LMFDB - Embedded newform 405.2.r.a.152.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

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

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, not 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			152.8
Character	$\chi$	$=$	405.152
Dual form			405.2.r.a.8.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0928047 - 0.0649826i) q^{2} +(-0.679650 - 1.86732i) q^{4} +(-0.584024 - 2.15845i) q^{5} +(0.344848 + 0.739528i) q^{7} +(-0.116914 + 0.436329i) q^{8} +O(q^{10})$	\(q+(-0.0928047 - 0.0649826i) q^{2} +(-0.679650 - 1.86732i) q^{4} +(-0.584024 - 2.15845i) q^{5} +(0.344848 + 0.739528i) q^{7} +(-0.116914 + 0.436329i) q^{8} +(-0.0860616 + 0.238266i) q^{10} +(0.792138 + 0.944033i) q^{11} +(-2.08344 - 2.97546i) q^{13} +(0.0160530 - 0.0910408i) q^{14} +(-3.00531 + 2.52175i) q^{16} +(-1.65815 - 6.18829i) q^{17} +(-2.78289 + 1.60671i) q^{19} +(-3.63360 + 2.55755i) q^{20} +(-0.0121684 - 0.139086i) q^{22} +(-0.471164 - 0.219707i) q^{23} +(-4.31783 + 2.52118i) q^{25} +0.411524i q^{26} +(1.14656 - 1.14656i) q^{28} +(-0.754929 - 4.28141i) q^{29} +(-6.93274 + 2.52331i) q^{31} +(1.34278 - 0.117478i) q^{32} +(-0.248247 + 0.682053i) q^{34} +(1.39484 - 1.17624i) q^{35} +(8.35299 - 2.23818i) q^{37} +(0.362674 + 0.0317298i) q^{38} +(1.01007 - 0.00247331i) q^{40} +(8.94143 + 1.57662i) q^{41} +(0.490289 - 5.60402i) q^{43} +(1.22444 - 2.12079i) q^{44} +(0.0294491 + 0.0510073i) q^{46} +(-2.14663 + 1.00099i) q^{47} +(4.07153 - 4.85226i) q^{49} +(0.564548 + 0.0466068i) q^{50} +(-4.14014 + 5.91273i) q^{52} +(-4.55111 - 4.55111i) q^{53} +(1.57502 - 2.26113i) q^{55} +(-0.362995 + 0.0640058i) q^{56} +(-0.208156 + 0.446393i) q^{58} +(10.5708 + 8.86992i) q^{59} +(3.01780 + 1.09839i) q^{61} +(0.807362 + 0.216332i) q^{62} +(6.66285 + 3.84680i) q^{64} +(-5.20561 + 6.23475i) q^{65} +(9.77239 - 6.84270i) q^{67} +(-10.4286 + 7.30217i) q^{68} +(-0.205883 + 0.0185205i) q^{70} +(-4.14187 - 2.39131i) q^{71} +(-5.46389 - 1.46405i) q^{73} +(-0.920640 - 0.335086i) q^{74} +(4.89163 + 4.10457i) q^{76} +(-0.424972 + 0.911356i) q^{77} +(9.54938 - 1.68381i) q^{79} +(7.19826 + 5.01405i) q^{80} +(-0.727355 - 0.727355i) q^{82} +(-4.76170 + 6.80042i) q^{83} +(-12.3887 + 7.19314i) q^{85} +(-0.409665 + 0.488220i) q^{86} +(-0.504521 + 0.235262i) q^{88} +(0.689073 + 1.19351i) q^{89} +(1.48197 - 2.56685i) q^{91} +(-0.0900380 + 1.02914i) q^{92} +(0.264265 + 0.0465970i) q^{94} +(5.09327 + 5.06839i) q^{95} +(-6.18004 - 0.540683i) q^{97} +(-0.693170 + 0.185734i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.0928047	−	0.0649826i	−0.0656229	−	0.0459496i	0.540305	−	0.841469i	$-0.318309\pi$
$2$	−0.0928047	−	0.0649826i	−0.0656229	−	0.0459496i	−0.605928	+	0.795520i	$0.707198\pi$
$3$		0			0
$3$		0			0
$4$	−0.679650	−	1.86732i	−0.339825	−	0.933662i
$5$	−0.584024	−	2.15845i	−0.261183	−	0.965289i
$5$	−0.584024	−	2.15845i	−0.261183	−	0.965289i
$6$		0			0
$7$	0.344848	+	0.739528i	0.130340	+	0.279515i	0.960637	−	0.277805i	$-0.0896071\pi$
$7$	0.344848	+	0.739528i	0.130340	+	0.279515i	−0.830297	+	0.557321i	$0.811829\pi$
$8$	−0.116914	+	0.436329i	−0.0413353	+	0.154265i
$9$		0			0
$10$	−0.0860616	+	0.238266i	−0.0272151	+	0.0753463i
$11$	0.792138	+	0.944033i	0.238839	+	0.284637i	0.872127	−	0.489279i	$-0.162740\pi$
$11$	0.792138	+	0.944033i	0.238839	+	0.284637i	−0.633289	+	0.773916i	$0.718295\pi$
$12$		0			0
$13$	−2.08344	−	2.97546i	−0.577843	−	0.825245i	0.418718	−	0.908116i	$-0.362480\pi$
$13$	−2.08344	−	2.97546i	−0.577843	−	0.825245i	−0.996560	+	0.0828718i	$0.973591\pi$
$14$	0.0160530	−	0.0910408i	0.00429033	−	0.0243317i
$15$		0			0
$16$	−3.00531	+	2.52175i	−0.751327	+	0.630438i
$17$	−1.65815	−	6.18829i	−0.402160	−	1.50088i	−0.809234	−	0.587486i	$-0.800118\pi$
$17$	−1.65815	−	6.18829i	−0.402160	−	1.50088i	0.407074	−	0.913395i	$-0.366549\pi$
$18$		0			0
$19$	−2.78289	+	1.60671i	−0.638440	+	0.368603i	−0.784013	−	0.620744i	$-0.786831\pi$
$19$	−2.78289	+	1.60671i	−0.638440	+	0.368603i	0.145573	+	0.989347i	$0.453497\pi$
$20$	−3.63360	+	2.55755i	−0.812497	+	0.571887i
$21$		0			0
$22$	−0.0121684	−	0.139086i	−0.00259432	−	0.0296532i
$23$	−0.471164	−	0.219707i	−0.0982444	−	0.0458121i	0.372875	−	0.927882i	$-0.378372\pi$
$23$	−0.471164	−	0.219707i	−0.0982444	−	0.0458121i	−0.471119	+	0.882070i	$0.656150\pi$
$24$		0			0
$25$	−4.31783	+	2.52118i	−0.863566	+	0.504235i
$26$			0.411524i			0.0807066i
$27$		0			0
$28$	1.14656	−	1.14656i	0.216680	−	0.216680i
$29$	−0.754929	−	4.28141i	−0.140187	−	0.795038i	−0.971107	−	0.238646i	$-0.923296\pi$
$29$	−0.754929	−	4.28141i	−0.140187	−	0.795038i	0.830920	−	0.556392i	$-0.187815\pi$
$30$		0			0
$31$	−6.93274	+	2.52331i	−1.24516	+	0.453200i	−0.878762	−	0.477260i	$-0.841630\pi$
$31$	−6.93274	+	2.52331i	−1.24516	+	0.453200i	−0.366394	+	0.930460i	$0.619408\pi$
$32$	1.34278	−	0.117478i	0.237372	−	0.0207674i
$33$		0			0
$34$	−0.248247	+	0.682053i	−0.0425740	+	0.116971i
$35$	1.39484	−	1.17624i	0.235771	−	0.198821i
$36$		0			0
$37$	8.35299	−	2.23818i	1.37322	−	0.367954i	0.504569	−	0.863372i	$-0.331652\pi$
$37$	8.35299	−	2.23818i	1.37322	−	0.367954i	0.868655	+	0.495417i	$0.164985\pi$
$38$	0.362674	+	0.0317298i	0.0588334	+	0.00514726i
$39$		0			0
$40$	1.01007	−	0.00247331i	0.159707	−	0.000391065i
$41$	8.94143	+	1.57662i	1.39642	+	0.246226i	0.820670	−	0.571402i	$-0.193600\pi$
$41$	8.94143	+	1.57662i	1.39642	+	0.246226i	0.575747	+	0.817628i	$0.304711\pi$
$42$		0			0
$43$	0.490289	−	5.60402i	0.0747683	−	0.854606i	−0.862514	−	0.506034i	$-0.831111\pi$
$43$	0.490289	−	5.60402i	0.0747683	−	0.854606i	0.937282	−	0.348572i	$-0.113333\pi$
$44$	1.22444	−	2.12079i	0.184591	−	0.319721i
$45$		0			0
$46$	0.0294491	+	0.0510073i	0.00434203	+	0.00752062i
$47$	−2.14663	+	1.00099i	−0.313118	+	0.146010i	−0.572824	−	0.819678i	$-0.694152\pi$
$47$	−2.14663	+	1.00099i	−0.313118	+	0.146010i	0.259706	+	0.965688i	$0.416374\pi$
$48$		0			0
$49$	4.07153	−	4.85226i	0.581647	−	0.693180i
$50$	0.564548	+	0.0466068i	0.0798391	+	0.00659120i
$51$		0			0
$52$	−4.14014	+	5.91273i	−0.574134	+	0.819949i
$53$	−4.55111	−	4.55111i	−0.625143	−	0.625143i	0.321699	−	0.946842i	$-0.395746\pi$
$53$	−4.55111	−	4.55111i	−0.625143	−	0.625143i	−0.946842	+	0.321699i	$0.895746\pi$
$54$		0			0
$55$	1.57502	−	2.26113i	0.212376	−	0.304891i
$56$	−0.362995	+	0.0640058i	−0.0485072	+	0.00855313i
$57$		0			0
$58$	−0.208156	+	0.446393i	−0.0273323	+	0.0586142i
$59$	10.5708	+	8.86992i	1.37620	+	1.15477i	0.970596	+	0.240714i	$0.0773817\pi$
$59$	10.5708	+	8.86992i	1.37620	+	1.15477i	0.405600	+	0.914051i	$0.367063\pi$
$60$		0			0
$61$	3.01780	+	1.09839i	0.386390	+	0.140634i	0.527908	−	0.849301i	$-0.322976\pi$
$61$	3.01780	+	1.09839i	0.386390	+	0.140634i	−0.141519	+	0.989936i	$0.545199\pi$
$62$	0.807362	+	0.216332i	0.102535	+	0.0274742i
$63$		0			0
$64$	6.66285	+	3.84680i	0.832856	+	0.480850i
$65$	−5.20561	+	6.23475i	−0.645677	+	0.773325i
$66$		0			0
$67$	9.77239	−	6.84270i	1.19389	−	0.835969i	0.204160	−	0.978938i	$-0.434554\pi$
$67$	9.77239	−	6.84270i	1.19389	−	0.835969i	0.989727	+	0.142969i	$0.0456649\pi$
$68$	−10.4286	+	7.30217i	−1.26465	+	0.885518i
$69$		0			0
$70$	−0.205883	+	0.0185205i	−0.0246077	+	0.00221362i
$71$	−4.14187	−	2.39131i	−0.491550	−	0.283796i	0.233667	−	0.972317i	$-0.424927\pi$
$71$	−4.14187	−	2.39131i	−0.491550	−	0.283796i	−0.725217	+	0.688520i	$0.758261\pi$
$72$		0			0
$73$	−5.46389	−	1.46405i	−0.639500	−	0.171354i	−0.0755232	−	0.997144i	$-0.524063\pi$
$73$	−5.46389	−	1.46405i	−0.639500	−	0.171354i	−0.563977	+	0.825790i	$0.690729\pi$
$74$	−0.920640	−	0.335086i	−0.107022	−	0.0389529i
$75$		0			0
$76$	4.89163	+	4.10457i	0.561109	+	0.470826i
$77$	−0.424972	+	0.911356i	−0.0484301	+	0.103859i
$78$		0			0
$79$	9.54938	−	1.68381i	1.07439	−	0.189444i	0.391656	−	0.920112i	$-0.371902\pi$
$79$	9.54938	−	1.68381i	1.07439	−	0.189444i	0.682733	+	0.730668i	$0.260791\pi$
$80$	7.19826	+	5.01405i	0.804790	+	0.560588i
$81$		0			0
$82$	−0.727355	−	0.727355i	−0.0803229	−	0.0803229i
$83$	−4.76170	+	6.80042i	−0.522665	+	0.746443i	−0.990521	−	0.137362i	$-0.956138\pi$
$83$	−4.76170	+	6.80042i	−0.522665	+	0.746443i	0.467856	+	0.883805i	$0.345027\pi$
$84$		0			0
$85$	−12.3887	+	7.19314i	−1.34375	+	0.780206i
$86$	−0.409665	+	0.488220i	−0.0441753	+	0.0526461i
$87$		0			0
$88$	−0.504521	+	0.235262i	−0.0537821	+	0.0250790i
$89$	0.689073	+	1.19351i	0.0730416	+	0.126512i	0.900233	−	0.435409i	$-0.143396\pi$
$89$	0.689073	+	1.19351i	0.0730416	+	0.126512i	−0.827191	+	0.561920i	$0.810063\pi$
$90$		0			0
$91$	1.48197	−	2.56685i	0.155353	−	0.269079i
$92$	−0.0900380	+	1.02914i	−0.00938711	+	0.107295i
$93$		0			0
$94$	0.264265	+	0.0465970i	0.0272568	+	0.00480611i
$95$	5.09327	+	5.06839i	0.522559	+	0.520006i
$96$		0			0
$97$	−6.18004	−	0.540683i	−0.627488	−	0.0548981i	−0.231023	−	0.972948i	$-0.574207\pi$
$97$	−6.18004	−	0.540683i	−0.627488	−	0.0548981i	−0.396464	+	0.918050i	$0.629763\pi$
$98$	−0.693170	+	0.185734i	−0.0700207	+	0.0187620i
$99$		0			0
$100$	7.64247	+	6.34927i	0.764247	+	0.634927i
$101$	0.358110	−	0.983900i	0.0356333	−	0.0979017i	−0.920600	−	0.390507i	$-0.872300\pi$
$101$	0.358110	−	0.983900i	0.0356333	−	0.0979017i	0.956233	+	0.292605i	$0.0945221\pi$
$102$		0			0
$103$	5.46070	−	0.477749i	0.538058	−	0.0470740i	0.185112	−	0.982717i	$-0.440735\pi$
$103$	5.46070	−	0.477749i	0.538058	−	0.0470740i	0.352947	+	0.935643i	$0.385180\pi$
$104$	1.54186	−	0.561192i	0.151192	−	0.0550294i
$105$		0			0
$106$	0.126622	+	0.718107i	0.0122986	+	0.0697487i
$107$	7.41541	−	7.41541i	0.716875	−	0.716875i	−0.251089	−	0.967964i	$-0.580789\pi$
$107$	7.41541	−	7.41541i	0.716875	−	0.716875i	0.967964	+	0.251089i	$0.0807888\pi$
$108$		0			0
$109$			13.2925i			1.27319i	0.771199	+	0.636595i	$0.219658\pi$
$109$			13.2925i			1.27319i	−0.771199	+	0.636595i	$0.780342\pi$
$110$	−0.293104	+	0.107495i	−0.0279463	+	0.0102492i
$111$		0			0
$112$	−2.90128	−	1.35289i	−0.274145	−	0.127836i
$113$	−1.20301	−	13.7505i	−0.113170	−	1.29353i	−0.814276	−	0.580477i	$-0.802866\pi$
$113$	−1.20301	−	13.7505i	−0.113170	−	1.29353i	0.701107	−	0.713056i	$-0.252690\pi$
$114$		0			0
$115$	−0.199057	+	1.14530i	−0.0185621	+	0.106800i
$116$	−7.48170	+	4.31956i	−0.694658	+	0.401061i
$117$		0			0
$118$	−0.404626	−	1.51009i	−0.0372489	−	0.139015i
$119$	4.00461	−	3.36027i	0.367102	−	0.308035i
$120$		0			0
$121$	1.64641	−	9.33728i	0.149674	−	0.848843i
$122$	−0.208690	−	0.298040i	−0.0188939	−	0.0269833i
$123$		0			0
$124$	9.42367	+	11.2307i	0.846271	+	1.00855i
$125$	7.96355	+	7.84741i	0.712282	+	0.701893i
$126$		0			0
$127$	3.01921	−	11.2678i	0.267911	−	0.999858i	−0.692533	−	0.721386i	$-0.743505\pi$
$127$	3.01921	−	11.2678i	0.267911	−	0.999858i	0.960444	−	0.278472i	$-0.0898280\pi$
$128$	−1.50767	−	3.23321i	−0.133261	−	0.285778i
$129$		0			0
$130$	0.888256	−	0.240340i	0.0779052	−	0.0210792i
$131$	2.06228	+	5.66608i	0.180182	+	0.495047i	0.996598	−	0.0824178i	$-0.0262642\pi$
$131$	2.06228	+	5.66608i	0.180182	+	0.495047i	−0.816415	+	0.577465i	$0.804042\pi$
$132$		0			0
$133$	−2.14788	−	1.50396i	−0.186245	−	0.130410i
$134$	−1.35158			−0.116759
$135$		0			0
$136$	2.89399			0.248157
$137$	10.9750	+	7.68477i	0.937657	+	0.656554i	0.939173	−	0.343444i	$-0.111594\pi$
$137$	10.9750	+	7.68477i	0.937657	+	0.656554i	−0.00151614	+	0.999999i	$0.500483\pi$
$138$		0			0
$139$	−2.32343	−	6.38357i	−0.197071	−	0.541447i	0.801315	−	0.598242i	$-0.204134\pi$
$139$	−2.32343	−	6.38357i	−0.197071	−	0.541447i	−0.998386	+	0.0567952i	$0.981912\pi$
$140$	−3.14442	−	1.80518i	−0.265752	−	0.152566i
$141$		0			0
$142$	0.228992	+	0.491074i	0.0192166	+	0.0412100i
$143$	1.15856	−	4.32381i	0.0968839	−	0.361575i
$144$		0			0
$145$	−8.80033	+	4.12993i	−0.730828	+	0.342972i
$146$	0.411938	+	0.490928i	0.0340922	+	0.0406295i
$147$		0			0
$148$	−9.85652	−	14.0766i	−0.810201	−	1.15709i
$149$	2.75408	−	15.6192i	0.225623	−	1.27957i	−0.635868	−	0.771798i	$-0.719358\pi$
$149$	2.75408	−	15.6192i	0.225623	−	1.27957i	0.861491	−	0.507773i	$-0.169531\pi$
$150$		0			0
$151$	−0.777628	+	0.652507i	−0.0632825	+	0.0531003i	−0.673880	−	0.738841i	$-0.735374\pi$
$151$	−0.777628	+	0.652507i	−0.0632825	+	0.0531003i	0.610598	+	0.791941i	$0.290929\pi$
$152$	−0.375692	−	1.40210i	−0.0304727	−	0.113726i
$153$		0			0
$154$	0.0986617	−	0.0569624i	0.00795039	−	0.00459016i
$155$	9.49533	+	13.4903i	0.762683	+	1.08357i
$156$		0			0
$157$	1.36005	+	15.5455i	0.108544	+	1.24066i	0.833754	+	0.552136i	$0.186187\pi$
$157$	1.36005	+	15.5455i	0.108544	+	1.24066i	−0.725210	+	0.688528i	$0.758257\pi$
$158$	−0.995646	−	0.464278i	−0.0792094	−	0.0369359i
$159$		0			0
$160$	−1.03779	−	2.82972i	−0.0820442	−	0.223709i
$161$		−	0.424205i		−	0.0334320i
$162$		0			0
$163$	1.25033	−	1.25033i	0.0979331	−	0.0979331i	−0.656443	−	0.754376i	$-0.727940\pi$
$163$	1.25033	−	1.25033i	0.0979331	−	0.0979331i	0.754376	+	0.656443i	$0.227940\pi$
$164$	−3.13299	−	17.7681i	−0.244646	−	1.38746i
$165$		0			0
$166$	0.883817	−	0.321683i	0.0685975	−	0.0249675i
$167$	−4.87345	+	0.426371i	−0.377119	+	0.0329936i	−0.274140	−	0.961690i	$-0.588393\pi$
$167$	−4.87345	+	0.426371i	−0.377119	+	0.0329936i	−0.102979	+	0.994684i	$0.532837\pi$
$168$		0			0
$169$	−0.0663864	+	0.182395i	−0.00510665	+	0.0140304i
$170$	1.61716	+	0.137494i	0.124031	+	0.0105453i
$171$		0			0
$172$	−10.7978	+	2.89325i	−0.823321	+	0.220608i
$173$	−2.34398	−	0.205071i	−0.178209	−	0.0155913i	−0.00229816	−	0.999997i	$-0.500732\pi$
$173$	−2.34398	−	0.205071i	−0.178209	−	0.0155913i	−0.175911	+	0.984406i	$0.556287\pi$
$174$		0			0
$175$	−3.35348	−	2.32374i	−0.253499	−	0.175658i
$176$	−4.76124	−	0.839535i	−0.358892	−	0.0632823i
$177$		0			0
$178$	0.0136081	−	0.155541i	0.00101997	−	0.0116583i
$179$	−9.70081	+	16.8023i	−0.725073	+	1.25586i	0.233871	+	0.972268i	$0.424861\pi$
$179$	−9.70081	+	16.8023i	−0.725073	+	1.25586i	−0.958944	+	0.283595i	$0.908473\pi$
$180$		0			0
$181$	−2.02017	−	3.49903i	−0.150158	−	0.260081i	0.781128	−	0.624371i	$-0.214645\pi$
$181$	−2.02017	−	3.49903i	−0.150158	−	0.260081i	−0.931285	+	0.364291i	$0.881312\pi$
$182$	−0.304334	+	0.141913i	−0.0225587	+	0.0105193i
$183$		0			0
$184$	0.150950	−	0.179895i	0.0111282	−	0.0132621i
$185$	−9.70935	−	16.7224i	−0.713846	−	1.22945i
$186$		0			0
$187$	4.52847	−	6.46733i	0.331155	−	0.472938i
$188$	3.32813	+	3.32813i	0.242729	+	0.242729i
$189$		0			0
$190$	−0.143323	−	0.801345i	−0.0103977	−	0.0581357i
$191$	0.548539	−	0.0967222i	0.0396909	−	0.00699857i	−0.153767	−	0.988107i	$-0.549141\pi$
$191$	0.548539	−	0.0967222i	0.0396909	−	0.00699857i	0.193458	+	0.981108i	$0.438030\pi$
$192$		0			0
$193$	−8.39357	+	18.0001i	−0.604183	+	1.29567i	0.331708	+	0.943382i	$0.392375\pi$
$193$	−8.39357	+	18.0001i	−0.604183	+	1.29567i	−0.935890	+	0.352292i	$0.885403\pi$
$194$	0.538402	+	0.451773i	0.0386550	+	0.0324354i
$195$		0			0
$196$	−11.8280	−	4.30503i	−0.844854	−	0.307502i
$197$	−16.1238	−	4.32035i	−1.14877	−	0.307812i	−0.366299	−	0.930497i	$-0.619375\pi$
$197$	−16.1238	−	4.32035i	−1.14877	−	0.307812i	−0.782473	+	0.622685i	$0.786042\pi$
$198$		0			0
$199$	−20.8934	−	12.0628i	−1.48110	−	0.855112i	−0.481327	−	0.876541i	$-0.659845\pi$
$199$	−20.8934	−	12.0628i	−1.48110	−	0.855112i	−0.999770	+	0.0214296i	$0.993178\pi$
$200$	−0.595246	−	2.17875i	−0.0420903	−	0.154061i
$201$		0			0
$202$	−0.0971707	+	0.0680397i	−0.00683691	+	0.00478725i
$203$	2.90589	−	2.03473i	0.203954	−	0.142810i
$204$		0			0
$205$	−1.81896	−	20.2204i	−0.127042	−	1.41226i
$206$	−0.537824	−	0.310513i	−0.0374720	−	0.0216344i
$207$		0			0
$208$	13.7648	+	3.68826i	0.954415	+	0.255735i
$209$	−3.72122	−	1.35441i	−0.257402	−	0.0936867i
$210$		0			0
$211$	21.4119	+	17.9667i	1.47406	+	1.23688i	0.912265	+	0.409601i	$0.134332\pi$
$211$	21.4119	+	17.9667i	1.47406	+	1.23688i	0.561792	+	0.827279i	$0.310112\pi$
$212$	−5.40523	+	11.5916i	−0.371233	+	0.796111i
$213$		0			0
$214$	−1.17006	+	0.206313i	−0.0799835	+	0.0141032i
$215$	−12.3824	+	2.21462i	−0.844470	+	0.151036i
$216$		0			0
$217$	−4.25680	−	4.25680i	−0.288970	−	0.288970i
$218$	0.863780	−	1.23361i	0.0585026	−	0.0835503i
$219$		0			0
$220$	−5.29273	−	1.40430i	−0.356836	−	0.0946779i
$221$	−14.9584	+	17.8267i	−1.00621	+	1.19915i
$222$		0			0
$223$	3.93150	−	1.83329i	0.263273	−	0.122766i	−0.286500	−	0.958080i	$-0.592492\pi$
$223$	3.93150	−	1.83329i	0.263273	−	0.122766i	0.549773	+	0.835314i	$0.314714\pi$
$224$	0.549933	+	0.952512i	0.0367440	+	0.0636424i
$225$		0			0
$226$	−0.781895	+	1.35428i	−0.0520109	+	0.0900855i
$227$	2.21851	−	25.3576i	0.147247	−	1.68305i	−0.459521	−	0.888167i	$-0.651979\pi$
$227$	2.21851	−	25.3576i	0.147247	−	1.68305i	0.606768	−	0.794879i	$-0.292466\pi$
$228$		0			0
$229$	−5.08120	−	0.895953i	−0.335775	−	0.0592062i	0.00321862	−	0.999995i	$-0.498975\pi$
$229$	−5.08120	−	0.895953i	−0.335775	−	0.0592062i	−0.338994	+	0.940789i	$0.610087\pi$
$230$	0.0928979	−	0.0933539i	0.00612550	−	0.00615558i
$231$		0			0
$232$	1.95636	+	0.171160i	0.128442	+	0.0112372i
$233$	7.55194	−	2.02354i	0.494744	−	0.132566i	−0.00281565	−	0.999996i	$-0.500896\pi$
$233$	7.55194	−	2.02354i	0.494744	−	0.132566i	0.497560	+	0.867430i	$0.334230\pi$
$234$		0			0
$235$	3.41428	+	4.04880i	0.222723	+	0.264115i
$236$	9.37859	−	25.7675i	0.610494	−	1.67732i
$237$		0			0
$238$	−0.590005	+	0.0516188i	−0.0382444	+	0.00334595i
$239$	10.8598	−	3.95265i	0.702462	−	0.255675i	0.0340005	−	0.999422i	$-0.489175\pi$
$239$	10.8598	−	3.95265i	0.702462	−	0.255675i	0.668462	+	0.743746i	$0.266953\pi$
$240$		0			0
$241$	2.63129	+	14.9228i	0.169496	+	0.961259i	0.944307	+	0.329066i	$0.106734\pi$
$241$	2.63129	+	14.9228i	0.169496	+	0.961259i	−0.774811	+	0.632193i	$0.782155\pi$
$242$	−0.759555	+	0.759555i	−0.0488261	+	0.0488261i
$243$		0			0
$244$		−	6.38173i		−	0.408548i
$245$	−12.8512	−	5.95437i	−0.821036	−	0.380411i
$246$		0			0
$247$	10.5787	+	4.93292i	0.673106	+	0.313874i
$248$	−0.290459	−	3.31996i	−0.0184442	−	0.210818i
$249$		0			0
$250$	−0.229111	−	1.24577i	−0.0144902	−	0.0787893i
$251$	13.8298	−	7.98465i	0.872930	−	0.503986i	0.00460934	−	0.999989i	$-0.498533\pi$
$251$	13.8298	−	7.98465i	0.872930	−	0.503986i	0.868321	+	0.496003i	$0.165199\pi$
$252$		0			0
$253$	−0.165816	−	0.618833i	−0.0104247	−	0.0389057i
$254$	−1.01241	+	0.849512i	−0.0635242	+	0.0533031i
$255$		0			0
$256$	2.60177	−	14.7554i	0.162611	−	0.922212i
$257$	−13.2591	−	18.9360i	−0.827080	−	1.18119i	−0.981172	−	0.193136i	$-0.938134\pi$
$257$	−13.2591	−	18.9360i	−0.827080	−	1.18119i	0.154092	−	0.988057i	$-0.450755\pi$
$258$		0			0
$259$	4.53571	+	5.40545i	0.281835	+	0.335878i
$260$	15.1803	+	5.48312i	0.941442	+	0.340048i
$261$		0			0
$262$	0.176807	−	0.659851i	0.0109231	−	0.0407657i
$263$	−0.0491363	−	0.105373i	−0.00302987	−	0.00649758i	0.904787	−	0.425864i	$-0.140030\pi$
$263$	−0.0491363	−	0.105373i	−0.00302987	−	0.00649758i	−0.907817	+	0.419367i	$0.862252\pi$
$264$		0			0
$265$	−7.16539	+	12.4813i	−0.440167	+	0.766721i
$266$	0.101602	+	0.279149i	0.00622962	+	0.0171158i
$267$		0			0
$268$	−19.4193	−	13.5976i	−1.18622	−	0.830604i
$269$	−16.5806			−1.01094			−0.505468	−	0.862845i	$-0.668680\pi$
$269$	−16.5806			−1.01094			−0.505468	+	0.862845i	$0.668680\pi$
$270$		0			0
$271$	−31.4952			−1.91320			−0.956599	−	0.291408i	$-0.905876\pi$
$271$	−31.4952			−1.91320			−0.956599	+	0.291408i	$0.905876\pi$
$272$	20.5886	+	14.4163i	1.24837	+	0.874116i
$273$		0			0
$274$	−0.519155	−	1.42637i	−0.0313633	−	0.0861700i
$275$	−5.80039	−	2.07906i	−0.349777	−	0.125372i
$276$		0			0
$277$	−0.477906	−	1.02487i	−0.0287146	−	0.0615786i	0.891427	−	0.453164i	$-0.149705\pi$
$277$	−0.477906	−	1.02487i	−0.0287146	−	0.0615786i	−0.920142	+	0.391585i	$0.871927\pi$
$278$	−0.199196	+	0.743408i	−0.0119470	+	0.0445866i
$279$		0			0
$280$	0.350151	+	0.746126i	0.0209255	+	0.0445896i
$281$	15.9976	+	19.0652i	0.954338	+	1.13734i	0.990434	+	0.137988i	$0.0440634\pi$
$281$	15.9976	+	19.0652i	0.954338	+	1.13734i	−0.0360958	+	0.999348i	$0.511492\pi$
$282$		0			0
$283$	13.1825	+	18.8266i	0.783618	+	1.11912i	0.990057	+	0.140664i	$0.0449236\pi$
$283$	13.1825	+	18.8266i	0.783618	+	1.11912i	−0.206439	+	0.978459i	$0.566187\pi$
$284$	−1.65033	+	9.35947i	−0.0979289	+	0.555382i
$285$		0			0
$286$	−0.388493	+	0.325984i	−0.0229721	+	0.0192758i
$287$	1.91748	+	7.15614i	0.113185	+	0.422413i
$288$		0			0
$289$	−20.8231	+	12.0222i	−1.22489	+	0.707188i
$290$	1.08509	+	0.188591i	0.0637184	+	0.0110745i
$291$		0			0
$292$	0.979689	+	11.1979i	0.0573320	+	0.655307i
$293$	15.8638	+	7.39741i	0.926773	+	0.432161i	0.826588	−	0.562807i	$-0.190279\pi$
$293$	15.8638	+	7.39741i	0.926773	+	0.432161i	0.100185	+	0.994969i	$0.468056\pi$
$294$		0			0
$295$	12.9717	−	27.9967i	0.755243	−	1.63003i
$296$			3.90632i			0.227050i
$297$		0			0
$298$	−1.27056	+	1.27056i	−0.0736018	+	0.0736018i
$299$	0.327911	+	1.85968i	0.0189636	+	0.107548i
$300$		0			0
$301$	4.31341	−	1.56995i	0.248621	−	0.0904906i
$302$	0.114569	−	0.0100235i	0.00659272	−	0.000576788i
$303$		0			0
$304$	4.31174	−	11.8464i	0.247295	−	0.679439i
$305$	0.608353	−	7.15526i	0.0348342	−	0.409709i
$306$		0			0
$307$	0.890598	−	0.238635i	0.0508291	−	0.0136196i	−0.233315	−	0.972401i	$-0.574957\pi$
$307$	0.890598	−	0.238635i	0.0508291	−	0.0136196i	0.284144	+	0.958782i	$0.408291\pi$
$308$	1.99063	+	0.174158i	0.113427	+	0.00992355i
$309$		0			0
$310$	−0.00457650	−	1.86900i	−0.000259928	−	0.106152i
$311$	−8.25248	−	1.45513i	−0.467955	−	0.0825131i	−0.0653015	−	0.997866i	$-0.520801\pi$
$311$	−8.25248	−	1.45513i	−0.467955	−	0.0825131i	−0.402653	+	0.915352i	$0.631912\pi$
$312$		0			0
$313$	0.138297	−	1.58074i	0.00781702	−	0.0893490i	−0.991284	−	0.131743i	$-0.957943\pi$
$313$	0.138297	−	1.58074i	0.00781702	−	0.0893490i	0.999101	+	0.0423936i	$0.0134983\pi$
$314$	0.883965	−	1.53107i	0.0498851	−	0.0864034i
$315$		0			0
$316$	−9.63446	−	16.6874i	−0.541981	−	0.938739i
$317$	9.24972	−	4.31321i	0.519516	−	0.242254i	−0.145130	−	0.989413i	$-0.546360\pi$
$317$	9.24972	−	4.31321i	0.519516	−	0.242254i	0.664646	+	0.747158i	$0.268582\pi$
$318$		0			0
$319$	3.44379	−	4.10415i	0.192815	−	0.229788i
$320$	4.41186	−	16.6281i	0.246631	−	0.929537i
$321$		0			0
$322$	−0.0275659	+	0.0393682i	−0.00153619	+	0.00219390i
$323$	14.5572	+	14.5572i	0.809985	+	0.809985i
$324$		0			0
$325$	16.4976	+	7.59482i	0.915123	+	0.421285i
$326$	−0.197286	+	0.0347868i	−0.0109266	+	0.00192666i
$327$		0			0
$328$	−1.73330	+	3.71707i	−0.0957055	+	0.205241i
$329$	−1.48052	−	1.24231i	−0.0816238	−	0.0684905i
$330$		0			0
$331$	7.45973	+	2.71512i	0.410024	+	0.149236i	0.538793	−	0.842438i	$-0.318880\pi$
$331$	7.45973	+	2.71512i	0.410024	+	0.149236i	−0.128769	+	0.991675i	$0.541103\pi$
$332$	15.9349	+	4.26974i	0.874540	+	0.234332i
$333$		0			0
$334$	0.479986	+	0.277120i	0.0262636	+	0.0151633i
$335$	−20.4769	−	17.0969i	−1.11878	−	0.934105i
$336$		0			0
$337$	1.96309	−	1.37457i	0.106937	−	0.0748778i	−0.518885	−	0.854844i	$-0.673653\pi$
$337$	1.96309	−	1.37457i	0.106937	−	0.0748778i	0.625822	+	0.779966i	$0.284764\pi$
$338$	0.0180135	−	0.0126132i	0.000979805	−	0.000686067i
$339$		0			0
$340$	21.8519	+	18.2450i	1.18509	+	0.989472i
$341$	−7.87377	−	4.54592i	−0.426389	−	0.246176i
$342$		0			0
$343$	10.5097	+	2.81606i	0.567469	+	0.152053i
$344$	2.38787	+	0.869115i	0.128746	+	0.0468595i
$345$		0			0
$346$	0.204206	+	0.171349i	0.0109782	+	0.00921179i
$347$	−10.1468	+	21.7598i	−0.544708	+	1.16813i	0.420656	+	0.907220i	$0.361800\pi$
$347$	−10.1468	+	21.7598i	−0.544708	+	1.16813i	−0.965363	+	0.260909i	$0.915978\pi$
$348$		0			0
$349$	18.2123	−	3.21131i	0.974880	−	0.171898i	0.336554	−	0.941664i	$-0.390738\pi$
$349$	18.2123	−	3.21131i	0.974880	−	0.171898i	0.638326	+	0.769767i	$0.279627\pi$
$350$	0.160216	+	0.433571i	0.00856391	+	0.0231754i
$351$		0			0
$352$	1.17457	+	1.17457i	0.0626048	+	0.0626048i
$353$	−16.5605	+	23.6509i	−0.881429	+	1.25881i	0.0835552	+	0.996503i	$0.473373\pi$
$353$	−16.5605	+	23.6509i	−0.881429	+	1.25881i	−0.964984	+	0.262308i	$0.915516\pi$
$354$		0			0
$355$	−2.74258	+	10.3366i	−0.145561	+	0.548610i
$356$	1.76034	−	2.09789i	0.0932978	−	0.111188i
$357$		0			0
$358$	1.99214	−	0.928949i	0.105288	−	0.0490965i
$359$	14.8587	+	25.7360i	0.784210	+	1.35829i	0.929470	+	0.368899i	$0.120265\pi$
$359$	14.8587	+	25.7360i	0.784210	+	1.35829i	−0.145259	+	0.989394i	$0.546402\pi$
$360$		0			0
$361$	−4.33700	+	7.51190i	−0.228263	+	0.395363i
$362$	−0.0398950	+	0.456002i	−0.00209684	+	0.0239670i
$363$		0			0
$364$	−5.80035	−	1.02276i	−0.304021	−	0.0536071i
$365$	0.0309719	+	12.6486i	0.00162114	+	0.662057i
$366$		0			0
$367$	−11.9998	−	1.04985i	−0.626385	−	0.0548016i	−0.230456	−	0.973083i	$-0.574022\pi$
$367$	−11.9998	−	1.04985i	−0.626385	−	0.0548016i	−0.395929	+	0.918281i	$0.629577\pi$
$368$	1.97004	−	0.527871i	0.102695	−	0.0275172i
$369$		0			0
$370$	−0.185590	+	2.18286i	−0.00964838	+	0.113481i
$371$	1.79623	−	4.93511i	0.0932558	−	0.256218i
$372$		0			0
$373$	10.0076	−	0.875548i	0.518172	−	0.0453341i	0.174929	−	0.984581i	$-0.444030\pi$
$373$	10.0076	−	0.875548i	0.518172	−	0.0453341i	0.343242	+	0.939247i	$0.388475\pi$
$374$	−0.840527	+	0.305927i	−0.0434626	+	0.0158191i
$375$		0			0
$376$	−0.185790	−	1.05367i	−0.00958138	−	0.0543387i
$377$	−11.1663	+	11.1663i	−0.575095	+	0.575095i
$378$		0			0
$379$		−	10.8604i		−	0.557863i	−0.960311	−	0.278932i	$-0.910020\pi$
$379$		−	10.8604i		−	0.557863i	0.960311	−	0.278932i	$-0.0899803\pi$
$380$	6.00268	−	12.9555i	0.307931	−	0.664604i
$381$		0			0
$382$	−0.0571923	−	0.0266692i	−0.00292621	−	0.00136451i
$383$	−0.230605	−	2.63583i	−0.0117834	−	0.134685i	0.988024	−	0.154299i	$-0.0493118\pi$
$383$	−0.230605	−	2.63583i	−0.0117834	−	0.134685i	−0.999808	+	0.0196141i	$0.993756\pi$
$384$		0			0
$385$	2.21531	+	0.385029i	0.112903	+	0.0196229i
$386$	1.94865	−	1.12506i	0.0991839	−	0.0572639i
$387$		0			0
$388$	3.19063	+	11.9076i	0.161980	+	0.604517i
$389$	−21.4540	+	18.0020i	−1.08776	+	0.912739i	−0.996542	−	0.0830919i	$-0.973520\pi$
$389$	−21.4540	+	18.0020i	−1.08776	+	0.912739i	−0.0912181	+	0.995831i	$0.529076\pi$
$390$		0			0
$391$	−0.578353	+	3.28001i	−0.0292486	+	0.165877i
$392$	1.64116	+	2.34382i	0.0828912	+	0.118381i
$393$		0			0
$394$	1.21561	+	1.44871i	0.0612418	+	0.0729851i
$395$	−9.21150	−	19.6285i	−0.463481	−	0.987617i
$396$		0			0
$397$	1.22098	−	4.55674i	0.0612790	−	0.228696i	−0.928494	−	0.371347i	$-0.878896\pi$
$397$	1.22098	−	4.55674i	0.0612790	−	0.228696i	0.989773	+	0.142651i	$0.0455626\pi$
$398$	1.15514	+	2.47720i	0.0579018	+	0.124171i
$399$		0			0
$400$	6.61863	−	18.4654i	0.330932	−	0.923271i
$401$	−1.42496	−	3.91506i	−0.0711593	−	0.195509i	0.899015	−	0.437919i	$-0.144284\pi$
$401$	−1.42496	−	3.91506i	−0.0711593	−	0.195509i	−0.970174	+	0.242410i	$0.922062\pi$
$402$		0			0
$403$	21.9520	+	15.3709i	1.09351	+	0.765681i
$404$	−2.08065			−0.103516
$405$		0			0
$406$	−0.401902			−0.0199461
$407$	8.72964	+	6.11256i	0.432712	+	0.302988i
$408$		0			0
$409$	−4.16426	−	11.4412i	−0.205910	−	0.565732i	0.793153	−	0.609023i	$-0.208438\pi$
$409$	−4.16426	−	11.4412i	−0.205910	−	0.565732i	−0.999063	+	0.0432906i	$0.986216\pi$
$410$	−1.14517	+	1.99475i	−0.0565558	+	0.0985138i
$411$		0			0
$412$	−4.60348	−	9.87218i	−0.226797	−	0.486368i
$413$	−2.91426	+	10.8761i	−0.143401	+	0.535180i
$414$		0			0
$415$	17.4593	+	6.30630i	0.857044	+	0.309564i
$416$	−3.14715	−	3.75063i	−0.154302	−	0.183890i
$417$		0			0
$418$	0.257334	+	0.367510i	0.0125866	+	0.0179755i
$419$	1.06706	−	6.05161i	0.0521294	−	0.295641i	−0.947586	−	0.319501i	$-0.896485\pi$
$419$	1.06706	−	6.05161i	0.0521294	−	0.295641i	0.999715	+	0.0238606i	$0.00759578\pi$
$420$		0			0
$421$	−3.35083	+	2.81168i	−0.163309	+	0.137033i	−0.720780	−	0.693164i	$-0.756216\pi$
$421$	−3.35083	+	2.81168i	−0.163309	+	0.137033i	0.557471	+	0.830197i	$0.311772\pi$
$422$	−0.819602	−	3.05880i	−0.0398976	−	0.148900i
$423$		0			0
$424$	2.51787	−	1.45369i	0.122278	−	0.0705975i
$425$	22.7614	+	22.5395i	1.10409	+	1.09333i
$426$		0			0
$427$	0.228391	+	2.61052i	0.0110526	+	0.126332i
$428$	−18.8869	−	8.80709i	−0.912931	−	0.425707i
$429$		0			0
$430$	1.29305	+	0.599110i	0.0623566	+	0.0288917i
$431$		−	30.2828i		−	1.45867i	−0.684157	−	0.729335i	$-0.739830\pi$
$431$		−	30.2828i		−	1.45867i	0.684157	−	0.729335i	$-0.260170\pi$
$432$		0			0
$433$	10.8459	−	10.8459i	0.521222	−	0.521222i	−0.396718	−	0.917941i	$-0.629851\pi$
$433$	10.8459	−	10.8459i	0.521222	−	0.521222i	0.917941	+	0.396718i	$0.129851\pi$
$434$	0.118433	+	0.671669i	0.00568498	+	0.0322411i
$435$		0			0
$436$	24.8214	−	9.03424i	1.18873	−	0.432662i
$437$	1.66420	−	0.145599i	0.0796097	−	0.00696494i
$438$		0			0
$439$	−7.27898	+	19.9988i	−0.347407	+	0.954492i	0.635777	+	0.771873i	$0.280680\pi$
$439$	−7.27898	+	19.9988i	−0.347407	+	0.954492i	−0.983184	+	0.182619i	$0.941543\pi$
$440$	0.802453	+	0.951585i	0.0382555	+	0.0453650i
$441$		0			0
$442$	2.54663	−	0.682368i	0.121131	−	0.0324569i
$443$	38.2232	+	3.34409i	1.81604	+	0.158883i	0.943869	−	0.330321i	$-0.107157\pi$
$443$	38.2232	+	3.34409i	1.81604	+	0.158883i	0.872169	+	0.489204i	$0.162713\pi$
$444$		0			0
$445$	2.17370	−	2.18437i	0.103043	−	0.103549i
$446$	−0.483993	−	0.0853411i	−0.0229177	−	0.00404102i
$447$		0			0
$448$	−0.547148	+	6.25393i	−0.0258503	+	0.295470i
$449$	−13.8474	+	23.9843i	−0.653497	+	1.13189i	0.328771	+	0.944410i	$0.393366\pi$
$449$	−13.8474	+	23.9843i	−0.653497	+	1.13189i	−0.982268	+	0.187481i	$0.939968\pi$
$450$		0			0
$451$	5.59447	+	9.68991i	0.263433	+	0.456280i
$452$	−24.8589	+	11.5919i	−1.16927	+	0.545237i
$453$		0			0
$454$	−1.85369	+	2.20915i	−0.0869981	+	0.103680i
$455$	−6.40592	−	1.69966i	−0.300314	−	0.0796813i
$456$		0			0
$457$	−9.23637	+	13.1909i	−0.432059	+	0.617044i	−0.974860	−	0.222817i	$-0.928475\pi$
$457$	−9.23637	+	13.1909i	−0.432059	+	0.617044i	0.542801	+	0.839861i	$0.317364\pi$
$458$	0.413338	+	0.413338i	0.0193140	+	0.0193140i
$459$		0			0
$460$	2.27393	−	0.406699i	0.106023	−	0.0189625i
$461$	4.66067	−	0.821802i	0.217069	−	0.0382751i	−0.0640559	−	0.997946i	$-0.520404\pi$
$461$	4.66067	−	0.821802i	0.217069	−	0.0382751i	0.281125	+	0.959671i	$0.409292\pi$
$462$		0			0
$463$	−0.268361	+	0.575502i	−0.0124718	+	0.0267458i	−0.912445	−	0.409199i	$-0.865808\pi$
$463$	−0.268361	+	0.575502i	−0.0124718	+	0.0267458i	0.899973	+	0.435945i	$0.143586\pi$
$464$	13.0655	+	10.9632i	0.606549	+	0.508955i
$465$		0			0
$466$	−0.832350	−	0.302951i	−0.0385579	−	0.0140339i
$467$	−10.3035	−	2.76083i	−0.476791	−	0.127756i	0.0124169	−	0.999923i	$-0.496047\pi$
$467$	−10.3035	−	2.76083i	−0.476791	−	0.127756i	−0.489208	+	0.872167i	$0.662714\pi$
$468$		0			0
$469$	8.43036	+	4.86727i	0.389278	+	0.224750i
$470$	−0.0537595	−	0.597616i	−0.00247974	−	0.0275660i
$471$		0			0
$472$	−5.10607	+	3.57531i	−0.235026	+	0.164567i
$473$	5.67876	−	3.97631i	0.261110	−	0.182831i
$474$		0			0
$475$	7.96529	−	13.9537i	0.365472	−	0.640237i
$476$	−8.99644	−	5.19410i	−0.412351	−	0.238071i
$477$		0			0
$478$	−1.26469	−	0.338874i	−0.0578458	−	0.0154997i
$479$	−6.25290	−	2.27587i	−0.285702	−	0.103987i	0.195194	−	0.980765i	$-0.437466\pi$
$479$	−6.25290	−	2.27587i	−0.285702	−	0.103987i	−0.480896	+	0.876777i	$0.659689\pi$
$480$		0			0
$481$	−24.0626	−	20.1909i	−1.09716	−	0.920626i
$482$	0.725524	−	1.55589i	0.0330467	−	0.0708689i
$483$		0			0
$484$	−18.5547	+	3.27169i	−0.843396	+	0.148713i
$485$	2.44225	+	13.6551i	0.110897	+	0.620045i
$486$		0			0
$487$	−9.82088	−	9.82088i	−0.445027	−	0.445027i	0.448671	−	0.893697i	$-0.351898\pi$
$487$	−9.82088	−	9.82088i	−0.445027	−	0.445027i	−0.893697	+	0.448671i	$0.851898\pi$
$488$	−0.832081	+	1.18833i	−0.0376665	+	0.0537934i
$489$		0			0
$490$	0.805726	+	1.38770i	0.0363990	+	0.0626899i
$491$	3.96956	−	4.73074i	0.179144	−	0.213495i	−0.668999	−	0.743264i	$-0.733277\pi$
$491$	3.96956	−	4.73074i	0.179144	−	0.213495i	0.848142	+	0.529769i	$0.177721\pi$
$492$		0			0
$493$	−25.2428	+	11.7709i	−1.13688	+	0.530136i
$494$	−0.661198	−	1.14523i	−0.0297487	−	0.0515263i
$495$		0			0
$496$	14.4719	−	25.0660i	0.649805	−	1.12550i
$497$	0.340127	−	3.88767i	0.0152568	−	0.174386i
$498$		0			0
$499$	−0.467311	−	0.0823996i	−0.0209197	−	0.00368871i	0.163179	−	0.986597i	$-0.447825\pi$
$499$	−0.467311	−	0.0823996i	−0.0209197	−	0.00368871i	−0.184098	+	0.982908i	$0.558936\pi$
$500$	9.24122	−	20.2040i	0.413280	−	0.903552i
$501$		0			0
$502$	−1.80234	−	0.157684i	−0.0804422	−	0.00703778i
$503$	18.5422	−	4.96837i	0.826756	−	0.221529i	0.179458	−	0.983766i	$-0.442566\pi$
$503$	18.5422	−	4.96837i	0.826756	−	0.221529i	0.647298	+	0.762237i	$0.275899\pi$
$504$		0			0
$505$	−2.33285	−	0.198343i	−0.103810	−	0.00882614i
$506$	−0.0248249	+	0.0682057i	−0.00110360	+	0.00303211i
$507$		0			0
$508$	−23.0927	+	2.02035i	−1.02457	+	0.0896385i
$509$	4.28872	−	1.56097i	0.190094	−	0.0691886i	−0.245219	−	0.969468i	$-0.578860\pi$
$509$	4.28872	−	1.56097i	0.190094	−	0.0691886i	0.435313	+	0.900279i	$0.356638\pi$
$510$		0			0
$511$	−0.801508	−	4.54558i	−0.0354566	−	0.201084i
$512$	−6.24544	+	6.24544i	−0.276012	+	0.276012i
$513$		0			0
$514$			2.61896i			0.115517i
$515$	−4.22038	−	11.5076i	−0.185972	−	0.507087i
$516$		0			0
$517$	−2.64540	−	1.23357i	−0.116344	−	0.0542523i
$518$	−0.0696754	−	0.796393i	−0.00306136	−	0.0349915i
$519$		0			0
$520$	−2.11179	−	3.00029i	−0.0926081	−	0.131571i
$521$	−12.7475	+	7.35977i	−0.558478	+	0.322437i	−0.752534	−	0.658553i	$-0.771169\pi$
$521$	−12.7475	+	7.35977i	−0.558478	+	0.322437i	0.194057	+	0.980990i	$0.437835\pi$
$522$		0			0
$523$	3.33822	+	12.4584i	0.145970	+	0.544768i	0.999710	+	0.0240685i	$0.00766199\pi$
$523$	3.33822	+	12.4584i	0.145970	+	0.544768i	−0.853740	+	0.520699i	$0.825671\pi$
$524$	9.17877	−	7.70190i	0.400976	−	0.336459i
$525$		0			0
$526$	−0.00228734	+	0.0129721i	−9.97326e−5	+	0.000565611i
$527$	27.1105	+	38.7178i	1.18095	+	1.68657i
$528$		0			0
$529$	−14.6104	−	17.4120i	−0.635234	−	0.757043i
$530$	1.47605	−	0.692699i	0.0641155	−	0.0300889i
$531$		0			0
$532$	−1.34858	+	5.03295i	−0.0584682	+	0.218206i
$533$	−13.9378	−	29.8897i	−0.603712	−	1.29467i
$534$		0			0
$535$	−20.3366	−	11.6750i	−0.879227	−	0.504756i
$536$	1.84314	+	5.06398i	0.0796114	+	0.218731i
$537$		0			0
$538$	1.53876	+	1.07745i	0.0663405	+	0.0464521i
$539$	7.80591			0.336224
$540$		0			0
$541$	26.5994			1.14360			0.571798	−	0.820394i	$-0.306246\pi$
$541$	26.5994			1.14360			0.571798	+	0.820394i	$0.306246\pi$
$542$	2.92290	+	2.04664i	0.125550	+	0.0879107i
$543$		0			0
$544$	−2.95352	−	8.11472i	−0.126631	−	0.347916i
$545$	28.6912	−	7.76313i	1.22900	−	0.332536i
$546$		0			0
$547$	2.39975	+	5.14628i	0.102606	+	0.220039i	0.950908	−	0.309473i	$-0.100153\pi$
$547$	2.39975	+	5.14628i	0.102606	+	0.220039i	−0.848302	+	0.529512i	$0.822375\pi$
$548$	6.89080	−	25.7168i	0.294360	−	1.09857i
$549$		0			0
$550$	0.403201	+	0.569871i	0.0171926	+	0.0242994i
$551$	8.97986	+	10.7018i	0.382555	+	0.455911i
$552$		0			0
$553$	4.53831	+	6.48138i	0.192989	+	0.275616i
$554$	−0.0222469	+	0.126169i	−0.000945181	+	0.00536039i
$555$		0			0
$556$	−10.3411	+	8.67719i	−0.438559	+	0.367995i
$557$	−8.94116	−	33.3689i	−0.378849	−	1.41388i	−0.847638	−	0.530575i	$-0.821976\pi$
$557$	−8.94116	−	33.3689i	−0.378849	−	1.41388i	0.468789	−	0.883310i	$-0.344690\pi$
$558$		0			0
$559$	−17.6960	+	10.2168i	−0.748463	+	0.432125i
$560$	−1.22573	+	7.05240i	−0.0517966	+	0.298018i
$561$		0			0
$562$	−0.245748	−	2.80891i	−0.0103662	−	0.118487i
$563$	20.2108	+	9.42446i	0.851785	+	0.397194i	0.798941	−	0.601409i	$-0.205394\pi$
$563$	20.2108	+	9.42446i	0.851785	+	0.397194i	0.0528435	+	0.998603i	$0.483172\pi$
$564$		0			0
$565$	−28.9771	+	10.6272i	−1.21908	+	0.447091i
$566$		−	2.60383i		−	0.109447i
$567$		0			0
$568$	1.52764	−	1.52764i	0.0640983	−	0.0640983i
$569$	−7.59648	−	43.0818i	−0.318461	−	1.80608i	−0.552121	−	0.833764i	$-0.686181\pi$
$569$	−7.59648	−	43.0818i	−0.318461	−	1.80608i	0.233660	−	0.972318i	$-0.424930\pi$
$570$		0			0
$571$	−6.30344	+	2.29426i	−0.263791	+	0.0960119i	−0.470530	−	0.882384i	$-0.655937\pi$
$571$	−6.30344	+	2.29426i	−0.263791	+	0.0960119i	0.206739	+	0.978396i	$0.433715\pi$
$572$	−8.86138	+	0.775270i	−0.370513	+	0.0324157i
$573$		0			0
$574$	0.287073	−	0.788726i	0.0119822	−	0.0329208i
$575$	2.58833	−	0.239228i	0.107941	−	0.00997648i
$576$		0			0
$577$	4.79931	−	1.28597i	0.199798	−	0.0535357i	−0.157532	−	0.987514i	$-0.550354\pi$
$577$	4.79931	−	1.28597i	0.199798	−	0.0535357i	0.357330	+	0.933978i	$0.383687\pi$
$578$	2.71371	+	0.237419i	0.112876	+	0.00987533i
$579$		0			0
$580$	13.6931	+	13.6262i	0.568573	+	0.565796i
$581$	−6.67116	−	1.17631i	−0.276767	−	0.0488014i
$582$		0			0
$583$	0.691292	−	7.90150i	0.0286304	−	0.327247i
$584$	1.27761	−	2.21288i	0.0528679	−	0.0915698i
$585$		0			0
$586$	−0.991533	−	1.71739i	−0.0409599	−	0.0709446i
$587$	−38.3006	+	17.8599i	−1.58084	+	0.737156i	−0.997194	−	0.0748562i	$-0.976150\pi$
$587$	−38.3006	+	17.8599i	−1.58084	+	0.737156i	−0.583641	+	0.812012i	$0.698372\pi$
$588$		0			0
$589$	15.2389	−	18.1610i	0.627906	−	0.748310i
$590$	−3.02314	+	1.75529i	−0.124461	+	0.0722643i
$591$		0			0
$592$	−19.4592	+	27.7906i	−0.799768	+	1.14219i
$593$	−5.82461	−	5.82461i	−0.239188	−	0.239188i	0.577326	−	0.816514i	$-0.304096\pi$
$593$	−5.82461	−	5.82461i	−0.239188	−	0.239188i	−0.816514	+	0.577326i	$0.804096\pi$
$594$		0			0
$595$	−9.59176	−	6.68128i	−0.393224	−	0.273906i
$596$	−31.0378	+	5.47281i	−1.27136	+	0.224175i
$597$		0			0
$598$	0.0904149	−	0.193895i	0.00369734	−	0.00792897i
$599$	−4.98951	−	4.18670i	−0.203866	−	0.171064i	0.535139	−	0.844764i	$-0.320259\pi$
$599$	−4.98951	−	4.18670i	−0.203866	−	0.171064i	−0.739005	+	0.673700i	$0.764704\pi$
$600$		0			0
$601$	22.5591	+	8.21084i	0.920205	+	0.334927i	0.758320	−	0.651882i	$-0.226020\pi$
$601$	22.5591	+	8.21084i	0.920205	+	0.334927i	0.161885	+	0.986810i	$0.448243\pi$
$602$	−0.502325	−	0.134597i	−0.0204732	−	0.00548578i
$603$		0			0
$604$	1.74696	+	1.00861i	0.0710827	+	0.0410396i
$605$	−21.1156	+	1.89949i	−0.858472	+	0.0772252i
$606$		0			0
$607$	−24.5836	+	17.2136i	−0.997817	+	0.698679i	−0.953828	−	0.300353i	$-0.902896\pi$
$607$	−24.5836	+	17.2136i	−0.997817	+	0.698679i	−0.0439890	+	0.999032i	$0.514007\pi$
$608$	−3.54806	+	2.48438i	−0.143893	+	0.100755i
$609$		0			0
$610$	−0.521425	+	0.624510i	−0.0211119	+	0.0252857i
$611$	7.45079	+	4.30172i	0.301427	+	0.174029i
$612$		0			0
$613$	−8.77093	−	2.35016i	−0.354255	−	0.0949223i	0.0773029	−	0.997008i	$-0.475369\pi$
$613$	−8.77093	−	2.35016i	−0.354255	−	0.0949223i	−0.431558	+	0.902085i	$0.642036\pi$
$614$	−0.0981589	−	0.0357269i	−0.00396137	−	0.00144182i
$615$		0			0
$616$	−0.347966	−	0.291978i	−0.0140199	−	0.0117641i
$617$	5.96112	−	12.7837i	0.239986	−	0.514651i	−0.749017	−	0.662551i	$-0.769474\pi$
$617$	5.96112	−	12.7837i	0.239986	−	0.514651i	0.989002	+	0.147900i	$0.0472515\pi$
$618$		0			0
$619$	3.14514	−	0.554573i	0.126414	−	0.0222902i	−0.110083	−	0.993922i	$-0.535112\pi$
$619$	3.14514	−	0.554573i	0.126414	−	0.0222902i	0.236497	+	0.971632i	$0.424001\pi$
$620$	18.7373	−	26.8995i	0.752507	−	1.08031i
$621$		0			0
$622$	0.671311	+	0.671311i	0.0269171	+	0.0269171i
$623$	−0.645009	+	0.921168i	−0.0258417	+	0.0369058i
$624$		0			0
$625$	12.2873	−	21.7720i	0.491494	−	0.870881i
$626$	−0.115556	+	0.137714i	−0.00461853	+	0.00550415i
$627$		0			0
$628$	28.1041	−	13.1051i	1.12147	−	0.522952i
$629$	−27.7010	−	47.9795i	−1.10451	−	1.91307i
$630$		0			0
$631$	4.87996	−	8.45234i	0.194268	−	0.336482i	−0.752392	−	0.658715i	$-0.771100\pi$
$631$	4.87996	−	8.45234i	0.194268	−	0.336482i	0.946660	+	0.322233i	$0.104434\pi$
$632$	−0.381759	+	4.36353i	−0.0151856	+	0.173572i
$633$		0			0
$634$	−1.13870	−	0.200784i	−0.0452236	−	0.00797414i
$635$	−26.0844	+	0.0638713i	−1.03513	+	0.00253465i
$636$		0			0
$637$	−22.9205	−	2.00529i	−0.908144	−	0.0794523i
$638$	−0.586298	+	0.157098i	−0.0232118	+	0.00621957i
$639$		0			0
$640$	−6.09822	+	5.14251i	−0.241053	+	0.203276i
$641$	3.49998	−	9.61611i	0.138241	−	0.379813i	−0.851183	−	0.524870i	$-0.824114\pi$
$641$	3.49998	−	9.61611i	0.138241	−	0.379813i	0.989423	+	0.145056i	$0.0463363\pi$
$642$		0			0
$643$	−13.9040	+	1.21644i	−0.548320	+	0.0479718i	−0.357950	−	0.933741i	$-0.616524\pi$
$643$	−13.9040	+	1.21644i	−0.548320	+	0.0479718i	−0.190370	+	0.981712i	$0.560969\pi$
$644$	−0.792127	+	0.288311i	−0.0312142	+	0.0113610i
$645$		0			0
$646$	−0.405013	−	2.29694i	−0.0159350	−	0.0903720i
$647$	26.7302	−	26.7302i	1.05087	−	1.05087i	0.0522394	−	0.998635i	$-0.483364\pi$
$647$	26.7302	−	26.7302i	1.05087	−	1.05087i	0.998635	−	0.0522394i	$-0.0166359\pi$
$648$		0			0
$649$			17.0053i			0.667518i
$650$	−1.03753	−	1.77689i	−0.0406951	−	0.0696955i
$651$		0			0
$652$	−3.18455	−	1.48498i	−0.124717	−	0.0581563i
$653$	−0.358345	−	4.09590i	−0.0140231	−	0.160285i	0.985954	−	0.167016i	$-0.0534131\pi$
$653$	−0.358345	−	4.09590i	−0.0140231	−	0.160285i	−0.999977	+	0.00673072i	$0.997858\pi$
$654$		0			0
$655$	11.0255	−	7.76046i	0.430803	−	0.303226i
$656$	−30.8476	+	17.8099i	−1.20440	+	0.695359i
$657$		0			0
$658$	0.0566713	+	0.211500i	0.00220928	+	0.00824513i
$659$	−23.3538	+	19.5962i	−0.909736	+	0.763359i	−0.972069	−	0.234697i	$-0.924590\pi$
$659$	−23.3538	+	19.5962i	−0.909736	+	0.763359i	0.0623330	+	0.998055i	$0.480146\pi$
$660$		0			0
$661$	−2.49857	+	14.1701i	−0.0971833	+	0.551154i	0.896873	+	0.442288i	$0.145833\pi$
$661$	−2.49857	+	14.1701i	−0.0971833	+	0.551154i	−0.994056	+	0.108866i	$0.965278\pi$
$662$	−0.515863	−	0.736728i	−0.0200496	−	0.0286338i
$663$		0			0
$664$	−2.41051	−	2.87273i	−0.0935458	−	0.111484i
$665$	−1.99182	+	5.51444i	−0.0772393	+	0.213841i
$666$		0			0
$667$	−0.584963	+	2.18311i	−0.0226498	+	0.0845304i
$668$	4.10841	+	8.81052i	0.158959	+	0.340889i
$669$		0			0
$670$	0.789355	+	2.91732i	0.0304955	+	0.112706i
$671$	1.35360	+	3.71898i	0.0522550	+	0.143570i
$672$		0			0
$673$	3.89377	+	2.72645i	0.150094	+	0.105097i	0.646211	−	0.763159i	$-0.276353\pi$
$673$	3.89377	+	2.72645i	0.150094	+	0.105097i	−0.496117	+	0.868255i	$0.665241\pi$
$674$	−0.271508			−0.0104581
$675$		0			0
$676$	0.385711			0.0148350
$677$	24.2852	+	17.0047i	0.933356	+	0.653543i	0.938070	−	0.346446i	$-0.112612\pi$
$677$	24.2852	+	17.0047i	0.933356	+	0.653543i	−0.00471373	+	0.999989i	$0.501500\pi$
$678$		0			0
$679$	−1.73132	−	4.75677i	−0.0664420	−	0.182548i
$680$	−1.69016	−	6.24654i	−0.0648146	−	0.239544i
$681$		0			0
$682$	0.435318	+	0.933541i	0.0166692	+	0.0357472i
$683$	−2.52954	+	9.44037i	−0.0967901	+	0.361226i	−0.997285	−	0.0736414i	$-0.976538\pi$
$683$	−2.52954	+	9.44037i	−0.0967901	+	0.361226i	0.900495	+	0.434867i	$0.143205\pi$
$684$		0			0
$685$	10.1776	−	28.1771i	0.388864	−	1.07659i
$686$	−0.792353	−	0.944289i	−0.0302522	−	0.0360531i
$687$		0			0
$688$	12.6585	+	18.0782i	0.482601	+	0.689225i
$689$	−4.05968	+	23.0236i	−0.154662	+	0.877130i
$690$		0			0
$691$	5.93833	−	4.98285i	0.225905	−	0.189556i	−0.522809	−	0.852450i	$-0.675116\pi$
$691$	5.93833	−	4.98285i	0.225905	−	0.189556i	0.748714	+	0.662893i	$0.230672\pi$
$692$	1.21015	+	4.51634i	0.0460030	+	0.171685i
$693$		0			0
$694$	2.35568	−	1.36005i	0.0894204	−	0.0516269i
$695$	−12.4217	+	8.74317i	−0.471181	+	0.331647i
$696$		0			0
$697$	−5.06966	−	57.9464i	−0.192027	−	2.19488i
$698$	−1.89886	−	0.885454i	−0.0718730	−	0.0335149i
$699$		0			0
$700$	−2.05998	+	7.84135i	−0.0778599	+	0.296375i
$701$			11.8234i			0.446564i	0.974754	+	0.223282i	$0.0716771\pi$
$701$			11.8234i			0.446564i	−0.974754	+	0.223282i	$0.928323\pi$
$702$		0			0
$703$	−19.6494	+	19.6494i	−0.741092	+	0.741092i
$704$	1.64639	+	9.33714i	0.0620507	+	0.351907i
$705$		0			0
$706$	3.07379	−	1.11877i	0.115684	−	0.0421055i
$707$	0.851116	−	0.0744630i	0.0320095	−	0.00280047i
$708$		0			0
$709$	−9.00610	+	24.7441i	−0.338231	+	0.929283i	0.647665	+	0.761925i	$0.275746\pi$
$709$	−9.00610	+	24.7441i	−0.338231	+	0.929283i	−0.985896	+	0.167357i	$0.946477\pi$
$710$	0.926224	−	0.781067i	0.0347606	−	0.0293129i
$711$		0			0
$712$	−0.601324	+	0.161124i	−0.0225356	+	0.00603839i
$713$	3.82084	+	0.334281i	0.143092	+	0.0125189i
$714$		0			0
$715$	−10.0094	+	0.0245094i	−0.374329	+	0.000916599i
$716$	37.9685	+	6.69487i	1.41895	+	0.250199i
$717$		0			0
$718$	0.293435	−	3.35397i	0.0109509	−	0.125169i
$719$	15.9538	−	27.6328i	0.594977	−	1.03053i	−0.398573	−	0.917136i	$-0.630495\pi$
$719$	15.9538	−	27.6328i	0.594977	−	1.03053i	0.993550	−	0.113393i	$-0.0361721\pi$
$720$		0			0
$721$	2.23642	+	3.87359i	0.0832885	+	0.144260i
$722$	0.890637	−	0.415311i	0.0331461	−	0.0154563i
$723$		0			0
$724$	−5.16082	+	6.15042i	−0.191800	+	0.228579i
$725$	14.0539	+	16.5831i	0.521947	+	0.615881i
$726$		0			0
$727$	12.2503	−	17.4952i	0.454338	−	0.648863i	−0.524997	−	0.851104i	$-0.675934\pi$
$727$	12.2503	−	17.4952i	0.454338	−	0.648863i	0.979336	+	0.202241i	$0.0648225\pi$
$728$	0.946725	+	0.946725i	0.0350880	+	0.0350880i
$729$		0			0
$730$	0.819064	−	1.17586i	0.0303149	−	0.0435206i
$731$	−35.4923	+	6.25825i	−1.31273	+	0.231470i
$732$		0			0
$733$	15.6653	−	33.5943i	0.578611	−	1.24083i	−0.371358	−	0.928490i	$-0.621108\pi$
$733$	15.6653	−	33.5943i	0.578611	−	1.24083i	0.949969	−	0.312345i	$-0.101114\pi$
$734$	1.04542	+	0.877209i	0.0385870	+	0.0323784i
$735$		0			0
$736$	−0.658480	−	0.239667i	−0.0242719	−	0.00883425i
$737$	14.2008	+	3.80510i	0.523094	+	0.140163i
$738$		0			0
$739$	−0.0105302	−	0.00607959i	−0.000387358	−	0.000223641i	0.499806	−	0.866137i	$-0.333405\pi$
$739$	−0.0105302	−	0.00607959i	−0.000387358	−	0.000223641i	−0.500194	+	0.865914i	$0.666738\pi$
$740$	−24.6272	+	29.4959i	−0.905312	+	1.08429i
$741$		0			0
$742$	−0.487396	+	0.341278i	−0.0178929	+	0.0125287i
$743$	16.1496	−	11.3081i	0.592471	−	0.414852i	−0.238521	−	0.971137i	$-0.576663\pi$
$743$	16.1496	−	11.3081i	0.592471	−	0.414852i	0.830992	+	0.556285i	$0.187774\pi$
$744$		0			0
$745$	−35.3216	+	3.17741i	−1.29408	+	0.116411i
$746$	−0.985644	−	0.569062i	−0.0360870	−	0.0208348i
$747$		0			0
$748$	−15.1544	−	4.06060i	−0.554099	−	0.148470i
$749$	8.04109	+	2.92672i	0.293815	+	0.106940i
$750$		0			0
$751$	−25.5632	−	21.4501i	−0.932814	−	0.782724i	0.0435062	−	0.999053i	$-0.486147\pi$
$751$	−25.5632	−	21.4501i	−0.932814	−	0.782724i	−0.976321	+	0.216329i	$0.930592\pi$
$752$	3.92704	−	8.42156i	0.143204	−	0.307103i
$753$		0			0
$754$	1.76191	−	0.310672i	0.0641648	−	0.0113140i
$755$	1.86256	+	1.29739i	0.0677855	+	0.0472170i
$756$		0			0
$757$	28.4224	+	28.4224i	1.03303	+	1.03303i	0.999436	+	0.0335950i	$0.0106956\pi$
$757$	28.4224	+	28.4224i	1.03303	+	1.03303i	0.0335950	+	0.999436i	$0.489304\pi$
$758$	−0.705739	+	1.00790i	−0.0256336	+	0.0366086i
$759$		0			0
$760$	−2.80696	+	1.62978i	−0.101819	+	0.0591182i
$761$	14.3996	−	17.1608i	0.521985	−	0.622078i	−0.439064	−	0.898456i	$-0.644690\pi$
$761$	14.3996	−	17.1608i	0.521985	−	0.622078i	0.961049	+	0.276378i	$0.0891342\pi$
$762$		0			0
$763$	−9.83017	+	4.58388i	−0.355876	+	0.165948i
$764$	−0.553426	−	0.958563i	−0.0200223	−	0.0346796i
$765$		0			0
$766$	−0.149882	+	0.259603i	−0.00541545	+	0.00937983i
$767$	4.36856	−	49.9328i	0.157739	−	1.80297i
$768$		0			0
$769$	3.68867	+	0.650412i	0.133017	+	0.0234545i	0.239760	−	0.970832i	$-0.422931\pi$
$769$	3.68867	+	0.650412i	0.133017	+	0.0234545i	−0.106743	+	0.994287i	$0.534042\pi$
$770$	−0.180571	−	0.179689i	−0.00650734	−	0.00647555i
$771$		0			0
$772$	39.3167	+	3.43976i	1.41504	+	0.123800i
$773$	−10.7936	+	2.89214i	−0.388220	+	0.104023i	−0.447649	−	0.894209i	$-0.647739\pi$
$773$	−10.7936	+	2.89214i	−0.388220	+	0.104023i	0.0594292	+	0.998233i	$0.481072\pi$
$774$		0			0
$775$	23.5727	−	28.3739i	0.846756	−	1.01922i
$776$	0.958447	−	2.63331i	0.0344063	−	0.0945304i
$777$		0			0
$778$	3.16085	−	0.276538i	0.113322	−	0.00991439i
$779$	−27.4162	+	9.97869i	−0.982288	+	0.357524i
$780$		0			0
$781$	−1.02346	−	5.80431i	−0.0366222	−	0.207695i
$782$	0.266817	−	0.266817i	0.00954136	−	0.00954136i
$783$		0			0
$784$			24.8499i			0.887498i
$785$	32.7598	−	12.0145i	1.16925	−	0.428817i
$786$		0			0
$787$	28.7051	+	13.3854i	1.02323	+	0.477138i	0.860456	−	0.509526i	$-0.170179\pi$
$787$	28.7051	+	13.3854i	1.02323	+	0.477138i	0.162771	+	0.986664i	$0.447957\pi$
$788$	2.89103	+	33.0446i	0.102989	+	1.17717i
$789$		0			0
$790$	−0.420640	+	2.42020i	−0.0149657	+	0.0861070i
$791$	9.75400	−	5.63147i	0.346812	−	0.200232i
$792$		0			0
$793$	−3.01919	−	11.2678i	−0.107215	−	0.400130i
$794$	−0.409421	+	0.343545i	−0.0145298	+	0.0121920i
$795$		0			0
$796$	−8.32498	+	47.2133i	−0.295071	+	1.67343i
$797$	−4.41609	−	6.30683i	−0.156426	−	0.223400i	0.733288	−	0.679919i	$-0.237985\pi$
$797$	−4.41609	−	6.30683i	−0.156426	−	0.223400i	−0.889714	+	0.456519i	$0.849096\pi$
$798$		0			0
$799$	9.75385	+	11.6242i	0.345067	+	0.411234i
$800$	−5.50172	+	3.89264i	−0.194515	+	0.137625i
$801$		0			0
$802$	−0.122167	+	0.455934i	−0.00431387	+	0.0160996i
$803$	−2.94605	−	6.31782i	−0.103964	−	0.222951i
$804$		0			0
$805$	−0.915625	+	0.247746i	−0.0322715	+	0.00873189i
$806$	−1.03840	−	2.85299i	−0.0365762	−	0.100492i
$807$		0			0
$808$	0.387436	+	0.271285i	0.0136299	+	0.00954378i
$809$	39.1614			1.37684			0.688421	−	0.725311i	$-0.258304\pi$
$809$	39.1614			1.37684			0.688421	+	0.725311i	$0.258304\pi$
$810$		0			0
$811$	17.1440			0.602008			0.301004	−	0.953623i	$-0.402678\pi$
$811$	17.1440			0.602008			0.301004	+	0.953623i	$0.402678\pi$
$812$	−5.77448	−	4.04334i	−0.202645	−	0.141893i
$813$		0			0
$814$	−0.412942	−	1.13455i	−0.0144736	−	0.0397659i
$815$	−3.42899	−	1.96855i	−0.120112	−	0.0689553i
$816$		0			0
$817$	7.63959	+	16.3832i	0.267276	+	0.573174i
$818$	−0.357017	+	1.33240i	−0.0124828	+	0.0465864i
$819$		0			0
$820$	−36.5218	+	17.1394i	−1.27540	+	0.598534i
$821$	26.7100	+	31.8317i	0.932184	+	1.11093i	0.993615	+	0.112822i	$0.0359890\pi$
$821$	26.7100	+	31.8317i	0.932184	+	1.11093i	−0.0614313	+	0.998111i	$0.519567\pi$
$822$		0			0
$823$	−6.39643	−	9.13505i	−0.222966	−	0.318428i	0.692048	−	0.721852i	$-0.256709\pi$
$823$	−6.39643	−	9.13505i	−0.222966	−	0.318428i	−0.915013	+	0.403424i	$0.867820\pi$
$824$	−0.429976	+	2.43851i	−0.0149789	+	0.0849496i
$825$		0			0
$826$	0.977217	−	0.819982i	0.0340017	−	0.0285308i
$827$	6.87074	+	25.6420i	0.238919	+	0.891658i	0.976343	+	0.216228i	$0.0693755\pi$
$827$	6.87074	+	25.6420i	0.238919	+	0.891658i	−0.737424	+	0.675430i	$0.763958\pi$
$828$		0			0
$829$	36.2779	−	20.9451i	1.25998	−	0.727453i	0.286914	−	0.957956i	$-0.407371\pi$
$829$	36.2779	−	20.9451i	1.25998	−	0.727453i	0.973071	+	0.230504i	$0.0740374\pi$
$830$	−1.21051	−	1.71981i	−0.0420173	−	0.0596954i
$831$		0			0
$832$	−2.43565	−	27.8396i	−0.0844410	−	0.965165i
$833$	−36.7784	−	17.1501i	−1.27430	−	0.594214i
$834$		0			0
$835$	3.76651	+	10.2701i	0.130345	+	0.355411i
$836$			7.86925i			0.272164i
$837$		0			0
$838$	−0.492278	+	0.492278i	−0.0170055	+	0.0170055i
$839$	1.94726	+	11.0435i	0.0672268	+	0.381262i	0.999795	+	0.0202674i	$0.00645175\pi$
$839$	1.94726	+	11.0435i	0.0672268	+	0.381262i	−0.932568	+	0.360995i	$0.882437\pi$
$840$		0			0
$841$	9.49050	−	3.45426i	0.327259	−	0.119112i
$842$	0.493683	−	0.0431917i	0.0170134	−	0.00148848i
$843$		0			0
$844$	18.9971	−	52.1940i	0.653906	−	1.79659i
$845$	0.432463	+	0.0367688i	0.0148772	+	0.00126488i
$846$		0			0
$847$	7.47294	−	2.00237i	0.256773	−	0.0688022i
$848$	25.1543	+	2.20071i	0.863801	+	0.0755728i
$849$		0			0
$850$	−0.647687	−	3.57087i	−0.0222155	−	0.122480i
$851$	−4.42737	−	0.780665i	−0.151768	−	0.0267609i
$852$		0			0
$853$	−3.28205	+	37.5140i	−0.112375	+	1.28446i	0.705355	+	0.708854i	$0.250787\pi$
$853$	−3.28205	+	37.5140i	−0.112375	+	1.28446i	−0.817731	+	0.575601i	$0.804768\pi$
$854$	0.148443	−	0.257111i	0.00507961	−	0.00879814i
$855$		0			0
$856$	2.36859	+	4.10252i	0.0809568	+	0.140221i
$857$	−27.5476	+	12.8457i	−0.941009	+	0.438800i	−0.831711	−	0.555209i	$-0.812638\pi$
$857$	−27.5476	+	12.8457i	−0.941009	+	0.438800i	−0.109299	+	0.994009i	$0.534860\pi$
$858$		0			0
$859$	−19.6543	+	23.4231i	−0.670598	+	0.799187i	−0.988865	−	0.148814i	$-0.952455\pi$
$859$	−19.6543	+	23.4231i	−0.670598	+	0.799187i	0.318268	+	0.948001i	$0.396899\pi$
$860$	12.5511	+	21.6167i	0.427989	+	0.737124i
$861$		0			0
$862$	−1.96785	+	2.81039i	−0.0670253	+	0.0957221i
$863$	−17.7157	−	17.7157i	−0.603051	−	0.603051i	0.338070	−	0.941121i	$-0.390226\pi$
$863$	−17.7157	−	17.7157i	−0.603051	−	0.603051i	−0.941121	+	0.338070i	$0.890226\pi$
$864$		0			0
$865$	0.926301	+	5.17912i	0.0314952	+	0.176096i
$866$	−1.71135	+	0.301757i	−0.0581541	+	0.0102541i
$867$		0			0
$868$	−5.05569	+	10.8420i	−0.171601	+	0.368000i
$869$	9.15400	+	7.68112i	0.310528	+	0.260564i
$870$		0			0
$871$	−40.7204	−	14.8210i	−1.37976	−	0.502191i
$872$	−5.79989	−	1.55408i	−0.196409	−	0.0526277i
$873$		0			0
$874$	−0.163907	−	0.0946320i	−0.00554425	−	0.00320097i
$875$	−3.05717	+	8.59544i	−0.103351	+	0.290579i
$876$		0			0
$877$	25.7226	−	18.0112i	0.868591	−	0.608194i	−0.0520323	−	0.998645i	$-0.516570\pi$
$877$	25.7226	−	18.0112i	0.868591	−	0.608194i	0.920624	+	0.390451i	$0.127681\pi$
$878$	1.97510	−	1.38298i	0.0666563	−	0.0466733i
$879$		0			0
$880$	0.968582	+	10.7672i	0.0326509	+	0.362963i
$881$	20.4197	+	11.7893i	0.687957	+	0.397192i	0.802846	−	0.596186i	$-0.203318\pi$
$881$	20.4197	+	11.7893i	0.687957	+	0.397192i	−0.114889	+	0.993378i	$0.536651\pi$
$882$		0			0
$883$	15.8726	+	4.25306i	0.534156	+	0.143127i	0.515807	−	0.856705i	$-0.327492\pi$
$883$	15.8726	+	4.25306i	0.534156	+	0.143127i	0.0183494	+	0.999832i	$0.494159\pi$
$884$	43.4547	+	15.8162i	1.46154	+	0.531957i
$885$		0			0
$886$	−3.32998	−	2.79419i	−0.111873	−	0.0938726i
$887$	16.4901	−	35.3631i	0.553683	−	1.18738i	−0.407941	−	0.913008i	$-0.633753\pi$
$887$	16.4901	−	35.3631i	0.553683	−	1.18738i	0.961624	−	0.274369i	$-0.0884691\pi$
$888$		0			0
$889$	9.37405	−	1.65290i	0.314395	−	0.0554364i
$890$	−0.343675	+	0.0614673i	−0.0115200	+	0.00206039i
$891$		0			0
$892$	−6.09538	−	6.09538i	−0.204089	−	0.204089i
$893$	4.36555	−	6.23466i	0.146088	−	0.208635i
$894$		0			0
$895$	41.9325	+	11.1258i	1.40165	+	0.371894i
$896$	1.87113	−	2.22993i	0.0625102	−	0.0744968i
$897$		0			0
$898$	2.84366	−	1.32602i	0.0948943	−	0.0442499i
$899$	16.0371	+	27.7770i	0.534866	+	0.926415i
$900$		0			0
$901$	−20.6172	+	35.7100i	−0.686858	+	1.18967i
$902$	0.110482	−	1.26281i	0.00367864	−	0.0420470i
$903$		0			0
$904$	6.14036	+	1.08271i	0.204225	+	0.0360105i
$905$	−6.37267	+	6.40395i	−0.211835	+	0.212875i
$906$		0			0
$907$	7.11684	+	0.622643i	0.236311	+	0.0206745i	0.204696	−	0.978826i	$-0.434379\pi$
$907$	7.11684	+	0.622643i	0.236311	+	0.0206745i	0.0316149	+	0.999500i	$0.489935\pi$
$908$	−48.8587	+	13.0917i	−1.62143	+	0.434462i
$909$		0			0
$910$	0.484051	+	0.574010i	0.0160461	+	0.0190282i
$911$	8.33512	−	22.9005i	0.276155	−	0.758729i	−0.721635	−	0.692274i	$-0.756609\pi$
$911$	8.33512	−	22.9005i	0.276155	−	0.758729i	0.997789	−	0.0664549i	$-0.0211688\pi$
$912$		0			0
$913$	−10.1917	+	0.891662i	−0.337297	+	0.0295097i
$914$	1.71436	−	0.623975i	0.0567059	−	0.0206393i
$915$		0			0
$916$	1.78041	+	10.0972i	0.0588263	+	0.333620i
$917$	−3.47905	+	3.47905i	−0.114888	+	0.114888i
$918$		0			0
$919$		−	22.6610i		−	0.747517i	−0.927526	−	0.373758i	$-0.878069\pi$
$919$		−	22.6610i		−	0.747517i	0.927526	−	0.373758i	$-0.121931\pi$
$920$	−0.476454	−	0.220755i	−0.0157082	−	0.00727809i
$921$		0			0
$922$	−0.485935	−	0.226595i	−0.0160034	−	0.00746251i
$923$	1.51409	+	17.3061i	0.0498369	+	0.569638i
$924$		0			0
$925$	−30.4240	+	30.7234i	−1.00033	+	1.01018i
$926$	0.0623027	−	0.0359705i	0.00204740	−	0.00118206i
$927$		0			0
$928$	−1.51668	−	5.66031i	−0.0497873	−	0.185809i
$929$	22.2920	−	18.7052i	0.731377	−	0.613698i	−0.199130	−	0.979973i	$-0.563811\pi$
$929$	22.2920	−	18.7052i	0.731377	−	0.613698i	0.930507	+	0.366275i	$0.119367\pi$
$930$		0			0
$931$	−3.53449	+	20.0451i	−0.115838	+	0.656951i
$932$	−8.91127	−	12.7266i	−0.291898	−	0.416874i
$933$		0			0
$934$	0.776812	+	0.925769i	0.0254181	+	0.0302921i
$935$	−16.6042	−	5.99741i	−0.543014	−	0.196136i
$936$		0			0
$937$	8.40546	−	31.3696i	0.274594	−	1.02480i	−0.681518	−	0.731801i	$-0.738680\pi$
$937$	8.40546	−	31.3696i	0.274594	−	1.02480i	0.956113	−	0.292999i	$-0.0946533\pi$
$938$	−0.466089	−	0.999532i	−0.0152184	−	0.0326359i
$939$		0			0
$940$	5.23991	−	9.12733i	0.170907	−	0.297701i
$941$	−7.58961	−	20.8523i	−0.247414	−	0.679765i	−0.999779	−	0.0210183i	$-0.993309\pi$
$941$	−7.58961	−	20.8523i	−0.247414	−	0.679765i	0.752365	−	0.658747i	$-0.228913\pi$
$942$		0			0
$943$	−3.86648	−	2.70734i	−0.125910	−	0.0881632i
$944$	−54.1361			−1.76198
$945$		0			0
$946$	−0.785407			−0.0255358
$947$	16.3365	+	11.4390i	0.530866	+	0.371716i	0.808062	−	0.589097i	$-0.200516\pi$
$947$	16.3365	+	11.4390i	0.530866	+	0.371716i	−0.277197	+	0.960813i	$0.589405\pi$
$948$		0			0
$949$	7.02749	+	19.3079i	0.228122	+	0.626760i
$950$	−1.64596	+	0.777360i	−0.0534020	+	0.0252209i
$951$		0			0
$952$	0.997985	+	2.14019i	0.0323449	+	0.0693638i
$953$	−6.93017	+	25.8637i	−0.224490	+	0.837809i	0.758118	+	0.652117i	$0.226119\pi$
$953$	−6.93017	+	25.8637i	−0.224490	+	0.837809i	−0.982608	+	0.185691i	$0.940548\pi$
$954$		0			0
$955$	−0.529130	−	1.12751i	−0.0171223	−	0.0364853i
$956$	−14.7617	−	17.5924i	−0.477429	−	0.568977i
$957$		0			0
$958$	0.432407	+	0.617541i	0.0139704	+	0.0199519i
$959$	−1.89841	+	10.7664i	−0.0613027	+	0.347665i
$960$		0			0
$961$	17.9484	−	15.0605i	0.578980	−	0.485822i
$962$	0.921065	+	3.43746i	0.0296963	+	0.110828i
$963$		0			0
$964$	26.0773	−	15.0557i	0.839892	−	0.484912i
$965$	43.7544	+	7.60465i	1.40850	+	0.244802i
$966$		0			0
$967$	4.84971	+	55.4324i	0.155956	+	1.78259i	0.522950	+	0.852363i	$0.324831\pi$
$967$	4.84971	+	55.4324i	0.155956	+	1.78259i	−0.366994	+	0.930223i	$0.619613\pi$
$968$	3.88163	+	1.81003i	0.124760	+	0.0581767i
$969$		0			0
$970$	0.660690	−	1.42596i	0.0212135	−	0.0457848i
$971$			31.2029i			1.00135i	0.865635	+	0.500675i	$0.166915\pi$
$971$			31.2029i			1.00135i	−0.865635	+	0.500675i	$0.833085\pi$
$972$		0			0
$973$	3.91960	−	3.91960i	0.125657	−	0.125657i
$974$	0.273238	+	1.54961i	0.00875512	+	0.0496527i
$975$		0			0
$976$	−11.8393	+	4.30915i	−0.378966	+	0.137932i
$977$	−6.15704	+	0.538672i	−0.196981	+	0.0172336i	−0.185219	−	0.982697i	$-0.559300\pi$
$977$	−6.15704	+	0.538672i	−0.196981	+	0.0172336i	−0.0117619	+	0.999931i	$0.503744\pi$
$978$		0			0
$979$	−0.580871	+	1.59593i	−0.0185647	+	0.0510062i
$980$	−2.38438	+	28.0443i	−0.0761662	+	0.895843i
$981$		0			0
$982$	−0.675810	+	0.181083i	−0.0215659	+	0.00577858i
$983$	−29.9051	−	2.61636i	−0.953824	−	0.0834488i	−0.400393	−	0.916344i	$-0.631126\pi$
$983$	−29.9051	−	2.61636i	−0.953824	−	0.0834488i	−0.553431	+	0.832895i	$0.686682\pi$
$984$		0			0
$985$	0.0913970	+	37.3256i	0.00291215	+	1.18929i
$986$	3.10756	+	0.547947i	0.0989649	+	0.0174502i
$987$		0			0
$988$	2.02156	−	23.1065i	0.0643143	−	0.735116i
$989$	−1.46225	+	2.53269i	−0.0464969	+	0.0805349i
$990$		0			0
$991$	12.6389	+	21.8911i	0.401486	+	0.695395i	0.993906	−	0.110235i	$-0.0351604\pi$
$991$	12.6389	+	21.8911i	0.401486	+	0.695395i	−0.592419	+	0.805630i	$0.701827\pi$
$992$	−9.01271	+	4.20270i	−0.286154	+	0.133436i
$993$		0			0
$994$	−0.284196	+	0.338692i	−0.00901416	+	0.0107427i
$995$	−13.8348	+	52.1425i	−0.438592	+	1.65303i
$996$		0			0
$997$	27.0029	−	38.5642i	0.855191	−	1.22134i	−0.118383	−	0.992968i	$-0.537771\pi$
$997$	27.0029	−	38.5642i	0.855191	−	1.22134i	0.973574	−	0.228371i	$-0.0733400\pi$
$998$	0.0380142	+	0.0380142i	0.00120332	+	0.00120332i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.152.8		192
3.2	odd	2		135.2.q.a.122.9	yes	192
5.3	odd	4	inner	405.2.r.a.233.8		192
15.2	even	4		675.2.ba.b.68.8		192
15.8	even	4		135.2.q.a.68.9	yes	192
15.14	odd	2		675.2.ba.b.257.8		192
27.2	odd	18	inner	405.2.r.a.332.8		192
27.25	even	9		135.2.q.a.2.9	✓	192
135.52	odd	36		675.2.ba.b.218.8		192
135.79	even	18		675.2.ba.b.407.8		192
135.83	even	36	inner	405.2.r.a.8.8		192
135.133	odd	36		135.2.q.a.83.9	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.9	✓	192	27.25	even	9
135.2.q.a.68.9	yes	192	15.8	even	4
135.2.q.a.83.9	yes	192	135.133	odd	36
135.2.q.a.122.9	yes	192	3.2	odd	2
405.2.r.a.8.8		192	135.83	even	36	inner
405.2.r.a.152.8		192	1.1	even	1	trivial
405.2.r.a.233.8		192	5.3	odd	4	inner
405.2.r.a.332.8		192	27.2	odd	18	inner
675.2.ba.b.68.8		192	15.2	even	4
675.2.ba.b.218.8		192	135.52	odd	36
675.2.ba.b.257.8		192	15.14	odd	2
675.2.ba.b.407.8		192	135.79	even	18

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:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0928047 - 0.0649826i) q^{2} +(-0.679650 - 1.86732i) q^{4} +(-0.584024 - 2.15845i) q^{5} +(0.344848 + 0.739528i) q^{7} +(-0.116914 + 0.436329i) q^{8} +O(q^{10})\)	\(q+(-0.0928047 - 0.0649826i) q^{2} +(-0.679650 - 1.86732i) q^{4} +(-0.584024 - 2.15845i) q^{5} +(0.344848 + 0.739528i) q^{7} +(-0.116914 + 0.436329i) q^{8} +(-0.0860616 + 0.238266i) q^{10} +(0.792138 + 0.944033i) q^{11} +(-2.08344 - 2.97546i) q^{13} +(0.0160530 - 0.0910408i) q^{14} +(-3.00531 + 2.52175i) q^{16} +(-1.65815 - 6.18829i) q^{17} +(-2.78289 + 1.60671i) q^{19} +(-3.63360 + 2.55755i) q^{20} +(-0.0121684 - 0.139086i) q^{22} +(-0.471164 - 0.219707i) q^{23} +(-4.31783 + 2.52118i) q^{25} +0.411524i q^{26} +(1.14656 - 1.14656i) q^{28} +(-0.754929 - 4.28141i) q^{29} +(-6.93274 + 2.52331i) q^{31} +(1.34278 - 0.117478i) q^{32} +(-0.248247 + 0.682053i) q^{34} +(1.39484 - 1.17624i) q^{35} +(8.35299 - 2.23818i) q^{37} +(0.362674 + 0.0317298i) q^{38} +(1.01007 - 0.00247331i) q^{40} +(8.94143 + 1.57662i) q^{41} +(0.490289 - 5.60402i) q^{43} +(1.22444 - 2.12079i) q^{44} +(0.0294491 + 0.0510073i) q^{46} +(-2.14663 + 1.00099i) q^{47} +(4.07153 - 4.85226i) q^{49} +(0.564548 + 0.0466068i) q^{50} +(-4.14014 + 5.91273i) q^{52} +(-4.55111 - 4.55111i) q^{53} +(1.57502 - 2.26113i) q^{55} +(-0.362995 + 0.0640058i) q^{56} +(-0.208156 + 0.446393i) q^{58} +(10.5708 + 8.86992i) q^{59} +(3.01780 + 1.09839i) q^{61} +(0.807362 + 0.216332i) q^{62} +(6.66285 + 3.84680i) q^{64} +(-5.20561 + 6.23475i) q^{65} +(9.77239 - 6.84270i) q^{67} +(-10.4286 + 7.30217i) q^{68} +(-0.205883 + 0.0185205i) q^{70} +(-4.14187 - 2.39131i) q^{71} +(-5.46389 - 1.46405i) q^{73} +(-0.920640 - 0.335086i) q^{74} +(4.89163 + 4.10457i) q^{76} +(-0.424972 + 0.911356i) q^{77} +(9.54938 - 1.68381i) q^{79} +(7.19826 + 5.01405i) q^{80} +(-0.727355 - 0.727355i) q^{82} +(-4.76170 + 6.80042i) q^{83} +(-12.3887 + 7.19314i) q^{85} +(-0.409665 + 0.488220i) q^{86} +(-0.504521 + 0.235262i) q^{88} +(0.689073 + 1.19351i) q^{89} +(1.48197 - 2.56685i) q^{91} +(-0.0900380 + 1.02914i) q^{92} +(0.264265 + 0.0465970i) q^{94} +(5.09327 + 5.06839i) q^{95} +(-6.18004 - 0.540683i) q^{97} +(-0.693170 + 0.185734i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

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Database

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