LMFDB - Embedded newform 31.5.f.a.15.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,5,Mod(15,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 5, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.15"); S:= CuspForms(chi, 5); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	31.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.20446885560$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			15.7
Character	$\chi$	$=$	31.15
Dual form			31.5.f.a.29.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.01837 - 2.19297i) q^{2} +(9.74278 - 13.4098i) q^{3} +(-0.642851 + 1.97849i) q^{4} -9.66586 q^{5} -61.8414i q^{6} +(-17.5449 + 53.9977i) q^{7} +(20.8451 + 64.1545i) q^{8} +(-59.8702 - 184.262i) q^{9} +(-29.1751 + 21.1970i) q^{10} +(109.657 + 35.6299i) q^{11} +(20.2680 + 27.8965i) q^{12} +(124.985 - 172.028i) q^{13} +(65.4585 + 201.460i) q^{14} +(-94.1724 + 129.617i) q^{15} +(176.679 + 128.365i) q^{16} +(-302.379 + 98.2489i) q^{17} +(-584.791 - 424.876i) q^{18} +(-259.704 + 188.686i) q^{19} +(6.21371 - 19.1238i) q^{20} +(553.161 + 761.361i) q^{21} +(409.122 - 132.932i) q^{22} +(107.186 - 34.8269i) q^{23} +(1063.39 + 345.515i) q^{24} -531.571 q^{25} -793.333i q^{26} +(-1777.31 - 577.485i) q^{27} +(-95.5552 - 69.4249i) q^{28} +(543.366 + 747.878i) q^{29} +597.750i q^{30} +(78.1052 - 957.821i) q^{31} -264.513 q^{32} +(1546.16 - 1123.35i) q^{33} +(-697.234 + 959.661i) q^{34} +(169.587 - 521.934i) q^{35} +403.048 q^{36} -1130.18i q^{37} +(-370.100 + 1139.05i) q^{38} +(-1089.15 - 3352.06i) q^{39} +(-201.485 - 620.108i) q^{40} +(-964.839 + 700.997i) q^{41} +(3339.29 + 1085.00i) q^{42} +(996.154 + 1371.09i) q^{43} +(-140.987 + 194.052i) q^{44} +(578.697 + 1781.05i) q^{45} +(247.153 - 340.177i) q^{46} +(-2131.73 - 1548.79i) q^{47} +(3442.69 - 1118.60i) q^{48} +(-665.474 - 483.495i) q^{49} +(-1604.48 + 1165.72i) q^{50} +(-1628.52 + 5012.05i) q^{51} +(260.008 + 357.871i) q^{52} +(1238.89 - 402.540i) q^{53} +(-6631.00 + 2154.54i) q^{54} +(-1059.93 - 344.393i) q^{55} -3829.92 q^{56} +5320.91i q^{57} +(3280.16 + 1065.79i) q^{58} +(-966.165 - 701.960i) q^{59} +(-195.908 - 269.644i) q^{60} -4448.70i q^{61} +(-1864.73 - 3062.34i) q^{62} +11000.1 q^{63} +(-3625.26 + 2633.91i) q^{64} +(-1208.09 + 1662.80i) q^{65} +(2203.40 - 6781.36i) q^{66} +7332.66 q^{67} -661.414i q^{68} +(577.270 - 1776.66i) q^{69} +(-632.712 - 1947.29i) q^{70} +(195.836 + 602.722i) q^{71} +(10573.2 - 7681.89i) q^{72} +(1328.01 + 431.495i) q^{73} +(-2478.46 - 3411.30i) q^{74} +(-5178.98 + 7128.25i) q^{75} +(-206.363 - 635.120i) q^{76} +(-3847.86 + 5296.12i) q^{77} +(-10638.4 - 7729.27i) q^{78} +(7288.17 - 2368.07i) q^{79} +(-1707.76 - 1240.76i) q^{80} +(-12363.8 + 8982.83i) q^{81} +(-1374.97 + 4231.73i) q^{82} +(-7048.71 - 9701.71i) q^{83} +(-1861.95 + 604.983i) q^{84} +(2922.75 - 949.660i) q^{85} +(6013.52 + 1953.91i) q^{86} +15322.8 q^{87} +7777.72i q^{88} +(-3209.57 - 1042.85i) q^{89} +(5652.51 + 4106.79i) q^{90} +(7096.23 + 9767.13i) q^{91} +234.456i q^{92} +(-12083.2 - 10379.2i) q^{93} -9830.82 q^{94} +(2510.27 - 1823.81i) q^{95} +(-2577.09 + 3547.06i) q^{96} +(682.240 - 2099.72i) q^{97} -3068.94 q^{98} -22338.8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 5 q^{3} - 79 q^{4} - 2 q^{5} - 73 q^{7} + 173 q^{8} + 62 q^{9} + 84 q^{10} + 100 q^{11} + 150 q^{12} - 260 q^{13} + 488 q^{14} - 1075 q^{15} + 777 q^{16} - 725 q^{17} - 786 q^{18} - 1581 q^{19}+ \cdots + 74456 q^{98}+O(q^{100}) $ 36 * q - 3 * q^2 - 5 * q^3 - 79 * q^4 - 2 * q^5 - 73 * q^7 + 173 * q^8 + 62 * q^9 + 84 * q^10 + 100 * q^11 + 150 * q^12 - 260 * q^13 + 488 * q^14 - 1075 * q^15 + 777 * q^16 - 725 * q^17 - 786 * q^18 - 1581 * q^19 + 827 * q^20 + 2335 * q^21 - 1030 * q^22 + 1675 * q^23 - 165 * q^24 + 1294 * q^25 - 2855 * q^27 + 352 * q^28 - 575 * q^29 + 895 * q^31 - 5470 * q^32 + 4468 * q^33 + 1815 * q^34 - 3042 * q^35 + 7808 * q^36 - 6604 * q^38 + 595 * q^39 + 1482 * q^40 - 1740 * q^41 + 3840 * q^42 - 10055 * q^43 - 5780 * q^44 + 6774 * q^45 + 16515 * q^46 + 693 * q^47 + 4710 * q^48 - 944 * q^49 - 6240 * q^50 + 12641 * q^51 + 15885 * q^52 - 10835 * q^53 - 25960 * q^54 - 14010 * q^55 - 19976 * q^56 + 4755 * q^58 - 6021 * q^59 + 35 * q^60 - 11088 * q^62 - 15564 * q^63 + 6935 * q^64 + 26645 * q^65 + 23988 * q^66 + 28596 * q^67 - 4229 * q^69 + 8041 * q^70 + 31101 * q^71 + 20690 * q^72 + 6125 * q^73 - 47295 * q^74 - 27475 * q^75 + 12511 * q^76 + 35950 * q^77 + 29801 * q^78 - 29050 * q^79 - 47358 * q^80 - 1965 * q^81 + 9198 * q^82 + 21640 * q^83 - 35875 * q^84 - 55360 * q^85 - 27935 * q^86 - 2262 * q^87 - 11645 * q^89 - 14916 * q^90 + 670 * q^91 - 36224 * q^93 - 52442 * q^94 + 73983 * q^95 + 29810 * q^96 + 55059 * q^97 + 74456 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	3.01837	−	2.19297i	0.754592	−	0.548243i	−0.142655	−	0.989773i	$-0.545564\pi$
$2$	3.01837	−	2.19297i	0.754592	−	0.548243i	0.897247	+	0.441529i	$0.145564\pi$
$3$	9.74278	−	13.4098i	1.08253	−	1.48998i	0.225827	−	0.974167i	$-0.427491\pi$
$3$	9.74278	−	13.4098i	1.08253	−	1.48998i	0.856704	−	0.515809i	$-0.172509\pi$
$4$	−0.642851	+	1.97849i	−0.0401782	+	0.123656i
$5$	−9.66586			−0.386634			−0.193317	−	0.981136i	$-0.561925\pi$
$5$	−9.66586			−0.386634			−0.193317	+	0.981136i	$0.561925\pi$
$6$		−	61.8414i		−	1.71782i
$7$	−17.5449	+	53.9977i	−0.358059	+	1.10199i	0.596155	+	0.802869i	$0.296694\pi$
$7$	−17.5449	+	53.9977i	−0.358059	+	1.10199i	−0.954214	+	0.299124i	$0.903306\pi$
$8$	20.8451	+	64.1545i	0.325704	+	1.00241i
$9$	−59.8702	−	184.262i	−0.739139	−	2.27483i
$10$	−29.1751	+	21.1970i	−0.291751	+	0.211970i
$11$	109.657	+	35.6299i	0.906260	+	0.294462i	0.724818	−	0.688940i	$-0.241924\pi$
$11$	109.657	+	35.6299i	0.906260	+	0.294462i	0.181441	+	0.983402i	$0.441924\pi$
$12$	20.2680	+	27.8965i	0.140750	+	0.193726i
$13$	124.985	−	172.028i	0.739559	−	1.01792i	−0.259085	−	0.965854i	$-0.583421\pi$
$13$	124.985	−	172.028i	0.739559	−	1.01792i	0.998644	−	0.0520607i	$-0.0165789\pi$
$14$	65.4585	+	201.460i	0.333972	+	1.02786i
$15$	−94.1724	+	129.617i	−0.418544	+	0.576076i
$16$	176.679	+	128.365i	0.690153	+	0.501425i
$17$	−302.379	+	98.2489i	−1.04629	+	0.339962i	−0.781213	−	0.624265i	$-0.785399\pi$
$17$	−302.379	+	98.2489i	−1.04629	+	0.339962i	−0.265081	+	0.964226i	$0.585399\pi$
$18$	−584.791	−	424.876i	−1.80491	−	1.31135i
$19$	−259.704	+	188.686i	−0.719402	+	0.522676i	−0.886193	−	0.463316i	$-0.846660\pi$
$19$	−259.704	+	188.686i	−0.719402	+	0.522676i	0.166791	+	0.985992i	$0.446660\pi$
$20$	6.21371	−	19.1238i	0.0155343	−	0.0478096i
$21$	553.161	+	761.361i	1.25433	+	1.72644i
$22$	409.122	−	132.932i	0.845293	−	0.274652i
$23$	107.186	−	34.8269i	0.202620	−	0.0658354i	−0.205949	−	0.978563i	$-0.566028\pi$
$23$	107.186	−	34.8269i	0.202620	−	0.0658354i	0.408569	+	0.912727i	$0.366028\pi$
$24$	1063.39	+	345.515i	1.84616	+	0.599853i
$25$	−531.571			−0.850514
$26$		−	793.333i		−	1.17357i
$27$	−1777.31	−	577.485i	−2.43802	−	0.792160i
$28$	−95.5552	−	69.4249i	−0.121882	−	0.0885522i
$29$	543.366	+	747.878i	0.646095	+	0.889273i	0.998922	−	0.0464155i	$-0.0147798\pi$
$29$	543.366	+	747.878i	0.646095	+	0.889273i	−0.352828	+	0.935688i	$0.614780\pi$
$30$			597.750i			0.664167i
$31$	78.1052	−	957.821i	0.0812749	−	0.996692i
$31$	78.1052	−	957.821i	0.0812749	−	0.996692i
$32$	−264.513			−0.258313
$33$	1546.16	−	1123.35i	1.41980	−	1.03154i
$34$	−697.234	+	959.661i	−0.603144	+	0.830156i
$35$	169.587	−	521.934i	0.138438	−	0.426069i
$36$	403.048			0.310994
$37$		−	1130.18i		−	0.825552i	−0.910833	−	0.412776i	$-0.864559\pi$
$37$		−	1130.18i		−	0.825552i	0.910833	−	0.412776i	$-0.135441\pi$
$38$	−370.100	+	1139.05i	−0.256302	+	0.788815i
$39$	−1089.15	−	3352.06i	−0.716074	−	2.20385i
$40$	−201.485	−	620.108i	−0.125928	−	0.387568i
$41$	−964.839	+	700.997i	−0.573967	+	0.417012i	−0.836544	−	0.547899i	$-0.815428\pi$
$41$	−964.839	+	700.997i	−0.573967	+	0.417012i	0.262577	+	0.964911i	$0.415428\pi$
$42$	3339.29	+	1085.00i	1.89302	+	0.615080i
$43$	996.154	+	1371.09i	0.538753	+	0.741530i	0.988433	−	0.151660i	$-0.0484619\pi$
$43$	996.154	+	1371.09i	0.538753	+	0.741530i	−0.449680	+	0.893190i	$0.648462\pi$
$44$	−140.987	+	194.052i	−0.0728238	+	0.100233i
$45$	578.697	+	1781.05i	0.285776	+	0.879530i
$46$	247.153	−	340.177i	0.116802	−	0.160764i
$47$	−2131.73	−	1548.79i	−0.965022	−	0.701129i	−0.0107101	−	0.999943i	$-0.503409\pi$
$47$	−2131.73	−	1548.79i	−0.965022	−	0.701129i	−0.954312	+	0.298813i	$0.903409\pi$
$48$	3442.69	−	1118.60i	1.49422	−	0.485503i
$49$	−665.474	−	483.495i	−0.277165	−	0.201372i
$50$	−1604.48	+	1165.72i	−0.641791	+	0.466289i
$51$	−1628.52	+	5012.05i	−0.626111	+	1.92697i
$52$	260.008	+	357.871i	0.0961569	+	0.132349i
$53$	1238.89	−	402.540i	0.441043	−	0.143304i	−0.0800735	−	0.996789i	$-0.525516\pi$
$53$	1238.89	−	402.540i	0.441043	−	0.143304i	0.521117	+	0.853485i	$0.325516\pi$
$54$	−6631.00	+	2154.54i	−2.27401	+	0.738869i
$55$	−1059.93	−	344.393i	−0.350391	−	0.113849i
$56$	−3829.92			−1.22127
$57$			5320.91i			1.63771i
$58$	3280.16	+	1065.79i	0.975076	+	0.316821i
$59$	−966.165	−	701.960i	−0.277554	−	0.201655i	0.440296	−	0.897853i	$-0.354874\pi$
$59$	−966.165	−	701.960i	−0.277554	−	0.201655i	−0.717850	+	0.696198i	$0.754874\pi$
$60$	−195.908	−	269.644i	−0.0544188	−	0.0749011i
$61$		−	4448.70i		−	1.19557i	−0.801658	−	0.597783i	$-0.796048\pi$
$61$		−	4448.70i		−	1.19557i	0.801658	−	0.597783i	$-0.203952\pi$
$62$	−1864.73	−	3062.34i	−0.485100	−	0.796654i
$63$	11000.1			2.77151
$64$	−3625.26	+	2633.91i	−0.885074	+	0.643044i
$65$	−1208.09	+	1662.80i	−0.285939	+	0.393561i
$66$	2203.40	−	6781.36i	0.505831	−	1.55679i
$67$	7332.66			1.63347			0.816736	−	0.577011i	$-0.195781\pi$
$67$	7332.66			1.63347			0.816736	+	0.577011i	$0.195781\pi$
$68$		−	661.414i		−	0.143039i
$69$	577.270	−	1776.66i	0.121250	−	0.373168i
$70$	−632.712	−	1947.29i	−0.129125	−	0.397406i
$71$	195.836	+	602.722i	0.0388487	+	0.119564i	0.968600	−	0.248624i	$-0.0799783\pi$
$71$	195.836	+	602.722i	0.0388487	+	0.119564i	−0.929751	+	0.368188i	$0.879978\pi$
$72$	10573.2	−	7681.89i	2.03959	−	1.48185i
$73$	1328.01	+	431.495i	0.249203	+	0.0809711i	0.430955	−	0.902373i	$-0.358177\pi$
$73$	1328.01	+	431.495i	0.249203	+	0.0809711i	−0.181752	+	0.983344i	$0.558177\pi$
$74$	−2478.46	−	3411.30i	−0.452603	−	0.622955i
$75$	−5178.98	+	7128.25i	−0.920708	+	1.26725i
$76$	−206.363	−	635.120i	−0.0357277	−	0.109958i
$77$	−3847.86	+	5296.12i	−0.648989	+	0.893257i
$78$	−10638.4	−	7729.27i	−1.74859	−	1.27043i
$79$	7288.17	−	2368.07i	1.16779	−	0.379438i	0.339972	−	0.940436i	$-0.389583\pi$
$79$	7288.17	−	2368.07i	1.16779	−	0.379438i	0.827817	+	0.560998i	$0.189583\pi$
$80$	−1707.76	−	1240.76i	−0.266837	−	0.193868i
$81$	−12363.8	+	8982.83i	−1.88444	+	1.36913i
$82$	−1374.97	+	4231.73i	−0.204487	+	0.629348i
$83$	−7048.71	−	9701.71i	−1.02318	−	1.40829i	−0.909948	−	0.414722i	$-0.863879\pi$
$83$	−7048.71	−	9701.71i	−1.02318	−	1.40829i	−0.113234	−	0.993568i	$-0.536121\pi$
$84$	−1861.95	+	604.983i	−0.263881	+	0.0857402i
$85$	2922.75	−	949.660i	0.404533	−	0.131441i
$86$	6013.52	+	1953.91i	0.813078	+	0.264185i
$87$	15322.8			2.02441
$88$			7777.72i			1.00435i
$89$	−3209.57	−	1042.85i	−0.405197	−	0.131657i	0.0993254	−	0.995055i	$-0.468332\pi$
$89$	−3209.57	−	1042.85i	−0.405197	−	0.131657i	−0.504523	+	0.863398i	$0.668332\pi$
$90$	5652.51	+	4106.79i	0.697841	+	0.507011i
$91$	7096.23	+	9767.13i	0.856930	+	1.17946i
$92$			234.456i			0.0277003i
$93$	−12083.2	−	10379.2i	−1.39706	−	1.20005i
$94$	−9830.82			−1.11259
$95$	2510.27	−	1823.81i	0.278146	−	0.202085i
$96$	−2577.09	+	3547.06i	−0.279632	+	0.384880i
$97$	682.240	−	2099.72i	0.0725093	−	0.223161i	−0.908234	−	0.418463i	$-0.862569\pi$
$97$	682.240	−	2099.72i	0.0725093	−	0.223161i	0.980743	+	0.195302i	$0.0625689\pi$
$98$	−3068.94			−0.319548
$99$		−	22338.8i		−	2.27924i
$100$	341.721	−	1051.71i	0.0341721	−	0.105171i
$101$	4877.05	+	15010.0i	0.478095	+	1.47143i	0.841738	+	0.539887i	$0.181533\pi$
$101$	4877.05	+	15010.0i	0.478095	+	1.47143i	−0.363642	+	0.931539i	$0.618467\pi$
$102$	6075.84	+	18699.5i	0.583991	+	1.79734i
$103$	7738.06	−	5622.03i	0.729387	−	0.529930i	−0.159983	−	0.987120i	$-0.551144\pi$
$103$	7738.06	−	5622.03i	0.729387	−	0.529930i	0.889369	+	0.457189i	$0.151144\pi$
$104$	13641.7	+	4432.45i	1.26125	+	0.409805i
$105$	−5346.78	−	7359.21i	−0.484969	−	0.667502i
$106$	2856.67	−	3931.87i	0.254243	−	0.349935i
$107$	4099.40	+	12616.7i	0.358058	+	1.10199i	0.954215	+	0.299121i	$0.0966934\pi$
$107$	4099.40	+	12616.7i	0.358058	+	1.10199i	−0.596157	+	0.802868i	$0.703307\pi$
$108$	2285.10	−	3145.17i	0.195910	−	0.269647i
$109$	8485.35	+	6164.97i	0.714195	+	0.518893i	0.884524	−	0.466494i	$-0.154483\pi$
$109$	8485.35	+	6164.97i	0.714195	+	0.518893i	−0.170329	+	0.985387i	$0.554483\pi$
$110$	−3954.52	+	1284.90i	−0.326820	+	0.106190i
$111$	−15155.5	−	11011.1i	−1.23005	−	0.893685i
$112$	−10031.2	+	7288.11i	−0.799683	+	0.581004i
$113$	−3519.08	+	10830.6i	−0.275596	+	0.848196i	0.713465	+	0.700690i	$0.247125\pi$
$113$	−3519.08	+	10830.6i	−0.275596	+	0.848196i	−0.989061	+	0.147506i	$0.952875\pi$
$114$	11668.6	+	16060.5i	0.897862	+	1.23580i
$115$	−1036.05	+	336.632i	−0.0783400	+	0.0254542i
$116$	−1828.97	+	594.270i	−0.135923	+	0.0441639i
$117$	−39181.0	−	12730.7i	−2.86222	−	0.929993i
$118$	−4455.62			−0.319996
$119$		−	18051.5i		−	1.27474i
$120$	−10278.5	−	3339.70i	−0.713788	−	0.231924i
$121$	−1089.55	−	791.606i	−0.0744179	−	0.0540678i
$122$	−9755.89	−	13427.8i	−0.655461	−	0.902165i
$123$			19767.9i			1.30663i
$124$	1844.83	+	770.266i	0.119981	+	0.0500954i
$125$	11179.3			0.715472
$126$	33202.4	−	24123.0i	2.09136	−	1.51946i
$127$	−1946.40	+	2678.99i	−0.120677	+	0.166098i	−0.865082	−	0.501631i	$-0.832733\pi$
$127$	−1946.40	+	2678.99i	−0.120677	+	0.166098i	0.744404	+	0.667729i	$0.232733\pi$
$128$	−3858.47	+	11875.1i	−0.235502	+	0.724802i
$129$	28091.3			1.68808
$130$			7668.25i			0.453742i
$131$	−2861.70	+	8807.42i	−0.166756	+	0.513223i	−0.999161	−	0.0409445i	$-0.986963\pi$
$131$	−2861.70	+	8807.42i	−0.166756	+	0.513223i	0.832405	+	0.554168i	$0.186963\pi$
$132$	1228.59	+	3781.21i	0.0705113	+	0.217011i
$133$	−5632.13	−	17333.9i	−0.318397	−	0.979926i
$134$	22132.7	−	16080.3i	1.23261	−	0.895541i
$135$	17179.3	+	5581.89i	0.942622	+	0.306276i
$136$	−12606.2	−	17351.0i	−0.681564	−	0.938093i
$137$	7704.14	−	10603.8i	0.410471	−	0.564965i	−0.552862	−	0.833273i	$-0.686464\pi$
$137$	7704.14	−	10603.8i	0.410471	−	0.564965i	0.963333	+	0.268307i	$0.0864643\pi$
$138$	−2153.74	−	6628.54i	−0.113093	−	0.348064i
$139$	−3375.22	+	4645.60i	−0.174692	+	0.240443i	−0.887381	−	0.461038i	$-0.847477\pi$
$139$	−3375.22	+	4645.60i	−0.174692	+	0.240443i	0.712689	+	0.701481i	$0.247477\pi$
$140$	923.623	+	671.052i	0.0471236	+	0.0342373i
$141$	−41538.0	+	13496.5i	−2.08933	+	0.678865i
$142$	1912.86	+	1389.77i	0.0948650	+	0.0689235i
$143$	19834.9	−	14410.9i	0.969969	−	0.704724i
$144$	13074.9	−	40240.4i	0.630541	−	1.94061i
$145$	−5252.10	−	7228.89i	−0.249802	−	0.343824i
$146$	4954.67	−	1609.87i	0.232439	−	0.0755240i
$147$	−12967.1	+	4213.28i	−0.600080	+	0.194978i
$148$	2236.05	+	726.537i	0.102084	+	0.0331692i
$149$	−18122.6			−0.816297			−0.408149	−	0.912916i	$-0.633825\pi$
$149$	−18122.6			−0.816297			−0.408149	+	0.912916i	$0.633825\pi$
$150$			32873.1i			1.46103i
$151$	−15625.2	−	5076.93i	−0.685286	−	0.222663i	−0.0543776	−	0.998520i	$-0.517317\pi$
$151$	−15625.2	−	5076.93i	−0.685286	−	0.222663i	−0.630908	+	0.775858i	$0.717317\pi$
$152$	−17518.6	−	12728.0i	−0.758250	−	0.550901i
$153$	36207.0	+	49834.7i	1.54671	+	2.12887i
$154$			24423.9i			1.02985i
$155$	−754.954	+	9258.16i	−0.0314237	+	0.385355i
$156$	7332.17			0.301289
$157$	−6858.51	+	4983.00i	−0.278247	+	0.202158i	−0.718152	−	0.695886i	$-0.755012\pi$
$157$	−6858.51	+	4983.00i	−0.278247	+	0.202158i	0.439905	+	0.898044i	$0.355012\pi$
$158$	16805.3	−	23130.5i	0.673180	−	0.926553i
$159$	6672.27	−	20535.1i	0.263924	−	0.812275i
$160$	2556.74			0.0998727
$161$			6398.84i			0.246859i
$162$	−17619.4	+	54227.0i	−0.671370	+	2.06626i
$163$	−16395.8	−	50461.2i	−0.617104	−	1.89925i	−0.360696	−	0.932684i	$-0.617461\pi$
$163$	−16395.8	−	50461.2i	−0.617104	−	1.89925i	−0.256409	−	0.966568i	$-0.582539\pi$
$164$	−766.668	−	2359.56i	−0.0285049	−	0.0877291i
$165$	−14944.9	+	10858.1i	−0.548942	+	0.398830i
$166$	−42551.2	−	13825.7i	−1.54417	−	0.501732i
$167$	16611.2	+	22863.3i	0.595617	+	0.819796i	0.995298	−	0.0968579i	$-0.0308792\pi$
$167$	16611.2	+	22863.3i	0.595617	+	0.819796i	−0.399681	+	0.916654i	$0.630879\pi$
$168$	−37314.0	+	51358.4i	−1.32207	+	1.81967i
$169$	−5146.33	−	15838.8i	−0.180187	−	0.554559i
$170$	6739.37	−	9275.95i	0.233196	−	0.320967i
$171$	50316.2	+	36556.8i	1.72074	+	1.25019i
$172$	−3353.07	+	1089.48i	−0.113341	+	0.0368266i
$173$	33099.3	+	24048.1i	1.10593	+	0.803504i	0.982018	−	0.188789i	$-0.0604563\pi$
$173$	33099.3	+	24048.1i	1.10593	+	0.803504i	0.123911	+	0.992293i	$0.460456\pi$
$174$	46249.8	−	33602.5i	1.52761	−	1.10987i
$175$	9326.36	−	28703.6i	0.304534	−	0.937260i
$176$	14800.6	+	20371.2i	0.477807	+	0.657645i
$177$	−18826.3	+	6117.03i	−0.600922	+	0.195251i
$178$	−11974.6	+	3890.79i	−0.377939	+	0.122800i
$179$	−25663.3	−	8338.51i	−0.800952	−	0.260245i	−0.120191	−	0.992751i	$-0.538351\pi$
$179$	−25663.3	−	8338.51i	−0.800952	−	0.260245i	−0.680761	+	0.732506i	$0.738351\pi$
$180$	−3895.80			−0.120241
$181$			19509.1i			0.595497i	0.954644	+	0.297749i	$0.0962357\pi$
$181$			19509.1i			0.595497i	−0.954644	+	0.297749i	$0.903764\pi$
$182$	42838.1	+	13918.9i	1.29327	+	0.420207i
$183$	−59656.1	−	43342.7i	−1.78137	−	1.29424i
$184$	4468.60	+	6150.51i	0.131989	+	0.181667i
$185$			10924.2i			0.319187i
$186$	−59232.9	−	4830.13i	−1.71213	−	0.139615i
$187$	−36658.7			−1.04832
$188$	4434.66	−	3221.97i	0.125471	−	0.0911604i
$189$	62365.6	−	85838.9i	1.74591	−	2.40304i
$190$	3577.33	−	11009.9i	0.0990951	−	0.304983i
$191$	21289.5			0.583577			0.291788	−	0.956483i	$-0.405750\pi$
$191$	21289.5			0.583577			0.291788	+	0.956483i	$0.405750\pi$
$192$			74275.6i			2.01485i
$193$	−11515.1	+	35439.8i	−0.309139	+	0.951431i	0.668962	+	0.743297i	$0.266739\pi$
$193$	−11515.1	+	35439.8i	−0.309139	+	0.951431i	−0.978100	+	0.208134i	$0.933261\pi$
$194$	−2545.38	−	7833.87i	−0.0676314	−	0.208148i
$195$	10527.6	+	32400.5i	0.276859	+	0.852084i
$196$	1384.39	−	1005.82i	0.0360369	−	0.0261823i
$197$	23757.0	+	7719.13i	0.612153	+	0.198901i	0.598653	−	0.801008i	$-0.295703\pi$
$197$	23757.0	+	7719.13i	0.612153	+	0.198901i	0.0134998	+	0.999909i	$0.495703\pi$
$198$	−48988.5	−	67426.8i	−1.24958	−	1.71990i
$199$	−20170.6	+	27762.5i	−0.509346	+	0.701054i	−0.983809	−	0.179221i	$-0.942642\pi$
$199$	−20170.6	+	27762.5i	−0.509346	+	0.701054i	0.474463	+	0.880275i	$0.342642\pi$
$200$	−11080.6	−	34102.7i	−0.277016	−	0.852567i
$201$	71440.5	−	98329.4i	1.76828	−	2.43384i
$202$	47637.3	+	34610.5i	1.16747	+	0.848214i
$203$	−49917.0	+	16219.0i	−1.21131	+	0.393579i
$204$	−8869.42	−	6444.01i	−0.213125	−	0.154845i
$205$	9326.00	−	6775.74i	0.221916	−	0.161231i
$206$	11027.4	−	33938.7i	0.259859	−	0.799763i
$207$	−12834.5	−	17665.2i	−0.299529	−	0.412267i
$208$	44164.6	−	14350.0i	1.02082	−	0.331683i
$209$	−35201.4	+	11437.6i	−0.805874	+	0.261844i
$210$	−32277.1	−	10487.5i	−0.731907	−	0.237811i
$211$	8620.08			0.193618			0.0968091	−	0.995303i	$-0.469136\pi$
$211$	8620.08			0.193618			0.0968091	+	0.995303i	$0.469136\pi$
$212$			2709.91i			0.0602952i
$213$	9990.36	+	3246.06i	0.220202	+	0.0715481i
$214$	40041.5	+	29091.9i	0.874346	+	0.635249i
$215$	−9628.69	−	13252.8i	−0.208300	−	0.286701i
$216$		−	126060.i		−	2.70191i
$217$	50349.7	+	21022.4i	1.06925	+	0.446439i
$218$	39131.5			0.823406
$219$	18724.7	−	13604.3i	0.390416	−	0.283653i
$220$	1362.76	−	1875.68i	0.0281562	−	0.0387536i
$221$	−20891.4	+	64297.2i	−0.427744	+	1.31646i
$222$	−69891.9			−1.41815
$223$		−	49941.9i		−	1.00428i	−0.864786	−	0.502141i	$-0.832546\pi$
$223$		−	49941.9i		−	1.00428i	0.864786	−	0.502141i	$-0.167454\pi$
$224$	4640.85	−	14283.1i	0.0924914	−	0.284659i
$225$	31825.3	+	97948.1i	0.628648	+	1.93478i
$226$	13129.4	+	40408.1i	0.257056	+	0.791136i
$227$	28283.8	−	20549.4i	0.548891	−	0.398793i	−0.278486	−	0.960440i	$-0.589832\pi$
$227$	28283.8	−	20549.4i	0.548891	−	0.398793i	0.827376	+	0.561648i	$0.189832\pi$
$228$	−10527.4	−	3420.55i	−0.202512	−	0.0658001i
$229$	18894.2	+	26005.6i	0.360294	+	0.495902i	0.950231	−	0.311548i	$-0.100847\pi$
$229$	18894.2	+	26005.6i	0.360294	+	0.495902i	−0.589937	+	0.807449i	$0.700847\pi$
$230$	−2388.95	+	3288.10i	−0.0451597	+	0.0621570i
$231$	33531.0	+	103198.i	0.628381	+	1.93396i
$232$	−36653.3	+	50448.9i	−0.680984	+	0.937294i
$233$	−56762.0	−	41240.0i	−1.04555	−	0.759639i	−0.0741910	−	0.997244i	$-0.523637\pi$
$233$	−56762.0	−	41240.0i	−1.04555	−	0.759639i	−0.971362	+	0.237606i	$0.923637\pi$
$234$	−146181.	+	47497.0i	−2.66968	+	0.867430i
$235$	20605.0	+	14970.4i	0.373111	+	0.271081i
$236$	2009.92	−	1460.29i	0.0360874	−	0.0262190i
$237$	39251.7	−	120804.i	0.698815	−	2.15073i
$238$	−39586.5	−	54486.2i	−0.698865	−	0.961906i
$239$	−6663.54	+	2165.12i	−0.116657	+	0.0379040i	−0.366764	−	0.930314i	$-0.619534\pi$
$239$	−6663.54	+	2165.12i	−0.116657	+	0.0379040i	0.250107	+	0.968218i	$0.419534\pi$
$240$	−33276.6	+	10812.2i	−0.577718	+	0.187712i
$241$	−50035.3	−	16257.4i	−0.861474	−	0.279910i	−0.155230	−	0.987878i	$-0.549612\pi$
$241$	−50035.3	−	16257.4i	−0.861474	−	0.279910i	−0.706244	+	0.707969i	$0.749612\pi$
$242$	−5024.64			−0.0857975
$243$			101943.i			1.72641i
$244$	8801.72	+	2859.85i	0.147839	+	0.0480357i
$245$	6432.38	+	4673.40i	0.107162	+	0.0778575i
$246$	43350.6	+	59667.0i	0.716349	+	0.985970i
$247$			68259.3i			1.11884i
$248$	63076.6	−	14955.0i	1.02557	−	0.243155i
$249$	−198772.			−3.20595
$250$	33743.1	−	24515.8i	0.539890	−	0.392253i
$251$	−4726.88	+	6506.00i	−0.0750287	+	0.103268i	−0.844882	−	0.534953i	$-0.820329\pi$
$251$	−4726.88	+	6506.00i	−0.0750287	+	0.103268i	0.769853	+	0.638221i	$0.220329\pi$
$252$	−7071.43	+	21763.6i	−0.111354	+	0.342713i
$253$	12994.6			0.203013
$254$			12354.6i			0.191497i
$255$	15741.0	−	48445.8i	0.242076	−	0.745034i
$256$	−7760.03	−	23882.9i	−0.118409	−	0.364424i
$257$	23407.1	+	72039.7i	0.354390	+	1.09070i	0.956362	+	0.292183i	$0.0943817\pi$
$257$	23407.1	+	72039.7i	0.354390	+	1.09070i	−0.601972	+	0.798517i	$0.705618\pi$
$258$	84790.0	−	61603.5i	1.27381	−	0.925478i
$259$	61027.1	+	19828.9i	0.909752	+	0.295596i
$260$	−2513.20	−	3459.13i	−0.0371776	−	0.0511706i
$261$	105274.	−	144897.i	1.54540	−	2.12705i
$262$	10676.8	+	32859.7i	0.155538	+	0.478697i
$263$	−23672.4	+	32582.3i	−0.342240	+	0.471053i	−0.945094	−	0.326798i	$-0.894030\pi$
$263$	−23672.4	+	32582.3i	−0.342240	+	0.471053i	0.602854	+	0.797852i	$0.294030\pi$
$264$	104298.	+	75776.6i	1.49646	+	1.08725i
$265$	−11975.0	+	3890.90i	−0.170523	+	0.0554062i
$266$	−55012.6	−	39969.0i	−0.777498	−	0.564885i
$267$	−45254.5	+	32879.4i	−0.634804	+	0.461212i
$268$	−4713.81	+	14507.6i	−0.0656300	+	0.201988i
$269$	−35822.6	−	49305.6i	−0.495055	−	0.681384i	0.486256	−	0.873817i	$-0.338362\pi$
$269$	−35822.6	−	49305.6i	−0.495055	−	0.681384i	−0.981310	+	0.192432i	$0.938362\pi$
$270$	64094.4	−	20825.5i	0.879209	−	0.285672i
$271$	95747.4	−	31110.2i	1.30373	−	0.423608i	0.426854	−	0.904320i	$-0.359622\pi$
$271$	95747.4	−	31110.2i	1.30373	−	0.423608i	0.876878	+	0.480712i	$0.159622\pi$
$272$	−66035.7	−	21456.3i	−0.892568	−	0.290013i
$273$	200112.			2.68502
$274$		−	48901.3i		−	0.651357i
$275$	−58290.7	−	18939.8i	−0.770786	−	0.250444i
$276$	3144.00	+	2284.25i	0.0412728	+	0.0299865i
$277$	−27618.9	−	38014.1i	−0.359953	−	0.495433i	0.590182	−	0.807270i	$-0.299056\pi$
$277$	−27618.9	−	38014.1i	−0.359953	−	0.495433i	−0.950136	+	0.311837i	$0.899056\pi$
$278$			21423.9i			0.277210i
$279$	−181166.	+	42953.2i	−2.32738	+	0.551806i
$280$	37019.4			0.472187
$281$	−70035.4	+	50883.7i	−0.886962	+	0.644415i	−0.935084	−	0.354426i	$-0.884676\pi$
$281$	−70035.4	+	50883.7i	−0.886962	+	0.644415i	0.0481225	+	0.998841i	$0.484676\pi$
$282$	−95779.5	+	131829.i	−1.20441	+	1.65773i
$283$	22945.7	−	70619.7i	0.286503	−	0.881766i	−0.699441	−	0.714690i	$-0.746568\pi$
$283$	22945.7	−	70619.7i	0.286503	−	0.881766i	0.985944	−	0.167075i	$-0.0534323\pi$
$284$	−1318.37			−0.0163456
$285$		−	51431.2i		−	0.633194i
$286$	28266.3	−	86994.8i	0.345571	−	1.06356i
$287$	−20924.2	−	64398.0i	−0.254030	−	0.781823i
$288$	15836.4	+	48739.5i	0.190929	+	0.587619i
$289$	14210.3	−	10324.4i	0.170140	−	0.123614i
$290$	−31705.5	−	10301.8i	−0.376998	−	0.122494i
$291$	−21509.9	−	29605.8i	−0.254011	−	0.349616i
$292$	−1707.42	+	2350.06i	−0.0200251	+	0.0275622i
$293$	25950.8	+	79868.4i	0.302284	+	0.930336i	0.980677	+	0.195636i	$0.0626770\pi$
$293$	25950.8	+	79868.4i	0.302284	+	0.930336i	−0.678392	+	0.734700i	$0.737323\pi$
$294$	−29900.0	+	41153.8i	−0.345921	+	0.476119i
$295$	9338.82	+	6785.05i	0.107312	+	0.0779667i
$296$	72506.1	−	23558.7i	0.827544	−	0.268885i
$297$	−174320.	−	126651.i	−1.97622	−	1.43581i
$298$	−54700.7	+	39742.4i	−0.615972	+	0.447530i
$299$	7405.52	−	22791.8i	0.0828349	−	0.254940i
$300$	−10773.9	−	14829.0i	−0.119710	−	0.164766i
$301$	−91513.0	+	29734.4i	−1.01007	+	0.328190i
$302$	−58296.2	+	18941.6i	−0.639185	+	0.207684i
$303$	248797.	+	80839.1i	2.70994	+	0.880513i
$304$	−70105.0			−0.758581
$305$			43000.5i			0.462247i
$306$	218572.	+	71018.4i	2.33428	+	0.758452i
$307$	−89206.6	−	64812.4i	−0.946499	−	0.687672i	0.00347736	−	0.999994i	$-0.498893\pi$
$307$	−89206.6	−	64812.4i	−0.946499	−	0.687672i	−0.949976	+	0.312322i	$0.898893\pi$
$308$	−8004.74	−	11017.6i	−0.0843812	−	0.116141i
$309$		−	158540.i		−	1.66043i
$310$	18024.2	+	29600.2i	0.187557	+	0.308014i
$311$	−60502.7			−0.625538			−0.312769	−	0.949829i	$-0.601257\pi$
$311$	−60502.7			−0.625538			−0.312769	+	0.949829i	$0.601257\pi$
$312$	192346.	−	139748.i	1.97594	−	1.43561i
$313$	29212.2	−	40207.2i	0.298178	−	0.410407i	−0.633471	−	0.773767i	$-0.718370\pi$
$313$	29212.2	−	40207.2i	0.298178	−	0.410407i	0.931649	+	0.363359i	$0.118370\pi$
$314$	−9773.93	+	30081.1i	−0.0991311	+	0.305094i
$315$	−106326.			−1.07156
$316$			15941.9i			0.159649i
$317$	−33280.2	+	102426.i	−0.331182	+	1.01927i	0.637390	+	0.770541i	$0.280014\pi$
$317$	−33280.2	+	102426.i	−0.331182	+	1.01927i	−0.968572	+	0.248733i	$0.919986\pi$
$318$	−24893.6	−	76614.7i	−0.246169	−	0.757631i
$319$	32937.3	+	101370.i	0.323673	+	0.996162i
$320$	35041.3	−	25459.0i	0.342200	−	0.248623i
$321$	209126.	+	67949.3i	2.02955	+	0.659439i
$322$	14032.5	+	19314.1i	0.135339	+	0.186278i
$323$	59990.9	−	82570.4i	0.575017	−	0.791442i
$324$	−9824.38	−	30236.3i	−0.0935869	−	0.288031i
$325$	−66438.6	+	91444.9i	−0.629005	+	0.865751i
$326$	−160149.	−	116355.i	−1.50691	−	1.09484i
$327$	165342.	−	53722.8i	1.54628	−	0.502416i
$328$	−65084.2	−	47286.4i	−0.604962	−	0.439530i
$329$	121032.	−	87935.1i	1.11817	−	0.812401i
$330$	−21297.7	+	65547.7i	−0.195572	+	0.601908i
$331$	−70385.9	−	96877.9i	−0.642436	−	0.884237i	0.356307	−	0.934369i	$-0.384036\pi$
$331$	−70385.9	−	96877.9i	−0.642436	−	0.884237i	−0.998743	+	0.0501320i	$0.984036\pi$
$332$	23726.0	−	7709.05i	0.215253	−	0.0699399i
$333$	−208249.	+	67664.1i	−1.87799	+	0.610197i
$334$	100277.	+	32582.0i	0.898896	+	0.292069i
$335$	−70876.5			−0.631557
$336$			205523.i			1.82046i
$337$	40796.1	+	13255.5i	0.359219	+	0.116717i	0.483066	−	0.875584i	$-0.339523\pi$
$337$	40796.1	+	13255.5i	0.359219	+	0.116717i	−0.123847	+	0.992301i	$0.539523\pi$
$338$	−50267.5	−	36521.5i	−0.440001	−	0.319680i
$339$	110951.	+	152710.i	0.965452	+	1.32883i
$340$			6393.13i			0.0553039i
$341$	42691.8	−	102249.i	0.367144	−	0.879329i
$342$	232041.			1.98387
$343$	−72502.2	+	52675.9i	−0.616259	+	0.447738i
$344$	−67196.6	+	92488.2i	−0.567846	+	0.781573i
$345$	−5579.81	+	17172.9i	−0.0468793	+	0.144280i
$346$	152643.			1.27504
$347$			181155.i			1.50449i	0.658881	+	0.752247i	$0.271030\pi$
$347$			181155.i			1.50449i	−0.658881	+	0.752247i	$0.728970\pi$
$348$	−9850.27	+	30316.0i	−0.0813372	+	0.250330i
$349$	−44849.8	−	138034.i	−0.368222	−	1.13327i	−0.947939	−	0.318453i	$-0.896837\pi$
$349$	−44849.8	−	138034.i	−0.368222	−	1.13327i	0.579716	−	0.814818i	$-0.303163\pi$
$350$	−34795.8	−	107091.i	−0.284048	−	0.874209i
$351$	−321482.	+	233570.i	−2.60941	+	1.89585i
$352$	−29005.8	−	9424.55i	−0.234099	−	0.0760633i
$353$	44443.4	+	61171.1i	0.356663	+	0.490904i	0.949215	−	0.314628i	$-0.101880\pi$
$353$	44443.4	+	61171.1i	0.356663	+	0.490904i	−0.592552	+	0.805532i	$0.701880\pi$
$354$	−43410.2	+	59749.0i	−0.346406	+	0.476786i
$355$	−1892.93	−	5825.82i	−0.0150202	−	0.0462275i
$356$	4126.55	−	5679.71i	0.0325602	−	0.0448153i
$357$	−242067.	−	175872.i	−1.89933	−	1.37994i
$358$	−95747.4	+	31110.2i	−0.747070	+	0.242738i
$359$	−27282.3	−	19821.8i	−0.211686	−	0.153799i	0.476890	−	0.878963i	$-0.341764\pi$
$359$	−27282.3	−	19821.8i	−0.211686	−	0.153799i	−0.688576	+	0.725164i	$0.741764\pi$
$360$	−102199.	+	74252.1i	−0.788574	+	0.572932i
$361$	−8427.57	+	25937.4i	−0.0646678	+	0.199027i
$362$	42782.9	+	58885.6i	0.326477	+	0.449358i
$363$	−21230.5	+	6898.22i	−0.161119	+	0.0523509i
$364$	−23886.0	+	7761.03i	−0.180277	+	0.0585756i
$365$	−12836.3	−	4170.77i	−0.0963506	−	0.0313062i
$366$	−275114.			−2.05376
$367$		−	234.833i		−	0.00174352i	−1.00000		0.000871762i	$-0.999723\pi$
$367$		−	234.833i		−	0.00174352i	1.00000		0.000871762i	$-0.000277490\pi$
$368$	23408.1	+	7605.76i	0.172851	+	0.0561625i
$369$	186932.	+	135814.i	1.37287	+	0.997451i
$370$	23956.4	+	32973.2i	0.174992	+	0.240856i
$371$			73959.8i			0.537338i
$372$	28302.9	−	17234.2i	0.204524	−	0.124539i
$373$	156658.			1.12599			0.562996	−	0.826460i	$-0.309649\pi$
$373$	156658.			1.12599			0.562996	+	0.826460i	$0.309649\pi$
$374$	−110649.	+	80391.6i	−0.791054	+	0.574735i
$375$	108917.	−	149911.i	0.774521	−	1.06604i
$376$	54926.0	−	169045.i	0.388510	−	1.19571i
$377$	196569.			1.38303
$378$		−	395860.i		−	2.77050i
$379$	38282.0	−	117820.i	0.266512	−	0.820239i	−0.724829	−	0.688928i	$-0.758081\pi$
$379$	38282.0	−	117820.i	0.266512	−	0.820239i	0.991341	−	0.131311i	$-0.0419185\pi$
$380$	1994.68	+	6138.98i	0.0138135	+	0.0425137i
$381$	16961.4	+	52201.7i	0.116845	+	0.359612i
$382$	64259.5	−	46687.2i	0.440362	−	0.319942i
$383$	−27877.8	−	9058.05i	−0.190047	−	0.0617500i	0.212447	−	0.977173i	$-0.431857\pi$
$383$	−27877.8	−	9058.05i	−0.190047	−	0.0617500i	−0.402494	+	0.915423i	$0.631857\pi$
$384$	121651.	+	167438.i	0.824998	+	1.13551i
$385$	37192.9	−	51191.6i	0.250922	−	0.345364i
$386$	42961.8	+	132223.i	0.288342	+	0.887426i
$387$	192999.	−	265640.i	1.28864	−	1.77367i
$388$	3715.70	+	2699.61i	0.0246818	+	0.0179324i
$389$	140556.	−	45669.4i	0.928859	−	0.301805i	0.194763	−	0.980850i	$-0.437606\pi$
$389$	140556.	−	45669.4i	0.928859	−	0.301805i	0.734096	+	0.679046i	$0.237606\pi$
$390$	102830.	+	74710.0i	0.676065	+	0.491190i
$391$	−28989.2	+	21061.9i	−0.189619	+	0.137766i
$392$	17146.5	−	52771.6i	0.111585	−	0.343422i
$393$	90224.7	+	124184.i	0.584171	+	0.804043i
$394$	88635.4	−	28799.4i	0.570972	−	0.185520i
$395$	−70446.4	+	22889.4i	−0.451507	+	0.146704i
$396$	44197.2	+	14360.5i	0.281841	+	0.0915757i
$397$	−70138.9			−0.445018			−0.222509	−	0.974931i	$-0.571425\pi$
$397$	−70138.9			−0.445018			−0.222509	+	0.974931i	$0.571425\pi$
$398$			128031.i			0.808256i
$399$	−287317.	−	93354.8i	−1.80474	−	0.586396i
$400$	−93917.5	−	68235.1i	−0.586984	−	0.426469i
$401$	−29420.8	−	40494.2i	−0.182964	−	0.251828i	0.707676	−	0.706537i	$-0.249743\pi$
$401$	−29420.8	−	40494.2i	−0.182964	−	0.251828i	−0.890640	+	0.454708i	$0.849743\pi$
$402$		−	453462.i		−	2.80600i
$403$	−155010.	−	133150.i	−0.954440	−	0.819843i
$404$	−32832.4			−0.201159
$405$	119507.	−	86826.8i	0.728589	−	0.529351i
$406$	−115100.	+	158422.i	−0.698270	+	0.961086i
$407$	40268.2	−	123933.i	0.243093	−	0.748164i
$408$	−355492.			−2.13555
$409$			107808.i			0.644472i	0.946659	+	0.322236i	$0.104434\pi$
$409$			107808.i			0.644472i	−0.946659	+	0.322236i	$0.895566\pi$
$410$	13290.3	−	40903.4i	0.0790619	−	0.243328i
$411$	−67135.5	−	206622.i	−0.397437	−	1.22319i
$412$	6148.72	+	18923.8i	0.0362235	+	0.111484i
$413$	54855.5	−	39854.8i	0.321603	−	0.233658i
$414$	−77478.7	−	25174.3i	−0.452045	−	0.146878i
$415$	68131.8	+	93775.4i	0.395598	+	0.544494i
$416$	−33060.2	+	45503.5i	−0.191038	+	0.262941i
$417$	29412.4	+	90522.1i	0.169145	+	0.520574i
$418$	−81168.3	+	111719.i	−0.464552	+	0.639401i
$419$	205322.	+	149175.i	1.16952	+	0.849706i	0.990951	−	0.134222i	$-0.0428535\pi$
$419$	205322.	+	149175.i	1.16952	+	0.849706i	0.178568	+	0.983928i	$0.442853\pi$
$420$	17997.3	−	5847.68i	0.102026	−	0.0331501i
$421$	165715.	+	120399.i	0.934970	+	0.679295i	0.947205	−	0.320630i	$-0.103895\pi$
$421$	165715.	+	120399.i	0.934970	+	0.679295i	−0.0122350	+	0.999925i	$0.503895\pi$
$422$	26018.6	−	18903.6i	0.146103	−	0.106150i
$423$	−157756.	+	485523.i	−0.881668	+	2.71350i
$424$	51649.5	+	71089.4i	0.287299	+	0.395433i
$425$	160736.	−	52226.3i	0.889887	−	0.289142i
$426$	37273.1	−	12110.8i	0.205389	−	0.0667348i
$427$	240219.	+	78052.0i	1.31751	+	0.428084i
$428$	−27597.3			−0.150653
$429$		−	406384.i		−	2.20812i
$430$	−58125.9	−	18886.2i	−0.314364	−	0.102143i
$431$	−6173.56	−	4485.35i	−0.0332339	−	0.0241458i	0.571044	−	0.820919i	$-0.306538\pi$
$431$	−6173.56	−	4485.35i	−0.0332339	−	0.0241458i	−0.604278	+	0.796773i	$0.706538\pi$
$432$	−239886.	−	330174.i	−1.28540	−	1.76920i
$433$			354405.i			1.89027i	0.326676	+	0.945136i	$0.394071\pi$
$433$			354405.i			1.89027i	−0.326676	+	0.945136i	$0.605929\pi$
$434$	198076.	−	46962.4i	1.05160	−	0.249328i
$435$	−148108.			−0.782708
$436$	−17652.2	+	12825.0i	−0.0928591	+	0.0674661i
$437$	−21265.4	+	29269.3i	−0.111355	+	0.153267i
$438$	26684.2	−	82125.6i	0.139093	−	0.428086i
$439$	−122852.			−0.637459			−0.318729	−	0.947846i	$-0.603256\pi$
$439$	−122852.			−0.637459			−0.318729	+	0.947846i	$0.603256\pi$
$440$		−	75178.4i		−	0.388318i
$441$	−49247.5	+	151568.i	−0.253225	+	0.779348i
$442$	77944.1	+	239887.i	0.398968	+	1.22790i
$443$	−55563.3	−	171006.i	−0.283127	−	0.871374i	−0.986954	−	0.161003i	$-0.948527\pi$
$443$	−55563.3	−	171006.i	−0.283127	−	0.871374i	0.703827	−	0.710371i	$-0.251473\pi$
$444$	31528.1	−	22906.5i	0.159931	−	0.116196i
$445$	31023.2	+	10080.1i	0.156663	+	0.0509030i
$446$	−109521.	−	150743.i	−0.550591	−	0.757823i
$447$	−176565.	+	243020.i	−0.883667	+	1.21626i
$448$	−78620.0	−	241967.i	−0.391721	−	1.20559i
$449$	−160614.	+	221066.i	−0.796691	+	1.09655i	0.196552	+	0.980493i	$0.437026\pi$
$449$	−160614.	+	221066.i	−0.796691	+	1.09655i	−0.993243	+	0.116057i	$0.962974\pi$
$450$	310858.	+	225852.i	1.53510	+	1.11532i
$451$	−130778.	+	42492.4i	−0.642957	+	0.208910i
$452$	−19166.1	−	13925.0i	−0.0938114	−	0.0681580i
$453$	−220313.	+	160067.i	−1.07361	+	0.780020i
$454$	40306.7	−	124051.i	0.195553	−	0.601852i
$455$	−68591.2	−	94407.7i	−0.331319	−	0.456021i
$456$	−341360.	+	110915.i	−1.64166	+	0.533407i
$457$	186056.	−	60453.1i	0.890862	−	0.289459i	0.172402	−	0.985027i	$-0.444847\pi$
$457$	186056.	−	60453.1i	0.890862	−	0.289459i	0.718460	+	0.695568i	$0.244847\pi$
$458$	114059.	+	37060.1i	0.543750	+	0.176675i
$459$	594160.			2.82019
$460$		−	2266.22i		−	0.0107099i
$461$	−89711.5	−	29149.0i	−0.422130	−	0.137158i	0.0902461	−	0.995919i	$-0.471235\pi$
$461$	−89711.5	−	29149.0i	−0.422130	−	0.137158i	−0.512376	+	0.858761i	$0.671235\pi$
$462$	327519.	+	237957.i	1.53445	+	1.11484i
$463$	−47503.2	−	65382.5i	−0.221595	−	0.305000i	0.683716	−	0.729748i	$-0.260363\pi$
$463$	−47503.2	−	65382.5i	−0.221595	−	0.305000i	−0.905312	+	0.424748i	$0.860363\pi$
$464$			201884.i			0.937702i
$465$	116795.	+	100324.i	0.540153	+	0.463980i
$466$	−261767.			−1.20543
$467$	128327.	−	93235.2i	0.588417	−	0.427510i	−0.253332	−	0.967379i	$-0.581527\pi$
$467$	128327.	−	93235.2i	0.588417	−	0.427510i	0.841749	+	0.539870i	$0.181527\pi$
$468$	50375.1	−	69335.4i	0.229998	−	0.316565i
$469$	−128651.	+	395946.i	−0.584880	+	1.80008i
$470$	95023.4			0.430165
$471$			140519.i			0.633424i
$472$	24894.1	−	76616.2i	0.111741	−	0.343904i
$473$	60384.0	+	185843.i	0.269898	+	0.830661i
$474$	−146445.	−	450710.i	−0.651804	−	2.00605i
$475$	138051.	−	100300.i	0.611862	−	0.444544i
$476$	35714.8	+	11604.4i	0.157628	+	0.0512166i
$477$	−148345.	−	204180.i	−0.651984	−	0.897380i
$478$	−15365.0	+	21148.1i	−0.0672476	+	0.0925583i
$479$	−23999.7	−	73863.6i	−0.104601	−	0.321928i	0.885036	−	0.465523i	$-0.154134\pi$
$479$	−23999.7	−	73863.6i	−0.104601	−	0.321928i	−0.989637	+	0.143595i	$0.954134\pi$
$480$	24909.8	−	34285.4i	0.108115	−	0.148808i
$481$	−194422.	−	141256.i	−0.840341	−	0.610544i
$482$	−186677.	+	60655.1i	−0.803520	+	0.261080i
$483$	85807.1	+	62342.5i	0.367814	+	0.267233i
$484$	2266.61	−	1646.79i	0.00967577	−	0.00702986i
$485$	−6594.44	+	20295.6i	−0.0280346	+	0.0862816i
$486$	223558.	+	307701.i	0.946492	+	1.30273i
$487$	177632.	−	57716.0i	0.748966	−	0.243354i	0.0904298	−	0.995903i	$-0.471176\pi$
$487$	177632.	−	57716.0i	0.748966	−	0.243354i	0.658536	+	0.752549i	$0.271176\pi$
$488$	285404.	−	92733.4i	1.19845	−	0.389401i
$489$	−836415.	−	271768.i	−3.49787	−	1.13653i
$490$	29664.0			0.123548
$491$		−	434028.i		−	1.80034i	−0.435536	−	0.900171i	$-0.643441\pi$
$491$		−	434028.i		−	1.80034i	0.435536	−	0.900171i	$-0.356559\pi$
$492$	−39110.7	−	12707.8i	−0.161572	−	0.0524979i
$493$	−237781.	−	172758.i	−0.978323	−	0.710794i
$494$	149691.	+	206032.i	0.613397	+	0.844269i
$495$			215924.i			0.881232i
$496$	136750.	−	159201.i	0.555858	−	0.647116i
$497$	−35981.5			−0.145669
$498$	−599967.	+	435901.i	−2.41918	+	1.75764i
$499$	170875.	−	235189.i	0.686243	−	0.944532i	−0.313745	−	0.949507i	$-0.601584\pi$
$499$	170875.	−	235189.i	0.686243	−	0.944532i	0.999988	+	0.00497507i	$0.00158362\pi$
$500$	−7186.60	+	22118.1i	−0.0287464	+	0.0884723i
$501$	468431.			1.86625
$502$			30003.4i			0.119059i
$503$	61029.2	−	187829.i	0.241213	−	0.742379i	−0.755023	−	0.655699i	$-0.772374\pi$
$503$	61029.2	−	187829.i	0.241213	−	0.742379i	0.996236	−	0.0866802i	$-0.0276258\pi$
$504$	229298.	+	705707.i	0.902691	+	2.77820i
$505$	−47140.9	−	145085.i	−0.184848	−	0.568904i
$506$	39222.6	−	28496.9i	0.153192	−	0.111300i
$507$	−262534.	−	85302.5i	−1.02134	−	0.331853i
$508$	−4049.12	−	5573.13i	−0.0156904	−	0.0215959i
$509$	148944.	−	205004.i	0.574893	−	0.791273i	−0.418231	−	0.908341i	$-0.637350\pi$
$509$	148944.	−	205004.i	0.574893	−	0.791273i	0.993124	+	0.117068i	$0.0373496\pi$
$510$	−58728.3	−	180747.i	−0.225791	−	0.694914i
$511$	−46599.4	+	64138.6i	−0.178459	+	0.245628i
$512$	−237423.	−	172498.i	−0.905696	−	0.658027i
$513$	570540.	−	185380.i	2.16796	−	0.704413i
$514$	228632.	+	166111.i	0.865389	+	0.628742i
$515$	−74795.0	+	54341.8i	−0.282006	+	0.204889i
$516$	−18058.5	+	55578.4i	−0.0678239	+	0.208741i
$517$	−178577.	−	245790.i	−0.668105	−	0.919567i
$518$	227687.	−	73979.8i	0.848551	−	0.275711i
$519$	644959.	−	209560.i	2.39440	−	0.777989i
$520$	−131859.	−	42843.4i	−0.487642	−	0.158445i
$521$	−203783.			−0.750744			−0.375372	−	0.926874i	$-0.622485\pi$
$521$	−203783.			−0.750744			−0.375372	+	0.926874i	$0.622485\pi$
$522$		−	668216.i		−	2.45231i
$523$	82933.2	+	26946.6i	0.303197	+	0.0985147i	0.456664	−	0.889639i	$-0.349044\pi$
$523$	82933.2	+	26946.6i	0.303197	+	0.0985147i	−0.153467	+	0.988154i	$0.549044\pi$
$524$	−15585.8	−	11323.7i	−0.0567630	−	0.0412407i
$525$	−294044.	−	404717.i	−1.06683	−	1.46836i
$526$			150258.i			0.543084i
$527$	70487.5	+	297299.i	0.253799	+	1.07046i
$528$	417372.			1.49712
$529$	−216120.	+	157020.i	−0.772296	+	0.561106i
$530$	−27612.2	+	38004.9i	−0.0982990	+	0.135297i
$531$	−71499.8	+	220054.i	−0.253580	+	0.780440i
$532$	37915.6			0.133966
$533$			253593.i			0.892655i
$534$	−64491.4	+	198484.i	−0.226162	+	0.696054i
$535$	−39624.3	−	121951.i	−0.138437	−	0.426067i
$536$	152850.	+	470423.i	0.532028	+	1.63742i
$537$	−361849.	+	262899.i	−1.25481	+	0.911675i
$538$	−216252.	−	70264.5i	−0.747129	−	0.242757i
$539$	−55747.3	−	76729.6i	−0.191887	−	0.264110i
$540$	−22087.4	+	30400.8i	−0.0757457	+	0.104255i
$541$	−138000.	−	424719.i	−0.471501	−	1.45113i	−0.850618	−	0.525784i	$-0.823772\pi$
$541$	−138000.	−	424719.i	−0.471501	−	1.45113i	0.379117	−	0.925349i	$-0.376228\pi$
$542$	220777.	−	303874.i	0.751546	−	1.03441i
$543$	261613.	+	190073.i	0.887277	+	0.644644i
$544$	79983.0	−	25988.1i	0.270271	−	0.0878165i
$545$	−82018.2	−	59589.7i	−0.276132	−	0.200622i
$546$	604012.	−	438841.i	2.02610	−	1.47205i
$547$	79773.9	−	245519.i	0.266616	−	0.820559i	−0.724701	−	0.689064i	$-0.758022\pi$
$547$	79773.9	−	245519.i	0.266616	−	0.820559i	0.991317	−	0.131496i	$-0.0419780\pi$
$548$	16027.0	+	22059.3i	0.0533692	+	0.0734564i
$549$	−819725.	+	266345.i	−2.71972	+	0.883689i
$550$	−217477.	+	70662.7i	−0.718934	+	0.233596i
$551$	−282229.	−	91701.7i	−0.929604	−	0.302047i
$552$	126014.			0.413561
$553$			435092.i			1.42276i
$554$	−166728.	−	54173.2i	−0.543236	−	0.176508i
$555$	146491.	+	106432.i	0.475581	+	0.345530i
$556$	−7021.51	−	9664.28i	−0.0227133	−	0.0312622i
$557$			36554.9i			0.117824i	0.998263	+	0.0589122i	$0.0187632\pi$
$557$			36554.9i			0.117824i	−0.998263	+	0.0589122i	$0.981237\pi$
$558$	−452630.	+	526940.i	−1.45370	+	1.69236i
$559$	360370.			1.15325
$560$	96960.4	−	70445.9i	0.309185	−	0.224636i
$561$	−357158.	+	491585.i	−1.13484	+	1.56197i
$562$	−99806.1	+	307171.i	−0.315998	+	0.972542i
$563$	42113.2			0.132862			0.0664311	−	0.997791i	$-0.478839\pi$
$563$	42113.2			0.132862			0.0664311	+	0.997791i	$0.478839\pi$
$564$		−	90858.9i		−	0.285633i
$565$	34015.0	−	104687.i	0.106555	−	0.327942i
$566$	−85608.5	−	263476.i	−0.267229	−	0.822447i
$567$	−268130.	−	825220.i	−0.834026	−	2.56687i
$568$	−34585.1	+	25127.5i	−0.107199	+	0.0778849i
$569$	−269455.	−	87551.4i	−0.832266	−	0.270420i	−0.138267	−	0.990395i	$-0.544153\pi$
$569$	−269455.	−	87551.4i	−0.832266	−	0.270420i	−0.694000	+	0.719975i	$0.744153\pi$
$570$	−112787.	−	155238.i	−0.347144	−	0.477803i
$571$	−274024.	+	377162.i	−0.840460	+	1.15679i	0.145425	+	0.989369i	$0.453545\pi$
$571$	−274024.	+	377162.i	−0.840460	+	1.15679i	−0.985885	+	0.167425i	$0.946455\pi$
$572$	15761.0	+	48507.3i	0.0481716	+	0.148257i
$573$	207418.	−	285487.i	0.631740	−	0.869515i
$574$	−204380.	−	148491.i	−0.620318	−	0.450688i
$575$	−56977.1	+	18513.0i	−0.172331	+	0.0559939i
$576$	702373.	+	510304.i	2.11701	+	1.53810i
$577$	78243.6	−	56847.3i	0.235016	−	0.170749i	−0.464044	−	0.885812i	$-0.653602\pi$
$577$	78243.6	−	56847.3i	0.235016	−	0.170749i	0.699060	+	0.715063i	$0.253602\pi$
$578$	20250.8	−	62325.6i	0.0606159	−	0.186557i
$579$	363052.	+	499698.i	1.08296	+	1.49056i
$580$	17678.6	−	5744.13i	0.0525524	−	0.0170753i
$581$	647539.	−	210398.i	1.91829	−	0.623289i
$582$	−129850.	−	42190.7i	−0.383349	−	0.124558i
$583$	150196.			0.441897
$584$			94192.0i			0.276178i
$585$	378718.	+	123053.i	1.10663	+	0.359567i
$586$	253478.	+	184163.i	0.738152	+	0.536299i
$587$	380519.	+	523740.i	1.10433	+	1.51999i	0.829510	+	0.558491i	$0.188620\pi$
$587$	380519.	+	523740.i	1.10433	+	1.51999i	0.274824	+	0.961495i	$0.411380\pi$
$588$		−	28363.9i		−	0.0820373i
$589$	160443.	+	263488.i	0.462478	+	0.759503i
$590$	43067.5			0.123722
$591$	334972.	−	243371.i	0.959032	−	0.696777i
$592$	145075.	−	199679.i	0.413952	−	0.569757i
$593$	10555.1	−	32485.2i	0.0300159	−	0.0923796i	−0.934926	−	0.354842i	$-0.884535\pi$
$593$	10555.1	−	32485.2i	0.0300159	−	0.0923796i	0.964942	+	0.262463i	$0.0845346\pi$
$594$	−803905.			−2.27841
$595$			174484.i			0.492857i
$596$	11650.1	−	35855.4i	0.0327973	−	0.100940i
$597$	175771.	+	540967.i	0.493172	+	1.51783i
$598$	−27629.3	−	85034.3i	−0.0772624	−	0.237789i
$599$	−72397.8	+	52600.0i	−0.201777	+	0.146599i	−0.684085	−	0.729402i	$-0.739798\pi$
$599$	−72397.8	+	52600.0i	−0.201777	+	0.146599i	0.482308	+	0.876001i	$0.339798\pi$
$600$	−565266.	−	183666.i	−1.57018	−	0.510183i
$601$	−263427.	−	362576.i	−0.729307	−	1.00381i	−0.999163	−	0.0409048i	$-0.986976\pi$
$601$	−263427.	−	362576.i	−0.729307	−	1.00381i	0.269856	−	0.962901i	$-0.413024\pi$
$602$	−211013.	+	290435.i	−0.582260	+	0.801412i
$603$	−439008.	−	1.35113e6i	−1.20736	−	3.71588i
$604$	20089.3	−	27650.6i	0.0550671	−	0.0757933i
$605$	10531.5	+	7651.56i	0.0287725	+	0.0209045i
$606$	928239.	−	301603.i	2.52764	−	0.821279i
$607$	2550.88	+	1853.32i	0.00692328	+	0.00503006i	0.591242	−	0.806495i	$-0.298638\pi$
$607$	2550.88	+	1853.32i	0.00692328	+	0.00503006i	−0.584318	+	0.811525i	$0.698638\pi$
$608$	68695.0	−	49909.9i	0.185831	−	0.135014i
$609$	−268837.	+	827394.i	−0.724860	+	2.23089i
$610$	94299.1	+	129792.i	0.253424	+	0.348808i
$611$	−532871.	+	173140.i	−1.42738	+	0.463784i
$612$	−121873.	+	39599.0i	−0.325391	+	0.105726i
$613$	410385.	+	133342.i	1.09212	+	0.354852i	0.799066	−	0.601244i	$-0.205328\pi$
$613$	410385.	+	133342.i	1.09212	+	0.354852i	0.293056	+	0.956095i	$0.405328\pi$
$614$	−411390.			−1.09123
$615$		−	191074.i		−	0.505187i
$616$	−419979.	−	136459.i	−1.10679	−	0.359618i
$617$	278342.	+	202227.i	0.731153	+	0.531214i	0.889928	−	0.456101i	$-0.150754\pi$
$617$	278342.	+	202227.i	0.731153	+	0.531214i	−0.158775	+	0.987315i	$0.550754\pi$
$618$	−347674.	−	478532.i	−0.910323	−	1.25295i
$619$			389568.i			1.01672i	0.861144	+	0.508361i	$0.169748\pi$
$619$			389568.i			1.01672i	−0.861144	+	0.508361i	$0.830252\pi$
$620$	−17831.9	−	7445.29i	−0.0463889	−	0.0193686i
$621$	−210616.			−0.546144
$622$	−182619.	+	132681.i	−0.472026	+	0.342947i
$623$	112623.	−	155012.i	0.290169	−	0.399384i
$624$	237856.	−	732046.i	0.610865	−	1.88005i
$625$	224175.			0.573887
$626$		−	185422.i		−	0.473164i
$627$	−189583.	+	583477.i	−0.482242	+	1.48419i
$628$	−5449.82	−	16772.8i	−0.0138186	−	0.0425292i
$629$	111039.	+	341743.i	0.280656	+	0.863770i
$630$	−320930.	+	233169.i	−0.808591	+	0.587476i
$631$	6991.11	+	2271.55i	0.0175585	+	0.00570511i	0.317783	−	0.948163i	$-0.397062\pi$
$631$	6991.11	+	2271.55i	0.0175585	+	0.00570511i	−0.300225	+	0.953869i	$0.597062\pi$
$632$	303845.	+	418206.i	0.760707	+	1.04702i
$633$	83983.5	−	115593.i	0.209598	−	0.288487i
$634$	124165.	+	382142.i	0.308903	+	0.950705i
$635$	18813.7	−	25894.8i	0.0466580	−	0.0642192i
$636$	36339.3	+	26402.1i	0.0898385	+	0.0652715i
$637$	−166349.	+	54050.1i	−0.409960	+	0.133204i
$638$	321720.	+	233743.i	0.790380	+	0.574245i
$639$	99333.7	−	72170.2i	0.243274	−	0.176749i
$640$	37295.4	−	114784.i	0.0910533	−	0.280233i
$641$	−32931.4	−	45326.1i	−0.0801482	−	0.110314i	0.767060	−	0.641575i	$-0.221719\pi$
$641$	−32931.4	−	45326.1i	−0.0801482	−	0.110314i	−0.847209	+	0.531260i	$0.821719\pi$
$642$	780232.	−	253513.i	1.89301	−	0.615077i
$643$	−706931.	+	229696.i	−1.70984	+	0.555560i	−0.990307	−	0.138899i	$-0.955644\pi$
$643$	−706931.	+	229696.i	−1.70984	+	0.555560i	−0.719532	+	0.694459i	$0.755644\pi$
$644$	−12660.1	−	4113.50i	−0.0305256	−	0.00991836i
$645$	−271527.			−0.652669
$646$		−	380786.i		−	0.912466i
$647$	−489461.	−	159036.i	−1.16926	−	0.379914i	−0.340891	−	0.940103i	$-0.610729\pi$
$647$	−489461.	−	159036.i	−1.16926	−	0.379914i	−0.828365	+	0.560189i	$0.810729\pi$
$648$	−834013.	−	605946.i	−1.98620	−	1.44306i
$649$	−80936.5	−	111399.i	−0.192156	−	0.264481i
$650$			421713.i			0.998137i
$651$	772452.	−	470363.i	1.82268	−	1.10987i
$652$	110377.			0.259648
$653$	−320273.	+	232692.i	−0.751094	+	0.545701i	−0.896166	−	0.443720i	$-0.853659\pi$
$653$	−320273.	+	232692.i	−0.751094	+	0.545701i	0.145072	+	0.989421i	$0.453659\pi$
$654$	381250.	−	524745.i	0.891362	−	1.22685i
$655$	27660.8	−	85131.3i	0.0644737	−	0.198430i
$656$	−260450.			−0.605225
$657$		−	270534.i		−	0.626745i
$658$	172481.	−	530842.i	0.398372	−	1.22606i
$659$	−99227.6	−	305391.i	−0.228487	−	0.703211i	−0.997919	−	0.0644818i	$-0.979461\pi$
$659$	−99227.6	−	305391.i	−0.228487	−	0.703211i	0.769432	−	0.638729i	$-0.220539\pi$
$660$	−11875.4	−	36548.6i	−0.0272621	−	0.0839041i
$661$	170976.	−	124221.i	0.391320	−	0.284310i	−0.374676	−	0.927156i	$-0.622246\pi$
$661$	170976.	−	124221.i	0.391320	−	0.284310i	0.765996	+	0.642845i	$0.222246\pi$
$662$	−424901.	−	138059.i	−0.969554	−	0.315027i
$663$	658671.	+	906583.i	1.49845	+	2.06244i
$664$	475478.	−	654439.i	1.07843	−	1.48434i
$665$	54439.4	+	167547.i	0.123103	+	0.378873i
$666$	−480186.	+	660920.i	−1.08258	+	1.49005i
$667$	84287.6	+	61238.5i	0.189458	+	0.137649i
$668$	−55913.4	+	18167.3i	−0.125303	+	0.0407135i
$669$	−669710.	−	486573.i	−1.49635	−	1.08717i
$670$	−213931.	+	155430.i	−0.476568	+	0.346247i
$671$	158507.	−	487833.i	0.352048	−	1.08349i
$672$	−146318.	−	201389.i	−0.324011	−	0.445962i
$673$	660349.	−	214560.i	1.45795	−	0.473717i	0.530508	−	0.847680i	$-0.322001\pi$
$673$	660349.	−	214560.i	1.45795	−	0.473717i	0.927444	+	0.373963i	$0.122001\pi$
$674$	152207.	−	49454.9i	0.335053	−	0.108865i
$675$	944769.	+	306974.i	2.07357	+	0.673743i
$676$	34645.2			0.0758140
$677$		−	657667.i		−	1.43492i	−0.696597	−	0.717462i	$-0.745304\pi$
$677$		−	657667.i		−	1.43492i	0.696597	−	0.717462i	$-0.254696\pi$
$678$	669780.	+	217625.i	1.45704	+	0.473423i
$679$	101410.	+	73678.8i	0.219959	+	0.159810i
$680$	121850.	+	167712.i	0.263516	+	0.362699i
$681$		−	579488.i		−	1.24954i
$682$	−95370.3	−	402248.i	−0.205043	−	0.864819i
$683$	406578.			0.871570			0.435785	−	0.900051i	$-0.356471\pi$
$683$	406578.			0.871570			0.435785	+	0.900051i	$0.356471\pi$
$684$	−104673.	+	76049.6i	−0.223730	+	0.162549i
$685$	−74467.1	+	102495.i	−0.158702	+	0.218435i
$686$	−103322.	+	317991.i	−0.219555	+	0.675720i
$687$	532811.			1.12891
$688$			370114.i			0.781913i
$689$	85595.3	−	263435.i	0.180306	−	0.554926i
$690$	20817.8	+	64070.6i	0.0437257	+	0.134574i
$691$	−224763.	−	691750.i	−0.470727	−	1.44875i	−0.851635	−	0.524136i	$-0.824388\pi$
$691$	−224763.	−	691750.i	−0.470727	−	1.44875i	0.380907	−	0.924613i	$-0.375612\pi$
$692$	−68856.9	+	50027.4i	−0.143792	+	0.104471i
$693$	1.20624e6	+	391932.i	2.51171	+	0.816103i
$694$	397268.	+	546792.i	0.824829	+	1.13528i
$695$	32624.4	−	44903.7i	0.0675419	−	0.0929635i
$696$	319404.	+	983025.i	0.659359	+	2.02930i
$697$	222875.	−	306761.i	0.458771	−	0.631444i
$698$	−438078.	−	318282.i	−0.899167	−	0.653283i
$699$	−1.10604e6	+	359374.i	−2.26369	+	0.735516i
$700$	50794.4	+	36904.3i	0.103662	+	0.0753148i
$701$	−250894.	+	182285.i	−0.510568	+	0.370950i	−0.813039	−	0.582209i	$-0.802189\pi$
$701$	−250894.	+	182285.i	−0.510568	+	0.370950i	0.302471	+	0.953159i	$0.402189\pi$
$702$	−458138.	+	1.41000e6i	−0.929655	+	2.86118i
$703$	213249.	+	293513.i	0.431496	+	0.593904i
$704$	−491383.	+	159660.i	−0.991458	+	0.322144i
$705$	401501.	−	130455.i	0.807808	−	0.262473i
$706$	268293.	+	87173.7i	0.538270	+	0.174895i
$707$	−896073.			−1.79269
$708$		−	41180.0i		−	0.0821523i
$709$	−730050.	−	237208.i	−1.45231	−	0.471885i	−0.526601	−	0.850113i	$-0.676534\pi$
$709$	−730050.	−	237208.i	−1.45231	−	0.471885i	−0.925713	+	0.378228i	$0.876534\pi$
$710$	−18489.4	−	13433.4i	−0.0366781	−	0.0266482i
$711$	−872689.	−	1.20115e6i	−1.72632	−	2.37607i
$712$		−	227647.i		−	0.449057i
$713$	−24986.1	−	105385.i	−0.0491496	−	0.207301i
$714$	−1.11633e6			−2.18976
$715$	−191721.	+	139294.i	−0.375024	+	0.272471i
$716$	32995.3	−	45414.2i	0.0643616	−	0.0885861i
$717$	−35887.7	+	110451.i	−0.0698083	+	0.214848i
$718$	−125817.			−0.244056
$719$		−	17004.5i		−	0.0328932i	−0.999865	−	0.0164466i	$-0.994765\pi$
$719$		−	17004.5i		−	0.0328932i	0.999865	−	0.0164466i	$-0.00523536\pi$
$720$	−126380.	+	388958.i	−0.243789	+	0.750305i
$721$	167813.	+	516475.i	0.322816	+	0.993526i
$722$	31442.5	+	96770.1i	0.0603174	+	0.185638i
$723$	−705491.	+	512570.i	−1.34963	+	0.980565i
$724$	−38598.6	−	12541.4i	−0.0736366	−	0.0239260i
$725$	−288837.	−	397551.i	−0.549512	−	0.756339i
$726$	−48954.0	+	67379.4i	−0.0928784	+	0.127836i
$727$	259879.	+	799825.i	0.491702	+	1.51330i	0.822034	+	0.569438i	$0.192839\pi$
$727$	259879.	+	799825.i	0.491702	+	1.51330i	−0.330332	+	0.943865i	$0.607161\pi$
$728$	−478684.	+	658852.i	−0.903204	+	1.24315i
$729$	365561.	+	265595.i	0.687867	+	0.499764i
$730$	−47891.1	+	15560.8i	−0.0898689	+	0.0292002i
$731$	−435924.	−	316717.i	−0.815786	−	0.592703i
$732$	124103.	−	90166.3i	0.231612	−	0.168276i
$733$	104588.	−	321889.i	0.194659	−	0.599099i	−0.805321	−	0.592839i	$-0.798007\pi$
$733$	104588.	−	321889.i	0.194659	−	0.599099i	0.999980	−	0.00626041i	$-0.00199276\pi$
$734$	−514.984	−	708.814i	−0.000955876	−	0.00131565i
$735$	125339.	−	40725.0i	0.232012	−	0.0753852i
$736$	−28352.1	+	9212.16i	−0.0523395	+	0.0170061i
$737$	804080.	+	261262.i	1.48035	+	0.480995i
$738$	862066.			1.58281
$739$			643653.i			1.17859i	0.807918	+	0.589295i	$0.200595\pi$
$739$			643653.i			1.17859i	−0.807918	+	0.589295i	$0.799405\pi$
$740$	−21613.4	−	7022.61i	−0.0394693	−	0.0128243i
$741$	915343.	+	665036.i	1.66705	+	1.21118i
$742$	162192.	+	223238.i	0.294592	+	0.405471i
$743$		−	333650.i		−	0.604384i	−0.953247	−	0.302192i	$-0.902282\pi$
$743$		−	333650.i		−	0.604384i	0.953247	−	0.302192i	$-0.0977184\pi$
$744$	413998.	−	991547.i	0.747915	−	1.79130i
$745$	175171.			0.315609
$746$	472852.	−	343547.i	0.849665	−	0.617318i
$747$	−1.36565e6	+	1.87965e6i	−2.44735	+	3.36849i
$748$	23566.1	−	72528.9i	0.0421196	−	0.129631i
$749$	−753194.			−1.34259
$750$		−	691340.i		−	1.22905i
$751$	224115.	−	689756.i	0.397367	−	1.22297i	−0.529736	−	0.848163i	$-0.677709\pi$
$751$	224115.	−	689756.i	0.397367	−	1.22297i	0.927103	−	0.374807i	$-0.122291\pi$
$752$	−177822.	−	547279.i	−0.314448	−	0.967772i
$753$	41191.1	+	126773.i	0.0726462	+	0.223582i
$754$	593317.	−	431070.i	1.04362	−	0.758237i
$755$	151031.	+	49072.9i	0.264955	+	0.0860891i
$756$	129740.	+	178572.i	0.227002	+	0.312442i
$757$	−318323.	+	438134.i	−0.555490	+	0.764566i	−0.990744	−	0.135741i	$-0.956658\pi$
$757$	−318323.	+	438134.i	−0.555490	+	0.764566i	0.435254	+	0.900308i	$0.356658\pi$
$758$	−142827.	−	439576.i	−0.248583	−	0.765060i
$759$	126604.	−	174255.i	0.219768	−	0.302484i
$760$	169333.	+	123027.i	0.293166	+	0.212997i
$761$	224195.	−	72845.2i	0.387129	−	0.125786i	−0.108985	−	0.994043i	$-0.534760\pi$
$761$	224195.	−	72845.2i	0.387129	−	0.125786i	0.496114	+	0.868258i	$0.334760\pi$
$762$	165673.	+	120368.i	0.285326	+	0.207301i
$763$	−481768.	+	350025.i	−0.827540	+	0.601243i
$764$	−13685.9	+	42121.0i	−0.0234471	+	0.0721626i
$765$	−349972.	−	481695.i	−0.598012	−	0.823093i
$766$	−104010.	+	33794.8i	−0.177262	+	0.0575959i
$767$	−241513.	+	78472.4i	−0.410535	+	0.133391i
$768$	−395869.	−	128626.i	−0.671164	−	0.218075i
$769$	660571.			1.11704			0.558518	−	0.829493i	$-0.311370\pi$
$769$	660571.			1.11704			0.558518	+	0.829493i	$0.311370\pi$
$770$		−	236078.i		−	0.398175i
$771$	1.19409e6	+	387982.i	2.00876	+	0.652684i
$772$	−62714.9	−	45565.1i	−0.105229	−	0.0764535i
$773$	371222.	+	510943.i	0.621261	+	0.855093i	0.997444	−	0.0714526i	$-0.0227635\pi$
$773$	371222.	+	510943.i	0.621261	+	0.855093i	−0.376183	+	0.926546i	$0.622763\pi$
$774$		−	1.22504e6i		−	2.04489i
$775$	−41518.4	+	509150.i	−0.0691254	+	0.847700i
$776$	148928.			0.247316
$777$	860475.	−	625171.i	1.42527	−	1.03552i
$778$	324098.	−	446083.i	0.535448	−	0.736980i
$779$	118304.	−	364104.i	0.194951	−	0.599999i
$780$	−70871.8			−0.116489
$781$			73070.5i			0.119795i
$782$	−41311.9	+	127145.i	−0.0675556	+	0.207915i
$783$	−533843.	−	1.64300e6i	−0.870744	−	2.67987i
$784$	−55511.6	−	170847.i	−0.0903132	−	0.277956i
$785$	66293.4	−	48165.0i	0.107580	−	0.0781614i
$786$	544663.	+	176972.i	0.881622	+	0.286456i
$787$	−75515.0	−	103937.i	−0.121922	−	0.167812i	0.743693	−	0.668521i	$-0.233072\pi$
$787$	−75515.0	−	103937.i	−0.121922	−	0.167812i	−0.865615	+	0.500710i	$0.833072\pi$
$788$	−30544.5	+	42040.9i	−0.0491904	+	0.0677048i
$789$	206286.	+	634884.i	0.331373	+	1.01986i
$790$	−162437.	+	223576.i	−0.260275	+	0.358237i
$791$	−523086.	−	380044.i	−0.836027	−	0.607409i
$792$	1.43314e6	−	465654.i	2.28474	−	0.742357i
$793$	−765300.	−	556023.i	−1.21698	−	0.884191i
$794$	−211705.	+	153813.i	−0.335807	+	0.243978i
$795$	−64493.2	+	198490.i	−0.102042	+	0.314054i
$796$	−41961.1	−	57754.5i	−0.0662248	−	0.0911506i
$797$	−50177.3	+	16303.6i	−0.0789933	+	0.0256665i	−0.348247	−	0.937403i	$-0.613223\pi$
$797$	−50177.3	+	16303.6i	−0.0789933	+	0.0256665i	0.269254	+	0.963069i	$0.413223\pi$
$798$	−1.07195e6	+	348298.i	−1.68333	+	0.546948i
$799$	796758.	+	258883.i	1.24805	+	0.405517i
$800$	140607.			0.219699
$801$			653836.i			1.01907i
$802$	−177606.	−	57707.6i	−0.276126	−	0.0897189i
$803$	130252.	+	94633.3i	0.202000	+	0.146762i
$804$	148618.	+	204556.i	0.229911	+	0.316446i
$805$		−	61850.3i		−	0.0954443i
$806$	−759871.	−	61963.4i	−1.16969	−	0.0953817i
$807$	−1.01019e6			−1.55116
$808$	−861297.	+	625769.i	−1.31926	+	0.958498i
$809$	−579042.	+	796983.i	−0.884735	+	1.21773i	0.0903524	+	0.995910i	$0.471201\pi$
$809$	−579042.	+	796983.i	−0.884735	+	1.21773i	−0.975087	+	0.221823i	$0.928799\pi$
$810$	170307.	−	524151.i	0.259575	−	0.798889i
$811$	236202.			0.359123			0.179561	−	0.983747i	$-0.442532\pi$
$811$	236202.			0.359123			0.179561	+	0.983747i	$0.442532\pi$
$812$		−	109187.i		−	0.165599i
$813$	515665.	−	1.58705e6i	0.780165	−	2.40110i
$814$	−150237.	−	462382.i	−0.226740	−	0.697833i
$815$	158480.	+	487751.i	0.238594	+	0.734316i
$816$	−931096.	+	676481.i	−1.39834	+	1.01596i
$817$	−517411.	−	168117.i	−0.775160	−	0.251865i
$818$	236420.	+	325404.i	0.353328	+	0.486314i
$819$	1.37485e6	−	1.89232e6i	2.04969	−	2.82116i
$820$	7410.51	+	22807.2i	0.0110210	+	0.0339191i
$821$	402755.	−	554344.i	0.597523	−	0.822419i	−0.397956	−	0.917404i	$-0.630280\pi$
$821$	402755.	−	554344.i	0.597523	−	0.822419i	0.995479	+	0.0949852i	$0.0302804\pi$
$822$	−655756.	−	476434.i	−0.970506	−	0.705114i
$823$	−496669.	+	161377.i	−0.733276	+	0.238256i	−0.651769	−	0.758417i	$-0.725973\pi$
$823$	−496669.	+	161377.i	−0.733276	+	0.238256i	−0.0815061	+	0.996673i	$0.525973\pi$
$824$	521979.	+	379240.i	0.768774	+	0.558547i
$825$	−821892.	+	597140.i	−1.20756	+	0.877340i
$826$	78173.5	−	240593.i	0.114578	−	0.352633i
$827$	−174111.	−	239643.i	−0.254575	−	0.350392i	0.662532	−	0.749034i	$-0.269482\pi$
$827$	−174111.	−	239643.i	−0.254575	−	0.350392i	−0.917107	+	0.398641i	$0.869482\pi$
$828$	43201.2	−	14036.9i	0.0630137	−	0.0204744i
$829$	859385.	−	279231.i	1.25049	−	0.406308i	0.392391	−	0.919799i	$-0.371648\pi$
$829$	859385.	−	279231.i	1.25049	−	0.406308i	0.858095	+	0.513491i	$0.171648\pi$
$830$	411294.	+	133638.i	0.597030	+	0.193987i
$831$	−778846.			−1.12784
$832$			952845.i			1.37650i
$833$	248728.	+	80816.7i	0.358455	+	0.116469i
$834$	287290.	+	208728.i	0.413036	+	0.300089i
$835$	−160561.	−	220993.i	−0.230286	−	0.316962i
$836$		−	76998.3i		−	0.110171i
$837$	−691944.	+	1.65724e6i	−0.987689	+	2.36557i
$838$	946875.			1.34836
$839$	−40847.3	+	29677.3i	−0.0580282	+	0.0421600i	−0.616421	−	0.787417i	$-0.711418\pi$
$839$	−40847.3	+	29677.3i	−0.0580282	+	0.0421600i	0.558393	+	0.829577i	$0.311418\pi$
$840$	360672.	−	496423.i	0.511157	−	0.703547i
$841$	−45514.3	+	140079.i	−0.0643511	+	0.198052i
$842$	764221.			1.07794
$843$			1.43491e6i			2.01915i
$844$	−5541.43	+	17054.8i	−0.00777923	+	0.0239420i
$845$	49743.7	+	153095.i	0.0696666	+	0.214412i
$846$	588574.	+	1.81144e6i	0.822356	+	2.53095i
$847$	61861.0	−	44944.6i	0.0862283	−	0.0626485i
$848$	270558.	+	87909.7i	0.376243	+	0.122249i
$849$	−723440.	−	995730.i	−1.00366	−	1.38142i
$850$	370630.	−	510128.i	0.512982	−	0.706059i
$851$	−39360.7	−	121140.i	−0.0543505	−	0.167274i
$852$	−12844.6	+	17679.1i	−0.0176947	+	0.0243546i
$853$	−902009.	−	655348.i	−1.23969	−	0.900687i	−0.242112	−	0.970248i	$-0.577840\pi$
$853$	−902009.	−	655348.i	−1.23969	−	0.900687i	−0.997578	+	0.0695612i	$0.977840\pi$
$854$	896237.	−	291205.i	1.22887	−	0.399285i
$855$	−486349.	−	353353.i	−0.665298	−	0.483367i
$856$	−723963.	+	525990.i	−0.988027	+	0.717844i
$857$	350044.	−	1.07733e6i	0.476608	−	1.46685i	−0.367168	−	0.930154i	$-0.619673\pi$
$857$	350044.	−	1.07733e6i	0.476608	−	1.46685i	0.843777	−	0.536695i	$-0.180327\pi$
$858$	−891189.	−	1.22662e6i	−1.21059	−	1.66623i
$859$	535724.	−	174067.i	0.726030	−	0.235902i	0.0773947	−	0.997001i	$-0.475340\pi$
$859$	535724.	−	174067.i	0.726030	−	0.235902i	0.648636	+	0.761099i	$0.275340\pi$
$860$	32410.3	−	10530.7i	0.0438214	−	0.0142384i
$861$	−1.06742e6	−	346827.i	−1.43989	−	0.467850i
$862$	−28470.3			−0.0383158
$863$			740144.i			0.993790i	0.867811	+	0.496895i	$0.165527\pi$
$863$			740144.i			0.993790i	−0.867811	+	0.496895i	$0.834473\pi$
$864$	470122.	+	152752.i	0.629772	+	0.204625i
$865$	−319934.	−	232445.i	−0.427590	−	0.310662i
$866$	777202.	+	1.06973e6i	1.03633	+	1.42639i
$867$		−	291145.i		−	0.387321i
$868$	−73960.0	+	86102.3i	−0.0981651	+	0.114281i
$869$	883576.			1.17005
$870$	−447044.	+	324797.i	−0.590625	+	0.429114i
$871$	916475.	−	1.26142e6i	1.20805	−	1.66274i
$872$	−218633.	+	672882.i	−0.287529	+	0.884924i
$873$	−427744.			−0.561248
$874$			134980.i			0.176704i
$875$	−196139.	+	603654.i	−0.256182	+	0.788446i
$876$	14878.8	+	45792.2i	0.0193892	+	0.0596738i
$877$	110122.	+	338920.i	0.143177	+	0.440654i	0.996772	−	0.0802832i	$-0.0255825\pi$
$877$	110122.	+	338920.i	0.143177	+	0.440654i	−0.853595	+	0.520937i	$0.825582\pi$
$878$	−370812.	+	269411.i	−0.481022	+	0.349483i
$879$	1.32385e6	+	430145.i	1.71341	+	0.556721i
$880$	−143060.	−	196905.i	−0.184737	−	0.254268i
$881$	−223355.	+	307422.i	−0.287769	+	0.396080i	−0.928288	−	0.371862i	$-0.878719\pi$
$881$	−223355.	+	307422.i	−0.287769	+	0.396080i	0.640519	+	0.767942i	$0.278719\pi$
$882$	183738.	+	565488.i	0.236190	+	0.726919i
$883$	−641350.	+	882743.i	−0.822572	+	1.13217i	0.166688	+	0.986010i	$0.446693\pi$
$883$	−641350.	+	882743.i	−0.822572	+	1.13217i	−0.989260	+	0.146164i	$0.953307\pi$
$884$	−113781.	−	82667.1i	−0.145602	−	0.105786i
$885$	181972.	−	59126.3i	0.232337	−	0.0754909i
$886$	−542723.	−	394311.i	−0.691371	−	0.502310i
$887$	793003.	−	576150.i	1.00792	−	0.732299i	0.0441507	−	0.999025i	$-0.485942\pi$
$887$	793003.	−	576150.i	1.00792	−	0.732299i	0.963772	+	0.266726i	$0.0859418\pi$
$888$	390494.	−	1.20182e6i	0.495209	−	1.52410i
$889$	−110510.	−	152104.i	−0.139829	−	0.192458i
$890$	115745.	−	37607.8i	0.146124	−	0.0474786i
$891$	−1.67584e6	+	544514.i	−2.11095	+	0.685888i
$892$	98809.6	+	32105.2i	0.124185	+	0.0403502i
$893$	845856.			1.06070
$894$			1.12073e6i			1.40225i
$895$	248058.	+	80598.9i	0.309675	+	0.100620i
$896$	−573534.	−	416697.i	−0.714403	−	0.519044i
$897$	−233483.	−	321362.i	−0.290182	−	0.399402i
$898$			1.01948e6i			1.26423i
$899$	758773.	−	462034.i	0.938842	−	0.571682i
$900$	−214249.			−0.264504
$901$	−335066.	+	243439.i	−0.412743	+	0.299876i
$902$	−301552.	+	415051.i	−0.370638	+	0.510139i
$903$	−492859.	+	1.51687e6i	−0.604432	+	1.86025i
$904$	−768188.			−0.940006
$905$		−	188572.i		−	0.230240i
$906$	−313964.	+	966283.i	−0.382494	+	1.17719i
$907$	225961.	+	695437.i	0.274675	+	0.845363i	0.989305	+	0.145861i	$0.0465951\pi$
$907$	225961.	+	695437.i	0.274675	+	0.845363i	−0.714630	+	0.699503i	$0.753405\pi$
$908$	22474.5	+	69169.5i	0.0272596	+	0.0838963i
$909$	2.47378e6	−	1.79731e6i	2.99387	−	2.17517i
$910$	−414067.	−	134539.i	−0.500021	−	0.162467i
$911$	−192694.	−	265220.i	−0.232183	−	0.319572i	0.676989	−	0.735993i	$-0.263284\pi$
$911$	−192694.	−	265220.i	−0.232183	−	0.319572i	−0.909172	+	0.416421i	$0.863284\pi$
$912$	−683018.	+	940093.i	−0.821187	+	1.13027i
$913$	−427272.	−	1.31501e6i	−0.512582	−	1.57756i
$914$	429012.	−	590485.i	0.513544	−	0.706832i
$915$	576628.	+	418945.i	0.688737	+	0.500397i
$916$	−63598.0	+	20664.2i	−0.0757970	+	0.0246280i
$917$	−425372.	−	309051.i	−0.505860	−	0.367529i
$918$	1.79339e6	−	1.30298e6i	2.12809	−	1.54615i
$919$	−408291.	+	1.25659e6i	−0.483435	+	1.48786i	0.350799	+	0.936451i	$0.385910\pi$
$919$	−408291.	+	1.25659e6i	−0.483435	+	1.48786i	−0.834234	+	0.551410i	$0.814090\pi$
$920$	−43192.9	−	59449.9i	−0.0510313	−	0.0702386i
$921$	−1.73824e6	+	564788.i	−2.04923	+	0.665835i
$922$	−334706.	+	108752.i	−0.393732	+	0.127931i
$923$	128161.	+	41642.2i	0.150437	+	0.0488799i
$924$	−225732.			−0.264392
$925$			600771.i			0.702143i
$926$	−286764.	−	93175.4i	−0.334429	−	0.108662i
$927$	−1.49920e6	−	1.08924e6i	−1.74462	−	1.26754i
$928$	−143727.	−	197823.i	−0.166895	−	0.229711i
$929$		−	423085.i		−	0.490226i	−0.969495	−	0.245113i	$-0.921175\pi$
$929$		−	423085.i		−	0.490226i	0.969495	−	0.245113i	$-0.0788250\pi$
$930$	572537.	+	46687.4i	0.661969	+	0.0539801i
$931$	264055.			0.304646
$932$	118083.	−	85792.0i	0.135942	−	0.0987677i
$933$	−589464.	+	811328.i	−0.677164	+	0.932037i
$934$	182877.	−	562836.i	0.209635	−	0.645191i
$935$	354338.			0.405317
$936$		−	2.77901e6i		−	3.17204i
$937$	63403.6	−	195136.i	0.0722162	−	0.222259i	−0.908433	−	0.418030i	$-0.862721\pi$
$937$	63403.6	−	195136.i	0.0722162	−	0.222259i	0.980650	+	0.195771i	$0.0627209\pi$
$938$	479985.	+	1.47724e6i	0.545534	+	1.67898i
$939$	−254561.	−	783459.i	−0.288710	−	0.888557i
$940$	−42864.9	+	31143.1i	−0.0485116	+	0.0352457i
$941$	−638799.	−	207558.i	−0.721414	−	0.234402i	−0.0747780	−	0.997200i	$-0.523825\pi$
$941$	−638799.	−	207558.i	−0.721414	−	0.234402i	−0.646636	+	0.762799i	$0.723825\pi$
$942$	308155.	+	424140.i	0.347271	+	0.477977i
$943$	−79003.9	+	108740.i	−0.0888434	+	0.122282i
$944$	−80594.2	−	248043.i	−0.0904398	−	0.278345i
$945$	−602818.	+	829707.i	−0.675029	+	0.929098i
$946$	589810.	+	428522.i	0.659067	+	0.478840i
$947$	128358.	−	41706.0i	0.143127	−	0.0465048i	−0.236577	−	0.971613i	$-0.576026\pi$
$947$	128358.	−	41706.0i	0.143127	−	0.0465048i	0.379705	+	0.925108i	$0.376026\pi$
$948$	213777.	+	155318.i	0.237873	+	0.172825i
$949$	240210.	−	174523.i	0.266722	−	0.193785i
$950$	196734.	−	605486.i	0.217988	−	0.670898i
$951$	1.04927e6	+	1.44419e6i	1.16018	+	1.59685i
$952$	1.15809e6	−	376285.i	1.27781	−	0.415186i
$953$	1.56519e6	−	508561.i	1.72338	−	0.559960i	0.730914	−	0.682470i	$-0.239094\pi$
$953$	1.56519e6	−	508561.i	1.72338	−	0.559960i	0.992467	+	0.122509i	$0.0390941\pi$
$954$	−895522.	−	290973.i	−0.983965	−	0.319710i
$955$	−205781.			−0.225631
$956$		−	14575.6i		−	0.0159482i
$957$	1.68026e6	+	545949.i	1.83464	+	0.596112i
$958$	−234421.	−	170317.i	−0.255426	−	0.185578i
$959$	437414.	+	602049.i	0.475615	+	0.654628i
$960$		−	717937.i		−	0.779012i
$961$	−911320.	−	149621.i	−0.986789	−	0.162012i
$962$	−896609.			−0.968842
$963$	2.07933e6	−	1.51073e6i	2.24219	−	1.62904i
$964$	64330.4	−	88543.3i	0.0692249	−	0.0952799i
$965$	111303.	−	342557.i	0.119524	−	0.367856i
$966$	395713.			0.424059
$967$			1.34289e6i			1.43610i	0.695989	+	0.718052i	$0.254966\pi$
$967$			1.34289e6i			1.43610i	−0.695989	+	0.718052i	$0.745034\pi$
$968$	28073.3	−	86400.7i	0.0299601	−	0.0922076i
$969$	−522773.	−	1.60893e6i	−0.556757	−	1.71352i
$970$	24603.3	+	75721.1i	0.0261486	+	0.0804773i
$971$	−1.20650e6	+	876576.i	−1.27965	+	0.929718i	−0.999542	−	0.0302519i	$-0.990369\pi$
$971$	−1.20650e6	+	876576.i	−1.27965	+	0.929718i	−0.280104	+	0.959970i	$0.590369\pi$
$972$	−201693.	−	65533.9i	−0.213480	−	0.0693639i
$973$	−191633.	−	263761.i	−0.202416	−	0.278602i
$974$	409588.	−	563750.i	0.431747	−	0.594249i
$975$	578960.	+	1.78186e6i	0.609031	+	1.87440i
$976$	571057.	−	785993.i	0.599487	−	0.825123i
$977$	1.46291e6	+	1.06286e6i	1.53259	+	1.11349i	0.954775	+	0.297329i	$0.0960959\pi$
$977$	1.46291e6	+	1.06286e6i	1.53259	+	1.11349i	0.577819	+	0.816165i	$0.303904\pi$
$978$	−3.12059e6	+	1.01394e6i	−3.26256	+	1.06007i
$979$	−314796.	−	228713.i	−0.328446	−	0.238630i
$980$	−13381.3	+	9722.12i	−0.0139331	+	0.0101230i
$981$	627947.	−	1.93262e6i	0.652507	−	2.00821i
$982$	−951813.	−	1.31006e6i	−0.987026	−	1.35852i
$983$	880483.	−	286086.i	0.911200	−	0.296067i	0.184348	−	0.982861i	$-0.440983\pi$
$983$	880483.	−	286086.i	0.911200	−	0.296067i	0.726852	+	0.686794i	$0.240983\pi$
$984$	−1.26820e6	+	412064.i	−1.30978	+	0.425573i
$985$	−229632.	−	74612.1i	−0.236679	−	0.0769018i
$986$	−1.09656e6			−1.12792
$987$		−	2.47975e6i		−	2.54550i
$988$	−135051.	−	43880.6i	−0.138351	−	0.0449530i
$989$	154525.	+	112269.i	0.157981	+	0.114780i
$990$	473516.	+	651738.i	0.483130	+	0.664971i
$991$		−	172185.i		−	0.175327i	−0.996150	−	0.0876635i	$-0.972060\pi$
$991$		−	172185.i		−	0.175327i	0.996150	−	0.0876635i	$-0.0279400\pi$
$992$	−20659.8	+	253356.i	−0.0209944	+	0.257458i
$993$	−1.98487e6			−2.01295
$994$	−108605.	+	78906.5i	−0.109921	+	0.0798619i
$995$	194966.	−	268348.i	0.196931	−	0.271052i
$996$	127781.	−	393268.i	0.128809	−	0.396434i
$997$	−687458.			−0.691602			−0.345801	−	0.938308i	$-0.612393\pi$
$997$	−687458.			−0.691602			−0.345801	+	0.938308i	$0.612393\pi$
$998$		−	1.08461e6i		−	1.08897i
$999$	−652662.	+	2.00869e6i	−0.653969	+	2.01271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.f.a.15.7	✓	36
31.29	odd	10	inner	31.5.f.a.29.7	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.f.a.15.7	✓	36	1.1	even	1	trivial
31.5.f.a.29.7	yes	36	31.29	odd	10	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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	31.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(3.01837 - 2.19297i) q^{2} +(9.74278 - 13.4098i) q^{3} +(-0.642851 + 1.97849i) q^{4} -9.66586 q^{5} -61.8414i q^{6} +(-17.5449 + 53.9977i) q^{7} +(20.8451 + 64.1545i) q^{8} +(-59.8702 - 184.262i) q^{9} +(-29.1751 + 21.1970i) q^{10} +(109.657 + 35.6299i) q^{11} +(20.2680 + 27.8965i) q^{12} +(124.985 - 172.028i) q^{13} +(65.4585 + 201.460i) q^{14} +(-94.1724 + 129.617i) q^{15} +(176.679 + 128.365i) q^{16} +(-302.379 + 98.2489i) q^{17} +(-584.791 - 424.876i) q^{18} +(-259.704 + 188.686i) q^{19} +(6.21371 - 19.1238i) q^{20} +(553.161 + 761.361i) q^{21} +(409.122 - 132.932i) q^{22} +(107.186 - 34.8269i) q^{23} +(1063.39 + 345.515i) q^{24} -531.571 q^{25} -793.333i q^{26} +(-1777.31 - 577.485i) q^{27} +(-95.5552 - 69.4249i) q^{28} +(543.366 + 747.878i) q^{29} +597.750i q^{30} +(78.1052 - 957.821i) q^{31} -264.513 q^{32} +(1546.16 - 1123.35i) q^{33} +(-697.234 + 959.661i) q^{34} +(169.587 - 521.934i) q^{35} +403.048 q^{36} -1130.18i q^{37} +(-370.100 + 1139.05i) q^{38} +(-1089.15 - 3352.06i) q^{39} +(-201.485 - 620.108i) q^{40} +(-964.839 + 700.997i) q^{41} +(3339.29 + 1085.00i) q^{42} +(996.154 + 1371.09i) q^{43} +(-140.987 + 194.052i) q^{44} +(578.697 + 1781.05i) q^{45} +(247.153 - 340.177i) q^{46} +(-2131.73 - 1548.79i) q^{47} +(3442.69 - 1118.60i) q^{48} +(-665.474 - 483.495i) q^{49} +(-1604.48 + 1165.72i) q^{50} +(-1628.52 + 5012.05i) q^{51} +(260.008 + 357.871i) q^{52} +(1238.89 - 402.540i) q^{53} +(-6631.00 + 2154.54i) q^{54} +(-1059.93 - 344.393i) q^{55} -3829.92 q^{56} +5320.91i q^{57} +(3280.16 + 1065.79i) q^{58} +(-966.165 - 701.960i) q^{59} +(-195.908 - 269.644i) q^{60} -4448.70i q^{61} +(-1864.73 - 3062.34i) q^{62} +11000.1 q^{63} +(-3625.26 + 2633.91i) q^{64} +(-1208.09 + 1662.80i) q^{65} +(2203.40 - 6781.36i) q^{66} +7332.66 q^{67} -661.414i q^{68} +(577.270 - 1776.66i) q^{69} +(-632.712 - 1947.29i) q^{70} +(195.836 + 602.722i) q^{71} +(10573.2 - 7681.89i) q^{72} +(1328.01 + 431.495i) q^{73} +(-2478.46 - 3411.30i) q^{74} +(-5178.98 + 7128.25i) q^{75} +(-206.363 - 635.120i) q^{76} +(-3847.86 + 5296.12i) q^{77} +(-10638.4 - 7729.27i) q^{78} +(7288.17 - 2368.07i) q^{79} +(-1707.76 - 1240.76i) q^{80} +(-12363.8 + 8982.83i) q^{81} +(-1374.97 + 4231.73i) q^{82} +(-7048.71 - 9701.71i) q^{83} +(-1861.95 + 604.983i) q^{84} +(2922.75 - 949.660i) q^{85} +(6013.52 + 1953.91i) q^{86} +15322.8 q^{87} +7777.72i q^{88} +(-3209.57 - 1042.85i) q^{89} +(5652.51 + 4106.79i) q^{90} +(7096.23 + 9767.13i) q^{91} +234.456i q^{92} +(-12083.2 - 10379.2i) q^{93} -9830.82 q^{94} +(2510.27 - 1823.81i) q^{95} +(-2577.09 + 3547.06i) q^{96} +(682.240 - 2099.72i) q^{97} -3068.94 q^{98} -22338.8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 5 q^{3} - 79 q^{4} - 2 q^{5} - 73 q^{7} + 173 q^{8} + 62 q^{9} + 84 q^{10} + 100 q^{11} + 150 q^{12} - 260 q^{13} + 488 q^{14} - 1075 q^{15} + 777 q^{16} - 725 q^{17} - 786 q^{18} - 1581 q^{19}+ \cdots + 74456 q^{98}+O(q^{100}) \) 36 * q - 3 * q^2 - 5 * q^3 - 79 * q^4 - 2 * q^5 - 73 * q^7 + 173 * q^8 + 62 * q^9 + 84 * q^10 + 100 * q^11 + 150 * q^12 - 260 * q^13 + 488 * q^14 - 1075 * q^15 + 777 * q^16 - 725 * q^17 - 786 * q^18 - 1581 * q^19 + 827 * q^20 + 2335 * q^21 - 1030 * q^22 + 1675 * q^23 - 165 * q^24 + 1294 * q^25 - 2855 * q^27 + 352 * q^28 - 575 * q^29 + 895 * q^31 - 5470 * q^32 + 4468 * q^33 + 1815 * q^34 - 3042 * q^35 + 7808 * q^36 - 6604 * q^38 + 595 * q^39 + 1482 * q^40 - 1740 * q^41 + 3840 * q^42 - 10055 * q^43 - 5780 * q^44 + 6774 * q^45 + 16515 * q^46 + 693 * q^47 + 4710 * q^48 - 944 * q^49 - 6240 * q^50 + 12641 * q^51 + 15885 * q^52 - 10835 * q^53 - 25960 * q^54 - 14010 * q^55 - 19976 * q^56 + 4755 * q^58 - 6021 * q^59 + 35 * q^60 - 11088 * q^62 - 15564 * q^63 + 6935 * q^64 + 26645 * q^65 + 23988 * q^66 + 28596 * q^67 - 4229 * q^69 + 8041 * q^70 + 31101 * q^71 + 20690 * q^72 + 6125 * q^73 - 47295 * q^74 - 27475 * q^75 + 12511 * q^76 + 35950 * q^77 + 29801 * q^78 - 29050 * q^79 - 47358 * q^80 - 1965 * q^81 + 9198 * q^82 + 21640 * q^83 - 35875 * q^84 - 55360 * q^85 - 27935 * q^86 - 2262 * q^87 - 11645 * q^89 - 14916 * q^90 + 670 * q^91 - 36224 * q^93 - 52442 * q^94 + 73983 * q^95 + 29810 * q^96 + 55059 * q^97 + 74456 * q^98

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