LMFDB - Embedded newform 80.12.j.a.67.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,12,Mod(43,80)] 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("80.43"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 3])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	80.j (of order $4$, 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:	$61.4674544448$
Analytic rank:	$0$
Dimension:	$260$
Relative dimension:	$130$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			67.16
Character	$\chi$	$=$	80.67
Dual form			80.12.j.a.43.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-41.9762 - 16.9115i) q^{2} -792.470i q^{3} +(1476.00 + 1419.76i) q^{4} +(6967.42 - 532.099i) q^{5} +(-13401.9 + 33264.9i) q^{6} +(40707.4 + 40707.4i) q^{7} +(-37946.5 - 84557.6i) q^{8} -450861. q^{9} +(-301465. - 95494.2i) q^{10} +(564272. + 564272. i) q^{11} +(1.12512e6 - 1.16969e6i) q^{12} -1.54176e6 q^{13} +(-1.02032e6 - 2.39717e6i) q^{14} +(-421673. - 5.52147e6i) q^{15} +(162853. + 4.19114e6i) q^{16} +(-4.72377e6 - 4.72377e6i) q^{17} +(1.89254e7 + 7.62475e6i) q^{18} +(4.10340e6 + 4.10340e6i) q^{19} +(1.10394e7 + 9.10671e6i) q^{20} +(3.22594e7 - 3.22594e7i) q^{21} +(-1.41433e7 - 3.32287e7i) q^{22} +(-5.99280e6 + 5.99280e6i) q^{23} +(-6.70094e7 + 3.00715e7i) q^{24} +(4.82619e7 - 7.41472e6i) q^{25} +(6.47173e7 + 2.60735e7i) q^{26} +2.16910e8i q^{27} +(2.28931e6 + 1.17879e8i) q^{28} +(-1.32874e8 + 1.32874e8i) q^{29} +(-7.56763e7 + 2.38902e8i) q^{30} +1.59076e8i q^{31} +(6.40426e7 - 1.78682e8i) q^{32} +(4.47169e8 - 4.47169e8i) q^{33} +(1.18400e8 + 2.78172e8i) q^{34} +(3.05286e8 + 2.61966e8i) q^{35} +(-6.65472e8 - 6.40116e8i) q^{36} +2.21122e8 q^{37} +(-1.02850e8 - 2.41640e8i) q^{38} +1.22180e9i q^{39} +(-3.09383e8 - 5.68958e8i) q^{40} -1.39383e8i q^{41} +(-1.89968e9 + 8.08571e8i) q^{42} +7.79378e8 q^{43} +(3.17337e7 + 1.63400e9i) q^{44} +(-3.14134e9 + 2.39903e8i) q^{45} +(3.52902e8 - 1.50208e8i) q^{46} +(8.64652e8 - 8.64652e8i) q^{47} +(3.32135e9 - 1.29056e8i) q^{48} +1.33686e9i q^{49} +(-2.15124e9 - 5.04940e8i) q^{50} +(-3.74345e9 + 3.74345e9i) q^{51} +(-2.27564e9 - 2.18894e9i) q^{52} +2.86989e9i q^{53} +(3.66829e9 - 9.10507e9i) q^{54} +(4.23177e9 + 3.63127e9i) q^{55} +(1.89742e9 - 4.98683e9i) q^{56} +(3.25182e9 - 3.25182e9i) q^{57} +(7.82467e9 - 3.33045e9i) q^{58} +(-1.76583e9 + 1.76583e9i) q^{59} +(7.21679e9 - 8.74837e9i) q^{60} +(5.93306e9 + 5.93306e9i) q^{61} +(2.69022e9 - 6.67741e9i) q^{62} +(-1.83534e10 - 1.83534e10i) q^{63} +(-5.71005e9 + 6.41734e9i) q^{64} +(-1.07421e10 + 8.20371e8i) q^{65} +(-2.63327e10 + 1.12081e10i) q^{66} +1.31443e10 q^{67} +(-2.65657e8 - 1.36789e10i) q^{68} +(4.74911e9 + 4.74911e9i) q^{69} +(-8.38452e9 - 1.61592e10i) q^{70} +1.60442e10 q^{71} +(1.71086e10 + 3.81238e10i) q^{72} +(1.88768e10 + 1.88768e10i) q^{73} +(-9.28184e9 - 3.73950e9i) q^{74} +(-5.87595e9 - 3.82461e10i) q^{75} +(2.30768e8 + 1.18825e10i) q^{76} +4.59401e10i q^{77} +(2.06625e10 - 5.12865e10i) q^{78} +2.36638e10 q^{79} +(3.36477e9 + 2.91148e10i) q^{80} +9.20262e10 q^{81} +(-2.35718e9 + 5.85077e9i) q^{82} -2.53798e10i q^{83} +(9.34156e10 - 1.81421e9i) q^{84} +(-3.54261e10 - 3.03990e10i) q^{85} +(-3.27153e10 - 1.31805e10i) q^{86} +(1.05299e11 + 1.05299e11i) q^{87} +(2.63013e10 - 6.91257e10i) q^{88} -3.26197e10 q^{89} +(1.35919e11 + 4.30547e10i) q^{90} +(-6.27612e10 - 6.27612e10i) q^{91} +(-1.73537e10 + 3.37025e8i) q^{92} +1.26063e11 q^{93} +(-5.09174e10 + 2.16722e10i) q^{94} +(3.07736e10 + 2.64067e10i) q^{95} +(-1.41600e11 - 5.07519e10i) q^{96} +(-4.74034e10 - 4.74034e10i) q^{97} +(2.26084e10 - 5.61164e10i) q^{98} +(-2.54409e11 - 2.54409e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 260 q - 2 q^{2} - 3956 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 74840 q^{8} - 14880348 q^{9} - 4098 q^{10} - 4 q^{11} - 114212 q^{12} - 4 q^{13} + 708588 q^{15} + 5740152 q^{16} - 4 q^{17} - 6791722 q^{18}+ \cdots - 189350900660 q^{99}+O(q^{100}) $ 260 * q - 2 * q^2 - 3956 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 74840 * q^8 - 14880348 * q^9 - 4098 * q^10 - 4 * q^11 - 114212 * q^12 - 4 * q^13 + 708588 * q^15 + 5740152 * q^16 - 4 * q^17 - 6791722 * q^18 - 11291288 * q^19 + 27599212 * q^20 - 4 * q^21 + 11921800 * q^22 - 4 * q^23 + 708588 * q^24 - 196875380 * q^26 + 185066800 * q^28 - 534157704 * q^30 - 894200972 * q^32 - 4 * q^33 - 122727336 * q^34 + 434731680 * q^35 + 917614156 * q^36 - 4 * q^37 - 169550316 * q^38 - 1417066568 * q^40 - 1572161236 * q^42 - 4763690660 * q^43 - 1456070840 * q^44 - 97301958 * q^45 - 3653567828 * q^46 + 5707353192 * q^47 - 447163780 * q^48 + 429408694 * q^50 + 112221284 * q^51 - 4957065880 * q^52 - 10995087044 * q^54 - 4 * q^55 - 8945492140 * q^56 + 708588 * q^57 + 33722126388 * q^58 - 11496390224 * q^59 - 6670533420 * q^60 - 2150827028 * q^61 + 15717297108 * q^62 + 708588 * q^63 - 11018267024 * q^64 - 4 * q^65 - 9909115916 * q^66 + 44333852084 * q^67 - 74998571352 * q^68 + 16194123612 * q^69 + 50947270608 * q^70 - 43677902056 * q^71 - 56634399632 * q^72 + 12278087704 * q^73 - 99553151276 * q^74 + 85400572304 * q^75 + 46613107196 * q^76 + 205137826492 * q^78 + 130159671844 * q^80 + 794986843420 * q^81 + 83904972628 * q^82 + 216982878048 * q^84 - 97656252 * q^85 + 56725646132 * q^86 - 50128110092 * q^87 + 346072249440 * q^88 + 174291105374 * q^90 - 46617621428 * q^91 - 51820450984 * q^92 + 708584 * q^93 - 82977932908 * q^94 - 20580862760 * q^95 - 62470624376 * q^96 - 4 * q^97 - 155418407946 * q^98 - 189350900660 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−41.9762	−	16.9115i	−0.927551	−	0.373695i
$2$	−41.9762	−	16.9115i	−0.927551	−	0.373695i
$3$		−	792.470i		−	1.88285i	−0.337222	−	0.941425i	$-0.609487\pi$
$3$		−	792.470i		−	1.88285i	0.337222	−	0.941425i	$-0.390513\pi$
$4$	1476.00	+	1419.76i	0.720704	+	0.693243i
$5$	6967.42	−	532.099i	0.997097	−	0.0761479i
$5$	6967.42	−	532.099i	0.997097	−	0.0761479i
$6$	−13401.9	+	33264.9i	−0.703613	+	1.74644i
$7$	40707.4	+	40707.4i	0.915450	+	0.915450i	0.996694	−	0.0812446i	$-0.0258895\pi$
$7$	40707.4	+	40707.4i	0.915450	+	0.915450i	−0.0812446	+	0.996694i	$0.525889\pi$
$8$	−37946.5	−	84557.6i	−0.409428	−	0.912343i
$9$	−450861.			−2.54513
$10$	−301465.	−	95494.2i	−0.953314	−	0.301979i
$11$	564272.	+	564272.i	1.05640	+	1.05640i	0.998311	+	0.0580897i	$0.0185009\pi$
$11$	564272.	+	564272.i	1.05640	+	1.05640i	0.0580897	+	0.998311i	$0.481499\pi$
$12$	1.12512e6	−	1.16969e6i	1.30527	−	1.35698i
$13$	−1.54176e6			−1.15167			−0.575836	−	0.817565i	$-0.695323\pi$
$13$	−1.54176e6			−1.15167			−0.575836	+	0.817565i	$0.695323\pi$
$14$	−1.02032e6	−	2.39717e6i	−0.507027	−	1.19123i
$15$	−421673.	−	5.52147e6i	−0.143375	−	1.87738i
$16$	162853.	+	4.19114e6i	0.0388271	+	0.999246i
$17$	−4.72377e6	−	4.72377e6i	−0.806901	−	0.806901i	0.177263	−	0.984164i	$-0.443276\pi$
$17$	−4.72377e6	−	4.72377e6i	−0.806901	−	0.806901i	−0.984164	+	0.177263i	$0.943276\pi$
$18$	1.89254e7	+	7.62475e6i	2.36074	+	0.951102i
$19$	4.10340e6	+	4.10340e6i	0.380189	+	0.380189i	0.871170	−	0.490981i	$-0.163362\pi$
$19$	4.10340e6	+	4.10340e6i	0.380189	+	0.380189i	−0.490981	+	0.871170i	$0.663362\pi$
$20$	1.10394e7	+	9.10671e6i	0.771400	+	0.636351i
$21$	3.22594e7	−	3.22594e7i	1.72365	−	1.72365i
$22$	−1.41433e7	−	3.32287e7i	−0.585094	−	1.37464i
$23$	−5.99280e6	+	5.99280e6i	−0.194145	+	0.194145i	−0.797485	−	0.603339i	$-0.793836\pi$
$23$	−5.99280e6	+	5.99280e6i	−0.194145	+	0.194145i	0.603339	+	0.797485i	$0.293836\pi$
$24$	−6.70094e7	+	3.00715e7i	−1.71780	+	0.770891i
$25$	4.82619e7	−	7.41472e6i	0.988403	−	0.151854i
$26$	6.47173e7	+	2.60735e7i	1.06824	+	0.430375i
$27$			2.16910e8i			2.90924i
$28$	2.28931e6	+	1.17879e8i	0.0251383	+	1.29440i
$29$	−1.32874e8	+	1.32874e8i	−1.20296	+	1.20296i	−0.229703	+	0.973261i	$0.573776\pi$
$29$	−1.32874e8	+	1.32874e8i	−1.20296	+	1.20296i	−0.973261	+	0.229703i	$0.926224\pi$
$30$	−7.56763e7	+	2.38902e8i	−0.568582	+	1.79495i
$31$			1.59076e8i			0.997965i	0.866612	+	0.498983i	$0.166293\pi$
$31$			1.59076e8i			0.997965i	−0.866612	+	0.498983i	$0.833707\pi$
$32$	6.40426e7	−	1.78682e8i	0.337399	−	0.941362i
$33$	4.47169e8	−	4.47169e8i	1.98905	−	1.98905i
$34$	1.18400e8	+	2.78172e8i	0.446907	+	1.04998i
$35$	3.05286e8	+	2.61966e8i	0.982501	+	0.843082i
$36$	−6.65472e8	−	6.40116e8i	−1.83428	−	1.76439i
$37$	2.21122e8			0.524230			0.262115	−	0.965037i	$-0.415580\pi$
$37$	2.21122e8			0.524230			0.262115	+	0.965037i	$0.415580\pi$
$38$	−1.02850e8	−	2.41640e8i	−0.210570	−	0.494720i
$39$			1.22180e9i			2.16843i
$40$	−3.09383e8	−	5.68958e8i	−0.477712	−	0.878517i
$41$		−	1.39383e8i		−	0.187888i	−0.995577	−	0.0939440i	$-0.970053\pi$
$41$		−	1.39383e8i		−	0.187888i	0.995577	−	0.0939440i	$-0.0299475\pi$
$42$	−1.89968e9	+	8.08571e8i	−2.24290	+	0.954657i
$43$	7.79378e8			0.808484			0.404242	−	0.914652i	$-0.367535\pi$
$43$	7.79378e8			0.808484			0.404242	+	0.914652i	$0.367535\pi$
$44$	3.17337e7	+	1.63400e9i	0.0290089	+	1.49369i
$45$	−3.14134e9	+	2.39903e8i	−2.53774	+	0.193806i
$46$	3.52902e8	−	1.50208e8i	0.252631	−	0.107528i
$47$	8.64652e8	−	8.64652e8i	0.549925	−	0.549925i	−0.376494	−	0.926419i	$-0.622871\pi$
$47$	8.64652e8	−	8.64652e8i	0.549925	−	0.549925i	0.926419	+	0.376494i	$0.122871\pi$
$48$	3.32135e9	−	1.29056e8i	1.88143	−	0.0731056i
$49$			1.33686e9i			0.676096i
$50$	−2.15124e9	−	5.04940e8i	−0.973542	−	0.228510i
$51$	−3.74345e9	+	3.74345e9i	−1.51927	+	1.51927i
$52$	−2.27564e9	−	2.18894e9i	−0.830014	−	0.798389i
$53$			2.86989e9i			0.942645i	0.881961	+	0.471322i	$0.156223\pi$
$53$			2.86989e9i			0.942645i	−0.881961	+	0.471322i	$0.843777\pi$
$54$	3.66829e9	−	9.10507e9i	1.08717	−	2.69847i
$55$	4.23177e9	+	3.63127e9i	1.13378	+	0.972891i
$56$	1.89742e9	−	4.98683e9i	0.460393	−	1.21001i
$57$	3.25182e9	−	3.25182e9i	0.715839	−	0.715839i
$58$	7.82467e9	−	3.33045e9i	1.56535	−	0.666269i
$59$	−1.76583e9	+	1.76583e9i	−0.321561	+	0.321561i	−0.849366	−	0.527804i	$-0.823015\pi$
$59$	−1.76583e9	+	1.76583e9i	−0.321561	+	0.321561i	0.527804	+	0.849366i	$0.323015\pi$
$60$	7.21679e9	−	8.74837e9i	1.19815	−	1.45243i
$61$	5.93306e9	+	5.93306e9i	0.899425	+	0.899425i	0.995385	−	0.0959603i	$-0.0305922\pi$
$61$	5.93306e9	+	5.93306e9i	0.899425	+	0.899425i	−0.0959603	+	0.995385i	$0.530592\pi$
$62$	2.69022e9	−	6.67741e9i	0.372935	−	0.925664i
$63$	−1.83534e10	−	1.83534e10i	−2.32993	−	2.32993i
$64$	−5.71005e9	+	6.41734e9i	−0.664738	+	0.747077i
$65$	−1.07421e10	+	8.20371e8i	−1.14833	+	0.0876974i
$66$	−2.63327e10	+	1.12081e10i	−2.58824	+	1.10164i
$67$	1.31443e10			1.18939			0.594697	−	0.803950i	$-0.297272\pi$
$67$	1.31443e10			1.18939			0.594697	+	0.803950i	$0.297272\pi$
$68$	−2.65657e8	−	1.36789e10i	−0.0221576	−	1.14091i
$69$	4.74911e9	+	4.74911e9i	0.365546	+	0.365546i
$70$	−8.38452e9	−	1.61592e10i	−0.596265	−	1.14916i
$71$	1.60442e10			1.05535			0.527676	−	0.849445i	$-0.323063\pi$
$71$	1.60442e10			1.05535			0.527676	+	0.849445i	$0.323063\pi$
$72$	1.71086e10	+	3.81238e10i	1.04205	+	2.32203i
$73$	1.88768e10	+	1.88768e10i	1.06574	+	1.06574i	0.997681	+	0.0680600i	$0.0216809\pi$
$73$	1.88768e10	+	1.88768e10i	1.06574	+	1.06574i	0.0680600	+	0.997681i	$0.478319\pi$
$74$	−9.28184e9	−	3.73950e9i	−0.486250	−	0.195902i
$75$	−5.87595e9	−	3.82461e10i	−0.285918	−	1.86102i
$76$	2.30768e8	+	1.18825e10i	0.0104400	+	0.537567i
$77$			4.59401e10i			1.93416i
$78$	2.06625e10	−	5.12865e10i	0.810331	−	2.01133i
$79$	2.36638e10			0.865237			0.432619	−	0.901577i	$-0.357590\pi$
$79$	2.36638e10			0.865237			0.432619	+	0.901577i	$0.357590\pi$
$80$	3.36477e9	+	2.91148e10i	0.114805	+	0.993388i
$81$	9.20262e10			2.93254
$82$	−2.35718e9	+	5.85077e9i	−0.0702129	+	0.174276i
$83$		−	2.53798e10i		−	0.707228i	−0.935391	−	0.353614i	$-0.884953\pi$
$83$		−	2.53798e10i		−	0.707228i	0.935391	−	0.353614i	$-0.115047\pi$
$84$	9.34156e10	−	1.81421e9i	2.43716	−	0.0473317i
$85$	−3.54261e10	−	3.03990e10i	−0.866002	−	0.743114i
$86$	−3.27153e10	−	1.31805e10i	−0.749911	−	0.302127i
$87$	1.05299e11	+	1.05299e11i	2.26500	+	2.26500i
$88$	2.63013e10	−	6.91257e10i	0.531280	−	1.39632i
$89$	−3.26197e10			−0.619205			−0.309603	−	0.950866i	$-0.600196\pi$
$89$	−3.26197e10			−0.619205			−0.309603	+	0.950866i	$0.600196\pi$
$90$	1.35919e11	+	4.30547e10i	2.42631	+	0.768575i
$91$	−6.27612e10	−	6.27612e10i	−1.05430	−	1.05430i
$92$	−1.73537e10	+	3.37025e8i	−0.274511	+	0.00533124i
$93$	1.26063e11			1.87902
$94$	−5.09174e10	+	2.16722e10i	−0.715588	+	0.304579i
$95$	3.07736e10	+	2.64067e10i	0.408036	+	0.350134i
$96$	−1.41600e11	−	5.07519e10i	−1.77244	−	0.635273i
$97$	−4.74034e10	−	4.74034e10i	−0.560486	−	0.560486i	0.368960	−	0.929445i	$-0.379714\pi$
$97$	−4.74034e10	−	4.74034e10i	−0.560486	−	0.560486i	−0.929445	+	0.368960i	$0.879714\pi$
$98$	2.26084e10	−	5.61164e10i	0.252654	−	0.627114i
$99$	−2.54409e11	−	2.54409e11i	−2.68867	−	2.68867i
$100$	8.17617e10	+	5.75762e10i	0.817617	+	0.575762i
$101$	−4.32195e10	+	4.32195e10i	−0.409178	+	0.409178i	−0.881452	−	0.472274i	$-0.843433\pi$
$101$	−4.32195e10	+	4.32195e10i	−0.409178	+	0.409178i	0.472274	+	0.881452i	$0.343433\pi$
$102$	2.20443e11	−	9.38283e10i	1.97695	−	0.841459i
$103$	−1.01202e11	+	1.01202e11i	−0.860166	+	0.860166i	−0.991357	−	0.131191i	$-0.958120\pi$
$103$	−1.01202e11	+	1.01202e11i	−0.860166	+	0.860166i	0.131191	+	0.991357i	$0.458120\pi$
$104$	5.85045e10	+	1.30368e11i	0.471527	+	1.05072i
$105$	2.07600e11	−	2.41930e11i	1.58740	−	1.84990i
$106$	4.85342e10	−	1.20467e11i	0.352262	−	0.874352i
$107$		−	6.21664e10i		−	0.428494i	−0.976779	−	0.214247i	$-0.931270\pi$
$107$		−	6.21664e10i		−	0.428494i	0.976779	−	0.214247i	$-0.0687298\pi$
$108$	−3.07961e11	+	3.20160e11i	−2.01681	+	2.09670i
$109$	1.06536e11	−	1.06536e11i	0.663207	−	0.663207i	−0.292928	−	0.956135i	$-0.594630\pi$
$109$	1.06536e11	−	1.06536e11i	0.663207	−	0.663207i	0.956135	+	0.292928i	$0.0946296\pi$
$110$	−1.16223e11	−	2.23993e11i	−0.688071	−	1.32609i
$111$		−	1.75232e11i		−	0.987046i
$112$	−1.63981e11	+	1.77240e11i	−0.879215	+	0.950304i
$113$	8.07727e10	−	8.07727e10i	0.412414	−	0.412414i	−0.470165	−	0.882579i	$-0.655806\pi$
$113$	8.07727e10	−	8.07727e10i	0.412414	−	0.412414i	0.882579	+	0.470165i	$0.155806\pi$
$114$	−1.91492e11	+	8.15059e10i	−0.931483	+	0.396472i
$115$	−3.85656e10	+	4.49431e10i	−0.178798	+	0.208365i
$116$	−3.84773e11	+	7.47263e9i	−1.70093	+	0.0330335i
$117$	6.95121e11			2.93115
$118$	1.03986e11	−	4.42601e10i	0.418431	−	0.178099i
$119$		−	3.84585e11i		−	1.47735i
$120$	−4.50882e11	+	2.45176e11i	−1.65412	+	0.899460i
$121$			3.51494e11i			1.23197i
$122$	−1.48710e11	−	3.49385e11i	−0.498152	−	1.17037i
$123$	−1.10457e11			−0.353765
$124$	−2.25850e11	+	2.34796e11i	−0.691833	+	0.719237i
$125$	3.32316e11	−	7.73416e10i	0.973970	−	0.226677i
$126$	4.60022e11	+	1.08079e12i	1.29045	+	3.03182i
$127$	−2.53368e11	+	2.53368e11i	−0.680504	+	0.680504i	−0.960114	−	0.279609i	$-0.909795\pi$
$127$	−2.53368e11	+	2.53368e11i	−0.680504	+	0.680504i	0.279609	+	0.960114i	$0.409795\pi$
$128$	3.48213e11	−	1.72810e11i	0.895758	−	0.444543i
$129$		−	6.17633e11i		−	1.52225i
$130$	4.64787e11	+	1.47229e11i	1.09791	+	0.347781i
$131$	3.27559e11	−	3.27559e11i	0.741818	−	0.741818i	−0.231110	−	0.972928i	$-0.574236\pi$
$131$	3.27559e11	−	3.27559e11i	0.741818	−	0.741818i	0.972928	+	0.231110i	$0.0742356\pi$
$132$	1.29489e12	−	2.51480e10i	2.81240	−	0.0546193i
$133$			3.34078e11i			0.696087i
$134$	−5.51748e11	−	2.22290e11i	−1.10322	−	0.444471i
$135$	1.15418e11	+	1.51131e12i	0.221533	+	2.90079i
$136$	−2.20180e11	+	5.78682e11i	−0.405802	+	1.06654i
$137$	−3.52771e11	+	3.52771e11i	−0.624496	+	0.624496i	−0.946678	−	0.322182i	$-0.895584\pi$
$137$	−3.52771e11	+	3.52771e11i	−0.624496	+	0.624496i	0.322182	+	0.946678i	$0.395584\pi$
$138$	−1.19035e11	−	2.79664e11i	−0.202460	−	0.475666i
$139$	−7.35279e11	+	7.35279e11i	−1.20191	+	1.20191i	−0.228320	+	0.973586i	$0.573323\pi$
$139$	−7.35279e11	+	7.35279e11i	−1.20191	+	1.20191i	−0.973586	+	0.228320i	$0.926677\pi$
$140$	7.86740e10	+	8.20095e11i	0.123631	+	1.28872i
$141$	−6.85211e11	−	6.85211e11i	−1.03543	−	1.03543i
$142$	−6.73475e11	−	2.71332e11i	−0.978894	−	0.394381i
$143$	−8.69974e11	−	8.69974e11i	−1.21663	−	1.21663i
$144$	−7.34240e10	−	1.88962e12i	−0.0988199	−	2.54321i
$145$	−8.55090e11	+	9.96495e11i	−1.10787	+	1.29107i
$146$	−4.73140e11	−	1.11161e12i	−0.590267	−	1.38679i
$147$	1.05942e12			1.27299
$148$	3.26376e11	+	3.13940e11i	0.377814	+	0.363419i
$149$	2.60731e11	+	2.60731e11i	0.290850	+	0.290850i	0.837416	−	0.546566i	$-0.184065\pi$
$149$	2.60731e11	+	2.60731e11i	0.290850	+	0.290850i	−0.546566	+	0.837416i	$0.684065\pi$
$150$	−4.00150e11	+	1.70480e12i	−0.430250	+	1.83303i
$151$	−1.96075e11			−0.203258			−0.101629	−	0.994822i	$-0.532405\pi$
$151$	−1.96075e11			−0.203258			−0.101629	+	0.994822i	$0.532405\pi$
$152$	1.91264e11	−	5.02684e11i	0.191203	−	0.502522i
$153$	2.12977e12	+	2.12977e12i	2.05366	+	2.05366i
$154$	7.76918e11	−	1.92839e12i	0.722788	−	1.79404i
$155$	8.46443e10	+	1.10835e12i	0.0759929	+	0.995068i
$156$	−1.73467e12	+	1.80338e12i	−1.50325	+	1.56279i
$157$			7.59772e11i			0.635675i	0.948145	+	0.317838i	$0.102957\pi$
$157$			7.59772e11i			0.635675i	−0.948145	+	0.317838i	$0.897043\pi$
$158$	−9.93316e11	−	4.00191e11i	−0.802552	−	0.323335i
$159$	2.27430e12			1.77486
$160$	3.51136e11	−	1.27903e12i	0.264737	−	0.964321i
$161$	−4.87903e11			−0.355460
$162$	−3.86291e12	−	1.55630e12i	−2.72008	−	1.09588i
$163$		−	1.27301e12i		−	0.866564i	−0.901258	−	0.433282i	$-0.857355\pi$
$163$		−	1.27301e12i		−	0.866564i	0.901258	−	0.433282i	$-0.142645\pi$
$164$	1.97891e11	−	2.05730e11i	0.130252	−	0.135412i
$165$	2.87768e12	−	3.35355e12i	1.83181	−	2.13473i
$166$	−4.29212e11	+	1.06535e12i	−0.264288	+	0.655991i
$167$	−3.68065e11	−	3.68065e11i	−0.219273	−	0.219273i	0.588919	−	0.808192i	$-0.299554\pi$
$167$	−3.68065e11	−	3.68065e11i	−0.219273	−	0.219273i	−0.808192	+	0.588919i	$0.799554\pi$
$168$	−3.95191e12	−	1.50365e12i	−2.27828	−	0.866851i
$169$	5.84871e11			0.326350
$170$	9.72957e11	+	1.87514e12i	0.525563	+	1.01290i
$171$	−1.85007e12	−	1.85007e12i	−0.967629	−	0.967629i
$172$	1.15036e12	+	1.10653e12i	0.582677	+	0.560476i
$173$	4.53814e11			0.222651			0.111325	−	0.993784i	$-0.464490\pi$
$173$	4.53814e11			0.222651			0.111325	+	0.993784i	$0.464490\pi$
$174$	−2.63928e12	−	6.20082e12i	−1.25448	−	2.94733i
$175$	2.26645e12	+	1.66278e12i	1.04385	+	0.765819i
$176$	−2.27305e12	+	2.45684e12i	−1.01459	+	1.09662i
$177$	1.39937e12	+	1.39937e12i	0.605452	+	0.605452i
$178$	1.36925e12	+	5.51649e11i	0.574345	+	0.231394i
$179$	3.28929e11	+	3.28929e11i	0.133786	+	0.133786i	0.770829	−	0.637043i	$-0.219842\pi$
$179$	3.28929e11	+	3.28929e11i	0.133786	+	0.133786i	−0.637043	+	0.770829i	$0.719842\pi$
$180$	−4.97723e12	−	4.10586e12i	−1.96331	−	1.61959i
$181$	8.00450e11	−	8.00450e11i	0.306268	−	0.306268i	−0.537192	−	0.843460i	$-0.680515\pi$
$181$	8.00450e11	−	8.00450e11i	0.306268	−	0.306268i	0.843460	+	0.537192i	$0.180515\pi$
$182$	1.57309e12	+	3.69586e12i	0.583929	+	1.37190i
$183$	4.70177e12	−	4.70177e12i	1.69348	−	1.69348i
$184$	7.34143e11	+	2.79331e11i	0.256615	+	0.0976385i
$185$	1.54065e12	−	1.17659e11i	0.522707	−	0.0399190i
$186$	−5.29164e12	−	2.13192e12i	−1.74289	−	0.702181i
$187$		−	5.33099e12i		−	1.70482i
$188$	2.50383e12	−	4.86265e10i	0.777564	−	0.0151010i
$189$	−8.82987e12	+	8.82987e12i	−2.66326	+	2.66326i
$190$	−8.45179e11	−	1.62888e12i	−0.247630	−	0.477249i
$191$			4.17284e12i			1.18781i	0.804534	+	0.593907i	$0.202415\pi$
$191$			4.17284e12i			1.18781i	−0.804534	+	0.593907i	$0.797585\pi$
$192$	5.08555e12	+	4.52505e12i	1.40663	+	1.25160i
$193$	−2.04022e11	+	2.04022e11i	−0.0548419	+	0.0548419i	−0.733996	−	0.679154i	$-0.762347\pi$
$193$	−2.04022e11	+	2.04022e11i	−0.0548419	+	0.0548419i	0.679154	+	0.733996i	$0.262347\pi$
$194$	1.18815e12	+	2.79148e12i	0.310428	+	0.729330i
$195$	6.50119e11	+	8.51280e12i	0.165121	+	2.16213i
$196$	−1.89803e12	+	1.97321e12i	−0.468699	+	0.487265i
$197$	−4.26749e8			−0.000102473			−5.12364e−5	−	1.00000i	$-0.500016\pi$
$197$	−4.26749e8			−0.000102473			−5.12364e−5		1.00000i	$0.500016\pi$
$198$	6.37666e12	+	1.49815e13i	1.48914	+	3.49863i
$199$		−	2.53974e11i		−	0.0576896i	−0.999584	−	0.0288448i	$-0.990817\pi$
$199$		−	2.53974e11i		−	0.0576896i	0.999584	−	0.0288448i	$-0.00918286\pi$
$200$	−2.45834e12	−	3.79955e12i	−0.543222	−	0.839589i
$201$		−	1.04165e13i		−	2.23945i
$202$	2.54510e12	−	1.08328e12i	0.532441	−	0.226626i
$203$	−1.08180e13			−2.20251
$204$	−1.08401e13	+	2.10525e11i	−2.14817	+	0.0417194i
$205$	−7.41657e10	−	9.71141e11i	−0.0143073	−	0.187342i
$206$	5.95953e12	−	2.53658e12i	1.11929	−	0.476408i
$207$	2.70192e12	−	2.70192e12i	0.494124	−	0.494124i
$208$	−2.51080e11	−	6.46174e12i	−0.0447161	−	1.15080i
$209$			4.63087e12i			0.803264i
$210$	−1.28057e13	+	6.64448e12i	−2.16369	+	1.12268i
$211$	3.50839e11	−	3.50839e11i	0.0577502	−	0.0577502i	−0.677642	−	0.735392i	$-0.736998\pi$
$211$	3.50839e11	−	3.50839e11i	0.0577502	−	0.0577502i	0.735392	+	0.677642i	$0.236998\pi$
$212$	−4.07456e12	+	4.23596e12i	−0.653482	+	0.679367i
$213$		−	1.27146e13i		−	1.98707i
$214$	−1.05133e12	+	2.60951e12i	−0.160126	+	0.397451i
$215$	5.43025e12	−	4.14706e11i	0.806137	−	0.0615643i
$216$	1.83414e13	−	8.23100e12i	2.65422	−	1.19112i
$217$	−6.47558e12	+	6.47558e12i	−0.913587	+	0.913587i
$218$	−6.27363e12	+	2.67028e12i	−0.862995	+	0.367321i
$219$	1.49593e13	−	1.49593e13i	2.00663	−	2.00663i
$220$	1.09055e12	+	1.13679e13i	0.142666	+	1.48715i
$221$	7.28294e12	+	7.28294e12i	0.929285	+	0.929285i
$222$	−2.96344e12	+	7.35558e12i	−0.368854	+	0.915536i
$223$	8.17936e12	+	8.17936e12i	0.993214	+	0.993214i	0.999977	−	0.00676355i	$-0.00215292\pi$
$223$	8.17936e12	+	8.17936e12i	0.993214	+	0.993214i	−0.00676355	+	0.999977i	$0.502153\pi$
$224$	9.88071e12	−	4.66668e12i	1.17064	−	0.552897i
$225$	−2.17594e13	+	3.34301e12i	−2.51561	+	0.386486i
$226$	−4.75652e12	+	2.02454e12i	−0.536652	+	0.228418i
$227$	−1.69441e12			−0.186585			−0.0932923	−	0.995639i	$-0.529739\pi$
$227$	−1.69441e12			−0.186585			−0.0932923	+	0.995639i	$0.529739\pi$
$228$	9.41651e12	−	1.82877e11i	1.01216	−	0.0196570i
$229$	−4.98269e11	−	4.98269e11i	−0.0522840	−	0.0522840i	0.680481	−	0.732765i	$-0.261771\pi$
$229$	−4.98269e11	−	4.98269e11i	−0.0522840	−	0.0522840i	−0.732765	+	0.680481i	$0.761771\pi$
$230$	2.37889e12	−	1.23434e12i	0.243709	−	0.126454i
$231$	3.64062e13			3.64174
$232$	1.62777e13	+	6.19343e12i	1.59004	+	0.604988i
$233$	6.35592e12	+	6.35592e12i	0.606347	+	0.606347i	0.941989	−	0.335643i	$-0.108953\pi$
$233$	6.35592e12	+	6.35592e12i	0.606347	+	0.606347i	−0.335643	+	0.941989i	$0.608953\pi$
$234$	−2.91785e13	−	1.17556e13i	−2.71879	−	1.09536i
$235$	5.56432e12	−	6.48448e12i	0.506452	−	0.590204i
$236$	−5.11344e12	+	9.93074e10i	−0.454671	+	0.00883010i
$237$		−	1.87528e13i		−	1.62911i
$238$	−6.50392e12	+	1.61434e13i	−0.552080	+	1.37032i
$239$	7.34770e12			0.609485			0.304742	−	0.952435i	$-0.401430\pi$
$239$	7.34770e12			0.609485			0.304742	+	0.952435i	$0.401430\pi$
$240$	2.30726e13	−	2.66648e12i	1.87040	−	0.216160i
$241$	1.13057e13			0.895786			0.447893	−	0.894087i	$-0.352175\pi$
$241$	1.13057e13			0.895786			0.447893	+	0.894087i	$0.352175\pi$
$242$	5.94430e12	−	1.47544e13i	0.460380	−	1.14271i
$243$		−	3.45030e13i		−	2.61229i
$244$	3.33665e11	+	1.71807e13i	0.0246983	+	1.27174i
$245$	7.11344e11	+	9.31449e12i	0.0514833	+	0.674133i
$246$	4.63656e12	+	1.86799e12i	0.328135	+	0.132200i
$247$	−6.32647e12	−	6.32647e12i	−0.437853	−	0.437853i
$248$	1.34511e13	−	6.03638e12i	0.910486	−	0.408595i
$249$	−2.01128e13			−1.33160
$250$	−1.52573e13	−	2.37345e12i	−0.988116	−	0.153713i
$251$	−1.53437e13	−	1.53437e13i	−0.972131	−	0.972131i	0.0274913	−	0.999622i	$-0.491248\pi$
$251$	−1.53437e13	−	1.53437e13i	−0.972131	−	0.972131i	−0.999622	+	0.0274913i	$0.991248\pi$
$252$	−1.03216e12	−	5.31471e13i	−0.0639802	−	3.29440i
$253$	−6.76314e12			−0.410190
$254$	1.49202e13	−	6.35058e12i	0.885504	−	0.376901i
$255$	−2.40903e13	+	2.80741e13i	−1.39917	+	1.63055i
$256$	−1.75391e13	+	1.36508e12i	−0.996985	+	0.0775956i
$257$	3.71251e12	+	3.71251e12i	0.206555	+	0.206555i	0.802801	−	0.596247i	$-0.203342\pi$
$257$	3.71251e12	+	3.71251e12i	0.206555	+	0.206555i	−0.596247	+	0.802801i	$0.703342\pi$
$258$	−1.04451e13	+	2.59259e13i	−0.568860	+	1.41197i
$259$	9.00129e12	+	9.00129e12i	0.479906	+	0.479906i
$260$	−1.70201e13	−	1.40404e13i	−0.888400	−	0.732867i
$261$	5.99080e13	−	5.99080e13i	3.06169	−	3.06169i
$262$	−1.92892e13	+	8.21016e12i	−0.965288	+	0.410860i
$263$	−1.56677e13	+	1.56677e13i	−0.767799	+	0.767799i	−0.977719	−	0.209920i	$-0.932680\pi$
$263$	−1.56677e13	+	1.56677e13i	−0.767799	+	0.767799i	0.209920	+	0.977719i	$0.432680\pi$
$264$	−5.47800e13	−	2.08430e13i	−2.62906	−	1.00032i
$265$	1.52707e12	+	1.99957e13i	0.0717804	+	0.939908i
$266$	5.64977e12	−	1.40233e13i	0.260125	−	0.645657i
$267$			2.58501e13i			1.16587i
$268$	1.94010e13	+	1.86618e13i	0.857201	+	0.824540i
$269$	−3.39402e12	+	3.39402e12i	−0.146919	+	0.146919i	−0.776740	−	0.629821i	$-0.783128\pi$
$269$	−3.39402e12	+	3.39402e12i	−0.146919	+	0.146919i	0.629821	+	0.776740i	$0.283128\pi$
$270$	2.07137e13	−	6.53908e13i	0.878531	−	2.77342i
$271$			4.73384e12i			0.196735i	0.995150	+	0.0983677i	$0.0313621\pi$
$271$			4.73384e12i			0.196735i	−0.995150	+	0.0983677i	$0.968638\pi$
$272$	1.90287e13	−	2.05673e13i	0.774963	−	0.837622i
$273$	−4.97363e13	+	4.97363e13i	−1.98509	+	1.98509i
$274$	2.07739e13	−	8.84208e12i	0.812623	−	0.345881i
$275$	3.14167e13	+	2.30489e13i	1.20457	+	0.883732i
$276$	2.67082e11	+	1.37523e13i	0.0100379	+	0.516863i
$277$	8.10466e12			0.298604			0.149302	−	0.988792i	$-0.452297\pi$
$277$	8.10466e12			0.298604			0.149302	+	0.988792i	$0.452297\pi$
$278$	4.32989e13	−	1.84295e13i	1.56398	−	0.665683i
$279$		−	7.17212e13i		−	2.53995i
$280$	1.05666e13	−	3.57550e13i	0.366916	−	1.24156i
$281$		−	2.61010e13i		−	0.888737i	−0.895844	−	0.444368i	$-0.853428\pi$
$281$		−	2.61010e13i		−	0.888737i	0.895844	−	0.444368i	$-0.146572\pi$
$282$	1.71746e13	+	4.03505e13i	0.573477	+	1.34734i
$283$	−2.48293e12			−0.0813092			−0.0406546	−	0.999173i	$-0.512944\pi$
$283$	−2.48293e12			−0.0813092			−0.0406546	+	0.999173i	$0.512944\pi$
$284$	2.36813e13	+	2.27790e13i	0.760597	+	0.731617i
$285$	2.09265e13	−	2.43871e13i	0.659251	−	0.768270i
$286$	2.18056e13	+	5.12307e13i	0.673837	+	1.58313i
$287$	5.67393e12	−	5.67393e12i	0.172002	−	0.172002i
$288$	−2.88744e13	+	8.05609e13i	−0.858724	+	2.39588i
$289$			1.03562e13i			0.302177i
$290$	5.27457e13	−	2.73682e13i	1.51007	−	0.783533i
$291$	−3.75657e13	+	3.75657e13i	−1.05531	+	1.05531i
$292$	1.06160e12	+	5.46626e13i	0.0292653	+	1.50690i
$293$		−	3.32371e12i		−	0.0899188i	−0.998989	−	0.0449594i	$-0.985684\pi$
$293$		−	3.32371e12i		−	0.0899188i	0.998989	−	0.0449594i	$-0.0143158\pi$
$294$	−4.44706e13	−	1.79165e13i	−1.18076	−	0.475710i
$295$	−1.13637e13	+	1.32429e13i	−0.296142	+	0.345114i
$296$	−8.39080e12	−	1.86975e13i	−0.214634	−	0.478277i
$297$	−1.22396e14	+	1.22396e14i	−3.07333	+	3.07333i
$298$	−6.53514e12	−	1.53539e13i	−0.161089	−	0.378467i
$299$	9.23947e12	−	9.23947e12i	0.223592	−	0.223592i
$300$	4.56274e13	−	6.47937e13i	1.08407	−	1.53945i
$301$	3.17265e13	+	3.17265e13i	0.740126	+	0.740126i
$302$	8.23046e12	+	3.31592e12i	0.188532	+	0.0759567i
$303$	3.42501e13	+	3.42501e13i	0.770420	+	0.770420i
$304$	−1.65297e13	+	1.78662e13i	−0.365141	+	0.394664i
$305$	4.44951e13	+	3.81812e13i	0.965303	+	0.828324i
$306$	−5.33819e13	−	1.25417e14i	−1.13743	−	2.67232i
$307$	−6.03614e13			−1.26328			−0.631638	−	0.775263i	$-0.717617\pi$
$307$	−6.03614e13			−1.26328			−0.631638	+	0.775263i	$0.717617\pi$
$308$	−6.52241e13	+	6.78077e13i	−1.34085	+	1.39396i
$309$	8.01992e13	+	8.01992e13i	1.61956	+	1.61956i
$310$	1.51908e13	−	4.79558e13i	0.301365	−	0.951375i
$311$	−8.42291e12			−0.164165			−0.0820824	−	0.996626i	$-0.526157\pi$
$311$	−8.42291e12			−0.164165			−0.0820824	+	0.996626i	$0.526157\pi$
$312$	1.03313e14	−	4.63631e13i	1.97835	−	0.887814i
$313$	6.68340e13	+	6.68340e13i	1.25749	+	1.25749i	0.952289	+	0.305198i	$0.0987227\pi$
$313$	6.68340e13	+	6.68340e13i	1.25749	+	1.25749i	0.305198	+	0.952289i	$0.401277\pi$
$314$	1.28489e13	−	3.18923e13i	0.237549	−	0.589621i
$315$	−1.37642e14	−	1.18110e14i	−2.50059	−	2.14575i
$316$	3.49278e13	+	3.35970e13i	0.623580	+	0.599820i
$317$		−	7.44082e12i		−	0.130555i	−0.997867	−	0.0652777i	$-0.979207\pi$
$317$		−	7.44082e12i		−	0.130555i	0.997867	−	0.0652777i	$-0.0207933\pi$
$318$	−9.54665e13	−	3.84619e13i	−1.64627	−	0.663257i
$319$	−1.49955e14			−2.54162
$320$	−3.63697e13	+	4.77506e13i	−0.605920	+	0.795526i
$321$	−4.92650e13			−0.806791
$322$	2.04803e13	+	8.25118e12i	0.329708	+	0.132834i
$323$		−	3.87671e13i		−	0.613549i
$324$	1.35831e14	+	1.30655e14i	2.11349	+	2.03296i
$325$	−7.44083e13	+	1.14317e13i	−1.13832	+	0.174886i
$326$	−2.15286e13	+	5.34362e13i	−0.323831	+	0.803783i
$327$	−8.44262e13	−	8.44262e13i	−1.24872	−	1.24872i
$328$	−1.17859e13	+	5.28911e12i	−0.171418	+	0.0769265i
$329$	7.03955e13			1.00686
$330$	−1.77507e14	+	9.21034e13i	−2.49684	+	1.29554i
$331$	1.87843e13	+	1.87843e13i	0.259861	+	0.259861i	0.824997	−	0.565137i	$-0.191177\pi$
$331$	1.87843e13	+	1.87843e13i	0.259861	+	0.259861i	−0.565137	+	0.824997i	$0.691177\pi$
$332$	3.60334e13	−	3.74607e13i	0.490281	−	0.509702i
$333$	−9.96952e13			−1.33423
$334$	9.22543e12	+	2.16745e13i	0.121445	+	0.285328i
$335$	9.15819e13	−	6.99407e12i	1.18594	−	0.0905699i
$336$	1.40457e14	+	1.29950e14i	1.78928	+	1.65543i
$337$	−8.66487e13	−	8.66487e13i	−1.08592	−	1.08592i	−0.995944	−	0.0899754i	$-0.971321\pi$
$337$	−8.66487e13	−	8.66487e13i	−1.08592	−	1.08592i	−0.0899754	−	0.995944i	$-0.528679\pi$
$338$	−2.45506e13	−	9.89106e12i	−0.302706	−	0.121955i
$339$	−6.40099e13	−	6.40099e13i	−0.776513	−	0.776513i
$340$	−9.12949e12	−	9.51656e13i	−0.108971	−	1.13591i
$341$	−8.97622e13	+	8.97622e13i	−1.05425	+	1.05425i
$342$	4.63713e13	+	1.08946e14i	0.535927	+	1.25912i
$343$	2.60716e13	−	2.60716e13i	0.296518	−	0.296518i
$344$	−2.95747e13	−	6.59023e13i	−0.331016	−	0.737614i
$345$	3.56161e13	+	3.05621e13i	0.392321	+	0.336649i
$346$	−1.90494e13	−	7.67469e12i	−0.206520	−	0.0832036i
$347$		−	9.17229e13i		−	0.978736i	−0.872077	−	0.489368i	$-0.837227\pi$
$347$		−	9.17229e13i		−	0.978736i	0.872077	−	0.489368i	$-0.162773\pi$
$348$	5.92183e12	+	3.04921e14i	0.0621971	+	3.20259i
$349$	−1.30208e14	+	1.30208e14i	−1.34616	+	1.34616i	−0.456372	+	0.889789i	$0.650851\pi$
$349$	−1.30208e14	+	1.30208e14i	−1.34616	+	1.34616i	−0.889789	+	0.456372i	$0.849149\pi$
$350$	−6.70168e13	−	1.08126e14i	−0.682039	−	1.10042i
$351$		−	3.34424e14i		−	3.35049i
$352$	1.36963e14	−	6.46879e13i	1.35088	−	0.638026i
$353$	1.31075e14	−	1.31075e14i	1.27280	−	1.27280i	0.328188	−	0.944612i	$-0.393562\pi$
$353$	1.31075e14	−	1.31075e14i	1.27280	−	1.27280i	0.944612	−	0.328188i	$-0.106438\pi$
$354$	−3.50748e13	−	8.24057e13i	−0.335333	−	0.787843i
$355$	1.11787e14	−	8.53712e12i	1.05229	−	0.0803629i
$356$	−4.81467e13	−	4.63122e13i	−0.446263	−	0.429260i
$357$	−3.04772e14			−2.78164
$358$	−8.24451e12	−	1.93699e13i	−0.0740983	−	0.174089i
$359$			7.48566e13i			0.662537i	0.943536	+	0.331269i	$0.107477\pi$
$359$			7.48566e13i			0.662537i	−0.943536	+	0.331269i	$0.892523\pi$
$360$	1.39489e14	+	2.56521e14i	1.21584	+	2.23594i
$361$		−	8.28144e13i		−	0.710913i
$362$	−4.71367e13	+	2.00630e13i	−0.398531	+	0.169629i
$363$	2.78549e14			2.31961
$364$	−3.52958e12	−	1.81742e14i	−0.0289511	−	1.49072i
$365$	1.41567e14	+	1.21478e14i	1.14380	+	0.981493i
$366$	−2.76877e14	+	1.17848e14i	−2.20364	+	0.937946i
$367$	−1.64745e14	+	1.64745e14i	−1.29166	+	1.29166i	−0.357903	+	0.933759i	$0.616508\pi$
$367$	−1.64745e14	+	1.64745e14i	−1.29166	+	1.29166i	−0.933759	+	0.357903i	$0.883492\pi$
$368$	−2.60926e13	−	2.41407e13i	−0.201537	−	0.186461i
$369$			6.28425e13i			0.478199i
$370$	−6.66603e13	−	2.11158e13i	−0.499756	−	0.158306i
$371$	−1.16826e14	+	1.16826e14i	−0.862944	+	0.862944i
$372$	1.86069e14	+	1.78979e14i	1.35422	+	1.30262i
$373$		−	7.58388e13i		−	0.543867i	−0.962316	−	0.271934i	$-0.912337\pi$
$373$		−	7.58388e13i		−	0.543867i	0.962316	−	0.271934i	$-0.0876631\pi$
$374$	−9.01551e13	+	2.23775e14i	−0.637084	+	1.58131i
$375$	−6.12909e13	−	2.63350e14i	−0.426800	−	1.83384i
$376$	−1.05923e14	−	4.03024e13i	−0.726874	−	0.276565i
$377$	2.04861e14	−	2.04861e14i	1.38542	−	1.38542i
$378$	5.19971e14	−	2.21318e14i	3.46556	−	1.47506i
$379$	5.08308e13	−	5.08308e13i	0.333896	−	0.333896i	−0.520168	−	0.854064i	$-0.674131\pi$
$379$	5.08308e13	−	5.08308e13i	0.333896	−	0.333896i	0.854064	+	0.520168i	$0.174131\pi$
$380$	7.93052e12	+	8.26675e13i	0.0513443	+	0.535211i
$381$	2.00786e14	+	2.00786e14i	1.28129	+	1.28129i
$382$	7.05691e13	−	1.75160e14i	0.443881	−	1.10176i
$383$	1.90727e14	+	1.90727e14i	1.18255	+	1.18255i	0.979082	+	0.203468i	$0.0652214\pi$
$383$	1.90727e14	+	1.90727e14i	1.18255	+	1.18255i	0.203468	+	0.979082i	$0.434779\pi$
$384$	−1.36947e14	−	2.75949e14i	−0.837007	−	1.68658i
$385$	2.44447e13	+	3.20084e14i	0.147282	+	1.92855i
$386$	1.20144e13	−	5.11375e12i	0.0713628	−	0.0303745i
$387$	−3.51391e14			−2.05769
$388$	−2.66588e12	−	1.37269e14i	−0.0153910	−	0.792497i
$389$	−1.11011e14	−	1.11011e14i	−0.631890	−	0.631890i	0.316652	−	0.948542i	$-0.397441\pi$
$389$	−1.11011e14	−	1.11011e14i	−0.631890	−	0.631890i	−0.948542	+	0.316652i	$0.897441\pi$
$390$	1.16675e14	−	3.68329e14i	0.654820	−	2.06719i
$391$	5.66173e13			0.313312
$392$	1.13042e14	−	5.07293e13i	0.616831	−	0.276812i
$393$	−2.59581e14	−	2.59581e14i	−1.39673	−	1.39673i
$394$	1.79133e10	+	7.21698e9i	9.50488e−5	+	3.82936e-5i
$395$	1.64876e14	−	1.25915e13i	0.862725	−	0.0658860i
$396$	−1.43075e13	−	7.36707e14i	−0.0738312	−	3.80164i
$397$		−	2.30061e14i		−	1.17083i	−0.810732	−	0.585417i	$-0.800931\pi$
$397$		−	2.30061e14i		−	1.17083i	0.810732	−	0.585417i	$-0.199069\pi$
$398$	−4.29509e12	+	1.06609e13i	−0.0215583	+	0.0535101i
$399$	2.64747e14			1.31063
$400$	3.89357e13	+	2.01065e14i	0.190116	+	0.981762i
$401$	−2.94570e14			−1.41871			−0.709357	−	0.704849i	$-0.751015\pi$
$401$	−2.94570e14			−1.41871			−0.709357	+	0.704849i	$0.751015\pi$
$402$	−1.76158e14	+	4.37243e14i	−0.836873	+	2.07721i
$403$		−	2.45257e14i		−	1.14933i
$404$	−1.25153e14	+	2.43059e12i	−0.578556	+	0.0112361i
$405$	6.41186e14	−	4.89671e13i	2.92403	−	0.223307i
$406$	4.54097e14	+	1.82948e14i	2.04294	+	0.823066i
$407$	1.24773e14	+	1.24773e14i	0.553797	+	0.553797i
$408$	4.58588e14	+	1.74486e14i	2.00813	+	0.764065i
$409$	3.64946e13			0.157670			0.0788352	−	0.996888i	$-0.474880\pi$
$409$	3.64946e13			0.157670			0.0788352	+	0.996888i	$0.474880\pi$
$410$	−1.33103e13	+	4.20191e13i	−0.0567383	+	0.179116i
$411$	2.79560e14	+	2.79560e14i	1.17583	+	1.17583i
$412$	−2.93056e14	+	5.69140e12i	−1.21623	+	0.0236202i
$413$	−1.43765e14			−0.588747
$414$	−1.59110e14	+	6.77228e13i	−0.642977	+	0.273674i
$415$	−1.35046e13	−	1.76832e14i	−0.0538539	−	0.705175i
$416$	−9.87385e13	+	2.75486e14i	−0.388574	+	1.08414i
$417$	5.82686e14	+	5.82686e14i	2.26301	+	2.26301i
$418$	7.83151e13	−	1.94386e14i	0.300176	−	0.745069i
$419$	−1.89706e14	−	1.89706e14i	−0.717637	−	0.717637i	0.250484	−	0.968121i	$-0.419410\pi$
$419$	−1.89706e14	−	1.89706e14i	−0.717637	−	0.717637i	−0.968121	+	0.250484i	$0.919410\pi$
$420$	6.49901e14	−	6.23468e13i	2.42648	−	0.232779i
$421$	−2.40215e14	+	2.40215e14i	−0.885215	+	0.885215i	−0.994059	−	0.108844i	$-0.965285\pi$
$421$	−2.40215e14	+	2.40215e14i	−0.885215	+	0.885215i	0.108844	+	0.994059i	$0.465285\pi$
$422$	−2.06601e13	+	8.79365e12i	−0.0751473	+	0.0319853i
$423$	−3.89838e14	+	3.89838e14i	−1.39963	+	1.39963i
$424$	2.42671e14	−	1.08902e14i	0.860015	−	0.385945i
$425$	−2.63004e14	−	1.92953e14i	−0.920074	−	0.675012i
$426$	−2.15023e14	+	5.33709e14i	−0.742560	+	1.84311i
$427$			4.83040e14i			1.64676i
$428$	8.82616e13	−	9.17577e13i	0.297051	−	0.308817i
$429$	−6.89428e14	+	6.89428e14i	−2.29073	+	2.29073i
$430$	−2.34955e14	−	7.44261e13i	−0.770740	−	0.244145i
$431$		−	3.54518e14i		−	1.14819i	−0.818789	−	0.574095i	$-0.805354\pi$
$431$		−	3.54518e14i		−	1.14819i	0.818789	−	0.574095i	$-0.194646\pi$
$432$	−9.09102e14	+	3.53244e13i	−2.90705	+	0.112957i
$433$	−5.36697e13	+	5.36697e13i	−0.169451	+	0.169451i	−0.786738	−	0.617287i	$-0.788232\pi$
$433$	−5.36697e13	+	5.36697e13i	−0.169451	+	0.169451i	0.617287	+	0.786738i	$0.288232\pi$
$434$	3.81332e14	−	1.62308e14i	1.18880	−	0.505996i
$435$	7.89692e14	+	6.77633e14i	2.43090	+	2.08595i
$436$	3.08502e14	−	5.99137e12i	0.937739	−	0.0182117i
$437$	−4.91817e13			−0.147624
$438$	−8.80917e14	+	3.74949e14i	−2.61112	+	1.11139i
$439$		−	2.76277e14i		−	0.808706i	−0.914603	−	0.404353i	$-0.867497\pi$
$439$		−	2.76277e14i		−	0.808706i	0.914603	−	0.404353i	$-0.132503\pi$
$440$	1.46471e14	−	4.95623e14i	0.423410	−	1.43272i
$441$		−	6.02740e14i		−	1.72075i
$442$	−1.82544e14	−	4.28875e14i	−0.514690	−	1.20923i
$443$	1.21918e14			0.339507			0.169753	−	0.985487i	$-0.445703\pi$
$443$	1.21918e14			0.339507			0.169753	+	0.985487i	$0.445703\pi$
$444$	2.48788e14	−	2.58643e14i	0.684263	−	0.711367i
$445$	−2.27275e14	+	1.73569e13i	−0.617408	+	0.0471512i
$446$	−2.05013e14	−	4.81664e14i	−0.550097	−	1.29242i
$447$	2.06622e14	−	2.06622e14i	0.547626	−	0.547626i
$448$	−4.93675e14	+	2.87918e13i	−1.29245	+	0.0753770i
$449$		−	3.49267e14i		−	0.903240i	−0.892210	−	0.451620i	$-0.850846\pi$
$449$		−	3.49267e14i		−	0.903240i	0.892210	−	0.451620i	$-0.149154\pi$
$450$	9.69913e14	+	2.27658e14i	2.47779	+	0.581586i
$451$	7.86500e13	−	7.86500e13i	0.198485	−	0.198485i
$452$	2.33899e14	−	4.54252e12i	0.583131	−	0.0113249i
$453$			1.55383e14i			0.382705i
$454$	7.11248e13	+	2.86550e13i	0.173067	+	0.0697258i
$455$	−4.70679e14	−	4.03889e14i	−1.13152	−	0.970954i
$456$	−3.98362e14	−	1.51571e14i	−0.946174	−	0.360006i
$457$	−4.47455e14	+	4.47455e14i	−1.05005	+	1.05005i	−0.0513717	+	0.998680i	$0.516359\pi$
$457$	−4.47455e14	+	4.47455e14i	−1.05005	+	1.05005i	−0.998680	+	0.0513717i	$0.983641\pi$
$458$	1.24889e13	+	2.93419e13i	0.0289578	+	0.0680343i
$459$	1.02464e15	−	1.02464e15i	2.34747	−	2.34747i
$460$	−1.20731e14	+	1.15821e13i	−0.273308	+	0.0262192i
$461$	−4.77050e13	−	4.77050e13i	−0.106711	−	0.106711i	0.651735	−	0.758446i	$-0.274041\pi$
$461$	−4.77050e13	−	4.77050e13i	−0.106711	−	0.106711i	−0.758446	+	0.651735i	$0.774041\pi$
$462$	−1.52819e15	−	6.15684e14i	−3.37790	−	1.36090i
$463$	−2.81984e14	−	2.81984e14i	−0.615927	−	0.615927i	0.328557	−	0.944484i	$-0.393438\pi$
$463$	−2.81984e14	−	2.81984e14i	−0.615927	−	0.615927i	−0.944484	+	0.328557i	$0.893438\pi$
$464$	−5.78535e14	−	5.35257e14i	−1.24876	−	1.15535i
$465$	8.78334e14	−	6.70780e13i	1.87356	−	0.143083i
$466$	−1.59309e14	−	3.74286e14i	−0.335829	−	0.789007i
$467$	6.70918e14			1.39774			0.698870	−	0.715249i	$-0.253687\pi$
$467$	6.70918e14			1.39774			0.698870	+	0.715249i	$0.253687\pi$
$468$	1.02600e15	+	9.86907e14i	2.11249	+	2.03200i
$469$	5.35071e14	+	5.35071e14i	1.08883	+	1.08883i
$470$	−3.43231e14	+	1.78093e14i	−0.690317	+	0.358185i
$471$	6.02096e14			1.19688
$472$	2.16322e14	+	8.23075e13i	0.425030	+	0.161718i
$473$	4.39781e14	+	4.39781e14i	0.854083	+	0.854083i
$474$	−3.17139e14	+	7.87173e14i	−0.608792	+	1.51109i
$475$	2.28463e14	+	1.67612e14i	0.433513	+	0.318047i
$476$	5.46020e14	−	5.67648e14i	1.02417	−	1.06473i
$477$		−	1.29392e15i		−	2.39915i
$478$	−3.08428e14	−	1.24261e14i	−0.565328	−	0.227762i
$479$	3.42742e14			0.621044			0.310522	−	0.950566i	$-0.399496\pi$
$479$	3.42742e14			0.621044			0.310522	+	0.950566i	$0.399496\pi$
$480$	−1.01359e15	−	2.78264e14i	−1.81567	−	0.498461i
$481$	−3.40917e14			−0.603741
$482$	−4.74571e14	−	1.91197e14i	−0.830888	−	0.334751i
$483$			3.86648e14i			0.669279i
$484$	−4.99039e14	+	5.18806e14i	−0.854052	+	0.887882i
$485$	−3.55503e14	−	3.05056e14i	−0.601538	−	0.516179i
$486$	−5.83498e14	+	1.44830e15i	−0.976202	+	2.42304i
$487$	−2.65597e14	−	2.65597e14i	−0.439353	−	0.439353i	0.452441	−	0.891794i	$-0.350553\pi$
$487$	−2.65597e14	−	2.65597e14i	−0.439353	−	0.439353i	−0.891794	+	0.452441i	$0.850553\pi$
$488$	2.76547e14	−	7.26825e14i	0.452334	−	1.18883i
$489$	−1.00882e15			−1.63161
$490$	1.27663e14	−	4.03017e14i	0.204167	−	0.644532i
$491$	8.35987e14	+	8.35987e14i	1.32206	+	1.32206i	0.912106	+	0.409954i	$0.134455\pi$
$491$	8.35987e14	+	8.35987e14i	1.32206	+	1.32206i	0.409954	+	0.912106i	$0.365545\pi$
$492$	−1.63034e14	−	1.56823e14i	−0.254960	−	0.245245i
$493$	1.25534e15			1.94134
$494$	1.58571e14	+	3.72552e14i	0.242508	+	0.569755i
$495$	−1.90794e15	−	1.63720e15i	−2.88560	−	2.47613i
$496$	−6.66710e14	+	2.59060e13i	−0.997213	+	0.0387481i
$497$	6.53119e14	+	6.53119e14i	0.966122	+	0.966122i
$498$	8.44257e14	+	3.40137e14i	1.23513	+	0.497615i
$499$	−9.36561e13	−	9.36561e13i	−0.135514	−	0.135514i	0.636096	−	0.771610i	$-0.280548\pi$
$499$	−9.36561e13	−	9.36561e13i	−0.135514	−	0.135514i	−0.771610	+	0.636096i	$0.780548\pi$
$500$	6.00305e14	+	3.57653e14i	0.859086	+	0.511831i
$501$	−2.91681e14	+	2.91681e14i	−0.412857	+	0.412857i
$502$	3.84585e14	+	9.03555e14i	0.538421	+	1.26498i
$503$	−4.09439e14	+	4.09439e14i	−0.566976	+	0.566976i	−0.931280	−	0.364304i	$-0.881307\pi$
$503$	−4.09439e14	+	4.09439e14i	−0.566976	+	0.566976i	0.364304	+	0.931280i	$0.381307\pi$
$504$	−8.55473e14	+	2.24837e15i	−1.17176	+	3.07964i
$505$	−2.78131e14	+	3.24125e14i	−0.376832	+	0.439148i
$506$	2.83891e14	+	1.14375e14i	0.380473	+	0.153286i
$507$		−	4.63492e14i		−	0.614468i
$508$	−7.33693e14	+	1.42490e13i	−0.962197	+	0.0186867i
$509$	−1.35335e14	+	1.35335e14i	−0.175575	+	0.175575i	−0.789424	−	0.613849i	$-0.789620\pi$
$509$	−1.35335e14	+	1.35335e14i	−0.175575	+	0.175575i	0.613849	+	0.789424i	$0.289620\pi$
$510$	1.48599e15	−	7.71039e14i	1.90713	−	0.989556i
$511$			1.53685e15i			1.95126i
$512$	7.59312e14	+	2.39313e14i	0.953752	+	0.300595i
$513$	−8.90071e14	+	8.90071e14i	−1.10606	+	1.10606i
$514$	−9.30528e13	−	2.18621e14i	−0.114402	−	0.268779i
$515$	−6.51265e14	+	7.58963e14i	−0.792169	+	0.923169i
$516$	8.76893e14	−	9.11627e14i	1.05529	−	1.09709i
$517$	9.75798e14			1.16188
$518$	−2.25614e14	−	5.30065e14i	−0.265799	−	0.624476i
$519$		−	3.59634e14i		−	0.419218i
$520$	4.76995e14	+	8.77197e14i	0.550168	+	1.01176i
$521$		−	1.49154e15i		−	1.70227i	−0.524948	−	0.851135i	$-0.675915\pi$
$521$		−	1.49154e15i		−	1.70227i	0.524948	−	0.851135i	$-0.324085\pi$
$522$	−3.52784e15	+	1.50157e15i	−3.98402	+	1.69574i
$523$	−4.36626e14			−0.487922			−0.243961	−	0.969785i	$-0.578447\pi$
$523$	−4.36626e14			−0.487922			−0.243961	+	0.969785i	$0.578447\pi$
$524$	9.48533e14	−	1.84213e13i	1.04889	−	0.0203704i
$525$	1.31770e15	−	1.79609e15i	1.44192	−	1.96541i
$526$	9.22633e14	−	3.92705e14i	0.999096	−	0.425250i
$527$	7.51439e14	−	7.51439e14i	0.805259	−	0.805259i
$528$	1.94697e15	+	1.80132e15i	2.06477	+	1.91032i
$529$			8.80982e14i			0.924615i
$530$	2.74058e14	−	8.65170e14i	0.284659	−	0.898637i
$531$	7.96147e14	−	7.96147e14i	0.818414	−	0.818414i
$532$	−4.74311e14	+	4.93099e14i	−0.482558	+	0.501673i
$533$			2.14896e14i			0.216385i
$534$	4.37165e14	−	1.08509e15i	0.435681	−	1.08141i
$535$	−3.30787e13	−	4.33140e14i	−0.0326289	−	0.427250i
$536$	−4.98781e14	−	1.11145e15i	−0.486971	−	1.08514i
$537$	2.60667e14	−	2.60667e14i	0.251899	−	0.251899i
$538$	1.99866e14	−	8.50701e13i	0.191178	−	0.0813719i
$539$	−7.54354e14	+	7.54354e14i	−0.714228	+	0.714228i
$540$	−1.97534e15	+	2.39456e15i	−1.85130	+	2.24419i
$541$	1.26068e15	+	1.26068e15i	1.16955	+	1.16955i	0.982315	+	0.187237i	$0.0599533\pi$
$541$	1.26068e15	+	1.26068e15i	1.16955	+	1.16955i	0.187237	+	0.982315i	$0.440047\pi$
$542$	8.00565e13	−	1.98709e14i	0.0735191	−	0.182482i
$543$	−6.34332e14	−	6.34332e14i	−0.576657	−	0.576657i
$544$	−1.14658e15	+	5.41531e14i	−1.03183	+	0.487337i
$545$	6.85591e14	−	7.98966e14i	0.610779	−	0.711783i
$546$	2.92886e15	−	1.24662e15i	2.58309	−	1.09945i
$547$	−5.29025e14			−0.461898			−0.230949	−	0.972966i	$-0.574183\pi$
$547$	−5.29025e14			−0.461898			−0.230949	+	0.972966i	$0.574183\pi$
$548$	−1.02154e15	+	1.98392e13i	−0.883004	+	0.0171487i
$549$	−2.67499e15	−	2.67499e15i	−2.28915	−	2.28915i
$550$	−9.28963e14	−	1.49881e15i	−0.787053	−	1.26985i
$551$	−1.09048e15			−0.914707
$552$	2.21361e14	−	5.81786e14i	0.183839	−	0.483168i
$553$	9.63292e14	+	9.63292e14i	0.792081	+	0.792081i
$554$	−3.40203e14	−	1.37062e14i	−0.276971	−	0.111587i
$555$	−9.32409e13	−	1.22092e15i	−0.0751614	−	0.984180i
$556$	−2.12919e15	+	4.13508e13i	−1.69943	+	0.0330044i
$557$		−	1.08250e14i		−	0.0855509i	−0.999085	−	0.0427755i	$-0.986380\pi$
$557$		−	1.08250e14i		−	0.0855509i	0.999085	−	0.0427755i	$-0.0136200\pi$
$558$	−1.21292e15	+	3.01058e15i	−0.949167	+	2.35593i
$559$	−1.20162e15			−0.931109
$560$	−1.04822e15	+	1.32216e15i	−0.804299	+	1.01449i
$561$	−4.22465e15			−3.20992
$562$	−4.41408e14	+	1.09562e15i	−0.332117	+	0.824349i
$563$			2.63593e15i			1.96398i	0.188924	+	0.981992i	$0.439500\pi$
$563$			2.63593e15i			1.96398i	−0.188924	+	0.981992i	$0.560500\pi$
$564$	−3.85350e13	−	1.98421e15i	−0.0284329	−	1.46404i
$565$	5.19799e14	−	6.05757e14i	0.379812	−	0.442621i
$566$	1.04224e14	+	4.19902e13i	0.0754185	+	0.0303849i
$567$	3.74615e15	+	3.74615e15i	2.68459	+	2.68459i
$568$	−6.08823e14	−	1.35666e15i	−0.432091	−	0.962843i
$569$	2.57946e14			0.181306			0.0906530	−	0.995883i	$-0.471105\pi$
$569$	2.57946e14			0.181306			0.0906530	+	0.995883i	$0.471105\pi$
$570$	−1.29084e15	+	6.69779e14i	−0.898588	+	0.466251i
$571$	−9.92503e14	−	9.92503e14i	−0.684279	−	0.684279i	0.276682	−	0.960961i	$-0.410765\pi$
$571$	−9.92503e14	−	9.92503e14i	−0.684279	−	0.684279i	−0.960961	+	0.276682i	$0.910765\pi$
$572$	−4.89258e13	−	2.51924e15i	−0.0334087	−	1.72025i
$573$	3.30685e15			2.23648
$574$	−3.34125e14	+	1.42215e14i	−0.223817	+	0.0952643i
$575$	−2.44789e14	+	3.33659e14i	−0.162412	+	0.221375i
$576$	2.57444e15	−	2.89333e15i	1.69184	−	1.90140i
$577$	−2.06402e15	−	2.06402e15i	−1.34353	−	1.34353i	−0.892519	−	0.451010i	$-0.851064\pi$
$577$	−2.06402e15	−	2.06402e15i	−1.34353	−	1.34353i	−0.451010	−	0.892519i	$-0.648936\pi$
$578$	1.75139e14	−	4.34713e14i	0.112922	−	0.280285i
$579$	1.61682e14	+	1.61682e14i	0.103259	+	0.103259i
$580$	−2.67690e15	+	2.56803e14i	−1.69347	+	0.162460i
$581$	1.03315e15	−	1.03315e15i	0.647432	−	0.647432i
$582$	2.21216e15	−	9.41573e14i	1.37322	−	0.584490i
$583$	−1.61940e15	+	1.61940e15i	−0.995811	+	0.995811i
$584$	8.79867e14	−	2.31248e15i	0.535977	−	1.40867i
$585$	4.84320e15	−	3.69874e14i	2.92264	−	0.223201i
$586$	−5.62089e13	+	1.39516e14i	−0.0336022	+	0.0834043i
$587$			9.73185e14i			0.576350i	0.957578	+	0.288175i	$0.0930484\pi$
$587$			9.73185e14i			0.576350i	−0.957578	+	0.288175i	$0.906952\pi$
$588$	1.56371e15	+	1.50413e15i	0.917447	+	0.882490i
$589$	−6.52753e14	+	6.52753e14i	−0.379415	+	0.379415i
$590$	7.00963e14	−	3.63709e14i	0.403654	−	0.209444i
$591$			3.38186e11i			0.000192941i
$592$	3.60102e13	+	9.26751e14i	0.0203543	+	0.523834i
$593$	1.19152e15	−	1.19152e15i	0.667267	−	0.667267i	−0.289815	−	0.957083i	$-0.593594\pi$
$593$	1.19152e15	−	1.19152e15i	0.667267	−	0.667267i	0.957083	+	0.289815i	$0.0935939\pi$
$594$	7.20765e15	−	3.06783e15i	3.99915	−	1.70218i
$595$	−2.04638e14	−	2.67957e15i	−0.112497	−	1.47306i
$596$	1.46631e13	+	7.55016e14i	0.00798675	+	0.411246i
$597$	−2.01267e14			−0.108621
$598$	−5.44091e14	+	2.31584e14i	−0.290948	+	0.123838i
$599$		−	2.18734e15i		−	1.15896i	−0.814986	−	0.579480i	$-0.803256\pi$
$599$		−	2.18734e15i		−	1.15896i	0.814986	−	0.579480i	$-0.196744\pi$
$600$	−3.01103e15	+	1.94816e15i	−1.58082	+	1.02281i
$601$			3.61875e15i			1.88256i	0.337626	+	0.941280i	$0.390376\pi$
$601$			3.61875e15i			1.88256i	−0.337626	+	0.941280i	$0.609624\pi$
$602$	−7.95213e14	−	1.86830e15i	−0.409924	−	0.963087i
$603$	−5.92626e15			−3.02716
$604$	−2.89406e14	−	2.78379e14i	−0.146489	−	0.140907i
$605$	1.87030e14	+	2.44901e15i	0.0938116	+	1.22839i
$606$	−8.58468e14	−	2.01691e15i	−0.426702	−	1.00251i
$607$	−1.64292e15	+	1.64292e15i	−0.809245	+	0.809245i	−0.984520	−	0.175275i	$-0.943919\pi$
$607$	−1.64292e15	+	1.64292e15i	−0.809245	+	0.809245i	0.175275	+	0.984520i	$0.443919\pi$
$608$	9.95998e14	−	4.70412e14i	0.486171	−	0.229620i
$609$			8.57290e15i			4.14699i
$610$	−1.22203e15	−	2.35518e15i	−0.585827	−	1.12904i
$611$	−1.33309e15	+	1.33309e15i	−0.633333	+	0.633333i
$612$	1.19774e14	+	6.16730e15i	0.0563938	+	2.90377i
$613$			1.38695e15i			0.647184i	0.946197	+	0.323592i	$0.104890\pi$
$613$			1.38695e15i			0.647184i	−0.946197	+	0.323592i	$0.895110\pi$
$614$	2.53374e15	+	1.02080e15i	1.17175	+	0.472081i
$615$	−7.69600e14	+	5.87741e13i	−0.352738	+	0.0269384i
$616$	3.88459e15	−	1.74327e15i	1.76462	−	0.791900i
$617$	−1.47836e14	+	1.47836e14i	−0.0665599	+	0.0665599i	−0.739603	−	0.673043i	$-0.764987\pi$
$617$	−1.47836e14	+	1.47836e14i	−0.0665599	+	0.0665599i	0.673043	+	0.739603i	$0.264987\pi$
$618$	−2.01017e15	−	4.72275e15i	−0.897006	−	2.10745i
$619$	1.34356e15	−	1.34356e15i	0.594234	−	0.594234i	−0.344538	−	0.938772i	$-0.611965\pi$
$619$	1.34356e15	−	1.34356e15i	0.594234	−	0.594234i	0.938772	+	0.344538i	$0.111965\pi$
$620$	−1.44866e15	+	1.75610e15i	−0.635056	+	0.769830i
$621$	−1.29990e15	−	1.29990e15i	−0.564815	−	0.564815i
$622$	3.53562e14	+	1.42444e14i	0.152271	+	0.0613476i
$623$	−1.32786e15	−	1.32786e15i	−0.566851	−	0.566851i
$624$	−5.12074e15	+	1.98973e14i	−2.16679	+	0.0841937i
$625$	2.27423e15	−	7.15697e14i	0.953881	−	0.300185i
$626$	−1.67517e15	−	3.93570e15i	−0.696467	−	1.63630i
$627$	3.66983e15			1.51243
$628$	−1.07870e15	+	1.12142e15i	−0.440678	+	0.458133i
$629$	−1.04453e15	−	1.04453e15i	−0.423001	−	0.423001i
$630$	3.78026e15	+	7.28555e15i	1.51757	+	2.92475i
$631$	3.87537e15			1.54224			0.771120	−	0.636690i	$-0.219697\pi$
$631$	3.87537e15			1.54224			0.771120	+	0.636690i	$0.219697\pi$
$632$	−8.97959e14	−	2.00095e15i	−0.354252	−	0.789393i
$633$	−2.78029e14	−	2.78029e14i	−0.108735	−	0.108735i
$634$	−1.25836e14	+	3.12337e14i	−0.0487880	+	0.121097i
$635$	−1.63050e15	+	1.90014e15i	−0.626710	+	0.730347i
$636$	3.35687e15	+	3.22897e15i	1.27915	+	1.23041i
$637$		−	2.06112e15i		−	0.778641i
$638$	6.29453e15	+	2.53596e15i	2.35749	+	0.949793i
$639$	−7.23372e15			−2.68601
$640$	2.33420e15	−	1.38932e15i	0.859306	−	0.511462i
$641$	5.84254e14			0.213247			0.106623	−	0.994299i	$-0.465996\pi$
$641$	5.84254e14			0.213247			0.106623	+	0.994299i	$0.465996\pi$
$642$	2.06796e15	+	8.33147e14i	0.748340	+	0.301494i
$643$			5.01369e15i			1.79886i	0.437066	+	0.899429i	$0.356018\pi$
$643$			5.01369e15i			1.79886i	−0.437066	+	0.899429i	$0.643982\pi$
$644$	−7.20145e14	−	6.92706e14i	−0.256181	−	0.246420i
$645$	−3.28642e14	−	4.30331e15i	−0.115916	−	1.51783i
$646$	−6.55611e14	+	1.62729e15i	−0.229281	+	0.569098i
$647$	1.63955e15	+	1.63955e15i	0.568528	+	0.568528i	0.931716	−	0.363188i	$-0.118312\pi$
$647$	1.63955e15	+	1.63955e15i	0.568528	+	0.568528i	−0.363188	+	0.931716i	$0.618312\pi$
$648$	−3.49208e15	−	7.78152e15i	−1.20066	−	2.67548i
$649$	−1.99282e15			−0.679396
$650$	3.31671e15	+	7.78497e14i	1.12120	+	0.263168i
$651$	5.13170e15	+	5.13170e15i	1.72015	+	1.72015i
$652$	1.80738e15	−	1.87897e15i	0.600740	−	0.624536i
$653$	−5.91529e14			−0.194964			−0.0974818	−	0.995237i	$-0.531079\pi$
$653$	−5.91529e14			−0.194964			−0.0974818	+	0.995237i	$0.531079\pi$
$654$	2.11611e15	+	4.97167e15i	0.691610	+	1.62489i
$655$	2.10795e15	−	2.45654e15i	0.683176	−	0.796152i
$656$	5.84174e14	−	2.26989e13i	0.187746	−	0.00729514i
$657$	−8.51080e15	−	8.51080e15i	−2.71245	−	2.71245i
$658$	−2.95494e15	−	1.19050e15i	−0.933911	−	0.376258i
$659$	−2.12686e15	−	2.12686e15i	−0.666606	−	0.666606i	0.290323	−	0.956929i	$-0.406237\pi$
$659$	−2.12686e15	−	2.12686e15i	−0.666606	−	0.666606i	−0.956929	+	0.290323i	$0.906237\pi$
$660$	9.00870e15	−	8.64229e14i	2.80008	−	0.268619i
$661$	2.79070e15	−	2.79070e15i	0.860211	−	0.860211i	−0.131151	−	0.991362i	$-0.541867\pi$
$661$	2.79070e15	−	2.79070e15i	0.860211	−	0.860211i	0.991362	+	0.131151i	$0.0418673\pi$
$662$	−4.70822e14	−	1.10616e15i	−0.143926	−	0.338143i
$663$	5.77151e15	−	5.77151e15i	1.74971	−	1.74971i
$664$	−2.14606e15	+	9.63077e14i	−0.645234	+	0.289559i
$665$	1.77763e14	+	2.32766e15i	0.0530056	+	0.694066i
$666$	4.18482e15	+	1.68600e15i	1.23757	+	0.498596i
$667$		−	1.59258e15i		−	0.467099i
$668$	−2.06993e13	−	1.06583e15i	−0.00602124	−	0.310040i
$669$	6.48190e15	−	6.48190e15i	1.87007	−	1.87007i
$670$	−3.96254e15	−	1.25520e15i	−1.13387	−	0.359173i
$671$			6.69572e15i			1.90031i
$672$	−3.69820e15	−	7.83016e15i	−1.04102	−	2.20414i
$673$	−2.53291e15	+	2.53291e15i	−0.707190	+	0.707190i	−0.965943	−	0.258753i	$-0.916688\pi$
$673$	−2.53291e15	+	2.53291e15i	−0.707190	+	0.707190i	0.258753	+	0.965943i	$0.416688\pi$
$674$	2.17182e15	+	5.10254e15i	0.601443	+	1.41305i
$675$	1.60833e15	+	1.04685e16i	0.441779	+	2.87550i
$676$	8.63270e14	+	8.30378e14i	0.235201	+	0.226240i
$677$	5.87173e14			0.158682			0.0793412	−	0.996848i	$-0.474718\pi$
$677$	5.87173e14			0.158682			0.0793412	+	0.996848i	$0.474718\pi$
$678$	1.60439e15	+	3.76940e15i	0.430077	+	1.01044i
$679$		−	3.85934e15i		−	1.02619i
$680$	−1.22617e15	+	4.14908e15i	−0.323409	+	1.09434i
$681$			1.34277e15i			0.351311i
$682$	5.28589e15	−	2.24986e15i	1.37184	−	0.583904i
$683$	5.98419e15			1.54061			0.770303	−	0.637678i	$-0.220105\pi$
$683$	5.98419e15			1.54061			0.770303	+	0.637678i	$0.220105\pi$
$684$	−1.04044e14	−	5.35735e15i	−0.0265712	−	1.36818i
$685$	−2.27019e15	+	2.64561e15i	−0.575128	+	0.670236i
$686$	−1.53530e15	+	6.53477e14i	−0.385843	+	0.164228i
$687$	−3.94863e14	+	3.94863e14i	−0.0984429	+	0.0984429i
$688$	1.26924e14	+	3.26648e15i	0.0313911	+	0.807874i
$689$		−	4.42469e15i		−	1.08562i
$690$	−9.78176e14	−	1.88520e15i	−0.238093	−	0.458868i
$691$	1.24669e14	−	1.24669e14i	0.0301044	−	0.0301044i	−0.691894	−	0.721999i	$-0.743224\pi$
$691$	1.24669e14	−	1.24669e14i	0.0301044	−	0.0301044i	0.721999	+	0.691894i	$0.243224\pi$
$692$	6.69830e14	+	6.44308e14i	0.160465	+	0.154351i
$693$		−	2.07126e16i		−	4.92269i
$694$	−1.55117e15	+	3.85018e15i	−0.365749	+	0.907828i
$695$	−4.73176e15	+	5.51424e15i	−1.10689	+	1.28994i
$696$	4.90810e15	−	1.28996e16i	1.13910	−	2.99381i
$697$	−6.58414e14	+	6.58414e14i	−0.151607	+	0.151607i
$698$	7.66764e15	−	3.26361e15i	1.75169	−	0.745579i
$699$	5.03688e15	−	5.03688e15i	1.14166	−	1.14166i
$700$	9.84527e14	+	5.67209e15i	0.221406	+	1.27557i
$701$	−2.10458e15	−	2.10458e15i	−0.469587	−	0.469587i	0.432194	−	0.901781i	$-0.357740\pi$
$701$	−2.10458e15	−	2.10458e15i	−0.469587	−	0.469587i	−0.901781	+	0.432194i	$0.857740\pi$
$702$	−5.65562e15	+	1.40379e16i	−1.25206	+	3.10775i
$703$	9.07351e14	+	9.07351e14i	0.199306	+	0.199306i
$704$	−6.84315e15	+	3.99101e14i	−1.49144	+	0.0869828i
$705$	−5.13875e15	−	4.40955e15i	−1.11126	−	0.953574i
$706$	−7.71873e15	+	3.28536e15i	−1.65623	+	0.704948i
$707$	−3.51871e15			−0.749163
$708$	7.86981e13	+	4.05225e15i	0.0166258	+	0.856077i
$709$	4.00661e14	+	4.00661e14i	0.0839891	+	0.0839891i	0.747853	−	0.663864i	$-0.231085\pi$
$709$	4.00661e14	+	4.00661e14i	0.0839891	+	0.0839891i	−0.663864	+	0.747853i	$0.731085\pi$
$710$	−4.83676e15	−	1.53213e15i	−1.00608	−	0.318695i
$711$	−1.06691e16			−2.20214
$712$	1.23780e15	+	2.75824e15i	0.253520	+	0.564927i
$713$	−9.53311e14	−	9.53311e14i	−0.193750	−	0.193750i
$714$	1.27932e16	+	5.15416e15i	2.58011	+	1.03948i
$715$	−6.52439e15	−	5.59856e15i	−1.30574	−	1.12045i
$716$	1.84984e13	+	9.52502e14i	0.00367378	+	0.189166i
$717$		−	5.82283e15i		−	1.14757i
$718$	1.26594e15	−	3.14219e15i	0.247587	−	0.614538i
$719$	2.88670e15			0.560264			0.280132	−	0.959961i	$-0.409622\pi$
$719$	2.88670e15			0.560264			0.280132	+	0.959961i	$0.409622\pi$
$720$	−1.51704e15	−	1.31267e16i	−0.292193	−	2.52830i
$721$	−8.23931e15			−1.57488
$722$	−1.40052e15	+	3.47623e15i	−0.265665	+	0.659408i
$723$		−	8.95944e15i		−	1.68663i
$724$	2.31791e15	−	4.50159e13i	0.433047	−	0.00841015i
$725$	−5.42754e15	+	7.39800e15i	−1.00634	+	1.37169i
$726$	−1.16924e16	−	4.71068e15i	−2.15156	−	0.866827i
$727$	5.05646e15	+	5.05646e15i	0.923438	+	0.923438i	0.997271	−	0.0738327i	$-0.0235231\pi$
$727$	5.05646e15	+	5.05646e15i	0.923438	+	0.923438i	−0.0738327	+	0.997271i	$0.523523\pi$
$728$	−2.92537e15	+	7.68851e15i	−0.530222	+	1.39354i
$729$	−1.10404e16			−1.98602
$730$	−3.88805e15	−	7.49330e15i	−0.694155	−	1.33782i
$731$	−3.68160e15	−	3.68160e15i	−0.652366	−	0.652366i
$732$	1.36152e16	−	2.64420e14i	2.39449	−	0.0465032i
$733$	−1.38851e15			−0.242370			−0.121185	−	0.992630i	$-0.538669\pi$
$733$	−1.38851e15			−0.242370			−0.121185	+	0.992630i	$0.538669\pi$
$734$	9.70145e15	−	4.12928e15i	1.68077	−	0.715395i
$735$	7.38145e15	−	5.63718e14i	1.26929	−	0.0969353i
$736$	6.87012e14	+	1.45460e15i	0.117256	+	0.248265i
$737$	7.41696e15	+	7.41696e15i	1.25648	+	1.25648i
$738$	1.06276e15	−	2.63789e15i	0.178701	−	0.443554i
$739$	−4.57270e14	−	4.57270e14i	−0.0763183	−	0.0763183i	0.667917	−	0.744236i	$-0.267186\pi$
$739$	−4.57270e14	−	4.57270e14i	−0.0763183	−	0.0763183i	−0.744236	+	0.667917i	$0.767186\pi$
$740$	2.44104e15	+	2.01369e15i	0.404391	+	0.333594i
$741$	−5.01354e15	+	5.01354e15i	−0.824412	+	0.824412i
$742$	6.87961e15	−	2.92820e15i	1.12290	−	0.477947i
$743$	−1.76850e15	+	1.76850e15i	−0.286528	+	0.286528i	−0.835706	−	0.549177i	$-0.814941\pi$
$743$	−1.76850e15	+	1.76850e15i	−0.286528	+	0.286528i	0.549177	+	0.835706i	$0.314941\pi$
$744$	−4.78365e15	−	1.06596e16i	−0.769323	−	1.71431i
$745$	1.95536e15	+	1.67789e15i	0.312153	+	0.267858i
$746$	−1.28255e15	+	3.18342e15i	−0.203241	+	0.504465i
$747$			1.14428e16i			1.79998i
$748$	7.56874e15	−	7.86854e15i	1.18186	−	1.22867i
$749$	2.53064e15	−	2.53064e15i	0.392265	−	0.392265i
$750$	−1.88089e15	+	1.20910e16i	−0.289419	+	1.86047i
$751$			4.85518e15i			0.741628i	0.928707	+	0.370814i	$0.120921\pi$
$751$			4.85518e15i			0.741628i	−0.928707	+	0.370814i	$0.879079\pi$
$752$	3.76469e15	+	3.48307e15i	0.570862	+	0.528158i
$753$	−1.21594e16	+	1.21594e16i	−1.83038	+	1.83038i
$754$	−1.20638e16	+	5.13477e15i	−1.80277	+	0.767324i
$755$	−1.36613e15	+	1.04331e14i	−0.202668	+	0.0154777i
$756$	−2.55692e16	+	4.96576e14i	−3.76571	+	0.0731334i
$757$	7.20654e15			1.05366			0.526829	−	0.849971i	$-0.323381\pi$
$757$	7.20654e15			1.05366			0.526829	+	0.849971i	$0.323381\pi$
$758$	−2.99331e15	+	1.27406e15i	−0.434481	+	0.184930i
$759$			5.35958e15i			0.772327i
$760$	1.06514e15	−	3.60418e15i	0.152381	−	0.515623i
$761$			1.05688e16i			1.50110i	0.660811	+	0.750552i	$0.270213\pi$
$761$			1.05688e16i			1.50110i	−0.660811	+	0.750552i	$0.729787\pi$
$762$	−5.03264e15	−	1.18238e16i	−0.709649	−	1.66727i
$763$	8.67358e15			1.21426
$764$	−5.92444e15	+	6.15912e15i	−0.823444	+	0.856062i
$765$	1.59722e16	+	1.37057e16i	2.20408	+	1.89132i
$766$	−4.78051e15	−	1.12315e16i	−0.654962	−	1.53879i
$767$	2.72250e15	−	2.72250e15i	0.370333	−	0.370333i
$768$	1.08178e15	+	1.38992e16i	0.146101	+	1.87717i
$769$			1.38272e16i			1.85413i	0.374905	+	0.927063i	$0.377675\pi$
$769$			1.38272e16i			1.85413i	−0.374905	+	0.927063i	$0.622325\pi$
$770$	4.38702e15	−	1.38493e16i	0.584077	−	1.84387i
$771$	2.94205e15	−	2.94205e15i	0.388912	−	0.388912i
$772$	−5.90800e14	+	1.14739e13i	−0.0775435	+	0.00150596i
$773$		−	7.76386e15i		−	1.01179i	−0.862595	−	0.505895i	$-0.831162\pi$
$773$		−	7.76386e15i		−	1.01179i	0.862595	−	0.505895i	$-0.168838\pi$
$774$	1.47501e16	+	5.94256e15i	1.90862	+	0.768951i
$775$	1.17950e15	+	7.67731e15i	0.151545	+	0.986392i
$776$	−2.20952e15	+	5.80711e15i	−0.281877	+	0.740834i
$777$	7.13325e15	−	7.13325e15i	0.903591	−	0.903591i
$778$	2.78244e15	+	6.53716e15i	0.349976	+	0.822245i
$779$	5.71945e14	−	5.71945e14i	0.0714329	−	0.0714329i
$780$	−1.11266e16	+	1.34879e16i	−1.37988	+	1.67272i
$781$	9.05331e15	+	9.05331e15i	1.11488	+	1.11488i
$782$	−2.37658e15	−	9.57484e14i	−0.290613	−	0.117083i
$783$	−2.88219e16	−	2.88219e16i	−3.49971	−	3.49971i
$784$	−5.60298e15	+	2.17712e14i	−0.675586	+	0.0262508i
$785$	4.04274e14	+	5.29365e15i	0.0484053	+	0.633830i
$786$	6.50630e15	+	1.52861e16i	0.773589	+	1.81749i
$787$	−8.80829e15			−1.03999			−0.519996	−	0.854168i	$-0.674067\pi$
$787$	−8.80829e15			−1.03999			−0.519996	+	0.854168i	$0.674067\pi$
$788$	−6.29882e11	−	6.05882e11i	−7.38525e−5	−	7.10386e-5i
$789$	1.24161e16	+	1.24161e16i	1.44565	+	1.44565i
$790$	−7.13379e15	−	2.25976e15i	−0.824843	−	0.261284i
$791$	6.57610e15			0.755088
$792$	−1.18583e16	+	3.11661e16i	−1.35217	+	3.55381i
$793$	−9.14737e15	−	9.14737e15i	−1.03584	−	1.03584i
$794$	−3.89068e15	+	9.65709e15i	−0.437535	+	1.08601i
$795$	1.58460e16	−	1.21015e15i	1.76971	−	0.135152i
$796$	3.60583e14	−	3.74866e14i	0.0399929	−	0.0415771i
$797$		−	1.40932e16i		−	1.55235i	−0.630516	−	0.776176i	$-0.717157\pi$
$797$		−	1.40932e16i		−	1.55235i	0.630516	−	0.776176i	$-0.282843\pi$
$798$	−1.11131e16	−	4.47727e15i	−1.21568	−	0.489776i
$799$	−8.16884e15			−0.887469
$800$	1.76594e15	−	9.09840e15i	0.190538	−	0.981680i
$801$	1.47070e16			1.57596
$802$	1.23649e16	+	4.98163e15i	1.31593	+	0.530167i
$803$			2.13033e16i			2.25170i
$804$	1.47889e16	−	1.53747e16i	1.55249	−	1.61398i
$805$	−3.39943e15	+	2.59613e14i	−0.354428	+	0.0270675i
$806$	−4.14768e15	+	1.02950e16i	−0.429499	+	1.06606i
$807$	2.68966e15	+	2.68966e15i	0.276626	+	0.276626i
$808$	5.29457e15	+	2.01451e15i	0.540839	+	0.205782i
$809$	6.49220e15			0.658681			0.329340	−	0.944211i	$-0.393174\pi$
$809$	6.49220e15			0.658681			0.329340	+	0.944211i	$0.393174\pi$
$810$	−2.77426e16	−	8.78797e15i	−2.79563	−	0.885566i
$811$	4.23176e15	+	4.23176e15i	0.423551	+	0.423551i	0.886425	−	0.462873i	$-0.153181\pi$
$811$	4.23176e15	+	4.23176e15i	0.423551	+	0.423551i	−0.462873	+	0.886425i	$0.653181\pi$
$812$	−1.59673e16	−	1.53589e16i	−1.58735	−	1.52687i
$813$	3.75143e15			0.370423
$814$	−3.12739e15	−	7.34758e15i	−0.306724	−	0.720626i
$815$	−6.77369e14	−	8.86962e15i	−0.0659870	−	0.864048i
$816$	−1.62990e16	−	1.50797e16i	−1.57712	−	1.45914i
$817$	3.19810e15	+	3.19810e15i	0.307377	+	0.307377i
$818$	−1.53190e15	−	6.17179e14i	−0.146248	−	0.0589207i
$819$	2.82966e16	+	2.82966e16i	2.68332	+	2.68332i
$820$	1.26932e15	−	1.53870e15i	0.119563	−	0.144937i
$821$	−1.05770e16	+	1.05770e16i	−0.989631	+	0.989631i	−0.999947	−	0.0103159i	$-0.996716\pi$
$821$	−1.05770e16	+	1.05770e16i	−0.989631	+	0.989631i	0.0103159	+	0.999947i	$0.496716\pi$
$822$	−7.00708e15	−	1.64627e16i	−0.651242	−	1.53005i
$823$	6.95676e15	−	6.95676e15i	0.642256	−	0.642256i	−0.308854	−	0.951109i	$-0.599945\pi$
$823$	6.95676e15	−	6.95676e15i	0.642256	−	0.642256i	0.951109	+	0.308854i	$0.0999454\pi$
$824$	1.23976e16	+	4.71712e15i	1.13694	+	0.432590i
$825$	1.82656e16	−	2.48968e16i	1.66393	−	2.26802i
$826$	6.03471e15	+	2.43129e15i	0.546093	+	0.220012i
$827$		−	1.83255e16i		−	1.64731i	−0.567090	−	0.823656i	$-0.691931\pi$
$827$		−	1.83255e16i		−	1.64731i	0.567090	−	0.823656i	$-0.308069\pi$
$828$	7.82413e15	−	1.51951e14i	0.698665	−	0.0135687i
$829$	−8.02019e15	+	8.02019e15i	−0.711434	+	0.711434i	−0.966835	−	0.255401i	$-0.917793\pi$
$829$	−8.02019e15	+	8.02019e15i	−0.711434	+	0.711434i	0.255401	+	0.966835i	$0.417793\pi$
$830$	−2.42363e15	+	7.65112e15i	−0.213568	+	0.674211i
$831$		−	6.42270e15i		−	0.562227i
$832$	8.80355e15	−	9.89401e15i	0.765560	−	0.860388i
$833$	6.31504e15	−	6.31504e15i	0.545542	−	0.545542i
$834$	−1.46048e16	−	3.43130e16i	−1.25338	−	2.94473i
$835$	−2.76031e15	−	2.36862e15i	−0.235333	−	0.201939i
$836$	−6.57474e15	+	6.83517e15i	−0.556857	+	0.578915i
$837$	−3.45052e16			−2.90332
$838$	4.75493e15	+	1.11714e16i	0.397468	+	0.933823i
$839$			5.18444e15i			0.430538i	0.976555	+	0.215269i	$0.0690628\pi$
$839$			5.18444e15i			0.430538i	−0.976555	+	0.215269i	$0.930937\pi$
$840$	−2.83347e16	−	8.37373e15i	−2.33767	−	0.690849i
$841$		−	2.31108e16i		−	1.89424i
$842$	1.41457e16	−	6.02091e15i	1.15188	−	0.490282i
$843$	−2.06843e16			−1.67336
$844$	1.01595e15	−	1.97305e13i	0.0816558	−	0.00158583i
$845$	4.07504e15	−	3.11209e14i	0.325402	−	0.0248508i
$846$	2.29567e16	−	9.77117e15i	1.82126	−	0.775192i
$847$	−1.43084e16	+	1.43084e16i	−1.12780	+	1.12780i
$848$	−1.20281e16	+	4.67369e14i	−0.941934	+	0.0366002i
$849$			1.96765e15i			0.153093i
$850$	7.77677e15	+	1.25472e16i	0.601167	+	0.969936i
$851$	−1.32514e15	+	1.32514e15i	−0.101777	+	0.101777i
$852$	1.80517e16	−	1.87667e16i	1.37752	−	1.43209i
$853$		−	1.99555e16i		−	1.51301i	−0.653987	−	0.756506i	$-0.726905\pi$
$853$		−	1.99555e16i		−	1.51301i	0.653987	−	0.756506i	$-0.273095\pi$
$854$	8.16893e15	−	2.02762e16i	0.615385	−	1.52745i
$855$	−1.38746e16	−	1.19058e16i	−1.03850	−	0.891136i
$856$	−5.25665e15	+	2.35900e15i	−0.390934	+	0.175438i
$857$	2.53526e15	−	2.53526e15i	0.187339	−	0.187339i	−0.607206	−	0.794545i	$-0.707710\pi$
$857$	2.53526e15	−	2.53526e15i	0.187339	−	0.187339i	0.794545	+	0.607206i	$0.207710\pi$
$858$	4.05988e16	−	1.72803e16i	2.98080	−	1.26873i
$859$	−1.05368e16	+	1.05368e16i	−0.768680	+	0.768680i	−0.977874	−	0.209194i	$-0.932916\pi$
$859$	−1.05368e16	+	1.05368e16i	−0.768680	+	0.768680i	0.209194	+	0.977874i	$0.432916\pi$
$860$	8.60385e15	+	7.09757e15i	0.623665	+	0.514479i
$861$	−4.49642e15	−	4.49642e15i	−0.323854	−	0.323854i
$862$	−5.99544e15	+	1.48813e16i	−0.429073	+	1.06500i
$863$	−1.32312e16	−	1.32312e16i	−0.940894	−	0.940894i	0.0574541	−	0.998348i	$-0.481702\pi$
$863$	−1.32312e16	−	1.32312e16i	−0.940894	−	0.940894i	−0.998348	+	0.0574541i	$0.981702\pi$
$864$	3.87580e16	+	1.38915e16i	2.73865	+	0.981576i
$865$	3.16192e15	−	2.41474e14i	0.222004	−	0.0169544i
$866$	3.16048e15	−	1.34521e15i	0.220498	−	0.0938517i
$867$	8.20696e15			0.568954
$868$	−1.87517e16	+	3.64175e14i	−1.29176	+	0.0250872i
$869$	1.33528e16	+	1.33528e16i	0.914038	+	0.914038i
$870$	−2.16885e16	−	4.17994e16i	−1.47528	−	2.84324i
$871$	−2.02654e16			−1.36979
$872$	−1.30510e16	−	4.96574e15i	−0.876607	−	0.333536i
$873$	2.13723e16	+	2.13723e16i	1.42651	+	1.42651i
$874$	2.06446e15	+	8.31738e14i	0.136929	+	0.0551663i
$875$	1.66761e16	+	1.03793e16i	1.09913	+	0.684109i
$876$	4.33185e16	−	8.41283e14i	2.83727	−	0.0551023i
$877$		−	1.56148e16i		−	1.01634i	−0.861256	−	0.508171i	$-0.830322\pi$
$877$		−	1.56148e16i		−	1.01634i	0.861256	−	0.508171i	$-0.169678\pi$
$878$	−4.67227e15	+	1.15971e16i	−0.302210	+	0.750116i
$879$	−2.63394e15			−0.169304
$880$	−1.45300e16	+	1.83273e16i	−0.928136	+	1.17070i
$881$	2.85943e16			1.81515			0.907574	−	0.419892i	$-0.137932\pi$
$881$	2.85943e16			1.81515			0.907574	+	0.419892i	$0.137932\pi$
$882$	−1.01932e16	+	2.53007e16i	−0.643036	+	1.59608i
$883$		−	4.91131e15i		−	0.307903i	−0.988078	−	0.153951i	$-0.950800\pi$
$883$		−	4.91131e15i		−	0.307903i	0.988078	−	0.153951i	$-0.0491999\pi$
$884$	4.09580e14	+	2.10897e16i	0.0255182	+	1.31396i
$885$	1.04946e16	+	9.00540e15i	0.649798	+	0.557590i
$886$	−5.11766e15	−	2.06182e15i	−0.314910	−	0.126872i
$887$	−1.79212e16	−	1.79212e16i	−1.09594	−	1.09594i	−0.994880	−	0.101059i	$-0.967777\pi$
$887$	−1.79212e16	−	1.79212e16i	−1.09594	−	1.09594i	−0.101059	−	0.994880i	$-0.532223\pi$
$888$	−1.48172e16	+	6.64945e15i	−0.900524	+	0.404124i
$889$	−2.06279e16			−1.24593
$890$	9.83368e15	+	3.11499e15i	0.590297	+	0.186987i
$891$	5.19278e16	+	5.19278e16i	3.09794	+	3.09794i
$892$	4.59993e14	+	2.36855e16i	0.0272737	+	1.40435i
$893$	7.09603e15			0.418150
$894$	−1.21675e16	+	5.17890e15i	−0.712597	+	0.303306i
$895$	2.46681e15	+	2.11677e15i	0.143585	+	0.123210i
$896$	2.12095e16	+	7.14023e15i	1.22698	+	0.413065i
$897$	−7.32200e15	−	7.32200e15i	−0.420990	−	0.420990i
$898$	−5.90664e15	+	1.46609e16i	−0.337537	+	0.837802i
$899$	−2.11371e16	−	2.11371e16i	−1.20052	−	1.20052i
$900$	−3.68632e16	−	2.59589e16i	−2.08094	−	1.46539i
$901$	1.35567e16	−	1.35567e16i	0.760621	−	0.760621i
$902$	−4.63152e15	+	1.97134e15i	−0.258278	+	0.109932i
$903$	2.51423e16	−	2.51423e16i	1.39355	−	1.39355i
$904$	−9.89499e15	−	3.76490e15i	−0.545116	−	0.207409i
$905$	5.15115e15	−	6.00299e15i	0.282057	−	0.328701i
$906$	2.62777e15	−	6.52239e15i	0.143015	−	0.354978i
$907$		−	4.64657e15i		−	0.251358i	−0.992071	−	0.125679i	$-0.959889\pi$
$907$		−	4.64657e15i		−	0.251358i	0.992071	−	0.125679i	$-0.0401109\pi$
$908$	−2.50095e15	−	2.40566e15i	−0.134472	−	0.129349i
$909$	1.94860e16	−	1.94860e16i	1.04141	−	1.04141i
$910$	1.29269e16	+	2.49136e16i	0.686701	+	1.32345i
$911$		−	3.38058e16i		−	1.78501i	−0.451042	−	0.892503i	$-0.648948\pi$
$911$		−	3.38058e16i		−	1.78501i	0.451042	−	0.892503i	$-0.351052\pi$
$912$	1.41584e16	+	1.30993e16i	0.743093	+	0.687505i
$913$	1.43211e16	−	1.43211e16i	0.747117	−	0.747117i
$914$	2.63496e16	−	1.12153e16i	1.36638	−	0.581577i
$915$	3.02574e16	−	3.52611e16i	1.55961	−	1.81752i
$916$	−2.80218e13	−	1.44287e15i	−0.00143572	−	0.0739268i
$917$	2.66682e16			1.35819
$918$	−6.03385e16	+	2.56822e16i	−3.05464	+	1.30016i
$919$			2.01885e16i			1.01594i	0.861374	+	0.507970i	$0.169604\pi$
$919$			2.01885e16i			1.01594i	−0.861374	+	0.507970i	$0.830396\pi$
$920$	5.26372e15	+	1.55558e15i	0.263305	+	0.0778143i
$921$			4.78346e16i			2.37856i
$922$	1.19571e15	+	2.80924e15i	0.0591025	+	0.138857i
$923$	−2.47364e16			−1.21542
$924$	5.37355e16	+	5.16881e16i	2.62462	+	2.52461i
$925$	1.06717e16	−	1.63955e15i	0.518150	−	0.0796061i
$926$	7.06784e15	+	1.66054e16i	0.341135	+	0.801473i
$927$	4.56279e16	−	4.56279e16i	2.18923	−	2.18923i
$928$	1.52327e16	+	3.22519e16i	0.726545	+	1.53830i
$929$			1.74996e16i			0.829741i	0.909881	+	0.414870i	$0.136173\pi$
$929$			1.74996e16i			0.829741i	−0.909881	+	0.414870i	$0.863827\pi$
$930$	−3.80035e16	−	1.20383e16i	−1.79130	−	0.567425i
$931$	−5.48569e15	+	5.48569e15i	−0.257044	+	0.257044i
$932$	3.57446e14	+	1.84052e16i	0.0166503	+	0.857342i
$933$			6.67490e15i			0.309098i
$934$	−2.81626e16	−	1.13462e16i	−1.29648	−	0.522329i
$935$	−2.83662e15	−	3.71432e16i	−0.129818	−	1.69987i
$936$	−2.63774e16	−	5.87778e16i	−1.20009	−	2.67421i
$937$	−1.60652e16	+	1.60652e16i	−0.726640	+	0.726640i	−0.969949	−	0.243309i	$-0.921767\pi$
$937$	−1.60652e16	+	1.60652e16i	−0.726640	+	0.726640i	0.243309	+	0.969949i	$0.421767\pi$
$938$	−1.34114e16	−	3.15091e16i	−0.603056	−	1.41684i
$939$	5.29639e16	−	5.29639e16i	2.36766	−	2.36766i
$940$	1.74194e16	−	1.67109e15i	0.774157	−	0.0742670i
$941$	−4.19882e15	−	4.19882e15i	−0.185517	−	0.185517i	0.608238	−	0.793755i	$-0.291877\pi$
$941$	−4.19882e15	−	4.19882e15i	−0.185517	−	0.185517i	−0.793755	+	0.608238i	$0.791877\pi$
$942$	−2.52737e16	−	1.01824e16i	−1.11017	−	0.447269i
$943$	8.35295e14	+	8.35295e14i	0.0364775	+	0.0364775i
$944$	−7.68843e15	−	7.11329e15i	−0.333804	−	0.308834i
$945$	−5.68230e16	+	6.62198e16i	−2.45273	+	2.85833i
$946$	−1.10230e16	−	2.58977e16i	−0.473039	−	1.11137i
$947$	3.37906e16			1.44169			0.720844	−	0.693098i	$-0.243755\pi$
$947$	3.37906e16			1.44169			0.720844	+	0.693098i	$0.243755\pi$
$948$	2.66246e16	−	2.76792e16i	1.12937	−	1.17411i
$949$	−2.91035e16	−	2.91035e16i	−1.22738	−	1.22738i
$950$	−6.75545e15	−	1.08994e16i	−0.283253	−	0.457007i
$951$	−5.89663e15			−0.245816
$952$	−3.25196e16	+	1.45937e16i	−1.34785	+	0.604870i
$953$	−2.82468e16	−	2.82468e16i	−1.16402	−	1.16402i	−0.983588	−	0.180427i	$-0.942252\pi$
$953$	−2.82468e16	−	2.82468e16i	−1.16402	−	1.16402i	−0.180427	−	0.983588i	$-0.557748\pi$
$954$	−2.18822e16	+	5.43140e16i	−0.896551	+	2.22533i
$955$	2.22037e15	+	2.90740e16i	0.0904495	+	1.18437i
$956$	1.08452e16	+	1.04320e16i	0.439258	+	0.422521i
$957$			1.18835e17i			4.78550i
$958$	−1.43870e16	−	5.79629e15i	−0.576050	−	0.232081i
$959$	−2.87208e16			−1.14339
$960$	3.78409e16	+	2.88219e16i	1.49786	+	1.14086i
$961$	1.03295e14			0.00406538
$962$	1.43104e16	+	5.76542e15i	0.560001	+	0.225615i
$963$			2.80285e16i			1.09057i
$964$	1.66872e16	+	1.60514e16i	0.645596	+	0.620998i
$965$	−1.31295e15	+	1.53007e15i	−0.0505066	+	0.0588588i
$966$	6.53881e15	−	1.62300e16i	0.250106	−	0.620790i
$967$	−3.36691e16	−	3.36691e16i	−1.28052	−	1.28052i	−0.940374	−	0.340143i	$-0.889524\pi$
$967$	−3.36691e16	−	3.36691e16i	−1.28052	−	1.28052i	−0.340143	−	0.940374i	$-0.610476\pi$
$968$	2.97215e16	−	1.33380e16i	1.12398	−	0.504401i
$969$	−3.07218e16			−1.15522
$970$	9.76368e15	+	1.88172e16i	0.365064	+	0.703574i
$971$	−1.31715e16	−	1.31715e16i	−0.489699	−	0.489699i	0.418512	−	0.908211i	$-0.362552\pi$
$971$	−1.31715e16	−	1.31715e16i	−0.489699	−	0.489699i	−0.908211	+	0.418512i	$0.862552\pi$
$972$	4.89860e16	−	5.09264e16i	1.81096	−	1.88269i
$973$	−5.98626e16			−2.20057
$974$	6.65710e15	+	1.56404e16i	0.243339	+	0.571707i
$975$	9.05931e15	+	5.89664e16i	0.329283	+	2.14328i
$976$	−2.39001e16	+	2.58325e16i	−0.863825	+	0.933669i
$977$	2.62919e16	+	2.62919e16i	0.944934	+	0.944934i	0.998561	−	0.0536269i	$-0.0170782\pi$
$977$	2.62919e16	+	2.62919e16i	0.944934	+	0.944934i	−0.0536269	+	0.998561i	$0.517078\pi$
$978$	4.23466e16	+	1.70607e16i	1.51340	+	0.609725i
$979$	−1.84064e16	−	1.84064e16i	−0.654129	−	0.654129i
$980$	−1.21744e16	+	1.47581e16i	−0.430234	+	0.521540i
$981$	−4.80328e16	+	4.80328e16i	−1.68794	+	1.68794i
$982$	−2.09537e16	−	4.92293e16i	−0.732231	−	1.72033i
$983$	−2.95751e15	+	2.95751e15i	−0.102774	+	0.102774i	−0.756624	−	0.653850i	$-0.773153\pi$
$983$	−2.95751e15	+	2.95751e15i	−0.102774	+	0.102774i	0.653850	+	0.756624i	$0.273153\pi$
$984$	4.19146e15	+	9.33998e15i	0.144841	+	0.322755i
$985$	−2.97334e12	+	2.27073e11i	−0.000102175	+	7.80308e-6i
$986$	−5.26943e16	−	2.12297e16i	−1.80070	−	0.725472i
$987$		−	5.57863e16i		−	1.89576i
$988$	−3.55790e14	−	1.83200e16i	−0.0120235	−	0.619101i
$989$	−4.67065e15	+	4.67065e15i	−0.156963	+	0.156963i
$990$	5.24006e16	+	1.00990e17i	1.75123	+	3.37508i
$991$		−	3.63611e16i		−	1.20846i	−0.796811	−	0.604229i	$-0.793481\pi$
$991$		−	3.63611e16i		−	1.20846i	0.796811	−	0.604229i	$-0.206519\pi$
$992$	2.84241e16	+	1.01876e16i	0.939446	+	0.336713i
$993$	1.48860e16	−	1.48860e16i	0.489279	−	0.489279i
$994$	−1.63702e16	−	3.84607e16i	−0.535093	−	1.25716i
$995$	−1.35140e14	−	1.76955e15i	−0.00439294	−	0.0575221i
$996$	−2.96865e16	−	2.85553e16i	−0.959692	−	0.923126i
$997$	4.91796e16			1.58111			0.790555	−	0.612391i	$-0.209792\pi$
$997$	4.91796e16			1.58111			0.790555	+	0.612391i	$0.209792\pi$
$998$	2.34746e15	+	5.51519e15i	0.0750551	+	0.176337i
$999$			4.79636e16i			1.52511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.12.j.a.67.16	yes	260
5.3	odd	4		80.12.s.a.3.50	yes	260
16.11	odd	4		80.12.s.a.27.50	yes	260
80.43	even	4	inner	80.12.j.a.43.16	✓	260

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.12.j.a.43.16	✓	260	80.43	even	4	inner
80.12.j.a.67.16	yes	260	1.1	even	1	trivial
80.12.s.a.3.50	yes	260	5.3	odd	4
80.12.s.a.27.50	yes	260	16.11	odd	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	80.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-41.9762 - 16.9115i) q^{2} -792.470i q^{3} +(1476.00 + 1419.76i) q^{4} +(6967.42 - 532.099i) q^{5} +(-13401.9 + 33264.9i) q^{6} +(40707.4 + 40707.4i) q^{7} +(-37946.5 - 84557.6i) q^{8} -450861. q^{9} +(-301465. - 95494.2i) q^{10} +(564272. + 564272. i) q^{11} +(1.12512e6 - 1.16969e6i) q^{12} -1.54176e6 q^{13} +(-1.02032e6 - 2.39717e6i) q^{14} +(-421673. - 5.52147e6i) q^{15} +(162853. + 4.19114e6i) q^{16} +(-4.72377e6 - 4.72377e6i) q^{17} +(1.89254e7 + 7.62475e6i) q^{18} +(4.10340e6 + 4.10340e6i) q^{19} +(1.10394e7 + 9.10671e6i) q^{20} +(3.22594e7 - 3.22594e7i) q^{21} +(-1.41433e7 - 3.32287e7i) q^{22} +(-5.99280e6 + 5.99280e6i) q^{23} +(-6.70094e7 + 3.00715e7i) q^{24} +(4.82619e7 - 7.41472e6i) q^{25} +(6.47173e7 + 2.60735e7i) q^{26} +2.16910e8i q^{27} +(2.28931e6 + 1.17879e8i) q^{28} +(-1.32874e8 + 1.32874e8i) q^{29} +(-7.56763e7 + 2.38902e8i) q^{30} +1.59076e8i q^{31} +(6.40426e7 - 1.78682e8i) q^{32} +(4.47169e8 - 4.47169e8i) q^{33} +(1.18400e8 + 2.78172e8i) q^{34} +(3.05286e8 + 2.61966e8i) q^{35} +(-6.65472e8 - 6.40116e8i) q^{36} +2.21122e8 q^{37} +(-1.02850e8 - 2.41640e8i) q^{38} +1.22180e9i q^{39} +(-3.09383e8 - 5.68958e8i) q^{40} -1.39383e8i q^{41} +(-1.89968e9 + 8.08571e8i) q^{42} +7.79378e8 q^{43} +(3.17337e7 + 1.63400e9i) q^{44} +(-3.14134e9 + 2.39903e8i) q^{45} +(3.52902e8 - 1.50208e8i) q^{46} +(8.64652e8 - 8.64652e8i) q^{47} +(3.32135e9 - 1.29056e8i) q^{48} +1.33686e9i q^{49} +(-2.15124e9 - 5.04940e8i) q^{50} +(-3.74345e9 + 3.74345e9i) q^{51} +(-2.27564e9 - 2.18894e9i) q^{52} +2.86989e9i q^{53} +(3.66829e9 - 9.10507e9i) q^{54} +(4.23177e9 + 3.63127e9i) q^{55} +(1.89742e9 - 4.98683e9i) q^{56} +(3.25182e9 - 3.25182e9i) q^{57} +(7.82467e9 - 3.33045e9i) q^{58} +(-1.76583e9 + 1.76583e9i) q^{59} +(7.21679e9 - 8.74837e9i) q^{60} +(5.93306e9 + 5.93306e9i) q^{61} +(2.69022e9 - 6.67741e9i) q^{62} +(-1.83534e10 - 1.83534e10i) q^{63} +(-5.71005e9 + 6.41734e9i) q^{64} +(-1.07421e10 + 8.20371e8i) q^{65} +(-2.63327e10 + 1.12081e10i) q^{66} +1.31443e10 q^{67} +(-2.65657e8 - 1.36789e10i) q^{68} +(4.74911e9 + 4.74911e9i) q^{69} +(-8.38452e9 - 1.61592e10i) q^{70} +1.60442e10 q^{71} +(1.71086e10 + 3.81238e10i) q^{72} +(1.88768e10 + 1.88768e10i) q^{73} +(-9.28184e9 - 3.73950e9i) q^{74} +(-5.87595e9 - 3.82461e10i) q^{75} +(2.30768e8 + 1.18825e10i) q^{76} +4.59401e10i q^{77} +(2.06625e10 - 5.12865e10i) q^{78} +2.36638e10 q^{79} +(3.36477e9 + 2.91148e10i) q^{80} +9.20262e10 q^{81} +(-2.35718e9 + 5.85077e9i) q^{82} -2.53798e10i q^{83} +(9.34156e10 - 1.81421e9i) q^{84} +(-3.54261e10 - 3.03990e10i) q^{85} +(-3.27153e10 - 1.31805e10i) q^{86} +(1.05299e11 + 1.05299e11i) q^{87} +(2.63013e10 - 6.91257e10i) q^{88} -3.26197e10 q^{89} +(1.35919e11 + 4.30547e10i) q^{90} +(-6.27612e10 - 6.27612e10i) q^{91} +(-1.73537e10 + 3.37025e8i) q^{92} +1.26063e11 q^{93} +(-5.09174e10 + 2.16722e10i) q^{94} +(3.07736e10 + 2.64067e10i) q^{95} +(-1.41600e11 - 5.07519e10i) q^{96} +(-4.74034e10 - 4.74034e10i) q^{97} +(2.26084e10 - 5.61164e10i) q^{98} +(-2.54409e11 - 2.54409e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 260 q - 2 q^{2} - 3956 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 74840 q^{8} - 14880348 q^{9} - 4098 q^{10} - 4 q^{11} - 114212 q^{12} - 4 q^{13} + 708588 q^{15} + 5740152 q^{16} - 4 q^{17} - 6791722 q^{18}+ \cdots - 189350900660 q^{99}+O(q^{100}) \) 260 * q - 2 * q^2 - 3956 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 74840 * q^8 - 14880348 * q^9 - 4098 * q^10 - 4 * q^11 - 114212 * q^12 - 4 * q^13 + 708588 * q^15 + 5740152 * q^16 - 4 * q^17 - 6791722 * q^18 - 11291288 * q^19 + 27599212 * q^20 - 4 * q^21 + 11921800 * q^22 - 4 * q^23 + 708588 * q^24 - 196875380 * q^26 + 185066800 * q^28 - 534157704 * q^30 - 894200972 * q^32 - 4 * q^33 - 122727336 * q^34 + 434731680 * q^35 + 917614156 * q^36 - 4 * q^37 - 169550316 * q^38 - 1417066568 * q^40 - 1572161236 * q^42 - 4763690660 * q^43 - 1456070840 * q^44 - 97301958 * q^45 - 3653567828 * q^46 + 5707353192 * q^47 - 447163780 * q^48 + 429408694 * q^50 + 112221284 * q^51 - 4957065880 * q^52 - 10995087044 * q^54 - 4 * q^55 - 8945492140 * q^56 + 708588 * q^57 + 33722126388 * q^58 - 11496390224 * q^59 - 6670533420 * q^60 - 2150827028 * q^61 + 15717297108 * q^62 + 708588 * q^63 - 11018267024 * q^64 - 4 * q^65 - 9909115916 * q^66 + 44333852084 * q^67 - 74998571352 * q^68 + 16194123612 * q^69 + 50947270608 * q^70 - 43677902056 * q^71 - 56634399632 * q^72 + 12278087704 * q^73 - 99553151276 * q^74 + 85400572304 * q^75 + 46613107196 * q^76 + 205137826492 * q^78 + 130159671844 * q^80 + 794986843420 * q^81 + 83904972628 * q^82 + 216982878048 * q^84 - 97656252 * q^85 + 56725646132 * q^86 - 50128110092 * q^87 + 346072249440 * q^88 + 174291105374 * q^90 - 46617621428 * q^91 - 51820450984 * q^92 + 708584 * q^93 - 82977932908 * q^94 - 20580862760 * q^95 - 62470624376 * q^96 - 4 * q^97 - 155418407946 * q^98 - 189350900660 * q^99

Introduction

L-functions

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