LMFDB - Embedded newform 42.12.f.a.5.13

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			5.13
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.13

$q$-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} +(357.546 - 222.054i) q^{3} +(512.000 + 886.810i) q^{4} +(4010.83 - 6946.96i) q^{5} +(-13461.5 + 433.002i) q^{6} +(8015.68 - 43738.7i) q^{7} -32768.0i q^{8} +(78531.2 - 158789. i) q^{9} +(-222303. + 128347. i) q^{10} +(-522703. + 301783. i) q^{11} +(379983. + 203384. i) q^{12} -1.04202e6i q^{13} +(-921957. + 1.08387e6i) q^{14} +(-108544. - 3.37448e6i) q^{15} +(-524288. + 908093. i) q^{16} +(-4.15462e6 - 7.19601e6i) q^{17} +(-4.71694e6 + 3.14399e6i) q^{18} +(1.78232e7 + 1.02902e7i) q^{19} +8.21418e6 q^{20} +(-6.84638e6 - 1.74185e7i) q^{21} +1.93141e7 q^{22} +(1.02018e7 + 5.88999e6i) q^{23} +(-7.27626e6 - 1.17161e7i) q^{24} +(-7.75944e6 - 1.34397e7i) q^{25} +(-1.66724e7 + 2.88774e7i) q^{26} +(-7.18118e6 - 7.42125e7i) q^{27} +(4.28920e7 - 1.52858e7i) q^{28} +2.49144e7i q^{29} +(-5.09836e7 + 9.52530e7i) q^{30} +(5.15959e7 - 2.97889e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(-1.19878e8 + 2.23969e8i) q^{33} +2.65896e8i q^{34} +(-2.71702e8 - 2.31113e8i) q^{35} +(1.81024e8 - 1.16577e7i) q^{36} +(-8.27814e7 + 1.43382e8i) q^{37} +(-3.29287e8 - 5.70341e8i) q^{38} +(-2.31385e8 - 3.72571e8i) q^{39} +(-2.27638e8 - 1.31427e8i) q^{40} -1.25022e9 q^{41} +(-8.89639e7 + 5.92258e8i) q^{42} -4.88272e8 q^{43} +(-5.35248e8 - 3.09026e8i) q^{44} +(-7.88125e8 - 1.18243e9i) q^{45} +(-1.88480e8 - 3.26456e8i) q^{46} +(4.52701e8 - 7.84102e8i) q^{47} +(1.41886e7 + 4.41105e8i) q^{48} +(-1.84882e9 - 7.01191e8i) q^{49} +4.96604e8i q^{50} +(-3.08337e9 - 1.65035e9i) q^{51} +(9.24076e8 - 5.33515e8i) q^{52} +(-2.37852e9 + 1.37324e9i) q^{53} +(-9.88389e8 + 2.17154e9i) q^{54} +4.84160e9i q^{55} +(-1.43323e9 - 2.62658e8i) q^{56} +(8.65758e9 - 2.78480e8i) q^{57} +(3.98630e8 - 6.90447e8i) q^{58} +(4.47891e9 + 7.75770e9i) q^{59} +(2.93695e9 - 1.82399e9i) q^{60} +(-8.04821e8 - 4.64664e8i) q^{61} -1.90649e9 q^{62} +(-6.31574e9 - 4.70765e9i) q^{63} -1.07374e9 q^{64} +(-7.23889e9 - 4.17937e9i) q^{65} +(6.90568e9 - 4.28877e9i) q^{66} +(-5.58269e9 - 9.66951e9i) q^{67} +(4.25433e9 - 7.36871e9i) q^{68} +(4.95549e9 - 1.59399e8i) q^{69} +(3.83180e9 + 1.07520e10i) q^{70} -1.63813e10i q^{71} +(-5.20319e9 - 2.57331e9i) q^{72} +(1.19200e10 - 6.88202e9i) q^{73} +(4.58821e9 - 2.64900e9i) q^{74} +(-5.75870e9 - 3.08231e9i) q^{75} +2.10743e10i q^{76} +(9.00977e9 + 2.52814e10i) q^{77} +(4.51198e8 + 1.40271e10i) q^{78} +(-1.19147e10 + 2.06368e10i) q^{79} +(4.20566e9 + 7.28442e9i) q^{80} +(-1.90468e10 - 2.49398e10i) q^{81} +(3.46470e10 + 2.00035e10i) q^{82} +6.13137e10 q^{83} +(1.19416e10 - 1.49897e10i) q^{84} -6.66539e10 q^{85} +(1.35314e10 + 7.81235e9i) q^{86} +(5.53233e9 + 8.90802e9i) q^{87} +(9.88882e9 + 1.71279e10i) q^{88} +(3.80667e9 - 6.59335e9i) q^{89} +(2.92231e9 + 4.53784e10i) q^{90} +(-4.55767e10 - 8.35252e9i) q^{91} +1.20627e10i q^{92} +(1.18332e10 - 2.21080e10i) q^{93} +(-2.50913e10 + 1.44864e10i) q^{94} +(1.42971e11 - 8.25446e10i) q^{95} +(6.66448e9 - 1.24513e10i) q^{96} -1.52185e11i q^{97} +(4.00171e10 + 4.90132e10i) q^{98} +(6.87126e9 + 1.06699e11i) 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
$3$	357.546	−	222.054i	0.849503	−	0.527584i
$3$	357.546	−	222.054i	0.849503	−	0.527584i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	4010.83	−	6946.96i	0.573983	−	0.994168i	−0.422168	−	0.906518i	$-0.638731\pi$
$5$	4010.83	−	6946.96i	0.573983	−	0.994168i	0.996151	−	0.0876505i	$-0.0279359\pi$
$6$	−13461.5	+	433.002i	−0.706741	+	0.0227331i
$7$	8015.68	−	43738.7i	0.180261	−	0.983619i
$7$	8015.68	−	43738.7i	0.180261	−	0.983619i
$8$		−	32768.0i		−	0.353553i
$9$	78531.2	−	158789.i	0.443311	−	0.896368i
$10$	−222303.	+	128347.i	−0.702983	+	0.405867i
$11$	−522703.	+	301783.i	−0.978578	+	0.564982i	−0.901840	−	0.432069i	$-0.857784\pi$
$11$	−522703.	+	301783.i	−0.978578	+	0.564982i	−0.0767371	+	0.997051i	$0.524450\pi$
$12$	379983.	+	203384.i	0.440826	+	0.235950i
$13$		−	1.04202e6i		−	0.778374i	−0.921159	−	0.389187i	$-0.872756\pi$
$13$		−	1.04202e6i		−	0.778374i	0.921159	−	0.389187i	$-0.127244\pi$
$14$	−921957.	+	1.08387e6i	−0.458149	+	0.538609i
$15$	−108544.	−	3.37448e6i	−0.0369064	−	1.14737i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	−4.15462e6	−	7.19601e6i	−0.709679	−	1.22920i	−0.964976	−	0.262338i	$-0.915507\pi$
$17$	−4.15462e6	−	7.19601e6i	−0.709679	−	1.22920i	0.255297	−	0.966863i	$-0.417827\pi$
$18$	−4.71694e6	+	3.14399e6i	−0.588385	+	0.392177i
$19$	1.78232e7	+	1.02902e7i	1.65135	+	0.953409i	0.976517	+	0.215443i	$0.0691194\pi$
$19$	1.78232e7	+	1.02902e7i	1.65135	+	0.953409i	0.674837	+	0.737967i	$0.264214\pi$
$20$	8.21418e6			0.573983
$21$	−6.84638e6	−	1.74185e7i	−0.365809	−	0.930690i
$22$	1.93141e7			0.799005
$23$	1.02018e7	+	5.88999e6i	0.330500	+	0.190814i	0.656063	−	0.754706i	$-0.272220\pi$
$23$	1.02018e7	+	5.88999e6i	0.330500	+	0.190814i	−0.325563	+	0.945520i	$0.605554\pi$
$24$	−7.27626e6	−	1.17161e7i	−0.186529	−	0.300345i
$25$	−7.75944e6	−	1.34397e7i	−0.158913	−	0.275246i
$26$	−1.66724e7	+	2.88774e7i	−0.275197	+	0.476655i
$27$	−7.18118e6	−	7.42125e7i	−0.0963153	−	0.995351i
$28$	4.28920e7	−	1.52858e7i	0.470985	−	0.167849i
$29$			2.49144e7i			0.225559i	0.993620	+	0.112780i	$0.0359754\pi$
$29$			2.49144e7i			0.225559i	−0.993620	+	0.112780i	$0.964025\pi$
$30$	−5.09836e7	+	9.52530e7i	−0.383057	+	0.715668i
$31$	5.15959e7	−	2.97889e7i	0.323688	−	0.186881i	−0.329347	−	0.944209i	$-0.606829\pi$
$31$	5.15959e7	−	2.97889e7i	0.323688	−	0.186881i	0.653035	+	0.757328i	$0.273495\pi$
$32$	2.90590e7	−	1.67772e7i	0.153093	−	0.0883883i
$33$	−1.19878e8	+	2.23969e8i	−0.533229	+	0.996235i
$34$			2.65896e8i			1.00364i
$35$	−2.71702e8	−	2.31113e8i	−0.874416	−	0.743790i
$36$	1.81024e8	−	1.16577e7i	0.498966	−	0.0321328i
$37$	−8.27814e7	+	1.43382e8i	−0.196256	+	0.339925i	−0.947312	−	0.320314i	$-0.896212\pi$
$37$	−8.27814e7	+	1.43382e8i	−0.196256	+	0.339925i	0.751056	+	0.660239i	$0.229545\pi$
$38$	−3.29287e8	−	5.70341e8i	−0.674162	−	1.16768i
$39$	−2.31385e8	−	3.72571e8i	−0.410658	−	0.661231i
$40$	−2.27638e8	−	1.31427e8i	−0.351491	−	0.202934i
$41$	−1.25022e9			−1.68529			−0.842645	−	0.538470i	$-0.819002\pi$
$41$	−1.25022e9			−1.68529			−0.842645	+	0.538470i	$0.819002\pi$
$42$	−8.89639e7	+	5.92258e8i	−0.105037	+	0.699262i
$43$	−4.88272e8			−0.506507			−0.253253	−	0.967400i	$-0.581501\pi$
$43$	−4.88272e8			−0.506507			−0.253253	+	0.967400i	$0.581501\pi$
$44$	−5.35248e8	−	3.09026e8i	−0.489289	−	0.282491i
$45$	−7.88125e8	−	1.18243e9i	−0.636687	−	0.955226i
$46$	−1.88480e8	−	3.26456e8i	−0.134926	−	0.233699i
$47$	4.52701e8	−	7.84102e8i	0.287921	−	0.498694i	−0.685392	−	0.728174i	$-0.740369\pi$
$47$	4.52701e8	−	7.84102e8i	0.287921	−	0.498694i	0.973313	+	0.229480i	$0.0737026\pi$
$48$	1.41886e7	+	4.41105e8i	0.00803735	+	0.249871i
$49$	−1.84882e9	−	7.01191e8i	−0.935012	−	0.354616i
$50$			4.96604e8i			0.224737i
$51$	−3.08337e9	−	1.65035e9i	−1.25138	−	0.669794i
$52$	9.24076e8	−	5.33515e8i	0.337046	−	0.194594i
$53$	−2.37852e9	+	1.37324e9i	−0.781249	+	0.451055i	−0.836873	−	0.547397i	$-0.815619\pi$
$53$	−2.37852e9	+	1.37324e9i	−0.781249	+	0.451055i	0.0556234	+	0.998452i	$0.482285\pi$
$54$	−9.88389e8	+	2.17154e9i	−0.292929	+	0.643578i
$55$			4.84160e9i			1.29716i
$56$	−1.43323e9	−	2.62658e8i	−0.347762	−	0.0637318i
$57$	8.65758e9	−	2.78480e8i	1.90583	−	0.0613031i
$58$	3.98630e8	−	6.90447e8i	0.0797472	−	0.138126i
$59$	4.47891e9	+	7.75770e9i	0.815617	+	1.41269i	0.908884	+	0.417049i	$0.136936\pi$
$59$	4.47891e9	+	7.75770e9i	0.815617	+	1.41269i	−0.0932672	+	0.995641i	$0.529731\pi$
$60$	2.93695e9	−	1.82399e9i	0.487600	−	0.302824i
$61$	−8.04821e8	−	4.64664e8i	−0.122007	−	0.0704408i	0.437754	−	0.899095i	$-0.355774\pi$
$61$	−8.04821e8	−	4.64664e8i	−0.122007	−	0.0704408i	−0.559762	+	0.828654i	$0.689107\pi$
$62$	−1.90649e9			−0.264290
$63$	−6.31574e9	−	4.70765e9i	−0.801773	−	0.597629i
$64$	−1.07374e9			−0.125000
$65$	−7.23889e9	−	4.17937e9i	−0.773835	−	0.446774i
$66$	6.90568e9	−	4.28877e9i	0.678757	−	0.421542i
$67$	−5.58269e9	−	9.66951e9i	−0.505164	−	0.874970i	−0.999982	−	0.00597304i	$-0.998099\pi$
$67$	−5.58269e9	−	9.66951e9i	−0.505164	−	0.874970i	0.494818	−	0.868996i	$-0.335235\pi$
$68$	4.25433e9	−	7.36871e9i	0.354840	−	0.614600i
$69$	4.95549e9	−	1.59399e8i	0.381432	−	0.0122691i
$70$	3.83180e9	+	1.07520e10i	0.272499	+	0.764629i
$71$		−	1.63813e10i		−	1.07753i	−0.842457	−	0.538763i	$-0.818892\pi$
$71$		−	1.63813e10i		−	1.07753i	0.842457	−	0.538763i	$-0.181108\pi$
$72$	−5.20319e9	−	2.57331e9i	−0.316914	−	0.156734i
$73$	1.19200e10	−	6.88202e9i	0.672978	−	0.388544i	−0.124226	−	0.992254i	$-0.539645\pi$
$73$	1.19200e10	−	6.88202e9i	0.672978	−	0.388544i	0.797204	+	0.603710i	$0.206311\pi$
$74$	4.58821e9	−	2.64900e9i	0.240364	−	0.138774i
$75$	−5.75870e9	−	3.08231e9i	−0.280213	−	0.149982i
$76$			2.10743e10i			0.953409i
$77$	9.00977e9	+	2.52814e10i	0.379328	+	1.06439i
$78$	4.51198e8	+	1.40271e10i	0.0176948	+	0.550109i
$79$	−1.19147e10	+	2.06368e10i	−0.435645	+	0.754559i	−0.997348	−	0.0727797i	$-0.976813\pi$
$79$	−1.19147e10	+	2.06368e10i	−0.435645	+	0.754559i	0.561703	+	0.827339i	$0.310146\pi$
$80$	4.20566e9	+	7.28442e9i	0.143496	+	0.248542i
$81$	−1.90468e10	−	2.49398e10i	−0.606951	−	0.794739i
$82$	3.46470e10	+	2.00035e10i	1.03202	+	0.595840i
$83$	6.13137e10			1.70855			0.854275	−	0.519821i	$-0.174002\pi$
$83$	6.13137e10			1.70855			0.854275	+	0.519821i	$0.174002\pi$
$84$	1.19416e10	−	1.49897e10i	0.311548	−	0.391072i
$85$	−6.66539e10			−1.62938
$86$	1.35314e10	+	7.81235e9i	0.310171	+	0.179077i
$87$	5.53233e9	+	8.90802e9i	0.119001	+	0.191613i
$88$	9.88882e9	+	1.71279e10i	0.199751	+	0.345979i
$89$	3.80667e9	−	6.59335e9i	0.0722604	−	0.125159i	−0.827631	−	0.561272i	$-0.810312\pi$
$89$	3.80667e9	−	6.59335e9i	0.0722604	−	0.125159i	0.899892	+	0.436114i	$0.143645\pi$
$90$	2.92231e9	+	4.53784e10i	0.0521666	+	0.810057i
$91$	−4.55767e10	−	8.35252e9i	−0.765624	−	0.140310i
$92$			1.20627e10i			0.190814i
$93$	1.18332e10	−	2.21080e10i	0.176378	−	0.329528i
$94$	−2.50913e10	+	1.44864e10i	−0.352630	+	0.203591i
$95$	1.42971e11	−	8.25446e10i	1.89570	−	1.09448i
$96$	6.66448e9	−	1.24513e10i	0.0834208	−	0.155856i
$97$		−	1.52185e11i		−	1.79939i	−0.436517	−	0.899696i	$-0.643788\pi$
$97$		−	1.52185e11i		−	1.79939i	0.436517	−	0.899696i	$-0.356212\pi$
$98$	4.00171e10	+	4.90132e10i	0.447200	+	0.547734i
$99$	6.87126e9	+	1.06699e11i	0.0726178	+	1.12763i
$100$	7.94567e9	−	1.37623e10i	0.0794567	−	0.137623i
$101$	5.38686e10	+	9.33032e10i	0.509998	+	0.883342i	0.999933	+	0.0115833i	$0.00368717\pi$
$101$	5.38686e10	+	9.33032e10i	0.509998	+	0.883342i	−0.489935	+	0.871759i	$0.662979\pi$
$102$	5.90431e10	+	9.50699e10i	0.529503	+	0.852593i
$103$	−3.06491e10	−	1.76953e10i	−0.260503	−	0.150401i	0.364061	−	0.931375i	$-0.381390\pi$
$103$	−3.06491e10	−	1.76953e10i	−0.260503	−	0.150401i	−0.624564	+	0.780974i	$0.714723\pi$
$104$	−3.41450e10			−0.275197
$105$	−1.48465e11	−	2.23012e10i	−1.13523	−	0.170525i
$106$	8.78874e10			0.637888
$107$	−1.40294e11	−	8.09986e10i	−0.967002	−	0.558299i	−0.0686808	−	0.997639i	$-0.521879\pi$
$107$	−1.40294e11	−	8.09986e10i	−0.967002	−	0.558299i	−0.898321	+	0.439340i	$0.855212\pi$
$108$	6.21356e10	−	4.43651e10i	0.406921	−	0.290543i
$109$	1.08487e11	+	1.87904e11i	0.675353	+	1.16975i	0.976366	+	0.216125i	$0.0693419\pi$
$109$	1.08487e11	+	1.87904e11i	0.675353	+	1.16975i	−0.301013	+	0.953620i	$0.597325\pi$
$110$	7.74655e10	−	1.34174e11i	0.458616	−	0.794345i
$111$	2.24028e9	+	6.96474e10i	0.0126190	+	0.392309i
$112$	3.55163e10	+	3.02107e10i	0.190427	+	0.161980i
$113$		−	2.01420e11i		−	1.02842i	−0.857663	−	0.514211i	$-0.828085\pi$
$113$		−	2.01420e11i		−	1.02842i	0.857663	−	0.514211i	$-0.171915\pi$
$114$	−2.44382e11	−	1.30804e11i	−1.18875	−	0.636273i
$115$	8.18350e10	−	4.72475e10i	0.379403	−	0.219049i
$116$	−2.20943e10	+	1.27561e10i	−0.0976700	+	0.0563898i
$117$	−1.65462e11	−	8.18312e10i	−0.697710	−	0.345062i
$118$		−	2.86650e11i		−	1.15346i
$119$	−3.48046e11	+	1.24037e11i	−1.33699	+	0.476477i
$120$	−1.10575e11	+	3.55676e9i	−0.405658	+	0.0130484i
$121$	3.94898e10	−	6.83983e10i	0.138409	−	0.239732i
$122$	1.48692e10	+	2.57543e10i	0.0498092	+	0.0862721i
$123$	−4.47010e11	+	2.77616e11i	−1.43166	+	0.889131i
$124$	5.28342e10	+	3.05039e10i	0.161844	+	0.0934406i
$125$	2.67195e11			0.783112
$126$	9.97045e10	+	2.31514e11i	0.279690	+	0.649441i
$127$	−4.33125e11			−1.16330			−0.581652	−	0.813438i	$-0.697593\pi$
$127$	−4.33125e11			−1.16330			−0.581652	+	0.813438i	$0.697593\pi$
$128$	2.97564e10	+	1.71799e10i	0.0765466	+	0.0441942i
$129$	−1.74580e11	+	1.08423e11i	−0.430279	+	0.267225i
$130$	1.33740e11	+	2.31644e11i	0.315917	+	0.547184i
$131$	2.69233e11	−	4.66326e11i	0.609729	−	1.05608i	−0.381556	−	0.924346i	$-0.624612\pi$
$131$	2.69233e11	−	4.66326e11i	0.609729	−	1.05608i	0.991285	−	0.131736i	$-0.0420551\pi$
$132$	−2.59996e11	+	8.36304e9i	−0.564690	+	0.0181638i
$133$	5.92945e11	−	6.97079e11i	1.23547	−	1.45244i
$134$			3.57292e11i			0.714410i
$135$	−5.44354e11	−	2.47766e11i	−1.04483	−	0.475561i
$136$	−2.35799e11	+	1.36139e11i	−0.434588	+	0.250909i
$137$	6.97165e9	−	4.02508e9i	0.0123416	−	0.00712544i	−0.493816	−	0.869566i	$-0.664399\pi$
$137$	6.97165e9	−	4.02508e9i	0.0123416	−	0.00712544i	0.506158	+	0.862441i	$0.331065\pi$
$138$	−1.39881e11	−	7.48705e10i	−0.237916	−	0.127343i
$139$			7.65627e11i			1.25151i	0.780018	+	0.625757i	$0.215210\pi$
$139$			7.65627e11i			1.25151i	−0.780018	+	0.625757i	$0.784790\pi$
$140$	6.58423e10	−	3.59278e11i	0.103467	−	0.564581i
$141$	−1.22513e10	−	3.80876e11i	−0.0185130	−	0.575545i
$142$	−2.62101e11	+	4.53973e11i	−0.380963	+	0.659848i
$143$	3.14464e11	+	5.44668e11i	0.439767	+	0.761699i
$144$	1.03022e11	+	1.54565e11i	0.138656	+	0.208026i
$145$	1.73079e11	+	9.99272e10i	0.224244	+	0.129467i
$146$	−4.40449e11			−0.549484
$147$	−8.16742e11	+	1.59830e11i	−0.981385	+	0.192050i
$148$	−1.69536e11			−0.196256
$149$	9.40175e11	+	5.42810e11i	1.04878	+	0.605513i	0.922307	−	0.386457i	$-0.126301\pi$
$149$	9.40175e11	+	5.42810e11i	1.04878	+	0.605513i	0.126472	+	0.991970i	$0.459635\pi$
$150$	1.10273e11	+	1.77559e11i	0.118568	+	0.190915i
$151$	−2.68297e11	−	4.64705e11i	−0.278127	−	0.481730i	0.692792	−	0.721137i	$-0.256380\pi$
$151$	−2.68297e11	−	4.64705e11i	−0.278127	−	0.481730i	−0.970919	+	0.239407i	$0.923047\pi$
$152$	3.37190e11	−	5.84030e11i	0.337081	−	0.583842i
$153$	−1.46891e12	+	9.45961e10i	−1.41642	+	0.0912159i
$154$	1.54816e11	−	8.44774e11i	0.144029	−	0.785917i
$155$		−	4.77913e11i		−	0.429066i
$156$	2.11930e11	−	3.95951e11i	0.183657	−	0.343128i
$157$	1.54599e12	−	8.92576e11i	1.29347	−	0.746788i	0.314206	−	0.949355i	$-0.398262\pi$
$157$	1.54599e12	−	8.92576e11i	1.29347	−	0.746788i	0.979268	+	0.202567i	$0.0649285\pi$
$158$	6.60378e11	−	3.81269e11i	0.533554	−	0.308048i
$159$	−5.45497e11	+	1.01916e12i	−0.425705	+	0.795347i
$160$		−	2.69162e11i		−	0.202934i
$161$	3.39395e11	−	3.98999e11i	0.247265	−	0.290690i
$162$	1.28803e11	+	9.95899e11i	0.0906974	+	0.701266i
$163$	−7.08630e11	+	1.22738e12i	−0.482378	+	0.835504i	−0.999795	−	0.0202298i	$-0.993560\pi$
$163$	−7.08630e11	+	1.22738e12i	−0.482378	+	0.835504i	0.517417	+	0.855733i	$0.326894\pi$
$164$	−6.40111e11	−	1.10871e12i	−0.421322	−	0.729752i
$165$	1.07510e12	+	1.73109e12i	0.684361	+	1.10194i
$166$	−1.69917e12	−	9.81018e11i	−1.04627	−	0.604064i
$167$	2.90111e12			1.72832			0.864158	−	0.503221i	$-0.167852\pi$
$167$	2.90111e12			1.72832			0.864158	+	0.503221i	$0.167852\pi$
$168$	−5.70770e11	+	2.24342e11i	−0.329049	+	0.129333i
$169$	7.06351e11			0.394134
$170$	1.84717e12	+	1.06646e12i	0.997785	+	0.576071i
$171$	3.03365e12	−	2.02202e12i	1.58667	−	1.05756i
$172$	−2.49995e11	−	4.33004e11i	−0.126627	−	0.219324i
$173$	−9.00323e10	+	1.55941e11i	−0.0441718	+	0.0765078i	−0.887266	−	0.461258i	$-0.847398\pi$
$173$	−9.00323e10	+	1.55941e11i	−0.0441718	+	0.0765078i	0.843094	+	0.537766i	$0.180732\pi$
$174$	−1.07880e10	−	3.35384e11i	−0.00512765	−	0.159412i
$175$	−6.50035e11	+	2.31659e11i	−0.299383	+	0.106694i
$176$		−	6.32884e11i		−	0.282491i
$177$	3.32404e12	+	1.77917e12i	1.43818	+	0.769778i
$178$	−2.10987e11	+	1.21814e11i	−0.0885006	+	0.0510959i
$179$	1.60000e12	−	9.23762e11i	0.650772	−	0.375724i	−0.137980	−	0.990435i	$-0.544061\pi$
$179$	1.60000e12	−	9.23762e11i	0.650772	−	0.375724i	0.788752	+	0.614711i	$0.210728\pi$
$180$	6.45069e11	−	1.30432e12i	0.254453	−	0.514500i
$181$			3.87802e12i			1.48381i	0.670505	+	0.741905i	$0.266077\pi$
$181$			3.87802e12i			1.48381i	−0.670505	+	0.741905i	$0.733923\pi$
$182$	1.12942e12	+	9.60699e11i	0.419240	+	0.356611i
$183$	−3.90941e11	+	1.25750e10i	−0.140809	+	0.00452926i
$184$	1.93003e11	−	3.34291e11i	0.0674631	−	0.116850i
$185$	6.64044e11	+	1.15016e12i	0.225295	+	0.390223i
$186$	−6.81658e11	+	4.23344e11i	−0.224515	+	0.139435i
$187$	4.34326e12	+	2.50758e12i	1.38895	+	0.801912i
$188$	9.27132e11			0.287921
$189$	−3.30352e12	−	2.80768e11i	−0.996408	−	0.0846852i
$190$	−5.28285e12			−1.54783
$191$	3.91283e10	+	2.25907e10i	0.0111380	+	0.00643053i	0.505559	−	0.862792i	$-0.331286\pi$
$191$	3.91283e10	+	2.25907e10i	0.0111380	+	0.00643053i	−0.494421	+	0.869223i	$0.664620\pi$
$192$	−3.83912e11	+	2.38429e11i	−0.106188	+	0.0659480i
$193$	−4.69314e11	−	8.12876e11i	−0.126153	−	0.218504i	0.796030	−	0.605257i	$-0.206930\pi$
$193$	−4.69314e11	−	8.12876e11i	−0.126153	−	0.218504i	−0.922183	+	0.386753i	$0.873596\pi$
$194$	−2.43495e12	+	4.21746e12i	−0.636181	+	1.10190i
$195$	−3.51628e12	+	1.13105e11i	−0.893086	+	0.0287270i
$196$	−3.24774e11	−	1.99857e12i	−0.0801998	−	0.493526i
$197$		−	3.69670e12i		−	0.887666i	−0.896109	−	0.443833i	$-0.853618\pi$
$197$		−	3.69670e12i		−	0.887666i	0.896109	−	0.443833i	$-0.146382\pi$
$198$	1.51676e12	−	3.06686e12i	0.354208	−	0.716203i
$199$	2.68746e12	−	1.55161e12i	0.610450	−	0.352444i	−0.162691	−	0.986677i	$-0.552018\pi$
$199$	2.68746e12	−	1.55161e12i	0.610450	−	0.352444i	0.773142	+	0.634233i	$0.218684\pi$
$200$	−4.40394e11	+	2.54261e11i	−0.0973142	+	0.0561844i
$201$	−4.14322e12	−	2.21763e12i	−0.890758	−	0.476773i
$202$		−	3.44759e12i		−	0.721246i
$203$	1.08972e12	+	1.99706e11i	0.221864	+	0.0406595i
$204$	−1.15133e11	−	3.57934e12i	−0.0228158	−	0.709312i
$205$	−5.01441e12	+	8.68521e12i	−0.967328	+	1.67546i
$206$	5.66248e11	+	9.80771e11i	0.106350	+	0.184203i
$207$	1.73642e12	−	1.15738e12i	0.317554	−	0.211660i
$208$	9.46253e11	+	5.46320e11i	0.168523	+	0.0972968i
$209$	−1.24216e13			−2.15464
$210$	3.75757e12	+	2.99347e12i	0.634894	+	0.505789i
$211$	1.03119e12			0.169740			0.0848702	−	0.996392i	$-0.472952\pi$
$211$	1.03119e12			0.169740			0.0848702	+	0.996392i	$0.472952\pi$
$212$	−2.43561e12	−	1.40620e12i	−0.390625	−	0.225527i
$213$	−3.63754e12	−	5.85708e12i	−0.568486	−	0.915362i
$214$	2.59195e12	+	4.48940e12i	0.394777	+	0.683773i
$215$	−1.95837e12	+	3.39200e12i	−0.290726	+	0.503553i
$216$	−2.43179e12	+	2.35313e11i	−0.351910	+	0.0340526i
$217$	−8.89353e11	−	2.49552e12i	−0.125472	−	0.352073i
$218$		−	6.94315e12i		−	0.955093i
$219$	2.73377e12	−	5.10752e12i	0.366707	−	0.685121i
$220$	−4.29358e12	+	2.47890e12i	−0.561687	+	0.324290i
$221$	−7.49840e12	+	4.32920e12i	−0.956778	+	0.552396i
$222$	1.05227e12	−	1.96597e12i	0.130975	−	0.244701i
$223$		−	1.34950e13i		−	1.63868i	−0.573307	−	0.819341i	$-0.694340\pi$
$223$		−	1.34950e13i		−	1.63868i	0.573307	−	0.819341i	$-0.305660\pi$
$224$	−5.00886e11	−	1.40548e12i	−0.0593438	−	0.166518i
$225$	−2.74344e12	+	1.76674e11i	−0.317170	+	0.0204253i
$226$	−3.22272e12	+	5.58192e12i	−0.363602	+	0.629778i
$227$	−2.99712e12	−	5.19116e12i	−0.330036	−	0.571639i	0.652483	−	0.757804i	$-0.273728\pi$
$227$	−2.99712e12	−	5.19116e12i	−0.330036	−	0.571639i	−0.982519	+	0.186165i	$0.940394\pi$
$228$	4.67964e12	+	7.53505e12i	0.503003	+	0.809924i
$229$	5.11041e12	+	2.95049e12i	0.536241	+	0.309599i	0.743554	−	0.668676i	$-0.233139\pi$
$229$	5.11041e12	+	2.95049e12i	0.536241	+	0.309599i	−0.207313	+	0.978275i	$0.566472\pi$
$230$	−3.02384e12			−0.309781
$231$	8.83523e12	+	7.03859e12i	0.883796	+	0.704077i
$232$	8.16393e11			0.0797472
$233$	7.27201e12	+	4.19850e12i	0.693740	+	0.400531i	0.805012	−	0.593259i	$-0.202159\pi$
$233$	7.27201e12	+	4.19850e12i	0.693740	+	0.400531i	−0.111271	+	0.993790i	$0.535492\pi$
$234$	3.27610e12	+	4.91516e12i	0.305260	+	0.457984i
$235$	−3.63142e12	−	6.28980e12i	−0.330524	−	0.572484i
$236$	−4.58640e12	+	7.94388e12i	−0.407808	+	0.706345i
$237$	3.22442e11	+	1.00243e13i	0.0280115	+	0.870840i
$238$	1.16299e13	+	2.13133e12i	0.987197	+	0.180917i
$239$		−	1.07980e13i		−	0.895681i	−0.894114	−	0.447840i	$-0.852193\pi$
$239$		−	1.07980e13i		−	0.895681i	0.894114	−	0.447840i	$-0.147807\pi$
$240$	3.12125e12	+	1.67063e12i	0.253027	+	0.135431i
$241$	6.66619e12	−	3.84873e12i	0.528183	−	0.304946i	−0.212093	−	0.977249i	$-0.568028\pi$
$241$	6.66619e12	−	3.84873e12i	0.528183	−	0.304946i	0.740276	+	0.672303i	$0.234695\pi$
$242$	−2.18875e12	+	1.26367e12i	−0.169516	+	0.0978702i
$243$	−1.23481e13	−	4.68770e12i	−0.934898	−	0.354916i
$244$		−	9.51631e11i		−	0.0704408i
$245$	−1.22865e13	+	1.00313e13i	−0.889229	+	0.726016i
$246$	1.68298e13	−	5.41347e11i	1.19106	−	0.0383118i
$247$	1.07226e13	−	1.85721e13i	0.742109	−	1.28537i
$248$	−9.76123e11	−	1.69070e12i	−0.0660725	−	0.114441i
$249$	2.19224e13	−	1.36149e13i	1.45142	−	0.901403i
$250$	−7.40474e12	−	4.27513e12i	−0.479556	−	0.276872i
$251$	−2.30366e13			−1.45953			−0.729763	−	0.683700i	$-0.760370\pi$
$251$	−2.30366e13			−1.45953			−0.729763	+	0.683700i	$0.760370\pi$
$252$	9.41135e11	−	8.01118e12i	0.0583377	−	0.496585i
$253$	−7.10999e12			−0.431227
$254$	1.20031e13	+	6.93000e12i	0.712375	+	0.411290i
$255$	−2.38318e13	+	1.48007e13i	−1.38416	+	0.859632i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	4.55613e12	−	7.89145e12i	0.253492	−	0.439061i	−0.710993	−	0.703199i	$-0.751754\pi$
$257$	4.55613e12	−	7.89145e12i	0.253492	−	0.439061i	0.964485	+	0.264138i	$0.0850876\pi$
$258$	6.57285e12	−	2.11423e11i	0.357969	−	0.0115144i
$259$	5.60777e12	+	4.77005e12i	0.298980	+	0.254316i
$260$		−	8.55935e12i		−	0.446774i
$261$	3.95612e12	+	1.95655e12i	0.202184	+	0.0999928i
$262$	−1.49224e13	+	8.61547e12i	−0.746762	+	0.431144i
$263$	1.53589e13	−	8.86749e12i	0.752670	−	0.434554i	−0.0739878	−	0.997259i	$-0.523573\pi$
$263$	1.53589e13	−	8.86749e12i	0.752670	−	0.434554i	0.826658	+	0.562705i	$0.190239\pi$
$264$	7.33903e12	+	3.92817e12i	0.352222	+	0.188525i
$265$			2.20313e13i			1.03559i
$266$	−2.75855e13	+	9.83090e12i	−1.27008	+	0.452631i
$267$	−1.03019e11	−	3.20271e12i	−0.00464626	−	0.144446i
$268$	5.71668e12	−	9.90158e12i	0.252582	−	0.437485i
$269$	1.90654e13	+	3.30223e13i	0.825295	+	1.42945i	0.901694	+	0.432376i	$0.142325\pi$
$269$	1.90654e13	+	3.30223e13i	0.825295	+	1.42945i	−0.0763986	+	0.997077i	$0.524342\pi$
$270$	1.11213e13	+	1.55760e13i	0.471688	+	0.660623i
$271$	−4.13329e12	−	2.38636e12i	−0.171777	−	0.0991754i	0.411647	−	0.911344i	$-0.364954\pi$
$271$	−4.13329e12	−	2.38636e12i	−0.171777	−	0.0991754i	−0.583423	+	0.812168i	$0.698287\pi$
$272$	8.71287e12			0.354840
$273$	−1.81505e13	+	7.13407e12i	−0.724425	+	0.284736i
$274$	−2.57605e11			−0.0100769
$275$	8.11177e12	+	4.68333e12i	0.311018	+	0.179566i
$276$	2.67857e12	+	4.31297e12i	0.100671	+	0.162097i
$277$	−3.71191e12	−	6.42922e12i	−0.136760	−	0.236875i	0.789508	−	0.613740i	$-0.210336\pi$
$277$	−3.71191e12	−	6.42922e12i	−0.136760	−	0.236875i	−0.926268	+	0.376865i	$0.877002\pi$
$278$	1.22500e13	−	2.12177e13i	0.442477	−	0.766393i
$279$	−6.78261e11	−	1.05322e13i	−0.0240200	−	0.372990i
$280$	−7.57312e12	+	8.90312e12i	−0.262970	+	0.309153i
$281$		−	1.39960e13i		−	0.476562i	−0.971196	−	0.238281i	$-0.923416\pi$
$281$		−	1.39960e13i		−	0.476562i	0.971196	−	0.238281i	$-0.0765839\pi$
$282$	−5.75451e12	+	1.07512e13i	−0.192149	+	0.358993i
$283$	1.18195e13	−	6.82398e12i	0.387055	−	0.223466i	−0.293828	−	0.955858i	$-0.594929\pi$
$283$	1.18195e13	−	6.82398e12i	0.387055	−	0.223466i	0.680883	+	0.732392i	$0.261596\pi$
$284$	1.45271e13	−	8.38724e12i	0.466583	−	0.269382i
$285$	3.27895e13	−	6.12608e13i	1.03297	−	1.92991i
$286$		−	2.01257e13i		−	0.621925i
$287$	−1.00213e13	+	5.46829e13i	−0.303792	+	1.65768i
$288$	−3.81999e11	−	5.93178e12i	−0.0113607	−	0.176411i
$289$	−1.73858e13	+	3.01130e13i	−0.507289	+	0.878650i
$290$	−3.19767e12	−	5.53853e12i	−0.0915471	−	0.158564i
$291$	−3.37932e13	−	5.44129e13i	−0.949330	−	1.52859i
$292$	1.22061e13	+	7.04719e12i	0.336489	+	0.194272i
$293$	−2.19643e13			−0.594218			−0.297109	−	0.954844i	$-0.596023\pi$
$293$	−2.19643e13			−0.594218			−0.297109	+	0.954844i	$0.596023\pi$
$294$	2.51915e13	+	8.63852e12i	0.668873	+	0.229366i
$295$	7.18566e13			1.87260
$296$	4.69833e12	+	2.71258e12i	0.120182	+	0.0693870i
$297$	2.61497e13	+	3.66239e13i	0.656607	+	0.919612i
$298$	−1.73699e13	−	3.00856e13i	−0.428162	−	0.741599i
$299$	6.13750e12	−	1.06305e13i	0.148525	−	0.257253i
$300$	−2.15031e11	−	6.68502e12i	−0.00510897	−	0.158831i
$301$	−3.91383e12	+	2.13564e13i	−0.0913033	+	0.498209i
$302$			1.71710e13i			0.393331i
$303$	3.99788e13	+	2.13984e13i	0.899282	+	0.481335i
$304$	−1.86889e13	+	1.07901e13i	−0.412838	+	0.238352i
$305$	−6.45600e12	+	3.72737e12i	−0.140060	+	0.0808637i
$306$	4.22213e13	+	2.08811e13i	0.899629	+	0.444923i
$307$		−	8.64144e12i		−	0.180853i	−0.995903	−	0.0904263i	$-0.971177\pi$
$307$		−	8.64144e12i		−	0.180853i	0.995903	−	0.0904263i	$-0.0288230\pi$
$308$	−1.78068e13	+	2.09340e13i	−0.366063	+	0.430352i
$309$	−1.48878e13	+	4.78880e11i	−0.300647	+	0.00967064i
$310$	−7.64661e12	+	1.32443e13i	−0.151698	+	0.262748i
$311$	2.00184e13	+	3.46728e13i	0.390163	+	0.675782i	0.992471	−	0.122482i	$-0.0390853\pi$
$311$	2.00184e13	+	3.46728e13i	0.390163	+	0.675782i	−0.602308	+	0.798264i	$0.705752\pi$
$312$	−1.22084e13	+	7.58202e12i	−0.233781	+	0.145189i
$313$	2.79777e13	+	1.61529e13i	0.526402	+	0.303918i	0.739550	−	0.673102i	$-0.235038\pi$
$313$	2.79777e13	+	1.61529e13i	0.526402	+	0.303918i	−0.213148	+	0.977020i	$0.568372\pi$
$314$	−5.71249e13			−1.05612
$315$	−5.80353e13	+	2.49936e13i	−1.05435	+	0.454068i
$316$	−2.44012e13			−0.435645
$317$	−4.14439e12	−	2.39277e12i	−0.0727168	−	0.0419831i	0.463201	−	0.886253i	$-0.346701\pi$
$317$	−4.14439e12	−	2.39277e12i	−0.0727168	−	0.0419831i	−0.535918	+	0.844270i	$0.680034\pi$
$318$	3.14238e13	−	1.95157e13i	0.541887	−	0.336539i
$319$	−7.51872e12	−	1.30228e13i	−0.127437	−	0.220727i
$320$	−4.30660e12	+	7.45924e12i	−0.0717479	+	0.124271i
$321$	−6.81475e13	+	2.19203e12i	−1.11602	+	0.0358979i
$322$	−1.57896e13	+	5.62709e12i	−0.254193	+	0.0905892i
$323$		−	1.71008e14i		−	2.70646i
$324$	1.23649e13	−	2.96600e13i	0.192394	−	0.461502i
$325$	−1.40045e13	+	8.08551e12i	−0.214244	+	0.123694i
$326$	3.92763e13	−	2.26762e13i	0.590790	−	0.341093i
$327$	8.05139e13	+	4.30946e13i	1.19085	+	0.637397i
$328$			4.09671e13i			0.595840i
$329$	−3.06669e13	−	2.60857e13i	−0.438624	−	0.373100i
$330$	−2.09642e12	−	6.51750e13i	−0.0294884	−	0.916757i
$331$	3.92110e13	−	6.79154e13i	0.542442	−	0.939538i	−0.456321	−	0.889815i	$-0.650833\pi$
$331$	3.92110e13	−	6.79154e13i	0.542442	−	0.939538i	0.998763	−	0.0497223i	$-0.0158336\pi$
$332$	3.13926e13	+	5.43736e13i	0.427137	+	0.739824i
$333$	1.62665e13	+	2.44047e13i	0.217696	+	0.326610i
$334$	−8.03978e13	−	4.64177e13i	−1.05837	−	0.611052i
$335$	−8.95649e13			−1.15982
$336$	1.94071e13	+	2.91517e12i	0.247226	+	0.0371362i
$337$	5.14094e13			0.644285			0.322143	−	0.946691i	$-0.395597\pi$
$337$	5.14094e13			0.644285			0.322143	+	0.946691i	$0.395597\pi$
$338$	−1.95750e13	−	1.13016e13i	−0.241357	−	0.139347i
$339$	−4.47261e13	−	7.20170e13i	−0.542579	−	0.873648i
$340$	−3.41268e13	−	5.91093e13i	−0.407344	−	0.705540i
$341$	−1.79796e13	+	3.11415e13i	−0.211169	+	0.365755i
$342$	−1.16423e14	+	7.49750e12i	−1.34554	+	0.0866509i
$343$	−4.54888e13	+	7.52447e13i	−0.517353	+	0.855772i
$344$			1.59997e13i			0.179077i
$345$	1.87683e13	−	3.50649e13i	0.206738	−	0.386249i
$346$	4.99010e12	−	2.88103e12i	0.0540992	−	0.0312342i
$347$	−8.30373e12	+	4.79416e12i	−0.0886056	+	0.0511565i	−0.543648	−	0.839313i	$-0.682957\pi$
$347$	−8.30373e12	+	4.79416e12i	−0.0886056	+	0.0511565i	0.455043	+	0.890470i	$0.349624\pi$
$348$	−5.06717e12	+	9.46703e12i	−0.0532206	+	0.0994324i
$349$			2.26985e12i			0.0234670i	0.999931	+	0.0117335i	$0.00373497\pi$
$349$			2.26985e12i			0.0234670i	−0.999931	+	0.0117335i	$0.996265\pi$
$350$	2.17208e13	+	3.98062e12i	0.221056	+	0.0405114i
$351$	−7.73310e13	+	7.48295e12i	−0.774755	+	0.0749694i
$352$	−1.01261e13	+	1.75390e13i	−0.0998756	+	0.172990i
$353$	−1.41850e13	−	2.45692e13i	−0.137743	−	0.238578i	0.788899	−	0.614523i	$-0.210651\pi$
$353$	−1.41850e13	−	2.45692e13i	−0.137743	−	0.238578i	−0.926642	+	0.375945i	$0.877318\pi$
$354$	−6.36518e13	−	1.02491e14i	−0.608545	−	0.979865i
$355$	−1.13800e14	−	6.57027e13i	−1.07124	−	0.618482i
$356$	7.79607e12			0.0722604
$357$	−9.68997e13	+	1.21634e14i	−0.884397	+	1.11014i
$358$	−5.91208e13			−0.531353
$359$	1.68524e14	+	9.72973e13i	1.49156	+	0.861155i	0.999953	−	0.00966081i	$-0.00307518\pi$
$359$	1.68524e14	+	9.72973e13i	1.49156	+	0.861155i	0.491610	+	0.870815i	$0.336409\pi$
$360$	−3.87458e13	+	2.58253e13i	−0.337723	+	0.225103i
$361$	1.53532e14	+	2.65925e14i	1.31798	+	2.28281i
$362$	6.20484e13	−	1.07471e14i	0.524606	−	0.908644i
$363$	−1.06870e12	−	3.32244e13i	−0.00889955	−	0.276675i
$364$	−1.59282e13	−	4.46944e13i	−0.130650	−	0.366602i
$365$		−	1.10410e14i		−	0.892071i
$366$	1.10353e13	+	5.90656e12i	0.0878288	+	0.0470099i
$367$	−2.70526e13	+	1.56188e13i	−0.212102	+	0.122457i	−0.602288	−	0.798279i	$-0.705744\pi$
$367$	−2.70526e13	+	1.56188e13i	−0.212102	+	0.122457i	0.390186	+	0.920736i	$0.372411\pi$
$368$	−1.06973e13	+	6.17610e12i	−0.0826251	+	0.0477036i
$369$	−9.81811e13	+	1.98521e14i	−0.747107	+	1.51064i
$370$		−	4.24988e13i		−	0.318616i
$371$	4.09983e13	+	1.15041e14i	0.302837	+	0.849759i
$372$	2.56642e13	−	8.25514e11i	0.186785	−	0.00600812i
$373$	−4.07039e13	+	7.05012e13i	−0.291902	+	0.505590i	−0.974260	−	0.225429i	$-0.927622\pi$
$373$	−4.07039e13	+	7.05012e13i	−0.291902	+	0.505590i	0.682357	+	0.731019i	$0.260955\pi$
$374$	−8.02427e13	−	1.38984e14i	−0.567037	−	0.982137i
$375$	9.55346e13	−	5.93318e13i	0.665256	−	0.413157i
$376$	−2.56934e13	−	1.48341e13i	−0.176315	−	0.101796i
$377$	2.59613e13			0.175569
$378$	8.70576e13	+	6.06372e13i	0.580232	+	0.404142i
$379$	1.94426e14			1.27714			0.638571	−	0.769563i	$-0.279526\pi$
$379$	1.94426e14			1.27714			0.638571	+	0.769563i	$0.279526\pi$
$380$	1.46403e14	+	8.45256e13i	0.947849	+	0.547241i
$381$	−1.54862e14	+	9.61771e13i	−0.988230	+	0.613740i
$382$	−7.22903e11	−	1.25210e12i	−0.00454707	−	0.00787575i
$383$	4.56479e13	−	7.90645e13i	0.283027	−	0.490217i	−0.689102	−	0.724664i	$-0.741995\pi$
$383$	4.56479e13	−	7.90645e13i	0.283027	−	0.490217i	0.972129	+	0.234448i	$0.0753281\pi$
$384$	1.44541e13	−	4.64932e11i	0.0883427	−	0.00284163i
$385$	2.11765e14	+	3.88087e13i	1.27591	+	0.233827i
$386$			3.00361e13i			0.178408i
$387$	−3.83446e13	+	7.75321e13i	−0.224540	+	0.454016i
$388$	1.34959e14	−	7.79185e13i	0.779160	−	0.449848i
$389$	2.35867e14	−	1.36178e14i	1.34259	−	0.775145i	0.355404	−	0.934713i	$-0.384343\pi$
$389$	2.35867e14	−	1.36178e14i	1.34259	−	0.775145i	0.987187	+	0.159567i	$0.0510099\pi$
$390$	9.92557e13	+	5.31260e13i	0.557057	+	0.298162i
$391$		−	9.78826e13i		−	0.541668i
$392$	−2.29766e13	+	6.05823e13i	−0.125376	+	0.330577i
$393$	−7.28616e12	−	2.26517e14i	−0.0392049	−	1.21883i
$394$	−5.91472e13	+	1.02446e14i	−0.313837	+	0.543582i
$395$	9.55753e13	+	1.65541e14i	0.500106	+	0.866209i
$396$	−9.11035e13	+	6.07233e13i	−0.470123	+	0.313351i
$397$	−2.02731e14	−	1.17047e14i	−1.03174	−	0.595678i	−0.114261	−	0.993451i	$-0.536450\pi$
$397$	−2.02731e14	−	1.17047e14i	−1.03174	−	0.595678i	−0.917484	+	0.397773i	$0.869783\pi$
$398$	−9.93028e13			−0.498430
$399$	5.72161e13	−	3.80904e14i	0.283248	−	1.88566i
$400$	1.62727e13			0.0794567
$401$	1.96148e14	+	1.13246e14i	0.944691	+	0.545418i	0.891428	−	0.453163i	$-0.149704\pi$
$401$	1.96148e14	+	1.13246e14i	0.944691	+	0.545418i	0.0532636	+	0.998580i	$0.483038\pi$
$402$	7.93381e13	+	1.27748e14i	0.376911	+	0.606893i
$403$	−3.10407e13	−	5.37641e13i	−0.145463	−	0.251950i
$404$	−5.51615e13	+	9.55425e13i	−0.254999	+	0.441671i
$405$	−2.49649e14	+	3.22880e13i	−1.13848	+	0.147244i
$406$	−2.70040e13	−	2.29700e13i	−0.121488	−	0.103340i
$407$		−	9.99279e13i		−	0.443525i
$408$	−5.40788e13	+	1.01036e14i	−0.236808	+	0.442430i
$409$	1.03950e11	−	6.00157e10i	0.000449104	−	0.000259291i	−0.499775	−	0.866155i	$-0.666584\pi$
$409$	1.03950e11	−	6.00157e10i	0.000449104	−	0.000259291i	0.500225	+	0.865896i	$0.333251\pi$
$410$	2.77927e14	−	1.60461e14i	1.18473	−	0.684004i
$411$	1.59890e12	−	2.98723e12i	0.00672498	−	0.0125643i
$412$		−	3.62399e13i		−	0.150401i
$413$	3.75213e14	−	1.33719e14i	1.53657	−	0.547604i
$414$	−6.66391e13	+	4.29147e12i	−0.269295	+	0.0173422i
$415$	2.45919e14	−	4.25943e14i	0.980679	−	1.69859i
$416$	−1.74822e13	−	3.02801e13i	−0.0687992	−	0.119164i
$417$	1.70010e14	+	2.73747e14i	0.660278	+	1.06316i
$418$	3.44238e14	+	1.98746e14i	1.31944	+	0.761779i
$419$	−1.63254e14			−0.617571			−0.308786	−	0.951132i	$-0.599923\pi$
$419$	−1.63254e14			−0.617571			−0.308786	+	0.951132i	$0.599923\pi$
$420$	−5.62374e13	−	1.43079e14i	−0.209968	−	0.534200i
$421$	−4.54006e14			−1.67305			−0.836526	−	0.547927i	$-0.815417\pi$
$421$	−4.54006e14			−1.67305			−0.836526	+	0.547927i	$0.815417\pi$
$422$	−2.85772e13	−	1.64990e13i	−0.103944	−	0.0600123i
$423$	−8.89555e13	−	1.33460e14i	−0.319375	−	0.479160i
$424$	4.49983e13	+	7.79394e13i	0.159472	+	0.276213i
$425$	−6.44750e13	+	1.11674e14i	−0.225555	+	0.390673i
$426$	7.09315e12	+	2.20517e14i	0.0244955	+	0.761533i
$427$	−2.67750e13	+	3.14772e13i	−0.0912800	+	0.107311i
$428$		−	1.65885e14i		−	0.558299i
$429$	2.33381e14	+	1.24916e14i	0.775444	+	0.415052i
$430$	1.08544e14	−	6.26680e13i	0.356065	−	0.205575i
$431$	−3.46980e14	+	2.00329e14i	−1.12378	+	0.648812i	−0.942362	−	0.334594i	$-0.891401\pi$
$431$	−3.46980e14	+	2.00329e14i	−1.12378	+	0.648812i	−0.181414	+	0.983407i	$0.558067\pi$
$432$	7.11569e13	+	3.23875e13i	0.227539	+	0.103566i
$433$			6.88888e12i			0.0217503i	0.999941	+	0.0108751i	$0.00346173\pi$
$433$			6.88888e12i			0.0217503i	−0.999941	+	0.0108751i	$0.996538\pi$
$434$	−1.52818e13	+	8.33875e13i	−0.0476411	+	0.259960i
$435$	8.40729e13	−	2.70429e12i	0.258801	−	0.00832459i
$436$	−1.11090e14	+	1.92414e14i	−0.337676	+	0.584873i
$437$	1.21218e14	+	2.09956e14i	0.363849	+	0.630204i
$438$	−1.57481e14	+	9.78035e13i	−0.466788	+	0.289899i
$439$	−5.01492e14	−	2.89537e14i	−1.46794	−	0.847518i	−0.468588	−	0.883417i	$-0.655237\pi$
$439$	−5.01492e14	−	2.89537e14i	−1.46794	−	0.847518i	−0.999355	+	0.0358988i	$0.988571\pi$
$440$	1.58649e14			0.458616
$441$	−2.56532e14	+	2.38507e14i	−0.732367	+	0.680910i
$442$	2.77069e14			0.781206
$443$	3.95238e13	+	2.28191e13i	0.110062	+	0.0635444i	0.554021	−	0.832503i	$-0.313093\pi$
$443$	3.95238e13	+	2.28191e13i	0.110062	+	0.0635444i	−0.443958	+	0.896047i	$0.646426\pi$
$444$	−6.06170e13	+	3.76462e13i	−0.166720	+	0.103541i
$445$	−3.05358e13	−	5.28896e13i	−0.0829526	−	0.143678i
$446$	−2.15919e14	+	3.73983e14i	−0.579362	+	1.00348i
$447$	4.56689e14	−	1.46899e13i	1.21040	−	0.0389338i
$448$	−8.60677e12	+	4.69641e13i	−0.0225326	+	0.122952i
$449$		−	1.91900e14i		−	0.496273i	−0.968725	−	0.248136i	$-0.920182\pi$
$449$		−	1.91900e14i		−	0.496273i	0.968725	−	0.248136i	$-0.0798181\pi$
$450$	7.88552e13	+	3.89989e13i	0.201447	+	0.0996285i
$451$	6.53493e14	−	3.77294e14i	1.64919	−	0.952158i
$452$	1.78622e14	−	1.03127e14i	0.445320	−	0.257106i
$453$	−1.99118e14	−	1.06577e14i	−0.490423	−	0.262496i
$454$			1.91815e14i			0.466741i
$455$	−2.40825e14	+	2.83119e14i	−0.578947	+	0.680623i
$456$	−9.12524e12	−	2.83692e14i	−0.0216739	−	0.673814i
$457$	−3.67119e14	+	6.35868e14i	−0.861524	+	1.49220i	0.00893406	+	0.999960i	$0.497156\pi$
$457$	−3.67119e14	+	6.35868e14i	−0.861524	+	1.49220i	−0.870458	+	0.492243i	$0.836177\pi$
$458$	−9.44158e13	−	1.63533e14i	−0.218920	−	0.379180i
$459$	−5.04199e14	+	3.60000e14i	−1.15513	+	0.824771i
$460$	8.37991e13	+	4.83814e13i	0.189702	+	0.109524i
$461$	−7.86474e14			−1.75926			−0.879629	−	0.475661i	$-0.842209\pi$
$461$	−7.86474e14			−1.75926			−0.879629	+	0.475661i	$0.842209\pi$
$462$	−1.32232e14	−	3.36423e14i	−0.292283	−	0.743626i
$463$	−5.54483e14			−1.21113			−0.605567	−	0.795794i	$-0.707054\pi$
$463$	−5.54483e14			−1.21113			−0.605567	+	0.795794i	$0.707054\pi$
$464$	−2.26246e13	−	1.30623e13i	−0.0488350	−	0.0281949i
$465$	−1.06122e14	−	1.70876e14i	−0.226368	−	0.364493i
$466$	−1.34352e14	−	2.32704e14i	−0.283218	−	0.490549i
$467$	3.95206e14	−	6.84517e14i	0.823343	−	1.42607i	−0.0798361	−	0.996808i	$-0.525440\pi$
$467$	3.95206e14	−	6.84517e14i	0.823343	−	1.42607i	0.903179	−	0.429264i	$-0.141227\pi$
$468$	−1.21476e13	−	1.88631e14i	−0.0250113	−	0.388383i
$469$	−4.67681e14	+	1.66672e14i	−0.951698	+	0.339166i
$470$			2.32411e14i			0.467431i
$471$	3.54561e14	−	6.62429e14i	0.704817	−	1.31681i
$472$	2.54204e14	−	1.46765e14i	0.499461	−	0.288364i
$473$	2.55221e14	−	1.47352e14i	0.495656	−	0.286167i
$474$	1.51453e14	−	2.82961e14i	0.290735	−	0.543182i
$475$		−	3.19385e14i		−	0.606038i
$476$	−2.88197e14	−	2.45144e14i	−0.540569	−	0.459815i
$477$	3.12672e13	+	4.85525e14i	0.0579746	+	0.900244i
$478$	−1.72767e14	+	2.99242e14i	−0.316671	+	0.548490i
$479$	−3.79423e14	−	6.57181e14i	−0.687510	−	1.19080i	−0.972641	−	0.232313i	$-0.925371\pi$
$479$	−3.79423e14	−	6.57181e14i	−0.687510	−	1.19080i	0.285131	−	0.958488i	$-0.407963\pi$
$480$	−5.97685e13	−	9.62378e13i	−0.107065	−	0.172393i
$481$	1.49407e14	+	8.62600e13i	0.264589	+	0.152761i
$482$	−2.46319e14			−0.431259
$483$	3.27498e13	−	2.18025e14i	0.0566890	−	0.377395i
$484$	8.08751e13			0.138409
$485$	−1.05722e15	−	6.10386e14i	−1.78890	−	1.03282i
$486$	2.67196e14	+	3.27478e14i	0.447024	+	0.547877i
$487$	2.69182e14	+	4.66237e14i	0.445283	+	0.771254i	0.998072	−	0.0620681i	$-0.0197696\pi$
$487$	2.69182e14	+	4.66237e14i	0.445283	+	0.771254i	−0.552788	+	0.833322i	$0.686436\pi$
$488$	−1.52261e13	+	2.63724e13i	−0.0249046	+	0.0431360i
$489$	1.91774e13	+	5.96200e14i	0.0310163	+	0.964258i
$490$	5.00994e14	−	8.14134e13i	0.801225	−	0.130202i
$491$			9.80146e14i			1.55004i	0.631937	+	0.775019i	$0.282260\pi$
$491$			9.80146e14i			1.55004i	−0.631937	+	0.775019i	$0.717740\pi$
$492$	−4.75062e14	−	2.54274e14i	−0.742920	−	0.397643i
$493$	1.79284e14	−	1.03510e14i	0.277257	−	0.160075i
$494$	−5.94308e14	+	3.43124e14i	−0.908895	+	0.524751i
$495$	7.68792e14	+	3.80216e14i	1.16273	+	0.575045i
$496$			6.24719e13i			0.0934406i
$497$	−7.16498e14	−	1.31308e14i	−1.05988	−	0.194236i
$498$	−8.25372e14	+	2.65489e13i	−1.20750	+	0.0388406i
$499$	−1.95208e14	+	3.38110e14i	−0.282452	+	0.489221i	−0.971988	−	0.235030i	$-0.924481\pi$
$499$	−1.95208e14	+	3.38110e14i	−0.282452	+	0.489221i	0.689536	+	0.724251i	$0.257814\pi$
$500$	1.36804e14	+	2.36952e14i	0.195778	+	0.339097i
$501$	1.03728e15	−	6.44202e14i	1.46821	−	0.911831i
$502$	6.38408e14	+	3.68585e14i	0.893774	+	0.516021i
$503$	−3.61386e13			−0.0500435			−0.0250218	−	0.999687i	$-0.507966\pi$
$503$	−3.61386e13			−0.0500435			−0.0250218	+	0.999687i	$0.507966\pi$
$504$	−1.54260e14	+	2.06954e14i	−0.211294	+	0.283470i
$505$	8.64232e14			1.17092
$506$	1.97038e14	+	1.13760e14i	0.264071	+	0.152462i
$507$	2.52553e14	−	1.56848e14i	0.334818	−	0.207938i
$508$	−2.21760e14	−	3.84100e14i	−0.290826	−	0.503725i
$509$	−6.39283e12	+	1.10727e13i	−0.00829364	+	0.0143650i	−0.870142	−	0.492800i	$-0.835973\pi$
$509$	−6.39283e12	+	1.10727e13i	−0.00829364	+	0.0143650i	0.861849	+	0.507165i	$0.169307\pi$
$510$	8.97259e14	−	2.88613e13i	1.15155	−	0.0370407i
$511$	−2.05464e14	−	5.76530e14i	−0.260868	−	0.731993i
$512$			3.51844e13i			0.0441942i
$513$	6.35670e14	−	1.39660e15i	0.789926	−	1.73550i
$514$	−2.52526e14	+	1.45796e14i	−0.310463	+	0.179246i
$515$	−2.45856e14	+	1.41945e14i	−0.299049	+	0.172656i
$516$	−1.85535e14	−	9.93065e13i	−0.223281	−	0.119510i
$517$			5.46470e14i			0.650681i
$518$	−7.90864e13	−	2.21916e14i	−0.0931726	−	0.261442i
$519$	2.43651e12	+	7.57479e13i	0.00284019	+	0.0882979i
$520$	−1.36950e14	+	2.37204e14i	−0.157958	+	0.273592i
$521$	8.17012e14	+	1.41511e15i	0.932440	+	1.61503i	0.779136	+	0.626854i	$0.215658\pi$
$521$	8.17012e14	+	1.41511e15i	0.932440	+	1.61503i	0.153304	+	0.988179i	$0.451009\pi$
$522$	−7.83304e13	−	1.17520e14i	−0.0884591	−	0.132716i
$523$	−9.15705e14	−	5.28682e14i	−1.02328	−	0.590793i	−0.108231	−	0.994126i	$-0.534518\pi$
$523$	−9.15705e14	−	5.28682e14i	−1.02328	−	0.590793i	−0.915053	+	0.403333i	$0.867852\pi$
$524$	5.51390e14			0.609729
$525$	−1.80976e14	+	2.27172e14i	−0.198037	+	0.248587i
$526$	−5.67519e14			−0.614552
$527$	−4.28723e14	−	2.47523e14i	−0.459429	−	0.265251i
$528$	−1.40534e14	−	2.26285e14i	−0.149038	−	0.239977i
$529$	−4.07021e14	−	7.04981e14i	−0.427180	−	0.739897i
$530$	3.52501e14	−	6.10550e14i	0.366137	−	0.634167i
$531$	1.58357e15	−	1.01980e14i	1.62786	−	0.104832i
$532$	9.21765e14	+	1.68925e14i	0.937791	+	0.171862i
$533$			1.30275e15i			1.31179i
$534$	−4.83885e13	+	9.04045e13i	−0.0482242	+	0.0900976i
$535$	−1.12539e15	+	6.49743e14i	−1.11009	+	0.640908i
$536$	−3.16850e14	+	1.82934e14i	−0.309348	+	0.178602i
$537$	3.66950e14	−	6.85574e14i	0.354607	−	0.662515i
$538$		−	1.22019e15i		−	1.16714i
$539$	1.17799e15	−	1.91428e14i	1.11533	−	0.181246i
$540$	−5.89875e13	−	6.09595e14i	−0.0552834	−	0.571315i
$541$	−4.37908e14	+	7.58478e14i	−0.406254	+	0.703652i	−0.994467	−	0.105054i	$-0.966498\pi$
$541$	−4.37908e14	+	7.58478e14i	−0.406254	+	0.703652i	0.588213	+	0.808706i	$0.299832\pi$
$542$	7.63634e13	+	1.32265e14i	0.0701276	+	0.121465i
$543$	8.61130e14	+	1.38657e15i	0.782834	+	1.26050i
$544$	−2.41458e14	−	1.39406e14i	−0.217294	−	0.125455i
$545$	1.74049e15			1.55056
$546$	6.17146e14	+	9.27023e13i	0.544287	+	0.0817582i
$547$	7.30768e14			0.638042			0.319021	−	0.947748i	$-0.396646\pi$
$547$	7.30768e14			0.638042			0.319021	+	0.947748i	$0.396646\pi$
$548$	7.13897e12	+	4.12168e12i	0.00617081	+	0.00356272i
$549$	−1.36987e14	+	9.13060e13i	−0.117228	+	0.0781361i
$550$	−1.49867e14	−	2.59577e14i	−0.126973	−	0.219923i
$551$	−2.56374e14	+	4.44053e14i	−0.215050	+	0.372478i
$552$	−5.22317e12	−	1.62382e14i	−0.00433780	−	0.134856i
$553$	8.07123e14	+	6.86550e14i	0.663669	+	0.564526i
$554$			2.37562e14i			0.193408i
$555$	4.92823e14	+	2.63781e14i	0.397264	+	0.212633i
$556$	−6.78966e14	+	3.92001e14i	−0.541921	+	0.312879i
$557$	−9.67776e14	+	5.58746e14i	−0.764841	+	0.441581i	−0.831031	−	0.556226i	$-0.812249\pi$
$557$	−9.67776e14	+	5.58746e14i	−0.764841	+	0.441581i	0.0661902	+	0.997807i	$0.478916\pi$
$558$	−1.49719e14	+	3.02730e14i	−0.117163	+	0.236901i
$559$			5.08790e14i			0.394252i
$560$	3.52322e14	−	1.25561e14i	0.270337	−	0.0963428i
$561$	2.10973e15	−	6.78618e13i	1.60299	−	0.0515620i
$562$	−2.23936e14	+	3.87869e14i	−0.168490	+	0.291833i
$563$	−1.29175e14	−	2.23738e14i	−0.0962459	−	0.166703i	0.813882	−	0.581030i	$-0.197350\pi$
$563$	−1.29175e14	−	2.23738e14i	−0.0962459	−	0.166703i	−0.910128	+	0.414327i	$0.864017\pi$
$564$	3.31492e14	−	2.05873e14i	0.244590	−	0.151903i
$565$	−1.39926e15	−	8.07862e14i	−1.02243	−	0.590297i
$566$	−4.36735e14			−0.316029
$567$	−1.24351e15	+	6.33172e14i	−0.891130	+	0.453748i
$568$	−5.36783e14			−0.380963
$569$	−1.45206e15	−	8.38346e14i	−1.02063	−	0.589259i	−0.106341	−	0.994330i	$-0.533913\pi$
$569$	−1.45206e15	−	8.38346e14i	−1.02063	−	0.589259i	−0.914285	+	0.405071i	$0.867247\pi$
$570$	−1.88886e15	+	1.17308e15i	−1.31489	+	0.816611i
$571$	2.14608e14	+	3.71712e14i	0.147961	+	0.256276i	0.930474	−	0.366358i	$-0.119396\pi$
$571$	2.14608e14	+	3.71712e14i	0.147961	+	0.256276i	−0.782513	+	0.622635i	$0.786062\pi$
$572$	−3.22011e14	+	5.57740e14i	−0.219884	+	0.380850i
$573$	1.90065e13	−	6.11364e11i	0.0128544	−	0.000413475i
$574$	1.15265e15	−	1.35508e15i	0.772113	−	0.907712i
$575$		−	1.82812e14i		−	0.121292i
$576$	−8.43222e13	+	1.70498e14i	−0.0554138	+	0.112046i
$577$	4.92763e14	−	2.84497e14i	0.320754	−	0.185187i	−0.330975	−	0.943640i	$-0.607378\pi$
$577$	4.92763e14	−	2.84497e14i	0.320754	−	0.185187i	0.651728	+	0.758452i	$0.274044\pi$
$578$	9.63616e14	−	5.56344e14i	0.621299	−	0.358707i
$579$	−3.48304e14	−	1.86428e14i	−0.222447	−	0.119063i
$580$			2.04651e14i			0.129467i
$581$	4.91471e14	−	2.68178e15i	0.307985	−	1.68056i
$582$	6.58962e13	+	2.04863e15i	0.0409057	+	1.27170i
$583$	8.28840e14	−	1.43559e15i	0.509675	−	0.882784i
$584$	−2.25510e14	−	3.90595e14i	−0.137371	−	0.237934i
$585$	−1.23212e15	+	8.21244e14i	−0.743523	+	0.495581i
$586$	6.08693e14	+	3.51429e14i	0.363883	+	0.210088i
$587$	1.56366e15			0.926048			0.463024	−	0.886346i	$-0.346764\pi$
$587$	1.56366e15			0.926048			0.463024	+	0.886346i	$0.346764\pi$
$588$	−5.59911e14	−	6.42462e14i	−0.328506	−	0.376940i
$589$	1.22614e15			0.712697
$590$	−1.99135e15	−	1.14971e15i	−1.14673	−	0.662065i
$591$	−8.20866e14	−	1.32174e15i	−0.468318	−	0.754075i
$592$	−8.68025e13	−	1.50346e14i	−0.0490640	−	0.0849814i
$593$	−1.13817e15	+	1.97137e15i	−0.637393	+	1.10400i	0.348610	+	0.937268i	$0.386654\pi$
$593$	−1.13817e15	+	1.97137e15i	−0.637393	+	1.10400i	−0.986003	+	0.166729i	$0.946680\pi$
$594$	−1.38698e14	−	1.43335e15i	−0.0769564	−	0.795291i
$595$	−5.34276e14	+	2.91535e15i	−0.293713	+	1.60268i
$596$			1.11168e15i			0.605513i
$597$	6.16351e14	−	1.15153e15i	0.332636	−	0.621465i
$598$	−3.40175e14	+	1.96400e14i	−0.181905	+	0.105023i
$599$	7.56407e14	−	4.36712e14i	0.400782	−	0.231392i	−0.286039	−	0.958218i	$-0.592339\pi$
$599$	7.56407e14	−	4.36712e14i	0.400782	−	0.231392i	0.686821	+	0.726826i	$0.259005\pi$
$600$	−1.01001e14	+	1.88701e14i	−0.0530267	+	0.0990702i
$601$		−	1.98408e15i		−	1.03216i	−0.856539	−	0.516082i	$-0.827390\pi$
$601$		−	1.98408e15i		−	1.03216i	0.856539	−	0.516082i	$-0.172610\pi$
$602$	4.50165e14	−	5.29224e14i	0.232055	−	0.272809i
$603$	−1.97383e15	+	1.27112e14i	−1.00824	+	0.0649293i
$604$	2.74737e14	−	4.75858e14i	0.139064	−	0.240865i
$605$	−3.16774e14	−	5.48668e14i	−0.158889	−	0.275204i
$606$	−7.65551e14	−	1.23267e15i	−0.380518	−	0.612701i
$607$	2.30212e15	+	1.32913e15i	1.13394	+	0.654681i	0.944923	−	0.327292i	$-0.106136\pi$
$607$	2.30212e15	+	1.32913e15i	1.13394	+	0.654681i	0.189018	+	0.981974i	$0.439470\pi$
$608$	6.90564e14			0.337081
$609$	4.33971e14	−	1.70573e14i	0.209926	−	0.0825116i
$610$	2.38552e14			0.114359
$611$	−8.17051e14	−	4.71725e14i	−0.388171	−	0.224110i
$612$	−8.35972e14	−	1.25421e15i	−0.393604	−	0.590526i
$613$	−5.92955e14	−	1.02703e15i	−0.276687	−	0.479236i	0.693872	−	0.720098i	$-0.255903\pi$
$613$	−5.92955e14	−	1.02703e15i	−0.276687	−	0.479236i	−0.970559	+	0.240862i	$0.922570\pi$
$614$	−1.38263e14	+	2.39478e14i	−0.0639411	+	0.110749i
$615$	1.35703e14	+	4.21883e15i	0.0621980	+	1.93366i
$616$	8.28419e14	−	2.95232e14i	0.376319	−	0.134113i
$617$			1.79072e15i			0.806229i	0.915150	+	0.403114i	$0.132072\pi$
$617$			1.79072e15i			0.806229i	−0.915150	+	0.403114i	$0.867928\pi$
$618$	4.20244e14	+	2.24933e14i	0.187527	+	0.100373i
$619$	6.85310e14	−	3.95664e14i	0.303102	−	0.174996i	−0.340734	−	0.940160i	$-0.610675\pi$
$619$	6.85310e14	−	3.95664e14i	0.303102	−	0.174996i	0.643836	+	0.765164i	$0.277342\pi$
$620$	4.23818e14	−	2.44692e14i	0.185791	−	0.107267i
$621$	3.63850e14	−	7.99395e14i	0.158095	−	0.347342i
$622$		−	1.28117e15i		−	0.551774i
$623$	−2.57872e14	−	2.19349e14i	−0.110083	−	0.0936380i
$624$	4.59641e14	−	1.47848e13i	0.194493	−	0.00625607i
$625$	1.45055e15	−	2.51243e15i	0.608406	−	1.05379i
$626$	−5.16893e14	−	8.95285e14i	−0.214903	−	0.372222i
$627$	−4.44130e15	+	2.75827e15i	−1.83037	+	1.13675i
$628$	1.58309e15	+	9.13998e14i	0.646737	+	0.373394i
$629$	1.37570e15			0.557115
$630$	2.00822e15	+	2.35921e14i	0.806191	+	0.0947094i
$631$	−2.02811e14			−0.0807107			−0.0403553	−	0.999185i	$-0.512849\pi$
$631$	−2.02811e14			−0.0807107			−0.0403553	+	0.999185i	$0.512849\pi$
$632$	6.76227e14	+	3.90420e14i	0.266777	+	0.154024i
$633$	3.68698e14	−	2.28980e14i	0.144195	−	0.0895523i
$634$	7.65685e13	+	1.32621e14i	0.0296865	+	0.0514186i
$635$	−1.73719e15	+	3.00890e15i	−0.667716	+	1.15652i
$636$	−1.18309e15	+	3.80554e13i	−0.450821	+	0.0145011i
$637$	−7.30657e14	+	1.92652e15i	−0.276024	+	0.727789i
$638$			4.81198e14i			0.180223i
$639$	−2.60117e15	−	1.28644e15i	−0.965860	−	0.477679i
$640$	2.38696e14	−	1.37811e14i	0.0878729	−	0.0507334i
$641$	2.42884e15	−	1.40229e15i	0.886503	−	0.511823i	0.0137060	−	0.999906i	$-0.495637\pi$
$641$	2.42884e15	−	1.40229e15i	0.886503	−	0.511823i	0.872797	+	0.488083i	$0.162304\pi$
$642$	1.92363e15	+	1.02961e15i	0.696112	+	0.372590i
$643$			2.41881e15i			0.867842i	0.900951	+	0.433921i	$0.142870\pi$
$643$			2.41881e15i			0.867842i	−0.900951	+	0.433921i	$0.857130\pi$
$644$	5.27607e14	+	9.66907e13i	0.187689	+	0.0343964i
$645$	5.29988e13	+	1.64766e15i	0.0186934	+	0.581152i
$646$	−2.73612e15	+	4.73910e15i	−0.956878	+	1.65736i
$647$	−1.55051e15	−	2.68556e15i	−0.537651	−	0.931239i	−0.999030	−	0.0440360i	$-0.985978\pi$
$647$	−1.55051e15	−	2.68556e15i	−0.537651	−	0.931239i	0.461379	−	0.887203i	$-0.347355\pi$
$648$	−8.17226e14	+	6.24125e14i	−0.280983	+	0.214590i
$649$	−4.68228e15	−	2.70331e15i	−1.59629	−	0.921618i
$650$	5.17473e14			0.174930
$651$	−8.72124e14	−	6.94778e14i	−0.292336	−	0.232890i
$652$	−1.45127e15			−0.482378
$653$	1.67755e15	+	9.68533e14i	0.552907	+	0.319221i	0.750294	−	0.661104i	$-0.229912\pi$
$653$	1.67755e15	+	9.68533e14i	0.552907	+	0.319221i	−0.197386	+	0.980326i	$0.563245\pi$
$654$	−1.54175e15	−	2.48249e15i	−0.503891	−	0.811354i
$655$	−2.15970e15	−	3.74071e15i	−0.699948	−	1.21235i
$656$	6.55474e14	−	1.13531e15i	0.210661	−	0.364876i
$657$	−1.56696e14	−	2.43322e15i	−0.0499400	−	0.775482i
$658$	4.32495e14	+	1.21358e15i	0.136691	+	0.383553i
$659$		−	2.02171e15i		−	0.633649i	−0.948484	−	0.316825i	$-0.897383\pi$
$659$		−	2.02171e15i		−	0.633649i	0.948484	−	0.316825i	$-0.102617\pi$
$660$	−9.84702e14	+	1.83972e15i	−0.306065	+	0.571822i
$661$	2.93692e15	−	1.69563e15i	0.905284	−	0.522666i	0.0263731	−	0.999652i	$-0.491604\pi$
$661$	2.93692e15	−	1.69563e15i	0.905284	−	0.522666i	0.878911	+	0.476986i	$0.158271\pi$
$662$	−2.17329e15	+	1.25475e15i	−0.664353	+	0.383565i
$663$	−1.71971e15	+	3.21294e15i	−0.521351	+	0.974042i
$664$		−	2.00913e15i		−	0.604064i
$665$	−2.46438e15	−	6.91503e15i	−0.734833	−	2.06194i
$666$	−6.03149e13	−	9.36586e14i	−0.0178368	−	0.276974i
$667$	−1.46745e14	+	2.54170e14i	−0.0430400	+	0.0745474i
$668$	1.48537e15	+	2.57273e15i	0.432079	+	0.748383i
$669$	−2.99661e15	−	4.82507e15i	−0.864542	−	1.39207i
$670$	2.48210e15	+	1.43304e15i	0.710243	+	0.410059i
$671$	5.60910e14			0.159191
$672$	−4.91183e14	−	3.91301e14i	−0.138265	−	0.110149i
$673$	−4.57617e14			−0.127767			−0.0638835	−	0.997957i	$-0.520349\pi$
$673$	−4.57617e14			−0.127767			−0.0638835	+	0.997957i	$0.520349\pi$
$674$	−1.42470e15	−	8.22551e14i	−0.394543	−	0.227789i
$675$	−9.41675e14	+	6.72361e14i	−0.258661	+	0.184685i
$676$	3.61652e14	+	6.26399e14i	0.0985334	+	0.170665i
$677$	−1.60538e14	+	2.78060e14i	−0.0433851	+	0.0751452i	−0.886903	−	0.461957i	$-0.847148\pi$
$677$	−1.60538e14	+	2.78060e14i	−0.0433851	+	0.0751452i	0.843517	+	0.537102i	$0.180481\pi$
$678$	8.72154e13	+	2.71141e15i	0.0233792	+	0.726829i
$679$	−6.65636e15	−	1.21986e15i	−1.76992	−	0.324360i
$680$			2.18411e15i			0.576071i
$681$	−2.22432e15	−	1.19056e15i	−0.581954	−	0.311488i
$682$	9.96529e14	−	5.75346e14i	0.258628	−	0.149319i
$683$	6.82405e14	−	3.93987e14i	0.175683	−	0.101430i	−0.409580	−	0.912274i	$-0.634325\pi$
$683$	6.82405e14	−	3.93987e14i	0.175683	−	0.101430i	0.585263	+	0.810844i	$0.300991\pi$
$684$	3.34637e15	+	1.65499e15i	0.854606	+	0.422657i
$685$		−	6.45757e13i		−	0.0163595i
$686$	2.46454e15	−	1.35742e15i	0.619374	−	0.341139i
$687$	2.48237e15	−	7.98481e13i	0.618878	−	0.0199069i
$688$	2.55995e14	−	4.43396e14i	0.0633133	−	0.109662i
$689$	1.43095e15	+	2.47847e15i	0.351089	+	0.608104i
$690$	−1.08116e15	+	6.71455e14i	−0.263160	+	0.163436i
$691$	−2.11082e15	−	1.21868e15i	−0.509707	−	0.294280i	0.223006	−	0.974817i	$-0.428413\pi$
$691$	−2.11082e15	−	1.21868e15i	−0.509707	−	0.294280i	−0.732713	+	0.680537i	$0.761746\pi$
$692$	−1.84386e14			−0.0441718
$693$	4.72195e15	+	5.54723e14i	1.12225	+	0.131839i
$694$	3.06826e14			0.0723462
$695$	5.31878e15	+	3.07080e15i	1.24422	+	0.718348i
$696$	2.91898e14	−	1.81283e14i	0.0677455	−	0.0420733i
$697$	5.19418e15	+	8.99658e15i	1.19601	+	2.07156i
$698$	3.63176e13	−	6.29040e13i	0.00829684	−	0.0143705i
$699$	3.53237e15	−	1.13622e14i	0.800648	−	0.0257537i
$700$	−5.38255e14	−	4.57848e14i	−0.121046	−	0.102963i
$701$			2.76465e15i			0.616866i	0.951246	+	0.308433i	$0.0998046\pi$
$701$			2.76465e15i			0.616866i	−0.951246	+	0.308433i	$0.900195\pi$
$702$	2.26279e15	+	1.02992e15i	0.500945	+	0.228008i
$703$	−2.95085e15	+	1.70367e15i	−0.648176	+	0.374225i
$704$	5.61248e14	−	3.24037e14i	0.122322	−	0.0706227i
$705$	−2.69507e15	−	1.44252e15i	−0.582814	−	0.311948i
$706$			9.07842e14i			0.194798i
$707$	4.51276e15	−	1.60826e15i	0.960805	−	0.342412i
$708$	1.24120e14	+	3.85873e15i	0.0262216	+	0.815195i
$709$	2.02799e15	−	3.51259e15i	0.425121	−	0.736330i	−0.571311	−	0.820734i	$-0.693565\pi$
$709$	2.02799e15	−	3.51259e15i	0.425121	−	0.736330i	0.996432	+	0.0844032i	$0.0268984\pi$
$710$	2.10249e15	+	3.64161e15i	0.437333	+	0.757483i
$711$	2.34122e15	+	3.51255e15i	0.483237	+	0.725002i
$712$	−2.16051e14	−	1.24737e14i	−0.0442503	−	0.0255479i
$713$	7.01825e14			0.142638
$714$	4.63151e15	−	1.82042e15i	0.934076	−	0.367140i
$715$	5.04505e15			1.00968
$716$	1.63840e15	+	9.45932e14i	0.325386	+	0.187862i
$717$	−2.39773e15	−	3.86077e15i	−0.472547	−	0.760883i
$718$	−3.11351e15	−	5.39276e15i	−0.608928	−	1.05469i
$719$	3.97543e15	−	6.88564e15i	0.771569	−	1.33640i	−0.165134	−	0.986271i	$-0.552806\pi$
$719$	3.97543e15	−	6.88564e15i	0.771569	−	1.33640i	0.936703	−	0.350125i	$-0.113861\pi$
$720$	1.48696e15	−	9.57583e13i	0.286398	−	0.0184437i
$721$	−1.01964e15	+	1.19871e15i	−0.194896	+	0.229124i
$722$		−	9.82603e15i		−	1.86390i
$723$	1.52885e15	−	2.85635e15i	0.287808	−	0.537714i
$724$	−3.43907e15	+	1.98555e15i	−0.642508	+	0.370952i
$725$	3.34843e14	−	1.93321e14i	0.0620843	−	0.0358444i
$726$	−5.01974e14	+	9.37841e14i	−0.0923697	+	0.172575i
$727$			5.49389e15i			1.00332i	0.865064	+	0.501662i	$0.167278\pi$
$727$			5.49389e15i			1.00332i	−0.865064	+	0.501662i	$0.832722\pi$
$728$	−2.73695e14	+	1.49346e15i	−0.0496072	+	0.270689i
$729$	−5.45592e15	+	1.06587e15i	−0.981447	+	0.191735i
$730$	−1.76657e15	+	3.05978e15i	−0.315395	+	0.546280i
$731$	2.02858e15	+	3.51361e15i	0.359457	+	0.622598i
$732$	−2.11313e14	−	3.40252e14i	−0.0371634	−	0.0598397i
$733$	−3.83186e15	−	2.21233e15i	−0.668864	−	0.386169i	0.126782	−	0.991931i	$-0.459535\pi$
$733$	−3.83186e15	−	2.21233e15i	−0.668864	−	0.386169i	−0.795646	+	0.605762i	$0.792868\pi$
$734$	9.99605e14			0.173181
$735$	−2.16548e15	+	6.31493e15i	−0.372369	+	1.08590i
$736$	3.95270e14			0.0674631
$737$	5.83618e15	+	3.36952e15i	0.988684	+	0.570817i
$738$	5.89720e15	−	3.93067e15i	0.991599	−	0.660932i
$739$	4.62948e15	+	8.01850e15i	0.772660	+	1.33829i	0.936100	+	0.351733i	$0.114407\pi$
$739$	4.62948e15	+	8.01850e15i	0.772660	+	1.33829i	−0.163441	+	0.986553i	$0.552259\pi$
$740$	−6.79981e14	+	1.17776e15i	−0.112648	+	0.195111i
$741$	−2.90182e14	−	9.02139e15i	−0.0477168	−	1.48345i
$742$	7.04477e14	−	3.84408e15i	0.114986	−	0.627438i
$743$			9.84819e15i			1.59558i	0.602937	+	0.797789i	$0.293997\pi$
$743$			9.84819e15i			1.59558i	−0.602937	+	0.797789i	$0.706003\pi$
$744$	−7.24434e14	−	3.87749e14i	−0.116506	−	0.0623591i
$745$	7.54176e15	−	4.35424e15i	1.20396	−	0.695109i
$746$	2.25604e15	−	1.30252e15i	0.357506	−	0.206406i
$747$	4.81503e15	−	9.73593e15i	0.757419	−	1.53149i
$748$			5.13553e15i			0.801912i
$749$	−4.66732e15	+	5.48701e15i	−0.723466	+	0.850522i
$750$	−3.59684e15	+	1.15696e14i	−0.553458	+	0.0178025i
$751$	3.24474e15	−	5.62005e15i	0.495633	−	0.858462i	−0.504354	−	0.863497i	$-0.668269\pi$
$751$	3.24474e15	−	5.62005e15i	0.495633	−	0.858462i	0.999987	+	0.00503520i	$0.00160276\pi$
$752$	4.74692e14	+	8.22190e14i	0.0719803	+	0.124674i
$753$	−8.23663e15	+	5.11536e15i	−1.23987	+	0.770023i
$754$	−7.19461e14	−	4.15381e14i	−0.107514	−	0.0620732i
$755$	−4.30438e15			−0.638561
$756$	−1.44241e15	−	3.07335e15i	−0.212432	−	0.452629i
$757$	2.47404e15			0.361726			0.180863	−	0.983508i	$-0.442111\pi$
$757$	2.47404e15			0.361726			0.180863	+	0.983508i	$0.442111\pi$
$758$	−5.38810e15	−	3.11082e15i	−0.782087	−	0.451538i
$759$	−2.54215e15	+	1.57880e15i	−0.366329	+	0.227508i
$760$	−2.70482e15	−	4.68489e15i	−0.386958	−	0.670231i
$761$	−1.42429e15	+	2.46694e15i	−0.202294	+	0.350383i	−0.949267	−	0.314471i	$-0.898173\pi$
$761$	−1.42429e15	+	2.46694e15i	−0.202294	+	0.350383i	0.746973	+	0.664854i	$0.231506\pi$
$762$	5.83050e15	−	1.87544e14i	0.822154	−	0.0264454i
$763$	9.08829e15	−	3.23889e15i	1.27232	−	0.453430i
$764$			4.62658e13i			0.00643053i
$765$	−5.23441e15	+	1.05839e16i	−0.722320	+	1.46052i
$766$	−2.53006e15	+	1.46073e15i	−0.346636	+	0.200130i
$767$	8.08369e15	−	4.66712e15i	1.09960	−	0.634855i
$768$	−4.08004e14	−	2.18382e14i	−0.0551033	−	0.0294937i
$769$			2.39551e15i			0.321221i	0.987018	+	0.160610i	$0.0513463\pi$
$769$			2.39551e15i			0.321221i	−0.987018	+	0.160610i	$0.948654\pi$
$770$	−5.24767e15	−	4.46374e15i	−0.698663	−	0.594292i
$771$	−1.23301e14	−	3.83326e15i	−0.0162992	−	0.506722i
$772$	4.80578e14	−	8.32385e14i	0.0630767	−	0.109252i
$773$	1.30633e15	+	2.26263e15i	0.170242	+	0.294867i	0.938504	−	0.345267i	$-0.112212\pi$
$773$	1.30633e15	+	2.26263e15i	0.170242	+	0.294867i	−0.768263	+	0.640135i	$0.778878\pi$
$774$	2.30315e15	−	1.53512e15i	0.298021	−	0.198640i
$775$	−8.00711e14	−	4.62291e14i	−0.102877	−	0.0593958i
$776$	−4.98678e15			−0.636181
$777$	3.06425e15	+	4.60284e14i	0.388157	+	0.0583057i
$778$	−8.71537e15			−1.09622
$779$	−2.22828e16	−	1.28650e16i	−2.78301	−	1.60677i
$780$	−1.90064e15	−	3.06036e15i	−0.235711	−	0.379536i
$781$	4.94360e15	+	8.56257e15i	0.608783	+	1.05444i
$782$	−1.56612e15	+	2.71260e15i	−0.191509	+	0.331703i
$783$	1.84896e15	−	1.78915e14i	0.224511	−	0.0217248i
$784$	1.60606e15	−	1.31128e15i	0.193653	−	0.158109i
$785$		−	1.43199e16i		−	1.71457i
$786$	−3.42236e15	+	6.39401e15i	−0.406913	+	0.760237i
$787$	−9.72378e15	+	5.61403e15i	−1.14808	+	0.662847i	−0.948420	−	0.317017i	$-0.897319\pi$
$787$	−9.72378e15	+	5.61403e15i	−1.14808	+	0.662847i	−0.199665	+	0.979864i	$0.563985\pi$
$788$	3.27827e15	−	1.89271e15i	0.384371	−	0.221917i
$789$	3.52247e15	−	6.58105e15i	0.410132	−	0.766252i
$790$		−	6.11682e15i		−	0.707256i
$791$	−8.80987e15	−	1.61452e15i	−1.01158	−	0.185384i
$792$	3.49631e15	−	2.25158e14i	0.398677	−	0.0256743i
$793$	−4.84190e14	+	8.38641e14i	−0.0548293	+	0.0949672i
$794$	3.74550e15	+	6.48739e15i	0.421208	+	0.729554i
$795$	4.89214e15	+	7.87721e15i	0.546361	+	0.879738i
$796$	2.75196e15	+	1.58884e15i	0.305225	+	0.176222i
$797$	−1.57364e16			−1.73335			−0.866674	−	0.498874i	$-0.833747\pi$
$797$	−1.57364e16			−1.73335			−0.866674	+	0.498874i	$0.833747\pi$
$798$	−7.68008e15	+	9.64046e15i	−0.840136	+	1.05459i
$799$	−7.52320e15			−0.817327
$800$	−4.50963e14	−	2.60364e14i	−0.0486571	−	0.0280922i
$801$	−7.48009e14	−	1.12224e15i	−0.0801545	−	0.120256i
$802$	−3.62388e15	−	6.27674e15i	−0.385669	−	0.667998i
$803$	−4.15375e15	+	7.19450e15i	−0.439041	+	0.760441i
$804$	−1.54708e14	−	4.80968e15i	−0.0162407	−	0.504903i
$805$	−1.41058e15	−	3.95808e15i	−0.147069	−	0.412674i
$806$			1.98661e15i			0.205716i
$807$	1.41495e16	+	7.57344e15i	1.45525	+	0.778912i
$808$	3.05736e15	−	1.76517e15i	0.312309	−	0.180311i
$809$	9.47848e15	−	5.47241e15i	0.961661	−	0.555215i	0.0649772	−	0.997887i	$-0.479303\pi$
$809$	9.47848e15	−	5.47241e15i	0.961661	−	0.555215i	0.896684	+	0.442672i	$0.145969\pi$
$810$	7.43508e15	+	3.09959e15i	0.749235	+	0.312346i
$811$		−	5.08111e15i		−	0.508562i	−0.967130	−	0.254281i	$-0.918161\pi$
$811$		−	5.08111e15i		−	0.508562i	0.967130	−	0.254281i	$-0.0818388\pi$
$812$	3.80837e14	+	1.06863e15i	0.0378600	+	0.106235i
$813$	−2.00774e15	+	6.45810e13i	−0.198248	+	0.00637686i
$814$	−1.59885e15	+	2.76928e15i	−0.156810	+	0.271602i
$815$	5.68439e15	+	9.84565e15i	0.553754	+	0.959130i
$816$	3.11525e15	−	1.93473e15i	0.301437	−	0.187208i
$817$	−8.70255e15	−	5.02442e15i	−0.836421	−	0.482908i
$818$	−3.84101e12			−0.000366692
$819$	−4.90548e15	+	6.58114e15i	−0.465179	+	0.624079i
$820$	−1.02695e16			−0.967328
$821$	−1.18852e16	−	6.86190e15i	−1.11203	−	0.642032i	−0.172677	−	0.984978i	$-0.555242\pi$
$821$	−1.18852e16	−	6.86190e15i	−1.11203	−	0.642032i	−0.939355	+	0.342946i	$0.888575\pi$
$822$	−9.21057e13	+	5.72022e13i	−0.00856035	+	0.00531640i
$823$	4.78435e15	+	8.28674e15i	0.441696	+	0.765041i	0.997816	−	0.0660619i	$-0.0210435\pi$
$823$	4.78435e15	+	8.28674e15i	0.441696	+	0.765041i	−0.556119	+	0.831103i	$0.687710\pi$
$824$	−5.79838e14	+	1.00431e15i	−0.0531749	+	0.0921017i
$825$	3.94028e15	−	1.26743e14i	0.358947	−	0.0115459i
$826$	−1.25377e16	−	2.29770e15i	−1.13456	−	0.207923i
$827$			1.11170e16i			0.999322i	0.866221	+	0.499661i	$0.166542\pi$
$827$			1.11170e16i			0.999322i	−0.866221	+	0.499661i	$0.833458\pi$
$828$	1.91542e15	+	9.47297e14i	0.171040	+	0.0845901i
$829$	1.48188e16	−	8.55562e15i	1.31450	−	0.758930i	0.331666	−	0.943397i	$-0.392389\pi$
$829$	1.48188e16	−	8.55562e15i	1.31450	−	0.758930i	0.982839	+	0.184467i	$0.0590559\pi$
$830$	−1.36302e16	+	7.86939e15i	−1.20108	+	0.693445i
$831$	−2.75481e15	−	1.47450e15i	−0.241149	−	0.129074i
$832$			1.11886e15i			0.0972968i
$833$	2.63538e15	+	1.62173e16i	0.227665	+	1.40098i
$834$	−3.31518e14	−	1.03065e16i	−0.0284508	−	0.884497i
$835$	1.16358e16	−	2.01539e16i	0.992024	−	1.71824i
$836$	−6.35987e15	−	1.10156e16i	−0.538659	−	0.932985i
$837$	−2.58123e15	−	3.61514e15i	−0.217188	−	0.304183i
$838$	4.52423e15	+	2.61207e15i	0.378183	+	0.218344i
$839$	−2.19193e16			−1.82027			−0.910137	−	0.414308i	$-0.864023\pi$
$839$	−2.19193e16			−1.82027			−0.910137	+	0.414308i	$0.864023\pi$
$840$	−7.30765e14	+	4.86491e15i	−0.0602895	+	0.401365i
$841$	1.15798e16			0.949123
$842$	1.25818e16	+	7.26409e15i	1.02453	+	0.591513i
$843$	−3.10787e15	−	5.00421e15i	−0.251426	−	0.404841i
$844$	5.27969e14	+	9.14469e14i	0.0424351	+	0.0734997i
$845$	2.83305e15	−	4.90699e15i	0.226226	−	0.391835i
$846$	3.29841e14	+	5.12185e15i	0.0261678	+	0.406340i
$847$	−2.67512e15	−	2.27549e15i	−0.210855	−	0.179356i
$848$		−	2.87989e15i		−	0.225527i
$849$	2.71072e15	−	5.06445e15i	0.210907	−	0.394039i
$850$	3.57357e15	−	2.06320e15i	0.276247	−	0.159491i
$851$	−1.68903e15	+	9.75162e14i	−0.129725	+	0.0748970i
$852$	3.33169e15	−	6.22463e15i	0.254242	−	0.475002i
$853$			1.05655e16i			0.801071i	0.916281	+	0.400535i	$0.131176\pi$
$853$			1.05655e16i			0.801071i	−0.916281	+	0.400535i	$0.868824\pi$
$854$	1.24565e15	−	4.43923e14i	0.0938375	−	0.0334418i
$855$	−1.87945e15	−	2.91846e16i	−0.140675	−	2.18444i
$856$	−2.65416e15	+	4.59714e15i	−0.197388	+	0.341887i
$857$	1.84229e15	+	3.19094e15i	0.136133	+	0.235789i	0.926030	−	0.377451i	$-0.123199\pi$
$857$	1.84229e15	+	3.19094e15i	0.136133	+	0.235789i	−0.789897	+	0.613240i	$0.789866\pi$
$858$	−4.46899e15	−	7.19587e15i	−0.328118	−	0.528327i
$859$	2.35691e16	+	1.36076e16i	1.71941	+	0.992703i	0.919998	+	0.391923i	$0.128190\pi$
$859$	2.35691e16	+	1.36076e16i	1.71941	+	0.992703i	0.799414	+	0.600780i	$0.205143\pi$
$860$	−4.01075e15			−0.290726
$861$	8.55946e15	+	2.17769e16i	0.616494	+	1.56848i
$862$	1.28211e16			0.917559
$863$	1.52179e16	+	8.78608e15i	1.08217	+	0.624792i	0.931481	−	0.363789i	$-0.118517\pi$
$863$	1.52179e16	+	8.78608e15i	1.08217	+	0.624792i	0.150690	+	0.988581i	$0.451850\pi$
$864$	−1.45376e15	−	2.03606e15i	−0.102723	−	0.143868i
$865$	7.22209e14	+	1.25090e15i	0.0507077	+	0.0878283i
$866$	1.10222e14	−	1.90910e14i	0.00768989	−	0.0133193i
$867$	4.70504e14	+	1.46274e16i	0.0326181	+	1.01405i
$868$	1.75770e15	−	2.06639e15i	0.121084	−	0.142349i
$869$		−	1.43826e16i		−	0.984526i
$870$	−2.37317e15	−	1.27022e15i	−0.161426	−	0.0864021i
$871$	−1.00758e16	+	5.81729e15i	−0.681054	+	0.393207i
$872$	6.15725e15	−	3.55489e15i	0.413567	−	0.238773i
$873$	−2.41652e16	−	1.19512e16i	−1.61292	−	0.797690i
$874$		−	7.75798e15i		−	0.514560i
$875$	2.14175e15	−	1.16868e16i	0.141164	−	0.770284i
$876$	5.92909e15	−	1.90715e14i	0.388343	−	0.0124915i
$877$	−6.51581e15	+	1.12857e16i	−0.424103	+	0.734567i	−0.996336	−	0.0855234i	$-0.972744\pi$
$877$	−6.51581e15	+	1.12857e16i	−0.424103	+	0.734567i	0.572234	+	0.820091i	$0.306077\pi$
$878$	9.26518e15	+	1.60478e16i	0.599286	+	1.03799i
$879$	−7.85326e15	+	4.87726e15i	−0.504790	+	0.313500i
$880$	−4.39662e15	−	2.53839e15i	−0.280844	−	0.162145i
$881$	−6.38611e15			−0.405386			−0.202693	−	0.979242i	$-0.564969\pi$
$881$	−6.38611e15			−0.405386			−0.202693	+	0.979242i	$0.564969\pi$
$882$	1.09253e16	−	2.50520e15i	0.689220	−	0.158039i
$883$	−5.48317e15			−0.343754			−0.171877	−	0.985118i	$-0.554983\pi$
$883$	−5.48317e15			−0.343754			−0.171877	+	0.985118i	$0.554983\pi$
$884$	−7.67836e15	−	4.43310e15i	−0.478389	−	0.276198i
$885$	2.56920e16	−	1.59560e16i	1.59078	−	0.987954i
$886$	−7.30210e14	−	1.26476e15i	−0.0449327	−	0.0778257i
$887$	−5.92970e15	+	1.02705e16i	−0.362621	+	0.628078i	−0.988391	−	0.151929i	$-0.951451\pi$
$887$	−5.92970e15	+	1.02705e16i	−0.362621	+	0.628078i	0.625770	+	0.780007i	$0.284785\pi$
$888$	2.28221e15	−	7.34095e13i	0.138702	−	0.00446150i
$889$	−3.47179e15	+	1.89443e16i	−0.209698	+	1.14425i
$890$			1.95429e15i			0.117313i
$891$	1.74822e16	+	7.28810e15i	1.04296	+	0.434797i
$892$	1.19675e16	−	6.90942e15i	0.709570	−	0.409670i
$893$	1.61371e16	−	9.31678e15i	0.950919	−	0.549013i
$894$	−1.28912e16	−	6.89992e15i	−0.754981	−	0.404099i
$895$		−	1.48202e16i		−	0.862636i
$896$	9.89943e14	−	1.16380e15i	0.0572686	−	0.0673262i
$897$	−1.66097e14	−	5.16373e15i	−0.00954998	−	0.296897i
$898$	−3.07040e15	+	5.31809e15i	−0.175459	+	0.303904i
$899$	7.42172e14	+	1.28548e15i	0.0421528	+	0.0730107i
$900$	−1.56132e15	−	2.34245e15i	−0.0881369	−	0.132232i
$901$	1.97637e16	+	1.14106e16i	1.10887	+	0.640208i
$902$	−2.41468e16			−1.34655
$903$	3.34289e15	+	8.50497e15i	0.185285	+	0.471401i
$904$	−6.60014e15			−0.363602
$905$	2.69405e16	+	1.55541e16i	1.47516	+	0.851682i
$906$	3.81289e15	+	6.13943e15i	0.207515	+	0.334136i
$907$	−1.78697e16	−	3.09513e16i	−0.966668	−	1.67432i	−0.705064	−	0.709144i	$-0.749082\pi$
$907$	−1.78697e16	−	3.09513e16i	−0.966668	−	1.67432i	−0.261605	−	0.965175i	$-0.584252\pi$
$908$	3.06905e15	−	5.31574e15i	0.165018	−	0.285820i
$909$	1.90459e16	−	1.22653e15i	1.01789	−	0.0655506i
$910$	1.12038e16	−	3.99282e15i	0.595168	−	0.212106i
$911$		−	2.65304e15i		−	0.140085i	−0.997544	−	0.0700427i	$-0.977686\pi$
$911$		−	2.65304e15i		−	0.140085i	0.997544	−	0.0700427i	$-0.0223136\pi$
$912$	−4.28618e15	+	8.00790e15i	−0.224957	+	0.420288i
$913$	−3.20488e16	+	1.85034e16i	−1.67195	+	0.965300i
$914$	2.03478e16	−	1.17478e16i	1.05515	−	0.609189i
$915$	−1.48064e15	+	2.76629e15i	−0.0763191	+	0.142587i
$916$			6.04261e15i			0.309599i
$917$	−1.82384e16	−	1.55138e16i	−0.928872	−	0.790111i
$918$	1.97328e16	−	1.90944e15i	0.998972	−	0.0966657i
$919$	−4.13737e15	+	7.16613e15i	−0.208204	+	0.360620i	−0.951149	−	0.308733i	$-0.900095\pi$
$919$	−4.13737e15	+	7.16613e15i	−0.208204	+	0.360620i	0.742945	+	0.669352i	$0.233428\pi$
$920$	−1.54820e15	−	2.68157e15i	−0.0774454	−	0.134139i
$921$	−1.91886e15	−	3.08971e15i	−0.0954149	−	0.153635i
$922$	2.17954e16	+	1.25836e16i	1.07732	+	0.621991i
$923$	−1.70697e16			−0.838719
$924$	−1.71826e15	+	1.14389e16i	−0.0839252	+	0.558714i
$925$	2.56935e15			0.124751
$926$	1.53663e16	+	8.87172e15i	0.741666	+	0.428201i
$927$	−5.21672e15	+	3.47710e15i	−0.250299	+	0.166832i
$928$	4.17993e14	+	7.23986e14i	0.0199368	+	0.0345316i
$929$	1.76195e15	−	3.05180e15i	0.0835427	−	0.144700i	−0.821227	−	0.570602i	$-0.806710\pi$
$929$	1.76195e15	−	3.05180e15i	0.0835427	−	0.144700i	0.904769	+	0.425902i	$0.140043\pi$
$930$	2.06937e14	+	6.43341e15i	0.00975400	+	0.303239i
$931$	−2.57365e16	−	3.15222e16i	−1.20594	−	1.47705i
$932$			8.59852e15i			0.400531i
$933$	1.48567e16	+	7.95197e15i	0.687977	+	0.368235i
$934$	−2.19045e16	+	1.26466e16i	−1.00839	+	0.582191i
$935$	3.48402e16	−	2.01150e16i	1.59447	−	0.920568i
$936$	−2.68145e15	+	5.42184e15i	−0.121998	+	0.246678i
$937$		−	8.54415e15i		−	0.386457i	−0.981154	−	0.193228i	$-0.938104\pi$
$937$		−	8.54415e15i		−	0.386457i	0.981154	−	0.193228i	$-0.0618959\pi$
$938$	1.56275e16	+	2.86394e15i	0.702707	+	0.128780i
$939$	1.35901e16	−	4.37140e14i	0.607523	−	0.0195416i
$940$	3.71857e15	−	6.44075e15i	0.165262	−	0.286242i
$941$	1.38257e16	+	2.39469e16i	0.610866	+	1.05805i	0.991095	+	0.133158i	$0.0425118\pi$
$941$	1.38257e16	+	2.39469e16i	0.610866	+	1.05805i	−0.380229	+	0.924892i	$0.624155\pi$
$942$	−2.04248e16	+	1.26848e16i	−0.897175	+	0.557190i
$943$	−1.27544e16	−	7.36377e15i	−0.556989	−	0.321578i
$944$	−9.39295e15			−0.407808
$945$	−1.52003e16	+	2.18233e16i	−0.656113	+	0.941989i
$946$	−9.43053e15			−0.404701
$947$	2.04518e16	+	1.18079e16i	0.872583	+	0.503786i	0.868206	−	0.496205i	$-0.165273\pi$
$947$	2.04518e16	+	1.18079e16i	0.872583	+	0.503786i	0.00437709	+	0.999990i	$0.498607\pi$
$948$	−8.72456e15	+	5.41839e15i	−0.370082	+	0.229839i
$949$	−7.17122e15	−	1.24209e16i	−0.302433	−	0.523829i
$950$	−5.11016e15	+	8.85106e15i	−0.214267	+	0.371121i
$951$	−2.01313e15	+	6.47545e13i	−0.0839227	+	0.00269946i
$952$	4.06444e15	+	1.14048e16i	0.168460	+	0.472698i
$953$		−	1.47620e16i		−	0.608325i	−0.952620	−	0.304162i	$-0.901623\pi$
$953$		−	1.47620e16i		−	0.608325i	0.952620	−	0.304162i	$-0.0983765\pi$
$954$	6.90190e15	−	1.39555e16i	0.282782	−	0.571782i
$955$	3.13874e14	−	1.81215e14i	0.0127860	−	0.00738203i
$956$	9.57574e15	−	5.52855e15i	0.387841	−	0.223920i
$957$	−5.58005e15	−	2.98669e15i	−0.224710	−	0.120275i
$958$			2.42831e16i			0.972286i
$959$	−1.20169e14	−	3.37195e14i	−0.00478400	−	0.0134239i
$960$	1.16548e14	+	3.62332e15i	0.00461331	+	0.143422i
$961$	−1.09295e16	+	1.89304e16i	−0.430151	+	0.745043i
$962$	−2.76032e15	−	4.78101e15i	−0.108018	−	0.187093i
$963$	−2.38791e16	+	1.59162e16i	−0.929123	+	0.619289i
$964$	6.82618e15	+	3.94110e15i	0.264091	+	0.152473i
$965$	−7.52936e15			−0.289640
$966$	−4.39598e15	+	5.51808e15i	−0.168144	+	0.211064i
$967$	−1.71796e16			−0.653381			−0.326691	−	0.945131i	$-0.605934\pi$
$967$	−1.71796e16			−0.653381			−0.326691	+	0.945131i	$0.605934\pi$
$968$	−2.24128e15	−	1.29400e15i	−0.0847580	−	0.0489351i
$969$	−3.79729e16	−	6.11431e16i	−1.42788	−	2.29915i
$970$	1.95324e16	+	3.38310e16i	0.730315	+	1.26494i
$971$	−4.41883e14	+	7.65363e14i	−0.0164286	+	0.0284552i	−0.874123	−	0.485705i	$-0.838563\pi$
$971$	−4.41883e14	+	7.65363e14i	−0.0164286	+	0.0284552i	0.857694	+	0.514160i	$0.171896\pi$
$972$	−2.16511e15	−	1.33505e16i	−0.0800415	−	0.493552i
$973$	3.34875e16	+	6.13702e15i	1.23101	+	0.225599i
$974$		−	1.72276e16i		−	0.629726i
$975$	−3.21184e15	+	6.00070e15i	−0.116742	+	0.218110i
$976$	8.43916e14	−	4.87235e14i	0.0305018	−	0.0176102i
$977$	−2.95352e16	+	1.70522e16i	−1.06150	+	0.612858i	−0.925847	−	0.377898i	$-0.876647\pi$
$977$	−2.95352e16	+	1.70522e16i	−1.06150	+	0.612858i	−0.135654	+	0.990756i	$0.543314\pi$
$978$	9.00774e15	−	1.68292e16i	0.321923	−	0.601451i
$979$			4.59515e15i			0.163303i
$980$	−1.51866e16	−	5.75971e15i	−0.536681	−	0.203544i
$981$	3.83567e16	−	2.47012e15i	1.34791	−	0.0868039i
$982$	1.56823e16	−	2.71626e16i	0.548022	−	0.949201i
$983$	9.94911e15	+	1.72324e16i	0.345732	+	0.598826i	0.985487	−	0.169754i	$-0.0542972\pi$
$983$	9.94911e15	+	1.72324e16i	0.345732	+	0.598826i	−0.639754	+	0.768580i	$0.720964\pi$
$984$	9.09691e15	+	1.46476e16i	0.314355	+	0.506168i
$985$	−2.56808e16	−	1.48268e16i	−0.882490	−	0.509506i
$986$	−6.62461e15			−0.226380
$987$	−1.67573e16	−	2.51713e15i	−0.569454	−	0.0855384i
$988$	2.19599e16			0.742109
$989$	−4.98123e15	−	2.87591e15i	−0.167401	−	0.0966488i
$990$	−1.52219e16	−	2.28375e16i	−0.508717	−	0.763230i
$991$	−1.89409e16	−	3.28066e16i	−0.629500	−	1.09033i	−0.987652	−	0.156663i	$-0.949927\pi$
$991$	−1.89409e16	−	3.28066e16i	−0.629500	−	1.09033i	0.358152	−	0.933663i	$-0.383407\pi$
$992$	9.99550e14	−	1.73127e15i	0.0330362	−	0.0572204i
$993$	−1.06115e15	−	3.29898e16i	−0.0348784	−	1.08432i
$994$	1.77553e16	+	1.51029e16i	0.580366	+	0.493667i
$995$		−	2.48929e16i		−	0.809187i
$996$	2.32982e16	+	1.24702e16i	0.753174	+	0.403132i
$997$	−3.77019e16	+	2.17672e16i	−1.21211	+	0.699809i	−0.963218	−	0.268723i	$-0.913398\pi$
$997$	−3.77019e16	+	2.17672e16i	−1.21211	+	0.699809i	−0.248888	+	0.968532i	$0.580065\pi$
$998$	1.08195e16	−	6.24665e15i	0.345931	−	0.199724i
$999$	1.12352e16	+	5.11376e15i	0.357248	+	0.162604i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.13	✓	60
3.2	odd	2	inner	42.12.f.a.5.29	yes	60
7.3	odd	6	inner	42.12.f.a.17.29	yes	60
21.17	even	6	inner	42.12.f.a.17.13	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.13	✓	60	1.1	even	1	trivial
42.12.f.a.5.29	yes	60	3.2	odd	2	inner
42.12.f.a.17.13	yes	60	21.17	even	6	inner
42.12.f.a.17.29	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} +(357.546 - 222.054i) q^{3} +(512.000 + 886.810i) q^{4} +(4010.83 - 6946.96i) q^{5} +(-13461.5 + 433.002i) q^{6} +(8015.68 - 43738.7i) q^{7} -32768.0i q^{8} +(78531.2 - 158789. i) q^{9} +(-222303. + 128347. i) q^{10} +(-522703. + 301783. i) q^{11} +(379983. + 203384. i) q^{12} -1.04202e6i q^{13} +(-921957. + 1.08387e6i) q^{14} +(-108544. - 3.37448e6i) q^{15} +(-524288. + 908093. i) q^{16} +(-4.15462e6 - 7.19601e6i) q^{17} +(-4.71694e6 + 3.14399e6i) q^{18} +(1.78232e7 + 1.02902e7i) q^{19} +8.21418e6 q^{20} +(-6.84638e6 - 1.74185e7i) q^{21} +1.93141e7 q^{22} +(1.02018e7 + 5.88999e6i) q^{23} +(-7.27626e6 - 1.17161e7i) q^{24} +(-7.75944e6 - 1.34397e7i) q^{25} +(-1.66724e7 + 2.88774e7i) q^{26} +(-7.18118e6 - 7.42125e7i) q^{27} +(4.28920e7 - 1.52858e7i) q^{28} +2.49144e7i q^{29} +(-5.09836e7 + 9.52530e7i) q^{30} +(5.15959e7 - 2.97889e7i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(-1.19878e8 + 2.23969e8i) q^{33} +2.65896e8i q^{34} +(-2.71702e8 - 2.31113e8i) q^{35} +(1.81024e8 - 1.16577e7i) q^{36} +(-8.27814e7 + 1.43382e8i) q^{37} +(-3.29287e8 - 5.70341e8i) q^{38} +(-2.31385e8 - 3.72571e8i) q^{39} +(-2.27638e8 - 1.31427e8i) q^{40} -1.25022e9 q^{41} +(-8.89639e7 + 5.92258e8i) q^{42} -4.88272e8 q^{43} +(-5.35248e8 - 3.09026e8i) q^{44} +(-7.88125e8 - 1.18243e9i) q^{45} +(-1.88480e8 - 3.26456e8i) q^{46} +(4.52701e8 - 7.84102e8i) q^{47} +(1.41886e7 + 4.41105e8i) q^{48} +(-1.84882e9 - 7.01191e8i) q^{49} +4.96604e8i q^{50} +(-3.08337e9 - 1.65035e9i) q^{51} +(9.24076e8 - 5.33515e8i) q^{52} +(-2.37852e9 + 1.37324e9i) q^{53} +(-9.88389e8 + 2.17154e9i) q^{54} +4.84160e9i q^{55} +(-1.43323e9 - 2.62658e8i) q^{56} +(8.65758e9 - 2.78480e8i) q^{57} +(3.98630e8 - 6.90447e8i) q^{58} +(4.47891e9 + 7.75770e9i) q^{59} +(2.93695e9 - 1.82399e9i) q^{60} +(-8.04821e8 - 4.64664e8i) q^{61} -1.90649e9 q^{62} +(-6.31574e9 - 4.70765e9i) q^{63} -1.07374e9 q^{64} +(-7.23889e9 - 4.17937e9i) q^{65} +(6.90568e9 - 4.28877e9i) q^{66} +(-5.58269e9 - 9.66951e9i) q^{67} +(4.25433e9 - 7.36871e9i) q^{68} +(4.95549e9 - 1.59399e8i) q^{69} +(3.83180e9 + 1.07520e10i) q^{70} -1.63813e10i q^{71} +(-5.20319e9 - 2.57331e9i) q^{72} +(1.19200e10 - 6.88202e9i) q^{73} +(4.58821e9 - 2.64900e9i) q^{74} +(-5.75870e9 - 3.08231e9i) q^{75} +2.10743e10i q^{76} +(9.00977e9 + 2.52814e10i) q^{77} +(4.51198e8 + 1.40271e10i) q^{78} +(-1.19147e10 + 2.06368e10i) q^{79} +(4.20566e9 + 7.28442e9i) q^{80} +(-1.90468e10 - 2.49398e10i) q^{81} +(3.46470e10 + 2.00035e10i) q^{82} +6.13137e10 q^{83} +(1.19416e10 - 1.49897e10i) q^{84} -6.66539e10 q^{85} +(1.35314e10 + 7.81235e9i) q^{86} +(5.53233e9 + 8.90802e9i) q^{87} +(9.88882e9 + 1.71279e10i) q^{88} +(3.80667e9 - 6.59335e9i) q^{89} +(2.92231e9 + 4.53784e10i) q^{90} +(-4.55767e10 - 8.35252e9i) q^{91} +1.20627e10i q^{92} +(1.18332e10 - 2.21080e10i) q^{93} +(-2.50913e10 + 1.44864e10i) q^{94} +(1.42971e11 - 8.25446e10i) q^{95} +(6.66448e9 - 1.24513e10i) q^{96} -1.52185e11i q^{97} +(4.00171e10 + 4.90132e10i) q^{98} +(6.87126e9 + 1.06699e11i) 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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