LMFDB - Embedded newform 42.12.f.a.5.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,12,Mod(5,42)] 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("42.5"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	42.f (of order $6$, degree $2$, 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:	$32.2704135835$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-27.7128 - 16.0000i) q^{2} +(-420.023 - 26.9724i) q^{3} +(512.000 + 886.810i) q^{4} +(956.472 - 1656.66i) q^{5} +(11208.5 + 7467.85i) q^{6} +(-43035.3 - 11193.3i) q^{7} -32768.0i q^{8} +(175692. + 22658.1i) q^{9} +(-53013.1 + 30607.1i) q^{10} +(-203585. + 117540. i) q^{11} +(-191132. - 386291. i) q^{12} -1.74455e6i q^{13} +(1.01354e6 + 998762. i) q^{14} +(-446425. + 670037. i) q^{15} +(-524288. + 908093. i) q^{16} +(-4.37909e6 - 7.58480e6i) q^{17} +(-4.50639e6 - 3.43899e6i) q^{18} +(-1.71739e7 - 9.91536e6i) q^{19} +1.95886e6 q^{20} +(1.77739e7 + 5.86221e6i) q^{21} +7.52257e6 q^{22} +(-7.44417e6 - 4.29789e6i) q^{23} +(-883833. + 1.37633e7i) q^{24} +(2.25844e7 + 3.91173e7i) q^{25} +(-2.79128e7 + 4.83463e7i) q^{26} +(-7.31836e7 - 1.42558e7i) q^{27} +(-1.21078e7 - 4.38951e7i) q^{28} +1.08965e8i q^{29} +(2.30923e7 - 1.14258e7i) q^{30} +(1.67899e8 - 9.69365e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(8.86809e7 - 4.38784e7i) q^{33} +2.80262e8i q^{34} +(-5.97055e7 + 6.05887e7i) q^{35} +(6.98609e7 + 1.67406e8i) q^{36} +(9.45932e7 - 1.63840e8i) q^{37} +(3.17291e8 + 5.49565e8i) q^{38} +(-4.70547e7 + 7.32750e8i) q^{39} +(-5.42854e7 - 3.13417e7i) q^{40} +1.03268e9 q^{41} +(-3.98770e8 - 4.46841e8i) q^{42} -3.63728e8 q^{43} +(-2.08471e8 - 1.20361e8i) q^{44} +(2.05581e8 - 2.69390e8i) q^{45} +(1.37533e8 + 2.38213e8i) q^{46} +(-1.44255e9 + 2.49857e9i) q^{47} +(2.44707e8 - 3.67279e8i) q^{48} +(1.72675e9 + 9.63412e8i) q^{49} -1.44540e9i q^{50} +(1.63474e9 + 3.30391e9i) q^{51} +(1.54708e9 - 8.93208e8i) q^{52} +(-1.74800e9 + 1.00921e9i) q^{53} +(1.80003e9 + 1.56600e9i) q^{54} +4.49695e8i q^{55} +(-3.66781e8 + 1.41018e9i) q^{56} +(6.94600e9 + 4.62790e9i) q^{57} +(1.74344e9 - 3.01972e9i) q^{58} +(3.77776e9 + 6.54327e9i) q^{59} +(-8.22765e8 - 5.28351e7i) q^{60} +(-4.68498e9 - 2.70487e9i) q^{61} -6.20393e9 q^{62} +(-7.30734e9 - 2.94167e9i) q^{63} -1.07374e9 q^{64} +(-2.89012e9 - 1.66861e9i) q^{65} +(-3.15965e9 - 2.02902e8i) q^{66} +(-4.18734e9 - 7.25268e9i) q^{67} +(4.48418e9 - 7.76684e9i) q^{68} +(3.01080e9 + 2.00600e9i) q^{69} +(2.62403e9 - 7.23796e8i) q^{70} -1.21731e9i q^{71} +(7.42461e8 - 5.75707e9i) q^{72} +(-1.88527e10 + 1.08846e10i) q^{73} +(-5.24289e9 + 3.02698e9i) q^{74} +(-8.43088e9 - 1.70393e10i) q^{75} -2.03067e10i q^{76} +(1.00770e10 - 2.77958e9i) q^{77} +(1.30280e10 - 1.95537e10i) q^{78} +(-8.17353e9 + 1.41570e10i) q^{79} +(1.00293e9 + 1.73713e9i) q^{80} +(3.03543e10 + 7.96169e9i) q^{81} +(-2.86185e10 - 1.65229e10i) q^{82} +2.10806e10 q^{83} +(3.90158e9 + 1.87635e10i) q^{84} -1.67539e10 q^{85} +(1.00799e10 + 5.81965e9i) q^{86} +(2.93905e9 - 4.57677e10i) q^{87} +(3.85155e9 + 6.67109e9i) q^{88} +(3.87321e10 - 6.70859e10i) q^{89} +(-1.00075e10 + 4.17625e9i) q^{90} +(-1.95272e10 + 7.50771e10i) q^{91} -8.80208e9i q^{92} +(-7.31360e10 + 3.61869e10i) q^{93} +(7.99542e10 - 4.61616e10i) q^{94} +(-3.28527e10 + 1.89675e10i) q^{95} +(-1.26580e10 + 6.26303e9i) q^{96} -3.84781e10i q^{97} +(-3.24384e10 - 5.43268e10i) q^{98} +(-3.84316e10 + 1.60380e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) $ 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−27.7128	−	16.0000i	−0.612372	−	0.353553i
$2$	−27.7128	−	16.0000i	−0.612372	−	0.353553i
$3$	−420.023	−	26.9724i	−0.997944	−	0.0640846i
$3$	−420.023	−	26.9724i	−0.997944	−	0.0640846i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	956.472	−	1656.66i	0.136879	−	0.237082i	−0.789435	−	0.613835i	$-0.789626\pi$
$5$	956.472	−	1656.66i	0.136879	−	0.237082i	0.926314	+	0.376753i	$0.122959\pi$
$6$	11208.5	+	7467.85i	0.588456	+	0.392070i
$7$	−43035.3	−	11193.3i	−0.967800	−	0.251720i
$7$	−43035.3	−	11193.3i	−0.967800	−	0.251720i
$8$		−	32768.0i		−	0.353553i
$9$	175692.	+	22658.1i	0.991786	+	0.127906i
$10$	−53013.1	+	30607.1i	−0.167642	+	0.0967882i
$11$	−203585.	+	117540.i	−0.381142	+	0.220052i	−0.678315	−	0.734771i	$-0.737290\pi$
$11$	−203585.	+	117540.i	−0.381142	+	0.220052i	0.297173	+	0.954824i	$0.403956\pi$
$12$	−191132.	−	386291.i	−0.221737	−	0.448144i
$13$		−	1.74455e6i		−	1.30315i	−0.758584	−	0.651575i	$-0.774109\pi$
$13$		−	1.74455e6i		−	1.30315i	0.758584	−	0.651575i	$-0.225891\pi$
$14$	1.01354e6	+	998762.i	0.503658	+	0.496316i
$15$	−446425.	+	670037.i	−0.151791	+	0.227823i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	−4.37909e6	−	7.58480e6i	−0.748022	−	1.29561i	−0.948769	−	0.315969i	$-0.897670\pi$
$17$	−4.37909e6	−	7.58480e6i	−0.748022	−	1.29561i	0.200747	−	0.979643i	$-0.435663\pi$
$18$	−4.50639e6	−	3.43899e6i	−0.562121	−	0.428975i
$19$	−1.71739e7	−	9.91536e6i	−1.59120	−	0.918679i	−0.993102	−	0.117254i	$-0.962591\pi$
$19$	−1.71739e7	−	9.91536e6i	−1.59120	−	0.918679i	−0.598096	−	0.801425i	$-0.704076\pi$
$20$	1.95886e6			0.136879
$21$	1.77739e7	+	5.86221e6i	0.949679	+	0.313224i
$22$	7.52257e6			0.311201
$23$	−7.44417e6	−	4.29789e6i	−0.241164	−	0.139236i	0.374547	−	0.927208i	$-0.377798\pi$
$23$	−7.44417e6	−	4.29789e6i	−0.241164	−	0.139236i	−0.615712	+	0.787971i	$0.711131\pi$
$24$	−883833.	+	1.37633e7i	−0.0226573	+	0.352827i
$25$	2.25844e7	+	3.91173e7i	0.462528	+	0.801122i
$26$	−2.79128e7	+	4.83463e7i	−0.460733	+	0.798013i
$27$	−7.31836e7	−	1.42558e7i	−0.981551	−	0.191201i
$28$	−1.21078e7	−	4.38951e7i	−0.132952	−	0.482000i
$29$			1.08965e8i			0.986500i	0.869887	+	0.493250i	$0.164191\pi$
$29$			1.08965e8i			0.986500i	−0.869887	+	0.493250i	$0.835809\pi$
$30$	2.30923e7	−	1.14258e7i	0.173500	−	0.0858460i
$31$	1.67899e8	−	9.69365e7i	1.05332	−	0.608132i	0.129740	−	0.991548i	$-0.458586\pi$
$31$	1.67899e8	−	9.69365e7i	1.05332	−	0.608132i	0.923576	+	0.383416i	$0.125252\pi$
$32$	2.90590e7	−	1.67772e7i	0.153093	−	0.0883883i
$33$	8.86809e7	−	4.38784e7i	0.394461	−	0.195175i
$34$			2.80262e8i			1.05786i
$35$	−5.97055e7	+	6.05887e7i	−0.192150	+	0.194992i
$36$	6.98609e7	+	1.67406e8i	0.192562	+	0.461432i
$37$	9.45932e7	−	1.63840e8i	0.224259	−	0.388429i	−0.731838	−	0.681479i	$-0.761337\pi$
$37$	9.45932e7	−	1.63840e8i	0.224259	−	0.388429i	0.956097	+	0.293050i	$0.0946704\pi$
$38$	3.17291e8	+	5.49565e8i	0.649604	+	1.12515i
$39$	−4.70547e7	+	7.32750e8i	−0.0835118	+	1.30047i
$40$	−5.42854e7	−	3.13417e7i	−0.0838210	−	0.0483941i
$41$	1.03268e9			1.39205			0.696025	−	0.718017i	$-0.254950\pi$
$41$	1.03268e9			1.39205			0.696025	+	0.718017i	$0.254950\pi$
$42$	−3.98770e8	−	4.46841e8i	−0.470816	−	0.527572i
$43$	−3.63728e8			−0.377312			−0.188656	−	0.982043i	$-0.560413\pi$
$43$	−3.63728e8			−0.377312			−0.188656	+	0.982043i	$0.560413\pi$
$44$	−2.08471e8	−	1.20361e8i	−0.190571	−	0.110026i
$45$	2.05581e8	−	2.69390e8i	0.166079	−	0.217627i
$46$	1.37533e8	+	2.38213e8i	0.0984549	+	0.170529i
$47$	−1.44255e9	+	2.49857e9i	−0.917472	+	1.58911i	−0.114230	+	0.993454i	$0.536440\pi$
$47$	−1.44255e9	+	2.49857e9i	−0.917472	+	1.58911i	−0.803242	+	0.595653i	$0.796893\pi$
$48$	2.44707e8	−	3.67279e8i	0.138618	−	0.208051i
$49$	1.72675e9	+	9.63412e8i	0.873274	+	0.487230i
$50$		−	1.44540e9i		−	0.654114i
$51$	1.63474e9	+	3.30391e9i	0.663456	+	1.34089i
$52$	1.54708e9	−	8.93208e8i	0.564281	−	0.325787i
$53$	−1.74800e9	+	1.00921e9i	−0.574148	+	0.331484i	−0.758804	−	0.651319i	$-0.774216\pi$
$53$	−1.74800e9	+	1.00921e9i	−0.574148	+	0.331484i	0.184656	+	0.982803i	$0.440883\pi$
$54$	1.80003e9	+	1.56600e9i	0.533475	+	0.464117i
$55$			4.49695e8i			0.120482i
$56$	−3.66781e8	+	1.41018e9i	−0.0889966	+	0.342169i
$57$	6.94600e9	+	4.62790e9i	1.52905	+	1.01876i
$58$	1.74344e9	−	3.01972e9i	0.348781	−	0.604106i
$59$	3.77776e9	+	6.54327e9i	0.687936	+	1.19154i	0.972504	+	0.232885i	$0.0748165\pi$
$59$	3.77776e9	+	6.54327e9i	0.687936	+	1.19154i	−0.284568	+	0.958656i	$0.591850\pi$
$60$	−8.22765e8	−	5.28351e7i	−0.136598	−	0.00877184i
$61$	−4.68498e9	−	2.70487e9i	−0.710221	−	0.410046i	0.100922	−	0.994894i	$-0.467821\pi$
$61$	−4.68498e9	−	2.70487e9i	−0.710221	−	0.410046i	−0.811143	+	0.584848i	$0.801154\pi$
$62$	−6.20393e9			−0.860029
$63$	−7.30734e9	−	2.94167e9i	−0.927654	−	0.373440i
$64$	−1.07374e9			−0.125000
$65$	−2.89012e9	−	1.66861e9i	−0.308953	−	0.178374i
$66$	−3.15965e9	−	2.02902e8i	−0.310562	−	0.0199432i
$67$	−4.18734e9	−	7.25268e9i	−0.378902	−	0.656277i	0.612001	−	0.790857i	$-0.290365\pi$
$67$	−4.18734e9	−	7.25268e9i	−0.378902	−	0.656277i	−0.990903	+	0.134580i	$0.957031\pi$
$68$	4.48418e9	−	7.76684e9i	0.374011	−	0.647806i
$69$	3.01080e9	+	2.00600e9i	0.231746	+	0.154405i
$70$	2.62403e9	−	7.23796e8i	0.186608	−	0.0514727i
$71$		−	1.21731e9i		−	0.0800719i	−0.999198	−	0.0400360i	$-0.987253\pi$
$71$		−	1.21731e9i		−	0.0800719i	0.999198	−	0.0400360i	$-0.0127473\pi$
$72$	7.42461e8	−	5.75707e9i	0.0452215	−	0.350649i
$73$	−1.88527e10	+	1.08846e10i	−1.06438	+	0.614522i	−0.926641	−	0.375947i	$-0.877318\pi$
$73$	−1.88527e10	+	1.08846e10i	−1.06438	+	0.614522i	−0.137741	+	0.990468i	$0.543984\pi$
$74$	−5.24289e9	+	3.02698e9i	−0.274661	+	0.158575i
$75$	−8.43088e9	−	1.70393e10i	−0.410238	−	0.829116i
$76$		−	2.03067e10i		−	0.918679i
$77$	1.00770e10	−	2.77958e9i	0.424261	−	0.117026i
$78$	1.30280e10	−	1.95537e10i	0.510926	−	0.766847i
$79$	−8.17353e9	+	1.41570e10i	−0.298855	+	0.517632i	−0.975874	−	0.218333i	$-0.929938\pi$
$79$	−8.17353e9	+	1.41570e10i	−0.298855	+	0.517632i	0.677019	+	0.735965i	$0.263271\pi$
$80$	1.00293e9	+	1.73713e9i	0.0342198	+	0.0592704i
$81$	3.03543e10	+	7.96169e9i	0.967280	+	0.253710i
$82$	−2.86185e10	−	1.65229e10i	−0.852453	−	0.492164i
$83$	2.10806e10			0.587427			0.293714	−	0.955893i	$-0.405109\pi$
$83$	2.10806e10			0.587427			0.293714	+	0.955893i	$0.405109\pi$
$84$	3.90158e9	+	1.87635e10i	0.101790	+	0.489529i
$85$	−1.67539e10			−0.409555
$86$	1.00799e10	+	5.81965e9i	0.231055	+	0.133400i
$87$	2.93905e9	−	4.57677e10i	0.0632194	−	0.984473i
$88$	3.85155e9	+	6.67109e9i	0.0778003	+	0.134754i
$89$	3.87321e10	−	6.70859e10i	0.735234	−	1.27346i	−0.219386	−	0.975638i	$-0.570405\pi$
$89$	3.87321e10	−	6.70859e10i	0.735234	−	1.27346i	0.954620	−	0.297825i	$-0.0962612\pi$
$90$	−1.00075e10	+	4.17625e9i	−0.178645	+	0.0745508i
$91$	−1.95272e10	+	7.50771e10i	−0.328029	+	1.26119i
$92$		−	8.80208e9i		−	0.139236i
$93$	−7.31360e10	+	3.61869e10i	−1.09012	+	0.539381i
$94$	7.99542e10	−	4.61616e10i	1.12367	−	0.648751i
$95$	−3.28527e10	+	1.89675e10i	−0.435604	+	0.251496i
$96$	−1.26580e10	+	6.26303e9i	−0.158443	+	0.0783958i
$97$		−	3.84781e10i		−	0.454956i	−0.973783	−	0.227478i	$-0.926952\pi$
$97$		−	3.84781e10i		−	0.454956i	0.973783	−	0.227478i	$-0.0730480\pi$
$98$	−3.24384e10	−	5.43268e10i	−0.362507	−	0.607115i
$99$	−3.84316e10	+	1.60380e10i	−0.406157	+	0.169495i
$100$	−2.31264e10	+	4.00561e10i	−0.231264	+	0.400561i
$101$	7.15381e10	+	1.23908e11i	0.677283	+	1.17309i	0.975796	+	0.218682i	$0.0701758\pi$
$101$	7.15381e10	+	1.23908e11i	0.677283	+	1.17309i	−0.298514	+	0.954405i	$0.596491\pi$
$102$	7.55934e9	−	1.17716e11i	0.0677927	−	1.05569i
$103$	−7.38504e10	−	4.26376e10i	−0.627694	−	0.362399i	0.152164	−	0.988355i	$-0.451376\pi$
$103$	−7.38504e10	−	4.26376e10i	−0.627694	−	0.362399i	−0.779859	+	0.625956i	$0.784709\pi$
$104$	−5.71653e10			−0.460733
$105$	2.67119e10	−	2.38383e10i	0.204251	−	0.182278i
$106$	6.45893e10			0.468790
$107$	6.00966e10	+	3.46968e10i	0.414228	+	0.239155i	0.692605	−	0.721317i	$-0.256463\pi$
$107$	6.00966e10	+	3.46968e10i	0.414228	+	0.239155i	−0.278377	+	0.960472i	$0.589796\pi$
$108$	−2.48278e10	−	7.21989e10i	−0.162595	−	0.472824i
$109$	−1.39394e10	−	2.41438e10i	−0.0867759	−	0.150300i	0.819371	−	0.573264i	$-0.194323\pi$
$109$	−1.39394e10	−	2.41438e10i	−0.0867759	−	0.150300i	−0.906147	+	0.422964i	$0.860990\pi$
$110$	7.19513e9	−	1.24623e10i	0.0425970	−	0.0737801i
$111$	−4.41505e10	+	6.62653e10i	−0.248691	+	0.373259i
$112$	3.27274e10	−	3.32116e10i	0.175474	−	0.178070i
$113$			2.22482e11i			1.13596i	0.823042	+	0.567980i	$0.192275\pi$
$113$			2.22482e11i			1.13596i	−0.823042	+	0.567980i	$0.807725\pi$
$114$	−1.18447e11	−	2.39388e11i	−0.576164	−	1.16446i
$115$	−1.42403e10	+	8.22163e9i	−0.0660208	+	0.0381171i
$116$	−9.66311e10	+	5.57900e10i	−0.427167	+	0.246625i
$117$	3.95281e10	−	3.06503e11i	0.166680	−	1.29245i
$118$		−	2.41777e11i		−	0.972889i
$119$	1.03557e11	+	3.75431e11i	0.397804	+	1.44219i
$120$	2.19558e10	+	1.46284e10i	0.0805474	+	0.0536663i
$121$	−1.15024e11	+	1.99228e11i	−0.403154	+	0.698283i
$122$	8.65560e10	+	1.49919e11i	0.289947	+	0.502202i
$123$	−4.33750e11	−	2.78539e10i	−1.38919	−	0.0892089i
$124$	1.71928e11	+	9.92630e10i	0.526658	+	0.304066i
$125$	1.79811e11			0.527000
$126$	1.55440e11	+	1.98439e11i	0.436039	+	0.556660i
$127$	5.47879e11			1.47151			0.735757	−	0.677245i	$-0.236826\pi$
$127$	5.47879e11			1.47151			0.735757	+	0.677245i	$0.236826\pi$
$128$	2.97564e10	+	1.71799e10i	0.0765466	+	0.0441942i
$129$	1.52774e11	+	9.81063e9i	0.376536	+	0.0241798i
$130$	5.33956e10	+	9.24838e10i	0.126130	+	0.218463i
$131$	−3.67879e11	+	6.37185e11i	−0.833130	+	1.44302i	0.0624144	+	0.998050i	$0.480120\pi$
$131$	−3.67879e11	+	6.37185e11i	−0.833130	+	1.44302i	−0.895544	+	0.444973i	$0.853213\pi$
$132$	8.43164e10	+	5.61774e10i	0.183128	+	0.122013i
$133$	6.28099e11	+	6.18943e11i	1.30871	+	1.28963i
$134$			2.67989e11i			0.535848i
$135$	−9.36150e10	+	1.07605e11i	−0.179684	+	0.206536i
$136$	−2.48539e11	+	1.43494e11i	−0.458068	+	0.264466i
$137$	1.26393e11	−	7.29730e10i	0.223748	−	0.129181i	−0.383936	−	0.923360i	$-0.625432\pi$
$137$	1.26393e11	−	7.29730e10i	0.223748	−	0.129181i	0.607685	+	0.794178i	$0.292098\pi$
$138$	−5.13417e10	−	1.03765e11i	−0.0873243	−	0.176488i
$139$			2.90312e11i			0.474551i	0.971442	+	0.237276i	$0.0762544\pi$
$139$			2.90312e11i			0.474551i	−0.971442	+	0.237276i	$0.923746\pi$
$140$	−8.42999e10	−	2.19260e10i	−0.132472	−	0.0344553i
$141$	6.73297e11	−	1.01055e12i	1.01742	−	1.52705i
$142$	−1.94770e10	+	3.37351e10i	−0.0283097	+	0.0490338i
$143$	2.05054e11	+	3.55164e11i	0.286761	+	0.496685i
$144$	−1.12689e11	+	1.47665e11i	−0.151666	+	0.198740i
$145$	1.80517e11	+	1.04222e11i	0.233881	+	0.135031i
$146$	6.96615e11			0.869065
$147$	−6.99288e11	−	4.51230e11i	−0.840255	−	0.542192i
$148$	1.93727e11			0.224259
$149$	−4.51305e11	−	2.60561e11i	−0.503437	−	0.290660i	0.226695	−	0.973966i	$-0.427208\pi$
$149$	−4.51305e11	−	2.60561e11i	−0.503437	−	0.290660i	−0.730132	+	0.683306i	$0.760541\pi$
$150$	−3.89860e10	+	6.07102e11i	−0.0419186	+	0.652769i
$151$	−6.97755e11	−	1.20855e12i	−0.723318	−	1.25282i	−0.959662	−	0.281155i	$-0.909283\pi$
$151$	−6.97755e11	−	1.20855e12i	−0.723318	−	1.25282i	0.236344	−	0.971669i	$-0.424051\pi$
$152$	−3.24906e11	+	5.62754e11i	−0.324802	+	0.562573i
$153$	−5.97513e11	−	1.43181e12i	−0.576162	−	1.38065i
$154$	−3.23736e11	−	8.42022e10i	−0.301181	−	0.0783357i
$155$		−	3.70868e11i		−	0.332962i
$156$	−6.73902e11	+	3.33440e11i	−0.583999	+	0.288956i
$157$	−2.90379e11	+	1.67650e11i	−0.242950	+	0.140267i	−0.616532	−	0.787330i	$-0.711463\pi$
$157$	−2.90379e11	+	1.67650e11i	−0.242950	+	0.140267i	0.373582	+	0.927597i	$0.378130\pi$
$158$	4.53023e11	−	2.61553e11i	0.366021	−	0.211323i
$159$	7.61421e11	−	3.76743e11i	0.594211	−	0.294009i
$160$		−	6.41878e10i		−	0.0483941i
$161$	2.72255e11	+	2.68286e11i	0.198350	+	0.195459i
$162$	−7.13815e11	−	7.06309e11i	−0.502636	−	0.497350i
$163$	3.40145e11	−	5.89148e11i	0.231543	−	0.401044i	−0.726719	−	0.686935i	$-0.758956\pi$
$163$	3.40145e11	−	5.89148e11i	0.231543	−	0.401044i	0.958262	+	0.285890i	$0.0922892\pi$
$164$	5.28733e11	+	9.15792e11i	0.348013	+	0.602776i
$165$	1.21294e10	−	1.88883e11i	0.00772106	−	0.120235i
$166$	−5.84204e11	−	3.37290e11i	−0.359724	−	0.207687i
$167$	1.56502e12			0.932350			0.466175	−	0.884693i	$-0.345632\pi$
$167$	1.56502e12			0.932350			0.466175	+	0.884693i	$0.345632\pi$
$168$	1.92093e11	−	5.82416e11i	0.110741	−	0.335762i
$169$	−1.25129e12			−0.698200
$170$	4.64298e11	+	2.68062e11i	0.250800	+	0.144799i
$171$	−2.79265e12	−	2.13118e12i	−1.46062	−	1.11466i
$172$	−1.86229e11	−	3.22558e11i	−0.0943279	−	0.163381i
$173$	8.02846e11	−	1.39057e12i	0.393893	−	0.682243i	−0.599066	−	0.800700i	$-0.704461\pi$
$173$	8.02846e11	−	1.39057e12i	0.393893	−	0.682243i	0.992959	+	0.118456i	$0.0377946\pi$
$174$	−8.13733e11	+	1.22133e12i	−0.386777	+	0.580512i
$175$	−5.34075e11	−	1.93622e12i	−0.245976	−	0.891754i
$176$		−	2.46499e11i		−	0.110026i
$177$	−1.41026e12	−	2.85022e12i	−0.610163	−	1.23318i
$178$	−2.14675e12	+	1.23943e12i	−0.900474	+	0.519889i
$179$	−3.35520e12	+	1.93713e12i	−1.36467	+	0.787891i	−0.990241	−	0.139366i	$-0.955494\pi$
$179$	−3.35520e12	+	1.93713e12i	−1.36467	+	0.787891i	−0.374426	+	0.927257i	$0.622160\pi$
$180$	3.44155e11	+	4.43839e10i	0.135755	+	0.0175076i
$181$		−	1.55933e11i		−	0.0596633i	−0.999555	−	0.0298316i	$-0.990503\pi$
$181$		−	1.55933e11i		−	0.0596633i	0.999555	−	0.0298316i	$-0.00949712\pi$
$182$	1.74239e12	−	1.76816e12i	0.646774	−	0.656341i
$183$	1.89484e12	+	1.26247e12i	0.682483	+	0.454718i
$184$	−1.40833e11	+	2.43931e11i	−0.0492275	+	0.0852645i
$185$	−1.80952e11	−	3.13417e11i	−0.0613929	−	0.106336i
$186$	2.60580e12	+	1.67335e11i	0.858261	+	0.0551146i
$187$	1.78304e12	+	1.02944e12i	0.570205	+	0.329208i
$188$	−2.95434e12			−0.917472
$189$	2.98991e12	+	1.43267e12i	0.901816	+	0.432121i
$190$	1.21392e12			0.355669
$191$	7.94729e11	+	4.58837e11i	0.226222	+	0.130610i	0.608828	−	0.793302i	$-0.291640\pi$
$191$	7.94729e11	+	4.58837e11i	0.226222	+	0.130610i	−0.382606	+	0.923912i	$0.624973\pi$
$192$	4.50996e11	+	2.89614e10i	0.124743	+	0.00801057i
$193$	5.18561e10	+	8.98175e10i	0.0139391	+	0.0241432i	0.872911	−	0.487880i	$-0.162230\pi$
$193$	5.18561e10	+	8.98175e10i	0.0139391	+	0.0241432i	−0.858972	+	0.512023i	$0.828896\pi$
$194$	−6.15650e11	+	1.06634e12i	−0.160851	+	0.278602i
$195$	1.16891e12	+	7.78809e11i	0.296887	+	0.197807i
$196$	2.97309e10	+	2.02456e12i	0.00734176	+	0.499946i
$197$			8.98069e11i			0.215648i	0.994170	+	0.107824i	$0.0343883\pi$
$197$			8.98069e11i			0.215648i	−0.994170	+	0.107824i	$0.965612\pi$
$198$	1.32165e12	+	1.70447e11i	0.308645	+	0.0398044i
$199$	−3.99886e12	+	2.30875e12i	−0.908332	+	0.524426i	−0.879894	−	0.475170i	$-0.842387\pi$
$199$	−3.99886e12	+	2.30875e12i	−0.908332	+	0.524426i	−0.0284380	+	0.999596i	$0.509053\pi$
$200$	1.28180e12	−	7.40045e11i	0.283240	−	0.163528i
$201$	1.56316e12	+	3.15924e12i	0.336065	+	0.679209i
$202$		−	4.57844e12i		−	0.957822i
$203$	1.21967e12	−	4.68933e12i	0.248322	−	0.954735i
$204$	−2.09295e12	+	3.14130e12i	−0.414757	+	0.622506i
$205$	9.87731e11	−	1.71080e12i	0.190543	−	0.330030i
$206$	1.36440e12	+	2.36321e12i	0.256255	+	0.443847i
$207$	−1.21050e12	−	9.23776e11i	−0.221374	−	0.168939i
$208$	1.58421e12	+	9.14645e11i	0.282140	+	0.162894i
$209$	4.66181e12			0.808630
$210$	−1.12168e12	+	2.33235e11i	−0.189523	+	0.0394082i
$211$	5.60718e12			0.922977			0.461488	−	0.887146i	$-0.347316\pi$
$211$	5.60718e12			0.922977			0.461488	+	0.887146i	$0.347316\pi$
$212$	−1.78995e12	−	1.03343e12i	−0.287074	−	0.165742i
$213$	−3.28338e10	+	5.11299e11i	−0.00513137	+	0.0799073i
$214$	−1.11030e12	−	1.92309e12i	−0.169108	−	0.292903i
$215$	−3.47896e11	+	6.02573e11i	−0.0516461	+	0.0894537i
$216$	−4.67133e11	+	2.39808e12i	−0.0675997	+	0.347031i
$217$	−8.31062e12	+	2.29235e12i	−1.17248	+	0.323409i
$218$			8.92123e11i			0.122720i
$219$	8.21216e12	−	4.06329e12i	1.10158	−	0.545048i
$220$	−3.98794e11	+	2.30244e11i	−0.0521704	+	0.0301206i
$221$	−1.32320e13	+	7.63953e12i	−1.68838	+	0.974785i
$222$	2.28378e12	−	1.12999e12i	0.284258	−	0.140648i
$223$			1.44009e12i			0.174869i	0.996170	+	0.0874345i	$0.0278668\pi$
$223$			1.44009e12i			0.174869i	−0.996170	+	0.0874345i	$0.972133\pi$
$224$	−1.43835e12	+	3.96747e11i	−0.170413	+	0.0470056i
$225$	3.08157e12	+	7.38432e12i	0.356261	+	0.853702i
$226$	3.55971e12	−	6.16560e12i	0.401623	−	0.695631i
$227$	−1.20358e12	−	2.08467e12i	−0.132536	−	0.229559i	0.792117	−	0.610369i	$-0.208979\pi$
$227$	−1.20358e12	−	2.08467e12i	−0.132536	−	0.229559i	−0.924654	+	0.380809i	$0.875645\pi$
$228$	−5.47720e11	+	8.52926e12i	−0.0588731	+	0.916790i
$229$	1.13374e13	+	6.54564e12i	1.18965	+	0.686843i	0.958226	−	0.286011i	$-0.0923295\pi$
$229$	1.13374e13	+	6.54564e12i	1.18965	+	0.686843i	0.231420	+	0.972854i	$0.425663\pi$
$230$	5.26184e11			0.0539057
$231$	−4.30755e12	+	8.95688e11i	−0.430888	+	0.0895965i
$232$	3.57056e12			0.348781
$233$	−4.38194e12	−	2.52991e12i	−0.418031	−	0.241350i	0.276203	−	0.961099i	$-0.410924\pi$
$233$	−4.38194e12	−	2.52991e12i	−0.418031	−	0.241350i	−0.694235	+	0.719749i	$0.744257\pi$
$234$	−5.99948e12	+	7.86161e12i	−0.559019	+	0.732528i
$235$	2.75952e12	+	4.77963e12i	0.251166	+	0.435032i
$236$	−3.86843e12	+	6.70031e12i	−0.343968	+	0.595770i
$237$	3.81492e12	−	5.72580e12i	0.331413	−	0.497416i
$238$	3.13705e12	−	1.20611e13i	0.266286	−	1.02380i
$239$			1.50748e12i			0.125044i	0.998044	+	0.0625222i	$0.0199144\pi$
$239$			1.50748e12i			0.125044i	−0.998044	+	0.0625222i	$0.980086\pi$
$240$	−3.74401e11	−	7.56688e11i	−0.0303511	−	0.0613416i
$241$	7.74699e12	−	4.47273e12i	0.613817	−	0.354388i	−0.160641	−	0.987013i	$-0.551356\pi$
$241$	7.74699e12	−	4.47273e12i	0.613817	−	0.354388i	0.774458	+	0.632625i	$0.218023\pi$
$242$	6.37530e12	−	3.68078e12i	0.493761	−	0.285073i
$243$	−1.25348e13	−	4.16283e12i	−0.949033	−	0.315176i
$244$		−	5.53958e12i		−	0.410046i
$245$	3.24763e12	−	1.93915e12i	0.235046	−	0.140346i
$246$	1.15748e13	+	7.71191e12i	0.819161	+	0.545782i
$247$	−1.72978e13	+	2.99607e13i	−1.19718	+	2.07357i
$248$	−3.17641e12	−	5.50171e12i	−0.215007	−	0.372403i
$249$	−8.85436e12	−	5.68596e11i	−0.586220	−	0.0376450i
$250$	−4.98306e12	−	2.87697e12i	−0.322720	−	0.186323i
$251$	1.96520e13			1.24509			0.622545	−	0.782584i	$-0.286099\pi$
$251$	1.96520e13			1.24509			0.622545	+	0.782584i	$0.286099\pi$
$252$	−1.13266e12	−	7.98636e12i	−0.0702094	−	0.495046i
$253$	2.02070e12			0.122557
$254$	−1.51833e13	−	8.76607e12i	−0.901115	−	0.520259i
$255$	7.03703e12	+	4.51894e11i	0.408713	+	0.0262461i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	1.98723e12	−	3.44198e12i	0.110564	−	0.191503i	−0.805434	−	0.592686i	$-0.798067\pi$
$257$	1.98723e12	−	3.44198e12i	0.110564	−	0.191503i	0.915998	+	0.401183i	$0.131401\pi$
$258$	−4.07683e12	−	2.71627e12i	−0.222031	−	0.147933i
$259$	−5.90476e12	+	5.99211e12i	−0.314814	+	0.319471i
$260$		−	3.41732e12i		−	0.178374i
$261$	−2.46894e12	+	1.91442e13i	−0.126179	+	0.978398i
$262$	2.03899e13	−	1.17721e13i	1.02037	−	0.589112i
$263$	1.56826e13	−	9.05438e12i	0.768533	−	0.443713i	−0.0638178	−	0.997962i	$-0.520328\pi$
$263$	1.56826e13	−	9.05438e12i	0.768533	−	0.443713i	0.832351	+	0.554249i	$0.186994\pi$
$264$	−1.43781e12	−	2.90590e12i	−0.0690047	−	0.139463i
$265$			3.86112e12i			0.181493i
$266$	−7.50330e12	−	2.72022e13i	−0.345464	−	1.25244i
$267$	−1.80778e13	+	2.71329e13i	−0.815332	+	1.22373i
$268$	4.28783e12	−	7.42674e12i	0.189451	−	0.328138i
$269$	−2.03153e13	−	3.51871e13i	−0.879398	−	1.52316i	−0.852002	−	0.523538i	$-0.824612\pi$
$269$	−2.03153e13	−	3.51871e13i	−0.879398	−	1.52316i	−0.0273962	−	0.999625i	$-0.508722\pi$
$270$	4.31601e12	−	1.48420e12i	0.183055	−	0.0629492i
$271$	−2.13908e13	−	1.23500e13i	−0.888990	−	0.513258i	−0.0153777	−	0.999882i	$-0.504895\pi$
$271$	−2.13908e13	−	1.23500e13i	−0.888990	−	0.513258i	−0.873612	+	0.486623i	$0.838228\pi$
$272$	9.18361e12			0.374011
$273$	1.02269e13	−	3.10074e13i	0.408178	−	1.23757i
$274$	−4.67027e12			−0.182690
$275$	−9.19570e12	−	5.30914e12i	−0.352578	−	0.203561i
$276$	−2.37414e11	+	3.69708e12i	−0.00892290	+	0.138950i
$277$	1.19885e13	+	2.07648e13i	0.441700	+	0.765047i	0.997816	−	0.0660579i	$-0.0210422\pi$
$277$	1.19885e13	+	2.07648e13i	0.441700	+	0.765047i	−0.556116	+	0.831105i	$0.687709\pi$
$278$	4.64499e12	−	8.04535e12i	0.167779	−	0.290602i
$279$	3.16949e13	−	1.32267e13i	1.12245	−	0.468412i
$280$	1.98537e12	+	1.95643e12i	0.0689402	+	0.0679353i
$281$		−	1.76519e13i		−	0.601046i	−0.953775	−	0.300523i	$-0.902839\pi$
$281$		−	1.76519e13i		−	0.601046i	0.953775	−	0.300523i	$-0.0971613\pi$
$282$	−3.48277e13	+	1.72324e13i	−1.16293	+	0.575407i
$283$	−2.25514e13	+	1.30201e13i	−0.738497	+	0.426372i	−0.821523	−	0.570176i	$-0.806875\pi$
$283$	−2.25514e13	+	1.30201e13i	−0.738497	+	0.426372i	0.0830255	+	0.996547i	$0.473542\pi$
$284$	1.07952e12	−	6.23263e11i	0.0346722	−	0.0200180i
$285$	1.43105e13	−	7.08068e12i	0.450825	−	0.223063i
$286$		−	1.31235e13i		−	0.405542i
$287$	−4.44417e13	−	1.15591e13i	−1.34723	−	0.350407i
$288$	5.48557e12	−	2.28920e12i	0.163141	−	0.0680809i
$289$	−2.12169e13	+	3.67487e13i	−0.619074	+	1.07227i
$290$	−3.33510e12	−	5.77656e12i	−0.0954816	−	0.165379i
$291$	−1.03785e12	+	1.61617e13i	−0.0291556	+	0.454021i
$292$	−1.93052e13	−	1.11458e13i	−0.532191	−	0.307261i
$293$	6.07096e13			1.64242			0.821212	−	0.570624i	$-0.193298\pi$
$293$	6.07096e13			1.64242			0.821212	+	0.570624i	$0.193298\pi$
$294$	1.21596e13	+	2.36935e13i	0.322855	+	0.629098i
$295$	1.44533e13			0.376657
$296$	−5.36872e12	−	3.09963e12i	−0.137330	−	0.0792877i
$297$	1.65747e13	−	5.69974e12i	0.416185	−	0.143118i
$298$	8.33795e12	+	1.44418e13i	0.205527	+	0.355984i
$299$	−7.49788e12	+	1.29867e13i	−0.181446	+	0.314273i
$300$	1.07940e13	−	1.62007e13i	0.256459	−	0.384917i
$301$	1.56531e13	+	4.07131e12i	0.365162	+	0.0949770i
$302$			4.46563e13i			1.02293i
$303$	−2.67056e13	−	5.39736e13i	−0.600714	−	1.21408i
$304$	1.80081e13	−	1.03970e13i	0.397799	−	0.229670i
$305$	−8.96210e12	+	5.17427e12i	−0.194429	+	0.112254i
$306$	−6.35020e12	+	4.92397e13i	−0.135307	+	1.04917i
$307$		−	6.52231e13i		−	1.36502i	−0.730874	−	0.682512i	$-0.760887\pi$
$307$		−	6.52231e13i		−	1.36502i	0.730874	−	0.682512i	$-0.239113\pi$
$308$	7.62440e12	+	7.51325e12i	0.156739	+	0.154454i
$309$	2.98688e13	+	1.99007e13i	0.603180	+	0.401880i
$310$	−5.93389e12	+	1.02778e13i	−0.117720	+	0.203897i
$311$	−4.15563e11	−	7.19776e11i	−0.00809943	−	0.0140286i	0.861947	−	0.506998i	$-0.169245\pi$
$311$	−4.15563e11	−	7.19776e11i	−0.00809943	−	0.0140286i	−0.870047	+	0.492969i	$0.835911\pi$
$312$	2.40108e13	+	1.54189e12i	0.459786	+	0.0295259i
$313$	1.67035e12	+	9.64379e11i	0.0314278	+	0.0181449i	0.515632	−	0.856810i	$-0.327557\pi$
$313$	1.67035e12	+	9.64379e11i	0.0314278	+	0.0181449i	−0.484204	+	0.874955i	$0.660891\pi$
$314$	1.07296e13			0.198368
$315$	−1.18626e13	+	9.29214e12i	−0.215512	+	0.168814i
$316$	−1.67394e13			−0.298855
$317$	−8.91452e13	−	5.14680e13i	−1.56413	−	0.903049i	−0.996832	−	0.0795347i	$-0.974657\pi$
$317$	−8.91452e13	−	5.14680e13i	−1.56413	−	0.903049i	−0.567295	−	0.823515i	$-0.692010\pi$
$318$	−2.71290e13	−	1.74213e12i	−0.467826	−	0.0300422i
$319$	−1.28077e13	−	2.21836e13i	−0.217082	−	0.375997i
$320$	−1.02700e12	+	1.77882e12i	−0.0171099	+	0.0296352i
$321$	−2.43061e13	−	1.61944e13i	−0.398050	−	0.265209i
$322$	−3.25237e12	−	1.17910e13i	−0.0523591	−	0.189821i
$323$			1.73681e14i			2.74877i
$324$	8.48088e12	+	3.09949e13i	0.131960	+	0.482272i
$325$	6.82420e13	−	3.93995e13i	1.04398	−	0.602744i
$326$	−1.88527e13	+	1.08846e13i	−0.283581	+	0.163726i
$327$	5.20366e12	+	1.05169e13i	0.0769656	+	0.155552i
$328$		−	3.38389e13i		−	0.492164i
$329$	9.00478e13	−	9.13799e13i	1.28794	−	1.30699i
$330$	−3.35826e12	+	5.04040e12i	−0.0472376	+	0.0708986i
$331$	−6.65592e13	+	1.15284e14i	−0.920777	+	1.59483i	−0.122561	+	0.992461i	$0.539111\pi$
$331$	−6.65592e13	+	1.15284e14i	−0.920777	+	1.59483i	−0.798216	+	0.602371i	$0.794223\pi$
$332$	1.07933e13	+	1.86945e13i	0.146857	+	0.254364i
$333$	2.03316e13	−	2.66421e13i	0.272100	−	0.356554i
$334$	−4.33711e13	−	2.50403e13i	−0.570945	−	0.329635i
$335$	−1.60203e13			−0.207455
$336$	−1.46421e13	+	1.30669e13i	−0.186525	+	0.166459i
$337$	1.21290e14			1.52005			0.760027	−	0.649892i	$-0.225186\pi$
$337$	1.21290e14			1.52005			0.760027	+	0.649892i	$0.225186\pi$
$338$	3.46767e13	+	2.00206e13i	0.427558	+	0.246851i
$339$	6.00088e12	−	9.34476e13i	0.0727976	−	1.13363i
$340$	−8.57800e12	−	1.48575e13i	−0.102389	−	0.177342i
$341$	−2.27878e13	+	3.94697e13i	−0.267642	+	0.463569i
$342$	4.32935e13	+	1.03743e14i	0.500356	+	1.19899i
$343$	−6.35274e13	−	6.07887e13i	−0.722509	−	0.691362i
$344$			1.19186e13i			0.133400i
$345$	6.20301e12	−	3.06918e12i	0.0683278	−	0.0338078i
$346$	−4.44982e13	+	2.56911e13i	−0.482419	+	0.278525i
$347$	−4.90521e13	+	2.83202e13i	−0.523414	+	0.302193i	−0.738330	−	0.674439i	$-0.764385\pi$
$347$	−4.90521e13	+	2.83202e13i	−0.523414	+	0.302193i	0.214916	+	0.976632i	$0.431052\pi$
$348$	4.20921e13	−	2.08267e13i	0.442094	−	0.218743i
$349$		−	8.80120e13i		−	0.909918i	−0.890512	−	0.454959i	$-0.849654\pi$
$349$		−	8.80120e13i		−	0.909918i	0.890512	−	0.454959i	$-0.150346\pi$
$350$	−1.61788e13	+	6.22032e13i	−0.164654	+	0.633051i
$351$	−2.48699e13	+	1.27672e14i	−0.249163	+	1.27911i
$352$	−3.94399e12	+	6.83119e12i	−0.0389002	+	0.0673770i
$353$	4.04210e13	+	7.00112e13i	0.392506	+	0.679840i	0.992779	−	0.119955i	$-0.0382750\pi$
$353$	4.04210e13	+	7.00112e13i	0.392506	+	0.679840i	−0.600274	+	0.799795i	$0.704942\pi$
$354$	−6.52131e12	+	1.01552e14i	−0.0623471	+	0.970889i
$355$	−2.01667e12	−	1.16432e12i	−0.0189836	−	0.0109602i
$356$	7.93233e13			0.735234
$357$	−3.33699e13	−	1.60483e14i	−0.304564	−	1.46471i
$358$	1.23976e14			1.11425
$359$	2.31255e13	+	1.33515e13i	0.204678	+	0.118171i	0.598836	−	0.800872i	$-0.295630\pi$
$359$	2.31255e13	+	1.33515e13i	0.204678	+	0.118171i	−0.394157	+	0.919043i	$0.628964\pi$
$360$	−8.82736e12	−	6.73649e12i	−0.0769427	−	0.0587178i
$361$	1.38383e14	+	2.39687e14i	1.18794	+	2.05757i
$362$	−2.49494e12	+	4.32136e12i	−0.0210942	+	0.0365362i
$363$	5.36866e13	−	8.05780e13i	0.447074	−	0.671012i
$364$	−7.65771e13	+	2.11226e13i	−0.628118	+	0.173256i
$365$			4.16433e13i			0.336461i
$366$	−3.23118e13	−	6.53042e13i	−0.257167	−	0.519751i
$367$	−5.79372e13	+	3.34501e13i	−0.454250	+	0.262261i	−0.709623	−	0.704581i	$-0.751135\pi$
$367$	−5.79372e13	+	3.34501e13i	−0.454250	+	0.262261i	0.255374	+	0.966842i	$0.417801\pi$
$368$	7.80578e12	−	4.50667e12i	0.0602911	−	0.0348091i
$369$	1.81434e14	+	2.33986e13i	1.38062	+	0.178051i
$370$			1.15809e13i			0.0868226i
$371$	8.65220e13	−	2.38657e13i	0.639102	−	0.176286i
$372$	−6.95366e13	−	4.63301e13i	−0.506089	−	0.337192i
$373$	3.98247e13	−	6.89785e13i	0.285597	−	0.494669i	−0.687156	−	0.726509i	$-0.741141\pi$
$373$	3.98247e13	−	6.89785e13i	0.285597	−	0.494669i	0.972754	+	0.231840i	$0.0744746\pi$
$374$	−3.29420e13	−	5.70572e13i	−0.232785	−	0.403196i
$375$	−7.55247e13	−	4.84994e12i	−0.525917	−	0.0337726i
$376$	8.18731e13	+	4.72695e13i	0.561834	+	0.324375i
$377$	1.90094e14			1.28556
$378$	−5.99361e13	−	8.75417e13i	−0.399469	−	0.583459i
$379$	−1.24451e14			−0.817491			−0.408746	−	0.912648i	$-0.634034\pi$
$379$	−1.24451e14			−0.817491			−0.408746	+	0.912648i	$0.634034\pi$
$380$	−3.36412e13	−	1.94228e13i	−0.217802	−	0.125748i
$381$	−2.30122e14	−	1.47776e13i	−1.46849	−	0.0943013i
$382$	−1.46828e13	−	2.54313e13i	−0.0923549	−	0.159963i
$383$	−6.82303e13	+	1.18178e14i	−0.423042	+	0.732731i	−0.996235	−	0.0866894i	$-0.972371\pi$
$383$	−6.82303e13	+	1.18178e14i	−0.423042	+	0.732731i	0.573193	+	0.819420i	$0.305705\pi$
$384$	−1.20350e13	−	8.01855e12i	−0.0735570	−	0.0490088i
$385$	5.03357e12	−	1.93528e13i	0.0303279	−	0.116603i
$386$		−	3.31879e12i		−	0.0197129i
$387$	−6.39041e13	−	8.24138e12i	−0.374212	−	0.0482603i
$388$	3.41228e13	−	1.97008e13i	0.197002	−	0.113739i
$389$	−1.07191e14	+	6.18865e13i	−0.610146	+	0.352268i	−0.773023	−	0.634379i	$-0.781256\pi$
$389$	−1.07191e14	+	6.18865e13i	−0.610146	+	0.352268i	0.162877	+	0.986646i	$0.447923\pi$
$390$	−1.99329e13	−	4.02856e13i	−0.111870	−	0.226097i
$391$			7.52834e13i			0.416607i
$392$	3.15691e13	−	5.65821e13i	0.172262	−	0.308749i
$393$	1.71704e14	−	2.57710e14i	0.923893	−	1.38667i
$394$	1.43691e13	−	2.48880e13i	0.0762431	−	0.132057i
$395$	1.56355e13	+	2.70815e13i	0.0818141	+	0.141706i
$396$	−3.38996e13	−	2.58700e13i	−0.174933	−	0.133498i
$397$	−1.11171e14	−	6.41846e13i	−0.565775	−	0.326650i	0.189685	−	0.981845i	$-0.439253\pi$
$397$	−1.11171e14	−	6.41846e13i	−0.565775	−	0.326650i	−0.755460	+	0.655195i	$0.772587\pi$
$398$	1.47760e14			0.741650
$399$	−2.47122e14	−	2.76912e14i	−1.22338	−	1.37085i
$400$	−4.73629e13			−0.231264
$401$	−1.25259e12	−	7.23185e11i	−0.00603276	−	0.00348302i	0.496981	−	0.867762i	$-0.334442\pi$
$401$	−1.25259e12	−	7.23185e11i	−0.00603276	−	0.00348302i	−0.503013	+	0.864279i	$0.667775\pi$
$402$	7.22833e12	−	1.12562e14i	0.0343396	−	0.534746i
$403$	−1.69110e14	−	2.92908e14i	−0.792487	−	1.37263i
$404$	−7.32550e13	+	1.26881e14i	−0.338641	+	0.586544i
$405$	4.22228e13	−	4.26715e13i	0.192551	−	0.194597i
$406$	−1.08830e14	+	1.10440e14i	−0.489615	+	0.496858i
$407$			4.44740e13i			0.197395i
$408$	1.08262e14	−	5.35671e13i	0.474075	−	0.234567i
$409$	−8.86713e13	+	5.11944e13i	−0.383093	+	0.221179i	−0.679163	−	0.733987i	$-0.737657\pi$
$409$	−8.86713e13	+	5.11944e13i	−0.383093	+	0.221179i	0.296070	+	0.955166i	$0.404324\pi$
$410$	−5.47456e13	+	3.16074e13i	−0.233366	+	0.134734i
$411$	−5.50562e13	+	2.72412e13i	−0.231567	+	0.114577i
$412$		−	8.73217e13i		−	0.362399i
$413$	−8.93363e13	−	3.23877e14i	−0.365850	−	1.32634i
$414$	1.87659e13	+	4.49684e13i	0.0758346	+	0.181721i
$415$	2.01630e13	−	3.49234e13i	0.0804066	−	0.139268i
$416$	−2.92687e13	−	5.06948e13i	−0.115183	−	0.199503i
$417$	7.83041e12	−	1.21938e14i	0.0304114	−	0.473576i
$418$	−1.29192e14	−	7.45889e13i	−0.495183	−	0.285894i
$419$	−2.35171e14			−0.889624			−0.444812	−	0.895624i	$-0.646730\pi$
$419$	−2.35171e14			−0.889624			−0.444812	+	0.895624i	$0.646730\pi$
$420$	3.48165e13	+	1.14832e13i	0.129991	+	0.0428738i
$421$	1.71453e14			0.631820			0.315910	−	0.948789i	$-0.397690\pi$
$421$	1.71453e14			0.631820			0.315910	+	0.948789i	$0.397690\pi$
$422$	−1.55391e14	−	8.97148e13i	−0.565205	−	0.326322i
$423$	−3.10057e14	+	4.06293e14i	−1.11319	+	1.45871i
$424$	3.30697e13	+	5.72784e13i	0.117197	+	0.202992i
$425$	1.97798e14	−	3.42596e14i	0.691963	−	1.19851i
$426$	9.09069e12	−	1.36442e13i	0.0313938	−	0.0471188i
$427$	1.71343e14	+	1.68845e14i	0.584135	+	0.575620i
$428$			7.10591e13i			0.239155i
$429$	−7.65479e13	−	1.54708e14i	−0.254342	−	0.514041i
$430$	1.92823e13	−	1.11327e13i	0.0632533	−	0.0365193i
$431$	1.31870e14	−	7.61352e13i	0.427092	−	0.246582i	−0.271015	−	0.962575i	$-0.587359\pi$
$431$	1.31870e14	−	7.61352e13i	0.427092	−	0.246582i	0.698107	+	0.715994i	$0.254026\pi$
$432$	5.13148e13	−	5.89834e13i	0.164090	−	0.188612i
$433$			5.99462e13i			0.189269i	0.995512	+	0.0946343i	$0.0301682\pi$
$433$			5.99462e13i			0.189269i	−0.995512	+	0.0946343i	$0.969832\pi$
$434$	2.66988e14	+	6.94424e13i	0.832336	+	0.216487i
$435$	−7.30104e13	−	4.86446e13i	−0.224747	−	0.149742i
$436$	1.42740e13	−	2.47232e13i	0.0433879	−	0.0751501i
$437$	8.52303e13	+	1.47623e14i	0.255827	+	0.443105i
$438$	−2.92595e14	−	1.87894e13i	−0.867278	−	0.0556936i
$439$	4.77841e14	+	2.75882e14i	1.39871	+	0.807547i	0.994258	−	0.107010i	$-0.0341278\pi$
$439$	4.77841e14	+	2.75882e14i	1.39871	+	0.807547i	0.404455	+	0.914558i	$0.367461\pi$
$440$	1.47356e13			0.0425970
$441$	2.81547e14	+	2.08389e14i	0.803782	+	0.594925i
$442$	4.88930e14			1.37855
$443$	2.03545e14	+	1.17517e14i	0.566812	+	0.327249i	0.755875	−	0.654716i	$-0.227212\pi$
$443$	2.03545e14	+	1.17517e14i	0.566812	+	0.327249i	−0.189063	+	0.981965i	$0.560545\pi$
$444$	−8.13698e13	−	5.22529e12i	−0.223798	−	0.0143716i
$445$	−7.40923e13	−	1.28332e14i	−0.201277	−	0.348621i
$446$	2.30414e13	−	3.99089e13i	0.0618255	−	0.107085i
$447$	1.82530e14	+	1.21614e14i	0.483776	+	0.322325i
$448$	4.62088e13	+	1.20187e13i	0.120975	+	0.0314650i
$449$			6.81733e14i			1.76303i	0.472156	+	0.881515i	$0.343476\pi$
$449$			6.81733e14i			1.76303i	−0.472156	+	0.881515i	$0.656524\pi$
$450$	3.27500e13	−	2.53945e14i	0.0836648	−	0.648741i
$451$	−2.10239e14	+	1.21381e14i	−0.530569	+	0.306324i
$452$	−1.97299e14	+	1.13911e14i	−0.491885	+	0.283990i
$453$	2.60476e14	+	5.26438e14i	0.641545	+	1.29660i
$454$			7.70294e13i			0.187434i
$455$	1.05700e14	+	1.04159e14i	0.254104	+	0.250400i
$456$	1.51647e14	−	2.27606e14i	0.360187	−	0.540602i
$457$	−2.40991e14	+	4.17409e14i	−0.565538	+	0.979540i	0.431462	+	0.902131i	$0.357998\pi$
$457$	−2.40991e14	+	4.17409e14i	−0.565538	+	0.979540i	−0.996999	+	0.0774090i	$0.975335\pi$
$458$	−2.09461e14	−	3.62796e14i	−0.485671	−	0.841207i
$459$	2.12350e14	+	6.17510e14i	0.486500	+	1.41473i
$460$	−1.45820e13	−	8.41895e12i	−0.0330104	−	0.0190586i
$461$	−3.78081e14			−0.845726			−0.422863	−	0.906194i	$-0.638975\pi$
$461$	−3.78081e14			−0.845726			−0.422863	+	0.906194i	$0.638975\pi$
$462$	1.33705e14	+	4.40988e13i	0.295541	+	0.0974757i
$463$	−1.19702e14			−0.261459			−0.130730	−	0.991418i	$-0.541732\pi$
$463$	−1.19702e14			−0.261459			−0.130730	+	0.991418i	$0.541732\pi$
$464$	−9.89502e13	−	5.71289e13i	−0.213584	−	0.123313i
$465$	−1.00032e13	+	1.55773e14i	−0.0213378	+	0.332278i
$466$	8.09572e13	+	1.40222e14i	0.170660	+	0.295593i
$467$	6.23555e13	−	1.08003e14i	0.129907	−	0.225005i	−0.793733	−	0.608266i	$-0.791866\pi$
$467$	6.23555e13	−	1.08003e14i	0.129907	−	0.225005i	0.923640	+	0.383261i	$0.125199\pi$
$468$	2.92048e14	−	1.21876e14i	0.601316	−	0.250937i
$469$	9.90220e13	+	3.58991e14i	0.201503	+	0.730522i
$470$		−	1.76609e14i		−	0.355202i
$471$	1.26488e14	−	6.25848e13i	0.251440	−	0.124410i
$472$	2.14410e14	−	1.23790e14i	0.421273	−	0.243222i
$473$	7.40497e13	−	4.27526e13i	0.143809	−	0.0830283i
$474$	−1.97335e14	+	9.76392e13i	−0.378812	+	0.187432i
$475$		−	8.95729e14i		−	1.69966i
$476$	−2.79915e14	+	2.84055e14i	−0.525034	+	0.532801i
$477$	−3.29976e14	+	1.37703e14i	−0.611831	+	0.255325i
$478$	2.41197e13	−	4.17766e13i	0.0442099	−	0.0765737i
$479$	3.93511e14	+	6.81581e14i	0.713036	+	1.23502i	0.963712	+	0.266944i	$0.0860139\pi$
$479$	3.93511e14	+	6.81581e14i	0.713036	+	1.23502i	−0.250676	+	0.968071i	$0.580653\pi$
$480$	−1.73130e12	+	2.69604e13i	−0.00310131	+	0.0482946i
$481$	−2.85827e14	−	1.65022e14i	−0.506181	−	0.292244i
$482$	−2.86254e14			−0.501180
$483$	−1.07117e14	−	1.20030e14i	−0.185417	−	0.207768i
$484$	−2.35570e14			−0.403154
$485$	−6.37451e13	−	3.68033e13i	−0.107862	−	0.0622740i
$486$	2.80768e14	+	3.15920e14i	0.469730	+	0.528539i
$487$	−3.40948e14	−	5.90540e14i	−0.564000	−	0.976877i	−0.997142	−	0.0755508i	$-0.975928\pi$
$487$	−3.40948e14	−	5.90540e14i	−0.564000	−	0.976877i	0.433142	−	0.901326i	$-0.357405\pi$
$488$	−8.86333e13	+	1.53517e14i	−0.144973	+	0.251101i
$489$	−1.58759e14	+	2.38281e14i	−0.256768	+	0.385382i
$490$	−1.21027e14	+	1.77730e12i	−0.193556	+	0.00284238i
$491$		−	7.66624e14i		−	1.21237i	−0.795325	−	0.606184i	$-0.792700\pi$
$491$		−	7.66624e14i		−	1.21237i	0.795325	−	0.606184i	$-0.207300\pi$
$492$	−1.97379e14	−	3.98915e14i	−0.308669	−	0.623839i
$493$	8.26476e14	−	4.77166e14i	1.27812	−	0.737924i
$494$	9.58742e14	−	5.53530e14i	1.46624	−	0.846531i
$495$	−1.01892e13	+	7.90079e13i	−0.0154104	+	0.119493i
$496$			2.03291e14i			0.304066i
$497$	−1.36257e13	+	5.23873e13i	−0.0201557	+	0.0774936i
$498$	2.36282e14	+	1.57427e14i	0.345675	+	0.230313i
$499$	−4.58436e14	+	7.94034e14i	−0.663323	+	1.14891i	0.316414	+	0.948621i	$0.397521\pi$
$499$	−4.58436e14	+	7.94034e14i	−0.663323	+	1.14891i	−0.979737	+	0.200288i	$0.935812\pi$
$500$	9.20632e13	+	1.59458e14i	0.131750	+	0.228198i
$501$	−6.57344e14	−	4.22124e13i	−0.930433	−	0.0597492i
$502$	−5.44612e14	−	3.14432e14i	−0.762459	−	0.440206i
$503$	−9.42284e13			−0.130484			−0.0652421	−	0.997869i	$-0.520782\pi$
$503$	−9.42284e13			−0.130484			−0.0652421	+	0.997869i	$0.520782\pi$
$504$	−9.63926e13	+	2.39447e14i	−0.132031	+	0.327975i
$505$	2.73697e14			0.370823
$506$	−5.59993e13	−	3.23312e13i	−0.0750506	−	0.0433305i
$507$	5.25569e14	+	3.37502e13i	0.696765	+	0.0447438i
$508$	2.80514e14	+	4.85865e14i	0.367879	+	0.637184i
$509$	−1.69071e14	+	2.92839e14i	−0.219342	+	0.379911i	−0.954607	−	0.297869i	$-0.903724\pi$
$509$	−1.69071e14	+	2.92839e14i	−0.219342	+	0.379911i	0.735265	+	0.677779i	$0.237058\pi$
$510$	−1.87786e14	−	1.25116e14i	−0.241005	−	0.160574i
$511$	9.33166e14	−	2.57399e14i	1.18480	−	0.326807i
$512$			3.51844e13i			0.0441942i
$513$	1.11550e15	+	9.70468e14i	1.38619	+	1.20597i
$514$	−1.10143e14	+	6.35913e13i	−0.135413	+	0.0781809i
$515$	−1.41272e14	+	8.15633e13i	−0.171837	+	0.0992099i
$516$	6.95202e13	+	1.40505e14i	0.0836638	+	0.169090i
$517$		−	6.78230e14i		−	0.807568i
$518$	2.59511e14	−	7.15820e13i	0.305733	−	0.0843316i
$519$	−3.74721e14	+	5.62417e14i	−0.436805	+	0.655598i
$520$	−5.46771e13	+	9.47035e13i	−0.0630648	+	0.109231i
$521$	−8.23494e14	−	1.42633e15i	−0.939838	−	1.62785i	−0.765771	−	0.643114i	$-0.777642\pi$
$521$	−8.23494e14	−	1.42633e15i	−0.939838	−	1.62785i	−0.174067	−	0.984734i	$-0.555691\pi$
$522$	3.74729e14	−	4.91038e14i	0.423184	−	0.554533i
$523$	−1.25811e15	−	7.26368e14i	−1.40591	−	0.811703i	−0.410920	−	0.911671i	$-0.634792\pi$
$523$	−1.25811e15	−	7.26368e14i	−1.40591	−	0.811703i	−0.994991	+	0.0999684i	$0.968126\pi$
$524$	−7.53416e14			−0.833130
$525$	1.72099e14	+	8.27662e14i	0.188323	+	0.905684i
$526$	−5.79480e14			−0.627505
$527$	−1.47049e15	−	8.48986e14i	−1.57581	−	0.909793i
$528$	−6.64869e12	+	1.03535e14i	−0.00705098	+	0.109800i
$529$	−4.39461e14	−	7.61169e14i	−0.461227	−	0.798868i
$530$	6.17778e13	−	1.07002e14i	0.0641676	−	0.111141i
$531$	5.15464e14	+	1.23520e15i	0.529881	+	1.26974i
$532$	−2.27298e14	+	8.73903e14i	−0.231250	+	0.889097i
$533$		−	1.80156e15i		−	1.81405i
$534$	9.35115e14	−	4.62685e14i	0.931940	−	0.461114i
$535$	1.14962e14	−	6.63731e13i	0.113398	−	0.0654706i
$536$	−2.37656e14	+	1.37211e14i	−0.232029	+	0.133962i
$537$	1.46151e15	−	7.23140e14i	1.41235	−	0.698817i
$538$			1.30018e15i			1.24366i
$539$	−4.64780e14	+	6.82535e12i	−0.440058	+	0.00646229i
$540$	−1.43356e14	−	2.79250e13i	−0.134354	−	0.0261714i
$541$	−1.36705e13	+	2.36779e13i	−0.0126823	+	0.0219664i	−0.872297	−	0.488977i	$-0.837370\pi$
$541$	−1.36705e13	+	2.36779e13i	−0.0126823	+	0.0219664i	0.859615	+	0.510943i	$0.170704\pi$
$542$	3.95200e14	+	6.84507e14i	0.362928	+	0.628611i
$543$	−4.20591e12	+	6.54957e13i	−0.00382350	+	0.0595407i
$544$	−2.54504e14	−	1.46938e14i	−0.229034	−	0.132233i
$545$	−5.33307e13			−0.0475112
$546$	−7.79535e14	+	6.95673e14i	−0.687505	+	0.613544i
$547$	5.79213e14			0.505717			0.252859	−	0.967503i	$-0.418629\pi$
$547$	5.79213e14			0.505717			0.252859	+	0.967503i	$0.418629\pi$
$548$	1.29426e14	+	7.47244e13i	0.111874	+	0.0645906i
$549$	−7.61826e14	−	5.81377e14i	−0.651940	−	0.497520i
$550$	1.69893e14	+	2.94262e14i	0.143939	+	0.249310i
$551$	1.08043e15	−	1.87135e15i	0.906277	−	1.56972i
$552$	6.57327e13	−	9.86579e13i	0.0545904	−	0.0819345i
$553$	5.10214e14	−	5.17761e14i	0.419531	−	0.425737i
$554$		−	7.67266e14i		−	0.624658i
$555$	6.75502e13	+	1.36523e14i	0.0544522	+	0.110051i
$556$	−2.57451e14	+	1.48640e14i	−0.205487	+	0.118638i
$557$	3.90582e14	−	2.25503e14i	0.308680	−	0.178217i	−0.337655	−	0.941270i	$-0.609634\pi$
$557$	3.90582e14	−	2.25503e14i	0.308680	−	0.178217i	0.646336	+	0.763053i	$0.276301\pi$
$558$	−1.08998e15	−	1.40569e14i	−0.852965	−	0.110003i
$559$			6.34541e14i			0.491694i
$560$	−2.37174e13	−	8.59841e13i	−0.0181984	−	0.0659757i
$561$	−7.21150e14	−	4.80480e14i	−0.547936	−	0.365073i
$562$	−2.82431e14	+	4.89185e14i	−0.212502	+	0.368064i
$563$	4.65527e14	+	8.06316e14i	0.346855	+	0.600771i	0.985689	−	0.168574i	$-0.0539161\pi$
$563$	4.65527e14	+	8.06316e14i	0.346855	+	0.600771i	−0.638834	+	0.769345i	$0.720583\pi$
$564$	1.24089e15	+	7.96858e13i	0.915586	+	0.0587958i
$565$	3.68577e14	+	2.12798e14i	0.269316	+	0.155489i
$566$	8.33285e14			0.602980
$567$	−1.21719e15	−	6.82398e14i	−0.872270	−	0.489025i
$568$	−3.98888e13			−0.0283097
$569$	2.01047e15	+	1.16074e15i	1.41312	+	0.815866i	0.995681	−	0.0928376i	$-0.0295937\pi$
$569$	2.01047e15	+	1.16074e15i	1.41312	+	0.815866i	0.417441	+	0.908704i	$0.362927\pi$
$570$	−5.09875e14	−	3.27424e13i	−0.354938	−	0.0227929i
$571$	−7.70508e14	−	1.33456e15i	−0.531225	−	0.920109i	−0.999336	−	0.0364393i	$-0.988398\pi$
$571$	−7.70508e14	−	1.33456e15i	−0.531225	−	0.920109i	0.468111	−	0.883670i	$-0.344935\pi$
$572$	−2.09976e14	+	3.63688e14i	−0.143381	+	0.248343i
$573$	−3.21429e14	−	2.14158e14i	−0.217387	−	0.144838i
$574$	1.04666e15	+	1.03140e15i	0.701117	+	0.690896i
$575$		−	3.88261e14i		−	0.257603i
$576$	−1.88648e14	−	2.43290e13i	−0.123973	−	0.0159882i
$577$	1.31350e15	−	7.58351e14i	0.854996	−	0.493632i	−0.00733761	−	0.999973i	$-0.502336\pi$
$577$	1.31350e15	−	7.58351e14i	0.854996	−	0.493632i	0.862333	+	0.506341i	$0.169002\pi$
$578$	1.17596e15	−	6.78939e14i	0.758208	−	0.437752i
$579$	−1.93582e13	−	3.91241e13i	−0.0123632	−	0.0249869i
$580$			2.13446e14i			0.135031i
$581$	−9.07212e14	−	2.35962e14i	−0.568512	−	0.147867i
$582$	2.87349e14	−	4.31281e14i	0.178375	−	0.267722i
$583$	2.37245e14	−	4.10920e14i	0.145888	−	0.252685i
$584$	3.56667e14	+	6.17765e14i	0.217266	+	0.376316i
$585$	−4.69963e14	−	3.58646e14i	−0.283600	−	0.216426i
$586$	−1.68243e15	−	9.71353e14i	−1.00577	−	0.580684i
$587$	−3.05613e15			−1.80993			−0.904967	−	0.425482i	$-0.860105\pi$
$587$	−3.05613e15			−1.80993			−0.904967	+	0.425482i	$0.860105\pi$
$588$	4.21198e13	−	8.51166e14i	0.0247122	−	0.499389i
$589$	−3.84464e15			−2.23471
$590$	−4.00541e14	−	2.31253e14i	−0.230654	−	0.133168i
$591$	2.42231e13	−	3.77210e14i	0.0138197	−	0.215205i
$592$	9.91882e13	+	1.71799e14i	0.0560648	+	0.0971072i
$593$	−2.76263e14	+	4.78502e14i	−0.154712	+	0.267968i	−0.932954	−	0.359996i	$-0.882778\pi$
$593$	−2.76263e14	+	4.78502e14i	−0.154712	+	0.267968i	0.778242	+	0.627964i	$0.216111\pi$
$594$	−5.50528e14	−	1.07240e14i	−0.305460	−	0.0595020i
$595$	7.21009e14	+	1.87531e14i	0.396367	+	0.103093i
$596$		−	5.33629e14i		−	0.290660i
$597$	1.74189e15	−	8.61867e14i	0.940073	−	0.465138i
$598$	4.15575e14	−	2.39932e14i	0.222225	−	0.128302i
$599$	−1.09045e14	+	6.29572e13i	−0.0577775	+	0.0333578i	−0.528610	−	0.848865i	$-0.677287\pi$
$599$	−1.09045e14	+	6.29572e13i	−0.0577775	+	0.0333578i	0.470833	+	0.882222i	$0.343953\pi$
$600$	−5.58345e14	+	2.76263e14i	−0.293137	+	0.145041i
$601$			1.01549e15i			0.528280i	0.964484	+	0.264140i	$0.0850881\pi$
$601$			1.01549e15i			0.528280i	−0.964484	+	0.264140i	$0.914912\pi$
$602$	−3.68652e14	−	3.63278e14i	−0.190036	−	0.187266i
$603$	−5.71349e14	−	1.36911e15i	−0.291848	−	0.699350i
$604$	7.14501e14	−	1.23755e15i	0.361659	−	0.626412i
$605$	2.20035e14	+	3.81113e14i	0.110367	+	0.191161i
$606$	−1.23492e14	+	1.92305e15i	−0.0613816	+	0.955853i
$607$	3.03618e15	+	1.75294e15i	1.49551	+	0.863434i	0.999987	−	0.00516001i	$-0.00164249\pi$
$607$	3.03618e15	+	1.75294e15i	1.49551	+	0.863434i	0.495525	+	0.868594i	$0.334976\pi$
$608$	−6.65408e14			−0.324802
$609$	−6.38774e14	+	1.93673e15i	−0.308996	+	0.936859i
$610$	3.31153e14			0.158751
$611$	4.35887e15	+	2.51660e15i	2.07085	+	1.19560i
$612$	9.63817e14	−	1.26297e15i	0.453797	−	0.594647i
$613$	1.19695e15	+	2.07318e15i	0.558527	+	0.967397i	0.997620	+	0.0689554i	$0.0219666\pi$
$613$	1.19695e15	+	2.07318e15i	0.558527	+	0.967397i	−0.439093	+	0.898442i	$0.644700\pi$
$614$	−1.04357e15	+	1.80752e15i	−0.482609	+	0.835903i
$615$	−4.61014e14	+	6.91934e14i	−0.211301	+	0.317140i
$616$	−9.10814e13	−	3.30204e14i	−0.0413748	−	0.149999i
$617$			2.98104e15i			1.34215i	0.741392	+	0.671073i	$0.234166\pi$
$617$			2.98104e15i			1.34215i	−0.741392	+	0.671073i	$0.765834\pi$
$618$	−5.09339e14	−	1.02941e15i	−0.227285	−	0.459356i
$619$	2.79426e15	−	1.61327e15i	1.23586	−	0.713523i	0.267614	−	0.963526i	$-0.413765\pi$
$619$	2.79426e15	−	1.61327e15i	1.23586	−	0.713523i	0.968245	+	0.250003i	$0.0804315\pi$
$620$	3.28890e14	−	1.89885e14i	0.144177	−	0.0832406i
$621$	4.83521e14	+	4.20657e14i	0.210093	+	0.182778i
$622$			2.65960e13i			0.0114543i
$623$	−2.41776e15	+	2.45352e15i	−1.03212	+	1.04738i
$624$	−6.40736e14	−	4.26902e14i	−0.271121	−	0.180640i
$625$	−9.30769e14	+	1.61214e15i	−0.390393	+	0.676180i
$626$	−3.08601e13	−	5.34513e13i	−0.0128304	−	0.0222228i
$627$	−1.95807e15	−	1.25740e14i	−0.806968	−	0.0518207i
$628$	−2.97348e14	−	1.71674e14i	−0.121475	−	0.0701336i
$629$	−1.65693e15			−0.671004
$630$	4.77420e14	−	6.77097e13i	0.191658	−	0.0271818i
$631$	−5.90004e14			−0.234797			−0.117399	−	0.993085i	$-0.537456\pi$
$631$	−5.90004e14			−0.234797			−0.117399	+	0.993085i	$0.537456\pi$
$632$	4.63896e14	+	2.67830e14i	0.183011	+	0.105661i
$633$	−2.35514e15	−	1.51239e14i	−0.921079	−	0.0591486i
$634$	1.64698e15	+	2.85265e15i	0.638552	+	1.10600i
$635$	5.24031e14	−	9.07649e14i	0.201420	−	0.348869i
$636$	7.23947e14	+	4.82343e14i	0.275862	+	0.183799i
$637$	1.68072e15	−	3.01239e15i	0.634933	−	1.13801i
$638$			8.19695e14i			0.307000i
$639$	2.75819e13	−	2.13872e14i	0.0102417	−	0.0794143i
$640$	5.69224e13	−	3.28641e13i	0.0209553	−	0.0120985i
$641$	8.49661e14	−	4.90552e14i	0.310118	−	0.179047i	−0.336861	−	0.941554i	$-0.609365\pi$
$641$	8.49661e14	−	4.90552e14i	0.310118	−	0.179047i	0.646979	+	0.762508i	$0.276032\pi$
$642$	4.14480e14	+	8.37691e14i	0.149990	+	0.303139i
$643$			2.21646e15i			0.795241i	0.917550	+	0.397621i	$0.130164\pi$
$643$			2.21646e15i			0.795241i	−0.917550	+	0.397621i	$0.869836\pi$
$644$	−9.85242e13	+	3.78800e14i	−0.0350486	+	0.134753i
$645$	1.62377e14	−	2.43711e14i	0.0572725	−	0.0859601i
$646$	2.77889e15	−	4.81318e15i	0.971836	−	1.68327i
$647$	7.28108e14	+	1.26112e15i	0.252477	+	0.437304i	0.964207	−	0.265150i	$-0.0854213\pi$
$647$	7.28108e14	+	1.26112e15i	0.252477	+	0.437304i	−0.711730	+	0.702453i	$0.752088\pi$
$648$	2.60889e14	−	9.94649e14i	0.0897001	−	0.341985i
$649$	−1.53819e15	−	8.88076e14i	−0.524403	−	0.302764i
$650$	−2.52157e15			−0.852408
$651$	3.55248e15	−	7.38683e14i	1.19079	−	0.247607i
$652$	6.96616e14			0.231543
$653$	2.57945e15	+	1.48924e15i	0.850167	+	0.490844i	0.860707	−	0.509100i	$-0.170022\pi$
$653$	2.57945e15	+	1.48924e15i	0.850167	+	0.490844i	−0.0105403	+	0.999944i	$0.503355\pi$
$654$	2.40627e13	−	3.74712e14i	0.00786443	−	0.122467i
$655$	7.03732e14	+	1.21890e15i	0.228076	+	0.395040i
$656$	−5.41422e14	+	9.37771e14i	−0.174006	+	0.301388i
$657$	−3.55889e15	+	1.48517e15i	−1.13424	+	0.473334i
$658$	−3.95755e15	+	1.09163e15i	−1.25079	+	0.345011i
$659$		−	4.71007e14i		−	0.147624i	−0.997272	−	0.0738121i	$-0.976483\pi$
$659$		−	4.71007e14i		−	0.147624i	0.997272	−	0.0738121i	$-0.0235165\pi$
$660$	1.73713e14	−	8.59514e13i	0.0539934	−	0.0267154i
$661$	−4.08343e15	+	2.35757e15i	−1.25868	+	0.726702i	−0.972819	−	0.231568i	$-0.925614\pi$
$661$	−4.08343e15	+	2.35757e15i	−1.25868	+	0.726702i	−0.285866	+	0.958270i	$0.592281\pi$
$662$	3.68909e15	−	2.12990e15i	1.12772	−	0.651088i
$663$	5.76382e15	−	2.85188e15i	1.74738	−	0.864582i
$664$		−	6.90770e14i		−	0.207687i
$665$	1.62614e15	−	4.48544e14i	0.484884	−	0.133747i
$666$	−9.89719e14	+	4.13023e14i	−0.292687	+	0.122142i
$667$	4.68319e14	−	8.11152e14i	0.137357	−	0.237909i
$668$	8.01290e14	+	1.38787e15i	0.233087	+	0.403719i
$669$	3.88427e13	−	6.04871e14i	0.0112064	−	0.174509i
$670$	4.43967e14	+	2.56325e14i	0.127040	+	0.0733464i
$671$	1.27172e15			0.360927
$672$	6.14844e14	−	1.27847e14i	0.173075	−	0.0359882i
$673$	−2.57699e15			−0.719498			−0.359749	−	0.933049i	$-0.617138\pi$
$673$	−2.57699e15			−0.719498			−0.359749	+	0.933049i	$0.617138\pi$
$674$	−3.36127e15	−	1.94063e15i	−0.930839	−	0.537420i
$675$	−1.09516e15	−	3.18470e15i	−0.300820	−	0.874778i
$676$	−6.40659e14	−	1.10965e15i	−0.174550	−	0.302329i
$677$	−3.02556e15	+	5.24042e15i	−0.817651	+	1.41621i	0.0897575	+	0.995964i	$0.471391\pi$
$677$	−3.02556e15	+	5.24042e15i	−0.817651	+	1.41621i	−0.907409	+	0.420250i	$0.861943\pi$
$678$	−1.66146e15	+	2.49368e15i	−0.445376	+	0.668463i
$679$	−4.30696e14	+	1.65592e15i	−0.114522	+	0.440306i
$680$			5.48992e14i			0.144799i
$681$	4.49305e14	+	9.08073e14i	0.117552	+	0.237581i
$682$	1.26303e15	−	7.29211e14i	0.327793	−	0.189251i
$683$	3.09537e15	−	1.78711e15i	0.796891	−	0.460085i	−0.0454918	−	0.998965i	$-0.514485\pi$
$683$	3.09537e15	−	1.78711e15i	0.796891	−	0.460085i	0.842383	+	0.538879i	$0.181152\pi$
$684$	4.60110e14	−	3.56772e15i	0.117504	−	0.911133i
$685$		−	2.79187e14i		−	0.0707288i
$686$	7.87902e14	+	2.70106e15i	0.198011	+	0.678816i
$687$	−4.58541e15	−	3.05512e15i	−1.14318	−	0.761669i
$688$	1.90698e14	−	3.30299e14i	0.0471639	−	0.0816903i
$689$	1.76061e15	+	3.04947e15i	0.431974	+	0.748201i
$690$	−2.21010e14	−	1.41925e13i	−0.0537949	−	0.00345452i
$691$	3.93558e15	+	2.27221e15i	0.950341	+	0.548680i	0.893187	−	0.449686i	$-0.148464\pi$
$691$	3.93558e15	+	2.27221e15i	0.950341	+	0.548680i	0.0571543	+	0.998365i	$0.481797\pi$
$692$	1.64423e15			0.393893
$693$	1.83343e15	−	2.60025e14i	0.435744	−	0.0617990i
$694$	1.81250e15			0.427366
$695$	4.80947e14	+	2.77675e14i	0.112507	+	0.0649562i
$696$	−1.49972e15	−	9.63067e13i	−0.348064	−	0.0223514i
$697$	−4.52220e15	−	7.83268e15i	−1.04128	−	1.80356i
$698$	−1.40819e15	+	2.43906e15i	−0.321705	+	0.557209i
$699$	1.77228e15	+	1.18081e15i	0.401705	+	0.267644i
$700$	1.44361e15	−	1.46497e15i	0.324647	−	0.329449i
$701$		−	5.31518e15i		−	1.18596i	−0.805219	−	0.592978i	$-0.797952\pi$
$701$		−	5.31518e15i		−	1.18596i	0.805219	−	0.592978i	$-0.202048\pi$
$702$	2.73197e15	−	3.14024e15i	0.604814	−	0.695198i
$703$	−3.24907e15	+	1.87585e15i	−0.713682	+	0.412045i
$704$	2.18598e14	−	1.26208e14i	0.0476428	−	0.0275066i
$705$	−1.03014e15	−	2.08198e15i	−0.222770	−	0.450233i
$706$		−	2.58694e15i		−	0.555087i
$707$	−1.69173e15	−	6.13315e15i	−0.360184	−	1.30580i
$708$	1.80555e15	−	2.70994e15i	0.381441	−	0.572503i
$709$	−4.43228e15	+	7.67693e15i	−0.929122	+	1.60929i	−0.144328	+	0.989530i	$0.546102\pi$
$709$	−4.43228e15	+	7.67693e15i	−0.929122	+	1.60929i	−0.784794	+	0.619757i	$0.787231\pi$
$710$	3.72584e13	+	6.45334e13i	0.00775002	+	0.0134234i
$711$	−1.75679e15	+	2.30207e15i	−0.362609	+	0.475156i
$712$	−2.19827e15	−	1.26917e15i	−0.450237	−	0.259945i
$713$	−1.66649e15			−0.338696
$714$	−1.64295e15	+	4.98134e15i	−0.331348	+	1.00463i
$715$	7.84515e14			0.157007
$716$	−3.43573e15	−	1.98362e15i	−0.682334	−	0.393946i
$717$	4.06605e13	−	6.33178e14i	0.00801341	−	0.124787i
$718$	−4.27249e14	−	7.40016e14i	−0.0835596	−	0.144729i
$719$	1.26658e15	−	2.19379e15i	0.245825	−	0.425781i	−0.716539	−	0.697547i	$-0.754275\pi$
$719$	1.26658e15	−	2.19379e15i	0.245825	−	0.425781i	0.962363	+	0.271767i	$0.0876080\pi$
$720$	1.36847e14	+	3.27925e14i	0.0263577	+	0.0631605i
$721$	2.70092e15	+	2.66155e15i	0.516259	+	0.508734i
$722$		−	8.85654e15i		−	1.68000i
$723$	−3.37455e15	+	1.66969e15i	−0.635266	+	0.314323i
$724$	1.38283e14	−	7.98379e13i	0.0258350	−	0.0149158i
$725$	−4.26241e15	+	2.46090e15i	−0.790307	+	0.456284i
$726$	−2.77706e15	+	1.37406e15i	−0.511014	+	0.252844i
$727$		−	1.57679e15i		−	0.287961i	−0.989581	−	0.143981i	$-0.954010\pi$
$727$		−	1.57679e15i		−	0.287961i	0.989581	−	0.143981i	$-0.0459903\pi$
$728$	2.46013e15	+	6.39868e14i	0.445898	+	0.115976i
$729$	5.15261e15	+	2.08658e15i	0.926884	+	0.375347i
$730$	6.66293e14	−	1.15405e15i	0.118957	−	0.206039i
$731$	1.59280e15	+	2.75880e15i	0.282237	+	0.488850i
$732$	−1.49416e14	+	2.32675e15i	−0.0262776	+	0.409203i
$733$	−3.58336e15	−	2.06885e15i	−0.625487	−	0.361125i	0.153515	−	0.988146i	$-0.450941\pi$
$733$	−3.58336e15	−	2.06885e15i	−0.625487	−	0.361125i	−0.779002	+	0.627021i	$0.784274\pi$
$734$	2.14081e15			0.370893
$735$	−1.41638e15	+	7.26893e14i	−0.243557	+	0.124994i
$736$	−2.88427e14			−0.0492275
$737$	1.70496e15	+	9.84360e14i	0.288831	+	0.166756i
$738$	−4.65366e15	−	3.55138e15i	−0.782501	−	0.597155i
$739$	−1.32831e15	−	2.30070e15i	−0.221694	−	0.383985i	0.733628	−	0.679551i	$-0.237825\pi$
$739$	−1.32831e15	−	2.30070e15i	−0.221694	−	0.383985i	−0.955322	+	0.295565i	$0.904492\pi$
$740$	1.85294e14	−	3.20939e14i	0.0306964	−	0.0531678i
$741$	8.07360e15	−	1.21176e16i	1.32760	−	1.99259i
$742$	−2.77962e15	−	7.22966e14i	−0.453695	−	0.118004i
$743$			5.22199e15i			0.846052i	0.906117	+	0.423026i	$0.139032\pi$
$743$			5.22199e15i			0.846052i	−0.906117	+	0.423026i	$0.860968\pi$
$744$	1.18577e15	+	2.39652e15i	0.190700	+	0.385416i
$745$	−8.63321e14	+	4.98439e14i	−0.137820	+	0.0795705i
$746$	−2.20731e15	+	1.27439e15i	−0.349784	+	0.201948i
$747$	3.70370e15	+	4.77647e14i	0.582603	+	0.0751353i
$748$			2.10829e15i			0.329208i
$749$	−2.19791e15	−	2.16587e15i	−0.340690	−	0.335723i
$750$	2.01540e15	+	1.34280e15i	0.310117	+	0.206621i
$751$	4.50346e15	−	7.80023e15i	0.687903	−	1.19148i	−0.284612	−	0.958643i	$-0.591865\pi$
$751$	4.50346e15	−	7.80023e15i	0.687903	−	1.19148i	0.972515	−	0.232840i	$-0.0748018\pi$
$752$	−1.51262e15	−	2.61994e15i	−0.229368	−	0.397277i
$753$	−8.25429e15	−	5.30062e14i	−1.24253	−	0.0797911i
$754$	−5.26805e15	−	3.04151e15i	−0.787240	−	0.454513i
$755$	−2.66953e15			−0.396029
$756$	2.60331e14	+	3.38500e15i	0.0383403	+	0.498528i
$757$	−6.52583e15			−0.954132			−0.477066	−	0.878867i	$-0.658300\pi$
$757$	−6.52583e15			−0.954132			−0.477066	+	0.878867i	$0.658300\pi$
$758$	3.44889e15	+	1.99122e15i	0.500609	+	0.289027i
$759$	−8.48740e14	−	5.45032e13i	−0.122305	−	0.00785402i
$760$	6.21528e14	+	1.07652e15i	0.0889172	+	0.154009i
$761$	1.28586e15	−	2.22718e15i	0.182633	−	0.316329i	−0.760144	−	0.649755i	$-0.774871\pi$
$761$	1.28586e15	−	2.22718e15i	0.182633	−	0.316329i	0.942776	+	0.333426i	$0.108205\pi$
$762$	6.14089e15	+	4.09148e15i	0.865922	+	0.576937i
$763$	3.29639e14	+	1.19506e15i	0.0461481	+	0.167304i
$764$			9.39698e14i			0.130610i
$765$	−2.94353e15	−	3.79612e14i	−0.406191	−	0.0523844i
$766$	3.78171e15	−	2.18337e15i	0.518119	−	0.299136i
$767$	1.14150e16	−	6.59048e15i	1.55276	−	0.896484i
$768$	2.05227e14	+	4.14776e14i	0.0277171	+	0.0560180i
$769$			9.38596e15i			1.25859i	0.777167	+	0.629295i	$0.216656\pi$
$769$			9.38596e15i			1.25859i	−0.777167	+	0.629295i	$0.783344\pi$
$770$	−4.49139e14	+	4.55783e14i	−0.0597973	+	0.0606819i
$771$	−9.27520e14	+	1.39211e15i	−0.122610	+	0.184024i
$772$	−5.31007e13	+	9.19731e13i	−0.00696955	+	0.0120716i
$773$	7.49802e15	+	1.29870e16i	0.977146	+	1.69247i	0.672663	+	0.739949i	$0.265151\pi$
$773$	7.49802e15	+	1.29870e16i	0.977146	+	1.69247i	0.304484	+	0.952518i	$0.401516\pi$
$774$	1.63910e15	+	1.25086e15i	0.212095	+	0.161857i
$775$	7.58379e15	+	4.37850e15i	0.974376	+	0.562556i
$776$	−1.26085e15			−0.160851
$777$	2.64176e15	−	2.35756e15i	0.334640	−	0.298639i
$778$	3.96074e15			0.498182
$779$	−1.77352e16	−	1.02394e16i	−2.21503	−	1.27885i
$780$	−9.21734e13	+	1.43535e15i	−0.0114310	+	0.178007i
$781$	1.43083e14	+	2.47827e14i	0.0176200	+	0.0305188i
$782$	1.20453e15	−	2.08631e15i	0.147293	−	0.255119i
$783$	1.55338e15	−	7.97443e15i	0.188620	−	0.968300i
$784$	−1.78018e15	+	1.06294e15i	−0.214648	+	0.128166i
$785$			6.41412e14i			0.0767987i
$786$	−8.88176e15	+	4.39460e15i	−1.05603	+	0.522511i
$787$	−1.16878e15	+	6.74797e14i	−0.137998	+	0.0796732i	−0.567410	−	0.823436i	$-0.692054\pi$
$787$	−1.16878e15	+	6.74797e14i	−0.137998	+	0.0796732i	0.429412	+	0.903109i	$0.358721\pi$
$788$	−7.96416e14	+	4.59811e14i	−0.0933783	+	0.0539120i
$789$	−6.83129e15	+	3.38005e15i	−0.795389	+	0.393550i
$790$		−	1.00067e15i		−	0.115703i
$791$	2.49030e15	−	9.57458e15i	0.285944	−	1.09938i
$792$	5.25533e14	+	1.25933e15i	0.0599255	+	0.143598i
$793$	−4.71878e15	+	8.17317e15i	−0.534352	+	0.925524i
$794$	2.05391e15	+	3.55747e15i	0.230976	+	0.400063i
$795$	1.04144e14	−	1.62176e15i	0.0116309	−	0.181120i
$796$	−4.09484e15	−	2.36416e15i	−0.454166	−	0.262213i
$797$	−1.13512e16			−1.25032			−0.625160	−	0.780497i	$-0.714966\pi$
$797$	−1.13512e16			−1.25032			−0.625160	+	0.780497i	$0.714966\pi$
$798$	2.41785e15	+	1.16279e16i	0.264492	+	1.27200i
$799$	2.52682e16			2.74516
$800$	1.31256e15	+	7.57806e14i	0.141620	+	0.0817642i
$801$	8.32495e15	−	1.09089e16i	0.892078	−	1.16896i
$802$	2.31419e13	+	4.00830e13i	0.00246286	+	0.00426580i
$803$	2.55876e15	−	4.43190e15i	0.270454	−	0.468440i
$804$	−2.00131e15	+	3.00375e15i	−0.210090	+	0.315323i
$805$	7.04862e14	−	1.94425e14i	0.0734897	−	0.0202710i
$806$			1.08231e16i			1.12075i
$807$	7.58381e15	+	1.53274e16i	0.779980	+	1.57639i
$808$	4.06021e15	−	2.34416e15i	0.414749	−	0.239456i
$809$	−1.01193e16	+	5.84236e15i	−1.02667	+	0.592750i	−0.916030	−	0.401110i	$-0.868625\pi$
$809$	−1.01193e16	+	5.84236e15i	−1.02667	+	0.592750i	−0.110644	+	0.993860i	$0.535291\pi$
$810$	−1.85286e15	+	5.06983e14i	−0.186713	+	0.0510888i
$811$		−	9.11784e15i		−	0.912593i	−0.889828	−	0.456297i	$-0.849176\pi$
$811$		−	9.11784e15i		−	0.912593i	0.889828	−	0.456297i	$-0.150824\pi$
$812$	4.78302e15	−	1.31932e15i	0.475493	−	0.131157i
$813$	8.65154e15	+	5.76425e15i	0.854270	+	0.569174i
$814$	7.11584e14	−	1.23250e15i	0.0697898	−	0.120879i
$815$	−6.50678e14	−	1.12701e15i	−0.0633869	−	0.109789i
$816$	−3.85733e15	−	2.47704e14i	−0.373242	−	0.0239683i
$817$	6.24663e15	+	3.60649e15i	0.600377	+	0.346628i
$818$	3.27644e15			0.312795
$819$	−5.13188e15	+	1.27480e16i	−0.486648	+	1.20887i
$820$	2.02287e15			0.190543
$821$	3.76813e15	+	2.17553e15i	0.352564	+	0.203553i	0.665814	−	0.746118i	$-0.268084\pi$
$821$	3.76813e15	+	2.17553e15i	0.352564	+	0.203553i	−0.313250	+	0.949671i	$0.601418\pi$
$822$	1.96162e15	+	1.25969e14i	0.182314	+	0.0117076i
$823$	6.18644e15	+	1.07152e16i	0.571139	+	0.989241i	0.996449	+	0.0841936i	$0.0268314\pi$
$823$	6.18644e15	+	1.07152e16i	0.571139	+	0.989241i	−0.425311	+	0.905047i	$0.639835\pi$
$824$	−1.39715e15	+	2.41993e15i	−0.128128	+	0.221923i
$825$	3.71921e15	+	2.47799e15i	0.338808	+	0.225737i
$826$	−2.70627e15	+	1.04049e16i	−0.244896	+	0.941562i
$827$			1.36985e16i			1.23138i	0.787989	+	0.615689i	$0.211122\pi$
$827$			1.36985e16i			1.23138i	−0.787989	+	0.615689i	$0.788878\pi$
$828$	1.99439e14	−	1.54646e15i	0.0178091	−	0.138093i
$829$	−2.45992e15	+	1.42023e15i	−0.218208	+	0.125982i	−0.605120	−	0.796134i	$-0.706875\pi$
$829$	−2.45992e15	+	1.42023e15i	−0.218208	+	0.125982i	0.386912	+	0.922117i	$0.373542\pi$
$830$	−1.11755e15	+	6.45218e14i	−0.0984776	+	0.0568560i
$831$	−4.47539e15	−	9.04504e15i	−0.391764	−	0.791781i
$832$			1.87319e15i			0.162894i
$833$	−2.54286e14	−	1.73159e16i	−0.0219672	−	1.49588i
$834$	−2.16800e15	+	3.25395e15i	−0.186057	+	0.279253i
$835$	1.49690e15	−	2.59270e15i	0.127619	−	0.221043i
$836$	2.38685e15	+	4.13414e15i	0.202157	+	0.350147i
$837$	−1.36693e16	+	4.70063e15i	−1.15016	+	0.395518i
$838$	6.51725e15	+	3.76274e15i	0.544781	+	0.314530i
$839$	4.42511e15			0.367480			0.183740	−	0.982975i	$-0.441180\pi$
$839$	4.42511e15			0.367480			0.183740	+	0.982975i	$0.441180\pi$
$840$	−7.81133e14	−	8.75297e14i	−0.0644449	−	0.0722136i
$841$	3.27180e14			0.0268169
$842$	−4.75144e15	−	2.74325e15i	−0.386909	−	0.223382i
$843$	−4.76116e14	+	7.41423e15i	−0.0385178	+	0.599811i
$844$	2.87087e15	+	4.97250e15i	0.230744	+	0.399661i
$845$	−1.19682e15	+	2.07295e15i	−0.0955690	+	0.165530i
$846$	1.50933e16	−	6.29861e15i	1.19742	−	0.499698i
$847$	7.18013e15	−	7.28635e15i	0.565944	−	0.574316i
$848$		−	2.11646e15i		−	0.165742i
$849$	9.82331e15	−	4.86047e15i	0.764303	−	0.378169i
$850$	−1.09631e16	+	6.32953e15i	−0.847478	+	0.489292i
$851$	−1.40834e15	+	8.13103e14i	−0.108167	+	0.0624501i
$852$	−4.70236e14	+	2.32667e14i	−0.0358837	+	0.0177549i
$853$		−	2.16300e16i		−	1.63997i	−0.572383	−	0.819986i	$-0.693981\pi$
$853$		−	2.16300e16i		−	1.63997i	0.572383	−	0.819986i	$-0.306019\pi$
$854$	−2.04687e15	−	7.42067e15i	−0.154196	−	0.559017i
$855$	−6.20173e15	+	2.58806e15i	−0.464194	+	0.193714i
$856$	1.13695e15	−	1.96925e15i	0.0845539	−	0.146452i
$857$	−7.95010e15	−	1.37700e16i	−0.587460	−	1.01751i	−0.994564	−	0.104128i	$-0.966795\pi$
$857$	−7.95010e15	−	1.37700e16i	−0.587460	−	1.01751i	0.407104	−	0.913382i	$-0.366539\pi$
$858$	−3.53972e14	+	5.51216e15i	−0.0259890	+	0.404708i
$859$	−2.91728e14	−	1.68429e14i	−0.0212822	−	0.0122873i	0.489321	−	0.872104i	$-0.337245\pi$
$859$	−2.91728e14	−	1.68429e14i	−0.0212822	−	0.0122873i	−0.510603	+	0.859816i	$0.670578\pi$
$860$	−7.12490e14			−0.0516461
$861$	1.83548e16	+	6.05379e15i	1.32200	+	0.436023i
$862$	−4.87265e15			−0.348719
$863$	−2.12165e16	−	1.22493e16i	−1.50874	−	0.871070i	−0.999948	−	0.0101781i	$-0.996760\pi$
$863$	−2.12165e16	−	1.22493e16i	−1.50874	−	0.871070i	−0.508789	−	0.860891i	$-0.669907\pi$
$864$	−2.36581e15	+	8.13558e14i	−0.167169	+	0.0574861i
$865$	−1.53580e15	−	2.66008e15i	−0.107832	−	0.186770i
$866$	9.59140e14	−	1.66128e15i	0.0669165	−	0.115903i
$867$	9.90277e15	−	1.48630e16i	0.686518	−	1.03039i
$868$	−6.28792e15	−	6.19625e15i	−0.433160	−	0.426846i
$869$		−	3.84287e15i		−	0.263055i
$870$	1.24501e15	+	2.51624e15i	0.0846871	+	0.171158i
$871$	−1.26526e16	+	7.30501e15i	−0.855227	+	0.493766i
$872$	−7.91143e14	+	4.56767e14i	−0.0531391	+	0.0306799i
$873$	8.71841e14	−	6.76030e15i	0.0581914	−	0.451219i
$874$		−	5.45474e15i		−	0.361794i
$875$	−7.73821e15	−	2.01267e15i	−0.510031	−	0.132657i
$876$	7.80799e15	+	5.20222e15i	0.511407	+	0.340734i
$877$	−3.35087e15	+	5.80388e15i	−0.218102	+	0.377764i	−0.954228	−	0.299081i	$-0.903320\pi$
$877$	−3.35087e15	+	5.80388e15i	−0.218102	+	0.377764i	0.736126	+	0.676845i	$0.236653\pi$
$878$	−8.82821e15	−	1.52909e16i	−0.571022	−	0.989040i
$879$	−2.54994e16	−	1.63748e15i	−1.63905	−	0.105254i
$880$	−4.08365e14	−	2.35770e14i	−0.0260852	−	0.0150603i
$881$	−1.52164e15			−0.0965928			−0.0482964	−	0.998833i	$-0.515379\pi$
$881$	−1.52164e15			−0.0965928			−0.0482964	+	0.998833i	$0.515379\pi$
$882$	−4.46823e15	−	1.02798e16i	−0.281876	−	0.648495i
$883$	−1.98308e16			−1.24325			−0.621623	−	0.783316i	$-0.713527\pi$
$883$	−1.98308e16			−1.24325			−0.621623	+	0.783316i	$0.713527\pi$
$884$	−1.35496e16	−	7.82287e15i	−0.844189	−	0.487393i
$885$	−6.07072e15	−	3.89840e14i	−0.375882	−	0.0241379i
$886$	−3.76053e15	−	6.51343e15i	−0.231400	−	0.400797i
$887$	−4.06770e15	+	7.04546e15i	−0.248753	+	0.430853i	−0.963180	−	0.268857i	$-0.913354\pi$
$887$	−4.06770e15	+	7.04546e15i	−0.248753	+	0.430853i	0.714427	+	0.699710i	$0.246687\pi$
$888$	2.17138e15	+	1.44672e15i	0.131967	+	0.0879254i
$889$	−2.35782e16	−	6.13257e15i	−1.42413	−	0.370410i
$890$			4.74191e15i			0.284648i
$891$	−7.11551e15	+	1.94696e15i	−0.424501	+	0.116153i
$892$	−1.27709e15	+	7.37326e14i	−0.0757205	+	0.0437172i
$893$	4.95484e16	−	2.86068e16i	2.91976	−	1.68572i
$894$	−3.11260e15	−	6.29077e15i	−0.182292	−	0.368423i
$895$			7.41123e15i			0.431384i
$896$	−1.08828e15	−	1.07241e15i	−0.0629572	−	0.0620394i
$897$	3.49957e15	−	5.25248e15i	0.201213	−	0.301999i
$898$	1.09077e16	−	1.88928e16i	0.623325	−	1.07963i
$899$	1.05627e16	+	1.82951e16i	0.599923	+	1.03910i
$900$	−4.97072e15	+	6.51354e15i	−0.280599	+	0.367691i
$901$	1.53093e16	+	8.83881e15i	0.858951	+	0.495915i
$902$	7.76841e15			0.433208
$903$	−6.46487e15	−	2.13225e15i	−0.358325	−	0.118183i
$904$	7.29029e15			0.401623
$905$	−2.58329e14	−	1.49146e14i	−0.0141451	−	0.00816666i
$906$	1.20449e15	−	1.87567e16i	0.0655538	−	1.02082i
$907$	5.20555e14	+	9.01628e14i	0.0281596	+	0.0487739i	0.879762	−	0.475415i	$-0.157702\pi$
$907$	5.20555e14	+	9.01628e14i	0.0281596	+	0.0487739i	−0.851602	+	0.524189i	$0.824369\pi$
$908$	1.23247e15	−	2.13470e15i	0.0662680	−	0.114780i
$909$	9.76116e15	+	2.33905e16i	0.521675	+	1.25008i
$910$	−1.26270e15	−	4.57774e15i	−0.0670767	−	0.243178i
$911$			2.47224e16i			1.30539i	0.757622	+	0.652694i	$0.226361\pi$
$911$			2.47224e16i			1.30539i	−0.757622	+	0.652694i	$0.773639\pi$
$912$	−7.84427e15	+	3.88126e15i	−0.411700	+	0.203705i
$913$	−4.29171e15	+	2.47782e15i	−0.223893	+	0.129265i
$914$	1.33571e16	−	7.71171e15i	0.692640	−	0.399896i
$915$	3.90385e15	−	1.93159e15i	0.201223	−	0.0995630i
$916$			1.34055e16i			0.686843i
$917$	2.29640e16	−	2.33037e16i	1.16954	−	1.18684i
$918$	3.99534e15	−	2.05105e16i	0.202264	−	1.03835i
$919$	−1.02833e16	+	1.78112e16i	−0.517483	+	0.896307i	0.482311	+	0.876000i	$0.339798\pi$
$919$	−1.02833e16	+	1.78112e16i	−0.517483	+	0.896307i	−0.999794	+	0.0203068i	$0.993536\pi$
$920$	2.69406e14	+	4.66626e14i	0.0134764	+	0.0233419i
$921$	−1.75923e15	+	2.73952e16i	−0.0874770	+	1.36222i
$922$	1.04777e16	+	6.04930e15i	0.517899	+	0.299009i
$923$	−2.12366e15			−0.104346
$924$	−2.99977e15	−	3.36139e15i	−0.146519	−	0.164181i
$925$	8.54532e15			0.414905
$926$	3.31727e15	+	1.91522e15i	0.160111	+	0.0924399i
$927$	−1.20088e16	−	9.16439e15i	−0.576186	−	0.439708i
$928$	1.82813e15	+	3.16641e15i	0.0871951	+	0.151026i
$929$	−1.13695e16	+	1.96925e16i	−0.539081	+	0.933715i	0.459873	+	0.887985i	$0.347895\pi$
$929$	−1.13695e16	+	1.96925e16i	−0.539081	+	0.933715i	−0.998954	+	0.0457307i	$0.985438\pi$
$930$	2.76959e15	−	4.15686e15i	0.130545	−	0.195934i
$931$	−2.01024e16	−	3.36669e16i	−0.941944	−	1.57754i
$932$		−	5.18126e15i		−	0.241350i
$933$	1.55132e14	+	3.13531e14i	0.00718377	+	0.0145188i
$934$	−3.45609e15	+	1.99538e15i	−0.159103	+	0.0918580i
$935$	3.41085e15	−	1.96926e15i	0.156099	−	0.0901235i
$936$	−1.00435e16	−	1.29526e15i	−0.456949	−	0.0589304i
$937$		−	5.76719e15i		−	0.260853i	−0.991458	−	0.130427i	$-0.958365\pi$
$937$		−	5.76719e15i		−	0.260853i	0.991458	−	0.130427i	$-0.0416347\pi$
$938$	2.99968e15	−	1.15330e16i	0.134884	−	0.518593i
$939$	−6.75575e14	−	4.50115e14i	−0.0302004	−	0.0201216i
$940$	−2.82575e15	+	4.89434e15i	−0.125583	+	0.217516i
$941$	−7.32079e15	−	1.26800e16i	−0.323456	−	0.560242i	0.657743	−	0.753243i	$-0.271511\pi$
$941$	−7.32079e15	−	1.26800e16i	−0.323456	−	0.560242i	−0.981199	+	0.193001i	$0.938178\pi$
$942$	−4.50669e15	−	2.89404e14i	−0.197960	−	0.0127123i
$943$	−7.68745e15	−	4.43835e15i	−0.335713	−	0.193824i
$944$	−7.92254e15			−0.343968
$945$	5.23320e15	−	3.58295e15i	0.225888	−	0.154656i
$946$	−2.73617e15			−0.117420
$947$	8.70090e15	+	5.02347e15i	0.371227	+	0.214328i	0.673994	−	0.738737i	$-0.264577\pi$
$947$	8.70090e15	+	5.02347e15i	0.371227	+	0.214328i	−0.302767	+	0.953064i	$0.597911\pi$
$948$	7.03094e15	+	4.51502e14i	0.298241	+	0.0191520i
$949$	1.89887e16	+	3.28894e16i	0.800814	+	1.38705i
$950$	−1.43317e16	+	2.48232e16i	−0.600920	+	1.04082i
$951$	3.60548e16	+	2.40222e16i	1.50304	+	1.00143i
$952$	1.23021e16	−	3.39334e15i	0.509890	−	0.140645i
$953$			1.99434e16i			0.821842i	0.911671	+	0.410921i	$0.134793\pi$
$953$			1.99434e16i			0.821842i	−0.911671	+	0.410921i	$0.865207\pi$
$954$	1.13478e16	+	1.46347e15i	0.464939	+	0.0599609i
$955$	1.52027e15	−	8.77730e14i	0.0619303	−	0.0357554i
$956$	−1.33685e15	+	7.71832e14i	−0.0541458	+	0.0312611i
$957$	4.78120e15	+	9.66310e15i	0.192540	+	0.389136i
$958$		−	2.51847e16i		−	1.00839i
$959$	−6.25617e15	+	1.72566e15i	−0.249061	+	0.0686995i
$960$	4.79345e14	−	7.19446e14i	0.0189739	−	0.0284778i
$961$	6.08912e15	−	1.05467e16i	0.239649	−	0.415085i
$962$	5.28072e15	+	9.14647e15i	0.206647	+	0.357924i
$963$	9.77233e15	+	7.45763e15i	0.380236	+	0.290172i
$964$	7.93291e15	+	4.58007e15i	0.306909	+	0.177194i
$965$	1.98396e14			0.00763189
$966$	1.04804e15	+	5.04023e15i	0.0400869	+	0.192786i
$967$	−6.30451e15			−0.239776			−0.119888	−	0.992787i	$-0.538254\pi$
$967$	−6.30451e15			−0.239776			−0.119888	+	0.992787i	$0.538254\pi$
$968$	6.52831e15	+	3.76912e15i	0.246880	+	0.142536i
$969$	4.68460e15	−	7.29500e16i	0.176154	−	2.74312i
$970$	1.17770e15	+	2.03984e15i	0.0440344	+	0.0762698i
$971$	3.78231e15	−	6.55115e15i	0.140621	−	0.243563i	−0.787109	−	0.616813i	$-0.788423\pi$
$971$	3.78231e15	−	6.55115e15i	0.140621	−	0.243563i	0.927731	+	0.373250i	$0.121757\pi$
$972$	−2.72616e15	−	1.32473e16i	−0.100783	−	0.489737i
$973$	3.24954e15	−	1.24936e16i	0.119454	−	0.459271i
$974$			2.18207e16i			0.797616i
$975$	−2.97259e16	+	1.47081e16i	−1.08046	+	0.534601i
$976$	4.91256e15	−	2.83627e15i	0.177555	−	0.102512i
$977$	−2.69044e16	+	1.55333e16i	−0.966948	+	0.558268i	−0.898304	−	0.439374i	$-0.855200\pi$
$977$	−2.69044e16	+	1.55333e16i	−0.966948	+	0.558268i	−0.0686434	+	0.997641i	$0.521867\pi$
$978$	8.21217e15	−	4.06329e15i	0.293491	−	0.145216i
$979$			1.82103e16i			0.647160i
$980$	3.38245e15	+	1.88719e15i	0.119533	+	0.0666916i
$981$	−1.90199e15	−	4.55771e15i	−0.0668389	−	0.160165i
$982$	−1.22660e16	+	2.12453e16i	−0.428637	+	0.742421i
$983$	1.70451e16	+	2.95230e16i	0.592319	+	1.02593i	0.993919	+	0.110111i	$0.0351207\pi$
$983$	1.70451e16	+	2.95230e16i	0.592319	+	1.02593i	−0.401600	+	0.915815i	$0.631546\pi$
$984$	−9.12718e14	+	1.42131e16i	−0.0315401	+	0.491152i
$985$	1.48779e15	+	8.58978e14i	0.0511262	+	0.0295177i
$986$	−3.05386e16			−1.04358
$987$	−4.02869e16	+	3.59528e16i	−1.36905	+	1.22177i
$988$	−3.54259e16			−1.19718
$989$	2.70765e15	+	1.56326e15i	0.0909941	+	0.0525355i
$990$	1.54650e15	−	2.02650e15i	0.0516840	−	0.0677257i
$991$	−8.71609e15	−	1.50967e16i	−0.289679	−	0.501738i	0.684054	−	0.729431i	$-0.260215\pi$
$991$	−8.71609e15	−	1.50967e16i	−0.289679	−	0.501738i	−0.973733	+	0.227693i	$0.926882\pi$
$992$	3.25265e15	−	5.63375e15i	0.107504	−	0.186202i
$993$	3.10659e16	−	4.66267e16i	1.02109	−	1.53255i
$994$	1.21580e15	−	1.23379e15i	0.0397409	−	0.0403288i
$995$			8.83300e15i			0.287132i
$996$	−4.02919e15	−	8.14325e15i	−0.130254	−	0.263252i
$997$	−1.71069e16	+	9.87666e15i	−0.549981	+	0.317532i	−0.749114	−	0.662441i	$-0.769521\pi$
$997$	−1.71069e16	+	9.87666e15i	−0.549981	+	0.317532i	0.199133	+	0.979972i	$0.436187\pi$
$998$	2.54091e16	−	1.46699e16i	0.812402	−	0.469040i
$999$	−9.25834e15	+	1.06419e16i	−0.294390	+	0.338384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.1	✓	60
3.2	odd	2	inner	42.12.f.a.5.21	yes	60
7.3	odd	6	inner	42.12.f.a.17.21	yes	60
21.17	even	6	inner	42.12.f.a.17.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.1	✓	60	1.1	even	1	trivial
42.12.f.a.5.21	yes	60	3.2	odd	2	inner
42.12.f.a.17.1	yes	60	21.17	even	6	inner
42.12.f.a.17.21	yes	60	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	42.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-27.7128 - 16.0000i) q^{2} +(-420.023 - 26.9724i) q^{3} +(512.000 + 886.810i) q^{4} +(956.472 - 1656.66i) q^{5} +(11208.5 + 7467.85i) q^{6} +(-43035.3 - 11193.3i) q^{7} -32768.0i q^{8} +(175692. + 22658.1i) q^{9} +(-53013.1 + 30607.1i) q^{10} +(-203585. + 117540. i) q^{11} +(-191132. - 386291. i) q^{12} -1.74455e6i q^{13} +(1.01354e6 + 998762. i) q^{14} +(-446425. + 670037. i) q^{15} +(-524288. + 908093. i) q^{16} +(-4.37909e6 - 7.58480e6i) q^{17} +(-4.50639e6 - 3.43899e6i) q^{18} +(-1.71739e7 - 9.91536e6i) q^{19} +1.95886e6 q^{20} +(1.77739e7 + 5.86221e6i) q^{21} +7.52257e6 q^{22} +(-7.44417e6 - 4.29789e6i) q^{23} +(-883833. + 1.37633e7i) q^{24} +(2.25844e7 + 3.91173e7i) q^{25} +(-2.79128e7 + 4.83463e7i) q^{26} +(-7.31836e7 - 1.42558e7i) q^{27} +(-1.21078e7 - 4.38951e7i) q^{28} +1.08965e8i q^{29} +(2.30923e7 - 1.14258e7i) q^{30} +(1.67899e8 - 9.69365e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(8.86809e7 - 4.38784e7i) q^{33} +2.80262e8i q^{34} +(-5.97055e7 + 6.05887e7i) q^{35} +(6.98609e7 + 1.67406e8i) q^{36} +(9.45932e7 - 1.63840e8i) q^{37} +(3.17291e8 + 5.49565e8i) q^{38} +(-4.70547e7 + 7.32750e8i) q^{39} +(-5.42854e7 - 3.13417e7i) q^{40} +1.03268e9 q^{41} +(-3.98770e8 - 4.46841e8i) q^{42} -3.63728e8 q^{43} +(-2.08471e8 - 1.20361e8i) q^{44} +(2.05581e8 - 2.69390e8i) q^{45} +(1.37533e8 + 2.38213e8i) q^{46} +(-1.44255e9 + 2.49857e9i) q^{47} +(2.44707e8 - 3.67279e8i) q^{48} +(1.72675e9 + 9.63412e8i) q^{49} -1.44540e9i q^{50} +(1.63474e9 + 3.30391e9i) q^{51} +(1.54708e9 - 8.93208e8i) q^{52} +(-1.74800e9 + 1.00921e9i) q^{53} +(1.80003e9 + 1.56600e9i) q^{54} +4.49695e8i q^{55} +(-3.66781e8 + 1.41018e9i) q^{56} +(6.94600e9 + 4.62790e9i) q^{57} +(1.74344e9 - 3.01972e9i) q^{58} +(3.77776e9 + 6.54327e9i) q^{59} +(-8.22765e8 - 5.28351e7i) q^{60} +(-4.68498e9 - 2.70487e9i) q^{61} -6.20393e9 q^{62} +(-7.30734e9 - 2.94167e9i) q^{63} -1.07374e9 q^{64} +(-2.89012e9 - 1.66861e9i) q^{65} +(-3.15965e9 - 2.02902e8i) q^{66} +(-4.18734e9 - 7.25268e9i) q^{67} +(4.48418e9 - 7.76684e9i) q^{68} +(3.01080e9 + 2.00600e9i) q^{69} +(2.62403e9 - 7.23796e8i) q^{70} -1.21731e9i q^{71} +(7.42461e8 - 5.75707e9i) q^{72} +(-1.88527e10 + 1.08846e10i) q^{73} +(-5.24289e9 + 3.02698e9i) q^{74} +(-8.43088e9 - 1.70393e10i) q^{75} -2.03067e10i q^{76} +(1.00770e10 - 2.77958e9i) q^{77} +(1.30280e10 - 1.95537e10i) q^{78} +(-8.17353e9 + 1.41570e10i) q^{79} +(1.00293e9 + 1.73713e9i) q^{80} +(3.03543e10 + 7.96169e9i) q^{81} +(-2.86185e10 - 1.65229e10i) q^{82} +2.10806e10 q^{83} +(3.90158e9 + 1.87635e10i) q^{84} -1.67539e10 q^{85} +(1.00799e10 + 5.81965e9i) q^{86} +(2.93905e9 - 4.57677e10i) q^{87} +(3.85155e9 + 6.67109e9i) q^{88} +(3.87321e10 - 6.70859e10i) q^{89} +(-1.00075e10 + 4.17625e9i) q^{90} +(-1.95272e10 + 7.50771e10i) q^{91} -8.80208e9i q^{92} +(-7.31360e10 + 3.61869e10i) q^{93} +(7.99542e10 - 4.61616e10i) q^{94} +(-3.28527e10 + 1.89675e10i) q^{95} +(-1.26580e10 + 6.26303e9i) q^{96} -3.84781e10i q^{97} +(-3.24384e10 - 5.43268e10i) q^{98} +(-3.84316e10 + 1.60380e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) \) 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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