LMFDB - Embedded newform 14.13.b.a.13.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,13,Mod(13,14)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 13, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("14.13");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	14.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.7959134419$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 154710x^{6} + 8245426887x^{4} + 174724076278260x^{2} + 1264170035276291934 $ x^8 + 154710x^6 + 8245426887x^4 + 174724076278260*x^2 + 1264170035276291934
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.3
Root			$-130.480i$ of defining polynomial
Character	$\chi$	$=$	14.13
Dual form			14.13.b.a.13.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-45.2548 q^{2} +102.042i q^{3} +2048.00 q^{4} +6916.58i q^{5} -4617.87i q^{6} +(-14384.7 - 116766. i) q^{7} -92681.9 q^{8} +521029. q^{9} +O(q^{10})$	\(q-45.2548 q^{2} +102.042i q^{3} +2048.00 q^{4} +6916.58i q^{5} -4617.87i q^{6} +(-14384.7 - 116766. i) q^{7} -92681.9 q^{8} +521029. q^{9} -313009. i q^{10} -1.34540e6 q^{11} +208981. i q^{12} +5.40570e6i q^{13} +(650975. + 5.28424e6i) q^{14} -705778. q^{15} +4.19430e6 q^{16} +4.33512e7i q^{17} -2.35791e7 q^{18} +4.81282e7i q^{19} +1.41652e7i q^{20} +(1.19150e7 - 1.46783e6i) q^{21} +6.08857e7 q^{22} -1.61270e8 q^{23} -9.45740e6i q^{24} +1.96302e8 q^{25} -2.44634e8i q^{26} +1.07396e8i q^{27} +(-2.94598e7 - 2.39137e8i) q^{28} -7.77122e7 q^{29} +3.19399e7 q^{30} +1.36270e8i q^{31} -1.89813e8 q^{32} -1.37286e8i q^{33} -1.96185e9i q^{34} +(8.07623e8 - 9.94926e7i) q^{35} +1.06707e9 q^{36} -1.35560e9 q^{37} -2.17803e9i q^{38} -5.51606e8 q^{39} -6.41042e8i q^{40} +4.10282e9i q^{41} +(-5.39212e8 + 6.64265e7i) q^{42} +2.00941e9 q^{43} -2.75537e9 q^{44} +3.60373e9i q^{45} +7.29824e9 q^{46} +1.64105e10i q^{47} +4.27993e8i q^{48} +(-1.34275e10 + 3.35929e9i) q^{49} -8.88359e9 q^{50} -4.42362e9 q^{51} +1.10709e10i q^{52} +2.76670e10 q^{53} -4.86017e9i q^{54} -9.30554e9i q^{55} +(1.33320e9 + 1.08221e10i) q^{56} -4.91107e9 q^{57} +3.51685e9 q^{58} -3.80747e10i q^{59} -1.44543e9 q^{60} -8.36798e10i q^{61} -6.16686e9i q^{62} +(-7.49481e9 - 6.08386e10i) q^{63} +8.58993e9 q^{64} -3.73889e10 q^{65} +6.21287e9i q^{66} +9.92030e10 q^{67} +8.87833e10i q^{68} -1.64562e10i q^{69} +(-3.65489e10 + 4.50252e9i) q^{70} -3.72326e10 q^{71} -4.82899e10 q^{72} +7.69138e10i q^{73} +6.13475e10 q^{74} +2.00309e10i q^{75} +9.85665e10i q^{76} +(1.93531e10 + 1.57097e11i) q^{77} +2.49628e10 q^{78} -2.27529e11 q^{79} +2.90102e10i q^{80} +2.65937e11 q^{81} -1.85672e11i q^{82} +1.32152e11i q^{83} +(2.44019e10 - 3.00612e9i) q^{84} -2.99842e11 q^{85} -9.09353e10 q^{86} -7.92987e9i q^{87} +1.24694e11 q^{88} +5.07290e11i q^{89} -1.63086e11i q^{90} +(6.31203e11 - 7.77591e10i) q^{91} -3.30281e11 q^{92} -1.39052e10 q^{93} -7.42656e11i q^{94} -3.32882e11 q^{95} -1.93688e10i q^{96} -2.74033e11i q^{97} +(6.07657e11 - 1.52024e11i) q^{98} -7.00990e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9}+O(q^{10}) $ 8 * q + 16384 * q^4 + 195160 * q^7 - 1478904 * q^9	\( 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9} - 213840 q^{11} - 8418816 q^{14} + 65882304 q^{15} + 33554432 q^{16} + 32547840 q^{18} - 4449984 q^{21} - 221337600 q^{22} + 156731760 q^{23} + 191237000 q^{25} + 399687680 q^{28} + 308853648 q^{29} - 2203567104 q^{30} - 3764734848 q^{35} - 3028795392 q^{36} - 3243600880 q^{37} + 13521315264 q^{39} - 12108579840 q^{42} + 21006302000 q^{43} - 437944320 q^{44} + 9664610304 q^{46} - 19258758904 q^{49} + 26259489792 q^{50} - 80965832832 q^{51} + 180445637520 q^{53} - 17241735168 q^{56} - 63145962240 q^{57} - 94193264640 q^{58} + 134926958592 q^{60} - 402706514280 q^{63} + 68719476736 q^{64} - 424890168192 q^{65} + 369211259440 q^{67} - 137936354304 q^{70} + 574058144304 q^{71} + 66657976320 q^{72} + 450517137408 q^{74} - 73915435440 q^{77} - 251000847360 q^{78} - 607826610128 q^{79} + 919051941384 q^{81} - 9113567232 q^{84} - 247202260608 q^{85} - 413092638720 q^{86} - 453299404800 q^{88} + 144527421696 q^{91} + 320986644480 q^{92} + 2292312458880 q^{93} - 1053641981376 q^{95} - 290797516800 q^{98} - 1800954256464 q^{99}+O(q^{100}) \) 8 * q + 16384 * q^4 + 195160 * q^7 - 1478904 * q^9 - 213840 * q^11 - 8418816 * q^14 + 65882304 * q^15 + 33554432 * q^16 + 32547840 * q^18 - 4449984 * q^21 - 221337600 * q^22 + 156731760 * q^23 + 191237000 * q^25 + 399687680 * q^28 + 308853648 * q^29 - 2203567104 * q^30 - 3764734848 * q^35 - 3028795392 * q^36 - 3243600880 * q^37 + 13521315264 * q^39 - 12108579840 * q^42 + 21006302000 * q^43 - 437944320 * q^44 + 9664610304 * q^46 - 19258758904 * q^49 + 26259489792 * q^50 - 80965832832 * q^51 + 180445637520 * q^53 - 17241735168 * q^56 - 63145962240 * q^57 - 94193264640 * q^58 + 134926958592 * q^60 - 402706514280 * q^63 + 68719476736 * q^64 - 424890168192 * q^65 + 369211259440 * q^67 - 137936354304 * q^70 + 574058144304 * q^71 + 66657976320 * q^72 + 450517137408 * q^74 - 73915435440 * q^77 - 251000847360 * q^78 - 607826610128 * q^79 + 919051941384 * q^81 - 9113567232 * q^84 - 247202260608 * q^85 - 413092638720 * q^86 - 453299404800 * q^88 + 144527421696 * q^91 + 320986644480 * q^92 + 2292312458880 * q^93 - 1053641981376 * q^95 - 290797516800 * q^98 - 1800954256464 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−45.2548			−0.707107
$2$	−45.2548			−0.707107
$3$			102.042i			0.139975i	0.997548	+	0.0699873i	$0.0222959\pi$
$3$			102.042i			0.139975i	−0.997548	+	0.0699873i	$0.977704\pi$
$4$	2048.00			0.500000
$5$			6916.58i			0.442661i	0.975199	+	0.221331i	$0.0710400\pi$
$5$			6916.58i			0.442661i	−0.975199	+	0.221331i	$0.928960\pi$
$6$		−	4617.87i		−	0.0989770i
$7$	−14384.7	−	116766.i	−0.122268	−	0.992497i
$7$	−14384.7	−	116766.i	−0.122268	−	0.992497i
$8$	−92681.9			−0.353553
$9$	521029.			0.980407
$10$		−	313009.i		−	0.313009i
$11$	−1.34540e6			−0.759442			−0.379721	−	0.925101i	$-0.623980\pi$
$11$	−1.34540e6			−0.759442			−0.379721	+	0.925101i	$0.623980\pi$
$12$			208981.i			0.0699873i
$13$			5.40570e6i			1.11993i	0.828516	+	0.559966i	$0.189186\pi$
$13$			5.40570e6i			1.11993i	−0.828516	+	0.559966i	$0.810814\pi$
$14$	650975.	+	5.28424e6i	0.0864562	+	0.701801i
$15$	−705778.			−0.0619613
$16$	4.19430e6			0.250000
$17$			4.33512e7i			1.79601i	0.439989	+	0.898003i	$0.354982\pi$
$17$			4.33512e7i			1.79601i	−0.439989	+	0.898003i	$0.645018\pi$
$18$	−2.35791e7			−0.693253
$19$			4.81282e7i			1.02300i	0.859282	+	0.511502i	$0.170911\pi$
$19$			4.81282e7i			1.02300i	−0.859282	+	0.511502i	$0.829089\pi$
$20$			1.41652e7i			0.221331i
$21$	1.19150e7	−	1.46783e6i	0.138924	−	0.0171144i
$22$	6.08857e7			0.537006
$23$	−1.61270e8			−1.08940			−0.544698	−	0.838632i	$-0.683356\pi$
$23$	−1.61270e8			−1.08940			−0.544698	+	0.838632i	$0.683356\pi$
$24$		−	9.45740e6i		−	0.0494885i
$25$	1.96302e8			0.804051
$26$		−	2.44634e8i		−	0.791912i
$27$			1.07396e8i			0.277207i
$28$	−2.94598e7	−	2.39137e8i	−0.0611338	−	0.496249i
$29$	−7.77122e7			−0.130647			−0.0653237	−	0.997864i	$-0.520808\pi$
$29$	−7.77122e7			−0.130647			−0.0653237	+	0.997864i	$0.520808\pi$
$30$	3.19399e7			0.0438133
$31$			1.36270e8i			0.153543i	0.997049	+	0.0767713i	$0.0244611\pi$
$31$			1.36270e8i			0.153543i	−0.997049	+	0.0767713i	$0.975539\pi$
$32$	−1.89813e8			−0.176777
$33$		−	1.37286e8i		−	0.106303i
$34$		−	1.96185e9i		−	1.26997i
$35$	8.07623e8	−	9.94926e7i	0.439340	−	0.0541231i
$36$	1.06707e9			0.490204
$37$	−1.35560e9			−0.528349			−0.264175	−	0.964475i	$-0.585100\pi$
$37$	−1.35560e9			−0.528349			−0.264175	+	0.964475i	$0.585100\pi$
$38$		−	2.17803e9i		−	0.723374i
$39$	−5.51606e8			−0.156762
$40$		−	6.41042e8i		−	0.156504i
$41$			4.10282e9i			0.863733i	0.901938	+	0.431866i	$0.142145\pi$
$41$			4.10282e9i			0.863733i	−0.901938	+	0.431866i	$0.857855\pi$
$42$	−5.39212e8	+	6.64265e7i	−0.0982344	+	0.0121017i
$43$	2.00941e9			0.317875			0.158938	−	0.987289i	$-0.449193\pi$
$43$	2.00941e9			0.317875			0.158938	+	0.987289i	$0.449193\pi$
$44$	−2.75537e9			−0.379721
$45$			3.60373e9i			0.433988i
$46$	7.29824e9			0.770320
$47$			1.64105e10i			1.52242i	0.648503	+	0.761212i	$0.275395\pi$
$47$			1.64105e10i			1.52242i	−0.648503	+	0.761212i	$0.724605\pi$
$48$			4.27993e8i			0.0349937i
$49$	−1.34275e10	+	3.35929e9i	−0.970101	+	0.242700i
$50$	−8.88359e9			−0.568550
$51$	−4.42362e9			−0.251395
$52$			1.10709e10i			0.559966i
$53$	2.76670e10			1.24827			0.624134	−	0.781318i	$-0.285452\pi$
$53$	2.76670e10			1.24827			0.624134	+	0.781318i	$0.285452\pi$
$54$		−	4.86017e9i		−	0.196015i
$55$		−	9.30554e9i		−	0.336175i
$56$	1.33320e9	+	1.08221e10i	0.0432281	+	0.350901i
$57$	−4.91107e9			−0.143195
$58$	3.51685e9			0.0923817
$59$		−	3.80747e10i		−	0.902661i	−0.892357	−	0.451331i	$-0.850950\pi$
$59$		−	3.80747e10i		−	0.902661i	0.892357	−	0.451331i	$-0.149050\pi$
$60$	−1.44543e9			−0.0309807
$61$		−	8.36798e10i		−	1.62421i	−0.583512	−	0.812104i	$-0.698322\pi$
$61$		−	8.36798e10i		−	1.62421i	0.583512	−	0.812104i	$-0.301678\pi$
$62$		−	6.16686e9i		−	0.108571i
$63$	−7.49481e9	−	6.08386e10i	−0.119872	−	0.973051i
$64$	8.58993e9			0.125000
$65$	−3.73889e10			−0.495750
$66$			6.21287e9i			0.0751673i
$67$	9.92030e10			1.09667			0.548335	−	0.836259i	$-0.315262\pi$
$67$	9.92030e10			1.09667			0.548335	+	0.836259i	$0.315262\pi$
$68$			8.87833e10i			0.898003i
$69$		−	1.64562e10i		−	0.152488i
$70$	−3.65489e10	+	4.50252e9i	−0.310660	+	0.0382708i
$71$	−3.72326e10			−0.290652			−0.145326	−	0.989384i	$-0.546423\pi$
$71$	−3.72326e10			−0.290652			−0.145326	+	0.989384i	$0.546423\pi$
$72$	−4.82899e10			−0.346626
$73$			7.69138e10i			0.508238i	0.967173	+	0.254119i	$0.0817855\pi$
$73$			7.69138e10i			0.508238i	−0.967173	+	0.254119i	$0.918214\pi$
$74$	6.13475e10			0.373599
$75$			2.00309e10i			0.112547i
$76$			9.85665e10i			0.511502i
$77$	1.93531e10	+	1.57097e11i	0.0928550	+	0.753744i
$78$	2.49628e10			0.110848
$79$	−2.27529e11			−0.935998			−0.467999	−	0.883729i	$-0.655025\pi$
$79$	−2.27529e11			−0.935998			−0.467999	+	0.883729i	$0.655025\pi$
$80$			2.90102e10i			0.110665i
$81$	2.65937e11			0.941605
$82$		−	1.85672e11i		−	0.610751i
$83$			1.32152e11i			0.404207i	0.979364	+	0.202104i	$0.0647777\pi$
$83$			1.32152e11i			0.404207i	−0.979364	+	0.202104i	$0.935222\pi$
$84$	2.44019e10	−	3.00612e9i	0.0694622	−	0.00855718i
$85$	−2.99842e11			−0.795022
$86$	−9.09353e10			−0.224772
$87$		−	7.92987e9i		−	0.0182873i
$88$	1.24694e11			0.268503
$89$			5.07290e11i			1.02074i	0.859954	+	0.510372i	$0.170492\pi$
$89$			5.07290e11i			1.02074i	−0.859954	+	0.510372i	$0.829508\pi$
$90$		−	1.63086e11i		−	0.306876i
$91$	6.31203e11	−	7.77591e10i	1.11153	−	0.136931i
$92$	−3.30281e11			−0.544698
$93$	−1.39052e10			−0.0214921
$94$		−	7.42656e11i		−	1.07652i
$95$	−3.32882e11			−0.452844
$96$		−	1.93688e10i		−	0.0247443i
$97$		−	2.74033e11i		−	0.328983i	−0.986379	−	0.164491i	$-0.947402\pi$
$97$		−	2.74033e11i		−	0.328983i	0.986379	−	0.164491i	$-0.0525983\pi$
$98$	6.07657e11	−	1.52024e11i	0.685965	−	0.171615i
$99$	−7.00990e11			−0.744562
$100$	4.02026e11			0.402026
$101$			7.12985e11i			0.671664i	0.941922	+	0.335832i	$0.109017\pi$
$101$			7.12985e11i			0.671664i	−0.941922	+	0.335832i	$0.890983\pi$
$102$	2.00190e11			0.177763
$103$		−	1.57416e12i		−	1.31833i	−0.751998	−	0.659165i	$-0.770910\pi$
$103$		−	1.57416e12i		−	1.31833i	0.751998	−	0.659165i	$-0.229090\pi$
$104$		−	5.01010e11i		−	0.395956i
$105$	1.01524e10	+	8.24111e10i	0.00757586	+	0.0614964i
$106$	−1.25207e12			−0.882658
$107$	7.57737e11			0.504912			0.252456	−	0.967608i	$-0.418762\pi$
$107$	7.57737e11			0.504912			0.252456	+	0.967608i	$0.418762\pi$
$108$			2.19946e11i			0.138603i
$109$	1.90661e12			1.13685			0.568426	−	0.822735i	$-0.307553\pi$
$109$	1.90661e12			1.13685			0.568426	+	0.822735i	$0.307553\pi$
$110$			4.21121e11i			0.237712i
$111$		−	1.38327e11i		−	0.0739555i
$112$	−6.03336e10	−	4.89753e11i	−0.0305669	−	0.248124i
$113$	−3.73652e12			−1.79472			−0.897360	−	0.441300i	$-0.854518\pi$
$113$	−3.73652e12			−1.79472			−0.897360	+	0.441300i	$0.854518\pi$
$114$	2.22250e11			0.101254
$115$		−	1.11544e12i		−	0.482234i
$116$	−1.59154e11			−0.0653237
$117$			2.81652e12i			1.09799i
$118$			1.72307e12i			0.638278i
$119$	5.06196e12	−	6.23592e11i	1.78253	−	0.219593i
$120$	6.54129e10			0.0219066
$121$	−1.32833e12			−0.423248
$122$			3.78692e12i			1.14849i
$123$	−4.18658e11			−0.120901
$124$			2.79080e11i			0.0767713i
$125$			3.04635e12i			0.798583i
$126$	3.39177e11	+	2.75324e12i	0.0847623	+	0.688051i
$127$	−6.59899e12			−1.57273			−0.786366	−	0.617760i	$-0.788040\pi$
$127$	−6.59899e12			−1.57273			−0.786366	+	0.617760i	$0.788040\pi$
$128$	−3.88736e11			−0.0883883
$129$			2.05043e11i			0.0444945i
$130$	1.69203e12			0.350548
$131$		−	3.36006e12i		−	0.664843i	−0.943131	−	0.332421i	$-0.892134\pi$
$131$		−	3.36006e12i		−	0.664843i	0.943131	−	0.332421i	$-0.107866\pi$
$132$		−	2.81163e11i		−	0.0531513i
$133$	5.61975e12	−	6.92307e11i	1.01533	−	0.125080i
$134$	−4.48941e12			−0.775463
$135$	−7.42810e11			−0.122709
$136$		−	4.01787e12i		−	0.634984i
$137$	5.70232e12			0.862439			0.431219	−	0.902247i	$-0.358084\pi$
$137$	5.70232e12			0.862439			0.431219	+	0.902247i	$0.358084\pi$
$138$			7.44724e11i			0.107825i
$139$		−	1.26130e13i		−	1.74876i	−0.485243	−	0.874379i	$-0.661269\pi$
$139$		−	1.26130e13i		−	1.74876i	0.485243	−	0.874379i	$-0.338731\pi$
$140$	1.65401e12	−	2.03761e11i	0.219670	−	0.0270615i
$141$	−1.67456e12			−0.213101
$142$	1.68495e12			0.205522
$143$		−	7.27281e12i		−	0.850523i
$144$	2.18535e12			0.245102
$145$		−	5.37502e11i		−	0.0578325i
$146$		−	3.48072e12i		−	0.359379i
$147$	−3.42787e11	−	1.37016e12i	−0.0339719	−	0.135790i
$148$	−2.77627e12			−0.264175
$149$	−1.72011e13			−1.57195			−0.785973	−	0.618260i	$-0.787838\pi$
$149$	−1.72011e13			−1.57195			−0.785973	+	0.618260i	$0.787838\pi$
$150$		−	9.06496e11i		−	0.0795826i
$151$	1.62926e13			1.37445			0.687226	−	0.726443i	$-0.258828\pi$
$151$	1.62926e13			1.37445			0.687226	+	0.726443i	$0.258828\pi$
$152$		−	4.46061e12i		−	0.361687i
$153$			2.25872e13i			1.76082i
$154$	−8.75820e11	−	7.10940e12i	−0.0656584	−	0.532977i
$155$	−9.42519e11			−0.0679673
$156$	−1.12969e12			−0.0783811
$157$			6.81019e12i			0.454738i	0.973809	+	0.227369i	$0.0730123\pi$
$157$			6.81019e12i			0.454738i	−0.973809	+	0.227369i	$0.926988\pi$
$158$	1.02968e13			0.661850
$159$			2.82319e12i			0.174726i
$160$		−	1.31285e12i		−	0.0782522i
$161$	2.31981e12	+	1.88309e13i	0.133198	+	1.08122i
$162$	−1.20349e13			−0.665815
$163$	−9.70032e12			−0.517202			−0.258601	−	0.965984i	$-0.583262\pi$
$163$	−9.70032e12			−0.517202			−0.258601	+	0.965984i	$0.583262\pi$
$164$			8.40258e12i			0.431866i
$165$	9.49552e11			0.0470560
$166$		−	5.98050e12i		−	0.285818i
$167$		−	7.66955e11i		−	0.0353567i	−0.999844	−	0.0176783i	$-0.994373\pi$
$167$		−	7.66955e11i		−	0.0353567i	0.999844	−	0.0176783i	$-0.00562748\pi$
$168$	−1.10431e12	+	1.36041e11i	−0.0491172	+	0.00605084i
$169$	−5.92349e12			−0.254248
$170$	1.35693e13			0.562165
$171$			2.50761e13i			1.00296i
$172$	4.11526e12			0.158938
$173$			2.86817e13i			1.06987i	0.844895	+	0.534933i	$0.179663\pi$
$173$			2.86817e13i			1.06987i	−0.844895	+	0.534933i	$0.820337\pi$
$174$			3.58865e11i			0.0129311i
$175$	−2.82373e12	−	2.29214e13i	−0.0983094	−	0.798019i
$176$	−5.64300e12			−0.189860
$177$	3.88520e12			0.126350
$178$		−	2.29573e13i		−	0.721774i
$179$	8.65371e12			0.263078			0.131539	−	0.991311i	$-0.458008\pi$
$179$	8.65371e12			0.263078			0.131539	+	0.991311i	$0.458008\pi$
$180$			7.38045e12i			0.216994i
$181$		−	2.96628e13i		−	0.843607i	−0.906687	−	0.421803i	$-0.861397\pi$
$181$		−	2.96628e13i		−	0.843607i	0.906687	−	0.421803i	$-0.138603\pi$
$182$	−2.85650e13	+	3.51897e12i	−0.785970	+	0.0968251i
$183$	8.53882e12			0.227348
$184$	1.49468e13			0.385160
$185$		−	9.37611e12i		−	0.233880i
$186$	6.29276e11			0.0151972
$187$		−	5.83246e13i		−	1.36396i
$188$			3.36088e13i			0.761212i
$189$	1.25402e13	−	1.54485e12i	0.275127	−	0.0338934i
$190$	1.50645e13			0.320209
$191$	−3.00697e13			−0.619340			−0.309670	−	0.950844i	$-0.600219\pi$
$191$	−3.00697e13			−0.619340			−0.309670	+	0.950844i	$0.600219\pi$
$192$			8.76530e11i			0.0174968i
$193$	−2.89263e13			−0.559693			−0.279846	−	0.960045i	$-0.590284\pi$
$193$	−2.89263e13			−0.559693			−0.279846	+	0.960045i	$0.590284\pi$
$194$			1.24013e13i			0.232626i
$195$		−	3.81522e12i		−	0.0693925i
$196$	−2.74994e13	+	6.87982e12i	−0.485051	+	0.121350i
$197$	8.13502e13			1.39175			0.695875	−	0.718163i	$-0.255017\pi$
$197$	8.13502e13			1.39175			0.695875	+	0.718163i	$0.255017\pi$
$198$	3.17232e13			0.526485
$199$		−	7.72999e13i		−	1.24469i	−0.782744	−	0.622344i	$-0.786181\pi$
$199$		−	7.72999e13i		−	1.24469i	0.782744	−	0.622344i	$-0.213819\pi$
$200$	−1.81936e13			−0.284275
$201$			1.01228e13i			0.153506i
$202$		−	3.22660e13i		−	0.474938i
$203$	1.11786e12	+	9.07416e12i	0.0159739	+	0.129667i
$204$	−9.05958e12			−0.125698
$205$	−2.83775e13			−0.382341
$206$			7.12381e13i			0.932200i
$207$	−8.40262e13			−1.06805
$208$			2.26731e13i			0.279983i
$209$		−	6.47515e13i		−	0.776912i
$210$	−4.59444e11	−	3.72950e12i	−0.00535694	−	0.0434846i
$211$	1.50952e14			1.71059			0.855293	−	0.518145i	$-0.173377\pi$
$211$	1.50952e14			1.71059			0.855293	+	0.518145i	$0.173377\pi$
$212$	5.66621e13			0.624134
$213$		−	3.79927e12i		−	0.0406839i
$214$	−3.42913e13			−0.357027
$215$			1.38982e13i			0.140711i
$216$		−	9.95363e12i		−	0.0980074i
$217$	1.59117e13	−	1.96019e12i	0.152391	−	0.0187733i
$218$	−8.62835e13			−0.803875
$219$	−7.84841e12			−0.0711405
$220$		−	1.90578e13i		−	0.168088i
$221$	−2.34344e14			−2.01140
$222$			6.25999e12i			0.0522945i
$223$			2.34517e14i			1.90697i	0.301437	+	0.953486i	$0.402534\pi$
$223$			2.34517e14i			1.90697i	−0.301437	+	0.953486i	$0.597466\pi$
$224$	2.73039e12	+	2.21637e13i	0.0216140	+	0.175450i
$225$	1.02279e14			0.788298
$226$	1.69096e14			1.26906
$227$			2.01371e14i			1.47178i	0.677104	+	0.735888i	$0.263235\pi$
$227$			2.01371e14i			1.47178i	−0.677104	+	0.735888i	$0.736765\pi$
$228$	−1.00579e13			−0.0715974
$229$			1.57658e13i			0.109321i	0.998505	+	0.0546604i	$0.0174076\pi$
$229$			1.57658e13i			0.109321i	−0.998505	+	0.0546604i	$0.982592\pi$
$230$			5.04788e13i			0.340991i
$231$	−1.60304e13	+	1.97482e12i	−0.105505	+	0.0129974i
$232$	7.20251e12			0.0461909
$233$	6.27812e13			0.392368			0.196184	−	0.980567i	$-0.437145\pi$
$233$	6.27812e13			0.392368			0.196184	+	0.980567i	$0.437145\pi$
$234$		−	1.27461e14i		−	0.776396i
$235$	−1.13505e14			−0.673918
$236$		−	7.79771e13i		−	0.451331i
$237$		−	2.32174e13i		−	0.131016i
$238$	−2.29078e14	+	2.82206e13i	−1.26044	+	0.155276i
$239$	2.45537e14			1.31743			0.658717	−	0.752391i	$-0.271100\pi$
$239$	2.45537e14			1.31743			0.658717	+	0.752391i	$0.271100\pi$
$240$	−2.96025e12			−0.0154903
$241$		−	5.69031e13i		−	0.290425i	−0.989401	−	0.145212i	$-0.953613\pi$
$241$		−	5.69031e13i		−	0.290425i	0.989401	−	0.145212i	$-0.0463865\pi$
$242$	6.01136e13			0.299282
$243$			8.42111e13i			0.409008i
$244$		−	1.71376e14i		−	0.812104i
$245$	−2.32348e13	−	9.28720e13i	−0.107434	−	0.429426i
$246$	1.89463e13			0.0854897
$247$	−2.60166e14			−1.14570
$248$		−	1.26297e13i		−	0.0542855i
$249$	−1.34850e13			−0.0565787
$250$		−	1.37862e14i		−	0.564684i
$251$		−	2.56371e14i		−	1.02524i	−0.858615	−	0.512621i	$-0.828675\pi$
$251$		−	2.56371e14i		−	1.02524i	0.858615	−	0.512621i	$-0.171325\pi$
$252$	−1.53494e13	−	1.24597e14i	−0.0599360	−	0.486526i
$253$	2.16972e14			0.827333
$254$	2.98636e14			1.11209
$255$		−	3.05963e13i		−	0.111283i
$256$	1.75922e13			0.0625000
$257$		−	3.28151e14i		−	1.13887i	−0.822036	−	0.569436i	$-0.807162\pi$
$257$		−	3.28151e14i		−	1.13887i	0.822036	−	0.569436i	$-0.192838\pi$
$258$		−	9.27918e12i		−	0.0314624i
$259$	1.94998e13	+	1.58288e14i	0.0646000	+	0.524385i
$260$	−7.65725e13			−0.247875
$261$	−4.04903e13			−0.128088
$262$			1.52059e14i			0.470115i
$263$	−8.77052e13			−0.265027			−0.132514	−	0.991181i	$-0.542305\pi$
$263$	−8.77052e13			−0.265027			−0.132514	+	0.991181i	$0.542305\pi$
$264$			1.27240e13i			0.0375836i
$265$			1.91361e14i			0.552559i
$266$	−2.54321e14	+	3.13302e13i	−0.717946	+	0.0884451i
$267$	−5.17647e13			−0.142878
$268$	2.03168e14			0.548335
$269$		−	4.84197e14i		−	1.27793i	−0.769234	−	0.638967i	$-0.779362\pi$
$269$		−	4.84197e14i		−	1.27793i	0.769234	−	0.638967i	$-0.220638\pi$
$270$	3.36157e13			0.0867681
$271$			4.77684e14i			1.20594i	0.797765	+	0.602968i	$0.206015\pi$
$271$			4.77684e14i			1.20594i	−0.797765	+	0.602968i	$0.793985\pi$
$272$			1.81828e14i			0.449001i
$273$	7.93466e12	+	6.44090e13i	0.0191669	+	0.155586i
$274$	−2.58058e14			−0.609836
$275$	−2.64104e14			−0.610630
$276$		−	3.37023e13i		−	0.0762440i
$277$	5.37806e14			1.19055			0.595274	−	0.803522i	$-0.297043\pi$
$277$	5.37806e14			1.19055			0.595274	+	0.803522i	$0.297043\pi$
$278$			5.70800e14i			1.23656i
$279$			7.10003e13i			0.150534i
$280$	−7.48521e13	+	9.22116e12i	−0.155330	+	0.0191354i
$281$	1.44271e14			0.293050			0.146525	−	0.989207i	$-0.453191\pi$
$281$	1.44271e14			0.293050			0.146525	+	0.989207i	$0.453191\pi$
$282$	7.57818e13			0.150685
$283$			8.29488e14i			1.61470i	0.590073	+	0.807350i	$0.299099\pi$
$283$			8.29488e14i			1.61470i	−0.590073	+	0.807350i	$0.700901\pi$
$284$	−7.62523e13			−0.145326
$285$		−	3.39678e13i		−	0.0633867i
$286$			3.29130e14i			0.601411i
$287$	4.79071e14	−	5.90177e13i	0.857252	−	0.105606i
$288$	−9.88977e13			−0.173313
$289$	−1.29671e15			−2.22564
$290$			2.43246e13i			0.0408938i
$291$	2.79628e13			0.0460492
$292$			1.57520e14i			0.254119i
$293$		−	7.24824e14i		−	1.14558i	−0.819701	−	0.572792i	$-0.805860\pi$
$293$		−	7.24824e14i		−	1.14558i	0.819701	−	0.572792i	$-0.194140\pi$
$294$	1.55128e13	+	6.20063e13i	0.0240218	+	0.0960177i
$295$	2.63347e14			0.399573
$296$	1.25640e14			0.186800
$297$		−	1.44490e14i		−	0.210522i
$298$	7.78431e14			1.11153
$299$		−	8.71776e14i		−	1.22005i
$300$			4.10233e13i			0.0562734i
$301$	−2.89046e13	−	2.34631e14i	−0.0388658	−	0.315490i
$302$	−7.37321e14			−0.971885
$303$	−7.27540e13			−0.0940159
$304$			2.01864e14i			0.255751i
$305$	5.78778e14			0.718974
$306$		−	1.02218e15i		−	1.24509i
$307$			3.18911e14i			0.380925i	0.981694	+	0.190462i	$0.0609987\pi$
$307$			3.18911e14i			0.380925i	−0.981694	+	0.190462i	$0.939001\pi$
$308$	3.96351e13	+	3.21735e14i	0.0464275	+	0.376872i
$309$	1.60629e14			0.184533
$310$	4.26536e13			0.0480601
$311$		−	1.19903e15i		−	1.32516i	−0.748993	−	0.662578i	$-0.769462\pi$
$311$		−	1.19903e15i		−	1.32516i	0.748993	−	0.662578i	$-0.230538\pi$
$312$	5.11239e13			0.0554238
$313$			7.64587e14i			0.813132i	0.913621	+	0.406566i	$0.133274\pi$
$313$			7.64587e14i			0.813132i	−0.913621	+	0.406566i	$0.866726\pi$
$314$		−	3.08194e14i		−	0.321548i
$315$	4.20795e14	−	5.18385e13i	0.430732	−	0.0530626i
$316$	−4.65980e14			−0.467999
$317$	−2.15173e14			−0.212047			−0.106024	−	0.994364i	$-0.533812\pi$
$317$	−2.15173e14			−0.212047			−0.106024	+	0.994364i	$0.533812\pi$
$318$		−	1.27763e14i		−	0.123550i
$319$	1.04554e14			0.0992191
$320$			5.94130e13i			0.0553326i
$321$			7.73207e13i			0.0706749i
$322$	−1.04983e14	−	8.52188e14i	−0.0941851	−	0.764540i
$323$	−2.08641e15			−1.83732
$324$	5.44639e14			0.470803
$325$			1.06115e15i			0.900483i
$326$	4.38986e14			0.365717
$327$			1.94554e14i			0.159130i
$328$		−	3.80257e14i		−	0.305376i
$329$	1.91620e15	−	2.36060e14i	1.51100	−	0.186143i
$330$	−4.29718e13			−0.0332736
$331$	8.82186e14			0.670799			0.335399	−	0.942076i	$-0.391129\pi$
$331$	8.82186e14			0.670799			0.335399	+	0.942076i	$0.391129\pi$
$332$			2.70646e14i			0.202104i
$333$	−7.06306e14			−0.517997
$334$			3.47084e13i			0.0250009i
$335$			6.86145e14i			0.485453i
$336$	4.99752e13	−	6.15653e12i	0.0347311	−	0.00427859i
$337$	−1.99560e15			−1.36237			−0.681185	−	0.732111i	$-0.738535\pi$
$337$	−1.99560e15			−1.36237			−0.681185	+	0.732111i	$0.738535\pi$
$338$	2.68066e14			0.179780
$339$		−	3.81280e14i		−	0.251215i
$340$	−6.14077e14			−0.397511
$341$		−	1.83337e14i		−	0.116607i
$342$		−	1.13482e15i		−	0.709201i
$343$	5.85401e14	+	1.51955e15i	0.359491	+	0.933148i
$344$	−1.86236e14			−0.112386
$345$	1.13821e14			0.0675005
$346$		−	1.29799e15i		−	0.756509i
$347$	1.66637e15			0.954541			0.477270	−	0.878756i	$-0.341626\pi$
$347$	1.66637e15			0.954541			0.477270	+	0.878756i	$0.341626\pi$
$348$		−	1.62404e13i		−	0.00914367i
$349$			1.13921e15i			0.630450i	0.949017	+	0.315225i	$0.102080\pi$
$349$			1.13921e15i			0.630450i	−0.949017	+	0.315225i	$0.897920\pi$
$350$	1.27787e14	+	1.03730e15i	0.0695152	+	0.564284i
$351$	−5.80548e14			−0.310453
$352$	2.55373e14			0.134252
$353$			2.56567e15i			1.32603i	0.748606	+	0.663015i	$0.230723\pi$
$353$			2.56567e15i			1.32603i	−0.748606	+	0.663015i	$0.769277\pi$
$354$	−1.75824e14			−0.0893427
$355$		−	2.57522e14i		−	0.128660i
$356$			1.03893e15i			0.510372i
$357$	6.36323e13	+	5.16530e14i	0.0307375	+	0.249509i
$358$	−3.91622e14			−0.186024
$359$	−1.78351e15			−0.833120			−0.416560	−	0.909108i	$-0.636764\pi$
$359$	−1.78351e15			−0.833120			−0.416560	+	0.909108i	$0.636764\pi$
$360$		−	3.34001e14i		−	0.153438i
$361$	−1.03004e14			−0.0465385
$362$			1.34238e15i			0.596520i
$363$		−	1.35545e14i		−	0.0592441i
$364$	1.29270e15	−	1.59251e14i	0.555765	−	0.0684657i
$365$	−5.31981e14			−0.224977
$366$	−3.86423e14			−0.160759
$367$		−	2.93506e15i		−	1.20121i	−0.799545	−	0.600607i	$-0.794926\pi$
$367$		−	2.93506e15i		−	1.20121i	0.799545	−	0.600607i	$-0.205074\pi$
$368$	−6.76415e14			−0.272349
$369$			2.13769e15i			0.846810i
$370$			4.24314e14i			0.165378i
$371$	−3.97981e14	−	3.23058e15i	−0.152623	−	1.23890i
$372$	−2.84778e13			−0.0107460
$373$	2.29973e15			0.853932			0.426966	−	0.904268i	$-0.359582\pi$
$373$	2.29973e15			0.853932			0.426966	+	0.904268i	$0.359582\pi$
$374$			2.63947e15i			0.964467i
$375$	−3.10855e14			−0.111781
$376$		−	1.52096e15i		−	0.538258i
$377$		−	4.20088e14i		−	0.146316i
$378$	−5.67504e14	+	6.99119e13i	−0.194544	+	0.0239662i
$379$	1.88145e15			0.634829			0.317414	−	0.948287i	$-0.397185\pi$
$379$	1.88145e15			0.634829			0.317414	+	0.948287i	$0.397185\pi$
$380$	−6.81743e14			−0.226422
$381$		−	6.73371e14i		−	0.220143i
$382$	1.36080e15			0.437940
$383$		−	1.19230e15i		−	0.377741i	−0.982002	−	0.188871i	$-0.939517\pi$
$383$		−	1.19230e15i		−	0.377741i	0.982002	−	0.188871i	$-0.0604827\pi$
$384$		−	3.96672e13i		−	0.0123721i
$385$	−1.08657e15	+	1.33857e14i	−0.333653	+	0.0411033i
$386$	1.30906e15			0.395763
$387$	1.04696e15			0.311647
$388$		−	5.61220e14i		−	0.164491i
$389$	−1.74555e15			−0.503774			−0.251887	−	0.967757i	$-0.581051\pi$
$389$	−1.74555e15			−0.503774			−0.251887	+	0.967757i	$0.581051\pi$
$390$			1.72657e14i			0.0490679i
$391$		−	6.99124e15i		−	1.95656i
$392$	1.24448e15	−	3.11345e14i	0.342983	−	0.0858075i
$393$	3.42865e14			0.0930611
$394$	−3.68149e15			−0.984116
$395$		−	1.57372e15i		−	0.414330i
$396$	−1.43563e15			−0.372281
$397$		−	6.00322e15i		−	1.53335i	−0.642035	−	0.766675i	$-0.721910\pi$
$397$		−	6.00322e15i		−	1.53335i	0.642035	−	0.766675i	$-0.278090\pi$
$398$			3.49819e15i			0.880127i
$399$	7.06440e13	+	5.73448e14i	0.0175081	+	0.142120i
$400$	8.23348e14			0.201013
$401$	2.06462e15			0.496563			0.248281	−	0.968688i	$-0.420134\pi$
$401$	2.06462e15			0.496563			0.248281	+	0.968688i	$0.420134\pi$
$402$		−	4.58107e14i		−	0.108545i
$403$	−7.36632e14			−0.171957
$404$			1.46019e15i			0.335832i
$405$			1.83937e15i			0.416812i
$406$	−5.05887e13	−	4.10650e14i	−0.0112953	−	0.0916886i
$407$	1.82382e15			0.401250
$408$	4.09990e14			0.0888817
$409$			3.12861e15i			0.668363i	0.942509	+	0.334181i	$0.108460\pi$
$409$			3.12861e15i			0.668363i	−0.942509	+	0.334181i	$0.891540\pi$
$410$	1.28422e15			0.270356
$411$			5.81873e14i			0.120720i
$412$		−	3.22387e15i		−	0.659165i
$413$	−4.44585e15	+	5.47692e14i	−0.895889	+	0.110366i
$414$	3.80259e15			0.755227
$415$	−9.14037e14			−0.178927
$416$		−	1.02607e15i		−	0.197978i
$417$	1.28705e15			0.244782
$418$			2.93032e15i			0.549360i
$419$			3.93360e15i			0.726952i	0.931603	+	0.363476i	$0.118410\pi$
$419$			3.93360e15i			0.726952i	−0.931603	+	0.363476i	$0.881590\pi$
$420$	2.07921e13	+	1.68778e14i	0.00378793	+	0.0307482i
$421$	4.51876e15			0.811572			0.405786	−	0.913968i	$-0.366998\pi$
$421$	4.51876e15			0.811572			0.405786	+	0.913968i	$0.366998\pi$
$422$	−6.83132e15			−1.20957
$423$			8.55036e15i			1.49260i
$424$	−2.56423e15			−0.441329
$425$			8.50991e15i			1.44408i
$426$			1.71935e14i			0.0287678i
$427$	−9.77098e15	+	1.20371e15i	−1.61202	+	0.198588i
$428$	1.55185e15			0.252456
$429$	7.42129e14			0.119052
$430$		−	6.28961e14i		−	0.0994977i
$431$	4.41573e15			0.688873			0.344436	−	0.938810i	$-0.388070\pi$
$431$	4.41573e15			0.688873			0.344436	+	0.938810i	$0.388070\pi$
$432$			4.50450e14i			0.0693017i
$433$			8.01909e15i			1.21674i	0.793654	+	0.608370i	$0.208176\pi$
$433$			8.01909e15i			1.21674i	−0.793654	+	0.608370i	$0.791824\pi$
$434$	−7.20081e14	+	8.87081e13i	−0.107756	+	0.0132747i
$435$	5.48475e13			0.00809509
$436$	3.90475e15			0.568426
$437$		−	7.76162e15i		−	1.11446i
$438$	3.55178e14			0.0503039
$439$		−	1.05956e15i		−	0.148026i	−0.997257	−	0.0740131i	$-0.976419\pi$
$439$		−	1.05956e15i		−	0.148026i	0.997257	−	0.0740131i	$-0.0235807\pi$
$440$			8.62456e14i			0.118856i
$441$	−6.99608e15	+	1.75028e15i	−0.951094	+	0.237945i
$442$	1.06052e16			1.42228
$443$	8.76266e15			1.15935			0.579674	−	0.814849i	$-0.303180\pi$
$443$	8.76266e15			1.15935			0.579674	+	0.814849i	$0.303180\pi$
$444$		−	2.83295e14i		−	0.0369778i
$445$	−3.50871e15			−0.451843
$446$		−	1.06130e16i		−	1.34843i
$447$		−	1.75522e15i		−	0.220033i
$448$	−1.23563e14	−	1.00301e15i	−0.0152834	−	0.124062i
$449$	−4.20903e15			−0.513693			−0.256847	−	0.966452i	$-0.582684\pi$
$449$	−4.20903e15			−0.513693			−0.256847	+	0.966452i	$0.582684\pi$
$450$	−4.62861e15			−0.557411
$451$		−	5.51992e15i		−	0.655955i
$452$	−7.65239e15			−0.897360
$453$			1.66253e15i			0.192389i
$454$		−	9.11301e15i		−	1.04070i
$455$	5.37827e14	+	4.36577e15i	0.0606142	+	0.492031i
$456$	4.55167e14			0.0506270
$457$	9.87545e15			1.08408			0.542038	−	0.840354i	$-0.317653\pi$
$457$	9.87545e15			1.08408			0.542038	+	0.840354i	$0.317653\pi$
$458$		−	7.13479e14i		−	0.0773015i
$459$	−4.65573e15			−0.497865
$460$		−	2.28441e15i		−	0.241117i
$461$		−	1.50600e16i		−	1.56898i	−0.620140	−	0.784491i	$-0.712924\pi$
$461$		−	1.50600e16i		−	1.56898i	0.620140	−	0.784491i	$-0.287076\pi$
$462$	7.25454e14	−	8.93700e13i	0.0746033	−	0.00919052i
$463$	4.17743e15			0.424056			0.212028	−	0.977264i	$-0.431993\pi$
$463$	4.17743e15			0.424056			0.212028	+	0.977264i	$0.431993\pi$
$464$	−3.25948e14			−0.0326619
$465$		−	9.61761e13i		−	0.00951370i
$466$	−2.84115e15			−0.277446
$467$			5.94993e14i			0.0573602i	0.999589	+	0.0286801i	$0.00913040\pi$
$467$			5.94993e14i			0.0573602i	−0.999589	+	0.0286801i	$0.990870\pi$
$468$			5.76824e15i			0.548995i
$469$	−1.42700e15	−	1.15836e16i	−0.134087	−	1.08844i
$470$	5.13664e15			0.476532
$471$	−6.94922e14			−0.0636518
$472$			3.52884e15i			0.319139i
$473$	−2.70345e15			−0.241408
$474$			1.05070e15i			0.0926423i
$475$			9.44763e15i			0.822548i
$476$	1.03669e16	−	1.27712e15i	0.891265	−	0.109797i
$477$	1.44153e16			1.22381
$478$	−1.11117e16			−0.931566
$479$			5.67964e15i			0.470227i	0.971968	+	0.235114i	$0.0755462\pi$
$479$			5.67964e15i			0.470227i	−0.971968	+	0.235114i	$0.924454\pi$
$480$	1.33966e14			0.0109533
$481$		−	7.32796e15i		−	0.591715i
$482$			2.57514e15i			0.205361i
$483$	−1.92153e15	+	2.36717e14i	−0.151344	+	0.0186443i
$484$	−2.72043e15			−0.211624
$485$	1.89537e15			0.145628
$486$		−	3.81096e15i		−	0.289212i
$487$	−1.44687e16			−1.08457			−0.542283	−	0.840196i	$-0.682440\pi$
$487$	−1.44687e16			−1.08457			−0.542283	+	0.840196i	$0.682440\pi$
$488$			7.75561e15i			0.574244i
$489$		−	9.89835e14i		−	0.0723952i
$490$	1.05149e15	+	4.20291e15i	0.0759673	+	0.303650i
$491$	−1.76959e16			−1.26294			−0.631472	−	0.775398i	$-0.717549\pi$
$491$	−1.76959e16			−1.26294			−0.631472	+	0.775398i	$0.717549\pi$
$492$	−8.57412e14			−0.0604504
$493$		−	3.36892e15i		−	0.234644i
$494$	1.17738e16			0.810129
$495$		−	4.84845e15i		−	0.329589i
$496$			5.71556e14i			0.0383856i
$497$	5.35578e14	+	4.34751e15i	0.0355373	+	0.288471i
$498$	6.10259e14			0.0400072
$499$	2.08779e16			1.35233			0.676165	−	0.736750i	$-0.263641\pi$
$499$	2.08779e16			1.35233			0.676165	+	0.736750i	$0.263641\pi$
$500$			6.23893e15i			0.399292i
$501$	7.82613e13			0.00494904
$502$			1.16020e16i			0.724955i
$503$			1.88109e16i			1.16146i	0.814098	+	0.580728i	$0.197232\pi$
$503$			1.88109e16i			1.16146i	−0.814098	+	0.580728i	$0.802768\pi$
$504$	6.94634e14	+	5.63863e15i	0.0423811	+	0.344026i
$505$	−4.93141e15			−0.297319
$506$	−9.81903e15			−0.585013
$507$		−	6.04442e14i		−	0.0355882i
$508$	−1.35147e16			−0.786366
$509$		−	1.03787e16i		−	0.596809i	−0.954440	−	0.298404i	$-0.903546\pi$
$509$		−	1.03787e16i		−	0.596809i	0.954440	−	0.298404i	$-0.0964544\pi$
$510$			1.38463e15i			0.0786889i
$511$	8.98094e15	−	1.10638e15i	0.504425	−	0.0621410i
$512$	−7.96131e14			−0.0441942
$513$	−5.16875e15			−0.283584
$514$			1.48504e16i			0.805304i
$515$	1.08878e16			0.583573
$516$			4.19928e14i			0.0222472i
$517$		−	2.20787e16i		−	1.15619i
$518$	−8.82462e14	−	7.16331e15i	−0.0456791	−	0.370796i
$519$	−2.92673e15			−0.149754
$520$	3.46528e15			0.175274
$521$			5.53480e15i			0.276742i	0.990380	+	0.138371i	$0.0441867\pi$
$521$			5.53480e15i			0.276742i	−0.990380	+	0.138371i	$0.955813\pi$
$522$	1.83238e15			0.0905717
$523$			2.91591e16i			1.42483i	0.701757	+	0.712416i	$0.252399\pi$
$523$			2.91591e16i			1.42483i	−0.701757	+	0.712416i	$0.747601\pi$
$524$		−	6.88140e15i		−	0.332421i
$525$	2.33894e15	−	2.88138e14i	0.111702	−	0.0137608i
$526$	3.96908e15			0.187403
$527$	−5.90745e15			−0.275763
$528$		−	5.75821e14i		−	0.0265756i
$529$	4.09334e15			0.186786
$530$		−	8.66002e15i		−	0.390718i
$531$		−	1.98380e16i		−	0.884976i
$532$	1.15092e16	−	1.41784e15i	0.507665	−	0.0625401i
$533$	−2.21786e16			−0.967322
$534$	2.34260e15			0.101030
$535$			5.24095e15i			0.223505i
$536$	−9.19432e15			−0.387731
$537$			8.83038e14i			0.0368242i
$538$			2.19122e16i			0.903635i
$539$	1.80653e16	−	4.51957e15i	0.736735	−	0.184317i
$540$	−1.52128e15			−0.0613543
$541$	2.54392e15			0.101466			0.0507329	−	0.998712i	$-0.483844\pi$
$541$	2.54392e15			0.101466			0.0507329	+	0.998712i	$0.483844\pi$
$542$		−	2.16175e16i		−	0.852726i
$543$	3.02683e15			0.118084
$544$		−	8.22860e15i		−	0.317492i
$545$			1.31872e16i			0.503240i
$546$	−3.59082e14	−	2.91482e15i	−0.0135531	−	0.110016i
$547$	−4.15289e16			−1.55034			−0.775169	−	0.631754i	$-0.782335\pi$
$547$	−4.15289e16			−1.55034			−0.775169	+	0.631754i	$0.782335\pi$
$548$	1.16784e16			0.431219
$549$		−	4.35996e16i		−	1.59239i
$550$	1.19520e16			0.431781
$551$		−	3.74014e15i		−	0.133653i
$552$			1.52519e15i			0.0539126i
$553$	3.27293e15	+	2.65678e16i	0.114442	+	0.928975i
$554$	−2.43383e16			−0.841845
$555$	9.56753e14			0.0327372
$556$		−	2.58314e16i		−	0.874379i
$557$	4.87696e16			1.63312			0.816560	−	0.577261i	$-0.195879\pi$
$557$	4.87696e16			1.63312			0.816560	+	0.577261i	$0.195879\pi$
$558$		−	3.21311e15i		−	0.106444i
$559$			1.08622e16i			0.355999i
$560$	3.38742e15	−	4.17302e14i	0.109835	−	0.0135308i
$561$	5.95153e15			0.190920
$562$	−6.52897e15			−0.207218
$563$			3.47426e16i			1.09097i	0.838121	+	0.545484i	$0.183654\pi$
$563$			3.47426e16i			1.09097i	−0.838121	+	0.545484i	$0.816346\pi$
$564$	−3.42949e15			−0.106550
$565$		−	2.58439e16i		−	0.794452i
$566$		−	3.75384e16i		−	1.14176i
$567$	−3.82541e15	−	3.10525e16i	−0.115128	−	0.934540i
$568$	3.45079e15			0.102761
$569$	−3.36101e16			−0.990366			−0.495183	−	0.868789i	$-0.664899\pi$
$569$	−3.36101e16			−0.990366			−0.495183	+	0.868789i	$0.664899\pi$
$570$			1.53721e15i			0.0448212i
$571$	4.27000e16			1.23200			0.616000	−	0.787746i	$-0.288752\pi$
$571$	4.27000e16			1.23200			0.616000	+	0.787746i	$0.288752\pi$
$572$		−	1.48947e16i		−	0.425261i
$573$		−	3.06836e15i		−	0.0866920i
$574$	−2.16803e16	+	2.67083e15i	−0.606169	+	0.0746751i
$575$	−3.16575e16			−0.875931
$576$	4.47560e15			0.122551
$577$			3.90242e16i			1.05750i	0.848778	+	0.528749i	$0.177339\pi$
$577$			3.90242e16i			1.05750i	−0.848778	+	0.528749i	$0.822661\pi$
$578$	5.86822e16			1.57376
$579$		−	2.95169e15i		−	0.0783428i
$580$		−	1.10080e15i		−	0.0289163i
$581$	1.54309e16	−	1.90095e15i	0.401174	−	0.0494214i
$582$	−1.26545e15			−0.0325617
$583$	−3.72232e16			−0.947986
$584$		−	7.12852e15i		−	0.179689i
$585$	−1.94807e16			−0.486037
$586$			3.28018e16i			0.810050i
$587$		−	1.17306e16i		−	0.286741i	−0.989669	−	0.143371i	$-0.954206\pi$
$587$		−	1.17306e16i		−	0.286741i	0.989669	−	0.143371i	$-0.0457941\pi$
$588$	−7.02027e14	−	2.80608e15i	−0.0169860	−	0.0678948i
$589$	−6.55840e15			−0.157075
$590$	−1.19177e16			−0.282541
$591$			8.30110e15i			0.194810i
$592$	−5.68580e15			−0.132087
$593$			5.92839e16i			1.36335i	0.731653	+	0.681677i	$0.238749\pi$
$593$			5.92839e16i			1.36335i	−0.731653	+	0.681677i	$0.761251\pi$
$594$			6.53886e15i			0.148862i
$595$	4.31312e15	+	3.50115e16i	0.0972054	+	0.789057i
$596$	−3.52278e16			−0.785973
$597$	7.88780e15			0.174225
$598$			3.94521e16i			0.862706i
$599$	4.21231e16			0.911926			0.455963	−	0.889999i	$-0.349295\pi$
$599$	4.21231e16			0.911926			0.455963	+	0.889999i	$0.349295\pi$
$600$		−	1.85650e15i		−	0.0397913i
$601$			8.27638e16i			1.75628i	0.478405	+	0.878139i	$0.341215\pi$
$601$			8.27638e16i			1.75628i	−0.478405	+	0.878139i	$0.658785\pi$
$602$	1.30807e15	+	1.06182e16i	0.0274823	+	0.223085i
$603$	5.16876e16			1.07518
$604$	3.33673e16			0.687226
$605$		−	9.18753e15i		−	0.187356i
$606$	3.29247e15			0.0664793
$607$		−	3.15849e16i		−	0.631461i	−0.948849	−	0.315731i	$-0.897750\pi$
$607$		−	3.15849e16i		−	0.631461i	0.948849	−	0.315731i	$-0.102250\pi$
$608$		−	9.13533e15i		−	0.180843i
$609$	−9.25941e14	+	1.14068e14i	−0.0181501	+	0.00223595i
$610$	−2.61925e16			−0.508391
$611$	−8.87104e16			−1.70501
$612$			4.62586e16i			0.880408i
$613$	−6.81811e16			−1.28499			−0.642497	−	0.766288i	$-0.722101\pi$
$613$	−6.81811e16			−1.28499			−0.642497	+	0.766288i	$0.722101\pi$
$614$		−	1.44323e16i		−	0.269355i
$615$		−	2.89568e15i		−	0.0535180i
$616$	−1.79368e15	−	1.45601e16i	−0.0328292	−	0.266489i
$617$	3.16558e16			0.573777			0.286888	−	0.957964i	$-0.407379\pi$
$617$	3.16558e16			0.573777			0.286888	+	0.957964i	$0.407379\pi$
$618$	−7.26925e15			−0.130484
$619$		−	7.12518e16i		−	1.26664i	−0.773892	−	0.633318i	$-0.781693\pi$
$619$		−	7.12518e16i		−	1.26664i	0.773892	−	0.633318i	$-0.218307\pi$
$620$	−1.93028e15			−0.0339837
$621$		−	1.73197e16i		−	0.301988i
$622$			5.42618e16i			0.937026i
$623$	5.92344e16	−	7.29719e15i	1.01308	−	0.124804i
$624$	−2.31360e15			−0.0391905
$625$	2.68548e16			0.450550
$626$		−	3.46013e16i		−	0.574971i
$627$	6.60734e15			0.108748
$628$			1.39473e16i			0.227369i
$629$		−	5.87669e16i		−	0.948919i
$630$	−1.90430e16	+	2.34594e15i	−0.304573	+	0.0375210i
$631$	4.94210e16			0.782953			0.391477	−	0.920188i	$-0.371964\pi$
$631$	4.94210e16			0.782953			0.391477	+	0.920188i	$0.371964\pi$
$632$	2.10879e16			0.330925
$633$			1.54034e16i			0.239439i
$634$	9.73764e15			0.149940
$635$		−	4.56424e16i		−	0.696187i
$636$			5.78189e15i			0.0873629i
$637$	−1.81593e16	−	7.25847e16i	−0.271808	−	1.08645i
$638$	−4.73156e15			−0.0701585
$639$	−1.93992e16			−0.284957
$640$		−	2.68872e15i		−	0.0391261i
$641$	−3.74467e16			−0.539841			−0.269920	−	0.962883i	$-0.586997\pi$
$641$	−3.74467e16			−0.539841			−0.269920	+	0.962883i	$0.586997\pi$
$642$		−	3.49913e15i		−	0.0499747i
$643$		−	1.35542e17i		−	1.91782i	−0.283717	−	0.958908i	$-0.591568\pi$
$643$		−	1.35542e17i		−	1.91782i	0.283717	−	0.958908i	$-0.408432\pi$
$644$	4.75097e15	+	3.85656e16i	0.0665989	+	0.540612i
$645$	−1.41819e15			−0.0196960
$646$	9.44203e16			1.29918
$647$		−	6.00611e16i		−	0.818781i	−0.912359	−	0.409390i	$-0.865741\pi$
$647$		−	6.00611e16i		−	0.818781i	0.912359	−	0.409390i	$-0.134259\pi$
$648$	−2.46476e16			−0.332908
$649$			5.12256e16i			0.685519i
$650$		−	4.80220e16i		−	0.636737i
$651$	2.00021e14	+	1.62365e15i	0.00262778	+	0.0213308i
$652$	−1.98663e16			−0.258601
$653$	−6.04546e15			−0.0779741			−0.0389870	−	0.999240i	$-0.512413\pi$
$653$	−6.04546e15			−0.0779741			−0.0389870	+	0.999240i	$0.512413\pi$
$654$		−	8.80450e15i		−	0.112522i
$655$	2.32401e16			0.294300
$656$			1.72085e16i			0.215933i
$657$			4.00743e16i			0.498280i
$658$	−8.67172e16	+	1.06829e16i	−1.06844	+	0.131623i
$659$	−3.39399e16			−0.414379			−0.207190	−	0.978301i	$-0.566432\pi$
$659$	−3.39399e16			−0.414379			−0.207190	+	0.978301i	$0.566432\pi$
$660$	1.94468e15			0.0235280
$661$			8.24221e15i			0.0988178i	0.998779	+	0.0494089i	$0.0157337\pi$
$661$			8.24221e15i			0.0988178i	−0.998779	+	0.0494089i	$0.984266\pi$
$662$	−3.99232e16			−0.474326
$663$		−	2.39128e16i		−	0.281546i
$664$		−	1.22481e16i		−	0.142909i
$665$	4.78839e15	+	3.88694e16i	0.0553681	+	0.449447i
$666$	3.19638e16			0.366280
$667$	1.25326e16			0.142327
$668$		−	1.57072e15i		−	0.0176783i
$669$	−2.39304e16			−0.266928
$670$		−	3.10514e16i		−	0.343267i
$671$			1.12583e17i			1.23349i
$672$	−2.26162e15	+	2.78613e14i	−0.0245586	+	0.00302542i
$673$	1.68997e17			1.81881			0.909406	−	0.415909i	$-0.136537\pi$
$673$	1.68997e17			1.81881			0.909406	+	0.415909i	$0.136537\pi$
$674$	9.03107e16			0.963341
$675$			2.10819e16i			0.222888i
$676$	−1.21313e16			−0.127124
$677$			1.83472e16i			0.190563i	0.995450	+	0.0952813i	$0.0303751\pi$
$677$			1.83472e16i			0.190563i	−0.995450	+	0.0952813i	$0.969625\pi$
$678$			1.72548e16i			0.177636i
$679$	−3.19979e16	+	3.94187e15i	−0.326514	+	0.0402239i
$680$	2.77899e16			0.281083
$681$	−2.05482e16			−0.206011
$682$			8.29687e15i			0.0824533i
$683$	−1.66013e17			−1.63537			−0.817686	−	0.575664i	$-0.804744\pi$
$683$	−1.66013e17			−1.63537			−0.817686	+	0.575664i	$0.804744\pi$
$684$			5.13559e16i			0.501481i
$685$			3.94405e16i			0.381768i
$686$	−2.64922e16	−	6.87671e16i	−0.254199	−	0.659836i
$687$	−1.60877e15			−0.0153022
$688$	8.42806e15			0.0794688
$689$			1.49560e17i			1.39797i
$690$	−5.15094e15			−0.0477300
$691$			1.12594e17i			1.03430i	0.855894	+	0.517151i	$0.173007\pi$
$691$			1.12594e17i			1.03430i	−0.855894	+	0.517151i	$0.826993\pi$
$692$			5.87402e16i			0.534933i
$693$	1.00835e16	+	8.18520e16i	0.0910357	+	0.738976i
$694$	−7.54113e16			−0.674962
$695$	8.72389e16			0.774107
$696$			7.34955e14i			0.00646555i
$697$	−1.77862e17			−1.55127
$698$		−	5.15547e16i		−	0.445795i
$699$			6.40629e15i			0.0549216i
$700$	−5.78300e15	−	4.69430e16i	−0.0491547	−	0.399009i
$701$	1.67852e17			1.41455			0.707276	−	0.706937i	$-0.249924\pi$
$701$	1.67852e17			1.41455			0.707276	+	0.706937i	$0.249924\pi$
$702$	2.62726e16			0.219523
$703$		−	6.52425e16i		−	0.540504i
$704$	−1.15569e16			−0.0949302
$705$		−	1.15822e16i		−	0.0943314i
$706$		−	1.16109e17i		−	0.937645i
$707$	8.32526e16	−	1.02560e16i	0.666624	−	0.0821227i
$708$	7.95690e15			0.0631749
$709$	5.82006e15			0.0458194			0.0229097	−	0.999738i	$-0.492707\pi$
$709$	5.82006e15			0.0458194			0.0229097	+	0.999738i	$0.492707\pi$
$710$			1.16541e16i			0.0909765i
$711$	−1.18549e17			−0.917659
$712$		−	4.70166e16i		−	0.360887i
$713$		−	2.19762e16i		−	0.167269i
$714$	−2.87967e15	−	2.33755e16i	−0.0217347	−	0.176430i
$715$	5.03030e16			0.376493
$716$	1.77228e16			0.131539
$717$			2.50549e16i			0.184407i
$718$	8.07122e16			0.589105
$719$			2.25497e16i			0.163218i	0.996664	+	0.0816090i	$0.0260059\pi$
$719$			2.25497e16i			0.163218i	−0.996664	+	0.0816090i	$0.973994\pi$
$720$			1.51152e16i			0.108497i
$721$	−1.83808e17	+	2.26437e16i	−1.30844	+	0.161189i
$722$	4.66144e15			0.0329077
$723$	5.80648e15			0.0406521
$724$		−	6.07493e16i		−	0.421803i
$725$	−1.52550e16			−0.105047
$726$			6.13408e15i			0.0418919i
$727$		−	8.48651e16i		−	0.574808i	−0.957809	−	0.287404i	$-0.907208\pi$
$727$		−	8.48651e16i		−	0.574808i	0.957809	−	0.287404i	$-0.0927922\pi$
$728$	−5.85011e16	+	7.20686e15i	−0.392985	+	0.0484125i
$729$	1.32737e17			0.884354
$730$	2.40747e16			0.159083
$731$			8.71102e16i			0.570906i
$732$	1.74875e16			0.113674
$733$		−	2.75348e17i		−	1.77525i	−0.460571	−	0.887623i	$-0.652355\pi$
$733$		−	2.75348e17i		−	1.77525i	0.460571	−	0.887623i	$-0.347645\pi$
$734$			1.32826e17i			0.849386i
$735$	9.47680e15	−	2.37091e15i	0.0601088	−	0.0150380i
$736$	3.06110e16			0.192580
$737$	−1.33467e17			−0.832857
$738$		−	9.67407e16i		−	0.598785i
$739$	2.12061e17			1.30195			0.650976	−	0.759098i	$-0.274360\pi$
$739$	2.12061e17			1.30195			0.650976	+	0.759098i	$0.274360\pi$
$740$		−	1.92023e16i		−	0.116940i
$741$		−	2.65478e16i		−	0.160368i
$742$	1.80106e16	+	1.46199e17i	0.107920	+	0.876036i
$743$	−7.72077e16			−0.458910			−0.229455	−	0.973319i	$-0.573694\pi$
$743$	−7.72077e16			−0.458910			−0.229455	+	0.973319i	$0.573694\pi$
$744$	1.28876e15			0.00759859
$745$		−	1.18973e17i		−	0.695839i
$746$	−1.04074e17			−0.603821
$747$			6.88548e16i			0.396287i
$748$		−	1.19449e17i		−	0.681981i
$749$	−1.08998e16	−	8.84782e16i	−0.0617344	−	0.501124i
$750$	1.40677e16			0.0790414
$751$	−2.38534e16			−0.132957			−0.0664785	−	0.997788i	$-0.521176\pi$
$751$	−2.38534e16			−0.132957			−0.0664785	+	0.997788i	$0.521176\pi$
$752$			6.88308e16i			0.380606i
$753$	2.61605e16			0.143508
$754$			1.90110e16i			0.103461i
$755$			1.12689e17i			0.608417i
$756$	2.56823e16	−	3.16385e15i	0.137563	−	0.0169467i
$757$	1.29851e17			0.690032			0.345016	−	0.938597i	$-0.387874\pi$
$757$	1.29851e17			0.690032			0.345016	+	0.938597i	$0.387874\pi$
$758$	−8.51446e16			−0.448892
$759$			2.21402e16i			0.115806i
$760$	3.08521e16			0.160105
$761$			7.58064e16i			0.390300i	0.980773	+	0.195150i	$0.0625193\pi$
$761$			7.58064e16i			0.390300i	−0.980773	+	0.195150i	$0.937481\pi$
$762$			3.04733e16i			0.155664i
$763$	−2.74260e16	−	2.22628e17i	−0.139000	−	1.12832i
$764$	−6.15828e16			−0.309670
$765$	−1.56226e17			−0.779445
$766$			5.39575e16i			0.267103i
$767$	2.05821e17			1.01092
$768$			1.79513e15i			0.00874842i
$769$		−	1.28136e17i		−	0.619601i	−0.950802	−	0.309800i	$-0.899738\pi$
$769$		−	1.28136e17i		−	0.619601i	0.950802	−	0.309800i	$-0.100262\pi$
$770$	4.91727e16	−	6.05768e15i	0.235928	−	0.0290644i
$771$	3.34850e16			0.159413
$772$	−5.92411e16			−0.279846
$773$		−	3.83485e17i		−	1.79751i	−0.438453	−	0.898754i	$-0.644473\pi$
$773$		−	3.83485e17i		−	1.79751i	0.438453	−	0.898754i	$-0.355527\pi$
$774$	−4.73799e16			−0.220368
$775$			2.67499e16i			0.123456i
$776$			2.53979e16i			0.116313i
$777$	−1.61520e16	+	1.98979e15i	−0.0734007	+	0.00904236i
$778$	7.89947e16			0.356222
$779$	−1.97461e17			−0.883603
$780$		−	7.81358e15i		−	0.0346962i
$781$	5.00926e16			0.220733
$782$			3.16388e17i			1.38350i
$783$		−	8.34594e15i		−	0.0362164i
$784$	−5.63188e16	+	1.40899e16i	−0.242525	+	0.0606751i
$785$	−4.71032e16			−0.201295
$786$	−1.55163e16			−0.0658041
$787$			1.10686e17i			0.465850i	0.972495	+	0.232925i	$0.0748297\pi$
$787$			1.10686e17i			0.465850i	−0.972495	+	0.232925i	$0.925170\pi$
$788$	1.66605e17			0.695875
$789$		−	8.94957e15i		−	0.0370971i
$790$			7.12186e16i			0.292975i
$791$	5.37485e16	+	4.36300e17i	0.219436	+	1.78125i
$792$	6.49691e16			0.263242
$793$	4.52348e17			1.81900
$794$			2.71675e17i			1.08424i
$795$	−1.95268e16			−0.0773443
$796$		−	1.58310e17i		−	0.622344i
$797$		−	6.75641e16i		−	0.263612i	−0.991276	−	0.131806i	$-0.957922\pi$
$797$		−	6.75641e16i		−	0.263612i	0.991276	−	0.131806i	$-0.0420776\pi$
$798$	−3.19698e15	−	2.59513e16i	−0.0123801	−	0.100494i
$799$	−7.11417e17			−2.73428
$800$	−3.72605e16			−0.142138
$801$			2.64313e17i			1.00074i
$802$	−9.34341e16			−0.351123
$803$		−	1.03480e17i		−	0.385977i
$804$			2.07315e16i			0.0767530i
$805$	−1.30245e17	+	1.60452e16i	−0.478615	+	0.0589615i
$806$	3.33362e16			0.121592
$807$	4.94082e16			0.178878
$808$		−	6.60808e16i		−	0.237469i
$809$	1.48164e17			0.528508			0.264254	−	0.964453i	$-0.414874\pi$
$809$	1.48164e17			0.528508			0.264254	+	0.964453i	$0.414874\pi$
$810$		−	8.32406e16i		−	0.294731i
$811$			3.91802e17i			1.37702i	0.725226	+	0.688511i	$0.241735\pi$
$811$			3.91802e17i			1.37702i	−0.725226	+	0.688511i	$0.758265\pi$
$812$	2.28938e15	+	1.85839e16i	0.00798697	+	0.0648336i
$813$	−4.87436e16			−0.168801
$814$	−8.25367e16			−0.283727
$815$		−	6.70930e16i		−	0.228945i
$816$	−1.85540e16			−0.0628488
$817$			9.67090e16i			0.325188i
$818$		−	1.41585e17i		−	0.472604i
$819$	3.28875e17	−	4.05147e16i	1.08975	−	0.134248i
$820$	−5.81171e16			−0.191170
$821$	1.01616e17			0.331819			0.165909	−	0.986141i	$-0.446944\pi$
$821$	1.01616e17			0.331819			0.165909	+	0.986141i	$0.446944\pi$
$822$		−	2.63326e16i		−	0.0853616i
$823$	3.66413e17			1.17916			0.589580	−	0.807710i	$-0.299293\pi$
$823$	3.66413e17			1.17916			0.589580	+	0.807710i	$0.299293\pi$
$824$			1.45896e17i			0.466100i
$825$		−	2.69495e16i		−	0.0854727i
$826$	2.01196e17	−	2.47857e16i	0.633489	−	0.0780407i
$827$	−2.85422e17			−0.892183			−0.446091	−	0.894987i	$-0.647184\pi$
$827$	−2.85422e17			−0.892183			−0.446091	+	0.894987i	$0.647184\pi$
$828$	−1.72086e17			−0.534026
$829$			2.56010e17i			0.788733i	0.918953	+	0.394367i	$0.129036\pi$
$829$			2.56010e17i			0.788733i	−0.918953	+	0.394367i	$0.870964\pi$
$830$	4.13646e16			0.126520
$831$			5.48786e16i			0.166647i
$832$			4.64346e16i			0.139992i
$833$	−1.45629e17	−	5.82096e17i	−0.435891	−	1.74231i
$834$	−5.82453e16			−0.173087
$835$	5.30471e15			0.0156510
$836$		−	1.32611e17i		−	0.388456i
$837$	−1.46348e16			−0.0425630
$838$		−	1.78014e17i		−	0.514033i
$839$		−	1.97080e17i		−	0.565028i	−0.959263	−	0.282514i	$-0.908832\pi$
$839$		−	1.97080e17i		−	0.565028i	0.959263	−	0.282514i	$-0.0911684\pi$
$840$	−9.40941e14	−	7.63802e15i	−0.00267847	−	0.0217423i
$841$	−3.47776e17			−0.982931
$842$	−2.04496e17			−0.573868
$843$			1.47217e16i			0.0410196i
$844$	3.09150e17			0.855293
$845$		−	4.09703e16i		−	0.112546i
$846$		−	3.86945e17i		−	1.05542i
$847$	1.91076e16	+	1.55105e17i	0.0517495	+	0.420073i
$848$	1.16044e17			0.312067
$849$	−8.46423e16			−0.226017
$850$		−	3.85115e17i		−	1.02112i
$851$	2.18617e17			0.575582
$852$		−	7.78090e15i		−	0.0203419i
$853$			2.02493e16i			0.0525673i	0.999655	+	0.0262836i	$0.00836731\pi$
$853$			2.02493e16i			0.0525673i	−0.999655	+	0.0262836i	$0.991633\pi$
$854$	4.42184e17	−	5.44735e16i	1.13987	−	0.140423i
$855$	−1.73441e17			−0.443972
$856$	−7.02285e16			−0.178513
$857$		−	5.47191e17i		−	1.38119i	−0.723241	−	0.690596i	$-0.757348\pi$
$857$		−	5.47191e17i		−	1.38119i	0.723241	−	0.690596i	$-0.242652\pi$
$858$	−3.35849e16			−0.0841822
$859$			8.67365e16i			0.215895i	0.994157	+	0.107948i	$0.0344278\pi$
$859$			8.67365e16i			0.215895i	−0.994157	+	0.107948i	$0.965572\pi$
$860$			2.84635e16i			0.0703555i
$861$	6.02225e15	+	4.88852e16i	0.0147822	+	0.119994i
$862$	−1.99833e17			−0.487106
$863$	2.08592e17			0.504931			0.252465	−	0.967606i	$-0.418759\pi$
$863$	2.08592e17			0.504931			0.252465	+	0.967606i	$0.418759\pi$
$864$		−	2.03850e16i		−	0.0490037i
$865$	−1.98380e17			−0.473588
$866$		−	3.62903e17i		−	0.860365i
$867$		−	1.32318e17i		−	0.311533i
$868$	3.25872e16	−	4.01447e15i	0.0761953	−	0.00938664i
$869$	3.06117e17			0.710836
$870$	−2.48212e15			−0.00572409
$871$			5.36261e17i			1.22820i
$872$	−1.76709e17			−0.401938
$873$		−	1.42779e17i		−	0.322537i
$874$			3.51251e17i			0.788041i
$875$	3.55711e17	−	4.38207e16i	0.792592	−	0.0976408i
$876$	−1.60735e16			−0.0355702
$877$	6.66040e17			1.46387			0.731935	−	0.681374i	$-0.238617\pi$
$877$	6.66040e17			1.46387			0.731935	+	0.681374i	$0.238617\pi$
$878$			4.79502e16i			0.104670i
$879$	7.39622e16			0.160353
$880$		−	3.90303e16i		−	0.0840438i
$881$		−	2.75630e16i		−	0.0589483i	−0.999566	−	0.0294742i	$-0.990617\pi$
$881$		−	2.75630e16i		−	0.0589483i	0.999566	−	0.0294742i	$-0.00938327\pi$
$882$	3.16607e17	−	7.92088e16i	0.672525	−	0.168253i
$883$	−9.14924e17			−1.93028			−0.965141	−	0.261730i	$-0.915707\pi$
$883$	−9.14924e17			−1.93028			−0.965141	+	0.261730i	$0.915707\pi$
$884$	−4.79936e17			−1.00570
$885$			2.68723e16i			0.0559301i
$886$	−3.96553e17			−0.819782
$887$		−	3.43433e17i		−	0.705181i	−0.935778	−	0.352590i	$-0.885301\pi$
$887$		−	3.43433e17i		−	0.705181i	0.935778	−	0.352590i	$-0.114699\pi$
$888$			1.28205e16i			0.0261472i
$889$	9.49241e16	+	7.70539e17i	0.192294	+	1.56093i
$890$	1.58786e17			0.319501
$891$	−3.57791e17			−0.715094
$892$			4.80290e17i			0.953486i
$893$	−7.89809e17			−1.55745
$894$			7.94323e16i			0.155587i
$895$			5.98540e16i			0.116454i
$896$	5.59183e15	+	4.53913e16i	0.0108070	+	0.0877252i
$897$	8.89574e16			0.170776
$898$	1.90479e17			0.363236
$899$		−	1.05898e16i		−	0.0200599i
$900$	2.09467e17			0.394149
$901$			1.19940e18i			2.24190i
$902$			2.49803e17i			0.463830i
$903$	2.39421e16	−	2.94947e15i	0.0441607	−	0.00544023i
$904$	3.46308e17			0.634529
$905$	2.05165e17			0.373432
$906$		−	7.52373e16i		−	0.136039i
$907$	6.54621e17			1.17583			0.587917	−	0.808921i	$-0.299948\pi$
$907$	6.54621e17			1.17583			0.587917	+	0.808921i	$0.299948\pi$
$908$			4.12408e17i			0.735888i
$909$			3.71485e17i			0.658504i
$910$	−2.43393e16	−	1.97572e17i	−0.0428607	−	0.347918i
$911$	−1.25928e17			−0.220298			−0.110149	−	0.993915i	$-0.535133\pi$
$911$	−1.25928e17			−0.220298			−0.110149	+	0.993915i	$0.535133\pi$
$912$	−2.05985e16			−0.0357987
$913$		−	1.77796e17i		−	0.306972i
$914$	−4.46912e17			−0.766558
$915$			5.90594e16i			0.100638i
$916$			3.22884e16i			0.0546604i
$917$	−3.92341e17	+	4.83332e16i	−0.659854	+	0.0812887i
$918$	2.10694e17			0.352044
$919$	4.38132e17			0.727297			0.363648	−	0.931536i	$-0.381531\pi$
$919$	4.38132e17			0.727297			0.363648	+	0.931536i	$0.381531\pi$
$920$			1.03381e17i			0.170495i
$921$	−3.25422e16			−0.0533198
$922$			6.81536e17i			1.10944i
$923$		−	2.01268e17i		−	0.325510i
$924$	−3.28303e16	+	4.04442e15i	−0.0527525	+	0.00649868i
$925$	−2.66106e17			−0.424820
$926$	−1.89049e17			−0.299853
$927$		−	8.20180e17i		−	1.29250i
$928$	1.47507e16			0.0230954
$929$		−	1.18179e18i		−	1.83842i	−0.393766	−	0.919211i	$-0.628828\pi$
$929$		−	1.18179e18i		−	1.83842i	0.393766	−	0.919211i	$-0.371172\pi$
$930$			4.35243e15i			0.00672720i
$931$	−1.61676e17	−	6.46238e17i	−0.248284	−	0.992418i
$932$	1.28576e17			0.196184
$933$	1.22351e17			0.185488
$934$		−	2.69263e16i		−	0.0405598i
$935$	4.03407e17			0.603773
$936$		−	2.61041e17i		−	0.388198i
$937$		−	2.14322e17i		−	0.316686i	−0.987384	−	0.158343i	$-0.949385\pi$
$937$		−	2.14322e17i		−	0.316686i	0.987384	−	0.158343i	$-0.0506152\pi$
$938$	6.45787e16	+	5.24212e17i	0.0948139	+	0.769645i
$939$	−7.80197e16			−0.113818
$940$	−2.32458e17			−0.336959
$941$			7.16473e17i			1.03196i	0.856601	+	0.515979i	$0.172572\pi$
$941$			7.16473e17i			1.03196i	−0.856601	+	0.515979i	$0.827428\pi$
$942$	3.14486e16			0.0450086
$943$		−	6.61661e17i		−	0.940948i
$944$		−	1.59697e17i		−	0.225665i
$945$	1.06851e16	+	8.67352e16i	0.0150033	+	0.121788i
$946$	1.22344e17			0.170701
$947$	−4.29466e17			−0.595427			−0.297713	−	0.954655i	$-0.596224\pi$
$947$	−4.29466e17			−0.595427			−0.297713	+	0.954655i	$0.596224\pi$
$948$		−	4.75493e16i		−	0.0655080i
$949$	−4.15773e17			−0.569192
$950$		−	4.27551e17i		−	0.581629i
$951$		−	2.19566e16i		−	0.0296813i
$952$	−4.69152e17	+	5.77957e16i	−0.630220	+	0.0776379i
$953$	1.43767e18			1.91911			0.959557	−	0.281515i	$-0.0908370\pi$
$953$	1.43767e18			1.91911			0.959557	+	0.281515i	$0.0908370\pi$
$954$	−6.52363e17			−0.865365
$955$		−	2.07980e17i		−	0.274158i
$956$	5.02859e17			0.658717
$957$			1.06688e16i			0.0138882i
$958$		−	2.57031e17i		−	0.332501i
$959$	−8.20259e16	−	6.65839e17i	−0.105448	−	0.855968i
$960$	−6.06259e15			−0.00774517
$961$	7.69093e17			0.976425
$962$			3.31626e17i			0.418406i
$963$	3.94803e17			0.495020
$964$		−	1.16538e17i		−	0.145212i
$965$		−	2.00071e17i		−	0.247754i
$966$	8.69586e16	−	1.07126e16i	0.107016	−	0.0131835i
$967$	−5.69655e17			−0.696712			−0.348356	−	0.937362i	$-0.613260\pi$
$967$	−5.69655e17			−0.696712			−0.348356	+	0.937362i	$0.613260\pi$
$968$	1.23113e17			0.149641
$969$		−	2.12901e17i		−	0.257179i
$970$	−8.57748e16			−0.102974
$971$			6.04240e17i			0.720932i	0.932772	+	0.360466i	$0.117382\pi$
$971$			6.04240e17i			0.720932i	−0.932772	+	0.360466i	$0.882618\pi$
$972$			1.72464e17i			0.204504i
$973$	−1.47277e18	+	1.81434e17i	−1.73564	+	0.213816i
$974$	6.54779e17			0.766904
$975$	−1.08281e17			−0.126045
$976$		−	3.50979e17i		−	0.406052i
$977$	−8.41436e17			−0.967506			−0.483753	−	0.875205i	$-0.660727\pi$
$977$	−8.41436e17			−0.967506			−0.483753	+	0.875205i	$0.660727\pi$
$978$			4.47948e16i			0.0511911i
$979$		−	6.82507e17i		−	0.775195i
$980$	−4.75848e16	−	1.90202e17i	−0.0537170	−	0.214713i
$981$	9.93400e17			1.11458
$982$	8.00826e17			0.893037
$983$			2.66147e17i			0.294985i	0.989063	+	0.147493i	$0.0471202\pi$
$983$			2.66147e17i			0.294985i	−0.989063	+	0.147493i	$0.952880\pi$
$984$	3.88020e16			0.0427449
$985$			5.62665e17i			0.616074i
$986$			1.52460e17i			0.165918i
$987$	2.40879e16	+	1.95532e17i	0.0260553	+	0.211502i
$988$	−5.32821e17			−0.572848
$989$	−3.24057e17			−0.346292
$990$			2.19416e17i			0.233054i
$991$	−1.36773e16			−0.0144397			−0.00721987	−	0.999974i	$-0.502298\pi$
$991$	−1.36773e16			−0.0144397			−0.00721987	+	0.999974i	$0.502298\pi$
$992$		−	2.58657e16i		−	0.0271427i
$993$			9.00196e16i			0.0938949i
$994$	−2.42375e16	−	1.96746e17i	−0.0251286	−	0.203980i
$995$	5.34651e17			0.550975
$996$	−2.76172e16			−0.0282894
$997$			2.28681e17i			0.232841i	0.993200	+	0.116421i	$0.0371420\pi$
$997$			2.28681e17i			0.232841i	−0.993200	+	0.116421i	$0.962858\pi$
$998$	−9.44824e17			−0.956242
$999$		−	1.45585e17i		−	0.146462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.13.b.a.13.3	yes	8
3.2	odd	2		126.13.c.a.55.6		8
4.3	odd	2		112.13.c.c.97.4		8
7.2	even	3		98.13.d.b.31.6		16
7.3	odd	6		98.13.d.b.19.6		16
7.4	even	3		98.13.d.b.19.7		16
7.5	odd	6		98.13.d.b.31.7		16
7.6	odd	2	inner	14.13.b.a.13.2	✓	8
21.20	even	2		126.13.c.a.55.7		8
28.27	even	2		112.13.c.c.97.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.b.a.13.2	✓	8	7.6	odd	2	inner
14.13.b.a.13.3	yes	8	1.1	even	1	trivial
98.13.d.b.19.6		16	7.3	odd	6
98.13.d.b.19.7		16	7.4	even	3
98.13.d.b.31.6		16	7.2	even	3
98.13.d.b.31.7		16	7.5	odd	6
112.13.c.c.97.4		8	4.3	odd	2
112.13.c.c.97.5		8	28.27	even	2
126.13.c.a.55.6		8	3.2	odd	2
126.13.c.a.55.7		8	21.20	even	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	14.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-45.2548 q^{2} +102.042i q^{3} +2048.00 q^{4} +6916.58i q^{5} -4617.87i q^{6} +(-14384.7 - 116766. i) q^{7} -92681.9 q^{8} +521029. q^{9} +O(q^{10})\)	\(q-45.2548 q^{2} +102.042i q^{3} +2048.00 q^{4} +6916.58i q^{5} -4617.87i q^{6} +(-14384.7 - 116766. i) q^{7} -92681.9 q^{8} +521029. q^{9} -313009. i q^{10} -1.34540e6 q^{11} +208981. i q^{12} +5.40570e6i q^{13} +(650975. + 5.28424e6i) q^{14} -705778. q^{15} +4.19430e6 q^{16} +4.33512e7i q^{17} -2.35791e7 q^{18} +4.81282e7i q^{19} +1.41652e7i q^{20} +(1.19150e7 - 1.46783e6i) q^{21} +6.08857e7 q^{22} -1.61270e8 q^{23} -9.45740e6i q^{24} +1.96302e8 q^{25} -2.44634e8i q^{26} +1.07396e8i q^{27} +(-2.94598e7 - 2.39137e8i) q^{28} -7.77122e7 q^{29} +3.19399e7 q^{30} +1.36270e8i q^{31} -1.89813e8 q^{32} -1.37286e8i q^{33} -1.96185e9i q^{34} +(8.07623e8 - 9.94926e7i) q^{35} +1.06707e9 q^{36} -1.35560e9 q^{37} -2.17803e9i q^{38} -5.51606e8 q^{39} -6.41042e8i q^{40} +4.10282e9i q^{41} +(-5.39212e8 + 6.64265e7i) q^{42} +2.00941e9 q^{43} -2.75537e9 q^{44} +3.60373e9i q^{45} +7.29824e9 q^{46} +1.64105e10i q^{47} +4.27993e8i q^{48} +(-1.34275e10 + 3.35929e9i) q^{49} -8.88359e9 q^{50} -4.42362e9 q^{51} +1.10709e10i q^{52} +2.76670e10 q^{53} -4.86017e9i q^{54} -9.30554e9i q^{55} +(1.33320e9 + 1.08221e10i) q^{56} -4.91107e9 q^{57} +3.51685e9 q^{58} -3.80747e10i q^{59} -1.44543e9 q^{60} -8.36798e10i q^{61} -6.16686e9i q^{62} +(-7.49481e9 - 6.08386e10i) q^{63} +8.58993e9 q^{64} -3.73889e10 q^{65} +6.21287e9i q^{66} +9.92030e10 q^{67} +8.87833e10i q^{68} -1.64562e10i q^{69} +(-3.65489e10 + 4.50252e9i) q^{70} -3.72326e10 q^{71} -4.82899e10 q^{72} +7.69138e10i q^{73} +6.13475e10 q^{74} +2.00309e10i q^{75} +9.85665e10i q^{76} +(1.93531e10 + 1.57097e11i) q^{77} +2.49628e10 q^{78} -2.27529e11 q^{79} +2.90102e10i q^{80} +2.65937e11 q^{81} -1.85672e11i q^{82} +1.32152e11i q^{83} +(2.44019e10 - 3.00612e9i) q^{84} -2.99842e11 q^{85} -9.09353e10 q^{86} -7.92987e9i q^{87} +1.24694e11 q^{88} +5.07290e11i q^{89} -1.63086e11i q^{90} +(6.31203e11 - 7.77591e10i) q^{91} -3.30281e11 q^{92} -1.39052e10 q^{93} -7.42656e11i q^{94} -3.32882e11 q^{95} -1.93688e10i q^{96} -2.74033e11i q^{97} +(6.07657e11 - 1.52024e11i) q^{98} -7.00990e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9}+O(q^{10}) \) 8 * q + 16384 * q^4 + 195160 * q^7 - 1478904 * q^9	\( 8 q + 16384 q^{4} + 195160 q^{7} - 1478904 q^{9} - 213840 q^{11} - 8418816 q^{14} + 65882304 q^{15} + 33554432 q^{16} + 32547840 q^{18} - 4449984 q^{21} - 221337600 q^{22} + 156731760 q^{23} + 191237000 q^{25} + 399687680 q^{28} + 308853648 q^{29} - 2203567104 q^{30} - 3764734848 q^{35} - 3028795392 q^{36} - 3243600880 q^{37} + 13521315264 q^{39} - 12108579840 q^{42} + 21006302000 q^{43} - 437944320 q^{44} + 9664610304 q^{46} - 19258758904 q^{49} + 26259489792 q^{50} - 80965832832 q^{51} + 180445637520 q^{53} - 17241735168 q^{56} - 63145962240 q^{57} - 94193264640 q^{58} + 134926958592 q^{60} - 402706514280 q^{63} + 68719476736 q^{64} - 424890168192 q^{65} + 369211259440 q^{67} - 137936354304 q^{70} + 574058144304 q^{71} + 66657976320 q^{72} + 450517137408 q^{74} - 73915435440 q^{77} - 251000847360 q^{78} - 607826610128 q^{79} + 919051941384 q^{81} - 9113567232 q^{84} - 247202260608 q^{85} - 413092638720 q^{86} - 453299404800 q^{88} + 144527421696 q^{91} + 320986644480 q^{92} + 2292312458880 q^{93} - 1053641981376 q^{95} - 290797516800 q^{98} - 1800954256464 q^{99}+O(q^{100}) \) 8 * q + 16384 * q^4 + 195160 * q^7 - 1478904 * q^9 - 213840 * q^11 - 8418816 * q^14 + 65882304 * q^15 + 33554432 * q^16 + 32547840 * q^18 - 4449984 * q^21 - 221337600 * q^22 + 156731760 * q^23 + 191237000 * q^25 + 399687680 * q^28 + 308853648 * q^29 - 2203567104 * q^30 - 3764734848 * q^35 - 3028795392 * q^36 - 3243600880 * q^37 + 13521315264 * q^39 - 12108579840 * q^42 + 21006302000 * q^43 - 437944320 * q^44 + 9664610304 * q^46 - 19258758904 * q^49 + 26259489792 * q^50 - 80965832832 * q^51 + 180445637520 * q^53 - 17241735168 * q^56 - 63145962240 * q^57 - 94193264640 * q^58 + 134926958592 * q^60 - 402706514280 * q^63 + 68719476736 * q^64 - 424890168192 * q^65 + 369211259440 * q^67 - 137936354304 * q^70 + 574058144304 * q^71 + 66657976320 * q^72 + 450517137408 * q^74 - 73915435440 * q^77 - 251000847360 * q^78 - 607826610128 * q^79 + 919051941384 * q^81 - 9113567232 * q^84 - 247202260608 * q^85 - 413092638720 * q^86 - 453299404800 * q^88 + 144527421696 * q^91 + 320986644480 * q^92 + 2292312458880 * q^93 - 1053641981376 * q^95 - 290797516800 * q^98 - 1800954256464 * q^99

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