LMFDB - Embedded newform 15.11.c.a.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,11,Mod(11,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("15.11");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	15.c (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:	$9.53035879011$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 11554 x^{12} + 52224391 x^{10} + 115670558124 x^{8} + 127683454012911 x^{6} + \cdots + 62\!\cdots\!00 $ x^14 + 11554x^12 + 52224391x^10 + 115670558124x^8 + 127683454012911x^6 + 62207430110604450x^4 + 9049402196955729225x^2 + 62911149236536050000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{20}\cdot 5^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.12
Root			$49.8576i$ of defining polynomial
Character	$\chi$	$=$	15.11
Dual form			15.11.c.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+52.0937i q^{2} +(196.615 + 142.800i) q^{3} -1689.75 q^{4} -1397.54i q^{5} +(-7438.96 + 10242.4i) q^{6} -32323.0 q^{7} -34681.6i q^{8} +(18265.6 + 56152.9i) q^{9} +O(q^{10})$	\(q+52.0937i q^{2} +(196.615 + 142.800i) q^{3} -1689.75 q^{4} -1397.54i q^{5} +(-7438.96 + 10242.4i) q^{6} -32323.0 q^{7} -34681.6i q^{8} +(18265.6 + 56152.9i) q^{9} +72803.2 q^{10} -10027.4i q^{11} +(-332230. - 241296. i) q^{12} -1865.46 q^{13} -1.68382e6i q^{14} +(199568. - 274777. i) q^{15} +76385.8 q^{16} +1.52077e6i q^{17} +(-2.92522e6 + 951522. i) q^{18} +3.08276e6 q^{19} +2.36150e6i q^{20} +(-6.35517e6 - 4.61571e6i) q^{21} +522364. q^{22} +8.67557e6i q^{23} +(4.95252e6 - 6.81891e6i) q^{24} -1.95312e6 q^{25} -97178.8i q^{26} +(-4.42733e6 + 1.36488e7i) q^{27} +5.46179e7 q^{28} +7.01771e6i q^{29} +(1.43142e7 + 1.03963e7i) q^{30} -7.59210e6 q^{31} -3.15348e7i q^{32} +(1.43191e6 - 1.97153e6i) q^{33} -7.92228e7 q^{34} +4.51728e7i q^{35} +(-3.08644e7 - 9.48847e7i) q^{36} -9.52445e7 q^{37} +1.60592e8i q^{38} +(-366777. - 266387. i) q^{39} -4.84690e7 q^{40} -6.27119e7i q^{41} +(2.40449e8 - 3.31065e8i) q^{42} +7.08486e7 q^{43} +1.69438e7i q^{44} +(7.84761e7 - 2.55269e7i) q^{45} -4.51943e8 q^{46} +3.66838e7i q^{47} +(1.50186e7 + 1.09079e7i) q^{48} +7.62301e8 q^{49} -1.01746e8i q^{50} +(-2.17166e8 + 2.99006e8i) q^{51} +3.15217e6 q^{52} +2.99567e8i q^{53} +(-7.11017e8 - 2.30636e8i) q^{54} -1.40137e7 q^{55} +1.12101e9i q^{56} +(6.06115e8 + 4.40216e8i) q^{57} -3.65579e8 q^{58} -2.34566e8i q^{59} +(-3.37222e8 + 4.64306e8i) q^{60} +7.97547e8 q^{61} -3.95501e8i q^{62} +(-5.90398e8 - 1.81503e9i) q^{63} +1.72098e9 q^{64} +2.60706e6i q^{65} +(1.02704e8 + 7.45933e7i) q^{66} +7.89899e8 q^{67} -2.56973e9i q^{68} +(-1.23887e9 + 1.70574e9i) q^{69} -2.35322e9 q^{70} +2.27167e9i q^{71} +(1.94748e9 - 6.33480e8i) q^{72} +6.29603e8 q^{73} -4.96164e9i q^{74} +(-3.84013e8 - 2.78905e8i) q^{75} -5.20910e9 q^{76} +3.24115e8i q^{77} +(1.38771e7 - 1.91068e7i) q^{78} -3.79241e9 q^{79} -1.06752e8i q^{80} +(-2.81952e9 + 2.05133e9i) q^{81} +3.26689e9 q^{82} +9.37970e8i q^{83} +(1.07387e10 + 7.79942e9i) q^{84} +2.12535e9 q^{85} +3.69077e9i q^{86} +(-1.00213e9 + 1.37978e9i) q^{87} -3.47766e8 q^{88} -6.91789e9i q^{89} +(1.32979e9 + 4.08811e9i) q^{90} +6.02973e7 q^{91} -1.46596e10i q^{92} +(-1.49272e9 - 1.08415e9i) q^{93} -1.91099e9 q^{94} -4.30828e9i q^{95} +(4.50315e9 - 6.20019e9i) q^{96} +7.43319e9 q^{97} +3.97111e10i q^{98} +(5.63067e8 - 1.83156e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9}+O(q^{10}) $ 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9	\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9} + 31250 q^{10} + 43756 q^{12} + 699408 q^{13} - 343750 q^{15} + 2871906 q^{16} - 3243880 q^{18} + 3814644 q^{19} - 2191008 q^{21} - 10493420 q^{22} + 9454542 q^{24} - 27343750 q^{25} + 13322636 q^{27} - 10989172 q^{28} + 20875000 q^{30} + 105444308 q^{31} - 187570700 q^{33} + 84960772 q^{34} + 80968490 q^{36} - 152902928 q^{37} - 262995952 q^{39} - 228656250 q^{40} + 1025108820 q^{42} - 82568592 q^{43} + 284500000 q^{45} + 302816052 q^{46} - 534917396 q^{48} + 1339929050 q^{49} - 519773324 q^{51} - 2117624528 q^{52} - 3171778694 q^{54} - 414437500 q^{55} + 2459677832 q^{57} + 2203542020 q^{58} + 918156250 q^{60} - 2372907732 q^{61} + 253855908 q^{63} + 5663115830 q^{64} + 915786920 q^{66} - 7807415008 q^{67} - 1032380604 q^{69} - 95812500 q^{70} + 2313658920 q^{72} + 10465834068 q^{73} - 85937500 q^{75} - 4927934540 q^{76} - 4082143640 q^{78} - 8333919076 q^{79} - 4284635426 q^{81} + 14404193720 q^{82} + 13837595568 q^{84} + 4711812500 q^{85} - 11735627260 q^{87} - 14973492180 q^{88} - 9226281250 q^{90} + 4013221984 q^{91} - 9561672552 q^{93} - 47501516708 q^{94} + 43132239458 q^{96} + 31262487532 q^{97} + 36258312560 q^{99}+O(q^{100}) \) 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9 + 31250 * q^10 + 43756 * q^12 + 699408 * q^13 - 343750 * q^15 + 2871906 * q^16 - 3243880 * q^18 + 3814644 * q^19 - 2191008 * q^21 - 10493420 * q^22 + 9454542 * q^24 - 27343750 * q^25 + 13322636 * q^27 - 10989172 * q^28 + 20875000 * q^30 + 105444308 * q^31 - 187570700 * q^33 + 84960772 * q^34 + 80968490 * q^36 - 152902928 * q^37 - 262995952 * q^39 - 228656250 * q^40 + 1025108820 * q^42 - 82568592 * q^43 + 284500000 * q^45 + 302816052 * q^46 - 534917396 * q^48 + 1339929050 * q^49 - 519773324 * q^51 - 2117624528 * q^52 - 3171778694 * q^54 - 414437500 * q^55 + 2459677832 * q^57 + 2203542020 * q^58 + 918156250 * q^60 - 2372907732 * q^61 + 253855908 * q^63 + 5663115830 * q^64 + 915786920 * q^66 - 7807415008 * q^67 - 1032380604 * q^69 - 95812500 * q^70 + 2313658920 * q^72 + 10465834068 * q^73 - 85937500 * q^75 - 4927934540 * q^76 - 4082143640 * q^78 - 8333919076 * q^79 - 4284635426 * q^81 + 14404193720 * q^82 + 13837595568 * q^84 + 4711812500 * q^85 - 11735627260 * q^87 - 14973492180 * q^88 - 9226281250 * q^90 + 4013221984 * q^91 - 9561672552 * q^93 - 47501516708 * q^94 + 43132239458 * q^96 + 31262487532 * q^97 + 36258312560 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$1$	$-1$

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 $

$2$			52.0937i			1.62793i	0.580915	+	0.813964i	$0.302695\pi$
$2$			52.0937i			1.62793i	−0.580915	+	0.813964i	$0.697305\pi$
$3$	196.615	+	142.800i	0.809113	+	0.587652i
$3$	196.615	+	142.800i	0.809113	+	0.587652i
$4$	−1689.75			−1.65015
$5$		−	1397.54i		−	0.447214i
$5$		−	1397.54i		−	0.447214i
$6$	−7438.96	+	10242.4i	−0.956656	+	1.31718i
$7$	−32323.0			−1.92319			−0.961593	−	0.274478i	$-0.911495\pi$
$7$	−32323.0			−1.92319			−0.961593	+	0.274478i	$0.911495\pi$
$8$		−	34681.6i		−	1.05840i
$9$	18265.6	+	56152.9i	0.309329	+	0.950955i
$10$	72803.2			0.728032
$11$		−	10027.4i		−	0.0622622i	−0.999515	−	0.0311311i	$-0.990089\pi$
$11$		−	10027.4i		−	0.0622622i	0.999515	−	0.0311311i	$-0.00991094\pi$
$12$	−332230.	−	241296.i	−1.33516	−	0.969715i
$13$	−1865.46			−0.00502423			−0.00251212	−	0.999997i	$-0.500800\pi$
$13$	−1865.46			−0.00502423			−0.00251212	+	0.999997i	$0.500800\pi$
$14$		−	1.68382e6i		−	3.13081i
$15$	199568.	−	274777.i	0.262806	−	0.361847i
$16$	76385.8			0.0728471
$17$			1.52077e6i			1.07108i	0.844511	+	0.535538i	$0.179891\pi$
$17$			1.52077e6i			1.07108i	−0.844511	+	0.535538i	$0.820109\pi$
$18$	−2.92522e6	+	951522.i	−1.54809	+	0.503566i
$19$	3.08276e6			1.24500			0.622502	−	0.782618i	$-0.286116\pi$
$19$	3.08276e6			1.24500			0.622502	+	0.782618i	$0.286116\pi$
$20$			2.36150e6i			0.737970i
$21$	−6.35517e6	−	4.61571e6i	−1.55608	−	1.13017i
$22$	522364.			0.101358
$23$			8.67557e6i			1.34790i	0.738775	+	0.673952i	$0.235404\pi$
$23$			8.67557e6i			1.34790i	−0.738775	+	0.673952i	$0.764596\pi$
$24$	4.95252e6	−	6.81891e6i	0.621971	−	0.856365i
$25$	−1.95312e6			−0.200000
$26$		−	97178.8i		−	0.00817909i
$27$	−4.42733e6	+	1.36488e7i	−0.308549	+	0.951209i
$28$	5.46179e7			3.17355
$29$			7.01771e6i			0.342141i	0.985259	+	0.171071i	$0.0547226\pi$
$29$			7.01771e6i			0.342141i	−0.985259	+	0.171071i	$0.945277\pi$
$30$	1.43142e7	+	1.03963e7i	0.589060	+	0.427830i
$31$	−7.59210e6			−0.265188			−0.132594	−	0.991170i	$-0.542331\pi$
$31$	−7.59210e6			−0.265188			−0.132594	+	0.991170i	$0.542331\pi$
$32$		−	3.15348e7i		−	0.939809i
$33$	1.43191e6	−	1.97153e6i	0.0365885	−	0.0503772i
$34$	−7.92228e7			−1.74363
$35$			4.51728e7i			0.860075i
$36$	−3.08644e7	−	9.48847e7i	−0.510440	−	1.56922i
$37$	−9.52445e7			−1.37351			−0.686754	−	0.726890i	$-0.740965\pi$
$37$	−9.52445e7			−1.37351			−0.686754	+	0.726890i	$0.740965\pi$
$38$			1.60592e8i			2.02678i
$39$	−366777.	−	266387.i	−0.00406517	−	0.00295250i
$40$	−4.84690e7			−0.473330
$41$		−	6.27119e7i		−	0.541291i	−0.962679	−	0.270645i	$-0.912763\pi$
$41$		−	6.27119e7i		−	0.541291i	0.962679	−	0.270645i	$-0.0872371\pi$
$42$	2.40449e8	−	3.31065e8i	1.83983	−	2.53318i
$43$	7.08486e7			0.481936			0.240968	−	0.970533i	$-0.422535\pi$
$43$	7.08486e7			0.481936			0.240968	+	0.970533i	$0.422535\pi$
$44$			1.69438e7i			0.102742i
$45$	7.84761e7	−	2.55269e7i	0.425280	−	0.138336i
$46$	−4.51943e8			−2.19429
$47$			3.66838e7i			0.159950i	0.996797	+	0.0799750i	$0.0254841\pi$
$47$			3.66838e7i			0.159950i	−0.996797	+	0.0799750i	$0.974516\pi$
$48$	1.50186e7	+	1.09079e7i	0.0589416	+	0.0428088i
$49$	7.62301e8			2.69865
$50$		−	1.01746e8i		−	0.325586i
$51$	−2.17166e8	+	2.99006e8i	−0.629420	+	0.866622i
$52$	3.15217e6			0.00829074
$53$			2.99567e8i			0.716332i	0.933658	+	0.358166i	$0.116598\pi$
$53$			2.99567e8i			0.716332i	−0.933658	+	0.358166i	$0.883402\pi$
$54$	−7.11017e8	−	2.30636e8i	−1.54850	−	0.502295i
$55$	−1.40137e7			−0.0278445
$56$			1.12101e9i			2.03550i
$57$	6.06115e8	+	4.40216e8i	1.00735	+	0.731630i
$58$	−3.65579e8			−0.556982
$59$		−	2.34566e8i		−	0.328099i	−0.986452	−	0.164049i	$-0.947544\pi$
$59$		−	2.34566e8i		−	0.328099i	0.986452	−	0.164049i	$-0.0524557\pi$
$60$	−3.37222e8	+	4.64306e8i	−0.433670	+	0.597101i
$61$	7.97547e8			0.944294			0.472147	−	0.881520i	$-0.343479\pi$
$61$	7.97547e8			0.944294			0.472147	+	0.881520i	$0.343479\pi$
$62$		−	3.95501e8i		−	0.431707i
$63$	−5.90398e8	−	1.81503e9i	−0.594898	−	1.82886i
$64$	1.72098e9			1.60279
$65$			2.60706e6i			0.00224690i
$66$	1.02704e8	+	7.45933e7i	0.0820105	+	0.0595635i
$67$	7.89899e8			0.585056			0.292528	−	0.956257i	$-0.405503\pi$
$67$	7.89899e8			0.585056			0.292528	+	0.956257i	$0.405503\pi$
$68$		−	2.56973e9i		−	1.76744i
$69$	−1.23887e9	+	1.70574e9i	−0.792099	+	1.09061i
$70$	−2.35322e9			−1.40014
$71$			2.27167e9i			1.25908i	0.776967	+	0.629541i	$0.216757\pi$
$71$			2.27167e9i			1.25908i	−0.776967	+	0.629541i	$0.783243\pi$
$72$	1.94748e9	−	6.33480e8i	1.00649	−	0.327394i
$73$	6.29603e8			0.303705			0.151853	−	0.988403i	$-0.451476\pi$
$73$	6.29603e8			0.303705			0.151853	+	0.988403i	$0.451476\pi$
$74$		−	4.96164e9i		−	2.23597i
$75$	−3.84013e8	−	2.78905e8i	−0.161823	−	0.117530i
$76$	−5.20910e9			−2.05445
$77$			3.24115e8i			0.119742i
$78$	1.38771e7	−	1.91068e7i	0.00480646	−	0.00661781i
$79$	−3.79241e9			−1.23248			−0.616239	−	0.787559i	$-0.711345\pi$
$79$	−3.79241e9			−1.23248			−0.616239	+	0.787559i	$0.711345\pi$
$80$		−	1.06752e8i		−	0.0325782i
$81$	−2.81952e9	+	2.05133e9i	−0.808631	+	0.588316i
$82$	3.26689e9			0.881182
$83$			9.37970e8i			0.238122i	0.992887	+	0.119061i	$0.0379883\pi$
$83$			9.37970e8i			0.238122i	−0.992887	+	0.119061i	$0.962012\pi$
$84$	1.07387e10	+	7.79942e9i	2.56776	+	1.86494i
$85$	2.12535e9			0.479000
$86$			3.69077e9i			0.784557i
$87$	−1.00213e9	+	1.37978e9i	−0.201060	+	0.276831i
$88$	−3.47766e8			−0.0658983
$89$		−	6.91789e9i		−	1.23886i	−0.785050	−	0.619432i	$-0.787363\pi$
$89$		−	6.91789e9i		−	1.23886i	0.785050	−	0.619432i	$-0.212637\pi$
$90$	1.32979e9	+	4.08811e9i	0.225201	+	0.692325i
$91$	6.02973e7			0.00966253
$92$		−	1.46596e10i		−	2.22424i
$93$	−1.49272e9	−	1.08415e9i	−0.214567	−	0.155838i
$94$	−1.91099e9			−0.260387
$95$		−	4.30828e9i		−	0.556783i
$96$	4.50315e9	−	6.20019e9i	0.552281	−	0.760412i
$97$	7.43319e9			0.865598			0.432799	−	0.901490i	$-0.357526\pi$
$97$	7.43319e9			0.865598			0.432799	+	0.901490i	$0.357526\pi$
$98$			3.97111e10i			4.39320i
$99$	5.63067e8	−	1.83156e8i	0.0592086	−	0.0192595i
$100$	3.30030e9			0.330030
$101$		−	7.65721e9i		−	0.728557i	−0.931290	−	0.364278i	$-0.881316\pi$
$101$		−	7.65721e9i		−	0.728557i	0.931290	−	0.364278i	$-0.118684\pi$
$102$	−1.55764e10	−	1.13130e10i	−1.41080	−	1.02465i
$103$	1.17553e10			1.01402			0.507012	−	0.861939i	$-0.330750\pi$
$103$	1.17553e10			1.01402			0.507012	+	0.861939i	$0.330750\pi$
$104$			6.46972e7i			0.00531764i
$105$	−6.45065e9	+	8.88162e9i	−0.505425	+	0.695898i
$106$	−1.56055e10			−1.16614
$107$			1.97974e10i			1.41153i	0.708448	+	0.705763i	$0.249396\pi$
$107$			1.97974e10i			1.41153i	−0.708448	+	0.705763i	$0.750604\pi$
$108$	7.48111e9	−	2.30631e10i	0.509152	−	1.56964i
$109$	−9.52377e9			−0.618980			−0.309490	−	0.950903i	$-0.600158\pi$
$109$	−9.52377e9			−0.618980			−0.309490	+	0.950903i	$0.600158\pi$
$110$		−	7.30026e8i		−	0.0453289i
$111$	−1.87265e10	−	1.36009e10i	−1.11132	−	0.807146i
$112$	−2.46902e9			−0.140099
$113$		−	3.01674e10i		−	1.63737i	−0.574246	−	0.818683i	$-0.694705\pi$
$113$		−	3.01674e10i		−	1.63737i	0.574246	−	0.818683i	$-0.305295\pi$
$114$	−2.29325e10	+	3.15748e10i	−1.19104	+	1.63989i
$115$	1.21245e10			0.602801
$116$		−	1.18582e10i		−	0.564585i
$117$	−3.40737e7	−	1.04751e8i	−0.00155414	−	0.00477782i
$118$	1.22194e10			0.534122
$119$		−	4.91560e10i		−	2.05988i
$120$	−9.52972e9	−	6.92136e9i	−0.382978	−	0.278154i
$121$	2.58369e10			0.996123
$122$			4.15472e10i			1.53724i
$123$	8.95523e9	−	1.23301e10i	0.318091	−	0.437966i
$124$	1.28288e10			0.437600
$125$			2.72958e9i			0.0894427i
$126$	9.45517e10	−	3.07560e10i	2.97726	−	0.968451i
$127$	−3.25707e10			−0.985844			−0.492922	−	0.870073i	$-0.664071\pi$
$127$	−3.25707e10			−0.985844			−0.492922	+	0.870073i	$0.664071\pi$
$128$			5.73607e10i			1.66942i
$129$	1.39299e10	+	1.01172e10i	0.389941	+	0.283211i
$130$	−1.35812e8			−0.00365780
$131$			6.90042e10i			1.78862i	0.447444	+	0.894312i	$0.352334\pi$
$131$			6.90042e10i			1.78862i	−0.447444	+	0.894312i	$0.647666\pi$
$132$	−2.41957e9	+	3.33140e9i	−0.0603766	+	0.0831300i
$133$	−9.96439e10			−2.39438
$134$			4.11488e10i			0.952430i
$135$	1.90748e10	+	6.18739e9i	0.425393	+	0.137987i
$136$	5.27429e10			1.13363
$137$			2.44876e10i			0.507392i	0.967284	+	0.253696i	$0.0816463\pi$
$137$			2.44876e10i			0.507392i	−0.967284	+	0.253696i	$0.918354\pi$
$138$	−8.88585e10	−	6.45372e10i	−1.77543	−	1.28948i
$139$	6.07840e9			0.117143			0.0585713	−	0.998283i	$-0.481345\pi$
$139$	6.07840e9			0.117143			0.0585713	+	0.998283i	$0.481345\pi$
$140$		−	7.63309e10i		−	1.41925i
$141$	−5.23842e9	+	7.21256e9i	−0.0939951	+	0.129418i
$142$	−1.18340e11			−2.04970
$143$			1.87057e7i			0.000312820i
$144$	1.39523e9	+	4.28929e9i	0.0225338	+	0.0692744i
$145$	9.80755e9			0.153010
$146$			3.27983e10i			0.494411i
$147$	1.49879e11	+	1.08856e11i	2.18351	+	1.58587i
$148$	1.60940e11			2.26650
$149$		−	3.01683e10i		−	0.410789i	−0.978679	−	0.205395i	$-0.934152\pi$
$149$		−	3.01683e10i		−	0.410789i	0.978679	−	0.205395i	$-0.0658478\pi$
$150$	1.45292e10	−	2.00047e10i	0.191331	−	0.263436i
$151$	−3.57314e10			−0.455161			−0.227581	−	0.973759i	$-0.573081\pi$
$151$	−3.57314e10			−0.455161			−0.227581	+	0.973759i	$0.573081\pi$
$152$		−	1.06915e11i		−	1.31771i
$153$	−8.53959e10	+	2.77778e10i	−1.01854	+	0.331315i
$154$	−1.68844e10			−0.194931
$155$			1.06103e10i			0.118596i
$156$	6.19763e8	+	4.50129e8i	0.00670815	+	0.00487207i
$157$	5.49690e10			0.576262			0.288131	−	0.957591i	$-0.406966\pi$
$157$	5.49690e10			0.576262			0.288131	+	0.957591i	$0.406966\pi$
$158$		−	1.97561e11i		−	2.00639i
$159$	−4.27780e10	+	5.88992e10i	−0.420954	+	0.579594i
$160$	−4.40712e10			−0.420295
$161$		−	2.80420e11i		−	2.59227i
$162$	−1.06862e11	−	1.46879e11i	−0.957737	−	1.31639i
$163$	1.23767e11			1.07564			0.537820	−	0.843060i	$-0.319248\pi$
$163$	1.23767e11			1.07564			0.537820	+	0.843060i	$0.319248\pi$
$164$			1.05968e11i			0.893211i
$165$	−2.75530e9	−	2.00115e9i	−0.0225294	−	0.0163629i
$166$	−4.88624e10			−0.387645
$167$			5.49575e10i			0.423101i	0.977367	+	0.211551i	$0.0678513\pi$
$167$			5.49575e10i			0.423101i	−0.977367	+	0.211551i	$0.932149\pi$
$168$	−1.60080e11	+	2.20408e11i	−1.19617	+	1.64695i
$169$	−1.37855e11			−0.999975
$170$			1.10717e11i			0.779777i
$171$	5.63083e10	+	1.73106e11i	0.385116	+	1.18394i
$172$	−1.19717e11			−0.795267
$173$			1.84142e11i			1.18829i	0.804358	+	0.594145i	$0.202510\pi$
$173$			1.84142e11i			1.18829i	−0.804358	+	0.594145i	$0.797490\pi$
$174$	−7.18781e10	−	5.22045e10i	−0.450661	−	0.327312i
$175$	6.31309e10			0.384637
$176$		−	7.65950e8i		−	0.00453562i
$177$	3.34959e10	−	4.61191e10i	0.192808	−	0.265469i
$178$	3.60378e11			2.01678
$179$		−	1.36499e11i		−	0.742788i	−0.928475	−	0.371394i	$-0.878880\pi$
$179$		−	1.36499e11i		−	0.742788i	0.928475	−	0.371394i	$-0.121120\pi$
$180$	−1.32605e11	+	4.31342e10i	−0.701776	+	0.228276i
$181$	−2.60188e10			−0.133935			−0.0669675	−	0.997755i	$-0.521332\pi$
$181$	−2.60188e10			−0.133935			−0.0669675	+	0.997755i	$0.521332\pi$
$182$			3.14111e9i			0.0157299i
$183$	1.56809e11	+	1.13889e11i	0.764041	+	0.554917i
$184$	3.00883e11			1.42662
$185$			1.33108e11i			0.614252i
$186$	5.64773e10	−	7.77612e10i	0.253694	−	0.349300i
$187$	1.52494e10			0.0666875
$188$		−	6.19865e10i		−	0.263942i
$189$	1.43105e11	−	4.41170e11i	0.593397	−	1.82935i
$190$	2.24434e11			0.906403
$191$		−	6.51058e10i		−	0.256126i	−0.991766	−	0.128063i	$-0.959124\pi$
$191$		−	6.51058e10i		−	0.256126i	0.991766	−	0.128063i	$-0.0408759\pi$
$192$	3.38370e11	+	2.45755e11i	1.29684	+	0.941883i
$193$	−2.01645e11			−0.753011			−0.376505	−	0.926414i	$-0.622874\pi$
$193$	−2.01645e11			−0.753011			−0.376505	+	0.926414i	$0.622874\pi$
$194$			3.87222e11i			1.40913i
$195$	−3.72287e8	+	5.12586e8i	−0.00132040	+	0.00181800i
$196$	−1.28810e12			−4.45317
$197$		−	2.69426e11i		−	0.908046i	−0.890990	−	0.454023i	$-0.849988\pi$
$197$		−	2.69426e11i		−	0.908046i	0.890990	−	0.454023i	$-0.150012\pi$
$198$	9.54128e9	+	2.93323e10i	0.0313531	+	0.0963873i
$199$	2.60623e11			0.835118			0.417559	−	0.908650i	$-0.362886\pi$
$199$	2.60623e11			0.835118			0.417559	+	0.908650i	$0.362886\pi$
$200$			6.77375e10i			0.211680i
$201$	1.55306e11	+	1.12797e11i	0.473377	+	0.343810i
$202$	3.98892e11			1.18604
$203$		−	2.26834e11i		−	0.658002i
$204$	3.66957e11	−	5.05247e11i	1.03864	−	1.43006i
$205$	−8.76425e10			−0.242073
$206$			6.12378e11i			1.65076i
$207$	−4.87159e11	+	1.58464e11i	−1.28180	+	0.416946i
$208$	−1.42495e8			−0.000366001
$209$		−	3.09120e10i		−	0.0775167i
$210$	−4.62677e11	−	3.36038e11i	−1.13287	−	0.822796i
$211$	−3.57579e11			−0.854988			−0.427494	−	0.904018i	$-0.640603\pi$
$211$	−3.57579e11			−0.854988			−0.427494	+	0.904018i	$0.640603\pi$
$212$		−	5.06194e11i		−	1.18206i
$213$	−3.24394e11	+	4.46644e11i	−0.739903	+	1.01874i
$214$	−1.03132e12			−2.29786
$215$		−	9.90140e10i		−	0.215528i
$216$	4.73363e11	+	1.53547e11i	1.00676	+	0.326568i
$217$	2.45400e11			0.510006
$218$		−	4.96129e11i		−	1.00766i
$219$	1.23789e11	+	8.99070e10i	0.245732	+	0.178473i
$220$	2.36797e10			0.0459476
$221$		−	2.83695e9i		−	0.00538133i
$222$	7.08520e11	−	9.75531e11i	1.31398	−	1.80916i
$223$	−2.96463e11			−0.537584			−0.268792	−	0.963198i	$-0.586624\pi$
$223$	−2.96463e11			−0.537584			−0.268792	+	0.963198i	$0.586624\pi$
$224$			1.01930e12i			1.80743i
$225$	−3.56750e10	−	1.09674e11i	−0.0618658	−	0.190191i
$226$	1.57153e12			2.66551
$227$			5.61330e11i			0.931299i	0.884969	+	0.465649i	$0.154179\pi$
$227$			5.61330e11i			0.931299i	−0.884969	+	0.465649i	$0.845821\pi$
$228$	−1.02418e12	−	7.43857e11i	−1.66228	−	1.20730i
$229$	3.69560e11			0.586824			0.293412	−	0.955986i	$-0.405209\pi$
$229$	3.69560e11			0.586824			0.293412	+	0.955986i	$0.405209\pi$
$230$			6.31609e11i			0.981316i
$231$	−4.62835e10	+	6.37258e10i	−0.0703666	+	0.0968847i
$232$	2.43386e11			0.362122
$233$		−	8.60579e11i		−	1.25317i	−0.779351	−	0.626587i	$-0.784451\pi$
$233$		−	8.60579e11i		−	1.25317i	0.779351	−	0.626587i	$-0.215549\pi$
$234$	5.45688e9	−	1.77503e9i	0.00777795	−	0.00253003i
$235$	5.12671e10			0.0715318
$236$			3.96359e11i			0.541413i
$237$	−7.45642e11	−	5.41554e11i	−0.997215	−	0.724269i
$238$	2.56072e12			3.35333
$239$			4.92606e11i			0.631699i	0.948809	+	0.315850i	$0.102289\pi$
$239$			4.92606e11i			0.631699i	−0.948809	+	0.315850i	$0.897711\pi$
$240$	1.52442e10	−	2.09891e10i	0.0191447	−	0.0263595i
$241$	−6.47039e11			−0.795875			−0.397938	−	0.917412i	$-0.630274\pi$
$241$	−6.47039e11			−0.795875			−0.397938	+	0.917412i	$0.630274\pi$
$242$			1.34594e12i			1.62162i
$243$	−8.47288e11	+	6.95469e8i	−1.00000	+	0.000820817i
$244$	−1.34766e12			−1.55823
$245$		−	1.06535e12i		−	1.20687i
$246$	6.42319e11	+	4.66511e11i	0.712977	+	0.517829i
$247$	−5.75076e9			−0.00625519
$248$			2.63307e11i			0.280675i
$249$	−1.33942e11	+	1.84419e11i	−0.139933	+	0.192667i
$250$	−1.42194e11			−0.145606
$251$			6.11429e11i			0.613731i	0.951753	+	0.306865i	$0.0992801\pi$
$251$			6.11429e11i			0.613731i	−0.951753	+	0.306865i	$0.900720\pi$
$252$	9.97628e11	+	3.06696e12i	0.981671	+	3.01790i
$253$	8.69933e10			0.0839234
$254$		−	1.69673e12i		−	1.60488i
$255$	4.17874e11	+	3.03498e11i	0.387565	+	0.281485i
$256$	−1.22585e12			−1.11490
$257$		−	1.52569e12i		−	1.36082i	−0.732832	−	0.680409i	$-0.761802\pi$
$257$		−	1.52569e12i		−	1.36082i	0.732832	−	0.680409i	$-0.238198\pi$
$258$	−5.27040e11	+	7.25659e11i	−0.461047	+	0.634796i
$259$	3.07859e12			2.64151
$260$		−	4.40530e9i		−	0.00370773i
$261$	−3.94065e11	+	1.28183e11i	−0.325361	+	0.105834i
$262$	−3.59469e12			−2.91175
$263$			2.12252e12i			1.68683i	0.537260	+	0.843417i	$0.319459\pi$
$263$			2.12252e12i			1.68683i	−0.537260	+	0.843417i	$0.680541\pi$
$264$	−6.83759e10	−	4.96608e10i	−0.0533192	−	0.0387253i
$265$	4.18657e11			0.320353
$266$		−	5.19082e12i		−	3.89787i
$267$	9.87871e11	−	1.36016e12i	0.728021	−	1.00238i
$268$	−1.33474e12			−0.965431
$269$			3.86755e9i			0.00274583i	0.999999	+	0.00137292i	$0.000437013\pi$
$269$			3.86755e9i			0.00274583i	−0.999999	+	0.00137292i	$0.999563\pi$
$270$	−3.22324e11	+	9.93676e11i	−0.224633	+	0.692510i
$271$	9.37751e11			0.641566			0.320783	−	0.947153i	$-0.396054\pi$
$271$	9.37751e11			0.641566			0.320783	+	0.947153i	$0.396054\pi$
$272$			1.16165e11i			0.0780248i
$273$	1.18553e10	+	8.61043e9i	0.00781809	+	0.00567821i
$274$	−1.27565e12			−0.825998
$275$			1.95847e10i			0.0124524i
$276$	2.09338e12	−	2.88229e12i	1.30708	−	1.79967i
$277$	−1.95575e12			−1.19926			−0.599632	−	0.800276i	$-0.704686\pi$
$277$	−1.95575e12			−1.19926			−0.599632	+	0.800276i	$0.704686\pi$
$278$			3.16646e11i			0.190700i
$279$	−1.38674e11	−	4.26319e11i	−0.0820304	−	0.252182i
$280$	1.56666e12			0.910303
$281$			5.39493e11i			0.307932i	0.988076	+	0.153966i	$0.0492046\pi$
$281$			5.39493e11i			0.307932i	−0.988076	+	0.153966i	$0.950795\pi$
$282$	−3.75729e11	−	2.72889e11i	−0.210683	−	0.153017i
$283$	1.19513e12			0.658389			0.329195	−	0.944262i	$-0.393223\pi$
$283$	1.19513e12			0.658389			0.329195	+	0.944262i	$0.393223\pi$
$284$		−	3.83857e12i		−	2.07768i
$285$	6.15221e11	−	8.47071e11i	0.327195	−	0.450501i
$286$	−9.74450e8			−0.000509248
$287$			2.02704e12i			1.04100i
$288$	1.77077e12	−	5.76001e11i	0.893716	−	0.290710i
$289$	−2.96760e11			−0.147203
$290$			5.10912e11i			0.249090i
$291$	1.46147e12	+	1.06146e12i	0.700367	+	0.508671i
$292$	−1.06387e12			−0.501160
$293$			2.33135e12i			1.07961i	0.841789	+	0.539807i	$0.181503\pi$
$293$			2.33135e12i			1.07961i	−0.841789	+	0.539807i	$0.818497\pi$
$294$	−5.67073e12	+	7.80778e12i	−2.58168	+	3.55460i
$295$	−3.27816e11			−0.146730
$296$			3.30323e12i			1.45372i
$297$	1.36862e11	+	4.43946e10i	0.0592243	+	0.0192109i
$298$	1.57158e12			0.668735
$299$		−	1.61839e10i		−	0.00677218i
$300$	6.48887e11	+	4.71282e11i	0.267032	+	0.193943i
$301$	−2.29004e12			−0.926852
$302$		−	1.86138e12i		−	0.740970i
$303$	1.09345e12	−	1.50552e12i	0.428138	−	0.589485i
$304$	2.35479e11			0.0906950
$305$		−	1.11461e12i		−	0.422301i
$306$	−1.44705e12	−	4.44859e12i	−0.539357	−	1.65812i
$307$	−1.37947e12			−0.505848			−0.252924	−	0.967486i	$-0.581392\pi$
$307$	−1.37947e12			−0.505848			−0.252924	+	0.967486i	$0.581392\pi$
$308$		−	5.47675e11i		−	0.197592i
$309$	2.31127e12	+	1.67865e12i	0.820460	+	0.595894i
$310$	−5.52729e11			−0.193065
$311$		−	1.61853e12i		−	0.556314i	−0.960536	−	0.278157i	$-0.910276\pi$
$311$		−	1.61853e12i		−	0.556314i	0.960536	−	0.278157i	$-0.0897235\pi$
$312$	−9.23874e9	+	1.27204e10i	−0.00312493	+	0.00430258i
$313$	6.89035e11			0.229361			0.114681	−	0.993402i	$-0.463416\pi$
$313$	6.89035e11			0.229361			0.114681	+	0.993402i	$0.463416\pi$
$314$			2.86354e12i			0.938113i
$315$	−2.53658e12	+	8.25107e11i	−0.817893	+	0.266046i
$316$	6.40824e12			2.03378
$317$			3.99522e11i			0.124809i	0.998051	+	0.0624043i	$0.0198768\pi$
$317$			3.99522e11i			0.124809i	−0.998051	+	0.0624043i	$0.980123\pi$
$318$	−3.06828e12	−	2.22846e12i	−0.943537	−	0.685283i
$319$	7.03693e10			0.0213025
$320$		−	2.40515e12i		−	0.716789i
$321$	−2.82706e12	+	3.89245e12i	−0.829487	+	1.14208i
$322$	1.46081e13			4.22003
$323$			4.68817e12i			1.33349i
$324$	4.76430e12	−	3.46625e12i	1.33436	−	0.970811i
$325$	3.64348e9			0.00100485
$326$			6.44748e12i			1.75107i
$327$	−1.87251e12	−	1.35999e12i	−0.500825	−	0.363745i
$328$	−2.17495e12			−0.572902
$329$		−	1.18573e12i		−	0.307614i
$330$	1.04247e11	−	1.43534e11i	0.0266376	−	0.0366762i
$331$	2.66426e12			0.670558			0.335279	−	0.942119i	$-0.391169\pi$
$331$	2.66426e12			0.670558			0.335279	+	0.942119i	$0.391169\pi$
$332$		−	1.58494e12i		−	0.392936i
$333$	−1.73970e12	−	5.34826e12i	−0.424866	−	1.30614i
$334$	−2.86294e12			−0.688779
$335$		−	1.10392e12i		−	0.261645i
$336$	−4.85445e11	−	3.52574e11i	−0.113356	−	0.0823293i
$337$	−2.09304e12			−0.481534			−0.240767	−	0.970583i	$-0.577399\pi$
$337$	−2.09304e12			−0.481534			−0.240767	+	0.970583i	$0.577399\pi$
$338$		−	7.18138e12i		−	1.62789i
$339$	4.30789e12	−	5.93135e12i	0.962202	−	1.32482i
$340$	−3.59131e12			−0.790422
$341$			7.61290e10i			0.0165112i
$342$	−9.01772e12	+	2.93331e12i	−1.92738	+	0.626942i
$343$	−1.55094e13			−3.26682
$344$		−	2.45715e12i		−	0.510080i
$345$	2.38385e12	+	1.73137e12i	0.487734	+	0.354237i
$346$	−9.59265e12			−1.93445
$347$			8.37421e12i			1.66455i	0.554365	+	0.832274i	$0.312961\pi$
$347$			8.37421e12i			1.66455i	−0.554365	+	0.832274i	$0.687039\pi$
$348$	1.69335e12	−	2.33150e12i	0.331780	−	0.456813i
$349$	−1.42259e12			−0.274760			−0.137380	−	0.990518i	$-0.543868\pi$
$349$	−1.42259e12			−0.274760			−0.137380	+	0.990518i	$0.543868\pi$
$350$			3.28872e12i			0.626162i
$351$	8.25902e9	−	2.54613e10i	0.00155022	−	0.00477909i
$352$	−3.16211e11			−0.0585146
$353$			1.34382e12i			0.245170i	0.992458	+	0.122585i	$0.0391184\pi$
$353$			1.34382e12i			0.245170i	−0.992458	+	0.122585i	$0.960882\pi$
$354$	2.40251e12	+	1.74493e12i	0.432165	+	0.313878i
$355$	3.17476e12			0.563079
$356$			1.16895e13i			2.04431i
$357$	7.01945e12	−	9.66478e12i	1.21049	−	1.66668i
$358$	7.11075e12			1.20921
$359$		−	6.92014e12i		−	1.16049i	−0.814441	−	0.580247i	$-0.802956\pi$
$359$		−	6.92014e12i		−	1.16049i	0.814441	−	0.580247i	$-0.197044\pi$
$360$	−8.85315e11	−	2.72168e12i	−0.146415	−	0.450116i
$361$	3.37231e12			0.550037
$362$		−	1.35541e12i		−	0.218037i
$363$	5.07991e12	+	3.68949e12i	0.805977	+	0.585374i
$364$	−1.01888e11			−0.0159446
$365$		−	8.79897e11i		−	0.135821i
$366$	−5.93292e12	+	8.16878e12i	−0.903364	+	1.24380i
$367$	3.85838e12			0.579529			0.289764	−	0.957098i	$-0.406423\pi$
$367$	3.85838e12			0.579529			0.289764	+	0.957098i	$0.406423\pi$
$368$			6.62690e11i			0.0981909i
$369$	3.52146e12	−	1.14547e12i	0.514743	−	0.167437i
$370$	−6.93410e12			−0.999958
$371$		−	9.68289e12i		−	1.37764i
$372$	2.52233e12	+	1.83195e12i	0.354068	+	0.257157i
$373$	5.54244e12			0.767638			0.383819	−	0.923408i	$-0.374609\pi$
$373$	5.54244e12			0.767638			0.383819	+	0.923408i	$0.374609\pi$
$374$			7.94398e11i			0.108563i
$375$	−3.89782e11	+	5.36674e11i	−0.0525612	+	0.0723693i
$376$	1.27225e12			0.169291
$377$		−	1.30913e10i		−	0.00171900i
$378$	2.29822e13	+	7.45486e12i	2.97805	+	0.966007i
$379$	2.18032e12			0.278820			0.139410	−	0.990235i	$-0.455479\pi$
$379$	2.18032e12			0.278820			0.139410	+	0.990235i	$0.455479\pi$
$380$			7.27994e12i			0.918776i
$381$	−6.40387e12	−	4.65108e12i	−0.797660	−	0.579334i
$382$	3.39160e12			0.416954
$383$		−	1.24412e13i		−	1.50963i	−0.655939	−	0.754814i	$-0.727727\pi$
$383$		−	1.24412e13i		−	1.50963i	0.655939	−	0.754814i	$-0.272273\pi$
$384$	−8.19109e12	+	1.12780e13i	−0.981037	+	1.35075i
$385$	4.52965e11			0.0535502
$386$		−	1.05044e13i		−	1.22585i
$387$	1.29409e12	+	3.97836e12i	0.149077	+	0.458299i
$388$	−1.25603e13			−1.42837
$389$			1.77168e13i			1.98901i	0.104691	+	0.994505i	$0.466615\pi$
$389$			1.77168e13i			1.98901i	−0.104691	+	0.994505i	$0.533385\pi$
$390$	−2.67025e10	−	1.93938e10i	−0.00295957	−	0.00214951i
$391$	−1.31936e13			−1.44371
$392$		−	2.64378e13i		−	2.85625i
$393$	−9.85377e12	+	1.35672e13i	−1.05109	+	1.44720i
$394$	1.40354e13			1.47823
$395$			5.30005e12i			0.551181i
$396$	−9.51446e11	+	3.09489e11i	−0.0977030	+	0.0317811i
$397$	1.25112e13			1.26866			0.634332	−	0.773061i	$-0.281275\pi$
$397$	1.25112e13			1.26866			0.634332	+	0.773061i	$0.281275\pi$
$398$			1.35768e13i			1.35951i
$399$	−1.95914e13	−	1.42291e13i	−1.93732	−	1.40706i
$400$	−1.49191e11			−0.0145694
$401$		−	6.26453e12i		−	0.604180i	−0.953279	−	0.302090i	$-0.902316\pi$
$401$		−	6.26453e12i		−	0.604180i	0.953279	−	0.302090i	$-0.0976844\pi$
$402$	−5.87603e12	+	8.09045e12i	−0.559698	+	0.770624i
$403$	1.41628e10			0.00133237
$404$			1.29388e13i			1.20223i
$405$	2.86682e12	+	3.94040e12i	0.263103	+	0.361631i
$406$	1.18166e13			1.07118
$407$			9.55054e11i			0.0855177i
$408$	1.03700e13	+	7.53166e12i	0.917232	+	0.666178i
$409$	−3.14255e12			−0.274578			−0.137289	−	0.990531i	$-0.543839\pi$
$409$	−3.14255e12			−0.274578			−0.137289	+	0.990531i	$0.543839\pi$
$410$		−	4.56562e12i		−	0.394077i
$411$	−3.49682e12	+	4.81462e12i	−0.298170	+	0.410538i
$412$	−1.98636e13			−1.67329
$413$			7.58187e12i			0.630996i
$414$	−8.25499e12	−	2.53779e13i	−0.678758	−	2.08667i
$415$	1.31085e12			0.106491
$416$			5.88269e10i			0.00472182i
$417$	1.19510e12	+	8.67992e11i	0.0947817	+	0.0688392i
$418$	1.61032e12			0.126192
$419$		−	1.25900e13i		−	0.974886i	−0.873155	−	0.487443i	$-0.837930\pi$
$419$		−	1.25900e13i		−	0.974886i	0.873155	−	0.487443i	$-0.162070\pi$
$420$	1.09000e13	−	1.50078e13i	0.834028	−	1.14834i
$421$	1.91520e13			1.44812			0.724060	−	0.689737i	$-0.242274\pi$
$421$	1.91520e13			1.44812			0.724060	+	0.689737i	$0.242274\pi$
$422$		−	1.86276e13i		−	1.39186i
$423$	−2.05990e12	+	6.70050e11i	−0.152105	+	0.0494772i
$424$	1.03895e13			0.758165
$425$		−	2.97026e12i		−	0.214215i
$426$	−2.32674e13	−	1.68989e13i	−1.65844	−	1.20451i
$427$	−2.57791e13			−1.81605
$428$		−	3.34527e13i		−	2.32923i
$429$	−2.67117e9	+	3.67782e9i	−0.000183829	+	0.000253107i
$430$	5.15800e12			0.350864
$431$			3.18338e12i			0.214044i	0.994257	+	0.107022i	$0.0341315\pi$
$431$			3.18338e12i			0.214044i	−0.994257	+	0.107022i	$0.965869\pi$
$432$	−3.38185e11	+	1.04257e12i	−0.0224769	+	0.0692928i
$433$	4.11495e12			0.270349			0.135175	−	0.990822i	$-0.456840\pi$
$433$	4.11495e12			0.270349			0.135175	+	0.990822i	$0.456840\pi$
$434$			1.27838e13i			0.830253i
$435$	1.92831e12	+	1.40051e12i	0.123803	+	0.0899169i
$436$	1.60928e13			1.02141
$437$			2.67447e13i			1.67815i
$438$	−4.68359e12	+	6.44863e12i	−0.290542	+	0.400034i
$439$	1.32207e13			0.810835			0.405418	−	0.914132i	$-0.367126\pi$
$439$	1.32207e13			0.810835			0.405418	+	0.914132i	$0.367126\pi$
$440$			4.86018e11i			0.0294706i
$441$	1.39239e13	+	4.28054e13i	0.834770	+	2.56629i
$442$	1.47787e11			0.00876042
$443$		−	2.00203e13i		−	1.17341i	−0.809800	−	0.586706i	$-0.800424\pi$
$443$		−	2.00203e13i		−	1.17341i	0.809800	−	0.586706i	$-0.199576\pi$
$444$	3.16431e13	+	2.29821e13i	1.83385	+	1.33191i
$445$	−9.66804e12			−0.554037
$446$		−	1.54439e13i		−	0.875148i
$447$	4.30801e12	−	5.93152e12i	0.241401	−	0.332375i
$448$	−5.56273e13			−3.08246
$449$		−	2.18773e12i		−	0.119884i	−0.998202	−	0.0599421i	$-0.980908\pi$
$449$		−	2.18773e12i		−	0.119884i	0.998202	−	0.0599421i	$-0.0190916\pi$
$450$	5.71331e12	−	1.85844e12i	0.309617	−	0.100713i
$451$	−6.28836e11			−0.0337019
$452$			5.09755e13i			2.70190i
$453$	−7.02531e12	−	5.10243e12i	−0.368277	−	0.267477i
$454$	−2.92418e13			−1.51609
$455$		−	8.42681e10i		−	0.00432122i
$456$	1.52674e13	−	2.10210e13i	0.774357	−	1.06618i
$457$	2.60002e13			1.30436			0.652178	−	0.758066i	$-0.273856\pi$
$457$	2.60002e13			1.30436			0.652178	+	0.758066i	$0.273856\pi$
$458$			1.92518e13i			0.955307i
$459$	−2.07567e13	−	6.73298e12i	−1.01882	−	0.330479i
$460$	−2.04874e13			−0.994712
$461$		−	3.32779e13i		−	1.59828i	−0.601147	−	0.799138i	$-0.705290\pi$
$461$		−	3.32779e13i		−	1.59828i	0.601147	−	0.799138i	$-0.294710\pi$
$462$	−3.31971e12	−	2.41108e12i	−0.157721	−	0.114552i
$463$	3.90586e13			1.83574			0.917872	−	0.396877i	$-0.129906\pi$
$463$	3.90586e13			1.83574			0.917872	+	0.396877i	$0.129906\pi$
$464$			5.36053e11i			0.0249240i
$465$	−1.51514e12	+	2.08614e12i	−0.0696930	+	0.0959573i
$466$	4.48308e13			2.04008
$467$			4.38166e13i			1.97267i	0.164750	+	0.986335i	$0.447318\pi$
$467$			4.38166e13i			1.97267i	−0.164750	+	0.986335i	$0.552682\pi$
$468$	5.75763e10	+	1.77004e11i	0.00256457	+	0.00788412i
$469$	−2.55319e13			−1.12517
$470$			2.67069e12i			0.116449i
$471$	1.08077e13	+	7.84955e12i	0.466261	+	0.338642i
$472$	−8.13513e12			−0.347260
$473$		−	7.10427e11i		−	0.0300064i
$474$	2.82116e13	−	3.88433e13i	1.17906	−	1.62339i
$475$	−6.02101e12			−0.249001
$476$			8.30615e13i			3.39911i
$477$	−1.68215e13	+	5.47176e12i	−0.681199	+	0.221582i
$478$	−2.56617e13			−1.02836
$479$			4.84957e13i			1.92321i	0.274443	+	0.961603i	$0.411507\pi$
$479$			4.84957e13i			1.92321i	−0.274443	+	0.961603i	$0.588493\pi$
$480$	−8.66504e12	−	6.29334e12i	−0.340067	−	0.246988i
$481$	1.77675e11			0.00690082
$482$		−	3.37066e13i		−	1.29563i
$483$	4.00439e13	−	5.51347e13i	1.52335	−	2.09744i
$484$	−4.36580e13			−1.64375
$485$		−	1.03882e13i		−	0.387107i
$486$	−3.62296e10	−	4.41384e13i	−0.00133623	−	1.62793i
$487$	1.86070e13			0.679253			0.339627	−	0.940560i	$-0.389699\pi$
$487$	1.86070e13			0.679253			0.339627	+	0.940560i	$0.389699\pi$
$488$		−	2.76602e13i		−	0.999440i
$489$	2.43344e13	+	1.76739e13i	0.870315	+	0.632103i
$490$	5.54979e13			1.96470
$491$		−	2.88351e13i		−	1.01045i	−0.862988	−	0.505224i	$-0.831410\pi$
$491$		−	2.88351e13i		−	1.01045i	0.862988	−	0.505224i	$-0.168590\pi$
$492$	−1.51321e13	+	2.08348e13i	−0.524898	+	0.722709i
$493$	−1.06724e13			−0.366459
$494$		−	2.99579e11i		−	0.0101830i
$495$	−2.55968e11	−	7.86911e11i	−0.00861312	−	0.0264789i
$496$	−5.79929e11			−0.0193182
$497$		−	7.34273e13i		−	2.42145i
$498$	−9.60705e12	−	6.97752e12i	−0.313649	−	0.227800i
$499$	2.27303e13			0.734687			0.367343	−	0.930085i	$-0.380267\pi$
$499$	2.27303e13			0.734687			0.367343	+	0.930085i	$0.380267\pi$
$500$		−	4.61231e12i		−	0.147594i
$501$	−7.84790e12	+	1.08054e13i	−0.248637	+	0.342337i
$502$	−3.18516e13			−0.999109
$503$			3.70818e12i			0.115165i	0.998341	+	0.0575826i	$0.0183392\pi$
$503$			3.70818e12i			0.115165i	−0.998341	+	0.0575826i	$0.981661\pi$
$504$	−6.29482e13	+	2.04760e13i	−1.93567	+	0.629639i
$505$	−1.07013e13			−0.325821
$506$			4.53180e12i			0.136621i
$507$	−2.71043e13	−	1.96856e13i	−0.809093	−	0.587638i
$508$	5.50365e13			1.62679
$509$		−	2.92019e13i		−	0.854717i	−0.904082	−	0.427359i	$-0.859444\pi$
$509$		−	2.92019e13i		−	0.854717i	0.904082	−	0.427359i	$-0.140556\pi$
$510$	−1.58104e13	+	2.17686e13i	−0.458238	+	0.630928i
$511$	−2.03507e13			−0.584082
$512$		−	5.12157e12i		−	0.145564i
$513$	−1.36484e13	+	4.20759e13i	−0.384144	+	1.18426i
$514$	7.94788e13			2.21531
$515$		−	1.64286e13i		−	0.453485i
$516$	−2.35381e13	−	1.70955e13i	−0.643461	−	0.467340i
$517$	3.67842e11			0.00995884
$518$			1.60375e14i			4.30019i
$519$	−2.62954e13	+	3.62050e13i	−0.698302	+	0.961462i
$520$	9.04171e10			0.00237812
$521$			5.27199e12i			0.137336i	0.997640	+	0.0686682i	$0.0218750\pi$
$521$			5.27199e12i			0.137336i	−0.997640	+	0.0686682i	$0.978125\pi$
$522$	−6.67751e12	−	2.05283e13i	−0.172291	−	0.529664i
$523$	−6.12340e13			−1.56489			−0.782446	−	0.622719i	$-0.786028\pi$
$523$	−6.12340e13			−1.56489			−0.782446	+	0.622719i	$0.786028\pi$
$524$		−	1.16600e14i		−	2.95150i
$525$	1.24124e13	+	9.01506e12i	0.311215	+	0.226033i
$526$	−1.10570e14			−2.74604
$527$		−	1.15459e13i		−	0.284036i
$528$	1.09377e11	−	1.50597e11i	0.00266537	−	0.00366983i
$529$	−3.38390e13			−0.816844
$530$			2.18094e13i			0.521512i
$531$	1.31716e13	−	4.28448e12i	0.312007	−	0.101491i
$532$	1.68374e14			3.95108
$533$			1.16987e11i			0.00271957i
$534$	7.08557e13	+	5.14619e13i	1.63181	+	1.18517i
$535$	2.76677e13			0.631254
$536$		−	2.73950e13i		−	0.619223i
$537$	1.94920e13	−	2.68377e13i	0.436501	−	0.601000i
$538$	−2.01475e11			−0.00447002
$539$		−	7.64389e12i		−	0.168024i
$540$	−3.22317e13	−	1.04552e13i	−0.701963	−	0.227700i
$541$	−3.51224e13			−0.757874			−0.378937	−	0.925422i	$-0.623710\pi$
$541$	−3.51224e13			−0.757874			−0.378937	+	0.925422i	$0.623710\pi$
$542$			4.88509e13i			1.04442i
$543$	−5.11567e12	−	3.71547e12i	−0.108369	−	0.0787072i
$544$	4.79573e13			1.00661
$545$			1.33099e13i			0.276816i
$546$	−4.48549e11	+	6.17588e11i	−0.00924372	+	0.0127273i
$547$	−9.50521e13			−1.94100			−0.970499	−	0.241105i	$-0.922490\pi$
$547$	−9.50521e13			−1.94100			−0.970499	+	0.241105i	$0.922490\pi$
$548$		−	4.13781e13i		−	0.837274i
$549$	1.45677e13	+	4.47846e13i	0.292098	+	0.897981i
$550$	−1.02024e12			−0.0202717
$551$			2.16339e13i			0.425968i
$552$	5.91579e13	+	4.29659e13i	1.15430	+	0.838357i
$553$	1.22582e14			2.37029
$554$		−	1.01882e14i		−	1.95232i
$555$	−1.90078e13	+	2.61710e13i	−0.360967	+	0.496999i
$556$	−1.02710e13			−0.193303
$557$		−	4.00180e13i		−	0.746414i	−0.927748	−	0.373207i	$-0.878258\pi$
$557$		−	4.00180e13i		−	0.746414i	0.927748	−	0.373207i	$-0.121742\pi$
$558$	2.22085e13	−	7.22405e12i	0.410534	−	0.133540i
$559$	−1.32165e11			−0.00242136
$560$			3.45056e12i			0.0626540i
$561$	2.99825e12	+	2.17761e12i	0.0539578	+	0.0391891i
$562$	−2.81042e13			−0.501291
$563$			2.48264e13i			0.438907i	0.975623	+	0.219453i	$0.0704274\pi$
$563$			2.48264e13i			0.438907i	−0.975623	+	0.219453i	$0.929573\pi$
$564$	8.85165e12	−	1.21875e13i	0.155106	−	0.213559i
$565$	−4.21602e13			−0.732252
$566$			6.22587e13i			1.07181i
$567$	9.11354e13	−	6.63052e13i	1.55515	−	1.13144i
$568$	7.87853e13			1.33261
$569$			9.21231e13i			1.54457i	0.635277	+	0.772284i	$0.280886\pi$
$569$			9.21231e13i			1.54457i	−0.635277	+	0.772284i	$0.719114\pi$
$570$	4.41271e13	+	3.20491e13i	0.733383	+	0.532650i
$571$	2.53770e13			0.418081			0.209040	−	0.977907i	$-0.432966\pi$
$571$	2.53770e13			0.418081			0.209040	+	0.977907i	$0.432966\pi$
$572$		−	3.16081e10i		−	0.000516200i
$573$	9.29708e12	−	1.28008e13i	0.150513	−	0.207235i
$574$	−1.05596e14			−1.69468
$575$		−	1.69445e13i		−	0.269581i
$576$	3.14347e13	+	9.66382e13i	0.495790	+	1.52418i
$577$	−1.12909e14			−1.76543			−0.882713	−	0.469913i	$-0.844285\pi$
$577$	−1.12909e14			−1.76543			−0.882713	+	0.469913i	$0.844285\pi$
$578$		−	1.54593e13i		−	0.239636i
$579$	−3.96464e13	−	2.87948e13i	−0.609271	−	0.442509i
$580$	−1.65724e13			−0.252490
$581$		−	3.03180e13i		−	0.457952i
$582$	−5.52952e13	+	7.61335e13i	−0.828080	+	1.14015i
$583$	3.00387e12			0.0446004
$584$		−	2.18357e13i		−	0.321441i
$585$	−1.46394e11	+	4.76195e10i	−0.00213671	+	0.000695033i
$586$	−1.21449e14			−1.75754
$587$			3.40736e13i			0.488909i	0.969661	+	0.244454i	$0.0786088\pi$
$587$			3.40736e13i			0.488909i	−0.969661	+	0.244454i	$0.921391\pi$
$588$	−2.53260e14	−	1.83940e14i	−3.60312	−	2.61692i
$589$	−2.34046e13			−0.330160
$590$		−	1.70771e13i		−	0.238866i
$591$	3.84739e13	−	5.29730e13i	0.533616	−	0.734713i
$592$	−7.27533e12			−0.100056
$593$		−	1.19631e14i		−	1.63144i	−0.578450	−	0.815718i	$-0.696342\pi$
$593$		−	1.19631e14i		−	1.63144i	0.578450	−	0.815718i	$-0.303658\pi$
$594$	−2.31268e12	+	7.12964e12i	−0.0312740	+	0.0964130i
$595$	−6.86976e13			−0.921206
$596$			5.09770e13i			0.677864i
$597$	5.12423e13	+	3.72169e13i	0.675705	+	0.490759i
$598$	8.43082e11			0.0110246
$599$			5.90145e13i			0.765288i	0.923896	+	0.382644i	$0.124986\pi$
$599$			5.90145e13i			0.765288i	−0.923896	+	0.382644i	$0.875014\pi$
$600$	−9.67289e12	+	1.33182e13i	−0.124394	+	0.171273i
$601$	8.10816e13			1.03407			0.517035	−	0.855964i	$-0.327036\pi$
$601$	8.10816e13			1.03407			0.517035	+	0.855964i	$0.327036\pi$
$602$		−	1.19297e14i		−	1.50885i
$603$	1.44280e13	+	4.43552e13i	0.180975	+	0.556362i
$604$	6.03773e13			0.751084
$605$		−	3.61081e13i		−	0.445480i
$606$	7.84280e13	+	5.69616e13i	0.959640	+	0.696978i
$607$	3.44451e13			0.418008			0.209004	−	0.977915i	$-0.432978\pi$
$607$	3.44451e13			0.418008			0.209004	+	0.977915i	$0.432978\pi$
$608$		−	9.72140e13i		−	1.17007i
$609$	3.23917e13	−	4.45988e13i	0.386676	−	0.532398i
$610$	5.80640e13			0.687476
$611$		−	6.84321e10i		−	0.000803626i
$612$	1.44298e14	−	4.69377e13i	1.68075	−	0.546720i
$613$	2.13648e13			0.246829			0.123415	−	0.992355i	$-0.460616\pi$
$613$	2.13648e13			0.246829			0.123415	+	0.992355i	$0.460616\pi$
$614$		−	7.18617e13i		−	0.823485i
$615$	−1.72318e13	−	1.25153e13i	−0.195864	−	0.142255i
$616$	1.12408e13			0.126735
$617$			1.12109e14i			1.25376i	0.779114	+	0.626882i	$0.215669\pi$
$617$			1.12109e14i			1.25376i	−0.779114	+	0.626882i	$0.784331\pi$
$618$	−8.74473e13	+	1.20402e14i	−0.970072	+	1.33565i
$619$	1.53149e14			1.68524			0.842619	−	0.538510i	$-0.181013\pi$
$619$	1.53149e14			1.68524			0.842619	+	0.538510i	$0.181013\pi$
$620$		−	1.79288e13i		−	0.195701i
$621$	−1.18411e14	−	3.84096e13i	−1.28214	−	0.415894i
$622$	8.43154e13			0.905639
$623$			2.23607e14i			2.38257i
$624$	−2.80165e10	−	2.03482e10i	−0.000296136	−	0.000215081i
$625$	3.81470e12			0.0400000
$626$			3.58944e13i			0.373383i
$627$	4.41422e12	−	6.07775e12i	0.0455529	−	0.0627198i
$628$	−9.28842e13			−0.950919
$629$		−	1.44845e14i		−	1.47113i
$630$	−4.29829e13	−	1.32140e14i	−0.433105	−	1.33147i
$631$	1.63287e14			1.63232			0.816159	−	0.577827i	$-0.196099\pi$
$631$	1.63287e14			1.63232			0.816159	+	0.577827i	$0.196099\pi$
$632$			1.31527e14i			1.30445i
$633$	−7.03053e13	−	5.10621e13i	−0.691782	−	0.502436i
$634$	−2.08126e13			−0.203179
$635$			4.55189e13i			0.440883i
$636$	7.22843e13	−	9.95251e13i	0.694638	−	0.956417i
$637$	−1.42204e12			−0.0135586
$638$			3.66580e12i			0.0346789i
$639$	−1.27561e14	+	4.14934e13i	−1.19733	+	0.389471i
$640$	8.01641e13			0.746586
$641$			5.57998e13i			0.515636i	0.966194	+	0.257818i	$0.0830034\pi$
$641$			5.57998e13i			0.515636i	−0.966194	+	0.257818i	$0.916997\pi$
$642$	−2.02772e14	−	1.47272e14i	−1.85923	−	1.35035i
$643$	7.98393e13			0.726377			0.363188	−	0.931716i	$-0.381688\pi$
$643$	7.98393e13			0.726377			0.363188	+	0.931716i	$0.381688\pi$
$644$			4.73842e14i			4.27764i
$645$	1.41391e13	−	1.94676e13i	0.126656	−	0.174387i
$646$	−2.44224e14			−2.17083
$647$		−	8.99383e13i		−	0.793274i	−0.917975	−	0.396637i	$-0.870177\pi$
$647$		−	8.99383e13i		−	0.793274i	0.917975	−	0.396637i	$-0.129823\pi$
$648$	7.11435e13	+	9.77856e13i	0.622674	+	0.855854i
$649$	−2.35208e12			−0.0204282
$650$			1.89802e11i			0.00163582i
$651$	4.82491e13	+	3.50430e13i	0.412653	+	0.299706i
$652$	−2.09136e14			−1.77497
$653$		−	1.17051e14i		−	0.985843i	−0.870074	−	0.492922i	$-0.835929\pi$
$653$		−	1.17051e14i		−	0.985843i	0.870074	−	0.492922i	$-0.164071\pi$
$654$	7.08470e13	−	9.75461e13i	0.592151	−	0.815307i
$655$	9.64363e13			0.799897
$656$		−	4.79029e12i		−	0.0394315i
$657$	1.15001e13	+	3.53541e13i	0.0939449	+	0.288810i
$658$	6.17690e13			0.500773
$659$			1.41996e14i			1.14248i	0.820783	+	0.571240i	$0.193537\pi$
$659$			1.41996e14i			1.14248i	−0.820783	+	0.571240i	$0.806463\pi$
$660$	4.65578e12	+	3.38145e12i	0.0371768	+	0.0270012i
$661$	−7.94016e13			−0.629248			−0.314624	−	0.949216i	$-0.601878\pi$
$661$	−7.94016e13			−0.629248			−0.314624	+	0.949216i	$0.601878\pi$
$662$			1.38791e14i			1.09162i
$663$	4.05115e11	−	5.57785e11i	0.00316235	−	0.00435411i
$664$	3.25303e13			0.252028
$665$			1.39257e14i			1.07080i
$666$	2.78611e14	−	9.06272e13i	2.12631	−	0.691652i
$667$	−6.08826e13			−0.461173
$668$		−	9.28646e13i		−	0.698181i
$669$	−5.82890e13	−	4.23348e13i	−0.434967	−	0.315913i
$670$	5.75072e13			0.425940
$671$		−	7.99731e12i		−	0.0587938i
$672$	−1.45555e14	+	2.00409e14i	−1.06214	+	1.46241i
$673$	7.21303e13			0.522447			0.261223	−	0.965278i	$-0.415874\pi$
$673$	7.21303e13			0.522447			0.261223	+	0.965278i	$0.415874\pi$
$674$		−	1.09034e14i		−	0.783903i
$675$	8.64714e12	−	2.66578e13i	0.0617097	−	0.190242i
$676$	2.32941e14			1.65011
$677$		−	1.17051e14i		−	0.823058i	−0.911397	−	0.411529i	$-0.864995\pi$
$677$		−	1.17051e14i		−	0.823058i	0.911397	−	0.411529i	$-0.135005\pi$
$678$	3.08986e14	+	2.24414e14i	2.15670	+	1.56640i
$679$	−2.40263e14			−1.66471
$680$		−	7.37105e13i		−	0.506973i
$681$	−8.01577e13	+	1.10366e14i	−0.547280	+	0.753526i
$682$	−3.96584e12			−0.0268790
$683$			1.40829e14i			0.947518i	0.880654	+	0.473759i	$0.157103\pi$
$683$			1.40829e14i			0.947518i	−0.880654	+	0.473759i	$0.842897\pi$
$684$	−9.51472e13	−	2.92506e14i	−0.635500	−	1.95369i
$685$	3.42225e13			0.226913
$686$		−	8.07943e14i		−	5.31814i
$687$	7.26609e13	+	5.27730e13i	0.474807	+	0.344848i
$688$	5.41183e12			0.0351076
$689$		−	5.58830e11i		−	0.00359902i
$690$	−9.01935e13	+	1.24184e14i	−0.576673	+	0.793996i
$691$	3.78789e13			0.240440			0.120220	−	0.992747i	$-0.461640\pi$
$691$	3.78789e13			0.240440			0.120220	+	0.992747i	$0.461640\pi$
$692$		−	3.11155e14i		−	1.96086i
$693$	−1.82000e13	+	5.92015e12i	−0.113869	+	0.0370397i
$694$	−4.36243e14			−2.70976
$695$		−	8.49482e12i		−	0.0523878i
$696$	4.78532e13	+	3.47554e13i	0.292998	+	0.212802i
$697$	9.53706e13			0.579763
$698$		−	7.41081e13i		−	0.447289i
$699$	1.22890e14	−	1.69202e14i	0.736431	−	1.01396i
$700$	−1.06676e14			−0.634710
$701$		−	8.79519e13i		−	0.519584i	−0.965665	−	0.259792i	$-0.916346\pi$
$701$		−	8.79519e13i		−	0.519584i	0.965665	−	0.259792i	$-0.0836539\pi$
$702$	1.32637e12	+	4.30243e11i	0.00778002	+	0.00252365i
$703$	−2.93616e14			−1.71002
$704$		−	1.72570e13i		−	0.0997932i
$705$	1.00799e13	+	7.32092e12i	0.0578774	+	0.0420359i
$706$	−7.00045e13			−0.399119
$707$			2.47504e14i			1.40115i
$708$	−5.65999e13	+	7.79299e13i	−0.318163	+	0.438064i
$709$	1.80344e14			1.00663			0.503315	−	0.864103i	$-0.332114\pi$
$709$	1.80344e14			1.00663			0.503315	+	0.864103i	$0.332114\pi$
$710$			1.65385e14i			0.916652i
$711$	−6.92705e13	−	2.12955e14i	−0.381242	−	1.17203i
$712$	−2.39924e14			−1.31121
$713$		−	6.58658e13i		−	0.357448i
$714$	5.03474e14	+	3.65669e14i	2.71323	+	1.97060i
$715$	2.61420e10			0.000139897
$716$			2.30650e14i			1.22571i
$717$	−7.03439e13	+	9.68535e13i	−0.371220	+	0.511116i
$718$	3.60496e14			1.88920
$719$			1.52331e14i			0.792765i	0.918086	+	0.396382i	$0.129735\pi$
$719$			1.52331e14i			0.792765i	−0.918086	+	0.396382i	$0.870265\pi$
$720$	5.99446e12	−	1.94989e12i	0.0309804	−	0.0100774i
$721$	−3.79967e14			−1.95016
$722$			1.75676e14i			0.895421i
$723$	−1.27217e14	−	9.23968e13i	−0.643953	−	0.467698i
$724$	4.39653e13			0.221013
$725$		−	1.37065e13i		−	0.0684283i
$726$	−1.92199e14	+	2.64631e14i	−0.952948	+	1.31207i
$727$	2.88764e14			1.42191			0.710954	−	0.703239i	$-0.248264\pi$
$727$	2.88764e14			1.42191			0.710954	+	0.703239i	$0.248264\pi$
$728$		−	2.09121e12i		−	0.0102268i
$729$	−1.66689e14	−	1.20856e14i	−0.809596	−	0.586988i
$730$	4.58371e13			0.221107
$731$			1.07745e14i			0.516190i
$732$	−2.64969e14	−	1.92445e14i	−1.26078	−	0.915696i
$733$	−1.76212e14			−0.832752			−0.416376	−	0.909193i	$-0.636700\pi$
$733$	−1.76212e14			−0.832752			−0.416376	+	0.909193i	$0.636700\pi$
$734$			2.00997e14i			0.943431i
$735$	1.52131e14	−	2.09463e14i	0.709221	−	0.976496i
$736$	2.73582e14			1.26677
$737$		−	7.92063e12i		−	0.0364269i
$738$	5.96717e13	+	1.83446e14i	0.272575	+	0.837965i
$739$	1.43897e14			0.652876			0.326438	−	0.945219i	$-0.394152\pi$
$739$	1.43897e14			0.652876			0.326438	+	0.945219i	$0.394152\pi$
$740$		−	2.24920e14i		−	1.01361i
$741$	−1.13068e12	−	8.21206e11i	−0.00506116	−	0.00367588i
$742$	5.04418e14			2.24270
$743$		−	3.20494e14i		−	1.41539i	−0.706519	−	0.707694i	$-0.749736\pi$
$743$		−	3.20494e14i		−	1.41539i	0.706519	−	0.707694i	$-0.250264\pi$
$744$	−3.76001e13	+	5.17699e13i	−0.164939	+	0.227098i
$745$	−4.21614e13			−0.183711
$746$			2.88726e14i			1.24966i
$747$	−5.26698e13	+	1.71326e13i	−0.226443	+	0.0736579i
$748$	−2.57677e13			−0.110044
$749$		−	6.39911e14i		−	2.71463i
$750$	−2.79574e13	−	2.03052e13i	−0.117812	−	0.0855659i
$751$	1.14203e14			0.478055			0.239027	−	0.971013i	$-0.423171\pi$
$751$	1.14203e14			0.478055			0.239027	+	0.971013i	$0.423171\pi$
$752$			2.80212e12i			0.0116519i
$753$	−8.73119e13	+	1.20216e14i	−0.360660	+	0.496578i
$754$	6.81973e11			0.00279840
$755$			4.99361e13i			0.203554i
$756$	−2.41812e14	+	7.45469e14i	−0.979194	+	3.01871i
$757$	−3.68180e14			−1.48109			−0.740544	−	0.672008i	$-0.765432\pi$
$757$	−3.68180e14			−1.48109			−0.740544	+	0.672008i	$0.765432\pi$
$758$			1.13581e14i			0.453900i
$759$	1.71042e13	+	1.24226e13i	0.0679036	+	0.0493178i
$760$	−1.49418e14			−0.589299
$761$			2.09034e14i			0.819019i	0.912306	+	0.409509i	$0.134300\pi$
$761$			2.09034e14i			0.819019i	−0.912306	+	0.409509i	$0.865700\pi$
$762$	2.42292e14	−	3.33601e14i	0.943114	−	1.29853i
$763$	3.07837e14			1.19041
$764$			1.10013e14i			0.422646i
$765$	3.88207e13	+	1.19344e14i	0.148169	+	0.455507i
$766$	6.48111e14			2.45757
$767$			4.37574e11i			0.00164844i
$768$	−2.41020e14	−	1.75051e14i	−0.902082	−	0.655175i
$769$	4.24700e14			1.57925			0.789624	−	0.613591i	$-0.210276\pi$
$769$	4.24700e14			1.57925			0.789624	+	0.613591i	$0.210276\pi$
$770$			2.35966e13i			0.0871759i
$771$	2.17868e14	−	2.99973e14i	0.799688	−	1.10106i
$772$	3.40731e14			1.24258
$773$		−	3.30626e14i		−	1.19795i	−0.800767	−	0.598976i	$-0.795574\pi$
$773$		−	3.30626e14i		−	1.19795i	0.800767	−	0.598976i	$-0.204426\pi$
$774$	−2.07247e14	+	6.74140e13i	−0.746078	+	0.242686i
$775$	1.48283e13			0.0530376
$776$		−	2.57795e14i		−	0.916149i
$777$	6.05295e14	+	4.39621e14i	2.13728	+	1.55229i
$778$	−9.22933e14			−3.23797
$779$		−	1.93325e14i		−	0.673909i
$780$	6.29074e11	−	8.66145e11i	0.00217886	−	0.00299998i
$781$	2.27790e13			0.0783933
$782$		−	6.87303e14i		−	2.35025i
$783$	−9.57834e13	−	3.10698e13i	−0.325448	−	0.105567i
$784$	5.82289e13			0.196589
$785$		−	7.68216e13i		−	0.257712i
$786$	−7.06767e14	−	5.13319e14i	−2.35594	−	1.71110i
$787$	−4.29857e14			−1.42381			−0.711903	−	0.702278i	$-0.752166\pi$
$787$	−4.29857e14			−1.42381			−0.711903	+	0.702278i	$0.752166\pi$
$788$			4.55263e14i			1.49841i
$789$	−3.03094e14	+	4.17318e14i	−0.991272	+	1.36484i
$790$	−2.76099e14			−0.897284
$791$			9.75101e14i			3.14896i
$792$	−6.35215e12	−	1.95281e13i	−0.0203843	−	0.0626663i
$793$	−1.48779e12			−0.00474435
$794$			6.51755e14i			2.06529i
$795$	8.23141e13	+	5.97840e13i	0.259202	+	0.188256i
$796$	−4.40389e14			−1.37807
$797$		−	2.03472e14i		−	0.632723i	−0.948639	−	0.316361i	$-0.897539\pi$
$797$		−	2.03472e14i		−	0.632723i	0.948639	−	0.316361i	$-0.102461\pi$
$798$	7.41247e14	−	1.02059e15i	2.29060	−	3.15382i
$799$	−5.57877e13			−0.171319
$800$			6.15913e13i			0.187962i
$801$	3.88460e14	−	1.26359e14i	1.17810	−	0.383217i
$802$	3.26343e14			0.983563
$803$		−	6.31327e12i		−	0.0189094i
$804$	−2.62429e14	−	1.90600e14i	−0.781143	−	0.567338i
$805$	−3.91899e14			−1.15930
$806$			7.37792e11i			0.00216900i
$807$	−5.52284e11	+	7.60416e11i	−0.00161359	+	0.00222169i
$808$	−2.65564e14			−0.771104
$809$		−	4.60403e14i		−	1.32860i	−0.747465	−	0.664301i	$-0.768729\pi$
$809$		−	4.60403e14i		−	1.32860i	0.747465	−	0.664301i	$-0.231271\pi$
$810$	−2.05270e14	+	1.49344e14i	−0.588709	+	0.428313i
$811$	−5.17782e14			−1.47585			−0.737926	−	0.674882i	$-0.764195\pi$
$811$	−5.17782e14			−1.47585			−0.737926	+	0.674882i	$0.764195\pi$
$812$			3.83293e14i			1.08580i
$813$	1.84376e14	+	1.33910e14i	0.519099	+	0.377018i
$814$	−4.97523e13			−0.139217
$815$		−	1.72970e14i		−	0.481041i
$816$	−1.65884e13	+	2.28398e13i	−0.0458515	+	0.0631309i
$817$	2.18409e14			0.600012
$818$		−	1.63707e14i		−	0.446994i
$819$	1.10137e12	+	3.38587e12i	0.00298890	+	0.00918864i
$820$	1.48094e14			0.399456
$821$		−	4.97126e13i		−	0.133276i	−0.997777	−	0.0666379i	$-0.978773\pi$
$821$		−	4.97126e13i		−	0.133276i	0.997777	−	0.0666379i	$-0.0212272\pi$
$822$	−2.50812e14	−	1.82162e14i	−0.668326	−	0.485400i
$823$	9.66371e13			0.255944			0.127972	−	0.991778i	$-0.459153\pi$
$823$	9.66371e13			0.255944			0.127972	+	0.991778i	$0.459153\pi$
$824$		−	4.07693e14i		−	1.07324i
$825$	−2.79669e12	+	3.85065e12i	−0.00731771	+	0.0100754i
$826$	−3.94968e14			−1.02722
$827$		−	2.50258e14i		−	0.646934i	−0.946240	−	0.323467i	$-0.895152\pi$
$827$		−	2.50258e14i		−	0.646934i	0.946240	−	0.323467i	$-0.104848\pi$
$828$	8.23179e14	−	2.67766e14i	2.11516	−	0.688024i
$829$	3.00805e14			0.768267			0.384134	−	0.923278i	$-0.374500\pi$
$829$	3.00805e14			0.768267			0.384134	+	0.923278i	$0.374500\pi$
$830$			6.82872e13i			0.173360i
$831$	−3.84529e14	−	2.79281e14i	−0.970341	−	0.704751i
$832$	−3.21043e12			−0.00805278
$833$			1.15929e15i			2.89045i
$834$	−4.52169e13	+	6.22573e13i	−0.112065	+	0.154298i
$835$	7.68054e13			0.189217
$836$			5.22337e13i			0.127914i
$837$	3.36128e13	−	1.03623e14i	0.0818234	−	0.252249i
$838$	6.55857e14			1.58705
$839$			2.58111e14i			0.620864i	0.950596	+	0.310432i	$0.100474\pi$
$839$			2.58111e14i			0.620864i	−0.950596	+	0.310432i	$0.899526\pi$
$840$	3.08029e14	+	2.23719e14i	0.736538	+	0.534942i
$841$	3.71459e14			0.882939
$842$			9.97701e14i			2.35744i
$843$	−7.70394e13	+	1.06072e14i	−0.180957	+	0.249152i
$844$	6.04221e14			1.41086
$845$			1.92658e14i			0.447202i
$846$	−3.49054e13	−	1.07308e14i	−0.0805454	−	0.247617i
$847$	−8.35125e14			−1.91573
$848$			2.28826e13i			0.0521827i
$849$	2.34980e14	+	1.70664e14i	0.532711	+	0.386904i
$850$	1.54732e14			0.348727
$851$		−	8.26300e14i		−	1.85136i
$852$	5.48146e14	−	7.54719e14i	1.22095	−	1.68108i
$853$	−5.93883e14			−1.31509			−0.657545	−	0.753415i	$-0.728405\pi$
$853$	−5.93883e14			−1.31509			−0.657545	+	0.753415i	$0.728405\pi$
$854$		−	1.34293e15i		−	2.95640i
$855$	2.41923e14	−	7.86933e13i	0.529476	−	0.172229i
$856$	6.86606e14			1.49396
$857$			4.02752e14i			0.871231i	0.900133	+	0.435615i	$0.143469\pi$
$857$			4.02752e14i			0.871231i	−0.900133	+	0.435615i	$0.856531\pi$
$858$	−1.91591e11	−	1.39151e11i	−0.000412039	−	0.000299261i
$859$	−1.00500e14			−0.214882			−0.107441	−	0.994211i	$-0.534266\pi$
$859$	−1.00500e14			−0.214882			−0.107441	+	0.994211i	$0.534266\pi$
$860$			1.67309e14i			0.355654i
$861$	−2.89460e14	+	3.98545e14i	−0.611748	+	0.842289i
$862$	−1.65834e14			−0.348448
$863$			2.88723e14i			0.603152i	0.953442	+	0.301576i	$0.0975127\pi$
$863$			2.88723e14i			0.603152i	−0.953442	+	0.301576i	$0.902487\pi$
$864$	4.30412e14	+	1.39615e14i	0.893955	+	0.289977i
$865$	2.57346e14			0.531420
$866$			2.14363e14i			0.440110i
$867$	−5.83473e13	−	4.23772e13i	−0.119104	−	0.0865041i
$868$	−4.14665e14			−0.841587
$869$			3.80279e13i			0.0767368i
$870$	−7.29580e13	+	1.00453e14i	−0.146378	+	0.201542i
$871$	−1.47353e12			−0.00293946
$872$			3.30300e14i			0.655128i
$873$	1.35771e14	+	4.17395e14i	0.267755	+	0.823145i
$874$	−1.39323e15			−2.73190
$875$		−	8.82281e13i		−	0.172015i
$876$	−2.09173e14	−	1.51921e14i	−0.405495	−	0.294508i
$877$	8.49756e14			1.63793			0.818967	−	0.573841i	$-0.194547\pi$
$877$	8.49756e14			1.63793			0.818967	+	0.573841i	$0.194547\pi$
$878$			6.88717e14i			1.31998i
$879$	−3.32915e14	+	4.58377e14i	−0.634438	+	0.873531i
$880$	−1.07045e12			−0.00202839
$881$			7.68303e14i			1.44762i	0.690002	+	0.723808i	$0.257610\pi$
$881$			7.68303e14i			1.44762i	−0.690002	+	0.723808i	$0.742390\pi$
$882$	−2.22989e15	+	7.25346e14i	−4.17774	+	1.35895i
$883$	7.54087e13			0.140481			0.0702406	−	0.997530i	$-0.477623\pi$
$883$	7.54087e13			0.140481			0.0702406	+	0.997530i	$0.477623\pi$
$884$			4.79374e12i			0.00888001i
$885$	−6.44534e13	−	4.68119e13i	−0.118721	−	0.0862264i
$886$	1.04293e15			1.91023
$887$		−	9.41528e14i		−	1.71481i	−0.514645	−	0.857404i	$-0.672076\pi$
$887$		−	9.41528e14i		−	1.71481i	0.514645	−	0.857404i	$-0.327924\pi$
$888$	−4.71700e14	+	6.49464e14i	−0.854282	+	1.17622i
$889$	1.05278e15			1.89596
$890$		−	5.03644e14i		−	0.901932i
$891$	2.05695e13	+	2.82724e13i	0.0366299	+	0.0503471i
$892$	5.00950e14			0.887095
$893$			1.13087e14i			0.199139i
$894$	3.08995e14	+	2.24420e14i	0.541083	+	0.392984i
$895$	−1.90763e14			−0.332185
$896$		−	1.85407e15i		−	3.21060i
$897$	2.31106e12	−	3.18200e12i	0.00397969	−	0.00547946i
$898$	1.13967e14			0.195163
$899$		−	5.32792e13i		−	0.0907318i
$900$	6.02819e13	+	1.85322e14i	0.102088	+	0.313844i
$901$	−4.55573e14			−0.767245
$902$		−	3.27584e13i		−	0.0548644i
$903$	−4.50255e14	−	3.27017e14i	−0.749929	−	0.544667i
$904$	−1.04625e15			−1.73299
$905$			3.63623e13i			0.0598975i
$906$	2.65804e14	−	3.65975e14i	0.435433	−	0.599529i
$907$	−6.01349e14			−0.979693			−0.489846	−	0.871809i	$-0.662947\pi$
$907$	−6.01349e14			−0.979693			−0.489846	+	0.871809i	$0.662947\pi$
$908$		−	9.48510e14i		−	1.53678i
$909$	4.29975e14	−	1.39863e14i	0.692825	−	0.225364i
$910$	4.38984e12			0.00703463
$911$		−	1.10100e15i		−	1.75467i	−0.479876	−	0.877336i	$-0.659319\pi$
$911$		−	1.10100e15i		−	1.75467i	0.479876	−	0.877336i	$-0.340681\pi$
$912$	4.62985e13	+	3.36262e13i	0.0733826	+	0.0532972i
$913$	9.40539e12			0.0148260
$914$			1.35445e15i			2.12340i
$915$	1.59165e14	−	2.19148e14i	0.248166	−	0.341689i
$916$	−6.24466e14			−0.968347
$917$		−	2.23042e15i		−	3.43986i
$918$	3.50746e14	−	1.08130e15i	0.537996	−	1.65856i
$919$	1.44104e14			0.219835			0.109918	−	0.993941i	$-0.464941\pi$
$919$	1.44104e14			0.219835			0.109918	+	0.993941i	$0.464941\pi$
$920$		−	4.20497e14i		−	0.638004i
$921$	−2.71224e14	−	1.96988e14i	−0.409289	−	0.297263i
$922$	1.73357e15			2.60188
$923$		−	4.23772e12i		−	0.00632592i
$924$	7.82078e13	−	1.07681e14i	0.116115	−	0.159874i
$925$	1.86024e14			0.274702
$926$			2.03471e15i			2.98846i
$927$	2.14718e14	+	6.60096e14i	0.313667	+	0.964291i
$928$	2.21302e14			0.321548
$929$			5.77264e14i			0.834249i	0.908849	+	0.417125i	$0.136962\pi$
$929$			5.77264e14i			0.834249i	−0.908849	+	0.417125i	$0.863038\pi$
$930$	−1.08675e14	−	7.89295e13i	−0.156212	−	0.113455i
$931$	2.34999e15			3.35983
$932$			1.45417e15i			2.06793i
$933$	2.31126e14	−	3.18227e14i	0.326919	−	0.450121i
$934$	−2.28257e15			−3.21137
$935$		−	2.13117e13i		−	0.0298236i
$936$	−3.63294e12	+	1.18173e12i	−0.00505684	+	0.00164490i
$937$	−3.26966e14			−0.452694			−0.226347	−	0.974047i	$-0.572678\pi$
$937$	−3.26966e14			−0.452694			−0.226347	+	0.974047i	$0.572678\pi$
$938$		−	1.33005e15i		−	1.83170i
$939$	1.35474e14	+	9.83939e13i	0.185579	+	0.134785i
$940$	−8.66288e13			−0.118038
$941$			6.47413e14i			0.877473i	0.898616	+	0.438736i	$0.144574\pi$
$941$			6.47413e14i			0.877473i	−0.898616	+	0.438736i	$0.855426\pi$
$942$	−4.08912e14	+	5.63014e14i	−0.551284	+	0.759040i
$943$	5.44061e14			0.729607
$944$		−	1.79175e13i		−	0.0239011i
$945$	−6.16554e14	−	1.99995e14i	−0.818111	−	0.265375i
$946$	3.70088e13			0.0488482
$947$			1.36195e15i			1.78817i	0.447893	+	0.894087i	$0.352175\pi$
$947$			1.36195e15i			1.78817i	−0.447893	+	0.894087i	$0.647825\pi$
$948$	1.25995e15	+	9.15093e14i	1.64556	+	1.19515i
$949$	−1.17450e12			−0.00152589
$950$		−	3.13657e14i		−	0.405356i
$951$	−5.70516e13	+	7.85518e13i	−0.0733441	+	0.100984i
$952$	−1.70481e15			−2.18017
$953$		−	7.14783e14i		−	0.909305i	−0.890669	−	0.454653i	$-0.849763\pi$
$953$		−	7.14783e14i		−	0.909305i	0.890669	−	0.454653i	$-0.150237\pi$
$954$	−2.85044e14	−	8.76297e14i	−0.360720	−	1.10894i
$955$	−9.09881e13			−0.114543
$956$		−	8.32383e14i		−	1.04240i
$957$	1.38356e13	+	1.00487e13i	0.0172361	+	0.0125185i
$958$	−2.52632e15			−3.13084
$959$		−	7.91514e14i		−	0.975810i
$960$	3.43454e14	−	4.72887e14i	0.421223	−	0.579964i
$961$	−7.61988e14			−0.929675
$962$			9.25575e12i			0.0112340i
$963$	−1.11168e15	+	3.61611e14i	−1.34230	+	0.436626i
$964$	1.09334e15			1.31331
$965$			2.81808e14i			0.336757i
$966$	2.87217e15	+	2.08604e15i	3.41448	+	2.47991i
$967$	−1.02397e15			−1.21103			−0.605517	−	0.795833i	$-0.707033\pi$
$967$	−1.02397e15			−1.21103			−0.605517	+	0.795833i	$0.707033\pi$
$968$		−	8.96065e14i		−	1.05430i
$969$	−6.69469e14	+	9.21763e14i	−0.783631	+	1.07895i
$970$	5.41160e14			0.630183
$971$		−	1.22441e14i		−	0.141850i	−0.997482	−	0.0709250i	$-0.977405\pi$
$971$		−	1.22441e14i		−	0.141850i	0.997482	−	0.0709250i	$-0.0225951\pi$
$972$	1.43171e15	−	1.17517e12i	1.65015	−	0.00135447i
$973$	−1.96472e14			−0.225287
$974$			9.69308e14i			1.10578i
$975$	7.16361e11	+	5.20287e11i	0.000813035	+	0.000590500i
$976$	6.09212e13			0.0687891
$977$		−	1.24499e14i		−	0.139860i	−0.997552	−	0.0699301i	$-0.977722\pi$
$977$		−	1.24499e14i		−	0.139860i	0.997552	−	0.0699301i	$-0.0222776\pi$
$978$	−9.20698e14	+	1.26767e15i	−1.02902	+	1.41681i
$979$	−6.93684e13			−0.0771344
$980$			1.80018e15i			1.99152i
$981$	−1.73957e14	−	5.34788e14i	−0.191469	−	0.588622i
$982$	1.50213e15			1.64494
$983$		−	3.64134e14i		−	0.396729i	−0.980128	−	0.198364i	$-0.936437\pi$
$983$		−	3.64134e14i		−	0.396729i	0.980128	−	0.198364i	$-0.0635629\pi$
$984$	−4.27627e14	−	3.10582e14i	−0.463542	−	0.336667i
$985$	−3.76534e14			−0.406091
$986$		−	5.55963e14i		−	0.596569i
$987$	1.69322e14	−	2.33132e14i	0.180770	−	0.248895i
$988$	9.71738e12			0.0103220
$989$			6.14652e14i			0.649603i
$990$	4.09931e13	−	1.33343e13i	0.0431057	−	0.0140215i
$991$	−9.30921e12			−0.00973968			−0.00486984	−	0.999988i	$-0.501550\pi$
$991$	−9.30921e12			−0.00973968			−0.00486984	+	0.999988i	$0.501550\pi$
$992$			2.39415e14i			0.249226i
$993$	5.23832e14	+	3.80455e14i	0.542558	+	0.394055i
$994$	3.82510e15			3.94195
$995$		−	3.64232e14i		−	0.373476i
$996$	2.26329e14	−	3.11622e14i	0.230910	−	0.317930i
$997$	−1.40222e15			−1.42345			−0.711723	−	0.702460i	$-0.752085\pi$
$997$	−1.40222e15			−1.42345			−0.711723	+	0.702460i	$0.752085\pi$
$998$			1.18411e15i			1.19602i
$999$	4.21679e14	−	1.29997e15i	0.423794	−	1.30649i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.11.c.a.11.12	yes	14
3.2	odd	2	inner	15.11.c.a.11.3	✓	14
4.3	odd	2		240.11.l.b.161.3		14
5.2	odd	4		75.11.d.d.74.5		28
5.3	odd	4		75.11.d.d.74.24		28
5.4	even	2		75.11.c.g.26.3		14
12.11	even	2		240.11.l.b.161.4		14
15.2	even	4		75.11.d.d.74.23		28
15.8	even	4		75.11.d.d.74.6		28
15.14	odd	2		75.11.c.g.26.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.11.c.a.11.3	✓	14	3.2	odd	2	inner
15.11.c.a.11.12	yes	14	1.1	even	1	trivial
75.11.c.g.26.3		14	5.4	even	2
75.11.c.g.26.12		14	15.14	odd	2
75.11.d.d.74.5		28	5.2	odd	4
75.11.d.d.74.6		28	15.8	even	4
75.11.d.d.74.23		28	15.2	even	4
75.11.d.d.74.24		28	5.3	odd	4
240.11.l.b.161.3		14	4.3	odd	2
240.11.l.b.161.4		14	12.11	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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	15.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+52.0937i q^{2} +(196.615 + 142.800i) q^{3} -1689.75 q^{4} -1397.54i q^{5} +(-7438.96 + 10242.4i) q^{6} -32323.0 q^{7} -34681.6i q^{8} +(18265.6 + 56152.9i) q^{9} +O(q^{10})\)	\(q+52.0937i q^{2} +(196.615 + 142.800i) q^{3} -1689.75 q^{4} -1397.54i q^{5} +(-7438.96 + 10242.4i) q^{6} -32323.0 q^{7} -34681.6i q^{8} +(18265.6 + 56152.9i) q^{9} +72803.2 q^{10} -10027.4i q^{11} +(-332230. - 241296. i) q^{12} -1865.46 q^{13} -1.68382e6i q^{14} +(199568. - 274777. i) q^{15} +76385.8 q^{16} +1.52077e6i q^{17} +(-2.92522e6 + 951522. i) q^{18} +3.08276e6 q^{19} +2.36150e6i q^{20} +(-6.35517e6 - 4.61571e6i) q^{21} +522364. q^{22} +8.67557e6i q^{23} +(4.95252e6 - 6.81891e6i) q^{24} -1.95312e6 q^{25} -97178.8i q^{26} +(-4.42733e6 + 1.36488e7i) q^{27} +5.46179e7 q^{28} +7.01771e6i q^{29} +(1.43142e7 + 1.03963e7i) q^{30} -7.59210e6 q^{31} -3.15348e7i q^{32} +(1.43191e6 - 1.97153e6i) q^{33} -7.92228e7 q^{34} +4.51728e7i q^{35} +(-3.08644e7 - 9.48847e7i) q^{36} -9.52445e7 q^{37} +1.60592e8i q^{38} +(-366777. - 266387. i) q^{39} -4.84690e7 q^{40} -6.27119e7i q^{41} +(2.40449e8 - 3.31065e8i) q^{42} +7.08486e7 q^{43} +1.69438e7i q^{44} +(7.84761e7 - 2.55269e7i) q^{45} -4.51943e8 q^{46} +3.66838e7i q^{47} +(1.50186e7 + 1.09079e7i) q^{48} +7.62301e8 q^{49} -1.01746e8i q^{50} +(-2.17166e8 + 2.99006e8i) q^{51} +3.15217e6 q^{52} +2.99567e8i q^{53} +(-7.11017e8 - 2.30636e8i) q^{54} -1.40137e7 q^{55} +1.12101e9i q^{56} +(6.06115e8 + 4.40216e8i) q^{57} -3.65579e8 q^{58} -2.34566e8i q^{59} +(-3.37222e8 + 4.64306e8i) q^{60} +7.97547e8 q^{61} -3.95501e8i q^{62} +(-5.90398e8 - 1.81503e9i) q^{63} +1.72098e9 q^{64} +2.60706e6i q^{65} +(1.02704e8 + 7.45933e7i) q^{66} +7.89899e8 q^{67} -2.56973e9i q^{68} +(-1.23887e9 + 1.70574e9i) q^{69} -2.35322e9 q^{70} +2.27167e9i q^{71} +(1.94748e9 - 6.33480e8i) q^{72} +6.29603e8 q^{73} -4.96164e9i q^{74} +(-3.84013e8 - 2.78905e8i) q^{75} -5.20910e9 q^{76} +3.24115e8i q^{77} +(1.38771e7 - 1.91068e7i) q^{78} -3.79241e9 q^{79} -1.06752e8i q^{80} +(-2.81952e9 + 2.05133e9i) q^{81} +3.26689e9 q^{82} +9.37970e8i q^{83} +(1.07387e10 + 7.79942e9i) q^{84} +2.12535e9 q^{85} +3.69077e9i q^{86} +(-1.00213e9 + 1.37978e9i) q^{87} -3.47766e8 q^{88} -6.91789e9i q^{89} +(1.32979e9 + 4.08811e9i) q^{90} +6.02973e7 q^{91} -1.46596e10i q^{92} +(-1.49272e9 - 1.08415e9i) q^{93} -1.91099e9 q^{94} -4.30828e9i q^{95} +(4.50315e9 - 6.20019e9i) q^{96} +7.43319e9 q^{97} +3.97111e10i q^{98} +(5.63067e8 - 1.83156e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9}+O(q^{10}) \) 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9	\( 14 q + 44 q^{3} - 8802 q^{4} + 21886 q^{6} - 50548 q^{7} + 116362 q^{9} + 31250 q^{10} + 43756 q^{12} + 699408 q^{13} - 343750 q^{15} + 2871906 q^{16} - 3243880 q^{18} + 3814644 q^{19} - 2191008 q^{21} - 10493420 q^{22} + 9454542 q^{24} - 27343750 q^{25} + 13322636 q^{27} - 10989172 q^{28} + 20875000 q^{30} + 105444308 q^{31} - 187570700 q^{33} + 84960772 q^{34} + 80968490 q^{36} - 152902928 q^{37} - 262995952 q^{39} - 228656250 q^{40} + 1025108820 q^{42} - 82568592 q^{43} + 284500000 q^{45} + 302816052 q^{46} - 534917396 q^{48} + 1339929050 q^{49} - 519773324 q^{51} - 2117624528 q^{52} - 3171778694 q^{54} - 414437500 q^{55} + 2459677832 q^{57} + 2203542020 q^{58} + 918156250 q^{60} - 2372907732 q^{61} + 253855908 q^{63} + 5663115830 q^{64} + 915786920 q^{66} - 7807415008 q^{67} - 1032380604 q^{69} - 95812500 q^{70} + 2313658920 q^{72} + 10465834068 q^{73} - 85937500 q^{75} - 4927934540 q^{76} - 4082143640 q^{78} - 8333919076 q^{79} - 4284635426 q^{81} + 14404193720 q^{82} + 13837595568 q^{84} + 4711812500 q^{85} - 11735627260 q^{87} - 14973492180 q^{88} - 9226281250 q^{90} + 4013221984 q^{91} - 9561672552 q^{93} - 47501516708 q^{94} + 43132239458 q^{96} + 31262487532 q^{97} + 36258312560 q^{99}+O(q^{100}) \) 14 * q + 44 * q^3 - 8802 * q^4 + 21886 * q^6 - 50548 * q^7 + 116362 * q^9 + 31250 * q^10 + 43756 * q^12 + 699408 * q^13 - 343750 * q^15 + 2871906 * q^16 - 3243880 * q^18 + 3814644 * q^19 - 2191008 * q^21 - 10493420 * q^22 + 9454542 * q^24 - 27343750 * q^25 + 13322636 * q^27 - 10989172 * q^28 + 20875000 * q^30 + 105444308 * q^31 - 187570700 * q^33 + 84960772 * q^34 + 80968490 * q^36 - 152902928 * q^37 - 262995952 * q^39 - 228656250 * q^40 + 1025108820 * q^42 - 82568592 * q^43 + 284500000 * q^45 + 302816052 * q^46 - 534917396 * q^48 + 1339929050 * q^49 - 519773324 * q^51 - 2117624528 * q^52 - 3171778694 * q^54 - 414437500 * q^55 + 2459677832 * q^57 + 2203542020 * q^58 + 918156250 * q^60 - 2372907732 * q^61 + 253855908 * q^63 + 5663115830 * q^64 + 915786920 * q^66 - 7807415008 * q^67 - 1032380604 * q^69 - 95812500 * q^70 + 2313658920 * q^72 + 10465834068 * q^73 - 85937500 * q^75 - 4927934540 * q^76 - 4082143640 * q^78 - 8333919076 * q^79 - 4284635426 * q^81 + 14404193720 * q^82 + 13837595568 * q^84 + 4711812500 * q^85 - 11735627260 * q^87 - 14973492180 * q^88 - 9226281250 * q^90 + 4013221984 * q^91 - 9561672552 * q^93 - 47501516708 * q^94 + 43132239458 * q^96 + 31262487532 * q^97 + 36258312560 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more