LMFDB - Embedded newform 930.2.be.b.37.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.13
Character	$\chi$	$=$	930.37
Dual form			930.2.be.b.553.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(0.260478 - 2.22084i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.587501 - 2.19258i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(0.260478 - 2.22084i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.587501 - 2.19258i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.75456 - 1.38619i) q^{10} +(-5.18915 - 2.99595i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-0.731893 + 0.196110i) q^{13} +(1.96582 - 1.13497i) q^{14} +(2.07775 + 0.826399i) q^{15} -1.00000 q^{16} +(-5.99105 - 1.60530i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(2.07086 - 1.19561i) q^{19} +(2.22084 + 0.260478i) q^{20} +(1.96582 + 1.13497i) q^{21} +(-1.55082 - 5.78774i) q^{22} +(-2.38785 - 2.38785i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.86430 - 1.15696i) q^{25} +(-0.656197 - 0.378856i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.19258 + 0.587501i) q^{28} -0.413869 q^{29} +(0.884842 + 2.05355i) q^{30} +(-5.55275 - 0.408678i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.23692 - 4.23692i) q^{33} +(-3.10119 - 5.37143i) q^{34} +(-4.71636 - 1.87587i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.75587 + 1.00638i) q^{37} +(2.30975 + 0.618895i) q^{38} -0.757711i q^{39} +(1.38619 + 1.75456i) q^{40} +(-1.22955 + 2.12965i) q^{41} +(0.587501 + 2.19258i) q^{42} +(-0.299644 + 1.11829i) q^{43} +(2.99595 - 5.18915i) q^{44} +(-1.33600 + 1.79307i) q^{45} -3.37693i q^{46} +(6.11972 + 6.11972i) q^{47} +(0.258819 - 0.965926i) q^{48} +(1.59991 + 0.923708i) q^{49} +(-2.62149 - 4.25768i) q^{50} +(3.10119 - 5.37143i) q^{51} +(-0.196110 - 0.731893i) q^{52} +(0.400077 - 0.107200i) q^{53} +1.00000 q^{54} +(-8.00521 + 10.7439i) q^{55} +(1.13497 + 1.96582i) q^{56} +(0.618895 + 2.30975i) q^{57} +(-0.292650 - 0.292650i) q^{58} +(9.59250 - 5.53823i) q^{59} +(-0.826399 + 2.07775i) q^{60} -1.49492i q^{61} +(-3.63740 - 4.21536i) q^{62} +(-1.60508 + 1.60508i) q^{63} -1.00000i q^{64} +(0.244888 + 1.67650i) q^{65} +5.99191 q^{66} +(13.5411 - 3.62833i) q^{67} +(1.60530 - 5.99105i) q^{68} +(2.92451 - 1.68847i) q^{69} +(-2.00853 - 4.66141i) q^{70} +(1.10218 - 1.90904i) q^{71} +(0.965926 - 0.258819i) q^{72} +(5.84213 - 1.56540i) q^{73} +(1.94418 + 3.36742i) q^{74} +(2.37651 - 4.39911i) q^{75} +(1.19561 + 2.07086i) q^{76} +(-9.61751 + 9.61751i) q^{77} +(0.535783 - 0.535783i) q^{78} +(-6.77438 - 11.7336i) q^{79} +(-0.260478 + 2.22084i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-2.37532 + 0.636464i) q^{82} +(-3.43940 + 0.921586i) q^{83} +(-1.13497 + 1.96582i) q^{84} +(-5.12565 + 12.8870i) q^{85} +(-1.00263 + 0.578869i) q^{86} +(0.107117 - 0.399767i) q^{87} +(5.78774 - 1.55082i) q^{88} +12.0649 q^{89} +(-2.21259 + 0.323195i) q^{90} +1.71995i q^{91} +(2.38785 - 2.38785i) q^{92} +(1.83191 - 5.25777i) q^{93} +8.65459i q^{94} +(-2.11586 - 4.91049i) q^{95} +(0.866025 - 0.500000i) q^{96} +(7.87927 + 7.87927i) q^{97} +(0.478147 + 1.78447i) q^{98} +(2.99595 + 5.18915i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$			1.00000i			0.500000i
$5$	0.260478	−	2.22084i	0.116489	−	0.993192i
$5$	0.260478	−	2.22084i	0.116489	−	0.993192i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	0.587501	−	2.19258i	0.222055	−	0.828719i	−0.761509	−	0.648155i	$-0.775541\pi$
$7$	0.587501	−	2.19258i	0.222055	−	0.828719i	0.983563	−	0.180564i	$-0.0577924\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	1.75456	−	1.38619i	0.554841	−	0.438351i
$11$	−5.18915	−	2.99595i	−1.56459	−	0.903314i	−0.996783	−	0.0801504i	$-0.974460\pi$
$11$	−5.18915	−	2.99595i	−1.56459	−	0.903314i	−0.567804	−	0.823164i	$-0.692207\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	−0.731893	+	0.196110i	−0.202991	+	0.0543911i	−0.358882	−	0.933383i	$-0.616842\pi$
$13$	−0.731893	+	0.196110i	−0.202991	+	0.0543911i	0.155891	+	0.987774i	$0.450175\pi$
$14$	1.96582	−	1.13497i	0.525387	−	0.303332i
$15$	2.07775	+	0.826399i	0.536474	+	0.213375i
$16$	−1.00000			−0.250000
$17$	−5.99105	−	1.60530i	−1.45304	−	0.389342i	−0.555962	−	0.831208i	$-0.687650\pi$
$17$	−5.99105	−	1.60530i	−1.45304	−	0.389342i	−0.897081	+	0.441866i	$0.854317\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	2.07086	−	1.19561i	0.475088	−	0.274292i	−0.243279	−	0.969956i	$-0.578223\pi$
$19$	2.07086	−	1.19561i	0.475088	−	0.274292i	0.718367	+	0.695664i	$0.244890\pi$
$20$	2.22084	+	0.260478i	0.496596	+	0.0582446i
$21$	1.96582	+	1.13497i	0.428976	+	0.247670i
$22$	−1.55082	−	5.78774i	−0.330636	−	1.23395i
$23$	−2.38785	−	2.38785i	−0.497902	−	0.497902i	0.412883	−	0.910784i	$-0.364522\pi$
$23$	−2.38785	−	2.38785i	−0.497902	−	0.497902i	−0.910784	+	0.412883i	$0.864522\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.86430	−	1.15696i	−0.972861	−	0.231392i
$26$	−0.656197	−	0.378856i	−0.128691	−	0.0742997i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.19258	+	0.587501i	0.414359	+	0.111027i
$29$	−0.413869			−0.0768535			−0.0384268	−	0.999261i	$-0.512235\pi$
$29$	−0.413869			−0.0768535			−0.0384268	+	0.999261i	$0.512235\pi$
$30$	0.884842	+	2.05355i	0.161549	+	0.374925i
$31$	−5.55275	−	0.408678i	−0.997303	−	0.0734008i
$31$	−5.55275	−	0.408678i	−0.997303	−	0.0734008i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	4.23692	−	4.23692i	0.737553	−	0.737553i
$34$	−3.10119	−	5.37143i	−0.531850	−	0.921192i
$35$	−4.71636	−	1.87587i	−0.797210	−	0.317080i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	3.75587	+	1.00638i	0.617461	+	0.165448i	0.553973	−	0.832534i	$-0.313111\pi$
$37$	3.75587	+	1.00638i	0.617461	+	0.165448i	0.0634879	+	0.997983i	$0.479778\pi$
$38$	2.30975	+	0.618895i	0.374690	+	0.100398i
$39$		−	0.757711i		−	0.121331i
$40$	1.38619	+	1.75456i	0.219176	+	0.277420i
$41$	−1.22955	+	2.12965i	−0.192024	+	0.332595i	−0.945921	−	0.324397i	$-0.894839\pi$
$41$	−1.22955	+	2.12965i	−0.192024	+	0.332595i	0.753897	+	0.656993i	$0.228172\pi$
$42$	0.587501	+	2.19258i	0.0906534	+	0.338323i
$43$	−0.299644	+	1.11829i	−0.0456954	+	0.170537i	−0.985003	−	0.172540i	$-0.944803\pi$
$43$	−0.299644	+	1.11829i	−0.0456954	+	0.170537i	0.939307	+	0.343077i	$0.111469\pi$
$44$	2.99595	−	5.18915i	0.451657	−	0.782293i
$45$	−1.33600	+	1.79307i	−0.199160	+	0.267295i
$46$		−	3.37693i		−	0.497902i
$47$	6.11972	+	6.11972i	0.892653	+	0.892653i	0.994772	−	0.102119i	$-0.0325624\pi$
$47$	6.11972	+	6.11972i	0.892653	+	0.892653i	−0.102119	+	0.994772i	$0.532562\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	1.59991	+	0.923708i	0.228559	+	0.131958i
$50$	−2.62149	−	4.25768i	−0.370734	−	0.602126i
$51$	3.10119	−	5.37143i	0.434254	−	0.752150i
$52$	−0.196110	−	0.731893i	−0.0271956	−	0.101495i
$53$	0.400077	−	0.107200i	0.0549548	−	0.0147251i	−0.231237	−	0.972897i	$-0.574277\pi$
$53$	0.400077	−	0.107200i	0.0549548	−	0.0147251i	0.286192	+	0.958172i	$0.407611\pi$
$54$	1.00000			0.136083
$55$	−8.00521	+	10.7439i	−1.07942	+	1.44871i
$56$	1.13497	+	1.96582i	0.151666	+	0.262693i
$57$	0.618895	+	2.30975i	0.0819746	+	0.305933i
$58$	−0.292650	−	0.292650i	−0.0384268	−	0.0384268i
$59$	9.59250	−	5.53823i	1.24884	−	0.721016i	0.277959	−	0.960593i	$-0.410342\pi$
$59$	9.59250	−	5.53823i	1.24884	−	0.721016i	0.970877	+	0.239577i	$0.0770087\pi$
$60$	−0.826399	+	2.07775i	−0.106688	+	0.268237i
$61$		−	1.49492i		−	0.191405i	−0.995410	−	0.0957024i	$-0.969490\pi$
$61$		−	1.49492i		−	0.191405i	0.995410	−	0.0957024i	$-0.0305097\pi$
$62$	−3.63740	−	4.21536i	−0.461951	−	0.535352i
$63$	−1.60508	+	1.60508i	−0.202221	+	0.202221i
$64$		−	1.00000i		−	0.125000i
$65$	0.244888	+	1.67650i	0.0303746	+	0.207945i
$66$	5.99191			0.737553
$67$	13.5411	−	3.62833i	1.65431	−	0.443271i	0.693495	−	0.720461i	$-0.256070\pi$
$67$	13.5411	−	3.62833i	1.65431	−	0.443271i	0.960815	+	0.277190i	$0.0894032\pi$
$68$	1.60530	−	5.99105i	0.194671	−	0.726521i
$69$	2.92451	−	1.68847i	0.352070	−	0.203268i
$70$	−2.00853	−	4.66141i	−0.240065	−	0.557145i
$71$	1.10218	−	1.90904i	0.130805	−	0.226561i	−0.793182	−	0.608985i	$-0.791577\pi$
$71$	1.10218	−	1.90904i	0.130805	−	0.226561i	0.923987	+	0.382423i	$0.124910\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	5.84213	−	1.56540i	0.683770	−	0.183216i	0.0998203	−	0.995005i	$-0.468173\pi$
$73$	5.84213	−	1.56540i	0.683770	−	0.183216i	0.583950	+	0.811790i	$0.301507\pi$
$74$	1.94418	+	3.36742i	0.226007	+	0.391455i
$75$	2.37651	−	4.39911i	0.274416	−	0.507966i
$76$	1.19561	+	2.07086i	0.137146	+	0.237544i
$77$	−9.61751	+	9.61751i	−1.09602	+	1.09602i
$78$	0.535783	−	0.535783i	0.0606654	−	0.0606654i
$79$	−6.77438	−	11.7336i	−0.762177	−	1.32013i	−0.941726	−	0.336380i	$-0.890797\pi$
$79$	−6.77438	−	11.7336i	−0.762177	−	1.32013i	0.179549	−	0.983749i	$-0.442536\pi$
$80$	−0.260478	+	2.22084i	−0.0291223	+	0.248298i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−2.37532	+	0.636464i	−0.262310	+	0.0702857i
$83$	−3.43940	+	0.921586i	−0.377524	+	0.101157i	−0.442591	−	0.896724i	$-0.645941\pi$
$83$	−3.43940	+	0.921586i	−0.377524	+	0.101157i	0.0650670	+	0.997881i	$0.479274\pi$
$84$	−1.13497	+	1.96582i	−0.123835	+	0.214488i
$85$	−5.12565	+	12.8870i	−0.555955	+	1.39780i
$86$	−1.00263	+	0.578869i	−0.108116	+	0.0624210i
$87$	0.107117	−	0.399767i	0.0114842	−	0.0428595i
$88$	5.78774	−	1.55082i	0.616975	−	0.165318i
$89$	12.0649			1.27888			0.639440	−	0.768841i	$-0.279166\pi$
$89$	12.0649			1.27888			0.639440	+	0.768841i	$0.279166\pi$
$90$	−2.21259	+	0.323195i	−0.233227	+	0.0340677i
$91$			1.71995i			0.180300i
$92$	2.38785	−	2.38785i	0.248951	−	0.248951i
$93$	1.83191	−	5.25777i	0.189960	−	0.545205i
$94$			8.65459i			0.892653i
$95$	−2.11586	−	4.91049i	−0.217082	−	0.503806i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	7.87927	+	7.87927i	0.800019	+	0.800019i	0.983098	−	0.183079i	$-0.0586064\pi$
$97$	7.87927	+	7.87927i	0.800019	+	0.800019i	−0.183079	+	0.983098i	$0.558606\pi$
$98$	0.478147	+	1.78447i	0.0483001	+	0.180258i
$99$	2.99595	+	5.18915i	0.301105	+	0.521529i
$100$	1.15696	−	4.86430i	0.115696	−	0.486430i
$101$	−13.2482			−1.31825			−0.659125	−	0.752034i	$-0.729073\pi$
$101$	−13.2482			−1.31825			−0.659125	+	0.752034i	$0.729073\pi$
$102$	5.99105	−	1.60530i	0.593202	−	0.158948i
$103$	−4.35888	−	16.2676i	−0.429493	−	1.60289i	−0.753911	−	0.656977i	$-0.771835\pi$
$103$	−4.35888	−	16.2676i	−0.429493	−	1.60289i	0.324418	−	0.945914i	$-0.394832\pi$
$104$	0.378856	−	0.656197i	0.0371498	−	0.0643454i
$105$	3.03263	−	4.07014i	0.295955	−	0.397205i
$106$	0.358699	+	0.207095i	0.0348400	+	0.0201149i
$107$	1.68329	−	6.28212i	0.162730	−	0.607315i	−0.835589	−	0.549355i	$-0.814874\pi$
$107$	1.68329	−	6.28212i	0.162730	−	0.607315i	0.998319	−	0.0579604i	$-0.0184597\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			15.2384i			1.45957i	0.683675	+	0.729787i	$0.260381\pi$
$109$			15.2384i			1.45957i	−0.683675	+	0.729787i	$0.739619\pi$
$110$	−13.2576	+	1.93655i	−1.26407	+	0.184643i
$111$	−1.94418	+	3.36742i	−0.184534	+	0.319622i
$112$	−0.587501	+	2.19258i	−0.0555136	+	0.207180i
$113$	−1.66247	−	6.20443i	−0.156392	−	0.583664i	−0.998982	−	0.0451081i	$-0.985637\pi$
$113$	−1.66247	−	6.20443i	−0.156392	−	0.583664i	0.842590	−	0.538556i	$-0.181030\pi$
$114$	−1.19561	+	2.07086i	−0.111979	+	0.193954i
$115$	−5.92503	+	4.68107i	−0.552512	+	0.436512i
$116$		−	0.413869i		−	0.0384268i
$117$	0.731893	+	0.196110i	0.0676635	+	0.0181304i
$118$	10.6990	+	2.86680i	0.984926	+	0.263910i
$119$	−7.03950	+	12.1928i	−0.645309	+	1.11771i
$120$	−2.05355	+	0.884842i	−0.187462	+	0.0807746i
$121$	12.4515	+	21.5666i	1.13195	+	1.96060i
$122$	1.05707	−	1.05707i	0.0957024	−	0.0957024i
$123$	−1.73885	−	1.73885i	−0.156787	−	0.156787i
$124$	0.408678	−	5.55275i	0.0367004	−	0.498651i
$125$	−3.83648	+	10.5015i	−0.343145	+	0.939283i
$126$	−2.26993			−0.202221
$127$	16.3693	+	4.38613i	1.45254	+	0.389206i	0.896905	−	0.442223i	$-0.145810\pi$
$127$	16.3693	+	4.38613i	1.45254	+	0.389206i	0.555631	+	0.831429i	$0.312477\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	−1.00263	−	0.578869i	−0.0882767	−	0.0509665i
$130$	−1.01230	+	1.35863i	−0.0887849	+	0.119160i
$131$	−6.28739	−	10.8901i	−0.549332	−	0.951470i	−0.998320	−	0.0579330i	$-0.981549\pi$
$131$	−6.28739	−	10.8901i	−0.549332	−	0.951470i	0.448989	−	0.893537i	$-0.351784\pi$
$132$	4.23692	+	4.23692i	0.368777	+	0.368777i
$133$	−1.40485	−	5.24296i	−0.121816	−	0.454623i
$134$	12.1406	+	7.00940i	1.04879	+	0.605520i
$135$	−1.38619	−	1.75456i	−0.119304	−	0.151008i
$136$	5.37143	−	3.10119i	0.460596	−	0.265925i
$137$	−2.59197	−	9.67335i	−0.221447	−	0.826450i	−0.983797	−	0.179286i	$-0.942621\pi$
$137$	−2.59197	−	9.67335i	−0.221447	−	0.826450i	0.762350	−	0.647165i	$-0.224045\pi$
$138$	3.26187	+	0.874015i	0.277669	+	0.0744011i
$139$	−18.5409			−1.57262			−0.786309	−	0.617833i	$-0.788011\pi$
$139$	−18.5409			−1.57262			−0.786309	+	0.617833i	$0.788011\pi$
$140$	1.87587	−	4.71636i	0.158540	−	0.398605i
$141$	−7.49509	+	4.32729i	−0.631201	+	0.364424i
$142$	2.12926	−	0.570532i	0.178683	−	0.0478780i
$143$	4.38543	+	1.17507i	0.366728	+	0.0982646i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	−0.107804	+	0.919139i	−0.00895261	+	0.0763303i
$146$	5.23791	+	3.02411i	0.433493	+	0.250277i
$147$	−1.30632	+	1.30632i	−0.107744	+	0.107744i
$148$	−1.00638	+	3.75587i	−0.0827241	+	0.308731i
$149$	−13.2621	+	7.65689i	−1.08648	+	0.627277i	−0.932636	−	0.360819i	$-0.882497\pi$
$149$	−13.2621	+	7.65689i	−1.08648	+	0.627277i	−0.153839	+	0.988096i	$0.549164\pi$
$150$	4.79109	−	1.43019i	0.391191	−	0.116775i
$151$		−	5.33429i		−	0.434098i	−0.976161	−	0.217049i	$-0.930357\pi$
$151$		−	5.33429i		−	0.434098i	0.976161	−	0.217049i	$-0.0696432\pi$
$152$	−0.618895	+	2.30975i	−0.0501990	+	0.187345i
$153$	4.38575	+	4.38575i	0.354567	+	0.354567i
$154$	−13.6012			−1.09602
$155$	−2.35398	+	12.2253i	−0.189076	+	0.981962i
$156$	0.757711			0.0606654
$157$	8.67159	+	8.67159i	0.692068	+	0.692068i	0.962687	−	0.270618i	$-0.0872282\pi$
$157$	8.67159	+	8.67159i	0.692068	+	0.692068i	−0.270618	+	0.962687i	$0.587228\pi$
$158$	3.50668	−	13.0871i	0.278976	−	1.04115i
$159$			0.414190i			0.0328474i
$160$	−1.75456	+	1.38619i	−0.138710	+	0.109588i
$161$	−6.63843	+	3.83270i	−0.523182	+	0.302059i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−5.88861	+	5.88861i	−0.461232	+	0.461232i	−0.899059	−	0.437827i	$-0.855748\pi$
$163$	−5.88861	+	5.88861i	−0.461232	+	0.461232i	0.437827	+	0.899059i	$0.355748\pi$
$164$	−2.12965	−	1.22955i	−0.166298	−	0.0960120i
$165$	−8.30592	−	10.5132i	−0.646615	−	0.818449i
$166$	−3.08369	−	1.78037i	−0.239340	−	0.138183i
$167$	−11.2472	−	3.01369i	−0.870337	−	0.233206i	−0.204104	−	0.978949i	$-0.565428\pi$
$167$	−11.2472	−	3.01369i	−0.870337	−	0.233206i	−0.666234	+	0.745743i	$0.732095\pi$
$168$	−2.19258	+	0.587501i	−0.169162	+	0.0453267i
$169$	−10.7611	+	6.21294i	−0.827779	+	0.477918i
$170$	−12.7369	+	5.48813i	−0.976875	+	0.420921i
$171$	−2.39123			−0.182862
$172$	−1.11829	−	0.299644i	−0.0852687	−	0.0228477i
$173$	−2.71681	−	10.1393i	−0.206555	−	0.770873i	−0.988970	−	0.148116i	$-0.952679\pi$
$173$	−2.71681	−	10.1393i	−0.206555	−	0.770873i	0.782415	−	0.622757i	$-0.213988\pi$
$174$	0.358421	−	0.206934i	0.0271718	−	0.0156877i
$175$	−5.39452	+	9.98568i	−0.407787	+	0.754846i
$176$	5.18915	+	2.99595i	0.391147	+	0.225829i
$177$	2.86680	+	10.6990i	0.215482	+	0.804189i
$178$	8.53119	+	8.53119i	0.639440	+	0.639440i
$179$	−9.94647	−	17.2278i	−0.743434	−	1.28767i	−0.950923	−	0.309428i	$-0.899862\pi$
$179$	−9.94647	−	17.2278i	−0.743434	−	1.28767i	0.207488	−	0.978237i	$-0.433471\pi$
$180$	−1.79307	−	1.33600i	−0.133647	−	0.0995798i
$181$	−16.0789	−	9.28316i	−1.19514	−	0.690012i	−0.235668	−	0.971834i	$-0.575728\pi$
$181$	−16.0789	−	9.28316i	−1.19514	−	0.690012i	−0.959467	+	0.281822i	$0.909061\pi$
$182$	−1.21619	+	1.21619i	−0.0901499	+	0.0901499i
$183$	1.44398	+	0.386913i	0.106742	+	0.0286015i
$184$	3.37693			0.248951
$185$	3.21334	−	8.07907i	0.236250	−	0.593985i
$186$	5.01316	−	2.42245i	0.367583	−	0.177622i
$187$	26.2790	+	26.2790i	1.92171	+	1.92171i
$188$	−6.11972	+	6.11972i	−0.446326	+	0.446326i
$189$	−1.13497	−	1.96582i	−0.0825566	−	0.142992i
$190$	1.97611	−	4.96838i	0.143362	−	0.360444i
$191$	9.34961	−	16.1940i	0.676514	−	1.17176i	−0.299510	−	0.954093i	$-0.596823\pi$
$191$	9.34961	−	16.1940i	0.676514	−	1.17176i	0.976024	−	0.217664i	$-0.0698436\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	−2.96472	−	0.794394i	−0.213405	−	0.0571817i	0.150532	−	0.988605i	$-0.451901\pi$
$193$	−2.96472	−	0.794394i	−0.213405	−	0.0571817i	−0.363938	+	0.931423i	$0.618568\pi$
$194$			11.1430i			0.800019i
$195$	−1.68276	−	0.197367i	−0.120505	−	0.0141337i
$196$	−0.923708	+	1.59991i	−0.0659792	+	0.114279i
$197$	−1.72089	−	6.42247i	−0.122609	−	0.457582i	0.877135	−	0.480245i	$-0.159452\pi$
$197$	−1.72089	−	6.42247i	−0.122609	−	0.457582i	−0.999743	+	0.0226631i	$0.992785\pi$
$198$	−1.55082	+	5.78774i	−0.110212	+	0.411317i
$199$	2.84478	−	4.92731i	0.201661	−	0.349288i	−0.747403	−	0.664371i	$-0.768699\pi$
$199$	2.84478	−	4.92731i	0.201661	−	0.349288i	0.949064	+	0.315084i	$0.102033\pi$
$200$	4.25768	−	2.62149i	0.301063	−	0.185367i
$201$			14.0188i			0.988809i
$202$	−9.36792	−	9.36792i	−0.659125	−	0.659125i
$203$	−0.243148	+	0.907442i	−0.0170657	+	0.0636900i
$204$	5.37143	+	3.10119i	0.376075	+	0.217127i
$205$	4.40935	+	3.28538i	0.307962	+	0.229461i
$206$	8.42071	−	14.5851i	0.586699	−	1.01619i
$207$	0.874015	+	3.26187i	0.0607482	+	0.226715i
$208$	0.731893	−	0.196110i	0.0507476	−	0.0135978i
$209$	−14.3280			−0.991089
$210$	5.02242	−	0.733629i	0.346580	−	0.0506252i
$211$	10.0774	+	17.4546i	0.693758	+	1.20162i	0.970598	+	0.240708i	$0.0773796\pi$
$211$	10.0774	+	17.4546i	0.693758	+	1.20162i	−0.276840	+	0.960916i	$0.589287\pi$
$212$	0.107200	+	0.400077i	0.00736255	+	0.0274774i
$213$	1.55872	+	1.55872i	0.106802	+	0.106802i
$214$	5.63239	−	3.25186i	0.385022	−	0.222293i
$215$	2.40549	+	0.956753i	0.164053	+	0.0652500i
$216$			1.00000i			0.0680414i
$217$	−4.15831	+	11.9348i	−0.282284	+	0.810185i
$218$	−10.7752	+	10.7752i	−0.729787	+	0.729787i
$219$			6.04822i			0.408701i
$220$	−10.7439	−	8.00521i	−0.724354	−	0.539711i
$221$	4.69962			0.316131
$222$	−3.75587	+	1.00638i	−0.252078	+	0.0675440i
$223$	5.08621	−	18.9820i	0.340598	−	1.27113i	−0.557074	−	0.830463i	$-0.688076\pi$
$223$	5.08621	−	18.9820i	0.340598	−	1.27113i	0.897672	−	0.440665i	$-0.145257\pi$
$224$	−1.96582	+	1.13497i	−0.131347	+	0.0758330i
$225$	3.63413	+	3.43411i	0.242275	+	0.228941i
$226$	3.21165	−	5.56274i	0.213636	−	0.370028i
$227$	−13.4750	+	3.61062i	−0.894368	+	0.239645i	−0.676596	−	0.736354i	$-0.736546\pi$
$227$	−13.4750	+	3.61062i	−0.894368	+	0.239645i	−0.217772	+	0.976000i	$0.569879\pi$
$228$	−2.30975	+	0.618895i	−0.152967	+	0.0409873i
$229$	−0.774144	−	1.34086i	−0.0511568	−	0.0886063i	0.839313	−	0.543648i	$-0.182958\pi$
$229$	−0.774144	−	1.34086i	−0.0511568	−	0.0886063i	−0.890470	+	0.455042i	$0.849624\pi$
$230$	−7.49965	−	0.879617i	−0.494512	−	0.0580002i
$231$	−6.80061	−	11.7790i	−0.447447	−	0.775001i
$232$	0.292650	−	0.292650i	0.0192134	−	0.0192134i
$233$	9.12763	−	9.12763i	0.597971	−	0.597971i	−0.341801	−	0.939772i	$-0.611037\pi$
$233$	9.12763	−	9.12763i	0.597971	−	0.597971i	0.939772	+	0.341801i	$0.111037\pi$
$234$	0.378856	+	0.656197i	0.0247666	+	0.0428969i
$235$	15.1850	−	11.9969i	0.990560	−	0.782591i
$236$	5.53823	+	9.59250i	0.360508	+	0.624418i
$237$	13.0871	−	3.50668i	0.850098	−	0.227783i
$238$	−13.5993	+	3.64391i	−0.881509	+	0.236200i
$239$	0.570069	−	0.987389i	0.0368747	−	0.0638689i	−0.846999	−	0.531594i	$-0.821593\pi$
$239$	0.570069	−	0.987389i	0.0368747	−	0.0638689i	0.883874	+	0.467726i	$0.154926\pi$
$240$	−2.07775	−	0.826399i	−0.134118	−	0.0533438i
$241$	2.55698	−	1.47627i	0.164710	−	0.0950952i	−0.415379	−	0.909648i	$-0.636351\pi$
$241$	2.55698	−	1.47627i	0.164710	−	0.0950952i	0.580089	+	0.814553i	$0.303018\pi$
$242$	−6.44537	+	24.0544i	−0.414324	+	1.54628i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	1.49492			0.0957024
$245$	2.46815	−	3.31255i	0.157685	−	0.211631i
$246$		−	2.45911i		−	0.156787i
$247$	−1.28118	+	1.28118i	−0.0815194	+	0.0815194i
$248$	4.21536	−	3.63740i	0.267676	−	0.230975i
$249$		−	3.56073i		−	0.225652i
$250$	−10.1385	+	4.71288i	−0.641214	+	0.298069i
$251$	−17.3865	+	10.0381i	−1.09743	+	0.633601i	−0.935544	−	0.353209i	$-0.885090\pi$
$251$	−17.3865	+	10.0381i	−1.09743	+	0.633601i	−0.161884	+	0.986810i	$0.551757\pi$
$252$	−1.60508	−	1.60508i	−0.101111	−	0.101111i
$253$	5.23702	+	19.5448i	0.329248	+	1.22877i
$254$	8.47335	+	14.6763i	0.531665	+	0.920871i
$255$	−11.1213	−	8.28641i	−0.696444	−	0.518915i
$256$	1.00000			0.0625000
$257$	25.4927	−	6.83075i	1.59019	−	0.426091i	0.648130	−	0.761530i	$-0.275551\pi$
$257$	25.4927	−	6.83075i	1.59019	−	0.426091i	0.942062	+	0.335439i	$0.108885\pi$
$258$	−0.299644	−	1.11829i	−0.0186551	−	0.0696216i
$259$	4.41316	−	7.64381i	0.274220	−	0.474963i
$260$	−1.67650	+	0.244888i	−0.103972	+	0.0151873i
$261$	0.358421	+	0.206934i	0.0221857	+	0.0128089i
$262$	3.25459	−	12.1463i	0.201069	−	0.750401i
$263$	10.1020	+	10.1020i	0.622914	+	0.622914i	0.946275	−	0.323362i	$-0.104813\pi$
$263$	10.1020	+	10.1020i	0.622914	+	0.622914i	−0.323362	+	0.946275i	$0.604813\pi$
$264$			5.99191i			0.368777i
$265$	−0.133864	−	0.916433i	−0.00822321	−	0.0562960i
$266$	2.71396	−	4.70071i	0.166403	−	0.288219i
$267$	−3.12263	+	11.6538i	−0.191102	+	0.713203i
$268$	3.62833	+	13.5411i	0.221636	+	0.827155i
$269$	−4.00747	+	6.94115i	−0.244340	+	0.423209i	−0.961946	−	0.273240i	$-0.911905\pi$
$269$	−4.00747	+	6.94115i	−0.244340	+	0.423209i	0.717606	+	0.696449i	$0.245238\pi$
$270$	0.260478	−	2.22084i	0.0158522	−	0.135156i
$271$			2.76259i			0.167815i	0.996474	+	0.0839076i	$0.0267401\pi$
$271$			2.76259i			0.167815i	−0.996474	+	0.0839076i	$0.973260\pi$
$272$	5.99105	+	1.60530i	0.363261	+	0.0973354i
$273$	−1.66135	−	0.445156i	−0.100549	−	0.0269421i
$274$	5.00730	−	8.67289i	0.302502	−	0.523948i
$275$	21.7754	+	20.5769i	1.31310	+	1.24083i
$276$	1.68847	+	2.92451i	0.101634	+	0.176035i
$277$	3.30326	−	3.30326i	0.198474	−	0.198474i	−0.600872	−	0.799345i	$-0.705180\pi$
$277$	3.30326	−	3.30326i	0.198474	−	0.198474i	0.799345	+	0.600872i	$0.205180\pi$
$278$	−13.1104	−	13.1104i	−0.786309	−	0.786309i
$279$	4.60448	+	3.13030i	0.275663	+	0.187406i
$280$	4.66141	−	2.00853i	0.278572	−	0.120033i
$281$	−11.8898			−0.709289			−0.354644	−	0.935001i	$-0.615398\pi$
$281$	−11.8898			−0.709289			−0.354644	+	0.935001i	$0.615398\pi$
$282$	−8.35969	−	2.23997i	−0.497812	−	0.133388i
$283$	3.75831	−	3.75831i	0.223409	−	0.223409i	−0.586524	−	0.809932i	$-0.699504\pi$
$283$	3.75831	−	3.75831i	0.223409	−	0.223409i	0.809932	+	0.586524i	$0.199504\pi$
$284$	1.90904	+	1.10218i	0.113281	+	0.0654026i
$285$	5.29080	−	0.772831i	0.313400	−	0.0457786i
$286$	2.27007	+	3.93187i	0.134232	+	0.232497i
$287$	3.94707	+	3.94707i	0.232988	+	0.232988i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	18.5932	+	10.7348i	1.09372	+	0.631460i
$290$	−0.726158	+	0.573700i	−0.0426415	+	0.0336888i
$291$	−9.65010	+	5.57149i	−0.565699	+	0.326606i
$292$	1.56540	+	5.84213i	0.0916078	+	0.341885i
$293$	17.4871	+	4.68565i	1.02161	+	0.273739i	0.730472	−	0.682943i	$-0.239300\pi$
$293$	17.4871	+	4.68565i	1.02161	+	0.273739i	0.291135	+	0.956682i	$0.405967\pi$
$294$	−1.84742			−0.107744
$295$	−9.80092	−	22.7460i	−0.570631	−	1.32433i
$296$	−3.36742	+	1.94418i	−0.195727	+	0.113003i
$297$	−5.78774	+	1.55082i	−0.335839	+	0.0899877i
$298$	−14.7920	−	3.96350i	−0.856876	−	0.229599i
$299$	2.21593	+	1.27937i	0.128151	+	0.0739879i
$300$	4.39911	+	2.37651i	0.253983	+	0.137208i
$301$	2.27590	+	1.31399i	0.131181	+	0.0757372i
$302$	3.77191	−	3.77191i	0.217049	−	0.217049i
$303$	3.42890	−	12.7968i	0.196985	−	0.735158i
$304$	−2.07086	+	1.19561i	−0.118772	+	0.0685731i
$305$	−3.31998	−	0.389393i	−0.190102	−	0.0222966i
$306$			6.20239i			0.354567i
$307$	7.51801	−	28.0576i	0.429076	−	1.60133i	−0.325783	−	0.945445i	$-0.605628\pi$
$307$	7.51801	−	28.0576i	0.429076	−	1.60133i	0.754859	−	0.655887i	$-0.227705\pi$
$308$	−9.61751	−	9.61751i	−0.548009	−	0.548009i
$309$	16.8414			0.958075
$310$	−10.3091	+	6.98010i	−0.585519	+	0.396443i
$311$	−21.0580			−1.19409			−0.597044	−	0.802208i	$-0.703658\pi$
$311$	−21.0580			−1.19409			−0.597044	+	0.802208i	$0.703658\pi$
$312$	0.535783	+	0.535783i	0.0303327	+	0.0303327i
$313$	6.12756	−	22.8684i	0.346350	−	1.29260i	−0.544676	−	0.838646i	$-0.683348\pi$
$313$	6.12756	−	22.8684i	0.346350	−	1.29260i	0.891027	−	0.453951i	$-0.149986\pi$
$314$			12.2635i			0.692068i
$315$	3.14655	+	3.98273i	0.177288	+	0.224401i
$316$	11.7336	−	6.77438i	0.660065	−	0.381088i
$317$	−5.43552	+	20.2856i	−0.305289	+	1.13935i	0.627407	+	0.778691i	$0.284116\pi$
$317$	−5.43552	+	20.2856i	−0.305289	+	1.13935i	−0.932696	+	0.360663i	$0.882550\pi$
$318$	−0.292877	+	0.292877i	−0.0164237	+	0.0164237i
$319$	2.14763	+	1.23993i	0.120244	+	0.0694229i
$320$	−2.22084	−	0.260478i	−0.124149	−	0.0145612i
$321$	5.63239	+	3.25186i	0.314369	+	0.181501i
$322$	−7.40421	−	1.98395i	−0.412621	−	0.110561i
$323$	−14.3259	+	3.83863i	−0.797117	+	0.213587i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	3.78704	−	0.107167i	0.210067	−	0.00594454i
$326$	−8.32776			−0.461232
$327$	−14.7192	−	3.94399i	−0.813971	−	0.218103i
$328$	−0.636464	−	2.37532i	−0.0351428	−	0.131155i
$329$	17.0133	−	9.82266i	0.937976	−	0.541541i
$330$	1.56076	−	13.3071i	0.0859170	−	0.732532i
$331$	−26.8776	−	15.5178i	−1.47733	−	0.852934i	−0.477653	−	0.878548i	$-0.658512\pi$
$331$	−26.8776	−	15.5178i	−1.47733	−	0.852934i	−0.999672	+	0.0256143i	$0.991846\pi$
$332$	−0.921586	−	3.43940i	−0.0505786	−	0.188762i
$333$	−2.74949	−	2.74949i	−0.150671	−	0.150671i
$334$	−5.82200	−	10.0840i	−0.318566	−	0.551772i
$335$	−4.53080	−	31.0178i	−0.247544	−	1.69468i
$336$	−1.96582	−	1.13497i	−0.107244	−	0.0619174i
$337$	10.9846	−	10.9846i	0.598369	−	0.598369i	−0.341510	−	0.939878i	$-0.610938\pi$
$337$	10.9846	−	10.9846i	0.598369	−	0.598369i	0.939878	+	0.341510i	$0.110938\pi$
$338$	−12.0025	−	3.21605i	−0.652848	−	0.174930i
$339$	6.42330			0.348866
$340$	−12.8870	−	5.12565i	−0.698898	−	0.277977i
$341$	27.5896	+	18.7565i	1.49406	+	1.01572i
$342$	−1.69085	−	1.69085i	−0.0914308	−	0.0914308i
$343$	14.2008	−	14.2008i	0.766773	−	0.766773i
$344$	−0.578869	−	1.00263i	−0.0312105	−	0.0540582i
$345$	−2.98805	−	6.93469i	−0.160871	−	0.373351i
$346$	5.24846	−	9.09061i	0.282159	−	0.488714i
$347$	6.34381	+	1.69982i	0.340553	+	0.0912510i	0.425042	−	0.905173i	$-0.360259\pi$
$347$	6.34381	+	1.69982i	0.340553	+	0.0912510i	−0.0844891	+	0.996424i	$0.526926\pi$
$348$	0.399767	+	0.107117i	0.0214297	+	0.00574208i
$349$		−	15.8163i		−	0.846629i	−0.905983	−	0.423314i	$-0.860867\pi$
$349$		−	15.8163i		−	0.846629i	0.905983	−	0.423314i	$-0.139133\pi$
$350$	−10.8754	+	3.24644i	−0.581317	+	0.173529i
$351$	−0.378856	+	0.656197i	−0.0202218	+	0.0350252i
$352$	1.55082	+	5.78774i	0.0826590	+	0.308488i
$353$	0.168760	−	0.629820i	0.00898218	−	0.0335220i	−0.961289	−	0.275541i	$-0.911143\pi$
$353$	0.168760	−	0.629820i	0.00898218	−	0.0335220i	0.970271	+	0.242019i	$0.0778097\pi$
$354$	−5.53823	+	9.59250i	−0.294354	+	0.509835i
$355$	−3.95258	−	2.94504i	−0.209781	−	0.156307i
$356$			12.0649i			0.639440i
$357$	−9.95535	−	9.95535i	−0.526893	−	0.526893i
$358$	5.14867	−	19.2151i	0.272116	−	1.01555i
$359$	10.5949	+	6.11698i	0.559179	+	0.322842i	0.752816	−	0.658231i	$-0.228695\pi$
$359$	10.5949	+	6.11698i	0.559179	+	0.322842i	−0.193637	+	0.981073i	$0.562028\pi$
$360$	−0.323195	−	2.21259i	−0.0170339	−	0.116614i
$361$	−6.64102	+	11.5026i	−0.349527	+	0.605399i
$362$	−4.80532	−	17.9337i	−0.252562	−	0.942573i
$363$	−24.0544	+	6.44537i	−1.26253	+	0.338294i
$364$	−1.71995			−0.0901499
$365$	−1.95475	−	13.3822i	−0.102316	−	0.700458i
$366$	0.747459	+	1.29464i	0.0390703	+	0.0676718i
$367$	1.71762	+	6.41023i	0.0896589	+	0.334611i	0.996156	−	0.0876014i	$-0.0279202\pi$
$367$	1.71762	+	6.41023i	0.0896589	+	0.334611i	−0.906497	+	0.422213i	$0.861254\pi$
$368$	2.38785	+	2.38785i	0.124475	+	0.124475i
$369$	2.12965	−	1.22955i	0.110865	−	0.0640080i
$370$	7.98494	−	3.44059i	0.415117	−	0.178868i
$371$		−	0.940183i		−	0.0488119i
$372$	5.25777	+	1.83191i	0.272602	+	0.0949801i
$373$	−7.43585	+	7.43585i	−0.385014	+	0.385014i	−0.872905	−	0.487891i	$-0.837766\pi$
$373$	−7.43585	+	7.43585i	−0.385014	+	0.385014i	0.487891	+	0.872905i	$0.337766\pi$
$374$			37.1642i			1.92171i
$375$	−9.15071	−	6.42374i	−0.472541	−	0.331720i
$376$	−8.65459			−0.446326
$377$	0.302908	−	0.0811639i	0.0156005	−	0.00418015i
$378$	0.587501	−	2.19258i	0.0302178	−	0.112774i
$379$	−5.46089	+	3.15285i	−0.280507	+	0.161951i	−0.633653	−	0.773617i	$-0.718445\pi$
$379$	−5.46089	+	3.15285i	−0.280507	+	0.161951i	0.353146	+	0.935568i	$0.385112\pi$
$380$	4.91049	−	2.11586i	0.251903	−	0.108541i
$381$	−8.47335	+	14.6763i	−0.434103	+	0.751888i
$382$	18.0621	−	4.83972i	0.924136	−	0.247621i
$383$	18.1412	−	4.86092i	0.926972	−	0.248381i	0.236409	−	0.971654i	$-0.424030\pi$
$383$	18.1412	−	4.86092i	0.926972	−	0.248381i	0.690563	+	0.723272i	$0.257363\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	18.8539	+	23.8642i	0.960881	+	1.21623i
$386$	−1.53465	−	2.65809i	−0.0781117	−	0.135293i
$387$	0.818644	−	0.818644i	0.0416140	−	0.0416140i
$388$	−7.87927	+	7.87927i	−0.400010	+	0.400010i
$389$	7.11438	+	12.3225i	0.360714	+	0.624774i	0.988078	−	0.153951i	$-0.0491998\pi$
$389$	7.11438	+	12.3225i	0.360714	+	0.624774i	−0.627365	+	0.778725i	$0.715867\pi$
$390$	−1.05033	−	1.32945i	−0.0531856	−	0.0673193i
$391$	10.4725	+	18.1390i	0.529619	+	0.917326i
$392$	−1.78447	+	0.478147i	−0.0901292	+	0.0241501i
$393$	12.1463	−	3.25459i	0.612700	−	0.164172i
$394$	3.32451	−	5.75822i	0.167487	−	0.290095i
$395$	−27.8230	+	11.9885i	−1.39993	+	0.603207i
$396$	−5.18915	+	2.99595i	−0.260764	+	0.150552i
$397$	−7.75644	+	28.9474i	−0.389284	+	1.45283i	0.442017	+	0.897007i	$0.354263\pi$
$397$	−7.75644	+	28.9474i	−0.389284	+	1.45283i	−0.831301	+	0.555822i	$0.812404\pi$
$398$	5.49570	−	1.47257i	0.275474	−	0.0738131i
$399$	5.42792			0.271736
$400$	4.86430	+	1.15696i	0.243215	+	0.0578481i
$401$			6.24284i			0.311752i	0.987777	+	0.155876i	$0.0498201\pi$
$401$			6.24284i			0.311752i	−0.987777	+	0.155876i	$0.950180\pi$
$402$	−9.91278	+	9.91278i	−0.494405	+	0.494405i
$403$	4.14416	−	0.789841i	0.206435	−	0.0393448i
$404$		−	13.2482i		−	0.659125i
$405$	2.05355	−	0.884842i	0.102042	−	0.0439681i
$406$	−0.813591	+	0.469727i	−0.0403778	+	0.0233121i
$407$	−16.4747	−	16.4747i	−0.816620	−	0.816620i
$408$	1.60530	+	5.99105i	0.0794740	+	0.296601i
$409$	16.0186	+	27.7450i	0.792068	+	1.37190i	0.924684	+	0.380734i	$0.124329\pi$
$409$	16.0186	+	27.7450i	0.792068	+	1.37190i	−0.132616	+	0.991167i	$0.542338\pi$
$410$	0.794771	+	5.44099i	0.0392509	+	0.268712i
$411$	10.0146			0.493983
$412$	16.2676	−	4.35888i	0.801445	−	0.214747i
$413$	−6.50743	−	24.2861i	−0.320210	−	1.19504i
$414$	−1.68847	+	2.92451i	−0.0829836	+	0.143732i
$415$	1.15081	+	7.87844i	0.0564910	+	0.386737i
$416$	0.656197	+	0.378856i	0.0321727	+	0.0185749i
$417$	4.79874	−	17.9091i	0.234995	−	0.877014i
$418$	−10.1314	−	10.1314i	−0.495545	−	0.495545i
$419$			29.0434i			1.41886i	0.704773	+	0.709432i	$0.251049\pi$
$419$			29.0434i			1.41886i	−0.704773	+	0.709432i	$0.748951\pi$
$420$	4.07014	+	3.03263i	0.198603	+	0.147977i
$421$	8.21698	−	14.2322i	0.400471	−	0.693636i	−0.593312	−	0.804973i	$-0.702180\pi$
$421$	8.21698	−	14.2322i	0.400471	−	0.693636i	0.993783	+	0.111337i	$0.0355132\pi$
$422$	−5.21645	+	19.4681i	−0.253933	+	0.947691i
$423$	−2.23997	−	8.35969i	−0.108911	−	0.406462i
$424$	−0.207095	+	0.358699i	−0.0100574	+	0.0174200i
$425$	27.2850	+	14.7401i	1.32352	+	0.714998i
$426$			2.20437i			0.106802i
$427$	−3.27773	−	0.878266i	−0.158621	−	0.0425023i
$428$	6.28212	+	1.68329i	0.303658	+	0.0813648i
$429$	−2.27007	+	3.93187i	−0.109600	+	0.189833i
$430$	1.02441	+	2.37747i	0.0494017	+	0.114652i
$431$	−7.70210	−	13.3404i	−0.370997	−	0.642586i	0.618722	−	0.785610i	$-0.287651\pi$
$431$	−7.70210	−	13.3404i	−0.370997	−	0.642586i	−0.989719	+	0.143024i	$0.954317\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	3.81068	+	3.81068i	0.183130	+	0.183130i	0.792718	−	0.609588i	$-0.208665\pi$
$433$	3.81068	+	3.81068i	0.183130	+	0.183130i	−0.609588	+	0.792718i	$0.708665\pi$
$434$	−11.3795	+	5.49879i	−0.546234	+	0.263950i
$435$	−0.859918	−	0.342021i	−0.0412299	−	0.0163986i
$436$	−15.2384			−0.729787
$437$	−7.79986	−	2.08997i	−0.373118	−	0.0999767i
$438$	−4.27674	+	4.27674i	−0.204350	+	0.204350i
$439$	−26.8176	−	15.4832i	−1.27993	−	0.738971i	−0.303099	−	0.952959i	$-0.598021\pi$
$439$	−26.8176	−	15.4832i	−1.27993	−	0.738971i	−0.976836	+	0.213989i	$0.931354\pi$
$440$	−1.93655	−	13.2576i	−0.0923215	−	0.632033i
$441$	−0.923708	−	1.59991i	−0.0439861	−	0.0761862i
$442$	3.32313	+	3.32313i	0.158065	+	0.158065i
$443$	0.269773	+	1.00681i	0.0128173	+	0.0478349i	0.972038	−	0.234822i	$-0.0754508\pi$
$443$	0.269773	+	1.00681i	0.0128173	+	0.0478349i	−0.959221	+	0.282657i	$0.908784\pi$
$444$	−3.36742	−	1.94418i	−0.159811	−	0.0922668i
$445$	3.14265	−	26.7943i	0.148976	−	1.27017i
$446$	17.0188	−	9.82580i	0.805863	−	0.465265i
$447$	−3.96350	−	14.7920i	−0.187467	−	0.699636i
$448$	−2.19258	−	0.587501i	−0.103590	−	0.0277568i
$449$	10.0761			0.475519			0.237759	−	0.971324i	$-0.423587\pi$
$449$	10.0761			0.475519			0.237759	+	0.971324i	$0.423587\pi$
$450$	0.141435	+	4.99800i	0.00666730	+	0.235608i
$451$	12.7607	−	7.36738i	0.600877	−	0.346916i
$452$	6.20443	−	1.66247i	0.291832	−	0.0781961i
$453$	5.15253	+	1.38062i	0.242087	+	0.0648670i
$454$	−12.0814	−	6.97518i	−0.567007	−	0.327362i
$455$	3.81974	+	0.448009i	0.179072	+	0.0210030i
$456$	−2.07086	−	1.19561i	−0.0969770	−	0.0559897i
$457$	−2.83689	+	2.83689i	−0.132704	+	0.132704i	−0.770339	−	0.637635i	$-0.779913\pi$
$457$	−2.83689	+	2.83689i	−0.132704	+	0.132704i	0.637635	+	0.770339i	$0.279913\pi$
$458$	0.400726	−	1.49553i	0.0187247	−	0.0698816i
$459$	−5.37143	+	3.10119i	−0.250717	+	0.144751i
$460$	−4.68107	−	5.92503i	−0.218256	−	0.276256i
$461$		−	25.6149i		−	1.19300i	−0.802612	−	0.596502i	$-0.796557\pi$
$461$		−	25.6149i		−	1.19300i	0.802612	−	0.596502i	$-0.203443\pi$
$462$	3.52025	−	13.1378i	0.163777	−	0.611224i
$463$	19.4241	+	19.4241i	0.902713	+	0.902713i	0.995670	−	0.0929573i	$-0.0296320\pi$
$463$	19.4241	+	19.4241i	0.902713	+	0.902713i	−0.0929573	+	0.995670i	$0.529632\pi$
$464$	0.413869			0.0192134
$465$	−11.1995	−	5.43792i	−0.519365	−	0.252177i
$466$	12.9084			0.597971
$467$	−26.5336	−	26.5336i	−1.22783	−	1.22783i	−0.964784	−	0.263042i	$-0.915274\pi$
$467$	−26.5336	−	26.5336i	−1.22783	−	1.22783i	−0.263042	−	0.964784i	$-0.584726\pi$
$468$	−0.196110	+	0.731893i	−0.00906519	+	0.0338318i
$469$		−	31.8217i		−	1.46939i
$470$	19.2205	+	2.25433i	0.886576	+	0.103984i
$471$	−10.6205	+	6.13174i	−0.489366	+	0.282536i
$472$	−2.86680	+	10.6990i	−0.131955	+	0.492463i
$473$	4.90524	−	4.90524i	0.225543	−	0.225543i
$474$	11.7336	+	6.77438i	0.538940	+	0.311157i
$475$	−11.4566	+	3.41991i	−0.525664	+	0.156916i
$476$	−12.1928	−	7.03950i	−0.558854	−	0.322655i
$477$	−0.400077	−	0.107200i	−0.0183183	−	0.00490837i
$478$	1.10129	−	0.295089i	0.0503718	−	0.0134971i
$479$	19.6961	−	11.3715i	0.899937	−	0.519579i	0.0227573	−	0.999741i	$-0.492756\pi$
$479$	19.6961	−	11.3715i	0.899937	−	0.519579i	0.877180	+	0.480162i	$0.159422\pi$
$480$	−0.884842	−	2.05355i	−0.0403873	−	0.0937312i
$481$	−2.94626			−0.134338
$482$	2.85194	+	0.764176i	0.129902	+	0.0348073i
$483$	−1.98395	−	7.40421i	−0.0902730	−	0.336903i
$484$	−21.5666	+	12.4515i	−0.980301	+	0.565977i
$485$	19.5510	−	15.4463i	0.887766	−	0.701379i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−1.50011	−	5.59850i	−0.0679766	−	0.253692i	0.923573	−	0.383424i	$-0.125255\pi$
$487$	−1.50011	−	5.59850i	−0.0679766	−	0.253692i	−0.991549	+	0.129732i	$0.958588\pi$
$488$	1.05707	+	1.05707i	0.0478512	+	0.0478512i
$489$	−4.16388	−	7.21205i	−0.188297	−	0.326140i
$490$	4.08757	−	0.597075i	0.184658	−	0.0269731i
$491$	27.7643	+	16.0297i	1.25298	+	0.723411i	0.971701	−	0.236214i	$-0.0759067\pi$
$491$	27.7643	+	16.0297i	1.25298	+	0.723411i	0.281283	+	0.959625i	$0.409240\pi$
$492$	1.73885	−	1.73885i	0.0783935	−	0.0783935i
$493$	2.47951	+	0.664382i	0.111671	+	0.0299223i
$494$	−1.81186			−0.0815194
$495$	12.3047	−	5.30189i	0.553054	−	0.238302i
$496$	5.55275	+	0.408678i	0.249326	+	0.0183502i
$497$	−3.53819	−	3.53819i	−0.158710	−	0.158710i
$498$	2.51782	−	2.51782i	0.112826	−	0.112826i
$499$	−3.42733	−	5.93631i	−0.153428	−	0.265746i	0.779057	−	0.626953i	$-0.215698\pi$
$499$	−3.42733	−	5.93631i	−0.153428	−	0.265746i	−0.932486	+	0.361207i	$0.882365\pi$
$500$	−10.5015	−	3.83648i	−0.469641	−	0.171572i
$501$	5.82200	−	10.0840i	0.260108	−	0.450520i
$502$	−19.3922	−	5.19611i	−0.865515	−	0.231914i
$503$	−16.0124	−	4.29051i	−0.713958	−	0.191305i	−0.116484	−	0.993193i	$-0.537162\pi$
$503$	−16.0124	−	4.29051i	−0.713958	−	0.191305i	−0.597474	+	0.801888i	$0.703829\pi$
$504$		−	2.26993i		−	0.101111i
$505$	−3.45087	+	29.4223i	−0.153562	+	1.30927i
$506$	−10.1171	+	17.5234i	−0.449762	+	0.779010i
$507$	−3.21605	−	12.0025i	−0.142830	−	0.533049i
$508$	−4.38613	+	16.3693i	−0.194603	+	0.726268i
$509$	16.3842	−	28.3783i	0.726217	−	1.25784i	−0.232254	−	0.972655i	$-0.574610\pi$
$509$	16.3842	−	28.3783i	0.726217	−	1.25784i	0.958471	−	0.285190i	$-0.0920566\pi$
$510$	−2.00458	−	13.7233i	−0.0887642	−	0.607679i
$511$		−	13.7290i		−	0.607337i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	0.618895	−	2.30975i	0.0273249	−	0.101978i
$514$	22.8561	+	13.1960i	1.00814	+	0.582051i
$515$	−37.2631	+	5.44306i	−1.64201	+	0.239850i
$516$	0.578869	−	1.00263i	0.0254833	−	0.0441383i
$517$	−13.4217	−	50.0905i	−0.590286	−	2.20298i
$518$	8.52556	−	2.28442i	0.374592	−	0.100372i
$519$	10.4969			0.460764
$520$	−1.35863	−	1.01230i	−0.0595798	−	0.0443925i
$521$	8.23348	+	14.2608i	0.360715	+	0.624777i	0.988079	−	0.153949i	$-0.0491992\pi$
$521$	8.23348	+	14.2608i	0.360715	+	0.624777i	−0.627363	+	0.778727i	$0.715866\pi$
$522$	0.107117	+	0.399767i	0.00468839	+	0.0174973i
$523$	30.3026	+	30.3026i	1.32504	+	1.32504i	0.909637	+	0.415404i	$0.136360\pi$
$523$	30.3026	+	30.3026i	1.32504	+	1.32504i	0.415404	+	0.909637i	$0.363640\pi$
$524$	10.8901	−	6.28739i	0.475735	−	0.274666i
$525$	−8.24922	−	7.79519i	−0.360025	−	0.340210i
$526$			14.2863i			0.622914i
$527$	32.6107	+	11.3622i	1.42055	+	0.494946i
$528$	−4.23692	+	4.23692i	−0.184388	+	0.184388i
$529$		−	11.5963i		−	0.504188i
$530$	0.553360	−	0.742672i	0.0240364	−	0.0322596i
$531$	−11.0765			−0.480677
$532$	5.24296	−	1.40485i	0.227311	−	0.0609079i
$533$	0.482256	−	1.79980i	0.0208888	−	0.0779581i
$534$	−10.4485	+	6.03247i	−0.452152	+	0.261050i
$535$	−13.5131	−	5.37467i	−0.584224	−	0.232367i
$536$	−7.00940	+	12.1406i	−0.302760	+	0.524395i
$537$	19.2151	−	5.14867i	0.829193	−	0.222182i
$538$	−7.74184	+	2.07442i	−0.333775	+	0.0894346i
$539$	−5.53478	−	9.58652i	−0.238400	−	0.412920i
$540$	1.75456	−	1.38619i	0.0755042	−	0.0596521i
$541$	−15.7397	−	27.2620i	−0.676702	−	1.17208i	−0.975968	−	0.217913i	$-0.930075\pi$
$541$	−15.7397	−	27.2620i	−0.676702	−	1.17208i	0.299266	−	0.954170i	$-0.403258\pi$
$542$	−1.95344	+	1.95344i	−0.0839076	+	0.0839076i
$543$	13.1284	−	13.1284i	0.563392	−	0.563392i
$544$	3.10119	+	5.37143i	0.132963	+	0.230298i
$545$	33.8421	+	3.96926i	1.44964	+	0.170025i
$546$	−0.859976	−	1.48952i	−0.0368036	−	0.0637456i
$547$	−34.9066	+	9.35320i	−1.49250	+	0.399914i	−0.910580	−	0.413333i	$-0.864365\pi$
$547$	−34.9066	+	9.35320i	−1.49250	+	0.399914i	−0.581919	+	0.813247i	$0.697698\pi$
$548$	9.67335	−	2.59197i	0.413225	−	0.110723i
$549$	−0.747459	+	1.29464i	−0.0319008	+	0.0552538i
$550$	0.847465	+	29.9476i	0.0361360	+	1.27697i
$551$	−0.857066	+	0.494827i	−0.0365122	+	0.0210803i
$552$	−0.874015	+	3.26187i	−0.0372005	+	0.138834i
$553$	−29.7068	+	7.95991i	−1.26326	+	0.338490i
$554$	4.67152			0.198474
$555$	6.97210	+	5.19486i	0.295949	+	0.220510i
$556$		−	18.5409i		−	0.786309i
$557$	−6.44198	+	6.44198i	−0.272955	+	0.272955i	−0.830289	−	0.557333i	$-0.811825\pi$
$557$	−6.44198	+	6.44198i	−0.272955	+	0.272955i	0.557333	+	0.830289i	$0.311825\pi$
$558$	1.04240	+	5.46931i	0.0441285	+	0.231535i
$559$		−	0.877230i		−	0.0371029i
$560$	4.71636	+	1.87587i	0.199303	+	0.0792699i
$561$	−32.1851	+	18.5821i	−1.35886	+	0.784536i
$562$	−8.40739	−	8.40739i	−0.354644	−	0.354644i
$563$	−2.27132	−	8.47667i	−0.0957246	−	0.357249i	0.901404	−	0.432980i	$-0.142538\pi$
$563$	−2.27132	−	8.47667i	−0.0957246	−	0.357249i	−0.997128	+	0.0757306i	$0.975871\pi$
$564$	−4.32729	−	7.49509i	−0.182212	−	0.315600i
$565$	−14.2121	+	2.07598i	−0.597908	+	0.0873370i
$566$	5.31506			0.223409
$567$	2.19258	−	0.587501i	0.0920799	−	0.0246727i
$568$	0.570532	+	2.12926i	0.0239390	+	0.0893416i
$569$	−3.89505	+	6.74642i	−0.163289	+	0.282825i	−0.936046	−	0.351877i	$-0.885544\pi$
$569$	−3.89505	+	6.74642i	−0.163289	+	0.282825i	0.772757	+	0.634702i	$0.218877\pi$
$570$	4.28763	+	3.19468i	0.179589	+	0.133811i
$571$	9.95019	+	5.74475i	0.416403	+	0.240410i	0.693537	−	0.720421i	$-0.256051\pi$
$571$	9.95019	+	5.74475i	0.416403	+	0.240410i	−0.277134	+	0.960831i	$0.589385\pi$
$572$	−1.17507	+	4.38543i	−0.0491323	+	0.183364i
$573$	13.2224	+	13.2224i	0.552372	+	0.552372i
$574$			5.58200i			0.232988i
$575$	8.85258	+	14.3779i	0.369178	+	0.599600i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−0.370348	+	1.38216i	−0.0154178	+	0.0575400i	−0.973206	−	0.229934i	$-0.926149\pi$
$577$	−0.370348	+	1.38216i	−0.0154178	+	0.0575400i	0.957788	+	0.287474i	$0.0928156\pi$
$578$	5.55675	+	20.7381i	0.231130	+	0.862590i
$579$	1.53465	−	2.65809i	0.0637779	−	0.110467i
$580$	−0.919139	−	0.107804i	−0.0381652	−	0.00447630i
$581$			8.08262i			0.335323i
$582$	−10.7633	−	2.88401i	−0.446153	−	0.119546i
$583$	−2.39723	−	0.642335i	−0.0992830	−	0.0266028i
$584$	−3.02411	+	5.23791i	−0.125139	+	0.216746i
$585$	0.626172	−	1.57434i	0.0258890	−	0.0650909i
$586$	9.05199	+	15.6785i	0.373934	+	0.647673i
$587$	3.21467	−	3.21467i	0.132684	−	0.132684i	−0.637646	−	0.770330i	$-0.720092\pi$
$587$	3.21467	−	3.21467i	0.132684	−	0.132684i	0.770330	+	0.637646i	$0.220092\pi$
$588$	−1.30632	−	1.30632i	−0.0538718	−	0.0538718i
$589$	−11.9876	+	5.79262i	−0.493940	+	0.238681i
$590$	9.15358	−	23.0142i	0.376847	−	0.947478i
$591$	6.64903			0.273504
$592$	−3.75587	−	1.00638i	−0.154365	−	0.0413621i
$593$	29.4665	−	29.4665i	1.21004	−	1.21004i	0.239033	−	0.971011i	$-0.423169\pi$
$593$	29.4665	−	29.4665i	1.21004	−	1.21004i	0.971011	−	0.239033i	$-0.0768306\pi$
$594$	−5.18915	−	2.99595i	−0.212913	−	0.122926i
$595$	25.2446	+	18.8096i	1.03493	+	0.771117i
$596$	−7.65689	−	13.2621i	−0.313638	−	0.543238i
$597$	4.02313	+	4.02313i	0.164656	+	0.164656i
$598$	0.662251	+	2.47155i	0.0270814	+	0.101069i
$599$	28.0079	+	16.1703i	1.14437	+	0.660702i	0.947509	−	0.319729i	$-0.103592\pi$
$599$	28.0079	+	16.1703i	1.14437	+	0.660702i	0.196861	+	0.980431i	$0.436925\pi$
$600$	1.43019	+	4.79109i	0.0583874	+	0.195595i
$601$	−11.2880	+	6.51711i	−0.460446	+	0.265838i	−0.712232	−	0.701944i	$-0.752315\pi$
$601$	−11.2880	+	6.51711i	−0.460446	+	0.265838i	0.251786	+	0.967783i	$0.418982\pi$
$602$	0.680172	+	2.53844i	0.0277217	+	0.103459i
$603$	−13.5411	−	3.62833i	−0.551437	−	0.147757i
$604$	5.33429			0.217049
$605$	51.1394	−	22.0352i	2.07911	−	0.895858i
$606$	11.4733	−	6.62412i	0.466072	−	0.269087i
$607$	21.3969	−	5.73329i	0.868475	−	0.232707i	0.203047	−	0.979169i	$-0.434916\pi$
$607$	21.3969	−	5.73329i	0.868475	−	0.232707i	0.665428	+	0.746462i	$0.268249\pi$
$608$	−2.30975	−	0.618895i	−0.0936726	−	0.0250995i
$609$	−0.813591	−	0.469727i	−0.0329684	−	0.0190343i
$610$	−2.07224	−	2.62292i	−0.0839025	−	0.106199i
$611$	−5.67912	−	3.27884i	−0.229752	−	0.132648i
$612$	−4.38575	+	4.38575i	−0.177283	+	0.177283i
$613$	−6.98467	+	26.0671i	−0.282108	+	1.05284i	0.668819	+	0.743425i	$0.266800\pi$
$613$	−6.98467	+	26.0671i	−0.282108	+	1.05284i	−0.950927	+	0.309416i	$0.899866\pi$
$614$	25.1558	−	14.5237i	1.01520	−	0.586128i
$615$	−4.31465	+	3.40879i	−0.173984	+	0.137456i
$616$		−	13.6012i		−	0.548009i
$617$	2.81776	−	10.5160i	0.113439	−	0.423359i	−0.885727	−	0.464207i	$-0.846339\pi$
$617$	2.81776	−	10.5160i	0.113439	−	0.423359i	0.999165	+	0.0408482i	$0.0130060\pi$
$618$	11.9087	+	11.9087i	0.479037	+	0.479037i
$619$	4.32362			0.173781			0.0868904	−	0.996218i	$-0.472307\pi$
$619$	4.32362			0.173781			0.0868904	+	0.996218i	$0.472307\pi$
$620$	−12.2253	−	2.35398i	−0.490981	−	0.0945380i
$621$	−3.37693			−0.135512
$622$	−14.8902	−	14.8902i	−0.597044	−	0.597044i
$623$	7.08816	−	26.4534i	0.283981	−	1.05983i
$624$			0.757711i			0.0303327i
$625$	22.3229	+	11.2556i	0.892915	+	0.450225i
$626$	20.5032	−	11.8375i	0.819474	−	0.473123i
$627$	3.70836	−	13.8398i	0.148098	−	0.552708i
$628$	−8.67159	+	8.67159i	−0.346034	+	0.346034i
$629$	−20.8861	−	12.0586i	−0.832782	−	0.480807i
$630$	−0.591267	+	5.04116i	−0.0235566	+	0.200845i
$631$	−29.1281	−	16.8171i	−1.15957	−	0.669478i	−0.208369	−	0.978050i	$-0.566815\pi$
$631$	−29.1281	−	16.8171i	−1.15957	−	0.669478i	−0.951201	+	0.308573i	$0.900149\pi$
$632$	13.0871	+	3.50668i	0.520576	+	0.139488i
$633$	−19.4681	+	5.21645i	−0.773786	+	0.207335i
$634$	−18.1876	+	10.5006i	−0.722322	+	0.417033i
$635$	14.0047	−	35.2111i	0.555761	−	1.39731i
$636$	−0.414190			−0.0164237
$637$	−1.35211	−	0.362297i	−0.0535726	−	0.0143547i
$638$	0.641836	+	2.39537i	0.0254105	+	0.0948334i
$639$	−1.90904	+	1.10218i	−0.0755204	+	0.0436017i
$640$	−1.38619	−	1.75456i	−0.0547939	−	0.0693551i
$641$	32.4150	+	18.7148i	1.28032	+	0.739190i	0.976906	−	0.213670i	$-0.0685418\pi$
$641$	32.4150	+	18.7148i	1.28032	+	0.739190i	0.303409	+	0.952860i	$0.401875\pi$
$642$	1.68329	+	6.28212i	0.0664341	+	0.247935i
$643$	−22.5162	−	22.5162i	−0.887950	−	0.887950i	0.106376	−	0.994326i	$-0.466075\pi$
$643$	−22.5162	−	22.5162i	−0.887950	−	0.887950i	−0.994326	+	0.106376i	$0.966075\pi$
$644$	−3.83270	−	6.63843i	−0.151030	−	0.261591i
$645$	−1.54674	+	2.07590i	−0.0609028	+	0.0817386i
$646$	−12.8443	−	7.41566i	−0.505352	−	0.291765i
$647$	−15.3746	+	15.3746i	−0.604437	+	0.604437i	−0.941487	−	0.337050i	$-0.890571\pi$
$647$	−15.3746	+	15.3746i	−0.604437	+	0.604437i	0.337050	+	0.941487i	$0.390571\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	−66.3692			−2.60522
$650$	2.75362	+	2.60206i	0.108006	+	0.102061i
$651$	−10.4518	−	7.10556i	−0.409640	−	0.278489i
$652$	−5.88861	−	5.88861i	−0.230616	−	0.230616i
$653$	−16.4609	+	16.4609i	−0.644166	+	0.644166i	−0.951577	−	0.307411i	$-0.900537\pi$
$653$	−16.4609	+	16.4609i	−0.644166	+	0.644166i	0.307411	+	0.951577i	$0.400537\pi$
$654$	−7.61920	−	13.1968i	−0.297934	−	0.516037i
$655$	−25.8229	+	11.1267i	−1.00898	+	0.434756i
$656$	1.22955	−	2.12965i	0.0480060	−	0.0831489i
$657$	−5.84213	−	1.56540i	−0.227923	−	0.0610719i
$658$	18.9759	+	5.08458i	0.739758	+	0.198218i
$659$			13.4475i			0.523840i	0.965090	+	0.261920i	$0.0843556\pi$
$659$			13.4475i			0.523840i	−0.965090	+	0.261920i	$0.915644\pi$
$660$	10.5132	−	8.30592i	0.409224	−	0.323307i
$661$	24.5329	−	42.4922i	0.954218	−	1.65275i	0.218071	−	0.975933i	$-0.430024\pi$
$661$	24.5329	−	42.4922i	0.954218	−	1.65275i	0.736147	−	0.676822i	$-0.236643\pi$
$662$	−8.03259	−	29.9780i	−0.312196	−	1.16513i
$663$	−1.21635	+	4.53948i	−0.0472392	+	0.176299i
$664$	1.78037	−	3.08369i	0.0690916	−	0.119670i
$665$	−12.0097	+	1.75427i	−0.465718	+	0.0680278i
$666$		−	3.88836i		−	0.150671i
$667$	0.988258	+	0.988258i	0.0382655	+	0.0382655i
$668$	3.01369	−	11.2472i	0.116603	−	0.435169i
$669$	17.0188	+	9.82580i	0.657984	+	0.379887i
$670$	18.7291	−	25.1367i	0.723570	−	0.971114i
$671$	−4.47871	+	7.75735i	−0.172899	+	0.299469i
$672$	−0.587501	−	2.19258i	−0.0226633	−	0.0845808i
$673$	−37.5606	+	10.0643i	−1.44786	+	0.387952i	−0.895277	−	0.445509i	$-0.853023\pi$
$673$	−37.5606	+	10.0643i	−1.44786	+	0.387952i	−0.552578	+	0.833461i	$0.686356\pi$
$674$	15.5346			0.598369
$675$	−4.25768	+	2.62149i	−0.163878	+	0.100901i
$676$	−6.21294	−	10.7611i	−0.238959	−	0.413889i
$677$	3.92459	+	14.6468i	0.150834	+	0.562922i	0.999426	+	0.0338734i	$0.0107843\pi$
$677$	3.92459	+	14.6468i	0.150834	+	0.562922i	−0.848592	+	0.529048i	$0.822549\pi$
$678$	4.54196	+	4.54196i	0.174433	+	0.174433i
$679$	21.9051	−	12.6469i	0.840639	−	0.485343i
$680$	−5.48813	−	12.7369i	−0.210460	−	0.488438i
$681$		−	13.9504i		−	0.534579i
$682$	6.24599	+	32.7716i	0.239171	+	1.25489i
$683$	0.0680949	−	0.0680949i	0.00260558	−	0.00260558i	−0.705803	−	0.708408i	$-0.749414\pi$
$683$	0.0680949	−	0.0680949i	0.00260558	−	0.00260558i	0.708408	+	0.705803i	$0.249414\pi$
$684$		−	2.39123i		−	0.0914308i
$685$	−22.1582	+	3.23666i	−0.846620	+	0.123666i
$686$	20.0830			0.766773
$687$	1.49553	−	0.400726i	0.0570581	−	0.0152887i
$688$	0.299644	−	1.11829i	0.0114238	−	0.0426343i
$689$	−0.271791	+	0.156918i	−0.0103544	+	0.00597811i
$690$	2.79070	−	7.01644i	0.106240	−	0.267111i
$691$	14.9261	−	25.8528i	0.567817	−	0.983487i	−0.428965	−	0.903321i	$-0.641122\pi$
$691$	14.9261	−	25.8528i	0.567817	−	0.983487i	0.996782	−	0.0801662i	$-0.0255451\pi$
$692$	10.1393	−	2.71681i	0.385437	−	0.103277i
$693$	13.1378	−	3.52025i	0.499063	−	0.133723i
$694$	3.28380	+	5.68770i	0.124651	+	0.215902i
$695$	−4.82949	+	41.1764i	−0.183193	+	1.56191i
$696$	0.206934	+	0.358421i	0.00784383	+	0.0135859i
$697$	10.7850	−	10.7850i	0.408512	−	0.408512i
$698$	11.1838	−	11.1838i	0.423314	−	0.423314i
$699$	6.45421	+	11.1790i	0.244121	+	0.422829i
$700$	−9.98568	−	5.39452i	−0.377423	−	0.203894i
$701$	6.40417	+	11.0923i	0.241882	+	0.418952i	0.961250	−	0.275677i	$-0.0889019\pi$
$701$	6.40417	+	11.0923i	0.241882	+	0.418952i	−0.719368	+	0.694629i	$0.755569\pi$
$702$	−0.731893	+	0.196110i	−0.0276235	+	0.00740170i
$703$	8.98113	−	2.40649i	0.338730	−	0.0907624i
$704$	−2.99595	+	5.18915i	−0.112914	+	0.195573i
$705$	7.65794	+	17.7726i	0.288415	+	0.669355i
$706$	0.564681	−	0.326019i	0.0212521	−	0.0122699i
$707$	−7.78336	+	29.0479i	−0.292723	+	1.09246i
$708$	−10.6990	+	2.86680i	−0.402095	+	0.107741i
$709$	13.1616			0.494293			0.247146	−	0.968978i	$-0.420507\pi$
$709$	13.1616			0.494293			0.247146	+	0.968978i	$0.420507\pi$
$710$	−0.712440	−	4.87736i	−0.0267374	−	0.183044i
$711$			13.5488i			0.508118i
$712$	−8.53119	+	8.53119i	−0.319720	+	0.319720i
$713$	12.2833	+	14.2350i	0.460012	+	0.533105i
$714$		−	14.0790i		−	0.526893i
$715$	3.75197	−	9.43329i	0.140316	−	0.352785i
$716$	17.2278	−	9.94647i	0.643833	−	0.371717i
$717$	0.806199	+	0.806199i	0.0301081	+	0.0301081i
$718$	3.16638	+	11.8171i	0.118168	+	0.441010i
$719$	−15.8007	−	27.3676i	−0.589267	−	1.02064i	−0.994329	−	0.106352i	$-0.966083\pi$
$719$	−15.8007	−	27.3676i	−0.589267	−	1.02064i	0.405061	−	0.914290i	$-0.367250\pi$
$720$	1.33600	−	1.79307i	0.0497899	−	0.0668237i
$721$	−38.2288			−1.42372
$722$	−12.8295	+	3.43764i	−0.477463	+	0.127936i
$723$	0.764176	+	2.85194i	0.0284200	+	0.106065i
$724$	9.28316	−	16.0789i	0.345006	−	0.597568i
$725$	2.01318	+	0.478831i	0.0747678	+	0.0177833i
$726$	−21.5666	−	12.4515i	−0.800412	−	0.462118i
$727$	6.93915	−	25.8973i	0.257359	−	0.960477i	−0.709404	−	0.704802i	$-0.751036\pi$
$727$	6.93915	−	25.8973i	0.257359	−	0.960477i	0.966763	−	0.255675i	$-0.0822976\pi$
$728$	−1.21619	−	1.21619i	−0.0450750	−	0.0450750i
$729$		−	1.00000i		−	0.0370370i
$730$	8.08044	−	10.8449i	0.299071	−	0.401387i
$731$	3.59037	−	6.21870i	0.132795	−	0.230007i
$732$	−0.386913	+	1.44398i	−0.0143007	+	0.0533711i
$733$	−3.76305	−	14.0439i	−0.138991	−	0.518723i	−0.999950	−	0.0100472i	$-0.996802\pi$
$733$	−3.76305	−	14.0439i	−0.138991	−	0.518723i	0.860958	−	0.508676i	$-0.169865\pi$
$734$	−3.31818	+	5.74726i	−0.122476	+	0.212135i
$735$	2.56087	+	3.24140i	0.0944590	+	0.119561i
$736$			3.37693i			0.124475i
$737$	−81.1371	−	21.7406i	−2.98872	−	0.800826i
$738$	2.37532	+	0.636464i	0.0874366	+	0.0234286i
$739$	−9.20613	+	15.9455i	−0.338653	+	0.586564i	−0.984180	−	0.177173i	$-0.943305\pi$
$739$	−9.20613	+	15.9455i	−0.338653	+	0.586564i	0.645527	+	0.763738i	$0.276638\pi$
$740$	8.07907	+	3.21334i	0.296992	+	0.118125i
$741$	−0.905929	−	1.56912i	−0.0332801	−	0.0576429i
$742$	0.664810	−	0.664810i	0.0244059	−	0.0244059i
$743$	3.08347	+	3.08347i	0.113122	+	0.113122i	0.761402	−	0.648280i	$-0.224511\pi$
$743$	3.08347	+	3.08347i	0.113122	+	0.113122i	−0.648280	+	0.761402i	$0.724511\pi$
$744$	2.42245	+	5.01316i	0.0888112	+	0.183791i
$745$	13.5503	+	31.4476i	0.496444	+	1.15215i
$746$	−10.5159			−0.385014
$747$	3.43940	+	0.921586i	0.125841	+	0.0337191i
$748$	−26.2790	+	26.2790i	−0.960856	+	0.960856i
$749$	−12.7851	−	7.38150i	−0.467159	−	0.269714i
$750$	−1.92826	−	11.0128i	−0.0704102	−	0.402131i
$751$	15.9437	+	27.6153i	0.581795	+	1.00770i	0.995267	+	0.0971814i	$0.0309827\pi$
$751$	15.9437	+	27.6153i	0.581795	+	1.00770i	−0.413472	+	0.910517i	$0.635684\pi$
$752$	−6.11972	−	6.11972i	−0.223163	−	0.223163i
$753$	−5.19611	−	19.3922i	−0.189357	−	0.706690i
$754$	0.271580	+	0.156797i	0.00989034	+	0.00571019i
$755$	−11.8466	−	1.38946i	−0.431143	−	0.0505678i
$756$	1.96582	−	1.13497i	0.0714961	−	0.0412783i
$757$	1.08749	+	4.05857i	0.0395255	+	0.147511i	0.982869	−	0.184308i	$-0.0590043\pi$
$757$	1.08749	+	4.05857i	0.0395255	+	0.147511i	−0.943343	+	0.331819i	$0.892338\pi$
$758$	−6.09084	−	1.63203i	−0.221229	−	0.0592782i
$759$	−20.2343			−0.734458
$760$	4.96838	+	1.97611i	0.180222	+	0.0716809i
$761$	−38.9327	+	22.4778i	−1.41131	+	0.814819i	−0.995512	−	0.0946390i	$-0.969830\pi$
$761$	−38.9327	+	22.4778i	−1.41131	+	0.814819i	−0.415796	+	0.909458i	$0.636497\pi$
$762$	−16.3693	+	4.38613i	−0.592995	+	0.158893i
$763$	33.4115	+	8.95257i	1.20958	+	0.324105i
$764$	16.1940	+	9.34961i	0.585879	+	0.338257i
$765$	10.8825	−	8.59768i	0.393456	−	0.310850i
$766$	16.2649	+	9.39057i	0.587676	+	0.339295i
$767$	−5.93458	+	5.93458i	−0.214285	+	0.214285i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	−16.9281	+	9.77342i	−0.610441	+	0.352438i	−0.773138	−	0.634238i	$-0.781314\pi$
$769$	−16.9281	+	9.77342i	−0.610441	+	0.352438i	0.162697	+	0.986676i	$0.447981\pi$
$770$	−3.54282	+	30.2062i	−0.127674	+	1.08856i
$771$			26.3920i			0.950485i
$772$	0.794394	−	2.96472i	0.0285909	−	0.106703i
$773$	18.9208	+	18.9208i	0.680532	+	0.680532i	0.960120	−	0.279588i	$-0.0901978\pi$
$773$	18.9208	+	18.9208i	0.680532	+	0.680532i	−0.279588	+	0.960120i	$0.590198\pi$
$774$	1.15774			0.0416140
$775$	26.5374	+	8.41225i	0.953252	+	0.302177i
$776$	−11.1430			−0.400010
$777$	6.24115	+	6.24115i	0.223900	+	0.223900i
$778$	−3.68268	+	13.7439i	−0.132030	+	0.492744i
$779$			5.88028i			0.210683i
$780$	0.197367	−	1.68276i	0.00706687	−	0.0602524i
$781$	−11.4388	+	6.60419i	−0.409312	+	0.236316i
$782$	−5.42098	+	20.2314i	−0.193854	+	0.723472i
$783$	−0.292650	+	0.292650i	−0.0104584	+	0.0104584i
$784$	−1.59991	−	0.923708i	−0.0571396	−	0.0329896i
$785$	21.5170	−	16.9995i	0.767975	−	0.606738i
$786$	10.8901	+	6.28739i	0.388436	+	0.224264i
$787$	33.3463	+	8.93512i	1.18867	+	0.318502i	0.798359	−	0.602182i	$-0.205702\pi$
$787$	33.3463	+	8.93512i	1.18867	+	0.318502i	0.390308	+	0.920684i	$0.372368\pi$
$788$	6.42247	−	1.72089i	0.228791	−	0.0613043i
$789$	−12.3723	+	7.14317i	−0.440467	+	0.254303i
$790$	−28.1510	−	11.1967i	−1.00157	−	0.398360i
$791$	−14.5804			−0.518421
$792$	−5.78774	−	1.55082i	−0.205658	−	0.0551060i
$793$	0.293169	+	1.09412i	0.0104107	+	0.0388533i
$794$	−25.9535	+	14.9843i	−0.921057	+	0.531772i
$795$	0.919853	+	0.107887i	0.0326238	+	0.00382637i
$796$	4.92731	+	2.84478i	0.174644	+	0.100831i
$797$	−2.21708	−	8.27425i	−0.0785329	−	0.293089i	0.915478	−	0.402367i	$-0.131813\pi$
$797$	−2.21708	−	8.27425i	−0.0785329	−	0.293089i	−0.994011	+	0.109279i	$0.965146\pi$
$798$	3.83812	+	3.83812i	0.135868	+	0.135868i
$799$	−26.8396	−	46.4875i	−0.949516	−	1.64461i
$800$	2.62149	+	4.25768i	0.0926835	+	0.150532i
$801$	−10.4485	−	6.03247i	−0.369181	−	0.213147i
$802$	−4.41435	+	4.41435i	−0.155876	+	0.155876i
$803$	−35.0055	−	9.37971i	−1.23532	−	0.331003i
$804$	−14.0188			−0.494405
$805$	6.78267	+	15.7413i	0.239058	+	0.554807i
$806$	3.48887	+	2.37186i	0.122890	+	0.0835453i
$807$	−5.66742	−	5.66742i	−0.199503	−	0.199503i
$808$	9.36792	−	9.36792i	0.329562	−	0.329562i
$809$	−4.73459	−	8.20055i	−0.166459	−	0.288316i	0.770713	−	0.637182i	$-0.219900\pi$
$809$	−4.73459	−	8.20055i	−0.166459	−	0.288316i	−0.937173	+	0.348866i	$0.886567\pi$
$810$	2.07775	+	0.826399i	0.0730049	+	0.0290367i
$811$	9.64418	−	16.7042i	0.338653	−	0.586564i	−0.645527	−	0.763738i	$-0.723362\pi$
$811$	9.64418	−	16.7042i	0.338653	−	0.586564i	0.984180	+	0.177173i	$0.0566954\pi$
$812$	−0.907442	−	0.243148i	−0.0318450	−	0.00853284i
$813$	−2.66845	−	0.715010i	−0.0935867	−	0.0250765i
$814$		−	23.2987i		−	0.816620i
$815$	11.5438	+	14.6115i	0.404363	+	0.511820i
$816$	−3.10119	+	5.37143i	−0.108564	+	0.188038i
$817$	0.716518	+	2.67408i	0.0250678	+	0.0935542i
$818$	−8.29183	+	30.9455i	−0.289917	+	1.08198i
$819$	0.859976	−	1.48952i	0.0300500	−	0.0520481i
$820$	−3.28538	+	4.40935i	−0.114730	+	0.153981i
$821$		−	7.70678i		−	0.268968i	−0.990916	−	0.134484i	$-0.957062\pi$
$821$		−	7.70678i		−	0.268968i	0.990916	−	0.134484i	$-0.0429378\pi$
$822$	7.08139	+	7.08139i	0.246992	+	0.246992i
$823$	−7.49510	+	27.9721i	−0.261263	+	0.975046i	0.703235	+	0.710957i	$0.251738\pi$
$823$	−7.49510	+	27.9721i	−0.261263	+	0.975046i	−0.964498	+	0.264089i	$0.914929\pi$
$824$	14.5851	+	8.42071i	0.508096	+	0.293349i
$825$	−25.5116	+	15.7077i	−0.888200	+	0.546872i
$826$	12.5714	−	21.7743i	0.437415	−	0.757625i
$827$	10.9720	+	40.9482i	0.381535	+	1.42391i	0.843557	+	0.537040i	$0.180458\pi$
$827$	10.9720	+	40.9482i	0.381535	+	1.42391i	−0.462021	+	0.886869i	$0.652876\pi$
$828$	−3.26187	+	0.874015i	−0.113358	+	0.0303741i
$829$	−8.90504			−0.309285			−0.154642	−	0.987971i	$-0.549423\pi$
$829$	−8.90504			−0.309285			−0.154642	+	0.987971i	$0.549423\pi$
$830$	−4.75715	+	6.38464i	−0.165123	+	0.221614i
$831$	2.33576	+	4.04565i	0.0810266	+	0.140342i
$832$	0.196110	+	0.731893i	0.00679889	+	0.0253738i
$833$	−8.10231	−	8.10231i	−0.280728	−	0.280728i
$834$	16.0569	−	9.27045i	0.556004	−	0.321009i
$835$	−9.62259	+	24.1934i	−0.333003	+	0.837246i
$836$		−	14.3280i		−	0.495545i
$837$	−4.21536	+	3.63740i	−0.145704	+	0.125727i
$838$	−20.5368	+	20.5368i	−0.709432	+	0.709432i
$839$		−	39.8908i		−	1.37718i	−0.725150	−	0.688591i	$-0.758230\pi$
$839$		−	39.8908i		−	1.37718i	0.725150	−	0.688591i	$-0.241770\pi$
$840$	0.733629	+	5.02242i	0.0253126	+	0.173290i
$841$	−28.8287			−0.994094
$842$	15.8740	−	4.25342i	0.547054	−	0.146583i
$843$	3.07732	−	11.4847i	0.105988	−	0.395554i
$844$	−17.4546	+	10.0774i	−0.600812	+	0.346879i
$845$	10.9949	+	25.5171i	0.378237	+	0.877815i
$846$	4.32729	−	7.49509i	0.148775	−	0.257687i
$847$	54.6019	−	14.6305i	1.87614	−	0.502711i
$848$	−0.400077	+	0.107200i	−0.0137387	+	0.00368128i
$849$	2.65753	+	4.60298i	0.0912062	+	0.157974i
$850$	8.87061	+	29.7162i	0.304260	+	1.01926i
$851$	−6.56537	−	11.3716i	−0.225058	−	0.389812i
$852$	−1.55872	+	1.55872i	−0.0534010	+	0.0534010i
$853$	12.7464	−	12.7464i	0.436429	−	0.436429i	−0.454379	−	0.890808i	$-0.650139\pi$
$853$	12.7464	−	12.7464i	0.436429	−	0.436429i	0.890808	+	0.454379i	$0.150139\pi$
$854$	−1.69668	−	2.93874i	−0.0580592	−	0.100562i
$855$	−0.622861	+	5.31054i	−0.0213014	+	0.181617i
$856$	3.25186	+	5.63239i	0.111146	+	0.192511i
$857$	−1.68561	+	0.451657i	−0.0575792	+	0.0154283i	−0.287494	−	0.957783i	$-0.592822\pi$
$857$	−1.68561	+	0.451657i	−0.0575792	+	0.0154283i	0.229914	+	0.973211i	$0.426155\pi$
$858$	−4.38543	+	1.17507i	−0.149716	+	0.0401164i
$859$	−10.3467	+	17.9211i	−0.353026	+	0.611460i	−0.986778	−	0.162077i	$-0.948181\pi$
$859$	−10.3467	+	17.9211i	−0.353026	+	0.611460i	0.633752	+	0.773537i	$0.281514\pi$
$860$	−0.956753	+	2.40549i	−0.0326250	+	0.0820267i
$861$	−4.83416	+	2.79100i	−0.164748	+	0.0951171i
$862$	3.98690	−	14.8793i	0.135794	−	0.506792i
$863$	5.93225	−	1.58954i	0.201936	−	0.0541086i	−0.156433	−	0.987689i	$-0.550000\pi$
$863$	5.93225	−	1.58954i	0.201936	−	0.0541086i	0.358369	+	0.933580i	$0.383333\pi$
$864$	−1.00000			−0.0340207
$865$	−23.2254	+	3.39255i	−0.789687	+	0.115350i
$866$			5.38912i			0.183130i
$867$	−15.1813	+	15.1813i	−0.515585	+	0.515585i
$868$	−11.9348	−	4.15831i	−0.405092	−	0.141142i
$869$			81.1829i			2.75394i
$870$	−0.366209	−	0.849899i	−0.0124156	−	0.0288143i
$871$	−9.19909	+	5.31110i	−0.311699	+	0.179960i
$872$	−10.7752	−	10.7752i	−0.364893	−	0.364893i
$873$	−2.88401	−	10.7633i	−0.0976091	−	0.364282i
$874$	−4.03751	−	6.99316i	−0.136571	−	0.236547i
$875$	20.7715	+	14.5814i	0.702204	+	0.492943i
$876$	−6.04822			−0.204350
$877$	−7.73474	+	2.07252i	−0.261184	+	0.0699839i	−0.387035	−	0.922065i	$-0.626501\pi$
$877$	−7.73474	+	2.07252i	−0.261184	+	0.0699839i	0.125851	+	0.992049i	$0.459834\pi$
$878$	−8.01467	−	29.9112i	−0.270482	−	1.00945i
$879$	−9.05199	+	15.6785i	−0.305316	+	0.528823i
$880$	8.00521	−	10.7439i	0.269856	−	0.362177i
$881$	38.1036	+	21.9991i	1.28374	+	0.741170i	0.977531	−	0.210793i	$-0.0676046\pi$
$881$	38.1036	+	21.9991i	1.28374	+	0.741170i	0.306213	+	0.951963i	$0.400938\pi$
$882$	0.478147	−	1.78447i	0.0161000	−	0.0600861i
$883$	−13.7755	−	13.7755i	−0.463581	−	0.463581i	0.436246	−	0.899827i	$-0.356308\pi$
$883$	−13.7755	−	13.7755i	−0.463581	−	0.463581i	−0.899827	+	0.436246i	$0.856308\pi$
$884$			4.69962i			0.158065i
$885$	24.5076	−	3.57985i	0.823815	−	0.120335i
$886$	−0.521162	+	0.902679i	−0.0175088	+	0.0303261i
$887$	−13.3506	+	49.8251i	−0.448269	+	1.67296i	0.258887	+	0.965908i	$0.416644\pi$
$887$	−13.3506	+	49.8251i	−0.448269	+	1.67296i	−0.707157	+	0.707057i	$0.750022\pi$
$888$	−1.00638	−	3.75587i	−0.0337720	−	0.126039i
$889$	19.2339	−	33.3141i	0.645085	−	1.11732i
$890$	21.1686	−	16.7243i	0.709575	−	0.560599i
$891$		−	5.99191i		−	0.200737i
$892$	18.9820	+	5.08621i	0.635564	+	0.170299i
$893$	19.9899	+	5.35628i	0.668937	+	0.179241i
$894$	7.65689	−	13.2621i	0.256085	−	0.443552i
$895$	−40.8511	+	17.6021i	−1.36550	+	0.588374i
$896$	−1.13497	−	1.96582i	−0.0379165	−	0.0656733i
$897$	−1.80930	+	1.80930i	−0.0604109	+	0.0604109i
$898$	7.12485	+	7.12485i	0.237759	+	0.237759i
$899$	2.29811	+	0.169139i	0.0766462	+	0.00564111i
$900$	−3.43411	+	3.63413i	−0.114470	+	0.121138i
$901$	−2.56897			−0.0855848
$902$	14.2327	+	3.81364i	0.473896	+	0.126980i
$903$	−1.85826	+	1.85826i	−0.0618392	+	0.0618392i
$904$	5.56274	+	3.21165i	0.185014	+	0.106818i
$905$	−24.8046	+	33.2907i	−0.824534	+	1.10662i
$906$	2.66714	+	4.61963i	0.0886100	+	0.153477i
$907$	2.24348	+	2.24348i	0.0744934	+	0.0744934i	0.743372	−	0.668878i	$-0.233225\pi$
$907$	2.24348	+	2.24348i	0.0744934	+	0.0744934i	−0.668878	+	0.743372i	$0.733225\pi$
$908$	−3.61062	−	13.4750i	−0.119823	−	0.447184i
$909$	11.4733	+	6.62412i	0.380546	+	0.219708i
$910$	2.38418	+	3.01776i	0.0790347	+	0.100038i
$911$	40.4965	−	23.3807i	1.34171	−	0.774637i	0.354652	−	0.934999i	$-0.384599\pi$
$911$	40.4965	−	23.3807i	1.34171	−	0.774637i	0.987058	+	0.160362i	$0.0512661\pi$
$912$	−0.618895	−	2.30975i	−0.0204937	−	0.0764834i
$913$	20.6086	+	5.52206i	0.682045	+	0.182753i
$914$	−4.01197			−0.132704
$915$	1.23540	−	3.10607i	0.0408410	−	0.102684i
$916$	1.34086	−	0.774144i	0.0443031	−	0.0255784i
$917$	−27.5713	+	7.38770i	−0.910483	+	0.243963i
$918$	−5.99105	−	1.60530i	−0.197734	−	0.0529827i
$919$	44.3335	+	25.5959i	1.46243	+	0.844332i	0.999123	−	0.0418680i	$-0.0133309\pi$
$919$	44.3335	+	25.5959i	1.46243	+	0.844332i	0.463303	+	0.886200i	$0.346664\pi$
$920$	0.879617	−	7.49965i	0.0290001	−	0.247256i
$921$	25.1558	+	14.5237i	0.828910	+	0.478572i
$922$	18.1125	−	18.1125i	0.596502	−	0.596502i
$923$	−0.432299	+	1.61336i	−0.0142293	+	0.0531044i
$924$	11.7790	−	6.80061i	0.387501	−	0.223724i
$925$	−17.1053	−	9.24075i	−0.562420	−	0.303834i
$926$			27.4698i			0.902713i
$927$	−4.35888	+	16.2676i	−0.143164	+	0.534297i
$928$	0.292650	+	0.292650i	0.00960669	+	0.00960669i
$929$	31.0927			1.02012			0.510059	−	0.860140i	$-0.329624\pi$
$929$	31.0927			1.02012			0.510059	+	0.860140i	$0.329624\pi$
$930$	−4.07406	−	11.7644i	−0.133594	−	0.385771i
$931$	4.41759			0.144781
$932$	9.12763	+	9.12763i	0.298985	+	0.298985i
$933$	5.45021	−	20.3405i	0.178432	−	0.665916i
$934$		−	37.5241i		−	1.22783i
$935$	65.2067	−	51.5165i	2.13249	−	1.68477i
$936$	−0.656197	+	0.378856i	−0.0214485	+	0.0123833i
$937$	−2.04793	+	7.64296i	−0.0669028	+	0.249685i	−0.991276	−	0.131806i	$-0.957922\pi$
$937$	−2.04793	+	7.64296i	−0.0669028	+	0.249685i	0.924373	+	0.381491i	$0.124589\pi$
$938$	22.5013	−	22.5013i	0.734694	−	0.734694i
$939$	20.5032	+	11.8375i	0.669097	+	0.386304i
$940$	11.9969	+	15.1850i	0.391296	+	0.495280i
$941$	39.2710	+	22.6731i	1.28020	+	0.739123i	0.976884	−	0.213768i	$-0.0685737\pi$
$941$	39.2710	+	22.6731i	1.28020	+	0.739123i	0.303314	+	0.952891i	$0.401907\pi$
$942$	−11.8456	−	3.17402i	−0.385951	−	0.103415i
$943$	8.02129	−	2.14930i	0.261209	−	0.0699907i
$944$	−9.59250	+	5.53823i	−0.312209	+	0.180254i
$945$	−4.66141	+	2.00853i	−0.151636	+	0.0653375i
$946$	6.93706			0.225543
$947$	15.9913	+	4.28485i	0.519647	+	0.139239i	0.509103	−	0.860705i	$-0.329977\pi$
$947$	15.9913	+	4.28485i	0.519647	+	0.139239i	0.0105436	+	0.999944i	$0.496644\pi$
$948$	3.50668	+	13.0871i	0.113892	+	0.425049i
$949$	−3.96883	+	2.29140i	−0.128834	+	0.0743821i
$950$	−10.5193	−	5.68278i	−0.341290	−	0.184374i
$951$	−18.1876	−	10.5006i	−0.589773	−	0.340506i
$952$	−3.64391	−	13.5993i	−0.118100	−	0.440755i
$953$	8.46963	+	8.46963i	0.274358	+	0.274358i	0.830852	−	0.556494i	$-0.187854\pi$
$953$	8.46963	+	8.46963i	0.274358	+	0.274358i	−0.556494	+	0.830852i	$0.687854\pi$
$954$	−0.207095	−	0.358699i	−0.00670496	−	0.0116133i
$955$	−33.5290	−	24.9822i	−1.08497	−	0.808406i
$956$	0.987389	+	0.570069i	0.0319344	+	0.0184374i
$957$	−1.75353	+	1.75353i	−0.0566836	+	0.0566836i
$958$	21.9681	+	5.88634i	0.709758	+	0.190179i
$959$	−22.7324			−0.734068
$960$	0.826399	−	2.07775i	0.0266719	−	0.0670592i
$961$	30.6660	+	4.53857i	0.989225	+	0.146406i
$962$	−2.08332	−	2.08332i	−0.0671689	−	0.0671689i
$963$	−4.59883	+	4.59883i	−0.148195	+	0.148195i
$964$	1.47627	+	2.55698i	0.0475476	+	0.0823548i
$965$	−2.53647	+	6.37726i	−0.0816519	+	0.205291i
$966$	3.83270	−	6.63843i	0.123315	−	0.213588i
$967$	28.7663	+	7.70791i	0.925063	+	0.247870i	0.689748	−	0.724050i	$-0.257721\pi$
$967$	28.7663	+	7.70791i	0.925063	+	0.247870i	0.235315	+	0.971919i	$0.424388\pi$
$968$	−24.0544	−	6.44537i	−0.773139	−	0.207162i
$969$		−	14.8313i		−	0.476450i
$970$	24.7468	+	2.90250i	0.794573	+	0.0931936i
$971$	−11.7407	+	20.3355i	−0.376778	+	0.652598i	−0.990591	−	0.136853i	$-0.956301\pi$
$971$	−11.7407	+	20.3355i	−0.376778	+	0.652598i	0.613814	+	0.789451i	$0.289635\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	−10.8928	+	40.6525i	−0.349207	+	1.30326i
$974$	2.89800	−	5.01948i	0.0928578	−	0.160834i
$975$	−0.876643	+	3.68574i	−0.0280750	+	0.118038i
$976$			1.49492i			0.0478512i
$977$	34.8552	+	34.8552i	1.11512	+	1.11512i	0.992448	+	0.122668i	$0.0391451\pi$
$977$	34.8552	+	34.8552i	1.11512	+	1.11512i	0.122668	+	0.992448i	$0.460855\pi$
$978$	2.15538	−	8.04399i	0.0689215	−	0.257219i
$979$	−62.6067	−	36.1460i	−2.00092	−	1.15523i
$980$	3.31255	+	2.46815i	0.105815	+	0.0788423i
$981$	7.61920	−	13.1968i	0.243262	−	0.421342i
$982$	8.29759	+	30.9670i	0.264787	+	0.988197i
$983$	−29.6716	+	7.95049i	−0.946378	+	0.253581i	−0.698825	−	0.715293i	$-0.746293\pi$
$983$	−29.6716	+	7.95049i	−0.946378	+	0.253581i	−0.247554	+	0.968874i	$0.579627\pi$
$984$	2.45911			0.0783935
$985$	−14.7116	+	2.14893i	−0.468749	+	0.0684706i
$986$	1.28349	+	2.22307i	0.0408746	+	0.0707969i
$987$	5.08458	+	18.9759i	0.161844	+	0.604010i
$988$	−1.28118	−	1.28118i	−0.0407597	−	0.0407597i
$989$	3.38582	−	1.95480i	0.107663	−	0.0621591i
$990$	12.4497	+	4.95171i	0.395678	+	0.157376i
$991$			51.2986i			1.62955i	0.579774	+	0.814777i	$0.303141\pi$
$991$			51.2986i			1.62955i	−0.579774	+	0.814777i	$0.696859\pi$
$992$	3.63740	+	4.21536i	0.115488	+	0.133838i
$993$	21.9454	−	21.9454i	0.696418	−	0.696418i
$994$		−	5.00376i		−	0.158710i
$995$	−10.2018	−	7.60127i	−0.323418	−	0.240977i
$996$	3.56073			0.112826
$997$	−20.2188	+	5.41761i	−0.640335	+	0.171577i	−0.564355	−	0.825532i	$-0.690875\pi$
$997$	−20.2188	+	5.41761i	−0.640335	+	0.171577i	−0.0759800	+	0.997109i	$0.524209\pi$
$998$	1.77412	−	6.62110i	0.0561587	−	0.209587i
$999$	3.36742	−	1.94418i	0.106541	−	0.0615112i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.37.13	yes	64
5.3	odd	4		930.2.be.a.223.15	✓	64
31.26	odd	6		930.2.be.a.367.15	yes	64
155.88	even	12	inner	930.2.be.b.553.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.15	✓	64	5.3	odd	4
930.2.be.a.367.15	yes	64	31.26	odd	6
930.2.be.b.37.13	yes	64	1.1	even	1	trivial
930.2.be.b.553.13	yes	64	155.88	even	12	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(0.260478 - 2.22084i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.587501 - 2.19258i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(0.260478 - 2.22084i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(0.587501 - 2.19258i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.75456 - 1.38619i) q^{10} +(-5.18915 - 2.99595i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-0.731893 + 0.196110i) q^{13} +(1.96582 - 1.13497i) q^{14} +(2.07775 + 0.826399i) q^{15} -1.00000 q^{16} +(-5.99105 - 1.60530i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(2.07086 - 1.19561i) q^{19} +(2.22084 + 0.260478i) q^{20} +(1.96582 + 1.13497i) q^{21} +(-1.55082 - 5.78774i) q^{22} +(-2.38785 - 2.38785i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-4.86430 - 1.15696i) q^{25} +(-0.656197 - 0.378856i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.19258 + 0.587501i) q^{28} -0.413869 q^{29} +(0.884842 + 2.05355i) q^{30} +(-5.55275 - 0.408678i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(4.23692 - 4.23692i) q^{33} +(-3.10119 - 5.37143i) q^{34} +(-4.71636 - 1.87587i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.75587 + 1.00638i) q^{37} +(2.30975 + 0.618895i) q^{38} -0.757711i q^{39} +(1.38619 + 1.75456i) q^{40} +(-1.22955 + 2.12965i) q^{41} +(0.587501 + 2.19258i) q^{42} +(-0.299644 + 1.11829i) q^{43} +(2.99595 - 5.18915i) q^{44} +(-1.33600 + 1.79307i) q^{45} -3.37693i q^{46} +(6.11972 + 6.11972i) q^{47} +(0.258819 - 0.965926i) q^{48} +(1.59991 + 0.923708i) q^{49} +(-2.62149 - 4.25768i) q^{50} +(3.10119 - 5.37143i) q^{51} +(-0.196110 - 0.731893i) q^{52} +(0.400077 - 0.107200i) q^{53} +1.00000 q^{54} +(-8.00521 + 10.7439i) q^{55} +(1.13497 + 1.96582i) q^{56} +(0.618895 + 2.30975i) q^{57} +(-0.292650 - 0.292650i) q^{58} +(9.59250 - 5.53823i) q^{59} +(-0.826399 + 2.07775i) q^{60} -1.49492i q^{61} +(-3.63740 - 4.21536i) q^{62} +(-1.60508 + 1.60508i) q^{63} -1.00000i q^{64} +(0.244888 + 1.67650i) q^{65} +5.99191 q^{66} +(13.5411 - 3.62833i) q^{67} +(1.60530 - 5.99105i) q^{68} +(2.92451 - 1.68847i) q^{69} +(-2.00853 - 4.66141i) q^{70} +(1.10218 - 1.90904i) q^{71} +(0.965926 - 0.258819i) q^{72} +(5.84213 - 1.56540i) q^{73} +(1.94418 + 3.36742i) q^{74} +(2.37651 - 4.39911i) q^{75} +(1.19561 + 2.07086i) q^{76} +(-9.61751 + 9.61751i) q^{77} +(0.535783 - 0.535783i) q^{78} +(-6.77438 - 11.7336i) q^{79} +(-0.260478 + 2.22084i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-2.37532 + 0.636464i) q^{82} +(-3.43940 + 0.921586i) q^{83} +(-1.13497 + 1.96582i) q^{84} +(-5.12565 + 12.8870i) q^{85} +(-1.00263 + 0.578869i) q^{86} +(0.107117 - 0.399767i) q^{87} +(5.78774 - 1.55082i) q^{88} +12.0649 q^{89} +(-2.21259 + 0.323195i) q^{90} +1.71995i q^{91} +(2.38785 - 2.38785i) q^{92} +(1.83191 - 5.25777i) q^{93} +8.65459i q^{94} +(-2.11586 - 4.91049i) q^{95} +(0.866025 - 0.500000i) q^{96} +(7.87927 + 7.87927i) q^{97} +(0.478147 + 1.78447i) q^{98} +(2.99595 + 5.18915i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more