LMFDB - Embedded newform 31.5.f.a.15.2

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			15.2
Character	$\chi$	$=$	31.15
Dual form			31.5.f.a.29.2

$q$-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 $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

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

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 $

$2$	−3.99299	+	2.90108i	−0.998247	+	0.725269i	−0.961712	−	0.274063i	$-0.911632\pi$
$2$	−3.99299	+	2.90108i	−0.998247	+	0.725269i	−0.0365358	+	0.999332i	$0.511632\pi$
$3$	−6.95155	+	9.56799i	−0.772395	+	1.06311i	0.223686	+	0.974661i	$0.428191\pi$
$3$	−6.95155	+	9.56799i	−0.772395	+	1.06311i	−0.996081	+	0.0884490i	$0.971809\pi$
$4$	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	−0.876673	−	0.481088i	$-0.840242\pi$
$7$	5.65199	−	17.3950i	0.115347	−	0.355001i	0.992019	+	0.126087i	$0.0402419\pi$
$8$	−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	0.0812903	−	0.996690i	$-0.474096\pi$
$11$	−53.0929	−	17.2509i	−0.438784	−	0.142570i	−0.520075	+	0.854121i	$0.674096\pi$
$12$	58.1165	+	79.9905i	0.403587	+	0.555489i
$13$	−35.4322	+	48.7682i	−0.209658	+	0.288569i	−0.900876	−	0.434077i	$-0.857074\pi$
$13$	−35.4322	+	48.7682i	−0.209658	+	0.288569i	0.691218	+	0.722646i	$0.257074\pi$
$14$	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	−0.955177	−	0.296034i	$-0.904336\pi$
$17$	−449.085	+	145.917i	−1.55393	+	0.504902i	−0.598750	+	0.800936i	$0.704336\pi$
$18$	235.070	+	170.788i	0.725523	+	0.527124i
$19$	209.081	−	151.907i	0.579173	−	0.420794i	−0.259253	−	0.965809i	$-0.583476\pi$
$19$	209.081	−	151.907i	0.579173	−	0.420794i	0.838426	+	0.545016i	$0.183476\pi$
$20$	−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	−0.612548	−	0.790433i	$-0.709855\pi$
$23$	−340.414	+	110.607i	−0.643505	+	0.209087i	−0.0309568	+	0.999521i	$0.509855\pi$
$24$	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	0.590881	−	0.806759i	$-0.298780\pi$
$29$	−301.906	−	415.537i	−0.358984	−	0.494099i	−0.949865	+	0.312659i	$0.898780\pi$
$30$			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	$0.157537\pi$
$37$			1300.44i			0.949917i	−0.880008	+	0.474959i	$0.842463\pi$
$38$	−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	−0.325247	+	0.945629i	$0.605448\pi$
$41$	−2227.49	+	1618.37i	−1.32510	+	0.962742i	−0.999854	+	0.0171133i	$0.994552\pi$
$42$	−1015.38	−	329.917i	−0.575613	−	0.187028i
$43$	641.579	+	883.057i	0.346987	+	0.477586i	0.946466	−	0.322804i	$-0.104625\pi$
$43$	641.579	+	883.057i	0.346987	+	0.477586i	−0.599479	+	0.800391i	$0.704625\pi$
$44$	−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	0.982990	+	0.183656i	$0.0587934\pi$
$47$	3228.27	+	2345.48i	1.46142	+	1.06178i	0.478428	+	0.878127i	$0.341207\pi$
$48$	−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	−0.646913	−	0.762564i	$-0.723940\pi$
$53$	−2028.25	+	659.017i	−0.722052	+	0.234609i	−0.0751396	+	0.997173i	$0.523940\pi$
$54$	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	0.300562	−	0.953762i	$-0.402826\pi$
$59$	−1787.98	−	1299.05i	−0.513641	−	0.373182i	−0.814203	+	0.580580i	$0.802826\pi$
$60$	−3.59667	−	4.95039i	−0.000999075	−	0.00137511i
$61$		−	1492.15i		−	0.401008i	−0.979693	−	0.200504i	$-0.935742\pi$
$61$		−	1492.15i		−	0.401008i	0.979693	−	0.200504i	$-0.0642580\pi$
$62$	−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	0.988420	−	0.151741i	$-0.0484878\pi$
$71$	501.986	+	1544.95i	0.0995806	+	0.306478i	−0.888840	+	0.458218i	$0.848488\pi$
$72$	−1795.88	+	1304.78i	−0.346428	+	0.251694i
$73$	−3900.95	−	1267.50i	−0.732023	−	0.237849i	−0.0807948	−	0.996731i	$-0.525746\pi$
$73$	−3900.95	−	1267.50i	−0.732023	−	0.237849i	−0.651228	+	0.758882i	$0.725746\pi$
$74$	−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	−0.769651	−	0.638465i	$-0.779570\pi$
$79$	−6347.29	+	2062.36i	−1.01703	+	0.330453i	−0.247380	+	0.968919i	$0.579570\pi$
$80$	−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	−0.989077	−	0.147399i	$-0.952910\pi$
$83$	−5673.92	−	7809.48i	−0.823621	−	1.13362i	0.165456	−	0.986217i	$-0.447090\pi$
$84$	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	0.963835	−	0.266501i	$-0.0858674\pi$
$89$	12570.2	+	4084.31i	1.58695	+	0.515631i	0.623114	+	0.782131i	$0.285867\pi$
$90$	−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	0.148274	+	0.988946i	$0.452628\pi$
$97$	−5202.90	+	16012.9i	−0.552970	+	1.70187i	−0.701245	+	0.712921i	$0.747372\pi$
$98$	−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	0.997432	−	0.0716179i	$-0.0228162\pi$
$101$	1513.79	+	4658.98i	0.148397	+	0.456718i	−0.849036	+	0.528336i	$0.822816\pi$
$102$	8517.42	+	26213.9i	0.818668	+	2.51960i
$103$	6168.25	−	4481.50i	0.581417	−	0.422424i	−0.257818	−	0.966194i	$-0.583003\pi$
$103$	6168.25	−	4481.50i	0.581417	−	0.422424i	0.839235	+	0.543770i	$0.183003\pi$
$104$	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	0.991491	+	0.130173i	$0.0415533\pi$
$107$	3043.97	+	9368.37i	0.265872	+	0.818269i	−0.725619	+	0.688096i	$0.758447\pi$
$108$	−1286.08	+	1770.14i	−0.110261	+	0.151761i
$109$	7018.45	+	5099.20i	0.590729	+	0.429189i	0.842576	−	0.538578i	$-0.181038\pi$
$109$	7018.45	+	5099.20i	0.590729	+	0.429189i	−0.251847	+	0.967767i	$0.581038\pi$
$110$	−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	−0.699370	−	0.714760i	$-0.746536\pi$
$113$	3659.06	−	11261.4i	0.286558	−	0.881934i	0.985927	−	0.167174i	$-0.0534642\pi$
$114$	−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	0.0886429	+	0.996063i	$0.471747\pi$
$127$	−14291.3	+	19670.3i	−0.886062	+	1.21956i	−0.974705	+	0.223496i	$0.928253\pi$
$128$	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	−0.652893	−	0.757450i	$-0.726445\pi$
$131$	5500.55	−	16929.0i	0.320526	−	0.986479i	0.973420	−	0.229029i	$-0.0735550\pi$
$132$	−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	−0.872480	−	0.488649i	$-0.837490\pi$
$137$	−2592.68	+	3568.52i	−0.138136	+	0.190128i	0.734344	+	0.678777i	$0.237490\pi$
$138$	6456.35	+	19870.6i	0.339023	+	1.04341i
$139$	5790.37	−	7969.76i	0.299693	−	0.412492i	−0.632439	−	0.774610i	$-0.717946\pi$
$139$	5790.37	−	7969.76i	0.299693	−	0.412492i	0.932132	+	0.362118i	$0.117946\pi$
$140$	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	0.652908	−	0.757437i	$-0.273549\pi$
$151$	16779.5	+	5451.99i	0.735911	+	0.239112i	0.0830031	+	0.996549i	$0.473549\pi$
$152$	−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	−0.280125	−	0.959963i	$-0.590376\pi$
$157$	13465.5	−	9783.27i	0.546291	−	0.396903i	0.826416	+	0.563060i	$0.190376\pi$
$158$	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	−0.895414	−	0.445234i	$-0.853121\pi$
$163$	−11496.7	−	35383.2i	−0.432711	−	1.33175i	0.462704	−	0.886513i	$-0.346879\pi$
$164$	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	0.953454	−	0.301538i	$-0.0975000\pi$
$167$	10375.9	+	14281.1i	0.372041	+	0.512071i	−0.581413	+	0.813608i	$0.697500\pi$
$168$	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	0.00309746	−	0.999995i	$-0.499014\pi$
$173$	−28342.7	−	20592.2i	−0.946997	−	0.688034i	−0.950095	+	0.311961i	$0.899014\pi$
$174$	−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	0.638125	−	0.769933i	$-0.279710\pi$
$179$	22487.1	+	7306.50i	0.701823	+	0.228036i	0.0636983	+	0.997969i	$0.479710\pi$
$180$	30.4591			0.000940096
$181$			22244.6i			0.678995i	0.940607	+	0.339498i	$0.110257\pi$
$181$			22244.6i			0.678995i	−0.940607	+	0.339498i	$0.889743\pi$
$182$	−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	−0.983631	−	0.180197i	$-0.942327\pi$
$193$	−3052.18	+	9393.63i	−0.0819398	+	0.252185i	0.901691	+	0.432381i	$0.142327\pi$
$194$	−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	0.818295	−	0.574799i	$-0.194920\pi$
$197$	44337.4	+	14406.1i	1.14245	+	0.371205i	0.324156	+	0.946003i	$0.394920\pi$
$198$	−9534.28	−	13122.8i	−0.243196	−	0.334731i
$199$	−13313.9	+	18325.1i	−0.336202	+	0.462742i	−0.943327	−	0.331864i	$-0.892323\pi$
$199$	−13313.9	+	18325.1i	−0.336202	+	0.462742i	0.607125	+	0.794606i	$0.292323\pi$
$200$	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	$-0.918549\pi$
$223$		−	25173.1i		−	0.506206i	0.967439	−	0.253103i	$-0.0814511\pi$
$224$	−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	0.314544	−	0.949243i	$-0.398149\pi$
$227$	67736.2	−	49213.3i	1.31453	−	0.955059i	0.999983	−	0.00581642i	$-0.00185143\pi$
$228$	24302.2	+	7896.25i	0.467493	+	0.151898i
$229$	−50878.4	−	70028.1i	−0.970203	−	1.33537i	−0.941944	−	0.335769i	$-0.891004\pi$
$229$	−50878.4	−	70028.1i	−0.970203	−	1.33537i	−0.0282587	−	0.999601i	$-0.508996\pi$
$230$	−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	0.935972	−	0.352075i	$-0.114524\pi$
$233$	48336.7	+	35118.7i	0.890359	+	0.646884i	−0.0456125	+	0.998959i	$0.514524\pi$
$234$	−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	−0.565685	−	0.824621i	$-0.691388\pi$
$239$	−30767.3	+	9996.90i	−0.538634	+	0.175013i	0.0270513	+	0.999634i	$0.491388\pi$
$240$	222.661	−	72.3470i	0.00386565	−	0.00125602i
$241$	−89598.2	−	29112.2i	−1.54264	−	0.501235i	−0.590538	−	0.807009i	$-0.701085\pi$
$241$	−89598.2	−	29112.2i	−1.54264	−	0.501235i	−0.952104	+	0.305775i	$0.901085\pi$
$242$	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	−0.237890	+	0.971292i	$0.576456\pi$
$251$	−68553.4	+	94355.6i	−1.08813	+	1.49768i	−0.850241	+	0.526393i	$0.823544\pi$
$252$	−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	0.920948	−	0.389687i	$-0.127417\pi$
$257$	−3511.61	−	10807.6i	−0.0531667	−	0.163630i	−0.974114	+	0.226056i	$0.927417\pi$
$258$	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	0.00252022	+	0.999997i	$0.499198\pi$
$263$	−65663.0	+	90377.3i	−0.949312	+	1.30662i	−0.951832	+	0.306619i	$0.900802\pi$
$264$	−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	0.992285	−	0.123976i	$-0.0395644\pi$
$269$	41082.6	+	56545.3i	0.567745	+	0.781433i	−0.424541	+	0.905409i	$0.639564\pi$
$270$	−76.0294	+	24.7035i	−0.00104293	+	0.000338868i
$271$	42361.6	−	13764.1i	0.576811	−	0.187417i	−0.00606028	−	0.999982i	$-0.501929\pi$
$271$	42361.6	−	13764.1i	0.576811	−	0.187417i	0.582872	+	0.812564i	$0.301929\pi$
$272$	−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	−0.957840	−	0.287302i	$-0.907242\pi$
$277$	−71748.7	−	98753.6i	−0.935092	−	1.28704i	0.0227480	−	0.999741i	$-0.492758\pi$
$278$			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	−0.298222	−	0.954496i	$-0.596394\pi$
$281$	40854.6	−	29682.6i	0.517402	−	0.375915i	0.815624	+	0.578582i	$0.196394\pi$
$282$	136910.	−	188440.i	1.72162	−	2.36961i
$283$	3984.85	−	12264.1i	0.0497553	−	0.153131i	−0.923092	−	0.384579i	$-0.874346\pi$
$283$	3984.85	−	12264.1i	0.0497553	−	0.153131i	0.972847	+	0.231449i	$0.0743465\pi$
$284$	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	−0.748965	−	0.662609i	$-0.769449\pi$
$293$	−45715.6	−	140698.i	−0.532512	−	1.63890i	0.216453	−	0.976293i	$-0.430551\pi$
$294$	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	0.821814	−	0.569756i	$-0.192962\pi$
$307$	50319.4	+	36559.2i	0.533898	+	0.387900i	−0.287916	+	0.957656i	$0.592962\pi$
$308$	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	−0.759177	−	0.650884i	$-0.774398\pi$
$313$	9253.08	−	12735.8i	0.0944491	−	0.129998i	0.853626	+	0.520886i	$0.174398\pi$
$314$	−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	0.404782	+	0.914413i	$0.367347\pi$
$317$	−46242.2	+	142319.i	−0.460172	+	1.41626i	−0.864954	+	0.501851i	$0.832653\pi$
$318$	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	0.993371	−	0.114950i	$-0.0366708\pi$
$331$	63225.3	+	87022.2i	0.577079	+	0.794281i	−0.416293	+	0.909231i	$0.636671\pi$
$332$	−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	0.671899	−	0.740643i	$-0.265479\pi$
$337$	88599.4	+	28787.7i	0.780137	+	0.253482i	0.108238	+	0.994125i	$0.465479\pi$
$338$	−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	$0.0920940\pi$
$347$			68706.0i			0.570605i	−0.958438	+	0.285302i	$0.907906\pi$
$348$	15693.3	−	48299.1i	0.129586	−	0.398824i
$349$	−58860.1	−	181153.i	−0.483248	−	1.48728i	−0.834502	−	0.551004i	$-0.814245\pi$
$349$	−58860.1	−	181153.i	−0.483248	−	1.48728i	0.351254	−	0.936280i	$-0.385755\pi$
$350$	−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	0.910885	−	0.412660i	$-0.135400\pi$
$353$	29525.3	+	40638.0i	0.236943	+	0.326124i	−0.673942	+	0.738784i	$0.735400\pi$
$354$	−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	0.816259	−	0.577686i	$-0.196044\pi$
$359$	66900.2	+	48605.8i	0.519085	+	0.377137i	−0.297174	+	0.954823i	$0.596044\pi$
$360$	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	$-0.734650\pi$
$367$		−	199439.i		−	1.48074i	0.672199	−	0.740370i	$-0.265350\pi$
$368$	−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	0.711682	+	0.702501i	$0.247934\pi$
$379$	−39788.7	+	122457.i	−0.277001	+	0.852520i	−0.988683	+	0.150019i	$0.952066\pi$
$380$	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	0.330922	−	0.943658i	$-0.392640\pi$
$383$	6450.60	+	2095.93i	0.0439747	+	0.0142882i	−0.286947	+	0.957946i	$0.592640\pi$
$384$	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	−0.672169	−	0.740398i	$-0.734637\pi$
$389$	−118147.	+	38388.2i	−0.780770	+	0.253687i	−0.108601	+	0.994085i	$0.534637\pi$
$390$	−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	0.529679	−	0.848198i	$-0.322312\pi$
$401$	−70862.7	−	97534.1i	−0.440686	−	0.606552i	−0.970364	+	0.241647i	$0.922312\pi$
$402$			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	$0.227134\pi$
$409$			218981.i			1.30906i	−0.756035	+	0.654532i	$0.772866\pi$
$410$	−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	0.602796	−	0.797895i	$-0.294053\pi$
$419$	5306.69	+	3855.54i	0.0302270	+	0.0219612i	−0.572569	+	0.819856i	$0.694053\pi$
$420$	−106.441	+	34.5846i	−0.000603404	+	0.000196058i
$421$	−64519.8	−	46876.4i	−0.364023	−	0.264478i	0.390705	−	0.920516i	$-0.372231\pi$
$421$	−64519.8	−	46876.4i	−0.364023	−	0.264478i	−0.754728	+	0.656038i	$0.772231\pi$
$422$	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	0.762218	−	0.647321i	$-0.224111\pi$
$431$	70982.5	+	51571.8i	0.382118	+	0.277625i	−0.380100	+	0.924945i	$0.624111\pi$
$432$	−49206.9	−	67727.5i	−0.263669	−	0.362909i
$433$		−	74035.4i		−	0.394879i	−0.980315	−	0.197439i	$-0.936737\pi$
$433$		−	74035.4i		−	0.394879i	0.980315	−	0.197439i	$-0.0632625\pi$
$434$	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	0.924042	−	0.382291i	$-0.124865\pi$
$443$	−9464.87	−	29129.9i	−0.0482289	−	0.148433i	−0.972271	+	0.233858i	$0.924865\pi$
$444$	−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	0.185083	+	0.982723i	$0.440745\pi$
$449$	−162639.	+	223853.i	−0.806736	+	1.11038i	−0.991819	+	0.127654i	$0.959255\pi$
$450$	−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	−0.352264	−	0.935901i	$-0.614588\pi$
$457$	−18199.8	+	5913.47i	−0.0871432	+	0.0283146i	0.265121	+	0.964215i	$0.414588\pi$
$458$	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	0.446010	−	0.895028i	$-0.352845\pi$
$461$	59666.5	+	19386.8i	0.280756	+	0.0912230i	−0.165254	+	0.986251i	$0.552845\pi$
$462$	48218.1	+	35032.5i	0.225905	+	0.164130i
$463$	−18756.5	−	25816.2i	−0.0874965	−	0.120429i	0.763025	−	0.646369i	$-0.223713\pi$
$463$	−18756.5	−	25816.2i	−0.0874965	−	0.120429i	−0.850521	+	0.525941i	$0.823713\pi$
$464$		−	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	−0.417604	−	0.908629i	$-0.637130\pi$
$467$	69244.9	−	50309.4i	0.317508	−	0.230683i	0.735111	+	0.677947i	$0.237130\pi$
$468$	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	−0.998379	−	0.0569130i	$-0.981874\pi$
$479$	−51423.7	−	158266.i	−0.224126	−	0.689789i	0.774253	−	0.632876i	$-0.218126\pi$
$480$	−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	−0.646822	−	0.762641i	$-0.723903\pi$
$487$	−171199.	+	55625.9i	−0.721844	+	0.234541i	−0.0750215	+	0.997182i	$0.523903\pi$
$488$	−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	$-0.973405\pi$
$491$		−	40238.7i		−	0.166909i	0.996512	−	0.0834547i	$-0.0265954\pi$
$492$	−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	−0.516662	+	0.856189i	$0.672826\pi$
$499$	−291652.	+	401425.i	−1.17129	+	1.61214i	−0.654627	+	0.755952i	$0.727174\pi$
$500$	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	0.184585	−	0.982816i	$-0.440906\pi$
$503$	155079.	−	477283.i	0.612938	−	1.88643i	0.428352	−	0.903612i	$-0.359094\pi$
$504$	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	−0.365817	−	0.930687i	$-0.619210\pi$
$509$	163833.	−	225497.i	0.632362	−	0.870372i	0.998179	+	0.0603147i	$0.0192104\pi$
$510$	−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	0.907389	−	0.420292i	$-0.138072\pi$
$523$	381420.	+	123931.i	1.39444	+	0.453081i	0.487052	+	0.873373i	$0.338072\pi$
$524$	−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	0.762441	+	0.647058i	$0.224001\pi$
$541$	153934.	+	473760.i	0.525944	+	1.61869i	−0.236497	+	0.971632i	$0.575999\pi$
$542$	−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	−0.680071	−	0.733147i	$-0.738051\pi$
$547$	90077.1	−	277229.i	0.301051	−	0.926539i	0.981121	−	0.193393i	$-0.0619491\pi$
$548$	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	$-0.934848\pi$
$557$		−	126119.i		−	0.406510i	0.979126	−	0.203255i	$-0.0651521\pi$
$558$	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	0.998193	−	0.0600850i	$-0.0191372\pi$
$569$	573197.	+	186243.i	1.77043	+	0.575248i	0.772238	+	0.635333i	$0.219137\pi$
$570$	548.759	+	755.302i	0.00168901	+	0.00232472i
$571$	224604.	−	309142.i	0.688884	−	0.948168i	−0.311113	−	0.950373i	$-0.600702\pi$
$571$	224604.	−	309142.i	0.688884	−	0.948168i	0.999998	+	0.00220504i	$0.000701886\pi$
$572$	−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	−0.792647	−	0.609681i	$-0.791297\pi$
$577$	−152397.	+	110723.i	−0.457746	+	0.332572i	0.334900	+	0.942254i	$0.391297\pi$
$578$	−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	−0.978239	−	0.207480i	$-0.933474\pi$
$587$	−300902.	−	414157.i	−0.873272	−	1.20196i	0.104968	−	0.994476i	$-0.466526\pi$
$588$			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	−0.790413	−	0.612575i	$-0.790134\pi$
$593$	73532.3	−	226309.i	0.209107	−	0.643565i	0.999520	−	0.0309905i	$-0.00986617\pi$
$594$	−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	−0.984041	−	0.177941i	$-0.943056\pi$
$599$	−401460.	+	291678.i	−1.11889	+	0.812924i	−0.134853	+	0.990866i	$0.543056\pi$
$600$	−265075.	−	86128.0i	−0.736319	−	0.239245i
$601$	116682.	+	160599.i	0.323040	+	0.444626i	0.939392	−	0.342844i	$-0.111390\pi$
$601$	116682.	+	160599.i	0.323040	+	0.444626i	−0.616353	+	0.787470i	$0.711390\pi$
$602$	−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	0.853179	−	0.521618i	$-0.174671\pi$
$607$	228710.	+	166168.i	0.620738	+	0.450992i	−0.232441	+	0.972610i	$0.574671\pi$
$608$	−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	0.279200	−	0.960233i	$-0.409931\pi$
$613$	−22296.0	−	7244.40i	−0.0593342	−	0.0192789i	−0.338534	+	0.940954i	$0.609931\pi$
$614$	−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	0.293682	−	0.955903i	$-0.405119\pi$
$617$	−199741.	−	145120.i	−0.524683	−	0.381205i	−0.818365	+	0.574698i	$0.805119\pi$
$618$	−261593.	−	360052.i	−0.684936	−	0.942733i
$619$		−	311178.i		−	0.812135i	−0.913843	−	0.406067i	$-0.866900\pi$
$619$		−	311178.i		−	0.812135i	0.913843	−	0.406067i	$-0.133100\pi$
$620$	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	0.427869	−	0.903841i	$-0.359265\pi$
$631$	96656.4	+	31405.6i	0.242757	+	0.0788765i	−0.185112	+	0.982718i	$0.559265\pi$
$632$	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	0.985153	+	0.171676i	$0.0549184\pi$
$641$	346783.	+	477306.i	0.843998	+	1.16166i	−0.141155	+	0.989987i	$0.545082\pi$
$642$	546849.	−	177682.i	1.32678	−	0.431096i
$643$	683554.	−	222100.i	1.65330	−	0.537189i	0.673846	−	0.738872i	$-0.264641\pi$
$643$	683554.	−	222100.i	1.65330	−	0.537189i	0.979451	+	0.201683i	$0.0646411\pi$
$644$	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	−0.344731	−	0.938702i	$-0.612030\pi$
$647$	−492024.	−	159868.i	−1.17538	−	0.381904i	−0.830648	+	0.556798i	$0.812030\pi$
$648$	−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	−0.425239	−	0.905081i	$-0.639810\pi$
$653$	129687.	−	94223.5i	0.304139	−	0.220970i	0.729377	+	0.684112i	$0.239810\pi$
$654$	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	0.950548	−	0.310579i	$-0.100523\pi$
$659$	−440.947	−	1357.09i	−0.00101535	−	0.00312492i	−0.951563	+	0.307454i	$0.900523\pi$
$660$	105.559	+	324.877i	0.000242330	+	0.000745814i
$661$	−688319.	+	500093.i	−1.57538	+	1.14458i	−0.653628	+	0.756816i	$0.726754\pi$
$661$	−688319.	+	500093.i	−1.57538	+	1.14458i	−0.921757	+	0.387768i	$0.873246\pi$
$662$	−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	−0.756667	−	0.653800i	$-0.773174\pi$
$673$	−445922.	+	144889.i	−0.984530	+	0.319893i	−0.227863	+	0.973693i	$0.573174\pi$
$674$	−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	$-0.944221\pi$
$677$		−	159810.i		−	0.348680i	0.984686	−	0.174340i	$-0.0557791\pi$
$678$	−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	0.892008	−	0.452020i	$-0.149297\pi$
$691$	−45519.5	−	140094.i	−0.0953325	−	0.293403i	−0.987340	+	0.158617i	$0.949297\pi$
$692$	−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	−0.298721	−	0.954340i	$-0.596560\pi$
$701$	253858.	−	184439.i	0.516601	−	0.375332i	0.815322	+	0.579008i	$0.196560\pi$
$702$	−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	−0.0139531	−	0.999903i	$-0.504442\pi$
$709$	−308128.	−	100117.i	−0.612969	−	0.199166i	−0.599016	+	0.800737i	$0.704442\pi$
$710$	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	$-0.749181\pi$
$719$		−	732971.i		−	1.41785i	0.705286	−	0.708923i	$-0.250819\pi$
$720$	−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	0.729951	+	0.683500i	$0.239543\pi$
$727$	286018.	+	880274.i	0.541159	+	1.66552i	−0.188791	+	0.982017i	$0.560457\pi$
$728$	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	0.629889	+	0.776685i	$0.283100\pi$
$733$	−180650.	+	555985.i	−0.336226	+	1.03480i	−0.966115	+	0.258112i	$0.916900\pi$
$734$	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	$-0.866767\pi$
$739$		−	443939.i		−	0.812896i	0.913674	−	0.406448i	$-0.133233\pi$
$740$	−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	$0.136593\pi$
$743$			459382.i			0.832140i	−0.909333	+	0.416070i	$0.863407\pi$
$744$	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	−0.995855	−	0.0909537i	$-0.971008\pi$
$751$	−77116.0	+	237338.i	−0.136730	+	0.420812i	0.859125	+	0.511766i	$0.171008\pi$
$752$	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	0.188555	+	0.982063i	$0.439620\pi$
$757$	−460564.	+	633913.i	−0.803709	+	1.10621i	−0.992264	+	0.124148i	$0.960380\pi$
$758$	−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	−0.603020	−	0.797726i	$-0.706036\pi$
$761$	−360203.	+	117037.i	−0.621982	+	0.202094i	−0.0189622	+	0.999820i	$0.506036\pi$
$762$	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	0.989954	−	0.141392i	$-0.0451578\pi$
$773$	328384.	+	451981.i	0.549569	+	0.756417i	−0.440384	+	0.897809i	$0.645158\pi$
$774$			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	−0.991503	−	0.130082i	$-0.958476\pi$
$787$	−500962.	−	689515.i	−0.808827	−	1.11325i	0.182676	−	0.983173i	$-0.441524\pi$
$788$	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	0.147711	−	0.989031i	$-0.452809\pi$
$797$	539007.	−	175134.i	0.848550	−	0.275711i	0.700839	+	0.713320i	$0.252809\pi$
$798$	−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	−0.402842	−	0.915270i	$-0.631977\pi$
$809$	387529.	−	533388.i	0.592116	−	0.814978i	0.994958	+	0.100291i	$0.0319775\pi$
$810$	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	−0.699324	−	0.714805i	$-0.746516\pi$
$821$	132515.	−	182392.i	0.196598	−	0.270595i	0.895923	+	0.444210i	$0.146516\pi$
$822$	208301.	+	151340.i	0.308282	+	0.223980i
$823$	703604.	−	228615.i	1.03879	−	0.337524i	0.260531	−	0.965465i	$-0.416102\pi$
$823$	703604.	−	228615.i	1.03879	−	0.337524i	0.778261	+	0.627941i	$0.216102\pi$
$824$	−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	−0.992247	−	0.124279i	$-0.960338\pi$
$827$	−549757.	−	756676.i	−0.803822	−	1.10637i	0.188425	−	0.982088i	$-0.439662\pi$
$828$	167542.	−	54437.6i	0.244378	−	0.0794033i
$829$	587850.	−	191004.i	0.855377	−	0.277929i	0.151681	−	0.988430i	$-0.451531\pi$
$829$	587850.	−	191004.i	0.855377	−	0.277929i	0.703697	+	0.710501i	$0.251531\pi$
$830$	−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	−0.965116	−	0.261821i	$-0.915677\pi$
$839$	−714020.	+	518766.i	−1.01435	+	0.736966i	−0.0492308	+	0.998787i	$0.515677\pi$
$840$	−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	0.531561	−	0.847020i	$-0.321605\pi$
$853$	−79848.4	−	58013.3i	−0.109741	−	0.0797314i	−0.641302	+	0.767288i	$0.721605\pi$
$854$	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	−0.802069	−	0.597232i	$-0.796267\pi$
$857$	145320.	−	447248.i	0.197862	−	0.608958i	0.999931	−	0.0117262i	$-0.00373266\pi$
$858$	−115460.	−	158917.i	−0.156840	−	0.215872i
$859$	−830400.	+	269813.i	−1.12538	+	0.365659i	−0.811820	−	0.583908i	$-0.801523\pi$
$859$	−830400.	+	269813.i	−1.12538	+	0.365659i	−0.313564	+	0.949567i	$0.601523\pi$
$860$	−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	$0.258845\pi$
$863$			1.08212e6i			1.45296i	−0.687188	+	0.726480i	$0.741155\pi$
$864$	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	0.989776	+	0.142633i	$0.0455568\pi$
$877$	209870.	+	645915.i	0.272868	+	0.839800i	−0.716908	+	0.697168i	$0.754443\pi$
$878$	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	−0.727177	−	0.686450i	$-0.759168\pi$
$881$	116723.	−	160656.i	0.150385	−	0.206988i	0.877563	+	0.479462i	$0.159168\pi$
$882$	185545.	+	571050.i	0.238513	+	0.734069i
$883$	168535.	−	231969.i	0.216157	−	0.297515i	−0.687145	−	0.726521i	$-0.741136\pi$
$883$	168535.	−	231969.i	0.216157	−	0.297515i	0.903302	+	0.429006i	$0.141136\pi$
$884$	−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	−0.999983	−	0.00590147i	$-0.998121\pi$
$887$	−1.02546e6	+	745040.i	−1.30338	+	0.946962i	−0.303399	+	0.952864i	$0.598121\pi$
$888$	−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	0.875005	+	0.484114i	$0.160858\pi$
$907$	371563.	+	1.14355e6i	0.451666	+	1.39009i	−0.423339	+	0.905971i	$0.639142\pi$
$908$	−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	0.649799	−	0.760106i	$-0.274853\pi$
$911$	−227318.	−	312877.i	−0.273903	−	0.376996i	−0.923703	+	0.383110i	$0.874853\pi$
$912$	−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	−0.981075	−	0.193630i	$-0.937974\pi$
$919$	−62122.3	+	191193.i	−0.0735557	+	0.226381i	0.907519	+	0.420011i	$0.137974\pi$
$920$	−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	$0.102689\pi$
$929$			547235.i			0.634078i	−0.948412	+	0.317039i	$0.897311\pi$
$930$	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	−0.979724	−	0.200350i	$-0.935792\pi$
$937$	−60885.4	+	187386.i	−0.0693480	+	0.213431i	0.910376	+	0.413781i	$0.135792\pi$
$938$	−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	0.308553	−	0.951207i	$-0.400155\pi$
$941$	−821.562	−	266.942i	−0.000927814	−	0.000301465i	−0.309481	+	0.950906i	$0.600155\pi$
$942$	−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	0.255637	−	0.966773i	$-0.417715\pi$
$947$	924347.	−	300339.i	1.03071	−	0.334897i	0.775070	+	0.631876i	$0.217715\pi$
$948$	−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	−0.132305	−	0.991209i	$-0.542238\pi$
$953$	311767.	−	101299.i	0.343277	−	0.111537i	0.475581	+	0.879672i	$0.342238\pi$
$954$	−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	$0.0432306\pi$
$967$			253214.i			0.270791i	−0.990792	+	0.135396i	$0.956769\pi$
$968$	−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	−0.832616	−	0.553851i	$-0.813158\pi$
$971$	−530975.	+	385776.i	−0.563165	+	0.409163i	0.269451	+	0.963014i	$0.413158\pi$
$972$	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	0.935294	−	0.353872i	$-0.115135\pi$
$977$	847396.	+	615669.i	0.887764	+	0.644998i	−0.0475303	+	0.998870i	$0.515135\pi$
$978$	−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	−0.251001	−	0.967987i	$-0.580760\pi$
$983$	111030.	−	36075.9i	0.114904	−	0.0373344i	0.365904	+	0.930652i	$0.380760\pi$
$984$	−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	$-0.708039\pi$
$991$		−	1.55938e6i		−	1.58783i	0.608027	−	0.793916i	$-0.291961\pi$
$992$	−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.15.2	✓	36
31.29	odd	10	inner	31.5.f.a.29.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.5.f.a.15.2	✓	36	1.1	even	1	trivial
31.5.f.a.29.2	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+(-3.99299 + 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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