LMFDB - Embedded newform 31.5.f.a.29.2

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			29.2
Character	$\chi$	$=$	31.29
Dual form			31.5.f.a.15.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.99299 - 2.90108i) q^{2} +(-6.95155 - 9.56799i) q^{3} +(2.58345 + 7.95104i) q^{4} -0.0618873 q^{5} +58.3719i q^{6} +(5.65199 + 17.3950i) q^{7} +(-11.6521 + 35.8615i) q^{8} +(-18.1920 + 55.9892i) q^{9} +(0.247115 + 0.179540i) q^{10} +(-53.0929 + 17.2509i) q^{11} +(58.1165 - 79.9905i) q^{12} +(-35.4322 - 48.7682i) q^{13} +(27.8960 - 85.8550i) q^{14} +(0.430213 + 0.592137i) q^{15} +(258.780 - 188.015i) q^{16} +(-449.085 - 145.917i) q^{17} +(235.070 - 170.788i) q^{18} +(209.081 + 151.907i) q^{19} +(-0.159883 - 0.492068i) q^{20} +(127.145 - 175.001i) q^{21} +(262.046 + 85.1438i) q^{22} +(-340.414 - 110.607i) q^{23} +(424.122 - 137.806i) q^{24} -624.996 q^{25} +297.522i q^{26} +(-248.908 + 80.8753i) q^{27} +(-123.707 + 89.8783i) q^{28} +(-301.906 + 415.537i) q^{29} -3.61248i q^{30} +(653.538 + 704.563i) q^{31} -975.442 q^{32} +(534.135 + 388.072i) q^{33} +(1369.88 + 1885.47i) q^{34} +(-0.349786 - 1.07653i) q^{35} -492.171 q^{36} -1300.44i q^{37} +(-394.168 - 1213.12i) q^{38} +(-220.305 + 678.029i) q^{39} +(0.721116 - 2.21937i) q^{40} +(-2227.49 - 1618.37i) q^{41} +(-1015.38 + 329.917i) q^{42} +(641.579 - 883.057i) q^{43} +(-274.326 - 377.577i) q^{44} +(1.12585 - 3.46502i) q^{45} +(1038.39 + 1429.22i) q^{46} +(3228.27 - 2345.48i) q^{47} +(-3597.85 - 1169.01i) q^{48} +(1671.81 - 1214.64i) q^{49} +(2495.60 + 1813.16i) q^{50} +(1725.71 + 5311.19i) q^{51} +(296.221 - 407.713i) q^{52} +(-2028.25 - 659.017i) q^{53} +(1228.51 + 399.169i) q^{54} +(3.28578 - 1.06761i) q^{55} -689.669 q^{56} -3056.48i q^{57} +(2411.01 - 783.385i) q^{58} +(-1787.98 + 1299.05i) q^{59} +(-3.59667 + 4.95039i) q^{60} +1492.15i q^{61} +(-565.579 - 4709.28i) q^{62} -1076.76 q^{63} +(-245.557 - 178.407i) q^{64} +(2.19280 + 3.01813i) q^{65} +(-1006.97 - 3099.13i) q^{66} -1071.78 q^{67} -3947.66i q^{68} +(1308.12 + 4025.97i) q^{69} +(-1.72641 + 5.31333i) q^{70} +(501.986 - 1544.95i) q^{71} +(-1795.88 - 1304.78i) q^{72} +(-3900.95 + 1267.50i) q^{73} +(-3772.67 + 5192.63i) q^{74} +(4344.69 + 5979.96i) q^{75} +(-667.664 + 2054.86i) q^{76} +(-600.161 - 826.051i) q^{77} +(2846.69 - 2068.24i) q^{78} +(-6347.29 - 2062.36i) q^{79} +(-16.0152 + 11.6357i) q^{80} +(6361.93 + 4622.21i) q^{81} +(4199.35 + 12924.3i) q^{82} +(-5673.92 + 7809.48i) q^{83} +(1719.91 + 558.833i) q^{84} +(27.7926 + 9.03038i) q^{85} +(-5123.63 + 1664.77i) q^{86} +6074.57 q^{87} -2105.00i q^{88} +(12570.2 - 4084.31i) q^{89} +(-14.5478 + 10.5696i) q^{90} +(648.062 - 891.981i) q^{91} -2992.39i q^{92} +(2198.15 - 11150.9i) q^{93} -19694.9 q^{94} +(-12.9395 - 9.40108i) q^{95} +(6780.84 + 9333.02i) q^{96} +(-5202.90 - 16012.9i) q^{97} -10199.3 q^{98} -3286.46i 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 $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

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

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 $

$2$	−3.99299	−	2.90108i	−0.998247	−	0.725269i	−0.0365358	−	0.999332i	$-0.511632\pi$
$2$	−3.99299	−	2.90108i	−0.998247	−	0.725269i	−0.961712	+	0.274063i	$0.911632\pi$
$3$	−6.95155	−	9.56799i	−0.772395	−	1.06311i	−0.996081	−	0.0884490i	$-0.971809\pi$
$3$	−6.95155	−	9.56799i	−0.772395	−	1.06311i	0.223686	−	0.974661i	$-0.428191\pi$
$4$	2.58345	+	7.95104i	0.161466	+	0.496940i
$5$	−0.0618873			−0.00247549			−0.00123775	−	0.999999i	$-0.500394\pi$
$5$	−0.0618873			−0.00247549			−0.00123775	+	0.999999i	$0.500394\pi$
$6$			58.3719i			1.62144i
$7$	5.65199	+	17.3950i	0.115347	+	0.355001i	0.992019	−	0.126087i	$-0.0402419\pi$
$7$	5.65199	+	17.3950i	0.115347	+	0.355001i	−0.876673	+	0.481088i	$0.840242\pi$
$8$	−11.6521	+	35.8615i	−0.182064	+	0.560335i
$9$	−18.1920	+	55.9892i	−0.224593	+	0.691225i
$10$	0.247115	+	0.179540i	0.00247115	+	0.00179540i
$11$	−53.0929	+	17.2509i	−0.438784	+	0.142570i	−0.520075	−	0.854121i	$-0.674096\pi$
$11$	−53.0929	+	17.2509i	−0.438784	+	0.142570i	0.0812903	+	0.996690i	$0.474096\pi$
$12$	58.1165	−	79.9905i	0.403587	−	0.555489i
$13$	−35.4322	−	48.7682i	−0.209658	−	0.288569i	0.691218	−	0.722646i	$-0.257074\pi$
$13$	−35.4322	−	48.7682i	−0.209658	−	0.288569i	−0.900876	+	0.434077i	$0.857074\pi$
$14$	27.8960	−	85.8550i	0.142326	−	0.438036i
$15$	0.430213	+	0.592137i	0.00191206	+	0.00263172i
$16$	258.780	−	188.015i	1.01086	−	0.734434i
$17$	−449.085	−	145.917i	−1.55393	−	0.504902i	−0.598750	−	0.800936i	$-0.704336\pi$
$17$	−449.085	−	145.917i	−1.55393	−	0.504902i	−0.955177	+	0.296034i	$0.904336\pi$
$18$	235.070	−	170.788i	0.725523	−	0.527124i
$19$	209.081	+	151.907i	0.579173	+	0.420794i	0.838426	−	0.545016i	$-0.183476\pi$
$19$	209.081	+	151.907i	0.579173	+	0.420794i	−0.259253	+	0.965809i	$0.583476\pi$
$20$	−0.159883	−	0.492068i	−0.000399706	−	0.00123017i
$21$	127.145	−	175.001i	0.288312	−	0.396827i
$22$	262.046	+	85.1438i	0.541417	+	0.175917i
$23$	−340.414	−	110.607i	−0.643505	−	0.209087i	−0.0309568	−	0.999521i	$-0.509855\pi$
$23$	−340.414	−	110.607i	−0.643505	−	0.209087i	−0.612548	+	0.790433i	$0.709855\pi$
$24$	424.122	−	137.806i	0.736324	−	0.239246i
$25$	−624.996			−0.999994
$26$			297.522i			0.440122i
$27$	−248.908	+	80.8753i	−0.341438	+	0.110940i
$28$	−123.707	+	89.8783i	−0.157789	+	0.114641i
$29$	−301.906	+	415.537i	−0.358984	+	0.494099i	−0.949865	−	0.312659i	$-0.898780\pi$
$29$	−301.906	+	415.537i	−0.358984	+	0.494099i	0.590881	+	0.806759i	$0.298780\pi$
$30$		−	3.61248i		−	0.00401386i
$31$	653.538	+	704.563i	0.680060	+	0.733156i
$31$	653.538	+	704.563i	0.680060	+	0.733156i
$32$	−975.442			−0.952580
$33$	534.135	+	388.072i	0.490482	+	0.356356i
$34$	1369.88	+	1885.47i	1.18501	+	1.63103i
$35$	−0.349786	−	1.07653i	−0.000285540	−	0.000878801i
$36$	−492.171			−0.379761
$37$		−	1300.44i		−	0.949917i	−0.880008	−	0.474959i	$-0.842463\pi$
$37$		−	1300.44i		−	0.949917i	0.880008	−	0.474959i	$-0.157537\pi$
$38$	−394.168	−	1213.12i	−0.272969	−	0.840113i
$39$	−220.305	+	678.029i	−0.144842	+	0.445779i
$40$	0.721116	−	2.21937i	0.000450698	−	0.00138710i
$41$	−2227.49	−	1618.37i	−1.32510	−	0.962742i	−0.999854	−	0.0171133i	$-0.994552\pi$
$41$	−2227.49	−	1618.37i	−1.32510	−	0.962742i	−0.325247	−	0.945629i	$-0.605448\pi$
$42$	−1015.38	+	329.917i	−0.575613	+	0.187028i
$43$	641.579	−	883.057i	0.346987	−	0.477586i	−0.599479	−	0.800391i	$-0.704625\pi$
$43$	641.579	−	883.057i	0.346987	−	0.477586i	0.946466	+	0.322804i	$0.104625\pi$
$44$	−274.326	−	377.577i	−0.141697	−	0.195029i
$45$	1.12585	−	3.46502i	0.000555977	−	0.00171112i
$46$	1038.39	+	1429.22i	0.490733	+	0.675435i
$47$	3228.27	−	2345.48i	1.46142	−	1.06178i	0.478428	−	0.878127i	$-0.341207\pi$
$47$	3228.27	−	2345.48i	1.46142	−	1.06178i	0.982990	−	0.183656i	$-0.0587934\pi$
$48$	−3597.85	−	1169.01i	−1.56157	−	0.507384i
$49$	1671.81	−	1214.64i	0.696296	−	0.505889i
$50$	2495.60	+	1813.16i	0.998241	+	0.725265i
$51$	1725.71	+	5311.19i	0.663479	+	2.04198i
$52$	296.221	−	407.713i	0.109549	−	0.150781i
$53$	−2028.25	−	659.017i	−0.722052	−	0.234609i	−0.0751396	−	0.997173i	$-0.523940\pi$
$53$	−2028.25	−	659.017i	−0.722052	−	0.234609i	−0.646913	+	0.762564i	$0.723940\pi$
$54$	1228.51	+	399.169i	0.421301	+	0.136889i
$55$	3.28578	−	1.06761i	0.00108621	−	0.000352930i
$56$	−689.669			−0.219920
$57$		−	3056.48i		−	0.940744i
$58$	2411.01	−	783.385i	0.716710	−	0.232873i
$59$	−1787.98	+	1299.05i	−0.513641	+	0.373182i	−0.814203	−	0.580580i	$-0.802826\pi$
$59$	−1787.98	+	1299.05i	−0.513641	+	0.373182i	0.300562	+	0.953762i	$0.402826\pi$
$60$	−3.59667	+	4.95039i	−0.000999075	+	0.00137511i
$61$			1492.15i			0.401008i	0.979693	+	0.200504i	$0.0642580\pi$
$61$			1492.15i			0.401008i	−0.979693	+	0.200504i	$0.935742\pi$
$62$	−565.579	−	4709.28i	−0.147133	−	1.22510i
$63$	−1076.76			−0.271291
$64$	−245.557	−	178.407i	−0.0599503	−	0.0435565i
$65$	2.19280	+	3.01813i	0.000519006	+	0.000714350i
$66$	−1006.97	−	3099.13i	−0.231168	−	0.711463i
$67$	−1071.78			−0.238757			−0.119379	−	0.992849i	$-0.538090\pi$
$67$	−1071.78			−0.238757			−0.119379	+	0.992849i	$0.538090\pi$
$68$		−	3947.66i		−	0.853733i
$69$	1308.12	+	4025.97i	0.274757	+	0.845615i
$70$	−1.72641	+	5.31333i	−0.000352328	+	0.00108435i
$71$	501.986	−	1544.95i	0.0995806	−	0.306478i	−0.888840	−	0.458218i	$-0.848488\pi$
$71$	501.986	−	1544.95i	0.0995806	−	0.306478i	0.988420	+	0.151741i	$0.0484878\pi$
$72$	−1795.88	−	1304.78i	−0.346428	−	0.251694i
$73$	−3900.95	+	1267.50i	−0.732023	+	0.237849i	−0.651228	−	0.758882i	$-0.725746\pi$
$73$	−3900.95	+	1267.50i	−0.732023	+	0.237849i	−0.0807948	+	0.996731i	$0.525746\pi$
$74$	−3772.67	+	5192.63i	−0.688946	+	0.948252i
$75$	4344.69	+	5979.96i	0.772390	+	1.06310i
$76$	−667.664	+	2054.86i	−0.115593	+	0.355758i
$77$	−600.161	−	826.051i	−0.101225	−	0.139324i
$78$	2846.69	−	2068.24i	0.467898	−	0.339948i
$79$	−6347.29	−	2062.36i	−1.01703	−	0.330453i	−0.247380	−	0.968919i	$-0.579570\pi$
$79$	−6347.29	−	2062.36i	−1.01703	−	0.330453i	−0.769651	+	0.638465i	$0.779570\pi$
$80$	−16.0152	+	11.6357i	−0.00250238	+	0.00181808i
$81$	6361.93	+	4622.21i	0.969658	+	0.704498i
$82$	4199.35	+	12924.3i	0.624531	+	1.92211i
$83$	−5673.92	+	7809.48i	−0.823621	+	1.13362i	0.165456	+	0.986217i	$0.447090\pi$
$83$	−5673.92	+	7809.48i	−0.823621	+	1.13362i	−0.989077	+	0.147399i	$0.952910\pi$
$84$	1719.91	+	558.833i	0.243751	+	0.0791996i
$85$	27.7926	+	9.03038i	0.00384673	+	0.00124988i
$86$	−5123.63	+	1664.77i	−0.692758	+	0.225091i
$87$	6074.57			0.802559
$88$		−	2105.00i		−	0.271823i
$89$	12570.2	−	4084.31i	1.58695	−	0.515631i	0.623114	−	0.782131i	$-0.285867\pi$
$89$	12570.2	−	4084.31i	1.58695	−	0.515631i	0.963835	+	0.266501i	$0.0858674\pi$
$90$	−14.5478	+	10.5696i	−0.00179603	+	0.00130489i
$91$	648.062	−	891.981i	0.0782589	−	0.107714i
$92$		−	2992.39i		−	0.353544i
$93$	2198.15	−	11150.9i	0.254151	−	1.28927i
$94$	−19694.9			−2.22894
$95$	−12.9395	−	9.40108i	−0.00143374	−	0.00104167i
$96$	6780.84	+	9333.02i	0.735768	+	1.01270i
$97$	−5202.90	−	16012.9i	−0.552970	−	1.70187i	−0.701245	−	0.712921i	$-0.747372\pi$
$97$	−5202.90	−	16012.9i	−0.552970	−	1.70187i	0.148274	−	0.988946i	$-0.452628\pi$
$98$	−10199.3			−1.06198
$99$		−	3286.46i		−	0.335319i
$100$	−1614.65	−	4969.37i	−0.161465	−	0.496937i
$101$	1513.79	−	4658.98i	0.148397	−	0.456718i	−0.849036	−	0.528336i	$-0.822816\pi$
$101$	1513.79	−	4658.98i	0.148397	−	0.456718i	0.997432	+	0.0716179i	$0.0228162\pi$
$102$	8517.42	−	26213.9i	0.818668	−	2.51960i
$103$	6168.25	+	4481.50i	0.581417	+	0.422424i	0.839235	−	0.543770i	$-0.183003\pi$
$103$	6168.25	+	4481.50i	0.581417	+	0.422424i	−0.257818	+	0.966194i	$0.583003\pi$
$104$	2161.76	−	702.398i	0.199867	−	0.0649406i
$105$	−7.86868	+	10.8303i	−0.000713713	+	0.000982341i
$106$	6186.90	+	8515.54i	0.550632	+	0.757880i
$107$	3043.97	−	9368.37i	0.265872	−	0.818269i	−0.725619	−	0.688096i	$-0.758447\pi$
$107$	3043.97	−	9368.37i	0.265872	−	0.818269i	0.991491	−	0.130173i	$-0.0415533\pi$
$108$	−1286.08	−	1770.14i	−0.110261	−	0.151761i
$109$	7018.45	−	5099.20i	0.590729	−	0.429189i	−0.251847	−	0.967767i	$-0.581038\pi$
$109$	7018.45	−	5099.20i	0.590729	−	0.429189i	0.842576	+	0.538578i	$0.181038\pi$
$110$	−16.2173	−	5.26932i	−0.00134027	−	0.000435481i
$111$	−12442.6	+	9040.05i	−1.00987	+	0.733711i
$112$	4733.15	+	3438.83i	0.377324	+	0.274142i
$113$	3659.06	+	11261.4i	0.286558	+	0.881934i	0.985927	+	0.167174i	$0.0534642\pi$
$113$	3659.06	+	11261.4i	0.286558	+	0.881934i	−0.699370	+	0.714760i	$0.746536\pi$
$114$	−8867.07	+	12204.5i	−0.682293	+	0.939095i
$115$	21.0673	+	6.84518i	0.00159299	+	0.000517594i
$116$	−4083.91	−	1326.94i	−0.303501	−	0.0986135i
$117$	3375.08	−	1096.63i	0.246554	−	0.0801102i
$118$	10908.0			0.783398
$119$		−	8636.56i		−	0.609884i
$120$	−26.2478	+	8.52842i	−0.00182276	+	0.000592251i
$121$	−9323.56	+	6773.96i	−0.636811	+	0.462671i
$122$	4328.85	−	5958.15i	0.290839	−	0.400306i
$123$			32562.8i			2.15235i
$124$	−3913.62	+	7016.51i	−0.254528	+	0.456329i
$125$	77.3588			0.00495097
$126$	4299.47	+	3123.75i	0.270816	+	0.196759i
$127$	−14291.3	−	19670.3i	−0.886062	−	1.21956i	−0.974705	−	0.223496i	$-0.928253\pi$
$127$	−14291.3	−	19670.3i	−0.886062	−	1.21956i	0.0886429	−	0.996063i	$-0.471747\pi$
$128$	5285.78	+	16268.0i	0.322619	+	0.992918i
$129$	−12909.1			−0.775738
$130$		−	18.4128i		−	0.00108952i
$131$	5500.55	+	16929.0i	0.320526	+	0.986479i	0.973420	+	0.229029i	$0.0735550\pi$
$131$	5500.55	+	16929.0i	0.320526	+	0.986479i	−0.652893	+	0.757450i	$0.726445\pi$
$132$	−1705.66	+	5249.49i	−0.0978916	+	0.301279i
$133$	−1460.69	+	4495.55i	−0.0825764	+	0.254144i
$134$	4279.61	+	3109.32i	0.238339	+	0.173163i
$135$	15.4043	−	5.00515i	0.000845227	−	0.000274631i
$136$	10465.6	−	14404.6i	0.565828	−	0.778796i
$137$	−2592.68	−	3568.52i	−0.138136	−	0.190128i	0.734344	−	0.678777i	$-0.237490\pi$
$137$	−2592.68	−	3568.52i	−0.138136	−	0.190128i	−0.872480	+	0.488649i	$0.837490\pi$
$138$	6456.35	−	19870.6i	0.339023	−	1.04341i
$139$	5790.37	+	7969.76i	0.299693	+	0.412492i	0.932132	−	0.362118i	$-0.117946\pi$
$139$	5790.37	+	7969.76i	0.299693	+	0.412492i	−0.632439	+	0.774610i	$0.717946\pi$
$140$	7.65588	−	5.56232i	0.000390606	−	0.000283792i
$141$	−44883.0	−	14583.4i	−2.25758	−	0.733534i
$142$	−6486.46	+	4712.69i	−0.321685	+	0.233718i
$143$	2722.49	+	1978.01i	0.133136	+	0.0967288i
$144$	5819.08	+	17909.3i	0.280627	+	0.863681i
$145$	18.6841	−	25.7165i	0.000888662	−	0.00122314i
$146$	19253.6	+	6255.86i	0.903244	+	0.293482i
$147$	−23243.3	−	7552.21i	−1.07563	−	0.349494i
$148$	10339.8	−	3359.61i	0.472052	−	0.153379i
$149$	−22000.2			−0.990956			−0.495478	−	0.868620i	$-0.665007\pi$
$149$	−22000.2			−0.990956			−0.495478	+	0.868620i	$0.665007\pi$
$150$		−	36482.2i		−	1.62143i
$151$	16779.5	−	5451.99i	0.735911	−	0.239112i	0.0830031	−	0.996549i	$-0.473549\pi$
$151$	16779.5	−	5451.99i	0.735911	−	0.239112i	0.652908	+	0.757437i	$0.273549\pi$
$152$	−7883.83	+	5727.94i	−0.341232	+	0.247920i
$153$	16339.5	−	22489.4i	0.698001	−	0.960716i
$154$			5039.52i			0.212495i
$155$	−40.4457	−	43.6035i	−0.00168348	−	0.00181492i
$156$	−5960.18			−0.244912
$157$	13465.5	+	9783.27i	0.546291	+	0.396903i	0.826416	−	0.563060i	$-0.190376\pi$
$157$	13465.5	+	9783.27i	0.546291	+	0.396903i	−0.280125	+	0.959963i	$0.590376\pi$
$158$	19361.6	+	26649.0i	0.775581	+	1.06750i
$159$	7793.99	+	23987.4i	0.308294	+	0.948832i
$160$	60.3675			0.00235810
$161$		−	6546.66i		−	0.252562i
$162$	−11993.7	−	36912.9i	−0.457008	−	1.40653i
$163$	−11496.7	+	35383.2i	−0.432711	+	1.33175i	0.462704	+	0.886513i	$0.346879\pi$
$163$	−11496.7	+	35383.2i	−0.432711	+	1.33175i	−0.895414	+	0.445234i	$0.853121\pi$
$164$	7113.10	−	21891.9i	0.264467	−	0.813945i
$165$	−33.0562	−	24.0167i	−0.00121418	−	0.000882156i
$166$	45311.8	−	14722.7i	1.64435	−	0.534283i
$167$	10375.9	−	14281.1i	0.372041	−	0.512071i	−0.581413	−	0.813608i	$-0.697500\pi$
$167$	10375.9	−	14281.1i	0.372041	−	0.512071i	0.953454	+	0.301538i	$0.0975000\pi$
$168$	4794.27	+	6598.74i	0.169865	+	0.233799i
$169$	7702.94	−	23707.2i	0.269701	−	0.830055i
$170$	−84.7779	−	116.687i	−0.00293349	−	0.00403761i
$171$	−12308.7	+	8942.83i	−0.420941	+	0.305832i
$172$	8678.71	+	2819.88i	0.293358	+	0.0953178i
$173$	−28342.7	+	20592.2i	−0.946997	+	0.688034i	−0.950095	−	0.311961i	$-0.899014\pi$
$173$	−28342.7	+	20592.2i	−0.946997	+	0.688034i	0.00309746	+	0.999995i	$0.499014\pi$
$174$	−24255.7	−	17622.8i	−0.801153	−	0.582072i
$175$	−3532.47	−	10871.8i	−0.115346	−	0.354998i
$176$	−10496.0	+	14446.5i	−0.338842	+	0.466376i
$177$	24858.5	+	8077.03i	0.793467	+	0.257813i
$178$	−62041.7	−	20158.6i	−1.95814	−	0.636238i
$179$	22487.1	−	7306.50i	0.701823	−	0.228036i	0.0636983	−	0.997969i	$-0.479710\pi$
$179$	22487.1	−	7306.50i	0.701823	−	0.228036i	0.638125	+	0.769933i	$0.279710\pi$
$180$	30.4591			0.000940096
$181$		−	22244.6i		−	0.678995i	−0.940607	−	0.339498i	$-0.889743\pi$
$181$		−	22244.6i		−	0.678995i	0.940607	−	0.339498i	$-0.110257\pi$
$182$	−5175.41	+	1681.59i	−0.156243	+	0.0507666i
$183$	14276.9	−	10372.8i	0.426316	−	0.309737i
$184$	7933.08	−	10918.9i	0.234318	−	0.322511i
$185$			80.4805i			0.00235151i
$186$	−41126.7	+	38148.3i	−1.18877	+	1.10268i
$187$	26360.4			0.753823
$188$	26989.1	+	19608.7i	0.763611	+	0.554796i
$189$	−2813.65	−	3872.66i	−0.0787675	−	0.108414i
$190$	24.3940	+	75.0769i	0.000675733	+	0.00207969i
$191$	35049.9			0.960773			0.480386	−	0.877057i	$-0.340496\pi$
$191$	35049.9			0.960773			0.480386	+	0.877057i	$0.340496\pi$
$192$			3589.69i			0.0973766i
$193$	−3052.18	−	9393.63i	−0.0819398	−	0.252185i	0.901691	−	0.432381i	$-0.142327\pi$
$193$	−3052.18	−	9393.63i	−0.0819398	−	0.252185i	−0.983631	+	0.180197i	$0.942327\pi$
$194$	−25679.4	+	79033.2i	−0.682311	+	2.09994i
$195$	13.6341	−	41.9614i	0.000358556	−	0.00110352i
$196$	13976.7	+	10154.6i	0.363824	+	0.264334i
$197$	44337.4	−	14406.1i	1.14245	−	0.371205i	0.324156	−	0.946003i	$-0.394920\pi$
$197$	44337.4	−	14406.1i	1.14245	−	0.371205i	0.818295	+	0.574799i	$0.194920\pi$
$198$	−9534.28	+	13122.8i	−0.243196	+	0.334731i
$199$	−13313.9	−	18325.1i	−0.336202	−	0.462742i	0.607125	−	0.794606i	$-0.292323\pi$
$199$	−13313.9	−	18325.1i	−0.336202	−	0.462742i	−0.943327	+	0.331864i	$0.892323\pi$
$200$	7282.52	−	22413.3i	0.182063	−	0.560332i
$201$	7450.54	+	10254.8i	0.184415	+	0.253825i
$202$	−19560.6	+	14211.6i	−0.479380	+	0.348290i
$203$	−8934.65	−	2903.04i	−0.216813	−	0.0704468i
$204$	−37771.2	+	27442.4i	−0.907612	+	0.659419i
$205$	137.854	+	100.156i	0.00328028	+	0.00238326i
$206$	−11628.6	−	35789.1i	−0.274027	−	0.843367i
$207$	12385.6	−	17047.4i	0.289053	−	0.397847i
$208$	−18338.3	−	5958.48i	−0.423870	−	0.137724i
$209$	−13721.3	−	4458.31i	−0.314125	−	0.102065i
$210$	62.8391	−	20.4177i	0.00142492	−	0.000462986i
$211$	−28662.4			−0.643795			−0.321898	−	0.946774i	$-0.604321\pi$
$211$	−28662.4			−0.643795			−0.321898	+	0.946774i	$0.604321\pi$
$212$		−	17829.2i		−	0.396698i
$213$	−18271.7	+	5936.83i	−0.402735	+	0.130857i
$214$	−39332.9	+	28577.0i	−0.858871	+	0.624007i
$215$	−39.7056	+	54.6500i	−0.000858963	+	0.00118226i
$216$		−	9868.59i		−	0.211518i
$217$	−8562.10	+	15350.5i	−0.181828	+	0.325989i
$218$	−42817.8			−0.900971
$219$	39245.0	+	28513.2i	0.818270	+	0.594508i
$220$	16.9773	+	23.3672i	0.000350770	+	0.000482793i
$221$	8795.97	+	27071.2i	0.180094	+	0.554272i
$222$	75908.9			1.54023
$223$			25173.1i			0.506206i	0.967439	+	0.253103i	$0.0814511\pi$
$223$			25173.1i			0.506206i	−0.967439	+	0.253103i	$0.918549\pi$
$224$	−5513.19	−	16967.8i	−0.109877	−	0.338167i
$225$	11369.9	−	34993.1i	0.224591	−	0.691221i
$226$	18059.7	−	55581.9i	0.353584	−	1.08822i
$227$	67736.2	+	49213.3i	1.31453	+	0.955059i	0.999983	+	0.00581642i	$0.00185143\pi$
$227$	67736.2	+	49213.3i	1.31453	+	0.955059i	0.314544	+	0.949243i	$0.398149\pi$
$228$	24302.2	−	7896.25i	0.467493	−	0.151898i
$229$	−50878.4	+	70028.1i	−0.970203	+	1.33537i	−0.0282587	+	0.999601i	$0.508996\pi$
$229$	−50878.4	+	70028.1i	−0.970203	+	1.33537i	−0.941944	+	0.335769i	$0.891004\pi$
$230$	−64.2631	−	88.4506i	−0.00121480	−	0.00167203i
$231$	−3731.60	+	11484.7i	−0.0699311	+	0.215226i
$232$	−11383.9	−	15668.7i	−0.211503	−	0.291109i
$233$	48336.7	−	35118.7i	0.890359	−	0.646884i	−0.0456125	−	0.998959i	$-0.514524\pi$
$233$	48336.7	−	35118.7i	0.890359	−	0.646884i	0.935972	+	0.352075i	$0.114524\pi$
$234$	−16658.1	−	5412.53i	−0.304223	−	0.0988481i
$235$	−199.789	+	145.155i	−0.00361773	+	0.00262843i
$236$	−14947.9	−	10860.3i	−0.268384	−	0.194993i
$237$	24390.9	+	75067.4i	0.434241	+	1.33646i
$238$	−25055.3	+	34485.7i	−0.442330	+	0.608815i
$239$	−30767.3	−	9996.90i	−0.538634	−	0.175013i	0.0270513	−	0.999634i	$-0.491388\pi$
$239$	−30767.3	−	9996.90i	−0.538634	−	0.175013i	−0.565685	+	0.824621i	$0.691388\pi$
$240$	222.661	+	72.3470i	0.00386565	+	0.00125602i
$241$	−89598.2	+	29112.2i	−1.54264	+	0.501235i	−0.952104	−	0.305775i	$-0.901085\pi$
$241$	−89598.2	+	29112.2i	−1.54264	+	0.501235i	−0.590538	+	0.807009i	$0.701085\pi$
$242$	56880.6			0.971256
$243$		−	71803.2i		−	1.21599i
$244$	−11864.2	+	3854.90i	−0.199277	+	0.0647490i
$245$	−103.464	+	75.1707i	−0.00172368	+	0.00125232i
$246$	94467.3	−	130023.i	1.56103	−	2.14857i
$247$		−	15578.9i		−	0.255354i
$248$	−32881.7	+	15227.2i	−0.534628	+	0.247581i
$249$	114164.			1.84132
$250$	−308.893	−	224.424i	−0.00494229	−	0.00359078i
$251$	−68553.4	−	94355.6i	−1.08813	−	1.49768i	−0.850241	−	0.526393i	$-0.823544\pi$
$251$	−68553.4	−	94355.6i	−1.08813	−	1.49768i	−0.237890	−	0.971292i	$-0.576456\pi$
$252$	−2781.74	−	8561.32i	−0.0438042	−	0.134815i
$253$	19981.7			0.312169
$254$			120003.i			1.86006i
$255$	−106.799	−	328.695i	−0.00164244	−	0.00505490i
$256$	24587.8	−	75673.6i	0.375181	−	1.15469i
$257$	−3511.61	+	10807.6i	−0.0531667	+	0.163630i	−0.974114	−	0.226056i	$-0.927417\pi$
$257$	−3511.61	+	10807.6i	−0.0531667	+	0.163630i	0.920948	+	0.389687i	$0.127417\pi$
$258$	51545.7	+	37450.2i	0.774378	+	0.562619i
$259$	22621.1	−	7350.05i	0.337221	−	0.109570i
$260$	−18.3323	+	25.2322i	−0.000271188	+	0.000373258i
$261$	−17773.4	−	24462.9i	−0.260909	−	0.359110i
$262$	27148.6	−	83554.7i	0.395498	−	1.21722i
$263$	−65663.0	−	90377.3i	−0.949312	−	1.30662i	−0.951832	−	0.306619i	$-0.900802\pi$
$263$	−65663.0	−	90377.3i	−0.949312	−	1.30662i	0.00252022	−	0.999997i	$-0.499198\pi$
$264$	−20140.6	+	14633.0i	−0.288978	+	0.209955i
$265$	125.523	+	40.7847i	0.00178743	+	0.000580772i
$266$	18874.5	−	13713.1i	0.266754	−	0.193808i
$267$	−126461.	−	91879.4i	−1.77392	−	1.28883i
$268$	−2768.89	−	8521.77i	−0.0385510	−	0.118648i
$269$	41082.6	−	56545.3i	0.567745	−	0.781433i	−0.424541	−	0.905409i	$-0.639564\pi$
$269$	41082.6	−	56545.3i	0.567745	−	0.781433i	0.992285	+	0.123976i	$0.0395644\pi$
$270$	−76.0294	−	24.7035i	−0.00104293	−	0.000338868i
$271$	42361.6	+	13764.1i	0.576811	+	0.187417i	0.582872	−	0.812564i	$-0.301929\pi$
$271$	42361.6	+	13764.1i	0.576811	+	0.187417i	−0.00606028	+	0.999982i	$0.501929\pi$
$272$	−143649.	+	46674.4i	−1.94162	+	0.630871i
$273$	−13039.5			−0.174959
$274$			21770.6i			0.289981i
$275$	33182.9	−	10781.8i	0.438782	−	0.142569i
$276$	−28631.2	+	20801.8i	−0.375856	+	0.273075i
$277$	−71748.7	+	98753.6i	−0.935092	+	1.28704i	0.0227480	+	0.999741i	$0.492758\pi$
$277$	−71748.7	+	98753.6i	−0.935092	+	1.28704i	−0.957840	+	0.287302i	$0.907242\pi$
$278$		−	48621.5i		−	0.629127i
$279$	−51337.1	+	23773.7i	−0.659513	+	0.305413i
$280$	42.6817			0.000544410
$281$	40854.6	+	29682.6i	0.517402	+	0.375915i	0.815624	−	0.578582i	$-0.196394\pi$
$281$	40854.6	+	29682.6i	0.517402	+	0.375915i	−0.298222	+	0.954496i	$0.596394\pi$
$282$	136910.	+	188440.i	1.72162	+	2.36961i
$283$	3984.85	+	12264.1i	0.0497553	+	0.153131i	0.972847	−	0.231449i	$-0.0743465\pi$
$283$	3984.85	+	12264.1i	0.0497553	+	0.153131i	−0.923092	+	0.384579i	$0.874346\pi$
$284$	13580.8			0.168380
$285$			189.157i			0.00232880i
$286$	−5132.54	−	15796.3i	−0.0627480	−	0.193119i
$287$	15561.8	−	47894.3i	0.188928	−	0.581461i
$288$	17745.3	−	54614.3i	0.213943	−	0.658447i
$289$	112816.	+	81965.4i	1.35075	+	0.981375i
$290$	−149.211	+	48.4816i	−0.00177421	+	0.000576475i
$291$	−117043.	+	161096.i	−1.38216	+	1.90238i
$292$	−20155.8	−	27742.1i	−0.236393	−	0.325367i
$293$	−45715.6	+	140698.i	−0.532512	+	1.63890i	0.216453	+	0.976293i	$0.430551\pi$
$293$	−45715.6	+	140698.i	−0.532512	+	1.63890i	−0.748965	+	0.662609i	$0.769449\pi$
$294$	70900.8	+	97586.6i	0.820269	+	1.12900i
$295$	110.653	−	80.3945i	0.00127151	−	0.000923809i
$296$	46635.6	+	15152.8i	0.532272	+	0.172946i
$297$	11820.1	−	8587.81i	0.134001	−	0.0973575i
$298$	87846.6	+	63824.3i	0.989219	+	0.718710i
$299$	6667.49	+	20520.4i	0.0745796	+	0.229533i
$300$	−36322.6	+	49993.7i	−0.403584	+	0.555486i
$301$	18987.0	+	6169.25i	0.209567	+	0.0680925i
$302$	−82817.1	−	26908.9i	−0.908042	−	0.295041i
$303$	−55100.3	+	17903.2i	−0.600162	+	0.195005i
$304$	82666.9			0.894509
$305$		−	92.3452i		−	0.000992692i
$306$	−130487.	+	42397.8i	−1.39356	+	0.452794i
$307$	50319.4	−	36559.2i	0.533898	−	0.387900i	−0.287916	−	0.957656i	$-0.592962\pi$
$307$	50319.4	−	36559.2i	0.533898	−	0.387900i	0.821814	+	0.569756i	$0.192962\pi$
$308$	5017.47	−	6905.96i	0.0528912	−	0.0727985i
$309$		−	90171.1i		−	0.944388i
$310$	35.0022	+	291.444i	0.000364226	+	0.00303272i
$311$	−69081.7			−0.714237			−0.357118	−	0.934059i	$-0.616241\pi$
$311$	−69081.7			−0.714237			−0.357118	+	0.934059i	$0.616241\pi$
$312$	−21748.1	−	15800.9i	−0.223415	−	0.162321i
$313$	9253.08	+	12735.8i	0.0944491	+	0.129998i	0.853626	−	0.520886i	$-0.174398\pi$
$313$	9253.08	+	12735.8i	0.0944491	+	0.129998i	−0.759177	+	0.650884i	$0.774398\pi$
$314$	−25385.7	−	78129.0i	−0.257471	−	0.792416i
$315$	66.6374			0.000671579
$316$		−	55795.5i		−	0.558760i
$317$	−46242.2	−	142319.i	−0.460172	−	1.41626i	−0.864954	−	0.501851i	$-0.832653\pi$
$317$	−46242.2	−	142319.i	−0.460172	−	1.41626i	0.404782	−	0.914413i	$-0.367347\pi$
$318$	38468.1	−	118392.i	0.380405	−	1.17077i
$319$	8860.64	−	27270.2i	0.0870730	−	0.267983i
$320$	15.1968	+	11.0411i	0.000148407	+	0.000107824i
$321$	−110797.	+	36000.0i	−1.07527	+	0.349376i
$322$	−18992.4	+	26140.8i	−0.183176	+	0.252120i
$323$	−71729.7	−	98727.4i	−0.687533	−	0.946308i
$324$	−20315.7	+	62525.1i	−0.193527	+	0.595614i
$325$	22145.0	+	30479.9i	0.209657	+	0.288567i
$326$	148556.	−	107932.i	1.39783	−	1.01558i
$327$	−97578.2	−	31705.1i	−0.912551	−	0.296506i
$328$	83992.1	−	61023.8i	0.780712	−	0.567220i
$329$	59045.8	+	42899.3i	0.545503	+	0.396331i
$330$	62.3186	+	191.797i	0.000572255	+	0.00176122i
$331$	63225.3	−	87022.2i	0.577079	−	0.794281i	−0.416293	−	0.909231i	$-0.636671\pi$
$331$	63225.3	−	87022.2i	0.577079	−	0.794281i	0.993371	+	0.114950i	$0.0366708\pi$
$332$	−76751.8	−	24938.2i	−0.696326	−	0.226250i
$333$	72810.5	+	23657.5i	0.656607	+	0.213344i
$334$	−82861.3	+	26923.3i	−0.742778	+	0.241343i
$335$	66.3296			0.000591041
$336$		−	69192.0i		−	0.612883i
$337$	88599.4	−	28787.7i	0.780137	−	0.253482i	0.108238	−	0.994125i	$-0.465479\pi$
$337$	88599.4	−	28787.7i	0.780137	−	0.253482i	0.671899	+	0.740643i	$0.265479\pi$
$338$	−99534.2	+	72315.8i	−0.871242	+	0.632994i
$339$	82313.1	−	113294.i	0.716258	−	0.985844i
$340$			244.310i			0.00211341i
$341$	−46852.6	−	26133.2i	−0.402926	−	0.224741i
$342$	75092.5			0.642014
$343$	66105.5	+	48028.5i	0.561888	+	0.408235i
$344$	24192.0	+	33297.4i	0.204435	+	0.281380i
$345$	−80.9558	−	249.156i	−0.000680158	−	0.00209331i
$346$	172912.			1.44435
$347$		−	68706.0i		−	0.570605i	−0.958438	−	0.285302i	$-0.907906\pi$
$347$		−	68706.0i		−	0.570605i	0.958438	−	0.285302i	$-0.0920940\pi$
$348$	15693.3	+	48299.1i	0.129586	+	0.398824i
$349$	−58860.1	+	181153.i	−0.483248	+	1.48728i	0.351254	+	0.936280i	$0.385755\pi$
$349$	−58860.1	+	181153.i	−0.483248	+	1.48728i	−0.834502	+	0.551004i	$0.814245\pi$
$350$	−17434.9	+	53659.1i	−0.142326	+	0.438033i
$351$	12763.5	+	9273.23i	0.103599	+	0.0752691i
$352$	51789.1	−	16827.3i	0.417977	−	0.135809i
$353$	29525.3	−	40638.0i	0.236943	−	0.326124i	−0.673942	−	0.738784i	$-0.735400\pi$
$353$	29525.3	−	40638.0i	0.236943	−	0.326124i	0.910885	+	0.412660i	$0.135400\pi$
$354$	−75827.8	−	104368.i	−0.605093	−	0.832839i
$355$	−31.0665	+	95.6130i	−0.000246511	+	0.000758683i
$356$	64949.0	+	89394.7i	0.512475	+	0.705361i
$357$	−82634.6	+	60037.5i	−0.648374	+	0.471071i
$358$	−110988.	−	36062.0i	−0.865981	−	0.281374i
$359$	66900.2	−	48605.8i	0.519085	−	0.377137i	−0.297174	−	0.954823i	$-0.596044\pi$
$359$	66900.2	−	48605.8i	0.519085	−	0.377137i	0.816259	+	0.577686i	$0.196044\pi$
$360$	111.142	+	80.7495i	0.000857579	+	0.000623067i
$361$	−19632.0	−	60420.9i	−0.150643	−	0.463632i
$362$	−64533.2	+	88822.3i	−0.492454	+	0.677805i
$363$	129626.	+	42118.2i	0.983740	+	0.319636i
$364$	8766.41	+	2848.38i	0.0661636	+	0.0214978i
$365$	241.419	−	78.4418i	0.00181212	−	0.000588792i
$366$	−87099.7			−0.650212
$367$			199439.i			1.48074i	0.672199	+	0.740370i	$0.265350\pi$
$367$			199439.i			1.48074i	−0.672199	+	0.740370i	$0.734650\pi$
$368$	−108888.	+	35380.0i	−0.804055	+	0.261253i
$369$	131134.	−	95274.4i	0.963080	−	0.699718i
$370$	233.480	−	321.358i	0.00170548	−	0.00234739i
$371$		−	39006.1i		−	0.283390i
$372$	94339.7	−	11330.1i	0.681724	−	0.0818743i
$373$	−67874.2			−0.487851			−0.243925	−	0.969794i	$-0.578435\pi$
$373$	−67874.2			−0.487851			−0.243925	+	0.969794i	$0.578435\pi$
$374$	−105257.	−	76473.6i	−0.752501	−	0.546724i
$375$	−537.764	−	740.169i	−0.00382410	−	0.00526342i
$376$	46496.1	+	143100.i	0.328883	+	1.01220i
$377$	30962.2			0.217846
$378$			23626.1i			0.165352i
$379$	−39788.7	−	122457.i	−0.277001	−	0.852520i	−0.988683	−	0.150019i	$-0.952066\pi$
$379$	−39788.7	−	122457.i	−0.277001	−	0.852520i	0.711682	−	0.702501i	$-0.247934\pi$
$380$	41.3199	−	127.170i	0.000286149	−	0.000880675i
$381$	−88858.4	+	273478.i	−0.612137	+	1.88396i
$382$	−139954.	−	101683.i	−0.959089	−	0.696819i
$383$	6450.60	−	2095.93i	0.0439747	−	0.0142882i	−0.286947	−	0.957946i	$-0.592640\pi$
$383$	6450.60	−	2095.93i	0.0439747	−	0.0142882i	0.330922	+	0.943658i	$0.392640\pi$
$384$	118907.	−	163662.i	0.806392	−	1.10990i
$385$	37.1423	+	51.1220i	0.000250581	+	0.000344895i
$386$	−15064.3	+	46363.3i	−0.101106	+	0.311171i
$387$	37770.1	+	51986.1i	0.252189	+	0.347109i
$388$	113877.	−	82736.8i	0.756440	−	0.549586i
$389$	−118147.	−	38388.2i	−0.780770	−	0.253687i	−0.108601	−	0.994085i	$-0.534637\pi$
$389$	−118147.	−	38388.2i	−0.780770	−	0.253687i	−0.672169	+	0.740398i	$0.734637\pi$
$390$	−176.174	+	127.998i	−0.00115828	+	0.000841538i
$391$	136735.	+	99344.1i	0.894391	+	0.649813i
$392$	24078.7	+	74106.6i	0.156697	+	0.482264i
$393$	123739.	−	170312.i	0.801163	−	1.10271i
$394$	−218832.	−	71102.8i	−1.40967	−	0.458030i
$395$	392.816	+	127.634i	0.00251765	+	0.000818034i
$396$	26130.8	−	8490.40i	0.166633	−	0.0541424i
$397$	−149728.			−0.949997			−0.474999	−	0.879987i	$-0.657551\pi$
$397$	−149728.			−0.949997			−0.474999	+	0.879987i	$0.657551\pi$
$398$			111797.i			0.705768i
$399$	53167.5	−	17275.2i	0.333965	−	0.108512i
$400$	−161737.	+	117509.i	−1.01085	+	0.734429i
$401$	−70862.7	+	97534.1i	−0.440686	+	0.606552i	−0.970364	−	0.241647i	$-0.922312\pi$
$401$	−70862.7	+	97534.1i	−0.440686	+	0.606552i	0.529679	+	0.848198i	$0.322312\pi$
$402$		−	62561.9i		−	0.387131i
$403$	11204.0	−	56836.1i	0.0689863	−	0.349956i
$404$	40954.5			0.250922
$405$	−393.722	−	286.056i	−0.00240038	−	0.00174398i
$406$	27254.0	+	37511.9i	0.165340	+	0.227571i
$407$	22433.7	+	69044.0i	0.135429	+	0.416809i
$408$	−210575.			−1.26499
$409$		−	218981.i		−	1.30906i	−0.756035	−	0.654532i	$-0.772866\pi$
$409$		−	218981.i		−	1.30906i	0.756035	−	0.654532i	$-0.227134\pi$
$410$	−259.886	−	799.848i	−0.00154602	−	0.00475817i
$411$	−16120.4	+	49613.5i	−0.0954316	+	0.293708i
$412$	−19697.2	+	60621.7i	−0.116041	+	0.357136i
$413$	−32702.6	−	23759.8i	−0.191727	−	0.139298i
$414$	−98911.4	+	32138.3i	−0.577093	+	0.187509i
$415$	351.144	−	483.308i	0.00203887	−	0.00280626i
$416$	34562.0	+	47570.6i	0.199716	+	0.274885i
$417$	36002.5	−	110804.i	0.207043	−	0.637214i
$418$	41855.0	+	57608.5i	0.239549	+	0.329711i
$419$	5306.69	−	3855.54i	0.0302270	−	0.0219612i	−0.572569	−	0.819856i	$-0.694053\pi$
$419$	5306.69	−	3855.54i	0.0302270	−	0.0219612i	0.602796	+	0.797895i	$0.294053\pi$
$420$	−106.441	−	34.5846i	−0.000603404	−	0.000196058i
$421$	−64519.8	+	46876.4i	−0.364023	+	0.264478i	−0.754728	−	0.656038i	$-0.772231\pi$
$421$	−64519.8	+	46876.4i	−0.364023	+	0.264478i	0.390705	+	0.920516i	$0.372231\pi$
$422$	114449.	+	83151.8i	0.642667	+	0.466925i
$423$	72592.8	+	223418.i	0.405707	+	1.24864i
$424$	47266.6	−	65056.9i	0.262919	−	0.361878i
$425$	280676.	+	91197.3i	1.55392	+	0.504898i
$426$	90181.9	+	29301.9i	0.496936	+	0.161464i
$427$	−25956.0	+	8433.62i	−0.142358	+	0.0462550i
$428$	82352.2			0.449560
$429$		−	39799.0i		−	0.216251i
$430$	317.088	−	103.028i	0.00171491	−	0.000557210i
$431$	70982.5	−	51571.8i	0.382118	−	0.277625i	−0.380100	−	0.924945i	$-0.624111\pi$
$431$	70982.5	−	51571.8i	0.382118	−	0.277625i	0.762218	+	0.647321i	$0.224111\pi$
$432$	−49206.9	+	67727.5i	−0.263669	+	0.362909i
$433$			74035.4i			0.394879i	0.980315	+	0.197439i	$0.0632625\pi$
$433$			74035.4i			0.394879i	−0.980315	+	0.197439i	$0.936737\pi$
$434$	78721.4	−	36455.0i	0.417939	−	0.193543i
$435$	−375.939			−0.00198673
$436$	58675.7	+	42630.4i	0.308664	+	0.224257i
$437$	−54372.3	−	74837.1i	−0.284718	−	0.391881i
$438$	−73986.1	−	227706.i	−0.385658	−	1.18693i
$439$	−284040.			−1.47384			−0.736920	−	0.675980i	$-0.763720\pi$
$439$	−284040.			−1.47384			−0.736920	+	0.675980i	$0.763720\pi$
$440$			130.273i			0.000672896i
$441$	37593.2	+	115700.i	0.193300	+	0.594917i
$442$	43413.4	−	133613.i	0.222218	−	0.683917i
$443$	−9464.87	+	29129.9i	−0.0482289	+	0.148433i	−0.972271	−	0.233858i	$-0.924865\pi$
$443$	−9464.87	+	29129.9i	−0.0482289	+	0.148433i	0.924042	+	0.382291i	$0.124865\pi$
$444$	−104023.	−	75576.8i	−0.527669	−	0.383374i
$445$	−777.936	+	252.767i	−0.00392848	+	0.00127644i
$446$	73029.1	−	100516.i	0.367136	−	0.505319i
$447$	152936.	+	210498.i	0.765409	+	1.05350i
$448$	1715.52	−	5279.82i	0.00854750	−	0.0263065i
$449$	−162639.	−	223853.i	−0.806736	−	1.11038i	−0.991819	−	0.127654i	$-0.959255\pi$
$449$	−162639.	−	223853.i	−0.806736	−	1.11038i	0.185083	−	0.982723i	$-0.440745\pi$
$450$	−146918.	+	106742.i	−0.725519	+	0.527120i
$451$	146183.	+	47497.6i	0.718691	+	0.233517i
$452$	−80087.0	+	58186.6i	−0.391999	+	0.284804i
$453$	−168808.	−	122646.i	−0.822616	−	0.597666i
$454$	−127699.	−	393016.i	−0.619548	−	1.90677i
$455$	−40.1068	+	55.2023i	−0.000193729	+	0.000266645i
$456$	109610.	+	35614.4i	0.527132	+	0.171276i
$457$	−18199.8	−	5913.47i	−0.0871432	−	0.0283146i	0.265121	−	0.964215i	$-0.414588\pi$
$457$	−18199.8	−	5913.47i	−0.0871432	−	0.0283146i	−0.352264	+	0.935901i	$0.614588\pi$
$458$	406314.	−	132019.i	1.93701	−	0.629371i
$459$	123582.			0.586584
$460$			185.191i			0.000875194i
$461$	59666.5	−	19386.8i	0.280756	−	0.0912230i	−0.165254	−	0.986251i	$-0.552845\pi$
$461$	59666.5	−	19386.8i	0.280756	−	0.0912230i	0.446010	+	0.895028i	$0.352845\pi$
$462$	48218.1	−	35032.5i	0.225905	−	0.164130i
$463$	−18756.5	+	25816.2i	−0.0874965	+	0.120429i	−0.850521	−	0.525941i	$-0.823713\pi$
$463$	−18756.5	+	25816.2i	−0.0874965	+	0.120429i	0.763025	+	0.646369i	$0.223713\pi$
$464$			164296.i			0.763116i
$465$	−136.037	+	690.096i	−0.000629147	+	0.00319156i
$466$	−294890.			−1.35796
$467$	69244.9	+	50309.4i	0.317508	+	0.230683i	0.735111	−	0.677947i	$-0.237130\pi$
$467$	69244.9	+	50309.4i	0.317508	+	0.230683i	−0.417604	+	0.908629i	$0.637130\pi$
$468$	17438.7	+	24002.3i	0.0796199	+	0.109587i
$469$	−6057.69	−	18643.7i	−0.0275398	−	0.0847589i
$470$	1218.86			0.00551771
$471$		−	196847.i		−	0.887333i
$472$	−25752.0	−	79256.4i	−0.115592	−	0.355754i
$473$	−18829.7	+	57951.9i	−0.0841631	+	0.259027i
$474$	120384.	−	370503.i	0.535811	−	1.64906i
$475$	−130675.	−	94941.0i	−0.579170	−	0.420791i
$476$	68669.6	−	22312.1i	0.303076	−	0.0984752i
$477$	73795.7	−	101571.i	0.324335	−	0.446409i
$478$	93851.8	+	129176.i	0.410759	+	0.565361i
$479$	−51423.7	+	158266.i	−0.224126	+	0.689789i	0.774253	+	0.632876i	$0.218126\pi$
$479$	−51423.7	+	158266.i	−0.224126	+	0.689789i	−0.998379	+	0.0569130i	$0.981874\pi$
$480$	−419.648	−	577.595i	−0.00182139	−	0.00250692i
$481$	−63419.9	+	46077.3i	−0.274117	+	0.199158i
$482$	442222.	+	143686.i	1.90347	+	0.618475i
$483$	−62638.4	+	45509.5i	−0.268501	+	0.195078i
$484$	−77946.9	−	56631.8i	−0.332743	−	0.241752i
$485$	321.993	+	990.993i	0.00136887	+	0.00421296i
$486$	−208307.	+	286710.i	−0.881923	+	1.21386i
$487$	−171199.	−	55625.9i	−0.721844	−	0.234541i	−0.0750215	−	0.997182i	$-0.523903\pi$
$487$	−171199.	−	55625.9i	−0.721844	−	0.234541i	−0.646822	+	0.762641i	$0.723903\pi$
$488$	−53510.8	−	17386.7i	−0.224699	−	0.0730092i
$489$	418466.	−	135968.i	1.75002	−	0.568615i
$490$	631.205			0.00262893
$491$			40238.7i			0.166909i	0.996512	+	0.0834547i	$0.0265954\pi$
$491$			40238.7i			0.166909i	−0.996512	+	0.0834547i	$0.973405\pi$
$492$	−258908.	+	84124.4i	−1.06959	+	0.347530i
$493$	196215.	−	142559.i	0.807307	−	0.586543i
$494$	−45195.6	+	62206.4i	−0.185201	+	0.254907i
$495$			203.390i			0.000830079i
$496$	301591.	+	59452.2i	1.22590	+	0.241660i
$497$	29711.7			0.120286
$498$	−455854.	−	331198.i	−1.83809	−	1.33545i
$499$	−291652.	−	401425.i	−1.17129	−	1.61214i	−0.654627	−	0.755952i	$-0.727174\pi$
$499$	−291652.	−	401425.i	−1.17129	−	1.61214i	−0.516662	−	0.856189i	$-0.672826\pi$
$500$	199.853	+	615.083i	0.000799410	+	0.00246033i
$501$	−208770.			−0.831750
$502$			575640.i			2.28425i
$503$	155079.	+	477283.i	0.612938	+	1.88643i	0.428352	+	0.903612i	$0.359094\pi$
$503$	155079.	+	477283.i	0.612938	+	1.88643i	0.184585	+	0.982816i	$0.440906\pi$
$504$	12546.5	−	38614.0i	0.0493924	−	0.152014i
$505$	−93.6846	+	288.331i	−0.000367354	+	0.00113060i
$506$	−79786.5	−	57968.3i	−0.311622	−	0.226407i
$507$	−280378.	+	91100.2i	−1.09076	+	0.354408i
$508$	119478.	−	164448.i	0.462979	−	0.637236i
$509$	163833.	+	225497.i	0.632362	+	0.870372i	0.998179	−	0.0603147i	$-0.0192104\pi$
$509$	163833.	+	225497.i	0.632362	+	0.870372i	−0.365817	+	0.930687i	$0.619210\pi$
$510$	−527.120	+	1622.31i	−0.00202661	+	0.00623725i
$511$	−44096.2	−	60693.3i	−0.168873	−	0.232433i
$512$	−96300.1	+	69966.1i	−0.367356	+	0.266900i
$513$	−64327.6	−	20901.3i	−0.244435	−	0.0794217i
$514$	45375.6	−	32967.3i	0.171750	−	0.124783i
$515$	−381.736	−	277.347i	−0.00143929	−	0.00104571i
$516$	−33349.9	−	102640.i	−0.125255	−	0.385495i
$517$	−130937.	+	180219.i	−0.489870	+	0.674248i
$518$	−111649.	−	36277.0i	−0.416098	−	0.135198i
$519$	394051.	+	128035.i	1.46291	+	0.475329i
$520$	−133.785	+	43.4695i	−0.000494768	+	0.000160760i
$521$	57647.9			0.212377			0.106189	−	0.994346i	$-0.466135\pi$
$521$	57647.9			0.212377			0.106189	+	0.994346i	$0.466135\pi$
$522$			149242.i			0.547710i
$523$	381420.	−	123931.i	1.39444	−	0.453081i	0.487052	−	0.873373i	$-0.338072\pi$
$523$	381420.	−	123931.i	1.39444	−	0.453081i	0.907389	+	0.420292i	$0.138072\pi$
$524$	−120392.	+	87470.2i	−0.438467	+	0.318565i
$525$	−79465.4	+	109375.i	−0.288310	+	0.396824i
$526$			551369.i			1.99283i
$527$	−190687.	−	411771.i	−0.686593	−	1.48263i
$528$	211187.			0.757529
$529$	−122748.	−	89181.9i	−0.438636	−	0.318688i
$530$	−382.891	−	527.004i	−0.00136308	−	0.00187613i
$531$	−40205.6	−	123740.i	−0.142593	−	0.438856i
$532$	−39517.9			−0.139627
$533$			165973.i			0.584230i
$534$	238409.	+	733747.i	0.836065	+	2.57314i
$535$	−188.383	+	579.783i	−0.000658163	+	0.00202562i
$536$	12488.5	−	38435.6i	0.0434691	−	0.133784i
$537$	−226229.	−	164365.i	−0.784512	−	0.569981i
$538$	−328084.	+	106601.i	−1.13350	+	0.368296i
$539$	−67807.5	+	93329.0i	−0.233400	+	0.321247i
$540$	79.5923	+	109.549i	0.000272950	+	0.000375684i
$541$	153934.	−	473760.i	0.525944	−	1.61869i	−0.236497	−	0.971632i	$-0.575999\pi$
$541$	153934.	−	473760.i	0.525944	−	1.61869i	0.762441	−	0.647058i	$-0.224001\pi$
$542$	−129219.	−	177854.i	−0.439872	−	0.605432i
$543$	−212836.	+	154634.i	−0.721847	+	0.524452i
$544$	438056.	+	142333.i	1.48024	+	0.480959i
$545$	−434.352	+	315.576i	−0.00146234	+	0.00106245i
$546$	52066.6	+	37828.6i	0.174652	+	0.126892i
$547$	90077.1	+	277229.i	0.301051	+	0.926539i	0.981121	+	0.193393i	$0.0619491\pi$
$547$	90077.1	+	277229.i	0.301051	+	0.926539i	−0.680071	+	0.733147i	$0.738051\pi$
$548$	21675.4	−	29833.6i	0.0721781	−	0.0993446i
$549$	−83544.5	−	27145.2i	−0.277187	−	0.0900635i
$550$	−163778.	−	53214.6i	−0.541413	−	0.175916i
$551$	−126246.	+	41019.7i	−0.415828	+	0.135111i
$552$	−159620.			−0.523851
$553$		−	122068.i		−	0.399163i
$554$	572983.	−	186174.i	1.86691	−	0.606595i
$555$	770.036	−	559.464i	0.00249992	−	0.00181629i
$556$	−48408.7	+	66628.9i	−0.156594	+	0.215533i
$557$			126119.i			0.406510i	0.979126	+	0.203255i	$0.0651521\pi$
$557$			126119.i			0.406510i	−0.979126	+	0.203255i	$0.934848\pi$
$558$	273958.	+	54004.8i	0.879864	+	0.173446i
$559$	−65797.6			−0.210565
$560$	−292.922	−	212.820i	−0.000934062	−	0.000678636i
$561$	−183246.	−	252216.i	−0.582249	−	0.801397i
$562$	−77020.4	−	237045.i	−0.243856	−	0.750512i
$563$	−136390.			−0.430295			−0.215148	−	0.976582i	$-0.569023\pi$
$563$	−136390.			−0.430295			−0.215148	+	0.976582i	$0.569023\pi$
$564$		−	394542.i		−	1.24032i
$565$	−226.449	−	696.939i	−0.000709371	−	0.00218322i
$566$	19667.6	−	60530.8i	0.0613931	−	0.188949i
$567$	−44445.9	+	136791.i	−0.138250	+	0.425491i
$568$	49555.1	+	36003.9i	0.153600	+	0.111597i
$569$	573197.	−	186243.i	1.77043	−	0.575248i	0.772238	−	0.635333i	$-0.219137\pi$
$569$	573197.	−	186243.i	1.77043	−	0.575248i	0.998193	+	0.0600850i	$0.0191372\pi$
$570$	548.759	−	755.302i	0.00168901	−	0.00232472i
$571$	224604.	+	309142.i	0.688884	+	0.948168i	0.999998	−	0.00220504i	$-0.000701886\pi$
$571$	224604.	+	309142.i	0.688884	+	0.948168i	−0.311113	+	0.950373i	$0.600702\pi$
$572$	−8693.79	+	26756.7i	−0.0265716	+	0.0817788i
$573$	−243652.	−	335358.i	−0.742096	−	1.02141i
$574$	−201083.	+	146096.i	−0.610313	+	0.443418i
$575$	212758.	+	69129.1i	0.643501	+	0.209086i
$576$	14456.1	−	10502.9i	0.0435717	−	0.0316567i
$577$	−152397.	−	110723.i	−0.457746	−	0.332572i	0.334900	−	0.942254i	$-0.391297\pi$
$577$	−152397.	−	110723.i	−0.457746	−	0.332572i	−0.792647	+	0.609681i	$0.791297\pi$
$578$	−212684.	−	654574.i	−0.636619	−	1.95931i
$579$	−68660.8	+	94503.5i	−0.204810	+	0.281897i
$580$	252.742	+	82.1209i	0.000751314	+	0.000244117i
$581$	−167915.	−	54558.9i	−0.497436	−	0.161627i
$582$	934701.	−	303703.i	2.75948	−	0.896609i
$583$	119054.			0.350273
$584$		−	154663.i		−	0.453482i
$585$	−208.874	+	67.8674i	−0.000610342	+	0.000198312i
$586$	590718.	−	429182.i	1.72022	−	1.24982i
$587$	−300902.	+	414157.i	−0.873272	+	1.20196i	0.104968	+	0.994476i	$0.466526\pi$
$587$	−300902.	+	414157.i	−0.873272	+	1.20196i	−0.978239	+	0.207480i	$0.933474\pi$
$588$		−	204319.i		−	0.590955i
$589$	29614.9	+	246588.i	0.0853651	+	0.710789i
$590$	−675.069			−0.00193930
$591$	−446051.	−	324075.i	−1.27706	−	0.927835i
$592$	−244502.	−	336528.i	−0.697651	−	0.960234i
$593$	73532.3	+	226309.i	0.209107	+	0.643565i	0.999520	+	0.0309905i	$0.00986617\pi$
$593$	73532.3	+	226309.i	0.209107	+	0.643565i	−0.790413	+	0.612575i	$0.790134\pi$
$594$	−72111.4			−0.204377
$595$			534.493i			0.00150976i
$596$	−56836.4	−	174925.i	−0.160005	−	0.492446i
$597$	−82781.5	+	254775.i	−0.232265	+	0.714839i
$598$	32908.1	−	101281.i	0.0920239	−	0.283221i
$599$	−401460.	−	291678.i	−1.11889	−	0.812924i	−0.134853	−	0.990866i	$-0.543056\pi$
$599$	−401460.	−	291678.i	−1.11889	−	0.812924i	−0.984041	+	0.177941i	$0.943056\pi$
$600$	−265075.	+	86128.0i	−0.736319	+	0.239245i
$601$	116682.	−	160599.i	0.323040	−	0.444626i	−0.616353	−	0.787470i	$-0.711390\pi$
$601$	116682.	−	160599.i	0.323040	−	0.444626i	0.939392	+	0.342844i	$0.111390\pi$
$602$	−57917.4	−	79716.5i	−0.159815	−	0.219966i
$603$	19497.8	−	60008.2i	0.0536231	−	0.165035i
$604$	86698.0	+	119330.i	0.237649	+	0.327095i
$605$	577.009	−	419.222i	0.00157642	−	0.00114534i
$606$	271953.	+	88363.0i	0.740541	+	0.240616i
$607$	228710.	−	166168.i	0.620738	−	0.450992i	−0.232441	−	0.972610i	$-0.574671\pi$
$607$	228710.	−	166168.i	0.620738	−	0.450992i	0.853179	+	0.521618i	$0.174671\pi$
$608$	−203947.	−	148176.i	−0.551709	−	0.400840i
$609$	34333.4	+	105667.i	0.0925726	+	0.284909i
$610$	−267.901	+	368.734i	−0.000719969	+	0.000990953i
$611$	−228770.	−	74331.7i	−0.612796	−	0.199109i
$612$	221026.	+	71815.8i	0.590121	+	0.191742i
$613$	−22296.0	+	7244.40i	−0.0593342	+	0.0192789i	−0.338534	−	0.940954i	$-0.609931\pi$
$613$	−22296.0	+	7244.40i	−0.0593342	+	0.0192789i	0.279200	+	0.960233i	$0.409931\pi$
$614$	−306986.			−0.814294
$615$		−	2015.23i		−	0.00532811i
$616$	36616.5	−	11897.4i	0.0964974	−	0.0313539i
$617$	−199741.	+	145120.i	−0.524683	+	0.381205i	−0.818365	−	0.574698i	$-0.805119\pi$
$617$	−199741.	+	145120.i	−0.524683	+	0.381205i	0.293682	+	0.955903i	$0.405119\pi$
$618$	−261593.	+	360052.i	−0.684936	+	0.942733i
$619$			311178.i			0.812135i	0.913843	+	0.406067i	$0.133100\pi$
$619$			311178.i			0.812135i	−0.913843	+	0.406067i	$0.866900\pi$
$620$	242.204	−	434.233i	0.000630082	−	0.00112964i
$621$	93677.4			0.242913
$622$	275843.	+	200411.i	0.712985	+	0.518014i
$623$	142093.	+	195575.i	0.366098	+	0.503891i
$624$	70469.1	+	216881.i	0.180979	+	0.556997i
$625$	390618.			0.999982
$626$		−	77697.7i		−	0.198271i
$627$	52727.1	+	162277.i	0.134122	+	0.412784i
$628$	−42999.7	+	132339.i	−0.109030	+	0.335560i
$629$	−189755.	+	584006.i	−0.479615	+	1.47610i
$630$	−266.083	−	193.320i	−0.000670402	−	0.000487076i
$631$	96656.4	−	31405.6i	0.242757	−	0.0788765i	−0.185112	−	0.982718i	$-0.559265\pi$
$631$	96656.4	−	31405.6i	0.242757	−	0.0788765i	0.427869	+	0.903841i	$0.359265\pi$
$632$	147918.	−	203592.i	0.370329	−	0.509715i
$633$	199248.	+	274242.i	0.497264	+	0.684425i
$634$	−228233.	+	702430.i	−0.567807	+	1.74753i
$635$	884.449	+	1217.34i	0.00219344	+	0.00301901i
$636$	−170590.	+	123941.i	−0.421734	+	0.306407i
$637$	−118472.	−	38493.7i	−0.291968	−	0.0948661i
$638$	−114494.	+	83184.4i	−0.281280	+	0.204362i
$639$	77368.7	+	56211.6i	0.189480	+	0.137665i
$640$	−327.123	−	1006.78i	−0.000798639	−	0.00245796i
$641$	346783.	−	477306.i	0.843998	−	1.16166i	−0.141155	−	0.989987i	$-0.545082\pi$
$641$	346783.	−	477306.i	0.843998	−	1.16166i	0.985153	−	0.171676i	$-0.0549184\pi$
$642$	546849.	+	177682.i	1.32678	+	0.431096i
$643$	683554.	+	222100.i	1.65330	+	0.537189i	0.979451	−	0.201683i	$-0.0646411\pi$
$643$	683554.	+	222100.i	1.65330	+	0.537189i	0.673846	+	0.738872i	$0.264641\pi$
$644$	52052.8	−	16913.0i	0.125508	−	0.0407801i
$645$	798.906			0.00192033
$646$			602311.i			1.44330i
$647$	−492024.	+	159868.i	−1.17538	+	0.381904i	−0.830648	−	0.556798i	$-0.812030\pi$
$647$	−492024.	+	159868.i	−1.17538	+	0.381904i	−0.344731	+	0.938702i	$0.612030\pi$
$648$	−239889.	+	174290.i	−0.571295	+	0.415070i
$649$	72519.5	−	99814.6i	0.172173	−	0.236976i
$650$		−	185950.i		−	0.440119i
$651$	206393.	−	24787.6i	0.487005	−	0.0584888i
$652$	−311034.			−0.731666
$653$	129687.	+	94223.5i	0.304139	+	0.220970i	0.729377	−	0.684112i	$-0.239810\pi$
$653$	129687.	+	94223.5i	0.304139	+	0.220970i	−0.425239	+	0.905081i	$0.639810\pi$
$654$	297650.	+	409680.i	0.695905	+	0.957832i
$655$	−340.414	−	1047.69i	−0.000793460	−	0.00244202i
$656$	−880710.			−2.04656
$657$		−	241470.i		−	0.559412i
$658$	−111315.	−	342593.i	−0.257100	−	0.791274i
$659$	−440.947	+	1357.09i	−0.00101535	+	0.00312492i	−0.951563	−	0.307454i	$-0.900523\pi$
$659$	−440.947	+	1357.09i	−0.00101535	+	0.00312492i	0.950548	+	0.310579i	$0.100523\pi$
$660$	105.559	−	324.877i	0.000242330	−	0.000745814i
$661$	−688319.	−	500093.i	−1.57538	−	1.14458i	−0.921757	−	0.387768i	$-0.873246\pi$
$661$	−688319.	−	500093.i	−1.57538	−	1.14458i	−0.653628	−	0.756816i	$-0.726754\pi$
$662$	−504916.	+	164057.i	−1.15213	+	0.374351i
$663$	197871.	−	272347.i	0.450149	−	0.619577i
$664$	−213946.	−	294472.i	−0.485254	−	0.667895i
$665$	90.3983	−	278.217i	0.000204417	−	0.000629131i
$666$	−222099.	−	305693.i	−0.500724	−	0.689187i
$667$	148734.	−	108062.i	0.334318	−	0.242896i
$668$	140355.	+	45604.2i	0.314540	+	0.102200i
$669$	240856.	−	174992.i	0.538153	−	0.390991i
$670$	−264.853	−	192.427i	−0.000590005	−	0.000428664i
$671$	−25741.0	−	79222.7i	−0.0571716	−	0.175956i
$672$	−124023.	+	170703.i	−0.274640	+	0.378009i
$673$	−445922.	−	144889.i	−0.984530	−	0.319893i	−0.227863	−	0.973693i	$-0.573174\pi$
$673$	−445922.	−	144889.i	−0.984530	−	0.319893i	−0.756667	+	0.653800i	$0.773174\pi$
$674$	−437292.	−	142085.i	−0.962613	−	0.312772i
$675$	155567.	−	50546.7i	0.341436	−	0.110939i
$676$	208397.			0.456035
$677$			159810.i			0.348680i	0.984686	+	0.174340i	$0.0557791\pi$
$677$			159810.i			0.348680i	−0.984686	+	0.174340i	$0.944221\pi$
$678$	−657350.	+	213586.i	−1.43000	+	0.464637i
$679$	249138.	−	181009.i	0.540381	−	0.392609i
$680$	−647.685	+	891.462i	−0.00140070	+	0.00192790i
$681$		−	990208.i		−	2.13517i
$682$	111268.	+	240272.i	0.239222	+	0.516577i
$683$	49288.1			0.105658			0.0528288	−	0.998604i	$-0.483176\pi$
$683$	49288.1			0.105658			0.0528288	+	0.998604i	$0.483176\pi$
$684$	−102904.	−	74764.0i	−0.219948	−	0.159801i
$685$	160.454	+	220.846i	0.000341955	+	0.000470661i
$686$	−124624.	−	383555.i	−0.264823	−	0.815040i
$687$	1.02371e6			2.16903
$688$		−	349144.i		−	0.737612i
$689$	39726.1	+	122264.i	0.0836830	+	0.257550i
$690$	−399.566	+	1229.74i	−0.000839248	+	0.00258294i
$691$	−45519.5	+	140094.i	−0.0953325	+	0.293403i	−0.987340	−	0.158617i	$-0.949297\pi$
$691$	−45519.5	+	140094.i	−0.0953325	+	0.293403i	0.892008	+	0.452020i	$0.149297\pi$
$692$	−236951.	−	172155.i	−0.494819	−	0.359507i
$693$	57168.1	−	18575.0i	0.119038	−	0.0386779i
$694$	−199321.	+	274342.i	−0.413842	+	0.569605i
$695$	−358.350	−	493.227i	−0.000741888	−	0.00102112i
$696$	−70781.5	+	217843.i	−0.146117	+	0.449702i
$697$	764187.	+	1.05181e6i	1.57302	+	2.16508i
$698$	760566.	−	552583.i	1.56108	−	1.13419i
$699$	−672030.	−	218356.i	−1.37542	−	0.446900i
$700$	77316.3	−	56173.6i	0.157788	−	0.114640i
$701$	253858.	+	184439.i	0.516601	+	0.375332i	0.815322	−	0.579008i	$-0.196560\pi$
$701$	253858.	+	184439.i	0.516601	+	0.375332i	−0.298721	+	0.954340i	$0.596560\pi$
$702$	−24062.2	−	74055.8i	−0.0488271	−	0.150274i
$703$	197545.	−	271897.i	0.399719	−	0.550166i
$704$	16115.0	+	5236.08i	0.0325151	+	0.0105648i
$705$	2777.69	+	902.526i	0.00558863	+	0.00181586i
$706$	−235788.	+	76612.2i	−0.473056	+	0.153705i
$707$	89599.0			0.179252
$708$			218518.i			0.435933i
$709$	−308128.	+	100117.i	−0.612969	+	0.199166i	−0.599016	−	0.800737i	$-0.704442\pi$
$709$	−308128.	+	100117.i	−0.612969	+	0.199166i	−0.0139531	+	0.999903i	$0.504442\pi$
$710$	401.429	−	291.655i	0.000796328	−	0.000578566i
$711$	230940.	−	317861.i	0.456835	−	0.628780i
$712$			498377.i			0.983101i
$713$	−144544.	−	312129.i	−0.284329	−	0.613982i
$714$	504133.			0.988891
$715$	−168.488	−	122.413i	−0.000329576	−	0.000239451i
$716$	116189.	+	159920.i	0.226640	+	0.311944i
$717$	118230.	+	363875.i	0.229980	+	0.707806i
$718$	−408141.			−0.791701
$719$			732971.i			1.41785i	0.705286	+	0.708923i	$0.250819\pi$
$719$			732971.i			1.41785i	−0.705286	+	0.708923i	$0.749181\pi$
$720$	−360.127	−	1108.36i	−0.000694690	−	0.00213803i
$721$	−43092.9	+	132626.i	−0.0828962	+	0.255128i
$722$	−96895.6	+	298214.i	−0.185879	+	0.572076i
$723$	901392.	+	654900.i	1.72440	+	1.25285i
$724$	176867.	−	57467.7i	0.337420	−	0.109634i
$725$	188690.	−	259709.i	0.358982	−	0.494096i
$726$	−395409.	−	544234.i	−0.750193	−	1.03255i
$727$	286018.	−	880274.i	0.541159	−	1.66552i	−0.188791	−	0.982017i	$-0.560457\pi$
$727$	286018.	−	880274.i	0.541159	−	1.66552i	0.729951	−	0.683500i	$-0.239543\pi$
$728$	24436.5	+	33633.9i	0.0461079	+	0.0634621i
$729$	−171697.	+	124745.i	−0.323078	+	0.234730i
$730$	−1191.55	−	387.158i	−0.00223597	−	0.000726512i
$731$	−416976.	+	302951.i	−0.780327	+	0.566940i
$732$	119358.	+	86718.6i	0.222756	+	0.161842i
$733$	−180650.	−	555985.i	−0.336226	−	1.03480i	−0.966115	−	0.258112i	$-0.916900\pi$
$733$	−180650.	−	555985.i	−0.336226	−	1.03480i	0.629889	−	0.776685i	$-0.283100\pi$
$734$	578589.	−	796360.i	1.07394	−	1.47815i
$735$	1438.47	+	467.386i	0.00266272	+	0.000865169i
$736$	332054.	+	107891.i	0.612990	+	0.199173i
$737$	56903.9	−	18489.2i	0.104763	−	0.0340395i
$738$	−800015.			−1.46888
$739$			443939.i			0.812896i	0.913674	+	0.406448i	$0.133233\pi$
$739$			443939.i			0.812896i	−0.913674	+	0.406448i	$0.866767\pi$
$740$	−639.903	+	207.917i	−0.00116856	+	0.000379688i
$741$	−149059.	+	108298.i	−0.271470	+	0.197234i
$742$	−113160.	+	155751.i	−0.205534	+	0.282894i
$743$		−	459382.i		−	0.832140i	−0.909333	−	0.416070i	$-0.863407\pi$
$743$		−	459382.i		−	0.832140i	0.909333	−	0.416070i	$-0.136593\pi$
$744$	374273.	+	208760.i	0.676149	+	0.377138i
$745$	1361.53			0.00245310
$746$	271021.	+	196908.i	0.486996	+	0.353823i
$747$	−334027.	−	459749.i	−0.598605	−	0.823909i
$748$	68100.8	+	209593.i	0.121716	+	0.374604i
$749$	180167.			0.321153
$750$			4515.58i			0.00802770i
$751$	−77116.0	−	237338.i	−0.136730	−	0.420812i	0.859125	−	0.511766i	$-0.171008\pi$
$751$	−77116.0	−	237338.i	−0.136730	−	0.420812i	−0.995855	+	0.0909537i	$0.971008\pi$
$752$	394429.	−	1.21393e6i	0.697483	−	2.14663i
$753$	−426242.	+	1.31184e6i	−0.751737	+	2.31361i
$754$	−123632.	−	89823.7i	−0.217464	−	0.157997i
$755$	−1038.44	+	337.409i	−0.00182174	+	0.000591920i
$756$	23522.8	−	32376.3i	0.0411571	−	0.0566479i
$757$	−460564.	−	633913.i	−0.803709	−	1.10621i	−0.992264	−	0.124148i	$-0.960380\pi$
$757$	−460564.	−	633913.i	−0.803709	−	1.10621i	0.188555	−	0.982063i	$-0.439620\pi$
$758$	−196381.	+	604399.i	−0.341792	+	1.05193i
$759$	−138904.	−	191184.i	−0.241118	−	0.331871i
$760$	487.909	−	354.486i	0.000844717	−	0.000613723i
$761$	−360203.	−	117037.i	−0.621982	−	0.202094i	−0.0189622	−	0.999820i	$-0.506036\pi$
$761$	−360203.	−	117037.i	−0.621982	−	0.202094i	−0.603020	+	0.797726i	$0.706036\pi$
$762$	1.14819e6	−	834210.i	1.97744	−	1.43670i
$763$	128369.	+	93265.4i	0.220501	+	0.160203i
$764$	90549.7	+	278683.i	0.155132	+	0.477446i
$765$	−1011.21	+	1391.81i	−0.00172790	+	0.00237824i
$766$	−31837.6	−	10344.7i	−0.0542604	−	0.0176303i
$767$	126704.	+	41168.7i	0.215378	+	0.0699805i
$768$	−894968.	+	290793.i	−1.51735	+	0.493016i
$769$	−470167.			−0.795059			−0.397530	−	0.917589i	$-0.630132\pi$
$769$	−470167.			−0.795059			−0.397530	+	0.917589i	$0.630132\pi$
$770$		−	311.882i		−	0.000526029i
$771$	127818.	−	41530.7i	0.215023	−	0.0698652i
$772$	66804.0	−	48535.9i	0.112090	−	0.0814383i
$773$	328384.	−	451981.i	0.549569	−	0.756417i	−0.440384	−	0.897809i	$-0.645158\pi$
$773$	328384.	−	451981.i	0.549569	−	0.756417i	0.989954	+	0.141392i	$0.0451578\pi$
$774$		−	317154.i		−	0.529405i
$775$	−408459.	−	440349.i	−0.680056	−	0.733152i
$776$	634870.			1.05429
$777$	−227577.	−	165345.i	−0.376953	−	0.273872i
$778$	360392.	+	496037.i	0.595410	+	0.819511i
$779$	−219887.	−	676742.i	−0.362347	−	1.11519i
$780$	368.860			0.000606278
$781$			90685.8i			0.148675i
$782$	−257778.	−	793360.i	−0.421534	−	1.29735i
$783$	41540.2	−	127847.i	0.0677555	−	0.208530i
$784$	204261.	−	628650.i	0.332317	−	1.02277i
$785$	−833.344	−	605.460i	−0.00135234	−	0.000982531i
$786$	−988175.	+	321078.i	−1.59952	+	0.519715i
$787$	−500962.	+	689515.i	−0.808827	+	1.11325i	0.182676	+	0.983173i	$0.441524\pi$
$787$	−500962.	+	689515.i	−0.808827	+	1.11325i	−0.991503	+	0.130082i	$0.958476\pi$
$788$	229087.	+	315311.i	0.368933	+	0.507793i
$789$	−408270.	+	1.25653e6i	−0.655833	+	2.01845i
$790$	−1198.24	−	1649.23i	−0.00191994	−	0.00264258i
$791$	−175212.	+	127299.i	−0.280034	+	0.203456i
$792$	117857.	+	38294.2i	0.187891	+	0.0610495i
$793$	72769.6	−	52870.2i	0.115719	−	0.0840745i
$794$	597863.	+	434373.i	0.948332	+	0.689004i
$795$	−482.349	−	1484.52i	−0.000763180	−	0.00234883i
$796$	111307.	−	153201.i	0.175670	−	0.241789i
$797$	539007.	+	175134.i	0.848550	+	0.275711i	0.700839	−	0.713320i	$-0.252809\pi$
$797$	539007.	+	175134.i	0.848550	+	0.275711i	0.147711	+	0.989031i	$0.452809\pi$
$798$	−262414.	−	85263.4i	−0.412079	−	0.133893i
$799$	−1.79201e6	+	582261.i	−2.80703	+	0.912061i
$800$	609648.			0.952574
$801$			778099.i			1.21275i
$802$	565908.	−	183875.i	0.879826	−	0.285873i
$803$	185247.	−	134590.i	0.287290	−	0.208729i
$804$	−62288.1	+	85732.2i	−0.0963592	+	0.132627i
$805$			405.155i			0.000625215i
$806$	−209623.	+	194442.i	−0.322678	+	0.299309i
$807$	−826613.			−1.26927
$808$	149439.	+	108574.i	0.228897	+	0.166304i
$809$	387529.	+	533388.i	0.592116	+	0.814978i	0.994958	−	0.100291i	$-0.0319775\pi$
$809$	387529.	+	533388.i	0.592116	+	0.814978i	−0.402842	+	0.915270i	$0.631977\pi$
$810$	742.258	+	2284.44i	0.00113132	+	0.00348184i
$811$	97857.8			0.148783			0.0743915	−	0.997229i	$-0.476299\pi$
$811$	97857.8			0.148783			0.0743915	+	0.997229i	$0.476299\pi$
$812$		−	78539.6i		−	0.119118i
$813$	−162784.	−	500997.i	−0.246281	−	0.757974i
$814$	110724.	−	340774.i	0.167107	−	0.514301i
$815$	711.499	−	2189.77i	0.00107117	−	0.00329673i
$816$	1.44516e6	+	1.04997e6i	2.17038	+	1.57688i
$817$	268284.	−	87170.9i	0.401931	−	0.130595i
$818$	−635282.	+	874391.i	−0.949423	+	1.30677i
$819$	38151.8	+	52511.4i	0.0568783	+	0.0782863i
$820$	−440.210	+	1354.83i	−0.000654685	+	0.00201491i
$821$	132515.	+	182392.i	0.196598	+	0.270595i	0.895923	−	0.444210i	$-0.146516\pi$
$821$	132515.	+	182392.i	0.196598	+	0.270595i	−0.699324	+	0.714805i	$0.746516\pi$
$822$	208301.	−	151340.i	0.308282	−	0.223980i
$823$	703604.	+	228615.i	1.03879	+	0.337524i	0.778261	−	0.627941i	$-0.216102\pi$
$823$	703604.	+	228615.i	1.03879	+	0.337524i	0.260531	+	0.965465i	$0.416102\pi$
$824$	−232586.	+	168984.i	−0.342554	+	0.248880i
$825$	−333832.	−	242543.i	−0.490479	−	0.356354i
$826$	61652.1	+	189746.i	0.0903624	+	0.278107i
$827$	−549757.	+	756676.i	−0.803822	+	1.10637i	0.188425	+	0.982088i	$0.439662\pi$
$827$	−549757.	+	756676.i	−0.803822	+	1.10637i	−0.992247	+	0.124279i	$0.960338\pi$
$828$	167542.	+	54437.6i	0.244378	+	0.0794033i
$829$	587850.	+	191004.i	0.855377	+	0.277929i	0.703697	−	0.710501i	$-0.251531\pi$
$829$	587850.	+	191004.i	0.855377	+	0.277929i	0.151681	+	0.988430i	$0.451531\pi$
$830$	−2804.23	+	911.148i	−0.00407058	+	0.00132261i
$831$	1.44364e6			2.09053
$832$			18296.7i			0.0264318i
$833$	−928020.	+	301532.i	−1.33742	+	0.434553i
$834$	−465210.	+	337995.i	−0.668832	+	0.485935i
$835$	−642.133	+	883.820i	−0.000920984	+	0.00126763i
$836$		−	120616.i		−	0.172581i
$837$	−219653.	−	122517.i	−0.313535	−	0.174882i
$838$	−32374.8			−0.0461019
$839$	−714020.	−	518766.i	−1.01435	−	0.736966i	−0.0492308	−	0.998787i	$-0.515677\pi$
$839$	−714020.	−	518766.i	−1.01435	−	0.736966i	−0.965116	+	0.261821i	$0.915677\pi$
$840$	−296.704	−	408.378i	−0.000420499	−	0.000578767i
$841$	137037.	+	421758.i	0.193753	+	0.596309i
$842$	393619.			0.555203
$843$		−	597236.i		−	0.840410i
$844$	−74047.9	−	227896.i	−0.103951	−	0.319927i
$845$	−476.714	+	1467.17i	−0.000667643	+	0.00205479i
$846$	358289.	−	1.10270e6i	0.500603	−	1.54070i
$847$	−170530.	−	123897.i	−0.237702	−	0.172701i
$848$	−648775.	+	210800.i	−0.902199	+	0.293142i
$849$	89642.0	−	123382.i	0.124364	−	0.171173i
$850$	−856168.	−	1.17841e6i	−1.18501	−	1.63102i
$851$	−143838.	+	442687.i	−0.198616	+	0.611276i
$852$	−94407.9	−	129941.i	−0.130056	−	0.179006i
$853$	−79848.4	+	58013.3i	−0.109741	+	0.0797314i	−0.641302	−	0.767288i	$-0.721605\pi$
$853$	−79848.4	+	58013.3i	−0.109741	+	0.0797314i	0.531561	+	0.847020i	$0.321605\pi$
$854$	128109.	+	41625.1i	0.175656	+	0.0570741i
$855$	761.755	−	553.447i	0.00104204	−	0.000757084i
$856$	300495.	+	218322.i	0.410100	+	0.297955i
$857$	145320.	+	447248.i	0.197862	+	0.608958i	0.999931	+	0.0117262i	$0.00373266\pi$
$857$	145320.	+	447248.i	0.197862	+	0.608958i	−0.802069	+	0.597232i	$0.796267\pi$
$858$	−115460.	+	158917.i	−0.156840	+	0.215872i
$859$	−830400.	−	269813.i	−1.12538	−	0.365659i	−0.313564	−	0.949567i	$-0.601523\pi$
$859$	−830400.	−	269813.i	−1.12538	−	0.365659i	−0.811820	+	0.583908i	$0.801523\pi$
$860$	−537.102	−	174.515i	−0.000726205	−	0.000235958i
$861$	−566431.	+	184045.i	−0.764084	+	0.248266i
$862$	−433046.			−0.582801
$863$		−	1.08212e6i		−	1.45296i	−0.687188	−	0.726480i	$-0.741155\pi$
$863$		−	1.08212e6i		−	1.45296i	0.687188	−	0.726480i	$-0.258845\pi$
$864$	242796.	−	78889.1i	0.325247	−	0.105679i
$865$	1754.05	−	1274.39i	0.00234428	−	0.00170322i
$866$	214782.	−	295623.i	0.286393	−	0.394186i
$867$		−	1.64921e6i		−	2.19400i
$868$	−144172.	−	28420.4i	−0.191356	−	0.0377216i
$869$	372574.			0.493370
$870$	1501.12	+	1090.63i	0.00198325	+	0.00144091i
$871$	37975.5	+	52268.8i	0.0500573	+	0.0688979i
$872$	101085.	+	311108.i	0.132940	+	0.409146i
$873$	991199.			1.30057
$874$			456562.i			0.597691i
$875$	437.231	+	1345.66i	0.000571077	+	0.00175760i
$876$	−125322.	+	385701.i	−0.163312	+	0.502624i
$877$	209870.	−	645915.i	0.272868	−	0.839800i	−0.716908	−	0.697168i	$-0.754443\pi$
$877$	209870.	−	645915.i	0.272868	−	0.839800i	0.989776	−	0.142633i	$-0.0455568\pi$
$878$	1.13417e6	+	824021.i	1.47126	+	1.06893i
$879$	1.66399e6	−	540664.i	2.15364	−	0.699761i
$880$	649.567	−	894.052i	0.000838801	−	0.00115451i
$881$	116723.	+	160656.i	0.150385	+	0.206988i	0.877563	−	0.479462i	$-0.159168\pi$
$881$	116723.	+	160656.i	0.150385	+	0.206988i	−0.727177	+	0.686450i	$0.759168\pi$
$882$	185545.	−	571050.i	0.238513	−	0.734069i
$883$	168535.	+	231969.i	0.216157	+	0.297515i	0.903302	−	0.429006i	$-0.141136\pi$
$883$	168535.	+	231969.i	0.216157	+	0.297515i	−0.687145	+	0.726521i	$0.741136\pi$
$884$	−192520.	+	139874.i	−0.246361	+	0.178992i
$885$	−1538.43	−	499.865i	−0.00196422	−	0.000638214i
$886$	122301.	−	88857.0i	0.155798	−	0.113194i
$887$	−1.02546e6	−	745040.i	−1.30338	−	0.946962i	−0.303399	−	0.952864i	$-0.598121\pi$
$887$	−1.02546e6	−	745040.i	−1.30338	−	0.946962i	−0.999983	+	0.00590147i	$0.998121\pi$
$888$	−179208.	−	551544.i	−0.227264	−	0.699446i
$889$	261391.	−	359774.i	0.330740	−	0.455225i
$890$	3839.59	+	1247.56i	0.00484735	+	0.00157500i
$891$	−417511.	−	135657.i	−0.525911	−	0.170879i
$892$	−200152.	+	65033.5i	−0.251554	+	0.0817348i
$893$	1.03127e6			1.29321
$894$		−	1.28419e6i		−	1.60678i
$895$	−1391.67	+	452.180i	−0.00173736	+	0.000564501i
$896$	−253107.	+	183893.i	−0.315273	+	0.229060i
$897$	149990.	−	206443.i	0.186413	−	0.256576i
$898$			1.36567e6i			1.69353i
$899$	−490079.	+	58858.0i	−0.606383	+	0.0728259i
$900$	307605.			0.379759
$901$	814693.	+	591909.i	1.00356	+	0.729131i
$902$	−445911.	−	613744.i	−0.548069	−	0.754353i
$903$	−72961.8	−	224553.i	−0.0894788	−	0.275387i
$904$	−446487.			−0.546351
$905$			1376.66i			0.00168085i
$906$	318243.	+	979451.i	0.387706	+	1.19324i
$907$	371563.	−	1.14355e6i	0.451666	−	1.39009i	−0.423339	−	0.905971i	$-0.639142\pi$
$907$	371563.	−	1.14355e6i	0.451666	−	1.39009i	0.875005	−	0.484114i	$-0.160858\pi$
$908$	−216303.	+	665713.i	−0.262356	+	0.807450i
$909$	233314.	+	169512.i	0.282366	+	0.205151i
$910$	320.292	−	104.069i	0.000386779	−	0.000125672i
$911$	−227318.	+	312877.i	−0.273903	+	0.376996i	−0.923703	−	0.383110i	$-0.874853\pi$
$911$	−227318.	+	312877.i	−0.273903	+	0.376996i	0.649799	+	0.760106i	$0.274853\pi$
$912$	−574664.	−	790956.i	−0.690914	−	0.950961i
$913$	166524.	−	512509.i	0.199773	−	0.614837i
$914$	55516.1	+	76411.4i	0.0664548	+	0.0914672i
$915$	−883.558	+	641.943i	−0.00105534	+	0.000766751i
$916$	−688238.	−	223622.i	−0.820253	−	0.266516i
$917$	−263391.	+	191365.i	−0.313229	+	0.227574i
$918$	−493462.	−	358521.i	−0.585556	−	0.425431i
$919$	−62122.3	−	191193.i	−0.0735557	−	0.226381i	0.907519	−	0.420011i	$-0.137974\pi$
$919$	−62122.3	−	191193.i	−0.0735557	−	0.226381i	−0.981075	+	0.193630i	$0.937974\pi$
$920$	−490.956	+	675.744i	−0.000580052	+	0.000798374i
$921$	−699596.	−	227312.i	−0.824761	−	0.267981i
$922$	−294490.	−	95685.7i	−0.346425	−	0.112560i
$923$	−93131.1	+	30260.1i	−0.109318	+	0.0355195i
$924$	−100955.			−0.118246
$925$			812768.i			0.949911i
$926$	149789.	−	48669.5i	0.174686	−	0.0567591i
$927$	−363128.	+	263828.i	−0.422572	+	0.307016i
$928$	294491.	−	405333.i	0.341961	−	0.470669i
$929$		−	547235.i		−	0.634078i	−0.948412	−	0.317039i	$-0.897311\pi$
$929$		−	547235.i		−	0.634078i	0.948412	−	0.317039i	$-0.102689\pi$
$930$	2545.22	−	2360.89i	0.00294279	−	0.00272967i
$931$	534056.			0.616151
$932$	404105.	+	293600.i	0.465225	+	0.338005i
$933$	480225.	+	660973.i	0.551673	+	0.759313i
$934$	−130543.	−	401770.i	−0.149644	−	0.460557i
$935$	−1631.37			−0.00186608
$936$			133813.i			0.152738i
$937$	−60885.4	−	187386.i	−0.0693480	−	0.213431i	0.910376	−	0.413781i	$-0.135792\pi$
$937$	−60885.4	−	187386.i	−0.0693480	−	0.213431i	−0.979724	+	0.200350i	$0.935792\pi$
$938$	−29898.4	+	92017.7i	−0.0339815	+	0.104584i
$939$	57532.5	−	177067.i	0.0652502	−	0.200820i
$940$	−1670.28	−	1213.53i	−0.00189031	−	0.00137339i
$941$	−821.562	+	266.942i	−0.000927814	+	0.000301465i	−0.309481	−	0.950906i	$-0.600155\pi$
$941$	−821.562	+	266.942i	−0.000927814	+	0.000301465i	0.308553	+	0.951207i	$0.400155\pi$
$942$	−571068.	+	786008.i	−0.643556	+	0.885778i
$943$	579267.	+	797293.i	0.651412	+	0.896591i
$944$	−218455.	+	672336.i	−0.245142	+	0.754471i
$945$	174.129	+	239.669i	0.000194988	+	0.000268378i
$946$	243310.	−	176775.i	0.271880	−	0.197532i
$947$	924347.	+	300339.i	1.03071	+	0.334897i	0.775070	−	0.631876i	$-0.217715\pi$
$947$	924347.	+	300339.i	1.03071	+	0.334897i	0.255637	+	0.966773i	$0.417715\pi$
$948$	−533851.	+	387866.i	−0.594023	+	0.431583i
$949$	200033.	+	145332.i	0.222110	+	0.161372i
$950$	246353.	+	758197.i	0.272968	+	0.840108i
$951$	−1.04025e6	+	1.43178e6i	−1.15021	+	1.58313i
$952$	309720.	+	100634.i	0.341739	+	0.111038i
$953$	311767.	+	101299.i	0.343277	+	0.111537i	0.475581	−	0.879672i	$-0.342238\pi$
$953$	311767.	+	101299.i	0.343277	+	0.111537i	−0.132305	+	0.991209i	$0.542238\pi$
$954$	−589331.	+	191485.i	−0.647534	+	0.210397i
$955$	−2169.15			−0.00237838
$956$		−	270458.i		−	0.295927i
$957$	−322517.	+	104792.i	−0.352151	+	0.114421i
$958$	664476.	−	482770.i	0.724016	−	0.526028i
$959$	47420.7	−	65268.9i	0.0515621	−	0.0709691i
$960$		−	222.156i		−	0.000241055i
$961$	−69297.0	+	920917.i	−0.0750357	+	0.997181i
$962$	386909.			0.418079
$963$	469152.	+	340859.i	0.505896	+	0.367555i
$964$	−462945.	−	637189.i	−0.498167	−	0.685668i
$965$	188.891	+	581.346i	0.000202841	+	0.000624281i
$966$	382141.			0.409515
$967$		−	253214.i		−	0.270791i	−0.990792	−	0.135396i	$-0.956769\pi$
$967$		−	253214.i		−	0.270791i	0.990792	−	0.135396i	$-0.0432306\pi$
$968$	−134285.	−	413287.i	−0.143310	−	0.441064i
$969$	−445991.	+	1.37262e6i	−0.474983	+	1.46185i
$970$	1589.23	−	4891.15i	0.00168905	−	0.00519837i
$971$	−530975.	−	385776.i	−0.563165	−	0.409163i	0.269451	−	0.963014i	$-0.413158\pi$
$971$	−530975.	−	385776.i	−0.563165	−	0.409163i	−0.832616	+	0.553851i	$0.813158\pi$
$972$	570910.	−	185500.i	0.604276	−	0.196341i
$973$	−105907.	+	145769.i	−0.111866	+	0.153971i
$974$	522221.	+	718775.i	0.550473	+	0.757662i
$975$	137690.	−	423766.i	0.144841	−	0.445776i
$976$	280547.	+	386140.i	0.294514	+	0.405364i
$977$	847396.	−	615669.i	0.887764	−	0.644998i	−0.0475303	−	0.998870i	$-0.515135\pi$
$977$	847396.	−	615669.i	0.887764	−	0.644998i	0.935294	+	0.353872i	$0.115135\pi$
$978$	−2.06538e6	−	671084.i	−2.15935	−	0.701615i
$979$	−596931.	+	433696.i	−0.622815	+	0.452501i
$980$	−864.978	−	628.443i	−0.000900644	−	0.000654356i
$981$	157821.	+	485722.i	0.163993	+	0.504719i
$982$	116735.	−	160673.i	0.121054	−	0.166617i
$983$	111030.	+	36075.9i	0.114904	+	0.0373344i	0.365904	−	0.930652i	$-0.380760\pi$
$983$	111030.	+	36075.9i	0.114904	+	0.0373344i	−0.251001	+	0.967987i	$0.580760\pi$
$984$	−1.16775e6	−	379425.i	−1.20604	−	0.391865i
$985$	−2743.92	+	891.554i	−0.00282813	+	0.000918914i
$986$	−1.19706e6			−1.23129
$987$		−	863167.i		−	0.886055i
$988$	123868.	−	40247.3i	0.126896	−	0.0412309i
$989$	−316075.	+	229642.i	−0.323145	+	0.234779i
$990$	590.050	−	812.135i	0.000602031	−	0.000828624i
$991$			1.55938e6i			1.58783i	0.608027	+	0.793916i	$0.291961\pi$
$991$			1.55938e6i			1.58783i	−0.608027	+	0.793916i	$0.708039\pi$
$992$	−637489.	−	687260.i	−0.647812	−	0.698390i
$993$	−1.27214e6			−1.29014
$994$	−118639.	−	86196.0i	−0.120075	−	0.0872398i
$995$	823.963	+	1134.09i	0.000832265	+	0.00114551i
$996$	294936.	+	907720.i	0.297310	+	0.915025i
$997$	1.12635e6			1.13314			0.566572	−	0.824012i	$-0.308269\pi$
$997$	1.12635e6			1.13314			0.566572	+	0.824012i	$0.308269\pi$
$998$			2.44899e6i			2.45882i
$999$	105173.	+	323690.i	0.105384	+	0.324338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.5.f.a.29.2	yes	36
31.15	odd	10	inner	31.5.f.a.15.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.f.a.15.2	✓	36	31.15	odd	10	inner
31.5.f.a.29.2	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-3.99299 - 2.90108i) q^{2} +(-6.95155 - 9.56799i) q^{3} +(2.58345 + 7.95104i) q^{4} -0.0618873 q^{5} +58.3719i q^{6} +(5.65199 + 17.3950i) q^{7} +(-11.6521 + 35.8615i) q^{8} +(-18.1920 + 55.9892i) q^{9} +(0.247115 + 0.179540i) q^{10} +(-53.0929 + 17.2509i) q^{11} +(58.1165 - 79.9905i) q^{12} +(-35.4322 - 48.7682i) q^{13} +(27.8960 - 85.8550i) q^{14} +(0.430213 + 0.592137i) q^{15} +(258.780 - 188.015i) q^{16} +(-449.085 - 145.917i) q^{17} +(235.070 - 170.788i) q^{18} +(209.081 + 151.907i) q^{19} +(-0.159883 - 0.492068i) q^{20} +(127.145 - 175.001i) q^{21} +(262.046 + 85.1438i) q^{22} +(-340.414 - 110.607i) q^{23} +(424.122 - 137.806i) q^{24} -624.996 q^{25} +297.522i q^{26} +(-248.908 + 80.8753i) q^{27} +(-123.707 + 89.8783i) q^{28} +(-301.906 + 415.537i) q^{29} -3.61248i q^{30} +(653.538 + 704.563i) q^{31} -975.442 q^{32} +(534.135 + 388.072i) q^{33} +(1369.88 + 1885.47i) q^{34} +(-0.349786 - 1.07653i) q^{35} -492.171 q^{36} -1300.44i q^{37} +(-394.168 - 1213.12i) q^{38} +(-220.305 + 678.029i) q^{39} +(0.721116 - 2.21937i) q^{40} +(-2227.49 - 1618.37i) q^{41} +(-1015.38 + 329.917i) q^{42} +(641.579 - 883.057i) q^{43} +(-274.326 - 377.577i) q^{44} +(1.12585 - 3.46502i) q^{45} +(1038.39 + 1429.22i) q^{46} +(3228.27 - 2345.48i) q^{47} +(-3597.85 - 1169.01i) q^{48} +(1671.81 - 1214.64i) q^{49} +(2495.60 + 1813.16i) q^{50} +(1725.71 + 5311.19i) q^{51} +(296.221 - 407.713i) q^{52} +(-2028.25 - 659.017i) q^{53} +(1228.51 + 399.169i) q^{54} +(3.28578 - 1.06761i) q^{55} -689.669 q^{56} -3056.48i q^{57} +(2411.01 - 783.385i) q^{58} +(-1787.98 + 1299.05i) q^{59} +(-3.59667 + 4.95039i) q^{60} +1492.15i q^{61} +(-565.579 - 4709.28i) q^{62} -1076.76 q^{63} +(-245.557 - 178.407i) q^{64} +(2.19280 + 3.01813i) q^{65} +(-1006.97 - 3099.13i) q^{66} -1071.78 q^{67} -3947.66i q^{68} +(1308.12 + 4025.97i) q^{69} +(-1.72641 + 5.31333i) q^{70} +(501.986 - 1544.95i) q^{71} +(-1795.88 - 1304.78i) q^{72} +(-3900.95 + 1267.50i) q^{73} +(-3772.67 + 5192.63i) q^{74} +(4344.69 + 5979.96i) q^{75} +(-667.664 + 2054.86i) q^{76} +(-600.161 - 826.051i) q^{77} +(2846.69 - 2068.24i) q^{78} +(-6347.29 - 2062.36i) q^{79} +(-16.0152 + 11.6357i) q^{80} +(6361.93 + 4622.21i) q^{81} +(4199.35 + 12924.3i) q^{82} +(-5673.92 + 7809.48i) q^{83} +(1719.91 + 558.833i) q^{84} +(27.7926 + 9.03038i) q^{85} +(-5123.63 + 1664.77i) q^{86} +6074.57 q^{87} -2105.00i q^{88} +(12570.2 - 4084.31i) q^{89} +(-14.5478 + 10.5696i) q^{90} +(648.062 - 891.981i) q^{91} -2992.39i q^{92} +(2198.15 - 11150.9i) q^{93} -19694.9 q^{94} +(-12.9395 - 9.40108i) q^{95} +(6780.84 + 9333.02i) q^{96} +(-5202.90 - 16012.9i) q^{97} -10199.3 q^{98} -3286.46i 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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