LMFDB - Embedded newform 49.7.h.a.3.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,7,Mod(3,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.3"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	49.h (of order $42$, degree $12$, 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:	$11.2726500974$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			3.2
Character	$\chi$	$=$	49.3
Dual form			49.7.h.a.33.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.28359 + 13.4624i) q^{2} +(11.4646 + 0.859156i) q^{3} +(-106.404 - 98.7284i) q^{4} +(-126.721 + 185.865i) q^{5} +(-72.1408 + 149.802i) q^{6} +(71.8347 + 335.393i) q^{7} +(1057.40 - 509.218i) q^{8} +(-590.158 - 88.9520i) q^{9} +(-1832.64 - 2688.00i) q^{10} +(-324.476 + 48.9069i) q^{11} +(-1135.06 - 1223.30i) q^{12} +(2769.33 - 2208.47i) q^{13} +(-4894.74 - 805.017i) q^{14} +(-1612.49 + 2022.00i) q^{15} +(574.179 + 7661.89i) q^{16} +(-1246.33 + 4040.49i) q^{17} +(4315.66 - 7474.94i) q^{18} +(5629.56 - 3250.23i) q^{19} +(31833.7 - 7265.84i) q^{20} +(535.404 + 3906.88i) q^{21} +(1056.00 - 4626.62i) q^{22} +(-8248.29 + 2544.26i) q^{23} +(12560.2 - 4929.52i) q^{24} +(-12779.2 - 32561.0i) q^{25} +(15099.2 + 48950.4i) q^{26} +(-14860.5 - 3391.82i) q^{27} +(25469.4 - 42779.3i) q^{28} +(2880.45 + 12620.1i) q^{29} +(-18701.2 - 32391.4i) q^{30} +(23514.6 + 13576.2i) q^{31} +(-34405.9 - 10612.8i) q^{32} +(-3762.02 + 281.924i) q^{33} +(-47809.5 - 38126.8i) q^{34} +(-71440.9 - 29149.7i) q^{35} +(54013.0 + 67730.2i) q^{36} +(-23601.9 + 21899.3i) q^{37} +(14011.5 + 92960.2i) q^{38} +(33646.8 - 22940.0i) q^{39} +(-39348.8 + 261062. i) q^{40} +(-17414.8 - 36162.3i) q^{41} +(-55424.8 - 13434.6i) q^{42} +(-128660. - 61959.2i) q^{43} +(39354.0 + 26831.1i) q^{44} +(91318.3 - 98417.7i) q^{45} +(9328.82 - 124484. i) q^{46} +(-110356. - 43311.5i) q^{47} +88334.1i q^{48} +(-107329. + 48185.8i) q^{49} +505868. q^{50} +(-17760.1 + 45252.0i) q^{51} +(-512706. - 38422.0i) q^{52} +(61083.2 + 56676.9i) q^{53} +(124179. - 182137. i) q^{54} +(32027.7 - 66506.2i) q^{55} +(246746. + 318066. i) q^{56} +(67333.3 - 32426.0i) q^{57} +(-185116. - 27901.7i) q^{58} +(-44912.6 - 65874.7i) q^{59} +(371205. - 55950.1i) q^{60} +(140173. + 151071. i) q^{61} +(-307009. + 244831. i) q^{62} +(-12559.9 - 204325. i) q^{63} +(18067.8 - 22656.3i) q^{64} +(59545.5 + 794580. i) q^{65} +(16081.6 - 52135.3i) q^{66} +(162480. - 281424. i) q^{67} +(531526. - 306876. i) q^{68} +(-96749.5 + 22082.4i) q^{69} +(769889. - 807749. i) q^{70} +(-103250. + 452368. i) q^{71} +(-669330. + 206461. i) q^{72} +(-380463. + 149321. i) q^{73} +(-170114. - 433445. i) q^{74} +(-118534. - 384279. i) q^{75} +(-919898. - 209961. i) q^{76} +(-39711.7 - 105314. i) q^{77} +(131051. + 574171. i) q^{78} +(-12541.4 - 21722.4i) q^{79} +(-1.49684e6 - 864200. i) q^{80} +(248298. + 76589.9i) q^{81} +(578843. - 43378.3i) q^{82} +(-540517. - 431048. i) q^{83} +(328751. - 468567. i) q^{84} +(-593051. - 743662. i) q^{85} +(1.51390e6 - 1.40470e6i) q^{86} +(22180.7 + 147160. i) q^{87} +(-318197. + 216943. i) q^{88} +(-48794.4 + 323729. i) q^{89} +(842447. + 1.74936e6i) q^{90} +(939639. + 770171. i) q^{91} +(1.12884e6 + 543621. i) q^{92} +(257922. + 175848. i) q^{93} +(1.16615e6 - 1.25681e6i) q^{94} +(-109278. + 1.45821e6i) q^{95} +(-385333. - 151232. i) q^{96} +955906. i q^{97} +(-81614.8 - 1.69949e6i) q^{98} +195842. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 13 q^{2} - 11 q^{3} + 819 q^{4} - 179 q^{5} + 770 q^{6} + 392 q^{7} + 828 q^{8} - 1160 q^{9} - 2594 q^{10} - 5305 q^{11} + 7497 q^{12} - 14 q^{13} - 11403 q^{14} - 6196 q^{15} + 27903 q^{16} - 5107 q^{17}+ \cdots - 4449616 q^{99}+O(q^{100}) $ 324 * q - 13 * q^2 - 11 * q^3 + 819 * q^4 - 179 * q^5 + 770 * q^6 + 392 * q^7 + 828 * q^8 - 1160 * q^9 - 2594 * q^10 - 5305 * q^11 + 7497 * q^12 - 14 * q^13 - 11403 * q^14 - 6196 * q^15 + 27903 * q^16 - 5107 * q^17 - 11538 * q^18 - 30006 * q^19 - 50190 * q^20 + 8953 * q^21 + 33042 * q^22 + 54531 * q^23 + 90184 * q^24 - 92804 * q^25 - 93366 * q^26 - 11774 * q^27 - 19180 * q^28 - 80398 * q^29 + 15851 * q^30 + 39378 * q^31 - 197841 * q^32 + 36697 * q^33 - 54698 * q^34 - 819 * q^35 + 706300 * q^36 + 15331 * q^37 - 304462 * q^38 - 179298 * q^39 - 515414 * q^40 - 116046 * q^41 + 1203482 * q^42 - 225018 * q^43 + 1373764 * q^44 + 465772 * q^45 + 1100364 * q^46 + 270021 * q^47 - 767900 * q^49 - 1164040 * q^50 - 1215743 * q^51 - 3954790 * q^52 + 141807 * q^53 - 1093487 * q^54 + 991354 * q^55 - 596680 * q^56 - 388207 * q^57 + 381012 * q^58 + 2015849 * q^59 + 5807298 * q^60 + 258821 * q^61 - 525742 * q^62 - 1265432 * q^63 + 872972 * q^64 - 70154 * q^65 + 497766 * q^66 - 324190 * q^67 - 799617 * q^68 - 2216774 * q^69 + 56140 * q^70 - 1031026 * q^71 + 4633092 * q^72 + 1268305 * q^73 - 1444192 * q^74 - 1699244 * q^75 - 5464011 * q^76 - 2274741 * q^77 - 1285956 * q^78 - 515710 * q^79 + 8314050 * q^80 - 1069027 * q^81 + 357910 * q^82 - 3183054 * q^83 - 10099096 * q^84 - 1596848 * q^85 - 5387681 * q^86 - 4197040 * q^87 - 1024645 * q^88 + 983769 * q^89 + 18547774 * q^90 + 13421086 * q^91 + 5294506 * q^92 + 15477850 * q^93 + 8903632 * q^94 + 5236430 * q^95 + 7804258 * q^96 - 10234553 * q^98 - 4449616 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{42}\right)$

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 $

$2$	−5.28359	+	13.4624i	−0.660449	+	1.68280i	0.0679892	+	0.997686i	$0.478342\pi$
$2$	−5.28359	+	13.4624i	−0.660449	+	1.68280i	−0.728438	+	0.685111i	$0.759754\pi$
$3$	11.4646	+	0.859156i	0.424616	+	0.0318206i	0.285325	−	0.958431i	$-0.407899\pi$
$3$	11.4646	+	0.859156i	0.424616	+	0.0318206i	0.139291	+	0.990251i	$0.455518\pi$
$4$	−106.404	−	98.7284i	−1.66256	−	1.54263i
$5$	−126.721	+	185.865i	−1.01377	+	1.48692i	−0.146414	+	0.989223i	$0.546773\pi$
$5$	−126.721	+	185.865i	−1.01377	+	1.48692i	−0.867351	+	0.497697i	$0.834179\pi$
$6$	−72.1408	+	149.802i	−0.333985	+	0.693527i
$7$	71.8347	+	335.393i	0.209431	+	0.977823i
$7$	71.8347	+	335.393i	0.209431	+	0.977823i
$8$	1057.40	−	509.218i	2.06524	−	0.994566i
$9$	−590.158	−	88.9520i	−0.809544	−	0.122019i
$10$	−1832.64	−	2688.00i	−1.83264	−	2.68800i
$11$	−324.476	+	48.9069i	−0.243784	+	0.0367445i	−0.269797	−	0.962917i	$-0.586957\pi$
$11$	−324.476	+	48.9069i	−0.243784	+	0.0367445i	0.0260138	+	0.999662i	$0.491719\pi$
$12$	−1135.06	−	1223.30i	−0.656863	−	0.707930i
$13$	2769.33	−	2208.47i	1.26051	−	1.00522i	0.261304	−	0.965257i	$-0.415847\pi$
$13$	2769.33	−	2208.47i	1.26051	−	1.00522i	0.999201	−	0.0399630i	$-0.0127240\pi$
$14$	−4894.74	−	805.017i	−1.78380	−	0.293373i
$15$	−1612.49	+	2022.00i	−0.477776	+	0.599112i
$16$	574.179	+	7661.89i	0.140180	+	1.87058i
$17$	−1246.33	+	4040.49i	−0.253679	+	0.822408i	0.735732	+	0.677272i	$0.236838\pi$
$17$	−1246.33	+	4040.49i	−0.253679	+	0.822408i	−0.989412	+	0.145136i	$0.953638\pi$
$18$	4315.66	−	7474.94i	0.739997	−	1.28171i
$19$	5629.56	−	3250.23i	0.820755	−	0.473863i	−0.0299215	−	0.999552i	$-0.509526\pi$
$19$	5629.56	−	3250.23i	0.820755	−	0.473863i	0.850677	+	0.525689i	$0.176192\pi$
$20$	31833.7	−	7265.84i	3.97922	−	0.908230i
$21$	535.404	+	3906.88i	0.0578127	+	0.421864i
$22$	1056.00	−	4626.62i	0.0991732	−	0.434506i
$23$	−8248.29	+	2544.26i	−0.677923	+	0.209111i	−0.614549	−	0.788878i	$-0.710662\pi$
$23$	−8248.29	+	2544.26i	−0.677923	+	0.209111i	−0.0633735	+	0.997990i	$0.520186\pi$
$24$	12560.2	−	4929.52i	0.908581	−	0.356592i
$25$	−12779.2	−	32561.0i	−0.817871	−	2.08390i
$26$	15099.2	+	48950.4i	0.859081	+	2.78507i
$27$	−14860.5	−	3391.82i	−0.754994	−	0.172322i
$28$	25469.4	−	42779.3i	1.16023	−	1.94877i
$29$	2880.45	+	12620.1i	0.118105	+	0.517450i	0.999023	+	0.0441828i	$0.0140684\pi$
$29$	2880.45	+	12620.1i	0.118105	+	0.517450i	−0.880919	+	0.473267i	$0.843074\pi$
$30$	−18701.2	−	32391.4i	−0.692637	−	1.19968i
$31$	23514.6	+	13576.2i	0.789319	+	0.455713i	0.839723	−	0.543015i	$-0.182718\pi$
$31$	23514.6	+	13576.2i	0.789319	+	0.455713i	−0.0504039	+	0.998729i	$0.516051\pi$
$32$	−34405.9	−	10612.8i	−1.04998	−	0.323877i
$33$	−3762.02	+	281.924i	−0.104684	+	0.00784496i
$34$	−47809.5	−	38126.8i	−1.21640	−	0.970050i
$35$	−71440.9	−	29149.7i	−1.66626	−	0.679877i
$36$	54013.0	+	67730.2i	1.15769	+	1.45169i
$37$	−23601.9	+	21899.3i	−0.465952	+	0.432341i	−0.877883	−	0.478874i	$-0.841045\pi$
$37$	−23601.9	+	21899.3i	−0.465952	+	0.432341i	0.411931	+	0.911215i	$0.364854\pi$
$38$	14011.5	+	92960.2i	0.255349	+	1.69413i
$39$	33646.8	−	22940.0i	0.567218	−	0.386722i
$40$	−39348.8	+	261062.i	−0.614825	+	4.07910i
$41$	−17414.8	−	36162.3i	−0.252678	−	0.524691i	0.735589	−	0.677428i	$-0.236906\pi$
$41$	−17414.8	−	36162.3i	−0.252678	−	0.524691i	−0.988267	+	0.152737i	$0.951191\pi$
$42$	−55424.8	−	13434.6i	−0.748094	−	0.181333i
$43$	−128660.	−	61959.2i	−1.61822	−	0.779293i	−0.618240	−	0.785989i	$-0.712154\pi$
$43$	−128660.	−	61959.2i	−1.61822	−	0.779293i	−0.999978	+	0.00669649i	$0.997868\pi$
$44$	39354.0	+	26831.1i	0.461988	+	0.314978i
$45$	91318.3	−	98417.7i	1.00212	−	1.08003i
$46$	9328.82	−	124484.i	0.0958414	−	1.27891i
$47$	−110356.	−	43311.5i	−1.06292	−	0.417167i	−0.231517	−	0.972831i	$-0.574369\pi$
$47$	−110356.	−	43311.5i	−1.06292	−	0.417167i	−0.831407	+	0.555664i	$0.812464\pi$
$48$			88334.1i			0.798738i
$49$	−107329.	+	48185.8i	−0.912278	+	0.409572i
$50$	505868.			4.04695
$51$	−17760.1	+	45252.0i	−0.133886	+	0.341136i
$52$	−512706.	−	38422.0i	−3.64635	−	0.273256i
$53$	61083.2	+	56676.9i	0.410293	+	0.380696i	0.858142	−	0.513413i	$-0.171619\pi$
$53$	61083.2	+	56676.9i	0.410293	+	0.380696i	−0.447848	+	0.894109i	$0.647810\pi$
$54$	124179.	−	182137.i	0.788619	−	1.15669i
$55$	32027.7	−	66506.2i	0.192503	−	0.399737i
$56$	246746.	+	318066.i	1.40503	+	1.81115i
$57$	67333.3	−	32426.0i	0.363585	−	0.175093i
$58$	−185116.	−	27901.7i	−0.948766	−	0.143003i
$59$	−44912.6	−	65874.7i	−0.218682	−	0.320747i	0.701184	−	0.712980i	$-0.252655\pi$
$59$	−44912.6	−	65874.7i	−0.218682	−	0.320747i	−0.919866	+	0.392233i	$0.871703\pi$
$60$	371205.	−	55950.1i	1.71854	−	0.259028i
$61$	140173.	+	151071.i	0.617555	+	0.665566i	0.961939	−	0.273263i	$-0.0881029\pi$
$61$	140173.	+	151071.i	0.617555	+	0.665566i	−0.344385	+	0.938829i	$0.611912\pi$
$62$	−307009.	+	244831.i	−1.28818	+	1.02729i
$63$	−12559.9	−	204325.i	−0.0502302	−	0.817146i
$64$	18067.8	−	22656.3i	0.0689231	−	0.0864269i
$65$	59545.5	+	794580.i	0.216825	+	2.89333i
$66$	16081.6	−	52135.3i	0.0559368	−	0.181343i
$67$	162480.	−	281424.i	0.540227	−	0.935700i	−0.458664	−	0.888610i	$-0.651672\pi$
$67$	162480.	−	281424.i	0.540227	−	0.935700i	0.998891	−	0.0470905i	$-0.0149949\pi$
$68$	531526.	−	306876.i	1.69043	−	0.975971i
$69$	−96749.5	+	22082.4i	−0.294511	+	0.0672202i
$70$	769889.	−	807749.i	2.24457	−	2.35495i
$71$	−103250.	+	452368.i	−0.288480	+	1.26391i	0.598132	+	0.801398i	$0.295910\pi$
$71$	−103250.	+	452368.i	−0.288480	+	1.26391i	−0.886612	+	0.462515i	$0.846947\pi$
$72$	−669330.	+	206461.i	−1.79326	+	0.553147i
$73$	−380463.	+	149321.i	−0.978012	+	0.383841i	−0.799876	−	0.600165i	$-0.795102\pi$
$73$	−380463.	+	149321.i	−0.978012	+	0.383841i	−0.178135	+	0.984006i	$0.557006\pi$
$74$	−170114.	−	433445.i	−0.419804	−	1.06964i
$75$	−118534.	−	384279.i	−0.280970	−	0.910884i
$76$	−919898.	−	209961.i	−2.09555	−	0.478296i
$77$	−39711.7	−	105314.i	−0.0869854	−	0.230682i
$78$	131051.	+	574171.i	0.276157	+	1.20992i
$79$	−12541.4	−	21722.4i	−0.0254370	−	0.0440582i	0.853027	−	0.521867i	$-0.174764\pi$
$79$	−12541.4	−	21722.4i	−0.0254370	−	0.0440582i	−0.878464	+	0.477809i	$0.841431\pi$
$80$	−1.49684e6	−	864200.i	−2.92351	−	1.68789i
$81$	248298.	+	76589.9i	0.467217	+	0.144117i
$82$	578843.	−	43378.3i	1.04983	−	0.0786739i
$83$	−540517.	−	431048.i	−0.945311	−	0.753860i	0.0239964	−	0.999712i	$-0.492361\pi$
$83$	−540517.	−	431048.i	−0.945311	−	0.753860i	−0.969307	+	0.245852i	$0.920932\pi$
$84$	328751.	−	468567.i	0.554663	−	0.790558i
$85$	−593051.	−	743662.i	−0.965684	−	1.21093i
$86$	1.51390e6	−	1.40470e6i	2.38014	−	2.20845i
$87$	22180.7	+	147160.i	0.0336836	+	0.223476i
$88$	−318197.	+	216943.i	−0.466926	+	0.318345i
$89$	−48794.4	+	323729.i	−0.0692149	+	0.459211i	0.927197	+	0.374574i	$0.122211\pi$
$89$	−48794.4	+	323729.i	−0.0692149	+	0.459211i	−0.996412	+	0.0846368i	$0.973027\pi$
$90$	842447.	+	1.74936e6i	1.15562	+	2.39967i
$91$	939639.	+	770171.i	1.24692	+	1.02203i
$92$	1.12884e6	+	543621.i	1.44967	+	0.698124i
$93$	257922.	+	175848.i	0.320656	+	0.218620i
$94$	1.16615e6	−	1.25681e6i	1.40401	−	1.51317i
$95$	−109278.	+	1.45821e6i	−0.127456	+	1.70078i
$96$	−385333.	−	151232.i	−0.435534	−	0.170934i
$97$			955906.i			1.04737i	0.851912	+	0.523685i	$0.175443\pi$
$97$			955906.i			1.04737i	−0.851912	+	0.523685i	$0.824557\pi$
$98$	−81614.8	−	1.69949e6i	−0.0867143	−	1.80568i
$99$	195842.			0.201837
$100$	−1.85493e6	+	4.72629e6i	−1.85493	+	4.72629i
$101$	−1.02987e6	−	77177.9i	−0.999579	−	0.0749081i	−0.435123	−	0.900371i	$-0.643295\pi$
$101$	−1.02987e6	−	77177.9i	−0.999579	−	0.0749081i	−0.564456	+	0.825463i	$0.690914\pi$
$102$	−515362.	−	478186.i	−0.485637	−	0.450606i
$103$	−268762.	+	394201.i	−0.245955	+	0.360750i	−0.929287	−	0.369358i	$-0.879578\pi$
$103$	−268762.	+	394201.i	−0.245955	+	0.360750i	0.683332	+	0.730108i	$0.260530\pi$
$104$	1.80370e6	−	3.74543e6i	1.60349	−	3.32967i
$105$	−793999.	−	395570.i	−0.685887	−	0.341708i
$106$	−1.08575e6	+	522867.i	−0.911613	+	0.439010i
$107$	123205.	+	18570.1i	0.100572	+	0.0151588i	0.199135	−	0.979972i	$-0.436187\pi$
$107$	123205.	+	18570.1i	0.100572	+	0.0151588i	−0.0985636	+	0.995131i	$0.531425\pi$
$108$	1.24635e6	+	1.82806e6i	0.989394	+	1.45117i
$109$	1.12747e6	−	169939.i	0.870614	−	0.131224i	0.301484	−	0.953471i	$-0.402518\pi$
$109$	1.12747e6	−	169939.i	0.870614	−	0.131224i	0.569130	+	0.822247i	$0.307280\pi$
$110$	726111.	+	782561.i	0.545538	+	0.587950i
$111$	−289402.	+	230790.i	−0.211608	+	0.168752i
$112$	−2.52850e6	+	742966.i	−1.79974	+	0.528828i
$113$	1.34466e6	−	1.68615e6i	0.931916	−	1.16859i	−0.0535248	−	0.998567i	$-0.517046\pi$
$113$	1.34466e6	−	1.68615e6i	0.931916	−	1.16859i	0.985441	−	0.170019i	$-0.0543830\pi$
$114$	80769.4	+	1.07779e6i	0.0545170	+	0.727479i
$115$	572339.	−	1.85548e6i	0.376322	−	1.22001i
$116$	939470.	−	1.62721e6i	0.601879	−	1.04248i
$117$	−1.83079e6	+	1.05701e6i	−1.14309	+	0.659964i
$118$	1.12413e6	−	256575.i	0.684180	−	0.156160i
$119$	−1.44468e6	−	127762.i	−0.857298	−	0.0758161i
$120$	−675413.	+	2.95918e6i	−0.390864	+	1.71249i
$121$	−1.58996e6	+	490439.i	−0.897493	+	0.276840i
$122$	−2.77439e6	+	1.08887e6i	−1.52788	+	0.599647i
$123$	−168586.	−	429549.i	−0.0905952	−	0.230833i
$124$	−1.16169e6	−	3.76612e6i	−0.609293	−	1.97528i
$125$	4.24457e6	+	968796.i	2.17322	+	0.496023i
$126$	2.81706e6	+	910484.i	1.40827	+	0.455156i
$127$	65123.0	+	285322.i	0.0317924	+	0.139291i	0.988333	−	0.152307i	$-0.0486701\pi$
$127$	65123.0	+	285322.i	0.0317924	+	0.139291i	−0.956541	+	0.291598i	$0.905813\pi$
$128$	−942631.	−	1.63268e6i	−0.449481	−	0.778524i
$129$	−1.42180e6	−	820879.i	−0.662324	−	0.382393i
$130$	−1.10116e7	−	3.39661e6i	−5.01209	−	1.54602i
$131$	587848.	−	44053.1i	0.261487	−	0.0195958i	0.0566587	−	0.998394i	$-0.481955\pi$
$131$	587848.	−	44053.1i	0.261487	−	0.0195958i	0.204829	+	0.978798i	$0.434336\pi$
$132$	428127.	+	341420.i	0.186145	+	0.148446i
$133$	1.49450e6	+	1.65464e6i	0.635246	+	0.703312i
$134$	2.93016e6	+	3.67430e6i	1.21780	+	1.52707i
$135$	2.51356e6	−	2.33224e6i	1.02162	−	0.947921i
$136$	739623.	+	4.90707e6i	0.294031	+	1.95077i
$137$	−36632.5	+	24975.6i	−0.0142464	+	0.00971302i	−0.570422	−	0.821352i	$-0.693220\pi$
$137$	−36632.5	+	24975.6i	−0.0142464	+	0.00971302i	0.556176	+	0.831065i	$0.312268\pi$
$138$	213903.	−	1.41915e6i	0.0813916	−	0.539998i
$139$	293249.	+	608937.i	0.109192	+	0.226740i	0.948404	−	0.317065i	$-0.102697\pi$
$139$	293249.	+	608937.i	0.109192	+	0.226740i	−0.839212	+	0.543805i	$0.816983\pi$
$140$	4.72368e6	+	1.01549e7i	1.72146	+	3.70076i
$141$	−1.22798e6	−	591364.i	−0.438060	−	0.210959i
$142$	−5.54442e6	−	3.78012e6i	−1.93638	−	1.32020i
$143$	−790572.	+	852034.i	−0.270354	+	0.291373i
$144$	342684.	−	4.57280e6i	0.114764	−	1.53142i
$145$	−2.71065e6	−	1.06385e6i	−0.889138	−	0.348961i
$146$		−	5.91089e6i		−	1.89930i
$147$	−1.27188e6	+	460221.i	−0.400401	+	0.144882i
$148$	4.67342e6			1.44162
$149$	1.38303e6	−	3.52391e6i	0.418094	−	1.06529i	−0.554378	−	0.832265i	$-0.687044\pi$
$149$	1.38303e6	−	3.52391e6i	0.418094	−	1.06529i	0.972472	−	0.233020i	$-0.0748609\pi$
$150$	5.79960e6	+	434620.i	1.71840	+	0.128776i
$151$	−268922.	−	249523.i	−0.0781080	−	0.0724737i	0.640153	−	0.768248i	$-0.278871\pi$
$151$	−268922.	−	249523.i	−0.0781080	−	0.0724737i	−0.718261	+	0.695774i	$0.755062\pi$
$152$	4.29763e6	−	6.30347e6i	1.22377	−	1.79494i
$153$	1.09494e6	−	2.27367e6i	0.305714	−	0.634822i
$154$	1.62760e6	+	21822.2i	0.445640	+	0.00597497i
$155$	−5.50312e6	+	2.65016e6i	−1.47779	+	0.711668i
$156$	−5.84498e6	−	880989.i	−1.53960	−	0.232058i
$157$	1.66905e6	+	2.44805e6i	0.431292	+	0.632589i	0.978947	−	0.204115i	$-0.0654318\pi$
$157$	1.66905e6	+	2.44805e6i	0.431292	+	0.632589i	−0.547655	+	0.836704i	$0.684479\pi$
$158$	358699.	−	54065.2i	0.0909409	−	0.0137071i
$159$	651603.	+	702260.i	0.162103	+	0.174706i
$160$	6.33248e6	−	5.04998e6i	1.54602	−	1.23291i
$161$	−1.44584e6	−	2.58366e6i	−0.346452	−	0.619094i
$162$	−2.34299e6	+	2.93802e6i	−0.551094	+	0.691050i
$163$	317377.	+	4.23510e6i	0.0732846	+	0.977915i	0.905743	+	0.423827i	$0.139314\pi$
$163$	317377.	+	4.23510e6i	0.0732846	+	0.977915i	−0.832458	+	0.554088i	$0.813067\pi$
$164$	−1.71724e6	+	5.56714e6i	−0.389313	+	1.26212i
$165$	424325.	−	734953.i	0.0944598	−	0.163609i
$166$	8.65880e6	−	4.99916e6i	1.89292	−	1.09288i
$167$	429839.	−	98107.9i	0.0922904	−	0.0210647i	−0.176126	−	0.984368i	$-0.556357\pi$
$167$	429839.	−	98107.9i	0.0922904	−	0.0210647i	0.268417	+	0.963303i	$0.413500\pi$
$168$	2.55559e6	+	3.85851e6i	0.538969	+	0.813751i
$169$	1.71780e6	−	7.52616e6i	0.355887	−	1.55924i
$170$	1.31449e7	−	4.05467e6i	2.67553	−	0.825293i
$171$	−3.61144e6	+	1.41739e6i	−0.722258	+	0.283466i
$172$	7.57276e6	+	1.92951e7i	1.48823	+	3.79194i
$173$	−1.66749e6	−	5.40587e6i	−0.322051	−	1.04406i	−0.961402	−	0.275149i	$-0.911273\pi$
$173$	−1.66749e6	−	5.40587e6i	−0.322051	−	1.04406i	0.639350	−	0.768916i	$-0.279203\pi$
$174$	−2.09831e6	−	478926.i	−0.398311	−	0.0909119i
$175$	1.00027e7	−	6.62508e6i	1.86640	−	1.23617i
$176$	−561026.	−	2.45802e6i	−0.102907	−	0.450865i
$177$	−458310.	−	793817.i	−0.0826494	−	0.143153i
$178$	−4.10036e6	−	2.36734e6i	−0.727046	−	0.419760i
$179$	3.72203e6	+	1.14809e6i	0.648965	+	0.200179i	0.601724	−	0.798704i	$-0.294481\pi$
$179$	3.72203e6	+	1.14809e6i	0.648965	+	0.200179i	0.0472411	+	0.998884i	$0.484957\pi$
$180$	−1.94332e7	+	1.45632e6i	−3.33217	+	0.249712i
$181$	−4.12724e6	−	3.29137e6i	−0.696024	−	0.555061i	0.210304	−	0.977636i	$-0.432555\pi$
$181$	−4.12724e6	−	3.29137e6i	−0.696024	−	0.555061i	−0.906328	+	0.422575i	$0.861126\pi$
$182$	−1.53330e7	+	8.58051e6i	−2.54339	+	1.42331i
$183$	1.47724e6	+	1.85240e6i	0.241045	+	0.302261i
$184$	−7.42617e6	+	6.89048e6i	−1.19210	+	1.10610i
$185$	−1.07948e6	−	7.16186e6i	−0.170490	−	1.13113i
$186$	−3.73009e6	+	2.54314e6i	−0.579670	+	0.395212i
$187$	206795.	−	1.37200e6i	0.0316239	−	0.209811i
$188$	7.46623e6	+	1.55038e7i	1.12364	+	2.33327i
$189$	70092.0	−	5.22778e6i	0.0103820	−	0.774340i
$190$	−1.90536e7	−	9.17573e6i	−2.77790	−	1.33776i
$191$	9.00693e6	+	6.14082e6i	1.29264	+	0.881305i	0.997253	−	0.0740731i	$-0.0235998\pi$
$191$	9.00693e6	+	6.14082e6i	1.29264	+	0.881305i	0.295385	+	0.955378i	$0.404552\pi$
$192$	226606.	−	244223.i	0.0320160	−	0.0345051i
$193$	−903759.	+	1.20598e7i	−0.125713	+	1.67753i	0.476488	+	0.879181i	$0.341910\pi$
$193$	−903759.	+	1.20598e7i	−0.125713	+	1.67753i	−0.602201	+	0.798345i	$0.705709\pi$
$194$	−1.28688e7	−	5.05062e6i	−1.76251	−	0.691735i
$195$			9.16073e6i			1.23545i
$196$	1.61775e7	+	5.46922e6i	2.14854	+	0.726369i
$197$	−6.55554e6			−0.857452			−0.428726	−	0.903435i	$-0.641037\pi$
$197$	−6.55554e6			−0.857452			−0.428726	+	0.903435i	$0.641037\pi$
$198$	−1.03475e6	+	2.63650e6i	−0.133303	+	0.339651i
$199$	2.90487e6	+	217690.i	0.368610	+	0.0276235i	0.257748	−	0.966212i	$-0.417020\pi$
$199$	2.90487e6	+	217690.i	0.368610	+	0.0276235i	0.110863	+	0.993836i	$0.464639\pi$
$200$	−3.00934e7	−	2.79226e7i	−3.76168	−	3.49033i
$201$	2.10456e6	−	3.08683e6i	0.259164	−	0.380123i
$202$	6.48040e6	−	1.34567e7i	0.786226	−	1.63262i
$203$	−4.02578e6	+	1.87265e6i	−0.481240	+	0.223855i
$204$	6.35740e6	−	3.06156e6i	0.748840	−	0.360622i
$205$	8.92812e6	+	1.34570e6i	1.03633	+	0.156202i
$206$	−3.88685e6	−	5.70097e6i	−0.444628	−	0.652149i
$207$	5.09411e6	−	767813.i	0.574324	−	0.0865655i
$208$	1.85111e7	+	1.99502e7i	2.05704	+	2.21696i
$209$	−1.66770e6	+	1.32995e6i	−0.182675	+	0.145678i
$210$	9.52048e6	−	8.59909e6i	1.02802	−	0.928527i
$211$	−8.37260e6	+	1.04989e7i	−0.891277	+	1.11763i	0.101160	+	0.994870i	$0.467745\pi$
$211$	−8.37260e6	+	1.04989e7i	−0.891277	+	1.11763i	−0.992437	+	0.122756i	$0.960827\pi$
$212$	−903869.	−	1.20613e7i	−0.0948633	−	1.26586i
$213$	−1.57238e6	+	5.09753e6i	−0.162712	+	0.527498i
$214$	−900962.	+	1.56051e6i	−0.0919316	+	0.159230i
$215$	2.78199e7	−	1.60618e7i	2.79924	−	1.61614i
$216$	−1.74407e7	+	3.98074e6i	−1.73063	+	0.395005i
$217$	−2.86419e6	+	8.86188e6i	−0.280300	+	0.867255i
$218$	−3.66931e6	+	1.60763e7i	−0.354173	+	1.55173i
$219$	−4.49016e6	+	1.38503e6i	−0.427494	+	0.131864i
$220$	−9.97393e6	+	3.91448e6i	−0.936695	+	0.367626i
$221$	5.47180e6	+	1.39419e7i	0.506937	+	1.29165i
$222$	−1.57790e6	−	5.11544e6i	−0.144219	−	0.467546i
$223$	−1.04938e7	−	2.39513e6i	−0.946273	−	0.215981i	−0.278576	−	0.960414i	$-0.589863\pi$
$223$	−1.04938e7	−	2.39513e6i	−0.946273	−	0.215981i	−0.667697	+	0.744433i	$0.732720\pi$
$224$	1.08793e6	−	1.23019e7i	0.0967958	−	1.09453i
$225$	4.64541e6	+	2.03529e7i	0.407827	+	1.78681i
$226$	1.55949e7	+	2.70112e7i	1.35101	+	2.34002i
$227$	1.84091e6	+	1.06285e6i	0.157382	+	0.0908644i	0.576623	−	0.817011i	$-0.304370\pi$
$227$	1.84091e6	+	1.06285e6i	0.157382	+	0.0908644i	−0.419241	+	0.907875i	$0.637704\pi$
$228$	−1.03659e7	−	3.19746e6i	−0.874586	−	0.269774i
$229$	−4.88544e6	+	366113.i	−0.406816	+	0.0304866i	−0.276567	−	0.960995i	$-0.589197\pi$
$229$	−4.88544e6	+	366113.i	−0.406816	+	0.0304866i	−0.130249	+	0.991481i	$0.541578\pi$
$230$	2.19551e7	+	1.75086e7i	1.80448	+	1.43903i
$231$	−364799.	−	1.24150e6i	−0.0295950	−	0.100719i
$232$	9.47217e6	+	1.18777e7i	0.758553	+	0.951195i
$233$	−1.29193e7	+	1.19873e7i	−1.02134	+	0.947664i	−0.998643	−	0.0520785i	$-0.983415\pi$
$233$	−1.29193e7	+	1.19873e7i	−1.02134	+	0.947664i	−0.0226958	+	0.999742i	$0.507225\pi$
$234$	−4.55668e6	−	3.02316e7i	−0.355632	−	2.35946i
$235$	2.20345e7	−	1.50228e7i	1.69785	−	1.15757i
$236$	−1.72483e6	+	1.14435e7i	−0.131223	+	0.870607i
$237$	−125120.	−	259815.i	−0.00939902	−	0.0195173i
$238$	9.35311e6	−	1.87738e7i	0.693785	−	1.39259i
$239$	1.13887e6	+	548449.i	0.0834217	+	0.0401738i	0.475129	−	0.879916i	$-0.342401\pi$
$239$	1.13887e6	+	548449.i	0.0834217	+	0.0401738i	−0.391708	+	0.920090i	$0.628116\pi$
$240$	−1.64182e7	−	1.11938e7i	−1.18766	−	0.809733i
$241$	3.17119e6	−	3.41773e6i	0.226554	−	0.244167i	−0.609538	−	0.792757i	$-0.708645\pi$
$241$	3.17119e6	−	3.41773e6i	0.226554	−	0.244167i	0.836091	+	0.548590i	$0.184835\pi$
$242$	1.79825e6	−	2.39960e7i	0.126883	−	1.69314i
$243$	1.31247e7	+	5.15105e6i	0.914680	+	0.358985i
$244$		−	2.99136e7i		−	2.05920i
$245$	4.64469e6	−	2.60548e7i	0.315834	−	1.77169i
$246$	6.67349e6			0.448278
$247$	8.41209e6	−	2.14337e7i	0.558230	−	1.42235i
$248$	3.17776e7	+	2.38140e6i	2.08337	+	0.156127i
$249$	−5.82649e6	−	5.40619e6i	−0.377406	−	0.350182i
$250$	−3.54689e7	+	5.20233e7i	−2.27001	+	3.32949i
$251$	−1.14228e7	+	2.37196e7i	−0.722354	+	1.49998i	0.138080	+	0.990421i	$0.455907\pi$
$251$	−1.14228e7	+	2.37196e7i	−0.722354	+	1.49998i	−0.860434	+	0.509562i	$0.829807\pi$
$252$	−1.88363e7	+	2.29810e7i	−1.17704	+	1.43604i
$253$	2.55194e6	−	1.22895e6i	0.157583	−	0.0758879i
$254$	−4.18520e6	−	630817.i	−0.255397	−	0.0384948i
$255$	−6.16019e6	−	9.03534e6i	−0.371513	−	0.544909i
$256$	2.87942e7	−	4.34003e6i	1.71627	−	0.258686i
$257$	−5.21228e6	−	5.61750e6i	−0.307064	−	0.330936i	0.560601	−	0.828086i	$-0.310570\pi$
$257$	−5.21228e6	−	5.61750e6i	−0.307064	−	0.330936i	−0.867664	+	0.497150i	$0.834380\pi$
$258$	1.85632e7	−	1.48037e7i	1.08092	−	0.862006i
$259$	−9.04033e6	−	6.34278e6i	−0.520337	−	0.365074i
$260$	7.21118e7	−	9.04253e7i	4.10285	−	5.14482i
$261$	−577340.	−	7.70407e6i	−0.0324721	−	0.433310i
$262$	−2.51289e6	+	8.14659e6i	−0.139723	+	0.452972i
$263$	−1.47921e6	+	2.56206e6i	−0.0813133	+	0.140839i	−0.903814	−	0.427925i	$-0.859245\pi$
$263$	−1.47921e6	+	2.56206e6i	−0.0813133	+	0.140839i	0.822501	+	0.568764i	$0.192578\pi$
$264$	−3.83440e6	+	2.21379e6i	−0.208394	+	0.120317i
$265$	−1.82748e7	+	4.17110e6i	−0.982006	+	0.224136i
$266$	−3.01717e7	+	1.13771e7i	−1.60308	+	0.604488i
$267$	−837544.	+	3.66952e6i	−0.0440021	+	0.192786i
$268$	−4.50731e7	+	1.39032e7i	−2.34160	+	0.722288i
$269$	−3.31852e7	+	1.30242e7i	−1.70486	+	0.669107i	−0.999221	−	0.0394668i	$-0.987434\pi$
$269$	−3.31852e7	+	1.30242e7i	−1.70486	+	0.669107i	−0.705637	+	0.708574i	$0.749339\pi$
$270$	1.81169e7	+	4.61611e7i	0.920434	+	2.34523i
$271$	−5.72037e6	−	1.85450e7i	−0.287420	−	0.931791i	−0.978012	−	0.208547i	$-0.933126\pi$
$271$	−5.72037e6	−	1.85450e7i	−0.287420	−	0.931791i	0.690593	−	0.723244i	$-0.257350\pi$
$272$	−3.16734e7	−	7.22925e6i	−1.57394	−	0.359242i
$273$	1.01109e7	+	9.63702e6i	0.496939	+	0.473647i
$274$	−142680.	−	625121.i	−0.00693603	−	0.0303887i
$275$	5.73901e6	+	9.94026e6i	0.275955	+	0.477969i
$276$	1.24747e7	+	7.20227e6i	0.593339	+	0.342564i
$277$	−1.33409e7	−	4.11512e6i	−0.627690	−	0.193617i	−0.0354410	−	0.999372i	$-0.511284\pi$
$277$	−1.33409e7	−	4.11512e6i	−0.627690	−	0.193617i	−0.592249	+	0.805755i	$0.701760\pi$
$278$	−9.74715e6	+	730448.i	−0.453673	+	0.0339981i
$279$	−1.26697e7	−	1.01037e7i	−0.583383	−	0.465232i
$280$	−9.03852e7	+	5.55600e6i	−4.11740	+	0.253098i
$281$	−1.24998e7	−	1.56743e7i	−0.563358	−	0.706428i	0.415817	−	0.909448i	$-0.363496\pi$
$281$	−1.24998e7	−	1.56743e7i	−0.563358	−	0.706428i	−0.979175	+	0.203020i	$0.934924\pi$
$282$	1.44493e7	−	1.34070e7i	0.644317	−	0.597839i
$283$	1.99612e6	+	1.32434e7i	0.0880701	+	0.584307i	0.988722	+	0.149765i	$0.0478516\pi$
$283$	1.99612e6	+	1.32434e7i	0.0880701	+	0.584307i	−0.900652	+	0.434542i	$0.856910\pi$
$284$	5.56478e7	−	3.79400e7i	2.42937	−	1.65631i
$285$	−2.50566e6	+	1.66240e7i	−0.108240	+	0.718125i
$286$	−7.29334e6	−	1.51448e7i	−0.311766	−	0.647388i
$287$	1.08776e7	−	8.43852e6i	0.460137	−	0.356961i
$288$	1.93609e7	+	9.32370e6i	0.810489	+	0.390311i
$289$	5.17115e6	+	3.52563e6i	0.214237	+	0.146064i
$290$	2.86439e7	−	3.08708e7i	1.17446	−	1.26577i
$291$	−821272.	+	1.09591e7i	−0.0333279	+	0.444730i
$292$	5.52250e7	+	2.16742e7i	2.21813	+	0.870552i
$293$			3.02872e7i			1.20408i	0.798466	+	0.602041i	$0.205645\pi$
$293$			3.02872e7i			1.20408i	−0.798466	+	0.602041i	$0.794355\pi$
$294$	524443.	−	1.95542e7i	0.0206375	−	0.769480i
$295$	1.79352e7			0.698617
$296$	−1.38051e7	+	3.51749e7i	−0.532311	+	1.35631i
$297$	4.98777e6	+	373782.i	0.190387	+	0.0142675i
$298$	4.01328e7	+	3.72378e7i	1.51653	+	1.40713i
$299$	−1.72233e7	+	2.52620e7i	−0.644322	+	0.945047i
$300$	−2.53267e7	+	5.25915e7i	−0.938027	+	1.94783i
$301$	1.15385e7	−	4.76024e7i	0.423106	−	1.74554i
$302$	4.78005e6	−	2.30195e6i	0.173545	−	0.0835748i
$303$	−1.17407e7	−	1.76963e6i	−0.422054	−	0.0636144i
$304$	2.81353e7	+	4.12669e7i	1.00145	+	1.46886i
$305$	−4.58416e7	+	6.90951e6i	−1.61570	+	0.243527i
$306$	2.48237e7	+	2.67536e7i	0.866369	+	0.933723i
$307$	1.94807e7	−	1.55353e7i	0.673269	−	0.536914i	−0.226100	−	0.974104i	$-0.572598\pi$
$307$	1.94807e7	−	1.55353e7i	0.673269	−	0.536914i	0.899369	+	0.437190i	$0.144026\pi$
$308$	−6.17200e6	+	1.51265e7i	−0.211239	+	0.517709i
$309$	−3.41993e6	+	4.28846e6i	−0.115916	+	0.145354i
$310$	−6.60124e6	−	8.80874e7i	−0.221585	−	2.95685i
$311$	2.19437e6	−	7.11398e6i	0.0729506	−	0.236500i	−0.911753	−	0.410740i	$-0.865271\pi$
$311$	2.19437e6	−	7.11398e6i	0.0729506	−	0.236500i	0.984703	+	0.174239i	$0.0557467\pi$
$312$	2.38967e7	−	4.13903e7i	0.786818	−	1.36281i
$313$	9.26049e6	−	5.34655e6i	0.301996	−	0.174357i	−0.341343	−	0.939939i	$-0.610882\pi$
$313$	9.26049e6	−	5.34655e6i	0.301996	−	0.174357i	0.643339	+	0.765581i	$0.277549\pi$
$314$	−4.17752e7	+	9.53492e6i	−1.34937	+	0.307984i
$315$	3.95685e7	+	2.35577e7i	1.26595	+	0.753706i
$316$	−810161.	+	3.54955e6i	−0.0256750	+	0.112489i
$317$	4.66290e7	−	1.43831e7i	1.46379	−	0.451519i	0.542386	−	0.840130i	$-0.317521\pi$
$317$	4.66290e7	−	1.43831e7i	1.46379	−	0.451519i	0.921402	+	0.388611i	$0.127045\pi$
$318$	−1.28969e7	+	5.06166e6i	−0.401055	+	0.157402i
$319$	−1.55185e6	−	3.95404e6i	−0.0478054	−	0.121806i
$320$	1.92145e6	+	6.22919e6i	0.0586380	+	0.190100i
$321$	1.39654e6	+	318752.i	0.0422220	+	0.00963690i
$322$	4.24214e7	−	5.81348e6i	1.27062	−	0.174128i
$323$	6.11625e6	+	2.67970e7i	0.181500	+	0.795205i
$324$	−1.88583e7	−	3.26636e7i	−0.554457	−	0.960348i
$325$	−1.07300e8	−	6.19495e7i	−3.12571	−	1.80463i
$326$	−5.86914e7	−	1.81039e7i	−1.69403	−	0.522540i
$327$	1.30720e7	−	979614.i	0.373852	−	0.0280164i
$328$	−3.68289e7	−	2.93701e7i	−1.04368	−	0.832307i
$329$	6.59901e6	−	4.01239e7i	0.185307	−	1.12672i
$330$	7.65225e6	+	9.59562e6i	0.212935	+	0.267012i
$331$	−2.22888e7	+	2.06810e7i	−0.614615	+	0.570280i	−0.924827	−	0.380388i	$-0.875791\pi$
$331$	−2.22888e7	+	2.06810e7i	−0.614615	+	0.570280i	0.310212	+	0.950667i	$0.399600\pi$
$332$	1.49564e7	+	9.92295e7i	0.408709	+	2.71161i
$333$	1.58768e7	−	1.08246e7i	0.429963	−	0.293144i
$334$	−950328.	+	6.30502e6i	−0.0255055	+	0.169218i
$335$	3.17173e7	+	6.58616e7i	0.843649	+	1.75185i
$336$	−2.96267e7	+	6.34545e6i	−0.781025	+	0.167280i
$337$	−4.76931e7	−	2.29678e7i	−1.24614	−	0.600107i	−0.309663	−	0.950846i	$-0.600216\pi$
$337$	−4.76931e7	−	2.29678e7i	−1.24614	−	0.600107i	−0.936473	+	0.350739i	$0.885930\pi$
$338$	9.22439e7	+	6.28908e7i	2.38884	+	1.62868i
$339$	1.68647e7	−	1.81758e7i	0.432892	−	0.466546i
$340$	−1.03177e7	+	1.37680e8i	−0.262509	+	3.50294i
$341$	−8.29389e6	−	3.25511e6i	−0.209168	−	0.0820924i
$342$		−	5.61075e7i		−	1.40263i
$343$	−2.38711e7	−	3.25359e7i	−0.591548	−	0.806269i
$344$	−1.67596e8			−4.11706
$345$	8.15581e6	−	2.07807e7i	0.198614	−	0.506060i
$346$	8.15862e7	+	6.11404e6i	1.96965	+	0.147605i
$347$	1.09838e7	+	1.01914e7i	0.262883	+	0.243920i	0.800591	−	0.599212i	$-0.204519\pi$
$347$	1.09838e7	+	1.01914e7i	0.262883	+	0.243920i	−0.537708	+	0.843131i	$0.680710\pi$
$348$	1.21687e7	−	1.78482e7i	0.288740	−	0.423504i
$349$	−2.19442e7	+	4.55676e7i	−0.516231	+	1.07196i	0.466086	+	0.884739i	$0.345664\pi$
$349$	−2.19442e7	+	4.55676e7i	−0.516231	+	1.07196i	−0.982317	+	0.187225i	$0.940051\pi$
$350$	3.63389e7	+	1.69665e8i	0.847555	+	3.95720i
$351$	−4.86445e7	+	2.34259e7i	−1.12490	+	0.541721i
$352$	1.16829e7	+	1.76092e6i	0.267869	+	0.0403748i
$353$	154371.	+	226421.i	0.00350948	+	0.00514746i	0.827990	−	0.560744i	$-0.189485\pi$
$353$	154371.	+	226421.i	0.00350948	+	0.00514746i	−0.824480	+	0.565891i	$0.808532\pi$
$354$	1.31082e7	−	1.97574e6i	0.295483	−	0.0445369i
$355$	−7.09955e7	−	7.65150e7i	−1.58689	−	1.71026i
$356$	3.71532e7	−	2.96287e7i	0.823467	−	0.656693i
$357$	−1.64530e7	−	2.70596e6i	−0.361610	−	0.0594725i
$358$	−3.51218e7	+	4.40413e7i	−0.765469	+	0.959868i
$359$	5.90587e6	+	7.88084e7i	0.127644	+	1.70329i	0.582585	+	0.812770i	$0.302041\pi$
$359$	5.90587e6	+	7.88084e7i	0.127644	+	1.70329i	−0.454941	+	0.890522i	$0.650340\pi$
$360$	4.64440e7	−	1.50568e8i	0.995457	−	3.22719i
$361$	−2.39496e6	+	4.14820e6i	−0.0509070	+	0.0881735i
$362$	6.61163e7	−	3.81723e7i	1.39374	−	0.804678i
$363$	−1.86497e7	+	4.25667e6i	−0.389899	+	0.0889919i
$364$	−2.39436e7	−	1.74718e8i	−0.496461	−	3.62272i
$365$	2.04590e7	−	8.96368e7i	0.420733	−	1.84335i
$366$	−3.27429e7	+	1.00998e7i	−0.667842	+	0.206002i
$367$	−1.82733e7	+	7.17176e6i	−0.369675	+	0.145087i	−0.542904	−	0.839795i	$-0.682675\pi$
$367$	−1.82733e7	+	7.17176e6i	−0.369675	+	0.145087i	0.173229	+	0.984882i	$0.444580\pi$
$368$	−2.42298e7	−	6.17366e7i	−0.486191	−	1.23879i
$369$	7.06079e6	+	2.28905e7i	0.140532	+	0.455593i
$370$	1.02119e8	+	2.33080e7i	2.01605	+	0.460151i
$371$	−1.46212e7	+	2.45583e7i	−0.286326	+	0.480924i
$372$	−1.00827e7	−	4.41752e7i	−0.195861	−	0.858124i
$373$	−2.03058e7	−	3.51707e7i	−0.391286	−	0.677727i	0.601334	−	0.798998i	$-0.294636\pi$
$373$	−2.03058e7	−	3.51707e7i	−0.391286	−	0.677727i	−0.992619	+	0.121271i	$0.961303\pi$
$374$	1.73777e7	+	1.00330e7i	0.332183	+	0.191786i
$375$	4.78301e7	+	1.47536e7i	0.907001	+	0.279773i
$376$	−1.38746e8	+	1.03975e7i	−2.61009	+	0.195599i
$377$	3.58480e7	+	2.85878e7i	0.669023	+	0.533528i
$378$	7.00080e7	+	2.85651e7i	1.29620	+	0.528883i
$379$	3.13458e7	+	3.93063e7i	0.575786	+	0.722013i	0.981388	−	0.192037i	$-0.0615094\pi$
$379$	3.13458e7	+	3.93063e7i	0.575786	+	0.722013i	−0.405602	+	0.914050i	$0.632938\pi$
$380$	1.55594e8	−	1.44370e8i	2.83559	−	2.63104i
$381$	501475.	+	3.32707e6i	0.00906722	+	0.0601571i
$382$	−1.30259e8	+	8.88091e7i	−2.33678	+	1.59319i
$383$	695733.	−	4.61589e6i	0.0123836	−	0.0821597i	−0.981785	−	0.189993i	$-0.939153\pi$
$383$	695733.	−	4.61589e6i	0.0123836	−	0.0821597i	0.994169	+	0.107834i	$0.0343914\pi$
$384$	−9.40419e6	−	1.95280e7i	−0.166084	−	0.344877i
$385$	2.46065e7	+	5.96443e6i	0.431188	+	0.104517i
$386$	−1.57579e8	−	7.58860e7i	−2.73991	−	1.31947i
$387$	7.04181e7	+	4.80103e7i	1.21493	+	0.828326i
$388$	9.43751e7	−	1.01712e8i	1.61571	−	1.74132i
$389$	−470856.	+	6.28314e6i	−0.00799907	+	0.106740i	−0.999774	−	0.0212529i	$-0.993234\pi$
$389$	−470856.	+	6.28314e6i	−0.00799907	+	0.106740i	0.991775	+	0.127993i	$0.0408535\pi$
$390$	−1.23325e8	−	4.84016e7i	−2.07902	−	0.815954i
$391$		−	3.64981e7i		−	0.610577i
$392$	−8.89523e7	+	1.05605e8i	−1.47672	+	1.75318i
$393$	6.77731e6			0.111655
$394$	3.46368e7	−	8.82532e7i	0.566303	−	1.44292i
$395$	5.62670e6	+	421663.i	0.0912982	+	0.00684186i
$396$	−2.08384e7	−	1.93352e7i	−0.335567	−	0.311360i
$397$	−2.45711e7	+	3.60392e7i	−0.392694	+	0.575976i	−0.970771	−	0.240006i	$-0.922851\pi$
$397$	−2.45711e7	+	3.60392e7i	−0.392694	+	0.575976i	0.578078	+	0.815982i	$0.303803\pi$
$398$	−1.82788e7	+	3.79563e7i	−0.289933	+	0.602053i
$399$	1.57123e7	+	2.02538e7i	0.247356	+	0.318852i
$400$	2.42141e8	−	1.16609e8i	3.78345	−	1.82201i
$401$	−3.92782e7	−	5.92023e6i	−0.609141	−	0.0918133i	−0.162774	−	0.986663i	$-0.552044\pi$
$401$	−3.92782e7	−	5.92023e6i	−0.609141	−	0.0918133i	−0.446367	+	0.894850i	$0.647282\pi$
$402$	3.04364e7	+	4.46420e7i	0.468506	+	0.687172i
$403$	9.51022e7	−	1.43343e7i	1.45303	−	0.219009i
$404$	1.01962e8	+	1.09889e8i	1.54631	+	1.66652i
$405$	−4.56999e7	+	3.64445e7i	−0.687940	+	0.548614i
$406$	−3.93968e6	−	6.40909e7i	−0.0588685	−	0.957675i
$407$	6.58721e6	−	8.26011e6i	0.0977054	−	0.122519i
$408$	4.26356e6	+	5.68933e7i	0.0627758	+	0.837685i
$409$	9.24009e6	−	2.99556e7i	0.135054	−	0.437833i	−0.862632	−	0.505833i	$-0.831185\pi$
$409$	9.24009e6	−	2.99556e7i	0.135054	−	0.437833i	0.997685	+	0.0679993i	$0.0216616\pi$
$410$	−6.52888e7	+	1.13084e8i	−0.947299	+	1.64077i
$411$	−441436.	+	254863.i	−0.00635832	+	0.00367098i
$412$	6.75161e7	−	1.54101e7i	0.965419	−	0.220351i
$413$	1.88677e7	−	1.97955e7i	0.267835	−	0.281006i
$414$	−1.65786e7	+	7.26356e7i	−0.233640	+	1.02364i
$415$	1.48611e8	−	4.58405e7i	2.07925	−	0.641365i
$416$	−1.18719e8	+	4.65938e7i	−1.64908	+	0.647215i
$417$	2.83882e6	+	7.23319e6i	0.0391498	+	0.0997520i
$418$	−9.09279e6	−	2.94781e7i	−0.124500	−	0.403618i
$419$	−2.81961e6	−	643557.i	−0.0383307	−	0.00874873i	0.203313	−	0.979114i	$-0.434829\pi$
$419$	−2.81961e6	−	643557.i	−0.0383307	−	0.00874873i	−0.241643	+	0.970365i	$0.577686\pi$
$420$	4.54307e7	+	1.20480e8i	0.613199	+	1.62618i
$421$	2.60000e7	+	1.13914e8i	0.348439	+	1.52661i	0.780724	+	0.624876i	$0.214850\pi$
$421$	2.60000e7	+	1.13914e8i	0.348439	+	1.52661i	−0.432285	+	0.901737i	$0.642292\pi$
$422$	−9.71028e7	−	1.68187e8i	−1.29210	−	2.23797i
$423$	6.12748e7	+	3.53770e7i	0.809582	+	0.467412i
$424$	9.34504e7	+	2.88256e7i	1.22598	+	0.378165i
$425$	1.47489e8	−	1.10528e7i	1.92130	−	0.143981i
$426$	−6.03171e7	−	4.81012e7i	−0.780210	−	0.622196i
$427$	−4.05988e7	+	5.78653e7i	−0.521471	+	0.743249i
$428$	−1.12761e7	−	1.41397e7i	−0.143822	−	0.180348i
$429$	−9.79565e6	+	9.08903e6i	−0.124068	+	0.115119i
$430$	6.92413e7	+	4.59386e8i	0.870883	+	5.77793i
$431$	6.57487e7	−	4.48267e7i	0.821212	−	0.559893i	−0.0782287	−	0.996935i	$-0.524926\pi$
$431$	6.57487e7	−	4.48267e7i	0.821212	−	0.559893i	0.899441	+	0.437042i	$0.143974\pi$
$432$	1.74552e7	−	1.15807e8i	0.216507	−	1.43643i
$433$	−3.31713e7	−	6.88810e7i	−0.408601	−	0.848468i	−0.999140	−	0.0414593i	$-0.986799\pi$
$433$	−3.31713e7	−	6.88810e7i	−0.408601	−	0.848468i	0.590540	−	0.807009i	$-0.298915\pi$
$434$	−1.04169e8	−	8.53814e7i	−1.27429	−	1.04447i
$435$	−3.01626e7	−	1.45255e7i	−0.366438	−	0.176467i
$436$	−1.36745e8	−	9.32312e7i	−1.64988	−	1.12487i
$437$	−3.81648e7	+	4.11319e7i	−0.457319	+	0.492872i
$438$	5.07838e6	−	6.77662e7i	0.0604369	−	0.806475i
$439$	5.36415e7	+	2.10528e7i	0.634027	+	0.248837i	0.660516	−	0.750812i	$-0.270338\pi$
$439$	5.36415e7	+	2.10528e7i	0.634027	+	0.248837i	−0.0264892	+	0.999649i	$0.508433\pi$
$440$		−	8.66329e7i		−	1.01701i
$441$	6.76270e7	−	1.88901e7i	0.788505	−	0.220252i
$442$	−2.16602e8			−2.50840
$443$	−4.85649e7	+	1.23741e8i	−0.558613	+	1.42332i	0.320747	+	0.947165i	$0.396066\pi$
$443$	−4.85649e7	+	1.23741e8i	−0.558613	+	1.42332i	−0.879360	+	0.476158i	$0.842029\pi$
$444$	5.35791e7	+	4.01520e6i	0.612134	+	0.0458731i
$445$	−5.39867e7	−	5.00924e7i	−0.612642	−	0.568449i
$446$	8.76889e7	−	1.28616e8i	0.988417	−	1.44974i
$447$	1.88835e7	−	3.92121e7i	0.211427	−	0.439033i
$448$	8.89666e6	+	4.43231e6i	0.0989448	+	0.0492942i
$449$	5.81906e7	−	2.80231e7i	0.642856	−	0.309583i	−0.0839049	−	0.996474i	$-0.526739\pi$
$449$	5.81906e7	−	2.80231e7i	0.642856	−	0.309583i	0.726761	+	0.686891i	$0.241025\pi$
$450$	−2.98542e8	−	4.49980e7i	−3.27618	−	0.493805i
$451$	7.41928e6	+	1.08821e7i	0.0808783	+	0.118627i
$452$	−3.09548e8	+	4.66568e7i	−3.35206	+	0.505242i
$453$	−2.86871e6	−	3.09174e6i	−0.0308598	−	0.0332589i
$454$	−2.40351e7	+	1.91673e7i	−0.256849	+	0.204830i
$455$	−2.62220e8	+	7.70496e7i	−2.78375	+	0.817968i
$456$	5.46865e7	−	6.85747e7i	0.576747	−	0.723218i
$457$	1.03911e7	+	1.38660e8i	0.108871	+	1.45278i	0.737641	+	0.675193i	$0.235940\pi$
$457$	1.03911e7	+	1.38660e8i	0.108871	+	1.45278i	−0.628770	+	0.777592i	$0.716441\pi$
$458$	2.08839e7	−	6.77041e7i	0.217378	−	0.704723i
$459$	3.22257e7	−	5.58166e7i	0.333246	−	0.577199i
$460$	−2.44088e8	+	1.40924e8i	−2.50768	+	1.44781i
$461$	1.73251e8	−	3.95434e7i	1.76837	−	0.403619i	0.790437	−	0.612544i	$-0.209854\pi$
$461$	1.73251e8	−	3.95434e7i	1.76837	−	0.403619i	0.977932	+	0.208925i	$0.0669966\pi$
$462$	1.86410e7	+	1.64854e6i	0.189036	+	0.0167176i
$463$	1.03815e7	−	4.54844e7i	0.104597	−	0.458268i	−0.895321	−	0.445422i	$-0.853054\pi$
$463$	1.03815e7	−	4.54844e7i	0.104597	−	0.458268i	0.999917	−	0.0128460i	$-0.00408911\pi$
$464$	−9.50399e7	+	2.93159e7i	−0.951375	+	0.293460i
$465$	−6.53681e7	+	2.56551e7i	−0.650141	+	0.255161i
$466$	−9.31177e7	−	2.37260e8i	−0.920184	−	2.34459i
$467$	−5.03658e7	−	1.63282e8i	−0.494521	−	1.60320i	−0.767412	−	0.641154i	$-0.778456\pi$
$467$	−5.03658e7	−	1.63282e8i	−0.494521	−	1.60320i	0.272891	−	0.962045i	$-0.412020\pi$
$468$	2.99160e8	+	6.82813e7i	2.91854	+	0.666138i
$469$	1.06060e8	+	3.42788e7i	1.02809	+	0.332282i
$470$	8.58221e7	+	3.76011e8i	0.826619	+	3.62165i
$471$	1.70318e7	+	2.95000e7i	0.163004	+	0.282331i
$472$	−8.10353e7	−	4.67857e7i	−0.770634	−	0.444926i
$473$	4.47772e7	+	1.38119e7i	0.423130	+	0.130518i
$474$	4.15881e6	−	311660.i	0.0390512	−	0.00292648i
$475$	−1.77772e8	−	1.41769e8i	−1.65876	−	1.32281i
$476$	1.41106e8	+	1.56226e8i	1.30836	+	1.44854i
$477$	−3.10072e7	−	3.88818e7i	−0.285698	−	0.358254i
$478$	−1.34007e7	+	1.24341e7i	−0.122700	+	0.113849i
$479$	−1.97274e7	−	1.30883e8i	−0.179499	−	1.19090i	−0.879196	−	0.476460i	$-0.841920\pi$
$479$	−1.97274e7	−	1.30883e8i	−0.179499	−	1.19090i	0.699697	−	0.714440i	$-0.253318\pi$
$480$	7.69383e7	−	5.24557e7i	0.695695	−	0.474317i
$481$	−1.69974e7	+	1.12770e8i	−0.152738	+	1.01335i
$482$	2.92555e7	+	6.07496e7i	0.261256	+	0.542503i
$483$	−1.43563e7	−	3.08629e7i	−0.127409	−	0.273902i
$484$	2.17599e8	+	1.04790e8i	1.91920	+	0.924237i
$485$	−1.77670e8	−	1.21133e8i	−1.55736	−	1.06179i
$486$	−1.38691e8	+	1.49473e8i	−1.20820	+	1.30213i
$487$	1.29028e6	−	1.72175e7i	0.0111711	−	0.149068i	−0.988829	−	0.149055i	$-0.952377\pi$
$487$	1.29028e6	−	1.72175e7i	0.0111711	−	0.149068i	1.00000		1.28818e-5i	$-4.10042e-6\pi$
$488$	2.25147e8	+	8.83638e7i	1.93735	+	0.760352i
$489$			4.88266e7i			0.417570i
$490$	3.26218e8	+	2.00191e8i	2.77281	+	1.70160i
$491$	2.20371e8			1.86170			0.930850	−	0.365402i	$-0.119069\pi$
$491$	2.20371e8			1.86170			0.930850	+	0.365402i	$0.119069\pi$
$492$	−2.44705e7	+	6.23499e7i	−0.205470	+	0.523529i
$493$	−5.45814e7	−	4.09031e6i	−0.455516	−	0.0341362i
$494$	2.44102e8	+	2.26494e8i	2.02484	+	1.87878i
$495$	−2.48173e7	+	3.64003e7i	−0.204615	+	0.300116i
$496$	−9.05174e7	+	1.87961e8i	−0.741801	+	1.54036i
$497$	−1.59138e8	−	2.13366e6i	−1.29630	−	0.0173803i
$498$	1.03565e8	−	4.98743e7i	0.838542	−	0.403821i
$499$	1.71061e8	+	2.57834e7i	1.37674	+	0.207510i	0.795366	−	0.606130i	$-0.207279\pi$
$499$	1.71061e8	+	2.57834e7i	1.37674	+	0.207510i	0.581370	+	0.813639i	$0.302517\pi$
$500$	−3.55991e8	−	5.22143e8i	−2.84793	−	4.17715i
$501$	5.01224e6	−	755473.i	0.0398583	−	0.00600767i
$502$	−2.58969e8	−	2.79102e8i	−2.04709	−	2.20624i
$503$	−7.92439e6	+	6.31949e6i	−0.0622676	+	0.0496567i	−0.654129	−	0.756383i	$-0.726965\pi$
$503$	−7.92439e6	+	6.31949e6i	−0.0622676	+	0.0496567i	0.591861	+	0.806040i	$0.298393\pi$
$504$	−1.17327e8	−	2.09658e8i	−0.916443	−	1.63764i
$505$	1.44850e8	−	1.81636e8i	1.12472	−	1.41036i
$506$	3.06117e6	+	4.08484e7i	0.0236285	+	0.315300i
$507$	2.61601e7	−	8.48088e7i	0.200731	−	0.650754i
$508$	2.12401e7	−	3.67889e7i	0.162019	−	0.280625i
$509$	−2.16411e8	+	1.24945e8i	−1.64107	+	0.947470i	−0.660611	+	0.750728i	$0.729703\pi$
$509$	−2.16411e8	+	1.24945e8i	−1.64107	+	0.947470i	−0.980455	+	0.196742i	$0.936964\pi$
$510$	1.54185e8	−	3.51918e7i	1.16234	−	0.265296i
$511$	−7.74117e7	−	1.16878e8i	−0.580155	−	0.875935i
$512$	−6.68611e7	+	2.92938e8i	−0.498154	+	2.18256i
$513$	−9.46826e7	+	2.92057e7i	−0.701323	+	0.216329i
$514$	1.03165e8	−	4.04891e7i	0.759698	−	0.298160i
$515$	−3.92105e7	−	9.99068e7i	−0.287065	−	0.731431i
$516$	7.02414e7	+	2.27717e8i	0.511263	+	1.65747i
$517$	3.79261e7	+	8.65638e6i	0.274452	+	0.0626419i
$518$	1.33154e8	−	8.81917e7i	0.958001	−	0.634510i
$519$	−1.44727e7	−	6.34090e7i	−0.103525	−	0.453575i
$520$	4.67578e8	+	8.09869e8i	3.32540	+	5.75976i
$521$	8.30917e7	+	4.79730e7i	0.587550	+	0.339222i	0.764128	−	0.645065i	$-0.223170\pi$
$521$	8.30917e7	+	4.79730e7i	0.587550	+	0.339222i	−0.176578	+	0.984287i	$0.556503\pi$
$522$	1.06766e8	+	3.29328e7i	0.750619	+	0.231535i
$523$	2.70665e8	−	2.02835e7i	1.89202	−	0.141788i	0.922376	−	0.386293i	$-0.126245\pi$
$523$	2.70665e8	−	2.02835e7i	1.89202	−	0.141788i	0.969648	+	0.244505i	$0.0786256\pi$
$524$	−6.68986e7	−	5.33499e7i	−0.464968	−	0.370800i
$525$	1.20370e8	−	6.73602e7i	0.831840	−	0.465506i
$526$	−2.66759e7	−	3.34505e7i	−0.183300	−	0.229851i
$527$	−8.41612e7	+	7.80902e7i	−0.575016	+	0.533537i
$528$	−4.32014e6	−	2.86623e7i	−0.0293492	−	0.194719i
$529$	−6.07520e7	+	4.14200e7i	−0.410387	+	0.279797i
$530$	4.04036e7	−	2.68060e8i	0.271389	−	1.80055i
$531$	2.06459e7	+	4.28716e7i	0.137895	+	0.286342i
$532$	4.33883e6	−	3.23610e8i	0.0288163	−	2.14925i
$533$	−1.28091e8	−	6.16852e7i	−0.845932	−	0.407379i
$534$	−4.49752e7	−	3.06636e7i	−0.295358	−	0.201372i
$535$	−1.90641e7	+	2.05462e7i	−0.124496	+	0.134175i
$536$	2.85007e7	−	3.80316e8i	0.185081	−	2.46973i
$537$	4.16854e7	+	1.63603e7i	0.269191	+	0.105650i
$538$		−	5.15567e8i		−	3.31084i
$539$	3.24689e7	−	2.08842e7i	0.207349	−	0.133368i
$540$	−4.97711e8			−3.16079
$541$	6.71442e7	−	1.71081e8i	0.424050	−	1.08046i	−0.546050	−	0.837753i	$-0.683869\pi$
$541$	6.71442e7	−	1.71081e8i	0.424050	−	1.08046i	0.970099	−	0.242708i	$-0.0780357\pi$
$542$	2.79884e8	+	2.09744e7i	1.75784	+	0.131732i
$543$	−4.44896e7	−	4.12803e7i	−0.277881	−	0.257836i
$544$	8.57619e7	−	1.25790e8i	0.532718	−	0.781354i
$545$	−1.11288e8	+	2.31092e8i	−0.687478	+	1.42756i
$546$	−1.83159e8	+	8.51990e7i	−1.12526	+	0.523428i
$547$	8.64975e7	−	4.16550e7i	0.528496	−	0.254510i	−0.150555	−	0.988602i	$-0.548106\pi$
$547$	8.64975e7	−	4.16550e7i	0.528496	−	0.254510i	0.679051	+	0.734091i	$0.262392\pi$
$548$	6.36364e6	+	959165.i	0.0386691	+	0.00582843i
$549$	−6.92863e7	−	1.01624e8i	−0.418726	−	0.614159i
$550$	−1.64142e8	+	2.47404e7i	−0.986579	+	0.148703i
$551$	5.72339e7	+	6.16835e7i	0.342136	+	0.368735i
$552$	−9.10583e7	+	7.26166e7i	−0.541380	+	0.431736i
$553$	6.38465e6	−	5.76674e6i	0.0377539	−	0.0341001i
$554$	1.25887e8	−	1.57857e8i	0.740375	−	0.928401i
$555$	−6.22266e6	−	8.30356e7i	−0.0363996	−	0.485719i
$556$	2.89166e7	−	9.37453e7i	0.168237	−	0.545413i
$557$	−1.35995e8	+	2.35550e8i	−0.786969	+	1.36307i	0.140847	+	0.990031i	$0.455017\pi$
$557$	−1.35995e8	+	2.35550e8i	−0.786969	+	1.36307i	−0.927816	+	0.373038i	$0.878316\pi$
$558$	2.02962e8	−	1.17180e8i	1.16819	−	0.674453i
$559$	−4.93136e8	+	1.12555e8i	−2.82313	+	0.644362i
$560$	1.82322e8	−	5.64109e8i	1.03819	−	3.21217i
$561$	3.54959e6	−	1.55518e7i	0.0201043	−	0.0880828i
$562$	2.77057e8	−	8.54607e7i	1.56084	−	0.481457i
$563$	−2.88793e8	+	1.13343e8i	−1.61831	+	0.635139i	−0.989774	−	0.142643i	$-0.954440\pi$
$563$	−2.88793e8	+	1.13343e8i	−1.61831	+	0.635139i	−0.628534	+	0.777782i	$0.716345\pi$
$564$	7.22774e7	+	1.84160e8i	0.402871	+	1.02650i
$565$	1.43000e8	+	4.63595e8i	0.792850	+	2.57036i
$566$	−1.88835e8	−	4.31003e7i	−1.04144	−	0.237701i
$567$	−7.85131e6	+	8.87795e7i	−0.0430718	+	0.487039i
$568$	1.21177e8	+	5.30912e8i	0.661265	+	2.89719i
$569$	−9.21622e6	−	1.59630e7i	−0.0500283	−	0.0866516i	0.839927	−	0.542700i	$-0.182598\pi$
$569$	−9.21622e6	−	1.59630e7i	−0.0500283	−	0.0866516i	−0.889955	+	0.456048i	$0.849264\pi$
$570$	−2.10559e8	−	1.21566e8i	−1.13697	−	0.656431i
$571$	−6.88388e7	−	2.12340e7i	−0.369764	−	0.114057i	0.104304	−	0.994546i	$-0.466739\pi$
$571$	−6.88388e7	−	2.12340e7i	−0.369764	−	0.114057i	−0.474068	+	0.880488i	$0.657215\pi$
$572$	1.68240e8	−	1.26078e7i	0.898961	−	0.0673678i
$573$	9.79853e7	+	7.81407e7i	0.520831	+	0.415349i
$574$	5.61298e7	+	1.91024e8i	0.296796	+	1.01007i
$575$	1.88250e8	+	2.36058e8i	0.990221	+	1.24170i
$576$	−1.26782e7	+	1.17636e7i	−0.0663421	+	0.0615564i
$577$	7.68282e6	+	5.09722e7i	0.0399938	+	0.265342i	0.999887	−	0.0150238i	$-0.00478241\pi$
$577$	7.68282e6	+	5.09722e7i	0.0399938	+	0.265342i	−0.959893	+	0.280366i	$0.909544\pi$
$578$	−7.47856e7	+	5.09880e7i	−0.387288	+	0.264049i
$579$	−2.07225e7	+	1.37485e8i	−0.106760	+	0.708304i
$580$	1.83391e8	+	3.80816e8i	0.939928	+	1.95178i
$581$	1.05743e8	−	2.12250e8i	0.539165	−	1.08223i
$582$	−1.43196e8	−	6.89598e7i	−0.726379	−	0.349806i
$583$	−2.25919e7	−	1.54029e7i	−0.114011	−	0.0777315i
$584$	−3.26266e8	+	3.51631e8i	−1.63807	+	1.76542i
$585$	3.55382e7	−	4.74224e8i	0.177512	−	2.36873i
$586$	−4.07737e8	−	1.60025e8i	−2.02622	−	0.795234i
$587$		−	4.23574e7i		−	0.209418i	−0.994503	−	0.104709i	$-0.966609\pi$
$587$		−	4.23574e7i		−	0.209418i	0.994503	−	0.104709i	$-0.0333912\pi$
$588$	1.80770e8	+	7.66016e7i	0.889190	+	0.376796i
$589$	1.76502e8			0.863784
$590$	−9.47621e7	+	2.41450e8i	−0.461401	+	1.17563i
$591$	−7.51569e7	−	5.63223e6i	−0.364088	−	0.0272846i
$592$	−1.81342e8	−	1.68261e8i	−0.874044	−	0.810995i
$593$	6.84094e7	−	1.00338e8i	0.328059	−	0.481174i	−0.626406	−	0.779497i	$-0.715475\pi$
$593$	6.84094e7	−	1.00338e8i	0.328059	−	0.481174i	0.954465	+	0.298323i	$0.0964272\pi$
$594$	−3.13854e7	+	6.51724e7i	−0.149750	+	0.310960i
$595$	2.06818e8	−	2.52326e8i	0.981832	−	1.19787i
$596$	−4.95070e8	+	2.38413e8i	−2.33845	+	1.12614i
$597$	3.31163e7	+	4.99147e6i	0.155639	+	0.0234588i
$598$	−2.49085e8	−	3.65341e8i	−1.16478	−	1.70842i
$599$	1.64417e7	−	2.47819e6i	0.0765010	−	0.0115307i	−0.110680	−	0.993856i	$-0.535303\pi$
$599$	1.64417e7	−	2.47819e6i	0.0765010	−	0.0115307i	0.187181	+	0.982325i	$0.440065\pi$
$600$	−3.21020e8	−	3.45977e8i	−1.48620	−	1.60175i
$601$	1.49402e8	−	1.19144e8i	0.688230	−	0.548845i	−0.215735	−	0.976452i	$-0.569215\pi$
$601$	1.49402e8	−	1.19144e8i	0.688230	−	0.548845i	0.903965	+	0.427607i	$0.140643\pi$
$602$	5.79877e8	+	4.06847e8i	2.65795	+	1.86484i
$603$	−1.20922e8	+	1.51632e8i	−0.551511	+	0.691573i
$604$	3.97933e6	+	5.31005e7i	0.0180592	+	0.240984i
$605$	1.10326e8	−	3.57667e8i	0.498208	−	1.61515i
$606$	8.58568e7	−	1.48708e8i	0.385795	−	0.668217i
$607$	5.54938e7	−	3.20393e7i	0.248129	−	0.143258i	−0.370778	−	0.928722i	$-0.620909\pi$
$607$	5.54938e7	−	3.20393e7i	0.248129	−	0.143258i	0.618907	+	0.785464i	$0.287576\pi$
$608$	−2.28184e8	+	5.20815e7i	−1.01525	+	0.231725i
$609$	−4.77630e7	+	1.80104e7i	−0.211466	+	0.0797393i
$610$	1.49190e8	−	6.53644e8i	0.657280	−	2.87973i
$611$	−4.01264e8	+	1.23774e8i	−1.75917	+	0.542631i
$612$	−3.40981e8	+	1.33825e8i	−1.48757	+	0.583827i
$613$	−1.02082e8	−	2.60102e8i	−0.443169	−	1.12918i	−0.961697	−	0.274116i	$-0.911615\pi$
$613$	−1.02082e8	−	2.60102e8i	−0.443169	−	1.12918i	0.518527	−	0.855061i	$-0.326480\pi$
$614$	1.06214e8	+	3.44339e8i	0.458858	+	1.48758i
$615$	1.01201e8	+	2.30986e7i	0.435072	+	0.0993024i
$616$	−9.56189e7	−	9.11372e7i	−0.409074	−	0.389900i
$617$	2.81543e7	+	1.23352e8i	0.119864	+	0.525160i	0.998834	+	0.0482817i	$0.0153745\pi$
$617$	2.81543e7	+	1.23352e8i	0.119864	+	0.525160i	−0.878969	+	0.476878i	$0.841768\pi$
$618$	−3.96634e7	−	6.86989e7i	−0.168044	−	0.291061i
$619$	3.64546e8	+	2.10470e8i	1.53702	+	0.887400i	0.999011	+	0.0444610i	$0.0141571\pi$
$619$	3.64546e8	+	2.10470e8i	1.53702	+	0.887400i	0.538010	+	0.842938i	$0.319176\pi$
$620$	8.47200e8	+	2.61327e8i	3.55476	+	1.09650i
$621$	1.31204e8	−	9.83236e6i	0.547862	−	0.0410566i
$622$	8.41769e7	+	6.71289e7i	0.349802	+	0.278958i
$623$	−1.12082e8	+	6.88970e6i	−0.463523	+	0.0284929i
$624$	1.95083e8	+	2.44626e8i	0.802907	+	1.00681i
$625$	−3.17294e8	+	2.94405e8i	−1.29963	+	1.20588i
$626$	2.30486e7	+	1.52917e8i	0.0939552	+	0.623352i
$627$	−2.02622e7	+	1.38145e7i	−0.0822023	+	0.0560446i
$628$	6.40984e7	−	4.25265e8i	0.258803	−	1.71704i
$629$	−5.90685e7	−	1.22657e8i	−0.237358	−	0.492879i
$630$	−5.26207e8	+	4.08216e8i	−2.10443	+	1.63256i
$631$	1.12011e7	+	5.39419e6i	0.0445835	+	0.0214703i	0.456043	−	0.889958i	$-0.349266\pi$
$631$	1.12011e7	+	5.39419e6i	0.0445835	+	0.0214703i	−0.411459	+	0.911428i	$0.634981\pi$
$632$	−2.43228e7	−	1.65830e7i	−0.0963523	−	0.0656919i
$633$	−1.05009e8	+	1.13173e8i	−0.414014	+	0.446201i
$634$	−5.27374e7	+	7.03732e8i	−0.206943	+	2.76146i
$635$	−6.12839e7	−	2.40521e7i	−0.239345	−	0.0939361i
$636$		−	1.39055e8i		−	0.540524i
$637$	−1.90811e8	+	3.70474e8i	−0.738221	+	1.43331i
$638$	6.14302e7			0.236548
$639$	1.01173e8	−	2.57784e8i	0.387759	−	0.987993i
$640$	4.22910e8	+	3.16927e7i	1.61327	+	0.120898i
$641$	7.25258e6	+	6.72941e6i	0.0275371	+	0.0255507i	0.693821	−	0.720147i	$-0.255926\pi$
$641$	7.25258e6	+	6.72941e6i	0.0275371	+	0.0255507i	−0.666284	+	0.745698i	$0.732116\pi$
$642$	−1.16699e7	+	1.71166e7i	−0.0441025	+	0.0646864i
$643$	−387572.	+	804802.i	−0.00145787	+	0.00302731i	−0.901697	−	0.432369i	$-0.857678\pi$
$643$	−387572.	+	804802.i	−0.00145787	+	0.00302731i	0.900239	+	0.435397i	$0.143392\pi$
$644$	−1.01237e8	+	4.17657e8i	−0.379037	+	1.56373i
$645$	3.32744e8	−	1.60241e8i	1.24003	−	0.597166i
$646$	−3.93068e8	−	5.92454e7i	−1.45804	−	0.219764i
$647$	1.30855e8	+	1.91930e8i	0.483147	+	0.708646i	0.987982	−	0.154570i	$-0.0493991\pi$
$647$	1.30855e8	+	1.91930e8i	0.483147	+	0.708646i	−0.504835	+	0.863216i	$0.668447\pi$
$648$	3.01552e8	−	4.54517e7i	1.10825	−	0.167042i
$649$	1.77948e7	+	1.91782e7i	0.0650967	+	0.0701575i
$650$	1.40092e9	−	1.11719e9i	5.10120	−	4.06807i
$651$	−4.04506e7	+	9.91375e7i	−0.146616	+	0.359331i
$652$	3.84355e8	−	4.81966e8i	1.38672	−	1.73889i
$653$	1.37911e7	+	1.84029e8i	0.0495290	+	0.660918i	0.965622	+	0.259952i	$0.0837066\pi$
$653$	1.37911e7	+	1.84029e8i	0.0495290	+	0.660918i	−0.916093	+	0.400967i	$0.868674\pi$
$654$	−5.58794e7	+	1.81157e8i	−0.199765	+	0.647621i
$655$	−6.63045e7	+	1.14843e8i	−0.235950	+	0.408677i
$656$	2.67072e8	−	1.54194e8i	0.946056	−	0.546206i
$657$	2.37816e8	−	5.42799e7i	0.838580	−	0.191400i
$658$	5.05297e8	+	3.00837e8i	1.77365	+	1.05597i
$659$	−2.11579e7	+	9.26987e7i	−0.0739292	+	0.323905i	−0.998347	−	0.0574768i	$-0.981694\pi$
$659$	−2.11579e7	+	9.26987e7i	−0.0739292	+	0.323905i	0.924418	+	0.381382i	$0.124552\pi$
$660$	−1.17711e8	+	3.63089e7i	−0.409434	+	0.126294i
$661$	−1.72177e8	+	6.75745e7i	−0.596171	+	0.233980i	−0.644189	−	0.764867i	$-0.722805\pi$
$661$	−1.72177e8	+	6.75745e7i	−0.596171	+	0.233980i	0.0480176	+	0.998846i	$0.484710\pi$
$662$	−1.60651e8	−	4.09331e8i	−0.553743	−	1.41091i
$663$	5.07540e7	+	1.64540e8i	0.174152	+	0.564588i
$664$	−7.91040e8	−	1.80550e8i	−2.70206	−	0.616727i
$665$	−4.96924e8	+	6.80991e7i	−1.68976	+	0.231567i
$666$	6.18387e7	+	2.70933e8i	0.209333	+	0.917147i
$667$	−5.58676e7	−	9.67655e7i	−0.188271	−	0.326094i
$668$	−5.54226e7	−	3.19983e7i	−0.185933	−	0.107349i
$669$	−1.18249e8	−	3.64751e7i	−0.394930	−	0.121820i
$670$	−1.05424e9	+	7.90040e7i	−3.50520	+	0.262679i
$671$	−5.28712e7	−	4.21634e7i	−0.175006	−	0.139562i
$672$	2.30419e7	−	1.40102e8i	0.0759296	−	0.461674i
$673$	6.64883e7	+	8.33737e7i	0.218122	+	0.273517i	0.878839	−	0.477119i	$-0.158319\pi$
$673$	6.64883e7	+	8.33737e7i	0.218122	+	0.273517i	−0.660716	+	0.750636i	$0.729747\pi$
$674$	5.61191e8	−	5.20710e8i	1.83287	−	1.70065i
$675$	7.94654e7	+	5.27219e8i	0.258385	+	1.71427i
$676$	−9.25826e8	+	6.31218e8i	−2.99702	+	2.04333i
$677$	−3.73388e7	+	2.47727e8i	−0.120336	+	0.798375i	0.844507	+	0.535545i	$0.179894\pi$
$677$	−3.73388e7	+	2.47727e8i	−0.120336	+	0.798375i	−0.964842	+	0.262830i	$0.915344\pi$
$678$	1.55583e8	+	3.23072e8i	0.499200	+	1.03660i
$679$	−3.20605e8	+	6.86672e7i	−1.02414	+	0.219351i
$680$	−1.00578e9	−	4.84358e8i	−3.19872	−	1.54042i
$681$	2.01922e7	+	1.37668e7i	0.0639355	+	0.0435905i
$682$	8.76431e7	−	9.44568e7i	0.276290	−	0.297769i
$683$	2.48798e7	−	3.31998e8i	0.0780881	−	1.04201i	−0.811231	−	0.584726i	$-0.801202\pi$
$683$	2.48798e7	−	3.31998e8i	0.0780881	−	1.04201i	0.889319	−	0.457288i	$-0.151179\pi$
$684$	5.24208e8	+	2.05737e8i	1.63808	+	0.642900i
$685$		−	9.97362e6i		−	0.0310300i
$686$	5.64136e8	−	1.49456e8i	1.74748	−	0.462956i
$687$	−5.63244e7			−0.173711
$688$	4.00851e8	−	1.02135e9i	1.23089	−	3.13624i
$689$	2.94329e8	+	2.20569e7i	0.899860	+	0.0674352i
$690$	2.36665e8	+	2.19593e8i	0.720422	+	0.668454i
$691$	3.70156e7	−	5.42919e7i	0.112189	−	0.164551i	−0.766038	−	0.642796i	$-0.777774\pi$
$691$	3.70156e7	−	5.42919e7i	0.112189	−	0.164551i	0.878227	+	0.478245i	$0.158727\pi$
$692$	−3.56286e8	+	7.39835e8i	−1.07518	+	2.23263i
$693$	1.40683e7	+	6.56843e7i	0.0422709	+	0.197361i
$694$	−1.95235e8	+	9.40200e7i	−0.584088	+	0.281282i
$695$	−1.50341e8	−	2.26602e7i	−0.447840	−	0.0675009i
$696$	9.83902e7	+	1.44312e8i	0.291826	+	0.428030i
$697$	1.67818e8	−	2.52945e7i	0.495610	−	0.0747012i
$698$	−4.97505e8	−	5.36182e8i	−1.46295	−	1.57669i
$699$	−1.58414e8	+	1.26331e8i	−0.463832	+	0.369894i
$700$	−1.71842e9	−	2.82620e8i	−5.00996	−	0.823966i
$701$	3.40615e8	−	4.27117e8i	0.988802	−	1.23992i	0.0180491	−	0.999837i	$-0.494254\pi$
$701$	3.40615e8	−	4.27117e8i	0.988802	−	1.23992i	0.970753	−	0.240081i	$-0.0771741\pi$
$702$	−5.83513e7	−	7.78644e8i	−0.168670	−	2.25075i
$703$	−6.16904e7	+	1.99995e8i	−0.177563	+	0.575644i
$704$	−4.75451e6	+	8.23506e6i	−0.0136266	+	0.0236020i
$705$	2.65524e8	−	1.53300e8i	0.757769	−	0.437498i
$706$	−3.86380e6	+	881887.i	−0.0109800	+	0.00250610i
$707$	−4.80953e7	−	3.50955e8i	−0.136096	−	0.993100i
$708$	−2.96063e7	+	1.29713e8i	−0.0834226	+	0.365498i
$709$	−1.15718e8	+	3.56944e7i	−0.324686	+	0.100152i	−0.452813	−	0.891605i	$-0.649580\pi$
$709$	−1.15718e8	+	3.56944e7i	−0.324686	+	0.100152i	0.128127	+	0.991758i	$0.459103\pi$
$710$	1.40518e9	−	5.51494e8i	3.92607	−	1.54087i
$711$	5.46918e6	+	1.39352e7i	0.0152165	+	0.0387709i
$712$	1.13254e8	+	3.67159e8i	0.313770	+	1.01722i
$713$	−2.28496e8	−	5.21528e7i	−0.630392	−	0.143883i
$714$	1.23360e8	−	2.07199e8i	0.338905	−	0.569238i
$715$	−5.81815e7	−	2.54910e8i	−0.159172	−	0.697379i
$716$	−2.82689e8	−	4.89632e8i	−0.770141	−	1.33392i
$717$	1.25855e7	+	7.26623e6i	0.0341438	+	0.0197130i
$718$	−1.09215e9	−	3.36884e8i	−2.95060	−	0.910138i
$719$	−4.60428e8	+	3.45043e7i	−1.23872	+	0.0928296i	−0.677931	−	0.735126i	$-0.737123\pi$
$719$	−4.60428e8	+	3.45043e7i	−1.23872	+	0.0928296i	−0.560794	+	0.827955i	$0.689504\pi$
$720$	8.06498e8	+	6.43161e8i	2.16076	+	1.72315i
$721$	−1.51519e8	−	6.18236e7i	−0.404260	−	0.164948i
$722$	−4.31906e7	−	5.41593e7i	−0.114757	−	0.143900i
$723$	3.92929e7	−	3.64585e7i	0.103968	−	0.0964680i
$724$	1.14203e8	+	7.57691e8i	0.300929	+	1.99653i
$725$	3.74112e8	−	2.55066e8i	0.981721	−	0.669326i
$726$	4.12325e7	−	2.73560e8i	0.107753	−	0.714896i
$727$	−2.96220e8	−	6.15108e8i	−0.770924	−	1.60084i	−0.799072	−	0.601236i	$-0.794675\pi$
$727$	−2.96220e8	−	6.15108e8i	−0.770924	−	1.60084i	0.0281478	−	0.999604i	$-0.491039\pi$
$728$	1.38576e9	+	3.35899e8i	3.59165	+	0.870591i
$729$	−2.46223e7	−	1.18575e7i	−0.0635544	−	0.0306062i
$730$	1.09863e9	+	7.49032e8i	2.82411	+	1.92545i
$731$	4.10698e8	−	4.42627e8i	1.05141	−	1.13315i
$732$	2.57004e7	−	3.42949e8i	0.0655251	−	0.874371i
$733$	4.25589e8	+	1.67031e8i	1.08063	+	0.424117i	0.837815	−	0.545955i	$-0.183833\pi$
$733$	4.25589e8	+	1.67031e8i	1.08063	+	0.424117i	0.242818	+	0.970072i	$0.421928\pi$
$734$		−	2.83895e8i		−	0.717910i
$735$	7.56348e7	−	2.94718e8i	0.190484	−	0.742240i
$736$	3.10791e8			0.779534
$737$	−3.89574e7	+	9.92617e7i	−0.0973166	+	0.247959i
$738$	−3.45467e8	−	2.58892e7i	−0.859484	−	0.0644094i
$739$	−8.55387e7	−	7.93683e7i	−0.211948	−	0.196659i	0.567054	−	0.823681i	$-0.308083\pi$
$739$	−8.55387e7	−	7.93683e7i	−0.211948	−	0.196659i	−0.779002	+	0.627022i	$0.784274\pi$
$740$	−5.92219e8	+	8.68626e8i	−1.46146	+	2.14357i
$741$	1.14856e8	−	2.38502e8i	0.282293	−	0.586188i
$742$	−2.53360e8	−	3.26592e8i	−0.620193	−	0.799454i
$743$	−3.17842e8	+	1.53065e8i	−0.774899	+	0.373172i	−0.779165	−	0.626819i	$-0.784357\pi$
$743$	−3.17842e8	+	1.53065e8i	−0.774899	+	0.373172i	0.00426554	+	0.999991i	$0.498642\pi$
$744$	3.62273e8	+	5.46038e7i	0.879664	+	0.132588i
$745$	4.79713e8	+	7.03609e8i	1.16015	+	1.70162i
$746$	5.80769e8	−	8.75369e7i	1.39890	−	0.210851i
$747$	2.80648e8	+	3.02466e8i	0.673286	+	0.725630i
$748$	−1.57459e8	+	1.25569e8i	−0.376238	+	0.300040i
$749$	2.62208e6	+	4.26560e7i	0.00624022	+	0.101516i
$750$	−4.51334e8	+	5.65955e8i	−1.06983	+	1.34152i
$751$	2.36569e6	+	3.15679e7i	0.00558518	+	0.0745291i	0.999300	−	0.0374134i	$-0.0119118\pi$
$751$	2.36569e6	+	3.15679e7i	0.00558518	+	0.0745291i	−0.993715	+	0.111942i	$0.964293\pi$
$752$	2.68484e8	−	8.70404e8i	0.631342	−	2.04676i
$753$	−1.51337e8	+	2.62123e8i	−0.354454	+	0.613931i
$754$	−5.74266e8	+	3.31553e8i	−1.33967	+	0.773461i
$755$	8.04556e7	−	1.83635e7i	0.186946	−	0.0426691i
$756$	−5.23589e8	+	5.49336e8i	−1.21178	+	1.27137i
$757$	−1.32423e8	+	5.80181e8i	−0.305263	+	1.33745i	0.556801	+	0.830646i	$0.312029\pi$
$757$	−1.32423e8	+	5.80181e8i	−0.305263	+	1.33745i	−0.862064	+	0.506799i	$0.830828\pi$
$758$	−6.94775e8	+	2.14310e8i	−1.59528	+	0.492078i
$759$	3.03129e7	−	1.18969e7i	0.0693270	−	0.0272088i
$760$	6.26996e8	+	1.59756e9i	1.42831	+	3.63929i
$761$	−1.59960e8	−	5.18577e8i	−0.362959	−	1.17668i	−0.934456	−	0.356079i	$-0.884113\pi$
$761$	−1.59960e8	−	5.18577e8i	−0.362959	−	1.17668i	0.571497	−	0.820604i	$-0.306363\pi$
$762$	−4.74398e7	−	1.08278e7i	−0.107221	−	0.0244724i
$763$	1.37988e8	+	3.65939e8i	0.310647	+	0.823824i
$764$	−3.52099e8	−	1.54265e9i	−0.789560	−	3.45929i
$765$	2.83843e8	+	4.91631e8i	0.634008	+	1.09813i
$766$	5.84649e7	+	3.37547e7i	0.130079	+	0.0751014i
$767$	−2.69860e8	−	8.32408e7i	−0.598071	−	0.184480i
$768$	3.33844e8	−	2.50181e7i	0.736987	−	0.0552295i
$769$	2.09315e8	+	1.66923e8i	0.460279	+	0.367060i	0.826005	−	0.563662i	$-0.190608\pi$
$769$	2.09315e8	+	1.66923e8i	0.460279	+	0.367060i	−0.365727	+	0.930722i	$0.619179\pi$
$770$	−2.10306e8	+	2.99748e8i	−0.460659	+	0.656574i
$771$	−5.49306e7	−	6.88808e7i	−0.119854	−	0.150292i
$772$	1.28681e9	−	1.19399e9i	2.79681	−	2.59506i
$773$	−6.05181e7	−	4.01511e8i	−0.131023	−	0.869279i	−0.953698	−	0.300767i	$-0.902757\pi$
$773$	−6.05181e7	−	4.01511e8i	−0.131023	−	0.869279i	0.822675	−	0.568512i	$-0.192481\pi$
$774$	−1.01839e9	+	6.94329e8i	−2.19630	+	1.49741i
$775$	1.41554e8	−	9.39151e8i	0.304101	−	2.01758i
$776$	4.86764e8	+	1.01078e9i	1.04168	+	2.16307i
$777$	−9.81947e7	−	8.04848e7i	−0.209327	−	0.171574i
$778$	−8.20981e7	−	3.95364e7i	−0.174339	−	0.0839572i
$779$	−2.15573e8	−	1.46975e8i	−0.456019	−	0.310908i
$780$	9.04425e8	−	9.74738e8i	1.90585	−	2.05402i
$781$	1.13783e7	−	1.51832e8i	0.0238849	−	0.318721i
$782$	4.91351e8	+	1.92841e8i	1.02748	+	0.403255i
$783$		−	1.97311e8i		−	0.411024i
$784$	−4.30820e8	−	7.94672e8i	−0.894021	−	1.64907i
$785$	−6.66511e8			−1.37784
$786$	−3.58085e7	+	9.12387e7i	−0.0737427	+	0.187893i
$787$	−7.34411e8	−	5.50365e7i	−1.50666	−	0.112908i	−0.704365	−	0.709838i	$-0.748768\pi$
$787$	−7.34411e8	−	5.50365e7i	−1.50666	−	0.112908i	−0.802293	+	0.596930i	$0.796387\pi$
$788$	6.97535e8	+	6.47218e8i	1.42557	+	1.32273i
$789$	−1.91598e7	+	2.81022e7i	−0.0390085	+	0.0572150i
$790$	−3.54058e7	+	7.35209e7i	−0.0718113	+	0.149118i
$791$	6.62116e8	+	3.29866e8i	1.33784	+	0.666512i
$792$	2.07084e8	−	9.97264e7i	0.416842	−	0.200740i
$793$	7.21821e8	+	1.08797e8i	1.44747	+	0.218171i
$794$	−3.55350e8	−	5.21203e8i	−0.709896	−	1.04123i
$795$	−2.13097e8	+	3.21192e7i	−0.424108	+	0.0639240i
$796$	−2.87598e8	−	3.09956e8i	−0.570225	−	0.614556i
$797$	−2.21899e8	+	1.76959e8i	−0.438309	+	0.349540i	−0.817649	−	0.575718i	$-0.804723\pi$
$797$	−2.21899e8	+	1.76959e8i	−0.438309	+	0.349540i	0.379339	+	0.925258i	$0.376151\pi$
$798$	−3.55683e8	+	1.04512e8i	−0.699929	+	0.205665i
$799$	3.12539e8	−	3.91912e8i	0.612723	−	0.768331i
$800$	9.41175e7	+	1.25591e9i	0.183823	+	2.45295i
$801$	5.75928e7	−	1.86711e8i	0.112065	−	0.363306i
$802$	2.87230e8	−	4.97497e8i	0.556810	−	0.964423i
$803$	1.16148e8	−	6.70583e7i	0.224319	−	0.129511i
$804$	−5.28692e8	+	1.20670e8i	−1.01727	+	0.232184i
$805$	6.63429e8	+	5.86711e7i	1.27176	+	0.112470i
$806$	−3.09507e8	+	1.35604e9i	−0.591106	+	2.58980i
$807$	−3.91647e8	+	1.20807e8i	−0.745201	+	0.229864i
$808$	−1.12828e9	+	4.42819e8i	−2.13887	+	0.839444i
$809$	5.87660e7	+	1.49733e8i	0.110989	+	0.282796i	0.975567	−	0.219704i	$-0.0705091\pi$
$809$	5.87660e7	+	1.49733e8i	0.110989	+	0.282796i	−0.864577	+	0.502500i	$0.832414\pi$
$810$	−2.49169e8	−	8.07787e8i	−0.468856	−	1.51999i
$811$	4.71737e8	+	1.07671e8i	0.884376	+	0.201853i	0.640504	−	0.767954i	$-0.278725\pi$
$811$	4.71737e8	+	1.07671e8i	0.884376	+	0.201853i	0.243872	+	0.969808i	$0.421582\pi$
$812$	6.13242e8	+	1.98202e8i	1.14542	+	0.370203i
$813$	−4.96489e7	−	2.17526e8i	−0.0923928	−	0.404799i
$814$	7.63965e7	+	1.32323e8i	0.141645	+	0.245336i
$815$	−8.27376e8	−	4.77685e8i	−1.52837	−	0.882408i
$816$	−3.56913e8	−	1.10093e8i	−0.656889	−	0.202623i
$817$	−9.25679e8	+	6.93701e7i	−1.69744	+	0.127205i
$818$	3.54453e8	+	2.82667e8i	0.647589	+	0.516435i
$819$	−4.86027e8	−	5.38105e8i	−0.884727	−	0.979525i
$820$	−8.17128e8	−	1.02465e9i	−1.48200	−	1.85837i
$821$	−3.78565e8	+	3.51257e8i	−0.684087	+	0.634740i	−0.943634	−	0.330990i	$-0.892617\pi$
$821$	−3.78565e8	+	3.51257e8i	−0.684087	+	0.634740i	0.259547	+	0.965730i	$0.416427\pi$
$822$	−1.09870e6	−	7.28937e6i	−0.00197816	−	0.0131243i
$823$	5.04537e8	−	3.43987e8i	0.905093	−	0.617082i	−0.0187623	−	0.999824i	$-0.505973\pi$
$823$	5.04537e8	−	3.43987e8i	0.905093	−	0.617082i	0.923855	+	0.382742i	$0.125020\pi$
$824$	−8.34549e7	+	5.53687e8i	−0.149166	+	0.989652i
$825$	5.72554e7	+	1.18892e8i	0.101966	+	0.211734i
$826$	1.66805e8	+	3.58595e8i	0.295985	+	0.636303i
$827$	3.90442e8	+	1.88027e8i	0.690304	+	0.332433i	0.745935	−	0.666019i	$-0.232003\pi$
$827$	3.90442e8	+	1.88027e8i	0.690304	+	0.332433i	−0.0556313	+	0.998451i	$0.517717\pi$
$828$	−6.17838e8	−	4.21235e8i	−1.08839	−	0.742050i
$829$	2.23317e7	−	2.40679e7i	0.0391975	−	0.0422449i	−0.713149	−	0.701013i	$-0.752732\pi$
$829$	2.23317e7	−	2.40679e7i	0.0391975	−	0.0422449i	0.752346	+	0.658768i	$0.228922\pi$
$830$	−1.68079e8	+	2.24286e9i	−0.293955	+	3.92255i
$831$	−1.49413e8	−	5.86402e7i	−0.260366	−	0.102186i
$832$		−	1.02645e8i		−	0.178224i
$833$	−6.09279e7	−	4.93715e8i	−0.105410	−	0.854165i
$834$	−1.12375e8			−0.193719
$835$	−3.62346e7	+	9.23243e7i	−0.0622393	+	0.158583i
$836$	3.08753e8	+	2.31379e7i	0.528436	+	0.0396008i
$837$	−3.03392e8	−	2.81506e8i	−0.517401	−	0.480078i
$838$	2.35615e7	−	3.45583e7i	0.0400378	−	0.0587247i
$839$	6.30307e7	−	1.30885e8i	0.106725	−	0.221617i	−0.840766	−	0.541398i	$-0.817895\pi$
$839$	6.30307e7	−	1.30885e8i	0.106725	−	0.221617i	0.947491	+	0.319781i	$0.103609\pi$
$840$	−1.04101e9	−	1.39574e7i	−1.75637	−	0.0235487i
$841$	3.84948e8	−	1.85381e8i	0.647163	−	0.311657i
$842$	−1.67092e9	−	2.51851e8i	−2.79911	−	0.421897i
$843$	−1.29839e8	−	1.90439e8i	−0.216732	−	0.317887i
$844$	1.92742e9	−	2.90511e8i	3.20589	−	0.483210i
$845$	1.18117e9	+	1.27300e9i	1.95768	+	2.10988i
$846$	−8.00010e8	+	6.37987e8i	−1.32125	+	1.05366i
$847$	−2.78704e8	−	4.98033e8i	−0.458663	−	0.819611i
$848$	−3.99180e8	+	5.00555e8i	−0.654607	+	0.820852i
$849$	1.15067e7	+	1.53546e8i	0.0188030	+	0.250909i
$850$	−6.30477e8	+	2.04396e9i	−1.02663	+	3.32824i
$851$	1.38957e8	−	2.40681e8i	0.225472	−	0.390529i
$852$	6.70578e8	−	3.87159e8i	1.08425	−	0.625994i
$853$	3.35652e8	−	7.66105e7i	0.540807	−	0.123436i	0.0566130	−	0.998396i	$-0.481970\pi$
$853$	3.35652e8	−	7.66105e7i	0.540807	−	0.123436i	0.484194	+	0.874960i	$0.339113\pi$
$854$	−5.64497e8	−	8.52294e8i	−0.906333	−	1.36841i
$855$	1.94202e8	−	8.50854e8i	0.310710	−	1.36131i
$856$	1.39733e8	−	4.31019e7i	0.222781	−	0.0687188i
$857$	3.04911e8	−	1.19669e8i	0.484429	−	0.190124i	−0.110542	−	0.993871i	$-0.535259\pi$
$857$	3.04911e8	−	1.19669e8i	0.484429	−	0.190124i	0.594971	+	0.803747i	$0.297164\pi$
$858$	−7.06038e7	−	1.79896e8i	−0.111781	−	0.284812i
$859$	2.18994e8	+	7.09962e8i	0.345504	+	1.12010i	0.947003	+	0.321224i	$0.104094\pi$
$859$	2.18994e8	+	7.09962e8i	0.345504	+	1.12010i	−0.601499	+	0.798873i	$0.705430\pi$
$860$	−4.54590e9	−	1.03757e9i	−7.14702	−	1.63126i
$861$	1.31958e8	−	8.73991e7i	0.206740	−	0.136930i
$862$	2.56085e8	+	1.12198e9i	0.399817	+	1.75171i
$863$	2.70543e8	+	4.68594e8i	0.420924	+	0.729061i	0.996030	−	0.0890175i	$-0.0283727\pi$
$863$	2.70543e8	+	4.68594e8i	0.420924	+	0.729061i	−0.575106	+	0.818079i	$0.695039\pi$
$864$	4.75293e8	+	2.74411e8i	0.736920	+	0.425461i
$865$	1.21607e9	+	3.75107e8i	1.87893	+	0.579572i
$866$	1.10257e9	−	8.26258e7i	1.69766	−	0.127222i
$867$	5.62563e7	+	4.48629e7i	0.0863205	+	0.0688383i
$868$	1.17968e9	−	6.60162e8i	1.80387	−	1.00947i
$869$	5.13177e6	+	6.43504e6i	0.00782003	+	0.00980600i
$870$	3.54915e8	−	3.29313e8i	0.538972	−	0.500093i
$871$	−1.71554e8	−	1.13819e9i	−0.259625	−	1.72250i
$872$	1.10565e9	−	7.53821e8i	1.66751	−	1.13689i
$873$	8.50297e7	−	5.64136e8i	0.127799	−	0.847892i
$874$	−3.52086e8	−	7.31113e8i	−0.527368	−	1.09509i
$875$	−2.00202e7	+	1.49319e9i	−0.0298843	+	2.22891i
$876$	6.14513e8	+	2.95934e8i	0.914153	+	0.440233i
$877$	−3.26500e8	−	2.22604e8i	−0.484043	−	0.330015i	0.296589	−	0.955005i	$-0.404151\pi$
$877$	−3.26500e8	−	2.22604e8i	−0.484043	−	0.330015i	−0.780633	+	0.624990i	$0.785103\pi$
$878$	−5.66840e8	+	6.10908e8i	−0.837485	+	0.902594i
$879$	−2.60214e7	+	3.47231e8i	−0.0383146	+	0.511272i
$880$	5.27953e8	+	2.07206e8i	0.774725	+	0.304057i
$881$			1.22161e8i			0.178650i	0.996003	+	0.0893252i	$0.0284711\pi$
$881$			1.22161e8i			0.178650i	−0.996003	+	0.0893252i	$0.971529\pi$
$882$	−1.03008e8	+	1.01023e9i	−0.150129	+	1.47236i
$883$	3.63382e8			0.527815			0.263907	−	0.964548i	$-0.414989\pi$
$883$	3.63382e8			0.527815			0.263907	+	0.964548i	$0.414989\pi$
$884$	7.94243e8	−	2.02370e9i	1.14973	−	2.92947i
$885$	2.05620e8	+	1.54091e7i	0.296644	+	0.0222304i
$886$	−1.40925e9	−	1.30760e9i	−2.02623	−	1.88007i
$887$	−4.58590e8	+	6.72627e8i	−0.657133	+	0.963837i	0.342570	+	0.939492i	$0.388702\pi$
$887$	−4.58590e8	+	6.72627e8i	−0.657133	+	0.963837i	−0.999704	+	0.0243451i	$0.992250\pi$
$888$	−1.88492e8	+	3.91407e8i	−0.269186	+	0.558971i
$889$	−9.10171e7	+	4.23379e7i	−0.129544	+	0.0602592i
$890$	9.59606e8	−	4.62122e8i	1.36120	−	0.655521i
$891$	−8.43126e7	−	1.27081e7i	−0.119195	−	0.0179658i
$892$	8.80110e8	+	1.29088e9i	1.24006	+	1.81883i
$893$	−7.62028e8	+	1.14857e8i	−1.07008	+	0.161289i
$894$	4.28115e8	+	4.61398e8i	0.599167	+	0.645748i
$895$	−6.85049e8	+	5.46308e8i	−0.955548	+	0.762024i
$896$	4.79878e8	−	4.33436e8i	0.667124	−	0.602560i
$897$	−2.19163e8	+	2.74822e8i	−0.303662	+	0.380780i
$898$	6.98022e7	+	9.31446e8i	0.0963919	+	1.28626i
$899$	−1.03600e8	+	3.35862e8i	−0.142587	+	0.462255i
$900$	1.51512e9	−	2.62426e9i	2.07835	−	3.59980i
$901$	−3.05132e8	+	1.76168e8i	−0.417171	+	0.240854i
$902$	−1.85699e8	+	4.23846e7i	−0.253041	+	0.0577549i
$903$	1.73182e8	−	5.35831e8i	0.235202	−	0.727721i
$904$	5.63227e8	−	2.46766e9i	0.762392	−	3.34026i
$905$	1.13476e9	−	3.50026e8i	1.53094	−	0.472231i
$906$	5.67793e7	−	2.22842e7i	0.0763494	−	0.0299649i
$907$	3.59854e8	+	9.16893e8i	0.482286	+	1.22884i	0.940436	+	0.339970i	$0.110417\pi$
$907$	3.59854e8	+	9.16893e8i	0.482286	+	1.22884i	−0.458151	+	0.888875i	$0.651488\pi$
$908$	−9.09465e7	−	2.94841e8i	−0.121487	−	0.393850i
$909$	6.00919e8	+	1.37156e8i	0.800063	+	0.182609i
$910$	3.48190e8	−	3.93720e9i	0.462054	−	5.22472i
$911$	−2.59923e8	−	1.13880e9i	−0.343787	−	1.50623i	−0.791009	−	0.611805i	$-0.790444\pi$
$911$	−2.59923e8	−	1.13880e9i	−0.343787	−	1.50623i	0.447222	−	0.894423i	$-0.352413\pi$
$912$	2.87106e8	+	4.97282e8i	0.378493	+	0.655569i
$913$	1.96466e8	+	1.13430e8i	0.258152	+	0.149044i
$914$	−1.92159e9	−	5.92732e8i	−2.51665	−	0.776282i
$915$	−5.31494e8	+	3.98300e7i	−0.693801	+	0.0519932i
$916$	5.55976e8	+	4.43376e8i	0.723385	+	0.576881i
$917$	5.70030e7	+	1.93996e8i	0.0739247	+	0.251585i
$918$	5.81156e8	+	7.28747e8i	0.751216	+	0.941996i
$919$	7.35487e8	−	6.82432e8i	0.947608	−	0.879251i	−0.0451993	−	0.998978i	$-0.514392\pi$
$919$	7.35487e8	−	6.82432e8i	0.947608	−	0.879251i	0.992807	+	0.119727i	$0.0382018\pi$
$920$	−3.39650e8	−	2.25343e9i	−0.436182	−	2.89388i
$921$	2.36686e8	−	1.61370e8i	0.302966	−	0.206559i
$922$	−3.83039e8	+	2.54130e9i	−0.488709	+	3.24237i
$923$	7.13107e8	+	1.48078e9i	0.906879	+	1.88315i
$924$	−8.37557e7	+	1.68117e8i	−0.106169	+	0.213106i
$925$	1.01468e9	+	4.88643e8i	1.28204	+	0.617400i
$926$	5.57476e8	+	3.80081e8i	0.702091	+	0.478678i
$927$	1.93677e8	−	2.08734e8i	0.243130	−	0.262032i
$928$	3.48301e7	−	4.64775e8i	0.0435823	−	0.581565i
$929$	−1.25399e9	−	4.92153e8i	−1.56403	−	0.613837i	−0.583836	−	0.811872i	$-0.698449\pi$
$929$	−1.25399e9	−	4.92153e8i	−1.56403	−	0.613837i	−0.980195	+	0.198035i	$0.936544\pi$
$930$		−	1.01556e9i		−	1.26258i
$931$	−4.47598e8	+	6.20107e8i	−0.554675	+	0.768454i
$932$	2.55815e9			3.15993
$933$	3.12697e7	−	7.96739e7i	0.0385016	−	0.0981005i
$934$	2.46428e9	+	1.84672e8i	3.02447	+	0.226652i
$935$	2.28801e8	+	2.12296e8i	0.279913	+	0.259721i
$936$	−1.39763e9	+	2.04995e9i	−1.70438	+	2.49986i
$937$	6.67567e7	−	1.38622e8i	0.0811476	−	0.168505i	−0.856447	−	0.516235i	$-0.827333\pi$
$937$	6.67567e7	−	1.38622e8i	0.0811476	−	0.168505i	0.937595	+	0.347730i	$0.113047\pi$
$938$	−1.02185e9	+	1.24670e9i	−1.23816	+	1.51061i
$939$	1.10762e8	−	5.33400e7i	0.133780	−	0.0644253i
$940$	−3.82774e9	−	5.76939e8i	−4.60849	−	0.694618i
$941$	−2.78238e7	−	4.08100e7i	−0.0333923	−	0.0489776i	0.809180	−	0.587561i	$-0.199912\pi$
$941$	−2.78238e7	−	4.08100e7i	−0.0333923	−	0.0489776i	−0.842572	+	0.538584i	$0.818960\pi$
$942$	−4.87129e8	+	7.34229e7i	−0.582763	+	0.0878373i
$943$	2.35649e8	+	2.53969e8i	0.281015	+	0.302862i
$944$	4.78937e8	−	3.81939e8i	0.569328	−	0.454024i
$945$	9.62779e8	+	6.75495e8i	1.14086	+	0.800437i
$946$	−4.22526e8	+	5.29831e8i	−0.499091	+	0.625841i
$947$	1.63593e7	+	2.18300e8i	0.0192626	+	0.257041i	0.998518	+	0.0544138i	$0.0173290\pi$
$947$	1.63593e7	+	2.18300e8i	0.0192626	+	0.257041i	−0.979256	+	0.202627i	$0.935052\pi$
$948$	−1.23378e7	+	3.99982e7i	−0.0144815	+	0.0469479i
$949$	−7.23858e8	+	1.25376e9i	−0.846944	+	1.46695i
$950$	2.84782e9	−	1.64419e9i	3.32155	−	1.91770i
$951$	5.46942e8	−	1.24836e8i	0.635916	−	0.145144i
$952$	−1.59267e9	+	6.00563e8i	−1.84593	+	0.696062i
$953$	−2.78897e8	+	1.22193e9i	−0.322229	+	1.41178i	0.511347	+	0.859374i	$0.329147\pi$
$953$	−2.78897e8	+	1.22193e9i	−0.322229	+	1.41178i	−0.833576	+	0.552404i	$0.813710\pi$
$954$	6.87271e8	−	2.11995e8i	0.791559	−	0.244163i
$955$	−2.28273e9	+	8.95905e8i	−2.62086	+	1.02861i
$956$	−6.70323e7	−	1.70796e8i	−0.0767203	−	0.195480i
$957$	−1.43942e7	−	4.66649e7i	−0.0164230	−	0.0532421i
$958$	1.86622e9	+	4.25953e8i	2.12259	+	0.484468i
$959$	−1.10081e7	−	1.04922e7i	−0.0124812	−	0.0118962i
$960$	1.66769e7	+	7.30662e7i	0.0188496	+	0.0825853i
$961$	−7.51277e7	−	1.30125e8i	−0.0846506	−	0.146619i
$962$	−1.42835e9	−	8.24659e8i	−1.60439	−	0.926295i
$963$	−7.10584e7	−	2.19186e7i	−0.0795676	−	0.0245434i
$964$	−6.74854e8	+	5.05733e7i	−0.753318	+	0.0564534i
$965$	−2.12698e9	−	1.69621e9i	−2.36690	−	1.88754i
$966$	4.91340e8	−	3.02028e7i	0.545069	−	0.0335055i
$967$	7.01196e8	+	8.79272e8i	0.775461	+	0.972397i	0.999998	−	0.00206816i	$-0.000658318\pi$
$967$	7.01196e8	+	8.79272e8i	0.775461	+	0.972397i	−0.224537	+	0.974466i	$0.572087\pi$
$968$	−1.43149e9	+	1.32823e9i	−1.57820	+	1.46436i
$969$	4.70978e7	+	3.12473e8i	0.0517641	+	0.343433i
$970$	2.56947e9	−	1.75184e9i	2.81533	−	1.91946i
$971$	3.37092e7	−	2.23646e8i	0.0368206	−	0.244289i	−0.962848	−	0.270045i	$-0.912961\pi$
$971$	3.37092e7	−	2.23646e8i	0.0368206	−	0.244289i	0.999668	+	0.0257565i	$0.00819944\pi$
$972$	−8.87960e8	−	1.84387e9i	−0.966930	−	2.00785i
$973$	−1.83168e8	+	1.42097e8i	−0.198843	+	0.154257i
$974$	2.24972e8	+	1.08341e8i	0.243473	+	0.117250i
$975$	−1.17693e9	−	8.02416e8i	−1.26980	−	0.865737i
$976$	−1.07700e9	+	1.16073e9i	−1.15842	+	1.24848i
$977$	1.14745e8	−	1.53116e9i	0.123041	−	1.64187i	−0.504592	−	0.863358i	$-0.668357\pi$
$977$	1.14745e8	−	1.53116e9i	0.123041	−	1.64187i	0.627633	−	0.778510i	$-0.284024\pi$
$978$	−6.57322e8	−	2.57980e8i	−0.702686	−	0.275784i
$979$		−	1.07429e8i		−	0.114491i
$980$	−3.06656e9	+	2.31377e9i	−3.25816	+	2.45834i
$981$	−6.80502e8			−0.720812
$982$	−1.16435e9	+	2.96671e9i	−1.22956	+	3.13286i
$983$	−7.26136e8	−	5.44164e7i	−0.764465	−	0.0572887i	−0.313210	−	0.949684i	$-0.601404\pi$
$983$	−7.26136e8	−	5.44164e7i	−0.764465	−	0.0572887i	−0.451255	+	0.892395i	$0.649023\pi$
$984$	−3.96997e8	−	3.68359e8i	−0.416679	−	0.386622i
$985$	8.30722e8	−	1.21845e9i	0.869255	−	1.27496i
$986$	3.43451e8	−	7.13184e8i	0.358290	−	0.743996i
$987$	1.10128e8	−	4.54337e8i	0.114537	−	0.472527i
$988$	−3.01119e9	+	1.45011e9i	−3.12225	+	1.50360i
$989$	1.21886e9	+	1.83714e8i	1.25999	+	0.189912i
$990$	−3.58910e8	−	5.26424e8i	−0.369896	−	0.542538i
$991$	8.76031e8	−	1.32040e8i	0.900116	−	0.135671i	0.317348	−	0.948309i	$-0.397208\pi$
$991$	8.76031e8	−	1.32040e8i	0.900116	−	0.135671i	0.582768	+	0.812639i	$0.301970\pi$
$992$	−6.64959e8	−	7.16655e8i	−0.681176	−	0.734134i
$993$	−2.73302e8	+	2.17951e8i	−0.279122	+	0.222593i
$994$	8.69546e8	−	2.13111e9i	0.885388	−	2.16993i
$995$	−4.08568e8	+	5.12328e8i	−0.414758	+	0.520091i
$996$	8.62166e7	+	1.15048e9i	0.0872595	+	1.16440i
$997$	1.93118e8	−	6.26074e8i	0.194867	−	0.631743i	−0.804423	−	0.594057i	$-0.797525\pi$
$997$	1.93118e8	−	6.26074e8i	0.194867	−	0.631743i	0.999290	−	0.0376856i	$-0.0119985\pi$
$998$	−1.25092e9	+	2.16667e9i	−1.25846	+	2.17972i
$999$	4.25015e8	−	2.45383e8i	0.426293	−	0.246120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.7.h.a.3.2	✓	324
49.33	odd	42	inner	49.7.h.a.33.2	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.7.h.a.3.2	✓	324	1.1	even	1	trivial
49.7.h.a.33.2	yes	324	49.33	odd	42	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:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	49.h (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.28359 + 13.4624i) q^{2} +(11.4646 + 0.859156i) q^{3} +(-106.404 - 98.7284i) q^{4} +(-126.721 + 185.865i) q^{5} +(-72.1408 + 149.802i) q^{6} +(71.8347 + 335.393i) q^{7} +(1057.40 - 509.218i) q^{8} +(-590.158 - 88.9520i) q^{9} +(-1832.64 - 2688.00i) q^{10} +(-324.476 + 48.9069i) q^{11} +(-1135.06 - 1223.30i) q^{12} +(2769.33 - 2208.47i) q^{13} +(-4894.74 - 805.017i) q^{14} +(-1612.49 + 2022.00i) q^{15} +(574.179 + 7661.89i) q^{16} +(-1246.33 + 4040.49i) q^{17} +(4315.66 - 7474.94i) q^{18} +(5629.56 - 3250.23i) q^{19} +(31833.7 - 7265.84i) q^{20} +(535.404 + 3906.88i) q^{21} +(1056.00 - 4626.62i) q^{22} +(-8248.29 + 2544.26i) q^{23} +(12560.2 - 4929.52i) q^{24} +(-12779.2 - 32561.0i) q^{25} +(15099.2 + 48950.4i) q^{26} +(-14860.5 - 3391.82i) q^{27} +(25469.4 - 42779.3i) q^{28} +(2880.45 + 12620.1i) q^{29} +(-18701.2 - 32391.4i) q^{30} +(23514.6 + 13576.2i) q^{31} +(-34405.9 - 10612.8i) q^{32} +(-3762.02 + 281.924i) q^{33} +(-47809.5 - 38126.8i) q^{34} +(-71440.9 - 29149.7i) q^{35} +(54013.0 + 67730.2i) q^{36} +(-23601.9 + 21899.3i) q^{37} +(14011.5 + 92960.2i) q^{38} +(33646.8 - 22940.0i) q^{39} +(-39348.8 + 261062. i) q^{40} +(-17414.8 - 36162.3i) q^{41} +(-55424.8 - 13434.6i) q^{42} +(-128660. - 61959.2i) q^{43} +(39354.0 + 26831.1i) q^{44} +(91318.3 - 98417.7i) q^{45} +(9328.82 - 124484. i) q^{46} +(-110356. - 43311.5i) q^{47} +88334.1i q^{48} +(-107329. + 48185.8i) q^{49} +505868. q^{50} +(-17760.1 + 45252.0i) q^{51} +(-512706. - 38422.0i) q^{52} +(61083.2 + 56676.9i) q^{53} +(124179. - 182137. i) q^{54} +(32027.7 - 66506.2i) q^{55} +(246746. + 318066. i) q^{56} +(67333.3 - 32426.0i) q^{57} +(-185116. - 27901.7i) q^{58} +(-44912.6 - 65874.7i) q^{59} +(371205. - 55950.1i) q^{60} +(140173. + 151071. i) q^{61} +(-307009. + 244831. i) q^{62} +(-12559.9 - 204325. i) q^{63} +(18067.8 - 22656.3i) q^{64} +(59545.5 + 794580. i) q^{65} +(16081.6 - 52135.3i) q^{66} +(162480. - 281424. i) q^{67} +(531526. - 306876. i) q^{68} +(-96749.5 + 22082.4i) q^{69} +(769889. - 807749. i) q^{70} +(-103250. + 452368. i) q^{71} +(-669330. + 206461. i) q^{72} +(-380463. + 149321. i) q^{73} +(-170114. - 433445. i) q^{74} +(-118534. - 384279. i) q^{75} +(-919898. - 209961. i) q^{76} +(-39711.7 - 105314. i) q^{77} +(131051. + 574171. i) q^{78} +(-12541.4 - 21722.4i) q^{79} +(-1.49684e6 - 864200. i) q^{80} +(248298. + 76589.9i) q^{81} +(578843. - 43378.3i) q^{82} +(-540517. - 431048. i) q^{83} +(328751. - 468567. i) q^{84} +(-593051. - 743662. i) q^{85} +(1.51390e6 - 1.40470e6i) q^{86} +(22180.7 + 147160. i) q^{87} +(-318197. + 216943. i) q^{88} +(-48794.4 + 323729. i) q^{89} +(842447. + 1.74936e6i) q^{90} +(939639. + 770171. i) q^{91} +(1.12884e6 + 543621. i) q^{92} +(257922. + 175848. i) q^{93} +(1.16615e6 - 1.25681e6i) q^{94} +(-109278. + 1.45821e6i) q^{95} +(-385333. - 151232. i) q^{96} +955906. i q^{97} +(-81614.8 - 1.69949e6i) q^{98} +195842. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 13 q^{2} - 11 q^{3} + 819 q^{4} - 179 q^{5} + 770 q^{6} + 392 q^{7} + 828 q^{8} - 1160 q^{9} - 2594 q^{10} - 5305 q^{11} + 7497 q^{12} - 14 q^{13} - 11403 q^{14} - 6196 q^{15} + 27903 q^{16} - 5107 q^{17}+ \cdots - 4449616 q^{99}+O(q^{100}) \) 324 * q - 13 * q^2 - 11 * q^3 + 819 * q^4 - 179 * q^5 + 770 * q^6 + 392 * q^7 + 828 * q^8 - 1160 * q^9 - 2594 * q^10 - 5305 * q^11 + 7497 * q^12 - 14 * q^13 - 11403 * q^14 - 6196 * q^15 + 27903 * q^16 - 5107 * q^17 - 11538 * q^18 - 30006 * q^19 - 50190 * q^20 + 8953 * q^21 + 33042 * q^22 + 54531 * q^23 + 90184 * q^24 - 92804 * q^25 - 93366 * q^26 - 11774 * q^27 - 19180 * q^28 - 80398 * q^29 + 15851 * q^30 + 39378 * q^31 - 197841 * q^32 + 36697 * q^33 - 54698 * q^34 - 819 * q^35 + 706300 * q^36 + 15331 * q^37 - 304462 * q^38 - 179298 * q^39 - 515414 * q^40 - 116046 * q^41 + 1203482 * q^42 - 225018 * q^43 + 1373764 * q^44 + 465772 * q^45 + 1100364 * q^46 + 270021 * q^47 - 767900 * q^49 - 1164040 * q^50 - 1215743 * q^51 - 3954790 * q^52 + 141807 * q^53 - 1093487 * q^54 + 991354 * q^55 - 596680 * q^56 - 388207 * q^57 + 381012 * q^58 + 2015849 * q^59 + 5807298 * q^60 + 258821 * q^61 - 525742 * q^62 - 1265432 * q^63 + 872972 * q^64 - 70154 * q^65 + 497766 * q^66 - 324190 * q^67 - 799617 * q^68 - 2216774 * q^69 + 56140 * q^70 - 1031026 * q^71 + 4633092 * q^72 + 1268305 * q^73 - 1444192 * q^74 - 1699244 * q^75 - 5464011 * q^76 - 2274741 * q^77 - 1285956 * q^78 - 515710 * q^79 + 8314050 * q^80 - 1069027 * q^81 + 357910 * q^82 - 3183054 * q^83 - 10099096 * q^84 - 1596848 * q^85 - 5387681 * q^86 - 4197040 * q^87 - 1024645 * q^88 + 983769 * q^89 + 18547774 * q^90 + 13421086 * q^91 + 5294506 * q^92 + 15477850 * q^93 + 8903632 * q^94 + 5236430 * q^95 + 7804258 * q^96 - 10234553 * q^98 - 4449616 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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