LMFDB - Embedded newform 25.8.d.a.11.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [25,8,Mod(6,25)] 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("25.6"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.80962563710$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	25.11
Dual form			25.8.d.a.16.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(10.7778 - 7.83056i) q^{2} +(-25.0139 + 76.9848i) q^{3} +(15.2900 - 47.0577i) q^{4} +(-143.017 - 240.148i) q^{5} +(333.238 + 1025.60i) q^{6} -1424.61 q^{7} +(323.251 + 994.865i) q^{8} +(-3531.64 - 2565.89i) q^{9} +(-3421.91 - 1468.38i) q^{10} +(-1784.52 + 1296.53i) q^{11} +(3240.26 + 2354.19i) q^{12} +(9275.70 + 6739.19i) q^{13} +(-15354.2 + 11155.5i) q^{14} +(22065.2 - 5003.09i) q^{15} +(16398.1 + 11913.9i) q^{16} +(982.238 + 3023.02i) q^{17} -58155.7 q^{18} +(-1330.23 - 4094.01i) q^{19} +(-13487.5 + 3058.19i) q^{20} +(35634.9 - 109673. i) q^{21} +(-9080.74 + 27947.6i) q^{22} +(-54260.5 + 39422.6i) q^{23} -84675.2 q^{24} +(-37217.3 + 68690.5i) q^{25} +152744. q^{26} +(142654. - 103644. i) q^{27} +(-21782.2 + 67038.7i) q^{28} +(34072.7 - 104865. i) q^{29} +(198638. - 226705. i) q^{30} +(47299.6 + 145573. i) q^{31} +136132. q^{32} +(-55175.4 - 169812. i) q^{33} +(34258.3 + 24890.1i) q^{34} +(203743. + 342117. i) q^{35} +(-174743. + 126958. i) q^{36} +(-102935. - 74786.4i) q^{37} +(-46395.4 - 33708.2i) q^{38} +(-750836. + 545514. i) q^{39} +(192685. - 219911. i) q^{40} +(-496058. - 360407. i) q^{41} +(-474734. - 1.46108e6i) q^{42} +687250. q^{43} +(33726.5 + 103800. i) q^{44} +(-111109. + 1.21508e6i) q^{45} +(-276110. + 849780. i) q^{46} +(-84119.5 + 258893. i) q^{47} +(-1.32737e6 + 964390. i) q^{48} +1.20596e6 q^{49} +(136763. + 1.03177e6i) q^{50} -257296. q^{51} +(458956. - 333451. i) q^{52} +(7268.64 - 22370.6i) q^{53} +(725908. - 2.23411e6i) q^{54} +(566577. + 243124. i) q^{55} +(-460506. - 1.41729e6i) q^{56} +348451. q^{57} +(-453922. - 1.39703e6i) q^{58} +(-1.12293e6 - 815859. i) q^{59} +(101942. - 1.11483e6i) q^{60} +(-1.55128e6 + 1.12707e6i) q^{61} +(1.64971e6 + 1.19858e6i) q^{62} +(5.03120e6 + 3.65538e6i) q^{63} +(-631742. + 458988. i) q^{64} +(291823. - 3.19136e6i) q^{65} +(-1.92440e6 - 1.39816e6i) q^{66} +(966986. + 2.97608e6i) q^{67} +157275. q^{68} +(-1.67767e6 - 5.16334e6i) q^{69} +(4.87488e6 + 2.09186e6i) q^{70} +(-1.41716e6 + 4.36158e6i) q^{71} +(1.41110e6 - 4.34293e6i) q^{72} +(80932.6 - 58801.0i) q^{73} -1.69503e6 q^{74} +(-4.35717e6 - 4.58338e6i) q^{75} -212994. q^{76} +(2.54225e6 - 1.84705e6i) q^{77} +(-3.82071e6 + 1.17589e7i) q^{78} +(-228557. + 703425. i) q^{79} +(515900. - 5.64186e6i) q^{80} +(1.46050e6 + 4.49494e6i) q^{81} -8.16862e6 q^{82} +(386535. + 1.18963e6i) q^{83} +(-4.61610e6 - 3.35380e6i) q^{84} +(585496. - 668226. i) q^{85} +(7.40707e6 - 5.38155e6i) q^{86} +(7.22072e6 + 5.24616e6i) q^{87} +(-1.86672e6 - 1.35625e6i) q^{88} +(1.52434e6 - 1.10750e6i) q^{89} +(8.31725e6 + 1.39660e7i) q^{90} +(-1.32142e7 - 9.60071e6i) q^{91} +(1.02549e6 + 3.15614e6i) q^{92} -1.23901e7 q^{93} +(1.12065e6 + 3.44901e6i) q^{94} +(-792925. + 904965. i) q^{95} +(-3.40520e6 + 1.04801e7i) q^{96} +(1.65618e6 - 5.09721e6i) q^{97} +(1.29977e7 - 9.44338e6i) q^{98} +9.62905e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16}+ \cdots + 71266232 q^{99}+O(q^{100}) $ 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	10.7778	−	7.83056i	0.952635	−	0.692130i	0.00120650	−	0.999999i	$-0.499616\pi$
$2$	10.7778	−	7.83056i	0.952635	−	0.692130i	0.951429	+	0.307869i	$0.0996160\pi$
$3$	−25.0139	+	76.9848i	−0.534880	+	1.64619i	0.209028	+	0.977910i	$0.432970\pi$
$3$	−25.0139	+	76.9848i	−0.534880	+	1.64619i	−0.743908	+	0.668282i	$0.767030\pi$
$4$	15.2900	−	47.0577i	0.119453	−	0.367638i
$5$	−143.017	−	240.148i	−0.511673	−	0.859180i
$5$	−143.017	−	240.148i	−0.511673	−	0.859180i
$6$	333.238	+	1025.60i	0.629833	+	1.93843i
$7$	−1424.61			−1.56983			−0.784914	−	0.619604i	$-0.787293\pi$
$7$	−1424.61			−1.56983			−0.784914	+	0.619604i	$0.787293\pi$
$8$	323.251	+	994.865i	0.223216	+	0.686988i
$9$	−3531.64	−	2565.89i	−1.61483	−	1.17324i
$10$	−3421.91	−	1468.38i	−1.08210	−	0.464341i
$11$	−1784.52	+	1296.53i	−0.404248	+	0.293703i	−0.771269	−	0.636509i	$-0.780378\pi$
$11$	−1784.52	+	1296.53i	−0.404248	+	0.293703i	0.367021	+	0.930213i	$0.380378\pi$
$12$	3240.26	+	2354.19i	0.541310	+	0.393285i
$13$	9275.70	+	6739.19i	1.17097	+	0.850758i	0.991124	−	0.132937i	$-0.0424408\pi$
$13$	9275.70	+	6739.19i	1.17097	+	0.850758i	0.179844	+	0.983695i	$0.442441\pi$
$14$	−15354.2	+	11155.5i	−1.49547	+	1.08653i
$15$	22065.2	−	5003.09i	1.68806	−	0.382753i
$16$	16398.1	+	11913.9i	1.00086	+	0.727167i
$17$	982.238	+	3023.02i	0.0484893	+	0.149235i	0.972369	−	0.233447i	$-0.0750006\pi$
$17$	982.238	+	3023.02i	0.0484893	+	0.149235i	−0.923880	+	0.382682i	$0.875001\pi$
$18$	−58155.7			−2.35038
$19$	−1330.23	−	4094.01i	−0.0444926	−	0.136934i	0.926343	−	0.376682i	$-0.122935\pi$
$19$	−1330.23	−	4094.01i	−0.0444926	−	0.136934i	−0.970835	+	0.239748i	$0.922935\pi$
$20$	−13487.5	+	3058.19i	−0.376988	+	0.0854789i
$21$	35634.9	−	109673.i	0.839670	−	2.58424i
$22$	−9080.74	+	27947.6i	−0.181820	+	0.559584i
$23$	−54260.5	+	39422.6i	−0.929901	+	0.675612i	−0.945969	−	0.324258i	$-0.894885\pi$
$23$	−54260.5	+	39422.6i	−0.929901	+	0.675612i	0.0160678	+	0.999871i	$0.494885\pi$
$24$	−84675.2			−1.25031
$25$	−37217.3	+	68690.5i	−0.476382	+	0.879239i
$26$	152744.			1.70434
$27$	142654.	−	103644.i	1.39479	−	1.01338i
$28$	−21782.2	+	67038.7i	−0.187521	+	0.577129i
$29$	34072.7	−	104865.i	0.259426	−	0.798432i	−0.733499	−	0.679691i	$-0.762114\pi$
$29$	34072.7	−	104865.i	0.259426	−	0.798432i	0.992925	−	0.118741i	$-0.0378859\pi$
$30$	198638.	−	226705.i	1.34319	−	1.53298i
$31$	47299.6	+	145573.i	0.285162	+	0.877637i	0.986350	+	0.164661i	$0.0526532\pi$
$31$	47299.6	+	145573.i	0.285162	+	0.877637i	−0.701188	+	0.712976i	$0.747347\pi$
$32$	136132.			0.734407
$33$	−55175.4	−	169812.i	−0.267268	−	0.822566i
$34$	34258.3	+	24890.1i	0.149482	+	0.108605i
$35$	203743.	+	342117.i	0.803239	+	1.34877i
$36$	−174743.	+	126958.i	−0.624226	+	0.453527i
$37$	−102935.	−	74786.4i	−0.334084	−	0.242726i	0.408078	−	0.912947i	$-0.366199\pi$
$37$	−102935.	−	74786.4i	−0.334084	−	0.242726i	−0.742162	+	0.670221i	$0.766199\pi$
$38$	−46395.4	−	33708.2i	−0.137161	−	0.0996536i
$39$	−750836.	+	545514.i	−2.02684	+	1.47258i
$40$	192685.	−	219911.i	0.476033	−	0.543296i
$41$	−496058.	−	360407.i	−1.12406	−	0.816677i	−0.139240	−	0.990259i	$-0.544466\pi$
$41$	−496058.	−	360407.i	−1.12406	−	0.816677i	−0.984819	+	0.173582i	$0.944466\pi$
$42$	−474734.	−	1.46108e6i	−0.988730	−	3.04300i
$43$	687250.			1.31818			0.659091	−	0.752064i	$-0.270941\pi$
$43$	687250.			1.31818			0.659091	+	0.752064i	$0.270941\pi$
$44$	33726.5	+	103800.i	0.0596880	+	0.183701i
$45$	−111109.	+	1.21508e6i	−0.181763	+	1.98775i
$46$	−276110.	+	849780.i	−0.418245	+	1.28722i
$47$	−84119.5	+	258893.i	−0.118183	+	0.363729i	−0.992598	−	0.121450i	$-0.961246\pi$
$47$	−84119.5	+	258893.i	−0.118183	+	0.363729i	0.874415	+	0.485179i	$0.161246\pi$
$48$	−1.32737e6	+	964390.i	−1.73240	+	1.25866i
$49$	1.20596e6			1.46436
$50$	136763.	+	1.03177e6i	0.154729	+	1.16731i
$51$	−257296.			−0.271605
$52$	458956.	−	333451.i	0.452647	−	0.328867i
$53$	7268.64	−	22370.6i	0.00670637	−	0.0206401i	−0.947647	−	0.319319i	$-0.896546\pi$
$53$	7268.64	−	22370.6i	0.00670637	−	0.0206401i	0.954354	+	0.298679i	$0.0965459\pi$
$54$	725908.	−	2.23411e6i	0.627340	−	1.93076i
$55$	566577.	+	243124.i	0.459187	+	0.197042i
$56$	−460506.	−	1.41729e6i	−0.350411	−	1.07845i
$57$	348451.			0.249218
$58$	−453922.	−	1.39703e6i	−0.305480	−	0.940171i
$59$	−1.12293e6	−	815859.i	−0.711823	−	0.517170i	0.171938	−	0.985108i	$-0.444997\pi$
$59$	−1.12293e6	−	815859.i	−0.711823	−	0.517170i	−0.883761	+	0.467938i	$0.844997\pi$
$60$	101942.	−	1.11483e6i	0.0609289	−	0.666316i
$61$	−1.55128e6	+	1.12707e6i	−0.875056	+	0.635765i	−0.931939	−	0.362616i	$-0.881884\pi$
$61$	−1.55128e6	+	1.12707e6i	−0.875056	+	0.635765i	0.0568829	+	0.998381i	$0.481884\pi$
$62$	1.64971e6	+	1.19858e6i	0.879094	+	0.638699i
$63$	5.03120e6	+	3.65538e6i	2.53501	+	1.84179i
$64$	−631742.	+	458988.i	−0.301238	+	0.218862i
$65$	291823.	−	3.19136e6i	0.131802	−	1.44138i
$66$	−1.92440e6	−	1.39816e6i	−0.823931	−	0.598621i
$67$	966986.	+	2.97608e6i	0.392788	+	1.20888i	0.930671	+	0.365858i	$0.119224\pi$
$67$	966986.	+	2.97608e6i	0.392788	+	1.20888i	−0.537883	+	0.843020i	$0.680776\pi$
$68$	157275.			0.0606565
$69$	−1.67767e6	−	5.16334e6i	−0.614802	−	1.89217i
$70$	4.87488e6	+	2.09186e6i	1.69871	+	0.728936i
$71$	−1.41716e6	+	4.36158e6i	−0.469911	+	1.44624i	0.382788	+	0.923836i	$0.374964\pi$
$71$	−1.41716e6	+	4.36158e6i	−0.469911	+	1.44624i	−0.852699	+	0.522402i	$0.825036\pi$
$72$	1.41110e6	−	4.34293e6i	0.445548	−	1.37126i
$73$	80932.6	−	58801.0i	0.0243497	−	0.0176911i	−0.575544	−	0.817771i	$-0.695210\pi$
$73$	80932.6	−	58801.0i	0.0243497	−	0.0176911i	0.599894	+	0.800080i	$0.295210\pi$
$74$	−1.69503e6			−0.486258
$75$	−4.35717e6	−	4.58338e6i	−1.19259	−	1.25450i
$76$	−212994.			−0.0556570
$77$	2.54225e6	−	1.84705e6i	0.634600	−	0.461064i
$78$	−3.82071e6	+	1.17589e7i	−0.911618	+	2.80567i
$79$	−228557.	+	703425.i	−0.0521554	+	0.160518i	−0.973742	−	0.227656i	$-0.926894\pi$
$79$	−228557.	+	703425.i	−0.0521554	+	0.160518i	0.921586	+	0.388174i	$0.126894\pi$
$80$	515900.	−	5.64186e6i	0.112655	−	1.23199i
$81$	1.46050e6	+	4.49494e6i	0.305353	+	0.939781i
$82$	−8.16862e6			−1.63606
$83$	386535.	+	1.18963e6i	0.0742019	+	0.228370i	0.981278	−	0.192597i	$-0.0616909\pi$
$83$	386535.	+	1.18963e6i	0.0742019	+	0.228370i	−0.907076	+	0.420967i	$0.861691\pi$
$84$	−4.61610e6	−	3.35380e6i	−0.849764	−	0.617389i
$85$	585496.	−	668226.i	0.103409	−	0.118020i
$86$	7.40707e6	−	5.38155e6i	1.25575	−	0.912353i
$87$	7.22072e6	+	5.24616e6i	1.17561	+	0.854130i
$88$	−1.86672e6	−	1.35625e6i	−0.292005	−	0.212154i
$89$	1.52434e6	−	1.10750e6i	0.229201	−	0.166524i	−0.467258	−	0.884121i	$-0.654758\pi$
$89$	1.52434e6	−	1.10750e6i	0.229201	−	0.166524i	0.696459	+	0.717597i	$0.254758\pi$
$90$	8.31725e6	+	1.39660e7i	1.20263	+	2.01940i
$91$	−1.32142e7	−	9.60071e6i	−1.83822	−	1.33554i
$92$	1.02549e6	+	3.15614e6i	0.137302	+	0.422571i
$93$	−1.23901e7			−1.59729
$94$	1.12065e6	+	3.44901e6i	0.139163	+	0.428299i
$95$	−792925.	+	904965.i	−0.0948855	+	0.108293i
$96$	−3.40520e6	+	1.04801e7i	−0.392819	+	1.20897i
$97$	1.65618e6	−	5.09721e6i	0.184250	−	0.567063i	−0.815685	−	0.578497i	$-0.803640\pi$
$97$	1.65618e6	−	5.09721e6i	0.184250	−	0.567063i	0.999935	+	0.0114337i	$0.00363955\pi$
$98$	1.29977e7	−	9.44338e6i	1.39500	−	1.01353i
$99$	9.62905e6			0.997379
$100$	2.66336e6	+	2.80164e6i	0.266336	+	0.280164i
$101$	1.77751e6			0.171667			0.0858337	−	0.996309i	$-0.472645\pi$
$101$	1.77751e6			0.171667			0.0858337	+	0.996309i	$0.472645\pi$
$102$	−2.77309e6	+	2.01477e6i	−0.258740	+	0.187986i
$103$	3.20132e6	−	9.85266e6i	0.288668	−	0.888430i	−0.696607	−	0.717453i	$-0.745308\pi$
$103$	3.20132e6	−	9.85266e6i	0.288668	−	0.888430i	0.985275	−	0.170977i	$-0.0546923\pi$
$104$	−3.70620e6	+	1.14065e7i	−0.323082	+	0.994344i
$105$	−3.14342e7	+	7.12744e6i	−2.64996	+	0.600857i
$106$	−96833.8	−	298024.i	−0.00789690	−	0.0243042i
$107$	1.19224e7			0.940848			0.470424	−	0.882440i	$-0.344101\pi$
$107$	1.19224e7			0.940848			0.470424	+	0.882440i	$0.344101\pi$
$108$	−2.69607e6	−	8.29766e6i	−0.205944	−	0.633830i
$109$	2.04666e6	+	1.48699e6i	0.151375	+	0.109980i	0.660895	−	0.750479i	$-0.270177\pi$
$109$	2.04666e6	+	1.48699e6i	0.151375	+	0.109980i	−0.509520	+	0.860459i	$0.670177\pi$
$110$	8.01027e6	−	1.81626e6i	0.573816	−	0.130108i
$111$	8.33221e6	−	6.05370e6i	0.578268	−	0.420137i
$112$	−2.33608e7	−	1.69726e7i	−1.57118	−	1.14153i
$113$	4.57136e6	+	3.32129e6i	0.298038	+	0.216537i	0.726747	−	0.686906i	$-0.241031\pi$
$113$	4.57136e6	+	3.32129e6i	0.298038	+	0.216537i	−0.428709	+	0.903443i	$0.641031\pi$
$114$	3.75555e6	−	2.72856e6i	0.237414	−	0.172491i
$115$	1.72274e7	+	7.39247e6i	1.05628	+	0.453260i
$116$	−4.41374e6	−	3.20677e6i	−0.262545	−	0.190750i
$117$	−1.54664e7	−	4.76008e7i	−0.892770	−	2.74766i
$118$	−1.84914e7			−1.03606
$119$	−1.39930e6	−	4.30662e6i	−0.0761198	−	0.234273i
$120$	1.21100e7	+	2.03346e7i	0.639748	+	1.07424i
$121$	−4.51834e6	+	1.39060e7i	−0.231862	+	0.713598i
$122$	−7.89385e6	+	2.42948e7i	−0.393577	+	1.21130i
$123$	4.01542e7	−	2.91737e7i	1.94564	−	1.41359i
$124$	7.57354e6			0.356716
$125$	2.18186e7	−	886230.i	0.999176	−	0.0405846i
$126$	8.28491e7			3.68970
$127$	1.32053e6	−	959422.i	0.0572052	−	0.0415620i	−0.558815	−	0.829292i	$-0.688744\pi$
$127$	1.32053e6	−	959422.i	0.0572052	−	0.0415620i	0.616020	+	0.787730i	$0.288744\pi$
$128$	−8.59929e6	+	2.64659e7i	−0.362433	+	1.11545i
$129$	−1.71908e7	+	5.29078e7i	−0.705069	+	2.16998i
$130$	−2.18449e7	−	3.66811e7i	−0.872065	−	1.46434i
$131$	−7.33624e6	−	2.25786e7i	−0.285118	−	0.877502i	−0.986363	−	0.164582i	$-0.947372\pi$
$131$	−7.33624e6	−	2.25786e7i	−0.285118	−	0.877502i	0.701246	−	0.712920i	$-0.252628\pi$
$132$	−8.83461e6			−0.334333
$133$	1.89505e6	+	5.83237e6i	0.0698458	+	0.214963i
$134$	3.37263e7	+	2.45036e7i	1.21088	+	0.879759i
$135$	−4.52918e7	−	1.94352e7i	−1.58435	−	0.679861i
$136$	−2.68999e6	+	1.95439e6i	−0.0916988	+	0.0666231i
$137$	3.71383e7	+	2.69825e7i	1.23396	+	0.896522i	0.997180	−	0.0750427i	$-0.0239093\pi$
$137$	3.71383e7	+	2.69825e7i	1.23396	+	0.896522i	0.236776	+	0.971564i	$0.423909\pi$
$138$	−5.85135e7	−	4.25126e7i	−1.89531	−	1.37702i
$139$	−4.03273e7	+	2.92995e7i	−1.27364	+	0.925355i	−0.999341	−	0.0362894i	$-0.988446\pi$
$139$	−4.03273e7	+	2.92995e7i	−1.27364	+	0.925355i	−0.274300	+	0.961644i	$0.588446\pi$
$140$	1.92145e7	−	4.35672e6i	0.591807	−	0.134187i
$141$	−1.78267e7	−	1.29518e7i	−0.535554	−	0.389103i
$142$	1.88797e7	+	5.81056e7i	0.553331	+	1.70298i
$143$	−2.52903e7			−0.723232
$144$	−2.73424e7	−	8.41512e7i	−0.763076	−	2.34851i
$145$	−3.00561e7	+	6.81497e6i	−0.818738	+	0.185642i
$146$	411834.	−	1.26749e6i	0.0109518	−	0.0337063i
$147$	−3.01658e7	+	9.28409e7i	−0.783258	+	2.41062i
$148$	−5.09314e6	+	3.70038e6i	−0.129143	+	0.0938276i
$149$	5.55852e7			1.37660			0.688299	−	0.725427i	$-0.258358\pi$
$149$	5.55852e7			1.37660			0.688299	+	0.725427i	$0.258358\pi$
$150$	−8.28513e7	−	1.52799e7i	−2.00438	−	0.369658i
$151$	−3.30040e7			−0.780095			−0.390047	−	0.920795i	$-0.627541\pi$
$151$	−3.30040e7			−0.780095			−0.390047	+	0.920795i	$0.627541\pi$
$152$	3.64299e6	−	2.64679e6i	0.0841406	−	0.0611318i
$153$	4.28781e6	−	1.31965e7i	0.0967867	−	0.297879i
$154$	1.29365e7	−	3.98144e7i	0.285426	−	0.878452i
$155$	2.81945e7	−	3.21783e7i	0.608139	−	0.694069i
$156$	1.41904e7	+	4.36735e7i	0.299266	+	0.921047i
$157$	−5.09739e7			−1.05123			−0.525617	−	0.850722i	$-0.676165\pi$
$157$	−5.09739e7			−1.05123			−0.525617	+	0.850722i	$0.676165\pi$
$158$	3.04486e6	+	9.37113e6i	0.0614141	+	0.189013i
$159$	1.54038e6	+	1.11915e6i	0.0303904	+	0.0220799i
$160$	−1.94692e7	−	3.26920e7i	−0.375776	−	0.630988i
$161$	7.73000e7	−	5.61617e7i	1.45978	−	1.06060i
$162$	5.09389e7	+	3.70093e7i	0.941341	+	0.683924i
$163$	8.18227e7	+	5.94477e7i	1.47985	+	1.07517i	0.977605	+	0.210446i	$0.0674917\pi$
$163$	8.18227e7	+	5.94477e7i	1.47985	+	1.07517i	0.502243	+	0.864727i	$0.332508\pi$
$164$	−2.45446e7	+	1.78327e7i	−0.434514	+	0.315693i
$165$	−3.28891e7	+	3.75363e7i	−0.569979	+	0.650516i
$166$	1.34815e7	+	9.79487e6i	0.228749	+	0.166196i
$167$	−1.17076e7	−	3.60322e7i	−0.194518	−	0.598665i	−0.999982	−	0.00601988i	$-0.998084\pi$
$167$	−1.17076e7	−	3.60322e7i	−0.194518	−	0.598665i	0.805464	−	0.592645i	$-0.201916\pi$
$168$	1.20629e8			1.96277
$169$	2.12316e7	+	6.53441e7i	0.338360	+	1.04136i
$170$	1.07780e6	−	1.17868e7i	0.0168255	−	0.184003i
$171$	−5.80690e6	+	1.78718e7i	−0.0888091	+	0.273326i
$172$	1.05080e7	−	3.23404e7i	0.157461	−	0.484614i
$173$	−3.52234e7	+	2.55913e7i	−0.517213	+	0.375778i	−0.815553	−	0.578682i	$-0.803567\pi$
$173$	−3.52234e7	+	2.55913e7i	−0.517213	+	0.375778i	0.298340	+	0.954460i	$0.403567\pi$
$174$	1.18904e8			1.71110
$175$	5.30201e7	−	9.78570e7i	0.747838	−	1.38025i
$176$	−4.47096e7			−0.618167
$177$	9.08976e7	−	6.60410e7i	1.23210	−	0.895174i
$178$	7.75676e6	−	2.38728e7i	0.103089	−	0.317274i
$179$	3.03098e7	−	9.32840e7i	0.395000	−	1.21569i	−0.533961	−	0.845509i	$-0.679297\pi$
$179$	3.03098e7	−	9.32840e7i	0.395000	−	1.21569i	0.928961	−	0.370177i	$-0.120703\pi$
$180$	5.54801e7	+	2.38071e7i	0.709061	+	0.304265i
$181$	−1.16991e7	−	3.60061e7i	−0.146648	−	0.451338i	0.850571	−	0.525860i	$-0.176257\pi$
$181$	−1.16991e7	−	3.60061e7i	−0.146648	−	0.451338i	−0.997219	+	0.0745229i	$0.976257\pi$
$182$	−2.17600e8			−2.67552
$183$	−4.79638e7	−	1.47617e8i	−0.578542	−	1.78057i
$184$	−5.67599e7	−	4.12385e7i	−0.671706	−	0.488023i
$185$	−3.23842e6	+	3.54153e7i	−0.0376039	+	0.411235i
$186$	−1.33538e8	+	9.70210e7i	−1.52163	+	1.10553i
$187$	−5.67227e6	−	4.12115e6i	−0.0634324	−	0.0460864i
$188$	1.08967e7	+	7.91694e6i	0.119603	+	0.0868970i
$189$	−2.03225e8	+	1.47652e8i	−2.18959	+	1.59083i
$190$	−1.45964e6	+	1.59626e7i	−0.0154386	+	0.168836i
$191$	7.32361e7	+	5.32091e7i	0.760516	+	0.552547i	0.899068	−	0.437808i	$-0.144245\pi$
$191$	7.32361e7	+	5.32091e7i	0.760516	+	0.552547i	−0.138553	+	0.990355i	$0.544245\pi$
$192$	−1.95327e7	−	6.01156e7i	−0.199163	−	0.612961i
$193$	−6.23811e6			−0.0624601			−0.0312300	−	0.999512i	$-0.509942\pi$
$193$	−6.23811e6			−0.0624601			−0.0312300	+	0.999512i	$0.509942\pi$
$194$	−2.20639e7	−	6.79057e7i	−0.216958	−	0.667729i
$195$	2.38387e8	+	1.02294e8i	2.30229	+	0.987938i
$196$	1.84392e7	−	5.67499e7i	0.174922	−	0.538355i
$197$	−8.74430e6	+	2.69122e7i	−0.0814879	+	0.250794i	−0.983497	−	0.180922i	$-0.942092\pi$
$197$	−8.74430e6	+	2.69122e7i	−0.0814879	+	0.250794i	0.902009	+	0.431716i	$0.142092\pi$
$198$	1.03780e8	−	7.54008e7i	0.950138	−	0.690316i
$199$	2.12424e8			1.91081			0.955405	−	0.295300i	$-0.0954196\pi$
$199$	2.12424e8			1.91081			0.955405	+	0.295300i	$0.0954196\pi$
$200$	−8.03683e7	−	1.48219e7i	−0.710362	−	0.131009i
$201$	−2.53301e8			−2.20014
$202$	1.91577e7	−	1.39189e7i	0.163536	−	0.118816i
$203$	−4.85403e7	+	1.49392e8i	−0.407255	+	1.25340i
$204$	−3.93405e6	+	1.21078e7i	−0.0324440	+	0.0998523i
$205$	−1.56065e7	+	1.70672e8i	−0.126522	+	1.38364i
$206$	−4.26485e7	−	1.31258e8i	−0.339913	−	1.04615i
$207$	2.92782e8			2.29429
$208$	7.18137e7	+	2.21020e8i	0.553332	+	1.70298i
$209$	7.68184e6	+	5.58119e6i	0.0582041	+	0.0422877i
$210$	−2.82981e8	+	3.22966e8i	−2.10858	+	2.40652i
$211$	3.40926e7	−	2.47697e7i	0.249846	−	0.181523i	−0.455813	−	0.890076i	$-0.650651\pi$
$211$	3.40926e7	−	2.47697e7i	0.249846	−	0.181523i	0.705658	+	0.708552i	$0.250651\pi$
$212$	−941570.	−	684091.i	−0.00678699	−	0.00493104i
$213$	−3.00327e8	−	2.18200e8i	−2.12944	−	1.54713i
$214$	1.28497e8	−	9.33588e7i	0.896285	−	0.651189i
$215$	−9.82884e7	−	1.65042e8i	−0.674478	−	1.13256i
$216$	1.49225e8	+	1.08418e8i	1.00752	+	0.732004i
$217$	−6.73833e7	−	2.07385e8i	−0.447655	−	1.37774i
$218$	3.37025e7			0.220326
$219$	2.50234e6	+	7.70142e6i	0.0160988	+	0.0495469i
$220$	2.01038e7	−	2.29444e7i	0.127291	−	0.145277i
$221$	−1.12618e7	+	3.46601e7i	−0.0701832	+	0.216002i
$222$	4.23993e7	−	1.30492e8i	0.260090	−	0.800474i
$223$	−2.33433e8	+	1.69599e8i	−1.40960	+	1.02413i	−0.416219	+	0.909264i	$0.636645\pi$
$223$	−2.33433e8	+	1.69599e8i	−1.40960	+	1.02413i	−0.993381	+	0.114870i	$0.963355\pi$
$224$	−1.93935e8			−1.15289
$225$	3.07690e8	−	1.47095e8i	1.80084	−	0.860911i
$226$	7.52770e7			0.433793
$227$	−4.44783e7	+	3.23154e7i	−0.252382	+	0.183366i	−0.706782	−	0.707432i	$-0.749854\pi$
$227$	−4.44783e7	+	3.23154e7i	−0.252382	+	0.183366i	0.454400	+	0.890798i	$0.349854\pi$
$228$	5.32780e6	−	1.63973e7i	0.0297698	−	0.0916221i
$229$	−5.80025e7	+	1.78513e8i	−0.319170	+	0.982305i	0.654834	+	0.755773i	$0.272739\pi$
$229$	−5.80025e7	+	1.78513e8i	−0.319170	+	0.982305i	−0.974004	+	0.226532i	$0.927261\pi$
$230$	2.43562e8	−	5.52255e7i	1.31996	−	0.299290i
$231$	7.86033e7	+	2.41916e8i	0.419565	+	1.29129i
$232$	1.15341e8			0.606421
$233$	7.74669e7	+	2.38419e8i	0.401209	+	1.23479i	0.924020	+	0.382345i	$0.124883\pi$
$233$	7.74669e7	+	2.38419e8i	0.401209	+	1.23479i	−0.522811	+	0.852449i	$0.675117\pi$
$234$	−5.39435e8	−	3.91923e8i	−2.75222	−	1.99961i
$235$	7.42032e7	−	1.68250e7i	0.372980	−	0.0845700i
$236$	−5.55621e7	+	4.03682e7i	−0.275161	+	0.199916i
$237$	−4.84359e7	−	3.51908e7i	−0.236346	−	0.171715i
$238$	−4.88047e7	−	3.54587e7i	−0.234662	−	0.170492i
$239$	−1.66949e8	+	1.21296e8i	−0.791028	+	0.574716i	−0.908268	−	0.418388i	$-0.862595\pi$
$239$	−1.66949e8	+	1.21296e8i	−0.791028	+	0.574716i	0.117240	+	0.993104i	$0.462595\pi$
$240$	4.21433e8	+	1.80841e8i	1.96784	+	0.844419i
$241$	−1.24956e8	−	9.07856e7i	−0.575037	−	0.417789i	0.261894	−	0.965097i	$-0.415653\pi$
$241$	−1.24956e8	−	9.07856e7i	−0.575037	−	0.417789i	−0.836932	+	0.547307i	$0.815653\pi$
$242$	6.01939e7	+	1.85258e8i	0.273023	+	0.840278i
$243$	3.05816e6			0.0136722
$244$	2.93183e7	+	9.02325e7i	0.129204	+	0.397648i
$245$	−1.72473e8	−	2.89610e8i	−0.749274	−	1.25815i
$246$	2.04329e8	−	6.28860e8i	0.875098	−	2.69328i
$247$	1.52516e7	−	4.69395e7i	0.0643984	−	0.198198i
$248$	−1.29536e8	+	9.41133e7i	−0.539274	+	0.391805i
$249$	−1.01252e8			−0.415630
$250$	2.28218e8	−	1.80404e8i	0.923760	−	0.730222i
$251$	1.68392e8			0.672144			0.336072	−	0.941836i	$-0.390901\pi$
$251$	1.68392e8			0.672144			0.336072	+	0.941836i	$0.390901\pi$
$252$	2.48941e8	−	1.80866e8i	0.979927	−	0.711959i
$253$	4.57166e7	−	1.40701e8i	0.177481	−	0.546230i
$254$	6.71966e6	−	2.06810e7i	0.0257294	−	0.0791869i
$255$	3.67977e7	+	6.17892e7i	0.138973	+	0.233357i
$256$	8.36740e7	+	2.57522e8i	0.311710	+	0.959345i
$257$	1.24299e8			0.456775			0.228388	−	0.973570i	$-0.426655\pi$
$257$	1.24299e8			0.456775			0.228388	+	0.973570i	$0.426655\pi$
$258$	2.29018e8	+	7.04845e8i	0.830234	+	2.55520i
$259$	1.46642e8	+	1.06541e8i	0.524454	+	0.381038i
$260$	−1.45716e8	−	6.25283e7i	−0.514163	−	0.220633i
$261$	−3.89404e8	+	2.82919e8i	−1.35569	+	0.984963i
$262$	−2.55872e8	−	1.85902e8i	−0.878958	−	0.638601i
$263$	−3.61837e8	−	2.62890e8i	−1.22650	−	0.891106i	−0.229879	−	0.973219i	$-0.573833\pi$
$263$	−3.61837e8	−	2.62890e8i	−1.22650	−	0.891106i	−0.996623	+	0.0821134i	$0.973833\pi$
$264$	1.51105e8	−	1.09784e8i	0.505434	−	0.367220i
$265$	−6.41179e6	+	1.45382e6i	−0.0211650	+	0.00479899i
$266$	6.60952e7	+	4.80210e7i	0.215320	+	0.156439i
$267$	4.71308e7	+	1.45054e8i	0.151536	+	0.466379i
$268$	1.54832e8			0.491349
$269$	−1.40805e8	−	4.33354e8i	−0.441048	−	1.35741i	−0.886760	−	0.462230i	$-0.847050\pi$
$269$	−1.40805e8	−	4.33354e8i	−0.441048	−	1.35741i	0.445712	−	0.895176i	$-0.352950\pi$
$270$	−6.40336e8	+	1.45191e8i	−1.97986	+	0.448917i
$271$	−1.76496e7	+	5.43200e7i	−0.0538696	+	0.165793i	−0.974372	−	0.224944i	$-0.927780\pi$
$271$	−1.76496e7	+	5.43200e7i	−0.0538696	+	0.165793i	0.920502	+	0.390738i	$0.127780\pi$
$272$	−1.99091e7	+	6.12740e7i	−0.0599876	+	0.184623i
$273$	1.06965e9	−	7.77144e8i	3.18179	−	2.31170i
$274$	6.11559e8			1.79602
$275$	−2.26443e7	−	1.70833e8i	−0.0656589	−	0.495346i
$276$	−2.68627e8			−0.769072
$277$	−3.34980e8	+	2.43377e8i	−0.946977	+	0.688019i	−0.950090	−	0.311976i	$-0.899009\pi$
$277$	−3.34980e8	+	2.43377e8i	−0.946977	+	0.688019i	0.00311304	+	0.999995i	$0.499009\pi$
$278$	−2.05210e8	+	6.31570e8i	−0.572850	+	1.76305i
$279$	2.06479e8	−	6.35477e8i	0.569195	−	1.75180i
$280$	−2.74500e8	+	3.13286e8i	−0.747290	+	0.852881i
$281$	−1.41940e8	−	4.36845e8i	−0.381620	−	1.17451i	−0.938902	−	0.344183i	$-0.888156\pi$
$281$	−1.41940e8	−	4.36845e8i	−0.381620	−	1.17451i	0.557282	−	0.830323i	$-0.311844\pi$
$282$	−2.93553e8			−0.779497
$283$	−2.72451e7	−	8.38517e7i	−0.0714555	−	0.219917i	0.908951	−	0.416903i	$-0.136885\pi$
$283$	−2.72451e7	−	8.38517e7i	−0.0714555	−	0.219917i	−0.980406	+	0.196986i	$0.936885\pi$
$284$	1.83578e8	+	1.33377e8i	0.475560	+	0.345515i
$285$	−4.98344e7	−	8.36798e7i	−0.127518	−	0.214123i
$286$	−2.72575e8	+	1.98037e8i	−0.688976	+	0.500571i
$287$	7.06688e8	+	5.13439e8i	1.76458	+	1.28204i
$288$	−4.80771e8	−	3.49300e8i	−1.18594	−	0.861639i
$289$	3.23797e8	−	2.35252e8i	0.789097	−	0.573313i
$290$	−2.70575e8	+	3.08807e8i	−0.651471	+	0.743522i
$291$	3.50980e8	+	2.55002e8i	0.834943	+	0.606621i
$292$	−1.52958e6	−	4.70757e6i	−0.00359528	−	0.0110651i
$293$	7.79412e7			0.181022			0.0905108	−	0.995895i	$-0.471150\pi$
$293$	7.79412e7			0.181022			0.0905108	+	0.995895i	$0.471150\pi$
$294$	4.01873e8	+	1.23684e9i	0.922303	+	2.83856i
$295$	−3.53286e7	+	3.86352e8i	−0.0801216	+	0.876206i
$296$	4.11286e7	−	1.26581e8i	0.0921771	−	0.283692i
$297$	−1.20191e8	+	3.69910e8i	−0.266210	+	0.819311i
$298$	5.99088e8	−	4.35263e8i	1.31140	−	0.952785i
$299$	−7.68981e8			−1.66367
$300$	−2.82304e8	+	1.34959e8i	−0.603661	+	0.288587i
$301$	−9.79062e8			−2.06932
$302$	−3.55712e8	+	2.58440e8i	−0.743146	+	0.539927i
$303$	−4.44625e7	+	1.36841e8i	−0.0918215	+	0.282597i
$304$	2.69626e7	−	8.29822e7i	0.0550432	−	0.169405i
$305$	4.92523e8	+	2.11347e8i	0.993979	+	0.426527i
$306$	−5.71228e7	−	1.75806e8i	−0.113968	−	0.350759i
$307$	−4.87410e8			−0.961414			−0.480707	−	0.876881i	$-0.659620\pi$
$307$	−4.87410e8			−0.961414			−0.480707	+	0.876881i	$0.659620\pi$
$308$	−4.80470e7	−	1.47874e8i	−0.0936999	−	0.288379i
$309$	6.78427e8	+	4.92906e8i	1.30812	+	0.950407i
$310$	5.19013e7	−	5.67591e8i	0.0989493	−	1.08211i
$311$	1.12623e8	−	8.18257e7i	0.212308	−	0.154251i	−0.476549	−	0.879148i	$-0.658113\pi$
$311$	1.12623e8	−	8.18257e7i	0.212308	−	0.154251i	0.688857	+	0.724897i	$0.258113\pi$
$312$	−7.85422e8	−	5.70642e8i	−1.46407	−	1.06371i
$313$	−5.56155e8	−	4.04070e8i	−1.02516	−	0.744821i	−0.0578240	−	0.998327i	$-0.518416\pi$
$313$	−5.56155e8	−	4.04070e8i	−1.02516	−	0.744821i	−0.967334	+	0.253506i	$0.918416\pi$
$314$	−5.49388e8	+	3.99154e8i	−1.00144	+	0.727590i
$315$	1.58286e8	−	1.73102e9i	0.285336	−	3.12043i
$316$	2.96069e7	+	2.15107e7i	0.0527823	+	0.0383486i
$317$	3.57224e7	+	1.09942e8i	0.0629844	+	0.193846i	0.977597	−	0.210485i	$-0.0675043\pi$
$317$	3.57224e7	+	1.09942e8i	0.0629844	+	0.193846i	−0.914613	+	0.404331i	$0.867504\pi$
$318$	2.53655e7			0.0442332
$319$	7.51574e7	+	2.31311e8i	0.129630	+	0.398959i
$320$	2.00575e8	+	8.60688e7i	0.342178	+	0.146832i
$321$	−2.98225e8	+	9.17841e8i	−0.503241	+	1.54882i
$322$	3.93349e8	−	1.21060e9i	0.656572	−	2.02072i
$323$	1.10697e7	−	8.04260e6i	0.0182779	−	0.0132797i
$324$	2.33852e8			0.381975
$325$	−8.08135e8	+	3.86338e8i	−1.30585	+	0.624275i
$326$	1.34738e9			2.15391
$327$	−1.65670e8	+	1.20367e8i	−0.262016	+	0.190366i
$328$	1.98205e8	−	6.10013e8i	0.310139	−	0.954510i
$329$	1.19837e8	−	3.68821e8i	0.185527	−	0.570992i
$330$	−6.05434e7	+	6.62101e8i	−0.0927402	+	1.01420i
$331$	5.81247e7	+	1.78889e8i	0.0880973	+	0.271136i	0.985393	−	0.170294i	$-0.0544716\pi$
$331$	5.81247e7	+	1.78889e8i	0.0880973	+	0.271136i	−0.897296	+	0.441429i	$0.854472\pi$
$332$	6.18914e7			0.0928212
$333$	1.71635e8	+	5.28237e8i	0.254712	+	0.783924i
$334$	−4.08335e8	−	2.96673e8i	−0.599658	−	0.435677i
$335$	5.76404e8	−	6.57849e8i	0.837665	−	0.956025i
$336$	1.89098e9	−	1.37388e9i	2.71957	−	1.97588i
$337$	9.33869e8	+	6.78495e8i	1.32917	+	0.965700i	0.999769	+	0.0215105i	$0.00684754\pi$
$337$	9.33869e8	+	6.78495e8i	1.32917	+	0.965700i	0.329403	+	0.944189i	$0.393152\pi$
$338$	7.40511e8	+	5.38013e8i	1.04309	+	0.757852i
$339$	−3.70036e8	+	2.68847e8i	−0.515876	+	0.374806i
$340$	−2.24929e7	−	3.77692e7i	−0.0310363	−	0.0521149i
$341$	−2.73147e8	−	1.98453e8i	−0.373041	−	0.271030i
$342$	7.73603e7	+	2.38090e8i	0.104575	+	0.321848i
$343$	−5.44801e8			−0.728968
$344$	2.22154e8	+	6.83721e8i	0.294239	+	0.905575i
$345$	−1.00003e9	+	1.14134e9i	−1.31113	+	1.49640i
$346$	−1.79238e8	+	5.51637e8i	−0.232629	+	0.715958i
$347$	−2.36507e8	+	7.27893e8i	−0.303872	+	0.935221i	0.676224	+	0.736696i	$0.263615\pi$
$347$	−2.36507e8	+	7.27893e8i	−0.303872	+	0.935221i	−0.980096	+	0.198525i	$0.936385\pi$
$348$	3.57277e8	−	2.59577e8i	0.454441	−	0.330171i
$349$	4.43515e8			0.558495			0.279248	−	0.960219i	$-0.409915\pi$
$349$	4.43515e8			0.558495			0.279248	+	0.960219i	$0.409915\pi$
$350$	−1.94833e8	−	1.46986e9i	−0.242898	−	1.83248i
$351$	2.02169e9			2.49540
$352$	−2.42932e8	+	1.76500e8i	−0.296883	+	0.215698i
$353$	9.01585e6	−	2.77479e7i	0.0109093	−	0.0335752i	−0.945454	−	0.325756i	$-0.894381\pi$
$353$	9.01585e6	−	2.77479e7i	0.0109093	−	0.0335752i	0.956363	+	0.292181i	$0.0943810\pi$
$354$	4.62542e8	−	1.42356e9i	0.554166	−	1.70555i
$355$	1.25011e9	−	2.83451e8i	1.48302	−	0.336262i
$356$	−2.88092e7	−	8.86655e7i	−0.0338420	−	0.104155i
$357$	3.66546e8			0.426373
$358$	−4.03791e8	−	1.24274e9i	−0.465122	−	1.43150i
$359$	−1.13666e9	−	8.25829e8i	−1.29658	−	0.942019i	−0.296662	−	0.954983i	$-0.595873\pi$
$359$	−1.13666e9	−	8.25829e8i	−1.29658	−	0.942019i	−0.999916	+	0.0129639i	$0.995873\pi$
$360$	−1.24476e9	+	2.82238e8i	−1.40613	+	0.318829i
$361$	7.08166e8	−	5.14513e8i	0.792246	−	0.575600i
$362$	−4.08039e8	−	2.96458e8i	−0.452087	−	0.328460i
$363$	−9.57530e8	−	6.95686e8i	−1.05070	−	0.763379i
$364$	−6.53832e8	+	4.75037e8i	−0.710578	+	0.516265i
$365$	−2.56957e7	−	1.10263e7i	−0.0276589	−	0.0118687i
$366$	−1.67287e9	−	1.21541e9i	−1.78352	−	1.29581i
$367$	3.20772e8	+	9.87235e8i	0.338739	+	1.04253i	0.964851	+	0.262799i	$0.0846455\pi$
$367$	3.20772e8	+	9.87235e8i	0.338739	+	1.04253i	−0.626111	+	0.779734i	$0.715354\pi$
$368$	−1.35945e9			−1.42198
$369$	8.27134e8	+	2.54566e9i	0.857006	+	2.63759i
$370$	2.42418e8	+	4.07059e8i	0.248805	+	0.417783i
$371$	−1.03550e7	+	3.18693e7i	−0.0105279	+	0.0324014i
$372$	−1.89443e8	+	5.83047e8i	−0.190800	+	0.587223i
$373$	−8.72171e8	+	6.33669e8i	−0.870204	+	0.632240i	−0.930642	−	0.365932i	$-0.880750\pi$
$373$	−8.72171e8	+	6.33669e8i	−0.870204	+	0.632240i	0.0604380	+	0.998172i	$0.480750\pi$
$374$	−9.34057e7			−0.0923257
$375$	−4.77542e8	+	1.70187e9i	−0.467629	+	1.66654i
$376$	−2.84755e8			−0.276258
$377$	1.02275e9	−	7.43075e8i	0.983052	−	0.714229i
$378$	−1.03413e9	+	3.18274e9i	−0.984817	+	3.03095i
$379$	−1.42288e8	+	4.37917e8i	−0.134255	+	0.413195i	−0.995473	−	0.0950405i	$-0.969702\pi$
$379$	−1.42288e8	+	4.37917e8i	−0.134255	+	0.413195i	0.861218	+	0.508235i	$0.169702\pi$
$380$	3.04617e7	+	5.11501e7i	0.0284782	+	0.0478194i
$381$	4.08293e7	+	1.25660e8i	0.0378211	+	0.116401i
$382$	1.20598e9			1.10693
$383$	−5.41184e8	−	1.66559e9i	−0.492209	−	1.51486i	−0.821262	−	0.570552i	$-0.806729\pi$
$383$	−5.41184e8	−	1.66559e9i	−0.492209	−	1.51486i	0.329053	−	0.944312i	$-0.393271\pi$
$384$	−1.82237e9	−	1.32403e9i	−1.64239	−	1.19327i
$385$	−8.07150e8	−	3.46357e8i	−0.720845	−	0.309322i
$386$	−6.72333e7	+	4.88479e7i	−0.0595016	+	0.0432305i
$387$	−2.42712e9	−	1.76340e9i	−2.12864	−	1.54655i
$388$	−2.14540e8	−	1.55872e8i	−0.186465	−	0.135475i
$389$	−4.97231e8	+	3.61259e8i	−0.428287	+	0.311168i	−0.780963	−	0.624577i	$-0.785272\pi$
$389$	−4.97231e8	+	3.61259e8i	−0.428287	+	0.311168i	0.352677	+	0.935745i	$0.385272\pi$
$390$	3.37031e9	−	7.64190e8i	2.87703	−	0.652342i
$391$	−1.72472e8	−	1.25308e8i	−0.145915	−	0.106013i
$392$	3.89830e8	+	1.19977e9i	0.326869	+	1.00600i
$393$	1.92172e9			1.59704
$394$	1.16493e8	+	3.58528e8i	0.0959538	+	0.295315i
$395$	2.01614e8	−	4.57142e7i	0.164600	−	0.0373217i
$396$	1.47228e8	−	4.53121e8i	0.119140	−	0.366675i
$397$	7.39959e8	−	2.27736e9i	0.593528	−	1.82669i	0.0316050	−	0.999500i	$-0.489938\pi$
$397$	7.39959e8	−	2.27736e9i	0.593528	−	1.82669i	0.561923	−	0.827190i	$-0.310062\pi$
$398$	2.28947e9	−	1.66340e9i	1.82030	−	1.32253i
$399$	−4.96406e8			−0.391230
$400$	−1.42867e9	+	6.82989e8i	−1.11614	+	0.533585i
$401$	1.06361e9			0.823713			0.411856	−	0.911249i	$-0.364881\pi$
$401$	1.06361e9			0.823713			0.411856	+	0.911249i	$0.364881\pi$
$402$	−2.73003e9	+	1.98348e9i	−2.09593	+	1.52278i
$403$	−5.42308e8	+	1.66905e9i	−0.412742	+	1.27029i
$404$	2.71781e7	−	8.36456e7i	0.0205062	−	0.0631115i
$405$	8.70577e8	−	9.93588e8i	0.651200	−	0.743214i
$406$	6.46660e8	+	1.99022e9i	0.479551	+	1.47591i
$407$	2.80652e8			0.206342
$408$	−8.31712e7	−	2.55975e8i	−0.0606265	−	0.186589i
$409$	1.63021e9	+	1.18442e9i	1.17818	+	0.855997i	0.991965	−	0.126512i	$-0.0403782\pi$
$409$	1.63021e9	+	1.18442e9i	1.17818	+	0.855997i	0.186214	+	0.982509i	$0.440378\pi$
$410$	1.16825e9	+	1.96168e9i	0.837130	+	1.40567i
$411$	−3.00622e9	+	2.18414e9i	−2.13586	+	1.55180i
$412$	−4.14695e8	−	3.01294e8i	−0.292138	−	0.212251i
$413$	1.59974e9	+	1.16228e9i	1.11744	+	0.811868i
$414$	3.15556e9	−	2.29265e9i	2.18562	−	1.58795i
$415$	2.30407e8	−	2.62963e8i	0.158244	−	0.180604i
$416$	1.26272e9	+	9.17423e8i	0.859967	+	0.624802i
$417$	−1.24687e9	−	3.83748e9i	−0.842066	−	2.59161i
$418$	1.26497e8			0.0847159
$419$	7.75288e7	+	2.38609e8i	0.0514890	+	0.158467i	0.973495	−	0.228709i	$-0.0734505\pi$
$419$	7.75288e7	+	2.38609e8i	0.0514890	+	0.158467i	−0.922006	+	0.387176i	$0.873451\pi$
$420$	−1.45227e8	+	1.58820e9i	−0.0956479	+	1.04600i
$421$	−4.31154e8	+	1.32696e9i	−0.281608	+	0.866700i	0.705787	+	0.708424i	$0.250594\pi$
$421$	−4.31154e8	+	1.32696e9i	−0.281608	+	0.866700i	−0.987395	+	0.158276i	$0.949406\pi$
$422$	1.73484e8	−	5.33928e8i	0.112374	−	0.345851i
$423$	9.61370e8	−	6.98476e8i	0.617588	−	0.448704i
$424$	2.46053e7			0.0156765
$425$	−2.44209e8	−	4.50382e7i	−0.154312	−	0.0284590i
$426$	−4.94550e9			−3.09939
$427$	2.20997e9	−	1.60563e9i	1.37369	−	0.998043i
$428$	1.82293e8	−	5.61039e8i	0.112387	−	0.345892i
$429$	6.32608e8	−	1.94697e9i	0.386842	−	1.19058i
$430$	−2.35171e9	−	1.00914e9i	−1.42641	−	0.612086i
$431$	−9.56473e8	−	2.94372e9i	−0.575443	−	1.77103i	−0.634667	−	0.772786i	$-0.718863\pi$
$431$	−9.56473e8	−	2.94372e9i	−0.575443	−	1.77103i	0.0592243	−	0.998245i	$-0.481137\pi$
$432$	3.57405e9			2.13289
$433$	8.88374e8	+	2.73413e9i	0.525882	+	1.61850i	0.762565	+	0.646911i	$0.223940\pi$
$433$	8.88374e8	+	2.73413e9i	0.525882	+	1.61850i	−0.236683	+	0.971587i	$0.576060\pi$
$434$	−2.35018e9	−	1.70751e9i	−1.38003	−	1.00265i
$435$	2.27171e8	−	2.48433e9i	0.132325	−	1.44710i
$436$	1.01268e8	−	7.35752e7i	0.0585151	−	0.0425137i
$437$	2.33575e8	+	1.69702e8i	0.133888	+	0.0972754i
$438$	8.72762e7	+	6.34099e7i	0.0496291	+	0.0360577i
$439$	−3.88433e8	+	2.82213e8i	−0.219124	+	0.159203i	−0.691932	−	0.721962i	$-0.743240\pi$
$439$	−3.88433e8	+	2.82213e8i	−0.219124	+	0.159203i	0.472808	+	0.881165i	$0.343240\pi$
$440$	−5.87290e7	+	6.42258e8i	−0.0328676	+	0.359439i
$441$	−4.25903e9	−	3.09437e9i	−2.36470	−	1.71805i
$442$	1.50031e8	+	4.61747e8i	0.0826422	+	0.254347i
$443$	−3.39447e8			−0.185506			−0.0927531	−	0.995689i	$-0.529567\pi$
$443$	−3.39447e8			−0.185506			−0.0927531	+	0.995689i	$0.529567\pi$
$444$	−1.57474e8	−	4.84655e8i	−0.0853824	−	0.262780i
$445$	−4.83970e8	−	2.07676e8i	−0.260350	−	0.111719i
$446$	−1.18785e9	+	3.65583e9i	−0.634000	+	1.95125i
$447$	−1.39040e9	+	4.27921e9i	−0.736315	+	2.26614i
$448$	8.99985e8	−	6.53877e8i	0.472892	−	0.343576i
$449$	1.24633e9			0.649788			0.324894	−	0.945750i	$-0.394671\pi$
$449$	1.24633e9			0.649788			0.324894	+	0.945750i	$0.394671\pi$
$450$	2.16440e9	−	3.99475e9i	1.11968	−	2.06655i
$451$	1.35251e9			0.694260
$452$	2.26188e8	−	1.64335e8i	0.115209	−	0.0837041i
$453$	8.25558e8	−	2.54081e9i	0.417257	−	1.28419i
$454$	−2.26333e8	+	6.96580e8i	−0.113515	+	0.349362i
$455$	−4.15733e8	+	4.54644e9i	−0.206907	+	2.26272i
$456$	1.12637e8	+	3.46661e8i	0.0556294	+	0.171210i
$457$	−1.58183e9			−0.775270			−0.387635	−	0.921813i	$-0.626708\pi$
$457$	−1.58183e9			−0.775270			−0.387635	+	0.921813i	$0.626708\pi$
$458$	7.72717e8	+	2.37818e9i	0.375830	+	1.15669i
$459$	4.53437e8	+	3.29442e8i	0.218863	+	0.159013i
$460$	6.11280e8	−	6.97652e8i	0.292811	−	0.334185i
$461$	1.29821e9	−	9.43205e8i	0.617152	−	0.448387i	−0.234774	−	0.972050i	$-0.575435\pi$
$461$	1.29821e9	−	9.43205e8i	0.617152	−	0.448387i	0.851925	+	0.523663i	$0.175435\pi$
$462$	2.74151e9	+	1.99182e9i	1.29343	+	0.939733i
$463$	−2.63172e9	−	1.91206e9i	−1.23227	−	0.895297i	−0.235213	−	0.971944i	$-0.575579\pi$
$463$	−2.63172e9	−	1.91206e9i	−1.23227	−	0.895297i	−0.997058	+	0.0766467i	$0.975579\pi$
$464$	1.80808e9	−	1.31365e9i	0.840243	−	0.610472i
$465$	1.77199e9	+	2.97545e9i	0.817288	+	1.37236i
$466$	2.70188e9	+	1.96303e9i	1.23684	+	0.898619i
$467$	1.11019e9	+	3.41682e9i	0.504416	+	1.55243i	0.801750	+	0.597660i	$0.203903\pi$
$467$	1.11019e9	+	3.41682e9i	0.504416	+	1.55243i	−0.297333	+	0.954774i	$0.596097\pi$
$468$	−2.47646e9			−1.11679
$469$	−1.37758e9	−	4.23974e9i	−0.616610	−	1.89773i
$470$	6.68002e8	−	7.62389e8i	0.296780	−	0.338715i
$471$	1.27505e9	−	3.92421e9i	0.562284	−	1.73053i
$472$	4.48680e8	−	1.38089e9i	0.196399	−	0.604455i
$473$	−1.22641e9	+	8.91042e8i	−0.532872	+	0.387154i
$474$	−7.97598e8			−0.344001
$475$	3.30727e8	+	6.09944e7i	0.141593	+	0.0261133i
$476$	−2.24055e8			−0.0952204
$477$	−8.30706e7	+	6.03543e7i	−0.0350455	+	0.0254621i
$478$	−8.49539e8	+	2.61461e9i	−0.355783	+	1.09499i
$479$	7.78330e8	−	2.39545e9i	0.323586	−	0.995895i	−0.648489	−	0.761224i	$-0.724599\pi$
$479$	7.78330e8	−	2.39545e9i	0.323586	−	0.995895i	0.972075	−	0.234671i	$-0.0754012\pi$
$480$	3.00378e9	−	6.81082e8i	1.23972	−	0.281096i
$481$	−4.50791e8	−	1.38739e9i	−0.184700	−	0.568449i
$482$	−2.05765e9			−0.836965
$483$	2.39003e9	+	7.35574e9i	0.965134	+	2.97038i
$484$	5.85299e8	+	4.25245e8i	0.234649	+	0.170483i
$485$	−1.46095e9	+	3.31258e8i	−0.581485	+	0.131847i
$486$	3.29604e7	−	2.39471e7i	0.0130246	−	0.00946295i
$487$	2.42526e8	+	1.76206e8i	0.0951497	+	0.0691303i	0.634343	−	0.773052i	$-0.281271\pi$
$487$	2.42526e8	+	1.76206e8i	0.0951497	+	0.0691303i	−0.539193	+	0.842182i	$0.681271\pi$
$488$	−1.62274e9	−	1.17899e9i	−0.632089	−	0.459240i
$489$	−6.62327e9	+	4.81208e9i	−2.56148	+	1.86103i
$490$	−4.12670e9	−	1.77081e9i	−1.58459	−	0.679964i
$491$	1.97831e9	+	1.43733e9i	0.754239	+	0.547987i	0.897138	−	0.441751i	$-0.145642\pi$
$491$	1.97831e9	+	1.43733e9i	0.754239	+	0.547987i	−0.142899	+	0.989737i	$0.545642\pi$
$492$	−7.58892e8	−	2.33563e9i	−0.287278	−	0.884150i
$493$	3.50477e8			0.131733
$494$	−2.03184e8	−	6.25335e8i	−0.0758305	−	0.233382i
$495$	−1.37712e9	−	2.31240e9i	−0.510332	−	0.856928i
$496$	−9.58722e8	+	2.95064e9i	−0.352782	+	1.08575i
$497$	2.01890e9	−	6.21355e9i	0.737680	−	2.27035i
$498$	−1.09128e9	+	7.92861e8i	−0.395944	+	0.287670i
$499$	−2.50818e9			−0.903663			−0.451831	−	0.892103i	$-0.649229\pi$
$499$	−2.50818e9			−0.903663			−0.451831	+	0.892103i	$0.649229\pi$
$500$	2.91902e8	−	1.04028e9i	0.104434	−	0.372183i
$501$	3.06679e9			1.08956
$502$	1.81490e9	−	1.31860e9i	0.640308	−	0.465211i
$503$	−1.42962e8	+	4.39990e8i	−0.0500877	+	0.154154i	−0.972972	−	0.230923i	$-0.925825\pi$
$503$	−1.42962e8	+	4.39990e8i	−0.0500877	+	0.154154i	0.922884	+	0.385078i	$0.125825\pi$
$504$	−2.01027e9	+	6.18697e9i	−0.699435	+	2.15264i
$505$	−2.54214e8	−	4.26867e8i	−0.0878376	−	0.147493i
$506$	−6.09042e8	−	1.87444e9i	−0.208988	−	0.643198i
$507$	−5.56158e9			−1.89527
$508$	−2.49573e7	−	7.68106e7i	−0.00844645	−	0.0259955i
$509$	1.41896e9	+	1.03093e9i	0.476933	+	0.346512i	0.800137	−	0.599817i	$-0.204760\pi$
$509$	1.41896e9	+	1.03093e9i	0.476933	+	0.346512i	−0.323204	+	0.946329i	$0.604760\pi$
$510$	8.80443e8	+	3.77807e8i	0.293904	+	0.126117i
$511$	−1.15297e8	+	8.37683e7i	−0.0382248	+	0.0277720i
$512$	3.66727e7	+	2.66443e7i	0.0120753	+	0.00877321i
$513$	−6.14081e8	−	4.46156e8i	−0.200824	−	0.145907i
$514$	1.33968e9	−	9.73332e8i	0.435140	−	0.316148i
$515$	−2.82394e9	+	6.40305e8i	−0.911025	+	0.206567i
$516$	2.22687e9	+	1.61792e9i	0.713544	+	0.518420i
$517$	−1.85550e8	−	5.71065e8i	−0.0590533	−	0.181747i
$518$	2.41476e9			0.763342
$519$	−1.08907e9	−	3.35180e9i	−0.341955	−	1.05243i
$520$	3.26931e9	−	7.41287e8i	1.01963	−	0.231193i
$521$	7.54893e8	−	2.32332e9i	0.233859	−	0.719743i	−0.763412	−	0.645912i	$-0.776477\pi$
$521$	7.54893e8	−	2.32332e9i	0.233859	−	0.719743i	0.997271	−	0.0738311i	$-0.0235226\pi$
$522$	−1.98152e9	+	6.09851e9i	−0.609751	+	1.87662i
$523$	4.63889e8	−	3.37035e8i	0.141794	−	0.103019i	−0.514627	−	0.857414i	$-0.672070\pi$
$523$	4.63889e8	−	3.37035e8i	0.141794	−	0.103019i	0.656421	+	0.754395i	$0.272070\pi$
$524$	−1.17467e9			−0.356661
$525$	6.20726e9	+	6.52952e9i	1.87216	+	1.96935i
$526$	−5.95840e9			−1.78517
$527$	−3.93611e8	+	2.85975e8i	−0.117147	+	0.0851120i
$528$	1.11836e9	−	3.44195e9i	0.330645	−	1.01762i
$529$	3.37916e8	−	1.04000e9i	0.0992462	−	0.305448i
$530$	−5.77210e7	+	6.58769e7i	−0.0168410	+	0.0192206i
$531$	1.87240e9	+	5.76264e9i	0.542709	+	1.67029i
$532$	3.03433e8			0.0873719
$533$	−2.17243e9	−	6.68606e9i	−0.621443	−	1.91260i
$534$	1.64382e9	+	1.19430e9i	0.467153	+	0.339407i
$535$	−1.70510e9	−	2.86314e9i	−0.481407	−	0.808358i
$536$	−2.64821e9	+	1.92404e9i	−0.742807	+	0.539681i
$537$	6.42328e9	+	4.66679e9i	1.78997	+	1.30049i
$538$	−4.91098e9	−	3.56803e9i	−1.35966	−	0.987850i
$539$	−2.15207e9	+	1.56357e9i	−0.591965	+	0.430088i
$540$	−1.60708e9	+	1.83416e9i	−0.439198	+	0.501256i
$541$	4.54232e9	+	3.30019e9i	1.23335	+	0.896083i	0.997137	−	0.0756171i	$-0.0240927\pi$
$541$	4.54232e9	+	3.30019e9i	1.23335	+	0.896083i	0.236216	+	0.971701i	$0.424093\pi$
$542$	2.35131e8	+	7.23659e8i	0.0634326	+	0.195225i
$543$	3.06456e9			0.821427
$544$	1.33714e8	+	4.11531e8i	0.0356108	+	0.109599i
$545$	6.43900e7	−	7.04167e8i	0.0170385	−	0.186332i
$546$	5.44301e9	−	1.67519e10i	1.43108	−	4.40442i
$547$	6.63383e8	−	2.04168e9i	0.173304	−	0.533375i	−0.826248	−	0.563306i	$-0.809529\pi$
$547$	6.63383e8	−	2.04168e9i	0.173304	−	0.533375i	0.999552	+	0.0299319i	$0.00952903\pi$
$548$	1.83758e9	−	1.33508e9i	0.476995	−	0.346557i
$549$	8.37050e9			2.15898
$550$	−1.58178e9	−	1.66390e9i	−0.405392	−	0.426439i
$551$	−4.74644e8			−0.120875
$552$	4.59452e9	−	3.33811e9i	1.16266	−	0.844723i
$553$	3.25604e8	−	1.00211e9i	0.0818750	−	0.251985i
$554$	−1.70458e9	+	5.24616e9i	−0.425925	+	1.31086i
$555$	−2.64543e9	−	1.13518e9i	−0.656857	−	0.281864i
$556$	7.62163e8	+	2.34570e9i	0.188056	+	0.578775i
$557$	−6.41675e9			−1.57334			−0.786669	−	0.617375i	$-0.788196\pi$
$557$	−6.41675e9			−1.57334			−0.786669	+	0.617375i	$0.788196\pi$
$558$	−2.75074e9	−	8.46591e9i	−0.670239	−	2.06278i
$559$	6.37473e9	+	4.63151e9i	1.54355	+	1.12145i
$560$	−7.34955e8	+	8.03744e9i	−0.176849	+	1.93401i
$561$	4.59151e8	−	3.33593e8i	0.109796	−	0.0797712i
$562$	−4.95054e9	−	3.59678e9i	−1.17646	−	0.854745i
$563$	5.68092e9	+	4.12743e9i	1.34165	+	0.974765i	0.999382	+	0.0351631i	$0.0111951\pi$
$563$	5.68092e9	+	4.12743e9i	1.34165	+	0.974765i	0.342268	+	0.939602i	$0.388805\pi$
$564$	−8.82053e8	+	6.40849e8i	−0.207023	+	0.150411i
$565$	1.43820e8	−	1.57281e9i	0.0335466	−	0.366864i
$566$	−9.50249e8	−	6.90396e8i	−0.220282	−	0.160045i
$567$	−2.08063e9	−	6.40353e9i	−0.479352	−	1.47529i
$568$	−4.79729e9			−1.09844
$569$	−6.59714e8	−	2.03039e9i	−0.150128	−	0.462048i	0.847506	−	0.530785i	$-0.178103\pi$
$569$	−6.59714e8	−	2.03039e9i	−0.150128	−	0.462048i	−0.997635	+	0.0687374i	$0.978103\pi$
$570$	−1.19237e9	−	5.11657e8i	−0.269679	−	0.115722i
$571$	−8.09244e8	+	2.49060e9i	−0.181908	+	0.559857i	−0.999881	−	0.0154000i	$-0.995098\pi$
$571$	−8.09244e8	+	2.49060e9i	−0.181908	+	0.559857i	0.817973	+	0.575257i	$0.195098\pi$
$572$	−3.86688e8	+	1.19010e9i	−0.0863922	+	0.265888i
$573$	−5.92821e9	+	4.30709e9i	−1.31638	+	0.956408i
$574$	1.16371e10			2.56834
$575$	−6.88525e8	−	5.19439e9i	−0.151037	−	1.13945i
$576$	3.40880e9			0.743228
$577$	−6.95404e8	+	5.05241e8i	−0.150703	+	0.109492i	−0.660582	−	0.750754i	$-0.729690\pi$
$577$	−6.95404e8	+	5.05241e8i	−0.150703	+	0.109492i	0.509879	+	0.860246i	$0.329690\pi$
$578$	1.64768e9	−	5.07102e9i	0.354915	−	1.09232i
$579$	1.56039e8	−	4.80239e8i	0.0334086	−	0.102821i
$580$	−1.38860e8	+	1.51857e9i	−0.0295516	+	0.323175i
$581$	−5.50660e8	−	1.69476e9i	−0.116484	−	0.358502i
$582$	5.77961e9			1.21526
$583$	1.60331e7	+	4.93449e7i	0.00335103	+	0.0103134i
$584$	8.46606e7	+	6.15095e7i	0.0175888	+	0.0127790i
$585$	−9.21928e9	+	1.05220e10i	−1.90393	+	2.17296i
$586$	8.40037e8	−	6.10323e8i	0.172448	−	0.125290i
$587$	−2.97865e9	−	2.16412e9i	−0.607836	−	0.441619i	0.240815	−	0.970571i	$-0.422585\pi$
$587$	−2.97865e9	−	2.16412e9i	−0.607836	−	0.441619i	−0.848652	+	0.528952i	$0.822585\pi$
$588$	3.90764e9	+	2.83907e9i	0.792673	+	0.575911i
$589$	5.33059e8	−	3.87290e8i	0.107491	−	0.0780968i
$590$	2.64459e9	+	4.44068e9i	0.530122	+	0.890160i
$591$	−1.85310e9	−	1.34636e9i	−0.369269	−	0.268289i
$592$	−7.96933e8	−	2.45271e9i	−0.157869	−	0.485870i
$593$	3.50439e9			0.690114			0.345057	−	0.938582i	$-0.387859\pi$
$593$	3.50439e9			0.690114			0.345057	+	0.938582i	$0.387859\pi$
$594$	1.60120e9	+	4.92799e9i	0.313468	+	0.964756i
$595$	−8.34102e8	+	9.51960e8i	−0.162334	+	0.185272i
$596$	8.49896e8	−	2.61571e9i	0.164439	−	0.506090i
$597$	−5.31354e9	+	1.63534e10i	−1.02205	+	3.14556i
$598$	−8.28795e9	+	6.02155e9i	−1.58487	+	1.15147i
$599$	1.55452e9			0.295531			0.147765	−	0.989022i	$-0.452792\pi$
$599$	1.55452e9			0.295531			0.147765	+	0.989022i	$0.452792\pi$
$600$	3.15138e9	−	5.81638e9i	0.595624	−	1.09932i
$601$	−7.36939e8			−0.138475			−0.0692374	−	0.997600i	$-0.522057\pi$
$601$	−7.36939e8			−0.138475			−0.0692374	+	0.997600i	$0.522057\pi$
$602$	−1.05522e10	+	7.66660e9i	−1.97131	+	1.43224i
$603$	4.22123e9	−	1.29916e10i	0.784022	−	2.41297i
$604$	−5.04630e8	+	1.55309e9i	−0.0931846	+	0.286793i
$605$	3.98570e9	−	9.03724e8i	0.731747	−	0.165917i
$606$	5.92335e8	+	1.82302e9i	0.108122	+	0.332765i
$607$	4.77840e9			0.867206			0.433603	−	0.901104i	$-0.357242\pi$
$607$	4.77840e9			0.867206			0.433603	+	0.901104i	$0.357242\pi$
$608$	−1.81087e8	−	5.57328e8i	−0.0326757	−	0.100565i
$609$	−1.02867e10	−	7.47372e9i	−1.84551	−	1.34084i
$610$	6.96330e9	−	1.57887e9i	1.24211	−	0.281638i
$611$	−2.52500e9	+	1.83452e9i	−0.447834	+	0.325370i
$612$	−5.55437e8	−	4.03549e8i	−0.0979501	−	0.0711649i
$613$	6.03441e9	+	4.38426e9i	1.05809	+	0.768749i	0.973734	−	0.227687i	$-0.0731163\pi$
$613$	6.03441e9	+	4.38426e9i	1.05809	+	0.768749i	0.0843573	+	0.996436i	$0.473116\pi$
$614$	−5.25323e9	+	3.81670e9i	−0.915877	+	0.665424i
$615$	−1.27488e10	−	5.47062e9i	−2.21006	−	0.948361i
$616$	2.65935e9	+	1.93213e9i	0.458398	+	0.333046i
$617$	−8.00977e8	−	2.46515e9i	−0.137285	−	0.422519i	0.858654	−	0.512556i	$-0.171301\pi$
$617$	−8.00977e8	−	2.46515e9i	−0.137285	−	0.422519i	−0.995938	+	0.0900374i	$0.971301\pi$
$618$	1.11717e10			1.90397
$619$	7.59094e7	+	2.33625e8i	0.0128641	+	0.0395915i	0.957283	−	0.289154i	$-0.0933741\pi$
$619$	7.59094e7	+	2.33625e8i	0.0128641	+	0.0395915i	−0.944418	+	0.328746i	$0.893374\pi$
$620$	−1.08314e9	−	1.81877e9i	−0.182522	−	0.306484i
$621$	−3.65455e9	+	1.12475e10i	−0.612369	+	1.88468i
$622$	5.73096e8	−	1.76381e9i	0.0954906	−	0.293890i
$623$	−2.17159e9	+	1.57775e9i	−0.359806	+	0.261415i
$624$	−1.88115e10			−3.09940
$625$	−3.33326e9	−	5.11295e9i	−0.546121	−	0.837706i
$626$	−9.15824e9			−1.49211
$627$	−6.21819e8	+	4.51778e8i	−0.100746	+	0.0731962i
$628$	−7.79389e8	+	2.39871e9i	−0.125573	+	0.386473i
$629$	1.24974e8	−	3.84631e8i	0.0200237	−	0.0616265i
$630$	−1.18488e10	−	1.98961e10i	−1.88792	−	3.17012i
$631$	1.06647e9	+	3.28226e9i	0.168984	+	0.520080i	0.999308	−	0.0372017i	$-0.0118444\pi$
$631$	1.06647e9	+	3.28226e9i	0.168984	+	0.520080i	−0.830324	+	0.557282i	$0.811844\pi$
$632$	−7.73694e8			−0.121916
$633$	1.05410e9	+	3.24420e9i	0.165185	+	0.508387i
$634$	1.24592e9	+	9.05212e8i	0.194168	+	0.141071i
$635$	−4.19262e8	−	1.79910e8i	−0.0649796	−	0.0278834i
$636$	7.62169e7	−	5.53748e7i	0.0117477	−	0.00853517i
$637$	1.11862e10	+	8.12723e9i	1.71472	+	1.24582i
$638$	2.62133e9	+	1.90450e9i	0.399621	+	0.290342i
$639$	1.61962e10	−	1.17673e10i	2.45562	−	1.78411i
$640$	7.58558e9	−	1.71997e9i	1.14382	−	0.259352i
$641$	−4.47537e9	−	3.25155e9i	−0.671160	−	0.487626i	0.199253	−	0.979948i	$-0.436148\pi$
$641$	−4.47537e9	−	3.25155e9i	−0.671160	−	0.487626i	−0.870413	+	0.492322i	$0.836148\pi$
$642$	3.97299e9	+	1.22276e10i	0.592577	+	1.82376i
$643$	−5.47801e8			−0.0812614			−0.0406307	−	0.999174i	$-0.512937\pi$
$643$	−5.47801e8			−0.0812614			−0.0406307	+	0.999174i	$0.512937\pi$
$644$	−1.46093e9	−	4.49627e9i	−0.215540	−	0.663364i
$645$	1.51643e10	−	3.43837e9i	2.22517	−	0.504538i
$646$	5.63292e7	−	1.73364e8i	0.00822091	−	0.0253014i
$647$	−5.31153e7	+	1.63472e8i	−0.00771001	+	0.0237290i	−0.954838	−	0.297128i	$-0.903971\pi$
$647$	−5.31153e7	+	1.63472e8i	−0.00771001	+	0.0237290i	0.947128	+	0.320857i	$0.103971\pi$
$648$	−3.99975e9	+	2.90599e9i	−0.577458	+	0.419548i
$649$	3.06169e9			0.439648
$650$	−5.68471e9	+	1.04920e10i	−0.811917	+	1.49852i
$651$	1.76510e10			2.50747
$652$	4.04854e9	−	2.94143e9i	0.572047	−	0.415616i
$653$	−2.08189e9	+	6.40741e9i	−0.292592	+	0.900506i	0.691427	+	0.722446i	$0.256982\pi$
$653$	−2.08189e9	+	6.40741e9i	−0.292592	+	0.900506i	−0.984020	+	0.178060i	$0.943018\pi$
$654$	−8.43031e8	+	2.59458e9i	−0.117848	+	0.362698i
$655$	−4.37301e9	+	4.99091e9i	−0.608045	+	0.693961i
$656$	−3.84055e9	−	1.18200e10i	−0.531165	−	1.63476i
$657$	−4.36701e8			−0.0600766
$658$	−1.59649e9	−	4.91349e9i	−0.218462	−	0.672356i
$659$	4.14834e9	+	3.01395e9i	0.564645	+	0.410239i	0.833156	−	0.553038i	$-0.186532\pi$
$659$	4.14834e9	+	3.01395e9i	0.564645	+	0.410239i	−0.268511	+	0.963277i	$0.586532\pi$
$660$	1.26350e9	+	2.12162e9i	0.171069	+	0.287252i
$661$	5.87612e9	−	4.26925e9i	0.791381	−	0.574972i	−0.116992	−	0.993133i	$-0.537325\pi$
$661$	5.87612e9	−	4.26925e9i	0.791381	−	0.574972i	0.908373	+	0.418161i	$0.137325\pi$
$662$	2.02726e9	+	1.47289e9i	0.271586	+	0.197318i
$663$	−2.38660e9	−	1.73397e9i	−0.318040	−	0.231070i
$664$	−1.05857e9	+	7.69100e8i	−0.140324	+	0.101952i
$665$	1.12961e9	−	1.28922e9i	0.148954	−	0.170001i
$666$	5.98624e9	+	4.34926e9i	0.785225	+	0.570500i
$667$	2.28525e9	+	7.03327e9i	0.298190	+	0.917734i
$668$	−1.87460e9			−0.243328
$669$	−7.21749e9	−	2.22131e10i	−0.931954	−	2.86826i
$670$	1.06106e9	−	1.16038e10i	0.136295	−	1.49052i
$671$	1.30701e9	−	4.02257e9i	0.167013	−	0.514014i
$672$	4.85107e9	−	1.49301e10i	0.616659	−	1.89788i
$673$	−5.04398e9	+	3.66467e9i	−0.637853	+	0.463427i	−0.859112	−	0.511788i	$-0.828983\pi$
$673$	−5.04398e9	+	3.66467e9i	−0.637853	+	0.463427i	0.221259	+	0.975215i	$0.428983\pi$
$674$	1.53781e10			1.93461
$675$	1.81017e9	+	1.36563e10i	0.226546	+	1.70911i
$676$	3.39957e9			0.423263
$677$	−7.06214e8	+	5.13095e8i	−0.0874734	+	0.0635532i	−0.630662	−	0.776057i	$-0.717217\pi$
$677$	−7.06214e8	+	5.13095e8i	−0.0874734	+	0.0635532i	0.543189	+	0.839610i	$0.317217\pi$
$678$	−1.88297e9	+	5.79518e9i	−0.232027	+	0.714107i
$679$	−2.35941e9	+	7.26152e9i	−0.289241	+	0.890192i
$680$	8.54056e8	+	3.66485e8i	0.104161	+	0.0446966i
$681$	−1.37522e9	−	4.23249e9i	−0.166862	−	0.513547i
$682$	−4.49794e9			−0.542960
$683$	−5.16949e8	−	1.59101e9i	−0.0620834	−	0.191073i	0.915204	−	0.402990i	$-0.132029\pi$
$683$	−5.16949e8	−	1.59101e9i	−0.0620834	−	0.191073i	−0.977288	+	0.211917i	$0.932029\pi$
$684$	7.52218e8	+	5.46518e8i	0.0898767	+	0.0652993i
$685$	1.16841e9	−	1.27776e10i	0.138892	−	1.51892i
$686$	−5.87178e9	+	4.26610e9i	−0.694441	+	0.504541i
$687$	−1.22919e10	−	8.93061e9i	−1.44634	−	1.05083i
$688$	1.12696e10	+	8.18783e9i	1.31931	+	0.958538i
$689$	2.18181e8	−	1.58518e8i	0.0254127	−	0.0184634i
$690$	−1.84089e9	+	2.01319e10i	−0.213332	+	2.33299i
$691$	−1.00034e10	−	7.26791e9i	−1.15339	−	0.837985i	−0.164460	−	0.986384i	$-0.552588\pi$
$691$	−1.00034e10	−	7.26791e9i	−1.15339	−	0.837985i	−0.988928	+	0.148398i	$0.952588\pi$
$692$	6.65702e8	+	2.04882e9i	0.0763675	+	0.235035i
$693$	−1.37176e10			−1.56571
$694$	3.15078e9	+	9.69709e9i	0.357816	+	1.10124i
$695$	1.28037e10	+	5.49420e9i	1.44673	+	0.620809i
$696$	−2.88511e9	+	8.87947e9i	−0.324363	+	0.998285i
$697$	6.02271e8	−	1.85360e9i	0.0673717	−	0.207349i
$698$	4.78013e9	−	3.47297e9i	0.532042	−	0.386551i
$699$	−2.02923e10			−2.24731
$700$	−3.79425e9	−	3.99123e9i	−0.418103	−	0.439809i
$701$	−8.64564e9			−0.947948			−0.473974	−	0.880539i	$-0.657181\pi$
$701$	−8.64564e9			−0.947948			−0.473974	+	0.880539i	$0.657181\pi$
$702$	2.17894e10	−	1.58309e10i	2.37720	−	1.72714i
$703$	−1.69250e8	+	5.20899e8i	−0.0183732	+	0.0565470i
$704$	5.32267e8	−	1.63815e9i	0.0574943	−	0.176949i
$705$	−5.60845e8	+	6.13337e9i	−0.0602810	+	0.659231i
$706$	−1.20110e8	−	3.69662e8i	−0.0128459	−	0.0395356i
$707$	−2.53226e9			−0.269488
$708$	−1.71791e9	−	5.28720e9i	−0.181922	−	0.559898i
$709$	−5.35717e9	−	3.89221e9i	−0.564513	−	0.410143i	0.268595	−	0.963253i	$-0.413441\pi$
$709$	−5.35717e9	−	3.89221e9i	−0.564513	−	0.410143i	−0.833108	+	0.553111i	$0.813441\pi$
$710$	1.12539e10	−	1.28440e10i	1.18004	−	1.34678i
$711$	2.61209e9	−	1.89779e9i	0.272549	−	0.198018i
$712$	1.59455e9	+	1.15851e9i	0.165561	+	0.120287i
$713$	−8.30537e9	−	6.03420e9i	−0.858115	−	0.623457i
$714$	3.95057e9	−	2.87026e9i	0.406178	−	0.295105i
$715$	3.61694e9	+	6.07342e9i	0.370058	+	0.621387i
$716$	−3.92629e9	−	2.85262e9i	−0.399749	−	0.290434i
$717$	−5.16188e9	−	1.58866e10i	−0.522987	−	1.60959i
$718$	−1.87174e10			−1.88716
$719$	3.38824e9	+	1.04279e10i	0.339956	+	1.04628i	0.964229	+	0.265071i	$0.0853953\pi$
$719$	3.38824e9	+	1.04279e10i	0.339956	+	1.04628i	−0.624273	+	0.781206i	$0.714605\pi$
$720$	−1.62983e10	+	1.86013e10i	−1.62735	+	1.85729i
$721$	−4.56063e9	+	1.40362e10i	−0.453160	+	1.39468i
$722$	3.60358e9	−	1.10907e10i	0.356331	−	1.09667i
$723$	1.01147e10	−	7.34878e9i	0.995337	−	0.723155i
$724$	−1.87324e9			−0.183446
$725$	5.93514e9	+	6.24327e9i	0.578426	+	0.608456i
$726$	−1.57677e10			−1.52929
$727$	−6.03880e9	+	4.38744e9i	−0.582881	+	0.423488i	−0.839762	−	0.542955i	$-0.817305\pi$
$727$	−6.03880e9	+	4.38744e9i	−0.582881	+	0.423488i	0.256881	+	0.966443i	$0.417305\pi$
$728$	5.27989e9	−	1.62498e10i	0.507183	−	1.56095i
$729$	−3.27060e9	+	1.00659e10i	−0.312666	+	0.962288i
$730$	−3.63286e8	+	8.23720e7i	−0.0345636	+	0.00783699i
$731$	6.75043e8	+	2.07757e9i	0.0639177	+	0.196718i
$732$	−7.67989e9			−0.723713
$733$	1.45696e9	+	4.48407e9i	0.136642	+	0.420541i	0.995842	−	0.0910991i	$-0.0290380\pi$
$733$	1.45696e9	+	4.48407e9i	0.136642	+	0.420541i	−0.859200	+	0.511640i	$0.829038\pi$
$734$	1.11878e10	+	8.12844e9i	1.04426	+	0.758701i
$735$	2.66098e10	−	6.03355e9i	2.47193	−	0.560489i
$736$	−7.38662e9	+	5.36669e9i	−0.682925	+	0.496174i
$737$	−5.58419e9	−	4.05715e9i	−0.513835	−	0.373323i
$738$	2.88486e10	+	2.09598e10i	2.64197	+	1.91950i
$739$	−7.29672e9	+	5.30138e9i	−0.665078	+	0.483207i	−0.868374	−	0.495910i	$-0.834835\pi$
$739$	−7.29672e9	+	5.30138e9i	−0.665078	+	0.483207i	0.203296	+	0.979117i	$0.434835\pi$
$740$	1.61705e9	+	6.93891e8i	0.146694	+	0.0629478i
$741$	3.23213e9	+	2.34828e9i	0.291826	+	0.212024i
$742$	1.37950e8	+	4.24567e8i	0.0123968	+	0.0381534i
$743$	1.50017e10			1.34178			0.670888	−	0.741558i	$-0.265913\pi$
$743$	1.50017e10			1.34178			0.670888	+	0.741558i	$0.265913\pi$
$744$	−4.00510e9	−	1.23264e10i	−0.356540	−	1.09732i
$745$	−7.94962e9	−	1.33487e10i	−0.704368	−	1.18275i
$746$	−4.43813e9	+	1.36592e10i	−0.391394	+	1.20459i
$747$	1.68736e9	−	5.19315e9i	0.148110	−	0.455836i
$748$	−2.80660e8	+	2.03912e8i	−0.0245203	+	0.0178150i
$749$	−1.69847e10			−1.47697
$750$	8.17971e9	+	2.20819e10i	0.707984	+	1.91127i
$751$	1.34523e10			1.15893			0.579463	−	0.814999i	$-0.303262\pi$
$751$	1.34523e10			1.15893			0.579463	+	0.814999i	$0.303262\pi$
$752$	−4.46383e9	+	3.24316e9i	−0.382776	+	0.278103i
$753$	−4.21212e9	+	1.29636e10i	−0.359516	+	1.10648i
$754$	5.20439e9	−	1.60175e10i	0.442151	−	1.36080i
$755$	4.72013e9	+	7.92586e9i	0.399153	+	0.670242i
$756$	3.84085e9	+	1.18209e10i	0.323296	+	0.995004i
$757$	1.90704e10			1.59781			0.798903	−	0.601460i	$-0.205414\pi$
$757$	1.90704e10			1.59781			0.798903	+	0.601460i	$0.205414\pi$
$758$	1.89558e9	+	5.83399e9i	0.158088	+	0.486546i
$759$	9.68829e9	+	7.03896e9i	0.804268	+	0.584335i
$760$	−1.15663e9	−	4.96323e8i	−0.0955757	−	0.0410125i
$761$	1.67582e10	−	1.21755e10i	1.37842	−	1.00148i	0.381389	−	0.924415i	$-0.375446\pi$
$761$	1.67582e10	−	1.21755e10i	1.37842	−	1.00148i	0.997026	−	0.0770625i	$-0.0245541\pi$
$762$	1.42404e9	+	1.03462e9i	0.116595	+	0.0847109i
$763$	−2.91569e9	−	2.11837e9i	−0.237632	−	0.172650i
$764$	3.62367e9	−	2.63275e9i	0.293983	−	0.213591i
$765$	−3.78235e9	+	8.57616e8i	−0.305455	+	0.0692593i
$766$	−1.88753e10	−	1.37137e10i	−1.51738	−	1.10244i
$767$	−4.91777e9	−	1.51353e10i	−0.393536	−	1.21118i
$768$	−2.19183e10			−1.74599
$769$	−3.85207e9	−	1.18555e10i	−0.305458	−	0.940104i	−0.979506	−	0.201416i	$-0.935446\pi$
$769$	−3.85207e9	−	1.18555e10i	−0.305458	−	0.940104i	0.674047	−	0.738688i	$-0.264554\pi$
$770$	−1.14115e10	+	2.58746e9i	−0.900793	+	0.204247i
$771$	−3.10920e9	+	9.56914e9i	−0.244320	+	0.751939i
$772$	−9.53805e7	+	2.93551e8i	−0.00746103	+	0.0229627i
$773$	−4.27118e9	+	3.10319e9i	−0.332598	+	0.241647i	−0.741532	−	0.670917i	$-0.765901\pi$
$773$	−4.27118e9	+	3.10319e9i	−0.332598	+	0.241647i	0.408934	+	0.912564i	$0.365901\pi$
$774$	−3.99675e10			−3.09823
$775$	−1.17599e10	−	2.16881e9i	−0.907499	−	0.167365i
$776$	5.60640e9			0.430693
$777$	−1.18701e10	+	8.62415e9i	−0.907782	+	0.659543i
$778$	−2.53021e9	+	7.78719e9i	−0.192632	+	0.592860i
$779$	−8.15644e8	+	2.51029e9i	−0.0618186	+	0.190258i
$780$	8.45865e9	−	9.65384e9i	0.638219	−	0.728399i
$781$	−3.12597e9	−	9.62075e9i	−0.234804	−	0.722654i
$782$	−2.84011e9			−0.212379
$783$	−6.00803e9	−	1.84908e10i	−0.447266	−	1.37654i
$784$	1.97755e10	+	1.43678e10i	1.46562	+	1.06484i
$785$	7.29013e9	+	1.22413e10i	0.537887	+	0.903199i
$786$	2.07120e10	−	1.50481e10i	1.52140	−	1.10536i
$787$	−9.24081e9	−	6.71384e9i	−0.675770	−	0.490975i	0.196182	−	0.980567i	$-0.437146\pi$
$787$	−9.24081e9	−	6.71384e9i	−0.675770	−	0.490975i	−0.871952	+	0.489592i	$0.837146\pi$
$788$	1.13273e9	+	8.22973e8i	0.0824675	+	0.0599161i
$789$	2.92895e10	−	2.12801e10i	2.12296	−	1.54242i
$790$	1.81499e9	−	2.07145e9i	0.130972	−	0.149479i
$791$	−6.51240e9	−	4.73154e9i	−0.467868	−	0.339926i
$792$	3.11260e9	+	9.57960e9i	0.222631	+	0.685187i
$793$	−2.19848e10			−1.56555
$794$	−9.85784e9	−	3.03393e10i	−0.698892	−	2.15097i
$795$	4.84618e7	−	5.29976e8i	0.00342069	−	0.0374086i
$796$	3.24795e9	−	9.99617e9i	0.228252	−	0.702486i
$797$	−3.22567e9	+	9.92760e9i	−0.225692	+	0.694609i	0.772528	+	0.634980i	$0.218992\pi$
$797$	−3.22567e9	+	9.92760e9i	−0.225692	+	0.694609i	−0.998221	+	0.0596288i	$0.981008\pi$
$798$	−5.35018e9	+	3.88713e9i	−0.372699	+	0.270782i
$799$	−8.65264e8			−0.0600116
$800$	−5.06648e9	+	9.35101e9i	−0.349858	+	0.645719i
$801$	−8.22513e9			−0.565495
$802$	1.14634e10	−	8.32863e9i	0.784698	−	0.570116i
$803$	−6.81888e7	+	2.09864e8i	−0.00464738	+	0.0143032i
$804$	−3.87296e9	+	1.19197e10i	−0.262813	+	0.808855i
$805$	−2.45423e10	−	1.05314e10i	−1.65818	−	0.711540i
$806$	7.22471e9	+	2.22354e10i	0.486013	+	1.49579i
$807$	3.68837e10			2.47046
$808$	5.74583e8	+	1.76838e9i	0.0383189	+	0.117933i
$809$	1.02361e10	+	7.43698e9i	0.679698	+	0.493829i	0.873257	−	0.487259i	$-0.162003\pi$
$809$	1.02361e10	+	7.43698e9i	0.679698	+	0.493829i	−0.193560	+	0.981089i	$0.562003\pi$
$810$	1.60259e9	−	1.75258e10i	0.105956	−	1.15873i
$811$	−1.52921e9	+	1.11104e9i	−0.100669	+	0.0731400i	−0.636981	−	0.770880i	$-0.719817\pi$
$811$	−1.52921e9	+	1.11104e9i	−0.100669	+	0.0731400i	0.536312	+	0.844020i	$0.319817\pi$
$812$	6.28784e9	+	4.56839e9i	0.412150	+	0.299445i
$813$	−3.74033e9	−	2.71751e9i	−0.244114	−	0.177359i
$814$	3.02483e9	−	2.19766e9i	0.196569	−	0.142816i
$815$	2.57422e9	−	2.81516e10i	0.166569	−	1.82159i
$816$	−4.21916e9	−	3.06540e9i	−0.271838	−	0.197502i
$817$	−9.14198e8	−	2.81361e9i	−0.0586493	−	0.180504i
$818$	2.68447e10			1.71484
$819$	2.20336e10	+	6.78125e10i	1.40150	+	4.31336i
$820$	7.79280e9	+	3.34397e9i	0.493566	+	0.211794i
$821$	4.36322e9	−	1.34286e10i	0.275173	−	0.846896i	−0.714000	−	0.700146i	$-0.753118\pi$
$821$	4.36322e9	−	1.34286e10i	0.275173	−	0.846896i	0.989173	−	0.146751i	$-0.0468816\pi$
$822$	−1.52974e10	+	4.70807e10i	−0.960655	+	2.95659i
$823$	−3.27339e9	+	2.37826e9i	−0.204691	+	0.148717i	−0.685408	−	0.728159i	$-0.740376\pi$
$823$	−3.27339e9	+	2.37826e9i	−0.204691	+	0.148717i	0.480717	+	0.876876i	$0.340376\pi$
$824$	1.08369e10			0.674776
$825$	1.37180e10	+	2.52994e9i	0.850553	+	0.156863i
$826$	2.63430e10			1.62643
$827$	−4.62053e9	+	3.35701e9i	−0.284068	+	0.206387i	−0.720690	−	0.693258i	$-0.756175\pi$
$827$	−4.62053e9	+	3.35701e9i	−0.284068	+	0.206387i	0.436622	+	0.899645i	$0.356175\pi$
$828$	4.47663e9	−	1.37777e10i	0.274060	−	0.843469i
$829$	3.63882e9	−	1.11991e10i	0.221830	−	0.682721i	−0.776768	−	0.629786i	$-0.783142\pi$
$829$	3.63882e9	−	1.11991e10i	0.221830	−	0.682721i	0.998598	−	0.0529348i	$-0.0168576\pi$
$830$	4.24141e8	−	4.63839e9i	0.0257476	−	0.281575i
$831$	−1.03572e10	−	3.18761e10i	−0.626092	−	1.92691i
$832$	−8.95306e9			−0.538939
$833$	1.18455e9	+	3.64565e9i	0.0710058	+	0.218534i
$834$	−4.34882e10	−	3.15960e10i	−2.59591	−	1.88604i
$835$	−6.97870e9	+	7.96478e9i	−0.414831	+	0.473446i
$836$	3.80093e8	−	2.76154e8i	0.0224992	−	0.0163466i
$837$	2.18352e10	+	1.58642e10i	1.28712	+	0.935146i
$838$	2.70404e9	+	1.96460e9i	0.158730	+	0.115324i
$839$	−2.03126e10	+	1.47579e10i	−1.18740	+	0.862698i	−0.992987	−	0.118221i	$-0.962281\pi$
$839$	−2.03126e10	+	1.47579e10i	−1.18740	+	0.862698i	−0.194415	+	0.980919i	$0.562281\pi$
$840$	−1.72520e10	−	2.89688e10i	−1.00430	−	1.68637i
$841$	4.11971e9	+	2.99315e9i	0.238826	+	0.173517i
$842$	5.74389e9	+	1.76779e10i	0.331600	+	1.02056i
$843$	3.71809e10			2.13758
$844$	−6.44331e8	−	1.98305e9i	−0.0368902	−	0.113536i
$845$	1.26558e10	−	1.44440e10i	0.721591	−	0.823550i
$846$	4.89203e9	−	1.50561e10i	0.277775	−	0.854903i
$847$	6.43686e9	−	1.98106e10i	0.363984	−	1.12023i
$848$	3.85713e8	−	2.80237e8i	0.0217209	−	0.0157812i
$849$	7.13681e9			0.400246
$850$	−2.98472e9	+	1.42688e9i	−0.166701	+	0.0796931i
$851$	8.53356e9			0.474654
$852$	−1.48600e10	+	1.07964e10i	−0.823151	+	0.598054i
$853$	−2.88829e9	+	8.88925e9i	−0.159338	+	0.490392i	−0.998575	−	0.0533744i	$-0.983002\pi$
$853$	−2.88829e9	+	8.88925e9i	−0.159338	+	0.490392i	0.839236	+	0.543767i	$0.183002\pi$
$854$	1.12456e10	−	3.46105e10i	0.617848	−	1.90154i
$855$	5.12236e9	−	1.16145e9i	0.280278	−	0.0635506i
$856$	3.85392e9	+	1.18612e10i	0.210012	+	0.646351i
$857$	2.87288e10			1.55914			0.779569	−	0.626317i	$-0.215438\pi$
$857$	2.87288e10			1.55914			0.779569	+	0.626317i	$0.215438\pi$
$858$	−8.42769e9	−	2.59378e10i	−0.455515	−	1.40193i
$859$	−6.15568e9	−	4.47237e9i	−0.331360	−	0.240747i	0.409647	−	0.912244i	$-0.365652\pi$
$859$	−6.15568e9	−	4.47237e9i	−0.331360	−	0.240747i	−0.741007	+	0.671497i	$0.765652\pi$
$860$	−9.26931e9	+	2.10174e9i	−0.496939	+	0.112677i
$861$	−5.72040e10	+	4.15611e10i	−3.05433	+	2.21910i
$862$	−3.33597e10	−	2.42372e10i	−1.77397	−	1.28886i
$863$	1.80664e10	+	1.31260e10i	0.956826	+	0.695174i	0.952411	−	0.304816i	$-0.0985949\pi$
$863$	1.80664e10	+	1.31260e10i	0.956826	+	0.695174i	0.00441421	+	0.999990i	$0.498595\pi$
$864$	1.94198e10	−	1.41093e10i	1.02435	−	0.744230i
$865$	1.11832e10	+	4.79885e9i	0.587505	+	0.252104i
$866$	3.09845e10	+	2.25116e10i	1.62118	+	1.17786i
$867$	1.00114e10	+	3.08120e10i	0.521710	+	1.60566i
$868$	−1.07893e10			−0.559984
$869$	−5.04149e8	−	1.55161e9i	−0.0260609	−	0.0802072i
$870$	−1.70053e10	−	2.85546e10i	−0.875522	−	1.47014i
$871$	−1.10869e10	+	3.41219e10i	−0.568520	+	1.74972i
$872$	−8.17765e8	+	2.51682e9i	−0.0417658	+	0.128542i
$873$	−1.89279e10	+	1.37519e10i	−0.962836	+	0.699542i
$874$	3.84630e9			0.194874
$875$	−3.10830e10	+	1.26253e9i	−1.56854	+	0.0637109i
$876$	4.00671e8			0.0201384
$877$	−2.82365e10	+	2.05150e10i	−1.41355	+	1.02701i	−0.420760	+	0.907172i	$0.638237\pi$
$877$	−2.82365e10	+	2.05150e10i	−1.41355	+	1.02701i	−0.992794	+	0.119835i	$0.961763\pi$
$878$	−1.97658e9	+	6.08330e9i	−0.0985563	+	0.303325i
$879$	−1.94961e9	+	6.00028e9i	−0.0968248	+	0.297996i
$880$	6.39422e9	+	1.07369e10i	0.316299	+	0.531117i
$881$	9.86813e9	+	3.03710e10i	0.486205	+	1.49638i	0.830229	+	0.557423i	$0.188210\pi$
$881$	9.86813e9	+	3.03710e10i	0.486205	+	1.49638i	−0.344024	+	0.938961i	$0.611790\pi$
$882$	−7.01338e10			−3.44181
$883$	−2.38918e9	−	7.35315e9i	−0.116785	−	0.359427i	0.875530	−	0.483163i	$-0.160512\pi$
$883$	−2.38918e9	−	7.35315e9i	−0.116785	−	0.359427i	−0.992315	+	0.123736i	$0.960512\pi$
$884$	1.45883e9	+	1.05990e9i	0.0710269	+	0.0516040i
$885$	−2.88595e10	−	1.23839e10i	−1.39955	−	0.600561i
$886$	−3.65850e9	+	2.65806e9i	−0.176720	+	0.128394i
$887$	−1.76998e10	−	1.28596e10i	−0.851598	−	0.618722i	0.0739880	−	0.997259i	$-0.476427\pi$
$887$	−1.76998e10	−	1.28596e10i	−0.851598	−	0.618722i	−0.925586	+	0.378537i	$0.876427\pi$
$888$	8.71601e9	+	6.33255e9i	0.417708	+	0.303482i
$889$	−1.88124e9	+	1.36680e9i	−0.0898023	+	0.0652452i
$890$	−6.84237e9	+	1.55145e9i	−0.325343	+	0.0737688i
$891$	−8.43413e9	−	6.12775e9i	−0.399455	−	0.290221i
$892$	4.41176e9	+	1.35780e10i	0.208130	+	0.640558i
$893$	1.17181e9			0.0550652
$894$	1.85231e10	+	5.70082e10i	0.867027	+	2.66843i
$895$	−2.67368e10	+	6.06234e9i	−1.24660	+	0.282657i
$896$	1.22506e10	−	3.77035e10i	0.568958	−	1.75107i
$897$	1.92352e10	−	5.91998e10i	0.889862	−	2.73871i
$898$	1.34328e10	−	9.75948e9i	0.619011	−	0.449738i
$899$	1.68772e10			0.774712
$900$	−2.21736e9	−	1.67283e10i	−0.101388	−	0.764895i
$901$	7.47662e7			0.00340540
$902$	1.45771e10	−	1.05909e10i	0.661376	−	0.480518i
$903$	2.44901e10	−	7.53728e10i	1.10684	−	3.40649i
$904$	−1.82654e9	+	5.62150e9i	−0.0822316	+	0.253083i
$905$	−6.97364e9	+	7.95900e9i	−0.312744	+	0.356935i
$906$	−1.09982e10	−	3.38490e10i	−0.491329	−	1.51216i
$907$	1.52412e9			0.0678258			0.0339129	−	0.999425i	$-0.489203\pi$
$907$	1.52412e9			0.0678258			0.0339129	+	0.999425i	$0.489203\pi$
$908$	8.40615e8	+	2.58715e9i	0.0372646	+	0.114689i
$909$	−6.27753e9	−	4.56089e9i	−0.277214	−	0.201408i
$910$	3.11204e10	+	5.22562e10i	1.36899	+	2.29876i
$911$	1.43853e10	−	1.04515e10i	0.630384	−	0.458001i	−0.226149	−	0.974093i	$-0.572614\pi$
$911$	1.43853e10	−	1.04515e10i	0.630384	−	0.458001i	0.856533	+	0.516092i	$0.172614\pi$
$912$	5.71393e9	+	4.15141e9i	0.249432	+	0.181223i
$913$	−2.23218e9	−	1.62177e9i	−0.0970691	−	0.0705248i
$914$	−1.70487e10	+	1.23866e10i	−0.738549	+	0.536588i
$915$	−2.85904e10	+	3.26302e10i	−1.23380	+	1.40814i
$916$	7.51356e9	+	5.45892e9i	0.323007	+	0.234678i
$917$	1.04513e10	+	3.21657e10i	0.447586	+	1.37753i
$918$	7.46679e9			0.318555
$919$	9.98696e9	+	3.07367e10i	0.424452	+	1.30633i	0.903518	+	0.428551i	$0.140976\pi$
$919$	9.98696e9	+	3.07367e10i	0.424452	+	1.30633i	−0.479065	+	0.877779i	$0.659024\pi$
$920$	−1.78572e9	+	1.95286e10i	−0.0756060	+	0.826825i
$921$	1.21920e10	−	3.75232e10i	0.514241	−	1.58267i
$922$	6.60608e9	−	2.03314e10i	0.277578	−	0.854298i
$923$	−4.25387e10	+	3.09062e10i	−1.78065	+	1.29372i
$924$	1.25859e10			0.524845
$925$	8.96807e9	−	4.28728e9i	0.372566	−	0.178109i
$926$	−4.33367e10			−1.79357
$927$	−3.65867e10	+	2.65818e10i	−1.50850	+	1.09599i
$928$	4.63840e9	−	1.42755e10i	0.190524	−	0.586374i
$929$	−1.10079e10	+	3.38790e10i	−0.450455	+	1.38636i	0.425934	+	0.904754i	$0.359945\pi$
$929$	−1.10079e10	+	3.38790e10i	−0.450455	+	1.38636i	−0.876389	+	0.481604i	$0.840055\pi$
$930$	4.23976e10	+	1.81933e10i	1.72843	+	0.741686i
$931$	−1.60421e9	−	4.93724e9i	−0.0651533	−	0.200521i
$932$	1.24039e10			0.501883
$933$	3.48218e9	+	1.07171e10i	0.140367	+	0.432006i
$934$	3.87211e10	+	2.81325e10i	1.55501	+	1.12978i
$935$	−1.78455e8	+	1.95158e9i	−0.00713984	+	0.0780810i
$936$	4.23568e10	−	3.07740e10i	1.68833	−	1.22664i
$937$	2.55190e10	+	1.85407e10i	1.01339	+	0.736269i	0.964917	−	0.262556i	$-0.0845653\pi$
$937$	2.55190e10	+	1.85407e10i	1.01339	+	0.736269i	0.0484705	+	0.998825i	$0.484565\pi$
$938$	−4.80468e10	−	3.49081e10i	−1.90088	−	1.38107i
$939$	4.50188e10	−	3.27081e10i	1.77445	−	1.28922i
$940$	3.42822e8	−	3.74908e9i	0.0134623	−	0.147224i
$941$	−1.35072e10	−	9.81358e9i	−0.528449	−	0.383941i	0.291328	−	0.956623i	$-0.405903\pi$
$941$	−1.35072e10	−	9.81358e9i	−0.528449	−	0.383941i	−0.819777	+	0.572683i	$0.805903\pi$
$942$	−1.69864e10	−	5.22789e10i	−0.662101	−	2.03774i
$943$	4.11246e10			1.59702
$944$	−8.69390e9	−	2.67571e10i	−0.336366	−	1.03523i
$945$	6.45230e10	+	2.76875e10i	2.48716	+	1.06727i
$946$	−6.24074e9	+	1.92070e10i	−0.239672	+	0.737634i
$947$	−3.44462e9	+	1.06015e10i	−0.131800	+	0.405640i	−0.995079	−	0.0990883i	$-0.968407\pi$
$947$	−3.44462e9	+	1.06015e10i	−0.131800	+	0.405640i	0.863278	+	0.504728i	$0.168407\pi$
$948$	−2.39658e9	+	1.74122e9i	−0.0913614	+	0.0663779i
$949$	1.14698e9			0.0435636
$950$	4.04215e9	−	1.93239e9i	0.152961	−	0.0731245i
$951$	−9.35742e9			−0.352797
$952$	3.83217e9	−	2.78424e9i	0.143951	−	0.104587i
$953$	7.57495e9	−	2.33133e10i	0.283501	−	0.872527i	−0.703343	−	0.710851i	$-0.748310\pi$
$953$	7.57495e9	−	2.33133e10i	0.283501	−	0.872527i	0.986844	−	0.161676i	$-0.0516899\pi$
$954$	−4.22713e8	+	1.30098e9i	−0.0157625	+	0.0485121i
$955$	2.30408e9	−	2.51973e10i	0.0856023	−	0.936143i
$956$	3.15525e9	+	9.71086e9i	0.116797	+	0.359464i
$957$	−1.96874e10			−0.726099
$958$	−1.03690e10	−	3.19126e10i	−0.381029	−	1.17269i
$959$	−5.29075e10	−	3.84395e10i	−1.93710	−	1.40739i
$960$	−1.16431e10	+	1.32883e10i	−0.424738	+	0.484752i
$961$	3.30390e9	−	2.40042e9i	0.120087	−	0.0872481i
$962$	−1.57226e10	−	1.14231e10i	−0.569393	−	0.413688i
$963$	−4.21055e10	−	3.05915e10i	−1.51931	−	1.10385i
$964$	−6.18273e9	+	4.49201e9i	−0.222285	+	0.161500i
$965$	8.92155e8	+	1.49807e9i	0.0319591	+	0.0536645i
$966$	8.33588e10	+	6.05637e10i	2.97531	+	2.16169i
$967$	−8.86625e9	−	2.72875e10i	−0.315317	−	0.970446i	−0.975624	−	0.219450i	$-0.929574\pi$
$967$	−8.86625e9	−	2.72875e10i	−0.315317	−	0.970446i	0.660307	−	0.750996i	$-0.270426\pi$
$968$	−1.52952e10			−0.541989
$969$	3.42262e8	+	1.05337e9i	0.0120844	+	0.0371920i
$970$	−1.31519e10	+	1.50103e10i	−0.462688	+	0.528065i
$971$	1.33839e10	−	4.11914e10i	0.469153	−	1.44391i	−0.384530	−	0.923113i	$-0.625636\pi$
$971$	1.33839e10	−	4.11914e10i	0.469153	−	1.44391i	0.853683	−	0.520793i	$-0.174364\pi$
$972$	4.67592e7	−	1.43910e8i	0.00163319	−	0.00502643i
$973$	5.74506e10	−	4.17403e10i	1.99940	−	1.45265i
$974$	3.99370e9			0.138490
$975$	−9.52755e9	−	7.18779e10i	−0.329204	−	2.48359i
$976$	−3.88658e10			−1.33812
$977$	4.12551e10	−	2.99736e10i	1.41529	−	1.02827i	0.422767	−	0.906238i	$-0.361059\pi$
$977$	4.12551e10	−	2.99736e10i	1.41529	−	1.02827i	0.992526	−	0.122032i	$-0.0389412\pi$
$978$	−3.37032e10	+	1.03728e11i	−1.15209	+	3.54576i
$979$	−1.28431e9	+	3.95271e9i	−0.0437453	+	0.134634i
$980$	−1.62655e10	+	3.68806e9i	−0.552047	+	0.125172i
$981$	−3.41263e9	−	1.05030e10i	−0.115411	−	0.355199i
$982$	3.25770e10			1.09779
$983$	1.06794e10	+	3.28679e10i	0.358601	+	1.10366i	0.953892	+	0.300150i	$0.0970366\pi$
$983$	1.06794e10	+	3.28679e10i	0.358601	+	1.10366i	−0.595291	+	0.803510i	$0.702963\pi$
$984$	4.20038e10	+	3.05176e10i	1.40542	+	1.02110i
$985$	7.71350e9	−	1.74897e9i	0.257172	−	0.0583117i
$986$	3.77738e9	−	2.74443e9i	0.125494	−	0.0911764i
$987$	2.53960e10	+	1.84513e10i	0.840728	+	0.610825i
$988$	−1.97567e9	−	1.43541e9i	−0.0651726	−	0.0473506i
$989$	−3.72905e10	+	2.70932e10i	−1.22578	+	0.890580i
$990$	−3.29497e10	−	1.41391e10i	−1.07927	−	0.463124i
$991$	3.19224e10	+	2.31930e10i	1.04193	+	0.757005i	0.970661	−	0.240452i	$-0.0772958\pi$
$991$	3.19224e10	+	2.31930e10i	1.04193	+	0.757005i	0.0712669	+	0.997457i	$0.477296\pi$
$992$	6.43900e9	+	1.98172e10i	0.209425	+	0.644543i
$993$	−1.52257e10			−0.493462
$994$	−2.68961e10	−	8.27777e10i	−0.868635	−	2.67338i
$995$	−3.03802e10	−	5.10132e10i	−0.977709	−	1.64173i
$996$	−1.54814e9	+	4.76469e9i	−0.0496482	+	0.152801i
$997$	−7.86263e9	+	2.41987e10i	−0.251267	+	0.773319i	0.743276	+	0.668985i	$0.233271\pi$
$997$	−7.86263e9	+	2.41987e10i	−0.251267	+	0.773319i	−0.994542	+	0.104334i	$0.966729\pi$
$998$	−2.70327e10	+	1.96404e10i	−0.860861	+	0.625452i
$999$	−2.24352e10			−0.711951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.8.d.a.11.13	✓	68
25.4	even	10		625.8.a.c.1.26		34
25.16	even	5	inner	25.8.d.a.16.13	yes	68
25.21	even	5		625.8.a.d.1.9		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.d.a.11.13	✓	68	1.1	even	1	trivial
25.8.d.a.16.13	yes	68	25.16	even	5	inner
625.8.a.c.1.26		34	25.4	even	10
625.8.a.d.1.9		34	25.21	even	5

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(10.7778 - 7.83056i) q^{2} +(-25.0139 + 76.9848i) q^{3} +(15.2900 - 47.0577i) q^{4} +(-143.017 - 240.148i) q^{5} +(333.238 + 1025.60i) q^{6} -1424.61 q^{7} +(323.251 + 994.865i) q^{8} +(-3531.64 - 2565.89i) q^{9} +(-3421.91 - 1468.38i) q^{10} +(-1784.52 + 1296.53i) q^{11} +(3240.26 + 2354.19i) q^{12} +(9275.70 + 6739.19i) q^{13} +(-15354.2 + 11155.5i) q^{14} +(22065.2 - 5003.09i) q^{15} +(16398.1 + 11913.9i) q^{16} +(982.238 + 3023.02i) q^{17} -58155.7 q^{18} +(-1330.23 - 4094.01i) q^{19} +(-13487.5 + 3058.19i) q^{20} +(35634.9 - 109673. i) q^{21} +(-9080.74 + 27947.6i) q^{22} +(-54260.5 + 39422.6i) q^{23} -84675.2 q^{24} +(-37217.3 + 68690.5i) q^{25} +152744. q^{26} +(142654. - 103644. i) q^{27} +(-21782.2 + 67038.7i) q^{28} +(34072.7 - 104865. i) q^{29} +(198638. - 226705. i) q^{30} +(47299.6 + 145573. i) q^{31} +136132. q^{32} +(-55175.4 - 169812. i) q^{33} +(34258.3 + 24890.1i) q^{34} +(203743. + 342117. i) q^{35} +(-174743. + 126958. i) q^{36} +(-102935. - 74786.4i) q^{37} +(-46395.4 - 33708.2i) q^{38} +(-750836. + 545514. i) q^{39} +(192685. - 219911. i) q^{40} +(-496058. - 360407. i) q^{41} +(-474734. - 1.46108e6i) q^{42} +687250. q^{43} +(33726.5 + 103800. i) q^{44} +(-111109. + 1.21508e6i) q^{45} +(-276110. + 849780. i) q^{46} +(-84119.5 + 258893. i) q^{47} +(-1.32737e6 + 964390. i) q^{48} +1.20596e6 q^{49} +(136763. + 1.03177e6i) q^{50} -257296. q^{51} +(458956. - 333451. i) q^{52} +(7268.64 - 22370.6i) q^{53} +(725908. - 2.23411e6i) q^{54} +(566577. + 243124. i) q^{55} +(-460506. - 1.41729e6i) q^{56} +348451. q^{57} +(-453922. - 1.39703e6i) q^{58} +(-1.12293e6 - 815859. i) q^{59} +(101942. - 1.11483e6i) q^{60} +(-1.55128e6 + 1.12707e6i) q^{61} +(1.64971e6 + 1.19858e6i) q^{62} +(5.03120e6 + 3.65538e6i) q^{63} +(-631742. + 458988. i) q^{64} +(291823. - 3.19136e6i) q^{65} +(-1.92440e6 - 1.39816e6i) q^{66} +(966986. + 2.97608e6i) q^{67} +157275. q^{68} +(-1.67767e6 - 5.16334e6i) q^{69} +(4.87488e6 + 2.09186e6i) q^{70} +(-1.41716e6 + 4.36158e6i) q^{71} +(1.41110e6 - 4.34293e6i) q^{72} +(80932.6 - 58801.0i) q^{73} -1.69503e6 q^{74} +(-4.35717e6 - 4.58338e6i) q^{75} -212994. q^{76} +(2.54225e6 - 1.84705e6i) q^{77} +(-3.82071e6 + 1.17589e7i) q^{78} +(-228557. + 703425. i) q^{79} +(515900. - 5.64186e6i) q^{80} +(1.46050e6 + 4.49494e6i) q^{81} -8.16862e6 q^{82} +(386535. + 1.18963e6i) q^{83} +(-4.61610e6 - 3.35380e6i) q^{84} +(585496. - 668226. i) q^{85} +(7.40707e6 - 5.38155e6i) q^{86} +(7.22072e6 + 5.24616e6i) q^{87} +(-1.86672e6 - 1.35625e6i) q^{88} +(1.52434e6 - 1.10750e6i) q^{89} +(8.31725e6 + 1.39660e7i) q^{90} +(-1.32142e7 - 9.60071e6i) q^{91} +(1.02549e6 + 3.15614e6i) q^{92} -1.23901e7 q^{93} +(1.12065e6 + 3.44901e6i) q^{94} +(-792925. + 904965. i) q^{95} +(-3.40520e6 + 1.04801e7i) q^{96} +(1.65618e6 - 5.09721e6i) q^{97} +(1.29977e7 - 9.44338e6i) q^{98} +9.62905e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16}+ \cdots + 71266232 q^{99}+O(q^{100}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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