LMFDB - Embedded newform 930.2.be.b.37.7

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			37.7
Character	$\chi$	$=$	930.37
Dual form			930.2.be.b.553.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(2.10363 - 0.758108i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-1.03988 + 3.88090i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(2.10363 - 0.758108i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-1.03988 + 3.88090i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.02356 - 0.951430i) q^{10} +(0.353977 + 0.204368i) q^{11} +(0.965926 + 0.258819i) q^{12} +(0.306524 - 0.0821329i) q^{13} +(3.47952 - 2.00890i) q^{14} +(-0.187816 - 2.22817i) q^{15} -1.00000 q^{16} +(4.10959 + 1.10116i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-2.92256 + 1.68734i) q^{19} +(0.758108 + 2.10363i) q^{20} +(3.47952 + 2.00890i) q^{21} +(-0.105789 - 0.394810i) q^{22} +(1.19975 + 1.19975i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.85054 - 3.18956i) q^{25} +(-0.274822 - 0.158668i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-3.88090 - 1.03988i) q^{28} +4.50807 q^{29} +(-1.44275 + 1.70836i) q^{30} +(3.52090 + 4.31315i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.289021 - 0.289021i) q^{33} +(-2.12728 - 3.68456i) q^{34} +(0.754605 + 8.95232i) q^{35} +(0.500000 - 0.866025i) q^{36} +(6.47723 + 1.73557i) q^{37} +(3.25969 + 0.873433i) q^{38} -0.317337i q^{39} +(0.951430 - 2.02356i) q^{40} +(-1.20690 + 2.09041i) q^{41} +(-1.03988 - 3.88090i) q^{42} +(0.287253 - 1.07204i) q^{43} +(-0.204368 + 0.353977i) q^{44} +(-2.20085 - 0.395276i) q^{45} -1.69670i q^{46} +(5.17767 + 5.17767i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(-7.91781 - 4.57135i) q^{49} +(-4.97811 - 0.467386i) q^{50} +(2.12728 - 3.68456i) q^{51} +(0.0821329 + 0.306524i) q^{52} +(-1.63249 + 0.437424i) q^{53} +1.00000 q^{54} +(0.899570 + 0.161564i) q^{55} +(2.00890 + 3.47952i) q^{56} +(0.873433 + 3.25969i) q^{57} +(-3.18769 - 3.18769i) q^{58} +(-7.87109 + 4.54438i) q^{59} +(2.22817 - 0.187816i) q^{60} -4.44745i q^{61} +(0.560205 - 5.53951i) q^{62} +(2.84101 - 2.84101i) q^{63} -1.00000i q^{64} +(0.582548 - 0.405156i) q^{65} -0.408737 q^{66} +(-1.22930 + 0.329390i) q^{67} +(-1.10116 + 4.10959i) q^{68} +(1.46939 - 0.848350i) q^{69} +(5.79666 - 6.86383i) q^{70} +(4.28466 - 7.42125i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(6.70182 - 1.79575i) q^{73} +(-3.35286 - 5.80733i) q^{74} +(-2.08429 - 4.54486i) q^{75} +(-1.68734 - 2.92256i) q^{76} +(-1.16123 + 1.16123i) q^{77} +(-0.224391 + 0.224391i) q^{78} +(-8.20268 - 14.2075i) q^{79} +(-2.10363 + 0.758108i) q^{80} +(0.500000 + 0.866025i) q^{81} +(2.33155 - 0.624738i) q^{82} +(9.88774 - 2.64941i) q^{83} +(-2.00890 + 3.47952i) q^{84} +(9.47987 - 0.799073i) q^{85} +(-0.961166 + 0.554930i) q^{86} +(1.16678 - 4.35446i) q^{87} +(0.394810 - 0.105789i) q^{88} -1.41670 q^{89} +(1.27674 + 1.83574i) q^{90} +1.27500i q^{91} +(-1.19975 + 1.19975i) q^{92} +(5.07746 - 2.28460i) q^{93} -7.32233i q^{94} +(-4.86881 + 5.76517i) q^{95} +(0.866025 - 0.500000i) q^{96} +(1.71748 + 1.71748i) q^{97} +(2.36631 + 8.83117i) q^{98} +(-0.204368 - 0.353977i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$			1.00000i			0.500000i
$5$	2.10363	−	0.758108i	0.940773	−	0.339036i
$5$	2.10363	−	0.758108i	0.940773	−	0.339036i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−1.03988	+	3.88090i	−0.393039	+	1.46684i	0.432056	+	0.901847i	$0.357788\pi$
$7$	−1.03988	+	3.88090i	−0.393039	+	1.46684i	−0.825095	+	0.564994i	$0.808879\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−2.02356	−	0.951430i	−0.639905	−	0.300869i
$11$	0.353977	+	0.204368i	0.106728	+	0.0616194i	0.552414	−	0.833570i	$-0.313707\pi$
$11$	0.353977	+	0.204368i	0.106728	+	0.0616194i	−0.445686	+	0.895189i	$0.647040\pi$
$12$	0.965926	+	0.258819i	0.278839	+	0.0747146i
$13$	0.306524	−	0.0821329i	0.0850145	−	0.0227796i	−0.216061	−	0.976380i	$-0.569321\pi$
$13$	0.306524	−	0.0821329i	0.0850145	−	0.0227796i	0.301076	+	0.953600i	$0.402654\pi$
$14$	3.47952	−	2.00890i	0.929940	−	0.536901i
$15$	−0.187816	−	2.22817i	−0.0484938	−	0.575310i
$16$	−1.00000			−0.250000
$17$	4.10959	+	1.10116i	0.996722	+	0.267071i	0.720072	−	0.693900i	$-0.244109\pi$
$17$	4.10959	+	1.10116i	0.996722	+	0.267071i	0.276650	+	0.960971i	$0.410776\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	−2.92256	+	1.68734i	−0.670482	+	0.387103i	−0.796259	−	0.604956i	$-0.793191\pi$
$19$	−2.92256	+	1.68734i	−0.670482	+	0.387103i	0.125777	+	0.992058i	$0.459858\pi$
$20$	0.758108	+	2.10363i	0.169518	+	0.470387i
$21$	3.47952	+	2.00890i	0.759292	+	0.438378i
$22$	−0.105789	−	0.394810i	−0.0225543	−	0.0841737i
$23$	1.19975	+	1.19975i	0.250165	+	0.250165i	0.821038	−	0.570873i	$-0.193395\pi$
$23$	1.19975	+	1.19975i	0.250165	+	0.250165i	−0.570873	+	0.821038i	$0.693395\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	3.85054	−	3.18956i	0.770109	−	0.637912i
$26$	−0.274822	−	0.158668i	−0.0538970	−	0.0311175i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−3.88090	−	1.03988i	−0.733420	−	0.196519i
$29$	4.50807			0.837128			0.418564	−	0.908187i	$-0.362534\pi$
$29$	4.50807			0.837128			0.418564	+	0.908187i	$0.362534\pi$
$30$	−1.44275	+	1.70836i	−0.263408	+	0.311902i
$31$	3.52090	+	4.31315i	0.632372	+	0.774665i
$31$	3.52090	+	4.31315i	0.632372	+	0.774665i
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.289021	−	0.289021i	0.0503120	−	0.0503120i
$34$	−2.12728	−	3.68456i	−0.364826	−	0.631896i
$35$	0.754605	+	8.95232i	0.127552	+	1.51322i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	6.47723	+	1.73557i	1.06485	+	0.285326i	0.748376	−	0.663275i	$-0.230834\pi$
$37$	6.47723	+	1.73557i	1.06485	+	0.285326i	0.316475	+	0.948601i	$0.397501\pi$
$38$	3.25969	+	0.873433i	0.528792	+	0.141689i
$39$		−	0.317337i		−	0.0508146i
$40$	0.951430	−	2.02356i	0.150434	−	0.319952i
$41$	−1.20690	+	2.09041i	−0.188486	+	0.326468i	−0.944746	−	0.327804i	$-0.893691\pi$
$41$	−1.20690	+	2.09041i	−0.188486	+	0.326468i	0.756259	+	0.654272i	$0.227025\pi$
$42$	−1.03988	−	3.88090i	−0.160457	−	0.598835i
$43$	0.287253	−	1.07204i	0.0438056	−	0.163485i	−0.940558	−	0.339633i	$-0.889697\pi$
$43$	0.287253	−	1.07204i	0.0438056	−	0.163485i	0.984364	+	0.176148i	$0.0563638\pi$
$44$	−0.204368	+	0.353977i	−0.0308097	+	0.0533640i
$45$	−2.20085	−	0.395276i	−0.328084	−	0.0589242i
$46$		−	1.69670i		−	0.250165i
$47$	5.17767	+	5.17767i	0.755241	+	0.755241i	0.975452	−	0.220211i	$-0.0706746\pi$
$47$	5.17767	+	5.17767i	0.755241	+	0.755241i	−0.220211	+	0.975452i	$0.570675\pi$
$48$	−0.258819	+	0.965926i	−0.0373573	+	0.139419i
$49$	−7.91781	−	4.57135i	−1.13112	−	0.653050i
$50$	−4.97811	−	0.467386i	−0.704011	−	0.0660983i
$51$	2.12728	−	3.68456i	0.297879	−	0.515941i
$52$	0.0821329	+	0.306524i	0.0113898	+	0.0425072i
$53$	−1.63249	+	0.437424i	−0.224240	+	0.0600848i	−0.369189	−	0.929354i	$-0.620365\pi$
$53$	−1.63249	+	0.437424i	−0.224240	+	0.0600848i	0.144950	+	0.989439i	$0.453698\pi$
$54$	1.00000			0.136083
$55$	0.899570	+	0.161564i	0.121298	+	0.0217853i
$56$	2.00890	+	3.47952i	0.268450	+	0.464970i
$57$	0.873433	+	3.25969i	0.115689	+	0.431757i
$58$	−3.18769	−	3.18769i	−0.418564	−	0.418564i
$59$	−7.87109	+	4.54438i	−1.02473	+	0.591627i	−0.915470	−	0.402386i	$-0.868181\pi$
$59$	−7.87109	+	4.54438i	−1.02473	+	0.591627i	−0.109259	+	0.994013i	$0.534848\pi$
$60$	2.22817	−	0.187816i	0.287655	−	0.0242469i
$61$		−	4.44745i		−	0.569438i	−0.958611	−	0.284719i	$-0.908100\pi$
$61$		−	4.44745i		−	0.569438i	0.958611	−	0.284719i	$-0.0919002\pi$
$62$	0.560205	−	5.53951i	0.0711461	−	0.703518i
$63$	2.84101	−	2.84101i	0.357934	−	0.357934i
$64$		−	1.00000i		−	0.125000i
$65$	0.582548	−	0.405156i	0.0722562	−	0.0502534i
$66$	−0.408737			−0.0503120
$67$	−1.22930	+	0.329390i	−0.150183	+	0.0402414i	−0.333127	−	0.942882i	$-0.608104\pi$
$67$	−1.22930	+	0.329390i	−0.150183	+	0.0402414i	0.182944	+	0.983123i	$0.441437\pi$
$68$	−1.10116	+	4.10959i	−0.133535	+	0.498361i
$69$	1.46939	−	0.848350i	0.176893	−	0.102129i
$70$	5.79666	−	6.86383i	0.692834	−	0.820385i
$71$	4.28466	−	7.42125i	0.508496	−	0.880741i	−0.491456	−	0.870903i	$-0.663535\pi$
$71$	4.28466	−	7.42125i	0.508496	−	0.880741i	0.999952	−	0.00983806i	$-0.00313160\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	6.70182	−	1.79575i	0.784389	−	0.210176i	0.155670	−	0.987809i	$-0.450246\pi$
$73$	6.70182	−	1.79575i	0.784389	−	0.210176i	0.628719	+	0.777633i	$0.283580\pi$
$74$	−3.35286	−	5.80733i	−0.389762	−	0.675088i
$75$	−2.08429	−	4.54486i	−0.240673	−	0.524795i
$76$	−1.68734	−	2.92256i	−0.193551	−	0.335241i
$77$	−1.16123	+	1.16123i	−0.132334	+	0.132334i
$78$	−0.224391	+	0.224391i	−0.0254073	+	0.0254073i
$79$	−8.20268	−	14.2075i	−0.922874	−	1.59846i	−0.794945	−	0.606681i	$-0.792501\pi$
$79$	−8.20268	−	14.2075i	−0.922874	−	1.59846i	−0.127928	−	0.991783i	$-0.540833\pi$
$80$	−2.10363	+	0.758108i	−0.235193	+	0.0847590i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	2.33155	−	0.624738i	0.257477	−	0.0689908i
$83$	9.88774	−	2.64941i	1.08532	−	0.290811i	0.328547	−	0.944488i	$-0.393441\pi$
$83$	9.88774	−	2.64941i	1.08532	−	0.290811i	0.756774	+	0.653677i	$0.226775\pi$
$84$	−2.00890	+	3.47952i	−0.219189	+	0.379646i
$85$	9.47987	−	0.799073i	1.02824	−	0.0866717i
$86$	−0.961166	+	0.554930i	−0.103645	+	0.0598396i
$87$	1.16678	−	4.35446i	0.125091	−	0.466848i
$88$	0.394810	−	0.105789i	0.0420868	−	0.0112771i
$89$	−1.41670			−0.150170			−0.0750852	−	0.997177i	$-0.523923\pi$
$89$	−1.41670			−0.150170			−0.0750852	+	0.997177i	$0.523923\pi$
$90$	1.27674	+	1.83574i	0.134580	+	0.193504i
$91$			1.27500i			0.133656i
$92$	−1.19975	+	1.19975i	−0.125082	+	0.125082i
$93$	5.07746	−	2.28460i	0.526508	−	0.236902i
$94$		−	7.32233i		−	0.755241i
$95$	−4.86881	+	5.76517i	−0.499530	+	0.591494i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	1.71748	+	1.71748i	0.174384	+	0.174384i	0.788902	−	0.614519i	$-0.210650\pi$
$97$	1.71748	+	1.71748i	0.174384	+	0.174384i	−0.614519	+	0.788902i	$0.710650\pi$
$98$	2.36631	+	8.83117i	0.239033	+	0.892083i
$99$	−0.204368	−	0.353977i	−0.0205398	−	0.0355760i
$100$	3.18956	+	3.85054i	0.318956	+	0.385054i
$101$	−3.43434			−0.341730			−0.170865	−	0.985294i	$-0.554656\pi$
$101$	−3.43434			−0.341730			−0.170865	+	0.985294i	$0.554656\pi$
$102$	−4.10959	+	1.10116i	−0.406910	+	0.109031i
$103$	3.67990	+	13.7336i	0.362591	+	1.35321i	0.870657	+	0.491891i	$0.163694\pi$
$103$	3.67990	+	13.7336i	0.362591	+	1.35321i	−0.508066	+	0.861318i	$0.669639\pi$
$104$	0.158668	−	0.274822i	0.0155587	−	0.0269485i
$105$	8.84259	+	1.58814i	0.862948	+	0.154986i
$106$	1.46365	+	0.845039i	0.142162	+	0.0820774i
$107$	3.51291	−	13.1103i	0.339606	−	1.26742i	−0.559184	−	0.829044i	$-0.688885\pi$
$107$	3.51291	−	13.1103i	0.339606	−	1.26742i	0.898789	−	0.438381i	$-0.144448\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$		−	10.6829i		−	1.02324i	−0.859213	−	0.511619i	$-0.829046\pi$
$109$		−	10.6829i		−	1.02324i	0.859213	−	0.511619i	$-0.170954\pi$
$110$	−0.521849	−	0.750335i	−0.0497564	−	0.0715416i
$111$	3.35286	−	5.80733i	0.318240	−	0.551207i
$112$	1.03988	−	3.88090i	0.0982597	−	0.366710i
$113$	5.34622	+	19.9524i	0.502930	+	1.87696i	0.480083	+	0.877223i	$0.340607\pi$
$113$	5.34622	+	19.9524i	0.502930	+	1.87696i	0.0228475	+	0.999739i	$0.492727\pi$
$114$	1.68734	−	2.92256i	0.158034	−	0.273723i
$115$	3.43337	+	1.61429i	0.320163	+	0.150534i
$116$			4.50807i			0.418564i
$117$	−0.306524	−	0.0821329i	−0.0283382	−	0.00759319i
$118$	8.77906	+	2.35234i	0.808178	+	0.216551i
$119$	−8.54698	+	14.8038i	−0.783501	+	1.35706i
$120$	−1.70836	−	1.44275i	−0.155951	−	0.131704i
$121$	−5.41647	−	9.38160i	−0.492406	−	0.852872i
$122$	−3.14482	+	3.14482i	−0.284719	+	0.284719i
$123$	1.70682	+	1.70682i	0.153898	+	0.153898i
$124$	−4.31315	+	3.52090i	−0.387332	+	0.316186i
$125$	5.68210	−	9.62880i	0.508223	−	0.861226i
$126$	−4.01780			−0.357934
$127$	1.59480	+	0.427325i	0.141516	+	0.0379190i	0.328882	−	0.944371i	$-0.393328\pi$
$127$	1.59480	+	0.427325i	0.141516	+	0.0379190i	−0.187366	+	0.982290i	$0.559995\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−0.961166	−	0.554930i	−0.0846260	−	0.0488588i
$130$	−0.698412	−	0.125436i	−0.0612548	−	0.0110014i
$131$	3.32035	+	5.75101i	0.290100	+	0.502468i	0.973833	−	0.227264i	$-0.0729781\pi$
$131$	3.32035	+	5.75101i	0.290100	+	0.502468i	−0.683733	+	0.729732i	$0.739645\pi$
$132$	0.289021	+	0.289021i	0.0251560	+	0.0251560i
$133$	−3.50928	−	13.0968i	−0.304293	−	1.13564i
$134$	1.10216	+	0.636333i	0.0952122	+	0.0549708i
$135$	−0.951430	+	2.02356i	−0.0818861	+	0.174160i
$136$	3.68456	−	2.12728i	0.315948	−	0.182413i
$137$	−2.02906	−	7.57257i	−0.173355	−	0.646969i	−0.996826	−	0.0796106i	$-0.974632\pi$
$137$	−2.02906	−	7.57257i	−0.173355	−	0.646969i	0.823471	−	0.567358i	$-0.192034\pi$
$138$	−1.63889	−	0.439138i	−0.139511	−	0.0373820i
$139$	−15.0318			−1.27498			−0.637490	−	0.770458i	$-0.720027\pi$
$139$	−15.0318			−1.27498			−0.637490	+	0.770458i	$0.720027\pi$
$140$	−8.95232	+	0.754605i	−0.756609	+	0.0637758i
$141$	6.34133	−	3.66117i	0.534036	−	0.308326i
$142$	−8.27733	+	2.21790i	−0.694618	+	0.186122i
$143$	0.125288	+	0.0335707i	0.0104771	+	0.00280733i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	9.48333	−	3.41761i	0.787548	−	0.283817i
$146$	−6.00869	−	3.46912i	−0.497283	−	0.287106i
$147$	−6.46487	+	6.46487i	−0.533213	+	0.533213i
$148$	−1.73557	+	6.47723i	−0.142663	+	0.532425i
$149$	−6.64792	+	3.83818i	−0.544619	+	0.314436i	−0.746949	−	0.664882i	$-0.768482\pi$
$149$	−6.64792	+	3.83818i	−0.544619	+	0.314436i	0.202330	+	0.979317i	$0.435149\pi$
$150$	−1.73989	+	4.68751i	−0.142061	+	0.382734i
$151$		−	3.96530i		−	0.322691i	−0.986898	−	0.161346i	$-0.948417\pi$
$151$		−	3.96530i		−	0.322691i	0.986898	−	0.161346i	$-0.0515834\pi$
$152$	−0.873433	+	3.25969i	−0.0708447	+	0.264396i
$153$	−3.00843	−	3.00843i	−0.243217	−	0.243217i
$154$	1.64222			0.132334
$155$	10.6765	+	6.40406i	0.857558	+	0.514387i
$156$	0.317337			0.0254073
$157$	−5.84146	−	5.84146i	−0.466200	−	0.466200i	0.434481	−	0.900681i	$-0.356932\pi$
$157$	−5.84146	−	5.84146i	−0.466200	−	0.466200i	−0.900681	+	0.434481i	$0.856932\pi$
$158$	−4.24602	+	15.8464i	−0.337795	+	1.26067i
$159$			1.69008i			0.134032i
$160$	2.02356	+	0.951430i	0.159976	+	0.0752171i
$161$	−5.90370	+	3.40850i	−0.465276	+	0.268627i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−4.40689	+	4.40689i	−0.345175	+	0.345175i	−0.858309	−	0.513134i	$-0.828484\pi$
$163$	−4.40689	+	4.40689i	−0.345175	+	0.345175i	0.513134	+	0.858309i	$0.328484\pi$
$164$	−2.09041	−	1.20690i	−0.163234	−	0.0942431i
$165$	0.388885	−	0.827102i	0.0302746	−	0.0643898i
$166$	−8.86510	−	5.11827i	−0.688065	−	0.397255i
$167$	−14.0872	−	3.77465i	−1.09010	−	0.292091i	−0.331373	−	0.943500i	$-0.607512\pi$
$167$	−14.0872	−	3.77465i	−1.09010	−	0.292091i	−0.758727	+	0.651408i	$0.774178\pi$
$168$	3.88090	−	1.03988i	0.299418	−	0.0802287i
$169$	−11.1711	+	6.44965i	−0.859317	+	0.496127i
$170$	−7.26831	−	6.13825i	−0.557454	−	0.470782i
$171$	3.37468			0.258069
$172$	1.07204	+	0.287253i	0.0817424	+	0.0219028i
$173$	−1.78612	−	6.66588i	−0.135796	−	0.506798i	−0.999993	−	0.00364467i	$-0.998840\pi$
$173$	−1.78612	−	6.66588i	−0.135796	−	0.506798i	0.864197	−	0.503153i	$-0.167827\pi$
$174$	−3.90411	+	2.25404i	−0.295970	+	0.170878i
$175$	8.37424	+	18.2603i	0.633033	+	1.38035i
$176$	−0.353977	−	0.204368i	−0.0266820	−	0.0154049i
$177$	2.35234	+	8.77906i	0.176813	+	0.659875i
$178$	1.00176	+	1.00176i	0.0750852	+	0.0750852i
$179$	7.67030	+	13.2854i	0.573305	+	0.992994i	0.996223	+	0.0868260i	$0.0276724\pi$
$179$	7.67030	+	13.2854i	0.573305	+	0.992994i	−0.422918	+	0.906168i	$0.638994\pi$
$180$	0.395276	−	2.20085i	0.0294621	−	0.164042i
$181$	−4.98344	−	2.87719i	−0.370416	−	0.213860i	0.303224	−	0.952919i	$-0.401937\pi$
$181$	−4.98344	−	2.87719i	−0.370416	−	0.213860i	−0.673640	+	0.739059i	$0.735270\pi$
$182$	0.901558	−	0.901558i	0.0668279	−	0.0668279i
$183$	−4.29591	−	1.15108i	−0.317563	−	0.0850906i
$184$	1.69670			0.125082
$185$	14.9415	−	1.25944i	1.09852	−	0.0925959i
$186$	−5.20576	−	1.97485i	−0.381705	−	0.144803i
$187$	1.22966	+	1.22966i	0.0899214	+	0.0899214i
$188$	−5.17767	+	5.17767i	−0.377621	+	0.377621i
$189$	−2.00890	−	3.47952i	−0.146126	−	0.253097i
$190$	7.51936	−	0.633819i	0.545512	−	0.0459820i
$191$	−9.00832	+	15.6029i	−0.651819	+	1.12898i	0.330862	+	0.943679i	$0.392660\pi$
$191$	−9.00832	+	15.6029i	−0.651819	+	1.12898i	−0.982681	+	0.185304i	$0.940673\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−4.62254	−	1.23861i	−0.332738	−	0.0891568i	0.0885823	−	0.996069i	$-0.471766\pi$
$193$	−4.62254	−	1.23861i	−0.332738	−	0.0891568i	−0.421320	+	0.906912i	$0.638433\pi$
$194$		−	2.42888i		−	0.174384i
$195$	−0.240576	−	0.667561i	−0.0172280	−	0.0478050i
$196$	4.57135	−	7.91781i	0.326525	−	0.565558i
$197$	−1.02326	−	3.81884i	−0.0729039	−	0.272081i	0.919846	−	0.392280i	$-0.128313\pi$
$197$	−1.02326	−	3.81884i	−0.0729039	−	0.272081i	−0.992750	+	0.120199i	$0.961647\pi$
$198$	−0.105789	+	0.394810i	−0.00751809	+	0.0280579i
$199$	−2.16943	+	3.75757i	−0.153787	+	0.266367i	−0.932617	−	0.360869i	$-0.882480\pi$
$199$	−2.16943	+	3.75757i	−0.153787	+	0.266367i	0.778830	+	0.627235i	$0.215814\pi$
$200$	0.467386	−	4.97811i	0.0330492	−	0.352005i
$201$			1.27267i			0.0897669i
$202$	2.42845	+	2.42845i	0.170865	+	0.170865i
$203$	−4.68787	+	17.4954i	−0.329024	+	1.22793i
$204$	3.68456	+	2.12728i	0.257971	+	0.148939i
$205$	−0.954118	+	5.31242i	−0.0666385	+	0.371036i
$206$	7.10902	−	12.3132i	0.495309	−	0.857900i
$207$	−0.439138	−	1.63889i	−0.0305222	−	0.113911i
$208$	−0.306524	+	0.0821329i	−0.0212536	+	0.00569489i
$209$	−1.37936			−0.0954122
$210$	−5.12967	−	7.37564i	−0.353981	−	0.508967i
$211$	−13.6611	−	23.6617i	−0.940466	−	1.62894i	−0.764584	−	0.644524i	$-0.777056\pi$
$211$	−13.6611	−	23.6617i	−0.940466	−	1.62894i	−0.175882	−	0.984411i	$-0.556278\pi$
$212$	−0.437424	−	1.63249i	−0.0300424	−	0.112120i
$213$	−6.05943	−	6.05943i	−0.415185	−	0.415185i
$214$	−11.7544	+	6.78641i	−0.803515	+	0.463910i
$215$	−0.208449	−	2.47295i	−0.0142161	−	0.168654i
$216$			1.00000i			0.0680414i
$217$	−20.4002	+	9.17908i	−1.38486	+	0.623116i
$218$	−7.55396	+	7.55396i	−0.511619	+	0.511619i
$219$		−	6.93824i		−	0.468843i
$220$	−0.161564	+	0.899570i	−0.0108926	+	0.0606490i
$221$	1.35013			0.0908195
$222$	−6.47723	+	1.73557i	−0.434724	+	0.116484i
$223$	−7.33359	+	27.3693i	−0.491094	+	1.83279i	0.0597981	+	0.998210i	$0.480954\pi$
$223$	−7.33359	+	27.3693i	−0.491094	+	1.83279i	−0.550892	+	0.834577i	$0.685712\pi$
$224$	−3.47952	+	2.00890i	−0.232485	+	0.134225i
$225$	−4.92945	+	0.836969i	−0.328630	+	0.0557979i
$226$	10.3281	−	17.8888i	0.687016	−	1.18995i
$227$	19.4470	−	5.21080i	1.29074	−	0.345853i	0.452799	−	0.891613i	$-0.350425\pi$
$227$	19.4470	−	5.21080i	1.29074	−	0.345853i	0.837942	+	0.545760i	$0.183759\pi$
$228$	−3.25969	+	0.873433i	−0.215879	+	0.0578445i
$229$	0.685986	+	1.18816i	0.0453312	+	0.0785159i	0.887801	−	0.460228i	$-0.152232\pi$
$229$	0.685986	+	1.18816i	0.0453312	+	0.0785159i	−0.842470	+	0.538744i	$0.818899\pi$
$230$	−1.28628	−	3.56924i	−0.0848149	−	0.235348i
$231$	0.821111	+	1.42221i	0.0540252	+	0.0935743i
$232$	3.18769	−	3.18769i	0.209282	−	0.209282i
$233$	−2.06905	+	2.06905i	−0.135548	+	0.135548i	−0.771625	−	0.636077i	$-0.780556\pi$
$233$	−2.06905	+	2.06905i	−0.135548	+	0.135548i	0.636077	+	0.771625i	$0.280556\pi$
$234$	0.158668	+	0.274822i	0.0103725	+	0.0179657i
$235$	14.8172	+	6.96669i	0.966565	+	0.454457i
$236$	−4.54438	−	7.87109i	−0.295814	−	0.512364i
$237$	−15.8464	+	4.24602i	−1.02933	+	0.275809i
$238$	16.5115	−	4.42424i	1.07028	−	0.286781i
$239$	13.2784	−	22.9989i	0.858910	−	1.48768i	−0.0140591	−	0.999901i	$-0.504475\pi$
$239$	13.2784	−	22.9989i	0.858910	−	1.48768i	0.872969	−	0.487775i	$-0.162191\pi$
$240$	0.187816	+	2.22817i	0.0121234	+	0.143828i
$241$	−10.7101	+	6.18347i	−0.689897	+	0.398312i	−0.803573	−	0.595206i	$-0.797071\pi$
$241$	−10.7101	+	6.18347i	−0.689897	+	0.398312i	0.113676	+	0.993518i	$0.463737\pi$
$242$	−2.80377	+	10.4638i	−0.180233	+	0.672639i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	4.44745			0.284719
$245$	−20.1218	−	3.61389i	−1.28553	−	0.230883i
$246$		−	2.41380i		−	0.153898i
$247$	−0.757249	+	0.757249i	−0.0481826	+	0.0481826i
$248$	5.53951	+	0.560205i	0.351759	+	0.0355730i
$249$		−	10.2365i		−	0.648714i
$250$	−10.8264	+	2.79073i	−0.684724	+	0.176502i
$251$	−16.8352	+	9.71980i	−1.06263	+	0.613508i	−0.926158	−	0.377136i	$-0.876909\pi$
$251$	−16.8352	+	9.71980i	−1.06263	+	0.613508i	−0.136470	+	0.990644i	$0.543576\pi$
$252$	2.84101	+	2.84101i	0.178967	+	0.178967i
$253$	0.179492	+	0.669874i	0.0112846	+	0.0421146i
$254$	−0.825529	−	1.42986i	−0.0517983	−	0.0897173i
$255$	1.68173	−	9.36367i	0.105314	−	0.586376i
$256$	1.00000			0.0625000
$257$	−9.32501	+	2.49863i	−0.581678	+	0.155860i	−0.537647	−	0.843170i	$-0.680687\pi$
$257$	−9.32501	+	2.49863i	−0.581678	+	0.155860i	−0.0440310	+	0.999030i	$0.514020\pi$
$258$	0.287253	+	1.07204i	0.0178836	+	0.0667424i
$259$	−13.4711	+	23.3327i	−0.837055	+	1.44982i
$260$	0.405156	+	0.582548i	0.0251267	+	0.0361281i
$261$	−3.90411	−	2.25404i	−0.241658	−	0.139521i
$262$	1.71874	−	6.41442i	0.106184	−	0.396284i
$263$	11.0569	+	11.0569i	0.681797	+	0.681797i	0.960405	−	0.278608i	$-0.0898731\pi$
$263$	11.0569	+	11.0569i	0.681797	+	0.681797i	−0.278608	+	0.960405i	$0.589873\pi$
$264$		−	0.408737i		−	0.0251560i
$265$	−3.10254	+	2.15778i	−0.190588	+	0.132552i
$266$	−6.77940	+	11.7423i	−0.415672	+	0.719965i
$267$	−0.366670	+	1.36843i	−0.0224399	+	0.0837467i
$268$	−0.329390	−	1.22930i	−0.0201207	−	0.0750915i
$269$	13.9185	−	24.1075i	0.848624	−	1.46986i	−0.0338121	−	0.999428i	$-0.510765\pi$
$269$	13.9185	−	24.1075i	0.848624	−	1.46986i	0.882436	−	0.470432i	$-0.155902\pi$
$270$	2.10363	−	0.758108i	0.128023	−	0.0461370i
$271$			19.5414i			1.18706i	0.804813	+	0.593529i	$0.202266\pi$
$271$			19.5414i			1.18706i	−0.804813	+	0.593529i	$0.797734\pi$
$272$	−4.10959	−	1.10116i	−0.249181	−	0.0667677i
$273$	1.23155	+	0.329993i	0.0745369	+	0.0199721i
$274$	−3.91985	+	6.78938i	−0.236807	+	0.410162i
$275$	2.01485	−	0.342100i	0.121500	−	0.0206294i
$276$	0.848350	+	1.46939i	0.0510647	+	0.0884466i
$277$	−8.76582	+	8.76582i	−0.526687	+	0.526687i	−0.919583	−	0.392896i	$-0.871473\pi$
$277$	−8.76582	+	8.76582i	−0.526687	+	0.526687i	0.392896	+	0.919583i	$0.371473\pi$
$278$	10.6291	+	10.6291i	0.637490	+	0.637490i
$279$	−0.892614	−	5.49575i	−0.0534394	−	0.329022i
$280$	6.86383	+	5.79666i	0.410193	+	0.346417i
$281$	21.4436			1.27922			0.639610	−	0.768699i	$-0.279096\pi$
$281$	21.4436			1.27922			0.639610	+	0.768699i	$0.279096\pi$
$282$	−7.07283	−	1.89516i	−0.421181	−	0.112855i
$283$	−9.65040	+	9.65040i	−0.573657	+	0.573657i	−0.933148	−	0.359492i	$-0.882950\pi$
$283$	−9.65040	+	9.65040i	−0.573657	+	0.573657i	0.359492	+	0.933148i	$0.382950\pi$
$284$	7.42125	+	4.28466i	0.440370	+	0.254248i
$285$	4.30858	+	6.19505i	0.255218	+	0.366963i
$286$	−0.0648537	−	0.112330i	−0.00383488	−	0.00664220i
$287$	−6.85764	−	6.85764i	−0.404794	−	0.404794i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	0.953745	+	0.550645i	0.0561027	+	0.0323909i
$290$	−9.12234	−	4.28912i	−0.535682	−	0.251866i
$291$	2.10347	−	1.21444i	0.123308	−	0.0711918i
$292$	1.79575	+	6.70182i	0.105088	+	0.392194i
$293$	−7.60756	−	2.03844i	−0.444438	−	0.119087i	0.0296575	−	0.999560i	$-0.490558\pi$
$293$	−7.60756	−	2.03844i	−0.444438	−	0.119087i	−0.474096	+	0.880473i	$0.657225\pi$
$294$	9.14270			0.533213
$295$	−13.1128	+	15.5268i	−0.763454	+	0.904007i
$296$	5.80733	−	3.35286i	0.337544	−	0.194881i
$297$	−0.394810	+	0.105789i	−0.0229092	+	0.00613849i
$298$	7.41479	+	1.98679i	0.429527	+	0.115091i
$299$	0.466291	+	0.269213i	0.0269663	+	0.0155690i
$300$	4.54486	−	2.08429i	0.262398	−	0.120336i
$301$	3.86177	+	2.22959i	0.222589	+	0.128512i
$302$	−2.80389	+	2.80389i	−0.161346	+	0.161346i
$303$	−0.888873	+	3.31732i	−0.0510644	+	0.190575i
$304$	2.92256	−	1.68734i	0.167620	−	0.0967757i
$305$	−3.37165	−	9.35580i	−0.193060	−	0.535712i
$306$			4.25456i			0.243217i
$307$	8.19844	−	30.5970i	0.467910	−	1.74626i	−0.179147	−	0.983822i	$-0.557334\pi$
$307$	8.19844	−	30.5970i	0.467910	−	1.74626i	0.647057	−	0.762441i	$-0.275999\pi$
$308$	−1.16123	−	1.16123i	−0.0661670	−	0.0661670i
$309$	14.2180			0.808836
$310$	−3.02108	−	12.0778i	−0.171586	−	0.685973i
$311$	23.1391			1.31210			0.656049	−	0.754719i	$-0.272227\pi$
$311$	23.1391			1.31210			0.656049	+	0.754719i	$0.272227\pi$
$312$	−0.224391	−	0.224391i	−0.0127036	−	0.0127036i
$313$	−5.10317	+	19.0453i	−0.288448	+	1.07650i	0.657834	+	0.753163i	$0.271473\pi$
$313$	−5.10317	+	19.0453i	−0.288448	+	1.07650i	−0.946283	+	0.323341i	$0.895194\pi$
$314$			8.26108i			0.466200i
$315$	3.82265	−	8.13024i	0.215382	−	0.458087i
$316$	14.2075	−	8.20268i	0.799232	−	0.461437i
$317$	−1.25494	+	4.68349i	−0.0704843	+	0.263051i	−0.992171	−	0.124883i	$-0.960144\pi$
$317$	−1.25494	+	4.68349i	−0.0704843	+	0.263051i	0.921687	+	0.387934i	$0.126811\pi$
$318$	1.19507	−	1.19507i	0.0670159	−	0.0670159i
$319$	1.59575	+	0.921308i	0.0893450	+	0.0515833i
$320$	−0.758108	−	2.10363i	−0.0423795	−	0.117597i
$321$	−11.7544	−	6.78641i	−0.656067	−	0.378781i
$322$	6.58472	+	1.76437i	0.366952	+	0.0983245i
$323$	−13.8686	+	3.71607i	−0.771668	+	0.206768i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	0.918317	−	1.29393i	0.0509390	−	0.0717745i
$326$	6.23229			0.345175
$327$	−10.3189	−	2.76494i	−0.570637	−	0.152902i
$328$	0.624738	+	2.33155i	0.0344954	+	0.128739i
$329$	−25.4782	+	14.7098i	−1.40466	+	0.810979i
$330$	−0.859833	+	0.309867i	−0.0473322	+	0.0170576i
$331$	17.3274	+	10.0040i	0.952398	+	0.549867i	0.893825	−	0.448416i	$-0.148012\pi$
$331$	17.3274	+	10.0040i	0.952398	+	0.549867i	0.0585730	+	0.998283i	$0.481345\pi$
$332$	2.64941	+	9.88774i	0.145405	+	0.542660i
$333$	−4.74166	−	4.74166i	−0.259842	−	0.259842i
$334$	7.29207	+	12.6302i	0.399004	+	0.691096i
$335$	−2.33629	+	1.62486i	−0.127645	+	0.0887755i
$336$	−3.47952	−	2.00890i	−0.189823	−	0.109594i
$337$	−2.56257	+	2.56257i	−0.139592	+	0.139592i	−0.773450	−	0.633858i	$-0.781471\pi$
$337$	−2.56257	+	2.56257i	−0.139592	+	0.139592i	0.633858	+	0.773450i	$0.281471\pi$
$338$	12.4598	+	3.33858i	0.677722	+	0.181595i
$339$	20.6562			1.12189
$340$	0.799073	+	9.47987i	0.0433358	+	0.514118i
$341$	0.364844	+	2.24631i	0.0197574	+	0.121645i
$342$	−2.38626	−	2.38626i	−0.129034	−	0.129034i
$343$	6.08744	−	6.08744i	0.328691	−	0.328691i
$344$	−0.554930	−	0.961166i	−0.0299198	−	0.0518226i
$345$	2.44791	−	2.89857i	0.131791	−	0.156054i
$346$	−3.45052	+	5.97647i	−0.185501	+	0.321297i
$347$	−22.4638	−	6.01916i	−1.20592	−	0.323125i	−0.400760	−	0.916183i	$-0.631254\pi$
$347$	−22.4638	−	6.01916i	−1.20592	−	0.323125i	−0.805160	+	0.593058i	$0.797920\pi$
$348$	4.35446	+	1.16678i	0.233424	+	0.0625457i
$349$		−	35.4053i		−	1.89520i	−0.319453	−	0.947602i	$-0.603499\pi$
$349$		−	35.4053i		−	1.89520i	0.319453	−	0.947602i	$-0.396501\pi$
$350$	6.99052	−	18.8335i	0.373659	−	1.00669i
$351$	−0.158668	+	0.274822i	−0.00846910	+	0.0146689i
$352$	0.105789	+	0.394810i	0.00563857	+	0.0210434i
$353$	9.05608	−	33.7978i	0.482007	−	1.79887i	−0.111170	−	0.993801i	$-0.535460\pi$
$353$	9.05608	−	33.7978i	0.482007	−	1.79887i	0.593177	−	0.805072i	$-0.297874\pi$
$354$	4.54438	−	7.87109i	0.241531	−	0.418344i
$355$	3.38725	−	18.8598i	0.179776	−	1.00098i
$356$		−	1.41670i		−	0.0750852i
$357$	12.0873	+	12.0873i	0.639726	+	0.639726i
$358$	3.97044	−	14.8179i	0.209844	−	0.783150i
$359$	−16.1435	−	9.32044i	−0.852020	−	0.491914i	0.00931174	−	0.999957i	$-0.497036\pi$
$359$	−16.1435	−	9.32044i	−0.852020	−	0.491914i	−0.861332	+	0.508043i	$0.830369\pi$
$360$	−1.83574	+	1.27674i	−0.0967520	+	0.0672899i
$361$	−3.80575	+	6.59176i	−0.200303	+	0.346935i
$362$	1.48934	+	5.55831i	0.0782782	+	0.292138i
$363$	−10.4638	+	2.80377i	−0.549208	+	0.147160i
$364$	−1.27500			−0.0668279
$365$	12.7368	−	8.85830i	0.666675	−	0.463664i
$366$	2.22373	+	3.85161i	0.116236	+	0.201327i
$367$	−3.26829	−	12.1974i	−0.170603	−	0.636700i	−0.997259	−	0.0739916i	$-0.976426\pi$
$367$	−3.26829	−	12.1974i	−0.170603	−	0.636700i	0.826656	−	0.562708i	$-0.190240\pi$
$368$	−1.19975	−	1.19975i	−0.0625412	−	0.0625412i
$369$	2.09041	−	1.20690i	0.108823	−	0.0628288i
$370$	−11.4558	−	9.67466i	−0.595557	−	0.502962i
$371$		−	6.79039i		−	0.352539i
$372$	2.28460	+	5.07746i	0.118451	+	0.263254i
$373$	13.3641	−	13.3641i	0.691969	−	0.691969i	−0.270696	−	0.962665i	$-0.587254\pi$
$373$	13.3641	−	13.3641i	0.691969	−	0.691969i	0.962665	+	0.270696i	$0.0872539\pi$
$374$		−	1.73900i		−	0.0899214i
$375$	−7.83007	−	7.98060i	−0.404343	−	0.412117i
$376$	7.32233			0.377621
$377$	1.38183	−	0.370261i	0.0711680	−	0.0190694i
$378$	−1.03988	+	3.88090i	−0.0534858	+	0.199612i
$379$	−8.39468	+	4.84667i	−0.431206	+	0.248957i	−0.699860	−	0.714280i	$-0.746754\pi$
$379$	−8.39468	+	4.84667i	−0.431206	+	0.248957i	0.268655	+	0.963237i	$0.413421\pi$
$380$	−5.76517	−	4.86881i	−0.295747	−	0.249765i
$381$	0.825529	−	1.42986i	0.0422932	−	0.0732539i
$382$	17.4027	−	4.66305i	0.890401	−	0.238582i
$383$	−3.97717	+	1.06568i	−0.203224	+	0.0544536i	−0.358995	−	0.933340i	$-0.616880\pi$
$383$	−3.97717	+	1.06568i	−0.203224	+	0.0544536i	0.155771	+	0.987793i	$0.450214\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−1.56246	+	3.32313i	−0.0796303	+	0.169362i
$386$	2.39280	+	4.14445i	0.121790	+	0.210947i
$387$	−0.784789	+	0.784789i	−0.0398931	+	0.0398931i
$388$	−1.71748	+	1.71748i	−0.0871918	+	0.0871918i
$389$	6.82974	+	11.8295i	0.346282	+	0.599777i	0.985586	−	0.169177i	$-0.0541108\pi$
$389$	6.82974	+	11.8295i	0.346282	+	0.599777i	−0.639304	+	0.768954i	$0.720777\pi$
$390$	−0.301924	+	0.642149i	−0.0152885	+	0.0325165i
$391$	3.60936	+	6.25159i	0.182533	+	0.316157i
$392$	−8.83117	+	2.36631i	−0.446042	+	0.119516i
$393$	6.41442	−	1.71874i	0.323565	−	0.0866988i
$394$	−1.97678	+	3.42388i	−0.0995886	+	0.172492i
$395$	−28.0262	−	23.6688i	−1.41015	−	1.19091i
$396$	0.353977	−	0.204368i	0.0177880	−	0.0102699i
$397$	4.82910	−	18.0224i	0.242365	−	0.904520i	−0.732324	−	0.680956i	$-0.761564\pi$
$397$	4.82910	−	18.0224i	0.242365	−	0.904520i	0.974689	−	0.223564i	$-0.0717690\pi$
$398$	4.19102	−	1.12298i	0.210077	−	0.0562899i
$399$	−13.5588			−0.678789
$400$	−3.85054	+	3.18956i	−0.192527	+	0.159478i
$401$			20.5193i			1.02469i	0.858781	+	0.512343i	$0.171222\pi$
$401$			20.5193i			1.02469i	−0.858781	+	0.512343i	$0.828778\pi$
$402$	0.899911	−	0.899911i	0.0448835	−	0.0448835i
$403$	1.43349	+	1.03290i	0.0714073	+	0.0514525i
$404$		−	3.43434i		−	0.170865i
$405$	1.70836	+	1.44275i	0.0848890	+	0.0716906i
$406$	15.6859	−	9.05627i	0.778479	−	0.449455i
$407$	1.93809	+	1.93809i	0.0960677	+	0.0960677i
$408$	−1.10116	−	4.10959i	−0.0545156	−	0.203455i
$409$	15.7704	+	27.3150i	0.779794	+	1.35064i	0.932060	+	0.362303i	$0.118009\pi$
$409$	15.7704	+	27.3150i	0.779794	+	1.35064i	−0.152267	+	0.988339i	$0.548657\pi$
$410$	4.43111	−	3.08179i	0.218837	−	0.152199i
$411$	−7.83970			−0.386704
$412$	−13.7336	+	3.67990i	−0.676604	+	0.181296i
$413$	−9.45124	−	35.2725i	−0.465065	−	1.73565i
$414$	−0.848350	+	1.46939i	−0.0416941	+	0.0722164i
$415$	18.7916	−	13.0694i	0.922445	−	0.641550i
$416$	0.274822	+	0.158668i	0.0134743	+	0.00777936i
$417$	−3.89052	+	14.5196i	−0.190519	+	0.711028i
$418$	0.975353	+	0.975353i	0.0477061	+	0.0477061i
$419$		−	27.7420i		−	1.35529i	−0.735391	−	0.677643i	$-0.763002\pi$
$419$		−	27.7420i		−	1.35529i	0.735391	−	0.677643i	$-0.236998\pi$
$420$	−1.58814	+	8.84259i	−0.0774932	+	0.431474i
$421$	9.50462	−	16.4625i	0.463227	−	0.802332i	−0.535893	−	0.844286i	$-0.680025\pi$
$421$	9.50462	−	16.4625i	0.463227	−	0.802332i	0.999120	+	0.0419538i	$0.0133582\pi$
$422$	−7.07149	+	26.3911i	−0.344235	+	1.28470i
$423$	−1.89516	−	7.07283i	−0.0921458	−	0.343893i
$424$	−0.845039	+	1.46365i	−0.0410387	+	0.0710811i
$425$	19.3364	−	8.86772i	0.937952	−	0.430148i
$426$			8.56932i			0.415185i
$427$	17.2601	+	4.62483i	0.835274	+	0.223811i
$428$	13.1103	+	3.51291i	0.633712	+	0.169803i
$429$	0.0648537	−	0.112330i	0.00313116	−	0.00542334i
$430$	−1.60124	+	1.89604i	−0.0772189	+	0.0914350i
$431$	−12.2303	−	21.1835i	−0.589114	−	1.02038i	−0.994349	−	0.106163i	$-0.966144\pi$
$431$	−12.2303	−	21.1835i	−0.589114	−	1.02038i	0.405235	−	0.914213i	$-0.367190\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−12.3774	−	12.3774i	−0.594820	−	0.594820i	0.344109	−	0.938930i	$-0.388181\pi$
$433$	−12.3774	−	12.3774i	−0.594820	−	0.594820i	−0.938930	+	0.344109i	$0.888181\pi$
$434$	20.9157	+	7.93454i	1.00399	+	0.380870i
$435$	−0.846687	−	10.0447i	−0.0405955	−	0.481608i
$436$	10.6829			0.511619
$437$	−5.53073	−	1.48195i	−0.264571	−	0.0708915i
$438$	−4.90607	+	4.90607i	−0.234421	+	0.234421i
$439$	−0.865709	−	0.499817i	−0.0413180	−	0.0238550i	0.479199	−	0.877706i	$-0.340927\pi$
$439$	−0.865709	−	0.499817i	−0.0413180	−	0.0238550i	−0.520517	+	0.853851i	$0.674261\pi$
$440$	0.750335	−	0.521849i	0.0357708	−	0.0248782i
$441$	4.57135	+	7.91781i	0.217683	+	0.377039i
$442$	−0.954686	−	0.954686i	−0.0454098	−	0.0454098i
$443$	−7.82836	−	29.2159i	−0.371937	−	1.38809i	−0.857769	−	0.514035i	$-0.828150\pi$
$443$	−7.82836	−	29.2159i	−0.371937	−	1.38809i	0.485832	−	0.874052i	$-0.338517\pi$
$444$	5.80733	+	3.35286i	0.275604	+	0.159120i
$445$	−2.98023	+	1.07402i	−0.141276	+	0.0509132i
$446$	24.5387	−	14.1674i	1.16194	−	0.670847i
$447$	1.98679	+	7.41479i	0.0939718	+	0.350708i
$448$	3.88090	+	1.03988i	0.183355	+	0.0491298i
$449$	16.6161			0.784164			0.392082	−	0.919930i	$-0.371755\pi$
$449$	16.6161			0.784164			0.392082	+	0.919930i	$0.371755\pi$
$450$	4.07747	+	2.89382i	0.192214	+	0.136416i
$451$	−0.854429	+	0.493305i	−0.0402335	+	0.0232288i
$452$	−19.9524	+	5.34622i	−0.938481	+	0.251465i
$453$	−3.83018	−	1.02629i	−0.179958	−	0.0482195i
$454$	−17.4357	−	10.0665i	−0.818297	−	0.472444i
$455$	0.966585	+	2.68212i	0.0453142	+	0.125740i
$456$	2.92256	+	1.68734i	0.136862	+	0.0790170i
$457$	−18.7490	+	18.7490i	−0.877041	+	0.877041i	−0.993227	−	0.116186i	$-0.962933\pi$
$457$	−18.7490	+	18.7490i	−0.877041	+	0.877041i	0.116186	+	0.993227i	$0.462933\pi$
$458$	0.355092	−	1.32522i	0.0165924	−	0.0619236i
$459$	−3.68456	+	2.12728i	−0.171980	+	0.0992930i
$460$	−1.61429	+	3.43337i	−0.0752668	+	0.160082i
$461$		−	1.47304i		−	0.0686064i	−0.999411	−	0.0343032i	$-0.989079\pi$
$461$		−	1.47304i		−	0.0686064i	0.999411	−	0.0343032i	$-0.0109212\pi$
$462$	0.425038	−	1.58627i	0.0197746	−	0.0737997i
$463$	28.3563	+	28.3563i	1.31783	+	1.31783i	0.915493	+	0.402335i	$0.131801\pi$
$463$	28.3563	+	28.3563i	1.31783	+	1.31783i	0.402335	+	0.915493i	$0.368199\pi$
$464$	−4.50807			−0.209282
$465$	8.94913	−	8.65523i	0.415006	−	0.401377i
$466$	2.92608			0.135548
$467$	12.0018	+	12.0018i	0.555378	+	0.555378i	0.927988	−	0.372610i	$-0.121537\pi$
$467$	12.0018	+	12.0018i	0.555378	+	0.555378i	−0.372610	+	0.927988i	$0.621537\pi$
$468$	0.0821329	−	0.306524i	0.00379659	−	0.0141691i
$469$		−	5.11332i		−	0.236111i
$470$	−5.55112	−	15.4035i	−0.256054	−	0.710511i
$471$	−7.15430	+	4.13054i	−0.329653	+	0.190325i
$472$	−2.35234	+	8.77906i	−0.108275	+	0.404089i
$473$	0.320772	−	0.320772i	0.0147491	−	0.0147491i
$474$	14.2075	+	8.20268i	0.652570	+	0.376762i
$475$	−5.87158	+	15.8189i	−0.269406	+	0.725820i
$476$	−14.8038	−	8.54698i	−0.678532	−	0.391750i
$477$	1.63249	+	0.437424i	0.0747465	+	0.0200283i
$478$	−25.6520	+	6.87342i	−1.17329	+	0.314383i
$479$	14.6284	−	8.44569i	0.668387	−	0.385893i	−0.127078	−	0.991893i	$-0.540560\pi$
$479$	14.6284	−	8.44569i	0.668387	−	0.385893i	0.795465	+	0.605999i	$0.207227\pi$
$480$	1.44275	−	1.70836i	0.0658520	−	0.0779755i
$481$	2.12798			0.0970273
$482$	11.9455	+	3.20080i	0.544105	+	0.145792i
$483$	1.76437	+	6.58472i	0.0802816	+	0.299615i
$484$	9.38160	−	5.41647i	0.426436	−	0.246203i
$485$	4.91498	+	2.31091i	0.223178	+	0.104933i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−7.05972	−	26.3472i	−0.319906	−	1.19391i	−0.919334	−	0.393478i	$-0.871272\pi$
$487$	−7.05972	−	26.3472i	−0.319906	−	1.19391i	0.599428	−	0.800429i	$-0.295395\pi$
$488$	−3.14482	−	3.14482i	−0.142359	−	0.142359i
$489$	3.11615	+	5.39732i	0.140917	+	0.244075i
$490$	11.6728	+	16.7836i	0.527324	+	0.758207i
$491$	3.90700	+	2.25571i	0.176320	+	0.101799i	0.585563	−	0.810627i	$-0.300874\pi$
$491$	3.90700	+	2.25571i	0.176320	+	0.101799i	−0.409242	+	0.912426i	$0.634207\pi$
$492$	−1.70682	+	1.70682i	−0.0769492	+	0.0769492i
$493$	18.5263	+	4.96412i	0.834384	+	0.223573i
$494$	1.07091			0.0481826
$495$	−0.698269	−	0.589703i	−0.0313848	−	0.0265052i
$496$	−3.52090	−	4.31315i	−0.158093	−	0.193666i
$497$	24.3456	+	24.3456i	1.09205	+	1.09205i
$498$	−7.23833	+	7.23833i	−0.324357	+	0.324357i
$499$	15.5665	+	26.9619i	0.696851	+	1.20698i	0.969553	+	0.244883i	$0.0787497\pi$
$499$	15.5665	+	26.9619i	0.696851	+	1.20698i	−0.272701	+	0.962099i	$0.587917\pi$
$500$	9.62880	+	5.68210i	0.430613	+	0.254111i
$501$	−7.29207	+	12.6302i	−0.325786	+	0.564277i
$502$	18.7772	+	5.03134i	0.838068	+	0.224560i
$503$	−17.8721	−	4.78880i	−0.796876	−	0.213522i	−0.162664	−	0.986682i	$-0.552009\pi$
$503$	−17.8721	−	4.78880i	−0.796876	−	0.213522i	−0.634212	+	0.773159i	$0.718675\pi$
$504$		−	4.01780i		−	0.178967i
$505$	−7.22460	+	2.60360i	−0.321490	+	0.115859i
$506$	0.346752	−	0.600592i	0.0154150	−	0.0266996i
$507$	3.33858	+	12.4598i	0.148272	+	0.553358i
$508$	−0.427325	+	1.59480i	−0.0189595	+	0.0707578i
$509$	1.33713	−	2.31597i	0.0592671	−	0.102654i	−0.834870	−	0.550448i	$-0.814457\pi$
$509$	1.33713	−	2.31597i	0.0592671	−	0.102654i	0.894137	+	0.447794i	$0.147790\pi$
$510$	−7.81027	+	5.43195i	−0.345845	+	0.240531i
$511$			27.8764i			1.23318i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	0.873433	−	3.25969i	0.0385630	−	0.143919i
$514$	8.36057	+	4.82698i	0.368769	+	0.212909i
$515$	18.1527	+	26.1006i	0.799903	+	1.15013i
$516$	0.554930	−	0.961166i	0.0244294	−	0.0423130i
$517$	0.774622	+	2.89093i	0.0340678	+	0.127143i
$518$	26.0242	−	6.97317i	1.14344	−	0.306383i
$519$	−6.90103			−0.302922
$520$	0.125436	−	0.698412i	0.00550072	−	0.0306274i
$521$	0.739992	+	1.28170i	0.0324197	+	0.0561525i	0.881780	−	0.471661i	$-0.156345\pi$
$521$	0.739992	+	1.28170i	0.0324197	+	0.0561525i	−0.849360	+	0.527813i	$0.823012\pi$
$522$	1.16678	+	4.35446i	0.0510684	+	0.190590i
$523$	−11.4997	−	11.4997i	−0.502845	−	0.502845i	0.409476	−	0.912321i	$-0.365712\pi$
$523$	−11.4997	−	11.4997i	−0.502845	−	0.502845i	−0.912321	+	0.409476i	$0.865712\pi$
$524$	−5.75101	+	3.32035i	−0.251234	+	0.145050i
$525$	19.8055	−	3.36277i	0.864385	−	0.146763i
$526$		−	15.6368i		−	0.681797i
$527$	9.71998	+	21.6024i	0.423409	+	0.941014i
$528$	−0.289021	+	0.289021i	−0.0125780	+	0.0125780i
$529$		−	20.1212i		−	0.874835i
$530$	3.71961	+	0.668047i	0.161570	+	0.0290181i
$531$	9.08875			0.394418
$532$	13.0968	−	3.50928i	0.567818	−	0.152146i
$533$	−0.198252	+	0.739888i	−0.00858727	+	0.0320481i
$534$	1.22690	−	0.708352i	0.0530933	−	0.0306534i
$535$	−2.54919	−	30.2425i	−0.110211	−	1.30750i
$536$	−0.636333	+	1.10216i	−0.0274854	+	0.0476061i
$537$	14.8179	−	3.97044i	0.639439	−	0.171337i
$538$	−26.8884	+	7.20473i	−1.15924	+	0.310618i
$539$	−1.86848	−	3.23630i	−0.0804811	−	0.139397i
$540$	−2.02356	−	0.951430i	−0.0870800	−	0.0409430i
$541$	0.0657260	+	0.113841i	0.00282578	+	0.00489440i	0.867435	−	0.497551i	$-0.165767\pi$
$541$	0.0657260	+	0.113841i	0.00282578	+	0.00489440i	−0.864609	+	0.502445i	$0.832434\pi$
$542$	13.8179	−	13.8179i	0.593529	−	0.593529i
$543$	−4.06896	+	4.06896i	−0.174616	+	0.174616i
$544$	2.12728	+	3.68456i	0.0912064	+	0.157974i
$545$	−8.09880	−	22.4729i	−0.346915	−	0.962635i
$546$	−0.637498	−	1.10418i	−0.0272824	−	0.0472545i
$547$	4.19662	−	1.12448i	0.179434	−	0.0480793i	−0.167983	−	0.985790i	$-0.553725\pi$
$547$	4.19662	−	1.12448i	0.179434	−	0.0480793i	0.347417	+	0.937711i	$0.387059\pi$
$548$	7.57257	−	2.02906i	0.323484	−	0.0866773i
$549$	−2.22373	+	3.85161i	−0.0949063	+	0.164383i
$550$	−1.66661	−	1.18281i	−0.0710647	−	0.0504353i
$551$	−13.1751	+	7.60666i	−0.561279	+	0.324055i
$552$	0.439138	−	1.63889i	0.0186910	−	0.0697557i
$553$	63.6675	−	17.0597i	2.70742	−	0.725450i
$554$	12.3967			0.526687
$555$	2.65061	−	14.7583i	0.112512	−	0.626456i
$556$		−	15.0318i		−	0.637490i
$557$	22.6818	−	22.6818i	0.961058	−	0.961058i	−0.0382114	−	0.999270i	$-0.512166\pi$
$557$	22.6818	−	22.6818i	0.961058	−	0.961058i	0.999270	+	0.0382114i	$0.0121660\pi$
$558$	−3.25491	+	4.51725i	−0.137791	+	0.191231i
$559$		−	0.352199i		−	0.0148964i
$560$	−0.754605	−	8.95232i	−0.0318879	−	0.378305i
$561$	1.50601	−	0.869498i	0.0635840	−	0.0367102i
$562$	−15.1629	−	15.1629i	−0.639610	−	0.639610i
$563$	5.73773	+	21.4135i	0.241817	+	0.902472i	0.974957	+	0.222395i	$0.0713873\pi$
$563$	5.73773	+	21.4135i	0.241817	+	0.902472i	−0.733140	+	0.680078i	$0.761946\pi$
$564$	3.66117	+	6.34133i	0.154163	+	0.267018i
$565$	26.3726	+	37.9195i	1.10950	+	1.59528i
$566$	13.6477			0.573657
$567$	−3.88090	+	1.03988i	−0.162982	+	0.0436710i
$568$	−2.21790	−	8.27733i	−0.0930612	−	0.347309i
$569$	5.54632	−	9.60651i	0.232514	−	0.402726i	−0.726033	−	0.687659i	$-0.758638\pi$
$569$	5.54632	−	9.60651i	0.232514	−	0.402726i	0.958547	+	0.284934i	$0.0919715\pi$
$570$	1.33393	−	7.42719i	0.0558722	−	0.311091i
$571$	−3.41967	−	1.97435i	−0.143109	−	0.0826239i	0.426736	−	0.904376i	$-0.359663\pi$
$571$	−3.41967	−	1.97435i	−0.143109	−	0.0826239i	−0.569845	+	0.821752i	$0.692997\pi$
$572$	−0.0335707	+	0.125288i	−0.00140366	+	0.00523854i
$573$	12.7397	+	12.7397i	0.532208	+	0.532208i
$574$			9.69817i			0.404794i
$575$	8.44636	+	0.793014i	0.352238	+	0.0330710i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	4.57213	−	17.0634i	0.190340	−	0.710360i	−0.803084	−	0.595866i	$-0.796809\pi$
$577$	4.57213	−	17.0634i	0.190340	−	0.710360i	0.993424	−	0.114494i	$-0.0365246\pi$
$578$	−0.285035	−	1.06376i	−0.0118559	−	0.0442468i
$579$	−2.39280	+	4.14445i	−0.0994415	+	0.172238i
$580$	3.41761	+	9.48333i	0.141908	+	0.393774i
$581$			41.1283i			1.70629i
$582$	−2.34612	−	0.628641i	−0.0972498	−	0.0260580i
$583$	−0.667259	−	0.178791i	−0.0276350	−	0.00740478i
$584$	3.46912	−	6.00869i	0.143553	−	0.248641i
$585$	−0.707080	+	0.0596009i	−0.0292341	+	0.00246419i
$586$	3.93796	+	6.82075i	0.162676	+	0.281763i
$587$	−6.61215	+	6.61215i	−0.272913	+	0.272913i	−0.830272	−	0.557359i	$-0.811815\pi$
$587$	−6.61215	+	6.61215i	−0.272913	+	0.272913i	0.557359	+	0.830272i	$0.311815\pi$
$588$	−6.46487	−	6.46487i	−0.266607	−	0.266607i
$589$	−17.5678	−	6.66449i	−0.723869	−	0.274605i
$590$	20.2513	−	1.70701i	0.833731	−	0.0702765i
$591$	−3.95355			−0.162627
$592$	−6.47723	−	1.73557i	−0.266213	−	0.0713315i
$593$	27.7102	−	27.7102i	1.13792	−	1.13792i	0.149099	−	0.988822i	$-0.452363\pi$
$593$	27.7102	−	27.7102i	1.13792	−	1.13792i	0.988822	−	0.149099i	$-0.0476372\pi$
$594$	0.353977	+	0.204368i	0.0145238	+	0.00838534i
$595$	−6.75683	+	37.6213i	−0.277003	+	1.54232i
$596$	−3.83818	−	6.64792i	−0.157218	−	0.272309i
$597$	3.06804	+	3.06804i	0.125567	+	0.125567i
$598$	−0.139355	−	0.520080i	−0.00569865	−	0.0212676i
$599$	−28.6668	−	16.5508i	−1.17130	−	0.676248i	−0.217311	−	0.976103i	$-0.569728\pi$
$599$	−28.6668	−	16.5508i	−1.17130	−	0.676248i	−0.953985	+	0.299855i	$0.903062\pi$
$600$	−4.68751	−	1.73989i	−0.191367	−	0.0710307i
$601$	−1.72514	+	0.996008i	−0.0703698	+	0.0406280i	−0.534772	−	0.844996i	$-0.679603\pi$
$601$	−1.72514	+	0.996008i	−0.0703698	+	0.0406280i	0.464402	+	0.885624i	$0.346269\pi$
$602$	−1.15412	−	4.30725i	−0.0470385	−	0.175550i
$603$	1.22930	+	0.329390i	0.0500610	+	0.0134138i
$604$	3.96530			0.161346
$605$	−18.5065	−	15.6292i	−0.752397	−	0.635416i
$606$	2.97423	−	1.71717i	0.120820	−	0.0697553i
$607$	0.834483	−	0.223599i	0.0338706	−	0.00907560i	−0.241844	−	0.970315i	$-0.577752\pi$
$607$	0.834483	−	0.223599i	0.0338706	−	0.00907560i	0.275715	+	0.961240i	$0.411086\pi$
$608$	−3.25969	−	0.873433i	−0.132198	−	0.0354224i
$609$	15.6859	+	9.05627i	0.635625	+	0.366978i
$610$	−4.23144	+	8.99967i	−0.171326	+	0.364386i
$611$	2.01234	+	1.16182i	0.0814105	+	0.0470024i
$612$	3.00843	−	3.00843i	0.121609	−	0.121609i
$613$	−0.235755	+	0.879849i	−0.00952205	+	0.0355368i	−0.970523	−	0.241007i	$-0.922522\pi$
$613$	−0.235755	+	0.879849i	−0.00952205	+	0.0355368i	0.961001	+	0.276544i	$0.0891890\pi$
$614$	−27.4325	+	15.8382i	−1.10709	+	0.639177i
$615$	4.88446	+	2.29656i	0.196961	+	0.0926064i
$616$			1.64222i			0.0661670i
$617$	1.87356	−	6.99221i	0.0754266	−	0.281496i	−0.917903	−	0.396805i	$-0.870119\pi$
$617$	1.87356	−	6.99221i	0.0754266	−	0.281496i	0.993330	+	0.115309i	$0.0367858\pi$
$618$	−10.0537	−	10.0537i	−0.404418	−	0.404418i
$619$	−48.3007			−1.94137			−0.970685	−	0.240355i	$-0.922736\pi$
$619$	−48.3007			−1.94137			−0.970685	+	0.240355i	$0.922736\pi$
$620$	−6.40406	+	10.6765i	−0.257193	+	0.428779i
$621$	−1.69670			−0.0680863
$622$	−16.3618	−	16.3618i	−0.656049	−	0.656049i
$623$	1.47321	−	5.49808i	0.0590228	−	0.220276i
$624$			0.317337i			0.0127036i
$625$	4.65339	−	24.5631i	0.186136	−	0.982524i
$626$	17.0755	−	9.85856i	0.682476	−	0.394028i
$627$	−0.357004	+	1.33236i	−0.0142574	+	0.0532092i
$628$	5.84146	−	5.84146i	0.233100	−	0.233100i
$629$	24.7076	+	14.2650i	0.985158	+	0.568781i
$630$	−8.45197	+	3.04592i	−0.336735	+	0.121353i
$631$	−40.6844	−	23.4892i	−1.61962	−	0.935089i	−0.987017	−	0.160613i	$-0.948653\pi$
$631$	−40.6844	−	23.4892i	−1.61962	−	0.935089i	−0.632604	−	0.774476i	$-0.718014\pi$
$632$	−15.8464	−	4.24602i	−0.630335	−	0.168898i
$633$	−26.3911	+	7.07149i	−1.04895	+	0.281066i
$634$	4.19910	−	2.42435i	0.166768	−	0.0962834i
$635$	3.67883	−	0.310095i	0.145990	−	0.0123057i
$636$	−1.69008			−0.0670159
$637$	−2.80246	−	0.750916i	−0.111037	−	0.0297524i
$638$	−0.476904	−	1.77983i	−0.0188808	−	0.0704642i
$639$	−7.42125	+	4.28466i	−0.293580	+	0.169499i
$640$	−0.951430	+	2.02356i	−0.0376086	+	0.0799881i
$641$	−9.39621	−	5.42490i	−0.371128	−	0.214271i	0.302823	−	0.953047i	$-0.402071\pi$
$641$	−9.39621	−	5.42490i	−0.371128	−	0.214271i	−0.673951	+	0.738776i	$0.735404\pi$
$642$	3.51291	+	13.1103i	0.138643	+	0.517424i
$643$	−7.80126	−	7.80126i	−0.307652	−	0.307652i	0.536346	−	0.843998i	$-0.319804\pi$
$643$	−7.80126	−	7.80126i	−0.307652	−	0.307652i	−0.843998	+	0.536346i	$0.819804\pi$
$644$	−3.40850	−	5.90370i	−0.134314	−	0.232638i
$645$	−2.44264	−	0.438701i	−0.0961788	−	0.0172738i
$646$	12.4342	+	7.17890i	0.489218	+	0.282450i
$647$	4.46137	−	4.46137i	0.175395	−	0.175395i	−0.613950	−	0.789345i	$-0.710420\pi$
$647$	4.46137	−	4.46137i	0.175395	−	0.175395i	0.789345	+	0.613950i	$0.210420\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	−3.71491			−0.145823
$650$	−1.56430	+	0.265601i	−0.0613568	+	0.0104177i
$651$	3.58634	+	22.0808i	0.140560	+	0.865415i
$652$	−4.40689	−	4.40689i	−0.172587	−	0.172587i
$653$	−20.8360	+	20.8360i	−0.815376	+	0.815376i	−0.985434	−	0.170058i	$-0.945604\pi$
$653$	−20.8360	+	20.8360i	−0.815376	+	0.815376i	0.170058	+	0.985434i	$0.445604\pi$
$654$	5.34146	+	9.25168i	0.208868	+	0.361769i
$655$	11.3447	+	9.58083i	0.443273	+	0.374354i
$656$	1.20690	−	2.09041i	0.0471216	−	0.0816169i
$657$	−6.70182	−	1.79575i	−0.261463	−	0.0700588i
$658$	28.4172	+	7.61437i	1.10782	+	0.296839i
$659$			13.6796i			0.532881i	0.963851	+	0.266440i	$0.0858475\pi$
$659$			13.6796i			0.532881i	−0.963851	+	0.266440i	$0.914152\pi$
$660$	0.827102	+	0.388885i	0.0321949	+	0.0151373i
$661$	10.9306	−	18.9324i	0.425151	−	0.736384i	−0.571283	−	0.820753i	$-0.693554\pi$
$661$	10.9306	−	18.9324i	0.425151	−	0.736384i	0.996435	+	0.0843692i	$0.0268875\pi$
$662$	−5.17843	−	19.3262i	−0.201265	−	0.751133i
$663$	0.349439	−	1.30413i	0.0135711	−	0.0506480i
$664$	5.11827	−	8.86510i	0.198627	−	0.344033i
$665$	−17.3110	−	24.8904i	−0.671292	−	0.965210i
$666$			6.70573i			0.259842i
$667$	5.40856	+	5.40856i	0.209420	+	0.209420i
$668$	3.77465	−	14.0872i	0.146046	−	0.545050i
$669$	24.5387	+	14.1674i	0.948720	+	0.547744i
$670$	2.80095	+	0.503054i	0.108210	+	0.0194347i
$671$	0.908919	−	1.57429i	0.0350884	−	0.0607749i
$672$	1.03988	+	3.88090i	0.0401143	+	0.149709i
$673$	−10.0284	+	2.68709i	−0.386565	+	0.103580i	−0.446867	−	0.894600i	$-0.647460\pi$
$673$	−10.0284	+	2.68709i	−0.386565	+	0.103580i	0.0603020	+	0.998180i	$0.480794\pi$
$674$	3.62402			0.139592
$675$	−0.467386	+	4.97811i	−0.0179897	+	0.191607i
$676$	−6.44965	−	11.1711i	−0.248063	−	0.429658i
$677$	−8.41381	−	31.4008i	−0.323369	−	1.20683i	−0.915941	−	0.401312i	$-0.868554\pi$
$677$	−8.41381	−	31.4008i	−0.323369	−	1.20683i	0.592573	−	0.805517i	$-0.298112\pi$
$678$	−14.6062	−	14.6062i	−0.560946	−	0.560946i
$679$	−8.45134	+	4.87938i	−0.324332	+	0.187253i
$680$	6.13825	−	7.26831i	0.235391	−	0.278727i
$681$		−	20.1330i		−	0.771498i
$682$	1.33040	−	1.84637i	0.0509437	−	0.0707011i
$683$	17.1759	−	17.1759i	0.657216	−	0.657216i	−0.297504	−	0.954720i	$-0.596154\pi$
$683$	17.1759	−	17.1759i	0.657216	−	0.657216i	0.954720	+	0.297504i	$0.0961543\pi$
$684$			3.37468i			0.129034i
$685$	−10.0092	−	14.3917i	−0.382433	−	0.549877i
$686$	−8.60895			−0.328691
$687$	1.32522	−	0.355092i	0.0505604	−	0.0135476i
$688$	−0.287253	+	1.07204i	−0.0109514	+	0.0408712i
$689$	−0.464470	+	0.268162i	−0.0176949	+	0.0102162i
$690$	−3.78053	+	0.318667i	−0.143922	+	0.0121314i
$691$	0.206158	−	0.357077i	0.00784264	−	0.0135838i	−0.862077	−	0.506777i	$-0.830837\pi$
$691$	0.206158	−	0.357077i	0.00784264	−	0.0135838i	0.869920	+	0.493193i	$0.164170\pi$
$692$	6.66588	−	1.78612i	0.253399	−	0.0678980i
$693$	1.58627	−	0.425038i	0.0602572	−	0.0161459i
$694$	11.6281	+	20.1405i	0.441397	+	0.764522i
$695$	−31.6214	+	11.3957i	−1.19947	+	0.432265i
$696$	−2.25404	−	3.90411i	−0.0854390	−	0.147985i
$697$	−7.26175	+	7.26175i	−0.275058	+	0.275058i
$698$	−25.0354	+	25.0354i	−0.947602	+	0.947602i
$699$	1.46304	+	2.53406i	0.0553373	+	0.0958470i
$700$	−18.2603	+	8.37424i	−0.690176	+	0.316517i
$701$	21.1693	+	36.6663i	0.799553	+	1.38487i	0.919907	+	0.392136i	$0.128264\pi$
$701$	21.1693	+	36.6663i	0.799553	+	1.38487i	−0.120354	+	0.992731i	$0.538403\pi$
$702$	0.306524	−	0.0821329i	0.0115690	−	0.00309990i
$703$	−21.8586	+	5.85700i	−0.824414	+	0.220901i
$704$	0.204368	−	0.353977i	0.00770243	−	0.0133410i
$705$	10.5643	−	12.5092i	0.397873	−	0.471122i
$706$	−30.3022	+	17.4950i	−1.14044	+	0.658433i
$707$	3.57131	−	13.3283i	0.134313	−	0.501263i
$708$	−8.77906	+	2.35234i	−0.329937	+	0.0884064i
$709$	−49.7930			−1.87002			−0.935009	−	0.354625i	$-0.884609\pi$
$709$	−49.7930			−1.87002			−0.935009	+	0.354625i	$0.884609\pi$
$710$	−15.7311	+	10.9408i	−0.590376	+	0.410600i
$711$			16.4054i			0.615249i
$712$	−1.00176	+	1.00176i	−0.0375426	+	0.0375426i
$713$	−0.950500	+	9.39889i	−0.0355965	+	0.351991i
$714$		−	17.0940i		−	0.639726i
$715$	0.289010	−	0.0243611i	0.0108083	−	0.000911052i
$716$	−13.2854	+	7.67030i	−0.496497	+	0.286653i
$717$	−18.7785	−	18.7785i	−0.701297	−	0.701297i
$718$	4.82462	+	18.0057i	0.180053	+	0.671967i
$719$	−17.1717	−	29.7422i	−0.640396	−	1.10920i	−0.985344	−	0.170577i	$-0.945437\pi$
$719$	−17.1717	−	29.7422i	−0.640396	−	1.10920i	0.344948	−	0.938622i	$-0.387896\pi$
$720$	2.20085	+	0.395276i	0.0820210	+	0.0147311i
$721$	−57.1252			−2.12745
$722$	7.35215	−	1.97000i	0.273619	−	0.0733159i
$723$	3.20080	+	11.9455i	0.119039	+	0.444260i
$724$	2.87719	−	4.98344i	0.106930	−	0.185208i
$725$	17.3585	−	14.3788i	0.644680	−	0.534014i
$726$	9.38160	+	5.41647i	0.348184	+	0.201024i
$727$	5.29177	−	19.7492i	0.196261	−	0.732456i	−0.795676	−	0.605723i	$-0.792884\pi$
$727$	5.29177	−	19.7492i	0.196261	−	0.732456i	0.991937	−	0.126733i	$-0.0404493\pi$
$728$	0.901558	+	0.901558i	0.0334140	+	0.0334140i
$729$		−	1.00000i		−	0.0370370i
$730$	−15.2700	−	2.74252i	−0.565170	−	0.101505i
$731$	2.36098	−	4.08934i	0.0873241	−	0.151250i
$732$	1.15108	−	4.29591i	0.0425453	−	0.158781i
$733$	−5.50927	−	20.5609i	−0.203489	−	0.759433i	−0.989905	−	0.141735i	$-0.954732\pi$
$733$	−5.50927	−	20.5609i	−0.203489	−	0.759433i	0.786415	−	0.617698i	$-0.211935\pi$
$734$	−6.31384	+	10.9359i	−0.233048	+	0.403651i
$735$	−8.69864	+	18.5008i	−0.320854	+	0.682411i
$736$			1.69670i			0.0625412i
$737$	−0.502461	−	0.134634i	−0.0185084	−	0.00495931i
$738$	−2.33155	−	0.624738i	−0.0858257	−	0.0229969i
$739$	−7.87372	+	13.6377i	−0.289640	+	0.501671i	−0.973724	−	0.227733i	$-0.926869\pi$
$739$	−7.87372	+	13.6377i	−0.289640	+	0.501671i	0.684084	+	0.729403i	$0.260202\pi$
$740$	1.25944	+	14.9415i	0.0462980	+	0.549260i
$741$	0.535456	+	0.927437i	0.0196705	+	0.0340703i
$742$	−4.80153	+	4.80153i	−0.176270	+	0.176270i
$743$	−32.4355	−	32.4355i	−1.18994	−	1.18994i	−0.977083	−	0.212858i	$-0.931723\pi$
$743$	−32.4355	−	32.4355i	−1.18994	−	1.18994i	−0.212858	−	0.977083i	$-0.568277\pi$
$744$	1.97485	−	5.20576i	0.0724014	−	0.190853i
$745$	−11.0750	+	13.1140i	−0.405758	+	0.480458i
$746$	−18.8997			−0.691969
$747$	−9.88774	−	2.64941i	−0.361773	−	0.0969369i
$748$	−1.22966	+	1.22966i	−0.0449607	+	0.0449607i
$749$	47.2269	+	27.2664i	1.72563	+	0.996294i
$750$	−0.106446	+	11.1798i	−0.00388687	+	0.408230i
$751$	−11.1321	−	19.2813i	−0.406215	−	0.703586i	0.588247	−	0.808682i	$-0.299818\pi$
$751$	−11.1321	−	19.2813i	−0.406215	−	0.703586i	−0.994462	+	0.105096i	$0.966485\pi$
$752$	−5.17767	−	5.17767i	−0.188810	−	0.188810i
$753$	5.03134	+	18.7772i	0.183352	+	0.684280i
$754$	−1.23892	−	0.715289i	−0.0451187	−	0.0260493i
$755$	−3.00612	−	8.34153i	−0.109404	−	0.303579i
$756$	3.47952	−	2.00890i	0.126549	−	0.0730630i
$757$	−2.49068	−	9.29533i	−0.0905252	−	0.337845i	0.905778	−	0.423753i	$-0.139287\pi$
$757$	−2.49068	−	9.29533i	−0.0905252	−	0.337845i	−0.996303	+	0.0859083i	$0.972621\pi$
$758$	9.36304	+	2.50882i	0.340081	+	0.0911244i
$759$	0.693504			0.0251726
$760$	0.633819	+	7.51936i	0.0229910	+	0.272756i
$761$	4.07779	−	2.35431i	0.147820	−	0.0853437i	−0.424266	−	0.905538i	$-0.639468\pi$
$761$	4.07779	−	2.35431i	0.147820	−	0.0853437i	0.572086	+	0.820194i	$0.306135\pi$
$762$	−1.59480	+	0.427325i	−0.0577735	+	0.0154804i
$763$	41.4593	+	11.1090i	1.50093	+	0.402172i
$764$	−15.6029	−	9.00832i	−0.564492	−	0.325909i
$765$	−8.60934	−	4.04792i	−0.311272	−	0.146353i
$766$	3.56583	+	2.05873i	0.128839	+	0.0743851i
$767$	−2.03944	+	2.03944i	−0.0736398	+	0.0736398i
$768$	0.258819	−	0.965926i	0.00933933	−	0.0348548i
$769$	−30.7836	+	17.7729i	−1.11009	+	0.640908i	−0.938852	−	0.344322i	$-0.888109\pi$
$769$	−30.7836	+	17.7729i	−1.11009	+	0.640908i	−0.171234	+	0.985230i	$0.554776\pi$
$770$	3.45463	−	1.24498i	0.124496	−	0.0448660i
$771$			9.65396i			0.347679i
$772$	1.23861	−	4.62254i	0.0445784	−	0.166369i
$773$	−13.3550	−	13.3550i	−0.480345	−	0.480345i	0.424897	−	0.905242i	$-0.360310\pi$
$773$	−13.3550	−	13.3550i	−0.480345	−	0.480345i	−0.905242	+	0.424897i	$0.860310\pi$
$774$	1.10986			0.0398931
$775$	27.3144	+	5.37785i	0.981164	+	0.193178i
$776$	2.42888			0.0871918
$777$	19.0511	+	19.0511i	0.683453	+	0.683453i
$778$	3.53533	−	13.1940i	0.126748	−	0.473030i
$779$		−	8.14582i		−	0.291854i
$780$	0.667561	−	0.240576i	0.0239025	−	0.00861399i
$781$	3.03334	−	1.75130i	0.108541	−	0.0626664i
$782$	1.86834	−	6.97275i	0.0668118	−	0.249345i
$783$	−3.18769	+	3.18769i	−0.113919	+	0.113919i
$784$	7.91781	+	4.57135i	0.282779	+	0.163263i
$785$	−16.7168	−	7.85984i	−0.596647	−	0.280530i
$786$	−5.75101	−	3.32035i	−0.205132	−	0.118433i
$787$	53.3053	+	14.2831i	1.90013	+	0.509138i	0.996775	+	0.0802426i	$0.0255695\pi$
$787$	53.3053	+	14.2831i	1.90013	+	0.509138i	0.903354	+	0.428896i	$0.141097\pi$
$788$	3.81884	−	1.02326i	0.136041	−	0.0364520i
$789$	13.5419	−	7.81840i	0.482103	−	0.278342i
$790$	3.08118	+	36.5539i	0.109624	+	1.30053i
$791$	−82.9925			−2.95088
$792$	−0.394810	−	0.105789i	−0.0140289	−	0.00375904i
$793$	−0.365282	−	1.36325i	−0.0129715	−	0.0484104i
$794$	−16.1585	+	9.32910i	−0.573443	+	0.331077i
$795$	1.28126	+	3.55530i	0.0454416	+	0.126094i
$796$	−3.75757	−	2.16943i	−0.133183	−	0.0768935i
$797$	−3.09324	−	11.5441i	−0.109568	−	0.408914i	0.889255	−	0.457411i	$-0.151223\pi$
$797$	−3.09324	−	11.5441i	−0.109568	−	0.408914i	−0.998823	+	0.0484977i	$0.984557\pi$
$798$	9.58752	+	9.58752i	0.339395	+	0.339395i
$799$	15.5767	+	26.9796i	0.551063	+	0.954468i
$800$	4.97811	+	0.467386i	0.176003	+	0.0165246i
$801$	1.22690	+	0.708352i	0.0433505	+	0.0250284i
$802$	14.5093	−	14.5093i	0.512343	−	0.512343i
$803$	2.73928	+	0.733988i	0.0966672	+	0.0259019i
$804$	−1.27267			−0.0448835
$805$	−9.83520	+	11.6459i	−0.346645	+	0.410463i
$806$	−0.283260	−	1.74400i	−0.00997739	−	0.0614299i
$807$	−19.6837	−	19.6837i	−0.692899	−	0.692899i
$808$	−2.42845	+	2.42845i	−0.0854325	+	0.0854325i
$809$	5.53744	+	9.59112i	0.194686	+	0.337206i	0.946798	−	0.321830i	$-0.104298\pi$
$809$	5.53744	+	9.59112i	0.194686	+	0.337206i	−0.752112	+	0.659036i	$0.770965\pi$
$810$	−0.187816	−	2.22817i	−0.00659917	−	0.0782898i
$811$	19.0919	−	33.0681i	0.670406	−	1.16118i	−0.307383	−	0.951586i	$-0.599453\pi$
$811$	19.0919	−	33.0681i	0.670406	−	1.16118i	0.977789	−	0.209592i	$-0.0672136\pi$
$812$	−17.4954	−	4.68787i	−0.613967	−	0.164512i
$813$	18.8756	+	5.05769i	0.661995	+	0.177381i
$814$		−	2.74088i		−	0.0960677i
$815$	−5.92959	+	12.6114i	−0.207704	+	0.441758i
$816$	−2.12728	+	3.68456i	−0.0744697	+	0.128985i
$817$	0.969387	+	3.61780i	0.0339146	+	0.126571i
$818$	8.16333	−	30.4660i	0.285424	−	1.06522i
$819$	0.637498	−	1.10418i	0.0222760	−	0.0385831i
$820$	−5.31242	−	0.954118i	−0.185518	−	0.0333192i
$821$			54.7250i			1.90992i	0.296740	+	0.954958i	$0.404101\pi$
$821$			54.7250i			1.90992i	−0.296740	+	0.954958i	$0.595899\pi$
$822$	5.54351	+	5.54351i	0.193352	+	0.193352i
$823$	−3.65260	+	13.6317i	−0.127322	+	0.475171i	−0.999912	−	0.0132823i	$-0.995772\pi$
$823$	−3.65260	+	13.6317i	−0.127322	+	0.475171i	0.872590	+	0.488453i	$0.162439\pi$
$824$	12.3132	+	7.10902i	0.428950	+	0.247654i
$825$	0.191038	−	2.03474i	0.00665108	−	0.0708404i
$826$	−18.2584	+	31.6245i	−0.635291	+	1.10036i
$827$	10.6290	+	39.6679i	0.369606	+	1.37939i	0.861068	+	0.508489i	$0.169796\pi$
$827$	10.6290	+	39.6679i	0.369606	+	1.37939i	−0.491463	+	0.870899i	$0.663538\pi$
$828$	1.63889	−	0.439138i	0.0569553	−	0.0152611i
$829$	53.7491			1.86678			0.933391	−	0.358860i	$-0.116835\pi$
$829$	53.7491			1.86678			0.933391	+	0.358860i	$0.116835\pi$
$830$	−22.5291	−	4.04626i	−0.781997	−	0.140448i
$831$	6.19837	+	10.7359i	0.215019	+	0.372424i
$832$	−0.0821329	−	0.306524i	−0.00284744	−	0.0106268i
$833$	−27.5052	−	27.5052i	−0.952998	−	0.952998i
$834$	13.0179	−	7.51590i	0.450774	−	0.260254i
$835$	−32.4959	+	2.73913i	−1.12457	+	0.0947915i
$836$		−	1.37936i		−	0.0477061i
$837$	−5.53951	−	0.560205i	−0.191473	−	0.0193635i
$838$	−19.6166	+	19.6166i	−0.677643	+	0.677643i
$839$		−	36.3997i		−	1.25666i	−0.777947	−	0.628329i	$-0.783739\pi$
$839$		−	36.3997i		−	1.25666i	0.777947	−	0.628329i	$-0.216261\pi$
$840$	7.37564	−	5.12967i	0.254484	−	0.176990i
$841$	−8.67727			−0.299216
$842$	−18.3615	+	4.91995i	−0.632779	+	0.169553i
$843$	5.55002	−	20.7130i	0.191153	−	0.713392i
$844$	23.6617	−	13.6611i	0.814468	−	0.470233i
$845$	−18.6104	+	22.0366i	−0.640217	+	0.758082i
$846$	−3.66117	+	6.34133i	−0.125874	+	0.218019i
$847$	42.0415	−	11.2650i	1.44456	−	0.387069i
$848$	1.63249	−	0.437424i	0.0560599	−	0.0150212i
$849$	6.82386	+	11.8193i	0.234194	+	0.405636i
$850$	−19.9433	−	7.40246i	−0.684050	−	0.253902i
$851$	5.68881	+	9.85330i	0.195010	+	0.337767i
$852$	6.05943	−	6.05943i	0.207593	−	0.207593i
$853$	−29.3798	+	29.3798i	−1.00595	+	1.00595i	−0.00596393	+	0.999982i	$0.501898\pi$
$853$	−29.3798	+	29.3798i	−1.00595	+	1.00595i	−0.999982	+	0.00596393i	$0.998102\pi$
$854$	−8.93448	−	15.4750i	−0.305732	−	0.529543i
$855$	7.09910	−	2.55837i	0.242784	−	0.0874946i
$856$	−6.78641	−	11.7544i	−0.231955	−	0.401758i
$857$	52.5751	−	14.0875i	1.79593	−	0.481219i	0.802602	−	0.596515i	$-0.203449\pi$
$857$	52.5751	−	14.0875i	1.79593	−	0.481219i	0.993331	+	0.115297i	$0.0367819\pi$
$858$	−0.125288	+	0.0335707i	−0.00427725	+	0.00114609i
$859$	11.0518	−	19.1423i	0.377082	−	0.653126i	−0.613554	−	0.789653i	$-0.710261\pi$
$859$	11.0518	−	19.1423i	0.377082	−	0.653126i	0.990636	+	0.136527i	$0.0435941\pi$
$860$	2.47295	−	0.208449i	0.0843269	−	0.00710805i
$861$	−8.39886	+	4.84908i	−0.286232	+	0.165256i
$862$	−6.33088	+	23.6272i	−0.215631	+	0.804744i
$863$	−20.3185	+	5.44434i	−0.691651	+	0.185327i	−0.587488	−	0.809233i	$-0.699883\pi$
$863$	−20.3185	+	5.44434i	−0.691651	+	0.185327i	−0.104163	+	0.994560i	$0.533216\pi$
$864$	−1.00000			−0.0340207
$865$	−8.81080	−	12.6685i	−0.299576	−	0.430742i
$866$			17.5043i			0.594820i
$867$	0.778730	−	0.778730i	0.0264470	−	0.0264470i
$868$	−9.17908	−	20.4002i	−0.311558	−	0.692428i
$869$		−	6.70548i		−	0.227468i
$870$	−6.50400	+	7.70140i	−0.220506	+	0.261102i
$871$	−0.349757	+	0.201932i	−0.0118510	+	0.00684221i
$872$	−7.55396	−	7.55396i	−0.255809	−	0.255809i
$873$	−0.628641	−	2.34612i	−0.0212763	−	0.0794042i
$874$	2.86292	+	4.95871i	0.0968395	+	0.167731i
$875$	31.4596	+	32.0645i	1.06353	+	1.08398i
$876$	6.93824			0.234421
$877$	−14.2383	+	3.81514i	−0.480793	+	0.128828i	−0.491072	−	0.871119i	$-0.663395\pi$
$877$	−14.2383	+	3.81514i	−0.480793	+	0.128828i	0.0102786	+	0.999947i	$0.496728\pi$
$878$	0.258724	+	0.965573i	0.00873152	+	0.0325865i
$879$	−3.93796	+	6.82075i	−0.132824	+	0.230058i
$880$	−0.899570	−	0.161564i	−0.0303245	−	0.00544632i
$881$	43.8545	+	25.3194i	1.47750	+	0.853033i	0.999677	−	0.0254244i	$-0.00809371\pi$
$881$	43.8545	+	25.3194i	1.47750	+	0.853033i	0.477820	+	0.878458i	$0.341427\pi$
$882$	2.36631	−	8.83117i	0.0796777	−	0.297361i
$883$	2.30578	+	2.30578i	0.0775956	+	0.0775956i	0.744839	−	0.667244i	$-0.232526\pi$
$883$	2.30578	+	2.30578i	0.0775956	+	0.0775956i	−0.667244	+	0.744839i	$0.732526\pi$
$884$			1.35013i			0.0454098i
$885$	11.6039	+	16.6846i	0.390062	+	0.560847i
$886$	−15.1232	+	26.1942i	−0.508075	+	0.880012i
$887$	−8.61763	+	32.1614i	−0.289352	+	1.07988i	0.656249	+	0.754545i	$0.272142\pi$
$887$	−8.61763	+	32.1614i	−0.289352	+	1.07988i	−0.945600	+	0.325331i	$0.894524\pi$
$888$	−1.73557	−	6.47723i	−0.0582419	−	0.217362i
$889$	−3.31681	+	5.74488i	−0.111242	+	0.192677i
$890$	2.86678	+	1.34790i	0.0960948	+	0.0451816i
$891$			0.408737i			0.0136932i
$892$	−27.3693	−	7.33359i	−0.916394	−	0.245547i
$893$	−23.8686	−	6.39557i	−0.798731	−	0.214019i
$894$	3.83818	−	6.64792i	0.128368	−	0.222340i
$895$	26.2072	+	22.1326i	0.876011	+	0.739811i
$896$	−2.00890	−	3.47952i	−0.0671126	−	0.116242i
$897$	0.380725	−	0.380725i	0.0127120	−	0.0127120i
$898$	−11.7494	−	11.7494i	−0.392082	−	0.392082i
$899$	15.8725	+	19.4440i	0.529377	+	0.648494i
$900$	−0.836969	−	4.92945i	−0.0278990	−	0.164315i
$901$	−7.19054			−0.239552
$902$	0.952992	+	0.255353i	0.0317312	+	0.00850234i
$903$	3.15312	−	3.15312i	0.104929	−	0.104929i
$904$	17.8888	+	10.3281i	0.594973	+	0.343508i
$905$	−12.6646	−	2.27457i	−0.420984	−	0.0756092i
$906$	1.98265	+	3.43405i	0.0658691	+	0.114089i
$907$	40.1307	+	40.1307i	1.33252	+	1.33252i	0.903111	+	0.429408i	$0.141278\pi$
$907$	40.1307	+	40.1307i	1.33252	+	1.33252i	0.429408	+	0.903111i	$0.358722\pi$
$908$	5.21080	+	19.4470i	0.172926	+	0.645370i
$909$	2.97423	+	1.71717i	0.0986489	+	0.0569550i
$910$	1.21307	−	2.58003i	0.0402129	−	0.0855270i
$911$	−9.74009	+	5.62345i	−0.322704	+	0.186313i	−0.652597	−	0.757705i	$-0.726321\pi$
$911$	−9.74009	+	5.62345i	−0.322704	+	0.186313i	0.329893	+	0.944018i	$0.392987\pi$
$912$	−0.873433	−	3.25969i	−0.0289222	−	0.107939i
$913$	4.04148	+	1.08291i	0.133754	+	0.0358392i
$914$	26.5151			0.877041
$915$	−9.90966	+	0.835301i	−0.327603	+	0.0276142i
$916$	−1.18816	+	0.685986i	−0.0392580	+	0.0226656i
$917$	−25.7718	+	6.90554i	−0.851061	+	0.228041i
$918$	4.10959	+	1.10116i	0.135637	+	0.0363437i
$919$	−45.9890	−	26.5518i	−1.51704	−	0.875862i	−0.999800	−	0.0200201i	$-0.993627\pi$
$919$	−45.9890	−	26.5518i	−1.51704	−	0.875862i	−0.517238	−	0.855842i	$-0.673040\pi$
$920$	3.56924	−	1.28628i	0.117674	−	0.0424075i
$921$	−27.4325	−	15.8382i	−0.903933	−	0.521886i
$922$	−1.04160	+	1.04160i	−0.0343032	+	0.0343032i
$923$	0.703823	−	2.62670i	0.0231666	−	0.0864590i
$924$	−1.42221	+	0.821111i	−0.0467872	+	0.0270126i
$925$	30.4766	−	13.9767i	1.00206	−	0.459549i
$926$		−	40.1018i		−	1.31783i
$927$	3.67990	−	13.7336i	0.120864	−	0.451070i
$928$	3.18769	+	3.18769i	0.104641	+	0.104641i
$929$	−9.53472			−0.312824			−0.156412	−	0.987692i	$-0.549993\pi$
$929$	−9.53472			−0.312824			−0.156412	+	0.987692i	$0.549993\pi$
$930$	−12.4482	−	0.207823i	−0.408191	−	0.00681478i
$931$	30.8537			1.01119
$932$	−2.06905	−	2.06905i	−0.0677741	−	0.0677741i
$933$	5.98884	−	22.3506i	0.196066	−	0.731727i
$934$		−	16.9731i		−	0.555378i
$935$	3.51896	+	1.65453i	0.115082	+	0.0541090i
$936$	−0.274822	+	0.158668i	−0.00898283	+	0.00518624i
$937$	4.03942	−	15.0753i	0.131962	−	0.492489i	−0.868030	−	0.496512i	$-0.834614\pi$
$937$	4.03942	−	15.0753i	0.131962	−	0.492489i	0.999992	+	0.00402311i	$0.00128060\pi$
$938$	−3.61566	+	3.61566i	−0.118055	+	0.118055i
$939$	17.0755	+	9.85856i	0.557239	+	0.321722i
$940$	−6.96669	+	14.8172i	−0.227228	+	0.483282i
$941$	12.6520	+	7.30462i	0.412442	+	0.238124i	0.691839	−	0.722052i	$-0.256801\pi$
$941$	12.6520	+	7.30462i	0.412442	+	0.238124i	−0.279396	+	0.960176i	$0.590134\pi$
$942$	7.97959	+	2.13812i	0.259989	+	0.0696638i
$943$	−3.95595	+	1.05999i	−0.128823	+	0.0345181i
$944$	7.87109	−	4.54438i	0.256182	−	0.147907i
$945$	−6.86383	−	5.79666i	−0.223281	−	0.188565i
$946$	−0.453640			−0.0147491
$947$	−28.6344	−	7.67257i	−0.930494	−	0.249325i	−0.238429	−	0.971160i	$-0.576632\pi$
$947$	−28.6344	−	7.67257i	−0.930494	−	0.249325i	−0.692065	+	0.721835i	$0.743299\pi$
$948$	−4.24602	−	15.8464i	−0.137904	−	0.514666i
$949$	1.90678	−	1.10088i	0.0618967	−	0.0357361i
$950$	15.3375	−	7.03381i	0.497613	−	0.228207i
$951$	4.19910	+	2.42435i	0.136165	+	0.0786150i
$952$	4.42424	+	16.5115i	0.143391	+	0.535141i
$953$	−19.7831	−	19.7831i	−0.640837	−	0.640837i	0.309924	−	0.950761i	$-0.399696\pi$
$953$	−19.7831	−	19.7831i	−0.640837	−	0.640837i	−0.950761	+	0.309924i	$0.899696\pi$
$954$	−0.845039	−	1.46365i	−0.0273591	−	0.0473874i
$955$	−7.12154	+	39.6520i	−0.230448	+	1.28311i
$956$	22.9989	+	13.2784i	0.743838	+	0.429455i
$957$	1.30293	−	1.30293i	0.0421176	−	0.0421176i
$958$	−16.3158	−	4.37181i	−0.527140	−	0.141247i
$959$	31.4983			1.01713
$960$	−2.22817	+	0.187816i	−0.0719138	+	0.00606172i
$961$	−6.20652	+	30.3723i	−0.200210	+	0.979753i
$962$	−1.50471	−	1.50471i	−0.0485137	−	0.0485137i
$963$	−9.59744	+	9.59744i	−0.309273	+	0.309273i
$964$	−6.18347	−	10.7101i	−0.199156	−	0.344949i
$965$	−10.6631	+	0.898811i	−0.343258	+	0.0289338i
$966$	3.40850	−	5.90370i	0.109667	−	0.189948i
$967$	15.1583	+	4.06164i	0.487457	+	0.130614i	0.494173	−	0.869364i	$-0.335471\pi$
$967$	15.1583	+	4.06164i	0.487457	+	0.130614i	−0.00671594	+	0.999977i	$0.502138\pi$
$968$	−10.4638	−	2.80377i	−0.336320	−	0.0901166i
$969$			14.3578i			0.461239i
$970$	−1.84136	−	5.10948i	−0.0591224	−	0.164055i
$971$	22.9135	−	39.6873i	0.735329	−	1.27363i	−0.219250	−	0.975669i	$-0.570361\pi$
$971$	22.9135	−	39.6873i	0.735329	−	1.27363i	0.954579	−	0.297958i	$-0.0963055\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	15.6313	−	58.3368i	0.501117	−	1.87019i
$974$	−13.6383	+	23.6223i	−0.437000	+	0.756907i
$975$	−1.01217	−	1.22192i	−0.0324153	−	0.0391328i
$976$			4.44745i			0.142359i
$977$	30.2771	+	30.2771i	0.968650	+	0.968650i	0.999523	−	0.0308734i	$-0.00982888\pi$
$977$	30.2771	+	30.2771i	0.968650	+	0.968650i	−0.0308734	+	0.999523i	$0.509829\pi$
$978$	1.61304	−	6.01993i	0.0515792	−	0.192496i
$979$	−0.501480	−	0.289530i	−0.0160274	−	0.00925341i
$980$	3.61389	−	20.1218i	0.115441	−	0.642766i
$981$	−5.34146	+	9.25168i	−0.170540	+	0.295383i
$982$	−1.16764	−	4.35769i	−0.0372609	−	0.139059i
$983$	22.0137	−	5.89856i	0.702128	−	0.188135i	0.109945	−	0.993938i	$-0.464933\pi$
$983$	22.0137	−	5.89856i	0.702128	−	0.188135i	0.592184	+	0.805803i	$0.298266\pi$
$984$	2.41380			0.0769492
$985$	−5.04765	−	7.25770i	−0.160831	−	0.231250i
$986$	−9.58994	−	16.6103i	−0.305406	−	0.528978i
$987$	7.61437	+	28.4172i	0.242368	+	0.904530i
$988$	−0.757249	−	0.757249i	−0.0240913	−	0.0240913i
$989$	1.63081	−	0.941549i	0.0518568	−	0.0299395i
$990$	0.0767672	+	0.910734i	0.00243982	+	0.0289450i
$991$		−	53.2759i		−	1.69236i	−0.532894	−	0.846182i	$-0.678896\pi$
$991$		−	53.2759i		−	1.69236i	0.532894	−	0.846182i	$-0.321104\pi$
$992$	−0.560205	+	5.53951i	−0.0177865	+	0.175880i
$993$	14.1477	−	14.1477i	0.448965	−	0.448965i
$994$		−	34.4298i		−	1.09205i
$995$	−1.71505	+	9.54921i	−0.0543707	+	0.302730i
$996$	10.2365			0.324357
$997$	−54.1509	+	14.5097i	−1.71498	+	0.459526i	−0.976636	−	0.214902i	$-0.931057\pi$
$997$	−54.1509	+	14.5097i	−1.71498	+	0.459526i	−0.738340	+	0.674429i	$0.764390\pi$
$998$	8.05780	−	30.0721i	0.255065	−	0.951917i
$999$	−5.80733	+	3.35286i	−0.183736	+	0.106080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.37.7	yes	64
5.3	odd	4		930.2.be.a.223.4	✓	64
31.26	odd	6		930.2.be.a.367.4	yes	64
155.88	even	12	inner	930.2.be.b.553.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.4	✓	64	5.3	odd	4
930.2.be.a.367.4	yes	64	31.26	odd	6
930.2.be.b.37.7	yes	64	1.1	even	1	trivial
930.2.be.b.553.7	yes	64	155.88	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(2.10363 - 0.758108i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-1.03988 + 3.88090i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.258819 - 0.965926i) q^{3} +1.00000i q^{4} +(2.10363 - 0.758108i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-1.03988 + 3.88090i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.02356 - 0.951430i) q^{10} +(0.353977 + 0.204368i) q^{11} +(0.965926 + 0.258819i) q^{12} +(0.306524 - 0.0821329i) q^{13} +(3.47952 - 2.00890i) q^{14} +(-0.187816 - 2.22817i) q^{15} -1.00000 q^{16} +(4.10959 + 1.10116i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-2.92256 + 1.68734i) q^{19} +(0.758108 + 2.10363i) q^{20} +(3.47952 + 2.00890i) q^{21} +(-0.105789 - 0.394810i) q^{22} +(1.19975 + 1.19975i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(3.85054 - 3.18956i) q^{25} +(-0.274822 - 0.158668i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-3.88090 - 1.03988i) q^{28} +4.50807 q^{29} +(-1.44275 + 1.70836i) q^{30} +(3.52090 + 4.31315i) q^{31} +(0.707107 + 0.707107i) q^{32} +(0.289021 - 0.289021i) q^{33} +(-2.12728 - 3.68456i) q^{34} +(0.754605 + 8.95232i) q^{35} +(0.500000 - 0.866025i) q^{36} +(6.47723 + 1.73557i) q^{37} +(3.25969 + 0.873433i) q^{38} -0.317337i q^{39} +(0.951430 - 2.02356i) q^{40} +(-1.20690 + 2.09041i) q^{41} +(-1.03988 - 3.88090i) q^{42} +(0.287253 - 1.07204i) q^{43} +(-0.204368 + 0.353977i) q^{44} +(-2.20085 - 0.395276i) q^{45} -1.69670i q^{46} +(5.17767 + 5.17767i) q^{47} +(-0.258819 + 0.965926i) q^{48} +(-7.91781 - 4.57135i) q^{49} +(-4.97811 - 0.467386i) q^{50} +(2.12728 - 3.68456i) q^{51} +(0.0821329 + 0.306524i) q^{52} +(-1.63249 + 0.437424i) q^{53} +1.00000 q^{54} +(0.899570 + 0.161564i) q^{55} +(2.00890 + 3.47952i) q^{56} +(0.873433 + 3.25969i) q^{57} +(-3.18769 - 3.18769i) q^{58} +(-7.87109 + 4.54438i) q^{59} +(2.22817 - 0.187816i) q^{60} -4.44745i q^{61} +(0.560205 - 5.53951i) q^{62} +(2.84101 - 2.84101i) q^{63} -1.00000i q^{64} +(0.582548 - 0.405156i) q^{65} -0.408737 q^{66} +(-1.22930 + 0.329390i) q^{67} +(-1.10116 + 4.10959i) q^{68} +(1.46939 - 0.848350i) q^{69} +(5.79666 - 6.86383i) q^{70} +(4.28466 - 7.42125i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(6.70182 - 1.79575i) q^{73} +(-3.35286 - 5.80733i) q^{74} +(-2.08429 - 4.54486i) q^{75} +(-1.68734 - 2.92256i) q^{76} +(-1.16123 + 1.16123i) q^{77} +(-0.224391 + 0.224391i) q^{78} +(-8.20268 - 14.2075i) q^{79} +(-2.10363 + 0.758108i) q^{80} +(0.500000 + 0.866025i) q^{81} +(2.33155 - 0.624738i) q^{82} +(9.88774 - 2.64941i) q^{83} +(-2.00890 + 3.47952i) q^{84} +(9.47987 - 0.799073i) q^{85} +(-0.961166 + 0.554930i) q^{86} +(1.16678 - 4.35446i) q^{87} +(0.394810 - 0.105789i) q^{88} -1.41670 q^{89} +(1.27674 + 1.83574i) q^{90} +1.27500i q^{91} +(-1.19975 + 1.19975i) q^{92} +(5.07746 - 2.28460i) q^{93} -7.32233i q^{94} +(-4.86881 + 5.76517i) q^{95} +(0.866025 - 0.500000i) q^{96} +(1.71748 + 1.71748i) q^{97} +(2.36631 + 8.83117i) q^{98} +(-0.204368 - 0.353977i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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