LMFDB - Embedded newform 40.8.d.a.21.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [40,8,Mod(21,40)] 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("40.21"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	40.d (of order $2$, degree $1$, 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:	$12.4954010194$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.10
Character	$\chi$	$=$	40.21
Dual form			40.8.d.a.21.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.11309 + 9.51999i) q^{2} +28.9351i q^{3} +(-53.2604 - 116.393i) q^{4} -125.000i q^{5} +(-275.462 - 176.883i) q^{6} +724.987 q^{7} +(1433.65 + 204.483i) q^{8} +1349.76 q^{9} +(1190.00 + 764.136i) q^{10} +635.952i q^{11} +(3367.84 - 1541.09i) q^{12} -4193.99i q^{13} +(-4431.91 + 6901.87i) q^{14} +3616.88 q^{15} +(-10710.7 + 12398.3i) q^{16} +2743.22 q^{17} +(-8251.21 + 12849.7i) q^{18} +40390.6i q^{19} +(-14549.1 + 6657.54i) q^{20} +20977.5i q^{21} +(-6054.26 - 3887.63i) q^{22} +47823.7 q^{23} +(-5916.72 + 41482.6i) q^{24} -15625.0 q^{25} +(39926.7 + 25638.2i) q^{26} +102336. i q^{27} +(-38613.1 - 84383.4i) q^{28} +121799. i q^{29} +(-22110.3 + 34432.7i) q^{30} +172575. q^{31} +(-52556.1 - 177757. i) q^{32} -18401.3 q^{33} +(-16769.5 + 26115.4i) q^{34} -90623.4i q^{35} +(-71888.8 - 157103. i) q^{36} -116482. i q^{37} +(-384518. - 246911. i) q^{38} +121353. q^{39} +(25560.3 - 179206. i) q^{40} +653497. q^{41} +(-199706. - 128238. i) q^{42} -277478. i q^{43} +(74020.4 - 33871.0i) q^{44} -168720. i q^{45} +(-292350. + 455281. i) q^{46} +884726. q^{47} +(-358745. - 309914. i) q^{48} -297937. q^{49} +(95517.0 - 148750. i) q^{50} +79375.2i q^{51} +(-488151. + 223373. i) q^{52} +568686. i q^{53} +(-974242. - 625592. i) q^{54} +79494.0 q^{55} +(1.03937e6 + 148247. i) q^{56} -1.16870e6 q^{57} +(-1.15952e6 - 744566. i) q^{58} -1.63412e6i q^{59} +(-192637. - 420980. i) q^{60} +2.45255e6i q^{61} +(-1.05497e6 + 1.64292e6i) q^{62} +978559. q^{63} +(2.01353e6 + 586311. i) q^{64} -524249. q^{65} +(112489. - 175180. i) q^{66} +838798. i q^{67} +(-146105. - 319291. i) q^{68} +1.38378e6i q^{69} +(862733. + 553988. i) q^{70} +4.53571e6 q^{71} +(1.93508e6 + 276003. i) q^{72} -2.64056e6 q^{73} +(1.10891e6 + 712066. i) q^{74} -452110. i q^{75} +(4.70118e6 - 2.15122e6i) q^{76} +461057. i q^{77} +(-741844. + 1.15528e6i) q^{78} -3.79614e6 q^{79} +(1.54978e6 + 1.33883e6i) q^{80} -9183.73 q^{81} +(-3.99488e6 + 6.22129e6i) q^{82} -4.04075e6i q^{83} +(2.44164e6 - 1.11727e6i) q^{84} -342902. i q^{85} +(2.64159e6 + 1.69625e6i) q^{86} -3.52426e6 q^{87} +(-130041. + 911730. i) q^{88} -1.18628e7 q^{89} +(1.60621e6 + 1.03140e6i) q^{90} -3.04059e6i q^{91} +(-2.54711e6 - 5.56634e6i) q^{92} +4.99348e6i q^{93} +(-5.40840e6 + 8.42258e6i) q^{94} +5.04882e6 q^{95} +(5.14341e6 - 1.52071e6i) q^{96} -1.28038e7 q^{97} +(1.82131e6 - 2.83636e6i) q^{98} +858384. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 14 q^{2} - 208 q^{4} - 228 q^{6} + 1372 q^{7} - 2024 q^{8} - 20412 q^{9} - 3250 q^{10} - 2788 q^{12} - 26620 q^{14} - 13500 q^{15} - 48824 q^{16} + 126562 q^{18} + 20500 q^{20} - 113892 q^{22} + 2588 q^{23}+ \cdots + 11064654 q^{98}+O(q^{100}) $ 28 * q - 14 * q^2 - 208 * q^4 - 228 * q^6 + 1372 * q^7 - 2024 * q^8 - 20412 * q^9 - 3250 * q^10 - 2788 * q^12 - 26620 * q^14 - 13500 * q^15 - 48824 * q^16 + 126562 * q^18 + 20500 * q^20 - 113892 * q^22 + 2588 * q^23 - 312408 * q^24 - 437500 * q^25 + 325932 * q^26 + 482476 * q^28 - 239000 * q^30 + 268024 * q^31 - 1445944 * q^32 - 99016 * q^33 + 651372 * q^34 + 1544216 * q^36 - 443660 * q^38 - 283944 * q^39 - 533000 * q^40 - 601208 * q^41 + 2692532 * q^42 + 239528 * q^44 - 142196 * q^46 - 2076460 * q^47 - 1158872 * q^48 + 4316268 * q^49 + 218750 * q^50 + 1591040 * q^52 + 4926168 * q^54 + 1331000 * q^55 + 2368232 * q^56 + 3788536 * q^57 - 5872008 * q^58 + 435500 * q^60 + 4008592 * q^62 - 14839060 * q^63 + 10179584 * q^64 - 9178320 * q^66 - 11198568 * q^68 - 2491000 * q^70 - 1001656 * q^71 - 8674904 * q^72 + 2534128 * q^73 - 21884804 * q^74 - 13848304 * q^76 + 25352888 * q^78 - 22040096 * q^79 - 7560000 * q^80 + 11166300 * q^81 + 20089464 * q^82 - 38088296 * q^84 + 17672012 * q^86 + 34127184 * q^87 + 11943152 * q^88 + 3807224 * q^89 + 13443750 * q^90 + 31988508 * q^92 + 17925028 * q^94 - 13718000 * q^95 - 30275488 * q^96 + 15198608 * q^97 + 11064654 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−6.11309	+	9.51999i	−0.540326	+	0.841456i
$2$	−6.11309	+	9.51999i	−0.540326	+	0.841456i
$3$			28.9351i			0.618729i	0.950944	+	0.309364i	$0.100116\pi$
$3$			28.9351i			0.618729i	−0.950944	+	0.309364i	$0.899884\pi$
$4$	−53.2604	−	116.393i	−0.416097	−	0.909320i
$5$		−	125.000i		−	0.447214i
$5$		−	125.000i		−	0.447214i
$6$	−275.462	−	176.883i	−0.520633	−	0.334315i
$7$	724.987			0.798890			0.399445	−	0.916757i	$-0.369203\pi$
$7$	724.987			0.798890			0.399445	+	0.916757i	$0.369203\pi$
$8$	1433.65	+	204.483i	0.989981	+	0.141202i
$9$	1349.76			0.617175
$10$	1190.00	+	764.136i	0.376311	+	0.241641i
$11$			635.952i			0.144062i	0.997402	+	0.0720311i	$0.0229481\pi$
$11$			635.952i			0.144062i	−0.997402	+	0.0720311i	$0.977052\pi$
$12$	3367.84	−	1541.09i	0.562623	−	0.257451i
$13$		−	4193.99i		−	0.529451i	−0.964324	−	0.264725i	$-0.914719\pi$
$13$		−	4193.99i		−	0.529451i	0.964324	−	0.264725i	$-0.0852813\pi$
$14$	−4431.91	+	6901.87i	−0.431661	+	0.672231i
$15$	3616.88			0.276704
$16$	−10710.7	+	12398.3i	−0.653727	+	0.756730i
$17$	2743.22			0.135422			0.0677110	−	0.997705i	$-0.478430\pi$
$17$	2743.22			0.135422			0.0677110	+	0.997705i	$0.478430\pi$
$18$	−8251.21	+	12849.7i	−0.333475	+	0.519326i
$19$			40390.6i			1.35096i	0.737378	+	0.675480i	$0.236064\pi$
$19$			40390.6i			1.35096i	−0.737378	+	0.675480i	$0.763936\pi$
$20$	−14549.1	+	6657.54i	−0.406660	+	0.186084i
$21$			20977.5i			0.494296i
$22$	−6054.26	−	3887.63i	−0.121222	−	0.0778405i
$23$	47823.7			0.819588			0.409794	−	0.912178i	$-0.365601\pi$
$23$	47823.7			0.819588			0.409794	+	0.912178i	$0.365601\pi$
$24$	−5916.72	+	41482.6i	−0.0873658	+	0.612529i
$25$	−15625.0			−0.200000
$26$	39926.7	+	25638.2i	0.445509	+	0.286076i
$27$			102336.i			1.00059i
$28$	−38613.1	−	84383.4i	−0.332415	−	0.726447i
$29$			121799.i			0.927363i	0.886002	+	0.463682i	$0.153472\pi$
$29$			121799.i			0.927363i	−0.886002	+	0.463682i	$0.846528\pi$
$30$	−22110.3	+	34432.7i	−0.149510	+	0.232834i
$31$	172575.			1.04043			0.520215	−	0.854035i	$-0.325852\pi$
$31$	172575.			1.04043			0.520215	+	0.854035i	$0.325852\pi$
$32$	−52556.1	−	177757.i	−0.283530	−	0.958964i
$33$	−18401.3			−0.0891354
$34$	−16769.5	+	26115.4i	−0.0731719	+	0.113952i
$35$		−	90623.4i		−	0.357274i
$36$	−71888.8	−	157103.i	−0.256804	−	0.561210i
$37$		−	116482.i		−	0.378054i	−0.981972	−	0.189027i	$-0.939467\pi$
$37$		−	116482.i		−	0.378054i	0.981972	−	0.189027i	$-0.0605333\pi$
$38$	−384518.	−	246911.i	−1.13677	−	0.729958i
$39$	121353.			0.327586
$40$	25560.3	−	179206.i	0.0631475	−	0.442733i
$41$	653497.			1.48081			0.740407	−	0.672159i	$-0.234633\pi$
$41$	653497.			1.48081			0.740407	+	0.672159i	$0.234633\pi$
$42$	−199706.	−	128238.i	−0.415928	−	0.267081i
$43$		−	277478.i		−	0.532218i	−0.963943	−	0.266109i	$-0.914262\pi$
$43$		−	277478.i		−	0.532218i	0.963943	−	0.266109i	$-0.0857381\pi$
$44$	74020.4	−	33871.0i	0.130999	−	0.0599438i
$45$		−	168720.i		−	0.276009i
$46$	−292350.	+	455281.i	−0.442844	+	0.689647i
$47$	884726.			1.24299			0.621493	−	0.783420i	$-0.286526\pi$
$47$	884726.			1.24299			0.621493	+	0.783420i	$0.286526\pi$
$48$	−358745.	−	309914.i	−0.468211	−	0.404480i
$49$	−297937.			−0.361775
$50$	95517.0	−	148750.i	0.108065	−	0.168291i
$51$			79375.2i			0.0837894i
$52$	−488151.	+	223373.i	−0.481440	+	0.220303i
$53$			568686.i			0.524695i	0.964973	+	0.262347i	$0.0844966\pi$
$53$			568686.i			0.524695i	−0.964973	+	0.262347i	$0.915503\pi$
$54$	−974242.	−	625592.i	−0.841954	−	0.540646i
$55$	79494.0			0.0644266
$56$	1.03937e6	+	148247.i	0.790886	+	0.112805i
$57$	−1.16870e6			−0.835877
$58$	−1.15952e6	−	744566.i	−0.780335	−	0.501078i
$59$		−	1.63412e6i		−	1.03586i	−0.855422	−	0.517932i	$-0.826702\pi$
$59$		−	1.63412e6i		−	1.03586i	0.855422	−	0.517932i	$-0.173298\pi$
$60$	−192637.	−	420980.i	−0.115135	−	0.251612i
$61$			2.45255e6i			1.38345i	0.722162	+	0.691724i	$0.243148\pi$
$61$			2.45255e6i			1.38345i	−0.722162	+	0.691724i	$0.756852\pi$
$62$	−1.05497e6	+	1.64292e6i	−0.562171	+	0.875476i
$63$	978559.			0.493055
$64$	2.01353e6	+	586311.i	0.960124	+	0.279575i
$65$	−524249.			−0.236778
$66$	112489.	−	175180.i	0.0481621	−	0.0750035i
$67$			838798.i			0.340718i	0.985382	+	0.170359i	$0.0544928\pi$
$67$			838798.i			0.340718i	−0.985382	+	0.170359i	$0.945507\pi$
$68$	−146105.	−	319291.i	−0.0563486	−	0.123142i
$69$			1.38378e6i			0.507102i
$70$	862733.	+	553988.i	0.300631	+	0.193045i
$71$	4.53571e6			1.50398			0.751988	−	0.659177i	$-0.229095\pi$
$71$	4.53571e6			1.50398			0.751988	+	0.659177i	$0.229095\pi$
$72$	1.93508e6	+	276003.i	0.610991	+	0.0871464i
$73$	−2.64056e6			−0.794450			−0.397225	−	0.917721i	$-0.630027\pi$
$73$	−2.64056e6			−0.794450			−0.397225	+	0.917721i	$0.630027\pi$
$74$	1.10891e6	+	712066.i	0.318116	+	0.204272i
$75$		−	452110.i		−	0.123746i
$76$	4.70118e6	−	2.15122e6i	1.22846	−	0.562130i
$77$			461057.i			0.115090i
$78$	−741844.	+	1.15528e6i	−0.177003	+	0.275649i
$79$	−3.79614e6			−0.866258			−0.433129	−	0.901332i	$-0.642591\pi$
$79$	−3.79614e6			−0.866258			−0.433129	+	0.901332i	$0.642591\pi$
$80$	1.54978e6	+	1.33883e6i	0.338420	+	0.292356i
$81$	−9183.73			−0.00192009
$82$	−3.99488e6	+	6.22129e6i	−0.800121	+	1.24604i
$83$		−	4.04075e6i		−	0.775692i	−0.921724	−	0.387846i	$-0.873219\pi$
$83$		−	4.04075e6i		−	0.775692i	0.921724	−	0.387846i	$-0.126781\pi$
$84$	2.44164e6	−	1.11727e6i	0.449474	−	0.205675i
$85$		−	342902.i		−	0.0605625i
$86$	2.64159e6	+	1.69625e6i	0.447838	+	0.287571i
$87$	−3.52426e6			−0.573786
$88$	−130041.	+	911730.i	−0.0203419	+	0.142619i
$89$	−1.18628e7			−1.78370			−0.891848	−	0.452334i	$-0.850591\pi$
$89$	−1.18628e7			−1.78370			−0.891848	+	0.452334i	$0.850591\pi$
$90$	1.60621e6	+	1.03140e6i	0.232249	+	0.149135i
$91$		−	3.04059e6i		−	0.422973i
$92$	−2.54711e6	−	5.56634e6i	−0.341028	−	0.745268i
$93$			4.99348e6i			0.643744i
$94$	−5.40840e6	+	8.42258e6i	−0.671617	+	1.04592i
$95$	5.04882e6			0.604168
$96$	5.14341e6	−	1.52071e6i	0.593338	−	0.175428i
$97$	−1.28038e7			−1.42442			−0.712208	−	0.701968i	$-0.752305\pi$
$97$	−1.28038e7			−1.42442			−0.712208	+	0.701968i	$0.752305\pi$
$98$	1.82131e6	−	2.83636e6i	0.195476	−	0.304418i
$99$			858384.i			0.0889116i
$100$	832193.	+	1.81864e6i	0.0832193	+	0.181864i
$101$		−	1.63109e7i		−	1.57526i	−0.616149	−	0.787629i	$-0.711308\pi$
$101$		−	1.63109e7i		−	1.57526i	0.616149	−	0.787629i	$-0.288692\pi$
$102$	−755651.	−	485227.i	−0.0705051	−	0.0452736i
$103$	1.26057e7			1.13668			0.568338	−	0.822795i	$-0.307587\pi$
$103$	1.26057e7			1.13668			0.568338	+	0.822795i	$0.307587\pi$
$104$	857598.	−	6.01269e6i	0.0747596	−	0.524146i
$105$	2.62219e6			0.221056
$106$	−5.41388e6	−	3.47642e6i	−0.441508	−	0.283506i
$107$		−	1.75324e7i		−	1.38356i	−0.722107	−	0.691782i	$-0.756826\pi$
$107$		−	1.75324e7i		−	1.38356i	0.722107	−	0.691782i	$-0.243174\pi$
$108$	1.19112e7	−	5.45048e6i	0.909859	−	0.416343i
$109$			7.43018e6i			0.549549i	0.961509	+	0.274775i	$0.0886032\pi$
$109$			7.43018e6i			0.549549i	−0.961509	+	0.274775i	$0.911397\pi$
$110$	−485954.	+	756782.i	−0.0348113	+	0.0542121i
$111$	3.37042e6			0.233913
$112$	−7.76509e6	+	8.98858e6i	−0.522256	+	0.604544i
$113$	−1.74971e7			−1.14075			−0.570375	−	0.821384i	$-0.693202\pi$
$113$	−1.74971e7			−1.14075			−0.570375	+	0.821384i	$0.693202\pi$
$114$	7.14439e6	−	1.11261e7i	0.451646	−	0.703354i
$115$		−	5.97796e6i		−	0.366531i
$116$	1.41765e7	−	6.48704e6i	0.843270	−	0.385873i
$117$		−	5.66088e6i		−	0.326764i
$118$	1.55568e7	+	9.98953e6i	0.871633	+	0.559703i
$119$	1.98880e6			0.108187
$120$	5.18533e6	+	739590.i	0.273931	+	0.0390712i
$121$	1.90827e7			0.979246
$122$	−2.33482e7	−	1.49926e7i	−1.16411	−	0.747512i
$123$			1.89090e7i			0.916221i
$124$	−9.19143e6	−	2.00866e7i	−0.432919	−	0.946085i
$125$			1.95312e6i			0.0894427i
$126$	−5.98202e6	+	9.31587e6i	−0.266410	+	0.414884i
$127$	−1.71199e7			−0.741632			−0.370816	−	0.928706i	$-0.620922\pi$
$127$	−1.71199e7			−0.741632			−0.370816	+	0.928706i	$0.620922\pi$
$128$	−1.78905e7	+	1.55846e7i	−0.754029	+	0.656841i
$129$	8.02886e6			0.329298
$130$	3.20478e6	−	4.99084e6i	0.127937	−	0.199238i
$131$			9.54213e6i			0.370848i	0.982659	+	0.185424i	$0.0593658\pi$
$131$			9.54213e6i			0.370848i	−0.982659	+	0.185424i	$0.940634\pi$
$132$	980061.	+	2.14178e6i	0.0370889	+	0.0810526i
$133$			2.92826e7i			1.07927i
$134$	−7.98535e6	−	5.12764e6i	−0.286699	−	0.184099i
$135$	1.27921e7			0.447478
$136$	3.93280e6	+	560940.i	0.134065	+	0.0191219i
$137$	3.76038e7			1.24942			0.624712	−	0.780855i	$-0.285216\pi$
$137$	3.76038e7			1.24942			0.624712	+	0.780855i	$0.285216\pi$
$138$	−1.31736e7	−	8.45917e6i	−0.426704	−	0.274000i
$139$			3.55473e7i			1.12268i	0.827586	+	0.561339i	$0.189714\pi$
$139$			3.55473e7i			1.12268i	−0.827586	+	0.561339i	$0.810286\pi$
$140$	−1.05479e7	+	4.82663e6i	−0.324877	+	0.148661i
$141$			2.55996e7i			0.769071i
$142$	−2.77272e7	+	4.31799e7i	−0.812636	+	1.26553i
$143$	2.66718e6			0.0762738
$144$	−1.44569e7	+	1.67347e7i	−0.403464	+	0.467035i
$145$	1.52248e7			0.414729
$146$	1.61420e7	−	2.51381e7i	0.429262	−	0.668495i
$147$		−	8.62083e6i		−	0.223840i
$148$	−1.35577e7	+	6.20388e6i	−0.343772	+	0.157307i
$149$			2.55870e7i			0.633677i	0.948479	+	0.316839i	$0.102621\pi$
$149$			2.55870e7i			0.633677i	−0.948479	+	0.316839i	$0.897379\pi$
$150$	4.30409e6	+	2.76379e6i	0.104127	+	0.0668630i
$151$	−8.75969e6			−0.207047			−0.103524	−	0.994627i	$-0.533012\pi$
$151$	−8.75969e6			−0.207047			−0.103524	+	0.994627i	$0.533012\pi$
$152$	−8.25917e6	+	5.79058e7i	−0.190758	+	1.33742i
$153$	3.70269e6			0.0835790
$154$	−4.38926e6	−	2.81848e6i	−0.0968430	−	0.0621860i
$155$		−	2.15719e7i		−	0.465295i
$156$	−6.46332e6	−	1.41247e7i	−0.136308	−	0.297881i
$157$		−	4.82895e7i		−	0.995873i	−0.867213	−	0.497937i	$-0.834091\pi$
$157$		−	4.82895e7i		−	0.995873i	0.867213	−	0.497937i	$-0.165909\pi$
$158$	2.32061e7	−	3.61392e7i	0.468061	−	0.728918i
$159$	−1.64550e7			−0.324644
$160$	−2.22196e7	+	6.56951e6i	−0.428862	+	0.126798i
$161$	3.46715e7			0.654760
$162$	56140.9	−	87429.0i	0.00103747	−	0.00161567i
$163$		−	1.65945e7i		−	0.300129i	−0.988676	−	0.150064i	$-0.952052\pi$
$163$		−	1.65945e7i		−	0.300129i	0.988676	−	0.150064i	$-0.0479481\pi$
$164$	−3.48055e7	−	7.60625e7i	−0.616161	−	1.34653i
$165$			2.30016e6i			0.0398625i
$166$	3.84679e7	+	2.47015e7i	0.652710	+	0.419126i
$167$	3.75161e7			0.623319			0.311660	−	0.950194i	$-0.399115\pi$
$167$	3.75161e7			0.623319			0.311660	+	0.950194i	$0.399115\pi$
$168$	−4.28954e6	+	3.00744e7i	−0.0697957	+	0.489344i
$169$	4.51590e7			0.719682
$170$	3.26443e6	+	2.09619e6i	0.0509607	+	0.0327235i
$171$			5.45177e7i			0.833779i
$172$	−3.22965e7	+	1.47786e7i	−0.483957	+	0.221454i
$173$		−	1.02982e8i		−	1.51217i	−0.654476	−	0.756083i	$-0.727111\pi$
$173$		−	1.02982e8i		−	1.51217i	0.654476	−	0.756083i	$-0.272889\pi$
$174$	2.15441e7	−	3.35509e7i	0.310031	−	0.482816i
$175$	−1.13279e7			−0.159778
$176$	−7.88470e6	−	6.81147e6i	−0.109016	−	0.0941774i
$177$	4.72834e7			0.640918
$178$	7.25181e7	−	1.12933e8i	0.963777	−	1.50090i
$179$			5.26588e7i			0.686255i	0.939289	+	0.343127i	$0.111486\pi$
$179$			5.26588e7i			0.686255i	−0.939289	+	0.343127i	$0.888514\pi$
$180$	−1.96379e7	+	8.98610e6i	−0.250981	+	0.114846i
$181$		−	6.39330e7i		−	0.801402i	−0.916209	−	0.400701i	$-0.868767\pi$
$181$		−	6.39330e7i		−	0.801402i	0.916209	−	0.400701i	$-0.131233\pi$
$182$	2.89463e7	+	1.85874e7i	0.355913	+	0.228543i
$183$	−7.09646e7			−0.855978
$184$	6.85622e7	+	9.77911e6i	0.811376	+	0.115728i
$185$	−1.45603e7			−0.169071
$186$	−4.75379e7	−	3.05256e7i	−0.541682	−	0.347831i
$187$			1.74455e6i			0.0195092i
$188$	−4.71208e7	−	1.02976e8i	−0.517202	−	1.13027i
$189$			7.41926e7i			0.799363i
$190$	−3.08639e7	+	4.80647e7i	−0.326447	+	0.508381i
$191$	−1.29743e8			−1.34730			−0.673652	−	0.739049i	$-0.735275\pi$
$191$	−1.29743e8			−1.34730			−0.673652	+	0.739049i	$0.735275\pi$
$192$	−1.69650e7	+	5.82615e7i	−0.172981	+	0.594056i
$193$	−1.11020e8			−1.11160			−0.555802	−	0.831315i	$-0.687589\pi$
$193$	−1.11020e8			−1.11160			−0.555802	+	0.831315i	$0.687589\pi$
$194$	7.82706e7	−	1.21892e8i	0.769649	−	1.19858i
$195$		−	1.51692e7i		−	0.146501i
$196$	1.58682e7	+	3.46778e7i	0.150533	+	0.328969i
$197$		−	1.82291e8i		−	1.69877i	−0.527774	−	0.849385i	$-0.676973\pi$
$197$		−	1.82291e8i		−	1.69877i	0.527774	−	0.849385i	$-0.323027\pi$
$198$	−8.17180e6	−	5.24737e6i	−0.0748152	−	0.0480412i
$199$	−1.49332e8			−1.34328			−0.671640	−	0.740878i	$-0.734410\pi$
$199$	−1.49332e8			−1.34328			−0.671640	+	0.740878i	$0.734410\pi$
$200$	−2.24007e7	−	3.19504e6i	−0.197996	−	0.0282404i
$201$	−2.42707e7			−0.210812
$202$	1.55279e8	+	9.97097e7i	1.32551	+	0.851153i
$203$			8.83025e7i			0.740861i
$204$	9.23872e6	−	4.22755e6i	0.0761914	−	0.0348645i
$205$		−	8.16871e7i		−	0.662240i
$206$	−7.70597e7	+	1.20006e8i	−0.614175	+	0.956462i
$207$	6.45505e7			0.505829
$208$	5.19982e7	+	4.49204e7i	0.400651	+	0.346116i
$209$	−2.56865e7			−0.194622
$210$	−1.60297e7	+	2.49632e7i	−0.119442	+	0.186009i
$211$			3.06835e7i			0.224862i	0.993660	+	0.112431i	$0.0358637\pi$
$211$			3.06835e7i			0.224862i	−0.993660	+	0.112431i	$0.964136\pi$
$212$	6.61910e7	−	3.02884e7i	0.477116	−	0.218324i
$213$			1.31241e8i			0.930552i
$214$	1.66909e8	+	1.07177e8i	1.16421	+	0.747575i
$215$	−3.46848e7			−0.238015
$216$	−2.09260e7	+	1.46714e8i	−0.141286	+	0.990567i
$217$	1.25115e8			0.831189
$218$	−7.07352e7	−	4.54213e7i	−0.462421	−	0.296935i
$219$		−	7.64049e7i		−	0.491549i
$220$	−4.23388e6	−	9.25255e6i	−0.0268077	−	0.0585844i
$221$		−	1.15050e7i		−	0.0716992i
$222$	−2.06037e7	+	3.20864e7i	−0.126389	+	0.196827i
$223$	7.89432e7			0.476703			0.238351	−	0.971179i	$-0.423393\pi$
$223$	7.89432e7			0.476703			0.238351	+	0.971179i	$0.423393\pi$
$224$	−3.81025e7	−	1.28872e8i	−0.226509	−	0.766106i
$225$	−2.10900e7			−0.123435
$226$	1.06961e8	−	1.66572e8i	0.616377	−	0.959892i
$227$		−	2.00872e8i		−	1.13980i	−0.821714	−	0.569900i	$-0.806982\pi$
$227$		−	2.00872e8i		−	1.13980i	0.821714	−	0.569900i	$-0.193018\pi$
$228$	6.22456e7	+	1.36029e8i	0.347806	+	0.760081i
$229$			2.38925e8i			1.31473i	0.753572	+	0.657365i	$0.228329\pi$
$229$			2.38925e8i			1.31473i	−0.753572	+	0.657365i	$0.771671\pi$
$230$	5.69101e7	+	3.65438e7i	0.308420	+	0.198046i
$231$	−1.33407e7			−0.0712094
$232$	−2.49057e7	+	1.74616e8i	−0.130946	+	0.918072i
$233$	1.13633e8			0.588519			0.294259	−	0.955726i	$-0.404927\pi$
$233$	1.13633e8			0.588519			0.294259	+	0.955726i	$0.404927\pi$
$234$	5.38916e7	+	3.46055e7i	0.274957	+	0.176559i
$235$		−	1.10591e8i		−	0.555880i
$236$	−1.90200e8	+	8.70339e7i	−0.941932	+	0.431019i
$237$		−	1.09842e8i		−	0.535979i
$238$	−1.21577e7	+	1.89333e7i	−0.0584563	+	0.0910348i
$239$	−1.48286e8			−0.702599			−0.351299	−	0.936263i	$-0.614260\pi$
$239$	−1.48286e8			−0.702599			−0.351299	+	0.936263i	$0.614260\pi$
$240$	−3.87392e7	+	4.48431e7i	−0.180889	+	0.209390i
$241$	−3.54688e8			−1.63225			−0.816126	−	0.577875i	$-0.803882\pi$
$241$	−3.54688e8			−1.63225			−0.816126	+	0.577875i	$0.803882\pi$
$242$	−1.16654e8	+	1.81667e8i	−0.529112	+	0.823993i
$243$			2.23544e8i			0.999404i
$244$	2.85459e8	−	1.30623e8i	1.25800	−	0.575648i
$245$			3.72421e7i			0.161791i
$246$	−1.80013e8	−	1.15592e8i	−0.770960	−	0.495058i
$247$	1.69398e8			0.715267
$248$	2.47412e8	+	3.52887e7i	1.03001	+	0.146911i
$249$	1.16920e8			0.479943
$250$	−1.85937e7	−	1.19396e7i	−0.0752621	−	0.0483282i
$251$			1.33392e8i			0.532443i	0.963912	+	0.266221i	$0.0857753\pi$
$251$			1.33392e8i			0.532443i	−0.963912	+	0.266221i	$0.914225\pi$
$252$	−5.21184e7	−	1.13897e8i	−0.205158	−	0.448345i
$253$			3.04136e7i			0.118072i
$254$	1.04656e8	−	1.62981e8i	0.400723	−	0.624051i
$255$	9.92190e6			0.0374718
$256$	−3.89986e7	−	2.65587e8i	−0.145281	−	0.989390i
$257$	5.09013e7			0.187052			0.0935261	−	0.995617i	$-0.470186\pi$
$257$	5.09013e7			0.187052			0.0935261	+	0.995617i	$0.470186\pi$
$258$	−4.90811e7	+	7.64346e7i	−0.177928	+	0.277090i
$259$		−	8.44481e7i		−	0.302023i
$260$	2.79217e7	+	6.10189e7i	0.0985223	+	0.215307i
$261$			1.64399e8i			0.572345i
$262$	−9.08410e7	−	5.83319e7i	−0.312052	−	0.200379i
$263$	1.65767e8			0.561892			0.280946	−	0.959724i	$-0.409352\pi$
$263$	1.65767e8			0.561892			0.280946	+	0.959724i	$0.409352\pi$
$264$	−2.63810e7	−	3.76275e6i	−0.0882423	−	0.0125861i
$265$	7.10857e7			0.234651
$266$	−2.78770e8	−	1.79007e8i	−0.908157	−	0.583156i
$267$		−	3.43250e8i		−	1.10362i
$268$	9.76302e7	−	4.46747e7i	0.309822	−	0.141772i
$269$			3.34898e8i			1.04901i	0.851407	+	0.524505i	$0.175750\pi$
$269$			3.34898e8i			1.04901i	−0.851407	+	0.524505i	$0.824250\pi$
$270$	−7.81989e7	+	1.21780e8i	−0.241784	+	0.376533i
$271$	1.88305e8			0.574736			0.287368	−	0.957820i	$-0.407220\pi$
$271$	1.88305e8			0.574736			0.287368	+	0.957820i	$0.407220\pi$
$272$	−2.93817e7	+	3.40111e7i	−0.0885290	+	0.102478i
$273$	8.79796e7			0.261705
$274$	−2.29875e8	+	3.57988e8i	−0.675096	+	1.05134i
$275$		−	9.93675e6i		−	0.0288124i
$276$	1.61062e8	−	7.37007e7i	0.461119	−	0.211004i
$277$		−	7.27368e7i		−	0.205625i	−0.994701	−	0.102812i	$-0.967216\pi$
$277$		−	7.27368e7i		−	0.205625i	0.994701	−	0.102812i	$-0.0327841\pi$
$278$	−3.38410e8	−	2.17304e8i	−0.944684	−	0.606612i
$279$	2.32936e8			0.642128
$280$	1.85309e7	−	1.29922e8i	0.0504479	−	0.353695i
$281$	−2.87068e8			−0.771814			−0.385907	−	0.922538i	$-0.626112\pi$
$281$	−2.87068e8			−0.771814			−0.385907	+	0.922538i	$0.626112\pi$
$282$	−2.43708e8	−	1.56493e8i	−0.647139	−	0.415549i
$283$			4.41650e8i			1.15831i	0.815216	+	0.579157i	$0.196618\pi$
$283$			4.41650e8i			1.15831i	−0.815216	+	0.579157i	$0.803382\pi$
$284$	−2.41573e8	−	5.27925e8i	−0.625799	−	1.36760i
$285$			1.46088e8i			0.373816i
$286$	−1.63047e7	+	2.53915e7i	−0.0412127	+	0.0641811i
$287$	4.73777e8			1.18301
$288$	−7.09382e7	−	2.39930e8i	−0.174987	−	0.591848i
$289$	−4.02813e8			−0.981661
$290$	−9.30708e7	+	1.44940e8i	−0.224089	+	0.348977i
$291$		−	3.70478e8i		−	0.881327i
$292$	1.40637e8	+	3.07343e8i	0.330568	+	0.722410i
$293$		−	5.90905e8i		−	1.37240i	−0.727412	−	0.686201i	$-0.759277\pi$
$293$		−	5.90905e8i		−	1.37240i	0.727412	−	0.686201i	$-0.240723\pi$
$294$	8.20702e7	+	5.26999e7i	0.188352	+	0.120947i
$295$	−2.04265e8			−0.463252
$296$	2.38186e7	−	1.66994e8i	0.0533820	−	0.374266i
$297$	−6.50811e7			−0.144147
$298$	−2.43588e8	−	1.56416e8i	−0.533212	−	0.342392i
$299$		−	2.00572e8i		−	0.433931i
$300$	−5.26225e7	+	2.40796e7i	−0.112525	+	0.0514902i
$301$		−	2.01168e8i		−	0.425184i
$302$	5.35487e7	−	8.33921e7i	0.111873	−	0.174221i
$303$	4.71956e8			0.974658
$304$	−5.00773e8	−	4.32610e8i	−1.02231	−	0.883159i
$305$	3.06568e8			0.618696
$306$	−2.26349e7	+	3.52496e7i	−0.0451599	+	0.0703281i
$307$		−	1.33591e8i		−	0.263507i	−0.991282	−	0.131754i	$-0.957939\pi$
$307$		−	1.33591e8i		−	0.263507i	0.991282	−	0.131754i	$-0.0420608\pi$
$308$	5.36638e7	−	2.45560e7i	0.104654	−	0.0478885i
$309$			3.64747e8i			0.703294i
$310$	2.05364e8	+	1.31871e8i	0.391525	+	0.251411i
$311$	7.26451e8			1.36945			0.684723	−	0.728804i	$-0.259923\pi$
$311$	7.26451e8			1.36945			0.684723	+	0.728804i	$0.259923\pi$
$312$	1.73978e8	+	2.48146e7i	0.324304	+	0.0462559i
$313$	−5.86492e8			−1.08108			−0.540539	−	0.841319i	$-0.681780\pi$
$313$	−5.86492e8			−1.08108			−0.540539	+	0.841319i	$0.681780\pi$
$314$	4.59716e8	+	2.95198e8i	0.837984	+	0.538096i
$315$		−	1.22320e8i		−	0.220501i
$316$	2.02184e8	+	4.41844e8i	0.360447	+	0.787706i
$317$			5.45883e8i			0.962482i	0.876588	+	0.481241i	$0.159814\pi$
$317$			5.45883e8i			0.962482i	−0.876588	+	0.481241i	$0.840186\pi$
$318$	1.00591e8	−	1.56651e8i	0.175413	−	0.273173i
$319$	−7.74581e7			−0.133598
$320$	7.32889e7	−	2.51691e8i	0.125030	−	0.429380i
$321$	5.07302e8			0.856050
$322$	−2.11950e8	+	3.30073e8i	−0.353784	+	0.550952i
$323$			1.10800e8i			0.182950i
$324$	489129.	+	1.06892e6i	0.000798943	+	0.00174598i
$325$			6.55311e7i			0.105890i
$326$	1.57979e8	+	1.01444e8i	0.252545	+	0.162167i
$327$	−2.14993e8			−0.340022
$328$	9.36883e8	+	1.33629e8i	1.46598	+	0.209094i
$329$	6.41414e8			0.993009
$330$	−2.18975e7	−	1.40611e7i	−0.0335426	−	0.0215388i
$331$			2.19781e8i			0.333114i	0.986032	+	0.166557i	$0.0532650\pi$
$331$			2.19781e8i			0.333114i	−0.986032	+	0.166557i	$0.946735\pi$
$332$	−4.70316e8	+	2.15212e8i	−0.705352	+	0.322763i
$333$		−	1.57223e8i		−	0.233325i
$334$	−2.29339e8	+	3.57153e8i	−0.336795	+	0.524496i
$335$	1.04850e8			0.152374
$336$	−2.60085e8	−	2.24684e8i	−0.374049	−	0.323135i
$337$	−1.17733e9			−1.67568			−0.837842	−	0.545913i	$-0.816183\pi$
$337$	−1.17733e9			−1.67568			−0.837842	+	0.545913i	$0.816183\pi$
$338$	−2.76061e8	+	4.29913e8i	−0.388863	+	0.605581i
$339$		−	5.06279e8i		−	0.705815i
$340$	−3.99114e7	+	1.82631e7i	−0.0550708	+	0.0251999i
$341$			1.09750e8i			0.149887i
$342$	−5.19007e8	−	3.33271e8i	−0.701588	−	0.450512i
$343$	−8.13058e8			−1.08791
$344$	5.67395e7	−	3.97805e8i	0.0751503	−	0.526885i
$345$	1.72973e8			0.226783
$346$	9.80387e8	+	6.29537e8i	1.27242	+	0.817062i
$347$			1.26996e9i			1.63169i	0.578270	+	0.815846i	$0.303728\pi$
$347$			1.26996e9i			1.63169i	−0.578270	+	0.815846i	$0.696272\pi$
$348$	1.87703e8	+	4.10199e8i	0.238750	+	0.521755i
$349$			4.38281e8i			0.551904i	0.961171	+	0.275952i	$0.0889931\pi$
$349$			4.38281e8i			0.551904i	−0.961171	+	0.275952i	$0.911007\pi$
$350$	6.92485e7	−	1.07842e8i	0.0863321	−	0.134446i
$351$	4.29198e8			0.529764
$352$	1.13045e8	−	3.34232e7i	0.138150	−	0.0408459i
$353$	−7.38394e8			−0.893463			−0.446731	−	0.894668i	$-0.647412\pi$
$353$	−7.38394e8			−0.893463			−0.446731	+	0.894668i	$0.647412\pi$
$354$	−2.89048e8	+	4.50138e8i	−0.346304	+	0.539304i
$355$		−	5.66963e8i		−	0.672598i
$356$	6.31815e8	+	1.38074e9i	0.742190	+	1.62195i
$357$			5.75460e7i			0.0669385i
$358$	−5.01311e8	−	3.21908e8i	−0.577453	−	0.370801i
$359$	−1.04520e9			−1.19225			−0.596127	−	0.802890i	$-0.703295\pi$
$359$	−1.04520e9			−1.19225			−0.596127	+	0.802890i	$0.703295\pi$
$360$	3.45003e7	−	2.41885e8i	0.0389731	−	0.273244i
$361$	−7.37527e8			−0.825093
$362$	6.08642e8	+	3.90828e8i	0.674345	+	0.433018i
$363$			5.52160e8i			0.605888i
$364$	−3.53903e8	+	1.61943e8i	−0.384618	+	0.175998i
$365$			3.30070e8i			0.355289i
$366$	4.33813e8	−	6.75582e8i	0.462507	−	0.720268i
$367$	−1.52124e9			−1.60644			−0.803222	−	0.595680i	$-0.796882\pi$
$367$	−1.52124e9			−1.60644			−0.803222	+	0.595680i	$0.796882\pi$
$368$	−5.12223e8	+	5.92931e8i	−0.535787	+	0.620207i
$369$	8.82065e8			0.913921
$370$	8.90082e7	−	1.38614e8i	0.0913533	−	0.142266i
$371$			4.12290e8i			0.419173i
$372$	5.81206e8	−	2.65955e8i	0.585370	−	0.267860i
$373$		−	1.71513e9i		−	1.71126i	−0.517587	−	0.855631i	$-0.673170\pi$
$373$		−	1.71513e9i		−	1.71126i	0.517587	−	0.855631i	$-0.326830\pi$
$374$	−1.66081e7	−	1.06646e7i	−0.0164161	−	0.0105413i
$375$	−5.65138e7			−0.0553408
$376$	1.26838e9	+	1.80911e8i	1.23053	+	0.175512i
$377$	5.10823e8			0.490993
$378$	−7.06313e8	−	4.53546e8i	−0.672629	−	0.431916i
$379$		−	1.49965e9i		−	1.41498i	−0.706721	−	0.707492i	$-0.749826\pi$
$379$		−	1.49965e9i		−	1.41498i	0.706721	−	0.707492i	$-0.250174\pi$
$380$	−2.68902e8	−	5.87648e8i	−0.251392	−	0.549382i
$381$		−	4.95366e8i		−	0.458869i
$382$	7.93127e8	−	1.23515e9i	0.727983	−	1.13370i
$383$	125718.			0.000114341			5.71705e−5	−	1.00000i	$-0.499982\pi$
$383$	125718.			0.000114341			5.71705e−5		1.00000i	$0.499982\pi$
$384$	−4.50941e8	−	5.17664e8i	−0.406406	−	0.466540i
$385$	5.76321e7			0.0514697
$386$	6.78674e8	−	1.05691e9i	0.600628	−	0.935366i
$387$		−	3.74530e8i		−	0.328472i
$388$	6.81934e8	+	1.49027e9i	0.592695	+	1.29525i
$389$			8.21407e8i			0.707513i	0.935338	+	0.353757i	$0.115096\pi$
$389$			8.21407e8i			0.707513i	−0.935338	+	0.353757i	$0.884904\pi$
$390$	1.44410e8	+	9.27304e7i	0.123274	+	0.0791583i
$391$	1.31191e8			0.110990
$392$	−4.27136e8	−	6.09229e7i	−0.358150	−	0.0510834i
$393$	−2.76102e8			−0.229454
$394$	1.73541e9	+	1.11436e9i	1.42944	+	0.917889i
$395$			4.74517e8i			0.387402i
$396$	9.99099e7	−	4.57178e7i	0.0808491	−	0.0369958i
$397$		−	9.97785e8i		−	0.800332i	−0.916443	−	0.400166i	$-0.868952\pi$
$397$		−	9.97785e8i		−	0.800332i	0.916443	−	0.400166i	$-0.131048\pi$
$398$	9.12878e8	−	1.42164e9i	0.725808	−	1.13031i
$399$	−8.47295e8			−0.667774
$400$	1.67354e8	−	1.93723e8i	0.130745	−	0.151346i
$401$	1.81089e9			1.40245			0.701225	−	0.712940i	$-0.252637\pi$
$401$	1.81089e9			1.40245			0.701225	+	0.712940i	$0.252637\pi$
$402$	1.48369e8	−	2.31057e8i	0.113907	−	0.177389i
$403$		−	7.23779e8i		−	0.550857i
$404$	−1.89847e9	+	8.68722e8i	−1.43242	+	0.655460i
$405$			1.14797e6i			0.000858690i
$406$	−8.40639e8	−	5.39801e8i	−0.623402	−	0.400306i
$407$	7.40771e7			0.0544632
$408$	−1.62308e7	+	1.13796e8i	−0.0118312	+	0.0829499i
$409$	7.95530e8			0.574943			0.287472	−	0.957789i	$-0.407185\pi$
$409$	7.95530e8			0.574943			0.287472	+	0.957789i	$0.407185\pi$
$410$	7.77661e8	+	4.99361e8i	0.557246	+	0.357825i
$411$			1.08807e9i			0.773055i
$412$	−6.71384e8	−	1.46721e9i	−0.472967	−	1.03360i
$413$		−	1.18472e9i		−	0.827541i
$414$	−3.94603e8	+	6.14520e8i	−0.273312	+	0.425633i
$415$	−5.05094e8			−0.346900
$416$	−7.45511e8	+	2.20420e8i	−0.507724	+	0.150115i
$417$	−1.02856e9			−0.694633
$418$	1.57024e8	−	2.44535e8i	0.105159	−	0.163766i
$419$		−	2.70680e9i		−	1.79765i	−0.438303	−	0.898827i	$-0.644420\pi$
$419$		−	2.70680e9i		−	1.79765i	0.438303	−	0.898827i	$-0.355580\pi$
$420$	−1.39659e8	−	3.05205e8i	−0.0919806	−	0.201011i
$421$		−	1.90994e9i		−	1.24748i	−0.781633	−	0.623739i	$-0.785613\pi$
$421$		−	1.90994e9i		−	1.24748i	0.781633	−	0.623739i	$-0.214387\pi$
$422$	−2.92106e8	−	1.87571e8i	−0.189211	−	0.121499i
$423$	1.19417e9			0.767140
$424$	−1.16286e8	+	8.15294e8i	−0.0740881	+	0.519438i
$425$	−4.28628e7			−0.0270844
$426$	−1.24941e9	−	8.02287e8i	−0.783019	−	0.502801i
$427$			1.77806e9i			1.10522i
$428$	−2.04065e9	+	9.33784e8i	−1.25810	+	0.575696i
$429$			7.71749e7i			0.0471928i
$430$	2.12031e8	−	3.30199e8i	0.128606	−	0.200279i
$431$	−1.23043e9			−0.740266			−0.370133	−	0.928979i	$-0.620688\pi$
$431$	−1.23043e9			−0.740266			−0.370133	+	0.928979i	$0.620688\pi$
$432$	−1.26879e9	−	1.09609e9i	−0.757178	−	0.654115i
$433$	1.30549e9			0.772799			0.386399	−	0.922332i	$-0.373719\pi$
$433$	1.30549e9			0.772799			0.386399	+	0.922332i	$0.373719\pi$
$434$	−7.64838e8	+	1.19109e9i	−0.449113	+	0.699409i
$435$			4.40532e8i			0.256605i
$436$	8.64821e8	−	3.95734e8i	0.499716	−	0.228665i
$437$			1.93163e9i			1.10723i
$438$	7.27374e8	+	4.67070e8i	0.413617	+	0.265597i
$439$	−1.03574e9			−0.584283			−0.292142	−	0.956375i	$-0.594368\pi$
$439$	−1.03574e9			−0.584283			−0.292142	+	0.956375i	$0.594368\pi$
$440$	1.13966e8	+	1.62551e7i	0.0637810	+	0.00909717i
$441$	−4.02144e8			−0.223278
$442$	1.09528e8	+	7.03312e7i	0.0603318	+	0.0387409i
$443$			3.39339e9i			1.85448i	0.374473	+	0.927238i	$0.377824\pi$
$443$			3.39339e9i			1.85448i	−0.374473	+	0.927238i	$0.622176\pi$
$444$	−1.79510e8	−	3.92294e8i	−0.0973303	−	0.212702i
$445$			1.48285e9i			0.797693i
$446$	−4.82586e8	+	7.51538e8i	−0.257575	+	0.401124i
$447$	−7.40363e8			−0.392074
$448$	1.45978e9	+	4.25068e8i	0.767033	+	0.223350i
$449$	3.03655e9			1.58314			0.791569	−	0.611080i	$-0.209265\pi$
$449$	3.03655e9			1.58314			0.791569	+	0.611080i	$0.209265\pi$
$450$	1.28925e8	−	2.00777e8i	0.0666951	−	0.103865i
$451$			4.15593e8i			0.213329i
$452$	9.31900e8	+	2.03654e9i	0.474662	+	1.03731i
$453$		−	2.53462e8i		−	0.128106i
$454$	1.91230e9	+	1.22795e9i	0.959092	+	0.615863i
$455$	−3.80073e8			−0.189159
$456$	−1.67551e9	−	2.38980e8i	−0.827503	−	0.118028i
$457$	1.73227e8			0.0849001			0.0424500	−	0.999099i	$-0.486484\pi$
$457$	1.73227e8			0.0849001			0.0424500	+	0.999099i	$0.486484\pi$
$458$	−2.27456e9	−	1.46057e9i	−1.10629	−	0.710382i
$459$			2.80731e8i			0.135502i
$460$	−6.95793e8	+	3.18388e8i	−0.333294	+	0.152512i
$461$		−	1.70634e9i		−	0.811171i	−0.914057	−	0.405586i	$-0.867068\pi$
$461$		−	1.70634e9i		−	0.811171i	0.914057	−	0.405586i	$-0.132932\pi$
$462$	8.15529e7	−	1.27003e8i	0.0384762	−	0.0599195i
$463$	3.50776e9			1.64247			0.821233	−	0.570593i	$-0.193286\pi$
$463$	3.50776e9			1.64247			0.821233	+	0.570593i	$0.193286\pi$
$464$	−1.51009e9	−	1.30455e9i	−0.701764	−	0.606243i
$465$	6.24185e8			0.287891
$466$	−6.94651e8	+	1.08179e9i	−0.317992	+	0.495213i
$467$			3.55199e9i			1.61385i	0.590655	+	0.806924i	$0.298870\pi$
$467$			3.55199e9i			1.61385i	−0.590655	+	0.806924i	$0.701130\pi$
$468$	−6.58887e8	+	3.01501e8i	−0.297133	+	0.135965i
$469$			6.08117e8i			0.272196i
$470$	1.05282e9	+	6.76051e8i	0.467749	+	0.300356i
$471$	1.39726e9			0.616175
$472$	3.34149e8	−	2.34275e9i	0.146266	−	1.02548i
$473$	1.76463e8			0.0766725
$474$	1.04569e9	+	6.71471e8i	0.451002	+	0.289603i
$475$		−	6.31103e8i		−	0.270192i
$476$	−1.05924e8	−	2.31482e8i	−0.0450163	−	0.0983769i
$477$			7.67590e8i			0.323829i
$478$	9.06485e8	−	1.41168e9i	0.379632	−	0.591206i
$479$	−9.68267e8			−0.402551			−0.201276	−	0.979535i	$-0.564509\pi$
$479$	−9.68267e8			−0.402551			−0.201276	+	0.979535i	$0.564509\pi$
$480$	−1.90089e8	−	6.42927e8i	−0.0784537	−	0.265349i
$481$	−4.88525e8			−0.200161
$482$	2.16824e9	−	3.37663e9i	0.881947	−	1.37347i
$483$			1.00322e9i			0.405119i
$484$	−1.01635e9	−	2.22110e9i	−0.407461	−	0.890449i
$485$			1.60047e9i			0.637019i
$486$	−2.12814e9	−	1.36654e9i	−0.840955	−	0.540004i
$487$	8.60336e8			0.337533			0.168767	−	0.985656i	$-0.446022\pi$
$487$	8.60336e8			0.337533			0.168767	+	0.985656i	$0.446022\pi$
$488$	−5.01503e8	+	3.51608e9i	−0.195346	+	1.36959i
$489$	4.80163e8			0.185698
$490$	−3.54545e8	−	2.27664e8i	−0.136140	−	0.0874196i
$491$			1.00221e9i			0.382097i	0.981581	+	0.191048i	$0.0611888\pi$
$491$			1.00221e9i			0.382097i	−0.981581	+	0.191048i	$0.938811\pi$
$492$	2.20087e9	−	1.00710e9i	0.833139	−	0.381236i
$493$			3.34120e8i			0.125585i
$494$	−1.03554e9	+	1.61266e9i	−0.386477	+	0.601865i
$495$	1.07298e8			0.0397625
$496$	−1.84840e9	+	2.13964e9i	−0.680158	+	0.787325i
$497$	3.28833e9			1.20151
$498$	−7.14739e8	+	1.11307e9i	−0.259325	+	0.403851i
$499$		−	5.40650e9i		−	1.94789i	−0.226788	−	0.973944i	$-0.572822\pi$
$499$		−	5.40650e9i		−	1.94789i	0.226788	−	0.973944i	$-0.427178\pi$
$500$	2.27330e8	−	1.04024e8i	0.0813321	−	0.0372168i
$501$			1.08553e9i			0.385665i
$502$	−1.26989e9	−	8.15439e8i	−0.448027	−	0.287693i
$503$	2.06071e9			0.721986			0.360993	−	0.932569i	$-0.382438\pi$
$503$	2.06071e9			0.721986			0.360993	+	0.932569i	$0.382438\pi$
$504$	1.40291e9	+	2.00098e8i	0.488115	+	0.0696204i
$505$	−2.03886e9			−0.704477
$506$	−2.89537e8	−	1.85921e8i	−0.0993520	−	0.0637971i
$507$			1.30668e9i			0.445288i
$508$	9.11813e8	+	1.99264e9i	0.308591	+	0.674381i
$509$		−	2.77559e9i		−	0.932917i	−0.884543	−	0.466459i	$-0.845530\pi$
$509$		−	2.77559e9i		−	0.932917i	0.884543	−	0.466459i	$-0.154470\pi$
$510$	−6.06534e7	+	9.44564e7i	−0.0202470	+	0.0315308i
$511$	−1.91437e9			−0.634678
$512$	2.76679e9	+	1.25229e9i	0.911028	+	0.412345i
$513$	−4.13343e9			−1.35176
$514$	−3.11164e8	+	4.84580e8i	−0.101069	+	0.157396i
$515$		−	1.57571e9i		−	0.508337i
$516$	−4.27620e8	−	9.34503e8i	−0.137020	−	0.299438i
$517$			5.62643e8i			0.179067i
$518$	8.03945e8	+	5.16238e8i	0.254139	+	0.163191i
$519$	2.97979e9			0.935621
$520$	−7.51587e8	−	1.07200e8i	−0.234405	−	0.0334335i
$521$	−2.62973e9			−0.814666			−0.407333	−	0.913280i	$-0.633541\pi$
$521$	−2.62973e9			−0.814666			−0.407333	+	0.913280i	$0.633541\pi$
$522$	−1.56508e9	−	1.00499e9i	−0.481603	−	0.309253i
$523$		−	2.10802e9i		−	0.644347i	−0.946681	−	0.322173i	$-0.895587\pi$
$523$		−	2.10802e9i		−	0.644347i	0.946681	−	0.322173i	$-0.104413\pi$
$524$	1.11064e9	−	5.08217e8i	0.337220	−	0.154309i
$525$		−	3.27774e8i		−	0.0988592i
$526$	−1.01335e9	+	1.57810e9i	−0.303605	+	0.472808i
$527$	4.73412e8			0.140897
$528$	1.97090e8	−	2.28144e8i	0.0582702	−	0.0674514i
$529$	−1.11772e9			−0.328276
$530$	−4.34553e8	+	6.76735e8i	−0.126788	+	0.197448i
$531$		−	2.20568e9i		−	0.639309i
$532$	3.40829e9	−	1.55960e9i	0.981401	−	0.449080i
$533$		−	2.74076e9i		−	0.784017i
$534$	3.26774e9	+	2.09832e9i	0.928651	+	0.596316i
$535$	−2.19155e9			−0.618748
$536$	−1.71520e8	+	1.20254e9i	−0.0481102	+	0.337305i
$537$	−1.52369e9			−0.424605
$538$	−3.18823e9	−	2.04726e9i	−0.882696	−	0.566807i
$539$		−	1.89474e8i		−	0.0521180i
$540$	−6.81309e8	−	1.48891e9i	−0.186194	−	0.406901i
$541$			1.57237e9i			0.426936i	0.976950	+	0.213468i	$0.0684760\pi$
$541$			1.57237e9i			0.426936i	−0.976950	+	0.213468i	$0.931524\pi$
$542$	−1.15112e9	+	1.79266e9i	−0.310544	+	0.483615i
$543$	1.84991e9			0.495850
$544$	−1.44173e8	−	4.87627e8i	−0.0383961	−	0.129865i
$545$	9.28772e8			0.245766
$546$	−5.37827e8	+	8.37565e8i	−0.141406	+	0.220214i
$547$		−	7.12156e9i		−	1.86046i	−0.366980	−	0.930229i	$-0.619608\pi$
$547$		−	7.12156e9i		−	1.86046i	0.366980	−	0.930229i	$-0.380392\pi$
$548$	−2.00279e9	−	4.37682e9i	−0.519881	−	1.13613i
$549$			3.31035e9i			0.853829i
$550$	9.45977e7	+	6.07442e7i	0.0242444	+	0.0155681i
$551$	−4.91952e9			−1.25283
$552$	−2.82959e8	+	1.98385e9i	−0.0716040	+	0.502022i
$553$	−2.75215e9			−0.692045
$554$	6.92454e8	+	4.44647e8i	0.173024	+	0.111104i
$555$		−	4.21303e8i		−	0.104609i
$556$	4.13746e9	−	1.89326e9i	1.02087	−	0.467142i
$557$			2.13776e9i			0.524161i	0.965046	+	0.262081i	$0.0844087\pi$
$557$			2.13776e9i			0.524161i	−0.965046	+	0.262081i	$0.915591\pi$
$558$	−1.42396e9	+	2.21754e9i	−0.346958	+	0.540322i
$559$	−1.16374e9			−0.281783
$560$	1.12357e9	+	9.70637e8i	0.270360	+	0.233560i
$561$	−5.04788e7			−0.0120709
$562$	1.75487e9	−	2.73289e9i	0.417031	−	0.649448i
$563$		−	1.62576e9i		−	0.383953i	−0.981400	−	0.191977i	$-0.938510\pi$
$563$		−	1.62576e9i		−	0.383953i	0.981400	−	0.191977i	$-0.0614897\pi$
$564$	2.97961e9	−	1.36344e9i	0.699332	−	0.320008i
$565$			2.18713e9i			0.510159i
$566$	−4.20451e9	−	2.69985e9i	−0.974670	−	0.625867i
$567$	−6.65808e6			−0.00153394
$568$	6.50259e9	+	9.27473e8i	1.48891	+	0.212365i
$569$	2.12335e9			0.483202			0.241601	−	0.970376i	$-0.422327\pi$
$569$	2.12335e9			0.483202			0.241601	+	0.970376i	$0.422327\pi$
$570$	−1.39076e9	−	8.93049e8i	−0.314550	−	0.201982i
$571$			4.99851e9i			1.12361i	0.827271	+	0.561803i	$0.189892\pi$
$571$			4.99851e9i			1.12361i	−0.827271	+	0.561803i	$0.810108\pi$
$572$	−1.42055e8	−	3.10441e8i	−0.0317373	−	0.0693573i
$573$		−	3.75411e9i		−	0.833616i
$574$	−2.89624e9	+	4.51035e9i	−0.639209	+	0.995448i
$575$	−7.47245e8			−0.163918
$576$	2.71778e9	+	7.91380e8i	0.592564	+	0.172547i
$577$	−4.67621e9			−1.01339			−0.506697	−	0.862124i	$-0.669134\pi$
$577$	−4.67621e9			−1.01339			−0.506697	+	0.862124i	$0.669134\pi$
$578$	2.46243e9	−	3.83478e9i	0.530416	−	0.826024i
$579$		−	3.21237e9i		−	0.687781i
$580$	−8.10881e8	−	1.77207e9i	−0.172567	−	0.377122i
$581$		−	2.92949e9i		−	0.619692i
$582$	3.52695e9	+	2.26477e9i	0.741598	+	0.476204i
$583$	−3.61657e8			−0.0755887
$584$	−3.78563e9	−	5.39949e8i	−0.786490	−	0.112178i
$585$	−7.07611e8			−0.146133
$586$	5.62541e9	+	3.61226e9i	1.15482	+	0.741544i
$587$			5.82916e8i			0.118952i	0.998230	+	0.0594761i	$0.0189430\pi$
$587$			5.82916e8i			0.118952i	−0.998230	+	0.0594761i	$0.981057\pi$
$588$	−1.00340e9	+	4.59148e8i	−0.203543	+	0.0931392i
$589$			6.97042e9i			1.40558i
$590$	1.24869e9	−	1.94460e9i	0.250307	−	0.389806i
$591$	5.27462e9			1.05108
$592$	1.44418e9	+	1.24760e9i	0.286085	+	0.247144i
$593$	−3.60198e9			−0.709333			−0.354666	−	0.934993i	$-0.615406\pi$
$593$	−3.60198e9			−0.709333			−0.354666	+	0.934993i	$0.615406\pi$
$594$	3.97846e8	−	6.19571e8i	0.0778866	−	0.121294i
$595$		−	2.48600e8i		−	0.0483828i
$596$	2.97815e9	−	1.36278e9i	0.576216	−	0.263671i
$597$		−	4.32092e9i		−	0.831125i
$598$	1.90944e9	+	1.22611e9i	0.365134	+	0.234464i
$599$	−7.85978e8			−0.149423			−0.0747114	−	0.997205i	$-0.523804\pi$
$599$	−7.85978e8			−0.149423			−0.0747114	+	0.997205i	$0.523804\pi$
$600$	9.24487e7	−	6.48166e8i	0.0174732	−	0.122506i
$601$	−6.82136e9			−1.28177			−0.640885	−	0.767637i	$-0.721433\pi$
$601$	−6.82136e9			−1.28177			−0.640885	+	0.767637i	$0.721433\pi$
$602$	1.91512e9	+	1.22976e9i	0.357773	+	0.229738i
$603$			1.13218e9i			0.210283i
$604$	4.66544e8	+	1.01957e9i	0.0861516	+	0.188272i
$605$		−	2.38534e9i		−	0.437932i
$606$	−2.88511e9	+	4.49301e9i	−0.526632	+	0.820132i
$607$	7.46800e9			1.35533			0.677663	−	0.735373i	$-0.262993\pi$
$607$	7.46800e9			1.35533			0.677663	+	0.735373i	$0.262993\pi$
$608$	7.17971e9	−	2.12277e9i	1.29552	−	0.383037i
$609$	−2.55504e9			−0.458392
$610$	−1.87408e9	+	2.91853e9i	−0.334298	+	0.520606i
$611$		−	3.71053e9i		−	0.658100i
$612$	−1.97207e8	−	4.30967e8i	−0.0347769	−	0.0760001i
$613$			3.65909e9i			0.641596i	0.947148	+	0.320798i	$0.103951\pi$
$613$			3.65909e9i			0.641596i	−0.947148	+	0.320798i	$0.896049\pi$
$614$	1.27178e9	+	8.16653e8i	0.221730	+	0.142380i
$615$	2.36362e9			0.409747
$616$	−9.42781e7	+	6.60992e8i	−0.0162509	+	0.113937i
$617$	5.11426e9			0.876567			0.438284	−	0.898837i	$-0.355587\pi$
$617$	5.11426e9			0.876567			0.438284	+	0.898837i	$0.355587\pi$
$618$	−3.47238e9	−	2.22973e9i	−0.591791	−	0.380008i
$619$			9.24516e9i			1.56674i	0.621555	+	0.783371i	$0.286501\pi$
$619$			9.24516e9i			1.56674i	−0.621555	+	0.783371i	$0.713499\pi$
$620$	−2.51082e9	+	1.14893e9i	−0.423102	+	0.193607i
$621$			4.89410e9i			0.820073i
$622$	−4.44086e9	+	6.91580e9i	−0.739946	+	1.15233i
$623$	−8.60035e9			−1.42498
$624$	−1.29978e9	+	1.50457e9i	−0.214152	+	0.247894i
$625$	2.44141e8			0.0400000
$626$	3.58528e9	−	5.58340e9i	0.584134	−	0.909679i
$627$		−	7.43240e8i		−	0.120418i
$628$	−5.62056e9	+	2.57192e9i	−0.905568	+	0.414379i
$629$		−	3.19536e8i		−	0.0511968i
$630$	1.16448e9	+	7.47752e8i	0.185542	+	0.119142i
$631$	9.02091e9			1.42938			0.714690	−	0.699442i	$-0.246568\pi$
$631$	9.02091e9			1.42938			0.714690	+	0.699442i	$0.246568\pi$
$632$	−5.44232e9	−	7.76244e8i	−0.857579	−	0.122318i
$633$	−8.87829e8			−0.139129
$634$	−5.19680e9	−	3.33703e9i	−0.809886	−	0.520054i
$635$			2.13999e9i			0.331668i
$636$	8.76397e8	+	1.91524e9i	0.135083	+	0.295205i
$637$			1.24954e9i			0.191542i
$638$	4.73508e8	−	7.37401e8i	0.0721864	−	0.112417i
$639$	6.12212e9			0.928216
$640$	1.94807e9	+	2.23632e9i	0.293748	+	0.337212i
$641$	2.21484e9			0.332154			0.166077	−	0.986113i	$-0.446890\pi$
$641$	2.21484e9			0.332154			0.166077	+	0.986113i	$0.446890\pi$
$642$	−3.10118e9	+	4.82951e9i	−0.462546	+	0.720329i
$643$		−	3.60818e8i		−	0.0535242i	−0.999642	−	0.0267621i	$-0.991480\pi$
$643$		−	3.60818e8i		−	0.0535242i	0.999642	−	0.0267621i	$-0.00851966\pi$
$644$	−1.84662e9	−	4.03552e9i	−0.272444	−	0.595387i
$645$		−	1.00361e9i		−	0.147267i
$646$	−1.05482e9	−	6.77331e8i	−0.153944	−	0.0988524i
$647$	−2.93899e9			−0.426612			−0.213306	−	0.976985i	$-0.568423\pi$
$647$	−2.93899e9			−0.426612			−0.213306	+	0.976985i	$0.568423\pi$
$648$	−1.31662e7	−	1.87791e6i	−0.00190085	−	0.000271121i
$649$	1.03922e9			0.149229
$650$	−6.23855e8	−	4.00597e8i	−0.0891019	−	0.0572151i
$651$			3.62021e9i			0.514281i
$652$	−1.93148e9	+	8.83829e8i	−0.272913	+	0.124883i
$653$			2.01978e8i			0.0283863i	0.999899	+	0.0141932i	$0.00451797\pi$
$653$			2.01978e8i			0.0283863i	−0.999899	+	0.0141932i	$0.995482\pi$
$654$	1.31427e9	−	2.04673e9i	0.183722	−	0.286113i
$655$	1.19277e9			0.165848
$656$	−6.99939e9	+	8.10223e9i	−0.968048	+	1.12058i
$657$	−3.56413e9			−0.490315
$658$	−3.92102e9	+	6.10626e9i	−0.536548	+	0.835573i
$659$		−	5.73039e9i		−	0.779983i	−0.920818	−	0.389992i	$-0.872478\pi$
$659$		−	5.73039e9i		−	0.779983i	0.920818	−	0.389992i	$-0.127522\pi$
$660$	2.67723e8	−	1.22508e8i	0.0362478	−	0.0165867i
$661$		−	2.92528e9i		−	0.393969i	−0.980407	−	0.196985i	$-0.936885\pi$
$661$		−	2.92528e9i		−	0.393969i	0.980407	−	0.196985i	$-0.0631149\pi$
$662$	−2.09232e9	−	1.34354e9i	−0.280301	−	0.179990i
$663$	3.32899e8			0.0443624
$664$	8.26264e8	−	5.79301e9i	0.109529	−	0.767920i
$665$	3.66033e9			0.482664
$666$	1.49676e9	+	9.61119e8i	0.196333	+	0.126072i
$667$			5.82486e9i			0.760055i
$668$	−1.99812e9	−	4.36662e9i	−0.259361	−	0.566797i
$669$			2.28423e9i			0.294949i
$670$	−6.40955e8	+	9.98168e8i	−0.0823315	+	0.128216i
$671$	−1.55970e9			−0.199302
$672$	3.72891e9	−	1.10250e9i	0.474012	−	0.140148i
$673$	1.38147e10			1.74699			0.873493	−	0.486837i	$-0.161849\pi$
$673$	1.38147e10			1.74699			0.873493	+	0.486837i	$0.161849\pi$
$674$	7.19709e9	−	1.12081e10i	0.905415	−	1.41001i
$675$		−	1.59901e9i		−	0.200118i
$676$	−2.40518e9	−	5.25619e9i	−0.299457	−	0.654422i
$677$		−	7.08067e9i		−	0.877029i	−0.898724	−	0.438514i	$-0.855505\pi$
$677$		−	7.08067e9i		−	0.877029i	0.898724	−	0.438514i	$-0.144495\pi$
$678$	4.81977e9	+	3.09493e9i	0.593912	+	0.381370i
$679$	−9.28257e9			−1.13795
$680$	7.01175e7	−	4.91600e8i	0.00855156	−	0.0599557i
$681$	5.81224e9			0.705227
$682$	−1.04482e9	−	6.70909e8i	−0.126123	−	0.0809876i
$683$			1.48335e10i			1.78144i	0.454554	+	0.890719i	$0.349799\pi$
$683$			1.48335e10i			1.78144i	−0.454554	+	0.890719i	$0.650201\pi$
$684$	6.34547e9	−	2.90363e9i	0.758172	−	0.346932i
$685$		−	4.70048e9i		−	0.558760i
$686$	4.97030e9	−	7.74031e9i	0.587825	−	0.915427i
$687$	−6.91330e9			−0.813461
$688$	3.44025e9	+	2.97198e9i	0.402745	+	0.347925i
$689$	2.38506e9			0.277800
$690$	−1.05740e9	+	1.64670e9i	−0.122537	+	0.190828i
$691$		−	8.98381e9i		−	1.03583i	−0.855433	−	0.517914i	$-0.826709\pi$
$691$		−	8.98381e9i		−	1.03583i	0.855433	−	0.517914i	$-0.173291\pi$
$692$	−1.19864e10	+	5.48485e9i	−1.37504	+	0.629207i
$693$			6.22317e8i			0.0710306i
$694$	−1.20900e10	−	7.76339e9i	−1.37300	−	0.881645i
$695$	4.44342e9			0.502077
$696$	−5.05253e9	−	7.20649e8i	−0.568037	−	0.0810198i
$697$	1.79269e9			0.200535
$698$	−4.17243e9	−	2.67925e9i	−0.464403	−	0.298208i
$699$			3.28799e9i			0.364133i
$700$	6.03329e8	+	1.31849e9i	0.0664831	+	0.145289i
$701$		−	1.43806e9i		−	0.157676i	−0.996887	−	0.0788379i	$-0.974879\pi$
$701$		−	1.43806e9i		−	0.157676i	0.996887	−	0.0788379i	$-0.0251209\pi$
$702$	−2.62372e9	+	4.08596e9i	−0.286245	+	0.445773i
$703$	4.70478e9			0.510736
$704$	−3.72866e8	+	1.28051e9i	−0.0402762	+	0.138318i
$705$	3.19995e9			0.343939
$706$	4.51386e9	−	7.02950e9i	0.482761	−	0.751810i
$707$		−	1.18252e10i		−	1.25846i
$708$	−2.51833e9	−	5.50346e9i	−0.266684	−	0.582800i
$709$			1.96630e9i			0.207199i	0.994619	+	0.103600i	$0.0330360\pi$
$709$			1.96630e9i			0.207199i	−0.994619	+	0.103600i	$0.966964\pi$
$710$	5.39748e9	+	3.46590e9i	0.565962	+	0.363422i
$711$	−5.12388e9			−0.534633
$712$	−1.70070e10	−	2.42573e9i	−1.76583	−	0.251862i
$713$	8.25319e9			0.852724
$714$	−5.47837e8	−	3.51784e8i	−0.0563258	−	0.0361686i
$715$		−	3.33397e8i		−	0.0341107i
$716$	6.12912e9	−	2.80463e9i	0.624025	−	0.285548i
$717$		−	4.29066e9i		−	0.434718i
$718$	6.38940e9	−	9.95030e9i	0.644206	−	1.00323i
$719$	−6.89945e9			−0.692251			−0.346125	−	0.938188i	$-0.612503\pi$
$719$	−6.89945e9			−0.692251			−0.346125	+	0.938188i	$0.612503\pi$
$720$	2.09184e9	+	1.80711e9i	0.208864	+	0.180435i
$721$	9.13896e9			0.908079
$722$	4.50857e9	−	7.02125e9i	0.445819	−	0.694279i
$723$		−	1.02629e10i		−	1.00992i
$724$	−7.44136e9	+	3.40510e9i	−0.728731	+	0.333461i
$725$		−	1.90311e9i		−	0.185473i
$726$	−5.25656e9	−	3.37540e9i	−0.509828	−	0.327377i
$727$	7.37008e9			0.711380			0.355690	−	0.934604i	$-0.384246\pi$
$727$	7.37008e9			0.711380			0.355690	+	0.934604i	$0.384246\pi$
$728$	6.21747e8	−	4.35912e9i	0.0597247	−	0.418735i
$729$	−6.48835e9			−0.620280
$730$	−3.14227e9	−	2.01775e9i	−0.298960	−	0.191972i
$731$		−	7.61183e8i		−	0.0720740i
$732$	3.77960e9	+	8.25978e9i	0.356170	+	0.778359i
$733$			1.50977e10i			1.41594i	0.706241	+	0.707971i	$0.250389\pi$
$733$			1.50977e10i			1.41594i	−0.706241	+	0.707971i	$0.749611\pi$
$734$	9.29945e9	−	1.44821e10i	0.868002	−	1.35175i
$735$	−1.07760e9			−0.100104
$736$	−2.51343e9	−	8.50100e9i	−0.232377	−	0.785955i
$737$	−5.33435e8			−0.0490846
$738$	−5.39214e9	+	8.39725e9i	−0.493815	+	0.769024i
$739$			1.89400e10i			1.72633i	0.504922	+	0.863165i	$0.331521\pi$
$739$			1.89400e10i			1.72633i	−0.504922	+	0.863165i	$0.668479\pi$
$740$	7.75486e8	+	1.69471e9i	0.0703498	+	0.153740i
$741$			4.90153e9i			0.442556i
$742$	−3.92499e9	−	2.52036e9i	−0.352716	−	0.226490i
$743$	−1.59965e10			−1.43075			−0.715375	−	0.698741i	$-0.753744\pi$
$743$	−1.59965e10			−1.43075			−0.715375	+	0.698741i	$0.753744\pi$
$744$	−1.02108e9	+	7.15888e9i	−0.0908980	+	0.637294i
$745$	3.19838e9			0.283389
$746$	1.63280e10	+	1.04847e10i	1.43995	+	0.924638i
$747$		−	5.45406e9i		−	0.478737i
$748$	2.03054e8	−	9.29156e7i	0.0177401	−	0.00811770i
$749$		−	1.27108e10i		−	1.10531i
$750$	3.45474e8	−	5.38011e8i	0.0299020	−	0.0465668i
$751$	7.15896e9			0.616752			0.308376	−	0.951265i	$-0.400215\pi$
$751$	7.15896e9			0.616752			0.308376	+	0.951265i	$0.400215\pi$
$752$	−9.47600e9	+	1.09691e10i	−0.812574	+	0.940605i
$753$	−3.85972e9			−0.329438
$754$	−3.12270e9	+	4.86302e9i	−0.265296	+	0.413149i
$755$			1.09496e9i			0.0925943i
$756$	8.63550e9	−	3.95152e9i	0.726877	−	0.332612i
$757$		−	1.93055e9i		−	0.161751i	−0.996724	−	0.0808754i	$-0.974228\pi$
$757$		−	1.93055e9i		−	0.161751i	0.996724	−	0.0808754i	$-0.0257716\pi$
$758$	1.42766e10	+	9.16747e9i	1.19065	+	0.764552i
$759$	−8.80018e8			−0.0730543
$760$	7.23822e9	+	1.03240e9i	0.598114	+	0.0853098i
$761$	1.10433e10			0.908348			0.454174	−	0.890913i	$-0.349934\pi$
$761$	1.10433e10			0.908348			0.454174	+	0.890913i	$0.349934\pi$
$762$	4.71588e9	+	3.02822e9i	0.386118	+	0.247939i
$763$			5.38678e9i			0.439029i
$764$	6.91013e9	+	1.51011e10i	0.560609	+	1.22513i
$765$		−	4.62836e8i		−	0.0373777i
$766$	−768526.	+	1.19684e6i	−6.17814e−5	+	9.62130e-5i
$767$	−6.85349e9			−0.548438
$768$	7.68479e9	−	1.12843e9i	0.612164	−	0.0898895i
$769$	−1.93885e10			−1.53746			−0.768728	−	0.639575i	$-0.779110\pi$
$769$	−1.93885e10			−1.53746			−0.768728	+	0.639575i	$0.779110\pi$
$770$	−3.52310e8	+	5.48657e8i	−0.0278104	+	0.0433095i
$771$			1.47283e9i			0.115735i
$772$	5.91296e9	+	1.29219e10i	0.462535	+	1.01080i
$773$		−	2.19721e9i		−	0.171097i	−0.996334	−	0.0855487i	$-0.972736\pi$
$773$		−	2.19721e9i		−	0.171097i	0.996334	−	0.0855487i	$-0.0272643\pi$
$774$	3.56552e9	+	2.28953e9i	0.276394	+	0.177482i
$775$	−2.69649e9			−0.208086
$776$	−1.83561e10	−	2.61815e9i	−1.41015	−	0.201131i
$777$	2.44351e9			0.186871
$778$	−7.81978e9	−	5.02133e9i	−0.595341	−	0.382287i
$779$			2.63951e10i			2.00052i
$780$	−1.76559e9	+	8.07915e8i	−0.133216	+	0.0609586i
$781$			2.88449e9i			0.216666i
$782$	−8.01980e8	+	1.24893e9i	−0.0599708	+	0.0933933i
$783$	−1.24645e10			−0.927912
$784$	3.19111e9	−	3.69390e9i	0.236502	−	0.273766i
$785$	−6.03619e9			−0.445368
$786$	1.68784e9	−	2.62849e9i	0.123980	−	0.193076i
$787$		−	1.04999e10i		−	0.767848i	−0.923365	−	0.383924i	$-0.874572\pi$
$787$		−	1.04999e10i		−	0.767848i	0.923365	−	0.383924i	$-0.125428\pi$
$788$	−2.12175e10	+	9.70891e9i	−1.54473	+	0.706852i
$789$			4.79648e9i			0.347659i
$790$	−4.51740e9	−	2.90077e9i	−0.325982	−	0.209323i
$791$	−1.26851e10			−0.911334
$792$	−1.75524e8	+	1.23062e9i	−0.0125545	+	0.0880207i
$793$	1.02859e10			0.732467
$794$	9.49890e9	+	6.09955e9i	0.673444	+	0.432440i
$795$			2.05687e9i			0.145185i
$796$	7.95346e9	+	1.73812e10i	0.558934	+	1.22147i
$797$		−	2.39080e10i		−	1.67278i	−0.548134	−	0.836390i	$-0.684662\pi$
$797$		−	2.39080e10i		−	1.67278i	0.548134	−	0.836390i	$-0.315338\pi$
$798$	5.17959e9	−	8.06624e9i	0.360815	−	0.561903i
$799$	2.42700e9			0.168328
$800$	8.21189e8	+	2.77745e9i	0.0567059	+	0.191793i
$801$	−1.60119e10			−1.10085
$802$	−1.10701e10	+	1.72397e10i	−0.757780	+	1.18010i
$803$		−	1.67927e9i		−	0.114450i
$804$	1.29266e9	+	2.82494e9i	0.0877182	+	0.191696i
$805$		−	4.33394e9i		−	0.292818i
$806$	6.89037e9	+	4.42453e9i	0.463522	+	0.297642i
$807$	−9.69030e9			−0.649053
$808$	3.33529e9	−	2.33840e10i	0.222430	−	1.55948i
$809$	−1.43285e9			−0.0951436			−0.0475718	−	0.998868i	$-0.515148\pi$
$809$	−1.43285e9			−0.0951436			−0.0475718	+	0.998868i	$0.515148\pi$
$810$	−1.09286e7	−	7.01762e6i	−0.000722550	−	0.000463972i
$811$			2.02071e9i			0.133024i	0.997786	+	0.0665120i	$0.0211871\pi$
$811$			2.02071e9i			0.133024i	−0.997786	+	0.0665120i	$0.978813\pi$
$812$	1.02778e10	−	4.70302e9i	0.673680	−	0.308270i
$813$			5.44860e9i			0.355605i
$814$	−4.52840e8	+	7.05213e8i	−0.0294279	+	0.0458284i
$815$	−2.07431e9			−0.134222
$816$	−9.84115e8	−	8.50162e8i	−0.0634060	−	0.0547754i
$817$	1.12075e10			0.719005
$818$	−4.86314e9	+	7.57343e9i	−0.310656	+	0.483789i
$819$		−	4.10407e9i		−	0.261048i
$820$	−9.50781e9	+	4.35069e9i	−0.602188	+	0.275556i
$821$			3.97118e9i			0.250448i	0.992128	+	0.125224i	$0.0399650\pi$
$821$			3.97118e9i			0.250448i	−0.992128	+	0.125224i	$0.960035\pi$
$822$	−1.03584e10	−	6.65146e9i	−0.650492	−	0.417701i
$823$	1.59915e10			0.999979			0.499989	−	0.866032i	$-0.333337\pi$
$823$	1.59915e10			0.999979			0.499989	+	0.866032i	$0.333337\pi$
$824$	1.80721e10	+	2.57765e9i	1.12529	+	0.160501i
$825$	2.87521e8			0.0178271
$826$	1.12785e10	+	7.24228e9i	0.696339	+	0.447141i
$827$			3.60022e9i			0.221340i	0.993857	+	0.110670i	$0.0352997\pi$
$827$			3.60022e9i			0.221340i	−0.993857	+	0.110670i	$0.964700\pi$
$828$	−3.43799e9	−	7.51323e9i	−0.210474	−	0.459961i
$829$		−	2.42858e10i		−	1.48051i	−0.672327	−	0.740254i	$-0.734705\pi$
$829$		−	2.42858e10i		−	1.48051i	0.672327	−	0.740254i	$-0.265295\pi$
$830$	3.08769e9	−	4.80849e9i	0.187439	−	0.291901i
$831$	2.10465e9			0.127226
$832$	2.45898e9	−	8.44470e9i	0.148021	−	0.508338i
$833$	−8.17306e8			−0.0489922
$834$	6.28770e9	−	9.79192e9i	0.375328	−	0.584503i
$835$		−	4.68952e9i		−	0.278757i
$836$	1.36807e9	+	2.98973e9i	0.0809816	+	0.176974i
$837$			1.76608e10i			1.04105i
$838$	2.57687e10	+	1.65469e10i	1.51265	+	0.971319i
$839$	9.51333e9			0.556117			0.278058	−	0.960564i	$-0.410309\pi$
$839$	9.51333e9			0.556117			0.278058	+	0.960564i	$0.410309\pi$
$840$	3.75930e9	+	5.36193e8i	0.218841	+	0.0312136i
$841$	2.41494e9			0.139998
$842$	1.81826e10	+	1.16756e10i	1.04970	+	0.674044i
$843$		−	8.30634e9i		−	0.477544i
$844$	3.57134e9	−	1.63421e9i	0.204472	−	0.0935643i
$845$		−	5.64487e9i		−	0.321852i
$846$	−7.30006e9	+	1.13685e10i	−0.414505	+	0.645514i
$847$	1.38347e10			0.782310
$848$	−7.05072e9	−	6.09100e9i	−0.397052	−	0.343007i
$849$	−1.27792e10			−0.716682
$850$	2.62024e8	−	4.08053e8i	0.0146344	−	0.0227903i
$851$		−	5.57061e9i		−	0.309848i
$852$	1.52755e10	−	6.98994e9i	0.846170	−	0.387200i
$853$		−	1.30130e10i		−	0.717887i	−0.933359	−	0.358944i	$-0.883137\pi$
$853$		−	1.30130e10i		−	0.717887i	0.933359	−	0.358944i	$-0.116863\pi$
$854$	−1.69271e10	−	1.08695e10i	−0.929996	−	0.597180i
$855$	6.81471e9			0.372877
$856$	3.58508e9	−	2.51353e10i	0.195362	−	1.36970i
$857$	−3.57734e8			−0.0194146			−0.00970728	−	0.999953i	$-0.503090\pi$
$857$	−3.57734e8			−0.0194146			−0.00970728	+	0.999953i	$0.503090\pi$
$858$	−7.34704e8	−	4.71777e8i	−0.0397107	−	0.0254995i
$859$		−	4.46756e8i		−	0.0240489i	−0.999928	−	0.0120244i	$-0.996172\pi$
$859$		−	4.46756e8i		−	0.0240489i	0.999928	−	0.0120244i	$-0.00382759\pi$
$860$	1.84732e9	+	4.03707e9i	0.0990372	+	0.216432i
$861$			1.37088e10i			0.731960i
$862$	7.52175e9	−	1.17137e10i	0.399985	−	0.622901i
$863$	−2.63664e10			−1.39641			−0.698206	−	0.715897i	$-0.746018\pi$
$863$	−2.63664e10			−1.39641			−0.698206	+	0.715897i	$0.746018\pi$
$864$	1.81910e10	−	5.37841e9i	0.959532	−	0.283697i
$865$	−1.28727e10			−0.676261
$866$	−7.98058e9	+	1.24283e10i	−0.417563	+	0.650276i
$867$		−	1.16554e10i		−	0.607382i
$868$	−6.66366e9	−	1.45625e10i	−0.345855	−	0.755817i
$869$		−	2.41416e9i		−	0.124795i
$870$	−4.19386e9	−	2.69301e9i	−0.215922	−	0.138650i
$871$	3.51791e9			0.180394
$872$	−1.51934e9	+	1.06522e10i	−0.0775975	+	0.544043i
$873$	−1.72820e10			−0.879114
$874$	−1.83891e10	−	1.18082e10i	−0.931685	−	0.598265i
$875$			1.41599e9i			0.0714549i
$876$	−8.89300e9	+	4.06935e9i	−0.446976	+	0.204532i
$877$			2.75765e10i			1.38051i	0.723564	+	0.690257i	$0.242503\pi$
$877$			2.75765e10i			1.38051i	−0.723564	+	0.690257i	$0.757497\pi$
$878$	6.33155e9	−	9.86020e9i	0.315703	−	0.491649i
$879$	1.70979e10			0.849144
$880$	−8.51434e8	+	9.85588e8i	−0.0421174	+	0.0487535i
$881$	−8.48952e9			−0.418280			−0.209140	−	0.977886i	$-0.567067\pi$
$881$	−8.48952e9			−0.418280			−0.209140	+	0.977886i	$0.567067\pi$
$882$	2.45834e9	−	3.82841e9i	0.120643	−	0.187879i
$883$		−	3.84331e10i		−	1.87864i	−0.343043	−	0.939320i	$-0.611458\pi$
$883$		−	3.84331e10i		−	1.87864i	0.343043	−	0.939320i	$-0.388542\pi$
$884$	−1.33910e9	+	6.12762e8i	−0.0651976	+	0.0298338i
$885$		−	5.91043e9i		−	0.286627i
$886$	−3.23051e10	−	2.07441e10i	−1.56046	−	1.00202i
$887$	3.67955e9			0.177036			0.0885181	−	0.996075i	$-0.471787\pi$
$887$	3.67955e9			0.177036			0.0885181	+	0.996075i	$0.471787\pi$
$888$	4.83199e9	+	6.89193e8i	0.231569	+	0.0330290i
$889$	−1.24117e10			−0.592483
$890$	−1.41167e10	−	9.06477e9i	−0.671224	−	0.431014i
$891$		−	5.84041e6i		−	0.000276612i
$892$	−4.20454e9	−	9.18843e9i	−0.198354	−	0.433475i
$893$			3.57346e10i			1.67922i
$894$	4.52590e9	−	7.04825e9i	0.211848	−	0.329913i
$895$	6.58235e9			0.306902
$896$	−1.29704e10	+	1.12986e10i	−0.602387	+	0.524743i
$897$	5.80356e9			0.268486
$898$	−1.85627e10	+	2.89079e10i	−0.855410	+	1.33214i
$899$			2.10195e10i			0.964857i
$900$	1.12326e9	+	2.45473e9i	0.0513609	+	0.112242i
$901$			1.56003e9i			0.0710552i
$902$	−3.95644e9	−	2.54055e9i	−0.179507	−	0.115267i
$903$	5.82081e9			0.263073
$904$	−2.50846e10	−	3.57785e9i	−1.12932	−	0.161076i
$905$	−7.99163e9			−0.358398
$906$	2.41296e9	+	1.54944e9i	0.107796	+	0.0692190i
$907$			1.43630e10i			0.639177i	0.947556	+	0.319588i	$0.103545\pi$
$907$			1.43630e10i			0.639177i	−0.947556	+	0.319588i	$0.896455\pi$
$908$	−2.33801e10	+	1.06985e10i	−1.03644	+	0.474267i
$909$		−	2.20158e10i		−	0.972210i
$910$	2.32342e9	−	3.61829e9i	0.102208	−	0.159169i
$911$	−1.87441e10			−0.821391			−0.410696	−	0.911772i	$-0.634714\pi$
$911$	−1.87441e10			−0.821391			−0.410696	+	0.911772i	$0.634714\pi$
$912$	1.25176e10	−	1.44899e10i	0.546436	−	0.632534i
$913$	2.56973e9			0.111748
$914$	−1.05895e9	+	1.64912e9i	−0.0458737	+	0.0714397i
$915$			8.87057e9i			0.382805i
$916$	2.78092e10	−	1.27252e10i	1.19551	−	0.547055i
$917$			6.91792e9i			0.296267i
$918$	−2.67256e9	−	1.71613e9i	−0.114019	−	0.0732153i
$919$	3.28361e10			1.39556			0.697778	−	0.716314i	$-0.254172\pi$
$919$	3.28361e10			1.39556			0.697778	+	0.716314i	$0.254172\pi$
$920$	1.22239e9	−	8.57027e9i	0.0517549	−	0.362858i
$921$	3.86546e9			0.163040
$922$	1.62443e10	+	1.04310e10i	0.682565	+	0.438297i
$923$		−	1.90227e10i		−	0.796281i
$924$	7.10531e8	+	1.55277e9i	0.0296300	+	0.0647521i
$925$			1.82003e9i			0.0756108i
$926$	−2.14432e10	+	3.33938e10i	−0.887467	+	1.38206i
$927$	1.70147e10			0.701528
$928$	2.16506e10	−	6.40127e9i	0.889307	−	0.262935i
$929$	3.86364e10			1.58103			0.790517	−	0.612440i	$-0.209812\pi$
$929$	3.86364e10			1.58103			0.790517	+	0.612440i	$0.209812\pi$
$930$	−3.81570e9	+	5.94224e9i	−0.155555	+	0.242248i
$931$		−	1.20338e10i		−	0.488743i
$932$	−6.05215e9	−	1.32261e10i	−0.244881	−	0.535152i
$933$			2.10199e10i			0.847315i
$934$	−3.38149e10	−	2.17136e10i	−1.35798	−	0.872004i
$935$	2.18069e8			0.00872477
$936$	1.15755e9	−	8.11570e9i	0.0461397	−	0.323490i
$937$	−4.10023e9			−0.162825			−0.0814123	−	0.996681i	$-0.525943\pi$
$937$	−4.10023e9			−0.162825			−0.0814123	+	0.996681i	$0.525943\pi$
$938$	−5.78927e9	−	3.71747e9i	−0.229041	−	0.147075i
$939$		−	1.69702e10i		−	0.668894i
$940$	−1.28720e10	+	5.89010e9i	−0.505473	+	0.231300i
$941$		−	1.80337e10i		−	0.705538i	−0.935710	−	0.352769i	$-0.885240\pi$
$941$		−	1.80337e10i		−	0.705538i	0.935710	−	0.352769i	$-0.114760\pi$
$942$	−8.54157e9	+	1.33019e10i	−0.332935	+	0.518484i
$943$	3.12526e10			1.21366
$944$	2.02603e10	+	1.75025e10i	0.783869	+	0.677172i
$945$	9.27407e9			0.357486
$946$	−1.07873e9	+	1.67992e9i	−0.0414281	+	0.0645165i
$947$			6.66183e9i			0.254899i	0.991845	+	0.127450i	$0.0406791\pi$
$947$			6.66183e9i			0.254899i	−0.991845	+	0.127450i	$0.959321\pi$
$948$	−1.27848e10	+	5.85020e9i	−0.487376	+	0.223019i
$949$			1.10745e10i			0.420622i
$950$	6.00809e9	+	3.85799e9i	0.227355	+	0.145992i
$951$	−1.57952e10			−0.595515
$952$	2.85123e9	+	4.06674e8i	0.107103	+	0.0152763i
$953$	1.09990e10			0.411651			0.205825	−	0.978589i	$-0.434012\pi$
$953$	1.09990e10			0.411651			0.205825	+	0.978589i	$0.434012\pi$
$954$	−7.30745e9	−	4.69235e9i	−0.272487	−	0.174973i
$955$			1.62178e10i			0.602533i
$956$	7.89776e9	+	1.72594e10i	0.292349	+	0.638887i
$957$		−	2.24126e9i		−	0.0826608i
$958$	5.91910e9	−	9.21790e9i	0.217509	−	0.338729i
$959$	2.72623e10			0.998153
$960$	7.28269e9	+	2.12062e9i	0.265670	+	0.0773594i
$961$	2.26966e9			0.0824951
$962$	2.98640e9	−	4.65075e9i	0.108152	−	0.168427i
$963$		−	2.36646e10i		−	0.853901i
$964$	1.88908e10	+	4.12832e10i	0.679174	+	1.48424i
$965$			1.38775e10i			0.497125i
$966$	−9.55067e9	−	6.13279e9i	−0.340890	−	0.218896i
$967$	1.48740e10			0.528975			0.264487	−	0.964389i	$-0.414797\pi$
$967$	1.48740e10			0.528975			0.264487	+	0.964389i	$0.414797\pi$
$968$	2.73579e10	+	3.90209e9i	0.969435	+	0.138272i
$969$	−3.20601e9			−0.113196
$970$	−1.52365e10	−	9.78383e9i	−0.536023	−	0.344197i
$971$			1.67742e10i			0.587995i	0.955806	+	0.293998i	$0.0949858\pi$
$971$			1.67742e10i			0.587995i	−0.955806	+	0.293998i	$0.905014\pi$
$972$	2.60190e10	−	1.19060e10i	0.908779	−	0.415849i
$973$			2.57713e10i			0.896896i
$974$	−5.25931e9	+	8.19039e9i	−0.182378	+	0.284019i
$975$	−1.89615e9			−0.0655173
$976$	−3.04073e10	−	2.62684e10i	−1.04690	−	0.904397i
$977$	1.07958e10			0.370361			0.185181	−	0.982705i	$-0.440713\pi$
$977$	1.07958e10			0.370361			0.185181	+	0.982705i	$0.440713\pi$
$978$	−2.93528e9	+	4.57115e9i	−0.100337	+	0.156257i
$979$		−	7.54415e9i		−	0.256963i
$980$	4.33472e9	−	1.98353e9i	0.147119	−	0.0673205i
$981$			1.00290e10i			0.339168i
$982$	−9.54103e9	−	6.12660e9i	−0.321518	−	0.206457i
$983$	1.18872e10			0.399154			0.199577	−	0.979882i	$-0.436043\pi$
$983$	1.18872e10			0.399154			0.199577	+	0.979882i	$0.436043\pi$
$984$	−3.86656e9	+	2.71088e10i	−0.129372	+	0.907041i
$985$	−2.27864e10			−0.759713
$986$	−3.18082e9	−	2.04251e9i	−0.105675	−	0.0678570i
$987$			1.85594e10i			0.614403i
$988$	−9.02218e9	−	1.97167e10i	−0.297620	−	0.650407i
$989$		−	1.32700e10i		−	0.436199i
$990$	−6.55922e8	+	1.02148e9i	−0.0214847	+	0.0334584i
$991$	−1.17102e10			−0.382213			−0.191106	−	0.981569i	$-0.561208\pi$
$991$	−1.17102e10			−0.382213			−0.191106	+	0.981569i	$0.561208\pi$
$992$	−9.06989e9	−	3.06765e10i	−0.294993	−	0.997735i
$993$	−6.35939e9			−0.206107
$994$	−2.01018e10	+	3.13048e10i	−0.649207	+	1.01102i
$995$			1.86665e10i			0.600733i
$996$	−6.22718e9	−	1.36086e10i	−0.199702	−	0.436422i
$997$		−	2.29607e9i		−	0.0733757i	−0.999327	−	0.0366879i	$-0.988319\pi$
$997$		−	2.29607e9i		−	0.0733757i	0.999327	−	0.0366879i	$-0.0116807\pi$
$998$	5.14698e10	+	3.30504e10i	1.63906	+	1.05249i
$999$	1.19204e10			0.378278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.8.d.a.21.10	yes	28
4.3	odd	2		160.8.d.a.81.10		28
8.3	odd	2		160.8.d.a.81.19		28
8.5	even	2	inner	40.8.d.a.21.9	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.8.d.a.21.9	✓	28	8.5	even	2	inner
40.8.d.a.21.10	yes	28	1.1	even	1	trivial
160.8.d.a.81.10		28	4.3	odd	2
160.8.d.a.81.19		28	8.3	odd	2

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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	40.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.11309 + 9.51999i) q^{2} +28.9351i q^{3} +(-53.2604 - 116.393i) q^{4} -125.000i q^{5} +(-275.462 - 176.883i) q^{6} +724.987 q^{7} +(1433.65 + 204.483i) q^{8} +1349.76 q^{9} +(1190.00 + 764.136i) q^{10} +635.952i q^{11} +(3367.84 - 1541.09i) q^{12} -4193.99i q^{13} +(-4431.91 + 6901.87i) q^{14} +3616.88 q^{15} +(-10710.7 + 12398.3i) q^{16} +2743.22 q^{17} +(-8251.21 + 12849.7i) q^{18} +40390.6i q^{19} +(-14549.1 + 6657.54i) q^{20} +20977.5i q^{21} +(-6054.26 - 3887.63i) q^{22} +47823.7 q^{23} +(-5916.72 + 41482.6i) q^{24} -15625.0 q^{25} +(39926.7 + 25638.2i) q^{26} +102336. i q^{27} +(-38613.1 - 84383.4i) q^{28} +121799. i q^{29} +(-22110.3 + 34432.7i) q^{30} +172575. q^{31} +(-52556.1 - 177757. i) q^{32} -18401.3 q^{33} +(-16769.5 + 26115.4i) q^{34} -90623.4i q^{35} +(-71888.8 - 157103. i) q^{36} -116482. i q^{37} +(-384518. - 246911. i) q^{38} +121353. q^{39} +(25560.3 - 179206. i) q^{40} +653497. q^{41} +(-199706. - 128238. i) q^{42} -277478. i q^{43} +(74020.4 - 33871.0i) q^{44} -168720. i q^{45} +(-292350. + 455281. i) q^{46} +884726. q^{47} +(-358745. - 309914. i) q^{48} -297937. q^{49} +(95517.0 - 148750. i) q^{50} +79375.2i q^{51} +(-488151. + 223373. i) q^{52} +568686. i q^{53} +(-974242. - 625592. i) q^{54} +79494.0 q^{55} +(1.03937e6 + 148247. i) q^{56} -1.16870e6 q^{57} +(-1.15952e6 - 744566. i) q^{58} -1.63412e6i q^{59} +(-192637. - 420980. i) q^{60} +2.45255e6i q^{61} +(-1.05497e6 + 1.64292e6i) q^{62} +978559. q^{63} +(2.01353e6 + 586311. i) q^{64} -524249. q^{65} +(112489. - 175180. i) q^{66} +838798. i q^{67} +(-146105. - 319291. i) q^{68} +1.38378e6i q^{69} +(862733. + 553988. i) q^{70} +4.53571e6 q^{71} +(1.93508e6 + 276003. i) q^{72} -2.64056e6 q^{73} +(1.10891e6 + 712066. i) q^{74} -452110. i q^{75} +(4.70118e6 - 2.15122e6i) q^{76} +461057. i q^{77} +(-741844. + 1.15528e6i) q^{78} -3.79614e6 q^{79} +(1.54978e6 + 1.33883e6i) q^{80} -9183.73 q^{81} +(-3.99488e6 + 6.22129e6i) q^{82} -4.04075e6i q^{83} +(2.44164e6 - 1.11727e6i) q^{84} -342902. i q^{85} +(2.64159e6 + 1.69625e6i) q^{86} -3.52426e6 q^{87} +(-130041. + 911730. i) q^{88} -1.18628e7 q^{89} +(1.60621e6 + 1.03140e6i) q^{90} -3.04059e6i q^{91} +(-2.54711e6 - 5.56634e6i) q^{92} +4.99348e6i q^{93} +(-5.40840e6 + 8.42258e6i) q^{94} +5.04882e6 q^{95} +(5.14341e6 - 1.52071e6i) q^{96} -1.28038e7 q^{97} +(1.82131e6 - 2.83636e6i) q^{98} +858384. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 14 q^{2} - 208 q^{4} - 228 q^{6} + 1372 q^{7} - 2024 q^{8} - 20412 q^{9} - 3250 q^{10} - 2788 q^{12} - 26620 q^{14} - 13500 q^{15} - 48824 q^{16} + 126562 q^{18} + 20500 q^{20} - 113892 q^{22} + 2588 q^{23}+ \cdots + 11064654 q^{98}+O(q^{100}) \) 28 * q - 14 * q^2 - 208 * q^4 - 228 * q^6 + 1372 * q^7 - 2024 * q^8 - 20412 * q^9 - 3250 * q^10 - 2788 * q^12 - 26620 * q^14 - 13500 * q^15 - 48824 * q^16 + 126562 * q^18 + 20500 * q^20 - 113892 * q^22 + 2588 * q^23 - 312408 * q^24 - 437500 * q^25 + 325932 * q^26 + 482476 * q^28 - 239000 * q^30 + 268024 * q^31 - 1445944 * q^32 - 99016 * q^33 + 651372 * q^34 + 1544216 * q^36 - 443660 * q^38 - 283944 * q^39 - 533000 * q^40 - 601208 * q^41 + 2692532 * q^42 + 239528 * q^44 - 142196 * q^46 - 2076460 * q^47 - 1158872 * q^48 + 4316268 * q^49 + 218750 * q^50 + 1591040 * q^52 + 4926168 * q^54 + 1331000 * q^55 + 2368232 * q^56 + 3788536 * q^57 - 5872008 * q^58 + 435500 * q^60 + 4008592 * q^62 - 14839060 * q^63 + 10179584 * q^64 - 9178320 * q^66 - 11198568 * q^68 - 2491000 * q^70 - 1001656 * q^71 - 8674904 * q^72 + 2534128 * q^73 - 21884804 * q^74 - 13848304 * q^76 + 25352888 * q^78 - 22040096 * q^79 - 7560000 * q^80 + 11166300 * q^81 + 20089464 * q^82 - 38088296 * q^84 + 17672012 * q^86 + 34127184 * q^87 + 11943152 * q^88 + 3807224 * q^89 + 13443750 * q^90 + 31988508 * q^92 + 17925028 * q^94 - 13718000 * q^95 - 30275488 * q^96 + 15198608 * q^97 + 11064654 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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