LMFDB - Embedded newform 738.2.ba.a.89.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [738,2,Mod(17,738)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("738.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(738, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 33])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.ba (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,-4,0,4,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$3$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			89.1
Character	$\chi$	$=$	738.89
Dual form			738.2.ba.a.539.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.891007 + 0.453990i) q^{2} +(0.587785 - 0.809017i) q^{4} +(-2.53900 + 0.402138i) q^{5} +(1.91317 + 0.150570i) q^{7} +(-0.156434 + 0.987688i) q^{8} +(2.07970 - 1.51099i) q^{10} +(-0.481597 - 2.00600i) q^{11} +(-1.04091 - 0.889022i) q^{13} +(-1.77301 + 0.734404i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-2.39754 + 3.91244i) q^{17} +(-2.79249 + 2.38501i) q^{19} +(-1.16705 + 2.29046i) q^{20} +(1.33981 + 1.56872i) q^{22} +(1.05344 - 3.24217i) q^{23} +(1.52952 - 0.496972i) q^{25} +(1.33107 + 0.319561i) q^{26} +(1.24635 - 1.45929i) q^{28} +(-2.25879 - 3.68601i) q^{29} +(1.46148 + 2.01155i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.360018 - 4.57447i) q^{34} +(-4.91810 + 0.387063i) q^{35} +(-7.99481 - 5.80857i) q^{37} +(1.40535 - 3.39282i) q^{38} -2.57065i q^{40} +(-6.13781 + 1.82408i) q^{41} +(-4.39530 - 8.62626i) q^{43} +(-1.90596 - 0.789475i) q^{44} +(0.533288 + 3.36705i) q^{46} +(0.0235479 + 0.299204i) q^{47} +(-3.27625 - 0.518907i) q^{49} +(-1.13719 + 1.13719i) q^{50} +(-1.33107 + 0.319561i) q^{52} +(0.335935 - 0.205861i) q^{53} +(2.02946 + 4.89955i) q^{55} +(-0.448003 + 1.86607i) q^{56} +(3.68601 + 2.25879i) q^{58} +(-3.35065 - 1.08869i) q^{59} +(1.10029 + 0.560625i) q^{61} +(-2.21541 - 1.12881i) q^{62} +(-0.951057 - 0.309017i) q^{64} +(3.00038 + 1.83864i) q^{65} +(0.716549 - 2.98464i) q^{67} +(1.75599 + 4.23933i) q^{68} +(4.20634 - 2.57765i) q^{70} +(-10.1802 + 2.44406i) q^{71} +(-7.20995 + 7.20995i) q^{73} +(9.76046 + 1.54590i) q^{74} +(0.288130 + 3.66104i) q^{76} +(-0.619336 - 3.91034i) q^{77} +(0.632092 + 0.261821i) q^{79} +(1.16705 + 2.29046i) q^{80} +(4.64072 - 4.41177i) q^{82} -12.6379i q^{83} +(4.51402 - 10.8978i) q^{85} +(7.83248 + 5.69063i) q^{86} +(2.05664 - 0.161861i) q^{88} +(0.333231 - 4.23410i) q^{89} +(-1.85759 - 1.85759i) q^{91} +(-2.00377 - 2.75795i) q^{92} +(-0.156817 - 0.255902i) q^{94} +(6.13102 - 7.17850i) q^{95} +(-3.33298 - 0.800177i) q^{97} +(3.15474 - 1.02504i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{5} + 4 q^{7} - 8 q^{11} - 4 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{17} - 4 q^{19} + 16 q^{20} + 20 q^{22} - 40 q^{25} - 20 q^{26} - 4 q^{28} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 52 q^{35} - 24 q^{37}+ \cdots + 16 q^{97}+O(q^{100}) $ 48 * q - 4 * q^5 + 4 * q^7 - 8 * q^11 - 4 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^17 - 4 * q^19 + 16 * q^20 + 20 * q^22 - 40 * q^25 - 20 * q^26 - 4 * q^28 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 52 * q^35 - 24 * q^37 + 16 * q^38 + 12 * q^41 - 20 * q^44 + 16 * q^46 - 8 * q^47 - 48 * q^49 - 16 * q^50 + 20 * q^52 + 64 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^58 + 20 * q^59 - 60 * q^61 - 36 * q^62 + 128 * q^65 - 12 * q^67 - 8 * q^68 + 8 * q^70 - 40 * q^71 + 8 * q^73 + 8 * q^74 + 12 * q^76 - 44 * q^77 + 36 * q^79 - 16 * q^80 + 68 * q^82 + 104 * q^85 - 16 * q^86 + 8 * q^88 - 60 * q^89 + 56 * q^91 - 12 * q^94 - 28 * q^95 + 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$-1$	$e\left(\frac{39}{40}\right)$

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 $

$2$	−0.891007	+	0.453990i	−0.630037	+	0.321020i
$2$	−0.891007	+	0.453990i	−0.630037	+	0.321020i
$3$		0			0
$3$		0			0
$4$	0.587785	−	0.809017i	0.293893	−	0.404508i
$5$	−2.53900	+	0.402138i	−1.13548	+	0.179842i	−0.695745	−	0.718289i	$-0.744926\pi$
$5$	−2.53900	+	0.402138i	−1.13548	+	0.179842i	−0.439730	+	0.898130i	$0.644926\pi$
$6$		0			0
$7$	1.91317	+	0.150570i	0.723112	+	0.0569102i	0.434673	−	0.900588i	$-0.356864\pi$
$7$	1.91317	+	0.150570i	0.723112	+	0.0569102i	0.288439	+	0.957498i	$0.406864\pi$
$8$	−0.156434	+	0.987688i	−0.0553079	+	0.349201i
$9$		0			0
$10$	2.07970	−	1.51099i	0.657658	−	0.477817i
$11$	−0.481597	−	2.00600i	−0.145207	−	0.604831i	−0.996751	−	0.0805471i	$-0.974333\pi$
$11$	−0.481597	−	2.00600i	−0.145207	−	0.604831i	0.851544	−	0.524283i	$-0.175667\pi$
$12$		0			0
$13$	−1.04091	−	0.889022i	−0.288697	−	0.246570i	0.493291	−	0.869865i	$-0.335794\pi$
$13$	−1.04091	−	0.889022i	−0.288697	−	0.246570i	−0.781987	+	0.623294i	$0.785794\pi$
$14$	−1.77301	+	0.734404i	−0.473857	+	0.196278i
$15$		0			0
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−2.39754	+	3.91244i	−0.581490	+	0.948905i	0.417697	+	0.908586i	$0.362837\pi$
$17$	−2.39754	+	3.91244i	−0.581490	+	0.948905i	−0.999187	+	0.0403188i	$0.987163\pi$
$18$		0			0
$19$	−2.79249	+	2.38501i	−0.640640	+	0.547158i	−0.909334	−	0.416067i	$-0.863408\pi$
$19$	−2.79249	+	2.38501i	−0.640640	+	0.547158i	0.268694	+	0.963226i	$0.413408\pi$
$20$	−1.16705	+	2.29046i	−0.260960	+	0.512163i
$21$		0			0
$22$	1.33981	+	1.56872i	0.285648	+	0.334451i
$23$	1.05344	−	3.24217i	0.219658	−	0.676039i	−0.779132	−	0.626860i	$-0.784340\pi$
$23$	1.05344	−	3.24217i	0.219658	−	0.676039i	0.998790	−	0.0491788i	$-0.0156604\pi$
$24$		0			0
$25$	1.52952	−	0.496972i	0.305904	−	0.0993943i
$26$	1.33107	+	0.319561i	0.261044	+	0.0626710i
$27$		0			0
$28$	1.24635	−	1.45929i	0.235538	−	0.275780i
$29$	−2.25879	−	3.68601i	−0.419447	−	0.684476i	0.571217	−	0.820799i	$-0.306471\pi$
$29$	−2.25879	−	3.68601i	−0.419447	−	0.684476i	−0.990664	+	0.136323i	$0.956471\pi$
$30$		0			0
$31$	1.46148	+	2.01155i	0.262489	+	0.361285i	0.919836	−	0.392303i	$-0.128322\pi$
$31$	1.46148	+	2.01155i	0.262489	+	0.361285i	−0.657347	+	0.753588i	$0.728322\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$		0			0
$34$	0.360018	−	4.57447i	0.0617427	−	0.784515i
$35$	−4.91810	+	0.387063i	−0.831311	+	0.0654256i
$36$		0			0
$37$	−7.99481	−	5.80857i	−1.31434	−	0.954922i	−0.999984	−	0.00561644i	$-0.998212\pi$
$37$	−7.99481	−	5.80857i	−1.31434	−	0.954922i	−0.314354	−	0.949306i	$-0.601788\pi$
$38$	1.40535	−	3.39282i	0.227978	−	0.550388i
$39$		0			0
$40$		−	2.57065i		−	0.406455i
$41$	−6.13781	+	1.82408i	−0.958565	+	0.284873i
$41$	−6.13781	+	1.82408i	−0.958565	+	0.284873i
$42$		0			0
$43$	−4.39530	−	8.62626i	−0.670277	−	1.31549i	−0.936190	−	0.351495i	$-0.885673\pi$
$43$	−4.39530	−	8.62626i	−0.670277	−	1.31549i	0.265913	−	0.963997i	$-0.414327\pi$
$44$	−1.90596	−	0.789475i	−0.287334	−	0.119018i
$45$		0			0
$46$	0.533288	+	3.36705i	0.0786290	+	0.496444i
$47$	0.0235479	+	0.299204i	0.00343481	+	0.0436434i	0.998396	−	0.0566186i	$-0.0180319\pi$
$47$	0.0235479	+	0.299204i	0.00343481	+	0.0436434i	−0.994961	+	0.100262i	$0.968032\pi$
$48$		0			0
$49$	−3.27625	−	0.518907i	−0.468036	−	0.0741296i
$50$	−1.13719	+	1.13719i	−0.160823	+	0.160823i
$51$		0			0
$52$	−1.33107	+	0.319561i	−0.184586	+	0.0443151i
$53$	0.335935	−	0.205861i	0.0461442	−	0.0282772i	−0.499235	−	0.866467i	$-0.666386\pi$
$53$	0.335935	−	0.205861i	0.0461442	−	0.0282772i	0.545379	+	0.838189i	$0.316386\pi$
$54$		0			0
$55$	2.02946	+	4.89955i	0.273653	+	0.660656i
$56$	−0.448003	+	1.86607i	−0.0598669	+	0.249364i
$57$		0			0
$58$	3.68601	+	2.25879i	0.483997	+	0.296594i
$59$	−3.35065	−	1.08869i	−0.436218	−	0.141736i	0.0826720	−	0.996577i	$-0.473655\pi$
$59$	−3.35065	−	1.08869i	−0.436218	−	0.141736i	−0.518890	+	0.854841i	$0.673655\pi$
$60$		0			0
$61$	1.10029	+	0.560625i	0.140878	+	0.0717807i	0.523008	−	0.852328i	$-0.324810\pi$
$61$	1.10029	+	0.560625i	0.140878	+	0.0717807i	−0.382131	+	0.924108i	$0.624810\pi$
$62$	−2.21541	−	1.12881i	−0.281357	−	0.143359i
$63$		0			0
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$	3.00038	+	1.83864i	0.372152	+	0.228055i
$66$		0			0
$67$	0.716549	−	2.98464i	0.0875404	−	0.364632i	−0.911355	−	0.411621i	$-0.864963\pi$
$67$	0.716549	−	2.98464i	0.0875404	−	0.364632i	0.998895	+	0.0469892i	$0.0149626\pi$
$68$	1.75599	+	4.23933i	0.212945	+	0.514094i
$69$		0			0
$70$	4.20634	−	2.57765i	0.502753	−	0.308088i
$71$	−10.1802	+	2.44406i	−1.20817	+	0.290057i	−0.787017	−	0.616931i	$-0.788376\pi$
$71$	−10.1802	+	2.44406i	−1.20817	+	0.290057i	−0.421156	+	0.906988i	$0.638376\pi$
$72$		0			0
$73$	−7.20995	+	7.20995i	−0.843861	+	0.843861i	−0.989359	−	0.145498i	$-0.953522\pi$
$73$	−7.20995	+	7.20995i	−0.843861	+	0.843861i	0.145498	+	0.989359i	$0.453522\pi$
$74$	9.76046	+	1.54590i	1.13463	+	0.179708i
$75$		0			0
$76$	0.288130	+	3.66104i	0.0330508	+	0.419950i
$77$	−0.619336	−	3.91034i	−0.0705799	−	0.445624i
$78$		0			0
$79$	0.632092	+	0.261821i	0.0711159	+	0.0294572i	0.417958	−	0.908466i	$-0.362746\pi$
$79$	0.632092	+	0.261821i	0.0711159	+	0.0294572i	−0.346842	+	0.937924i	$0.612746\pi$
$80$	1.16705	+	2.29046i	0.130480	+	0.256082i
$81$		0			0
$82$	4.64072	−	4.41177i	0.512481	−	0.487199i
$83$		−	12.6379i		−	1.38719i	−0.720367	−	0.693593i	$-0.756027\pi$
$83$		−	12.6379i		−	1.38719i	0.720367	−	0.693593i	$-0.243973\pi$
$84$		0			0
$85$	4.51402	−	10.8978i	0.489615	−	1.18203i
$86$	7.83248	+	5.69063i	0.844598	+	0.613636i
$87$		0			0
$88$	2.05664	−	0.161861i	0.219238	−	0.0172544i
$89$	0.333231	−	4.23410i	0.0353224	−	0.448813i	−0.953671	−	0.300852i	$-0.902729\pi$
$89$	0.333231	−	4.23410i	0.0353224	−	0.448813i	0.988993	−	0.147961i	$-0.0472711\pi$
$90$		0			0
$91$	−1.85759	−	1.85759i	−0.194728	−	0.194728i
$92$	−2.00377	−	2.75795i	−0.208908	−	0.287537i
$93$		0			0
$94$	−0.156817	−	0.255902i	−0.0161744	−	0.0263943i
$95$	6.13102	−	7.17850i	0.629029	−	0.736499i
$96$		0			0
$97$	−3.33298	−	0.800177i	−0.338413	−	0.0812457i	0.0606774	−	0.998157i	$-0.480674\pi$
$97$	−3.33298	−	0.800177i	−0.338413	−	0.0812457i	−0.399090	+	0.916912i	$0.630674\pi$
$98$	3.15474	−	1.02504i	0.318677	−	0.103544i
$99$		0			0
$100$	0.496972	−	1.52952i	0.0496972	−	0.152952i
$101$	8.59715	+	10.0660i	0.855448	+	1.00160i	0.999927	+	0.0120932i	$0.00384949\pi$
$101$	8.59715	+	10.0660i	0.855448	+	1.00160i	−0.144479	+	0.989508i	$0.546151\pi$
$102$		0			0
$103$	−3.44361	+	6.75846i	−0.339309	+	0.665931i	−0.996109	−	0.0881342i	$-0.971910\pi$
$103$	−3.44361	+	6.75846i	−0.339309	+	0.665931i	0.656800	+	0.754065i	$0.271910\pi$
$104$	1.04091	−	0.889022i	0.102070	−	0.0871758i
$105$		0			0
$106$	−0.205861	+	0.335935i	−0.0199950	+	0.0326289i
$107$	−0.115813	−	0.356436i	−0.0111961	−	0.0344580i	0.945302	−	0.326195i	$-0.105767\pi$
$107$	−0.115813	−	0.356436i	−0.0111961	−	0.0344580i	−0.956498	+	0.291737i	$0.905767\pi$
$108$		0			0
$109$	−7.04095	+	2.91646i	−0.674400	+	0.279346i	−0.693484	−	0.720472i	$-0.743925\pi$
$109$	−7.04095	+	2.91646i	−0.674400	+	0.279346i	0.0190835	+	0.999818i	$0.493925\pi$
$110$	−4.03262	−	3.44418i	−0.384495	−	0.328390i
$111$		0			0
$112$	−0.448003	−	1.86607i	−0.0423323	−	0.176327i
$113$	9.26527	−	6.73161i	0.871603	−	0.633257i	−0.0594132	−	0.998233i	$-0.518923\pi$
$113$	9.26527	−	6.73161i	0.871603	−	0.633257i	0.931017	+	0.364976i	$0.118923\pi$
$114$		0			0
$115$	−1.37090	+	8.65550i	−0.127837	+	0.807129i
$116$	−4.30973	−	0.339183i	−0.400149	−	0.0314924i
$117$		0			0
$118$	3.47971	−	0.551132i	0.320333	−	0.0507358i
$119$	−5.17602	+	7.12418i	−0.474485	+	0.653072i
$120$		0			0
$121$	6.00899	−	3.06173i	0.546272	−	0.278339i
$122$	−1.23488			−0.111801
$123$		0			0
$124$	2.48641			0.223286
$125$	7.76872	−	3.95836i	0.694855	−	0.354047i
$126$		0			0
$127$	−7.82662	+	10.7724i	−0.694501	+	0.955898i	0.305493	+	0.952194i	$0.401179\pi$
$127$	−7.82662	+	10.7724i	−0.694501	+	0.955898i	−0.999993	+	0.00370359i	$0.998821\pi$
$128$	0.987688	−	0.156434i	0.0873001	−	0.0138270i
$129$		0			0
$130$	−3.50809	−	0.276092i	−0.307679	−	0.0242149i
$131$	0.811861	−	5.12589i	0.0709327	−	0.447851i	−0.926503	−	0.376287i	$-0.877201\pi$
$131$	0.811861	−	5.12589i	0.0709327	−	0.447851i	0.997436	−	0.0715646i	$-0.0227992\pi$
$132$		0			0
$133$	−5.70162	+	4.14247i	−0.494394	+	0.359198i
$134$	0.716549	+	2.98464i	0.0619004	+	0.257834i
$135$		0			0
$136$	−3.48921	−	2.98007i	−0.299197	−	0.255539i
$137$	0.168936	−	0.0699756i	0.0144332	−	0.00597842i	−0.375455	−	0.926841i	$-0.622514\pi$
$137$	0.168936	−	0.0699756i	0.0144332	−	0.00597842i	0.389888	+	0.920862i	$0.372514\pi$
$138$		0			0
$139$	3.49345	+	10.7517i	0.296310	+	0.911949i	0.982778	+	0.184789i	$0.0591602\pi$
$139$	3.49345	+	10.7517i	0.296310	+	0.911949i	−0.686468	+	0.727160i	$0.740840\pi$
$140$	−2.57765	+	4.20634i	−0.217851	+	0.355500i
$141$		0			0
$142$	7.96109	−	6.79941i	0.668080	−	0.570594i
$143$	−1.28208	+	2.51622i	−0.107213	+	0.210416i
$144$		0			0
$145$	7.21736	+	8.45044i	0.599369	+	0.701771i
$146$	3.15086	−	9.69736i	0.260767	−	0.802559i
$147$		0			0
$148$	−9.39846	+	3.05374i	−0.772548	+	0.251016i
$149$	20.1245	+	4.83146i	1.64866	+	0.395809i	0.948148	−	0.317830i	$-0.102954\pi$
$149$	20.1245	+	4.83146i	1.64866	+	0.395809i	0.700514	+	0.713638i	$0.252954\pi$
$150$		0			0
$151$	−8.65374	+	10.1322i	−0.704232	+	0.824549i	−0.991058	−	0.133433i	$-0.957400\pi$
$151$	−8.65374	+	10.1322i	−0.704232	+	0.824549i	0.286826	+	0.957983i	$0.407400\pi$
$152$	−1.91880	−	3.13120i	−0.155636	−	0.253974i
$153$		0			0
$154$	2.32709	+	3.20296i	0.187522	+	0.258102i
$155$	−4.51960	−	4.51960i	−0.363023	−	0.363023i
$156$		0			0
$157$	1.16204	−	14.7651i	0.0927408	−	1.17838i	−0.757805	−	0.652482i	$-0.773728\pi$
$157$	1.16204	−	14.7651i	0.0927408	−	1.17838i	0.850545	−	0.525902i	$-0.176272\pi$
$158$	−0.682062	+	0.0536795i	−0.0542620	+	0.00427051i
$159$		0			0
$160$	−2.07970	−	1.51099i	−0.164415	−	0.119454i
$161$	2.50360	−	6.04422i	0.197311	−	0.476351i
$162$		0			0
$163$			12.7606i			0.999490i	0.866173	+	0.499745i	$0.166573\pi$
$163$			12.7606i			0.999490i	−0.866173	+	0.499745i	$0.833427\pi$
$164$	−2.13201	+	6.03776i	−0.166482	+	0.471470i
$165$		0			0
$166$	5.73747	+	11.2604i	0.445314	+	0.873978i
$167$	18.1191	+	7.50516i	1.40210	+	0.580767i	0.950295	−	0.311352i	$-0.100782\pi$
$167$	18.1191	+	7.50516i	1.40210	+	0.580767i	0.451801	+	0.892119i	$0.350782\pi$
$168$		0			0
$169$	−1.74051	−	10.9892i	−0.133886	−	0.845320i
$170$	0.925481	+	11.7593i	0.0709811	+	0.901901i
$171$		0			0
$172$	−9.56228	−	1.51452i	−0.729117	−	0.115481i
$173$	−7.16154	+	7.16154i	−0.544482	+	0.544482i	−0.924840	−	0.380357i	$-0.875801\pi$
$173$	−7.16154	+	7.16154i	−0.544482	+	0.544482i	0.380357	+	0.924840i	$0.375801\pi$
$174$		0			0
$175$	3.00107	−	0.720493i	0.226860	−	0.0544642i
$176$	−1.75899	+	1.07791i	−0.132589	+	0.0812507i
$177$		0			0
$178$	1.62533	+	3.92389i	0.121824	+	0.294108i
$179$	−0.435114	+	1.81238i	−0.0325220	+	0.135464i	−0.986269	−	0.165146i	$-0.947190\pi$
$179$	−0.435114	+	1.81238i	−0.0325220	+	0.135464i	0.953747	+	0.300610i	$0.0971903\pi$
$180$		0			0
$181$	1.96858	+	1.20634i	0.146323	+	0.0896669i	0.593733	−	0.804662i	$-0.297654\pi$
$181$	1.96858	+	1.20634i	0.146323	+	0.0896669i	−0.447410	+	0.894329i	$0.647654\pi$
$182$	2.49845	+	0.811795i	0.185197	+	0.0601742i
$183$		0			0
$184$	3.03746	+	1.54766i	0.223924	+	0.114095i
$185$	22.6347	+	11.5329i	1.66413	+	0.847918i
$186$		0			0
$187$	9.00298	+	2.92525i	0.658363	+	0.213915i
$188$	0.255902	+	0.156817i	0.0186636	+	0.0114371i
$189$		0			0
$190$	−2.20381	+	9.17951i	−0.159881	+	0.665952i
$191$	0.763208	+	1.84255i	0.0552238	+	0.133322i	0.949083	−	0.315025i	$-0.102013\pi$
$191$	0.763208	+	1.84255i	0.0552238	+	0.133322i	−0.893860	+	0.448347i	$0.852013\pi$
$192$		0			0
$193$	14.6704	−	8.99000i	1.05600	−	0.647115i	0.117735	−	0.993045i	$-0.462437\pi$
$193$	14.6704	−	8.99000i	1.05600	−	0.647115i	0.938260	+	0.345930i	$0.112437\pi$
$194$	3.33298	−	0.800177i	0.239294	−	0.0574494i
$195$		0			0
$196$	−2.34554	+	2.34554i	−0.167538	+	0.167538i
$197$	−9.22733	−	1.46147i	−0.657420	−	0.104125i	−0.181193	−	0.983448i	$-0.557996\pi$
$197$	−9.22733	−	1.46147i	−0.657420	−	0.104125i	−0.476227	+	0.879322i	$0.657996\pi$
$198$		0			0
$199$	1.75167	+	22.2571i	0.124173	+	1.57776i	0.671604	+	0.740911i	$0.265606\pi$
$199$	1.75167	+	22.2571i	0.124173	+	1.57776i	−0.547431	+	0.836851i	$0.684394\pi$
$200$	0.251583	+	1.58843i	0.0177896	+	0.112319i
$201$		0			0
$202$	−12.2300	−	5.06582i	−0.860498	−	0.356430i
$203$	−3.76646	−	7.39210i	−0.264354	−	0.518823i
$204$		0			0
$205$	14.8504	−	7.09958i	1.03720	−	0.495856i
$206$		−	7.58519i		−	0.528486i
$207$		0			0
$208$	−0.523851	+	1.26469i	−0.0363225	+	0.0876904i
$209$	6.12917	+	4.45310i	0.423964	+	0.308028i
$210$		0			0
$211$	14.6251	−	1.15102i	1.00683	−	0.0792395i	0.435696	−	0.900094i	$-0.356502\pi$
$211$	14.6251	−	1.15102i	1.00683	−	0.0792395i	0.571138	+	0.820854i	$0.306502\pi$
$212$	0.0309124	−	0.392779i	0.00212307	−	0.0269762i
$213$		0			0
$214$	0.265009	+	0.265009i	0.0181157	+	0.0181157i
$215$	14.6286	+	20.1346i	0.997663	+	1.37317i
$216$		0			0
$217$	2.49318	+	4.06850i	0.169248	+	0.276188i
$218$	4.94949	−	5.79510i	0.335222	−	0.392494i
$219$		0			0
$220$	5.15671	+	1.23802i	0.347665	+	0.0834671i
$221$	5.97387	−	1.94103i	0.401846	−	0.130568i
$222$		0			0
$223$	1.77149	−	5.45209i	0.118628	−	0.365099i	−0.874058	−	0.485821i	$-0.838521\pi$
$223$	1.77149	−	5.45209i	0.118628	−	0.365099i	0.992686	+	0.120721i	$0.0385208\pi$
$224$	1.24635	+	1.45929i	0.0832752	+	0.0975028i
$225$		0			0
$226$	−5.19933	+	10.2043i	−0.345854	+	0.678777i
$227$	−15.5710	+	13.2989i	−1.03348	+	0.882677i	−0.993189	−	0.116511i	$-0.962829\pi$
$227$	−15.5710	+	13.2989i	−1.03348	+	0.882677i	−0.0402926	+	0.999188i	$0.512829\pi$
$228$		0			0
$229$	−1.62599	+	2.65338i	−0.107448	+	0.175340i	−0.901845	−	0.432059i	$-0.857787\pi$
$229$	−1.62599	+	2.65338i	−0.107448	+	0.175340i	0.794397	+	0.607399i	$0.207787\pi$
$230$	−2.70804	−	8.33448i	−0.178563	−	0.549559i
$231$		0			0
$232$	3.99399	−	1.65436i	0.262218	−	0.108614i
$233$	−12.3687	−	10.5639i	−0.810302	−	0.692064i	0.144435	−	0.989514i	$-0.453864\pi$
$233$	−12.3687	−	10.5639i	−0.810302	−	0.692064i	−0.954737	+	0.297451i	$0.903864\pi$
$234$		0			0
$235$	−0.180109	−	0.750209i	−0.0117490	−	0.0489383i
$236$	−2.85024	+	2.07082i	−0.185535	+	0.134799i
$237$		0			0
$238$	1.37756	−	8.69755i	0.0892937	−	0.563778i
$239$	−27.4961	−	2.16399i	−1.77858	−	0.139977i	−0.853827	−	0.520557i	$-0.825724\pi$
$239$	−27.4961	−	2.16399i	−1.77858	−	0.139977i	−0.924748	+	0.380580i	$0.875724\pi$
$240$		0			0
$241$	23.1443	−	3.66569i	1.49085	−	0.236128i	0.642799	−	0.766035i	$-0.277773\pi$
$241$	23.1443	−	3.66569i	1.49085	−	0.236128i	0.848056	+	0.529907i	$0.177773\pi$
$242$	−3.96405	+	5.45605i	−0.254819	+	0.350728i
$243$		0			0
$244$	1.10029	−	0.560625i	0.0704388	−	0.0358903i
$245$	8.52707			0.544775
$246$		0			0
$247$	5.02706			0.319864
$248$	−2.21541	+	1.12881i	−0.140679	+	0.0716793i
$249$		0			0
$250$	−5.12492	+	7.05385i	−0.324129	+	0.446125i
$251$	25.3508	−	4.01517i	1.60013	−	0.253435i	0.708334	−	0.705877i	$-0.249447\pi$
$251$	25.3508	−	4.01517i	1.60013	−	0.253435i	0.891794	+	0.452442i	$0.149447\pi$
$252$		0			0
$253$	−7.01112	−	0.551787i	−0.440785	−	0.0346905i
$254$	2.08300	−	13.1515i	0.130699	−	0.825199i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	0.857305	+	3.57093i	0.0534772	+	0.222749i	0.992709	−	0.120535i	$-0.0384609\pi$
$257$	0.857305	+	3.57093i	0.0534772	+	0.222749i	−0.939232	+	0.343283i	$0.888461\pi$
$258$		0			0
$259$	−14.4209	−	12.3166i	−0.896069	−	0.765315i
$260$	3.25107	−	1.34664i	0.201623	−	0.0835149i
$261$		0			0
$262$	1.60373	+	4.93578i	0.0990789	+	0.304934i
$263$	−14.3466	+	23.4116i	−0.884652	+	1.44362i	0.0115298	+	0.999934i	$0.496330\pi$
$263$	−14.3466	+	23.4116i	−0.884652	+	1.44362i	−0.896182	+	0.443687i	$0.853670\pi$
$264$		0			0
$265$	−0.770154	+	0.657774i	−0.0473102	+	0.0404067i
$266$	3.19954	−	6.27945i	0.196176	−	0.385018i
$267$		0			0
$268$	−1.99345	−	2.33403i	−0.121769	−	0.142574i
$269$	1.35339	−	4.16531i	0.0825177	−	0.253963i	−0.901282	−	0.433232i	$-0.857373\pi$
$269$	1.35339	−	4.16531i	0.0825177	−	0.253963i	0.983800	+	0.179269i	$0.0573731\pi$
$270$		0			0
$271$	−7.25283	+	2.35659i	−0.440578	+	0.143152i	−0.520902	−	0.853616i	$-0.674404\pi$
$271$	−7.25283	+	2.35659i	−0.440578	+	0.143152i	0.0803244	+	0.996769i	$0.474404\pi$
$272$	4.46183	+	1.07119i	0.270538	+	0.0649505i
$273$		0			0
$274$	−0.118755	+	0.139044i	−0.00717425	+	0.00839997i
$275$	−1.73354	−	2.82887i	−0.104536	−	0.170588i
$276$		0			0
$277$	9.77554	+	13.4549i	0.587355	+	0.808425i	0.994478	−	0.104948i	$-0.0334678\pi$
$277$	9.77554	+	13.4549i	0.587355	+	0.808425i	−0.407122	+	0.913374i	$0.633468\pi$
$278$	−7.99386	−	7.99386i	−0.479440	−	0.479440i
$279$		0			0
$280$	0.387063	−	4.91810i	0.0231314	−	0.293913i
$281$	7.67457	−	0.604002i	0.457827	−	0.0360317i	0.152551	−	0.988296i	$-0.451251\pi$
$281$	7.67457	−	0.604002i	0.457827	−	0.0360317i	0.305276	+	0.952264i	$0.401251\pi$
$282$		0			0
$283$	−8.53895	−	6.20391i	−0.507588	−	0.368784i	0.304320	−	0.952570i	$-0.401571\pi$
$283$	−8.53895	−	6.20391i	−0.507588	−	0.368784i	−0.811908	+	0.583786i	$0.801571\pi$
$284$	−4.00651	+	9.67258i	−0.237743	+	0.573962i
$285$		0			0
$286$		−	2.82401i		−	0.166987i
$287$	−12.0174	+	2.56561i	−0.709362	+	0.151443i
$288$		0			0
$289$	−1.84110	−	3.61336i	−0.108300	−	0.212551i
$290$	−10.2671	−	4.25279i	−0.602907	−	0.249732i
$291$		0			0
$292$	1.59507	+	10.0709i	0.0933444	+	0.589353i
$293$	−1.43752	−	18.2655i	−0.0839810	−	1.06708i	−0.884118	−	0.467263i	$-0.845240\pi$
$293$	−1.43752	−	18.2655i	−0.0839810	−	1.06708i	0.800137	−	0.599817i	$-0.204760\pi$
$294$		0			0
$295$	8.94512	+	1.41677i	0.520805	+	0.0824874i
$296$	6.98772	−	6.98772i	0.406153	−	0.406153i
$297$		0			0
$298$	−20.1245	+	4.83146i	−1.16578	+	0.279879i
$299$	−3.97891	+	2.43828i	−0.230106	+	0.141009i
$300$		0			0
$301$	−7.11012	−	17.1653i	−0.409820	−	0.989394i
$302$	3.11060	−	12.9566i	0.178995	−	0.745569i
$303$		0			0
$304$	3.13120	+	1.91880i	0.179587	+	0.110051i
$305$	−3.01908	−	0.980959i	−0.172872	−	0.0561695i
$306$		0			0
$307$	−27.0545	−	13.7850i	−1.54408	−	0.786750i	−0.545406	−	0.838172i	$-0.683625\pi$
$307$	−27.0545	−	13.7850i	−1.54408	−	0.786750i	−0.998677	+	0.0514219i	$0.983625\pi$
$308$	−3.52756	−	1.79738i	−0.201002	−	0.102415i
$309$		0			0
$310$	6.07886	+	1.97514i	0.345256	+	0.112180i
$311$	−7.47254	−	4.57918i	−0.423729	−	0.259661i	0.294247	−	0.955729i	$-0.404931\pi$
$311$	−7.47254	−	4.57918i	−0.423729	−	0.259661i	−0.717976	+	0.696068i	$0.754931\pi$
$312$		0			0
$313$	6.39853	−	26.6518i	0.361666	−	1.50645i	−0.434111	−	0.900859i	$-0.642937\pi$
$313$	6.39853	−	26.6518i	0.361666	−	1.50645i	0.795777	−	0.605589i	$-0.207063\pi$
$314$	5.66783	+	13.6834i	0.319854	+	0.772196i
$315$		0			0
$316$	0.583352	−	0.357479i	0.0328161	−	0.0201097i
$317$	−22.8603	+	5.48827i	−1.28396	+	0.308252i	−0.817315	−	0.576191i	$-0.804538\pi$
$317$	−22.8603	+	5.48827i	−1.28396	+	0.308252i	−0.466648	+	0.884443i	$0.654538\pi$
$318$		0			0
$319$	−6.30630	+	6.30630i	−0.353085	+	0.353085i
$320$	2.53900	+	0.402138i	0.141934	+	0.0224802i
$321$		0			0
$322$	0.513296	+	6.52205i	0.0286049	+	0.363460i
$323$	−2.63608	−	16.6436i	−0.146676	−	0.926074i
$324$		0			0
$325$	−2.03392	−	0.842475i	−0.112821	−	0.0467321i
$326$	−5.79321	−	11.3698i	−0.320856	−	0.629715i
$327$		0			0
$328$	−0.841455	−	6.34759i	−0.0464616	−	0.350487i
$329$			0.575975i			0.0317545i
$330$		0			0
$331$	4.82306	−	11.6439i	0.265099	−	0.640006i	−0.734140	−	0.678998i	$-0.762415\pi$
$331$	4.82306	−	11.6439i	0.265099	−	0.640006i	0.999240	+	0.0389917i	$0.0124146\pi$
$332$	−10.2242	−	7.42835i	−0.561128	−	0.407684i
$333$		0			0
$334$	−19.5515	+	1.53873i	−1.06981	+	0.0841958i
$335$	−0.619080	+	7.86616i	−0.0338240	+	0.429774i
$336$		0			0
$337$	−20.4989	−	20.4989i	−1.11665	−	1.11665i	−0.992230	−	0.124418i	$-0.960294\pi$
$337$	−20.4989	−	20.4989i	−1.11665	−	1.11665i	−0.124418	−	0.992230i	$-0.539706\pi$
$338$	6.53978	+	9.00124i	0.355717	+	0.489603i
$339$		0			0
$340$	−6.16324	−	10.0575i	−0.334249	−	0.545444i
$341$	3.33132	−	3.90047i	0.180401	−	0.211222i
$342$		0			0
$343$	−19.2524	−	4.62209i	−1.03953	−	0.249569i
$344$	9.20763	−	2.99174i	0.496442	−	0.161304i
$345$		0			0
$346$	3.12971	−	9.63226i	0.168254	−	0.517833i
$347$	−16.5885	−	19.4226i	−0.890515	−	1.04266i	−0.998821	−	0.0485415i	$-0.984543\pi$
$347$	−16.5885	−	19.4226i	−0.890515	−	1.04266i	0.108306	−	0.994118i	$-0.465457\pi$
$348$		0			0
$349$	12.2921	−	24.1246i	0.657980	−	1.29136i	−0.285007	−	0.958526i	$-0.591996\pi$
$349$	12.2921	−	24.1246i	0.657980	−	1.29136i	0.942986	−	0.332832i	$-0.108004\pi$
$350$	−2.34688	+	2.00442i	−0.125446	+	0.107141i
$351$		0			0
$352$	1.07791	−	1.75899i	0.0574529	−	0.0937547i
$353$	3.50640	+	10.7916i	0.186627	+	0.574378i	0.999973	−	0.00740243i	$-0.00235629\pi$
$353$	3.50640	+	10.7916i	0.186627	+	0.574378i	−0.813346	+	0.581780i	$0.802356\pi$
$354$		0			0
$355$	24.8648	−	10.2993i	1.31969	−	0.546632i
$356$	−3.22959	−	2.75833i	−0.171168	−	0.146191i
$357$		0			0
$358$	−0.435114	−	1.81238i	−0.0229965	−	0.0957873i
$359$	−17.9672	+	13.0539i	−0.948273	+	0.688961i	−0.950398	−	0.311037i	$-0.899324\pi$
$359$	−17.9672	+	13.0539i	−0.948273	+	0.688961i	0.00212446	+	0.999998i	$0.499324\pi$
$360$		0			0
$361$	−0.862542	+	5.44588i	−0.0453969	+	0.286625i
$362$	−2.30168	−	0.181146i	−0.120974	−	0.00952084i
$363$		0			0
$364$	−2.59468	+	0.410957i	−0.135998	+	0.0215400i
$365$	15.4067	−	21.2055i	0.806422	−	1.10994i
$366$		0			0
$367$	15.3346	−	7.81339i	0.800462	−	0.407856i	−0.00538058	−	0.999986i	$-0.501713\pi$
$367$	15.3346	−	7.81339i	0.800462	−	0.407856i	0.805843	+	0.592130i	$0.201713\pi$
$368$	−3.40902			−0.177707
$369$		0			0
$370$	−25.4035			−1.32066
$371$	0.673699	−	0.343267i	0.0349767	−	0.0178215i
$372$		0			0
$373$	−8.85992	+	12.1946i	−0.458749	+	0.631414i	−0.974249	−	0.225476i	$-0.927606\pi$
$373$	−8.85992	+	12.1946i	−0.458749	+	0.631414i	0.515499	+	0.856890i	$0.327606\pi$
$374$	−9.34975	+	1.48085i	−0.483464	+	0.0765732i
$375$		0			0
$376$	−0.299204	−	0.0235479i	−0.0154303	−	0.00121439i
$377$	−0.925746	+	5.84493i	−0.0476784	+	0.301029i
$378$		0			0
$379$	−7.58056	+	5.50760i	−0.389387	+	0.282906i	−0.765204	−	0.643788i	$-0.777362\pi$
$379$	−7.58056	+	5.50760i	−0.389387	+	0.282906i	0.375817	+	0.926694i	$0.377362\pi$
$380$	−2.20381	−	9.17951i	−0.113053	−	0.470899i
$381$		0			0
$382$	−1.51652	−	1.29523i	−0.0775921	−	0.0662699i
$383$	10.9579	−	4.53890i	0.559921	−	0.231927i	−0.0847298	−	0.996404i	$-0.527003\pi$
$383$	10.9579	−	4.53890i	0.559921	−	0.231927i	0.644651	+	0.764477i	$0.277003\pi$
$384$		0			0
$385$	3.14499	+	9.67928i	0.160283	+	0.493302i
$386$	−8.99000	+	14.6704i	−0.457579	+	0.746701i
$387$		0			0
$388$	−2.60643	+	2.22610i	−0.132322	+	0.113013i
$389$	−2.94937	+	5.78846i	−0.149539	+	0.293487i	−0.953609	−	0.301048i	$-0.902664\pi$
$389$	−2.94937	+	5.78846i	−0.149539	+	0.293487i	0.804070	+	0.594535i	$0.202664\pi$
$390$		0			0
$391$	10.1591	+	11.8948i	0.513768	+	0.601545i
$392$	1.02504	−	3.15474i	0.0517722	−	0.159338i
$393$		0			0
$394$	8.88511	−	2.88695i	0.447625	−	0.145442i
$395$	−1.71017	−	0.410575i	−0.0860479	−	0.0206583i
$396$		0			0
$397$	14.6930	−	17.2033i	0.737419	−	0.863406i	−0.257269	−	0.966340i	$-0.582823\pi$
$397$	14.6930	−	17.2033i	0.737419	−	0.863406i	0.994688	+	0.102933i	$0.0328228\pi$
$398$	−11.6652	−	19.0359i	−0.584726	−	0.954186i
$399$		0			0
$400$	−0.945296	−	1.30109i	−0.0472648	−	0.0650544i
$401$	7.80732	+	7.80732i	0.389879	+	0.389879i	0.874644	−	0.484765i	$-0.161095\pi$
$401$	7.80732	+	7.80732i	0.389879	+	0.389879i	−0.484765	+	0.874644i	$0.661095\pi$
$402$		0			0
$403$	0.267045	−	3.39313i	0.0133025	−	0.169024i
$404$	13.1968	−	1.03861i	0.656566	−	0.0516729i
$405$		0			0
$406$	6.71188	+	4.87647i	0.333105	+	0.242015i
$407$	−7.80169	+	18.8349i	−0.386715	+	0.933613i
$408$		0			0
$409$		−	8.26551i		−	0.408703i	−0.978898	−	0.204352i	$-0.934491\pi$
$409$		−	8.26551i		−	0.408703i	0.978898	−	0.204352i	$-0.0655086\pi$
$410$	−10.0086	+	13.0677i	−0.494291	+	0.645368i
$411$		0			0
$412$	3.44361	+	6.75846i	0.169654	+	0.332965i
$413$	−6.24646	−	2.58737i	−0.307368	−	0.127316i
$414$		0			0
$415$	5.08216	+	32.0875i	0.249474	+	1.57511i
$416$	−0.107402	−	1.36467i	−0.00526581	−	0.0669084i
$417$		0			0
$418$	−7.48280	−	1.18516i	−0.365996	−	0.0579680i
$419$	−4.06301	+	4.06301i	−0.198491	+	0.198491i	−0.799353	−	0.600862i	$-0.794824\pi$
$419$	−4.06301	+	4.06301i	−0.198491	+	0.198491i	0.600862	+	0.799353i	$0.294824\pi$
$420$		0			0
$421$	−3.80998	+	0.914694i	−0.185687	+	0.0445795i	−0.325222	−	0.945638i	$-0.605439\pi$
$421$	−3.80998	+	0.914694i	−0.185687	+	0.0445795i	0.139535	+	0.990217i	$0.455439\pi$
$422$	−12.5085	+	7.66523i	−0.608905	+	0.373137i
$423$		0			0
$424$	0.150775	+	0.364003i	0.00732227	+	0.0176775i
$425$	−1.72273	+	7.17567i	−0.0835644	+	0.348071i
$426$		0			0
$427$	2.02063	+	1.23824i	0.0977852	+	0.0599228i
$428$	−0.356436	−	0.115813i	−0.0172290	−	0.00559804i
$429$		0			0
$430$	−22.1751	−	11.2988i	−1.06938	−	0.544875i
$431$	29.9852	+	15.2782i	1.44433	+	0.735925i	0.988082	−	0.153925i	$-0.0491916\pi$
$431$	29.9852	+	15.2782i	1.44433	+	0.735925i	0.456252	+	0.889851i	$0.349192\pi$
$432$		0			0
$433$	−15.9904	−	5.19561i	−0.768451	−	0.249685i	−0.101549	−	0.994831i	$-0.532380\pi$
$433$	−15.9904	−	5.19561i	−0.768451	−	0.249685i	−0.666902	+	0.745146i	$0.732380\pi$
$434$	−4.06850	−	2.49318i	−0.195294	−	0.119676i
$435$		0			0
$436$	−1.77910	+	7.41050i	−0.0852036	+	0.354898i
$437$	4.79087	+	11.5662i	0.229179	+	0.553286i
$438$		0			0
$439$	16.2516	−	9.95896i	0.775644	−	0.475315i	−0.0774988	−	0.996992i	$-0.524693\pi$
$439$	16.2516	−	9.95896i	0.775644	−	0.475315i	0.853143	+	0.521677i	$0.174693\pi$
$440$	−5.15671	+	1.23802i	−0.245837	+	0.0590201i
$441$		0			0
$442$	−4.44155	+	4.44155i	−0.211263	+	0.211263i
$443$	3.10369	+	0.491577i	0.147461	+	0.0233555i	0.229728	−	0.973255i	$-0.426216\pi$
$443$	3.10369	+	0.491577i	0.147461	+	0.0233555i	−0.0822676	+	0.996610i	$0.526216\pi$
$444$		0			0
$445$	0.856619	+	10.8844i	0.0406076	+	0.515969i
$446$	0.896787	+	5.66209i	0.0424641	+	0.268108i
$447$		0			0
$448$	−1.77301	−	0.734404i	−0.0837668	−	0.0346973i
$449$	−12.4359	−	24.4068i	−0.586886	−	1.15183i	−0.973307	−	0.229506i	$-0.926289\pi$
$449$	−12.4359	−	24.4068i	−0.586886	−	1.15183i	0.386421	−	0.922322i	$-0.373711\pi$
$450$		0			0
$451$	6.61504	+	11.4340i	0.311490	+	0.538404i
$452$		−	11.4525i		−	0.538681i
$453$		0			0
$454$	7.83628	−	18.9185i	0.367775	−	0.887887i
$455$	5.46341	+	3.96940i	0.256129	+	0.186088i
$456$		0			0
$457$	20.6523	−	1.62537i	0.966076	−	0.0760318i	0.414404	−	0.910093i	$-0.363990\pi$
$457$	20.6523	−	1.62537i	0.966076	−	0.0760318i	0.551672	+	0.834061i	$0.313990\pi$
$458$	0.244161	−	3.10236i	0.0114089	−	0.144964i
$459$		0			0
$460$	6.19665	+	6.19665i	0.288920	+	0.288920i
$461$	13.3255	+	18.3410i	0.620630	+	0.854224i	0.997399	−	0.0720832i	$-0.0229647\pi$
$461$	13.3255	+	18.3410i	0.620630	+	0.854224i	−0.376768	+	0.926308i	$0.622965\pi$
$462$		0			0
$463$	−4.34044	−	7.08296i	−0.201717	−	0.329173i	0.735745	−	0.677258i	$-0.236832\pi$
$463$	−4.34044	−	7.08296i	−0.201717	−	0.329173i	−0.937463	+	0.348085i	$0.886832\pi$
$464$	−2.80760	+	3.28728i	−0.130340	+	0.152608i
$465$		0			0
$466$	15.8165	+	3.79721i	0.732686	+	0.175902i
$467$	12.8235	−	4.16659i	0.593399	−	0.192807i	0.00310468	−	0.999995i	$-0.499012\pi$
$467$	12.8235	−	4.16659i	0.593399	−	0.192807i	0.590294	+	0.807188i	$0.299012\pi$
$468$		0			0
$469$	1.82028	−	5.60225i	0.0840528	−	0.258688i
$470$	0.501067	+	0.586674i	0.0231125	+	0.0270612i
$471$		0			0
$472$	1.59945	−	3.13909i	0.0736206	−	0.144488i
$473$	−15.1875	+	12.9713i	−0.698321	+	0.596423i
$474$		0			0
$475$	−3.08589	+	5.03571i	−0.141590	+	0.231054i
$476$	2.72119	+	8.37497i	0.124726	+	0.383866i
$477$		0			0
$478$	25.4816	−	10.5548i	1.16550	−	0.482767i
$479$	−22.4383	−	19.1641i	−1.02523	−	0.875630i	−0.0329272	−	0.999458i	$-0.510483\pi$
$479$	−22.4383	−	19.1641i	−1.02523	−	0.875630i	−0.992304	+	0.123828i	$0.960483\pi$
$480$		0			0
$481$	3.15794	+	13.1538i	0.143990	+	0.599760i
$482$	−18.9575	+	13.7734i	−0.863491	+	0.627363i
$483$		0			0
$484$	1.05500	−	6.66101i	0.0479546	−	0.302773i
$485$	8.78421	+	0.691332i	0.398870	+	0.0313918i
$486$		0			0
$487$	38.6574	−	6.12272i	1.75173	−	0.277447i	0.803564	−	0.595218i	$-0.202934\pi$
$487$	38.6574	−	6.12272i	1.75173	−	0.277447i	0.948168	+	0.317771i	$0.102934\pi$
$488$	−0.725846	+	0.999041i	−0.0328575	+	0.0452245i
$489$		0			0
$490$	−7.59768	+	3.87121i	−0.343228	+	0.174883i
$491$	−12.1593			−0.548744			−0.274372	−	0.961624i	$-0.588470\pi$
$491$	−12.1593			−0.548744			−0.274372	+	0.961624i	$0.588470\pi$
$492$		0			0
$493$	19.8368			0.893407
$494$	−4.47914	+	2.28224i	−0.201526	+	0.102683i
$495$		0			0
$496$	1.46148	−	2.01155i	0.0656222	−	0.0903212i
$497$	−19.8446	+	3.14308i	−0.890152	+	0.140986i
$498$		0			0
$499$	−25.0086	−	1.96822i	−1.11954	−	0.0881097i	−0.494847	−	0.868980i	$-0.664776\pi$
$499$	−25.0086	−	1.96822i	−1.11954	−	0.0881097i	−0.624693	+	0.780870i	$0.714776\pi$
$500$	1.36396	−	8.61169i	0.0609981	−	0.385127i
$501$		0			0
$502$	−20.7649	+	15.0866i	−0.926782	+	0.673346i
$503$	−7.02443	−	29.2588i	−0.313204	−	1.30459i	−0.877723	−	0.479168i	$-0.840939\pi$
$503$	−7.02443	−	29.2588i	−0.313204	−	1.30459i	0.564520	−	0.825420i	$-0.309061\pi$
$504$		0			0
$505$	−25.8761	−	22.1002i	−1.15147	−	0.983448i
$506$	6.49746	−	2.69133i	0.288847	−	0.119644i
$507$		0			0
$508$	4.11470	+	12.6637i	0.182560	+	0.561863i
$509$	−20.5299	+	33.5018i	−0.909973	+	1.48494i	−0.0357824	+	0.999360i	$0.511392\pi$
$509$	−20.5299	+	33.5018i	−0.909973	+	1.48494i	−0.874191	+	0.485582i	$0.838608\pi$
$510$		0			0
$511$	−14.8795	+	12.7083i	−0.658230	+	0.562182i
$512$	0.453990	−	0.891007i	0.0200637	−	0.0393773i
$513$		0			0
$514$	−2.38503	−	2.79251i	−0.105199	−	0.123173i
$515$	6.02548	−	18.5445i	0.265514	−	0.817170i
$516$		0			0
$517$	0.588862	−	0.191333i	0.0258981	−	0.00841480i
$518$	18.4407	+	4.42722i	0.810238	+	0.194521i
$519$		0			0
$520$	−2.28536	+	2.67582i	−0.100220	+	0.117342i
$521$	2.99896	+	4.89386i	0.131387	+	0.214404i	0.911568	−	0.411150i	$-0.134873\pi$
$521$	2.99896	+	4.89386i	0.131387	+	0.214404i	−0.780181	+	0.625554i	$0.784873\pi$
$522$		0			0
$523$	−14.3430	−	19.7415i	−0.627176	−	0.863234i	0.370674	−	0.928763i	$-0.379127\pi$
$523$	−14.3430	−	19.7415i	−0.627176	−	0.863234i	−0.997851	+	0.0655289i	$0.979127\pi$
$524$	−3.66973	−	3.66973i	−0.160313	−	0.160313i
$525$		0			0
$526$	2.15431	−	27.3731i	0.0939324	−	1.19352i
$527$	−11.3740	+	0.895153i	−0.495459	+	0.0389935i
$528$		0			0
$529$	9.20547	+	6.68816i	0.400238	+	0.290790i
$530$	0.387589	−	0.935723i	0.0168358	−	0.0406452i
$531$		0			0
$532$			7.04760i			0.305552i
$533$	8.01057	+	3.55795i	0.346976	+	0.154112i
$534$		0			0
$535$	0.437386	+	0.858419i	0.0189099	+	0.0371127i
$536$	2.83580	+	1.17463i	0.122488	+	0.0507362i
$537$		0			0
$538$	0.685131	+	4.32574i	0.0295381	+	0.186496i
$539$	0.536907	+	6.82205i	0.0231262	+	0.293847i
$540$		0			0
$541$	36.8518	+	5.83675i	1.58438	+	0.250941i	0.885619	−	0.464412i	$-0.153734\pi$
$541$	36.8518	+	5.83675i	1.58438	+	0.250941i	0.698763	+	0.715354i	$0.253734\pi$
$542$	5.39245	−	5.39245i	0.231625	−	0.231625i
$543$		0			0
$544$	−4.46183	+	1.07119i	−0.191299	+	0.0459269i
$545$	16.7041	−	10.2363i	0.715527	−	0.438475i
$546$		0			0
$547$	−12.4529	−	30.0640i	−0.532448	−	1.28544i	−0.929898	−	0.367818i	$-0.880105\pi$
$547$	−12.4529	−	30.0640i	−0.532448	−	1.28544i	0.397450	−	0.917624i	$-0.369895\pi$
$548$	0.0426867	−	0.177803i	0.00182349	−	0.00759536i
$549$		0			0
$550$	2.82887	+	1.73354i	0.120624	+	0.0739182i
$551$	15.0988	+	4.90590i	0.643231	+	0.208999i
$552$		0			0
$553$	1.16988	+	0.596084i	0.0497483	+	0.0253481i
$554$	−14.8185	−	7.55038i	−0.629576	−	0.320785i
$555$		0			0
$556$	10.7517	+	3.49345i	0.455975	+	0.148155i
$557$	−3.55029	−	2.17562i	−0.150431	−	0.0921840i	0.445246	−	0.895408i	$-0.353116\pi$
$557$	−3.55029	−	2.17562i	−0.150431	−	0.0921840i	−0.595677	+	0.803224i	$0.703116\pi$
$558$		0			0
$559$	−3.09382	+	12.8867i	−0.130855	+	0.545049i
$560$	1.88790	+	4.55778i	0.0797781	+	0.192601i
$561$		0			0
$562$	−6.56388	+	4.02235i	−0.276881	+	0.169673i
$563$	1.67568	−	0.402294i	0.0706213	−	0.0169547i	−0.197981	−	0.980206i	$-0.563438\pi$
$563$	1.67568	−	0.402294i	0.0706213	−	0.0169547i	0.268602	+	0.963251i	$0.413438\pi$
$564$		0			0
$565$	−20.8175	+	20.8175i	−0.875798	+	0.875798i
$566$	10.4248	+	1.65112i	0.438186	+	0.0694019i
$567$		0			0
$568$	−0.821429	−	10.4372i	−0.0344664	−	0.437937i
$569$	−2.53041	−	15.9764i	−0.106080	−	0.669765i	−0.982224	−	0.187715i	$-0.939892\pi$
$569$	−2.53041	−	15.9764i	−0.106080	−	0.669765i	0.876143	−	0.482051i	$-0.160108\pi$
$570$		0			0
$571$	34.4968	+	14.2891i	1.44365	+	0.597978i	0.960680	−	0.277659i	$-0.0895587\pi$
$571$	34.4968	+	14.2891i	1.44365	+	0.597978i	0.482968	+	0.875638i	$0.339559\pi$
$572$	1.28208	+	2.51622i	0.0536063	+	0.105208i
$573$		0			0
$574$	9.54278	−	7.74174i	0.398308	−	0.323134i
$575$		−	5.48250i		−	0.228636i
$576$		0			0
$577$	3.26807	−	7.88982i	0.136052	−	0.328458i	−0.841140	−	0.540818i	$-0.818115\pi$
$577$	3.26807	−	7.88982i	0.136052	−	0.328458i	0.977192	+	0.212360i	$0.0681149\pi$
$578$	3.28086	+	2.38369i	0.136466	+	0.0991483i
$579$		0			0
$580$	11.0788	−	0.871921i	0.460022	−	0.0362046i
$581$	1.90288	−	24.1784i	0.0789449	−	1.00309i
$582$		0			0
$583$	−0.574742	−	0.574742i	−0.0238034	−	0.0238034i
$584$	−5.99330	−	8.24907i	−0.248005	−	0.341349i
$585$		0			0
$586$	9.57319	+	15.6220i	0.395465	+	0.645340i
$587$	−2.11936	+	2.48145i	−0.0874754	+	0.102420i	−0.802417	−	0.596763i	$-0.796453\pi$
$587$	−2.11936	+	2.48145i	−0.0874754	+	0.102420i	0.714942	+	0.699184i	$0.246453\pi$
$588$		0			0
$589$	−8.87871	−	2.13159i	−0.365841	−	0.0878306i
$590$	−8.61336	+	2.79865i	−0.354606	+	0.115219i
$591$		0			0
$592$	−3.05374	+	9.39846i	−0.125508	+	0.386274i
$593$	9.99778	+	11.7059i	0.410560	+	0.480704i	0.926701	−	0.375800i	$-0.122632\pi$
$593$	9.99778	+	11.7059i	0.410560	+	0.480704i	−0.516141	+	0.856504i	$0.672632\pi$
$594$		0			0
$595$	10.2770	−	20.1698i	0.421316	−	0.826879i
$596$	15.7376	−	13.4412i	0.644638	−	0.550573i
$597$		0			0
$598$	2.43828	−	3.97891i	0.0997085	−	0.162710i
$599$	−1.75393	−	5.39803i	−0.0716635	−	0.220558i	0.908810	−	0.417211i	$-0.136993\pi$
$599$	−1.75393	−	5.39803i	−0.0716635	−	0.220558i	−0.980473	+	0.196654i	$0.936993\pi$
$600$		0			0
$601$	−34.7984	+	14.4140i	−1.41946	+	0.587958i	−0.954724	−	0.297494i	$-0.903849\pi$
$601$	−34.7984	+	14.4140i	−1.41946	+	0.587958i	−0.464732	+	0.885451i	$0.653849\pi$
$602$	14.1281	+	12.0665i	0.575817	+	0.491794i
$603$		0			0
$604$	3.11060	+	12.9566i	0.126569	+	0.527197i
$605$	−14.0256	+	10.1902i	−0.570221	+	0.414290i
$606$		0			0
$607$	−4.92019	+	31.0649i	−0.199704	+	1.26088i	0.660458	+	0.750863i	$0.270362\pi$
$607$	−4.92019	+	31.0649i	−0.199704	+	1.26088i	−0.860162	+	0.510021i	$0.829638\pi$
$608$	−3.66104	−	0.288130i	−0.148475	−	0.0116852i
$609$		0			0
$610$	3.13537	−	0.496593i	0.126947	−	0.0201065i
$611$	0.241488	−	0.332380i	0.00976955	−	0.0134466i
$612$		0			0
$613$	−39.5322	+	20.1427i	−1.59669	+	0.813555i	−0.596754	+	0.802424i	$0.703543\pi$
$613$	−39.5322	+	20.1427i	−1.59669	+	0.813555i	−0.999938	+	0.0111307i	$0.996457\pi$
$614$	30.3640			1.22539
$615$		0			0
$616$	3.95908			0.159516
$617$	−41.0480	+	20.9150i	−1.65253	+	0.842006i	−0.656371	+	0.754438i	$0.727909\pi$
$617$	−41.0480	+	20.9150i	−1.65253	+	0.842006i	−0.996159	+	0.0875674i	$0.972091\pi$
$618$		0			0
$619$	18.8961	−	26.0082i	0.759498	−	1.04536i	−0.237758	−	0.971325i	$-0.576412\pi$
$619$	18.8961	−	26.0082i	0.759498	−	1.04536i	0.997256	−	0.0740348i	$-0.0235876\pi$
$620$	−6.31299	+	0.999880i	−0.253536	+	0.0401561i
$621$		0			0
$622$	8.73699	+	0.687616i	0.350321	+	0.0275709i
$623$	1.27506	−	8.05039i	0.0510841	−	0.322532i
$624$		0			0
$625$	−24.6384	+	17.9009i	−0.985537	+	0.716034i
$626$	6.39853	+	26.6518i	0.255737	+	1.06522i
$627$		0			0
$628$	−11.2622	−	9.61882i	−0.449410	−	0.383833i
$629$	41.8935	−	17.3529i	1.67040	−	0.691904i
$630$		0			0
$631$	10.1193	+	31.1441i	0.402844	+	1.23983i	0.922682	+	0.385562i	$0.125992\pi$
$631$	10.1193	+	31.1441i	0.402844	+	1.23983i	−0.519838	+	0.854265i	$0.674008\pi$
$632$	−0.357479	+	0.583352i	−0.0142197	+	0.0232045i
$633$		0			0
$634$	17.8771	−	15.2685i	0.709989	−	0.606388i
$635$	15.5398	−	30.4986i	0.616678	−	1.21030i
$636$		0			0
$637$	2.94897	+	3.45280i	0.116842	+	0.136805i
$638$	2.75595	−	8.48196i	0.109109	−	0.335804i
$639$		0			0
$640$	−2.44483	+	0.794374i	−0.0966405	+	0.0314004i
$641$	18.4721	+	4.43476i	0.729605	+	0.175163i	0.581196	−	0.813763i	$-0.302585\pi$
$641$	18.4721	+	4.43476i	0.729605	+	0.175163i	0.148409	+	0.988926i	$0.452585\pi$
$642$		0			0
$643$	−25.7785	+	30.1828i	−1.01661	+	1.19029i	−0.0349971	+	0.999387i	$0.511142\pi$
$643$	−25.7785	+	30.1828i	−1.01661	+	1.19029i	−0.981609	+	0.190905i	$0.938858\pi$
$644$	−3.41830	−	5.57816i	−0.134700	−	0.219810i
$645$		0			0
$646$	9.90480	+	13.6328i	0.389699	+	0.536375i
$647$	−1.85156	−	1.85156i	−0.0727923	−	0.0727923i	0.669773	−	0.742566i	$-0.266391\pi$
$647$	−1.85156	−	1.85156i	−0.0727923	−	0.0727923i	−0.742566	+	0.669773i	$0.766391\pi$
$648$		0			0
$649$	−0.570250	+	7.24571i	−0.0223843	+	0.284419i
$650$	2.19471	−	0.172727i	0.0860835	−	0.00677492i
$651$		0			0
$652$	10.3236	+	7.50051i	0.404302	+	0.293743i
$653$	−3.56423	+	8.60482i	−0.139479	+	0.336733i	−0.978148	−	0.207909i	$-0.933334\pi$
$653$	−3.56423	+	8.60482i	−0.139479	+	0.336733i	0.838669	+	0.544642i	$0.183334\pi$
$654$		0			0
$655$			13.3411i			0.521281i
$656$	3.63149	+	5.27374i	0.141786	+	0.205905i
$657$		0			0
$658$	−0.261487	−	0.513198i	−0.0101938	−	0.0200065i
$659$	13.7702	+	5.70379i	0.536410	+	0.222188i	0.634408	−	0.772998i	$-0.281244\pi$
$659$	13.7702	+	5.70379i	0.536410	+	0.222188i	−0.0979983	+	0.995187i	$0.531244\pi$
$660$		0			0
$661$	−0.820561	−	5.18082i	−0.0319161	−	0.201510i	0.966578	−	0.256374i	$-0.0825277\pi$
$661$	−0.820561	−	5.18082i	−0.0319161	−	0.201510i	−0.998494	+	0.0548632i	$0.982528\pi$
$662$	0.988840	+	12.5644i	0.0384324	+	0.488329i
$663$		0			0
$664$	12.4823	+	1.97700i	0.484406	+	0.0767224i
$665$	12.8106	−	12.8106i	0.496773	−	0.496773i
$666$		0			0
$667$	−14.3302	+	3.44038i	−0.554867	+	0.133212i
$668$	16.7219	−	10.2472i	0.646991	−	0.396476i
$669$		0			0
$670$	−3.01956	−	7.28986i	−0.116656	−	0.281632i
$671$	0.594716	−	2.47717i	0.0229588	−	0.0956301i
$672$		0			0
$673$	2.44361	+	1.49745i	0.0941942	+	0.0577223i	0.568798	−	0.822477i	$-0.307409\pi$
$673$	2.44361	+	1.49745i	0.0941942	+	0.0577223i	−0.474604	+	0.880200i	$0.657409\pi$
$674$	27.5710	+	8.95836i	1.06200	+	0.345063i
$675$		0			0
$676$	−9.91347	−	5.05116i	−0.381287	−	0.194275i
$677$	28.6167	+	14.5809i	1.09983	+	0.560391i	0.907123	−	0.420866i	$-0.138274\pi$
$677$	28.6167	+	14.5809i	1.09983	+	0.560391i	0.192706	+	0.981257i	$0.438274\pi$
$678$		0			0
$679$	−6.25609	−	2.03273i	−0.240087	−	0.0780089i
$680$	10.0575	+	6.16324i	0.385687	+	0.236350i
$681$		0			0
$682$	−1.19745	+	4.98773i	−0.0458526	+	0.190990i
$683$	9.25948	+	22.3544i	0.354304	+	0.855365i	0.996079	+	0.0884722i	$0.0281984\pi$
$683$	9.25948	+	22.3544i	0.354304	+	0.855365i	−0.641775	+	0.766893i	$0.721802\pi$
$684$		0			0
$685$	−0.400789	+	0.245604i	−0.0153134	+	0.00938404i
$686$	19.2524	−	4.62209i	0.735059	−	0.176472i
$687$		0			0
$688$	−6.84584	+	6.84584i	−0.260995	+	0.260995i
$689$	−0.532694	−	0.0843704i	−0.0202940	−	0.00321426i
$690$		0			0
$691$	3.00192	+	38.1430i	0.114198	+	1.45103i	0.740820	+	0.671704i	$0.234437\pi$
$691$	3.00192	+	38.1430i	0.114198	+	1.45103i	−0.626621	+	0.779324i	$0.715563\pi$
$692$	1.58436	+	10.0033i	0.0602284	+	0.380267i
$693$		0			0
$694$	23.5981	+	9.77465i	0.895771	+	0.371041i
$695$	−13.1935	−	25.8938i	−0.500459	−	0.982207i
$696$		0			0
$697$	7.57909	−	28.3871i	0.287078	−	1.07524i
$698$			27.0756i			1.02483i
$699$		0			0
$700$	1.18109	−	2.85141i	0.0446412	−	0.107773i
$701$	−6.51759	−	4.73531i	−0.246166	−	0.178850i	0.457860	−	0.889024i	$-0.348616\pi$
$701$	−6.51759	−	4.73531i	−0.246166	−	0.178850i	−0.704026	+	0.710174i	$0.748616\pi$
$702$		0			0
$703$	36.1789	−	2.84734i	1.36451	−	0.107389i
$704$	−0.161861	+	2.05664i	−0.00610036	+	0.0775124i
$705$		0			0
$706$	−8.02350	−	8.02350i	−0.301968	−	0.301968i
$707$	14.9322	+	20.5524i	0.561584	+	0.772954i
$708$		0			0
$709$	1.00203	+	1.63517i	0.0376321	+	0.0614100i	0.870903	−	0.491455i	$-0.163535\pi$
$709$	1.00203	+	1.63517i	0.0376321	+	0.0614100i	−0.833271	+	0.552865i	$0.813535\pi$
$710$	−17.4789	+	20.4652i	−0.655971	+	0.768044i
$711$		0			0
$712$	4.12984	+	0.991487i	0.154772	+	0.0371575i
$713$	8.06136	−	2.61930i	0.301900	−	0.0980934i
$714$		0			0
$715$	2.24332	−	6.90424i	0.0838955	−	0.258204i
$716$	1.21049	+	1.41731i	0.0452383	+	0.0529672i
$717$		0			0
$718$	10.0825	−	19.7881i	0.376277	−	0.738485i
$719$	−14.3964	+	12.2957i	−0.536896	+	0.458553i	−0.876079	−	0.482168i	$-0.839850\pi$
$719$	−14.3964	+	12.2957i	−0.536896	+	0.458553i	0.339183	+	0.940721i	$0.389850\pi$
$720$		0			0
$721$	−7.60584	+	12.4116i	−0.283256	+	0.462232i
$722$	−1.70385	−	5.24390i	−0.0634106	−	0.195158i
$723$		0			0
$724$	2.13305	−	0.883540i	0.0792743	−	0.0328365i
$725$	−5.28672	−	4.51528i	−0.196344	−	0.167693i
$726$		0			0
$727$	−8.98890	−	37.4414i	−0.333380	−	1.38863i	−0.847449	−	0.530877i	$-0.821862\pi$
$727$	−8.98890	−	37.4414i	−0.333380	−	1.38863i	0.514069	−	0.857749i	$-0.328138\pi$
$728$	2.12531	−	1.54413i	0.0787691	−	0.0572291i
$729$		0			0
$730$	−4.10036	+	25.8887i	−0.151761	+	0.958183i
$731$	44.2876	+	3.48551i	1.63804	+	0.128916i
$732$		0			0
$733$	0.0567772	−	0.00899262i	0.00209711	−	0.000332150i	−0.155386	−	0.987854i	$-0.549662\pi$
$733$	0.0567772	−	0.00899262i	0.00209711	−	0.000332150i	0.157483	+	0.987522i	$0.449662\pi$
$734$	−10.1161	+	13.9236i	−0.373391	+	0.513928i
$735$		0			0
$736$	3.03746	−	1.54766i	0.111962	−	0.0570476i
$737$	−6.33227			−0.233252
$738$		0			0
$739$	−35.0489			−1.28929			−0.644647	−	0.764480i	$-0.722996\pi$
$739$	−35.0489			−1.28929			−0.644647	+	0.764480i	$0.722996\pi$
$740$	22.6347	−	11.5329i	0.832066	−	0.423959i
$741$		0			0
$742$	−0.444430	+	0.611706i	−0.0163155	+	0.0224564i
$743$	−31.1010	+	4.92591i	−1.14098	+	0.180714i	−0.698192	−	0.715911i	$-0.746012\pi$
$743$	−31.1010	+	4.92591i	−1.14098	+	0.180714i	−0.442792	+	0.896625i	$0.646012\pi$
$744$		0			0
$745$	−53.0390	−	4.17426i	−1.94320	−	0.152933i
$746$	2.35800	−	14.8878i	0.0863325	−	0.545082i
$747$		0			0
$748$	7.65839	−	5.56415i	0.280019	−	0.203445i
$749$	−0.167902	−	0.699363i	−0.00613502	−	0.0255542i
$750$		0			0
$751$	21.3264	+	18.2145i	0.778212	+	0.664656i	0.947085	−	0.320982i	$-0.104013\pi$
$751$	21.3264	+	18.2145i	0.778212	+	0.664656i	−0.168873	+	0.985638i	$0.554013\pi$
$752$	0.277283	−	0.114854i	0.0101115	−	0.00418831i
$753$		0			0
$754$	−1.82870	−	5.62815i	−0.0665972	−	0.204965i
$755$	17.8973	−	29.2057i	0.651349	−	1.06291i
$756$		0			0
$757$	18.9999	−	16.2274i	0.690562	−	0.589796i	−0.233353	−	0.972392i	$-0.574970\pi$
$757$	18.9999	−	16.2274i	0.690562	−	0.589796i	0.923916	+	0.382596i	$0.124970\pi$
$758$	4.25393	−	8.34880i	0.154510	−	0.303242i
$759$		0			0
$760$	6.13102	+	7.17850i	0.222395	+	0.260392i
$761$	4.39303	−	13.5203i	0.159247	−	0.490112i	−0.839319	−	0.543639i	$-0.817046\pi$
$761$	4.39303	−	13.5203i	0.159247	−	0.490112i	0.998566	+	0.0535265i	$0.0170462\pi$
$762$		0			0
$763$	−13.9097	+	4.51953i	−0.503565	+	0.163618i
$764$	1.93926	+	0.465574i	0.0701598	+	0.0168439i
$765$		0			0
$766$	−7.70292	+	9.01896i	−0.278318	+	0.325868i
$767$	2.51986	+	4.11204i	0.0909870	+	0.148477i
$768$		0			0
$769$	24.8770	+	34.2402i	0.897087	+	1.23473i	0.971388	+	0.237498i	$0.0763274\pi$
$769$	24.8770	+	34.2402i	0.897087	+	1.23473i	−0.0743012	+	0.997236i	$0.523673\pi$
$770$	−7.19651	−	7.19651i	−0.259344	−	0.259344i
$771$		0			0
$772$	1.34995	−	17.1528i	0.0485858	−	0.617341i
$773$	−36.3392	+	2.85995i	−1.30703	+	0.102865i	−0.712764	−	0.701404i	$-0.752557\pi$
$773$	−36.3392	+	2.85995i	−1.30703	+	0.102865i	−0.594265	+	0.804269i	$0.702557\pi$
$774$		0			0
$775$	3.23504	+	2.35039i	0.116206	+	0.0844286i
$776$	1.31172	−	3.16677i	0.0470879	−	0.113680i
$777$		0			0
$778$		−	6.49655i		−	0.232912i
$779$	12.7893	−	19.7324i	0.458225	−	0.706988i
$780$		0			0
$781$	9.80556	+	19.2445i	0.350870	+	0.688622i
$782$	−14.4519	−	5.98619i	−0.516800	−	0.214066i
$783$		0			0
$784$	0.518907	+	3.27625i	0.0185324	+	0.117009i
$785$	2.98719	+	37.9559i	0.106617	+	1.35470i
$786$		0			0
$787$	−6.04660	−	0.957688i	−0.215538	−	0.0341379i	0.0477314	−	0.998860i	$-0.484801\pi$
$787$	−6.04660	−	0.957688i	−0.215538	−	0.0341379i	−0.263270	+	0.964722i	$0.584801\pi$
$788$	−6.60604	+	6.60604i	−0.235330	+	0.235330i
$789$		0			0
$790$	1.71017	−	0.410575i	0.0608451	−	0.0146076i
$791$	18.7397	−	11.4837i	0.666306	−	0.408313i
$792$		0			0
$793$	−0.646895	−	1.56174i	−0.0229719	−	0.0554591i
$794$	−5.28142	+	21.9987i	−0.187430	+	0.780704i
$795$		0			0
$796$	19.0359	+	11.6652i	0.674711	+	0.413464i
$797$	−15.3688	−	4.99361i	−0.544389	−	0.176883i	0.0238960	−	0.999714i	$-0.492393\pi$
$797$	−15.3688	−	4.99361i	−0.544389	−	0.176883i	−0.568285	+	0.822832i	$0.692393\pi$
$798$		0			0
$799$	−1.22707	−	0.625225i	−0.0434107	−	0.0221189i
$800$	1.43295	+	0.730123i	0.0506623	+	0.0258137i
$801$		0			0
$802$	−10.5008	−	3.41192i	−0.370797	−	0.120479i
$803$	17.9354	+	10.9908i	0.632927	+	0.387858i
$804$		0			0
$805$	−3.92602	+	16.3531i	−0.138374	+	0.576370i
$806$	1.30251	+	3.14453i	0.0458789	+	0.110762i
$807$		0			0
$808$	−11.2869	+	6.91664i	−0.397073	+	0.243327i
$809$	−13.9338	+	3.34520i	−0.489885	+	0.117611i	−0.470860	−	0.882208i	$-0.656056\pi$
$809$	−13.9338	+	3.34520i	−0.489885	+	0.117611i	−0.0190254	+	0.999819i	$0.506056\pi$
$810$		0			0
$811$	−21.9664	+	21.9664i	−0.771344	+	0.771344i	−0.978341	−	0.206998i	$-0.933631\pi$
$811$	−21.9664	+	21.9664i	−0.771344	+	0.771344i	0.206998	+	0.978341i	$0.433631\pi$
$812$	−8.19420	−	1.29783i	−0.287560	−	0.0455450i
$813$		0			0
$814$	−1.59953	−	20.3239i	−0.0560635	−	0.712354i
$815$	−5.13153	−	32.3992i	−0.179750	−	1.13490i
$816$		0			0
$817$	32.8475	+	13.6059i	1.14919	+	0.476010i
$818$	3.75246	+	7.36463i	0.131202	+	0.257498i
$819$		0			0
$820$	2.98515	−	16.1872i	0.104246	−	0.565283i
$821$		−	50.3598i		−	1.75757i	−0.477220	−	0.878784i	$-0.658356\pi$
$821$		−	50.3598i		−	1.75757i	0.477220	−	0.878784i	$-0.341644\pi$
$822$		0			0
$823$	16.4943	−	39.8208i	0.574955	−	1.38806i	−0.322336	−	0.946625i	$-0.604468\pi$
$823$	16.4943	−	39.8208i	0.574955	−	1.38806i	0.897291	−	0.441439i	$-0.145532\pi$
$824$	−6.13655	−	4.45847i	−0.213777	−	0.155318i
$825$		0			0
$826$	6.74028	−	0.530472i	0.234524	−	0.0184575i
$827$	−1.67663	+	21.3037i	−0.0583023	+	0.740801i	0.896402	+	0.443243i	$0.146172\pi$
$827$	−1.67663	+	21.3037i	−0.0583023	+	0.740801i	−0.954704	+	0.297558i	$0.903828\pi$
$828$		0			0
$829$	−30.0283	−	30.0283i	−1.04292	−	1.04292i	−0.999036	−	0.0438883i	$-0.986025\pi$
$829$	−30.0283	−	30.0283i	−1.04292	−	1.04292i	−0.0438883	−	0.999036i	$-0.513975\pi$
$830$	−19.0957	−	26.2829i	−0.662820	−	0.912294i
$831$		0			0
$832$	0.715243	+	1.16717i	0.0247966	+	0.0404643i
$833$	9.88515	−	11.5740i	0.342500	−	0.401016i
$834$		0			0
$835$	−49.0224	−	11.7692i	−1.69649	−	0.407291i
$836$	7.20527	−	2.34113i	0.249200	−	0.0809698i
$837$		0			0
$838$	1.77560	−	5.46473i	0.0613370	−	0.188776i
$839$	12.2766	+	14.3741i	0.423836	+	0.496248i	0.930703	−	0.365776i	$-0.119196\pi$
$839$	12.2766	+	14.3741i	0.423836	+	0.496248i	−0.506867	+	0.862024i	$0.669196\pi$
$840$		0			0
$841$	4.68117	−	9.18731i	0.161420	−	0.316804i
$842$	2.97945	−	2.54469i	0.102679	−	0.0876959i
$843$		0			0
$844$	7.66523	−	12.5085i	0.263848	−	0.430561i
$845$	8.83832	+	27.2015i	0.304047	+	0.935762i
$846$		0			0
$847$	11.9572	−	4.95285i	0.410856	−	0.170182i
$848$	−0.299595	−	0.255878i	−0.0102881	−	0.00878690i
$849$		0			0
$850$	−1.72273	−	7.17567i	−0.0590890	−	0.246123i
$851$	−27.2544	+	19.8015i	−0.934270	+	0.678787i
$852$		0			0
$853$	−7.58809	+	47.9093i	−0.259811	+	1.64038i	0.420379	+	0.907349i	$0.361897\pi$
$853$	−7.58809	+	47.9093i	−0.259811	+	1.64038i	−0.680190	+	0.733036i	$0.738103\pi$
$854$	−2.36255	−	0.185936i	−0.0808447	−	0.00636261i
$855$		0			0
$856$	0.370165	−	0.0586284i	0.0126520	−	0.00200388i
$857$	27.3166	−	37.5981i	0.933117	−	1.28433i	−0.0255145	−	0.999674i	$-0.508122\pi$
$857$	27.3166	−	37.5981i	0.933117	−	1.28433i	0.958631	−	0.284651i	$-0.0918776\pi$
$858$		0			0
$859$	−44.1205	+	22.4805i	−1.50537	+	0.767025i	−0.995637	−	0.0933076i	$-0.970256\pi$
$859$	−44.1205	+	22.4805i	−1.50537	+	0.767025i	−0.509733	+	0.860332i	$0.670256\pi$
$860$	24.8877			0.848663
$861$		0			0
$862$	−33.6531			−1.14623
$863$	6.61004	−	3.36798i	0.225008	−	0.114647i	−0.337853	−	0.941199i	$-0.609701\pi$
$863$	6.61004	−	3.36798i	0.225008	−	0.114647i	0.562861	+	0.826552i	$0.309701\pi$
$864$		0			0
$865$	15.3032	−	21.0631i	0.520325	−	0.716166i
$866$	16.6063	−	2.63018i	0.564306	−	0.0893773i
$867$		0			0
$868$	4.75694	+	0.374379i	0.161461	+	0.0127073i
$869$	0.220798	−	1.39407i	0.00749007	−	0.0472904i
$870$		0			0
$871$	−3.39928	+	2.46972i	−0.115180	+	0.0836833i
$872$	−1.77910	−	7.41050i	−0.0602480	−	0.250951i
$873$		0			0
$874$	−9.51964	−	8.13054i	−0.322007	−	0.275020i
$875$	15.4589	−	6.40330i	0.522607	−	0.216471i
$876$		0			0
$877$	−4.64883	−	14.3076i	−0.156980	−	0.483134i	0.841376	−	0.540450i	$-0.181746\pi$
$877$	−4.64883	−	14.3076i	−0.156980	−	0.483134i	−0.998356	+	0.0573158i	$0.981746\pi$
$878$	−9.95896	+	16.2516i	−0.336099	+	0.548463i
$879$		0			0
$880$	4.03262	−	3.44418i	0.135939	−	0.116103i
$881$	22.8919	−	44.9279i	0.771248	−	1.51366i	−0.0845900	−	0.996416i	$-0.526958\pi$
$881$	22.8919	−	44.9279i	0.771248	−	1.51366i	0.855838	−	0.517244i	$-0.173042\pi$
$882$		0			0
$883$	−28.4318	−	33.2893i	−0.956805	−	1.12028i	−0.992662	−	0.120918i	$-0.961416\pi$
$883$	−28.4318	−	33.2893i	−0.956805	−	1.12028i	0.0358572	−	0.999357i	$-0.488584\pi$
$884$	1.94103	−	5.97387i	0.0652839	−	0.200923i
$885$		0			0
$886$	−2.98858	+	0.971049i	−0.100403	+	0.0326230i
$887$	13.8847	+	3.33341i	0.466201	+	0.111925i	0.459739	−	0.888054i	$-0.347943\pi$
$887$	13.8847	+	3.33341i	0.466201	+	0.111925i	0.00646224	+	0.999979i	$0.497943\pi$
$888$		0			0
$889$	−16.5957	+	19.4311i	−0.556602	+	0.651697i
$890$	−5.70466	−	9.30915i	−0.191221	−	0.312044i
$891$		0			0
$892$	−3.36958	−	4.63783i	−0.112822	−	0.155286i
$893$	−0.779361	−	0.779361i	−0.0260803	−	0.0260803i
$894$		0			0
$895$	0.375928	−	4.77661i	0.0125659	−	0.159665i
$896$	1.91317	−	0.150570i	0.0639147	−	0.00503019i
$897$		0			0
$898$	22.1609	+	16.1008i	0.739519	+	0.537292i
$899$	4.11343	−	9.93069i	0.137190	−	0.331207i
$900$		0			0
$901$			1.80788i			0.0602294i
$902$	−11.0850	−	7.18456i	−0.369089	−	0.239220i
$903$		0			0
$904$	5.19933	+	10.2043i	0.172927	+	0.339389i
$905$	−5.48333	−	2.27127i	−0.182272	−	0.0754996i
$906$		0			0
$907$	−5.60391	−	35.3817i	−0.186075	−	1.17483i	−0.887060	−	0.461654i	$-0.847256\pi$
$907$	−5.60391	−	35.3817i	−0.186075	−	1.17483i	0.700985	−	0.713176i	$-0.252744\pi$
$908$	1.60662	+	20.4141i	0.0533176	+	0.677465i
$909$		0			0
$910$	−6.67001	−	1.05643i	−0.221109	−	0.0350202i
$911$	−3.39834	+	3.39834i	−0.112592	+	0.112592i	−0.761158	−	0.648566i	$-0.775369\pi$
$911$	−3.39834	+	3.39834i	−0.112592	+	0.112592i	0.648566	+	0.761158i	$0.275369\pi$
$912$		0			0
$913$	−25.3515	+	6.08636i	−0.839012	+	0.201429i
$914$	−17.6635	+	10.8242i	−0.584255	+	0.358032i
$915$		0			0
$916$	1.19089	+	2.87507i	0.0393482	+	0.0949950i
$917$	2.32504	−	9.68448i	0.0767796	−	0.319810i
$918$		0			0
$919$	44.7086	+	27.3975i	1.47480	+	0.903759i	0.999716	+	0.0238192i	$0.00758259\pi$
$919$	44.7086	+	27.3975i	1.47480	+	0.903759i	0.475085	+	0.879940i	$0.342417\pi$
$920$	−8.33448	−	2.70804i	−0.274780	−	0.0892813i
$921$		0			0
$922$	−20.1997	−	10.2923i	−0.665243	−	0.338958i
$923$	12.7696	+	6.50642i	0.420315	+	0.214161i
$924$		0			0
$925$	−15.1149	−	4.91113i	−0.496975	−	0.161477i
$926$	7.08296	+	4.34044i	0.232760	+	0.142636i
$927$		0			0
$928$	1.00920	−	4.20361i	0.0331286	−	0.137990i
$929$	−3.15654	−	7.62056i	−0.103563	−	0.250023i	0.863601	−	0.504175i	$-0.168203\pi$
$929$	−3.15654	−	7.62056i	−0.103563	−	0.250023i	−0.967164	+	0.254153i	$0.918203\pi$
$930$		0			0
$931$	10.3865	−	6.36485i	0.340403	−	0.208599i
$932$	−15.8165	+	3.79721i	−0.518088	+	0.124382i
$933$		0			0
$934$	−9.53419	+	9.53419i	−0.311968	+	0.311968i
$935$	−24.0349	−	3.80676i	−0.786026	−	0.124494i
$936$		0			0
$937$	0.729381	+	9.26766i	0.0238278	+	0.302761i	0.997271	+	0.0738314i	$0.0235227\pi$
$937$	0.729381	+	9.26766i	0.0238278	+	0.302761i	−0.973443	+	0.228930i	$0.926477\pi$
$938$	0.921486	+	5.81804i	0.0300876	+	0.189966i
$939$		0			0
$940$	−0.712798	−	0.295251i	−0.0232489	−	0.00963001i
$941$	16.5117	+	32.4061i	0.538268	+	1.05641i	0.986694	+	0.162590i	$0.0519847\pi$
$941$	16.5117	+	32.4061i	0.538268	+	1.05641i	−0.448426	+	0.893820i	$0.648015\pi$
$942$		0			0
$943$	−0.551878	+	21.8214i	−0.0179716	+	0.710602i
$944$			3.52309i			0.114667i
$945$		0			0
$946$	7.64328	−	18.4525i	0.248505	−	0.599943i
$947$	−14.8525	−	10.7910i	−0.482642	−	0.350660i	0.319706	−	0.947517i	$-0.396416\pi$
$947$	−14.8525	−	10.7910i	−0.482642	−	0.350660i	−0.802348	+	0.596857i	$0.796416\pi$
$948$		0			0
$949$	13.9147	−	1.09511i	0.451691	−	0.0355489i
$950$	0.463381	−	5.88781i	0.0150341	−	0.191026i
$951$		0			0
$952$	−6.22676	−	6.22676i	−0.201810	−	0.201810i
$953$	−23.6593	−	32.5643i	−0.766400	−	1.05486i	−0.996655	−	0.0817292i	$-0.973956\pi$
$953$	−23.6593	−	32.5643i	−0.766400	−	1.05486i	0.230254	−	0.973131i	$-0.426044\pi$
$954$		0			0
$955$	−2.67874	−	4.37131i	−0.0866821	−	0.141452i
$956$	−17.9125	+	20.9729i	−0.579332	+	0.678311i
$957$		0			0
$958$	28.6930	+	6.88857i	0.927028	+	0.222560i
$959$	0.333741	−	0.108439i	0.0107770	−	0.00350168i
$960$		0			0
$961$	7.66911	−	23.6031i	0.247391	−	0.761390i
$962$	−8.78543	−	10.2864i	−0.283254	−	0.331647i
$963$		0			0
$964$	10.6383	−	20.8788i	0.342635	−	0.672460i
$965$	−33.6328	+	28.7251i	−1.08268	+	0.924694i
$966$		0			0
$967$	−4.15671	+	6.78314i	−0.133671	+	0.218131i	−0.912471	−	0.409141i	$-0.865828\pi$
$967$	−4.15671	+	6.78314i	−0.133671	+	0.218131i	0.778800	+	0.627272i	$0.215828\pi$
$968$	2.08402	+	6.41397i	0.0669831	+	0.206153i
$969$		0			0
$970$	−8.14065	+	3.37197i	−0.261380	+	0.108267i
$971$	13.9486	+	11.9132i	0.447631	+	0.382313i	0.844494	−	0.535565i	$-0.179901\pi$
$971$	13.9486	+	11.9132i	0.447631	+	0.382313i	−0.396863	+	0.917878i	$0.629901\pi$
$972$		0			0
$973$	5.06469	+	21.0959i	0.162366	+	0.676305i
$974$	−31.6643	+	23.0055i	−1.01459	+	0.737142i
$975$		0			0
$976$	0.193178	−	1.21968i	0.00618348	−	0.0390410i
$977$	18.1586	+	1.42912i	0.580946	+	0.0457215i	0.365528	−	0.930800i	$-0.380888\pi$
$977$	18.1586	+	1.42912i	0.580946	+	0.0457215i	0.215418	+	0.976522i	$0.430888\pi$
$978$		0			0
$979$	−8.65407	+	1.37067i	−0.276585	+	0.0438068i
$980$	5.01209	−	6.89855i	0.160105	−	0.220366i
$981$		0			0
$982$	10.8341	−	5.52023i	0.345729	−	0.176158i
$983$	−40.1665			−1.28111			−0.640556	−	0.767912i	$-0.721296\pi$
$983$	−40.1665			−1.28111			−0.640556	+	0.767912i	$0.721296\pi$
$984$		0			0
$985$	24.0159			0.765210
$986$	−17.6748	+	9.00574i	−0.562879	+	0.286801i
$987$		0			0
$988$	2.95483	−	4.06697i	0.0940057	−	0.129388i
$989$	−32.5980	+	5.16302i	−1.03656	+	0.164174i
$990$		0			0
$991$	23.6864	+	1.86416i	0.752423	+	0.0592170i	0.448870	−	0.893597i	$-0.351827\pi$
$991$	23.6864	+	1.86416i	0.752423	+	0.0592170i	0.303554	+	0.952814i	$0.401827\pi$
$992$	−0.388960	+	2.45580i	−0.0123495	+	0.0779717i
$993$		0			0
$994$	16.2547	−	11.8098i	0.515569	−	0.374583i
$995$	−13.3979	−	55.8063i	−0.424742	−	1.76918i
$996$		0			0
$997$	−6.90844	−	5.90037i	−0.218793	−	0.186867i	0.533296	−	0.845929i	$-0.320953\pi$
$997$	−6.90844	−	5.90037i	−0.218793	−	0.186867i	−0.752088	+	0.659062i	$0.770953\pi$
$998$	23.1764	−	9.59999i	0.733637	−	0.303882i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.ba.a.89.1	✓	48
3.2	odd	2		738.2.ba.b.89.3	yes	48
41.6	odd	40		738.2.ba.b.539.3	yes	48
123.47	even	40	inner	738.2.ba.a.539.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.ba.a.89.1	✓	48	1.1	even	1	trivial
738.2.ba.a.539.1	yes	48	123.47	even	40	inner
738.2.ba.b.89.3	yes	48	3.2	odd	2
738.2.ba.b.539.3	yes	48	41.6	odd	40

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.ba (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 + 0.453990i) q^{2} +(0.587785 - 0.809017i) q^{4} +(-2.53900 + 0.402138i) q^{5} +(1.91317 + 0.150570i) q^{7} +(-0.156434 + 0.987688i) q^{8} +(2.07970 - 1.51099i) q^{10} +(-0.481597 - 2.00600i) q^{11} +(-1.04091 - 0.889022i) q^{13} +(-1.77301 + 0.734404i) q^{14} +(-0.309017 - 0.951057i) q^{16} +(-2.39754 + 3.91244i) q^{17} +(-2.79249 + 2.38501i) q^{19} +(-1.16705 + 2.29046i) q^{20} +(1.33981 + 1.56872i) q^{22} +(1.05344 - 3.24217i) q^{23} +(1.52952 - 0.496972i) q^{25} +(1.33107 + 0.319561i) q^{26} +(1.24635 - 1.45929i) q^{28} +(-2.25879 - 3.68601i) q^{29} +(1.46148 + 2.01155i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.360018 - 4.57447i) q^{34} +(-4.91810 + 0.387063i) q^{35} +(-7.99481 - 5.80857i) q^{37} +(1.40535 - 3.39282i) q^{38} -2.57065i q^{40} +(-6.13781 + 1.82408i) q^{41} +(-4.39530 - 8.62626i) q^{43} +(-1.90596 - 0.789475i) q^{44} +(0.533288 + 3.36705i) q^{46} +(0.0235479 + 0.299204i) q^{47} +(-3.27625 - 0.518907i) q^{49} +(-1.13719 + 1.13719i) q^{50} +(-1.33107 + 0.319561i) q^{52} +(0.335935 - 0.205861i) q^{53} +(2.02946 + 4.89955i) q^{55} +(-0.448003 + 1.86607i) q^{56} +(3.68601 + 2.25879i) q^{58} +(-3.35065 - 1.08869i) q^{59} +(1.10029 + 0.560625i) q^{61} +(-2.21541 - 1.12881i) q^{62} +(-0.951057 - 0.309017i) q^{64} +(3.00038 + 1.83864i) q^{65} +(0.716549 - 2.98464i) q^{67} +(1.75599 + 4.23933i) q^{68} +(4.20634 - 2.57765i) q^{70} +(-10.1802 + 2.44406i) q^{71} +(-7.20995 + 7.20995i) q^{73} +(9.76046 + 1.54590i) q^{74} +(0.288130 + 3.66104i) q^{76} +(-0.619336 - 3.91034i) q^{77} +(0.632092 + 0.261821i) q^{79} +(1.16705 + 2.29046i) q^{80} +(4.64072 - 4.41177i) q^{82} -12.6379i q^{83} +(4.51402 - 10.8978i) q^{85} +(7.83248 + 5.69063i) q^{86} +(2.05664 - 0.161861i) q^{88} +(0.333231 - 4.23410i) q^{89} +(-1.85759 - 1.85759i) q^{91} +(-2.00377 - 2.75795i) q^{92} +(-0.156817 - 0.255902i) q^{94} +(6.13102 - 7.17850i) q^{95} +(-3.33298 - 0.800177i) q^{97} +(3.15474 - 1.02504i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{5} + 4 q^{7} - 8 q^{11} - 4 q^{13} + 4 q^{14} + 12 q^{16} - 16 q^{17} - 4 q^{19} + 16 q^{20} + 20 q^{22} - 40 q^{25} - 20 q^{26} - 4 q^{28} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 52 q^{35} - 24 q^{37}+ \cdots + 16 q^{97}+O(q^{100}) \) 48 * q - 4 * q^5 + 4 * q^7 - 8 * q^11 - 4 * q^13 + 4 * q^14 + 12 * q^16 - 16 * q^17 - 4 * q^19 + 16 * q^20 + 20 * q^22 - 40 * q^25 - 20 * q^26 - 4 * q^28 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 52 * q^35 - 24 * q^37 + 16 * q^38 + 12 * q^41 - 20 * q^44 + 16 * q^46 - 8 * q^47 - 48 * q^49 - 16 * q^50 + 20 * q^52 + 64 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^58 + 20 * q^59 - 60 * q^61 - 36 * q^62 + 128 * q^65 - 12 * q^67 - 8 * q^68 + 8 * q^70 - 40 * q^71 + 8 * q^73 + 8 * q^74 + 12 * q^76 - 44 * q^77 + 36 * q^79 - 16 * q^80 + 68 * q^82 + 104 * q^85 - 16 * q^86 + 8 * q^88 - 60 * q^89 + 56 * q^91 - 12 * q^94 - 28 * q^95 + 16 * q^97

Introduction

L-functions

Modular forms

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Database

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