LMFDB - Embedded newform 645.2.bn.b.491.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [645,2,Mod(26,645)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("645.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(645, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([21, 0, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 645 = 3 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	645.bn (of order $42$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [348,0,0,-56,29] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.15035093037$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			491.22
Character	$\chi$	$=$	645.491
Dual form			645.2.bn.b.356.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.38802 + 0.668438i) q^{2} +(1.12387 + 1.31792i) q^{3} +(0.232825 + 0.291953i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(0.679017 + 2.58054i) q^{6} +(1.44966 + 0.836959i) q^{7} +(-0.557614 - 2.44306i) q^{8} +(-0.473820 + 2.96235i) q^{9} +(-1.47215 + 0.454097i) q^{10} +(4.56741 + 3.64239i) q^{11} +(-0.123105 + 0.634962i) q^{12} +(0.430596 + 0.132821i) q^{13} +(1.45270 + 2.13072i) q^{14} +(-1.72027 - 0.201675i) q^{15} +(1.02524 - 4.49188i) q^{16} +(-1.38096 + 1.48832i) q^{17} +(-2.63782 + 3.79509i) q^{18} +(-5.29367 - 2.07761i) q^{19} +(-0.369251 - 0.0556556i) q^{20} +(0.526184 + 2.85116i) q^{21} +(3.90497 + 8.10875i) q^{22} +(-0.0998868 + 0.662706i) q^{23} +(2.59307 - 3.48058i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(0.508895 + 0.472186i) q^{26} +(-4.43664 + 2.70484i) q^{27} +(0.0931629 + 0.618096i) q^{28} +(4.06967 - 2.77465i) q^{29} +(-2.25297 - 1.42982i) q^{30} +(0.0537718 + 0.717535i) q^{31} +(1.30081 - 1.63116i) q^{32} +(0.332817 + 10.1130i) q^{33} +(-2.91165 + 1.14274i) q^{34} +(-1.63195 + 0.372482i) q^{35} +(-0.975183 + 0.551374i) q^{36} +(-1.07219 + 0.619028i) q^{37} +(-5.95899 - 6.42227i) q^{38} +(0.308888 + 0.716765i) q^{39} +(2.07047 + 1.41162i) q^{40} +(0.260977 - 0.541924i) q^{41} +(-1.17547 + 4.30921i) q^{42} +(1.63737 + 6.34973i) q^{43} +2.18150i q^{44} +(-1.66757 - 2.49383i) q^{45} +(-0.581623 + 0.853084i) q^{46} +(9.84801 - 7.85353i) q^{47} +(7.07218 - 3.69712i) q^{48} +(-2.09900 - 3.63557i) q^{49} +(0.770296 - 1.33419i) q^{50} +(-3.51351 - 0.147309i) q^{51} +(0.0614758 + 0.156638i) q^{52} +(-3.43201 - 11.1263i) q^{53} +(-7.96619 + 0.788772i) q^{54} +(-5.82560 + 0.436568i) q^{55} +(1.23640 - 4.00830i) q^{56} +(-3.21129 - 9.31160i) q^{57} +(7.50348 - 1.13097i) q^{58} +(1.52445 + 0.347946i) q^{59} +(-0.341642 - 0.549193i) q^{60} +(-6.25924 - 0.469065i) q^{61} +(-0.404991 + 1.03190i) q^{62} +(-3.16624 + 3.89781i) q^{63} +(-5.40636 + 2.60357i) q^{64} +(-0.405991 + 0.195515i) q^{65} +(-6.29798 + 14.2596i) q^{66} +(5.63190 - 14.3498i) q^{67} +(-0.756041 - 0.0566574i) q^{68} +(-0.985652 + 0.613154i) q^{69} +(-2.51417 - 0.573842i) q^{70} +(8.78026 - 1.32341i) q^{71} +(7.50141 - 0.494273i) q^{72} +(-1.45189 + 4.70690i) q^{73} +(-1.90200 + 0.142536i) q^{74} +(1.39822 - 1.02224i) q^{75} +(-0.625932 - 2.02922i) q^{76} +(3.57264 + 9.10293i) q^{77} +(-0.0503689 + 1.20136i) q^{78} +(1.41284 - 2.44710i) q^{79} +(2.30370 + 3.99013i) q^{80} +(-8.55099 - 2.80724i) q^{81} +(0.724484 - 0.577757i) q^{82} +(6.70685 - 9.83714i) q^{83} +(-0.709897 + 0.817442i) q^{84} -2.03031i q^{85} +(-1.97169 + 9.90806i) q^{86} +(8.23055 + 2.24513i) q^{87} +(6.35173 - 13.1895i) q^{88} +(-10.3970 - 7.08855i) q^{89} +(-0.647661 - 4.57617i) q^{90} +(0.513050 + 0.552936i) q^{91} +(-0.216735 + 0.125132i) q^{92} +(-0.885220 + 0.877285i) q^{93} +(18.9189 - 4.31811i) q^{94} +(5.29367 - 2.07761i) q^{95} +(3.61168 - 0.118859i) q^{96} +(-3.15513 + 3.95641i) q^{97} +(-0.483310 - 6.44932i) q^{98} +(-12.9541 + 11.8044i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q - 56 q^{4} + 29 q^{5} - 4 q^{6} - 3 q^{7} - 8 q^{9} - 7 q^{12} + 5 q^{13} - 42 q^{14} - 7 q^{15} - 68 q^{16} - 22 q^{18} - 30 q^{19} + 28 q^{20} + 4 q^{21} - 42 q^{22} + 6 q^{23} + 9 q^{24} + 29 q^{25}+ \cdots - q^{99}+O(q^{100}) $ 348 * q - 56 * q^4 + 29 * q^5 - 4 * q^6 - 3 * q^7 - 8 * q^9 - 7 * q^12 + 5 * q^13 - 42 * q^14 - 7 * q^15 - 68 * q^16 - 22 * q^18 - 30 * q^19 + 28 * q^20 + 4 * q^21 - 42 * q^22 + 6 * q^23 + 9 * q^24 + 29 * q^25 + 182 * q^26 + 6 * q^27 + 18 * q^28 + 2 * q^29 + 2 * q^30 + 72 * q^31 - 23 * q^33 - 84 * q^34 - 21 * q^35 + 56 * q^36 - 39 * q^37 - 4 * q^39 - 84 * q^42 + 6 * q^43 + 4 * q^45 - 94 * q^46 - 28 * q^47 - 72 * q^48 + 175 * q^49 + 103 * q^51 - 56 * q^52 + 94 * q^53 + 22 * q^54 - 90 * q^56 + 74 * q^57 - 40 * q^58 - 7 * q^60 + 30 * q^61 - 104 * q^62 + q^63 - 76 * q^64 - 10 * q^65 - 22 * q^66 + 9 * q^67 + 98 * q^68 - 244 * q^69 - 8 * q^71 + 85 * q^72 - 75 * q^73 - 42 * q^74 - 14 * q^75 + 30 * q^76 - 16 * q^77 + 44 * q^78 + 20 * q^79 - 148 * q^80 - 136 * q^81 - 30 * q^83 - 124 * q^84 + 38 * q^86 + 42 * q^87 + 42 * q^88 - 102 * q^89 - 82 * q^90 - 13 * q^91 + 24 * q^92 - 167 * q^93 - 56 * q^94 + 30 * q^95 - 494 * q^96 - 64 * q^97 - 12 * q^98 - q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/645\mathbb{Z}\right)^\times$.

$n$	$46$	$431$	$517$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$-1$	$1$

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 $

$2$	1.38802	+	0.668438i	0.981482	+	0.472657i	0.854615	−	0.519263i	$-0.173793\pi$
$2$	1.38802	+	0.668438i	0.981482	+	0.472657i	0.126867	+	0.991920i	$0.459508\pi$
$3$	1.12387	+	1.31792i	0.648868	+	0.760901i
$3$	1.12387	+	1.31792i	0.648868	+	0.760901i
$4$	0.232825	+	0.291953i	0.116412	+	0.145976i
$5$	−0.733052	+	0.680173i	−0.327831	+	0.304182i
$5$	−0.733052	+	0.680173i	−0.327831	+	0.304182i
$6$	0.679017	+	2.58054i	0.277208	+	1.05350i
$7$	1.44966	+	0.836959i	0.547918	+	0.316341i	0.748282	−	0.663381i	$-0.230879\pi$
$7$	1.44966	+	0.836959i	0.547918	+	0.316341i	−0.200364	+	0.979722i	$0.564212\pi$
$8$	−0.557614	−	2.44306i	−0.197146	−	0.863754i
$9$	−0.473820	+	2.96235i	−0.157940	+	0.987449i
$10$	−1.47215	+	0.454097i	−0.465534	+	0.143598i
$11$	4.56741	+	3.64239i	1.37712	+	1.09822i	0.983889	+	0.178783i	$0.0572160\pi$
$11$	4.56741	+	3.64239i	1.37712	+	1.09822i	0.393236	+	0.919437i	$0.371355\pi$
$12$	−0.123105	+	0.634962i	−0.0355373	+	0.183298i
$13$	0.430596	+	0.132821i	0.119426	+	0.0368380i	0.353892	−	0.935286i	$-0.384858\pi$
$13$	0.430596	+	0.132821i	0.119426	+	0.0368380i	−0.234466	+	0.972124i	$0.575334\pi$
$14$	1.45270	+	2.13072i	0.388251	+	0.569460i
$15$	−1.72027	−	0.201675i	−0.444172	−	0.0520723i
$16$	1.02524	−	4.49188i	0.256311	−	1.12297i
$17$	−1.38096	+	1.48832i	−0.334932	+	0.360971i	−0.877952	−	0.478749i	$-0.841090\pi$
$17$	−1.38096	+	1.48832i	−0.334932	+	0.360971i	0.543020	+	0.839720i	$0.317281\pi$
$18$	−2.63782	+	3.79509i	−0.621739	+	0.894512i
$19$	−5.29367	−	2.07761i	−1.21445	−	0.476637i	−0.330317	−	0.943870i	$-0.607156\pi$
$19$	−5.29367	−	2.07761i	−1.21445	−	0.476637i	−0.884134	+	0.467233i	$0.845251\pi$
$20$	−0.369251	−	0.0556556i	−0.0825670	−	0.0124450i
$21$	0.526184	+	2.85116i	0.114823	+	0.622175i
$22$	3.90497	+	8.10875i	0.832542	+	1.72879i
$23$	−0.0998868	+	0.662706i	−0.0208278	+	0.138184i	−0.996828	−	0.0795862i	$-0.974640\pi$
$23$	−0.0998868	+	0.662706i	−0.0208278	+	0.138184i	0.976000	+	0.217770i	$0.0698782\pi$
$24$	2.59307	−	3.48058i	0.529309	−	0.710471i
$25$	0.0747301	−	0.997204i	0.0149460	−	0.199441i
$26$	0.508895	+	0.472186i	0.0998026	+	0.0926033i
$27$	−4.43664	+	2.70484i	−0.853833	+	0.520548i
$28$	0.0931629	+	0.618096i	0.0176061	+	0.116809i
$29$	4.06967	−	2.77465i	0.755718	−	0.515240i	−0.123101	−	0.992394i	$-0.539284\pi$
$29$	4.06967	−	2.77465i	0.755718	−	0.515240i	0.878820	+	0.477154i	$0.158332\pi$
$30$	−2.25297	−	1.42982i	−0.411334	−	0.261049i
$31$	0.0537718	+	0.717535i	0.00965770	+	0.128873i	0.999949	−	0.0101374i	$-0.00322688\pi$
$31$	0.0537718	+	0.717535i	0.00965770	+	0.128873i	−0.990291	+	0.139010i	$0.955608\pi$
$32$	1.30081	−	1.63116i	0.229953	−	0.288352i
$33$	0.332817	+	10.1130i	0.0579359	+	1.76046i
$34$	−2.91165	+	1.14274i	−0.499345	+	0.195978i
$35$	−1.63195	+	0.372482i	−0.275850	+	0.0629609i
$36$	−0.975183	+	0.551374i	−0.162530	+	0.0918957i
$37$	−1.07219	+	0.619028i	−0.176267	+	0.101768i	−0.585537	−	0.810645i	$-0.699116\pi$
$37$	−1.07219	+	0.619028i	−0.176267	+	0.101768i	0.409271	+	0.912413i	$0.365783\pi$
$38$	−5.95899	−	6.42227i	−0.966677	−	1.04183i
$39$	0.308888	+	0.716765i	0.0494616	+	0.114774i
$40$	2.07047	+	1.41162i	0.327369	+	0.223197i
$41$	0.260977	−	0.541924i	0.0407577	−	0.0846343i	−0.879596	−	0.475722i	$-0.842187\pi$
$41$	0.260977	−	0.541924i	0.0407577	−	0.0846343i	0.920353	+	0.391088i	$0.127901\pi$
$42$	−1.17547	+	4.30921i	−0.181379	+	0.664925i
$43$	1.63737	+	6.34973i	0.249696	+	0.968324i
$43$	1.63737	+	6.34973i	0.249696	+	0.968324i
$44$			2.18150i			0.328874i
$45$	−1.66757	−	2.49383i	−0.248587	−	0.371759i
$46$	−0.581623	+	0.853084i	−0.0857556	+	0.125780i
$47$	9.84801	−	7.85353i	1.43648	−	1.14555i	0.471937	−	0.881633i	$-0.343555\pi$
$47$	9.84801	−	7.85353i	1.43648	−	1.14555i	0.964544	−	0.263922i	$-0.0850163\pi$
$48$	7.07218	−	3.69712i	1.02078	−	0.533633i
$49$	−2.09900	−	3.63557i	−0.299857	−	0.519368i
$50$	0.770296	−	1.33419i	0.108936	−	0.188683i
$51$	−3.51351	−	0.147309i	−0.491989	−	0.0206275i
$52$	0.0614758	+	0.156638i	0.00852517	+	0.0217218i
$53$	−3.43201	−	11.1263i	−0.471423	−	1.52832i	−0.809456	−	0.587181i	$-0.800238\pi$
$53$	−3.43201	−	11.1263i	−0.471423	−	1.52832i	0.338033	−	0.941134i	$-0.390239\pi$
$54$	−7.96619	+	0.788772i	−1.08406	+	0.107338i
$55$	−5.82560	+	0.436568i	−0.785523	+	0.0588668i
$56$	1.23640	−	4.00830i	0.165220	−	0.535632i
$57$	−3.21129	−	9.31160i	−0.425346	−	1.23335i
$58$	7.50348	−	1.13097i	0.985255	−	0.148503i
$59$	1.52445	+	0.347946i	0.198466	+	0.0452987i	0.320598	−	0.947215i	$-0.396116\pi$
$59$	1.52445	+	0.347946i	0.198466	+	0.0452987i	−0.122132	+	0.992514i	$0.538973\pi$
$60$	−0.341642	−	0.549193i	−0.0441057	−	0.0709005i
$61$	−6.25924	−	0.469065i	−0.801414	−	0.0600577i	−0.332275	−	0.943182i	$-0.607816\pi$
$61$	−6.25924	−	0.469065i	−0.801414	−	0.0600577i	−0.469138	+	0.883125i	$0.655435\pi$
$62$	−0.404991	+	1.03190i	−0.0514339	+	0.131051i
$63$	−3.16624	+	3.89781i	−0.398908	+	0.491078i
$64$	−5.40636	+	2.60357i	−0.675795	+	0.325446i
$65$	−0.405991	+	0.195515i	−0.0503570	+	0.0242506i
$66$	−6.29798	+	14.2596i	−0.775228	+	1.75524i
$67$	5.63190	−	14.3498i	0.688046	−	1.75311i	0.0306944	−	0.999529i	$-0.490228\pi$
$67$	5.63190	−	14.3498i	0.688046	−	1.75311i	0.657352	−	0.753584i	$-0.271677\pi$
$68$	−0.756041	−	0.0566574i	−0.0916834	−	0.00687072i
$69$	−0.985652	+	0.613154i	−0.118659	+	0.0738151i
$70$	−2.51417	−	0.573842i	−0.300500	−	0.0685873i
$71$	8.78026	−	1.32341i	1.04203	−	0.157060i	0.394338	−	0.918966i	$-0.370974\pi$
$71$	8.78026	−	1.32341i	1.04203	−	0.157060i	0.647688	+	0.761906i	$0.275736\pi$
$72$	7.50141	−	0.494273i	0.884050	−	0.0582506i
$73$	−1.45189	+	4.70690i	−0.169930	+	0.550901i	−0.999977	−	0.00679340i	$-0.997838\pi$
$73$	−1.45189	+	4.70690i	−0.169930	+	0.550901i	0.830047	+	0.557694i	$0.188314\pi$
$74$	−1.90200	+	0.142536i	−0.221104	+	0.0165694i
$75$	1.39822	−	1.02224i	0.161453	−	0.118038i
$76$	−0.625932	−	2.02922i	−0.0717994	−	0.232768i
$77$	3.57264	+	9.10293i	0.407140	+	1.03738i
$78$	−0.0503689	+	1.20136i	−0.00570316	+	0.136027i
$79$	1.41284	−	2.44710i	0.158956	−	0.275321i	−0.775536	−	0.631303i	$-0.782520\pi$
$79$	1.41284	−	2.44710i	0.158956	−	0.275321i	0.934493	+	0.355983i	$0.115854\pi$
$80$	2.30370	+	3.99013i	0.257561	+	0.446110i
$81$	−8.55099	−	2.80724i	−0.950110	−	0.311915i
$82$	0.724484	−	0.577757i	0.0800059	−	0.0638026i
$83$	6.70685	−	9.83714i	0.736173	−	1.07977i	−0.257371	−	0.966313i	$-0.582856\pi$
$83$	6.70685	−	9.83714i	0.736173	−	1.07977i	0.993543	−	0.113454i	$-0.0361915\pi$
$84$	−0.709897	+	0.817442i	−0.0774561	+	0.0891903i
$85$		−	2.03031i		−	0.220218i
$86$	−1.97169	+	9.90806i	−0.212613	+	1.06841i
$87$	8.23055	+	2.24513i	0.882408	+	0.240704i
$88$	6.35173	−	13.1895i	0.677097	−	1.40601i
$89$	−10.3970	−	7.08855i	−1.10208	−	0.751385i	−0.131296	−	0.991343i	$-0.541914\pi$
$89$	−10.3970	−	7.08855i	−1.10208	−	0.751385i	−0.970783	+	0.239958i	$0.922866\pi$
$90$	−0.647661	−	4.57617i	−0.0682695	−	0.482371i
$91$	0.513050	+	0.552936i	0.0537823	+	0.0579635i
$92$	−0.216735	+	0.125132i	−0.0225962	+	0.0130459i
$93$	−0.885220	+	0.877285i	−0.0917930	+	0.0909702i
$94$	18.9189	−	4.31811i	1.95133	−	0.445379i
$95$	5.29367	−	2.07761i	0.543119	−	0.213159i
$96$	3.61168	−	0.118859i	0.368616	−	0.0121310i
$97$	−3.15513	+	3.95641i	−0.320355	+	0.401713i	−0.915768	−	0.401707i	$-0.868417\pi$
$97$	−3.15513	+	3.95641i	−0.320355	+	0.401713i	0.595413	+	0.803420i	$0.296988\pi$
$98$	−0.483310	−	6.44932i	−0.0488216	−	0.651480i
$99$	−12.9541	+	11.8044i	−1.30194	+	1.18639i
$100$	0.308536	−	0.210356i	0.0308536	−	0.0210356i
$101$	1.47377	+	9.77780i	0.146645	+	0.972928i	0.934217	+	0.356705i	$0.116100\pi$
$101$	1.47377	+	9.77780i	0.146645	+	0.972928i	−0.787572	+	0.616223i	$0.788662\pi$
$102$	−4.77837	−	2.55303i	−0.473129	−	0.252788i
$103$	−0.536731	−	0.498013i	−0.0528856	−	0.0490707i	0.653287	−	0.757110i	$-0.273389\pi$
$103$	−0.536731	−	0.498013i	−0.0528856	−	0.0490707i	−0.706173	+	0.708039i	$0.749580\pi$
$104$	0.0843848	−	1.12604i	0.00827461	−	0.110417i
$105$	−2.32500	−	1.73215i	−0.226897	−	0.169041i
$106$	2.67352	−	17.7377i	0.259676	−	1.72283i
$107$	4.22589	+	8.77515i	0.408532	+	0.848326i	0.999144	+	0.0413702i	$0.0131723\pi$
$107$	4.22589	+	8.77515i	0.408532	+	0.848326i	−0.590612	+	0.806956i	$0.701113\pi$
$108$	−1.82265	−	0.665537i	−0.175384	−	0.0640413i
$109$	−4.84372	−	0.730073i	−0.463944	−	0.0699283i	−0.0870890	−	0.996201i	$-0.527756\pi$
$109$	−4.84372	−	0.730073i	−0.463944	−	0.0699283i	−0.376855	+	0.926272i	$0.622995\pi$
$110$	−8.37789	−	3.28808i	−0.798801	−	0.313506i
$111$	−2.02083	−	0.717348i	−0.191809	−	0.0680876i
$112$	5.24577	−	5.65359i	0.495679	−	0.534215i
$113$	3.23269	−	14.1634i	0.304106	−	1.33238i	−0.559760	−	0.828655i	$-0.689107\pi$
$113$	3.23269	−	14.1634i	0.304106	−	1.33238i	0.863866	−	0.503722i	$-0.168036\pi$
$114$	1.76688	−	15.0713i	0.165483	−	1.41156i
$115$	−0.377532	−	0.553738i	−0.0352050	−	0.0516363i
$116$	1.75759	+	0.542144i	0.163188	+	0.0503368i
$117$	−0.597488	+	1.21264i	−0.0552378	+	0.112109i
$118$	1.88339	+	1.50196i	0.173380	+	0.138266i
$119$	−3.24758	+	1.00174i	−0.297705	+	0.0918298i
$120$	0.466540	+	4.31519i	0.0425891	+	0.393921i
$121$	5.14650	+	22.5483i	0.467864	+	2.04985i
$122$	−8.37444	−	4.83499i	−0.758186	−	0.437739i
$123$	1.00752	−	0.265107i	0.0908447	−	0.0239039i
$124$	−0.196967	+	0.182759i	−0.0176882	+	0.0164122i
$125$	0.623490	+	0.781831i	0.0557666	+	0.0699291i
$126$	−7.00026	+	3.29383i	−0.623633	+	0.293438i
$127$	−12.0406	−	5.79846i	−1.06843	−	0.514530i	−0.184831	−	0.982770i	$-0.559174\pi$
$127$	−12.0406	−	5.79846i	−1.06843	−	0.514530i	−0.883601	+	0.468241i	$0.844888\pi$
$128$	−13.4172			−1.18592
$129$	−6.52823	+	9.29420i	−0.574779	+	0.818309i
$130$	−0.694215			−0.0608867
$131$	−8.49220	−	4.08963i	−0.741967	−	0.357312i	0.0244114	−	0.999702i	$-0.492229\pi$
$131$	−8.49220	−	4.08963i	−0.741967	−	0.357312i	−0.766378	+	0.642390i	$0.777943\pi$
$132$	−2.87505	+	2.45173i	−0.250241	+	0.213396i
$133$	−5.93512	−	7.44241i	−0.514640	−	0.645339i
$134$	17.4092	−	16.1534i	1.50393	−	1.39544i
$135$	1.41253	−	5.00048i	0.121571	−	0.430372i
$136$	4.40610	+	2.54387i	0.377820	+	0.218135i
$137$	3.70642	+	16.2389i	0.316661	+	1.38738i	0.843368	+	0.537336i	$0.180569\pi$
$137$	3.70642	+	16.2389i	0.316661	+	1.38738i	−0.526707	+	0.850047i	$0.676573\pi$
$138$	−1.77796	+	0.192226i	−0.151350	+	0.0163634i
$139$	−2.22886	+	0.687511i	−0.189049	+	0.0583139i	−0.387834	−	0.921729i	$-0.626777\pi$
$139$	−2.22886	+	0.687511i	−0.189049	+	0.0583139i	0.198785	+	0.980043i	$0.436300\pi$
$140$	−0.488705	−	0.389729i	−0.0413031	−	0.0329381i
$141$	21.4182	+	4.15251i	1.80374	+	0.349705i
$142$	13.0718	+	4.03213i	1.09696	+	0.338369i
$143$	1.48292	+	2.17505i	0.124008	+	0.181887i
$144$	12.8207	+	5.16547i	1.06839	+	0.430456i
$145$	−1.09603	+	4.80204i	−0.0910207	+	0.398788i
$146$	−5.16152	+	5.56280i	−0.427170	+	0.460380i
$147$	2.43238	−	6.85223i	0.200620	−	0.565163i
$148$	−0.430359	−	0.168903i	−0.0353753	−	0.0138838i
$149$	13.2949	+	2.00388i	1.08916	+	0.164165i	0.668984	−	0.743277i	$-0.266730\pi$
$149$	13.2949	+	2.00388i	1.08916	+	0.164165i	0.420178	+	0.907442i	$0.361968\pi$
$150$	2.62407	−	0.484274i	0.214254	−	0.0395408i
$151$	8.12593	+	16.8737i	0.661279	+	1.37316i	0.914037	+	0.405630i	$0.132948\pi$
$151$	8.12593	+	16.8737i	0.661279	+	1.37316i	−0.252759	+	0.967529i	$0.581338\pi$
$152$	−2.12392	+	14.0913i	−0.172273	+	1.14295i
$153$	−3.75459	−	4.79607i	−0.303541	−	0.387740i
$154$	−1.12583	+	15.0232i	−0.0907221	+	1.21060i
$155$	−0.527465	−	0.489416i	−0.0423670	−	0.0393109i
$156$	−0.137345	+	0.257061i	−0.0109964	+	0.0205814i
$157$	−0.300405	−	1.99306i	−0.0239749	−	0.159063i	0.973640	−	0.228091i	$-0.0732484\pi$
$157$	−0.300405	−	1.99306i	−0.0239749	−	0.159063i	−0.997615	+	0.0690278i	$0.978010\pi$
$158$	3.59679	−	2.45225i	0.286145	−	0.195090i
$159$	10.8064	−	17.0277i	0.857005	−	1.35038i
$160$	0.155912	+	2.08050i	0.0123259	+	0.164478i
$161$	−0.699459	+	0.877093i	−0.0551251	+	0.0691246i
$162$	−9.99253	−	9.61231i	−0.785087	−	0.755215i
$163$	−14.0676	+	5.52113i	−1.10186	+	0.432448i	−0.845415	−	0.534110i	$-0.820647\pi$
$163$	−14.0676	+	5.52113i	−1.10186	+	0.432448i	−0.256446	+	0.966559i	$0.582551\pi$
$164$	0.218978	−	0.0499803i	0.0170993	−	0.00390281i
$165$	−7.12259	−	7.18702i	−0.554493	−	0.559508i
$166$	15.8848	−	9.17109i	1.23290	−	0.711815i
$167$	0.927448	+	0.999551i	0.0717681	+	0.0773476i	0.767915	−	0.640552i	$-0.221294\pi$
$167$	0.927448	+	0.999551i	0.0717681	+	0.0773476i	−0.696147	+	0.717899i	$0.745104\pi$
$168$	6.67217	−	2.87535i	0.514769	−	0.221838i
$169$	−10.5733	−	7.20878i	−0.813333	−	0.554521i
$170$	1.35713	−	2.81812i	0.104087	−	0.216140i
$171$	8.66286	−	14.6973i	0.662465	−	1.12393i
$172$	−1.47260	+	1.95641i	−0.112285	+	0.149175i
$173$			15.6634i			1.19086i	0.803406	+	0.595431i	$0.203019\pi$
$173$			15.6634i			1.19086i	−0.803406	+	0.595431i	$0.796981\pi$
$174$	9.92348	+	8.61791i	0.752297	+	0.653322i
$175$	0.942951	−	1.38306i	0.0712804	−	0.104549i
$176$	21.0439	−	16.7819i	1.58624	−	1.26499i
$177$	1.25472	+	2.40015i	0.0943108	+	0.180406i
$178$	−9.69303	−	16.7888i	−0.726523	−	1.25838i
$179$	−9.39647	+	16.2752i	−0.702325	+	1.21646i	0.265323	+	0.964160i	$0.414521\pi$
$179$	−9.39647	+	16.2752i	−0.702325	+	1.21646i	−0.967648	+	0.252303i	$0.918812\pi$
$180$	0.339830	−	1.06748i	0.0253294	−	0.0795652i
$181$	−5.21847	−	13.2965i	−0.387886	−	0.988318i	−0.982824	−	0.184546i	$-0.940919\pi$
$181$	−5.21847	−	13.2965i	−0.387886	−	0.988318i	0.594938	−	0.803772i	$-0.297177\pi$
$182$	0.342523	+	1.11043i	0.0253895	+	0.0823107i
$183$	−6.41640	−	8.77634i	−0.474314	−	0.648766i
$184$	1.67473	−	0.125504i	0.123463	−	0.00925226i
$185$	0.364923	−	1.18305i	0.0268297	−	0.0869797i
$186$	−1.81512	+	0.625979i	−0.133091	+	0.0458990i
$187$	−11.7284	+	1.76778i	−0.857668	+	0.129273i
$188$	4.58572	+	1.04666i	0.334448	+	0.0763356i
$189$	−8.69545	+	0.207804i	−0.632501	+	0.0151155i
$190$	8.73650	+	0.654711i	0.633813	+	0.0474977i
$191$	−4.51606	+	11.5067i	−0.326771	+	0.832599i	0.669213	+	0.743070i	$0.266631\pi$
$191$	−4.51606	+	11.5067i	−0.326771	+	0.832599i	−0.995984	+	0.0895283i	$0.971464\pi$
$192$	−9.50735	−	4.19907i	−0.686134	−	0.303042i
$193$	7.83450	−	3.77290i	0.563940	−	0.271579i	−0.130118	−	0.991499i	$-0.541536\pi$
$193$	7.83450	−	3.77290i	0.563940	−	0.271579i	0.694058	+	0.719919i	$0.255821\pi$
$194$	−7.02402	+	3.38259i	−0.504295	+	0.242856i
$195$	−0.713955	−	0.315329i	−0.0511274	−	0.0225812i
$196$	0.572718	−	1.45926i	0.0409084	−	0.104233i
$197$	23.3368	+	1.74885i	1.66268	+	0.124600i	0.872610	−	0.488418i	$-0.162426\pi$
$197$	23.3368	+	1.74885i	1.66268	+	0.124600i	0.790068	+	0.613019i	$0.210045\pi$
$198$	−25.8712	+	7.72578i	−1.83858	+	0.549047i
$199$	−0.488616	−	0.111523i	−0.0346371	−	0.00790568i	0.205167	−	0.978727i	$-0.434226\pi$
$199$	−0.488616	−	0.111523i	−0.0346371	−	0.00790568i	−0.239804	+	0.970821i	$0.577083\pi$
$200$	−2.47790	+	0.373484i	−0.175214	+	0.0264093i
$201$	25.2415	−	8.70502i	1.78040	−	0.614005i
$202$	−4.49023	+	14.5570i	−0.315931	+	1.02422i
$203$	8.22188	−	0.616145i	0.577063	−	0.0432449i
$204$	−0.775024	−	1.06008i	−0.0542625	−	0.0742202i
$205$	0.177292	+	0.574768i	0.0123826	+	0.0401435i
$206$	−0.412105	−	1.05003i	−0.0287127	−	0.0731587i
$207$	−1.91583	−	0.609902i	−0.133160	−	0.0423911i
$208$	1.03808	−	1.79801i	0.0719781	−	0.124670i
$209$	−16.6109	−	28.7709i	−1.14900	−	1.99012i
$210$	−2.06933	−	3.95839i	−0.142797	−	0.273155i
$211$	−0.544222	+	0.434003i	−0.0374658	+	0.0298780i	−0.642044	−	0.766668i	$-0.721913\pi$
$211$	−0.544222	+	0.434003i	−0.0374658	+	0.0298780i	0.604578	+	0.796546i	$0.293342\pi$
$212$	2.44930	−	3.59246i	0.168219	−	0.246731i
$213$	11.6121	+	10.0843i	0.795645	+	0.690967i
$214$			15.0049i			1.02571i
$215$	−5.51919	−	3.54099i	−0.376405	−	0.241493i
$216$	9.08204	+	9.33075i	0.617955	+	0.634877i
$217$	−0.522597	+	1.08518i	−0.0354762	+	0.0736670i
$218$	−6.23519	−	4.25108i	−0.422301	−	0.287920i
$219$	−7.83504	+	3.37649i	−0.529443	+	0.228162i
$220$	−1.48380	−	1.59916i	−0.100038	−	0.107815i
$221$	−0.792316	+	0.457444i	−0.0532970	+	0.0307710i
$222$	−2.32546	−	2.34650i	−0.156075	−	0.157486i
$223$	−15.9654	+	3.64400i	−1.06912	+	0.244020i	−0.720651	−	0.693298i	$-0.756157\pi$
$223$	−15.9654	+	3.64400i	−1.06912	+	0.244020i	−0.348473	+	0.937319i	$0.613300\pi$
$224$	3.25094	−	1.27590i	0.217213	−	0.0852497i
$225$	2.91865	+	0.693871i	0.194577	+	0.0462581i
$226$	13.9544	−	17.4982i	0.928231	−	1.16397i
$227$	−1.63299	−	21.7907i	−0.108385	−	1.44630i	−0.740828	−	0.671694i	$-0.765567\pi$
$227$	−1.63299	−	21.7907i	−0.108385	−	1.44630i	0.632443	−	0.774607i	$-0.282052\pi$
$228$	1.97088	−	3.10552i	0.130525	−	0.205668i
$229$	−5.94191	+	4.05113i	−0.392653	+	0.267706i	−0.743513	−	0.668722i	$-0.766842\pi$
$229$	−5.94191	+	4.05113i	−0.392653	+	0.267706i	0.350860	+	0.936428i	$0.385889\pi$
$230$	−0.153885	−	1.02096i	−0.0101469	−	0.0673200i
$231$	−7.98174	+	14.9390i	−0.525160	+	0.982913i
$232$	−9.04795	−	8.39527i	−0.594027	−	0.551177i
$233$	0.706378	−	9.42595i	0.0462763	−	0.617515i	−0.925062	−	0.379815i	$-0.875988\pi$
$233$	0.706378	−	9.42595i	0.0462763	−	0.617515i	0.971339	−	0.237700i	$-0.0763934\pi$
$234$	−1.63990	+	1.28379i	−0.107204	+	0.0839242i
$235$	−1.87735	+	12.4554i	−0.122465	+	0.812500i
$236$	0.253346	+	0.526078i	0.0164914	+	0.0342447i
$237$	4.81293	−	0.888230i	0.312633	−	0.0576967i
$238$	−5.17732	−	0.780356i	−0.335596	−	0.0505830i
$239$	−27.2646	−	10.7006i	−1.76360	−	0.692162i	−0.998856	−	0.0478288i	$-0.984770\pi$
$239$	−27.2646	−	10.7006i	−1.76360	−	0.692162i	−0.764745	−	0.644333i	$-0.777135\pi$
$240$	−2.66959	+	7.52048i	−0.172322	+	0.485445i
$241$	−3.24649	+	3.49889i	−0.209125	+	0.225383i	−0.828901	−	0.559396i	$-0.811033\pi$
$241$	−3.24649	+	3.49889i	−0.209125	+	0.225383i	0.619776	+	0.784779i	$0.287224\pi$
$242$	−7.92866	+	34.7377i	−0.509673	+	2.23303i
$243$	−5.91052	−	14.4245i	−0.379160	−	0.925331i
$244$	−1.32036	−	1.93661i	−0.0845275	−	0.123979i
$245$	4.01149	+	1.23738i	0.256285	+	0.0790534i
$246$	1.57567	+	0.305486i	0.100461	+	0.0194771i
$247$	−2.00348	−	1.59773i	−0.127479	−	0.101661i
$248$	1.72300	−	0.531475i	0.109411	−	0.0337487i
$249$	20.5022	−	2.21661i	1.29927	−	0.140472i
$250$	0.342814	+	1.50197i	0.0216815	+	0.0949926i
$251$	12.9949	+	7.50263i	0.820233	+	0.473562i	0.850497	−	0.525980i	$-0.176301\pi$
$251$	12.9949	+	7.50263i	0.820233	+	0.473562i	−0.0302637	+	0.999542i	$0.509635\pi$
$252$	−1.87516	−	0.0168850i	−0.118124	−	0.00106365i
$253$	−2.87005	+	2.66302i	−0.180439	+	0.167423i
$254$	−12.8368	−	16.0968i	−0.805451	−	1.01000i
$255$	2.67578	−	2.28181i	0.167564	−	0.142892i
$256$	−7.81063	−	3.76140i	−0.488164	−	0.235087i
$257$	−18.3378			−1.14388			−0.571940	−	0.820295i	$-0.693809\pi$
$257$	−18.3378			−1.14388			−0.571940	+	0.820295i	$0.693809\pi$
$258$	−15.2739	+	8.53687i	−0.950914	+	0.531482i
$259$	−2.07240			−0.128773
$260$	−0.151606	−	0.0730095i	−0.00940219	−	0.00452786i
$261$	6.29119	+	13.3704i	0.389415	+	0.827610i
$262$	−9.05372	−	11.3530i	−0.559341	−	0.701391i
$263$	−1.53767	+	1.42675i	−0.0948166	+	0.0879769i	−0.726157	−	0.687529i	$-0.758696\pi$
$263$	−1.53767	+	1.42675i	−0.0948166	+	0.0879769i	0.631341	+	0.775506i	$0.282505\pi$
$264$	24.5212	−	6.45227i	1.50918	−	0.397109i
$265$	10.0836	+	5.82180i	0.619434	+	0.357630i
$266$	−3.26331	−	14.2975i	−0.200087	−	0.876637i
$267$	−2.34277	−	21.6690i	−0.143375	−	1.32612i
$268$	5.50073	−	1.69675i	0.336010	−	0.103645i
$269$	11.8246	+	9.42982i	0.720960	+	0.574946i	0.913742	−	0.406295i	$-0.133180\pi$
$269$	11.8246	+	9.42982i	0.720960	+	0.574946i	−0.192782	+	0.981242i	$0.561751\pi$
$270$	5.30313	−	5.99660i	0.322738	−	0.364941i
$271$	−16.4948	−	5.08796i	−1.00198	−	0.309071i	−0.249996	−	0.968247i	$-0.580429\pi$
$271$	−16.4948	−	5.08796i	−1.00198	−	0.309071i	−0.751989	+	0.659176i	$0.770905\pi$
$272$	5.26954	+	7.72900i	0.319513	+	0.468639i
$273$	−0.152122	+	1.29759i	−0.00920686	+	0.0785336i
$274$	−5.71009	+	25.0175i	−0.344959	+	1.51136i
$275$	3.97352	−	4.28244i	0.239612	−	0.258241i
$276$	−0.408496	−	0.145007i	−0.0245886	−	0.00872837i
$277$	20.7445	+	8.14161i	1.24642	+	0.489182i	0.894592	−	0.446884i	$-0.147466\pi$
$277$	20.7445	+	8.14161i	1.24642	+	0.489182i	0.351824	+	0.936066i	$0.385562\pi$
$278$	−3.55327	−	0.535569i	−0.213111	−	0.0321213i
$279$	−2.15107	−	0.180691i	−0.128781	−	0.0108177i
$280$	1.81999	+	3.77926i	0.108765	+	0.225854i
$281$	−0.839269	+	5.56818i	−0.0500666	+	0.332170i	0.949750	+	0.313010i	$0.101337\pi$
$281$	−0.839269	+	5.56818i	−0.0500666	+	0.332170i	−0.999816	+	0.0191601i	$0.993901\pi$
$282$	26.9533	+	20.0805i	1.60505	+	1.19578i
$283$	0.190657	−	2.54415i	0.0113334	−	0.151234i	−0.988666	−	0.150132i	$-0.952030\pi$
$283$	0.190657	−	2.54415i	0.0113334	−	0.151234i	0.999999	−	0.00110197i	$-0.000350769\pi$
$284$	2.43064	+	2.25530i	0.144232	+	0.133827i
$285$	8.68754	+	4.64166i	0.514606	+	0.274948i
$286$	0.604449	+	4.01026i	0.0357418	+	0.237132i
$287$	0.831894	−	0.567176i	0.0491052	−	0.0334793i
$288$	4.21572	+	4.62632i	0.248414	+	0.272609i
$289$	0.962363	+	12.8418i	0.0566096	+	0.755403i
$290$	−4.73119	+	5.93272i	−0.277825	+	0.348381i
$291$	−8.76020	+	0.288295i	−0.513532	+	0.0169001i
$292$	−1.71223	+	0.672000i	−0.100201	+	0.0393258i
$293$	−24.5968	+	5.61407i	−1.43696	+	0.327977i	−0.868892	−	0.495002i	$-0.835167\pi$
$293$	−24.5968	+	5.61407i	−1.43696	+	0.327977i	−0.568071	+	0.822979i	$0.692310\pi$
$294$	7.95650	−	7.88518i	0.464032	−	0.459873i
$295$	−1.35416	+	0.781827i	−0.0788424	+	0.0455197i
$296$	2.11019	+	2.27425i	0.122652	+	0.132188i
$297$	−30.1160	−	3.80584i	−1.74751	−	0.220837i
$298$	17.1142	+	11.6683i	0.991398	+	0.675924i
$299$	−0.131032	+	0.272091i	−0.00757779	+	0.0157355i
$300$	0.623987	+	0.170211i	0.0360259	+	0.00982716i
$301$	−2.94084	+	10.5753i	−0.169507	+	0.609551i
$302$			28.8527i			1.66029i
$303$	−11.2300	+	12.9313i	−0.645148	+	0.742885i
$304$	−14.7597	+	21.6485i	−0.846527	+	1.24163i
$305$	4.90739	−	3.91352i	0.280997	−	0.224087i
$306$	−2.00559	−	9.16678i	−0.114652	−	0.524030i
$307$	−4.16166	−	7.20820i	−0.237518	−	0.411394i	0.722483	−	0.691389i	$-0.243001\pi$
$307$	−4.16166	−	7.20820i	−0.237518	−	0.411394i	−0.960002	+	0.279995i	$0.909667\pi$
$308$	−1.82583	+	3.16243i	−0.104036	+	0.180196i
$309$	0.0531240	−	1.26707i	0.00302212	−	0.0720811i
$310$	−0.404991	−	1.03190i	−0.0230019	−	0.0586079i
$311$	7.32296	+	23.7404i	0.415247	+	1.34620i	0.885899	+	0.463878i	$0.153542\pi$
$311$	7.32296	+	23.7404i	0.415247	+	1.34620i	−0.470652	+	0.882319i	$0.655981\pi$
$312$	1.57886	−	1.15431i	0.0893855	−	0.0653500i
$313$	11.4035	−	0.854576i	0.644566	−	0.0483035i	0.251563	−	0.967841i	$-0.419055\pi$
$313$	11.4035	−	0.854576i	0.644566	−	0.0483035i	0.393002	+	0.919537i	$0.371436\pi$
$314$	0.915264	−	2.96721i	0.0516514	−	0.167450i
$315$	−0.330170	−	5.01089i	−0.0186030	−	0.282332i
$316$	1.04338	−	0.157264i	0.0586948	−	0.00884682i
$317$	6.32190	+	1.44293i	0.355073	+	0.0810432i	0.396337	−	0.918105i	$-0.370281\pi$
$317$	6.32190	+	1.44293i	0.355073	+	0.0810432i	−0.0412636	+	0.999148i	$0.513138\pi$
$318$	26.3815	−	16.4114i	1.47940	−	0.920306i
$319$	28.6942	+	2.15033i	1.60657	+	0.120395i
$320$	2.19227	−	5.58581i	0.122552	−	0.312256i
$321$	−6.81558	+	15.4315i	−0.380408	+	0.861305i
$322$	−1.55715	+	0.749883i	−0.0867765	+	0.0417893i
$323$	10.4025	−	5.00958i	0.578811	−	0.278741i
$324$	−1.17130	−	3.15008i	−0.0650723	−	0.175004i
$325$	0.164628	−	0.419466i	0.00913194	−	0.0232678i
$326$	−23.2167	−	1.73985i	−1.28586	−	0.0963615i
$327$	−4.48155	−	7.20414i	−0.247830	−	0.398390i
$328$	−1.46948	−	0.335399i	−0.0811384	−	0.0185193i
$329$	20.8493	−	3.14253i	1.14946	−	0.173253i
$330$	−5.08226	−	14.7368i	−0.279769	−	0.811232i
$331$	5.85056	−	18.9671i	0.321576	−	1.04252i	−0.640090	−	0.768300i	$-0.721103\pi$
$331$	5.85056	−	18.9671i	0.321576	−	1.04252i	0.961666	−	0.274224i	$-0.0884209\pi$
$332$	4.43350	−	0.332245i	0.243320	−	0.0182343i
$333$	−1.32575	−	3.46950i	−0.0726507	−	0.190127i
$334$	0.619183	+	2.00734i	0.0338802	+	0.109837i
$335$	5.63190	+	14.3498i	0.307704	+	0.784016i
$336$	13.3466	+	0.559576i	0.728114	+	0.0305274i
$337$	6.06180	−	10.4993i	0.330207	−	0.571936i	−0.652345	−	0.757922i	$-0.726215\pi$
$337$	6.06180	−	10.4993i	0.330207	−	0.571936i	0.982552	+	0.185986i	$0.0595480\pi$
$338$	−9.85743	−	17.0736i	−0.536174	−	0.928680i
$339$	22.2993	−	11.6574i	1.21113	−	0.633142i
$340$	0.592754	−	0.472706i	0.0321466	−	0.0256361i
$341$	−2.36794	+	3.47313i	−0.128231	+	0.188081i
$342$	21.8485	−	14.6096i	1.18143	−	0.789997i
$343$		−	18.7445i		−	1.01211i
$344$	14.5998	−	7.54089i	0.787167	−	0.406577i
$345$	0.305483	−	1.11989i	0.0164467	−	0.0602927i
$346$	−10.4700	+	21.7411i	−0.562869	+	1.16881i
$347$	−9.10188	−	6.20556i	−0.488615	−	0.333132i	0.293824	−	0.955860i	$-0.405072\pi$
$347$	−9.10188	−	6.20556i	−0.488615	−	0.333132i	−0.782439	+	0.622728i	$0.786024\pi$
$348$	1.26080	+	2.92566i	0.0675861	+	0.156832i
$349$	15.1713	+	16.3507i	0.812099	+	0.875235i	0.994145	−	0.108055i	$-0.0344623\pi$
$349$	15.1713	+	16.3507i	0.812099	+	0.875235i	−0.182046	+	0.983290i	$0.558272\pi$
$350$	2.23333	−	1.28941i	0.119376	−	0.0689219i
$351$	−2.26966	+	0.575415i	−0.121146	+	0.0307134i
$352$	11.8826	−	2.71214i	0.633347	−	0.144557i
$353$	−16.0782	+	6.31024i	−0.855758	+	0.335860i	−0.752338	−	0.658777i	$-0.771074\pi$
$353$	−16.0782	+	6.31024i	−0.855758	+	0.335860i	−0.103420	+	0.994638i	$0.532979\pi$
$354$	0.137239	+	4.17017i	0.00729415	+	0.221642i
$355$	−5.53624	+	6.94223i	−0.293833	+	0.368455i
$356$	−0.351154	−	4.68582i	−0.0186111	−	0.248348i
$357$	−4.97008	−	3.15421i	−0.263045	−	0.166938i
$358$	−23.9215	+	16.3094i	−1.26429	+	0.861978i
$359$	3.53311	+	23.4407i	0.186471	+	1.23715i	0.864695	+	0.502297i	$0.167512\pi$
$359$	3.53311	+	23.4407i	0.186471	+	1.23715i	−0.678224	+	0.734855i	$0.737250\pi$
$360$	−5.16273	+	5.46458i	−0.272100	+	0.288009i
$361$	9.77851	+	9.07313i	0.514658	+	0.477533i
$362$	1.64448	−	21.9440i	0.0864319	−	1.15335i
$363$	−23.9328	+	32.1241i	−1.25615	+	1.68608i
$364$	−0.0419807	+	0.278524i	−0.00220039	+	0.0145986i
$365$	−2.13720	−	4.43793i	−0.111866	−	0.232292i
$366$	−3.03969	−	16.4707i	−0.158887	−	0.860940i
$367$	−17.1492	−	2.58483i	−0.895183	−	0.134927i	−0.314692	−	0.949194i	$-0.601901\pi$
$367$	−17.1492	−	2.58483i	−0.895183	−	0.134927i	−0.580491	+	0.814267i	$0.697139\pi$
$368$	2.87439	+	1.12811i	0.149838	+	0.0588070i
$369$	1.48171	+	1.02988i	0.0771347	+	0.0536133i
$370$	1.29732	−	1.39818i	0.0674444	−	0.0726878i
$371$	4.33703	−	19.0018i	0.225167	−	0.986522i
$372$	−0.462227	−	0.0541890i	−0.0239654	−	0.00280957i
$373$	5.28246	+	7.74795i	0.273515	+	0.401173i	0.938278	−	0.345881i	$-0.112420\pi$
$373$	5.28246	+	7.74795i	0.273515	+	0.401173i	−0.664763	+	0.747054i	$0.731467\pi$
$374$	−17.4610	−	5.38601i	−0.902887	−	0.278504i
$375$	−0.329667	+	1.70039i	−0.0170239	+	0.0878077i
$376$	−24.6781	−	19.6801i	−1.27267	−	1.01492i
$377$	2.12092	−	0.654216i	0.109233	−	0.0336938i
$378$	−12.2084	−	5.52393i	−0.627932	−	0.284120i
$379$	4.77194	+	20.9073i	0.245118	+	1.07393i	0.936286	+	0.351239i	$0.114240\pi$
$379$	4.77194	+	20.9073i	0.245118	+	1.07393i	−0.691168	+	0.722695i	$0.742903\pi$
$380$	1.83906	+	1.06178i	0.0943419	+	0.0544683i
$381$	−5.89023	−	22.3853i	−0.301766	−	1.14683i
$382$	−13.9599	+	12.9529i	−0.714253	+	0.662730i
$383$	13.2727	+	16.6434i	0.678201	+	0.850437i	0.995187	−	0.0979932i	$-0.0312423\pi$
$383$	13.2727	+	16.6434i	0.678201	+	0.850437i	−0.316986	+	0.948430i	$0.602671\pi$
$384$	−15.0792	−	17.6827i	−0.769506	−	0.902368i
$385$	−8.81050	−	4.24291i	−0.449024	−	0.216239i
$386$	13.3964			0.681861
$387$	−19.5859	+	1.84182i	−0.995608	+	0.0936251i
$388$	−1.88968			−0.0959339
$389$	11.8666	+	5.71466i	0.601661	+	0.289745i	0.709814	−	0.704390i	$-0.248779\pi$
$389$	11.8666	+	5.71466i	0.601661	+	0.289745i	−0.108152	+	0.994134i	$0.534493\pi$
$390$	−0.780209	−	0.914919i	−0.0395074	−	0.0463287i
$391$	−0.848378	−	1.06383i	−0.0429043	−	0.0538003i
$392$	−7.71151	+	7.15524i	−0.389490	+	0.361394i
$393$	−4.15436	−	15.7882i	−0.209560	−	0.796412i
$394$	31.2231	+	18.0266i	1.57300	+	0.908169i
$395$	0.628771	+	2.75482i	0.0316369	+	0.138610i
$396$	−6.46237	−	1.03364i	−0.324746	−	0.0519423i
$397$	−3.22434	+	0.994576i	−0.161825	+	0.0499164i	−0.374609	−	0.927183i	$-0.622223\pi$
$397$	−3.22434	+	0.994576i	−0.161825	+	0.0499164i	0.212784	+	0.977099i	$0.431747\pi$
$398$	−0.603665	−	0.481406i	−0.0302590	−	0.0241307i
$399$	3.13817	−	16.1863i	0.157105	−	0.810330i
$400$	−4.40271	−	1.35805i	−0.220135	−	0.0679027i
$401$	−3.78745	−	5.55518i	−0.189136	−	0.277412i	0.719945	−	0.694032i	$-0.244167\pi$
$401$	−3.78745	−	5.55518i	−0.189136	−	0.277412i	−0.909081	+	0.416619i	$0.863215\pi$
$402$	40.8545	+	4.78957i	2.03764	+	0.238882i
$403$	−0.0721500	+	0.316110i	−0.00359405	+	0.0157466i
$404$	−2.51153	+	2.70678i	−0.124953	+	0.134668i
$405$	8.17772	−	3.75830i	0.406354	−	0.186751i
$406$	11.8240	+	4.64059i	0.586817	+	0.230309i
$407$	−7.15185	−	1.07797i	−0.354504	−	0.0534329i
$408$	1.59929	+	8.66587i	0.0791768	+	0.429024i
$409$	8.90974	+	18.5013i	0.440558	+	0.914829i	0.996499	+	0.0836066i	$0.0266439\pi$
$409$	8.90974	+	18.5013i	0.440558	+	0.914829i	−0.555941	+	0.831222i	$0.687642\pi$
$410$	−0.138110	+	0.916300i	−0.00682077	+	0.0452529i
$411$	−17.2360	+	23.1352i	−0.850190	+	1.14118i
$412$	0.0204323	−	0.272650i	0.00100663	−	0.0134325i
$413$	1.91871	+	1.78030i	0.0944135	+	0.0876029i
$414$	−2.25155	−	2.12718i	−0.110657	−	0.104545i
$415$	1.77449	+	11.7730i	0.0871062	+	0.577912i
$416$	0.776777	−	0.529597i	0.0380846	−	0.0259656i
$417$	−3.41103	−	2.16478i	−0.167039	−	0.106010i
$418$	−3.82477	−	51.0381i	−0.187076	−	2.49635i
$419$	−21.2546	+	26.6525i	−1.03836	+	1.30206i	−0.0862569	+	0.996273i	$0.527491\pi$
$419$	−21.2546	+	26.6525i	−1.03836	+	1.30206i	−0.952100	+	0.305786i	$0.901081\pi$
$420$	−0.0356108	−	1.08208i	−0.00173763	−	0.0528001i
$421$	0.373883	−	0.146738i	0.0182220	−	0.00715159i	−0.356213	−	0.934405i	$-0.615932\pi$
$421$	0.373883	−	0.146738i	0.0182220	−	0.00715159i	0.374435	+	0.927253i	$0.377837\pi$
$422$	−1.04550	+	0.238628i	−0.0508940	+	0.0116162i
$423$	18.5987	+	32.8944i	0.904299	+	1.59938i
$424$	−25.2685	+	14.5888i	−1.22715	+	0.708495i
$425$	1.38096	+	1.48832i	0.0669864	+	0.0721941i
$426$	9.37707	+	21.7592i	0.454321	+	1.05424i
$427$	−8.68115	−	5.91871i	−0.420110	−	0.286426i
$428$	−1.57804	+	3.27683i	−0.0762775	+	0.158392i
$429$	−1.19992	+	4.39885i	−0.0579326	+	0.212378i
$430$	−5.29384	−	8.60421i	−0.255292	−	0.414932i
$431$		−	2.25520i		−	0.108629i	−0.998524	−	0.0543146i	$-0.982703\pi$
$431$		−	2.25520i		−	0.108629i	0.998524	−	0.0543146i	$-0.0172974\pi$
$432$	7.60121	+	22.7020i	0.365713	+	1.09225i
$433$	16.0565	−	23.5505i	0.771625	−	1.13177i	−0.216224	−	0.976344i	$-0.569374\pi$
$433$	16.0565	−	23.5505i	0.771625	−	1.13177i	0.987848	−	0.155422i	$-0.0496736\pi$
$434$	−1.45075	+	1.15694i	−0.0696384	+	0.0555348i
$435$	−7.56050	+	3.95240i	−0.362498	+	0.189503i
$436$	−0.914590	−	1.58412i	−0.0438009	−	0.0758654i
$437$	1.90561	−	3.30062i	0.0911579	−	0.157890i
$438$	−13.1322	−	0.550589i	−0.627481	−	0.0263082i
$439$	−3.14400	−	8.01077i	−0.150055	−	0.382333i	0.836006	−	0.548721i	$-0.184885\pi$
$439$	−3.14400	−	8.01077i	−0.150055	−	0.382333i	−0.986060	+	0.166387i	$0.946790\pi$
$440$	4.31500	+	13.9889i	0.205709	+	0.666893i
$441$	11.7644	−	4.49536i	0.560208	−	0.214065i
$442$	−1.40553	+	0.105330i	−0.0668541	+	0.00501003i
$443$	6.39322	−	20.7263i	0.303751	−	0.984737i	−0.667083	−	0.744984i	$-0.732457\pi$
$443$	6.39322	−	20.7263i	0.303751	−	0.984737i	0.970834	−	0.239754i	$-0.0770666\pi$
$444$	−0.261068	−	0.757004i	−0.0123897	−	0.0359258i
$445$	12.4430	−	1.87548i	0.589853	−	0.0889061i
$446$	−24.5962	−	5.61392i	−1.16466	−	0.265827i
$447$	12.3008	+	19.7737i	0.581809	+	0.935265i
$448$	−10.0164	−	0.750628i	−0.473232	−	0.0354639i
$449$	−8.76879	+	22.3425i	−0.413825	+	1.05441i	0.560279	+	0.828304i	$0.310694\pi$
$449$	−8.76879	+	22.3425i	−0.413825	+	1.05441i	−0.974103	+	0.226104i	$0.927401\pi$
$450$	3.58736	+	2.91405i	0.169110	+	0.137370i
$451$	3.16588	−	1.52461i	0.149076	−	0.0717910i
$452$	4.88768	−	2.35378i	0.229897	−	0.110713i
$453$	−13.1056	+	29.6732i	−0.615755	+	1.39417i
$454$	12.2991	−	31.3376i	0.577226	−	1.47075i
$455$	−0.752185	−	0.0563684i	−0.0352630	−	0.00264259i
$456$	−20.9582	+	13.0377i	−0.981457	+	0.610545i
$457$	−1.49010	−	0.340106i	−0.0697040	−	0.0159095i	0.187527	−	0.982260i	$-0.439953\pi$
$457$	−1.49010	−	0.340106i	−0.0697040	−	0.0159095i	−0.257231	+	0.966350i	$0.582810\pi$
$458$	−10.9554	+	1.65127i	−0.511914	+	0.0771587i
$459$	2.10115	−	10.3384i	0.0980733	−	0.482556i
$460$	0.0737666	−	0.239145i	0.00343939	−	0.0111502i
$461$	−10.9651	+	0.821719i	−0.510694	+	0.0382713i	−0.327586	−	0.944821i	$-0.606235\pi$
$461$	−10.9651	+	0.821719i	−0.510694	+	0.0382713i	−0.183109	+	0.983093i	$0.558616\pi$
$462$	−21.0646	+	15.4004i	−0.980015	+	0.716491i
$463$	3.55641	+	11.5296i	0.165280	+	0.535826i	0.999887	−	0.0150202i	$-0.00478127\pi$
$463$	3.55641	+	11.5296i	0.165280	+	0.535826i	−0.834607	+	0.550846i	$0.814305\pi$
$464$	−8.29101	−	21.1252i	−0.384901	−	0.980711i
$465$	0.0522069	−	1.24520i	0.00242104	−	0.0577447i
$466$	7.28113	−	12.6113i	0.337292	−	0.584207i
$467$	−13.1720	−	22.8147i	−0.609530	−	1.05574i	−0.991318	−	0.131487i	$-0.958025\pi$
$467$	−13.1720	−	22.8147i	−0.609530	−	1.05574i	0.381788	−	0.924250i	$-0.375308\pi$
$468$	−0.493144	+	0.107895i	−0.0227956	+	0.00498743i
$469$	20.1745	−	16.0887i	0.931574	−	0.742905i
$470$	−10.9315	+	16.0335i	−0.504231	+	0.739571i
$471$	2.28907	−	2.63585i	0.105475	−	0.121454i
$472$		−	3.91835i		−	0.180357i
$473$	−15.6496	+	34.9657i	−0.719571	+	1.60772i
$474$	7.27419	+	1.98426i	0.334115	+	0.0911399i
$475$	−2.46740	+	5.12361i	−0.113212	+	0.235087i
$476$	−1.04858	−	0.714909i	−0.0480615	−	0.0327678i
$477$	34.5861	−	4.89494i	1.58359	−	0.224124i
$478$	−30.6913	−	33.0773i	−1.40379	−	1.51292i
$479$	35.5571	−	20.5289i	1.62464	−	0.937989i	0.638989	−	0.769216i	$-0.279353\pi$
$479$	35.5571	−	20.5289i	1.62464	−	0.937989i	0.985655	−	0.168773i	$-0.0539804\pi$
$480$	−2.56671	+	2.54370i	−0.117154	+	0.116103i
$481$	−0.543900	+	0.124142i	−0.0247997	+	0.00566037i
$482$	−6.84500	+	2.68646i	−0.311781	+	0.122365i
$483$	−1.94204	+	0.0639118i	−0.0883659	+	0.00290809i
$484$	−5.38481	+	6.75234i	−0.244764	+	0.306924i
$485$	−0.378167	−	5.04629i	−0.0171717	−	0.229140i
$486$	1.43792	−	23.9724i	0.0652254	−	1.08741i
$487$	12.9821	−	8.85105i	0.588276	−	0.401080i	−0.232278	−	0.972650i	$-0.574618\pi$
$487$	12.9821	−	8.85105i	0.588276	−	0.401080i	0.820553	+	0.571570i	$0.193665\pi$
$488$	2.34428	+	15.5533i	0.106121	+	0.704064i
$489$	−23.0866	−	12.3349i	−1.04401	−	0.557804i
$490$	4.74094	+	4.39895i	0.214174	+	0.198724i
$491$	−1.39167	+	18.5705i	−0.0628051	+	0.838076i	0.873485	+	0.486850i	$0.161854\pi$
$491$	−1.39167	+	18.5705i	−0.0628051	+	0.838076i	−0.936291	+	0.351226i	$0.885765\pi$
$492$	0.311974	+	0.232424i	0.0140649	+	0.0104785i
$493$	−1.49047	+	9.88865i	−0.0671276	+	0.445362i
$494$	−1.71291	−	3.55689i	−0.0770673	−	0.160032i
$495$	1.46702	−	17.4643i	0.0659375	−	0.784961i
$496$	3.27821	+	0.494111i	0.147196	+	0.0221862i
$497$	13.8360	+	5.43023i	0.620629	+	0.243579i
$498$	29.9392	+	10.6277i	1.34161	+	0.476240i
$499$	9.80937	−	10.5720i	0.439128	−	0.473267i	−0.474244	−	0.880393i	$-0.657279\pi$
$499$	9.80937	−	10.5720i	0.439128	−	0.473267i	0.913372	+	0.407126i	$0.133469\pi$
$500$	−0.0830942	+	0.364059i	−0.00371608	+	0.0162812i
$501$	−0.274994	+	2.34567i	−0.0122858	+	0.104797i
$502$	13.0223	+	19.1001i	0.581212	+	0.852481i
$503$	20.5070	+	6.32558i	0.914364	+	0.282044i	0.716013	−	0.698087i	$-0.245965\pi$
$503$	20.5070	+	6.32558i	0.914364	+	0.282044i	0.198351	+	0.980131i	$0.436441\pi$
$504$	11.2881	+	5.56185i	0.502814	+	0.247744i
$505$	−7.73094	−	6.16522i	−0.344022	−	0.274349i
$506$	−5.76377	+	1.77789i	−0.256231	+	0.0790367i
$507$	−2.38250	−	22.0365i	−0.105811	−	0.978677i
$508$	−1.11048	−	4.86532i	−0.0492694	−	0.215864i
$509$	5.50571	+	3.17872i	0.244036	+	0.140894i	0.617030	−	0.786939i	$-0.288336\pi$
$509$	5.50571	+	3.17872i	0.244036	+	0.140894i	−0.372994	+	0.927834i	$0.621669\pi$
$510$	5.23929	−	1.37861i	0.232000	−	0.0610460i
$511$	−6.04421	+	5.60821i	−0.267380	+	0.248093i
$512$	8.40384	+	10.5381i	0.371401	+	0.465722i
$513$	29.1058	−	5.10093i	1.28505	−	0.225212i
$514$	−25.4533	−	12.2577i	−1.12270	−	0.540663i
$515$	0.732186			0.0322640
$516$	−4.23340	+	0.257983i	−0.186365	+	0.0113571i
$517$	73.5855			3.23628
$518$	−2.87655	−	1.38527i	−0.126388	−	0.0608654i
$519$	−20.6430	+	17.6036i	−0.906128	+	0.772713i
$520$	0.704041	+	0.882840i	0.0308743	+	0.0387151i
$521$	−4.73885	+	4.39701i	−0.207613	+	0.192637i	−0.777125	−	0.629346i	$-0.783323\pi$
$521$	−4.73885	+	4.39701i	−0.207613	+	0.192637i	0.569512	+	0.821983i	$0.307132\pi$
$522$	−0.204978	+	22.7638i	−0.00897163	+	0.996344i
$523$	−5.94402	−	3.43178i	−0.259914	−	0.150061i	0.364381	−	0.931250i	$-0.381280\pi$
$523$	−5.94402	−	3.43178i	−0.259914	−	0.150061i	−0.624295	+	0.781188i	$0.714614\pi$
$524$	−0.783215	−	3.43149i	−0.0342149	−	0.149905i
$525$	2.88251	−	0.311645i	0.125803	−	0.0136013i
$526$	−3.08801	+	0.952525i	−0.134644	+	0.0415321i
$527$	−1.14218	−	0.910857i	−0.0497541	−	0.0396775i
$528$	45.7678	+	8.87336i	1.99179	+	0.386163i
$529$	21.5490	+	6.64698i	0.936912	+	0.288999i
$530$	10.1048	+	14.8211i	0.438927	+	0.643787i
$531$	−1.75305	+	4.35108i	−0.0760758	+	0.188821i
$532$	0.790990	−	3.46555i	0.0342938	−	0.150251i
$533$	0.184355	−	0.198687i	0.00798529	−	0.00860609i
$534$	11.2326	−	31.6431i	0.486081	−	1.36933i
$535$	−9.06642	−	3.55831i	−0.391975	−	0.153839i
$536$	−38.1980	−	5.75743i	−1.64990	−	0.248683i
$537$	−32.0098	+	5.90743i	−1.38132	+	0.254925i
$538$	10.1096	+	20.9928i	0.435857	+	0.905066i
$539$	3.65518	−	24.2505i	0.157440	−	1.04454i
$540$	1.78878	−	0.751842i	0.0769766	−	0.0323541i
$541$	1.56776	−	20.9203i	0.0674032	−	0.899434i	−0.856338	−	0.516416i	$-0.827266\pi$
$541$	1.56776	−	20.9203i	0.0674032	−	0.899434i	0.923741	−	0.383018i	$-0.125115\pi$
$542$	−19.4941	−	18.0879i	−0.837345	−	0.776943i
$543$	11.6587	−	21.8211i	0.500325	−	0.936431i
$544$	0.631328	+	4.18859i	0.0270680	+	0.179584i
$545$	4.04727	−	2.75938i	0.173366	−	0.118199i
$546$	−1.07851	+	1.69940i	−0.0461558	+	0.0727276i
$547$	−3.17597	−	42.3804i	−0.135795	−	1.81205i	−0.484467	−	0.874810i	$-0.660986\pi$
$547$	−3.17597	−	42.3804i	−0.135795	−	1.81205i	0.348672	−	0.937245i	$-0.386633\pi$
$548$	−3.87805	+	4.86292i	−0.165662	+	0.207734i
$549$	4.35528	−	18.3198i	0.185879	−	0.781870i
$550$	8.37789	−	3.28808i	0.357235	−	0.140204i
$551$	−27.3081	+	6.23290i	−1.16337	+	0.265531i
$552$	2.04759	+	2.06611i	0.0871511	+	0.0879394i
$553$	4.09625	−	2.36497i	0.174190	−	0.100569i
$554$	23.3517	+	25.1672i	0.992119	+	1.06925i
$555$	1.96929	−	0.848661i	0.0835919	−	0.0360237i
$556$	−0.719654	−	0.490652i	−0.0305201	−	0.0208083i
$557$	−6.76918	+	14.0564i	−0.286819	+	0.595587i	−0.993741	−	0.111705i	$-0.964369\pi$
$557$	−6.76918	+	14.0564i	−0.286819	+	0.595587i	0.706922	+	0.707292i	$0.250083\pi$
$558$	−2.86495	−	1.68866i	−0.121283	−	0.0714865i
$559$	−0.138335	+	2.95165i	−0.00585096	+	0.124841i
$560$			7.71241i			0.325909i
$561$	−15.5111	−	13.4704i	−0.654877	−	0.568719i
$562$	−4.88691	+	7.16778i	−0.206142	+	0.302355i
$563$	25.5986	−	20.4142i	1.07885	−	0.860356i	0.0881095	−	0.996111i	$-0.471917\pi$
$563$	25.5986	−	20.4142i	1.07885	−	0.860356i	0.990742	+	0.135755i	$0.0433460\pi$
$564$	3.77435	+	7.21992i	0.158929	+	0.304014i
$565$	7.26380	+	12.5813i	0.305590	+	0.529298i
$566$	1.96524	−	3.40390i	0.0826052	−	0.143076i
$567$	−10.0464	−	11.2263i	−0.421911	−	0.471462i
$568$	−8.12917	−	20.7128i	−0.341093	−	0.869090i
$569$	7.33818	+	23.7898i	0.307632	+	0.997319i	0.968959	+	0.247221i	$0.0795175\pi$
$569$	7.33818	+	23.7898i	0.307632	+	0.997319i	−0.661327	+	0.750098i	$0.730006\pi$
$570$	8.95587	+	12.2498i	0.375120	+	0.513088i
$571$	−42.4631	+	3.18217i	−1.77702	+	0.133170i	−0.922439	−	0.386142i	$-0.873807\pi$
$571$	−42.4631	+	3.18217i	−1.77702	+	0.133170i	−0.854585	+	0.519312i	$0.826188\pi$
$572$	−0.289750	+	0.939348i	−0.0121151	+	0.0392761i
$573$	−20.2404	+	6.98031i	−0.845556	+	0.291607i
$574$	1.53381	−	0.231185i	0.0640201	−	0.00964947i
$575$	0.653388	+	0.149132i	0.0272482	+	0.00621921i
$576$	−5.15103	−	17.2491i	−0.214626	−	0.718714i
$577$	−29.1897	−	2.18747i	−1.21518	−	0.0910655i	−0.548335	−	0.836258i	$-0.684738\pi$
$577$	−29.1897	−	2.18747i	−1.21518	−	0.0910655i	−0.666849	+	0.745193i	$0.732357\pi$
$578$	−7.24819	+	18.4681i	−0.301485	+	0.768171i
$579$	13.7774	+	6.08498i	0.572568	+	0.252883i
$580$	−1.65715	+	0.798043i	−0.0688096	+	0.0331369i
$581$	17.9559	−	8.64711i	0.744937	−	0.358743i
$582$	−12.3521	−	5.45549i	−0.512010	−	0.226137i
$583$	24.8509	−	63.3191i	1.02922	−	2.62241i
$584$	12.3088	+	0.922420i	0.509344	+	0.0381700i
$585$	−0.386816	−	1.29532i	−0.0159929	−	0.0535551i
$586$	−37.8937	−	8.64899i	−1.56537	−	0.357286i
$587$	−35.8053	+	5.39678i	−1.47784	+	0.222749i	−0.837963	−	0.545726i	$-0.816254\pi$
$587$	−35.8053	+	5.39678i	−1.47784	+	0.222749i	−0.639879	+	0.768475i	$0.721016\pi$
$588$	2.56685	−	0.885228i	0.105855	−	0.0365062i
$589$	1.20611	−	3.91011i	0.0496969	−	0.161113i
$590$	−2.40221	+	0.180021i	−0.0988976	+	0.00741135i
$591$	23.9228	+	32.7215i	0.984051	+	1.34598i
$592$	1.68135	+	5.45080i	0.0691030	+	0.224026i
$593$	1.98374	+	5.05449i	0.0814624	+	0.207563i	0.965802	−	0.259282i	$-0.0834859\pi$
$593$	1.98374	+	5.05449i	0.0814624	+	0.207563i	−0.884339	+	0.466845i	$0.845391\pi$
$594$	−39.2579	−	25.4133i	−1.61077	−	1.04272i
$595$	1.69928	−	2.94324i	0.0696638	−	0.120661i
$596$	2.51034	+	4.34804i	0.102828	+	0.178103i
$597$	−0.402163	−	0.769294i	−0.0164595	−	0.0314851i
$598$	−0.363752	+	0.290083i	−0.0148749	+	0.0118624i
$599$	−24.6978	+	36.2250i	−1.00912	+	1.48011i	−0.137155	+	0.990550i	$0.543796\pi$
$599$	−24.6978	+	36.2250i	−1.00912	+	1.48011i	−0.871968	+	0.489562i	$0.837157\pi$
$600$	−3.27707	−	2.84593i	−0.133786	−	0.116184i
$601$		−	33.0711i		−	1.34900i	−0.738277	−	0.674498i	$-0.764360\pi$
$601$		−	33.0711i		−	1.34900i	0.738277	−	0.674498i	$-0.235640\pi$
$602$	−11.1509	+	12.7130i	−0.454477	+	0.518145i
$603$	39.8407	+	23.4829i	1.62244	+	0.956297i
$604$	−3.03440	+	6.30099i	−0.123468	+	0.256384i
$605$	−19.1094	−	13.0286i	−0.776907	−	0.529686i
$606$	−24.2313	+	10.4424i	−0.984330	+	0.424194i
$607$	2.93454	+	3.16269i	0.119109	+	0.128369i	0.789791	−	0.613376i	$-0.210189\pi$
$607$	2.93454	+	3.16269i	0.119109	+	0.128369i	−0.670682	+	0.741745i	$0.733998\pi$
$608$	−10.2750	+	5.93226i	−0.416706	+	0.240585i
$609$	10.0524	+	10.1433i	0.407343	+	0.411027i
$610$	9.42753	−	2.15177i	0.381709	−	0.0871227i
$611$	5.28363	−	2.07367i	0.213753	−	0.0838918i
$612$	0.526066	−	2.21281i	0.0212650	−	0.0894475i
$613$	25.7694	−	32.3138i	1.04082	−	1.30514i	0.0898144	−	0.995959i	$-0.471373\pi$
$613$	25.7694	−	32.3138i	1.04082	−	1.30514i	0.951002	−	0.309184i	$-0.100056\pi$
$614$	−0.958251	−	12.7870i	−0.0386719	−	0.516040i
$615$	−0.558243	+	0.879623i	−0.0225105	+	0.0354698i
$616$	20.2469	−	13.8041i	0.815771	−	0.556183i
$617$	−3.17755	−	21.0816i	−0.127923	−	0.848715i	−0.957106	−	0.289738i	$-0.906432\pi$
$617$	−3.17755	−	21.0816i	−0.127923	−	0.848715i	0.829183	−	0.558977i	$-0.188806\pi$
$618$	0.920695	−	1.72322i	0.0370358	−	0.0693179i
$619$	−31.2374	−	28.9841i	−1.25554	−	1.16497i	−0.978976	−	0.203973i	$-0.934614\pi$
$619$	−31.2374	−	28.9841i	−1.25554	−	1.16497i	−0.276562	−	0.960996i	$-0.589195\pi$
$620$	0.0200796	−	0.267943i	0.000806415	−	0.0107609i
$621$	−1.34935	−	3.21037i	−0.0541477	−	0.128828i
$622$	−5.70456	+	37.8473i	−0.228732	+	1.51754i
$623$	−9.13923	−	18.9778i	−0.366156	−	0.760330i
$624$	3.53631	−	0.652629i	0.141566	−	0.0261261i
$625$	−0.988831	−	0.149042i	−0.0395532	−	0.00596169i
$626$	16.3996	+	6.43637i	0.655460	+	0.257249i
$627$	19.2492	−	54.2266i	0.768738	−	2.16560i
$628$	0.511937	−	0.551737i	0.0204285	−	0.0220167i
$629$	0.559336	−	2.45061i	0.0223022	−	0.0977122i
$630$	2.89118	−	7.17593i	0.115187	−	0.285896i
$631$	3.16688	+	4.64495i	0.126071	+	0.184913i	0.884085	−	0.467326i	$-0.154782\pi$
$631$	3.16688	+	4.64495i	0.126071	+	0.184913i	−0.758014	+	0.652238i	$0.773830\pi$
$632$	−6.76624	−	2.08711i	−0.269147	−	0.0830208i
$633$	−1.18362	−	0.229477i	−0.0470446	−	0.00912088i
$634$	7.81045	+	6.22862i	0.310192	+	0.247370i
$635$	12.7703	−	3.93913i	0.506776	−	0.156320i
$636$	7.48728	−	0.809494i	0.296890	−	0.0320985i
$637$	−0.420940	−	1.84426i	−0.0166782	−	0.0730721i
$638$	38.3909	+	22.1650i	1.51991	+	0.877520i
$639$	−0.239857	+	26.6372i	−0.00948858	+	1.05375i
$640$	9.83547	−	9.12598i	0.388781	−	0.360736i
$641$	−3.76183	−	4.71718i	−0.148583	−	0.186318i	0.701970	−	0.712207i	$-0.252304\pi$
$641$	−3.76183	−	4.71718i	−0.148583	−	0.186318i	−0.850553	+	0.525889i	$0.823733\pi$
$642$	−19.7752	+	16.8636i	−0.780465	+	0.665552i
$643$	−1.72655	−	0.831461i	−0.0680883	−	0.0327896i	0.399530	−	0.916720i	$-0.369173\pi$
$643$	−1.72655	−	0.831461i	−0.0680883	−	0.0327896i	−0.467618	+	0.883931i	$0.654888\pi$
$644$	−0.418921			−0.0165078
$645$	−1.53613	−	11.2535i	−0.0604851	−	0.443104i
$646$	17.7875			0.699841
$647$	7.57024	+	3.64564i	0.297617	+	0.143325i	0.576733	−	0.816933i	$-0.304327\pi$
$647$	7.57024	+	3.64564i	0.297617	+	0.143325i	−0.279116	+	0.960257i	$0.590042\pi$
$648$	−2.09011	+	22.4560i	−0.0821072	+	0.882154i
$649$	5.69543	+	7.14184i	0.223565	+	0.280342i
$650$	0.508895	−	0.472186i	0.0199605	−	0.0185207i
$651$	−2.01752	+	0.530868i	−0.0790727	+	0.0208064i
$652$	−4.88720	−	2.82162i	−0.191397	−	0.110503i
$653$	0.636648	+	2.78934i	0.0249140	+	0.109155i	0.985856	−	0.167594i	$-0.0535999\pi$
$653$	0.636648	+	2.78934i	0.0249140	+	0.109155i	−0.960942	+	0.276750i	$0.910743\pi$
$654$	−1.40498	−	12.9952i	−0.0549392	−	0.508151i
$655$	9.00688	−	2.77825i	0.351928	−	0.108555i
$656$	−2.16669	−	1.72788i	−0.0845952	−	0.0674624i
$657$	−13.2555	−	6.53121i	−0.517147	−	0.254807i
$658$	31.0399	+	9.57455i	1.21006	+	0.373255i
$659$	−15.0427	−	22.0636i	−0.585981	−	0.859477i	0.412697	−	0.910868i	$-0.364587\pi$
$659$	−15.0427	−	22.0636i	−0.585981	−	0.859477i	−0.998679	+	0.0513915i	$0.983634\pi$
$660$	0.439955	−	3.75278i	0.0171252	−	0.146077i
$661$	6.69797	−	29.3457i	0.260521	−	1.14142i	−0.660167	−	0.751118i	$-0.729515\pi$
$661$	6.69797	−	29.3457i	0.260521	−	1.14142i	0.920688	−	0.390298i	$-0.127628\pi$
$662$	20.7990	−	22.4160i	0.808377	−	0.871223i
$663$	−1.49334	−	0.530100i	−0.0579964	−	0.0205874i
$664$	−27.7726	−	10.8999i	−1.07779	−	0.423000i
$665$	9.41288	+	1.41876i	0.365016	+	0.0550173i
$666$	0.478967	−	5.70193i	0.0185596	−	0.220945i
$667$	1.43227	+	2.97414i	0.0554578	+	0.115159i
$668$	−0.0758891	+	0.503491i	−0.00293624	+	0.0194807i
$669$	−22.7456	−	16.9457i	−0.879396	−	0.655160i
$670$	−1.77476	+	23.6825i	−0.0685649	+	0.914935i
$671$	−26.8800	−	24.9410i	−1.03769	−	0.962836i
$672$	5.33518	+	2.85053i	0.205809	+	0.109961i
$673$	7.19734	+	47.7513i	0.277437	+	1.84068i	0.500333	+	0.865833i	$0.333211\pi$
$673$	7.19734	+	47.7513i	0.277437	+	1.84068i	−0.222896	+	0.974842i	$0.571551\pi$
$674$	15.4321	−	10.5214i	0.594422	−	0.405270i
$675$	2.36573	+	4.62637i	0.0910570	+	0.178069i
$676$	−0.357110	−	4.76530i	−0.0137350	−	0.183281i
$677$	14.2218	−	17.8336i	0.546588	−	0.685400i	−0.429427	−	0.903102i	$-0.641284\pi$
$677$	14.2218	−	17.8336i	0.546588	−	0.685400i	0.976015	+	0.217701i	$0.0698559\pi$
$678$	38.7442	−	1.27506i	1.48796	−	0.0489683i
$679$	−7.88521	+	3.09472i	−0.302607	+	0.118764i
$680$	−4.96017	+	1.13213i	−0.190214	+	0.0434151i
$681$	26.8831	−	26.6422i	1.03016	−	1.02093i
$682$	−5.60833	+	3.23797i	−0.214754	+	0.123988i
$683$	4.21830	+	4.54624i	0.161409	+	0.173957i	0.808578	−	0.588389i	$-0.200238\pi$
$683$	4.21830	+	4.54624i	0.161409	+	0.173957i	−0.647169	+	0.762346i	$0.724047\pi$
$684$	6.30784	−	0.892743i	0.241186	−	0.0341349i
$685$	−13.7623	−	9.38295i	−0.525829	−	0.358504i
$686$	12.5295	−	26.0179i	0.478380	−	0.993367i
$687$	−12.0170	−	3.27800i	−0.458477	−	0.125064i
$688$	30.2009	−	0.844848i	1.15140	−	0.0322095i
$689$		−	5.24679i		−	0.199887i
$690$	1.17259	−	1.35024i	0.0446399	−	0.0514026i
$691$	−14.1400	+	20.7396i	−0.537911	+	0.788970i	−0.994939	−	0.100482i	$-0.967962\pi$
$691$	−14.1400	+	20.7396i	−0.537911	+	0.788970i	0.457028	+	0.889452i	$0.348914\pi$
$692$	−4.57296	+	3.64682i	−0.173838	+	0.138631i
$693$	−28.6588	+	6.27024i	−1.08866	+	0.238187i
$694$	−8.48561	−	14.6975i	−0.322109	−	0.557910i
$695$	1.16624	−	2.01999i	0.0442380	−	0.0766225i
$696$	0.895539	−	21.3597i	0.0339453	−	0.809637i
$697$	0.446158	+	1.13679i	0.0168994	+	0.0430591i
$698$	10.1286	+	32.8363i	0.383375	+	1.24287i
$699$	13.2165	−	9.66263i	0.499895	−	0.365474i
$700$	0.623330	−	0.0467121i	0.0235596	−	0.00176555i
$701$	8.09685	−	26.2493i	0.305814	−	0.991424i	−0.664032	−	0.747704i	$-0.731156\pi$
$701$	8.09685	−	26.2493i	0.305814	−	0.991424i	0.969846	−	0.243720i	$-0.0783677\pi$
$702$	−3.53498	−	0.718438i	−0.133419	−	0.0271157i
$703$	6.96191	−	1.04934i	0.262573	−	0.0395766i
$704$	−34.1762	−	7.80050i	−1.28807	−	0.293993i
$705$	−18.5251	+	11.5241i	−0.697696	+	0.434022i
$706$	−26.5350	−	1.98852i	−0.998658	−	0.0748391i
$707$	−6.04717	+	15.4079i	−0.227427	+	0.579475i
$708$	−0.408599	+	0.925133i	−0.0153561	+	0.0347686i
$709$	−18.2261	+	8.77724i	−0.684496	+	0.329636i	−0.743608	−	0.668615i	$-0.766887\pi$
$709$	−18.2261	+	8.77724i	−0.684496	+	0.329636i	0.0591123	+	0.998251i	$0.481173\pi$
$710$	−12.3249	+	5.93535i	−0.462545	+	0.222750i
$711$	6.57973	+	5.34479i	0.246759	+	0.200445i
$712$	−11.5203	+	29.3532i	−0.431741	+	1.10006i
$713$	−0.480885	−	0.0360374i	−0.0180093	−	0.00134961i
$714$	−4.79021	−	7.70031i	−0.179269	−	0.288177i
$715$	−2.56647	−	0.585779i	−0.0959804	−	0.0219069i
$716$	−6.93931	+	1.04593i	−0.259334	+	0.0390884i
$717$	−16.5395	−	47.9586i	−0.617678	−	1.79105i
$718$	−10.7646	+	34.8979i	−0.401731	+	1.30238i
$719$	−31.0341	+	2.32568i	−1.15738	+	0.0867333i	−0.639548	−	0.768752i	$-0.720878\pi$
$719$	−31.0341	+	2.32568i	−1.15738	+	0.0867333i	−0.517828	+	0.855485i	$0.673259\pi$
$720$	−12.9117	+	4.93376i	−0.481190	+	0.183870i
$721$	−0.361258	−	1.17117i	−0.0134539	−	0.0436166i
$722$	7.50799	+	19.1301i	0.279419	+	0.711947i
$723$	−8.25989	−	0.346309i	−0.307189	−	0.0128794i
$724$	2.66695	−	4.61929i	0.0991164	−	0.171675i
$725$	−2.46277	−	4.26564i	−0.0914649	−	0.158422i
$726$	−54.6923	+	28.5915i	−2.02982	+	1.06113i
$727$	−18.0380	+	14.3849i	−0.668994	+	0.533505i	−0.898042	−	0.439910i	$-0.855010\pi$
$727$	−18.0380	+	14.3849i	−0.668994	+	0.533505i	0.229048	+	0.973415i	$0.426439\pi$
$728$	1.06478	−	1.56174i	0.0394632	−	0.0578819i
$729$	12.3676	−	24.0009i	0.458060	−	0.888921i
$730$		−	7.58854i		−	0.280865i
$731$	−11.7116	−	6.33179i	−0.433168	−	0.234190i
$732$	1.06838	−	3.91664i	0.0394885	−	0.144763i
$733$	−1.20857	+	2.50961i	−0.0446394	+	0.0926946i	−0.922096	−	0.386962i	$-0.873524\pi$
$733$	−1.20857	+	2.50961i	−0.0446394	+	0.0926946i	0.877456	+	0.479657i	$0.159239\pi$
$734$	−22.0758	−	15.0510i	−0.814831	−	0.555543i
$735$	2.87764	+	6.67748i	0.106143	+	0.246303i
$736$	0.951047	+	1.02498i	0.0350561	+	0.0377814i
$737$	77.9908	−	45.0280i	2.87283	−	1.65863i
$738$	1.36824	+	2.41993i	0.0503657	+	0.0890787i
$739$	45.0112	−	10.2735i	1.65576	−	0.377917i	0.710365	−	0.703833i	$-0.248530\pi$
$739$	45.0112	−	10.2735i	1.65576	−	0.377917i	0.945399	+	0.325916i	$0.105673\pi$
$740$	0.430359	−	0.168903i	0.0158203	−	0.00620901i
$741$	−0.145989	−	4.43607i	−0.00536305	−	0.162963i
$742$	18.7214	−	23.4759i	0.687284	−	0.861827i
$743$	−3.06750	−	40.9329i	−0.112536	−	1.50168i	−0.712509	−	0.701663i	$-0.752441\pi$
$743$	−3.06750	−	40.9329i	−0.112536	−	1.50168i	0.599974	−	0.800020i	$-0.295178\pi$
$744$	2.63687	+	1.67346i	0.0966725	+	0.0613522i
$745$	−11.1088	+	7.57388i	−0.406997	+	0.277486i
$746$	2.15317	+	14.2853i	0.0788331	+	0.523023i
$747$	25.9632	+	24.5290i	0.949943	+	0.897471i
$748$	−3.24678	−	3.01257i	−0.118714	−	0.110150i
$749$	−1.21836	+	16.2578i	−0.0445178	+	0.594049i
$750$	−1.59419	+	2.13982i	−0.0582116	+	0.0781351i
$751$	1.98565	−	13.1740i	0.0724575	−	0.480724i	−0.922944	−	0.384934i	$-0.874224\pi$
$751$	1.98565	−	13.1740i	0.0724575	−	0.480724i	0.995402	−	0.0957901i	$-0.0305378\pi$
$752$	−25.1805	−	52.2879i	−0.918239	−	1.90674i
$753$	4.71680	+	25.5583i	0.171890	+	0.931395i
$754$	3.38119	+	0.509632i	0.123136	+	0.0185597i
$755$	−17.4337	−	6.84224i	−0.634478	−	0.249014i
$756$	−2.08518	−	2.49028i	−0.0758374	−	0.0905706i
$757$	3.41775	−	3.68346i	0.124220	−	0.133878i	−0.667879	−	0.744270i	$-0.732798\pi$
$757$	3.41775	−	3.68346i	0.124220	−	0.133878i	0.792099	+	0.610392i	$0.208988\pi$
$758$	−7.35162	+	32.2095i	−0.267023	+	1.16990i
$759$	−6.73522	−	0.789600i	−0.244473	−	0.0286607i
$760$	−8.02757	−	11.7743i	−0.291190	−	0.427098i
$761$	19.5009	+	6.01524i	0.706908	+	0.218052i	0.627304	−	0.778774i	$-0.284158\pi$
$761$	19.5009	+	6.01524i	0.706908	+	0.218052i	0.0796039	+	0.996827i	$0.474634\pi$
$762$	6.78738	−	35.0086i	0.245881	−	1.26823i
$763$	−6.41068	−	5.11235i	−0.232082	−	0.185079i
$764$	−4.41088	+	1.36058i	−0.159580	+	0.0492239i
$765$	6.01447	+	0.961999i	0.217454	+	0.0347811i
$766$	7.29771	+	31.9734i	0.263677	+	1.15524i
$767$	0.610207	+	0.352303i	0.0220333	+	0.0127209i
$768$	−3.82093	−	14.5211i	−0.137876	−	0.523985i
$769$	−22.1018	+	20.5075i	−0.797011	+	0.739518i	−0.969394	−	0.245512i	$-0.921044\pi$
$769$	−22.1018	+	20.5075i	−0.797011	+	0.739518i	0.172382	+	0.985030i	$0.444854\pi$
$770$	−9.39307	−	11.7785i	−0.338503	−	0.424469i
$771$	−20.6094	−	24.1677i	−0.742228	−	0.870379i
$772$	2.92557	+	1.40888i	0.105294	+	0.0507068i
$773$	49.9817			1.79772			0.898859	−	0.438238i	$-0.144397\pi$
$773$	49.9817			1.79772			0.898859	+	0.438238i	$0.144397\pi$
$774$	−28.4169	−	10.5355i	−1.02142	−	0.378689i
$775$	0.719547			0.0258469
$776$	11.4251	+	5.50205i	0.410138	+	0.197512i
$777$	−2.32912	−	2.73126i	−0.0835566	−	0.0979834i
$778$	12.6513	+	15.8642i	0.453570	+	0.568758i
$779$	−2.50743	+	2.32656i	−0.0898381	+	0.0833576i
$780$	−0.0741651	−	0.281858i	−0.00265554	−	0.0100921i
$781$	44.9234	+	25.9365i	1.60749	+	0.928083i
$782$	−0.466464	−	2.04371i	−0.0166807	−	0.0730831i
$783$	−10.5507	+	23.3180i	−0.377050	+	0.833316i
$784$	−18.4826	+	5.70111i	−0.660091	+	0.203611i
$785$	1.57584	+	1.25669i	0.0562440	+	0.0448531i
$786$	4.78711	−	24.6914i	0.170751	−	0.880713i
$787$	51.2146	+	15.7976i	1.82560	+	0.563124i	0.999999	−	0.00112521i	$-0.000358166\pi$
$787$	51.2146	+	15.7976i	1.82560	+	0.563124i	0.825604	+	0.564249i	$0.190834\pi$
$788$	4.92280	+	7.22042i	0.175368	+	0.257217i
$789$	−3.60848	−	0.423038i	−0.128465	−	0.0150606i
$790$	−0.968679	+	4.24406i	−0.0344640	+	0.150997i
$791$	16.5404	−	17.8264i	0.588110	−	0.633832i
$792$	36.0623	+	25.0655i	1.28142	+	0.890663i
$793$	−2.63290	−	1.03334i	−0.0934972	−	0.0366949i
$794$	−5.14027	−	0.774771i	−0.182421	−	0.0274956i
$795$	3.66008	+	19.8324i	0.129810	+	0.703382i
$796$	−0.0812023	−	0.168618i	−0.00287814	−	0.00597651i
$797$	0.420630	−	2.79070i	0.0148995	−	0.0988516i	−0.980145	−	0.198282i	$-0.936464\pi$
$797$	0.420630	−	2.79070i	0.0148995	−	0.0988516i	0.995045	+	0.0994302i	$0.0317020\pi$
$798$	15.1754	−	20.3694i	0.537204	−	0.721068i
$799$	−1.91114	+	25.5024i	−0.0676113	+	0.902210i
$800$	−1.52939	−	1.41907i	−0.0540722	−	0.0501717i
$801$	25.9250	−	27.4408i	0.916016	−	0.969573i
$802$	−1.54379	−	10.2424i	−0.0545132	−	0.361672i
$803$	−23.7757	+	16.2100i	−0.839026	+	0.572038i
$804$	8.41829	+	5.34258i	0.296890	+	0.188418i
$805$	−0.0838355	−	1.11871i	−0.00295481	−	0.0394293i
$806$	−0.311446	+	0.390541i	−0.0109702	+	0.0137562i
$807$	0.861634	+	26.1818i	0.0303309	+	0.921643i
$808$	23.0660	−	9.05274i	0.811460	−	0.318474i
$809$	25.6237	−	5.84845i	0.900883	−	0.205621i	0.253095	−	0.967441i	$-0.418551\pi$
$809$	25.6237	−	5.84845i	0.900883	−	0.205621i	0.647788	+	0.761821i	$0.275694\pi$
$810$	13.8631	+	0.249682i	0.487099	+	0.00877293i
$811$	−21.5645	+	12.4503i	−0.757232	+	0.437188i	−0.828301	−	0.560283i	$-0.810692\pi$
$811$	−21.5645	+	12.4503i	−0.757232	+	0.437188i	0.0710690	+	0.997471i	$0.477359\pi$
$812$	2.09414	+	2.25695i	0.0734900	+	0.0792034i
$813$	−11.8325	−	27.4570i	−0.414984	−	0.962957i
$814$	−9.20640	−	6.27682i	−0.322684	−	0.220002i
$815$	6.55697	−	13.6157i	0.229680	−	0.476936i
$816$	−4.26390	+	15.6312i	−0.149266	+	0.547203i
$817$	4.52459	−	37.0152i	0.158295	−	1.29500i
$818$			31.6358i			1.10612i
$819$	−1.88108	+	1.25784i	−0.0657303	+	0.0439525i
$820$	−0.126527	+	0.185581i	−0.00441852	+	0.00648077i
$821$	22.3024	−	17.7856i	0.778359	−	0.620721i	−0.151575	−	0.988446i	$-0.548435\pi$
$821$	22.3024	−	17.7856i	0.778359	−	0.620721i	0.929935	+	0.367725i	$0.119863\pi$
$822$	−39.3885	+	20.5911i	−1.37383	+	0.718196i
$823$	−7.24092	−	12.5416i	−0.252403	−	0.437174i	0.711784	−	0.702398i	$-0.247887\pi$
$823$	−7.24092	−	12.5416i	−0.252403	−	0.437174i	−0.964187	+	0.265224i	$0.914554\pi$
$824$	−0.917390	+	1.58897i	−0.0319588	+	0.0553543i
$825$	10.1096	+	0.423863i	0.351973	+	0.0147570i
$826$	1.47320	+	3.75364i	0.0512590	+	0.130606i
$827$	−0.361347	−	1.17146i	−0.0125653	−	0.0407356i	0.949073	−	0.315056i	$-0.102023\pi$
$827$	−0.361347	−	1.17146i	−0.0125653	−	0.0407356i	−0.961638	+	0.274320i	$0.911547\pi$
$828$	−0.267991	−	0.701334i	−0.00931333	−	0.0243730i
$829$	−35.5105	+	2.66115i	−1.23333	+	0.0924255i	−0.675394	−	0.737457i	$-0.736026\pi$
$829$	−35.5105	+	2.66115i	−1.23333	+	0.0924255i	−0.557938	+	0.829882i	$0.688407\pi$
$830$	−5.40645	+	17.5273i	−0.187661	+	0.608381i
$831$	12.5842	+	36.4897i	0.436540	+	1.26581i
$832$	−2.67377	+	0.403006i	−0.0926962	+	0.0139717i
$833$	8.30953	+	1.89660i	0.287908	+	0.0657132i
$834$	−3.28758	−	5.28483i	−0.113840	−	0.182999i
$835$	−1.35973	−	0.101898i	−0.0470556	−	0.00352633i
$836$	4.53232	−	11.5482i	0.156754	−	0.399402i
$837$	−2.17939	−	3.03800i	−0.0753306	−	0.105009i
$838$	−47.3175	+	22.7869i	−1.63456	+	0.787160i
$839$	5.57793	−	2.68619i	0.192572	−	0.0927376i	−0.335113	−	0.942178i	$-0.608775\pi$
$839$	5.57793	−	2.68619i	0.192572	−	0.0927376i	0.527685	+	0.849440i	$0.323060\pi$
$840$	−2.93531	+	6.64601i	−0.101278	+	0.229309i
$841$	−1.73140	+	4.41152i	−0.0597033	+	0.152121i
$842$	0.617045	+	0.0462411i	0.0212648	+	0.00159357i
$843$	−8.28165	+	5.15184i	−0.285235	+	0.177439i
$844$	−0.253417	−	0.0578407i	−0.00872297	−	0.00199096i
$845$	12.6540	−	1.90729i	0.435311	−	0.0656126i
$846$	3.82760	+	58.0903i	0.131596	+	1.99719i
$847$	−11.4113	+	36.9947i	−0.392098	+	1.27115i
$848$	−53.4967	+	4.00902i	−1.83708	+	0.137670i
$849$	3.56725	−	2.60803i	0.122428	−	0.0895072i
$850$	0.921957	+	2.98891i	0.0316229	+	0.102519i
$851$	−0.303136	−	0.772377i	−0.0103914	−	0.0264768i
$852$	−0.240577	+	5.73805i	−0.00824204	+	0.196582i
$853$	−23.0240	+	39.8788i	−0.788327	+	1.36542i	0.138664	+	0.990339i	$0.455719\pi$
$853$	−23.0240	+	39.8788i	−0.788327	+	1.36542i	−0.926991	+	0.375083i	$0.877614\pi$
$854$	−8.09337	−	14.0181i	−0.276949	−	0.479690i
$855$	3.64636	+	16.6661i	0.124703	+	0.569969i
$856$	19.0819	−	15.2173i	0.652204	−	0.520116i
$857$	−1.26115	+	1.84976i	−0.0430799	+	0.0631866i	−0.847174	−	0.531315i	$-0.821698\pi$
$857$	−1.26115	+	1.84976i	−0.0430799	+	0.0631866i	0.804095	+	0.594501i	$0.202651\pi$
$858$	−4.60587	+	5.30364i	−0.157242	+	0.181063i
$859$			25.0062i			0.853202i	0.904440	+	0.426601i	$0.140289\pi$
$859$			25.0062i			0.853202i	−0.904440	+	0.426601i	$0.859711\pi$
$860$	−0.251201	−	2.43577i	−0.00856589	−	0.0830591i
$861$	1.68244	+	0.458935i	0.0573372	+	0.0156405i
$862$	1.50746	−	3.13027i	0.0513443	−	0.106618i
$863$	9.55911	+	6.51729i	0.325396	+	0.221851i	0.714989	−	0.699136i	$-0.246432\pi$
$863$	9.55911	+	6.51729i	0.325396	+	0.221851i	−0.389593	+	0.920987i	$0.627384\pi$
$864$	−1.35918	+	10.7554i	−0.0462404	+	0.365905i
$865$	−10.6538	−	11.4820i	−0.362240	−	0.390401i
$866$	38.0288	−	21.9560i	1.29227	−	0.746094i
$867$	−15.8429	+	15.7009i	−0.538054	+	0.533231i
$868$	−0.438496	+	0.100084i	−0.0148835	+	0.00339707i
$869$	15.3663	−	6.03082i	0.521265	−	0.204582i
$870$	−13.1361	+	0.432304i	−0.445355	+	0.0146565i
$871$	4.33104	−	5.43095i	0.146752	−	0.184021i
$872$	0.917307	+	12.2406i	0.0310639	+	0.414520i
$873$	−10.2253	−	11.2212i	−0.346074	−	0.379781i
$874$	4.85130	−	3.30756i	0.164098	−	0.111880i
$875$	0.249484	+	1.65522i	0.00843411	+	0.0559567i
$876$	−2.80997	−	1.50133i	−0.0949400	−	0.0507254i
$877$	−5.17822	−	4.80469i	−0.174856	−	0.162243i	0.587890	−	0.808941i	$-0.299959\pi$
$877$	−5.17822	−	4.80469i	−0.174856	−	0.162243i	−0.762746	+	0.646698i	$0.776149\pi$
$878$	0.990756	−	13.2207i	0.0334364	−	0.446178i
$879$	−35.0426	−	26.1071i	−1.18196	−	0.880572i
$880$	−4.01164	+	26.6155i	−0.135232	+	0.897208i
$881$	2.60018	+	5.39934i	0.0876024	+	0.181908i	0.940167	−	0.340713i	$-0.110668\pi$
$881$	2.60018	+	5.39934i	0.0876024	+	0.181908i	−0.852565	+	0.522621i	$0.824954\pi$
$882$	19.3341	+	1.62408i	0.651014	+	0.0546857i
$883$	−1.84943	−	0.278757i	−0.0622383	−	0.00938092i	0.117849	−	0.993031i	$-0.462400\pi$
$883$	−1.84943	−	0.278757i	−0.0622383	−	0.00938092i	−0.180088	+	0.983651i	$0.557638\pi$
$884$	−0.318023	−	0.124815i	−0.0106963	−	0.00419798i
$885$	−2.55229	−	0.906004i	−0.0857943	−	0.0304550i
$886$	22.7282	−	24.4952i	0.763569	−	0.822932i
$887$	8.88091	−	38.9098i	0.298192	−	1.30646i	−0.574625	−	0.818417i	$-0.694852\pi$
$887$	8.88091	−	38.9098i	0.298192	−	1.30646i	0.872817	−	0.488047i	$-0.162291\pi$
$888$	−0.625684	+	5.33702i	−0.0209966	+	0.179099i
$889$	−12.6017	−	18.4833i	−0.422647	−	0.619909i
$890$	18.5248	+	5.71414i	0.620953	+	0.191538i
$891$	−28.8308	−	43.9678i	−0.965869	−	1.47298i
$892$	−4.78102	−	3.81274i	−0.160080	−	0.127660i
$893$	−68.4488	+	21.1136i	−2.29055	+	0.706541i
$894$	3.85636	+	35.6687i	0.128976	+	1.19294i
$895$	−4.18182	−	18.3218i	−0.139783	−	0.612429i
$896$	−19.4503	−	11.2296i	−0.649787	−	0.375155i
$897$	−0.505858	+	0.133106i	−0.0168901	+	0.00444429i
$898$	−27.1059	+	25.1506i	−0.904534	+	0.839285i
$899$	2.20974	+	2.77093i	0.0736991	+	0.0924157i
$900$	0.476957	+	1.01366i	0.0158986	+	0.0337887i
$901$	21.2990	+	10.2570i	0.709572	+	0.341712i
$902$	5.41343			0.180247
$903$	−17.2425	+	8.00953i	−0.573796	+	0.266540i
$904$	−36.4046			−1.21080
$905$	12.8693	+	6.19753i	0.427790	+	0.206013i
$906$	−38.0256	+	32.4268i	−1.26331	+	1.07731i
$907$	5.04944	+	6.33180i	0.167664	+	0.210244i	0.858564	−	0.512706i	$-0.171357\pi$
$907$	5.04944	+	6.33180i	0.167664	+	0.210244i	−0.690900	+	0.722950i	$0.742786\pi$
$908$	5.98167	−	5.55018i	0.198509	−	0.184189i
$909$	−29.6635	−	0.267107i	−0.983878	−	0.00885938i
$910$	−1.00637	−	0.581029i	−0.0333609	−	0.0192609i
$911$	−4.87219	−	21.3464i	−0.161423	−	0.707239i	−0.989247	−	0.146252i	$-0.953279\pi$
$911$	−4.87219	−	21.3464i	−0.161423	−	0.707239i	0.827825	−	0.560987i	$-0.189578\pi$
$912$	−45.1190	+	4.87808i	−1.49404	+	0.161529i
$913$	66.4636	−	20.5013i	2.19962	−	0.678494i
$914$	−1.84096	−	1.46812i	−0.0608935	−	0.0485609i
$915$	10.6730	+	2.06925i	0.352838	+	0.0684074i
$916$	−2.56616	−	0.791556i	−0.0847884	−	0.0261537i
$917$	−8.88791	−	13.0362i	−0.293505	−	0.430492i
$918$	9.82704	−	12.9455i	0.324341	−	0.427265i
$919$	−10.7684	+	47.1794i	−0.355216	+	1.55630i	0.409728	+	0.912208i	$0.365624\pi$
$919$	−10.7684	+	47.1794i	−0.355216	+	1.55630i	−0.764944	+	0.644097i	$0.777233\pi$
$920$	−1.14230	+	1.23111i	−0.0376605	+	0.0405884i
$921$	4.82265	−	13.5858i	0.158912	−	0.447668i
$922$	−15.7691	−	6.18890i	−0.519326	−	0.203821i
$923$	3.95653	+	0.596350i	0.130231	+	0.0196291i
$924$	−6.21983	+	1.14787i	−0.204617	+	0.0377623i
$925$	0.537172	+	1.11545i	0.0176621	+	0.0366758i
$926$	−2.77043	+	18.3806i	−0.0910420	+	0.604024i
$927$	1.72960	−	1.35401i	0.0568075	−	0.0444716i
$928$	0.767950	−	10.2476i	0.0252092	−	0.336393i
$929$	29.3440	+	27.2273i	0.962745	+	0.893297i	0.994344	−	0.106204i	$-0.0338695\pi$
$929$	29.3440	+	27.2273i	0.962745	+	0.893297i	−0.0315991	+	0.999501i	$0.510060\pi$
$930$	0.904802	−	1.69347i	0.0296696	−	0.0555310i
$931$	3.55810	+	23.6065i	0.116612	+	0.773670i
$932$	2.91640	−	1.98837i	0.0955298	−	0.0651311i
$933$	−23.0579	+	36.3323i	−0.754882	+	1.18947i
$934$	−3.03296	−	40.4720i	−0.0992414	−	1.32428i
$935$	7.39516	−	9.27324i	0.241848	−	0.303267i
$936$	3.29573	+	0.783516i	0.107724	+	0.0256100i
$937$	−24.7136	+	9.69937i	−0.807358	+	0.316865i	−0.732880	−	0.680358i	$-0.761824\pi$
$937$	−24.7136	+	9.69937i	−0.807358	+	0.316865i	−0.0744781	+	0.997223i	$0.523729\pi$
$938$	38.7570	−	8.84604i	1.26546	−	0.288833i
$939$	13.9424	+	14.0685i	0.454992	+	0.459108i
$940$	−4.07348	+	2.35183i	−0.132862	+	0.0767081i
$941$	33.0031	+	35.5689i	1.07587	+	1.15951i	0.986542	+	0.163510i	$0.0522817\pi$
$941$	33.0031	+	35.5689i	1.07587	+	1.15951i	0.0893286	+	0.996002i	$0.471528\pi$
$942$	4.93919	−	2.12853i	0.160927	−	0.0693512i
$943$	0.333068	+	0.227082i	0.0108462	+	0.00739480i
$944$	3.12586	−	6.49092i	0.101738	−	0.211261i
$945$	6.23287	−	6.06674i	0.202755	−	0.197351i
$946$	−45.0945	+	38.0725i	−1.46615	+	1.23784i
$947$		−	48.4003i		−	1.57280i	−0.617718	−	0.786400i	$-0.711943\pi$
$947$		−	48.4003i		−	1.57280i	0.617718	−	0.786400i	$-0.288057\pi$
$948$	1.37989	+	1.19835i	0.0448167	+	0.0389205i
$949$	−1.25035	+	1.83393i	−0.0405882	+	0.0595319i
$950$	−6.84963	+	5.46240i	−0.222231	+	0.177224i
$951$	5.20335	+	9.95343i	0.168730	+	0.322762i
$952$	4.25822	+	7.37545i	0.138010	+	0.239040i
$953$	0.276655	−	0.479180i	0.00896173	−	0.0155222i	−0.861510	−	0.507741i	$-0.830481\pi$
$953$	0.276655	−	0.479180i	0.00896173	−	0.0155222i	0.870471	+	0.492219i	$0.163814\pi$
$954$	51.2784	+	16.3244i	1.66020	+	0.528521i
$955$	−4.51606	−	11.5067i	−0.146136	−	0.372349i
$956$	−3.22381	−	10.4513i	−0.104265	−	0.338020i
$957$	29.4146	+	40.2333i	0.950840	+	1.30056i
$958$	63.0764	−	4.72692i	2.03791	−	0.152720i
$959$	−8.21826	+	26.6429i	−0.265381	+	0.860345i
$960$	9.82547	−	3.38851i	0.317116	−	0.109364i
$961$	30.1418	−	4.54314i	0.972316	−	0.146553i
$962$	−0.837928	−	0.191252i	−0.0270159	−	0.00616620i
$963$	−27.9974	+	8.36071i	−0.902202	+	0.269420i
$964$	−1.77737	−	0.133196i	−0.0572454	−	0.00428995i
$965$	−3.17688	+	8.09455i	−0.102267	+	0.260573i
$966$	−2.73832	−	1.20942i	−0.0881040	−	0.0389125i
$967$	28.2485	−	13.6038i	0.908411	−	0.437468i	0.0794915	−	0.996836i	$-0.474670\pi$
$967$	28.2485	−	13.6038i	0.908411	−	0.437468i	0.828920	+	0.559368i	$0.188956\pi$
$968$	52.2172	−	25.1465i	1.67832	−	0.808238i
$969$	18.2933	+	8.07952i	0.587666	+	0.259552i
$970$	2.84822	−	7.25716i	0.0914510	−	0.233013i
$971$	0.0677939	+	0.00508045i	0.00217561	+	0.000163039i	0.0758179	−	0.997122i	$-0.475843\pi$
$971$	0.0677939	+	0.00508045i	0.00217561	+	0.000163039i	−0.0736422	+	0.997285i	$0.523462\pi$
$972$	2.83516	−	5.08397i	0.0909377	−	0.163068i
$973$	−3.80649	−	0.868807i	−0.122031	−	0.0278527i
$974$	23.9359	−	3.60775i	0.766955	−	0.115600i
$975$	0.737844	−	0.254460i	0.0236299	−	0.00814924i
$976$	−8.52423	+	27.6349i	−0.272854	+	0.884571i
$977$	−27.6399	+	2.07133i	−0.884280	+	0.0662676i	−0.509123	−	0.860694i	$-0.670030\pi$
$977$	−27.6399	+	2.07133i	−0.884280	+	0.0662676i	−0.375157	+	0.926961i	$0.622411\pi$
$978$	−23.7997	−	32.5531i	−0.761029	−	1.04093i
$979$	−21.6681	−	70.2461i	−0.692514	−	2.24508i
$980$	0.572718	+	1.45926i	0.0182948	+	0.0466144i
$981$	4.45778	−	14.0028i	0.142326	−	0.447077i
$982$	−14.3449	+	24.8461i	−0.457765	+	0.792871i
$983$	21.4285	+	37.1153i	0.683464	+	1.18379i	0.973917	+	0.226905i	$0.0728608\pi$
$983$	21.4285	+	37.1153i	0.683464	+	1.18379i	−0.290453	+	0.956889i	$0.593806\pi$
$984$	−1.20948	−	2.31360i	−0.0385568	−	0.0737549i
$985$	−18.2966	+	14.5911i	−0.582978	+	0.464910i
$986$	−8.67876	+	12.7294i	−0.276388	+	0.405387i
$987$	27.5736	+	23.9459i	0.877676	+	0.762206i
$988$		−	0.956913i		−	0.0304435i
$989$	−4.37155	+	0.450838i	−0.139007	+	0.0143358i
$990$	13.7100	−	23.2603i	0.435734	−	0.739260i
$991$	−22.9847	+	47.7283i	−0.730134	+	1.51614i	0.121837	+	0.992550i	$0.461122\pi$
$991$	−22.9847	+	47.7283i	−0.730134	+	1.51614i	−0.851971	+	0.523589i	$0.824593\pi$
$992$	1.24036	+	0.845665i	0.0393816	+	0.0268499i
$993$	31.5723	−	13.6060i	1.00192	−	0.431773i
$994$	15.5749	+	16.7858i	0.494007	+	0.532413i
$995$	0.434036	−	0.250591i	0.0137599	−	0.00794426i
$996$	5.42057	+	5.46960i	0.171757	+	0.173311i
$997$	−5.79112	+	1.32179i	−0.183407	+	0.0418614i	−0.313238	−	0.949675i	$-0.601414\pi$
$997$	−5.79112	+	1.32179i	−0.183407	+	0.0418614i	0.129831	+	0.991536i	$0.458557\pi$
$998$	20.6824	−	8.11723i	0.654689	−	0.256946i
$999$	3.08254	−	5.64651i	0.0975273	−	0.178648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	645.2.bn.b.491.22	yes	348
3.2	odd	2		645.2.bn.a.491.8	yes	348
43.12	odd	42		645.2.bn.a.356.8	✓	348
129.98	even	42	inner	645.2.bn.b.356.22	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
645.2.bn.a.356.8	✓	348	43.12	odd	42
645.2.bn.a.491.8	yes	348	3.2	odd	2
645.2.bn.b.356.22	yes	348	129.98	even	42	inner
645.2.bn.b.491.22	yes	348	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 645 = 3 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	645.bn (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38802 + 0.668438i) q^{2} +(1.12387 + 1.31792i) q^{3} +(0.232825 + 0.291953i) q^{4} +(-0.733052 + 0.680173i) q^{5} +(0.679017 + 2.58054i) q^{6} +(1.44966 + 0.836959i) q^{7} +(-0.557614 - 2.44306i) q^{8} +(-0.473820 + 2.96235i) q^{9} +(-1.47215 + 0.454097i) q^{10} +(4.56741 + 3.64239i) q^{11} +(-0.123105 + 0.634962i) q^{12} +(0.430596 + 0.132821i) q^{13} +(1.45270 + 2.13072i) q^{14} +(-1.72027 - 0.201675i) q^{15} +(1.02524 - 4.49188i) q^{16} +(-1.38096 + 1.48832i) q^{17} +(-2.63782 + 3.79509i) q^{18} +(-5.29367 - 2.07761i) q^{19} +(-0.369251 - 0.0556556i) q^{20} +(0.526184 + 2.85116i) q^{21} +(3.90497 + 8.10875i) q^{22} +(-0.0998868 + 0.662706i) q^{23} +(2.59307 - 3.48058i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(0.508895 + 0.472186i) q^{26} +(-4.43664 + 2.70484i) q^{27} +(0.0931629 + 0.618096i) q^{28} +(4.06967 - 2.77465i) q^{29} +(-2.25297 - 1.42982i) q^{30} +(0.0537718 + 0.717535i) q^{31} +(1.30081 - 1.63116i) q^{32} +(0.332817 + 10.1130i) q^{33} +(-2.91165 + 1.14274i) q^{34} +(-1.63195 + 0.372482i) q^{35} +(-0.975183 + 0.551374i) q^{36} +(-1.07219 + 0.619028i) q^{37} +(-5.95899 - 6.42227i) q^{38} +(0.308888 + 0.716765i) q^{39} +(2.07047 + 1.41162i) q^{40} +(0.260977 - 0.541924i) q^{41} +(-1.17547 + 4.30921i) q^{42} +(1.63737 + 6.34973i) q^{43} +2.18150i q^{44} +(-1.66757 - 2.49383i) q^{45} +(-0.581623 + 0.853084i) q^{46} +(9.84801 - 7.85353i) q^{47} +(7.07218 - 3.69712i) q^{48} +(-2.09900 - 3.63557i) q^{49} +(0.770296 - 1.33419i) q^{50} +(-3.51351 - 0.147309i) q^{51} +(0.0614758 + 0.156638i) q^{52} +(-3.43201 - 11.1263i) q^{53} +(-7.96619 + 0.788772i) q^{54} +(-5.82560 + 0.436568i) q^{55} +(1.23640 - 4.00830i) q^{56} +(-3.21129 - 9.31160i) q^{57} +(7.50348 - 1.13097i) q^{58} +(1.52445 + 0.347946i) q^{59} +(-0.341642 - 0.549193i) q^{60} +(-6.25924 - 0.469065i) q^{61} +(-0.404991 + 1.03190i) q^{62} +(-3.16624 + 3.89781i) q^{63} +(-5.40636 + 2.60357i) q^{64} +(-0.405991 + 0.195515i) q^{65} +(-6.29798 + 14.2596i) q^{66} +(5.63190 - 14.3498i) q^{67} +(-0.756041 - 0.0566574i) q^{68} +(-0.985652 + 0.613154i) q^{69} +(-2.51417 - 0.573842i) q^{70} +(8.78026 - 1.32341i) q^{71} +(7.50141 - 0.494273i) q^{72} +(-1.45189 + 4.70690i) q^{73} +(-1.90200 + 0.142536i) q^{74} +(1.39822 - 1.02224i) q^{75} +(-0.625932 - 2.02922i) q^{76} +(3.57264 + 9.10293i) q^{77} +(-0.0503689 + 1.20136i) q^{78} +(1.41284 - 2.44710i) q^{79} +(2.30370 + 3.99013i) q^{80} +(-8.55099 - 2.80724i) q^{81} +(0.724484 - 0.577757i) q^{82} +(6.70685 - 9.83714i) q^{83} +(-0.709897 + 0.817442i) q^{84} -2.03031i q^{85} +(-1.97169 + 9.90806i) q^{86} +(8.23055 + 2.24513i) q^{87} +(6.35173 - 13.1895i) q^{88} +(-10.3970 - 7.08855i) q^{89} +(-0.647661 - 4.57617i) q^{90} +(0.513050 + 0.552936i) q^{91} +(-0.216735 + 0.125132i) q^{92} +(-0.885220 + 0.877285i) q^{93} +(18.9189 - 4.31811i) q^{94} +(5.29367 - 2.07761i) q^{95} +(3.61168 - 0.118859i) q^{96} +(-3.15513 + 3.95641i) q^{97} +(-0.483310 - 6.44932i) q^{98} +(-12.9541 + 11.8044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q - 56 q^{4} + 29 q^{5} - 4 q^{6} - 3 q^{7} - 8 q^{9} - 7 q^{12} + 5 q^{13} - 42 q^{14} - 7 q^{15} - 68 q^{16} - 22 q^{18} - 30 q^{19} + 28 q^{20} + 4 q^{21} - 42 q^{22} + 6 q^{23} + 9 q^{24} + 29 q^{25}+ \cdots - q^{99}+O(q^{100}) \) 348 * q - 56 * q^4 + 29 * q^5 - 4 * q^6 - 3 * q^7 - 8 * q^9 - 7 * q^12 + 5 * q^13 - 42 * q^14 - 7 * q^15 - 68 * q^16 - 22 * q^18 - 30 * q^19 + 28 * q^20 + 4 * q^21 - 42 * q^22 + 6 * q^23 + 9 * q^24 + 29 * q^25 + 182 * q^26 + 6 * q^27 + 18 * q^28 + 2 * q^29 + 2 * q^30 + 72 * q^31 - 23 * q^33 - 84 * q^34 - 21 * q^35 + 56 * q^36 - 39 * q^37 - 4 * q^39 - 84 * q^42 + 6 * q^43 + 4 * q^45 - 94 * q^46 - 28 * q^47 - 72 * q^48 + 175 * q^49 + 103 * q^51 - 56 * q^52 + 94 * q^53 + 22 * q^54 - 90 * q^56 + 74 * q^57 - 40 * q^58 - 7 * q^60 + 30 * q^61 - 104 * q^62 + q^63 - 76 * q^64 - 10 * q^65 - 22 * q^66 + 9 * q^67 + 98 * q^68 - 244 * q^69 - 8 * q^71 + 85 * q^72 - 75 * q^73 - 42 * q^74 - 14 * q^75 + 30 * q^76 - 16 * q^77 + 44 * q^78 + 20 * q^79 - 148 * q^80 - 136 * q^81 - 30 * q^83 - 124 * q^84 + 38 * q^86 + 42 * q^87 + 42 * q^88 - 102 * q^89 - 82 * q^90 - 13 * q^91 + 24 * q^92 - 167 * q^93 - 56 * q^94 + 30 * q^95 - 494 * q^96 - 64 * q^97 - 12 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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