LMFDB - Embedded newform 600.2.w.j.293.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(293,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("600.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			293.6
Character	$\chi$	$=$	600.293
Dual form			600.2.w.j.557.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.533177 + 1.30986i) q^{2} +(-1.59834 + 0.667305i) q^{3} +(-1.43144 - 1.39677i) q^{4} +(-0.0218716 - 2.44939i) q^{6} +(-0.582772 + 0.582772i) q^{7} +(2.59278 - 1.13026i) q^{8} +(2.10941 - 2.13317i) q^{9} +O(q^{10})$	\(q+(-0.533177 + 1.30986i) q^{2} +(-1.59834 + 0.667305i) q^{3} +(-1.43144 - 1.39677i) q^{4} +(-0.0218716 - 2.44939i) q^{6} +(-0.582772 + 0.582772i) q^{7} +(2.59278 - 1.13026i) q^{8} +(2.10941 - 2.13317i) q^{9} -3.68607 q^{11} +(3.22001 + 1.27731i) q^{12} +(3.88771 - 3.88771i) q^{13} +(-0.452626 - 1.07407i) q^{14} +(0.0980619 + 3.99880i) q^{16} +(0.880105 + 0.880105i) q^{17} +(1.66945 + 3.90038i) q^{18} +6.32919 q^{19} +(0.542584 - 1.32036i) q^{21} +(1.96533 - 4.82821i) q^{22} +(-2.06626 + 2.06626i) q^{23} +(-3.38993 + 3.53672i) q^{24} +(3.01950 + 7.16518i) q^{26} +(-1.94809 + 4.81715i) q^{27} +(1.64820 - 0.0202063i) q^{28} +1.37122i q^{29} +3.32075 q^{31} +(-5.29013 - 2.00362i) q^{32} +(5.89160 - 2.45973i) q^{33} +(-1.62206 + 0.683558i) q^{34} +(-5.99904 + 0.107144i) q^{36} +(2.44147 + 2.44147i) q^{37} +(-3.37458 + 8.29032i) q^{38} +(-3.61961 + 8.80819i) q^{39} +0.648104i q^{41} +(1.44018 + 1.41469i) q^{42} +(0.819412 - 0.819412i) q^{43} +(5.27640 + 5.14859i) q^{44} +(-1.60482 - 3.80818i) q^{46} +(6.28508 + 6.28508i) q^{47} +(-2.82515 - 6.32602i) q^{48} +6.32075i q^{49} +(-1.99401 - 0.819412i) q^{51} +(-10.9953 + 0.134798i) q^{52} +(5.60782 + 5.60782i) q^{53} +(-5.27109 - 5.12011i) q^{54} +(-0.852318 + 2.16968i) q^{56} +(-10.1162 + 4.22349i) q^{57} +(-1.79611 - 0.731106i) q^{58} -6.12026i q^{59} -5.13471i q^{61} +(-1.77055 + 4.34971i) q^{62} +(0.0138443 + 2.47245i) q^{63} +(5.44503 - 5.86102i) q^{64} +(0.0806201 + 9.02862i) q^{66} +(4.90636 + 4.90636i) q^{67} +(-0.0305156 - 2.48912i) q^{68} +(1.92377 - 4.68141i) q^{69} +4.13251i q^{71} +(3.05821 - 7.91501i) q^{72} +(-4.69820 - 4.69820i) q^{73} +(-4.49972 + 1.89624i) q^{74} +(-9.05987 - 8.84042i) q^{76} +(2.14814 - 2.14814i) q^{77} +(-9.60756 - 9.43750i) q^{78} -1.10079i q^{79} +(-0.100786 - 8.99944i) q^{81} +(-0.848922 - 0.345554i) q^{82} +(-6.27439 - 6.27439i) q^{83} +(-2.62091 + 1.13215i) q^{84} +(0.636420 + 1.51020i) q^{86} +(-0.915024 - 2.19169i) q^{87} +(-9.55717 + 4.16621i) q^{88} +15.3562 q^{89} +4.53130i q^{91} +(5.84382 - 0.0716428i) q^{92} +(-5.30771 + 2.21595i) q^{93} +(-11.5836 + 4.88148i) q^{94} +(9.79248 - 0.327652i) q^{96} +(5.42154 - 5.42154i) q^{97} +(-8.27927 - 3.37008i) q^{98} +(-7.77542 + 7.86299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{6}+O(q^{10}) $ 32 * q - 4 * q^6	$ 32 q - 4 q^{6} + 8 q^{12} + 28 q^{16} + 20 q^{18} + 52 q^{22} - 12 q^{28} - 32 q^{31} - 8 q^{33} - 20 q^{36} - 16 q^{42} + 24 q^{46} - 44 q^{48} - 8 q^{52} + 16 q^{57} - 28 q^{58} - 48 q^{63} + 16 q^{66} - 32 q^{72} + 64 q^{73} - 88 q^{76} - 64 q^{78} + 48 q^{81} - 64 q^{82} + 8 q^{87} + 52 q^{88} - 52 q^{96} - 16 q^{97}+O(q^{100}) $ 32 * q - 4 * q^6 + 8 * q^12 + 28 * q^16 + 20 * q^18 + 52 * q^22 - 12 * q^28 - 32 * q^31 - 8 * q^33 - 20 * q^36 - 16 * q^42 + 24 * q^46 - 44 * q^48 - 8 * q^52 + 16 * q^57 - 28 * q^58 - 48 * q^63 + 16 * q^66 - 32 * q^72 + 64 * q^73 - 88 * q^76 - 64 * q^78 + 48 * q^81 - 64 * q^82 + 8 * q^87 + 52 * q^88 - 52 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.533177	+	1.30986i	−0.377013	+	0.926208i
$2$	−0.533177	+	1.30986i	−0.377013	+	0.926208i
$3$	−1.59834	+	0.667305i	−0.922805	+	0.385268i
$3$	−1.59834	+	0.667305i	−0.922805	+	0.385268i
$4$	−1.43144	−	1.39677i	−0.715722	−	0.698385i
$5$		0			0
$5$		0			0
$6$	−0.0218716	−	2.44939i	−0.00892904	−	0.999960i
$7$	−0.582772	+	0.582772i	−0.220267	+	0.220267i	−0.808611	−	0.588344i	$-0.799780\pi$
$7$	−0.582772	+	0.582772i	−0.220267	+	0.220267i	0.588344	+	0.808611i	$0.299780\pi$
$8$	2.59278	−	1.13026i	0.916687	−	0.399606i
$9$	2.10941	−	2.13317i	0.703136	−	0.711055i
$10$		0			0
$11$	−3.68607			−1.11139			−0.555695	−	0.831386i	$-0.687548\pi$
$11$	−3.68607			−1.11139			−0.555695	+	0.831386i	$0.687548\pi$
$12$	3.22001	+	1.27731i	0.929537	+	0.368728i
$13$	3.88771	−	3.88771i	1.07826	−	1.07826i	0.0815911	−	0.996666i	$-0.474000\pi$
$13$	3.88771	−	3.88771i	1.07826	−	1.07826i	0.996666	−	0.0815911i	$-0.0260002\pi$
$14$	−0.452626	−	1.07407i	−0.120969	−	0.287057i
$15$		0			0
$16$	0.0980619	+	3.99880i	0.0245155	+	0.999699i
$17$	0.880105	+	0.880105i	0.213457	+	0.213457i	0.805734	−	0.592277i	$-0.201771\pi$
$17$	0.880105	+	0.880105i	0.213457	+	0.213457i	−0.592277	+	0.805734i	$0.701771\pi$
$18$	1.66945	+	3.90038i	0.393493	+	0.919328i
$19$	6.32919			1.45201			0.726007	−	0.687687i	$-0.241374\pi$
$19$	6.32919			1.45201			0.726007	+	0.687687i	$0.241374\pi$
$20$		0			0
$21$	0.542584	−	1.32036i	0.118402	−	0.288125i
$22$	1.96533	−	4.82821i	0.419009	−	1.02938i
$23$	−2.06626	+	2.06626i	−0.430844	+	0.430844i	−0.888916	−	0.458071i	$-0.848540\pi$
$23$	−2.06626	+	2.06626i	−0.430844	+	0.430844i	0.458071	+	0.888916i	$0.348540\pi$
$24$	−3.38993	+	3.53672i	−0.691967	+	0.721929i
$25$		0			0
$26$	3.01950	+	7.16518i	0.592173	+	1.40521i
$27$	−1.94809	+	4.81715i	−0.374910	+	0.927061i
$28$	1.64820	−	0.0202063i	0.311481	−	0.00381863i
$29$			1.37122i			0.254630i	0.991862	+	0.127315i	$0.0406359\pi$
$29$			1.37122i			0.254630i	−0.991862	+	0.127315i	$0.959364\pi$
$30$		0			0
$31$	3.32075			0.596425			0.298212	−	0.954500i	$-0.403610\pi$
$31$	3.32075			0.596425			0.298212	+	0.954500i	$0.403610\pi$
$32$	−5.29013	−	2.00362i	−0.935172	−	0.354194i
$33$	5.89160	−	2.45973i	1.02560	−	0.428184i
$34$	−1.62206	+	0.683558i	−0.278181	+	0.117229i
$35$		0			0
$36$	−5.99904	+	0.107144i	−0.999841	+	0.0178574i
$37$	2.44147	+	2.44147i	0.401376	+	0.401376i	0.878718	−	0.477342i	$-0.158400\pi$
$37$	2.44147	+	2.44147i	0.401376	+	0.401376i	−0.477342	+	0.878718i	$0.658400\pi$
$38$	−3.37458	+	8.29032i	−0.547429	+	1.34487i
$39$	−3.61961	+	8.80819i	−0.579602	+	1.41044i
$40$		0			0
$41$			0.648104i			0.101217i	0.998719	+	0.0506084i	$0.0161160\pi$
$41$			0.648104i			0.101217i	−0.998719	+	0.0506084i	$0.983884\pi$
$42$	1.44018	+	1.41469i	0.222225	+	0.218292i
$43$	0.819412	−	0.819412i	0.124959	−	0.124959i	−0.641861	−	0.766821i	$-0.721838\pi$
$43$	0.819412	−	0.819412i	0.124959	−	0.124959i	0.766821	+	0.641861i	$0.221838\pi$
$44$	5.27640	+	5.14859i	0.795447	+	0.776179i
$45$		0			0
$46$	−1.60482	−	3.80818i	−0.236617	−	0.561485i
$47$	6.28508	+	6.28508i	0.916772	+	0.916772i	0.996793	−	0.0800208i	$-0.0254987\pi$
$47$	6.28508	+	6.28508i	0.916772	+	0.916772i	−0.0800208	+	0.996793i	$0.525499\pi$
$48$	−2.82515	−	6.32602i	−0.407776	−	0.913082i
$49$			6.32075i			0.902965i
$50$		0			0
$51$	−1.99401	−	0.819412i	−0.279217	−	0.114741i
$52$	−10.9953	+	0.134798i	−1.52477	+	0.0186931i
$53$	5.60782	+	5.60782i	0.770293	+	0.770293i	0.978158	−	0.207864i	$-0.0666512\pi$
$53$	5.60782	+	5.60782i	0.770293	+	0.770293i	−0.207864	+	0.978158i	$0.566651\pi$
$54$	−5.27109	−	5.12011i	−0.717305	−	0.696759i
$55$		0			0
$56$	−0.852318	+	2.16968i	−0.113896	+	0.289936i
$57$	−10.1162	+	4.22349i	−1.33993	+	0.559415i
$58$	−1.79611	−	0.731106i	−0.235840	−	0.0959989i
$59$		−	6.12026i		−	0.796790i	−0.917214	−	0.398395i	$-0.869567\pi$
$59$		−	6.12026i		−	0.796790i	0.917214	−	0.398395i	$-0.130433\pi$
$60$		0			0
$61$		−	5.13471i		−	0.657432i	−0.944429	−	0.328716i	$-0.893384\pi$
$61$		−	5.13471i		−	0.657432i	0.944429	−	0.328716i	$-0.106616\pi$
$62$	−1.77055	+	4.34971i	−0.224860	+	0.552413i
$63$	0.0138443	+	2.47245i	0.00174421	+	0.311500i
$64$	5.44503	−	5.86102i	0.680629	−	0.732628i
$65$		0			0
$66$	0.0806201	+	9.02862i	0.00992365	+	1.11135i
$67$	4.90636	+	4.90636i	0.599408	+	0.599408i	0.940155	−	0.340747i	$-0.110680\pi$
$67$	4.90636	+	4.90636i	0.599408	+	0.599408i	−0.340747	+	0.940155i	$0.610680\pi$
$68$	−0.0305156	−	2.48912i	−0.00370056	−	0.301851i
$69$	1.92377	−	4.68141i	0.231594	−	0.563576i
$70$		0			0
$71$			4.13251i			0.490439i	0.969468	+	0.245220i	$0.0788601\pi$
$71$			4.13251i			0.490439i	−0.969468	+	0.245220i	$0.921140\pi$
$72$	3.05821	−	7.91501i	0.360414	−	0.932793i
$73$	−4.69820	−	4.69820i	−0.549883	−	0.549883i	0.376524	−	0.926407i	$-0.377119\pi$
$73$	−4.69820	−	4.69820i	−0.549883	−	0.549883i	−0.926407	+	0.376524i	$0.877119\pi$
$74$	−4.49972	+	1.89624i	−0.523082	+	0.220433i
$75$		0			0
$76$	−9.05987	−	8.84042i	−1.03924	−	1.01407i
$77$	2.14814	−	2.14814i	0.244803	−	0.244803i
$78$	−9.60756	−	9.43750i	−1.08784	−	1.06859i
$79$		−	1.10079i		−	0.123848i	−0.998081	−	0.0619241i	$-0.980276\pi$
$79$		−	1.10079i		−	0.123848i	0.998081	−	0.0619241i	$-0.0197237\pi$
$80$		0			0
$81$	−0.100786	−	8.99944i	−0.0111985	−	0.999937i
$82$	−0.848922	−	0.345554i	−0.0937478	−	0.0381601i
$83$	−6.27439	−	6.27439i	−0.688703	−	0.688703i	0.273242	−	0.961945i	$-0.411904\pi$
$83$	−6.27439	−	6.27439i	−0.688703	−	0.688703i	−0.961945	+	0.273242i	$0.911904\pi$
$84$	−2.62091	+	1.13215i	−0.285965	+	0.123528i
$85$		0			0
$86$	0.636420	+	1.51020i	0.0686269	+	0.162849i
$87$	−0.915024	−	2.19169i	−0.0981009	−	0.234974i
$88$	−9.55717	+	4.16621i	−1.01880	+	0.444119i
$89$	15.3562			1.62775			0.813875	−	0.581040i	$-0.197354\pi$
$89$	15.3562			1.62775			0.813875	+	0.581040i	$0.197354\pi$
$90$		0			0
$91$			4.53130i			0.475009i
$92$	5.84382	−	0.0716428i	0.609260	−	0.00746928i
$93$	−5.30771	+	2.21595i	−0.550384	+	0.229784i
$94$	−11.5836	+	4.88148i	−1.19476	+	0.503486i
$95$		0			0
$96$	9.79248	−	0.327652i	0.999441	−	0.0334409i
$97$	5.42154	−	5.42154i	0.550474	−	0.550474i	−0.376104	−	0.926578i	$-0.622736\pi$
$97$	5.42154	−	5.42154i	0.550474	−	0.550474i	0.926578	+	0.376104i	$0.122736\pi$
$98$	−8.27927	−	3.37008i	−0.836333	−	0.340430i
$99$	−7.77542	+	7.86299i	−0.781459	+	0.790260i
$100$		0			0
$101$	9.84442			0.979556			0.489778	−	0.871847i	$-0.337078\pi$
$101$	9.84442			0.979556			0.489778	+	0.871847i	$0.337078\pi$
$102$	2.13647	−	2.17497i	0.211542	−	0.215354i
$103$	8.28098	+	8.28098i	0.815949	+	0.815949i	0.985518	−	0.169569i	$-0.0542377\pi$
$103$	8.28098	+	8.28098i	0.815949	+	0.815949i	−0.169569	+	0.985518i	$0.554238\pi$
$104$	5.68587	−	14.4741i	0.557545	−	1.41930i
$105$		0			0
$106$	−10.3354	+	4.35547i	−1.00386	+	0.423041i
$107$	5.84678	−	5.84678i	0.565230	−	0.565230i	−0.365559	−	0.930788i	$-0.619122\pi$
$107$	5.84678	−	5.84678i	0.565230	−	0.565230i	0.930788	+	0.365559i	$0.119122\pi$
$108$	9.51704	−	4.17444i	0.915777	−	0.401686i
$109$	11.7033			1.12097			0.560487	−	0.828163i	$-0.310614\pi$
$109$	11.7033			1.12097			0.560487	+	0.828163i	$0.310614\pi$
$110$		0			0
$111$	−5.53152	−	2.27311i	−0.525029	−	0.215754i
$112$	−2.38754	−	2.27324i	−0.225601	−	0.214801i
$113$	8.58333	−	8.58333i	0.807452	−	0.807452i	−0.176796	−	0.984248i	$-0.556573\pi$
$113$	8.58333	−	8.58333i	0.807452	−	0.807452i	0.984248	+	0.176796i	$0.0565731\pi$
$114$	−0.138429	−	15.5027i	−0.0129651	−	1.45196i
$115$		0			0
$116$	1.91529	−	1.96283i	0.177830	−	0.182244i
$117$	−0.0923560	−	16.4939i	−0.00853832	−	1.52486i
$118$	8.01666	+	3.26318i	0.737993	+	0.300400i
$119$	−1.02580			−0.0940350
$120$		0			0
$121$	2.58708			0.235189
$122$	6.72573	+	2.73771i	0.608919	+	0.247861i
$123$	−0.432483	−	1.03589i	−0.0389956	−	0.0934033i
$124$	−4.75347	−	4.63833i	−0.426874	−	0.416535i
$125$		0			0
$126$	−3.24594	−	1.30012i	−0.289171	−	0.115824i
$127$	0.0146460	−	0.0146460i	0.00129962	−	0.00129962i	−0.706457	−	0.707756i	$-0.749707\pi$
$127$	0.0146460	−	0.0146460i	0.00129962	−	0.00129962i	0.707756	+	0.706457i	$0.249707\pi$
$128$	4.77393	+	10.2572i	0.421959	+	0.906615i
$129$	−0.762905	+	1.85650i	−0.0671701	+	0.163456i
$130$		0			0
$131$	5.23989			0.457811			0.228906	−	0.973449i	$-0.426485\pi$
$131$	5.23989			0.457811			0.228906	+	0.973449i	$0.426485\pi$
$132$	−11.8692	−	4.70826i	−1.03308	−	0.409801i
$133$	−3.68847	+	3.68847i	−0.319831	+	0.319831i
$134$	−9.04259	+	3.81066i	−0.781161	+	0.329191i
$135$		0			0
$136$	3.27666	+	1.28717i	0.280972	+	0.110374i
$137$	−14.0984	−	14.0984i	−1.20450	−	1.20450i	−0.972782	−	0.231722i	$-0.925564\pi$
$137$	−14.0984	−	14.0984i	−1.20450	−	1.20450i	−0.231722	−	0.972782i	$-0.574436\pi$
$138$	5.10627	+	5.01588i	0.434674	+	0.426980i
$139$	−9.22166			−0.782171			−0.391085	−	0.920354i	$-0.627900\pi$
$139$	−9.22166			−0.782171			−0.391085	+	0.920354i	$0.627900\pi$
$140$		0			0
$141$	−14.2398	−	5.85165i	−1.19921	−	0.492798i
$142$	−5.41300	−	2.20336i	−0.454249	−	0.184902i
$143$	−14.3304	+	14.3304i	−1.19836	+	1.19836i
$144$	8.73695	+	8.22592i	0.728079	+	0.685493i
$145$		0			0
$146$	8.65895	−	3.64899i	0.716619	−	0.301993i
$147$	−4.21787	−	10.1027i	−0.347884	−	0.833260i
$148$	−0.0846526	−	6.90501i	−0.00695840	−	0.567589i
$149$			14.0054i			1.14737i	0.819076	+	0.573685i	$0.194487\pi$
$149$			14.0054i			1.14737i	−0.819076	+	0.573685i	$0.805513\pi$
$150$		0			0
$151$	13.1301			1.06851			0.534255	−	0.845323i	$-0.320592\pi$
$151$	13.1301			1.06851			0.534255	+	0.845323i	$0.320592\pi$
$152$	16.4102	−	7.15361i	1.33104	−	0.580234i
$153$	3.73391	−	0.0209077i	0.301869	−	0.00169028i
$154$	1.66841	+	3.95909i	0.134444	+	0.319032i
$155$		0			0
$156$	17.4843	−	7.55265i	1.39986	−	0.604696i
$157$	6.36936	+	6.36936i	0.508330	+	0.508330i	0.914014	−	0.405683i	$-0.132966\pi$
$157$	6.36936	+	6.36936i	0.508330	+	0.508330i	−0.405683	+	0.914014i	$0.632966\pi$
$158$	1.44187	+	0.586914i	0.114709	+	0.0466924i
$159$	−12.7054	−	5.22110i	−1.00760	−	0.414060i
$160$		0			0
$161$		−	2.40831i		−	0.189802i
$162$	11.8417	+	4.66628i	0.930372	+	0.366618i
$163$	3.46013	−	3.46013i	0.271018	−	0.271018i	−0.558492	−	0.829510i	$-0.688620\pi$
$163$	3.46013	−	3.46013i	0.271018	−	0.271018i	0.829510	+	0.558492i	$0.188620\pi$
$164$	0.905253	−	0.927724i	0.0706884	−	0.0724431i
$165$		0			0
$166$	11.5639	−	4.87318i	0.897533	−	0.378232i
$167$	0.954151	+	0.954151i	0.0738345	+	0.0738345i	0.743060	−	0.669225i	$-0.233374\pi$
$167$	0.954151	+	0.954151i	0.0738345	+	0.0738345i	−0.669225	+	0.743060i	$0.733374\pi$
$168$	−0.0855420	−	4.03666i	−0.00659971	−	0.311435i
$169$		−	17.2286i		−	1.32528i
$170$		0			0
$171$	13.3508	−	13.5012i	1.02096	−	1.03246i
$172$	−2.31747	+	0.0284113i	−0.176706	+	0.00216634i
$173$	−1.80240	−	1.80240i	−0.137034	−	0.137034i	0.635262	−	0.772296i	$-0.280892\pi$
$173$	−1.80240	−	1.80240i	−0.137034	−	0.137034i	−0.772296	+	0.635262i	$0.780892\pi$
$174$	3.35867	−	0.0299909i	0.254620	−	0.00227360i
$175$		0			0
$176$	−0.361463	−	14.7398i	−0.0272463	−	1.11106i
$177$	4.08408	+	9.78228i	0.306978	+	0.735281i
$178$	−8.18756	+	20.1144i	−0.613683	+	1.50763i
$179$		−	24.0166i		−	1.79508i	−0.440930	−	0.897541i	$-0.645351\pi$
$179$		−	24.0166i		−	1.79508i	0.440930	−	0.897541i	$-0.354649\pi$
$180$		0			0
$181$			21.7210i			1.61451i	0.590205	+	0.807253i	$0.299047\pi$
$181$			21.7210i			1.61451i	−0.590205	+	0.807253i	$0.700953\pi$
$182$	−5.93535	−	2.41599i	−0.439957	−	0.179085i
$183$	3.42641	+	8.20703i	0.253288	+	0.606681i
$184$	−3.02195	+	7.69276i	−0.222781	+	0.567117i
$185$		0			0
$186$	−0.0726302	−	8.13383i	−0.00532550	−	0.596401i
$187$	−3.24412	−	3.24412i	−0.237234	−	0.237234i
$188$	−0.217921	−	17.7755i	−0.0158935	−	1.29641i
$189$	−1.67201	−	3.94259i	−0.121621	−	0.286781i
$190$		0			0
$191$			12.9839i			0.939479i	0.882805	+	0.469739i	$0.155652\pi$
$191$			12.9839i			0.939479i	−0.882805	+	0.469739i	$0.844348\pi$
$192$	−4.79195	+	13.0014i	−0.345829	+	0.938297i
$193$	−9.48630	−	9.48630i	−0.682839	−	0.682839i	0.277800	−	0.960639i	$-0.410395\pi$
$193$	−9.48630	−	9.48630i	−0.682839	−	0.682839i	−0.960639	+	0.277800i	$0.910395\pi$
$194$	4.21079	+	9.99208i	0.302317	+	0.717389i
$195$		0			0
$196$	8.82864	−	9.04780i	0.630617	−	0.646272i
$197$	−12.8606	+	12.8606i	−0.916280	+	0.916280i	−0.996757	−	0.0804765i	$-0.974356\pi$
$197$	−12.8606	+	12.8606i	−0.916280	+	0.916280i	0.0804765	+	0.996757i	$0.474356\pi$
$198$	−6.15370	−	14.3770i	−0.437324	−	1.02173i
$199$			0.0463625i			0.00328655i	0.999999	+	0.00164328i	$0.000523071\pi$
$199$			0.0463625i			0.00328655i	−0.999999	+	0.00164328i	$0.999477\pi$
$200$		0			0
$201$	−11.1161	−	4.56802i	−0.784069	−	0.322203i
$202$	−5.24882	+	12.8948i	−0.369306	+	0.907273i
$203$	−0.799111	−	0.799111i	−0.0560866	−	0.0560866i
$204$	1.70978	+	3.95812i	0.119708	+	0.277123i
$205$		0			0
$206$	−15.2621	+	6.43165i	−1.06336	+	0.448115i
$207$	0.0490858	+	8.76625i	0.00341170	+	0.609296i
$208$	15.9274	+	15.1649i	1.10437	+	1.05150i
$209$	−23.3298			−1.61376
$210$		0			0
$211$			0.591066i			0.0406907i	0.999793	+	0.0203453i	$0.00647657\pi$
$211$			0.591066i			0.0406907i	−0.999793	+	0.0203453i	$0.993523\pi$
$212$	−0.194439	−	15.8601i	−0.0133541	−	1.08928i
$213$	−2.75765	−	6.60518i	−0.188951	−	0.452579i
$214$	4.54107	+	10.7758i	0.310421	+	0.736619i
$215$		0			0
$216$	0.393647	+	14.6917i	0.0267843	+	0.999641i
$217$	−1.93524	+	1.93524i	−0.131373	+	0.131373i
$218$	−6.23994	+	15.3296i	−0.422622	+	1.03825i
$219$	10.6445	+	4.37421i	0.719287	+	0.295582i
$220$		0			0
$221$	6.84318			0.460322
$222$	5.92673	−	6.03353i	0.397776	−	0.404944i
$223$	−16.8577	−	16.8577i	−1.12888	−	1.12888i	−0.990360	−	0.138517i	$-0.955767\pi$
$223$	−16.8577	−	16.8577i	−1.12888	−	1.12888i	−0.138517	−	0.990360i	$-0.544233\pi$
$224$	4.25060	−	1.91529i	0.284005	−	0.127970i
$225$		0			0
$226$	6.66649	+	15.8194i	0.443448	+	1.05229i
$227$	−7.23390	+	7.23390i	−0.480131	+	0.480131i	−0.905173	−	0.425043i	$-0.860259\pi$
$227$	−7.23390	+	7.23390i	−0.480131	+	0.480131i	0.425043	+	0.905173i	$0.360259\pi$
$228$	20.3800	+	8.08434i	1.34970	+	0.535399i
$229$	−23.0081			−1.52042			−0.760210	−	0.649677i	$-0.774904\pi$
$229$	−23.0081			−1.52042			−0.760210	+	0.649677i	$0.774904\pi$
$230$		0			0
$231$	−2.00000	+	4.86692i	−0.131590	+	0.320220i
$232$	1.54984	+	3.55529i	0.101752	+	0.233416i
$233$	−4.45082	+	4.45082i	−0.291583	+	0.291583i	−0.837705	−	0.546122i	$-0.816103\pi$
$233$	−4.45082	+	4.45082i	−0.291583	+	0.291583i	0.546122	+	0.837705i	$0.316103\pi$
$234$	21.6539	+	8.67320i	1.41556	+	0.566985i
$235$		0			0
$236$	−8.54860	+	8.76081i	−0.556466	+	0.570280i
$237$	0.734560	+	1.75944i	0.0477148	+	0.114288i
$238$	0.546934	−	1.34365i	0.0354524	−	0.0870959i
$239$	−4.03472			−0.260984			−0.130492	−	0.991449i	$-0.541656\pi$
$239$	−4.03472			−0.260984			−0.130492	+	0.991449i	$0.541656\pi$
$240$		0			0
$241$	−11.4612			−0.738279			−0.369139	−	0.929374i	$-0.620347\pi$
$241$	−11.4612			−0.738279			−0.369139	+	0.929374i	$0.620347\pi$
$242$	−1.37937	+	3.38871i	−0.0886696	+	0.217834i
$243$	6.16646	+	14.3169i	0.395578	+	0.918432i
$244$	−7.17201	+	7.35005i	−0.459141	+	0.470538i
$245$		0			0
$246$	1.58746	−	0.0141751i	0.101213	−	0.000903769i
$247$	24.6060	−	24.6060i	1.56564	−	1.56564i
$248$	8.60999	−	3.75331i	0.546735	−	0.238335i
$249$	14.2156	+	5.84170i	0.900874	+	0.370203i
$250$		0			0
$251$	−17.4804			−1.10335			−0.551677	−	0.834058i	$-0.686012\pi$
$251$	−17.4804			−1.10335			−0.551677	+	0.834058i	$0.686012\pi$
$252$	3.43363	−	3.55851i	0.216299	−	0.224165i
$253$	7.61636	−	7.61636i	0.478836	−	0.478836i
$254$	0.0113752	+	0.0269930i	0.000713745	+	0.00169369i
$255$		0			0
$256$	−15.9808	+	0.784260i	−0.998798	+	0.0490162i
$257$	6.77283	+	6.77283i	0.422477	+	0.422477i	0.886056	−	0.463578i	$-0.153435\pi$
$257$	6.77283	+	6.77283i	0.422477	+	0.422477i	−0.463578	+	0.886056i	$0.653435\pi$
$258$	−2.02498	−	1.98914i	−0.126070	−	0.123838i
$259$	−2.84565			−0.176820
$260$		0			0
$261$	2.92505	+	2.89247i	0.181056	+	0.179040i
$262$	−2.79379	+	6.86350i	−0.172601	+	0.424028i
$263$	15.3708	−	15.3708i	0.947805	−	0.947805i	−0.0508987	−	0.998704i	$-0.516209\pi$
$263$	15.3708	−	15.3708i	0.947805	−	0.947805i	0.998704	+	0.0508987i	$0.0162086\pi$
$264$	12.4955	−	13.0366i	0.769046	−	0.802345i
$265$		0			0
$266$	−2.86476	−	6.79798i	−0.175649	−	0.416811i
$267$	−24.5444	+	10.2472i	−1.50209	+	0.627121i
$268$	−0.170117	−	13.8762i	−0.0103916	−	0.847627i
$269$			9.58859i			0.584627i	0.956323	+	0.292313i	$0.0944250\pi$
$269$			9.58859i			0.584627i	−0.956323	+	0.292313i	$0.905575\pi$
$270$		0			0
$271$	−20.9078			−1.27006			−0.635030	−	0.772487i	$-0.719012\pi$
$271$	−20.9078			−1.27006			−0.635030	+	0.772487i	$0.719012\pi$
$272$	−3.43306	+	3.60567i	−0.208160	+	0.218626i
$273$	−3.02376	−	7.24257i	−0.183006	−	0.438341i
$274$	25.9837	−	10.9499i	1.56974	−	0.661507i
$275$		0			0
$276$	−9.29263	+	4.01412i	−0.559350	+	0.241621i
$277$	−8.86336	−	8.86336i	−0.532547	−	0.532547i	0.388782	−	0.921330i	$-0.372896\pi$
$277$	−8.86336	−	8.86336i	−0.532547	−	0.532547i	−0.921330	+	0.388782i	$0.872896\pi$
$278$	4.91678	−	12.0790i	0.294889	−	0.724453i
$279$	7.00483	−	7.08372i	0.419368	−	0.424091i
$280$		0			0
$281$			12.1925i			0.727341i	0.931528	+	0.363670i	$0.118477\pi$
$281$			12.1925i			0.727341i	−0.931528	+	0.363670i	$0.881523\pi$
$282$	15.2571	−	15.5321i	0.908550	−	0.924922i
$283$	−11.6799	+	11.6799i	−0.694298	+	0.694298i	−0.963175	−	0.268877i	$-0.913348\pi$
$283$	−11.6799	+	11.6799i	−0.694298	+	0.694298i	0.268877	+	0.963175i	$0.413348\pi$
$284$	5.77217	−	5.91546i	0.342516	−	0.351018i
$285$		0			0
$286$	−11.1301	−	26.4113i	−0.658135	−	1.56173i
$287$	−0.377697	−	0.377697i	−0.0222947	−	0.0222947i
$288$	−15.4331	+	7.05827i	−0.909405	+	0.415912i
$289$		−	15.4508i		−	0.908872i
$290$		0			0
$291$	−5.04767	+	12.2833i	−0.295900	+	0.720060i
$292$	0.162900	+	13.2875i	0.00953298	+	0.777594i
$293$	5.16432	+	5.16432i	0.301703	+	0.301703i	0.841680	−	0.539977i	$-0.181567\pi$
$293$	5.16432	+	5.16432i	0.301703	+	0.301703i	−0.539977	+	0.841680i	$0.681567\pi$
$294$	15.4820	−	0.138245i	0.902929	−	0.00806261i
$295$		0			0
$296$	9.08971	+	3.57071i	0.528328	+	0.207544i
$297$	7.18079	−	17.7563i	0.416672	−	1.03033i
$298$	−18.3451	−	7.46739i	−1.06270	−	0.432574i
$299$			16.0660i			0.929122i
$300$		0			0
$301$			0.955061i			0.0550488i
$302$	−7.00066	+	17.1985i	−0.402843	+	0.989663i
$303$	−15.7348	+	6.56923i	−0.903939	+	0.377392i
$304$	0.620652	+	25.3091i	0.0355968	+	1.45158i
$305$		0			0
$306$	−1.96345	+	4.90203i	−0.112243	+	0.280230i
$307$	9.19824	+	9.19824i	0.524972	+	0.524972i	0.919069	−	0.394097i	$-0.128943\pi$
$307$	9.19824	+	9.19824i	0.524972	+	0.524972i	−0.394097	+	0.919069i	$0.628943\pi$
$308$	−6.07539	+	0.0744818i	−0.346177	+	0.00424399i
$309$	−18.7618	−	7.70992i	−1.06732	−	0.438602i
$310$		0			0
$311$		−	30.5690i		−	1.73341i	−0.498821	−	0.866705i	$-0.666233\pi$
$311$		−	30.5690i		−	1.73341i	0.498821	−	0.866705i	$-0.333767\pi$
$312$	0.570656	+	26.9288i	0.0323071	+	1.52454i
$313$	16.4612	+	16.4612i	0.930440	+	0.930440i	0.997733	−	0.0672931i	$-0.0214363\pi$
$313$	16.4612	+	16.4612i	0.930440	+	0.930440i	−0.0672931	+	0.997733i	$0.521436\pi$
$314$	−11.7389	+	4.94694i	−0.662467	+	0.279172i
$315$		0			0
$316$	−1.53755	+	1.57571i	−0.0864937	+	0.0886408i
$317$	0.000616701	0	0.000616701i	3.46374e−5	0	3.46374e-5i	−0.707089	−	0.707124i	$-0.749992\pi$
$317$	0.000616701	0	0.000616701i	3.46374e−5	0	3.46374e-5i	0.707124	+	0.707089i	$0.249992\pi$
$318$	13.6131	−	13.8584i	0.763385	−	0.777141i
$319$		−	5.05442i		−	0.282993i
$320$		0			0
$321$	−5.44358	+	13.2468i	−0.303831	+	0.739362i
$322$	3.15454	+	1.28406i	0.175796	+	0.0715578i
$323$	5.57034	+	5.57034i	0.309942	+	0.309942i
$324$	−12.4259	+	13.0230i	−0.690327	+	0.723498i
$325$		0			0
$326$	2.68740	+	6.37713i	0.148842	+	0.353196i
$327$	−18.7059	+	7.80967i	−1.03444	+	0.431876i
$328$	0.732524	+	1.68039i	0.0404469	+	0.0927841i
$329$	−7.32553			−0.403870
$330$		0			0
$331$			8.28613i			0.455447i	0.973726	+	0.227724i	$0.0731283\pi$
$331$			8.28613i			0.455447i	−0.973726	+	0.227724i	$0.926872\pi$
$332$	0.217550	+	17.7453i	0.0119396	+	0.973901i
$333$	10.3581	−	0.0579994i	0.567622	−	0.00317835i
$334$	−1.75853	+	0.741069i	−0.0962226	+	0.0405495i
$335$		0			0
$336$	5.33305	+	2.04021i	0.290942	+	0.111302i
$337$	−2.27666	+	2.27666i	−0.124018	+	0.124018i	−0.766392	−	0.642374i	$-0.777950\pi$
$337$	−2.27666	+	2.27666i	−0.124018	+	0.124018i	0.642374	+	0.766392i	$0.277950\pi$
$338$	22.5670	+	9.18590i	1.22748	+	0.499647i
$339$	−7.99142	+	19.4468i	−0.434035	+	1.05621i
$340$		0			0
$341$	−12.2405			−0.662861
$342$	10.5663	+	24.6862i	0.571357	+	1.33488i
$343$	−7.76296	−	7.76296i	−0.419161	−	0.419161i
$344$	1.19841	−	3.05070i	0.0646139	−	0.164483i
$345$		0			0
$346$	3.32189	−	1.39989i	0.178586	−	0.0752584i
$347$	18.6384	−	18.6384i	1.00056	−	1.00056i	0.000564305	−	1.00000i	$-0.499820\pi$
$347$	18.6384	−	18.6384i	1.00056	−	1.00056i	1.00000		0.000564305i	$-0.000179624\pi$
$348$	−1.75148	+	4.41536i	−0.0938892	+	0.236688i
$349$	17.7267			0.948889			0.474445	−	0.880285i	$-0.342649\pi$
$349$	17.7267			0.948889			0.474445	+	0.880285i	$0.342649\pi$
$350$		0			0
$351$	11.1541	+	26.3013i	0.595360	+	1.40386i
$352$	19.4998	+	7.38548i	1.03934	+	0.393648i
$353$	−10.5779	+	10.5779i	−0.563007	+	0.563007i	−0.930160	−	0.367153i	$-0.880332\pi$
$353$	−10.5779	+	10.5779i	−0.563007	+	0.563007i	0.367153	+	0.930160i	$0.380332\pi$
$354$	−14.9909	+	0.133860i	−0.796758	+	0.00711457i
$355$		0			0
$356$	−21.9815	−	21.4490i	−1.16502	−	1.13680i
$357$	1.63958	−	0.684521i	0.0867759	−	0.0362287i
$358$	31.4582	+	12.8051i	1.66262	+	0.676770i
$359$	24.7266			1.30502			0.652510	−	0.757780i	$-0.273716\pi$
$359$	24.7266			1.30502			0.652510	+	0.757780i	$0.273716\pi$
$360$		0			0
$361$	21.0586			1.10835
$362$	−28.4513	−	11.5811i	−1.49537	−	0.608691i
$363$	−4.13505	+	1.72637i	−0.217034	+	0.0906111i
$364$	6.32919	−	6.48630i	0.331739	−	0.339974i
$365$		0			0
$366$	−12.5769	+	0.112304i	−0.657406	+	0.00587024i
$367$	−9.33767	+	9.33767i	−0.487423	+	0.487423i	−0.907492	−	0.420069i	$-0.862006\pi$
$367$	−9.33767	+	9.33767i	−0.487423	+	0.487423i	0.420069	+	0.907492i	$0.362006\pi$
$368$	−8.46516	−	8.05992i	−0.441277	−	0.420152i
$369$	1.38251	+	1.36712i	0.0719707	+	0.0711692i
$370$		0			0
$371$	−6.53616			−0.339341
$372$	10.6929	+	4.24164i	0.554399	+	0.219919i
$373$	−11.9025	+	11.9025i	−0.616291	+	0.616291i	−0.944578	−	0.328287i	$-0.893529\pi$
$373$	−11.9025	+	11.9025i	−0.616291	+	0.616291i	0.328287	+	0.944578i	$0.393529\pi$
$374$	5.97903	−	2.51964i	0.309168	−	0.130288i
$375$		0			0
$376$	23.3996	+	9.19207i	1.20674	+	0.474045i
$377$	5.33092	+	5.33092i	0.274557	+	0.274557i
$378$	6.05570	−	0.0879865i	0.311472	−	0.00452554i
$379$	2.73341			0.140406			0.0702029	−	0.997533i	$-0.477635\pi$
$379$	2.73341			0.140406			0.0702029	+	0.997533i	$0.477635\pi$
$380$		0			0
$381$	−0.0136360	+	0.0331827i	−0.000698593	+	0.00170000i
$382$	−17.0070	−	6.92270i	−0.870153	−	0.354196i
$383$	17.6065	−	17.6065i	0.899651	−	0.899651i	−0.0957539	−	0.995405i	$-0.530526\pi$
$383$	17.6065	−	17.6065i	0.899651	−	0.899651i	0.995405	+	0.0957539i	$0.0305262\pi$
$384$	−14.4750	−	13.2088i	−0.738676	−	0.674060i
$385$		0			0
$386$	17.4836	−	7.36780i	0.889890	−	0.375011i
$387$	−0.0194659	−	3.47642i	−0.000989506	−	0.176716i
$388$	−15.3333	+	0.187980i	−0.778429	+	0.00954322i
$389$			25.1335i			1.27432i	0.770731	+	0.637160i	$0.219891\pi$
$389$			25.1335i			1.27432i	−0.770731	+	0.637160i	$0.780109\pi$
$390$		0			0
$391$	−3.63704			−0.183933
$392$	7.14408	+	16.3883i	0.360831	+	0.827736i
$393$	−8.37515	+	3.49660i	−0.422470	+	0.176380i
$394$	−9.98855	−	23.7025i	−0.503216	−	1.19412i
$395$		0			0
$396$	22.1129	−	0.394941i	1.11121	−	0.0198465i
$397$	5.42664	+	5.42664i	0.272355	+	0.272355i	0.830048	−	0.557692i	$-0.188313\pi$
$397$	5.42664	+	5.42664i	0.272355	+	0.272355i	−0.557692	+	0.830048i	$0.688313\pi$
$398$	−0.0607282	−	0.0247195i	−0.00304403	−	0.00123907i
$399$	3.43411	−	8.35678i	0.171921	−	0.418362i
$400$		0			0
$401$		−	5.15831i		−	0.257594i	−0.991671	−	0.128797i	$-0.958888\pi$
$401$		−	5.15831i		−	0.257594i	0.991671	−	0.128797i	$-0.0411115\pi$
$402$	11.9103	−	12.1249i	0.594032	−	0.604736i
$403$	12.9101	−	12.9101i	0.643099	−	0.643099i
$404$	−14.0917	−	13.7504i	−0.701090	−	0.684108i
$405$		0			0
$406$	1.47279	−	0.620652i	0.0730933	−	0.0308025i
$407$	−8.99944	−	8.99944i	−0.446085	−	0.446085i
$408$	−6.09617	+	0.129186i	−0.301806	+	0.00639565i
$409$			14.1638i			0.700356i	0.936683	+	0.350178i	$0.113879\pi$
$409$			14.1638i			0.700356i	−0.936683	+	0.350178i	$0.886121\pi$
$410$		0			0
$411$	31.9419	+	13.1261i	1.57558	+	0.647464i
$412$	−0.287124	−	23.4204i	−0.0141456	−	1.15384i
$413$	3.56672	+	3.56672i	0.175507	+	0.175507i
$414$	−11.5087	−	4.60967i	−0.565621	−	0.226553i
$415$		0			0
$416$	−28.3560	+	12.7770i	−1.39027	+	0.626444i
$417$	14.7394	−	6.15365i	0.721791	−	0.301346i
$418$	12.4389	−	30.5587i	0.608407	−	1.49467i
$419$			4.80514i			0.234746i	0.993088	+	0.117373i	$0.0374474\pi$
$419$			4.80514i			0.234746i	−0.993088	+	0.117373i	$0.962553\pi$
$420$		0			0
$421$		−	15.2187i		−	0.741716i	−0.928690	−	0.370858i	$-0.879064\pi$
$421$		−	15.2187i		−	0.741716i	0.928690	−	0.370858i	$-0.120936\pi$
$422$	−0.774212	−	0.315143i	−0.0376880	−	0.0153409i
$423$	26.6649	−	0.149308i	1.29649	−	0.00725958i
$424$	20.8781	+	8.20157i	1.01393	+	0.398304i
$425$		0			0
$426$	10.1221	−	0.0903846i	0.490420	−	0.00437915i
$427$	2.99236	+	2.99236i	0.144811	+	0.144811i
$428$	−16.5359	+	0.202724i	−0.799295	+	0.00979903i
$429$	13.3421	−	32.4676i	0.644164	−	1.56755i
$430$		0			0
$431$		−	27.8760i		−	1.34274i	−0.741122	−	0.671370i	$-0.765706\pi$
$431$		−	27.8760i		−	1.34274i	0.741122	−	0.671370i	$-0.234294\pi$
$432$	−19.4538	−	7.31764i	−0.935974	−	0.352070i
$433$	2.78003	+	2.78003i	0.133600	+	0.133600i	0.770744	−	0.637145i	$-0.219885\pi$
$433$	2.78003	+	2.78003i	0.133600	+	0.133600i	−0.637145	+	0.770744i	$0.719885\pi$
$434$	−1.50306	−	3.56672i	−0.0721492	−	0.171208i
$435$		0			0
$436$	−16.7526	−	16.3468i	−0.802305	−	0.782872i
$437$	−13.0777	+	13.0777i	−0.625592	+	0.625592i
$438$	−11.4050	+	11.6105i	−0.544951	+	0.554771i
$439$			10.8174i			0.516286i	0.966107	+	0.258143i	$0.0831105\pi$
$439$			10.8174i			0.516286i	−0.966107	+	0.258143i	$0.916889\pi$
$440$		0			0
$441$	13.4832	+	13.3331i	0.642058	+	0.634907i
$442$	−3.64863	+	8.96358i	−0.173548	+	0.426354i
$443$	−5.74963	−	5.74963i	−0.273173	−	0.273173i	0.557203	−	0.830376i	$-0.311874\pi$
$443$	−5.74963	−	5.74963i	−0.273173	−	0.273173i	−0.830376	+	0.557203i	$0.811874\pi$
$444$	4.74305	+	10.9801i	0.225095	+	0.521092i
$445$		0			0
$446$	31.0693	−	13.0930i	1.47118	−	0.619973i
$447$	−9.34590	−	22.3855i	−0.442046	−	1.05880i
$448$	0.242427	+	6.58885i	0.0114536	+	0.311294i
$449$	−6.91183			−0.326189			−0.163095	−	0.986610i	$-0.552148\pi$
$449$	−6.91183			−0.326189			−0.163095	+	0.986610i	$0.552148\pi$
$450$		0			0
$451$		−	2.38895i		−	0.112491i
$452$	−24.2755	+	0.297608i	−1.14182	+	0.0139983i
$453$	−20.9864	+	8.76176i	−0.986026	+	0.411663i
$454$	−5.61841	−	13.3323i	−0.263685	−	0.625716i
$455$		0			0
$456$	−21.4555	+	22.3845i	−1.00475	+	1.04825i
$457$	5.15748	−	5.15748i	0.241257	−	0.241257i	−0.576113	−	0.817370i	$-0.695431\pi$
$457$	5.15748	−	5.15748i	0.241257	−	0.241257i	0.817370	+	0.576113i	$0.195431\pi$
$458$	12.2674	−	30.1373i	0.573219	−	1.40823i
$459$	−5.95412	+	2.52507i	−0.277915	+	0.117860i
$460$		0			0
$461$	18.4555			0.859558			0.429779	−	0.902934i	$-0.358592\pi$
$461$	18.4555			0.859558			0.429779	+	0.902934i	$0.358592\pi$
$462$	−5.30861	−	5.21464i	−0.246979	−	0.242607i
$463$	19.6899	+	19.6899i	0.915068	+	0.915068i	0.996665	−	0.0815977i	$-0.0260023\pi$
$463$	19.6899	+	19.6899i	0.915068	+	0.915068i	−0.0815977	+	0.996665i	$0.526002\pi$
$464$	−5.48325	+	0.134465i	−0.254553	+	0.00624238i
$465$		0			0
$466$	−3.45685	−	8.20301i	−0.160136	−	0.379997i
$467$	−2.07946	+	2.07946i	−0.0962257	+	0.0962257i	−0.753581	−	0.657355i	$-0.771675\pi$
$467$	−2.07946	+	2.07946i	−0.0962257	+	0.0962257i	0.657355	+	0.753581i	$0.271675\pi$
$468$	−22.9060	+	23.7391i	−1.05883	+	1.09734i
$469$	−5.71858			−0.264060
$470$		0			0
$471$	−14.4307	−	5.93013i	−0.664933	−	0.273246i
$472$	−6.91747	−	15.8685i	−0.318402	−	0.730407i
$473$	−3.02041	+	3.02041i	−0.138879	+	0.138879i
$474$	−2.69626	+	0.0240759i	−0.123843	+	0.00110584i
$475$		0			0
$476$	1.46838	+	1.43281i	0.0673029	+	0.0656727i
$477$	23.7916	−	0.133219i	1.08934	−	0.00609967i
$478$	2.15122	−	5.28490i	0.0983945	−	0.241725i
$479$	−19.7088			−0.900517			−0.450259	−	0.892898i	$-0.648668\pi$
$479$	−19.7088			−0.900517			−0.450259	+	0.892898i	$0.648668\pi$
$480$		0			0
$481$	18.9835			0.865573
$482$	6.11083	−	15.0125i	0.278341	−	0.683799i
$483$	1.60708	+	3.84931i	0.0731246	+	0.175150i
$484$	−3.70326	−	3.61356i	−0.168330	−	0.164253i
$485$		0			0
$486$	−22.0409	+	0.443697i	−0.999797	+	0.0201265i
$487$	−4.21395	+	4.21395i	−0.190952	+	0.190952i	−0.796107	−	0.605155i	$-0.793111\pi$
$487$	−4.21395	+	4.21395i	−0.190952	+	0.190952i	0.605155	+	0.796107i	$0.293111\pi$
$488$	−5.80354	−	13.3132i	−0.262714	−	0.602659i
$489$	−3.22151	+	7.83943i	−0.145682	+	0.354511i
$490$		0			0
$491$	−27.7215			−1.25105			−0.625527	−	0.780203i	$-0.715116\pi$
$491$	−27.7215			−1.25105			−0.625527	+	0.780203i	$0.715116\pi$
$492$	−0.827831	+	2.08690i	−0.0373215	+	0.0940848i
$493$	−1.20682	+	1.20682i	−0.0543525	+	0.0543525i
$494$	19.1110	+	45.3497i	0.859843	+	2.04038i
$495$		0			0
$496$	0.325640	+	13.2790i	0.0146216	+	0.596246i
$497$	−2.40831	−	2.40831i	−0.108028	−	0.108028i
$498$	−15.2312	+	15.5057i	−0.682527	+	0.694825i
$499$	5.14705			0.230414			0.115207	−	0.993342i	$-0.463247\pi$
$499$	5.14705			0.230414			0.115207	+	0.993342i	$0.463247\pi$
$500$		0			0
$501$	−2.16177	−	0.888353i	−0.0965809	−	0.0396887i
$502$	9.32016	−	22.8968i	0.415979	−	1.02193i
$503$	12.2281	−	12.2281i	0.545224	−	0.545224i	−0.379832	−	0.925056i	$-0.624018\pi$
$503$	12.2281	−	12.2281i	0.545224	−	0.545224i	0.925056	+	0.379832i	$0.124018\pi$
$504$	2.83040	+	6.39488i	0.126076	+	0.284851i
$505$		0			0
$506$	5.91546	+	14.0372i	0.262974	+	0.624030i
$507$	11.4967	+	27.5372i	0.510587	+	1.22297i
$508$	−0.0414220		0.000507817i	−0.00183780		2.25307e-5i
$509$		−	35.8361i		−	1.58841i	−0.607651	−	0.794204i	$-0.707888\pi$
$509$		−	35.8361i		−	1.58841i	0.607651	−	0.794204i	$-0.292112\pi$
$510$		0			0
$511$	5.47596			0.242242
$512$	7.49332	−	21.3506i	0.331161	−	0.943574i
$513$	−12.3298	+	30.4886i	−0.544375	+	1.34611i
$514$	−12.4825	+	5.26031i	−0.550581	+	0.232022i
$515$		0			0
$516$	3.68516	−	1.59187i	0.162230	−	0.0700783i
$517$	−23.1672	−	23.1672i	−1.01889	−	1.01889i
$518$	1.51723	−	3.72738i	0.0666634	−	0.163772i
$519$	4.08361	+	1.67811i	0.179251	+	0.0736608i
$520$		0			0
$521$		−	18.1715i		−	0.796107i	−0.917362	−	0.398054i	$-0.869686\pi$
$521$		−	18.1715i		−	0.796107i	0.917362	−	0.398054i	$-0.130314\pi$
$522$	−5.34829	+	2.28919i	−0.234088	+	0.100195i
$523$	21.7444	−	21.7444i	0.950815	−	0.950815i	−0.0480305	−	0.998846i	$-0.515294\pi$
$523$	21.7444	−	21.7444i	0.950815	−	0.950815i	0.998846	+	0.0480305i	$0.0152945\pi$
$524$	−7.50061	−	7.31893i	−0.327666	−	0.319729i
$525$		0			0
$526$	11.9382	+	28.3289i	0.520529	+	1.23520i
$527$	2.92261	+	2.92261i	0.127311	+	0.127311i
$528$	10.4137	+	23.3181i	0.453198	+	1.01479i
$529$			14.4612i			0.628746i
$530$		0			0
$531$	−13.0555	−	12.9101i	−0.566561	−	0.560252i
$532$	10.4318	−	0.127889i	0.452275	−	0.00554471i
$533$	2.51964	+	2.51964i	0.109138	+	0.109138i
$534$	−0.335864	−	37.6133i	−0.0145342	−	1.62768i
$535$		0			0
$536$	18.2666	+	7.17567i	0.788996	+	0.309942i
$537$	16.0264	+	38.3867i	0.691589	+	1.65651i
$538$	−12.5597	−	5.11242i	−0.541486	−	0.220412i
$539$		−	23.2987i		−	1.00355i
$540$		0			0
$541$		−	26.6843i		−	1.14725i	−0.819119	−	0.573623i	$-0.805537\pi$
$541$		−	26.6843i		−	1.14725i	0.819119	−	0.573623i	$-0.194463\pi$
$542$	11.1476	−	27.3862i	0.478830	−	1.17634i
$543$	−14.4945	−	34.7176i	−0.622019	−	1.48987i
$544$	−2.89247	−	6.41927i	−0.124014	−	0.275224i
$545$		0			0
$546$	11.0989	−	0.0991067i	0.474990	−	0.00424138i
$547$	−22.2551	−	22.2551i	−0.951559	−	0.951559i	0.0473207	−	0.998880i	$-0.484932\pi$
$547$	−22.2551	−	22.2551i	−0.951559	−	0.951559i	−0.998880	+	0.0473207i	$0.984932\pi$
$548$	0.488829	+	39.8732i	0.0208817	+	1.70330i
$549$	−10.9532	−	10.8312i	−0.467470	−	0.462264i
$550$		0			0
$551$			8.67873i			0.369726i
$552$	−0.303295	−	14.3122i	−0.0129091	−	0.609169i
$553$	0.641507	+	0.641507i	0.0272797	+	0.0272797i
$554$	16.3355	−	6.88398i	0.694027	−	0.292472i
$555$		0			0
$556$	13.2003	+	12.8805i	0.559817	+	0.546257i
$557$	7.30615	−	7.30615i	0.309572	−	0.309572i	−0.535172	−	0.844743i	$-0.679753\pi$
$557$	7.30615	−	7.30615i	0.309572	−	0.309572i	0.844743	+	0.535172i	$0.179753\pi$
$558$	5.54383	+	12.9522i	0.234689	+	0.548310i
$559$		−	6.37128i		−	0.269476i
$560$		0			0
$561$	7.35005	+	3.02041i	0.310319	+	0.127522i
$562$	−15.9704	−	6.50074i	−0.673669	−	0.274217i
$563$	−21.3458	−	21.3458i	−0.899616	−	0.899616i	0.0957856	−	0.995402i	$-0.469464\pi$
$563$	−21.3458	−	21.3458i	−0.899616	−	0.899616i	−0.995402	+	0.0957856i	$0.969464\pi$
$564$	12.2100	+	28.2660i	0.514134	+	1.19021i
$565$		0			0
$566$	−9.07152	−	21.5264i	−0.381304	−	0.904823i
$567$	5.30335	+	5.18588i	0.222720	+	0.217787i
$568$	4.67081	+	10.7147i	0.195983	+	0.449579i
$569$	−35.6410			−1.49415			−0.747075	−	0.664740i	$-0.768542\pi$
$569$	−35.6410			−1.49415			−0.747075	+	0.664740i	$0.768542\pi$
$570$		0			0
$571$		−	9.49296i		−	0.397268i	−0.980074	−	0.198634i	$-0.936350\pi$
$571$		−	9.49296i		−	0.397268i	0.980074	−	0.198634i	$-0.0636505\pi$
$572$	40.5293	−	0.496873i	1.69462	−	0.0207753i
$573$	−8.66419	−	20.7527i	−0.361952	−	0.866955i
$574$	0.696108	−	0.293349i	0.0290550	−	0.0122441i
$575$		0			0
$576$	−1.01673	−	23.9785i	−0.0423636	−	0.999102i
$577$	−10.6312	+	10.6312i	−0.442582	+	0.442582i	−0.892879	−	0.450297i	$-0.851318\pi$
$577$	−10.6312	+	10.6312i	−0.442582	+	0.442582i	0.450297	+	0.892879i	$0.351318\pi$
$578$	20.2384	+	8.23803i	0.841805	+	0.342657i
$579$	21.4926	+	8.83212i	0.893203	+	0.367050i
$580$		0			0
$581$	7.31307			0.303397
$582$	−13.3981	−	13.1609i	−0.555367	−	0.545537i
$583$	−20.6708	−	20.6708i	−0.856097	−	0.856097i
$584$	−17.4916	−	6.87124i	−0.723808	−	0.284334i
$585$		0			0
$586$	−9.51801	+	4.01102i	−0.393186	+	0.165694i
$587$	17.1910	−	17.1910i	0.709550	−	0.709550i	−0.256891	−	0.966441i	$-0.582698\pi$
$587$	17.1910	−	17.1910i	0.709550	−	0.709550i	0.966441	+	0.256891i	$0.0826980\pi$
$588$	−8.07357	+	20.3529i	−0.332949	+	0.839339i
$589$	21.0177			0.866018
$590$		0			0
$591$	11.9737	−	29.1376i	0.492534	−	1.19856i
$592$	−9.52355	+	10.0024i	−0.391415	+	0.411095i
$593$	−9.69544	+	9.69544i	−0.398144	+	0.398144i	−0.877578	−	0.479434i	$-0.840842\pi$
$593$	−9.69544	+	9.69544i	−0.398144	+	0.398144i	0.479434	+	0.877578i	$0.340842\pi$
$594$	19.4296	+	18.8731i	0.797206	+	0.774372i
$595$		0			0
$596$	19.5624	−	20.0480i	0.801307	−	0.821198i
$597$	−0.0309379	−	0.0741033i	−0.00126621	−	0.00303285i
$598$	−21.0442	−	8.56604i	−0.860560	−	0.350291i
$599$	26.8502			1.09707			0.548535	−	0.836128i	$-0.315186\pi$
$599$	26.8502			1.09707			0.548535	+	0.836128i	$0.315186\pi$
$600$		0			0
$601$	−42.9566			−1.75224			−0.876119	−	0.482095i	$-0.839876\pi$
$601$	−42.9566			−1.75224			−0.876119	+	0.482095i	$0.839876\pi$
$602$	−1.25099	−	0.509217i	−0.0509866	−	0.0207541i
$603$	20.8156	−	0.116555i	0.847677	−	0.00474649i
$604$	−18.7950	−	18.3397i	−0.764756	−	0.746232i
$605$		0			0
$606$	−0.215313	−	24.1128i	−0.00874650	−	0.979517i
$607$	−32.0417	+	32.0417i	−1.30053	+	1.30053i	−0.372498	+	0.928033i	$0.621499\pi$
$607$	−32.0417	+	32.0417i	−1.30053	+	1.30053i	−0.928033	+	0.372498i	$0.878501\pi$
$608$	−33.4822	−	12.6813i	−1.35788	−	0.514294i
$609$	1.81051	+	0.744004i	0.0733654	+	0.0301486i
$610$		0			0
$611$	48.8691			1.97703
$612$	−5.37408	−	5.18549i	−0.217234	−	0.209611i
$613$	20.1419	−	20.1419i	0.813522	−	0.813522i	−0.171638	−	0.985160i	$-0.554906\pi$
$613$	20.1419	−	20.1419i	0.813522	−	0.813522i	0.985160	+	0.171638i	$0.0549060\pi$
$614$	−16.9527	+	7.14408i	−0.684154	+	0.288311i
$615$		0			0
$616$	3.14170	−	7.99760i	0.126583	−	0.322232i
$617$	7.33463	+	7.33463i	0.295281	+	0.295281i	0.839162	−	0.543881i	$-0.183046\pi$
$617$	7.33463	+	7.33463i	0.295281	+	0.295281i	−0.543881	+	0.839162i	$0.683046\pi$
$618$	20.1022	−	20.4645i	0.808631	−	0.823202i
$619$	11.9287			0.479456			0.239728	−	0.970840i	$-0.422942\pi$
$619$	11.9287			0.479456			0.239728	+	0.970840i	$0.422942\pi$
$620$		0			0
$621$	−5.92821	−	13.9787i	−0.237891	−	0.560947i
$622$	40.0410	+	16.2987i	1.60550	+	0.653519i
$623$	−8.94914	+	8.94914i	−0.358540	+	0.358540i
$624$	−35.5771	−	13.6104i	−1.42422	−	0.544850i
$625$		0			0
$626$	−30.3385	+	12.7850i	−1.21257	+	0.510993i
$627$	37.2890	−	15.5681i	1.48918	−	0.621729i
$628$	−0.220843	−	18.0139i	−0.00881260	−	0.718834i
$629$			4.29751i			0.171353i
$630$		0			0
$631$	7.13985			0.284233			0.142116	−	0.989850i	$-0.454609\pi$
$631$	7.13985			0.284233			0.142116	+	0.989850i	$0.454609\pi$
$632$	−1.24417	−	2.85410i	−0.0494905	−	0.113530i
$633$	−0.394421	−	0.944728i	−0.0156768	−	0.0375496i
$634$	0.000478978		0.00113660i	1.90227e−5		4.51402e-5i
$635$		0			0
$636$	10.8943	+	25.2202i	0.431988	+	1.00005i
$637$	24.5733	+	24.5733i	0.973628	+	0.973628i
$638$	6.62057	+	2.69490i	0.262111	+	0.106692i
$639$	8.81533	+	8.71716i	0.348729	+	0.344846i
$640$		0			0
$641$			30.0187i			1.18567i	0.805325	+	0.592834i	$0.201991\pi$
$641$			30.0187i			1.18567i	−0.805325	+	0.592834i	$0.798009\pi$
$642$	−14.4489	−	14.1932i	−0.570254	−	0.560160i
$643$	−32.7048	+	32.7048i	−1.28975	+	1.28975i	−0.354812	+	0.934938i	$0.615455\pi$
$643$	−32.7048	+	32.7048i	−1.28975	+	1.28975i	−0.934938	+	0.354812i	$0.884545\pi$
$644$	−3.36386	+	3.44736i	−0.132555	+	0.135845i
$645$		0			0
$646$	−10.2663	+	4.32637i	−0.403923	+	0.170219i
$647$	−2.53026	−	2.53026i	−0.0994747	−	0.0994747i	0.655618	−	0.755093i	$-0.272408\pi$
$647$	−2.53026	−	2.53026i	−0.0994747	−	0.0994747i	−0.755093	+	0.655618i	$0.772408\pi$
$648$	−10.4330	−	23.2197i	−0.409847	−	0.912154i
$649$			22.5597i			0.885545i
$650$		0			0
$651$	1.80179	−	4.38458i	0.0706176	−	0.171845i
$652$	−9.78598	+	0.119972i	−0.383248	+	0.00469847i
$653$	−23.8061	−	23.8061i	−0.931604	−	0.931604i	0.0662023	−	0.997806i	$-0.478912\pi$
$653$	−23.8061	−	23.8061i	−0.931604	−	0.931604i	−0.997806	+	0.0662023i	$0.978912\pi$
$654$	−0.255970	−	28.6660i	−0.0100092	−	1.12093i
$655$		0			0
$656$	−2.59164	+	0.0635543i	−0.101186	+	0.00248138i
$657$	−19.9325	+	0.111610i	−0.777640	+	0.00435432i
$658$	3.90581	−	9.59539i	0.152264	−	0.374067i
$659$		−	15.7130i		−	0.612093i	−0.952017	−	0.306047i	$-0.900994\pi$
$659$		−	15.7130i		−	0.612093i	0.952017	−	0.306047i	$-0.0990063\pi$
$660$		0			0
$661$			25.2637i			0.982643i	0.870978	+	0.491322i	$0.163486\pi$
$661$			25.2637i			0.982643i	−0.870978	+	0.491322i	$0.836514\pi$
$662$	−10.8536	−	4.41798i	−0.421839	−	0.171710i
$663$	−10.9378	+	4.56649i	−0.424788	+	0.177348i
$664$	−23.3598	−	9.17644i	−0.906536	−	0.356115i
$665$		0			0
$666$	−5.44675	+	13.5986i	−0.211057	+	0.526935i
$667$	−2.83330	−	2.83330i	−0.109706	−	0.109706i
$668$	−0.0330830	−	2.69854i	−0.00128002	−	0.104410i
$669$	38.1937	+	15.6952i	1.47665	+	0.606812i
$670$		0			0
$671$			18.9269i			0.730664i
$672$	−5.51584	+	5.89773i	−0.212778	+	0.227510i
$673$	15.4486	+	15.4486i	0.595498	+	0.595498i	0.939111	−	0.343613i	$-0.111651\pi$
$673$	15.4486	+	15.4486i	0.595498	+	0.595498i	−0.343613	+	0.939111i	$0.611651\pi$
$674$	−1.76824	−	4.19597i	−0.0681099	−	0.161623i
$675$		0			0
$676$	−24.0644	+	24.6618i	−0.925554	+	0.948529i
$677$	−3.86002	+	3.86002i	−0.148353	+	0.148353i	−0.777382	−	0.629029i	$-0.783453\pi$
$677$	−3.86002	+	3.86002i	−0.148353	+	0.148353i	0.629029	+	0.777382i	$0.283453\pi$
$678$	−21.2117	−	20.8362i	−0.814630	−	0.800210i
$679$			6.31904i			0.242503i
$680$		0			0
$681$	6.73505	−	16.3895i	0.258088	−	0.628046i
$682$	6.52637	−	16.0333i	0.249908	−	0.613947i
$683$	20.9584	+	20.9584i	0.801949	+	0.801949i	0.983400	−	0.181451i	$-0.0580793\pi$
$683$	20.9584	+	20.9584i	0.801949	+	0.801949i	−0.181451	+	0.983400i	$0.558079\pi$
$684$	−37.9691	+	0.678136i	−1.45178	+	0.0259292i
$685$		0			0
$686$	14.3074	−	6.02932i	0.546259	−	0.230201i
$687$	36.7749	−	15.3534i	1.40305	−	0.585770i
$688$	3.35702	+	3.19631i	0.127985	+	0.121858i
$689$	43.6032			1.66115
$690$		0			0
$691$		−	26.8902i		−	1.02295i	−0.859298	−	0.511475i	$-0.829099\pi$
$691$		−	26.8902i		−	1.02295i	0.859298	−	0.511475i	$-0.170901\pi$
$692$	0.0624943	+	5.09759i	0.00237568	+	0.193781i
$693$	−0.0510309	−	9.11363i	−0.00193850	−	0.346198i
$694$	14.4761	+	34.3513i	0.549504	+	1.30396i
$695$		0			0
$696$	−4.84963	−	4.64836i	−0.183825	−	0.176196i
$697$	−0.570399	+	0.570399i	−0.0216054	+	0.0216054i
$698$	−9.45148	+	23.2194i	−0.357744	+	0.878869i
$699$	4.14389	−	10.0840i	0.156736	−	0.381412i
$700$		0			0
$701$	−35.7956			−1.35198			−0.675990	−	0.736911i	$-0.736284\pi$
$701$	−35.7956			−1.35198			−0.675990	+	0.736911i	$0.736284\pi$
$702$	−40.3980	+	0.586964i	−1.52472	+	0.0221535i
$703$	15.4525	+	15.4525i	0.582804	+	0.582804i
$704$	−20.0708	+	21.6041i	−0.756445	+	0.814236i
$705$		0			0
$706$	−8.21566	−	19.4955i	−0.309200	−	0.733723i
$707$	−5.73705	+	5.73705i	−0.215764	+	0.215764i
$708$	7.81748	−	19.7073i	0.293799	−	0.740646i
$709$	−31.6856			−1.18998			−0.594988	−	0.803735i	$-0.702843\pi$
$709$	−31.6856			−1.18998			−0.594988	+	0.803735i	$0.702843\pi$
$710$		0			0
$711$	−2.34816	−	2.32201i	−0.0880628	−	0.0870821i
$712$	39.8152	−	17.3564i	1.49214	−	0.650459i
$713$	−6.86153	+	6.86153i	−0.256966	+	0.256966i
$714$	0.0224359	+	2.51259i	0.000839642	+	0.0940312i
$715$		0			0
$716$	−33.5456	+	34.3784i	−1.25366	+	1.28478i
$717$	6.44887	−	2.69238i	0.240837	−	0.100549i
$718$	−13.1837	+	32.3883i	−0.492010	+	1.20872i
$719$	47.9558			1.78845			0.894225	−	0.447618i	$-0.147728\pi$
$719$	47.9558			1.78845			0.894225	+	0.447618i	$0.147728\pi$
$720$		0			0
$721$	−9.65184			−0.359453
$722$	−11.2280	+	27.5837i	−0.417861	+	1.02656i
$723$	18.3189	−	7.64809i	0.681287	−	0.284435i
$724$	30.3392	−	31.0923i	1.12755	−	1.15554i
$725$		0			0
$726$	−0.0565836	−	6.33678i	−0.00210002	−	0.235180i
$727$	−20.8052	+	20.8052i	−0.771622	+	0.771622i	−0.978390	−	0.206768i	$-0.933705\pi$
$727$	−20.8052	+	20.8052i	−0.771622	+	0.771622i	0.206768	+	0.978390i	$0.433705\pi$
$728$	5.12153	+	11.7487i	0.189817	+	0.435435i
$729$	−19.4099	−	18.7685i	−0.718884	−	0.695130i
$730$		0			0
$731$	1.44234			0.0533468
$732$	6.55862	−	16.5338i	0.242414	−	0.611108i
$733$	−11.3990	+	11.3990i	−0.421033	+	0.421033i	−0.885559	−	0.464526i	$-0.846225\pi$
$733$	−11.3990	+	11.3990i	−0.421033	+	0.421033i	0.464526	+	0.885559i	$0.346225\pi$
$734$	−7.25237	−	17.2096i	−0.267690	−	0.635219i
$735$		0			0
$736$	15.0708	−	6.79077i	0.555516	−	0.250311i
$737$	−18.0852	−	18.0852i	−0.666176	−	0.666176i
$738$	−2.52785	+	1.08198i	−0.0930514	+	0.0398281i
$739$	9.60683			0.353393			0.176697	−	0.984265i	$-0.443459\pi$
$739$	9.60683			0.353393			0.176697	+	0.984265i	$0.443459\pi$
$740$		0			0
$741$	−22.9092	+	55.7487i	−0.841591	+	2.04798i
$742$	3.48493	−	8.56143i	0.127936	−	0.314300i
$743$	2.71436	−	2.71436i	0.0995802	−	0.0995802i	−0.655562	−	0.755142i	$-0.727568\pi$
$743$	2.71436	−	2.71436i	0.0995802	−	0.0995802i	0.755142	+	0.655562i	$0.227568\pi$
$744$	−11.2571	+	11.7446i	−0.412706	+	0.430577i
$745$		0			0
$746$	−9.24445	−	21.9368i	−0.338463	−	0.803163i
$747$	−26.6196	+	0.149054i	−0.973958	+	0.00545359i
$748$	0.112483	+	9.17508i	0.00411277	+	0.335474i
$749$			6.81468i			0.249003i
$750$		0			0
$751$	−18.9690			−0.692189			−0.346094	−	0.938200i	$-0.612492\pi$
$751$	−18.9690			−0.692189			−0.346094	+	0.938200i	$0.612492\pi$
$752$	−24.5164	+	25.7491i	−0.894022	+	0.938972i
$753$	27.9397	−	11.6648i	1.01818	−	0.425087i
$754$	−9.82507	+	4.14041i	−0.357808	+	0.150785i
$755$		0			0
$756$	−3.11352	+	7.97901i	−0.113237	+	0.290194i
$757$	−0.279592	−	0.279592i	−0.0101620	−	0.0101620i	0.702008	−	0.712170i	$-0.252287\pi$
$757$	−0.279592	−	0.279592i	−0.0101620	−	0.0101620i	−0.712170	+	0.702008i	$0.752287\pi$
$758$	−1.45739	+	3.58037i	−0.0529349	+	0.130045i
$759$	−7.09113	+	17.2560i	−0.257392	+	0.626353i
$760$		0			0
$761$			20.3237i			0.736733i	0.929681	+	0.368366i	$0.120083\pi$
$761$			20.3237i			0.736733i	−0.929681	+	0.368366i	$0.879917\pi$
$762$	−0.0361941	−	0.0355534i	−0.00131117	−	0.00128797i
$763$	−6.82036	+	6.82036i	−0.246914	+	0.246914i
$764$	18.1355	−	18.5857i	0.656118	−	0.672406i
$765$		0			0
$766$	13.6746	+	32.4494i	0.494083	+	1.17244i
$767$	−23.7938	−	23.7938i	−0.859144	−	0.859144i
$768$	25.0194	−	11.9176i	0.902811	−	0.430038i
$769$			25.1716i			0.907711i	0.891075	+	0.453855i	$0.149952\pi$
$769$			25.1716i			0.907711i	−0.891075	+	0.453855i	$0.850048\pi$
$770$		0			0
$771$	−15.3448	−	6.30577i	−0.552631	−	0.227097i
$772$	0.328916	+	26.8293i	0.0118379	+	0.965607i
$773$	−24.0474	−	24.0474i	−0.864925	−	0.864925i	0.126980	−	0.991905i	$-0.459472\pi$
$773$	−24.0474	−	24.0474i	−0.864925	−	0.864925i	−0.991905	+	0.126980i	$0.959472\pi$
$774$	4.56398	+	1.82805i	0.164049	+	0.0657079i
$775$		0			0
$776$	7.92913	−	20.1846i	0.284639	−	0.724585i
$777$	4.54832	−	1.89891i	0.163170	−	0.0681231i
$778$	−32.9213	−	13.4006i	−1.18029	−	0.480436i
$779$			4.10197i			0.146968i
$780$		0			0
$781$		−	15.2327i		−	0.545070i
$782$	1.93919	−	4.76400i	0.0693453	−	0.170360i
$783$	−6.60539	−	2.67127i	−0.236058	−	0.0954634i
$784$	−25.2754	+	0.619825i	−0.902693	+	0.0221366i
$785$		0			0
$786$	−0.114605	−	12.8345i	−0.00408782	−	0.457793i
$787$	−6.79695	−	6.79695i	−0.242285	−	0.242285i	0.575510	−	0.817795i	$-0.304804\pi$
$787$	−6.79695	−	6.79695i	−0.242285	−	0.242285i	−0.817795	+	0.575510i	$0.804804\pi$
$788$	36.3725	−	0.445912i	1.29572	−	0.0158850i
$789$	−14.3108	+	34.8249i	−0.509479	+	1.23980i
$790$		0			0
$791$			10.0043i			0.355710i
$792$	−11.2728	+	29.1752i	−0.400560	+	1.03670i
$793$	−19.9623	−	19.9623i	−0.708881	−	0.708881i
$794$	−10.0015	+	4.21476i	−0.354939	+	0.149576i
$795$		0			0
$796$	0.0647578	−	0.0663654i	0.00229528	−	0.00235226i
$797$	−6.72322	+	6.72322i	−0.238149	+	0.238149i	−0.816083	−	0.577935i	$-0.803859\pi$
$797$	−6.72322	+	6.72322i	−0.238149	+	0.238149i	0.577935	+	0.816083i	$0.303859\pi$
$798$	9.11519	+	8.95384i	0.322674	+	0.316963i
$799$			11.0630i			0.391382i
$800$		0			0
$801$	32.3924	−	32.7572i	1.14453	−	1.15742i
$802$	6.75665	+	2.75030i	0.238585	+	0.0971164i
$803$	17.3179	+	17.3179i	0.611135	+	0.611135i
$804$	9.53159	+	22.0655i	0.336153	+	0.778190i
$805$		0			0
$806$	10.0270	+	23.7938i	0.353187	+	0.838101i
$807$	−6.39851	−	15.3259i	−0.225238	−	0.539496i
$808$	25.5244	−	11.1267i	0.897946	−	0.391437i
$809$	−35.3381			−1.24242			−0.621212	−	0.783643i	$-0.713359\pi$
$809$	−35.3381			−1.24242			−0.621212	+	0.783643i	$0.713359\pi$
$810$		0			0
$811$		−	37.1596i		−	1.30485i	−0.757854	−	0.652425i	$-0.773752\pi$
$811$		−	37.1596i		−	1.30485i	0.757854	−	0.652425i	$-0.226248\pi$
$812$	0.0277074	+	2.26006i	0.000972338	+	0.0793125i
$813$	33.4179	−	13.9519i	1.17202	−	0.489314i
$814$	16.5863	−	6.98967i	0.581348	−	0.244988i
$815$		0			0
$816$	3.08113	−	8.05399i	0.107861	−	0.281946i
$817$	5.18621	−	5.18621i	0.181443	−	0.181443i
$818$	−18.5526	−	7.55184i	−0.648676	−	0.264044i
$819$	9.66601	+	9.55836i	0.337758	+	0.333996i
$820$		0			0
$821$	28.5674			0.997010			0.498505	−	0.866887i	$-0.333882\pi$
$821$	28.5674			0.997010			0.498505	+	0.866887i	$0.333882\pi$
$822$	−34.2241	+	34.8408i	−1.19370	+	1.21521i
$823$	28.5682	+	28.5682i	0.995823	+	0.995823i	0.999991	−	0.00416817i	$-0.00132677\pi$
$823$	28.5682	+	28.5682i	0.995823	+	0.995823i	−0.00416817	+	0.999991i	$0.501327\pi$
$824$	30.8304	+	12.1111i	1.07403	+	0.421911i
$825$		0			0
$826$	−6.57357	+	2.77019i	−0.228724	+	0.0963872i
$827$	5.31276	−	5.31276i	0.184743	−	0.184743i	−0.608676	−	0.793419i	$-0.708299\pi$
$827$	5.31276	−	5.31276i	0.184743	−	0.184743i	0.793419	+	0.608676i	$0.208299\pi$
$828$	12.1742	−	12.6170i	0.423082	−	0.438469i
$829$	4.51176			0.156700			0.0783500	−	0.996926i	$-0.475035\pi$
$829$	4.51176			0.156700			0.0783500	+	0.996926i	$0.475035\pi$
$830$		0			0
$831$	20.0813	+	8.25214i	0.696611	+	0.286263i
$832$	−1.61725	−	43.9547i	−0.0560679	−	1.52385i
$833$	−5.56292	+	5.56292i	−0.192744	+	0.192744i
$834$	0.201692	+	22.5875i	0.00698403	+	0.782140i
$835$		0			0
$836$	33.3953	+	32.5864i	1.15500	+	1.12702i
$837$	−6.46913	+	15.9966i	−0.223606	+	0.552922i
$838$	−6.29404	−	2.56199i	−0.217424	−	0.0885025i
$839$	−42.7255			−1.47505			−0.737523	−	0.675322i	$-0.764005\pi$
$839$	−42.7255			−1.47505			−0.737523	+	0.675322i	$0.764005\pi$
$840$		0			0
$841$	27.1197			0.935164
$842$	19.9343	+	8.11428i	0.686983	+	0.279637i
$843$	−8.13608	−	19.4877i	−0.280221	−	0.671193i
$844$	0.825584	−	0.846078i	0.0284178	−	0.0291232i
$845$		0			0
$846$	−14.0215	+	35.0068i	−0.482071	+	1.20356i
$847$	−1.50768	+	1.50768i	−0.0518045	+	0.0518045i
$848$	−21.8746	+	22.9745i	−0.751178	+	0.788946i
$849$	10.8744	−	26.4625i	0.373210	−	0.908192i
$850$		0			0
$851$	−10.0894			−0.345861
$852$	−5.27851	+	13.3067i	−0.180839	+	0.455881i
$853$	−28.1027	+	28.1027i	−0.962217	+	0.962217i	−0.999312	−	0.0370946i	$-0.988190\pi$
$853$	−28.1027	+	28.1027i	−0.962217	+	0.962217i	0.0370946	+	0.999312i	$0.488190\pi$
$854$	−5.51503	+	2.32410i	−0.188720	+	0.0795292i
$855$		0			0
$856$	8.55106	−	21.7678i	0.292269	−	0.744008i
$857$	35.8406	+	35.8406i	1.22429	+	1.22429i	0.966092	+	0.258198i	$0.0831287\pi$
$857$	35.8406	+	35.8406i	1.22429	+	1.22429i	0.258198	+	0.966092i	$0.416871\pi$
$858$	35.4141	+	34.7872i	1.20902	+	1.18762i
$859$	1.55128			0.0529289			0.0264645	−	0.999650i	$-0.491575\pi$
$859$	1.55128			0.0529289			0.0264645	+	0.999650i	$0.491575\pi$
$860$		0			0
$861$	0.855728	+	0.351651i	0.0291631	+	0.0119842i
$862$	36.5136	+	14.8629i	1.24366	+	0.506231i
$863$	22.7893	−	22.7893i	0.775758	−	0.775758i	−0.203348	−	0.979107i	$-0.565182\pi$
$863$	22.7893	−	22.7893i	0.775758	−	0.775758i	0.979107	+	0.203348i	$0.0651823\pi$
$864$	19.9574	−	21.5801i	0.678965	−	0.734171i
$865$		0			0
$866$	−5.12369	+	2.15919i	−0.174110	+	0.0733723i
$867$	10.3104	+	24.6957i	0.350160	+	0.838712i
$868$	5.47328	−	0.0671001i	0.185775	−	0.00227753i
$869$			4.05757i			0.137644i
$870$		0			0
$871$	38.1490			1.29263
$872$	30.3441	−	13.2278i	1.02758	−	0.447948i
$873$	−0.128793	−	23.0013i	−0.00435900	−	0.778476i
$874$	−10.1572	−	24.1027i	−0.343572	−	0.815285i
$875$		0			0
$876$	−9.12720	−	21.1293i	−0.308379	−	0.713894i
$877$	22.8089	+	22.8089i	0.770202	+	0.770202i	0.978142	−	0.207940i	$-0.0666758\pi$
$877$	22.8089	+	22.8089i	0.770202	+	0.770202i	−0.207940	+	0.978142i	$0.566676\pi$
$878$	−14.1692	−	5.76759i	−0.478188	−	0.194647i
$879$	−11.7005	−	4.80819i	−0.394649	−	0.162176i
$880$		0			0
$881$			1.47551i			0.0497114i	0.999691	+	0.0248557i	$0.00791262\pi$
$881$			1.47551i			0.0497114i	−0.999691	+	0.0248557i	$0.992087\pi$
$882$	−24.6533	+	10.5522i	−0.830121	+	0.355310i
$883$	−3.02812	+	3.02812i	−0.101904	+	0.101904i	−0.756221	−	0.654316i	$-0.772956\pi$
$883$	−3.02812	+	3.02812i	−0.101904	+	0.101904i	0.654316	+	0.756221i	$0.272956\pi$
$884$	−9.79563	−	9.55836i	−0.329463	−	0.321482i
$885$		0			0
$886$	10.5968	−	4.46561i	0.356005	−	0.150025i
$887$	19.9170	+	19.9170i	0.668749	+	0.668749i	0.957426	−	0.288678i	$-0.0932156\pi$
$887$	19.9170	+	19.9170i	0.668749	+	0.668749i	−0.288678	+	0.957426i	$0.593216\pi$
$888$	−16.9112	+	0.358371i	−0.567504	+	0.0120261i
$889$			0.0170705i			0.000572528i
$890$		0			0
$891$	0.371504	+	33.1725i	0.0124459	+	1.11132i
$892$	0.584504	+	47.6773i	0.0195706	+	1.59635i
$893$	39.7794	+	39.7794i	1.33117	+	1.33117i
$894$	34.3048	−	0.306321i	1.14733	−	0.0102449i
$895$		0			0
$896$	−8.75970	−	3.19548i	−0.292641	−	0.106754i
$897$	−10.7209	−	25.6790i	−0.357961	−	0.857398i
$898$	3.68523	−	9.05349i	0.122978	−	0.302119i
$899$			4.55350i			0.151868i
$900$		0			0
$901$			9.87094i			0.328849i
$902$	3.12918	+	1.27374i	0.104190	+	0.0424108i
$903$	−0.637317	−	1.52652i	−0.0212086	−	0.0507993i
$904$	12.5533	−	31.9561i	0.417518	−	1.06284i
$905$		0			0
$906$	−0.287176	−	32.1607i	−0.00954077	−	1.06847i
$907$	6.11318	+	6.11318i	0.202985	+	0.202985i	0.801278	−	0.598293i	$-0.204154\pi$
$907$	6.11318	+	6.11318i	0.202985	+	0.202985i	−0.598293	+	0.801278i	$0.704154\pi$
$908$	20.4590	−	0.250819i	0.678956	−	0.00832372i
$909$	20.7659	−	20.9998i	0.688762	−	0.696518i
$910$		0			0
$911$		−	28.1492i		−	0.932625i	−0.884620	−	0.466313i	$-0.845582\pi$
$911$		−	28.1492i		−	0.932625i	0.884620	−	0.466313i	$-0.154418\pi$
$912$	−17.8809	−	40.0385i	−0.592096	−	1.32581i
$913$	23.1278	+	23.1278i	0.765419	+	0.765419i
$914$	4.00570	+	9.50541i	0.132497	+	0.314411i
$915$		0			0
$916$	32.9349	+	32.1371i	1.08820	+	1.06184i
$917$	−3.05366	+	3.05366i	−0.100841	+	0.100841i
$918$	−0.132878	−	9.14535i	−0.00438561	−	0.301842i
$919$		−	49.4285i		−	1.63049i	−0.579113	−	0.815247i	$-0.696601\pi$
$919$		−	49.4285i		−	1.63049i	0.579113	−	0.815247i	$-0.303399\pi$
$920$		0			0
$921$	−20.8400	−	8.56393i	−0.686701	−	0.282191i
$922$	−9.84005	+	24.1740i	−0.324065	+	0.796129i
$923$	16.0660	+	16.0660i	0.528819	+	0.528819i
$924$	9.66086	−	4.17318i	0.317819	−	0.137288i
$925$		0			0
$926$	−36.2892	+	15.2927i	−1.19254	+	0.502550i
$927$	35.1327	−	0.196722i	1.15391	−	0.00646120i
$928$	2.74741	−	7.25396i	0.0901883	−	0.238123i
$929$	38.9204			1.27694			0.638468	−	0.769649i	$-0.279569\pi$
$929$	38.9204			1.27694			0.638468	+	0.769649i	$0.279569\pi$
$930$		0			0
$931$			40.0052i			1.31112i
$932$	12.5879	−	0.154322i	0.412329	−	0.00505499i
$933$	20.3988	+	48.8598i	0.667828	+	1.59960i
$934$	−1.61507	−	3.83251i	−0.0528466	−	0.125403i
$935$		0			0
$936$	−18.8818	−	42.6607i	−0.617172	−	1.39441i
$937$	4.49303	−	4.49303i	0.146781	−	0.146781i	−0.629897	−	0.776678i	$-0.716903\pi$
$937$	4.49303	−	4.49303i	0.146781	−	0.146781i	0.776678	+	0.629897i	$0.216903\pi$
$938$	3.04902	−	7.49052i	0.0995540	−	0.244574i
$939$	−37.2952	−	15.3260i	−1.21708	−	0.500145i
$940$		0			0
$941$	−23.2736			−0.758696			−0.379348	−	0.925254i	$-0.623852\pi$
$941$	−23.2736			−0.758696			−0.379348	+	0.925254i	$0.623852\pi$
$942$	15.4618	−	15.7404i	0.503771	−	0.512849i
$943$	−1.33915	−	1.33915i	−0.0436087	−	0.0436087i
$944$	24.4737	−	0.600164i	0.796550	−	0.0195337i
$945$		0			0
$946$	−2.34589	−	5.56671i	−0.0762713	−	0.180989i
$947$	−28.1797	+	28.1797i	−0.915717	+	0.915717i	−0.996714	−	0.0809978i	$-0.974189\pi$
$947$	−28.1797	+	28.1797i	−0.915717	+	0.915717i	0.0809978	+	0.996714i	$0.474189\pi$
$948$	1.40605	−	3.54454i	0.0456663	−	0.115121i
$949$	−36.5305			−1.18583
$950$		0			0
$951$	−0.000574173		0.00139723i	−1.86188e−5		4.53082e-5i
$952$	−2.65968	+	1.15942i	−0.0862006	+	0.0375770i
$953$	28.5653	−	28.5653i	0.925321	−	0.925321i	−0.0720776	−	0.997399i	$-0.522963\pi$
$953$	28.5653	−	28.5653i	0.925321	−	0.925321i	0.997399	+	0.0720776i	$0.0229629\pi$
$954$	−12.5106	+	31.2346i	−0.405047	+	1.01126i
$955$		0			0
$956$	5.77547	+	5.63557i	0.186792	+	0.182267i
$957$	3.37284	+	8.07871i	0.109028	+	0.261148i
$958$	10.5083	−	25.8157i	0.339507	−	0.834066i
$959$	16.4323			0.530625
$960$		0			0
$961$	−19.9726			−0.644277
$962$	−10.1216	+	24.8656i	−0.326332	+	0.801700i
$963$	−0.138895	−	24.8054i	−0.00447584	−	0.799343i
$964$	16.4060	+	16.0086i	0.528402	+	0.515603i
$965$		0			0
$966$	−5.89890	+	0.0526736i	−0.189794	+	0.00169475i
$967$	37.0606	−	37.0606i	1.19179	−	1.19179i	0.215225	−	0.976565i	$-0.430952\pi$
$967$	37.0606	−	37.0606i	1.19179	−	1.19179i	0.976565	−	0.215225i	$-0.0690484\pi$
$968$	6.70774	−	2.92407i	0.215595	−	0.0939832i
$969$	−12.6204	−	5.18621i	−0.405427	−	0.166605i
$970$		0			0
$971$	11.8114			0.379044			0.189522	−	0.981876i	$-0.439306\pi$
$971$	11.8114			0.379044			0.189522	+	0.981876i	$0.439306\pi$
$972$	11.1706	−	29.1070i	0.358296	−	0.933608i
$973$	5.37412	−	5.37412i	0.172287	−	0.172287i
$974$	−3.27288	−	7.76644i	−0.104870	−	0.248853i
$975$		0			0
$976$	20.5327	−	0.503519i	0.657234	−	0.0161173i
$977$	−5.34002	−	5.34002i	−0.170842	−	0.170842i	0.616507	−	0.787349i	$-0.288547\pi$
$977$	−5.34002	−	5.34002i	−0.170842	−	0.170842i	−0.787349	+	0.616507i	$0.788547\pi$
$978$	−8.55088	−	8.39953i	−0.273427	−	0.268587i
$979$	−56.6038			−1.80907
$980$		0			0
$981$	24.6871	−	24.9651i	0.788197	−	0.797074i
$982$	14.7805	−	36.3111i	0.471664	−	1.15874i
$983$	−42.6490	+	42.6490i	−1.36029	+	1.36029i	−0.486753	+	0.873540i	$0.661819\pi$
$983$	−42.6490	+	42.6490i	−1.36029	+	1.36029i	−0.873540	+	0.486753i	$0.838181\pi$
$984$	−2.29216	−	2.19703i	−0.0730714	−	0.0700387i
$985$		0			0
$986$	−0.937311	−	2.22421i	−0.0298501	−	0.0708333i
$987$	11.7087	−	4.88836i	0.372693	−	0.155598i
$988$	−69.5912	+	0.853159i	−2.21399	+	0.0271426i
$989$			3.38623i			0.107676i
$990$		0			0
$991$	−31.5197			−1.00126			−0.500629	−	0.865662i	$-0.666898\pi$
$991$	−31.5197			−1.00126			−0.500629	+	0.865662i	$0.666898\pi$
$992$	−17.5672	−	6.65353i	−0.557760	−	0.211250i
$993$	−5.52938	−	13.2441i	−0.175469	−	0.420289i
$994$	4.43860	−	1.87048i	0.140784	−	0.0593282i
$995$		0			0
$996$	−12.1892	−	28.2179i	−0.386231	−	0.894120i
$997$	−38.3474	−	38.3474i	−1.21447	−	1.21447i	−0.969540	−	0.244935i	$-0.921233\pi$
$997$	−38.3474	−	38.3474i	−1.21447	−	1.21447i	−0.244935	−	0.969540i	$-0.578767\pi$
$998$	−2.74429	+	6.74190i	−0.0868690	+	0.213411i
$999$	−16.5172	+	7.00473i	−0.522580	+	0.221620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.w.j.293.6		32
3.2	odd	2	inner	600.2.w.j.293.11		32
5.2	odd	4	inner	600.2.w.j.557.3		32
5.3	odd	4		120.2.w.c.77.14	yes	32
5.4	even	2		120.2.w.c.53.11	yes	32
8.5	even	2	inner	600.2.w.j.293.14		32
15.2	even	4	inner	600.2.w.j.557.14		32
15.8	even	4		120.2.w.c.77.3	yes	32
15.14	odd	2		120.2.w.c.53.6	yes	32
20.3	even	4		480.2.bi.c.17.11		32
20.19	odd	2		480.2.bi.c.113.3		32
24.5	odd	2	inner	600.2.w.j.293.3		32
40.3	even	4		480.2.bi.c.17.6		32
40.13	odd	4		120.2.w.c.77.6	yes	32
40.19	odd	2		480.2.bi.c.113.14		32
40.29	even	2		120.2.w.c.53.3	✓	32
40.37	odd	4	inner	600.2.w.j.557.11		32
60.23	odd	4		480.2.bi.c.17.14		32
60.59	even	2		480.2.bi.c.113.6		32
120.29	odd	2		120.2.w.c.53.14	yes	32
120.53	even	4		120.2.w.c.77.11	yes	32
120.59	even	2		480.2.bi.c.113.11		32
120.77	even	4	inner	600.2.w.j.557.6		32
120.83	odd	4		480.2.bi.c.17.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.w.c.53.3	✓	32	40.29	even	2
120.2.w.c.53.6	yes	32	15.14	odd	2
120.2.w.c.53.11	yes	32	5.4	even	2
120.2.w.c.53.14	yes	32	120.29	odd	2
120.2.w.c.77.3	yes	32	15.8	even	4
120.2.w.c.77.6	yes	32	40.13	odd	4
120.2.w.c.77.11	yes	32	120.53	even	4
120.2.w.c.77.14	yes	32	5.3	odd	4
480.2.bi.c.17.3		32	120.83	odd	4
480.2.bi.c.17.6		32	40.3	even	4
480.2.bi.c.17.11		32	20.3	even	4
480.2.bi.c.17.14		32	60.23	odd	4
480.2.bi.c.113.3		32	20.19	odd	2
480.2.bi.c.113.6		32	60.59	even	2
480.2.bi.c.113.11		32	120.59	even	2
480.2.bi.c.113.14		32	40.19	odd	2
600.2.w.j.293.3		32	24.5	odd	2	inner
600.2.w.j.293.6		32	1.1	even	1	trivial
600.2.w.j.293.11		32	3.2	odd	2	inner
600.2.w.j.293.14		32	8.5	even	2	inner
600.2.w.j.557.3		32	5.2	odd	4	inner
600.2.w.j.557.6		32	120.77	even	4	inner
600.2.w.j.557.11		32	40.37	odd	4	inner
600.2.w.j.557.14		32	15.2	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.533177 + 1.30986i) q^{2} +(-1.59834 + 0.667305i) q^{3} +(-1.43144 - 1.39677i) q^{4} +(-0.0218716 - 2.44939i) q^{6} +(-0.582772 + 0.582772i) q^{7} +(2.59278 - 1.13026i) q^{8} +(2.10941 - 2.13317i) q^{9} +O(q^{10})\)	\(q+(-0.533177 + 1.30986i) q^{2} +(-1.59834 + 0.667305i) q^{3} +(-1.43144 - 1.39677i) q^{4} +(-0.0218716 - 2.44939i) q^{6} +(-0.582772 + 0.582772i) q^{7} +(2.59278 - 1.13026i) q^{8} +(2.10941 - 2.13317i) q^{9} -3.68607 q^{11} +(3.22001 + 1.27731i) q^{12} +(3.88771 - 3.88771i) q^{13} +(-0.452626 - 1.07407i) q^{14} +(0.0980619 + 3.99880i) q^{16} +(0.880105 + 0.880105i) q^{17} +(1.66945 + 3.90038i) q^{18} +6.32919 q^{19} +(0.542584 - 1.32036i) q^{21} +(1.96533 - 4.82821i) q^{22} +(-2.06626 + 2.06626i) q^{23} +(-3.38993 + 3.53672i) q^{24} +(3.01950 + 7.16518i) q^{26} +(-1.94809 + 4.81715i) q^{27} +(1.64820 - 0.0202063i) q^{28} +1.37122i q^{29} +3.32075 q^{31} +(-5.29013 - 2.00362i) q^{32} +(5.89160 - 2.45973i) q^{33} +(-1.62206 + 0.683558i) q^{34} +(-5.99904 + 0.107144i) q^{36} +(2.44147 + 2.44147i) q^{37} +(-3.37458 + 8.29032i) q^{38} +(-3.61961 + 8.80819i) q^{39} +0.648104i q^{41} +(1.44018 + 1.41469i) q^{42} +(0.819412 - 0.819412i) q^{43} +(5.27640 + 5.14859i) q^{44} +(-1.60482 - 3.80818i) q^{46} +(6.28508 + 6.28508i) q^{47} +(-2.82515 - 6.32602i) q^{48} +6.32075i q^{49} +(-1.99401 - 0.819412i) q^{51} +(-10.9953 + 0.134798i) q^{52} +(5.60782 + 5.60782i) q^{53} +(-5.27109 - 5.12011i) q^{54} +(-0.852318 + 2.16968i) q^{56} +(-10.1162 + 4.22349i) q^{57} +(-1.79611 - 0.731106i) q^{58} -6.12026i q^{59} -5.13471i q^{61} +(-1.77055 + 4.34971i) q^{62} +(0.0138443 + 2.47245i) q^{63} +(5.44503 - 5.86102i) q^{64} +(0.0806201 + 9.02862i) q^{66} +(4.90636 + 4.90636i) q^{67} +(-0.0305156 - 2.48912i) q^{68} +(1.92377 - 4.68141i) q^{69} +4.13251i q^{71} +(3.05821 - 7.91501i) q^{72} +(-4.69820 - 4.69820i) q^{73} +(-4.49972 + 1.89624i) q^{74} +(-9.05987 - 8.84042i) q^{76} +(2.14814 - 2.14814i) q^{77} +(-9.60756 - 9.43750i) q^{78} -1.10079i q^{79} +(-0.100786 - 8.99944i) q^{81} +(-0.848922 - 0.345554i) q^{82} +(-6.27439 - 6.27439i) q^{83} +(-2.62091 + 1.13215i) q^{84} +(0.636420 + 1.51020i) q^{86} +(-0.915024 - 2.19169i) q^{87} +(-9.55717 + 4.16621i) q^{88} +15.3562 q^{89} +4.53130i q^{91} +(5.84382 - 0.0716428i) q^{92} +(-5.30771 + 2.21595i) q^{93} +(-11.5836 + 4.88148i) q^{94} +(9.79248 - 0.327652i) q^{96} +(5.42154 - 5.42154i) q^{97} +(-8.27927 - 3.37008i) q^{98} +(-7.77542 + 7.86299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{6}+O(q^{10}) \) 32 * q - 4 * q^6	\( 32 q - 4 q^{6} + 8 q^{12} + 28 q^{16} + 20 q^{18} + 52 q^{22} - 12 q^{28} - 32 q^{31} - 8 q^{33} - 20 q^{36} - 16 q^{42} + 24 q^{46} - 44 q^{48} - 8 q^{52} + 16 q^{57} - 28 q^{58} - 48 q^{63} + 16 q^{66} - 32 q^{72} + 64 q^{73} - 88 q^{76} - 64 q^{78} + 48 q^{81} - 64 q^{82} + 8 q^{87} + 52 q^{88} - 52 q^{96} - 16 q^{97}+O(q^{100}) \) 32 * q - 4 * q^6 + 8 * q^12 + 28 * q^16 + 20 * q^18 + 52 * q^22 - 12 * q^28 - 32 * q^31 - 8 * q^33 - 20 * q^36 - 16 * q^42 + 24 * q^46 - 44 * q^48 - 8 * q^52 + 16 * q^57 - 28 * q^58 - 48 * q^63 + 16 * q^66 - 32 * q^72 + 64 * q^73 - 88 * q^76 - 64 * q^78 + 48 * q^81 - 64 * q^82 + 8 * q^87 + 52 * q^88 - 52 * q^96 - 16 * q^97

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