LMFDB - Embedded newform 7.13.b.b.6.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7,13,Mod(6,7)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7, 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("7.6");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 7 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	7.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:	$6.39795672093$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 238188x^{4} - 14589496x^{3} + 11212054600x^{2} - 101757597480x + 81251686776288 $ x^6 - x^5 + 238188x^4 - 14589496x^3 + 11212054600x^2 - 101757597480x + 81251686776288
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{11}\cdot 3\cdot 7^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			6.1
Root			$-1.79648 + 93.6923i$ of defining polynomial
Character	$\chi$	$=$	7.6
Dual form			7.13.b.b.6.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-108.657 q^{2} -1048.40i q^{3} +7710.33 q^{4} -23251.4i q^{5} +113916. i q^{6} +(-98544.2 - 64267.7i) q^{7} -392722. q^{8} -567695. q^{9} +O(q^{10})$	\(q-108.657 q^{2} -1048.40i q^{3} +7710.33 q^{4} -23251.4i q^{5} +113916. i q^{6} +(-98544.2 - 64267.7i) q^{7} -392722. q^{8} -567695. q^{9} +2.52642e6i q^{10} +1.17023e6 q^{11} -8.08348e6i q^{12} +1.30280e6i q^{13} +(1.07075e7 + 6.98313e6i) q^{14} -2.43766e7 q^{15} +1.10904e7 q^{16} -1.42965e7i q^{17} +6.16839e7 q^{18} +5.15402e7i q^{19} -1.79276e8i q^{20} +(-6.73780e7 + 1.03313e8i) q^{21} -1.27153e8 q^{22} +1.32381e8 q^{23} +4.11728e8i q^{24} -2.96485e8 q^{25} -1.41558e8i q^{26} +3.80082e7i q^{27} +(-7.59808e8 - 4.95525e8i) q^{28} +1.43502e8 q^{29} +2.64869e9 q^{30} -6.22541e8i q^{31} +4.03536e8 q^{32} -1.22686e9i q^{33} +1.55341e9i q^{34} +(-1.49431e9 + 2.29129e9i) q^{35} -4.37711e9 q^{36} +5.77404e8 q^{37} -5.60020e9i q^{38} +1.36585e9 q^{39} +9.13131e9i q^{40} +3.87419e9i q^{41} +(7.32109e9 - 1.12257e10i) q^{42} -1.05376e10 q^{43} +9.02284e9 q^{44} +1.31997e10i q^{45} -1.43842e10 q^{46} -1.69221e10i q^{47} -1.16272e10i q^{48} +(5.58062e9 + 1.26664e10i) q^{49} +3.22151e10 q^{50} -1.49884e10 q^{51} +1.00450e10i q^{52} -1.48137e10 q^{53} -4.12985e9i q^{54} -2.72094e10i q^{55} +(3.87004e10 + 2.52393e10i) q^{56} +5.40345e10 q^{57} -1.55925e10 q^{58} -6.12158e10i q^{59} -1.87952e11 q^{60} +4.42202e10i q^{61} +6.76434e10i q^{62} +(5.59430e10 + 3.64844e10i) q^{63} -8.92734e10 q^{64} +3.02918e10 q^{65} +1.33307e11i q^{66} +1.23400e11 q^{67} -1.10231e11i q^{68} -1.38788e11i q^{69} +(1.62367e11 - 2.48964e11i) q^{70} -1.23655e11 q^{71} +2.22946e11 q^{72} -1.13587e11i q^{73} -6.27390e10 q^{74} +3.10834e11i q^{75} +3.97391e11i q^{76} +(-1.15319e11 - 7.52078e10i) q^{77} -1.48409e11 q^{78} +1.22580e11 q^{79} -2.57867e11i q^{80} -2.61849e11 q^{81} -4.20957e11i q^{82} +1.49210e11i q^{83} +(-5.19506e11 + 7.96580e11i) q^{84} -3.32413e11 q^{85} +1.14499e12 q^{86} -1.50447e11i q^{87} -4.59574e11 q^{88} +2.82175e11i q^{89} -1.43424e12i q^{90} +(8.37276e10 - 1.28383e11i) q^{91} +1.02070e12 q^{92} -6.52670e11 q^{93} +1.83871e12i q^{94} +1.19838e12 q^{95} -4.23066e11i q^{96} +7.83396e11i q^{97} +(-6.06373e11 - 1.37629e12i) q^{98} -6.64332e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 16288 q^{4} - 314650 q^{7} - 1036800 q^{8} - 1680762 q^{9}+O(q^{10}) $ 6 * q + 16288 * q^4 - 314650 * q^7 - 1036800 * q^8 - 1680762 * q^9	\( 6 q + 16288 q^{4} - 314650 q^{7} - 1036800 q^{8} - 1680762 q^{9} + 1704780 q^{11} + 27863136 q^{14} - 40526880 q^{15} + 15993088 q^{16} + 128356800 q^{18} - 32694816 q^{21} - 83177600 q^{22} - 266735700 q^{23} - 1115987130 q^{25} - 150488800 q^{28} + 2090185452 q^{29} + 3469961280 q^{30} - 666316800 q^{32} + 1813281120 q^{35} - 5110975584 q^{36} - 4824866900 q^{37} - 9660671328 q^{39} + 26387188800 q^{42} - 28724189300 q^{43} + 40254705216 q^{44} - 56843757056 q^{46} + 23216390022 q^{49} + 30589686720 q^{50} + 74552249088 q^{51} - 104521857300 q^{53} + 110766507264 q^{56} + 6945343200 q^{57} + 169979689600 q^{58} - 621243786240 q^{60} + 209517066150 q^{63} - 404530321408 q^{64} + 420221360160 q^{65} - 129746603700 q^{67} + 715652629440 q^{70} - 15017604660 q^{71} + 550229836800 q^{72} - 538689695616 q^{74} + 272839020300 q^{77} - 336774849600 q^{78} - 172527631668 q^{79} - 1648796648346 q^{81} - 343188486144 q^{84} + 62636728320 q^{85} + 1808205928704 q^{86} - 462937446400 q^{88} - 474685856736 q^{91} + 2013091790400 q^{92} - 2143380662400 q^{93} + 3657881967840 q^{95} - 2066720745600 q^{98} + 65572191564 q^{99}+O(q^{100}) \) 6 * q + 16288 * q^4 - 314650 * q^7 - 1036800 * q^8 - 1680762 * q^9 + 1704780 * q^11 + 27863136 * q^14 - 40526880 * q^15 + 15993088 * q^16 + 128356800 * q^18 - 32694816 * q^21 - 83177600 * q^22 - 266735700 * q^23 - 1115987130 * q^25 - 150488800 * q^28 + 2090185452 * q^29 + 3469961280 * q^30 - 666316800 * q^32 + 1813281120 * q^35 - 5110975584 * q^36 - 4824866900 * q^37 - 9660671328 * q^39 + 26387188800 * q^42 - 28724189300 * q^43 + 40254705216 * q^44 - 56843757056 * q^46 + 23216390022 * q^49 + 30589686720 * q^50 + 74552249088 * q^51 - 104521857300 * q^53 + 110766507264 * q^56 + 6945343200 * q^57 + 169979689600 * q^58 - 621243786240 * q^60 + 209517066150 * q^63 - 404530321408 * q^64 + 420221360160 * q^65 - 129746603700 * q^67 + 715652629440 * q^70 - 15017604660 * q^71 + 550229836800 * q^72 - 538689695616 * q^74 + 272839020300 * q^77 - 336774849600 * q^78 - 172527631668 * q^79 - 1648796648346 * q^81 - 343188486144 * q^84 + 62636728320 * q^85 + 1808205928704 * q^86 - 462937446400 * q^88 - 474685856736 * q^91 + 2013091790400 * q^92 - 2143380662400 * q^93 + 3657881967840 * q^95 - 2066720745600 * q^98 + 65572191564 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/7\mathbb{Z}\right)^\times$.

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

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 $

$2$	−108.657			−1.69776			−0.848882	−	0.528582i	$-0.822724\pi$
$2$	−108.657			−1.69776			−0.848882	+	0.528582i	$0.822724\pi$
$3$		−	1048.40i		−	1.43813i	−0.694943	−	0.719065i	$-0.744570\pi$
$3$		−	1048.40i		−	1.43813i	0.694943	−	0.719065i	$-0.255430\pi$
$4$	7710.33			1.88240
$5$		−	23251.4i		−	1.48809i	−0.668131	−	0.744043i	$-0.732906\pi$
$5$		−	23251.4i		−	1.48809i	0.668131	−	0.744043i	$-0.267094\pi$
$6$			113916.i			2.44161i
$7$	−98544.2	−	64267.7i	−0.837612	−	0.546266i
$7$	−98544.2	−	64267.7i	−0.837612	−	0.546266i
$8$	−392722.			−1.49811
$9$	−567695.			−1.06822
$10$			2.52642e6i			2.52642i
$11$	1.17023e6			0.660563			0.330282	−	0.943882i	$-0.392856\pi$
$11$	1.17023e6			0.660563			0.330282	+	0.943882i	$0.392856\pi$
$12$		−	8.08348e6i		−	2.70714i
$13$			1.30280e6i			0.269908i	0.990852	+	0.134954i	$0.0430887\pi$
$13$			1.30280e6i			0.269908i	−0.990852	+	0.134954i	$0.956911\pi$
$14$	1.07075e7	+	6.98313e6i	1.42207	+	0.927431i
$15$	−2.43766e7			−2.14006
$16$	1.10904e7			0.661041
$17$		−	1.42965e7i		−	0.592293i	−0.955143	−	0.296146i	$-0.904298\pi$
$17$		−	1.42965e7i		−	0.592293i	0.955143	−	0.296146i	$-0.0957016\pi$
$18$	6.16839e7			1.81358
$19$			5.15402e7i			1.09553i	0.836632	+	0.547765i	$0.184521\pi$
$19$			5.15402e7i			1.09553i	−0.836632	+	0.547765i	$0.815479\pi$
$20$		−	1.79276e8i		−	2.80118i
$21$	−6.73780e7	+	1.03313e8i	−0.785602	+	1.20459i
$22$	−1.27153e8			−1.12148
$23$	1.32381e8			0.894252			0.447126	−	0.894471i	$-0.352448\pi$
$23$	1.32381e8			0.894252			0.447126	+	0.894471i	$0.352448\pi$
$24$			4.11728e8i			2.15448i
$25$	−2.96485e8			−1.21440
$26$		−	1.41558e8i		−	0.458241i
$27$			3.80082e7i			0.0981057i
$28$	−7.59808e8	−	4.95525e8i	−1.57672	−	1.02829i
$29$	1.43502e8			0.241252			0.120626	−	0.992698i	$-0.461510\pi$
$29$	1.43502e8			0.241252			0.120626	+	0.992698i	$0.461510\pi$
$30$	2.64869e9			3.63332
$31$		−	6.22541e8i		−	0.701452i	−0.936478	−	0.350726i	$-0.885935\pi$
$31$		−	6.22541e8i		−	0.701452i	0.936478	−	0.350726i	$-0.114065\pi$
$32$	4.03536e8			0.375823
$33$		−	1.22686e9i		−	0.949976i
$34$			1.55341e9i			1.00557i
$35$	−1.49431e9	+	2.29129e9i	−0.812891	+	1.24644i
$36$	−4.37711e9			−2.01082
$37$	5.77404e8			0.225045			0.112523	−	0.993649i	$-0.464107\pi$
$37$	5.77404e8			0.225045			0.112523	+	0.993649i	$0.464107\pi$
$38$		−	5.60020e9i		−	1.85995i
$39$	1.36585e9			0.388163
$40$			9.13131e9i			2.22932i
$41$			3.87419e9i			0.815600i	0.913071	+	0.407800i	$0.133704\pi$
$41$			3.87419e9i			0.815600i	−0.913071	+	0.407800i	$0.866296\pi$
$42$	7.32109e9	−	1.12257e10i	1.33377	−	2.04512i
$43$	−1.05376e10			−1.66699			−0.833493	−	0.552530i	$-0.813663\pi$
$43$	−1.05376e10			−1.66699			−0.833493	+	0.552530i	$0.813663\pi$
$44$	9.02284e9			1.24345
$45$			1.31997e10i			1.58960i
$46$	−1.43842e10			−1.51823
$47$		−	1.69221e10i		−	1.56988i	−0.619569	−	0.784942i	$-0.712692\pi$
$47$		−	1.69221e10i		−	1.56988i	0.619569	−	0.784942i	$-0.287308\pi$
$48$		−	1.16272e10i		−	0.950662i
$49$	5.58062e9	+	1.26664e10i	0.403187	+	0.915118i
$50$	3.22151e10			2.06177
$51$	−1.49884e10			−0.851794
$52$			1.00450e10i			0.508076i
$53$	−1.48137e10			−0.668355			−0.334178	−	0.942510i	$-0.608459\pi$
$53$	−1.48137e10			−0.668355			−0.334178	+	0.942510i	$0.608459\pi$
$54$		−	4.12985e9i		−	0.166560i
$55$		−	2.72094e10i		−	0.982975i
$56$	3.87004e10	+	2.52393e10i	1.25484	+	0.818369i
$57$	5.40345e10			1.57551
$58$	−1.55925e10			−0.409589
$59$		−	6.12158e10i		−	1.45128i	−0.688074	−	0.725641i	$-0.741543\pi$
$59$		−	6.12158e10i		−	1.45128i	0.688074	−	0.725641i	$-0.258457\pi$
$60$	−1.87952e11			−4.02846
$61$			4.42202e10i			0.858304i	0.903232	+	0.429152i	$0.141188\pi$
$61$			4.42202e10i			0.858304i	−0.903232	+	0.429152i	$0.858812\pi$
$62$			6.76434e10i			1.19090i
$63$	5.59430e10	+	3.64844e10i	0.894752	+	0.583531i
$64$	−8.92734e10			−1.29910
$65$	3.02918e10			0.401647
$66$			1.33307e11i			1.61283i
$67$	1.23400e11			1.36417			0.682084	−	0.731274i	$-0.261074\pi$
$67$	1.23400e11			1.36417			0.682084	+	0.731274i	$0.261074\pi$
$68$		−	1.10231e11i		−	1.11493i
$69$		−	1.38788e11i		−	1.28605i
$70$	1.62367e11	−	2.48964e11i	1.38010	−	2.11616i
$71$	−1.23655e11			−0.965297			−0.482648	−	0.875814i	$-0.660325\pi$
$71$	−1.23655e11			−0.965297			−0.482648	+	0.875814i	$0.660325\pi$
$72$	2.22946e11			1.60031
$73$		−	1.13587e11i		−	0.750569i	−0.926910	−	0.375284i	$-0.877545\pi$
$73$		−	1.13587e11i		−	0.750569i	0.926910	−	0.375284i	$-0.122455\pi$
$74$	−6.27390e10			−0.382074
$75$			3.10834e11i			1.74647i
$76$			3.97391e11i			2.06223i
$77$	−1.15319e11	−	7.52078e10i	−0.553295	−	0.360843i
$78$	−1.48409e11			−0.659009
$79$	1.22580e11			0.504265			0.252132	−	0.967693i	$-0.418868\pi$
$79$	1.22580e11			0.504265			0.252132	+	0.967693i	$0.418868\pi$
$80$		−	2.57867e11i		−	0.983686i
$81$	−2.61849e11			−0.927129
$82$		−	4.20957e11i		−	1.38470i
$83$			1.49210e11i			0.456383i	0.973616	+	0.228191i	$0.0732812\pi$
$83$			1.49210e11i			0.456383i	−0.973616	+	0.228191i	$0.926719\pi$
$84$	−5.19506e11	+	7.96580e11i	−1.47882	+	2.26753i
$85$	−3.32413e11			−0.881383
$86$	1.14499e12			2.83015
$87$		−	1.50447e11i		−	0.346951i
$88$	−4.59574e11			−0.989599
$89$			2.82175e11i			0.567779i	0.958857	+	0.283889i	$0.0916248\pi$
$89$			2.82175e11i			0.567779i	−0.958857	+	0.283889i	$0.908375\pi$
$90$		−	1.43424e12i		−	2.69877i
$91$	8.37276e10	−	1.28383e11i	0.147442	−	0.226078i
$92$	1.02070e12			1.68334
$93$	−6.52670e11			−1.00878
$94$			1.83871e12i			2.66529i
$95$	1.19838e12			1.63024
$96$		−	4.23066e11i		−	0.540482i
$97$			7.83396e11i			0.940484i	0.882538	+	0.470242i	$0.155833\pi$
$97$			7.83396e11i			0.940484i	−0.882538	+	0.470242i	$0.844167\pi$
$98$	−6.06373e11	−	1.37629e12i	−0.684516	−	1.55365i
$99$	−6.64332e11			−0.705625
$100$	−2.28600e12			−2.28600
$101$		−	1.00723e12i		−	0.948854i	−0.880295	−	0.474427i	$-0.842655\pi$
$101$		−	1.00723e12i		−	0.948854i	0.880295	−	0.474427i	$-0.157345\pi$
$102$	1.62859e12			1.44615
$103$		−	4.90157e11i		−	0.410499i	−0.978710	−	0.205249i	$-0.934199\pi$
$103$		−	4.90157e11i		−	0.410499i	0.978710	−	0.205249i	$-0.0658006\pi$
$104$		−	5.11636e11i		−	0.404353i
$105$	2.40218e12	+	1.56663e12i	1.79254	+	1.16904i
$106$	1.60961e12			1.13471
$107$	−4.91858e11			−0.327746			−0.163873	−	0.986481i	$-0.552399\pi$
$107$	−4.91858e11			−0.327746			−0.163873	+	0.986481i	$0.552399\pi$
$108$			2.93055e11i			0.184675i
$109$	−3.39847e11			−0.202639			−0.101320	−	0.994854i	$-0.532307\pi$
$109$	−3.39847e11			−0.202639			−0.101320	+	0.994854i	$0.532307\pi$
$110$			2.95649e12i			1.66886i
$111$		−	6.05349e11i		−	0.323644i
$112$	−1.09290e12	−	7.12755e11i	−0.553695	−	0.361104i
$113$	−3.33025e12			−1.59958			−0.799791	−	0.600278i	$-0.795057\pi$
$113$	−3.33025e12			−1.59958			−0.799791	+	0.600278i	$0.795057\pi$
$114$	−5.87123e12			−2.67485
$115$		−	3.07805e12i		−	1.33073i
$116$	1.10645e12			0.454133
$117$		−	7.39590e11i		−	0.288321i
$118$			6.65152e12i			2.46393i
$119$	−9.18803e11	+	1.40884e12i	−0.323549	+	0.496111i
$120$	9.57324e12			3.20606
$121$	−1.76899e12			−0.563656
$122$		−	4.80483e12i		−	1.45720i
$123$	4.06168e12			1.17294
$124$		−	4.80000e12i		−	1.32042i
$125$			1.21708e12i			0.319049i
$126$	−6.07859e12	−	3.96428e12i	−1.51908	−	0.990698i
$127$	4.99992e12			1.19163			0.595814	−	0.803123i	$-0.296830\pi$
$127$	4.99992e12			1.19163			0.595814	+	0.803123i	$0.296830\pi$
$128$	8.04729e12			1.82974
$129$			1.10476e13i			2.39734i
$130$	−3.29141e12			−0.681902
$131$		−	1.90805e12i		−	0.377539i	−0.982021	−	0.188770i	$-0.939550\pi$
$131$		−	1.90805e12i		−	0.377539i	0.982021	−	0.188770i	$-0.0604499\pi$
$132$		−	9.45952e12i		−	1.78824i
$133$	3.31237e12	−	5.07898e12i	0.598451	−	0.917629i
$134$	−1.34083e13			−2.31603
$135$	8.83742e11			0.145990
$136$			5.61455e12i			0.887322i
$137$	4.10693e12			0.621146			0.310573	−	0.950550i	$-0.399479\pi$
$137$	4.10693e12			0.621146			0.310573	+	0.950550i	$0.399479\pi$
$138$			1.50803e13i			2.18341i
$139$		−	1.32224e13i		−	1.83325i	−0.399743	−	0.916627i	$-0.630901\pi$
$139$		−	1.32224e13i		−	1.83325i	0.399743	−	0.916627i	$-0.369099\pi$
$140$	−1.15216e13	+	1.76666e13i	−1.53019	+	2.34630i
$141$	−1.77411e13			−2.25770
$142$	1.34359e13			1.63885
$143$			1.52457e12i			0.178291i
$144$	−6.29597e12			−0.706135
$145$		−	3.33662e12i		−	0.359004i
$146$			1.23420e13i			1.27429i
$147$	1.32794e13	−	5.85071e12i	1.31606	−	0.579835i
$148$	4.45198e12			0.423626
$149$	−3.14929e11			−0.0287802			−0.0143901	−	0.999896i	$-0.504581\pi$
$149$	−3.14929e11			−0.0287802			−0.0143901	+	0.999896i	$0.504581\pi$
$150$		−	3.37742e13i		−	2.96509i
$151$	1.14143e13			0.962915			0.481458	−	0.876469i	$-0.340108\pi$
$151$	1.14143e13			0.962915			0.481458	+	0.876469i	$0.340108\pi$
$152$		−	2.02409e13i		−	1.64123i
$153$			8.11605e12i			0.632698i
$154$	1.25302e13	+	8.17185e12i	0.939365	+	0.612627i
$155$	−1.44749e13			−1.04382
$156$	1.05311e13			0.730680
$157$			1.92523e13i			1.28553i	0.766062	+	0.642767i	$0.222214\pi$
$157$			1.92523e13i			1.28553i	−0.766062	+	0.642767i	$0.777786\pi$
$158$	−1.33192e13			−0.856123
$159$			1.55306e13i			0.961182i
$160$		−	9.38277e12i		−	0.559257i
$161$	−1.30454e13	−	8.50784e12i	−0.749036	−	0.488500i
$162$	2.84517e13			1.57405
$163$	−1.23076e13			−0.656217			−0.328109	−	0.944640i	$-0.606411\pi$
$163$	−1.23076e13			−0.656217			−0.328109	+	0.944640i	$0.606411\pi$
$164$			2.98712e13i			1.53529i
$165$	−2.85262e13			−1.41365
$166$		−	1.62127e13i		−	0.774830i
$167$			2.20066e13i			1.01451i	0.861797	+	0.507253i	$0.169339\pi$
$167$			2.20066e13i			1.01451i	−0.861797	+	0.507253i	$0.830661\pi$
$168$	2.64608e13	−	4.05734e13i	1.17692	−	1.80462i
$169$	2.16008e13			0.927150
$170$	3.61190e13			1.49638
$171$		−	2.92591e13i		−	1.17026i
$172$	−8.12486e13			−3.13794
$173$		−	9.88290e12i		−	0.368644i	−0.982866	−	0.184322i	$-0.940991\pi$
$173$		−	9.88290e12i		−	0.368644i	0.982866	−	0.184322i	$-0.0590090\pi$
$174$			1.63471e13i			0.589042i
$175$	2.92169e13	+	1.90544e13i	1.01720	+	0.663387i
$176$	1.29783e13			0.436659
$177$	−6.41785e13			−2.08713
$178$		−	3.06603e13i		−	0.963954i
$179$	5.94852e12			0.180838			0.0904192	−	0.995904i	$-0.471179\pi$
$179$	5.94852e12			0.180838			0.0904192	+	0.995904i	$0.471179\pi$
$180$			1.01774e14i			2.99227i
$181$			2.25728e13i			0.641969i	0.947085	+	0.320984i	$0.104014\pi$
$181$			2.25728e13i			0.641969i	−0.947085	+	0.320984i	$0.895986\pi$
$182$	−9.09758e12	+	1.39497e13i	−0.250321	+	0.383828i
$183$	4.63603e13			1.23435
$184$	−5.19890e13			−1.33969
$185$		−	1.34254e13i		−	0.334887i
$186$	7.09171e13			1.71267
$187$		−	1.67302e13i		−	0.391247i
$188$		−	1.30475e14i		−	2.95516i
$189$	2.44270e12	−	3.74548e12i	0.0535918	−	0.0821745i
$190$	−1.30212e14			−2.76777
$191$	3.35988e13			0.692027			0.346013	−	0.938230i	$-0.387535\pi$
$191$	3.35988e13			0.692027			0.346013	+	0.938230i	$0.387535\pi$
$192$			9.35939e13i			1.86827i
$193$	1.15361e13			0.223212			0.111606	−	0.993753i	$-0.464401\pi$
$193$	1.15361e13			0.223212			0.111606	+	0.993753i	$0.464401\pi$
$194$		−	8.51214e13i		−	1.59672i
$195$		−	3.17578e13i		−	0.577620i
$196$	4.30284e13	+	9.76621e13i	0.758960	+	1.72262i
$197$	4.77036e13			0.816120			0.408060	−	0.912955i	$-0.366205\pi$
$197$	4.77036e13			0.816120			0.408060	+	0.912955i	$0.366205\pi$
$198$	7.21843e13			1.19799
$199$		−	4.23415e13i		−	0.681785i	−0.940102	−	0.340893i	$-0.889271\pi$
$199$		−	4.23415e13i		−	0.681785i	0.940102	−	0.340893i	$-0.110729\pi$
$200$	1.16436e14			1.81931
$201$		−	1.29373e14i		−	1.96185i
$202$			1.09442e14i			1.61093i
$203$	−1.41413e13	−	9.22255e12i	−0.202075	−	0.131788i
$204$	−1.15566e14			−1.60342
$205$	9.00801e13			1.21368
$206$			5.32590e13i			0.696930i
$207$	−7.51522e13			−0.955256
$208$			1.44486e13i			0.178420i
$209$			6.03137e13i			0.723667i
$210$	−2.61013e14	−	1.70225e14i	−3.04331	−	1.98476i
$211$	3.09776e13			0.351037			0.175519	−	0.984476i	$-0.443840\pi$
$211$	3.09776e13			0.351037			0.175519	+	0.984476i	$0.443840\pi$
$212$	−1.14218e14			−1.25811
$213$			1.29639e14i			1.38822i
$214$	5.34438e13			0.556435
$215$			2.45014e14i			2.48062i
$216$		−	1.49266e13i		−	0.146974i
$217$	−4.00093e13	+	6.13478e13i	−0.383180	+	0.587545i
$218$	3.69267e13			0.344034
$219$	−1.19084e14			−1.07942
$220$		−	2.09793e14i		−	1.85036i
$221$	1.86254e13			0.159865
$222$			6.57753e13i			0.549471i
$223$		−	2.37590e14i		−	1.93196i	−0.258613	−	0.965981i	$-0.583266\pi$
$223$		−	2.37590e14i		−	1.93196i	0.258613	−	0.965981i	$-0.416734\pi$
$224$	−3.97662e13	−	2.59343e13i	−0.314793	−	0.205299i
$225$	1.68313e14			1.29725
$226$	3.61855e14			2.71571
$227$		−	2.56461e14i		−	1.87442i	−0.348772	−	0.937208i	$-0.613401\pi$
$227$		−	2.56461e14i		−	1.87442i	0.348772	−	0.937208i	$-0.386599\pi$
$228$	4.16624e14			2.96575
$229$			8.45082e13i			0.585984i	0.956115	+	0.292992i	$0.0946510\pi$
$229$			8.45082e13i			0.585984i	−0.956115	+	0.292992i	$0.905349\pi$
$230$			3.34451e14i			2.25926i
$231$	−7.88476e13	+	1.20900e14i	−0.518939	+	0.795711i
$232$	−5.63564e13			−0.361423
$233$	−2.69656e14			−1.68529			−0.842645	−	0.538470i	$-0.819003\pi$
$233$	−2.69656e14			−1.68529			−0.842645	+	0.538470i	$0.819003\pi$
$234$			8.03616e13i			0.489501i
$235$	−3.93462e14			−2.33613
$236$		−	4.71994e14i		−	2.73190i
$237$		−	1.28513e14i		−	0.725199i
$238$	9.98343e13	−	1.53080e14i	0.549311	−	0.842280i
$239$	2.10380e14			1.12880			0.564399	−	0.825502i	$-0.309108\pi$
$239$	2.10380e14			1.12880			0.564399	+	0.825502i	$0.309108\pi$
$240$	−2.70347e14			−1.41467
$241$			2.37000e13i			0.120961i	0.998169	+	0.0604805i	$0.0192633\pi$
$241$			2.37000e13i			0.120961i	−0.998169	+	0.0604805i	$0.980737\pi$
$242$	1.92214e14			0.956956
$243$			2.94720e14i			1.43144i
$244$			3.40952e14i			1.61568i
$245$	2.94511e14	−	1.29757e14i	1.36177	−	0.599977i
$246$	−4.41330e14			−1.99137
$247$	−6.71463e13			−0.295692
$248$			2.44485e14i			1.05086i
$249$	1.56431e14			0.656338
$250$		−	1.32244e14i		−	0.541670i
$251$			1.21922e14i			0.487572i	0.969829	+	0.243786i	$0.0783894\pi$
$251$			1.21922e14i			0.487572i	−0.969829	+	0.243786i	$0.921611\pi$
$252$	4.31339e14	+	2.81307e14i	1.68428	+	1.09844i
$253$	1.54916e14			0.590710
$254$	−5.43276e14			−2.02310
$255$			3.48501e14i			1.26754i
$256$	−5.08730e14			−1.80737
$257$		−	5.52269e14i		−	1.91669i	−0.285613	−	0.958345i	$-0.592197\pi$
$257$		−	5.52269e14i		−	1.91669i	0.285613	−	0.958345i	$-0.407803\pi$
$258$		−	1.20040e15i		−	4.07012i
$259$	−5.68998e13	−	3.71084e13i	−0.188500	−	0.122935i
$260$	2.33559e14			0.756062
$261$	−8.14654e13			−0.257709
$262$			2.07323e14i			0.640973i
$263$	1.09419e14			0.330641			0.165321	−	0.986240i	$-0.447134\pi$
$263$	1.09419e14			0.330641			0.165321	+	0.986240i	$0.447134\pi$
$264$			4.81816e14i			1.42317i
$265$			3.44438e14i			0.994571i
$266$	−3.59911e14	+	5.51867e14i	−1.01603	+	1.55792i
$267$	2.95832e14			0.816539
$268$	9.51457e14			2.56791
$269$		−	3.94590e14i		−	1.04144i	−0.853729	−	0.520718i	$-0.825664\pi$
$269$		−	3.94590e14i		−	1.04144i	0.853729	−	0.520718i	$-0.174336\pi$
$270$	−9.60246e13			−0.247856
$271$			1.46417e14i			0.369638i	0.982773	+	0.184819i	$0.0591698\pi$
$271$			1.46417e14i			0.369638i	−0.982773	+	0.184819i	$0.940830\pi$
$272$		−	1.58554e14i		−	0.391530i
$273$	−1.34596e14	−	8.77797e13i	−0.325130	−	0.212040i
$274$	−4.46246e14			−1.05456
$275$	−3.46955e14			−0.802189
$276$		−	1.07010e15i		−	2.42087i
$277$	−8.96979e14			−1.98565			−0.992827	−	0.119559i	$-0.961852\pi$
$277$	−8.96979e14			−1.98565			−0.992827	+	0.119559i	$0.961852\pi$
$278$			1.43671e15i			3.11243i
$279$			3.53413e14i			0.749304i
$280$	5.86848e14	−	8.99837e14i	1.21780	−	1.86731i
$281$	5.68256e14			1.15427			0.577133	−	0.816650i	$-0.304171\pi$
$281$	5.68256e14			1.15427			0.577133	+	0.816650i	$0.304171\pi$
$282$	1.92769e15			3.83304
$283$			4.81105e14i			0.936530i	0.883588	+	0.468265i	$0.155121\pi$
$283$			4.81105e14i			0.936530i	−0.883588	+	0.468265i	$0.844879\pi$
$284$	−9.53419e14			−1.81708
$285$		−	1.25638e15i		−	2.34450i
$286$		−	1.65655e14i		−	0.302697i
$287$	2.48985e14	−	3.81779e14i	0.445535	−	0.683156i
$288$	−2.29085e14			−0.401460
$289$	3.78232e14			0.649189
$290$			3.62547e14i			0.609503i
$291$	8.21310e14			1.35254
$292$		−	8.75791e14i		−	1.41287i
$293$			4.87781e14i			0.770937i	0.922721	+	0.385469i	$0.125960\pi$
$293$			4.87781e14i			0.770937i	−0.922721	+	0.385469i	$0.874040\pi$
$294$	−1.44290e15	+	6.35720e14i	−2.23436	+	0.984423i
$295$	−1.42335e15			−2.15963
$296$	−2.26759e14			−0.337143
$297$			4.44782e13i			0.0648050i
$298$	3.42192e13			0.0488621
$299$			1.72466e14i			0.241366i
$300$			2.39663e15i			3.28756i
$301$	1.03842e15	+	6.77229e14i	1.39629	+	0.910618i
$302$	−1.24024e15			−1.63480
$303$	−1.05597e15			−1.36458
$304$			5.71602e14i			0.724190i
$305$	1.02818e15			1.27723
$306$		−	8.81865e14i		−	1.07417i
$307$		−	9.30882e14i		−	1.11190i	−0.831217	−	0.555949i	$-0.812355\pi$
$307$		−	9.30882e14i		−	1.11190i	0.831217	−	0.555949i	$-0.187645\pi$
$308$	−8.89148e14	−	5.79877e14i	−1.04153	−	0.679253i
$309$	−5.13879e14			−0.590351
$310$	1.57280e15			1.77216
$311$		−	3.43906e14i		−	0.380082i	−0.981776	−	0.190041i	$-0.939138\pi$
$311$		−	3.43906e14i		−	0.380082i	0.981776	−	0.190041i	$-0.0608620\pi$
$312$	−5.36397e14			−0.581512
$313$			1.12089e15i			1.19206i	0.802962	+	0.596030i	$0.203256\pi$
$313$			1.12089e15i			1.19206i	−0.802962	+	0.596030i	$0.796744\pi$
$314$		−	2.09189e15i		−	2.18253i
$315$	8.48312e14	−	1.30075e15i	0.868345	−	1.33147i
$316$	9.45136e14			0.949230
$317$	6.80310e14			0.670427			0.335214	−	0.942142i	$-0.391192\pi$
$317$	6.80310e14			0.670427			0.335214	+	0.942142i	$0.391192\pi$
$318$		−	1.68751e15i		−	1.63186i
$319$	1.67930e14			0.159362
$320$			2.07573e15i			1.93317i
$321$			5.15662e14i			0.471341i
$322$	1.41748e15	+	9.24436e14i	1.27169	+	0.829357i
$323$	7.36844e14			0.648874
$324$	−2.01894e15			−1.74523
$325$		−	3.86259e14i		−	0.327777i
$326$	1.33731e15			1.11410
$327$			3.56294e14i			0.291422i
$328$		−	1.52148e15i		−	1.22186i
$329$	−1.08755e15	+	1.66758e15i	−0.857575	+	1.31495i
$330$	3.09957e15			2.40004
$331$	−1.48816e15			−1.13157			−0.565785	−	0.824553i	$-0.691427\pi$
$331$	−1.48816e15			−1.13157			−0.565785	+	0.824553i	$0.691427\pi$
$332$			1.15046e15i			0.859097i
$333$	−3.27789e14			−0.240397
$334$		−	2.39117e15i		−	1.72239i
$335$		−	2.86923e15i		−	2.03000i
$336$	−7.47250e14	+	1.14579e15i	−0.519315	+	0.796286i
$337$	−9.38277e14			−0.640548			−0.320274	−	0.947325i	$-0.603775\pi$
$337$	−9.38277e14			−0.640548			−0.320274	+	0.947325i	$0.603775\pi$
$338$	−2.34708e15			−1.57408
$339$			3.49143e15i			2.30041i
$340$	−2.56301e15			−1.65912
$341$		−	7.28515e14i		−	0.463353i
$342$			3.17920e15i			1.98683i
$343$	2.64102e14	−	1.60685e15i	0.162184	−	0.986761i
$344$	4.13835e15			2.49734
$345$	−3.22702e15			−1.91376
$346$			1.07385e15i			0.625871i
$347$	−5.02825e14			−0.288031			−0.144016	−	0.989575i	$-0.546002\pi$
$347$	−5.02825e14			−0.288031			−0.144016	+	0.989575i	$0.546002\pi$
$348$		−	1.16000e15i		−	0.653103i
$349$			3.81292e14i			0.211011i	0.994419	+	0.105506i	$0.0336461\pi$
$349$			3.81292e14i			0.211011i	−0.994419	+	0.105506i	$0.966354\pi$
$350$	−3.17461e15	−	2.07039e15i	−1.72696	−	1.12627i
$351$	−4.95169e13			−0.0264795
$352$	4.72230e14			0.248255
$353$		−	4.76560e14i		−	0.246303i	−0.992388	−	0.123151i	$-0.960700\pi$
$353$		−	4.76560e14i		−	0.246303i	0.992388	−	0.123151i	$-0.0393001\pi$
$354$	6.97344e15			3.54346
$355$			2.87514e15i			1.43645i
$356$			2.17566e15i			1.06879i
$357$	1.47702e15	+	9.63270e14i	0.713473	+	0.465306i
$358$	−6.46348e14			−0.307021
$359$	3.34600e15			1.56300			0.781501	−	0.623905i	$-0.214455\pi$
$359$	3.34600e15			1.56300			0.781501	+	0.623905i	$0.214455\pi$
$360$		−	5.18380e15i		−	2.38140i
$361$	−4.43073e14			−0.200185
$362$		−	2.45269e15i		−	1.08991i
$363$			1.85461e15i			0.810611i
$364$	6.45567e14	−	9.89874e14i	0.277545	−	0.425571i
$365$	−2.64105e15			−1.11691
$366$	−5.03736e15			−2.09564
$367$		−	2.05536e15i		−	0.841186i	−0.907249	−	0.420593i	$-0.861822\pi$
$367$		−	2.05536e15i		−	0.841186i	0.907249	−	0.420593i	$-0.138178\pi$
$368$	1.46817e15			0.591137
$369$		−	2.19936e15i		−	0.871239i
$370$			1.45877e15i			0.568559i
$371$	1.45980e15	+	9.52040e14i	0.559822	+	0.365100i
$372$	−5.03230e15			−1.89893
$373$	−7.10343e14			−0.263764			−0.131882	−	0.991265i	$-0.542102\pi$
$373$	−7.10343e14			−0.263764			−0.131882	+	0.991265i	$0.542102\pi$
$374$			1.81785e15i			0.664245i
$375$	1.27598e15			0.458834
$376$			6.64569e15i			2.35187i
$377$			1.86954e14i			0.0651158i
$378$	−2.65416e14	+	4.06973e14i	−0.0909863	+	0.139513i
$379$	1.76573e15			0.595785			0.297892	−	0.954599i	$-0.403716\pi$
$379$	1.76573e15			0.595785			0.297892	+	0.954599i	$0.403716\pi$
$380$	9.23989e15			3.06878
$381$		−	5.24190e15i		−	1.71372i
$382$	−3.65074e15			−1.17490
$383$		−	4.12262e14i		−	0.130611i	−0.997865	−	0.0653056i	$-0.979198\pi$
$383$		−	4.12262e14i		−	0.130611i	0.997865	−	0.0653056i	$-0.0208022\pi$
$384$		−	8.43675e15i		−	2.63141i
$385$	−1.74868e15	+	2.68133e15i	−0.536966	+	0.823352i
$386$	−1.25348e15			−0.378961
$387$	5.98215e15			1.78070
$388$			6.04024e15i			1.77037i
$389$	6.16527e15			1.77932			0.889661	−	0.456622i	$-0.150941\pi$
$389$	6.16527e15			1.77932			0.889661	+	0.456622i	$0.150941\pi$
$390$			3.45070e15i			0.980663i
$391$		−	1.89259e15i		−	0.529659i
$392$	−2.19163e15	−	4.97437e15i	−0.604020	−	1.37095i
$393$	−2.00039e15			−0.542950
$394$	−5.18333e15			−1.38558
$395$		−	2.85016e15i		−	0.750390i
$396$	−5.12222e15			−1.32827
$397$			8.72469e14i			0.222847i	0.993773	+	0.111424i	$0.0355410\pi$
$397$			8.72469e14i			0.222847i	−0.993773	+	0.111424i	$0.964459\pi$
$398$			4.60070e15i			1.15751i
$399$	−5.32479e15	−	3.47267e15i	−1.31967	−	0.860650i
$400$	−3.28814e15			−0.802769
$401$	1.45325e15			0.349523			0.174761	−	0.984611i	$-0.444085\pi$
$401$	1.45325e15			0.349523			0.174761	+	0.984611i	$0.444085\pi$
$402$			1.40572e16i			3.33076i
$403$	8.11044e14			0.189328
$404$		−	7.76606e15i		−	1.78613i
$405$			6.08833e15i			1.37965i
$406$	1.53655e15	+	1.00209e15i	0.343076	+	0.223744i
$407$	6.75695e14			0.148657
$408$	5.88627e15			1.27608
$409$		−	5.01466e15i		−	1.07128i	−0.844448	−	0.535638i	$-0.820071\pi$
$409$		−	5.01466e15i		−	1.07128i	0.844448	−	0.535638i	$-0.179929\pi$
$410$	−9.78783e15			−2.06055
$411$		−	4.30569e15i		−	0.893288i
$412$		−	3.77927e15i		−	0.772725i
$413$	−3.93420e15	+	6.03246e15i	−0.792786	+	1.21561i
$414$	8.16581e15			1.62180
$415$	3.46933e15			0.679137
$416$			5.25725e14i			0.101438i
$417$	−1.38624e16			−2.63646
$418$		−	6.55350e15i		−	1.22862i
$419$		−	1.56282e15i		−	0.288819i	−0.989518	−	0.144410i	$-0.953872\pi$
$419$		−	1.56282e15i		−	0.288819i	0.989518	−	0.144410i	$-0.0461283\pi$
$420$	1.85216e16	+	1.20792e16i	3.37429	+	2.20061i
$421$	7.16312e15			1.28650			0.643249	−	0.765657i	$-0.277586\pi$
$421$	7.16312e15			1.28650			0.643249	+	0.765657i	$0.277586\pi$
$422$	−3.36593e15			−0.595979
$423$			9.60660e15i			1.67698i
$424$	5.81765e15			1.00127
$425$			4.23870e15i			0.719282i
$426$		−	1.40862e16i		−	2.35687i
$427$	2.84193e15	−	4.35764e15i	0.468862	−	0.718926i
$428$	−3.79239e15			−0.616950
$429$	1.59835e15			0.256406
$430$		−	2.66225e16i		−	4.21151i
$431$	−5.80586e15			−0.905739			−0.452869	−	0.891577i	$-0.649600\pi$
$431$	−5.80586e15			−0.905739			−0.452869	+	0.891577i	$0.649600\pi$
$432$			4.21527e14i			0.0648519i
$433$			2.32511e15i			0.352790i	0.984319	+	0.176395i	$0.0564436\pi$
$433$			2.32511e15i			0.352790i	−0.984319	+	0.176395i	$0.943556\pi$
$434$	4.34728e15	−	6.66587e15i	0.650549	−	0.997512i
$435$	−3.49810e15			−0.516294
$436$	−2.62033e15			−0.381449
$437$			6.82296e15i			0.979680i
$438$	1.29393e16			1.83259
$439$			9.39452e15i			1.31246i	0.754559	+	0.656232i	$0.227851\pi$
$439$			9.39452e15i			1.31246i	−0.754559	+	0.656232i	$0.772149\pi$
$440$			1.06857e16i			1.47261i
$441$	−3.16809e15	−	7.19065e15i	−0.430691	−	0.977545i
$442$	−2.02378e15			−0.271413
$443$	−1.29412e16			−1.71218			−0.856092	−	0.516823i	$-0.827115\pi$
$443$	−1.29412e16			−1.71218			−0.856092	+	0.516823i	$0.827115\pi$
$444$		−	4.66744e15i		−	0.609229i
$445$	6.56096e15			0.844904
$446$			2.58158e16i			3.28002i
$447$			3.30170e14i			0.0413897i
$448$	8.79737e15	+	5.73739e15i	1.08814	+	0.709654i
$449$	7.13603e15			0.870921			0.435460	−	0.900208i	$-0.356586\pi$
$449$	7.13603e15			0.870921			0.435460	+	0.900208i	$0.356586\pi$
$450$	−1.82884e16			−2.20242
$451$			4.53368e15i			0.538756i
$452$	−2.56773e16			−3.01106
$453$		−	1.19667e16i		−	1.38480i
$454$			2.78662e16i			3.18232i
$455$	−2.98508e15	−	1.94678e15i	−0.336424	−	0.219406i
$456$	−2.12205e16			−2.36030
$457$	1.06628e16			1.17051			0.585254	−	0.810850i	$-0.300995\pi$
$457$	1.06628e16			1.17051			0.585254	+	0.810850i	$0.300995\pi$
$458$		−	9.18240e15i		−	0.994864i
$459$	5.43384e14			0.0581073
$460$		−	2.37328e16i		−	2.50496i
$461$		−	1.26948e16i		−	1.32258i	−0.750132	−	0.661288i	$-0.770010\pi$
$461$		−	1.26948e16i		−	1.32258i	0.750132	−	0.661288i	$-0.229990\pi$
$462$	8.56734e15	−	1.31366e16i	0.881037	−	1.35093i
$463$	−8.25194e15			−0.837664			−0.418832	−	0.908064i	$-0.637560\pi$
$463$	−8.25194e15			−0.837664			−0.418832	+	0.908064i	$0.637560\pi$
$464$	1.59150e15			0.159477
$465$			1.51755e16i			1.50115i
$466$	2.93000e16			2.86122
$467$		−	4.00512e15i		−	0.386113i	−0.981188	−	0.193057i	$-0.938160\pi$
$467$		−	4.00512e15i		−	0.386113i	0.981188	−	0.193057i	$-0.0618401\pi$
$468$		−	5.70248e15i		−	0.542736i
$469$	−1.21604e16	−	7.93065e15i	−1.14264	−	0.745198i
$470$	4.27524e16			3.96619
$471$	2.01840e16			1.84877
$472$			2.40408e16i			2.17419i
$473$	−1.23314e16			−1.10115
$474$			1.39638e16i			1.23122i
$475$		−	1.52809e16i		−	1.33041i
$476$	−7.08427e15	+	1.08626e16i	−0.609051	+	0.933882i
$477$	8.40964e15			0.713949
$478$	−2.28592e16			−1.91643
$479$		−	8.38590e15i		−	0.694283i	−0.937813	−	0.347142i	$-0.887152\pi$
$479$		−	8.38590e15i		−	0.694283i	0.937813	−	0.347142i	$-0.112848\pi$
$480$	−9.83686e15			−0.804284
$481$			7.52239e14i			0.0607415i
$482$		−	2.57516e15i		−	0.205363i
$483$	−8.91960e15	+	1.36768e16i	−0.702526	+	1.07721i
$484$	−1.36395e16			−1.06103
$485$	1.82150e16			1.39952
$486$		−	3.20234e16i		−	2.43024i
$487$	1.22862e16			0.920965			0.460482	−	0.887669i	$-0.347676\pi$
$487$	1.22862e16			0.920965			0.460482	+	0.887669i	$0.347676\pi$
$488$		−	1.73662e16i		−	1.28584i
$489$			1.29032e16i			0.943725i
$490$	−3.20007e16	+	1.40990e16i	−2.31197	+	1.01862i
$491$	−2.40564e15			−0.171689			−0.0858444	−	0.996309i	$-0.527359\pi$
$491$	−2.40564e15			−0.171689			−0.0858444	+	0.996309i	$0.527359\pi$
$492$	3.13169e16			2.20795
$493$		−	2.05158e15i		−	0.142892i
$494$	7.29591e15			0.502016
$495$			1.54466e16i			1.05003i
$496$		−	6.90425e15i		−	0.463688i
$497$	1.21855e16	+	7.94700e15i	0.808544	+	0.527309i
$498$	−1.69973e16			−1.11431
$499$	−1.38752e16			−0.898747			−0.449373	−	0.893344i	$-0.648353\pi$
$499$	−1.38752e16			−0.898747			−0.449373	+	0.893344i	$0.648353\pi$
$500$			9.38405e15i			0.600579i
$501$	2.30717e16			1.45899
$502$		−	1.32476e16i		−	0.827782i
$503$			2.13753e16i			1.31979i	0.751358	+	0.659895i	$0.229399\pi$
$503$			2.13753e16i			1.31979i	−0.751358	+	0.659895i	$0.770601\pi$
$504$	−2.19700e16	−	1.43282e16i	−1.34044	−	0.874196i
$505$	−2.34194e16			−1.41198
$506$	−1.68327e16			−1.00289
$507$		−	2.26462e16i		−	1.33336i
$508$	3.85510e16			2.24313
$509$		−	2.46667e16i		−	1.41842i	−0.704997	−	0.709210i	$-0.749052\pi$
$509$		−	2.46667e16i		−	1.41842i	0.704997	−	0.709210i	$-0.250948\pi$
$510$		−	3.78670e16i		−	2.15199i
$511$	−7.29996e15	+	1.11933e16i	−0.410010	+	0.628685i
$512$	2.23153e16			1.23875
$513$	−1.95895e15			−0.107478
$514$			6.00078e16i			3.25409i
$515$	−1.13968e16			−0.610858
$516$			8.51807e16i			4.51277i
$517$		−	1.98027e16i		−	1.03701i
$518$	6.18256e15	+	4.03209e15i	0.320029	+	0.208714i
$519$	−1.03612e16			−0.530159
$520$	−1.18962e16			−0.601713
$521$			8.97454e15i			0.448731i	0.974505	+	0.224365i	$0.0720309\pi$
$521$			8.97454e15i			0.448731i	−0.974505	+	0.224365i	$0.927969\pi$
$522$	8.85178e15			0.437530
$523$		−	1.42563e16i		−	0.696622i	−0.937379	−	0.348311i	$-0.886755\pi$
$523$		−	1.42563e16i		−	0.696622i	0.937379	−	0.348311i	$-0.113245\pi$
$524$		−	1.47117e16i		−	0.710681i
$525$	1.99766e16	−	3.06309e16i	0.954036	−	1.46286i
$526$	−1.18891e16			−0.561351
$527$	−8.90017e15			−0.415465
$528$		−	1.36064e16i		−	0.627973i
$529$	−4.38978e15			−0.200313
$530$		−	3.74256e16i		−	1.68855i
$531$			3.47519e16i			1.55028i
$532$	2.55394e16	−	3.91606e16i	1.12653	−	1.72735i
$533$	−5.04727e15			−0.220137
$534$	−3.21442e16			−1.38629
$535$			1.14364e16i			0.487714i
$536$	−4.84620e16			−2.04368
$537$		−	6.23641e15i		−	0.260069i
$538$			4.28750e16i			1.76811i
$539$	6.53060e15	+	1.48226e16i	0.266330	+	0.604493i
$540$	6.81394e15			0.274812
$541$	1.21619e16			0.485086			0.242543	−	0.970141i	$-0.422019\pi$
$541$	1.21619e16			0.485086			0.242543	+	0.970141i	$0.422019\pi$
$542$		−	1.59092e16i		−	0.627558i
$543$	2.36652e16			0.923234
$544$		−	5.76916e15i		−	0.222597i
$545$			7.90190e15i			0.301545i
$546$	1.46248e16	+	9.53788e15i	0.551994	+	0.359994i
$547$	1.94006e16			0.724256			0.362128	−	0.932128i	$-0.382050\pi$
$547$	1.94006e16			0.724256			0.362128	+	0.932128i	$0.382050\pi$
$548$	3.16657e16			1.16925
$549$		−	2.51035e16i		−	0.916856i
$550$	3.76991e16			1.36193
$551$			7.39612e15i			0.264298i
$552$			5.45051e16i			1.92665i
$553$	−1.20796e16	−	7.87796e15i	−0.422378	−	0.275463i
$554$	9.74630e16			3.37117
$555$	−1.40752e16			−0.481611
$556$		−	1.01949e17i		−	3.45092i
$557$	7.86285e15			0.263299			0.131649	−	0.991296i	$-0.457973\pi$
$557$	7.86285e15			0.263299			0.131649	+	0.991296i	$0.457973\pi$
$558$		−	3.84008e16i		−	1.27214i
$559$		−	1.37284e16i		−	0.449933i
$560$	−1.65725e16	+	2.54113e16i	−0.537354	+	0.823947i
$561$	−1.75399e16			−0.562664
$562$	−6.17450e16			−1.95967
$563$		−	3.67350e16i		−	1.15353i	−0.816910	−	0.576766i	$-0.804315\pi$
$563$		−	3.67350e16i		−	1.15353i	0.816910	−	0.576766i	$-0.195685\pi$
$564$	−1.36790e17			−4.24990
$565$			7.74329e16i			2.38032i
$566$		−	5.22754e16i		−	1.59001i
$567$	2.58037e16	+	1.68284e16i	0.776574	+	0.506459i
$568$	4.85619e16			1.44612
$569$	−2.12670e16			−0.626661			−0.313331	−	0.949644i	$-0.601445\pi$
$569$	−2.12670e16			−0.626661			−0.313331	+	0.949644i	$0.601445\pi$
$570$			1.36514e17i			3.98041i
$571$	−1.45840e16			−0.420786			−0.210393	−	0.977617i	$-0.567474\pi$
$571$	−1.45840e16			−0.420786			−0.210393	+	0.977617i	$0.567474\pi$
$572$			1.17549e16i			0.335616i
$573$		−	3.52248e16i		−	0.995225i
$574$	−2.70539e16	+	4.14829e16i	−0.756413	+	1.15984i
$575$	−3.92491e16			−1.08598
$576$	5.06800e16			1.38772
$577$			3.74881e16i			1.01587i	0.861395	+	0.507935i	$0.169591\pi$
$577$			3.74881e16i			1.01587i	−0.861395	+	0.507935i	$0.830409\pi$
$578$	−4.10975e16			−1.10217
$579$		−	1.20945e16i		−	0.321007i
$580$		−	2.57264e16i		−	0.675790i
$581$	9.58937e15	−	1.47038e16i	0.249306	−	0.382272i
$582$	−8.92410e16			−2.29629
$583$	−1.73354e16			−0.441491
$584$			4.46080e16i			1.12444i
$585$	−1.71965e16			−0.429046
$586$		−	5.30008e16i		−	1.30887i
$587$			2.44373e16i			0.597343i	0.954356	+	0.298672i	$0.0965435\pi$
$587$			2.44373e16i			0.597343i	−0.954356	+	0.298672i	$0.903456\pi$
$588$	1.02389e17	−	4.51109e16i	2.47735	−	1.09148i
$589$	3.20859e16			0.768462
$590$	1.54657e17			3.66655
$591$		−	5.00123e16i		−	1.17369i
$592$	6.40366e15			0.148764
$593$			7.85587e16i			1.80662i	0.428991	+	0.903309i	$0.358869\pi$
$593$			7.85587e16i			1.80662i	−0.428991	+	0.903309i	$0.641131\pi$
$594$		−	4.83287e15i		−	0.110024i
$595$	3.27574e16	+	2.13634e16i	0.738257	+	0.481470i
$596$	−2.42820e15			−0.0541761
$597$	−4.43907e16			−0.980496
$598$		−	1.87396e16i		−	0.409783i
$599$	1.28530e16			0.278256			0.139128	−	0.990274i	$-0.455570\pi$
$599$	1.28530e16			0.278256			0.139128	+	0.990274i	$0.455570\pi$
$600$		−	1.22071e17i		−	2.61641i
$601$		−	1.85101e16i		−	0.392791i	−0.980525	−	0.196395i	$-0.937076\pi$
$601$		−	1.85101e16i		−	0.392791i	0.980525	−	0.196395i	$-0.0629236\pi$
$602$	−1.12832e17	−	7.35856e16i	−2.37057	−	1.54602i
$603$	−7.00537e16			−1.45723
$604$	8.80081e16			1.81260
$605$			4.11315e16i			0.838769i
$606$	1.14739e17			2.31673
$607$		−	4.20346e16i		−	0.840377i	−0.907437	−	0.420189i	$-0.861964\pi$
$607$		−	4.20346e16i		−	0.840377i	0.907437	−	0.420189i	$-0.138036\pi$
$608$			2.07983e16i			0.411725i
$609$	−9.66889e15	+	1.48257e16i	−0.189528	+	0.290611i
$610$	−1.11719e17			−2.16844
$611$	2.20461e16			0.423725
$612$			6.25774e16i			1.19099i
$613$	5.33061e16			1.00465			0.502324	−	0.864679i	$-0.332478\pi$
$613$	5.33061e16			1.00465			0.502324	+	0.864679i	$0.332478\pi$
$614$			1.01147e17i			1.88774i
$615$		−	9.44397e16i		−	1.74544i
$616$	4.52883e16	+	2.95357e16i	0.828900	+	0.540584i
$617$	−1.35803e16			−0.246149			−0.123074	−	0.992397i	$-0.539275\pi$
$617$	−1.35803e16			−0.246149			−0.123074	+	0.992397i	$0.539275\pi$
$618$	5.58365e16			1.00228
$619$			1.28458e16i			0.228358i	0.993460	+	0.114179i	$0.0364237\pi$
$619$			1.28458e16i			0.228358i	−0.993460	+	0.114179i	$0.963576\pi$
$620$	−1.11606e17			−1.96489
$621$			5.03158e15i			0.0877313i
$622$			3.73677e16i			0.645289i
$623$	1.81347e16	−	2.78067e16i	0.310158	−	0.475578i
$624$	1.51478e16			0.256592
$625$	−4.40853e16			−0.739629
$626$		−	1.21793e17i		−	2.02384i
$627$	6.32327e16			1.04073
$628$			1.48441e17i			2.41989i
$629$		−	8.25487e15i		−	0.133293i
$630$	−9.21750e16	+	1.41336e17i	−1.47424	+	2.26052i
$631$	−7.93590e15			−0.125725			−0.0628623	−	0.998022i	$-0.520023\pi$
$631$	−7.93590e15			−0.125725			−0.0628623	+	0.998022i	$0.520023\pi$
$632$	−4.81400e16			−0.755446
$633$		−	3.24768e16i		−	0.504837i
$634$	−7.39204e16			−1.13823
$635$		−	1.16255e17i		−	1.77325i
$636$			1.19746e17i			1.80933i
$637$	−1.65017e16	+	7.27041e15i	−0.246998	+	0.108823i
$638$	−1.82468e16			−0.270559
$639$	7.01982e16			1.03115
$640$		−	1.87110e17i		−	2.72281i
$641$	−7.48894e16			−1.07962			−0.539811	−	0.841786i	$-0.681504\pi$
$641$	−7.48894e16			−1.07962			−0.539811	+	0.841786i	$0.681504\pi$
$642$		−	5.60303e16i		−	0.800226i
$643$			8.01964e16i			1.13472i	0.823470	+	0.567360i	$0.192035\pi$
$643$			8.01964e16i			1.13472i	−0.823470	+	0.567360i	$0.807965\pi$
$644$	−1.00584e17	−	6.55983e16i	−1.40999	−	0.919554i
$645$	2.56872e17			3.56745
$646$	−8.00632e16			−1.10164
$647$			1.11934e17i			1.52593i	0.646439	+	0.762966i	$0.276258\pi$
$647$			1.11934e17i			1.52593i	−0.646439	+	0.762966i	$0.723742\pi$
$648$	1.02834e17			1.38894
$649$		−	7.16365e16i		−	0.958663i
$650$			4.19697e16i			0.556488i
$651$	6.43169e16	+	4.19456e16i	0.844965	+	0.551062i
$652$	−9.48956e16			−1.23527
$653$	3.83393e16			0.494499			0.247250	−	0.968952i	$-0.420473\pi$
$653$	3.83393e16			0.494499			0.247250	+	0.968952i	$0.420473\pi$
$654$		−	3.87138e16i		−	0.494766i
$655$	−4.43648e16			−0.561811
$656$			4.29664e16i			0.539145i
$657$			6.44826e16i			0.801771i
$658$	1.18169e17	−	1.81194e17i	1.45596	−	2.23248i
$659$	1.23435e17			1.50705			0.753523	−	0.657422i	$-0.228353\pi$
$659$	1.23435e17			1.50705			0.753523	+	0.657422i	$0.228353\pi$
$660$	−2.19947e17			−2.66105
$661$			4.24258e16i			0.508652i	0.967119	+	0.254326i	$0.0818537\pi$
$661$			4.24258e16i			0.508652i	−0.967119	+	0.254326i	$0.918146\pi$
$662$	1.61699e17			1.92114
$663$		−	1.95268e16i		−	0.229906i
$664$		−	5.85980e16i		−	0.683713i
$665$	−1.18093e17	−	7.70170e16i	−1.36551	−	0.890547i
$666$	3.56166e16			0.408138
$667$	1.89970e16			0.215740
$668$			1.69678e17i			1.90971i
$669$	−2.49088e17			−2.77841
$670$			3.11761e17i			3.44646i
$671$			5.17477e16i			0.566964i
$672$	−2.71895e16	+	4.16907e16i	−0.295247	+	0.452714i
$673$	−7.15750e16			−0.770320			−0.385160	−	0.922850i	$-0.625854\pi$
$673$	−7.15750e16			−0.770320			−0.385160	+	0.922850i	$0.625854\pi$
$674$	1.01950e17			1.08750
$675$		−	1.12689e16i		−	0.119140i
$676$	1.66549e17			1.74527
$677$		−	5.18212e16i		−	0.538239i	−0.963107	−	0.269120i	$-0.913267\pi$
$677$		−	5.18212e16i		−	0.538239i	0.963107	−	0.269120i	$-0.0867327\pi$
$678$		−	3.79368e17i		−	3.90555i
$679$	5.03471e16	−	7.71992e16i	0.513754	−	0.787760i
$680$	1.30546e17			1.32041
$681$	−2.68873e17			−2.69565
$682$			7.91582e16i			0.786665i
$683$	9.10982e16			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$683$	9.10982e16			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$684$		−	2.25597e17i		−	2.20291i
$685$		−	9.54916e16i		−	0.924319i
$686$	−2.86965e16	+	1.74596e17i	−0.275350	+	1.67529i
$687$	8.85981e16			0.842722
$688$	−1.16867e17			−1.10195
$689$		−	1.92992e16i		−	0.180395i
$690$	3.50638e17			3.24911
$691$		−	1.65562e17i		−	1.52087i	−0.649413	−	0.760435i	$-0.724986\pi$
$691$		−	1.65562e17i		−	1.52087i	0.649413	−	0.760435i	$-0.275014\pi$
$692$		−	7.62004e16i		−	0.693938i
$693$	6.54661e16	+	4.26951e16i	0.591040	+	0.385459i
$694$	5.46354e16			0.489010
$695$	−3.07440e17			−2.72804
$696$			5.90839e16i			0.519773i
$697$	5.53874e16			0.483074
$698$		−	4.14301e16i		−	0.358247i
$699$			2.82706e17i			2.42367i
$700$	2.25272e17	+	1.46916e17i	1.91478	+	1.24876i
$701$	−6.62930e16			−0.558675			−0.279338	−	0.960193i	$-0.590115\pi$
$701$	−6.62930e16			−0.558675			−0.279338	+	0.960193i	$0.590115\pi$
$702$	5.38035e15			0.0449560
$703$			2.97595e16i			0.246544i
$704$	−1.04470e17			−0.858137
$705$			4.12505e17i			3.35965i
$706$			5.17815e16i			0.418164i
$707$	−6.47322e16	+	9.92565e16i	−0.518327	+	0.794772i
$708$	−4.94837e17			−3.92883
$709$	2.51430e17			1.97942			0.989712	−	0.143071i	$-0.0456978\pi$
$709$	2.51430e17			1.97942			0.989712	+	0.143071i	$0.0456978\pi$
$710$		−	3.12404e17i		−	2.43875i
$711$	−6.95883e16			−0.538665
$712$		−	1.10816e17i		−	0.850597i
$713$		−	8.24129e16i		−	0.627275i
$714$	−1.60489e17	−	1.04666e17i	−1.21131	−	0.789980i
$715$	3.54483e16			0.265313
$716$	4.58650e16			0.340411
$717$		−	2.20561e17i		−	1.62336i
$718$	−3.63566e17			−2.65361
$719$			1.47269e17i			1.06595i	0.846131	+	0.532976i	$0.178926\pi$
$719$			1.47269e17i			1.06595i	−0.846131	+	0.532976i	$0.821074\pi$
$720$			1.46390e17i			1.05079i
$721$	−3.15012e16	+	4.83021e16i	−0.224242	+	0.343839i
$722$	4.81430e16			0.339867
$723$	2.48470e16			0.173958
$724$			1.74044e17i			1.20844i
$725$	−4.25462e16			−0.292977
$726$		−	2.01516e17i		−	1.37623i
$727$		−	2.15669e17i		−	1.46077i	−0.683038	−	0.730383i	$-0.739342\pi$
$727$		−	2.15669e17i		−	1.46077i	0.683038	−	0.730383i	$-0.260658\pi$
$728$	−3.28816e16	+	5.04187e16i	−0.220884	+	0.338691i
$729$	1.69827e17			1.13146
$730$	2.86968e17			1.89625
$731$			1.50651e17i			0.987344i
$732$	3.57453e17			2.32355
$733$		−	5.23058e16i		−	0.337230i	−0.985682	−	0.168615i	$-0.946071\pi$
$733$		−	5.23058e16i		−	0.337230i	0.985682	−	0.168615i	$-0.0539295\pi$
$734$			2.23329e17i			1.42814i
$735$	−1.36037e17	−	3.08765e17i	−0.862845	−	1.95841i
$736$	5.34207e16			0.336080
$737$	1.44407e17			0.901119
$738$			2.38975e17i			1.47916i
$739$	−1.23421e17			−0.757741			−0.378871	−	0.925450i	$-0.623687\pi$
$739$	−1.23421e17			−0.757741			−0.378871	+	0.925450i	$0.623687\pi$
$740$		−	1.03514e17i		−	0.630392i
$741$			7.03959e16i			0.425244i
$742$	−1.58617e17	−	1.03446e17i	−0.950446	−	0.619853i
$743$	8.82572e16			0.524587			0.262293	−	0.964988i	$-0.415521\pi$
$743$	8.82572e16			0.524587			0.262293	+	0.964988i	$0.415521\pi$
$744$	2.56318e17			1.51127
$745$			7.32252e15i			0.0428275i
$746$	7.71837e16			0.447809
$747$		−	8.47057e16i		−	0.487516i
$748$		−	1.28995e17i		−	0.736485i
$749$	4.84697e16	+	3.16106e16i	0.274524	+	0.179036i
$750$	−1.38644e17			−0.778992
$751$	1.65761e17			0.923939			0.461969	−	0.886896i	$-0.347143\pi$
$751$	1.65761e17			0.923939			0.461969	+	0.886896i	$0.347143\pi$
$752$		−	1.87674e17i		−	1.03776i
$753$	1.27822e17			0.701192
$754$		−	2.03138e16i		−	0.110551i
$755$		−	2.65398e17i		−	1.43290i
$756$	1.88340e16	−	2.88789e16i	0.100881	−	0.154686i
$757$	1.51696e16			0.0806120			0.0403060	−	0.999187i	$-0.487167\pi$
$757$	1.51696e16			0.0806120			0.0403060	+	0.999187i	$0.487167\pi$
$758$	−1.91859e17			−1.01150
$759$		−	1.62414e17i		−	0.849518i
$760$	−4.70629e17			−2.44229
$761$		−	1.89084e16i		−	0.0973525i	−0.998815	−	0.0486762i	$-0.984500\pi$
$761$		−	1.89084e16i		−	0.0973525i	0.998815	−	0.0486762i	$-0.0155003\pi$
$762$			5.69569e17i			2.90949i
$763$	3.34899e16	+	2.18412e16i	0.169733	+	0.110695i
$764$	2.59057e17			1.30267
$765$	1.88709e17			0.941509
$766$			4.47951e16i			0.221747i
$767$	7.97517e16			0.391713
$768$			5.33351e17i			2.59923i
$769$			1.49855e17i			0.724623i	0.932057	+	0.362311i	$0.118012\pi$
$769$			1.49855e17i			0.724623i	−0.932057	+	0.362311i	$0.881988\pi$
$770$	1.90007e17	−	2.91345e17i	0.911642	−	1.39786i
$771$	−5.78997e17			−2.75645
$772$	8.89475e16			0.420175
$773$			2.05313e16i			0.0962366i	0.998842	+	0.0481183i	$0.0153225\pi$
$773$			2.05313e16i			0.0962366i	−0.998842	+	0.0481183i	$0.984678\pi$
$774$	−6.50003e17			−3.02322
$775$			1.84574e17i			0.851845i
$776$		−	3.07657e17i		−	1.40895i
$777$	−3.89043e16	+	5.96536e16i	−0.176796	+	0.271088i
$778$	−6.69899e17			−3.02087
$779$	−1.99676e17			−0.893514
$780$		−	2.44863e17i		−	1.08731i
$781$	−1.44704e17			−0.637639
$782$			2.05643e17i			0.899237i
$783$			5.45426e15i			0.0236682i
$784$	6.18915e16	+	1.40476e17i	0.266523	+	0.604930i
$785$	4.47641e17			1.91299
$786$	2.17357e17			0.921802
$787$			1.04119e17i			0.438210i	0.975701	+	0.219105i	$0.0703137\pi$
$787$			1.04119e17i			0.438210i	−0.975701	+	0.219105i	$0.929686\pi$
$788$	3.67810e17			1.53627
$789$		−	1.14714e17i		−	0.475505i
$790$			3.09690e17i			1.27399i
$791$	3.28177e17	+	2.14028e17i	1.33983	+	0.873798i
$792$	2.60898e17			1.05711
$793$	−5.76098e16			−0.231663
$794$		−	9.47998e16i		−	0.378342i
$795$	3.61108e17			1.43032
$796$		−	3.26467e17i		−	1.28340i
$797$		−	4.50891e17i		−	1.75922i	−0.475691	−	0.879612i	$-0.657802\pi$
$797$		−	4.50891e17i		−	1.75922i	0.475691	−	0.879612i	$-0.342198\pi$
$798$	5.78575e17	+	3.77330e17i	2.24049	+	1.46118i
$799$	−2.41927e17			−0.929832
$800$	−1.19642e17			−0.456400
$801$		−	1.60189e17i		−	0.606511i
$802$	−1.57906e17			−0.593407
$803$		−	1.32922e17i		−	0.495798i
$804$		−	9.97504e17i		−	3.69299i
$805$	−1.97819e17	+	3.03324e17i	−0.726930	+	1.11463i
$806$	−8.81255e16			−0.321434
$807$	−4.13687e17			−1.49772
$808$			3.95560e17i			1.42149i
$809$	−1.55381e17			−0.554250			−0.277125	−	0.960834i	$-0.589382\pi$
$809$	−1.55381e17			−0.554250			−0.277125	+	0.960834i	$0.589382\pi$
$810$		−	6.61540e17i		−	2.34232i
$811$			3.51222e17i			1.23440i	0.786806	+	0.617201i	$0.211733\pi$
$811$			3.51222e17i			1.23440i	−0.786806	+	0.617201i	$0.788267\pi$
$812$	−1.09034e17	−	7.11089e16i	−0.380387	−	0.248078i
$813$	1.53503e17			0.531587
$814$	−7.34189e16			−0.252384
$815$			2.86168e17i			0.976508i
$816$	−1.66228e17			−0.563071
$817$		−	5.43111e17i		−	1.82623i
$818$			5.44877e17i			1.81877i
$819$	−4.75317e16	+	7.28823e16i	−0.157500	+	0.241501i
$820$	6.94547e17			2.28464
$821$	−1.12917e17			−0.368723			−0.184362	−	0.982858i	$-0.559022\pi$
$821$	−1.12917e17			−0.368723			−0.184362	+	0.982858i	$0.559022\pi$
$822$			4.67843e17i			1.51659i
$823$	2.90624e17			0.935259			0.467630	−	0.883925i	$-0.345108\pi$
$823$	2.90624e17			0.935259			0.467630	+	0.883925i	$0.345108\pi$
$824$			1.92495e17i			0.614974i
$825$			3.63746e17i			1.15365i
$826$	4.27478e17	−	6.55469e17i	1.34596	−	2.06382i
$827$	−4.07036e17			−1.27233			−0.636164	−	0.771554i	$-0.719480\pi$
$827$	−4.07036e17			−1.27233			−0.636164	+	0.771554i	$0.719480\pi$
$828$	−5.79448e17			−1.79818
$829$		−	2.25156e17i		−	0.693676i	−0.937925	−	0.346838i	$-0.887255\pi$
$829$		−	2.25156e17i		−	0.693676i	0.937925	−	0.346838i	$-0.112745\pi$
$830$	−3.76967e17			−1.15301
$831$			9.40390e17i			2.85563i
$832$		−	1.16305e17i		−	0.350637i
$833$	1.81085e17	−	7.97835e16i	0.542018	−	0.238805i
$834$	1.50624e18			4.47608
$835$	5.11684e17			1.50967
$836$			4.65039e17i			1.36223i
$837$	2.36617e16			0.0688165
$838$			1.69812e17i			0.490347i
$839$		−	2.80993e17i		−	0.805607i	−0.915286	−	0.402804i	$-0.868036\pi$
$839$		−	2.80993e17i		−	0.805607i	0.915286	−	0.402804i	$-0.131964\pi$
$840$	−9.43387e17	−	6.15249e17i	−2.68543	−	1.75136i
$841$	−3.33222e17			−0.941798
$842$	−7.78322e17			−2.18417
$843$		−	5.95758e17i		−	1.65999i
$844$	2.38848e17			0.660794
$845$		−	5.02248e17i		−	1.37968i
$846$		−	1.04382e18i		−	2.84711i
$847$	1.74324e17	+	1.13689e17i	0.472125	+	0.307906i
$848$	−1.64290e17			−0.441810
$849$	5.04389e17			1.34685
$850$		−	4.60564e17i		−	1.22117i
$851$	7.64376e16			0.201247
$852$			9.99561e17i			2.61319i
$853$			3.22249e17i			0.836561i	0.908318	+	0.418281i	$0.137367\pi$
$853$			3.22249e17i			0.836561i	−0.908318	+	0.418281i	$0.862633\pi$
$854$	−3.08795e17	+	4.73488e17i	−0.796018	+	1.22057i
$855$	−6.80313e17			−1.74145
$856$	1.93163e17			0.491000
$857$		−	1.79668e17i		−	0.453508i	−0.973952	−	0.226754i	$-0.927189\pi$
$857$		−	1.79668e17i		−	0.453508i	0.973952	−	0.226754i	$-0.0728114\pi$
$858$	−1.73672e17			−0.435317
$859$			1.71260e17i			0.426283i	0.977021	+	0.213142i	$0.0683695\pi$
$859$			1.71260e17i			0.426283i	−0.977021	+	0.213142i	$0.931630\pi$
$860$			1.88914e18i			4.66953i
$861$	−4.00255e17	−	2.61035e17i	−0.982468	−	0.640737i
$862$	6.30847e17			1.53773
$863$	1.57698e17			0.381735			0.190867	−	0.981616i	$-0.438870\pi$
$863$	1.57698e17			0.381735			0.190867	+	0.981616i	$0.438870\pi$
$864$			1.53377e16i			0.0368704i
$865$	−2.29791e17			−0.548575
$866$		−	2.52639e17i		−	0.598954i
$867$		−	3.96537e17i		−	0.933618i
$868$	−3.08485e17	+	4.73012e17i	−0.721299	+	1.10600i
$869$	1.43447e17			0.333099
$870$	3.80093e17			0.876545
$871$			1.60765e17i			0.368200i
$872$	1.33465e17			0.303577
$873$		−	4.44730e17i		−	1.00464i
$874$		−	7.41362e17i		−	1.66327i
$875$	7.82186e16	−	1.19936e17i	0.174286	−	0.267239i
$876$	−9.18177e17			−2.03190
$877$	−2.40301e17			−0.528151			−0.264075	−	0.964502i	$-0.585067\pi$
$877$	−2.40301e17			−0.528151			−0.264075	+	0.964502i	$0.585067\pi$
$878$		−	1.02078e18i		−	2.22826i
$879$	5.11388e17			1.10871
$880$		−	3.01764e17i		−	0.649787i
$881$			4.73891e17i			1.01350i	0.862093	+	0.506750i	$0.169153\pi$
$881$			4.73891e17i			1.01350i	−0.862093	+	0.506750i	$0.830847\pi$
$882$	3.44235e17	+	7.81314e17i	0.731212	+	1.65964i
$883$	−8.50525e17			−1.79441			−0.897207	−	0.441610i	$-0.854408\pi$
$883$	−8.50525e17			−1.79441			−0.897207	+	0.441610i	$0.854408\pi$
$884$	1.43608e17			0.300930
$885$			1.49224e18i			3.10583i
$886$	1.40615e18			2.90689
$887$			7.96966e17i			1.63643i	0.574911	+	0.818216i	$0.305037\pi$
$887$			7.96966e17i			1.63643i	−0.574911	+	0.818216i	$0.694963\pi$
$888$			2.37734e17i			0.484856i
$889$	−4.92713e17	−	3.21333e17i	−0.998121	−	0.650946i
$890$	−7.12894e17			−1.43445
$891$	−3.06422e17			−0.612427
$892$		−	1.83189e18i		−	3.63673i
$893$	8.72169e17			1.71986
$894$		−	3.58753e16i		−	0.0702700i
$895$		−	1.38311e17i		−	0.269103i
$896$	−7.93013e17	−	5.17180e17i	−1.53261	−	0.999526i
$897$	1.80813e17			0.347116
$898$	−7.75379e17			−1.47862
$899$		−	8.93360e16i		−	0.169227i
$900$	1.29775e18			2.44194
$901$			2.11784e17i			0.395862i
$902$		−	4.92616e17i		−	0.914680i
$903$	7.10004e17	−	1.08868e18i	1.30959	−	2.00804i
$904$	1.30786e18			2.39636
$905$	5.24848e17			0.955305
$906$			1.30027e18i			2.35106i
$907$	−6.42928e16			−0.115483			−0.0577416	−	0.998332i	$-0.518390\pi$
$907$	−6.42928e16			−0.115483			−0.0577416	+	0.998332i	$0.518390\pi$
$908$		−	1.97740e18i		−	3.52841i
$909$			5.71798e17i			1.01358i
$910$	3.24349e17	+	2.11531e17i	0.571169	+	0.372500i
$911$	−2.23708e17			−0.391355			−0.195677	−	0.980668i	$-0.562691\pi$
$911$	−2.23708e17			−0.391355			−0.195677	+	0.980668i	$0.562691\pi$
$912$	5.99266e17			1.04148
$913$			1.74610e17i			0.301470i
$914$	−1.15859e18			−1.98725
$915$		−	1.07794e18i		−	1.83682i
$916$			6.51586e17i			1.10306i
$917$	−1.22626e17	+	1.88027e17i	−0.206237	+	0.316231i
$918$	−5.90425e16			−0.0986526
$919$	5.37739e17			0.892644			0.446322	−	0.894873i	$-0.352734\pi$
$919$	5.37739e17			0.892644			0.446322	+	0.894873i	$0.352734\pi$
$920$			1.20882e18i			1.99358i
$921$	−9.75934e17			−1.59905
$922$			1.37938e18i			2.24542i
$923$		−	1.61097e17i		−	0.260541i
$924$	−6.07941e17	+	9.32180e17i	−0.976854	+	1.49785i
$925$	−1.71192e17			−0.273295
$926$	8.96630e17			1.42216
$927$			2.78260e17i			0.438502i
$928$	5.79084e16			0.0906679
$929$			4.19994e16i			0.0653355i	0.999466	+	0.0326678i	$0.0104003\pi$
$929$			4.19994e16i			0.0653355i	−0.999466	+	0.0326678i	$0.989600\pi$
$930$		−	1.64892e18i		−	2.54860i
$931$	−6.52829e17	+	2.87626e17i	−1.00254	+	0.441703i
$932$	−2.07914e18			−3.17240
$933$	−3.60549e17			−0.546607
$934$			4.35184e17i			0.655529i
$935$	−3.88999e17			−0.582209
$936$			2.90453e17i			0.431937i
$937$		−	5.95424e17i		−	0.879810i	−0.898044	−	0.439905i	$-0.855012\pi$
$937$		−	5.95424e17i		−	0.879810i	0.898044	−	0.439905i	$-0.144988\pi$
$938$	1.32131e18	+	8.61720e17i	1.93994	+	1.26517i
$939$	1.17514e18			1.71434
$940$	−3.03372e18			−4.39753
$941$		−	2.18896e17i		−	0.315282i	−0.987496	−	0.157641i	$-0.949611\pi$
$941$		−	2.18896e17i		−	0.315282i	0.987496	−	0.157641i	$-0.0503889\pi$
$942$	−2.19313e18			−3.13877
$943$			5.12870e17i			0.729353i
$944$		−	6.78910e17i		−	0.959356i
$945$	−8.70876e16	−	5.67960e16i	−0.122283	−	0.0797493i
$946$	1.33989e18			1.86949
$947$	1.10218e18			1.52811			0.764054	−	0.645152i	$-0.223206\pi$
$947$	1.10218e18			1.52811			0.764054	+	0.645152i	$0.223206\pi$
$948$		−	9.90877e17i		−	1.36512i
$949$	1.47980e17			0.202585
$950$			1.66037e18i			2.25873i
$951$		−	7.13235e17i		−	0.964161i
$952$	3.60834e17	−	5.53281e17i	0.484714	−	0.743232i
$953$	9.84874e17			1.31469			0.657345	−	0.753590i	$-0.271679\pi$
$953$	9.84874e17			1.31469			0.657345	+	0.753590i	$0.271679\pi$
$954$	−9.13766e17			−1.21212
$955$		−	7.81217e17i		−	1.02980i
$956$	1.62210e18			2.12485
$957$		−	1.76058e17i		−	0.229183i
$958$			9.11186e17i			1.17873i
$959$	−4.04714e17	−	2.63943e17i	−0.520279	−	0.339311i
$960$	2.17619e18			2.78015
$961$	4.00105e17			0.507965
$962$		−	8.17360e16i		−	0.103125i
$963$	2.79225e17			0.350104
$964$			1.82734e17i			0.227697i
$965$		−	2.68231e17i		−	0.332158i
$966$	9.69176e17	−	1.48608e18i	1.19272	−	1.82885i
$967$	4.11124e17			0.502821			0.251411	−	0.967881i	$-0.419106\pi$
$967$	4.11124e17			0.502821			0.251411	+	0.967881i	$0.419106\pi$
$968$	6.94723e17			0.844421
$969$		−	7.72505e17i		−	0.933166i
$970$	−1.97919e18			−2.37606
$971$			8.20292e16i			0.0978708i	0.998802	+	0.0489354i	$0.0155828\pi$
$971$			8.20292e16i			0.0978708i	−0.998802	+	0.0489354i	$0.984417\pi$
$972$			2.27239e18i			2.69454i
$973$	−8.49775e17	+	1.30299e18i	−1.00144	+	1.53556i
$974$	−1.33498e18			−1.56358
$975$	−4.04953e17			−0.471386
$976$			4.90420e17i			0.567374i
$977$	−2.65255e17			−0.304998			−0.152499	−	0.988304i	$-0.548732\pi$
$977$	−2.65255e17			−0.304998			−0.152499	+	0.988304i	$0.548732\pi$
$978$		−	1.40203e18i		−	1.60222i
$979$			3.30209e17i			0.375054i
$980$	2.27078e18	−	1.00047e18i	2.56341	−	1.12940i
$981$	1.92929e17			0.216463
$982$	2.61390e17			0.291487
$983$		−	5.38986e17i		−	0.597388i	−0.954349	−	0.298694i	$-0.903449\pi$
$983$		−	5.38986e17i		−	0.597388i	0.954349	−	0.298694i	$-0.0965510\pi$
$984$	−1.59511e18			−1.75720
$985$		−	1.10917e18i		−	1.21446i
$986$			2.22918e17i			0.242596i
$987$	1.74828e18	+	1.14018e18i	1.89107	+	1.23330i
$988$	−5.17720e17			−0.556613
$989$	−1.39499e18			−1.49071
$990$		−	1.67838e18i		−	1.78271i
$991$	1.24787e18			1.31743			0.658716	−	0.752392i	$-0.271100\pi$
$991$	1.24787e18			1.31743			0.658716	+	0.752392i	$0.271100\pi$
$992$		−	2.51218e17i		−	0.263622i
$993$			1.56018e18i			1.62735i
$994$	−1.32403e18	−	8.63497e17i	−1.37272	−	0.895246i
$995$	−9.84497e17			−1.01456
$996$	1.20614e18			1.23549
$997$			1.79370e18i			1.82633i	0.407592	+	0.913164i	$0.366368\pi$
$997$			1.79370e18i			1.82633i	−0.407592	+	0.913164i	$0.633632\pi$
$998$	1.50764e18			1.52586
$999$			2.19461e16i			0.0220782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7.13.b.b.6.1	✓	6
3.2	odd	2		63.13.d.d.55.6		6
4.3	odd	2		112.13.c.b.97.6		6
7.2	even	3		49.13.d.b.31.6		12
7.3	odd	6		49.13.d.b.19.6		12
7.4	even	3		49.13.d.b.19.5		12
7.5	odd	6		49.13.d.b.31.5		12
7.6	odd	2	inner	7.13.b.b.6.2	yes	6
21.20	even	2		63.13.d.d.55.5		6
28.27	even	2		112.13.c.b.97.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.13.b.b.6.1	✓	6	1.1	even	1	trivial
7.13.b.b.6.2	yes	6	7.6	odd	2	inner
49.13.d.b.19.5		12	7.4	even	3
49.13.d.b.19.6		12	7.3	odd	6
49.13.d.b.31.5		12	7.5	odd	6
49.13.d.b.31.6		12	7.2	even	3
63.13.d.d.55.5		6	21.20	even	2
63.13.d.d.55.6		6	3.2	odd	2
112.13.c.b.97.1		6	28.27	even	2
112.13.c.b.97.6		6	4.3	odd	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:	\( N \)	\(=\)	\( 7 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	7.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-108.657 q^{2} -1048.40i q^{3} +7710.33 q^{4} -23251.4i q^{5} +113916. i q^{6} +(-98544.2 - 64267.7i) q^{7} -392722. q^{8} -567695. q^{9} +O(q^{10})\)	\(q-108.657 q^{2} -1048.40i q^{3} +7710.33 q^{4} -23251.4i q^{5} +113916. i q^{6} +(-98544.2 - 64267.7i) q^{7} -392722. q^{8} -567695. q^{9} +2.52642e6i q^{10} +1.17023e6 q^{11} -8.08348e6i q^{12} +1.30280e6i q^{13} +(1.07075e7 + 6.98313e6i) q^{14} -2.43766e7 q^{15} +1.10904e7 q^{16} -1.42965e7i q^{17} +6.16839e7 q^{18} +5.15402e7i q^{19} -1.79276e8i q^{20} +(-6.73780e7 + 1.03313e8i) q^{21} -1.27153e8 q^{22} +1.32381e8 q^{23} +4.11728e8i q^{24} -2.96485e8 q^{25} -1.41558e8i q^{26} +3.80082e7i q^{27} +(-7.59808e8 - 4.95525e8i) q^{28} +1.43502e8 q^{29} +2.64869e9 q^{30} -6.22541e8i q^{31} +4.03536e8 q^{32} -1.22686e9i q^{33} +1.55341e9i q^{34} +(-1.49431e9 + 2.29129e9i) q^{35} -4.37711e9 q^{36} +5.77404e8 q^{37} -5.60020e9i q^{38} +1.36585e9 q^{39} +9.13131e9i q^{40} +3.87419e9i q^{41} +(7.32109e9 - 1.12257e10i) q^{42} -1.05376e10 q^{43} +9.02284e9 q^{44} +1.31997e10i q^{45} -1.43842e10 q^{46} -1.69221e10i q^{47} -1.16272e10i q^{48} +(5.58062e9 + 1.26664e10i) q^{49} +3.22151e10 q^{50} -1.49884e10 q^{51} +1.00450e10i q^{52} -1.48137e10 q^{53} -4.12985e9i q^{54} -2.72094e10i q^{55} +(3.87004e10 + 2.52393e10i) q^{56} +5.40345e10 q^{57} -1.55925e10 q^{58} -6.12158e10i q^{59} -1.87952e11 q^{60} +4.42202e10i q^{61} +6.76434e10i q^{62} +(5.59430e10 + 3.64844e10i) q^{63} -8.92734e10 q^{64} +3.02918e10 q^{65} +1.33307e11i q^{66} +1.23400e11 q^{67} -1.10231e11i q^{68} -1.38788e11i q^{69} +(1.62367e11 - 2.48964e11i) q^{70} -1.23655e11 q^{71} +2.22946e11 q^{72} -1.13587e11i q^{73} -6.27390e10 q^{74} +3.10834e11i q^{75} +3.97391e11i q^{76} +(-1.15319e11 - 7.52078e10i) q^{77} -1.48409e11 q^{78} +1.22580e11 q^{79} -2.57867e11i q^{80} -2.61849e11 q^{81} -4.20957e11i q^{82} +1.49210e11i q^{83} +(-5.19506e11 + 7.96580e11i) q^{84} -3.32413e11 q^{85} +1.14499e12 q^{86} -1.50447e11i q^{87} -4.59574e11 q^{88} +2.82175e11i q^{89} -1.43424e12i q^{90} +(8.37276e10 - 1.28383e11i) q^{91} +1.02070e12 q^{92} -6.52670e11 q^{93} +1.83871e12i q^{94} +1.19838e12 q^{95} -4.23066e11i q^{96} +7.83396e11i q^{97} +(-6.06373e11 - 1.37629e12i) q^{98} -6.64332e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 16288 q^{4} - 314650 q^{7} - 1036800 q^{8} - 1680762 q^{9}+O(q^{10}) \) 6 * q + 16288 * q^4 - 314650 * q^7 - 1036800 * q^8 - 1680762 * q^9	\( 6 q + 16288 q^{4} - 314650 q^{7} - 1036800 q^{8} - 1680762 q^{9} + 1704780 q^{11} + 27863136 q^{14} - 40526880 q^{15} + 15993088 q^{16} + 128356800 q^{18} - 32694816 q^{21} - 83177600 q^{22} - 266735700 q^{23} - 1115987130 q^{25} - 150488800 q^{28} + 2090185452 q^{29} + 3469961280 q^{30} - 666316800 q^{32} + 1813281120 q^{35} - 5110975584 q^{36} - 4824866900 q^{37} - 9660671328 q^{39} + 26387188800 q^{42} - 28724189300 q^{43} + 40254705216 q^{44} - 56843757056 q^{46} + 23216390022 q^{49} + 30589686720 q^{50} + 74552249088 q^{51} - 104521857300 q^{53} + 110766507264 q^{56} + 6945343200 q^{57} + 169979689600 q^{58} - 621243786240 q^{60} + 209517066150 q^{63} - 404530321408 q^{64} + 420221360160 q^{65} - 129746603700 q^{67} + 715652629440 q^{70} - 15017604660 q^{71} + 550229836800 q^{72} - 538689695616 q^{74} + 272839020300 q^{77} - 336774849600 q^{78} - 172527631668 q^{79} - 1648796648346 q^{81} - 343188486144 q^{84} + 62636728320 q^{85} + 1808205928704 q^{86} - 462937446400 q^{88} - 474685856736 q^{91} + 2013091790400 q^{92} - 2143380662400 q^{93} + 3657881967840 q^{95} - 2066720745600 q^{98} + 65572191564 q^{99}+O(q^{100}) \) 6 * q + 16288 * q^4 - 314650 * q^7 - 1036800 * q^8 - 1680762 * q^9 + 1704780 * q^11 + 27863136 * q^14 - 40526880 * q^15 + 15993088 * q^16 + 128356800 * q^18 - 32694816 * q^21 - 83177600 * q^22 - 266735700 * q^23 - 1115987130 * q^25 - 150488800 * q^28 + 2090185452 * q^29 + 3469961280 * q^30 - 666316800 * q^32 + 1813281120 * q^35 - 5110975584 * q^36 - 4824866900 * q^37 - 9660671328 * q^39 + 26387188800 * q^42 - 28724189300 * q^43 + 40254705216 * q^44 - 56843757056 * q^46 + 23216390022 * q^49 + 30589686720 * q^50 + 74552249088 * q^51 - 104521857300 * q^53 + 110766507264 * q^56 + 6945343200 * q^57 + 169979689600 * q^58 - 621243786240 * q^60 + 209517066150 * q^63 - 404530321408 * q^64 + 420221360160 * q^65 - 129746603700 * q^67 + 715652629440 * q^70 - 15017604660 * q^71 + 550229836800 * q^72 - 538689695616 * q^74 + 272839020300 * q^77 - 336774849600 * q^78 - 172527631668 * q^79 - 1648796648346 * q^81 - 343188486144 * q^84 + 62636728320 * q^85 + 1808205928704 * q^86 - 462937446400 * q^88 - 474685856736 * q^91 + 2013091790400 * q^92 - 2143380662400 * q^93 + 3657881967840 * q^95 - 2066720745600 * q^98 + 65572191564 * q^99

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