LMFDB - Embedded newform 14.13.b.a.13.1

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			13.1
Root			$242.361i$ of defining polynomial
Character	$\chi$	$=$	14.13
Dual form			14.13.b.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-45.2548 q^{2} -1265.70i q^{3} +2048.00 q^{4} +23188.3i q^{5} +57279.1i q^{6} +(109682. + 42556.3i) q^{7} -92681.9 q^{8} -1.07056e6 q^{9} +O(q^{10})$	\(q-45.2548 q^{2} -1265.70i q^{3} +2048.00 q^{4} +23188.3i q^{5} +57279.1i q^{6} +(109682. + 42556.3i) q^{7} -92681.9 q^{8} -1.07056e6 q^{9} -1.04938e6i q^{10} +2.51467e6 q^{11} -2.59216e6i q^{12} +4.20204e6i q^{13} +(-4.96366e6 - 1.92588e6i) q^{14} +2.93495e7 q^{15} +4.19430e6 q^{16} +2.05062e6i q^{17} +4.84479e7 q^{18} -5.17019e7i q^{19} +4.74896e7i q^{20} +(5.38636e7 - 1.38825e8i) q^{21} -1.13801e8 q^{22} +1.47063e8 q^{23} +1.17308e8i q^{24} -2.93557e8 q^{25} -1.90163e8i q^{26} +6.82360e8i q^{27} +(2.24630e8 + 8.71554e7i) q^{28} +6.75275e8 q^{29} -1.32820e9 q^{30} +2.35058e8i q^{31} -1.89813e8 q^{32} -3.18282e9i q^{33} -9.28005e7i q^{34} +(-9.86809e8 + 2.54335e9i) q^{35} -2.19250e9 q^{36} -1.94408e9 q^{37} +2.33976e9i q^{38} +5.31853e9 q^{39} -2.14914e9i q^{40} +4.99826e9i q^{41} +(-2.43759e9 + 6.28251e9i) q^{42} +5.52421e9 q^{43} +5.15004e9 q^{44} -2.48244e10i q^{45} -6.65530e9 q^{46} -4.82717e9i q^{47} -5.30873e9i q^{48} +(1.02192e10 + 9.33537e9i) q^{49} +1.32849e10 q^{50} +2.59547e9 q^{51} +8.60579e9i q^{52} +2.56862e10 q^{53} -3.08801e10i q^{54} +5.83108e10i q^{55} +(-1.01656e10 - 3.94420e9i) q^{56} -6.54391e10 q^{57} -3.05594e10 q^{58} -8.26012e9i q^{59} +6.01077e10 q^{60} +3.69504e10i q^{61} -1.06375e10i q^{62} +(-1.17421e11 - 4.55590e10i) q^{63} +8.58993e9 q^{64} -9.74383e10 q^{65} +1.44038e11i q^{66} +7.26978e8 q^{67} +4.19967e9i q^{68} -1.86138e11i q^{69} +(4.46579e10 - 1.15099e11i) q^{70} +1.17803e11 q^{71} +9.92213e10 q^{72} +4.53135e10i q^{73} +8.79790e10 q^{74} +3.71555e11i q^{75} -1.05885e11i q^{76} +(2.75815e11 + 1.07015e11i) q^{77} -2.40689e11 q^{78} -1.42006e11 q^{79} +9.72588e10i q^{80} +2.94726e11 q^{81} -2.26196e11i q^{82} -5.47779e11i q^{83} +(1.10313e11 - 2.84314e11i) q^{84} -4.75504e10 q^{85} -2.49997e11 q^{86} -8.54696e11i q^{87} -2.33064e11 q^{88} +6.34439e11i q^{89} +1.12342e12i q^{90} +(-1.78824e11 + 4.60891e11i) q^{91} +3.01185e11 q^{92} +2.97513e11 q^{93} +2.18453e11i q^{94} +1.19888e12 q^{95} +2.40246e11i q^{96} +1.64607e11i q^{97} +(-4.62468e11 - 4.22470e11i) q^{98} -2.69210e12 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
$3$		−	1265.70i		−	1.73622i	−0.496376	−	0.868108i	$-0.665336\pi$
$3$		−	1265.70i		−	1.73622i	0.496376	−	0.868108i	$-0.334664\pi$
$4$	2048.00			0.500000
$5$			23188.3i			1.48405i	0.670371	+	0.742026i	$0.266135\pi$
$5$			23188.3i			1.48405i	−0.670371	+	0.742026i	$0.733865\pi$
$6$			57279.1i			1.22769i
$7$	109682.	+	42556.3i	0.932286	+	0.361723i
$7$	109682.	+	42556.3i	0.932286	+	0.361723i
$8$	−92681.9			−0.353553
$9$	−1.07056e6			−2.01444
$10$		−	1.04938e6i		−	1.04938i
$11$	2.51467e6			1.41946			0.709732	−	0.704472i	$-0.248816\pi$
$11$	2.51467e6			1.41946			0.709732	+	0.704472i	$0.248816\pi$
$12$		−	2.59216e6i		−	0.868108i
$13$			4.20204e6i			0.870564i	0.900294	+	0.435282i	$0.143351\pi$
$13$			4.20204e6i			0.870564i	−0.900294	+	0.435282i	$0.856649\pi$
$14$	−4.96366e6	−	1.92588e6i	−0.659226	−	0.255777i
$15$	2.93495e7			2.57663
$16$	4.19430e6			0.250000
$17$			2.05062e6i			0.0849555i	0.999097	+	0.0424778i	$0.0135252\pi$
$17$			2.05062e6i			0.0849555i	−0.999097	+	0.0424778i	$0.986475\pi$
$18$	4.84479e7			1.42443
$19$		−	5.17019e7i		−	1.09897i	−0.835505	−	0.549483i	$-0.814825\pi$
$19$		−	5.17019e7i		−	1.09897i	0.835505	−	0.549483i	$-0.185175\pi$
$20$			4.74896e7i			0.742026i
$21$	5.38636e7	−	1.38825e8i	0.628029	−	1.61865i
$22$	−1.13801e8			−1.00371
$23$	1.47063e8			0.993427			0.496714	−	0.867915i	$-0.334540\pi$
$23$	1.47063e8			0.993427			0.496714	+	0.867915i	$0.334540\pi$
$24$			1.17308e8i			0.613845i
$25$	−2.93557e8			−1.20241
$26$		−	1.90163e8i		−	0.615581i
$27$			6.82360e8i			1.76129i
$28$	2.24630e8	+	8.71554e7i	0.466143	+	0.180861i
$29$	6.75275e8			1.13525			0.567626	−	0.823286i	$-0.307862\pi$
$29$	6.75275e8			1.13525			0.567626	+	0.823286i	$0.307862\pi$
$30$	−1.32820e9			−1.82195
$31$			2.35058e8i			0.264852i	0.991193	+	0.132426i	$0.0422768\pi$
$31$			2.35058e8i			0.264852i	−0.991193	+	0.132426i	$0.957723\pi$
$32$	−1.89813e8			−0.176777
$33$		−	3.18282e9i		−	2.46449i
$34$		−	9.28005e7i		−	0.0600726i
$35$	−9.86809e8	+	2.54335e9i	−0.536815	+	1.38356i
$36$	−2.19250e9			−1.00722
$37$	−1.94408e9			−0.757711			−0.378856	−	0.925456i	$-0.623682\pi$
$37$	−1.94408e9			−0.757711			−0.378856	+	0.925456i	$0.623682\pi$
$38$			2.33976e9i			0.777087i
$39$	5.31853e9			1.51149
$40$		−	2.14914e9i		−	0.524691i
$41$			4.99826e9i			1.05224i	0.850409	+	0.526121i	$0.176354\pi$
$41$			4.99826e9i			1.05224i	−0.850409	+	0.526121i	$0.823646\pi$
$42$	−2.43759e9	+	6.28251e9i	−0.444083	+	1.14456i
$43$	5.52421e9			0.873895			0.436947	−	0.899487i	$-0.356060\pi$
$43$	5.52421e9			0.873895			0.436947	+	0.899487i	$0.356060\pi$
$44$	5.15004e9			0.709732
$45$		−	2.48244e10i		−	2.98954i
$46$	−6.65530e9			−0.702459
$47$		−	4.82717e9i		−	0.447822i	−0.974610	−	0.223911i	$-0.928118\pi$
$47$		−	4.82717e9i		−	0.447822i	0.974610	−	0.223911i	$-0.0718825\pi$
$48$		−	5.30873e9i		−	0.434054i
$49$	1.02192e10	+	9.33537e9i	0.738313	+	0.674458i
$50$	1.32849e10			0.850232
$51$	2.59547e9			0.147501
$52$			8.60579e9i			0.435282i
$53$	2.56862e10			1.15890			0.579449	−	0.815009i	$-0.303268\pi$
$53$	2.56862e10			1.15890			0.579449	+	0.815009i	$0.303268\pi$
$54$		−	3.08801e10i		−	1.24542i
$55$			5.83108e10i			2.10656i
$56$	−1.01656e10	−	3.94420e9i	−0.329613	−	0.127888i
$57$	−6.54391e10			−1.90804
$58$	−3.05594e10			−0.802745
$59$		−	8.26012e9i		−	0.195828i	−0.995195	−	0.0979138i	$-0.968783\pi$
$59$		−	8.26012e9i		−	0.195828i	0.995195	−	0.0979138i	$-0.0312170\pi$
$60$	6.01077e10			1.28832
$61$			3.69504e10i			0.717200i	0.933491	+	0.358600i	$0.116746\pi$
$61$			3.69504e10i			0.717200i	−0.933491	+	0.358600i	$0.883254\pi$
$62$		−	1.06375e10i		−	0.187279i
$63$	−1.17421e11	−	4.55590e10i	−1.87804	−	0.728670i
$64$	8.58993e9			0.125000
$65$	−9.74383e10			−1.29196
$66$			1.44038e11i			1.74266i
$67$	7.26978e8			0.00803660			0.00401830	−	0.999992i	$-0.498721\pi$
$67$	7.26978e8			0.00803660			0.00401830	+	0.999992i	$0.498721\pi$
$68$			4.19967e9i			0.0424778i
$69$		−	1.86138e11i		−	1.72480i
$70$	4.46579e10	−	1.15099e11i	0.379586	−	0.978325i
$71$	1.17803e11			0.919618			0.459809	−	0.888018i	$-0.347918\pi$
$71$	1.17803e11			0.919618			0.459809	+	0.888018i	$0.347918\pi$
$72$	9.92213e10			0.712213
$73$			4.53135e10i			0.299426i	0.988729	+	0.149713i	$0.0478350\pi$
$73$			4.53135e10i			0.299426i	−0.988729	+	0.149713i	$0.952165\pi$
$74$	8.79790e10			0.535783
$75$			3.71555e11i			2.08764i
$76$		−	1.05885e11i		−	0.549483i
$77$	2.75815e11	+	1.07015e11i	1.32335	+	0.513452i
$78$	−2.40689e11			−1.06878
$79$	−1.42006e11			−0.584176			−0.292088	−	0.956391i	$-0.594350\pi$
$79$	−1.42006e11			−0.584176			−0.292088	+	0.956391i	$0.594350\pi$
$80$			9.72588e10i			0.371013i
$81$	2.94726e11			1.04354
$82$		−	2.26196e11i		−	0.744048i
$83$		−	5.47779e11i		−	1.67547i	−0.546075	−	0.837736i	$-0.683879\pi$
$83$		−	5.47779e11i		−	1.67547i	0.546075	−	0.837736i	$-0.316121\pi$
$84$	1.10313e11	−	2.84314e11i	0.314014	−	0.809324i
$85$	−4.75504e10			−0.126078
$86$	−2.49997e11			−0.617937
$87$		−	8.54696e11i		−	1.97104i
$88$	−2.33064e11			−0.501856
$89$			6.34439e11i			1.27659i	0.769794	+	0.638293i	$0.220359\pi$
$89$			6.34439e11i			1.27659i	−0.769794	+	0.638293i	$0.779641\pi$
$90$			1.12342e12i			2.11392i
$91$	−1.78824e11	+	4.60891e11i	−0.314903	+	0.811614i
$92$	3.01185e11			0.496714
$93$	2.97513e11			0.459841
$94$			2.18453e11i			0.316658i
$95$	1.19888e12			1.63092
$96$			2.40246e11i			0.306922i
$97$			1.64607e11i			0.197614i	0.995107	+	0.0988072i	$0.0315027\pi$
$97$			1.64607e11i			0.197614i	−0.995107	+	0.0988072i	$0.968497\pi$
$98$	−4.62468e11	−	4.22470e11i	−0.522066	−	0.476914i
$99$	−2.69210e12			−2.85943
$100$	−6.01204e11			−0.601204
$101$		−	7.38422e11i		−	0.695627i	−0.937564	−	0.347813i	$-0.886924\pi$
$101$		−	7.38422e11i		−	0.695627i	0.937564	−	0.347813i	$-0.113076\pi$
$102$	−1.17458e11			−0.104299
$103$		−	1.58377e12i		−	1.32639i	−0.748448	−	0.663193i	$-0.769201\pi$
$103$		−	1.58377e12i		−	1.32639i	0.748448	−	0.663193i	$-0.230799\pi$
$104$		−	3.89453e11i		−	0.307791i
$105$	3.21912e12	+	1.24901e12i	2.40216	+	0.932027i
$106$	−1.16243e12			−0.819464
$107$	−5.21160e11			−0.347271			−0.173636	−	0.984810i	$-0.555551\pi$
$107$	−5.21160e11			−0.347271			−0.173636	+	0.984810i	$0.555551\pi$
$108$			1.39747e12i			0.880646i
$109$	−2.83446e12			−1.69010			−0.845048	−	0.534690i	$-0.820428\pi$
$109$	−2.83446e12			−1.69010			−0.845048	+	0.534690i	$0.820428\pi$
$110$		−	2.63885e12i		−	1.48956i
$111$			2.46062e12i			1.31555i
$112$	4.60042e11	+	1.78494e11i	0.233071	+	0.0904307i
$113$	−2.60388e10			−0.0125069			−0.00625347	−	0.999980i	$-0.501991\pi$
$113$	−2.60388e10			−0.0125069			−0.00625347	+	0.999980i	$0.501991\pi$
$114$	2.96143e12			1.34919
$115$			3.41014e12i			1.47430i
$116$	1.38296e12			0.567626
$117$		−	4.49853e12i		−	1.75370i
$118$			3.73810e11i			0.138471i
$119$	−8.72669e10	+	2.24917e11i	−0.0307304	+	0.0792028i
$120$	−2.72016e12			−0.910977
$121$	3.18512e12			1.01488
$122$		−	1.67218e12i		−	0.507137i
$123$	6.32631e12			1.82692
$124$			4.81398e11i			0.132426i
$125$		−	1.14588e12i		−	0.300385i
$126$	5.31389e12	+	2.06176e12i	1.32797	+	0.515247i
$127$	−7.39213e12			−1.76176			−0.880882	−	0.473337i	$-0.843049\pi$
$127$	−7.39213e12			−1.76176			−0.880882	+	0.473337i	$0.843049\pi$
$128$	−3.88736e11			−0.0883883
$129$		−	6.99199e12i		−	1.51727i
$130$	4.40955e12			0.913555
$131$			7.68637e12i			1.52087i	0.649412	+	0.760437i	$0.275015\pi$
$131$			7.68637e12i			1.52087i	−0.649412	+	0.760437i	$0.724985\pi$
$132$		−	6.51841e12i		−	1.23225i
$133$	2.20024e12	−	5.67079e12i	0.397521	−	1.02455i
$134$	−3.28993e10			−0.00568274
$135$	−1.58228e13			−2.61385
$136$		−	1.90055e11i		−	0.0300363i
$137$	1.68160e12			0.254331			0.127165	−	0.991882i	$-0.459412\pi$
$137$	1.68160e12			0.254331			0.127165	+	0.991882i	$0.459412\pi$
$138$			8.42363e12i			1.21962i
$139$			4.09346e12i			0.567547i	0.958891	+	0.283774i	$0.0915865\pi$
$139$			4.09346e12i			0.567547i	−0.958891	+	0.283774i	$0.908414\pi$
$140$	−2.02098e12	+	5.20878e12i	−0.268408	+	0.691780i
$141$	−6.10975e12			−0.777515
$142$	−5.33117e12			−0.650268
$143$			1.05667e13i			1.23573i
$144$	−4.49024e12			−0.503611
$145$			1.56585e13i			1.68477i
$146$		−	2.05065e12i		−	0.211726i
$147$	1.18158e13	−	1.29345e13i	1.17100	−	1.28187i
$148$	−3.98147e12			−0.378856
$149$	6.73518e12			0.615505			0.307753	−	0.951466i	$-0.400423\pi$
$149$	6.73518e12			0.615505			0.307753	+	0.951466i	$0.400423\pi$
$150$		−	1.68147e13i		−	1.47618i
$151$	−4.58454e12			−0.386753			−0.193377	−	0.981125i	$-0.561944\pi$
$151$	−4.58454e12			−0.386753			−0.193377	+	0.981125i	$0.561944\pi$
$152$			4.79183e12i			0.388543i
$153$		−	2.19531e12i		−	0.171138i
$154$	−1.24820e13	−	4.84294e12i	−0.935747	−	0.363066i
$155$	−5.45059e12			−0.393055
$156$	1.08924e13			0.755743
$157$			6.34897e12i			0.423941i	0.977276	+	0.211970i	$0.0679881\pi$
$157$			6.34897e12i			0.423941i	−0.977276	+	0.211970i	$0.932012\pi$
$158$	6.42645e12			0.413075
$159$		−	3.25111e13i		−	2.01210i
$160$		−	4.40143e12i		−	0.262346i
$161$	1.61302e13	+	6.25845e12i	0.926158	+	0.359345i
$162$	−1.33378e13			−0.737893
$163$	−1.81117e13			−0.965678			−0.482839	−	0.875709i	$-0.660394\pi$
$163$	−1.81117e13			−0.965678			−0.482839	+	0.875709i	$0.660394\pi$
$164$			1.02364e13i			0.526121i
$165$	7.38041e13			3.65744
$166$			2.47897e13i			1.18474i
$167$		−	3.67149e13i		−	1.69256i	−0.532738	−	0.846280i	$-0.678837\pi$
$167$		−	3.67149e13i		−	1.69256i	0.532738	−	0.846280i	$-0.321163\pi$
$168$	−4.99218e12	+	1.28666e13i	−0.222042	+	0.572279i
$169$	5.64091e12			0.242119
$170$	2.15189e12			0.0891509
$171$			5.53498e13i			2.21381i
$172$	1.13136e13			0.436947
$173$		−	3.01346e13i		−	1.12406i	−0.827117	−	0.562030i	$-0.810021\pi$
$173$		−	3.01346e13i		−	1.12406i	0.827117	−	0.562030i	$-0.189979\pi$
$174$			3.86791e13i			1.39374i
$175$	−3.21980e13	−	1.24927e13i	−1.12099	−	0.434939i
$176$	1.05473e13			0.354866
$177$	−1.04548e13			−0.339999
$178$		−	2.87114e13i		−	0.902682i
$179$	−4.33930e13			−1.31917			−0.659586	−	0.751630i	$-0.729268\pi$
$179$	−4.33930e13			−1.31917			−0.659586	+	0.751630i	$0.729268\pi$
$180$		−	5.08404e13i		−	1.49477i
$181$			2.71254e13i			0.771443i	0.922615	+	0.385722i	$0.126048\pi$
$181$			2.71254e13i			0.771443i	−0.922615	+	0.385722i	$0.873952\pi$
$182$	8.09263e12	−	2.08575e13i	0.222670	−	0.573898i
$183$	4.67681e13			1.24521
$184$	−1.36301e13			−0.351229
$185$		−	4.50799e13i		−	1.12448i
$186$	−1.34639e13			−0.325157
$187$			5.15663e12i			0.120591i
$188$		−	9.88604e12i		−	0.223911i
$189$	−2.90388e13	+	7.48430e13i	−0.637099	+	1.64203i
$190$	−5.42550e13			−1.15324
$191$	5.66925e12			0.116768			0.0583842	−	0.998294i	$-0.481405\pi$
$191$	5.66925e12			0.116768			0.0583842	+	0.998294i	$0.481405\pi$
$192$		−	1.08723e13i		−	0.217027i
$193$	−7.45868e13			−1.44317			−0.721586	−	0.692325i	$-0.756586\pi$
$193$	−7.45868e13			−1.44317			−0.721586	+	0.692325i	$0.756586\pi$
$194$		−	7.44928e12i		−	0.139735i
$195$			1.23328e14i			2.24312i
$196$	2.09289e13	+	1.91188e13i	0.369157	+	0.337229i
$197$	1.78184e13			0.304840			0.152420	−	0.988316i	$-0.451293\pi$
$197$	1.78184e13			0.304840			0.152420	+	0.988316i	$0.451293\pi$
$198$	1.21830e14			2.02192
$199$		−	8.73527e13i		−	1.40656i	−0.710913	−	0.703280i	$-0.751718\pi$
$199$		−	8.73527e13i		−	1.40656i	0.710913	−	0.703280i	$-0.248282\pi$
$200$	2.72074e13			0.425116
$201$		−	9.20137e11i		−	0.0139533i
$202$			3.34172e13i			0.491883i
$203$	7.40658e13	+	2.87372e13i	1.05838	+	0.410647i
$204$	5.31553e12			0.0737505
$205$	−1.15901e14			−1.56158
$206$			7.16735e13i			0.937897i
$207$	−1.57439e14			−2.00120
$208$			1.76247e13i			0.217641i
$209$		−	1.30013e14i		−	1.55994i
$210$	−1.45681e14	−	5.65235e13i	−1.69858	−	0.659042i
$211$	8.44210e13			0.956656			0.478328	−	0.878181i	$-0.341243\pi$
$211$	8.44210e13			0.956656			0.478328	+	0.878181i	$0.341243\pi$
$212$	5.26054e13			0.579449
$213$		−	1.49104e14i		−	1.59665i
$214$	2.35850e13			0.245558
$215$			1.28097e14i			1.29690i
$216$		−	6.32425e13i		−	0.622711i
$217$	−1.00032e13	+	2.57817e13i	−0.0958032	+	0.246918i
$218$	1.28273e14			1.19508
$219$	5.73533e13			0.519869
$220$			1.19421e14i			1.05328i
$221$	−8.61680e12			−0.0739592
$222$		−	1.11355e14i		−	0.930234i
$223$		−	1.22959e14i		−	0.999844i	−0.866071	−	0.499922i	$-0.833362\pi$
$223$		−	1.22959e14i		−	0.999844i	0.866071	−	0.499922i	$-0.166638\pi$
$224$	−2.08191e13	−	8.07772e12i	−0.164806	−	0.0639442i
$225$	3.14270e14			2.42218
$226$	1.17838e12			0.00884374
$227$			2.60509e14i			1.90400i	0.306096	+	0.952001i	$0.400977\pi$
$227$			2.60509e14i			1.90400i	−0.306096	+	0.952001i	$0.599023\pi$
$228$	−1.34019e14			−0.954021
$229$			1.82809e14i			1.26761i	0.773494	+	0.633803i	$0.218507\pi$
$229$			1.82809e14i			1.26761i	−0.773494	+	0.633803i	$0.781493\pi$
$230$		−	1.54325e14i		−	1.04249i
$231$	1.35449e14	−	3.49099e14i	0.891464	−	2.29761i
$232$	−6.25857e13			−0.401372
$233$	2.37534e12			0.0148454			0.00742269	−	0.999972i	$-0.497637\pi$
$233$	2.37534e12			0.0148454			0.00742269	+	0.999972i	$0.497637\pi$
$234$			2.03580e14i			1.24005i
$235$	1.11934e14			0.664591
$236$		−	1.69167e13i		−	0.0979138i
$237$			1.79737e14i			1.01426i
$238$	3.94925e12	−	1.01786e13i	0.0217296	−	0.0560049i
$239$	−8.33178e13			−0.447044			−0.223522	−	0.974699i	$-0.571755\pi$
$239$	−8.33178e13			−0.447044			−0.223522	+	0.974699i	$0.571755\pi$
$240$	1.23101e14			0.644158
$241$		−	2.21182e14i		−	1.12888i	−0.825473	−	0.564441i	$-0.809092\pi$
$241$		−	2.21182e14i		−	1.12888i	0.825473	−	0.564441i	$-0.190908\pi$
$242$	−1.44142e14			−0.717626
$243$		−	1.04005e13i		−	0.0505147i
$244$			7.56744e13i			0.358600i
$245$	−2.16471e14	+	2.36966e14i	−1.00093	+	1.09569i
$246$	−2.86296e14			−1.29183
$247$	2.17254e14			0.956720
$248$		−	2.17856e13i		−	0.0936395i
$249$	−6.93325e14			−2.90898
$250$			5.18566e13i			0.212405i
$251$		−	3.70158e14i		−	1.48028i	−0.672452	−	0.740141i	$-0.734759\pi$
$251$		−	3.70158e14i		−	1.48028i	0.672452	−	0.740141i	$-0.265241\pi$
$252$	−2.40479e14	−	9.33048e13i	−0.939018	−	0.364335i
$253$	3.69814e14			1.41013
$254$	3.34530e14			1.24575
$255$			6.01846e13i			0.218899i
$256$	1.75922e13			0.0625000
$257$		−	1.67460e13i		−	0.0581181i	−0.999578	−	0.0290590i	$-0.990749\pi$
$257$		−	1.67460e13i		−	0.0581181i	0.999578	−	0.0290590i	$-0.00925108\pi$
$258$			3.16421e14i			1.07287i
$259$	−2.13231e14	−	8.27329e13i	−0.706403	−	0.274081i
$260$	−1.99554e14			−0.645981
$261$	−7.22921e14			−2.28690
$262$		−	3.47845e14i		−	1.07542i
$263$	2.62812e14			0.794166			0.397083	−	0.917783i	$-0.370023\pi$
$263$	2.62812e14			0.794166			0.397083	+	0.917783i	$0.370023\pi$
$264$			2.94989e14i			0.871330i
$265$			5.95620e14i			1.71986i
$266$	−9.95715e13	+	2.56631e14i	−0.281090	+	0.724467i
$267$	8.03010e14			2.21643
$268$	1.48885e12			0.00401830
$269$		−	7.43175e13i		−	0.196145i	−0.995179	−	0.0980725i	$-0.968732\pi$
$269$		−	7.43175e13i		−	0.196145i	0.995179	−	0.0980725i	$-0.0312677\pi$
$270$	7.16057e14			1.84827
$271$		−	1.39097e14i		−	0.351157i	−0.984465	−	0.175579i	$-0.943820\pi$
$271$		−	1.39097e14i		−	0.351157i	0.984465	−	0.175579i	$-0.0561796\pi$
$272$			8.60092e12i			0.0212389i
$273$	5.83350e14	+	2.26337e14i	1.40914	+	0.546739i
$274$	−7.61005e13			−0.179839
$275$	−7.38198e14			−1.70678
$276$		−	3.81210e14i		−	0.862402i
$277$	5.61259e14			1.24247			0.621233	−	0.783626i	$-0.286632\pi$
$277$	5.61259e14			1.24247			0.621233	+	0.783626i	$0.286632\pi$
$278$		−	1.85249e14i		−	0.401317i
$279$		−	2.51643e14i		−	0.533530i
$280$	9.14593e13	−	2.35723e14i	0.189793	−	0.489162i
$281$	−7.54933e14			−1.53345			−0.766727	−	0.641973i	$-0.778116\pi$
$281$	−7.54933e14			−1.53345			−0.766727	+	0.641973i	$0.778116\pi$
$282$	2.76496e14			0.549786
$283$		−	8.87646e12i		−	0.0172791i	−0.999963	−	0.00863955i	$-0.997250\pi$
$283$		−	8.87646e12i		−	0.0172791i	0.999963	−	0.00863955i	$-0.00275009\pi$
$284$	2.41261e14			0.459809
$285$		−	1.51742e15i		−	2.83163i
$286$		−	4.78196e14i		−	0.873795i
$287$	−2.12708e14	+	5.48222e14i	−0.380620	+	0.980991i
$288$	2.03205e14			0.356107
$289$	5.78417e14			0.992783
$290$		−	7.08622e14i		−	1.19131i
$291$	2.08344e14			0.343101
$292$			9.28020e13i			0.149713i
$293$			3.25301e14i			0.514138i	0.966393	+	0.257069i	$0.0827567\pi$
$293$			3.25301e14i			0.514138i	−0.966393	+	0.257069i	$0.917243\pi$
$294$	−5.34721e14	+	5.85347e14i	−0.828025	+	0.906419i
$295$	1.91538e14			0.290618
$296$	1.80181e14			0.267891
$297$			1.71591e15i			2.50009i
$298$	−3.04800e14			−0.435228
$299$			6.17965e14i			0.864841i
$300$			7.60945e14i			1.04382i
$301$	6.05909e14	+	2.35090e14i	0.814720	+	0.316108i
$302$	2.07473e14			0.273476
$303$	−9.34621e14			−1.20776
$304$		−	2.16853e14i		−	0.274742i
$305$	−8.56817e14			−1.06436
$306$			9.93483e13i			0.121013i
$307$		−	5.19001e14i		−	0.619923i	−0.950749	−	0.309962i	$-0.899684\pi$
$307$		−	5.19001e14i		−	0.619923i	0.950749	−	0.309962i	$-0.100316\pi$
$308$	5.64869e14	+	2.19167e14i	0.661673	+	0.256726i
$309$	−2.00458e15			−2.30289
$310$	2.46665e14			0.277932
$311$			4.87134e14i			0.538377i	0.963088	+	0.269188i	$0.0867554\pi$
$311$			4.87134e14i			0.538377i	−0.963088	+	0.269188i	$0.913245\pi$
$312$	−4.92932e14			−0.534391
$313$		−	1.57844e15i		−	1.67865i	−0.543628	−	0.839326i	$-0.682950\pi$
$313$		−	1.57844e15i		−	1.67865i	0.543628	−	0.839326i	$-0.317050\pi$
$314$		−	2.87322e14i		−	0.299771i
$315$	1.05644e15	−	2.72280e15i	1.08138	−	2.78710i
$316$	−2.90828e14			−0.292088
$317$	−1.26151e15			−1.24319			−0.621593	−	0.783341i	$-0.713514\pi$
$317$	−1.26151e15			−1.24319			−0.621593	+	0.783341i	$0.713514\pi$
$318$			1.47128e15i			1.42277i
$319$	1.69809e15			1.61145
$320$			1.99186e14i			0.185506i
$321$			6.59633e14i			0.602937i
$322$	−7.29970e14	−	2.83225e14i	−0.654892	−	0.254095i
$323$	1.06021e14			0.0933633
$324$	6.03599e14			0.521769
$325$		−	1.23354e15i		−	1.04677i
$326$	8.19640e14			0.682838
$327$			3.58758e15i			2.93437i
$328$		−	4.63249e14i		−	0.372024i
$329$	2.05427e14	−	5.29456e14i	0.161987	−	0.417498i
$330$	−3.33999e15			−2.58620
$331$	−1.33315e15			−1.01370			−0.506850	−	0.862034i	$-0.669190\pi$
$331$	−1.33315e15			−1.01370			−0.506850	+	0.862034i	$0.669190\pi$
$332$		−	1.12185e15i		−	0.837736i
$333$	2.08125e15			1.52637
$334$			1.66153e15i			1.19682i
$335$			1.68574e13i			0.0119267i
$336$	2.25920e14	−	5.82275e14i	0.157007	−	0.404662i
$337$	1.79086e15			1.22260			0.611299	−	0.791400i	$-0.290647\pi$
$337$	1.79086e15			1.22260			0.611299	+	0.791400i	$0.290647\pi$
$338$	−2.55278e14			−0.171204
$339$			3.29574e13i			0.0217147i
$340$	−9.73832e13			−0.0630392
$341$			5.91091e14i			0.375948i
$342$		−	2.50485e15i		−	1.56540i
$343$	7.23589e14	+	1.45882e15i	0.444352	+	0.895852i
$344$	−5.11994e14			−0.308968
$345$	4.31621e15			2.55970
$346$			1.36374e15i			0.794830i
$347$	−2.78892e15			−1.59757			−0.798785	−	0.601617i	$-0.794523\pi$
$347$	−2.78892e15			−1.59757			−0.798785	+	0.601617i	$0.794523\pi$
$348$		−	1.75042e15i		−	0.985521i
$349$			5.41692e13i			0.0299778i	0.999888	+	0.0149889i	$0.00477129\pi$
$349$			5.41692e13i			0.0299778i	−0.999888	+	0.0149889i	$0.995229\pi$
$350$	1.45712e15	+	5.65355e14i	0.792659	+	0.307548i
$351$	−2.86731e15			−1.53332
$352$	−4.77315e14			−0.250928
$353$		−	3.73671e15i		−	1.93126i	−0.259916	−	0.965631i	$-0.583695\pi$
$353$		−	3.73671e15i		−	1.93126i	0.259916	−	0.965631i	$-0.416305\pi$
$354$	4.73132e14			0.240416
$355$			2.73166e15i			1.36476i
$356$			1.29933e15i			0.638293i
$357$	2.84678e14	+	1.10454e14i	0.137513	+	0.0533545i
$358$	1.96374e15			0.932795
$359$	3.86240e15			1.80422			0.902111	−	0.431504i	$-0.142017\pi$
$359$	3.86240e15			1.80422			0.902111	+	0.431504i	$0.142017\pi$
$360$			2.30077e15i			1.05696i
$361$	−4.59767e14			−0.207728
$362$		−	1.22755e15i		−	0.545493i
$363$		−	4.03141e15i		−	1.76204i
$364$	−3.66231e14	+	9.43904e14i	−0.157451	+	0.405807i
$365$	−1.05074e15			−0.444364
$366$	−2.11648e15			−0.880498
$367$		−	3.76724e15i		−	1.54180i	−0.636958	−	0.770899i	$-0.719807\pi$
$367$		−	3.76724e15i		−	1.54180i	0.636958	−	0.770899i	$-0.280193\pi$
$368$	6.16826e14			0.248357
$369$		−	5.35093e15i		−	2.11968i
$370$			2.04008e15i			0.795129i
$371$	2.81733e15	+	1.09311e15i	1.08042	+	0.419200i
$372$	6.09306e14			0.229920
$373$	−3.19475e15			−1.18627			−0.593135	−	0.805103i	$-0.702110\pi$
$373$	−3.19475e15			−1.18627			−0.593135	+	0.805103i	$0.702110\pi$
$374$		−	2.33362e14i		−	0.0852709i
$375$	−1.45034e15			−0.521534
$376$			4.47391e14i			0.158329i
$377$			2.83753e15i			0.988310i
$378$	1.31414e15	−	3.38701e15i	0.450497	−	1.16109i
$379$	−5.20525e15			−1.75633			−0.878165	−	0.478358i	$-0.841232\pi$
$379$	−5.20525e15			−1.75633			−0.878165	+	0.478358i	$0.841232\pi$
$380$	2.45530e15			0.815462
$381$			9.35623e15i			3.05880i
$382$	−2.56561e14			−0.0825677
$383$			4.01746e15i			1.27279i	0.771361	+	0.636397i	$0.219576\pi$
$383$			4.01746e15i			1.27279i	−0.771361	+	0.636397i	$0.780424\pi$
$384$			4.92024e14i			0.153461i
$385$	−2.48150e15	+	6.39568e15i	−0.761990	+	1.96391i
$386$	3.37541e15			1.02048
$387$	−5.91398e15			−1.76041
$388$			3.37116e14i			0.0988072i
$389$	2.85911e15			0.825150			0.412575	−	0.910924i	$-0.364630\pi$
$389$	2.85911e15			0.825150			0.412575	+	0.910924i	$0.364630\pi$
$390$		−	5.58118e15i		−	1.58613i
$391$			3.01570e14i			0.0843971i
$392$	−9.47135e14	−	8.65220e14i	−0.261033	−	0.238457i
$393$	9.72864e15			2.64056
$394$	−8.06370e14			−0.215554
$395$		−	3.29287e15i		−	0.866947i
$396$	−5.51341e15			−1.42971
$397$		−	6.17908e15i		−	1.57827i	−0.614221	−	0.789134i	$-0.710530\pi$
$397$		−	6.17908e15i		−	1.57827i	0.614221	−	0.789134i	$-0.289470\pi$
$398$			3.95313e15i			0.994588i
$399$	−7.17752e15	−	2.78485e15i	−1.77884	−	0.690183i
$400$	−1.23127e15			−0.300602
$401$	−4.77895e15			−1.14939			−0.574694	−	0.818368i	$-0.694879\pi$
$401$	−4.77895e15			−1.14939			−0.574694	+	0.818368i	$0.694879\pi$
$402$			4.16406e13i			0.00986645i
$403$	−9.87722e14			−0.230571
$404$		−	1.51229e15i		−	0.347813i
$405$			6.83419e15i			1.54866i
$406$	−3.35184e15	−	1.30050e15i	−0.748388	−	0.290371i
$407$	−4.88871e15			−1.07554
$408$	−2.40553e14			−0.0521495
$409$		−	4.49714e15i		−	0.960719i	−0.877072	−	0.480360i	$-0.840506\pi$
$409$		−	4.49714e15i		−	0.960719i	0.877072	−	0.480360i	$-0.159494\pi$
$410$	5.24509e15			1.10421
$411$		−	2.12840e15i		−	0.441573i
$412$		−	3.24357e15i		−	0.663193i
$413$	3.51520e14	−	9.05990e14i	0.0708353	−	0.182567i
$414$	7.12489e15			1.41506
$415$	1.27021e16			2.48649
$416$		−	7.97601e14i		−	0.153895i
$417$	5.18110e15			0.985385
$418$			5.88371e15i			1.10305i
$419$		−	2.76956e15i		−	0.511831i	−0.966699	−	0.255916i	$-0.917623\pi$
$419$		−	2.76956e15i		−	0.511831i	0.966699	−	0.255916i	$-0.0823769\pi$
$420$	6.59276e15	+	2.55796e15i	1.20108	+	0.466013i
$421$	−2.03251e15			−0.365039			−0.182519	−	0.983202i	$-0.558425\pi$
$421$	−2.03251e15			−0.365039			−0.182519	+	0.983202i	$0.558425\pi$
$422$	−3.82046e15			−0.676458
$423$			5.16776e15i			0.902112i
$424$	−2.38065e15			−0.409732
$425$		−	6.01974e14i		−	0.102151i
$426$			6.74767e15i			1.12901i
$427$	−1.57247e15	+	4.05281e15i	−0.259427	+	0.668635i
$428$	−1.06734e15			−0.173636
$429$	1.33743e16			2.14550
$430$		−	5.79701e15i		−	0.917050i
$431$	−8.25480e14			−0.128778			−0.0643892	−	0.997925i	$-0.520510\pi$
$431$	−8.25480e14			−0.128778			−0.0643892	+	0.997925i	$0.520510\pi$
$432$			2.86203e15i			0.440323i
$433$		−	8.15758e15i		−	1.23775i	−0.785489	−	0.618876i	$-0.787588\pi$
$433$		−	8.15758e15i		−	1.23775i	0.785489	−	0.618876i	$-0.212412\pi$
$434$	4.52693e14	−	1.16675e15i	0.0677431	−	0.174598i
$435$	1.98189e16			2.92513
$436$	−5.80498e15			−0.845048
$437$		−	7.60342e15i		−	1.09174i
$438$	−2.59551e15			−0.367603
$439$			7.94126e15i			1.10944i	0.832038	+	0.554718i	$0.187174\pi$
$439$			7.94126e15i			1.10944i	−0.832038	+	0.554718i	$0.812826\pi$
$440$		−	5.40436e15i		−	0.744780i
$441$	−1.09402e16	−	9.99405e15i	−1.48729	−	1.35866i
$442$	3.89952e14			0.0522971
$443$	1.81587e15			0.240249			0.120124	−	0.992759i	$-0.461671\pi$
$443$	1.81587e15			0.240249			0.120124	+	0.992759i	$0.461671\pi$
$444$			5.03936e15i			0.657775i
$445$	−1.47116e16			−1.89452
$446$			5.56450e15i			0.706996i
$447$		−	8.52472e15i		−	1.06865i
$448$	9.42165e14	+	3.65556e14i	0.116536	+	0.0452153i
$449$	1.20368e15			0.146904			0.0734518	−	0.997299i	$-0.476598\pi$
$449$	1.20368e15			0.146904			0.0734518	+	0.997299i	$0.476598\pi$
$450$	−1.42222e16			−1.71274
$451$			1.25690e16i			1.49362i
$452$	−5.33275e13			−0.00625347
$453$			5.80266e15i			0.671487i
$454$		−	1.17893e16i		−	1.34633i
$455$	−1.06873e16	−	4.14662e15i	−1.20448	−	0.467332i
$456$	6.06502e15			0.674595
$457$	−1.83352e15			−0.201274			−0.100637	−	0.994923i	$-0.532088\pi$
$457$	−1.83352e15			−0.201274			−0.100637	+	0.994923i	$0.532088\pi$
$458$		−	8.27299e15i		−	0.896333i
$459$	−1.39926e15			−0.149631
$460$			6.98396e15i			0.737148i
$461$		−	1.88290e15i		−	0.196165i	−0.995178	−	0.0980823i	$-0.968729\pi$
$461$		−	1.88290e15i		−	0.196165i	0.995178	−	0.0980823i	$-0.0312708\pi$
$462$	−6.12972e15	+	1.57984e16i	−0.630360	+	1.62466i
$463$	4.08763e15			0.414940			0.207470	−	0.978241i	$-0.433477\pi$
$463$	4.08763e15			0.414940			0.207470	+	0.978241i	$0.433477\pi$
$464$	2.83231e15			0.283813
$465$			6.89881e15i			0.682428i
$466$	−1.07496e14			−0.0104973
$467$			1.49916e16i			1.44526i	0.691236	+	0.722629i	$0.257067\pi$
$467$			1.49916e16i			1.44526i	−0.691236	+	0.722629i	$0.742933\pi$
$468$		−	9.21299e15i		−	0.876850i
$469$	7.97368e13	+	3.09375e13i	0.00749241	+	0.00290702i
$470$	−5.06555e15			−0.469937
$471$	8.03590e15			0.736053
$472$			7.65563e14i			0.0692355i
$473$	1.38915e16			1.24046
$474$		−	8.13396e15i		−	0.717187i
$475$			1.51774e16i			1.32141i
$476$	−1.78723e14	+	4.60630e14i	−0.0153652	+	0.0396014i
$477$	−2.74986e16			−2.33453
$478$	3.77053e15			0.316108
$479$			2.44254e15i			0.202222i	0.994875	+	0.101111i	$0.0322398\pi$
$479$			2.44254e15i			0.202222i	−0.994875	+	0.101111i	$0.967760\pi$
$480$	−5.57089e15			−0.455489
$481$		−	8.16911e15i		−	0.659636i
$482$			1.00096e16i			0.798240i
$483$	7.92133e15	−	2.04160e16i	0.623901	−	1.60801i
$484$	6.52312e15			0.507438
$485$	−3.81696e15			−0.293270
$486$			4.70674e14i			0.0357193i
$487$	1.20432e15			0.0902752			0.0451376	−	0.998981i	$-0.485627\pi$
$487$	1.20432e15			0.0902752			0.0451376	+	0.998981i	$0.485627\pi$
$488$		−	3.42463e15i		−	0.253568i
$489$			2.29239e16i			1.67663i
$490$	9.79637e15	−	1.07239e16i	0.707765	−	0.774773i
$491$	1.11932e14			0.00798852			0.00399426	−	0.999992i	$-0.498729\pi$
$491$	1.11932e14			0.00798852			0.00399426	+	0.999992i	$0.498729\pi$
$492$	1.29563e16			0.913460
$493$			1.38473e15i			0.0964460i
$494$	−9.83177e15			−0.676504
$495$		−	6.24251e16i		−	4.24354i
$496$			9.85903e14i			0.0662131i
$497$	1.29210e16	+	5.01328e15i	0.857347	+	0.332647i
$498$	3.13763e16			2.05696
$499$	−8.33426e15			−0.539839			−0.269919	−	0.962883i	$-0.586997\pi$
$499$	−8.33426e15			−0.539839			−0.269919	+	0.962883i	$0.586997\pi$
$500$		−	2.34676e15i		−	0.150193i
$501$	−4.64701e16			−2.93865
$502$			1.67514e16i			1.04672i
$503$			6.23381e15i			0.384898i	0.981307	+	0.192449i	$0.0616430\pi$
$503$			6.23381e15i			0.384898i	−0.981307	+	0.192449i	$0.938357\pi$
$504$	1.08828e16	+	4.22249e15i	0.663986	+	0.257624i
$505$	1.71228e16			1.03235
$506$	−1.67359e16			−0.997115
$507$		−	7.13970e15i		−	0.420370i
$508$	−1.51391e16			−0.880882
$509$			2.30193e16i			1.32369i	0.749642	+	0.661844i	$0.230226\pi$
$509$			2.30193e16i			1.32369i	−0.749642	+	0.661844i	$0.769774\pi$
$510$		−	2.72364e15i		−	0.154785i
$511$	−1.92837e15	+	4.97009e15i	−0.108309	+	0.279151i
$512$	−7.96131e14			−0.0441942
$513$	3.52793e16			1.93560
$514$			7.57835e14i			0.0410957i
$515$	3.67250e16			1.96843
$516$		−	1.43196e16i		−	0.758635i
$517$		−	1.21387e16i		−	0.635667i
$518$	9.64975e15	+	3.74406e15i	0.499503	+	0.193805i
$519$	−3.81414e16			−1.95161
$520$	9.03077e15			0.456777
$521$			3.57803e15i			0.178903i	0.995991	+	0.0894515i	$0.0285114\pi$
$521$			3.57803e15i			0.178903i	−0.995991	+	0.0894515i	$0.971489\pi$
$522$	3.27156e16			1.61708
$523$		−	1.20775e16i		−	0.590157i	−0.955473	−	0.295078i	$-0.904654\pi$
$523$		−	1.20775e16i		−	0.590157i	0.955473	−	0.295078i	$-0.0953458\pi$
$524$			1.57417e16i			0.760437i
$525$	−1.58120e16	+	4.07531e16i	−0.755147	+	1.94628i
$526$	−1.18935e16			−0.561560
$527$	−4.82014e14			−0.0225007
$528$		−	1.33497e16i		−	0.616124i
$529$	−2.87143e14			−0.0131028
$530$		−	2.69547e16i		−	1.21613i
$531$			8.84293e15i			0.394484i
$532$	4.50609e15	−	1.16138e16i	0.198761	−	0.512275i
$533$	−2.10029e16			−0.916045
$534$	−3.63401e16			−1.56725
$535$		−	1.20848e16i		−	0.515368i
$536$	−6.73777e13			−0.00284137
$537$			5.49225e16i			2.29036i
$538$			3.36322e15i			0.138695i
$539$	2.56979e16	+	2.34753e16i	1.04801	+	0.957368i
$540$	−3.24051e16			−1.30692
$541$	7.58133e15			0.302386			0.151193	−	0.988504i	$-0.451688\pi$
$541$	7.58133e15			0.302386			0.151193	+	0.988504i	$0.451688\pi$
$542$			6.29481e15i			0.248306i
$543$	3.43326e16			1.33939
$544$		−	3.89233e14i		−	0.0150182i
$545$		−	6.57263e16i		−	2.50819i
$546$	−2.63994e16	−	1.02429e16i	−0.996410	−	0.386603i
$547$	7.62005e15			0.284468			0.142234	−	0.989833i	$-0.454571\pi$
$547$	7.62005e15			0.284468			0.142234	+	0.989833i	$0.454571\pi$
$548$	3.44392e15			0.127165
$549$		−	3.95575e16i		−	1.44476i
$550$	3.34070e16			1.20687
$551$		−	3.49130e16i		−	1.24760i
$552$			1.72516e16i			0.609810i
$553$	−1.55756e16	−	6.04325e15i	−0.544619	−	0.211310i
$554$	−2.53997e16			−0.878556
$555$	−5.70577e16			−1.95234
$556$			8.38341e15i			0.283774i
$557$	−1.88829e16			−0.632322			−0.316161	−	0.948706i	$-0.602394\pi$
$557$	−1.88829e16			−0.632322			−0.316161	+	0.948706i	$0.602394\pi$
$558$			1.13880e16i			0.377263i
$559$			2.32130e16i			0.760781i
$560$	−4.13898e15	+	1.06676e16i	−0.134204	+	0.345890i
$561$	6.52674e15			0.209372
$562$	3.41644e16			1.08432
$563$			2.62360e16i			0.823848i	0.911218	+	0.411924i	$0.135143\pi$
$563$			2.62360e16i			0.823848i	−0.911218	+	0.411924i	$0.864857\pi$
$564$	−1.25128e16			−0.388758
$565$		−	6.03797e14i		−	0.0185609i
$566$			4.01703e14i			0.0122182i
$567$	3.23263e16	+	1.25425e16i	0.972875	+	0.377471i
$568$	−1.09182e16			−0.325134
$569$	−1.64822e16			−0.485670			−0.242835	−	0.970068i	$-0.578077\pi$
$569$	−1.64822e16			−0.485670			−0.242835	+	0.970068i	$0.578077\pi$
$570$			6.86707e16i			2.00227i
$571$	−1.15534e16			−0.333344			−0.166672	−	0.986012i	$-0.553302\pi$
$571$	−1.15534e16			−0.333344			−0.166672	+	0.986012i	$0.553302\pi$
$572$			2.16407e16i			0.617867i
$573$		−	7.17557e15i		−	0.202735i
$574$	9.62605e15	−	2.48097e16i	0.269139	−	0.693665i
$575$	−4.31713e16			−1.19451
$576$	−9.19602e15			−0.251805
$577$		−	2.02709e16i		−	0.549312i	−0.961543	−	0.274656i	$-0.911436\pi$
$577$		−	2.02709e16i		−	0.549312i	0.961543	−	0.274656i	$-0.0885640\pi$
$578$	−2.61762e16			−0.702003
$579$			9.44045e16i			2.50566i
$580$			3.20686e16i			0.842387i
$581$	2.33115e16	−	6.00818e16i	0.606056	−	1.56202i
$582$	−9.42856e15			−0.242609
$583$	6.45923e16			1.64501
$584$		−	4.19974e15i		−	0.105863i
$585$	1.04313e17			2.60258
$586$		−	1.47214e16i		−	0.363550i
$587$		−	6.03675e16i		−	1.47562i	−0.675008	−	0.737810i	$-0.735860\pi$
$587$		−	6.03675e16i		−	1.47562i	0.675008	−	0.737810i	$-0.264140\pi$
$588$	2.41987e16	−	2.64898e16i	0.585502	−	0.640935i
$589$	1.21529e16			0.291064
$590$	−8.66802e15			−0.205498
$591$		−	2.25528e16i		−	0.529268i
$592$	−8.15406e15			−0.189428
$593$			2.03032e16i			0.466913i	0.972367	+	0.233456i	$0.0750036\pi$
$593$			2.03032e16i			0.466913i	−0.972367	+	0.233456i	$0.924996\pi$
$594$		−	7.76532e16i		−	1.76783i
$595$	−5.21545e15	−	2.02357e15i	−0.117541	−	0.0456054i
$596$	1.37937e16			0.307753
$597$	−1.10562e17			−2.44209
$598$		−	2.79659e16i		−	0.611535i
$599$	4.96916e16			1.07578			0.537888	−	0.843016i	$-0.319222\pi$
$599$	4.96916e16			1.07578			0.537888	+	0.843016i	$0.319222\pi$
$600$		−	3.44364e16i		−	0.738092i
$601$			7.10138e14i			0.0150694i	0.999972	+	0.00753470i	$0.00239839\pi$
$601$			7.10138e14i			0.0150694i	−0.999972	+	0.00753470i	$0.997602\pi$
$602$	−2.74203e16	−	1.06390e16i	−0.576094	−	0.223522i
$603$	−7.78272e14			−0.0161893
$604$	−9.38914e15			−0.193377
$605$			7.38575e16i			1.50613i
$606$	4.22961e16			0.854014
$607$		−	5.96824e16i		−	1.19320i	−0.802538	−	0.596601i	$-0.796517\pi$
$607$		−	5.96824e16i		−	1.19320i	0.802538	−	0.596601i	$-0.203483\pi$
$608$			9.81366e15i			0.194272i
$609$	3.63727e16	−	9.37452e16i	0.712971	−	1.83758i
$610$	3.87751e16			0.752617
$611$	2.02840e16			0.389858
$612$		−	4.49599e15i		−	0.0855690i
$613$	7.09993e16			1.33811			0.669054	−	0.743214i	$-0.266700\pi$
$613$	7.09993e16			1.33811			0.669054	+	0.743214i	$0.266700\pi$
$614$			2.34873e16i			0.438352i
$615$			1.46696e17i			2.71124i
$616$	−2.55630e16	−	9.91835e15i	−0.467873	−	0.181533i
$617$	3.75441e15			0.0680505			0.0340252	−	0.999421i	$-0.489167\pi$
$617$	3.75441e15			0.0680505			0.0340252	+	0.999421i	$0.489167\pi$
$618$	9.07172e16			1.62839
$619$		−	9.15472e15i		−	0.162743i	−0.996684	−	0.0813713i	$-0.974070\pi$
$619$		−	9.15472e15i		−	0.162743i	0.996684	−	0.0813713i	$-0.0259300\pi$
$620$	−1.11628e16			−0.196527
$621$			1.00350e17i			1.74971i
$622$		−	2.20452e16i		−	0.380690i
$623$	−2.69994e16	+	6.95869e16i	−0.461770	+	1.19014i
$624$	2.23075e16			0.377871
$625$	−4.50982e16			−0.756622
$626$			7.14319e16i			1.18699i
$627$	−1.64557e17			−2.70840
$628$			1.30027e16i			0.211970i
$629$		−	3.98657e15i		−	0.0643718i
$630$	−4.78088e16	+	1.23220e17i	−0.764654	+	1.97078i
$631$	−3.19085e16			−0.505510			−0.252755	−	0.967530i	$-0.581337\pi$
$631$	−3.19085e16			−0.505510			−0.252755	+	0.967530i	$0.581337\pi$
$632$	1.31614e16			0.206537
$633$		−	1.06852e17i		−	1.66096i
$634$	5.70895e16			0.879065
$635$		−	1.71411e17i		−	2.61455i
$636$		−	6.65827e16i		−	1.00605i
$637$	−3.92276e16	+	4.29416e16i	−0.587159	+	0.642749i
$638$	−7.68468e16			−1.13947
$639$	−1.26115e17			−1.85252
$640$		−	9.01413e15i		−	0.131173i
$641$	−4.40486e16			−0.635015			−0.317507	−	0.948256i	$-0.602846\pi$
$641$	−4.40486e16			−0.635015			−0.317507	+	0.948256i	$0.602846\pi$
$642$		−	2.98516e16i		−	0.426341i
$643$		−	1.80148e16i		−	0.254897i	−0.991845	−	0.127448i	$-0.959321\pi$
$643$		−	1.80148e16i		−	0.254897i	0.991845	−	0.127448i	$-0.0406787\pi$
$644$	3.30347e16	+	1.28173e16i	0.463079	+	0.179673i
$645$	1.62132e17			2.25171
$646$	−4.79796e15			−0.0660178
$647$			6.80291e16i			0.927404i	0.885991	+	0.463702i	$0.153479\pi$
$647$			6.80291e16i			0.927404i	−0.885991	+	0.463702i	$0.846521\pi$
$648$	−2.73158e16			−0.368946
$649$		−	2.07714e16i		−	0.277970i
$650$			5.58236e16i			0.740181i
$651$	3.26319e16	+	1.26610e16i	0.428703	+	0.166335i
$652$	−3.70927e16			−0.482839
$653$	−4.06622e16			−0.524460			−0.262230	−	0.965005i	$-0.584458\pi$
$653$	−4.06622e16			−0.524460			−0.262230	+	0.965005i	$0.584458\pi$
$654$		−	1.62355e17i		−	2.07491i
$655$	−1.78234e17			−2.25706
$656$			2.09642e16i			0.263061i
$657$		−	4.85107e16i		−	0.603177i
$658$	−9.29655e15	+	2.39604e16i	−0.114542	+	0.295216i
$659$	−3.81768e16			−0.466109			−0.233054	−	0.972464i	$-0.574872\pi$
$659$	−3.81768e16			−0.466109			−0.233054	+	0.972464i	$0.574872\pi$
$660$	1.51151e17			1.82872
$661$			1.62699e17i			1.95063i	0.220810	+	0.975317i	$0.429130\pi$
$661$			1.62699e17i			1.95063i	−0.220810	+	0.975317i	$0.570870\pi$
$662$	6.03313e16			0.716795
$663$			1.09063e16i			0.128409i
$664$			5.07692e16i			0.592369i
$665$	1.31496e17	+	5.10199e16i	1.52049	+	0.589942i
$666$	−9.41866e16			−1.07930
$667$	9.93078e16			1.12779
$668$		−	7.51922e16i		−	0.846280i
$669$	−1.55630e17			−1.73594
$670$		−	7.62878e14i		−	0.00843347i
$671$			9.29179e16i			1.01804i
$672$	−1.02240e16	+	2.63508e16i	−0.111021	+	0.286139i
$673$	6.85032e16			0.737259			0.368630	−	0.929576i	$-0.379827\pi$
$673$	6.85032e16			0.737259			0.368630	+	0.929576i	$0.379827\pi$
$674$	−8.10453e16			−0.864507
$675$		−	2.00312e17i		−	2.11779i
$676$	1.15526e16			0.121059
$677$		−	1.04790e17i		−	1.08839i	−0.838957	−	0.544197i	$-0.816834\pi$
$677$		−	1.04790e17i		−	1.08839i	0.838957	−	0.544197i	$-0.183166\pi$
$678$		−	1.49148e15i		−	0.0153546i
$679$	−7.00508e15	+	1.80545e16i	−0.0714817	+	0.184233i
$680$	4.40706e15			0.0445754
$681$	3.29726e17			3.30576
$682$		−	2.67497e16i		−	0.265836i
$683$	1.57618e17			1.55268			0.776338	−	0.630317i	$-0.217075\pi$
$683$	1.57618e17			1.55268			0.776338	+	0.630317i	$0.217075\pi$
$684$			1.13356e17i			1.10690i
$685$			3.89935e16i			0.377440i
$686$	−3.27459e16	−	6.60186e16i	−0.314204	−	0.633463i
$687$	2.31381e17			2.20084
$688$	2.31702e16			0.218474
$689$			1.07935e17i			1.00889i
$690$	−1.95330e17			−1.80998
$691$		−	9.57058e15i		−	0.0879164i	−0.999033	−	0.0439582i	$-0.986003\pi$
$691$		−	9.57058e15i		−	0.0879164i	0.999033	−	0.0439582i	$-0.0139968\pi$
$692$		−	6.17157e16i		−	0.562030i
$693$	−2.95276e17	−	1.14566e17i	−2.66580	−	1.03432i
$694$	1.26212e17			1.12965
$695$	−9.49205e16			−0.842270
$696$			7.92148e16i			0.696869i
$697$	−1.02495e16			−0.0893939
$698$		−	2.45142e15i		−	0.0211975i
$699$		−	3.00648e15i		−	0.0257748i
$700$	−6.59416e16	−	2.55851e16i	−0.560494	−	0.217469i
$701$	1.88814e17			1.59120			0.795601	−	0.605821i	$-0.207155\pi$
$701$	1.88814e17			1.59120			0.795601	+	0.605821i	$0.207155\pi$
$702$	1.29760e17			1.08422
$703$			1.00513e17i			0.832699i
$704$	2.16008e16			0.177433
$705$		−	1.41675e17i		−	1.15387i
$706$			1.69104e17i			1.36561i
$707$	3.14245e16	−	8.09920e16i	0.251624	−	0.648523i
$708$	−2.14115e16			−0.169999
$709$	−4.52849e16			−0.356514			−0.178257	−	0.983984i	$-0.557046\pi$
$709$	−4.52849e16			−0.356514			−0.178257	+	0.983984i	$0.557046\pi$
$710$		−	1.23621e17i		−	0.965032i
$711$	1.52025e17			1.17679
$712$		−	5.88010e16i		−	0.451341i
$713$			3.45682e16i			0.263112i
$714$	−1.28830e16	−	4.99857e15i	−0.0972365	−	0.0377273i
$715$	−2.45025e17			−1.83389
$716$	−8.88688e16			−0.659586
$717$			1.05455e17i			0.776165i
$718$	−1.74792e17			−1.27578
$719$		−	1.28671e16i		−	0.0931337i	−0.998915	−	0.0465668i	$-0.985172\pi$
$719$		−	1.28671e16i		−	0.0931337i	0.998915	−	0.0465668i	$-0.0148281\pi$
$720$		−	1.04121e17i		−	0.747384i
$721$	6.73996e16	−	1.73712e17i	0.479784	−	1.23657i
$722$	2.08067e16			0.146886
$723$	−2.79951e17			−1.95998
$724$			5.55527e16i			0.385722i
$725$	−1.98232e17			−1.36504
$726$			1.82441e17i			1.24595i
$727$		−	2.64500e17i		−	1.79151i	−0.444547	−	0.895756i	$-0.646635\pi$
$727$		−	2.64500e17i		−	1.79151i	0.444547	−	0.895756i	$-0.353365\pi$
$728$	1.65737e16	−	4.27162e16i	0.111335	−	0.286949i
$729$	1.43465e17			0.955833
$730$	4.75512e16			0.314213
$731$			1.13280e16i			0.0742422i
$732$	9.57812e16			0.622606
$733$			1.45082e17i			0.935383i	0.883892	+	0.467692i	$0.154914\pi$
$733$			1.45082e17i			0.935383i	−0.883892	+	0.467692i	$0.845086\pi$
$734$			1.70486e17i			1.09022i
$735$	2.99928e17	+	2.73988e17i	1.90236	+	1.73783i
$736$	−2.79144e16			−0.175615
$737$	1.82811e15			0.0114077
$738$			2.42155e17i			1.49884i
$739$	8.28814e16			0.508851			0.254425	−	0.967092i	$-0.418114\pi$
$739$	8.28814e16			0.508851			0.254425	+	0.967092i	$0.418114\pi$
$740$		−	9.23236e16i		−	0.562241i
$741$		−	2.74978e17i		−	1.66107i
$742$	−1.27498e17	−	4.94686e16i	−0.763975	−	0.296419i
$743$	9.81364e16			0.583307			0.291654	−	0.956524i	$-0.405795\pi$
$743$	9.81364e16			0.583307			0.291654	+	0.956524i	$0.405795\pi$
$744$	−2.75740e16			−0.162578
$745$			1.56177e17i			0.913441i
$746$	1.44578e17			0.838820
$747$			5.86429e17i			3.37514i
$748$			1.05608e16i			0.0602956i
$749$	−5.71622e16	−	2.21787e16i	−0.323756	−	0.125616i
$750$	6.56349e16			0.368780
$751$	−9.06358e16			−0.505196			−0.252598	−	0.967571i	$-0.581285\pi$
$751$	−9.06358e16			−0.505196			−0.252598	+	0.967571i	$0.581285\pi$
$752$		−	2.02466e16i		−	0.111955i
$753$	−4.68509e17			−2.57009
$754$		−	1.28412e17i		−	0.698841i
$755$		−	1.06308e17i		−	0.573962i
$756$	−5.94714e16	+	1.53278e17i	−0.318550	+	0.821013i
$757$	−1.02358e17			−0.543936			−0.271968	−	0.962306i	$-0.587674\pi$
$757$	−1.02358e17			−0.543936			−0.271968	+	0.962306i	$0.587674\pi$
$758$	2.35563e17			1.24191
$759$		−	4.68074e17i		−	2.44829i
$760$	−1.11114e17			−0.576618
$761$			1.72185e17i			0.886516i	0.896394	+	0.443258i	$0.146177\pi$
$761$			1.72185e17i			0.886516i	−0.896394	+	0.443258i	$0.853823\pi$
$762$		−	4.23415e17i		−	2.16290i
$763$	−3.10891e17	−	1.20624e17i	−1.57565	−	0.611346i
$764$	1.16106e16			0.0583842
$765$	5.09054e16			0.253978
$766$		−	1.81809e17i		−	0.900002i
$767$	3.47094e16			0.170480
$768$		−	2.22664e16i		−	0.108513i
$769$			1.63589e17i			0.791037i	0.918458	+	0.395518i	$0.129435\pi$
$769$			1.63589e17i			0.791037i	−0.918458	+	0.395518i	$0.870565\pi$
$770$	1.12300e17	−	2.89435e17i	0.538808	−	1.38870i
$771$	−2.11954e16			−0.100905
$772$	−1.52754e17			−0.721586
$773$		−	2.42218e17i		−	1.13535i	−0.823253	−	0.567675i	$-0.807843\pi$
$773$		−	2.42218e17i		−	1.13535i	0.823253	−	0.567675i	$-0.192157\pi$
$774$	2.67636e17			1.24480
$775$		−	6.90028e16i		−	0.318461i
$776$		−	1.52561e16i		−	0.0698673i
$777$	−1.04715e17	+	2.69887e17i	−0.475864	+	1.22647i
$778$	−1.29388e17			−0.583469
$779$	2.58420e17			1.15638
$780$			2.52575e17i			1.12156i
$781$	2.96236e17			1.30536
$782$		−	1.36475e16i		−	0.0596778i
$783$			4.60781e17i			1.99951i
$784$	4.28625e16	+	3.91554e16i	0.184578	+	0.168614i
$785$	−1.47222e17			−0.629150
$786$	−4.40268e17			−1.86716
$787$			2.96207e17i			1.24666i	0.781959	+	0.623329i	$0.214220\pi$
$787$			2.96207e17i			1.24666i	−0.781959	+	0.623329i	$0.785780\pi$
$788$	3.64921e16			0.152420
$789$		−	3.32642e17i		−	1.37884i
$790$			1.49019e17i			0.613024i
$791$	−2.85600e15	−	1.10812e15i	−0.0116600	−	0.00452404i
$792$	2.49508e17			1.01096
$793$	−1.55267e17			−0.624368
$794$			2.79633e17i			1.11600i
$795$	7.53877e17			2.98605
$796$		−	1.78898e17i		−	0.703280i
$797$			1.55317e17i			0.605994i	0.952991	+	0.302997i	$0.0979873\pi$
$797$			1.55317e17i			0.605994i	−0.952991	+	0.302997i	$0.902013\pi$
$798$	3.24818e17	+	1.26028e17i	1.25783	+	0.488033i
$799$	9.89869e15			0.0380450
$800$	5.57208e16			0.212558
$801$		−	6.79204e17i		−	2.57161i
$802$	2.16271e17			0.812740
$803$			1.13948e17i			0.425025i
$804$		−	1.88444e15i		−	0.00697664i
$805$	−1.45123e17	+	3.74032e17i	−0.533287	+	1.37447i
$806$	4.46992e16			0.163038
$807$	−9.40637e16			−0.340550
$808$			6.84384e16i			0.245941i
$809$	4.53583e15			0.0161795			0.00808976	−	0.999967i	$-0.497425\pi$
$809$	4.53583e15			0.0161795			0.00808976	+	0.999967i	$0.497425\pi$
$810$		−	3.09280e17i		−	1.09507i
$811$		−	4.16680e17i		−	1.46446i	−0.681057	−	0.732231i	$-0.738479\pi$
$811$		−	4.16680e17i		−	1.46446i	0.681057	−	0.732231i	$-0.261521\pi$
$812$	1.51687e17	+	5.88538e16i	0.529190	+	0.205323i
$813$	−1.76055e17			−0.609684
$814$	2.21238e17			0.760524
$815$		−	4.19978e17i		−	1.43312i
$816$	1.08862e16			0.0368753
$817$		−	2.85612e17i		−	0.960381i
$818$			2.03517e17i			0.679331i
$819$	1.91441e17	−	4.93410e17i	0.634354	−	1.63495i
$820$	−2.37366e17			−0.780791
$821$	−1.37823e17			−0.450052			−0.225026	−	0.974353i	$-0.572247\pi$
$821$	−1.37823e17			−0.450052			−0.225026	+	0.974353i	$0.572247\pi$
$822$			9.63205e16i			0.312239i
$823$	2.31880e16			0.0746217			0.0373109	−	0.999304i	$-0.488121\pi$
$823$	2.31880e16			0.0746217			0.0373109	+	0.999304i	$0.488121\pi$
$824$			1.46787e17i			0.468948i
$825$			9.34337e17i			2.96333i
$826$	−1.59080e16	+	4.10004e16i	−0.0500881	+	0.129095i
$827$	−3.60692e17			−1.12746			−0.563732	−	0.825957i	$-0.690635\pi$
$827$	−3.60692e17			−1.12746			−0.563732	+	0.825957i	$0.690635\pi$
$828$	−3.22436e17			−1.00060
$829$			6.48621e16i			0.199831i	0.994996	+	0.0999157i	$0.0318573\pi$
$829$			6.48621e16i			0.199831i	−0.994996	+	0.0999157i	$0.968143\pi$
$830$	−5.74830e17			−1.75821
$831$		−	7.10386e17i		−	2.15719i
$832$			3.60953e16i			0.108820i
$833$	−1.91433e16	+	2.09557e16i	−0.0572989	+	0.0627238i
$834$	−2.34470e17			−0.696772
$835$	8.51357e17			2.51185
$836$		−	2.66266e17i		−	0.779972i
$837$	−1.60394e17			−0.466482
$838$			1.25336e17i			0.361919i
$839$			8.40214e16i			0.240890i	0.992720	+	0.120445i	$0.0384321\pi$
$839$			8.40214e16i			0.240890i	−0.992720	+	0.120445i	$0.961568\pi$
$840$	−2.98354e17	−	1.15760e17i	−0.849291	−	0.329521i
$841$	1.02181e17			0.288799
$842$	9.19807e16			0.258122
$843$			9.55520e17i			2.66241i
$844$	1.72894e17			0.478328
$845$			1.30803e17i			0.359317i
$846$		−	2.33866e17i		−	0.637889i
$847$	3.49352e17	+	1.35547e17i	0.946155	+	0.367104i
$848$	1.07736e17			0.289724
$849$	−1.12349e16			−0.0300002
$850$			2.72422e16i			0.0722319i
$851$	−2.85902e17			−0.752731
$852$		−	3.05365e17i		−	0.798327i
$853$		−	4.46870e17i		−	1.16008i	−0.814589	−	0.580039i	$-0.803037\pi$
$853$		−	4.46870e17i		−	1.16008i	0.814589	−	0.580039i	$-0.196963\pi$
$854$	7.11620e16	−	1.83409e17i	0.183443	−	0.472796i
$855$	−1.28347e18			−3.28540
$856$	4.83021e16			0.122779
$857$			7.28771e17i			1.83953i	0.392473	+	0.919763i	$0.371620\pi$
$857$			7.28771e17i			1.83953i	−0.392473	+	0.919763i	$0.628380\pi$
$858$	−6.05253e17			−1.51710
$859$			6.42025e17i			1.59806i	0.601291	+	0.799030i	$0.294653\pi$
$859$			6.42025e17i			1.59806i	−0.601291	+	0.799030i	$0.705347\pi$
$860$			2.62343e17i			0.648452i
$861$	6.93885e17	+	2.69224e17i	1.70321	+	0.660839i
$862$	3.73570e16			0.0910601
$863$	−6.51220e17			−1.57639			−0.788194	−	0.615427i	$-0.788984\pi$
$863$	−6.51220e17			−1.57639			−0.788194	+	0.615427i	$0.788984\pi$
$864$		−	1.29521e17i		−	0.311355i
$865$	6.98771e17			1.66816
$866$			3.69170e17i			0.875223i
$867$		−	7.32103e17i		−	1.72368i
$868$	−2.04865e16	+	5.28009e16i	−0.0479016	+	0.123459i
$869$	−3.57097e17			−0.829216
$870$	−8.96903e17			−2.06838
$871$			3.05479e15i			0.00699638i
$872$	2.62703e17			0.597539
$873$		−	1.76222e17i		−	0.398083i
$874$			3.44092e17i			0.771979i
$875$	4.87644e16	−	1.25683e17i	0.108656	−	0.280045i
$876$	1.17460e17			0.259934
$877$	7.18483e17			1.57913			0.789567	−	0.613664i	$-0.210305\pi$
$877$	7.18483e17			1.57913			0.789567	+	0.613664i	$0.210305\pi$
$878$		−	3.59380e17i		−	0.784490i
$879$	4.11733e17			0.892653
$880$			2.44573e17i			0.526639i
$881$		−	2.08936e17i		−	0.446847i	−0.974722	−	0.223423i	$-0.928277\pi$
$881$		−	2.08936e17i		−	0.446847i	0.974722	−	0.223423i	$-0.0717232\pi$
$882$	4.95099e17	+	4.52279e17i	1.05167	+	0.960716i
$883$	−3.89085e17			−0.820881			−0.410441	−	0.911887i	$-0.634625\pi$
$883$	−3.89085e17			−0.820881			−0.410441	+	0.911887i	$0.634625\pi$
$884$	−1.76472e16			−0.0369796
$885$		−	2.42430e17i		−	0.504576i
$886$	−8.21767e16			−0.169882
$887$		−	3.20242e17i		−	0.657561i	−0.944406	−	0.328780i	$-0.893362\pi$
$887$		−	3.20242e17i		−	0.657561i	0.944406	−	0.328780i	$-0.106638\pi$
$888$		−	2.28055e17i		−	0.465117i
$889$	−8.10788e17	−	3.14582e17i	−1.64247	−	0.637270i
$890$	6.65770e17			1.33963
$891$	7.41137e17			1.48126
$892$		−	2.51821e17i		−	0.499922i
$893$	−2.49574e17			−0.492141
$894$			3.85785e17i			0.755649i
$895$		−	1.00621e18i		−	1.95772i
$896$	−4.26375e16	−	1.65432e16i	−0.0824032	−	0.0319721i
$897$	7.82158e17			1.50155
$898$	−5.44723e16			−0.103877
$899$			1.58728e17i			0.300674i
$900$	6.43624e17			1.21109
$901$			5.26727e16i			0.0984548i
$902$		−	5.68806e17i		−	1.05615i
$903$	2.97553e17	−	7.66899e17i	0.548831	−	1.41453i
$904$	2.41333e15			0.00442187
$905$	−6.28991e17			−1.14486
$906$		−	2.62598e17i		−	0.474813i
$907$	−3.11575e17			−0.559654			−0.279827	−	0.960050i	$-0.590277\pi$
$907$	−3.11575e17			−0.559654			−0.279827	+	0.960050i	$0.590277\pi$
$908$			5.33522e17i			0.952001i
$909$			7.90523e17i			1.40130i
$910$	4.83651e17	+	1.87654e17i	0.851694	+	0.330454i
$911$	5.87201e17			1.02725			0.513626	−	0.858014i	$-0.328302\pi$
$911$	5.87201e17			1.02725			0.513626	+	0.858014i	$0.328302\pi$
$912$	−2.74471e17			−0.477011
$913$		−	1.37748e18i		−	2.37827i
$914$	8.29755e16			0.142322
$915$			1.08447e18i			1.84796i
$916$			3.74393e17i			0.633803i
$917$	−3.27104e17	+	8.43060e17i	−0.550135	+	1.41789i
$918$	6.33234e16			0.105805
$919$	6.86145e17			1.13900			0.569499	−	0.821992i	$-0.307137\pi$
$919$	6.86145e17			1.13900			0.569499	+	0.821992i	$0.307137\pi$
$920$		−	3.16058e17i		−	0.521243i
$921$	−6.56900e17			−1.07632
$922$			8.52101e16i			0.138709i
$923$			4.95015e17i			0.800586i
$924$	2.77399e17	−	7.14955e17i	0.445732	−	1.14881i
$925$	5.70698e17			0.911079
$926$	−1.84985e17			−0.293407
$927$			1.69552e18i			2.67193i
$928$	−1.28176e17			−0.200686
$929$			2.41271e16i			0.0375328i	0.999824	+	0.0187664i	$0.00597389\pi$
$929$			2.41271e16i			0.0375328i	−0.999824	+	0.0187664i	$0.994026\pi$
$930$		−	3.12205e17i		−	0.482549i
$931$	4.82656e17	−	5.28352e17i	0.741207	−	0.811382i
$932$	4.86471e15			0.00742269
$933$	6.16566e17			0.934738
$934$		−	6.78441e17i		−	1.02195i
$935$	−1.19573e17			−0.178964
$936$			4.16932e17i			0.620027i
$937$		−	3.87468e17i		−	0.572530i	−0.958151	−	0.286265i	$-0.907586\pi$
$937$		−	3.87468e17i		−	0.572530i	0.958151	−	0.286265i	$-0.0924137\pi$
$938$	−3.60847e15	−	1.40007e15i	−0.00529793	−	0.00205558i
$939$	−1.99783e18			−2.91450
$940$	2.29241e17			0.332295
$941$			5.04751e17i			0.727008i	0.931593	+	0.363504i	$0.118420\pi$
$941$			5.04751e17i			0.727008i	−0.931593	+	0.363504i	$0.881580\pi$
$942$	−3.63663e17			−0.520468
$943$			7.35059e17i			1.04533i
$944$		−	3.46454e16i		−	0.0489569i
$945$	−1.73548e18	−	6.73359e17i	−2.43685	−	0.945488i
$946$	−6.28659e17			−0.877139
$947$	−1.14177e18			−1.58299			−0.791497	−	0.611173i	$-0.790698\pi$
$947$	−1.14177e18			−1.58299			−0.791497	+	0.611173i	$0.790698\pi$
$948$			3.68101e17i			0.507128i
$949$	−1.90409e17			−0.260670
$950$		−	6.86852e17i		−	0.934376i
$951$			1.59670e18i			2.15844i
$952$	8.08806e15	−	2.08457e16i	0.0108648	−	0.0280024i
$953$	1.03407e18			1.38036			0.690182	−	0.723636i	$-0.257531\pi$
$953$	1.03407e18			1.38036			0.690182	+	0.723636i	$0.257531\pi$
$954$	1.24444e18			1.65076
$955$			1.31460e17i			0.173290i
$956$	−1.70635e17			−0.223522
$957$		−	2.14927e18i		−	2.79782i
$958$		−	1.10537e17i		−	0.142993i
$959$	1.84442e17	+	7.15627e16i	0.237109	+	0.0919973i
$960$	2.52110e17			0.322079
$961$	7.32411e17			0.929853
$962$			3.69692e17i			0.466433i
$963$	5.57932e17			0.699558
$964$		−	4.52982e17i		−	0.564441i
$965$		−	1.72954e18i		−	2.14174i
$966$	−3.58479e17	+	9.23924e17i	−0.441164	+	1.13703i
$967$	−1.55498e18			−1.90180			−0.950900	−	0.309498i	$-0.899839\pi$
$967$	−1.55498e18			−1.90180			−0.950900	+	0.309498i	$0.899839\pi$
$968$	−2.95203e17			−0.358813
$969$		−	1.34191e17i		−	0.162099i
$970$	1.72736e17			0.207373
$971$		−	2.93946e17i		−	0.350714i	−0.984505	−	0.175357i	$-0.943892\pi$
$971$		−	2.93946e17i		−	0.350714i	0.984505	−	0.175357i	$-0.0561079\pi$
$972$		−	2.13003e16i		−	0.0252574i
$973$	−1.74203e17	+	4.48981e17i	−0.205295	+	0.529116i
$974$	−5.45014e16			−0.0638342
$975$	−1.56129e18			−1.81742
$976$			1.54981e17i			0.179300i
$977$	−4.44830e17			−0.511478			−0.255739	−	0.966746i	$-0.582319\pi$
$977$	−4.44830e17			−0.511478			−0.255739	+	0.966746i	$0.582319\pi$
$978$		−	1.03742e18i		−	1.18555i
$979$			1.59540e18i			1.81207i
$980$	−4.43333e17	+	4.85306e17i	−0.500465	+	0.547847i
$981$	3.03445e18			3.40460
$982$	−5.06548e15			−0.00564874
$983$		−	7.23090e17i		−	0.801440i	−0.916201	−	0.400720i	$-0.868760\pi$
$983$		−	7.23090e17i		−	0.801440i	0.916201	−	0.400720i	$-0.131240\pi$
$984$	−5.86334e17			−0.645914
$985$			4.13179e17i			0.452398i
$986$		−	6.26658e16i		−	0.0681976i
$987$	−6.70133e17	−	2.60009e17i	−0.724866	−	0.281245i
$988$	4.44935e17			0.478360
$989$	8.12405e17			0.868151
$990$			2.82504e18i			3.00064i
$991$	5.29003e17			0.558491			0.279245	−	0.960220i	$-0.409916\pi$
$991$	5.29003e17			0.558491			0.279245	+	0.960220i	$0.409916\pi$
$992$		−	4.46169e16i		−	0.0468197i
$993$			1.68736e18i			1.76000i
$994$	−5.84736e17	−	2.26875e17i	−0.606236	−	0.235217i
$995$	2.02556e18			2.08741
$996$	−1.41993e18			−1.45449
$997$			2.70445e17i			0.275365i	0.990476	+	0.137683i	$0.0439654\pi$
$997$			2.70445e17i			0.275365i	−0.990476	+	0.137683i	$0.956035\pi$
$998$	3.77166e17			0.381724
$999$		−	1.32656e18i		−	1.33455i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.13.b.a.13.1	✓	8
3.2	odd	2		126.13.c.a.55.5		8
4.3	odd	2		112.13.c.c.97.8		8
7.2	even	3		98.13.d.b.31.8		16
7.3	odd	6		98.13.d.b.19.8		16
7.4	even	3		98.13.d.b.19.5		16
7.5	odd	6		98.13.d.b.31.5		16
7.6	odd	2	inner	14.13.b.a.13.4	yes	8
21.20	even	2		126.13.c.a.55.8		8
28.27	even	2		112.13.c.c.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.13.b.a.13.1	✓	8	1.1	even	1	trivial
14.13.b.a.13.4	yes	8	7.6	odd	2	inner
98.13.d.b.19.5		16	7.4	even	3
98.13.d.b.19.8		16	7.3	odd	6
98.13.d.b.31.5		16	7.5	odd	6
98.13.d.b.31.8		16	7.2	even	3
112.13.c.c.97.1		8	28.27	even	2
112.13.c.c.97.8		8	4.3	odd	2
126.13.c.a.55.5		8	3.2	odd	2
126.13.c.a.55.8		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)

\(f(q)\)	\(=\)	\(q-45.2548 q^{2} -1265.70i q^{3} +2048.00 q^{4} +23188.3i q^{5} +57279.1i q^{6} +(109682. + 42556.3i) q^{7} -92681.9 q^{8} -1.07056e6 q^{9} +O(q^{10})\)	\(q-45.2548 q^{2} -1265.70i q^{3} +2048.00 q^{4} +23188.3i q^{5} +57279.1i q^{6} +(109682. + 42556.3i) q^{7} -92681.9 q^{8} -1.07056e6 q^{9} -1.04938e6i q^{10} +2.51467e6 q^{11} -2.59216e6i q^{12} +4.20204e6i q^{13} +(-4.96366e6 - 1.92588e6i) q^{14} +2.93495e7 q^{15} +4.19430e6 q^{16} +2.05062e6i q^{17} +4.84479e7 q^{18} -5.17019e7i q^{19} +4.74896e7i q^{20} +(5.38636e7 - 1.38825e8i) q^{21} -1.13801e8 q^{22} +1.47063e8 q^{23} +1.17308e8i q^{24} -2.93557e8 q^{25} -1.90163e8i q^{26} +6.82360e8i q^{27} +(2.24630e8 + 8.71554e7i) q^{28} +6.75275e8 q^{29} -1.32820e9 q^{30} +2.35058e8i q^{31} -1.89813e8 q^{32} -3.18282e9i q^{33} -9.28005e7i q^{34} +(-9.86809e8 + 2.54335e9i) q^{35} -2.19250e9 q^{36} -1.94408e9 q^{37} +2.33976e9i q^{38} +5.31853e9 q^{39} -2.14914e9i q^{40} +4.99826e9i q^{41} +(-2.43759e9 + 6.28251e9i) q^{42} +5.52421e9 q^{43} +5.15004e9 q^{44} -2.48244e10i q^{45} -6.65530e9 q^{46} -4.82717e9i q^{47} -5.30873e9i q^{48} +(1.02192e10 + 9.33537e9i) q^{49} +1.32849e10 q^{50} +2.59547e9 q^{51} +8.60579e9i q^{52} +2.56862e10 q^{53} -3.08801e10i q^{54} +5.83108e10i q^{55} +(-1.01656e10 - 3.94420e9i) q^{56} -6.54391e10 q^{57} -3.05594e10 q^{58} -8.26012e9i q^{59} +6.01077e10 q^{60} +3.69504e10i q^{61} -1.06375e10i q^{62} +(-1.17421e11 - 4.55590e10i) q^{63} +8.58993e9 q^{64} -9.74383e10 q^{65} +1.44038e11i q^{66} +7.26978e8 q^{67} +4.19967e9i q^{68} -1.86138e11i q^{69} +(4.46579e10 - 1.15099e11i) q^{70} +1.17803e11 q^{71} +9.92213e10 q^{72} +4.53135e10i q^{73} +8.79790e10 q^{74} +3.71555e11i q^{75} -1.05885e11i q^{76} +(2.75815e11 + 1.07015e11i) q^{77} -2.40689e11 q^{78} -1.42006e11 q^{79} +9.72588e10i q^{80} +2.94726e11 q^{81} -2.26196e11i q^{82} -5.47779e11i q^{83} +(1.10313e11 - 2.84314e11i) q^{84} -4.75504e10 q^{85} -2.49997e11 q^{86} -8.54696e11i q^{87} -2.33064e11 q^{88} +6.34439e11i q^{89} +1.12342e12i q^{90} +(-1.78824e11 + 4.60891e11i) q^{91} +3.01185e11 q^{92} +2.97513e11 q^{93} +2.18453e11i q^{94} +1.19888e12 q^{95} +2.40246e11i q^{96} +1.64607e11i q^{97} +(-4.62468e11 - 4.22470e11i) q^{98} -2.69210e12 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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