LMFDB - Embedded newform 42.12.f.a.5.16

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			5.16
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.16

$q$-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} +(-411.940 - 86.3257i) q^{3} +(512.000 + 886.810i) q^{4} +(-6258.52 + 10840.1i) q^{5} +(-10034.8 - 8983.37i) q^{6} +(-41292.3 + 16500.6i) q^{7} +32768.0i q^{8} +(162243. + 71122.1i) q^{9} +(-346882. + 200273. i) q^{10} +(-435052. + 251177. i) q^{11} +(-134359. - 409512. i) q^{12} +563130. i q^{13} +(-1.40834e6 - 203398. i) q^{14} +(3.51391e6 - 3.92519e6i) q^{15} +(-524288. + 908093. i) q^{16} +(329541. + 570781. i) q^{17} +(3.35825e6 + 4.56688e6i) q^{18} +(6.21252e6 + 3.58680e6i) q^{19} -1.28174e7 q^{20} +(1.84344e7 - 3.23269e6i) q^{21} -1.60754e7 q^{22} +(8.20976e6 + 4.73991e6i) q^{23} +(2.82872e6 - 1.34985e7i) q^{24} +(-5.39240e7 - 9.33991e7i) q^{25} +(-9.01008e6 + 1.56059e7i) q^{26} +(-6.06947e7 - 4.33038e7i) q^{27} +(-3.57746e7 - 2.81701e7i) q^{28} -1.28782e8i q^{29} +(1.60183e8 - 5.25555e7i) q^{30} +(-1.63510e8 + 9.44024e7i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(2.00899e8 - 6.59139e7i) q^{33} +2.10906e7i q^{34} +(7.95606e7 - 5.50881e8i) q^{35} +(1.99965e7 + 1.80293e8i) q^{36} +(7.10853e7 - 1.23123e8i) q^{37} +(1.14778e8 + 1.98801e8i) q^{38} +(4.86126e7 - 2.31976e8i) q^{39} +(-3.55207e8 - 2.05079e8i) q^{40} +1.33125e9 q^{41} +(5.62592e8 + 2.05363e8i) q^{42} -8.00252e8 q^{43} +(-4.45493e8 - 2.57206e8i) q^{44} +(-1.78637e9 + 1.31360e9i) q^{45} +(1.51677e8 + 2.62712e8i) q^{46} +(-8.34818e8 + 1.44595e9i) q^{47} +(2.94367e8 - 3.28821e8i) q^{48} +(1.43278e9 - 1.36270e9i) q^{49} -3.45113e9i q^{50} +(-8.64781e7 - 2.63576e8i) q^{51} +(-4.99389e8 + 2.88323e8i) q^{52} +(5.10052e9 - 2.94479e9i) q^{53} +(-9.89160e8 - 2.17118e9i) q^{54} -6.28799e9i q^{55} +(-5.40693e8 - 1.35307e9i) q^{56} +(-2.24956e9 - 2.01385e9i) q^{57} +(2.06051e9 - 3.56890e9i) q^{58} +(3.40089e9 + 5.89051e9i) q^{59} +(5.28002e9 + 1.10647e9i) q^{60} +(-7.55358e9 - 4.36106e9i) q^{61} -6.04176e9 q^{62} +(-7.87294e9 - 2.59686e8i) q^{63} -1.07374e9 q^{64} +(-6.10437e9 - 3.52436e9i) q^{65} +(6.62209e9 + 1.38772e9i) q^{66} +(3.88865e9 + 6.73534e9i) q^{67} +(-3.37450e8 + 5.84480e8i) q^{68} +(-2.97276e9 - 2.66127e9i) q^{69} +(1.10189e10 - 1.39935e10i) q^{70} +1.50248e10i q^{71} +(-2.33053e9 + 5.31637e9i) q^{72} +(-2.86914e10 + 1.65650e10i) q^{73} +(3.93995e9 - 2.27473e9i) q^{74} +(1.41507e10 + 4.31299e10i) q^{75} +7.34577e9i q^{76} +(1.38197e10 - 1.75503e10i) q^{77} +(5.05881e9 - 5.65090e9i) q^{78} +(4.77500e8 - 8.27054e8i) q^{79} +(-6.56253e9 - 1.13666e10i) q^{80} +(2.12644e10 + 2.30781e10i) q^{81} +(3.68927e10 + 2.13000e10i) q^{82} +1.04978e10 q^{83} +(1.23052e10 + 1.46927e10i) q^{84} -8.24975e9 q^{85} +(-2.21772e10 - 1.28040e10i) q^{86} +(-1.11172e10 + 5.30504e10i) q^{87} +(-8.23058e9 - 1.42558e10i) q^{88} +(-1.87137e10 + 3.24132e10i) q^{89} +(-7.05229e10 + 7.82178e9i) q^{90} +(-9.29200e9 - 2.32529e10i) q^{91} +9.70733e9i q^{92} +(7.55057e10 - 2.47731e10i) q^{93} +(-4.62703e10 + 2.67142e10i) q^{94} +(-7.77623e10 + 4.48961e10i) q^{95} +(1.34189e10 - 4.40268e9i) q^{96} +2.70123e10i q^{97} +(6.15097e10 - 1.48397e10i) q^{98} +(-8.84483e10 + 9.80991e9i) 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
$3$	−411.940	−	86.3257i	−0.978740	−	0.205104i
$3$	−411.940	−	86.3257i	−0.978740	−	0.205104i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	−6258.52	+	10840.1i	−0.895646	+	1.55130i	−0.0626426	+	0.998036i	$0.519953\pi$
$5$	−6258.52	+	10840.1i	−0.895646	+	1.55130i	−0.833003	+	0.553268i	$0.813380\pi$
$6$	−10034.8	−	8983.37i	−0.526839	−	0.471637i
$7$	−41292.3	+	16500.6i	−0.928603	+	0.371075i
$7$	−41292.3	+	16500.6i	−0.928603	+	0.371075i
$8$			32768.0i			0.353553i
$9$	162243.	+	71122.1i	0.915865	+	0.401486i
$10$	−346882.	+	200273.i	−1.09694	+	0.633317i
$11$	−435052.	+	251177.i	−0.814482	+	0.470241i	−0.848510	−	0.529180i	$-0.822500\pi$
$11$	−435052.	+	251177.i	−0.814482	+	0.470241i	0.0340281	+	0.999421i	$0.489166\pi$
$12$	−134359.	−	409512.i	−0.155873	−	0.475083i
$13$			563130.i			0.420649i	0.977632	+	0.210325i	$0.0674521\pi$
$13$			563130.i			0.420649i	−0.977632	+	0.210325i	$0.932548\pi$
$14$	−1.40834e6	−	203398.i	−0.699846	−	0.101075i
$15$	3.51391e6	−	3.92519e6i	1.19478	−	1.33462i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	329541.	+	570781.i	0.0562912	+	0.0974991i	0.892798	−	0.450458i	$-0.148739\pi$
$17$	329541.	+	570781.i	0.0562912	+	0.0974991i	−0.836507	+	0.547957i	$0.815406\pi$
$18$	3.35825e6	+	4.56688e6i	0.418904	+	0.569666i
$19$	6.21252e6	+	3.58680e6i	0.575603	+	0.332325i	0.759384	−	0.650643i	$-0.225500\pi$
$19$	6.21252e6	+	3.58680e6i	0.575603	+	0.332325i	−0.183781	+	0.982967i	$0.558834\pi$
$20$	−1.28174e7			−0.895646
$21$	1.84344e7	−	3.23269e6i	0.984970	−	0.172726i
$22$	−1.60754e7			−0.665022
$23$	8.20976e6	+	4.73991e6i	0.265967	+	0.153556i	0.627053	−	0.778976i	$-0.284261\pi$
$23$	8.20976e6	+	4.73991e6i	0.265967	+	0.153556i	−0.361087	+	0.932532i	$0.617594\pi$
$24$	2.82872e6	−	1.34985e7i	0.0725150	−	0.346037i
$25$	−5.39240e7	−	9.33991e7i	−1.10436	−	1.91281i
$26$	−9.01008e6	+	1.56059e7i	−0.148722	+	0.257594i
$27$	−6.06947e7	−	4.33038e7i	−0.814048	−	0.580798i
$28$	−3.57746e7	−	2.81701e7i	−0.392831	−	0.309328i
$29$		−	1.28782e8i		−	1.16591i	−0.812504	−	0.582955i	$-0.801896\pi$
$29$		−	1.28782e8i		−	1.16591i	0.812504	−	0.582955i	$-0.198104\pi$
$30$	1.60183e8	−	5.25555e7i	1.20351	−	0.394867i
$31$	−1.63510e8	+	9.44024e7i	−1.02578	+	0.592235i	−0.915773	−	0.401696i	$-0.868421\pi$
$31$	−1.63510e8	+	9.44024e7i	−1.02578	+	0.592235i	−0.110008	+	0.993931i	$0.535088\pi$
$32$	−2.90590e7	+	1.67772e7i	−0.153093	+	0.0883883i
$33$	2.00899e8	−	6.59139e7i	0.893614	−	0.293191i
$34$			2.10906e7i			0.0796077i
$35$	7.95606e7	−	5.50881e8i	0.256049	−	1.77290i
$36$	1.99965e7	+	1.80293e8i	0.0551177	+	0.496953i
$37$	7.10853e7	−	1.23123e8i	0.168527	−	0.291898i	−0.769375	−	0.638797i	$-0.779432\pi$
$37$	7.10853e7	−	1.23123e8i	0.168527	−	0.291898i	0.937902	+	0.346899i	$0.112765\pi$
$38$	1.14778e8	+	1.98801e8i	0.234989	+	0.407013i
$39$	4.86126e7	−	2.31976e8i	0.0862767	−	0.411706i
$40$	−3.55207e8	−	2.05079e8i	−0.548469	−	0.316659i
$41$	1.33125e9			1.79452			0.897261	−	0.441500i	$-0.145553\pi$
$41$	1.33125e9			1.79452			0.897261	+	0.441500i	$0.145553\pi$
$42$	5.62592e8	+	2.05363e8i	0.664236	+	0.242467i
$43$	−8.00252e8			−0.830138			−0.415069	−	0.909790i	$-0.636243\pi$
$43$	−8.00252e8			−0.830138			−0.415069	+	0.909790i	$0.636243\pi$
$44$	−4.45493e8	−	2.57206e8i	−0.407241	−	0.235121i
$45$	−1.78637e9	+	1.31360e9i	−1.44312	+	1.06120i
$46$	1.51677e8	+	2.62712e8i	0.108580	+	0.188067i
$47$	−8.34818e8	+	1.44595e9i	−0.530950	+	0.919633i	0.468397	+	0.883518i	$0.344832\pi$
$47$	−8.34818e8	+	1.44595e9i	−0.530950	+	0.919633i	−0.999348	+	0.0361148i	$0.988502\pi$
$48$	2.94367e8	−	3.28821e8i	0.166749	−	0.186266i
$49$	1.43278e9	−	1.36270e9i	0.724607	−	0.689162i
$50$		−	3.45113e9i		−	1.56181i
$51$	−8.64781e7	−	2.63576e8i	−0.0350970	−	0.106972i
$52$	−4.99389e8	+	2.88323e8i	−0.182146	+	0.105162i
$53$	5.10052e9	−	2.94479e9i	1.67532	−	0.967246i	0.710739	−	0.703456i	$-0.248361\pi$
$53$	5.10052e9	−	2.94479e9i	1.67532	−	0.967246i	0.964580	−	0.263790i	$-0.0849725\pi$
$54$	−9.89160e8	−	2.17118e9i	−0.293157	−	0.643474i
$55$		−	6.28799e9i		−	1.68468i
$56$	−5.40693e8	−	1.35307e9i	−0.131195	−	0.328311i
$57$	−2.24956e9	−	2.01385e9i	−0.495205	−	0.443318i
$58$	2.06051e9	−	3.56890e9i	0.412212	−	0.713972i
$59$	3.40089e9	+	5.89051e9i	0.619307	+	1.07267i	0.989612	+	0.143762i	$0.0459199\pi$
$59$	3.40089e9	+	5.89051e9i	0.619307	+	1.07267i	−0.370305	+	0.928910i	$0.620747\pi$
$60$	5.28002e9	+	1.10647e9i	0.876605	+	0.183700i
$61$	−7.55358e9	−	4.36106e9i	−1.14509	−	0.661117i	−0.197402	−	0.980323i	$-0.563250\pi$
$61$	−7.55358e9	−	4.36106e9i	−1.14509	−	0.661117i	−0.947685	+	0.319206i	$0.896584\pi$
$62$	−6.04176e9			−0.837546
$63$	−7.87294e9	−	2.59686e8i	−0.999456	−	0.0329667i
$64$	−1.07374e9			−0.125000
$65$	−6.10437e9	−	3.52436e9i	−0.652555	−	0.376753i
$66$	6.62209e9	+	1.38772e9i	0.650883	+	0.136398i
$67$	3.88865e9	+	6.73534e9i	0.351874	+	0.609464i	0.986578	−	0.163291i	$-0.0522111\pi$
$67$	3.88865e9	+	6.73534e9i	0.351874	+	0.609464i	−0.634703	+	0.772756i	$0.718878\pi$
$68$	−3.37450e8	+	5.84480e8i	−0.0281456	+	0.0487496i
$69$	−2.97276e9	−	2.66127e9i	−0.228818	−	0.204842i
$70$	1.10189e10	−	1.39935e10i	0.783611	−	0.995146i
$71$			1.50248e10i			0.988299i	0.869377	+	0.494149i	$0.164520\pi$
$71$			1.50248e10i			0.988299i	−0.869377	+	0.494149i	$0.835480\pi$
$72$	−2.33053e9	+	5.31637e9i	−0.141947	+	0.323807i
$73$	−2.86914e10	+	1.65650e10i	−1.61985	+	0.935222i	−0.632895	+	0.774238i	$0.718133\pi$
$73$	−2.86914e10	+	1.65650e10i	−1.61985	+	0.935222i	−0.986957	+	0.160984i	$0.948533\pi$
$74$	3.93995e9	−	2.27473e9i	0.206403	−	0.119167i
$75$	1.41507e10	+	4.31299e10i	0.688560	+	2.09866i
$76$			7.34577e9i			0.332325i
$77$	1.38197e10	−	1.75503e10i	0.581835	−	0.738901i
$78$	5.05881e9	−	5.65090e9i	0.198394	−	0.221614i
$79$	4.77500e8	−	8.27054e8i	0.0174592	−	0.0302402i	−0.857164	−	0.515044i	$-0.827776\pi$
$79$	4.77500e8	−	8.27054e8i	0.0174592	−	0.0302402i	0.874623	+	0.484804i	$0.161109\pi$
$80$	−6.56253e9	−	1.13666e10i	−0.223911	−	0.387826i
$81$	2.12644e10	+	2.30781e10i	0.677618	+	0.735414i
$82$	3.68927e10	+	2.13000e10i	1.09892	+	0.634460i
$83$	1.04978e10			0.292528			0.146264	−	0.989246i	$-0.453275\pi$
$83$	1.04978e10			0.292528			0.146264	+	0.989246i	$0.453275\pi$
$84$	1.23052e10	+	1.46927e10i	0.321035	+	0.383323i
$85$	−8.24975e9			−0.201668
$86$	−2.21772e10	−	1.28040e10i	−0.508354	−	0.293498i
$87$	−1.11172e10	+	5.30504e10i	−0.239132	+	1.14112i
$88$	−8.23058e9	−	1.42558e10i	−0.166255	−	0.287963i
$89$	−1.87137e10	+	3.24132e10i	−0.355235	+	0.615285i	−0.987158	−	0.159746i	$-0.948932\pi$
$89$	−1.87137e10	+	3.24132e10i	−0.355235	+	0.615285i	0.631923	+	0.775031i	$0.282266\pi$
$90$	−7.05229e10	+	7.82178e9i	−1.25892	+	0.139628i
$91$	−9.29200e9	−	2.32529e10i	−0.156092	−	0.390616i
$92$			9.70733e9i			0.153556i
$93$	7.55057e10	−	2.47731e10i	1.12544	−	0.369253i
$94$	−4.62703e10	+	2.67142e10i	−0.650278	+	0.375438i
$95$	−7.77623e10	+	4.48961e10i	−1.03107	+	0.595290i
$96$	1.34189e10	−	4.40268e9i	0.167967	−	0.0551093i
$97$			2.70123e10i			0.319386i	0.987167	+	0.159693i	$0.0510505\pi$
$97$			2.70123e10i			0.319386i	−0.987167	+	0.159693i	$0.948950\pi$
$98$	6.15097e10	−	1.48397e10i	0.687385	−	0.165837i
$99$	−8.84483e10	+	9.80991e9i	−0.934751	+	0.103674i
$100$	5.52182e10	−	9.56406e10i	0.552182	−	0.956406i
$101$	−8.86810e9	−	1.53600e10i	−0.0839582	−	0.145420i	0.820989	−	0.570945i	$-0.193423\pi$
$101$	−8.86810e9	−	1.53600e10i	−0.0839582	−	0.145420i	−0.904947	+	0.425525i	$0.860090\pi$
$102$	1.82066e9	−	8.68808e9i	0.0163278	−	0.0779153i
$103$	1.74172e11	+	1.00558e11i	1.48038	+	0.854699i	0.999753	−	0.0222250i	$-0.00707502\pi$
$103$	1.74172e11	+	1.00558e11i	1.48038	+	0.854699i	0.480629	+	0.876924i	$0.340408\pi$
$104$	−1.84526e10			−0.148722
$105$	−8.03294e10	+	2.20062e11i	−0.614233	+	1.68269i
$106$	1.88466e11			1.36789
$107$	−7.11129e10	−	4.10571e10i	−0.490160	−	0.282994i	0.234481	−	0.972121i	$-0.424661\pi$
$107$	−7.11129e10	−	4.10571e10i	−0.490160	−	0.282994i	−0.724641	+	0.689127i	$0.757994\pi$
$108$	7.32654e9	−	7.59962e10i	0.0479809	−	0.497693i
$109$	−8.08839e10	−	1.40095e11i	−0.503519	−	0.872121i	−0.999992	−	0.00406864i	$-0.998705\pi$
$109$	−8.08839e10	−	1.40095e11i	−0.503519	−	0.872121i	0.496472	−	0.868053i	$-0.334628\pi$
$110$	1.00608e11	−	1.74258e11i	0.595624	−	1.03165i
$111$	−3.99116e10	+	4.45830e10i	−0.224814	+	0.251127i
$112$	6.66495e9	−	4.61484e10i	0.0357353	−	0.247433i
$113$		−	2.76208e11i		−	1.41028i	−0.709069	−	0.705139i	$-0.750884\pi$
$113$		−	2.76208e11i		−	1.41028i	0.709069	−	0.705139i	$-0.249116\pi$
$114$	−3.01199e10	−	9.18023e10i	−0.146513	−	0.446557i
$115$	−1.02762e11	+	5.93296e10i	−0.476424	+	0.275064i
$116$	1.14205e11	−	6.59362e10i	0.504854	−	0.291478i
$117$	−4.00510e10	+	9.13637e10i	−0.168885	+	0.385258i
$118$			2.17657e11i			0.875833i
$119$	−2.30258e10	−	1.81313e10i	−0.0884516	−	0.0696498i
$120$	1.28621e11	+	1.15144e11i	0.471861	+	0.422419i
$121$	−1.64757e10	+	2.85368e10i	−0.0577463	+	0.100020i
$122$	−1.39554e11	−	2.41714e11i	−0.467480	−	0.809699i
$123$	−5.48396e11	−	1.14921e11i	−1.75637	−	0.368063i
$124$	−1.67434e11	−	9.66681e10i	−0.512890	−	0.296117i
$125$	7.38753e11			2.16518
$126$	−2.14026e11	−	1.33164e11i	−0.600384	−	0.373549i
$127$	−6.44469e11			−1.73094			−0.865469	−	0.500963i	$-0.832979\pi$
$127$	−6.44469e11			−1.73094			−0.865469	+	0.500963i	$0.832979\pi$
$128$	−2.97564e10	−	1.71799e10i	−0.0765466	−	0.0441942i
$129$	3.29656e11	+	6.90823e10i	0.812489	+	0.170264i
$130$	−1.12779e11	−	1.95340e11i	−0.266404	−	0.461426i
$131$	3.25683e11	−	5.64100e11i	0.737570	−	1.27751i	−0.216017	−	0.976390i	$-0.569307\pi$
$131$	3.25683e11	−	5.64100e11i	0.737570	−	1.27751i	0.953587	−	0.301118i	$-0.0973600\pi$
$132$	1.61313e11	+	1.44411e11i	0.350359	+	0.313649i
$133$	−3.15714e11	−	4.55968e10i	−0.657824	−	0.0950058i
$134$			2.48874e11i			0.497626i
$135$	8.49274e11	−	3.86917e11i	1.63009	−	0.742647i
$136$	−1.87034e10	+	1.07984e10i	−0.0344712	+	0.0199019i
$137$	−1.30107e9	+	7.51175e8i	−0.00230324	+	0.00132977i	−0.501151	−	0.865360i	$-0.667090\pi$
$137$	−1.30107e9	+	7.51175e8i	−0.00230324	+	0.00132977i	0.498848	+	0.866690i	$0.333757\pi$
$138$	−3.98031e10	−	1.21315e11i	−0.0676989	−	0.206339i
$139$		−	7.47761e10i		−	0.122231i	−0.998131	−	0.0611155i	$-0.980534\pi$
$139$		−	7.47761e10i		−	0.122231i	0.998131	−	0.0611155i	$-0.0194658\pi$
$140$	5.29262e11	−	2.11496e11i	0.831699	−	0.332352i
$141$	4.68718e11	−	5.23578e11i	0.708282	−	0.791182i
$142$	−2.40397e11	+	4.16380e11i	−0.349416	+	0.605207i
$143$	−1.41445e11	−	2.44991e11i	−0.197807	−	0.342611i
$144$	−1.49647e11	+	1.10043e11i	−0.201407	+	0.148105i
$145$	1.39600e12	+	8.05982e11i	1.80868	+	1.04424i
$146$	−1.06016e12			−1.32260
$147$	−7.07858e11	+	4.37665e11i	−0.850552	+	0.525892i
$148$	1.45583e11			0.168527
$149$	4.48317e11	+	2.58836e11i	0.500105	+	0.288735i	0.728757	−	0.684773i	$-0.240099\pi$
$149$	4.48317e11	+	2.58836e11i	0.500105	+	0.288735i	−0.228652	+	0.973508i	$0.573432\pi$
$150$	−2.97922e11	+	1.42166e12i	−0.320332	+	1.52860i
$151$	−3.31782e10	−	5.74662e10i	−0.0343937	−	0.0595716i	0.848316	−	0.529490i	$-0.177617\pi$
$151$	−3.31782e10	−	5.74662e10i	−0.0343937	−	0.0595716i	−0.882710	+	0.469918i	$0.844283\pi$
$152$	−1.17532e11	+	2.03572e11i	−0.117495	+	0.203506i
$153$	1.28705e10	+	1.16043e11i	0.0124105	+	0.111896i
$154$	6.63789e11	−	2.65254e11i	0.617541	−	0.246773i
$155$		−	2.36328e12i		−	2.12173i
$156$	2.30608e11	−	7.56616e10i	0.199843	−	0.0655677i
$157$	−1.08687e12	+	6.27508e11i	−0.909351	+	0.525014i	−0.880222	−	0.474562i	$-0.842607\pi$
$157$	−1.08687e12	+	6.27508e11i	−0.909351	+	0.525014i	−0.0291286	+	0.999576i	$0.509273\pi$
$158$	2.64657e10	−	1.52800e10i	0.0213831	−	0.0123455i
$159$	−2.35532e12	+	7.72771e11i	−1.83809	+	0.603069i
$160$		−	4.20002e11i		−	0.316659i
$161$	−4.17212e11	−	6.02555e10i	−0.303958	−	0.0438990i
$162$	2.20046e11	+	9.79788e11i	0.154946	+	0.689922i
$163$	5.75602e11	−	9.96973e11i	0.391824	−	0.678659i	−0.600866	−	0.799349i	$-0.705178\pi$
$163$	5.75602e11	−	9.96973e11i	0.391824	−	0.678659i	0.992690	+	0.120691i	$0.0385110\pi$
$164$	6.81601e11	+	1.18057e12i	0.448631	+	0.777051i
$165$	−5.42815e11	+	2.59028e12i	−0.345534	+	1.64886i
$166$	2.90922e11	+	1.67964e11i	0.179136	+	0.103424i
$167$	−1.96526e12			−1.17079			−0.585395	−	0.810748i	$-0.699061\pi$
$167$	−1.96526e12			−1.17079			−0.585395	+	0.810748i	$0.699061\pi$
$168$	1.05929e11	+	6.04059e11i	0.0610679	+	0.348239i
$169$	1.47505e12			0.823054
$170$	−2.28624e11	−	1.31996e11i	−0.123496	−	0.0713003i
$171$	7.52836e11	+	1.02378e12i	0.393751	+	0.535461i
$172$	−4.09729e11	−	7.09672e11i	−0.207534	−	0.359460i
$173$	6.93882e11	−	1.20184e12i	0.340433	−	0.589647i	−0.644080	−	0.764958i	$-0.722760\pi$
$173$	6.93882e11	−	1.20184e12i	0.340433	−	0.589647i	0.984513	+	0.175311i	$0.0560930\pi$
$174$	−1.15689e12	+	1.29230e12i	−0.549886	+	0.614247i
$175$	3.76779e12	+	2.96688e12i	1.73531	+	1.36644i
$176$		−	5.26757e11i		−	0.235121i
$177$	−8.92461e11	−	2.72012e12i	−0.386132	−	1.17689i
$178$	−1.03722e12	+	5.98840e11i	−0.435072	+	0.251189i
$179$	−1.98766e11	+	1.14757e11i	−0.0808443	+	0.0466755i	−0.539877	−	0.841744i	$-0.681529\pi$
$179$	−1.98766e11	+	1.14757e11i	−0.0808443	+	0.0466755i	0.459033	+	0.888419i	$0.348196\pi$
$180$	−2.07954e12	−	9.11603e11i	−0.820291	−	0.359589i
$181$		−	3.99811e12i		−	1.52976i	−0.644175	−	0.764878i	$-0.722799\pi$
$181$		−	3.99811e12i		−	1.52976i	0.644175	−	0.764878i	$-0.277201\pi$
$182$	1.14539e11	−	7.93076e11i	0.0425170	−	0.294390i
$183$	2.73515e12	+	2.44856e12i	0.985146	+	0.881923i
$184$	−1.55317e11	+	2.69017e11i	−0.0542902	+	0.0940335i
$185$	8.89777e11	+	1.54114e12i	0.301882	+	0.522875i
$186$	2.48884e12	+	5.21559e11i	0.819740	+	0.171784i
$187$	−2.86735e11	−	1.65546e11i	−0.0916962	−	0.0529408i
$188$	−1.70971e12			−0.530950
$189$	3.22076e12	+	7.86612e11i	0.971447	+	0.237258i
$190$	−2.87335e12			−0.841868
$191$	−2.03265e12	−	1.17355e12i	−0.578601	−	0.334056i	0.181976	−	0.983303i	$-0.441751\pi$
$191$	−2.03265e12	−	1.17355e12i	−0.578601	−	0.334056i	−0.760577	+	0.649247i	$0.775084\pi$
$192$	4.42318e11	+	9.26915e10i	0.122343	+	0.0256379i
$193$	−3.21534e12	−	5.56913e12i	−0.864294	−	1.49700i	−0.867747	−	0.497007i	$-0.834432\pi$
$193$	−3.21534e12	−	5.56913e12i	−0.864294	−	1.49700i	0.00345278	−	0.999994i	$-0.498901\pi$
$194$	−4.32196e11	+	7.48586e11i	−0.112920	+	0.195583i
$195$	2.21039e12	+	1.97879e12i	0.561409	+	0.502584i
$196$	1.94204e12	+	5.72906e11i	0.479568	+	0.141473i
$197$			2.83497e11i			0.0680745i	0.999421	+	0.0340372i	$0.0108365\pi$
$197$			2.83497e11i			0.0680745i	−0.999421	+	0.0340372i	$0.989164\pi$
$198$	−2.60811e12	−	1.14331e12i	−0.609070	−	0.266997i
$199$	1.05318e12	−	6.08055e11i	0.239228	−	0.138118i	−0.375594	−	0.926784i	$-0.622561\pi$
$199$	1.05318e12	−	6.08055e11i	0.239228	−	0.138118i	0.614822	+	0.788666i	$0.289228\pi$
$200$	3.06050e12	−	1.76698e12i	0.676281	−	0.390451i
$201$	−1.02046e12	−	3.11025e12i	−0.219390	−	0.668678i
$202$		−	5.67559e11i		−	0.118735i
$203$	2.12498e12	+	5.31770e12i	0.432640	+	1.08267i
$204$	1.89465e11	−	2.11640e11i	0.0375459	−	0.0419404i
$205$	−8.33166e12	+	1.44309e13i	−1.60726	+	2.78385i
$206$	3.21787e12	+	5.57351e12i	0.604363	+	1.04679i
$207$	9.94862e11	+	1.35291e12i	0.181939	+	0.247419i
$208$	−5.11375e11	−	2.95242e11i	−0.0910732	−	0.0525812i
$209$	−3.60369e12			−0.625091
$210$	−5.74715e12	+	4.81327e12i	−0.971060	+	0.813268i
$211$	−6.89868e12			−1.13557			−0.567783	−	0.823178i	$-0.692199\pi$
$211$	−6.89868e12			−1.13557			−0.567783	+	0.823178i	$0.692199\pi$
$212$	5.22294e12	+	3.01546e12i	0.837659	+	0.483623i
$213$	1.29703e12	−	6.18933e12i	0.202704	−	0.967288i
$214$	−1.31383e12	−	2.27561e12i	−0.200107	−	0.346595i
$215$	5.00839e12	−	8.67479e12i	0.743510	−	1.28780i
$216$	1.41898e12	−	1.98884e12i	0.205343	−	0.287809i
$217$	5.19400e12	−	6.59611e12i	0.732780	−	0.930592i
$218$		−	5.17657e12i		−	0.712084i
$219$	1.32491e13	−	4.34698e12i	1.77723	−	0.583102i
$220$	5.57625e12	−	3.21945e12i	0.729487	−	0.421170i
$221$	−3.21424e11	+	1.85574e11i	−0.0410129	+	0.0236788i
$222$	−1.81939e12	+	5.96935e11i	−0.226457	+	0.0742994i
$223$			8.88493e12i			1.07889i	0.842021	+	0.539445i	$0.181366\pi$
$223$			8.88493e12i			1.07889i	−0.842021	+	0.539445i	$0.818634\pi$
$224$	9.23078e11	−	1.17226e12i	0.109364	−	0.138887i
$225$	−2.10604e12	−	1.89885e13i	−0.243480	−	2.19527i
$226$	4.41933e12	−	7.65450e12i	0.498609	−	0.863616i
$227$	−6.23327e12	−	1.07963e13i	−0.686395	−	1.18887i	−0.972996	−	0.230821i	$-0.925859\pi$
$227$	−6.23327e12	−	1.07963e13i	−0.686395	−	1.18887i	0.286602	−	0.958050i	$-0.407474\pi$
$228$	6.34129e11	−	3.02602e12i	0.0681610	−	0.325260i
$229$	−1.51422e11	−	8.74238e10i	−0.0158889	−	0.00917349i	0.492034	−	0.870576i	$-0.336253\pi$
$229$	−1.51422e11	−	8.74238e10i	−0.0158889	−	0.00917349i	−0.507923	+	0.861402i	$0.669587\pi$
$230$	−3.79709e12			−0.388999
$231$	−7.20794e12	+	6.03669e12i	−0.721017	+	0.603856i
$232$	4.21992e12			0.412212
$233$	4.78942e12	+	2.76518e12i	0.456905	+	0.263794i	0.710742	−	0.703453i	$-0.248359\pi$
$233$	4.78942e12	+	2.76518e12i	0.456905	+	0.263794i	−0.253837	+	0.967247i	$0.581693\pi$
$234$	−2.57174e12	+	1.89113e12i	−0.239630	+	0.176212i
$235$	−1.04494e13	−	1.80990e13i	−0.951087	−	1.64733i
$236$	−3.48251e12	+	6.03188e12i	−0.309654	+	0.536336i
$237$	−2.68098e11	+	2.99476e11i	−0.0232904	+	0.0260164i
$238$	−3.48009e11	−	8.70880e11i	−0.0295404	−	0.0739240i
$239$			1.16852e13i			0.969280i	0.874714	+	0.484640i	$0.161049\pi$
$239$			1.16852e13i			0.969280i	−0.874714	+	0.484640i	$0.838951\pi$
$240$	1.72214e12	+	5.24889e12i	0.139607	+	0.425506i
$241$	1.73798e12	−	1.00342e12i	0.137706	−	0.0795043i	−0.429564	−	0.903036i	$-0.641333\pi$
$241$	1.73798e12	−	1.00342e12i	0.137706	−	0.0795043i	0.567270	+	0.823532i	$0.308000\pi$
$242$	−9.13176e11	+	5.27223e11i	−0.0707245	+	0.0408328i
$243$	−6.76742e12	−	1.13425e13i	−0.512376	−	0.858761i
$244$		−	8.93145e12i		−	0.661117i
$245$	5.80465e12	+	2.40600e13i	0.420109	+	1.74133i
$246$	−1.33589e13	−	1.19591e13i	−0.945424	−	0.846363i
$247$	−2.01984e12	+	3.49846e12i	−0.139792	+	0.242127i
$248$	−3.09338e12	−	5.35789e12i	−0.209387	−	0.362668i
$249$	−4.32445e12	−	9.06226e11i	−0.286309	−	0.0599985i
$250$	2.04729e13	+	1.18200e13i	1.32590	+	0.765507i
$251$	2.35605e12			0.149273			0.0746363	−	0.997211i	$-0.476220\pi$
$251$	2.35605e12			0.149273			0.0746363	+	0.997211i	$0.476220\pi$
$252$	−3.80065e12	−	7.11476e12i	−0.235589	−	0.441019i
$253$	−4.76223e12			−0.288833
$254$	−1.78600e13	−	1.03115e13i	−1.05998	−	0.611979i
$255$	3.39840e12	+	7.12165e11i	0.197380	+	0.0413628i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−9.60767e12	+	1.66410e13i	−0.534547	+	0.925862i	0.464638	+	0.885501i	$0.346184\pi$
$257$	−9.60767e12	+	1.66410e13i	−0.534547	+	0.925862i	−0.999185	+	0.0403618i	$0.987149\pi$
$258$	8.03038e12	+	7.18896e12i	0.437349	+	0.391524i
$259$	−9.03663e11	+	6.25700e12i	−0.0481790	+	0.333594i
$260$		−	7.21788e12i		−	0.376753i
$261$	9.15922e12	−	2.08939e13i	0.468097	−	1.06782i
$262$	1.80512e13	−	1.04219e13i	0.903335	−	0.521540i
$263$	−1.43021e13	+	8.25730e12i	−0.700878	+	0.404652i	−0.807674	−	0.589629i	$-0.799274\pi$
$263$	−1.43021e13	+	8.25730e12i	−0.700878	+	0.404652i	0.106796	+	0.994281i	$0.465941\pi$
$264$	2.15987e12	+	6.58304e12i	0.103659	+	0.315940i
$265$			7.37200e13i			3.46524i
$266$	−8.01977e12	−	6.31504e12i	−0.369244	−	0.290755i
$267$	1.05070e13	−	1.17368e13i	0.473880	−	0.529344i
$268$	−3.98198e12	+	6.89699e12i	−0.175937	+	0.304732i
$269$	6.01234e12	+	1.04137e13i	0.260259	+	0.450782i	0.966311	−	0.257378i	$-0.0828586\pi$
$269$	6.01234e12	+	1.04137e13i	0.260259	+	0.450782i	−0.706051	+	0.708161i	$0.749525\pi$
$270$	2.97265e13	+	2.86583e12i	1.26079	+	0.121549i
$271$	−4.32589e12	−	2.49755e12i	−0.179781	−	0.103797i	0.407409	−	0.913246i	$-0.366432\pi$
$271$	−4.32589e12	−	2.49755e12i	−0.179781	−	0.103797i	−0.587190	+	0.809449i	$0.699766\pi$
$272$	−6.91097e11			−0.0281456
$273$	1.82043e12	+	1.03810e13i	0.0726571	+	0.414327i
$274$	−4.80752e10			−0.00188058
$275$	4.69195e13	+	2.70890e13i	1.79897	+	1.03863i
$276$	8.37992e11	−	3.99884e12i	0.0314949	−	0.150291i
$277$	1.59776e13	+	2.76741e13i	0.588673	+	1.01961i	0.994407	+	0.105620i	$0.0336827\pi$
$277$	1.59776e13	+	2.76741e13i	0.588673	+	1.01961i	−0.405734	+	0.913991i	$0.632984\pi$
$278$	1.19642e12	−	2.07226e12i	0.0432152	−	0.0748509i
$279$	−3.32424e13	+	3.68695e12i	−1.17725	+	0.130570i
$280$	1.80513e13	+	2.60704e12i	0.626814	+	0.0905271i
$281$			1.81369e13i			0.617560i	0.951133	+	0.308780i	$0.0999207\pi$
$281$			1.81369e13i			0.617560i	−0.951133	+	0.308780i	$0.900079\pi$
$282$	2.13667e13	−	7.01033e12i	0.713458	−	0.234082i
$283$	−2.74714e13	+	1.58606e13i	−0.899613	+	0.519392i	−0.877075	−	0.480354i	$-0.840508\pi$
$283$	−2.74714e13	+	1.58606e13i	−0.899613	+	0.519392i	−0.0225382	+	0.999746i	$0.507175\pi$
$284$	−1.33242e13	+	7.69270e12i	−0.427946	+	0.247075i
$285$	3.59091e13	−	1.17816e13i	1.13125	−	0.371158i
$286$		−	9.05251e12i		−	0.279741i
$287$	−5.49705e13	+	2.19665e13i	−1.66640	+	0.665902i
$288$	−5.90784e12	+	6.55246e11i	−0.175699	+	0.0194870i
$289$	1.69188e13	−	2.93041e13i	0.493663	−	0.855049i
$290$	2.57914e13	+	4.46721e13i	0.738391	+	1.27893i
$291$	2.33185e12	−	1.11274e13i	0.0655073	−	0.312596i
$292$	−2.93799e13	−	1.69625e13i	−0.809926	−	0.467611i
$293$	−5.90556e13			−1.59768			−0.798839	−	0.601545i	$-0.794552\pi$
$293$	−5.90556e13			−1.59768			−0.798839	+	0.601545i	$0.794552\pi$
$294$	−2.66194e13	+	8.03197e11i	−0.706785	+	0.0213261i
$295$	−8.51380e13			−2.21872
$296$	4.03451e12	+	2.32932e12i	0.103202	+	0.0595834i
$297$	3.72823e13	+	3.59426e12i	0.936142	+	0.0902504i
$298$	8.28275e12	+	1.43461e13i	0.204167	+	0.353627i
$299$	−2.66918e12	+	4.62316e12i	−0.0645932	+	0.111879i
$300$	−3.10028e13	+	3.46315e13i	−0.736605	+	0.822819i
$301$	3.30443e13	−	1.32047e13i	0.770869	−	0.308043i
$302$		−	2.12340e12i		−	0.0486400i
$303$	2.32717e12	+	7.09295e12i	0.0523472	+	0.159548i
$304$	−6.51430e12	+	3.76103e12i	−0.143901	+	0.0830812i
$305$	9.45484e13	−	5.45875e13i	2.05119	−	1.18425i
$306$	−1.50001e12	+	3.42180e12i	−0.0319614	+	0.0729099i
$307$		−	5.78462e13i		−	1.21064i	−0.795983	−	0.605319i	$-0.793046\pi$
$307$		−	5.78462e13i		−	1.21064i	0.795983	−	0.605319i	$-0.206954\pi$
$308$	2.26395e13	+	3.26969e12i	0.465412	+	0.0672169i
$309$	−6.30678e13	−	5.64595e13i	−1.27361	−	1.14016i
$310$	3.78124e13	−	6.54930e13i	0.750145	−	1.29929i
$311$	−3.81509e13	−	6.60793e13i	−0.743571	−	1.28790i	−0.950859	−	0.309623i	$-0.899797\pi$
$311$	−3.81509e13	−	6.60793e13i	−0.743571	−	1.28790i	0.207288	−	0.978280i	$-0.433536\pi$
$312$	7.60139e12	+	1.59294e12i	0.145560	+	0.0305034i
$313$	−3.77329e12	−	2.17851e12i	−0.0709947	−	0.0409888i	0.464082	−	0.885792i	$-0.346384\pi$
$313$	−3.77329e12	−	2.17851e12i	−0.0709947	−	0.0409888i	−0.535077	+	0.844803i	$0.679717\pi$
$314$	−4.01605e13			−0.742482
$315$	5.20879e13	−	8.37179e13i	0.946300	−	1.52093i
$316$	9.77920e11			0.0174592
$317$	3.35580e13	+	1.93747e13i	0.588804	+	0.339946i	0.764624	−	0.644476i	$-0.222925\pi$
$317$	3.35580e13	+	1.93747e13i	0.588804	+	0.339946i	−0.175821	+	0.984422i	$0.556258\pi$
$318$	−7.76370e13	−	1.62695e13i	−1.33881	−	0.280560i
$319$	3.23471e13	+	5.60267e13i	0.548259	+	0.949613i
$320$	6.72003e12	−	1.16394e13i	0.111956	−	0.193913i
$321$	2.57500e13	+	2.30519e13i	0.421696	+	0.377511i
$322$	−1.05980e13	−	8.34523e12i	−0.170615	−	0.134348i
$323$			4.72799e12i			0.0748278i
$324$	−9.57852e12	+	3.06734e13i	−0.149039	+	0.477271i
$325$	5.25958e13	−	3.03662e13i	0.804623	−	0.464550i
$326$	3.19031e13	−	1.84193e13i	0.479884	−	0.277061i
$327$	2.12255e13	+	6.46931e13i	0.313940	+	0.956854i
$328$			4.36225e13i			0.634460i
$329$	1.06125e13	−	7.34816e13i	0.151789	−	1.05100i
$330$	−5.64874e13	+	6.30988e13i	−0.794556	+	0.887554i
$331$	5.95979e13	−	1.03227e14i	0.824474	−	1.42803i	−0.0778461	−	0.996965i	$-0.524804\pi$
$331$	5.95979e13	−	1.03227e14i	0.824474	−	1.42803i	0.902320	−	0.431066i	$-0.141862\pi$
$332$	5.37485e12	+	9.30952e12i	0.0731319	+	0.126668i
$333$	2.02899e13	−	1.49201e13i	0.271541	−	0.199678i
$334$	−5.44629e13	−	3.14442e13i	−0.716960	−	0.413937i
$335$	−9.73488e13			−1.26062
$336$	−6.72935e12	+	1.84350e13i	−0.0857249	+	0.234843i
$337$	−6.70814e13			−0.840694			−0.420347	−	0.907364i	$-0.638092\pi$
$337$	−6.70814e13			−0.840694			−0.420347	+	0.907364i	$0.638092\pi$
$338$	4.08776e13	+	2.36007e13i	0.504016	+	0.290994i
$339$	−2.38439e13	+	1.13781e14i	−0.289253	+	1.38030i
$340$	−4.22387e12	−	7.31596e12i	−0.0504169	−	0.0873247i
$341$	4.74235e13	−	8.21399e13i	0.556986	−	0.964729i
$342$	4.48272e12	+	4.04172e13i	0.0518082	+	0.467114i
$343$	−3.66776e13	+	7.99109e13i	−0.417141	+	0.908842i
$344$		−	2.62227e13i		−	0.293498i
$345$	4.74534e13	−	1.55693e13i	0.522712	−	0.171500i
$346$	3.84588e13	−	2.22042e13i	0.416944	−	0.240723i
$347$	4.15394e13	−	2.39828e13i	0.443249	−	0.255910i	−0.261726	−	0.965142i	$-0.584292\pi$
$347$	4.15394e13	−	2.39828e13i	0.443249	−	0.255910i	0.704975	+	0.709232i	$0.250958\pi$
$348$	−5.27376e13	+	1.73030e13i	−0.553904	+	0.181734i
$349$			7.88994e13i			0.815707i	0.913047	+	0.407853i	$0.133723\pi$
$349$			7.88994e13i			0.815707i	−0.913047	+	0.407853i	$0.866277\pi$
$350$	5.69459e13	+	1.42505e14i	0.579547	+	1.45030i
$351$	2.43856e13	−	3.41790e13i	0.244312	−	0.342429i
$352$	8.42811e12	−	1.45979e13i	0.0831277	−	0.143981i
$353$	6.52510e12	+	1.13018e13i	0.0633616	+	0.109745i	0.895966	−	0.444123i	$-0.146485\pi$
$353$	6.52510e12	+	1.13018e13i	0.0633616	+	0.109745i	−0.832604	+	0.553868i	$0.813151\pi$
$354$	1.87894e13	−	8.96616e13i	0.179636	−	0.857213i
$355$	−1.62870e14	−	9.40330e13i	−1.53315	−	0.885166i
$356$	−3.83258e13			−0.355235
$357$	7.92005e12	+	9.45671e12i	0.0722857	+	0.0863108i
$358$	−7.34447e12			−0.0660091
$359$	3.91784e13	+	2.26196e13i	0.346758	+	0.200201i	0.663257	−	0.748392i	$-0.269174\pi$
$359$	3.91784e13	+	2.26196e13i	0.346758	+	0.200201i	−0.316498	+	0.948593i	$0.602507\pi$
$360$	−4.30442e13	−	5.85357e13i	−0.375189	−	0.510219i
$361$	−3.25148e13	−	5.63173e13i	−0.279121	−	0.483451i
$362$	6.39697e13	−	1.10799e14i	0.540851	−	0.936781i
$363$	9.25046e12	−	1.03332e13i	0.0770330	−	0.0860492i
$364$	1.58634e13	−	2.01457e13i	0.130119	−	0.165244i
$365$		−	4.14688e14i		−	3.35051i
$366$	3.66217e13	+	1.11619e14i	0.291469	+	0.888367i
$367$	1.30726e14	−	7.54749e13i	1.02494	−	0.591751i	0.109411	−	0.993997i	$-0.465103\pi$
$367$	1.30726e14	−	7.54749e13i	1.02494	−	0.591751i	0.915532	+	0.402245i	$0.131770\pi$
$368$	−8.60856e12	+	4.97015e12i	−0.0664917	+	0.0383890i
$369$	2.15986e14	+	9.46814e13i	1.64354	+	0.720476i
$370$			5.69458e13i			0.426925i
$371$	−1.62022e14	+	2.05759e14i	−1.19679	+	1.51986i
$372$	6.06279e13	+	5.42754e13i	0.441252	+	0.395018i
$373$	−8.29658e13	+	1.43701e14i	−0.594978	+	1.03053i	0.398573	+	0.917137i	$0.369506\pi$
$373$	−8.29658e13	+	1.43701e14i	−0.594978	+	1.03053i	−0.993550	+	0.113394i	$0.963828\pi$
$374$	−5.29748e12	−	9.17551e12i	−0.0374348	−	0.0648390i
$375$	−3.04322e14	−	6.37734e13i	−2.11915	−	0.444086i
$376$	−4.73808e13	−	2.73553e13i	−0.325139	−	0.187719i
$377$	7.25208e13			0.490439
$378$	7.66706e13	+	7.33315e13i	0.511004	+	0.488748i
$379$	−4.45474e12			−0.0292622			−0.0146311	−	0.999893i	$-0.504657\pi$
$379$	−4.45474e12			−0.0292622			−0.0146311	+	0.999893i	$0.504657\pi$
$380$	−7.96286e13	−	4.59736e13i	−0.515537	−	0.297645i
$381$	2.65483e14	+	5.56342e13i	1.69414	+	0.355021i
$382$	−3.75537e13	−	6.50449e13i	−0.236213	−	0.409133i
$383$	−7.12045e13	+	1.23330e14i	−0.441483	+	0.764671i	−0.997800	−	0.0662994i	$-0.978881\pi$
$383$	−7.12045e13	+	1.23330e14i	−0.441483	+	0.764671i	0.556317	+	0.830970i	$0.312214\pi$
$384$	1.07748e13	+	9.64582e12i	0.0658548	+	0.0589546i
$385$	1.03756e14	+	2.59646e14i	0.625142	+	1.56440i
$386$		−	2.05782e14i		−	1.22230i
$387$	−1.29835e14	−	5.69156e13i	−0.760294	−	0.333289i
$388$	−2.39547e13	+	1.38303e13i	−0.138298	+	0.0798466i
$389$	1.04221e14	−	6.01722e13i	0.593244	−	0.342510i	−0.173135	−	0.984898i	$-0.555390\pi$
$389$	1.04221e14	−	6.01722e13i	0.593244	−	0.342510i	0.766379	+	0.642388i	$0.222056\pi$
$390$	2.95956e13	+	9.02041e13i	0.166101	+	0.506257i
$391$			6.24797e12i			0.0345754i
$392$	4.46529e13	+	4.69495e13i	0.243656	+	0.256187i
$393$	−1.82858e14	+	2.04261e14i	−0.983910	+	1.09907i
$394$	−4.53595e12	+	7.85650e12i	−0.0240680	+	0.0416869i
$395$	5.97688e12	+	1.03523e13i	0.0312745	+	0.0541691i
$396$	−5.39850e13	−	7.34141e13i	−0.278580	−	0.378840i
$397$	5.22418e12	+	3.01618e12i	0.0265871	+	0.0153501i	0.513235	−	0.858248i	$-0.328447\pi$
$397$	5.22418e12	+	3.01618e12i	0.0265871	+	0.0153501i	−0.486648	+	0.873598i	$0.661780\pi$
$398$	3.89155e13			0.195329
$399$	1.26119e14	+	4.60374e13i	0.624353	+	0.227908i
$400$	1.13087e14			0.552182
$401$	2.14159e14	+	1.23645e14i	1.03143	+	0.595499i	0.917395	−	0.397977i	$-0.130288\pi$
$401$	2.14159e14	+	1.23645e14i	1.03143	+	0.595499i	0.114039	+	0.993476i	$0.463621\pi$
$402$	2.14842e13	−	1.02521e14i	0.102065	−	0.487046i
$403$	−5.31608e13	−	9.20773e13i	−0.249123	−	0.431494i
$404$	9.08094e12	−	1.57286e13i	0.0419791	−	0.0727099i
$405$	−3.83251e14	+	8.60726e13i	−1.74776	+	0.392520i
$406$	−2.61939e13	+	1.81368e14i	−0.117844	+	0.815957i
$407$			7.14201e13i			0.316994i
$408$	8.63685e12	−	2.83371e12i	0.0378203	−	0.0124087i
$409$	1.76829e14	−	1.02092e14i	0.763970	−	0.441078i	−0.0667495	−	0.997770i	$-0.521263\pi$
$409$	1.76829e14	−	1.02092e14i	0.763970	−	0.441078i	0.830719	+	0.556692i	$0.187929\pi$
$410$	−4.61787e14	+	2.66613e14i	−1.96848	+	1.13650i
$411$	6.00810e11	−	1.97123e11i	0.00252701	−	0.000829101i
$412$			2.05943e14i			0.854699i
$413$	−2.37628e14	−	1.87116e14i	−0.973132	−	0.766277i
$414$	5.92385e12	+	5.34108e13i	0.0239388	+	0.215837i
$415$	−6.57004e13	+	1.13796e14i	−0.262001	+	0.453799i
$416$	−9.44775e12	−	1.63640e13i	−0.0371805	−	0.0643985i
$417$	−6.45510e12	+	3.08033e13i	−0.0250700	+	0.119632i
$418$	−9.98685e13	−	5.76591e13i	−0.382789	−	0.221003i
$419$	8.37838e13			0.316944			0.158472	−	0.987363i	$-0.449343\pi$
$419$	8.37838e13			0.316944			0.158472	+	0.987363i	$0.449343\pi$
$420$	−2.36282e14	+	4.14348e13i	−0.882184	+	0.154701i
$421$	3.96767e14			1.46212			0.731061	−	0.682312i	$-0.239025\pi$
$421$	3.96767e14			1.46212			0.731061	+	0.682312i	$0.239025\pi$
$422$	−1.91182e14	−	1.10379e14i	−0.695390	−	0.401484i
$423$	−2.38282e14	+	1.75221e14i	−0.855499	+	0.629090i
$424$	9.64948e13	+	1.67134e14i	0.341973	+	0.592315i
$425$	3.55403e13	−	6.15576e13i	0.124332	−	0.215349i
$426$	1.34974e14	−	1.50771e14i	0.466118	−	0.520674i
$427$	3.83865e14	+	5.54394e13i	1.30866	+	0.189002i
$428$		−	8.40849e13i		−	0.282994i
$429$	3.71181e13	+	1.13132e14i	0.123331	+	0.375898i
$430$	2.77593e14	−	1.60268e14i	0.910610	−	0.525741i
$431$	7.34302e13	−	4.23950e13i	0.237821	−	0.137306i	−0.376354	−	0.926476i	$-0.622822\pi$
$431$	7.34302e13	−	4.23950e13i	0.237821	−	0.137306i	0.614175	+	0.789170i	$0.289489\pi$
$432$	7.11454e13	−	3.24128e13i	0.227502	−	0.103647i
$433$			3.07354e14i			0.970412i	0.874400	+	0.485206i	$0.161255\pi$
$433$			3.07354e14i			0.970412i	−0.874400	+	0.485206i	$0.838745\pi$
$434$	2.49478e14	−	9.96928e13i	0.777748	−	0.310792i
$435$	−5.05493e14	−	4.52528e14i	−1.55605	−	1.39301i
$436$	8.28251e13	−	1.43457e14i	0.251760	−	0.436061i
$437$	3.40022e13	+	5.88936e13i	0.102061	+	0.176775i
$438$	4.36722e14	+	9.15188e13i	1.29449	+	0.271271i
$439$	−2.27200e14	−	1.31174e14i	−0.665049	−	0.383966i	0.129149	−	0.991625i	$-0.458775\pi$
$439$	−2.27200e14	−	1.31174e14i	−0.665049	−	0.383966i	−0.794198	+	0.607659i	$0.792109\pi$
$440$	2.06045e14			0.595624
$441$	3.29377e14	−	1.19185e14i	0.940331	−	0.340260i
$442$	−1.18768e13			−0.0334869
$443$	6.78562e13	+	3.91768e13i	0.188960	+	0.109096i	0.591495	−	0.806308i	$-0.298538\pi$
$443$	6.78562e13	+	3.91768e13i	0.188960	+	0.109096i	−0.402536	+	0.915404i	$0.631871\pi$
$444$	−5.99714e13	−	1.25675e13i	−0.164945	−	0.0345656i
$445$	−2.34241e14	−	4.05717e14i	−0.636329	−	1.10215i
$446$	−1.42159e14	+	2.46226e14i	−0.381445	+	0.660683i
$447$	−1.62336e14	−	1.45326e14i	−0.430252	−	0.385170i
$448$	4.43373e13	−	1.77174e13i	0.116075	−	0.0463844i
$449$			5.21675e14i			1.34910i	0.738227	+	0.674552i	$0.235663\pi$
$449$			5.21675e14i			1.34910i	−0.738227	+	0.674552i	$0.764337\pi$
$450$	2.45452e14	−	5.59922e14i	0.627043	−	1.43040i
$451$	−5.79164e14	+	3.34380e14i	−1.46161	+	0.843859i
$452$	2.44944e14	−	1.41419e14i	0.610669	−	0.352570i
$453$	8.70661e12	+	2.65368e13i	0.0214442	+	0.0653594i
$454$		−	3.98929e14i		−	0.970709i
$455$	3.10218e14	+	4.48030e13i	0.745768	+	0.107707i
$456$	6.59898e13	−	7.37134e13i	0.156737	−	0.175081i
$457$	−6.82177e12	+	1.18157e13i	−0.0160088	+	0.0277280i	−0.873919	−	0.486072i	$-0.838429\pi$
$457$	−6.82177e12	+	1.18157e13i	−0.0160088	+	0.0277280i	0.857910	+	0.513800i	$0.171763\pi$
$458$	−2.79756e12	−	4.84552e12i	−0.00648664	−	0.0112352i
$459$	4.71561e12	−	4.89138e13i	0.0108036	−	0.112063i
$460$	−1.05228e14	−	6.07535e13i	−0.238212	−	0.137532i
$461$	−7.83162e14			−1.75185			−0.875924	−	0.482449i	$-0.839747\pi$
$461$	−7.83162e14			−1.75185			−0.875924	+	0.482449i	$0.839747\pi$
$462$	−2.96339e14	+	5.19666e13i	−0.655026	+	0.114867i
$463$	−4.16047e14			−0.908756			−0.454378	−	0.890809i	$-0.650138\pi$
$463$	−4.16047e14			−0.908756			−0.454378	+	0.890809i	$0.650138\pi$
$464$	1.16946e14	+	6.75187e13i	0.252427	+	0.145739i
$465$	−2.04011e14	+	9.73529e14i	−0.435174	+	2.07662i
$466$	8.84856e13	+	1.53262e14i	0.186531	+	0.323081i
$467$	2.06714e14	−	3.58039e14i	0.430653	−	0.745912i	−0.566277	−	0.824215i	$-0.691617\pi$
$467$	2.06714e14	−	3.58039e14i	0.430653	−	0.745912i	0.996930	+	0.0783027i	$0.0249501\pi$
$468$	−1.01528e14	+	1.12606e13i	−0.209043	+	0.0231852i
$469$	−2.71709e14	−	2.13953e14i	−0.552909	−	0.435379i
$470$		−	6.68765e14i		−	1.34504i
$471$	5.01898e14	−	1.64670e14i	0.997701	−	0.327341i
$472$	−1.93020e14	+	1.11440e14i	−0.379247	+	0.218958i
$473$	3.48151e14	−	2.01005e14i	0.676132	−	0.390365i
$474$	−1.22214e13	+	4.00978e12i	−0.0234606	+	0.00769731i
$475$		−	7.73658e14i		−	1.46803i
$476$	4.28979e12	−	2.97027e13i	0.00804633	−	0.0557131i
$477$	1.03696e15	−	1.15011e14i	1.92270	−	0.213249i
$478$	−1.86964e14	+	3.23831e14i	−0.342692	+	0.593560i
$479$	1.26739e14	+	2.19518e14i	0.229649	+	0.397763i	0.957704	−	0.287755i	$-0.0929090\pi$
$479$	1.26739e14	+	2.19518e14i	0.229649	+	0.397763i	−0.728055	+	0.685518i	$0.759576\pi$
$480$	−3.62570e13	+	1.73016e14i	−0.0649478	+	0.309927i
$481$	6.93345e13	+	4.00303e13i	0.122787	+	0.0708909i
$482$	6.42191e13			0.112436
$483$	1.66665e14	+	6.08377e13i	0.288492	+	0.105309i
$484$	−3.37422e13			−0.0577463
$485$	−2.92815e14	−	1.69057e14i	−0.495465	−	0.286057i
$486$	−6.06492e12	−	4.22610e14i	−0.0101467	−	0.707034i
$487$	4.24273e13	+	7.34862e13i	0.0701837	+	0.121562i	0.898982	−	0.437986i	$-0.144308\pi$
$487$	4.24273e13	+	7.34862e13i	0.0701837	+	0.121562i	−0.828798	+	0.559548i	$0.810975\pi$
$488$	1.42903e14	−	2.47516e14i	0.233740	−	0.404850i
$489$	−3.23178e14	+	3.61004e14i	−0.522689	+	0.583866i
$490$	−2.24096e14	+	7.59643e14i	−0.358390	+	1.21487i
$491$			7.84932e14i			1.24132i	0.784080	+	0.620660i	$0.213135\pi$
$491$			7.84932e14i			1.24132i	−0.784080	+	0.620660i	$0.786865\pi$
$492$	−1.78866e14	−	5.45163e14i	−0.279717	−	0.852547i
$493$	7.35062e13	−	4.24388e13i	0.113675	−	0.0656305i
$494$	−1.11951e14	+	6.46347e13i	−0.171210	+	0.0988480i
$495$	4.47215e14	−	1.02018e15i	0.676375	−	1.54294i
$496$		−	1.97976e14i		−	0.296117i
$497$	−2.47919e14	−	6.20409e14i	−0.366733	−	0.917737i
$498$	−1.05343e14	−	9.43053e13i	−0.154115	−	0.137967i
$499$	−1.03883e14	+	1.79930e14i	−0.150311	+	0.260345i	−0.931342	−	0.364147i	$-0.881361\pi$
$499$	−1.03883e14	+	1.79930e14i	−0.150311	+	0.260345i	0.781031	+	0.624492i	$0.214694\pi$
$500$	3.78242e14	+	6.55134e14i	0.541295	+	0.937551i
$501$	8.09570e14	+	1.69652e14i	1.14590	+	0.240133i
$502$	6.52929e13	+	3.76969e13i	0.0914104	+	0.0527758i
$503$	7.31678e14			1.01320			0.506601	−	0.862180i	$-0.330902\pi$
$503$	7.31678e14			1.01320			0.506601	+	0.862180i	$0.330902\pi$
$504$	8.50940e12	−	2.57980e14i	0.0116555	−	0.353361i
$505$	2.22005e14			0.300787
$506$	−1.31975e14	−	7.61957e13i	−0.176874	−	0.102118i
$507$	−6.07631e14	−	1.27334e14i	−0.805556	−	0.168811i
$508$	−3.29968e14	−	5.71521e14i	−0.432734	−	0.749518i
$509$	−1.66437e14	+	2.88277e14i	−0.215925	+	0.373992i	−0.953558	−	0.301209i	$-0.902610\pi$
$509$	−1.66437e14	+	2.88277e14i	−0.215925	+	0.373992i	0.737634	+	0.675201i	$0.235943\pi$
$510$	8.27847e13	+	7.41106e13i	0.106246	+	0.0951139i
$511$	9.11400e14	−	1.15743e15i	1.15716	−	1.46954i
$512$		−	3.51844e13i		−	0.0441942i
$513$	−2.21745e14	−	4.86725e14i	−0.275555	−	0.604837i
$514$	−5.32511e14	+	3.07445e14i	−0.654684	+	0.377982i
$515$	−2.18012e15	+	1.25869e15i	−2.65180	+	1.53102i
$516$	1.07521e14	+	3.27712e14i	0.129396	+	0.394384i
$517$		−	8.38750e14i		−	0.998699i
$518$	−1.25155e14	+	1.58941e14i	−0.147447	+	0.187250i
$519$	−3.89587e14	+	4.35186e14i	−0.454134	+	0.507288i
$520$	1.15486e14	−	2.00028e14i	0.133202	−	0.230713i
$521$	−2.20669e14	−	3.82210e14i	−0.251845	−	0.436209i	0.712189	−	0.701988i	$-0.247704\pi$
$521$	−2.20669e14	−	3.82210e14i	−0.251845	−	0.436209i	−0.964034	+	0.265779i	$0.914371\pi$
$522$	5.88130e14	−	4.32481e14i	0.664180	−	0.488404i
$523$	1.01024e15	+	5.83260e14i	1.12892	+	0.651783i	0.943663	−	0.330907i	$-0.107355\pi$
$523$	1.01024e15	+	5.83260e14i	1.12892	+	0.651783i	0.185257	+	0.982690i	$0.440688\pi$
$524$	6.66999e14			0.737570
$525$	−1.29599e15	−	1.54744e15i	−1.41816	−	1.69331i
$526$	−5.28467e14			−0.572264
$527$	−1.07766e14	−	6.22189e13i	−0.115485	−	0.0666752i
$528$	−4.54727e13	+	2.16993e14i	−0.0482241	+	0.230122i
$529$	−4.31471e14	−	7.47330e14i	−0.452841	−	0.784344i
$530$	−1.17952e15	+	2.04299e15i	−1.22515	+	2.12202i
$531$	1.32824e14	+	1.19757e15i	0.136539	+	1.23107i
$532$	−1.21210e14	−	3.03324e14i	−0.123317	−	0.308598i
$533$			7.49668e14i			0.754865i
$534$	4.78969e14	−	1.57148e14i	0.477342	−	0.156614i
$535$	8.90123e14	−	5.13913e14i	0.878019	−	0.506925i
$536$	−2.20704e14	+	1.27423e14i	−0.215478	+	0.124406i
$537$	9.17860e13	−	3.01146e13i	0.0886989	−	0.0291017i
$538$			3.84790e14i			0.368062i
$539$	−2.81057e14	+	9.52728e14i	−0.266106	+	0.902050i
$540$	7.77950e14	+	5.55043e14i	0.729099	+	0.520189i
$541$	−7.85100e14	+	1.35983e15i	−0.728349	+	1.26154i	0.229231	+	0.973372i	$0.426379\pi$
$541$	−7.85100e14	+	1.35983e15i	−0.728349	+	1.26154i	−0.957580	+	0.288166i	$0.906954\pi$
$542$	−7.99217e13	−	1.38429e14i	−0.0733954	−	0.127125i
$543$	−3.45139e14	+	1.64698e15i	−0.313758	+	1.49723i
$544$	−1.91522e13	−	1.10576e13i	−0.0172356	−	0.00995096i
$545$	2.02485e15			1.80390
$546$	−1.15646e14	+	3.16813e14i	−0.101993	+	0.279411i
$547$	1.36524e15			1.19201			0.596004	−	0.802982i	$-0.296754\pi$
$547$	1.36524e15			1.19201			0.596004	+	0.802982i	$0.296754\pi$
$548$	−1.33230e12	−	7.69203e11i	−0.00115162	−	0.000664887i
$549$	−9.15346e14	−	1.24478e15i	−0.783316	−	1.06523i
$550$	8.66847e14	+	1.50142e15i	0.734425	+	1.27206i
$551$	4.61915e14	−	8.00059e14i	0.387461	−	0.671102i
$552$	8.72046e13	−	9.74113e13i	0.0724226	−	0.0808992i
$553$	−6.07016e12	+	4.20300e13i	−0.00499128	+	0.0345598i
$554$			1.02257e15i			0.832509i
$555$	−2.33495e14	−	7.11668e14i	−0.188220	−	0.573675i
$556$	6.63122e13	−	3.82854e13i	0.0529276	−	0.0305577i
$557$	−1.91258e14	+	1.10423e14i	−0.151152	+	0.0872679i	−0.573669	−	0.819087i	$-0.694480\pi$
$557$	−1.91258e14	+	1.10423e14i	−0.151152	+	0.0872679i	0.422516	+	0.906355i	$0.361147\pi$
$558$	−9.80231e14	−	4.29702e14i	−0.767080	−	0.336263i
$559$		−	4.50646e14i		−	0.349197i
$560$	4.58539e14	+	3.61069e14i	0.351837	+	0.277048i
$561$	1.03827e14	+	9.29478e13i	0.0788884	+	0.0706226i
$562$	−2.90191e14	+	5.02625e14i	−0.218340	+	0.378177i
$563$	−1.03336e15	−	1.78983e15i	−0.769938	−	1.33357i	−0.937596	−	0.347726i	$-0.886954\pi$
$563$	−1.03336e15	−	1.78983e15i	−0.769938	−	1.33357i	0.167658	−	0.985845i	$-0.446379\pi$
$564$	7.04298e14	+	1.47592e14i	0.519662	+	0.108900i
$565$	2.99411e15	+	1.72865e15i	2.18777	+	1.26311i
$566$	−1.01508e15			−0.734531
$567$	−1.25886e15	−	6.02072e14i	−0.902132	−	0.431461i
$568$	−4.92333e14			−0.349416
$569$	1.87412e15	+	1.08202e15i	1.31728	+	0.760533i	0.983291	−	0.182043i	$-0.0582709\pi$
$569$	1.87412e15	+	1.08202e15i	1.31728	+	0.760533i	0.333992	+	0.942576i	$0.391604\pi$
$570$	1.18365e15	+	2.48044e14i	0.823970	+	0.172670i
$571$	1.31105e14	+	2.27081e14i	0.0903901	+	0.156560i	0.907675	−	0.419673i	$-0.137855\pi$
$571$	1.31105e14	+	2.27081e14i	0.0903901	+	0.156560i	−0.817285	+	0.576233i	$0.804522\pi$
$572$	1.44840e14	−	2.50871e14i	0.0989033	−	0.171306i
$573$	7.36024e14	+	6.58904e14i	0.497785	+	0.445627i
$574$	−1.87485e15	−	2.70774e14i	−1.25589	−	0.181381i
$575$		−	1.02238e15i		−	0.678326i
$576$	−1.74207e14	−	7.63667e13i	−0.114483	−	0.0501858i
$577$	1.72763e15	−	9.97446e14i	1.12456	−	0.649265i	0.181999	−	0.983299i	$-0.441743\pi$
$577$	1.72763e15	−	9.97446e14i	1.12456	−	0.649265i	0.942561	+	0.334033i	$0.108410\pi$
$578$	9.37733e14	−	5.41400e14i	0.604611	−	0.349072i
$579$	8.43769e14	+	2.57172e15i	0.538879	+	1.64244i
$580$			1.65065e15i			1.04424i
$581$	−4.33477e14	+	1.73220e14i	−0.271642	+	0.108550i
$582$	2.42661e14	−	2.71063e14i	0.150634	−	0.168265i
$583$	−1.47933e15	+	2.56227e15i	−0.909678	+	1.57561i
$584$	−5.42801e14	−	9.40158e14i	−0.330651	−	0.572704i
$585$	−7.39730e14	−	1.00596e15i	−0.446391	−	0.607047i
$586$	−1.63660e15	−	9.44890e14i	−0.978374	−	0.564864i
$587$	8.14518e14			0.482382			0.241191	−	0.970478i	$-0.422462\pi$
$587$	8.14518e14			0.482382			0.241191	+	0.970478i	$0.422462\pi$
$588$	−7.50549e14	−	4.03651e14i	−0.440356	−	0.236827i
$589$	−1.35441e15			−0.787257
$590$	−2.35941e15	−	1.36221e15i	−1.35868	−	0.784436i
$591$	2.44731e13	−	1.16784e14i	0.0139623	−	0.0666272i
$592$	7.45384e13	+	1.29104e14i	0.0421319	+	0.0729745i
$593$	−9.34195e14	+	1.61807e15i	−0.523162	+	0.906144i	0.476474	+	0.879188i	$0.341915\pi$
$593$	−9.34195e14	+	1.61807e15i	−0.523162	+	0.906144i	−0.999637	+	0.0269554i	$0.991419\pi$
$594$	9.75688e14	+	6.96123e14i	0.541359	+	0.386243i
$595$	3.40651e14	−	1.36126e14i	0.187269	−	0.0748338i
$596$			5.30096e14i			0.288735i
$597$	−4.86339e14	+	1.59566e14i	−0.262470	+	0.0861153i
$598$	−1.47941e14	+	8.54139e13i	−0.0791102	+	0.0456743i
$599$	−9.88456e14	+	5.70685e14i	−0.523733	+	0.302377i	−0.738461	−	0.674297i	$-0.764447\pi$
$599$	−9.88456e14	+	5.70685e14i	−0.523733	+	0.302377i	0.214728	+	0.976674i	$0.431114\pi$
$600$	−1.41328e15	+	4.63691e14i	−0.741987	+	0.243443i
$601$		−	2.12879e15i		−	1.10745i	−0.832701	−	0.553723i	$-0.813206\pi$
$601$		−	2.12879e15i		−	1.10745i	0.832701	−	0.553723i	$-0.186794\pi$
$602$	1.12702e15	+	1.62770e14i	0.580968	+	0.0839060i
$603$	1.51874e14	+	1.36933e15i	0.0775780	+	0.699460i
$604$	3.39744e13	−	5.88454e13i	0.0171969	−	0.0297858i
$605$	−2.06227e14	−	3.57196e14i	−0.103441	−	0.179164i
$606$	−4.89949e13	+	2.33800e14i	−0.0243529	+	0.116211i
$607$	−2.18703e15	−	1.26268e15i	−1.07725	−	0.621951i	−0.147098	−	0.989122i	$-0.546993\pi$
$607$	−2.18703e15	−	1.26268e15i	−1.07725	−	0.621951i	−0.930154	+	0.367171i	$0.880326\pi$
$608$	−2.40706e14			−0.117495
$609$	−4.16312e14	−	2.37401e15i	−0.201383	−	1.14839i
$610$	3.49360e15			1.67479
$611$	−8.14256e14	−	4.70111e14i	−0.386843	−	0.223344i
$612$	−9.63182e13	+	7.08276e13i	−0.0453498	+	0.0333480i
$613$	−1.91486e15	−	3.31664e15i	−0.893521	−	1.54762i	−0.835624	−	0.549301i	$-0.814894\pi$
$613$	−1.91486e15	−	3.31664e15i	−0.893521	−	1.54762i	−0.0578966	−	0.998323i	$-0.518439\pi$
$614$	9.25540e14	−	1.60308e15i	0.428025	−	0.741361i
$615$	4.67790e15	−	5.22542e15i	2.14406	−	2.39501i
$616$	5.75089e14	+	4.52844e14i	0.261241	+	0.205710i
$617$			1.14687e15i			0.516354i	0.966098	+	0.258177i	$0.0831217\pi$
$617$			1.14687e15i			0.516354i	−0.966098	+	0.258177i	$0.916878\pi$
$618$	−8.44432e14	−	2.57374e15i	−0.376815	−	1.14849i
$619$	−1.41022e15	+	8.14191e14i	−0.623718	+	0.360104i	−0.778315	−	0.627874i	$-0.783925\pi$
$619$	−1.41022e15	+	8.14191e14i	−0.623718	+	0.360104i	0.154597	+	0.987978i	$0.450592\pi$
$620$	2.09578e15	−	1.21000e15i	0.918736	−	0.530433i
$621$	−2.93033e14	−	6.43201e14i	−0.127325	−	0.279475i
$622$		−	2.44166e15i		−	1.05157i
$623$	2.37896e14	−	1.64720e15i	0.101555	−	0.703174i
$624$	1.85169e14	+	1.65767e14i	0.0783525	+	0.0701427i
$625$	−1.99049e15	+	3.44763e15i	−0.834872	+	1.44604i
$626$	−6.97123e13	−	1.20745e14i	−0.0289835	−	0.0502008i
$627$	1.48451e15	+	3.11091e14i	0.611802	+	0.128208i
$628$	−1.11296e15	−	6.42568e14i	−0.454675	−	0.262507i
$629$	9.37021e13			0.0379464
$630$	2.78299e15	−	1.48665e15i	1.11722	−	0.596811i
$631$	7.71425e14			0.306996			0.153498	−	0.988149i	$-0.450946\pi$
$631$	7.71425e14			0.306996			0.153498	+	0.988149i	$0.450946\pi$
$632$	2.71009e13	+	1.56467e13i	0.0106915	+	0.00617276i
$633$	2.84185e15	+	5.95534e14i	1.11143	+	0.232909i
$634$	6.19992e14	+	1.07386e15i	0.240378	+	0.416347i
$635$	4.03342e15	−	6.98609e15i	1.55031	−	2.68521i
$636$	−1.89123e15	−	1.69306e15i	−0.720658	−	0.645148i
$637$	7.67377e14	+	8.06844e14i	0.289896	+	0.304805i
$638$			2.07021e15i			0.775356i
$639$	−1.06860e15	+	2.43767e15i	−0.396788	+	0.905148i
$640$	3.72462e14	−	2.15041e14i	0.137117	−	0.0791647i
$641$	−1.56856e15	+	9.05610e14i	−0.572510	+	0.330539i	−0.758151	−	0.652079i	$-0.773897\pi$
$641$	−1.56856e15	+	9.05610e14i	−0.572510	+	0.330539i	0.185641	+	0.982618i	$0.440564\pi$
$642$	3.44774e14	+	1.05083e15i	0.124765	+	0.380270i
$643$		−	3.36872e15i		−	1.20866i	−0.796734	−	0.604331i	$-0.793441\pi$
$643$		−	3.36872e15i		−	1.20866i	0.796734	−	0.604331i	$-0.206559\pi$
$644$	−1.60177e14	−	4.00838e14i	−0.0569808	−	0.142593i
$645$	−2.81201e15	+	3.14114e15i	−0.991834	+	1.10792i
$646$	−7.56479e13	+	1.31026e14i	−0.0264556	+	0.0458225i
$647$	−1.62584e15	−	2.81604e15i	−0.563773	−	0.976484i	−0.997163	−	0.0752770i	$-0.976016\pi$
$647$	−1.62584e15	−	2.81604e15i	−0.563773	−	0.976484i	0.433390	−	0.901207i	$-0.357317\pi$
$648$	−7.56223e14	+	6.96791e14i	−0.260008	+	0.239574i
$649$	−2.95913e15	−	1.70845e15i	−1.00883	−	0.582448i
$650$	1.94344e15			0.656972
$651$	−2.70903e15	+	2.26883e15i	−0.908069	+	0.760513i
$652$	1.17883e15			0.391824
$653$	−1.35242e14	−	7.80819e13i	−0.0445747	−	0.0257352i	0.477547	−	0.878606i	$-0.341526\pi$
$653$	−1.35242e14	−	7.80819e13i	−0.0445747	−	0.0257352i	−0.522122	+	0.852871i	$0.674859\pi$
$654$	−4.46871e14	+	2.13244e15i	−0.146051	+	0.696945i
$655$	4.07658e15	+	7.06085e15i	1.32120	+	2.28839i
$656$	−6.97959e14	+	1.20890e15i	−0.224315	+	0.388526i
$657$	−5.83310e15	+	6.46956e14i	−1.85904	+	0.206189i
$658$	1.46981e15	−	1.86658e15i	0.464535	−	0.589935i
$659$			1.22672e15i			0.384483i	0.981348	+	0.192241i	$0.0615757\pi$
$659$			1.22672e15i			0.384483i	−0.981348	+	0.192241i	$0.938424\pi$
$660$	−2.57500e15	+	8.44848e14i	−0.800362	+	0.262595i
$661$	−1.23609e15	+	7.13655e14i	−0.381014	+	0.219979i	−0.678259	−	0.734823i	$-0.737265\pi$
$661$	−1.23609e15	+	7.13655e14i	−0.381014	+	0.219979i	0.297245	+	0.954801i	$0.403932\pi$
$662$	3.30325e15	−	1.90713e15i	1.00977	−	0.582991i
$663$	1.48427e14	−	4.86984e13i	0.0449976	−	0.0147635i
$664$			3.43991e14i			0.103424i
$665$	2.47017e15	−	3.13699e15i	0.736560	−	0.935394i
$666$	8.01012e14	−	8.88412e13i	0.236881	−	0.0262728i
$667$	6.10414e14	−	1.05727e15i	0.179033	−	0.310094i
$668$	−1.00621e15	−	1.74281e15i	−0.292698	−	0.506967i
$669$	7.66998e14	−	3.66006e15i	0.221284	−	1.05595i
$670$	−2.69781e15	−	1.55758e15i	−0.771969	−	0.445696i
$671$	4.38160e15			1.24354
$672$	−4.81450e14	+	4.03217e14i	−0.135525	+	0.113503i
$673$	−3.73740e14			−0.104349			−0.0521743	−	0.998638i	$-0.516615\pi$
$673$	−3.73740e14			−0.104349			−0.0521743	+	0.998638i	$0.516615\pi$
$674$	−1.85901e15	−	1.07330e15i	−0.514818	−	0.297230i
$675$	−7.71633e14	+	8.00394e15i	−0.211953	+	2.19853i
$676$	7.55223e14	+	1.30808e15i	0.205764	+	0.356393i
$677$	−2.02924e15	+	3.51474e15i	−0.548397	+	0.949851i	0.449988	+	0.893035i	$0.351428\pi$
$677$	−2.02924e15	+	3.51474e15i	−0.548397	+	0.949851i	−0.998385	+	0.0568162i	$0.981905\pi$
$678$	−2.48128e15	+	2.77170e15i	−0.665139	+	0.742989i
$679$	−4.45720e14	−	1.11540e15i	−0.118516	−	0.296583i
$680$		−	2.70328e14i		−	0.0713003i
$681$	1.63573e15	+	4.98554e15i	0.427961	+	1.30438i
$682$	2.62848e15	−	1.51755e15i	0.682166	−	0.393849i
$683$	−1.38633e15	+	8.00399e14i	−0.356906	+	0.206060i	−0.667723	−	0.744410i	$-0.732731\pi$
$683$	−1.38633e15	+	8.00399e14i	−0.356906	+	0.206060i	0.310817	+	0.950470i	$0.399397\pi$
$684$	−5.22446e14	+	1.19180e15i	−0.133424	+	0.304365i
$685$		−	1.88050e13i		−	0.00476403i
$686$	−2.29501e15	+	1.62771e15i	−0.576770	+	0.409068i
$687$	5.48301e13	+	4.90850e13i	0.0136696	+	0.0122373i
$688$	4.19563e14	−	7.26704e14i	0.103767	−	0.179730i
$689$	1.65830e15	+	2.87226e15i	0.406871	+	0.704722i
$690$	1.56418e15	+	3.27787e14i	0.380729	+	0.0797850i
$691$	2.03451e15	+	1.17463e15i	0.491282	+	0.283642i	0.725106	−	0.688637i	$-0.241791\pi$
$691$	2.03451e15	+	1.17463e15i	0.491282	+	0.283642i	−0.233824	+	0.972279i	$0.575124\pi$
$692$	1.42107e15			0.340433
$693$	3.49036e15	−	1.86453e15i	0.829541	−	0.443135i
$694$	1.53490e15			0.361912
$695$	8.10578e14	+	4.67987e14i	0.189617	+	0.109476i
$696$	−1.73836e15	−	3.64287e14i	−0.403448	−	0.0845461i
$697$	4.38702e14	+	7.59854e14i	0.101016	+	0.174964i
$698$	−1.26239e15	+	2.18653e15i	−0.288396	+	0.499516i
$699$	−1.73425e15	−	1.55254e15i	−0.393086	−	0.351899i
$700$	−7.01954e14	+	4.86036e15i	−0.157859	+	1.09302i
$701$		−	1.68670e15i		−	0.376348i	−0.982136	−	0.188174i	$-0.939743\pi$
$701$		−	1.68670e15i		−	0.376348i	0.982136	−	0.188174i	$-0.0602568\pi$
$702$	1.22266e15	−	5.57026e14i	0.270677	−	0.123316i
$703$	8.83239e14	−	5.09938e14i	0.194010	−	0.112012i
$704$	4.67133e14	−	2.69700e14i	0.101810	−	0.0587802i
$705$	2.74214e15	+	8.35775e15i	0.592994	+	1.80738i
$706$			4.17606e14i			0.0896068i
$707$	6.19634e14	+	4.87921e14i	0.131926	+	0.103883i
$708$	1.95529e15	−	2.18415e15i	0.413075	−	0.461423i
$709$	1.73718e15	−	3.00889e15i	0.364159	−	0.630742i	−0.624482	−	0.781039i	$-0.714690\pi$
$709$	1.73718e15	−	3.00889e15i	0.364159	−	0.630742i	0.988641	+	0.150298i	$0.0480232\pi$
$710$	−3.00906e15	−	5.21184e15i	−0.625907	−	1.08410i
$711$	1.36293e14	−	1.00223e14i	0.0281313	−	0.0206863i
$712$	−1.06211e15	−	6.13212e14i	−0.217536	−	0.125595i
$713$	−1.78984e15			−0.363765
$714$	6.81794e13	+	3.88793e14i	0.0137503	+	0.0784112i
$715$	3.54096e15			0.708659
$716$	−2.03536e14	−	1.17512e14i	−0.0404221	−	0.0233377i
$717$	1.00874e15	−	4.81362e15i	0.198803	−	0.948673i
$718$	7.23829e14	+	1.25371e15i	0.141564	+	0.245195i
$719$	2.28021e15	−	3.94944e15i	0.442554	−	0.766526i	−0.555324	−	0.831634i	$-0.687406\pi$
$719$	2.28021e15	−	3.94944e15i	0.442554	−	0.766526i	0.997878	+	0.0651081i	$0.0207392\pi$
$720$	−2.56304e14	−	2.31089e15i	−0.0493659	−	0.445094i
$721$	−8.85125e15	−	1.27833e15i	−1.69184	−	0.244343i
$722$		−	2.08095e15i		−	0.394736i
$723$	−8.02566e14	+	2.63318e14i	−0.151085	+	0.0495702i
$724$	3.54556e15	−	2.04703e15i	0.662404	−	0.382439i
$725$	−1.20281e16	+	6.94442e15i	−2.23017	+	1.28759i
$726$	4.21687e14	−	1.38354e14i	0.0775959	−	0.0254589i
$727$			8.66288e15i			1.58206i	0.611777	+	0.791030i	$0.290455\pi$
$727$			8.66288e15i			1.58206i	−0.611777	+	0.791030i	$0.709545\pi$
$728$	7.61952e14	−	3.04480e14i	0.138104	−	0.0551870i
$729$	1.80863e15	+	5.25662e15i	0.325348	+	0.945594i
$730$	6.63501e15	−	1.14922e16i	1.18458	−	2.05176i
$731$	−2.63716e14	−	4.56769e14i	−0.0467294	−	0.0809377i
$732$	−7.71014e14	+	3.67923e15i	−0.135597	+	0.647061i
$733$	−5.10594e15	−	2.94791e15i	−0.891258	−	0.514568i	−0.0169043	−	0.999857i	$-0.505381\pi$
$733$	−5.10594e15	−	2.94791e15i	−0.891258	−	0.514568i	−0.874354	+	0.485289i	$0.838714\pi$
$734$	4.83039e15			0.836863
$735$	−3.14176e14	−	1.04124e16i	−0.0540248	−	1.79048i
$736$	−3.18090e14			−0.0542902
$737$	−3.38353e15	−	1.95348e15i	−0.573191	−	0.330932i
$738$	4.47068e15	+	6.07966e15i	0.751732	+	1.02228i
$739$	−4.01666e15	−	6.95706e15i	−0.670379	−	1.16113i	−0.977797	−	0.209556i	$-0.932798\pi$
$739$	−4.01666e15	−	6.95706e15i	−0.670379	−	1.16113i	0.307418	−	0.951575i	$-0.400535\pi$
$740$	−9.11132e14	+	1.57813e15i	−0.150941	+	0.261437i
$741$	1.13406e15	−	1.26679e15i	0.186481	−	0.208308i
$742$	−7.78222e15	+	3.10982e15i	−1.27023	+	0.507590i
$743$			8.49682e15i			1.37663i	0.725411	+	0.688316i	$0.241650\pi$
$743$			8.49682e15i			1.37663i	−0.725411	+	0.688316i	$0.758350\pi$
$744$	8.11764e14	+	2.47417e15i	0.130551	+	0.397904i
$745$	−5.61160e15	+	3.23986e15i	−0.895833	+	0.517209i
$746$	−4.59843e15	+	2.65491e15i	−0.728696	+	0.420713i
$747$	1.70319e15	+	7.46622e14i	0.267916	+	0.117446i
$748$		−	3.39039e14i		−	0.0529408i
$749$	3.61389e15	+	5.21933e14i	0.560176	+	0.0809030i
$750$	−7.41325e15	−	6.63649e15i	−1.14070	−	1.02118i
$751$	−3.42821e15	+	5.93784e15i	−0.523658	+	0.907003i	0.475962	+	0.879466i	$0.342100\pi$
$751$	−3.42821e15	+	5.93784e15i	−0.523658	+	0.907003i	−0.999621	+	0.0275373i	$0.991234\pi$
$752$	−8.75370e14	−	1.51619e15i	−0.132738	−	0.229908i
$753$	−9.70554e14	−	2.03388e14i	−0.146099	−	0.0306163i
$754$	2.00976e15	+	1.16033e15i	0.300332	+	0.173397i
$755$	8.30584e14			0.123218
$756$	9.51456e14	+	3.25895e15i	0.140126	+	0.479963i
$757$	−2.23307e15			−0.326495			−0.163247	−	0.986585i	$-0.552197\pi$
$757$	−2.23307e15			−0.326495			−0.163247	+	0.986585i	$0.552197\pi$
$758$	−1.23453e14	−	7.12758e13i	−0.0179194	−	0.0103457i
$759$	1.96175e15	+	4.11103e14i	0.282693	+	0.0592408i
$760$	−1.47116e15	−	2.54812e15i	−0.210467	−	0.364539i
$761$	3.83893e15	−	6.64922e15i	0.545249	−	0.944399i	−0.453342	−	0.891336i	$-0.649769\pi$
$761$	3.83893e15	−	6.64922e15i	0.545249	−	0.944399i	0.998591	−	0.0530621i	$-0.0168981\pi$
$762$	6.46713e15	+	5.78950e15i	0.911925	+	0.816374i
$763$	5.65154e15	+	4.45021e15i	0.791192	+	0.623011i
$764$		−	2.40344e15i		−	0.334056i
$765$	−1.33846e15	−	5.86739e14i	−0.184700	−	0.0809668i
$766$	−3.94655e15	+	2.27854e15i	−0.540704	+	0.312176i
$767$	−3.31712e15	+	1.91514e15i	−0.451219	+	0.260511i
$768$	1.44267e14	+	4.39710e14i	0.0194841	+	0.0593854i
$769$		−	1.28901e15i		−	0.172846i	−0.996259	−	0.0864232i	$-0.972456\pi$
$769$		−	1.28901e15i		−	0.172846i	0.996259	−	0.0864232i	$-0.0275437\pi$
$770$	−1.27896e15	+	8.85561e15i	−0.170278	+	1.17901i
$771$	5.39433e15	−	6.02570e15i	0.713080	−	0.796541i
$772$	3.29251e15	−	5.70279e15i	0.432147	−	0.748500i
$773$	−1.18145e15	−	2.04632e15i	−0.153967	−	0.266678i	0.778716	−	0.627377i	$-0.215872\pi$
$773$	−1.18145e15	−	2.04632e15i	−0.153967	−	0.266678i	−0.932682	+	0.360699i	$0.882538\pi$
$774$	−2.68745e15	−	3.65465e15i	−0.347748	−	0.472902i
$775$	1.76342e16	+	1.01811e16i	2.26567	+	1.30808i
$776$	−8.85138e14			−0.112920
$777$	9.12396e14	−	2.49950e15i	0.115576	−	0.316620i
$778$	3.85102e15			0.484382
$779$	8.27043e15	+	4.77494e15i	1.03293	+	0.596364i
$780$	−6.23089e14	+	2.97334e15i	−0.0772733	+	0.368743i
$781$	−3.77389e15	−	6.53657e15i	−0.464739	−	0.804951i
$782$	−9.99676e13	+	1.73149e14i	−0.0122242	+	0.0211730i
$783$	−5.57673e15	+	7.81637e15i	−0.677158	+	0.949107i
$784$	4.86267e14	+	2.01555e15i	0.0586322	+	0.243027i
$785$		−	1.57091e16i		−	1.88091i
$786$	−8.33569e15	+	2.73490e15i	−0.991100	+	0.325176i
$787$	−1.27557e15	+	7.36452e14i	−0.150607	+	0.0869527i	−0.573409	−	0.819269i	$-0.694380\pi$
$787$	−1.27557e15	+	7.36452e14i	−0.150607	+	0.0869527i	0.422803	+	0.906222i	$0.361046\pi$
$788$	−2.51408e14	+	1.45150e14i	−0.0294771	+	0.0170186i
$789$	6.60442e15	−	2.16688e15i	0.768973	−	0.252297i
$790$			3.82520e14i			0.0442288i
$791$	4.55761e15	+	1.14053e16i	0.523319	+	1.30959i
$792$	−3.21451e14	−	2.89827e15i	−0.0366544	−	0.330484i
$793$	2.45584e15	−	4.25365e15i	0.278098	−	0.481680i
$794$	9.65179e13	+	1.67174e14i	0.0108541	+	0.0187999i
$795$	6.36393e15	−	3.03683e16i	0.710733	−	3.39157i
$796$	1.07846e15	+	6.22648e14i	0.119614	+	0.0690591i
$797$	−6.99029e15			−0.769971			−0.384985	−	0.922923i	$-0.625794\pi$
$797$	−6.99029e15			−0.769971			−0.384985	+	0.922923i	$0.625794\pi$
$798$	2.75852e15	+	3.29373e15i	0.301759	+	0.360307i
$799$	−1.10043e15			−0.119551
$800$	3.13395e15	+	1.80939e15i	0.338141	+	0.195226i
$801$	−5.34146e15	+	3.92784e15i	−0.572376	+	0.420896i
$802$	3.95663e15	+	6.85308e15i	0.421081	+	0.729334i
$803$	8.32149e15	−	1.44132e16i	0.879560	−	1.52344i
$804$	2.23573e15	−	2.49740e15i	0.234698	−	0.262168i
$805$	3.26430e15	−	4.14549e15i	0.340340	−	0.432214i
$806$		−	3.40229e15i		−	0.352313i
$807$	−1.57776e15	−	4.80884e15i	−0.162269	−	0.494579i
$808$	5.03317e14	−	2.90590e14i	0.0514137	−	0.0296837i
$809$	−1.20713e15	+	6.96935e14i	−0.122472	+	0.0707092i	−0.559984	−	0.828503i	$-0.689193\pi$
$809$	−1.20713e15	+	6.96935e14i	−0.122472	+	0.0707092i	0.437513	+	0.899212i	$0.355860\pi$
$810$	−1.19981e16	−	3.74671e15i	−1.20905	−	0.377557i
$811$			8.96106e15i			0.896901i	0.893808	+	0.448451i	$0.148024\pi$
$811$			8.96106e15i			0.896901i	−0.893808	+	0.448451i	$0.851976\pi$
$812$	−3.62780e15	+	4.60711e15i	−0.360649	+	0.458006i
$813$	1.56641e15	+	1.40228e15i	0.154670	+	0.138464i
$814$	−1.14272e15	+	1.97925e15i	−0.112074	+	0.194118i
$815$	7.20483e15	+	1.24791e16i	0.701871	+	1.21568i
$816$	2.84691e14	+	5.96594e13i	0.0275472	+	0.00577276i
$817$	−4.97158e15	−	2.87035e15i	−0.477830	−	0.275875i
$818$	6.53392e15			0.623779
$819$	1.46237e14	−	4.43349e15i	0.0138674	−	0.420421i
$820$	−1.70632e16			−1.60726
$821$	1.11603e16	+	6.44339e15i	1.04421	+	0.602875i	0.921023	−	0.389509i	$-0.127355\pi$
$821$	1.11603e16	+	6.44339e15i	1.04421	+	0.602875i	0.123187	+	0.992383i	$0.460689\pi$
$822$	1.98041e13	+	4.15012e12i	0.00184060	+	0.000385715i
$823$	−7.49448e14	−	1.29808e15i	−0.0691899	−	0.119840i	0.829355	−	0.558722i	$-0.188708\pi$
$823$	−7.49448e14	−	1.29808e15i	−0.0691899	−	0.119840i	−0.898545	+	0.438882i	$0.855375\pi$
$824$	−3.29509e15	+	5.70727e15i	−0.302182	+	0.523394i
$825$	−1.69895e16	−	1.52094e16i	−1.54769	−	1.38553i
$826$	−3.59148e15	−	8.98756e15i	−0.325000	−	0.813301i
$827$		−	9.78197e15i		−	0.879318i	−0.898165	−	0.439659i	$-0.855099\pi$
$827$		−	9.78197e15i		−	0.879318i	0.898165	−	0.439659i	$-0.144901\pi$
$828$	−6.90406e14	+	1.57494e15i	−0.0616506	+	0.140637i
$829$	−7.48383e15	+	4.32079e15i	−0.663856	+	0.383277i	−0.793745	−	0.608251i	$-0.791871\pi$
$829$	−7.48383e15	+	4.32079e15i	−0.663856	+	0.383277i	0.129889	+	0.991529i	$0.458538\pi$
$830$	−3.64148e15	+	2.10241e15i	−0.320885	+	0.185263i
$831$	−4.19285e15	−	1.27794e16i	−0.367032	−	1.11867i
$832$		−	6.04656e14i		−	0.0525812i
$833$	1.24996e15	+	3.68742e14i	0.107982	+	0.0318548i
$834$	−6.71741e14	+	7.50364e14i	−0.0576486	+	0.0643960i
$835$	1.22996e16	−	2.13035e16i	1.04861	−	1.81625i
$836$	−1.84509e15	−	3.19579e15i	−0.156273	−	0.270672i
$837$	1.40122e16	+	1.35087e15i	1.17900	+	0.113664i
$838$	2.32188e15	+	1.34054e15i	0.194088	+	0.112057i
$839$	−1.01251e16			−0.840831			−0.420416	−	0.907332i	$-0.638116\pi$
$839$	−1.01251e16			−0.840831			−0.420416	+	0.907332i	$0.638116\pi$
$840$	−7.21099e15	−	2.63223e15i	−0.594921	−	0.217164i
$841$	−4.38422e15			−0.359348
$842$	1.09955e16	+	6.34827e15i	0.895364	+	0.516938i
$843$	1.56568e15	−	7.47134e15i	0.126664	−	0.604431i
$844$	−3.53213e15	−	6.11782e15i	−0.283892	−	0.491715i
$845$	−9.23159e15	+	1.59896e16i	−0.737165	+	1.27681i
$846$	−9.40699e15	+	1.04334e15i	−0.746301	+	0.0827731i
$847$	2.09445e14	−	1.45021e15i	0.0165087	−	0.114307i
$848$			6.17567e15i			0.483623i
$849$	1.26858e16	−	4.16214e15i	0.987016	−	0.323836i
$850$	1.96984e15	−	1.13729e15i	0.152275	−	0.0879158i
$851$	1.16719e15	−	6.73876e14i	0.0896454	−	0.0517568i
$852$	6.15284e15	−	2.01872e15i	0.469524	−	0.154049i
$853$			1.24721e16i			0.945627i	0.881163	+	0.472813i	$0.156762\pi$
$853$			1.24721e16i			0.945627i	−0.881163	+	0.472813i	$0.843238\pi$
$854$	9.75095e15	+	7.67822e15i	0.734562	+	0.578419i
$855$	−1.58095e16	+	1.75345e15i	−1.18332	+	0.131244i
$856$	1.34536e15	−	2.33023e15i	0.100053	−	0.173298i
$857$	−7.85377e15	−	1.36031e16i	−0.580342	−	1.00518i	−0.995439	−	0.0954043i	$-0.969586\pi$
$857$	−7.85377e15	−	1.36031e16i	−0.580342	−	1.00518i	0.415097	−	0.909777i	$-0.363748\pi$
$858$	−7.81464e14	+	3.72909e15i	−0.0573758	+	0.273794i
$859$	5.05801e15	+	2.92024e15i	0.368992	+	0.213038i	0.673018	−	0.739626i	$-0.264998\pi$
$859$	5.05801e15	+	2.92024e15i	0.368992	+	0.213038i	−0.304026	+	0.952664i	$0.598331\pi$
$860$	1.02572e16			0.743510
$861$	2.45408e16	−	4.30353e15i	1.76755	−	0.309961i
$862$	2.71328e15			0.194180
$863$	−1.99363e16	−	1.15102e16i	−1.41770	−	0.818510i	−0.421604	−	0.906780i	$-0.638533\pi$
$863$	−1.99363e16	−	1.15102e16i	−1.41770	−	0.818510i	−0.996097	+	0.0882703i	$0.971866\pi$
$864$	2.49024e15	+	2.40076e14i	0.175961	+	0.0169638i
$865$	8.68534e15	+	1.50434e16i	0.609815	+	1.05623i
$866$	−4.91767e15	+	8.51765e15i	−0.343092	+	0.594253i
$867$	−9.49922e15	+	1.06110e16i	−0.658541	+	0.735619i
$868$	8.50883e15	+	1.22888e15i	0.586153	+	0.0846548i
$869$			4.79749e14i			0.0328401i
$870$	−6.76819e15	−	2.06287e16i	−0.460380	−	1.40319i
$871$	−3.79287e15	+	2.18982e15i	−0.256371	+	0.148016i
$872$	4.59063e15	−	2.65040e15i	0.308341	−	0.178021i
$873$	−1.92117e15	+	4.38254e15i	−0.128229	+	0.292515i
$874$			2.17614e15i			0.144336i
$875$	−3.05048e16	+	1.21899e16i	−2.01059	+	0.803444i
$876$	1.06385e16	+	9.52379e15i	0.696798	+	0.623788i
$877$	−6.81149e15	+	1.17978e16i	−0.443347	+	0.767900i	−0.997935	−	0.0642247i	$-0.979543\pi$
$877$	−6.81149e15	+	1.17978e16i	−0.443347	+	0.767900i	0.554588	+	0.832125i	$0.312876\pi$
$878$	−4.19757e15	−	7.27040e15i	−0.271505	−	0.470260i
$879$	2.43274e16	+	5.09802e15i	1.56371	+	0.327689i
$880$	5.71008e15	+	3.29672e15i	0.364744	+	0.210585i
$881$	−1.84948e15			−0.117404			−0.0587018	−	0.998276i	$-0.518696\pi$
$881$	−1.84948e15			−0.117404			−0.0587018	+	0.998276i	$0.518696\pi$
$882$	1.10349e16	+	1.96707e15i	0.696133	+	0.124091i
$883$	−2.58256e16			−1.61908			−0.809538	−	0.587068i	$-0.800282\pi$
$883$	−2.58256e16			−1.61908			−0.809538	+	0.587068i	$0.800282\pi$
$884$	−3.29138e14	−	1.90028e14i	−0.0205065	−	0.0118394i
$885$	3.50718e16	+	7.34960e15i	2.17155	+	0.455067i
$886$	1.25366e15	+	2.17140e15i	0.0771424	+	0.133615i
$887$	−8.12393e15	+	1.40711e16i	−0.496806	+	0.860492i	−0.999993	−	0.00368469i	$-0.998827\pi$
$887$	−8.12393e15	+	1.40711e16i	−0.496806	+	0.860492i	0.503188	+	0.864177i	$0.332160\pi$
$888$	−1.46090e15	−	1.30782e15i	−0.0887867	−	0.0794837i
$889$	2.66116e16	−	1.06341e16i	1.60735	−	0.642308i
$890$		−	1.49914e16i		−	0.899906i
$891$	−1.50478e16	−	4.69904e15i	−0.897729	−	0.280338i
$892$	−7.87925e15	+	4.54908e15i	−0.467173	+	0.269723i
$893$	−1.03727e16	+	5.98866e15i	−0.611233	+	0.352896i
$894$	−2.17356e15	−	6.62477e15i	−0.127296	−	0.387985i
$895$		−	2.87284e15i		−	0.167219i
$896$	1.51219e15	+	2.18397e14i	0.0874807	+	0.0126343i
$897$	1.49864e15	−	1.67405e15i	0.0861667	−	0.0962519i
$898$	−8.34680e15	+	1.44571e16i	−0.476980	+	0.826154i
$899$	1.21573e16	+	2.10571e16i	0.690493	+	1.19597i
$900$	1.57609e16	−	1.15898e16i	0.889708	−	0.654246i
$901$	3.36166e15	+	1.94086e15i	0.188611	+	0.108895i
$902$	−2.14003e16			−1.19340
$903$	−1.47522e16	+	2.58697e15i	−0.817661	+	0.143387i
$904$	9.05079e15			0.498609
$905$	4.33397e16	+	2.50222e16i	2.37312	+	1.37012i
$906$	−1.83304e14	+	8.74715e14i	−0.00997625	+	0.0476060i
$907$	−8.41397e15	−	1.45734e16i	−0.455157	−	0.788355i	0.543540	−	0.839383i	$-0.317083\pi$
$907$	−8.41397e15	−	1.45734e16i	−0.455157	−	0.788355i	−0.998697	+	0.0510283i	$0.983750\pi$
$908$	6.38287e15	−	1.10555e16i	0.343197	−	0.594435i
$909$	−3.46350e14	−	3.12277e15i	−0.0185103	−	0.166893i
$910$	7.88015e15	+	6.20510e15i	0.418608	+	0.329626i
$911$			5.35338e14i			0.0282668i	0.999900	+	0.0141334i	$0.00449895\pi$
$911$			5.35338e14i			0.0282668i	−0.999900	+	0.0141334i	$0.995501\pi$
$912$	3.00818e15	−	9.86970e14i	0.157882	−	0.0518003i
$913$	−4.56707e15	+	2.63680e15i	−0.238258	+	0.137559i
$914$	−3.78101e14	+	2.18297e14i	−0.0196067	+	0.0113199i
$915$	−4.36606e16	+	1.43249e16i	−2.25047	+	0.738370i
$916$		−	1.79044e14i		−	0.00917349i
$917$	−4.14020e15	+	2.86670e16i	−0.210858	+	1.45999i
$918$	9.13303e14	−	1.28009e15i	0.0462360	−	0.0648045i
$919$	−6.52935e15	+	1.13092e16i	−0.328575	+	0.569109i	−0.982229	−	0.187685i	$-0.939902\pi$
$919$	−6.52935e15	+	1.13092e16i	−0.328575	+	0.569109i	0.653654	+	0.756793i	$0.273235\pi$
$920$	−1.94411e15	−	3.36730e15i	−0.0972497	−	0.168441i
$921$	−4.99361e15	+	2.38292e16i	−0.248306	+	1.18490i
$922$	−2.17036e16	−	1.25306e16i	−1.07278	−	0.619372i
$923$	−8.46092e15			−0.415727
$924$	−9.04387e15	−	3.30129e15i	−0.441731	−	0.161246i
$925$	−1.53328e16			−0.744462
$926$	−1.15298e16	−	6.65676e15i	−0.556497	−	0.321294i
$927$	2.11062e16	+	2.87023e16i	1.01268	+	1.37714i
$928$	2.16060e15	+	3.74227e15i	0.103053	+	0.178493i
$929$	1.64315e16	−	2.84602e16i	0.779096	−	1.34943i	−0.153367	−	0.988169i	$-0.549012\pi$
$929$	1.64315e16	−	2.84602e16i	0.779096	−	1.34943i	0.932463	−	0.361265i	$-0.117655\pi$
$930$	−2.12302e16	+	2.37150e16i	−1.00069	+	1.11781i
$931$	1.37889e16	−	3.32669e15i	0.646112	−	0.155879i
$932$			5.66308e15i			0.263794i
$933$	1.00116e16	+	3.05141e16i	0.463610	+	1.41303i
$934$	1.14573e16	−	6.61485e15i	0.527440	−	0.304517i
$935$	3.58907e15	−	2.07215e15i	0.164255	−	0.0948325i
$936$	−2.99381e15	−	1.31239e15i	−0.136209	−	0.0597098i
$937$			2.54407e15i			0.115070i	0.998344	+	0.0575348i	$0.0183240\pi$
$937$			2.54407e15i			0.115070i	−0.998344	+	0.0575348i	$0.981676\pi$
$938$	−4.10658e15	−	1.02766e16i	−0.184656	−	0.462097i
$939$	1.36631e15	+	1.22315e15i	0.0610784	+	0.0546787i
$940$	1.07002e16	−	1.85333e16i	0.475543	−	0.823665i
$941$	−1.55904e16	−	2.70034e16i	−0.688835	−	1.19310i	−0.972215	−	0.234090i	$-0.924789\pi$
$941$	−1.55904e16	−	2.70034e16i	−0.688835	−	1.19310i	0.283380	−	0.959008i	$-0.408544\pi$
$942$	1.65437e16	+	3.46688e15i	0.726697	+	0.152286i
$943$	1.09293e16	+	6.31001e15i	0.477283	+	0.275560i
$944$	−7.13218e15			−0.309654
$945$	−2.86841e16	+	2.99903e16i	−1.23813	+	1.29451i
$946$	1.28643e16			0.552060
$947$	4.54360e15	+	2.62325e15i	0.193854	+	0.111922i	0.593786	−	0.804623i	$-0.297633\pi$
$947$	4.54360e15	+	2.62325e15i	0.193854	+	0.111922i	−0.399932	+	0.916545i	$0.630966\pi$
$948$	−4.02845e14	−	8.44196e13i	−0.0170880	−	0.00358094i
$949$	−9.32822e15	−	1.61570e16i	−0.393400	−	0.681390i
$950$	1.23785e16	−	2.14403e16i	0.519026	−	0.898980i
$951$	−1.21514e16	−	1.08782e16i	−0.506562	−	0.453485i
$952$	5.94125e14	−	7.54508e14i	0.0246249	−	0.0312724i
$953$		−	3.80591e16i		−	1.56837i	−0.620529	−	0.784184i	$-0.713082\pi$
$953$		−	3.80591e16i		−	1.56837i	0.620529	−	0.784184i	$-0.286918\pi$
$954$	3.05773e16	+	1.34041e16i	1.25280	+	0.549190i
$955$	2.54428e16	−	1.46894e16i	1.03644	−	0.598391i
$956$	−1.03626e16	+	5.98284e15i	−0.419711	+	0.242320i
$957$	−8.48851e15	−	2.58721e16i	−0.341834	−	1.04187i
$958$			8.11127e15i			0.324772i
$959$	4.13294e13	−	5.24863e13i	0.00164535	−	0.00208951i
$960$	−3.77303e15	+	4.21464e15i	−0.149348	+	0.166828i
$961$	5.11940e15	−	8.86706e15i	0.201484	−	0.348981i
$962$	1.28097e15	+	2.21870e15i	0.0501275	+	0.0868233i
$963$	−8.61749e15	−	1.17189e16i	−0.335302	−	0.455977i
$964$	1.77969e15	+	1.02751e15i	0.0688528	+	0.0397522i
$965$	8.04930e16			3.09640
$966$	3.64534e15	+	4.35262e15i	0.139433	+	0.166486i
$967$	5.13204e15			0.195184			0.0975920	−	0.995227i	$-0.468886\pi$
$967$	5.13204e15			0.195184			0.0975920	+	0.995227i	$0.468886\pi$
$968$	−9.35093e14	−	5.39876e14i	−0.0353623	−	0.0204164i
$969$	4.08147e14	−	1.94765e15i	0.0153474	−	0.0732369i
$970$	−5.40981e15	−	9.37007e15i	−0.202273	−	0.350347i
$971$	6.71621e15	−	1.16328e16i	0.249700	−	0.432493i	−0.713743	−	0.700408i	$-0.753001\pi$
$971$	6.71621e15	−	1.16328e16i	0.249700	−	0.432493i	0.963443	+	0.267915i	$0.0863347\pi$
$972$	6.59368e15	−	1.18088e16i	0.243761	−	0.436556i
$973$	1.23385e15	+	3.08768e15i	0.0453568	+	0.113504i
$974$			2.71535e15i			0.0992547i
$975$	−2.42877e16	+	7.96870e15i	−0.882798	+	0.289642i
$976$	7.92050e15	−	4.57290e15i	0.286272	−	0.165279i
$977$	−1.42630e16	+	8.23477e15i	−0.512616	+	0.295959i	−0.733908	−	0.679249i	$-0.762306\pi$
$977$	−1.42630e16	+	8.23477e15i	−0.512616	+	0.295959i	0.221293	+	0.975207i	$0.428972\pi$
$978$	−1.47322e16	+	4.83358e15i	−0.526508	+	0.172745i
$979$		−	1.88019e16i		−	0.668185i
$980$	−1.83646e16	+	1.74663e16i	−0.648991	+	0.617245i
$981$	−3.15898e15	−	2.84820e16i	−0.111011	−	1.00090i
$982$	−1.25589e16	+	2.17527e16i	−0.438873	+	0.760150i
$983$	−1.53597e16	−	2.66038e16i	−0.533751	−	0.924483i	−0.999223	−	0.0394205i	$-0.987449\pi$
$983$	−1.53597e16	−	2.66038e16i	−0.533751	−	0.924483i	0.465472	−	0.885063i	$-0.345885\pi$
$984$	3.76574e15	−	1.79699e16i	0.130130	−	0.620971i
$985$	−3.07313e15	−	1.77427e15i	−0.105604	−	0.0609706i
$986$	2.71609e15			0.0928155
$987$	−1.07151e16	+	2.93539e16i	−0.364125	+	0.997519i
$988$	−4.13662e15			−0.139792
$989$	−6.56988e15	−	3.79312e15i	−0.220789	−	0.127473i
$990$	2.87165e16	−	2.11166e16i	0.959705	−	0.705718i
$991$	−8.93500e15	−	1.54759e16i	−0.296954	−	0.514340i	0.678483	−	0.734616i	$-0.262638\pi$
$991$	−8.93500e15	−	1.54759e16i	−0.296954	−	0.514340i	−0.975438	+	0.220276i	$0.929304\pi$
$992$	3.16762e15	−	5.48648e15i	0.104693	−	0.181334i
$993$	−3.34619e16	+	3.73784e16i	−1.09984	+	1.22857i
$994$	3.05602e15	−	2.11600e16i	0.0998920	−	0.691656i
$995$			1.52221e16i			0.494820i
$996$	−1.41047e15	−	4.29895e15i	−0.0455971	−	0.138975i
$997$	−5.16492e15	+	2.98197e15i	−0.166050	+	0.0958692i	−0.580722	−	0.814102i	$-0.697230\pi$
$997$	−5.16492e15	+	2.98197e15i	−0.166050	+	0.0958692i	0.414672	+	0.909971i	$0.363896\pi$
$998$	−5.75775e15	+	3.32424e15i	−0.184092	+	0.106286i
$999$	−9.64621e15	+	4.39467e15i	−0.306723	+	0.139739i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.16	yes	60
3.2	odd	2	inner	42.12.f.a.5.6	✓	60
7.3	odd	6	inner	42.12.f.a.17.6	yes	60
21.17	even	6	inner	42.12.f.a.17.16	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.6	✓	60	3.2	odd	2	inner
42.12.f.a.5.16	yes	60	1.1	even	1	trivial
42.12.f.a.17.6	yes	60	7.3	odd	6	inner
42.12.f.a.17.16	yes	60	21.17	even	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} +(-411.940 - 86.3257i) q^{3} +(512.000 + 886.810i) q^{4} +(-6258.52 + 10840.1i) q^{5} +(-10034.8 - 8983.37i) q^{6} +(-41292.3 + 16500.6i) q^{7} +32768.0i q^{8} +(162243. + 71122.1i) q^{9} +(-346882. + 200273. i) q^{10} +(-435052. + 251177. i) q^{11} +(-134359. - 409512. i) q^{12} +563130. i q^{13} +(-1.40834e6 - 203398. i) q^{14} +(3.51391e6 - 3.92519e6i) q^{15} +(-524288. + 908093. i) q^{16} +(329541. + 570781. i) q^{17} +(3.35825e6 + 4.56688e6i) q^{18} +(6.21252e6 + 3.58680e6i) q^{19} -1.28174e7 q^{20} +(1.84344e7 - 3.23269e6i) q^{21} -1.60754e7 q^{22} +(8.20976e6 + 4.73991e6i) q^{23} +(2.82872e6 - 1.34985e7i) q^{24} +(-5.39240e7 - 9.33991e7i) q^{25} +(-9.01008e6 + 1.56059e7i) q^{26} +(-6.06947e7 - 4.33038e7i) q^{27} +(-3.57746e7 - 2.81701e7i) q^{28} -1.28782e8i q^{29} +(1.60183e8 - 5.25555e7i) q^{30} +(-1.63510e8 + 9.44024e7i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(2.00899e8 - 6.59139e7i) q^{33} +2.10906e7i q^{34} +(7.95606e7 - 5.50881e8i) q^{35} +(1.99965e7 + 1.80293e8i) q^{36} +(7.10853e7 - 1.23123e8i) q^{37} +(1.14778e8 + 1.98801e8i) q^{38} +(4.86126e7 - 2.31976e8i) q^{39} +(-3.55207e8 - 2.05079e8i) q^{40} +1.33125e9 q^{41} +(5.62592e8 + 2.05363e8i) q^{42} -8.00252e8 q^{43} +(-4.45493e8 - 2.57206e8i) q^{44} +(-1.78637e9 + 1.31360e9i) q^{45} +(1.51677e8 + 2.62712e8i) q^{46} +(-8.34818e8 + 1.44595e9i) q^{47} +(2.94367e8 - 3.28821e8i) q^{48} +(1.43278e9 - 1.36270e9i) q^{49} -3.45113e9i q^{50} +(-8.64781e7 - 2.63576e8i) q^{51} +(-4.99389e8 + 2.88323e8i) q^{52} +(5.10052e9 - 2.94479e9i) q^{53} +(-9.89160e8 - 2.17118e9i) q^{54} -6.28799e9i q^{55} +(-5.40693e8 - 1.35307e9i) q^{56} +(-2.24956e9 - 2.01385e9i) q^{57} +(2.06051e9 - 3.56890e9i) q^{58} +(3.40089e9 + 5.89051e9i) q^{59} +(5.28002e9 + 1.10647e9i) q^{60} +(-7.55358e9 - 4.36106e9i) q^{61} -6.04176e9 q^{62} +(-7.87294e9 - 2.59686e8i) q^{63} -1.07374e9 q^{64} +(-6.10437e9 - 3.52436e9i) q^{65} +(6.62209e9 + 1.38772e9i) q^{66} +(3.88865e9 + 6.73534e9i) q^{67} +(-3.37450e8 + 5.84480e8i) q^{68} +(-2.97276e9 - 2.66127e9i) q^{69} +(1.10189e10 - 1.39935e10i) q^{70} +1.50248e10i q^{71} +(-2.33053e9 + 5.31637e9i) q^{72} +(-2.86914e10 + 1.65650e10i) q^{73} +(3.93995e9 - 2.27473e9i) q^{74} +(1.41507e10 + 4.31299e10i) q^{75} +7.34577e9i q^{76} +(1.38197e10 - 1.75503e10i) q^{77} +(5.05881e9 - 5.65090e9i) q^{78} +(4.77500e8 - 8.27054e8i) q^{79} +(-6.56253e9 - 1.13666e10i) q^{80} +(2.12644e10 + 2.30781e10i) q^{81} +(3.68927e10 + 2.13000e10i) q^{82} +1.04978e10 q^{83} +(1.23052e10 + 1.46927e10i) q^{84} -8.24975e9 q^{85} +(-2.21772e10 - 1.28040e10i) q^{86} +(-1.11172e10 + 5.30504e10i) q^{87} +(-8.23058e9 - 1.42558e10i) q^{88} +(-1.87137e10 + 3.24132e10i) q^{89} +(-7.05229e10 + 7.82178e9i) q^{90} +(-9.29200e9 - 2.32529e10i) q^{91} +9.70733e9i q^{92} +(7.55057e10 - 2.47731e10i) q^{93} +(-4.62703e10 + 2.67142e10i) q^{94} +(-7.77623e10 + 4.48961e10i) q^{95} +(1.34189e10 - 4.40268e9i) q^{96} +2.70123e10i q^{97} +(6.15097e10 - 1.48397e10i) q^{98} +(-8.84483e10 + 9.80991e9i) 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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