q^{50} +(1.20247 + 6.82225i) q^{52} +(9.59125 - 4.88699i) q^{53} +(-4.81186 - 6.28055i) q^{55} +(-6.82103 + 7.18641i) q^{56} +(-0.361245 + 1.14559i) q^{58} +(-7.12122 - 5.17387i) q^{59} +(8.17083 - 5.93646i) q^{61} +(5.81867e-5 + 0.000173921i) q^{62} +(-7.98912 + 0.417073i) q^{64} +(1.40579 + 7.61643i) q^{65} +(4.18342 - 8.21042i) q^{67} +(-7.86965 - 3.83894i) q^{68} +(-7.56119 + 8.09582i) q^{70} +(-1.99288 - 0.647527i) q^{71} +(12.5935 + 1.99462i) q^{73} +(1.20589 + 7.20758i) q^{74} +(-3.82176 - 11.1016i) q^{76} +(1.93900 - 12.2424i) q^{77} +(-0.609102 + 1.87462i) q^{79} +(-8.92806 + 0.538226i) q^{80} +(-4.29510 + 6.02107i) q^{82} +(14.4825 + 7.37922i) q^{83} +(-8.83282 - 4.22106i) q^{85} +(6.52791 + 6.41539i) q^{86} +(7.94045 - 6.09165i) q^{88} +(3.49423 + 4.80940i) q^{89} +(-7.13192 + 9.81624i) q^{91} +(-0.0217248 + 0.154504i) q^{92} +(-8.46447 - 16.2614i) q^{94} +(-4.37269 - 12.3772i) q^{95} +(-1.72335 - 3.38227i) q^{97} +(-7.45458 + 0.0648039i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8}+O(q^{10}) $ 240 * q - 12 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	0.0122935	+	1.41416i	0.00869285	+	0.999962i
$2$	0.0122935	+	1.41416i	0.00869285	+	0.999962i
$3$		0			0
$3$		0			0
$4$	−1.99970	+	0.0347701i	−0.999849	+	0.0173850i
$5$	−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	$-0.480298\pi$
$7$	−2.47703	−	2.47703i	−0.936230	−	0.936230i	−0.998085	+	0.0618548i	$0.980298\pi$
$8$	−0.0737538	−	2.82747i	−0.0260759	−	0.999660i
$9$		0			0
$10$	−0.107917	−	3.16044i	−0.0341264	−	0.999418i
$11$	2.07978	+	2.86258i	0.627079	+	0.863100i	0.997844	−	0.0656267i	$-0.0209047\pi$
$11$	2.07978	+	2.86258i	0.627079	+	0.863100i	−0.370766	+	0.928726i	$0.620905\pi$
$12$		0			0
$13$	−0.541843	−	3.42106i	−0.150280	−	0.948832i	−0.941430	−	0.337209i	$-0.890517\pi$
$13$	−0.541843	−	3.42106i	−0.150280	−	0.948832i	0.791150	−	0.611623i	$-0.209483\pi$
$14$	3.47247	−	3.53337i	0.928056	−	0.944333i
$15$		0			0
$16$	3.99758	−	0.139059i	0.999396	−	0.0347648i
$17$	3.90086	+	1.98759i	0.946097	+	0.482061i	0.857772	−	0.514031i	$-0.171848\pi$
$17$	3.90086	+	1.98759i	0.946097	+	0.482061i	0.0883256	+	0.996092i	$0.471848\pi$
$18$		0			0
$19$	1.81409	+	5.58320i	0.416181	+	1.28087i	0.911190	+	0.411986i	$0.135165\pi$
$19$	1.81409	+	5.58320i	0.416181	+	1.28087i	−0.495009	+	0.868888i	$0.664835\pi$
$20$	4.46804	−	0.191465i	0.999083	−	0.0428129i
$21$		0			0
$22$	−4.02258	+	2.97634i	−0.857616	+	0.634558i
$23$	0.0122038	−	0.0770517i	0.00254466	−	0.0160664i	−0.986383	−	0.164462i	$-0.947411\pi$
$23$	0.0122038	−	0.0770517i	0.00254466	−	0.0160664i	0.988928	+	0.148396i	$0.0474111\pi$
$24$		0			0
$25$	4.99353	−	0.254291i	0.998706	−	0.0508581i
$26$	4.83127	−	0.808310i	0.947489	−	0.158523i
$27$		0			0
$28$	5.03944	+	4.86719i	0.952365	+	0.919812i
$29$	0.807803	+	0.262471i	0.150005	+	0.0487397i	0.383057	−	0.923725i	$-0.374871\pi$
$29$	0.807803	+	0.262471i	0.150005	+	0.0487397i	−0.233052	+	0.972464i	$0.574871\pi$
$30$		0			0
$31$	0.000123334	0	4.00736e-5i	2.21514e−5	0	7.19743e-6i	−0.309006	−	0.951060i	$-0.599996\pi$
$31$	0.000123334	0	4.00736e-5i	2.21514e−5	0	7.19743e-6i	0.309028	+	0.951053i	$0.399996\pi$
$32$	0.245797	+	5.65151i	0.0434511	+	0.999056i
$33$		0			0
$34$	−2.76281	+	5.54087i	−0.473818	+	0.950252i
$35$	5.67791	+	5.39613i	0.959743	+	0.912112i
$36$		0			0
$37$	5.10375	−	0.808354i	0.839051	−	0.132893i	0.277904	−	0.960609i	$-0.410360\pi$
$37$	5.10375	−	0.808354i	0.839051	−	0.132893i	0.561147	+	0.827716i	$0.310360\pi$
$38$	−7.87324	+	2.63405i	−1.27721	+	0.427300i
$39$		0			0
$40$	0.325690	+	6.31616i	0.0514961	+	0.998673i
$41$	4.23098	+	3.07399i	0.660768	+	0.480076i	0.866922	−	0.498443i	$-0.166095\pi$
$41$	4.23098	+	3.07399i	0.660768	+	0.480076i	−0.206154	+	0.978520i	$0.566095\pi$
$42$		0			0
$43$	4.57632	−	4.57632i	0.697883	−	0.697883i	−0.266071	−	0.963954i	$-0.585725\pi$
$43$	4.57632	−	4.57632i	0.697883	−	0.697883i	0.963954	+	0.266071i	$0.0857255\pi$
$44$	−4.25847	−	5.65198i	−0.641989	−	0.852068i
$45$		0			0
$46$	0.109113	+	0.0163109i	0.0160879	+	0.00240491i
$47$	−11.5502	+	5.88510i	−1.68476	+	0.858430i	−0.694457	+	0.719534i	$0.744356\pi$
$47$	−11.5502	+	5.88510i	−1.68476	+	0.858430i	−0.990307	+	0.138896i	$0.955644\pi$
$48$		0			0
$49$			5.27138i			0.753054i
$50$	0.420996	+	7.05852i	0.0595378	+	0.998226i
$51$		0			0
$52$	1.20247	+	6.82225i	0.166753	+	0.946076i
$53$	9.59125	−	4.88699i	1.31746	−	0.671279i	0.353029	−	0.935613i	$-0.385152\pi$
$53$	9.59125	−	4.88699i	1.31746	−	0.671279i	0.964431	+	0.264333i	$0.0851519\pi$
$54$		0			0
$55$	−4.81186	−	6.28055i	−0.648831	−	0.846869i
$56$	−6.82103	+	7.18641i	−0.911499	+	0.960325i
$57$		0			0
$58$	−0.361245	+	1.14559i	−0.0474338	+	0.150423i
$59$	−7.12122	−	5.17387i	−0.927104	−	0.673580i	0.0181782	−	0.999835i	$-0.494213\pi$
$59$	−7.12122	−	5.17387i	−0.927104	−	0.673580i	−0.945282	+	0.326254i	$0.894213\pi$
$60$		0			0
$61$	8.17083	−	5.93646i	1.04617	−	0.760085i	0.0746877	−	0.997207i	$-0.476204\pi$
$61$	8.17083	−	5.93646i	1.04617	−	0.760085i	0.971480	+	0.237122i	$0.0762040\pi$
$62$	5.81867e−5	0	0.000173921i	7.38972e−6	0	2.20880e-5i
$63$		0			0
$64$	−7.98912	+	0.417073i	−0.998640	+	0.0521341i
$65$	1.40579	+	7.61643i	0.174367	+	0.944702i
$66$		0			0
$67$	4.18342	−	8.21042i	0.511086	−	1.00306i	−0.480907	−	0.876771i	$-0.659693\pi$
$67$	4.18342	−	8.21042i	0.511086	−	1.00306i	0.991993	−	0.126291i	$-0.0403073\pi$
$68$	−7.86965	−	3.83894i	−0.954335	−	0.465540i
$69$		0			0
$70$	−7.56119	+	8.09582i	−0.903735	+	0.967635i
$71$	−1.99288	−	0.647527i	−0.236512	−	0.0768473i	0.188363	−	0.982099i	$-0.439682\pi$
$71$	−1.99288	−	0.647527i	−0.236512	−	0.0768473i	−0.424875	+	0.905252i	$0.639682\pi$
$72$		0			0
$73$	12.5935	+	1.99462i	1.47396	+	0.233453i	0.841129	−	0.540835i	$-0.181892\pi$
$73$	12.5935	+	1.99462i	1.47396	+	0.233453i	0.632834	+	0.774288i	$0.281892\pi$
$74$	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	$-0.935368\pi$
$79$	−0.609102	+	1.87462i	−0.0685293	+	0.210911i	0.910927	+	0.412567i	$0.135368\pi$
$80$	−8.92806	+	0.538226i	−0.998188	+	0.0601755i
$81$		0			0
$82$	−4.29510	+	6.02107i	−0.474314	+	0.664916i
$83$	14.4825	+	7.37922i	1.58966	+	0.809974i	0.999997	+	0.00232773i	$0.000740939\pi$
$83$	14.4825	+	7.37922i	1.58966	+	0.809974i	0.589667	+	0.807647i	$0.299259\pi$
$84$		0			0
$85$	−8.83282	−	4.22106i	−0.958053	−	0.457838i
$86$	6.52791	+	6.41539i	0.703923	+	0.691790i
$87$		0			0
$88$	7.94045	−	6.09165i	0.846455	−	0.649372i
$89$	3.49423	+	4.80940i	0.370388	+	0.509795i	0.953006	−	0.302951i	$-0.0979718\pi$
$89$	3.49423	+	4.80940i	0.370388	+	0.509795i	−0.582618	+	0.812746i	$0.697972\pi$
$90$		0			0
$91$	−7.13192	+	9.81624i	−0.747628	+	1.02902i
$92$	−0.0217248	+	0.154504i	−0.00226497	+	0.0161082i
$93$		0			0
$94$	−8.46447	−	16.2614i	−0.873043	−	1.67724i
$95$	−4.37269	−	12.3772i	−0.448628	−	1.26987i
$96$		0			0
$97$	−1.72335	−	3.38227i	−0.174980	−	0.343417i	0.786815	−	0.617189i	$-0.211729\pi$
$97$	−1.72335	−	3.38227i	−0.174980	−	0.343417i	−0.961795	+	0.273772i	$0.911729\pi$
$98$	−7.45458	+	0.0648039i	−0.753026	+	0.00654619i
$99$		0			0
$100$	−9.97671	+	0.682130i	−0.997671	+	0.0682130i
$101$	−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	0.897083	+	0.441862i	$0.145682\pi$
$103$	7.38093	+	14.4859i	0.727265	+	1.42734i	−0.169818	+	0.985475i	$0.554318\pi$
$104$	−9.63297	+	1.78436i	−0.944590	+	0.174971i
$105$		0			0
$106$	7.02889	+	13.5035i	0.682706	+	1.31157i
$107$	−0.755111	−	0.755111i	−0.0729993	−	0.0729993i	0.669664	−	0.742664i	$-0.266438\pi$
$107$	−0.755111	−	0.755111i	−0.0729993	−	0.0729993i	−0.742664	+	0.669664i	$0.766438\pi$
$108$		0			0
$109$	−4.88498	+	6.72359i	−0.467896	+	0.644003i	−0.976123	−	0.217220i	$-0.930301\pi$
$109$	−4.88498	+	6.72359i	−0.467896	+	0.644003i	0.508227	+	0.861223i	$0.330301\pi$
$110$	8.82255	−	6.88195i	0.841197	−	0.656168i
$111$		0			0
$112$	−10.2466	−	9.55769i	−0.968212	−	0.903117i
$113$	−2.07827	−	13.1217i	−0.195508	−	1.23439i	−0.868858	−	0.495062i	$-0.835145\pi$
$113$	−2.07827	−	13.1217i	−0.195508	−	1.23439i	0.673350	−	0.739324i	$-0.264855\pi$
$114$		0			0
$115$	−0.0228970	+	0.172931i	−0.00213516	+	0.0161259i
$116$	−1.62449	−	0.496776i	−0.150830	−	0.0461244i
$117$		0			0
$118$	7.22913	−	10.1342i	0.665496	−	0.932924i
$119$	−4.73924	−	14.5859i	−0.434445	−	1.33708i
$120$		0			0
$121$	−0.469662	+	1.44547i	−0.0426965	+	0.131406i
$122$	8.49555	+	11.4819i	0.769151	+	1.03952i
$123$		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	$-0.234920\pi$
$127$	13.9231	+	2.20521i	1.23548	+	0.195680i	0.495677	+	0.868507i	$0.334920\pi$
$128$	−0.688022	−	11.2928i	−0.0608131	−	0.998149i
$129$		0			0
$130$	−10.7536	+	2.08165i	−0.943151	+	0.182573i
$131$	9.73405	−	3.16278i	0.850468	−	0.276334i	0.148826	−	0.988863i	$-0.452451\pi$
$131$	9.73405	−	3.16278i	0.850468	−	0.276334i	0.701642	+	0.712530i	$0.252451\pi$
$132$		0			0
$133$	9.33620	−	18.3233i	0.809551	−	1.58883i
$134$	11.6623	+	5.81509i	1.00747	+	0.502347i
$135$		0			0
$136$	5.33213	−	11.1761i	0.457226	−	0.958346i
$137$	−2.60954	+	0.413311i	−0.222948	+	0.0353115i	−0.266909	−	0.963722i	$-0.586002\pi$
$137$	−2.60954	+	0.413311i	−0.222948	+	0.0353115i	0.0439608	+	0.999033i	$0.486002\pi$
$138$		0			0
$139$	−5.28116	+	3.83699i	−0.447942	+	0.325449i	−0.788783	−	0.614672i	$-0.789288\pi$
$139$	−5.28116	+	3.83699i	−0.447942	+	0.325449i	0.340841	+	0.940121i	$0.389288\pi$
$140$	−11.5417	−	10.5932i	−0.975455	−	0.895289i
$141$		0			0
$142$	0.891207	−	2.82621i	0.0747884	−	0.237171i
$143$	8.66614	−	8.66614i	0.724699	−	0.724699i
$144$		0			0
$145$	−1.82065	−	0.540766i	−0.151197	−	0.0449082i
$146$	−2.66589	+	17.8338i	−0.220631	+	1.47594i
$147$		0			0
$148$	−10.1778	+	1.79392i	−0.836614	+	0.147460i
$149$			1.66225i			0.136177i	0.997679	+	0.0680885i	$0.0216900\pi$
$149$			1.66225i			0.136177i	−0.997679	+	0.0680885i	$0.978310\pi$
$150$		0			0
$151$			14.2155i			1.15684i	0.815738	+	0.578422i	$0.196331\pi$
$151$			14.2155i			1.15684i	−0.815738	+	0.578422i	$0.803669\pi$
$152$	15.6525	−	5.54106i	1.26959	−	0.449440i
$153$		0			0
$154$	17.3365	+	2.59156i	1.39702	+	0.208834i
$155$	−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	−0.986800	−	0.161943i	$-0.948224\pi$
$157$	−10.3354	+	10.3354i	−0.824857	+	0.824857i	0.161943	+	0.986800i	$0.448224\pi$
$158$	−2.65850	−	0.838321i	−0.211499	−	0.0666933i
$159$		0			0
$160$	−0.870895	−	12.6191i	−0.0688503	−	0.997627i
$161$	−0.221089	+	0.160630i	−0.0174242	+	0.0126594i
$162$		0			0
$163$	−23.5826	+	3.73511i	−1.84713	+	0.292556i	−0.979012	−	0.203804i	$-0.934669\pi$
$163$	−23.5826	+	3.73511i	−1.84713	+	0.292556i	−0.868117	+	0.496360i	$0.834669\pi$
$164$	−8.56756	−	5.99993i	−0.669014	−	0.468516i
$165$		0			0
$166$	−10.2574	+	20.5713i	−0.796125	+	1.59665i
$167$	−3.90289	+	7.65985i	−0.302015	+	0.592737i	−0.991280	−	0.131772i	$-0.957933\pi$
$167$	−3.90289	+	7.65985i	−0.302015	+	0.592737i	0.689266	+	0.724509i	$0.257933\pi$
$168$		0			0
$169$	0.953668	−	0.309865i	0.0733591	−	0.0238358i
$170$	5.86067	−	12.5429i	0.449493	−	0.961997i
$171$		0			0
$172$	−8.99214	+	9.31038i	−0.685645	+	0.709910i
$173$	24.3562	+	3.85764i	1.85176	+	0.293291i	0.980351	−	0.197260i	$-0.0632043\pi$
$173$	24.3562	+	3.85764i	1.85176	+	0.293291i	0.871413	+	0.490551i	$0.163204\pi$
$174$		0			0
$175$	−12.9990	−	11.7392i	−0.982634	−	0.887404i
$176$	8.71218	+	11.1542i	0.656705	+	0.840778i
$177$		0			0
$178$	−6.75830	+	5.00053i	−0.506556	+	0.374805i
$179$	−2.88996	+	8.89439i	−0.216006	+	0.664798i	0.783075	+	0.621928i	$0.213650\pi$
$179$	−2.88996	+	8.89439i	−0.216006	+	0.664798i	−0.999081	+	0.0428703i	$0.986350\pi$
$180$		0			0
$181$	−1.13761	−	3.50121i	−0.0845580	−	0.260243i	0.899834	−	0.436233i	$-0.143687\pi$
$181$	−1.13761	−	3.50121i	−0.0845580	−	0.260243i	−0.984392	+	0.175990i	$0.943687\pi$
$182$	−13.9694	−	9.96500i	−1.03548	−	0.738655i
$183$		0			0
$184$	−0.218761	−	0.0288229i	−0.0161273	−	0.00212485i
$185$	−11.3627	+	2.09725i	−0.835399	+	0.154193i
$186$		0			0
$187$	2.42332	+	15.3003i	0.177211	+	1.11887i
$188$	22.8922	−	12.1700i	1.66959	−	0.887590i
$189$		0			0
$190$	17.4496	−	6.33584i	1.26592	−	0.459650i
$191$	0.778612	−	1.07167i	0.0563384	−	0.0775431i	−0.779918	−	0.625881i	$-0.784739\pi$
$191$	0.778612	−	1.07167i	0.0563384	−	0.0775431i	0.836257	+	0.548338i	$0.184739\pi$
$192$		0			0
$193$	−8.28171	−	8.28171i	−0.596131	−	0.596131i	0.343150	−	0.939281i	$-0.388506\pi$
$193$	−8.28171	−	8.28171i	−0.596131	−	0.596131i	−0.939281	+	0.343150i	$0.888506\pi$
$194$	4.76188	−	2.47867i	0.341883	−	0.177958i
$195$		0			0
$196$	−0.183286	−	10.5412i	−0.0130919	−	0.752941i
$197$	−7.57112	−	14.8592i	−0.539420	−	1.05867i	−0.986436	−	0.164146i	$-0.947513\pi$
$197$	−7.57112	−	14.8592i	−0.539420	−	1.05867i	0.447016	−	0.894526i	$-0.352487\pi$
$198$		0			0
$199$	18.7284			1.32762			0.663811	−	0.747900i	$-0.268938\pi$
$199$	18.7284			1.32762			0.663811	+	0.747900i	$0.268938\pi$
$200$	−1.08729	−	14.1003i	−0.0768830	−	0.997040i
$201$		0			0
$202$	−0.0685055	−	7.88038i	−0.00482003	−	0.554461i
$203$	−1.35080	−	2.65110i	−0.0948079	−	0.186071i
$204$		0			0
$205$	−9.63254	−	6.63076i	−0.672766	−	0.463113i
$206$	−20.3946	+	10.6159i	−1.42096	+	0.739645i
$207$		0			0
$208$	−2.64179	−	13.6006i	−0.183175	−	0.943034i
$209$	−12.2094	+	16.8048i	−0.844544	+	1.16241i
$210$		0			0
$211$	−9.53944	−	13.1299i	−0.656722	−	0.903901i	0.342645	−	0.939465i	$-0.388677\pi$
$211$	−9.53944	−	13.1299i	−0.656722	−	0.903901i	−0.999367	+	0.0355641i	$0.988677\pi$
$212$	−19.0097	+	10.1060i	−1.30559	+	0.694082i
$213$		0			0
$214$	1.05856	−	1.07713i	0.0723620	−	0.0736311i
$215$	−9.96936	+	10.4900i	−0.679905	+	0.715409i
$216$		0			0
$217$	−0.000404766	0	0.000206238i	−2.74773e−5	0	1.40004e-5i
$218$	−9.56829	−	6.82548i	−0.648046	−	0.462280i
$219$		0			0
$220$	9.84064	+	12.3919i	0.663455	+	0.835461i
$221$	4.68600	−	14.4220i	0.315215	−	0.970131i
$222$		0			0
$223$	2.09027	−	13.1975i	0.139975	−	0.883768i	−0.813340	−	0.581789i	$-0.802353\pi$
$223$	2.09027	−	13.1975i	0.139975	−	0.883768i	0.953315	−	0.301979i	$-0.0976471\pi$
$224$	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	$-0.187025\pi$
$227$	21.8851	+	3.46626i	1.45256	+	0.230064i	0.620266	+	0.784392i	$0.287025\pi$
$228$		0			0
$229$	21.0179	+	6.82911i	1.38890	+	0.451281i	0.905584	−	0.424166i	$-0.139433\pi$
$229$	21.0179	+	6.82911i	1.38890	+	0.451281i	0.483314	+	0.875447i	$0.339433\pi$
$230$	−0.244834	−	0.0302541i	−0.0161439	−	0.00199490i
$231$		0			0
$232$	0.682549	−	2.30339i	0.0448116	−	0.151225i
$233$	−6.93889	+	13.6183i	−0.454582	+	0.892167i	0.544008	+	0.839080i	$0.316906\pi$
$233$	−6.93889	+	13.6183i	−0.454582	+	0.892167i	−0.998590	+	0.0530874i	$0.983094\pi$
$234$		0			0
$235$	25.4838	−	13.8122i	1.66238	−	0.901008i
$236$	14.4202	+	10.0986i	0.938674	+	0.657361i
$237$		0			0
$238$	20.5685	−	6.88135i	1.33326	−	0.446052i
$239$	−1.66547	+	1.21003i	−0.107730	+	0.0782704i	−0.640346	−	0.768087i	$-0.721209\pi$
$239$	−1.66547	+	1.21003i	−0.107730	+	0.0782704i	0.532616	+	0.846357i	$0.321209\pi$
$240$		0			0
$241$	16.0774	+	11.6809i	1.03564	+	0.752434i	0.969429	−	0.245371i	$-0.0789099\pi$
$241$	16.0774	+	11.6809i	1.03564	+	0.752434i	0.0662080	+	0.997806i	$0.478910\pi$
$242$	−2.04990	−	0.646407i	−0.131773	−	0.0415526i
$243$		0			0
$244$	−16.1328	+	12.1552i	−1.03280	+	0.778158i
$245$	−0.299834	−	11.7834i	−0.0191557	−	0.752811i
$246$		0			0
$247$	18.1175	−	9.23133i	1.15279	−	0.587376i
$248$	−0.000122403	0	0.000345767i	−7.77261e−6	0	2.19562e-5i
$249$		0			0
$250$	−1.34256	−	15.7543i	−0.0849107	−	0.996389i
$251$		−	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
$254$	−2.94735	+	19.7166i	−0.184933	+	1.23713i
$255$		0			0
$256$	15.9613	−	1.11180i	0.997583	−	0.0694876i
$257$	5.28943	−	5.28943i	0.329946	−	0.329946i	−0.522620	−	0.852566i	$-0.675045\pi$
$257$	5.28943	−	5.28943i	0.329946	−	0.329946i	0.852566	+	0.522620i	$0.175045\pi$
$258$		0			0
$259$	−14.6445	−	10.6398i	−0.909963	−	0.661127i
$260$	−3.07599	−	15.1817i	−0.190765	−	0.941528i
$261$		0			0
$262$	4.59235	+	13.7266i	0.283716	+	0.848034i
$263$	−13.9709	+	2.21277i	−0.861481	+	0.136445i	−0.571515	−	0.820592i	$-0.693644\pi$
$263$	−13.9709	+	2.21277i	−0.861481	+	0.136445i	−0.289966	+	0.957037i	$0.593644\pi$
$264$		0			0
$265$	−21.1618	+	11.4696i	−1.29996	+	0.704575i
$266$	26.0269	+	12.9776i	1.59581	+	0.795709i
$267$		0			0
$268$	−8.08010	+	16.5638i	−0.493570	+	1.01180i
$269$	−9.22474	+	2.99730i	−0.562443	+	0.182749i	−0.576420	−	0.817154i	$-0.695551\pi$
$269$	−9.22474	+	2.99730i	−0.562443	+	0.182749i	0.0139774	+	0.999902i	$0.495551\pi$
$270$		0			0
$271$	11.2200	+	3.64559i	0.681564	+	0.221454i	0.629280	−	0.777179i	$-0.283350\pi$
$271$	11.2200	+	3.64559i	0.681564	+	0.221454i	0.0522842	+	0.998632i	$0.483350\pi$
$272$	15.8704	+	7.40309i	0.962284	+	0.448878i
$273$		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	−0.532642	−	0.846341i	$-0.678801\pi$
$277$	3.91891	−	24.7430i	0.235464	−	1.48666i	0.768106	−	0.640322i	$-0.221199\pi$
$278$	−5.49104	−	7.42123i	−0.329331	−	0.445096i
$279$		0			0
$280$	14.8386	−	16.4521i	0.886776	−	0.983200i
$281$	−4.75790	−	14.6433i	−0.283832	−	0.873546i	−0.986746	−	0.162271i	$-0.948118\pi$
$281$	−4.75790	−	14.6433i	−0.283832	−	0.873546i	0.702914	−	0.711275i	$-0.251882\pi$
$282$		0			0
$283$	−13.9254	−	7.09534i	−0.827778	−	0.421774i	−0.0118519	−	0.999930i	$-0.503773\pi$
$283$	−13.9254	−	7.09534i	−0.827778	−	0.421774i	−0.815927	+	0.578156i	$0.803773\pi$
$284$	4.00768	+	1.22556i	0.237812	+	0.0727239i
$285$		0			0
$286$	12.3618	+	12.1488i	0.730971	+	0.718372i
$287$	−2.86591	−	18.0946i	−0.169169	−	1.06809i
$288$		0			0
$289$	1.27385	+	1.75330i	0.0749323	+	0.103135i
$290$	0.742347	−	2.58133i	0.0435921	−	0.151581i
$291$		0			0
$292$	−25.2526	−	3.55076i	−1.47780	−	0.207792i
$293$	−12.3367	−	12.3367i	−0.720717	−	0.720717i	0.248035	−	0.968751i	$-0.420215\pi$
$293$	−12.3367	−	12.3367i	−0.720717	−	0.720717i	−0.968751	+	0.248035i	$0.920215\pi$
$294$		0			0
$295$	16.2127	+	11.1603i	0.943938	+	0.649779i
$296$	−2.66202	−	14.3711i	−0.154726	−	0.835301i
$297$		0			0
$298$	−2.35069	+	0.0204350i	−0.136172	+	0.00118377i
$299$	−0.270211			−0.0156267
$300$		0			0
$301$	−22.6714			−1.30676
$302$	−20.1030	+	0.174759i	−1.15680	+	0.0100563i
$303$		0			0
$304$	8.02837	+	22.0670i	0.460459	+	1.26563i
$305$	−17.9270	+	13.7348i	−1.02649	+	0.786451i
$306$		0			0
$307$	−21.4864	−	21.4864i	−1.22629	−	1.22629i	−0.965356	−	0.260937i	$-0.915969\pi$
$307$	−21.4864	−	21.4864i	−1.22629	−	1.22629i	−0.260937	−	0.965356i	$-0.584031\pi$
$308$	−3.45175	+	24.5485i	−0.196682	+	1.39878i
$309$		0			0
$310$	−0.000139960	0	0.000385464i	−7.94919e−6	0	2.18929e-5i
$311$	7.60468	+	10.4670i	0.431222	+	0.593526i	0.968233	−	0.250049i	$-0.0804467\pi$
$311$	7.60468	+	10.4670i	0.431222	+	0.593526i	−0.537011	+	0.843575i	$0.680447\pi$
$312$		0			0
$313$	0.282072	+	1.78093i	0.0159436	+	0.100664i	0.994377	−	0.105899i	$-0.0337721\pi$
$313$	0.282072	+	1.78093i	0.0159436	+	0.100664i	−0.978433	+	0.206563i	$0.933772\pi$
$314$	−14.7430	−	14.4889i	−0.831997	−	0.817656i
$315$		0			0
$316$	1.15284	−	3.76986i	0.0648522	−	0.212071i
$317$	−0.555856	−	0.283223i	−0.0312200	−	0.0159074i	0.438311	−	0.898823i	$-0.355577\pi$
$317$	−0.555856	−	0.283223i	−0.0312200	−	0.0159074i	−0.469531	+	0.882916i	$0.655577\pi$
$318$		0			0
$319$	0.928712	+	2.85828i	0.0519979	+	0.160033i
$320$	17.8347	−	1.38672i	0.996991	−	0.0775199i
$321$		0			0
$322$	−0.229875	−	0.310680i	−0.0128104	−	0.0173135i
$323$	−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
$328$	8.37954	−	12.1897i	0.462683	−	0.673062i
$329$	43.1877	+	14.0325i	2.38102	+	0.773639i
$330$		0			0
$331$	10.1209	−	3.28849i	0.556297	−	0.180752i	−0.0173575	−	0.999849i	$-0.505525\pi$
$331$	10.1209	−	3.28849i	0.556297	−	0.180752i	0.573654	+	0.819098i	$0.305525\pi$
$332$	−29.2173	−	14.2526i	−1.60351	−	0.782216i
$333$		0			0
$334$	−10.8802	−	5.42514i	−0.595340	−	0.296851i
$335$	−8.88438	+	18.5911i	−0.485405	+	1.01574i
$336$		0			0
$337$	−16.9393	+	2.68292i	−0.922741	+	0.146148i	−0.599689	−	0.800233i	$-0.704709\pi$
$337$	−16.9393	+	2.68292i	−0.922741	+	0.146148i	−0.323052	+	0.946381i	$0.604709\pi$
$338$	0.449923	+	1.34483i	0.0244726	+	0.0731491i
$339$		0			0
$340$	17.8097	+	8.13373i	0.965868	+	0.441113i
$341$	0.000371222	0	0.000269708i	2.01028e−5	0	1.46055e-5i
$342$		0			0
$343$	−4.28185	+	4.28185i	−0.231198	+	0.231198i
$344$	−13.2769	−	12.6019i	−0.715843	−	0.679448i
$345$		0			0
$346$	−5.15589	+	34.4909i	−0.277182	+	1.85424i
$347$	−4.15803	+	2.11862i	−0.223215	+	0.113734i	−0.562022	−	0.827122i	$-0.689977\pi$
$347$	−4.15803	+	2.11862i	−0.223215	+	0.113734i	0.338807	+	0.940856i	$0.389977\pi$
$348$		0			0
$349$			27.0365i			1.44723i	0.690203	+	0.723616i	$0.257521\pi$
$349$			27.0365i			1.44723i	−0.690203	+	0.723616i	$0.742479\pi$
$350$	16.4414	−	18.5270i	0.878828	−	0.990311i
$351$		0			0
$352$	−15.6667	+	12.4575i	−0.835037	+	0.663989i
$353$	10.5828	−	5.39221i	0.563266	−	0.286998i	−0.149082	−	0.988825i	$-0.547632\pi$
$353$	10.5828	−	5.39221i	0.563266	−	0.286998i	0.712348	+	0.701826i	$0.247632\pi$
$354$		0			0
$355$	4.49161	+	1.33409i	0.238390	+	0.0708062i
$356$	−7.15463	−	9.49585i	−0.379195	−	0.503279i
$357$		0			0
$358$	−12.6136	−	3.97753i	−0.666651	−	0.210219i
$359$	12.3154	+	8.94766i	0.649981	+	0.472239i	0.863265	−	0.504751i	$-0.168416\pi$
$359$	12.3154	+	8.94766i	0.649981	+	0.472239i	−0.213283	+	0.976990i	$0.568416\pi$
$360$		0			0
$361$	−12.5099	+	9.08895i	−0.658414	+	0.478366i
$362$	4.93729	−	1.65181i	0.259498	−	0.0868171i
$363$		0			0
$364$	13.9204	−	19.8775i	0.729626	−	1.04186i
$365$	−28.2643	−	3.74235i	−1.47942	−	0.195884i
$366$		0			0
$367$	−10.8842	+	21.3614i	−0.568149	+	1.11505i	0.410948	+	0.911659i	$0.365198\pi$
$367$	−10.8842	+	21.3614i	−0.568149	+	1.11505i	−0.979097	+	0.203396i	$0.934802\pi$
$368$	0.0380709	−	0.309717i	0.00198458	−	0.0161451i
$369$		0			0
$370$	−3.10553	−	16.0428i	−0.161449	−	0.834027i
$371$	−35.8631	−	11.6526i	−1.86192	−	0.604974i
$372$		0			0
$373$	21.4232	+	3.39311i	1.10925	+	0.175689i	0.684068	−	0.729418i	$-0.260209\pi$
$373$	21.4232	+	3.39311i	1.10925	+	0.175689i	0.425185	+	0.905106i	$0.360209\pi$
$374$	−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	$-0.851243\pi$
$379$	1.83578	−	5.64994i	0.0942976	−	0.290218i	0.987070	+	0.160290i	$0.0512429\pi$
$380$	9.17441	+	24.5986i	0.470637	+	1.26188i
$381$		0			0
$382$	1.52508	+	1.08791i	0.0780299	+	0.0556622i
$383$	4.12547	+	2.10203i	0.210802	+	0.107409i	0.556204	−	0.831046i	$-0.312257\pi$
$383$	4.12547	+	2.10203i	0.210802	+	0.107409i	−0.345402	+	0.938455i	$0.612257\pi$
$384$		0			0
$385$	−3.63800	+	27.4763i	−0.185410	+	1.40032i
$386$	11.6099	−	11.8135i	0.590926	−	0.601290i
$387$		0			0
$388$	3.56378	+	6.70359i	0.180924	+	0.340323i
$389$	5.61572	+	7.72937i	0.284728	+	0.391895i	0.927293	−	0.374337i	$-0.122130\pi$
$389$	5.61572	+	7.72937i	0.284728	+	0.391895i	−0.642565	+	0.766231i	$0.722130\pi$
$390$		0			0
$391$	0.200752	−	0.276312i	0.0101525	−	0.0139737i
$392$	14.9046	−	0.388784i	0.752798	−	0.0196366i
$393$		0			0
$394$	20.9202	−	10.8895i	1.05394	−	0.548603i
$395$	1.25492	−	4.22507i	0.0631421	−	0.212586i
$396$		0			0
$397$	9.59631	+	18.8338i	0.481625	+	0.945242i	0.996142	+	0.0877616i	$0.0279714\pi$
$397$	9.59631	+	18.8338i	0.481625	+	0.945242i	−0.514517	+	0.857480i	$0.672029\pi$
$398$	0.230239	+	26.4850i	0.0115408	+	1.32757i
$399$		0			0
$400$	19.9267	−	1.71094i	0.996334	−	0.0855472i
$401$	−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
$404$	11.1433	−	0.193755i	0.554398	−	0.00963969i
$405$		0			0
$406$	3.73248	−	1.94285i	0.185240	−	0.0964218i
$407$	12.9287	+	12.9287i	0.640851	+	0.640851i
$408$		0			0
$409$	−6.44004	+	8.86395i	−0.318439	+	0.438294i	−0.937990	−	0.346663i	$-0.887315\pi$
$409$	−6.44004	+	8.86395i	−0.318439	+	0.438294i	0.619551	+	0.784957i	$0.287315\pi$
$410$	9.25854	−	13.7035i	0.457247	−	0.676766i
$411$		0			0
$412$	−15.2633	−	28.7108i	−0.751969	−	1.41448i
$413$	4.82365	+	30.4553i	0.237356	+	1.49861i
$414$		0			0
$415$	−32.7932	−	15.6713i	−1.60975	−	0.769275i
$416$	19.2010	−	3.90312i	0.941406	−	0.191366i
$417$		0			0
$418$	−23.9148	−	17.0595i	−1.16971	−	0.834407i
$419$	5.83515	+	17.9587i	0.285066	+	0.877342i	0.986379	+	0.164489i	$0.0525974\pi$
$419$	5.83515	+	17.9587i	0.285066	+	0.877342i	−0.701313	+	0.712853i	$0.747403\pi$
$420$		0			0
$421$	4.18623	−	12.8839i	0.204024	−	0.627922i	−0.795728	−	0.605654i	$-0.792911\pi$
$421$	4.18623	−	12.8839i	0.204024	−	0.627922i	0.999752	−	0.0222675i	$-0.00708854\pi$
$422$	18.4505	−	13.6517i	0.898158	−	0.664555i
$423$		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
$428$	1.53625	+	1.48374i	0.0742574	+	0.0717192i
$429$		0			0
$430$	−14.9570	−	13.9693i	−0.721292	−	0.673660i
$431$	−8.92558	+	2.90010i	−0.429930	+	0.139693i	−0.515985	−	0.856598i	$-0.672574\pi$
$431$	−8.92558	+	2.90010i	−0.429930	+	0.139693i	0.0860549	+	0.996290i	$0.472574\pi$
$432$		0			0
$433$	−13.2636	+	26.0312i	−0.637406	+	1.25098i	0.315848	+	0.948810i	$0.397711\pi$
$433$	−13.2636	+	26.0312i	−0.637406	+	1.25098i	−0.953254	+	0.302170i	$0.902289\pi$
$434$	0.000286678	0	0.000574939i	1.37610e−5	0	2.75980e-5i
$435$		0			0
$436$	9.53469	−	13.6150i	0.456629	−	0.652040i
$437$	0.452334	−	0.0716426i	0.0216380	−	0.00342713i
$438$		0			0
$439$	−8.37262	+	6.08307i	−0.399603	+	0.290329i	−0.769379	−	0.638792i	$-0.779434\pi$
$439$	−8.37262	+	6.08307i	−0.399603	+	0.290329i	0.369776	+	0.929121i	$0.379434\pi$
$440$	−17.4031	+	14.0686i	−0.829662	+	0.670693i
$441$		0			0
$442$	20.4527	+	6.44946i	0.972835	+	0.306770i
$443$	−1.22412	+	1.22412i	−0.0581596	+	0.0581596i	−0.735588	−	0.677429i	$-0.763094\pi$
$443$	−1.22412	+	1.22412i	−0.0581596	+	0.0581596i	0.677429	+	0.735588i	$0.263094\pi$
$444$		0			0
$445$	−8.08437	−	10.5519i	−0.383236	−	0.500208i
$446$	18.6890	+	2.79374i	0.884951	+	0.132287i
$447$		0			0
$448$	20.8224	+	18.7562i	0.983767	+	0.886148i
$449$			36.0614i			1.70184i	0.525292	+	0.850922i	$0.323956\pi$
$449$			36.0614i			1.70184i	−0.525292	+	0.850922i	$0.676044\pi$
$450$		0			0
$451$			18.5047i			0.871354i
$452$	4.61216	+	26.1672i	0.216938	+	1.23080i
$453$		0			0
$454$	−4.63280	+	30.9916i	−0.217428	+	1.45451i
$455$	15.3840	−	22.3483i	0.721211	−	1.04771i
$456$		0			0
$457$	−2.22184	+	2.22184i	−0.103933	+	0.103933i	−0.757161	−	0.653228i	$-0.773414\pi$
$457$	−2.22184	+	2.22184i	−0.103933	+	0.103933i	0.653228	+	0.757161i	$0.273414\pi$
$458$	−9.39908	+	29.8066i	−0.439190	+	1.39277i
$459$		0			0
$460$	0.0397742	−	0.346606i	0.00185448	−	0.0161606i
$461$	−21.0778	+	15.3139i	−0.981692	+	0.713241i	−0.958086	−	0.286481i	$-0.907515\pi$
$461$	−21.0778	+	15.3139i	−0.981692	+	0.713241i	−0.0236057	+	0.999721i	$0.507515\pi$
$462$		0			0
$463$	25.1759	−	3.98747i	1.17002	−	0.185314i	0.458970	−	0.888452i	$-0.348218\pi$
$463$	25.1759	−	3.98747i	1.17002	−	0.185314i	0.711053	+	0.703138i	$0.248218\pi$
$464$	3.26576	+	0.936917i	0.151609	+	0.0434953i
$465$		0			0
$466$	−19.3438	−	9.64529i	−0.896085	−	0.446809i
$467$	17.3078	−	33.9686i	0.800911	−	1.57188i	−0.0192980	−	0.999814i	$-0.506143\pi$
$467$	17.3078	−	33.9686i	0.800911	−	1.57188i	0.820209	−	0.572063i	$-0.193857\pi$
$468$		0			0
$469$	−30.6999	+	9.97502i	−1.41759	+	0.460603i
$470$	19.8459	+	35.8684i	0.915425	+	1.65449i
$471$		0			0
$472$	−14.1037	+	20.5166i	−0.649176	+	0.944353i
$473$	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
$478$	−1.73165	−	2.34036i	−0.0792039	−	0.107046i
$479$	2.02143	−	6.22131i	0.0923613	−	0.284259i	−0.894196	−	0.447676i	$-0.852252\pi$
$479$	2.02143	−	6.22131i	0.0923613	−	0.284259i	0.986557	+	0.163417i	$0.0522517\pi$
$480$		0			0
$481$	−5.53086	−	17.0222i	−0.252186	−	0.776147i
$482$	−16.3210	+	22.8796i	−0.743403	+	1.04214i
$483$		0			0
$484$	0.888923	−	2.90683i	0.0404056	−	0.132129i
$485$	4.04466	+	7.46251i	0.183659	+	0.338855i
$486$		0			0
$487$	1.93534	+	12.2192i	0.0876986	+	0.553707i	0.991942	+	0.126690i	$0.0404354\pi$
$487$	1.93534	+	12.2192i	0.0876986	+	0.553707i	−0.904244	+	0.427017i	$0.859565\pi$
$488$	−17.3878	−	22.6649i	−0.787107	−	1.02599i
$489$		0			0
$490$	16.6599	−	0.568872i	0.752616	−	0.0256990i
$491$	1.51867	−	2.09027i	0.0685365	−	0.0943323i	−0.773373	−	0.633952i	$-0.781432\pi$
$491$	1.51867	−	2.09027i	0.0685365	−	0.0943323i	0.841909	+	0.539619i	$0.181432\pi$
$492$		0			0
$493$	2.62944	+	2.62944i	0.118424	+	0.118424i
$494$	13.2773	+	25.5076i	0.597375	+	1.14764i
$495$		0			0
$496$	0.000487465	0	0.000177348i	2.18878e−5	0	7.96317e-6i
$497$	3.33249	+	6.54038i	0.149483	+	0.293376i
$498$		0			0
$499$	1.41851			0.0635014			0.0317507	−	0.999496i	$-0.489892\pi$
$499$	1.41851			0.0635014			0.0317507	+	0.999496i	$0.489892\pi$
$500$	22.2626	−	2.09227i	0.995613	−	0.0935689i
$501$		0			0
$502$	36.7176	−	0.319192i	1.63879	−	0.0142463i
$503$	−5.08096	−	9.97194i	−0.226549	−	0.444627i	0.749552	−	0.661945i	$-0.230269\pi$
$503$	−5.08096	−	9.97194i	−0.226549	−	0.444627i	−0.976101	+	0.217319i	$0.930269\pi$
$504$		0			0
$505$	12.4564	−	0.316960i	0.554303	−	0.0141045i
$506$	0.180241	+	0.346269i	0.00801270	+	0.0153935i
$507$		0			0
$508$	−27.9187	−	3.92564i	−1.23869	−	0.174172i
$509$	6.17501	−	8.49917i	0.273702	−	0.376719i	−0.649933	−	0.759992i	$-0.725203\pi$
$509$	6.17501	−	8.49917i	0.273702	−	0.376719i	0.923635	+	0.383273i	$0.125203\pi$
$510$		0			0
$511$	−26.2539	−	36.1353i	−1.16140	−	1.59853i
$512$	1.76849	+	22.5582i	0.0781568	+	0.996941i
$513$		0			0
$514$	7.54513	+	7.41508i	0.332801	+	0.327065i
$515$	−17.3229	−	31.9611i	−0.763337	−	1.40838i
$516$		0			0
$517$	−40.8684	−	20.8235i	−1.79739	−	0.915816i
$518$	14.8664	−	20.8404i	0.653192	−	0.915676i
$519$		0			0
$520$	21.4315	−	4.53657i	0.939834	−	0.198942i
$521$	−5.86783	+	18.0593i	−0.257074	+	0.791193i	0.736340	+	0.676612i	$0.236553\pi$
$521$	−5.86783	+	18.0593i	−0.257074	+	0.791193i	−0.993414	+	0.114581i	$0.963447\pi$
$522$		0			0
$523$	0.798016	−	5.03848i	0.0348948	−	0.220317i	−0.964079	−	0.265617i	$-0.914424\pi$
$523$	0.798016	−	5.03848i	0.0348948	−	0.220317i	0.998973	+	0.0452999i	$0.0144243\pi$
$524$	−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
$530$	−16.4801	−	29.7852i	−0.715848	−	1.29378i
$531$		0			0
$532$	−18.0325	+	36.9657i	−0.781807	+	1.60267i
$533$	8.22377	−	16.1401i	0.356211	−	0.699104i
$534$		0			0
$535$	1.73088	+	1.64498i	0.0748326	+	0.0711188i
$536$	−23.5232	−	11.2229i	−1.01605	−	0.484756i
$537$		0			0
$538$	−4.35207	−	13.0084i	−0.187631	−	0.560833i
$539$	−15.0897	+	10.9633i	−0.649961	+	0.472224i
$540$		0			0
$541$	3.67152	+	2.66752i	0.157851	+	0.114685i	0.663907	−	0.747815i	$-0.268897\pi$
$541$	3.67152	+	2.66752i	0.157851	+	0.114685i	−0.506056	+	0.862501i	$0.668897\pi$
$542$	−5.01751	+	15.9116i	−0.215521	+	0.683464i
$543$		0			0
$544$	−10.2741	+	22.5343i	−0.440496	+	0.966150i
$545$	10.5372	−	15.3074i	0.451363	−	0.655697i
$546$		0			0
$547$	10.6451	−	5.42393i	0.455150	−	0.231910i	−0.211358	−	0.977409i	$-0.567788\pi$
$547$	10.6451	−	5.42393i	0.455150	−	0.231910i	0.666507	+	0.745498i	$0.267788\pi$
$548$	5.20393	−	0.917231i	0.222301	−	0.0391822i
$549$		0			0
$550$	−19.3300	+	15.8853i	−0.824234	+	0.677353i
$551$			4.98627i			0.212422i
$552$		0			0
$553$	6.15226	−	3.13474i	0.261621	−	0.133302i
$554$	35.0387	+	5.23778i	1.48865	+	0.222532i
$555$		0			0
$556$	10.4273	−	7.85644i	0.442216	−	0.333187i
$557$	−10.4828	+	10.4828i	−0.444172	+	0.444172i	−0.893412	−	0.449239i	$-0.851695\pi$
$557$	−10.4828	+	10.4828i	−0.444172	+	0.444172i	0.449239	+	0.893412i	$0.351695\pi$
$558$		0			0
$559$	−18.1355	−	13.1762i	−0.767051	−	0.557295i
$560$	23.4483	+	20.7819i	0.990872	+	0.878196i
$561$		0			0
$562$	20.6495	−	6.90845i	0.871046	−	0.291415i
$563$	−8.04485	+	1.27418i	−0.339050	+	0.0537002i	−0.323638	−	0.946181i	$-0.604906\pi$
$563$	−8.04485	+	1.27418i	−0.339050	+	0.0537002i	−0.0154120	+	0.999881i	$0.504906\pi$
$564$		0			0
$565$	5.39201	+	29.2133i	0.226844	+	1.22901i
$566$	9.86275	−	19.7800i	0.414562	−	0.831414i
$567$		0			0
$568$	−1.68388	+	5.68256i	−0.0706539	+	0.238435i
$569$	−25.0837	+	8.15020i	−1.05157	+	0.341674i	−0.783283	−	0.621666i	$-0.786456\pi$
$569$	−25.0837	+	8.15020i	−1.05157	+	0.341674i	−0.268283	+	0.963340i	$0.586456\pi$
$570$		0			0
$571$	32.3724	+	10.5184i	1.35474	+	0.440182i	0.894284	−	0.447500i	$-0.147686\pi$
$571$	32.3724	+	10.5184i	1.35474	+	0.440182i	0.460457	+	0.887682i	$0.347686\pi$
$572$	−17.0283	+	17.6310i	−0.711990	+	0.737188i
$573$		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	−0.921594	−	0.388155i	$-0.873113\pi$
$577$	1.79773	−	11.3504i	0.0748405	−	0.472524i	0.996435	−	0.0843691i	$-0.0268875\pi$
$578$	−2.46379	+	1.82298i	−0.102480	+	0.0758260i
$579$		0			0
$580$	3.65955	+	1.01806i	0.151954	+	0.0422728i
$581$	−17.5951	−	54.1523i	−0.729969	−	2.24661i
$582$		0			0
$583$	33.9371	+	17.2918i	1.40553	+	0.716154i
$584$	4.71090	−	35.7549i	0.194938	−	1.47955i
$585$		0			0
$586$	17.2944	−	17.5977i	0.714424	−	0.726954i
$587$	−4.04749	−	25.5549i	−0.167058	−	1.05476i	−0.918632	−	0.395114i	$-0.870705\pi$
$587$	−4.04749	−	25.5549i	−0.167058	−	1.05476i	0.751574	−	0.659649i	$-0.229295\pi$
$588$		0			0
$589$	0.000447478	0	0.000615901i	1.84380e−5	0	2.53777e-5i
$590$	−15.5832	+	23.0645i	−0.641549	+	0.949551i
$591$		0			0
$592$	20.2902	−	3.94119i	0.833924	−	0.161982i
$593$	20.9734	+	20.9734i	0.861274	+	0.861274i	0.991486	−	0.130212i	$-0.0415658\pi$
$593$	20.9734	+	20.9734i	0.861274	+	0.861274i	−0.130212	+	0.991486i	$0.541566\pi$
$594$		0			0
$595$	11.4235	+	32.3349i	0.468316	+	1.32560i
$596$	−0.0577967	−	3.32400i	−0.00236744	−	0.136157i
$597$		0			0
$598$	−0.00332185	−	0.382122i	−0.000135841	−	0.0156261i
$599$	3.33851			0.136408			0.0682039	−	0.997671i	$-0.478273\pi$
$599$	3.33851			0.136408			0.0682039	+	0.997671i	$0.478273\pi$
$600$		0			0
$601$	−10.9587			−0.447013			−0.223506	−	0.974702i	$-0.571750\pi$
$601$	−10.9587			−0.447013			−0.223506	+	0.974702i	$0.571750\pi$
$602$	−0.278712	−	32.0610i	−0.0113594	−	1.30671i
$603$		0			0
$604$	−0.494275	−	28.4268i	−0.0201118	−	1.15667i
$605$	0.967638	−	3.25784i	0.0393401	−	0.132450i
$606$		0			0
$607$	5.16417	+	5.16417i	0.209607	+	0.209607i	0.804101	−	0.594493i	$-0.202647\pi$
$607$	5.16417	+	5.16417i	0.209607	+	0.209607i	−0.594493	+	0.804101i	$0.702647\pi$
$608$	−31.1076	+	11.6247i	−1.26158	+	0.471443i
$609$		0			0
$610$	−19.6436	−	25.1827i	−0.795344	−	1.01962i
$611$	26.3917	+	36.3250i	1.06769	+	1.46955i
$612$		0			0
$613$	2.23054	+	14.0831i	0.0900905	+	0.568809i	0.990901	+	0.134596i	$0.0429736\pi$
$613$	2.23054	+	14.0831i	0.0900905	+	0.568809i	−0.900810	+	0.434213i	$0.857026\pi$
$614$	30.1210	−	30.6493i	1.21559	−	1.23691i
$615$		0			0
$616$	−34.7580	−	4.57955i	−1.40044	−	0.184515i
$617$	−5.96590	−	3.03978i	−0.240178	−	0.122377i	0.329759	−	0.944065i	$-0.393032\pi$
$617$	−5.96590	−	3.03978i	−0.240178	−	0.122377i	−0.569937	+	0.821688i	$0.693032\pi$
$618$		0			0
$619$	−3.98349	−	12.2599i	−0.160110	−	0.492768i	0.838533	−	0.544851i	$-0.183414\pi$
$619$	−3.98349	−	12.2599i	−0.160110	−	0.492768i	−0.998643	+	0.0520830i	$0.983414\pi$
$620$	0.000543388	0	0.000202664i	2.18230e−5	0	8.13920e-6i
$621$		0			0
$622$	−14.7085	+	10.8829i	−0.589755	+	0.436365i
$623$	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
$628$	20.3084	−	21.0271i	0.810393	−	0.839073i
$629$	21.5157	+	6.99087i	0.857886	+	0.278744i
$630$		0			0
$631$	6.89142	−	2.23916i	0.274343	−	0.0891394i	−0.168614	−	0.985682i	$-0.553929\pi$
$631$	6.89142	−	2.23916i	0.274343	−	0.0891394i	0.442957	+	0.896543i	$0.353929\pi$
$632$	5.34535	+	1.58395i	0.212627	+	0.0630063i
$633$		0			0
$634$	0.393689	−	0.789551i	0.0156354	−	0.0313571i
$635$	−31.2484	−	4.13745i	−1.24005	−	0.164190i
$636$		0			0
$637$	18.0337	−	2.85626i	0.714522	−	0.113169i
$638$	−4.03065	+	1.34849i	−0.159575	+	0.0533871i
$639$		0			0
$640$	2.18029	+	25.2041i	0.0861837	+	0.996279i
$641$	−32.0344	−	23.2743i	−1.26528	−	0.919281i	−0.266278	−	0.963896i	$-0.585794\pi$
$641$	−32.0344	−	23.2743i	−1.26528	−	0.919281i	−0.999004	+	0.0446150i	$0.985794\pi$
$642$		0			0
$643$	−8.11866	+	8.11866i	−0.320169	+	0.320169i	−0.848832	−	0.528663i	$-0.822694\pi$
$643$	−8.11866	+	8.11866i	−0.320169	+	0.320169i	0.528663	+	0.848832i	$0.322694\pi$
$644$	0.436525	−	0.328899i	0.0172015	−	0.0129604i
$645$		0			0
$646$	−35.9478	−	5.37367i	−1.41435	−	0.211424i
$647$	−27.6446	+	14.0856i	−1.08682	+	0.553763i	−0.903194	−	0.429233i	$-0.858784\pi$
$647$	−27.6446	+	14.0856i	−1.08682	+	0.553763i	−0.183628	+	0.982996i	$0.558784\pi$
$648$		0			0
$649$		−	31.1456i		−	1.22257i
$650$	23.9195	−	5.26486i	0.938201	−	0.206505i
$651$		0			0
$652$	47.0281	−	8.28906i	1.84176	−	0.324625i
$653$	14.2708	−	7.27133i	0.558459	−	0.284549i	−0.151891	−	0.988397i	$-0.548536\pi$
$653$	14.2708	−	7.27133i	0.558459	−	0.284549i	0.710351	+	0.703848i	$0.248536\pi$
$654$		0			0
$655$	−21.5791	+	7.62358i	−0.843164	+	0.297878i
$656$	17.3412	+	11.7002i	0.677058	+	0.456814i
$657$		0			0
$658$	−19.3133	+	61.2469i	−0.752912	+	2.38765i
$659$	−11.4410	−	8.31238i	−0.445679	−	0.323804i	0.342209	−	0.939624i	$-0.388825\pi$
$659$	−11.4410	−	8.31238i	−0.445679	−	0.323804i	−0.787887	+	0.615820i	$0.788825\pi$
$660$		0			0
$661$	−30.5608	+	22.2037i	−1.18868	+	0.863623i	−0.993124	−	0.117070i	$-0.962650\pi$
$661$	−30.5608	+	22.2037i	−1.18868	+	0.863623i	−0.195552	+	0.980693i	$0.562650\pi$
$662$	4.77487	+	14.2722i	0.185581	+	0.554704i
$663$		0			0
$664$	19.7963	−	41.4931i	0.768247	−	1.61024i
$665$	−19.8274	+	41.4900i	−0.768874	+	1.60891i
$666$		0			0
$667$	0.0300821	−	0.0590394i	0.00116478	−	0.00228602i
$668$	7.53826	−	15.4531i	0.291664	−	0.597898i
$669$		0			0
$670$	−26.4000	−	12.3354i	−1.01992	−	0.476557i
$671$	33.9871	+	11.0431i	1.31206	+	0.426314i
$672$		0			0
$673$	6.11086	+	0.967866i	0.235556	+	0.0373085i	0.273096	−	0.961987i	$-0.411952\pi$
$673$	6.11086	+	0.967866i	0.235556	+	0.0373085i	−0.0375400	+	0.999295i	$0.511952\pi$
$674$	−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	−0.757441	−	0.652904i	$-0.773551\pi$
$677$	4.28502	−	27.0545i	0.164687	−	1.03979i	0.922127	−	0.386886i	$-0.126449\pi$
$678$		0			0
$679$	−4.10919	+	12.6468i	−0.157696	+	0.485339i
$680$	−11.2835	+	25.2858i	−0.432701	+	0.969666i
$681$		0			0
$682$	−0.000376847	0	0.000528283i	−1.44302e−5	0	2.02290e-5i
$683$	−38.8244	−	19.7820i	−1.48558	−	0.756939i	−0.492052	−	0.870566i	$-0.663753\pi$
$683$	−38.8244	−	19.7820i	−1.48558	−	0.756939i	−0.993523	+	0.113627i	$0.963753\pi$
$684$		0			0
$685$	5.80972	−	1.07232i	0.221978	−	0.0409713i
$686$	−6.10785	−	6.00258i	−0.233199	−	0.229179i
$687$		0			0
$688$	17.6578	−	18.9306i	0.673199	−	0.721723i
$689$	−21.9156	−	30.1643i	−0.834919	−	1.14917i
$690$		0			0
$691$	24.1230	−	33.2025i	0.917682	−	1.26308i	−0.0467925	−	0.998905i	$-0.514900\pi$
$691$	24.1230	−	33.2025i	0.917682	−	1.26308i	0.964474	−	0.264176i	$-0.0851000\pi$
$692$	−48.8391	−	6.86724i	−1.85658	−	0.261053i
$693$		0			0
$694$	−3.04719	−	5.85408i	−0.115670	−	0.222218i
$695$	11.5870	−	8.87738i	0.439519	−	0.336738i
$696$		0			0
$697$	10.3946	+	20.4006i	0.393725	+	0.772729i
$698$	−38.2340	+	0.332375i	−1.44718	+	0.0125806i
$699$		0			0
$700$	26.4023	+	23.0230i	0.997913	+	0.870187i
$701$	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
$704$	−17.8096	−	22.0021i	−0.671223	−	0.829234i
$705$		0			0
$706$	7.75555	+	14.8995i	0.291884	+	0.560750i
$707$	13.8032	+	13.8032i	0.519123	+	0.519123i
$708$		0			0
$709$	4.19370	−	5.77214i	0.157498	−	0.216777i	−0.722974	−	0.690875i	$-0.757226\pi$
$709$	4.19370	−	5.77214i	0.157498	−	0.216777i	0.880472	+	0.474098i	$0.157226\pi$
$710$	−1.83140	+	6.36825i	−0.0687312	+	0.238996i
$711$		0			0
$712$	13.3407	−	10.2345i	0.499964	−	0.383555i
$713$	−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
$716$	5.46979	−	17.8866i	0.204416	−	0.668453i
$717$		0			0
$718$	−12.5020	+	17.5259i	−0.466571	+	0.654062i
$719$	4.73921	+	14.5858i	0.176743	+	0.543958i	0.999709	−	0.0241324i	$-0.00768234\pi$
$719$	4.73921	+	14.5858i	0.176743	+	0.543958i	−0.822966	+	0.568091i	$0.807682\pi$
$720$		0			0
$721$	17.5992	−	54.1648i	0.655429	−	2.01720i
$722$	−13.0070	−	17.5792i	−0.484071	−	0.654231i
$723$		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	$-0.462897\pi$
$727$	−2.15735	−	0.341691i	−0.0800117	−	0.0126726i	−0.196312	+	0.980541i	$0.562897\pi$
$728$	28.2811	+	19.4413i	1.04817	+	0.720541i
$729$		0			0
$730$	4.94481	−	40.0163i	0.183016	−	1.48107i
$731$	26.9474	−	8.75575i	0.996687	−	0.323843i
$732$		0			0
$733$	6.40810	−	12.5766i	0.236689	−	0.464528i	−0.741857	−	0.670558i	$-0.766055\pi$
$733$	6.40810	−	12.5766i	0.236689	−	0.464528i	0.978546	+	0.206031i	$0.0660546\pi$
$734$	−30.3422	−	15.1293i	−1.11995	−	0.558434i
$735$		0			0
$736$	0.438458	+	0.0500308i	0.0161618	+	0.00184416i
$737$	32.2036	−	5.10055i	1.18623	−	0.187881i
$738$		0			0
$739$	14.6312	−	10.6302i	0.538218	−	0.391039i	−0.285205	−	0.958467i	$-0.592062\pi$
$739$	14.6312	−	10.6302i	0.538218	−	0.391039i	0.823423	+	0.567428i	$0.192062\pi$
$740$	22.6490	−	4.58895i	0.832592	−	0.168693i
$741$		0			0
$742$	16.0378	−	50.8594i	0.588766	−	1.86711i
$743$	9.25021	−	9.25021i	0.339357	−	0.339357i	−0.516768	−	0.856125i	$-0.672865\pi$
$743$	9.25021	−	9.25021i	0.339357	−	0.339357i	0.856125	+	0.516768i	$0.172865\pi$
$744$		0			0
$745$	−0.0945482	−	3.71571i	−0.00346398	−	0.136133i
$746$	−4.53503	+	30.3376i	−0.166039	+	1.11074i
$747$		0			0
$748$	−5.37791	−	30.5116i	−0.196636	−	1.11562i
$749$			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	$-0.154944\pi$
$752$	−45.3543	+	25.1323i	−1.65390	+	0.916482i
$753$		0			0
$754$	4.11487	+	0.615113i	0.149855	+	0.0224011i
$755$	−0.808572	−	31.7766i	−0.0294270	−	1.15647i
$756$		0			0
$757$	24.1240	−	24.1240i	0.876803	−	0.876803i	−0.116400	−	0.993202i	$-0.537135\pi$
$757$	24.1240	−	24.1240i	0.876803	−	0.876803i	0.993202	+	0.116400i	$0.0371353\pi$
$758$	8.01249	+	2.52663i	0.291027	+	0.0917712i
$759$		0			0
$760$	−34.6736	+	13.2765i	−1.25774	+	0.481589i
$761$	−10.8763	+	7.90212i	−0.394267	+	0.286452i	−0.767202	−	0.641406i	$-0.778352\pi$
$761$	−10.8763	+	7.90212i	−0.394267	+	0.286452i	0.372935	+	0.927858i	$0.378352\pi$
$762$		0			0
$763$	28.7548	−	4.55431i	1.04099	−	0.164877i
$764$	−1.51973	+	2.17008i	−0.0549818	+	0.0785109i
$765$		0			0
$766$	−2.92190	+	5.85992i	−0.105572	+	0.211728i
$767$	−13.8415	+	27.1656i	−0.499789	+	0.980891i
$768$		0			0
$769$	37.1381	−	12.0669i	1.33924	−	0.435144i	0.450178	−	0.892939i	$-0.351361\pi$
$769$	37.1381	−	12.0669i	1.33924	−	0.435144i	0.889058	+	0.457795i	$0.151361\pi$
$770$	−38.9006	−	4.80694i	−1.40188	−	0.173230i
$771$		0			0
$772$	16.8489	+	16.2730i	0.606404	+	0.585677i
$773$	19.5920	+	3.10306i	0.704674	+	0.111609i	0.498479	−	0.866902i	$-0.333892\pi$
$773$	19.5920	+	3.10306i	0.704674	+	0.111609i	0.206195	+	0.978511i	$0.433892\pi$
$774$		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
$778$	−10.8615	+	8.03655i	−0.389405	+	0.288124i
$779$	−9.48730	+	29.1989i	−0.339918	+	1.04616i
$780$		0			0
$781$	−2.29117	−	7.05150i	−0.0819845	−	0.252322i
$782$	0.393217	+	0.280499i	0.0140614	+	0.0100306i
$783$		0			0
$784$	0.733034	+	21.0728i	0.0261798	+	0.752599i
$785$	22.5154	−	23.6911i	0.803608	−	0.845573i
$786$		0			0
$787$	2.45311	+	15.4883i	0.0874439	+	0.552099i	0.992049	+	0.125849i	$0.0401655\pi$
$787$	2.45311	+	15.4883i	0.0874439	+	0.552099i	−0.904606	+	0.426250i	$0.859834\pi$
$788$	15.6566	+	29.4506i	0.557744	+	1.04913i
$789$		0			0
$790$	5.99035	+	1.72272i	0.213127	+	0.0612917i
$791$	−27.3549	+	37.6508i	−0.972629	+	1.33871i
$792$		0			0
$793$	−24.7363	−	24.7363i	−0.878411	−	0.878411i
$794$	−26.5161	+	13.8022i	−0.941020	+	0.489824i
$795$		0			0
$796$	−37.4512	+	0.651188i	−1.32742	+	0.0230808i
$797$	−8.18837	−	16.0706i	−0.290047	−	0.569249i	0.699300	−	0.714829i	$-0.253495\pi$
$797$	−8.18837	−	16.0706i	−0.290047	−	0.569249i	−0.989347	+	0.145580i	$0.953495\pi$
$798$		0			0
$799$	−56.7527			−2.00777
$800$	2.66452	+	28.1585i	0.0942049	+	0.995553i
$801$		0			0
$802$	−0.206200	−	23.7197i	−0.00728116	−	0.837572i
$803$	20.4821	+	40.1984i	0.722797	+	1.41857i
$804$		0			0
$805$	0.485073	−	0.371639i	0.0170966	−	0.0130986i
$806$	0.000563467	0	0.000293298i	1.98473e−5	0	1.03310e-5i
$807$		0			0
$808$	0.410992	+	15.7560i	0.0144586	+	0.554294i
$809$	19.5336	−	26.8857i	0.686765	−	0.945251i	−0.313225	−	0.949679i	$-0.601409\pi$
$809$	19.5336	−	26.8857i	0.686765	−	0.945251i	0.999990	+	0.00442775i	$0.00140940\pi$
$810$		0			0
$811$	6.93113	+	9.53989i	0.243385	+	0.334991i	0.913181	−	0.407555i	$-0.133618\pi$
$811$	6.93113	+	9.53989i	0.243385	+	0.334991i	−0.669796	+	0.742545i	$0.733618\pi$
$812$	2.79338	+	5.25444i	0.0980284	+	0.184395i
$813$		0			0
$814$	−18.1243	+	18.4422i	−0.635256	+	0.646397i
$815$	52.5027	−	9.69062i	1.83909	−	0.339448i
$816$		0			0
$817$	33.8524	+	17.2487i	1.18435	+	0.603454i
$818$	−12.6142	−	8.99827i	−0.441046	−	0.314617i
$819$		0			0
$820$	19.4927	+	12.9246i	0.680716	+	0.451347i
$821$	10.4922	−	32.2916i	0.366180	−	1.12699i	−0.583059	−	0.812430i	$-0.698144\pi$
$821$	10.4922	−	32.2916i	0.366180	−	1.12699i	0.949239	−	0.314556i	$-0.101856\pi$
$822$		0			0
$823$	1.35624	−	8.56297i	0.0472756	−	0.298486i	−0.952710	−	0.303881i	$-0.901717\pi$
$823$	1.35624	−	8.56297i	0.0472756	−	0.298486i	0.999985	+	0.00539505i	$0.00171731\pi$
$824$	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	$-0.412076\pi$
$827$	6.75206	+	1.06942i	0.234792	+	0.0371874i	−0.0379294	+	0.999280i	$0.512076\pi$
$828$		0			0
$829$	−1.59946	−	0.519697i	−0.0555516	−	0.0180498i	0.281109	−	0.959676i	$-0.409298\pi$
$829$	−1.59946	−	0.519697i	−0.0555516	−	0.0180498i	−0.336661	+	0.941626i	$0.609298\pi$
$830$	21.7586	−	46.5674i	0.755253	−	1.61638i
$831$		0			0
$832$	5.75568	+	27.1053i	0.199542	+	0.939707i
$833$	−10.4773	+	20.5629i	−0.363018	+	0.712463i
$834$		0			0
$835$	8.28861	−	17.3444i	0.286839	−	0.600228i
$836$	23.8309	−	34.0291i	0.824207	−	1.17692i
$837$		0			0
$838$	−25.3248	+	8.47261i	−0.874830	+	0.292681i
$839$	32.2588	−	23.4374i	1.11370	−	0.809148i	0.130455	−	0.991454i	$-0.458356\pi$
$839$	32.2588	−	23.4374i	1.11370	−	0.809148i	0.983242	+	0.182307i	$0.0583563\pi$
$840$		0			0
$841$	−22.8778	−	16.6217i	−0.788891	−	0.573163i
$842$	18.2713	+	5.76160i	0.629672	+	0.198558i
$843$		0			0
$844$	19.5325	+	25.9242i	0.672338	+	0.892347i
$845$	−2.11415	+	0.746900i	−0.0727290	+	0.0256941i
$846$		0			0
$847$	4.74385	−	2.41711i	0.163000	−	0.0830529i
$848$	37.6622	−	20.8699i	1.29333	−	0.716675i
$849$		0			0
$850$	−12.3872	+	28.3711i	−0.424877	+	0.973120i
$851$		−	0.403117i		−	0.0138187i
$852$		0			0
$853$	−11.5438	+	5.88186i	−0.395252	+	0.201391i	−0.640309	−	0.768118i	$-0.721194\pi$
$853$	−11.5438	+	5.88186i	−0.395252	+	0.201391i	0.245056	+	0.969509i	$0.421194\pi$
$854$	7.39725	−	49.4847i	0.253129	−	1.69333i
$855$		0			0
$856$	−2.07936	+	2.19074i	−0.0710710	+	0.0748780i
$857$	11.9042	−	11.9042i	0.406640	−	0.406640i	−0.473925	−	0.880565i	$-0.657163\pi$
$857$	11.9042	−	11.9042i	0.406640	−	0.406640i	0.880565	+	0.473925i	$0.157163\pi$
$858$		0			0
$859$	28.2976	+	20.5594i	0.965502	+	0.701478i	0.954422	−	0.298460i	$-0.0964730\pi$
$859$	28.2976	+	20.5594i	0.965502	+	0.701478i	0.0110802	+	0.999939i	$0.496473\pi$
$860$	19.5710	−	21.3234i	0.667365	−	0.727121i
$861$		0			0
$862$	−4.21093	−	12.5865i	−0.143425	−	0.428699i
$863$	−27.6579	+	4.38058i	−0.941485	+	0.149117i	−0.608266	−	0.793733i	$-0.708135\pi$
$863$	−27.6579	+	4.38058i	−0.941485	+	0.149117i	−0.333219	+	0.942850i	$0.608135\pi$
$864$		0			0
$865$	−54.6638	−	7.23778i	−1.85863	−	0.246092i
$866$	−36.9754	−	18.4368i	−1.25647	−	0.626508i
$867$		0			0
$868$	0.000816580	0	0.000398341i	2.77165e−5	0	1.35206e-5i
$869$	−6.63305	+	2.15521i	−0.225011	+	0.0731105i
$870$		0			0
$871$	−30.3551	−	9.86297i	−1.02854	−	0.334194i
$872$	19.3710	+	13.3162i	0.655985	+	0.450944i
$873$		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	−0.994158	−	0.107934i	$-0.965577\pi$
$877$	−0.453223	+	2.86154i	−0.0153043	+	0.0966273i	0.978854	+	0.204561i	$0.0655766\pi$
$878$	−8.70536	−	11.7654i	−0.293792	−	0.397065i
$879$		0			0
$880$	−20.1092	−	24.4379i	−0.677880	−	0.823801i
$881$	13.8508	+	42.6283i	0.466645	+	1.43619i	0.856902	+	0.515479i	$0.172386\pi$
$881$	13.8508	+	42.6283i	0.466645	+	1.43619i	−0.390257	+	0.920706i	$0.627614\pi$
$882$		0			0
$883$	−24.6083	−	12.5385i	−0.828134	−	0.421955i	−0.0120772	−	0.999927i	$-0.503844\pi$
$883$	−24.6083	−	12.5385i	−0.828134	−	0.421955i	−0.816057	+	0.577972i	$0.803844\pi$
$884$	−8.86914	+	29.0026i	−0.298301	+	0.975465i
$885$		0			0
$886$	−1.74615	−	1.71605i	−0.0586630	−	0.0576518i
$887$	−5.07182	−	32.0222i	−0.170295	−	1.07520i	−0.913709	−	0.406369i	$-0.866795\pi$
$887$	−5.07182	−	32.0222i	−0.170295	−	1.07520i	0.743414	−	0.668831i	$-0.233205\pi$
$888$		0			0
$889$	−29.0257	−	39.9504i	−0.973489	−	1.33989i
$890$	14.8227	−	11.5623i	0.496858	−	0.387569i
$891$		0			0
$892$	−3.72104	+	26.4636i	−0.124590	+	0.886068i
$893$	−53.8107	−	53.8107i	−1.80071	−	1.80071i
$894$		0			0
$895$	5.95415	−	20.0464i	0.199025	−	0.670077i
$896$	−26.2683	+	29.6768i	−0.877562	+	0.991433i
$897$		0			0
$898$	−50.9966	+	0.443323i	−1.70178	+	0.0147939i
$899$	0.000110148	0		3.67363e−6	0
$900$		0			0
$901$	47.1274			1.57004
$902$	−26.1687	+	0.227489i	−0.871321	+	0.00757455i
$903$		0			0
$904$	−36.9479	+	6.84402i	−1.22887	+	0.227629i
$905$	2.74210	+	7.76170i	0.0911506	+	0.258008i
$906$		0			0
$907$	−11.7557	−	11.7557i	−0.390343	−	0.390343i	0.484467	−	0.874810i	$-0.339014\pi$
$907$	−11.7557	−	11.7557i	−0.390343	−	0.390343i	−0.874810	+	0.484467i	$0.839014\pi$
$908$	−43.8841	−	6.17052i	−1.45634	−	0.204776i
$909$		0			0
$910$	31.7933	+	21.4806i	1.05394	+	0.712076i
$911$	9.75815	+	13.4309i	0.323302	+	0.444987i	0.939472	−	0.342626i	$-0.111316\pi$
$911$	9.75815	+	13.4309i	0.323302	+	0.444987i	−0.616170	+	0.787613i	$0.711316\pi$
$912$		0			0
$913$	8.99696	+	56.8046i	0.297756	+	1.87996i
$914$	−3.16936	−	3.11473i	−0.104833	−	0.103026i
$915$		0			0
$916$	−42.2668	−	12.9254i	−1.39653	−	0.427066i
$917$	−31.9459	−	16.2772i	−1.05495	−	0.537522i
$918$		0			0
$919$	−6.92595	−	21.3159i	−0.228466	−	0.703146i	−0.997921	−	0.0644452i	$-0.979472\pi$
$919$	−6.92595	−	21.3159i	−0.228466	−	0.703146i	0.769455	−	0.638701i	$-0.220528\pi$
$920$	0.490646	+	0.0519861i	0.0161761	+	0.00171393i
$921$		0			0
$922$	−21.9155	−	29.6191i	−0.721748	−	0.975455i
$923$	−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
$928$	−1.28480	+	4.62982i	−0.0421757	+	0.151981i
$929$	−8.61163	−	2.79809i	−0.282539	−	0.0918023i	0.164320	−	0.986407i	$-0.447457\pi$
$929$	−8.61163	−	2.79809i	−0.282539	−	0.0918023i	−0.446858	+	0.894605i	$0.647457\pi$
$930$		0			0
$931$	−29.4312	+	9.56277i	−0.964568	+	0.313407i
$932$	13.4022	−	27.4738i	0.439003	−	0.899936i
$933$		0			0
$934$	48.2497	+	24.0585i	1.57878	+	0.787217i
$935$	−6.28724	−	34.0635i	−0.205615	−	1.11400i
$936$		0			0
$937$	50.3586	−	7.97602i	1.64514	−	0.260565i	0.735980	−	0.677004i	$-0.236722\pi$
$937$	50.3586	−	7.97602i	1.64514	−	0.260565i	0.909164	+	0.416438i	$0.136722\pi$
$938$	−14.4837	−	43.2920i	−0.472909	−	1.41353i
$939$		0			0
$940$	−50.4797	+	28.5063i	−1.64647	+	0.929773i
$941$	25.8577	+	18.7867i	0.842937	+	0.612429i	0.923189	−	0.384345i	$-0.125573\pi$
$941$	25.8577	+	18.7867i	0.842937	+	0.612429i	−0.0802527	+	0.996775i	$0.525573\pi$
$942$		0			0
$943$	0.288490	−	0.288490i	0.00939452	−	0.00939452i
$944$	−29.1871	−	19.6927i	−0.949960	−	0.640943i
$945$		0			0
$946$	−4.78791	+	32.0293i	−0.155669	+	1.04136i
$947$	2.86881	−	1.46173i	0.0932239	−	0.0474999i	−0.406757	−	0.913536i	$-0.633340\pi$
$947$	2.86881	−	1.46173i	0.0932239	−	0.0474999i	0.499981	+	0.866036i	$0.333340\pi$
$948$		0			0
$949$		−	44.1640i		−	1.43363i
$950$	−38.6454	+	15.1553i	−1.25382	+	0.491703i
$951$		0			0
$952$	−40.8915	+	14.4758i	−1.32530	+	0.469163i
$953$	−28.9987	+	14.7756i	−0.939360	+	0.478628i	−0.855473	−	0.517848i	$-0.826733\pi$
$953$	−28.9987	+	14.7756i	−0.939360	+	0.478628i	−0.0838869	+	0.996475i	$0.526733\pi$
$954$		0			0
$955$	−1.67951	+	2.43983i	−0.0543477	+	0.0789511i
$956$	3.28835	−	2.47761i	0.106353	−	0.0801315i
$957$		0			0
$958$	8.82278	+	2.78214i	0.285051	+	0.0898868i
$959$	7.48771	+	5.44014i	0.241791	+	0.175671i
$960$		0			0
$961$	−25.0795	+	18.2213i	−0.809017	+	0.587785i
$962$	24.0042	−	8.03079i	0.773926	−	0.258923i
$963$		0			0
$964$	−32.5561	−	22.7993i	−1.04856	−	0.734316i
$965$	18.9835	+	18.0414i	0.611102	+	0.580774i
$966$		0			0
$967$	6.18287	−	12.1346i	0.198828	−	0.390221i	−0.769968	−	0.638083i	$-0.779728\pi$
$967$	6.18287	−	12.1346i	0.198828	−	0.390221i	0.968796	+	0.247861i	$0.0797277\pi$
$968$	4.12166	+	1.22134i	0.132475	+	0.0392555i
$969$		0			0
$970$	−10.5035	+	5.81154i	−0.337246	+	0.186597i
$971$	−21.7239	−	7.05851i	−0.697152	−	0.226518i	−0.0610628	−	0.998134i	$-0.519449\pi$
$971$	−21.7239	−	7.05851i	−0.697152	−	0.226518i	−0.636089	+	0.771616i	$0.719449\pi$
$972$		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	0.948702	+	0.316171i	$0.102397\pi$
$977$	−1.60253	+	10.1180i	−0.0512695	+	0.323703i	−0.999972	+	0.00753150i	$0.997603\pi$
$978$		0			0
$979$	−6.50003	+	20.0050i	−0.207742	+	0.639363i
$980$	1.00928	+	23.5527i	0.0322404	+	0.752364i
$981$		0			0
$982$	2.97464	+	2.12194i	0.0949246	+	0.0677139i
$983$	−31.8803	−	16.2438i	−1.01682	−	0.518097i	−0.135583	−	0.990766i	$-0.543291\pi$
$983$	−31.8803	−	16.2438i	−1.01682	−	0.518097i	−0.881240	+	0.472669i	$0.843291\pi$
$984$		0			0
$985$	17.7692	+	32.7847i	0.566175	+	1.04461i
$986$	−3.68613	+	3.75078i	−0.117390	+	0.119449i
$987$		0			0
$988$	−35.9086	+	19.0898i	−1.14240	+	0.607328i
$989$	−0.296765	−	0.408462i	−0.00943657	−	0.0129883i
$990$		0			0
$991$	17.5929	−	24.2146i	0.558858	−	0.769202i	−0.432323	−	0.901719i	$-0.642306\pi$
$991$	17.5929	−	24.2146i	0.558858	−	0.769202i	0.991181	+	0.132517i	$0.0423059\pi$
$992$	0.000256792	0	0.000687173i	8.15314e−6	0	2.18178e-5i
$993$		0			0
$994$	−9.20817	+	4.79308i	−0.292066	+	0.152027i
$995$	−41.8645	+	1.06526i	−1.32719	+	0.0337711i
$996$		0			0
$997$	−18.8432	−	36.9818i	−0.596769	−	1.17123i	−0.969913	−	0.243452i	$-0.921720\pi$
$997$	−18.8432	−	36.9818i	−0.596769	−	1.17123i	0.373144	−	0.927773i	$-0.378280\pi$
$998$	0.0174386	+	2.00601i	0.000552008	+	0.0634990i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.16	✓	240	300.287	odd	20
300.2.w.a.187.19	yes	240	75.62	even	20
300.2.w.a.223.16	yes	240	3.2	odd	2
300.2.w.a.223.19	yes	240	12.11	even	2
900.2.bj.f.487.12		240	25.12	odd	20	inner
900.2.bj.f.487.15		240	100.87	even	20	inner
900.2.bj.f.523.12		240	4.3	odd	2	inner
900.2.bj.f.523.15		240	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.0122935 + 1.41416i) q^{2} +(-1.99970 + 0.0347701i) q^{4} +(-2.23534 + 0.0568795i) q^{5} +(-2.47703 - 2.47703i) q^{7} +(-0.0737538 - 2.82747i) q^{8} +O(q^{10})\)	\(q+(0.0122935 + 1.41416i) q^{2} +(-1.99970 + 0.0347701i) q^{4} +(-2.23534 + 0.0568795i) q^{5} +(-2.47703 - 2.47703i) q^{7} +(-0.0737538 - 2.82747i) q^{8} +(-0.107917 - 3.16044i) q^{10} +(2.07978 + 2.86258i) q^{11} +(-0.541843 - 3.42106i) q^{13} +(3.47247 - 3.53337i) q^{14} +(3.99758 - 0.139059i) q^{16} +(3.90086 + 1.98759i) q^{17} +(1.81409 + 5.58320i) q^{19} +(4.46804 - 0.191465i) q^{20} +(-4.02258 + 2.97634i) q^{22} +(0.0122038 - 0.0770517i) q^{23} +(4.99353 - 0.254291i) q^{25} +(4.83127 - 0.808310i) q^{26} +(5.03944 + 4.86719i) q^{28} +(0.807803 + 0.262471i) q^{29} +(0.000123334 - 4.00736e-5i) q^{31} +(0.245797 + 5.65151i) q^{32} +(-2.76281 + 5.54087i) q^{34} +(5.67791 + 5.39613i) q^{35} +(5.10375 - 0.808354i) q^{37} +(-7.87324 + 2.63405i) q^{38} +(0.325690 + 6.31616i) q^{40} +(4.23098 + 3.07399i) q^{41} +(4.57632 - 4.57632i) q^{43} +(-4.25847 - 5.65198i) q^{44} +(0.109113 + 0.0163109i) q^{46} +(-11.5502 + 5.88510i) q^{47} +5.27138i q^{49} +(0.420996 + 7.05852i) q^{50} +(1.20247 + 6.82225i) q^{52} +(9.59125 - 4.88699i) q^{53} +(-4.81186 - 6.28055i) q^{55} +(-6.82103 + 7.18641i) q^{56} +(-0.361245 + 1.14559i) q^{58} +(-7.12122 - 5.17387i) q^{59} +(8.17083 - 5.93646i) q^{61} +(5.81867e-5 + 0.000173921i) q^{62} +(-7.98912 + 0.417073i) q^{64} +(1.40579 + 7.61643i) q^{65} +(4.18342 - 8.21042i) q^{67} +(-7.86965 - 3.83894i) q^{68} +(-7.56119 + 8.09582i) q^{70} +(-1.99288 - 0.647527i) q^{71} +(12.5935 + 1.99462i) q^{73} +(1.20589 + 7.20758i) q^{74} +(-3.82176 - 11.1016i) q^{76} +(1.93900 - 12.2424i) q^{77} +(-0.609102 + 1.87462i) q^{79} +(-8.92806 + 0.538226i) q^{80} +(-4.29510 + 6.02107i) q^{82} +(14.4825 + 7.37922i) q^{83} +(-8.83282 - 4.22106i) q^{85} +(6.52791 + 6.41539i) q^{86} +(7.94045 - 6.09165i) q^{88} +(3.49423 + 4.80940i) q^{89} +(-7.13192 + 9.81624i) q^{91} +(-0.0217248 + 0.154504i) q^{92} +(-8.46447 - 16.2614i) q^{94} +(-4.37269 - 12.3772i) q^{95} +(-1.72335 - 3.38227i) q^{97} +(-7.45458 + 0.0648039i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 240 * q - 12 * q^8	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) \) 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

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