LMFDB - Embedded newform 31.8.g.a.7.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,8,Mod(7,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.7"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, 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:	$9.68393579001$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			7.17
Character	$\chi$	$=$	31.7
Dual form			31.8.g.a.9.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.20562 + 16.0213i) q^{2} +(-55.0184 + 11.6945i) q^{3} +(-126.028 + 91.5648i) q^{4} +(247.149 - 428.075i) q^{5} +(-473.766 - 820.587i) q^{6} +(-708.649 - 315.511i) q^{7} +(-378.590 - 275.062i) q^{8} +(892.338 - 397.295i) q^{9} +(8144.86 + 1731.24i) q^{10} +(-373.854 - 3556.99i) q^{11} +(5863.06 - 6511.59i) q^{12} +(1535.91 + 1705.80i) q^{13} +(1365.92 - 12995.9i) q^{14} +(-8591.61 + 26442.3i) q^{15} +(-3725.68 + 11466.5i) q^{16} +(3080.40 - 29308.0i) q^{17} +(11010.3 + 12228.2i) q^{18} +(8961.08 - 9952.29i) q^{19} +(8048.84 + 76579.6i) q^{20} +(42678.5 + 9071.59i) q^{21} +(55041.3 - 24505.9i) q^{22} +(-47721.1 - 34671.4i) q^{23} +(24046.2 + 10706.0i) q^{24} +(-83102.8 - 143938. i) q^{25} +(-19333.7 + 33487.0i) q^{26} +(55071.1 - 40011.5i) q^{27} +(118199. - 25124.0i) q^{28} +(-30936.1 - 95211.6i) q^{29} -468363. q^{30} +(152410. + 65450.6i) q^{31} -263001. q^{32} +(62166.1 + 191328. i) q^{33} +(485587. - 103215. i) q^{34} +(-310204. + 225376. i) q^{35} +(-76081.5 + 131777. i) q^{36} +(-27965.3 - 48437.4i) q^{37} +(206096. + 91760.0i) q^{38} +(-104452. - 75888.7i) q^{39} +(-211315. + 94083.7i) q^{40} +(-525862. - 111775. i) q^{41} +(76829.7 + 730986. i) q^{42} +(-563959. + 626340. i) q^{43} +(372811. + 414048. i) q^{44} +(50468.8 - 480178. i) q^{45} +(307062. - 945039. i) q^{46} +(-107644. + 331294. i) q^{47} +(70886.1 - 674437. i) q^{48} +(-148422. - 164839. i) q^{49} +(1.87347e6 - 2.08070e6i) q^{50} +(173265. + 1.64850e6i) q^{51} +(-349759. - 74343.6i) q^{52} +(1.84961e6 - 823499. i) q^{53} +(927713. + 674023. i) q^{54} +(-1.61505e6 - 719068. i) q^{55} +(181503. + 314372. i) q^{56} +(-376637. + 652355. i) q^{57} +(1.36437e6 - 991272. i) q^{58} +(-1.27166e6 + 270300. i) q^{59} +(-1.33840e6 - 4.11916e6i) q^{60} +1.80614e6 q^{61} +(-255212. + 2.78251e6i) q^{62} -757705. q^{63} +(-892197. - 2.74590e6i) q^{64} +(1.10981e6 - 235897. i) q^{65} +(-2.74170e6 + 1.99196e6i) q^{66} +(-1.96317e6 + 3.40031e6i) q^{67} +(2.29537e6 + 3.97569e6i) q^{68} +(3.03101e6 + 1.34949e6i) q^{69} +(-5.22562e6 - 3.79663e6i) q^{70} +(4.23583e6 - 1.88591e6i) q^{71} +(-447111. - 95036.5i) q^{72} +(-189172. - 1.79985e6i) q^{73} +(630451. - 700187. i) q^{74} +(6.25547e6 + 6.94740e6i) q^{75} +(-218069. + 2.07479e6i) q^{76} +(-857336. + 2.63861e6i) q^{77} +(672095. - 2.06850e6i) q^{78} +(-204604. + 1.94667e6i) q^{79} +(3.98771e6 + 4.42880e6i) q^{80} +(-3.99142e6 + 4.43293e6i) q^{81} +(-946656. - 9.00683e6i) q^{82} +(-6.65062e6 - 1.41363e6i) q^{83} +(-6.20932e6 + 2.76457e6i) q^{84} +(-1.17847e7 - 8.56209e6i) q^{85} +(-1.29705e7 - 5.77484e6i) q^{86} +(2.81551e6 + 4.87661e6i) q^{87} +(-836854. + 1.44947e6i) q^{88} +(7.48326e6 - 5.43691e6i) q^{89} +(7.95578e6 - 1.69105e6i) q^{90} +(-550222. - 1.69341e6i) q^{91} +9.18888e6 q^{92} +(-9.15077e6 - 1.81863e6i) q^{93} -5.86810e6 q^{94} +(-2.04560e6 - 6.29571e6i) q^{95} +(1.44699e7 - 3.07567e6i) q^{96} +(-9.64317e6 + 7.00617e6i) q^{97} +(1.86830e6 - 3.23600e6i) q^{98} +(-1.74678e6 - 3.02550e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{2} - 8 q^{3} - 2362 q^{4} - 75 q^{5} - 1637 q^{6} + 5518 q^{7} + 3401 q^{8} + 14542 q^{9} - 5312 q^{10} + 1361 q^{11} - 18281 q^{12} + 22457 q^{13} + 28470 q^{14} - 86918 q^{15} - 155730 q^{16}+ \cdots - 102755966 q^{99}+O(q^{100}) $ 144 * q - 6 * q^2 - 8 * q^3 - 2362 * q^4 - 75 * q^5 - 1637 * q^6 + 5518 * q^7 + 3401 * q^8 + 14542 * q^9 - 5312 * q^10 + 1361 * q^11 - 18281 * q^12 + 22457 * q^13 + 28470 * q^14 - 86918 * q^15 - 155730 * q^16 + 51582 * q^17 - 24915 * q^18 + 206748 * q^19 + 53815 * q^20 - 28547 * q^21 + 471441 * q^22 - 10235 * q^23 + 69278 * q^24 - 974301 * q^25 - 279651 * q^26 - 948323 * q^27 + 550632 * q^28 - 32990 * q^29 + 2457990 * q^30 + 899715 * q^31 - 1048518 * q^32 + 780887 * q^33 - 1741528 * q^34 + 40023 * q^35 - 2118881 * q^36 - 787972 * q^37 + 580274 * q^38 + 2541281 * q^39 + 2341817 * q^40 + 1129504 * q^41 - 4390379 * q^42 + 481927 * q^43 - 3123681 * q^44 - 1715971 * q^45 + 2065430 * q^46 - 3123106 * q^47 + 1041890 * q^48 + 76766 * q^49 + 7537425 * q^50 + 6145978 * q^51 + 3260257 * q^52 + 141486 * q^53 - 8979668 * q^54 - 8182779 * q^55 - 5240874 * q^56 - 5487037 * q^57 + 5315215 * q^58 + 7471552 * q^59 + 8590679 * q^60 + 10667852 * q^61 + 27020951 * q^62 - 23783686 * q^63 - 3962521 * q^64 + 935148 * q^65 + 3015728 * q^66 - 17382495 * q^67 - 29462568 * q^68 - 26986306 * q^69 - 31811186 * q^70 - 6186650 * q^71 + 35811589 * q^72 + 6470154 * q^73 + 55339663 * q^74 + 17367737 * q^75 + 2919592 * q^76 + 31865334 * q^77 - 7291717 * q^78 + 4223078 * q^79 + 77431338 * q^80 - 5164601 * q^81 - 19477394 * q^82 - 28867780 * q^83 - 76561164 * q^84 - 45198987 * q^85 - 60993764 * q^86 + 18253055 * q^87 - 45197061 * q^88 - 8429459 * q^89 + 83458809 * q^90 - 53128088 * q^91 + 77469728 * q^92 + 41662009 * q^93 - 16867972 * q^94 - 12744274 * q^95 + 119555444 * q^96 + 20643027 * q^97 + 49624796 * q^98 - 102755966 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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 $

$2$	5.20562	+	16.0213i	0.460116	+	1.41609i	0.865022	+	0.501734i	$0.167304\pi$
$2$	5.20562	+	16.0213i	0.460116	+	1.41609i	−0.404905	+	0.914359i	$0.632696\pi$
$3$	−55.0184	+	11.6945i	−1.17648	+	0.250068i	−0.754352	−	0.656470i	$-0.772049\pi$
$3$	−55.0184	+	11.6945i	−1.17648	+	0.250068i	−0.422125	+	0.906538i	$0.638716\pi$
$4$	−126.028	+	91.5648i	−0.984595	+	0.715350i
$5$	247.149	−	428.075i	0.884227	−	1.53153i	0.0376304	−	0.999292i	$-0.488019\pi$
$5$	247.149	−	428.075i	0.884227	−	1.53153i	0.846597	−	0.532235i	$-0.178648\pi$
$6$	−473.766	−	820.587i	−0.895436	−	1.55094i
$7$	−708.649	−	315.511i	−0.780886	−	0.347673i	−0.0227265	−	0.999742i	$-0.507235\pi$
$7$	−708.649	−	315.511i	−0.780886	−	0.347673i	−0.758160	+	0.652069i	$0.773901\pi$
$8$	−378.590	−	275.062i	−0.261430	−	0.189940i
$9$	892.338	−	397.295i	0.408019	−	0.181662i
$10$	8144.86	+	1731.24i	2.57563	+	0.547467i
$11$	−373.854	−	3556.99i	−0.0846892	−	0.805764i	−0.951608	−	0.307314i	$-0.900570\pi$
$11$	−373.854	−	3556.99i	−0.0846892	−	0.805764i	0.866919	−	0.498449i	$-0.166097\pi$
$12$	5863.06	−	6511.59i	0.979467	−	1.08781i
$13$	1535.91	+	1705.80i	0.193894	+	0.215341i	0.832250	−	0.554400i	$-0.187052\pi$
$13$	1535.91	+	1705.80i	0.193894	+	0.215341i	−0.638357	+	0.769741i	$0.720386\pi$
$14$	1365.92	−	12995.9i	0.133039	−	1.26578i
$15$	−8591.61	+	26442.3i	−0.657288	+	2.02292i
$16$	−3725.68	+	11466.5i	−0.227398	+	0.699858i
$17$	3080.40	−	29308.0i	0.152067	−	1.44682i	−0.606426	−	0.795140i	$-0.707397\pi$
$17$	3080.40	−	29308.0i	0.152067	−	1.44682i	0.758493	−	0.651682i	$-0.225936\pi$
$18$	11010.3	+	12228.2i	0.444986	+	0.494208i
$19$	8961.08	−	9952.29i	0.299725	−	0.332878i	−0.574404	−	0.818572i	$-0.694766\pi$
$19$	8961.08	−	9952.29i	0.299725	−	0.332878i	0.874129	+	0.485693i	$0.161433\pi$
$20$	8048.84	+	76579.6i	0.224972	+	2.14046i
$21$	42678.5	+	9071.59i	1.00564	+	0.213755i
$22$	55041.3	−	24505.9i	1.10207	−	0.490673i
$23$	−47721.1	−	34671.4i	−0.817830	−	0.594188i	0.0982599	−	0.995161i	$-0.468672\pi$
$23$	−47721.1	−	34671.4i	−0.817830	−	0.594188i	−0.916090	+	0.400972i	$0.868672\pi$
$24$	24046.2	+	10706.0i	0.355064	+	0.158085i
$25$	−83102.8	−	143938.i	−1.06372	−	1.84241i
$26$	−19333.7	+	33487.0i	−0.215729	+	0.373653i
$27$	55071.1	−	40011.5i	0.538456	−	0.391211i
$28$	118199.	−	25124.0i	1.01756	−	0.216290i
$29$	−30936.1	−	95211.6i	−0.235545	−	0.724932i	−0.997049	−	0.0767715i	$-0.975539\pi$
$29$	−30936.1	−	95211.6i	−0.235545	−	0.724932i	0.761504	−	0.648160i	$-0.224461\pi$
$30$	−468363.			−3.16708
$31$	152410.	+	65450.6i	0.918857	+	0.394592i
$31$	152410.	+	65450.6i	0.918857	+	0.394592i
$32$	−263001.			−1.41884
$33$	62166.1	+	191328.i	0.301131	+	0.926785i
$34$	485587.	−	103215.i	2.11880	−	0.450365i
$35$	−310204.	+	225376.i	−1.22295	+	0.888526i
$36$	−76081.5	+	131777.i	−0.271782	+	0.470740i
$37$	−27965.3	−	48437.4i	−0.0907641	−	0.157208i	0.817069	−	0.576540i	$-0.195598\pi$
$37$	−27965.3	−	48437.4i	−0.0907641	−	0.157208i	−0.907833	+	0.419332i	$0.862264\pi$
$38$	206096.	+	91760.0i	0.609295	+	0.271276i
$39$	−104452.	−	75888.7i	−0.281961	−	0.204857i
$40$	−211315.	+	94083.7i	−0.522061	+	0.232436i
$41$	−525862.	−	111775.i	−1.19159	−	0.253281i	−0.430905	−	0.902397i	$-0.641805\pi$
$41$	−525862.	−	111775.i	−1.19159	−	0.253281i	−0.760689	+	0.649116i	$0.775139\pi$
$42$	76829.7	+	730986.i	0.160014	+	1.52243i
$43$	−563959.	+	626340.i	−1.08170	+	1.20135i	−0.103298	+	0.994650i	$0.532940\pi$
$43$	−563959.	+	626340.i	−1.08170	+	1.20135i	−0.978404	+	0.206702i	$0.933727\pi$
$44$	372811.	+	414048.i	0.659788	+	0.732768i
$45$	50468.8	−	480178.i	0.0825618	−	0.785523i
$46$	307062.	−	945039.i	0.465129	−	1.43152i
$47$	−107644.	+	331294.i	−0.151233	+	0.465448i	−0.997760	−	0.0668986i	$-0.978690\pi$
$47$	−107644.	+	331294.i	−0.151233	+	0.465448i	0.846527	+	0.532346i	$0.178690\pi$
$48$	70886.1	−	674437.i	0.0925160	−	0.880231i
$49$	−148422.	−	164839.i	−0.180224	−	0.200158i
$50$	1.87347e6	−	2.08070e6i	2.11959	−	2.35404i
$51$	173265.	+	1.64850e6i	0.182900	+	1.74018i
$52$	−349759.	−	74343.6i	−0.344951	−	0.0733216i
$53$	1.84961e6	−	823499.i	1.70653	−	0.759797i	0.707967	−	0.706245i	$-0.249612\pi$
$53$	1.84961e6	−	823499.i	1.70653	−	0.759797i	0.998565	−	0.0535522i	$-0.0170544\pi$
$54$	927713.	+	674023.i	0.801744	+	0.582501i
$55$	−1.61505e6	−	719068.i	−1.30893	−	0.582775i
$56$	181503.	+	314372.i	0.138110	+	0.239213i
$57$	−376637.	+	652355.i	−0.269377	+	0.466575i
$58$	1.36437e6	−	991272.i	0.918192	−	0.667106i
$59$	−1.27166e6	+	270300.i	−0.806100	+	0.171342i	−0.592490	−	0.805577i	$-0.701855\pi$
$59$	−1.27166e6	+	270300.i	−0.806100	+	0.171342i	−0.213609	+	0.976919i	$0.568522\pi$
$60$	−1.33840e6	−	4.11916e6i	−0.799936	−	2.46195i
$61$	1.80614e6			1.01882			0.509409	−	0.860524i	$-0.329864\pi$
$61$	1.80614e6			1.01882			0.509409	+	0.860524i	$0.329864\pi$
$62$	−255212.	+	2.78251e6i	−0.135997	+	1.48274i
$63$	−757705.			−0.381776
$64$	−892197.	−	2.74590e6i	−0.425433	−	1.30935i
$65$	1.10981e6	−	235897.i	0.501246	−	0.106543i
$66$	−2.74170e6	+	1.99196e6i	−1.17386	+	0.852858i
$67$	−1.96317e6	+	3.40031e6i	−0.797436	+	1.38120i	0.123844	+	0.992302i	$0.460478\pi$
$67$	−1.96317e6	+	3.40031e6i	−0.797436	+	1.38120i	−0.921281	+	0.388899i	$0.872856\pi$
$68$	2.29537e6	+	3.97569e6i	0.885259	+	1.53331i
$69$	3.03101e6	+	1.34949e6i	1.11075	+	0.494536i
$70$	−5.22562e6	−	3.79663e6i	−1.82094	−	1.32299i
$71$	4.23583e6	−	1.88591e6i	1.40454	−	0.625341i	0.442131	−	0.896950i	$-0.354222\pi$
$71$	4.23583e6	−	1.88591e6i	1.40454	−	0.625341i	0.962408	+	0.271609i	$0.0875558\pi$
$72$	−447111.	−	95036.5i	−0.141173	−	0.0300073i
$73$	−189172.	−	1.79985e6i	−0.0569150	−	0.541510i	−0.985414	−	0.170175i	$-0.945567\pi$
$73$	−189172.	−	1.79985e6i	−0.0569150	−	0.541510i	0.928499	−	0.371335i	$-0.121100\pi$
$74$	630451.	−	700187.i	0.180859	−	0.200864i
$75$	6.25547e6	+	6.94740e6i	1.71216	+	1.90155i
$76$	−218069.	+	2.07479e6i	−0.0569832	+	0.542158i
$77$	−857336.	+	2.63861e6i	−0.214010	+	0.658654i
$78$	672095.	−	2.06850e6i	0.160361	−	0.493542i
$79$	−204604.	+	1.94667e6i	−0.0466894	+	0.444220i	0.946058	+	0.323998i	$0.105027\pi$
$79$	−204604.	+	1.94667e6i	−0.0466894	+	0.444220i	−0.992747	+	0.120222i	$0.961639\pi$
$80$	3.98771e6	+	4.42880e6i	0.870779	+	0.967098i
$81$	−3.99142e6	+	4.43293e6i	−0.834508	+	0.926815i
$82$	−946656.	−	9.00683e6i	−0.189602	−	1.80395i
$83$	−6.65062e6	−	1.41363e6i	−1.27670	−	0.271371i	−0.480816	−	0.876821i	$-0.659660\pi$
$83$	−6.65062e6	−	1.41363e6i	−1.27670	−	0.271371i	−0.795883	+	0.605451i	$0.792993\pi$
$84$	−6.20932e6	+	2.76457e6i	−1.14305	+	0.508921i
$85$	−1.17847e7	−	8.56209e6i	−2.08138	−	1.51221i
$86$	−1.29705e7	−	5.77484e6i	−2.19894	−	0.979029i
$87$	2.81551e6	+	4.87661e6i	0.458395	+	0.793963i
$88$	−836854.	+	1.44947e6i	−0.130906	+	0.226736i
$89$	7.48326e6	−	5.43691e6i	1.12519	−	0.817498i	0.140202	−	0.990123i	$-0.455225\pi$
$89$	7.48326e6	−	5.43691e6i	1.12519	−	0.817498i	0.984988	+	0.172625i	$0.0552248\pi$
$90$	7.95578e6	−	1.69105e6i	1.15036	−	0.244517i
$91$	−550222.	−	1.69341e6i	−0.0765408	−	0.235568i
$92$	9.18888e6			1.23028
$93$	−9.15077e6	−	1.81863e6i	−1.17969	−	0.234452i
$94$	−5.86810e6			−0.728702
$95$	−2.04560e6	−	6.29571e6i	−0.244787	−	0.753377i
$96$	1.44699e7	−	3.07567e6i	1.66923	−	0.354806i
$97$	−9.64317e6	+	7.00617e6i	−1.07280	+	0.779435i	−0.976413	−	0.215909i	$-0.930729\pi$
$97$	−9.64317e6	+	7.00617e6i	−1.07280	+	0.779435i	−0.0963867	+	0.995344i	$0.530729\pi$
$98$	1.86830e6	−	3.23600e6i	0.200519	−	0.347309i
$99$	−1.74678e6	−	3.02550e6i	−0.180931	−	0.313382i
$100$	2.36530e7	+	1.05310e7i	2.36530	+	1.05310i
$101$	9.88964e6	+	7.18524e6i	0.955115	+	0.693931i	0.952011	−	0.306064i	$-0.0990121\pi$
$101$	9.88964e6	+	7.18524e6i	0.955115	+	0.693931i	0.00310362	+	0.999995i	$0.499012\pi$
$102$	−2.55092e7	+	1.13574e7i	−2.38010	+	1.05969i
$103$	7.38501e6	+	1.56973e6i	0.665918	+	0.141545i	0.528454	−	0.848962i	$-0.322772\pi$
$103$	7.38501e6	+	1.56973e6i	0.665918	+	0.141545i	0.137463	+	0.990507i	$0.456105\pi$
$104$	−112280.	−	1.06827e6i	−0.00978779	−	0.0931246i
$105$	1.44313e7	−	1.60275e7i	1.21658	−	1.35115i
$106$	2.28219e7	+	2.53463e7i	1.86115	+	2.06701i
$107$	710532.	−	6.76026e6i	0.0560713	−	0.533483i	−0.930047	−	0.367440i	$-0.880234\pi$
$107$	710532.	−	6.76026e6i	0.0560713	−	0.533483i	0.986119	−	0.166043i	$-0.0530990\pi$
$108$	−3.27686e6	+	1.00851e7i	−0.250308	+	0.770369i
$109$	1.52269e6	−	4.68636e6i	0.112621	−	0.346611i	−0.878823	−	0.477149i	$-0.841670\pi$
$109$	1.52269e6	−	4.68636e6i	0.112621	−	0.346611i	0.991443	+	0.130537i	$0.0416703\pi$
$110$	3.11302e6	−	2.96184e7i	0.223001	−	2.12171i
$111$	2.10506e6	+	2.33791e6i	0.146095	+	0.162254i
$112$	6.25799e6	−	6.95020e6i	0.420893	−	0.467449i
$113$	−4269.35	−	40620.2i	−0.000278347	−	0.00264830i	0.994382	−	0.105853i	$-0.0337571\pi$
$113$	−4269.35	−	40620.2i	−0.000278347	−	0.00264830i	−0.994660	+	0.103204i	$0.967090\pi$
$114$	−1.24122e7	−	2.63829e6i	−0.784659	−	0.166784i
$115$	−2.66362e7	+	1.18592e7i	−1.63316	+	0.727131i
$116$	1.26169e7	+	9.16668e6i	0.750496	+	0.545267i
$117$	2.04826e6	+	911942.i	0.118232	+	0.0526401i
$118$	−1.09503e7	−	1.89665e7i	−0.613535	−	1.06267i
$119$	−1.14299e7	+	1.97972e7i	−0.621768	+	1.07693i
$120$	1.05260e7	−	7.64756e6i	0.556068	−	0.404007i
$121$	6.54895e6	−	1.39202e6i	0.336065	−	0.0714327i
$122$	9.40208e6	+	2.89366e7i	0.468775	+	1.44274i
$123$	3.02392e7			1.46522
$124$	−2.52009e7	+	5.70678e6i	−1.18697	+	0.268791i
$125$	−4.35380e7			−1.99381
$126$	−3.94433e6	−	1.21394e7i	−0.175661	−	0.540630i
$127$	7.29139e6	−	1.54983e6i	0.315862	−	0.0671386i	−0.0472527	−	0.998883i	$-0.515047\pi$
$127$	7.29139e6	−	1.54983e6i	0.315862	−	0.0671386i	0.363115	+	0.931744i	$0.381713\pi$
$128$	1.21135e7	−	8.80097e6i	0.510546	−	0.370933i
$129$	2.37034e7	−	4.10554e7i	0.972178	−	1.68386i
$130$	9.55661e6	+	1.65525e7i	0.381507	+	0.660789i
$131$	2.90845e7	+	1.29492e7i	1.13035	+	0.503263i	0.884730	−	0.466104i	$-0.154343\pi$
$131$	2.90845e7	+	1.29492e7i	1.13035	+	0.503263i	0.245617	+	0.969367i	$0.421009\pi$
$132$	−2.53535e7	−	1.84204e7i	−0.959467	−	0.697094i
$133$	−9.49032e6	+	4.22536e6i	−0.349784	+	0.155734i
$134$	−6.46968e7	−	1.37517e7i	−2.32282	−	0.493731i
$135$	−3.51714e6	−	3.34633e7i	−0.123033	−	1.17058i
$136$	−9.22773e6	+	1.02484e7i	−0.314564	+	0.349358i
$137$	−6.43916e6	−	7.15142e6i	−0.213948	−	0.237613i	0.626613	−	0.779331i	$-0.284441\pi$
$137$	−6.43916e6	−	7.15142e6i	−0.213948	−	0.237613i	−0.840560	+	0.541718i	$0.817774\pi$
$138$	−5.84227e6	+	5.55855e7i	−0.189236	+	1.80046i
$139$	6.92970e6	−	2.13274e7i	0.218858	−	0.673576i	−0.779999	−	0.625781i	$-0.784780\pi$
$139$	6.92970e6	−	2.13274e7i	0.218858	−	0.673576i	0.998857	−	0.0477955i	$-0.0152196\pi$
$140$	1.84579e7	−	5.68075e7i	0.568504	−	1.74968i
$141$	2.04807e6	−	1.94861e7i	0.0615288	−	0.585407i
$142$	5.22648e7	+	5.80459e7i	1.53179	+	1.70123i
$143$	5.49330e6	−	6.10093e6i	0.157093	−	0.174470i
$144$	1.23100e6	+	1.17122e7i	0.0343549	+	0.326865i
$145$	−4.84035e7	−	1.02885e7i	−1.31853	−	0.280262i
$146$	2.78511e7	−	1.24001e7i	0.740641	−	0.329755i
$147$	1.00936e7	+	7.33346e6i	0.262082	+	0.190414i
$148$	7.95958e6	+	3.54383e6i	0.201825	+	0.0898581i
$149$	−1.80720e6	−	3.13016e6i	−0.0447563	−	0.0775202i	0.842779	−	0.538259i	$-0.180918\pi$
$149$	−1.80720e6	−	3.13016e6i	−0.0447563	−	0.0775202i	−0.887536	+	0.460739i	$0.847584\pi$
$150$	−7.87425e7	+	1.36386e8i	−1.90498	+	3.29952i
$151$	2.75672e6	−	2.00287e6i	0.0651589	−	0.0473407i	−0.554729	−	0.832031i	$-0.687178\pi$
$151$	2.75672e6	−	2.00287e6i	0.0651589	−	0.0473407i	0.619888	+	0.784690i	$0.287178\pi$
$152$	−6.13008e6	+	1.30299e6i	−0.141584	+	0.0300946i
$153$	−8.89516e6	−	2.73765e7i	−0.200786	−	0.617956i
$154$	−4.67368e7			−1.03118
$155$	6.56858e7	−	4.90668e7i	1.41681	−	1.05834i
$156$	2.01126e7			0.424162
$157$	2.78899e7	+	8.58361e7i	0.575172	+	1.77020i	0.635594	+	0.772023i	$0.280755\pi$
$157$	2.78899e7	+	8.58361e7i	0.575172	+	1.77020i	−0.0604228	+	0.998173i	$0.519245\pi$
$158$	−3.22533e7	+	6.85564e6i	−0.650540	+	0.138277i
$159$	−9.21321e7	+	6.69379e7i	−1.81770	+	1.32063i
$160$	−6.50005e7	+	1.12584e8i	−1.25457	+	2.17299i
$161$	2.28783e7	+	3.96264e7i	0.432049	+	0.748331i
$162$	−9.17989e7	−	4.08715e7i	−1.69643	−	0.755298i
$163$	7.66456e6	+	5.56863e6i	0.138621	+	0.100714i	0.654935	−	0.755685i	$-0.272696\pi$
$163$	7.66456e6	+	5.56863e6i	0.138621	+	0.100714i	−0.516313	+	0.856400i	$0.672696\pi$
$164$	7.65081e7	−	3.40636e7i	1.35442	−	0.603027i
$165$	9.72668e7	+	2.06747e7i	1.68566	+	0.358299i
$166$	−1.19724e7	−	1.13910e8i	−0.203144	−	1.93279i
$167$	1.93128e7	−	2.14491e7i	0.320877	−	0.356370i	−0.561028	−	0.827797i	$-0.689594\pi$
$167$	1.93128e7	−	2.14491e7i	0.320877	−	0.356370i	0.881905	+	0.471427i	$0.156261\pi$
$168$	−1.36624e7	−	1.51736e7i	−0.222303	−	0.246892i
$169$	6.00827e6	−	5.71649e7i	0.0957516	−	0.911015i
$170$	7.58287e7	−	2.33377e8i	1.18376	−	3.64323i
$171$	4.04233e6	−	1.24410e7i	0.0618223	−	0.190269i
$172$	1.37240e7	−	1.30575e8i	0.205651	−	1.95664i
$173$	1.82568e7	+	2.02762e7i	0.268079	+	0.297732i	0.862121	−	0.506702i	$-0.169136\pi$
$173$	1.82568e7	+	2.02762e7i	0.268079	+	0.297732i	−0.594042	+	0.804434i	$0.702469\pi$
$174$	−6.34729e7	+	7.04938e7i	−0.913411	+	1.01445i
$175$	1.34766e7	+	1.28221e8i	0.190085	+	1.80854i
$176$	4.21789e7	+	8.96541e6i	0.583178	+	0.123958i
$177$	6.68036e7	−	2.97429e7i	0.905511	−	0.403159i
$178$	1.26061e8	+	9.15888e7i	1.67537	+	1.21723i
$179$	3.35714e7	+	1.49470e7i	0.437506	+	0.194790i	0.613657	−	0.789573i	$-0.289698\pi$
$179$	3.35714e7	+	1.49470e7i	0.437506	+	0.194790i	−0.176150	+	0.984363i	$0.556365\pi$
$180$	3.76069e7	+	6.51371e7i	0.480634	+	0.832482i
$181$	2.76306e7	−	4.78576e7i	0.346350	−	0.599896i	−0.639248	−	0.769001i	$-0.720754\pi$
$181$	2.76306e7	−	4.78576e7i	0.346350	−	0.599896i	0.985598	+	0.169105i	$0.0540876\pi$
$182$	2.42663e7	−	1.76305e7i	0.298369	−	0.216778i
$183$	−9.93709e7	+	2.11219e7i	−1.19862	+	0.254774i
$184$	8.52997e6	+	2.62525e7i	0.100945	+	0.310677i
$185$	−2.76464e7			−0.321024
$186$	−1.84988e7	−	1.56074e8i	−0.210789	−	1.77842i
$187$	−1.05400e8			−1.17868
$188$	−1.67687e7	−	5.16087e7i	−0.184055	−	0.566462i
$189$	−5.16501e7	+	1.09786e7i	−0.556487	+	0.118285i
$190$	9.02166e7	−	6.55462e7i	0.954221	−	0.693282i
$191$	3.72113e7	−	6.44519e7i	0.386419	−	0.669297i	−0.605546	−	0.795810i	$-0.707045\pi$
$191$	3.72113e7	−	6.44519e7i	0.386419	−	0.669297i	0.991965	+	0.126513i	$0.0403785\pi$
$192$	8.11993e7	+	1.40641e8i	0.827938	+	1.43403i
$193$	1.19960e8	+	5.34094e7i	1.20111	+	0.534770i	0.907053	−	0.421016i	$-0.138326\pi$
$193$	1.19960e8	+	5.34094e7i	1.20111	+	0.534770i	0.294061	+	0.955787i	$0.404993\pi$
$194$	−1.62446e8	−	1.18024e8i	−1.59737	−	1.16055i
$195$	−5.83012e7	+	2.59573e7i	−0.563062	+	0.250691i
$196$	3.37988e7	+	7.18415e6i	0.320630	+	0.0681521i
$197$	−8.26745e6	−	7.86595e7i	−0.0770441	−	0.733026i	−0.963045	−	0.269342i	$-0.913194\pi$
$197$	−8.26745e6	−	7.86595e7i	−0.0770441	−	0.733026i	0.886001	−	0.463684i	$-0.153473\pi$
$198$	3.93793e7	−	4.37352e7i	0.360529	−	0.400408i
$199$	−2.46259e7	−	2.73499e7i	−0.221517	−	0.246019i	0.622135	−	0.782910i	$-0.286265\pi$
$199$	−2.46259e7	−	2.73499e7i	−0.221517	−	0.246019i	−0.843652	+	0.536891i	$0.819599\pi$
$200$	−8.13003e6	+	7.73521e7i	−0.0718600	+	0.683702i
$201$	6.82455e7	−	2.10038e8i	0.592772	−	1.82436i
$202$	−6.36349e7	+	1.95848e8i	−0.543207	+	1.67182i
$203$	−8.11744e6	+	7.72323e7i	−0.0681056	+	0.647982i
$204$	−1.72781e8	−	1.91893e8i	−1.42492	−	1.58253i
$205$	−1.77814e8	+	1.97483e8i	−1.44155	+	1.60100i
$206$	1.32945e7	+	1.26489e8i	0.105959	+	1.00813i
$207$	−5.63581e7	−	1.19793e7i	−0.441632	−	0.0938718i
$208$	−2.52818e7	+	1.12562e7i	−0.194799	+	0.0867300i
$209$	−3.87503e7	−	2.81537e7i	−0.293605	−	0.213316i
$210$	3.31905e8	+	1.47774e8i	2.47313	+	1.10111i
$211$	−7.82686e7	−	1.35565e8i	−0.573586	−	0.993481i	−0.996194	−	0.0871677i	$-0.972218\pi$
$211$	−7.82686e7	−	1.35565e8i	−0.573586	−	0.993481i	0.422607	−	0.906313i	$-0.361115\pi$
$212$	−1.57699e8	+	2.73143e8i	−1.13672	+	1.96886i
$213$	−2.10993e8	+	1.53296e8i	−1.49603	+	1.08693i
$214$	1.12007e8	−	2.38078e7i	0.781261	−	0.166062i
$215$	1.28738e8	+	3.96216e8i	0.883432	+	2.71892i
$216$	−3.18550e7			−0.215075
$217$	−8.73548e7	−	9.44685e7i	−0.580334	−	0.627593i
$218$	8.30079e7			0.542653
$219$	3.14564e7	+	9.68127e7i	0.202374	+	0.622842i
$220$	2.69383e8	−	5.72592e7i	1.70566	−	0.362548i
$221$	5.47248e7	−	3.97599e7i	0.341045	−	0.247783i
$222$	−2.64980e7	+	4.58960e7i	−0.162547	+	0.281539i
$223$	−7.87295e7	−	1.36364e8i	−0.475412	−	0.823438i	0.524191	−	0.851601i	$-0.324368\pi$
$223$	−7.87295e7	−	1.36364e8i	−0.475412	−	0.823438i	−0.999603	+	0.0281623i	$0.991034\pi$
$224$	1.86375e8	+	8.29797e7i	1.10795	+	0.493291i
$225$	−1.31342e8	−	9.54253e7i	−0.768712	−	0.558502i
$226$	628561.	−	279854.i	0.00362216	−	0.00161269i
$227$	−1.76240e8	−	3.74610e7i	−1.00003	−	0.212564i	−0.321323	−	0.946970i	$-0.604128\pi$
$227$	−1.76240e8	−	3.74610e7i	−1.00003	−	0.212564i	−0.678711	+	0.734406i	$0.737461\pi$
$228$	−1.22658e7	−	1.16702e8i	−0.0685371	−	0.652087i
$229$	5.97384e7	−	6.63462e7i	0.328723	−	0.365083i	−0.556015	−	0.831172i	$-0.687670\pi$
$229$	5.97384e7	−	6.63462e7i	0.328723	−	0.365083i	0.884738	+	0.466088i	$0.154337\pi$
$230$	−3.28657e8	−	3.65011e8i	−1.78113	−	1.97815i
$231$	1.63120e7	−	1.55198e8i	0.0870692	−	0.828409i
$232$	−1.44770e7	+	4.45556e7i	−0.0761150	+	0.234258i
$233$	−1.18744e7	+	3.65457e7i	−0.0614988	+	0.189274i	−0.977086	−	0.212846i	$-0.931727\pi$
$233$	−1.18744e7	+	3.65457e7i	−0.0614988	+	0.189274i	0.915587	+	0.402120i	$0.131727\pi$
$234$	−3.94802e6	+	3.75629e7i	−0.0201430	+	0.191647i
$235$	1.15214e8	+	1.27959e8i	0.579121	+	0.643179i
$236$	1.35515e8	−	1.50505e8i	0.671112	−	0.745345i
$237$	−1.15085e7	−	1.09496e8i	−0.0561562	−	0.534291i
$238$	−3.76676e8	−	8.00649e7i	−1.81112	−	0.384966i
$239$	1.28105e8	−	5.70361e7i	0.606980	−	0.270245i	−0.0801461	−	0.996783i	$-0.525539\pi$
$239$	1.28105e8	−	5.70361e7i	0.606980	−	0.270245i	0.687126	+	0.726538i	$0.258872\pi$
$240$	−2.71190e8	−	1.97031e8i	−1.26629	−	0.920015i
$241$	5.15646e7	+	2.29580e7i	0.237297	+	0.105651i	0.521940	−	0.852982i	$-0.325208\pi$
$241$	5.15646e7	+	2.29580e7i	0.237297	+	0.105651i	−0.284643	+	0.958634i	$0.591875\pi$
$242$	5.63933e7	+	9.76761e7i	0.255784	+	0.443031i
$243$	9.33245e7	−	1.61643e8i	0.417228	−	0.722661i
$244$	−2.27624e8	+	1.65379e8i	−1.00312	+	0.728812i
$245$	−1.07246e8	+	2.27958e7i	−0.465907	+	0.0990315i
$246$	1.57414e8	+	4.84471e8i	0.674172	+	2.07489i
$247$	3.07400e7			0.129797
$248$	−3.96980e7	−	6.67012e7i	−0.165268	−	0.277685i
$249$	3.82438e8			1.56987
$250$	−2.26643e8	−	6.97534e8i	−0.917385	−	2.82342i
$251$	1.75760e8	−	3.73590e7i	0.701556	−	0.149120i	0.156695	−	0.987647i	$-0.449916\pi$
$251$	1.75760e8	−	3.73590e7i	0.701556	−	0.149120i	0.544861	+	0.838527i	$0.316583\pi$
$252$	9.54921e7	−	6.93791e7i	0.375894	−	0.273103i
$253$	−1.05485e8	+	1.82705e8i	−0.409514	+	0.709299i
$254$	6.27865e7	+	1.08749e8i	0.240408	+	0.416399i
$255$	7.48505e8	+	3.33256e8i	2.82686	+	1.25860i
$256$	−9.49218e7	−	6.89647e7i	−0.353611	−	0.256914i
$257$	−4.68537e8	+	2.08606e8i	−1.72178	+	0.766587i	−0.724800	+	0.688960i	$0.758068\pi$
$257$	−4.68537e8	+	2.08606e8i	−1.72178	+	0.766587i	−0.996982	+	0.0776273i	$0.975266\pi$
$258$	7.81151e8	+	1.66039e8i	2.83182	+	0.601922i
$259$	4.53508e6	+	4.31484e7i	0.0162195	+	0.154318i
$260$	−1.18267e8	+	1.31349e8i	−0.417309	+	0.463468i
$261$	−6.54325e7	−	7.26702e7i	−0.227799	−	0.252997i
$262$	−5.60604e7	+	5.33379e8i	−0.192576	+	1.83224i
$263$	−1.04066e8	+	3.20281e8i	−0.352746	+	1.08564i	0.604558	+	0.796561i	$0.293350\pi$
$263$	−1.04066e8	+	3.20281e8i	−0.352746	+	1.08564i	−0.957305	+	0.289081i	$0.906650\pi$
$264$	2.90915e7	−	8.95343e7i	0.0973088	−	0.299486i
$265$	1.04610e8	−	9.95298e8i	0.345313	−	3.28543i
$266$	−1.17099e8	−	1.30051e8i	−0.381475	−	0.423671i
$267$	−3.48135e8	+	3.86643e8i	−1.11933	+	1.24314i
$268$	−6.39340e7	−	6.08292e8i	−0.202890	−	1.93037i
$269$	8.13669e7	+	1.72951e7i	0.254868	+	0.0541738i	0.333574	−	0.942724i	$-0.391745\pi$
$269$	8.13669e7	+	1.72951e7i	0.254868	+	0.0541738i	−0.0787058	+	0.996898i	$0.525079\pi$
$270$	5.17816e8	−	2.30546e8i	1.60104	−	0.712829i
$271$	7.12363e7	+	5.17562e7i	0.217425	+	0.157968i	0.691167	−	0.722695i	$-0.257097\pi$
$271$	7.12363e7	+	5.17562e7i	0.217425	+	0.157968i	−0.473742	+	0.880664i	$0.657097\pi$
$272$	3.24583e8	+	1.44514e8i	0.977990	+	0.435429i
$273$	5.00759e7	+	8.67341e7i	0.148957	+	0.258000i
$274$	8.10548e7	−	1.40391e8i	0.238041	−	0.412299i
$275$	−4.80918e8	+	3.49407e8i	−1.39446	+	1.01314i
$276$	−5.05558e8	+	1.07460e8i	−1.44740	+	0.307655i
$277$	−1.46368e8	−	4.50473e8i	−0.413776	−	1.27347i	−0.913341	−	0.407196i	$-0.866507\pi$
$277$	−1.46368e8	−	4.50473e8i	−0.413776	−	1.27347i	0.499564	−	0.866277i	$-0.333493\pi$
$278$	3.77766e8			1.05455
$279$	1.62004e8	−	2.14760e6i	0.446593	−	0.00592022i
$280$	1.79433e8			0.488482
$281$	3.74468e7	+	1.15249e8i	0.100680	+	0.309860i	0.988692	−	0.149959i	$-0.0479142\pi$
$281$	3.74468e7	+	1.15249e8i	0.100680	+	0.309860i	−0.888012	+	0.459819i	$0.847914\pi$
$282$	3.22853e8	−	6.86246e7i	0.857301	−	0.182225i
$283$	−2.32402e8	+	1.68850e8i	−0.609520	+	0.442842i	−0.849245	−	0.527999i	$-0.822943\pi$
$283$	−2.32402e8	+	1.68850e8i	−0.609520	+	0.442842i	0.239726	+	0.970841i	$0.422943\pi$
$284$	−3.61150e8	+	6.25530e8i	−0.935564	+	1.62044i
$285$	1.86171e8	+	3.22458e8i	0.476382	+	0.825117i
$286$	1.26341e8	+	5.62505e7i	0.319346	+	0.142182i
$287$	3.37385e8	+	2.45125e8i	0.842440	+	0.612069i
$288$	−2.34686e8	+	1.04489e8i	−0.578913	+	0.257749i
$289$	−4.48099e8	−	9.52463e7i	−1.09202	−	0.232116i
$290$	−8.71360e7	−	8.29043e8i	−0.209800	−	1.99611i
$291$	4.48618e8	−	4.98241e8i	1.06721	−	1.18526i
$292$	1.88644e8	+	2.09510e8i	0.443408	+	0.492454i
$293$	−1.78415e7	+	1.69751e8i	−0.0414377	+	0.394253i	0.954071	+	0.299581i	$0.0968469\pi$
$293$	−1.78415e7	+	1.69751e8i	−0.0414377	+	0.394253i	−0.995509	+	0.0946721i	$0.969820\pi$
$294$	−6.49476e7	+	1.99888e8i	−0.149055	+	0.458745i
$295$	−1.98581e8	+	6.11169e8i	−0.450361	+	1.38607i
$296$	−2.73588e6	+	2.60301e7i	−0.00613162	+	0.0583385i
$297$	−1.62909e8	−	1.80929e8i	−0.360825	−	0.400737i
$298$	4.07416e7	−	4.52481e7i	0.0891827	−	0.0990475i
$299$	−1.41528e7	−	1.34655e8i	−0.0306191	−	0.291322i
$300$	−1.42450e9	−	3.02787e8i	−3.04606	−	0.647461i
$301$	5.97266e8	−	2.65920e8i	1.26236	−	0.562041i
$302$	4.64390e7	+	3.37399e7i	0.0970195	+	0.0704888i
$303$	−6.28140e8	−	2.79666e8i	−1.29720	−	0.577551i
$304$	8.07315e7	+	1.39831e8i	0.164811	+	0.285461i
$305$	4.46386e8	−	7.73162e8i	0.900867	−	1.56035i
$306$	3.92301e8	−	2.85023e8i	0.782698	−	0.568663i
$307$	8.14677e8	−	1.73165e8i	1.60695	−	0.341567i	0.684896	−	0.728640i	$-0.259847\pi$
$307$	8.14677e8	−	1.73165e8i	1.60695	−	0.341567i	0.922049	+	0.387074i	$0.126514\pi$
$308$	−1.33555e8	−	4.11041e8i	−0.260455	−	0.801599i
$309$	−4.24668e8			−0.818833
$310$	1.12805e9	+	7.96945e8i	2.15061	+	1.51937i
$311$	−7.02749e7			−0.132476			−0.0662382	−	0.997804i	$-0.521100\pi$
$311$	−7.02749e7			−0.132476			−0.0662382	+	0.997804i	$0.521100\pi$
$312$	1.86704e7	+	5.74614e7i	0.0348026	+	0.107111i
$313$	−4.10176e8	+	8.71855e7i	−0.756075	+	0.160709i	−0.569794	−	0.821788i	$-0.692977\pi$
$313$	−4.10176e8	+	8.71855e7i	−0.756075	+	0.160709i	−0.186281	+	0.982496i	$0.559644\pi$
$314$	−1.23002e9	+	8.93661e8i	−2.24212	+	1.62899i
$315$	−1.87266e8	+	3.24354e8i	−0.337576	+	0.584700i
$316$	−1.52461e8	−	2.64070e8i	−0.271803	−	0.470776i
$317$	6.24924e8	+	2.78234e8i	1.10184	+	0.490572i	0.875374	−	0.483446i	$-0.160615\pi$
$317$	6.24924e8	+	2.78234e8i	1.10184	+	0.490572i	0.226469	+	0.974018i	$0.427282\pi$
$318$	−1.55203e9	−	1.12762e9i	−2.70649	−	1.96638i
$319$	−3.27101e8	+	1.45635e8i	−0.564175	+	0.251187i
$320$	−1.39596e9	−	2.96720e8i	−2.38148	−	0.506199i
$321$	3.99657e7	+	3.80248e8i	0.0674403	+	0.641652i
$322$	−5.15769e8	+	5.72819e8i	−0.860914	+	0.956141i
$323$	−2.64078e8	−	2.93289e8i	−0.436037	−	0.484269i
$324$	9.71318e7	−	9.24147e8i	0.158655	−	1.50950i
$325$	1.17892e8	−	3.62833e8i	0.190498	−	0.586293i
$326$	−4.93176e7	+	1.51784e8i	−0.0788389	+	0.242641i
$327$	−2.89713e7	+	2.75643e8i	−0.0458195	+	0.435943i
$328$	1.68341e8	+	1.86962e8i	0.263410	+	0.292546i
$329$	1.80809e8	−	2.00808e8i	0.279920	−	0.310882i
$330$	1.75100e8	+	1.66596e9i	0.268217	+	2.55191i
$331$	−8.34277e8	−	1.77331e8i	−1.26448	−	0.268774i	−0.473598	−	0.880741i	$-0.657045\pi$
$331$	−8.34277e8	−	1.77331e8i	−1.26448	−	0.268774i	−0.790883	+	0.611967i	$0.790379\pi$
$332$	9.67604e8	−	4.30805e8i	1.45116	−	0.646096i
$333$	−4.41984e7	−	3.21120e7i	−0.0655922	−	0.0476555i
$334$	4.44177e8	+	1.97760e8i	0.652293	+	0.290420i
$335$	9.70391e8	+	1.68077e9i	1.41023	+	2.44259i
$336$	−2.63025e8	+	4.55573e8i	−0.378277	+	0.655195i
$337$	5.58717e8	−	4.05931e8i	0.795219	−	0.577761i	−0.114289	−	0.993448i	$-0.536459\pi$
$337$	5.58717e8	−	4.05931e8i	0.795219	−	0.577761i	0.909508	+	0.415687i	$0.136459\pi$
$338$	9.47130e8	−	2.01319e8i	1.33414	−	0.283580i
$339$	709926.	+	2.18493e6i	0.000989724	+	0.00304606i
$340$	2.26919e9			3.13108
$341$	1.75828e8	−	5.66589e8i	0.240130	−	0.773799i
$342$	2.20363e8			0.297885
$343$	2.50581e8	+	7.71208e8i	0.335288	+	1.03191i
$344$	3.85792e8	−	8.20026e7i	0.510973	−	0.108611i
$345$	1.32679e9	−	9.63971e8i	1.73955	−	1.26385i
$346$	−2.29812e8	+	3.98047e8i	−0.298268	+	0.516616i
$347$	−1.33300e8	−	2.30882e8i	−0.171268	−	0.296645i	0.767595	−	0.640935i	$-0.221453\pi$
$347$	−1.33300e8	−	2.30882e8i	−0.171268	−	0.296645i	−0.938863	+	0.344290i	$0.888120\pi$
$348$	−8.01359e8	−	3.56788e8i	−1.01929	−	0.453819i
$349$	−9.11910e8	−	6.62541e8i	−1.14832	−	0.834303i	−0.160063	−	0.987107i	$-0.551170\pi$
$349$	−9.11910e8	−	6.62541e8i	−1.14832	−	0.834303i	−0.988257	+	0.152804i	$0.951170\pi$
$350$	−1.98412e9	+	8.83385e8i	−2.47360	+	1.10132i
$351$	1.52836e8	+	3.24862e7i	0.188647	+	0.0400982i
$352$	9.83241e7	+	9.35491e8i	0.120160	+	1.14325i
$353$	8.13807e7	−	9.03825e7i	0.0984714	−	0.109364i	−0.691895	−	0.721999i	$-0.743224\pi$
$353$	8.13807e7	−	9.03825e7i	0.0984714	−	0.109364i	0.790366	+	0.612635i	$0.209890\pi$
$354$	8.24273e8	+	9.15448e8i	0.987551	+	1.09679i
$355$	2.39569e8	−	2.27935e9i	0.284205	−	2.70403i
$356$	−4.45272e8	+	1.37041e9i	−0.523059	+	1.60981i
$357$	3.97337e8	−	1.22288e9i	0.462189	−	1.42247i
$358$	−6.47090e7	+	6.15665e8i	−0.0745374	+	0.709176i
$359$	−2.30123e8	−	2.55578e8i	−0.262500	−	0.291536i	0.597458	−	0.801900i	$-0.296177\pi$
$359$	−2.30123e8	−	2.55578e8i	−0.262500	−	0.291536i	−0.859959	+	0.510364i	$0.829511\pi$
$360$	−1.51186e8	+	1.67909e8i	−0.170786	+	0.189677i
$361$	7.46879e7	+	7.10608e8i	0.0835556	+	0.794978i
$362$	9.10574e8	+	1.93548e8i	1.00887	+	0.214442i
$363$	−3.44034e8	+	1.53174e8i	−0.377509	+	0.168078i
$364$	2.24400e8	+	1.63036e8i	0.243875	+	0.177186i
$365$	−8.17225e8	−	3.63852e8i	−0.879663	−	0.391651i
$366$	−8.55687e8	−	1.48209e9i	−0.912287	−	1.58013i
$367$	−2.56246e8	+	4.43831e8i	−0.270599	+	0.468691i	−0.969015	−	0.247001i	$-0.920555\pi$
$367$	−2.56246e8	+	4.43831e8i	−0.270599	+	0.468691i	0.698417	+	0.715691i	$0.253888\pi$
$368$	5.75352e8	−	4.18018e8i	0.601820	−	0.437248i
$369$	−5.13654e8	+	1.09181e8i	−0.532205	+	0.113124i
$370$	−1.43917e8	−	4.42930e8i	−0.147709	−	0.454600i
$371$	−1.57055e9			−1.59677
$372$	1.31978e9	−	6.08690e8i	1.32923	−	0.613050i
$373$	−2.72667e8			−0.272052			−0.136026	−	0.990705i	$-0.543433\pi$
$373$	−2.72667e8			−0.272052			−0.136026	+	0.990705i	$0.543433\pi$
$374$	−5.48672e8	−	1.68864e9i	−0.542328	−	1.66911i
$375$	2.39539e9	−	5.09157e8i	2.34567	−	0.498588i
$376$	1.31879e8	−	9.58160e7i	0.127944	−	0.0929566i
$377$	1.14897e8	−	1.99007e8i	0.110437	−	0.191282i
$378$	−4.44761e8	−	7.70349e8i	−0.423551	−	0.733612i
$379$	−1.28862e9	−	5.73730e8i	−1.21587	−	0.541340i	−0.304336	−	0.952565i	$-0.598435\pi$
$379$	−1.28862e9	−	5.73730e8i	−1.21587	−	0.541340i	−0.911534	+	0.411225i	$0.865101\pi$
$380$	8.34269e8	+	6.06132e8i	0.779944	+	0.566663i
$381$	−3.83036e8	+	1.70539e8i	−0.354815	+	0.157974i
$382$	1.22631e9	+	2.60660e8i	1.12559	+	0.239250i
$383$	−1.54926e8	−	1.47402e9i	−0.140906	−	1.34063i	−0.805131	−	0.593097i	$-0.797905\pi$
$383$	−1.54926e8	−	1.47402e9i	−0.140906	−	1.34063i	0.664225	−	0.747533i	$-0.268762\pi$
$384$	−5.63542e8	+	6.25877e8i	−0.507887	+	0.564066i
$385$	9.17632e8	+	1.01913e9i	0.819513	+	0.910161i
$386$	−2.31222e8	+	2.19993e9i	−0.204632	+	1.94695i
$387$	−2.54401e8	+	7.82965e8i	−0.223115	+	0.686679i
$388$	5.73792e8	−	1.76595e9i	0.498705	−	1.53486i
$389$	1.76272e8	−	1.67712e9i	0.151831	−	1.44458i	−0.607732	−	0.794142i	$-0.707921\pi$
$389$	1.76272e8	−	1.67712e9i	0.151831	−	1.44458i	0.759563	−	0.650433i	$-0.225413\pi$
$390$	−7.19363e8	−	7.98934e8i	−0.614076	−	0.682001i
$391$	−1.16315e9	+	1.29181e9i	−0.984050	+	1.09290i
$392$	1.08501e7	+	1.03232e8i	0.00909771	+	0.0865590i
$393$	−1.75162e9	−	3.72318e8i	−1.45568	−	0.309414i
$394$	1.21719e9	−	5.41927e8i	1.00258	−	0.446379i
$395$	7.82754e8	+	5.68704e8i	0.639051	+	0.464298i
$396$	4.97172e8	+	2.21355e8i	0.402322	+	0.179125i
$397$	−1.84412e8	−	3.19411e8i	−0.147918	−	0.256202i	0.782540	−	0.622601i	$-0.213924\pi$
$397$	−1.84412e8	−	3.19411e8i	−0.147918	−	0.256202i	−0.930458	+	0.366399i	$0.880591\pi$
$398$	3.09986e8	−	5.36912e8i	0.246463	−	0.426886i
$399$	4.72728e8	−	3.43457e8i	0.372569	−	0.270687i
$400$	1.96008e9	−	4.16627e8i	1.53131	−	0.325490i
$401$	7.85189e8	+	2.41656e9i	0.608092	+	1.87151i	0.473950	+	0.880551i	$0.342828\pi$
$401$	7.85189e8	+	2.41656e9i	0.608092	+	1.87151i	0.134141	+	0.990962i	$0.457172\pi$
$402$	3.72033e9			2.85621
$403$	1.22442e8	+	3.60507e8i	0.0931889	+	0.274376i
$404$	−1.90429e9			−1.43680
$405$	9.11146e8	+	2.80422e9i	0.681547	+	2.09758i
$406$	−1.27961e9	+	2.71991e8i	−0.948939	+	0.201703i
$407$	−1.61836e8	+	1.17581e8i	−0.118986	+	0.0864482i
$408$	3.87844e8	−	6.71766e8i	0.282714	−	0.489675i
$409$	4.75318e8	+	8.23276e8i	0.343521	+	0.594996i	0.985084	−	0.172075i	$-0.0550471\pi$
$409$	4.75318e8	+	8.23276e8i	0.343521	+	0.594996i	−0.641563	+	0.767070i	$0.721714\pi$
$410$	−4.08956e9	−	1.82079e9i	−2.93044	−	1.30472i
$411$	4.37905e8	+	3.18156e8i	0.311124	+	0.226045i
$412$	−1.07445e9	+	4.78376e8i	−0.756913	+	0.337000i
$413$	9.86442e8	+	2.09675e8i	0.689043	+	0.146461i
$414$	−1.01456e8	−	9.65288e8i	−0.0702710	−	0.668584i
$415$	−2.24883e9	+	2.49758e9i	−1.54450	+	1.71535i
$416$	−4.03946e8	−	4.48627e8i	−0.275104	−	0.305534i
$417$	−1.31847e8	+	1.25444e9i	−0.0890419	+	0.847177i
$418$	2.49339e8	−	7.67387e8i	0.166983	−	0.513922i
$419$	2.60081e8	−	8.00448e8i	0.172727	−	0.531599i	−0.826795	−	0.562503i	$-0.809839\pi$
$419$	2.60081e8	−	8.00448e8i	0.172727	−	0.531599i	0.999522	+	0.0309039i	$0.00983859\pi$
$420$	−3.51186e8	+	3.34132e9i	−0.231294	+	2.20062i
$421$	−8.51008e7	−	9.45140e7i	−0.0555836	−	0.0617318i	0.714712	−	0.699419i	$-0.246558\pi$
$421$	−8.51008e7	−	9.45140e7i	−0.0555836	−	0.0617318i	−0.770295	+	0.637687i	$0.779891\pi$
$422$	1.76449e9	−	1.95966e9i	1.14294	−	1.26937i
$423$	3.55665e7	+	3.38393e8i	0.0228481	+	0.217385i
$424$	−9.26758e8	−	1.96989e8i	−0.590454	−	0.125505i
$425$	−4.47453e9	+	1.99219e9i	−2.82739	+	1.25884i
$426$	−3.55434e9	−	2.58238e9i	−2.22754	−	1.61840i
$427$	−1.27992e9	−	5.69856e8i	−0.795582	−	0.354216i
$428$	5.29455e8	+	9.17043e8i	0.326419	+	0.565375i
$429$	−2.30885e8	+	3.99905e8i	−0.141187	+	0.244543i
$430$	−5.67771e9	+	4.12510e9i	−3.44377	+	2.50204i
$431$	2.76282e9	−	5.87256e8i	1.66220	−	0.353311i	0.721462	−	0.692454i	$-0.243471\pi$
$431$	2.76282e9	−	5.87256e8i	1.66220	−	0.353311i	0.940735	+	0.339144i	$0.110137\pi$
$432$	2.53613e8	+	7.80540e8i	0.151349	+	0.465803i
$433$	3.29958e8			0.195322			0.0976609	−	0.995220i	$-0.468864\pi$
$433$	3.29958e8			0.195322			0.0976609	+	0.995220i	$0.468864\pi$
$434$	1.05877e9	−	1.89130e9i	0.621709	−	1.11057i
$435$	2.78340e9			1.62130
$436$	2.37204e8	+	7.30038e8i	0.137063	+	0.421835i
$437$	−7.72693e8	+	1.64241e8i	−0.442917	+	0.0941448i
$438$	−1.38731e9	+	1.00794e9i	−0.788887	+	0.573160i
$439$	1.68014e9	−	2.91008e9i	0.947805	−	1.64165i	0.197769	−	0.980249i	$-0.436630\pi$
$439$	1.68014e9	−	2.91008e9i	0.947805	−	1.64165i	0.750035	−	0.661398i	$-0.230036\pi$
$440$	4.13655e8	+	7.16472e8i	0.231502	+	0.400973i
$441$	−1.97932e8	−	8.81251e7i	−0.109896	−	0.0489288i
$442$	9.21880e8	+	6.69785e8i	0.507805	+	0.368942i
$443$	2.94193e9	−	1.30983e9i	1.60775	−	0.715817i	0.610650	−	0.791900i	$-0.290908\pi$
$443$	2.94193e9	−	1.30983e9i	1.60775	−	0.715817i	0.997101	+	0.0760833i	$0.0242415\pi$
$444$	−4.79366e8	−	1.01892e8i	−0.259913	−	0.0552461i
$445$	−4.77922e8	−	4.54712e9i	−0.257097	−	2.44611i
$446$	1.77488e9	−	1.97120e9i	0.947320	−	1.05211i
$447$	1.36035e8	+	1.51082e8i	0.0720401	+	0.0800087i
$448$	−2.34107e8	+	2.22738e9i	−0.123010	+	1.17036i
$449$	−9.34049e8	+	2.87471e9i	−0.486976	+	1.49876i	0.342122	+	0.939655i	$0.388854\pi$
$449$	−9.34049e8	+	2.87471e9i	−0.486976	+	1.49876i	−0.829098	+	0.559103i	$0.811146\pi$
$450$	8.45118e8	−	2.60101e9i	0.437194	−	1.34554i
$451$	−2.00988e8	+	1.91227e9i	−0.103170	+	0.981593i
$452$	4.25743e6	+	4.72836e6i	0.00216852	+	0.00240839i
$453$	−1.28248e8	+	1.42433e8i	−0.0648195	+	0.0719894i
$454$	−3.17268e8	−	3.01860e9i	−0.159122	−	1.51395i
$455$	−8.60892e8	−	1.82988e8i	−0.428459	−	0.0910717i
$456$	3.22029e8	−	1.43377e8i	0.159044	−	0.0708111i
$457$	2.35404e9	+	1.71031e9i	1.15374	+	0.838238i	0.988973	−	0.148095i	$-0.0473141\pi$
$457$	2.35404e9	+	1.71031e9i	1.15374	+	0.838238i	0.164763	+	0.986333i	$0.447314\pi$
$458$	1.37393e9	+	6.11711e8i	0.668243	+	0.297521i
$459$	−1.00302e9	−	1.73727e9i	−0.484132	−	0.838540i
$460$	2.27102e9	−	3.93353e9i	1.08785	−	1.88421i
$461$	−2.33865e8	+	1.69913e8i	−0.111176	+	0.0807742i	−0.641984	−	0.766718i	$-0.721889\pi$
$461$	−2.33865e8	+	1.69913e8i	−0.111176	+	0.0807742i	0.530808	+	0.847492i	$0.321889\pi$
$462$	2.57138e9	−	5.46565e8i	1.21317	−	0.257866i
$463$	3.48597e8	+	1.07287e9i	0.163226	+	0.502360i	0.998901	−	0.0468652i	$-0.0149231\pi$
$463$	3.48597e8	+	1.07287e9i	0.163226	+	0.502360i	−0.835675	+	0.549225i	$0.814923\pi$
$464$	1.20700e9			0.560911
$465$	−3.04011e9	+	3.46774e9i	−1.40218	+	1.59942i
$466$	−6.47322e8			−0.296326
$467$	1.50786e8	+	4.64072e8i	0.0685098	+	0.210851i	0.979450	−	0.201687i	$-0.0646423\pi$
$467$	1.50786e8	+	4.64072e8i	0.0685098	+	0.210851i	−0.910940	+	0.412538i	$0.864642\pi$
$468$	−3.41640e8	+	7.26177e7i	−0.154066	+	0.0327478i
$469$	2.46403e9	−	1.79022e9i	1.10291	−	0.801313i
$470$	−1.45030e9	+	2.51199e9i	−0.644338	+	1.11603i
$471$	−2.53827e9	−	4.39641e9i	−1.11935	−	1.93876i
$472$	5.55787e8	+	2.47452e8i	0.243283	+	0.108317i
$473$	2.43872e9	+	1.77183e9i	1.05961	+	0.769855i
$474$	1.69435e9	−	7.54373e8i	0.730767	−	0.325358i
$475$	−2.17721e9	−	4.62780e8i	−0.932120	−	0.198128i
$476$	−3.72235e8	−	3.54158e9i	−0.158195	−	1.50513i
$477$	1.32331e9	−	1.46968e9i	0.558272	−	0.620024i
$478$	1.58066e9	+	1.75550e9i	0.661973	+	0.735196i
$479$	−6.68453e7	+	6.35991e8i	−0.0277905	+	0.264409i	0.971800	+	0.235805i	$0.0757728\pi$
$479$	−6.68453e7	+	6.35991e8i	−0.0277905	+	0.264409i	−0.999591	+	0.0286038i	$0.990894\pi$
$480$	2.25960e9	−	6.95435e9i	0.932584	−	2.87020i
$481$	3.96723e7	−	1.22099e8i	0.0162547	−	0.0500268i
$482$	−9.93909e7	+	9.45641e8i	−0.0404280	+	0.384646i
$483$	−1.72214e9	−	1.91263e9i	−0.695430	−	0.772353i
$484$	−6.97892e8	+	7.75087e8i	−0.279788	+	0.310736i
$485$	6.15865e8	+	5.85957e9i	0.245126	+	2.33222i
$486$	3.07553e9	+	6.53725e8i	1.21533	+	0.258326i
$487$	1.12417e9	−	5.00513e8i	0.441043	−	0.196365i	−0.174187	−	0.984713i	$-0.555730\pi$
$487$	1.12417e9	−	5.00513e8i	0.441043	−	0.196365i	0.615230	+	0.788348i	$0.289063\pi$
$488$	−6.83787e8	−	4.96800e8i	−0.266349	−	0.193514i
$489$	−4.86814e8	−	2.16744e8i	−0.188270	−	0.0838234i
$490$	−9.23498e8	−	1.59955e9i	−0.354609	−	0.614201i
$491$	1.10391e9	−	1.91202e9i	0.420869	−	0.728966i	−0.575156	−	0.818044i	$-0.695059\pi$
$491$	1.10391e9	−	1.91202e9i	0.420869	−	0.728966i	0.996025	+	0.0890778i	$0.0283920\pi$
$492$	−3.81099e9	+	2.76885e9i	−1.44265	+	1.04815i
$493$	−2.88576e9	+	6.13387e8i	−1.08467	+	0.230553i
$494$	1.60021e8	+	4.92494e8i	0.0597218	+	0.183805i
$495$	−1.72686e9			−0.639938
$496$	−1.31832e9	+	1.50376e9i	−0.485104	+	0.553340i
$497$	−3.59674e9			−1.31420
$498$	1.99083e9	+	6.12714e9i	0.722322	+	2.22308i
$499$	−1.71883e8	+	3.65349e7i	−0.0619273	+	0.0131630i	−0.238771	−	0.971076i	$-0.576745\pi$
$499$	−1.71883e8	+	3.65349e7i	−0.0619273	+	0.0131630i	0.176844	+	0.984239i	$0.443411\pi$
$500$	5.48702e9	−	3.98655e9i	1.96310	−	1.42627i
$501$	−8.11724e8	+	1.40595e9i	−0.288388	+	0.499502i
$502$	1.51348e9	+	2.62142e9i	0.533966	+	0.924856i
$503$	5.21446e8	+	2.32163e8i	0.182693	+	0.0813400i	0.496045	−	0.868297i	$-0.334785\pi$
$503$	5.21446e8	+	2.32163e8i	0.182693	+	0.0813400i	−0.313352	+	0.949637i	$0.601452\pi$
$504$	2.86860e8	+	2.08416e8i	0.0998074	+	0.0725144i
$505$	5.52003e9	−	2.45768e9i	1.90731	−	0.849190i
$506$	−3.47629e9	−	7.38907e8i	−1.19286	−	0.253550i
$507$	3.37950e8	+	3.21538e9i	0.115166	+	1.09573i
$508$	−7.77011e8	+	8.62958e8i	−0.262969	+	0.292056i
$509$	6.54152e8	+	7.26509e8i	0.219870	+	0.244191i	0.842981	−	0.537943i	$-0.180798\pi$
$509$	6.54152e8	+	7.26509e8i	0.219870	+	0.244191i	−0.623111	+	0.782133i	$0.714132\pi$
$510$	−1.44274e9	+	1.37268e10i	−0.481608	+	4.58219i
$511$	−4.33816e8	+	1.33515e9i	−0.143824	+	0.442646i
$512$	1.20302e9	−	3.70253e9i	0.396122	−	1.21914i
$513$	9.52906e7	−	9.06629e8i	0.0311630	−	0.296496i
$514$	−5.78116e9	−	6.42063e9i	−1.87778	−	2.08548i
$515$	2.49716e9	−	2.77338e9i	0.805603	−	0.894712i
$516$	7.71941e8	+	7.34453e9i	0.247349	+	2.35337i
$517$	1.21865e9	+	2.59032e8i	0.387849	+	0.0824398i
$518$	−6.67685e8	+	2.97272e8i	−0.211065	+	0.0939724i
$519$	−1.24158e9	−	9.02059e8i	−0.389842	−	0.283237i
$520$	−4.85049e8	−	2.15958e8i	−0.151277	−	0.0673530i
$521$	1.92727e9	+	3.33813e9i	0.597050	+	1.03412i	0.993254	+	0.115958i	$0.0369938\pi$
$521$	1.92727e9	+	3.33813e9i	0.597050	+	1.03412i	−0.396204	+	0.918162i	$0.629673\pi$
$522$	8.23651e8	−	1.42661e9i	0.253452	−	0.438993i
$523$	1.59899e9	−	1.16173e9i	0.488752	−	0.355099i	−0.315952	−	0.948775i	$-0.602324\pi$
$523$	1.59899e9	−	1.16173e9i	0.488752	−	0.355099i	0.804704	+	0.593676i	$0.202324\pi$
$524$	−4.85116e9	+	1.03115e9i	−1.47294	+	0.313084i
$525$	−2.24095e9	−	6.89694e9i	−0.675888	−	2.08017i
$526$	−5.67304e9			−1.69967
$527$	2.38771e9	−	4.26522e9i	0.710632	−	1.26942i
$528$	−2.42546e9			−0.717094
$529$	2.30487e7	+	7.09365e7i	0.00676942	+	0.0208341i
$530$	1.64905e10	−	3.50516e9i	4.81136	−	1.02269i
$531$	−1.02736e9	+	7.46422e8i	−0.297778	+	0.216348i
$532$	8.09152e8	−	1.40149e9i	0.232991	−	0.403553i
$533$	−6.17010e8	−	1.06869e9i	−0.176501	−	0.305708i
$534$	−8.00677e9	−	3.56484e9i	−2.27543	−	1.01309i
$535$	−2.71829e9	−	1.97495e9i	−0.767463	−	0.557595i
$536$	1.67853e9	−	7.47331e8i	0.470818	−	0.209622i
$537$	−2.02184e9	−	4.29756e8i	−0.563427	−	0.119760i
$538$	1.46477e8	+	1.39363e9i	0.0405537	+	0.385843i
$539$	−5.30842e8	+	5.89560e8i	−0.146017	+	0.162169i
$540$	3.50732e9	+	3.89527e9i	0.958511	+	1.06453i
$541$	−1.42337e8	+	1.35424e9i	−0.0386480	+	0.367711i	0.958056	+	0.286582i	$0.0925191\pi$
$541$	−1.42337e8	+	1.35424e9i	−0.0386480	+	0.367711i	−0.996704	+	0.0811287i	$0.974148\pi$
$542$	−4.58370e8	+	1.41072e9i	−0.123657	+	0.380577i
$543$	−9.60519e8	+	2.95617e9i	−0.257458	+	0.792375i
$544$	−8.10147e8	+	7.70804e9i	−0.215758	+	2.05280i
$545$	−1.62978e9	−	1.81005e9i	−0.431262	−	0.478965i
$546$	−1.12891e9	+	1.25378e9i	−0.296815	+	0.329647i
$547$	−5.05431e8	−	4.80886e9i	−0.132040	−	1.25628i	−0.837068	−	0.547099i	$-0.815732\pi$
$547$	−5.05431e8	−	4.80886e9i	−0.132040	−	1.25628i	0.705028	−	0.709180i	$-0.250935\pi$
$548$	1.46633e9	+	3.11679e8i	0.380628	+	0.0809050i
$549$	1.61169e9	−	7.17569e8i	0.415698	−	0.185080i
$550$	−8.10142e9	−	5.88603e9i	−2.07631	−	1.50853i
$551$	−1.22480e9	−	5.45314e8i	−0.311913	−	0.138872i
$552$	−7.76316e8	−	1.34462e9i	−0.196450	−	0.340261i
$553$	7.59189e8	−	1.31495e9i	0.190903	−	0.330653i
$554$	6.45521e9	−	4.68999e9i	1.61297	−	1.17189i
$555$	1.52106e9	−	3.23312e8i	0.377678	−	0.0802779i
$556$	1.07950e9	+	3.32237e9i	0.266356	+	0.819760i
$557$	−6.46848e9			−1.58602			−0.793011	−	0.609208i	$-0.791488\pi$
$557$	−6.46848e9			−1.58602			−0.793011	+	0.609208i	$0.791488\pi$
$558$	8.77742e8	+	2.58434e9i	0.213869	+	0.629694i
$559$	−1.93460e9			−0.468435
$560$	−1.42855e9	−	4.39662e9i	−0.343746	−	1.05794i
$561$	5.79893e9	−	1.23260e9i	1.38668	−	0.294749i
$562$	−1.65150e9	+	1.19989e9i	−0.392467	+	0.285144i
$563$	−9.50581e8	+	1.64645e9i	−0.224496	+	0.388839i	−0.956168	−	0.292818i	$-0.905407\pi$
$563$	−9.50581e8	+	1.64645e9i	−0.224496	+	0.388839i	0.731672	+	0.681657i	$0.238740\pi$
$564$	1.52613e9	+	2.64333e9i	0.358190	+	0.620404i
$565$	−1.84436e7	−	8.21163e6i	−0.00430206	−	0.00191540i
$566$	−3.91499e9	−	2.84441e9i	−0.907555	−	0.659377i
$567$	4.22715e9	−	1.88205e9i	0.973884	−	0.433601i
$568$	−2.12239e9	−	4.51127e8i	−0.485965	−	0.103295i
$569$	6.40474e7	+	6.09370e8i	0.0145750	+	0.138672i	0.999389	−	0.0349382i	$-0.0111234\pi$
$569$	6.40474e7	+	6.09370e8i	0.0145750	+	0.138672i	−0.984814	+	0.173610i	$0.944457\pi$
$570$	−4.19704e9	+	4.66129e9i	−0.949252	+	1.05425i
$571$	−2.36027e7	−	2.62134e7i	−0.00530560	−	0.00589247i	0.740486	−	0.672072i	$-0.234595\pi$
$571$	−2.36027e7	−	2.62134e7i	−0.00530560	−	0.00589247i	−0.745792	+	0.666179i	$0.767929\pi$
$572$	−1.33680e8	+	1.27188e9i	−0.0298662	+	0.284158i
$573$	−1.29357e9	+	3.98121e9i	−0.287243	+	0.884044i
$574$	−2.17091e9	+	6.68136e9i	−0.479125	+	1.47460i
$575$	−1.02479e9	+	9.75019e9i	−0.224800	+	2.13883i
$576$	−1.88707e9	−	2.09581e9i	−0.411443	−	0.456954i
$577$	2.84334e8	−	3.15785e8i	0.0616188	−	0.0684346i	−0.711547	−	0.702638i	$-0.752005\pi$
$577$	2.84334e8	−	3.15785e8i	0.0616188	−	0.0684346i	0.773166	+	0.634204i	$0.218672\pi$
$578$	−8.06667e8	−	7.67492e9i	−0.173759	−	1.65320i
$579$	−7.22458e9	−	1.53563e9i	−1.54681	−	0.328785i
$580$	7.04227e9	−	3.13542e9i	1.49870	−	0.667264i
$581$	4.26694e9	+	3.10011e9i	0.902609	+	0.655784i
$582$	1.03178e10	+	4.59377e9i	2.16948	+	0.965915i
$583$	−3.62066e9	−	6.27117e9i	−0.756742	−	1.31072i
$584$	−4.23452e8	+	7.33441e8i	−0.0879751	+	0.152377i
$585$	8.96604e8	−	6.51421e8i	0.185163	−	0.134529i
$586$	−2.81250e9	+	5.97815e8i	−0.577365	+	0.122723i
$587$	−6.60790e8	−	2.03370e9i	−0.134844	−	0.415006i	0.860722	−	0.509075i	$-0.170013\pi$
$587$	−6.60790e8	−	2.03370e9i	−0.134844	−	0.415006i	−0.995566	+	0.0940692i	$0.970013\pi$
$588$	−1.94357e9			−0.394257
$589$	2.01714e9	−	9.30321e8i	0.406755	−	0.187598i
$590$	−1.08254e10			−2.17002
$591$	1.37475e9	+	4.23104e9i	0.273947	+	0.843122i
$592$	6.59595e8	−	1.40201e8i	0.130663	−	0.0277732i
$593$	7.46647e9	−	5.42471e9i	1.47036	−	1.06828i	0.489851	−	0.871806i	$-0.337051\pi$
$593$	7.46647e9	−	5.42471e9i	1.47036	−	1.06828i	0.980509	−	0.196473i	$-0.0629488\pi$
$594$	2.05066e9	−	3.55185e9i	0.401459	−	0.695348i
$595$	5.64978e9	+	9.78571e9i	1.09957	+	1.90451i
$596$	5.14371e8	+	2.29013e8i	0.0995209	+	0.0443096i
$597$	1.67472e9	+	1.21676e9i	0.322131	+	0.234042i
$598$	2.08367e9	−	9.27708e8i	0.398450	−	0.177401i
$599$	−8.14433e9	−	1.73113e9i	−1.54832	−	0.329106i	−0.647080	−	0.762422i	$-0.724010\pi$
$599$	−8.14433e9	−	1.73113e9i	−1.54832	−	0.329106i	−0.901242	+	0.433316i	$0.857343\pi$
$600$	−4.57294e8	−	4.35086e9i	−0.0864304	−	0.822330i
$601$	2.96967e9	−	3.29816e9i	0.558018	−	0.619742i	−0.396450	−	0.918056i	$-0.629758\pi$
$601$	2.96967e9	−	3.29816e9i	0.558018	−	0.619742i	0.954468	+	0.298315i	$0.0964245\pi$
$602$	7.36951e9	+	8.18467e9i	1.37674	+	1.52902i
$603$	−4.00887e8	+	3.81418e9i	−0.0744580	+	0.708420i
$604$	−1.64032e8	+	5.04837e8i	−0.0302899	+	0.0932228i
$605$	1.02268e9	−	3.14748e9i	0.187756	−	0.577855i
$606$	1.21074e9	−	1.15194e10i	0.221002	−	2.10270i
$607$	2.43484e9	+	2.70416e9i	0.441885	+	0.490763i	0.922407	−	0.386220i	$-0.126219\pi$
$607$	2.43484e9	+	2.70416e9i	0.441885	+	0.490763i	−0.480522	+	0.876983i	$0.659553\pi$
$608$	−2.35677e9	+	2.61746e9i	−0.425261	+	0.472300i
$609$	−4.56586e8	−	4.34413e9i	−0.0819147	−	0.779367i
$610$	1.47108e10	+	3.12687e9i	2.62410	+	0.557770i
$611$	−7.30452e8	+	3.25218e8i	−0.129553	+	0.0576807i
$612$	3.62776e9	+	2.63572e9i	0.639748	+	0.464804i
$613$	7.05698e9	+	3.14197e9i	1.23739	+	0.550923i	0.917955	−	0.396685i	$-0.129839\pi$
$613$	7.05698e9	+	3.14197e9i	1.23739	+	0.550923i	0.319438	+	0.947607i	$0.396506\pi$
$614$	7.01522e9	+	1.21507e10i	1.22307	+	2.11842i
$615$	7.47360e9	−	1.29447e10i	1.29559	−	2.24402i
$616$	1.05036e9	−	7.63131e8i	0.181053	−	0.131543i
$617$	−6.13168e9	+	1.30333e9i	−1.05095	+	0.223386i	−0.700837	−	0.713322i	$-0.747190\pi$
$617$	−6.13168e9	+	1.30333e9i	−1.05095	+	0.223386i	−0.350112	+	0.936708i	$0.613857\pi$
$618$	−2.21066e9	−	6.80372e9i	−0.376758	−	1.15954i
$619$	8.04771e9			1.36381			0.681907	−	0.731439i	$-0.261151\pi$
$619$	8.04771e9			1.36381			0.681907	+	0.731439i	$0.261151\pi$
$620$	−3.78546e9	+	1.21983e10i	−0.637893	+	2.05555i
$621$	−4.01531e9			−0.672819
$622$	−3.65824e8	−	1.12589e9i	−0.0609546	−	0.187599i
$623$	−7.01840e9	+	1.49181e9i	−1.16287	+	0.247175i
$624$	1.25933e9	−	9.14956e8i	0.207488	−	0.150749i
$625$	−4.26798e9	+	7.39236e9i	−0.699266	+	1.21116i
$626$	−3.53204e9	−	6.11768e9i	−0.575461	−	0.996727i
$627$	2.46122e9	+	1.09581e9i	0.398763	+	0.177541i
$628$	−1.13745e10	−	8.26404e9i	−1.83262	−	1.33148i
$629$	−1.50575e9	+	6.70402e8i	−0.241254	+	0.107413i
$630$	−6.17140e9	−	1.31177e9i	−0.983313	−	0.209010i
$631$	6.25577e8	+	5.95197e9i	0.0991238	+	0.943100i	0.925184	+	0.379518i	$0.123910\pi$
$631$	6.25577e8	+	5.95197e9i	0.0991238	+	0.943100i	−0.826060	+	0.563582i	$0.809423\pi$
$632$	6.12917e8	−	6.80714e8i	0.0965811	−	0.107264i
$633$	5.89158e9	+	6.54326e9i	0.923249	+	1.02537i
$634$	−1.20454e9	+	1.14605e10i	−0.187720	+	1.78603i
$635$	1.13862e9	−	3.50430e9i	0.176469	−	0.543117i
$636$	5.48208e9	−	1.68721e10i	0.844979	−	2.60058i
$637$	5.32201e7	−	5.06356e8i	0.00815808	−	0.0776190i
$638$	−4.03601e9	−	4.48245e9i	−0.615291	−	0.683350i
$639$	3.03053e9	−	3.36574e9i	0.459478	−	0.510302i
$640$	−7.73634e8	−	7.36063e9i	−0.116656	−	1.10990i
$641$	1.86819e9	+	3.97095e8i	0.280167	+	0.0595513i	0.345852	−	0.938289i	$-0.387590\pi$
$641$	1.86819e9	+	3.97095e8i	0.280167	+	0.0595513i	−0.0656850	+	0.997840i	$0.520923\pi$
$642$	−5.88401e9	+	2.61973e9i	−0.877608	+	0.390736i
$643$	−1.75049e9	−	1.27180e9i	−0.259669	−	0.188661i	0.450332	−	0.892861i	$-0.351306\pi$
$643$	−1.75049e9	−	1.27180e9i	−0.259669	−	0.188661i	−0.710001	+	0.704200i	$0.751306\pi$
$644$	−6.51169e9	−	2.89919e9i	−0.960712	−	0.427737i
$645$	−1.17165e10	−	2.02936e10i	−1.71925	−	2.97783i
$646$	3.32416e9	−	5.75762e9i	0.485141	−	0.840289i
$647$	−6.13450e9	+	4.45697e9i	−0.890459	+	0.646956i	−0.935998	−	0.352006i	$-0.885500\pi$
$647$	−6.13450e9	+	4.45697e9i	−0.890459	+	0.646956i	0.0455386	+	0.998963i	$0.485500\pi$
$648$	2.73044e9	−	5.80374e8i	0.394204	−	0.0837906i
$649$	1.43687e9	+	4.42222e9i	0.206329	+	0.635015i
$650$	6.42674e9			0.917897
$651$	5.91089e9	+	4.17593e9i	0.839690	+	0.593226i
$652$	−1.47584e9			−0.208532
$653$	−3.11399e8	−	9.58387e8i	−0.0437644	−	0.134693i	0.926787	−	0.375588i	$-0.122559\pi$
$653$	−3.11399e8	−	9.58387e8i	−0.0437644	−	0.134693i	−0.970551	+	0.240895i	$0.922559\pi$
$654$	−4.56696e9	+	9.70738e8i	−0.638418	+	0.135700i
$655$	1.27314e10	−	9.24994e9i	1.77024	−	1.28616i
$656$	3.24086e9	−	5.61334e9i	0.448226	−	0.776350i
$657$	−8.83877e8	−	1.53092e9i	−0.121594	−	0.210607i
$658$	4.15842e9	+	1.85145e9i	0.569034	+	0.253350i
$659$	−1.55074e9	−	1.12668e9i	−0.211077	−	0.153356i	0.477224	−	0.878782i	$-0.341643\pi$
$659$	−1.55074e9	−	1.12668e9i	−0.211077	−	0.153356i	−0.688301	+	0.725426i	$0.741643\pi$
$660$	−1.41514e10	+	6.30062e9i	−1.91600	+	0.853060i
$661$	4.40146e9	+	9.35560e8i	0.592778	+	0.125999i	0.494526	−	0.869163i	$-0.335342\pi$
$661$	4.40146e9	+	9.35560e8i	0.592778	+	0.125999i	0.0982517	+	0.995162i	$0.468675\pi$
$662$	−1.50187e9	−	1.42893e10i	−0.201200	−	1.91429i
$663$	−2.54590e9	+	2.82751e9i	−0.339269	+	0.376796i
$664$	2.12902e9	+	2.36452e9i	0.282223	+	0.313440i
$665$	−5.36752e8	+	5.10686e9i	−0.0707780	+	0.673408i
$666$	2.84395e8	−	8.75278e8i	0.0373046	−	0.114812i
$667$	−1.82482e9	+	5.61620e9i	−0.238111	+	0.732829i
$668$	−4.69980e8	+	4.47156e9i	−0.0610045	+	0.580419i
$669$	5.92628e9	+	6.58180e9i	0.765227	+	0.849871i
$670$	−2.18765e10	+	2.42963e10i	−2.81006	+	3.12089i
$671$	−6.75233e8	−	6.42441e9i	−0.0862829	−	0.820927i
$672$	−1.12245e10	−	2.38584e9i	−1.42684	−	0.303283i
$673$	−2.94752e9	+	1.31232e9i	−0.372738	+	0.165954i	−0.584552	−	0.811356i	$-0.698730\pi$
$673$	−2.94752e9	+	1.31232e9i	−0.372738	+	0.165954i	0.211814	+	0.977310i	$0.432063\pi$
$674$	9.41200e9	+	6.83822e9i	1.18406	+	0.860267i
$675$	−1.03357e10	−	4.60177e9i	−1.29354	−	0.575919i
$676$	4.47708e9	+	7.75453e9i	0.557418	+	0.965477i
$677$	−3.17979e9	+	5.50755e9i	−0.393856	+	0.682179i	−0.992954	−	0.118497i	$-0.962193\pi$
$677$	−3.17979e9	+	5.50755e9i	−0.393856	+	0.682179i	0.599098	+	0.800676i	$0.295526\pi$
$678$	−3.13097e7	+	2.27478e7i	−0.00385811	+	0.00280308i
$679$	9.04415e9	−	1.92239e9i	1.10872	−	0.235666i
$680$	2.10647e9	+	6.48305e9i	0.256906	+	0.790675i
$681$	1.01346e10			1.22967
$682$	9.99277e9	−	1.32468e8i	1.20626	−	0.0159906i
$683$	−2.18386e8			−0.0262272			−0.0131136	−	0.999914i	$-0.504174\pi$
$683$	−2.18386e8			−0.0262272			−0.0131136	+	0.999914i	$0.504174\pi$
$684$	6.29711e8	+	1.93805e9i	0.0752393	+	0.231563i
$685$	−4.65277e9	+	9.88977e8i	−0.553089	+	0.117563i
$686$	−1.10513e10	+	8.02923e9i	−1.30701	+	0.949598i
$687$	−2.51082e9	+	4.34888e9i	−0.295439	+	0.511715i
$688$	−5.08077e9	−	8.80016e9i	−0.594799	−	1.03022i
$689$	4.24556e9	+	1.89024e9i	0.494501	+	0.220166i
$690$	2.23508e10	+	1.62388e10i	2.59013	+	1.88184i
$691$	−2.27063e9	+	1.01095e9i	−0.261802	+	0.116562i	−0.533441	−	0.845837i	$-0.679101\pi$
$691$	−2.27063e9	+	1.01095e9i	−0.261802	+	0.116562i	0.271638	+	0.962399i	$0.412435\pi$
$692$	−4.15745e9	−	8.83694e8i	−0.476931	−	0.101375i
$693$	2.83271e8	+	2.69515e9i	0.0323323	+	0.307621i
$694$	3.00511e9	−	3.33751e9i	0.341273	−	0.379022i
$695$	−7.41707e9	−	8.23749e9i	−0.838080	−	0.930782i
$696$	2.75444e8	−	2.62068e9i	0.0309672	−	0.294633i
$697$	−4.89578e9	+	1.50677e10i	−0.547655	+	1.68551i
$698$	5.86769e9	−	1.80589e10i	0.653090	−	2.01000i
$699$	2.25927e8	−	2.14955e9i	0.0250206	−	0.238055i
$700$	−1.34390e10	−	1.49255e10i	−1.48089	−	1.64470i
$701$	−4.86031e9	+	5.39792e9i	−0.532906	+	0.591852i	−0.948136	−	0.317864i	$-0.897034\pi$
$701$	−4.86031e9	+	5.39792e9i	−0.532906	+	0.591852i	0.415230	+	0.909716i	$0.363701\pi$
$702$	2.75135e8	+	2.61773e9i	0.0300169	+	0.285591i
$703$	−7.32663e8	−	1.55732e8i	−0.0795354	−	0.0169058i
$704$	−9.43358e9	+	4.20010e9i	−1.01900	+	0.453686i
$705$	−7.83533e9	−	5.69270e9i	−0.842161	−	0.611866i
$706$	1.87168e9	+	8.33325e8i	0.200177	+	0.0891247i
$707$	−4.74126e9	−	8.21210e9i	−0.504575	−	0.873949i
$708$	−5.69573e9	+	9.86530e9i	−0.603161	+	1.04471i
$709$	−4.17999e9	+	3.03694e9i	−0.440467	+	0.320018i	−0.785821	−	0.618454i	$-0.787759\pi$
$709$	−4.17999e9	+	3.03694e9i	−0.440467	+	0.320018i	0.345353	+	0.938473i	$0.387759\pi$
$710$	3.77652e10	−	8.02724e9i	3.95993	−	0.841709i
$711$	5.90827e8	+	1.81838e9i	0.0616477	+	0.189732i
$712$	−4.32858e9			−0.449433
$713$	−5.00391e9	−	8.40765e9i	−0.517007	−	0.868683i
$714$	2.16604e10			2.22701
$715$	−1.25399e9	−	3.85938e9i	−0.128299	−	0.394863i
$716$	−5.59956e9	+	1.19022e9i	−0.570110	+	0.121181i
$717$	−6.38114e9	+	4.63617e9i	−0.646519	+	0.469723i
$718$	2.89674e9	−	5.01731e9i	0.292062	−	0.505865i
$719$	1.55805e9	+	2.69862e9i	0.156326	+	0.270764i	0.933541	−	0.358471i	$-0.116702\pi$
$719$	1.55805e9	+	2.69862e9i	0.156326	+	0.270764i	−0.777215	+	0.629235i	$0.783368\pi$
$720$	5.31792e9	+	2.36769e9i	0.530980	+	0.236407i
$721$	−4.73811e9	−	3.44244e9i	−0.470795	−	0.342052i
$722$	−1.09960e10	+	4.89575e9i	−1.08732	+	0.484105i
$723$	−3.10549e9	−	6.60091e8i	−0.305594	−	0.0649561i
$724$	8.99839e8	+	8.56139e9i	0.0881210	+	0.838416i
$725$	−1.11337e10	+	1.23652e10i	−1.08507	+	1.20509i
$726$	−4.24494e9	−	4.71449e9i	−0.411712	−	0.457253i
$727$	7.75355e7	−	7.37701e8i	0.00748394	−	0.0712049i	−0.990142	−	0.140064i	$-0.955269\pi$
$727$	7.75355e7	−	7.37701e8i	0.00748394	−	0.0712049i	0.997626	+	0.0688590i	$0.0219359\pi$
$728$	−2.57484e8	+	7.92454e8i	−0.0247338	+	0.0761227i
$729$	7.87097e8	−	2.42244e9i	0.0752458	−	0.231583i
$730$	1.57520e9	−	1.49870e10i	0.149867	−	1.42589i
$731$	1.66196e10	+	1.84579e10i	1.57365	+	1.74772i
$732$	1.05895e10	−	1.17608e10i	0.997899	−	1.10828i
$733$	9.50285e7	+	9.04136e8i	0.00891230	+	0.0847949i	0.998074	−	0.0620360i	$-0.0197594\pi$
$733$	9.50285e7	+	9.04136e8i	0.00891230	+	0.0847949i	−0.989162	+	0.146831i	$0.953093\pi$
$734$	−8.44465e9	−	1.79497e9i	−0.788216	−	0.167541i
$735$	5.63390e9	−	2.50838e9i	0.523364	−	0.233017i
$736$	1.25507e10	+	9.11862e9i	1.16037	+	0.843057i
$737$	1.28288e10	+	5.71175e9i	1.18046	+	0.525573i
$738$	−4.42310e9	−	7.66104e9i	−0.405070	−	0.701601i
$739$	3.61591e9	−	6.26294e9i	0.329581	−	0.570851i	−0.652848	−	0.757489i	$-0.726426\pi$
$739$	3.61591e9	−	6.26294e9i	0.329581	−	0.570851i	0.982429	+	0.186638i	$0.0597592\pi$
$740$	3.48423e9	−	2.53144e9i	0.316079	−	0.229645i
$741$	−1.69127e9	+	3.59490e8i	−0.152703	+	0.0324581i
$742$	−8.17567e9	−	2.51621e10i	−0.734700	−	2.26117i
$743$	−1.40030e9			−0.125245			−0.0626227	−	0.998037i	$-0.519946\pi$
$743$	−1.40030e9			−0.125245			−0.0626227	+	0.998037i	$0.519946\pi$
$744$	2.96416e9	+	3.20554e9i	0.263874	+	0.285362i
$745$	−1.78659e9			−0.158299
$746$	−1.41940e9	−	4.36847e9i	−0.125175	−	0.385250i
$747$	−6.49623e9	+	1.38082e9i	−0.570216	+	0.121203i
$748$	1.32833e10	−	9.65091e9i	1.16052	−	0.843165i
$749$	−2.63645e9	+	4.56647e9i	−0.229263	+	0.397095i
$750$	2.06268e10	+	3.57267e10i	1.78533	+	3.09228i
$751$	−8.19689e9	−	3.64949e9i	−0.706171	−	0.314407i	0.0220437	−	0.999757i	$-0.492983\pi$
$751$	−8.19689e9	−	3.64949e9i	−0.706171	−	0.314407i	−0.728214	+	0.685350i	$0.759649\pi$
$752$	−3.39772e9	−	2.46859e9i	−0.291357	−	0.211683i
$753$	−9.23315e9	+	4.11086e9i	−0.788075	+	0.350873i
$754$	3.78646e9	+	8.04836e8i	0.321687	+	0.0683767i
$755$	−1.76059e8	−	1.67509e9i	−0.0148883	−	0.141652i
$756$	5.50411e9	−	6.11294e9i	0.463299	−	0.514545i
$757$	−5.41765e9	−	6.01691e9i	−0.453916	−	0.504124i	0.472134	−	0.881527i	$-0.343484\pi$
$757$	−5.41765e9	−	6.01691e9i	−0.453916	−	0.504124i	−0.926049	+	0.377403i	$0.876817\pi$
$758$	2.48381e9	−	2.36319e10i	0.207146	−	1.97086i
$759$	3.66696e9	−	1.12858e10i	0.304411	−	0.936881i
$760$	−9.57267e8	+	2.94616e9i	−0.0791016	+	0.243450i
$761$	−1.41926e9	+	1.35034e10i	−0.116739	+	1.11070i	0.766652	+	0.642063i	$0.221921\pi$
$761$	−1.41926e9	+	1.35034e10i	−0.116739	+	1.11070i	−0.883391	+	0.468637i	$0.844745\pi$
$762$	−4.72619e9	−	5.24896e9i	−0.386962	−	0.429765i
$763$	−2.55765e9	+	2.84056e9i	−0.208452	+	0.231509i
$764$	1.21185e9	+	1.15300e10i	0.0983157	+	0.935412i
$765$	−1.39176e10	−	2.95828e9i	−1.12396	−	0.238904i
$766$	2.28092e10	−	1.01553e10i	1.83362	−	0.816382i
$767$	−2.41423e9	−	1.75404e9i	−0.193195	−	0.140364i
$768$	6.02896e9	+	2.68426e9i	0.480262	+	0.213826i
$769$	−9.92278e9	−	1.71868e10i	−0.786848	−	1.36286i	−0.927889	−	0.372857i	$-0.878378\pi$
$769$	−9.92278e9	−	1.71868e10i	−0.786848	−	1.36286i	0.141040	−	0.990004i	$-0.454955\pi$
$770$	−1.15510e10	+	2.00068e10i	−0.911802	+	1.57929i
$771$	2.33386e10	−	1.69565e10i	1.83394	−	1.33243i
$772$	−2.00087e10	+	4.25298e9i	−1.56516	+	0.332685i
$773$	5.12571e9	+	1.57753e10i	0.399141	+	1.22843i	0.925690	+	0.378284i	$0.123486\pi$
$773$	5.12571e9	+	1.57753e10i	0.399141	+	1.22843i	−0.526549	+	0.850145i	$0.676514\pi$
$774$	−1.38684e10			−1.07506
$775$	−3.24485e9	−	2.73768e10i	−0.250403	−	2.11264i
$776$	5.57795e9			0.428507
$777$	−7.54113e8	−	2.32092e9i	−0.0576717	−	0.177495i
$778$	2.77872e10	−	5.90634e9i	2.11551	−	0.449666i
$779$	−5.82471e9	+	4.23190e9i	−0.441462	+	0.320741i
$780$	4.97081e9	−	8.60969e9i	0.375056	−	0.649616i
$781$	−8.29174e9	−	1.43617e10i	−0.622826	−	1.07877i
$782$	−2.67513e10	−	1.19105e10i	−2.00042	−	0.890646i
$783$	−5.51324e9	−	4.00561e9i	−0.410432	−	0.298196i
$784$	2.44309e9	−	1.08774e9i	0.181065	−	0.0806152i
$785$	4.36372e10	+	9.27538e9i	3.21968	+	0.684365i
$786$	−3.15326e9	−	3.00013e10i	−0.231623	−	2.20374i
$787$	−2.88745e9	+	3.20684e9i	−0.211156	+	0.234513i	−0.839414	−	0.543493i	$-0.817102\pi$
$787$	−2.88745e9	+	3.20684e9i	−0.211156	+	0.234513i	0.628258	+	0.778005i	$0.283768\pi$
$788$	8.24437e9	+	9.15630e9i	0.600227	+	0.666620i
$789$	1.97999e9	−	1.88384e10i	0.143514	−	1.36544i
$790$	−5.03664e9	+	1.55012e10i	−0.363451	+	1.11859i
$791$	−9.79063e6	+	3.01324e7i	−0.000703384	+	0.00216479i
$792$	−1.70889e8	+	1.62590e9i	−0.0122229	+	0.116293i
$793$	2.77407e9	+	3.08091e9i	0.197543	+	0.219393i
$794$	4.15739e9	−	4.61725e9i	0.294747	−	0.327349i
$795$	5.88406e9	+	5.59831e10i	0.415329	+	3.95159i
$796$	5.60784e9	+	1.19198e9i	0.394094	+	0.0837673i
$797$	−6.21771e9	+	2.76830e9i	−0.435037	+	0.193691i	−0.612557	−	0.790426i	$-0.709859\pi$
$797$	−6.21771e9	+	2.76830e9i	−0.435037	+	0.193691i	0.177520	+	0.984117i	$0.443193\pi$
$798$	7.96347e9	+	5.78580e9i	0.554743	+	0.403045i
$799$	9.37798e9	+	4.17535e9i	0.650422	+	0.289587i
$800$	2.18561e10	+	3.78559e10i	1.50924	+	2.61408i
$801$	4.51754e9	−	7.82462e9i	0.310591	−	0.537959i
$802$	−3.46290e10	+	2.51594e10i	−2.37044	+	1.72223i
$803$	−6.33133e9	+	1.34576e9i	−0.431509	+	0.0917201i
$804$	1.06312e10	+	3.27196e10i	0.721419	+	2.22030i
$805$	2.26174e10			1.52812
$806$	−5.13839e9	+	3.83835e9i	−0.345664	+	0.258209i
$807$	−4.67893e9			−0.313393
$808$	−1.76773e9	−	5.44053e9i	−0.117890	−	0.362828i
$809$	1.52015e10	−	3.23118e9i	1.00941	−	0.214556i	0.326606	−	0.945161i	$-0.394095\pi$
$809$	1.52015e10	−	3.23118e9i	1.00941	−	0.214556i	0.682801	+	0.730604i	$0.260762\pi$
$810$	−4.01841e10	+	2.91954e10i	−2.65678	+	1.93027i
$811$	−7.31110e9	+	1.26632e10i	−0.481293	+	0.833624i	−0.999770	−	0.0214679i	$-0.993166\pi$
$811$	−7.31110e9	+	1.26632e10i	−0.481293	+	0.833624i	0.518477	+	0.855092i	$0.326499\pi$
$812$	−6.04873e9	−	1.04767e10i	−0.396477	−	0.686719i
$813$	−4.52457e9	−	2.01447e9i	−0.295298	−	0.131475i
$814$	−2.72625e9	−	1.98074e9i	−0.177166	−	0.128719i
$815$	4.27808e9	−	1.90472e9i	0.276820	−	0.123248i
$816$	−1.95480e10	−	4.15506e9i	−1.25947	−	0.267708i
$817$	1.17983e9	+	1.12254e10i	0.0756909	+	0.720151i
$818$	−1.07156e10	+	1.19009e10i	−0.684509	+	0.760225i
$819$	−1.16377e9	−	1.29249e9i	−0.0740239	−	0.0822119i
$820$	4.32714e9	−	4.11700e10i	0.274064	−	2.60755i
$821$	5.80896e9	−	1.78781e10i	0.366351	−	1.12751i	−0.582780	−	0.812630i	$-0.698035\pi$
$821$	5.80896e9	−	1.78781e10i	0.366351	−	1.12751i	0.949131	−	0.314882i	$-0.101965\pi$
$822$	−2.81770e9	+	8.67199e9i	−0.176947	+	0.544587i
$823$	−9.90226e8	+	9.42137e9i	−0.0619206	+	0.589135i	0.918936	+	0.394406i	$0.129049\pi$
$823$	−9.90226e8	+	9.42137e9i	−0.0619206	+	0.589135i	−0.980857	+	0.194729i	$0.937617\pi$
$824$	−2.36412e9	−	2.62562e9i	−0.147206	−	0.163488i
$825$	2.23732e10	−	2.48479e10i	1.38720	−	1.54064i
$826$	1.77579e9	+	1.68955e10i	0.109638	+	1.04314i
$827$	−1.45877e10	−	3.10071e9i	−0.896844	−	0.190630i	−0.263646	−	0.964620i	$-0.584925\pi$
$827$	−1.45877e10	−	3.10071e9i	−0.896844	−	0.190630i	−0.633198	+	0.773989i	$0.718258\pi$
$828$	8.19959e9	−	3.65069e9i	0.501980	−	0.223496i
$829$	3.99402e9	+	2.90183e9i	0.243484	+	0.176901i	0.702834	−	0.711354i	$-0.251918\pi$
$829$	3.99402e9	+	2.90183e9i	0.243484	+	0.176901i	−0.459350	+	0.888255i	$0.651918\pi$
$830$	−5.17210e10	−	2.30277e10i	−3.13974	−	1.39790i
$831$	1.33210e10	+	2.30726e10i	0.805253	+	1.39474i
$832$	3.31362e9	−	5.73936e9i	0.199467	−	0.345487i
$833$	−5.28830e9	+	3.84218e9i	−0.317000	+	0.230314i
$834$	−2.07841e10	+	4.41779e9i	−1.24065	+	0.263708i
$835$	−4.40866e9	−	1.35685e10i	−0.262062	−	0.806543i
$836$	7.46152e9			0.441678
$837$	1.10122e10	−	2.49372e9i	0.649133	−	0.146997i
$838$	1.41781e10			0.832268
$839$	4.37078e9	+	1.34519e10i	0.255501	+	0.786350i	0.993731	+	0.111801i	$0.0356620\pi$
$839$	4.37078e9	+	1.34519e10i	0.255501	+	0.786350i	−0.738230	+	0.674549i	$0.764338\pi$
$840$	−9.87210e9	+	2.09838e9i	−0.574688	+	0.122154i
$841$	5.84723e9	−	4.24826e9i	0.338973	−	0.246278i
$842$	1.07123e9	−	1.85543e9i	0.0618430	−	0.107115i
$843$	−3.40804e9	−	5.90291e9i	−0.195934	−	0.339367i
$844$	2.22770e10	+	9.91837e9i	1.27544	+	0.567861i
$845$	−2.29859e10	−	1.67002e10i	−1.31058	−	0.952191i
$846$	−5.23633e9	+	2.33136e9i	−0.297325	+	0.132377i
$847$	−5.08010e9	−	1.07981e9i	−0.287264	−	0.0610598i
$848$	2.55157e9	+	2.42766e10i	0.143689	+	1.36711i
$849$	1.08118e10	−	1.20077e10i	0.606345	−	0.673415i
$850$	−5.52101e10	−	6.13171e10i	−3.08356	−	3.42464i
$851$	−3.44856e8	+	3.28108e9i	−0.0191816	+	0.182500i
$852$	1.25546e10	−	3.86391e10i	0.695449	−	2.14037i
$853$	−9.65337e9	+	2.97100e10i	−0.532547	+	1.63901i	0.216345	+	0.976317i	$0.430586\pi$
$853$	−9.65337e9	+	2.97100e10i	−0.532547	+	1.63901i	−0.748892	+	0.662693i	$0.769414\pi$
$854$	2.46704e9	−	2.34724e10i	0.135542	−	1.28960i
$855$	−4.32662e9	−	4.80520e9i	−0.236738	−	0.262924i
$856$	−2.12849e9	+	2.36393e9i	−0.115988	+	0.128818i
$857$	−2.31043e9	−	2.19823e10i	−0.125389	−	1.19300i	−0.858473	−	0.512859i	$-0.828586\pi$
$857$	−2.31043e9	−	2.19823e10i	−0.125389	−	1.19300i	0.733084	−	0.680139i	$-0.238080\pi$
$858$	−7.60888e9	−	1.61732e9i	−0.411259	−	0.0874158i
$859$	−2.58231e10	+	1.14972e10i	−1.39006	+	0.618893i	−0.958993	−	0.283430i	$-0.908528\pi$
$859$	−2.58231e10	+	1.14972e10i	−1.39006	+	0.618893i	−0.431062	+	0.902322i	$0.641861\pi$
$860$	−5.25041e10	−	3.81464e10i	−2.81480	−	2.04508i
$861$	−2.14290e10	−	9.54080e9i	−1.14417	−	0.509418i
$862$	2.37908e10	+	4.12068e10i	1.26512	+	2.19126i
$863$	−1.68977e10	+	2.92677e10i	−0.894934	+	1.55007i	−0.0610469	+	0.998135i	$0.519444\pi$
$863$	−1.68977e10	+	2.92677e10i	−0.894934	+	1.55007i	−0.833887	+	0.551936i	$0.813889\pi$
$864$	−1.44837e10	+	1.05231e10i	−0.763982	+	0.555065i
$865$	1.31919e10	−	2.80402e9i	0.693027	−	0.147307i
$866$	1.71764e9	+	5.28634e9i	0.0898707	+	0.276594i
$867$	2.57675e10			1.34278
$868$	1.96592e10	+	3.90706e9i	1.02034	+	0.202783i
$869$	7.00078e9			0.361891
$870$	1.44893e10	+	4.45936e10i	0.745987	+	2.29591i
$871$	−8.81550e9	+	1.87379e9i	−0.452047	+	0.0960855i
$872$	−1.86552e9	+	1.35538e9i	−0.0952777	+	0.0692233i
$873$	−5.82146e9	+	1.00831e10i	−0.296130	+	0.512911i
$874$	−6.65370e9	−	1.15245e10i	−0.337111	−	0.583893i
$875$	3.08532e10	+	1.37367e10i	1.55694	+	0.693194i
$876$	−1.28290e10	−	9.32083e9i	−0.644806	−	0.468479i
$877$	6.18766e9	−	2.75492e9i	0.309762	−	0.137915i	−0.245968	−	0.969278i	$-0.579106\pi$
$877$	6.18766e9	−	2.75492e9i	0.309762	−	0.137915i	0.555729	+	0.831363i	$0.312439\pi$
$878$	5.53694e10	+	1.17691e10i	2.76082	+	0.586831i
$879$	−1.00354e9	−	9.54807e9i	−0.0498396	−	0.474192i
$880$	1.42623e10	−	1.58399e10i	0.705507	−	0.783545i
$881$	1.08722e10	+	1.20748e10i	0.535675	+	0.594928i	0.948851	−	0.315723i	$-0.102247\pi$
$881$	1.08722e10	+	1.20748e10i	0.535675	+	0.594928i	−0.413176	+	0.910651i	$0.635581\pi$
$882$	3.81515e8	−	3.62987e9i	0.0187228	−	0.178136i
$883$	5.95103e9	−	1.83154e10i	0.290890	−	0.895269i	−0.693681	−	0.720283i	$-0.744012\pi$
$883$	5.95103e9	−	1.83154e10i	0.290890	−	0.895269i	0.984571	−	0.174986i	$-0.0559880\pi$
$884$	−3.25626e9	+	1.00217e10i	−0.158539	+	0.487933i
$885$	3.77827e9	−	3.59479e10i	0.183228	−	1.74330i
$886$	3.62997e10	+	4.03149e10i	1.75342	+	1.94737i
$887$	1.16422e10	−	1.29299e10i	0.560146	−	0.622106i	−0.394842	−	0.918749i	$-0.629201\pi$
$887$	1.16422e10	−	1.29299e10i	0.560146	−	0.622106i	0.954988	+	0.296644i	$0.0958673\pi$
$888$	−1.53886e8	−	1.46413e9i	−0.00737488	−	0.0701672i
$889$	−5.65603e9	−	1.20223e9i	−0.269995	−	0.0573891i
$890$	7.03627e10	−	3.13275e10i	3.34563	−	1.48957i
$891$	1.72601e10	+	1.25402e10i	0.817467	+	0.593925i
$892$	2.24082e10	+	9.97679e9i	1.05714	+	0.470667i
$893$	2.33253e9	+	4.04006e9i	0.109609	+	0.189849i
$894$	−1.71238e9	+	2.96593e9i	−0.0801529	+	0.138829i
$895$	1.46956e10	−	1.06770e10i	0.685182	−	0.497814i
$896$	−1.13610e10	+	2.41486e9i	−0.527642	+	0.112154i
$897$	2.35339e9	+	7.24298e9i	0.108873	+	0.335076i
$898$	−5.09188e10			−2.34645
$899$	1.51668e9	−	1.65360e10i	0.0696203	−	0.759052i
$900$	2.52903e10			1.15639
$901$	−1.84376e10	−	5.67451e10i	−0.839784	−	2.58459i
$902$	−3.16833e10	+	6.73448e9i	−1.43750	+	0.305549i
$903$	−2.97508e10	+	2.16152e10i	−1.34459	+	0.976905i
$904$	−9.55673e6	+	1.65527e7i	−0.000430249	+	0.000745213i
$905$	−1.36577e10	−	2.36559e10i	−0.612504	−	1.06089i
$906$	−2.94957e9	−	1.31323e9i	−0.131768	−	0.0586670i
$907$	1.40761e10	+	1.02269e10i	0.626406	+	0.455110i	0.855153	−	0.518375i	$-0.173463\pi$
$907$	1.40761e10	+	1.02269e10i	0.626406	+	0.455110i	−0.228747	+	0.973486i	$0.573463\pi$
$908$	2.56414e10	−	1.14163e10i	1.13669	−	0.506085i
$909$	1.16796e10	+	2.48257e9i	0.515766	+	0.109629i
$910$	−1.54978e9	−	1.47451e10i	−0.0681749	−	0.648641i
$911$	2.17404e9	−	2.41452e9i	0.0952693	−	0.105807i	−0.693625	−	0.720337i	$-0.743987\pi$
$911$	2.17404e9	−	2.41452e9i	0.0952693	−	0.105807i	0.788894	+	0.614529i	$0.210654\pi$
$912$	−6.07697e9	−	6.74916e9i	−0.265281	−	0.294624i
$913$	−2.54191e9	+	2.41846e10i	−0.110538	+	1.05170i
$914$	−1.51471e10	+	4.66179e10i	−0.656170	+	2.01948i
$915$	−1.55177e10	+	4.77584e10i	−0.669657	+	2.06099i
$916$	−1.45374e9	+	1.38314e10i	−0.0624961	+	0.594611i
$917$	−1.65251e10	−	1.83529e10i	−0.707702	−	0.785983i
$918$	2.26120e10	−	2.51132e10i	0.964694	−	1.07140i
$919$	−7.79351e8	−	7.41503e9i	−0.0331229	−	0.315144i	−0.998521	−	0.0543637i	$-0.982687\pi$
$919$	−7.79351e8	−	7.41503e9i	−0.0331229	−	0.315144i	0.965398	−	0.260780i	$-0.0839797\pi$
$920$	1.33462e10	+	2.83683e9i	0.565068	+	0.120109i
$921$	−4.27971e10	+	1.90545e10i	−1.80512	+	0.803691i
$922$	−3.93963e9	−	2.86231e9i	−0.165538	−	0.120270i
$923$	9.72283e9	+	4.32888e9i	0.406993	+	0.181205i
$924$	1.21549e10	+	2.10529e10i	0.506874	+	0.877932i
$925$	−4.64799e9	+	8.05056e9i	−0.193094	+	0.334449i
$926$	−1.53741e10	+	1.11699e10i	−0.636284	+	0.462288i
$927$	7.21357e9	−	1.53329e9i	0.297421	−	0.0632187i
$928$	8.13624e9	+	2.50408e10i	0.334199	+	1.02856i
$929$	−1.58198e10			−0.647362			−0.323681	−	0.946166i	$-0.604920\pi$
$929$	−1.58198e10			−0.647362			−0.323681	+	0.946166i	$0.604920\pi$
$930$	−7.13833e10	−	3.06547e10i	−2.91009	−	1.24970i
$931$	−2.97055e9			−0.120646
$932$	−1.84979e9	−	5.69306e9i	−0.0748456	−	0.230351i
$933$	3.86641e9	−	8.21831e8i	0.155856	−	0.0331281i
$934$	−6.65009e9	+	4.83157e9i	−0.267063	+	0.194032i
$935$	−2.60495e10	+	4.51190e10i	−1.04222	+	1.80517i
$936$	−5.24609e8	−	9.08650e8i	−0.0209108	−	0.0362186i
$937$	3.26798e10	+	1.45500e10i	1.29775	+	0.577796i	0.935184	−	0.354162i	$-0.115234\pi$
$937$	3.26798e10	+	1.45500e10i	1.29775	+	0.577796i	0.362567	+	0.931958i	$0.381900\pi$
$938$	4.15085e10	+	3.01577e10i	1.64220	+	1.19313i
$939$	2.15476e10	−	9.59362e9i	0.849317	−	0.378140i
$940$	−2.62368e10	−	5.57680e9i	−1.03030	−	0.218997i
$941$	−3.67867e9	−	3.50002e10i	−0.143922	−	1.36933i	−0.793286	−	0.608850i	$-0.791631\pi$
$941$	−3.67867e9	−	3.50002e10i	−0.143922	−	1.36933i	0.649364	−	0.760478i	$-0.275035\pi$
$942$	5.72227e10	−	6.35523e10i	2.23044	−	2.47715i
$943$	2.12193e10	+	2.35664e10i	0.824025	+	0.915172i
$944$	1.63842e9	−	1.55885e10i	0.0633902	−	0.603118i
$945$	−8.06562e9	+	2.48234e10i	−0.310904	+	0.956865i
$946$	−1.56920e10	+	4.82949e10i	−0.602640	+	1.85474i
$947$	5.33816e9	−	5.07892e10i	0.204252	−	1.94333i	−0.109866	−	0.993946i	$-0.535042\pi$
$947$	5.33816e9	−	5.07892e10i	0.204252	−	1.94333i	0.314118	−	0.949384i	$-0.398291\pi$
$948$	1.14763e10	+	1.27458e10i	0.437496	+	0.485888i
$949$	2.77964e9	−	3.08710e9i	0.105574	−	0.117252i
$950$	−3.91941e9	−	3.72906e10i	−0.148316	−	1.41113i
$951$	−3.76361e10	−	7.99981e9i	−1.41897	−	0.301611i
$952$	9.77271e9	−	4.35109e9i	0.367101	−	0.163444i
$953$	−3.11797e10	−	2.26534e10i	−1.16694	−	0.847829i	−0.176298	−	0.984337i	$-0.556412\pi$
$953$	−3.11797e10	−	2.26534e10i	−1.16694	−	0.847829i	−0.990639	+	0.136508i	$0.956412\pi$
$954$	3.04348e10	+	1.35504e10i	1.13488	+	0.505282i
$955$	−1.83935e10	−	3.18585e10i	−0.683365	−	1.18362i
$956$	−1.09224e10	+	1.89181e10i	−0.404310	+	0.700285i
$957$	1.62934e10	−	1.18379e10i	0.600926	−	0.436598i
$958$	−1.05373e10	+	2.23978e9i	−0.387215	+	0.0823050i
$959$	2.30676e9	+	7.09947e9i	0.0844572	+	0.259932i
$960$	8.02733e10			2.92834
$961$	1.89450e10	+	1.99507e10i	0.688595	+	0.725146i
$962$	2.16269e9			0.0783217
$963$	−2.05178e9	−	6.31473e9i	−0.0740353	−	0.227857i
$964$	−8.60074e9	+	1.82814e9i	−0.309219	+	0.0657265i
$965$	5.25111e10	−	3.81516e10i	1.88107	−	1.36668i
$966$	2.16779e10	−	3.75473e10i	0.773745	−	1.34017i
$967$	−1.35636e10	−	2.34928e10i	−0.482371	−	0.835491i	0.517424	−	0.855729i	$-0.326891\pi$
$967$	−1.35636e10	−	2.34928e10i	−0.482371	−	0.835491i	−0.999795	+	0.0202379i	$0.993558\pi$
$968$	−2.86226e9	−	1.27436e9i	−0.101425	−	0.0451574i
$969$	1.79590e10	+	1.30480e10i	0.634088	+	0.460692i
$970$	−9.06717e10	+	4.03696e10i	−3.18985	+	1.42021i
$971$	3.98637e10	+	8.47330e9i	1.39737	+	0.297020i	0.844190	−	0.536044i	$-0.180082\pi$
$971$	3.98637e10	+	8.47330e9i	1.39737	+	0.297020i	0.553178	+	0.833063i	$0.313415\pi$
$972$	3.03928e9	+	2.89168e10i	0.106154	+	1.00999i
$973$	−1.16398e10	+	1.29273e10i	−0.405088	+	0.449896i
$974$	1.38708e10	+	1.54051e10i	0.481002	+	0.534207i
$975$	−2.24305e9	+	2.13412e10i	−0.0775036	+	0.737398i
$976$	−6.72910e9	+	2.07100e10i	−0.231677	+	0.713028i
$977$	−1.05120e9	+	3.23525e9i	−0.0360622	+	0.110988i	−0.967467	−	0.252996i	$-0.918584\pi$
$977$	−1.05120e9	+	3.23525e9i	−0.0360622	+	0.110988i	0.931405	+	0.363985i	$0.118584\pi$
$978$	9.38335e8	−	8.92766e9i	0.0320754	−	0.305177i
$979$	−2.21366e10	−	2.45852e10i	−0.754002	−	0.837404i
$980$	1.14287e10	−	1.26928e10i	0.387887	−	0.430792i
$981$	−5.03110e8	−	4.78677e9i	−0.0170146	−	0.161883i
$982$	3.63795e10	+	7.73270e9i	1.22593	+	0.260580i
$983$	4.01768e10	−	1.78879e10i	1.34908	−	0.600650i	0.400243	−	0.916409i	$-0.368926\pi$
$983$	4.01768e10	−	1.78879e10i	1.34908	−	0.600650i	0.948839	+	0.315759i	$0.102259\pi$
$984$	−1.14483e10	−	8.31767e9i	−0.383052	−	0.278304i
$985$	−3.57154e10	−	1.59015e10i	−1.19077	−	0.530166i
$986$	−2.48494e10	−	4.30404e10i	−0.825556	−	1.42991i
$987$	−7.59944e9	+	1.31626e10i	−0.251577	+	0.435745i
$988$	−3.87411e9	+	2.81470e9i	−0.127798	+	0.0928503i
$989$	4.86288e10	−	1.03364e10i	1.59848	−	0.339767i
$990$	−8.98936e9	−	2.76664e10i	−0.294446	−	0.906211i
$991$	−1.99079e10			−0.649783			−0.324891	−	0.945751i	$-0.605328\pi$
$991$	−1.99079e10			−0.649783			−0.324891	+	0.945751i	$0.605328\pi$
$992$	−4.00840e10	−	1.72136e10i	−1.30371	−	0.559861i
$993$	4.79744e10			1.55485
$994$	−1.87233e10	−	5.76243e10i	−0.604685	−	1.86103i
$995$	−1.77941e10	+	3.78224e9i	−0.572657	+	0.121722i
$996$	−4.81979e10	+	3.50179e10i	−1.54568	+	1.12301i
$997$	−1.18393e10	+	2.05063e10i	−0.378350	+	0.655322i	−0.990822	−	0.135170i	$-0.956842\pi$
$997$	−1.18393e10	+	2.05063e10i	−0.378350	+	0.655322i	0.612472	+	0.790492i	$0.290175\pi$
$998$	−1.48010e9	−	2.56360e9i	−0.0471338	−	0.0816382i
$999$	−3.47813e9	−	1.54856e9i	−0.110374	−	0.0491417i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.8.g.a.7.17	✓	144
31.9	even	15	inner	31.8.g.a.9.17	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.8.g.a.7.17	✓	144	1.1	even	1	trivial
31.8.g.a.9.17	yes	144	31.9	even	15	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(5.20562 + 16.0213i) q^{2} +(-55.0184 + 11.6945i) q^{3} +(-126.028 + 91.5648i) q^{4} +(247.149 - 428.075i) q^{5} +(-473.766 - 820.587i) q^{6} +(-708.649 - 315.511i) q^{7} +(-378.590 - 275.062i) q^{8} +(892.338 - 397.295i) q^{9} +(8144.86 + 1731.24i) q^{10} +(-373.854 - 3556.99i) q^{11} +(5863.06 - 6511.59i) q^{12} +(1535.91 + 1705.80i) q^{13} +(1365.92 - 12995.9i) q^{14} +(-8591.61 + 26442.3i) q^{15} +(-3725.68 + 11466.5i) q^{16} +(3080.40 - 29308.0i) q^{17} +(11010.3 + 12228.2i) q^{18} +(8961.08 - 9952.29i) q^{19} +(8048.84 + 76579.6i) q^{20} +(42678.5 + 9071.59i) q^{21} +(55041.3 - 24505.9i) q^{22} +(-47721.1 - 34671.4i) q^{23} +(24046.2 + 10706.0i) q^{24} +(-83102.8 - 143938. i) q^{25} +(-19333.7 + 33487.0i) q^{26} +(55071.1 - 40011.5i) q^{27} +(118199. - 25124.0i) q^{28} +(-30936.1 - 95211.6i) q^{29} -468363. q^{30} +(152410. + 65450.6i) q^{31} -263001. q^{32} +(62166.1 + 191328. i) q^{33} +(485587. - 103215. i) q^{34} +(-310204. + 225376. i) q^{35} +(-76081.5 + 131777. i) q^{36} +(-27965.3 - 48437.4i) q^{37} +(206096. + 91760.0i) q^{38} +(-104452. - 75888.7i) q^{39} +(-211315. + 94083.7i) q^{40} +(-525862. - 111775. i) q^{41} +(76829.7 + 730986. i) q^{42} +(-563959. + 626340. i) q^{43} +(372811. + 414048. i) q^{44} +(50468.8 - 480178. i) q^{45} +(307062. - 945039. i) q^{46} +(-107644. + 331294. i) q^{47} +(70886.1 - 674437. i) q^{48} +(-148422. - 164839. i) q^{49} +(1.87347e6 - 2.08070e6i) q^{50} +(173265. + 1.64850e6i) q^{51} +(-349759. - 74343.6i) q^{52} +(1.84961e6 - 823499. i) q^{53} +(927713. + 674023. i) q^{54} +(-1.61505e6 - 719068. i) q^{55} +(181503. + 314372. i) q^{56} +(-376637. + 652355. i) q^{57} +(1.36437e6 - 991272. i) q^{58} +(-1.27166e6 + 270300. i) q^{59} +(-1.33840e6 - 4.11916e6i) q^{60} +1.80614e6 q^{61} +(-255212. + 2.78251e6i) q^{62} -757705. q^{63} +(-892197. - 2.74590e6i) q^{64} +(1.10981e6 - 235897. i) q^{65} +(-2.74170e6 + 1.99196e6i) q^{66} +(-1.96317e6 + 3.40031e6i) q^{67} +(2.29537e6 + 3.97569e6i) q^{68} +(3.03101e6 + 1.34949e6i) q^{69} +(-5.22562e6 - 3.79663e6i) q^{70} +(4.23583e6 - 1.88591e6i) q^{71} +(-447111. - 95036.5i) q^{72} +(-189172. - 1.79985e6i) q^{73} +(630451. - 700187. i) q^{74} +(6.25547e6 + 6.94740e6i) q^{75} +(-218069. + 2.07479e6i) q^{76} +(-857336. + 2.63861e6i) q^{77} +(672095. - 2.06850e6i) q^{78} +(-204604. + 1.94667e6i) q^{79} +(3.98771e6 + 4.42880e6i) q^{80} +(-3.99142e6 + 4.43293e6i) q^{81} +(-946656. - 9.00683e6i) q^{82} +(-6.65062e6 - 1.41363e6i) q^{83} +(-6.20932e6 + 2.76457e6i) q^{84} +(-1.17847e7 - 8.56209e6i) q^{85} +(-1.29705e7 - 5.77484e6i) q^{86} +(2.81551e6 + 4.87661e6i) q^{87} +(-836854. + 1.44947e6i) q^{88} +(7.48326e6 - 5.43691e6i) q^{89} +(7.95578e6 - 1.69105e6i) q^{90} +(-550222. - 1.69341e6i) q^{91} +9.18888e6 q^{92} +(-9.15077e6 - 1.81863e6i) q^{93} -5.86810e6 q^{94} +(-2.04560e6 - 6.29571e6i) q^{95} +(1.44699e7 - 3.07567e6i) q^{96} +(-9.64317e6 + 7.00617e6i) q^{97} +(1.86830e6 - 3.23600e6i) q^{98} +(-1.74678e6 - 3.02550e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{2} - 8 q^{3} - 2362 q^{4} - 75 q^{5} - 1637 q^{6} + 5518 q^{7} + 3401 q^{8} + 14542 q^{9} - 5312 q^{10} + 1361 q^{11} - 18281 q^{12} + 22457 q^{13} + 28470 q^{14} - 86918 q^{15} - 155730 q^{16}+ \cdots - 102755966 q^{99}+O(q^{100}) \) 144 * q - 6 * q^2 - 8 * q^3 - 2362 * q^4 - 75 * q^5 - 1637 * q^6 + 5518 * q^7 + 3401 * q^8 + 14542 * q^9 - 5312 * q^10 + 1361 * q^11 - 18281 * q^12 + 22457 * q^13 + 28470 * q^14 - 86918 * q^15 - 155730 * q^16 + 51582 * q^17 - 24915 * q^18 + 206748 * q^19 + 53815 * q^20 - 28547 * q^21 + 471441 * q^22 - 10235 * q^23 + 69278 * q^24 - 974301 * q^25 - 279651 * q^26 - 948323 * q^27 + 550632 * q^28 - 32990 * q^29 + 2457990 * q^30 + 899715 * q^31 - 1048518 * q^32 + 780887 * q^33 - 1741528 * q^34 + 40023 * q^35 - 2118881 * q^36 - 787972 * q^37 + 580274 * q^38 + 2541281 * q^39 + 2341817 * q^40 + 1129504 * q^41 - 4390379 * q^42 + 481927 * q^43 - 3123681 * q^44 - 1715971 * q^45 + 2065430 * q^46 - 3123106 * q^47 + 1041890 * q^48 + 76766 * q^49 + 7537425 * q^50 + 6145978 * q^51 + 3260257 * q^52 + 141486 * q^53 - 8979668 * q^54 - 8182779 * q^55 - 5240874 * q^56 - 5487037 * q^57 + 5315215 * q^58 + 7471552 * q^59 + 8590679 * q^60 + 10667852 * q^61 + 27020951 * q^62 - 23783686 * q^63 - 3962521 * q^64 + 935148 * q^65 + 3015728 * q^66 - 17382495 * q^67 - 29462568 * q^68 - 26986306 * q^69 - 31811186 * q^70 - 6186650 * q^71 + 35811589 * q^72 + 6470154 * q^73 + 55339663 * q^74 + 17367737 * q^75 + 2919592 * q^76 + 31865334 * q^77 - 7291717 * q^78 + 4223078 * q^79 + 77431338 * q^80 - 5164601 * q^81 - 19477394 * q^82 - 28867780 * q^83 - 76561164 * q^84 - 45198987 * q^85 - 60993764 * q^86 + 18253055 * q^87 - 45197061 * q^88 - 8429459 * q^89 + 83458809 * q^90 - 53128088 * q^91 + 77469728 * q^92 + 41662009 * q^93 - 16867972 * q^94 - 12744274 * q^95 + 119555444 * q^96 + 20643027 * q^97 + 49624796 * q^98 - 102755966 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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