LMFDB - Embedded newform 42.12.f.a.5.12

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			5.12
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.12

$q$-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} +(300.225 + 294.978i) q^{3} +(512.000 + 886.810i) q^{4} +(407.491 - 705.796i) q^{5} +(-3600.42 - 12978.3i) q^{6} +(-18834.9 - 40281.2i) q^{7} -32768.0i q^{8} +(3122.76 + 177119. i) q^{9} +(-22585.5 + 13039.7i) q^{10} +(-9547.45 + 5512.22i) q^{11} +(-107875. + 417271. i) q^{12} +1.39427e6i q^{13} +(-122529. + 1.41766e6i) q^{14} +(330533. - 91696.3i) q^{15} +(-524288. + 908093. i) q^{16} +(691798. + 1.19823e6i) q^{17} +(2.74737e6 - 4.95844e6i) q^{18} +(-7.16131e6 - 4.13459e6i) q^{19} +834542. q^{20} +(6.22735e6 - 1.76493e7i) q^{21} +352782. q^{22} +(-1.03976e7 - 6.00304e6i) q^{23} +(9.66584e6 - 9.83776e6i) q^{24} +(2.40820e7 + 4.17112e7i) q^{25} +(2.23083e7 - 3.86391e7i) q^{26} +(-5.13088e7 + 5.40968e7i) q^{27} +(2.60782e7 - 3.73270e7i) q^{28} -1.59853e8i q^{29} +(-1.06271e7 - 2.74737e6i) q^{30} +(-1.21971e8 + 7.04202e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(-4.49237e6 - 1.16138e6i) q^{33} -4.42750e7i q^{34} +(-3.61053e7 - 3.12061e6i) q^{35} +(-1.55472e8 + 9.34545e7i) q^{36} +(-3.26843e8 + 5.66109e8i) q^{37} +(1.32307e8 + 2.29162e8i) q^{38} +(-4.11279e8 + 4.18594e8i) q^{39} +(-2.31275e7 - 1.33527e7i) q^{40} +5.00579e7 q^{41} +(-4.54966e8 + 3.89474e8i) q^{42} -1.88708e9 q^{43} +(-9.77659e6 - 5.64452e6i) q^{44} +(1.26283e8 + 6.99706e7i) q^{45} +(1.92097e8 + 3.32722e8i) q^{46} +(-8.25384e8 + 1.42961e9i) q^{47} +(-4.25272e8 + 1.17979e8i) q^{48} +(-1.26782e9 + 1.51739e9i) q^{49} -1.54125e9i q^{50} +(-1.45757e8 + 5.63803e8i) q^{51} +(-1.23645e9 + 7.13866e8i) q^{52} +(1.41137e8 - 8.14854e7i) q^{53} +(2.28746e9 - 6.78233e8i) q^{54} +8.98473e6i q^{55} +(-1.31993e9 + 6.17183e8i) q^{56} +(-9.30391e8 - 3.35374e9i) q^{57} +(-2.55765e9 + 4.42998e9i) q^{58} +(-3.77159e9 - 6.53258e9i) q^{59} +(2.50550e8 + 2.46172e8i) q^{60} +(1.46189e8 + 8.44025e7i) q^{61} +4.50690e9 q^{62} +(7.07576e9 - 3.46182e9i) q^{63} -1.07374e9 q^{64} +(9.84070e8 + 5.68153e8i) q^{65} +(1.05914e8 + 1.04063e8i) q^{66} +(-4.23419e9 - 7.33384e9i) q^{67} +(-7.08401e8 + 1.22699e9i) q^{68} +(-1.35084e9 - 4.86932e9i) q^{69} +(9.50651e8 + 6.64166e8i) q^{70} +1.72414e10i q^{71} +(5.80385e9 - 1.02327e8i) q^{72} +(-2.52586e9 + 1.45831e9i) q^{73} +(1.81155e10 - 1.04590e10i) q^{74} +(-5.07389e9 + 1.96264e10i) q^{75} -8.46763e9i q^{76} +(4.01864e8 + 2.80760e8i) q^{77} +(1.80952e10 - 5.01996e9i) q^{78} +(7.28778e8 - 1.26228e9i) q^{79} +(4.27286e8 + 7.40080e8i) q^{80} +(-3.13616e10 + 1.10620e9i) q^{81} +(-1.38724e9 - 8.00926e8i) q^{82} -9.16160e9 q^{83} +(1.88400e10 - 3.51396e9i) q^{84} +1.12761e9 q^{85} +(5.22962e10 + 3.01932e10i) q^{86} +(4.71532e10 - 4.79919e10i) q^{87} +(1.80625e8 + 3.12851e8i) q^{88} +(-2.54222e10 + 4.40326e10i) q^{89} +(-2.38012e9 - 3.95960e9i) q^{90} +(5.61628e10 - 2.62610e10i) q^{91} -1.22942e10i q^{92} +(-5.73913e10 - 1.48370e10i) q^{93} +(4.57474e10 - 2.64123e10i) q^{94} +(-5.83635e9 + 3.36962e9i) q^{95} +(1.36731e10 + 3.53483e9i) q^{96} -6.03089e10i q^{97} +(5.94130e10 - 2.17660e10i) q^{98} +(-1.00614e9 - 1.67383e9i) 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
$3$	300.225	+	294.978i	0.713312	+	0.700847i
$3$	300.225	+	294.978i	0.713312	+	0.700847i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	407.491	−	705.796i	0.0583154	−	0.101005i	−0.835394	−	0.549652i	$-0.814760\pi$
$5$	407.491	−	705.796i	0.0583154	−	0.101005i	0.893709	+	0.448646i	$0.148094\pi$
$6$	−3600.42	−	12978.3i	−0.189026	−	0.681373i
$7$	−18834.9	−	40281.2i	−0.423570	−	0.905863i
$7$	−18834.9	−	40281.2i	−0.423570	−	0.905863i
$8$		−	32768.0i		−	0.353553i
$9$	3122.76	+	177119.i	0.0176281	+	0.999845i
$10$	−22585.5	+	13039.7i	−0.0714215	+	0.0412352i
$11$	−9547.45	+	5512.22i	−0.0178742	+	0.0103197i	−0.508910	−	0.860819i	$-0.669952\pi$
$11$	−9547.45	+	5512.22i	−0.0178742	+	0.0103197i	0.491036	+	0.871139i	$0.336618\pi$
$12$	−107875.	+	417271.i	−0.125147	+	0.484085i
$13$			1.39427e6i			1.04150i	0.853710	+	0.520749i	$0.174347\pi$
$13$			1.39427e6i			1.04150i	−0.853710	+	0.520749i	$0.825653\pi$
$14$	−122529.	+	1.41766e6i	−0.0608886	+	0.704480i
$15$	330533.	−	91696.3i	0.112386	−	0.0311781i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	691798.	+	1.19823e6i	0.118171	+	0.204678i	0.919043	−	0.394158i	$-0.128964\pi$
$17$	691798.	+	1.19823e6i	0.118171	+	0.204678i	−0.800872	+	0.598836i	$0.795630\pi$
$18$	2.74737e6	−	4.95844e6i	0.342704	−	0.618510i
$19$	−7.16131e6	−	4.13459e6i	−0.663511	−	0.383078i	0.130103	−	0.991501i	$-0.458469\pi$
$19$	−7.16131e6	−	4.13459e6i	−0.663511	−	0.383078i	−0.793613	+	0.608423i	$0.791803\pi$
$20$	834542.			0.0583154
$21$	6.22735e6	−	1.76493e7i	0.332734	−	0.943021i
$22$	352782.			0.0145943
$23$	−1.03976e7	−	6.00304e6i	−0.336844	−	0.194477i	0.322032	−	0.946729i	$-0.395634\pi$
$23$	−1.03976e7	−	6.00304e6i	−0.336844	−	0.194477i	−0.658876	+	0.752252i	$0.728968\pi$
$24$	9.66584e6	−	9.83776e6i	0.247787	−	0.252194i
$25$	2.40820e7	+	4.17112e7i	0.493199	+	0.854245i
$26$	2.23083e7	−	3.86391e7i	0.368225	−	0.637785i
$27$	−5.13088e7	+	5.40968e7i	−0.688163	+	0.725556i
$28$	2.60782e7	−	3.73270e7i	0.286358	−	0.409877i
$29$		−	1.59853e8i		−	1.44721i	−0.690213	−	0.723606i	$-0.742483\pi$
$29$		−	1.59853e8i		−	1.44721i	0.690213	−	0.723606i	$-0.257517\pi$
$30$	−1.06271e7	−	2.74737e6i	−0.0798454	−	0.0206419i
$31$	−1.21971e8	+	7.04202e7i	−0.765189	+	0.441782i	−0.831156	−	0.556040i	$-0.812320\pi$
$31$	−1.21971e8	+	7.04202e7i	−0.765189	+	0.441782i	0.0659666	+	0.997822i	$0.478987\pi$
$32$	2.90590e7	−	1.67772e7i	0.153093	−	0.0883883i
$33$	−4.49237e6	−	1.16138e6i	−0.0199824	−	0.00516594i
$34$		−	4.42750e7i		−	0.167119i
$35$	−3.61053e7	−	3.12061e6i	−0.116198	−	0.0100430i
$36$	−1.55472e8	+	9.34545e7i	−0.428538	+	0.257594i
$37$	−3.26843e8	+	5.66109e8i	−0.774872	+	1.34212i	0.159994	+	0.987118i	$0.448852\pi$
$37$	−3.26843e8	+	5.66109e8i	−0.774872	+	1.34212i	−0.934866	+	0.355000i	$0.884481\pi$
$38$	1.32307e8	+	2.29162e8i	0.270877	+	0.469173i
$39$	−4.11279e8	+	4.18594e8i	−0.729930	+	0.742913i
$40$	−2.31275e7	−	1.33527e7i	−0.0357107	−	0.0206176i
$41$	5.00579e7			0.0674779			0.0337389	−	0.999431i	$-0.489259\pi$
$41$	5.00579e7			0.0674779			0.0337389	+	0.999431i	$0.489259\pi$
$42$	−4.54966e8	+	3.89474e8i	−0.537165	+	0.459841i
$43$	−1.88708e9			−1.95755			−0.978776	−	0.204933i	$-0.934302\pi$
$43$	−1.88708e9			−1.95755			−0.978776	+	0.204933i	$0.934302\pi$
$44$	−9.77659e6	−	5.64452e6i	−0.00893712	−	0.00515985i
$45$	1.26283e8	+	6.99706e7i	0.102018	+	0.0565258i
$46$	1.92097e8	+	3.32722e8i	0.137516	+	0.238185i
$47$	−8.25384e8	+	1.42961e9i	−0.524950	+	0.909240i	0.474628	+	0.880186i	$0.342583\pi$
$47$	−8.25384e8	+	1.42961e9i	−0.524950	+	0.909240i	−0.999578	+	0.0290534i	$0.990751\pi$
$48$	−4.25272e8	+	1.17979e8i	−0.240902	+	0.0668308i
$49$	−1.26782e9	+	1.51739e9i	−0.641177	+	0.767393i
$50$		−	1.54125e9i		−	0.697488i
$51$	−1.45757e8	+	5.63803e8i	−0.0591551	+	0.228819i
$52$	−1.23645e9	+	7.13866e8i	−0.450982	+	0.260375i
$53$	1.41137e8	−	8.14854e7i	0.0463578	−	0.0267647i	−0.476642	−	0.879098i	$-0.658146\pi$
$53$	1.41137e8	−	8.14854e7i	0.0463578	−	0.0267647i	0.523000	+	0.852333i	$0.324813\pi$
$54$	2.28746e9	−	6.78233e8i	0.677935	−	0.201008i
$55$			8.98473e6i			0.00240719i
$56$	−1.31993e9	+	6.17183e8i	−0.320271	+	0.149755i
$57$	−9.30391e8	−	3.35374e9i	−0.204811	−	0.738273i
$58$	−2.55765e9	+	4.42998e9i	−0.511667	+	0.886233i
$59$	−3.77159e9	−	6.53258e9i	−0.686812	−	1.18959i	−0.972864	−	0.231379i	$-0.925676\pi$
$59$	−3.77159e9	−	6.53258e9i	−0.686812	−	1.18959i	0.286052	−	0.958214i	$-0.407657\pi$
$60$	2.50550e8	+	2.46172e8i	0.0415971	+	0.0408702i
$61$	1.46189e8	+	8.44025e7i	0.0221616	+	0.0127950i	0.511040	−	0.859557i	$-0.329260\pi$
$61$	1.46189e8	+	8.44025e7i	0.0221616	+	0.0127950i	−0.488878	+	0.872352i	$0.662594\pi$
$62$	4.50690e9			0.624774
$63$	7.07576e9	−	3.46182e9i	0.898256	−	0.439473i
$64$	−1.07374e9			−0.125000
$65$	9.84070e8	+	5.68153e8i	0.105197	+	0.0607354i
$66$	1.05914e8	+	1.04063e8i	0.0104103	+	0.0102283i
$67$	−4.23419e9	−	7.33384e9i	−0.383142	−	0.663621i	0.608368	−	0.793655i	$-0.291825\pi$
$67$	−4.23419e9	−	7.33384e9i	−0.383142	−	0.663621i	−0.991509	+	0.130034i	$0.958491\pi$
$68$	−7.08401e8	+	1.22699e9i	−0.0590854	+	0.102339i
$69$	−1.35084e9	−	4.86932e9i	−0.103976	−	0.374799i
$70$	9.50651e8	+	6.64166e8i	0.0676055	+	0.0472321i
$71$			1.72414e10i			1.13410i	0.823683	+	0.567050i	$0.191916\pi$
$71$			1.72414e10i			1.13410i	−0.823683	+	0.567050i	$0.808084\pi$
$72$	5.80385e9	−	1.02327e8i	0.353498	−	0.00623246i
$73$	−2.52586e9	+	1.45831e9i	−0.142605	+	0.0823329i	−0.569605	−	0.821919i	$-0.692904\pi$
$73$	−2.52586e9	+	1.45831e9i	−0.142605	+	0.0823329i	0.427000	+	0.904252i	$0.359570\pi$
$74$	1.81155e10	−	1.04590e10i	0.949020	−	0.547917i
$75$	−5.07389e9	+	1.96264e10i	−0.246890	+	0.955000i
$76$		−	8.46763e9i		−	0.383078i
$77$	4.01864e8	+	2.80760e8i	0.0169192	+	0.0118205i
$78$	1.80952e10	−	5.01996e9i	0.709649	−	0.196870i
$79$	7.28778e8	−	1.26228e9i	0.0266469	−	0.0461537i	−0.852394	−	0.522899i	$-0.824850\pi$
$79$	7.28778e8	−	1.26228e9i	0.0266469	−	0.0461537i	0.879041	+	0.476746i	$0.158184\pi$
$80$	4.27286e8	+	7.40080e8i	0.0145789	+	0.0252513i
$81$	−3.13616e10	+	1.10620e9i	−0.999379	+	0.0352506i
$82$	−1.38724e9	−	8.00926e8i	−0.0413216	−	0.0238570i
$83$	−9.16160e9			−0.255295			−0.127647	−	0.991820i	$-0.540743\pi$
$83$	−9.16160e9			−0.255295			−0.127647	+	0.991820i	$0.540743\pi$
$84$	1.88400e10	−	3.51396e9i	0.491523	−	0.0916772i
$85$	1.12761e9			0.0275647
$86$	5.22962e10	+	3.01932e10i	1.19875	+	0.692099i
$87$	4.71532e10	−	4.79919e10i	1.01427	−	1.03231i
$88$	1.80625e8	+	3.12851e8i	0.00364856	+	0.00631950i
$89$	−2.54222e10	+	4.40326e10i	−0.482579	+	0.835852i	−0.999800	−	0.0200002i	$-0.993633\pi$
$89$	−2.54222e10	+	4.40326e10i	−0.482579	+	0.835852i	0.517221	+	0.855852i	$0.326967\pi$
$90$	−2.38012e9	−	3.95960e9i	−0.0424878	−	0.0706835i
$91$	5.61628e10	−	2.62610e10i	0.943455	−	0.441147i
$92$		−	1.22942e10i		−	0.194477i
$93$	−5.73913e10	−	1.48370e10i	−0.855440	−	0.221152i
$94$	4.57474e10	−	2.64123e10i	0.642930	−	0.371196i
$95$	−5.83635e9	+	3.36962e9i	−0.0773858	+	0.0446787i
$96$	1.36731e10	+	3.53483e9i	0.171150	+	0.0442463i
$97$		−	6.03089e10i		−	0.713077i	−0.934281	−	0.356539i	$-0.883957\pi$
$97$		−	6.03089e10i		−	0.713077i	0.934281	−	0.356539i	$-0.116043\pi$
$98$	5.94130e10	−	2.17660e10i	0.663954	−	0.243240i
$99$	−1.00614e9	−	1.67383e9i	−0.0106332	−	0.0176896i
$100$	−2.46599e10	+	4.27123e10i	−0.246599	+	0.427123i
$101$	−4.58170e10	−	7.93573e10i	−0.433769	−	0.751310i	0.563425	−	0.826167i	$-0.309483\pi$
$101$	−4.58170e10	−	7.93573e10i	−0.433769	−	0.751310i	−0.997194	+	0.0748569i	$0.976150\pi$
$102$	1.30602e10	−	1.32925e10i	0.117125	−	0.119208i
$103$	−4.74769e10	−	2.74108e10i	−0.403532	−	0.232979i	0.284475	−	0.958683i	$-0.408181\pi$
$103$	−4.74769e10	−	2.74108e10i	−0.403532	−	0.232979i	−0.688007	+	0.725704i	$0.741514\pi$
$104$	4.56874e10			0.368225
$105$	−9.91920e9	−	1.15872e10i	−0.0758465	−	0.0886005i
$106$	−5.21507e9			−0.0378510
$107$	2.08910e11	+	1.20614e11i	1.43995	+	0.831356i	0.997846	−	0.0656072i	$-0.0208984\pi$
$107$	2.08910e11	+	1.20614e11i	1.43995	+	0.831356i	0.442105	+	0.896963i	$0.354232\pi$
$108$	−7.42437e10	−	1.78036e10i	−0.486216	−	0.116595i
$109$	6.01702e9	+	1.04218e10i	0.0374572	+	0.0648778i	0.884146	−	0.467210i	$-0.154741\pi$
$109$	6.01702e9	+	1.04218e10i	0.0374572	+	0.0648778i	−0.846689	+	0.532088i	$0.821408\pi$
$110$	1.43756e8	−	2.48992e8i	0.000851070	−	0.00147410i
$111$	−2.65116e11	+	7.35483e10i	−1.49334	+	0.414282i
$112$	4.64540e10	+	4.01504e9i	0.249071	+	0.0215274i
$113$		−	1.59227e10i		−	0.0812988i	−0.999173	−	0.0406494i	$-0.987057\pi$
$113$		−	1.59227e10i		−	0.0812988i	0.999173	−	0.0406494i	$-0.0129427\pi$
$114$	−2.78760e10	+	1.07828e11i	−0.135598	+	0.524510i
$115$	−8.47384e9	+	4.89237e9i	−0.0392864	+	0.0226820i
$116$	1.41759e11	−	8.18448e10i	0.626661	−	0.361803i
$117$	−2.46952e11	+	4.35397e9i	−1.04134	+	0.0183596i
$118$			2.41381e11i			0.971299i
$119$	3.52361e10	−	5.04350e10i	0.135357	−	0.193742i
$120$	−3.00470e9	−	1.08309e10i	−0.0110231	−	0.0397345i
$121$	−1.42595e11	+	2.46982e11i	−0.499787	+	0.865656i
$122$	−2.70088e9	−	4.67806e9i	−0.00904745	−	0.0156706i
$123$	1.50286e10	+	1.47660e10i	0.0481328	+	0.0472916i
$124$	−1.24899e11	−	7.21103e10i	−0.382595	−	0.220891i
$125$	7.90468e10			0.231675
$126$	−2.51478e11	−	1.72753e10i	−0.705444	−	0.0484606i
$127$	1.16990e11			0.314215			0.157107	−	0.987582i	$-0.449783\pi$
$127$	1.16990e11			0.314215			0.157107	+	0.987582i	$0.449783\pi$
$128$	2.97564e10	+	1.71799e10i	0.0765466	+	0.0441942i
$129$	−5.66547e11	−	5.56647e11i	−1.39635	−	1.37194i
$130$	−1.81809e10	−	3.14902e10i	−0.0429464	−	0.0743853i
$131$	−2.10645e11	+	3.64847e11i	−0.477044	+	0.826264i	−0.999654	−	0.0263080i	$-0.991625\pi$
$131$	−2.10645e11	+	3.64847e11i	−0.477044	+	0.826264i	0.522610	+	0.852572i	$0.324958\pi$
$132$	−1.27016e9	−	4.57850e9i	−0.00275869	−	0.00994413i
$133$	−3.16630e10	+	3.66341e11i	−0.0659733	+	0.763310i
$134$			2.70988e11i			0.541844i
$135$	1.72734e10	+	5.82575e10i	0.0331544	+	0.111819i
$136$	3.92636e10	−	2.26688e10i	0.0723645	−	0.0417797i
$137$	4.40499e11	−	2.54322e11i	0.779798	−	0.450217i	−0.0565607	−	0.998399i	$-0.518013\pi$
$137$	4.40499e11	−	2.54322e11i	0.779798	−	0.450217i	0.836359	+	0.548183i	$0.184680\pi$
$138$	−4.04735e10	+	1.56556e11i	−0.0688391	+	0.266278i
$139$		−	4.12592e11i		−	0.674434i	−0.941427	−	0.337217i	$-0.890514\pi$
$139$		−	4.12592e11i		−	0.674434i	0.941427	−	0.337217i	$-0.109486\pi$
$140$	−1.57185e10	−	3.36163e10i	−0.0247006	−	0.0528258i
$141$	−6.69504e11	+	1.85733e11i	−1.01169	+	0.280662i
$142$	2.75862e11	−	4.77808e11i	0.400965	−	0.694492i
$143$	−7.68553e9	−	1.33117e10i	−0.0107479	−	0.0186160i
$144$	−1.62478e11	−	9.00259e10i	−0.218676	−	0.121164i
$145$	−1.12824e11	−	6.51388e10i	−0.146176	−	0.0843948i
$146$	9.33317e10			0.116436
$147$	−8.28226e11	+	8.15785e10i	−0.995184	+	0.0980236i
$148$	−6.69375e11			−0.774872
$149$	1.23743e12	+	7.14432e11i	1.38038	+	0.796960i	0.992204	−	0.124627i	$-0.0397733\pi$
$149$	1.23743e12	+	7.14432e11i	1.38038	+	0.796960i	0.388172	+	0.921587i	$0.373107\pi$
$150$	4.54634e11	−	4.62720e11i	0.488832	−	0.497527i
$151$	6.61198e11	+	1.14523e12i	0.685422	+	1.18719i	0.973304	+	0.229520i	$0.0737158\pi$
$151$	6.61198e11	+	1.14523e12i	0.685422	+	1.18719i	−0.287881	+	0.957666i	$0.592951\pi$
$152$	−1.35482e11	+	2.34662e11i	−0.135439	+	0.234586i
$153$	−2.10069e11	+	1.26273e11i	−0.202563	+	0.121760i
$154$	−6.64463e9	−	1.42105e10i	−0.00618169	−	0.0132204i
$155$			1.14783e11i			0.103051i
$156$	−5.81789e11	−	1.50406e11i	−0.504173	−	0.130341i
$157$	4.83638e11	−	2.79228e11i	0.404643	−	0.233621i	−0.283842	−	0.958871i	$-0.591609\pi$
$157$	4.83638e11	−	2.79228e11i	0.404643	−	0.233621i	0.688485	+	0.725250i	$0.258276\pi$
$158$	−4.03930e10	+	2.33209e10i	−0.0326356	+	0.0188422i
$159$	6.64092e10	+	1.71684e10i	0.0518256	+	0.0133981i
$160$		−	2.73463e10i		−	0.0206176i
$161$	−4.59718e10	+	5.31893e11i	−0.0334926	+	0.387509i
$162$	8.86816e11	+	4.71129e11i	0.624455	+	0.331747i
$163$	5.32943e11	−	9.23084e11i	0.362784	−	0.628361i	−0.625634	−	0.780117i	$-0.715159\pi$
$163$	5.32943e11	−	9.23084e11i	0.362784	−	0.628361i	0.988418	+	0.151756i	$0.0484928\pi$
$164$	2.56296e10	+	4.43918e10i	0.0168695	+	0.0292188i
$165$	−2.65030e9	+	2.69744e9i	−0.00168707	+	0.00171708i
$166$	2.53894e11	+	1.46586e11i	0.156335	+	0.0902603i
$167$	3.32274e12			1.97950			0.989751	−	0.142805i	$-0.0456123\pi$
$167$	3.32274e12			1.97950			0.989751	+	0.142805i	$0.0456123\pi$
$168$	−5.78332e11	−	2.04058e11i	−0.333408	−	0.117639i
$169$	−1.51829e11			−0.0847182
$170$	−3.12491e10	−	1.80417e10i	−0.0168799	−	0.00974559i
$171$	7.09953e11	−	1.28132e12i	0.371322	−	0.670160i
$172$	−9.66184e11	−	1.67348e12i	−0.489388	−	0.847645i
$173$	1.24581e12	−	2.15781e12i	0.611222	−	1.05867i	−0.379813	−	0.925063i	$-0.624012\pi$
$173$	1.24581e12	−	2.15781e12i	0.611222	−	1.05867i	0.991035	−	0.133604i	$-0.0426551\pi$
$174$	−2.07462e12	+	5.75539e11i	−0.986092	+	0.273561i
$175$	1.22659e12	−	1.75568e12i	0.564925	−	0.808603i
$176$		−	1.15600e10i		−	0.00515985i
$177$	7.94645e11	−	3.07378e12i	0.343811	−	1.32990i
$178$	1.40904e12	−	8.13512e11i	0.591037	−	0.341235i
$179$	2.53842e12	−	1.46556e12i	1.03246	−	0.596089i	0.114770	−	0.993392i	$-0.463387\pi$
$179$	2.53842e12	−	1.46556e12i	1.03246	−	0.596089i	0.917688	+	0.397303i	$0.130054\pi$
$180$	2.60607e9	+	1.47814e11i	0.00102799	+	0.0583063i
$181$			1.53245e12i			0.586345i	0.956060	+	0.293173i	$0.0947111\pi$
$181$			1.53245e12i			0.586345i	−0.956060	+	0.293173i	$0.905289\pi$
$182$	−1.97661e12	−	1.70839e11i	−0.733715	−	0.0634154i
$183$	1.89928e10	+	6.84624e10i	0.00684081	+	0.0246587i
$184$	−1.96708e11	+	3.40708e11i	−0.0687580	+	0.119092i
$185$	2.66371e11	+	4.61369e11i	0.0903739	+	0.156532i
$186$	1.35308e12	+	1.32944e12i	0.445659	+	0.437871i
$187$	−1.32098e10	−	7.62669e9i	−0.00422443	−	0.00243897i
$188$	−1.69039e12			−0.524950
$189$	3.14548e12	+	1.04787e12i	0.948740	+	0.316059i
$190$	2.15655e11			0.0631852
$191$	−3.88269e11	−	2.24167e11i	−0.110522	−	0.0638099i	0.443720	−	0.896165i	$-0.353658\pi$
$191$	−3.88269e11	−	2.24167e11i	−0.110522	−	0.0638099i	−0.554242	+	0.832356i	$0.686992\pi$
$192$	−3.22364e11	−	3.16730e11i	−0.0891640	−	0.0876058i
$193$	6.19416e11	+	1.07286e12i	0.166501	+	0.288389i	0.937187	−	0.348826i	$-0.113420\pi$
$193$	6.19416e11	+	1.07286e12i	0.166501	+	0.288389i	−0.770686	+	0.637215i	$0.780086\pi$
$194$	−9.64942e11	+	1.67133e12i	−0.252111	+	0.436669i
$195$	1.27849e11	+	4.60853e11i	0.0324719	+	0.117050i
$196$	−1.99476e12	−	3.47411e11i	−0.492585	−	0.0857897i
$197$			4.66428e12i			1.12001i	0.828490	+	0.560003i	$0.189200\pi$
$197$			4.66428e12i			1.12001i	−0.828490	+	0.560003i	$0.810800\pi$
$198$	1.10165e9	+	6.24846e10i	0.000257268	+	0.0145920i
$199$	−3.82778e12	+	2.20997e12i	−0.869472	+	0.501990i	−0.867173	−	0.498008i	$-0.834065\pi$
$199$	−3.82778e12	+	2.20997e12i	−0.869472	+	0.501990i	−0.00229903	+	0.999997i	$0.500732\pi$
$200$	1.36679e12	−	7.89118e11i	0.302021	−	0.174372i
$201$	8.92113e11	−	3.45079e12i	0.191797	−	0.741892i
$202$			2.93229e12i			0.613442i
$203$	−6.43907e12	+	3.01082e12i	−1.31098	+	0.612995i
$204$	−5.74613e11	+	1.59409e11i	−0.113870	+	0.0315898i
$205$	2.03982e10	−	3.53306e10i	0.00393500	−	0.00681562i
$206$	8.77145e11	+	1.51926e12i	0.164741	+	0.285340i
$207$	1.03079e12	−	1.86036e12i	0.188509	−	0.340220i
$208$	−1.26613e12	−	7.30999e11i	−0.225491	−	0.130187i
$209$	9.11630e10			0.0158130
$210$	8.94943e10	+	4.79820e11i	0.0151213	+	0.0810723i
$211$	−9.25525e12			−1.52347			−0.761736	−	0.647887i	$-0.775653\pi$
$211$	−9.25525e12			−1.52347			−0.761736	+	0.647887i	$0.775653\pi$
$212$	1.44524e11	+	8.34411e10i	0.0231789	+	0.0133824i
$213$	−5.08584e12	+	5.17630e12i	−0.794831	+	0.808968i
$214$	−3.85965e12	−	6.68511e12i	−0.587857	−	1.01820i
$215$	−7.68968e11	+	1.33189e12i	−0.114155	+	0.197723i
$216$	1.77264e12	+	1.68129e12i	0.256523	+	0.243303i
$217$	5.13393e12	+	3.58679e12i	0.724305	+	0.506031i
$218$		−	3.85089e11i		−	0.0529725i
$219$	−1.18850e12	−	3.07255e11i	−0.159424	−	0.0412150i
$220$	−7.96775e9	+	4.60018e9i	−0.00104234	+	0.000601797i
$221$	−1.67065e12	+	9.64553e11i	−0.213171	+	0.123075i
$222$	8.52389e12	+	2.20363e12i	1.06095	+	0.274282i
$223$			1.08217e13i			1.31407i	0.753859	+	0.657036i	$0.228190\pi$
$223$			1.08217e13i			1.31407i	−0.753859	+	0.657036i	$0.771810\pi$
$224$	−1.22313e12	−	8.54532e11i	−0.144913	−	0.101243i
$225$	−7.31266e12	+	4.39564e12i	−0.845418	+	0.508181i
$226$	−2.54762e11	+	4.41261e11i	−0.0287435	+	0.0497851i
$227$	−6.65328e12	−	1.15238e13i	−0.732645	−	1.26898i	−0.955749	−	0.294183i	$-0.904952\pi$
$227$	−6.65328e12	−	1.15238e13i	−0.732645	−	1.26898i	0.223104	−	0.974795i	$-0.428381\pi$
$228$	2.49777e12	−	2.54219e12i	0.268479	−	0.273254i
$229$	5.66471e12	+	3.27052e12i	0.594405	+	0.343180i	0.766837	−	0.641841i	$-0.221829\pi$
$229$	5.66471e12	+	3.27052e12i	0.594405	+	0.343180i	−0.172432	+	0.985021i	$0.555163\pi$
$230$	3.13112e11			0.0320772
$231$	3.78315e10	+	2.02832e11i	0.00378432	+	0.0202895i
$232$	−5.23807e12			−0.511667
$233$	−7.17664e12	−	4.14344e12i	−0.684642	−	0.395278i	0.116960	−	0.993137i	$-0.462685\pi$
$233$	−7.17664e12	−	4.14344e12i	−0.684642	−	0.395278i	−0.801602	+	0.597858i	$0.796019\pi$
$234$	6.91341e12	+	3.83058e12i	0.644177	+	0.356925i
$235$	6.72674e11	+	1.16510e12i	0.0612253	+	0.106045i
$236$	3.86210e12	−	6.68936e12i	0.343406	−	0.594797i
$237$	5.91142e11	−	1.63994e11i	0.0513542	−	0.0142466i
$238$	−1.78345e12	+	8.33918e11i	−0.151387	+	0.0707864i
$239$		−	2.16705e13i		−	1.79754i	−0.438415	−	0.898772i	$-0.644460\pi$
$239$		−	2.16705e13i		−	1.79754i	0.438415	−	0.898772i	$-0.355540\pi$
$240$	−9.00259e10	+	3.48230e11i	−0.00729803	+	0.0282296i
$241$	3.60752e12	−	2.08280e12i	0.285834	−	0.165027i	−0.350227	−	0.936665i	$-0.613896\pi$
$241$	3.60752e12	−	2.08280e12i	0.285834	−	0.165027i	0.636062	+	0.771638i	$0.280562\pi$
$242$	7.90342e12	−	4.56304e12i	0.612112	−	0.353403i
$243$	−9.74182e12	−	8.91887e12i	−0.737574	−	0.675266i
$244$			1.72856e11i			0.0127950i
$245$	5.54340e11	+	1.51314e12i	0.0401202	+	0.109513i
$246$	−1.80229e11	−	6.49665e11i	−0.0127551	−	0.0459776i
$247$	5.76473e12	−	9.98480e12i	0.398975	−	0.691045i
$248$	2.30753e12	+	3.99676e12i	0.156194	+	0.270535i
$249$	−2.75054e12	−	2.70247e12i	−0.182105	−	0.178922i
$250$	−2.19061e12	−	1.26475e12i	−0.141871	−	0.0819095i
$251$	−1.20516e13			−0.763553			−0.381776	−	0.924255i	$-0.624688\pi$
$251$	−1.20516e13			−0.763553			−0.381776	+	0.924255i	$0.624688\pi$
$252$	6.69277e12	+	4.50240e12i	0.414861	+	0.279088i
$253$	1.32360e11			0.00802778
$254$	−3.24211e12	−	1.87183e12i	−0.192417	−	0.111092i
$255$	3.38535e11	+	3.32619e11i	0.0196622	+	0.0193186i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−9.94506e12	+	1.72254e13i	−0.553319	+	0.958376i	0.444714	+	0.895673i	$0.353305\pi$
$257$	−9.94506e12	+	1.72254e13i	−0.553319	+	0.958376i	−0.998032	+	0.0627032i	$0.980028\pi$
$258$	6.79427e12	+	2.44910e13i	0.370028	+	1.33382i
$259$	2.89596e13	+	2.50299e12i	1.54399	+	0.133448i
$260$			1.16358e12i			0.0607354i
$261$	2.83131e13	−	4.99183e11i	1.44699	−	0.0255115i
$262$	1.16751e13	−	6.74062e12i	0.584257	−	0.337321i
$263$	−3.40724e13	+	1.96717e13i	−1.66973	+	0.964018i	−0.701944	+	0.712232i	$0.747684\pi$
$263$	−3.40724e13	+	1.96717e13i	−1.66973	+	0.964018i	−0.967783	+	0.251786i	$0.918982\pi$
$264$	−3.80562e10	+	1.47206e11i	−0.00182643	+	0.00706486i
$265$		−	1.32818e11i		−	0.00624318i
$266$	6.73892e12	−	9.64572e12i	0.310271	−	0.444105i
$267$	−2.06210e13	+	5.72067e12i	−0.930034	+	0.258009i
$268$	4.33581e12	−	7.50985e12i	0.191571	−	0.331810i
$269$	1.79453e13	+	3.10821e13i	0.776807	+	1.34547i	0.933774	+	0.357865i	$0.116495\pi$
$269$	1.79453e13	+	3.10821e13i	0.776807	+	1.34547i	−0.156967	+	0.987604i	$0.550172\pi$
$270$	4.53427e11	−	1.89085e12i	0.0192312	−	0.0801968i
$271$	−7.55576e12	−	4.36232e12i	−0.314013	−	0.181295i	0.334708	−	0.942322i	$-0.391362\pi$
$271$	−7.55576e12	−	4.36232e12i	−0.314013	−	0.181295i	−0.648721	+	0.761027i	$0.724696\pi$
$272$	−1.45080e12			−0.0590854
$273$	2.46079e13	+	8.68261e12i	0.982154	+	0.346542i
$274$	−1.62766e13			−0.636702
$275$	−4.59843e11	−	2.65490e11i	−0.0176311	−	0.0101793i
$276$	3.62653e12	−	3.69103e12i	0.136299	−	0.138723i
$277$	−4.10799e12	−	7.11525e12i	−0.151353	−	0.262151i	0.780372	−	0.625315i	$-0.215030\pi$
$277$	−4.10799e12	−	7.11525e12i	−0.151353	−	0.262151i	−0.931725	+	0.363164i	$0.881696\pi$
$278$	−6.60147e12	+	1.14341e13i	−0.238448	+	0.413005i
$279$	−1.28537e13	−	2.13836e13i	−0.455202	−	0.757283i
$280$	−1.02256e11	+	1.18310e12i	−0.00355075	+	0.0410821i
$281$		−	3.63883e13i		−	1.23902i	−0.784990	−	0.619509i	$-0.787332\pi$
$281$		−	3.63883e13i		−	1.23902i	0.784990	−	0.619509i	$-0.212668\pi$
$282$	2.15256e13	+	5.56487e12i	0.718761	+	0.185817i
$283$	3.81698e13	−	2.20373e13i	1.24996	−	0.721662i	0.278855	−	0.960333i	$-0.410045\pi$
$283$	3.81698e13	−	2.20373e13i	1.24996	−	0.721662i	0.971100	+	0.238671i	$0.0767118\pi$
$284$	−1.52898e13	+	8.82760e12i	−0.491080	+	0.283525i
$285$	−2.74618e12	−	7.09953e11i	−0.0865131	−	0.0223657i
$286$			4.91874e11i			0.0151999i
$287$	−9.42837e11	−	2.01639e12i	−0.0285816	−	0.0611257i
$288$	3.06232e12	+	5.09452e12i	0.0910733	+	0.151511i
$289$	1.61788e13	−	2.80225e13i	0.472071	−	0.817652i
$290$	2.08444e12	+	3.61036e12i	0.0596761	+	0.103362i
$291$	1.77898e13	−	1.81062e13i	0.499758	−	0.508647i
$292$	−2.58648e12	−	1.49331e12i	−0.0713024	−	0.0411665i
$293$	−3.01460e13			−0.815564			−0.407782	−	0.913079i	$-0.633698\pi$
$293$	−3.01460e13			−0.815564			−0.407782	+	0.913079i	$0.633698\pi$
$294$	2.42577e13	+	1.09908e13i	0.644080	+	0.291824i
$295$	−6.14755e12			−0.160207
$296$	1.85503e13	+	1.07100e13i	0.474510	+	0.273959i
$297$	1.91675e11	−	7.99312e11i	0.00481288	−	0.0200704i
$298$	−2.28618e13	−	3.95979e13i	−0.563536	−	0.976073i
$299$	8.36986e12	−	1.44970e13i	0.202547	−	0.350822i
$300$	−2.00027e13	+	5.54913e12i	−0.475250	+	0.131843i
$301$	3.55430e13	+	7.60137e13i	0.829160	+	1.77327i
$302$		−	4.23167e13i		−	0.969334i
$303$	9.65329e12	−	3.73400e13i	0.217140	−	0.839924i
$304$	7.50918e12	−	4.33543e12i	0.165878	−	0.0957695i
$305$	1.19142e11	−	6.87865e10i	0.00258473	−	0.00149229i
$306$	7.84197e12	−	1.38260e11i	0.167093	−	0.00294598i
$307$			9.07225e13i			1.89869i	0.314236	+	0.949345i	$0.398252\pi$
$307$			9.07225e13i			1.89869i	−0.314236	+	0.949345i	$0.601748\pi$
$308$	−4.32262e10	+	5.00127e11i	−0.000888625	+	0.0102814i
$309$	−6.16815e12	−	2.22340e13i	−0.124561	−	0.449001i
$310$	1.83652e12	−	3.18095e12i	0.0364340	−	0.0631055i
$311$	−2.49650e13	−	4.32407e13i	−0.486575	−	0.842772i	0.513306	−	0.858206i	$-0.328421\pi$
$311$	−2.49650e13	−	4.32407e13i	−0.486575	−	0.842772i	−0.999881	+	0.0154334i	$0.995087\pi$
$312$	1.37165e13	+	1.34768e13i	0.262659	+	0.258069i
$313$	−5.62363e13	−	3.24681e13i	−1.05809	−	0.610889i	−0.133188	−	0.991091i	$-0.542521\pi$
$313$	−5.62363e13	−	3.24681e13i	−1.05809	−	0.610889i	−0.924904	+	0.380202i	$0.875855\pi$
$314$	−1.78706e13			−0.330390
$315$	4.39972e11	−	6.40470e12i	0.00799313	−	0.116357i
$316$	1.49254e12			0.0266469
$317$	4.53598e13	+	2.61885e13i	0.795876	+	0.459499i	0.842027	−	0.539435i	$-0.181362\pi$
$317$	4.53598e13	+	2.61885e13i	0.795876	+	0.459499i	−0.0461513	+	0.998934i	$0.514696\pi$
$318$	−1.56569e12	−	1.53833e12i	−0.0269996	−	0.0265278i
$319$	8.81146e11	+	1.52619e12i	0.0149348	+	0.0258678i
$320$	−4.37540e11	+	7.57842e11i	−0.00728943	+	0.0126257i
$321$	2.71413e13	+	9.78351e13i	0.444481	+	1.60220i
$322$	9.78430e12	−	1.40047e13i	0.157515	−	0.225459i
$323$		−	1.14412e13i		−	0.181074i
$324$	−1.70381e13	−	2.72454e13i	−0.265109	−	0.423931i
$325$	−5.81567e13	+	3.35768e13i	−0.889695	+	0.513665i
$326$	−2.95387e13	+	1.70542e13i	−0.444318	+	0.256527i
$327$	−1.26774e12	+	4.90377e12i	−0.0187507	+	0.0725299i
$328$		−	1.64030e12i		−	0.0238570i
$329$	7.31323e13	+	6.32087e12i	1.04600	+	0.0904064i
$330$	1.16606e11	−	3.23488e10i	0.00164019	−	0.000455021i
$331$	−2.89309e12	+	5.01097e12i	−0.0400228	+	0.0693215i	−0.885343	−	0.464939i	$-0.846076\pi$
$331$	−2.89309e12	+	5.01097e12i	−0.0400228	+	0.0693215i	0.845320	+	0.534260i	$0.179410\pi$
$332$	−4.69074e12	−	8.12460e12i	−0.0638237	−	0.110546i
$333$	−1.01290e14	−	5.61225e13i	−1.35557	−	0.751093i
$334$	−9.20825e13	−	5.31639e13i	−1.21219	−	0.699859i
$335$	−6.90159e12			−0.0893722
$336$	1.27623e13	+	1.49083e13i	0.162578	+	0.189917i
$337$	−1.26800e14			−1.58912			−0.794558	−	0.607188i	$-0.792297\pi$
$337$	−1.26800e14			−1.58912			−0.794558	+	0.607188i	$0.792297\pi$
$338$	4.20760e12	+	2.42926e12i	0.0518791	+	0.0299524i
$339$	4.69683e12	−	4.78037e12i	0.0569780	−	0.0579914i
$340$	5.77334e11	+	9.99972e11i	0.00689117	+	0.0119359i
$341$	7.76344e11	−	1.34467e12i	0.00911812	−	0.0157930i
$342$	−4.01759e13	+	2.41497e13i	−0.464325	+	0.279106i
$343$	8.50013e13	+	2.24893e13i	0.966736	+	0.255775i
$344$			6.18358e13i			0.692099i
$345$	−3.98720e12	−	1.03079e12i	−0.0439201	−	0.0113544i
$346$	−6.90499e13	+	3.98660e13i	−0.748591	+	0.432199i
$347$	9.52884e13	−	5.50148e13i	1.01678	−	0.587040i	0.103612	−	0.994618i	$-0.466960\pi$
$347$	9.52884e13	−	5.50148e13i	1.01678	−	0.587040i	0.913170	+	0.407578i	$0.133627\pi$
$348$	6.67021e13	+	1.72441e13i	0.700574	+	0.181115i
$349$			1.55630e14i			1.60899i	0.593961	+	0.804494i	$0.297563\pi$
$349$			1.55630e14i			1.60899i	−0.593961	+	0.804494i	$0.702437\pi$
$350$	−6.20832e13	+	2.90293e13i	−0.631829	+	0.295435i
$351$	−7.54255e13	−	7.15384e13i	−0.755665	−	0.716721i
$352$	−1.84960e11	+	3.20359e11i	−0.00182428	+	0.00315975i
$353$	8.58455e13	+	1.48689e14i	0.833598	+	1.44383i	0.895167	+	0.445731i	$0.147056\pi$
$353$	8.58455e13	+	1.48689e14i	0.833598	+	1.44383i	−0.0615691	+	0.998103i	$0.519610\pi$
$354$	−7.12023e13	+	7.24687e13i	−0.680732	+	0.692839i
$355$	1.21689e13	+	7.02572e12i	0.114550	+	0.0661356i
$356$	−5.20647e13			−0.482579
$357$	2.54560e13	−	4.74795e12i	0.232335	−	0.0433342i
$358$	−9.37957e13			−0.842998
$359$	−4.46157e13	−	2.57589e13i	−0.394883	−	0.227986i	0.289391	−	0.957211i	$-0.406547\pi$
$359$	−4.46157e13	−	2.57589e13i	−0.394883	−	0.227986i	−0.684274	+	0.729225i	$0.739881\pi$
$360$	2.29280e12	−	4.13803e12i	0.0199849	−	0.0360686i
$361$	−2.40555e13	−	4.16654e13i	−0.206502	−	0.357673i
$362$	2.45192e13	−	4.24684e13i	0.207304	−	0.359062i
$363$	−1.15665e14	+	3.20876e13i	−0.963196	+	0.267209i
$364$	5.20439e13	+	3.63601e13i	0.426886	+	0.298241i
$365$			2.37699e12i			0.0192051i
$366$	5.69055e11	−	2.20117e12i	0.00452906	−	0.0175189i
$367$	1.90417e14	−	1.09937e14i	1.49294	−	0.861950i	0.492975	−	0.870044i	$-0.335909\pi$
$367$	1.90417e14	−	1.09937e14i	1.49294	−	0.861950i	0.999967	+	0.00809311i	$0.00257615\pi$
$368$	1.09026e13	−	6.29464e12i	0.0842110	−	0.0486192i
$369$	1.56319e11	+	8.86623e12i	0.00118950	+	0.0674674i
$370$		−	1.70478e13i		−	0.127808i
$371$	−5.94063e12	−	4.15038e12i	−0.0438810	−	0.0306572i
$372$	−1.62267e13	−	5.84917e13i	−0.118099	−	0.425704i
$373$	4.16016e13	−	7.20560e13i	0.298340	−	0.516740i	−0.677417	−	0.735600i	$-0.736901\pi$
$373$	4.16016e13	−	7.20560e13i	0.298340	−	0.516740i	0.975756	+	0.218860i	$0.0702338\pi$
$374$	2.44054e11	+	4.22714e11i	0.00172461	+	0.00298712i
$375$	2.37318e13	+	2.33171e13i	0.165257	+	0.162369i
$376$	4.68454e13	+	2.70462e13i	0.321465	+	0.185598i
$377$	2.22879e14			1.50727
$378$	−7.04042e13	−	7.93671e13i	−0.469238	−	0.528976i
$379$	−8.90884e13			−0.585202			−0.292601	−	0.956235i	$-0.594521\pi$
$379$	−8.90884e13			−0.585202			−0.292601	+	0.956235i	$0.594521\pi$
$380$	−5.97642e12	−	3.45049e12i	−0.0386929	−	0.0223393i
$381$	3.51232e13	+	3.45094e13i	0.224133	+	0.220216i
$382$	7.17335e12	+	1.24246e13i	0.0451204	+	0.0781509i
$383$	−1.33101e13	+	2.30537e13i	−0.0825253	+	0.142938i	−0.904334	−	0.426825i	$-0.859632\pi$
$383$	−1.33101e13	+	2.30537e13i	−0.0825253	+	0.142938i	0.821809	+	0.569764i	$0.192965\pi$
$384$	3.86592e12	+	1.39353e13i	0.0236282	+	0.0851716i
$385$	3.61915e11	−	1.69227e11i	0.00218059	−	0.00101961i
$386$		−	3.96426e13i		−	0.235468i
$387$	−5.89289e12	−	3.34238e14i	−0.0345078	−	1.95725i
$388$	5.34825e13	−	3.08781e13i	0.308771	−	0.178269i
$389$	1.69145e14	−	9.76560e13i	0.962801	−	0.555874i	0.0657672	−	0.997835i	$-0.479051\pi$
$389$	1.69145e14	−	9.76560e13i	0.962801	−	0.555874i	0.897034	+	0.441961i	$0.145717\pi$
$390$	3.83058e12	−	1.48171e13i	0.0214985	−	0.0831588i
$391$		−	1.66116e13i		−	0.0919260i
$392$	4.97217e13	+	4.15438e13i	0.271314	+	0.226690i
$393$	−1.70863e14	+	4.74006e13i	−0.919365	+	0.255049i
$394$	7.46285e13	−	1.29260e14i	0.395982	−	0.685861i
$395$	−5.93941e11	−	1.02874e12i	−0.00310785	−	0.00538295i
$396$	9.69224e11	−	1.74925e12i	0.00500150	−	0.00902669i
$397$	1.67129e14	+	9.64918e13i	0.850557	+	0.491069i	0.860839	−	0.508878i	$-0.169940\pi$
$397$	1.67129e14	+	9.64918e13i	0.850557	+	0.491069i	−0.0102818	+	0.999947i	$0.503273\pi$
$398$	1.41438e14			0.709921
$399$	−1.17569e14	+	1.00645e14i	−0.582023	+	0.498241i
$400$	−5.05035e13			−0.246599
$401$	1.21684e14	+	7.02541e13i	0.586055	+	0.338359i	0.763536	−	0.645765i	$-0.223462\pi$
$401$	1.21684e14	+	7.02541e13i	0.586055	+	0.338359i	−0.177481	+	0.984124i	$0.556795\pi$
$402$	−7.99357e13	+	8.13574e13i	−0.379750	+	0.386504i
$403$	−9.81848e13	−	1.70061e14i	−0.460115	−	0.796943i
$404$	4.69166e13	−	8.12619e13i	0.216885	−	0.375655i
$405$	−1.19988e13	+	2.25856e13i	−0.0547187	+	0.102998i
$406$	2.26618e14	+	1.95867e13i	1.01953	+	0.0881188i
$407$		−	7.20653e12i		−	0.0319858i
$408$	1.84747e13	+	4.77615e12i	0.0808996	+	0.0209145i
$409$	1.82561e14	−	1.05402e14i	0.788732	−	0.455374i	−0.0507842	−	0.998710i	$-0.516172\pi$
$409$	1.82561e14	−	1.05402e14i	0.788732	−	0.455374i	0.839516	+	0.543335i	$0.182839\pi$
$410$	−1.13058e12	+	6.52741e11i	−0.00481937	+	0.00278246i
$411$	2.07268e14	+	5.35838e13i	0.871772	+	0.225374i
$412$		−	5.61373e13i		−	0.232979i
$413$	−1.92102e14	+	2.74965e14i	−0.786696	+	1.12603i
$414$	−5.83317e13	+	3.50632e13i	−0.235724	+	0.141693i
$415$	−3.73327e12	+	6.46622e12i	−0.0148876	+	0.0257861i
$416$	2.33920e13	+	4.05161e13i	0.0920563	+	0.159446i
$417$	1.21706e14	−	1.23870e14i	0.472675	−	0.481082i
$418$	−2.52638e12	−	1.45861e12i	−0.00968345	−	0.00559074i
$419$	−3.33287e14			−1.26078			−0.630392	−	0.776277i	$-0.717106\pi$
$419$	−3.33287e14			−1.26078			−0.630392	+	0.776277i	$0.717106\pi$
$420$	5.19699e12	−	1.47291e13i	0.0194035	−	0.0549926i
$421$	1.86837e14			0.688511			0.344255	−	0.938876i	$-0.388131\pi$
$421$	1.86837e14			0.688511			0.344255	+	0.938876i	$0.388131\pi$
$422$	2.56489e14	+	1.48084e14i	0.932933	+	0.538629i
$423$	−2.55789e14	−	1.41727e14i	−0.918352	−	0.508840i
$424$	−2.67011e12	−	4.62477e12i	−0.00946275	−	0.0163900i
$425$	−3.33197e13	+	5.77114e13i	−0.116563	+	0.201894i
$426$	2.23764e14	−	6.20763e13i	0.772746	−	0.214374i
$427$	6.46362e11	−	7.47839e12i	0.00220355	−	0.0254950i
$428$			2.47018e14i			0.831356i
$429$	1.61928e12	−	6.26357e12i	0.00538031	−	0.0208117i
$430$	4.26205e13	−	2.46070e13i	0.139811	−	0.0807201i
$431$	2.03904e14	−	1.17724e14i	0.660391	−	0.381277i	−0.132035	−	0.991245i	$-0.542151\pi$
$431$	2.03904e14	−	1.17724e14i	0.660391	−	0.381277i	0.792426	+	0.609968i	$0.208818\pi$
$432$	−2.22243e13	−	7.49555e13i	−0.0710670	−	0.239686i
$433$			1.09511e14i			0.345758i	0.984943	+	0.172879i	$0.0553070\pi$
$433$			1.09511e14i			0.345758i	−0.984943	+	0.172879i	$0.944693\pi$
$434$	−8.48871e13	−	1.81543e14i	−0.264636	−	0.565960i
$435$	−1.46579e13	−	5.28368e13i	−0.0451213	−	0.162647i
$436$	−6.16143e12	+	1.06719e13i	−0.0187286	+	0.0324389i
$437$	4.96402e13	+	8.59793e13i	0.149000	+	0.258075i
$438$	2.80205e13	+	2.75308e13i	0.0830554	+	0.0816040i
$439$	−4.09842e14	−	2.36623e14i	−1.19967	−	0.692630i	−0.239189	−	0.970973i	$-0.576882\pi$
$439$	−4.09842e14	−	2.36623e14i	−1.19967	−	0.692630i	−0.960482	+	0.278343i	$0.910215\pi$
$440$	2.94412e11			0.000851070
$441$	−2.72718e14	−	2.19817e14i	−0.778576	−	0.627550i
$442$	6.17314e13			0.174054
$443$	−5.27104e14	−	3.04324e14i	−1.46783	−	0.847452i	−0.468479	−	0.883475i	$-0.655198\pi$
$443$	−5.27104e14	−	3.04324e14i	−1.46783	−	0.847452i	−0.999351	+	0.0360227i	$0.988531\pi$
$444$	−2.00963e14	−	1.97451e14i	−0.552725	−	0.543066i
$445$	2.07187e13	+	3.58858e13i	0.0562836	+	0.0974861i
$446$	1.73147e14	−	2.99900e14i	0.464595	−	0.804702i
$447$	1.60766e14	+	5.79506e14i	0.426092	+	1.53591i
$448$	2.02239e13	+	4.32516e13i	0.0529462	+	0.113233i
$449$			3.63033e14i			0.938839i	0.882975	+	0.469420i	$0.155537\pi$
$449$			3.63033e14i			0.938839i	−0.882975	+	0.469420i	$0.844463\pi$
$450$	2.72985e14	−	4.81294e12i	0.697380	−	0.0122954i
$451$	−4.77925e11	+	2.75930e11i	−0.00120612	+	0.000696351i
$452$	1.41204e13	−	8.15240e12i	0.0352034	−	0.0203247i
$453$	−1.39309e14	+	5.38865e14i	−0.343116	+	1.32721i
$454$			4.25810e14i			1.03612i
$455$	4.35097e12	−	5.03406e13i	0.0104598	−	0.121020i
$456$	−1.09895e14	+	3.04870e13i	−0.261019	+	0.0724117i
$457$	−3.72352e13	+	6.44933e13i	−0.0873806	+	0.151348i	−0.906403	−	0.422414i	$-0.861183\pi$
$457$	−3.72352e13	+	6.44933e13i	−0.0873806	+	0.151348i	0.819023	+	0.573761i	$0.194516\pi$
$458$	−1.04657e14	−	1.81271e14i	−0.242665	−	0.420308i
$459$	−1.00316e14	−	2.40557e13i	−0.229826	−	0.0551123i
$460$	−8.67721e12	−	5.00979e12i	−0.0196432	−	0.0113410i
$461$	−2.84148e14			−0.635608			−0.317804	−	0.948156i	$-0.602945\pi$
$461$	−2.84148e14			−0.635608			−0.317804	+	0.948156i	$0.602945\pi$
$462$	2.19690e12	−	6.22636e12i	0.00485601	−	0.0137627i
$463$	−8.60751e13			−0.188011			−0.0940053	−	0.995572i	$-0.529967\pi$
$463$	−8.60751e13			−0.188011			−0.0940053	+	0.995572i	$0.529967\pi$
$464$	1.45162e14	+	8.38091e13i	0.313331	+	0.180902i
$465$	−3.38583e13	+	3.44606e13i	−0.0722228	+	0.0735074i
$466$	1.32590e14	+	2.29653e14i	0.279504	+	0.484115i
$467$	1.26850e12	−	2.19710e12i	0.00264269	−	0.00457727i	−0.864701	−	0.502287i	$-0.832492\pi$
$467$	1.26850e12	−	2.19710e12i	0.00264269	−	0.00457727i	0.867344	+	0.497710i	$0.165825\pi$
$468$	−1.30301e14	−	2.16771e14i	−0.268284	−	0.446322i
$469$	−2.15665e14	+	3.08691e14i	−0.438863	+	0.628164i
$470$		−	4.30511e13i		−	0.0865857i
$471$	2.27566e14	+	5.88313e13i	0.452369	+	0.116948i
$472$	−2.14060e14	+	1.23587e14i	−0.420585	+	0.242825i
$473$	1.80168e13	−	1.04020e13i	0.0349898	−	0.0202013i
$474$	−1.90061e13	−	4.91354e12i	−0.0364849	−	0.00943221i
$475$		−	3.98276e14i		−	0.755734i
$476$	6.27671e13	+	5.42500e12i	0.117732	+	0.0101756i
$477$	1.48734e13	+	2.47436e13i	0.0275778	+	0.0458788i
$478$	−3.46727e14	+	6.00549e14i	−0.635528	+	1.10077i
$479$	−2.74211e14	−	4.74948e14i	−0.496867	−	0.860598i	0.503127	−	0.864213i	$-0.332183\pi$
$479$	−2.74211e14	−	4.74948e14i	−0.496867	−	0.860598i	−0.999993	+	0.00361444i	$0.998849\pi$
$480$	8.06655e12	−	8.21003e12i	0.0144498	−	0.0147068i
$481$	−7.89309e14	−	4.55708e14i	−1.39781	−	0.807028i
$482$	−1.33299e14			−0.233383
$483$	−1.70699e14	+	1.46127e14i	−0.295475	+	0.252942i
$484$	−2.92035e14			−0.499787
$485$	−4.25657e13	−	2.45753e13i	−0.0720245	−	0.0415834i
$486$	1.27271e14	+	4.03036e14i	0.212927	+	0.674286i
$487$	7.55239e12	+	1.30811e13i	0.0124932	+	0.0216389i	0.872204	−	0.489142i	$-0.162690\pi$
$487$	7.55239e12	+	1.30811e13i	0.0124932	+	0.0216389i	−0.859711	+	0.510780i	$0.829357\pi$
$488$	2.76570e12	−	4.79033e12i	0.00452372	−	0.00783532i
$489$	4.32292e14	−	1.19926e14i	0.699163	−	0.193961i
$490$	8.84793e12	−	5.08028e13i	0.0141502	−	0.0812474i
$491$		−	3.45137e14i		−	0.545812i	−0.962041	−	0.272906i	$-0.912015\pi$
$491$		−	3.45137e14i		−	0.545812i	0.962041	−	0.272906i	$-0.0879848\pi$
$492$	−5.39997e12	+	2.08877e13i	−0.00844468	+	0.0326650i
$493$	1.91541e14	−	1.10586e14i	0.296212	−	0.171018i
$494$	−3.19514e14	+	1.84471e14i	−0.488643	+	0.282118i
$495$	−1.59137e12	+	2.80571e10i	−0.00240682	+	4.24341e-5i
$496$		−	1.47682e14i		−	0.220891i
$497$	6.94504e14	−	3.24741e14i	1.02734	−	0.480371i
$498$	3.29856e13	+	1.18902e14i	0.0482573	+	0.173951i
$499$	−4.54750e14	+	7.87650e14i	−0.657990	+	1.13967i	0.323145	+	0.946349i	$0.395260\pi$
$499$	−4.54750e14	+	7.87650e14i	−0.657990	+	1.13967i	−0.981135	+	0.193323i	$0.938073\pi$
$500$	4.04720e13	+	7.00995e13i	0.0579188	+	0.100318i
$501$	9.97569e14	+	9.80136e14i	1.41200	+	1.38733i
$502$	3.33983e14	+	1.92825e14i	0.467579	+	0.269957i
$503$	−2.46131e14			−0.340834			−0.170417	−	0.985372i	$-0.554511\pi$
$503$	−2.46131e14			−0.340834			−0.170417	+	0.985372i	$0.554511\pi$
$504$	−1.13437e14	−	2.31859e14i	−0.155377	−	0.317581i
$505$	−7.46800e13			−0.101182
$506$	−3.66808e12	−	2.11777e12i	−0.00491599	−	0.00283825i
$507$	−4.55827e13	−	4.47861e13i	−0.0604305	−	0.0593745i
$508$	5.98987e13	+	1.03748e14i	0.0785537	+	0.136059i
$509$	−5.65067e14	+	9.78725e14i	−0.733081	+	1.26973i	0.222479	+	0.974938i	$0.428585\pi$
$509$	−5.65067e14	+	9.78725e14i	−0.733081	+	1.26973i	−0.955560	+	0.294796i	$0.904748\pi$
$510$	−4.05986e12	−	1.46344e13i	−0.00521044	−	0.0187818i
$511$	1.06317e14	+	7.42776e13i	0.134985	+	0.0943068i
$512$			3.51844e13i			0.0441942i
$513$	5.91107e14	−	1.75263e14i	0.734548	−	0.217794i
$514$	5.51211e14	−	3.18242e14i	0.677674	−	0.391255i
$515$	−3.86928e13	+	2.23393e13i	−0.0470642	+	0.0271725i
$516$	2.03568e14	−	7.87423e14i	0.244983	−	0.947621i
$517$		−	1.81988e13i		−	0.0216693i
$518$	−7.62504e14	−	5.32719e14i	−0.898315	−	0.627602i
$519$	1.01053e15	−	2.80341e14i	1.17796	−	0.326787i
$520$	1.86172e13	−	3.22460e13i	0.0214732	−	0.0371927i
$521$	−6.47609e14	−	1.12169e15i	−0.739104	−	1.28016i	−0.952899	−	0.303287i	$-0.901916\pi$
$521$	−6.47609e14	−	1.12169e15i	−0.739104	−	1.28016i	0.213796	−	0.976878i	$-0.431417\pi$
$522$	−7.92623e14	−	4.39176e14i	−0.895115	−	0.495965i
$523$	−3.87601e14	−	2.23781e14i	−0.433137	−	0.250072i	0.267545	−	0.963545i	$-0.413788\pi$
$523$	−3.87601e14	−	2.23781e14i	−0.433137	−	0.250072i	−0.700682	+	0.713474i	$0.747121\pi$
$524$	−4.31400e14			−0.477044
$525$	8.86140e14	−	1.65280e14i	0.969675	−	0.180860i
$526$	1.25899e15			1.36333
$527$	−1.68759e14	−	9.74331e13i	−0.180846	−	0.104411i
$528$	3.40994e12	−	3.47059e12i	0.00361626	−	0.00368058i
$529$	−4.04332e14	−	7.00323e14i	−0.424357	−	0.735009i
$530$	−2.12509e12	+	3.68077e12i	−0.00220730	+	0.00382315i
$531$	1.14527e15	−	6.88421e14i	1.17730	−	0.707676i
$532$	−3.41086e14	+	1.59487e14i	−0.347016	+	0.162260i
$533$			6.97942e13i			0.0702781i
$534$	6.62998e14	+	1.71401e14i	0.660747	+	0.170819i
$535$	1.70258e14	−	9.82983e13i	0.167943	−	0.0969617i
$536$	−2.40315e14	+	1.38746e14i	−0.234625	+	0.135461i
$537$	1.19440e15	+	3.08782e14i	1.15423	+	0.298396i
$538$		−	1.14850e15i		−	1.09857i
$539$	3.74025e12	−	2.14757e13i	0.00354130	−	0.0203333i
$540$	−4.28194e13	+	4.51461e13i	−0.0401305	+	0.0423111i
$541$	−1.39802e14	+	2.42145e14i	−0.129697	+	0.224642i	−0.923559	−	0.383456i	$-0.874734\pi$
$541$	−1.39802e14	+	2.42145e14i	−0.129697	+	0.224642i	0.793862	+	0.608098i	$0.208067\pi$
$542$	1.39594e14	+	2.41784e14i	0.128195	+	0.222040i
$543$	−4.52039e14	+	4.60079e14i	−0.410938	+	0.418247i
$544$	4.02059e13	+	2.32129e13i	0.0361823	+	0.0208898i
$545$	9.80753e12			0.00873734
$546$	−5.43032e14	−	6.34346e14i	−0.478923	−	0.559457i
$547$	1.31043e15			1.14415			0.572077	−	0.820200i	$-0.306138\pi$
$547$	1.31043e15			1.14415			0.572077	+	0.820200i	$0.306138\pi$
$548$	4.51071e14	+	2.60426e14i	0.389899	+	0.225108i
$549$	−1.44928e13	+	2.61566e13i	−0.0124024	+	0.0223837i
$550$	8.49569e12	+	1.47150e13i	0.00719787	+	0.0124671i
$551$	−6.60927e14	+	1.14476e15i	−0.554395	+	0.960241i
$552$	−1.59558e14	+	4.42644e13i	−0.132511	+	0.0367612i
$553$	−6.45726e13	−	5.58105e12i	−0.0530958	−	0.00458910i
$554$			2.62911e14i			0.214045i
$555$	−5.61225e13	+	2.17088e14i	−0.0452403	+	0.174995i
$556$	3.65891e14	−	2.11247e14i	0.292038	−	0.168608i
$557$	1.13899e15	−	6.57595e14i	0.900152	−	0.519703i	0.0229022	−	0.999738i	$-0.492709\pi$
$557$	1.13899e15	−	6.57595e14i	0.900152	−	0.519703i	0.877249	+	0.480035i	$0.159376\pi$
$558$	1.40739e13	+	7.98259e14i	0.0110136	+	0.624677i
$559$		−	2.63110e15i		−	2.03879i
$560$	2.17634e13	−	3.11509e13i	0.0166991	−	0.0239021i
$561$	−1.71620e12	−	6.18632e12i	−0.00130399	−	0.00470042i
$562$	−5.82213e14	+	1.00842e15i	−0.438059	+	0.758740i
$563$	9.93366e14	+	1.72056e15i	0.740139	+	1.28196i	0.952432	+	0.304752i	$0.0985734\pi$
$563$	9.93366e14	+	1.72056e15i	0.740139	+	1.28196i	−0.212293	+	0.977206i	$0.568093\pi$
$564$	−5.07496e14	−	4.98627e14i	−0.374453	−	0.367909i
$565$	−1.12381e13	−	6.48834e12i	−0.00821160	−	0.00474097i
$566$	−1.41039e15			−1.02058
$567$	6.35252e14	+	1.24244e15i	0.455239	+	0.890369i
$568$	5.64966e14			0.400965
$569$	−1.00143e15	−	5.78178e14i	−0.703890	−	0.406391i	0.104904	−	0.994482i	$-0.466546\pi$
$569$	−1.00143e15	−	5.78178e14i	−0.703890	−	0.406391i	−0.808795	+	0.588091i	$0.799880\pi$
$570$	6.47451e13	+	6.36136e13i	0.0450708	+	0.0442831i
$571$	7.17124e14	+	1.24210e15i	0.494420	+	0.856360i	0.999979	−	0.00643184i	$-0.00204733\pi$
$571$	7.17124e14	+	1.24210e15i	0.494420	+	0.856360i	−0.505560	+	0.862792i	$0.668714\pi$
$572$	7.86998e12	−	1.36312e13i	0.00537397	−	0.00930800i
$573$	−5.04435e13	−	1.81831e14i	−0.0341157	−	0.122975i
$574$	−6.13357e12	+	7.09652e13i	−0.00410864	+	0.0475368i
$575$		−	5.78260e14i		−	0.383663i
$576$	−3.35304e12	−	1.90181e14i	−0.00220351	−	0.124981i
$577$	−1.23957e15	+	7.15668e14i	−0.806874	+	0.465849i	−0.845869	−	0.533391i	$-0.820918\pi$
$577$	−1.23957e15	+	7.15668e14i	−0.806874	+	0.465849i	0.0389954	+	0.999239i	$0.487584\pi$
$578$	−8.96719e14	+	5.17721e14i	−0.578167	+	0.333805i
$579$	−1.30506e14	+	5.04814e14i	−0.0833488	+	0.322403i
$580$		−	1.33404e14i		−	0.0843948i
$581$	1.72558e14	+	3.69040e14i	0.108135	+	0.231262i
$582$	−7.82705e14	+	2.17137e14i	−0.485872	+	0.134790i
$583$	−8.98332e11	+	1.55596e12i	−0.000552408	+	0.000956798i
$584$	4.77858e13	+	8.27675e13i	0.0291091	+	0.0504184i
$585$	−9.75579e13	+	1.76072e14i	−0.0588715	+	0.106251i
$586$	8.35431e14	+	4.82337e14i	0.499429	+	0.288346i
$587$	3.01314e15			1.78447			0.892235	−	0.451572i	$-0.149137\pi$
$587$	3.01314e15			1.78447			0.892235	+	0.451572i	$0.149137\pi$
$588$	−4.96396e14	−	6.92711e14i	−0.291241	−	0.406421i
$589$	1.16463e15			0.676948
$590$	1.70366e14	+	9.83609e13i	0.0981063	+	0.0566417i
$591$	−1.37586e15	+	1.40033e15i	−0.784953	+	0.798914i
$592$	−3.42720e14	−	5.93608e14i	−0.193718	−	0.335529i
$593$	4.52648e14	−	7.84010e14i	0.253490	−	0.439057i	−0.710995	−	0.703197i	$-0.751755\pi$
$593$	4.52648e14	−	7.84010e14i	0.253490	−	0.439057i	0.964484	+	0.264141i	$0.0850883\pi$
$594$	−1.81009e13	+	1.90844e13i	−0.0100432	+	0.0105889i
$595$	−2.12384e13	−	4.54213e13i	−0.0116756	−	0.0249699i
$596$			1.46316e15i			0.796960i
$597$	−1.80109e15	−	4.65624e14i	−0.972022	−	0.251291i
$598$	−4.63905e14	+	2.67836e14i	−0.248069	+	0.143223i
$599$	−1.14772e14	+	6.62639e13i	−0.0608121	+	0.0351099i	−0.530098	−	0.847937i	$-0.677845\pi$
$599$	−1.14772e14	+	6.62639e13i	−0.0608121	+	0.0351099i	0.469286	+	0.883046i	$0.344511\pi$
$600$	6.43117e14	+	1.66261e14i	0.337643	+	0.0872889i
$601$		−	2.81988e15i		−	1.46697i	−0.679705	−	0.733486i	$-0.737892\pi$
$601$		−	2.81988e15i		−	1.46697i	0.679705	−	0.733486i	$-0.262108\pi$
$602$	2.31223e14	−	2.67524e15i	0.119193	−	1.37906i
$603$	1.28574e15	−	7.72860e14i	0.656763	−	0.394780i
$604$	−6.77067e14	+	1.17271e15i	−0.342711	+	0.593593i
$605$	1.16212e14	+	2.01286e14i	0.0582906	+	0.100962i
$606$	−8.64960e14	+	8.80344e14i	−0.429929	+	0.437576i
$607$	8.01213e12	+	4.62581e12i	0.00394648	+	0.00227850i	0.501972	−	0.864884i	$-0.332608\pi$
$607$	8.01213e12	+	4.62581e12i	0.00394648	+	0.00227850i	−0.498025	+	0.867162i	$0.665941\pi$
$608$	−2.77467e14			−0.135439
$609$	−2.82130e15	−	9.95462e14i	−1.36475	−	0.481537i
$610$	−4.40234e12			−0.00211042
$611$	−1.99326e15	−	1.15081e15i	−0.946972	−	0.546734i
$612$	−2.19535e14	−	1.21640e14i	−0.103365	−	0.0572722i
$613$	1.29886e15	+	2.24969e15i	0.606079	+	1.04976i	0.991880	+	0.127178i	$0.0405918\pi$
$613$	1.29886e15	+	2.24969e15i	0.606079	+	1.04976i	−0.385801	+	0.922582i	$0.626075\pi$
$614$	1.45156e15	−	2.51418e15i	0.671288	−	1.16271i
$615$	1.65458e13	−	4.59012e12i	0.00758358	−	0.00210383i
$616$	9.19994e12	−	1.31683e13i	0.00417918	−	0.00598185i
$617$		−	2.23031e15i		−	1.00415i	−0.864825	−	0.502073i	$-0.832571\pi$
$617$		−	2.23031e15i		−	1.00415i	0.864825	−	0.502073i	$-0.167429\pi$
$618$	−1.84808e14	+	7.14858e14i	−0.0824677	+	0.318995i
$619$	1.26381e14	−	7.29663e13i	0.0558965	−	0.0322719i	−0.471791	−	0.881710i	$-0.656392\pi$
$619$	1.26381e14	−	7.29663e13i	0.0558965	−	0.0322719i	0.527688	+	0.849438i	$0.323059\pi$
$620$	−1.01790e14	+	5.87687e13i	−0.0446223	+	0.0257627i
$621$	8.58233e14	−	2.54466e14i	0.372908	−	0.110567i
$622$			1.59776e15i			0.688121i
$623$	2.25251e15	+	1.94686e14i	0.961574	+	0.0831094i
$624$	−1.64494e14	−	5.92944e14i	−0.0696041	−	0.250899i
$625$	−1.14367e15	+	1.98089e15i	−0.479688	+	0.830845i
$626$	1.03898e15	+	1.79956e15i	0.431964	+	0.748183i
$627$	2.73694e13	+	2.68911e13i	0.0112796	+	0.0110825i
$628$	4.95245e14	+	2.85930e14i	0.202321	+	0.116810i
$629$	−9.04437e14			−0.366269
$630$	−1.14668e14	+	1.70453e14i	−0.0460330	+	0.0684276i
$631$	3.65245e14			0.145353			0.0726763	−	0.997356i	$-0.476846\pi$
$631$	3.65245e14			0.145353			0.0726763	+	0.997356i	$0.476846\pi$
$632$	−4.13624e13	−	2.38806e13i	−0.0163178	−	0.00942109i
$633$	−2.77866e15	−	2.73010e15i	−1.08671	−	1.06772i
$634$	−8.38032e14	−	1.45151e15i	−0.324915	−	0.562769i
$635$	4.76722e13	−	8.25707e13i	0.0183236	−	0.0317374i
$636$	1.87764e13	+	6.76825e13i	0.00715482	+	0.0257907i
$637$	−2.11565e15	−	1.76768e15i	−0.799238	−	0.667785i
$638$		−	5.63934e13i		−	0.0211210i
$639$	−3.05379e15	+	5.38407e13i	−1.13392	+	0.0199920i
$640$	2.42510e13	−	1.40013e13i	0.00892769	−	0.00515440i
$641$	−1.04470e15	+	6.03155e14i	−0.381303	+	0.220145i	−0.678385	−	0.734707i	$-0.737320\pi$
$641$	−1.04470e15	+	6.03155e14i	−0.381303	+	0.220145i	0.297082	+	0.954852i	$0.403987\pi$
$642$	8.13199e14	−	3.14555e15i	0.294276	−	1.13829i
$643$			1.14740e15i			0.411675i	0.978586	+	0.205837i	$0.0659918\pi$
$643$			1.14740e15i			0.411675i	−0.978586	+	0.205837i	$0.934008\pi$
$644$	−4.95226e14	+	2.31561e14i	−0.176170	+	0.0823746i
$645$	−6.23742e14	+	1.73038e14i	−0.220002	+	0.0610328i
$646$	−1.83059e14	+	3.17067e14i	−0.0640195	+	0.110885i
$647$	2.37948e15	+	4.12137e15i	0.825102	+	1.42912i	0.901841	+	0.432068i	$0.142216\pi$
$647$	2.37948e15	+	4.12137e15i	0.825102	+	1.42912i	−0.0767389	+	0.997051i	$0.524451\pi$
$648$	3.62480e13	+	1.02766e15i	0.0124630	+	0.353334i
$649$	7.20181e13	+	4.15796e13i	0.0245525	+	0.0141754i
$650$	2.14891e15			0.726433
$651$	4.83309e14	+	2.59124e15i	0.162005	+	0.868585i
$652$	1.09147e15			0.362784
$653$	−3.04172e15	−	1.75614e15i	−1.00253	−	0.578810i	−0.0935327	−	0.995616i	$-0.529816\pi$
$653$	−3.04172e15	−	1.75614e15i	−1.00253	−	0.578810i	−0.908995	+	0.416806i	$0.863149\pi$
$654$	1.13593e14	−	1.15613e14i	0.0371256	−	0.0377859i
$655$	1.71672e14	+	2.97344e14i	0.0556380	+	0.0963678i
$656$	−2.62448e13	+	4.54572e13i	−0.00843473	+	0.0146094i
$657$	−2.66182e14	−	4.42826e14i	−0.0848340	−	0.141131i
$658$	−1.92557e15	−	1.34529e15i	−0.608578	−	0.425179i
$659$			2.98301e15i			0.934943i	0.884008	+	0.467471i	$0.154835\pi$
$659$			2.98301e15i			0.934943i	−0.884008	+	0.467471i	$0.845165\pi$
$660$	−3.74907e12	−	9.69224e11i	−0.00116528	−	0.000301254i
$661$	−3.53472e15	+	2.04077e15i	−1.08955	+	0.629052i	−0.933457	−	0.358691i	$-0.883223\pi$
$661$	−3.53472e15	+	2.04077e15i	−1.08955	+	0.629052i	−0.156093	+	0.987742i	$0.549890\pi$
$662$	1.60351e14	−	9.25788e13i	0.0490177	−	0.0283004i
$663$	−7.86094e14	−	2.03224e14i	−0.238314	−	0.0616099i
$664$			3.00207e14i			0.0902603i
$665$	2.45659e14	+	1.71628e14i	0.0732511	+	0.0511764i
$666$	1.90906e15	+	3.17594e15i	0.564561	+	0.939214i
$667$	−9.59605e14	+	1.66208e15i	−0.281450	+	0.487485i
$668$	1.70124e15	+	2.94664e15i	0.494875	+	0.857149i
$669$	−3.19217e15	+	3.24895e15i	−0.920963	+	0.937344i
$670$	1.91262e14	+	1.10425e14i	0.0547291	+	0.0315979i
$671$	−1.86098e12			−0.000528163
$672$	−1.15146e14	−	6.17348e14i	−0.0324128	−	0.173780i
$673$	5.44670e15			1.52072			0.760362	−	0.649499i	$-0.225021\pi$
$673$	5.44670e15			1.52072			0.760362	+	0.649499i	$0.225021\pi$
$674$	3.51399e15	+	2.02880e15i	0.973131	+	0.561837i
$675$	−3.49206e15	−	8.37396e14i	−0.959204	−	0.230017i
$676$	−7.77362e13	−	1.34643e14i	−0.0211795	−	0.0366840i
$677$	−2.78534e15	+	4.82435e15i	−0.752733	+	1.30377i	0.193761	+	0.981049i	$0.437932\pi$
$677$	−2.78534e15	+	4.82435e15i	−0.752733	+	1.30377i	−0.946494	+	0.322723i	$0.895402\pi$
$678$	−2.06648e14	+	5.73282e13i	−0.0553948	+	0.0153676i
$679$	−2.42931e15	+	1.13591e15i	−0.645951	+	0.302038i
$680$		−	3.69494e13i		−	0.00974559i
$681$	1.40180e15	−	5.42230e15i	0.366755	−	1.41865i
$682$	−4.30294e13	+	2.48430e13i	−0.0111674	+	0.00644748i
$683$	4.95135e15	−	2.85866e15i	1.27471	−	0.735951i	0.298836	−	0.954305i	$-0.403402\pi$
$683$	4.95135e15	−	2.85866e15i	1.27471	−	0.735951i	0.975870	+	0.218353i	$0.0700685\pi$
$684$	1.49978e15	−	2.64424e13i	0.383018	−	0.00675292i
$685$		−	4.14537e14i		−	0.105018i
$686$	−1.99580e15	−	1.98326e15i	−0.501573	−	0.498422i
$687$	7.35953e14	+	2.65286e15i	0.183480	+	0.661381i
$688$	9.89372e14	−	1.71364e15i	0.244694	−	0.423822i
$689$	1.13613e14	+	1.96783e14i	0.0278754	+	0.0482816i
$690$	9.40039e13	+	9.23612e13i	0.0228811	+	0.0224812i
$691$	−3.62558e15	−	2.09323e15i	−0.875484	−	0.505461i	−0.00631714	−	0.999980i	$-0.502011\pi$
$691$	−3.62558e15	−	2.09323e15i	−0.875484	−	0.505461i	−0.869167	+	0.494519i	$0.835344\pi$
$692$	2.55142e15			0.611222
$693$	−4.84731e13	+	7.20548e13i	−0.0115204	+	0.0171250i
$694$	−3.52095e15			−0.830199
$695$	−2.91206e14	−	1.68128e14i	−0.0681213	−	0.0393299i
$696$	−1.57260e15	−	1.54512e15i	−0.364978	−	0.358600i
$697$	3.46299e13	+	5.99808e13i	0.00797391	+	0.0138112i
$698$	2.49008e15	−	4.31294e15i	0.568863	−	0.985300i
$699$	−9.32382e14	−	3.36091e15i	−0.211334	−	0.761786i
$700$	2.18497e15	+	1.88848e14i	0.491367	+	0.0424691i
$701$		−	3.25683e15i		−	0.726684i	−0.931656	−	0.363342i	$-0.881636\pi$
$701$		−	3.25683e15i		−	0.726684i	0.931656	−	0.363342i	$-0.118364\pi$
$702$	9.45639e14	+	3.18934e15i	0.209349	+	0.706068i
$703$	4.68125e15	−	2.70272e15i	1.02827	−	0.593673i
$704$	1.02515e13	−	5.91870e12i	0.00223428	−	0.00128996i
$705$	−1.41727e14	+	5.48217e14i	−0.0306488	+	0.118553i
$706$		−	5.49411e15i		−	1.17889i
$707$	−2.33364e15	+	3.34025e15i	−0.496853	+	0.711168i
$708$	3.13271e15	−	8.69075e14i	0.661817	−	0.183601i
$709$	3.29807e15	−	5.71243e15i	0.691363	−	1.19748i	−0.280028	−	0.959992i	$-0.590344\pi$
$709$	3.29807e15	−	5.71243e15i	0.691363	−	1.19748i	0.971391	−	0.237484i	$-0.0763228\pi$
$710$	−2.24823e14	−	3.89405e14i	−0.0467649	−	0.0809992i
$711$	2.25850e14	+	1.25139e14i	0.0466163	+	0.0258291i
$712$	1.44286e15	+	8.33036e14i	0.295518	+	0.170618i
$713$	1.69094e15			0.343666
$714$	−7.81423e14	−	2.75716e14i	−0.157596	−	0.0556061i
$715$	−1.25271e13			−0.00250708
$716$	2.59934e15	+	1.50073e15i	0.516229	+	0.298045i
$717$	6.39231e15	−	6.50601e15i	1.25980	−	1.28221i
$718$	8.24285e14	+	1.42770e15i	0.161210	+	0.279224i
$719$	−1.76876e15	+	3.06359e15i	−0.343290	+	0.594596i	−0.985042	−	0.172317i	$-0.944875\pi$
$719$	−1.76876e15	+	3.06359e15i	−0.343290	+	0.594596i	0.641752	+	0.766913i	$0.278208\pi$
$720$	−1.29748e14	+	7.79917e13i	−0.0249904	+	0.0150217i
$721$	−2.09914e14	+	2.42870e15i	−0.0401234	+	0.464227i
$722$			1.53955e15i			0.292039i
$723$	1.69745e15	+	4.38830e14i	0.319548	+	0.0826107i
$724$	−1.35899e15	+	7.84613e14i	−0.253895	+	0.146586i
$725$	6.66767e15	−	3.84958e15i	1.23627	−	0.713763i
$726$	3.71880e15	+	9.61399e14i	0.684308	+	0.176910i
$727$		−	2.96482e15i		−	0.541452i	−0.962657	−	0.270726i	$-0.912736\pi$
$727$		−	2.96482e15i		−	0.541452i	0.962657	−	0.270726i	$-0.0872637\pi$
$728$	−8.60520e14	−	1.84034e15i	−0.155969	−	0.333562i
$729$	−2.93864e14	−	5.55129e15i	−0.0528623	−	0.998602i
$730$	3.80319e13	−	6.58731e13i	0.00679003	−	0.0117607i
$731$	−1.30548e15	−	2.26115e15i	−0.231325	−	0.400667i
$732$	−5.09888e13	+	5.18957e13i	−0.00896735	+	0.00912684i
$733$	7.23241e15	+	4.17563e15i	1.26244	+	0.728870i	0.973546	−	0.228491i	$-0.0733790\pi$
$733$	7.23241e15	+	4.17563e15i	1.26244	+	0.728870i	0.288894	+	0.957361i	$0.406712\pi$
$734$	−7.03600e15			−1.21898
$735$	−2.79917e14	+	6.17801e14i	−0.0481337	+	0.106235i
$736$	−4.02857e14			−0.0687580
$737$	8.08515e13	+	4.66796e13i	0.0136967	+	0.00790781i
$738$	1.37528e14	−	2.48209e14i	0.0231249	−	0.0417357i
$739$	7.76577e14	+	1.34507e15i	0.129611	+	0.224492i	0.923526	−	0.383536i	$-0.125294\pi$
$739$	7.76577e14	+	1.34507e15i	0.129611	+	0.224492i	−0.793915	+	0.608029i	$0.791961\pi$
$740$	−2.72764e14	+	4.72442e14i	−0.0451870	+	0.0782661i
$741$	4.67601e15	−	1.29722e15i	0.768910	−	0.213310i
$742$	9.82254e13	+	2.10069e14i	0.0160325	+	0.0342879i
$743$			5.43590e15i			0.880710i	0.897824	+	0.440355i	$0.145147\pi$
$743$			5.43590e15i			0.880710i	−0.897824	+	0.440355i	$0.854853\pi$
$744$	−4.86179e14	+	1.88060e15i	−0.0781889	+	0.302444i
$745$	1.00849e15	−	5.82250e14i	0.160994	−	0.0929501i
$746$	−2.30579e15	+	1.33125e15i	−0.365390	+	0.210958i
$747$	−2.86094e13	−	1.62270e15i	−0.00450035	−	0.255255i
$748$		−	1.56195e13i		−	0.00243897i
$749$	9.23673e14	−	1.06869e16i	0.143175	−	1.65654i
$750$	−2.84602e14	−	1.02589e15i	−0.0437926	−	0.157857i
$751$	−1.65252e15	+	2.86225e15i	−0.252422	+	0.437208i	−0.964192	−	0.265205i	$-0.914560\pi$
$751$	−1.65252e15	+	2.86225e15i	−0.252422	+	0.437208i	0.711770	+	0.702413i	$0.247894\pi$
$752$	−8.65478e14	−	1.49905e15i	−0.131237	−	0.227310i
$753$	−3.61819e15	−	3.55496e15i	−0.544651	−	0.535133i
$754$	−6.17659e15	−	3.56606e15i	−0.923010	−	0.532900i
$755$	1.07773e15			0.159883
$756$	6.81224e14	+	3.32595e15i	0.100328	+	0.489831i
$757$	−1.27744e15			−0.186773			−0.0933865	−	0.995630i	$-0.529769\pi$
$757$	−1.27744e15			−0.186773			−0.0933865	+	0.995630i	$0.529769\pi$
$758$	2.46889e15	+	1.42541e15i	0.358361	+	0.206900i
$759$	3.97379e13	+	3.90434e13i	0.00572631	+	0.00562624i
$760$	1.10416e14	+	1.91245e14i	0.0157963	+	0.0273600i
$761$	−5.68960e15	+	9.85467e15i	−0.808102	+	1.39967i	0.106076	+	0.994358i	$0.466171\pi$
$761$	−5.68960e15	+	9.85467e15i	−0.808102	+	1.39967i	−0.914177	+	0.405315i	$0.867162\pi$
$762$	−4.21212e14	−	1.51832e15i	−0.0593948	−	0.214098i
$763$	3.06471e14	−	4.38666e14i	0.0429047	−	0.0614114i
$764$		−	4.59094e14i		−	0.0638099i
$765$	3.52124e12	+	1.99721e14i	0.000485912	+	0.0275604i
$766$	7.37719e14	−	4.25922e14i	0.101072	−	0.0583542i
$767$	9.10818e15	−	5.25861e15i	1.23896	−	0.715313i
$768$	1.15829e14	−	4.48041e14i	0.0156434	−	0.0605106i
$769$			1.29438e16i			1.73567i	0.496848	+	0.867837i	$0.334491\pi$
$769$			1.29438e16i			1.73567i	−0.496848	+	0.867837i	$0.665509\pi$
$770$	−1.27373e13	−	1.10089e12i	−0.00169582	−	0.000146571i
$771$	−8.06686e15	+	2.23790e15i	−1.06636	+	0.295830i
$772$	−6.34282e14	+	1.09861e15i	−0.0832506	+	0.144194i
$773$	4.74294e14	+	8.21501e14i	0.0618102	+	0.107058i	0.895275	−	0.445515i	$-0.146979\pi$
$773$	4.74294e14	+	8.21501e14i	0.0618102	+	0.107058i	−0.833464	+	0.552573i	$0.813646\pi$
$774$	−5.18450e15	+	9.35697e15i	−0.670860	+	1.21076i
$775$	−5.87462e15	−	3.39172e15i	−0.754780	−	0.435773i
$776$	−1.97620e15			−0.252111
$777$	7.95606e15	+	9.29391e15i	1.00782	+	1.17729i
$778$	−6.24998e15			−0.786124
$779$	−3.58480e14	−	2.06969e14i	−0.0447723	−	0.0258493i
$780$	−3.43230e14	+	3.49335e14i	−0.0425662	+	0.0433233i
$781$	−9.50385e13	−	1.64611e14i	−0.0117036	−	0.0202712i
$782$	−2.65785e14	+	4.60353e14i	−0.0325007	+	0.0562929i
$783$	8.64754e15	+	8.20188e15i	1.05003	+	0.995919i
$784$	−7.13227e14	−	1.94684e15i	−0.0859983	−	0.234743i
$785$		−	4.55132e14i		−	0.0544947i
$786$	5.49349e15	+	1.42020e15i	0.653167	+	0.168859i
$787$	7.06654e15	−	4.07987e15i	0.834345	−	0.481710i	−0.0209928	−	0.999780i	$-0.506683\pi$
$787$	7.06654e15	−	4.07987e15i	0.834345	−	0.481710i	0.855338	+	0.518070i	$0.173349\pi$
$788$	−4.13633e15	+	2.38811e15i	−0.484977	+	0.280002i
$789$	−1.60321e16	−	4.14468e15i	−1.86666	−	0.482577i
$790$			3.80122e13i			0.00439516i
$791$	−6.41383e14	+	2.99902e14i	−0.0736456	+	0.0344357i
$792$	−5.48479e13	+	3.29691e13i	−0.00625420	+	0.00375940i
$793$	−1.17680e14	+	2.03827e14i	−0.0133260	+	0.0230813i
$794$	−3.08774e15	−	5.34812e15i	−0.347238	−	0.601435i
$795$	3.91785e13	−	3.98754e13i	0.00437551	−	0.00445334i
$796$	−3.91965e15	−	2.26301e15i	−0.434736	−	0.250995i
$797$	−1.62650e16			−1.79156			−0.895782	−	0.444494i	$-0.853383\pi$
$797$	−1.62650e16			−1.79156			−0.895782	+	0.444494i	$0.853383\pi$
$798$	4.86847e15	−	9.08049e14i	0.532570	−	0.0993330i
$799$	−2.28399e15			−0.248135
$800$	1.39960e15	+	8.08057e14i	0.151011	+	0.0871860i
$801$	−7.87842e15	−	4.36527e15i	−0.844229	−	0.467770i
$802$	−2.24813e15	−	3.89388e15i	−0.239256	−	0.414403i
$803$	1.60770e13	−	2.78463e13i	0.00169930	−	0.00294328i
$804$	3.51696e15	−	9.75672e14i	0.369198	−	0.102423i
$805$	3.56675e14	+	2.49189e14i	0.0371873	+	0.0259807i
$806$			6.28383e15i			0.650701i
$807$	−3.78094e15	+	1.46251e16i	−0.388862	+	1.50416i
$808$	−2.60038e15	+	1.50133e15i	−0.265628	+	0.153361i
$809$	6.32713e15	−	3.65297e15i	0.641933	−	0.370620i	−0.143426	−	0.989661i	$-0.545812\pi$
$809$	6.32713e15	−	3.65297e15i	0.641933	−	0.370620i	0.785359	+	0.619041i	$0.212478\pi$
$810$	6.93891e14	−	4.33930e14i	0.0699235	−	0.0437272i
$811$			1.07253e16i			1.07348i	0.843747	+	0.536741i	$0.180345\pi$
$811$			1.07253e16i			1.07348i	−0.843747	+	0.536741i	$0.819655\pi$
$812$	−5.96683e15	−	4.16869e15i	−0.593179	−	0.414421i
$813$	−9.81637e14	−	3.53846e15i	−0.0969288	−	0.349395i
$814$	−1.15304e14	+	1.99713e14i	−0.0113087	+	0.0195872i
$815$	−4.34339e14	−	7.52297e14i	−0.0423118	−	0.0732863i
$816$	−4.35567e14	−	4.27956e14i	−0.0421463	−	0.0414098i
$817$	1.35140e16	+	7.80229e15i	1.29886	+	0.749895i
$818$	−6.74570e15			−0.643997
$819$	4.82672e15	+	9.86552e15i	0.457710	+	0.935532i
$820$	4.17754e13			0.00393500
$821$	−4.34728e15	−	2.50990e15i	−0.406752	−	0.234838i	0.282641	−	0.959226i	$-0.408789\pi$
$821$	−4.34728e15	−	2.50990e15i	−0.406752	−	0.234838i	−0.689393	+	0.724387i	$0.742123\pi$
$822$	−4.88665e15	−	4.80125e15i	−0.454168	−	0.446231i
$823$	−8.73207e14	−	1.51244e15i	−0.0806154	−	0.139630i	0.822899	−	0.568188i	$-0.192355\pi$
$823$	−8.73207e14	−	1.51244e15i	−0.0806154	−	0.139630i	−0.903514	+	0.428558i	$0.859022\pi$
$824$	−8.98197e14	+	1.55572e15i	−0.0823705	+	0.142670i
$825$	−5.97423e13	−	2.15350e14i	−0.00544233	−	0.0196177i
$826$	9.72313e15	−	4.54641e15i	0.879864	−	0.411413i
$827$		−	7.65932e15i		−	0.688510i	−0.938876	−	0.344255i	$-0.888132\pi$
$827$		−	7.65932e15i		−	0.688510i	0.938876	−	0.344255i	$-0.111868\pi$
$828$	2.17755e15	−	3.83919e13i	0.194447	−	0.00342825i
$829$	−1.18523e16	+	6.84290e15i	−1.05136	+	0.607002i	−0.923030	−	0.384729i	$-0.874295\pi$
$829$	−1.18523e16	+	6.84290e15i	−1.05136	+	0.607002i	−0.128330	+	0.991732i	$0.540962\pi$
$830$	2.06919e14	−	1.19465e14i	0.0182335	−	0.0105271i
$831$	8.65523e14	−	3.34794e15i	0.0757657	−	0.293071i
$832$		−	1.49709e15i		−	0.130187i
$833$	−2.69525e15	−	4.69410e14i	−0.232837	−	0.0405513i
$834$	−5.35473e15	+	1.48550e15i	−0.459541	+	0.127485i
$835$	1.35399e15	−	2.34518e15i	0.115435	−	0.199940i
$836$	4.66755e13	+	8.08443e13i	0.00395325	+	0.00684723i
$837$	2.44871e15	−	1.02114e16i	0.206038	−	0.859206i
$838$	9.23631e15	+	5.33259e15i	0.772070	+	0.445755i
$839$	−9.68430e15			−0.804225			−0.402112	−	0.915590i	$-0.631724\pi$
$839$	−9.68430e15			−0.804225			−0.402112	+	0.915590i	$0.631724\pi$
$840$	−3.79688e14	+	3.25032e14i	−0.0313250	+	0.0268158i
$841$	−1.33525e16			−1.09442
$842$	−5.17777e15	−	2.98939e15i	−0.421625	−	0.243425i
$843$	1.07338e16	−	1.09247e16i	0.868361	−	0.883806i
$844$	−4.73869e15	−	8.20765e15i	−0.380868	−	0.659683i
$845$	−6.18688e13	+	1.07160e14i	−0.00494038	+	0.00855698i
$846$	4.82099e15	+	8.02028e15i	0.382472	+	0.636286i
$847$	1.26345e16	+	1.09201e15i	0.995861	+	0.0860729i
$848$			1.70887e14i			0.0133824i
$849$	1.79601e16	+	4.64310e15i	1.39738	+	0.361257i
$850$	1.84676e15	−	1.06623e15i	0.142760	−	0.0824227i
$851$	6.79675e15	−	3.92411e15i	0.522022	−	0.301390i
$852$	−7.19434e15	−	1.85991e15i	−0.549001	−	0.141930i
$853$			1.65754e16i			1.25674i	0.777915	+	0.628369i	$0.216277\pi$
$853$			1.65754e16i			1.25674i	−0.777915	+	0.628369i	$0.783723\pi$
$854$	−1.37567e14	+	1.96906e14i	−0.0103632	+	0.0148334i
$855$	−6.15050e14	−	1.02321e15i	−0.0460359	−	0.0765862i
$856$	3.95228e15	−	6.84555e15i	0.293929	−	0.509099i
$857$	1.44593e15	+	2.50443e15i	0.106845	+	0.185061i	0.914490	−	0.404608i	$-0.132592\pi$
$857$	1.44593e15	+	2.50443e15i	0.106845	+	0.185061i	−0.807646	+	0.589668i	$0.799259\pi$
$858$	−1.45092e14	+	1.47673e14i	−0.0106528	+	0.0108423i
$859$	−7.03677e15	−	4.06268e15i	−0.513347	−	0.296381i	0.220862	−	0.975305i	$-0.429113\pi$
$859$	−7.03677e15	−	4.06268e15i	−0.513347	−	0.296381i	−0.734208	+	0.678924i	$0.762446\pi$
$860$	−1.57485e15			−0.114155
$861$	3.11728e14	−	8.83486e14i	0.0224522	−	0.0636330i
$862$	−7.53435e15			−0.539207
$863$	−6.94070e15	−	4.00721e15i	−0.493564	−	0.284960i	0.232488	−	0.972599i	$-0.425313\pi$
$863$	−6.94070e15	−	4.00721e15i	−0.493564	−	0.284960i	−0.726052	+	0.687640i	$0.758647\pi$
$864$	−5.83390e14	+	2.43282e15i	−0.0412224	+	0.171903i
$865$	−1.01532e15	−	1.75858e15i	−0.0712873	−	0.123473i
$866$	1.75217e15	−	3.03485e15i	0.122244	−	0.211733i
$867$	1.31233e16	−	3.64065e15i	0.909782	−	0.252391i
$868$	−5.52227e14	+	6.38926e15i	−0.0380417	+	0.440141i
$869$			1.60687e13i			0.00109995i
$870$	−4.39176e14	+	1.69878e15i	−0.0298733	+	0.115553i
$871$	1.02254e16	−	5.90361e15i	0.691160	−	0.399041i
$872$	3.41501e14	−	1.97166e14i	0.0229378	−	0.0132431i
$873$	1.06819e16	−	1.88330e14i	0.712966	−	0.0125702i
$874$		−	3.17697e15i		−	0.210717i
$875$	−1.48884e15	−	3.18410e15i	−0.0981306	−	0.209866i
$876$	−3.36033e14	−	1.21128e15i	−0.0220095	−	0.0793366i
$877$	1.26277e16	−	2.18718e16i	0.821912	−	1.42359i	−0.0823437	−	0.996604i	$-0.526241\pi$
$877$	1.26277e16	−	2.18718e16i	0.821912	−	1.42359i	0.904256	−	0.426990i	$-0.140426\pi$
$878$	7.57192e15	+	1.31150e16i	0.489764	+	0.848295i
$879$	−9.05058e15	−	8.89242e15i	−0.581752	−	0.571586i
$880$	−8.15898e12	−	4.71059e12i	−0.000521172	−	0.000300899i
$881$	−1.03982e16			−0.660069			−0.330034	−	0.943969i	$-0.607060\pi$
$881$	−1.03982e16			−0.660069			−0.330034	+	0.943969i	$0.607060\pi$
$882$	4.04071e15	+	1.04552e16i	0.254906	+	0.659563i
$883$	5.49567e15			0.344538			0.172269	−	0.985050i	$-0.444890\pi$
$883$	5.49567e15			0.344538			0.172269	+	0.985050i	$0.444890\pi$
$884$	−1.71075e15	−	9.87702e14i	−0.106586	−	0.0615373i
$885$	−1.84565e15	−	1.81339e15i	−0.114278	−	0.112280i
$886$	9.73835e15	+	1.68673e16i	0.599239	+	1.03791i
$887$	−8.76349e15	+	1.51788e16i	−0.535917	+	0.928235i	0.463202	+	0.886253i	$0.346700\pi$
$887$	−8.76349e15	+	1.51788e16i	−0.535917	+	0.928235i	−0.999118	+	0.0419818i	$0.986633\pi$
$888$	2.41003e15	+	8.68733e15i	0.146471	+	0.527977i
$889$	−2.20349e15	−	4.71248e15i	−0.133092	−	0.284636i
$890$		−	1.32600e15i		−	0.0795971i
$891$	2.93325e14	−	1.83433e14i	0.0174994	−	0.0109434i
$892$	−9.59680e15	+	5.54072e15i	−0.569010	+	0.328518i
$893$	1.18217e16	−	6.82524e15i	0.696620	−	0.402193i
$894$	4.81682e15	−	1.86320e16i	0.282100	−	1.09120i
$895$		−	2.38881e15i		−	0.139045i
$896$	1.31565e14	−	1.52220e15i	0.00761108	−	0.0880600i
$897$	6.78914e15	−	1.88344e15i	0.390352	−	0.108291i
$898$	5.80853e15	−	1.00607e16i	0.331930	−	0.574919i
$899$	1.12569e16	+	1.94975e16i	0.639353	+	1.10739i
$900$	−7.64218e15	−	4.23437e15i	−0.431403	−	0.239032i
$901$	1.95276e14	+	1.12743e14i	0.0109563	+	0.00632561i
$902$	1.76595e13			0.000984789
$903$	−1.17515e16	+	3.33056e16i	−0.651344	+	1.84601i
$904$	−5.21753e14			−0.0287435
$905$	1.08159e15	+	6.24459e14i	0.0592239	+	0.0341930i
$906$	1.24825e16	−	1.27045e16i	0.679354	−	0.691437i
$907$	−6.49745e15	−	1.12539e16i	−0.351482	−	0.608785i	0.635027	−	0.772490i	$-0.280989\pi$
$907$	−6.49745e15	−	1.12539e16i	−0.351482	−	0.608785i	−0.986509	+	0.163705i	$0.947656\pi$
$908$	6.81295e15	−	1.18004e16i	0.366322	−	0.634489i
$909$	1.39126e16	−	8.36289e15i	0.743547	−	0.446946i
$910$	−9.26027e14	+	1.32546e15i	−0.0491922	+	0.0704110i
$911$		−	4.08779e14i		−	0.0215843i	−0.999942	−	0.0107921i	$-0.996565\pi$
$911$		−	4.08779e14i		−	0.0215843i	0.999942	−	0.0107921i	$-0.00343531\pi$
$912$	3.53330e15	+	9.13442e14i	0.185442	+	0.0479412i
$913$	8.74699e13	−	5.05008e13i	0.00456320	−	0.00263456i
$914$	2.06379e15	−	1.19153e15i	0.107019	−	0.0617874i
$915$	5.60598e13	+	1.44928e13i	0.00288959	+	0.000747027i
$916$			6.69803e15i			0.343180i
$917$	1.86639e16	+	1.61313e15i	0.950543	+	0.0821560i
$918$	2.39514e15	+	2.27170e15i	0.121254	+	0.115005i
$919$	1.80355e16	−	3.12384e16i	0.907598	−	1.57201i	0.0902056	−	0.995923i	$-0.471248\pi$
$919$	1.80355e16	−	3.12384e16i	0.907598	−	1.57201i	0.817392	−	0.576082i	$-0.195419\pi$
$920$	1.60313e14	+	2.77671e14i	0.00801930	+	0.0138898i
$921$	−2.67612e16	+	2.72371e16i	−1.33069	+	1.35436i
$922$	7.87454e15	+	4.54637e15i	0.389229	+	0.224721i
$923$	−2.40392e16			−1.18116
$924$	−1.60504e14	+	1.37400e14i	−0.00783953	+	0.00671103i
$925$	−3.14841e16			−1.52866
$926$	2.38538e15	+	1.37720e15i	0.115132	+	0.0664718i
$927$	4.70673e15	−	8.49468e15i	0.225829	−	0.407576i
$928$	−2.68189e15	−	4.64517e15i	−0.127917	−	0.221558i
$929$	8.59148e15	−	1.48809e16i	0.407363	−	0.705574i	−0.587230	−	0.809420i	$-0.699782\pi$
$929$	8.59148e15	−	1.48809e16i	0.407363	−	0.705574i	0.994593	+	0.103846i	$0.0331150\pi$
$930$	1.48968e15	−	4.13265e14i	0.0702161	−	0.0194793i
$931$	1.53530e16	−	5.62458e15i	0.719399	−	0.263552i
$932$		−	8.48576e15i		−	0.395278i
$933$	5.25994e15	−	2.03460e16i	0.243574	−	0.942174i
$934$	−7.03071e13	+	4.05918e13i	−0.00323662	+	0.00186866i
$935$	−1.07658e13	+	6.21562e12i	−0.000492698	+	0.000284459i
$936$	1.42671e14	+	8.09214e15i	0.00649109	+	0.368168i
$937$			2.18914e16i			0.990160i	0.868847	+	0.495080i	$0.164861\pi$
$937$			2.18914e16i			0.990160i	−0.868847	+	0.495080i	$0.835139\pi$
$938$	1.09157e16	−	5.10405e15i	0.490837	−	0.229509i
$939$	−7.30617e15	−	2.63362e16i	−0.326610	−	1.17731i
$940$	−6.88818e14	+	1.19307e15i	−0.0306127	+	0.0530227i
$941$	1.53247e16	+	2.65432e16i	0.677095	+	1.17276i	0.975852	+	0.218434i	$0.0700947\pi$
$941$	1.53247e16	+	2.65432e16i	0.677095	+	1.17276i	−0.298757	+	0.954329i	$0.596572\pi$
$942$	−5.36520e15	−	5.27144e15i	−0.235671	−	0.231552i
$943$	−5.20480e14	−	3.00500e14i	−0.0227295	−	0.0131229i
$944$	7.90959e15			0.343406
$945$	2.02134e15	−	1.79307e15i	0.0872497	−	0.0773966i
$946$	−6.65728e14			−0.0285690
$947$	−3.37010e16	−	1.94573e16i	−1.43786	−	0.830152i	−0.440164	−	0.897918i	$-0.645080\pi$
$947$	−3.37010e16	−	1.94573e16i	−1.43786	−	0.830152i	−0.997701	+	0.0677660i	$0.978413\pi$
$948$	4.48097e14	+	4.40266e14i	0.0190075	+	0.0186754i
$949$	−2.03328e15	−	3.52174e15i	−0.0857496	−	0.148523i
$950$	−6.37241e15	+	1.10373e16i	−0.267192	+	0.462791i
$951$	5.89310e15	+	2.12426e16i	0.245669	+	0.885553i
$952$	−1.65265e15	−	1.15462e15i	−0.0684981	−	0.0478558i
$953$			1.23673e16i			0.509642i	0.966988	+	0.254821i	$0.0820165\pi$
$953$			1.23673e16i			0.509642i	−0.966988	+	0.254821i	$0.917984\pi$
$954$	−1.62854e13	−	9.23690e14i	−0.000667240	−	0.0378451i
$955$	−3.16432e14	+	1.82692e14i	−0.0128903	+	0.00744220i
$956$	1.92176e16	−	1.10953e16i	0.778360	−	0.449386i
$957$	−1.85651e14	+	7.18119e14i	−0.00747621	+	0.0289188i
$958$			1.75495e16i			0.702675i
$959$	−1.85412e16	−	1.29537e16i	−0.738134	−	0.515692i
$960$	−3.54907e14	+	9.84581e13i	−0.0140483	+	0.00389726i
$961$	−2.78622e15	+	4.82587e15i	−0.109657	+	0.189932i
$962$	1.45826e16	+	2.52579e16i	0.570655	+	0.988403i
$963$	−2.07107e16	+	3.73786e16i	−0.805843	+	1.45438i
$964$	3.69410e15	+	2.13279e15i	0.142917	+	0.0825133i
$965$	1.00963e15			0.0388383
$966$	7.06857e15	−	1.31840e15i	0.270369	−	0.0504283i
$967$	−1.69793e16			−0.645764			−0.322882	−	0.946439i	$-0.604652\pi$
$967$	−1.69793e16			−0.645764			−0.322882	+	0.946439i	$0.604652\pi$
$968$	8.09310e15	+	4.67256e15i	0.306056	+	0.176701i
$969$	3.37490e15	−	3.43493e15i	0.126905	−	0.129163i
$970$	7.86411e14	+	1.36210e15i	0.0294039	+	0.0509290i
$971$	2.11145e16	−	3.65713e16i	0.785009	−	1.35968i	−0.143985	−	0.989580i	$-0.545992\pi$
$971$	2.11145e16	−	3.65713e16i	0.785009	−	1.35968i	0.928994	−	0.370095i	$-0.120675\pi$
$972$	2.92153e15	−	1.32056e16i	0.108005	−	0.488195i
$973$	−1.66197e16	+	7.77114e15i	−0.610945	+	0.285670i
$974$		−	4.83353e14i		−	0.0176681i
$975$	−2.73645e16	−	7.07437e15i	−0.994630	−	0.257136i
$976$	−1.53291e14	+	8.85024e13i	−0.00554041	+	0.00319876i
$977$	−2.48351e16	+	1.43386e16i	−0.892577	+	0.515330i	−0.874785	−	0.484512i	$-0.838997\pi$
$977$	−2.48351e16	+	1.43386e16i	−0.892577	+	0.515330i	−0.0177926	+	0.999842i	$0.505664\pi$
$978$	−1.38988e16	−	3.59318e15i	−0.496724	−	0.128415i
$979$		−	5.60532e14i		−	0.0199203i
$980$	−1.05805e15	+	1.26632e15i	−0.0373905	+	0.0447508i
$981$	−1.82711e15	+	1.09828e15i	−0.0642075	+	0.0385951i
$982$	−5.52219e15	+	9.56471e15i	−0.192974	+	0.334240i
$983$	2.05991e16	+	3.56787e16i	0.715821	+	1.23984i	0.962642	+	0.270778i	$0.0872808\pi$
$983$	2.05991e16	+	3.56787e16i	0.715821	+	1.23984i	−0.246821	+	0.969061i	$0.579386\pi$
$984$	4.83852e14	−	4.92458e14i	0.0167201	−	0.0170175i
$985$	3.29203e15	+	1.90065e15i	0.113127	+	0.0653136i
$986$	−7.07751e15			−0.241856
$987$	2.00916e16	+	2.34701e16i	0.682763	+	0.797574i
$988$	1.18062e16			0.398975
$989$	1.96210e16	+	1.13282e16i	0.659390	+	0.380699i
$990$	4.45503e13	+	2.46844e13i	0.00148887	+	0.000824952i
$991$	−6.32339e15	−	1.09524e16i	−0.210157	−	0.364003i	0.741606	−	0.670835i	$-0.234064\pi$
$991$	−6.32339e15	−	1.09524e16i	−0.210157	−	0.364003i	−0.951764	+	0.306832i	$0.900731\pi$
$992$	−2.36291e15	+	4.09268e15i	−0.0780968	+	0.135268i
$993$	−2.34670e15	+	6.51021e14i	−0.0771325	+	0.0213980i
$994$	−2.44425e16	−	2.11258e15i	−0.798952	−	0.0690539i
$995$			3.60218e15i			0.117095i
$996$	9.88303e14	−	3.82287e15i	0.0319495	−	0.123584i
$997$	−4.51992e16	+	2.60958e16i	−1.45314	+	0.838971i	−0.998658	−	0.0517842i	$-0.983509\pi$
$997$	−4.51992e16	+	2.60958e16i	−1.45314	+	0.838971i	−0.454483	+	0.890756i	$0.650176\pi$
$998$	2.52048e16	−	1.45520e16i	0.805870	−	0.465269i
$999$	−1.38547e16	−	4.67276e16i	−0.440543	−	1.48581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.12	✓	60
3.2	odd	2	inner	42.12.f.a.5.22	yes	60
7.3	odd	6	inner	42.12.f.a.17.22	yes	60
21.17	even	6	inner	42.12.f.a.17.12	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.12	✓	60	1.1	even	1	trivial
42.12.f.a.5.22	yes	60	3.2	odd	2	inner
42.12.f.a.17.12	yes	60	21.17	even	6	inner
42.12.f.a.17.22	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} +(300.225 + 294.978i) q^{3} +(512.000 + 886.810i) q^{4} +(407.491 - 705.796i) q^{5} +(-3600.42 - 12978.3i) q^{6} +(-18834.9 - 40281.2i) q^{7} -32768.0i q^{8} +(3122.76 + 177119. i) q^{9} +(-22585.5 + 13039.7i) q^{10} +(-9547.45 + 5512.22i) q^{11} +(-107875. + 417271. i) q^{12} +1.39427e6i q^{13} +(-122529. + 1.41766e6i) q^{14} +(330533. - 91696.3i) q^{15} +(-524288. + 908093. i) q^{16} +(691798. + 1.19823e6i) q^{17} +(2.74737e6 - 4.95844e6i) q^{18} +(-7.16131e6 - 4.13459e6i) q^{19} +834542. q^{20} +(6.22735e6 - 1.76493e7i) q^{21} +352782. q^{22} +(-1.03976e7 - 6.00304e6i) q^{23} +(9.66584e6 - 9.83776e6i) q^{24} +(2.40820e7 + 4.17112e7i) q^{25} +(2.23083e7 - 3.86391e7i) q^{26} +(-5.13088e7 + 5.40968e7i) q^{27} +(2.60782e7 - 3.73270e7i) q^{28} -1.59853e8i q^{29} +(-1.06271e7 - 2.74737e6i) q^{30} +(-1.21971e8 + 7.04202e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(-4.49237e6 - 1.16138e6i) q^{33} -4.42750e7i q^{34} +(-3.61053e7 - 3.12061e6i) q^{35} +(-1.55472e8 + 9.34545e7i) q^{36} +(-3.26843e8 + 5.66109e8i) q^{37} +(1.32307e8 + 2.29162e8i) q^{38} +(-4.11279e8 + 4.18594e8i) q^{39} +(-2.31275e7 - 1.33527e7i) q^{40} +5.00579e7 q^{41} +(-4.54966e8 + 3.89474e8i) q^{42} -1.88708e9 q^{43} +(-9.77659e6 - 5.64452e6i) q^{44} +(1.26283e8 + 6.99706e7i) q^{45} +(1.92097e8 + 3.32722e8i) q^{46} +(-8.25384e8 + 1.42961e9i) q^{47} +(-4.25272e8 + 1.17979e8i) q^{48} +(-1.26782e9 + 1.51739e9i) q^{49} -1.54125e9i q^{50} +(-1.45757e8 + 5.63803e8i) q^{51} +(-1.23645e9 + 7.13866e8i) q^{52} +(1.41137e8 - 8.14854e7i) q^{53} +(2.28746e9 - 6.78233e8i) q^{54} +8.98473e6i q^{55} +(-1.31993e9 + 6.17183e8i) q^{56} +(-9.30391e8 - 3.35374e9i) q^{57} +(-2.55765e9 + 4.42998e9i) q^{58} +(-3.77159e9 - 6.53258e9i) q^{59} +(2.50550e8 + 2.46172e8i) q^{60} +(1.46189e8 + 8.44025e7i) q^{61} +4.50690e9 q^{62} +(7.07576e9 - 3.46182e9i) q^{63} -1.07374e9 q^{64} +(9.84070e8 + 5.68153e8i) q^{65} +(1.05914e8 + 1.04063e8i) q^{66} +(-4.23419e9 - 7.33384e9i) q^{67} +(-7.08401e8 + 1.22699e9i) q^{68} +(-1.35084e9 - 4.86932e9i) q^{69} +(9.50651e8 + 6.64166e8i) q^{70} +1.72414e10i q^{71} +(5.80385e9 - 1.02327e8i) q^{72} +(-2.52586e9 + 1.45831e9i) q^{73} +(1.81155e10 - 1.04590e10i) q^{74} +(-5.07389e9 + 1.96264e10i) q^{75} -8.46763e9i q^{76} +(4.01864e8 + 2.80760e8i) q^{77} +(1.80952e10 - 5.01996e9i) q^{78} +(7.28778e8 - 1.26228e9i) q^{79} +(4.27286e8 + 7.40080e8i) q^{80} +(-3.13616e10 + 1.10620e9i) q^{81} +(-1.38724e9 - 8.00926e8i) q^{82} -9.16160e9 q^{83} +(1.88400e10 - 3.51396e9i) q^{84} +1.12761e9 q^{85} +(5.22962e10 + 3.01932e10i) q^{86} +(4.71532e10 - 4.79919e10i) q^{87} +(1.80625e8 + 3.12851e8i) q^{88} +(-2.54222e10 + 4.40326e10i) q^{89} +(-2.38012e9 - 3.95960e9i) q^{90} +(5.61628e10 - 2.62610e10i) q^{91} -1.22942e10i q^{92} +(-5.73913e10 - 1.48370e10i) q^{93} +(4.57474e10 - 2.64123e10i) q^{94} +(-5.83635e9 + 3.36962e9i) q^{95} +(1.36731e10 + 3.53483e9i) q^{96} -6.03089e10i q^{97} +(5.94130e10 - 2.17660e10i) q^{98} +(-1.00614e9 - 1.67383e9i) 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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