LMFDB - Embedded newform 930.2.bg.g.421.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, 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:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			421.1
Character	$\chi$	$=$	930.421
Dual form			930.2.bg.g.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.348368 - 0.386902i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.348368 - 0.386902i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(0.913545 + 0.406737i) q^{10} +(5.88702 - 1.25132i) q^{11} +(-0.104528 - 0.994522i) q^{12} +(0.258587 - 2.46029i) q^{13} +(0.509251 + 0.108245i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-7.02008 - 1.49216i) q^{17} +(-0.104528 + 0.994522i) q^{18} +(-0.0465940 - 0.443313i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(-0.475618 - 0.211759i) q^{21} +(-4.02719 + 4.47265i) q^{22} +(-0.199250 - 0.613230i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.23692 + 2.14241i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.475618 + 0.211759i) q^{28} +(-6.09750 + 4.43009i) q^{29} +1.00000 q^{30} +(5.30251 - 1.69807i) q^{31} +1.00000 q^{32} +(4.86910 - 3.53761i) q^{33} +(6.55644 - 2.91911i) q^{34} +(-0.160883 + 0.495147i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.31327 - 7.47081i) q^{37} +(0.298268 + 0.331260i) q^{38} +(-0.764459 - 2.35276i) q^{39} +(0.669131 - 0.743145i) q^{40} +(2.12414 + 0.945726i) q^{41} +(0.509251 - 0.108245i) q^{42} +(-0.994643 - 9.46340i) q^{43} +(0.629109 - 5.98557i) q^{44} +(-0.978148 - 0.207912i) q^{45} +(0.521644 + 0.378997i) q^{46} +(4.39186 + 3.19087i) q^{47} +(-0.978148 - 0.207912i) q^{48} +(0.703366 - 6.69208i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(-7.02008 + 1.49216i) q^{51} +(-2.25997 - 1.00620i) q^{52} +(-2.03184 + 2.25659i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-4.02719 - 4.47265i) q^{55} +(0.260314 - 0.450877i) q^{56} +(-0.222877 - 0.386035i) q^{57} +(2.32904 - 7.16804i) q^{58} +(1.45656 - 0.648504i) q^{59} +(-0.809017 + 0.587785i) q^{60} -2.82408 q^{61} +(-3.29172 + 4.49050i) q^{62} -0.520628 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-2.25997 + 1.00620i) q^{65} +(-1.85983 + 5.72397i) q^{66} +(-0.993857 - 1.72141i) q^{67} +(-3.58846 + 6.21539i) q^{68} +(-0.431447 - 0.479171i) q^{69} +(-0.160883 - 0.495147i) q^{70} +(4.52395 - 5.02436i) q^{71} +(0.913545 + 0.406737i) q^{72} +(9.08652 - 1.93140i) q^{73} +(0.901720 + 8.57929i) q^{74} +(-0.104528 + 0.994522i) q^{75} +(-0.436014 - 0.0926776i) q^{76} +(-2.53499 - 1.84178i) q^{77} +(2.00138 + 1.45409i) q^{78} +(-7.14657 - 1.51905i) q^{79} +(-0.104528 + 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-2.27435 + 0.483427i) q^{82} +(-1.51001 - 0.672298i) q^{83} +(-0.348368 + 0.386902i) q^{84} +(2.21779 + 6.82565i) q^{85} +(6.36713 + 7.07141i) q^{86} +(-3.76846 + 6.52717i) q^{87} +(3.00927 + 5.21221i) q^{88} +(1.51616 - 4.66627i) q^{89} +(0.913545 - 0.406737i) q^{90} +(-1.04198 + 0.757040i) q^{91} -0.644788 q^{92} +(4.15341 - 3.70798i) q^{93} -5.42863 q^{94} +(-0.360623 + 0.262008i) q^{95} +(0.913545 - 0.406737i) q^{96} +(2.39031 - 7.35660i) q^{97} +(3.36447 + 5.82744i) q^{98} +(3.00927 - 5.21221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 3 * q^20 + 4 * q^21 + 3 * q^22 + 5 * q^23 + 3 * q^24 - 12 * q^25 - 3 * q^26 - 6 * q^27 + 4 * q^28 - 15 * q^29 + 24 * q^30 + 15 * q^31 + 24 * q^32 + 4 * q^33 - 9 * q^34 - 3 * q^35 - 12 * q^36 + 6 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 - 6 * q^42 - 13 * q^43 - 2 * q^44 + 3 * q^45 - 10 * q^46 + 4 * q^47 + 3 * q^48 + 3 * q^50 - 9 * q^51 - 3 * q^52 - 6 * q^54 + 3 * q^55 - 11 * q^56 - 14 * q^57 + 22 * q^59 - 6 * q^60 + 16 * q^61 - 5 * q^62 + 22 * q^63 - 6 * q^64 - 3 * q^65 - 6 * q^66 - 19 * q^67 - 9 * q^68 - 10 * q^69 - 3 * q^70 - 45 * q^71 + 3 * q^72 + 11 * q^73 - 35 * q^74 + 3 * q^75 + 6 * q^76 - 50 * q^77 + 6 * q^78 + 36 * q^79 + 3 * q^80 + 3 * q^81 - 20 * q^82 - 4 * q^83 + 9 * q^84 - 12 * q^85 + 22 * q^86 - 15 * q^87 - 2 * q^88 - 7 * q^89 + 3 * q^90 - 32 * q^91 + 10 * q^92 + 7 * q^93 + 54 * q^94 - 2 * q^95 + 3 * q^96 + 11 * q^97 - 15 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.348368	−	0.386902i	−0.131671	−	0.146235i	0.673704	−	0.739002i	$-0.264702\pi$
$7$	−0.348368	−	0.386902i	−0.131671	−	0.146235i	−0.805375	+	0.592766i	$0.798036\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.669131	−	0.743145i	0.223044	−	0.247715i
$10$	0.913545	+	0.406737i	0.288888	+	0.128621i
$11$	5.88702	−	1.25132i	1.77500	−	0.377289i	0.800091	−	0.599879i	$-0.204784\pi$
$11$	5.88702	−	1.25132i	1.77500	−	0.377289i	0.974912	+	0.222590i	$0.0714511\pi$
$12$	−0.104528	−	0.994522i	−0.0301748	−	0.287094i
$13$	0.258587	−	2.46029i	0.0717191	−	0.682362i	−0.898308	−	0.439366i	$-0.855203\pi$
$13$	0.258587	−	2.46029i	0.0717191	−	0.682362i	0.970027	−	0.242996i	$-0.0781302\pi$
$14$	0.509251	+	0.108245i	0.136103	+	0.0289296i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−7.02008	−	1.49216i	−1.70262	−	0.361903i	−0.748919	−	0.662662i	$-0.769427\pi$
$17$	−7.02008	−	1.49216i	−1.70262	−	0.361903i	−0.953700	+	0.300759i	$0.902760\pi$
$18$	−0.104528	+	0.994522i	−0.0246376	+	0.234411i
$19$	−0.0465940	−	0.443313i	−0.0106894	−	0.101703i	0.987876	−	0.155243i	$-0.0496161\pi$
$19$	−0.0465940	−	0.443313i	−0.0106894	−	0.101703i	−0.998566	+	0.0535403i	$0.982949\pi$
$20$	−0.978148	+	0.207912i	−0.218720	+	0.0464905i
$21$	−0.475618	−	0.211759i	−0.103788	−	0.0462095i
$22$	−4.02719	+	4.47265i	−0.858599	+	0.953571i
$23$	−0.199250	−	0.613230i	−0.0415466	−	0.127867i	0.928132	−	0.372252i	$-0.121414\pi$
$23$	−0.199250	−	0.613230i	−0.0415466	−	0.127867i	−0.969678	+	0.244384i	$0.921414\pi$
$24$	0.669131	+	0.743145i	0.136586	+	0.151694i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.23692	+	2.14241i	0.242580	+	0.420161i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−0.475618	+	0.211759i	−0.0898833	+	0.0400186i
$29$	−6.09750	+	4.43009i	−1.13228	+	0.822648i	−0.986025	−	0.166599i	$-0.946721\pi$
$29$	−6.09750	+	4.43009i	−1.13228	+	0.822648i	−0.146253	+	0.989247i	$0.546721\pi$
$30$	1.00000			0.182574
$31$	5.30251	−	1.69807i	0.952358	−	0.304982i
$31$	5.30251	−	1.69807i	0.952358	−	0.304982i
$32$	1.00000			0.176777
$33$	4.86910	−	3.53761i	0.847602	−	0.615819i
$34$	6.55644	−	2.91911i	1.12442	−	0.500624i
$35$	−0.160883	+	0.495147i	−0.0271942	+	0.0836951i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	4.31327	−	7.47081i	0.709098	−	1.22819i	−0.256094	−	0.966652i	$-0.582436\pi$
$37$	4.31327	−	7.47081i	0.709098	−	1.22819i	0.965192	−	0.261542i	$-0.0842310\pi$
$38$	0.298268	+	0.331260i	0.0483855	+	0.0537375i
$39$	−0.764459	−	2.35276i	−0.122411	−	0.376744i
$40$	0.669131	−	0.743145i	0.105799	−	0.117502i
$41$	2.12414	+	0.945726i	0.331734	+	0.147698i	0.565843	−	0.824513i	$-0.308551\pi$
$41$	2.12414	+	0.945726i	0.331734	+	0.147698i	−0.234109	+	0.972210i	$0.575217\pi$
$42$	0.509251	−	0.108245i	0.0785792	−	0.0167025i
$43$	−0.994643	−	9.46340i	−0.151682	−	1.44315i	−0.760238	−	0.649644i	$-0.774918\pi$
$43$	−0.994643	−	9.46340i	−0.151682	−	1.44315i	0.608557	−	0.793510i	$-0.291749\pi$
$44$	0.629109	−	5.98557i	0.0948417	−	0.902358i
$45$	−0.978148	−	0.207912i	−0.145814	−	0.0309936i
$46$	0.521644	+	0.378997i	0.0769122	+	0.0558800i
$47$	4.39186	+	3.19087i	0.640618	+	0.465436i	0.860062	−	0.510189i	$-0.170424\pi$
$47$	4.39186	+	3.19087i	0.640618	+	0.465436i	−0.219444	+	0.975625i	$0.570424\pi$
$48$	−0.978148	−	0.207912i	−0.141183	−	0.0300095i
$49$	0.703366	−	6.69208i	0.100481	−	0.956012i
$50$	−0.104528	−	0.994522i	−0.0147826	−	0.140647i
$51$	−7.02008	+	1.49216i	−0.983008	+	0.208945i
$52$	−2.25997	−	1.00620i	−0.313401	−	0.139535i
$53$	−2.03184	+	2.25659i	−0.279095	+	0.309967i	−0.866352	−	0.499434i	$-0.833541\pi$
$53$	−2.03184	+	2.25659i	−0.279095	+	0.309967i	0.587257	+	0.809401i	$0.300208\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	−4.02719	−	4.47265i	−0.543026	−	0.603091i
$56$	0.260314	−	0.450877i	0.0347859	−	0.0602510i
$57$	−0.222877	−	0.386035i	−0.0295208	−	0.0511315i
$58$	2.32904	−	7.16804i	0.305818	−	0.941210i
$59$	1.45656	−	0.648504i	0.189628	−	0.0844280i	−0.309726	−	0.950826i	$-0.600237\pi$
$59$	1.45656	−	0.648504i	0.189628	−	0.0844280i	0.499354	+	0.866398i	$0.333571\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	−2.82408			−0.361586			−0.180793	−	0.983521i	$-0.557866\pi$
$61$	−2.82408			−0.361586			−0.180793	+	0.983521i	$0.557866\pi$
$62$	−3.29172	+	4.49050i	−0.418049	+	0.570294i
$63$	−0.520628			−0.0655930
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−2.25997	+	1.00620i	−0.280314	+	0.124804i
$66$	−1.85983	+	5.72397i	−0.228929	+	0.704572i
$67$	−0.993857	−	1.72141i	−0.121419	−	0.210304i	0.798909	−	0.601453i	$-0.205411\pi$
$67$	−0.993857	−	1.72141i	−0.121419	−	0.210304i	−0.920327	+	0.391149i	$0.872078\pi$
$68$	−3.58846	+	6.21539i	−0.435164	+	0.753727i
$69$	−0.431447	−	0.479171i	−0.0519401	−	0.0576854i
$70$	−0.160883	−	0.495147i	−0.0192292	−	0.0591814i
$71$	4.52395	−	5.02436i	0.536895	−	0.596282i	−0.412270	−	0.911062i	$-0.635264\pi$
$71$	4.52395	−	5.02436i	0.536895	−	0.596282i	0.949165	+	0.314780i	$0.101931\pi$
$72$	0.913545	+	0.406737i	0.107662	+	0.0479344i
$73$	9.08652	−	1.93140i	1.06350	−	0.226053i	0.357243	−	0.934012i	$-0.383717\pi$
$73$	9.08652	−	1.93140i	1.06350	−	0.226053i	0.706254	+	0.707958i	$0.250384\pi$
$74$	0.901720	+	8.57929i	0.104823	+	0.997322i
$75$	−0.104528	+	0.994522i	−0.0120699	+	0.114837i
$76$	−0.436014	−	0.0926776i	−0.0500142	−	0.0106308i
$77$	−2.53499	−	1.84178i	−0.288889	−	0.209890i
$78$	2.00138	+	1.45409i	0.226612	+	0.164643i
$79$	−7.14657	−	1.51905i	−0.804052	−	0.170907i	−0.212487	−	0.977164i	$-0.568156\pi$
$79$	−7.14657	−	1.51905i	−0.804052	−	0.170907i	−0.591565	+	0.806257i	$0.701490\pi$
$80$	−0.104528	+	0.994522i	−0.0116866	+	0.111191i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	−2.27435	+	0.483427i	−0.251160	+	0.0533856i
$83$	−1.51001	−	0.672298i	−0.165745	−	0.0737943i	0.322187	−	0.946676i	$-0.395582\pi$
$83$	−1.51001	−	0.672298i	−0.165745	−	0.0737943i	−0.487932	+	0.872882i	$0.662249\pi$
$84$	−0.348368	+	0.386902i	−0.0380101	+	0.0422145i
$85$	2.21779	+	6.82565i	0.240553	+	0.740346i
$86$	6.36713	+	7.07141i	0.686585	+	0.762530i
$87$	−3.76846	+	6.52717i	−0.404022	+	0.699786i
$88$	3.00927	+	5.21221i	0.320789	+	0.555623i
$89$	1.51616	−	4.66627i	0.160713	−	0.494623i	−0.837982	−	0.545698i	$-0.816265\pi$
$89$	1.51616	−	4.66627i	0.160713	−	0.494623i	0.998695	+	0.0510745i	$0.0162646\pi$
$90$	0.913545	−	0.406737i	0.0962961	−	0.0428738i
$91$	−1.04198	+	0.757040i	−0.109229	+	0.0793593i
$92$	−0.644788			−0.0672238
$93$	4.15341	−	3.70798i	0.430689	−	0.384500i
$94$	−5.42863			−0.559921
$95$	−0.360623	+	0.262008i	−0.0369991	+	0.0268814i
$96$	0.913545	−	0.406737i	0.0932383	−	0.0415124i
$97$	2.39031	−	7.35660i	0.242699	−	0.746950i	−0.753308	−	0.657668i	$-0.771543\pi$
$97$	2.39031	−	7.35660i	0.242699	−	0.746950i	0.996006	−	0.0892817i	$-0.0284571\pi$
$98$	3.36447	+	5.82744i	0.339863	+	0.588660i
$99$	3.00927	−	5.21221i	0.302443	−	0.523847i
$100$	0.669131	+	0.743145i	0.0669131	+	0.0743145i
$101$	3.00827	+	9.25851i	0.299334	+	0.921256i	0.981731	+	0.190274i	$0.0609377\pi$
$101$	3.00827	+	9.25851i	0.299334	+	0.921256i	−0.682397	+	0.730982i	$0.739062\pi$
$102$	4.80229	−	5.33349i	0.475498	−	0.528094i
$103$	3.05621	+	1.36071i	0.301137	+	0.134075i	0.551743	−	0.834014i	$-0.313963\pi$
$103$	3.05621	+	1.36071i	0.301137	+	0.134075i	−0.250606	+	0.968089i	$0.580630\pi$
$104$	2.41978	−	0.514341i	0.237279	−	0.0504353i
$105$	0.0544205	+	0.517776i	0.00531090	+	0.0505298i
$106$	0.317405	−	3.01991i	0.0308291	−	0.293319i
$107$	−19.1909	−	4.07914i	−1.85525	−	0.394346i	−0.861670	−	0.507470i	$-0.830581\pi$
$107$	−19.1909	−	4.07914i	−1.85525	−	0.394346i	−0.993581	+	0.113124i	$0.963914\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	7.66654	+	5.57007i	0.734322	+	0.533516i	0.890928	−	0.454145i	$-0.150055\pi$
$109$	7.66654	+	5.57007i	0.734322	+	0.533516i	−0.156606	+	0.987661i	$0.550055\pi$
$110$	5.88702	+	1.25132i	0.561305	+	0.119309i
$111$	0.901720	−	8.57929i	0.0855875	−	0.814310i
$112$	0.0544205	+	0.517776i	0.00514225	+	0.0489253i
$113$	−1.39166	+	0.295806i	−0.130916	+	0.0278271i	−0.272904	−	0.962041i	$-0.587984\pi$
$113$	−1.39166	+	0.295806i	−0.130916	+	0.0278271i	0.141988	+	0.989868i	$0.454651\pi$
$114$	0.407217	+	0.181305i	0.0381394	+	0.0169807i
$115$	−0.431447	+	0.479171i	−0.0402327	+	0.0446829i
$116$	2.32904	+	7.16804i	0.216246	+	0.665536i
$117$	−1.65532	−	1.83842i	−0.153035	−	0.169962i
$118$	−0.797204	+	1.38080i	−0.0733886	+	0.127113i
$119$	1.86825	+	3.23591i	0.171262	+	0.296635i
$120$	0.309017	−	0.951057i	0.0282093	−	0.0868192i
$121$	23.0422	−	10.2590i	2.09474	−	0.932640i
$122$	2.28473	−	1.65995i	0.206850	−	0.150285i
$123$	2.32516			0.209652
$124$	0.0236072	−	5.56771i	0.00211999	−	0.499996i
$125$	1.00000			0.0894427
$126$	0.421197	−	0.306018i	0.0375232	−	0.0272622i
$127$	2.04431	−	0.910187i	0.181403	−	0.0807660i	−0.314025	−	0.949415i	$-0.601678\pi$
$127$	2.04431	−	0.910187i	0.181403	−	0.0807660i	0.495429	+	0.868649i	$0.335011\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−4.75776	−	8.24068i	−0.418898	−	0.725552i
$130$	1.23692	−	2.14241i	0.108485	−	0.187902i
$131$	10.6263	+	11.8017i	0.928428	+	1.03112i	0.999434	+	0.0336474i	$0.0107123\pi$
$131$	10.6263	+	11.8017i	0.928428	+	1.03112i	−0.0710062	+	0.997476i	$0.522621\pi$
$132$	−1.85983	−	5.72397i	−0.161877	−	0.498208i
$133$	−0.155287	+	0.172463i	−0.0134651	+	0.0149545i
$134$	1.81587	+	0.808476i	0.156867	+	0.0698417i
$135$	−0.978148	+	0.207912i	−0.0841855	+	0.0178942i
$136$	−0.750192	−	7.13760i	−0.0643284	−	0.612044i
$137$	0.213966	−	2.03575i	0.0182804	−	0.173926i	−0.981572	−	0.191091i	$-0.938797\pi$
$137$	0.213966	−	2.03575i	0.0182804	−	0.173926i	0.999853	+	0.0171650i	$0.00546406\pi$
$138$	0.630698	+	0.134059i	0.0536885	+	0.0114119i
$139$	1.21388	+	0.881933i	0.102960	+	0.0748046i	0.638074	−	0.769975i	$-0.279731\pi$
$139$	1.21388	+	0.881933i	0.102960	+	0.0748046i	−0.535114	+	0.844780i	$0.679731\pi$
$140$	0.421197	+	0.306018i	0.0355977	+	0.0258632i
$141$	5.31000	+	1.12868i	0.447183	+	0.0950517i
$142$	−0.706711	+	6.72391i	−0.0593059	+	0.564258i
$143$	−1.55632	−	14.8074i	−0.130146	−	1.23825i
$144$	−0.978148	+	0.207912i	−0.0815123	+	0.0173260i
$145$	6.88533	+	3.06554i	0.571795	+	0.254580i
$146$	−6.21590	+	6.90346i	−0.514432	+	0.571334i
$147$	−2.07936	−	6.39961i	−0.171503	−	0.527831i
$148$	−5.77229	−	6.41078i	−0.474479	−	0.526962i
$149$	1.34911	−	2.33672i	0.110523	−	0.191432i	−0.805458	−	0.592653i	$-0.798081\pi$
$149$	1.34911	−	2.33672i	0.110523	−	0.191432i	0.915981	+	0.401221i	$0.131414\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−4.85963	+	14.9564i	−0.395471	+	1.21714i	0.533122	+	0.846038i	$0.321019\pi$
$151$	−4.85963	+	14.9564i	−0.395471	+	1.21714i	−0.928594	+	0.371098i	$0.878981\pi$
$152$	0.407217	−	0.181305i	0.0330297	−	0.0147058i
$153$	−5.80624	+	4.21848i	−0.469407	+	0.341044i
$154$	3.13342			0.252498
$155$	−4.12182	−	3.74307i	−0.331073	−	0.300651i
$156$	−2.47384			−0.198066
$157$	−19.4889	+	14.1595i	−1.55538	+	1.13005i	−0.615711	+	0.787972i	$0.711131\pi$
$157$	−19.4889	+	14.1595i	−1.55538	+	1.13005i	−0.939671	+	0.342079i	$0.888869\pi$
$158$	6.67458	−	2.97171i	0.531001	−	0.236417i
$159$	−0.938344	+	2.88792i	−0.0744155	+	0.229027i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−0.167847	+	0.290720i	−0.0132282	+	0.0229120i
$162$	0.669131	+	0.743145i	0.0525719	+	0.0583870i
$163$	6.01923	+	18.5253i	0.471462	+	1.45101i	0.850670	+	0.525700i	$0.176197\pi$
$163$	6.01923	+	18.5253i	0.471462	+	1.45101i	−0.379208	+	0.925311i	$0.623803\pi$
$164$	1.55583	−	1.72793i	0.121490	−	0.134929i
$165$	−5.49821	−	2.44796i	−0.428035	−	0.190573i
$166$	1.61679	−	0.343659i	0.125487	−	0.0266731i
$167$	1.11763	+	10.6335i	0.0864845	+	0.822845i	0.948673	+	0.316258i	$0.102426\pi$
$167$	1.11763	+	10.6335i	0.0864845	+	0.822845i	−0.862189	+	0.506587i	$0.830907\pi$
$168$	0.0544205	−	0.517776i	0.00419863	−	0.0399473i
$169$	6.72976	+	1.43045i	0.517674	+	0.110035i
$170$	−5.80624	−	4.21848i	−0.445319	−	0.323543i
$171$	−0.360623	−	0.262008i	−0.0275775	−	0.0200362i
$172$	−9.30759	−	1.97839i	−0.709697	−	0.150851i
$173$	−1.59752	+	15.1994i	−0.121457	+	1.15559i	0.748734	+	0.662871i	$0.230662\pi$
$173$	−1.59752	+	15.1994i	−0.121457	+	1.15559i	−0.870191	+	0.492715i	$0.836005\pi$
$174$	−0.787823	−	7.49564i	−0.0597247	−	0.568243i
$175$	0.509251	−	0.108245i	0.0384958	−	0.00818253i
$176$	−5.49821	−	2.44796i	−0.414443	−	0.184522i
$177$	1.06687	−	1.18488i	0.0801906	−	0.0890607i
$178$	1.51616	+	4.66627i	0.113641	+	0.349752i
$179$	12.2489	+	13.6038i	0.915528	+	1.01680i	0.999793	+	0.0203534i	$0.00647913\pi$
$179$	12.2489	+	13.6038i	0.915528	+	1.01680i	−0.0842649	+	0.996443i	$0.526854\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	1.24883	+	2.16304i	0.0928249	+	0.160777i	0.908699	−	0.417453i	$-0.137077\pi$
$181$	1.24883	+	2.16304i	0.0928249	+	0.160777i	−0.815874	+	0.578230i	$0.803744\pi$
$182$	0.397999	−	1.22492i	0.0295017	−	0.0907968i
$183$	−2.57993	+	1.14866i	−0.190714	+	0.0849112i
$184$	0.521644	−	0.378997i	0.0384561	−	0.0279400i
$185$	−8.62655			−0.634237
$186$	−1.18068	+	5.44114i	−0.0865720	+	0.398964i
$187$	−43.1945			−3.15870
$188$	4.39186	−	3.19087i	0.320309	−	0.232718i
$189$	−0.475618	+	0.211759i	−0.0345961	+	0.0154032i
$190$	0.137746	−	0.423938i	0.00999312	−	0.0307557i
$191$	−5.30024	−	9.18029i	−0.383512	−	0.664262i	0.608050	−	0.793899i	$-0.291952\pi$
$191$	−5.30024	−	9.18029i	−0.383512	−	0.664262i	−0.991562	+	0.129637i	$0.958619\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	3.87073	+	4.29888i	0.278621	+	0.309440i	0.866171	−	0.499748i	$-0.166574\pi$
$193$	3.87073	+	4.29888i	0.278621	+	0.309440i	−0.587550	+	0.809188i	$0.699907\pi$
$194$	2.39031	+	7.35660i	0.171614	+	0.528173i
$195$	−1.65532	+	1.83842i	−0.118540	+	0.131652i
$196$	−6.14720	−	2.73691i	−0.439086	−	0.195493i
$197$	3.67318	−	0.780759i	0.261704	−	0.0556268i	−0.0751912	−	0.997169i	$-0.523957\pi$
$197$	3.67318	−	0.780759i	0.261704	−	0.0556268i	0.336895	+	0.941542i	$0.390623\pi$
$198$	0.629109	+	5.98557i	0.0447088	+	0.425376i
$199$	−1.89393	+	18.0195i	−0.134257	+	1.27737i	0.695207	+	0.718810i	$0.255313\pi$
$199$	−1.89393	+	18.0195i	−0.134257	+	1.27737i	−0.829464	+	0.558560i	$0.811354\pi$
$200$	−0.978148	−	0.207912i	−0.0691655	−	0.0147016i
$201$	−1.60809	−	1.16835i	−0.113426	−	0.0824090i
$202$	−7.87576	−	5.72207i	−0.554136	−	0.402604i
$203$	3.83819	+	0.815833i	0.269388	+	0.0572602i
$204$	−0.750192	+	7.13760i	−0.0525239	+	0.499732i
$205$	−0.243045	−	2.31242i	−0.0169750	−	0.161506i
$206$	−3.27233	+	0.695555i	−0.227994	+	0.0484616i
$207$	−0.589043	−	0.262259i	−0.0409413	−	0.0182282i
$208$	−1.65532	+	1.83842i	−0.114776	+	0.127472i
$209$	−0.829028	−	2.55149i	−0.0573451	−	0.176490i
$210$	−0.348368	−	0.386902i	−0.0240397	−	0.0266988i
$211$	12.2807	−	21.2708i	0.845440	−	1.46434i	−0.0397987	−	0.999208i	$-0.512672\pi$
$211$	12.2807	−	21.2708i	0.845440	−	1.46434i	0.885239	−	0.465137i	$-0.153995\pi$
$212$	1.51827	+	2.62972i	0.104275	+	0.180610i
$213$	2.08925	−	6.43004i	0.143153	−	0.440579i
$214$	17.9234	−	7.98001i	1.22522	−	0.545502i
$215$	−7.69822	+	5.59308i	−0.525014	+	0.381445i
$216$	1.00000			0.0680414
$217$	−2.50421	−	1.46000i	−0.169997	−	0.0991112i
$218$	−9.47637			−0.641821
$219$	7.51538	−	5.46024i	0.507842	−	0.368969i
$220$	−5.49821	+	2.44796i	−0.370689	+	0.165041i
$221$	−5.48646	+	16.8856i	−0.369059	+	1.13585i
$222$	4.31327	+	7.47081i	0.289488	+	0.501408i
$223$	−7.82744	+	13.5575i	−0.524164	+	0.907878i	0.475440	+	0.879748i	$0.342289\pi$
$223$	−7.82744	+	13.5575i	−0.524164	+	0.907878i	−0.999604	+	0.0281305i	$0.991045\pi$
$224$	−0.348368	−	0.386902i	−0.0232763	−	0.0258510i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	0.952004	−	1.05731i	0.0633264	−	0.0703311i
$227$	−6.15522	−	2.74048i	−0.408536	−	0.181892i	0.192171	−	0.981362i	$-0.438447\pi$
$227$	−6.15522	−	2.74048i	−0.408536	−	0.181892i	−0.600707	+	0.799470i	$0.705114\pi$
$228$	−0.436014	+	0.0926776i	−0.0288757	+	0.00613772i
$229$	0.410388	+	3.90458i	0.0271192	+	0.258022i	0.999678	+	0.0253657i	$0.00807502\pi$
$229$	0.410388	+	3.90458i	0.0271192	+	0.258022i	−0.972559	+	0.232656i	$0.925258\pi$
$230$	0.0673987	−	0.641256i	0.00444414	−	0.0422831i
$231$	−3.06495	−	0.651475i	−0.201659	−	0.0428639i
$232$	−6.09750	−	4.43009i	−0.400321	−	0.290850i
$233$	15.5499	+	11.2977i	1.01871	+	0.740136i	0.966018	−	0.258475i	$-0.0832201\pi$
$233$	15.5499	+	11.2977i	1.01871	+	0.740136i	0.0526913	+	0.998611i	$0.483220\pi$
$234$	2.41978	+	0.514341i	0.158186	+	0.0336235i
$235$	0.567447	−	5.39889i	0.0370161	−	0.352185i
$236$	−0.166661	−	1.58567i	−0.0108487	−	0.103219i
$237$	−7.14657	+	1.51905i	−0.464220	+	0.0986730i
$238$	−3.41347	−	1.51977i	−0.221262	−	0.0985123i
$239$	4.45822	−	4.95136i	0.288378	−	0.320277i	−0.581497	−	0.813549i	$-0.697533\pi$
$239$	4.45822	−	4.95136i	0.288378	−	0.320277i	0.869875	+	0.493272i	$0.164199\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	−10.3428	−	11.4868i	−0.666237	−	0.739932i	0.311389	−	0.950283i	$-0.399206\pi$
$241$	−10.3428	−	11.4868i	−0.666237	−	0.739932i	−0.977626	+	0.210351i	$0.932539\pi$
$242$	−12.6114	+	21.8436i	−0.810692	+	1.40416i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−0.872689	+	2.68586i	−0.0558682	+	0.171945i
$245$	−6.14720	+	2.73691i	−0.392730	+	0.174855i
$246$	−1.88109	+	1.36669i	−0.119934	+	0.0871371i
$247$	−1.10273			−0.0701648
$248$	3.25352	+	4.51825i	0.206599	+	0.286909i
$249$	−1.65291			−0.104749
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	−27.1982	+	12.1094i	−1.71673	+	0.764338i	−0.719149	+	0.694856i	$0.755468\pi$
$251$	−27.1982	+	12.1094i	−1.71673	+	0.764338i	−0.997583	+	0.0694825i	$0.977865\pi$
$252$	−0.160883	+	0.495147i	−0.0101347	+	0.0311913i
$253$	−1.94034	−	3.36077i	−0.121988	−	0.211290i
$254$	−1.11889	+	1.93797i	−0.0702054	+	0.121599i
$255$	4.80229	+	5.33349i	0.300731	+	0.333996i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	7.76893	−	8.62827i	0.484613	−	0.538217i	−0.450402	−	0.892826i	$-0.648719\pi$
$257$	7.76893	−	8.62827i	0.484613	−	0.538217i	0.935015	+	0.354609i	$0.115386\pi$
$258$	8.69286	+	3.87031i	0.541194	+	0.240955i
$259$	−4.39308	+	0.933778i	−0.272973	+	0.0580222i
$260$	0.258587	+	2.46029i	0.0160369	+	0.152581i
$261$	−0.787823	+	7.49564i	−0.0487650	+	0.463968i
$262$	−15.5338	−	3.30181i	−0.959680	−	0.203986i
$263$	−3.31638	−	2.40949i	−0.204497	−	0.148576i	0.480823	−	0.876817i	$-0.340338\pi$
$263$	−3.31638	−	2.40949i	−0.204497	−	0.148576i	−0.685320	+	0.728242i	$0.740338\pi$
$264$	4.86910	+	3.53761i	0.299672	+	0.217725i
$265$	2.97019	+	0.631333i	0.182457	+	0.0387825i
$266$	0.0242582	−	0.230801i	0.00148736	−	0.0141513i
$267$	−0.512859	−	4.87953i	−0.0313865	−	0.298622i
$268$	−1.94428	+	0.413269i	−0.118766	+	0.0252444i
$269$	9.59367	+	4.27138i	0.584936	+	0.260430i	0.677798	−	0.735249i	$-0.262935\pi$
$269$	9.59367	+	4.27138i	0.584936	+	0.260430i	−0.0928611	+	0.995679i	$0.529601\pi$
$270$	0.669131	−	0.743145i	0.0407220	−	0.0452264i
$271$	0.438049	+	1.34818i	0.0266096	+	0.0818958i	0.963479	−	0.267783i	$-0.0862909\pi$
$271$	0.438049	+	1.34818i	0.0266096	+	0.0818958i	−0.936870	+	0.349678i	$0.886291\pi$
$272$	4.80229	+	5.33349i	0.291182	+	0.323390i
$273$	−0.643976	+	1.11540i	−0.0389752	+	0.0675071i
$274$	1.02348	+	1.77273i	0.0618309	+	0.107094i
$275$	−1.85983	+	5.72397i	−0.112152	+	0.345168i
$276$	−0.589043	+	0.262259i	−0.0354562	+	0.0157861i
$277$	−6.26425	+	4.55125i	−0.376382	+	0.273458i	−0.759853	−	0.650095i	$-0.774729\pi$
$277$	−6.26425	+	4.55125i	−0.376382	+	0.273458i	0.383470	+	0.923553i	$0.374729\pi$
$278$	−1.50043			−0.0899901
$279$	2.28616	−	5.07676i	0.136869	−	0.303938i
$280$	−0.520628			−0.0311135
$281$	−3.32053	+	2.41251i	−0.198086	+	0.143918i	−0.682407	−	0.730972i	$-0.739067\pi$
$281$	−3.32053	+	2.41251i	−0.198086	+	0.143918i	0.484321	+	0.874891i	$0.339067\pi$
$282$	−4.95930	+	2.20802i	−0.295322	+	0.131486i
$283$	9.41520	−	28.9770i	0.559675	−	1.72250i	−0.123590	−	0.992333i	$-0.539441\pi$
$283$	9.41520	−	28.9770i	0.559675	−	1.72250i	0.683265	−	0.730170i	$-0.260559\pi$
$284$	−3.38047	−	5.85515i	−0.200594	−	0.347439i
$285$	−0.222877	+	0.386035i	−0.0132021	+	0.0228667i
$286$	9.96263	+	11.0646i	0.589103	+	0.654265i
$287$	−0.374078	−	1.15129i	−0.0220811	−	0.0679588i
$288$	0.669131	−	0.743145i	0.0394289	−	0.0437902i
$289$	31.5247	+	14.0357i	1.85439	+	0.825629i
$290$	−7.37223	+	1.56702i	−0.432912	+	0.0920183i
$291$	−0.808548	−	7.69282i	−0.0473979	−	0.450961i
$292$	0.971019	−	9.23863i	0.0568246	−	0.540650i
$293$	−7.41498	−	1.57610i	−0.433188	−	0.0920770i	−0.0138436	−	0.999904i	$-0.504407\pi$
$293$	−7.41498	−	1.57610i	−0.433188	−	0.0920770i	−0.419344	+	0.907827i	$0.637740\pi$
$294$	5.44383	+	3.95518i	0.317491	+	0.230671i
$295$	−1.28990	−	0.937169i	−0.0751010	−	0.0545641i
$296$	8.43804	+	1.79356i	0.490451	+	0.104249i
$297$	0.629109	−	5.98557i	0.0365046	−	0.347318i
$298$	0.282040	+	2.68344i	0.0163382	+	0.155447i
$299$	−1.56025	+	0.331641i	−0.0902314	+	0.0191793i
$300$	0.913545	+	0.406737i	0.0527436	+	0.0234830i
$301$	−3.31491	+	3.68158i	−0.191068	+	0.212203i
$302$	−4.85963	−	14.9564i	−0.279641	−	0.860645i
$303$	6.51397	+	7.23449i	0.374218	+	0.415611i
$304$	−0.222877	+	0.386035i	−0.0127829	+	0.0221406i
$305$	1.41204	+	2.44573i	0.0808532	+	0.140042i
$306$	2.21779	−	6.82565i	0.126782	−	0.390196i
$307$	−15.9098	+	7.08352i	−0.908023	+	0.404278i	−0.806963	−	0.590602i	$-0.798890\pi$
$307$	−15.9098	+	7.08352i	−0.908023	+	0.404278i	−0.101060	+	0.994880i	$0.532224\pi$
$308$	−2.53499	+	1.84178i	−0.144445	+	0.104945i
$309$	3.34544			0.190315
$310$	5.53475	+	0.605462i	0.314352	+	0.0343880i
$311$	−14.5413			−0.824561			−0.412281	−	0.911057i	$-0.635268\pi$
$311$	−14.5413			−0.824561			−0.412281	+	0.911057i	$0.635268\pi$
$312$	2.00138	−	1.45409i	0.113306	−	0.0823215i
$313$	−20.0669	+	8.93437i	−1.13425	+	0.505001i	−0.885995	−	0.463694i	$-0.846524\pi$
$313$	−20.0669	+	8.93437i	−1.13425	+	0.505001i	−0.248255	+	0.968695i	$0.579857\pi$
$314$	7.44409	−	22.9106i	0.420094	−	1.29292i
$315$	0.260314	+	0.450877i	0.0146670	+	0.0254041i
$316$	−3.65312	+	6.32738i	−0.205504	+	0.355943i
$317$	19.1333	+	21.2497i	1.07463	+	1.19350i	0.980209	+	0.197968i	$0.0634341\pi$
$317$	19.1333	+	21.2497i	1.07463	+	1.19350i	0.0944236	+	0.995532i	$0.469899\pi$
$318$	−0.938344	−	2.88792i	−0.0526197	−	0.161947i
$319$	−30.3526	+	33.7100i	−1.69942	+	1.88740i
$320$	0.913545	+	0.406737i	0.0510687	+	0.0227373i
$321$	−19.1909	+	4.07914i	−1.07113	+	0.227676i
$322$	−0.0350897	−	0.333856i	−0.00195547	−	0.0186051i
$323$	−0.334401	+	3.18162i	−0.0186066	+	0.177030i
$324$	−0.978148	−	0.207912i	−0.0543415	−	0.0115506i
$325$	2.00138	+	1.45409i	0.111017	+	0.0806583i
$326$	−15.7585	−	11.4492i	−0.872785	−	0.634115i
$327$	9.26929	+	1.97025i	0.512593	+	0.108955i
$328$	−0.243045	+	2.31242i	−0.0134199	+	0.127682i
$329$	−0.295429	−	2.81082i	−0.0162875	−	0.154965i
$330$	5.88702	−	1.25132i	0.324070	−	0.0688832i
$331$	28.7091	+	12.7821i	1.57799	+	0.702568i	0.994019	−	0.109203i	$-0.0348299\pi$
$331$	28.7091	+	12.7821i	1.57799	+	0.702568i	0.583975	+	0.811772i	$0.301497\pi$
$332$	−1.10601	+	1.22835i	−0.0607002	+	0.0674144i
$333$	−2.66575	−	8.20434i	−0.146082	−	0.449595i
$334$	−7.15439	−	7.94576i	−0.391471	−	0.434773i
$335$	−0.993857	+	1.72141i	−0.0543002	+	0.0940507i
$336$	0.260314	+	0.450877i	0.0142013	+	0.0245974i
$337$	−8.90462	+	27.4056i	−0.485066	+	1.49288i	0.346820	+	0.937932i	$0.387261\pi$
$337$	−8.90462	+	27.4056i	−0.485066	+	1.49288i	−0.831886	+	0.554947i	$0.812739\pi$
$338$	−6.28529	+	2.79839i	−0.341875	+	0.152212i
$339$	−1.15103	+	0.836270i	−0.0625152	+	0.0454200i
$340$	7.17691			0.389223
$341$	29.0911	−	16.6317i	1.57537	−	0.900657i
$342$	0.445754			0.0241036
$343$	−5.78259	+	4.20130i	−0.312231	+	0.226849i
$344$	8.69286	−	3.87031i	0.468688	−	0.208673i
$345$	−0.199250	+	0.613230i	−0.0107273	+	0.0330152i
$346$	−7.64154	−	13.2355i	−0.410812	−	0.711547i
$347$	17.3046	−	29.9724i	0.928959	−	1.60900i	0.143892	−	0.989593i	$-0.454038\pi$
$347$	17.3046	−	29.9724i	0.928959	−	1.60900i	0.785067	−	0.619411i	$-0.212628\pi$
$348$	5.04319	+	5.60103i	0.270343	+	0.300247i
$349$	−4.25612	−	13.0990i	−0.227825	−	0.701174i	−0.997993	−	0.0633318i	$-0.979827\pi$
$349$	−4.25612	−	13.0990i	−0.227825	−	0.701174i	0.770167	−	0.637842i	$-0.220173\pi$
$350$	−0.348368	+	0.386902i	−0.0186211	+	0.0206808i
$351$	−2.25997	−	1.00620i	−0.120628	−	0.0537071i
$352$	5.88702	−	1.25132i	0.313779	−	0.0666958i
$353$	−3.12514	−	29.7337i	−0.166334	−	1.58257i	−0.685616	−	0.727963i	$-0.740467\pi$
$353$	−3.12514	−	29.7337i	−0.166334	−	1.58257i	0.519282	−	0.854603i	$-0.326199\pi$
$354$	−0.166661	+	1.58567i	−0.00885793	+	0.0842776i
$355$	−6.61320	−	1.40568i	−0.350992	−	0.0746057i
$356$	−3.96936	−	2.88391i	−0.210376	−	0.152847i
$357$	3.02290	+	2.19626i	0.159989	+	0.116239i
$358$	−17.9057	−	3.80598i	−0.946346	−	0.201152i
$359$	−3.02904	+	28.8194i	−0.159866	+	1.52103i	0.560920	+	0.827870i	$0.310448\pi$
$359$	−3.02904	+	28.8194i	−0.159866	+	1.52103i	−0.720786	+	0.693158i	$0.756219\pi$
$360$	−0.104528	−	0.994522i	−0.00550913	−	0.0524159i
$361$	18.3904	−	3.90901i	0.967918	−	0.205737i
$362$	−2.28173	−	1.01589i	−0.119925	−	0.0533940i
$363$	16.8774	−	18.7442i	0.885831	−	0.983815i
$364$	0.397999	+	1.22492i	0.0208608	+	0.0642030i
$365$	−6.21590	−	6.90346i	−0.325355	−	0.361343i
$366$	1.41204	−	2.44573i	0.0738085	−	0.127840i
$367$	11.5429	+	19.9929i	0.602534	+	1.04362i	0.992436	+	0.122763i	$0.0391756\pi$
$367$	11.5429	+	19.9929i	0.602534	+	1.04362i	−0.389902	+	0.920856i	$0.627491\pi$
$368$	−0.199250	+	0.613230i	−0.0103866	+	0.0319668i
$369$	2.12414	−	0.945726i	0.110578	−	0.0492326i
$370$	6.97902	−	5.07056i	0.362822	−	0.263606i
$371$	1.58091			0.0820768
$372$	−2.24303	−	5.09596i	−0.116296	−	0.264213i
$373$	24.4111			1.26396			0.631979	−	0.774985i	$-0.282243\pi$
$373$	24.4111			1.26396			0.631979	+	0.774985i	$0.282243\pi$
$374$	34.9451	−	25.3891i	1.80697	−	1.31284i
$375$	0.913545	−	0.406737i	0.0471753	−	0.0210038i
$376$	−1.67754	+	5.16294i	−0.0865125	+	0.266258i
$377$	9.32259	+	16.1472i	0.480138	+	0.831623i
$378$	0.260314	−	0.450877i	0.0133891	−	0.0231906i
$379$	6.58653	+	7.31508i	0.338327	+	0.375751i	0.888168	−	0.459519i	$-0.151978\pi$
$379$	6.58653	+	7.31508i	0.338327	+	0.375751i	−0.549841	+	0.835270i	$0.685312\pi$
$380$	0.137746	+	0.423938i	0.00706621	+	0.0217475i
$381$	1.49737	−	1.66299i	0.0767124	−	0.0851978i
$382$	9.68402	+	4.31160i	0.495478	+	0.220601i
$383$	−8.12861	+	1.72779i	−0.415352	+	0.0882859i	−0.410848	−	0.911704i	$-0.634767\pi$
$383$	−8.12861	+	1.72779i	−0.415352	+	0.0882859i	−0.00450467	+	0.999990i	$0.501434\pi$
$384$	−0.104528	−	0.994522i	−0.00533420	−	0.0507515i
$385$	−0.327532	+	3.11626i	−0.0166926	+	0.158819i
$386$	−5.65830	−	1.20271i	−0.288000	−	0.0612163i
$387$	−7.69822	−	5.59308i	−0.391323	−	0.284312i
$388$	−6.25790	−	4.54663i	−0.317697	−	0.230820i
$389$	−12.6615	−	2.69129i	−0.641965	−	0.136454i	−0.124584	−	0.992209i	$-0.539760\pi$
$389$	−12.6615	−	2.69129i	−0.641965	−	0.136454i	−0.517381	+	0.855755i	$0.673093\pi$
$390$	0.258587	−	2.46029i	0.0130941	−	0.124582i
$391$	0.483714	+	4.60223i	0.0244625	+	0.232745i
$392$	6.58190	−	1.39903i	0.332436	−	0.0706615i
$393$	14.5078	+	6.45931i	0.731824	+	0.325829i
$394$	−2.51275	+	2.79069i	−0.126590	+	0.140593i
$395$	2.25775	+	6.94864i	0.113600	+	0.349624i
$396$	−4.02719	−	4.47265i	−0.202374	−	0.224759i
$397$	−0.444570	+	0.770019i	−0.0223124	+	0.0386461i	−0.876966	−	0.480552i	$-0.840436\pi$
$397$	−0.444570	+	0.770019i	−0.0223124	+	0.0386461i	0.854654	+	0.519199i	$0.173769\pi$
$398$	−9.05939	−	15.6913i	−0.454106	−	0.786535i
$399$	−0.0717143	+	0.220714i	−0.00359021	+	0.0110495i
$400$	0.913545	−	0.406737i	0.0456773	−	0.0203368i
$401$	19.5779	−	14.2242i	0.977675	−	0.710323i	0.0204873	−	0.999790i	$-0.493478\pi$
$401$	19.5779	−	14.2242i	0.977675	−	0.710323i	0.957188	+	0.289468i	$0.0934782\pi$
$402$	1.98771			0.0991382
$403$	−2.80658	−	13.4848i	−0.139806	−	0.671726i
$404$	9.73497			0.484333
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$	−3.58470	+	1.59601i	−0.177905	+	0.0792086i
$407$	16.0439	−	49.3781i	0.795268	−	2.44758i
$408$	−3.58846	−	6.21539i	−0.177655	−	0.307708i
$409$	−10.6586	+	18.4612i	−0.527033	+	0.912847i	0.472471	+	0.881346i	$0.343362\pi$
$409$	−10.6586	+	18.4612i	−0.527033	+	0.912847i	−0.999504	+	0.0315012i	$0.989971\pi$
$410$	1.55583	+	1.72793i	0.0768371	+	0.0853363i
$411$	−0.632548	−	1.94678i	−0.0312013	−	0.0960276i
$412$	2.23853	−	2.48614i	0.110285	−	0.122484i
$413$	−0.758328	−	0.337630i	−0.0373149	−	0.0166137i
$414$	0.630698	−	0.134059i	0.0309971	−	0.00658864i
$415$	0.172776	+	1.64385i	0.00848123	+	0.0806935i
$416$	0.258587	−	2.46029i	0.0126783	−	0.120626i
$417$	1.46765	+	0.311958i	0.0718710	+	0.0152766i
$418$	2.17042	+	1.57690i	0.106159	+	0.0771289i
$419$	−17.5803	−	12.7728i	−0.858853	−	0.623993i	0.0687196	−	0.997636i	$-0.478109\pi$
$419$	−17.5803	−	12.7728i	−0.858853	−	0.623993i	−0.927573	+	0.373643i	$0.878109\pi$
$420$	0.509251	+	0.108245i	0.0248489	+	0.00528180i
$421$	4.12246	−	39.2226i	0.200916	−	1.91159i	−0.174364	−	0.984681i	$-0.555787\pi$
$421$	4.12246	−	39.2226i	0.200916	−	1.91159i	0.375280	−	0.926911i	$-0.377547\pi$
$422$	2.56737	+	24.4269i	0.124978	+	1.18908i
$423$	5.31000	−	1.12868i	0.258181	−	0.0548781i
$424$	−2.77402	−	1.23507i	−0.134718	−	0.0599805i
$425$	4.80229	−	5.33349i	0.232945	−	0.258712i
$426$	2.08925	+	6.43004i	0.101224	+	0.311536i
$427$	0.983820	+	1.09264i	0.0476104	+	0.0528767i
$428$	−9.80980	+	16.9911i	−0.474174	+	0.821294i
$429$	−7.44446	−	12.8942i	−0.359422	−	0.622537i
$430$	2.94046	−	9.04980i	0.141801	−	0.436420i
$431$	−2.94036	+	1.30913i	−0.141632	+	0.0630588i	−0.476329	−	0.879267i	$-0.658033\pi$
$431$	−2.94036	+	1.30913i	−0.141632	+	0.0630588i	0.334697	+	0.942326i	$0.391366\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	22.8815			1.09961			0.549806	−	0.835292i	$-0.314702\pi$
$433$	22.8815			1.09961			0.549806	+	0.835292i	$0.314702\pi$
$434$	2.88412	−	0.290774i	0.138442	−	0.0139576i
$435$	7.53693			0.361368
$436$	7.66654	−	5.57007i	0.367161	−	0.266758i
$437$	−0.262569	+	0.116903i	−0.0125604	+	0.00559223i
$438$	−2.87062	+	8.83486i	−0.137163	+	0.422146i
$439$	−16.7979	−	29.0948i	−0.801721	−	1.38862i	−0.918483	−	0.395461i	$-0.870585\pi$
$439$	−16.7979	−	29.0948i	−0.801721	−	1.38862i	0.116762	−	0.993160i	$-0.462748\pi$
$440$	3.00927	−	5.21221i	0.143461	−	0.248482i
$441$	−4.50254	−	5.00058i	−0.214407	−	0.238123i
$442$	−5.48646	−	16.8856i	−0.260964	−	0.803165i
$443$	−10.1270	+	11.2471i	−0.481147	+	0.534368i	−0.934026	−	0.357204i	$-0.883730\pi$
$443$	−10.1270	+	11.2471i	−0.481147	+	0.534368i	0.452879	+	0.891572i	$0.350397\pi$
$444$	−7.88074	−	3.50873i	−0.374004	−	0.166517i
$445$	−4.79919	+	1.02010i	−0.227503	+	0.0483573i
$446$	−1.63638	−	15.5691i	−0.0774848	−	0.737219i
$447$	0.282040	−	2.68344i	0.0133401	−	0.126922i
$448$	0.509251	+	0.108245i	0.0240599	+	0.00511408i
$449$	32.9890	+	23.9679i	1.55685	+	1.13112i	0.938535	+	0.345184i	$0.112183\pi$
$449$	32.9890	+	23.9679i	1.55685	+	1.13112i	0.618313	+	0.785932i	$0.287817\pi$
$450$	−0.809017	−	0.587785i	−0.0381374	−	0.0277085i
$451$	13.6882	+	2.90953i	0.644554	+	0.137004i
$452$	−0.148718	+	1.41495i	−0.00699509	+	0.0665538i
$453$	1.64383	+	15.6400i	0.0772337	+	0.734829i
$454$	6.59049	−	1.40085i	0.309307	−	0.0657452i
$455$	1.17660	+	0.523858i	0.0551600	+	0.0245588i
$456$	0.298268	−	0.331260i	0.0139677	−	0.0155127i
$457$	6.92835	+	21.3233i	0.324095	+	0.997461i	0.971848	+	0.235610i	$0.0757090\pi$
$457$	6.92835	+	21.3233i	0.324095	+	0.997461i	−0.647753	+	0.761851i	$0.724291\pi$
$458$	−2.62707	−	2.91765i	−0.122755	−	0.136333i
$459$	−3.58846	+	6.21539i	−0.167495	+	0.290109i
$460$	0.322394	+	0.558403i	0.0150317	+	0.0260357i
$461$	5.43418	−	16.7247i	0.253095	−	0.778946i	−0.741104	−	0.671390i	$-0.765698\pi$
$461$	5.43418	−	16.7247i	0.253095	−	0.778946i	0.994199	−	0.107556i	$-0.0343024\pi$
$462$	2.86252	−	1.27448i	0.133177	−	0.0592941i
$463$	2.94560	−	2.14010i	0.136894	−	0.0994590i	−0.517231	−	0.855846i	$-0.673037\pi$
$463$	2.94560	−	2.14010i	0.136894	−	0.0994590i	0.654125	+	0.756387i	$0.273037\pi$
$464$	7.53693			0.349893
$465$	−5.28792	−	1.74297i	−0.245221	−	0.0808283i
$466$	−19.2208			−0.890384
$467$	16.7382	−	12.1610i	0.774550	−	0.562744i	−0.128788	−	0.991672i	$-0.541109\pi$
$467$	16.7382	−	12.1610i	0.774550	−	0.562744i	0.903338	+	0.428928i	$0.141109\pi$
$468$	−2.25997	+	1.00620i	−0.104467	+	0.0465117i
$469$	−0.319789	+	0.984211i	−0.0147665	+	0.0454466i
$470$	2.71432	+	4.70133i	0.125202	+	0.216856i
$471$	−12.0448	+	20.8622i	−0.554995	+	0.961279i
$472$	1.06687	+	1.18488i	0.0491065	+	0.0545383i
$473$	−17.6973	−	54.4666i	−0.813721	−	2.50438i
$474$	4.88882	−	5.42959i	0.224551	−	0.249389i
$475$	0.407217	+	0.181305i	0.0186844	+	0.00831883i
$476$	3.65485	−	0.776863i	0.167520	−	0.0356075i
$477$	0.317405	+	3.01991i	0.0145330	+	0.138272i
$478$	−0.696442	+	6.62621i	−0.0318545	+	0.303076i
$479$	−18.6139	−	3.95650i	−0.850490	−	0.180777i	−0.238010	−	0.971263i	$-0.576495\pi$
$479$	−18.6139	−	3.95650i	−0.850490	−	0.180777i	−0.612481	+	0.790485i	$0.709828\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	−17.2650	−	12.5438i	−0.787217	−	0.571946i
$482$	15.1193	+	3.21370i	0.688664	+	0.146380i
$483$	−0.0350897	+	0.333856i	−0.00159663	+	0.0151910i
$484$	−2.63650	−	25.0846i	−0.119841	−	1.14021i
$485$	−7.56616	+	1.60824i	−0.343562	+	0.0730263i
$486$	0.913545	+	0.406737i	0.0414393	+	0.0184499i
$487$	−6.80586	+	7.55867i	−0.308403	+	0.342516i	−0.877344	−	0.479862i	$-0.840687\pi$
$487$	−6.80586	+	7.55867i	−0.308403	+	0.342516i	0.568941	+	0.822378i	$0.307353\pi$
$488$	−0.872689	−	2.68586i	−0.0395048	−	0.121583i
$489$	13.0337	+	14.4754i	0.589406	+	0.654602i
$490$	3.36447	−	5.82744i	0.151991	−	0.263257i
$491$	−18.2848	−	31.6702i	−0.825182	−	1.42926i	−0.901780	−	0.432196i	$-0.857739\pi$
$491$	−18.2848	−	31.6702i	−0.825182	−	1.42926i	0.0765973	−	0.997062i	$-0.475594\pi$
$492$	0.718513	−	2.21136i	0.0323931	−	0.0996956i
$493$	49.4154	−	22.0011i	2.22556	−	0.990882i
$494$	0.892124	−	0.648166i	0.0401386	−	0.0291624i
$495$	−6.01854			−0.270513
$496$	−5.28792	−	1.74297i	−0.237434	−	0.0782617i
$497$	−3.51994			−0.157891
$498$	1.33723	−	0.971554i	0.0599227	−	0.0435364i
$499$	20.8643	−	9.28940i	0.934016	−	0.415851i	0.117434	−	0.993081i	$-0.462533\pi$
$499$	20.8643	−	9.28940i	0.934016	−	0.415851i	0.816582	+	0.577230i	$0.195866\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	5.34604	+	9.25961i	0.238843	+	0.413689i
$502$	14.8860	−	25.7834i	0.664397	−	1.15077i
$503$	21.3685	+	23.7321i	0.952773	+	1.05816i	0.998246	+	0.0591965i	$0.0188538\pi$
$503$	21.3685	+	23.7321i	0.952773	+	1.05816i	−0.0454730	+	0.998966i	$0.514479\pi$
$504$	−0.160883	−	0.495147i	−0.00716630	−	0.0220556i
$505$	6.51397	−	7.23449i	0.289868	−	0.321931i
$506$	3.54518	+	1.57841i	0.157602	+	0.0701691i
$507$	6.72976	−	1.43045i	0.298879	−	0.0635287i
$508$	−0.233912	−	2.22552i	−0.0103781	−	0.0987415i
$509$	1.40727	−	13.3892i	0.0623760	−	0.593468i	−0.918034	−	0.396501i	$-0.870224\pi$
$509$	1.40727	−	13.3892i	0.0623760	−	0.593468i	0.980410	−	0.196967i	$-0.0631091\pi$
$510$	−7.02008	−	1.49216i	−0.310854	−	0.0660741i
$511$	−3.91272	−	2.84276i	−0.173088	−	0.125756i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−0.436014	−	0.0926776i	−0.0192505	−	0.00409181i
$514$	−1.21363	+	11.5469i	−0.0535308	+	0.509311i
$515$	−0.349693	−	3.32711i	−0.0154093	−	0.146610i
$516$	−9.30759	+	1.97839i	−0.409744	+	0.0870937i
$517$	29.8478	+	13.2891i	1.31270	+	0.584453i
$518$	3.00522	−	3.33763i	0.132042	−	0.146647i
$519$	4.72273	+	14.5351i	0.207305	+	0.638019i
$520$	−1.65532	−	1.83842i	−0.0725908	−	0.0806202i
$521$	−13.7799	+	23.8675i	−0.603710	+	1.04566i	0.388544	+	0.921430i	$0.372978\pi$
$521$	−13.7799	+	23.8675i	−0.603710	+	1.04566i	−0.992254	+	0.124226i	$0.960355\pi$
$522$	−3.76846	−	6.52717i	−0.164941	−	0.285686i
$523$	−1.64127	+	5.05131i	−0.0717677	+	0.220878i	−0.980506	−	0.196487i	$-0.937047\pi$
$523$	−1.64127	+	5.05131i	−0.0717677	+	0.220878i	0.908739	+	0.417366i	$0.137047\pi$
$524$	14.5078	−	6.45931i	0.633778	−	0.282176i
$525$	0.421197	−	0.306018i	0.0183826	−	0.0133557i
$526$	4.09927			0.178737
$527$	−39.7578	+	4.00835i	−1.73188	+	0.174607i
$528$	−6.01854			−0.261923
$529$	18.2710	−	13.2747i	0.794393	−	0.577160i
$530$	−2.77402	+	1.23507i	−0.120496	+	0.0536482i
$531$	0.492699	−	1.51637i	0.0213813	−	0.0658049i
$532$	0.116036	+	0.200981i	0.00503081	+	0.00871361i
$533$	2.87604	−	4.98144i	0.124575	−	0.215770i
$534$	3.28303	+	3.64617i	0.142070	+	0.157785i
$535$	6.06279	+	18.6593i	0.262117	+	0.806714i
$536$	1.33004	−	1.47716i	0.0574490	−	0.0638036i
$537$	16.7231	+	7.44561i	0.721656	+	0.321302i
$538$	−10.2721	+	2.18340i	−0.442862	+	0.0941331i
$539$	−4.23324	−	40.2766i	−0.182338	−	1.73483i
$540$	−0.104528	+	0.994522i	−0.00449819	+	0.0427974i
$541$	9.25741	+	1.96772i	0.398007	+	0.0845990i	0.402567	−	0.915391i	$-0.368118\pi$
$541$	9.25741	+	1.96772i	0.398007	+	0.0845990i	−0.00455970	+	0.999990i	$0.501451\pi$
$542$	−1.14683	−	0.833218i	−0.0492604	−	0.0357898i
$543$	2.02065	+	1.46809i	0.0867144	+	0.0630017i
$544$	−7.02008	−	1.49216i	−0.300983	−	0.0639760i
$545$	0.990550	−	9.42446i	0.0424305	−	0.403699i
$546$	−0.134628	−	1.28090i	−0.00576153	−	0.0548173i
$547$	−32.9541	+	7.00460i	−1.40901	+	0.299495i	−0.848739	−	0.528812i	$-0.822638\pi$
$547$	−32.9541	+	7.00460i	−1.40901	+	0.299495i	−0.560275	+	0.828307i	$0.689304\pi$
$548$	−1.87000	−	0.832576i	−0.0798823	−	0.0355659i
$549$	−1.88968	+	2.09870i	−0.0806495	+	0.0895704i
$550$	−1.85983	−	5.72397i	−0.0793035	−	0.244071i
$551$	2.24802	+	2.49668i	0.0957690	+	0.106362i
$552$	0.322394	−	0.558403i	0.0137220	−	0.0237672i
$553$	1.90192	+	3.29422i	0.0808777	+	0.140084i
$554$	2.39273	−	7.36407i	0.101657	−	0.312869i
$555$	−7.88074	+	3.50873i	−0.334519	+	0.148937i
$556$	1.21388	−	0.881933i	0.0514799	−	0.0374023i
$557$	19.2737			0.816653			0.408327	−	0.912836i	$-0.366112\pi$
$557$	19.2737			0.816653			0.408327	+	0.912836i	$0.366112\pi$
$558$	1.13450	+	5.45095i	0.0480273	+	0.230757i
$559$	−23.5399			−0.995632
$560$	0.421197	−	0.306018i	0.0177988	−	0.0129316i
$561$	−39.4602	+	17.5688i	−1.66601	+	0.741755i
$562$	1.26833	−	3.90352i	0.0535013	−	0.164660i
$563$	5.82505	+	10.0893i	0.245496	+	0.425212i	0.962271	−	0.272093i	$-0.0877157\pi$
$563$	5.82505	+	10.0893i	0.245496	+	0.425212i	−0.716775	+	0.697305i	$0.754382\pi$
$564$	2.71432	−	4.70133i	0.114293	−	0.197962i
$565$	0.952004	+	1.05731i	0.0400511	+	0.0444813i
$566$	9.41520	+	28.9770i	0.395750	+	1.21799i
$567$	−0.348368	+	0.386902i	−0.0146301	+	0.0162484i
$568$	6.17643	+	2.74992i	0.259157	+	0.115384i
$569$	6.86874	−	1.46000i	0.287953	−	0.0612062i	−0.0616708	−	0.998097i	$-0.519643\pi$
$569$	6.86874	−	1.46000i	0.287953	−	0.0612062i	0.349623	+	0.936890i	$0.386310\pi$
$570$	−0.0465940	−	0.443313i	−0.00195161	−	0.0185683i
$571$	−0.667978	+	6.35539i	−0.0279540	+	0.265965i	0.971614	+	0.236572i	$0.0760239\pi$
$571$	−0.667978	+	6.35539i	−0.0279540	+	0.265965i	−0.999568	+	0.0293925i	$0.990643\pi$
$572$	−14.5636	−	3.09558i	−0.608933	−	0.129433i
$573$	−8.57597	−	6.23081i	−0.358266	−	0.260296i
$574$	0.979349	+	0.711539i	0.0408773	+	0.0296991i
$575$	0.630698	+	0.134059i	0.0263019	+	0.00559064i
$576$	−0.104528	+	0.994522i	−0.00435535	+	0.0414384i
$577$	2.81201	+	26.7545i	0.117065	+	1.11380i	0.882507	+	0.470298i	$0.155854\pi$
$577$	2.81201	+	26.7545i	0.117065	+	1.11380i	−0.765442	+	0.643505i	$0.777480\pi$
$578$	−33.7540	+	7.17463i	−1.40398	+	0.298425i
$579$	5.28460	+	2.35285i	0.219620	+	0.0977813i
$580$	5.04319	−	5.60103i	0.209407	−	0.232570i
$581$	0.265925	+	0.818432i	0.0110324	+	0.0339543i
$582$	5.17585	+	5.74837i	0.214546	+	0.238277i
$583$	−9.13778	+	15.8271i	−0.378448	+	0.655491i
$584$	4.64476	+	8.04496i	0.192201	+	0.332903i
$585$	−0.764459	+	2.35276i	−0.0316065	+	0.0972748i
$586$	6.92526	−	3.08332i	0.286080	−	0.127371i
$587$	24.0264	−	17.4562i	0.991676	−	0.720495i	0.0313885	−	0.999507i	$-0.490007\pi$
$587$	24.0264	−	17.4562i	0.991676	−	0.720495i	0.960287	+	0.279012i	$0.0900071\pi$
$588$	−6.72895			−0.277497
$589$	−0.999839	−	2.27155i	−0.0411977	−	0.0935975i
$590$	1.59441			0.0656407
$591$	3.03806	−	2.20728i	0.124969	−	0.0907953i
$592$	−7.88074	+	3.50873i	−0.323897	+	0.144208i
$593$	−2.33389	+	7.18298i	−0.0958414	+	0.294970i	−0.987472	−	0.157794i	$-0.949562\pi$
$593$	−2.33389	+	7.18298i	−0.0958414	+	0.294970i	0.891631	+	0.452764i	$0.149562\pi$
$594$	3.00927	+	5.21221i	0.123472	+	0.213859i
$595$	1.86825	−	3.23591i	0.0765909	−	0.132659i
$596$	−1.80546	−	2.00517i	−0.0739545	−	0.0821348i
$597$	5.59901	+	17.2320i	0.229152	+	0.705258i
$598$	1.06733	−	1.18539i	0.0436465	−	0.0484743i
$599$	0.0433857	+	0.0193165i	0.00177269	+	0.000789252i	0.407623	−	0.913150i	$-0.366358\pi$
$599$	0.0433857	+	0.0193165i	0.00177269	+	0.000789252i	−0.405850	+	0.913940i	$0.633025\pi$
$600$	−0.978148	+	0.207912i	−0.0399327	+	0.00848796i
$601$	−0.141973	−	1.35078i	−0.00579119	−	0.0550995i	0.991245	−	0.132038i	$-0.0421521\pi$
$601$	−0.141973	−	1.35078i	−0.00579119	−	0.0550995i	−0.997036	+	0.0769386i	$0.975485\pi$
$602$	0.517839	−	4.92691i	0.0211056	−	0.200806i
$603$	−1.94428	−	0.413269i	−0.0791771	−	0.0168296i
$604$	12.7227	+	9.24357i	0.517679	+	0.376116i
$605$	−20.4057	−	14.8256i	−0.829609	−	0.602746i
$606$	−9.52224	−	2.02401i	−0.386815	−	0.0822200i
$607$	−0.00666645	+	0.0634270i	−0.000270583	+	0.00257442i	−0.994656	−	0.103241i	$-0.967079\pi$
$607$	−0.00666645	+	0.0634270i	−0.000270583	+	0.00257442i	0.994386	+	0.105816i	$0.0337453\pi$
$608$	−0.0465940	−	0.443313i	−0.00188964	−	0.0179787i
$609$	3.83819	−	0.815833i	0.155531	−	0.0330592i
$610$	−2.57993	−	1.14866i	−0.104458	−	0.0465078i
$611$	8.98615	−	9.98013i	0.363541	−	0.403753i
$612$	2.21779	+	6.82565i	0.0896488	+	0.275911i
$613$	25.2982	+	28.0965i	1.02179	+	1.13481i	0.990806	+	0.135287i	$0.0431957\pi$
$613$	25.2982	+	28.0965i	1.02179	+	1.13481i	0.0309786	+	0.999520i	$0.490138\pi$
$614$	8.70775	−	15.0823i	0.351416	−	0.608671i
$615$	−1.16258	−	2.01364i	−0.0468797	−	0.0811980i
$616$	0.968281	−	2.98006i	0.0390131	−	0.120070i
$617$	−0.181533	+	0.0808238i	−0.00730825	+	0.00325384i	−0.410388	−	0.911911i	$-0.634607\pi$
$617$	−0.181533	+	0.0808238i	−0.00730825	+	0.00325384i	0.403079	+	0.915165i	$0.367940\pi$
$618$	−2.70652	+	1.96640i	−0.108872	+	0.0791002i
$619$	12.5058			0.502651			0.251326	−	0.967903i	$-0.419133\pi$
$619$	12.5058			0.502651			0.251326	+	0.967903i	$0.419133\pi$
$620$	−4.83359	+	2.76341i	−0.194121	+	0.110981i
$621$	−0.644788			−0.0258744
$622$	11.7642	−	8.54716i	0.471700	−	0.342710i
$623$	−2.33357	+	1.03897i	−0.0934926	+	0.0416256i
$624$	−0.764459	+	2.35276i	−0.0306029	+	0.0941859i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.9830	−	19.0231i	0.438969	−	0.760316i
$627$	−1.79514	−	1.99370i	−0.0716909	−	0.0796208i
$628$	7.44409	+	22.9106i	0.297052	+	0.914231i
$629$	−41.4272	+	46.0096i	−1.65181	+	1.83452i
$630$	−0.475618	−	0.211759i	−0.0189491	−	0.00843667i
$631$	−16.3084	+	3.46645i	−0.649226	+	0.137997i	−0.520742	−	0.853714i	$-0.674345\pi$
$631$	−16.3084	+	3.46645i	−0.649226	+	0.137997i	−0.128484	+	0.991712i	$0.541011\pi$
$632$	−0.763709	−	7.26621i	−0.0303787	−	0.289034i
$633$	2.56737	−	24.4269i	0.102044	−	0.970882i
$634$	−27.9694	−	5.94508i	−1.11081	−	0.236109i
$635$	−1.81040	−	1.31533i	−0.0718436	−	0.0521974i
$636$	2.45662	+	1.78484i	0.0974111	+	0.0707733i
$637$	−16.2826	−	3.46097i	−0.645140	−	0.137129i
$638$	4.74155	−	45.1128i	0.187720	−	1.78603i
$639$	−0.706711	−	6.72391i	−0.0279571	−	0.265994i
$640$	−0.978148	+	0.207912i	−0.0386647	+	0.00821843i
$641$	24.4079	+	10.8671i	0.964053	+	0.429224i	0.827535	−	0.561414i	$-0.189742\pi$
$641$	24.4079	+	10.8671i	0.964053	+	0.429224i	0.136518	+	0.990638i	$0.456409\pi$
$642$	13.1281	−	14.5802i	0.518124	−	0.575435i
$643$	−11.8534	−	36.4811i	−0.467454	−	1.43868i	−0.855870	−	0.517191i	$-0.826978\pi$
$643$	−11.8534	−	36.4811i	−0.467454	−	1.43868i	0.388416	−	0.921484i	$-0.373022\pi$
$644$	0.224624	+	0.249470i	0.00885141	+	0.00983049i
$645$	−4.75776	+	8.24068i	−0.187337	+	0.324477i
$646$	−1.59957	−	2.77054i	−0.0629343	−	0.109005i
$647$	13.6744	−	42.0855i	0.537596	−	1.65455i	−0.200376	−	0.979719i	$-0.564216\pi$
$647$	13.6744	−	42.0855i	0.537596	−	1.65455i	0.737972	−	0.674831i	$-0.235784\pi$
$648$	0.913545	−	0.406737i	0.0358875	−	0.0159781i
$649$	7.76333	−	5.64039i	0.304737	−	0.221405i
$650$	−2.47384			−0.0970321
$651$	−2.88155	−	0.315221i	−0.112937	−	0.0123545i
$652$	19.4786			0.762842
$653$	26.6319	−	19.3492i	1.04219	−	0.757194i	0.0714763	−	0.997442i	$-0.477229\pi$
$653$	26.6319	−	19.3492i	1.04219	−	0.757194i	0.970711	+	0.240249i	$0.0772290\pi$
$654$	−8.65709	+	3.85439i	−0.338519	+	0.150718i
$655$	4.90744	−	15.1036i	0.191750	−	0.590145i
$656$	−1.16258	−	2.01364i	−0.0453911	−	0.0786196i
$657$	4.64476	−	8.04496i	0.181209	−	0.313864i
$658$	1.89116	+	2.10035i	0.0737252	+	0.0818802i
$659$	0.907740	+	2.79374i	0.0353605	+	0.108829i	0.967179	−	0.254097i	$-0.0817781\pi$
$659$	0.907740	+	2.79374i	0.0353605	+	0.108829i	−0.931818	+	0.362925i	$0.881778\pi$
$660$	−4.02719	+	4.47265i	−0.156758	+	0.174098i
$661$	2.03375	+	0.905482i	0.0791035	+	0.0352192i	0.445907	−	0.895079i	$-0.352881\pi$
$661$	2.03375	+	0.905482i	0.0791035	+	0.0352192i	−0.366803	+	0.930298i	$0.619548\pi$
$662$	−30.7393	+	6.53384i	−1.19472	+	0.253945i
$663$	1.85586	+	17.6573i	0.0720755	+	0.685752i
$664$	0.172776	−	1.64385i	0.00670500	−	0.0637938i
$665$	0.227001	+	0.0482506i	0.00880272	+	0.00187108i
$666$	6.97902	+	5.07056i	0.270432	+	0.196480i
$667$	3.93159	+	2.85647i	0.152232	+	0.110603i
$668$	10.4584	+	2.22301i	0.404649	+	0.0860107i
$669$	−1.63638	+	15.5691i	−0.0632661	+	0.601937i
$670$	−0.207773	−	1.97683i	−0.00802696	−	0.0763714i
$671$	−16.6254	+	3.53384i	−0.641817	+	0.136422i
$672$	−0.475618	−	0.211759i	−0.0183473	−	0.00816877i
$673$	−11.9369	+	13.2573i	−0.460134	+	0.511030i	−0.927904	−	0.372820i	$-0.878391\pi$
$673$	−11.9369	+	13.2573i	−0.460134	+	0.511030i	0.467770	+	0.883850i	$0.345058\pi$
$674$	−8.90462	−	27.4056i	−0.342993	−	1.05562i
$675$	0.669131	+	0.743145i	0.0257548	+	0.0286037i
$676$	3.44005	−	5.95834i	0.132310	−	0.229167i
$677$	15.5881	+	26.9994i	0.599100	+	1.03767i	0.992954	+	0.118499i	$0.0378083\pi$
$677$	15.5881	+	26.9994i	0.599100	+	1.03767i	−0.393854	+	0.919173i	$0.628858\pi$
$678$	0.439653	−	1.35311i	0.0168848	−	0.0519660i
$679$	−3.67899	+	1.63799i	−0.141187	+	0.0628604i
$680$	−5.80624	+	4.21848i	−0.222659	+	0.161771i
$681$	−6.73772			−0.258190
$682$	−13.7593	+	30.5547i	−0.526872	+	1.17000i
$683$	−35.1451			−1.34479			−0.672394	−	0.740193i	$-0.734734\pi$
$683$	−35.1451			−1.34479			−0.672394	+	0.740193i	$0.734734\pi$
$684$	−0.360623	+	0.262008i	−0.0137888	+	0.0100181i
$685$	−1.87000	+	0.832576i	−0.0714489	+	0.0318111i
$686$	2.20875	−	6.79785i	0.0843306	−	0.259543i
$687$	1.96304	+	3.40009i	0.0748948	+	0.129722i
$688$	−4.75776	+	8.24068i	−0.181388	+	0.314173i
$689$	5.02646	+	5.58245i	0.191493	+	0.212675i
$690$	−0.199250	−	0.613230i	−0.00758533	−	0.0233453i
$691$	−12.2529	+	13.6083i	−0.466123	+	0.517683i	−0.929672	−	0.368389i	$-0.879909\pi$
$691$	−12.2529	+	13.6083i	−0.466123	+	0.517683i	0.463548	+	0.886072i	$0.346576\pi$
$692$	13.9618	+	6.21619i	0.530747	+	0.236304i
$693$	−3.06495	+	0.651475i	−0.116428	+	0.0247475i
$694$	3.61764	+	34.4196i	0.137324	+	1.30655i
$695$	0.156838	−	1.49222i	0.00594921	−	0.0566030i
$696$	−7.37223	−	1.56702i	−0.279444	−	0.0593976i
$697$	−13.5004	−	9.80863i	−0.511365	−	0.371529i
$698$	11.1427	+	8.09563i	0.421757	+	0.306424i
$699$	18.8007	+	3.99622i	0.711109	+	0.151151i
$700$	0.0544205	−	0.517776i	0.00205690	−	0.0195701i
$701$	−1.88689	−	17.9526i	−0.0712669	−	0.678060i	−0.970584	−	0.240763i	$-0.922602\pi$
$701$	−1.88689	−	17.9526i	−0.0712669	−	0.678060i	0.899317	−	0.437297i	$-0.144064\pi$
$702$	2.41978	−	0.514341i	0.0913288	−	0.0194125i
$703$	−3.51288	−	1.56403i	−0.132491	−	0.0589887i
$704$	−4.02719	+	4.47265i	−0.151780	+	0.168569i
$705$	−1.67754	−	5.16294i	−0.0631798	−	0.194447i
$706$	20.0053	+	22.2182i	0.752911	+	0.836192i
$707$	2.53415	−	4.38928i	0.0953066	−	0.165076i
$708$	−0.797204	−	1.38080i	−0.0299608	−	0.0518935i
$709$	−4.15714	+	12.7944i	−0.156125	+	0.480502i	−0.998273	−	0.0587435i	$-0.981291\pi$
$709$	−4.15714	+	12.7944i	−0.156125	+	0.480502i	0.842148	+	0.539246i	$0.181291\pi$
$710$	6.17643	−	2.74992i	0.231797	−	0.103203i
$711$	−5.91087	+	4.29450i	−0.221675	+	0.161056i
$712$	4.90640			0.183875
$713$	−2.09783	−	2.91331i	−0.0785644	−	0.109104i
$714$	−3.73650			−0.139835
$715$	−12.0454	+	8.75149i	−0.450472	+	0.327287i
$716$	16.7231	−	7.44561i	0.624972	−	0.278256i
$717$	2.05889	−	6.33661i	0.0768906	−	0.236645i
$718$	−14.4891	−	25.0958i	−0.540727	−	0.936566i
$719$	−20.7979	+	36.0231i	−0.775632	+	1.34343i	0.158807	+	0.987310i	$0.449235\pi$
$719$	−20.7979	+	36.0231i	−0.775632	+	1.34343i	−0.934439	+	0.356124i	$0.884098\pi$
$720$	0.669131	+	0.743145i	0.0249370	+	0.0276954i
$721$	−0.538224	−	1.65648i	−0.0200445	−	0.0616907i
$722$	−12.5805	+	13.9721i	−0.468199	+	0.519987i
$723$	−14.1207	−	6.28695i	−0.525155	−	0.233814i
$724$	2.44308	−	0.519293i	0.0907964	−	0.0192994i
$725$	−0.787823	−	7.49564i	−0.0292590	−	0.278381i
$726$	−2.63650	+	25.0846i	−0.0978498	+	0.930978i
$727$	−12.3379	−	2.62250i	−0.457587	−	0.0972631i	−0.0266493	−	0.999645i	$-0.508484\pi$
$727$	−12.3379	−	2.62250i	−0.457587	−	0.0972631i	−0.430938	+	0.902382i	$0.641817\pi$
$728$	−1.04198	−	0.757040i	−0.0386182	−	0.0280578i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	9.08652	+	1.93140i	0.336307	+	0.0714843i
$731$	−7.13847	+	67.9180i	−0.264026	+	2.51204i
$732$	0.295197	+	2.80861i	0.0109108	+	0.103809i
$733$	−5.75193	+	1.22261i	−0.212452	+	0.0451582i	−0.312908	−	0.949783i	$-0.601303\pi$
$733$	−5.75193	+	1.22261i	−0.212452	+	0.0451582i	0.100456	+	0.994942i	$0.467970\pi$
$734$	−21.0899	−	9.38984i	−0.778443	−	0.346585i
$735$	−4.50254	+	5.00058i	−0.166079	+	0.184449i
$736$	−0.199250	−	0.613230i	−0.00734447	−	0.0226039i
$737$	−8.00490	−	8.89034i	−0.294864	−	0.327480i
$738$	−1.16258	+	2.01364i	−0.0427951	+	0.0741233i
$739$	−15.6332	−	27.0776i	−0.575078	−	0.996065i	−0.996033	−	0.0889833i	$-0.971638\pi$
$739$	−15.6332	−	27.0776i	−0.575078	−	0.996065i	0.420955	−	0.907082i	$-0.361695\pi$
$740$	−2.66575	+	8.20434i	−0.0979949	+	0.301597i
$741$	−1.00739	+	0.448519i	−0.0370074	+	0.0164768i
$742$	−1.27898	+	0.929236i	−0.0469530	+	0.0341133i
$743$	33.0429			1.21223			0.606113	−	0.795378i	$-0.292728\pi$
$743$	33.0429			1.21223			0.606113	+	0.795378i	$0.292728\pi$
$744$	4.80998	+	2.80430i	0.176342	+	0.102811i
$745$	−2.69822			−0.0988550
$746$	−19.7490	+	14.3485i	−0.723062	+	0.525335i
$747$	−1.51001	+	0.672298i	−0.0552482	+	0.0245981i
$748$	−13.3478	+	41.0804i	−0.488045	+	1.50205i
$749$	5.10726	+	8.84603i	0.186615	+	0.323227i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	18.0278	+	20.0219i	0.657844	+	0.730610i	0.976082	−	0.217401i	$-0.0697580\pi$
$751$	18.0278	+	20.0219i	0.657844	+	0.730610i	−0.318239	+	0.948011i	$0.603091\pi$
$752$	−1.67754	−	5.16294i	−0.0611736	−	0.188273i
$753$	−19.9214	+	22.1250i	−0.725977	+	0.806279i
$754$	−17.0332	−	7.58367i	−0.620313	−	0.276181i
$755$	15.3825	−	3.26964i	0.559825	−	0.118994i
$756$	0.0544205	+	0.517776i	0.00197925	+	0.0188313i
$757$	2.34307	−	22.2929i	0.0851604	−	0.810247i	−0.865687	−	0.500586i	$-0.833118\pi$
$757$	2.34307	−	22.2929i	0.0851604	−	0.810247i	0.950847	−	0.309661i	$-0.100216\pi$
$758$	−9.62831	−	2.04656i	−0.349716	−	0.0743345i
$759$	−3.13954	−	2.28101i	−0.113958	−	0.0827953i
$760$	−0.360623	−	0.262008i	−0.0130812	−	0.00950403i
$761$	−41.8149	−	8.88803i	−1.51579	−	0.322191i	−0.626457	−	0.779456i	$-0.715496\pi$
$761$	−41.8149	−	8.88803i	−1.51579	−	0.322191i	−0.889330	+	0.457265i	$0.848829\pi$
$762$	−0.233912	+	2.22552i	−0.00847372	+	0.0806221i
$763$	−0.515709	−	4.90664i	−0.0186699	−	0.177632i
$764$	−10.3688	+	2.20396i	−0.375131	+	0.0797366i
$765$	6.55644	+	2.91911i	0.237048	+	0.105541i
$766$	5.56061	−	6.17569i	0.200913	−	0.223137i
$767$	−1.21886	−	3.75126i	−0.0440105	−	0.135450i
$768$	0.669131	+	0.743145i	0.0241452	+	0.0268159i
$769$	−25.6031	+	44.3459i	−0.923271	+	1.59915i	−0.128953	+	0.991651i	$0.541162\pi$
$769$	−25.6031	+	44.3459i	−0.923271	+	1.59915i	−0.794318	+	0.607502i	$0.792172\pi$
$770$	−1.56671	−	2.71362i	−0.0564603	−	0.0977922i
$771$	3.58784	−	11.0422i	0.129213	−	0.397676i
$772$	5.28460	−	2.35285i	0.190197	−	0.0846811i
$773$	−6.06922	+	4.40955i	−0.218295	+	0.158600i	−0.691559	−	0.722320i	$-0.743076\pi$
$773$	−6.06922	+	4.40955i	−0.218295	+	0.158600i	0.473264	+	0.880921i	$0.343076\pi$
$774$	9.51552			0.342028
$775$	−1.18068	+	5.44114i	−0.0424114	+	0.195451i
$776$	7.73519			0.277677
$777$	−3.63348	+	2.63988i	−0.130350	+	0.0947050i
$778$	11.8253	−	5.26496i	0.423958	−	0.188758i
$779$	0.320280	−	0.985722i	0.0114752	−	0.0353171i
$780$	1.23692	+	2.14241i	0.0442889	+	0.0767106i
$781$	20.3455	−	35.2394i	0.728019	−	1.26097i
$782$	−3.09646	−	3.43897i	−0.110729	−	0.122977i
$783$	2.32904	+	7.16804i	0.0832330	+	0.256165i
$784$	−4.50254	+	5.00058i	−0.160805	+	0.178592i
$785$	22.0069	+	9.79811i	0.785461	+	0.349710i
$786$	−15.5338	+	3.30181i	−0.554072	+	0.117772i
$787$	1.15131	+	10.9540i	0.0410397	+	0.390467i	0.995690	+	0.0927388i	$0.0295622\pi$
$787$	1.15131	+	10.9540i	0.0410397	+	0.390467i	−0.954651	+	0.297728i	$0.903771\pi$
$788$	0.392530	−	3.73467i	0.0139833	−	0.133042i
$789$	−4.00969	−	0.852287i	−0.142749	−	0.0303422i
$790$	−5.91087	−	4.29450i	−0.210299	−	0.152791i
$791$	0.599257	+	0.435386i	0.0213071	+	0.0154805i
$792$	5.88702	+	1.25132i	0.209186	+	0.0444639i
$793$	−0.730270	+	6.94806i	−0.0259327	+	0.246733i
$794$	−0.0929405	−	0.884270i	−0.00329834	−	0.0313816i
$795$	2.97019	−	0.631333i	0.105342	−	0.0223911i
$796$	16.5523	+	7.36957i	0.586682	+	0.261208i
$797$	−28.6268	+	31.7933i	−1.01401	+	1.12618i	−0.0220366	+	0.999757i	$0.507015\pi$
$797$	−28.6268	+	31.7933i	−1.01401	+	1.12618i	−0.991977	+	0.126419i	$0.959652\pi$
$798$	−0.0717143	−	0.220714i	−0.00253866	−	0.00781319i
$799$	−26.0699	−	28.9535i	−0.922286	−	1.02430i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−2.45320	−	4.24907i	−0.0866796	−	0.150134i
$802$	−7.47810	+	23.0152i	−0.264061	+	0.812696i
$803$	51.0757	−	22.7404i	1.80242	−	0.802490i
$804$	−1.60809	+	1.16835i	−0.0567131	+	0.0412045i
$805$	0.335695			0.0118317
$806$	10.1967	+	9.25977i	0.359165	+	0.326161i
$807$	10.5016			0.369673
$808$	−7.87576	+	5.72207i	−0.277068	+	0.201302i
$809$	−41.1995	+	18.3432i	−1.44850	+	0.644913i	−0.972153	−	0.234346i	$-0.924705\pi$
$809$	−41.1995	+	18.3432i	−1.44850	+	0.644913i	−0.476344	+	0.879259i	$0.658038\pi$
$810$	0.309017	−	0.951057i	0.0108578	−	0.0334167i
$811$	10.2497	+	17.7530i	0.359915	+	0.623391i	0.987946	−	0.154797i	$-0.0494724\pi$
$811$	10.2497	+	17.7530i	0.359915	+	0.623391i	−0.628031	+	0.778188i	$0.716139\pi$
$812$	1.96197	−	3.39823i	0.0688516	−	0.119254i
$813$	0.948530	+	1.05345i	0.0332664	+	0.0369461i
$814$	16.0439	+	49.3781i	0.562339	+	1.73070i
$815$	13.0337	−	14.4754i	0.456552	−	0.507053i
$816$	6.55644	+	2.91911i	0.229521	+	0.102189i
$817$	−4.14890	+	0.881876i	−0.145152	+	0.0308529i
$818$	−2.22825	−	21.2004i	−0.0779089	−	0.741254i
$819$	−0.134628	+	1.28090i	−0.00470427	+	0.0447582i
$820$	−2.27435	−	0.483427i	−0.0794236	−	0.0168820i
$821$	−17.3176	−	12.5820i	−0.604389	−	0.439114i	0.243045	−	0.970015i	$-0.421854\pi$
$821$	−17.3176	−	12.5820i	−0.604389	−	0.439114i	−0.847434	+	0.530901i	$0.821854\pi$
$822$	1.65603	+	1.20318i	0.0577607	+	0.0419656i
$823$	−28.5659	−	6.07188i	−0.995746	−	0.211652i	−0.318909	−	0.947785i	$-0.603316\pi$
$823$	−28.5659	−	6.07188i	−0.995746	−	0.211652i	−0.676837	+	0.736133i	$0.736650\pi$
$824$	−0.349693	+	3.32711i	−0.0121821	+	0.115905i
$825$	0.629109	+	5.98557i	0.0219028	+	0.208391i
$826$	0.811954	−	0.172586i	0.0282515	−	0.00600504i
$827$	11.0521	+	4.92069i	0.384318	+	0.171109i	0.589796	−	0.807552i	$-0.299208\pi$
$827$	11.0521	+	4.92069i	0.384318	+	0.171109i	−0.205478	+	0.978662i	$0.565875\pi$
$828$	−0.431447	+	0.479171i	−0.0149938	+	0.0166523i
$829$	−9.06801	−	27.9085i	−0.314945	−	0.969301i	−0.975777	−	0.218767i	$-0.929796\pi$
$829$	−9.06801	−	27.9085i	−0.314945	−	0.969301i	0.660832	−	0.750534i	$-0.270204\pi$
$830$	−1.10601	−	1.22835i	−0.0383902	−	0.0426366i
$831$	−3.87152	+	6.70567i	−0.134302	+	0.232617i
$832$	1.23692	+	2.14241i	0.0428825	+	0.0742747i
$833$	−14.9234	+	45.9294i	−0.517064	+	1.59136i
$834$	−1.37072	+	0.610282i	−0.0474640	+	0.0211323i
$835$	8.65007	−	6.28464i	0.299348	−	0.217489i
$836$	−2.68279			−0.0927863
$837$	0.0236072	−	5.56771i	0.000815984	−	0.192448i
$838$	21.7304			0.750665
$839$	40.0771	−	29.1177i	1.38361	−	1.00525i	0.387082	−	0.922045i	$-0.373483\pi$
$839$	40.0771	−	29.1177i	1.38361	−	1.00525i	0.996532	−	0.0832089i	$-0.0265169\pi$
$840$	−0.475618	+	0.211759i	−0.0164104	+	0.00730637i
$841$	8.59230	−	26.4444i	0.296286	−	0.911875i
$842$	19.7193	+	34.1549i	0.679573	+	1.17705i
$843$	−2.05220	+	3.55452i	−0.0706816	+	0.122424i
$844$	−16.4348	−	18.2527i	−0.565710	−	0.628284i
$845$	−2.12607	−	6.54337i	−0.0731390	−	0.225099i
$846$	−3.63246	+	4.03426i	−0.124887	+	0.138701i
$847$	−11.9964	−	5.34115i	−0.412202	−	0.183524i
$848$	2.97019	−	0.631333i	0.101997	−	0.0216801i
$849$	−3.18480	−	30.3013i	−0.109302	−	1.03994i
$850$	−0.750192	+	7.13760i	−0.0257314	+	0.244818i
$851$	−5.44074	−	1.15647i	−0.186506	−	0.0396431i
$852$	−5.46972	−	3.97398i	−0.187389	−	0.136146i
$853$	−10.2675	−	7.45979i	−0.351553	−	0.255418i	0.397967	−	0.917400i	$-0.369716\pi$
$853$	−10.2675	−	7.45979i	−0.351553	−	0.255418i	−0.749520	+	0.661981i	$0.769716\pi$
$854$	−1.43817	−	0.305692i	−0.0492131	−	0.0104606i
$855$	−0.0465940	+	0.443313i	−0.00159348	+	0.0151610i
$856$	−2.05081	−	19.5121i	−0.0700951	−	0.666910i
$857$	46.4983	−	9.88351i	1.58835	−	0.337614i	0.672802	−	0.739822i	$-0.265091\pi$
$857$	46.4983	−	9.88351i	1.58835	−	0.337614i	0.915548	+	0.402208i	$0.131757\pi$
$858$	13.6017	+	6.05587i	0.464355	+	0.206744i
$859$	−22.9134	+	25.4480i	−0.781797	+	0.868273i	−0.994048	−	0.108942i	$-0.965254\pi$
$859$	−22.9134	+	25.4480i	−0.781797	+	0.868273i	0.212252	+	0.977215i	$0.431920\pi$
$860$	2.94046	+	9.04980i	0.100269	+	0.308596i
$861$	−0.810011	−	0.899608i	−0.0276051	−	0.0306586i
$862$	1.60931	−	2.78741i	0.0548135	−	0.0949397i
$863$	8.89812	+	15.4120i	0.302895	+	0.524630i	0.976791	−	0.214197i	$-0.0687134\pi$
$863$	8.89812	+	15.4120i	0.302895	+	0.524630i	−0.673895	+	0.738827i	$0.735380\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	13.9618	−	6.21619i	0.474715	−	0.211357i
$866$	−18.5115	+	13.4494i	−0.629046	+	0.457029i
$867$	34.5081			1.17196
$868$	−2.16239	+	1.93048i	−0.0733961	+	0.0655248i
$869$	−43.9728			−1.49168
$870$	−6.09750	+	4.43009i	−0.206725	+	0.150194i
$871$	−4.49217	+	2.00004i	−0.152211	+	0.0677689i
$872$	−2.92836	+	9.01256i	−0.0991668	+	0.305204i
$873$	−3.86760	−	6.69887i	−0.130898	−	0.226722i
$874$	0.143709	−	0.248910i	0.00486101	−	0.00841952i
$875$	−0.348368	−	0.386902i	−0.0117770	−	0.0130797i
$876$	−2.87062	−	8.83486i	−0.0969892	−	0.298502i
$877$	25.3795	−	28.1868i	0.857005	−	0.951800i	−0.142272	−	0.989828i	$-0.545441\pi$
$877$	25.3795	−	28.1868i	0.857005	−	0.951800i	0.999277	+	0.0380272i	$0.0121074\pi$
$878$	30.6913	+	13.6647i	1.03578	+	0.461160i
$879$	−7.41498	+	1.57610i	−0.250101	+	0.0531607i
$880$	0.629109	+	5.98557i	0.0212072	+	0.201773i
$881$	3.62958	−	34.5331i	0.122284	−	1.16345i	−0.745499	−	0.666507i	$-0.767789\pi$
$881$	3.62958	−	34.5331i	0.122284	−	1.16345i	0.867783	−	0.496944i	$-0.165545\pi$
$882$	6.58190	+	1.39903i	0.221624	+	0.0471077i
$883$	−11.2547	−	8.17702i	−0.378751	−	0.275179i	0.382079	−	0.924129i	$-0.375208\pi$
$883$	−11.2547	−	8.17702i	−0.378751	−	0.275179i	−0.760830	+	0.648951i	$0.775208\pi$
$884$	14.3637	+	10.4359i	0.483105	+	0.350996i
$885$	−1.55957	−	0.331496i	−0.0524242	−	0.0111431i
$886$	1.58199	−	15.0516i	0.0531479	−	0.505669i
$887$	−3.70033	−	35.2063i	−0.124245	−	1.18211i	−0.861952	−	0.506991i	$-0.830758\pi$
$887$	−3.70033	−	35.2063i	−0.124245	−	1.18211i	0.737707	−	0.675121i	$-0.235909\pi$
$888$	8.43804	−	1.79356i	0.283162	−	0.0601879i
$889$	−1.06433	−	0.473869i	−0.0356964	−	0.0158931i
$890$	3.28303	−	3.64617i	0.110047	−	0.122220i
$891$	−1.85983	−	5.72397i	−0.0623067	−	0.191760i
$892$	10.4752	+	11.6338i	0.350734	+	0.389530i
$893$	1.20992	−	2.09564i	0.0404884	−	0.0701279i
$894$	1.34911	+	2.33672i	0.0451209	+	0.0781517i
$895$	5.65678	−	17.4098i	0.189085	−	0.581945i
$896$	−0.475618	+	0.211759i	−0.0158893	+	0.00707436i
$897$	−1.29047	+	0.937578i	−0.0430874	+	0.0313048i
$898$	−40.7767			−1.36073
$899$	−24.8094	+	33.8446i	−0.827441	+	1.12878i
$900$	1.00000			0.0333333
$901$	17.6309	−	12.8096i	0.587371	−	0.426750i
$902$	−12.7842	+	5.69189i	−0.425667	+	0.189519i
$903$	−1.53089	+	4.71158i	−0.0509447	+	0.156792i
$904$	−0.711374	−	1.23214i	−0.0236599	−	0.0409802i
$905$	1.24883	−	2.16304i	0.0415125	−	0.0719018i
$906$	−10.5228	−	11.6868i	−0.349597	−	0.388267i
$907$	−4.21461	−	12.9712i	−0.139944	−	0.430703i	0.856382	−	0.516342i	$-0.172707\pi$
$907$	−4.21461	−	12.9712i	−0.139944	−	0.430703i	−0.996326	+	0.0856391i	$0.972707\pi$
$908$	−4.50842	+	5.00710i	−0.149617	+	0.166167i
$909$	8.89334	+	3.95957i	0.294973	+	0.131331i
$910$	−1.25981	+	0.267780i	−0.0417622	+	0.00887683i
$911$	−1.57027	−	14.9401i	−0.0520253	−	0.494987i	−0.989247	−	0.146254i	$-0.953278\pi$
$911$	−1.57027	−	14.9401i	−0.0520253	−	0.494987i	0.937222	−	0.348734i	$-0.113388\pi$
$912$	−0.0465940	+	0.443313i	−0.00154288	+	0.0146795i
$913$	−9.73070	−	2.06832i	−0.322039	−	0.0684515i
$914$	−18.1387	−	13.1785i	−0.599974	−	0.435906i
$915$	2.28473	+	1.65995i	0.0755308	+	0.0548763i
$916$	3.84029	+	0.816280i	0.126887	+	0.0269706i
$917$	0.864242	−	8.22271i	0.0285398	−	0.271538i
$918$	−0.750192	−	7.13760i	−0.0247600	−	0.235576i
$919$	−44.2182	+	9.39886i	−1.45862	+	0.310040i	−0.867861	−	0.496807i	$-0.834506\pi$
$919$	−44.2182	+	9.39886i	−1.45862	+	0.310040i	−0.590761	+	0.806846i	$0.701173\pi$
$920$	−0.589043	−	0.262259i	−0.0194202	−	0.00864642i
$921$	−11.6532	+	12.9422i	−0.383987	+	0.426461i
$922$	5.43418	+	16.7247i	0.178965	+	0.550798i
$923$	−11.1916	−	12.4295i	−0.368374	−	0.409121i
$924$	−1.56671	+	2.71362i	−0.0515410	+	0.0892716i
$925$	4.31327	+	7.47081i	0.141820	+	0.245639i
$926$	−1.12512	+	3.46276i	−0.0369737	+	0.113793i
$927$	3.05621	−	1.36071i	0.100379	−	0.0446916i
$928$	−6.09750	+	4.43009i	−0.200160	+	0.145425i
$929$	8.41301			0.276022			0.138011	−	0.990431i	$-0.455929\pi$
$929$	8.41301			0.276022			0.138011	+	0.990431i	$0.455929\pi$
$930$	5.30251	−	1.69807i	0.173876	−	0.0556818i
$931$	−2.99946			−0.0983033
$932$	15.5499	−	11.2977i	0.509355	−	0.370068i
$933$	−13.2841	+	5.91448i	−0.434903	+	0.193631i
$934$	−6.39341	+	19.6769i	−0.209199	+	0.643848i
$935$	21.5973	+	37.4076i	0.706306	+	1.22336i
$936$	1.23692	−	2.14241i	0.0404300	−	0.0700269i
$937$	36.3632	+	40.3855i	1.18794	+	1.31934i	0.936170	+	0.351547i	$0.114344\pi$
$937$	36.3632	+	40.3855i	1.18794	+	1.31934i	0.251765	+	0.967788i	$0.418989\pi$
$938$	−0.319789	−	0.984211i	−0.0104415	−	0.0321356i
$939$	−14.6981	+	16.3239i	−0.479655	+	0.532711i
$940$	−4.95930	−	2.20802i	−0.161755	−	0.0720178i
$941$	−8.94746	+	1.90184i	−0.291679	+	0.0619982i	−0.351427	−	0.936215i	$-0.614303\pi$
$941$	−8.94746	+	1.90184i	−0.291679	+	0.0619982i	0.0597484	+	0.998213i	$0.480970\pi$
$942$	−2.51805	−	23.9576i	−0.0820424	−	0.780581i
$943$	0.156712	−	1.49102i	0.00510326	−	0.0485543i
$944$	−1.55957	−	0.331496i	−0.0507595	−	0.0107893i
$945$	0.421197	+	0.306018i	0.0137015	+	0.00995476i
$946$	46.3320	+	33.6622i	1.50638	+	1.09445i
$947$	22.5481	+	4.79274i	0.732714	+	0.155743i	0.559135	−	0.829077i	$-0.311133\pi$
$947$	22.5481	+	4.79274i	0.732714	+	0.155743i	0.173579	+	0.984820i	$0.444467\pi$
$948$	−0.763709	+	7.26621i	−0.0248041	+	0.235995i
$949$	−2.40215	−	22.8549i	−0.0779770	−	0.741902i
$950$	−0.436014	+	0.0926776i	−0.0141462	+	0.00300686i
$951$	26.1221	+	11.6303i	0.847068	+	0.377139i
$952$	−2.50021	+	2.77676i	−0.0810322	+	0.0899954i
$953$	−17.5152	−	53.9061i	−0.567372	−	1.74619i	−0.660797	−	0.750565i	$-0.729781\pi$
$953$	−17.5152	−	53.9061i	−0.567372	−	1.74619i	0.0934247	−	0.995626i	$-0.470219\pi$
$954$	−2.03184	−	2.25659i	−0.0657834	−	0.0730599i
$955$	−5.30024	+	9.18029i	−0.171512	+	0.297067i
$956$	−3.33135	−	5.77007i	−0.107744	−	0.186617i
$957$	−14.0174	+	43.1411i	−0.453118	+	1.39456i
$958$	17.3845	−	7.74009i	0.561669	−	0.250071i
$959$	−0.862177	+	0.626408i	−0.0278411	+	0.0202278i
$960$	1.00000			0.0322749
$961$	25.2331	−	18.0080i	0.813972	−	0.580904i
$962$	21.3407			0.688053
$963$	−15.8726	+	11.5321i	−0.511487	+	0.371617i
$964$	−14.1207	+	6.28695i	−0.454798	+	0.202489i
$965$	1.78757	−	5.50159i	0.0575441	−	0.177102i
$966$	−0.167847	−	0.290720i	−0.00540040	−	0.00935377i
$967$	26.4035	−	45.7323i	0.849080	−	1.47065i	−0.0329496	−	0.999457i	$-0.510490\pi$
$967$	26.4035	−	45.7323i	0.849080	−	1.47065i	0.882030	−	0.471193i	$-0.156177\pi$
$968$	16.8774	+	18.7442i	0.542459	+	0.602461i
$969$	0.988589	+	3.04256i	0.0317580	+	0.0977412i
$970$	5.17585	−	5.74837i	0.166187	−	0.184569i
$971$	20.1637	+	8.97744i	0.647083	+	0.288100i	0.703915	−	0.710284i	$-0.251433\pi$
$971$	20.1637	+	8.97744i	0.647083	+	0.288100i	−0.0568327	+	0.998384i	$0.518100\pi$
$972$	−0.978148	+	0.207912i	−0.0313741	+	0.00666877i
$973$	−0.0816544	−	0.776890i	−0.00261772	−	0.0249059i
$974$	1.06318	−	10.1155i	0.0340665	−	0.324121i
$975$	2.41978	+	0.514341i	0.0774951	+	0.0164721i
$976$	2.28473	+	1.65995i	0.0731324	+	0.0531338i
$977$	10.2624	+	7.45608i	0.328324	+	0.238541i	0.739719	−	0.672916i	$-0.234958\pi$
$977$	10.2624	+	7.45608i	0.328324	+	0.238541i	−0.411395	+	0.911457i	$0.634958\pi$
$978$	−19.0530	−	4.04983i	−0.609247	−	0.129499i
$979$	3.08666	−	29.3676i	0.0986501	−	0.938593i
$980$	0.703366	+	6.69208i	0.0224682	+	0.213771i
$981$	9.26929	−	1.97025i	0.295946	−	0.0629052i
$982$	33.4080	+	14.8742i	1.06609	+	0.474655i
$983$	−28.7680	+	31.9501i	−0.917556	+	1.01905i	0.0821925	+	0.996616i	$0.473808\pi$
$983$	−28.7680	+	31.9501i	−0.917556	+	1.01905i	−0.999748	+	0.0224325i	$0.992859\pi$
$984$	0.718513	+	2.21136i	0.0229054	+	0.0704954i
$985$	−2.51275	−	2.79069i	−0.0800629	−	0.0889188i
$986$	−27.0459	+	46.8449i	−0.861318	+	1.49185i
$987$	−1.41315	−	2.44765i	−0.0449811	−	0.0779095i
$988$	−0.340761	+	1.04876i	−0.0108411	+	0.0333653i
$989$	−5.60505	+	2.49553i	−0.178230	+	0.0793532i
$990$	4.86910	−	3.53761i	0.154750	−	0.112433i
$991$	48.5075			1.54089			0.770446	−	0.637506i	$-0.220034\pi$
$991$	48.5075			1.54089			0.770446	+	0.637506i	$0.220034\pi$
$992$	5.30251	−	1.69807i	0.168355	−	0.0539137i
$993$	31.4260			0.997274
$994$	2.84769	−	2.06897i	0.0903233	−	0.0656237i
$995$	16.5523	−	7.36957i	0.524744	−	0.233631i
$996$	−0.510776	+	1.57201i	−0.0161846	+	0.0498110i
$997$	17.6544	+	30.5783i	0.559120	+	0.968424i	0.997570	+	0.0696684i	$0.0221941\pi$
$997$	17.6544	+	30.5783i	0.559120	+	0.968424i	−0.438450	+	0.898755i	$0.644473\pi$
$998$	−11.4194	+	19.7790i	−0.361476	+	0.626094i
$999$	−5.77229	−	6.41078i	−0.182627	−	0.202828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.g.421.1	yes	24
31.19	even	15	inner	930.2.bg.g.391.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.g.391.1	✓	24	31.19	even	15	inner
930.2.bg.g.421.1	yes	24	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.348368 - 0.386902i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.348368 - 0.386902i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(0.913545 + 0.406737i) q^{10} +(5.88702 - 1.25132i) q^{11} +(-0.104528 - 0.994522i) q^{12} +(0.258587 - 2.46029i) q^{13} +(0.509251 + 0.108245i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-7.02008 - 1.49216i) q^{17} +(-0.104528 + 0.994522i) q^{18} +(-0.0465940 - 0.443313i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(-0.475618 - 0.211759i) q^{21} +(-4.02719 + 4.47265i) q^{22} +(-0.199250 - 0.613230i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(1.23692 + 2.14241i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.475618 + 0.211759i) q^{28} +(-6.09750 + 4.43009i) q^{29} +1.00000 q^{30} +(5.30251 - 1.69807i) q^{31} +1.00000 q^{32} +(4.86910 - 3.53761i) q^{33} +(6.55644 - 2.91911i) q^{34} +(-0.160883 + 0.495147i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.31327 - 7.47081i) q^{37} +(0.298268 + 0.331260i) q^{38} +(-0.764459 - 2.35276i) q^{39} +(0.669131 - 0.743145i) q^{40} +(2.12414 + 0.945726i) q^{41} +(0.509251 - 0.108245i) q^{42} +(-0.994643 - 9.46340i) q^{43} +(0.629109 - 5.98557i) q^{44} +(-0.978148 - 0.207912i) q^{45} +(0.521644 + 0.378997i) q^{46} +(4.39186 + 3.19087i) q^{47} +(-0.978148 - 0.207912i) q^{48} +(0.703366 - 6.69208i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(-7.02008 + 1.49216i) q^{51} +(-2.25997 - 1.00620i) q^{52} +(-2.03184 + 2.25659i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-4.02719 - 4.47265i) q^{55} +(0.260314 - 0.450877i) q^{56} +(-0.222877 - 0.386035i) q^{57} +(2.32904 - 7.16804i) q^{58} +(1.45656 - 0.648504i) q^{59} +(-0.809017 + 0.587785i) q^{60} -2.82408 q^{61} +(-3.29172 + 4.49050i) q^{62} -0.520628 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-2.25997 + 1.00620i) q^{65} +(-1.85983 + 5.72397i) q^{66} +(-0.993857 - 1.72141i) q^{67} +(-3.58846 + 6.21539i) q^{68} +(-0.431447 - 0.479171i) q^{69} +(-0.160883 - 0.495147i) q^{70} +(4.52395 - 5.02436i) q^{71} +(0.913545 + 0.406737i) q^{72} +(9.08652 - 1.93140i) q^{73} +(0.901720 + 8.57929i) q^{74} +(-0.104528 + 0.994522i) q^{75} +(-0.436014 - 0.0926776i) q^{76} +(-2.53499 - 1.84178i) q^{77} +(2.00138 + 1.45409i) q^{78} +(-7.14657 - 1.51905i) q^{79} +(-0.104528 + 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(-2.27435 + 0.483427i) q^{82} +(-1.51001 - 0.672298i) q^{83} +(-0.348368 + 0.386902i) q^{84} +(2.21779 + 6.82565i) q^{85} +(6.36713 + 7.07141i) q^{86} +(-3.76846 + 6.52717i) q^{87} +(3.00927 + 5.21221i) q^{88} +(1.51616 - 4.66627i) q^{89} +(0.913545 - 0.406737i) q^{90} +(-1.04198 + 0.757040i) q^{91} -0.644788 q^{92} +(4.15341 - 3.70798i) q^{93} -5.42863 q^{94} +(-0.360623 + 0.262008i) q^{95} +(0.913545 - 0.406737i) q^{96} +(2.39031 - 7.35660i) q^{97} +(3.36447 + 5.82744i) q^{98} +(3.00927 - 5.21221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 3 * q^20 + 4 * q^21 + 3 * q^22 + 5 * q^23 + 3 * q^24 - 12 * q^25 - 3 * q^26 - 6 * q^27 + 4 * q^28 - 15 * q^29 + 24 * q^30 + 15 * q^31 + 24 * q^32 + 4 * q^33 - 9 * q^34 - 3 * q^35 - 12 * q^36 + 6 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 - 6 * q^42 - 13 * q^43 - 2 * q^44 + 3 * q^45 - 10 * q^46 + 4 * q^47 + 3 * q^48 + 3 * q^50 - 9 * q^51 - 3 * q^52 - 6 * q^54 + 3 * q^55 - 11 * q^56 - 14 * q^57 + 22 * q^59 - 6 * q^60 + 16 * q^61 - 5 * q^62 + 22 * q^63 - 6 * q^64 - 3 * q^65 - 6 * q^66 - 19 * q^67 - 9 * q^68 - 10 * q^69 - 3 * q^70 - 45 * q^71 + 3 * q^72 + 11 * q^73 - 35 * q^74 + 3 * q^75 + 6 * q^76 - 50 * q^77 + 6 * q^78 + 36 * q^79 + 3 * q^80 + 3 * q^81 - 20 * q^82 - 4 * q^83 + 9 * q^84 - 12 * q^85 + 22 * q^86 - 15 * q^87 - 2 * q^88 - 7 * q^89 + 3 * q^90 - 32 * q^91 + 10 * q^92 + 7 * q^93 + 54 * q^94 - 2 * q^95 + 3 * q^96 + 11 * q^97 - 15 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more