LMFDB - Embedded newform 930.2.be.a.37.5

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			37.5
Character	$\chi$	$=$	930.37
Dual form			930.2.be.a.553.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(0.303557 - 2.21537i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.35687 + 5.06392i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(0.303557 - 2.21537i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.35687 + 5.06392i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.78115 + 1.35185i) q^{10} +(4.89763 + 2.82765i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-2.98284 + 0.799250i) q^{13} +(4.54018 - 2.62128i) q^{14} +(2.06131 + 0.866592i) q^{15} -1.00000 q^{16} +(-6.10981 - 1.63712i) q^{17} +(0.258819 + 0.965926i) q^{18} +(1.97643 - 1.14109i) q^{19} +(2.21537 + 0.303557i) q^{20} +(-4.54018 - 2.62128i) q^{21} +(-1.46370 - 5.46259i) q^{22} +(-4.69302 - 4.69302i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.81571 - 1.34498i) q^{25} +(2.67434 + 1.54403i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-5.06392 - 1.35687i) q^{28} +2.75885 q^{29} +(-0.844796 - 2.07034i) q^{30} +(-4.39045 + 3.42402i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.99889 + 3.99889i) q^{33} +(3.16267 + 5.47791i) q^{34} +(10.8065 + 4.54316i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.09183 + 0.828455i) q^{37} +(-2.20443 - 0.590674i) q^{38} -3.08806i q^{39} +(-1.35185 - 1.78115i) q^{40} +(-4.15298 + 7.19318i) q^{41} +(1.35687 + 5.06392i) q^{42} +(-1.62969 + 6.08210i) q^{43} +(-2.82765 + 4.89763i) q^{44} +(-1.37057 + 1.76679i) q^{45} +6.63694i q^{46} +(-1.83462 - 1.83462i) q^{47} +(0.258819 - 0.965926i) q^{48} +(-17.7400 - 10.2422i) q^{49} +(2.45418 + 4.35626i) q^{50} +(3.16267 - 5.47791i) q^{51} +(-0.799250 - 2.98284i) q^{52} +(6.83165 - 1.83053i) q^{53} -1.00000 q^{54} +(7.75098 - 9.99169i) q^{55} +(2.62128 + 4.54018i) q^{56} +(0.590674 + 2.20443i) q^{57} +(-1.95080 - 1.95080i) q^{58} +(-6.91399 + 3.99179i) q^{59} +(-0.866592 + 2.06131i) q^{60} -2.01855i q^{61} +(5.52567 + 0.683370i) q^{62} +(3.70704 - 3.70704i) q^{63} -1.00000i q^{64} +(0.865172 + 6.85071i) q^{65} +5.65529 q^{66} +(4.78436 - 1.28196i) q^{67} +(1.63712 - 6.10981i) q^{68} +(5.74776 - 3.31847i) q^{69} +(-4.42889 - 10.8539i) q^{70} +(-6.93286 + 12.0081i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-16.3130 + 4.37105i) q^{73} +(-1.60045 - 2.77206i) q^{74} +(2.54555 - 4.30351i) q^{75} +(1.14109 + 1.97643i) q^{76} +(-20.9644 + 20.9644i) q^{77} +(-2.18359 + 2.18359i) q^{78} +(1.90156 + 3.29360i) q^{79} +(-0.303557 + 2.21537i) q^{80} +(0.500000 + 0.866025i) q^{81} +(8.02295 - 2.14974i) q^{82} +(-7.65140 + 2.05019i) q^{83} +(2.62128 - 4.54018i) q^{84} +(-5.48149 + 13.0385i) q^{85} +(5.45306 - 3.14833i) q^{86} +(-0.714043 + 2.66484i) q^{87} +(5.46259 - 1.46370i) q^{88} +1.97417 q^{89} +(2.21845 - 0.280166i) q^{90} -16.1893i q^{91} +(4.69302 - 4.69302i) q^{92} +(-2.17102 - 5.12705i) q^{93} +2.59455i q^{94} +(-1.92798 - 4.72491i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-2.48474 - 2.48474i) q^{97} +(5.30174 + 19.7864i) q^{98} +(-2.82765 - 4.89763i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) $ 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * 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
$5$	0.303557	−	2.21537i	0.135755	−	0.990742i
$5$	0.303557	−	2.21537i	0.135755	−	0.990742i
$6$	0.866025	−	0.500000i	0.353553	−	0.204124i
$7$	−1.35687	+	5.06392i	−0.512850	+	1.91398i	−0.125343	+	0.992113i	$0.540003\pi$
$7$	−1.35687	+	5.06392i	−0.512850	+	1.91398i	−0.387506	+	0.921867i	$0.626663\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−1.78115	+	1.35185i	−0.563249	+	0.427494i
$11$	4.89763	+	2.82765i	1.47669	+	0.852567i	0.999654	−	0.0263166i	$-0.00837780\pi$
$11$	4.89763	+	2.82765i	1.47669	+	0.852567i	0.477036	+	0.878884i	$0.341711\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	−2.98284	+	0.799250i	−0.827291	+	0.221672i	−0.647532	−	0.762038i	$-0.724199\pi$
$13$	−2.98284	+	0.799250i	−0.827291	+	0.221672i	−0.179760	+	0.983711i	$0.557532\pi$
$14$	4.54018	−	2.62128i	1.21342	−	0.700565i
$15$	2.06131	+	0.866592i	0.532229	+	0.223753i
$16$	−1.00000			−0.250000
$17$	−6.10981	−	1.63712i	−1.48185	−	0.397060i	−0.574871	−	0.818244i	$-0.694948\pi$
$17$	−6.10981	−	1.63712i	−1.48185	−	0.397060i	−0.906975	+	0.421184i	$0.861615\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	1.97643	−	1.14109i	0.453425	−	0.261785i	−0.255851	−	0.966716i	$-0.582356\pi$
$19$	1.97643	−	1.14109i	0.453425	−	0.261785i	0.709276	+	0.704931i	$0.249022\pi$
$20$	2.21537	+	0.303557i	0.495371	+	0.0678773i
$21$	−4.54018	−	2.62128i	−0.990749	−	0.572009i
$22$	−1.46370	−	5.46259i	−0.312061	−	1.16463i
$23$	−4.69302	−	4.69302i	−0.978563	−	0.978563i	0.0212119	−	0.999775i	$-0.493248\pi$
$23$	−4.69302	−	4.69302i	−0.978563	−	0.978563i	−0.999775	+	0.0212119i	$0.993248\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−4.81571	−	1.34498i	−0.963141	−	0.268996i
$26$	2.67434	+	1.54403i	0.524482	+	0.302810i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−5.06392	−	1.35687i	−0.956990	−	0.256425i
$29$	2.75885			0.512306			0.256153	−	0.966636i	$-0.417545\pi$
$29$	2.75885			0.512306			0.256153	+	0.966636i	$0.417545\pi$
$30$	−0.844796	−	2.07034i	−0.154238	−	0.377991i
$31$	−4.39045	+	3.42402i	−0.788549	+	0.614972i
$31$	−4.39045	+	3.42402i	−0.788549	+	0.614972i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−3.99889	+	3.99889i	−0.696118	+	0.696118i
$34$	3.16267	+	5.47791i	0.542393	+	0.939453i
$35$	10.8065	+	4.54316i	1.82664	+	0.767933i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	3.09183	+	0.828455i	0.508294	+	0.136197i	0.503847	−	0.863793i	$-0.331918\pi$
$37$	3.09183	+	0.828455i	0.508294	+	0.136197i	0.00444763	+	0.999990i	$0.498584\pi$
$38$	−2.20443	−	0.590674i	−0.357605	−	0.0958200i
$39$		−	3.08806i		−	0.494486i
$40$	−1.35185	−	1.78115i	−0.213747	−	0.281624i
$41$	−4.15298	+	7.19318i	−0.648587	+	1.12339i	0.334874	+	0.942263i	$0.391306\pi$
$41$	−4.15298	+	7.19318i	−0.648587	+	1.12339i	−0.983461	+	0.181122i	$0.942027\pi$
$42$	1.35687	+	5.06392i	0.209370	+	0.781379i
$43$	−1.62969	+	6.08210i	−0.248526	+	0.927511i	0.723052	+	0.690793i	$0.242738\pi$
$43$	−1.62969	+	6.08210i	−0.248526	+	0.927511i	−0.971578	+	0.236718i	$0.923928\pi$
$44$	−2.82765	+	4.89763i	−0.426284	+	0.738345i
$45$	−1.37057	+	1.76679i	−0.204313	+	0.263377i
$46$			6.63694i			0.978563i
$47$	−1.83462	−	1.83462i	−0.267607	−	0.267607i	0.560528	−	0.828135i	$-0.310598\pi$
$47$	−1.83462	−	1.83462i	−0.267607	−	0.267607i	−0.828135	+	0.560528i	$0.810598\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	−17.7400	−	10.2422i	−2.53428	−	1.46317i
$50$	2.45418	+	4.35626i	0.347073	+	0.616069i
$51$	3.16267	−	5.47791i	0.442862	−	0.767060i
$52$	−0.799250	−	2.98284i	−0.110836	−	0.413646i
$53$	6.83165	−	1.83053i	0.938399	−	0.251443i	0.242966	−	0.970035i	$-0.421880\pi$
$53$	6.83165	−	1.83053i	0.938399	−	0.251443i	0.695432	+	0.718592i	$0.255213\pi$
$54$	−1.00000			−0.136083
$55$	7.75098	−	9.99169i	1.04514	−	1.34728i
$56$	2.62128	+	4.54018i	0.350283	+	0.606708i
$57$	0.590674	+	2.20443i	0.0782367	+	0.291983i
$58$	−1.95080	−	1.95080i	−0.256153	−	0.256153i
$59$	−6.91399	+	3.99179i	−0.900124	+	0.519687i	−0.877240	−	0.480051i	$-0.840618\pi$
$59$	−6.91399	+	3.99179i	−0.900124	+	0.519687i	−0.0228837	+	0.999738i	$0.507285\pi$
$60$	−0.866592	+	2.06131i	−0.111877	+	0.266115i
$61$		−	2.01855i		−	0.258449i	−0.991615	−	0.129225i	$-0.958751\pi$
$61$		−	2.01855i		−	0.258449i	0.991615	−	0.129225i	$-0.0412488\pi$
$62$	5.52567	+	0.683370i	0.701761	+	0.0867881i
$63$	3.70704	−	3.70704i	0.467044	−	0.467044i
$64$		−	1.00000i		−	0.125000i
$65$	0.865172	+	6.85071i	0.107311	+	0.849726i
$66$	5.65529			0.696118
$67$	4.78436	−	1.28196i	0.584502	−	0.156617i	0.0455628	−	0.998961i	$-0.485492\pi$
$67$	4.78436	−	1.28196i	0.584502	−	0.156617i	0.538939	+	0.842345i	$0.318825\pi$
$68$	1.63712	−	6.10981i	0.198530	−	0.740923i
$69$	5.74776	−	3.31847i	0.691949	−	0.399497i
$70$	−4.42889	−	10.8539i	−0.529353	−	1.29729i
$71$	−6.93286	+	12.0081i	−0.822779	+	1.42510i	0.0808256	+	0.996728i	$0.474244\pi$
$71$	−6.93286	+	12.0081i	−0.822779	+	1.42510i	−0.903605	+	0.428367i	$0.859089\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	−16.3130	+	4.37105i	−1.90929	+	0.511593i	−0.915206	+	0.402985i	$0.867973\pi$
$73$	−16.3130	+	4.37105i	−1.90929	+	0.511593i	−0.994085	+	0.108608i	$0.965361\pi$
$74$	−1.60045	−	2.77206i	−0.186049	−	0.322246i
$75$	2.54555	−	4.30351i	0.293934	−	0.496926i
$76$	1.14109	+	1.97643i	0.130893	+	0.226713i
$77$	−20.9644	+	20.9644i	−2.38912	+	2.38912i
$78$	−2.18359	+	2.18359i	−0.247243	+	0.247243i
$79$	1.90156	+	3.29360i	0.213942	+	0.370559i	0.952945	−	0.303144i	$-0.0980362\pi$
$79$	1.90156	+	3.29360i	0.213942	+	0.370559i	−0.739002	+	0.673703i	$0.764703\pi$
$80$	−0.303557	+	2.21537i	−0.0339386	+	0.247686i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	8.02295	−	2.14974i	0.885986	−	0.237399i
$83$	−7.65140	+	2.05019i	−0.839850	+	0.225037i	−0.653006	−	0.757352i	$-0.726493\pi$
$83$	−7.65140	+	2.05019i	−0.839850	+	0.225037i	−0.186844	+	0.982390i	$0.559826\pi$
$84$	2.62128	−	4.54018i	0.286005	−	0.495375i
$85$	−5.48149	+	13.0385i	−0.594551	+	1.41423i
$86$	5.45306	−	3.14833i	0.588019	−	0.339493i
$87$	−0.714043	+	2.66484i	−0.0765534	+	0.285701i
$88$	5.46259	−	1.46370i	0.582314	−	0.156031i
$89$	1.97417			0.209262			0.104631	−	0.994511i	$-0.466634\pi$
$89$	1.97417			0.209262			0.104631	+	0.994511i	$0.466634\pi$
$90$	2.21845	−	0.280166i	0.233845	−	0.0295321i
$91$		−	16.1893i		−	1.69710i
$92$	4.69302	−	4.69302i	0.489282	−	0.489282i
$93$	−2.17102	−	5.12705i	−0.225124	−	0.531651i
$94$			2.59455i			0.267607i
$95$	−1.92798	−	4.72491i	−0.197807	−	0.484766i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−2.48474	−	2.48474i	−0.252287	−	0.252287i	0.569621	−	0.821908i	$-0.307090\pi$
$97$	−2.48474	−	2.48474i	−0.252287	−	0.252287i	−0.821908	+	0.569621i	$0.807090\pi$
$98$	5.30174	+	19.7864i	0.535557	+	1.99872i
$99$	−2.82765	−	4.89763i	−0.284189	−	0.492230i
$100$	1.34498	−	4.81571i	0.134498	−	0.481571i
$101$	13.5988			1.35313			0.676566	−	0.736382i	$-0.263467\pi$
$101$	13.5988			1.35313			0.676566	+	0.736382i	$0.263467\pi$
$102$	−6.10981	+	1.63712i	−0.604961	+	0.162099i
$103$	−1.34979	−	5.03749i	−0.132999	−	0.496358i	0.866999	−	0.498309i	$-0.166046\pi$
$103$	−1.34979	−	5.03749i	−0.132999	−	0.496358i	−0.999998	+	0.00195103i	$0.999379\pi$
$104$	−1.54403	+	2.67434i	−0.151405	+	0.262241i
$105$	−7.18529	+	9.26247i	−0.701213	+	0.903924i
$106$	−6.12509	−	3.53632i	−0.594921	−	0.343478i
$107$	−1.62256	+	6.05549i	−0.156859	+	0.585406i	0.842080	+	0.539353i	$0.181331\pi$
$107$	−1.62256	+	6.05549i	−0.156859	+	0.585406i	−0.998939	+	0.0460532i	$0.985336\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$		−	4.25182i		−	0.407250i	−0.979049	−	0.203625i	$-0.934728\pi$
$109$		−	4.25182i		−	0.407250i	0.979049	−	0.203625i	$-0.0652724\pi$
$110$	−12.5460	+	1.58442i	−1.19621	+	0.151069i
$111$	−1.60045	+	2.77206i	−0.151908	+	0.263113i
$112$	1.35687	−	5.06392i	0.128212	−	0.478495i
$113$	0.453643	+	1.69302i	0.0426751	+	0.159266i	0.983975	−	0.178305i	$-0.0570614\pi$
$113$	0.453643	+	1.69302i	0.0426751	+	0.159266i	−0.941300	+	0.337571i	$0.890395\pi$
$114$	1.14109	−	1.97643i	0.106873	−	0.185110i
$115$	−11.8214	+	8.97217i	−1.10235	+	0.836660i
$116$			2.75885i			0.256153i
$117$	2.98284	+	0.799250i	0.275764	+	0.0738907i
$118$	7.71155	+	2.06630i	0.709906	+	0.190219i
$119$	16.5805	−	28.7182i	1.51993	−	2.63259i
$120$	2.07034	−	0.844796i	0.188996	−	0.0771190i
$121$	10.4912	+	18.1712i	0.953742	+	1.65193i
$122$	−1.42733	+	1.42733i	−0.129225	+	0.129225i
$123$	−5.87320	−	5.87320i	−0.529569	−	0.529569i
$124$	−3.42402	−	4.39045i	−0.307486	−	0.394274i
$125$	−4.44146	+	10.2603i	−0.397256	+	0.917708i
$126$	−5.24255			−0.467044
$127$	18.3983	+	4.92981i	1.63259	+	0.437450i	0.954664	−	0.297685i	$-0.0962144\pi$
$127$	18.3983	+	4.92981i	1.63259	+	0.437450i	0.677921	+	0.735135i	$0.262881\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−5.45306	−	3.14833i	−0.480115	−	0.277195i
$130$	4.23241	−	5.45595i	0.371207	−	0.478519i
$131$	−4.19474	−	7.26550i	−0.366496	−	0.634790i	0.622519	−	0.782605i	$-0.286109\pi$
$131$	−4.19474	−	7.26550i	−0.366496	−	0.634790i	−0.989015	+	0.147815i	$0.952776\pi$
$132$	−3.99889	−	3.99889i	−0.348059	−	0.348059i
$133$	3.09664	+	11.5568i	0.268513	+	1.00210i
$134$	−4.28954	−	2.47657i	−0.370560	−	0.213943i
$135$	−1.35185	−	1.78115i	−0.116349	−	0.153297i
$136$	−5.47791	+	3.16267i	−0.469727	+	0.271197i
$137$	−1.80200	−	6.72515i	−0.153955	−	0.574569i	−0.999193	−	0.0401776i	$-0.987208\pi$
$137$	−1.80200	−	6.72515i	−0.153955	−	0.574569i	0.845237	−	0.534391i	$-0.179459\pi$
$138$	−6.41079	−	1.71777i	−0.545723	−	0.146226i
$139$	2.63661			0.223635			0.111817	−	0.993729i	$-0.464333\pi$
$139$	2.63661			0.223635			0.111817	+	0.993729i	$0.464333\pi$
$140$	−4.54316	+	10.8065i	−0.383967	+	0.913320i
$141$	2.24694	−	1.29727i	0.189227	−	0.109250i
$142$	13.3933	−	3.58871i	1.12394	−	0.301158i
$143$	−16.8688	−	4.51999i	−1.41064	−	0.377981i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	0.837467	−	6.11187i	0.0695478	−	0.507563i
$146$	14.6258	+	8.44423i	1.21044	+	0.698849i
$147$	14.4846	−	14.4846i	1.19467	−	1.19467i
$148$	−0.828455	+	3.09183i	−0.0680985	+	0.254147i
$149$	1.16507	−	0.672654i	0.0954464	−	0.0551060i	−0.451517	−	0.892262i	$-0.649117\pi$
$149$	1.16507	−	0.672654i	0.0954464	−	0.0551060i	0.546963	+	0.837156i	$0.315784\pi$
$150$	−4.84301	+	1.24307i	−0.395430	+	0.101496i
$151$			0.922868i			0.0751019i	0.999295	+	0.0375510i	$0.0119557\pi$
$151$			0.922868i			0.0751019i	−0.999295	+	0.0375510i	$0.988044\pi$
$152$	0.590674	−	2.20443i	0.0479100	−	0.178803i
$153$	4.47269	+	4.47269i	0.361596	+	0.361596i
$154$	29.6482			2.38912
$155$	6.25272	+	10.7659i	0.502230	+	0.864734i
$156$	3.08806			0.247243
$157$	5.73785	+	5.73785i	0.457930	+	0.457930i	0.897975	−	0.440046i	$-0.145038\pi$
$157$	5.73785	+	5.73785i	0.457930	+	0.457930i	−0.440046	+	0.897975i	$0.645038\pi$
$158$	0.984321	−	3.67354i	0.0783084	−	0.292251i
$159$			7.07264i			0.560897i
$160$	1.78115	−	1.35185i	0.140812	−	0.106873i
$161$	30.1329	−	17.3972i	2.37481	−	1.37110i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−9.85246	+	9.85246i	−0.771704	+	0.771704i	−0.978404	−	0.206700i	$-0.933728\pi$
$163$	−9.85246	+	9.85246i	−0.771704	+	0.771704i	0.206700	+	0.978404i	$0.433728\pi$
$164$	−7.19318	−	4.15298i	−0.561693	−	0.324293i
$165$	7.64513	+	10.0729i	0.595173	+	0.784175i
$166$	6.86006	+	3.96066i	0.532444	+	0.307407i
$167$	9.52730	+	2.55283i	0.737245	+	0.197544i	0.607853	−	0.794050i	$-0.292031\pi$
$167$	9.52730	+	2.55283i	0.737245	+	0.197544i	0.129391	+	0.991594i	$0.458698\pi$
$168$	−5.06392	+	1.35687i	−0.390690	+	0.104685i
$169$	−2.99979	+	1.73193i	−0.230753	+	0.133225i
$170$	13.0956	−	5.34362i	1.00439	−	0.409837i
$171$	−2.28219			−0.174523
$172$	−6.08210	−	1.62969i	−0.463756	−	0.124263i
$173$	0.0794472	+	0.296501i	0.00604026	+	0.0225426i	0.968880	−	0.247530i	$-0.0796189\pi$
$173$	0.0794472	+	0.296501i	0.00604026	+	0.0225426i	−0.962840	+	0.270073i	$0.912952\pi$
$174$	2.38923	−	1.37942i	0.181127	−	0.104574i
$175$	13.3452	−	22.5614i	1.00880	−	1.70548i
$176$	−4.89763	−	2.82765i	−0.369172	−	0.213142i
$177$	−2.06630	−	7.71155i	−0.155313	−	0.579635i
$178$	−1.39595	−	1.39595i	−0.104631	−	0.104631i
$179$	0.729188	+	1.26299i	0.0545021	+	0.0944004i	0.891989	−	0.452057i	$-0.149310\pi$
$179$	0.729188	+	1.26299i	0.0545021	+	0.0944004i	−0.837487	+	0.546457i	$0.815976\pi$
$180$	−1.76679	−	1.37057i	−0.131688	−	0.102156i
$181$	−1.75602	−	1.01384i	−0.130524	−	0.0753580i	0.433316	−	0.901242i	$-0.357343\pi$
$181$	−1.75602	−	1.01384i	−0.130524	−	0.0753580i	−0.563840	+	0.825884i	$0.690677\pi$
$182$	−11.4476	+	11.4476i	−0.848552	+	0.848552i
$183$	1.94977	+	0.522440i	0.144131	+	0.0386199i
$184$	−6.63694			−0.489282
$185$	2.77388	−	6.59807i	0.203940	−	0.485100i
$186$	−2.09023	+	5.16052i	−0.153263	+	0.378387i
$187$	−25.2944	−	25.2944i	−1.84971	−	1.84971i
$188$	1.83462	−	1.83462i	0.133804	−	0.133804i
$189$	2.62128	+	4.54018i	0.190670	+	0.330250i
$190$	−1.97773	+	4.70431i	−0.143479	+	0.341287i
$191$	7.16590	−	12.4117i	0.518507	−	0.898080i	−0.481262	−	0.876577i	$-0.659821\pi$
$191$	7.16590	−	12.4117i	0.518507	−	0.898080i	0.999769	−	0.0215032i	$-0.00684520\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	7.76749	+	2.08129i	0.559116	+	0.149815i	0.527300	−	0.849679i	$-0.323204\pi$
$193$	7.76749	+	2.08129i	0.559116	+	0.149815i	0.0318158	+	0.999494i	$0.489871\pi$
$194$			3.51395i			0.252287i
$195$	−6.84120	−	0.937402i	−0.489908	−	0.0671288i
$196$	10.2422	−	17.7400i	0.731584	−	1.26714i
$197$	0.467297	+	1.74398i	0.0332935	+	0.124253i	0.980573	−	0.196157i	$-0.0628461\pi$
$197$	0.467297	+	1.74398i	0.0332935	+	0.124253i	−0.947279	+	0.320410i	$0.896179\pi$
$198$	−1.46370	+	5.46259i	−0.104020	+	0.388209i
$199$	2.49314	−	4.31825i	0.176734	−	0.306113i	−0.764026	−	0.645186i	$-0.776780\pi$
$199$	2.49314	−	4.31825i	0.176734	−	0.306113i	0.940760	+	0.339073i	$0.110113\pi$
$200$	−4.35626	+	2.45418i	−0.308034	+	0.173536i
$201$			4.95313i			0.349367i
$202$	−9.61581	−	9.61581i	−0.676566	−	0.676566i
$203$	−3.74341	+	13.9706i	−0.262736	+	0.980543i
$204$	5.47791	+	3.16267i	0.383530	+	0.221431i
$205$	14.6749	+	11.3839i	1.02494	+	0.795087i
$206$	−2.60760	+	4.51649i	−0.181680	+	0.314679i
$207$	1.71777	+	6.41079i	0.119393	+	0.445581i
$208$	2.98284	−	0.799250i	0.206823	−	0.0554180i
$209$	12.9064			0.892757
$210$	11.6303	−	1.46879i	0.802569	−	0.101356i
$211$	−3.33567	−	5.77754i	−0.229637	−	0.397742i	0.728064	−	0.685509i	$-0.240420\pi$
$211$	−3.33567	−	5.77754i	−0.229637	−	0.397742i	−0.957700	+	0.287767i	$0.907087\pi$
$212$	1.83053	+	6.83165i	0.125722	+	0.469199i
$213$	−9.80455	−	9.80455i	−0.671796	−	0.671796i
$214$	5.42920	−	3.13455i	0.371132	−	0.214273i
$215$	12.9794	+	5.45663i	0.885186	+	0.372139i
$216$		−	1.00000i		−	0.0680414i
$217$	−11.3817	−	26.8788i	−0.772639	−	1.82465i
$218$	−3.00649	+	3.00649i	−0.203625	+	0.203625i
$219$		−	16.8885i		−	1.14122i
$220$	9.99169	+	7.75098i	0.673640	+	0.522571i
$221$	19.5331			1.31394
$222$	3.09183	−	0.828455i	0.207510	−	0.0556022i
$223$	−6.44409	+	24.0497i	−0.431528	+	1.61049i	0.317712	+	0.948187i	$0.397086\pi$
$223$	−6.44409	+	24.0497i	−0.431528	+	1.61049i	−0.749240	+	0.662298i	$0.769581\pi$
$224$	−4.54018	+	2.62128i	−0.303354	+	0.175141i
$225$	3.49804	+	3.57264i	0.233202	+	0.238176i
$226$	0.876371	−	1.51792i	0.0582953	−	0.100970i
$227$	22.0302	−	5.90296i	1.46219	−	0.391793i	0.561946	−	0.827174i	$-0.310053\pi$
$227$	22.0302	−	5.90296i	1.46219	−	0.391793i	0.900247	+	0.435380i	$0.143386\pi$
$228$	−2.20443	+	0.590674i	−0.145992	+	0.0391183i
$229$	−5.46051	−	9.45788i	−0.360841	−	0.624994i	0.627259	−	0.778811i	$-0.284177\pi$
$229$	−5.46051	−	9.45788i	−0.360841	−	0.624994i	−0.988099	+	0.153817i	$0.950843\pi$
$230$	14.7033	+	2.01469i	0.969504	+	0.132844i
$231$	−14.8241	−	25.6761i	−0.975353	−	1.68936i
$232$	1.95080	−	1.95080i	0.128076	−	0.128076i
$233$	14.5803	−	14.5803i	0.955187	−	0.955187i	−0.0438513	−	0.999038i	$-0.513963\pi$
$233$	14.5803	−	14.5803i	0.955187	−	0.955187i	0.999038	+	0.0438513i	$0.0139628\pi$
$234$	−1.54403	−	2.67434i	−0.100937	−	0.174827i
$235$	−4.62127	+	3.50745i	−0.301459	+	0.228801i
$236$	−3.99179	−	6.91399i	−0.259843	−	0.450062i
$237$	−3.67354	+	0.984321i	−0.238622	+	0.0639385i
$238$	−32.0310	+	8.58268i	−2.07626	+	0.556332i
$239$	0.0712953	−	0.123487i	0.00461171	−	0.00798771i	−0.863710	−	0.503989i	$-0.831865\pi$
$239$	0.0712953	−	0.123487i	0.00461171	−	0.00798771i	0.868322	+	0.496001i	$0.165199\pi$
$240$	−2.06131	−	0.866592i	−0.133057	−	0.0559383i
$241$	−8.13357	+	4.69592i	−0.523929	+	0.302491i	−0.738541	−	0.674209i	$-0.764485\pi$
$241$	−8.13357	+	4.69592i	−0.523929	+	0.302491i	0.214612	+	0.976699i	$0.431151\pi$
$242$	5.43062	−	20.2674i	0.349094	−	1.30284i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	2.01855			0.129225
$245$	−28.0753	+	36.1915i	−1.79366	+	2.31219i
$246$			8.30597i			0.529569i
$247$	−4.98337	+	4.98337i	−0.317084	+	0.317084i
$248$	−0.683370	+	5.52567i	−0.0433940	+	0.350880i
$249$		−	7.92131i		−	0.501993i
$250$	10.3957	−	4.11453i	0.657482	−	0.260226i
$251$	−5.77871	+	3.33634i	−0.364749	+	0.210588i	−0.671162	−	0.741311i	$-0.734204\pi$
$251$	−5.77871	+	3.33634i	−0.364749	+	0.210588i	0.306413	+	0.951899i	$0.400871\pi$
$252$	3.70704	+	3.70704i	0.233522	+	0.233522i
$253$	−9.71447	−	36.2549i	−0.610743	−	2.27932i
$254$	−9.52366	−	16.4955i	−0.597568	−	1.03502i
$255$	−11.1755	−	8.66933i	−0.699839	−	0.542895i
$256$	1.00000			0.0625000
$257$	6.45955	−	1.73083i	0.402936	−	0.107966i	−0.0516589	−	0.998665i	$-0.516451\pi$
$257$	6.45955	−	1.73083i	0.402936	−	0.107966i	0.454594	+	0.890699i	$0.349784\pi$
$258$	1.62969	+	6.08210i	0.101460	+	0.378655i
$259$	−8.39045	+	14.5327i	−0.521357	+	0.903017i
$260$	−6.85071	+	0.865172i	−0.424863	+	0.0536557i
$261$	−2.38923	−	1.37942i	−0.147890	−	0.0853843i
$262$	−2.17136	+	8.10361i	−0.134147	+	0.500643i
$263$	6.88641	+	6.88641i	0.424634	+	0.424634i	0.886796	−	0.462162i	$-0.152926\pi$
$263$	6.88641	+	6.88641i	0.424634	+	0.424634i	−0.462162	+	0.886796i	$0.652926\pi$
$264$			5.65529i			0.348059i
$265$	−1.98151	−	15.6903i	−0.121723	−	0.963846i
$266$	5.98225	−	10.3616i	0.366795	−	0.635308i
$267$	−0.510954	+	1.90691i	−0.0312699	+	0.116701i
$268$	1.28196	+	4.78436i	0.0783084	+	0.292251i
$269$	13.3047	−	23.0444i	0.811200	−	1.40504i	−0.100824	−	0.994904i	$-0.532148\pi$
$269$	13.3047	−	23.0444i	0.811200	−	1.40504i	0.912024	−	0.410136i	$-0.134519\pi$
$270$	−0.303557	+	2.21537i	−0.0184739	+	0.134823i
$271$			6.45144i			0.391897i	0.980614	+	0.195949i	$0.0627786\pi$
$271$			6.45144i			0.391897i	−0.980614	+	0.195949i	$0.937221\pi$
$272$	6.10981	+	1.63712i	0.370462	+	0.0992649i
$273$	15.6377	+	4.19011i	0.946437	+	0.253597i
$274$	−3.48120	+	6.02961i	−0.210307	+	0.364262i
$275$	−19.7824	−	20.2043i	−1.19292	−	1.21837i
$276$	3.31847	+	5.74776i	0.199748	+	0.345974i
$277$	11.5029	−	11.5029i	0.691144	−	0.691144i	−0.271340	−	0.962484i	$-0.587467\pi$
$277$	11.5029	−	11.5029i	0.691144	−	0.691144i	0.962484	+	0.271340i	$0.0874667\pi$
$278$	−1.86437	−	1.86437i	−0.111817	−	0.111817i
$279$	5.51425	−	0.770064i	0.330130	−	0.0461025i
$280$	10.8539	−	4.42889i	0.648643	−	0.264677i
$281$	−6.44525			−0.384492			−0.192246	−	0.981347i	$-0.561577\pi$
$281$	−6.44525			−0.384492			−0.192246	+	0.981347i	$0.561577\pi$
$282$	−2.50614	−	0.671518i	−0.149238	−	0.0399883i
$283$	4.33073	−	4.33073i	0.257435	−	0.257435i	−0.566575	−	0.824010i	$-0.691732\pi$
$283$	4.33073	−	4.33073i	0.257435	−	0.257435i	0.824010	+	0.566575i	$0.191732\pi$
$284$	−12.0081	−	6.93286i	−0.712548	−	0.411390i
$285$	5.06292	−	0.639392i	0.299901	−	0.0378743i
$286$	8.73195	+	15.1242i	0.516331	+	0.894312i
$287$	−30.7906	−	30.7906i	−1.81751	−	1.81751i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	19.9272	+	11.5050i	1.17219	+	0.676763i
$290$	−4.91392	+	3.72956i	−0.288555	+	0.219008i
$291$	3.04317	−	1.75698i	0.178394	−	0.102996i
$292$	−4.37105	−	16.3130i	−0.255797	−	0.954646i
$293$	17.1790	+	4.60311i	1.00361	+	0.268917i	0.722957	−	0.690893i	$-0.242782\pi$
$293$	17.1790	+	4.60311i	1.00361	+	0.268917i	0.280653	+	0.959809i	$0.409449\pi$
$294$	−20.4844			−1.19467
$295$	6.74450	+	16.5288i	0.392680	+	0.962341i
$296$	2.77206	−	1.60045i	0.161123	−	0.0930243i
$297$	5.46259	−	1.46370i	0.316972	−	0.0849323i
$298$	−1.29947	−	0.348192i	−0.0752762	−	0.0201702i
$299$	17.7494	+	10.2476i	1.02648	+	0.592637i
$300$	4.30351	+	2.54555i	0.248463	+	0.146967i
$301$	−28.5880	−	16.5053i	−1.64778	−	0.951348i
$302$	0.652566	−	0.652566i	0.0375510	−	0.0375510i
$303$	−3.51963	+	13.1354i	−0.202197	+	0.754611i
$304$	−1.97643	+	1.14109i	−0.113356	+	0.0654463i
$305$	−4.47184	−	0.612745i	−0.256057	−	0.0350857i
$306$		−	6.32534i		−	0.361596i
$307$	−5.71154	+	21.3158i	−0.325975	+	1.21655i	0.587353	+	0.809331i	$0.300170\pi$
$307$	−5.71154	+	21.3158i	−0.325975	+	1.21655i	−0.913328	+	0.407224i	$0.866497\pi$
$308$	−20.9644	−	20.9644i	−1.19456	−	1.19456i
$309$	5.21519			0.296682
$310$	3.19127	−	12.0339i	0.181252	−	0.683482i
$311$	−23.6076			−1.33866			−0.669331	−	0.742964i	$-0.733419\pi$
$311$	−23.6076			−1.33866			−0.669331	+	0.742964i	$0.733419\pi$
$312$	−2.18359	−	2.18359i	−0.123622	−	0.123622i
$313$	−4.23889	+	15.8198i	−0.239596	+	0.894186i	0.736426	+	0.676518i	$0.236512\pi$
$313$	−4.23889	+	15.8198i	−0.239596	+	0.894186i	−0.976023	+	0.217668i	$0.930155\pi$
$314$		−	8.11454i		−	0.457930i
$315$	−7.08717	−	9.33776i	−0.399317	−	0.526123i
$316$	−3.29360	+	1.90156i	−0.185280	+	0.106971i
$317$	5.50971	−	20.5625i	0.309456	−	1.15491i	−0.619585	−	0.784929i	$-0.712699\pi$
$317$	5.50971	−	20.5625i	0.309456	−	1.15491i	0.929041	−	0.369976i	$-0.120634\pi$
$318$	5.00111	−	5.00111i	0.280448	−	0.280448i
$319$	13.5118	+	7.80105i	0.756516	+	0.436775i
$320$	−2.21537	−	0.303557i	−0.123843	−	0.0169693i
$321$	−5.42920	−	3.13455i	−0.303028	−	0.174954i
$322$	−33.6089	−	9.00548i	−1.87295	−	0.501856i
$323$	−13.9437	+	3.73621i	−0.775851	+	0.207889i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	15.4395	+	0.162904i	0.856427	+	0.00903629i
$326$	13.9335			0.771704
$327$	4.10694	+	1.10045i	0.227114	+	0.0608551i
$328$	2.14974	+	8.02295i	0.118700	+	0.442993i
$329$	11.7797	−	6.80102i	0.649437	−	0.374953i
$330$	1.71670	−	12.5285i	0.0945012	−	0.689674i
$331$	−8.04428	−	4.64437i	−0.442154	−	0.255278i	0.262357	−	0.964971i	$-0.415500\pi$
$331$	−8.04428	−	4.64437i	−0.442154	−	0.255278i	−0.704511	+	0.709693i	$0.748834\pi$
$332$	−2.05019	−	7.65140i	−0.112519	−	0.419925i
$333$	−2.26338	−	2.26338i	−0.124032	−	0.124032i
$334$	−4.93169	−	8.54194i	−0.269850	−	0.467394i
$335$	−1.38770	−	10.9883i	−0.0758181	−	0.600353i
$336$	4.54018	+	2.62128i	0.247687	+	0.143002i
$337$	−20.8436	+	20.8436i	−1.13542	+	1.13542i	−0.146160	+	0.989261i	$0.546691\pi$
$337$	−20.8436	+	20.8436i	−1.13542	+	1.13542i	−0.989261	+	0.146160i	$0.953309\pi$
$338$	3.34583	+	0.896512i	0.181989	+	0.0487638i
$339$	−1.75274			−0.0951958
$340$	−13.0385	−	5.48149i	−0.707113	−	0.297276i
$341$	−31.1847	+	4.35493i	−1.68875	+	0.235833i
$342$	1.61375	+	1.61375i	0.0872617	+	0.0872617i
$343$	49.9871	−	49.9871i	2.69905	−	2.69905i
$344$	3.14833	+	5.45306i	0.169746	+	0.294009i
$345$	−5.60686	−	13.7407i	−0.301863	−	0.739776i
$346$	0.153480	−	0.265836i	0.00825115	−	0.0142914i
$347$	32.8916	+	8.81328i	1.76571	+	0.473121i	0.987863	−	0.155328i	$-0.0496435\pi$
$347$	32.8916	+	8.81328i	1.76571	+	0.473121i	0.777850	+	0.628450i	$0.216310\pi$
$348$	−2.66484	−	0.714043i	−0.142851	−	0.0382767i
$349$			19.7580i			1.05762i	0.848740	+	0.528810i	$0.177361\pi$
$349$			19.7580i			1.05762i	−0.848740	+	0.528810i	$0.822639\pi$
$350$	−25.3898	+	6.51685i	−1.35714	+	0.348340i
$351$	−1.54403	+	2.67434i	−0.0824144	+	0.142746i
$352$	1.46370	+	5.46259i	0.0780153	+	0.291157i
$353$	−7.35212	+	27.4385i	−0.391314	+	1.46040i	0.436654	+	0.899629i	$0.356163\pi$
$353$	−7.35212	+	27.4385i	−0.391314	+	1.46040i	−0.827968	+	0.560775i	$0.810503\pi$
$354$	−3.99179	+	6.91399i	−0.212161	+	0.367474i
$355$	24.4978	+	19.0040i	1.30021	+	1.00863i
$356$			1.97417i			0.104631i
$357$	23.4483	+	23.4483i	1.24102	+	1.24102i
$358$	0.377456	−	1.40868i	0.0199492	−	0.0744513i
$359$	−31.8374	−	18.3813i	−1.68031	−	0.970129i	−0.961451	−	0.274976i	$-0.911330\pi$
$359$	−31.8374	−	18.3813i	−1.68031	−	0.970129i	−0.718862	−	0.695153i	$-0.755337\pi$
$360$	0.280166	+	2.21845i	0.0147661	+	0.116922i
$361$	−6.89581	+	11.9439i	−0.362937	+	0.628626i
$362$	0.524801	+	1.95858i	0.0275829	+	0.102941i
$363$	−20.2674	+	5.43062i	−1.06376	+	0.285034i
$364$	16.1893			0.848552
$365$	4.73157	+	37.4661i	0.247662	+	1.96107i
$366$	−1.00928	−	1.74812i	−0.0527557	−	0.0913756i
$367$	1.69107	+	6.31114i	0.0882729	+	0.329439i	0.995914	−	0.0903084i	$-0.0287853\pi$
$367$	1.69107	+	6.31114i	0.0882729	+	0.329439i	−0.907641	+	0.419748i	$0.862119\pi$
$368$	4.69302	+	4.69302i	0.244641	+	0.244641i
$369$	7.19318	−	4.15298i	0.374462	−	0.216196i
$370$	−6.62697	+	2.70411i	−0.344520	+	0.140580i
$371$			37.0787i			1.92503i
$372$	5.12705	−	2.17102i	0.265825	−	0.112562i
$373$	20.8924	−	20.8924i	1.08177	−	1.08177i	0.0854248	−	0.996345i	$-0.472775\pi$
$373$	20.8924	−	20.8924i	1.08177	−	1.08177i	0.996345	−	0.0854248i	$-0.0272247\pi$
$374$			35.7716i			1.84971i
$375$	−8.76114	−	6.94568i	−0.452423	−	0.358673i
$376$	−2.59455			−0.133804
$377$	−8.22921	+	2.20501i	−0.423826	+	0.113564i
$378$	1.35687	−	5.06392i	0.0697900	−	0.260460i
$379$	7.07358	−	4.08393i	0.363345	−	0.209777i	−0.307202	−	0.951644i	$-0.599393\pi$
$379$	7.07358	−	4.08393i	0.363345	−	0.209777i	0.670547	+	0.741867i	$0.266059\pi$
$380$	4.72491	−	1.92798i	0.242383	−	0.0989035i
$381$	−9.52366	+	16.4955i	−0.487912	+	0.845088i
$382$	−13.8435	+	3.70935i	−0.708293	+	0.189787i
$383$	18.9219	−	5.07010i	0.966863	−	0.259070i	0.259360	−	0.965781i	$-0.416488\pi$
$383$	18.9219	−	5.07010i	0.966863	−	0.259070i	0.707503	+	0.706710i	$0.249822\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	40.0800	+	52.8078i	2.04267	+	2.69133i
$386$	−4.02075	−	6.96414i	−0.204651	−	0.354465i
$387$	4.45241	−	4.45241i	0.226328	−	0.226328i
$388$	2.48474	−	2.48474i	0.126144	−	0.126144i
$389$	12.8859	+	22.3190i	0.653340	+	1.13162i	0.982307	+	0.187276i	$0.0599659\pi$
$389$	12.8859	+	22.3190i	0.653340	+	1.13162i	−0.328968	+	0.944341i	$0.606701\pi$
$390$	4.17461	+	5.50030i	0.211390	+	0.278519i
$391$	20.9904	+	36.3565i	1.06153	+	1.83863i
$392$	−19.7864	+	5.30174i	−0.999362	+	0.267778i
$393$	8.10361	−	2.17136i	0.408773	−	0.109530i
$394$	0.902749	−	1.56361i	0.0454798	−	0.0787734i
$395$	7.87377	−	3.21286i	0.396172	−	0.161657i
$396$	4.89763	−	2.82765i	0.246115	−	0.142095i
$397$	−7.52980	+	28.1016i	−0.377910	+	1.41038i	0.471136	+	0.882061i	$0.343844\pi$
$397$	−7.52980	+	28.1016i	−0.377910	+	1.41038i	−0.849046	+	0.528319i	$0.822823\pi$
$398$	−4.81638	+	1.29055i	−0.241424	+	0.0646892i
$399$	−11.9645			−0.598974
$400$	4.81571	+	1.34498i	0.240785	+	0.0672489i
$401$		−	18.6513i		−	0.931400i	−0.884943	−	0.465700i	$-0.845803\pi$
$401$		−	18.6513i		−	0.931400i	0.884943	−	0.465700i	$-0.154197\pi$
$402$	3.50239	−	3.50239i	0.174683	−	0.174683i
$403$	10.3594	−	13.7224i	0.516037	−	0.683561i
$404$			13.5988i			0.676566i
$405$	2.07034	−	0.844796i	0.102876	−	0.0419783i
$406$	12.5257	−	7.23171i	0.621639	−	0.358904i
$407$	12.8001	+	12.8001i	0.634476	+	0.634476i
$408$	−1.63712	−	6.10981i	−0.0810494	−	0.302481i
$409$	12.2786	+	21.2672i	0.607140	+	1.05160i	0.991709	+	0.128501i	$0.0410166\pi$
$409$	12.2786	+	21.2672i	0.607140	+	1.05160i	−0.384569	+	0.923096i	$0.625650\pi$
$410$	−2.32705	−	18.4263i	−0.114925	−	0.910012i
$411$	6.96239			0.343429
$412$	5.03749	−	1.34979i	0.248179	−	0.0664994i
$413$	−10.8327	−	40.4282i	−0.533042	−	1.98934i
$414$	3.31847	−	5.74776i	0.163094	−	0.282487i
$415$	2.21928	+	17.5730i	0.108940	+	0.862625i
$416$	−2.67434	−	1.54403i	−0.131120	−	0.0757024i
$417$	−0.682406	+	2.54677i	−0.0334175	+	0.124716i
$418$	−9.12623	−	9.12623i	−0.446379	−	0.446379i
$419$		−	0.267659i		−	0.0130760i	−0.999979	−	0.00653800i	$-0.997919\pi$
$419$		−	0.267659i		−	0.0130760i	0.999979	−	0.00653800i	$-0.00208113\pi$
$420$	−9.26247	−	7.18529i	−0.451962	−	0.350606i
$421$	8.74168	−	15.1410i	0.426044	−	0.737929i	−0.570474	−	0.821316i	$-0.693240\pi$
$421$	8.74168	−	15.1410i	0.426044	−	0.737929i	0.996517	+	0.0833868i	$0.0265737\pi$
$422$	−1.72667	+	6.44401i	−0.0840529	+	0.313690i
$423$	0.671518	+	2.50614i	0.0326503	+	0.121853i
$424$	3.53632	−	6.12509i	0.171739	−	0.297460i
$425$	27.2212	+	16.1014i	1.32042	+	0.781035i
$426$			13.8657i			0.671796i
$427$	10.2218	+	2.73892i	0.494667	+	0.132546i
$428$	−6.05549	−	1.62256i	−0.292703	−	0.0784295i
$429$	8.73195	−	15.1242i	0.421583	−	0.730203i
$430$	−5.31939	−	13.0362i	−0.256524	−	0.628663i
$431$	−8.31263	−	14.3979i	−0.400405	−	0.693522i	0.593369	−	0.804930i	$-0.297797\pi$
$431$	−8.31263	−	14.3979i	−0.400405	−	0.693522i	−0.993775	+	0.111408i	$0.964464\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	7.93949	+	7.93949i	0.381548	+	0.381548i	0.871660	−	0.490112i	$-0.163044\pi$
$433$	7.93949	+	7.93949i	0.381548	+	0.381548i	−0.490112	+	0.871660i	$0.663044\pi$
$434$	−10.9582	+	27.0543i	−0.526008	+	1.29865i
$435$	5.68686	+	2.39080i	0.272664	+	0.114630i
$436$	4.25182			0.203625
$437$	−14.6306	−	3.92027i	−0.699878	−	0.187532i
$438$	−11.9419	+	11.9419i	−0.570608	+	0.570608i
$439$	5.25354	+	3.03314i	0.250738	+	0.144764i	0.620102	−	0.784521i	$-0.287091\pi$
$439$	5.25354	+	3.03314i	0.250738	+	0.144764i	−0.369364	+	0.929285i	$0.620424\pi$
$440$	−1.58442	−	12.5460i	−0.0755343	−	0.598105i
$441$	10.2422	+	17.7400i	0.487723	+	0.844760i
$442$	−13.8120	−	13.8120i	−0.656968	−	0.656968i
$443$	−1.92177	−	7.17213i	−0.0913058	−	0.340758i	0.905128	−	0.425140i	$-0.139775\pi$
$443$	−1.92177	−	7.17213i	−0.0913058	−	0.340758i	−0.996433	+	0.0843819i	$0.973108\pi$
$444$	−2.77206	−	1.60045i	−0.131556	−	0.0759541i
$445$	0.599273	−	4.37352i	0.0284083	−	0.207325i
$446$	21.5624	−	12.4490i	1.02101	−	0.589479i
$447$	0.348192	+	1.29947i	0.0164689	+	0.0614628i
$448$	5.06392	+	1.35687i	0.239248	+	0.0641062i
$449$	11.0212			0.520120			0.260060	−	0.965592i	$-0.416258\pi$
$449$	11.0212			0.520120			0.260060	+	0.965592i	$0.416258\pi$
$450$	0.0527528	−	4.99972i	0.00248679	−	0.235689i
$451$	−40.6795	+	23.4863i	−1.91552	+	1.10593i
$452$	−1.69302	+	0.453643i	−0.0796329	+	0.0213376i
$453$	−0.891422	−	0.238856i	−0.0418827	−	0.0112224i
$454$	−19.7517	−	11.4036i	−0.926993	−	0.535200i
$455$	−35.8653	−	4.91438i	−1.68139	−	0.230390i
$456$	1.97643	+	1.14109i	0.0925550	+	0.0534367i
$457$	−20.3742	+	20.3742i	−0.953065	+	0.953065i	−0.998947	−	0.0458816i	$-0.985390\pi$
$457$	−20.3742	+	20.3742i	−0.953065	+	0.953065i	0.0458816	+	0.998947i	$0.485390\pi$
$458$	−2.82657	+	10.5489i	−0.132077	+	0.492917i
$459$	−5.47791	+	3.16267i	−0.255687	+	0.147621i
$460$	−8.97217	−	11.8214i	−0.418330	−	0.551174i
$461$			30.9759i			1.44269i	0.692574	+	0.721346i	$0.256476\pi$
$461$			30.9759i			1.44269i	−0.692574	+	0.721346i	$0.743524\pi$
$462$	−7.67351	+	28.6379i	−0.357004	+	1.33236i
$463$	2.99113	+	2.99113i	0.139010	+	0.139010i	0.773187	−	0.634178i	$-0.218661\pi$
$463$	2.99113	+	2.99113i	0.139010	+	0.139010i	−0.634178	+	0.773187i	$0.718661\pi$
$464$	−2.75885			−0.128076
$465$	−12.0173	+	3.25325i	−0.557291	+	0.150866i
$466$	−20.6196			−0.955187
$467$	−3.02661	−	3.02661i	−0.140055	−	0.140055i	0.633603	−	0.773658i	$-0.281575\pi$
$467$	−3.02661	−	3.02661i	−0.140055	−	0.140055i	−0.773658	+	0.633603i	$0.781575\pi$
$468$	−0.799250	+	2.98284i	−0.0369453	+	0.137882i
$469$			25.9670i			1.19905i
$470$	5.74788	+	0.787592i	0.265130	+	0.0363289i
$471$	−7.02740	+	4.05727i	−0.323805	+	0.186949i
$472$	−2.06630	+	7.71155i	−0.0951093	+	0.354953i
$473$	−25.1796	+	25.1796i	−1.15776	+	1.15776i
$474$	3.29360	+	1.90156i	0.151280	+	0.0873416i
$475$	−11.0527	+	2.83692i	−0.507131	+	0.130167i
$476$	28.7182	+	16.5805i	1.31630	+	0.759964i
$477$	−6.83165	−	1.83053i	−0.312800	−	0.0838144i
$478$	−0.137732	+	0.0369051i	−0.00629971	+	0.00168800i
$479$	−1.52175	+	0.878584i	−0.0695306	+	0.0401435i	−0.534362	−	0.845256i	$-0.679448\pi$
$479$	−1.52175	+	0.878584i	−0.0695306	+	0.0401435i	0.464832	+	0.885399i	$0.346115\pi$
$480$	0.844796	+	2.07034i	0.0385595	+	0.0944978i
$481$	−9.88459			−0.450699
$482$	9.07181	+	2.43079i	0.413210	+	0.110719i
$483$	9.00548	+	33.6089i	0.409763	+	1.52926i
$484$	−18.1712	+	10.4912i	−0.825964	+	0.476871i
$485$	−6.25887	+	4.75035i	−0.284201	+	0.215702i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	0.0929698	+	0.346968i	0.00421287	+	0.0157226i	0.968000	−	0.250949i	$-0.0807427\pi$
$487$	0.0929698	+	0.346968i	0.00421287	+	0.0157226i	−0.963787	+	0.266672i	$0.914076\pi$
$488$	−1.42733	−	1.42733i	−0.0646123	−	0.0646123i
$489$	−6.96674	−	12.0667i	−0.315047	−	0.545677i
$490$	45.4435	−	5.73902i	2.05293	−	0.259263i
$491$	13.5861	+	7.84393i	0.613132	+	0.353992i	0.774190	−	0.632953i	$-0.218157\pi$
$491$	13.5861	+	7.84393i	0.613132	+	0.353992i	−0.161059	+	0.986945i	$0.551491\pi$
$492$	5.87320	−	5.87320i	0.264785	−	0.264785i
$493$	−16.8560	−	4.51656i	−0.759158	−	0.203416i
$494$	7.04755			0.317084
$495$	−11.7084	+	4.77757i	−0.526253	+	0.214736i
$496$	4.39045	−	3.42402i	0.197137	−	0.153743i
$497$	−51.4008	−	51.4008i	−2.30564	−	2.30564i
$498$	−5.60121	+	5.60121i	−0.250996	+	0.250996i
$499$	2.98464	+	5.16955i	0.133611	+	0.231421i	0.925066	−	0.379807i	$-0.124009\pi$
$499$	2.98464	+	5.16955i	0.133611	+	0.231421i	−0.791455	+	0.611227i	$0.790676\pi$
$500$	−10.2603	−	4.44146i	−0.458854	−	0.198628i
$501$	−4.93169	+	8.54194i	−0.220332	+	0.381626i
$502$	6.44531	+	1.72702i	0.287668	+	0.0770805i
$503$	29.2894	+	7.84808i	1.30595	+	0.349928i	0.843697	−	0.536819i	$-0.180374\pi$
$503$	29.2894	+	7.84808i	1.30595	+	0.349928i	0.462253	+	0.886748i	$0.347041\pi$
$504$		−	5.24255i		−	0.233522i
$505$	4.12801	−	30.1264i	0.183694	−	1.34061i
$506$	−18.7669	+	32.5052i	−0.834291	+	1.44503i
$507$	−0.896512	−	3.34583i	−0.0398155	−	0.148593i
$508$	−4.92981	+	18.3983i	−0.218725	+	0.816293i
$509$	−13.4306	+	23.2625i	−0.595300	+	1.03109i	0.398204	+	0.917297i	$0.369634\pi$
$509$	−13.4306	+	23.2625i	−0.595300	+	1.03109i	−0.993504	+	0.113794i	$0.963700\pi$
$510$	1.77215	+	14.0324i	0.0784720	+	0.621367i
$511$		−	88.5386i		−	3.91672i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.590674	−	2.20443i	0.0260789	−	0.0973278i
$514$	−5.79147	−	3.34371i	−0.255451	−	0.147485i
$515$	−11.5696	+	1.46112i	−0.509819	+	0.0643847i
$516$	3.14833	−	5.45306i	0.138597	−	0.240058i
$517$	−3.79763	−	14.1730i	−0.167020	−	0.623326i
$518$	16.2091	−	4.34322i	0.712187	−	0.190830i
$519$	−0.306960			−0.0134741
$520$	5.45595	+	4.23241i	0.239259	+	0.185604i
$521$	−10.0508	−	17.4085i	−0.440334	−	0.762682i	0.557380	−	0.830258i	$-0.311807\pi$
$521$	−10.0508	−	17.4085i	−0.440334	−	0.762682i	−0.997714	+	0.0675761i	$0.978473\pi$
$522$	0.714043	+	2.66484i	0.0312528	+	0.116637i
$523$	−20.1521	−	20.1521i	−0.881190	−	0.881190i	0.112465	−	0.993656i	$-0.464125\pi$
$523$	−20.1521	−	20.1521i	−0.881190	−	0.881190i	−0.993656	+	0.112465i	$0.964125\pi$
$524$	7.26550	−	4.19474i	0.317395	−	0.183248i
$525$	18.3386	+	18.7297i	0.800364	+	0.817433i
$526$		−	9.73885i		−	0.424634i
$527$	32.4304	−	13.7324i	1.41269	−	0.598194i
$528$	3.99889	−	3.99889i	0.174030	−	0.174030i
$529$			21.0489i			0.915172i
$530$	−9.69356	+	12.4958i	−0.421061	+	0.542785i
$531$	7.98358			0.346458
$532$	−11.5568	+	3.09664i	−0.501052	+	0.134256i
$533$	6.63854	−	24.7754i	0.287547	−	1.07314i
$534$	1.70968	−	0.987087i	0.0739853	−	0.0427154i
$535$	12.9226	+	5.43275i	0.558692	+	0.234878i
$536$	2.47657	−	4.28954i	0.106971	−	0.185280i
$537$	−1.40868	+	0.377456i	−0.0607892	+	0.0162884i
$538$	−25.7027	+	6.88701i	−1.10812	+	0.296920i
$539$	−57.9225	−	100.325i	−2.49490	−	4.32129i
$540$	1.78115	−	1.35185i	0.0766484	−	0.0581746i
$541$	−4.84566	−	8.39293i	−0.208331	−	0.360840i	0.742858	−	0.669449i	$-0.233470\pi$
$541$	−4.84566	−	8.39293i	−0.208331	−	0.360840i	−0.951189	+	0.308609i	$0.900137\pi$
$542$	4.56186	−	4.56186i	0.195949	−	0.195949i
$543$	1.43378	−	1.43378i	0.0615295	−	0.0615295i
$544$	−3.16267	−	5.47791i	−0.135598	−	0.234863i
$545$	−9.41934	−	1.29067i	−0.403480	−	0.0552861i
$546$	−8.09467	−	14.0204i	−0.346420	−	0.600017i
$547$	−28.4389	+	7.62018i	−1.21596	+	0.325816i	−0.809098	−	0.587674i	$-0.800044\pi$
$547$	−28.4389	+	7.62018i	−1.21596	+	0.325816i	−0.406862	+	0.913490i	$0.633377\pi$
$548$	6.72515	−	1.80200i	0.287284	−	0.0769776i
$549$	−1.00928	+	1.74812i	−0.0430749	+	0.0746079i
$550$	−0.298332	+	28.2749i	−0.0127209	+	1.20564i
$551$	5.45268	−	3.14811i	0.232292	−	0.134114i
$552$	1.71777	−	6.41079i	0.0731130	−	0.272861i
$553$	−19.2587	+	5.16035i	−0.818963	+	0.219441i
$554$	−16.2676			−0.691144
$555$	5.65531	+	4.38707i	0.240055	+	0.186221i
$556$			2.63661i			0.111817i
$557$	−19.6368	+	19.6368i	−0.832037	+	0.832037i	−0.987795	−	0.155758i	$-0.950218\pi$
$557$	−19.6368	+	19.6368i	−0.832037	+	0.832037i	0.155758	+	0.987795i	$0.450218\pi$
$558$	−4.44368	−	3.35465i	−0.188116	−	0.142014i
$559$		−	19.4445i		−	0.822414i
$560$	−10.8065	−	4.54316i	−0.456660	−	0.191983i
$561$	30.9791	−	17.8858i	1.30794	−	0.755140i
$562$	4.55748	+	4.55748i	0.192246	+	0.192246i
$563$	1.29838	+	4.84562i	0.0547202	+	0.204218i	0.987874	−	0.155260i	$-0.0496214\pi$
$563$	1.29838	+	4.84562i	0.0547202	+	0.204218i	−0.933154	+	0.359478i	$0.882955\pi$
$564$	1.29727	+	2.24694i	0.0546251	+	0.0946134i
$565$	3.88836	−	0.491059i	0.163585	−	0.0206590i
$566$	−6.12458			−0.257435
$567$	−5.06392	+	1.35687i	−0.212665	+	0.0569833i
$568$	3.58871	+	13.3933i	0.150579	+	0.561969i
$569$	11.1525	−	19.3167i	0.467538	−	0.809800i	−0.531774	−	0.846886i	$-0.678474\pi$
$569$	11.1525	−	19.3167i	0.467538	−	0.809800i	0.999312	+	0.0370864i	$0.0118077\pi$
$570$	−4.03214	−	3.12790i	−0.168888	−	0.131013i
$571$	14.7653	+	8.52474i	0.617908	+	0.356749i	0.776054	−	0.630666i	$-0.217218\pi$
$571$	14.7653	+	8.52474i	0.617908	+	0.356749i	−0.158146	+	0.987416i	$0.550552\pi$
$572$	4.51999	−	16.8688i	0.188990	−	0.705322i
$573$	10.1341	+	10.1341i	0.423359	+	0.423359i
$574$			43.5445i			1.81751i
$575$	16.2882	+	28.9122i	0.679265	+	1.20572i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	4.42600	−	16.5181i	0.184257	−	0.687656i	−0.810532	−	0.585695i	$-0.800822\pi$
$577$	4.42600	−	16.5181i	0.184257	−	0.687656i	0.994788	−	0.101961i	$-0.0325117\pi$
$578$	−5.95541	−	22.2259i	−0.247712	−	0.924475i
$579$	−4.02075	+	6.96414i	−0.167097	+	0.289420i
$580$	6.11187	+	0.837467i	0.253781	+	0.0347739i
$581$		−	41.5279i		−	1.72287i
$582$	−3.39422	−	0.909478i	−0.140695	−	0.0376991i
$583$	38.6349	+	10.3522i	1.60010	+	0.428744i
$584$	−8.44423	+	14.6258i	−0.349425	+	0.605221i
$585$	2.67609	−	6.36547i	0.110643	−	0.263180i
$586$	−8.89253	−	15.4023i	−0.367347	−	0.636264i
$587$	11.9620	−	11.9620i	0.493724	−	0.493724i	−0.415753	−	0.909478i	$-0.636482\pi$
$587$	11.9620	−	11.9620i	0.493724	−	0.493724i	0.909478	+	0.415753i	$0.136482\pi$
$588$	14.4846	+	14.4846i	0.597336	+	0.597336i
$589$	−4.77031	+	11.7773i	−0.196557	+	0.485274i
$590$	6.91851	−	16.4567i	0.284831	−	0.677511i
$591$	−1.80550			−0.0742682
$592$	−3.09183	−	0.828455i	−0.127074	−	0.0340493i
$593$	−21.3221	+	21.3221i	−0.875594	+	0.875594i	−0.993075	−	0.117481i	$-0.962518\pi$
$593$	−21.3221	+	21.3221i	−0.875594	+	0.875594i	0.117481	+	0.993075i	$0.462518\pi$
$594$	−4.89763	−	2.82765i	−0.200952	−	0.116020i
$595$	−58.5883	−	45.4494i	−2.40188	−	1.86324i
$596$	0.672654	+	1.16507i	0.0275530	+	0.0477232i
$597$	3.52584	+	3.52584i	0.144303	+	0.144303i
$598$	−5.30457	−	19.7969i	−0.216920	−	0.809557i
$599$	−19.9169	−	11.4990i	−0.813783	−	0.469838i	0.0344849	−	0.999405i	$-0.489021\pi$
$599$	−19.9169	−	11.4990i	−0.813783	−	0.469838i	−0.848268	+	0.529567i	$0.822354\pi$
$600$	−1.24307	−	4.84301i	−0.0507480	−	0.197715i
$601$	−32.9929	+	19.0485i	−1.34581	+	0.777003i	−0.987653	−	0.156658i	$-0.949928\pi$
$601$	−32.9929	+	19.0485i	−1.34581	+	0.777003i	−0.358157	+	0.933662i	$0.616595\pi$
$602$	8.54375	+	31.8857i	0.348217	+	1.29957i
$603$	−4.78436	−	1.28196i	−0.194834	−	0.0522056i
$604$	−0.922868			−0.0375510
$605$	43.4406	−	17.7258i	1.76611	−	0.720655i
$606$	11.7769	−	6.79940i	0.478404	−	0.276207i
$607$	−2.36657	+	0.634119i	−0.0960559	+	0.0257381i	−0.306527	−	0.951862i	$-0.599167\pi$
$607$	−2.36657	+	0.634119i	−0.0960559	+	0.0257381i	0.210471	+	0.977600i	$0.432500\pi$
$608$	2.20443	+	0.590674i	0.0894013	+	0.0239550i
$609$	−12.5257	−	7.23171i	−0.507566	−	0.293044i
$610$	2.72879	+	3.59534i	0.110485	+	0.145571i
$611$	6.93871	+	4.00607i	0.280710	+	0.162068i
$612$	−4.47269	+	4.47269i	−0.180798	+	0.180798i
$613$	−1.71217	+	6.38990i	−0.0691538	+	0.258086i	−0.991844	−	0.127456i	$-0.959319\pi$
$613$	−1.71217	+	6.38990i	−0.0691538	+	0.258086i	0.922690	+	0.385542i	$0.125985\pi$
$614$	19.1112	−	11.0339i	0.771265	−	0.445290i
$615$	−14.7942	+	11.2285i	−0.596558	+	0.452775i
$616$			29.6482i			1.19456i
$617$	−6.87996	+	25.6764i	−0.276977	+	1.03369i	0.677528	+	0.735497i	$0.263051\pi$
$617$	−6.87996	+	25.6764i	−0.276977	+	1.03369i	−0.954505	+	0.298195i	$0.903615\pi$
$618$	−3.68770	−	3.68770i	−0.148341	−	0.148341i
$619$	32.6492			1.31228			0.656142	−	0.754638i	$-0.272187\pi$
$619$	32.6492			1.31228			0.656142	+	0.754638i	$0.272187\pi$
$620$	−10.7659	+	6.25272i	−0.432367	+	0.251115i
$621$	−6.63694			−0.266331
$622$	16.6931	+	16.6931i	0.669331	+	0.669331i
$623$	−2.67870	+	9.99705i	−0.107320	+	0.400523i
$624$			3.08806i			0.123622i
$625$	21.3821	+	12.9540i	0.855283	+	0.518162i
$626$	14.1836	−	8.18891i	0.566891	−	0.327295i
$627$	−3.34043	+	12.4667i	−0.133404	+	0.497871i
$628$	−5.73785	+	5.73785i	−0.228965	+	0.228965i
$629$	−17.5342	−	10.1234i	−0.699136	−	0.403646i
$630$	−1.59141	+	11.6142i	−0.0634033	+	0.462720i
$631$	31.1996	+	18.0131i	1.24204	+	0.717090i	0.969509	−	0.245057i	$-0.0788068\pi$
$631$	31.1996	+	18.0131i	1.24204	+	0.717090i	0.272528	+	0.962148i	$0.412140\pi$
$632$	3.67354	+	0.984321i	0.146125	+	0.0391542i
$633$	6.44401	−	1.72667i	0.256126	−	0.0686289i
$634$	−18.4358	+	10.6439i	−0.732181	+	0.422725i
$635$	16.5063	−	39.2625i	0.655031	−	1.55809i
$636$	−7.07264			−0.280448
$637$	61.1016	+	16.3721i	2.42093	+	0.648687i
$638$	−4.03812	−	15.0705i	−0.159871	−	0.596646i
$639$	12.0081	−	6.93286i	0.475032	−	0.274260i
$640$	1.35185	+	1.78115i	0.0534367	+	0.0704061i
$641$	4.84137	+	2.79517i	0.191223	+	0.110402i	0.592555	−	0.805530i	$-0.298119\pi$
$641$	4.84137	+	2.79517i	0.191223	+	0.110402i	−0.401332	+	0.915933i	$0.631453\pi$
$642$	1.62256	+	6.05549i	0.0640374	+	0.238991i
$643$	−8.52945	−	8.52945i	−0.336369	−	0.336369i	0.518630	−	0.854999i	$-0.326442\pi$
$643$	−8.52945	−	8.52945i	−0.336369	−	0.336369i	−0.854999	+	0.518630i	$0.826442\pi$
$644$	17.3972	+	30.1329i	0.685548	+	1.18740i
$645$	−8.63001	+	11.1248i	−0.339806	+	0.438040i
$646$	12.5016	+	7.21781i	0.491870	+	0.283981i
$647$	9.47969	−	9.47969i	0.372685	−	0.372685i	−0.495769	−	0.868454i	$-0.665114\pi$
$647$	9.47969	−	9.47969i	0.372685	−	0.372685i	0.868454	+	0.495769i	$0.165114\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−45.1495			−1.77227
$650$	−10.8022	−	11.0325i	−0.423696	−	0.432732i
$651$	28.9088	−	4.03710i	1.13302	−	0.158226i
$652$	−9.85246	−	9.85246i	−0.385852	−	0.385852i
$653$	−11.1980	+	11.1980i	−0.438212	+	0.438212i	−0.891410	−	0.453198i	$-0.850283\pi$
$653$	−11.1980	+	11.1980i	−0.438212	+	0.438212i	0.453198	+	0.891410i	$0.350283\pi$
$654$	−2.12591	−	3.68218i	−0.0831297	−	0.143985i
$655$	−17.3691	+	7.08740i	−0.678667	+	0.276928i
$656$	4.15298	−	7.19318i	0.162147	−	0.280846i
$657$	16.3130	+	4.37105i	0.636430	+	0.170531i
$658$	−13.1386	−	3.52047i	−0.512195	−	0.137242i
$659$			29.2065i			1.13772i	0.822433	+	0.568862i	$0.192616\pi$
$659$			29.2065i			1.13772i	−0.822433	+	0.568862i	$0.807384\pi$
$660$	−10.0729	+	7.64513i	−0.392088	+	0.297586i
$661$	−11.6701	+	20.2132i	−0.453915	+	0.786203i	−0.998625	−	0.0524210i	$-0.983306\pi$
$661$	−11.6701	+	20.2132i	−0.453915	+	0.786203i	0.544710	+	0.838624i	$0.316640\pi$
$662$	2.40410	+	8.97223i	0.0934381	+	0.348716i
$663$	−5.05553	+	18.8675i	−0.196340	+	0.732753i
$664$	−3.96066	+	6.86006i	−0.153703	+	0.266222i
$665$	26.5426	−	3.35205i	1.02928	−	0.129987i
$666$			3.20090i			0.124032i
$667$	−12.9473	−	12.9473i	−0.501323	−	0.501323i
$668$	−2.55283	+	9.52730i	−0.0987720	+	0.368622i
$669$	−21.5624	−	12.4490i	−0.833649	−	0.481307i
$670$	−6.78862	+	8.75112i	−0.262267	+	0.338085i
$671$	5.70775	−	9.88612i	0.220345	−	0.381649i
$672$	−1.35687	−	5.06392i	−0.0523425	−	0.195345i
$673$	4.35545	−	1.16704i	0.167890	−	0.0449861i	−0.173895	−	0.984764i	$-0.555635\pi$
$673$	4.35545	−	1.16704i	0.167890	−	0.0449861i	0.341785	+	0.939778i	$0.388969\pi$
$674$	29.4772			1.13542
$675$	−4.35626	+	2.45418i	−0.167673	+	0.0944613i
$676$	−1.73193	−	2.99979i	−0.0666126	−	0.115376i
$677$	−7.48529	−	27.9355i	−0.287683	−	1.07365i	−0.946856	−	0.321657i	$-0.895760\pi$
$677$	−7.48529	−	27.9355i	−0.287683	−	1.07365i	0.659173	−	0.751991i	$-0.270906\pi$
$678$	1.23938	+	1.23938i	0.0475979	+	0.0475979i
$679$	15.9540	−	9.21104i	0.612258	−	0.353487i
$680$	5.34362	+	13.0956i	0.204919	+	0.502194i
$681$			22.8073i			0.873977i
$682$	25.1303	+	18.9715i	0.962290	+	0.726457i
$683$	−4.12588	+	4.12588i	−0.157872	+	0.157872i	−0.781623	−	0.623751i	$-0.785608\pi$
$683$	−4.12588	+	4.12588i	−0.157872	+	0.157872i	0.623751	+	0.781623i	$0.285608\pi$
$684$		−	2.28219i		−	0.0872617i
$685$	−15.4457	+	1.95063i	−0.590150	+	0.0745296i
$686$	−70.6924			−2.69905
$687$	10.5489	−	2.82657i	0.402465	−	0.107840i
$688$	1.62969	−	6.08210i	0.0621315	−	0.231878i
$689$	−18.9147	+	10.9204i	−0.720591	+	0.416034i
$690$	−5.75152	+	13.6808i	−0.218957	+	0.520820i
$691$	1.83779	−	3.18315i	0.0699129	−	0.121093i	−0.828950	−	0.559323i	$-0.811061\pi$
$691$	1.83779	−	3.18315i	0.0699129	−	0.121093i	0.898863	+	0.438230i	$0.144395\pi$
$692$	−0.296501	+	0.0794472i	−0.0112713	+	0.00302013i
$693$	28.6379	−	7.67351i	1.08786	−	0.291492i
$694$	−17.0259	−	29.4898i	−0.646296	−	1.11942i
$695$	0.800361	−	5.84107i	0.0303594	−	0.221564i
$696$	1.37942	+	2.38923i	0.0522870	+	0.0905637i
$697$	37.1500	−	37.1500i	1.40716	−	1.40716i
$698$	13.9710	−	13.9710i	0.528810	−	0.528810i
$699$	10.3098	+	17.8571i	0.389953	+	0.675419i
$700$	22.5614	+	13.3452i	0.852740	+	0.504400i
$701$	−9.78185	−	16.9427i	−0.369455	−	0.639915i	0.620025	−	0.784582i	$-0.287122\pi$
$701$	−9.78185	−	16.9427i	−0.369455	−	0.639915i	−0.989480	+	0.144667i	$0.953789\pi$
$702$	2.98284	−	0.799250i	0.112580	−	0.0301657i
$703$	7.05615	−	1.89069i	0.266128	−	0.0713087i
$704$	2.82765	−	4.89763i	0.106571	−	0.184586i
$705$	−2.19186	−	5.37160i	−0.0825504	−	0.202306i
$706$	24.6007	−	14.2032i	0.925859	−	0.534545i
$707$	−18.4518	+	68.8632i	−0.693953	+	2.58987i
$708$	7.71155	−	2.06630i	0.289818	−	0.0776564i
$709$	−23.3942			−0.878586			−0.439293	−	0.898344i	$-0.644771\pi$
$709$	−23.3942			−0.878586			−0.439293	+	0.898344i	$0.644771\pi$
$710$	−3.88471	−	30.7604i	−0.145790	−	1.15442i
$711$		−	3.80312i		−	0.142628i
$712$	1.39595	−	1.39595i	0.0523155	−	0.0523155i
$713$	36.6735	+	4.53548i	1.37343	+	0.169855i
$714$		−	33.1609i		−	1.24102i
$715$	−15.1341	+	35.9986i	−0.565983	+	1.34627i
$716$	−1.26299	+	0.729188i	−0.0472002	+	0.0272511i
$717$	0.100827	+	0.100827i	0.00376544	+	0.00376544i
$718$	9.51487	+	35.5100i	0.355092	+	1.32522i
$719$	4.39261	+	7.60822i	0.163817	+	0.283739i	0.936234	−	0.351376i	$-0.114286\pi$
$719$	4.39261	+	7.60822i	0.163817	+	0.283739i	−0.772418	+	0.635115i	$0.780953\pi$
$720$	1.37057	−	1.76679i	0.0510782	−	0.0658442i
$721$	27.3409			1.01823
$722$	13.3217	−	3.56953i	0.495781	−	0.132844i
$723$	−2.43079	−	9.07181i	−0.0904019	−	0.337384i
$724$	1.01384	−	1.75602i	0.0376790	−	0.0652619i
$725$	−13.2858	−	3.71059i	−0.493423	−	0.137808i
$726$	18.1712	+	10.4912i	0.674397	+	0.389363i
$727$	1.51023	−	5.63624i	0.0560112	−	0.209037i	−0.932249	−	0.361818i	$-0.882156\pi$
$727$	1.51023	−	5.63624i	0.0560112	−	0.209037i	0.988260	+	0.152781i	$0.0488229\pi$
$728$	−11.4476	−	11.4476i	−0.424276	−	0.424276i
$729$		−	1.00000i		−	0.0370370i
$730$	23.1468	−	29.8383i	0.856703	−	1.10436i
$731$	19.9142	−	34.4925i	0.736555	−	1.27575i
$732$	−0.522440	+	1.94977i	−0.0193099	+	0.0720657i
$733$	1.94016	+	7.24079i	0.0716616	+	0.267445i	0.992456	−	0.122604i	$-0.0391246\pi$
$733$	1.94016	+	7.24079i	0.0716616	+	0.267445i	−0.920794	+	0.390049i	$0.872458\pi$
$734$	3.26689	−	5.65842i	0.120583	−	0.208856i
$735$	−27.6919	−	36.4857i	−1.02143	−	1.34579i
$736$		−	6.63694i		−	0.244641i
$737$	27.0569	+	7.24988i	0.996655	+	0.267053i
$738$	−8.02295	−	2.14974i	−0.295329	−	0.0791331i
$739$	5.80153	−	10.0486i	0.213413	−	0.369642i	−0.739368	−	0.673302i	$-0.764875\pi$
$739$	5.80153	−	10.0486i	0.213413	−	0.369642i	0.952780	+	0.303660i	$0.0982087\pi$
$740$	6.59807	+	2.77388i	0.242550	+	0.101970i
$741$	−3.52377	−	6.10336i	−0.129449	−	0.224212i
$742$	26.2186	−	26.2186i	0.962515	−	0.962515i
$743$	3.21148	+	3.21148i	0.117818	+	0.117818i	0.763558	−	0.645740i	$-0.223451\pi$
$743$	3.21148	+	3.21148i	0.117818	+	0.117818i	−0.645740	+	0.763558i	$0.723451\pi$
$744$	−5.16052	−	2.09023i	−0.189194	−	0.0766316i
$745$	−1.13651	−	2.78525i	−0.0416386	−	0.102044i
$746$	−29.5464			−1.08177
$747$	7.65140	+	2.05019i	0.279950	+	0.0750124i
$748$	25.2944	−	25.2944i	0.924854	−	0.924854i
$749$	−28.4629	−	16.4330i	−1.04001	−	0.600450i
$750$	1.28372	+	11.1064i	0.0468750	+	0.405548i
$751$	−15.9088	−	27.5548i	−0.580519	−	1.00549i	−0.995418	−	0.0956206i	$-0.969516\pi$
$751$	−15.9088	−	27.5548i	−0.580519	−	1.00549i	0.414899	−	0.909867i	$-0.363817\pi$
$752$	1.83462	+	1.83462i	0.0669018	+	0.0669018i
$753$	−1.72702	−	6.44531i	−0.0629359	−	0.234880i
$754$	7.37811	+	4.25975i	0.268695	+	0.155131i
$755$	2.04449	+	0.280143i	0.0744067	+	0.0101954i
$756$	−4.54018	+	2.62128i	−0.165125	+	0.0953349i
$757$	−9.86472	−	36.8157i	−0.358539	−	1.33809i	−0.875971	−	0.482363i	$-0.839779\pi$
$757$	−9.86472	−	36.8157i	−0.358539	−	1.33809i	0.517432	−	0.855724i	$-0.326888\pi$
$758$	−7.88955	−	2.11400i	−0.286561	−	0.0767839i
$759$	37.5338			1.36239
$760$	−4.70431	−	1.97773i	−0.170643	−	0.0717397i
$761$	−3.32178	+	1.91783i	−0.120414	+	0.0695213i	−0.558997	−	0.829169i	$-0.688814\pi$
$761$	−3.32178	+	1.91783i	−0.120414	+	0.0695213i	0.438583	+	0.898691i	$0.355481\pi$
$762$	18.3983	−	4.92981i	0.666500	−	0.178588i
$763$	21.5309	+	5.76918i	0.779470	+	0.208858i
$764$	12.4117	+	7.16590i	0.449040	+	0.259253i
$765$	11.2664	−	8.55094i	0.407336	−	0.309160i
$766$	−16.9649	−	9.79469i	−0.612967	−	0.353896i
$767$	17.4329	−	17.4329i	0.629465	−	0.629465i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	−10.5180	+	6.07259i	−0.379290	+	0.218983i	−0.677509	−	0.735514i	$-0.736941\pi$
$769$	−10.5180	+	6.07259i	−0.379290	+	0.218983i	0.298219	+	0.954497i	$0.403607\pi$
$770$	8.99989	−	65.6816i	0.324334	−	2.36700i
$771$			6.68742i			0.240841i
$772$	−2.08129	+	7.76749i	−0.0749073	+	0.279558i
$773$	−8.96410	−	8.96410i	−0.322416	−	0.322416i	0.527277	−	0.849693i	$-0.323213\pi$
$773$	−8.96410	−	8.96410i	−0.322416	−	0.322416i	−0.849693	+	0.527277i	$0.823213\pi$
$774$	−6.29665			−0.226328
$775$	25.7484	−	10.5840i	0.924909	−	0.380189i
$776$	−3.51395			−0.126144
$777$	−11.8659	−	11.8659i	−0.425686	−	0.425686i
$778$	6.67022	−	24.8936i	0.239139	−	0.892478i
$779$			18.9558i			0.679161i
$780$	0.937402	−	6.84120i	0.0335644	−	0.244954i
$781$	−67.9091	+	39.2073i	−2.42998	+	1.40295i
$782$	10.8655	−	40.5504i	0.388548	−	1.45008i
$783$	1.95080	−	1.95080i	0.0697160	−	0.0697160i
$784$	17.7400	+	10.2422i	0.633570	+	0.365792i
$785$	14.4532	−	10.9697i	0.515857	−	0.391525i
$786$	−7.26550	−	4.19474i	−0.259152	−	0.149621i
$787$	31.4182	+	8.41848i	1.11994	+	0.300086i	0.770858	−	0.637007i	$-0.219828\pi$
$787$	31.4182	+	8.41848i	1.11994	+	0.300086i	0.349079	+	0.937093i	$0.386494\pi$
$788$	−1.74398	+	0.467297i	−0.0621266	+	0.0166468i
$789$	−8.43409	+	4.86943i	−0.300262	+	0.173356i
$790$	−7.83943	−	3.29576i	−0.278915	−	0.117258i
$791$	−9.18884			−0.326717
$792$	−5.46259	−	1.46370i	−0.194105	−	0.0520102i
$793$	1.61333	+	6.02102i	0.0572910	+	0.213813i
$794$	25.1952	−	14.5465i	0.894145	−	0.516235i
$795$	15.6685	+	2.14695i	0.555704	+	0.0761443i
$796$	4.31825	+	2.49314i	0.153056	+	0.0883671i
$797$	−8.09875	−	30.2250i	−0.286873	−	1.07062i	−0.947460	−	0.319874i	$-0.896359\pi$
$797$	−8.09875	−	30.2250i	−0.286873	−	1.07062i	0.660588	−	0.750749i	$-0.270307\pi$
$798$	8.46018	+	8.46018i	0.299487	+	0.299487i
$799$	8.20570	+	14.2127i	0.290297	+	0.502809i
$800$	−2.45418	−	4.35626i	−0.0867682	−	0.154017i
$801$	−1.70968	−	0.987087i	−0.0604087	−	0.0348770i
$802$	−13.1884	+	13.1884i	−0.465700	+	0.465700i
$803$	−92.2547	−	24.7196i	−3.25560	−	0.872335i
$804$	−4.95313			−0.174683
$805$	−29.3943	−	72.0365i	−1.03601	−	2.53895i
$806$	−17.0284	+	2.37801i	−0.599799	+	0.0837617i
$807$	18.8157	+	18.8157i	0.662342	+	0.662342i
$808$	9.61581	−	9.61581i	0.338283	−	0.338283i
$809$	21.8797	+	37.8968i	0.769251	+	1.33238i	0.937970	+	0.346717i	$0.112704\pi$
$809$	21.8797	+	37.8968i	0.769251	+	1.33238i	−0.168719	+	0.985664i	$0.553963\pi$
$810$	−2.06131	−	0.866592i	−0.0724272	−	0.0304490i
$811$	20.4349	−	35.3942i	0.717566	−	1.24286i	−0.244396	−	0.969675i	$-0.578590\pi$
$811$	20.4349	−	35.3942i	0.717566	−	1.24286i	0.961962	−	0.273185i	$-0.0880770\pi$
$812$	−13.9706	−	3.74341i	−0.490271	−	0.131368i
$813$	−6.23162	−	1.66976i	−0.218552	−	0.0585609i
$814$		−	18.1020i		−	0.634476i
$815$	18.8360	+	24.8176i	0.659798	+	0.869322i
$816$	−3.16267	+	5.47791i	−0.110716	+	0.191765i
$817$	3.71927	+	13.8805i	0.130121	+	0.485617i
$818$	6.35589	−	23.7205i	0.222229	−	0.829369i
$819$	−8.09467	+	14.0204i	−0.282851	+	0.489912i
$820$	−11.3839	+	14.6749i	−0.397544	+	0.512469i
$821$			17.4622i			0.609436i	0.952443	+	0.304718i	$0.0985622\pi$
$821$			17.4622i			0.609436i	−0.952443	+	0.304718i	$0.901438\pi$
$822$	−4.92315	−	4.92315i	−0.171715	−	0.171715i
$823$	5.16953	−	19.2929i	0.180198	−	0.672509i	−0.815409	−	0.578885i	$-0.803488\pi$
$823$	5.16953	−	19.2929i	0.180198	−	0.672509i	0.995608	−	0.0936245i	$-0.0298453\pi$
$824$	−4.51649	−	2.60760i	−0.157339	−	0.0908399i
$825$	24.6359	−	13.8791i	0.857713	−	0.483207i
$826$	−20.9272	+	36.2469i	−0.728150	+	1.26119i
$827$	7.89604	+	29.4684i	0.274572	+	1.02472i	0.956127	+	0.292951i	$0.0946372\pi$
$827$	7.89604	+	29.4684i	0.274572	+	1.02472i	−0.681555	+	0.731767i	$0.738696\pi$
$828$	−6.41079	+	1.71777i	−0.222790	+	0.0596965i
$829$	−0.512710			−0.0178072			−0.00890359	−	0.999960i	$-0.502834\pi$
$829$	−0.512710			−0.0178072			−0.00890359	+	0.999960i	$0.502834\pi$
$830$	10.8567	−	13.9953i	0.376842	−	0.485783i
$831$	8.13380	+	14.0881i	0.282158	+	0.488712i
$832$	0.799250	+	2.98284i	0.0277090	+	0.103411i
$833$	91.6202	+	91.6202i	3.17445	+	3.17445i
$834$	2.28337	−	1.31831i	0.0790668	−	0.0456492i
$835$	8.54753	−	20.3315i	0.295800	−	0.703602i
$836$			12.9064i			0.446379i
$837$	−0.683370	+	5.52567i	−0.0236207	+	0.190995i
$838$	−0.189264	+	0.189264i	−0.00653800	+	0.00653800i
$839$		−	4.47058i		−	0.154341i	−0.997018	−	0.0771707i	$-0.975411\pi$
$839$		−	4.47058i		−	0.154341i	0.997018	−	0.0771707i	$-0.0245887\pi$
$840$	1.46879	+	11.6303i	0.0506779	+	0.401284i
$841$	−21.3887			−0.737543
$842$	−16.8876	+	4.52503i	−0.581986	+	0.155943i
$843$	1.66815	−	6.22564i	0.0574543	−	0.214422i
$844$	5.77754	−	3.33567i	0.198871	−	0.114818i
$845$	2.92625	+	7.17137i	0.100666	+	0.246703i
$846$	1.29727	−	2.24694i	0.0446012	−	0.0772515i
$847$	−106.253	+	28.4703i	−3.65089	+	0.978252i
$848$	−6.83165	+	1.83053i	−0.234600	+	0.0628608i
$849$	3.06229	+	5.30404i	0.105097	+	0.182034i
$850$	−7.86283	−	30.6337i	−0.269693	−	1.05073i
$851$	−10.6221	−	18.3980i	−0.364121	−	0.630676i
$852$	9.80455	−	9.80455i	0.335898	−	0.335898i
$853$	37.2729	−	37.2729i	1.27620	−	1.27620i	0.333422	−	0.942778i	$-0.391797\pi$
$853$	37.2729	−	37.2729i	1.27620	−	1.27620i	0.942778	−	0.333422i	$-0.108203\pi$
$854$	−5.29119	−	9.16460i	−0.181061	−	0.313606i
$855$	−0.692773	+	5.05589i	−0.0236924	+	0.172908i
$856$	3.13455	+	5.42920i	0.107137	+	0.185566i
$857$	−19.6911	+	5.27622i	−0.672636	+	0.180232i	−0.578942	−	0.815369i	$-0.696534\pi$
$857$	−19.6911	+	5.27622i	−0.672636	+	0.180232i	−0.0936942	+	0.995601i	$0.529868\pi$
$858$	−16.8688	+	4.51999i	−0.575893	+	0.154310i
$859$	8.65773	−	14.9956i	0.295398	−	0.511644i	−0.679679	−	0.733509i	$-0.737881\pi$
$859$	8.65773	−	14.9956i	0.295398	−	0.511644i	0.975077	+	0.221865i	$0.0712144\pi$
$860$	−5.45663	+	12.9794i	−0.186070	+	0.442593i
$861$	37.7106	−	21.7722i	1.28517	−	0.741996i
$862$	−4.30293	+	16.0588i	−0.146559	+	0.546964i
$863$	−55.1442	+	14.7759i	−1.87713	+	0.502976i	−0.877402	+	0.479757i	$0.840725\pi$
$863$	−55.1442	+	14.7759i	−1.87713	+	0.502976i	−0.999730	+	0.0232192i	$0.992608\pi$
$864$	1.00000			0.0340207
$865$	0.680975	−	0.0859999i	0.0231539	−	0.00292409i
$866$		−	11.2281i		−	0.381548i
$867$	−16.2705	+	16.2705i	−0.552574	+	0.552574i
$868$	26.8788	−	11.3817i	0.912327	−	0.386319i
$869$			21.5078i			0.729601i
$870$	−2.33067	−	5.71176i	−0.0790170	−	0.193647i
$871$	−13.2464	+	7.64779i	−0.448836	+	0.259136i
$872$	−3.00649	−	3.00649i	−0.101813	−	0.101813i
$873$	0.909478	+	3.39422i	0.0307812	+	0.114877i
$874$	7.57337	+	13.1175i	0.256173	+	0.443705i
$875$	−45.9307	−	36.4131i	−1.55274	−	1.23099i
$876$	16.8885			0.570608
$877$	−28.3196	+	7.58822i	−0.956286	+	0.256236i	−0.703028	−	0.711163i	$-0.748169\pi$
$877$	−28.3196	+	7.58822i	−0.956286	+	0.256236i	−0.253258	+	0.967399i	$0.581502\pi$
$878$	−1.57007	−	5.85957i	−0.0529872	−	0.197751i
$879$	−8.89253	+	15.4023i	−0.299938	+	0.519507i
$880$	−7.75098	+	9.99169i	−0.261285	+	0.336820i
$881$	22.9399	+	13.2444i	0.772865	+	0.446214i	0.833896	−	0.551922i	$-0.186105\pi$
$881$	22.9399	+	13.2444i	0.772865	+	0.446214i	−0.0610306	+	0.998136i	$0.519439\pi$
$882$	5.30174	−	19.7864i	0.178519	−	0.666242i
$883$	16.2929	+	16.2929i	0.548300	+	0.548300i	0.925949	−	0.377649i	$-0.123267\pi$
$883$	16.2929	+	16.2929i	0.548300	+	0.548300i	−0.377649	+	0.925949i	$0.623267\pi$
$884$			19.5331i			0.656968i
$885$	−17.7112	+	2.23673i	−0.595354	+	0.0751869i
$886$	−3.71257	+	6.43035i	−0.124726	+	0.216032i
$887$	8.11106	−	30.2709i	0.272343	−	1.01640i	−0.685258	−	0.728300i	$-0.740311\pi$
$887$	8.11106	−	30.2709i	0.272343	−	1.01640i	0.957601	−	0.288097i	$-0.0930226\pi$
$888$	0.828455	+	3.09183i	0.0278011	+	0.103755i
$889$	−49.9283	+	86.4783i	−1.67454	+	2.90039i
$890$	−3.51630	+	2.66880i	−0.117867	+	0.0894582i
$891$			5.65529i			0.189459i
$892$	−24.0497	−	6.44409i	−0.805243	−	0.215764i
$893$	−5.71949	−	1.53253i	−0.191395	−	0.0512842i
$894$	0.672654	−	1.16507i	0.0224969	−	0.0389658i
$895$	3.01934	−	1.23203i	0.100925	−	0.0411823i
$896$	−2.62128	−	4.54018i	−0.0875707	−	0.151677i
$897$	−14.4924	+	14.4924i	−0.483886	+	0.483886i
$898$	−7.79313	−	7.79313i	−0.260060	−	0.260060i
$899$	−12.1126	+	9.44636i	−0.403978	+	0.315054i
$900$	−3.57264	+	3.49804i	−0.119088	+	0.116601i
$901$	−44.7369			−1.49040
$902$	45.3721	+	12.1574i	1.51073	+	0.404798i
$903$	23.3420	−	23.3420i	0.776772	−	0.776772i
$904$	1.51792	+	0.876371i	0.0504852	+	0.0291477i
$905$	−2.77907	+	3.58247i	−0.0923795	+	0.119085i
$906$	0.461434	+	0.799227i	0.0153301	+	0.0265525i
$907$	19.7283	+	19.7283i	0.655066	+	0.655066i	0.954208	−	0.299142i	$-0.0967006\pi$
$907$	19.7283	+	19.7283i	0.655066	+	0.655066i	−0.299142	+	0.954208i	$0.596701\pi$
$908$	5.90296	+	22.0302i	0.195897	+	0.731096i
$909$	−11.7769	−	6.79940i	−0.390616	−	0.225522i
$910$	21.8856	+	28.8356i	0.725502	+	0.955891i
$911$	6.65832	−	3.84418i	0.220600	−	0.127363i	−0.385628	−	0.922654i	$-0.626015\pi$
$911$	6.65832	−	3.84418i	0.220600	−	0.127363i	0.606228	+	0.795291i	$0.292682\pi$
$912$	−0.590674	−	2.20443i	−0.0195592	−	0.0729958i
$913$	−43.2709	−	11.5944i	−1.43206	−	0.383719i
$914$	28.8135			0.953065
$915$	1.74926	−	4.16087i	0.0578288	−	0.137554i
$916$	9.45788	−	5.46051i	0.312497	−	0.180420i
$917$	42.4836	−	11.3834i	1.40293	−	0.375915i
$918$	6.10981	+	1.63712i	0.201654	+	0.0540330i
$919$	10.0471	+	5.80068i	0.331422	+	0.191347i	0.656472	−	0.754350i	$-0.272048\pi$
$919$	10.0471	+	5.80068i	0.331422	+	0.191347i	−0.325050	+	0.945697i	$0.605381\pi$
$920$	−2.01469	+	14.7033i	−0.0664222	+	0.484752i
$921$	−19.1112	−	11.0339i	−0.629735	−	0.363578i
$922$	21.9033	−	21.9033i	0.721346	−	0.721346i
$923$	11.0822	−	41.3593i	0.364774	−	1.36136i
$924$	25.6761	−	14.8241i	0.844680	−	0.487676i
$925$	−13.7751	−	8.14804i	−0.452923	−	0.267906i
$926$		−	4.23010i		−	0.139010i
$927$	−1.34979	+	5.03749i	−0.0443329	+	0.165453i
$928$	1.95080	+	1.95080i	0.0640382	+	0.0640382i
$929$	23.9393			0.785423			0.392712	−	0.919662i	$-0.371537\pi$
$929$	23.9393			0.785423			0.392712	+	0.919662i	$0.371537\pi$
$930$	10.7979	+	6.19714i	0.354078	+	0.203212i
$931$	−46.7492			−1.53214
$932$	14.5803	+	14.5803i	0.477593	+	0.477593i
$933$	6.11009	−	22.8032i	0.200035	−	0.746542i
$934$			4.28027i			0.140055i
$935$	−63.7146	+	48.3581i	−2.08369	+	1.58148i
$936$	2.67434	−	1.54403i	0.0874136	−	0.0504683i
$937$	7.42634	−	27.7155i	0.242608	−	0.905425i	−0.731963	−	0.681345i	$-0.761396\pi$
$937$	7.42634	−	27.7155i	0.242608	−	0.905425i	0.974571	−	0.224080i	$-0.0719378\pi$
$938$	18.3615	−	18.3615i	0.599523	−	0.599523i
$939$	−14.1836	−	8.18891i	−0.462865	−	0.267235i
$940$	−3.50745	−	4.62127i	−0.114400	−	0.150729i
$941$	9.07706	+	5.24064i	0.295904	+	0.170840i	0.640601	−	0.767874i	$-0.278685\pi$
$941$	9.07706	+	5.24064i	0.295904	+	0.170840i	−0.344698	+	0.938714i	$0.612019\pi$
$942$	7.83804	+	2.10020i	0.255377	+	0.0684281i
$943$	53.2478	−	14.2677i	1.73399	−	0.464620i
$944$	6.91399	−	3.99179i	0.225031	−	0.129922i
$945$	10.8539	−	4.42889i	0.353077	−	0.144072i
$946$	35.6094			1.15776
$947$	−23.1770	−	6.21026i	−0.753152	−	0.201806i	−0.138236	−	0.990399i	$-0.544143\pi$
$947$	−23.1770	−	6.21026i	−0.753152	−	0.201806i	−0.614916	+	0.788593i	$0.710810\pi$
$948$	−0.984321	−	3.67354i	−0.0319693	−	0.119311i
$949$	45.1655	−	26.0763i	1.46613	−	0.846473i
$950$	9.82142	+	5.80942i	0.318649	+	0.188482i
$951$	18.4358	+	10.6439i	0.597823	+	0.345153i
$952$	−8.58268	−	32.0310i	−0.278166	−	1.03813i
$953$	−10.4864	−	10.4864i	−0.339687	−	0.339687i	0.516562	−	0.856250i	$-0.327211\pi$
$953$	−10.4864	−	10.4864i	−0.339687	−	0.339687i	−0.856250	+	0.516562i	$0.827211\pi$
$954$	3.53632	+	6.12509i	0.114493	+	0.198307i
$955$	−25.3212	−	19.6428i	−0.819376	−	0.635625i
$956$	0.123487	+	0.0712953i	0.00399385	+	0.00230585i
$957$	−11.0323	+	11.0323i	−0.356625	+	0.356625i
$958$	1.69729	+	0.454788i	0.0548371	+	0.0146935i
$959$	36.5007			1.17867
$960$	0.866592	−	2.06131i	0.0279691	−	0.0665286i
$961$	7.55215	−	30.0660i	0.243618	−	0.969871i
$962$	6.98946	+	6.98946i	0.225349	+	0.225349i
$963$	4.43292	−	4.43292i	0.142849	−	0.142849i
$964$	−4.69592	−	8.13357i	−0.151245	−	0.261965i
$965$	6.96870	−	16.5761i	0.224330	−	0.533602i
$966$	17.3972	−	30.1329i	0.559747	−	0.969511i
$967$	38.3470	+	10.2750i	1.23316	+	0.330423i	0.815807	−	0.578324i	$-0.196293\pi$
$967$	38.3470	+	10.2750i	1.23316	+	0.330423i	0.417348	+	0.908747i	$0.362960\pi$
$968$	20.2674	+	5.43062i	0.651418	+	0.174547i
$969$		−	14.4356i		−	0.463739i
$970$	7.78469	+	1.06668i	0.249951	+	0.0342491i
$971$	−18.6410	+	32.2872i	−0.598218	+	1.03614i	0.394866	+	0.918739i	$0.370791\pi$
$971$	−18.6410	+	32.2872i	−0.598218	+	1.03614i	−0.993084	+	0.117406i	$0.962542\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	−3.57755	+	13.3516i	−0.114691	+	0.428032i
$974$	0.179604	−	0.311083i	0.00575488	−	0.00996775i
$975$	−4.15338	+	14.8712i	−0.133015	+	0.476260i
$976$			2.01855i			0.0646123i
$977$	7.79216	+	7.79216i	0.249293	+	0.249293i	0.820681	−	0.571387i	$-0.193595\pi$
$977$	7.79216	+	7.79216i	0.249293	+	0.249293i	−0.571387	+	0.820681i	$0.693595\pi$
$978$	−3.60625	+	13.4587i	−0.115315	+	0.430362i
$979$	9.66876	+	5.58226i	0.309015	+	0.178410i
$980$	−36.1915	−	28.0753i	−1.15609	−	0.896832i
$981$	−2.12591	+	3.68218i	−0.0678751	+	0.117563i
$982$	−4.06032	−	15.1533i	−0.129570	−	0.483562i
$983$	−5.29457	+	1.41868i	−0.168871	+	0.0452487i	−0.342264	−	0.939604i	$-0.611194\pi$
$983$	−5.29457	+	1.41868i	−0.168871	+	0.0452487i	0.173393	+	0.984853i	$0.444527\pi$
$984$	−8.30597			−0.264785
$985$	4.00540	−	0.505839i	0.127623	−	0.0161174i
$986$	8.72533	+	15.1127i	0.277871	+	0.481287i
$987$	3.52047	+	13.1386i	0.112058	+	0.418205i
$988$	−4.98337	−	4.98337i	−0.158542	−	0.158542i
$989$	36.1916	−	20.8952i	1.15083	−	0.664430i
$990$	11.6573	+	4.90083i	0.370494	+	0.155759i
$991$			51.2575i			1.62825i	0.580691	+	0.814124i	$0.302783\pi$
$991$			51.2575i			1.62825i	−0.580691	+	0.814124i	$0.697217\pi$
$992$	−5.52567	−	0.683370i	−0.175440	−	0.0216970i
$993$	6.56813	−	6.56813i	0.208433	−	0.208433i
$994$			72.6918i			2.30564i
$995$	−8.80970	−	6.83406i	−0.279286	−	0.216654i
$996$	7.92131			0.250996
$997$	32.2299	−	8.63597i	1.02073	−	0.273504i	0.290624	−	0.956837i	$-0.406137\pi$
$997$	32.2299	−	8.63597i	1.02073	−	0.273504i	0.730106	+	0.683334i	$0.239470\pi$
$998$	1.54496	−	5.76588i	0.0489049	−	0.182516i
$999$	2.77206	−	1.60045i	0.0877042	−	0.0506360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.37.5	✓	64
5.3	odd	4		930.2.be.b.223.6	yes	64
31.26	odd	6		930.2.be.b.367.6	yes	64
155.88	even	12	inner	930.2.be.a.553.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.37.5	✓	64	1.1	even	1	trivial
930.2.be.a.553.5	yes	64	155.88	even	12	inner
930.2.be.b.223.6	yes	64	5.3	odd	4
930.2.be.b.367.6	yes	64	31.26	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(0.303557 - 2.21537i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.35687 + 5.06392i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(0.303557 - 2.21537i) q^{5} +(0.866025 - 0.500000i) q^{6} +(-1.35687 + 5.06392i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.78115 + 1.35185i) q^{10} +(4.89763 + 2.82765i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-2.98284 + 0.799250i) q^{13} +(4.54018 - 2.62128i) q^{14} +(2.06131 + 0.866592i) q^{15} -1.00000 q^{16} +(-6.10981 - 1.63712i) q^{17} +(0.258819 + 0.965926i) q^{18} +(1.97643 - 1.14109i) q^{19} +(2.21537 + 0.303557i) q^{20} +(-4.54018 - 2.62128i) q^{21} +(-1.46370 - 5.46259i) q^{22} +(-4.69302 - 4.69302i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.81571 - 1.34498i) q^{25} +(2.67434 + 1.54403i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-5.06392 - 1.35687i) q^{28} +2.75885 q^{29} +(-0.844796 - 2.07034i) q^{30} +(-4.39045 + 3.42402i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.99889 + 3.99889i) q^{33} +(3.16267 + 5.47791i) q^{34} +(10.8065 + 4.54316i) q^{35} +(0.500000 - 0.866025i) q^{36} +(3.09183 + 0.828455i) q^{37} +(-2.20443 - 0.590674i) q^{38} -3.08806i q^{39} +(-1.35185 - 1.78115i) q^{40} +(-4.15298 + 7.19318i) q^{41} +(1.35687 + 5.06392i) q^{42} +(-1.62969 + 6.08210i) q^{43} +(-2.82765 + 4.89763i) q^{44} +(-1.37057 + 1.76679i) q^{45} +6.63694i q^{46} +(-1.83462 - 1.83462i) q^{47} +(0.258819 - 0.965926i) q^{48} +(-17.7400 - 10.2422i) q^{49} +(2.45418 + 4.35626i) q^{50} +(3.16267 - 5.47791i) q^{51} +(-0.799250 - 2.98284i) q^{52} +(6.83165 - 1.83053i) q^{53} -1.00000 q^{54} +(7.75098 - 9.99169i) q^{55} +(2.62128 + 4.54018i) q^{56} +(0.590674 + 2.20443i) q^{57} +(-1.95080 - 1.95080i) q^{58} +(-6.91399 + 3.99179i) q^{59} +(-0.866592 + 2.06131i) q^{60} -2.01855i q^{61} +(5.52567 + 0.683370i) q^{62} +(3.70704 - 3.70704i) q^{63} -1.00000i q^{64} +(0.865172 + 6.85071i) q^{65} +5.65529 q^{66} +(4.78436 - 1.28196i) q^{67} +(1.63712 - 6.10981i) q^{68} +(5.74776 - 3.31847i) q^{69} +(-4.42889 - 10.8539i) q^{70} +(-6.93286 + 12.0081i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-16.3130 + 4.37105i) q^{73} +(-1.60045 - 2.77206i) q^{74} +(2.54555 - 4.30351i) q^{75} +(1.14109 + 1.97643i) q^{76} +(-20.9644 + 20.9644i) q^{77} +(-2.18359 + 2.18359i) q^{78} +(1.90156 + 3.29360i) q^{79} +(-0.303557 + 2.21537i) q^{80} +(0.500000 + 0.866025i) q^{81} +(8.02295 - 2.14974i) q^{82} +(-7.65140 + 2.05019i) q^{83} +(2.62128 - 4.54018i) q^{84} +(-5.48149 + 13.0385i) q^{85} +(5.45306 - 3.14833i) q^{86} +(-0.714043 + 2.66484i) q^{87} +(5.46259 - 1.46370i) q^{88} +1.97417 q^{89} +(2.21845 - 0.280166i) q^{90} -16.1893i q^{91} +(4.69302 - 4.69302i) q^{92} +(-2.17102 - 5.12705i) q^{93} +2.59455i q^{94} +(-1.92798 - 4.72491i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-2.48474 - 2.48474i) q^{97} +(5.30174 + 19.7864i) q^{98} +(-2.82765 - 4.89763i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

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