LMFDB - Embedded newform 76.7.b.a.39.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,7,Mod(39,76)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	76.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$17.4841103551$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.17
Character	$\chi$	$=$	76.39
Dual form			76.7.b.a.39.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.87964 - 6.33949i) q^{2} -47.1905i q^{3} +(-16.3782 + 61.8689i) q^{4} +222.735 q^{5} +(-299.163 + 230.273i) q^{6} -51.2381i q^{7} +(472.136 - 198.069i) q^{8} -1497.94 q^{9} +O(q^{10})$	\(q+(-4.87964 - 6.33949i) q^{2} -47.1905i q^{3} +(-16.3782 + 61.8689i) q^{4} +222.735 q^{5} +(-299.163 + 230.273i) q^{6} -51.2381i q^{7} +(472.136 - 198.069i) q^{8} -1497.94 q^{9} +(-1086.87 - 1412.03i) q^{10} -2340.87i q^{11} +(2919.62 + 772.893i) q^{12} +2482.94 q^{13} +(-324.823 + 250.024i) q^{14} -10511.0i q^{15} +(-3559.51 - 2026.60i) q^{16} -5852.47 q^{17} +(7309.42 + 9496.18i) q^{18} -1573.56i q^{19} +(-3647.99 + 13780.4i) q^{20} -2417.95 q^{21} +(-14839.9 + 11422.6i) q^{22} +1334.15i q^{23} +(-9346.97 - 22280.3i) q^{24} +33985.9 q^{25} +(-12115.9 - 15740.6i) q^{26} +36286.7i q^{27} +(3170.05 + 839.186i) q^{28} -3450.03 q^{29} +(-66634.2 + 51289.8i) q^{30} +7825.76i q^{31} +(4521.58 + 32454.5i) q^{32} -110467. q^{33} +(28558.0 + 37101.6i) q^{34} -11412.5i q^{35} +(24533.5 - 92676.0i) q^{36} +45898.8 q^{37} +(-9975.58 + 7678.42i) q^{38} -117171. i q^{39} +(105161. - 44116.9i) q^{40} -88106.1 q^{41} +(11798.7 + 15328.6i) q^{42} +59673.3i q^{43} +(144827. + 38339.1i) q^{44} -333644. q^{45} +(8457.81 - 6510.17i) q^{46} -41950.6i q^{47} +(-95636.0 + 167975. i) q^{48} +115024. q^{49} +(-165839. - 215453. i) q^{50} +276181. i q^{51} +(-40666.0 + 153617. i) q^{52} -138956. q^{53} +(230039. - 177066. i) q^{54} -521394. i q^{55} +(-10148.7 - 24191.4i) q^{56} -74257.2 q^{57} +(16834.9 + 21871.4i) q^{58} +275336. i q^{59} +(650302. + 172150. i) q^{60} +201103. q^{61} +(49611.3 - 38186.9i) q^{62} +76751.8i q^{63} +(183681. - 187031. i) q^{64} +553038. q^{65} +(539039. + 700303. i) q^{66} +160517. i q^{67} +(95852.6 - 362086. i) q^{68} +62959.1 q^{69} +(-72349.6 + 55689.1i) q^{70} -541240. i q^{71} +(-707233. + 296696. i) q^{72} -200444. q^{73} +(-223970. - 290975. i) q^{74} -1.60381e6i q^{75} +(97354.5 + 25772.0i) q^{76} -119942. q^{77} +(-742806. + 571754. i) q^{78} +347234. i q^{79} +(-792828. - 451394. i) q^{80} +620389. q^{81} +(429926. + 558547. i) q^{82} -273705. i q^{83} +(39601.6 - 149596. i) q^{84} -1.30355e6 q^{85} +(378298. - 291184. i) q^{86} +162809. i q^{87} +(-463654. - 1.10521e6i) q^{88} +165590. q^{89} +(1.62806e6 + 2.11513e6i) q^{90} -127221. i q^{91} +(-82542.2 - 21850.9i) q^{92} +369301. q^{93} +(-265945. + 204704. i) q^{94} -350487. i q^{95} +(1.53155e6 - 213376. i) q^{96} -510222. q^{97} +(-561274. - 729191. i) q^{98} +3.50649e6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) $ 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

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 $

$2$	−4.87964	−	6.33949i	−0.609955	−	0.792436i
$2$	−4.87964	−	6.33949i	−0.609955	−	0.792436i
$3$		−	47.1905i		−	1.74780i	−0.486110	−	0.873898i	$-0.661584\pi$
$3$		−	47.1905i		−	1.74780i	0.486110	−	0.873898i	$-0.338416\pi$
$4$	−16.3782	+	61.8689i	−0.255909	+	0.966701i
$5$	222.735			1.78188			0.890940	−	0.454121i	$-0.150047\pi$
$5$	222.735			1.78188			0.890940	+	0.454121i	$0.150047\pi$
$6$	−299.163	+	230.273i	−1.38502	+	1.06608i
$7$		−	51.2381i		−	0.149382i	−0.997207	−	0.0746912i	$-0.976203\pi$
$7$		−	51.2381i		−	0.149382i	0.997207	−	0.0746912i	$-0.0237971\pi$
$8$	472.136	−	198.069i	0.922141	−	0.386853i
$9$	−1497.94			−2.05479
$10$	−1086.87	−	1412.03i	−1.08687	−	1.41203i
$11$		−	2340.87i		−	1.75873i	−0.476147	−	0.879365i	$-0.657967\pi$
$11$		−	2340.87i		−	1.75873i	0.476147	−	0.879365i	$-0.342033\pi$
$12$	2919.62	+	772.893i	1.68960	+	0.447276i
$13$	2482.94			1.13015			0.565076	−	0.825039i	$-0.308847\pi$
$13$	2482.94			1.13015			0.565076	+	0.825039i	$0.308847\pi$
$14$	−324.823	+	250.024i	−0.118376	+	0.0911166i
$15$		−	10511.0i		−	3.11436i
$16$	−3559.51	−	2026.60i	−0.869022	−	0.494774i
$17$	−5852.47			−1.19122			−0.595610	−	0.803273i	$-0.703090\pi$
$17$	−5852.47			−1.19122			−0.595610	+	0.803273i	$0.703090\pi$
$18$	7309.42	+	9496.18i	1.25333	+	1.62829i
$19$		−	1573.56i		−	0.229416i
$19$		−	1573.56i		−	0.229416i
$20$	−3647.99	+	13780.4i	−0.455998	+	1.72254i
$21$	−2417.95			−0.261090
$22$	−14839.9	+	11422.6i	−1.39368	+	1.07275i
$23$			1334.15i			0.109653i	0.998496	+	0.0548265i	$0.0174606\pi$
$23$			1334.15i			0.109653i	−0.998496	+	0.0548265i	$0.982539\pi$
$24$	−9346.97	−	22280.3i	−0.676141	−	1.61171i
$25$	33985.9			2.17510
$26$	−12115.9	−	15740.6i	−0.689342	−	0.895572i
$27$			36286.7i			1.84356i
$28$	3170.05	+	839.186i	0.144408	+	0.0382282i
$29$	−3450.03			−0.141458			−0.0707292	−	0.997496i	$-0.522533\pi$
$29$	−3450.03			−0.141458			−0.0707292	+	0.997496i	$0.522533\pi$
$30$	−66634.2	+	51289.8i	−2.46793	+	1.89962i
$31$			7825.76i			0.262689i	0.991337	+	0.131344i	$0.0419293\pi$
$31$			7825.76i			0.262689i	−0.991337	+	0.131344i	$0.958071\pi$
$32$	4521.58	+	32454.5i	0.137988	+	0.990434i
$33$	−110467.			−3.07390
$34$	28558.0	+	37101.6i	0.726592	+	0.943966i
$35$		−	11412.5i		−	0.266181i
$36$	24533.5	−	92676.0i	0.525839	−	1.98637i
$37$	45898.8			0.906141			0.453071	−	0.891475i	$-0.350329\pi$
$37$	45898.8			0.906141			0.453071	+	0.891475i	$0.350329\pi$
$38$	−9975.58	+	7678.42i	−0.181797	+	0.139933i
$39$		−	117171.i		−	1.97527i
$40$	105161.	−	44116.9i	1.64314	−	0.689326i
$41$	−88106.1			−1.27836			−0.639182	−	0.769056i	$-0.720727\pi$
$41$	−88106.1			−1.27836			−0.639182	+	0.769056i	$0.720727\pi$
$42$	11798.7	+	15328.6i	0.159253	+	0.206897i
$43$			59673.3i			0.750541i	0.926915	+	0.375270i	$0.122450\pi$
$43$			59673.3i			0.750541i	−0.926915	+	0.375270i	$0.877550\pi$
$44$	144827.	+	38339.1i	1.70017	+	0.450074i
$45$	−333644.			−3.66139
$46$	8457.81	−	6510.17i	0.0868929	−	0.0668834i
$47$		−	41950.6i		−	0.404059i	−0.979379	−	0.202029i	$-0.935246\pi$
$47$		−	41950.6i		−	0.404059i	0.979379	−	0.202029i	$-0.0647537\pi$
$48$	−95636.0	+	167975.i	−0.864764	+	1.51887i
$49$	115024.			0.977685
$50$	−165839.	−	215453.i	−1.32671	−	1.72362i
$51$			276181.i			2.08201i
$52$	−40666.0	+	153617.i	−0.289216	+	1.09252i
$53$	−138956.			−0.933363			−0.466682	−	0.884425i	$-0.654551\pi$
$53$	−138956.			−0.933363			−0.466682	+	0.884425i	$0.654551\pi$
$54$	230039.	−	177066.i	1.46090	−	1.12449i
$55$		−	521394.i		−	3.13385i
$56$	−10148.7	−	24191.4i	−0.0577891	−	0.137752i
$57$	−74257.2			−0.400972
$58$	16834.9	+	21871.4i	0.0862833	+	0.112097i
$59$			275336.i			1.34063i	0.742079	+	0.670313i	$0.233840\pi$
$59$			275336.i			1.34063i	−0.742079	+	0.670313i	$0.766160\pi$
$60$	650302.	+	172150.i	3.01066	+	0.796992i
$61$	201103.			0.885991			0.442995	−	0.896524i	$-0.353916\pi$
$61$	201103.			0.885991			0.442995	+	0.896524i	$0.353916\pi$
$62$	49611.3	−	38186.9i	0.208164	−	0.160228i
$63$			76751.8i			0.306949i
$64$	183681.	−	187031.i	0.700689	−	0.713467i
$65$	553038.			2.01379
$66$	539039.	+	700303.i	1.87494	+	2.43587i
$67$			160517.i			0.533700i	0.963738	+	0.266850i	$0.0859827\pi$
$67$			160517.i			0.533700i	−0.963738	+	0.266850i	$0.914017\pi$
$68$	95852.6	−	362086.i	0.304844	−	1.15155i
$69$	62959.1			0.191651
$70$	−72349.6	+	55689.1i	−0.210932	+	0.162359i
$71$		−	541240.i		−	1.51222i	−0.654445	−	0.756110i	$-0.727098\pi$
$71$		−	541240.i		−	1.51222i	0.654445	−	0.756110i	$-0.272902\pi$
$72$	−707233.	+	296696.i	−1.89481	+	0.794903i
$73$	−200444.			−0.515257			−0.257629	−	0.966244i	$-0.582941\pi$
$73$	−200444.			−0.515257			−0.257629	+	0.966244i	$0.582941\pi$
$74$	−223970.	−	290975.i	−0.552706	−	0.718058i
$75$		−	1.60381e6i		−	3.80162i
$76$	97354.5	+	25772.0i	0.221776	+	0.0587095i
$77$	−119942.			−0.262723
$78$	−742806.	+	571754.i	−1.56528	+	1.20483i
$79$			347234.i			0.704273i	0.935949	+	0.352136i	$0.114545\pi$
$79$			347234.i			0.704273i	−0.935949	+	0.352136i	$0.885455\pi$
$80$	−792828.	−	451394.i	−1.54849	−	0.881628i
$81$	620389.			1.16737
$82$	429926.	+	558547.i	0.779745	+	1.01302i
$83$		−	273705.i		−	0.478683i	−0.970935	−	0.239342i	$-0.923068\pi$
$83$		−	273705.i		−	0.478683i	0.970935	−	0.239342i	$-0.0769316\pi$
$84$	39601.6	−	149596.i	0.0668151	−	0.252396i
$85$	−1.30355e6			−2.12261
$86$	378298.	−	291184.i	0.594755	−	0.457797i
$87$			162809.i			0.247240i
$88$	−463654.	−	1.10521e6i	−0.680371	−	1.62180i
$89$	165590.			0.234890			0.117445	−	0.993079i	$-0.462530\pi$
$89$	165590.			0.234890			0.117445	+	0.993079i	$0.462530\pi$
$90$	1.62806e6	+	2.11513e6i	2.23328	+	2.90142i
$91$		−	127221.i		−	0.168825i
$92$	−82542.2	−	21850.9i	−0.106002	−	0.0280611i
$93$	369301.			0.459126
$94$	−265945.	+	204704.i	−0.320191	+	0.246458i
$95$		−	350487.i		−	0.408791i
$96$	1.53155e6	−	213376.i	1.73108	−	0.241174i
$97$	−510222.			−0.559042			−0.279521	−	0.960140i	$-0.590176\pi$
$97$	−510222.			−0.559042			−0.279521	+	0.960140i	$0.590176\pi$
$98$	−561274.	−	729191.i	−0.596344	−	0.774752i
$99$			3.50649e6i			3.61382i
$100$	−556626.	+	2.10267e6i	−0.556626	+	2.10267i
$101$	230678.			0.223894			0.111947	−	0.993714i	$-0.464291\pi$
$101$	230678.			0.223894			0.111947	+	0.993714i	$0.464291\pi$
$102$	1.75084e6	−	1.34766e6i	1.64986	−	1.26993i
$103$		−	414709.i		−	0.379517i	−0.981831	−	0.189759i	$-0.939229\pi$
$103$		−	414709.i		−	0.379517i	0.981831	−	0.189759i	$-0.0607705\pi$
$104$	1.17229e6	−	491794.i	1.04216	−	0.437203i
$105$	−538563.			−0.465231
$106$	678057.	+	880911.i	0.569310	+	0.739630i
$107$			94767.7i			0.0773587i	0.999252	+	0.0386794i	$0.0123151\pi$
$107$			94767.7i			0.0773587i	−0.999252	+	0.0386794i	$0.987685\pi$
$108$	−2.24502e6	−	594310.i	−1.78217	−	0.471782i
$109$	366838.			0.283266			0.141633	−	0.989919i	$-0.454765\pi$
$109$	366838.			0.283266			0.141633	+	0.989919i	$0.454765\pi$
$110$	−3.30537e6	+	2.54422e6i	−2.48337	+	1.91151i
$111$		−	2.16598e6i		−	1.58375i
$112$	−103839.	+	182383.i	−0.0739105	+	0.129816i
$113$	759799.			0.526579			0.263289	−	0.964717i	$-0.415193\pi$
$113$	759799.			0.526579			0.263289	+	0.964717i	$0.415193\pi$
$114$	362349.	+	470752.i	0.244575	+	0.317744i
$115$			297161.i			0.195388i
$116$	56505.1	−	213449.i	0.0362004	−	0.136748i
$117$	−3.71930e6			−2.32222
$118$	1.74549e6	−	1.34354e6i	1.06236	−	0.817722i
$119$			299870.i			0.177947i
$120$	−2.08190e6	−	4.96261e6i	−1.20480	−	2.87188i
$121$	−3.70812e6			−2.09313
$122$	−981312.	−	1.27489e6i	−0.540415	−	0.702091i
$123$			4.15777e6i			2.23432i
$124$	−484171.	−	128171.i	−0.253941	−	0.0672243i
$125$	4.08961e6			2.09388
$126$	486567.	−	374521.i	0.243238	−	0.187225i
$127$			520319.i			0.254015i	0.991902	+	0.127007i	$0.0405372\pi$
$127$			520319.i			0.254015i	−0.991902	+	0.127007i	$0.959463\pi$
$128$	−2.08198e6	−	251800.i	−0.992766	−	0.120068i
$129$	2.81601e6			1.31179
$130$	−2.69863e6	−	3.50598e6i	−1.22832	−	1.59580i
$131$		−	919584.i		−	0.409051i	−0.978861	−	0.204525i	$-0.934435\pi$
$131$		−	919584.i		−	0.409051i	0.978861	−	0.204525i	$-0.0655651\pi$
$132$	1.80924e6	−	6.83446e6i	0.786638	−	2.97154i
$133$	−80626.4			−0.0342707
$134$	1.01760e6	−	783266.i	0.422923	−	0.325533i
$135$			8.08233e6i			3.28500i
$136$	−2.76316e6	+	1.15919e6i	−1.09847	+	0.460828i
$137$	3.48023e6			1.35346			0.676732	−	0.736229i	$-0.263396\pi$
$137$	3.48023e6			1.35346			0.676732	+	0.736229i	$0.263396\pi$
$138$	−307218.	−	399128.i	−0.116899	−	0.151871i
$139$		−	2.71782e6i		−	1.01199i	−0.862536	−	0.505996i	$-0.831125\pi$
$139$		−	2.71782e6i		−	1.01199i	0.862536	−	0.505996i	$-0.168875\pi$
$140$	706080.	+	186916.i	0.257318	+	0.0681181i
$141$	−1.97967e6			−0.706212
$142$	−3.43118e6	+	2.64106e6i	−1.19834	+	0.922387i
$143$		−	5.81225e6i		−	1.98763i
$144$	5.33194e6	+	3.03572e6i	1.78566	+	1.01666i
$145$	−768442.			−0.252062
$146$	978095.	+	1.27071e6i	0.314284	+	0.408308i
$147$		−	5.42802e6i		−	1.70879i
$148$	−751737.	+	2.83970e6i	−0.231889	+	0.875967i
$149$	4.16100e6			1.25788			0.628940	−	0.777454i	$-0.283489\pi$
$149$	4.16100e6			1.25788			0.628940	+	0.777454i	$0.283489\pi$
$150$	−1.01673e7	+	7.82602e6i	−3.01254	+	2.31882i
$151$			2.64361e6i			0.767833i	0.923368	+	0.383916i	$0.125425\pi$
$151$			2.64361e6i			0.767833i	−0.923368	+	0.383916i	$0.874575\pi$
$152$	−311674.	−	742936.i	−0.0887503	−	0.211554i
$153$	8.76666e6			2.44771
$154$	585274.	+	760370.i	0.160250	+	0.208191i
$155$			1.74307e6i			0.468080i
$156$	7.24925e6	+	1.91905e6i	1.90950	+	0.505490i
$157$	5.74515e6			1.48458			0.742288	−	0.670081i	$-0.233741\pi$
$157$	5.74515e6			1.48458			0.742288	+	0.670081i	$0.233741\pi$
$158$	2.20128e6	−	1.69438e6i	0.558091	−	0.429575i
$159$			6.55742e6i			1.63133i
$160$	1.00711e6	+	7.22876e6i	0.245877	+	1.76483i
$161$	68359.3			0.0163802
$162$	−3.02728e6	−	3.93295e6i	−0.712045	−	0.925067i
$163$		−	5.89269e6i		−	1.36066i	−0.732904	−	0.680332i	$-0.761836\pi$
$163$		−	5.89269e6i		−	1.36066i	0.732904	−	0.680332i	$-0.238164\pi$
$164$	1.44301e6	−	5.45102e6i	0.327144	−	1.23579i
$165$	−2.46048e7			−5.47732
$166$	−1.73515e6	+	1.33558e6i	−0.379326	+	0.291976i
$167$		−	2.43169e6i		−	0.522106i	−0.965324	−	0.261053i	$-0.915930\pi$
$167$		−	2.43169e6i		−	0.522106i	0.965324	−	0.261053i	$-0.0840698\pi$
$168$	−1.14160e6	+	478921.i	−0.240762	+	0.101003i
$169$	1.33820e6			0.277242
$170$	6.36086e6	+	8.26383e6i	1.29470	+	1.68203i
$171$			2.35711e6i			0.471401i
$172$	−3.69192e6	−	977338.i	−0.725549	−	0.192070i
$173$	812895.			0.156999			0.0784994	−	0.996914i	$-0.474987\pi$
$173$	812895.			0.156999			0.0784994	+	0.996914i	$0.474987\pi$
$174$	1.03212e6	−	794448.i	0.195922	−	0.150806i
$175$		−	1.74137e6i		−	0.324921i
$176$	−4.74400e6	+	8.33236e6i	−0.870175	+	1.52838i
$177$	1.29933e7			2.34314
$178$	−808021.	−	1.04976e6i	−0.143272	−	0.186135i
$179$			7.93287e6i			1.38316i	0.722302	+	0.691578i	$0.243084\pi$
$179$			7.93287e6i			1.38316i	−0.722302	+	0.691578i	$0.756916\pi$
$180$	5.46447e6	−	2.06422e7i	0.936981	−	3.53947i
$181$	2.51643e6			0.424374			0.212187	−	0.977229i	$-0.431941\pi$
$181$	2.51643e6			0.424374			0.212187	+	0.977229i	$0.431941\pi$
$182$	−806518.	+	620795.i	−0.133783	+	0.102976i
$183$		−	9.49015e6i		−	1.54853i
$184$	264253.	+	629900.i	0.0424196	+	0.101116i
$185$	1.02233e7			1.61463
$186$	−1.80206e6	−	2.34118e6i	−0.280046	−	0.363828i
$187$			1.36999e7i			2.09504i
$188$	2.59544e6	+	687073.i	0.390604	+	0.103402i
$189$	1.85927e6			0.275395
$190$	−2.22191e6	+	1.71025e6i	−0.323941	+	0.249344i
$191$		−	3.70523e6i		−	0.531759i	−0.964006	−	0.265879i	$-0.914338\pi$
$191$		−	3.70523e6i		−	0.531759i	0.964006	−	0.265879i	$-0.0856623\pi$
$192$	−8.82609e6	−	8.66801e6i	−1.24699	−	1.22466i
$193$	1.28518e7			1.78769			0.893844	−	0.448377i	$-0.147998\pi$
$193$	1.28518e7			1.78769			0.893844	+	0.448377i	$0.147998\pi$
$194$	2.48970e6	+	3.23455e6i	0.340991	+	0.443005i
$195$		−	2.60981e7i		−	3.51970i
$196$	−1.88388e6	+	7.11638e6i	−0.250198	+	0.945129i
$197$	−2.06576e6			−0.270197			−0.135098	−	0.990832i	$-0.543135\pi$
$197$	−2.06576e6			−0.270197			−0.135098	+	0.990832i	$0.543135\pi$
$198$	2.22293e7	−	1.71104e7i	2.86372	−	2.20427i
$199$			1.38360e7i			1.75570i	0.478933	+	0.877852i	$0.341024\pi$
$199$			1.38360e7i			1.75570i	−0.478933	+	0.877852i	$0.658976\pi$
$200$	1.60460e7	−	6.73155e6i	2.00575	−	0.841443i
$201$	7.57488e6			0.932798
$202$	−1.12563e6	−	1.46238e6i	−0.136565	−	0.177422i
$203$			176773.i			0.0211314i
$204$	−1.70870e7	−	4.52333e6i	−2.01268	−	0.532805i
$205$	−1.96243e7			−2.27789
$206$	−2.62904e6	+	2.02363e6i	−0.300743	+	0.231489i
$207$		−	1.99848e6i		−	0.225314i
$208$	−8.83807e6	−	5.03192e6i	−0.982126	−	0.559170i
$209$	−3.68351e6			−0.403481
$210$	2.62799e6	+	3.41421e6i	0.283770	+	0.368665i
$211$		−	8.84341e6i		−	0.941396i	−0.882294	−	0.470698i	$-0.844002\pi$
$211$		−	8.84341e6i		−	0.941396i	0.882294	−	0.470698i	$-0.155998\pi$
$212$	2.27585e6	−	8.59707e6i	0.238856	−	0.902283i
$213$	−2.55414e7			−2.64305
$214$	600779.	−	462433.i	0.0613018	−	0.0471854i
$215$			1.32913e7i			1.33737i
$216$	7.18728e6	+	1.71323e7i	0.713187	+	1.70002i
$217$	400977.			0.0392410
$218$	−1.79004e6	−	2.32557e6i	−0.172780	−	0.224470i
$219$			9.45904e6i			0.900565i
$220$	3.22580e7	+	8.53947e6i	3.02949	+	0.801979i
$221$	−1.45313e7			−1.34626
$222$	−1.37312e7	+	1.05692e7i	−1.25502	+	0.966017i
$223$		−	3.09962e6i		−	0.279508i	−0.990186	−	0.139754i	$-0.955369\pi$
$223$		−	3.09962e6i		−	0.279508i	0.990186	−	0.139754i	$-0.0446311\pi$
$224$	1.66291e6	−	231677.i	0.147953	−	0.0206129i
$225$	−5.09089e7			−4.46937
$226$	−3.70755e6	−	4.81673e6i	−0.321189	−	0.417280i
$227$			8.03323e6i			0.686772i	0.939194	+	0.343386i	$0.111574\pi$
$227$			8.03323e6i			0.686772i	−0.939194	+	0.343386i	$0.888426\pi$
$228$	1.21620e6	−	4.59421e6i	0.102612	−	0.387620i
$229$	1.82202e7			1.51721			0.758607	−	0.651549i	$-0.225880\pi$
$229$	1.82202e7			1.51721			0.758607	+	0.651549i	$0.225880\pi$
$230$	1.88385e6	−	1.45004e6i	0.154833	−	0.119178i
$231$			5.66012e6i			0.459187i
$232$	−1.62888e6	+	683344.i	−0.130445	+	0.0547237i
$233$	−1.27589e7			−1.00866			−0.504331	−	0.863510i	$-0.668261\pi$
$233$	−1.27589e7			−1.00866			−0.504331	+	0.863510i	$0.668261\pi$
$234$	1.81489e7	+	2.35785e7i	1.41645	+	1.84021i
$235$		−	9.34387e6i		−	0.719984i
$236$	−1.70347e7	−	4.50950e6i	−1.29598	−	0.343078i
$237$	1.63861e7			1.23092
$238$	1.90102e6	−	1.46326e6i	0.141012	−	0.108540i
$239$		−	1.65843e7i		−	1.21480i	−0.794398	−	0.607398i	$-0.792213\pi$
$239$		−	1.65843e7i		−	1.21480i	0.794398	−	0.607398i	$-0.207787\pi$
$240$	−2.13015e7	+	3.74139e7i	−1.54091	+	2.70645i
$241$	8.89659e6			0.635583			0.317792	−	0.948161i	$-0.397059\pi$
$241$	8.89659e6			0.635583			0.317792	+	0.948161i	$0.397059\pi$
$242$	1.80943e7	+	2.35075e7i	1.27672	+	1.65867i
$243$		−	2.82344e6i		−	0.196771i
$244$	−3.29370e6	+	1.24420e7i	−0.226733	+	0.856488i
$245$	2.56198e7			1.74212
$246$	2.63581e7	−	2.02884e7i	1.77055	−	1.36283i
$247$		−	3.90707e6i		−	0.259275i
$248$	1.55004e6	+	3.69482e6i	0.101622	+	0.242236i
$249$	−1.29163e7			−0.836641
$250$	−1.99558e7	−	2.59260e7i	−1.27717	−	1.65926i
$251$		−	2.51030e7i		−	1.58747i	−0.608266	−	0.793734i	$-0.708134\pi$
$251$		−	2.51030e7i		−	1.58747i	0.608266	−	0.793734i	$-0.291866\pi$
$252$	−4.74854e6	−	1.25705e6i	−0.296728	−	0.0785510i
$253$	3.12307e6			0.192850
$254$	3.29856e6	−	2.53897e6i	0.201290	−	0.154938i
$255$			6.15151e7i			3.70989i
$256$	8.56304e6	+	1.44274e7i	0.510397	+	0.859939i
$257$	−1.55216e7			−0.914402			−0.457201	−	0.889363i	$-0.651148\pi$
$257$	−1.55216e7			−0.914402			−0.457201	+	0.889363i	$0.651148\pi$
$258$	−1.37411e7	−	1.78521e7i	−0.800135	−	1.03951i
$259$		−	2.35177e6i		−	0.135361i
$260$	−9.05774e6	+	3.42158e7i	−0.515347	+	1.94674i
$261$	5.16794e6			0.290667
$262$	−5.82969e6	+	4.48724e6i	−0.324147	+	0.249503i
$263$		−	1.94334e7i		−	1.06827i	−0.845399	−	0.534136i	$-0.820637\pi$
$263$		−	1.94334e7i		−	1.06827i	0.845399	−	0.534136i	$-0.179363\pi$
$264$	−5.21554e7	+	2.18800e7i	−2.83457	+	1.18915i
$265$	−3.09504e7			−1.66314
$266$	393428.	+	511130.i	0.0209036	+	0.0271573i
$267$		−	7.81428e6i		−	0.410540i
$268$	−9.93101e6	−	2.62897e6i	−0.515928	−	0.136578i
$269$	−1.38219e7			−0.710084			−0.355042	−	0.934850i	$-0.615533\pi$
$269$	−1.38219e7			−0.710084			−0.355042	+	0.934850i	$0.615533\pi$
$270$	5.12378e7	−	3.94389e7i	2.60315	−	2.00370i
$271$		−	1.46439e7i		−	0.735782i	−0.929869	−	0.367891i	$-0.880080\pi$
$271$		−	1.46439e7i		−	0.735782i	0.929869	−	0.367891i	$-0.119920\pi$
$272$	2.08319e7	+	1.18606e7i	1.03520	+	0.589385i
$273$	−6.00364e6			−0.295071
$274$	−1.69823e7	−	2.20629e7i	−0.825553	−	1.07253i
$275$		−	7.95565e7i		−	3.82541i
$276$	−1.03115e6	+	3.89521e6i	−0.0490452	+	0.185269i
$277$	2.60966e7			1.22785			0.613924	−	0.789365i	$-0.289590\pi$
$277$	2.60966e7			1.22785			0.613924	+	0.789365i	$0.289590\pi$
$278$	−1.72296e7	+	1.32620e7i	−0.801938	+	0.617270i
$279$		−	1.17225e7i		−	0.539770i
$280$	−2.26047e6	−	5.38827e6i	−0.102973	−	0.245457i
$281$	1.25925e7			0.567537			0.283768	−	0.958893i	$-0.408415\pi$
$281$	1.25925e7			0.567537			0.283768	+	0.958893i	$0.408415\pi$
$282$	9.66008e6	+	1.25501e7i	0.430758	+	0.559628i
$283$			1.27737e7i			0.563581i	0.959476	+	0.281791i	$0.0909283\pi$
$283$			1.27737e7i			0.563581i	−0.959476	+	0.281791i	$0.909072\pi$
$284$	3.34859e7	+	8.86451e6i	1.46186	+	0.386990i
$285$	−1.65397e7			−0.714484
$286$	−3.68467e7	+	2.83617e7i	−1.57507	+	1.21237i
$287$			4.51439e6i			0.190965i
$288$	−6.77306e6	−	4.86150e7i	−0.283536	−	2.03513i
$289$	1.01138e7			0.419007
$290$	3.74972e6	+	4.87153e6i	0.153747	+	0.199743i
$291$			2.40776e7i			0.977091i
$292$	3.28290e6	−	1.24012e7i	0.131859	−	0.498100i
$293$	2.21475e7			0.880486			0.440243	−	0.897879i	$-0.354892\pi$
$293$	2.21475e7			0.880486			0.440243	+	0.897879i	$0.354892\pi$
$294$	−3.44109e7	+	2.64868e7i	−1.35411	+	1.04229i
$295$			6.13270e7i			2.38883i
$296$	2.16705e7	−	9.09112e6i	0.835590	−	0.350544i
$297$	8.49426e7			3.24232
$298$	−2.03042e7	−	2.63786e7i	−0.767251	−	0.996789i
$299$			3.31261e6i			0.123924i
$300$	9.92259e7	+	2.62674e7i	3.67503	+	0.972868i
$301$	3.05755e6			0.112118
$302$	1.67591e7	−	1.28999e7i	0.608458	−	0.468344i
$303$		−	1.08858e7i		−	0.391321i
$304$	−3.18897e6	+	5.60111e6i	−0.113509	+	0.199367i
$305$	4.47927e7			1.57873
$306$	−4.27782e7	−	5.55761e7i	−1.49299	−	1.93965i
$307$		−	2.08366e7i		−	0.720131i	−0.932927	−	0.360066i	$-0.882754\pi$
$307$		−	2.08366e7i		−	0.720131i	0.932927	−	0.360066i	$-0.117246\pi$
$308$	1.96443e6	−	7.42067e6i	0.0672332	−	0.253975i
$309$	−1.95703e7			−0.663318
$310$	1.10502e7	−	8.50556e6i	0.370923	−	0.285508i
$311$			4.63620e6i			0.154128i	0.997026	+	0.0770640i	$0.0245546\pi$
$311$			4.63620e6i			0.154128i	−0.997026	+	0.0770640i	$0.975445\pi$
$312$	−2.32080e7	−	5.53208e7i	−0.764141	−	1.82148i
$313$	−5.62384e7			−1.83400			−0.917001	−	0.398885i	$-0.869397\pi$
$313$	−5.62384e7			−1.83400			−0.917001	+	0.398885i	$0.869397\pi$
$314$	−2.80343e7	−	3.64213e7i	−0.905525	−	1.17643i
$315$			1.70953e7i			0.546947i
$316$	−2.14830e7	−	5.68705e6i	−0.680821	−	0.180229i
$317$	−5.73045e6			−0.179892			−0.0899458	−	0.995947i	$-0.528669\pi$
$317$	−5.73045e6			−0.179892			−0.0899458	+	0.995947i	$0.528669\pi$
$318$	4.15706e7	−	3.19979e7i	1.29272	−	0.995038i
$319$			8.07607e6i			0.248787i
$320$	4.09123e7	−	4.16584e7i	1.24854	−	1.27131i
$321$	4.47214e6			0.135207
$322$	−333569.	−	433363.i	−0.00999121	−	0.0129803i
$323$			9.20923e6i			0.273285i
$324$	−1.01608e7	+	3.83828e7i	−0.298741	+	1.12850i
$325$	8.43850e7			2.45819
$326$	−3.73566e7	+	2.87542e7i	−1.07824	+	0.829944i
$327$		−	1.73113e7i		−	0.495092i
$328$	−4.15981e7	+	1.74511e7i	−1.17883	+	0.494539i
$329$	−2.14947e6			−0.0603593
$330$	1.20063e8	+	1.55982e8i	3.34092	+	4.34043i
$331$			6.14693e7i			1.69502i	0.530781	+	0.847509i	$0.321898\pi$
$331$			6.14693e7i			1.69502i	−0.530781	+	0.847509i	$0.678102\pi$
$332$	1.69338e7	+	4.48278e6i	0.462744	+	0.122499i
$333$	−6.87537e7			−1.86193
$334$	−1.54157e7	+	1.18658e7i	−0.413736	+	0.318462i
$335$			3.57528e7i			0.950988i
$336$	8.60673e6	+	4.90021e6i	0.226893	+	0.129181i
$337$	−5.42593e7			−1.41770			−0.708851	−	0.705358i	$-0.750786\pi$
$337$	−5.42593e7			−1.41770			−0.708851	+	0.705358i	$0.750786\pi$
$338$	−6.52992e6	−	8.48348e6i	−0.169106	−	0.219697i
$339$		−	3.58553e7i		−	0.920352i
$340$	2.13497e7	−	8.06491e7i	0.543195	−	2.05193i
$341$	1.83191e7			0.461999
$342$	1.49428e7	−	1.15018e7i	0.373555	−	0.287534i
$343$		−	1.19217e7i		−	0.295431i
$344$	1.18194e7	+	2.81739e7i	0.290349	+	0.692105i
$345$	1.40232e7			0.341499
$346$	−3.96664e6	−	5.15334e6i	−0.0957622	−	0.124411i
$347$		−	6.83139e6i		−	0.163501i	−0.996653	−	0.0817506i	$-0.973949\pi$
$347$		−	6.83139e6i		−	0.163501i	0.996653	−	0.0817506i	$-0.0260511\pi$
$348$	−1.00728e7	−	2.66650e6i	−0.239008	−	0.0632710i
$349$	3.96819e7			0.933504			0.466752	−	0.884388i	$-0.345424\pi$
$349$	3.96819e7			0.933504			0.466752	+	0.884388i	$0.345424\pi$
$350$	−1.10394e7	+	8.49728e6i	−0.257479	+	0.198187i
$351$			9.00979e7i			2.08350i
$352$	7.59719e7	−	1.05844e7i	1.74191	−	0.242683i
$353$	−3.78798e7			−0.861160			−0.430580	−	0.902553i	$-0.641691\pi$
$353$	−3.78798e7			−0.861160			−0.430580	+	0.902553i	$0.641691\pi$
$354$	−6.34024e7	−	8.23705e7i	−1.42921	−	1.85679i
$355$		−	1.20553e8i		−	2.69459i
$356$	−2.71206e6	+	1.02449e7i	−0.0601104	+	0.227068i
$357$	1.41510e7			0.311016
$358$	5.02903e7	−	3.87096e7i	1.09606	−	0.843664i
$359$			5.83918e7i			1.26203i	0.775772	+	0.631013i	$0.217361\pi$
$359$			5.83918e7i			1.26203i	−0.775772	+	0.631013i	$0.782639\pi$
$360$	−1.57525e8	+	6.60845e7i	−3.37632	+	1.41642i
$361$	−2.47610e6			−0.0526316
$362$	−1.22793e7	−	1.59528e7i	−0.258849	−	0.336289i
$363$			1.74988e8i			3.65837i
$364$	7.87104e6	+	2.08365e6i	0.163203	+	0.0432037i
$365$	−4.46459e7			−0.918127
$366$	−6.01627e7	+	4.63086e7i	−1.22711	+	0.944535i
$367$			4.33332e7i			0.876642i	0.898819	+	0.438321i	$0.144427\pi$
$367$			4.33332e7i			0.876642i	−0.898819	+	0.438321i	$0.855573\pi$
$368$	2.70378e6	−	4.74892e6i	0.0542535	−	0.0952908i
$369$	1.31978e8			2.62677
$370$	−4.98859e7	−	6.48102e7i	−0.984855	−	1.27949i
$371$			7.11986e6i			0.139428i
$372$	−6.04847e6	+	2.28482e7i	−0.117494	+	0.443838i
$373$	−9.94335e7			−1.91605			−0.958023	−	0.286690i	$-0.907445\pi$
$373$	−9.94335e7			−1.91605			−0.958023	+	0.286690i	$0.907445\pi$
$374$	8.68501e7	−	6.68505e7i	1.66018	−	1.27788i
$375$		−	1.92991e8i		−	3.65967i
$376$	−8.30911e6	−	1.98064e7i	−0.156312	−	0.372599i
$377$	−8.56623e6			−0.159869
$378$	−9.07255e6	−	1.17868e7i	−0.167979	−	0.218233i
$379$		−	1.75461e7i		−	0.322302i	−0.986930	−	0.161151i	$-0.948479\pi$
$379$		−	1.75461e7i		−	0.322302i	0.986930	−	0.161151i	$-0.0515206\pi$
$380$	2.16843e7	+	5.74034e6i	0.395179	+	0.104613i
$381$	2.45541e7			0.443966
$382$	−2.34892e7	+	1.80802e7i	−0.421384	+	0.324349i
$383$			5.90011e7i			1.05018i	0.851046	+	0.525090i	$0.175968\pi$
$383$			5.90011e7i			1.05018i	−0.851046	+	0.525090i	$0.824032\pi$
$384$	−1.18826e7	+	9.82497e7i	−0.209854	+	1.73515i
$385$	−2.67153e7			−0.468141
$386$	−6.27122e7	−	8.14738e7i	−1.09041	−	1.41663i
$387$		−	8.93871e7i		−	1.54220i
$388$	8.35650e6	−	3.15669e7i	0.143064	−	0.540426i
$389$	1.04056e8			1.76775			0.883873	−	0.467727i	$-0.154927\pi$
$389$	1.04056e8			1.76775			0.883873	+	0.467727i	$0.154927\pi$
$390$	−1.65449e8	+	1.27350e8i	−2.78914	+	2.14686i
$391$		−	7.80806e6i		−	0.130621i
$392$	5.43068e7	−	2.27826e7i	0.901564	−	0.378221i
$393$	−4.33956e7			−0.714937
$394$	1.00802e7	+	1.30958e7i	0.164808	+	0.214114i
$395$			7.73411e7i			1.25493i
$396$	−2.16942e8	−	5.74298e7i	−3.49349	−	0.924809i
$397$	1.05811e8			1.69106			0.845530	−	0.533928i	$-0.179285\pi$
$397$	1.05811e8			1.69106			0.845530	+	0.533928i	$0.179285\pi$
$398$	8.77131e7	−	6.75147e7i	1.39128	−	1.07090i
$399$			3.80480e6i			0.0598981i
$400$	−1.20973e8	−	6.88756e7i	−1.89021	−	1.07618i
$401$	7.30526e7			1.13293			0.566465	−	0.824086i	$-0.308311\pi$
$401$	7.30526e7			1.13293			0.566465	+	0.824086i	$0.308311\pi$
$402$	−3.69627e7	−	4.80208e7i	−0.568965	−	0.739182i
$403$			1.94309e7i			0.296878i
$404$	−3.77808e6	+	1.42718e7i	−0.0572964	+	0.216439i
$405$	1.38182e8			2.08012
$406$	1.12065e6	−	862590.i	0.0167453	−	0.0128892i
$407$		−	1.07443e8i		−	1.59366i
$408$	5.47028e7	+	1.30395e8i	0.805433	+	1.91991i
$409$	−3.75892e7			−0.549406			−0.274703	−	0.961529i	$-0.588580\pi$
$409$	−3.75892e7			−0.549406			−0.274703	+	0.961529i	$0.588580\pi$
$410$	9.57596e7	+	1.24408e8i	1.38941	+	1.80508i
$411$		−	1.64234e8i		−	2.36558i
$412$	2.56576e7	+	6.79216e6i	0.366880	+	0.0971217i
$413$	1.41077e7			0.200266
$414$	−1.26693e7	+	9.75185e6i	−0.178547	+	0.137431i
$415$		−	6.09637e7i		−	0.852956i
$416$	1.12268e7	+	8.05828e7i	0.155947	+	1.11934i
$417$	−1.28255e8			−1.76876
$418$	1.79742e7	+	2.33515e7i	0.246105	+	0.319732i
$419$			8.92053e7i			1.21269i	0.795203	+	0.606343i	$0.207364\pi$
$419$			8.92053e7i			1.21269i	−0.795203	+	0.606343i	$0.792636\pi$
$420$	8.82066e6	−	3.33203e7i	0.119057	−	0.449739i
$421$	1.26558e8			1.69607			0.848033	−	0.529944i	$-0.177787\pi$
$421$	1.26558e8			1.69607			0.848033	+	0.529944i	$0.177787\pi$
$422$	−5.60626e7	+	4.31527e7i	−0.745996	+	0.574209i
$423$			6.28396e7i			0.830256i
$424$	−6.56063e7	+	2.75229e7i	−0.860693	+	0.361075i
$425$	−1.98901e8			−2.59102
$426$	1.24633e8	+	1.61919e8i	1.61214	+	2.09445i
$427$		−	1.03042e7i		−	0.132351i
$428$	−5.86317e6	−	1.55212e6i	−0.0747827	−	0.0197968i
$429$	−2.74283e8			−3.47398
$430$	8.42601e7	−	6.48569e7i	1.05978	−	0.815738i
$431$			6.08496e7i			0.760022i	0.924982	+	0.380011i	$0.124080\pi$
$431$			6.08496e7i			0.760022i	−0.924982	+	0.380011i	$0.875920\pi$
$432$	7.35386e7	−	1.29163e8i	0.912145	−	1.60209i
$433$	3.68142e7			0.453474			0.226737	−	0.973956i	$-0.427194\pi$
$433$	3.68142e7			0.453474			0.226737	+	0.973956i	$0.427194\pi$
$434$	−1.95663e6	−	2.54199e6i	−0.0239353	−	0.0310960i
$435$			3.62632e7i			0.440553i
$436$	−6.00813e6	+	2.26959e7i	−0.0724903	+	0.273834i
$437$	2.09937e6			0.0251561
$438$	5.99655e7	−	4.61568e7i	0.713640	−	0.549304i
$439$			1.20204e8i			1.42078i	0.703808	+	0.710390i	$0.251482\pi$
$439$			1.20204e8i			1.42078i	−0.703808	+	0.710390i	$0.748518\pi$
$440$	−1.03272e8	−	2.46169e8i	−1.21234	−	2.88985i
$441$	−1.72299e8			−2.00894
$442$	7.09078e7	+	9.21213e7i	0.821159	+	1.06682i
$443$			1.96190e7i			0.225666i	0.993614	+	0.112833i	$0.0359925\pi$
$443$			1.96190e7i			0.225666i	−0.993614	+	0.112833i	$0.964007\pi$
$444$	1.34007e8	+	3.54748e7i	1.53101	+	0.405295i
$445$	3.68827e7			0.418546
$446$	−1.96500e7	+	1.51250e7i	−0.221492	+	0.170487i
$447$		−	1.96360e8i		−	2.19852i
$448$	−9.58313e6	−	9.41149e6i	−0.106579	−	0.104671i
$449$	−2.88353e7			−0.318556			−0.159278	−	0.987234i	$-0.550917\pi$
$449$	−2.88353e7			−0.318556			−0.159278	+	0.987234i	$0.550917\pi$
$450$	2.48417e8	+	3.22736e8i	2.72611	+	3.54168i
$451$			2.06245e8i			2.24830i
$452$	−1.24441e7	+	4.70079e7i	−0.134756	+	0.509044i
$453$	1.24753e8			1.34201
$454$	5.09265e7	−	3.91993e7i	0.544223	−	0.418900i
$455$		−	2.83367e7i		−	0.300825i
$456$	−3.50595e7	+	1.47080e7i	−0.369753	+	0.155117i
$457$	−1.72924e8			−1.81179			−0.905893	−	0.423507i	$-0.860799\pi$
$457$	−1.72924e8			−1.81179			−0.905893	+	0.423507i	$0.860799\pi$
$458$	−8.89081e7	−	1.15507e8i	−0.925433	−	1.20229i
$459$		−	2.12367e8i		−	2.19608i
$460$	−1.83850e7	−	4.86696e6i	−0.188882	−	0.0500016i
$461$	−1.41810e8			−1.44745			−0.723725	−	0.690088i	$-0.757572\pi$
$461$	−1.41810e8			−1.44745			−0.723725	+	0.690088i	$0.757572\pi$
$462$	3.58822e7	−	2.76193e7i	0.363876	−	0.280083i
$463$			7.64440e7i			0.770194i	0.922876	+	0.385097i	$0.125832\pi$
$463$			7.64440e7i			0.770194i	−0.922876	+	0.385097i	$0.874168\pi$
$464$	1.22804e7	+	6.99181e6i	0.122930	+	0.0699900i
$465$	8.22563e7			0.818107
$466$	6.22589e7	+	8.08849e7i	0.615239	+	0.799300i
$467$		−	1.51182e8i		−	1.48439i	−0.670184	−	0.742195i	$-0.733785\pi$
$467$		−	1.51182e8i		−	1.48439i	0.670184	−	0.742195i	$-0.266215\pi$
$468$	6.09153e7	−	2.30109e8i	0.594277	−	2.24490i
$469$	8.22460e6			0.0797253
$470$	−5.92353e7	+	4.55947e7i	−0.570541	+	0.439158i
$471$		−	2.71116e8i		−	2.59474i
$472$	5.45356e7	+	1.29996e8i	0.518625	+	1.23625i
$473$	1.39687e8			1.32000
$474$	−7.99585e7	−	1.03880e8i	−0.750809	−	0.975429i
$475$		−	5.34789e7i		−	0.499001i
$476$	−1.85526e7	−	4.91131e6i	−0.172022	−	0.0455383i
$477$	2.08148e8			1.91787
$478$	−1.05136e8	+	8.09254e7i	−0.962647	+	0.740971i
$479$			7.36109e7i			0.669785i	0.942256	+	0.334893i	$0.108700\pi$
$479$			7.36109e7i			0.669785i	−0.942256	+	0.334893i	$0.891300\pi$
$480$	3.41129e8	−	4.75262e7i	3.08457	−	0.429744i
$481$	1.13964e8			1.02408
$482$	−4.34122e7	−	5.63998e7i	−0.387678	−	0.503659i
$483$		−	3.22591e6i		−	0.0286293i
$484$	6.07321e7	−	2.29417e8i	0.535651	−	2.02344i
$485$	−1.13644e8			−0.996145
$486$	−1.78992e7	+	1.37774e7i	−0.155928	+	0.120021i
$487$		−	2.21059e7i		−	0.191391i	−0.995411	−	0.0956957i	$-0.969492\pi$
$487$		−	2.21059e7i		−	0.191391i	0.995411	−	0.0956957i	$-0.0305076\pi$
$488$	9.49481e7	−	3.98323e7i	0.817009	−	0.342749i
$489$	−2.78079e8			−2.37816
$490$	−1.25015e8	−	1.62416e8i	−1.06261	−	1.38052i
$491$		−	9.31723e7i		−	0.787123i	−0.919298	−	0.393561i	$-0.871243\pi$
$491$		−	9.31723e7i		−	0.787123i	0.919298	−	0.393561i	$-0.128757\pi$
$492$	−2.57236e8	−	6.80966e7i	−2.15992	−	0.571781i
$493$	2.01912e7			0.168508
$494$	−2.47688e7	+	1.90651e7i	−0.205458	+	0.158146i
$495$			7.81018e8i			6.43940i
$496$	1.58596e7	−	2.78559e7i	0.129972	−	0.228282i
$497$	−2.77321e7			−0.225899
$498$	6.30268e7	+	8.18825e7i	0.510314	+	0.662984i
$499$		−	2.69347e7i		−	0.216776i	−0.994109	−	0.108388i	$-0.965431\pi$
$499$		−	2.69347e7i		−	0.216776i	0.994109	−	0.108388i	$-0.0345688\pi$
$500$	−6.69802e7	+	2.53019e8i	−0.535842	+	2.02416i
$501$	−1.14753e8			−0.912535
$502$	−1.59140e8	+	1.22494e8i	−1.25797	+	0.968284i
$503$			1.00693e8i			0.791218i	0.918419	+	0.395609i	$0.129466\pi$
$503$			1.00693e8i			0.791218i	−0.918419	+	0.395609i	$0.870534\pi$
$504$	1.52021e7	+	3.62373e7i	0.118744	+	0.283051i
$505$	5.13801e7			0.398952
$506$	−1.52395e7	−	1.97986e7i	−0.117630	−	0.152821i
$507$		−	6.31501e7i		−	0.484563i
$508$	−3.21916e7	−	8.52187e6i	−0.245556	−	0.0650045i
$509$	2.00123e8			1.51755			0.758776	−	0.651352i	$-0.225798\pi$
$509$	2.00123e8			1.51755			0.758776	+	0.651352i	$0.225798\pi$
$510$	3.89974e8	−	3.00172e8i	2.93985	−	2.26287i
$511$			1.02704e7i			0.0769704i
$512$	4.96776e7	−	1.24686e8i	0.370127	−	0.928981i
$513$	5.70995e7			0.422941
$514$	7.57399e7	+	9.83990e7i	0.557745	+	0.724605i
$515$		−	9.23701e7i		−	0.676254i
$516$	−4.61210e7	+	1.74223e8i	−0.335699	+	1.26811i
$517$	−9.82009e7			−0.710631
$518$	−1.49090e7	+	1.14758e7i	−0.107265	+	0.0825645i
$519$		−	3.83609e7i		−	0.274402i
$520$	2.61109e8	−	1.09540e8i	1.85700	−	0.779043i
$521$	2.84002e7			0.200820			0.100410	−	0.994946i	$-0.467984\pi$
$521$	2.84002e7			0.200820			0.100410	+	0.994946i	$0.467984\pi$
$522$	−2.52177e7	−	3.27621e7i	−0.177294	−	0.230335i
$523$			1.92155e8i			1.34322i	0.740906	+	0.671609i	$0.234396\pi$
$523$			1.92155e8i			1.34322i	−0.740906	+	0.671609i	$0.765604\pi$
$524$	5.68936e7	+	1.50611e7i	0.395430	+	0.104680i
$525$	−8.21762e7			−0.567895
$526$	−1.23198e8	+	9.48281e7i	−0.846536	+	0.651598i
$527$		−	4.58000e7i		−	0.312920i
$528$	3.93208e8	+	2.23872e8i	2.67129	+	1.52089i
$529$	1.46256e8			0.987976
$530$	1.51027e8	+	1.96210e8i	1.01444	+	1.31793i
$531$		−	4.12438e8i		−	2.75470i
$532$	1.32051e6	−	4.98827e6i	0.00877016	−	0.0331295i
$533$	−2.18762e8			−1.44474
$534$	−4.95385e7	+	3.81309e7i	−0.325326	+	0.250411i
$535$			2.11081e7i			0.137844i
$536$	3.17934e7	+	7.57859e7i	0.206463	+	0.492146i
$537$	3.74356e8			2.41747
$538$	6.74457e7	+	8.76234e7i	0.433119	+	0.562696i
$539$		−	2.69256e8i		−	1.71948i
$540$	−5.00044e8	−	1.32374e8i	−3.17561	−	0.840659i
$541$	−9.70079e7			−0.612654			−0.306327	−	0.951926i	$-0.599100\pi$
$541$	−9.70079e7			−0.612654			−0.306327	+	0.951926i	$0.599100\pi$
$542$	−9.28349e7	+	7.14571e7i	−0.583060	+	0.448794i
$543$		−	1.18751e8i		−	0.741718i
$544$	−2.64624e7	−	1.89939e8i	−0.164374	−	1.17983i
$545$	8.17077e7			0.504747
$546$	2.92956e7	+	3.80600e7i	0.179980	+	0.233825i
$547$			1.43698e8i			0.877989i	0.898490	+	0.438995i	$0.144665\pi$
$547$			1.43698e8i			0.877989i	−0.898490	+	0.438995i	$0.855335\pi$
$548$	−5.69998e7	+	2.15318e8i	−0.346363	+	1.30840i
$549$	−3.01241e8			−1.82053
$550$	−5.04348e8	+	3.88208e8i	−3.03139	+	2.33333i
$551$			5.42884e6i			0.0324528i
$552$	2.97253e7	−	1.24702e7i	0.176729	−	0.0741409i
$553$	1.77916e7			0.105206
$554$	−1.27342e8	−	1.65439e8i	−0.748932	−	0.972990i
$555$		−	4.82441e8i		−	2.82205i
$556$	1.68149e8	+	4.45129e7i	0.978293	+	0.258977i
$557$	−7.24309e7			−0.419139			−0.209570	−	0.977794i	$-0.567206\pi$
$557$	−7.24309e7			−0.419139			−0.209570	+	0.977794i	$0.567206\pi$
$558$	−7.43148e7	+	5.72018e7i	−0.427733	+	0.329236i
$559$			1.48165e8i			0.848225i
$560$	−2.31286e7	+	4.06230e7i	−0.131700	+	0.231317i
$561$	6.46504e8			3.66170
$562$	−6.14471e7	−	7.98302e7i	−0.346172	−	0.449736i
$563$			6.81230e7i			0.381741i	0.981615	+	0.190871i	$0.0611311\pi$
$563$			6.81230e7i			0.381741i	−0.981615	+	0.190871i	$0.938869\pi$
$564$	3.24233e7	−	1.22480e8i	0.180726	−	0.682696i
$565$	1.69234e8			0.938300
$566$	8.09785e7	−	6.23310e7i	0.446602	−	0.343759i
$567$		−	3.17876e7i		−	0.174385i
$568$	−1.07203e8	−	2.55539e8i	−0.585007	−	1.39448i
$569$	−5.00476e7			−0.271673			−0.135836	−	0.990731i	$-0.543372\pi$
$569$	−5.00476e7			−0.271673			−0.135836	+	0.990731i	$0.543372\pi$
$570$	8.07077e7	+	1.04853e8i	0.435803	+	0.566182i
$571$			1.38064e8i			0.741605i	0.928712	+	0.370802i	$0.120917\pi$
$571$			1.38064e8i			0.741605i	−0.928712	+	0.370802i	$0.879083\pi$
$572$	3.59597e8	+	9.51939e7i	1.92145	+	0.508652i
$573$	−1.74851e8			−0.929405
$574$	2.86189e7	−	2.20286e7i	0.151327	−	0.116480i
$575$			4.53422e7i			0.238506i
$576$	−2.75144e8	+	2.80162e8i	−1.43977	+	1.46602i
$577$	1.14511e8			0.596101			0.298051	−	0.954550i	$-0.403664\pi$
$577$	1.14511e8			0.596101			0.298051	+	0.954550i	$0.403664\pi$
$578$	−4.93518e7	−	6.41164e7i	−0.255576	−	0.332036i
$579$		−	6.06483e8i		−	3.12452i
$580$	1.25857e7	−	4.75427e7i	0.0645048	−	0.243669i
$581$	−1.40241e7			−0.0715068
$582$	1.52640e8	−	1.17490e8i	0.774282	−	0.595982i
$583$			3.25279e8i			1.64153i
$584$	−9.46368e7	+	3.97017e7i	−0.475140	+	0.199329i
$585$	−8.28419e8			−4.13792
$586$	−1.08072e8	−	1.40404e8i	−0.537057	−	0.697728i
$587$			2.18180e8i			1.07870i	0.842082	+	0.539350i	$0.181330\pi$
$587$			2.18180e8i			1.07870i	−0.842082	+	0.539350i	$0.818670\pi$
$588$	3.35826e8	+	8.89010e7i	1.65189	+	0.437295i
$589$	1.23143e7			0.0602649
$590$	3.88782e8	−	2.99254e8i	1.89300	−	1.45708i
$591$			9.74840e7i			0.472249i
$592$	−1.63377e8	−	9.30182e7i	−0.787456	−	0.448335i
$593$	1.84372e8			0.884162			0.442081	−	0.896975i	$-0.354240\pi$
$593$	1.84372e8			0.884162			0.442081	+	0.896975i	$0.354240\pi$
$594$	−4.14490e8	−	5.38492e8i	−1.97767	−	2.56933i
$595$			6.67915e7i			0.317081i
$596$	−6.81496e7	+	2.57437e8i	−0.321902	+	1.21599i
$597$	6.52927e8			3.06861
$598$	2.10003e7	−	1.61644e7i	0.0982022	−	0.0755884i
$599$		−	3.16263e8i		−	1.47153i	−0.677238	−	0.735764i	$-0.736823\pi$
$599$		−	3.16263e8i		−	1.47153i	0.677238	−	0.735764i	$-0.263177\pi$
$600$	−3.17665e8	−	7.57217e8i	−1.47067	−	3.50563i
$601$	8.53213e7			0.393037			0.196519	−	0.980500i	$-0.437036\pi$
$601$	8.53213e7			0.393037			0.196519	+	0.980500i	$0.437036\pi$
$602$	−1.49197e7	−	1.93833e7i	−0.0683867	−	0.0888460i
$603$		−	2.40445e8i		−	1.09664i
$604$	−1.63557e8	−	4.32975e7i	−0.742265	−	0.196495i
$605$	−8.25927e8			−3.72971
$606$	−6.90105e7	+	5.31189e7i	−0.310097	+	0.238688i
$607$			1.39501e8i			0.623752i	0.950123	+	0.311876i	$0.100957\pi$
$607$			1.39501e8i			0.623752i	−0.950123	+	0.311876i	$0.899043\pi$
$608$	5.10692e7	−	7.11499e6i	0.227221	−	0.0316565i
$609$	8.34201e6			0.0369334
$610$	−2.18572e8	−	2.83963e8i	−0.962955	−	1.25104i
$611$		−	1.04161e8i		−	0.456648i
$612$	−1.43582e8	+	5.42383e8i	−0.626390	+	2.36620i
$613$	−1.73042e8			−0.751226			−0.375613	−	0.926777i	$-0.622568\pi$
$613$	−1.73042e8			−0.751226			−0.375613	+	0.926777i	$0.622568\pi$
$614$	−1.32093e8	+	1.01675e8i	−0.570658	+	0.439248i
$615$			9.26080e8i			3.98129i
$616$	−5.66289e7	+	2.37568e7i	−0.242268	+	0.101635i
$617$	−1.45145e7			−0.0617941			−0.0308970	−	0.999523i	$-0.509836\pi$
$617$	−1.45145e7			−0.0617941			−0.0308970	+	0.999523i	$0.509836\pi$
$618$	9.54961e7	+	1.24066e8i	0.404595	+	0.525637i
$619$			6.10693e7i			0.257485i	0.991678	+	0.128742i	$0.0410940\pi$
$619$			6.10693e7i			0.257485i	−0.991678	+	0.128742i	$0.958906\pi$
$620$	−1.07842e8	−	2.85483e7i	−0.452493	−	0.119786i
$621$	−4.84119e7			−0.202152
$622$	2.93911e7	−	2.26230e7i	0.122136	−	0.0940112i
$623$		−	8.48454e6i		−	0.0350884i
$624$	−2.37459e8	+	4.17073e8i	−0.977315	+	1.71656i
$625$	3.79870e8			1.55595
$626$	2.74423e8	+	3.56522e8i	1.11866	+	1.45333i
$627$			1.73826e8i			0.705202i
$628$	−9.40950e7	+	3.55446e8i	−0.379916	+	1.43514i
$629$	−2.68621e8			−1.07941
$630$	1.08375e8	−	8.34190e7i	0.433420	−	0.333613i
$631$			2.85304e8i			1.13559i	0.823172	+	0.567793i	$0.192202\pi$
$631$			2.85304e8i			1.13559i	−0.823172	+	0.567793i	$0.807798\pi$
$632$	6.87763e7	+	1.63942e8i	0.272450	+	0.649439i
$633$	−4.17325e8			−1.64537
$634$	2.79626e7	+	3.63281e7i	0.109726	+	0.142553i
$635$			1.15893e8i			0.452623i
$636$	−4.05700e8	−	1.07398e8i	−1.57701	−	0.417471i
$637$	2.85597e8			1.10493
$638$	5.11982e7	−	3.94084e7i	0.197148	−	0.151749i
$639$			8.10746e8i			3.10729i
$640$	−4.63730e8	−	5.60848e7i	−1.76899	−	0.213946i
$641$	−1.67746e8			−0.636908			−0.318454	−	0.947938i	$-0.603164\pi$
$641$	−1.67746e8			−0.636908			−0.318454	+	0.947938i	$0.603164\pi$
$642$	−2.18224e7	−	2.83510e7i	−0.0824704	−	0.107143i
$643$		−	3.28618e8i		−	1.23611i	−0.786133	−	0.618057i	$-0.787920\pi$
$643$		−	3.28618e8i		−	1.23611i	0.786133	−	0.618057i	$-0.212080\pi$
$644$	−1.11960e6	+	4.22931e6i	−0.00419184	+	0.0158348i
$645$	6.27224e8			2.33746
$646$	5.83818e7	−	4.49377e7i	0.216561	−	0.166692i
$647$		−	1.04253e8i		−	0.384926i	−0.981304	−	0.192463i	$-0.938352\pi$
$647$		−	1.04253e8i		−	0.384926i	0.981304	−	0.192463i	$-0.0616475\pi$
$648$	2.92908e8	−	1.22880e8i	1.07648	−	0.451602i
$649$	6.44527e8			2.35780
$650$	−4.11769e8	−	5.34957e8i	−1.49939	−	1.94796i
$651$		−	1.89223e7i		−	0.0685853i
$652$	3.64574e8	+	9.65114e7i	1.31536	+	0.348206i
$653$	−1.37481e8			−0.493745			−0.246873	−	0.969048i	$-0.579403\pi$
$653$	−1.37481e8			−0.493745			−0.246873	+	0.969048i	$0.579403\pi$
$654$	−1.09745e8	+	8.44729e7i	−0.392329	+	0.301984i
$655$		−	2.04823e8i		−	0.728880i
$656$	3.13615e8	+	1.78555e8i	1.11093	+	0.632501i
$657$	3.00253e8			1.05875
$658$	1.04887e7	+	1.36265e7i	0.0368165	+	0.0478308i
$659$			1.71785e8i			0.600245i	0.953901	+	0.300123i	$0.0970276\pi$
$659$			1.71785e8i			0.600245i	−0.953901	+	0.300123i	$0.902972\pi$
$660$	4.02982e8	−	1.52227e9i	1.40169	−	5.29494i
$661$	−2.07149e7			−0.0717264			−0.0358632	−	0.999357i	$-0.511418\pi$
$661$	−2.07149e7			−0.0717264			−0.0358632	+	0.999357i	$0.511418\pi$
$662$	3.89684e8	−	2.99948e8i	1.34319	−	1.03389i
$663$			6.85741e8i			2.35299i
$664$	−5.42124e7	−	1.29226e8i	−0.185180	−	0.441414i
$665$	−1.79583e7			−0.0610662
$666$	3.35493e8	+	4.35863e8i	1.13569	+	1.47546i
$667$		−	4.60285e6i		−	0.0155113i
$668$	1.50446e8	+	3.98266e7i	0.504721	+	0.133611i
$669$	−1.46273e8			−0.488522
$670$	2.26654e8	−	1.74461e8i	0.753597	−	0.580061i
$671$		−	4.70756e8i		−	1.55822i
$672$	−1.09330e7	−	7.84736e7i	−0.0360272	−	0.258592i
$673$	−5.51279e8			−1.80853			−0.904266	−	0.426969i	$-0.859581\pi$
$673$	−5.51279e8			−1.80853			−0.904266	+	0.426969i	$0.859581\pi$
$674$	2.64766e8	+	3.43976e8i	0.864735	+	1.12344i
$675$			1.23324e9i			4.00991i
$676$	−2.19172e7	+	8.27927e7i	−0.0709487	+	0.268011i
$677$	2.77987e8			0.895896			0.447948	−	0.894060i	$-0.352155\pi$
$677$	2.77987e8			0.895896			0.447948	+	0.894060i	$0.352155\pi$
$678$	−2.27304e8	+	1.74961e8i	−0.729320	+	0.561374i
$679$			2.61428e7i			0.0835110i
$680$	−6.15453e8	+	2.58193e8i	−1.95735	+	0.821140i
$681$	3.79092e8			1.20034
$682$	−8.93906e7	−	1.16134e8i	−0.281799	−	0.366104i
$683$			3.86546e8i			1.21322i	0.795000	+	0.606610i	$0.207471\pi$
$683$			3.86546e8i			1.21322i	−0.795000	+	0.606610i	$0.792529\pi$
$684$	−1.45831e8	−	3.86050e7i	−0.455704	−	0.120636i
$685$	7.75170e8			2.41171
$686$	−7.55775e7	+	5.81737e7i	−0.234110	+	0.180200i
$687$		−	8.59820e8i		−	2.65178i
$688$	1.20934e8	−	2.12408e8i	0.371348	−	0.652236i
$689$	−3.45021e8			−1.05484
$690$	−6.84282e7	−	8.88998e7i	−0.208299	−	0.270616i
$691$		−	4.53808e8i		−	1.37543i	−0.725981	−	0.687714i	$-0.758614\pi$
$691$		−	4.53808e8i		−	1.37543i	0.725981	−	0.687714i	$-0.241386\pi$
$692$	−1.33137e7	+	5.02929e7i	−0.0401773	+	0.151771i
$693$	1.79666e8			0.539841
$694$	−4.33075e7	+	3.33348e7i	−0.129564	+	0.0997284i
$695$		−	6.05355e8i		−	1.80325i
$696$	3.22473e7	+	7.68678e7i	0.0956458	+	0.227991i
$697$	5.15638e8			1.52281
$698$	−1.93634e8	−	2.51563e8i	−0.569396	−	0.739742i
$699$			6.02099e8i			1.76294i
$700$	1.07737e8	+	2.85205e7i	0.314101	+	0.0831501i
$701$	−4.45362e8			−1.29288			−0.646441	−	0.762964i	$-0.723743\pi$
$701$	−4.45362e8			−1.29288			−0.646441	+	0.762964i	$0.723743\pi$
$702$	5.71174e8	−	4.39646e8i	1.65104	−	1.27084i
$703$		−	7.22246e7i		−	0.207883i
$704$	−4.37816e8	−	4.29974e8i	−1.25480	−	1.23232i
$705$	−4.40942e8			−1.25839
$706$	1.84840e8	+	2.40138e8i	0.525269	+	0.682414i
$707$		−	1.18195e7i		−	0.0334458i
$708$	−2.12806e8	+	8.03878e8i	−0.599630	+	2.26512i
$709$	7.01549e7			0.196843			0.0984214	−	0.995145i	$-0.468621\pi$
$709$	7.01549e7			0.196843			0.0984214	+	0.995145i	$0.468621\pi$
$710$	−7.64245e8	+	5.88256e8i	−2.13529	+	1.64358i
$711$		−	5.20136e8i		−	1.44713i
$712$	7.81812e7	−	3.27983e7i	0.216602	−	0.0908680i
$713$	−1.04407e7			−0.0288046
$714$	−6.90518e7	−	8.97100e7i	−0.189706	−	0.246460i
$715$		−	1.29459e9i		−	3.54172i
$716$	−4.90798e8	−	1.29926e8i	−1.33710	−	0.353962i
$717$	−7.82621e8			−2.12321
$718$	3.70174e8	−	2.84931e8i	1.00007	−	0.769780i
$719$		−	5.60762e8i		−	1.50866i	−0.656494	−	0.754331i	$-0.727961\pi$
$719$		−	5.60762e8i		−	1.50866i	0.656494	−	0.754331i	$-0.272039\pi$
$720$	1.18761e9	+	6.76162e8i	3.18183	+	1.81156i
$721$	−2.12489e7			−0.0566932
$722$	1.20825e7	+	1.56972e7i	0.0321029	+	0.0417071i
$723$		−	4.19834e8i		−	1.11087i
$724$	−4.12144e7	+	1.55688e8i	−0.108601	+	0.410242i
$725$	−1.17252e8			−0.307686
$726$	1.10933e9	−	8.53878e8i	2.89902	−	2.23144i
$727$		−	2.22030e8i		−	0.577841i	−0.957353	−	0.288921i	$-0.906704\pi$
$727$		−	2.22030e8i		−	0.577841i	0.957353	−	0.288921i	$-0.0932964\pi$
$728$	−2.51986e7	−	6.00658e7i	−0.0653104	−	0.155680i
$729$	3.19024e8			0.823458
$730$	2.17856e8	+	2.83032e8i	0.560016	+	0.727556i
$731$		−	3.49236e8i		−	0.894060i
$732$	5.87145e8	+	1.55431e8i	1.49697	+	0.396283i
$733$	−6.79609e8			−1.72563			−0.862814	−	0.505521i	$-0.831300\pi$
$733$	−6.79609e8			−1.72563			−0.862814	+	0.505521i	$0.831300\pi$
$734$	2.74710e8	−	2.11450e8i	0.694682	−	0.534712i
$735$		−	1.20901e9i		−	3.04486i
$736$	−4.32992e7	+	6.03246e6i	−0.108604	+	0.0151308i
$737$	3.75750e8			0.938634
$738$	−6.44005e8	−	8.36671e8i	−1.60221	−	2.08154i
$739$		−	1.70549e8i		−	0.422587i	−0.977423	−	0.211294i	$-0.932232\pi$
$739$		−	1.70549e8i		−	0.422587i	0.977423	−	0.211294i	$-0.0677677\pi$
$740$	−1.67438e8	+	6.32501e8i	−0.413199	+	1.56087i
$741$	−1.84376e8			−0.453159
$742$	4.51363e7	−	3.47424e7i	0.110488	−	0.0850449i
$743$			3.12503e8i			0.761882i	0.924599	+	0.380941i	$0.124400\pi$
$743$			3.12503e8i			0.761882i	−0.924599	+	0.380941i	$0.875600\pi$
$744$	1.74361e8	−	7.31471e7i	0.423379	−	0.177614i
$745$	9.26801e8			2.24139
$746$	4.85200e8	+	6.30357e8i	1.16870	+	1.51834i
$747$			4.09994e8i			0.983594i
$748$	−8.47596e8	−	2.24379e8i	−2.02527	−	0.536138i
$749$	4.85572e6			0.0115560
$750$	−1.22346e9	+	9.41725e8i	−2.90006	+	2.23224i
$751$			4.22256e8i			0.996910i	0.866915	+	0.498455i	$0.166099\pi$
$751$			4.22256e8i			0.996910i	−0.866915	+	0.498455i	$0.833901\pi$
$752$	−8.50169e7	+	1.49324e8i	−0.199918	+	0.351136i
$753$	−1.18462e9			−2.77457
$754$	4.18001e7	+	5.43055e7i	0.0975133	+	0.126686i
$755$			5.88825e8i			1.36819i
$756$	−3.04513e7	+	1.15031e8i	−0.0704760	+	0.266225i
$757$	5.50286e8			1.26853			0.634265	−	0.773116i	$-0.281303\pi$
$757$	5.50286e8			1.26853			0.634265	+	0.773116i	$0.281303\pi$
$758$	−1.11233e8	+	8.56187e7i	−0.255403	+	0.196590i
$759$		−	1.47379e8i		−	0.337063i
$760$	−6.94207e7	−	1.65478e8i	−0.158142	−	0.376963i
$761$	3.90355e8			0.885740			0.442870	−	0.896586i	$-0.353960\pi$
$761$	3.90355e8			0.885740			0.442870	+	0.896586i	$0.353960\pi$
$762$	−1.19815e8	−	1.55660e8i	−0.270799	−	0.351814i
$763$		−	1.87961e7i		−	0.0423150i
$764$	2.29238e8	+	6.06847e7i	0.514052	+	0.136082i
$765$	1.95264e9			4.36152
$766$	3.74037e8	−	2.87905e8i	0.832201	−	0.640563i
$767$			6.83644e8i			1.51511i
$768$	6.80835e8	−	4.04094e8i	1.50300	−	0.892069i
$769$	2.25189e8			0.495186			0.247593	−	0.968864i	$-0.420360\pi$
$769$	2.25189e8			0.495186			0.247593	+	0.968864i	$0.420360\pi$
$770$	1.30361e8	+	1.69361e8i	0.285545	+	0.370972i
$771$			7.32472e8i			1.59819i
$772$	−2.10489e8	+	7.95126e8i	−0.457485	+	1.72816i
$773$	−3.38741e8			−0.733381			−0.366690	−	0.930343i	$-0.619509\pi$
$773$	−3.38741e8			−0.733381			−0.366690	+	0.930343i	$0.619509\pi$
$774$	−5.66668e8	+	4.36177e8i	−1.22210	+	0.940676i
$775$			2.65965e8i			0.571373i
$776$	−2.40894e8	+	1.01059e8i	−0.515515	+	0.216267i
$777$	−1.10981e8			−0.236584
$778$	−5.07758e8	−	6.59664e8i	−1.07825	−	1.40082i
$779$			1.38640e8i			0.293277i
$780$	1.61466e9	+	4.27439e8i	3.40250	+	0.900722i
$781$	−1.26697e9			−2.65959
$782$	−4.94991e7	+	3.81005e7i	−0.103509	+	0.0796730i
$783$		−	1.25190e8i		−	0.260787i
$784$	−4.09428e8	−	2.33106e8i	−0.849629	−	0.483733i
$785$	1.27965e9			2.64534
$786$	2.11755e8	+	2.75106e8i	0.436080	+	0.566542i
$787$		−	9.30874e8i		−	1.90971i	−0.297076	−	0.954854i	$-0.596012\pi$
$787$		−	9.30874e8i		−	1.90971i	0.297076	−	0.954854i	$-0.403988\pi$
$788$	3.38333e7	−	1.27806e8i	0.0691457	−	0.261200i
$789$	−9.17071e8			−1.86712
$790$	4.90303e8	−	3.77397e8i	0.994451	−	0.765451i
$791$		−	3.89307e7i		−	0.0786615i
$792$	6.94527e8	+	1.65554e9i	1.39802	+	3.33246i
$793$	4.99328e8			1.00130
$794$	−5.16320e8	−	6.70787e8i	−1.03147	−	1.34006i
$795$			1.46057e9i			2.90683i
$796$	−8.56017e8	−	2.26608e8i	−1.69724	−	0.449300i
$797$	1.23561e8			0.244065			0.122032	−	0.992526i	$-0.461059\pi$
$797$	1.23561e8			0.244065			0.122032	+	0.992526i	$0.461059\pi$
$798$	2.41205e7	−	1.85661e7i	0.0474654	−	0.0365352i
$799$			2.45515e8i			0.481323i
$800$	1.53670e8	+	1.10300e9i	0.300136	+	2.15429i
$801$	−2.48045e8			−0.482650
$802$	−3.56471e8	−	4.63116e8i	−0.691036	−	0.897774i
$803$			4.69213e8i			0.906199i
$804$	−1.24063e8	+	4.68649e8i	−0.238711	+	0.901736i
$805$	1.52260e7			0.0291876
$806$	1.23182e8	−	9.48159e7i	0.235257	−	0.181082i
$807$			6.52260e8i			1.24108i
$808$	1.08912e8	−	4.56902e7i	0.206462	−	0.0866141i
$809$	−8.78005e8			−1.65826			−0.829128	−	0.559059i	$-0.811162\pi$
$809$	−8.78005e8			−1.65826			−0.829128	+	0.559059i	$0.811162\pi$
$810$	−6.74281e8	−	8.76006e8i	−1.26878	−	1.64836i
$811$			6.56702e8i			1.23114i	0.788084	+	0.615568i	$0.211073\pi$
$811$			6.56702e8i			1.23114i	−0.788084	+	0.615568i	$0.788927\pi$
$812$	−1.09368e7	−	2.89522e6i	−0.0204277	−	0.00540771i
$813$	−6.91053e8			−1.28600
$814$	−6.81134e8	+	5.24284e8i	−1.26287	+	0.972061i
$815$		−	1.31251e9i		−	2.42454i
$816$	5.59707e8	−	9.83069e8i	1.03013	−	1.80931i
$817$	9.38996e7			0.172186
$818$	1.83422e8	+	2.38296e8i	0.335113	+	0.435369i
$819$			1.90570e8i			0.346899i
$820$	3.21410e8	−	1.21413e9i	0.582932	−	2.20204i
$821$	3.47026e8			0.627095			0.313547	−	0.949573i	$-0.398483\pi$
$821$	3.47026e8			0.627095			0.313547	+	0.949573i	$0.398483\pi$
$822$	−1.04116e9	+	8.01403e8i	−1.87457	+	1.44290i
$823$		−	1.49790e8i		−	0.268710i	−0.990933	−	0.134355i	$-0.957104\pi$
$823$		−	1.49790e8i		−	0.268710i	0.990933	−	0.134355i	$-0.0428962\pi$
$824$	−8.21409e7	−	1.95799e8i	−0.146817	−	0.349968i
$825$	−3.75431e9			−6.68603
$826$	−6.88407e7	−	8.94357e7i	−0.122153	−	0.158698i
$827$			8.83011e7i			0.156117i	0.996949	+	0.0780584i	$0.0248721\pi$
$827$			8.83011e7i			0.156117i	−0.996949	+	0.0780584i	$0.975128\pi$
$828$	1.23643e8	+	3.27313e7i	0.217811	+	0.0576598i
$829$	−4.42558e8			−0.776795			−0.388397	−	0.921492i	$-0.626971\pi$
$829$	−4.42558e8			−0.776795			−0.388397	+	0.921492i	$0.626971\pi$
$830$	−3.86478e8	+	2.97481e8i	−0.675913	+	0.520265i
$831$		−	1.23151e9i		−	2.14603i
$832$	4.56070e8	−	4.64387e8i	0.791885	−	0.806326i
$833$	−6.73172e8			−1.16464
$834$	6.25841e8	+	8.13074e8i	1.07886	+	1.40162i
$835$		−	5.41623e8i		−	0.930331i
$836$	6.03290e7	−	2.27894e8i	0.103254	−	0.390045i
$837$	−2.83971e8			−0.484282
$838$	5.65516e8	−	4.35290e8i	0.960976	−	0.739685i
$839$		−	2.53074e8i		−	0.428511i	−0.976778	−	0.214255i	$-0.931268\pi$
$839$		−	2.53074e8i		−	0.428511i	0.976778	−	0.214255i	$-0.0687325\pi$
$840$	−2.54275e8	+	1.06673e8i	−0.429008	+	0.179976i
$841$	−5.82921e8			−0.979990
$842$	−6.17557e8	−	8.02311e8i	−1.03452	−	1.34402i
$843$		−	5.94248e8i		−	0.991938i
$844$	5.47131e8	+	1.44839e8i	0.910048	+	0.240911i
$845$	2.98063e8			0.494013
$846$	3.98371e8	−	3.06635e8i	0.657925	−	0.506419i
$847$			1.89997e8i			0.312677i
$848$	4.94617e8	+	2.81608e8i	0.811113	+	0.461804i
$849$	6.02796e8			0.985025
$850$	9.70567e8	+	1.26093e9i	1.58041	+	2.05322i
$851$			6.12357e7i			0.0993611i
$852$	4.18321e8	−	1.58022e9i	0.676380	−	2.55504i
$853$	−3.84998e8			−0.620314			−0.310157	−	0.950685i	$-0.600382\pi$
$853$	−3.84998e8			−0.620314			−0.310157	+	0.950685i	$0.600382\pi$
$854$	−6.53230e7	+	5.02806e7i	−0.104880	+	0.0807285i
$855$			5.25010e8i			0.839980i
$856$	1.87705e7	+	4.47433e7i	0.0299265	+	0.0713356i
$857$	−9.53981e8			−1.51564			−0.757822	−	0.652461i	$-0.773736\pi$
$857$	−9.53981e8			−1.51564			−0.757822	+	0.652461i	$0.773736\pi$
$858$	1.33840e9	+	1.73881e9i	2.11897	+	2.75290i
$859$			1.31911e8i			0.208113i	0.994571	+	0.104057i	$0.0331823\pi$
$859$			1.31911e8i			0.208113i	−0.994571	+	0.104057i	$0.966818\pi$
$860$	−8.22319e8	−	2.17687e8i	−1.29284	−	0.342246i
$861$	2.13036e8			0.333768
$862$	3.85755e8	−	2.96924e8i	0.602268	−	0.463579i
$863$			1.85669e8i			0.288872i	0.989514	+	0.144436i	$0.0461368\pi$
$863$			1.85669e8i			0.288872i	−0.989514	+	0.144436i	$0.953863\pi$
$864$	−1.17767e9	+	1.64073e8i	−1.82592	+	0.254388i
$865$	1.81060e8			0.279753
$866$	−1.79640e8	−	2.33383e8i	−0.276599	−	0.359349i
$867$		−	4.77276e8i		−	0.732339i
$868$	−6.56727e6	+	2.48080e7i	−0.0100421	+	0.0379344i
$869$	8.12830e8			1.23863
$870$	2.29890e8	−	1.76951e8i	0.349110	−	0.268718i
$871$			3.98555e8i			0.603161i
$872$	1.73198e8	−	7.26593e7i	0.261212	−	0.109583i
$873$	7.64283e8			1.14871
$874$	−1.02442e7	−	1.33089e7i	−0.0153441	−	0.0199346i
$875$		−	2.09544e8i		−	0.312789i
$876$	−5.85220e8	−	1.54922e8i	−0.870577	−	0.230462i
$877$	−1.34408e9			−1.99263			−0.996315	−	0.0857664i	$-0.972666\pi$
$877$	−1.34408e9			−1.99263			−0.996315	+	0.0857664i	$0.972666\pi$
$878$	7.62034e8	−	5.86555e8i	1.12588	−	0.866613i
$879$		−	1.04515e9i		−	1.53891i
$880$	−1.05665e9	+	1.85591e9i	−1.55055	+	2.72338i
$881$	1.91138e8			0.279523			0.139762	−	0.990185i	$-0.455366\pi$
$881$	1.91138e8			0.279523			0.139762	+	0.990185i	$0.455366\pi$
$882$	8.40757e8	+	1.09229e9i	1.22536	+	1.59195i
$883$		−	7.49483e8i		−	1.08863i	−0.838881	−	0.544314i	$-0.816790\pi$
$883$		−	7.49483e8i		−	1.08863i	0.838881	−	0.544314i	$-0.183210\pi$
$884$	2.37997e8	−	8.99038e8i	0.344520	−	1.30143i
$885$	2.89405e9			4.17519
$886$	1.24375e8	−	9.57339e7i	0.178826	−	0.137646i
$887$			2.28983e8i			0.328120i	0.986450	+	0.164060i	$0.0524591\pi$
$887$			2.28983e8i			0.328120i	−0.986450	+	0.164060i	$0.947541\pi$
$888$	−4.29014e8	−	1.02264e9i	−0.612679	−	1.46044i
$889$	2.66602e7			0.0379453
$890$	−1.79975e8	−	2.33818e8i	−0.255294	−	0.331671i
$891$		−	1.45225e9i		−	2.05309i
$892$	1.91770e8	+	5.07660e7i	0.270200	+	0.0715284i
$893$	−6.60119e7			−0.0926975
$894$	−1.24482e9	+	9.58166e8i	−1.74218	+	1.34100i
$895$			1.76693e9i			2.46462i
$896$	−1.29018e7	+	1.06677e8i	−0.0179360	+	0.148302i
$897$	1.56324e8			0.216595
$898$	1.40706e8	+	1.82801e8i	0.194305	+	0.252435i
$899$		−	2.69991e7i		−	0.0371595i
$900$	8.33793e8	−	3.14967e9i	1.14375	−	4.32054i
$901$	8.13237e8			1.11184
$902$	1.30749e9	−	1.00640e9i	1.78163	−	1.37136i
$903$		−	1.44287e8i		−	0.195959i
$904$	3.58729e8	−	1.50493e8i	0.485580	−	0.203709i
$905$	5.60496e8			0.756183
$906$	−6.08752e8	−	7.90872e8i	−0.818569	−	1.06346i
$907$			1.36745e9i			1.83269i	0.400387	+	0.916346i	$0.368876\pi$
$907$			1.36745e9i			1.83269i	−0.400387	+	0.916346i	$0.631124\pi$
$908$	−4.97007e8	−	1.31569e8i	−0.663903	−	0.175751i
$909$	−3.45543e8			−0.460055
$910$	−1.79640e8	+	1.38273e8i	−0.238385	+	0.183490i
$911$			1.62708e8i			0.215206i	0.994194	+	0.107603i	$0.0343175\pi$
$911$			1.62708e8i			0.215206i	−0.994194	+	0.107603i	$0.965682\pi$
$912$	2.64319e8	+	1.50489e8i	0.348453	+	0.198391i
$913$	−6.40708e8			−0.841875
$914$	8.43808e8	+	1.09625e9i	1.10511	+	1.43572i
$915$		−	2.11379e9i		−	2.75930i
$916$	−2.98413e8	+	1.12726e9i	−0.388268	+	1.46669i
$917$	−4.71178e7			−0.0611050
$918$	−1.34630e9	+	1.03628e9i	−1.74026	+	1.33951i
$919$			9.10502e8i			1.17310i	0.809914	+	0.586549i	$0.199514\pi$
$919$			9.10502e8i			1.17310i	−0.809914	+	0.586549i	$0.800486\pi$
$920$	5.88584e7	+	1.40301e8i	0.0755867	+	0.180176i
$921$	−9.83289e8			−1.25864
$922$	6.91982e8	+	8.99002e8i	0.882880	+	1.14701i
$923$		−	1.34387e9i		−	1.70904i
$924$	−3.50185e8	−	9.27022e7i	−0.443896	−	0.117510i
$925$	1.55991e9			1.97094
$926$	4.84616e8	−	3.73019e8i	0.610330	−	0.469784i
$927$			6.21209e8i			0.779828i
$928$	−1.55996e7	−	1.11969e8i	−0.0195195	−	0.140105i
$929$	−6.04931e7			−0.0754499			−0.0377250	−	0.999288i	$-0.512011\pi$
$929$	−6.04931e7			−0.0754499			−0.0377250	+	0.999288i	$0.512011\pi$
$930$	−4.01381e8	−	5.21463e8i	−0.499009	−	0.648298i
$931$		−	1.80997e8i		−	0.224296i
$932$	2.08967e8	−	7.89379e8i	0.258125	−	0.975075i
$933$	2.18785e8			0.269384
$934$	−9.58413e8	+	7.37712e8i	−1.17628	+	0.905412i
$935$			3.05144e9i			3.73310i
$936$	−1.75602e9	+	7.36679e8i	−2.14142	+	0.898360i
$937$	−7.45493e8			−0.906201			−0.453100	−	0.891459i	$-0.649682\pi$
$937$	−7.45493e8			−0.906201			−0.453100	+	0.891459i	$0.649682\pi$
$938$	−4.01331e7	−	5.21397e7i	−0.0486289	−	0.0631772i
$939$			2.65392e9i			3.20546i
$940$	5.78094e8	+	1.53035e8i	0.696010	+	0.184250i
$941$	4.32809e8			0.519430			0.259715	−	0.965685i	$-0.416371\pi$
$941$	4.32809e8			0.519430			0.259715	+	0.965685i	$0.416371\pi$
$942$	−1.71874e9	+	1.32295e9i	−2.05616	+	1.58267i
$943$		−	1.17547e8i		−	0.140176i
$944$	5.57995e8	−	9.80063e8i	0.663307	−	1.16503i
$945$	4.14123e8			0.490721
$946$	−6.81625e8	−	8.85546e8i	−0.805141	−	1.04601i
$947$			6.16017e8i			0.725342i	0.931917	+	0.362671i	$0.118135\pi$
$947$			6.16017e8i			0.725342i	−0.931917	+	0.362671i	$0.881865\pi$
$948$	−2.68375e8	+	1.01379e9i	−0.315004	+	1.18994i
$949$	−4.97691e8			−0.582319
$950$	−3.39029e8	+	2.60958e8i	−0.395426	+	0.304369i
$951$			2.70423e8i			0.314414i
$952$	5.93949e7	+	1.41579e8i	0.0688396	+	0.164093i
$953$	1.36034e9			1.57170			0.785850	−	0.618417i	$-0.212226\pi$
$953$	1.36034e9			1.57170			0.785850	+	0.618417i	$0.212226\pi$
$954$	−1.01569e9	−	1.31955e9i	−1.16981	−	1.51978i
$955$		−	8.25283e8i		−	0.947530i
$956$	1.02605e9	+	2.71620e8i	1.17434	+	0.310877i
$957$	3.81114e8			0.434829
$958$	4.66655e8	−	3.59195e8i	0.530762	−	0.408539i
$959$		−	1.78321e8i		−	0.202184i
$960$	−1.96588e9	−	1.93067e9i	−2.22199	−	2.18220i
$961$	8.26261e8			0.930995
$962$	−5.56104e8	−	7.22473e8i	−0.624641	−	0.811515i
$963$		−	1.41957e8i		−	0.158956i
$964$	−1.45710e8	+	5.50422e8i	−0.162651	+	0.614419i
$965$	2.86255e9			3.18545
$966$	−2.04506e7	+	1.57413e7i	−0.0226869	+	0.0174626i
$967$		−	1.58799e9i		−	1.75617i	−0.478502	−	0.878086i	$-0.658820\pi$
$967$		−	1.58799e9i		−	1.75617i	0.478502	−	0.878086i	$-0.341180\pi$
$968$	−1.75074e9	+	7.34462e8i	−1.93017	+	0.809736i
$969$	4.34588e8			0.477646
$970$	5.54544e8	+	7.20447e8i	0.607604	+	0.789381i
$971$		−	8.52937e8i		−	0.931664i	−0.884873	−	0.465832i	$-0.845755\pi$
$971$		−	8.52937e8i		−	0.931664i	0.884873	−	0.465832i	$-0.154245\pi$
$972$	1.74683e8	+	4.62428e7i	0.190218	+	0.0503553i
$973$	−1.39256e8			−0.151174
$974$	−1.40140e8	+	1.07869e8i	−0.151665	+	0.116740i
$975$		−	3.98217e9i		−	4.29641i
$976$	−7.15829e8	−	4.07555e8i	−0.769945	−	0.438366i
$977$	1.11916e9			1.20007			0.600036	−	0.799973i	$-0.295153\pi$
$977$	1.11916e9			1.20007			0.600036	+	0.799973i	$0.295153\pi$
$978$	1.35693e9	+	1.76288e9i	1.45057	+	1.88454i
$979$		−	3.87625e8i		−	0.413108i
$980$	−4.19605e8	+	1.58507e9i	−0.445823	+	1.68411i
$981$	−5.49503e8			−0.582053
$982$	−5.90665e8	+	4.54648e8i	−0.623744	+	0.480110i
$983$		−	1.24153e9i		−	1.30706i	−0.756899	−	0.653532i	$-0.773287\pi$
$983$		−	1.24153e9i		−	1.30706i	0.756899	−	0.653532i	$-0.226713\pi$
$984$	8.23525e8	+	1.96303e9i	0.864353	+	2.06036i
$985$	−4.60116e8			−0.481458
$986$	−9.85258e7	−	1.28002e8i	−0.102783	−	0.133532i
$987$			1.01435e8i			0.105496i
$988$	2.41726e8	+	6.39905e7i	0.250641	+	0.0663506i
$989$	−7.96130e7			−0.0822991
$990$	4.95125e9	−	3.81109e9i	5.10281	−	3.92775i
$991$			8.29506e8i			0.852312i	0.904650	+	0.426156i	$0.140133\pi$
$991$			8.29506e8i			0.852312i	−0.904650	+	0.426156i	$0.859867\pi$
$992$	−2.53981e8	+	3.53848e7i	−0.260176	+	0.0362478i
$993$	2.90077e9			2.96254
$994$	1.35323e8	+	1.75807e8i	0.137788	+	0.179010i
$995$			3.08176e9i			3.12845i
$996$	2.11545e8	−	7.99115e8i	0.214104	−	0.808781i
$997$	2.77319e8			0.279830			0.139915	−	0.990163i	$-0.455317\pi$
$997$	2.77319e8			0.279830			0.139915	+	0.990163i	$0.455317\pi$
$998$	−1.70752e8	+	1.31432e8i	−0.171781	+	0.132223i
$999$			1.66552e9i			1.67052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.7.b.a.39.17	✓	54
4.3	odd	2	inner	76.7.b.a.39.18	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.7.b.a.39.17	✓	54	1.1	even	1	trivial
76.7.b.a.39.18	yes	54	4.3	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.87964 - 6.33949i) q^{2} -47.1905i q^{3} +(-16.3782 + 61.8689i) q^{4} +222.735 q^{5} +(-299.163 + 230.273i) q^{6} -51.2381i q^{7} +(472.136 - 198.069i) q^{8} -1497.94 q^{9} +O(q^{10})\)	\(q+(-4.87964 - 6.33949i) q^{2} -47.1905i q^{3} +(-16.3782 + 61.8689i) q^{4} +222.735 q^{5} +(-299.163 + 230.273i) q^{6} -51.2381i q^{7} +(472.136 - 198.069i) q^{8} -1497.94 q^{9} +(-1086.87 - 1412.03i) q^{10} -2340.87i q^{11} +(2919.62 + 772.893i) q^{12} +2482.94 q^{13} +(-324.823 + 250.024i) q^{14} -10511.0i q^{15} +(-3559.51 - 2026.60i) q^{16} -5852.47 q^{17} +(7309.42 + 9496.18i) q^{18} -1573.56i q^{19} +(-3647.99 + 13780.4i) q^{20} -2417.95 q^{21} +(-14839.9 + 11422.6i) q^{22} +1334.15i q^{23} +(-9346.97 - 22280.3i) q^{24} +33985.9 q^{25} +(-12115.9 - 15740.6i) q^{26} +36286.7i q^{27} +(3170.05 + 839.186i) q^{28} -3450.03 q^{29} +(-66634.2 + 51289.8i) q^{30} +7825.76i q^{31} +(4521.58 + 32454.5i) q^{32} -110467. q^{33} +(28558.0 + 37101.6i) q^{34} -11412.5i q^{35} +(24533.5 - 92676.0i) q^{36} +45898.8 q^{37} +(-9975.58 + 7678.42i) q^{38} -117171. i q^{39} +(105161. - 44116.9i) q^{40} -88106.1 q^{41} +(11798.7 + 15328.6i) q^{42} +59673.3i q^{43} +(144827. + 38339.1i) q^{44} -333644. q^{45} +(8457.81 - 6510.17i) q^{46} -41950.6i q^{47} +(-95636.0 + 167975. i) q^{48} +115024. q^{49} +(-165839. - 215453. i) q^{50} +276181. i q^{51} +(-40666.0 + 153617. i) q^{52} -138956. q^{53} +(230039. - 177066. i) q^{54} -521394. i q^{55} +(-10148.7 - 24191.4i) q^{56} -74257.2 q^{57} +(16834.9 + 21871.4i) q^{58} +275336. i q^{59} +(650302. + 172150. i) q^{60} +201103. q^{61} +(49611.3 - 38186.9i) q^{62} +76751.8i q^{63} +(183681. - 187031. i) q^{64} +553038. q^{65} +(539039. + 700303. i) q^{66} +160517. i q^{67} +(95852.6 - 362086. i) q^{68} +62959.1 q^{69} +(-72349.6 + 55689.1i) q^{70} -541240. i q^{71} +(-707233. + 296696. i) q^{72} -200444. q^{73} +(-223970. - 290975. i) q^{74} -1.60381e6i q^{75} +(97354.5 + 25772.0i) q^{76} -119942. q^{77} +(-742806. + 571754. i) q^{78} +347234. i q^{79} +(-792828. - 451394. i) q^{80} +620389. q^{81} +(429926. + 558547. i) q^{82} -273705. i q^{83} +(39601.6 - 149596. i) q^{84} -1.30355e6 q^{85} +(378298. - 291184. i) q^{86} +162809. i q^{87} +(-463654. - 1.10521e6i) q^{88} +165590. q^{89} +(1.62806e6 + 2.11513e6i) q^{90} -127221. i q^{91} +(-82542.2 - 21850.9i) q^{92} +369301. q^{93} +(-265945. + 204704. i) q^{94} -350487. i q^{95} +(1.53155e6 - 213376. i) q^{96} -510222. q^{97} +(-561274. - 729191. i) q^{98} +3.50649e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9}+O(q^{10}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9	\( 54 q - 10 q^{2} + 90 q^{4} - 44 q^{5} - 510 q^{6} + 440 q^{8} - 13122 q^{9} - 2088 q^{10} - 2384 q^{12} - 828 q^{13} + 4116 q^{14} - 7782 q^{16} + 12220 q^{17} + 15790 q^{18} - 7000 q^{20} - 16048 q^{21} - 51864 q^{22} + 19294 q^{24} + 218346 q^{25} - 18110 q^{26} + 97926 q^{28} - 101996 q^{29} + 50076 q^{30} - 235160 q^{32} + 9072 q^{33} - 51156 q^{34} - 48028 q^{36} - 63420 q^{37} + 157260 q^{40} - 135700 q^{41} + 302290 q^{42} + 137784 q^{44} - 50348 q^{45} - 177084 q^{46} + 111320 q^{48} - 1099338 q^{49} + 485770 q^{50} + 232980 q^{52} + 892932 q^{53} - 730010 q^{54} - 298644 q^{56} - 702534 q^{58} + 1231628 q^{60} + 323700 q^{61} + 1573116 q^{62} - 1065942 q^{64} + 587512 q^{65} - 74604 q^{66} - 1235974 q^{68} + 217376 q^{69} + 1163796 q^{70} - 1228320 q^{72} - 739428 q^{73} - 1852264 q^{74} - 563144 q^{77} - 2516852 q^{78} - 1597436 q^{80} + 4660886 q^{81} - 919236 q^{82} + 4928476 q^{84} - 737904 q^{85} - 1444124 q^{86} + 2679960 q^{88} - 3415940 q^{89} + 4702636 q^{90} - 3230670 q^{92} - 5021584 q^{93} + 1881960 q^{94} + 1838870 q^{96} + 3483660 q^{97} - 3419858 q^{98}+O(q^{100}) \) 54 * q - 10 * q^2 + 90 * q^4 - 44 * q^5 - 510 * q^6 + 440 * q^8 - 13122 * q^9 - 2088 * q^10 - 2384 * q^12 - 828 * q^13 + 4116 * q^14 - 7782 * q^16 + 12220 * q^17 + 15790 * q^18 - 7000 * q^20 - 16048 * q^21 - 51864 * q^22 + 19294 * q^24 + 218346 * q^25 - 18110 * q^26 + 97926 * q^28 - 101996 * q^29 + 50076 * q^30 - 235160 * q^32 + 9072 * q^33 - 51156 * q^34 - 48028 * q^36 - 63420 * q^37 + 157260 * q^40 - 135700 * q^41 + 302290 * q^42 + 137784 * q^44 - 50348 * q^45 - 177084 * q^46 + 111320 * q^48 - 1099338 * q^49 + 485770 * q^50 + 232980 * q^52 + 892932 * q^53 - 730010 * q^54 - 298644 * q^56 - 702534 * q^58 + 1231628 * q^60 + 323700 * q^61 + 1573116 * q^62 - 1065942 * q^64 + 587512 * q^65 - 74604 * q^66 - 1235974 * q^68 + 217376 * q^69 + 1163796 * q^70 - 1228320 * q^72 - 739428 * q^73 - 1852264 * q^74 - 563144 * q^77 - 2516852 * q^78 - 1597436 * q^80 + 4660886 * q^81 - 919236 * q^82 + 4928476 * q^84 - 737904 * q^85 - 1444124 * q^86 + 2679960 * q^88 - 3415940 * q^89 + 4702636 * q^90 - 3230670 * q^92 - 5021584 * q^93 + 1881960 * q^94 + 1838870 * q^96 + 3483660 * q^97 - 3419858 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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