LMFDB - Embedded newform 28.9.c.a.15.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [28,9,Mod(15,28)] 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("28.15"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(28, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 28 = 2^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	28.c (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:	$11.4066010817$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			15.12
Character	$\chi$	$=$	28.15
Dual form			28.9.c.a.15.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.480763 + 15.9928i) q^{2} +113.792i q^{3} +(-255.538 + 15.3775i) q^{4} -421.707 q^{5} +(-1819.85 + 54.7071i) q^{6} -907.493i q^{7} +(-368.781 - 4079.36i) q^{8} -6387.68 q^{9} +(-202.741 - 6744.26i) q^{10} +20043.8i q^{11} +(-1749.84 - 29078.2i) q^{12} +26178.6 q^{13} +(14513.3 - 436.289i) q^{14} -47987.0i q^{15} +(65063.1 - 7859.04i) q^{16} -108872. q^{17} +(-3070.96 - 102157. i) q^{18} -20820.6i q^{19} +(107762. - 6484.78i) q^{20} +103266. q^{21} +(-320556. + 9636.31i) q^{22} -557432. i q^{23} +(464200. - 41964.5i) q^{24} -212789. q^{25} +(12585.7 + 418668. i) q^{26} +19722.3i q^{27} +(13954.9 + 231899. i) q^{28} -582737. q^{29} +(767445. - 23070.3i) q^{30} +668311. i q^{31} +(156968. + 1.03676e6i) q^{32} -2.28083e6 q^{33} +(-52341.5 - 1.74116e6i) q^{34} +382696. i q^{35} +(1.63229e6 - 98226.3i) q^{36} -720436. q^{37} +(332980. - 10009.8i) q^{38} +2.97892e6i q^{39} +(155517. + 1.72030e6i) q^{40} -1.10993e6 q^{41} +(49646.3 + 1.65150e6i) q^{42} +3.46610e6i q^{43} +(-308223. - 5.12195e6i) q^{44} +2.69373e6 q^{45} +(8.91488e6 - 267992. i) q^{46} -343843. i q^{47} +(894298. + 7.40367e6i) q^{48} -823543. q^{49} +(-102301. - 3.40308e6i) q^{50} -1.23888e7i q^{51} +(-6.68962e6 + 402560. i) q^{52} -1.06271e7 q^{53} +(-315414. + 9481.73i) q^{54} -8.45260e6i q^{55} +(-3.70199e6 + 334666. i) q^{56} +2.36923e6 q^{57} +(-280158. - 9.31959e6i) q^{58} -9.34340e6i q^{59} +(737917. + 1.22625e7i) q^{60} +4.84615e6 q^{61} +(-1.06881e7 + 321299. i) q^{62} +5.79677e6i q^{63} +(-1.65052e7 + 3.00879e6i) q^{64} -1.10397e7 q^{65} +(-1.09654e6 - 3.64768e7i) q^{66} +6.60142e6i q^{67} +(2.78208e7 - 1.67417e6i) q^{68} +6.34314e7 q^{69} +(-6.12037e6 + 183986. i) q^{70} +3.04115e7i q^{71} +(2.35566e6 + 2.60577e7i) q^{72} +2.91778e7 q^{73} +(-346359. - 1.15218e7i) q^{74} -2.42137e7i q^{75} +(320169. + 5.32046e6i) q^{76} +1.81896e7 q^{77} +(-4.76412e7 + 1.43215e6i) q^{78} +4.10436e7i q^{79} +(-2.74375e7 + 3.31421e6i) q^{80} -4.41538e7 q^{81} +(-533614. - 1.77509e7i) q^{82} +8.03486e7i q^{83} +(-2.63883e7 + 1.58796e6i) q^{84} +4.59119e7 q^{85} +(-5.54325e7 + 1.66637e6i) q^{86} -6.63110e7i q^{87} +(8.17660e7 - 7.39178e6i) q^{88} -1.08138e8 q^{89} +(1.29504e6 + 4.30802e7i) q^{90} -2.37569e7i q^{91} +(8.57188e6 + 1.42445e8i) q^{92} -7.60486e7 q^{93} +(5.49900e6 - 165307. i) q^{94} +8.78020e6i q^{95} +(-1.17975e8 + 1.78617e7i) q^{96} +1.14406e8 q^{97} +(-395929. - 1.31707e7i) q^{98} -1.28033e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 383 q^{4} - 336 q^{5} + 5502 q^{6} - 12069 q^{8} - 56296 q^{9} + 41972 q^{10} - 31290 q^{12} - 28560 q^{13} + 7203 q^{14} + 166193 q^{16} - 165648 q^{17} - 11609 q^{18} - 71568 q^{20} - 955748 q^{22}+ \cdots - 2470629 q^{98}+O(q^{100}) $ 24 * q + 3 * q^2 - 383 * q^4 - 336 * q^5 + 5502 * q^6 - 12069 * q^8 - 56296 * q^9 + 41972 * q^10 - 31290 * q^12 - 28560 * q^13 + 7203 * q^14 + 166193 * q^16 - 165648 * q^17 - 11609 * q^18 - 71568 * q^20 - 955748 * q^22 + 133322 * q^24 + 989640 * q^25 - 1066632 * q^26 - 372155 * q^28 + 997296 * q^29 + 3246560 * q^30 - 2265357 * q^32 - 5521600 * q^33 + 1423618 * q^34 - 649451 * q^36 + 5387056 * q^37 + 3945690 * q^38 + 11452504 * q^40 - 12346320 * q^41 + 5642350 * q^42 - 2412372 * q^44 + 17486448 * q^45 + 537288 * q^46 + 20895070 * q^48 - 19765032 * q^49 - 28121691 * q^50 - 12804764 * q^52 + 10812720 * q^53 - 42610652 * q^54 - 7109361 * q^56 + 6748288 * q^57 + 36144266 * q^58 - 98388944 * q^60 + 33644464 * q^61 + 12180756 * q^62 - 1102631 * q^64 - 9084960 * q^65 + 83635608 * q^66 + 106943886 * q^68 - 90944448 * q^69 + 11611236 * q^70 - 48881753 * q^72 - 7651728 * q^73 - 66897318 * q^74 + 64861986 * q^76 - 47482176 * q^77 - 41838760 * q^78 + 154560168 * q^80 + 299710744 * q^81 - 13781390 * q^82 + 571438 * q^84 - 280618528 * q^85 - 139907676 * q^86 - 65086060 * q^88 + 215250672 * q^89 + 40480132 * q^90 + 111569640 * q^92 + 181272192 * q^93 + 171294732 * q^94 - 684707590 * q^96 + 114327024 * q^97 - 2470629 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/28\mathbb{Z}\right)^\times$.

$n$	$15$	$17$
$\chi(n)$	$-1$	$1$

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 $

$2$	0.480763	+	15.9928i	0.0300477	+	0.999548i
$2$	0.480763	+	15.9928i	0.0300477	+	0.999548i
$3$			113.792i			1.40484i	0.711761	+	0.702421i	$0.247898\pi$
$3$			113.792i			1.40484i	−0.711761	+	0.702421i	$0.752102\pi$
$4$	−255.538	+	15.3775i	−0.998194	+	0.0600682i
$5$	−421.707			−0.674731			−0.337365	−	0.941374i	$-0.609536\pi$
$5$	−421.707			−0.674731			−0.337365	+	0.941374i	$0.609536\pi$
$6$	−1819.85	+	54.7071i	−1.40421	+	0.0422122i
$7$		−	907.493i		−	0.377964i
$7$		−	907.493i		−	0.377964i
$8$	−368.781	−	4079.36i	−0.0900345	−	0.995939i
$9$	−6387.68			−0.973584
$10$	−202.741	−	6744.26i	−0.0202741	−	0.674426i
$11$			20043.8i			1.36902i	0.729004	+	0.684509i	$0.239983\pi$
$11$			20043.8i			1.36902i	−0.729004	+	0.684509i	$0.760017\pi$
$12$	−1749.84	−	29078.2i	−0.0843864	−	1.40231i
$13$	26178.6			0.916585			0.458293	−	0.888801i	$-0.348461\pi$
$13$	26178.6			0.916585			0.458293	+	0.888801i	$0.348461\pi$
$14$	14513.3	−	436.289i	0.377794	−	0.0113569i
$15$		−	47987.0i		−	0.947890i
$16$	65063.1	−	7859.04i	0.992784	−	0.119919i
$17$	−108872.			−1.30353			−0.651763	−	0.758423i	$-0.725970\pi$
$17$	−108872.			−1.30353			−0.651763	+	0.758423i	$0.725970\pi$
$18$	−3070.96	−	102157.i	−0.0292539	−	0.973144i
$19$		−	20820.6i		−	0.159764i	−0.996804	−	0.0798821i	$-0.974546\pi$
$19$		−	20820.6i		−	0.159764i	0.996804	−	0.0798821i	$-0.0254544\pi$
$20$	107762.	−	6484.78i	0.673512	−	0.0405298i
$21$	103266.			0.530981
$22$	−320556.	+	9636.31i	−1.36840	+	0.0411358i
$23$		−	557432.i		−	1.99196i	−0.0895803	−	0.995980i	$-0.528553\pi$
$23$		−	557432.i		−	1.99196i	0.0895803	−	0.995980i	$-0.471447\pi$
$24$	464200.	−	41964.5i	1.39914	−	0.126484i
$25$	−212789.			−0.544739
$26$	12585.7	+	418668.i	0.0275412	+	0.916171i
$27$			19722.3i			0.0371109i
$28$	13954.9	+	231899.i	0.0227036	+	0.377282i
$29$	−582737.			−0.823912			−0.411956	−	0.911204i	$-0.635154\pi$
$29$	−582737.			−0.823912			−0.411956	+	0.911204i	$0.635154\pi$
$30$	767445.	−	23070.3i	0.947462	−	0.0284819i
$31$			668311.i			0.723655i	0.932245	+	0.361828i	$0.117847\pi$
$31$			668311.i			0.723655i	−0.932245	+	0.361828i	$0.882153\pi$
$32$	156968.	+	1.03676e6i	0.149696	+	0.988732i
$33$	−2.28083e6			−1.92326
$34$	−52341.5	−	1.74116e6i	−0.0391679	−	1.30294i
$35$			382696.i			0.255024i
$36$	1.63229e6	−	98226.3i	0.971826	−	0.0584814i
$37$	−720436.			−0.384404			−0.192202	−	0.981355i	$-0.561563\pi$
$37$	−720436.			−0.384404			−0.192202	+	0.981355i	$0.561563\pi$
$38$	332980.	−	10009.8i	0.159692	−	0.00480054i
$39$			2.97892e6i			1.28766i
$40$	155517.	+	1.72030e6i	0.0607490	+	0.671990i
$41$	−1.10993e6			−0.392791			−0.196395	−	0.980525i	$-0.562924\pi$
$41$	−1.10993e6			−0.392791			−0.196395	+	0.980525i	$0.562924\pi$
$42$	49646.3	+	1.65150e6i	0.0159547	+	0.530741i
$43$			3.46610e6i			1.01383i	0.861995	+	0.506917i	$0.169215\pi$
$43$			3.46610e6i			1.01383i	−0.861995	+	0.506917i	$0.830785\pi$
$44$	−308223.	−	5.12195e6i	−0.0822345	−	1.36655i
$45$	2.69373e6			0.656907
$46$	8.91488e6	−	267992.i	1.99106	−	0.0598537i
$47$		−	343843.i		−	0.0704642i	−0.999379	−	0.0352321i	$-0.988783\pi$
$47$		−	343843.i		−	0.0704642i	0.999379	−	0.0352321i	$-0.0112170\pi$
$48$	894298.	+	7.40367e6i	0.168468	+	1.39471i
$49$	−823543.			−0.142857
$50$	−102301.	−	3.40308e6i	−0.0163681	−	0.544493i
$51$		−	1.23888e7i		−	1.83125i
$52$	−6.68962e6	+	402560.i	−0.914930	+	0.0550576i
$53$	−1.06271e7			−1.34682			−0.673410	−	0.739269i	$-0.735171\pi$
$53$	−1.06271e7			−1.34682			−0.673410	+	0.739269i	$0.735171\pi$
$54$	−315414.	+	9481.73i	−0.0370942	+	0.00111510i
$55$		−	8.45260e6i		−	0.923719i
$56$	−3.70199e6	+	334666.i	−0.376429	+	0.0340298i
$57$	2.36923e6			0.224444
$58$	−280158.	−	9.31959e6i	−0.0247566	−	0.823540i
$59$		−	9.34340e6i		−	0.771075i	−0.922692	−	0.385538i	$-0.874016\pi$
$59$		−	9.34340e6i		−	0.771075i	0.922692	−	0.385538i	$-0.125984\pi$
$60$	737917.	+	1.22625e7i	0.0569381	+	0.946179i
$61$	4.84615e6			0.350008			0.175004	−	0.984568i	$-0.444006\pi$
$61$	4.84615e6			0.350008			0.175004	+	0.984568i	$0.444006\pi$
$62$	−1.06881e7	+	321299.i	−0.723329	+	0.0217442i
$63$			5.79677e6i			0.367980i
$64$	−1.65052e7	+	3.00879e6i	−0.983788	+	0.179338i
$65$	−1.10397e7			−0.618448
$66$	−1.09654e6	−	3.64768e7i	−0.0577893	−	1.92239i
$67$			6.60142e6i			0.327596i	0.986494	+	0.163798i	$0.0523745\pi$
$67$			6.60142e6i			0.327596i	−0.986494	+	0.163798i	$0.947626\pi$
$68$	2.78208e7	−	1.67417e6i	1.30117	−	0.0783004i
$69$	6.34314e7			2.79839
$70$	−6.12037e6	+	183986.i	−0.254909	+	0.00766288i
$71$			3.04115e7i			1.19675i	0.801216	+	0.598376i	$0.204187\pi$
$71$			3.04115e7i			1.19675i	−0.801216	+	0.598376i	$0.795813\pi$
$72$	2.35566e6	+	2.60577e7i	0.0876561	+	0.969630i
$73$	2.91778e7			1.02745			0.513726	−	0.857954i	$-0.328265\pi$
$73$	2.91778e7			1.02745			0.513726	+	0.857954i	$0.328265\pi$
$74$	−346359.	−	1.15218e7i	−0.0115505	−	0.384231i
$75$		−	2.42137e7i		−	0.765272i
$76$	320169.	+	5.32046e6i	0.00959675	+	0.159476i
$77$	1.81896e7			0.517440
$78$	−4.76412e7	+	1.43215e6i	−1.28708	+	0.0386911i
$79$			4.10436e7i			1.05375i	0.849943	+	0.526875i	$0.176636\pi$
$79$			4.10436e7i			1.05375i	−0.849943	+	0.526875i	$0.823364\pi$
$80$	−2.74375e7	+	3.31421e6i	−0.669861	+	0.0809133i
$81$	−4.41538e7			−1.02572
$82$	−533614.	−	1.77509e7i	−0.0118024	−	0.392613i
$83$			8.03486e7i			1.69303i	0.532361	+	0.846517i	$0.321305\pi$
$83$			8.03486e7i			1.69303i	−0.532361	+	0.846517i	$0.678695\pi$
$84$	−2.63883e7	+	1.58796e6i	−0.530022	+	0.0318951i
$85$	4.59119e7			0.879528
$86$	−5.54325e7	+	1.66637e6i	−1.01338	+	0.0304633i
$87$		−	6.63110e7i		−	1.15747i
$88$	8.17660e7	−	7.39178e6i	1.36346	−	0.123259i
$89$	−1.08138e8			−1.72352			−0.861760	−	0.507316i	$-0.830638\pi$
$89$	−1.08138e8			−1.72352			−0.861760	+	0.507316i	$0.830638\pi$
$90$	1.29504e6	+	4.30802e7i	0.0197385	+	0.656610i
$91$		−	2.37569e7i		−	0.346437i
$92$	8.57188e6	+	1.42445e8i	0.119653	+	1.98836i
$93$	−7.60486e7			−1.01662
$94$	5.49900e6	−	165307.i	0.0704324	−	0.00211728i
$95$			8.78020e6i			0.107798i
$96$	−1.17975e8	+	1.78617e7i	−1.38901	+	0.210300i
$97$	1.14406e8			1.29229			0.646147	−	0.763213i	$-0.276379\pi$
$97$	1.14406e8			1.29229			0.646147	+	0.763213i	$0.276379\pi$
$98$	−395929.	−	1.31707e7i	−0.00429252	−	0.142793i
$99$		−	1.28033e8i		−	1.33285i
$100$	5.43755e7	−	3.27215e6i	0.543755	−	0.0327215i
$101$	1.86131e8			1.78869			0.894343	−	0.447383i	$-0.147644\pi$
$101$	1.86131e8			1.78869			0.894343	+	0.447383i	$0.147644\pi$
$102$	1.98131e8	−	5.95605e6i	1.83042	−	0.0550247i
$103$		−	6.13641e7i		−	0.545212i	−0.962126	−	0.272606i	$-0.912114\pi$
$103$		−	6.13641e7i		−	0.545212i	0.962126	−	0.272606i	$-0.0878855\pi$
$104$	−9.65417e6	−	1.06792e8i	−0.0825243	−	0.912862i
$105$	−4.35478e7			−0.358269
$106$	−5.10910e6	−	1.69956e8i	−0.0404688	−	1.34621i
$107$			4.37566e7i			0.333817i	0.985972	+	0.166908i	$0.0533784\pi$
$107$			4.37566e7i			0.333817i	−0.985972	+	0.166908i	$0.946622\pi$
$108$	−303278.	−	5.03978e6i	−0.00222919	−	0.0370439i
$109$	−7.45205e7			−0.527922			−0.263961	−	0.964533i	$-0.585029\pi$
$109$	−7.45205e7			−0.527922			−0.263961	+	0.964533i	$0.585029\pi$
$110$	1.35181e8	−	4.06370e6i	0.923301	−	0.0277556i
$111$		−	8.19800e7i		−	0.540028i
$112$	−7.13202e6	−	5.90443e7i	−0.0453253	−	0.375237i
$113$	−2.94412e8			−1.80568			−0.902841	−	0.429975i	$-0.858522\pi$
$113$	−2.94412e8			−1.80568			−0.902841	+	0.429975i	$0.858522\pi$
$114$	1.13904e6	+	3.78905e7i	0.00674401	+	0.224342i
$115$			2.35073e8i			1.34404i
$116$	1.48911e8	−	8.96102e6i	0.822424	−	0.0494909i
$117$	−1.67220e8			−0.892372
$118$	1.49427e8	−	4.49196e6i	0.770727	−	0.0231690i
$119$			9.88003e7i			0.492686i
$120$	−1.95756e8	+	1.76967e7i	−0.944041	+	0.0853428i
$121$	−1.87395e8			−0.874211
$122$	2.32985e6	+	7.75034e7i	0.0105169	+	0.349850i
$123$		−	1.26302e8i		−	0.551809i
$124$	−1.02769e7	−	1.70779e8i	−0.0434687	−	0.722349i
$125$	2.54463e8			1.04228
$126$	−9.27065e7	+	2.78687e6i	−0.367814	+	0.0110569i
$127$		−	1.40357e8i		−	0.539535i	−0.962926	−	0.269767i	$-0.913053\pi$
$127$		−	1.40357e8i		−	0.539535i	0.962926	−	0.269767i	$-0.0869468\pi$
$128$	−5.60539e7	−	2.62518e8i	−0.208817	−	0.977955i
$129$	−3.94415e8			−1.42428
$130$	−5.30747e6	−	1.76555e8i	−0.0185829	−	0.618169i
$131$			2.56569e8i			0.871202i	0.900140	+	0.435601i	$0.143464\pi$
$131$			2.56569e8i			0.871202i	−0.900140	+	0.435601i	$0.856536\pi$
$132$	5.82838e8	−	3.50734e7i	1.91978	−	0.115526i
$133$	−1.88946e7			−0.0603852
$134$	−1.05575e8	+	3.17372e6i	−0.327448	+	0.00984349i
$135$		−	8.31701e6i		−	0.0250399i
$136$	4.01498e7	+	4.44127e8i	0.117362	+	1.29823i
$137$	4.52210e8			1.28368			0.641842	−	0.766837i	$-0.278171\pi$
$137$	4.52210e8			1.28368			0.641842	+	0.766837i	$0.278171\pi$
$138$	3.04955e7	+	1.01444e9i	0.0840851	+	2.79713i
$139$		−	5.26618e8i		−	1.41071i	−0.708856	−	0.705353i	$-0.750789\pi$
$139$		−	5.26618e8i		−	1.41071i	0.708856	−	0.705353i	$-0.249211\pi$
$140$	−5.88489e6	−	9.77932e7i	−0.0153188	−	0.254564i
$141$	3.91266e7			0.0989911
$142$	−4.86364e8	+	1.46207e7i	−1.19621	+	0.0359596i
$143$			5.24718e8i			1.25482i
$144$	−4.15602e8	+	5.02011e7i	−0.966558	+	0.116752i
$145$	2.45744e8			0.555919
$146$	1.40276e7	+	4.66634e8i	0.0308725	+	1.02699i
$147$		−	9.37128e7i		−	0.200692i
$148$	1.84098e8	−	1.10785e7i	0.383710	−	0.0230905i
$149$	−4.05691e8			−0.823096			−0.411548	−	0.911388i	$-0.635012\pi$
$149$	−4.05691e8			−0.823096			−0.411548	+	0.911388i	$0.635012\pi$
$150$	3.87244e8	−	1.16410e7i	0.764927	−	0.0229946i
$151$			7.92336e8i			1.52406i	0.647543	+	0.762029i	$0.275797\pi$
$151$			7.92336e8i			1.52406i	−0.647543	+	0.762029i	$0.724203\pi$
$152$	−8.49350e7	+	7.67826e6i	−0.159115	+	0.0143843i
$153$	6.95438e8			1.26909
$154$	8.74488e6	+	2.90902e8i	0.0155479	+	0.517207i
$155$		−	2.81831e8i		−	0.488272i
$156$	−4.58082e7	−	7.61227e8i	−0.0773473	−	1.28533i
$157$	2.77859e8			0.457326			0.228663	−	0.973506i	$-0.426565\pi$
$157$	2.77859e8			0.457326			0.228663	+	0.973506i	$0.426565\pi$
$158$	−6.56401e8	+	1.97322e7i	−1.05327	+	0.0316627i
$159$		−	1.20928e9i		−	1.89207i
$160$	−6.61944e7	−	4.37209e8i	−0.101005	−	0.667128i
$161$	−5.05865e8			−0.752890
$162$	−2.12275e7	−	7.06142e8i	−0.0308204	−	1.02526i
$163$			1.65174e8i			0.233987i	0.993133	+	0.116993i	$0.0373256\pi$
$163$			1.65174e8i			0.233987i	−0.993133	+	0.116993i	$0.962674\pi$
$164$	2.83630e8	−	1.70679e7i	0.392081	−	0.0235942i
$165$	9.61841e8			1.29768
$166$	−1.28500e9	+	3.86286e7i	−1.69227	+	0.0508717i
$167$			7.97740e8i			1.02564i	0.858496	+	0.512821i	$0.171399\pi$
$167$			7.97740e8i			1.02564i	−0.858496	+	0.512821i	$0.828601\pi$
$168$	−3.80824e7	−	4.21258e8i	−0.0478066	−	0.528824i
$169$	−1.30412e8			−0.159872
$170$	2.20727e7	+	7.34259e8i	0.0264278	+	0.879131i
$171$			1.32996e8i			0.155544i
$172$	−5.32998e7	−	8.85719e8i	−0.0608992	−	1.01200i
$173$	7.25228e8			0.809637			0.404818	−	0.914397i	$-0.367335\pi$
$173$	7.25228e8			0.809637			0.404818	+	0.914397i	$0.367335\pi$
$174$	1.06050e9	−	3.18799e7i	1.15694	−	0.0347792i
$175$			1.93104e8i			0.205892i
$176$	1.57525e8	+	1.30411e9i	0.164172	+	1.35914i
$177$	1.06321e9			1.08324
$178$	−5.19885e7	−	1.72942e9i	−0.0517877	−	1.72274i
$179$		−	2.08752e8i		−	0.203338i	−0.994818	−	0.101669i	$-0.967582\pi$
$179$		−	2.08752e8i		−	0.203338i	0.994818	−	0.101669i	$-0.0324183\pi$
$180$	−6.88349e8	+	4.14227e7i	−0.655720	+	0.0394592i
$181$	−1.87673e9			−1.74859			−0.874294	−	0.485397i	$-0.838675\pi$
$181$	−1.87673e9			−1.74859			−0.874294	+	0.485397i	$0.838675\pi$
$182$	3.79938e8	−	1.14214e7i	0.346280	−	0.0104096i
$183$			5.51455e8i			0.491706i
$184$	−2.27397e9	+	2.05570e8i	−1.98387	+	0.179345i
$185$	3.03812e8			0.259369
$186$	−3.65613e7	−	1.21623e9i	−0.0305471	−	1.01616i
$187$		−	2.18220e9i		−	1.78455i
$188$	5.28743e6	+	8.78648e7i	0.00423266	+	0.0703369i
$189$	1.78978e7			0.0140266
$190$	−1.40420e8	+	4.22119e6i	−0.107749	+	0.00323907i
$191$			1.15398e9i			0.867094i	0.901131	+	0.433547i	$0.142738\pi$
$191$			1.15398e9i			0.867094i	−0.901131	+	0.433547i	$0.857262\pi$
$192$	−3.42377e8	−	1.87817e9i	−0.251941	−	1.38207i
$193$	2.01198e9			1.45009			0.725045	−	0.688702i	$-0.241819\pi$
$193$	2.01198e9			1.45009			0.725045	+	0.688702i	$0.241819\pi$
$194$	5.50020e7	+	1.82967e9i	0.0388304	+	1.29171i
$195$		−	1.25623e9i		−	0.868822i
$196$	2.10446e8	−	1.26640e7i	0.142599	−	0.00858117i
$197$	−2.04195e9			−1.35575			−0.677876	−	0.735176i	$-0.737100\pi$
$197$	−2.04195e9			−1.35575			−0.677876	+	0.735176i	$0.737100\pi$
$198$	2.04761e9	−	6.15537e7i	1.33225	−	0.0400491i
$199$		−	1.98787e9i		−	1.26758i	−0.773505	−	0.633790i	$-0.781498\pi$
$199$		−	1.98787e9i		−	1.26758i	0.773505	−	0.633790i	$-0.218502\pi$
$200$	7.84724e7	+	8.68042e8i	0.0490453	+	0.542526i
$201$	−7.51191e8			−0.460221
$202$	8.94850e7	+	2.97676e9i	0.0537458	+	1.78788i
$203$			5.28830e8i			0.311409i
$204$	1.90508e8	+	3.16580e9i	0.110000	+	1.82794i
$205$	4.68066e8			0.265028
$206$	9.81382e8	−	2.95016e7i	0.544966	−	0.0163823i
$207$			3.56070e9i			1.93934i
$208$	1.70326e9	−	2.05739e8i	0.909971	−	0.109916i
$209$	4.17325e8			0.218720
$210$	−2.09362e7	−	6.96450e8i	−0.0107651	−	0.358107i
$211$		−	1.74166e9i		−	0.878684i	−0.898320	−	0.439342i	$-0.855212\pi$
$211$		−	1.74166e9i		−	0.878684i	0.898320	−	0.439342i	$-0.144788\pi$
$212$	2.71562e9	−	1.63417e8i	1.34439	−	0.0809011i
$213$	−3.46059e9			−1.68125
$214$	−6.99789e8	+	2.10365e7i	−0.333666	+	0.0100304i
$215$		−	1.46168e9i		−	0.684065i
$216$	8.04543e7	−	7.27320e6i	0.0369602	−	0.00334126i
$217$	6.06487e8			0.273516
$218$	−3.58267e7	−	1.19179e9i	−0.0158628	−	0.527683i
$219$			3.32021e9i			1.44341i
$220$	1.29980e8	+	2.15996e9i	0.0554861	+	0.922051i
$221$	−2.85011e9			−1.19479
$222$	1.31109e9	−	3.94129e7i	0.539784	−	0.0162266i
$223$			1.93537e9i			0.782607i	0.920262	+	0.391303i	$0.127976\pi$
$223$			1.93537e9i			0.782607i	−0.920262	+	0.391303i	$0.872024\pi$
$224$	9.40853e8	−	1.42447e8i	0.373706	−	0.0565798i
$225$	1.35923e9			0.530349
$226$	−1.41542e8	−	4.70846e9i	−0.0542565	−	1.80487i
$227$			9.19491e8i			0.346293i	0.984896	+	0.173147i	$0.0553935\pi$
$227$			9.19491e8i			0.346293i	−0.984896	+	0.173147i	$0.944607\pi$
$228$	−6.05427e8	+	3.64327e7i	−0.224038	+	0.0134819i
$229$	1.00898e9			0.366896			0.183448	−	0.983029i	$-0.441274\pi$
$229$	1.00898e9			0.366896			0.183448	+	0.983029i	$0.441274\pi$
$230$	−3.75946e9	+	1.13014e8i	−1.34343	+	0.0403851i
$231$			2.06984e9i			0.726922i
$232$	2.14903e8	+	2.37720e9i	0.0741805	+	0.820566i
$233$	−2.28993e9			−0.776960			−0.388480	−	0.921457i	$-0.627000\pi$
$233$	−2.28993e9			−0.776960			−0.388480	+	0.921457i	$0.627000\pi$
$234$	−8.03934e7	−	2.67432e9i	−0.0268137	−	0.891969i
$235$			1.45001e8i			0.0475443i
$236$	1.43678e8	+	2.38759e9i	0.0463171	+	0.769683i
$237$	−4.67045e9			−1.48035
$238$	−1.58009e9	+	4.74995e7i	−0.492464	+	0.0148041i
$239$		−	1.86010e8i		−	0.0570090i	−0.999594	−	0.0285045i	$-0.990926\pi$
$239$		−	1.86010e8i		−	0.0570090i	0.999594	−	0.0285045i	$-0.00907450\pi$
$240$	−3.77131e8	−	3.12218e9i	−0.113671	−	0.941050i
$241$	1.91210e9			0.566817			0.283408	−	0.958999i	$-0.408535\pi$
$241$	1.91210e9			0.566817			0.283408	+	0.958999i	$0.408535\pi$
$242$	−9.00925e7	−	2.99697e9i	−0.0262680	−	0.873817i
$243$		−	4.89497e9i		−	1.40386i
$244$	−1.23837e9	+	7.45215e7i	−0.349376	+	0.0210243i
$245$	3.47294e8			0.0963901
$246$	2.01992e9	−	6.07212e7i	0.551560	−	0.0165806i
$247$		−	5.45055e8i		−	0.146438i
$248$	2.72628e9	−	2.46461e8i	0.720716	−	0.0651539i
$249$	−9.14305e9			−2.37845
$250$	1.22337e8	+	4.06958e9i	0.0313182	+	1.04181i
$251$		−	5.15337e9i		−	1.29836i	−0.760633	−	0.649182i	$-0.775111\pi$
$251$		−	5.15337e9i		−	1.29836i	0.760633	−	0.649182i	$-0.224889\pi$
$252$	−8.91397e7	−	1.48129e9i	−0.0221039	−	0.367316i
$253$	1.11731e10			2.72703
$254$	2.24470e9	−	6.74784e7i	0.539291	−	0.0162118i
$255$			5.22442e9i			1.23560i
$256$	4.17144e9	−	1.02267e9i	0.971239	−	0.238108i
$257$	3.79879e8			0.0870789			0.0435394	−	0.999052i	$-0.486137\pi$
$257$	3.79879e8			0.0870789			0.0435394	+	0.999052i	$0.486137\pi$
$258$	−1.89620e8	−	6.30779e9i	−0.0427962	−	1.42363i
$259$			6.53790e8i			0.145291i
$260$	2.82106e9	−	1.69762e8i	0.617331	−	0.0371491i
$261$	3.72234e9			0.802147
$262$	−4.10325e9	+	1.23349e8i	−0.870809	+	0.0261776i
$263$			1.77115e9i			0.370196i	0.982720	+	0.185098i	$0.0592603\pi$
$263$			1.77115e9i			0.370196i	−0.982720	+	0.185098i	$0.940740\pi$
$264$	8.41127e8	+	9.30433e9i	0.173159	+	1.91544i
$265$	4.48150e9			0.908741
$266$	−9.08381e6	−	3.02177e8i	−0.00181443	−	0.0603580i
$267$		−	1.23052e10i		−	2.42127i
$268$	−1.01513e8	−	1.68691e9i	−0.0196781	−	0.327004i
$269$	5.98251e9			1.14255			0.571274	−	0.820760i	$-0.306450\pi$
$269$	5.98251e9			1.14255			0.571274	+	0.820760i	$0.306450\pi$
$270$	1.33012e8	−	3.99851e6i	0.0250286	−	0.000752389i
$271$		−	5.53681e8i		−	0.102656i	−0.998682	−	0.0513278i	$-0.983655\pi$
$271$		−	5.53681e8i		−	0.102656i	0.998682	−	0.0513278i	$-0.0163453\pi$
$272$	−7.08353e9	+	8.55627e8i	−1.29412	+	0.156318i
$273$	2.70335e9			0.486689
$274$	2.17406e8	+	7.23209e9i	0.0385717	+	1.28310i
$275$		−	4.26509e9i		−	0.745757i
$276$	−1.62091e10	+	9.75414e8i	−2.79334	+	0.168094i
$277$	−1.65972e9			−0.281913			−0.140957	−	0.990016i	$-0.545018\pi$
$277$	−1.65972e9			−0.281913			−0.140957	+	0.990016i	$0.545018\pi$
$278$	8.42208e9	−	2.53178e8i	1.41007	−	0.0423884i
$279$		−	4.26896e9i		−	0.704539i
$280$	1.56116e9	−	1.41131e8i	0.253988	−	0.0229610i
$281$	−6.52132e9			−1.04595			−0.522975	−	0.852348i	$-0.675178\pi$
$281$	−6.52132e9			−1.04595			−0.522975	+	0.852348i	$0.675178\pi$
$282$	1.88106e7	+	6.25744e8i	0.00297445	+	0.0989464i
$283$			8.04314e9i			1.25395i	0.779040	+	0.626975i	$0.215707\pi$
$283$			8.04314e9i			1.25395i	−0.779040	+	0.626975i	$0.784293\pi$
$284$	−4.67651e8	−	7.77128e9i	−0.0718867	−	1.19459i
$285$	−9.99119e8			−0.151439
$286$	−8.39170e9	+	2.52265e8i	−1.25426	+	0.0377045i
$287$			1.00726e9i			0.148461i
$288$	−1.00266e9	−	6.62250e9i	−0.145742	−	0.962613i
$289$	4.87729e9			0.699178
$290$	1.18145e8	+	3.93013e9i	0.0167041	+	0.555668i
$291$			1.30185e10i			1.81547i
$292$	−7.45603e9	+	4.48681e8i	−1.02560	+	0.0617172i
$293$	−1.78929e9			−0.242779			−0.121390	−	0.992605i	$-0.538735\pi$
$293$	−1.78929e9			−0.242779			−0.121390	+	0.992605i	$0.538735\pi$
$294$	1.49873e9	−	4.50536e7i	0.200601	−	0.00603032i
$295$			3.94017e9i			0.520268i
$296$	2.65683e8	+	2.93892e9i	0.0346096	+	0.382843i
$297$	−3.95309e8			−0.0508055
$298$	−1.95041e8	−	6.48813e9i	−0.0247321	−	0.822725i
$299$		−	1.45928e10i		−	1.82580i
$300$	3.72345e8	+	6.18751e9i	0.0459685	+	0.763890i
$301$	3.14546e9			0.383193
$302$	−1.26717e10	+	3.80926e8i	−1.52337	+	0.0457944i
$303$			2.11803e10i			2.51282i
$304$	−1.63630e8	−	1.35465e9i	−0.0191588	−	0.158611i
$305$	−2.04365e9			−0.236161
$306$	3.34341e8	+	1.11220e10i	0.0381332	+	1.26852i
$307$			3.27610e9i			0.368811i	0.982850	+	0.184405i	$0.0590359\pi$
$307$			3.27610e9i			0.368811i	−0.982850	+	0.184405i	$0.940964\pi$
$308$	−4.64813e9	+	2.79710e8i	−0.516506	+	0.0310817i
$309$	6.98276e9			0.765937
$310$	4.50726e9	−	1.35494e8i	0.488052	−	0.0146714i
$311$			1.33236e10i			1.42423i	0.702062	+	0.712116i	$0.252263\pi$
$311$			1.33236e10i			1.42423i	−0.702062	+	0.712116i	$0.747737\pi$
$312$	1.21521e10	−	1.09857e9i	1.28243	−	0.115934i
$313$	3.94528e9			0.411056			0.205528	−	0.978651i	$-0.434109\pi$
$313$	3.94528e9			0.411056			0.205528	+	0.978651i	$0.434109\pi$
$314$	1.33584e8	+	4.44374e9i	0.0137416	+	0.457120i
$315$		−	2.44454e9i		−	0.248287i
$316$	−6.31147e8	−	1.04882e10i	−0.0632968	−	1.05185i
$317$	4.85851e9			0.481134			0.240567	−	0.970633i	$-0.422667\pi$
$317$	4.85851e9			0.481134			0.240567	+	0.970633i	$0.422667\pi$
$318$	1.93397e10	−	5.81376e8i	1.89122	−	0.0568523i
$319$		−	1.16803e10i		−	1.12795i
$320$	6.96036e9	−	1.26883e9i	0.663792	−	0.121005i
$321$	−4.97916e9			−0.468960
$322$	−2.43201e8	−	8.09019e9i	−0.0226226	−	0.752550i
$323$			2.26678e9i			0.208257i
$324$	1.12830e10	−	6.78974e8i	1.02387	−	0.0616131i
$325$	−5.57050e9			−0.499299
$326$	−2.64159e9	+	7.94095e7i	−0.233881	+	0.00703076i
$327$		−	8.47985e9i		−	0.741647i
$328$	4.09322e8	+	4.52782e9i	0.0353647	+	0.391195i
$329$	−3.12035e8			−0.0266330
$330$	4.62417e8	+	1.53825e10i	0.0389922	+	1.29709i
$331$			8.78441e9i			0.731814i	0.930651	+	0.365907i	$0.119241\pi$
$331$			8.78441e9i			0.731814i	−0.930651	+	0.365907i	$0.880759\pi$
$332$	−1.23556e9	−	2.05321e10i	−0.101698	−	1.68998i
$333$	4.60191e9			0.374250
$334$	−1.27581e10	+	3.83524e8i	−1.02518	+	0.0308181i
$335$		−	2.78386e9i		−	0.221039i
$336$	6.71878e9	−	8.11569e8i	0.527149	−	0.0636749i
$337$	−2.76498e9			−0.214374			−0.107187	−	0.994239i	$-0.534184\pi$
$337$	−2.76498e9			−0.214374			−0.107187	+	0.994239i	$0.534184\pi$
$338$	−6.26974e7	−	2.08566e9i	−0.00480378	−	0.159800i
$339$		−	3.35018e10i		−	2.53670i
$340$	−1.17322e10	+	7.06009e8i	−0.877940	+	0.0528317i
$341$	−1.33955e10			−0.990697
$342$	−2.12697e9	+	6.39393e7i	−0.155474	+	0.00467373i
$343$			7.47359e8i			0.0539949i
$344$	1.41395e10	−	1.27823e9i	1.00972	−	0.0912800i
$345$	−2.67495e10			−1.88816
$346$	3.48662e8	+	1.15984e10i	0.0243277	+	0.809271i
$347$		−	3.87636e9i		−	0.267366i	−0.991024	−	0.133683i	$-0.957320\pi$
$347$		−	3.87636e9i		−	0.267366i	0.991024	−	0.133683i	$-0.0426803\pi$
$348$	1.01969e9	+	1.69450e10i	0.0695270	+	1.15538i
$349$	7.86220e9			0.529959			0.264979	−	0.964254i	$-0.414635\pi$
$349$	7.86220e9			0.529959			0.264979	+	0.964254i	$0.414635\pi$
$350$	−3.08827e9	+	9.28372e7i	−0.205799	+	0.00618657i
$351$			5.16301e8i			0.0340153i
$352$	−2.07806e10	+	3.14623e9i	−1.35359	+	0.204937i
$353$	−1.22133e10			−0.786563			−0.393281	−	0.919418i	$-0.628660\pi$
$353$	−1.22133e10			−0.786563			−0.393281	+	0.919418i	$0.628660\pi$
$354$	5.11150e8	+	1.70036e10i	0.0325488	+	1.08275i
$355$		−	1.28247e10i		−	0.807485i
$356$	2.76332e10	−	1.66288e9i	1.72041	−	0.103529i
$357$	−1.12427e10			−0.692147
$358$	3.33853e9	−	1.00360e8i	0.203246	−	0.00610984i
$359$		−	5.63090e9i		−	0.339000i	−0.985530	−	0.169500i	$-0.945785\pi$
$359$		−	5.63090e9i		−	0.339000i	0.985530	−	0.169500i	$-0.0542153\pi$
$360$	−9.93396e8	−	1.09887e10i	−0.0591442	−	0.654239i
$361$	1.65501e10			0.974475
$362$	−9.02262e8	−	3.00141e10i	−0.0525410	−	1.74780i
$363$		−	2.13241e10i		−	1.22813i
$364$	3.65320e8	+	6.07078e9i	0.0208098	+	0.345811i
$365$	−1.23045e10			−0.693253
$366$	−8.81929e9	+	2.65119e8i	−0.491484	+	0.0147746i
$367$			1.70730e10i			0.941120i	0.882368	+	0.470560i	$0.155948\pi$
$367$			1.70730e10i			0.941120i	−0.882368	+	0.470560i	$0.844052\pi$
$368$	−4.38088e9	−	3.62682e10i	−0.238875	−	1.97758i
$369$	7.08990e9			0.382415
$370$	1.46062e8	+	4.85880e9i	0.00779344	+	0.259252i
$371$			9.64398e9i			0.509050i
$372$	1.94333e10	−	1.16943e9i	1.01479	−	0.0610667i
$373$	−4.23927e8			−0.0219006			−0.0109503	−	0.999940i	$-0.503486\pi$
$373$	−4.23927e8			−0.0219006			−0.0109503	+	0.999940i	$0.503486\pi$
$374$	3.48995e10	−	1.04912e9i	1.78374	−	0.0536216i
$375$			2.89560e10i			1.46424i
$376$	−1.40266e9	+	1.26803e8i	−0.0701780	+	0.00634421i
$377$	−1.52552e10			−0.755185
$378$	8.60460e6	+	2.86236e8i	0.000421467	+	0.0140203i
$379$		−	3.68579e9i		−	0.178638i	−0.996003	−	0.0893191i	$-0.971531\pi$
$379$		−	3.68579e9i		−	0.178638i	0.996003	−	0.0893191i	$-0.0284691\pi$
$380$	−1.35017e8	−	2.24367e9i	−0.00647522	−	0.107603i
$381$	1.59715e10			0.757961
$382$	−1.84554e10	+	5.54792e8i	−0.866702	+	0.0260541i
$383$			1.68400e10i			0.782611i	0.920261	+	0.391306i	$0.127976\pi$
$383$			1.68400e10i			0.782611i	−0.920261	+	0.391306i	$0.872024\pi$
$384$	2.98725e10	−	6.37850e9i	1.37387	−	0.293355i
$385$	−7.67067e9			−0.349133
$386$	9.67286e8	+	3.21772e10i	0.0435718	+	1.44943i
$387$		−	2.21403e10i		−	0.987052i
$388$	−2.92350e10	+	1.75927e9i	−1.28996	+	0.0776257i
$389$	1.17832e9			0.0514592			0.0257296	−	0.999669i	$-0.491809\pi$
$389$	1.17832e9			0.0514592			0.0257296	+	0.999669i	$0.491809\pi$
$390$	2.00906e10	−	6.03949e8i	0.868430	−	0.0261061i
$391$			6.06886e10i			2.59657i
$392$	3.03707e8	+	3.35953e9i	0.0128621	+	0.142277i
$393$	−2.91956e10			−1.22390
$394$	−9.81694e8	−	3.26565e10i	−0.0407372	−	1.35514i
$395$		−	1.73084e10i		−	0.710997i
$396$	1.96883e9	+	3.27174e10i	0.0800621	+	1.33045i
$397$	2.28317e10			0.919128			0.459564	−	0.888145i	$-0.348006\pi$
$397$	2.28317e10			0.919128			0.459564	+	0.888145i	$0.348006\pi$
$398$	3.17916e10	−	9.55694e8i	1.26701	−	0.0380878i
$399$		−	2.15006e9i		−	0.0848317i
$400$	−1.38447e10	+	1.67231e9i	−0.540808	+	0.0653248i
$401$	3.80794e10			1.47270			0.736348	−	0.676603i	$-0.236549\pi$
$401$	3.80794e10			1.47270			0.736348	+	0.676603i	$0.236549\pi$
$402$	−3.61145e8	−	1.20136e10i	−0.0138286	−	0.460013i
$403$			1.74954e10i			0.663292i
$404$	−4.75636e10	+	2.86223e9i	−1.78546	+	0.107443i
$405$	1.86200e10			0.692084
$406$	−8.45746e9	+	2.54242e8i	−0.311269	+	0.00935713i
$407$		−	1.44403e10i		−	0.526257i
$408$	−5.05383e10	+	4.56874e9i	−1.82381	+	0.164875i
$409$	−1.20508e10			−0.430649			−0.215325	−	0.976542i	$-0.569081\pi$
$409$	−1.20508e10			−0.430649			−0.215325	+	0.976542i	$0.569081\pi$
$410$	2.25029e8	+	7.48567e9i	0.00796347	+	0.264908i
$411$			5.14580e10i			1.80337i
$412$	9.43623e8	+	1.56808e10i	0.0327499	+	0.544227i
$413$	−8.47906e9			−0.291439
$414$	−5.69454e10	+	1.71185e9i	−1.93846	+	0.0582726i
$415$		−	3.38835e10i		−	1.14234i
$416$	4.10919e9	+	2.71409e10i	0.137209	+	0.906257i
$417$	5.99250e10			1.98182
$418$	2.00634e8	+	6.67418e9i	0.00657203	+	0.218621i
$419$		−	5.42002e9i		−	0.175851i	−0.996127	−	0.0879256i	$-0.971976\pi$
$419$		−	5.42002e9i		−	0.175851i	0.996127	−	0.0879256i	$-0.0280238\pi$
$420$	1.11281e10	−	6.69655e8i	0.357622	−	0.0215206i
$421$	−1.80269e10			−0.573842			−0.286921	−	0.957954i	$-0.592632\pi$
$421$	−1.80269e10			−0.573842			−0.286921	+	0.957954i	$0.592632\pi$
$422$	2.78539e10	−	8.37323e8i	0.878287	−	0.0264024i
$423$			2.19636e9i			0.0686028i
$424$	3.91906e9	+	4.33517e10i	0.121260	+	1.34135i
$425$	2.31667e10			0.710080
$426$	−1.66372e9	−	5.53444e10i	−0.0505176	−	1.68049i
$427$		−	4.39785e9i		−	0.132291i
$428$	−6.72865e8	−	1.11815e10i	−0.0200518	−	0.333214i
$429$	−5.97089e10			−1.76283
$430$	2.33763e10	−	7.02719e8i	0.683756	−	0.0205546i
$431$		−	5.65231e10i		−	1.63801i	−0.573785	−	0.819006i	$-0.694525\pi$
$431$		−	5.65231e10i		−	1.63801i	0.573785	−	0.819006i	$-0.305475\pi$
$432$	1.54998e8	+	1.28319e9i	0.00445032	+	0.0368431i
$433$	5.51824e10			1.56982			0.784909	−	0.619611i	$-0.212710\pi$
$433$	5.51824e10			1.56982			0.784909	+	0.619611i	$0.212710\pi$
$434$	2.91576e8	+	9.69941e9i	0.00821852	+	0.273393i
$435$			2.79638e10i			0.780978i
$436$	1.90428e10	−	1.14594e9i	0.526968	−	0.0317113i
$437$	−1.16061e10			−0.318244
$438$	−5.30994e10	+	1.59623e9i	−1.44276	+	0.0433710i
$439$		−	4.01558e10i		−	1.08116i	−0.841292	−	0.540580i	$-0.818205\pi$
$439$		−	4.01558e10i		−	1.08116i	0.841292	−	0.540580i	$-0.181795\pi$
$440$	−3.44812e10	+	3.11716e9i	−0.919967	+	0.0831665i
$441$	5.26053e9			0.139083
$442$	−1.37023e9	−	4.55811e10i	−0.0359007	−	1.19425i
$443$		−	6.46594e9i		−	0.167887i	−0.996471	−	0.0839435i	$-0.973248\pi$
$443$		−	6.46594e9i		−	0.167887i	0.996471	−	0.0839435i	$-0.0267515\pi$
$444$	1.26064e9	+	2.09490e10i	0.0324385	+	0.539053i
$445$	4.56023e10			1.16291
$446$	−3.09519e10	+	9.30452e8i	−0.782253	+	0.0235155i
$447$		−	4.61645e10i		−	1.15632i
$448$	2.73045e9	+	1.49784e10i	0.0677833	+	0.371837i
$449$	2.13689e10			0.525770			0.262885	−	0.964827i	$-0.415326\pi$
$449$	2.13689e10			0.525770			0.262885	+	0.964827i	$0.415326\pi$
$450$	6.53465e8	+	2.17378e10i	0.0159357	+	0.530109i
$451$		−	2.22473e10i		−	0.537738i
$452$	7.52333e10	−	4.52730e9i	1.80242	−	0.108464i
$453$	−9.01617e10			−2.14106
$454$	−1.47052e10	+	4.42057e8i	−0.346137	+	0.0104053i
$455$			1.00184e10i			0.233751i
$456$	−8.73727e8	−	9.66495e9i	−0.0202077	−	0.223532i
$457$	3.93231e10			0.901535			0.450768	−	0.892641i	$-0.351150\pi$
$457$	3.93231e10			0.901535			0.450768	+	0.892641i	$0.351150\pi$
$458$	4.85082e8	+	1.61365e10i	0.0110244	+	0.366730i
$459$		−	2.14720e9i		−	0.0483750i
$460$	−3.61482e9	−	6.00699e10i	−0.0807338	−	1.34161i
$461$	−2.57663e9			−0.0570490			−0.0285245	−	0.999593i	$-0.509081\pi$
$461$	−2.57663e9			−0.0570490			−0.0285245	+	0.999593i	$0.509081\pi$
$462$	−3.31024e10	+	9.95100e8i	−0.726594	+	0.0218423i
$463$			1.21173e10i			0.263684i	0.991271	+	0.131842i	$0.0420891\pi$
$463$			1.21173e10i			0.263684i	−0.991271	+	0.131842i	$0.957911\pi$
$464$	−3.79147e10	+	4.57976e9i	−0.817966	+	0.0988031i
$465$	3.20702e10			0.685946
$466$	−1.10091e9	−	3.66224e10i	−0.0233458	−	0.776609i
$467$			8.39380e10i			1.76478i	0.470517	+	0.882391i	$0.344068\pi$
$467$			8.39380e10i			1.76478i	−0.470517	+	0.882391i	$0.655932\pi$
$468$	4.27311e10	−	2.57143e9i	0.890761	−	0.0536032i
$469$	5.99074e9			0.123820
$470$	−2.31896e9	+	6.97109e7i	−0.0475229	+	0.00142860i
$471$			3.16182e10i			0.642471i
$472$	−3.81151e10	+	3.44567e9i	−0.767944	+	0.0694233i
$473$	−6.94738e10			−1.38796
$474$	−2.24538e9	−	7.46934e10i	−0.0444811	−	1.47968i
$475$			4.43039e9i			0.0870298i
$476$	−1.51930e9	−	2.52472e10i	−0.0295948	−	0.491797i
$477$	6.78823e10			1.31124
$478$	2.97481e9	−	8.94264e7i	0.0569833	−	0.00171299i
$479$			3.20517e10i			0.608848i	0.952537	+	0.304424i	$0.0984640\pi$
$479$			3.20517e10i			0.608848i	−0.952537	+	0.304424i	$0.901536\pi$
$480$	4.97510e10	−	7.53241e9i	0.937210	−	0.141896i
$481$	−1.88600e10			−0.352339
$482$	9.19267e8	+	3.05798e10i	0.0170315	+	0.566561i
$483$		−	5.75636e10i		−	1.05769i
$484$	4.78865e10	−	2.88166e9i	0.872633	−	0.0525123i
$485$	−4.82457e10			−0.871950
$486$	7.82841e10	−	2.35332e9i	1.40323	−	0.0421828i
$487$		−	9.05554e10i		−	1.60990i	−0.593344	−	0.804949i	$-0.702193\pi$
$487$		−	9.05554e10i		−	1.60990i	0.593344	−	0.804949i	$-0.297807\pi$
$488$	−1.78717e9	−	1.97692e10i	−0.0315128	−	0.348586i
$489$	−1.87955e10			−0.328715
$490$	1.66966e8	+	5.55419e9i	0.00289630	+	0.0963466i
$491$			3.57660e10i			0.615382i	0.951486	+	0.307691i	$0.0995563\pi$
$491$			3.57660e10i			0.615382i	−0.951486	+	0.307691i	$0.900444\pi$
$492$	1.94220e9	+	3.22749e10i	0.0331462	+	0.550813i
$493$	6.34436e10			1.07399
$494$	8.71694e9	−	2.62042e8i	0.146371	−	0.00440011i
$495$			5.39925e10i			0.899317i
$496$	5.25228e9	+	4.34824e10i	0.0867804	+	0.718433i
$497$	2.75982e10			0.452329
$498$	−4.39564e9	−	1.46223e11i	−0.0714668	−	2.37737i
$499$			8.01000e9i			0.129191i	0.997912	+	0.0645953i	$0.0205756\pi$
$499$			8.01000e9i			0.129191i	−0.997912	+	0.0645953i	$0.979424\pi$
$500$	−6.50250e10	+	3.91300e9i	−1.04040	+	0.0626080i
$501$	−9.07767e10			−1.44086
$502$	8.24167e10	−	2.47755e9i	1.29778	−	0.0390128i
$503$			2.50451e10i			0.391246i	0.980679	+	0.195623i	$0.0626729\pi$
$503$			2.50451e10i			0.391246i	−0.980679	+	0.195623i	$0.937327\pi$
$504$	2.36472e10	−	2.13774e9i	0.366486	−	0.0331309i
$505$	−7.84928e10			−1.20688
$506$	5.37159e9	+	1.78688e11i	0.0819408	+	2.72580i
$507$		−	1.48399e10i		−	0.224595i
$508$	2.15833e9	+	3.58665e10i	0.0324089	+	0.538560i
$509$	9.42879e9			0.140470			0.0702352	−	0.997530i	$-0.477625\pi$
$509$	9.42879e9			0.140470			0.0702352	+	0.997530i	$0.477625\pi$
$510$	−8.35530e10	+	2.51171e9i	−1.23504	+	0.0371269i
$511$		−	2.64787e10i		−	0.388340i
$512$	1.83608e10	+	6.62212e10i	0.267184	+	0.963646i
$513$	4.10630e8			0.00592900
$514$	1.82632e8	+	6.07532e9i	0.00261652	+	0.0870395i
$515$			2.58776e10i			0.367871i
$516$	1.00788e11	−	6.06510e9i	1.42171	−	0.0855538i
$517$	6.89191e9			0.0964667
$518$	−1.04559e10	+	3.14318e8i	−0.145226	+	0.00436566i
$519$			8.25253e10i			1.13741i
$520$	4.07123e9	+	4.50349e10i	0.0556816	+	0.615936i
$521$	−2.88643e10			−0.391752			−0.195876	−	0.980629i	$-0.562755\pi$
$521$	−2.88643e10			−0.391752			−0.195876	+	0.980629i	$0.562755\pi$
$522$	1.78956e9	+	5.95306e10i	0.0241027	+	0.801785i
$523$			1.81241e10i			0.242243i	0.992638	+	0.121121i	$0.0386490\pi$
$523$			1.81241e10i			0.242243i	−0.992638	+	0.121121i	$0.961351\pi$
$524$	−3.94538e9	−	6.55631e10i	−0.0523315	−	0.869629i
$525$	−2.19737e10			−0.289246
$526$	−2.83256e10	+	8.51502e8i	−0.370029	+	0.0111235i
$527$		−	7.27602e10i		−	0.943303i
$528$	−1.48398e11	+	1.79251e10i	−1.90938	+	0.230636i
$529$	−2.32419e11			−2.96790
$530$	2.15454e9	+	7.16717e10i	0.0273056	+	0.908331i
$531$			5.96826e10i			0.750706i
$532$	4.82828e9	−	2.90551e8i	0.0602762	−	0.00362723i
$533$	−2.90565e10			−0.360026
$534$	1.96795e11	−	5.91589e9i	2.42018	−	0.0727537i
$535$		−	1.84524e10i		−	0.225236i
$536$	2.69296e10	−	2.43448e9i	0.326265	−	0.0294949i
$537$	2.37544e10			0.285658
$538$	2.87617e9	+	9.56769e10i	0.0343309	+	1.14203i
$539$		−	1.65069e10i		−	0.195574i
$540$	1.27894e8	+	2.12531e9i	0.00150410	+	0.0249947i
$541$	−8.46099e9			−0.0987716			−0.0493858	−	0.998780i	$-0.515726\pi$
$541$	−8.46099e9			−0.0987716			−0.0493858	+	0.998780i	$0.515726\pi$
$542$	8.85489e9	−	2.66189e8i	0.102609	−	0.00308456i
$543$		−	2.13557e11i		−	2.45649i
$544$	−1.70894e10	−	1.12874e11i	−0.195133	−	1.28884i
$545$	3.14258e10			0.356205
$546$	1.29967e9	+	4.32341e10i	0.0146239	+	0.486469i
$547$		−	9.80343e10i		−	1.09504i	−0.836794	−	0.547518i	$-0.815573\pi$
$547$		−	9.80343e10i		−	1.09504i	0.836794	−	0.547518i	$-0.184427\pi$
$548$	−1.15557e11	+	6.95384e9i	−1.28137	+	0.0771085i
$549$	−3.09557e10			−0.340762
$550$	6.82106e10	−	2.05050e9i	0.745420	−	0.0224083i
$551$			1.21330e10i			0.131632i
$552$	−2.33923e10	−	2.58760e11i	−0.251952	−	2.78702i
$553$	3.72468e10			0.398280
$554$	−7.97930e8	−	2.65435e10i	−0.00847083	−	0.281786i
$555$			3.45715e10i			0.364373i
$556$	8.09804e9	+	1.34571e11i	0.0847385	+	1.40816i
$557$	1.29450e11			1.34487			0.672434	−	0.740157i	$-0.265249\pi$
$557$	1.29450e11			1.34487			0.672434	+	0.740157i	$0.265249\pi$
$558$	6.82725e10	−	2.05236e9i	0.704221	−	0.0211698i
$559$			9.07375e10i			0.929265i
$560$	3.00762e9	+	2.48994e10i	0.0305824	+	0.253184i
$561$	2.48318e11			2.50701
$562$	−3.13521e9	−	1.04294e11i	−0.0314283	−	1.04548i
$563$			2.66759e10i			0.265512i	0.991149	+	0.132756i	$0.0423827\pi$
$563$			2.66759e10i			0.265512i	−0.991149	+	0.132756i	$0.957617\pi$
$564$	−9.99833e9	+	6.01668e8i	−0.0988123	+	0.00594622i
$565$	1.24155e11			1.21835
$566$	−1.28632e11	+	3.86684e9i	−1.25338	+	0.0376783i
$567$			4.00693e10i			0.387685i
$568$	1.24059e11	−	1.12152e10i	1.19189	−	0.107749i
$569$	3.51924e10			0.335737			0.167869	−	0.985809i	$-0.446312\pi$
$569$	3.51924e10			0.335737			0.167869	+	0.985809i	$0.446312\pi$
$570$	−4.80339e8	−	1.59787e10i	−0.00455039	−	0.151371i
$571$			1.71511e11i			1.61342i	0.590947	+	0.806710i	$0.298754\pi$
$571$			1.71511e11i			1.61342i	−0.590947	+	0.806710i	$0.701246\pi$
$572$	−8.06883e9	−	1.34085e11i	−0.0753749	−	1.25256i
$573$	−1.31314e11			−1.21813
$574$	−1.61088e10	+	4.84251e8i	−0.148394	+	0.00446090i
$575$			1.18615e11i			1.08510i
$576$	1.05430e11	−	1.92192e10i	0.957799	−	0.174600i
$577$	−9.24032e10			−0.833650			−0.416825	−	0.908987i	$-0.636857\pi$
$577$	−9.24032e10			−0.833650			−0.416825	+	0.908987i	$0.636857\pi$
$578$	2.34482e9	+	7.80015e10i	0.0210087	+	0.698862i
$579$			2.28948e11i			2.03715i
$580$	−6.27969e10	+	3.77892e9i	−0.554915	+	0.0333930i
$581$	7.29157e10			0.639907
$582$	−2.08202e11	+	6.25881e9i	−1.81465	+	0.0545506i
$583$		−	2.13007e11i		−	1.84382i
$584$	−1.07602e10	−	1.19027e11i	−0.0925061	−	1.02328i
$585$	7.05180e10			0.602111
$586$	−8.60226e8	−	2.86158e10i	−0.00729494	−	0.242669i
$587$		−	1.84582e11i		−	1.55467i	−0.629089	−	0.777334i	$-0.716572\pi$
$587$		−	1.84582e11i		−	1.55467i	0.629089	−	0.777334i	$-0.283428\pi$
$588$	1.44107e9	+	2.39472e10i	0.0120552	+	0.200329i
$589$	1.39147e10			0.115614
$590$	−6.30143e10	+	1.89429e9i	−0.520033	+	0.0156328i
$591$		−	2.32358e11i		−	1.90462i
$592$	−4.68738e10	+	5.66193e9i	−0.381630	+	0.0460976i
$593$	−1.56367e11			−1.26452			−0.632262	−	0.774755i	$-0.717873\pi$
$593$	−1.56367e11			−1.26452			−0.632262	+	0.774755i	$0.717873\pi$
$594$	−1.90050e8	−	6.32209e9i	−0.00152659	−	0.0507826i
$595$		−	4.16647e10i		−	0.332430i
$596$	1.03669e11	−	6.23850e9i	0.821610	−	0.0494419i
$597$	2.26204e11			1.78075
$598$	2.33379e11	−	7.01566e9i	1.82498	−	0.0548610i
$599$		−	3.74209e10i		−	0.290675i	−0.989382	−	0.145337i	$-0.953573\pi$
$599$		−	3.74209e10i		−	0.290675i	0.989382	−	0.145337i	$-0.0464267\pi$
$600$	−9.87765e10	+	8.92955e9i	−0.762164	+	0.0689009i
$601$	−1.71728e11			−1.31626			−0.658132	−	0.752903i	$-0.728653\pi$
$601$	−1.71728e11			−1.31626			−0.658132	+	0.752903i	$0.728653\pi$
$602$	1.51222e9	+	5.03046e10i	0.0115141	+	0.383020i
$603$		−	4.21678e10i		−	0.318942i
$604$	−1.21841e10	−	2.02472e11i	−0.0915474	−	1.52131i
$605$	7.90257e10			0.589857
$606$	−3.38732e11	+	1.01827e10i	−2.51169	+	0.0755044i
$607$			6.14409e10i			0.452588i	0.974059	+	0.226294i	$0.0726610\pi$
$607$			6.14409e10i			0.452588i	−0.974059	+	0.226294i	$0.927339\pi$
$608$	2.15860e10	−	3.26817e9i	0.157964	−	0.0239161i
$609$	−6.01768e10			−0.437481
$610$	−9.82513e8	−	3.26837e10i	−0.00709609	−	0.236054i
$611$		−	9.00132e9i		−	0.0645864i
$612$	−1.77711e11	+	1.06941e10i	−1.26680	+	0.0762320i
$613$	1.77862e10			0.125962			0.0629812	−	0.998015i	$-0.479939\pi$
$613$	1.77862e10			0.125962			0.0629812	+	0.998015i	$0.479939\pi$
$614$	−5.23939e10	+	1.57503e9i	−0.368644	+	0.0110819i
$615$			5.32623e10i			0.372323i
$616$	−6.70798e9	−	7.42020e10i	−0.0465875	−	0.515339i
$617$	−1.27291e11			−0.878331			−0.439166	−	0.898406i	$-0.644726\pi$
$617$	−1.27291e11			−0.878331			−0.439166	+	0.898406i	$0.644726\pi$
$618$	3.35705e9	+	1.11674e11i	0.0230146	+	0.765591i
$619$			2.92211e10i			0.199037i	0.995036	+	0.0995185i	$0.0317302\pi$
$619$			2.92211e10i			0.199037i	−0.995036	+	0.0995185i	$0.968270\pi$
$620$	4.33385e9	+	7.20185e10i	0.0293296	+	0.487391i
$621$	1.09938e10			0.0739234
$622$	−2.13082e11	+	6.40550e9i	−1.42359	+	0.0427948i
$623$			9.81340e10i			0.651429i
$624$	2.34115e10	+	1.93818e11i	0.154415	+	1.27837i
$625$	−2.41884e10			−0.158521
$626$	1.89674e9	+	6.30960e10i	0.0123513	+	0.410870i
$627$			4.74883e10i			0.307268i
$628$	−7.10035e10	+	4.27277e9i	−0.456500	+	0.0274708i
$629$	7.84351e10			0.501081
$630$	3.90950e10	−	1.17524e9i	0.248175	−	0.00746046i
$631$		−	6.85093e9i		−	0.0432148i	−0.999767	−	0.0216074i	$-0.993122\pi$
$631$		−	6.85093e9i		−	0.0432148i	0.999767	−	0.0216074i	$-0.00687838\pi$
$632$	1.67432e11	−	1.51361e10i	1.04947	−	0.0948738i
$633$	1.98187e11			1.23441
$634$	2.33579e9	+	7.77010e10i	0.0144569	+	0.480916i
$635$			5.91895e10i			0.364040i
$636$	1.85956e10	+	3.09016e11i	0.113653	+	1.88866i
$637$	−2.15592e10			−0.130941
$638$	1.86800e11	−	5.61544e9i	1.12744	−	0.0338923i
$639$		−	1.94259e11i		−	1.16514i
$640$	2.36383e10	+	1.10705e11i	0.140895	+	0.659856i
$641$	2.64600e11			1.56732			0.783661	−	0.621188i	$-0.213350\pi$
$641$	2.64600e11			1.56732			0.783661	+	0.621188i	$0.213350\pi$
$642$	−2.39379e9	−	7.96306e10i	−0.0140912	−	0.468748i
$643$			8.11868e10i			0.474943i	0.971395	+	0.237471i	$0.0763186\pi$
$643$			8.11868e10i			0.474943i	−0.971395	+	0.237471i	$0.923681\pi$
$644$	1.29268e11	−	7.77892e9i	0.751530	−	0.0452247i
$645$	1.66327e11			0.961004
$646$	−3.62521e10	+	1.08978e9i	−0.208163	+	0.00625763i
$647$			3.40689e10i			0.194420i	0.995264	+	0.0972100i	$0.0309918\pi$
$647$			3.40689e10i			0.194420i	−0.995264	+	0.0972100i	$0.969008\pi$
$648$	1.62831e10	+	1.80120e11i	0.0923500	+	1.02155i
$649$	1.87277e11			1.05562
$650$	−2.67809e9	−	8.90878e10i	−0.0150028	−	0.499074i
$651$			6.90136e10i			0.384247i
$652$	−2.53996e9	−	4.22082e10i	−0.0140552	−	0.233564i
$653$	1.25556e11			0.690533			0.345266	−	0.938505i	$-0.387789\pi$
$653$	1.25556e11			0.690533			0.345266	+	0.938505i	$0.387789\pi$
$654$	1.35616e11	−	4.07680e9i	0.741312	−	0.0222848i
$655$		−	1.08197e11i		−	0.587827i
$656$	−7.22156e10	+	8.72301e9i	−0.389956	+	0.0471032i
$657$	−1.86379e11			−1.00031
$658$	−1.50015e8	−	4.99030e9i	−0.000800258	−	0.0266209i
$659$			1.22224e11i			0.648060i	0.946047	+	0.324030i	$0.105038\pi$
$659$			1.22224e11i			0.648060i	−0.946047	+	0.324030i	$0.894962\pi$
$660$	−2.45787e11	+	1.47907e10i	−1.29534	+	0.0779493i
$661$	−3.14513e11			−1.64753			−0.823763	−	0.566934i	$-0.808129\pi$
$661$	−3.14513e11			−1.64753			−0.823763	+	0.566934i	$0.808129\pi$
$662$	−1.40487e11	+	4.22321e9i	−0.731483	+	0.0219893i
$663$		−	3.24320e11i		−	1.67849i
$664$	3.27771e11	−	2.96310e10i	1.68616	−	0.152431i
$665$	7.96797e9			0.0407438
$666$	2.21243e9	+	7.35974e10i	0.0112453	+	0.374081i
$667$			3.24836e11i			1.64120i
$668$	−1.22672e10	−	2.03853e11i	−0.0616084	−	1.02379i
$669$	−2.20230e11			−1.09944
$670$	4.45217e10	−	1.33838e9i	0.220939	−	0.00664170i
$671$			9.71353e10i			0.479167i
$672$	1.62094e10	+	1.07062e11i	0.0794858	+	0.524998i
$673$	−3.43018e11			−1.67208			−0.836040	−	0.548669i	$-0.815135\pi$
$673$	−3.43018e11			−1.67208			−0.836040	+	0.548669i	$0.815135\pi$
$674$	−1.32930e9	−	4.42198e10i	−0.00644145	−	0.214278i
$675$		−	4.19667e9i		−	0.0202157i
$676$	3.33253e10	−	2.00541e9i	0.159583	−	0.00960321i
$677$	2.23631e11			1.06458			0.532290	−	0.846562i	$-0.321332\pi$
$677$	2.23631e11			1.06458			0.532290	+	0.846562i	$0.321332\pi$
$678$	5.35786e11	−	1.61064e10i	2.53555	−	0.0762219i
$679$		−	1.03822e11i		−	0.488441i
$680$	−1.69315e10	−	1.87291e11i	−0.0791879	−	0.875956i
$681$	−1.04631e11			−0.486488
$682$	−6.44005e9	−	2.14231e11i	−0.0297681	−	0.990250i
$683$			2.31081e11i			1.06190i	0.847405	+	0.530948i	$0.178164\pi$
$683$			2.31081e11i			1.06190i	−0.847405	+	0.530948i	$0.821836\pi$
$684$	−2.04513e9	−	3.39854e10i	−0.00934324	−	0.155263i
$685$	−1.90700e11			−0.866140
$686$	−1.19523e10	+	3.59302e8i	−0.0539705	+	0.00162242i
$687$			1.14815e11i			0.515431i
$688$	2.72402e10	+	2.25515e11i	0.121578	+	1.00652i
$689$	−2.78202e11			−1.23448
$690$	−1.28601e10	−	4.27798e11i	−0.0567348	−	1.88731i
$691$			1.18106e11i			0.518037i	0.965872	+	0.259018i	$0.0833990\pi$
$691$			1.18106e11i			0.518037i	−0.965872	+	0.259018i	$0.916601\pi$
$692$	−1.85323e11	+	1.11522e10i	−0.808175	+	0.0486334i
$693$	−1.16189e11			−0.503771
$694$	6.19937e10	−	1.86361e9i	0.267245	−	0.00803372i
$695$			2.22078e11i			0.951846i
$696$	−2.70507e11	+	2.44543e10i	−1.15277	+	0.104212i
$697$	1.20840e11			0.512012
$698$	3.77985e9	+	1.25738e11i	0.0159240	+	0.529720i
$699$		−	2.60577e11i		−	1.09151i
$700$	−2.96945e9	−	4.93454e10i	−0.0123676	−	0.205520i
$701$	−3.05577e11			−1.26546			−0.632731	−	0.774372i	$-0.718066\pi$
$701$	−3.05577e11			−1.26546			−0.632731	+	0.774372i	$0.718066\pi$
$702$	−8.25708e9	+	2.48218e8i	−0.0339999	+	0.00102208i
$703$			1.49999e10i			0.0614141i
$704$	−6.03075e10	−	3.30827e11i	−0.245517	−	1.34682i
$705$	−1.65000e10			−0.0667923
$706$	−5.87169e9	−	1.95324e11i	−0.0236344	−	0.786208i
$707$		−	1.68913e11i		−	0.676059i
$708$	−2.71689e11	+	1.63494e10i	−1.08128	+	0.0650682i
$709$	−2.46346e11			−0.974903			−0.487451	−	0.873150i	$-0.662073\pi$
$709$	−2.46346e11			−0.974903			−0.487451	+	0.873150i	$0.662073\pi$
$710$	2.05103e11	−	6.16564e9i	0.807120	−	0.0242630i
$711$		−	2.62174e11i		−	1.02591i
$712$	3.98791e10	+	4.41132e11i	0.155176	+	1.71652i
$713$	3.72538e11			1.44149
$714$	−5.40507e9	−	1.79802e11i	−0.0207974	−	0.691834i
$715$		−	2.21277e11i		−	0.846667i
$716$	3.21008e9	+	5.33440e10i	0.0122142	+	0.202971i
$717$	2.11664e10			0.0800887
$718$	9.00537e10	−	2.70713e9i	0.338847	−	0.0101862i
$719$		−	4.05715e11i		−	1.51812i	−0.651021	−	0.759060i	$-0.725659\pi$
$719$		−	4.05715e11i		−	1.51812i	0.651021	−	0.759060i	$-0.274341\pi$
$720$	1.75262e11	−	2.11701e10i	0.652166	−	0.0787759i
$721$	−5.56874e10			−0.206071
$722$	7.95665e9	+	2.64681e11i	0.0292807	+	0.974035i
$723$			2.17582e11i			0.796288i
$724$	4.79575e11	−	2.88593e10i	1.74543	−	0.105035i
$725$	1.24000e11			0.448817
$726$	3.41032e11	−	1.02518e10i	1.22757	−	0.0369024i
$727$			2.53597e11i			0.907835i	0.891044	+	0.453917i	$0.149974\pi$
$727$			2.53597e11i			0.907835i	−0.891044	+	0.453917i	$0.850026\pi$
$728$	−9.69130e10	+	8.76109e9i	−0.345030	+	0.0311912i
$729$	2.67316e11			0.946488
$730$	−5.91553e9	−	1.96783e11i	−0.0208306	−	0.692940i
$731$		−	3.77360e11i		−	1.32156i
$732$	−8.47997e9	−	1.40917e11i	−0.0295359	−	0.490818i
$733$	−3.11643e11			−1.07955			−0.539774	−	0.841810i	$-0.681490\pi$
$733$	−3.11643e11			−1.07955			−0.539774	+	0.841810i	$0.681490\pi$
$734$	−2.73044e11	+	8.20805e9i	−0.940695	+	0.0282785i
$735$			3.95193e10i			0.135413i
$736$	5.77923e11	−	8.74988e10i	1.96951	−	0.298189i
$737$	−1.32318e11			−0.448485
$738$	3.40856e9	+	1.13387e11i	0.0114907	+	0.382242i
$739$			4.01482e11i			1.34613i	0.739582	+	0.673066i	$0.235023\pi$
$739$			4.01482e11i			1.34613i	−0.739582	+	0.673066i	$0.764977\pi$
$740$	−7.76356e10	+	4.67186e9i	−0.258901	+	0.0155798i
$741$	6.20230e10			0.205722
$742$	−1.54234e11	+	4.63647e9i	−0.508821	+	0.0152958i
$743$		−	4.06133e11i		−	1.33264i	−0.745665	−	0.666321i	$-0.767868\pi$
$743$		−	4.06133e11i		−	1.33264i	0.745665	−	0.666321i	$-0.232132\pi$
$744$	2.80453e10	+	3.10230e11i	0.0915310	+	1.01249i
$745$	1.71083e11			0.555368
$746$	−2.03808e8	−	6.77977e9i	−0.000658062	−	0.0218907i
$747$		−	5.13241e11i		−	1.64831i
$748$	3.35567e10	+	5.57635e11i	0.107195	+	1.78133i
$749$	3.97088e10			0.126171
$750$	−4.63086e11	+	1.39210e10i	−1.46358	+	0.0439971i
$751$		−	2.28029e11i		−	0.716853i	−0.933558	−	0.358426i	$-0.883313\pi$
$751$		−	2.28029e11i		−	0.716853i	0.933558	−	0.358426i	$-0.116687\pi$
$752$	−2.70227e9	−	2.23715e10i	−0.00845003	−	0.0699557i
$753$	5.86414e11			1.82400
$754$	−7.33415e9	−	2.43974e11i	−0.0226916	−	0.754844i
$755$		−	3.34133e11i		−	1.02833i
$756$	−4.57356e9	+	2.75223e8i	−0.0140013	+	0.000842553i
$757$	1.80433e11			0.549454			0.274727	−	0.961522i	$-0.411413\pi$
$757$	1.80433e11			0.549454			0.274727	+	0.961522i	$0.411413\pi$
$758$	5.89461e10	−	1.77199e9i	0.178557	−	0.00536766i
$759$			1.27141e12i			3.83105i
$760$	3.58176e10	−	3.23797e9i	0.107360	−	0.00970552i
$761$	−2.36144e11			−0.704108			−0.352054	−	0.935980i	$-0.614517\pi$
$761$	−2.36144e11			−0.704108			−0.352054	+	0.935980i	$0.614517\pi$
$762$	7.67852e9	+	2.55429e11i	0.0227750	+	0.757619i
$763$			6.76268e10i			0.199536i
$764$	−1.77453e10	−	2.94886e11i	−0.0520847	−	0.865528i
$765$	−2.93271e11			−0.856294
$766$	−2.69318e11	+	8.09603e9i	−0.782258	+	0.0235156i
$767$		−	2.44597e11i		−	0.706756i
$768$	1.16372e11	+	4.74677e11i	0.334505	+	1.36444i
$769$	3.05517e11			0.873634			0.436817	−	0.899550i	$-0.356106\pi$
$769$	3.05517e11			0.873634			0.436817	+	0.899550i	$0.356106\pi$
$770$	−3.68777e9	−	1.22675e11i	−0.0104906	−	0.348975i
$771$			4.32273e10i			0.122332i
$772$	−5.14137e11	+	3.09392e10i	−1.44747	+	0.0871043i
$773$	9.39666e10			0.263182			0.131591	−	0.991304i	$-0.457992\pi$
$773$	9.39666e10			0.263182			0.131591	+	0.991304i	$0.457992\pi$
$774$	3.54085e11	−	1.06442e10i	0.986607	−	0.0296586i
$775$		−	1.42209e11i		−	0.394203i
$776$	−4.21907e10	−	4.66703e11i	−0.116351	−	1.28705i
$777$	−7.43963e10			−0.204111
$778$	5.66490e8	+	1.88445e10i	0.00154623	+	0.0514360i
$779$			2.31095e10i			0.0627539i
$780$	1.93176e10	+	3.21014e11i	0.0521886	+	0.867253i
$781$	−6.09561e11			−1.63837
$782$	−9.70579e11	+	2.91768e10i	−2.59540	+	0.0780208i
$783$		−	1.14929e10i		−	0.0305761i
$784$	−5.35822e10	+	6.47226e9i	−0.141826	+	0.0171314i
$785$	−1.17175e11			−0.308572
$786$	−1.40361e10	−	4.66918e11i	−0.0367754	−	1.22335i
$787$			2.79468e11i			0.728506i	0.931300	+	0.364253i	$0.118676\pi$
$787$			2.79468e11i			0.728506i	−0.931300	+	0.364253i	$0.881324\pi$
$788$	5.21796e11	−	3.14000e10i	1.35330	−	0.0814376i
$789$	−2.01543e11			−0.520068
$790$	2.76809e11	−	8.32122e9i	0.710676	−	0.0213638i
$791$			2.67176e11i			0.682484i
$792$	−5.22295e11	+	4.72163e10i	−1.32744	+	0.120003i
$793$	1.26865e11			0.320812
$794$	1.09766e10	+	3.65142e11i	0.0276177	+	0.918713i
$795$			5.09960e11i			1.27664i
$796$	3.05684e10	+	5.07976e11i	0.0761413	+	1.26529i
$797$	5.46838e11			1.35527			0.677634	−	0.735399i	$-0.263005\pi$
$797$	5.46838e11			1.35527			0.677634	+	0.735399i	$0.263005\pi$
$798$	3.43854e10	−	1.03367e9i	0.0847934	−	0.00254900i
$799$			3.74347e10i			0.0918518i
$800$	−3.34009e10	−	2.20611e11i	−0.0815453	−	0.538601i
$801$	6.90748e11			1.67799
$802$	1.83072e10	+	6.08996e11i	0.0442511	+	1.47203i
$803$			5.84834e11i			1.40660i
$804$	1.91958e11	−	1.15514e10i	0.459390	−	0.0276446i
$805$	2.13327e11			0.507998
$806$	−2.79801e11	+	8.41115e9i	−0.662992	+	0.0199304i
$807$			6.80763e11i			1.60510i
$808$	−6.86417e10	−	7.59297e11i	−0.161043	−	1.78142i
$809$	−4.77340e11			−1.11438			−0.557190	−	0.830385i	$-0.688121\pi$
$809$	−4.77340e11			−1.11438			−0.557190	+	0.830385i	$0.688121\pi$
$810$	8.95178e9	+	2.97785e11i	0.0207955	+	0.691771i
$811$		−	4.08290e11i		−	0.943812i	−0.881649	−	0.471906i	$-0.843566\pi$
$811$		−	4.08290e11i		−	0.943812i	0.881649	−	0.471906i	$-0.156434\pi$
$812$	−8.13206e9	−	1.35136e11i	−0.0187058	−	0.310847i
$813$	6.30046e10			0.144215
$814$	2.30940e11	−	6.94234e9i	0.526019	−	0.0158128i
$815$		−	6.96550e10i		−	0.157878i
$816$	−9.73638e10	−	8.06051e11i	−0.219602	−	1.81803i
$817$	7.21664e10			0.161974
$818$	−5.79359e9	−	1.92726e11i	−0.0129400	−	0.430455i
$819$			1.51751e11i			0.337285i
$820$	−1.19608e11	+	7.19766e9i	−0.264549	+	0.0159197i
$821$	5.10432e11			1.12348			0.561740	−	0.827314i	$-0.310132\pi$
$821$	5.10432e11			1.12348			0.561740	+	0.827314i	$0.310132\pi$
$822$	−8.22956e11	+	2.47391e10i	−1.80256	+	0.0541872i
$823$			1.70406e11i			0.371438i	0.982603	+	0.185719i	$0.0594614\pi$
$823$			1.70406e11i			0.371438i	−0.982603	+	0.185719i	$0.940539\pi$
$824$	−2.50326e11	+	2.26299e10i	−0.542998	+	0.0490879i
$825$	4.85334e11			1.04767
$826$	−4.07642e9	−	1.35604e11i	−0.00875706	−	0.291307i
$827$		−	6.55361e11i		−	1.40107i	−0.713620	−	0.700533i	$-0.752946\pi$
$827$		−	6.55361e11i		−	1.40107i	0.713620	−	0.700533i	$-0.247054\pi$
$828$	−5.47545e10	−	9.09893e11i	−0.116493	−	1.93584i
$829$	3.93066e10			0.0832239			0.0416119	−	0.999134i	$-0.486751\pi$
$829$	3.93066e10			0.0832239			0.0416119	+	0.999134i	$0.486751\pi$
$830$	5.41892e11	−	1.62899e10i	1.14183	−	0.0343247i
$831$		−	1.88863e11i		−	0.396044i
$832$	−4.32083e11	+	7.87658e10i	−0.901725	+	0.164378i
$833$	8.96605e10			0.186218
$834$	2.88097e10	+	9.58368e11i	0.0595491	+	1.98092i
$835$		−	3.36412e11i		−	0.692032i
$836$	−1.06642e11	+	6.41739e9i	−0.218325	+	0.0131381i
$837$	−1.31806e10			−0.0268555
$838$	8.66812e10	−	2.60574e9i	0.175772	−	0.00528392i
$839$		−	2.91635e11i		−	0.588562i	−0.955719	−	0.294281i	$-0.904920\pi$
$839$		−	2.91635e11i		−	0.588562i	0.955719	−	0.294281i	$-0.0950802\pi$
$840$	1.60596e10	+	1.77647e11i	0.0322566	+	0.356814i
$841$	−1.60664e11			−0.321169
$842$	−8.66666e9	−	2.88300e11i	−0.0172426	−	0.573583i
$843$		−	7.42076e11i		−	1.46939i
$844$	2.67822e10	+	4.45059e11i	0.0527809	+	0.877097i
$845$	5.49958e10			0.107870
$846$	−3.51259e10	+	1.05593e9i	−0.0685718	+	0.00206135i
$847$			1.70060e11i			0.330421i
$848$	−6.91429e11	+	8.35185e10i	−1.33710	+	0.161510i
$849$	−9.15248e11			−1.76160
$850$	1.11377e10	+	3.70499e11i	0.0213363	+	0.709760i
$851$			4.01594e11i			0.765718i
$852$	8.84311e11	−	5.32151e10i	1.67821	−	0.100990i
$853$	9.36628e11			1.76918			0.884588	−	0.466373i	$-0.154440\pi$
$853$	9.36628e11			1.76918			0.884588	+	0.466373i	$0.154440\pi$
$854$	7.03338e10	−	2.11432e9i	0.132231	−	0.00397502i
$855$		−	5.60851e10i		−	0.104950i
$856$	1.78499e11	−	1.61366e10i	0.332461	−	0.0300550i
$857$	7.42624e11			1.37672			0.688360	−	0.725369i	$-0.258331\pi$
$857$	7.42624e11			1.37672			0.688360	+	0.725369i	$0.258331\pi$
$858$	−2.87058e10	−	9.54911e11i	−0.0529688	−	1.76203i
$859$		−	1.05691e12i		−	1.94118i	−0.240743	−	0.970589i	$-0.577391\pi$
$859$		−	1.05691e12i		−	1.94118i	0.240743	−	0.970589i	$-0.422609\pi$
$860$	2.24769e10	+	3.73513e11i	0.0410905	+	0.682830i
$861$	−1.14618e11			−0.208564
$862$	9.03962e11	−	2.71742e10i	1.63727	−	0.0492184i
$863$			3.86556e11i			0.696898i	0.937328	+	0.348449i	$0.113291\pi$
$863$			3.86556e11i			0.696898i	−0.937328	+	0.348449i	$0.886709\pi$
$864$	−2.04473e10	+	3.09576e9i	−0.0366927	+	0.00555536i
$865$	−3.05833e11			−0.546287
$866$	2.65297e10	+	8.82520e11i	0.0471694	+	1.56911i
$867$			5.54998e11i			0.982235i
$868$	−1.54980e11	+	9.32623e9i	−0.273022	+	0.0164296i
$869$	−8.22670e11			−1.44260
$870$	−4.47219e11	+	1.34439e10i	−0.780626	+	0.0234666i
$871$			1.72816e11i			0.300269i
$872$	2.74817e10	+	3.03996e11i	0.0475312	+	0.525778i
$873$	−7.30788e11			−1.25816
$874$	−5.57977e9	−	1.85614e11i	−0.00956249	−	0.318100i
$875$		−	2.30924e11i		−	0.393946i
$876$	−5.10564e10	−	8.48439e11i	−0.0867029	−	1.44080i
$877$	1.02216e11			0.172791			0.0863956	−	0.996261i	$-0.472465\pi$
$877$	1.02216e11			0.172791			0.0863956	+	0.996261i	$0.472465\pi$
$878$	6.42203e11	−	1.93054e10i	1.08067	−	0.0324864i
$879$		−	2.03608e11i		−	0.341066i
$880$	−6.64294e10	−	5.49952e11i	−0.110772	−	0.917053i
$881$	−1.14116e12			−1.89427			−0.947135	−	0.320834i	$-0.896037\pi$
$881$	−1.14116e12			−1.89427			−0.947135	+	0.320834i	$0.896037\pi$
$882$	2.52907e9	+	8.41305e10i	0.00417913	+	0.139021i
$883$		−	4.52318e11i		−	0.744048i	−0.928223	−	0.372024i	$-0.878664\pi$
$883$		−	4.52318e11i		−	0.744048i	0.928223	−	0.372024i	$-0.121336\pi$
$884$	7.28310e11	−	4.38274e10i	1.19263	−	0.0717690i
$885$	−4.48361e11			−0.730895
$886$	1.03408e11	−	3.10858e9i	0.167811	−	0.00504461i
$887$		−	6.85217e11i		−	1.10696i	−0.832861	−	0.553482i	$-0.813299\pi$
$887$		−	6.85217e11i		−	1.10696i	0.832861	−	0.553482i	$-0.186701\pi$
$888$	−3.34426e11	+	3.02327e10i	−0.537834	+	0.0486211i
$889$	−1.27373e11			−0.203925
$890$	2.19239e10	+	7.29307e11i	0.0349428	+	1.16239i
$891$		−	8.85010e11i		−	1.40423i
$892$	−2.97610e10	−	4.94559e11i	−0.0470098	−	0.781194i
$893$	−7.15902e9			−0.0112577
$894$	7.38299e11	−	2.21942e10i	1.15580	−	0.0347447i
$895$			8.80322e10i			0.137198i
$896$	−2.38233e11	+	5.08685e10i	−0.369632	+	0.0789255i
$897$	1.66055e12			2.56496
$898$	1.02734e10	+	3.41747e11i	0.0157982	+	0.525533i
$899$		−	3.89450e11i		−	0.596228i
$900$	−3.47333e11	+	2.09014e10i	−0.529391	+	0.0318571i
$901$	1.15699e12			1.75561
$902$	3.55795e11	−	1.06957e10i	0.537495	−	0.0161578i
$903$			3.57929e11i			0.538326i
$904$	1.08573e11	+	1.20101e12i	0.162574	+	1.79835i
$905$	7.91429e11			1.17983
$906$	−4.33464e10	−	1.44194e12i	−0.0643339	−	2.14010i
$907$			3.55160e11i			0.524801i	0.964959	+	0.262401i	$0.0845142\pi$
$907$			3.55160e11i			0.524801i	−0.964959	+	0.262401i	$0.915486\pi$
$908$	−1.41394e10	−	2.34965e11i	−0.0208012	−	0.345668i
$909$	−1.18895e12			−1.74143
$910$	−1.60223e11	+	4.81649e9i	−0.233646	+	0.00702368i
$911$			4.48352e11i			0.650947i	0.945551	+	0.325473i	$0.105524\pi$
$911$			4.48352e11i			0.650947i	−0.945551	+	0.325473i	$0.894476\pi$
$912$	1.54149e11	−	1.86199e10i	0.222824	−	0.0269152i
$913$	−1.61049e12			−2.31780
$914$	1.89051e10	+	6.28885e11i	0.0270890	+	0.901128i
$915$		−	2.32552e11i		−	0.331769i
$916$	−2.57834e11	+	1.55156e10i	−0.366233	+	0.0220388i
$917$	2.32835e11			0.329284
$918$	3.43396e10	−	1.03229e9i	0.0483532	−	0.00145356i
$919$			7.28279e11i			1.02102i	0.859871	+	0.510512i	$0.170544\pi$
$919$			7.28279e11i			1.02102i	−0.859871	+	0.510512i	$0.829456\pi$
$920$	9.58947e11	−	8.66904e10i	1.33858	−	0.121010i
$921$	−3.72795e11			−0.518121
$922$	−1.23875e9	−	4.12074e10i	−0.00171419	−	0.0570232i
$923$			7.96129e11i			1.09692i
$924$	−3.18288e10	−	5.28921e11i	−0.0436649	−	0.725610i
$925$	1.53300e11			0.209400
$926$	−1.93790e11	+	5.82556e9i	−0.263564	+	0.00792308i
$927$			3.91974e11i			0.530809i
$928$	−9.14710e10	−	6.04159e11i	−0.123336	−	0.814628i
$929$	−1.05867e12			−1.42134			−0.710672	−	0.703523i	$-0.751609\pi$
$929$	−1.05867e12			−1.42134			−0.710672	+	0.703523i	$0.751609\pi$
$930$	1.54182e10	+	5.12892e11i	0.0206111	+	0.685636i
$931$			1.71467e10i			0.0228235i
$932$	5.85164e11	−	3.52133e10i	0.775557	−	0.0466706i
$933$	−1.51613e12			−2.00082
$934$	−1.34240e12	+	4.03543e10i	−1.76399	+	0.0530276i
$935$			9.20249e11i			1.20409i
$936$	6.16678e10	+	6.82153e11i	0.0803443	+	0.888748i
$937$	9.40055e10			0.121954			0.0609769	−	0.998139i	$-0.480578\pi$
$937$	9.40055e10			0.121954			0.0609769	+	0.998139i	$0.480578\pi$
$938$	2.88013e9	+	9.58086e10i	0.00372049	+	0.123764i
$939$			4.48942e11i			0.577468i
$940$	−2.22974e9	−	3.70532e10i	−0.00285590	−	0.0474585i
$941$	−6.08618e10			−0.0776223			−0.0388111	−	0.999247i	$-0.512357\pi$
$941$	−6.08618e10			−0.0776223			−0.0388111	+	0.999247i	$0.512357\pi$
$942$	−5.05663e11	+	1.52009e10i	−0.642181	+	0.0193048i
$943$			6.18712e11i			0.782423i
$944$	−7.34301e10	−	6.07910e11i	−0.0924669	−	0.765511i
$945$	−7.54762e9			−0.00946418
$946$	−3.34004e10	−	1.11108e12i	−0.0417049	−	1.38733i
$947$			8.74488e11i			1.08731i	0.839308	+	0.543656i	$0.182960\pi$
$947$			8.74488e11i			1.08731i	−0.839308	+	0.543656i	$0.817040\pi$
$948$	1.19348e12	−	7.18196e10i	1.47768	−	0.0889221i
$949$	7.63834e11			0.941747
$950$	−7.08543e10	+	2.12997e9i	−0.0869905	+	0.00261504i
$951$			5.52860e11i			0.675917i
$952$	4.03042e11	−	3.64357e10i	0.490685	−	0.0443587i
$953$	−7.13631e11			−0.865171			−0.432586	−	0.901593i	$-0.642399\pi$
$953$	−7.13631e11			−0.865171			−0.432586	+	0.901593i	$0.642399\pi$
$954$	3.26353e10	+	1.08563e12i	0.0393998	+	1.31065i
$955$		−	4.86642e11i		−	0.585055i
$956$	2.86035e9	+	4.75325e10i	0.00342443	+	0.0569061i
$957$	1.32912e12			1.58459
$958$	−5.12596e11	+	1.54093e10i	−0.608573	+	0.0182945i
$959$		−	4.10377e11i		−	0.485187i
$960$	1.44382e11	+	7.92035e11i	0.169992	+	0.932523i
$961$	4.06252e11			0.476323
$962$	−9.06718e9	−	3.01624e11i	−0.0105870	−	0.352180i
$963$		−	2.79503e11i		−	0.324999i
$964$	−4.88614e11	+	2.94032e10i	−0.565793	+	0.0340477i
$965$	−8.48466e11			−0.978420
$966$	9.20601e11	−	2.76744e10i	1.05721	−	0.0317812i
$967$			8.10942e11i			0.927436i	0.885983	+	0.463718i	$0.153485\pi$
$967$			8.10942e11i			0.927436i	−0.885983	+	0.463718i	$0.846515\pi$
$968$	6.91077e10	+	7.64452e11i	0.0787092	+	0.870661i
$969$	−2.57942e11			−0.292568
$970$	−2.31947e10	−	7.71583e11i	−0.0262001	−	0.871556i
$971$		−	5.92702e11i		−	0.666744i	−0.942795	−	0.333372i	$-0.891813\pi$
$971$		−	5.92702e11i		−	0.666744i	0.942795	−	0.333372i	$-0.108187\pi$
$972$	7.52721e10	+	1.25085e12i	0.0843275	+	1.40133i
$973$	−4.77902e11			−0.533197
$974$	1.44823e12	−	4.35356e10i	1.60917	−	0.0483737i
$975$		−	6.33880e11i		−	0.701437i
$976$	3.15306e11	−	3.80861e10i	0.347482	−	0.0419727i
$977$	2.47964e11			0.272152			0.136076	−	0.990698i	$-0.456551\pi$
$977$	2.47964e11			0.272152			0.136076	+	0.990698i	$0.456551\pi$
$978$	−9.03619e9	−	3.00593e11i	−0.00987711	−	0.328566i
$979$		−	2.16749e12i		−	2.35953i
$980$	−8.87466e10	+	5.34049e9i	−0.0962160	+	0.00578998i
$981$	4.76013e11			0.513976
$982$	−5.71998e11	+	1.71950e10i	−0.615104	+	0.0184908i
$983$		−	1.34877e11i		−	0.144452i	−0.997388	−	0.0722261i	$-0.976990\pi$
$983$		−	1.34877e11i		−	0.144452i	0.997388	−	0.0722261i	$-0.0230103\pi$
$984$	−5.15231e11	+	4.65777e10i	−0.549568	+	0.0496818i
$985$	8.61105e11			0.914768
$986$	3.05013e10	+	1.01464e12i	0.0322709	+	1.07351i
$987$		−	3.55071e10i		−	0.0374151i
$988$	8.38156e9	+	1.39282e11i	0.00879624	+	0.146173i
$989$	1.93211e12			2.01952
$990$	−8.63490e11	+	2.59576e10i	−0.898911	+	0.0270224i
$991$		−	1.29401e12i		−	1.34166i	−0.741610	−	0.670831i	$-0.765938\pi$
$991$		−	1.29401e12i		−	1.34166i	0.741610	−	0.670831i	$-0.234062\pi$
$992$	−6.92878e11	+	1.04903e11i	−0.715501	+	0.108328i
$993$	−9.99598e11			−1.02808
$994$	1.32682e10	+	4.41372e11i	0.0135914	+	0.452125i
$995$			8.38298e11i			0.855276i
$996$	2.33639e12	−	1.40597e11i	2.37415	−	0.142869i
$997$	9.36520e11			0.947843			0.473922	−	0.880567i	$-0.342838\pi$
$997$	9.36520e11			0.947843			0.473922	+	0.880567i	$0.342838\pi$
$998$	−1.28102e11	+	3.85091e9i	−0.129132	+	0.00388187i
$999$		−	1.42086e10i		−	0.0142656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	28.9.c.a.15.12	yes	24
4.3	odd	2	inner	28.9.c.a.15.11	✓	24
8.3	odd	2		448.9.d.d.127.21		24
8.5	even	2		448.9.d.d.127.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.9.c.a.15.11	✓	24	4.3	odd	2	inner
28.9.c.a.15.12	yes	24	1.1	even	1	trivial
448.9.d.d.127.4		24	8.5	even	2
448.9.d.d.127.21		24	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:	\( N \)	\(=\)	\( 28 = 2^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	28.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.480763 + 15.9928i) q^{2} +113.792i q^{3} +(-255.538 + 15.3775i) q^{4} -421.707 q^{5} +(-1819.85 + 54.7071i) q^{6} -907.493i q^{7} +(-368.781 - 4079.36i) q^{8} -6387.68 q^{9} +(-202.741 - 6744.26i) q^{10} +20043.8i q^{11} +(-1749.84 - 29078.2i) q^{12} +26178.6 q^{13} +(14513.3 - 436.289i) q^{14} -47987.0i q^{15} +(65063.1 - 7859.04i) q^{16} -108872. q^{17} +(-3070.96 - 102157. i) q^{18} -20820.6i q^{19} +(107762. - 6484.78i) q^{20} +103266. q^{21} +(-320556. + 9636.31i) q^{22} -557432. i q^{23} +(464200. - 41964.5i) q^{24} -212789. q^{25} +(12585.7 + 418668. i) q^{26} +19722.3i q^{27} +(13954.9 + 231899. i) q^{28} -582737. q^{29} +(767445. - 23070.3i) q^{30} +668311. i q^{31} +(156968. + 1.03676e6i) q^{32} -2.28083e6 q^{33} +(-52341.5 - 1.74116e6i) q^{34} +382696. i q^{35} +(1.63229e6 - 98226.3i) q^{36} -720436. q^{37} +(332980. - 10009.8i) q^{38} +2.97892e6i q^{39} +(155517. + 1.72030e6i) q^{40} -1.10993e6 q^{41} +(49646.3 + 1.65150e6i) q^{42} +3.46610e6i q^{43} +(-308223. - 5.12195e6i) q^{44} +2.69373e6 q^{45} +(8.91488e6 - 267992. i) q^{46} -343843. i q^{47} +(894298. + 7.40367e6i) q^{48} -823543. q^{49} +(-102301. - 3.40308e6i) q^{50} -1.23888e7i q^{51} +(-6.68962e6 + 402560. i) q^{52} -1.06271e7 q^{53} +(-315414. + 9481.73i) q^{54} -8.45260e6i q^{55} +(-3.70199e6 + 334666. i) q^{56} +2.36923e6 q^{57} +(-280158. - 9.31959e6i) q^{58} -9.34340e6i q^{59} +(737917. + 1.22625e7i) q^{60} +4.84615e6 q^{61} +(-1.06881e7 + 321299. i) q^{62} +5.79677e6i q^{63} +(-1.65052e7 + 3.00879e6i) q^{64} -1.10397e7 q^{65} +(-1.09654e6 - 3.64768e7i) q^{66} +6.60142e6i q^{67} +(2.78208e7 - 1.67417e6i) q^{68} +6.34314e7 q^{69} +(-6.12037e6 + 183986. i) q^{70} +3.04115e7i q^{71} +(2.35566e6 + 2.60577e7i) q^{72} +2.91778e7 q^{73} +(-346359. - 1.15218e7i) q^{74} -2.42137e7i q^{75} +(320169. + 5.32046e6i) q^{76} +1.81896e7 q^{77} +(-4.76412e7 + 1.43215e6i) q^{78} +4.10436e7i q^{79} +(-2.74375e7 + 3.31421e6i) q^{80} -4.41538e7 q^{81} +(-533614. - 1.77509e7i) q^{82} +8.03486e7i q^{83} +(-2.63883e7 + 1.58796e6i) q^{84} +4.59119e7 q^{85} +(-5.54325e7 + 1.66637e6i) q^{86} -6.63110e7i q^{87} +(8.17660e7 - 7.39178e6i) q^{88} -1.08138e8 q^{89} +(1.29504e6 + 4.30802e7i) q^{90} -2.37569e7i q^{91} +(8.57188e6 + 1.42445e8i) q^{92} -7.60486e7 q^{93} +(5.49900e6 - 165307. i) q^{94} +8.78020e6i q^{95} +(-1.17975e8 + 1.78617e7i) q^{96} +1.14406e8 q^{97} +(-395929. - 1.31707e7i) q^{98} -1.28033e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 383 q^{4} - 336 q^{5} + 5502 q^{6} - 12069 q^{8} - 56296 q^{9} + 41972 q^{10} - 31290 q^{12} - 28560 q^{13} + 7203 q^{14} + 166193 q^{16} - 165648 q^{17} - 11609 q^{18} - 71568 q^{20} - 955748 q^{22}+ \cdots - 2470629 q^{98}+O(q^{100}) \) 24 * q + 3 * q^2 - 383 * q^4 - 336 * q^5 + 5502 * q^6 - 12069 * q^8 - 56296 * q^9 + 41972 * q^10 - 31290 * q^12 - 28560 * q^13 + 7203 * q^14 + 166193 * q^16 - 165648 * q^17 - 11609 * q^18 - 71568 * q^20 - 955748 * q^22 + 133322 * q^24 + 989640 * q^25 - 1066632 * q^26 - 372155 * q^28 + 997296 * q^29 + 3246560 * q^30 - 2265357 * q^32 - 5521600 * q^33 + 1423618 * q^34 - 649451 * q^36 + 5387056 * q^37 + 3945690 * q^38 + 11452504 * q^40 - 12346320 * q^41 + 5642350 * q^42 - 2412372 * q^44 + 17486448 * q^45 + 537288 * q^46 + 20895070 * q^48 - 19765032 * q^49 - 28121691 * q^50 - 12804764 * q^52 + 10812720 * q^53 - 42610652 * q^54 - 7109361 * q^56 + 6748288 * q^57 + 36144266 * q^58 - 98388944 * q^60 + 33644464 * q^61 + 12180756 * q^62 - 1102631 * q^64 - 9084960 * q^65 + 83635608 * q^66 + 106943886 * q^68 - 90944448 * q^69 + 11611236 * q^70 - 48881753 * q^72 - 7651728 * q^73 - 66897318 * q^74 + 64861986 * q^76 - 47482176 * q^77 - 41838760 * q^78 + 154560168 * q^80 + 299710744 * q^81 - 13781390 * q^82 + 571438 * q^84 - 280618528 * q^85 - 139907676 * q^86 - 65086060 * q^88 + 215250672 * q^89 + 40480132 * q^90 + 111569640 * q^92 + 181272192 * q^93 + 171294732 * q^94 - 684707590 * q^96 + 114327024 * q^97 - 2470629 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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