LMFDB - Embedded newform 42.12.f.a.5.17

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			5.17
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.17

$q$-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} +(-409.456 + 97.4316i) q^{3} +(512.000 + 886.810i) q^{4} +(6887.81 - 11930.0i) q^{5} +(-12906.1 - 3851.19i) q^{6} +(-11166.0 - 43042.4i) q^{7} +32768.0i q^{8} +(158161. - 79787.9i) q^{9} +(381761. - 220410. i) q^{10} +(-791882. + 457193. i) q^{11} +(-296045. - 313225. i) q^{12} +417129. i q^{13} +(379236. - 1.37148e6i) q^{14} +(-1.65789e6 + 5.55591e6i) q^{15} +(-524288. + 908093. i) q^{16} +(1.68518e6 + 2.91882e6i) q^{17} +(5.65970e6 + 319431. i) q^{18} +(57829.4 + 33387.8i) q^{19} +1.41062e7 q^{20} +(8.76568e6 + 1.65360e7i) q^{21} -2.92604e7 q^{22} +(-3.35476e7 - 1.93687e7i) q^{23} +(-3.19264e6 - 1.34170e7i) q^{24} +(-7.04698e7 - 1.22057e8i) q^{25} +(-6.67407e6 + 1.15598e7i) q^{26} +(-5.69861e7 + 4.80795e7i) q^{27} +(3.24534e7 - 3.19398e7i) q^{28} -3.71986e6i q^{29} +(-1.34839e8 + 1.27444e8i) q^{30} +(-1.31414e8 + 7.58718e7i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(2.79696e8 - 2.64355e8i) q^{33} +1.07852e8i q^{34} +(-5.90407e8 - 1.63257e8i) q^{35} +(1.51735e8 + 9.94075e7i) q^{36} +(-4.85486e7 + 8.40887e7i) q^{37} +(1.06841e6 + 1.85054e6i) q^{38} +(-4.06416e7 - 1.70796e8i) q^{39} +(3.90924e8 + 2.25700e8i) q^{40} +4.90067e7 q^{41} +(-2.16548e7 + 5.98511e8i) q^{42} +8.91002e8 q^{43} +(-8.10887e8 - 4.68166e8i) q^{44} +(1.37511e8 - 2.43643e9i) q^{45} +(-6.19800e8 - 1.07352e9i) q^{46} +(-7.83090e8 + 1.35635e9i) q^{47} +(1.26196e8 - 4.22906e8i) q^{48} +(-1.72797e9 + 9.61224e8i) q^{49} -4.51007e9i q^{50} +(-9.74394e8 - 1.03094e9i) q^{51} +(-3.69915e8 + 2.13570e8i) q^{52} +(-1.37510e9 + 7.93915e8i) q^{53} +(-2.34852e9 + 4.20641e8i) q^{54} +1.25962e10i q^{55} +(1.41041e9 - 3.65888e8i) q^{56} +(-2.69316e7 - 8.03642e6i) q^{57} +(5.95177e7 - 1.03088e8i) q^{58} +(-4.04457e9 - 7.00540e9i) q^{59} +(-5.77588e9 + 1.37439e9i) q^{60} +(-2.62501e9 - 1.51555e9i) q^{61} -4.85579e9 q^{62} +(-5.20029e9 - 5.91672e9i) q^{63} -1.07374e9 q^{64} +(4.97637e9 + 2.87311e9i) q^{65} +(1.19808e10 - 2.85089e9i) q^{66} +(-9.50217e9 - 1.64582e10i) q^{67} +(-1.72563e9 + 2.98887e9i) q^{68} +(1.56234e10 + 4.66204e9i) q^{69} +(-1.37497e10 - 1.39708e10i) q^{70} -4.59153e8i q^{71} +(2.61449e9 + 5.18262e9i) q^{72} +(1.08123e10 - 6.24246e9i) q^{73} +(-2.69084e9 + 1.55356e9i) q^{74} +(4.07465e10 + 4.31111e10i) q^{75} +6.83782e7i q^{76} +(2.85209e10 + 2.89795e10i) q^{77} +(1.60644e9 - 5.38351e9i) q^{78} +(-1.69739e10 + 2.93997e10i) q^{79} +(7.22239e9 + 1.25096e10i) q^{80} +(1.86488e10 - 2.52387e10i) q^{81} +(1.35811e9 + 7.84107e8i) q^{82} -2.18126e10 q^{83} +(-1.01763e10 + 1.62399e10i) q^{84} +4.64289e10 q^{85} +(2.46922e10 + 1.42560e10i) q^{86} +(3.62432e8 + 1.52312e9i) q^{87} +(-1.49813e10 - 2.59484e10i) q^{88} +(2.38097e9 - 4.12397e9i) q^{89} +(4.27938e10 - 6.53202e10i) q^{90} +(1.79542e10 - 4.65768e9i) q^{91} -3.96672e10i q^{92} +(4.64158e10 - 4.38700e10i) q^{93} +(-4.34032e10 + 2.50589e10i) q^{94} +(7.96635e8 - 4.59938e8i) q^{95} +(1.02637e10 - 9.70079e9i) q^{96} +7.92567e10i q^{97} +(-6.32664e10 - 1.00923e9i) q^{98} +(-8.87665e10 + 1.35493e11i) 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
$3$	−409.456	+	97.4316i	−0.972837	+	0.231490i
$3$	−409.456	+	97.4316i	−0.972837	+	0.231490i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	6887.81	−	11930.0i	0.985703	−	1.70729i	0.346935	−	0.937889i	$-0.387222\pi$
$5$	6887.81	−	11930.0i	0.985703	−	1.70729i	0.638768	−	0.769399i	$-0.279444\pi$
$6$	−12906.1	−	3851.19i	−0.677583	−	0.202192i
$7$	−11166.0	−	43042.4i	−0.251107	−	0.967959i
$7$	−11166.0	−	43042.4i	−0.251107	−	0.967959i
$8$			32768.0i			0.353553i
$9$	158161.	−	79787.9i	0.892824	−	0.450405i
$10$	381761.	−	220410.i	1.20724	−	0.696998i
$11$	−791882.	+	457193.i	−1.48252	+	0.855934i	−0.999803	−	0.0198424i	$-0.993684\pi$
$11$	−791882.	+	457193.i	−1.48252	+	0.855934i	−0.482717	+	0.875776i	$0.660350\pi$
$12$	−296045.	−	313225.i	−0.343448	−	0.363378i
$13$			417129.i			0.311589i	0.987789	+	0.155795i	$0.0497938\pi$
$13$			417129.i			0.311589i	−0.987789	+	0.155795i	$0.950206\pi$
$14$	379236.	−	1.37148e6i	0.188454	−	0.681531i
$15$	−1.65789e6	+	5.55591e6i	−0.563708	+	1.88909i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	1.68518e6	+	2.91882e6i	0.287858	+	0.498584i	0.973298	−	0.229544i	$-0.0737236\pi$
$17$	1.68518e6	+	2.91882e6i	0.287858	+	0.498584i	−0.685440	+	0.728129i	$0.740390\pi$
$18$	5.65970e6	+	319431.i	0.705983	+	0.0398454i
$19$	57829.4	+	33387.8i	0.00535801	+	0.00309345i	0.502677	−	0.864475i	$-0.332349\pi$
$19$	57829.4	+	33387.8i	0.00535801	+	0.00309345i	−0.497319	+	0.867568i	$0.665682\pi$
$20$	1.41062e7			0.985703
$21$	8.76568e6	+	1.65360e7i	0.468360	+	0.883538i
$22$	−2.92604e7			−1.21047
$23$	−3.35476e7	−	1.93687e7i	−1.08682	−	0.627478i	−0.154094	−	0.988056i	$-0.549246\pi$
$23$	−3.35476e7	−	1.93687e7i	−1.08682	−	0.627478i	−0.932729	+	0.360578i	$0.882579\pi$
$24$	−3.19264e6	−	1.34170e7i	−0.0818442	−	0.343950i
$25$	−7.04698e7	−	1.22057e8i	−1.44322	−	2.49973i
$26$	−6.67407e6	+	1.15598e7i	−0.110163	+	0.190809i
$27$	−5.69861e7	+	4.80795e7i	−0.764308	+	0.644851i
$28$	3.24534e7	−	3.19398e7i	0.356362	−	0.350722i
$29$		−	3.71986e6i		−	0.0336773i	−0.999858	−	0.0168387i	$-0.994640\pi$
$29$		−	3.71986e6i		−	0.0336773i	0.999858	−	0.0168387i	$-0.00536016\pi$
$30$	−1.34839e8	+	1.27444e8i	−1.01309	+	0.957528i
$31$	−1.31414e8	+	7.58718e7i	−0.824426	+	0.475982i	−0.851940	−	0.523639i	$-0.824574\pi$
$31$	−1.31414e8	+	7.58718e7i	−0.824426	+	0.475982i	0.0275145	+	0.999621i	$0.491241\pi$
$32$	−2.90590e7	+	1.67772e7i	−0.153093	+	0.0883883i
$33$	2.79696e8	−	2.64355e8i	1.24411	−	1.17587i
$34$			1.07852e8i			0.407092i
$35$	−5.90407e8	−	1.63257e8i	−1.90010	−	0.525408i
$36$	1.51735e8	+	9.94075e7i	0.418237	+	0.274003i
$37$	−4.85486e7	+	8.40887e7i	−0.115098	+	0.199355i	−0.917819	−	0.396999i	$-0.870052\pi$
$37$	−4.85486e7	+	8.40887e7i	−0.115098	+	0.199355i	0.802721	+	0.596355i	$0.203385\pi$
$38$	1.06841e6	+	1.85054e6i	0.00218740	+	0.00378869i
$39$	−4.06416e7	−	1.70796e8i	−0.0721299	−	0.303126i
$40$	3.90924e8	+	2.25700e8i	0.603618	+	0.348499i
$41$	4.90067e7			0.0660608			0.0330304	−	0.999454i	$-0.489484\pi$
$41$	4.90067e7			0.0660608			0.0330304	+	0.999454i	$0.489484\pi$
$42$	−2.16548e7	+	5.98511e8i	−0.0255671	+	0.706644i
$43$	8.91002e8			0.924277			0.462138	−	0.886808i	$-0.347082\pi$
$43$	8.91002e8			0.924277			0.462138	+	0.886808i	$0.347082\pi$
$44$	−8.10887e8	−	4.68166e8i	−0.741260	−	0.427967i
$45$	1.37511e8	−	2.43643e9i	0.111089	−	1.96827i
$46$	−6.19800e8	−	1.07352e9i	−0.443694	−	0.768500i
$47$	−7.83090e8	+	1.35635e9i	−0.498050	+	0.862648i	−0.999997	−	0.00224983i	$-0.999284\pi$
$47$	−7.83090e8	+	1.35635e9i	−0.498050	+	0.862648i	0.501947	+	0.864898i	$0.332617\pi$
$48$	1.26196e8	−	4.22906e8i	0.0714855	−	0.239562i
$49$	−1.72797e9	+	9.61224e8i	−0.873890	+	0.486123i
$50$		−	4.51007e9i		−	2.04102i
$51$	−9.74394e8	−	1.03094e9i	−0.395456	−	0.418405i
$52$	−3.69915e8	+	2.13570e8i	−0.134922	+	0.0778973i
$53$	−1.37510e9	+	7.93915e8i	−0.451666	+	0.260769i	−0.708533	−	0.705677i	$-0.750643\pi$
$53$	−1.37510e9	+	7.93915e8i	−0.451666	+	0.260769i	0.256868	+	0.966447i	$0.417310\pi$
$54$	−2.34852e9	+	4.20641e8i	−0.696031	+	0.124665i
$55$			1.25962e10i			3.37479i
$56$	1.41041e9	−	3.65888e8i	0.342225	−	0.0887798i
$57$	−2.69316e7	−	8.03642e6i	−0.00592858	−	0.00176909i
$58$	5.95177e7	−	1.03088e8i	0.0119067	−	0.0206231i
$59$	−4.04457e9	−	7.00540e9i	−0.736522	−	1.27569i	−0.954052	−	0.299641i	$-0.903133\pi$
$59$	−4.04457e9	−	7.00540e9i	−0.736522	−	1.27569i	0.217530	−	0.976054i	$-0.430200\pi$
$60$	−5.77588e9	+	1.37439e9i	−0.958929	+	0.228181i
$61$	−2.62501e9	−	1.51555e9i	−0.397939	−	0.229750i	0.287655	−	0.957734i	$-0.407124\pi$
$61$	−2.62501e9	−	1.51555e9i	−0.397939	−	0.229750i	−0.685594	+	0.727984i	$0.740458\pi$
$62$	−4.85579e9			−0.673141
$63$	−5.20029e9	−	5.91672e9i	−0.660168	−	0.751118i
$64$	−1.07374e9			−0.125000
$65$	4.97637e9	+	2.87311e9i	0.531973	+	0.307135i
$66$	1.19808e10	−	2.85089e9i	1.17759	−	0.280213i
$67$	−9.50217e9	−	1.64582e10i	−0.859828	−	1.48927i	−0.872093	−	0.489341i	$-0.837237\pi$
$67$	−9.50217e9	−	1.64582e10i	−0.859828	−	1.48927i	0.0122649	−	0.999925i	$-0.496096\pi$
$68$	−1.72563e9	+	2.98887e9i	−0.143929	+	0.249292i
$69$	1.56234e10	+	4.66204e9i	1.20256	+	0.358844i
$70$	−1.37497e10	−	1.39708e10i	−0.977811	−	0.993533i
$71$		−	4.59153e8i		−	0.0302020i	−0.999886	−	0.0151010i	$-0.995193\pi$
$71$		−	4.59153e8i		−	0.0302020i	0.999886	−	0.0151010i	$-0.00480699\pi$
$72$	2.61449e9	+	5.18262e9i	0.159242	+	0.315661i
$73$	1.08123e10	−	6.24246e9i	0.610437	−	0.352436i	−0.162699	−	0.986676i	$-0.552020\pi$
$73$	1.08123e10	−	6.24246e9i	0.610437	−	0.352436i	0.773137	+	0.634240i	$0.218687\pi$
$74$	−2.69084e9	+	1.55356e9i	−0.140966	+	0.0813865i
$75$	4.07465e10	+	4.31111e10i	1.98268	+	2.09774i
$76$			6.83782e7i			0.00309345i
$77$	2.85209e10	+	2.89795e10i	1.20078	+	1.22009i
$78$	1.60644e9	−	5.38351e9i	0.0630007	−	0.211128i
$79$	−1.69739e10	+	2.93997e10i	−0.620630	+	1.07496i	0.368739	+	0.929533i	$0.379790\pi$
$79$	−1.69739e10	+	2.93997e10i	−0.620630	+	1.07496i	−0.989369	+	0.145430i	$0.953544\pi$
$80$	7.22239e9	+	1.25096e10i	0.246426	+	0.426822i
$81$	1.86488e10	−	2.52387e10i	0.594271	−	0.804265i
$82$	1.35811e9	+	7.84107e8i	0.0404538	+	0.0233560i
$83$	−2.18126e10			−0.607824			−0.303912	−	0.952700i	$-0.598293\pi$
$83$	−2.18126e10			−0.607824			−0.303912	+	0.952700i	$0.598293\pi$
$84$	−1.01763e10	+	1.62399e10i	−0.265493	+	0.423690i
$85$	4.64289e10			1.13497
$86$	2.46922e10	+	1.42560e10i	0.566002	+	0.326781i
$87$	3.62432e8	+	1.52312e9i	0.00779598	+	0.0327625i
$88$	−1.49813e10	−	2.59484e10i	−0.302618	−	0.524150i
$89$	2.38097e9	−	4.12397e9i	0.0451970	−	0.0782835i	−0.842542	−	0.538631i	$-0.818942\pi$
$89$	2.38097e9	−	4.12397e9i	0.0451970	−	0.0782835i	0.887739	+	0.460347i	$0.152275\pi$
$90$	4.27938e10	−	6.53202e10i	0.763918	−	1.16604i
$91$	1.79542e10	−	4.65768e9i	0.301606	−	0.0782423i
$92$		−	3.96672e10i		−	0.627478i
$93$	4.64158e10	−	4.38700e10i	0.691847	−	0.653900i
$94$	−4.34032e10	+	2.50589e10i	−0.609985	+	0.352175i
$95$	7.96635e8	−	4.59938e8i	0.0105628	−	0.00609845i
$96$	1.02637e10	−	9.70079e9i	0.128474	−	0.121427i
$97$			7.92567e10i			0.937112i	0.883434	+	0.468556i	$0.155226\pi$
$97$			7.92567e10i			0.937112i	−0.883434	+	0.468556i	$0.844774\pi$
$98$	−6.32664e10	−	1.00923e9i	−0.707017	−	0.0112784i
$99$	−8.87665e10	+	1.35493e11i	−0.938114	+	1.43193i
$100$	7.21611e10	−	1.24987e11i	0.721611	−	1.24987i
$101$	−3.92888e10	−	6.80502e10i	−0.371964	−	0.644261i	0.617903	−	0.786254i	$-0.287982\pi$
$101$	−3.92888e10	−	6.80502e10i	−0.371964	−	0.644261i	−0.989868	+	0.141993i	$0.954649\pi$
$102$	−1.05082e10	−	4.41605e10i	−0.0942380	−	0.396035i
$103$	6.18514e8	+	3.57099e8i	0.00525708	+	0.00303518i	0.502626	−	0.864504i	$-0.332367\pi$
$103$	6.18514e8	+	3.57099e8i	0.00525708	+	0.00303518i	−0.497369	+	0.867539i	$0.665701\pi$
$104$	−1.36685e10			−0.110163
$105$	2.57652e11	+	9.32212e9i	1.97012	+	0.0712809i
$106$	−5.08105e10			−0.368784
$107$	2.82918e10	+	1.63343e10i	0.195007	+	0.112587i	0.594324	−	0.804226i	$-0.297420\pi$
$107$	2.82918e10	+	1.63343e10i	0.195007	+	0.112587i	−0.399318	+	0.916813i	$0.630753\pi$
$108$	−7.18143e10	−	2.59192e10i	−0.470306	−	0.169742i
$109$	1.42456e11	+	2.46741e11i	0.886819	+	1.53601i	0.843615	+	0.536948i	$0.180423\pi$
$109$	1.42456e11	+	2.46741e11i	0.886819	+	1.53601i	0.0432035	+	0.999066i	$0.486244\pi$
$110$	−2.01540e11	+	3.49077e11i	−1.19317	+	2.06663i
$111$	1.16856e10	−	3.91608e10i	0.0658227	−	0.220584i
$112$	4.49407e10	+	1.24268e10i	0.240958	+	0.0666286i
$113$		−	1.63241e11i		−	0.833484i	−0.909025	−	0.416742i	$-0.863172\pi$
$113$		−	1.63241e11i		−	0.833484i	0.909025	−	0.416742i	$-0.136828\pi$
$114$	−6.17768e8	−	6.53617e8i	−0.00300503	−	0.00317941i
$115$	−4.62140e11	+	2.66816e11i	−2.14257	+	1.23701i
$116$	3.29881e9	−	1.90457e9i	0.0145827	−	0.00841933i
$117$	3.32819e10	+	6.59737e10i	0.140341	+	0.278194i
$118$		−	2.58852e11i		−	1.04160i
$119$	1.06816e11	−	1.05126e11i	0.410326	−	0.403833i
$120$	−1.82056e11	−	5.43258e10i	−0.667896	−	0.199301i
$121$	2.75396e11	−	4.76999e11i	0.965245	−	1.67185i
$122$	−4.84976e10	−	8.40002e10i	−0.162458	−	0.281385i
$123$	−2.00661e10	+	4.77480e9i	−0.0642664	+	0.0152924i
$124$	−1.34568e11	−	7.76927e10i	−0.412213	−	0.237991i
$125$	−1.26889e12			−3.71895
$126$	−4.94472e10	−	2.47174e11i	−0.138709	−	0.693368i
$127$	4.39423e11			1.18022			0.590109	−	0.807324i	$-0.299085\pi$
$127$	4.39423e11			1.18022			0.590109	+	0.807324i	$0.299085\pi$
$128$	−2.97564e10	−	1.71799e10i	−0.0765466	−	0.0441942i
$129$	−3.64826e11	+	8.68117e10i	−0.899171	+	0.213961i
$130$	9.19395e10	+	1.59244e11i	0.217177	+	0.376161i
$131$	2.08883e11	−	3.61795e11i	0.473053	−	0.819352i	−0.526471	−	0.850193i	$-0.676485\pi$
$131$	2.08883e11	−	3.61795e11i	0.473053	−	0.819352i	0.999524	+	0.0308407i	$0.00981846\pi$
$132$	3.77637e11	+	1.12687e11i	0.820196	+	0.244747i
$133$	7.91366e8	−	2.86192e9i	0.00164890	−	0.00596312i
$134$		−	6.08139e11i		−	1.21598i
$135$	1.81081e11	+	1.01101e12i	0.347566	+	1.94053i
$136$	−9.56440e10	+	5.52201e10i	−0.176276	+	0.101773i
$137$	−3.87098e11	+	2.23491e11i	−0.685263	+	0.395637i	−0.801835	−	0.597545i	$-0.796143\pi$
$137$	−3.87098e11	+	2.23491e11i	−0.685263	+	0.395637i	0.116572	+	0.993182i	$0.462809\pi$
$138$	3.58376e11	+	3.79173e11i	0.609542	+	0.644915i
$139$		−	1.18801e11i		−	0.194195i	−0.995275	−	0.0970975i	$-0.969044\pi$
$139$		−	1.18801e11i		−	0.194195i	0.995275	−	0.0970975i	$-0.0309559\pi$
$140$	−1.57511e11	−	6.07166e11i	−0.247517	−	0.954121i
$141$	1.88489e11	−	6.31664e11i	0.284827	−	0.954510i
$142$	7.34644e9	−	1.27244e10i	0.0106780	−	0.0184949i
$143$	−1.90709e11	−	3.30317e11i	−0.266700	−	0.461937i
$144$	−1.04671e10	+	1.85457e11i	−0.0140875	+	0.249603i
$145$	−4.43781e10	−	2.56217e10i	−0.0574969	−	0.0331958i
$146$	3.99518e11			0.498420
$147$	6.13872e11	−	5.61938e11i	0.737620	−	0.675216i
$148$	−9.94276e10			−0.115098
$149$	−7.39189e11	−	4.26771e11i	−0.824577	−	0.476070i	0.0274155	−	0.999624i	$-0.491272\pi$
$149$	−7.39189e11	−	4.26771e11i	−0.824577	−	0.476070i	−0.851992	+	0.523555i	$0.824606\pi$
$150$	4.39423e11	+	1.84667e12i	0.472478	+	1.98558i
$151$	−4.07571e11	−	7.05933e11i	−0.422503	−	0.731797i	0.573681	−	0.819079i	$-0.305515\pi$
$151$	−4.07571e11	−	7.05933e11i	−0.422503	−	0.731797i	−0.996184	+	0.0872825i	$0.972182\pi$
$152$	−1.09405e9	+	1.89495e9i	−0.00109370	+	0.00189434i
$153$	4.99417e11	+	3.27187e11i	0.481571	+	0.315496i
$154$	3.26722e11	+	1.25944e12i	0.303959	+	1.17169i
$155$			2.09036e12i			1.87671i
$156$	1.30655e11	−	1.23489e11i	0.113225	−	0.107015i
$157$	6.02984e11	−	3.48133e11i	0.504496	−	0.291271i	−0.226072	−	0.974111i	$-0.572589\pi$
$157$	6.02984e11	−	3.48133e11i	0.504496	−	0.291271i	0.730568	+	0.682840i	$0.239255\pi$
$158$	−9.40789e11	+	5.43165e11i	−0.760113	+	0.438852i
$159$	4.85691e11	−	4.59051e11i	0.379032	−	0.358242i
$160$			4.62233e11i			0.348499i
$161$	−4.59083e11	+	1.66024e12i	−0.334464	+	1.20956i
$162$	9.20631e11	−	4.01054e11i	0.648266	−	0.282403i
$163$	9.67100e11	−	1.67507e12i	0.658324	−	1.14025i	−0.322725	−	0.946493i	$-0.604599\pi$
$163$	9.67100e11	−	1.67507e12i	0.658324	−	1.14025i	0.981049	−	0.193758i	$-0.0620677\pi$
$164$	2.50914e10	+	4.34596e10i	0.0165152	+	0.0286052i
$165$	−1.22727e12	−	5.15761e12i	−0.781231	−	3.28312i
$166$	−6.04488e11	−	3.49001e11i	−0.372215	−	0.214898i
$167$	1.06354e12			0.633594			0.316797	−	0.948493i	$-0.397393\pi$
$167$	1.06354e12			0.633594			0.316797	+	0.948493i	$0.397393\pi$
$168$	−5.41853e11	+	2.87234e11i	−0.312378	+	0.165590i
$169$	1.61816e12			0.902912
$170$	1.28668e12	+	7.42862e11i	0.695024	+	0.401272i
$171$	1.18103e10	+	6.66569e8i	0.00617707	+	0.000348631i
$172$	4.56193e11	+	7.90149e11i	0.231069	+	0.400224i
$173$	5.10520e11	−	8.84247e11i	0.250472	−	0.433830i	−0.713184	−	0.700977i	$-0.752748\pi$
$173$	5.10520e11	−	8.84247e11i	0.250472	−	0.433830i	0.963656	+	0.267147i	$0.0860809\pi$
$174$	−1.43259e10	+	4.80088e10i	−0.00680927	+	0.0228192i
$175$	−4.46677e12	+	4.39608e12i	−2.05724	+	2.02468i
$176$		−	9.58804e11i		−	0.427967i
$177$	2.33862e12	+	2.47433e12i	1.01183	+	1.07054i
$178$	1.31967e11	−	7.61912e10i	0.0553548	−	0.0319591i
$179$	−1.16778e12	+	6.74218e11i	−0.474973	+	0.274226i	−0.718319	−	0.695714i	$-0.755088\pi$
$179$	−1.16778e12	+	6.74218e11i	−0.474973	+	0.274226i	0.243346	+	0.969940i	$0.421755\pi$
$180$	2.23106e12	−	1.12551e12i	0.880060	−	0.443966i
$181$			2.05828e12i			0.787541i	0.919209	+	0.393770i	$0.128829\pi$
$181$			2.05828e12i			0.787541i	−0.919209	+	0.393770i	$0.871171\pi$
$182$	5.72085e11	+	1.58191e11i	0.212358	+	0.0587203i
$183$	1.22249e12	+	3.64792e11i	0.440315	+	0.131390i
$184$	6.34675e11	−	1.09929e12i	0.221847	−	0.384250i
$185$	6.68788e11	+	1.15837e12i	0.226905	+	0.393011i
$186$	1.98823e12	−	4.73108e11i	0.654856	−	0.155826i
$187$	−2.66893e12	−	1.54091e12i	−0.853510	−	0.492774i
$188$	−1.60377e12			−0.498050
$189$	2.70577e12	+	1.91596e12i	0.816113	+	0.577892i
$190$	2.94360e10			0.00862451
$191$	−2.94234e12	−	1.69876e12i	−0.837549	−	0.483559i	0.0188817	−	0.999822i	$-0.493989\pi$
$191$	−2.94234e12	−	1.69876e12i	−0.837549	−	0.483559i	−0.856430	+	0.516263i	$0.827323\pi$
$192$	4.39650e11	−	1.04616e11i	0.121605	−	0.0289363i
$193$	−1.83279e12	−	3.17449e12i	−0.492660	−	0.853313i	0.507304	−	0.861767i	$-0.330642\pi$
$193$	−1.83279e12	−	3.17449e12i	−0.492660	−	0.853313i	−0.999964	+	0.00845460i	$0.997309\pi$
$194$	−1.26811e12	+	2.19643e12i	−0.331319	+	0.573861i
$195$	−2.31754e12	−	6.91555e11i	−0.588621	−	0.175645i
$196$	−1.73714e12	−	1.04023e12i	−0.428970	−	0.256875i
$197$		−	4.41279e12i		−	1.05962i	−0.848117	−	0.529809i	$-0.822264\pi$
$197$		−	4.41279e12i		−	1.05962i	0.848117	−	0.529809i	$-0.177736\pi$
$198$	−4.62785e12	+	2.33462e12i	−1.08074	+	0.545203i
$199$	5.80937e12	−	3.35404e12i	1.31958	−	0.761863i	0.335923	−	0.941889i	$-0.390952\pi$
$199$	5.80937e12	−	3.35404e12i	1.31958	−	0.761863i	0.983662	+	0.180027i	$0.0576184\pi$
$200$	3.99957e12	−	2.30916e12i	0.883789	−	0.510256i
$201$	5.49427e12	+	5.81311e12i	1.18122	+	1.24977i
$202$		−	2.51448e12i		−	0.526037i
$203$	−1.60112e11	+	4.15360e10i	−0.0325983	+	0.00845662i
$204$	4.15357e11	−	1.39194e12i	0.0823106	−	0.275839i
$205$	3.37549e11	−	5.84651e11i	0.0651164	−	0.112785i
$206$	1.14272e10	+	1.97924e10i	0.00214619	+	0.00371732i
$207$	−6.85133e12	−	3.86686e11i	−1.25296	−	0.0707167i
$208$	−3.78793e11	−	2.18696e11i	−0.0674610	−	0.0389487i
$209$	−6.10587e10			−0.0105911
$210$	6.99110e12	+	4.38077e12i	1.18124	+	0.740192i
$211$	1.23398e10			0.00203121			0.00101561	−	0.999999i	$-0.499677\pi$
$211$	1.23398e10			0.00203121			0.00101561	+	0.999999i	$0.499677\pi$
$212$	−1.40810e12	−	8.12969e11i	−0.225833	−	0.130385i
$213$	4.47360e10	+	1.88003e11i	0.00699148	+	0.0293817i
$214$	5.22696e11	+	9.05337e11i	0.0796111	+	0.137891i
$215$	6.13705e12	−	1.06297e13i	0.911063	−	1.57801i
$216$	−1.57547e12	−	1.86732e12i	−0.227989	−	0.270224i
$217$	4.73307e12	+	4.80918e12i	0.667751	+	0.678488i
$218$			9.11718e12i			1.25415i
$219$	−3.81893e12	+	3.60947e12i	−0.512270	+	0.484173i
$220$	−1.11705e13	+	6.44928e12i	−1.46133	+	0.843697i
$221$	−1.21753e12	+	7.02940e11i	−0.155354	+	0.0896934i
$222$	9.50414e11	−	8.98285e11i	0.118296	−	0.111808i
$223$			5.92842e12i			0.719883i	0.932975	+	0.359942i	$0.117203\pi$
$223$			5.92842e12i			0.719883i	−0.932975	+	0.359942i	$0.882797\pi$
$224$	1.04660e12	+	1.06343e12i	0.123999	+	0.125993i
$225$	−2.08843e13	−	1.36821e13i	−2.41444	−	1.58179i
$226$	2.61185e12	−	4.52386e12i	0.294681	−	0.510403i
$227$	4.97002e12	+	8.60833e12i	0.547288	+	0.947931i	0.998459	+	0.0554936i	$0.0176732\pi$
$227$	4.97002e12	+	8.60833e12i	0.547288	+	0.947931i	−0.451171	+	0.892438i	$0.648993\pi$
$228$	−6.66220e9	−	2.79979e10i	−0.000716104	−	0.00300942i
$229$	−8.21927e12	−	4.74540e12i	−0.862458	−	0.497941i	0.00237632	−	0.999997i	$-0.499244\pi$
$229$	−8.21927e12	−	4.74540e12i	−0.862458	−	0.497941i	−0.864835	+	0.502057i	$0.832577\pi$
$230$	−1.70763e13			−1.74940
$231$	−1.45015e13	−	9.08697e12i	−1.45060	−	0.908978i
$232$	1.21892e11			0.0119067
$233$	−4.96973e12	−	2.86927e12i	−0.474105	−	0.273725i	0.243851	−	0.969813i	$-0.421589\pi$
$233$	−4.96973e12	−	2.86927e12i	−0.474105	−	0.273725i	−0.717957	+	0.696088i	$0.754922\pi$
$234$	−1.33244e11	+	2.36083e12i	−0.0124154	+	0.219977i
$235$	1.07875e13	+	1.86846e13i	0.981860	+	1.70063i
$236$	4.14164e12	−	7.17353e12i	0.368261	−	0.637847i
$237$	4.08561e12	−	1.36917e13i	0.354928	−	1.18943i
$238$	4.64220e12	−	1.20427e12i	0.394049	−	0.102224i
$239$		−	1.87955e13i		−	1.55907i	−0.626357	−	0.779537i	$-0.715455\pi$
$239$		−	1.87955e13i		−	1.55907i	0.626357	−	0.779537i	$-0.284545\pi$
$240$	−4.17608e12	−	4.41842e12i	−0.338537	−	0.358183i
$241$	−4.08324e12	+	2.35746e12i	−0.323527	+	0.186789i	−0.652964	−	0.757389i	$-0.726475\pi$
$241$	−4.08324e12	+	2.35746e12i	−0.323527	+	0.186789i	0.329436	+	0.944178i	$0.393141\pi$
$242$	1.52640e13	−	8.81266e12i	1.18218	−	0.682531i
$243$	−5.17683e12	+	1.21511e13i	−0.391949	+	0.919987i
$244$		−	3.10384e12i		−	0.229750i
$245$	−4.34462e11	+	2.72354e13i	−0.0314441	+	1.97116i
$246$	−6.32484e11	−	1.88734e11i	−0.0447617	−	0.0133569i
$247$	−1.39270e10	+	2.41223e10i	−0.000963885	+	0.00166950i
$248$	−2.48617e12	−	4.30617e12i	−0.168285	−	0.291479i
$249$	8.93129e12	−	2.12524e12i	0.591314	−	0.140705i
$250$	−3.51646e13	−	2.03023e13i	−2.27738	−	1.31485i
$251$	−1.58758e12			−0.100584			−0.0502922	−	0.998735i	$-0.516015\pi$
$251$	−1.58758e12			−0.100584			−0.0502922	+	0.998735i	$0.516015\pi$
$252$	2.58446e12	−	7.64103e12i	0.160201	−	0.473641i
$253$	3.54210e13			2.14832
$254$	1.21776e13	+	7.03076e12i	0.722733	+	0.417270i
$255$	−1.90106e13	+	4.52364e12i	−1.10414	+	0.262735i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−9.13158e12	+	1.58164e13i	−0.508058	+	0.879983i	0.491898	+	0.870653i	$0.336303\pi$
$257$	−9.13158e12	+	1.58164e13i	−0.508058	+	0.879983i	−0.999956	+	0.00933013i	$0.997030\pi$
$258$	−1.14993e13	−	3.43142e12i	−0.626274	−	0.186881i
$259$	4.16147e12	+	1.15071e12i	0.221870	+	0.0613505i
$260$			5.88413e12i			0.307135i
$261$	−2.96800e11	−	5.88337e11i	−0.0151684	−	0.0300679i
$262$	1.15774e13	−	6.68424e12i	0.579370	−	0.334499i
$263$	2.67077e13	−	1.54197e13i	1.30882	−	0.755648i	0.326922	−	0.945051i	$-0.393989\pi$
$263$	2.67077e13	−	1.54197e13i	1.30882	−	0.755648i	0.981899	+	0.189403i	$0.0606553\pi$
$264$	8.66238e12	+	9.16507e12i	0.415734	+	0.439860i
$265$			2.18733e13i			1.02817i
$266$	6.77217e10	−	6.66501e10i	0.00311802	−	0.00306868i
$267$	−5.73099e11	+	1.92057e12i	−0.0258474	+	0.0866198i
$268$	9.73022e12	−	1.68532e13i	0.429914	−	0.744633i
$269$	7.26118e12	+	1.25767e13i	0.314318	+	0.544416i	0.979292	−	0.202451i	$-0.0648907\pi$
$269$	7.26118e12	+	1.25767e13i	0.314318	+	0.544416i	−0.664974	+	0.746867i	$0.731557\pi$
$270$	−1.11579e13	+	3.09152e13i	−0.473240	+	1.31121i
$271$	2.92095e13	+	1.68641e13i	1.21393	+	0.700863i	0.963613	−	0.267301i	$-0.0861319\pi$
$271$	2.92095e13	+	1.68641e13i	1.21393	+	0.700863i	0.250317	+	0.968164i	$0.419465\pi$
$272$	−3.53409e12			−0.143929
$273$	−6.89767e12	+	3.65642e12i	−0.275301	+	0.145936i
$274$	−1.43034e13			−0.559515
$275$	1.11608e14	+	6.44367e13i	4.27921	+	2.47060i
$276$	3.86484e12	+	1.62420e13i	0.145255	+	0.610434i
$277$	−3.24975e12	−	5.62873e12i	−0.119732	−	0.207382i	0.799929	−	0.600094i	$-0.204870\pi$
$277$	−3.24975e12	−	5.62873e12i	−0.119732	−	0.207382i	−0.919662	+	0.392712i	$0.871537\pi$
$278$	1.90081e12	−	3.29231e12i	0.0686583	−	0.118920i
$279$	−1.47309e13	+	2.24852e13i	−0.521682	+	0.796294i
$280$	5.34960e12	−	1.93464e13i	0.185760	−	0.671788i
$281$		−	4.80986e13i		−	1.63775i	−0.573972	−	0.818875i	$-0.694598\pi$
$281$		−	4.80986e13i		−	1.63775i	0.573972	−	0.818875i	$-0.305402\pi$
$282$	1.53302e13	−	1.44893e13i	0.511891	−	0.483814i
$283$	3.92352e13	−	2.26525e13i	1.28485	−	0.741806i	0.307115	−	0.951672i	$-0.400636\pi$
$283$	3.92352e13	−	2.26525e13i	1.28485	−	0.741806i	0.977730	+	0.209867i	$0.0673030\pi$
$284$	4.07181e11	−	2.35086e11i	0.0130779	−	0.00755051i
$285$	−2.81375e11	+	2.65942e11i	−0.00886417	+	0.00837799i
$286$		−	1.22054e13i		−	0.377170i
$287$	−5.47210e11	−	2.10936e12i	−0.0165884	−	0.0639442i
$288$	−3.25738e12	+	4.97206e12i	−0.0968747	+	0.147869i
$289$	1.14563e13	−	1.98428e13i	0.334276	−	0.578983i
$290$	−8.19894e11	−	1.42010e12i	−0.0234730	−	0.0406564i
$291$	−7.72211e12	−	3.24521e13i	−0.216932	−	0.911657i
$292$	1.10718e13	+	6.39228e12i	0.305219	+	0.176218i
$293$	−4.61180e13			−1.24767			−0.623833	−	0.781558i	$-0.714426\pi$
$293$	−4.61180e13			−1.24767			−0.623833	+	0.781558i	$0.714426\pi$
$294$	2.60031e13	−	5.75091e12i	0.690423	−	0.152696i
$295$	−1.11433e14			−2.90397
$296$	−2.75542e12	−	1.59084e12i	−0.0704828	−	0.0406933i
$297$	2.31447e13	−	6.41270e13i	0.581153	−	1.61020i
$298$	−1.36567e13	−	2.36540e13i	−0.336632	−	0.583064i
$299$	8.07927e12	−	1.39937e13i	0.195515	−	0.338642i
$300$	−1.73691e13	+	5.82073e13i	−0.412678	+	1.38296i
$301$	−9.94894e12	−	3.83508e13i	−0.232093	−	0.894662i
$302$		−	2.60845e13i		−	0.597509i
$303$	2.27173e13	+	2.40356e13i	0.511001	+	0.540655i
$304$	−6.06385e10	+	3.50096e10i	−0.00133950	+	0.000773362i
$305$	−3.61611e13	+	2.08776e13i	−0.784500	+	0.452931i
$306$	8.60526e12	+	1.70580e13i	0.183357	+	0.363462i
$307$			6.28632e13i			1.31563i	0.753178	+	0.657817i	$0.228520\pi$
$307$			6.28632e13i			1.31563i	−0.753178	+	0.657817i	$0.771480\pi$
$308$	−1.10966e13	+	4.01301e13i	−0.228119	+	0.824975i
$309$	−2.88047e11	−	8.59535e10i	−0.00581690	−	0.00173577i
$310$	−3.34458e13	+	5.79298e13i	−0.663517	+	1.14925i
$311$	−1.24960e13	−	2.16436e13i	−0.243550	−	0.421841i	0.718173	−	0.695864i	$-0.244979\pi$
$311$	−1.24960e13	−	2.16436e13i	−0.243550	−	0.421841i	−0.961723	+	0.274024i	$0.911645\pi$
$312$	5.59665e12	−	1.33174e12i	0.107171	−	0.0255018i
$313$	3.86524e13	+	2.23160e13i	0.727248	+	0.419877i	0.817414	−	0.576050i	$-0.195407\pi$
$313$	3.86524e13	+	2.23160e13i	0.727248	+	0.419877i	−0.0901666	+	0.995927i	$0.528740\pi$
$314$	2.22805e13			0.411919
$315$	−1.06405e14	+	2.12864e13i	−1.93310	+	0.386719i
$316$	−3.47626e13			−0.620630
$317$	−2.14800e13	−	1.24015e13i	−0.376884	−	0.217594i	0.299578	−	0.954072i	$-0.403154\pi$
$317$	−2.14800e13	−	1.24015e13i	−0.376884	−	0.217594i	−0.676462	+	0.736478i	$0.736488\pi$
$318$	2.08047e13	−	4.95055e12i	0.358766	−	0.0853699i
$319$	1.70069e12	+	2.94569e12i	0.0288255	+	0.0499273i
$320$	−7.39573e12	+	1.28098e13i	−0.123213	+	0.213411i
$321$	−1.31757e13	−	3.93165e12i	−0.215773	−	0.0643868i
$322$	−3.92864e13	+	3.86647e13i	−0.632462	+	0.622453i
$323$			2.25058e11i			0.00356189i
$324$	3.19301e13	+	3.61577e12i	0.496825	+	0.0562604i
$325$	5.09137e13	−	2.93950e13i	0.778890	−	0.449692i
$326$	5.36022e13	−	3.09472e13i	0.806279	−	0.465505i
$327$	−8.23698e13	−	8.71498e13i	−1.21830	−	1.28900i
$328$			1.60585e12i			0.0233560i
$329$	6.71246e13	+	1.85610e13i	0.960073	+	0.265475i
$330$	4.85105e13	−	1.62568e14i	0.682353	−	2.28670i
$331$	−5.06478e13	+	8.77246e13i	−0.700659	+	1.21358i	0.267576	+	0.963537i	$0.413777\pi$
$331$	−5.06478e13	+	8.77246e13i	−0.700659	+	1.21358i	−0.968235	+	0.250040i	$0.919556\pi$
$332$	−1.11680e13	−	1.93436e13i	−0.151956	−	0.263195i
$333$	−9.69247e11	+	1.71732e13i	−0.0129715	+	0.229830i
$334$	2.94736e13	+	1.70166e13i	0.387996	+	0.224009i
$335$	−2.61797e14			−3.39014
$336$	−1.96120e13	−	7.09583e11i	−0.249837	−	0.00903935i
$337$	1.09085e13			0.136710			0.0683548	−	0.997661i	$-0.478225\pi$
$337$	1.09085e13			0.136710			0.0683548	+	0.997661i	$0.478225\pi$
$338$	4.48439e13	+	2.58906e13i	0.552919	+	0.319228i
$339$	1.59048e13	+	6.68399e13i	0.192944	+	0.810844i
$340$	2.37716e13	+	4.11736e13i	0.283742	+	0.491456i
$341$	6.93761e13	−	1.20163e14i	0.814819	−	1.41131i
$342$	3.16632e11	+	2.07437e11i	0.00365941	+	0.00239742i
$343$	6.06679e13	+	6.36427e13i	0.689988	+	0.723821i
$344$			2.91963e13i			0.326781i
$345$	1.63229e14	−	1.54277e14i	1.79802	−	1.69940i
$346$	2.82959e13	−	1.63366e13i	0.306764	−	0.177110i
$347$	3.25924e12	−	1.88172e12i	0.0347779	−	0.0200791i	−0.482510	−	0.875890i	$-0.660275\pi$
$347$	3.25924e12	−	1.88172e12i	0.0347779	−	0.0200791i	0.517288	+	0.855811i	$0.326942\pi$
$348$	−1.16515e12	+	1.10124e12i	−0.0122376	+	0.0115664i
$349$		−	1.71601e14i		−	1.77411i	−0.461665	−	0.887054i	$-0.652748\pi$
$349$		−	1.71601e14i		−	1.77411i	0.461665	−	0.887054i	$-0.347252\pi$
$350$	−1.94124e14	+	5.03595e13i	−1.97563	+	0.512516i
$351$	−2.00554e13	−	2.37706e13i	−0.200929	−	0.238150i
$352$	1.53409e13	−	2.65712e13i	0.151309	−	0.262075i
$353$	−2.54333e12	−	4.40517e12i	−0.0246968	−	0.0427762i	0.853413	−	0.521236i	$-0.174529\pi$
$353$	−2.54333e12	−	4.40517e12i	−0.0246968	−	0.0427762i	−0.878110	+	0.478459i	$0.841195\pi$
$354$	2.52204e13	+	1.05989e14i	0.241120	+	1.01331i
$355$	−5.47771e12	−	3.16256e12i	−0.0515636	−	0.0297703i
$356$	4.87624e12			0.0451970
$357$	−3.34940e13	+	5.34517e13i	−0.305697	+	0.487850i
$358$	−4.31499e13			−0.387814
$359$	−1.38572e14	−	8.00047e13i	−1.22647	−	0.708102i	−0.260179	−	0.965560i	$-0.583782\pi$
$359$	−1.38572e14	−	8.00047e13i	−1.22647	−	0.708102i	−0.966289	+	0.257458i	$0.917115\pi$
$360$	7.98370e13	+	4.50597e12i	0.695890	+	0.0392758i
$361$	−5.82429e13	−	1.00880e14i	−0.499981	−	0.865992i
$362$	−3.29325e13	+	5.70408e13i	−0.278438	+	0.482268i
$363$	−6.62875e13	+	2.22142e14i	−0.552008	+	1.84989i
$364$	1.33230e13	+	1.35373e13i	0.109281	+	0.111039i
$365$		−	1.71988e14i		−	1.38959i
$366$	2.80419e13	+	2.96692e13i	0.223183	+	0.236135i
$367$	−1.34630e14	+	7.77289e13i	−1.05555	+	0.609424i	−0.924199	−	0.381912i	$-0.875266\pi$
$367$	−1.34630e14	+	7.77289e13i	−1.05555	+	0.609424i	−0.131354	+	0.991336i	$0.541932\pi$
$368$	3.51773e13	−	2.03096e13i	0.271706	−	0.156869i
$369$	7.75095e12	−	3.91014e12i	0.0589807	−	0.0297541i
$370$			4.28024e13i			0.320892i
$371$	4.95264e13	+	5.03227e13i	0.365831	+	0.371713i
$372$	6.26693e13	+	1.87006e13i	0.456109	+	0.136103i
$373$	−8.25996e13	+	1.43067e14i	−0.592351	+	1.02598i	0.401563	+	0.915831i	$0.368467\pi$
$373$	−8.25996e13	+	1.43067e14i	−0.592351	+	1.02598i	−0.993915	+	0.110152i	$0.964866\pi$
$374$	−4.93091e13	−	8.54059e13i	−0.348444	−	0.603523i
$375$	5.19556e14	−	1.23630e14i	3.61793	−	0.860901i
$376$	−4.44449e13	−	2.56603e13i	−0.304992	−	0.176087i
$377$	1.55166e12			0.0104935
$378$	4.43290e13	+	9.63890e13i	0.295449	+	0.642425i
$379$	−9.41219e13			−0.618266			−0.309133	−	0.951019i	$-0.600039\pi$
$379$	−9.41219e13			−0.618266			−0.309133	+	0.951019i	$0.600039\pi$
$380$	8.15755e11	+	4.70976e11i	0.00528141	+	0.00304922i
$381$	−1.79924e14	+	4.28137e13i	−1.14816	+	0.273209i
$382$	−5.43604e13	−	9.41550e13i	−0.341928	−	0.592236i
$383$	−1.39046e14	+	2.40835e14i	−0.862116	+	1.49323i	0.00776747	+	0.999970i	$0.497528\pi$
$383$	−1.39046e14	+	2.40835e14i	−0.862116	+	1.49323i	−0.869883	+	0.493258i	$0.835806\pi$
$384$	1.38578e13	+	4.13518e12i	0.0846979	+	0.0252739i
$385$	5.42172e14	−	1.40650e14i	3.26666	−	0.847434i
$386$		−	1.17299e14i		−	0.696727i
$387$	1.40922e14	−	7.10911e13i	0.825217	−	0.416299i
$388$	−7.02856e13	+	4.05794e13i	−0.405781	+	0.234278i
$389$	−1.44538e14	+	8.34492e13i	−0.822735	+	0.475006i	−0.851359	−	0.524584i	$-0.824221\pi$
$389$	−1.44538e14	+	8.34492e13i	−0.822735	+	0.475006i	0.0286240	+	0.999590i	$0.490887\pi$
$390$	−5.31605e13	−	5.62455e13i	−0.298356	−	0.315669i
$391$		−	1.30560e14i		−	0.722498i
$392$	−3.14974e13	−	5.66220e13i	−0.171871	−	0.308967i
$393$	−5.02779e13	+	1.68491e14i	−0.270532	+	0.906604i
$394$	7.06046e13	−	1.22291e14i	0.374631	−	0.648880i
$395$	2.33826e14	+	4.04999e14i	1.22351	+	2.11919i
$396$	−1.65605e14	−	9.34668e12i	−0.854574	−	0.0482318i
$397$	−1.30900e14	−	7.55749e13i	−0.666178	−	0.384618i	0.128449	−	0.991716i	$-0.459000\pi$
$397$	−1.30900e14	−	7.55749e13i	−0.666178	−	0.384618i	−0.794627	+	0.607098i	$0.792334\pi$
$398$	2.14659e14			1.07744
$399$	−4.51878e10	+	1.24893e12i	−0.000223702	+	0.00618285i
$400$	1.47786e14			0.721611
$401$	2.01189e14	+	1.16157e14i	0.968970	+	0.559435i	0.898922	−	0.438108i	$-0.144351\pi$
$401$	2.01189e14	+	1.16157e14i	0.968970	+	0.559435i	0.0700481	+	0.997544i	$0.477685\pi$
$402$	5.92520e13	+	2.49006e14i	0.281488	+	1.18295i
$403$	−3.16484e13	−	5.48166e13i	−0.148311	−	0.256882i
$404$	4.02317e13	−	6.96834e13i	0.185982	−	0.322130i
$405$	−1.72649e14	−	3.96321e14i	−0.787338	−	1.80736i
$406$	−5.10172e12	−	1.41071e12i	−0.0229521	−	0.00634663i
$407$		−	8.87844e13i		−	0.394065i
$408$	3.37818e13	−	3.19289e13i	0.147929	−	0.139815i
$409$	1.15197e13	−	6.65089e12i	0.0497694	−	0.0287344i	−0.474909	−	0.880035i	$-0.657519\pi$
$409$	1.15197e13	−	6.65089e12i	0.0497694	−	0.0287344i	0.524678	+	0.851301i	$0.324186\pi$
$410$	1.87088e13	−	1.08016e13i	0.0797509	−	0.0460442i
$411$	1.36724e14	−	1.29225e14i	0.575063	−	0.543522i
$412$			7.31339e11i			0.00303518i
$413$	−2.56367e14	+	2.52310e14i	−1.04987	+	1.03326i
$414$	−1.83683e14	−	1.20337e14i	−0.742277	−	0.486294i
$415$	−1.50241e14	+	2.60225e14i	−0.599134	+	1.03773i
$416$	−6.99827e12	−	1.21214e13i	−0.0275409	−	0.0477022i
$417$	1.15750e13	+	4.86437e13i	0.0449543	+	0.188920i
$418$	−1.69211e12	−	9.76939e11i	−0.00648573	−	0.00374454i
$419$	−9.20120e13			−0.348071			−0.174035	−	0.984739i	$-0.555681\pi$
$419$	−9.20120e13			−0.348071			−0.174035	+	0.984739i	$0.555681\pi$
$420$	1.23651e14	+	2.33261e14i	0.461664	+	0.870906i
$421$	2.80568e14			1.03392			0.516960	−	0.856010i	$-0.327064\pi$
$421$	2.80568e14			1.03392			0.516960	+	0.856010i	$0.327064\pi$
$422$	3.41971e11	+	1.97437e11i	0.00124386	+	0.000718142i
$423$	−1.56340e13	+	2.77003e14i	−0.0561302	+	0.994518i
$424$	−2.60150e13	−	4.50593e13i	−0.0921959	−	0.159688i
$425$	2.37509e14	−	4.11378e14i	0.830886	−	1.43914i
$426$	−1.76828e12	+	5.92586e12i	−0.00610660	+	0.0204644i
$427$	−3.59219e13	+	1.29909e14i	−0.122463	+	0.442881i
$428$			3.34526e13i			0.112587i
$429$	1.10270e14	+	1.16669e14i	0.366389	+	0.387651i
$430$	3.40150e14	−	1.96386e14i	1.11582	−	0.644219i
$431$	2.01906e14	−	1.16571e14i	0.653921	−	0.377541i	−0.136036	−	0.990704i	$-0.543436\pi$
$431$	2.01906e14	−	1.16571e14i	0.653921	−	0.377541i	0.789957	+	0.613163i	$0.210103\pi$
$432$	−1.37835e13	−	7.69563e13i	−0.0440758	−	0.246084i
$433$			2.43128e14i			0.767628i	0.923410	+	0.383814i	$0.125390\pi$
$433$			2.43128e14i			0.767628i	−0.923410	+	0.383814i	$0.874610\pi$
$434$	5.42199e13	+	2.09005e14i	0.169031	+	0.651573i
$435$	2.06672e13	+	6.16712e12i	0.0636196	+	0.0189842i
$436$	−1.45875e14	+	2.52663e14i	−0.443409	+	0.768007i
$437$	−1.29336e12	−	2.24016e12i	−0.00388214	−	0.00672407i
$438$	−1.63585e14	+	3.89257e13i	−0.484881	+	0.115379i
$439$	1.78502e14	+	1.03058e14i	0.522502	+	0.301667i	0.737958	−	0.674847i	$-0.235790\pi$
$439$	1.78502e14	+	1.03058e14i	0.522502	+	0.301667i	−0.215456	+	0.976514i	$0.569124\pi$
$440$	−4.12754e14			−1.19317
$441$	−1.96603e14	+	2.89899e14i	−0.561278	+	0.827627i
$442$	−4.49881e13			−0.126846
$443$	−3.92351e14	−	2.26524e14i	−1.09258	−	0.630804i	−0.158321	−	0.987388i	$-0.550608\pi$
$443$	−3.92351e14	−	2.26524e14i	−1.09258	−	0.630804i	−0.934263	+	0.356584i	$0.883941\pi$
$444$	4.07112e13	−	9.68739e12i	0.111972	−	0.0266441i
$445$	−3.27994e13	−	5.68102e13i	−0.0891017	−	0.154329i
$446$	−9.48547e13	+	1.64293e14i	−0.254517	+	0.440837i
$447$	3.44246e14	+	1.02723e14i	0.912384	+	0.272257i
$448$	1.19894e13	+	4.62164e13i	0.0313884	+	0.120995i
$449$		−	5.92829e14i		−	1.53311i	−0.642176	−	0.766557i	$-0.721968\pi$
$449$		−	5.92829e14i		−	1.53311i	0.642176	−	0.766557i	$-0.278032\pi$
$450$	−3.59849e14	−	7.13318e14i	−0.919288	−	1.82228i
$451$	−3.88075e13	+	2.24055e13i	−0.0979365	+	0.0565437i
$452$	1.44764e14	−	8.35793e13i	0.360909	−	0.208371i
$453$	2.35662e14	+	2.49338e14i	0.580430	+	0.614113i
$454$			3.18082e14i			0.773983i
$455$	6.80992e13	−	2.46276e14i	0.163712	−	0.592052i
$456$	2.63337e11	−	8.82495e11i	0.000625469	−	0.00209607i
$457$	2.15653e14	−	3.73522e14i	0.506077	−	0.876552i	−0.493898	−	0.869520i	$-0.664428\pi$
$457$	2.15653e14	−	3.73522e14i	0.506077	−	0.876552i	0.999975	−	0.00703183i	$-0.00223832\pi$
$458$	−1.51853e14	−	2.63017e14i	−0.352097	−	0.609850i
$459$	−2.36368e14	−	8.53097e13i	−0.541525	−	0.195447i
$460$	−4.73231e14	−	2.73220e14i	−1.07129	−	0.618507i
$461$	3.90634e13			0.0873807			0.0436903	−	0.999045i	$-0.486089\pi$
$461$	3.90634e13			0.0873807			0.0436903	+	0.999045i	$0.486089\pi$
$462$	−2.56487e14	−	4.83850e14i	−0.566937	−	1.06950i
$463$	2.89629e14			0.632624			0.316312	−	0.948655i	$-0.397555\pi$
$463$	2.89629e14			0.632624			0.316312	+	0.948655i	$0.397555\pi$
$464$	3.37798e12	+	1.95028e12i	0.00729135	+	0.00420966i
$465$	−2.03667e14	−	8.55911e14i	−0.434440	−	1.82573i
$466$	−9.18167e13	−	1.59031e14i	−0.193553	−	0.335243i
$467$	5.95394e13	−	1.03125e14i	0.124040	−	0.214843i	−0.797317	−	0.603560i	$-0.793748\pi$
$467$	5.95394e13	−	1.03125e14i	0.124040	−	0.214843i	0.921357	+	0.388717i	$0.127082\pi$
$468$	−4.14658e13	+	6.32932e13i	−0.0853764	+	0.130318i
$469$	−6.02301e14	+	5.92769e14i	−1.22564	+	1.20624i
$470$			6.90403e14i			1.38856i
$471$	−2.12976e14	+	2.01295e14i	−0.423366	+	0.400145i
$472$	2.29553e14	−	1.32532e14i	0.451026	−	0.260400i
$473$	−7.05568e14	+	4.07360e14i	−1.37026	+	0.791120i
$474$	3.32290e14	−	3.14065e14i	0.637877	−	0.602890i
$475$		−	9.41133e12i		−	0.0178581i
$476$	1.47917e14	+	4.09013e13i	0.277446	+	0.0767182i
$477$	−1.54143e14	+	2.35283e14i	−0.285806	+	0.436254i
$478$	3.00729e14	−	5.20878e14i	0.551216	−	0.954734i
$479$	2.22814e14	+	3.85925e14i	0.403736	+	0.699291i	0.994173	−	0.107793i	$-0.0343782\pi$
$479$	2.22814e14	+	3.85925e14i	0.403736	+	0.699291i	−0.590438	+	0.807083i	$0.701045\pi$
$480$	−4.50361e13	−	1.89264e14i	−0.0806741	−	0.339033i
$481$	−3.50759e13	−	2.02511e13i	−0.0621170	−	0.0358633i
$482$	−1.50877e14			−0.264159
$483$	2.62141e13	−	7.24525e14i	0.0453759	−	1.25413i
$484$	5.64010e14			0.965245
$485$	9.45535e14	+	5.45905e14i	1.59992	+	0.923714i
$486$	−3.37882e14	+	2.53912e14i	−0.565283	+	0.424800i
$487$	−4.97118e14	−	8.61033e14i	−0.822337	−	1.42433i	−0.903937	−	0.427665i	$-0.859336\pi$
$487$	−4.97118e14	−	8.61033e14i	−0.822337	−	1.42433i	0.0816001	−	0.996665i	$-0.473997\pi$
$488$	4.96615e13	−	8.60163e13i	0.0812290	−	0.140693i
$489$	−2.32780e14	+	7.80092e14i	−0.376485	+	1.26167i
$490$	−4.47807e14	+	7.47819e14i	−0.716164	+	1.19596i
$491$		−	4.20524e14i		−	0.665033i	−0.943097	−	0.332516i	$-0.892102\pi$
$491$		−	4.20524e14i		−	0.665033i	0.943097	−	0.332516i	$-0.107898\pi$
$492$	−1.45082e13	−	1.53501e13i	−0.0226884	−	0.0240051i
$493$	1.08576e13	−	6.26864e12i	0.0167910	−	0.00969428i
$494$	−7.71915e11	+	4.45665e11i	−0.00118051	+	0.000681570i
$495$	1.00503e15	+	1.99224e15i	1.52002	+	3.01309i
$496$		−	1.59115e14i		−	0.237991i
$497$	−1.97630e13	+	5.12691e12i	−0.0292343	+	0.00758395i
$498$	2.81515e14	+	8.40044e13i	0.411851	+	0.122897i
$499$	−4.40924e14	+	7.63702e14i	−0.637985	+	1.10502i	0.347889	+	0.937536i	$0.386898\pi$
$499$	−4.40924e14	+	7.63702e14i	−0.637985	+	1.10502i	−0.985874	+	0.167487i	$0.946435\pi$
$500$	−6.49674e14	−	1.12527e15i	−0.929737	−	1.61035i
$501$	−4.35471e14	+	1.03622e14i	−0.616384	+	0.146671i
$502$	−4.39964e13	−	2.54013e13i	−0.0615952	−	0.0355620i
$503$	5.77122e14			0.799179			0.399589	−	0.916694i	$-0.369153\pi$
$503$	5.77122e14			0.799179			0.399589	+	0.916694i	$0.369153\pi$
$504$	1.93879e14	−	1.70403e14i	0.265560	−	0.233405i
$505$	−1.08246e15			−1.46659
$506$	9.81617e14	+	5.66737e14i	1.31557	+	0.759545i
$507$	−6.62566e14	+	1.57660e14i	−0.878387	+	0.209016i
$508$	2.24984e14	+	3.89685e14i	0.295054	+	0.511049i
$509$	−1.66719e14	+	2.88765e14i	−0.216290	+	0.374625i	−0.953671	−	0.300852i	$-0.902729\pi$
$509$	−1.66719e14	+	2.88765e14i	−0.216290	+	0.374625i	0.737381	+	0.675477i	$0.236062\pi$
$510$	−5.99215e14	−	1.78806e14i	−0.769036	−	0.229481i
$511$	−3.89421e14	−	3.95682e14i	−0.494429	−	0.502379i
$512$		−	3.51844e13i		−	0.0441942i
$513$	−4.90074e12	+	8.77766e11i	−0.00608999	+	0.00109077i
$514$	−5.06123e14	+	2.92210e14i	−0.622242	+	0.359252i
$515$	8.52041e12	−	4.91926e12i	0.0103638	−	0.00598357i
$516$	−2.63776e14	−	2.79084e14i	−0.317441	−	0.335862i
$517$		−	1.43209e15i		−	1.70519i
$518$	9.69147e13	+	9.84730e13i	0.114176	+	0.116012i
$519$	−1.22882e14	+	4.11801e14i	−0.143241	+	0.480028i
$520$	−9.41460e13	+	1.63066e14i	−0.108588	+	0.188081i
$521$	−1.43251e14	−	2.48118e14i	−0.163490	−	0.283173i	0.772628	−	0.634859i	$-0.218942\pi$
$521$	−1.43251e14	−	2.48118e14i	−0.163490	−	0.283173i	−0.936118	+	0.351686i	$0.885608\pi$
$522$	1.18824e12	−	2.10533e13i	0.00134189	−	0.0237756i
$523$	−2.65452e14	−	1.53259e14i	−0.296637	−	0.171264i	0.344294	−	0.938862i	$-0.388118\pi$
$523$	−2.65452e14	−	1.53259e14i	−0.296637	−	0.171264i	−0.640931	+	0.767598i	$0.721452\pi$
$524$	4.27792e14			0.473053
$525$	1.40063e15	−	2.23521e15i	1.53266	−	2.44592i
$526$	9.86862e14			1.06865
$527$	−4.42913e14	−	2.55716e14i	−0.474635	−	0.274031i
$528$	9.34178e13	+	3.92588e14i	0.0990702	+	0.416342i
$529$	2.73892e14	+	4.74394e14i	0.287457	+	0.497890i
$530$	−3.49973e14	+	6.06172e14i	−0.363511	+	0.629620i
$531$	−1.19864e15	−	7.85274e14i	−1.23216	−	0.807237i
$532$	2.94316e12	−	7.63513e11i	0.00299433	−	0.000776788i
$533$			2.04421e13i			0.0205838i
$534$	−4.66112e13	+	4.40547e13i	−0.0464530	+	0.0439051i
$535$	3.89737e14	−	2.25015e14i	0.384437	−	0.221955i
$536$	5.39304e14	−	3.11367e14i	0.526535	−	0.303995i
$537$	4.12464e14	−	3.89841e14i	0.398591	−	0.376729i
$538$			4.64716e14i			0.444513i
$539$	9.28880e14	−	1.55119e15i	0.879471	−	1.46868i
$540$	−8.03860e14	+	6.78221e14i	−0.753381	+	0.635632i
$541$	7.05021e13	−	1.22113e14i	0.0654059	−	0.113286i	−0.831468	−	0.555573i	$-0.812499\pi$
$541$	7.05021e13	−	1.22113e14i	0.0654059	−	0.113286i	0.896874	+	0.442286i	$0.145832\pi$
$542$	5.39652e14	+	9.34705e14i	0.495585	+	0.858378i
$543$	−2.00542e14	−	8.42776e14i	−0.182308	−	0.766149i
$544$	−9.79395e13	−	5.65454e13i	−0.0881381	−	0.0508866i
$545$	3.92484e15			3.49656
$546$	−2.49657e14	−	9.03284e12i	−0.220183	−	0.00796645i
$547$	−3.28147e14			−0.286509			−0.143255	−	0.989686i	$-0.545757\pi$
$547$	−3.28147e14			−0.286509			−0.143255	+	0.989686i	$0.545757\pi$
$548$	−3.96388e14	−	2.28855e14i	−0.342632	−	0.197818i
$549$	−5.36097e14	−	3.02571e13i	−0.458770	−	0.0258928i
$550$	2.06197e15	+	3.57144e15i	1.74698	+	3.02586i
$551$	1.24198e11	−	2.15117e11i	0.000104179	−	0.000180443i
$552$	−1.52766e14	+	5.11948e14i	−0.126871	+	0.425168i
$553$	1.45496e15	+	4.02320e14i	1.19636	+	0.330814i
$554$		−	2.07984e14i		−	0.169327i
$555$	−3.86701e14	−	4.09142e14i	−0.311720	−	0.329809i
$556$	1.05354e14	−	6.08260e13i	0.0840889	−	0.0485488i
$557$	−1.91444e15	+	1.10530e15i	−1.51299	+	0.873528i	−0.513110	+	0.858323i	$0.671507\pi$
$557$	−1.91444e15	+	1.10530e15i	−1.51299	+	0.873528i	−0.999884	+	0.0152054i	$0.995160\pi$
$558$	−7.67998e14	+	3.87434e14i	−0.600997	+	0.303186i
$559$			3.71663e14i			0.287995i
$560$	4.57796e14	−	4.50551e14i	0.351267	−	0.345708i
$561$	1.24294e15	+	3.70896e14i	0.944399	+	0.281810i
$562$	7.69577e14	−	1.33295e15i	0.579032	−	1.00291i
$563$	6.19267e14	+	1.07260e15i	0.461405	+	0.799176i	0.999031	−	0.0440068i	$-0.0140123\pi$
$563$	6.19267e14	+	1.07260e15i	0.461405	+	0.799176i	−0.537627	+	0.843183i	$0.680679\pi$
$564$	6.56672e14	−	1.56258e14i	0.484522	−	0.115294i
$565$	−1.94747e15	−	1.12437e15i	−1.42300	−	0.821568i
$566$	1.44976e15			1.04907
$567$	−1.29457e15	−	5.20875e14i	−0.927722	−	0.373273i
$568$	1.50455e13			0.0106780
$569$	−5.55897e14	−	3.20947e14i	−0.390730	−	0.225588i	0.291746	−	0.956496i	$-0.405764\pi$
$569$	−5.55897e14	−	3.20947e14i	−0.390730	−	0.225588i	−0.682476	+	0.730908i	$0.739097\pi$
$570$	−1.20527e13	+	2.86800e12i	−0.00839024	+	0.00199649i
$571$	3.88577e14	+	6.73035e14i	0.267904	+	0.464023i	0.968320	−	0.249712i	$-0.0803358\pi$
$571$	3.88577e14	+	6.73035e14i	0.267904	+	0.464023i	−0.700417	+	0.713734i	$0.747002\pi$
$572$	1.95286e14	−	3.38245e14i	0.133350	−	0.230969i
$573$	1.37027e15	+	4.08891e14i	0.926738	+	0.276540i
$574$	1.85851e13	−	6.72117e13i	0.0124494	−	0.0450225i
$575$			5.45965e15i			3.62236i
$576$	−1.69824e14	+	8.56716e13i	−0.111603	+	0.0563006i
$577$	6.33994e14	−	3.66036e14i	0.412684	−	0.238263i	−0.279258	−	0.960216i	$-0.590089\pi$
$577$	6.33994e14	−	3.66036e14i	0.412684	−	0.238263i	0.691942	+	0.721953i	$0.256755\pi$
$578$	6.34971e14	−	3.66600e14i	0.409402	−	0.236369i
$579$	1.05974e15	+	1.12124e15i	0.676812	+	0.716088i
$580$		−	5.24732e13i		−	0.0331958i
$581$	2.43560e14	+	9.38866e14i	0.152629	+	0.588349i
$582$	3.05232e14	−	1.02289e15i	0.189476	−	0.634971i
$583$	7.25945e14	−	1.25737e15i	0.446403	−	0.773192i
$584$	2.04553e14	+	3.54296e14i	0.124605	+	0.215822i
$585$	1.01631e15	+	5.73600e13i	0.613293	+	0.0346140i
$586$	−1.27806e15	−	7.37888e14i	−0.764036	−	0.441117i
$587$	−1.98220e15			−1.17392			−0.586960	−	0.809616i	$-0.699675\pi$
$587$	−1.98220e15			−1.17392			−0.586960	+	0.809616i	$0.699675\pi$
$588$	8.12634e14	+	2.56676e14i	0.476782	+	0.150595i
$589$	−1.01328e13			−0.00588971
$590$	−3.08812e15	−	1.78293e15i	−1.77831	−	1.02671i
$591$	4.29945e14	+	1.80684e15i	0.245291	+	1.03084i
$592$	−5.09069e13	−	8.81734e13i	−0.0287745	−	0.0498389i
$593$	−3.18858e14	+	5.52278e14i	−0.178565	+	0.309284i	−0.941389	−	0.337322i	$-0.890479\pi$
$593$	−3.18858e14	+	5.52278e14i	−0.178565	+	0.309284i	0.762824	+	0.646606i	$0.223812\pi$
$594$	1.66744e15	−	1.40682e15i	0.925174	−	0.780575i
$595$	−5.18426e14	−	1.99841e15i	−0.284999	−	1.09860i
$596$		−	8.74027e14i		−	0.476070i
$597$	−2.05189e15	+	1.93935e15i	−1.10738	+	1.04664i
$598$	4.47799e14	−	2.58537e14i	0.239456	−	0.138250i
$599$	1.62968e15	−	9.40897e14i	0.863486	−	0.498534i	−0.00169231	−	0.999999i	$-0.500539\pi$
$599$	1.62968e15	−	9.40897e14i	0.863486	−	0.498534i	0.865178	+	0.501465i	$0.167205\pi$
$600$	−1.41266e15	+	1.33518e15i	−0.741664	+	0.700985i
$601$		−	2.46227e15i		−	1.28093i	−0.767986	−	0.640467i	$-0.778741\pi$
$601$		−	2.46227e15i		−	1.28093i	0.767986	−	0.640467i	$-0.221259\pi$
$602$	3.37900e14	−	1.22199e15i	0.174184	−	0.629924i
$603$	−2.81604e15	−	1.84490e15i	−1.43845	−	0.942382i
$604$	4.17352e14	−	7.22876e14i	0.211251	−	0.365898i
$605$	−3.79375e15	−	6.57096e15i	−1.90289	−	3.29590i
$606$	2.44990e14	+	1.02957e15i	0.121772	+	0.511748i
$607$	−9.54240e14	−	5.50931e14i	−0.470024	−	0.271368i	0.246226	−	0.969212i	$-0.420809\pi$
$607$	−9.54240e14	−	5.50931e14i	−0.470024	−	0.271368i	−0.716250	+	0.697844i	$0.754143\pi$
$608$	−2.24062e12			−0.00109370
$609$	6.15117e13	−	3.26071e13i	0.0297552	−	0.0157731i
$610$	−1.33617e15			−0.640541
$611$	−5.65774e14	−	3.26650e14i	−0.268792	−	0.155187i
$612$	−3.44512e13	+	6.10408e14i	−0.0162208	+	0.287400i
$613$	−4.85492e14	−	8.40897e14i	−0.226542	−	0.392383i	0.730239	−	0.683192i	$-0.239409\pi$
$613$	−4.85492e14	−	8.40897e14i	−0.226542	−	0.392383i	−0.956781	+	0.290809i	$0.906076\pi$
$614$	−1.00581e15	+	1.74212e15i	−0.465147	+	0.805658i
$615$	−8.12477e13	+	2.72277e14i	−0.0372390	+	0.124795i
$616$	−9.49599e14	+	9.34572e14i	−0.431366	+	0.424540i
$617$			2.12067e15i			0.954785i	0.878690	+	0.477392i	$0.158418\pi$
$617$			2.12067e15i			0.954785i	−0.878690	+	0.477392i	$0.841582\pi$
$618$	−6.60733e12	−	6.99076e12i	−0.00294842	−	0.00311952i
$619$	1.37481e15	−	7.93748e14i	0.608058	−	0.351062i	−0.164147	−	0.986436i	$-0.552487\pi$
$619$	1.37481e15	−	7.93748e14i	0.608058	−	0.351062i	0.772205	+	0.635374i	$0.219154\pi$
$620$	−1.85375e15	+	1.07027e15i	−0.812639	+	0.469177i
$621$	2.84299e15	−	5.09205e14i	1.23530	−	0.221253i
$622$		−	7.99742e14i		−	0.344431i
$623$	−2.04091e14	−	5.64345e13i	−0.0871245	−	0.0240913i
$624$	1.76407e14	+	5.26400e13i	0.0746449	+	0.0222741i
$625$	−5.29899e15	+	9.17812e15i	−2.22256	+	3.84958i
$626$	7.14111e14	+	1.23688e15i	0.296898	+	0.514242i
$627$	2.50008e13	−	5.94905e12i	0.0103035	−	0.00245175i
$628$	6.17456e14	+	3.56488e14i	0.252248	+	0.145635i
$629$	−3.27253e14			−0.132527
$630$	−3.28937e15	−	1.11258e15i	−1.32051	−	0.446640i
$631$	3.94202e15			1.56876			0.784382	−	0.620278i	$-0.212980\pi$
$631$	3.94202e15			1.56876			0.784382	+	0.620278i	$0.212980\pi$
$632$	−9.63368e14	−	5.56201e14i	−0.380057	−	0.219426i
$633$	−5.05261e12	+	1.20229e12i	−0.00197604	+	0.000470206i
$634$	−3.96847e14	−	6.87359e14i	−0.153862	−	0.266497i
$635$	3.02666e15	−	5.24233e15i	1.16334	−	2.01497i
$636$	6.55765e14	+	1.95681e14i	0.249881	+	0.0745649i
$637$	−4.00955e14	−	7.20786e14i	−0.151471	−	0.272295i
$638$			1.08844e14i			0.0407655i
$639$	−3.66348e13	−	7.26201e13i	−0.0136032	−	0.0269651i
$640$	−4.09913e14	+	2.36663e14i	−0.150904	+	0.0871247i
$641$	−2.89790e15	+	1.67310e15i	−1.05770	+	0.610665i	−0.924796	−	0.380464i	$-0.875764\pi$
$641$	−2.89790e15	+	1.67310e15i	−1.05770	+	0.610665i	−0.132907	+	0.991129i	$0.542431\pi$
$642$	−3.02230e14	−	3.19768e14i	−0.109369	−	0.115716i
$643$			2.14867e15i			0.770921i	0.922724	+	0.385461i	$0.125957\pi$
$643$			2.14867e15i			0.770921i	−0.922724	+	0.385461i	$0.874043\pi$
$644$	−1.70737e15	+	4.42925e14i	−0.607373	+	0.157564i
$645$	−1.47718e15	+	4.95033e15i	−0.521022	+	1.74605i
$646$	−3.60093e12	+	6.23700e12i	−0.00125932	+	0.00218121i
$647$	−2.06135e15	−	3.57036e15i	−0.714788	−	1.23805i	−0.963041	−	0.269354i	$-0.913190\pi$
$647$	−2.06135e15	−	3.57036e15i	−0.714788	−	1.23805i	0.248253	−	0.968695i	$-0.420144\pi$
$648$	8.27022e14	+	6.11085e14i	0.284351	+	0.210106i
$649$	6.40564e15	+	3.69830e15i	2.18382	+	1.26083i
$650$	1.88128e15			0.635961
$651$	−2.40655e15	−	1.50799e15i	−0.806676	−	0.505480i
$652$	1.98062e15			0.658324
$653$	−2.18628e15	−	1.26225e15i	−0.720581	−	0.416028i	0.0943854	−	0.995536i	$-0.469911\pi$
$653$	−2.18628e15	−	1.26225e15i	−0.720581	−	0.416028i	−0.814967	+	0.579508i	$0.803245\pi$
$654$	−8.88302e14	−	3.73308e15i	−0.290324	−	1.22008i
$655$	−2.87749e15	−	4.98395e15i	−0.932580	−	1.61528i
$656$	−2.56936e13	+	4.45026e13i	−0.00825760	+	0.0143026i
$657$	1.21201e15	−	1.85000e15i	0.386274	−	0.589607i
$658$	1.56323e15	+	1.58837e15i	0.494062	+	0.502007i
$659$		−	4.57637e14i		−	0.143434i	−0.997425	−	0.0717169i	$-0.977152\pi$
$659$		−	4.57637e14i		−	0.143434i	0.997425	−	0.0717169i	$-0.0228478\pi$
$660$	3.94545e15	−	3.72905e15i	1.22632	−	1.15906i
$661$	2.51725e14	−	1.45333e14i	0.0775922	−	0.0447979i	−0.460702	−	0.887555i	$-0.652402\pi$
$661$	2.51725e14	−	1.45333e14i	0.0775922	−	0.0447979i	0.538294	+	0.842757i	$0.319069\pi$
$662$	−2.80719e15	+	1.62073e15i	−0.858129	+	0.495441i
$663$	4.30035e14	−	4.06448e14i	0.130371	−	0.123220i
$664$		−	7.14755e14i		−	0.214898i
$665$	−2.86921e13	−	2.91534e13i	−0.00855545	−	0.00869301i
$666$	−3.01631e14	+	4.60409e14i	−0.0892006	+	0.136155i
$667$	−7.20490e13	+	1.24793e14i	−0.0211318	+	0.0366013i
$668$	5.44530e14	+	9.43154e14i	0.158399	+	0.274354i
$669$	−5.77616e14	−	2.42743e15i	−0.166646	−	0.700329i
$670$	−7.25512e15	−	4.18875e15i	−2.07603	−	1.19860i
$671$	2.77160e15			0.786604
$672$	−5.32150e14	−	3.33457e14i	−0.149797	−	0.0938660i
$673$	−1.12838e15			−0.315044			−0.157522	−	0.987515i	$-0.550351\pi$
$673$	−1.12838e15			−0.315044			−0.157522	+	0.987515i	$0.550351\pi$
$674$	3.02304e14	+	1.74535e14i	0.0837172	+	0.0483341i
$675$	9.88426e15	+	3.56742e15i	2.71502	+	0.979904i
$676$	8.28500e14	+	1.43500e15i	0.225728	+	0.390972i
$677$	−2.11177e15	+	3.65770e15i	−0.570702	+	0.988486i	0.425792	+	0.904821i	$0.359996\pi$
$677$	−2.11177e15	+	3.65770e15i	−0.570702	+	0.988486i	−0.996494	+	0.0836643i	$0.973338\pi$
$678$	−6.28671e14	+	2.10680e15i	−0.168523	+	0.564754i
$679$	3.41140e15	−	8.84982e14i	0.907086	−	0.235316i
$680$			1.52138e15i			0.401272i
$681$	−2.87373e15	−	3.04049e15i	−0.751860	−	0.795491i
$682$	3.84522e15	−	2.22004e15i	0.997945	−	0.576164i
$683$	−2.43031e15	+	1.40314e15i	−0.625673	+	0.361233i	−0.779074	−	0.626931i	$-0.784311\pi$
$683$	−2.43031e15	+	1.40314e15i	−0.625673	+	0.361233i	0.153401	+	0.988164i	$0.450977\pi$
$684$	5.45575e12	+	1.08148e13i	0.00139331	+	0.00276191i
$685$			6.15745e15i			1.55992i
$686$	6.62994e14	+	2.73441e15i	0.166620	+	0.687196i
$687$	3.82778e15	+	1.14221e15i	0.954300	+	0.284764i
$688$	−4.67141e14	+	8.09113e14i	−0.115535	+	0.200112i
$689$	−3.31165e14	−	5.73595e14i	−0.0812529	−	0.140734i
$690$	6.99197e15	−	1.66377e15i	1.70188	−	0.404970i
$691$	5.48229e15	+	3.16520e15i	1.32383	+	0.764314i	0.984338	−	0.176294i	$-0.0564109\pi$
$691$	5.48229e15	+	3.16520e15i	1.32383	+	0.764314i	0.339494	+	0.940608i	$0.389744\pi$
$692$	1.04555e15			0.250472
$693$	6.82310e15	+	2.30780e15i	1.62162	+	0.548487i
$694$	1.20430e14			0.0283961
$695$	−1.41730e15	−	8.18278e14i	−0.331547	−	0.191419i
$696$	−4.99095e13	+	1.18762e13i	−0.0115833	+	0.00275629i
$697$	8.25852e13	+	1.43042e14i	0.0190161	+	0.0329369i
$698$	2.74562e15	−	4.75555e15i	0.627242	−	1.08642i
$699$	2.31444e15	+	6.90632e14i	0.524592	+	0.156539i
$700$	−6.18548e15	−	1.71038e15i	−1.39102	−	0.384639i
$701$			3.91865e14i			0.0874353i	0.999044	+	0.0437177i	$0.0139202\pi$
$701$			3.91865e14i			0.0874353i	−0.999044	+	0.0437177i	$0.986080\pi$
$702$	−1.75462e14	−	9.79636e14i	−0.0388444	−	0.216876i
$703$	−5.61507e12	+	3.24186e12i	−0.00123339	+	0.000712099i
$704$	8.50277e14	−	4.90908e14i	0.185315	−	0.106992i
$705$	−6.23749e15	−	6.59946e15i	−1.34887	−	1.42715i
$706$		−	1.62773e14i		−	0.0349266i
$707$	−2.49034e15	+	2.45093e15i	−0.530215	+	0.521825i
$708$	−9.96889e14	+	3.34077e15i	−0.210603	+	0.705770i
$709$	−2.28626e15	+	3.95992e15i	−0.479260	+	0.830103i	−0.999717	−	0.0237851i	$-0.992428\pi$
$709$	−2.28626e15	+	3.95992e15i	−0.479260	+	0.830103i	0.520457	+	0.853888i	$0.325762\pi$
$710$	−1.01202e14	−	1.75287e14i	−0.0210507	−	0.0364610i
$711$	−3.38875e14	+	6.00420e15i	−0.0699449	+	1.23929i
$712$	1.35134e14	+	7.80198e13i	0.0276774	+	0.0159796i
$713$	5.87816e15			1.19467
$714$	−1.78344e15	+	9.45394e14i	−0.359682	+	0.190666i
$715$	−5.25427e15			−1.05155
$716$	−1.19581e15	−	6.90399e14i	−0.237487	−	0.137113i
$717$	1.83128e15	+	7.69595e15i	0.360911	+	1.51672i
$718$	−2.56015e15	−	4.43431e15i	−0.500704	−	0.867244i
$719$	2.14198e15	−	3.71002e15i	0.415726	−	0.720058i	−0.579778	−	0.814774i	$-0.696861\pi$
$719$	2.14198e15	−	3.71002e15i	0.415726	−	0.720058i	0.995504	+	0.0947158i	$0.0301942\pi$
$720$	2.14041e15	+	1.40227e15i	0.412258	+	0.270086i
$721$	8.46406e12	−	3.06097e13i	0.00161784	−	0.00585079i
$722$		−	3.72755e15i		−	0.707080i
$723$	1.44221e15	−	1.36311e15i	0.271500	−	0.256608i
$724$	−1.82531e15	+	1.05384e15i	−0.341015	+	0.196885i
$725$	−4.54036e14	+	2.62138e14i	−0.0841843	+	0.0486038i
$726$	−5.39129e15	+	5.09559e15i	−0.992068	+	0.937655i
$727$		−	8.99038e15i		−	1.64187i	−0.571022	−	0.820935i	$-0.693453\pi$
$727$		−	8.99038e15i		−	1.64187i	0.571022	−	0.820935i	$-0.306547\pi$
$728$	1.52623e14	+	5.88325e14i	0.0276628	+	0.106634i
$729$	9.35780e14	−	5.47973e15i	0.168334	−	0.985730i
$730$	2.75180e15	−	4.76626e15i	0.491294	−	0.850946i
$731$	1.50150e15	+	2.60068e15i	0.266060	+	0.460830i
$732$	3.02413e14	+	1.27089e15i	0.0531850	+	0.223510i
$733$	−1.03375e15	−	5.96837e14i	−0.180445	−	0.104180i	0.407057	−	0.913403i	$-0.366555\pi$
$733$	−1.03375e15	−	5.96837e14i	−0.180445	−	0.104180i	−0.587502	+	0.809223i	$0.699888\pi$
$734$	−4.97465e15			−0.861855
$735$	−2.47570e15	−	1.11940e16i	−0.425714	−	1.92489i
$736$	1.29981e15			0.221847
$737$	1.50492e16	+	8.68866e15i	2.54942	+	1.47191i
$738$	2.77363e14	+	1.56543e13i	0.0466378	+	0.00263222i
$739$	−3.39468e14	−	5.87976e14i	−0.0566571	−	0.0981331i	0.836306	−	0.548263i	$-0.184711\pi$
$739$	−3.39468e14	−	5.87976e14i	−0.0566571	−	0.0981331i	−0.892963	+	0.450130i	$0.851378\pi$
$740$	−6.84838e14	+	1.18618e15i	−0.113452	+	0.196505i
$741$	3.35223e12	−	1.12340e13i	0.000551231	−	0.00184728i
$742$	5.67352e14	+	2.18701e15i	0.0926043	+	0.356968i
$743$			3.17202e15i			0.513922i	0.966422	+	0.256961i	$0.0827212\pi$
$743$			3.17202e15i			0.513922i	−0.966422	+	0.256961i	$0.917279\pi$
$744$	1.43753e15	+	1.52095e15i	0.231189	+	0.244605i
$745$	−1.01828e16	+	5.87904e15i	−1.62558	+	0.938527i
$746$	−4.57814e15	+	2.64319e15i	−0.725479	+	0.418856i
$747$	−3.44990e15	+	1.74038e15i	−0.542680	+	0.273767i
$748$		−	3.15578e15i		−	0.492774i
$749$	3.87159e14	−	1.40013e15i	0.0600122	−	0.217030i
$750$	1.63764e16	+	4.88675e15i	2.51990	+	0.751940i
$751$	6.91784e14	−	1.19821e15i	0.105670	−	0.183025i	−0.808342	−	0.588713i	$-0.799635\pi$
$751$	6.91784e14	−	1.19821e15i	0.105670	−	0.183025i	0.914012	+	0.405688i	$0.132968\pi$
$752$	−8.21129e14	−	1.42224e15i	−0.124513	−	0.215662i
$753$	6.50045e14	−	1.54681e14i	0.0978523	−	0.0232843i
$754$	4.30009e13	+	2.48266e13i	0.00642592	+	0.00371001i
$755$	−1.12291e16			−1.66585
$756$	−3.13742e14	+	3.38047e15i	−0.0462065	+	0.497860i
$757$	−1.56770e15			−0.229211			−0.114605	−	0.993411i	$-0.536560\pi$
$757$	−1.56770e15			−0.229211			−0.114605	+	0.993411i	$0.536560\pi$
$758$	−2.60838e15	−	1.50595e15i	−0.378609	−	0.218590i
$759$	−1.45034e16	+	3.45113e15i	−2.08996	+	0.497315i
$760$	1.50712e13	+	2.61042e13i	0.00215613	+	0.00373452i
$761$	−2.37880e15	+	4.12020e15i	−0.337864	+	0.585197i	−0.984031	−	0.177999i	$-0.943038\pi$
$761$	−2.37880e15	+	4.12020e15i	−0.337864	+	0.585197i	0.646167	+	0.763196i	$0.276371\pi$
$762$	−5.67123e15	−	1.69230e15i	−0.799695	−	0.238630i
$763$	9.02965e15	−	8.88676e15i	1.26411	−	1.24411i
$764$		−	3.47907e15i		−	0.483559i
$765$	7.34325e15	−	3.70446e15i	1.01333	−	0.511196i
$766$	−7.70672e15	+	4.44947e15i	−1.05587	+	0.609608i
$767$	2.92216e15	−	1.68711e15i	0.397493	−	0.229492i
$768$	3.17876e14	+	3.36322e14i	0.0429310	+	0.0454223i
$769$		−	7.19211e15i		−	0.964410i	−0.876058	−	0.482205i	$-0.839836\pi$
$769$		−	7.19211e15i		−	0.964410i	0.876058	−	0.482205i	$-0.160164\pi$
$770$	1.72755e16	+	4.77695e15i	2.30002	+	0.635992i
$771$	2.19796e15	−	7.36580e15i	0.290550	−	0.973691i
$772$	1.87678e15	−	3.25067e15i	0.246330	−	0.426656i
$773$	6.00492e14	+	1.04008e15i	0.0782565	+	0.135544i	0.902498	−	0.430695i	$-0.141731\pi$
$773$	6.00492e14	+	1.04008e15i	0.0782565	+	0.135544i	−0.824241	+	0.566239i	$0.808398\pi$
$774$	5.04280e15	+	2.84614e14i	0.652524	+	0.0368282i
$775$	1.85214e16	+	1.06933e16i	2.37966	+	1.37390i
$776$	−2.59708e15			−0.331319
$777$	−1.81605e15	−	6.57068e13i	−0.230045	−	0.00832328i
$778$	−5.34075e15			−0.671760
$779$	2.83402e12	+	1.63622e12i	0.000353955	+	0.000204356i
$780$	−5.73300e14	−	2.40929e15i	−0.0710987	−	0.298792i
$781$	2.09922e14	+	3.63595e14i	0.0258509	+	0.0447752i
$782$	2.08895e15	−	3.61817e15i	0.255441	−	0.442438i
$783$	1.78849e14	+	2.11980e14i	0.0217169	+	0.0257398i
$784$	3.30705e13	−	2.07311e15i	0.00398752	−	0.249968i
$785$		−	9.59150e15i		−	1.14843i
$786$	−4.08920e15	+	3.86491e15i	−0.486199	+	0.459532i
$787$	−4.32874e15	+	2.49920e15i	−0.511093	+	0.295080i	−0.733283	−	0.679924i	$-0.762013\pi$
$787$	−4.32874e15	+	2.49920e15i	−0.511093	+	0.295080i	0.222190	+	0.975003i	$0.428680\pi$
$788$	3.91331e15	−	2.25935e15i	0.458828	−	0.264904i
$789$	−9.43327e15	+	8.91587e15i	−1.09834	+	1.03810i
$790$			1.49649e16i			1.73031i
$791$	−7.02627e15	+	1.82275e15i	−0.806779	+	0.209294i
$792$	−4.43983e15	−	2.90870e15i	−0.506265	−	0.331673i
$793$	6.32180e14	−	1.09497e15i	0.0715877	−	0.123993i
$794$	−2.41840e15	−	4.18879e15i	−0.271966	−	0.471059i
$795$	−2.13116e15	−	8.95617e15i	−0.238010	−	1.00024i
$796$	5.94880e15	+	3.43454e15i	0.659792	+	0.380931i
$797$	4.73410e15			0.521455			0.260728	−	0.965412i	$-0.416038\pi$
$797$	4.73410e15			0.521455			0.260728	+	0.965412i	$0.416038\pi$
$798$	−2.12352e13	+	3.38885e13i	−0.00232296	+	0.00370712i
$799$	−5.27860e15			−0.573471
$800$	4.09556e15	+	2.36458e15i	0.441895	+	0.255128i
$801$	4.75348e13	−	8.42225e14i	0.00509370	−	0.0902504i
$802$	3.71701e15	+	6.43805e15i	0.395580	+	0.685165i
$803$	−5.70803e15	+	9.88659e15i	−0.603324	+	1.04499i
$804$	−2.34206e15	+	7.84869e15i	−0.245861	+	0.823927i
$805$	1.66447e16	+	1.69123e16i	1.73539	+	1.76330i
$806$		−	2.02549e15i		−	0.209743i
$807$	−4.19851e15	−	4.44215e15i	−0.431808	−	0.456866i
$808$	2.22987e15	−	1.28742e15i	0.227781	−	0.131509i
$809$	−3.90707e15	+	2.25575e15i	−0.396401	+	0.228862i	−0.684930	−	0.728609i	$-0.740167\pi$
$809$	−3.90707e15	+	2.25575e15i	−0.396401	+	0.228862i	0.288529	+	0.957471i	$0.406834\pi$
$810$	1.55655e15	−	1.37455e16i	0.156853	−	1.38514i
$811$		−	1.06078e16i		−	1.06172i	−0.847459	−	0.530860i	$-0.821869\pi$
$811$		−	1.06078e16i		−	1.06172i	0.847459	−	0.530860i	$-0.178131\pi$
$812$	−1.18812e14	−	1.20722e14i	−0.0118114	−	0.0120013i
$813$	−1.36031e16	−	4.05918e15i	−1.34320	−	0.400812i
$814$	1.42055e15	−	2.46047e15i	0.139323	−	0.241314i
$815$	−1.33224e16	−	2.30751e16i	−1.29782	−	2.24790i
$816$	1.44705e15	−	3.44332e14i	0.140019	−	0.0333182i
$817$	5.15261e13	+	2.97486e13i	0.00495228	+	0.00285920i
$818$	4.25657e14			0.0406365
$819$	2.46804e15	−	2.16920e15i	0.234040	−	0.205701i
$820$	6.91300e14			0.0651164
$821$	3.96542e15	+	2.28944e15i	0.371024	+	0.214211i	0.673906	−	0.738817i	$-0.264615\pi$
$821$	3.96542e15	+	2.28944e15i	0.371024	+	0.214211i	−0.302882	+	0.953028i	$0.597949\pi$
$822$	5.85662e15	−	1.39361e15i	0.544317	−	0.129522i
$823$	−1.99873e15	−	3.46191e15i	−0.184525	−	0.319607i	0.758891	−	0.651217i	$-0.225741\pi$
$823$	−1.99873e15	−	3.46191e15i	−0.184525	−	0.319607i	−0.943416	+	0.331610i	$0.892408\pi$
$824$	−1.17014e13	+	2.02675e13i	−0.00107310	+	0.00185866i
$825$	−5.19765e16	−	1.55099e16i	−4.73490	−	1.41290i
$826$	−1.11416e16	+	2.89035e15i	−1.00823	+	0.261553i
$827$		−	2.07346e15i		−	0.186387i	−0.995648	−	0.0931936i	$-0.970292\pi$
$827$		−	2.07346e15i		−	0.186387i	0.995648	−	0.0931936i	$-0.0297076\pi$
$828$	−3.16496e15	−	6.27381e15i	−0.282619	−	0.560227i
$829$	−2.90311e15	+	1.67611e15i	−0.257521	+	0.148680i	−0.623203	−	0.782060i	$-0.714169\pi$
$829$	−2.90311e15	+	1.67611e15i	−0.257521	+	0.148680i	0.365682	+	0.930740i	$0.380836\pi$
$830$	−8.32720e15	+	4.80771e15i	−0.733786	+	0.423652i
$831$	1.87905e15	+	1.98809e15i	0.164487	+	0.174032i
$832$		−	4.47889e14i		−	0.0389487i
$833$	−5.71758e15	−	3.42379e15i	−0.493930	−	0.295774i
$834$	−4.57524e14	+	1.53325e15i	−0.0392646	+	0.131583i
$835$	7.32543e15	−	1.26880e16i	0.624536	−	1.08173i
$836$	−3.12621e13	−	5.41475e13i	−0.00264779	−	0.00458610i
$837$	3.84088e15	−	1.06420e16i	0.323178	−	0.895429i
$838$	−2.54991e15	−	1.47219e15i	−0.213149	−	0.123062i
$839$	2.34205e16			1.94494			0.972468	−	0.233036i	$-0.0748660\pi$
$839$	2.34205e16			1.94494			0.972468	+	0.233036i	$0.0748660\pi$
$840$	−3.05467e14	+	8.44274e15i	−0.0252016	+	0.696542i
$841$	1.21867e16			0.998866
$842$	7.77533e15	+	4.48909e15i	0.633144	+	0.365546i
$843$	4.68632e15	+	1.96942e16i	0.379123	+	1.59326i
$844$	6.31799e12	+	1.09431e13i	0.000507803	+	0.000879541i
$845$	1.11456e16	−	1.93048e16i	0.890004	−	1.54153i
$846$	−4.86531e15	+	7.42639e15i	−0.385988	+	0.589170i
$847$	−2.36063e16	−	6.52750e15i	−1.86067	−	0.514503i
$848$		−	1.66496e15i		−	0.130385i
$849$	−1.38580e16	+	1.30979e16i	−1.07822	+	1.01909i
$850$	1.31641e16	−	7.60029e15i	1.01762	−	0.587525i
$851$	3.25738e15	−	1.88065e15i	0.250182	−	0.144443i
$852$	−1.43818e14	+	1.35930e14i	−0.0109748	+	0.0103728i
$853$			2.21235e16i			1.67739i	0.544603	+	0.838694i	$0.316680\pi$
$853$			2.21235e16i			1.67739i	−0.544603	+	0.838694i	$0.683320\pi$
$854$	−3.07405e15	+	3.02540e15i	−0.231575	+	0.227911i
$855$	8.92993e13	−	1.36306e14i	0.00668397	−	0.0102024i
$856$	−5.35241e14	+	9.27065e14i	−0.0398056	+	0.0689453i
$857$	1.10070e16	+	1.90646e16i	0.813341	+	1.40875i	0.910513	+	0.413481i	$0.135687\pi$
$857$	1.10070e16	+	1.90646e16i	0.813341	+	1.40875i	−0.0971712	+	0.995268i	$0.530979\pi$
$858$	1.18919e15	+	4.99756e15i	0.0873113	+	0.366925i
$859$	−1.00102e16	−	5.77940e15i	−0.730266	−	0.421619i	0.0882534	−	0.996098i	$-0.471871\pi$
$859$	−1.00102e16	−	5.77940e15i	−0.730266	−	0.421619i	−0.818520	+	0.574479i	$0.805205\pi$
$860$	1.25687e16			0.911063
$861$	4.29577e14	+	8.10376e14i	0.0309402	+	0.0583672i
$862$	7.46053e15			0.533924
$863$	7.18232e13	+	4.14671e13i	0.00510746	+	0.00294880i	0.502552	−	0.864547i	$-0.332395\pi$
$863$	7.18232e13	+	4.14671e13i	0.00510746	+	0.00294880i	−0.497444	+	0.867496i	$0.665728\pi$
$864$	8.49319e14	−	2.35321e15i	0.0600130	−	0.166278i
$865$	−7.03273e15	−	1.21810e16i	−0.493782	−	0.855256i
$866$	−3.89004e15	+	6.73775e15i	−0.271398	+	0.470074i
$867$	−2.75751e15	+	9.24096e15i	−0.191167	+	0.640637i
$868$	−1.84149e15	+	6.65963e15i	−0.126856	+	0.458767i
$869$		−	3.10414e16i		−	2.12487i
$870$	4.74073e14	+	5.01584e14i	0.0322470	+	0.0341183i
$871$	6.86522e15	−	3.96364e15i	0.464039	−	0.267913i
$872$	−8.08521e15	+	4.66800e15i	−0.543063	+	0.313538i
$873$	6.32372e15	+	1.25353e16i	0.422080	+	0.836676i
$874$		−	8.27750e13i		−	0.00549018i
$875$	1.41685e16	+	5.46162e16i	0.933855	+	3.59979i
$876$	−5.15621e15	−	1.53862e15i	−0.337721	−	0.100776i
$877$	−5.12465e14	+	8.87616e14i	−0.0333554	+	0.0577733i	−0.882221	−	0.470835i	$-0.843953\pi$
$877$	−5.12465e14	+	8.87616e14i	−0.0333554	+	0.0577733i	0.848866	+	0.528608i	$0.177286\pi$
$878$	3.29786e15	+	5.71206e15i	0.213311	+	0.369465i
$879$	1.88833e16	−	4.49335e15i	1.21378	−	0.288823i
$880$	−1.14386e16	−	6.60406e15i	−0.730663	−	0.421848i
$881$	−4.20815e15			−0.267131			−0.133565	−	0.991040i	$-0.542643\pi$
$881$	−4.20815e15			−0.267131			−0.133565	+	0.991040i	$0.542643\pi$
$882$	−1.00868e16	+	4.88827e15i	−0.636322	+	0.308374i
$883$	−1.44664e16			−0.906937			−0.453469	−	0.891272i	$-0.649814\pi$
$883$	−1.44664e16			−0.906937			−0.453469	+	0.891272i	$0.649814\pi$
$884$	−1.24675e15	−	7.19810e14i	−0.0776768	−	0.0448467i
$885$	4.56268e16	−	1.08571e16i	2.82509	−	0.672241i
$886$	−7.24878e15	−	1.25552e16i	−0.446046	−	0.772573i
$887$	8.14794e15	−	1.41126e16i	0.498273	−	0.863035i	−0.501725	−	0.865027i	$-0.667301\pi$
$887$	8.14794e15	−	1.41126e16i	0.498273	−	0.863035i	0.999998	+	0.00199262i	$0.000634270\pi$
$888$	1.28322e15	+	3.82914e14i	0.0779884	+	0.0232718i
$889$	−4.90660e15	−	1.89138e16i	−0.296361	−	1.14240i
$890$		−	2.09916e15i		−	0.126009i
$891$	−3.22872e15	+	2.85122e16i	−0.192621	+	1.70100i
$892$	−5.25738e15	+	3.03535e15i	−0.311719	+	0.179971i
$893$	−9.05711e13	+	5.22913e13i	−0.00533712	+	0.00308139i
$894$	7.89646e15	+	8.35470e15i	0.462462	+	0.489299i
$895$			1.85755e16i			1.08122i
$896$	−4.07202e14	+	1.47262e15i	−0.0235568	+	0.0851914i
$897$	−1.94468e15	+	6.51698e15i	−0.111812	+	0.374704i
$898$	9.48526e15	−	1.64290e16i	0.542038	−	0.938837i
$899$	2.82232e14	+	4.88841e14i	0.0160298	+	0.0277644i
$900$	1.44066e15	−	2.55256e16i	0.0813255	−	1.44093i
$901$	−4.63459e15	−	2.67578e15i	−0.260031	−	0.150129i
$902$	−1.43395e15			−0.0799648
$903$	7.81024e15	+	1.47336e16i	0.432894	+	0.816633i
$904$	5.34907e15			0.294681
$905$	2.45554e16	+	1.41771e16i	1.34456	+	0.776282i
$906$	2.54146e15	+	1.06805e16i	0.138318	+	0.581279i
$907$	1.74637e16	+	3.02480e16i	0.944704	+	1.63627i	0.756344	+	0.654174i	$0.226984\pi$
$907$	1.74637e16	+	3.02480e16i	0.944704	+	1.63627i	0.188360	+	0.982100i	$0.439683\pi$
$908$	−5.08930e15	+	8.81493e15i	−0.273644	+	0.473966i
$909$	−1.16435e16	−	7.62813e15i	−0.622277	−	0.407677i
$910$	5.82764e15	−	5.73542e15i	0.309574	−	0.304675i
$911$			9.10493e15i			0.480757i	0.970679	+	0.240379i	$0.0772716\pi$
$911$			9.10493e15i			0.480757i	−0.970679	+	0.240379i	$0.922728\pi$
$912$	2.14177e13	−	2.02430e13i	0.00112409	−	0.00106244i
$913$	1.72730e16	−	9.97257e15i	0.901111	−	0.520257i
$914$	1.19527e16	−	6.90090e15i	0.619816	−	0.357851i
$915$	1.27722e16	−	1.20717e16i	0.658341	−	0.622232i
$916$		−	9.71858e15i		−	0.497941i
$917$	−1.79049e16	−	4.95099e15i	−0.911887	−	0.252151i
$918$	−5.18546e15	−	6.14605e15i	−0.262514	−	0.311144i
$919$	1.00746e16	−	1.74497e16i	0.506981	−	0.878117i	−0.492986	−	0.870037i	$-0.664095\pi$
$919$	1.00746e16	−	1.74497e16i	0.506981	−	0.878117i	0.999967	−	0.00807967i	$-0.00257187\pi$
$920$	−8.74304e15	−	1.51434e16i	−0.437350	−	0.757513i
$921$	−6.12486e15	−	2.57397e16i	−0.304557	−	1.27990i
$922$	1.08256e15	+	6.25015e14i	0.0535095	+	0.0308937i
$923$	1.91526e14			0.00941063
$924$	6.33626e14	−	1.75127e16i	0.0309483	−	0.855374i
$925$	1.36849e16			0.664447
$926$	8.02642e15	+	4.63406e15i	0.387402	+	0.223667i
$927$	1.26317e14	+	7.12929e12i	0.00606071	+	0.000342064i
$928$	6.24089e13	+	1.08095e14i	0.00297668	+	0.00515576i
$929$	1.10188e16	−	1.90850e16i	0.522451	−	0.904913i	−0.477207	−	0.878791i	$-0.658351\pi$
$929$	1.10188e16	−	1.90850e16i	0.522451	−	0.904913i	0.999659	−	0.0261218i	$-0.00831576\pi$
$930$	8.05038e15	−	2.69784e16i	0.379455	−	1.27163i
$931$	−1.32020e14	−	2.10600e12i	−0.00618611	−	9.86814e-5i
$932$		−	5.87627e15i		−	0.273725i
$933$	7.22532e15	+	7.64462e15i	0.334586	+	0.354003i
$934$	3.30001e15	−	1.90526e15i	0.151917	−	0.0877094i
$935$	−3.67662e16	+	2.12270e16i	−1.68262	+	0.971459i
$936$	−2.16183e15	+	1.09058e15i	−0.0983566	+	0.0496182i
$937$			3.94095e16i			1.78251i	0.453500	+	0.891256i	$0.350175\pi$
$937$			3.94095e16i			1.78251i	−0.453500	+	0.891256i	$0.649825\pi$
$938$	−2.61758e16	+	6.79049e15i	−1.17702	+	0.305341i
$939$	−1.80007e16	−	5.37144e15i	−0.804691	−	0.240121i
$940$	−1.10464e16	+	1.91330e16i	−0.490930	+	0.850315i
$941$	−8.27624e15	−	1.43349e16i	−0.365671	−	0.633360i	0.623213	−	0.782052i	$-0.285827\pi$
$941$	−8.27624e15	−	1.43349e16i	−0.365671	−	0.633360i	−0.988884	+	0.148692i	$0.952494\pi$
$942$	−9.12289e15	+	2.17083e15i	−0.400730	+	0.0953554i
$943$	−1.64406e15	−	9.49197e14i	−0.0717964	−	0.0414517i
$944$	8.48207e15			0.368261
$945$	4.14943e16	−	1.90831e16i	1.79107	−	0.823710i
$946$	−2.60710e16			−1.11881
$947$	7.37167e15	+	4.25603e15i	0.314515	+	0.181585i	0.648945	−	0.760835i	$-0.275211\pi$
$947$	7.37167e15	+	4.25603e15i	0.314515	+	0.181585i	−0.334430	+	0.942420i	$0.608544\pi$
$948$	1.42337e16	−	3.38697e15i	0.603772	−	0.143670i
$949$	2.60392e15	+	4.51011e15i	0.109815	+	0.190206i
$950$	1.50581e14	−	2.60814e14i	0.00631380	−	0.0109358i
$951$	1.00034e16	+	2.98502e15i	0.417017	+	0.124438i
$952$	3.44477e15	+	3.50016e15i	0.142776	+	0.145072i
$953$			4.04004e16i			1.66485i	0.554139	+	0.832424i	$0.313048\pi$
$953$			4.04004e16i			1.66485i	−0.554139	+	0.832424i	$0.686952\pi$
$954$	−8.03625e15	+	4.05407e15i	−0.329259	+	0.166102i
$955$	−4.05326e16	+	2.34015e16i	−1.65115	+	0.953291i
$956$	1.66681e16	−	9.62332e15i	0.675099	−	0.389768i
$957$	−9.83363e14	−	1.04043e15i	−0.0396003	−	0.0418983i
$958$			1.42601e16i			0.570968i
$959$	1.39419e16	+	1.41661e16i	0.555035	+	0.563959i
$960$	1.78015e15	−	5.96562e15i	0.0704635	−	0.236137i
$961$	−1.19119e15	+	2.06319e15i	−0.0468814	+	0.0812010i
$962$	−6.48034e14	−	1.12243e15i	−0.0253592	−	0.0439234i
$963$	5.77794e15	+	3.26105e14i	0.224817	+	0.0126886i
$964$	−4.18124e15	−	2.41404e15i	−0.161764	−	0.0933943i
$965$	−5.04956e16			−1.94247
$966$	1.23189e16	−	1.96592e16i	0.471191	−	0.751955i
$967$	1.66004e16			0.631356			0.315678	−	0.948866i	$-0.397768\pi$
$967$	1.66004e16			0.631356			0.315678	+	0.948866i	$0.397768\pi$
$968$	1.56303e16	+	9.02416e15i	0.591089	+	0.341266i
$969$	−2.19278e13	−	9.21514e13i	−0.000824545	−	0.00346514i
$970$	1.74690e16	+	3.02571e16i	0.653164	+	1.13131i
$971$	1.38048e16	−	2.39106e16i	0.513244	−	0.888965i	−0.486638	−	0.873604i	$-0.661777\pi$
$971$	1.38048e16	−	2.39106e16i	0.513244	−	0.888965i	0.999882	−	0.0153612i	$-0.00488982\pi$
$972$	−1.34263e16	+	1.63051e15i	−0.496353	+	0.0602779i
$973$	−5.11347e15	+	1.32653e15i	−0.187973	+	0.0487638i
$974$		−	3.18155e16i		−	1.16296i
$975$	−1.79829e16	+	1.69966e16i	−0.653634	+	0.617783i
$976$	2.75252e15	−	1.58917e15i	0.0994847	−	0.0574375i
$977$	9.82707e15	−	5.67366e15i	0.353187	−	0.203912i	−0.312901	−	0.949786i	$-0.601301\pi$
$977$	9.82707e15	−	5.67366e15i	0.353187	−	0.203912i	0.666088	+	0.745873i	$0.267968\pi$
$978$	−1.89325e16	+	1.78941e16i	−0.676618	+	0.639507i
$979$			4.35426e15i			0.154743i
$980$	−2.43751e16	+	1.35593e16i	−0.861397	+	0.479173i
$981$	4.22179e16	+	2.76586e16i	1.48360	+	0.971964i
$982$	6.72839e15	−	1.16539e16i	0.235125	−	0.407248i
$983$	−5.36302e15	−	9.28902e15i	−0.186365	−	0.322794i	0.757670	−	0.652637i	$-0.226337\pi$
$983$	−5.36302e15	−	9.28902e15i	−0.186365	−	0.322794i	−0.944036	+	0.329843i	$0.893004\pi$
$984$	−1.56461e14	−	6.57525e14i	−0.00540670	−	0.0227216i
$985$	−5.26448e16	−	3.03945e16i	−1.80907	−	1.04447i
$986$	4.01193e14			0.0137098
$987$	−2.92930e16	−	1.05985e15i	−0.995449	−	0.0360164i
$988$	−2.85226e13			−0.000963885
$989$	−2.98910e16	−	1.72576e16i	−1.00453	−	0.579963i
$990$	−4.02363e15	+	7.12909e16i	−0.134470	+	2.38254i
$991$	3.98738e15	+	6.90634e15i	0.132520	+	0.229532i	0.924647	−	0.380824i	$-0.124360\pi$
$991$	3.98738e15	+	6.90634e15i	0.132520	+	0.229532i	−0.792127	+	0.610356i	$0.791026\pi$
$992$	2.54583e15	−	4.40951e15i	0.0841426	−	0.145739i
$993$	1.21909e16	−	4.08540e16i	0.400696	−	1.34281i
$994$	−6.29720e14	−	1.74127e14i	−0.0205836	−	0.00569170i
$995$		−	9.24081e16i		−	3.00388i
$996$	6.45750e15	+	6.83224e15i	0.208756	+	0.220870i
$997$	2.56157e16	−	1.47892e16i	0.823536	−	0.475468i	−0.0280986	−	0.999605i	$-0.508945\pi$
$997$	2.56157e16	−	1.47892e16i	0.823536	−	0.475468i	0.851634	+	0.524137i	$0.175612\pi$
$998$	−2.44385e16	+	1.41096e16i	−0.781369	+	0.451123i
$999$	−1.27635e15	−	7.12608e15i	−0.0405843	−	0.226590i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.17	yes	60
3.2	odd	2	inner	42.12.f.a.5.5	✓	60
7.3	odd	6	inner	42.12.f.a.17.5	yes	60
21.17	even	6	inner	42.12.f.a.17.17	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.5	✓	60	3.2	odd	2	inner
42.12.f.a.5.17	yes	60	1.1	even	1	trivial
42.12.f.a.17.5	yes	60	7.3	odd	6	inner
42.12.f.a.17.17	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} +(-409.456 + 97.4316i) q^{3} +(512.000 + 886.810i) q^{4} +(6887.81 - 11930.0i) q^{5} +(-12906.1 - 3851.19i) q^{6} +(-11166.0 - 43042.4i) q^{7} +32768.0i q^{8} +(158161. - 79787.9i) q^{9} +(381761. - 220410. i) q^{10} +(-791882. + 457193. i) q^{11} +(-296045. - 313225. i) q^{12} +417129. i q^{13} +(379236. - 1.37148e6i) q^{14} +(-1.65789e6 + 5.55591e6i) q^{15} +(-524288. + 908093. i) q^{16} +(1.68518e6 + 2.91882e6i) q^{17} +(5.65970e6 + 319431. i) q^{18} +(57829.4 + 33387.8i) q^{19} +1.41062e7 q^{20} +(8.76568e6 + 1.65360e7i) q^{21} -2.92604e7 q^{22} +(-3.35476e7 - 1.93687e7i) q^{23} +(-3.19264e6 - 1.34170e7i) q^{24} +(-7.04698e7 - 1.22057e8i) q^{25} +(-6.67407e6 + 1.15598e7i) q^{26} +(-5.69861e7 + 4.80795e7i) q^{27} +(3.24534e7 - 3.19398e7i) q^{28} -3.71986e6i q^{29} +(-1.34839e8 + 1.27444e8i) q^{30} +(-1.31414e8 + 7.58718e7i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(2.79696e8 - 2.64355e8i) q^{33} +1.07852e8i q^{34} +(-5.90407e8 - 1.63257e8i) q^{35} +(1.51735e8 + 9.94075e7i) q^{36} +(-4.85486e7 + 8.40887e7i) q^{37} +(1.06841e6 + 1.85054e6i) q^{38} +(-4.06416e7 - 1.70796e8i) q^{39} +(3.90924e8 + 2.25700e8i) q^{40} +4.90067e7 q^{41} +(-2.16548e7 + 5.98511e8i) q^{42} +8.91002e8 q^{43} +(-8.10887e8 - 4.68166e8i) q^{44} +(1.37511e8 - 2.43643e9i) q^{45} +(-6.19800e8 - 1.07352e9i) q^{46} +(-7.83090e8 + 1.35635e9i) q^{47} +(1.26196e8 - 4.22906e8i) q^{48} +(-1.72797e9 + 9.61224e8i) q^{49} -4.51007e9i q^{50} +(-9.74394e8 - 1.03094e9i) q^{51} +(-3.69915e8 + 2.13570e8i) q^{52} +(-1.37510e9 + 7.93915e8i) q^{53} +(-2.34852e9 + 4.20641e8i) q^{54} +1.25962e10i q^{55} +(1.41041e9 - 3.65888e8i) q^{56} +(-2.69316e7 - 8.03642e6i) q^{57} +(5.95177e7 - 1.03088e8i) q^{58} +(-4.04457e9 - 7.00540e9i) q^{59} +(-5.77588e9 + 1.37439e9i) q^{60} +(-2.62501e9 - 1.51555e9i) q^{61} -4.85579e9 q^{62} +(-5.20029e9 - 5.91672e9i) q^{63} -1.07374e9 q^{64} +(4.97637e9 + 2.87311e9i) q^{65} +(1.19808e10 - 2.85089e9i) q^{66} +(-9.50217e9 - 1.64582e10i) q^{67} +(-1.72563e9 + 2.98887e9i) q^{68} +(1.56234e10 + 4.66204e9i) q^{69} +(-1.37497e10 - 1.39708e10i) q^{70} -4.59153e8i q^{71} +(2.61449e9 + 5.18262e9i) q^{72} +(1.08123e10 - 6.24246e9i) q^{73} +(-2.69084e9 + 1.55356e9i) q^{74} +(4.07465e10 + 4.31111e10i) q^{75} +6.83782e7i q^{76} +(2.85209e10 + 2.89795e10i) q^{77} +(1.60644e9 - 5.38351e9i) q^{78} +(-1.69739e10 + 2.93997e10i) q^{79} +(7.22239e9 + 1.25096e10i) q^{80} +(1.86488e10 - 2.52387e10i) q^{81} +(1.35811e9 + 7.84107e8i) q^{82} -2.18126e10 q^{83} +(-1.01763e10 + 1.62399e10i) q^{84} +4.64289e10 q^{85} +(2.46922e10 + 1.42560e10i) q^{86} +(3.62432e8 + 1.52312e9i) q^{87} +(-1.49813e10 - 2.59484e10i) q^{88} +(2.38097e9 - 4.12397e9i) q^{89} +(4.27938e10 - 6.53202e10i) q^{90} +(1.79542e10 - 4.65768e9i) q^{91} -3.96672e10i q^{92} +(4.64158e10 - 4.38700e10i) q^{93} +(-4.34032e10 + 2.50589e10i) q^{94} +(7.96635e8 - 4.59938e8i) q^{95} +(1.02637e10 - 9.70079e9i) q^{96} +7.92567e10i q^{97} +(-6.32664e10 - 1.00923e9i) q^{98} +(-8.87665e10 + 1.35493e11i) 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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