LMFDB - Embedded newform 930.2.j.h.683.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(497,930)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("930.497"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [40,0,-4,0,0,8,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			683.1
Character	$\chi$	$=$	930.683
Dual form			930.2.j.h.497.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.73016 - 0.0809240i) q^{3} +1.00000i q^{4} +(-0.662050 + 2.13581i) q^{5} +(1.16619 + 1.28063i) q^{6} +(2.89525 - 2.89525i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.98690 + 0.280023i) q^{9} +(1.97839 - 1.04211i) q^{10} +1.62335i q^{11} +(0.0809240 - 1.73016i) q^{12} +(-1.74736 - 1.74736i) q^{13} -4.09450 q^{14} +(1.31829 - 3.64172i) q^{15} -1.00000 q^{16} +(-0.396012 - 0.396012i) q^{17} +(-1.91405 - 2.31007i) q^{18} +4.55776i q^{19} +(-2.13581 - 0.662050i) q^{20} +(-5.24354 + 4.77495i) q^{21} +(1.14789 - 1.14789i) q^{22} +(0.0718525 - 0.0718525i) q^{23} +(-1.28063 + 1.16619i) q^{24} +(-4.12338 - 2.82803i) q^{25} +2.47114i q^{26} +(-5.14516 - 0.726196i) q^{27} +(2.89525 + 2.89525i) q^{28} +3.20334 q^{29} +(-3.50726 + 1.64291i) q^{30} -1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.131368 - 2.80866i) q^{33} +0.560046i q^{34} +(4.26691 + 8.10050i) q^{35} +(-0.280023 + 2.98690i) q^{36} +(5.51900 - 5.51900i) q^{37} +(3.22282 - 3.22282i) q^{38} +(2.88181 + 3.16462i) q^{39} +(1.04211 + 1.97839i) q^{40} -4.20851i q^{41} +(7.08414 + 0.331343i) q^{42} +(7.67725 + 7.67725i) q^{43} -1.62335 q^{44} +(-2.57555 + 6.19407i) q^{45} -0.101615 q^{46} +(6.63515 + 6.63515i) q^{47} +(1.73016 + 0.0809240i) q^{48} -9.76493i q^{49} +(0.915953 + 4.91539i) q^{50} +(0.653117 + 0.717211i) q^{51} +(1.74736 - 1.74736i) q^{52} +(-2.49463 + 2.49463i) q^{53} +(3.12468 + 4.15167i) q^{54} +(-3.46718 - 1.07474i) q^{55} -4.09450i q^{56} +(0.368832 - 7.88565i) q^{57} +(-2.26510 - 2.26510i) q^{58} +6.90534 q^{59} +(3.64172 + 1.31829i) q^{60} +8.74025 q^{61} +(0.707107 + 0.707107i) q^{62} +(9.45856 - 7.83709i) q^{63} -1.00000i q^{64} +(4.88888 - 2.57520i) q^{65} +(-2.07892 + 1.89313i) q^{66} +(7.82013 - 7.82013i) q^{67} +(0.396012 - 0.396012i) q^{68} +(-0.130131 + 0.118502i) q^{69} +(2.71076 - 8.74508i) q^{70} +7.38175i q^{71} +(2.31007 - 1.91405i) q^{72} +(7.37382 + 7.37382i) q^{73} -7.80505 q^{74} +(6.90525 + 5.22662i) q^{75} -4.55776 q^{76} +(4.70002 + 4.70002i) q^{77} +(0.199975 - 4.27547i) q^{78} +0.229093i q^{79} +(0.662050 - 2.13581i) q^{80} +(8.84317 + 1.67280i) q^{81} +(-2.97586 + 2.97586i) q^{82} +(-0.833196 + 0.833196i) q^{83} +(-4.77495 - 5.24354i) q^{84} +(1.10799 - 0.583627i) q^{85} -10.8573i q^{86} +(-5.54228 - 0.259227i) q^{87} +(1.14789 + 1.14789i) q^{88} -10.4607 q^{89} +(6.20106 - 2.55868i) q^{90} -10.1181 q^{91} +(0.0718525 + 0.0718525i) q^{92} +(1.73016 + 0.0809240i) q^{93} -9.38351i q^{94} +(-9.73452 - 3.01746i) q^{95} +(-1.16619 - 1.28063i) q^{96} +(7.96436 - 7.96436i) q^{97} +(-6.90485 + 6.90485i) q^{98} +(-0.454576 + 4.84880i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−1.73016	−	0.0809240i	−0.998908	−	0.0467215i
$3$	−1.73016	−	0.0809240i	−0.998908	−	0.0467215i
$4$			1.00000i			0.500000i
$5$	−0.662050	+	2.13581i	−0.296078	+	0.955164i
$5$	−0.662050	+	2.13581i	−0.296078	+	0.955164i
$6$	1.16619	+	1.28063i	0.476093	+	0.522815i
$7$	2.89525	−	2.89525i	1.09430	−	1.09430i	0.0992373	−	0.995064i	$-0.468360\pi$
$7$	2.89525	−	2.89525i	1.09430	−	1.09430i	0.995064	−	0.0992373i	$-0.0316403\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.98690	+	0.280023i	0.995634	+	0.0933409i
$10$	1.97839	−	1.04211i	0.625621	−	0.329543i
$11$			1.62335i			0.489460i	0.969591	+	0.244730i	$0.0786993\pi$
$11$			1.62335i			0.489460i	−0.969591	+	0.244730i	$0.921301\pi$
$12$	0.0809240	−	1.73016i	0.0233607	−	0.499454i
$13$	−1.74736	−	1.74736i	−0.484631	−	0.484631i	0.421976	−	0.906607i	$-0.361337\pi$
$13$	−1.74736	−	1.74736i	−0.484631	−	0.484631i	−0.906607	+	0.421976i	$0.861337\pi$
$14$	−4.09450			−1.09430
$15$	1.31829	−	3.64172i	0.340381	−	0.940288i
$16$	−1.00000			−0.250000
$17$	−0.396012	−	0.396012i	−0.0960470	−	0.0960470i	0.657451	−	0.753498i	$-0.271635\pi$
$17$	−0.396012	−	0.396012i	−0.0960470	−	0.0960470i	−0.753498	+	0.657451i	$0.771635\pi$
$18$	−1.91405	−	2.31007i	−0.451147	−	0.544488i
$19$			4.55776i			1.04562i	0.852449	+	0.522811i	$0.175117\pi$
$19$			4.55776i			1.04562i	−0.852449	+	0.522811i	$0.824883\pi$
$20$	−2.13581	−	0.662050i	−0.477582	−	0.148039i
$21$	−5.24354	+	4.77495i	−1.14423	+	1.04198i
$22$	1.14789	−	1.14789i	0.244730	−	0.244730i
$23$	0.0718525	−	0.0718525i	0.0149823	−	0.0149823i	−0.699576	−	0.714558i	$-0.746628\pi$
$23$	0.0718525	−	0.0718525i	0.0149823	−	0.0149823i	0.714558	+	0.699576i	$0.246628\pi$
$24$	−1.28063	+	1.16619i	−0.261407	+	0.238047i
$25$	−4.12338	−	2.82803i	−0.824676	−	0.565605i
$26$			2.47114i			0.484631i
$27$	−5.14516	−	0.726196i	−0.990186	−	0.139756i
$28$	2.89525	+	2.89525i	0.547151	+	0.547151i
$29$	3.20334			0.594845			0.297422	−	0.954746i	$-0.403873\pi$
$29$	3.20334			0.594845			0.297422	+	0.954746i	$0.403873\pi$
$30$	−3.50726	+	1.64291i	−0.640334	+	0.299953i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	0.131368	−	2.80866i	0.0228683	−	0.488925i
$34$			0.560046i			0.0960470i
$35$	4.26691	+	8.10050i	0.721239	+	1.36923i
$36$	−0.280023	+	2.98690i	−0.0466705	+	0.497817i
$37$	5.51900	−	5.51900i	0.907319	−	0.907319i	−0.0887366	−	0.996055i	$-0.528283\pi$
$37$	5.51900	−	5.51900i	0.907319	−	0.907319i	0.996055	+	0.0887366i	$0.0282829\pi$
$38$	3.22282	−	3.22282i	0.522811	−	0.522811i
$39$	2.88181	+	3.16462i	0.461459	+	0.506745i
$40$	1.04211	+	1.97839i	0.164772	+	0.312810i
$41$		−	4.20851i		−	0.657258i	−0.944459	−	0.328629i	$-0.893413\pi$
$41$		−	4.20851i		−	0.657258i	0.944459	−	0.328629i	$-0.106587\pi$
$42$	7.08414	+	0.331343i	1.09311	+	0.0511274i
$43$	7.67725	+	7.67725i	1.17077	+	1.17077i	0.982026	+	0.188744i	$0.0604417\pi$
$43$	7.67725	+	7.67725i	1.17077	+	1.17077i	0.188744	+	0.982026i	$0.439558\pi$
$44$	−1.62335			−0.244730
$45$	−2.57555	+	6.19407i	−0.383941	+	0.923358i
$46$	−0.101615			−0.0149823
$47$	6.63515	+	6.63515i	0.967835	+	0.967835i	0.999499	−	0.0316631i	$-0.0100804\pi$
$47$	6.63515	+	6.63515i	0.967835	+	0.967835i	−0.0316631	+	0.999499i	$0.510080\pi$
$48$	1.73016	+	0.0809240i	0.249727	+	0.0116804i
$49$		−	9.76493i		−	1.39499i
$50$	0.915953	+	4.91539i	0.129535	+	0.695141i
$51$	0.653117	+	0.717211i	0.0914547	+	0.100430i
$52$	1.74736	−	1.74736i	0.242316	−	0.242316i
$53$	−2.49463	+	2.49463i	−0.342664	+	0.342664i	−0.857368	−	0.514704i	$-0.827902\pi$
$53$	−2.49463	+	2.49463i	−0.342664	+	0.342664i	0.514704	+	0.857368i	$0.327902\pi$
$54$	3.12468	+	4.15167i	0.425215	+	0.564971i
$55$	−3.46718	−	1.07474i	−0.467514	−	0.144918i
$56$		−	4.09450i		−	0.547151i
$57$	0.368832	−	7.88565i	0.0488530	−	1.04448i
$58$	−2.26510	−	2.26510i	−0.297422	−	0.297422i
$59$	6.90534			0.898998			0.449499	−	0.893281i	$-0.351602\pi$
$59$	6.90534			0.898998			0.449499	+	0.893281i	$0.351602\pi$
$60$	3.64172	+	1.31829i	0.470144	+	0.170191i
$61$	8.74025			1.11907			0.559537	−	0.828805i	$-0.310979\pi$
$61$	8.74025			1.11907			0.559537	+	0.828805i	$0.310979\pi$
$62$	0.707107	+	0.707107i	0.0898027	+	0.0898027i
$63$	9.45856	−	7.83709i	1.19167	−	0.987381i
$64$		−	1.00000i		−	0.125000i
$65$	4.88888	−	2.57520i	0.606391	−	0.319414i
$66$	−2.07892	+	1.89313i	−0.255897	+	0.233029i
$67$	7.82013	−	7.82013i	0.955381	−	0.955381i	−0.0436654	−	0.999046i	$-0.513904\pi$
$67$	7.82013	−	7.82013i	0.955381	−	0.955381i	0.999046	+	0.0436654i	$0.0139036\pi$
$68$	0.396012	−	0.396012i	0.0480235	−	0.0480235i
$69$	−0.130131	+	0.118502i	−0.0156659	+	0.0142659i
$70$	2.71076	−	8.74508i	0.323998	−	1.04524i
$71$			7.38175i			0.876053i	0.898962	+	0.438026i	$0.144322\pi$
$71$			7.38175i			0.876053i	−0.898962	+	0.438026i	$0.855678\pi$
$72$	2.31007	−	1.91405i	0.272244	−	0.225573i
$73$	7.37382	+	7.37382i	0.863040	+	0.863040i	0.991690	−	0.128650i	$-0.0410643\pi$
$73$	7.37382	+	7.37382i	0.863040	+	0.863040i	−0.128650	+	0.991690i	$0.541064\pi$
$74$	−7.80505			−0.907319
$75$	6.90525	+	5.22662i	0.797350	+	0.603518i
$76$	−4.55776			−0.522811
$77$	4.70002	+	4.70002i	0.535617	+	0.535617i
$78$	0.199975	−	4.27547i	0.0226427	−	0.484102i
$79$			0.229093i			0.0257750i	0.999917	+	0.0128875i	$0.00410233\pi$
$79$			0.229093i			0.0257750i	−0.999917	+	0.0128875i	$0.995898\pi$
$80$	0.662050	−	2.13581i	0.0740194	−	0.238791i
$81$	8.84317	+	1.67280i	0.982575	+	0.185867i
$82$	−2.97586	+	2.97586i	−0.328629	+	0.328629i
$83$	−0.833196	+	0.833196i	−0.0914551	+	0.0914551i	−0.751354	−	0.659899i	$-0.770599\pi$
$83$	−0.833196	+	0.833196i	−0.0914551	+	0.0914551i	0.659899	+	0.751354i	$0.270599\pi$
$84$	−4.77495	−	5.24354i	−0.520989	−	0.572117i
$85$	1.10799	−	0.583627i	0.120178	−	0.0633033i
$86$		−	10.8573i		−	1.17077i
$87$	−5.54228	−	0.259227i	−0.594195	−	0.0277920i
$88$	1.14789	+	1.14789i	0.122365	+	0.122365i
$89$	−10.4607			−1.10883			−0.554415	−	0.832241i	$-0.687058\pi$
$89$	−10.4607			−1.10883			−0.554415	+	0.832241i	$0.687058\pi$
$90$	6.20106	−	2.55868i	0.653649	−	0.269708i
$91$	−10.1181			−1.06067
$92$	0.0718525	+	0.0718525i	0.00749115	+	0.00749115i
$93$	1.73016	+	0.0809240i	0.179409	+	0.00839143i
$94$		−	9.38351i		−	0.967835i
$95$	−9.73452	−	3.01746i	−0.998740	−	0.309585i
$96$	−1.16619	−	1.28063i	−0.119023	−	0.130704i
$97$	7.96436	−	7.96436i	0.808658	−	0.808658i	−0.175772	−	0.984431i	$-0.556242\pi$
$97$	7.96436	−	7.96436i	0.808658	−	0.808658i	0.984431	+	0.175772i	$0.0562423\pi$
$98$	−6.90485	+	6.90485i	−0.697495	+	0.697495i
$99$	−0.454576	+	4.84880i	−0.0456866	+	0.487323i
$100$	2.82803	−	4.12338i	0.282803	−	0.412338i
$101$			13.5753i			1.35079i	0.737456	+	0.675395i	$0.236027\pi$
$101$			13.5753i			1.35079i	−0.737456	+	0.675395i	$0.763973\pi$
$102$	0.0453211	−	0.968968i	0.00448746	−	0.0959421i
$103$	−1.42399	−	1.42399i	−0.140310	−	0.140310i	0.633463	−	0.773773i	$-0.281633\pi$
$103$	−1.42399	−	1.42399i	−0.140310	−	0.140310i	−0.773773	+	0.633463i	$0.781633\pi$
$104$	−2.47114			−0.242316
$105$	−6.72690	−	14.3605i	−0.656478	−	1.40144i
$106$	3.52794			0.342664
$107$	−3.00041	−	3.00041i	−0.290061	−	0.290061i	0.547044	−	0.837104i	$-0.315753\pi$
$107$	−3.00041	−	3.00041i	−0.290061	−	0.290061i	−0.837104	+	0.547044i	$0.815753\pi$
$108$	0.726196	−	5.14516i	0.0698782	−	0.495093i
$109$			7.90833i			0.757481i	0.925503	+	0.378740i	$0.123643\pi$
$109$			7.90833i			0.757481i	−0.925503	+	0.378740i	$0.876357\pi$
$110$	1.69171	+	3.21162i	0.161298	+	0.306216i
$111$	−9.99537	+	9.10214i	−0.948719	+	0.863936i
$112$	−2.89525	+	2.89525i	−0.273575	+	0.273575i
$113$	13.5684	−	13.5684i	1.27641	−	1.27641i	0.333747	−	0.942663i	$-0.391687\pi$
$113$	13.5684	−	13.5684i	1.27641	−	1.27641i	0.942663	−	0.333747i	$-0.108313\pi$
$114$	−5.83680	+	5.31519i	−0.546667	+	0.497814i
$115$	0.105894	+	0.201033i	0.00987462	+	0.0187465i
$116$			3.20334i			0.297422i
$117$	−4.72990	−	5.70851i	−0.437280	−	0.527751i
$118$	−4.88281	−	4.88281i	−0.449499	−	0.449499i
$119$	−2.29311			−0.210209
$120$	−1.64291	−	3.50726i	−0.149977	−	0.320167i
$121$	8.36472			0.760429
$122$	−6.18029	−	6.18029i	−0.559537	−	0.559537i
$123$	−0.340569	+	7.28139i	−0.0307081	+	0.656541i
$124$		−	1.00000i		−	0.0898027i
$125$	8.77002	−	6.93447i	0.784414	−	0.620238i
$126$	−12.2299	−	1.14655i	−1.08952	−	0.102143i
$127$	−1.53100	+	1.53100i	−0.135854	+	0.135854i	−0.771764	−	0.635910i	$-0.780625\pi$
$127$	−1.53100	+	1.53100i	−0.135854	+	0.135854i	0.635910	+	0.771764i	$0.280625\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−12.6616	−	13.9041i	−1.11479	−	1.22419i
$130$	−5.27790	−	1.63602i	−0.462902	−	0.143489i
$131$		−	1.63084i		−	0.142487i	−0.997459	−	0.0712437i	$-0.977303\pi$
$131$		−	1.63084i		−	0.142487i	0.997459	−	0.0712437i	$-0.0226968\pi$
$132$	2.80866	+	0.131368i	0.244463	+	0.0114341i
$133$	13.1959	+	13.1959i	1.14423	+	1.14423i
$134$	−11.0593			−0.955381
$135$	4.95737	−	10.5083i	0.426662	−	0.904411i
$136$	−0.560046			−0.0480235
$137$	−10.3702	−	10.3702i	−0.885989	−	0.885989i	0.108146	−	0.994135i	$-0.465509\pi$
$137$	−10.3702	−	10.3702i	−0.885989	−	0.885989i	−0.994135	+	0.108146i	$0.965509\pi$
$138$	0.175810	+	0.00822308i	0.0149659	+	0.000699995i
$139$			15.9812i			1.35551i	0.735289	+	0.677754i	$0.237046\pi$
$139$			15.9812i			1.35551i	−0.735289	+	0.677754i	$0.762954\pi$
$140$	−8.10050	+	4.26691i	−0.684617	+	0.360619i
$141$	−10.9429	−	12.0168i	−0.921560	−	1.01200i
$142$	5.21969	−	5.21969i	0.438026	−	0.438026i
$143$	2.83659	−	2.83659i	0.237208	−	0.237208i
$144$	−2.98690	−	0.280023i	−0.248909	−	0.0233352i
$145$	−2.12077	+	6.84172i	−0.176120	+	0.568174i
$146$		−	10.4282i		−	0.863040i
$147$	−0.790217	+	16.8949i	−0.0651760	+	1.39347i
$148$	5.51900	+	5.51900i	0.453659	+	0.453659i
$149$	17.6969			1.44979			0.724894	−	0.688860i	$-0.241889\pi$
$149$	17.6969			1.44979			0.724894	+	0.688860i	$0.241889\pi$
$150$	−1.18697	−	8.57853i	−0.0969158	−	0.700434i
$151$	−7.84423			−0.638354			−0.319177	−	0.947695i	$-0.603406\pi$
$151$	−7.84423			−0.638354			−0.319177	+	0.947695i	$0.603406\pi$
$152$	3.22282	+	3.22282i	0.261406	+	0.261406i
$153$	−1.07196	−	1.29374i	−0.0866626	−	0.104593i
$154$		−	6.64683i		−	0.535617i
$155$	0.662050	−	2.13581i	0.0531771	−	0.171552i
$156$	−3.16462	+	2.88181i	−0.253372	+	0.230730i
$157$	−15.3315	+	15.3315i	−1.22359	+	1.22359i	−0.257241	+	0.966347i	$0.582814\pi$
$157$	−15.3315	+	15.3315i	−1.22359	+	1.22359i	−0.966347	+	0.257241i	$0.917186\pi$
$158$	0.161993	−	0.161993i	0.0128875	−	0.0128875i
$159$	4.51798	−	4.11423i	0.358299	−	0.326280i
$160$	−1.97839	+	1.04211i	−0.156405	+	0.0823858i
$161$		−	0.416062i		−	0.0327903i
$162$	−5.07022	−	7.43592i	−0.398354	−	0.584221i
$163$	13.3507	+	13.3507i	1.04571	+	1.04571i	0.998904	+	0.0468022i	$0.0149030\pi$
$163$	13.3507	+	13.3507i	1.04571	+	1.04571i	0.0468022	+	0.998904i	$0.485097\pi$
$164$	4.20851			0.328629
$165$	5.91180	+	2.14005i	0.460233	+	0.166603i
$166$	1.17832			0.0914551
$167$	3.74931	+	3.74931i	0.290130	+	0.290130i	0.837132	−	0.547002i	$-0.184231\pi$
$167$	3.74931	+	3.74931i	0.290130	+	0.290130i	−0.547002	+	0.837132i	$0.684231\pi$
$168$	−0.331343	+	7.08414i	−0.0255637	+	0.546553i
$169$		−	6.89344i		−	0.530265i
$170$	−1.19615	−	0.370778i	−0.0917406	−	0.0284374i
$171$	−1.27628	+	13.6136i	−0.0975993	+	1.04106i
$172$	−7.67725	+	7.67725i	−0.585385	+	0.585385i
$173$	0.496896	−	0.496896i	0.0377783	−	0.0377783i	−0.687965	−	0.725744i	$-0.741496\pi$
$173$	0.496896	−	0.496896i	0.0377783	−	0.0377783i	0.725744	+	0.687965i	$0.241496\pi$
$174$	3.73569	+	4.10229i	0.283202	+	0.310994i
$175$	−20.1261	+	3.75037i	−1.52139	+	0.283501i
$176$		−	1.62335i		−	0.122365i
$177$	−11.9473	−	0.558807i	−0.898017	−	0.0420025i
$178$	7.39681	+	7.39681i	0.554415	+	0.554415i
$179$	−5.69409			−0.425596			−0.212798	−	0.977096i	$-0.568258\pi$
$179$	−5.69409			−0.425596			−0.212798	+	0.977096i	$0.568258\pi$
$180$	−6.19407	−	2.57555i	−0.461679	−	0.191970i
$181$	16.1019			1.19684			0.598422	−	0.801181i	$-0.295795\pi$
$181$	16.1019			1.19684			0.598422	+	0.801181i	$0.295795\pi$
$182$	7.15458	+	7.15458i	0.530333	+	0.530333i
$183$	−15.1220	−	0.707296i	−1.11785	−	0.0522848i
$184$		−	0.101615i		−	0.00749115i
$185$	8.13369	+	15.4414i	0.598001	+	1.13527i
$186$	−1.16619	−	1.28063i	−0.0855089	−	0.0939003i
$187$	0.642868	−	0.642868i	0.0470112	−	0.0470112i
$188$	−6.63515	+	6.63515i	−0.483918	+	0.483918i
$189$	−16.9990	+	12.7940i	−1.23650	+	0.930626i
$190$	4.74967	+	9.01701i	0.344578	+	0.654163i
$191$			13.8091i			0.999191i	0.866259	+	0.499595i	$0.166518\pi$
$191$			13.8091i			0.999191i	−0.866259	+	0.499595i	$0.833482\pi$
$192$	−0.0809240	+	1.73016i	−0.00584019	+	0.124863i
$193$	9.32773	+	9.32773i	0.671425	+	0.671425i	0.958044	−	0.286620i	$-0.0925317\pi$
$193$	9.32773	+	9.32773i	0.671425	+	0.671425i	−0.286620	+	0.958044i	$0.592532\pi$
$194$	−11.2633			−0.808658
$195$	−8.66694	+	4.05987i	−0.620652	+	0.290734i
$196$	9.76493			0.697495
$197$	−17.6217	−	17.6217i	−1.25549	−	1.25549i	−0.953223	−	0.302269i	$-0.902256\pi$
$197$	−17.6217	−	17.6217i	−1.25549	−	1.25549i	−0.302269	−	0.953223i	$-0.597744\pi$
$198$	3.75006	−	3.10719i	0.266505	−	0.220818i
$199$			4.43694i			0.314527i	0.987557	+	0.157263i	$0.0502671\pi$
$199$			4.43694i			0.314527i	−0.987557	+	0.157263i	$0.949733\pi$
$200$	−4.91539	+	0.915953i	−0.347570	+	0.0647677i
$201$	−14.1629	+	12.8972i	−0.998974	+	0.909701i
$202$	9.59917	−	9.59917i	0.675395	−	0.675395i
$203$	9.27446	−	9.27446i	0.650939	−	0.650939i
$204$	−0.717211	+	0.653117i	−0.0502148	+	0.0457273i
$205$	8.98858	+	2.78624i	0.627789	+	0.194600i
$206$			2.01383i			0.140310i
$207$	0.234737	−	0.194496i	0.0163153	−	0.0135184i
$208$	1.74736	+	1.74736i	0.121158	+	0.121158i
$209$	−7.39886			−0.511790
$210$	−5.39774	+	14.9110i	−0.372479	+	1.02896i
$211$	14.6718			1.01005			0.505023	−	0.863106i	$-0.331484\pi$
$211$	14.6718			1.01005			0.505023	+	0.863106i	$0.331484\pi$
$212$	−2.49463	−	2.49463i	−0.171332	−	0.171332i
$213$	0.597361	−	12.7716i	0.0409305	−	0.875096i
$214$			4.24322i			0.290061i
$215$	−21.4799	+	11.3144i	−1.46492	+	0.771639i
$216$	−4.15167	+	3.12468i	−0.282486	+	0.212607i
$217$	−2.89525	+	2.89525i	−0.196542	+	0.196542i
$218$	5.59204	−	5.59204i	0.378740	−	0.378740i
$219$	−12.1612	−	13.3546i	−0.821775	−	0.902420i
$220$	1.07474	−	3.46718i	0.0724591	−	0.233757i
$221$			1.38395i			0.0930948i
$222$	13.5040	+	0.631616i	0.906328	+	0.0423913i
$223$	−20.1771	−	20.1771i	−1.35116	−	1.35116i	−0.884367	−	0.466793i	$-0.845409\pi$
$223$	−20.1771	−	20.1771i	−1.35116	−	1.35116i	−0.466793	−	0.884367i	$-0.654591\pi$
$224$	4.09450			0.273575
$225$	−11.5242	−	9.60168i	−0.768282	−	0.640112i
$226$	−19.1886			−1.27641
$227$	14.0570	+	14.0570i	0.932999	+	0.932999i	0.997892	−	0.0648933i	$-0.0206707\pi$
$227$	14.0570	+	14.0570i	0.932999	+	0.932999i	−0.0648933	+	0.997892i	$0.520671\pi$
$228$	7.88565	+	0.368832i	0.522240	+	0.0244265i
$229$		−	9.05951i		−	0.598669i	−0.954148	−	0.299335i	$-0.903235\pi$
$229$		−	9.05951i		−	0.598669i	0.954148	−	0.299335i	$-0.0967647\pi$
$230$	0.0672741	−	0.217030i	0.00443592	−	0.0143105i
$231$	−7.75143	−	8.51212i	−0.510007	−	0.560056i
$232$	2.26510	−	2.26510i	0.148711	−	0.148711i
$233$	1.24516	−	1.24516i	0.0815733	−	0.0815733i	−0.665143	−	0.746716i	$-0.731629\pi$
$233$	1.24516	−	1.24516i	0.0815733	−	0.0815733i	0.746716	+	0.665143i	$0.231629\pi$
$234$	−0.691977	+	7.38107i	−0.0452359	+	0.482516i
$235$	−18.5642	+	9.77862i	−1.21100	+	0.637887i
$236$			6.90534i			0.449499i
$237$	0.0185391	−	0.396368i	0.00120425	−	0.0257468i
$238$	1.62147	+	1.62147i	0.105104	+	0.105104i
$239$	−15.7892			−1.02132			−0.510659	−	0.859784i	$-0.670598\pi$
$239$	−15.7892			−1.02132			−0.510659	+	0.859784i	$0.670598\pi$
$240$	−1.31829	+	3.64172i	−0.0850953	+	0.235072i
$241$	9.56070			0.615859			0.307929	−	0.951409i	$-0.400364\pi$
$241$	9.56070			0.615859			0.307929	+	0.951409i	$0.400364\pi$
$242$	−5.91475	−	5.91475i	−0.380214	−	0.380214i
$243$	−15.1647	−	3.60984i	−0.972818	−	0.231571i
$244$			8.74025i			0.559537i
$245$	20.8560	+	6.46487i	1.33244	+	0.413025i
$246$	5.38954	−	4.90790i	0.343624	−	0.312916i
$247$	7.96406	−	7.96406i	0.506741	−	0.506741i
$248$	−0.707107	+	0.707107i	−0.0449013	+	0.0449013i
$249$	1.50899	−	1.37414i	0.0956281	−	0.0870823i
$250$	−11.1047	−	1.29793i	−0.702326	−	0.0820882i
$251$		−	8.18335i		−	0.516529i	−0.966074	−	0.258264i	$-0.916849\pi$
$251$		−	8.18335i		−	0.516529i	0.966074	−	0.258264i	$-0.0831505\pi$
$252$	7.83709	+	9.45856i	0.493690	+	0.595833i
$253$	0.116642	+	0.116642i	0.00733323	+	0.00733323i
$254$	2.16516			0.135854
$255$	−1.96422	+	0.920105i	−0.123004	+	0.0576192i
$256$	1.00000			0.0625000
$257$	−4.02526	−	4.02526i	−0.251089	−	0.251089i	0.570328	−	0.821417i	$-0.306816\pi$
$257$	−4.02526	−	4.02526i	−0.251089	−	0.251089i	−0.821417	+	0.570328i	$0.806816\pi$
$258$	−0.878614	+	18.7848i	−0.0547001	+	1.16949i
$259$		−	31.9578i		−	1.98576i
$260$	2.57520	+	4.88888i	0.159707	+	0.303195i
$261$	9.56806	+	0.897007i	0.592248	+	0.0555234i
$262$	−1.15318	+	1.15318i	−0.0712437	+	0.0712437i
$263$	15.2841	−	15.2841i	0.942457	−	0.942457i	−0.0559749	−	0.998432i	$-0.517827\pi$
$263$	15.2841	−	15.2841i	0.942457	−	0.942457i	0.998432	+	0.0559749i	$0.0178267\pi$
$264$	−1.89313	−	2.07892i	−0.116514	−	0.127948i
$265$	−3.67649	−	6.97963i	−0.225845	−	0.428755i
$266$		−	18.6618i		−	1.14423i
$267$	18.0986	+	0.846519i	1.10762	+	0.0518061i
$268$	7.82013	+	7.82013i	0.477690	+	0.477690i
$269$	−15.0385			−0.916912			−0.458456	−	0.888717i	$-0.651597\pi$
$269$	−15.0385			−0.916912			−0.458456	+	0.888717i	$0.651597\pi$
$270$	−10.9359	+	3.92511i	−0.665537	+	0.238874i
$271$	−12.6980			−0.771349			−0.385674	−	0.922635i	$-0.626031\pi$
$271$	−12.6980			−0.771349			−0.385674	+	0.922635i	$0.626031\pi$
$272$	0.396012	+	0.396012i	0.0240118	+	0.0240118i
$273$	17.5059	+	0.818797i	1.05951	+	0.0495558i
$274$			14.6657i			0.885989i
$275$	4.59089	−	6.69371i	0.276841	−	0.403646i
$276$	−0.118502	−	0.130131i	−0.00713297	−	0.00783296i
$277$	−11.3481	+	11.3481i	−0.681838	+	0.681838i	−0.960414	−	0.278576i	$-0.910138\pi$
$277$	−11.3481	+	11.3481i	−0.681838	+	0.681838i	0.278576	+	0.960414i	$0.410138\pi$
$278$	11.3004	−	11.3004i	0.677754	−	0.677754i
$279$	−2.98690	−	0.280023i	−0.178821	−	0.0167645i
$280$	8.74508	+	2.71076i	0.522618	+	0.161999i
$281$		−	28.4115i		−	1.69489i	−0.530884	−	0.847444i	$-0.678140\pi$
$281$		−	28.4115i		−	1.69489i	0.530884	−	0.847444i	$-0.321860\pi$
$282$	−0.759351	+	16.2350i	−0.0452187	+	0.966779i
$283$	−7.62439	−	7.62439i	−0.453223	−	0.453223i	0.443200	−	0.896423i	$-0.353843\pi$
$283$	−7.62439	−	7.62439i	−0.453223	−	0.453223i	−0.896423	+	0.443200i	$0.853843\pi$
$284$	−7.38175			−0.438026
$285$	16.5981	+	6.00845i	0.983185	+	0.355910i
$286$	−4.01154			−0.237208
$287$	−12.1847	−	12.1847i	−0.719239	−	0.719239i
$288$	1.91405	+	2.31007i	0.112787	+	0.136122i
$289$		−	16.6863i		−	0.981550i
$290$	6.33744	−	3.33822i	0.372147	−	0.196027i
$291$	−14.4241	+	13.1351i	−0.845557	+	0.769994i
$292$	−7.37382	+	7.37382i	−0.431520	+	0.431520i
$293$	−5.08033	+	5.08033i	−0.296796	+	0.296796i	−0.839758	−	0.542962i	$-0.817303\pi$
$293$	−5.08033	+	5.08033i	−0.296796	+	0.296796i	0.542962	+	0.839758i	$0.317303\pi$
$294$	12.5053	−	11.3877i	0.729321	−	0.664145i
$295$	−4.57168	+	14.7485i	−0.266173	+	0.858691i
$296$		−	7.80505i		−	0.453659i
$297$	1.17887	−	8.35242i	0.0684052	−	0.484656i
$298$	−12.5136	−	12.5136i	−0.724894	−	0.724894i
$299$	−0.251105			−0.0145218
$300$	−5.22662	+	6.90525i	−0.301759	+	0.398675i
$301$	44.4551			2.56235
$302$	5.54671	+	5.54671i	0.319177	+	0.319177i
$303$	1.09857	−	23.4874i	0.0631109	−	1.34931i
$304$		−	4.55776i		−	0.261406i
$305$	−5.78648	+	18.6675i	−0.331333	+	1.06890i
$306$	−0.156825	+	1.67280i	−0.00896512	+	0.0956277i
$307$	−19.6876	+	19.6876i	−1.12363	+	1.12363i	−0.132439	+	0.991191i	$0.542281\pi$
$307$	−19.6876	+	19.6876i	−1.12363	+	1.12363i	−0.991191	+	0.132439i	$0.957719\pi$
$308$	−4.70002	+	4.70002i	−0.267808	+	0.267808i
$309$	2.34850	+	2.57897i	0.133601	+	0.146713i
$310$	−1.97839	+	1.04211i	−0.112365	+	0.0591877i
$311$		−	6.92495i		−	0.392678i	−0.980536	−	0.196339i	$-0.937095\pi$
$311$		−	6.92495i		−	0.392678i	0.980536	−	0.196339i	$-0.0629053\pi$
$312$	4.27547	+	0.199975i	0.242051	+	0.0113213i
$313$	−10.5189	−	10.5189i	−0.594565	−	0.594565i	0.344296	−	0.938861i	$-0.388118\pi$
$313$	−10.5189	−	10.5189i	−0.594565	−	0.594565i	−0.938861	+	0.344296i	$0.888118\pi$
$314$	21.6820			1.22359
$315$	10.4765	+	25.3902i	0.590284	+	1.43058i
$316$	−0.229093			−0.0128875
$317$	−17.5631	−	17.5631i	−0.986441	−	0.986441i	0.0134684	−	0.999909i	$-0.495713\pi$
$317$	−17.5631	−	17.5631i	−0.986441	−	0.986441i	−0.999909	+	0.0134684i	$0.995713\pi$
$318$	−6.10390	−	0.285495i	−0.342290	−	0.0160098i
$319$			5.20015i			0.291153i
$320$	2.13581	+	0.662050i	0.119395	+	0.0370097i
$321$	4.94838	+	5.43399i	0.276192	+	0.303296i
$322$	−0.294200	+	0.294200i	−0.0163951	+	0.0163951i
$323$	1.80493	−	1.80493i	0.100429	−	0.100429i
$324$	−1.67280	+	8.84317i	−0.0929334	+	0.491287i
$325$	2.26345	+	12.1466i	0.125554	+	0.673774i
$326$		−	18.8807i		−	1.04571i
$327$	0.639974	−	13.6827i	0.0353906	−	0.756654i
$328$	−2.97586	−	2.97586i	−0.164315	−	0.164315i
$329$	38.4208			2.11821
$330$	−2.66703	−	5.69352i	−0.146815	−	0.313418i
$331$	−19.1502			−1.05259			−0.526295	−	0.850302i	$-0.676419\pi$
$331$	−19.1502			−1.05259			−0.526295	+	0.850302i	$0.676419\pi$
$332$	−0.833196	−	0.833196i	−0.0457276	−	0.0457276i
$333$	18.0302	−	14.9393i	0.988047	−	0.818667i
$334$		−	5.30232i		−	0.290130i
$335$	11.5250	+	21.8796i	0.629678	+	1.19541i
$336$	5.24354	−	4.77495i	0.286058	−	0.260495i
$337$	0.640755	−	0.640755i	0.0349041	−	0.0349041i	−0.689439	−	0.724343i	$-0.742143\pi$
$337$	0.640755	−	0.640755i	0.0349041	−	0.0349041i	0.724343	+	0.689439i	$0.242143\pi$
$338$	−4.87440	+	4.87440i	−0.265132	+	0.265132i
$339$	−24.5735	+	22.3775i	−1.33465	+	1.21538i
$340$	0.583627	+	1.10799i	0.0316516	+	0.0600890i
$341$		−	1.62335i		−	0.0879096i
$342$	10.5287	−	8.72380i	0.569328	−	0.471729i
$343$	−8.00515	−	8.00515i	−0.432238	−	0.432238i
$344$	10.8573			0.585385
$345$	−0.166944	−	0.356389i	−0.00898797	−	0.0191873i
$346$	−0.702717			−0.0377783
$347$	−11.8865	−	11.8865i	−0.638103	−	0.638103i	0.311984	−	0.950087i	$-0.399006\pi$
$347$	−11.8865	−	11.8865i	−0.638103	−	0.638103i	−0.950087	+	0.311984i	$0.899006\pi$
$348$	0.259227	−	5.54228i	0.0138960	−	0.297098i
$349$		−	9.01900i		−	0.482776i	−0.970429	−	0.241388i	$-0.922397\pi$
$349$		−	9.01900i		−	0.482776i	0.970429	−	0.241388i	$-0.0776026\pi$
$350$	16.8832	+	11.5794i	0.902444	+	0.618943i
$351$	7.72153	+	10.2594i	0.412145	+	0.547605i
$352$	−1.14789	+	1.14789i	−0.0611825	+	0.0611825i
$353$	−20.0852	+	20.0852i	−1.06903	+	1.06903i	−0.0715963	+	0.997434i	$0.522809\pi$
$353$	−20.0852	+	20.0852i	−1.06903	+	1.06903i	−0.997434	+	0.0715963i	$0.977191\pi$
$354$	8.05291	+	8.84318i	0.428007	+	0.470010i
$355$	−15.7660	−	4.88709i	−0.836774	−	0.259380i
$356$		−	10.4607i		−	0.554415i
$357$	3.96744	+	0.185567i	0.209979	+	0.00982126i
$358$	4.02633	+	4.02633i	0.212798	+	0.212798i
$359$	26.3374			1.39003			0.695017	−	0.718993i	$-0.255397\pi$
$359$	26.3374			1.39003			0.695017	+	0.718993i	$0.255397\pi$
$360$	2.55868	+	6.20106i	0.134854	+	0.326825i
$361$	−1.77319			−0.0933256
$362$	−11.3858	−	11.3858i	−0.598422	−	0.598422i
$363$	−14.4723	−	0.676906i	−0.759599	−	0.0355284i
$364$		−	10.1181i		−	0.530333i
$365$	−20.6309	+	10.8673i	−1.07987	+	0.568818i
$366$	10.1928	+	11.1930i	0.532784	+	0.585069i
$367$	6.04081	−	6.04081i	0.315328	−	0.315328i	−0.531642	−	0.846969i	$-0.678425\pi$
$367$	6.04081	−	6.04081i	0.315328	−	0.315328i	0.846969	+	0.531642i	$0.178425\pi$
$368$	−0.0718525	+	0.0718525i	−0.00374557	+	0.00374557i
$369$	1.17848	−	12.5704i	0.0613491	−	0.654389i
$370$	5.16733	−	16.6701i	0.268637	−	0.866638i
$371$			14.4452i			0.749955i
$372$	−0.0809240	+	1.73016i	−0.00419571	+	0.0897046i
$373$	−10.5024	−	10.5024i	−0.543796	−	0.543796i	0.380844	−	0.924639i	$-0.375634\pi$
$373$	−10.5024	−	10.5024i	−0.543796	−	0.543796i	−0.924639	+	0.380844i	$0.875634\pi$
$374$	−0.909153			−0.0470112
$375$	−15.7347	+	11.2880i	−0.812536	+	0.582911i
$376$	9.38351			0.483918
$377$	−5.59739	−	5.59739i	−0.288280	−	0.288280i
$378$	21.0668	+	2.97341i	1.08356	+	0.152936i
$379$			1.55688i			0.0799714i	0.999200	+	0.0399857i	$0.0127312\pi$
$379$			1.55688i			0.0799714i	−0.999200	+	0.0399857i	$0.987269\pi$
$380$	3.01746	−	9.73452i	0.154793	−	0.499370i
$381$	2.77276	−	2.52497i	0.142053	−	0.129358i
$382$	9.76450	−	9.76450i	0.499595	−	0.499595i
$383$	−3.53739	+	3.53739i	−0.180752	+	0.180752i	−0.791684	−	0.610931i	$-0.790795\pi$
$383$	−3.53739	+	3.53739i	−0.180752	+	0.180752i	0.610931	+	0.791684i	$0.290795\pi$
$384$	1.28063	−	1.16619i	0.0653518	−	0.0595117i
$385$	−13.1500	+	6.92670i	−0.670186	+	0.353017i
$386$		−	13.1914i		−	0.671425i
$387$	20.7814	+	25.0810i	1.05638	+	1.27494i
$388$	7.96436	+	7.96436i	0.404329	+	0.404329i
$389$	32.6543			1.65564			0.827819	−	0.560995i	$-0.189581\pi$
$389$	32.6543			1.65564			0.827819	+	0.560995i	$0.189581\pi$
$390$	8.99921	+	3.25769i	0.455693	+	0.164959i
$391$	−0.0569089			−0.00287801
$392$	−6.90485	−	6.90485i	−0.348747	−	0.348747i
$393$	−0.131974	+	2.82162i	−0.00665722	+	0.142332i
$394$			24.9208i			1.25549i
$395$	−0.489300	−	0.151671i	−0.0246193	−	0.00763140i
$396$	−4.84880	−	0.454576i	−0.243662	−	0.0228433i
$397$	−8.53863	+	8.53863i	−0.428542	+	0.428542i	−0.888131	−	0.459590i	$-0.847996\pi$
$397$	−8.53863	+	8.53863i	−0.428542	+	0.428542i	0.459590	+	0.888131i	$0.347996\pi$
$398$	3.13739	−	3.13739i	0.157263	−	0.157263i
$399$	−21.7631	−	23.8988i	−1.08952	−	1.19644i
$400$	4.12338	+	2.82803i	0.206169	+	0.141401i
$401$			31.6949i			1.58277i	0.611321	+	0.791383i	$0.290638\pi$
$401$			31.6949i			1.58277i	−0.611321	+	0.791383i	$0.709362\pi$
$402$	19.1344	+	0.894965i	0.954337	+	0.0446368i
$403$	1.74736	+	1.74736i	0.0870424	+	0.0870424i
$404$	−13.5753			−0.675395
$405$	−9.42741	+	17.7799i	−0.468452	+	0.883489i
$406$	−13.1161			−0.650939
$407$	8.95930	+	8.95930i	0.444096	+	0.444096i
$408$	0.968968	+	0.0453211i	0.0479711	+	0.00224373i
$409$		−	18.9112i		−	0.935098i	−0.883967	−	0.467549i	$-0.845137\pi$
$409$		−	18.9112i		−	0.935098i	0.883967	−	0.467549i	$-0.154863\pi$
$410$	−4.38571	−	8.32605i	−0.216595	−	0.411195i
$411$	17.1030	+	18.7814i	0.843627	+	0.926416i
$412$	1.42399	−	1.42399i	0.0701551	−	0.0701551i
$413$	19.9927	−	19.9927i	0.983775	−	0.983775i
$414$	−0.303514	−	0.0284545i	−0.0149169	−	0.00139846i
$415$	−1.22793	−	2.33117i	−0.0602768	−	0.114432i
$416$		−	2.47114i		−	0.121158i
$417$	1.29326	−	27.6500i	0.0633313	−	1.35403i
$418$	5.23179	+	5.23179i	0.255895	+	0.255895i
$419$	7.06832			0.345310			0.172655	−	0.984982i	$-0.444765\pi$
$419$	7.06832			0.345310			0.172655	+	0.984982i	$0.444765\pi$
$420$	14.3605	−	6.72690i	0.700719	−	0.328239i
$421$	29.7297			1.44894			0.724468	−	0.689308i	$-0.242085\pi$
$421$	29.7297			1.44894			0.724468	+	0.689308i	$0.242085\pi$
$422$	−10.3745	−	10.3745i	−0.505023	−	0.505023i
$423$	17.9605	+	21.6765i	0.873271	+	1.05395i
$424$			3.52794i			0.171332i
$425$	0.512975	+	2.75284i	0.0248830	+	0.133532i
$426$	−9.45329	+	8.60849i	−0.458013	+	0.417083i
$427$	25.3052	−	25.3052i	1.22460	−	1.22460i
$428$	3.00041	−	3.00041i	0.145030	−	0.145030i
$429$	−5.13730	+	4.67821i	−0.248031	+	0.225866i
$430$	23.1891	+	7.18806i	1.11828	+	0.346639i
$431$			27.1832i			1.30937i	0.755903	+	0.654684i	$0.227198\pi$
$431$			27.1832i			1.30937i	−0.755903	+	0.654684i	$0.772802\pi$
$432$	5.14516	+	0.726196i	0.247546	+	0.0349391i
$433$	12.0553	+	12.0553i	0.579342	+	0.579342i	0.934722	−	0.355380i	$-0.115648\pi$
$433$	12.0553	+	12.0553i	0.579342	+	0.579342i	−0.355380	+	0.934722i	$0.615648\pi$
$434$	4.09450			0.196542
$435$	4.22293	−	11.6657i	0.202474	−	0.559325i
$436$	−7.90833			−0.378740
$437$	0.327487	+	0.327487i	0.0156658	+	0.0156658i
$438$	−0.843888	+	18.0424i	−0.0403225	+	0.862098i
$439$		−	4.38472i		−	0.209271i	−0.994511	−	0.104636i	$-0.966632\pi$
$439$		−	4.38472i		−	0.209271i	0.994511	−	0.104636i	$-0.0333676\pi$
$440$	−3.21162	+	1.69171i	−0.153108	+	0.0806491i
$441$	2.73440	−	29.1669i	0.130210	−	1.38890i
$442$	0.978603	−	0.978603i	0.0465474	−	0.0465474i
$443$	−18.6578	+	18.6578i	−0.886457	+	0.886457i	−0.994181	−	0.107724i	$-0.965644\pi$
$443$	−18.6578	+	18.6578i	−0.886457	+	0.886457i	0.107724	+	0.994181i	$0.465644\pi$
$444$	−9.10214	−	9.99537i	−0.431968	−	0.474359i
$445$	6.92549	−	22.3420i	0.328300	−	1.05911i
$446$			28.5347i			1.35116i
$447$	−30.6185	−	1.43211i	−1.44820	−	0.0677362i
$448$	−2.89525	−	2.89525i	−0.136788	−	0.136788i
$449$	10.1528			0.479142			0.239571	−	0.970879i	$-0.422993\pi$
$449$	10.1528			0.479142			0.239571	+	0.970879i	$0.422993\pi$
$450$	1.35944	+	14.9383i	0.0640847	+	0.704197i
$451$	6.83190			0.321702
$452$	13.5684	+	13.5684i	0.638205	+	0.638205i
$453$	13.5718	+	0.634786i	0.637657	+	0.0298249i
$454$		−	19.8797i		−	0.932999i
$455$	6.69869	−	21.6104i	0.314039	−	1.01311i
$456$	−5.31519	−	5.83680i	−0.248907	−	0.273333i
$457$	−6.23308	+	6.23308i	−0.291571	+	0.291571i	−0.837701	−	0.546130i	$-0.816101\pi$
$457$	−6.23308	+	6.23308i	−0.291571	+	0.291571i	0.546130	+	0.837701i	$0.316101\pi$
$458$	−6.40604	+	6.40604i	−0.299335	+	0.299335i
$459$	1.74996	+	2.32513i	0.0816812	+	0.108528i
$460$	−0.201033	+	0.105894i	−0.00937323	+	0.00493731i
$461$		−	7.19713i		−	0.335204i	−0.985855	−	0.167602i	$-0.946398\pi$
$461$		−	7.19713i		−	0.335204i	0.985855	−	0.167602i	$-0.0536023\pi$
$462$	−0.537888	+	11.5001i	−0.0250248	+	0.535032i
$463$	−15.5749	−	15.5749i	−0.723826	−	0.723826i	0.245557	−	0.969382i	$-0.421029\pi$
$463$	−15.5749	−	15.5749i	−0.723826	−	0.723826i	−0.969382	+	0.245557i	$0.921029\pi$
$464$	−3.20334			−0.148711
$465$	−1.31829	+	3.64172i	−0.0611342	+	0.168881i
$466$	−1.76092			−0.0815733
$467$	−27.0181	−	27.0181i	−1.25025	−	1.25025i	−0.955608	−	0.294640i	$-0.904800\pi$
$467$	−27.0181	−	27.0181i	−1.25025	−	1.25025i	−0.294640	−	0.955608i	$-0.595200\pi$
$468$	5.70851	−	4.72990i	0.263876	−	0.218640i
$469$		−	45.2824i		−	2.09095i
$470$	20.0414	+	6.21235i	0.924441	+	0.286554i
$471$	27.7667	−	25.2853i	1.27942	−	1.16508i
$472$	4.88281	−	4.88281i	0.224750	−	0.224750i
$473$	−12.4629	+	12.4629i	−0.573045	+	0.573045i
$474$	−0.293383	+	0.267165i	−0.0134755	+	0.0122713i
$475$	12.8895	−	18.7934i	0.591410	−	0.862299i
$476$		−	2.29311i		−	0.105104i
$477$	−8.14977	+	6.75267i	−0.373152	+	0.309183i
$478$	11.1646	+	11.1646i	0.510659	+	0.510659i
$479$	20.0787			0.917419			0.458710	−	0.888586i	$-0.348312\pi$
$479$	20.0787			0.917419			0.458710	+	0.888586i	$0.348312\pi$
$480$	3.50726	−	1.64291i	0.160084	−	0.0749883i
$481$	−19.2874			−0.879430
$482$	−6.76044	−	6.76044i	−0.307929	−	0.307929i
$483$	−0.0336694	+	0.719853i	−0.00153201	+	0.0327545i
$484$			8.36472i			0.380214i
$485$	11.7376	+	22.2832i	0.532976	+	1.01183i
$486$	8.17054	+	13.2756i	0.370623	+	0.602195i
$487$	1.10651	−	1.10651i	0.0501406	−	0.0501406i	−0.681592	−	0.731733i	$-0.738712\pi$
$487$	1.10651	−	1.10651i	0.0501406	−	0.0501406i	0.731733	+	0.681592i	$0.238712\pi$
$488$	6.18029	−	6.18029i	0.279769	−	0.279769i
$489$	−22.0184	−	24.1792i	−0.995707	−	1.09342i
$490$	−10.1761	−	19.3188i	−0.459709	−	0.872734i
$491$		−	39.8508i		−	1.79844i	−0.437496	−	0.899220i	$-0.644135\pi$
$491$		−	39.8508i		−	1.79844i	0.437496	−	0.899220i	$-0.355865\pi$
$492$	−7.28139	−	0.340569i	−0.328270	−	0.0153540i
$493$	−1.26856	−	1.26856i	−0.0571331	−	0.0571331i
$494$	−11.2629			−0.506741
$495$	−10.0552	−	4.18104i	−0.451947	−	0.187924i
$496$	1.00000			0.0449013
$497$	21.3720	+	21.3720i	0.958666	+	0.958666i
$498$	−2.03868	−	0.0953541i	−0.0913552	−	0.00427292i
$499$			1.93331i			0.0865468i	0.999063	+	0.0432734i	$0.0137787\pi$
$499$			1.93331i			0.0865468i	−0.999063	+	0.0432734i	$0.986221\pi$
$500$	6.93447	+	8.77002i	0.310119	+	0.392207i
$501$	−6.18349	−	6.79031i	−0.276258	−	0.303369i
$502$	−5.78650	+	5.78650i	−0.258264	+	0.258264i
$503$	−1.63114	+	1.63114i	−0.0727289	+	0.0727289i	−0.742536	−	0.669807i	$-0.766377\pi$
$503$	−1.63114	+	1.63114i	−0.0727289	+	0.0727289i	0.669807	+	0.742536i	$0.266377\pi$
$504$	1.14655	−	12.2299i	0.0510715	−	0.544762i
$505$	−28.9942	−	8.98751i	−1.29023	−	0.399939i
$506$		−	0.164957i		−	0.00733323i
$507$	−0.557845	+	11.9268i	−0.0247748	+	0.529686i
$508$	−1.53100	−	1.53100i	−0.0679270	−	0.0679270i
$509$	−40.9970			−1.81716			−0.908581	−	0.417709i	$-0.862833\pi$
$509$	−40.9970			−1.81716			−0.908581	+	0.417709i	$0.862833\pi$
$510$	2.03953	+	0.738302i	0.0903118	+	0.0326926i
$511$	42.6981			1.88885
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	3.30983	−	23.4504i	0.146132	−	1.03536i
$514$			5.69257i			0.251089i
$515$	3.98414	−	2.09863i	0.175562	−	0.0924765i
$516$	13.9041	−	12.6616i	0.612096	−	0.557396i
$517$	−10.7712	+	10.7712i	−0.473717	+	0.473717i
$518$	−22.5976	+	22.5976i	−0.992880	+	0.992880i
$519$	−0.899920	+	0.819498i	−0.0395021	+	0.0359720i
$520$	1.63602	−	5.27790i	0.0717443	−	0.231451i
$521$			33.9332i			1.48664i	0.668936	+	0.743320i	$0.266750\pi$
$521$			33.9332i			1.48664i	−0.668936	+	0.743320i	$0.733250\pi$
$522$	−6.13136	−	7.39992i	−0.268362	−	0.323886i
$523$	27.3843	+	27.3843i	1.19743	+	1.19743i	0.974933	+	0.222500i	$0.0714217\pi$
$523$	27.3843	+	27.3843i	1.19743	+	1.19743i	0.222500	+	0.974933i	$0.428578\pi$
$524$	1.63084			0.0712437
$525$	35.1248	−	4.86006i	1.53297	−	0.212110i
$526$	−21.6150			−0.942457
$527$	0.396012	+	0.396012i	0.0172506	+	0.0172506i
$528$	−0.131368	+	2.80866i	−0.00571707	+	0.122231i
$529$			22.9897i			0.999551i
$530$	−2.33567	+	7.53501i	−0.101455	+	0.327300i
$531$	20.6256	+	1.93365i	0.895074	+	0.0839133i
$532$	−13.1959	+	13.1959i	−0.572113	+	0.572113i
$533$	−7.35379	+	7.35379i	−0.318528	+	0.318528i
$534$	−12.1991	−	13.3962i	−0.527906	−	0.579712i
$535$	8.39473	−	4.42189i	0.362936	−	0.191175i
$536$		−	11.0593i		−	0.477690i
$537$	9.85169	+	0.460789i	0.425132	+	0.0198845i
$538$	10.6338	+	10.6338i	0.458456	+	0.458456i
$539$	15.8519			0.682792
$540$	10.5083	+	4.95737i	0.452206	+	0.213331i
$541$	−24.7593			−1.06449			−0.532243	−	0.846592i	$-0.678651\pi$
$541$	−24.7593			−1.06449			−0.532243	+	0.846592i	$0.678651\pi$
$542$	8.97885	+	8.97885i	0.385674	+	0.385674i
$543$	−27.8588	−	1.30303i	−1.19554	−	0.0559183i
$544$		−	0.560046i		−	0.0240118i
$545$	−16.8907	−	5.23571i	−0.723518	−	0.224273i
$546$	−11.7996	−	12.9575i	−0.504976	−	0.554531i
$547$	−16.5080	+	16.5080i	−0.705831	+	0.705831i	−0.965656	−	0.259825i	$-0.916335\pi$
$547$	−16.5080	+	16.5080i	−0.705831	+	0.705831i	0.259825	+	0.965656i	$0.416335\pi$
$548$	10.3702	−	10.3702i	0.442995	−	0.442995i
$549$	26.1063	+	2.44747i	1.11419	+	0.104455i
$550$	−7.97942	+	1.48692i	−0.340244	+	0.0634023i
$551$			14.6000i			0.621983i
$552$	−0.00822308	+	0.175810i	−0.000349997	+	0.00748296i
$553$	0.663281	+	0.663281i	0.0282056	+	0.0282056i
$554$	16.0486			0.681838
$555$	−12.8230	−	27.3743i	−0.544306	−	1.16197i
$556$	−15.9812			−0.677754
$557$	−32.1980	−	32.1980i	−1.36427	−	1.36427i	−0.868387	−	0.495887i	$-0.834843\pi$
$557$	−32.1980	−	32.1980i	−1.36427	−	1.36427i	−0.495887	−	0.868387i	$-0.665157\pi$
$558$	1.91405	+	2.31007i	0.0810283	+	0.0977929i
$559$		−	26.8299i		−	1.13478i
$560$	−4.26691	−	8.10050i	−0.180310	−	0.342309i
$561$	−1.16429	+	1.06024i	−0.0491563	+	0.0447634i
$562$	−20.0900	+	20.0900i	−0.847444	+	0.847444i
$563$	6.51375	−	6.51375i	0.274522	−	0.274522i	−0.556396	−	0.830917i	$-0.687816\pi$
$563$	6.51375	−	6.51375i	0.274522	−	0.274522i	0.830917	+	0.556396i	$0.187816\pi$
$564$	12.0168	−	10.9429i	0.505999	−	0.460780i
$565$	19.9966	+	37.9626i	0.841264	+	1.59710i
$566$			10.7825i			0.453223i
$567$	30.4464	−	20.7600i	1.27863	−	0.871839i
$568$	5.21969	+	5.21969i	0.219013	+	0.219013i
$569$	1.99748			0.0837389			0.0418694	−	0.999123i	$-0.486669\pi$
$569$	1.99748			0.0837389			0.0418694	+	0.999123i	$0.486669\pi$
$570$	−7.48800	−	15.9852i	−0.313638	−	0.669548i
$571$	−10.3526			−0.433244			−0.216622	−	0.976256i	$-0.569504\pi$
$571$	−10.3526			−0.433244			−0.216622	+	0.976256i	$0.569504\pi$
$572$	2.83659	+	2.83659i	0.118604	+	0.118604i
$573$	1.11749	−	23.8919i	0.0466837	−	0.998100i
$574$			17.2317i			0.719239i
$575$	−0.499476	+	0.0930744i	−0.0208296	+	0.00388147i
$576$	0.280023	−	2.98690i	0.0116676	−	0.124454i
$577$	31.4080	−	31.4080i	1.30753	−	1.30753i	0.384344	−	0.923190i	$-0.374428\pi$
$577$	31.4080	−	31.4080i	1.30753	−	1.30753i	0.923190	−	0.384344i	$-0.125572\pi$
$578$	−11.7990	+	11.7990i	−0.490775	+	0.490775i
$579$	−15.3836	−	16.8933i	−0.639321	−	0.702061i
$580$	−6.84172	−	2.12077i	−0.284087	−	0.0880601i
$581$			4.82462i			0.200159i
$582$	19.4873	+	0.911472i	0.807775	+	0.0377817i
$583$	−4.04967	−	4.04967i	−0.167720	−	0.167720i
$584$	10.4282			0.431520
$585$	15.3237	−	6.32286i	0.633558	−	0.261418i
$586$	7.18467			0.296796
$587$	29.2278	+	29.2278i	1.20636	+	1.20636i	0.972198	+	0.234162i	$0.0752345\pi$
$587$	29.2278	+	29.2278i	1.20636	+	1.20636i	0.234162	+	0.972198i	$0.424765\pi$
$588$	−16.8949	−	0.790217i	−0.696733	−	0.0325880i
$589$		−	4.55776i		−	0.187799i
$590$	13.6614	−	7.19610i	0.562432	−	0.296259i
$591$	29.0623	+	31.9143i	1.19546	+	1.31278i
$592$	−5.51900	+	5.51900i	−0.226830	+	0.226830i
$593$	10.4703	−	10.4703i	0.429964	−	0.429964i	−0.458652	−	0.888616i	$-0.651667\pi$
$593$	10.4703	−	10.4703i	0.429964	−	0.429964i	0.888616	+	0.458652i	$0.151667\pi$
$594$	−6.73964	+	5.07246i	−0.276531	+	0.208126i
$595$	1.51815	−	4.89764i	0.0622381	−	0.200784i
$596$			17.6969i			0.724894i
$597$	0.359055	−	7.67662i	0.0146951	−	0.314183i
$598$	0.177558	+	0.177558i	0.00726089	+	0.00726089i
$599$	10.7834			0.440598			0.220299	−	0.975432i	$-0.429297\pi$
$599$	10.7834			0.440598			0.220299	+	0.975432i	$0.429297\pi$
$600$	8.57853	−	1.18697i	0.350217	−	0.0484579i
$601$	−38.9612			−1.58926			−0.794630	−	0.607094i	$-0.792335\pi$
$601$	−38.9612			−1.58926			−0.794630	+	0.607094i	$0.792335\pi$
$602$	−31.4345	−	31.4345i	−1.28118	−	1.28118i
$603$	25.5478	−	21.1681i	1.04039	−	0.862034i
$604$		−	7.84423i		−	0.319177i
$605$	−5.53786	+	17.8655i	−0.225146	+	0.726334i
$606$	−17.3849	+	15.8313i	−0.706213	+	0.643102i
$607$	8.11174	−	8.11174i	0.329245	−	0.329245i	−0.523054	−	0.852300i	$-0.675207\pi$
$607$	8.11174	−	8.11174i	0.329245	−	0.329245i	0.852300	+	0.523054i	$0.175207\pi$
$608$	−3.22282	+	3.22282i	−0.130703	+	0.130703i
$609$	−16.7968	+	15.2958i	−0.680641	+	0.619816i
$610$	17.2916	−	9.10828i	0.700117	−	0.368783i
$611$		−	23.1880i		−	0.938087i
$612$	1.29374	−	1.07196i	0.0522964	−	0.0433313i
$613$	27.0043	+	27.0043i	1.09069	+	1.09069i	0.995454	+	0.0952399i	$0.0303618\pi$
$613$	27.0043	+	27.0043i	1.09069	+	1.09069i	0.0952399	+	0.995454i	$0.469638\pi$
$614$	27.8425			1.12363
$615$	−15.3262	−	5.54803i	−0.618012	−	0.223718i
$616$	6.64683			0.267808
$617$	−7.33375	−	7.33375i	−0.295246	−	0.295246i	0.543903	−	0.839148i	$-0.316946\pi$
$617$	−7.33375	−	7.33375i	−0.295246	−	0.295246i	−0.839148	+	0.543903i	$0.816946\pi$
$618$	0.162967	−	3.48425i	0.00655550	−	0.140157i
$619$			34.5763i			1.38974i	0.719137	+	0.694869i	$0.244537\pi$
$619$			34.5763i			1.38974i	−0.719137	+	0.694869i	$0.755463\pi$
$620$	2.13581	+	0.662050i	0.0857762	+	0.0265886i
$621$	−0.421872	+	0.317514i	−0.0169291	+	0.0127414i
$622$	−4.89668	+	4.89668i	−0.196339	+	0.196339i
$623$	−30.2863	+	30.2863i	−1.21339	+	1.21339i
$624$	−2.88181	−	3.16462i	−0.115365	−	0.126686i
$625$	9.00453	+	23.3221i	0.360181	+	0.932882i
$626$			14.8760i			0.594565i
$627$	12.8012	+	0.598746i	0.511231	+	0.0239116i
$628$	−15.3315	−	15.3315i	−0.611794	−	0.611794i
$629$	−4.37118			−0.174290
$630$	10.5456	−	25.3616i	0.420147	−	1.01043i
$631$	−12.9099			−0.513935			−0.256968	−	0.966420i	$-0.582723\pi$
$631$	−12.9099			−0.513935			−0.256968	+	0.966420i	$0.582723\pi$
$632$	0.161993	+	0.161993i	0.00644375	+	0.00644375i
$633$	−25.3845	−	1.18730i	−1.00894	−	0.0471909i
$634$			24.8379i			0.986441i
$635$	−2.25632	−	4.28352i	−0.0895395	−	0.169986i
$636$	4.11423	+	4.51798i	0.163140	+	0.179150i
$637$	−17.0629	+	17.0629i	−0.676056	+	0.676056i
$638$	3.67706	−	3.67706i	0.145576	−	0.145576i
$639$	−2.06706	+	22.0486i	−0.0817716	+	0.872228i
$640$	−1.04211	−	1.97839i	−0.0411929	−	0.0782026i
$641$		−	24.4580i		−	0.966032i	−0.875611	−	0.483016i	$-0.839541\pi$
$641$		−	24.4580i		−	0.966032i	0.875611	−	0.483016i	$-0.160459\pi$
$642$	0.343378	−	7.34145i	0.0135521	−	0.289744i
$643$	−25.1274	−	25.1274i	−0.990929	−	0.990929i	0.00903042	−	0.999959i	$-0.497125\pi$
$643$	−25.1274	−	25.1274i	−0.990929	−	0.990929i	−0.999959	+	0.00903042i	$0.997125\pi$
$644$	0.416062			0.0163951
$645$	38.0792	−	17.8375i	1.49937	−	0.702353i
$646$	−2.55255			−0.100429
$647$	34.1529	+	34.1529i	1.34269	+	1.34269i	0.893372	+	0.449317i	$0.148333\pi$
$647$	34.1529	+	34.1529i	1.34269	+	1.34269i	0.449317	+	0.893372i	$0.351667\pi$
$648$	7.43592	−	5.07022i	0.292110	−	0.199177i
$649$			11.2098i			0.440024i
$650$	6.98846	−	10.1895i	0.274110	−	0.399664i
$651$	5.24354	−	4.77495i	0.205510	−	0.187145i
$652$	−13.3507	+	13.3507i	−0.522853	+	0.522853i
$653$	−17.7976	+	17.7976i	−0.696473	+	0.696473i	−0.963648	−	0.267175i	$-0.913910\pi$
$653$	−17.7976	+	17.7976i	−0.696473	+	0.696473i	0.267175	+	0.963648i	$0.413910\pi$
$654$	−10.1276	+	9.22258i	−0.396022	+	0.360632i
$655$	3.48317	+	1.07970i	0.136099	+	0.0421873i
$656$			4.20851i			0.164315i
$657$	19.9600	+	24.0897i	0.778716	+	0.939829i
$658$	−27.1676	−	27.1676i	−1.05910	−	1.05910i
$659$	39.0933			1.52286			0.761428	−	0.648249i	$-0.224498\pi$
$659$	39.0933			1.52286			0.761428	+	0.648249i	$0.224498\pi$
$660$	−2.14005	+	5.91180i	−0.0833014	+	0.230117i
$661$	−19.6035			−0.762488			−0.381244	−	0.924474i	$-0.624504\pi$
$661$	−19.6035			−0.762488			−0.381244	+	0.924474i	$0.624504\pi$
$662$	13.5412	+	13.5412i	0.526295	+	0.526295i
$663$	0.111995	−	2.39446i	0.00434953	−	0.0929931i
$664$			1.17832i			0.0457276i
$665$	−36.9202	+	19.4475i	−1.43170	+	0.754143i
$666$	−23.3129	−	2.18559i	−0.903357	−	0.0846899i
$667$	0.230168	−	0.230168i	0.00891214	−	0.00891214i
$668$	−3.74931	+	3.74931i	−0.145065	+	0.145065i
$669$	33.2768	+	36.5424i	1.28656	+	1.41281i
$670$	7.32183	−	23.6206i	0.282867	−	0.912545i
$671$			14.1885i			0.547742i
$672$	−7.08414	−	0.331343i	−0.273277	−	0.0127818i
$673$	1.80880	+	1.80880i	0.0697242	+	0.0697242i	0.741109	−	0.671385i	$-0.234300\pi$
$673$	1.80880	+	1.80880i	0.0697242	+	0.0697242i	−0.671385	+	0.741109i	$0.734300\pi$
$674$	−0.906164			−0.0349041
$675$	19.1617	+	17.5450i	0.737536	+	0.675308i
$676$	6.89344			0.265132
$677$	−21.5329	−	21.5329i	−0.827578	−	0.827578i	0.159603	−	0.987181i	$-0.448979\pi$
$677$	−21.5329	−	21.5329i	−0.827578	−	0.827578i	−0.987181	+	0.159603i	$0.948979\pi$
$678$	33.1994	+	1.55282i	1.27502	+	0.0596357i
$679$		−	46.1176i		−	1.76983i
$680$	0.370778	−	1.19615i	0.0142187	−	0.0458703i
$681$	−23.1834	−	25.4585i	−0.888389	−	0.975571i
$682$	−1.14789	+	1.14789i	−0.0439548	+	0.0439548i
$683$	−4.74586	+	4.74586i	−0.181595	+	0.181595i	−0.792051	−	0.610455i	$-0.790987\pi$
$683$	−4.74586	+	4.74586i	−0.181595	+	0.181595i	0.610455	+	0.792051i	$0.290987\pi$
$684$	−13.6136	−	1.27628i	−0.520529	−	0.0487997i
$685$	29.0145	−	15.2833i	1.10859	−	0.583943i
$686$			11.3210i			0.432238i
$687$	−0.733132	+	15.6744i	−0.0279707	+	0.598016i
$688$	−7.67725	−	7.67725i	−0.292693	−	0.292693i
$689$	8.71805			0.332131
$690$	−0.133958	+	0.370053i	−0.00509969	+	0.0140877i
$691$	−39.0929			−1.48716			−0.743582	−	0.668644i	$-0.766875\pi$
$691$	−39.0929			−1.48716			−0.743582	+	0.668644i	$0.766875\pi$
$692$	0.496896	+	0.496896i	0.0188891	+	0.0188891i
$693$	12.7224	+	15.3546i	0.483283	+	0.583273i
$694$			16.8101i			0.638103i
$695$	−34.1328	−	10.5804i	−1.29473	−	0.401336i
$696$	−4.10229	+	3.73569i	−0.155497	+	0.141601i
$697$	−1.66662	+	1.66662i	−0.0631277	+	0.0631277i
$698$	−6.37740	+	6.37740i	−0.241388	+	0.241388i
$699$	−2.25509	+	2.05357i	−0.0852954	+	0.0776730i
$700$	−3.75037	−	20.1261i	−0.141751	−	0.760693i
$701$		−	5.93509i		−	0.224165i	−0.993699	−	0.112083i	$-0.964248\pi$
$701$		−	5.93509i		−	0.224165i	0.993699	−	0.112083i	$-0.0357521\pi$
$702$	1.79454	−	12.7144i	0.0677304	−	0.479875i
$703$	25.1543	+	25.1543i	0.948712	+	0.948712i
$704$	1.62335			0.0611825
$705$	32.9104	−	15.4163i	1.23948	−	0.580611i
$706$	28.4048			1.06903
$707$	39.3038	+	39.3038i	1.47817	+	1.47817i
$708$	0.558807	−	11.9473i	0.0210013	−	0.449008i
$709$		−	39.1504i		−	1.47032i	−0.677891	−	0.735162i	$-0.737106\pi$
$709$		−	39.1504i		−	1.47032i	0.677891	−	0.735162i	$-0.262894\pi$
$710$	7.69257	+	14.6040i	0.288697	+	0.548077i
$711$	−0.0641513	+	0.684279i	−0.00240586	+	0.0256625i
$712$	−7.39681	+	7.39681i	−0.277207	+	0.277207i
$713$	−0.0718525	+	0.0718525i	−0.00269090	+	0.00269090i
$714$	−2.67419	−	2.93662i	−0.100079	−	0.109900i
$715$	4.18046	+	7.93639i	0.156340	+	0.296804i
$716$		−	5.69409i		−	0.212798i
$717$	27.3178	+	1.27772i	1.02020	+	0.0477174i
$718$	−18.6233	−	18.6233i	−0.695017	−	0.695017i
$719$	40.4594			1.50888			0.754441	−	0.656368i	$-0.227908\pi$
$719$	40.4594			1.50888			0.754441	+	0.656368i	$0.227908\pi$
$720$	2.57555	−	6.19407i	0.0959852	−	0.230839i
$721$	−8.24563			−0.307083
$722$	1.25383	+	1.25383i	0.0466628	+	0.0466628i
$723$	−16.5415	−	0.773690i	−0.615186	−	0.0287738i
$724$			16.1019i			0.598422i
$725$	−13.2086	−	9.05912i	−0.490554	−	0.336447i
$726$	9.75481	+	10.7121i	0.362035	+	0.397563i
$727$	−7.03815	+	7.03815i	−0.261031	+	0.261031i	−0.825473	−	0.564442i	$-0.809091\pi$
$727$	−7.03815	+	7.03815i	−0.261031	+	0.261031i	0.564442	+	0.825473i	$0.309091\pi$
$728$	−7.15458	+	7.15458i	−0.265166	+	0.265166i
$729$	25.9453	+	7.47278i	0.960936	+	0.276770i
$730$	22.2726	+	6.90396i	0.824345	+	0.255527i
$731$		−	6.08057i		−	0.224898i
$732$	0.707296	−	15.1220i	0.0261424	−	0.558926i
$733$	−25.0986	−	25.0986i	−0.927040	−	0.927040i	0.0704741	−	0.997514i	$-0.477549\pi$
$733$	−25.0986	−	25.0986i	−0.927040	−	0.927040i	−0.997514	+	0.0704741i	$0.977549\pi$
$734$	−8.54300			−0.315328
$735$	−35.5611	−	12.8730i	−1.31169	−	0.474828i
$736$	0.101615			0.00374557
$737$	12.6948	+	12.6948i	0.467621	+	0.467621i
$738$	−9.72193	+	8.05531i	−0.357869	+	0.296520i
$739$			27.0688i			0.995740i	0.867252	+	0.497870i	$0.165884\pi$
$739$			27.0688i			0.995740i	−0.867252	+	0.497870i	$0.834116\pi$
$740$	−15.4414	+	8.13369i	−0.567637	+	0.299001i
$741$	−14.4236	+	13.1346i	−0.529864	+	0.482512i
$742$	10.2143	−	10.2143i	0.374977	−	0.374977i
$743$	17.7922	−	17.7922i	0.652731	−	0.652731i	−0.300919	−	0.953650i	$-0.597293\pi$
$743$	17.7922	−	17.7922i	0.652731	−	0.652731i	0.953650	+	0.300919i	$0.0972933\pi$
$744$	1.28063	−	1.16619i	0.0469501	−	0.0427544i
$745$	−11.7162	+	37.7973i	−0.429250	+	1.38479i
$746$			14.8527i			0.543796i
$747$	−2.72199	+	2.25536i	−0.0995923	+	0.0825193i
$748$	0.642868	+	0.642868i	0.0235056	+	0.0235056i
$749$	−17.3739			−0.634827
$750$	19.1079	+	3.14426i	0.697724	+	0.114812i
$751$	−17.7423			−0.647424			−0.323712	−	0.946156i	$-0.604931\pi$
$751$	−17.7423			−0.647424			−0.323712	+	0.946156i	$0.604931\pi$
$752$	−6.63515	−	6.63515i	−0.241959	−	0.241959i
$753$	−0.662229	+	14.1585i	−0.0241330	+	0.515964i
$754$			7.91591i			0.288280i
$755$	5.19327	−	16.7538i	0.189002	−	0.609733i
$756$	−12.7940	−	16.9990i	−0.465313	−	0.618249i
$757$	−23.0320	+	23.0320i	−0.837113	+	0.837113i	−0.988478	−	0.151365i	$-0.951633\pi$
$757$	−23.0320	+	23.0320i	−0.837113	+	0.837113i	0.151365	+	0.988478i	$0.451633\pi$
$758$	1.10088	−	1.10088i	0.0399857	−	0.0399857i
$759$	−0.192370	−	0.211249i	−0.00698260	−	0.00766784i
$760$	−9.01701	+	4.74967i	−0.327081	+	0.172289i
$761$			0.261797i			0.00949014i	0.999989	+	0.00474507i	$0.00151041\pi$
$761$			0.261797i			0.00949014i	−0.999989	+	0.00474507i	$0.998490\pi$
$762$	−3.74607	−	0.175213i	−0.135706	−	0.00634730i
$763$	22.8966	+	22.8966i	0.828912	+	0.828912i
$764$	−13.8091			−0.499595
$765$	3.47288	−	1.43298i	0.125562	−	0.0518094i
$766$	5.00263			0.180752
$767$	−12.0661	−	12.0661i	−0.435683	−	0.435683i
$768$	−1.73016	−	0.0809240i	−0.0624317	−	0.00292009i
$769$			7.62321i			0.274900i	0.990509	+	0.137450i	$0.0438906\pi$
$769$			7.62321i			0.274900i	−0.990509	+	0.137450i	$0.956109\pi$
$770$	14.1964	+	4.40053i	0.511602	+	0.158584i
$771$	6.63860	+	7.29008i	0.239083	+	0.262546i
$772$	−9.32773	+	9.32773i	−0.335712	+	0.335712i
$773$	20.6595	−	20.6595i	0.743070	−	0.743070i	−0.230097	−	0.973168i	$-0.573904\pi$
$773$	20.6595	−	20.6595i	0.743070	−	0.743070i	0.973168	+	0.230097i	$0.0739045\pi$
$774$	3.04028	−	32.4296i	0.109281	−	1.16566i
$775$	4.12338	+	2.82803i	0.148116	+	0.101586i
$776$		−	11.2633i		−	0.404329i
$777$	−2.58615	+	55.2920i	−0.0927776	+	1.98359i
$778$	−23.0901	−	23.0901i	−0.827819	−	0.827819i
$779$	19.1814			0.687244
$780$	−4.05987	−	8.66694i	−0.145367	−	0.310326i
$781$	−11.9832			−0.428793
$782$	0.0402407	+	0.0402407i	0.00143900	+	0.00143900i
$783$	−16.4817	−	2.32625i	−0.589007	−	0.0831334i
$784$			9.76493i			0.348747i
$785$	−22.5950	−	42.8955i	−0.806450	−	1.53100i
$786$	2.08851	−	1.90187i	0.0744945	−	0.0678373i
$787$	−1.98539	+	1.98539i	−0.0707716	+	0.0707716i	−0.741607	−	0.670835i	$-0.765936\pi$
$787$	−1.98539	+	1.98539i	−0.0707716	+	0.0707716i	0.670835	+	0.741607i	$0.265936\pi$
$788$	17.6217	−	17.6217i	0.627746	−	0.627746i
$789$	−27.6808	+	25.2071i	−0.985461	+	0.897395i
$790$	0.238739	+	0.453235i	0.00849397	+	0.0161254i
$791$		−	78.5679i		−	2.79355i
$792$	3.10719	+	3.75006i	0.110409	+	0.133252i
$793$	−15.2724	−	15.2724i	−0.542339	−	0.542339i
$794$	12.0754			0.428542
$795$	5.79609	+	12.3734i	0.205566	+	0.438839i
$796$	−4.43694			−0.157263
$797$	−32.7775	−	32.7775i	−1.16104	−	1.16104i	−0.984249	−	0.176790i	$-0.943429\pi$
$797$	−32.7775	−	32.7775i	−1.16104	−	1.16104i	−0.176790	−	0.984249i	$-0.556571\pi$
$798$	−1.51018	+	32.2878i	−0.0534599	+	1.14298i
$799$		−	5.25519i		−	0.185915i
$800$	−0.915953	−	4.91539i	−0.0323838	−	0.173785i
$801$	−31.2450	−	2.92923i	−1.10399	−	0.103499i
$802$	22.4116	−	22.4116i	0.791383	−	0.791383i
$803$	−11.9703	+	11.9703i	−0.422424	+	0.422424i
$804$	−12.8972	−	14.1629i	−0.454850	−	0.499487i
$805$	0.888630	+	0.275454i	0.0313201	+	0.00970847i
$806$		−	2.47114i		−	0.0870424i
$807$	26.0190	+	1.21697i	0.915911	+	0.0428395i
$808$	9.59917	+	9.59917i	0.337698	+	0.337698i
$809$	−11.4242			−0.401655			−0.200827	−	0.979627i	$-0.564363\pi$
$809$	−11.4242			−0.401655			−0.200827	+	0.979627i	$0.564363\pi$
$810$	19.2385	−	5.90608i	0.675970	−	0.207519i
$811$	−30.9776			−1.08777			−0.543886	−	0.839159i	$-0.683048\pi$
$811$	−30.9776			−1.08777			−0.543886	+	0.839159i	$0.683048\pi$
$812$	9.27446	+	9.27446i	0.325470	+	0.325470i
$813$	21.9696	+	1.02757i	0.770507	+	0.0360386i
$814$		−	12.6704i		−	0.444096i
$815$	−37.3534	+	19.6757i	−1.30843	+	0.689211i
$816$	−0.653117	−	0.717211i	−0.0228637	−	0.0251074i
$817$	−34.9911	+	34.9911i	−1.22418	+	1.22418i
$818$	−13.3722	+	13.3722i	−0.467549	+	0.467549i
$819$	−30.2218	−	2.83330i	−1.05603	−	0.0990035i
$820$	−2.78624	+	8.98858i	−0.0972998	+	0.313895i
$821$			1.02880i			0.0359054i	0.999839	+	0.0179527i	$0.00571482\pi$
$821$			1.02880i			0.0359054i	−0.999839	+	0.0179527i	$0.994285\pi$
$822$	1.18681	−	25.3741i	0.0413947	−	0.885022i
$823$	24.6895	+	24.6895i	0.860621	+	0.860621i	0.991410	−	0.130789i	$-0.0417511\pi$
$823$	24.6895	+	24.6895i	0.860621	+	0.860621i	−0.130789	+	0.991410i	$0.541751\pi$
$824$	−2.01383			−0.0701551
$825$	−8.48466	+	11.2097i	−0.295398	+	0.390271i
$826$	−28.2739			−0.983775
$827$	6.48529	+	6.48529i	0.225516	+	0.225516i	0.810816	−	0.585301i	$-0.199024\pi$
$827$	6.48529	+	6.48529i	0.225516	+	0.225516i	−0.585301	+	0.810816i	$0.699024\pi$
$828$	0.194496	+	0.234737i	0.00675921	+	0.00815767i
$829$			17.3145i			0.601356i	0.953726	+	0.300678i	$0.0972129\pi$
$829$			17.3145i			0.601356i	−0.953726	+	0.300678i	$0.902787\pi$
$830$	−0.780104	+	2.51666i	−0.0270778	+	0.0873546i
$831$	20.5523	−	18.7156i	0.712950	−	0.649237i
$832$	−1.74736	+	1.74736i	−0.0605789	+	0.0605789i
$833$	−3.86703	+	3.86703i	−0.133985	+	0.133985i
$834$	−20.4660	+	18.6370i	−0.708679	+	0.645348i
$835$	−10.4900	+	5.52558i	−0.363023	+	0.191221i
$836$		−	7.39886i		−	0.255895i
$837$	5.14516	+	0.726196i	0.177843	+	0.0251010i
$838$	−4.99806	−	4.99806i	−0.172655	−	0.172655i
$839$	13.9786			0.482594			0.241297	−	0.970451i	$-0.422427\pi$
$839$	13.9786			0.482594			0.241297	+	0.970451i	$0.422427\pi$
$840$	−14.9110	−	5.39774i	−0.514479	−	0.186240i
$841$	−18.7386			−0.646160
$842$	−21.0221	−	21.0221i	−0.724468	−	0.724468i
$843$	−2.29917	+	49.1564i	−0.0791877	+	1.69304i
$844$			14.6718i			0.505023i
$845$	14.7231	+	4.56380i	0.506490	+	0.157000i
$846$	2.62760	−	28.0276i	0.0903386	−	0.963610i
$847$	24.2179	−	24.2179i	0.832138	−	0.832138i
$848$	2.49463	−	2.49463i	0.0856660	−	0.0856660i
$849$	12.5744	+	13.8084i	0.431552	+	0.473903i
$850$	1.58382	−	2.30928i	0.0543247	−	0.0792077i
$851$		−	0.793109i		−	0.0271874i
$852$	12.7716	+	0.597361i	0.437548	+	0.0204652i
$853$	−37.6051	−	37.6051i	−1.28757	−	1.28757i	−0.936256	−	0.351319i	$-0.885733\pi$
$853$	−37.6051	−	37.6051i	−1.28757	−	1.28757i	−0.351319	−	0.936256i	$-0.614267\pi$
$854$	−35.7870			−1.22460
$855$	−28.2311	−	11.7388i	−0.965483	−	0.401457i
$856$	−4.24322			−0.145030
$857$	−10.2076	−	10.2076i	−0.348686	−	0.348686i	0.510934	−	0.859620i	$-0.329300\pi$
$857$	−10.2076	−	10.2076i	−0.348686	−	0.348686i	−0.859620	+	0.510934i	$0.829300\pi$
$858$	6.94061	+	0.324630i	0.236949	+	0.0110827i
$859$			42.2900i			1.44292i	0.692458	+	0.721458i	$0.256528\pi$
$859$			42.2900i			1.44292i	−0.692458	+	0.721458i	$0.743472\pi$
$860$	−11.3144	−	21.4799i	−0.385819	−	0.732458i
$861$	20.0954	+	22.0675i	0.684849	+	0.752057i
$862$	19.2214	−	19.2214i	0.654684	−	0.654684i
$863$	−2.70566	+	2.70566i	−0.0921017	+	0.0921017i	−0.751656	−	0.659555i	$-0.770745\pi$
$863$	−2.70566	+	2.70566i	−0.0921017	+	0.0921017i	0.659555	+	0.751656i	$0.270745\pi$
$864$	−3.12468	−	4.15167i	−0.106304	−	0.141243i
$865$	0.732306	+	1.39025i	0.0248991	+	0.0472698i
$866$		−	17.0488i		−	0.579342i
$867$	−1.35033	+	28.8700i	−0.0458595	+	0.980478i
$868$	−2.89525	−	2.89525i	−0.0982711	−	0.0982711i
$869$	−0.371899			−0.0126158
$870$	−11.2349	+	5.26280i	−0.380899	+	0.178426i
$871$	−27.3292			−0.926015
$872$	5.59204	+	5.59204i	0.189370	+	0.189370i
$873$	26.0190	−	21.5586i	0.880609	−	0.729647i
$874$		−	0.463136i		−	0.0156658i
$875$	5.31437	−	45.4684i	0.179658	−	1.53711i
$876$	13.3546	−	12.1612i	0.451210	−	0.410888i
$877$	27.0903	−	27.0903i	0.914774	−	0.914774i	−0.0818686	−	0.996643i	$-0.526089\pi$
$877$	27.0903	−	27.0903i	0.914774	−	0.914774i	0.996643	+	0.0818686i	$0.0260888\pi$
$878$	−3.10046	+	3.10046i	−0.104636	+	0.104636i
$879$	9.20090	−	8.37866i	0.310339	−	0.282605i
$880$	3.46718	+	1.07474i	0.116879	+	0.0362295i
$881$		−	14.3326i		−	0.482878i	−0.970416	−	0.241439i	$-0.922381\pi$
$881$		−	14.3326i		−	0.482878i	0.970416	−	0.241439i	$-0.0776193\pi$
$882$	−22.5576	+	18.6906i	−0.759554	+	0.629345i
$883$	−3.56870	−	3.56870i	−0.120096	−	0.120096i	0.644504	−	0.764601i	$-0.277064\pi$
$883$	−3.56870	−	3.56870i	−0.120096	−	0.120096i	−0.764601	+	0.644504i	$0.777064\pi$
$884$	−1.38395			−0.0465474
$885$	9.10324	−	25.1473i	0.306002	−	0.845317i
$886$	26.3861			0.886457
$887$	−29.8263	−	29.8263i	−1.00147	−	1.00147i	−0.999999	−	0.00147171i	$-0.999532\pi$
$887$	−29.8263	−	29.8263i	−1.00147	−	1.00147i	−0.00147171	−	0.999999i	$-0.500468\pi$
$888$	−0.631616	+	13.5040i	−0.0211956	+	0.453164i
$889$			8.86524i			0.297330i
$890$	−20.6953	+	10.9011i	−0.693707	+	0.365407i
$891$	−2.71555	+	14.3556i	−0.0909744	+	0.480931i
$892$	20.1771	−	20.1771i	0.675580	−	0.675580i
$893$	−30.2414	+	30.2414i	−1.01199	+	1.01199i
$894$	20.6379	+	22.6632i	0.690234	+	0.757971i
$895$	3.76977	−	12.1615i	0.126010	−	0.406514i
$896$			4.09450i			0.136788i
$897$	0.434452	+	0.0203204i	0.0145059	+	0.000678479i
$898$	−7.17914	−	7.17914i	−0.239571	−	0.239571i
$899$	−3.20334			−0.106837
$900$	9.60168	−	11.5242i	0.320056	−	0.384141i
$901$	1.97581			0.0658237
$902$	−4.83088	−	4.83088i	−0.160851	−	0.160851i
$903$	−76.9144	−	3.59749i	−2.55955	−	0.119717i
$904$		−	19.1886i		−	0.638205i
$905$	−10.6603	+	34.3906i	−0.354359	+	1.14318i
$906$	−9.14782	−	10.0455i	−0.303916	−	0.333741i
$907$	−12.9671	+	12.9671i	−0.430564	+	0.430564i	−0.888820	−	0.458256i	$-0.848474\pi$
$907$	−12.9671	+	12.9671i	−0.430564	+	0.430564i	0.458256	+	0.888820i	$0.348474\pi$
$908$	−14.0570	+	14.0570i	−0.466499	+	0.466499i
$909$	−3.80139	+	40.5480i	−0.126084	+	1.34489i
$910$	−20.0175	+	10.5441i	−0.663574	+	0.349535i
$911$			10.4211i			0.345266i	0.984986	+	0.172633i	$0.0552275\pi$
$911$			10.4211i			0.345266i	−0.984986	+	0.172633i	$0.944773\pi$
$912$	−0.368832	+	7.88565i	−0.0122133	+	0.261120i
$913$	−1.35257	−	1.35257i	−0.0447636	−	0.0447636i
$914$	8.81490			0.291571
$915$	11.5222	−	31.8295i	0.380912	−	1.05225i
$916$	9.05951			0.299335
$917$	−4.72170	−	4.72170i	−0.155924	−	0.155924i
$918$	0.406703	−	2.88152i	0.0134232	−	0.0951044i
$919$			6.66283i			0.219787i	0.993943	+	0.109893i	$0.0350509\pi$
$919$			6.66283i			0.219787i	−0.993943	+	0.109893i	$0.964949\pi$
$920$	0.217030	+	0.0672741i	0.00715527	+	0.00221796i
$921$	35.6559	−	32.4695i	1.17490	−	1.06991i
$922$	−5.08914	+	5.08914i	−0.167602	+	0.167602i
$923$	12.8986	−	12.8986i	0.424563	−	0.424563i
$924$	8.51212	−	7.75143i	0.280028	−	0.255003i
$925$	−38.3648	+	7.14906i	−1.26143	+	0.235060i
$926$			22.0262i			0.723826i
$927$	−3.85458	−	4.65208i	−0.126601	−	0.152794i
$928$	2.26510	+	2.26510i	0.0743556	+	0.0743556i
$929$	−7.60114			−0.249385			−0.124693	−	0.992195i	$-0.539795\pi$
$929$	−7.60114			−0.249385			−0.124693	+	0.992195i	$0.539795\pi$
$930$	3.50726	−	1.64291i	0.115007	−	0.0538732i
$931$	44.5062			1.45863
$932$	1.24516	+	1.24516i	0.0407866	+	0.0407866i
$933$	−0.560395	+	11.9813i	−0.0183465	+	0.392249i
$934$			38.2093i			1.25025i
$935$	0.947434	+	1.79866i	0.0309844	+	0.0588223i
$936$	−7.38107	−	0.691977i	−0.241258	−	0.0226180i
$937$	−34.7274	+	34.7274i	−1.13449	+	1.13449i	−0.145073	+	0.989421i	$0.546342\pi$
$937$	−34.7274	+	34.7274i	−1.13449	+	1.13449i	−0.989421	+	0.145073i	$0.953658\pi$
$938$	−32.0195	+	32.0195i	−1.04547	+	1.04547i
$939$	17.3482	+	19.0507i	0.566137	+	0.621695i
$940$	−9.77862	−	18.5642i	−0.318943	−	0.605498i
$941$			11.3755i			0.370832i	0.982660	+	0.185416i	$0.0593632\pi$
$941$			11.3755i			0.370832i	−0.982660	+	0.185416i	$0.940637\pi$
$942$	−37.5134	−	1.75460i	−1.22225	−	0.0571679i
$943$	−0.302392	−	0.302392i	−0.00984724	−	0.00984724i
$944$	−6.90534			−0.224750
$945$	−16.0713	−	44.7770i	−0.522801	−	1.45659i
$946$	17.6252			0.573045
$947$	−2.49401	−	2.49401i	−0.0810444	−	0.0810444i	0.665423	−	0.746467i	$-0.268251\pi$
$947$	−2.49401	−	2.49401i	−0.0810444	−	0.0810444i	−0.746467	+	0.665423i	$0.768251\pi$
$948$	0.396368	+	0.0185391i	0.0128734	+	0.000602123i
$949$		−	25.7695i		−	0.836513i
$950$	−22.4032	+	4.17469i	−0.726854	+	0.135445i
$951$	28.9657	+	31.8082i	0.939276	+	1.03145i
$952$	−1.62147	+	1.62147i	−0.0525522	+	0.0525522i
$953$	20.1590	−	20.1590i	0.653013	−	0.653013i	−0.300704	−	0.953717i	$-0.597222\pi$
$953$	20.1590	−	20.1590i	0.653013	−	0.653013i	0.953717	+	0.300704i	$0.0972217\pi$
$954$	10.5376	+	0.987904i	0.341168	+	0.0319846i
$955$	−29.4936	−	9.14231i	−0.954391	−	0.295838i
$956$		−	15.7892i		−	0.510659i
$957$	0.420817	−	8.99709i	0.0136031	−	0.290835i
$958$	−14.1978	−	14.1978i	−0.458710	−	0.458710i
$959$	−60.0488			−1.93908
$960$	−3.64172	−	1.31829i	−0.117536	−	0.0425476i
$961$	1.00000			0.0322581
$962$	13.6383	+	13.6383i	0.439715	+	0.439715i
$963$	−8.12175	−	9.80211i	−0.261720	−	0.315869i
$964$			9.56070i			0.307929i
$965$	−26.0977	+	13.7468i	−0.840114	+	0.442527i
$966$	0.532821	−	0.485205i	0.0171432	−	0.0156112i
$967$	42.9073	−	42.9073i	1.37981	−	1.37981i	0.534877	−	0.844930i	$-0.320358\pi$
$967$	42.9073	−	42.9073i	1.37981	−	1.37981i	0.844930	−	0.534877i	$-0.179642\pi$
$968$	5.91475	−	5.91475i	0.190107	−	0.190107i
$969$	−3.26887	+	2.97675i	−0.105011	+	0.0956270i
$970$	7.45687	−	24.0563i	0.239426	−	0.772401i
$971$			13.1853i			0.423137i	0.977363	+	0.211568i	$0.0678571\pi$
$971$			13.1853i			0.423137i	−0.977363	+	0.211568i	$0.932143\pi$
$972$	3.60984	−	15.1647i	0.115786	−	0.486409i
$973$	46.2695	+	46.2695i	1.48333	+	1.48333i
$974$	−1.56484			−0.0501406
$975$	−2.93318	−	21.1988i	−0.0939369	−	0.678904i
$976$	−8.74025			−0.279769
$977$	13.9002	+	13.9002i	0.444706	+	0.444706i	0.893590	−	0.448884i	$-0.148178\pi$
$977$	13.9002	+	13.9002i	0.444706	+	0.444706i	−0.448884	+	0.893590i	$0.648178\pi$
$978$	−1.52790	+	32.6667i	−0.0488569	+	1.04456i
$979$		−	16.9814i		−	0.542728i
$980$	−6.46487	+	20.8560i	−0.206513	+	0.666222i
$981$	−2.21451	+	23.6214i	−0.0707040	+	0.754174i
$982$	−28.1788	+	28.1788i	−0.899220	+	0.899220i
$983$	−30.0974	+	30.0974i	−0.959958	+	0.959958i	−0.999229	−	0.0392708i	$-0.987496\pi$
$983$	−30.0974	+	30.0974i	−0.959958	+	0.959958i	0.0392708	+	0.999229i	$0.487496\pi$
$984$	4.90790	+	5.38954i	0.156458	+	0.171812i
$985$	49.3030	−	25.9701i	1.57092	−	0.827477i
$986$			1.79401i			0.0571331i
$987$	−66.4741	−	3.10916i	−2.11589	−	0.0989658i
$988$	7.96406	+	7.96406i	0.253371	+	0.253371i
$989$	1.10326			0.0350816
$990$	4.15364	+	10.0665i	0.132011	+	0.319935i
$991$	42.9669			1.36489			0.682444	−	0.730937i	$-0.260917\pi$
$991$	42.9669			1.36489			0.682444	+	0.730937i	$0.260917\pi$
$992$	−0.707107	−	0.707107i	−0.0224507	−	0.0224507i
$993$	33.1329	+	1.54971i	1.05144	+	0.0491786i
$994$		−	30.2246i		−	0.958666i
$995$	−9.47647	−	2.93748i	−0.300424	−	0.0931243i
$996$	1.37414	+	1.50899i	0.0435412	+	0.0478141i
$997$	−26.5138	+	26.5138i	−0.839701	+	0.839701i	−0.988819	−	0.149118i	$-0.952357\pi$
$997$	−26.5138	+	26.5138i	−0.839701	+	0.839701i	0.149118	+	0.988819i	$0.452357\pi$
$998$	1.36706	−	1.36706i	0.0432734	−	0.0432734i
$999$	−32.4040	+	24.3883i	−1.02522	+	0.771610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.h.683.1	yes	40
3.2	odd	2	inner	930.2.j.h.683.16	yes	40
5.2	odd	4	inner	930.2.j.h.497.16	yes	40
15.2	even	4	inner	930.2.j.h.497.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.1	✓	40	15.2	even	4	inner
930.2.j.h.497.16	yes	40	5.2	odd	4	inner
930.2.j.h.683.1	yes	40	1.1	even	1	trivial
930.2.j.h.683.16	yes	40	3.2	odd	2	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-1.73016 - 0.0809240i) q^{3} +1.00000i q^{4} +(-0.662050 + 2.13581i) q^{5} +(1.16619 + 1.28063i) q^{6} +(2.89525 - 2.89525i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.98690 + 0.280023i) q^{9} +(1.97839 - 1.04211i) q^{10} +1.62335i q^{11} +(0.0809240 - 1.73016i) q^{12} +(-1.74736 - 1.74736i) q^{13} -4.09450 q^{14} +(1.31829 - 3.64172i) q^{15} -1.00000 q^{16} +(-0.396012 - 0.396012i) q^{17} +(-1.91405 - 2.31007i) q^{18} +4.55776i q^{19} +(-2.13581 - 0.662050i) q^{20} +(-5.24354 + 4.77495i) q^{21} +(1.14789 - 1.14789i) q^{22} +(0.0718525 - 0.0718525i) q^{23} +(-1.28063 + 1.16619i) q^{24} +(-4.12338 - 2.82803i) q^{25} +2.47114i q^{26} +(-5.14516 - 0.726196i) q^{27} +(2.89525 + 2.89525i) q^{28} +3.20334 q^{29} +(-3.50726 + 1.64291i) q^{30} -1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} +(0.131368 - 2.80866i) q^{33} +0.560046i q^{34} +(4.26691 + 8.10050i) q^{35} +(-0.280023 + 2.98690i) q^{36} +(5.51900 - 5.51900i) q^{37} +(3.22282 - 3.22282i) q^{38} +(2.88181 + 3.16462i) q^{39} +(1.04211 + 1.97839i) q^{40} -4.20851i q^{41} +(7.08414 + 0.331343i) q^{42} +(7.67725 + 7.67725i) q^{43} -1.62335 q^{44} +(-2.57555 + 6.19407i) q^{45} -0.101615 q^{46} +(6.63515 + 6.63515i) q^{47} +(1.73016 + 0.0809240i) q^{48} -9.76493i q^{49} +(0.915953 + 4.91539i) q^{50} +(0.653117 + 0.717211i) q^{51} +(1.74736 - 1.74736i) q^{52} +(-2.49463 + 2.49463i) q^{53} +(3.12468 + 4.15167i) q^{54} +(-3.46718 - 1.07474i) q^{55} -4.09450i q^{56} +(0.368832 - 7.88565i) q^{57} +(-2.26510 - 2.26510i) q^{58} +6.90534 q^{59} +(3.64172 + 1.31829i) q^{60} +8.74025 q^{61} +(0.707107 + 0.707107i) q^{62} +(9.45856 - 7.83709i) q^{63} -1.00000i q^{64} +(4.88888 - 2.57520i) q^{65} +(-2.07892 + 1.89313i) q^{66} +(7.82013 - 7.82013i) q^{67} +(0.396012 - 0.396012i) q^{68} +(-0.130131 + 0.118502i) q^{69} +(2.71076 - 8.74508i) q^{70} +7.38175i q^{71} +(2.31007 - 1.91405i) q^{72} +(7.37382 + 7.37382i) q^{73} -7.80505 q^{74} +(6.90525 + 5.22662i) q^{75} -4.55776 q^{76} +(4.70002 + 4.70002i) q^{77} +(0.199975 - 4.27547i) q^{78} +0.229093i q^{79} +(0.662050 - 2.13581i) q^{80} +(8.84317 + 1.67280i) q^{81} +(-2.97586 + 2.97586i) q^{82} +(-0.833196 + 0.833196i) q^{83} +(-4.77495 - 5.24354i) q^{84} +(1.10799 - 0.583627i) q^{85} -10.8573i q^{86} +(-5.54228 - 0.259227i) q^{87} +(1.14789 + 1.14789i) q^{88} -10.4607 q^{89} +(6.20106 - 2.55868i) q^{90} -10.1181 q^{91} +(0.0718525 + 0.0718525i) q^{92} +(1.73016 + 0.0809240i) q^{93} -9.38351i q^{94} +(-9.73452 - 3.01746i) q^{95} +(-1.16619 - 1.28063i) q^{96} +(7.96436 - 7.96436i) q^{97} +(-6.90485 + 6.90485i) q^{98} +(-0.454576 + 4.84880i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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