LMFDB - Embedded newform 450.2.h.g.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(91,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("450.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.h (of order $5$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 6 x^{10} - 26 x^{9} + 61 x^{8} - 120 x^{7} + 465 x^{6} - 600 x^{5} + 1525 x^{4} + \cdots + 15625 $ x^12 - x^11 + 6x^10 - 26x^9 + 61x^8 - 120x^7 + 465x^6 - 600x^5 + 1525x^4 - 3250x^3 + 3750x^2 - 3125x + 15625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.2
Root			$0.220100 - 2.22521i$ of defining polynomial
Character	$\chi$	$=$	450.91
Dual form			450.2.h.g.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.220100 + 2.22521i) q^{5} +1.64173 q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.220100 + 2.22521i) q^{5} +1.64173 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-1.48601 + 1.67086i) q^{10} +(0.232788 + 0.169130i) q^{11} +(1.02912 - 0.747697i) q^{13} +(1.32819 + 0.964983i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-1.52297 + 4.68721i) q^{17} +(-0.745417 + 2.29416i) q^{19} +(-2.18431 + 0.478300i) q^{20} +(0.0889172 + 0.273659i) q^{22} +(-0.588076 - 0.427262i) q^{23} +(-4.90311 - 0.979536i) q^{25} +1.27206 q^{26} +(0.507322 + 1.56138i) q^{28} +(1.43158 + 4.40594i) q^{29} +(2.27323 - 6.99629i) q^{31} -1.00000 q^{32} +(-3.98718 + 2.89686i) q^{34} +(-0.361344 + 3.65319i) q^{35} +(6.70462 - 4.87119i) q^{37} +(-1.95153 + 1.41787i) q^{38} +(-2.04829 - 0.896955i) q^{40} +(2.21533 - 1.60953i) q^{41} +5.96937 q^{43} +(-0.0889172 + 0.273659i) q^{44} +(-0.224625 - 0.691324i) q^{46} +(1.71263 + 5.27092i) q^{47} -4.30473 q^{49} +(-3.39094 - 3.67444i) q^{50} +(1.02912 + 0.747697i) q^{52} +(-1.99918 - 6.15285i) q^{53} +(-0.427587 + 0.480777i) q^{55} +(-0.507322 + 1.56138i) q^{56} +(-1.43158 + 4.40594i) q^{58} +(7.03842 - 5.11371i) q^{59} +(-8.45598 - 6.14363i) q^{61} +(5.95140 - 4.32394i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(1.43727 + 2.45457i) q^{65} +(3.78815 - 11.6587i) q^{67} -4.92843 q^{68} +(-2.43962 + 2.74310i) q^{70} +(-4.76911 - 14.6778i) q^{71} +(5.40292 + 3.92545i) q^{73} +8.28736 q^{74} -2.41222 q^{76} +(0.382175 + 0.277666i) q^{77} +(2.98419 + 9.18438i) q^{79} +(-1.12988 - 1.92960i) q^{80} +2.73830 q^{82} +(0.898338 - 2.76480i) q^{83} +(-10.0948 - 4.42058i) q^{85} +(4.82932 + 3.50871i) q^{86} +(-0.232788 + 0.169130i) q^{88} +(-12.4011 - 9.00992i) q^{89} +(1.68953 - 1.22751i) q^{91} +(0.224625 - 0.691324i) q^{92} +(-1.71263 + 5.27092i) q^{94} +(-4.94091 - 2.16365i) q^{95} +(0.560804 + 1.72598i) q^{97} +(-3.48260 - 2.53026i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 - q^5 - 2 * q^7 + 3 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8} + q^{10} - q^{11} + 4 q^{13} - 8 q^{14} - 3 q^{16} + 8 q^{17} - 8 q^{19} - q^{20} - 4 q^{22} - 11 q^{25} + 16 q^{26} - 7 q^{28} + 6 q^{29} - 3 q^{31} - 12 q^{32} + 2 q^{34} + 18 q^{35} - 8 q^{37} - 2 q^{38} + q^{40} - 20 q^{41} + 32 q^{43} + 4 q^{44} - 10 q^{46} + 34 q^{49} - 9 q^{50} + 4 q^{52} - 2 q^{53} + 44 q^{55} + 7 q^{56} - 6 q^{58} + 19 q^{59} - 26 q^{61} - 2 q^{62} - 3 q^{64} - 16 q^{65} - 16 q^{67} - 12 q^{68} - 23 q^{70} - 48 q^{71} - 30 q^{73} + 8 q^{74} + 12 q^{76} + 39 q^{77} - 18 q^{79} + 4 q^{80} - 40 q^{82} + 29 q^{83} - 4 q^{85} - 12 q^{86} + q^{88} - 62 q^{89} - 26 q^{91} + 10 q^{92} - 6 q^{95} + 23 q^{97} + 6 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 - q^5 - 2 * q^7 + 3 * q^8 + q^10 - q^11 + 4 * q^13 - 8 * q^14 - 3 * q^16 + 8 * q^17 - 8 * q^19 - q^20 - 4 * q^22 - 11 * q^25 + 16 * q^26 - 7 * q^28 + 6 * q^29 - 3 * q^31 - 12 * q^32 + 2 * q^34 + 18 * q^35 - 8 * q^37 - 2 * q^38 + q^40 - 20 * q^41 + 32 * q^43 + 4 * q^44 - 10 * q^46 + 34 * q^49 - 9 * q^50 + 4 * q^52 - 2 * q^53 + 44 * q^55 + 7 * q^56 - 6 * q^58 + 19 * q^59 - 26 * q^61 - 2 * q^62 - 3 * q^64 - 16 * q^65 - 16 * q^67 - 12 * q^68 - 23 * q^70 - 48 * q^71 - 30 * q^73 + 8 * q^74 + 12 * q^76 + 39 * q^77 - 18 * q^79 + 4 * q^80 - 40 * q^82 + 29 * q^83 - 4 * q^85 - 12 * q^86 + q^88 - 62 * q^89 - 26 * q^91 + 10 * q^92 - 6 * q^95 + 23 * q^97 + 6 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.220100	+	2.22521i	−0.0984316	+	0.995144i
$5$	−0.220100	+	2.22521i	−0.0984316	+	0.995144i
$6$		0			0
$7$	1.64173			0.620515			0.310257	−	0.950653i	$-0.399585\pi$
$7$	1.64173			0.620515			0.310257	+	0.950653i	$0.399585\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$		0			0
$10$	−1.48601	+	1.67086i	−0.469918	+	0.528373i
$11$	0.232788	+	0.169130i	0.0701883	+	0.0509948i	0.622326	−	0.782758i	$-0.286188\pi$
$11$	0.232788	+	0.169130i	0.0701883	+	0.0509948i	−0.552138	+	0.833753i	$0.686188\pi$
$12$		0			0
$13$	1.02912	−	0.747697i	0.285426	−	0.207374i	−0.435855	−	0.900017i	$-0.643554\pi$
$13$	1.02912	−	0.747697i	0.285426	−	0.207374i	0.721280	+	0.692643i	$0.243554\pi$
$14$	1.32819	+	0.964983i	0.354972	+	0.257903i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.52297	+	4.68721i	−0.369374	+	1.13682i	0.577822	+	0.816163i	$0.303903\pi$
$17$	−1.52297	+	4.68721i	−0.369374	+	1.13682i	−0.947196	+	0.320654i	$0.896097\pi$
$18$		0			0
$19$	−0.745417	+	2.29416i	−0.171010	+	0.526316i	−0.999429	−	0.0337940i	$-0.989241\pi$
$19$	−0.745417	+	2.29416i	−0.171010	+	0.526316i	0.828419	+	0.560110i	$0.189241\pi$
$20$	−2.18431	+	0.478300i	−0.488428	+	0.106951i
$21$		0			0
$22$	0.0889172	+	0.273659i	0.0189572	+	0.0583443i
$23$	−0.588076	−	0.427262i	−0.122622	−	0.0890903i	0.524784	−	0.851236i	$-0.324146\pi$
$23$	−0.588076	−	0.427262i	−0.122622	−	0.0890903i	−0.647406	+	0.762145i	$0.724146\pi$
$24$		0			0
$25$	−4.90311	−	0.979536i	−0.980622	−	0.195907i
$26$	1.27206			0.249471
$27$		0			0
$28$	0.507322	+	1.56138i	0.0958748	+	0.295072i
$29$	1.43158	+	4.40594i	0.265837	+	0.818162i	0.991499	+	0.130111i	$0.0415334\pi$
$29$	1.43158	+	4.40594i	0.265837	+	0.818162i	−0.725662	+	0.688051i	$0.758467\pi$
$30$		0			0
$31$	2.27323	−	6.99629i	0.408284	−	1.25657i	−0.509837	−	0.860271i	$-0.670294\pi$
$31$	2.27323	−	6.99629i	0.408284	−	1.25657i	0.918121	−	0.396299i	$-0.129706\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−3.98718	+	2.89686i	−0.683796	+	0.496807i
$35$	−0.361344	+	3.65319i	−0.0610783	+	0.617501i
$36$		0			0
$37$	6.70462	−	4.87119i	1.10223	−	0.800819i	0.120810	−	0.992676i	$-0.461451\pi$
$37$	6.70462	−	4.87119i	1.10223	−	0.800819i	0.981423	+	0.191857i	$0.0614509\pi$
$38$	−1.95153	+	1.41787i	−0.316579	+	0.230008i
$39$		0			0
$40$	−2.04829	−	0.896955i	−0.323862	−	0.141821i
$41$	2.21533	−	1.60953i	0.345976	−	0.251367i	−0.401203	−	0.915989i	$-0.631408\pi$
$41$	2.21533	−	1.60953i	0.345976	−	0.251367i	0.747179	+	0.664623i	$0.231408\pi$
$42$		0			0
$43$	5.96937			0.910320			0.455160	−	0.890410i	$-0.349582\pi$
$43$	5.96937			0.910320			0.455160	+	0.890410i	$0.349582\pi$
$44$	−0.0889172	+	0.273659i	−0.0134048	+	0.0412556i
$45$		0			0
$46$	−0.224625	−	0.691324i	−0.0331191	−	0.101930i
$47$	1.71263	+	5.27092i	0.249812	+	0.768843i	0.994808	+	0.101773i	$0.0324517\pi$
$47$	1.71263	+	5.27092i	0.249812	+	0.768843i	−0.744995	+	0.667070i	$0.767548\pi$
$48$		0			0
$49$	−4.30473			−0.614962
$50$	−3.39094	−	3.67444i	−0.479552	−	0.519644i
$51$		0			0
$52$	1.02912	+	0.747697i	0.142713	+	0.103687i
$53$	−1.99918	−	6.15285i	−0.274609	−	0.845159i	−0.989323	−	0.145742i	$-0.953443\pi$
$53$	−1.99918	−	6.15285i	−0.274609	−	0.845159i	0.714714	−	0.699417i	$-0.246557\pi$
$54$		0			0
$55$	−0.427587	+	0.480777i	−0.0576559	+	0.0648279i
$56$	−0.507322	+	1.56138i	−0.0677937	+	0.208648i
$57$		0			0
$58$	−1.43158	+	4.40594i	−0.187975	+	0.578528i
$59$	7.03842	−	5.11371i	0.916324	−	0.665748i	−0.0262825	−	0.999655i	$-0.508367\pi$
$59$	7.03842	−	5.11371i	0.916324	−	0.665748i	0.942606	+	0.333906i	$0.108367\pi$
$60$		0			0
$61$	−8.45598	−	6.14363i	−1.08268	−	0.786611i	−0.104529	−	0.994522i	$-0.533334\pi$
$61$	−8.45598	−	6.14363i	−1.08268	−	0.786611i	−0.978148	+	0.207911i	$0.933334\pi$
$62$	5.95140	−	4.32394i	0.755828	−	0.549141i
$63$		0			0
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.43727	+	2.45457i	0.178272	+	0.304452i
$66$		0			0
$67$	3.78815	−	11.6587i	0.462797	−	1.42434i	−0.398936	−	0.916979i	$-0.630620\pi$
$67$	3.78815	−	11.6587i	0.462797	−	1.42434i	0.861733	−	0.507363i	$-0.169380\pi$
$68$	−4.92843			−0.597660
$69$		0			0
$70$	−2.43962	+	2.74310i	−0.291591	+	0.327863i
$71$	−4.76911	−	14.6778i	−0.565989	−	1.74194i	−0.664994	−	0.746849i	$-0.731566\pi$
$71$	−4.76911	−	14.6778i	−0.565989	−	1.74194i	0.0990047	−	0.995087i	$-0.468434\pi$
$72$		0			0
$73$	5.40292	+	3.92545i	0.632364	+	0.459440i	0.857219	−	0.514953i	$-0.172191\pi$
$73$	5.40292	+	3.92545i	0.632364	+	0.459440i	−0.224854	+	0.974392i	$0.572191\pi$
$74$	8.28736			0.963387
$75$		0			0
$76$	−2.41222			−0.276700
$77$	0.382175	+	0.277666i	0.0435528	+	0.0316430i
$78$		0			0
$79$	2.98419	+	9.18438i	0.335747	+	1.03332i	0.966353	+	0.257220i	$0.0828066\pi$
$79$	2.98419	+	9.18438i	0.335747	+	1.03332i	−0.630605	+	0.776104i	$0.717193\pi$
$80$	−1.12988	−	1.92960i	−0.126324	−	0.215736i
$81$		0			0
$82$	2.73830			0.302394
$83$	0.898338	−	2.76480i	0.0986054	−	0.303476i	−0.889571	−	0.456797i	$-0.848997\pi$
$83$	0.898338	−	2.76480i	0.0986054	−	0.303476i	0.988177	+	0.153321i	$0.0489967\pi$
$84$		0			0
$85$	−10.0948	−	4.42058i	−1.09494	−	0.479479i
$86$	4.82932	+	3.50871i	0.520759	+	0.378354i
$87$		0			0
$88$	−0.232788	+	0.169130i	−0.0248153	+	0.0180294i
$89$	−12.4011	−	9.00992i	−1.31451	−	0.955049i	−0.999983	−	0.00580136i	$-0.998153\pi$
$89$	−12.4011	−	9.00992i	−1.31451	−	0.955049i	−0.314529	−	0.949248i	$-0.601847\pi$
$90$		0			0
$91$	1.68953	−	1.22751i	0.177111	−	0.128679i
$92$	0.224625	−	0.691324i	0.0234188	−	0.0720755i
$93$		0			0
$94$	−1.71263	+	5.27092i	−0.176644	+	0.543654i
$95$	−4.94091	−	2.16365i	−0.506927	−	0.221986i
$96$		0			0
$97$	0.560804	+	1.72598i	0.0569410	+	0.175246i	0.975482	−	0.220079i	$-0.0706317\pi$
$97$	0.560804	+	1.72598i	0.0569410	+	0.175246i	−0.918541	+	0.395326i	$0.870632\pi$
$98$	−3.48260	−	2.53026i	−0.351796	−	0.255595i
$99$		0			0
$100$	−0.583551	−	4.96583i	−0.0583551	−	0.496583i
$101$	1.35931			0.135257			0.0676283	−	0.997711i	$-0.478457\pi$
$101$	1.35931			0.135257			0.0676283	+	0.997711i	$0.478457\pi$
$102$		0			0
$103$	5.53474	+	17.0342i	0.545354	+	1.67843i	0.720146	+	0.693823i	$0.244075\pi$
$103$	5.53474	+	17.0342i	0.545354	+	1.67843i	−0.174791	+	0.984606i	$0.555925\pi$
$104$	0.393088	+	1.20980i	0.0385454	+	0.118631i
$105$		0			0
$106$	1.99918	−	6.15285i	0.194178	−	0.597617i
$107$	−6.32873			−0.611821			−0.305911	−	0.952060i	$-0.598961\pi$
$107$	−6.32873			−0.611821			−0.305911	+	0.952060i	$0.598961\pi$
$108$		0			0
$109$	−6.65751	+	4.83696i	−0.637673	+	0.463297i	−0.859050	−	0.511891i	$-0.828945\pi$
$109$	−6.65751	+	4.83696i	−0.637673	+	0.463297i	0.221377	+	0.975188i	$0.428945\pi$
$110$	−0.628519	+	0.137627i	−0.0599269	+	0.0131222i
$111$		0			0
$112$	−1.32819	+	0.964983i	−0.125502	+	0.0911823i
$113$	10.1263	−	7.35719i	0.952602	−	0.692106i	0.00118151	−	0.999999i	$-0.499624\pi$
$113$	10.1263	−	7.35719i	0.952602	−	0.692106i	0.951421	+	0.307893i	$0.0996239\pi$
$114$		0			0
$115$	1.08018	−	1.21455i	0.100728	−	0.113257i
$116$	−3.74791	+	2.72302i	−0.347985	+	0.252826i
$117$		0			0
$118$	8.69996			0.800896
$119$	−2.50030	+	7.69513i	−0.229202	+	0.705411i
$120$		0			0
$121$	−3.37360	−	10.3829i	−0.306691	−	0.943898i
$122$	−3.22990	−	9.94060i	−0.292421	−	0.899980i
$123$		0			0
$124$	7.35633			0.660618
$125$	3.25885	−	10.6949i	0.291480	−	0.956577i
$126$		0			0
$127$	16.4816	+	11.9746i	1.46250	+	1.06257i	0.982702	+	0.185192i	$0.0592905\pi$
$127$	16.4816	+	11.9746i	1.46250	+	1.06257i	0.479799	+	0.877378i	$0.340709\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$		0			0
$130$	−0.279980	+	2.83060i	−0.0245559	+	0.248260i
$131$	3.51255	−	10.8105i	0.306893	−	0.944519i	−0.672071	−	0.740486i	$-0.734595\pi$
$131$	3.51255	−	10.8105i	0.306893	−	0.944519i	0.978964	−	0.204033i	$-0.0654048\pi$
$132$		0			0
$133$	−1.22377	+	3.76638i	−0.106114	+	0.326587i
$134$	9.91751	−	7.20550i	0.856743	−	0.622460i
$135$		0			0
$136$	−3.98718	−	2.89686i	−0.341898	−	0.248404i
$137$	3.96485	−	2.88063i	0.338740	−	0.246109i	−0.405390	−	0.914144i	$-0.632864\pi$
$137$	3.96485	−	2.88063i	0.338740	−	0.246109i	0.744130	+	0.668035i	$0.232864\pi$
$138$		0			0
$139$	7.61833	+	5.53504i	0.646178	+	0.469476i	0.861967	−	0.506964i	$-0.169232\pi$
$139$	7.61833	+	5.53504i	0.646178	+	0.469476i	−0.215789	+	0.976440i	$0.569232\pi$
$140$	−3.58605	+	0.785238i	−0.303076	+	0.0663647i
$141$		0			0
$142$	4.76911	−	14.6778i	0.400215	−	1.23173i
$143$	0.366025			0.0306085
$144$		0			0
$145$	−10.1192	+	2.21581i	−0.840356	+	0.184013i
$146$	2.06373	+	6.35152i	0.170796	+	0.525655i
$147$		0			0
$148$	6.70462	+	4.87119i	0.551116	+	0.400409i
$149$	−15.0495			−1.23290			−0.616452	−	0.787392i	$-0.711431\pi$
$149$	−15.0495			−1.23290			−0.616452	+	0.787392i	$0.711431\pi$
$150$		0			0
$151$	3.06961			0.249801			0.124901	−	0.992169i	$-0.460139\pi$
$151$	3.06961			0.249801			0.124901	+	0.992169i	$0.460139\pi$
$152$	−1.95153	−	1.41787i	−0.158290	−	0.115004i
$153$		0			0
$154$	0.145978	+	0.449273i	0.0117632	+	0.0362035i
$155$	15.0679	+	6.59830i	1.21028	+	0.529988i
$156$		0			0
$157$	−15.6140			−1.24613			−0.623066	−	0.782170i	$-0.714113\pi$
$157$	−15.6140			−1.24613			−0.623066	+	0.782170i	$0.714113\pi$
$158$	−2.98419	+	9.18438i	−0.237409	+	0.730670i
$159$		0			0
$160$	0.220100	−	2.22521i	0.0174004	−	0.175918i
$161$	−0.965460	−	0.701447i	−0.0760889	−	0.0552818i
$162$		0			0
$163$	7.16908	−	5.20864i	0.561526	−	0.407972i	−0.270491	−	0.962722i	$-0.587186\pi$
$163$	7.16908	−	5.20864i	0.561526	−	0.407972i	0.832017	+	0.554750i	$0.187186\pi$
$164$	2.21533	+	1.60953i	0.172988	+	0.125683i
$165$		0			0
$166$	2.35188	−	1.70874i	0.182541	−	0.132624i
$167$	−5.42191	+	16.6869i	−0.419560	+	1.29127i	0.488548	+	0.872537i	$0.337527\pi$
$167$	−5.42191	+	16.6869i	−0.419560	+	1.29127i	−0.908108	+	0.418736i	$0.862473\pi$
$168$		0			0
$169$	−3.51719	+	10.8248i	−0.270553	+	0.832677i
$170$	−5.56854	−	9.50991i	−0.427087	−	0.729377i
$171$		0			0
$172$	1.84464	+	5.67721i	0.140652	+	0.432883i
$173$	13.9942	+	10.1674i	1.06396	+	0.773012i	0.974817	−	0.223007i	$-0.0715871\pi$
$173$	13.9942	+	10.1674i	1.06396	+	0.773012i	0.0891431	+	0.996019i	$0.471587\pi$
$174$		0			0
$175$	−8.04957	−	1.60813i	−0.608491	−	0.121563i
$176$	−0.287742			−0.0216894
$177$		0			0
$178$	−4.73679	−	14.5783i	−0.355038	−	1.09269i
$179$	1.22409	+	3.76738i	0.0914931	+	0.281587i	0.986324	−	0.164819i	$-0.0527039\pi$
$179$	1.22409	+	3.76738i	0.0914931	+	0.281587i	−0.894831	+	0.446406i	$0.852704\pi$
$180$		0			0
$181$	1.61586	−	4.97310i	0.120106	−	0.369647i	−0.872872	−	0.487949i	$-0.837745\pi$
$181$	1.61586	−	4.97310i	0.120106	−	0.369647i	0.992978	+	0.118302i	$0.0377451\pi$
$182$	2.08837			0.154801
$183$		0			0
$184$	0.588076	−	0.427262i	0.0433535	−	0.0314982i
$185$	9.36373	+	15.9913i	0.688435	+	1.17571i
$186$		0			0
$187$	−1.14728	+	0.833548i	−0.0838974	+	0.0609550i
$188$	−4.48371	+	3.25761i	−0.327008	+	0.237586i
$189$		0			0
$190$	−2.72552	−	4.65463i	−0.197730	−	0.337682i
$191$	−9.68041	+	7.03323i	−0.700450	+	0.508906i	−0.880079	−	0.474828i	$-0.842510\pi$
$191$	−9.68041	+	7.03323i	−0.700450	+	0.508906i	0.179629	+	0.983734i	$0.442510\pi$
$192$		0			0
$193$	−13.9654			−1.00525			−0.502624	−	0.864505i	$-0.667632\pi$
$193$	−13.9654			−1.00525			−0.502624	+	0.864505i	$0.667632\pi$
$194$	−0.560804	+	1.72598i	−0.0402634	+	0.123918i
$195$		0			0
$196$	−1.33024	−	4.09404i	−0.0950168	−	0.292432i
$197$	−4.24836	−	13.0751i	−0.302683	−	0.931563i	−0.980532	−	0.196362i	$-0.937087\pi$
$197$	−4.24836	−	13.0751i	−0.302683	−	0.931563i	0.677848	−	0.735202i	$-0.262913\pi$
$198$		0			0
$199$	−13.0562			−0.925531			−0.462765	−	0.886481i	$-0.653143\pi$
$199$	−13.0562			−0.925531			−0.462765	+	0.886481i	$0.653143\pi$
$200$	2.44674	−	4.36044i	0.173011	−	0.308330i
$201$		0			0
$202$	1.09971	+	0.798984i	0.0773751	+	0.0562163i
$203$	2.35026	+	7.23335i	0.164956	+	0.507682i
$204$		0			0
$205$	3.09395	+	5.28383i	0.216091	+	0.369039i
$206$	−5.53474	+	17.0342i	−0.385624	+	1.18683i
$207$		0			0
$208$	−0.393088	+	1.20980i	−0.0272557	+	0.0838845i
$209$	−0.561536	+	0.407980i	−0.0388423	+	0.0282205i
$210$		0			0
$211$	−6.54646	−	4.75628i	−0.450677	−	0.327436i	0.339186	−	0.940719i	$-0.389848\pi$
$211$	−6.54646	−	4.75628i	−0.450677	−	0.327436i	−0.789863	+	0.613283i	$0.789848\pi$
$212$	5.23392	−	3.80267i	0.359467	−	0.261168i
$213$		0			0
$214$	−5.12005	−	3.71993i	−0.349999	−	0.254289i
$215$	−1.31386	+	13.2831i	−0.0896043	+	0.905900i
$216$		0			0
$217$	3.73203	−	11.4860i	0.253346	−	0.779720i
$218$	−8.22913			−0.557347
$219$		0			0
$220$	−0.589378	−	0.258092i	−0.0397358	−	0.0174005i
$221$	1.93730	+	5.96241i	0.130317	+	0.401075i
$222$		0			0
$223$	4.11685	+	2.99107i	0.275685	+	0.200297i	0.717033	−	0.697039i	$-0.245500\pi$
$223$	4.11685	+	2.99107i	0.275685	+	0.200297i	−0.441348	+	0.897336i	$0.645500\pi$
$224$	−1.64173			−0.109693
$225$		0			0
$226$	12.5168			0.832605
$227$	20.0528	+	14.5692i	1.33095	+	0.966993i	0.999725	+	0.0234412i	$0.00746225\pi$
$227$	20.0528	+	14.5692i	1.33095	+	0.966993i	0.331226	+	0.943551i	$0.392538\pi$
$228$		0			0
$229$	−0.457059	−	1.40668i	−0.0302033	−	0.0929562i	0.934819	−	0.355126i	$-0.115562\pi$
$229$	−0.457059	−	1.40668i	−0.0302033	−	0.0929562i	−0.965022	+	0.262170i	$0.915562\pi$
$230$	1.58778	−	0.347677i	0.104695	−	0.0229251i
$231$		0			0
$232$	−4.63268			−0.304150
$233$	−0.215440	+	0.663055i	−0.0141139	+	0.0434382i	−0.957865	−	0.287217i	$-0.907270\pi$
$233$	−0.215440	+	0.663055i	−0.0141139	+	0.0434382i	0.943752	+	0.330656i	$0.107270\pi$
$234$		0			0
$235$	−12.1059	+	2.65082i	−0.789699	+	0.172921i
$236$	7.03842	+	5.11371i	0.458162	+	0.332874i
$237$		0			0
$238$	−6.54587	+	4.75585i	−0.424306	+	0.308276i
$239$	−23.6136	−	17.1563i	−1.52744	−	1.10975i	−0.957642	−	0.287961i	$-0.907023\pi$
$239$	−23.6136	−	17.1563i	−1.52744	−	1.10975i	−0.569795	−	0.821787i	$-0.692977\pi$
$240$		0			0
$241$	−14.0170	+	10.1840i	−0.902915	+	0.656006i	−0.939213	−	0.343335i	$-0.888443\pi$
$241$	−14.0170	+	10.1840i	−0.902915	+	0.656006i	0.0362980	+	0.999341i	$0.488443\pi$
$242$	3.37360	−	10.3829i	0.216863	−	0.667437i
$243$		0			0
$244$	3.22990	−	9.94060i	0.206773	−	0.636382i
$245$	0.947471	−	9.57893i	0.0605317	−	0.611975i
$246$		0			0
$247$	0.948214	+	2.91830i	0.0603334	+	0.185687i
$248$	5.95140	+	4.32394i	0.377914	+	0.274571i
$249$		0			0
$250$	8.92274	−	6.73682i	0.564324	−	0.426074i
$251$	−1.10083			−0.0694837			−0.0347419	−	0.999396i	$-0.511061\pi$
$251$	−1.10083			−0.0694837			−0.0347419	+	0.999396i	$0.511061\pi$
$252$		0			0
$253$	−0.0646340	−	0.198923i	−0.00406350	−	0.0125062i
$254$	6.29540	+	19.3752i	0.395008	+	1.21571i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−29.4887			−1.83945			−0.919726	−	0.392560i	$-0.871590\pi$
$257$	−29.4887			−1.83945			−0.919726	+	0.392560i	$0.871590\pi$
$258$		0			0
$259$	11.0072	−	7.99717i	0.683951	−	0.496920i
$260$	−1.89029	+	2.12543i	−0.117231	+	0.131814i
$261$		0			0
$262$	9.19597	−	6.68126i	0.568129	−	0.412770i
$263$	0.647992	−	0.470794i	0.0399569	−	0.0290304i	−0.567628	−	0.823285i	$-0.692139\pi$
$263$	0.647992	−	0.470794i	0.0399569	−	0.0290304i	0.607584	+	0.794255i	$0.292139\pi$
$264$		0			0
$265$	14.1314	−	3.09436i	0.868084	−	0.190085i
$266$	−3.20387	+	2.32775i	−0.196442	+	0.142724i
$267$		0			0
$268$	12.2587			0.748821
$269$	−8.75585	+	26.9477i	−0.533853	+	1.64303i	0.212260	+	0.977213i	$0.431918\pi$
$269$	−8.75585	+	26.9477i	−0.533853	+	1.64303i	−0.746114	+	0.665819i	$0.768082\pi$
$270$		0			0
$271$	8.05031	+	24.7763i	0.489021	+	1.50505i	0.826071	+	0.563566i	$0.190571\pi$
$271$	8.05031	+	24.7763i	0.489021	+	1.50505i	−0.337049	+	0.941487i	$0.609429\pi$
$272$	−1.52297	−	4.68721i	−0.0923435	−	0.284204i
$273$		0			0
$274$	4.90083			0.296070
$275$	−0.975717	−	1.05729i	−0.0588379	−	0.0637570i
$276$		0			0
$277$	−1.13826	−	0.826993i	−0.0683913	−	0.0496892i	0.553064	−	0.833139i	$-0.313458\pi$
$277$	−1.13826	−	0.826993i	−0.0683913	−	0.0496892i	−0.621456	+	0.783449i	$0.713458\pi$
$278$	2.90994	+	8.95588i	0.174527	+	0.537138i
$279$		0			0
$280$	−3.36273	−	1.47256i	−0.200961	−	0.0880020i
$281$	−5.01989	+	15.4496i	−0.299461	+	0.921647i	0.682225	+	0.731142i	$0.261012\pi$
$281$	−5.01989	+	15.4496i	−0.299461	+	0.921647i	−0.981686	+	0.190505i	$0.938988\pi$
$282$		0			0
$283$	4.18580	−	12.8826i	0.248820	−	0.765790i	−0.746164	−	0.665762i	$-0.768107\pi$
$283$	4.18580	−	12.8826i	0.248820	−	0.765790i	0.994985	−	0.100028i	$-0.0318932\pi$
$284$	12.4857	−	9.07139i	0.740890	−	0.538288i
$285$		0			0
$286$	0.296120	+	0.215144i	0.0175099	+	0.0127217i
$287$	3.63697	−	2.64241i	0.214683	−	0.155977i
$288$		0			0
$289$	−5.89726	−	4.28461i	−0.346898	−	0.252036i
$290$	−9.48904	−	4.15530i	−0.557216	−	0.244008i
$291$		0			0
$292$	−2.06373	+	6.35152i	−0.120771	+	0.371694i
$293$	23.3958			1.36679			0.683397	−	0.730047i	$-0.260502\pi$
$293$	23.3958			1.36679			0.683397	+	0.730047i	$0.260502\pi$
$294$		0			0
$295$	9.82992	+	16.7875i	0.572320	+	0.977405i
$296$	2.56094	+	7.88175i	0.148851	+	0.458118i
$297$		0			0
$298$	−12.1753	−	8.84588i	−0.705297	−	0.512428i
$299$	−0.924661			−0.0534745
$300$		0			0
$301$	9.80008			0.564867
$302$	2.48337	+	1.80427i	0.142902	+	0.103824i
$303$		0			0
$304$	−0.745417	−	2.29416i	−0.0427526	−	0.131579i
$305$	15.5320	−	17.4641i	0.889361	−	0.999992i
$306$		0			0
$307$	−1.94345			−0.110919			−0.0554593	−	0.998461i	$-0.517662\pi$
$307$	−1.94345			−0.110919			−0.0554593	+	0.998461i	$0.517662\pi$
$308$	−0.145978	+	0.449273i	−0.00831785	+	0.0255997i
$309$		0			0
$310$	8.31178	+	14.1948i	0.472077	+	0.806211i
$311$	−7.84831	−	5.70213i	−0.445037	−	0.323338i	0.342596	−	0.939483i	$-0.388694\pi$
$311$	−7.84831	−	5.70213i	−0.445037	−	0.323338i	−0.787633	+	0.616144i	$0.788694\pi$
$312$		0			0
$313$	−4.04903	+	2.94179i	−0.228865	+	0.166280i	−0.696308	−	0.717743i	$-0.745175\pi$
$313$	−4.04903	+	2.94179i	−0.228865	+	0.166280i	0.467443	+	0.884023i	$0.345175\pi$
$314$	−12.6320	−	9.17767i	−0.712864	−	0.517926i
$315$		0			0
$316$	−7.81270	+	5.67626i	−0.439499	+	0.319315i
$317$	−2.72402	+	8.38366i	−0.152996	+	0.470873i	−0.997952	−	0.0639620i	$-0.979626\pi$
$317$	−2.72402	+	8.38366i	−0.152996	+	0.470873i	0.844956	+	0.534835i	$0.179626\pi$
$318$		0			0
$319$	−0.411924	+	1.26777i	−0.0230633	+	0.0709817i
$320$	1.48601	−	1.67086i	0.0830705	−	0.0934039i
$321$		0			0
$322$	−0.368773	−	1.13497i	−0.0205509	−	0.0632492i
$323$	−9.61796	−	6.98786i	−0.535158	−	0.388815i
$324$		0			0
$325$	−5.77827	+	2.65799i	−0.320521	+	0.147439i
$326$	8.86147			0.490791
$327$		0			0
$328$	0.846180	+	2.60428i	0.0467225	+	0.143797i
$329$	2.81167	+	8.65342i	0.155012	+	0.477078i
$330$		0			0
$331$	−0.197287	+	0.607187i	−0.0108439	+	0.0333740i	−0.956332	−	0.292282i	$-0.905585\pi$
$331$	−0.197287	+	0.607187i	−0.0108439	+	0.0333740i	0.945488	+	0.325656i	$0.105585\pi$
$332$	2.90708			0.159547
$333$		0			0
$334$	−14.1947	+	10.3131i	−0.776702	+	0.564307i
$335$	25.1094	+	10.9955i	1.37187	+	0.600749i
$336$		0			0
$337$	−4.75679	+	3.45601i	−0.259119	+	0.188261i	−0.709759	−	0.704445i	$-0.751196\pi$
$337$	−4.75679	+	3.45601i	−0.259119	+	0.188261i	0.450640	+	0.892706i	$0.351196\pi$
$338$	−9.20812	+	6.69009i	−0.500856	+	0.363893i
$339$		0			0
$340$	1.08475	−	10.9668i	0.0588286	−	0.594757i
$341$	1.71247	−	1.24418i	0.0927353	−	0.0673761i
$342$		0			0
$343$	−18.5593			−1.00211
$344$	−1.84464	+	5.67721i	−0.0994561	+	0.306095i
$345$		0			0
$346$	5.34531	+	16.4512i	0.287366	+	0.884421i
$347$	−6.69935	−	20.6185i	−0.359640	−	1.10686i	−0.953270	−	0.302120i	$-0.902306\pi$
$347$	−6.69935	−	20.6185i	−0.359640	−	1.10686i	0.593630	−	0.804738i	$-0.297694\pi$
$348$		0			0
$349$	−1.18292			−0.0633205			−0.0316602	−	0.999499i	$-0.510079\pi$
$349$	−1.18292			−0.0633205			−0.0316602	+	0.999499i	$0.510079\pi$
$350$	−5.56701	−	6.03243i	−0.297569	−	0.322447i
$351$		0			0
$352$	−0.232788	−	0.169130i	−0.0124076	−	0.00901468i
$353$	0.639222	+	1.96732i	0.0340223	+	0.104710i	0.966626	−	0.256193i	$-0.0824684\pi$
$353$	0.639222	+	1.96732i	0.0340223	+	0.104710i	−0.932603	+	0.360903i	$0.882468\pi$
$354$		0			0
$355$	33.7109	−	7.38168i	1.78919	−	0.391779i
$356$	4.73679	−	14.5783i	0.251050	−	0.772651i
$357$		0			0
$358$	−1.22409	+	3.76738i	−0.0646954	+	0.199112i
$359$	29.6026	−	21.5076i	1.56237	−	1.13513i	0.628331	−	0.777946i	$-0.283738\pi$
$359$	29.6026	−	21.5076i	1.56237	−	1.13513i	0.934036	−	0.357179i	$-0.116262\pi$
$360$		0			0
$361$	10.6638	+	7.74771i	0.561253	+	0.407774i
$362$	4.23037	−	3.07354i	0.222343	−	0.161542i
$363$		0			0
$364$	1.68953	+	1.22751i	0.0885554	+	0.0643393i
$365$	−9.92414	+	11.1586i	−0.519453	+	0.584070i
$366$		0			0
$367$	−2.35254	+	7.24037i	−0.122801	+	0.377944i	−0.993494	−	0.113883i	$-0.963671\pi$
$367$	−2.35254	+	7.24037i	−0.122801	+	0.377944i	0.870693	+	0.491828i	$0.163671\pi$
$368$	0.726901			0.0378924
$369$		0			0
$370$	−1.82405	+	18.4411i	−0.0948277	+	0.958708i
$371$	−3.28211	−	10.1013i	−0.170399	−	0.524433i
$372$		0			0
$373$	−8.22653	−	5.97692i	−0.425953	−	0.309473i	0.354075	−	0.935217i	$-0.384796\pi$
$373$	−8.22653	−	5.97692i	−0.425953	−	0.309473i	−0.780029	+	0.625744i	$0.784796\pi$
$374$	−1.41812			−0.0733290
$375$		0			0
$376$	−5.54218			−0.285816
$377$	4.76757	+	3.46384i	0.245542	+	0.178397i
$378$		0			0
$379$	−10.9182	−	33.6026i	−0.560828	−	1.72605i	−0.680034	−	0.733181i	$-0.738035\pi$
$379$	−10.9182	−	33.6026i	−0.560828	−	1.72605i	0.119206	−	0.992870i	$-0.461965\pi$
$380$	0.530929	−	5.36769i	0.0272361	−	0.275357i
$381$		0			0
$382$	−11.9656			−0.612215
$383$	3.41810	−	10.5198i	0.174657	−	0.537538i	−0.824961	−	0.565190i	$-0.808803\pi$
$383$	3.41810	−	10.5198i	0.174657	−	0.537538i	0.999618	+	0.0276519i	$0.00880299\pi$
$384$		0			0
$385$	−0.701982	+	0.789304i	−0.0357763	+	0.0402267i
$386$	−11.2982	−	8.20863i	−0.575064	−	0.417808i
$387$		0			0
$388$	−1.46820	+	1.06671i	−0.0745367	+	0.0541541i
$389$	−27.6451	−	20.0853i	−1.40166	−	1.01837i	−0.994470	−	0.105024i	$-0.966508\pi$
$389$	−27.6451	−	20.0853i	−1.40166	−	1.01837i	−0.407191	−	0.913343i	$-0.633492\pi$
$390$		0			0
$391$	2.89829	−	2.10573i	0.146573	−	0.106491i
$392$	1.33024	−	4.09404i	0.0671870	−	0.206780i
$393$		0			0
$394$	4.24836	−	13.0751i	0.214029	−	0.658715i
$395$	−21.0940	+	4.61896i	−1.06135	+	0.232405i
$396$		0			0
$397$	5.60979	+	17.2652i	0.281547	+	0.866514i	0.987412	+	0.158167i	$0.0505585\pi$
$397$	5.60979	+	17.2652i	0.281547	+	0.866514i	−0.705865	+	0.708346i	$0.749441\pi$
$398$	−10.5627	−	7.67425i	−0.529460	−	0.384676i
$399$		0			0
$400$	4.54246	−	2.08952i	0.227123	−	0.104476i
$401$	2.68524			0.134094			0.0670472	−	0.997750i	$-0.478642\pi$
$401$	2.68524			0.134094			0.0670472	+	0.997750i	$0.478642\pi$
$402$		0			0
$403$	−2.89168	−	8.89969i	−0.144045	−	0.443325i
$404$	0.420051	+	1.29278i	0.0208983	+	0.0643184i
$405$		0			0
$406$	−2.35026	+	7.23335i	−0.116641	+	0.358985i
$407$	2.38462			0.118201
$408$		0			0
$409$	26.9131	−	19.5535i	1.33077	−	0.966858i	0.331036	−	0.943618i	$-0.392602\pi$
$409$	26.9131	−	19.5535i	1.33077	−	0.966858i	0.999730	−	0.0232401i	$-0.00739821\pi$
$410$	−0.602699	+	6.09329i	−0.0297652	+	0.300926i
$411$		0			0
$412$	−14.4901	+	10.5277i	−0.713878	+	0.518663i
$413$	11.5552	−	8.39532i	0.568592	−	0.413106i
$414$		0			0
$415$	5.95453	+	2.60752i	0.292297	+	0.127998i
$416$	−1.02912	+	0.747697i	−0.0504566	+	0.0366589i
$417$		0			0
$418$	−0.694097			−0.0339494
$419$	3.70892	−	11.4149i	0.181192	−	0.557653i	−0.818670	−	0.574265i	$-0.805288\pi$
$419$	3.70892	−	11.4149i	0.181192	−	0.557653i	0.999862	+	0.0166119i	$0.00528798\pi$
$420$		0			0
$421$	7.31823	+	22.5232i	0.356669	+	1.09771i	0.955035	+	0.296492i	$0.0958167\pi$
$421$	7.31823	+	22.5232i	0.356669	+	1.09771i	−0.598367	+	0.801223i	$0.704183\pi$
$422$	−2.50053	−	7.69583i	−0.121724	−	0.374627i
$423$		0			0
$424$	6.46949			0.314186
$425$	12.0586	−	21.4901i	0.584927	−	1.04242i
$426$		0			0
$427$	−13.8824	−	10.0862i	−0.671817	−	0.488104i
$428$	−1.95568	−	6.01898i	−0.0945316	−	0.290938i
$429$		0			0
$430$	−8.87054	+	9.97398i	−0.427775	+	0.480988i
$431$	8.82145	−	27.1496i	0.424914	−	1.30775i	−0.478162	−	0.878271i	$-0.658697\pi$
$431$	8.82145	−	27.1496i	0.424914	−	1.30775i	0.903076	−	0.429480i	$-0.141303\pi$
$432$		0			0
$433$	10.2515	−	31.5507i	0.492653	−	1.51623i	−0.327928	−	0.944703i	$-0.606350\pi$
$433$	10.2515	−	31.5507i	0.492653	−	1.51623i	0.820582	−	0.571529i	$-0.193650\pi$
$434$	9.77057	−	7.09874i	0.469002	−	0.340750i
$435$		0			0
$436$	−6.65751	−	4.83696i	−0.318837	−	0.231648i
$437$	1.41857	−	1.03065i	0.0678593	−	0.0493026i
$438$		0			0
$439$	14.9511	+	10.8626i	0.713575	+	0.518442i	0.884325	−	0.466872i	$-0.154619\pi$
$439$	14.9511	+	10.8626i	0.713575	+	0.518442i	−0.170750	+	0.985314i	$0.554619\pi$
$440$	−0.325114	−	0.555228i	−0.0154992	−	0.0264695i
$441$		0			0
$442$	−1.93730	+	5.96241i	−0.0921482	+	0.283603i
$443$	−18.7642			−0.891515			−0.445757	−	0.895154i	$-0.647066\pi$
$443$	−18.7642			−0.891515			−0.445757	+	0.895154i	$0.647066\pi$
$444$		0			0
$445$	22.7784	−	25.6119i	1.07980	−	1.21412i
$446$	1.57250	+	4.83965i	0.0744599	+	0.229164i
$447$		0			0
$448$	−1.32819	−	0.964983i	−0.0627509	−	0.0455912i
$449$	−4.33462			−0.204563			−0.102282	−	0.994755i	$-0.532614\pi$
$449$	−4.33462			−0.204563			−0.102282	+	0.994755i	$0.532614\pi$
$450$		0			0
$451$	0.787923			0.0371018
$452$	10.1263	+	7.35719i	0.476301	+	0.346053i
$453$		0			0
$454$	7.65949	+	23.5735i	0.359478	+	1.10636i
$455$	2.35961	+	4.02973i	0.110620	+	0.188917i
$456$		0			0
$457$	−27.6962			−1.29557			−0.647786	−	0.761822i	$-0.724305\pi$
$457$	−27.6962			−1.29557			−0.647786	+	0.761822i	$0.724305\pi$
$458$	0.457059	−	1.40668i	0.0213570	−	0.0657299i
$459$		0			0
$460$	1.48890	+	0.651998i	0.0694204	+	0.0303995i
$461$	−9.30766	−	6.76241i	−0.433501	−	0.314957i	0.349546	−	0.936919i	$-0.386336\pi$
$461$	−9.30766	−	6.76241i	−0.433501	−	0.314957i	−0.783047	+	0.621962i	$0.786336\pi$
$462$		0			0
$463$	−0.940376	+	0.683223i	−0.0437030	+	0.0317521i	−0.609422	−	0.792846i	$-0.708599\pi$
$463$	−0.940376	+	0.683223i	−0.0437030	+	0.0317521i	0.565719	+	0.824598i	$0.308599\pi$
$464$	−3.74791	−	2.72302i	−0.173993	−	0.126413i
$465$		0			0
$466$	−0.564028	+	0.409791i	−0.0261281	+	0.0189832i
$467$	−6.68977	+	20.5890i	−0.309566	+	0.952745i	0.668368	+	0.743831i	$0.266993\pi$
$467$	−6.68977	+	20.5890i	−0.309566	+	0.952745i	−0.977934	+	0.208915i	$0.933007\pi$
$468$		0			0
$469$	6.21911	−	19.1405i	0.287172	−	0.883825i
$470$	−11.3520	−	4.97108i	−0.523627	−	0.229299i
$471$		0			0
$472$	2.68844	+	8.27415i	0.123745	+	0.380849i
$473$	1.38960	+	1.00960i	0.0638938	+	0.0464216i
$474$		0			0
$475$	5.90207	−	10.5183i	0.270806	−	0.482615i
$476$	−8.09114			−0.370857
$477$		0			0
$478$	−9.01959	−	27.7595i	−0.412547	−	1.26969i
$479$	7.53007	+	23.1752i	0.344058	+	1.05890i	0.962086	+	0.272745i	$0.0879315\pi$
$479$	7.53007	+	23.1752i	0.344058	+	1.05890i	−0.618029	+	0.786156i	$0.712068\pi$
$480$		0			0
$481$	3.25766	−	10.0260i	0.148537	−	0.457148i
$482$	−17.3260			−0.789177
$483$		0			0
$484$	8.83220	−	6.41697i	0.401464	−	0.291681i
$485$	−3.96409	+	0.868018i	−0.180000	+	0.0394147i
$486$		0			0
$487$	−19.3197	+	14.0366i	−0.875458	+	0.636058i	−0.932046	−	0.362340i	$-0.881978\pi$
$487$	−19.3197	+	14.0366i	−0.875458	+	0.636058i	0.0565877	+	0.998398i	$0.481978\pi$
$488$	8.45598	−	6.14363i	0.382784	−	0.278109i
$489$		0			0
$490$	6.39687	−	7.19261i	0.288981	−	0.324929i
$491$	22.2993	−	16.2014i	1.00635	−	0.731158i	0.0429114	−	0.999079i	$-0.486337\pi$
$491$	22.2993	−	16.2014i	1.00635	−	0.731158i	0.963441	+	0.267921i	$0.0863367\pi$
$492$		0			0
$493$	−22.8318			−1.02829
$494$	−0.948214	+	2.91830i	−0.0426621	+	0.131301i
$495$		0			0
$496$	2.27323	+	6.99629i	0.102071	+	0.314143i
$497$	−7.82958	−	24.0970i	−0.351205	−	1.08090i
$498$		0			0
$499$	12.7308			0.569911			0.284955	−	0.958541i	$-0.408021\pi$
$499$	12.7308			0.569911			0.284955	+	0.958541i	$0.408021\pi$
$500$	11.1785	−	0.205544i	0.499915	−	0.00919219i
$501$		0			0
$502$	−0.890590	−	0.647051i	−0.0397490	−	0.0288793i
$503$	−8.58376	−	26.4181i	−0.382731	−	1.17792i	−0.938113	−	0.346329i	$-0.887428\pi$
$503$	−8.58376	−	26.4181i	−0.382731	−	1.17792i	0.555382	−	0.831595i	$-0.312572\pi$
$504$		0			0
$505$	−0.299185	+	3.02476i	−0.0133135	+	0.134600i
$506$	0.0646340	−	0.198923i	0.00287333	−	0.00884321i
$507$		0			0
$508$	−6.29540	+	19.3752i	−0.279313	+	0.859637i
$509$	18.2595	−	13.2663i	0.809338	−	0.588019i	−0.104300	−	0.994546i	$-0.533260\pi$
$509$	18.2595	−	13.2663i	0.809338	−	0.588019i	0.913639	+	0.406527i	$0.133260\pi$
$510$		0			0
$511$	8.87013	+	6.44452i	0.392391	+	0.285089i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$		0			0
$514$	−23.8568	−	17.3330i	−1.05228	−	0.764526i
$515$	−39.1228	+	8.56674i	−1.72396	+	0.377496i
$516$		0			0
$517$	−0.492794	+	1.51667i	−0.0216731	+	0.0667029i
$518$	13.6056			0.597795
$519$		0			0
$520$	−2.77858	+	0.608426i	−0.121849	+	0.0266812i
$521$	7.98129	+	24.5639i	0.349667	+	1.07616i	0.959038	+	0.283278i	$0.0914220\pi$
$521$	7.98129	+	24.5639i	0.349667	+	1.07616i	−0.609371	+	0.792885i	$0.708578\pi$
$522$		0			0
$523$	−23.0192	−	16.7244i	−1.00656	−	0.731308i	−0.0430742	−	0.999072i	$-0.513715\pi$
$523$	−23.0192	−	16.7244i	−1.00656	−	0.731308i	−0.963484	+	0.267764i	$0.913715\pi$
$524$	11.3668			0.496563
$525$		0			0
$526$	0.800963			0.0349236
$527$	29.3310	+	21.3102i	1.27768	+	0.928289i
$528$		0			0
$529$	−6.94411	−	21.3718i	−0.301918	−	0.929208i
$530$	13.2514	+	5.80284i	0.575602	+	0.252059i
$531$		0			0
$532$	−3.96021			−0.171697
$533$	1.07639	−	3.31279i	0.0466237	−	0.143493i
$534$		0			0
$535$	1.39295	−	14.0827i	0.0602226	−	0.608850i
$536$	9.91751	+	7.20550i	0.428371	+	0.311230i
$537$		0			0
$538$	−22.9231	+	16.6546i	−0.988285	+	0.718031i
$539$	−1.00209	−	0.728061i	−0.0431631	−	0.0313598i
$540$		0			0
$541$	−20.3737	+	14.8024i	−0.875933	+	0.636403i	−0.932172	−	0.362014i	$-0.882089\pi$
$541$	−20.3737	+	14.8024i	−0.875933	+	0.636403i	0.0562391	+	0.998417i	$0.482089\pi$
$542$	−8.05031	+	24.7763i	−0.345790	+	1.06423i
$543$		0			0
$544$	1.52297	−	4.68721i	0.0652967	−	0.200963i
$545$	−9.29794	−	15.8790i	−0.398280	−	0.680180i
$546$		0			0
$547$	−2.56321	−	7.88874i	−0.109595	−	0.337298i	0.881187	−	0.472769i	$-0.156745\pi$
$547$	−2.56321	−	7.88874i	−0.109595	−	0.337298i	−0.990781	+	0.135471i	$0.956745\pi$
$548$	3.96485	+	2.88063i	0.169370	+	0.123055i
$549$		0			0
$550$	−0.167912	−	1.42888i	−0.00715979	−	0.0609275i
$551$	−11.1750			−0.476072
$552$		0			0
$553$	4.89922	+	15.0783i	0.208336	+	0.641193i
$554$	−0.434776	−	1.33810i	−0.0184719	−	0.0568506i
$555$		0			0
$556$	−2.90994	+	8.95588i	−0.123409	+	0.379814i
$557$	−14.4884			−0.613894			−0.306947	−	0.951727i	$-0.599307\pi$
$557$	−14.4884			−0.613894			−0.306947	+	0.951727i	$0.599307\pi$
$558$		0			0
$559$	6.14318	−	4.46328i	0.259829	−	0.188777i
$560$	−1.85496	−	3.16788i	−0.0783862	−	0.133867i
$561$		0			0
$562$	−13.1422	+	9.54839i	−0.554372	+	0.402775i
$563$	−31.7433	+	23.0629i	−1.33782	+	0.971984i	−0.338300	+	0.941038i	$0.609852\pi$
$563$	−31.7433	+	23.0629i	−1.33782	+	0.971984i	−0.999521	+	0.0309456i	$0.990148\pi$
$564$		0			0
$565$	14.1425	+	24.1525i	0.594979	+	1.01610i
$566$	10.9586	−	7.96187i	0.460623	−	0.334662i
$567$		0			0
$568$	15.4332			0.647561
$569$	−7.49004	+	23.0520i	−0.313999	+	0.966389i	0.662166	+	0.749357i	$0.269637\pi$
$569$	−7.49004	+	23.0520i	−0.313999	+	0.966389i	−0.976165	+	0.217031i	$0.930363\pi$
$570$		0			0
$571$	−7.52079	−	23.1466i	−0.314735	−	0.968656i	−0.975863	−	0.218383i	$-0.929922\pi$
$571$	−7.52079	−	23.1466i	−0.314735	−	0.968656i	0.661128	−	0.750273i	$-0.270078\pi$
$572$	0.113108	+	0.348110i	0.00472928	+	0.0145552i
$573$		0			0
$574$	4.49554			0.187640
$575$	2.46488	+	2.67095i	0.102793	+	0.111386i
$576$		0			0
$577$	13.6665	+	9.92928i	0.568943	+	0.413361i	0.834721	−	0.550673i	$-0.185629\pi$
$577$	13.6665	+	9.92928i	0.568943	+	0.413361i	−0.265778	+	0.964034i	$0.585629\pi$
$578$	−2.25255	−	6.93264i	−0.0936938	−	0.288360i
$579$		0			0
$580$	−5.23437	−	8.93923i	−0.217345	−	0.371181i
$581$	1.47483	−	4.53905i	0.0611861	−	0.188311i
$582$		0			0
$583$	0.575248	−	1.77043i	0.0238244	−	0.0733238i
$584$	−5.40292	+	3.92545i	−0.223575	+	0.162436i
$585$		0			0
$586$	18.9276	+	13.7517i	0.781890	+	0.568077i
$587$	27.9308	−	20.2929i	1.15283	−	0.837577i	0.163972	−	0.986465i	$-0.447569\pi$
$587$	27.9308	−	20.2929i	1.15283	−	0.837577i	0.988854	+	0.148888i	$0.0475693\pi$
$588$		0			0
$589$	14.3561	+	10.4303i	0.591532	+	0.429773i
$590$	−1.91486	+	19.3592i	−0.0788335	+	0.797007i
$591$		0			0
$592$	−2.56094	+	7.88175i	−0.105254	+	0.323938i
$593$	2.75615			0.113181			0.0565907	−	0.998397i	$-0.481977\pi$
$593$	2.75615			0.113181			0.0565907	+	0.998397i	$0.481977\pi$
$594$		0			0
$595$	−16.5730	−	7.25738i	−0.679425	−	0.297524i
$596$	−4.65056	−	14.3129i	−0.190494	−	0.586281i
$597$		0			0
$598$	−0.748066	−	0.543502i	−0.0305907	−	0.0222255i
$599$	21.3977			0.874286			0.437143	−	0.899392i	$-0.355990\pi$
$599$	21.3977			0.874286			0.437143	+	0.899392i	$0.355990\pi$
$600$		0			0
$601$	17.1818			0.700860			0.350430	−	0.936589i	$-0.386036\pi$
$601$	17.1818			0.700860			0.350430	+	0.936589i	$0.386036\pi$
$602$	7.92843	+	5.76034i	0.323139	+	0.234774i
$603$		0			0
$604$	0.948562	+	2.91937i	0.0385964	+	0.118788i
$605$	23.8466	−	5.22170i	0.969502	−	0.212292i
$606$		0			0
$607$	−22.8963			−0.929332			−0.464666	−	0.885486i	$-0.653826\pi$
$607$	−22.8963			−0.929332			−0.464666	+	0.885486i	$0.653826\pi$
$608$	0.745417	−	2.29416i	0.0302306	−	0.0930403i
$609$		0			0
$610$	22.8308	−	4.99927i	0.924393	−	0.202415i
$611$	5.70355	+	4.14387i	0.230741	+	0.167643i
$612$		0			0
$613$	36.4310	−	26.4687i	1.47143	−	1.06906i	0.491239	−	0.871025i	$-0.336544\pi$
$613$	36.4310	−	26.4687i	1.47143	−	1.06906i	0.980195	−	0.198035i	$-0.0634560\pi$
$614$	−1.57228	−	1.14233i	−0.0634522	−	0.0461007i
$615$		0			0
$616$	−0.382175	+	0.277666i	−0.0153983	+	0.0111875i
$617$	−3.64878	+	11.2298i	−0.146894	+	0.452094i	−0.997250	−	0.0741144i	$-0.976387\pi$
$617$	−3.64878	+	11.2298i	−0.146894	+	0.452094i	0.850355	+	0.526209i	$0.176387\pi$
$618$		0			0
$619$	2.47764	−	7.62539i	0.0995848	−	0.306490i	−0.888837	−	0.458224i	$-0.848486\pi$
$619$	2.47764	−	7.62539i	0.0995848	−	0.306490i	0.988421	+	0.151734i	$0.0484857\pi$
$620$	−1.61913	+	16.3694i	−0.0650257	+	0.657410i
$621$		0			0
$622$	−2.99779	−	9.22625i	−0.120200	−	0.369939i
$623$	−20.3592	−	14.7918i	−0.815674	−	0.592622i
$624$		0			0
$625$	23.0810	+	9.60555i	0.923241	+	0.384222i
$626$	−5.00488			−0.200035
$627$		0			0
$628$	−4.82499	−	14.8498i	−0.192538	−	0.592571i
$629$	12.6214	+	38.8447i	0.503248	+	1.54884i
$630$		0			0
$631$	−14.7444	+	45.3785i	−0.586964	+	1.80649i	0.00427117	+	0.999991i	$0.498640\pi$
$631$	−14.7444	+	45.3785i	−0.586964	+	1.80649i	−0.591235	+	0.806499i	$0.701360\pi$
$632$	−9.65703			−0.384136
$633$		0			0
$634$	−7.13157	+	5.18139i	−0.283231	+	0.205779i
$635$	−30.2735	+	34.0393i	−1.20137	+	1.35081i
$636$		0			0
$637$	−4.43007	+	3.21864i	−0.175526	+	0.127527i
$638$	−1.07843	+	0.783527i	−0.0426955	+	0.0310201i
$639$		0			0
$640$	2.18431	−	0.478300i	0.0863426	−	0.0189065i
$641$	−6.95681	+	5.05442i	−0.274778	+	0.199638i	−0.716636	−	0.697447i	$-0.754319\pi$
$641$	−6.95681	+	5.05442i	−0.274778	+	0.199638i	0.441859	+	0.897085i	$0.354319\pi$
$642$		0			0
$643$	−30.8943			−1.21835			−0.609176	−	0.793035i	$-0.708500\pi$
$643$	−30.8943			−1.21835			−0.609176	+	0.793035i	$0.708500\pi$
$644$	0.368773	−	1.13497i	0.0145317	−	0.0447239i
$645$		0			0
$646$	−3.67373	−	11.3066i	−0.144541	−	0.444852i
$647$	14.5077	+	44.6503i	0.570358	+	1.75538i	0.651466	+	0.758677i	$0.274154\pi$
$647$	14.5077	+	44.6503i	0.570358	+	1.75538i	−0.0811081	+	0.996705i	$0.525846\pi$
$648$		0			0
$649$	2.50334			0.0982648
$650$	−6.23704	−	1.24603i	−0.244637	−	0.0488732i
$651$		0			0
$652$	7.16908	+	5.20864i	0.280763	+	0.203986i
$653$	11.9897	+	36.9004i	0.469192	+	1.44402i	0.853633	+	0.520875i	$0.174394\pi$
$653$	11.9897	+	36.9004i	0.469192	+	1.44402i	−0.384441	+	0.923150i	$0.625606\pi$
$654$		0			0
$655$	23.2825	+	10.1955i	0.909724	+	0.398373i
$656$	−0.846180	+	2.60428i	−0.0330378	+	0.101680i
$657$		0			0
$658$	−2.81167	+	8.65342i	−0.109610	+	0.337345i
$659$	39.8805	−	28.9749i	1.55352	−	1.12870i	0.612445	−	0.790513i	$-0.290186\pi$
$659$	39.8805	−	28.9749i	1.55352	−	1.12870i	0.941079	−	0.338188i	$-0.109814\pi$
$660$		0			0
$661$	2.16132	+	1.57029i	0.0840658	+	0.0610773i	0.629024	−	0.777386i	$-0.283455\pi$
$661$	2.16132	+	1.57029i	0.0840658	+	0.0610773i	−0.544959	+	0.838463i	$0.683455\pi$
$662$	−0.516504	+	0.375262i	−0.0200745	+	0.0145850i
$663$		0			0
$664$	2.35188	+	1.70874i	0.0912706	+	0.0663120i
$665$	−8.11163	−	3.55213i	−0.314556	−	0.137746i
$666$		0			0
$667$	1.04061	−	3.20268i	0.0402928	−	0.124008i
$668$	−17.5457			−0.678863
$669$		0			0
$670$	13.8509	+	23.6545i	0.535107	+	0.913852i
$671$	−0.929377	−	2.86033i	−0.0358782	−	0.110422i
$672$		0			0
$673$	7.04983	+	5.12200i	0.271751	+	0.197439i	0.715311	−	0.698806i	$-0.246285\pi$
$673$	7.04983	+	5.12200i	0.271751	+	0.197439i	−0.443560	+	0.896244i	$0.646285\pi$
$674$	−5.87972			−0.226478
$675$		0			0
$676$	−11.3819			−0.437764
$677$	−10.4655	−	7.60363i	−0.402222	−	0.292231i	0.368224	−	0.929737i	$-0.379966\pi$
$677$	−10.4655	−	7.60363i	−0.402222	−	0.292231i	−0.770445	+	0.637506i	$0.779966\pi$
$678$		0			0
$679$	0.920687	+	2.83358i	0.0353327	+	0.108743i
$680$	7.32369	−	8.23472i	0.280851	−	0.315787i
$681$		0			0
$682$	2.11673			0.0810536
$683$	−7.56254	+	23.2751i	−0.289373	+	0.890597i	0.695681	+	0.718351i	$0.255103\pi$
$683$	−7.56254	+	23.2751i	−0.289373	+	0.890597i	−0.985054	+	0.172247i	$0.944897\pi$
$684$		0			0
$685$	5.53735	+	9.45665i	0.211571	+	0.361320i
$686$	−15.0148	−	10.9089i	−0.573267	−	0.416503i
$687$		0			0
$688$	−4.82932	+	3.50871i	−0.184116	+	0.133768i
$689$	−6.65786	−	4.83722i	−0.253644	−	0.184283i
$690$		0			0
$691$	20.9259	−	15.2036i	0.796060	−	0.578371i	−0.113696	−	0.993516i	$-0.536269\pi$
$691$	20.9259	−	15.2036i	0.796060	−	0.578371i	0.909756	+	0.415144i	$0.136269\pi$
$692$	−5.34531	+	16.4512i	−0.203198	+	0.625380i
$693$		0			0
$694$	6.69935	−	20.6185i	0.254304	−	0.782667i
$695$	−13.9934	+	15.7341i	−0.530800	+	0.596829i
$696$		0			0
$697$	4.17034	+	12.8350i	0.157963	+	0.486160i
$698$	−0.957006	−	0.695305i	−0.0362232	−	0.0263177i
$699$		0			0
$700$	−0.958031	−	8.15254i	−0.0362102	−	0.308137i
$701$	2.50610			0.0946542			0.0473271	−	0.998879i	$-0.484930\pi$
$701$	2.50610			0.0946542			0.0473271	+	0.998879i	$0.484930\pi$
$702$		0			0
$703$	6.17754	+	19.0125i	0.232990	+	0.717070i
$704$	−0.0889172	−	0.273659i	−0.00335119	−	0.0103139i
$705$		0			0
$706$	−0.639222	+	1.96732i	−0.0240574	+	0.0740411i
$707$	2.23162			0.0839288
$708$		0			0
$709$	1.52309	−	1.10659i	0.0572009	−	0.0415589i	−0.558817	−	0.829291i	$-0.688745\pi$
$709$	1.52309	−	1.10659i	0.0572009	−	0.0415589i	0.616018	+	0.787732i	$0.288745\pi$
$710$	31.6115	+	13.8429i	1.18636	+	0.519513i
$711$		0			0
$712$	12.4011	−	9.00992i	0.464750	−	0.337661i
$713$	−4.32608	+	3.14308i	−0.162013	+	0.117709i
$714$		0			0
$715$	−0.0805619	+	0.814481i	−0.00301285	+	0.0304599i
$716$	−3.20472	+	2.32837i	−0.119766	+	0.0870151i
$717$		0			0
$718$	36.5909			1.36556
$719$	−8.94181	+	27.5201i	−0.333473	+	1.02632i	0.633996	+	0.773336i	$0.281414\pi$
$719$	−8.94181	+	27.5201i	−0.333473	+	1.02632i	−0.967469	+	0.252989i	$0.918586\pi$
$720$		0			0
$721$	9.08654	+	27.9655i	0.338400	+	1.04149i
$722$	4.07321	+	12.5361i	0.151589	+	0.466544i
$723$		0			0
$724$	5.22902			0.194335
$725$	−2.70340	−	23.0051i	−0.100402	−	0.854388i
$726$		0			0
$727$	−7.04183	−	5.11619i	−0.261167	−	0.189749i	0.449494	−	0.893283i	$-0.351604\pi$
$727$	−7.04183	−	5.11619i	−0.261167	−	0.189749i	−0.710661	+	0.703534i	$0.751604\pi$
$728$	0.645343	+	1.98616i	0.0239180	+	0.0736120i
$729$		0			0
$730$	−14.5877	+	3.19427i	−0.539914	+	0.118225i
$731$	−9.09116	+	27.9797i	−0.336249	+	1.03487i
$732$		0			0
$733$	−6.34806	+	19.5373i	−0.234471	+	0.721627i	0.762720	+	0.646729i	$0.223863\pi$
$733$	−6.34806	+	19.5373i	−0.234471	+	0.721627i	−0.997191	+	0.0748988i	$0.976137\pi$
$734$	−6.15902	+	4.47479i	−0.227334	+	0.165168i
$735$		0			0
$736$	0.588076	+	0.427262i	0.0216768	+	0.0157491i
$737$	2.85368	−	2.07332i	0.105117	−	0.0763718i
$738$		0			0
$739$	−30.9932	−	22.5179i	−1.14010	−	0.828333i	−0.152969	−	0.988231i	$-0.548884\pi$
$739$	−30.9932	−	22.5179i	−1.14010	−	0.828333i	−0.987134	+	0.159898i	$0.948884\pi$
$740$	−12.3151	+	13.8470i	−0.452712	+	0.509027i
$741$		0			0
$742$	3.28211	−	10.1013i	0.120490	−	0.370830i
$743$	−5.03337			−0.184657			−0.0923283	−	0.995729i	$-0.529431\pi$
$743$	−5.03337			−0.184657			−0.0923283	+	0.995729i	$0.529431\pi$
$744$		0			0
$745$	3.31240	−	33.4883i	0.121357	−	1.22692i
$746$	−3.14225	−	9.67086i	−0.115046	−	0.354075i
$747$		0			0
$748$	−1.14728	−	0.833548i	−0.0419487	−	0.0304775i
$749$	−10.3900			−0.379644
$750$		0			0
$751$	−41.7544			−1.52364			−0.761820	−	0.647789i	$-0.775694\pi$
$751$	−41.7544			−1.52364			−0.761820	+	0.647789i	$0.775694\pi$
$752$	−4.48371	−	3.25761i	−0.163504	−	0.118793i
$753$		0			0
$754$	1.82105	+	5.60461i	0.0663187	+	0.204108i
$755$	−0.675621	+	6.83052i	−0.0245884	+	0.248588i
$756$		0			0
$757$	42.0525			1.52843			0.764213	−	0.644964i	$-0.223128\pi$
$757$	42.0525			1.52843			0.764213	+	0.644964i	$0.223128\pi$
$758$	10.9182	−	33.6026i	0.396565	−	1.22050i
$759$		0			0
$760$	3.58458	−	4.03048i	0.130026	−	0.146201i
$761$	30.9063	+	22.4548i	1.12035	+	0.813984i	0.984263	−	0.176712i	$-0.0565462\pi$
$761$	30.9063	+	22.4548i	1.12035	+	0.813984i	0.136090	+	0.990696i	$0.456546\pi$
$762$		0			0
$763$	−10.9298	+	7.94097i	−0.395686	+	0.287482i
$764$	−9.68041	−	7.03323i	−0.350225	−	0.254453i
$765$		0			0
$766$	8.94869	−	6.50161i	0.323329	−	0.234913i
$767$	3.41985	−	10.5252i	0.123484	−	0.380043i
$768$		0			0
$769$	−10.2945	+	31.6832i	−0.371229	+	1.14253i	0.574758	+	0.818323i	$0.305096\pi$
$769$	−10.2945	+	31.6832i	−0.371229	+	1.14253i	−0.945988	+	0.324203i	$0.894904\pi$
$770$	−1.03186	+	0.225946i	−0.0371855	+	0.00814253i
$771$		0			0
$772$	−4.31553	−	13.2818i	−0.155319	−	0.478024i
$773$	3.70547	+	2.69218i	0.133277	+	0.0968311i	0.652426	−	0.757852i	$-0.273751\pi$
$773$	3.70547	+	2.69218i	0.133277	+	0.0968311i	−0.519150	+	0.854683i	$0.673751\pi$
$774$		0			0
$775$	−17.9990	+	32.0769i	−0.646544	+	1.15224i
$776$	−1.81480			−0.0651475
$777$		0			0
$778$	−10.5595	−	32.4987i	−0.378576	−	1.16514i
$779$	2.04117	+	6.28208i	0.0731326	+	0.225079i
$780$		0			0
$781$	1.37227	−	4.22342i	0.0491038	−	0.151126i
$782$	3.58248			0.128109
$783$		0			0
$784$	3.48260	−	2.53026i	0.124379	−	0.0903663i
$785$	3.43663	−	34.7444i	0.122659	−	1.24008i
$786$		0			0
$787$	−12.1753	+	8.84587i	−0.434002	+	0.315321i	−0.783247	−	0.621710i	$-0.786438\pi$
$787$	−12.1753	+	8.84587i	−0.434002	+	0.315321i	0.349245	+	0.937032i	$0.386438\pi$
$788$	11.1224	−	8.08087i	0.396218	−	0.287869i
$789$		0			0
$790$	−19.7804	−	8.66192i	−0.703754	−	0.308177i
$791$	16.6246	−	12.0785i	0.591104	−	0.429462i
$792$		0			0
$793$	−13.2958			−0.472146
$794$	−5.60979	+	17.2652i	−0.199084	+	0.612718i
$795$		0			0
$796$	−4.03459	−	12.4172i	−0.143002	−	0.440116i
$797$	−8.77965	−	27.0210i	−0.310991	−	0.957132i	−0.977373	−	0.211522i	$-0.932158\pi$
$797$	−8.77965	−	27.0210i	−0.310991	−	0.957132i	0.666382	−	0.745610i	$-0.267842\pi$
$798$		0			0
$799$	−27.3142			−0.966308
$800$	4.90311	+	0.979536i	0.173351	+	0.0346318i
$801$		0			0
$802$	2.17240	+	1.57834i	0.0767102	+	0.0557332i
$803$	0.593823	+	1.82760i	0.0209555	+	0.0644945i
$804$		0			0
$805$	1.77336	−	1.99396i	0.0625029	−	0.0702779i
$806$	2.89168	−	8.89969i	0.101855	−	0.313478i
$807$		0			0
$808$	−0.420051	+	1.29278i	−0.0147773	+	0.0454800i
$809$	25.1848	−	18.2978i	0.885449	−	0.643317i	−0.0492382	−	0.998787i	$-0.515679\pi$
$809$	25.1848	−	18.2978i	0.885449	−	0.643317i	0.934688	+	0.355470i	$0.115679\pi$
$810$		0			0
$811$	3.32933	+	2.41890i	0.116909	+	0.0849390i	0.644703	−	0.764433i	$-0.276981\pi$
$811$	3.32933	+	2.41890i	0.116909	+	0.0849390i	−0.527795	+	0.849372i	$0.676981\pi$
$812$	−6.15305	+	4.47046i	−0.215930	+	0.156882i
$813$		0			0
$814$	1.92920	+	1.40165i	0.0676184	+	0.0491277i
$815$	10.0124	+	17.0991i	0.350719	+	0.598956i
$816$		0			0
$817$	−4.44967	+	13.6947i	−0.155674	+	0.479116i
$818$	33.2664			1.16313
$819$		0			0
$820$	−4.06914	+	4.57531i	−0.142100	+	0.159777i
$821$	6.29922	+	19.3870i	0.219844	+	0.676611i	0.998774	+	0.0494998i	$0.0157627\pi$
$821$	6.29922	+	19.3870i	0.219844	+	0.676611i	−0.778930	+	0.627111i	$0.784237\pi$
$822$		0			0
$823$	−5.60716	−	4.07384i	−0.195453	−	0.142005i	0.485754	−	0.874095i	$-0.338545\pi$
$823$	−5.60716	−	4.07384i	−0.195453	−	0.142005i	−0.681208	+	0.732090i	$0.738545\pi$
$824$	−17.9108			−0.623952
$825$		0			0
$826$	14.2830			0.496968
$827$	1.96999	+	1.43128i	0.0685032	+	0.0497705i	0.621510	−	0.783406i	$-0.286520\pi$
$827$	1.96999	+	1.43128i	0.0685032	+	0.0497705i	−0.553007	+	0.833177i	$0.686520\pi$
$828$		0			0
$829$	−3.46417	−	10.6616i	−0.120316	−	0.370293i	0.872703	−	0.488251i	$-0.162365\pi$
$829$	−3.46417	−	10.6616i	−0.120316	−	0.370293i	−0.993019	+	0.117958i	$0.962365\pi$
$830$	3.28466	+	5.60952i	0.114012	+	0.194709i
$831$		0			0
$832$	−1.27206			−0.0441007
$833$	6.55597	−	20.1772i	0.227151	−	0.699099i
$834$		0			0
$835$	−35.9385	−	15.7377i	−1.24370	−	0.544625i
$836$	−0.561536	−	0.407980i	−0.0194211	−	0.0141103i
$837$		0			0
$838$	9.71007	−	7.05478i	0.335429	−	0.243703i
$839$	−23.2407	−	16.8854i	−0.802359	−	0.582948i	0.109246	−	0.994015i	$-0.465156\pi$
$839$	−23.2407	−	16.8854i	−0.802359	−	0.582948i	−0.911605	+	0.411067i	$0.865156\pi$
$840$		0			0
$841$	6.09861	−	4.43090i	0.210297	−	0.152790i
$842$	−7.31823	+	22.5232i	−0.252203	+	0.776201i
$843$		0			0
$844$	2.50053	−	7.69583i	0.0860717	−	0.264901i
$845$	−23.3133	−	10.2090i	−0.802002	−	0.351201i
$846$		0			0
$847$	−5.53853	−	17.0459i	−0.190306	−	0.585703i
$848$	5.23392	+	3.80267i	0.179734	+	0.130584i
$849$		0			0
$850$	22.3872	−	10.2980i	0.767874	−	0.353219i
$851$	−6.02410			−0.206503
$852$		0			0
$853$	6.31242	+	19.4276i	0.216133	+	0.665190i	0.999071	+	0.0430898i	$0.0137202\pi$
$853$	6.31242	+	19.4276i	0.216133	+	0.665190i	−0.782938	+	0.622100i	$0.786280\pi$
$854$	−5.30261	−	16.3198i	−0.181452	−	0.558450i
$855$		0			0
$856$	1.95568	−	6.01898i	0.0668439	−	0.205724i
$857$	−14.6791			−0.501427			−0.250714	−	0.968061i	$-0.580665\pi$
$857$	−14.6791			−0.501427			−0.250714	+	0.968061i	$0.580665\pi$
$858$		0			0
$859$	−18.4207	+	13.3834i	−0.628506	+	0.456637i	−0.855882	−	0.517170i	$-0.826985\pi$
$859$	−18.4207	+	13.3834i	−0.628506	+	0.456637i	0.227376	+	0.973807i	$0.426985\pi$
$860$	−13.0390	+	2.85515i	−0.444626	+	0.0973598i
$861$		0			0
$862$	23.0948	−	16.7794i	0.786614	−	0.571508i
$863$	1.33585	−	0.970550i	0.0454728	−	0.0330379i	−0.564817	−	0.825216i	$-0.691053\pi$
$863$	1.33585	−	0.970550i	0.0454728	−	0.0330379i	0.610289	+	0.792178i	$0.291053\pi$
$864$		0			0
$865$	−25.7047	+	28.9022i	−0.873986	+	0.982704i
$866$	26.8387	−	19.4994i	0.912015	−	0.662617i
$867$		0			0
$868$	12.0771			0.409923
$869$	−0.858676	+	2.64273i	−0.0291286	+	0.0896486i
$870$		0			0
$871$	−4.81875	−	14.8306i	−0.163277	−	0.502515i
$872$	−2.54294	−	7.82637i	−0.0861149	−	0.265034i
$873$		0			0
$874$	1.75345			0.0593112
$875$	5.35014	−	17.5580i	0.180868	−	0.593570i
$876$		0			0
$877$	−35.4144	−	25.7301i	−1.19586	−	0.868844i	−0.201990	−	0.979388i	$-0.564741\pi$
$877$	−35.4144	−	25.7301i	−1.19586	−	0.868844i	−0.993871	+	0.110544i	$0.964741\pi$
$878$	5.71079	+	17.5760i	0.192730	+	0.593162i
$879$		0			0
$880$	0.0633320	−	0.640286i	0.00213492	−	0.0215840i
$881$	−9.65827	+	29.7251i	−0.325396	+	1.00146i	0.645866	+	0.763451i	$0.276496\pi$
$881$	−9.65827	+	29.7251i	−0.325396	+	1.00146i	−0.971262	+	0.238014i	$0.923504\pi$
$882$		0			0
$883$	14.0459	−	43.2290i	0.472684	−	1.45477i	−0.376372	−	0.926468i	$-0.622829\pi$
$883$	14.0459	−	43.2290i	0.472684	−	1.45477i	0.849056	−	0.528303i	$-0.177171\pi$
$884$	−5.07193	+	3.68497i	−0.170587	+	0.123939i
$885$		0			0
$886$	−15.1806	−	11.0293i	−0.510001	−	0.370537i
$887$	19.5953	−	14.2368i	0.657945	−	0.478025i	−0.208024	−	0.978124i	$-0.566703\pi$
$887$	19.5953	−	14.2368i	0.657945	−	0.478025i	0.865968	+	0.500099i	$0.166703\pi$
$888$		0			0
$889$	27.0582	+	19.6590i	0.907504	+	0.659340i
$890$	33.4824	−	7.33166i	1.12233	−	0.245758i
$891$		0			0
$892$	−1.57250	+	4.83965i	−0.0526511	+	0.162043i
$893$	−13.3689			−0.447375
$894$		0			0
$895$	−8.65262	+	1.89467i	−0.289225	+	0.0633318i
$896$	−0.507322	−	1.56138i	−0.0169484	−	0.0521619i
$897$		0			0
$898$	−3.50678	−	2.54782i	−0.117023	−	0.0850220i
$899$	34.0795			1.13662
$900$		0			0
$901$	31.8844			1.06222
$902$	0.637443	+	0.463130i	0.0212245	+	0.0154205i
$903$		0			0
$904$	3.86790	+	11.9042i	0.128645	+	0.395927i
$905$	10.7105	+	4.69020i	0.356030	+	0.155907i
$906$		0			0
$907$	48.7013			1.61710			0.808550	−	0.588428i	$-0.200253\pi$
$907$	48.7013			1.61710			0.808550	+	0.588428i	$0.200253\pi$
$908$	−7.65949	+	23.5735i	−0.254189	+	0.782313i
$909$		0			0
$910$	−0.459651	+	4.64707i	−0.0152373	+	0.154049i
$911$	−43.4094	−	31.5388i	−1.43822	−	1.04493i	−0.988411	−	0.151802i	$-0.951493\pi$
$911$	−43.4094	−	31.5388i	−1.43822	−	1.04493i	−0.449808	−	0.893125i	$-0.648507\pi$
$912$		0			0
$913$	0.676734	−	0.491676i	0.0223966	−	0.0162721i
$914$	−22.4067	−	16.2794i	−0.741147	−	0.538475i
$915$		0			0
$916$	1.19660	−	0.869377i	0.0395366	−	0.0287250i
$917$	5.76665	−	17.7479i	0.190431	−	0.586088i
$918$		0			0
$919$	−12.3715	+	38.0755i	−0.408097	+	1.25599i	0.510184	+	0.860065i	$0.329577\pi$
$919$	−12.3715	+	38.0755i	−0.408097	+	1.25599i	−0.918281	+	0.395929i	$0.870423\pi$
$920$	0.821312	+	1.40263i	0.0270778	+	0.0462434i
$921$		0			0
$922$	−3.55521	−	10.9418i	−0.117085	−	0.360349i
$923$	−15.8825	−	11.5393i	−0.522780	−	0.379822i
$924$		0			0
$925$	−37.6450	+	17.3166i	−1.23776	+	0.569366i
$926$	−1.16237			−0.0381978
$927$		0			0
$928$	−1.43158	−	4.40594i	−0.0469938	−	0.144632i
$929$	−0.00519461	−	0.0159874i	−0.000170430	−	0.000524528i	0.950971	−	0.309279i	$-0.100088\pi$
$929$	−0.00519461	−	0.0159874i	−0.000170430	−	0.000524528i	−0.951142	+	0.308755i	$0.900088\pi$
$930$		0			0
$931$	3.20882	−	9.87573i	0.105165	−	0.323664i
$932$	−0.697178			−0.0228368
$933$		0			0
$934$	−17.5140	+	12.7247i	−0.573077	+	0.416365i
$935$	−1.60230	−	2.73640i	−0.0524009	−	0.0894899i
$936$		0			0
$937$	44.0518	−	32.0055i	1.43911	−	1.04557i	0.450881	−	0.892584i	$-0.351110\pi$
$937$	44.0518	−	32.0055i	1.43911	−	1.04557i	0.988228	−	0.152990i	$-0.0488902\pi$
$938$	16.2819	−	11.8295i	0.531621	−	0.386246i
$939$		0			0
$940$	−6.26200	−	10.6942i	−0.204244	−	0.348806i
$941$	−15.3671	+	11.1649i	−0.500954	+	0.363964i	−0.809381	−	0.587284i	$-0.800197\pi$
$941$	−15.3671	+	11.1649i	−0.500954	+	0.363964i	0.308427	+	0.951248i	$0.400197\pi$
$942$		0			0
$943$	−1.99047			−0.0648187
$944$	−2.68844	+	8.27415i	−0.0875011	+	0.269301i
$945$		0			0
$946$	0.530779	+	1.63357i	0.0172571	+	0.0531120i
$947$	−15.8661	−	48.8308i	−0.515578	−	1.58679i	−0.782227	−	0.622994i	$-0.785916\pi$
$947$	−15.8661	−	48.8308i	−0.515578	−	1.58679i	0.266648	−	0.963794i	$-0.414084\pi$
$948$		0			0
$949$	8.49529			0.275769
$950$	10.9574	−	5.04037i	0.355505	−	0.163531i
$951$		0			0
$952$	−6.54587	−	4.75585i	−0.212153	−	0.154138i
$953$	0.235824	+	0.725791i	0.00763908	+	0.0235107i	0.954803	−	0.297238i	$-0.0960655\pi$
$953$	0.235824	+	0.725791i	0.00763908	+	0.0235107i	−0.947164	+	0.320749i	$0.896065\pi$
$954$		0			0
$955$	−13.5197	−	23.0889i	−0.437489	−	0.747141i
$956$	9.01959	−	27.7595i	0.291715	−	0.897805i
$957$		0			0
$958$	−7.53007	+	23.1752i	−0.243286	+	0.748756i
$959$	6.50920	−	4.72921i	0.210193	−	0.152714i
$960$		0			0
$961$	−18.7009	−	13.5870i	−0.603256	−	0.438291i
$962$	8.52867	−	6.19644i	0.274975	−	0.199781i
$963$		0			0
$964$	−14.0170	−	10.1840i	−0.451458	−	0.328003i
$965$	3.07377	−	31.0759i	0.0989483	−	1.00037i
$966$		0			0
$967$	−9.05202	+	27.8593i	−0.291093	+	0.895893i	0.693412	+	0.720541i	$0.256106\pi$
$967$	−9.05202	+	27.8593i	−0.291093	+	0.895893i	−0.984506	+	0.175352i	$0.943894\pi$
$968$	10.9172			0.350892
$969$		0			0
$970$	−3.71723	−	1.62779i	−0.119353	−	0.0522653i
$971$	2.22232	+	6.83961i	0.0713177	+	0.219493i	0.980362	−	0.197206i	$-0.0631868\pi$
$971$	2.22232	+	6.83961i	0.0713177	+	0.219493i	−0.909044	+	0.416699i	$0.863187\pi$
$972$		0			0
$973$	12.5072	+	9.08703i	0.400963	+	0.291317i
$974$	−23.8804			−0.765179
$975$		0			0
$976$	10.4522			0.334566
$977$	−30.6811	−	22.2911i	−0.981576	−	0.713157i	−0.0235158	−	0.999723i	$-0.507486\pi$
$977$	−30.6811	−	22.2911i	−0.981576	−	0.713157i	−0.958060	+	0.286567i	$0.907486\pi$
$978$		0			0
$979$	−1.36297	−	4.19480i	−0.0435608	−	0.134066i
$980$	9.40289	−	2.05895i	0.300364	−	0.0657709i
$981$		0			0
$982$	27.5634			0.879584
$983$	−4.92956	+	15.1716i	−0.157228	+	0.483899i	−0.998380	−	0.0569002i	$-0.981878\pi$
$983$	−4.92956	+	15.1716i	−0.157228	+	0.483899i	0.841151	+	0.540800i	$0.181878\pi$
$984$		0			0
$985$	30.0299	−	6.57566i	0.956833	−	0.209518i
$986$	−18.4713	−	13.4202i	−0.588247	−	0.427386i
$987$		0			0
$988$	−2.48246	+	1.80361i	−0.0789774	+	0.0573805i
$989$	−3.51044	−	2.55048i	−0.111626	−	0.0811007i
$990$		0			0
$991$	4.72420	−	3.43233i	0.150069	−	0.109032i	−0.510217	−	0.860046i	$-0.670435\pi$
$991$	4.72420	−	3.43233i	0.150069	−	0.109032i	0.660286	+	0.751014i	$0.270435\pi$
$992$	−2.27323	+	6.99629i	−0.0721752	+	0.222132i
$993$		0			0
$994$	7.82958	−	24.0970i	0.248339	−	0.764309i
$995$	2.87367	−	29.0528i	0.0911015	−	0.921036i
$996$		0			0
$997$	2.89258	+	8.90245i	0.0916090	+	0.281944i	0.986355	−	0.164632i	$-0.0526435\pi$
$997$	2.89258	+	8.90245i	0.0916090	+	0.281944i	−0.894746	+	0.446575i	$0.852644\pi$
$998$	10.2995	+	7.48300i	0.326024	+	0.236870i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.h.g.91.2	yes	12
3.2	odd	2		450.2.h.f.91.2	✓	12
25.11	even	5	inner	450.2.h.g.361.2	yes	12
75.11	odd	10		450.2.h.f.361.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.h.f.91.2	✓	12	3.2	odd	2
450.2.h.f.361.2	yes	12	75.11	odd	10
450.2.h.g.91.2	yes	12	1.1	even	1	trivial
450.2.h.g.361.2	yes	12	25.11	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.220100 + 2.22521i) q^{5} +1.64173 q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-0.220100 + 2.22521i) q^{5} +1.64173 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-1.48601 + 1.67086i) q^{10} +(0.232788 + 0.169130i) q^{11} +(1.02912 - 0.747697i) q^{13} +(1.32819 + 0.964983i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-1.52297 + 4.68721i) q^{17} +(-0.745417 + 2.29416i) q^{19} +(-2.18431 + 0.478300i) q^{20} +(0.0889172 + 0.273659i) q^{22} +(-0.588076 - 0.427262i) q^{23} +(-4.90311 - 0.979536i) q^{25} +1.27206 q^{26} +(0.507322 + 1.56138i) q^{28} +(1.43158 + 4.40594i) q^{29} +(2.27323 - 6.99629i) q^{31} -1.00000 q^{32} +(-3.98718 + 2.89686i) q^{34} +(-0.361344 + 3.65319i) q^{35} +(6.70462 - 4.87119i) q^{37} +(-1.95153 + 1.41787i) q^{38} +(-2.04829 - 0.896955i) q^{40} +(2.21533 - 1.60953i) q^{41} +5.96937 q^{43} +(-0.0889172 + 0.273659i) q^{44} +(-0.224625 - 0.691324i) q^{46} +(1.71263 + 5.27092i) q^{47} -4.30473 q^{49} +(-3.39094 - 3.67444i) q^{50} +(1.02912 + 0.747697i) q^{52} +(-1.99918 - 6.15285i) q^{53} +(-0.427587 + 0.480777i) q^{55} +(-0.507322 + 1.56138i) q^{56} +(-1.43158 + 4.40594i) q^{58} +(7.03842 - 5.11371i) q^{59} +(-8.45598 - 6.14363i) q^{61} +(5.95140 - 4.32394i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(1.43727 + 2.45457i) q^{65} +(3.78815 - 11.6587i) q^{67} -4.92843 q^{68} +(-2.43962 + 2.74310i) q^{70} +(-4.76911 - 14.6778i) q^{71} +(5.40292 + 3.92545i) q^{73} +8.28736 q^{74} -2.41222 q^{76} +(0.382175 + 0.277666i) q^{77} +(2.98419 + 9.18438i) q^{79} +(-1.12988 - 1.92960i) q^{80} +2.73830 q^{82} +(0.898338 - 2.76480i) q^{83} +(-10.0948 - 4.42058i) q^{85} +(4.82932 + 3.50871i) q^{86} +(-0.232788 + 0.169130i) q^{88} +(-12.4011 - 9.00992i) q^{89} +(1.68953 - 1.22751i) q^{91} +(0.224625 - 0.691324i) q^{92} +(-1.71263 + 5.27092i) q^{94} +(-4.94091 - 2.16365i) q^{95} +(0.560804 + 1.72598i) q^{97} +(-3.48260 - 2.53026i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 - q^5 - 2 * q^7 + 3 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} - q^{5} - 2 q^{7} + 3 q^{8} + q^{10} - q^{11} + 4 q^{13} - 8 q^{14} - 3 q^{16} + 8 q^{17} - 8 q^{19} - q^{20} - 4 q^{22} - 11 q^{25} + 16 q^{26} - 7 q^{28} + 6 q^{29} - 3 q^{31} - 12 q^{32} + 2 q^{34} + 18 q^{35} - 8 q^{37} - 2 q^{38} + q^{40} - 20 q^{41} + 32 q^{43} + 4 q^{44} - 10 q^{46} + 34 q^{49} - 9 q^{50} + 4 q^{52} - 2 q^{53} + 44 q^{55} + 7 q^{56} - 6 q^{58} + 19 q^{59} - 26 q^{61} - 2 q^{62} - 3 q^{64} - 16 q^{65} - 16 q^{67} - 12 q^{68} - 23 q^{70} - 48 q^{71} - 30 q^{73} + 8 q^{74} + 12 q^{76} + 39 q^{77} - 18 q^{79} + 4 q^{80} - 40 q^{82} + 29 q^{83} - 4 q^{85} - 12 q^{86} + q^{88} - 62 q^{89} - 26 q^{91} + 10 q^{92} - 6 q^{95} + 23 q^{97} + 6 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 - q^5 - 2 * q^7 + 3 * q^8 + q^10 - q^11 + 4 * q^13 - 8 * q^14 - 3 * q^16 + 8 * q^17 - 8 * q^19 - q^20 - 4 * q^22 - 11 * q^25 + 16 * q^26 - 7 * q^28 + 6 * q^29 - 3 * q^31 - 12 * q^32 + 2 * q^34 + 18 * q^35 - 8 * q^37 - 2 * q^38 + q^40 - 20 * q^41 + 32 * q^43 + 4 * q^44 - 10 * q^46 + 34 * q^49 - 9 * q^50 + 4 * q^52 - 2 * q^53 + 44 * q^55 + 7 * q^56 - 6 * q^58 + 19 * q^59 - 26 * q^61 - 2 * q^62 - 3 * q^64 - 16 * q^65 - 16 * q^67 - 12 * q^68 - 23 * q^70 - 48 * q^71 - 30 * q^73 + 8 * q^74 + 12 * q^76 + 39 * q^77 - 18 * q^79 + 4 * q^80 - 40 * q^82 + 29 * q^83 - 4 * q^85 - 12 * q^86 + q^88 - 62 * q^89 - 26 * q^91 + 10 * q^92 - 6 * q^95 + 23 * q^97 + 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more