LMFDB - Embedded newform 6.13.b.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,13,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, 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("6.5");

S:= CuspForms(chi, 13);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 13 $
Character orbit:	$[\chi]$	$=$	6.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:	$5.48396290366$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{1009})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 499x^{2} + 500x + 64518 $ x^4 - 2x^3 - 499x^2 + 500*x + 64518
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{9}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.1
Root			$16.3824 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.13.b.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-45.2548i q^{2} +(4.41144 - 728.987i) q^{3} -2048.00 q^{4} +1793.38i q^{5} +(-32990.2 - 199.639i) q^{6} -136690. q^{7} +92681.9i q^{8} +(-531402. - 6431.76i) q^{9} +O(q^{10})$	\(q-45.2548i q^{2} +(4.41144 - 728.987i) q^{3} -2048.00 q^{4} +1793.38i q^{5} +(-32990.2 - 199.639i) q^{6} -136690. q^{7} +92681.9i q^{8} +(-531402. - 6431.76i) q^{9} +81159.0 q^{10} -1.76028e6i q^{11} +(-9034.62 + 1.49296e6i) q^{12} +6.95914e6 q^{13} +6.18590e6i q^{14} +(1.30735e6 + 7911.37i) q^{15} +4.19430e6 q^{16} -3.90909e7i q^{17} +(-291068. + 2.40485e7i) q^{18} -6.02734e7 q^{19} -3.67284e6i q^{20} +(-603001. + 9.96454e7i) q^{21} -7.96610e7 q^{22} -1.16231e8i q^{23} +(6.75639e7 + 408860. i) q^{24} +2.40924e8 q^{25} -3.14935e8i q^{26} +(-7.03291e6 + 3.87357e8i) q^{27} +2.79942e8 q^{28} +1.81306e8i q^{29} +(358028. - 5.91638e7i) q^{30} +2.39099e8 q^{31} -1.89813e8i q^{32} +(-1.28322e9 - 7.76535e6i) q^{33} -1.76905e9 q^{34} -2.45137e8i q^{35} +(1.08831e9 + 1.31722e7i) q^{36} -1.10731e8 q^{37} +2.72766e9i q^{38} +(3.06998e7 - 5.07312e9i) q^{39} -1.66214e8 q^{40} +3.21831e9i q^{41} +(4.50944e9 + 2.72887e7i) q^{42} +6.08967e9 q^{43} +3.60504e9i q^{44} +(1.15346e7 - 9.53004e8i) q^{45} -5.26002e9 q^{46} -3.06152e9i q^{47} +(1.85029e7 - 3.05759e9i) q^{48} +4.84295e9 q^{49} -1.09030e10i q^{50} +(-2.84967e10 - 1.72447e8i) q^{51} -1.42523e10 q^{52} +2.76061e10i q^{53} +(1.75298e10 + 3.18273e8i) q^{54} +3.15684e9 q^{55} -1.26687e10i q^{56} +(-2.65892e8 + 4.39385e10i) q^{57} +8.20496e9 q^{58} -7.62703e10i q^{59} +(-2.67745e9 - 1.62025e7i) q^{60} +3.69791e10 q^{61} -1.08204e10i q^{62} +(7.26375e10 + 8.79159e8i) q^{63} -8.58993e9 q^{64} +1.24804e10i q^{65} +(-3.51419e8 + 5.80718e10i) q^{66} -5.88864e10 q^{67} +8.00581e10i q^{68} +(-8.47310e10 - 5.12747e8i) q^{69} -1.10936e10 q^{70} -1.03143e11i q^{71} +(5.96108e8 - 4.92514e10i) q^{72} -1.32650e11 q^{73} +5.01112e9i q^{74} +(1.06282e9 - 1.75631e11i) q^{75} +1.23440e11 q^{76} +2.40613e11i q^{77} +(-2.29583e11 - 1.38932e9i) q^{78} +1.57563e11 q^{79} +7.52197e9i q^{80} +(2.82347e11 + 6.83570e9i) q^{81} +1.45644e11 q^{82} +3.02225e11i q^{83} +(1.23495e9 - 2.04074e11i) q^{84} +7.01046e10 q^{85} -2.75587e11i q^{86} +(1.32169e11 + 7.99819e8i) q^{87} +1.63146e11 q^{88} +5.40489e10i q^{89} +(-4.31280e10 - 5.21995e8i) q^{90} -9.51247e11 q^{91} +2.38042e11i q^{92} +(1.05477e9 - 1.74300e11i) q^{93} -1.38549e11 q^{94} -1.08093e11i q^{95} +(-1.38371e11 - 8.37346e8i) q^{96} -1.33559e11 q^{97} -2.19167e11i q^{98} +(-1.13217e10 + 9.35414e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 780 q^{3} - 8192 q^{4} - 9984 q^{6} + 153080 q^{7} - 1530972 q^{9}+O(q^{10}) $ 4 * q + 780 * q^3 - 8192 * q^4 - 9984 * q^6 + 153080 * q^7 - 1530972 * q^9	\( 4 q + 780 q^{3} - 8192 q^{4} - 9984 q^{6} + 153080 q^{7} - 1530972 q^{9} + 1641984 q^{10} - 1597440 q^{12} + 7253000 q^{13} - 17613792 q^{15} + 16777216 q^{16} + 42600960 q^{18} - 120268072 q^{19} + 163232328 q^{21} - 159244800 q^{22} + 20447232 q^{24} + 435605764 q^{25} - 784941300 q^{27} - 313507840 q^{28} + 571258368 q^{30} + 2731727672 q^{31} - 2567489760 q^{33} - 3097810944 q^{34} + 3135430656 q^{36} - 15280120 q^{37} - 2508657000 q^{39} - 3362783232 q^{40} + 20958988800 q^{42} + 1629119960 q^{43} - 15576677568 q^{45} - 29905849344 q^{46} + 3271557120 q^{48} + 72937649100 q^{49} - 63012636288 q^{51} - 14854144000 q^{52} + 38602586880 q^{54} + 6285799872 q^{55} - 424311000 q^{57} - 62351992320 q^{58} + 36073046016 q^{60} + 45477065096 q^{61} + 45447449400 q^{63} - 34359738368 q^{64} - 673085952 q^{66} - 213433609960 q^{67} + 95560926912 q^{69} + 293322353664 q^{70} - 87246766080 q^{72} - 254383625080 q^{73} - 15705158772 q^{75} + 246309011456 q^{76} - 645782208000 q^{78} + 308580159032 q^{79} + 219015659268 q^{81} + 234603709440 q^{82} - 334299807744 q^{84} - 18844054272 q^{85} + 1341091294560 q^{87} + 326133350400 q^{88} - 432622121472 q^{90} - 3323734346000 q^{91} + 871044956040 q^{93} + 775668172800 q^{94} - 41875931136 q^{96} + 1276228475720 q^{97} - 23456841408 q^{99}+O(q^{100}) \) 4 * q + 780 * q^3 - 8192 * q^4 - 9984 * q^6 + 153080 * q^7 - 1530972 * q^9 + 1641984 * q^10 - 1597440 * q^12 + 7253000 * q^13 - 17613792 * q^15 + 16777216 * q^16 + 42600960 * q^18 - 120268072 * q^19 + 163232328 * q^21 - 159244800 * q^22 + 20447232 * q^24 + 435605764 * q^25 - 784941300 * q^27 - 313507840 * q^28 + 571258368 * q^30 + 2731727672 * q^31 - 2567489760 * q^33 - 3097810944 * q^34 + 3135430656 * q^36 - 15280120 * q^37 - 2508657000 * q^39 - 3362783232 * q^40 + 20958988800 * q^42 + 1629119960 * q^43 - 15576677568 * q^45 - 29905849344 * q^46 + 3271557120 * q^48 + 72937649100 * q^49 - 63012636288 * q^51 - 14854144000 * q^52 + 38602586880 * q^54 + 6285799872 * q^55 - 424311000 * q^57 - 62351992320 * q^58 + 36073046016 * q^60 + 45477065096 * q^61 + 45447449400 * q^63 - 34359738368 * q^64 - 673085952 * q^66 - 213433609960 * q^67 + 95560926912 * q^69 + 293322353664 * q^70 - 87246766080 * q^72 - 254383625080 * q^73 - 15705158772 * q^75 + 246309011456 * q^76 - 645782208000 * q^78 + 308580159032 * q^79 + 219015659268 * q^81 + 234603709440 * q^82 - 334299807744 * q^84 - 18844054272 * q^85 + 1341091294560 * q^87 + 326133350400 * q^88 - 432622121472 * q^90 - 3323734346000 * q^91 + 871044956040 * q^93 + 775668172800 * q^94 - 41875931136 * q^96 + 1276228475720 * q^97 - 23456841408 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	45.2548i		−	0.707107i
$2$		−	45.2548i		−	0.707107i
$3$	4.41144	−	728.987i	0.00605136	−	0.999982i
$3$	4.41144	−	728.987i	0.00605136	−	0.999982i
$4$	−2048.00			−0.500000
$5$			1793.38i			0.114776i	0.998352	+	0.0573881i	$0.0182772\pi$
$5$			1793.38i			0.114776i	−0.998352	+	0.0573881i	$0.981723\pi$
$6$	−32990.2	−	199.639i	−0.707094	−	0.00427895i
$7$	−136690.			−1.16185			−0.580924	−	0.813958i	$-0.697309\pi$
$7$	−136690.			−1.16185			−0.580924	+	0.813958i	$0.697309\pi$
$8$			92681.9i			0.353553i
$9$	−531402.	−	6431.76i	−0.999927	−	0.0121025i
$10$	81159.0			0.0811590
$11$		−	1.76028e6i		−	0.993630i	−0.867857	−	0.496815i	$-0.834503\pi$
$11$		−	1.76028e6i		−	0.993630i	0.867857	−	0.496815i	$-0.165497\pi$
$12$	−9034.62	+	1.49296e6i	−0.00302568	+	0.499991i
$13$	6.95914e6			1.44177			0.720884	−	0.693055i	$-0.243736\pi$
$13$	6.95914e6			1.44177			0.720884	+	0.693055i	$0.243736\pi$
$14$			6.18590e6i			0.821551i
$15$	1.30735e6	+	7911.37i	0.114774	+	0.000694551i
$16$	4.19430e6			0.250000
$17$		−	3.90909e7i		−	1.61950i	−0.586773	−	0.809751i	$-0.699602\pi$
$17$		−	3.90909e7i		−	1.61950i	0.586773	−	0.809751i	$-0.300398\pi$
$18$	−291068.	+	2.40485e7i	−0.00855775	+	0.707055i
$19$	−6.02734e7			−1.28116			−0.640581	−	0.767891i	$-0.721306\pi$
$19$	−6.02734e7			−1.28116			−0.640581	+	0.767891i	$0.721306\pi$
$20$		−	3.67284e6i		−	0.0573881i
$21$	−603001.	+	9.96454e7i	−0.00703076	+	1.16183i
$22$	−7.96610e7			−0.702602
$23$		−	1.16231e8i		−	0.785156i	−0.919719	−	0.392578i	$-0.871583\pi$
$23$		−	1.16231e8i		−	0.785156i	0.919719	−	0.392578i	$-0.128417\pi$
$24$	6.75639e7	+	408860.i	0.353547	+	0.00213948i
$25$	2.40924e8			0.986826
$26$		−	3.14935e8i		−	1.01948i
$27$	−7.03291e6	+	3.87357e8i	−0.0181532	+	0.999835i
$28$	2.79942e8			0.580924
$29$			1.81306e8i			0.304806i	0.988318	+	0.152403i	$0.0487011\pi$
$29$			1.81306e8i			0.304806i	−0.988318	+	0.152403i	$0.951299\pi$
$30$	358028.	−	5.91638e7i	0.000491122	−	0.0811575i
$31$	2.39099e8			0.269406			0.134703	−	0.990886i	$-0.456992\pi$
$31$	2.39099e8			0.269406			0.134703	+	0.990886i	$0.456992\pi$
$32$		−	1.89813e8i		−	0.176777i
$33$	−1.28322e9	−	7.76535e6i	−0.993612	−	0.00601281i
$34$	−1.76905e9			−1.14516
$35$		−	2.45137e8i		−	0.133352i
$36$	1.08831e9	+	1.31722e7i	0.499963	+	0.00605124i
$37$	−1.10731e8			−0.0431578			−0.0215789	−	0.999767i	$-0.506869\pi$
$37$	−1.10731e8			−0.0431578			−0.0215789	+	0.999767i	$0.506869\pi$
$38$			2.72766e9i			0.905918i
$39$	3.06998e7	−	5.07312e9i	0.00872465	−	1.44174i
$40$	−1.66214e8			−0.0405795
$41$			3.21831e9i			0.677524i	0.940872	+	0.338762i	$0.110008\pi$
$41$			3.21831e9i			0.677524i	−0.940872	+	0.338762i	$0.889992\pi$
$42$	4.50944e9	+	2.72887e7i	0.821536	+	0.00497150i
$43$	6.08967e9			0.963348			0.481674	−	0.876351i	$-0.340029\pi$
$43$	6.08967e9			0.963348			0.481674	+	0.876351i	$0.340029\pi$
$44$			3.60504e9i			0.496815i
$45$	1.15346e7	−	9.53004e8i	0.00138908	−	0.114768i
$46$	−5.26002e9			−0.555189
$47$		−	3.06152e9i		−	0.284021i	−0.989865	−	0.142010i	$-0.954643\pi$
$47$		−	3.06152e9i		−	0.284021i	0.989865	−	0.142010i	$-0.0453567\pi$
$48$	1.85029e7	−	3.05759e9i	0.00151284	−	0.249995i
$49$	4.84295e9			0.349892
$50$		−	1.09030e10i		−	0.697792i
$51$	−2.84967e10	−	1.72447e8i	−1.61947	−	0.00980019i
$52$	−1.42523e10			−0.720884
$53$			2.76061e10i			1.24552i	0.782414	+	0.622758i	$0.213988\pi$
$53$			2.76061e10i			1.24552i	−0.782414	+	0.622758i	$0.786012\pi$
$54$	1.75298e10	+	3.18273e8i	0.706990	+	0.0128362i
$55$	3.15684e9			0.114045
$56$		−	1.26687e10i		−	0.410775i
$57$	−2.65892e8	+	4.39385e10i	−0.00775277	+	1.28114i
$58$	8.20496e9			0.215530
$59$		−	7.62703e10i		−	1.80819i	−0.427335	−	0.904093i	$-0.640547\pi$
$59$		−	7.62703e10i		−	1.80819i	0.427335	−	0.904093i	$-0.359453\pi$
$60$	−2.67745e9	−	1.62025e7i	−0.0573870	−	0.000347275i
$61$	3.69791e10			0.717757			0.358879	−	0.933384i	$-0.383159\pi$
$61$	3.69791e10			0.717757			0.358879	+	0.933384i	$0.383159\pi$
$62$		−	1.08204e10i		−	0.190499i
$63$	7.26375e10	+	8.79159e8i	1.16176	+	0.0140613i
$64$	−8.58993e9			−0.125000
$65$			1.24804e10i			0.165481i
$66$	−3.51419e8	+	5.80718e10i	−0.00425170	+	0.702589i
$67$	−5.88864e10			−0.650977			−0.325489	−	0.945546i	$-0.605529\pi$
$67$	−5.88864e10			−0.650977			−0.325489	+	0.945546i	$0.605529\pi$
$68$			8.00581e10i			0.809751i
$69$	−8.47310e10	−	5.12747e8i	−0.785141	−	0.00475126i
$70$	−1.10936e10			−0.0942944
$71$		−	1.03143e11i		−	0.805174i	−0.915382	−	0.402587i	$-0.868111\pi$
$71$		−	1.03143e11i		−	0.805174i	0.915382	−	0.402587i	$-0.131889\pi$
$72$	5.96108e8	−	4.92514e10i	0.00427888	−	0.353527i
$73$	−1.32650e11			−0.876540			−0.438270	−	0.898843i	$-0.644409\pi$
$73$	−1.32650e11			−0.876540			−0.438270	+	0.898843i	$0.644409\pi$
$74$			5.01112e9i			0.0305172i
$75$	1.06282e9	−	1.75631e11i	0.00597164	−	0.986808i
$76$	1.23440e11			0.640581
$77$			2.40613e11i			1.15445i
$78$	−2.29583e11	−	1.38932e9i	−1.01947	−	0.00616926i
$79$	1.57563e11			0.648175			0.324088	−	0.946027i	$-0.394943\pi$
$79$	1.57563e11			0.648175			0.324088	+	0.946027i	$0.394943\pi$
$80$			7.52197e9i			0.0286940i
$81$	2.82347e11	+	6.83570e9i	0.999707	+	0.0242032i
$82$	1.45644e11			0.479082
$83$			3.02225e11i			0.924403i	0.886775	+	0.462201i	$0.152940\pi$
$83$			3.02225e11i			0.924403i	−0.886775	+	0.462201i	$0.847060\pi$
$84$	1.23495e9	−	2.04074e11i	0.00351538	−	0.580914i
$85$	7.01046e10			0.185880
$86$		−	2.75587e11i		−	0.681190i
$87$	1.32169e11	+	7.99819e8i	0.304800	+	0.00184449i
$88$	1.63146e11			0.351301
$89$			5.40489e10i			0.108754i	0.998520	+	0.0543772i	$0.0173174\pi$
$89$			5.40489e10i			0.108754i	−0.998520	+	0.0543772i	$0.982683\pi$
$90$	−4.31280e10	−	5.21995e8i	−0.0811530	−	0.000982225i
$91$	−9.51247e11			−1.67512
$92$			2.38042e11i			0.392578i
$93$	1.05477e9	−	1.74300e11i	0.00163027	−	0.269401i
$94$	−1.38549e11			−0.200833
$95$		−	1.08093e11i		−	0.147047i
$96$	−1.38371e11	−	8.37346e8i	−0.176773	−	0.00106974i
$97$	−1.33559e11			−0.160341			−0.0801704	−	0.996781i	$-0.525546\pi$
$97$	−1.33559e11			−0.160341			−0.0801704	+	0.996781i	$0.525546\pi$
$98$		−	2.19167e11i		−	0.247411i
$99$	−1.13217e10	+	9.35414e11i	−0.0120254	+	0.993557i
$100$	−4.93413e11			−0.493413
$101$		−	1.79448e12i		−	1.69048i	−0.534384	−	0.845242i	$-0.679456\pi$
$101$		−	1.79448e12i		−	1.69048i	0.534384	−	0.845242i	$-0.320544\pi$
$102$	−7.80406e9	+	1.28961e12i	−0.00692978	+	1.14514i
$103$	1.16132e12			0.972584			0.486292	−	0.873796i	$-0.338349\pi$
$103$	1.16132e12			0.972584			0.486292	+	0.873796i	$0.338349\pi$
$104$			6.44986e11i			0.509742i
$105$	−1.78702e11	−	1.08141e9i	−0.133350	−	0.000806963i
$106$	1.24931e12			0.880713
$107$		−	8.99772e10i		−	0.0599556i	−0.999551	−	0.0299778i	$-0.990456\pi$
$107$		−	8.99772e10i		−	0.0599556i	0.999551	−	0.0299778i	$-0.00954366\pi$
$108$	1.44034e10	−	7.93306e11i	0.00907659	−	0.499918i
$109$	1.11742e12			0.666284			0.333142	−	0.942877i	$-0.391891\pi$
$109$	1.11742e12			0.666284			0.333142	+	0.942877i	$0.391891\pi$
$110$		−	1.42862e11i		−	0.0806420i
$111$	−4.88483e8	+	8.07215e10i	−0.000261163	+	0.0431570i
$112$	−5.73321e11			−0.290462
$113$		−	1.23497e12i		−	0.593177i	−0.955005	−	0.296589i	$-0.904151\pi$
$113$		−	1.23497e12i		−	0.593177i	0.955005	−	0.296589i	$-0.0958490\pi$
$114$	1.98843e12	+	1.20329e10i	0.905902	+	0.00548203i
$115$	2.08446e11			0.0901171
$116$		−	3.71314e11i		−	0.152403i
$117$	−3.69810e12	−	4.47595e10i	−1.44166	−	0.0174490i
$118$	−3.45160e12			−1.27858
$119$			5.34334e12i			1.88162i
$120$	−7.33241e8	+	1.21167e11i	−0.000245561	+	0.0405787i
$121$	3.98581e10			0.0127000
$122$		−	1.67348e12i		−	0.507531i
$123$	2.34610e12	+	1.41974e10i	0.677511	+	0.00409994i
$124$	−4.89674e11			−0.134703
$125$			8.69904e11i			0.228040i
$126$	3.97862e10	−	3.28720e12i	0.00994281	−	0.821491i
$127$	−4.44366e12			−1.05905			−0.529527	−	0.848293i	$-0.677631\pi$
$127$	−4.44366e12			−1.05905			−0.529527	+	0.848293i	$0.677631\pi$
$128$			3.88736e11i			0.0883883i
$129$	2.68642e10	−	4.43929e12i	0.00582956	−	0.963330i
$130$	5.64797e11			0.117012
$131$		−	5.54105e11i		−	0.109639i	−0.998496	−	0.0548194i	$-0.982542\pi$
$131$		−	5.54105e11i		−	0.109639i	0.998496	−	0.0548194i	$-0.0174583\pi$
$132$	2.62803e12	+	1.59034e10i	0.496806	+	0.00300640i
$133$	8.23879e12			1.48852
$134$			2.66489e12i			0.460310i
$135$	−6.94676e11	−	1.26127e10i	−0.114757	−	0.00208355i
$136$	3.62302e12			0.572581
$137$			7.09613e12i			1.07324i	0.843823	+	0.536622i	$0.180300\pi$
$137$			7.09613e12i			1.07324i	−0.843823	+	0.536622i	$0.819700\pi$
$138$	−2.32043e10	+	3.83449e12i	−0.00335964	+	0.555179i
$139$	2.92962e12			0.406184			0.203092	−	0.979160i	$-0.434901\pi$
$139$	2.92962e12			0.406184			0.203092	+	0.979160i	$0.434901\pi$
$140$			5.02041e11i			0.0666762i
$141$	−2.23181e12	−	1.35057e10i	−0.284016	−	0.00171871i
$142$	−4.66772e12			−0.569344
$143$		−	1.22500e13i		−	1.43258i
$144$	−2.22886e12	−	2.69768e10i	−0.249982	−	0.00302562i
$145$	−3.25149e11			−0.0349844
$146$			6.00308e12i			0.619807i
$147$	2.13644e10	−	3.53045e12i	0.00211732	−	0.349885i
$148$	2.26777e11			0.0215789
$149$		−	1.27596e13i		−	1.16605i	−0.812453	−	0.583027i	$-0.801868\pi$
$149$		−	1.27596e13i		−	1.16605i	0.812453	−	0.583027i	$-0.198132\pi$
$150$	−7.94814e12	−	4.80979e10i	−0.697779	−	0.00422259i
$151$	−1.57990e13			−1.33281			−0.666405	−	0.745590i	$-0.732168\pi$
$151$	−1.57990e13			−1.33281			−0.666405	+	0.745590i	$0.732168\pi$
$152$		−	5.58625e12i		−	0.452959i
$153$	−2.51423e11	+	2.07730e13i	−0.0196000	+	1.61938i
$154$	1.08889e13			0.816317
$155$			4.28794e11i			0.0309214i
$156$	−6.28732e10	+	1.03898e13i	−0.00436233	+	0.720871i
$157$	−1.25698e13			−0.839324			−0.419662	−	0.907680i	$-0.637851\pi$
$157$	−1.25698e13			−0.839324			−0.419662	+	0.907680i	$0.637851\pi$
$158$		−	7.13050e12i		−	0.458329i
$159$	2.01245e13	+	1.21783e11i	1.24549	+	0.00753707i
$160$	3.40405e11			0.0202897
$161$			1.58877e13i			0.912232i
$162$	3.09348e11	−	1.27776e13i	0.0171143	−	0.706900i
$163$	5.32661e12			0.284005			0.142002	−	0.989866i	$-0.454646\pi$
$163$	5.32661e12			0.284005			0.142002	+	0.989866i	$0.454646\pi$
$164$		−	6.59109e12i		−	0.338762i
$165$	1.39262e10	−	2.30129e12i	0.000690126	−	0.114043i
$166$	1.36771e13			0.653651
$167$		−	1.40888e13i		−	0.649492i	−0.945801	−	0.324746i	$-0.894721\pi$
$167$		−	1.40888e13i		−	0.649492i	0.945801	−	0.324746i	$-0.105279\pi$
$168$	−9.23533e12	−	5.58873e10i	−0.410768	−	0.00248575i
$169$	2.51316e13			1.07870
$170$		−	3.17257e12i		−	0.131437i
$171$	3.20294e13	+	3.87664e11i	1.28107	+	0.0155052i
$172$	−1.24716e13			−0.481674
$173$			3.38119e13i			1.26123i	0.776098	+	0.630613i	$0.217196\pi$
$173$			3.38119e13i			1.26123i	−0.776098	+	0.630613i	$0.782804\pi$
$174$	3.61957e10	−	5.98130e12i	0.00130425	−	0.215526i
$175$	−3.29320e13			−1.14654
$176$		−	7.38313e12i		−	0.248407i
$177$	−5.56000e13	−	3.36462e11i	−1.80815	−	0.0109420i
$178$	2.44598e12			0.0769010
$179$		−	1.48281e13i		−	0.450782i	−0.974268	−	0.225391i	$-0.927634\pi$
$179$		−	1.48281e13i		−	0.450782i	0.974268	−	0.225391i	$-0.0723659\pi$
$180$	−2.36228e10	+	1.95175e12i	−0.000694538	+	0.0573839i
$181$	2.23824e13			0.636553			0.318276	−	0.947998i	$-0.396896\pi$
$181$	2.23824e13			0.636553			0.318276	+	0.947998i	$0.396896\pi$
$182$			4.30485e13i			1.18449i
$183$	1.63131e11	−	2.69573e13i	0.00434341	−	0.717744i
$184$	1.07725e13			0.277594
$185$		−	1.98583e11i		−	0.00495348i
$186$	−7.88791e12	−	4.77334e10i	−0.190495	−	0.00115278i
$187$	−6.88107e13			−1.60919
$188$			6.27000e12i			0.142010i
$189$	9.61331e11	−	5.29479e13i	0.0210912	−	1.16166i
$190$	−4.89173e12			−0.103978
$191$			6.90387e13i			1.42198i	0.703204	+	0.710988i	$0.251752\pi$
$191$			6.90387e13i			1.42198i	−0.703204	+	0.710988i	$0.748248\pi$
$192$	−3.78940e10	+	6.26195e12i	−0.000756419	+	0.124998i
$193$	7.07749e13			1.36942			0.684708	−	0.728818i	$-0.259930\pi$
$193$	7.07749e13			1.36942			0.684708	+	0.728818i	$0.259930\pi$
$194$			6.04421e12i			0.113378i
$195$	9.09802e12	+	5.50563e10i	0.165478	+	0.00100138i
$196$	−9.91836e12			−0.174946
$197$		−	1.06670e14i		−	1.82493i	−0.409154	−	0.912466i	$-0.634176\pi$
$197$		−	1.06670e14i		−	1.82493i	0.409154	−	0.912466i	$-0.365824\pi$
$198$	4.23320e13	+	5.12360e11i	0.702551	+	0.00850324i
$199$	8.61383e13			1.38700			0.693502	−	0.720455i	$-0.256067\pi$
$199$	8.61383e13			1.38700			0.693502	+	0.720455i	$0.256067\pi$
$200$			2.23293e13i			0.348896i
$201$	−2.59774e11	+	4.29274e13i	−0.00393929	+	0.650965i
$202$	−8.12090e13			−1.19535
$203$		−	2.47827e13i		−	0.354138i
$204$	5.83613e13	+	3.53171e11i	0.809737	+	0.00490009i
$205$	−5.77164e12			−0.0777635
$206$		−	5.25552e13i		−	0.687721i
$207$	−7.47571e11	+	6.17655e13i	−0.00950234	+	0.785098i
$208$	2.91888e13			0.360442
$209$			1.06098e14i			1.27300i
$210$	−4.89389e10	+	8.08712e12i	−0.000570609	+	0.0942927i
$211$	−7.93013e13			−0.898640			−0.449320	−	0.893371i	$-0.648334\pi$
$211$	−7.93013e13			−0.898640			−0.449320	+	0.893371i	$0.648334\pi$
$212$		−	5.65373e13i		−	0.622758i
$213$	−7.51899e13	−	4.55009e11i	−0.805160	−	0.00487240i
$214$	−4.07190e12			−0.0423950
$215$			1.09211e13i			0.110569i
$216$	−3.59010e13	−	6.51824e11i	−0.353495	−	0.00641812i
$217$	−3.26825e13			−0.313009
$218$		−	5.05689e13i		−	0.471134i
$219$	−5.85179e11	+	9.67004e13i	−0.00530425	+	0.876524i
$220$	−6.46520e12			−0.0570225
$221$		−	2.72039e14i		−	2.33495i
$222$	3.65304e12	+	2.21062e10i	0.0305166	+	0.000184670i
$223$	4.73883e13			0.385338			0.192669	−	0.981264i	$-0.438286\pi$
$223$	4.73883e13			0.385338			0.192669	+	0.981264i	$0.438286\pi$
$224$			2.59455e13i			0.205388i
$225$	−1.28028e14	−	1.54957e12i	−0.986754	−	0.0119431i
$226$	−5.58882e13			−0.419440
$227$			1.96565e14i			1.43665i	0.695708	+	0.718325i	$0.255091\pi$
$227$			1.96565e14i			1.43665i	−0.695708	+	0.718325i	$0.744909\pi$
$228$	5.44548e11	−	8.99861e13i	0.00387638	−	0.640569i
$229$	1.47104e14			1.02003			0.510014	−	0.860166i	$-0.329640\pi$
$229$	1.47104e14			1.02003			0.510014	+	0.860166i	$0.329640\pi$
$230$		−	9.43320e12i		−	0.0637224i
$231$	1.75403e14	+	1.06145e12i	1.15443	+	0.00698597i
$232$	−1.68037e13			−0.107765
$233$			9.97295e13i			0.623287i	0.950199	+	0.311644i	$0.100879\pi$
$233$			9.97295e13i			0.623287i	−0.950199	+	0.311644i	$0.899121\pi$
$234$	−2.02558e12	+	1.67357e14i	−0.0123383	+	1.01941i
$235$	5.49046e12			0.0325988
$236$			1.56202e14i			0.904093i
$237$	6.95081e11	−	1.14862e14i	0.00392234	−	0.648164i
$238$	2.41812e14			1.33050
$239$		−	1.87505e14i		−	1.00607i	−0.864267	−	0.503033i	$-0.832218\pi$
$239$		−	1.87505e14i		−	1.00607i	0.864267	−	0.503033i	$-0.167782\pi$
$240$	5.48341e12	+	3.31827e10i	0.0286935	+	0.000173638i
$241$	6.67375e13			0.340618			0.170309	−	0.985391i	$-0.445523\pi$
$241$	6.67375e13			0.340618			0.170309	+	0.985391i	$0.445523\pi$
$242$		−	1.80377e12i		−	0.00898027i
$243$	6.22869e12	−	2.05797e14i	0.0302523	−	0.999542i
$244$	−7.57333e13			−0.358879
$245$			8.68524e12i			0.0401592i
$246$	6.42499e11	−	1.06173e14i	0.00289909	−	0.479073i
$247$	−4.19451e14			−1.84714
$248$			2.21601e13i			0.0952494i
$249$	2.20318e14	+	1.33324e12i	0.924386	+	0.00559389i
$250$	3.93674e13			0.161249
$251$		−	2.35650e13i		−	0.0942377i	−0.998889	−	0.0471188i	$-0.984996\pi$
$251$		−	2.35650e13i		−	0.0942377i	0.998889	−	0.0471188i	$-0.0150039\pi$
$252$	−1.48762e14	−	1.80052e12i	−0.580882	−	0.00703063i
$253$	−2.04599e14			−0.780154
$254$			2.01097e14i			0.748864i
$255$	3.09262e11	−	5.11054e13i	0.00112483	−	0.185877i
$256$	1.75922e13			0.0625000
$257$			4.62487e14i			1.60509i	0.596589	+	0.802547i	$0.296522\pi$
$257$			4.62487e14i			1.60509i	−0.596589	+	0.802547i	$0.703478\pi$
$258$	−2.00899e14	−	1.21574e12i	−0.681177	−	0.00412212i
$259$	1.51359e13			0.0501428
$260$		−	2.55598e13i		−	0.0827403i
$261$	1.16611e12	−	9.63462e13i	0.00368891	−	0.304784i
$262$	−2.50759e13			−0.0775263
$263$			1.82217e14i			0.550624i	0.961355	+	0.275312i	$0.0887811\pi$
$263$			1.82217e14i			0.550624i	−0.961355	+	0.275312i	$0.911219\pi$
$264$	7.19707e11	−	1.18931e14i	0.00212585	−	0.351295i
$265$	−4.95081e13			−0.142956
$266$		−	3.72845e14i		−	1.05254i
$267$	3.94010e13	+	2.38434e11i	0.108752	+	0.000658112i
$268$	1.20599e14			0.325489
$269$		−	3.28807e14i		−	0.867814i	−0.900958	−	0.433907i	$-0.857135\pi$
$269$		−	3.28807e14i		−	0.867814i	0.900958	−	0.433907i	$-0.142865\pi$
$270$	−5.70784e11	+	3.14375e13i	−0.00147329	+	0.0811456i
$271$	2.14710e14			0.542047			0.271024	−	0.962573i	$-0.412638\pi$
$271$	2.14710e14			0.542047			0.271024	+	0.962573i	$0.412638\pi$
$272$		−	1.63959e14i		−	0.404876i
$273$	−4.19637e12	+	6.93446e14i	−0.0101367	+	1.67509i
$274$	3.21134e14			0.758898
$275$		−	4.24093e14i		−	0.980540i
$276$	1.73529e14	+	1.05011e12i	0.392571	+	0.00237563i
$277$	3.91069e14			0.865715			0.432857	−	0.901462i	$-0.357505\pi$
$277$	3.91069e14			0.865715			0.432857	+	0.901462i	$0.357505\pi$
$278$		−	1.32580e14i		−	0.287215i
$279$	−1.27058e14	−	1.53783e12i	−0.269386	−	0.00326048i
$280$	2.27198e13			0.0471472
$281$			4.97511e14i			1.01057i	0.862953	+	0.505284i	$0.168612\pi$
$281$			4.97511e14i			1.01057i	−0.862953	+	0.505284i	$0.831388\pi$
$282$	−6.11199e11	+	1.01000e14i	−0.00121531	+	0.200829i
$283$	4.29612e14			0.836291			0.418146	−	0.908380i	$-0.362680\pi$
$283$	4.29612e14			0.836291			0.418146	+	0.908380i	$0.362680\pi$
$284$			2.11237e14i			0.402587i
$285$	−7.87983e13	−	4.76845e11i	−0.147044	−	0.000889832i
$286$	−5.54372e14			−1.01299
$287$		−	4.39911e14i		−	0.787180i
$288$	−1.22083e12	+	1.00867e14i	−0.00213944	+	0.176764i
$289$	−9.45473e14			−1.62279
$290$			1.47146e13i			0.0247377i
$291$	−5.89189e11	+	9.73631e13i	−0.000970280	+	0.160338i
$292$	2.71668e14			0.438270
$293$		−	1.59482e14i		−	0.252062i	−0.992026	−	0.126031i	$-0.959776\pi$
$293$		−	1.59482e14i		−	0.252062i	0.992026	−	0.126031i	$-0.0402238\pi$
$294$	−1.59770e14	−	9.66841e11i	−0.247406	−	0.00149717i
$295$	1.36781e14			0.207537
$296$		−	1.02628e13i		−	0.0152586i
$297$	6.81854e14	+	1.23799e13i	0.993466	+	0.0180375i
$298$	−5.77432e14			−0.824524
$299$		−	8.08869e14i		−	1.13201i
$300$	−2.17666e12	+	3.59692e14i	−0.00298582	+	0.493404i
$301$	−8.32399e14			−1.11926
$302$			7.14982e14i			0.942439i
$303$	−1.30815e15	−	7.91625e12i	−1.69045	−	0.0102297i
$304$	−2.52805e14			−0.320291
$305$			6.63175e13i			0.0823814i
$306$	9.40077e14	+	1.13781e13i	1.14508	+	0.0138593i
$307$	8.26344e14			0.987030			0.493515	−	0.869737i	$-0.335712\pi$
$307$	8.26344e14			0.987030			0.493515	+	0.869737i	$0.335712\pi$
$308$		−	4.92775e14i		−	0.577224i
$309$	5.12307e12	−	8.46584e14i	0.00588545	−	0.972566i
$310$	1.94050e13			0.0218647
$311$			7.33313e14i			0.810451i	0.914217	+	0.405226i	$0.132807\pi$
$311$			7.33313e14i			0.810451i	−0.914217	+	0.405226i	$0.867193\pi$
$312$	4.70186e14	+	2.84532e12i	0.509733	+	0.00308463i
$313$	9.99817e14			1.06330			0.531648	−	0.846965i	$-0.321573\pi$
$313$	9.99817e14			1.06330			0.531648	+	0.846965i	$0.321573\pi$
$314$			5.68843e14i			0.593492i
$315$	−1.57666e12	+	1.30266e14i	−0.00161390	+	0.133343i
$316$	−3.22690e14			−0.324088
$317$		−	4.75088e14i		−	0.468186i	−0.972214	−	0.234093i	$-0.924788\pi$
$317$		−	4.75088e14i		−	0.468186i	0.972214	−	0.234093i	$-0.0752120\pi$
$318$	5.51125e12	−	9.10729e14i	0.00532951	−	0.880697i
$319$	3.19148e14			0.302864
$320$		−	1.54050e13i		−	0.0143470i
$321$	−6.55921e13	−	3.96929e11i	−0.0599545	−	0.000362813i
$322$	7.18994e14			0.645045
$323$			2.35614e15i			2.07485i
$324$	−5.78246e14	−	1.39995e13i	−0.499854	−	0.0121016i
$325$	1.67663e15			1.42278
$326$		−	2.41055e14i		−	0.200822i
$327$	4.92945e12	−	8.14588e14i	0.00403192	−	0.666272i
$328$	−2.98279e14			−0.239541
$329$			4.18480e14i			0.329989i
$330$	−1.04145e14	−	6.30227e11i	−0.0806405	−	0.000487993i
$331$	−1.17559e15			−0.893895			−0.446948	−	0.894560i	$-0.647489\pi$
$331$	−1.17559e15			−0.893895			−0.446948	+	0.894560i	$0.647489\pi$
$332$		−	6.18956e14i		−	0.462201i
$333$	5.88427e13	+	7.12195e11i	0.0431546	+	0.000522317i
$334$	−6.37584e14			−0.459260
$335$		−	1.05605e14i		−	0.0747166i
$336$	−2.52917e12	+	4.17943e14i	−0.00175769	+	0.290457i
$337$	−1.80768e15			−1.23408			−0.617039	−	0.786932i	$-0.711668\pi$
$337$	−1.80768e15			−1.23408			−0.617039	+	0.786932i	$0.711668\pi$
$338$		−	1.13732e15i		−	0.762754i
$339$	−9.00274e14	−	5.44798e12i	−0.593167	−	0.00358953i
$340$	−1.43574e14			−0.0929401
$341$		−	4.20880e14i		−	0.267690i
$342$	1.75437e13	−	1.44949e15i	0.0109639	−	0.905852i
$343$	1.22999e15			0.755327
$344$			5.64402e14i			0.340595i
$345$	9.19548e11	−	1.51955e14i	0.000545331	−	0.0901155i
$346$	1.53015e15			0.891821
$347$			1.07187e15i			0.613995i	0.951710	+	0.306997i	$0.0993243\pi$
$347$			1.07187e15i			0.613995i	−0.951710	+	0.306997i	$0.900676\pi$
$348$	−2.70683e14	−	1.63803e12i	−0.152400	−	0.000922244i
$349$	−3.35896e15			−1.85889			−0.929443	−	0.368965i	$-0.879712\pi$
$349$	−3.35896e15			−1.85889			−0.929443	+	0.368965i	$0.879712\pi$
$350$			1.49033e15i			0.810728i
$351$	−4.89430e13	+	2.69567e15i	−0.0261727	+	1.44153i
$352$	−3.34122e14			−0.175651
$353$		−	3.05843e15i		−	1.58070i	−0.612653	−	0.790352i	$-0.709898\pi$
$353$		−	3.05843e15i		−	1.58070i	0.612653	−	0.790352i	$-0.290102\pi$
$354$	−1.52265e13	+	2.51617e15i	−0.00773715	+	1.27856i
$355$	1.84974e14			0.0924148
$356$		−	1.10692e14i		−	0.0543772i
$357$	3.89522e15	+	2.35718e13i	1.88158	+	0.0113863i
$358$	−6.71042e14			−0.318751
$359$		−	1.15467e15i		−	0.539374i	−0.962948	−	0.269687i	$-0.913080\pi$
$359$		−	1.15467e15i		−	0.539374i	0.962948	−	0.269687i	$-0.0869203\pi$
$360$	8.83262e13	+	1.06905e12i	0.0405765	+	0.000491113i
$361$	1.41957e15			0.641376
$362$		−	1.01291e15i		−	0.450111i
$363$	1.75832e11	−	2.90560e13i	7.68523e−5	−	0.0126998i
$364$	1.94815e15			0.837558
$365$		−	2.37892e14i		−	0.100606i
$366$	−1.21995e15	−	7.38247e12i	−0.507522	−	0.00307125i
$367$	3.94032e15			1.61263			0.806315	−	0.591487i	$-0.201459\pi$
$367$	3.94032e15			1.61263			0.806315	+	0.591487i	$0.201459\pi$
$368$		−	4.87509e14i		−	0.196289i
$369$	2.06994e13	−	1.71022e15i	0.00819972	−	0.677474i
$370$	−8.98682e12			−0.00350264
$371$		−	3.77348e15i		−	1.44710i
$372$	−2.16017e12	+	3.56966e14i	−0.000815136	+	0.134701i
$373$	−4.39222e15			−1.63092			−0.815458	−	0.578817i	$-0.803515\pi$
$373$	−4.39222e15			−1.63092			−0.815458	+	0.578817i	$0.803515\pi$
$374$			3.11402e15i			1.13787i
$375$	6.34149e14	+	3.83753e12i	0.228036	+	0.00137995i
$376$	2.83748e14			0.100417
$377$			1.26173e15i			0.439459i
$378$	−2.39615e15	−	4.35049e13i	−0.821415	−	0.0149138i
$379$	−1.19032e15			−0.401633			−0.200817	−	0.979629i	$-0.564360\pi$
$379$	−1.19032e15			−0.401633			−0.200817	+	0.979629i	$0.564360\pi$
$380$			2.21374e14i			0.0735234i
$381$	−1.96029e13	+	3.23937e15i	−0.00640871	+	1.05903i
$382$	3.12434e15			1.00549
$383$			3.21031e15i			1.01708i	0.861039	+	0.508539i	$0.169814\pi$
$383$			3.21031e15i			1.01708i	−0.861039	+	0.508539i	$0.830186\pi$
$384$	2.83383e14	+	1.71489e12i	0.0883867	+	0.000534869i
$385$	−4.31509e14			−0.132503
$386$		−	3.20290e15i		−	0.968323i
$387$	−3.23606e15	−	3.91673e13i	−0.963277	−	0.0116589i
$388$	2.73530e14			0.0801704
$389$			5.57085e14i			0.160777i	0.996764	+	0.0803885i	$0.0256161\pi$
$389$			5.57085e14i			0.160777i	−0.996764	+	0.0803885i	$0.974384\pi$
$390$	2.49157e12	−	4.11729e14i	0.000708084	−	0.117010i
$391$	−4.54358e15			−1.27156
$392$			4.48854e14i			0.123705i
$393$	−4.03935e14	−	2.44440e12i	−0.109637	−	0.000663463i
$394$	−4.82735e15			−1.29042
$395$			2.82570e14i			0.0743951i
$396$	2.31868e13	−	1.91573e15i	0.00601270	−	0.496778i
$397$	5.52035e15			1.41001			0.705007	−	0.709200i	$-0.250944\pi$
$397$	5.52035e15			1.41001			0.705007	+	0.709200i	$0.250944\pi$
$398$		−	3.89817e15i		−	0.980760i
$399$	3.63449e13	−	6.00597e15i	0.00900754	−	1.48849i
$400$	1.01051e15			0.246707
$401$			3.33946e15i			0.803176i	0.915820	+	0.401588i	$0.131542\pi$
$401$			3.33946e15i			0.803176i	−0.915820	+	0.401588i	$0.868458\pi$
$402$	1.94267e15	+	1.17560e13i	0.460302	+	0.00278550i
$403$	1.66392e15			0.388421
$404$			3.67510e15i			0.845242i
$405$	−1.22590e13	+	5.06354e14i	−0.00277795	+	0.114742i
$406$	−1.12154e15			−0.250414
$407$			1.94917e14i			0.0428829i
$408$	1.59827e13	−	2.64113e15i	0.00346489	−	0.572570i
$409$	2.13091e15			0.455225			0.227613	−	0.973752i	$-0.426908\pi$
$409$	2.13091e15			0.455225			0.227613	+	0.973752i	$0.426908\pi$
$410$			2.61195e14i			0.0549871i
$411$	5.17298e15	+	3.13041e13i	1.07322	+	0.00649458i
$412$	−2.37837e15			−0.486292
$413$			1.04254e16i			2.10084i
$414$	2.79519e15	+	3.38312e13i	0.555148	+	0.00671917i
$415$	−5.42002e14			−0.106099
$416$		−	1.32093e15i		−	0.254871i
$417$	1.29238e13	−	2.13566e15i	0.00245796	−	0.406176i
$418$	4.80144e15			0.900147
$419$		−	2.50176e15i		−	0.462340i	−0.972913	−	0.231170i	$-0.925745\pi$
$419$		−	2.50176e15i		−	0.462340i	0.972913	−	0.231170i	$-0.0742554\pi$
$420$	3.65981e14	+	2.21472e12i	0.0666750	+	0.000403481i
$421$	2.58203e15			0.463733			0.231867	−	0.972748i	$-0.425517\pi$
$421$	2.58203e15			0.463733			0.231867	+	0.972748i	$0.425517\pi$
$422$			3.58877e15i			0.635434i
$423$	−1.96910e13	+	1.62690e15i	−0.00343736	+	0.284000i
$424$	−2.55858e15			−0.440357
$425$		−	9.41794e15i		−	1.59817i
$426$	−2.05914e13	+	3.40271e15i	−0.00344530	+	0.569334i
$427$	−5.05469e15			−0.833925
$428$			1.84273e14i			0.0299778i
$429$	−8.93009e15	−	5.40401e13i	−1.43256	−	0.00866907i
$430$	4.94231e14			0.0781843
$431$		−	8.92494e15i		−	1.39233i	−0.717883	−	0.696164i	$-0.754889\pi$
$431$		−	8.92494e15i		−	1.39233i	0.717883	−	0.696164i	$-0.245111\pi$
$432$	−2.94982e13	+	1.62469e15i	−0.00453829	+	0.249959i
$433$	−1.92914e15			−0.292709			−0.146355	−	0.989232i	$-0.546754\pi$
$433$	−1.92914e15			−0.292709			−0.146355	+	0.989232i	$0.546754\pi$
$434$			1.47904e15i			0.221331i
$435$	−1.43438e12	+	2.37029e14i	−0.000211703	+	0.0349838i
$436$	−2.28849e15			−0.333142
$437$			7.00565e15i			1.00591i
$438$	4.37616e15	+	2.64822e13i	0.619796	+	0.00375067i
$439$	7.28685e15			1.01801			0.509006	−	0.860763i	$-0.330013\pi$
$439$	7.28685e15			1.01801			0.509006	+	0.860763i	$0.330013\pi$
$440$			2.92582e14i			0.0403210i
$441$	−2.57355e15	−	3.11487e13i	−0.349866	−	0.00423456i
$442$	−1.23111e16			−1.65106
$443$		−	3.15613e14i		−	0.0417573i	−0.999782	−	0.0208786i	$-0.993354\pi$
$443$		−	3.15613e14i		−	0.0417573i	0.999782	−	0.0208786i	$-0.00664636\pi$
$444$	1.00041e12	−	1.65318e14i	0.000130582	−	0.0215785i
$445$	−9.69301e13			−0.0124824
$446$		−	2.14455e15i		−	0.272475i
$447$	−9.30156e15	−	5.62881e13i	−1.16603	−	0.00705620i
$448$	1.17416e15			0.145231
$449$		−	1.17600e16i		−	1.43526i	−0.696427	−	0.717628i	$-0.745228\pi$
$449$		−	1.17600e16i		−	1.43526i	0.696427	−	0.717628i	$-0.254772\pi$
$450$	−7.01254e13	+	5.79387e15i	−0.00844502	+	0.697741i
$451$	5.66511e15			0.673208
$452$			2.52921e15i			0.296589i
$453$	−6.96964e13	+	1.15173e16i	−0.00806531	+	1.33279i
$454$	8.89551e15			1.01586
$455$		−	1.70594e15i		−	0.192263i
$456$	−4.07230e15	−	2.46434e13i	−0.452951	−	0.00274102i
$457$	2.09774e15			0.230279			0.115140	−	0.993349i	$-0.463268\pi$
$457$	2.09774e15			0.230279			0.115140	+	0.993349i	$0.463268\pi$
$458$		−	6.65717e15i		−	0.721269i
$459$	1.51421e16	+	2.74923e14i	1.61924	+	0.0293991i
$460$	−4.26898e14			−0.0450586
$461$			3.28649e15i			0.342395i	0.985237	+	0.171197i	$0.0547636\pi$
$461$			3.28649e15i			0.342395i	−0.985237	+	0.171197i	$0.945236\pi$
$462$	4.80356e13	−	7.93785e15i	0.00493983	−	0.816302i
$463$	−4.69598e15			−0.476694			−0.238347	−	0.971180i	$-0.576606\pi$
$463$	−4.69598e15			−0.476694			−0.238347	+	0.971180i	$0.576606\pi$
$464$			7.60451e14i			0.0762015i
$465$	3.12585e14	+	1.89160e12i	0.0309208	+	0.000187116i
$466$	4.51324e15			0.440731
$467$			1.21461e16i			1.17094i	0.810694	+	0.585470i	$0.199090\pi$
$467$			1.21461e16i			1.17094i	−0.810694	+	0.585470i	$0.800910\pi$
$468$	7.57371e15	+	9.16675e13i	0.720831	+	0.00872449i
$469$	8.04919e15			0.756337
$470$		−	2.48470e14i		−	0.0230508i
$471$	−5.54508e13	+	9.16320e15i	−0.00507905	+	0.839309i
$472$	7.06888e15			0.639291
$473$		−	1.07195e16i		−	0.957211i
$474$	−5.19804e15	−	3.14558e13i	−0.458321	−	0.00277351i
$475$	−1.45213e16			−1.26428
$476$		−	1.09432e16i		−	0.940808i
$477$	1.77556e14	−	1.46699e16i	0.0150739	−	1.24543i
$478$	−8.48552e15			−0.711396
$479$			1.56379e16i			1.29469i	0.762196	+	0.647346i	$0.224121\pi$
$479$			1.56379e16i			1.29469i	−0.762196	+	0.647346i	$0.775879\pi$
$480$	1.50168e12	−	2.48151e14i	0.000122780	−	0.0202894i
$481$	−7.70593e14			−0.0622235
$482$		−	3.02019e15i		−	0.240853i
$483$	1.15819e16	+	7.00875e13i	0.912215	+	0.00552024i
$484$	−8.16294e13			−0.00635001
$485$		−	2.39522e14i		−	0.0184033i
$486$	−9.31330e15	−	2.81878e14i	−0.706783	−	0.0213916i
$487$	−1.84287e16			−1.38141			−0.690703	−	0.723139i	$-0.742699\pi$
$487$	−1.84287e16			−1.38141			−0.690703	+	0.723139i	$0.742699\pi$
$488$			3.42730e15i			0.253766i
$489$	2.34980e13	−	3.88303e15i	0.00171861	−	0.284000i
$490$	3.93049e14			0.0283968
$491$		−	3.47790e15i		−	0.248215i	−0.992269	−	0.124108i	$-0.960393\pi$
$491$		−	3.47790e15i		−	0.248215i	0.992269	−	0.124108i	$-0.0396068\pi$
$492$	−4.80482e15	−	2.90762e13i	−0.338756	−	0.00204997i
$493$	7.08739e15			0.493634
$494$			1.89822e16i			1.30612i
$495$	−1.67755e15	−	2.03040e13i	−0.114037	−	0.00138023i
$496$	1.00285e15			0.0673515
$497$			1.40987e16i			0.935490i
$498$	6.03358e13	−	9.97044e15i	0.00395548	−	0.653639i
$499$	−1.02285e16			−0.662532			−0.331266	−	0.943537i	$-0.607476\pi$
$499$	−1.02285e16			−0.662532			−0.331266	+	0.943537i	$0.607476\pi$
$500$		−	1.78156e15i		−	0.114020i
$501$	−1.02705e16	−	6.21517e13i	−0.649480	−	0.00393031i
$502$	−1.06643e15			−0.0666361
$503$			7.96034e15i			0.491500i	0.969333	+	0.245750i	$0.0790342\pi$
$503$			7.96034e15i			0.491500i	−0.969333	+	0.245750i	$0.920966\pi$
$504$	−8.14821e13	+	6.73218e15i	−0.00497141	+	0.410745i
$505$	3.21818e15			0.194027
$506$			9.25909e15i			0.551652i
$507$	1.10866e14	−	1.83206e16i	0.00652758	−	1.07868i
$508$	9.10061e15			0.529527
$509$		−	1.45032e16i		−	0.833985i	−0.908910	−	0.416993i	$-0.863084\pi$
$509$		−	1.45032e16i		−	0.833985i	0.908910	−	0.416993i	$-0.136916\pi$
$510$	−2.31276e15	−	1.39956e13i	−0.131435	−	0.000795373i
$511$	1.81320e16			1.01841
$512$		−	7.96131e14i		−	0.0441942i
$513$	4.23898e14	−	2.33473e16i	0.0232572	−	1.28095i
$514$	2.09298e16			1.13497
$515$			2.08268e15i			0.111629i
$516$	−5.50179e13	+	9.09166e15i	−0.00291478	+	0.481665i
$517$	−5.38912e15			−0.282212
$518$		−	6.84971e14i		−	0.0354563i
$519$	2.46484e16	+	1.49159e14i	1.26120	+	0.00763212i
$520$	−1.15670e15			−0.0585062
$521$		−	2.20555e16i		−	1.10279i	−0.834246	−	0.551393i	$-0.814097\pi$
$521$		−	2.20555e16i		−	1.10279i	0.834246	−	0.551393i	$-0.185903\pi$
$522$	−4.36013e15	−	5.27723e13i	−0.215514	−	0.00260845i
$523$	−5.41153e14			−0.0264429			−0.0132215	−	0.999913i	$-0.504209\pi$
$523$	−5.41153e14			−0.0264429			−0.0132215	+	0.999913i	$0.504209\pi$
$524$			1.13481e15i			0.0548194i
$525$	−1.45278e14	+	2.40070e16i	−0.00693814	+	1.14652i
$526$	8.24621e15			0.389350
$527$		−	9.34658e15i		−	0.436304i
$528$	−5.38220e15	−	3.25702e13i	−0.248403	−	0.00150320i
$529$	8.40493e15			0.383531
$530$			2.24048e15i			0.101085i
$531$	−4.90552e14	+	4.05302e16i	−0.0218836	+	1.80805i
$532$	−1.68730e16			−0.744258
$533$			2.23967e16i			0.976832i
$534$	1.07903e13	−	1.78308e15i	0.000465355	−	0.0768996i
$535$	1.61363e14			0.00688147
$536$		−	5.45770e15i		−	0.230155i
$537$	−1.08095e16	−	6.54131e13i	−0.450774	−	0.00272784i
$538$	−1.48801e16			−0.613637
$539$		−	8.52493e15i		−	0.347663i
$540$	1.42270e15	+	2.58307e13i	0.0573786	+	0.00104178i
$541$	4.33377e15			0.172855			0.0864275	−	0.996258i	$-0.472455\pi$
$541$	4.33377e15			0.172855			0.0864275	+	0.996258i	$0.472455\pi$
$542$		−	9.71668e15i		−	0.383285i
$543$	9.87384e13	−	1.63164e16i	0.00385201	−	0.636541i
$544$	−7.41994e15			−0.286290
$545$			2.00396e15i			0.0764735i
$546$	3.13818e16	+	1.89906e14i	1.18446	+	0.00716775i
$547$	−3.60740e16			−1.34670			−0.673349	−	0.739325i	$-0.735145\pi$
$547$	−3.60740e16			−1.34670			−0.673349	+	0.739325i	$0.735145\pi$
$548$		−	1.45329e16i		−	0.536622i
$549$	−1.96508e16	−	2.37841e14i	−0.717705	−	0.00868665i
$550$	−1.91923e16			−0.693347
$551$		−	1.09279e16i		−	0.390506i
$552$	4.75223e13	−	7.85303e15i	0.00167982	−	0.277589i
$553$	−2.15374e16			−0.753082
$554$		−	1.76978e16i		−	0.612153i
$555$	−1.44764e14	−	8.76034e11i	−0.00495339	−	2.99753e-5i
$556$	−5.99986e15			−0.203092
$557$		−	3.61689e15i		−	0.121117i	−0.998165	−	0.0605584i	$-0.980712\pi$
$557$		−	3.61689e15i		−	0.121117i	0.998165	−	0.0605584i	$-0.0192881\pi$
$558$	−6.95941e13	+	5.74997e15i	−0.00230551	+	0.190485i
$559$	4.23789e16			1.38892
$560$		−	1.02818e15i		−	0.0333381i
$561$	−3.03554e14	+	5.01621e16i	−0.00973776	+	1.60916i
$562$	2.25148e16			0.714579
$563$		−	1.11795e16i		−	0.351052i	−0.984475	−	0.175526i	$-0.943837\pi$
$563$		−	1.11795e16i		−	0.351052i	0.984475	−	0.175526i	$-0.0561627\pi$
$564$	4.57074e15	+	2.76597e13i	0.142008	+	0.000859356i
$565$	2.21476e15			0.0680826
$566$		−	1.94420e16i		−	0.591347i
$567$	−3.85941e16	−	9.34374e14i	−1.16151	−	0.0281205i
$568$	9.55949e15			0.284672
$569$			6.08528e16i			1.79311i	0.442933	+	0.896555i	$0.353938\pi$
$569$			6.08528e16i			1.79311i	−0.442933	+	0.896555i	$0.646062\pi$
$570$	−2.15795e13	+	3.56600e15i	−0.000629207	+	0.103976i
$571$	1.73121e15			0.0499497			0.0249748	−	0.999688i	$-0.492049\pi$
$571$	1.73121e15			0.0499497			0.0249748	+	0.999688i	$0.492049\pi$
$572$			2.50880e16i			0.716292i
$573$	5.03283e16	+	3.04560e14i	1.42195	+	0.00860489i
$574$	−1.99081e16			−0.556620
$575$		−	2.80029e16i		−	0.774812i
$576$	4.56471e15	+	5.52484e13i	0.124991	+	0.00151281i
$577$	5.53494e16			1.49988			0.749942	−	0.661503i	$-0.230081\pi$
$577$	5.53494e16			1.49988			0.749942	+	0.661503i	$0.230081\pi$
$578$			4.27872e16i			1.14749i
$579$	3.12219e14	−	5.15939e16i	0.00828682	−	1.36939i
$580$	6.65906e14			0.0174922
$581$		−	4.13112e16i		−	1.07402i
$582$	4.40615e15	+	2.66637e13i	0.113376	+	0.000686091i
$583$	4.85943e16			1.23758
$584$		−	1.22943e16i		−	0.309904i
$585$	8.02707e13	−	6.63209e15i	0.00200273	−	0.165468i
$586$	−7.21734e15			−0.178234
$587$			1.60341e16i			0.391936i	0.980610	+	0.195968i	$0.0627848\pi$
$587$			1.60341e16i			0.391936i	−0.980610	+	0.195968i	$0.937215\pi$
$588$	−4.37542e13	+	7.23035e15i	−0.00105866	+	0.174943i
$589$	−1.44113e16			−0.345153
$590$		−	6.19002e15i		−	0.146751i
$591$	−7.77613e16	−	4.70570e14i	−1.82490	−	0.0110433i
$592$	−4.64440e14			−0.0107894
$593$			2.24316e16i			0.515861i	0.966163	+	0.257931i	$0.0830406\pi$
$593$			2.24316e16i			0.515861i	−0.966163	+	0.257931i	$0.916959\pi$
$594$	5.60249e14	−	3.08572e16i	0.0127545	−	0.702487i
$595$	−9.58263e15			−0.215965
$596$			2.61316e16i			0.583027i
$597$	3.79994e14	−	6.27936e16i	0.00839325	−	1.38698i
$598$	−3.66053e16			−0.800454
$599$			1.33120e16i			0.288193i	0.989564	+	0.144097i	$0.0460276\pi$
$599$			1.33120e16i			0.288193i	−0.989564	+	0.144097i	$0.953972\pi$
$600$	1.62778e16	+	9.85045e13i	0.348889	+	0.00211129i
$601$	−4.25822e16			−0.903611			−0.451805	−	0.892117i	$-0.649220\pi$
$601$	−4.25822e16			−0.903611			−0.451805	+	0.892117i	$0.649220\pi$
$602$			3.76701e16i			0.791439i
$603$	3.12923e16	+	3.78743e14i	0.650930	+	0.00787845i
$604$	3.23564e16			0.666405
$605$			7.14806e13i			0.00145766i
$606$	−3.58249e14	+	5.92003e16i	−0.00723350	+	1.19533i
$607$	4.89540e15			0.0978714			0.0489357	−	0.998802i	$-0.484417\pi$
$607$	4.89540e15			0.0978714			0.0489357	+	0.998802i	$0.484417\pi$
$608$			1.14406e16i			0.226480i
$609$	−1.80663e16	−	1.09327e14i	−0.354132	−	0.00214302i
$610$	3.00119e15			0.0582525
$611$		−	2.13056e16i		−	0.409492i
$612$	5.14914e14	−	4.25430e16i	0.00980001	−	0.809692i
$613$	−8.61136e16			−1.62296			−0.811482	−	0.584377i	$-0.801339\pi$
$613$	−8.61136e16			−1.62296			−0.811482	+	0.584377i	$0.801339\pi$
$614$		−	3.73960e16i		−	0.697936i
$615$	−2.54612e13	+	4.20745e15i	−0.000470575	+	0.0777621i
$616$	−2.23004e16			−0.408159
$617$			7.09153e16i			1.28537i	0.766130	+	0.642686i	$0.222180\pi$
$617$			7.09153e16i			1.28537i	−0.766130	+	0.642686i	$0.777820\pi$
$618$	−3.83120e16	−	2.31844e14i	−0.687708	−	0.00416164i
$619$	−5.89878e16			−1.04862			−0.524310	−	0.851527i	$-0.675677\pi$
$619$	−5.89878e16			−1.04862			−0.524310	+	0.851527i	$0.675677\pi$
$620$		−	8.78171e14i		−	0.0154607i
$621$	4.50229e16	+	8.17444e14i	0.785026	+	0.0142531i
$622$	3.31860e16			0.573076
$623$		−	7.38796e15i		−	0.126356i
$624$	1.28764e14	−	2.12782e16i	0.00218116	−	0.360436i
$625$	5.72594e16			0.960653
$626$		−	4.52466e16i		−	0.751864i
$627$	7.73439e16	+	4.68044e14i	1.27298	+	0.00770338i
$628$	2.57429e16			0.419662
$629$			4.32857e15i			0.0698942i
$630$	5.89519e15	+	7.13516e13i	0.0942875	+	0.00114120i
$631$	5.31674e16			0.842304			0.421152	−	0.906990i	$-0.361626\pi$
$631$	5.31674e16			0.842304			0.421152	+	0.906990i	$0.361626\pi$
$632$			1.46033e16i			0.229165i
$633$	−3.49833e14	+	5.78096e16i	−0.00543799	+	0.898623i
$634$	−2.15000e16			−0.331058
$635$		−	7.96915e15i		−	0.121554i
$636$	−4.12149e16	−	2.49411e14i	−0.622747	−	0.00376853i
$637$	3.37028e16			0.504463
$638$		−	1.44430e16i		−	0.214157i
$639$	−6.63391e14	+	5.48104e16i	−0.00974461	+	0.805115i
$640$	−6.97150e14			−0.0101449
$641$		−	1.10730e17i		−	1.59630i	−0.602456	−	0.798152i	$-0.705811\pi$
$641$		−	1.10730e17i		−	1.59630i	0.602456	−	0.798152i	$-0.294189\pi$
$642$	−1.79629e13	+	2.96836e15i	−0.000256547	+	0.0423942i
$643$	4.77717e16			0.675935			0.337968	−	0.941158i	$-0.390261\pi$
$643$	4.77717e16			0.675935			0.337968	+	0.941158i	$0.390261\pi$
$644$		−	3.25380e16i		−	0.456116i
$645$	7.96132e15	+	4.81776e13i	0.110567	+	0.000669094i
$646$	1.06627e17			1.46714
$647$			1.03565e17i			1.41185i	0.708288	+	0.705923i	$0.249468\pi$
$647$			1.03565e17i			1.41185i	−0.708288	+	0.705923i	$0.750532\pi$
$648$	−6.33546e14	+	2.61684e16i	−0.00855713	+	0.353450i
$649$	−1.34257e17			−1.79667
$650$		−	7.58755e16i		−	1.00605i
$651$	−1.44177e14	+	2.38251e16i	−0.00189413	+	0.313003i
$652$	−1.09089e16			−0.142002
$653$		−	1.16931e17i		−	1.50817i	−0.656777	−	0.754085i	$-0.728081\pi$
$653$		−	1.16931e17i		−	1.50817i	0.656777	−	0.754085i	$-0.271919\pi$
$654$	−3.68640e16	−	2.23081e14i	−0.471125	−	0.00285100i
$655$	9.93718e14			0.0125839
$656$			1.34986e16i			0.169381i
$657$	7.04907e16	+	8.53176e14i	0.876476	+	0.0106083i
$658$	1.89383e16			0.233338
$659$			9.35126e16i			1.14172i	0.821049	+	0.570858i	$0.193389\pi$
$659$			9.35126e16i			1.14172i	−0.821049	+	0.570858i	$0.806611\pi$
$660$	−2.85208e13	+	4.71305e15i	−0.000345063	+	0.0570214i
$661$	−1.50669e16			−0.180641			−0.0903205	−	0.995913i	$-0.528789\pi$
$661$	−1.50669e16			−0.180641			−0.0903205	+	0.995913i	$0.528789\pi$
$662$			5.32010e16i			0.632079i
$663$	−1.98313e17	−	1.20008e15i	−2.33491	−	0.0141296i
$664$	−2.80107e16			−0.326826
$665$			1.47753e16i			0.170846i
$666$	3.22303e13	−	2.66292e15i	0.000369334	−	0.0305149i
$667$	2.10734e16			0.239320
$668$			2.88538e16i			0.324746i
$669$	2.09050e14	−	3.45454e16i	0.00233182	−	0.385331i
$670$	−4.77916e15			−0.0528326
$671$		−	6.50935e16i		−	0.713185i
$672$	1.89139e16	+	1.14457e14i	0.205384	+	0.00124287i
$673$	−7.21757e16			−0.776785			−0.388392	−	0.921494i	$-0.626969\pi$
$673$	−7.21757e16			−0.776785			−0.388392	+	0.921494i	$0.626969\pi$
$674$			8.18064e16i			0.872625i
$675$	−1.69440e15	+	9.33237e16i	−0.0179140	+	0.986664i
$676$	−5.14694e16			−0.539348
$677$		−	1.40180e17i		−	1.45597i	−0.685593	−	0.727985i	$-0.740457\pi$
$677$		−	1.40180e17i		−	1.45597i	0.685593	−	0.727985i	$-0.259543\pi$
$678$	−2.46547e14	+	4.07418e16i	−0.00253818	+	0.419432i
$679$	1.82563e16			0.186292
$680$			6.49743e15i			0.0657186i
$681$	1.43293e17	+	8.67134e14i	1.43662	+	0.00869367i
$682$	−1.90468e16			−0.189285
$683$		−	1.28372e17i		−	1.26458i	−0.774733	−	0.632289i	$-0.782116\pi$
$683$		−	1.28372e17i		−	1.26458i	0.774733	−	0.632289i	$-0.217884\pi$
$684$	−6.55962e16	−	7.93936e14i	−0.640534	−	0.00775262i
$685$	−1.27260e16			−0.123183
$686$		−	5.56628e16i		−	0.534097i
$687$	6.48941e14	−	1.07237e17i	0.00617255	−	1.02001i
$688$	2.55419e16			0.240837
$689$			1.92115e17i			1.79575i
$690$	−6.87668e15	−	4.16140e13i	−0.0637213	−	0.000385607i
$691$	−2.62529e16			−0.241162			−0.120581	−	0.992703i	$-0.538476\pi$
$691$	−2.62529e16			−0.241162			−0.120581	+	0.992703i	$0.538476\pi$
$692$		−	6.92467e16i		−	0.630613i
$693$	1.54756e15	−	1.27862e17i	0.0139717	−	1.15436i
$694$	4.85072e16			0.434160
$695$			5.25392e15i			0.0466202i
$696$	−7.41287e13	+	1.22497e16i	−0.000652125	+	0.107763i
$697$	1.25806e17			1.09725
$698$			1.52009e17i			1.31443i
$699$	7.27015e16	+	4.39951e14i	0.623276	+	0.00377173i
$700$	6.74448e16			0.573271
$701$			3.77892e16i			0.318463i	0.987241	+	0.159232i	$0.0509017\pi$
$701$			3.77892e16i			0.318463i	−0.987241	+	0.159232i	$0.949098\pi$
$702$	1.21992e17	+	2.21491e15i	1.01932	+	0.0185069i
$703$	6.67414e15			0.0552921
$704$			1.51207e16i			0.124204i
$705$	2.42208e13	−	4.00247e15i	0.000197267	−	0.0325982i
$706$	−1.38409e17			−1.11773
$707$			2.45288e17i			1.96409i
$708$	1.13869e17	+	6.89073e14i	0.904077	+	0.00547099i
$709$	7.26971e16			0.572321			0.286161	−	0.958182i	$-0.407621\pi$
$709$	7.26971e16			0.572321			0.286161	+	0.958182i	$0.407621\pi$
$710$		−	8.37098e15i		−	0.0653471i
$711$	−8.37295e16	−	1.01341e15i	−0.648128	−	0.00784454i
$712$	−5.00936e15			−0.0384505
$713$		−	2.77907e16i		−	0.211526i
$714$	1.06674e15	−	1.76278e17i	0.00805135	−	1.33048i
$715$	2.19689e16			0.164426
$716$			3.03679e16i			0.225391i
$717$	−1.36689e17	−	8.27168e14i	−1.00605	−	0.00608806i
$718$	−5.22543e16			−0.381395
$719$			5.03837e16i			0.364684i	0.983235	+	0.182342i	$0.0583678\pi$
$719$			5.03837e16i			0.364684i	−0.983235	+	0.182342i	$0.941632\pi$
$720$	4.83795e13	−	3.99719e15i	0.000347269	−	0.0286919i
$721$	−1.58741e17			−1.12999
$722$		−	6.42423e16i		−	0.453522i
$723$	2.94408e14	−	4.86507e16i	0.00206120	−	0.340612i
$724$	−4.58391e16			−0.318276
$725$			4.36810e16i			0.300790i
$726$	−1.31493e15	−	7.95723e12i	−0.00898010	−	5.43428e-5i
$727$	2.56056e17			1.73432			0.867158	−	0.498032i	$-0.165944\pi$
$727$	2.56056e17			1.73432			0.867158	+	0.498032i	$0.165944\pi$
$728$		−	8.81634e16i		−	0.592243i
$729$	−1.49996e17	−	5.44849e15i	−0.999341	−	0.0363004i
$730$	−1.07658e16			−0.0711391
$731$		−	2.38051e17i		−	1.56014i
$732$	−3.34093e14	+	5.52085e16i	−0.00217170	+	0.358872i
$733$	5.75511e16			0.371047			0.185524	−	0.982640i	$-0.440602\pi$
$733$	5.75511e16			0.371047			0.185524	+	0.982640i	$0.440602\pi$
$734$		−	1.78318e17i		−	1.14030i
$735$	6.33142e15	+	3.83144e13i	0.0401585	+	0.000243018i
$736$	−2.20621e16			−0.138797
$737$			1.03656e17i			0.646830i
$738$	−7.73955e16	−	9.36747e14i	−0.479046	−	0.00579808i
$739$	−2.93210e17			−1.80016			−0.900082	−	0.435721i	$-0.856493\pi$
$739$	−2.93210e17			−1.80016			−0.900082	+	0.435721i	$0.856493\pi$
$740$			4.06697e14i			0.00247674i
$741$	−1.85038e15	+	3.05774e17i	−0.0111777	+	1.84711i
$742$	−1.70768e17			−1.02326
$743$			1.10591e17i			0.657337i	0.944445	+	0.328669i	$0.106600\pi$
$743$			1.10591e17i			0.657337i	−0.944445	+	0.328669i	$0.893400\pi$
$744$	1.61544e16	+	9.77580e13i	0.0952477	+	0.000576388i
$745$	2.28827e16			0.133835
$746$			1.98769e17i			1.15323i
$747$	1.94384e15	−	1.60603e17i	0.0111876	−	0.924335i
$748$	1.40924e17			0.804593
$749$			1.22990e16i			0.0696593i
$750$	1.73667e14	−	2.86983e16i	0.000975774	−	0.161246i
$751$	1.86384e17			1.03889			0.519445	−	0.854504i	$-0.326139\pi$
$751$	1.86384e17			1.03889			0.519445	+	0.854504i	$0.326139\pi$
$752$		−	1.28410e16i		−	0.0710052i
$753$	−1.71785e16	−	1.03955e14i	−0.0942359	−	0.000570266i
$754$	5.70994e16			0.310745
$755$		−	2.83336e16i		−	0.152975i
$756$	−1.96881e15	+	1.08437e17i	−0.0105456	+	0.580828i
$757$	9.23272e16			0.490630			0.245315	−	0.969443i	$-0.421109\pi$
$757$	9.23272e16			0.490630			0.245315	+	0.969443i	$0.421109\pi$
$758$			5.38679e16i			0.283997i
$759$	−9.02576e14	+	1.49150e17i	−0.00472099	+	0.780140i
$760$	1.00183e16			0.0519889
$761$		−	7.00101e16i		−	0.360456i	−0.983625	−	0.180228i	$-0.942316\pi$
$761$		−	7.00101e16i		−	0.360456i	0.983625	−	0.180228i	$-0.0576836\pi$
$762$	1.46597e17	+	8.87127e14i	0.748851	+	0.00453164i
$763$	−1.52741e17			−0.774121
$764$		−	1.41391e17i		−	0.710988i
$765$	−3.72538e16	−	4.50896e14i	−0.185867	−	0.00224961i
$766$	1.45282e17			0.719182
$767$		−	5.30776e17i		−	2.60699i
$768$	7.76068e13	−	1.28245e16i	0.000378210	−	0.0624989i
$769$	1.77848e17			0.859987			0.429994	−	0.902832i	$-0.358516\pi$
$769$	1.77848e17			0.859987			0.429994	+	0.902832i	$0.358516\pi$
$770$			1.95279e16i			0.0936937i
$771$	3.37147e17	+	2.04023e15i	1.60506	+	0.00971299i
$772$	−1.44947e17			−0.684708
$773$			7.55535e16i			0.354142i	0.984198	+	0.177071i	$0.0566622\pi$
$773$			7.55535e16i			0.354142i	−0.984198	+	0.177071i	$0.943338\pi$
$774$	−1.77251e15	+	1.46448e17i	−0.00824409	+	0.681140i
$775$	5.76047e16			0.265857
$776$		−	1.23785e16i		−	0.0566891i
$777$	6.67709e13	−	1.10338e16i	0.000303432	−	0.0501419i
$778$	2.52108e16			0.113687
$779$		−	1.93978e17i		−	0.868018i
$780$	−1.86327e16	−	1.12755e14i	−0.0827388	−	0.000500691i
$781$	−1.81560e17			−0.800045
$782$			2.05619e17i			0.899130i
$783$	−7.02299e16	−	1.27511e15i	−0.304756	−	0.00553320i
$784$	2.03128e16			0.0874729
$785$		−	2.25423e16i		−	0.0963344i
$786$	−1.10621e14	+	1.82800e16i	−0.000469139	+	0.0775249i
$787$	−3.57950e17			−1.50652			−0.753258	−	0.657725i	$-0.771519\pi$
$787$	−3.57950e17			−1.50652			−0.753258	+	0.657725i	$0.771519\pi$
$788$			2.18461e17i			0.912466i
$789$	1.32834e17	+	8.03840e14i	0.550614	+	0.00333202i
$790$	1.27877e16			0.0526053
$791$			1.68808e17i			0.689182i
$792$	−8.66960e16	−	1.04931e15i	−0.351275	−	0.00425162i
$793$	2.57343e17			1.03484
$794$		−	2.49822e17i		−	0.997031i
$795$	−2.18402e14	+	3.60908e16i	−0.000865075	+	0.142953i
$796$	−1.76411e17			−0.693502
$797$			1.64375e17i			0.641336i	0.947192	+	0.320668i	$0.103907\pi$
$797$			1.64375e17i			0.641336i	−0.947192	+	0.320668i	$0.896093\pi$
$798$	−2.71799e17	−	1.64478e15i	−1.05252	−	0.00636929i
$799$	−1.19678e17			−0.459973
$800$		−	4.57305e16i		−	0.174448i
$801$	3.47630e14	−	2.87217e16i	0.00131620	−	0.108746i
$802$	1.51127e17			0.567931
$803$			2.33501e17i			0.870956i
$804$	5.32016e14	−	8.79152e16i	0.00196965	−	0.325483i
$805$	−2.84926e16			−0.104702
$806$		−	7.53005e16i		−	0.274655i
$807$	−2.39696e17	−	1.45051e15i	−0.867799	−	0.00525145i
$808$	1.66316e17			0.597676
$809$		−	3.05986e17i		−	1.09147i	−0.837959	−	0.545733i	$-0.816251\pi$
$809$		−	3.05986e17i		−	1.09147i	0.837959	−	0.545733i	$-0.183749\pi$
$810$	2.29150e16	+	5.54778e14i	0.0811352	+	0.00196431i
$811$	−3.60456e17			−1.26685			−0.633427	−	0.773802i	$-0.718352\pi$
$811$	−3.60456e17			−1.26685			−0.633427	+	0.773802i	$0.718352\pi$
$812$			5.07550e16i			0.177069i
$813$	9.47182e14	−	1.56521e17i	0.00328012	−	0.542038i
$814$	8.82095e15			0.0303228
$815$			9.55263e15i			0.0325970i
$816$	−1.19524e17	−	7.23295e14i	−0.404868	−	0.00245005i
$817$	−3.67045e17			−1.23420
$818$		−	9.64342e16i		−	0.321893i
$819$	5.05495e17	+	6.11819e15i	1.67499	+	0.0202731i
$820$	1.18203e16			0.0388818
$821$			4.84675e17i			1.58268i	0.611379	+	0.791338i	$0.290615\pi$
$821$			4.84675e17i			1.58268i	−0.611379	+	0.791338i	$0.709385\pi$
$822$	1.41666e15	−	2.34103e17i	0.00459236	−	0.758884i
$823$	3.72014e17			1.19718			0.598591	−	0.801055i	$-0.295728\pi$
$823$	3.72014e17			1.19718			0.598591	+	0.801055i	$0.295728\pi$
$824$			1.07633e17i			0.343860i
$825$	−3.09158e17	−	1.87086e15i	−0.980522	−	0.00593360i
$826$	4.71800e17			1.48552
$827$			2.67343e17i			0.835671i	0.908523	+	0.417836i	$0.137211\pi$
$827$			2.67343e17i			0.835671i	−0.908523	+	0.417836i	$0.862789\pi$
$828$	1.53103e15	−	1.26496e17i	0.00475117	−	0.392549i
$829$	3.62105e17			1.11560			0.557799	−	0.829976i	$-0.311646\pi$
$829$	3.62105e17			1.11560			0.557799	+	0.829976i	$0.311646\pi$
$830$			2.45282e16i			0.0750236i
$831$	1.72518e15	−	2.85084e17i	0.00523875	−	0.865699i
$832$	−5.97786e16			−0.180221
$833$		−	1.89315e17i		−	0.566651i
$834$	−9.66487e16	−	5.84866e14i	−0.287210	−	0.00173804i
$835$	2.52664e16			0.0745462
$836$		−	2.17288e17i		−	0.636500i
$837$	−1.68156e15	+	9.26165e16i	−0.00489058	+	0.269362i
$838$	−1.13217e17			−0.326924
$839$			5.20240e17i			1.49153i	0.666209	+	0.745765i	$0.267916\pi$
$839$			5.20240e17i			1.49153i	−0.666209	+	0.745765i	$0.732084\pi$
$840$	1.00227e14	−	1.65624e16i	0.000285304	−	0.0471463i
$841$	3.20943e17			0.907093
$842$		−	1.16849e17i		−	0.327909i
$843$	3.62679e17	+	2.19474e15i	1.01055	+	0.00611530i
$844$	1.62409e17			0.449320
$845$			4.50704e16i			0.123809i
$846$	7.36251e16	+	8.91112e14i	0.200818	+	0.00243058i
$847$	−5.44821e15			−0.0147555
$848$			1.15788e17i			0.311379i
$849$	1.89521e15	−	3.13181e17i	0.00506069	−	0.836276i
$850$	−4.26207e17			−1.13008
$851$			1.28704e16i			0.0338856i
$852$	1.53989e17	+	9.31859e14i	0.402580	+	0.00243620i
$853$	−1.90970e17			−0.495761			−0.247880	−	0.968791i	$-0.579734\pi$
$853$	−1.90970e17			−0.495761			−0.247880	+	0.968791i	$0.579734\pi$
$854$			2.28749e17i			0.589674i
$855$	−6.95228e14	+	5.74408e16i	−0.00177963	+	0.147036i
$856$	8.33925e15			0.0211975
$857$		−	4.42309e17i		−	1.11645i	−0.829688	−	0.558227i	$-0.811482\pi$
$857$		−	4.42309e17i		−	1.11645i	0.829688	−	0.558227i	$-0.188518\pi$
$858$	−2.44558e15	+	4.04130e17i	−0.00612996	+	1.01297i
$859$	−1.02172e16			−0.0254315			−0.0127157	−	0.999919i	$-0.504048\pi$
$859$	−1.02172e16			−0.0254315			−0.0127157	+	0.999919i	$0.504048\pi$
$860$		−	2.23664e16i		−	0.0552847i
$861$	−3.20690e17	−	1.94064e15i	−0.787165	−	0.00476350i
$862$	−4.03896e17			−0.984524
$863$		−	2.39726e17i		−	0.580297i	−0.956982	−	0.290148i	$-0.906295\pi$
$863$		−	2.39726e17i		−	0.580297i	0.956982	−	0.290148i	$-0.0937046\pi$
$864$	7.35251e16	+	1.33494e15i	0.176748	+	0.00320906i
$865$	−6.06374e16			−0.144759
$866$			8.73029e16i			0.206977i
$867$	−4.17090e15	+	6.89238e17i	−0.00982008	+	1.62276i
$868$	6.69337e16			0.156504
$869$		−	2.77355e17i		−	0.644046i
$870$	1.07267e16	+	6.49124e13i	0.0247373	+	0.000149697i
$871$	−4.09798e17			−0.938559
$872$			1.03565e17i			0.235567i
$873$	7.09738e16	+	8.59022e14i	0.160329	+	0.00194052i
$874$	3.17040e17			0.711287
$875$		−	1.18907e17i		−	0.264948i
$876$	1.19845e15	−	1.98042e17i	0.00265213	−	0.438262i
$877$	−5.25806e17			−1.15565			−0.577827	−	0.816159i	$-0.696099\pi$
$877$	−5.25806e17			−1.15565			−0.577827	+	0.816159i	$0.696099\pi$
$878$		−	3.29765e17i		−	0.719843i
$879$	−1.16260e17	−	7.03546e14i	−0.252057	−	0.00152531i
$880$	1.32407e16			0.0285112
$881$		−	6.44606e17i		−	1.37860i	−0.724475	−	0.689301i	$-0.757918\pi$
$881$		−	6.44606e17i		−	1.37860i	0.724475	−	0.689301i	$-0.242082\pi$
$882$	−1.40963e15	+	1.16466e17i	−0.00299429	+	0.247393i
$883$	−2.82719e17			−0.596473			−0.298236	−	0.954492i	$-0.596398\pi$
$883$	−2.82719e17			−0.596473			−0.298236	+	0.954492i	$0.596398\pi$
$884$			5.57136e17i			1.16747i
$885$	6.03402e14	−	9.97118e16i	0.00125588	−	0.207533i
$886$	−1.42830e16			−0.0295268
$887$		−	4.06806e16i		−	0.0835306i	−0.999127	−	0.0417653i	$-0.986702\pi$
$887$		−	4.06806e16i		−	0.0835306i	0.999127	−	0.0417653i	$-0.0132982\pi$
$888$	−7.48142e15	−	4.52736e13i	−0.0152583	−	9.23351e-5i
$889$	6.07405e17			1.23046
$890$			4.38656e15i			0.00882640i
$891$	1.20327e16	−	4.97008e17i	0.0240490	−	0.993339i
$892$	−9.70511e16			−0.192669
$893$			1.84528e17i			0.363877i
$894$	−2.54731e15	+	4.20940e17i	−0.00498949	+	0.824509i
$895$	2.65923e16			0.0517390
$896$		−	5.31364e16i		−	0.102694i
$897$	−5.89655e17	−	3.56828e15i	−1.13199	−	0.00685021i
$898$	−5.32197e17			−1.01488
$899$			4.33500e16i			0.0821165i
$900$	2.62201e17	+	3.17351e15i	0.493377	+	0.00597153i
$901$	1.07915e18			2.01712
$902$		−	2.56374e17i		−	0.476030i
$903$	−3.67208e15	+	6.06808e17i	−0.00677306	+	1.11924i
$904$	1.14459e17			0.209720
$905$			4.01400e16i			0.0730610i
$906$	5.21212e17	+	3.15410e15i	0.942422	+	0.00570304i
$907$	9.01955e17			1.62010			0.810049	−	0.586362i	$-0.199440\pi$
$907$	9.01955e17			1.62010			0.810049	+	0.586362i	$0.199440\pi$
$908$		−	4.02565e17i		−	0.718325i
$909$	−1.15417e16	+	9.53592e17i	−0.0204591	+	1.69036i
$910$	−7.72022e16			−0.135951
$911$			3.67660e17i			0.643185i	0.946878	+	0.321592i	$0.104218\pi$
$911$			3.67660e17i			0.643185i	−0.946878	+	0.321592i	$0.895782\pi$
$912$	−1.11523e15	+	1.84291e17i	−0.00193819	+	0.320285i
$913$	5.31999e17			0.918514
$914$		−	9.49330e16i		−	0.162832i
$915$	4.83446e16	+	2.92556e14i	0.0823799	+	0.000498519i
$916$	−3.01269e17			−0.510014
$917$			7.57407e16i			0.127384i
$918$	1.24416e16	−	6.85254e17i	0.0207883	−	1.14497i
$919$	−4.07315e17			−0.676141			−0.338070	−	0.941121i	$-0.609774\pi$
$919$	−4.07315e17			−0.676141			−0.338070	+	0.941121i	$0.609774\pi$
$920$			1.93192e16i			0.0318612i
$921$	3.64536e15	−	6.02394e17i	0.00597287	−	0.987012i
$922$	1.48730e17			0.242110
$923$		−	7.17787e17i		−	1.16087i
$924$	−3.59226e17	−	2.17384e15i	−0.577213	−	0.00349298i
$925$	−2.66778e16			−0.0425892
$926$			2.12516e17i			0.337074i
$927$	−6.17126e17	−	7.46930e15i	−0.972513	−	0.0117707i
$928$	3.44141e16			0.0538826
$929$			3.42950e17i			0.533502i	0.963765	+	0.266751i	$0.0859501\pi$
$929$			3.42950e17i			0.533502i	−0.963765	+	0.266751i	$0.914050\pi$
$930$	8.56040e13	−	1.41460e16i	0.000132311	−	0.0218643i
$931$	−2.91901e17			−0.448268
$932$		−	2.04246e17i		−	0.311644i
$933$	5.34575e17	+	3.23496e15i	0.810437	+	0.00490433i
$934$	5.49669e17			0.827980
$935$		−	1.23403e17i		−	0.184696i
$936$	4.14840e15	−	3.42747e17i	0.00616915	−	0.509705i
$937$	−1.16771e18			−1.72543			−0.862715	−	0.505691i	$-0.831238\pi$
$937$	−1.16771e18			−1.72543			−0.862715	+	0.505691i	$0.831238\pi$
$938$		−	3.64265e17i		−	0.534811i
$939$	4.41063e15	−	7.28853e17i	0.00643439	−	1.06328i
$940$	−1.12445e16			−0.0162994
$941$			8.77973e17i			1.26457i	0.774735	+	0.632286i	$0.217883\pi$
$941$			8.77973e17i			1.26457i	−0.774735	+	0.632286i	$0.782117\pi$
$942$	4.14679e17	+	2.50942e15i	0.593481	+	0.00359143i
$943$	3.74068e17			0.531961
$944$		−	3.19901e17i		−	0.452047i
$945$	9.49555e16	+	1.72403e15i	0.133330	+	0.00242077i
$946$	−4.85109e17			−0.676850
$947$			1.14869e18i			1.59259i	0.604910	+	0.796294i	$0.293209\pi$
$947$			1.14869e18i			1.59259i	−0.604910	+	0.796294i	$0.706791\pi$
$948$	−1.42353e15	+	2.35236e17i	−0.00196117	+	0.324082i
$949$	−9.23133e17			−1.26377
$950$			6.57161e17i			0.893984i
$951$	−3.46333e17	−	2.09582e15i	−0.468177	−	0.00283316i
$952$	−4.95231e17			−0.665252
$953$			9.51372e17i			1.26997i	0.772525	+	0.634984i	$0.218993\pi$
$953$			9.51372e17i			1.26997i	−0.772525	+	0.634984i	$0.781007\pi$
$954$	−6.63885e17	−	8.03525e15i	−0.880649	−	0.0106588i
$955$	−1.23812e17			−0.163209
$956$			3.84011e17i			0.503033i
$957$	1.40790e15	−	2.32655e17i	0.00183274	−	0.302859i
$958$	7.07693e17			0.915486
$959$		−	9.69972e17i		−	1.24695i
$960$	−1.12300e16	−	6.79582e13i	−0.0143468	−	8.68189e-5i
$961$	−7.30495e17			−0.927420
$962$			3.48731e16i			0.0439987i
$963$	−5.78711e14	+	4.78140e16i	−0.000725612	+	0.0599512i
$964$	−1.36678e17			−0.170309
$965$			1.26926e17i			0.157176i
$966$	3.17180e15	−	5.24137e17i	0.00390340	−	0.645033i
$967$	1.35642e18			1.65896			0.829481	−	0.558535i	$-0.188636\pi$
$967$	1.35642e18			1.65896			0.829481	+	0.558535i	$0.188636\pi$
$968$			3.69412e15i			0.00449013i
$969$	1.71759e18	+	1.03940e16i	2.07481	+	0.0125556i
$970$	−1.08395e16			−0.0130131
$971$		−	6.96300e17i		−	0.830770i	−0.909646	−	0.415385i	$-0.863647\pi$
$971$		−	6.96300e17i		−	0.830770i	0.909646	−	0.415385i	$-0.136353\pi$
$972$	−1.27564e16	+	4.21472e17i	−0.0151262	+	0.499771i
$973$	−4.00451e17			−0.471924
$974$			8.33988e17i			0.976801i
$975$	7.39634e15	−	1.22224e18i	0.00860972	−	1.42275i
$976$	1.55102e17			0.179439
$977$		−	1.14608e18i		−	1.31779i	−0.752235	−	0.658895i	$-0.771024\pi$
$977$		−	1.14608e18i		−	1.31779i	0.752235	−	0.658895i	$-0.228976\pi$
$978$	−1.75726e17	−	1.06340e15i	−0.200818	−	0.00121524i
$979$	9.51410e16			0.108062
$980$		−	1.77874e16i		−	0.0200796i
$981$	−5.93802e17	−	7.18701e15i	−0.666235	−	0.00806369i
$982$	−1.57392e17			−0.175515
$983$			4.84387e17i			0.536873i	0.963297	+	0.268436i	$0.0865069\pi$
$983$			4.84387e17i			0.536873i	−0.963297	+	0.268436i	$0.913493\pi$
$984$	−1.31584e15	+	2.17441e17i	−0.00144955	+	0.239536i
$985$	1.91300e17			0.209458
$986$		−	3.20739e17i		−	0.349052i
$987$	3.05067e17	+	1.84610e15i	0.329983	+	0.00199688i
$988$	8.59036e17			0.923570
$989$		−	7.07810e17i		−	0.756378i
$990$	−9.18855e14	+	7.59172e16i	−0.000975968	+	0.0806361i
$991$	1.40621e18			1.48460			0.742300	−	0.670068i	$-0.233735\pi$
$991$	1.40621e18			1.48460			0.742300	+	0.670068i	$0.233735\pi$
$992$		−	4.53839e16i		−	0.0476247i
$993$	−5.18603e15	+	8.56987e17i	−0.00540928	+	0.893879i
$994$	6.38032e17			0.661492
$995$			1.54478e17i			0.159195i
$996$	−4.51211e17	−	2.73049e15i	−0.462193	−	0.00279694i
$997$	1.09471e18			1.11462			0.557310	−	0.830304i	$-0.311833\pi$
$997$	1.09471e18			1.11462			0.557310	+	0.830304i	$0.311833\pi$
$998$			4.62887e17i			0.468481i
$999$	7.78762e14	−	4.28924e16i	0.000783451	−	0.0431507i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.13.b.a.5.1	✓	4
3.2	odd	2	inner	6.13.b.a.5.3	yes	4
4.3	odd	2		48.13.e.c.17.4		4
5.2	odd	4		150.13.b.a.149.5		8
5.3	odd	4		150.13.b.a.149.4		8
5.4	even	2		150.13.d.a.101.4		4
8.3	odd	2		192.13.e.h.65.1		4
8.5	even	2		192.13.e.e.65.4		4
9.2	odd	6		162.13.d.d.53.3		8
9.4	even	3		162.13.d.d.107.3		8
9.5	odd	6		162.13.d.d.107.2		8
9.7	even	3		162.13.d.d.53.2		8
12.11	even	2		48.13.e.c.17.3		4
15.2	even	4		150.13.b.a.149.3		8
15.8	even	4		150.13.b.a.149.6		8
15.14	odd	2		150.13.d.a.101.2		4
24.5	odd	2		192.13.e.e.65.3		4
24.11	even	2		192.13.e.h.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.13.b.a.5.1	✓	4	1.1	even	1	trivial
6.13.b.a.5.3	yes	4	3.2	odd	2	inner
48.13.e.c.17.3		4	12.11	even	2
48.13.e.c.17.4		4	4.3	odd	2
150.13.b.a.149.3		8	15.2	even	4
150.13.b.a.149.4		8	5.3	odd	4
150.13.b.a.149.5		8	5.2	odd	4
150.13.b.a.149.6		8	15.8	even	4
150.13.d.a.101.2		4	15.14	odd	2
150.13.d.a.101.4		4	5.4	even	2
162.13.d.d.53.2		8	9.7	even	3
162.13.d.d.53.3		8	9.2	odd	6
162.13.d.d.107.2		8	9.5	odd	6
162.13.d.d.107.3		8	9.4	even	3
192.13.e.e.65.3		4	24.5	odd	2
192.13.e.e.65.4		4	8.5	even	2
192.13.e.h.65.1		4	8.3	odd	2
192.13.e.h.65.2		4	24.11	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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 13 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-45.2548i q^{2} +(4.41144 - 728.987i) q^{3} -2048.00 q^{4} +1793.38i q^{5} +(-32990.2 - 199.639i) q^{6} -136690. q^{7} +92681.9i q^{8} +(-531402. - 6431.76i) q^{9} +O(q^{10})\)	\(q-45.2548i q^{2} +(4.41144 - 728.987i) q^{3} -2048.00 q^{4} +1793.38i q^{5} +(-32990.2 - 199.639i) q^{6} -136690. q^{7} +92681.9i q^{8} +(-531402. - 6431.76i) q^{9} +81159.0 q^{10} -1.76028e6i q^{11} +(-9034.62 + 1.49296e6i) q^{12} +6.95914e6 q^{13} +6.18590e6i q^{14} +(1.30735e6 + 7911.37i) q^{15} +4.19430e6 q^{16} -3.90909e7i q^{17} +(-291068. + 2.40485e7i) q^{18} -6.02734e7 q^{19} -3.67284e6i q^{20} +(-603001. + 9.96454e7i) q^{21} -7.96610e7 q^{22} -1.16231e8i q^{23} +(6.75639e7 + 408860. i) q^{24} +2.40924e8 q^{25} -3.14935e8i q^{26} +(-7.03291e6 + 3.87357e8i) q^{27} +2.79942e8 q^{28} +1.81306e8i q^{29} +(358028. - 5.91638e7i) q^{30} +2.39099e8 q^{31} -1.89813e8i q^{32} +(-1.28322e9 - 7.76535e6i) q^{33} -1.76905e9 q^{34} -2.45137e8i q^{35} +(1.08831e9 + 1.31722e7i) q^{36} -1.10731e8 q^{37} +2.72766e9i q^{38} +(3.06998e7 - 5.07312e9i) q^{39} -1.66214e8 q^{40} +3.21831e9i q^{41} +(4.50944e9 + 2.72887e7i) q^{42} +6.08967e9 q^{43} +3.60504e9i q^{44} +(1.15346e7 - 9.53004e8i) q^{45} -5.26002e9 q^{46} -3.06152e9i q^{47} +(1.85029e7 - 3.05759e9i) q^{48} +4.84295e9 q^{49} -1.09030e10i q^{50} +(-2.84967e10 - 1.72447e8i) q^{51} -1.42523e10 q^{52} +2.76061e10i q^{53} +(1.75298e10 + 3.18273e8i) q^{54} +3.15684e9 q^{55} -1.26687e10i q^{56} +(-2.65892e8 + 4.39385e10i) q^{57} +8.20496e9 q^{58} -7.62703e10i q^{59} +(-2.67745e9 - 1.62025e7i) q^{60} +3.69791e10 q^{61} -1.08204e10i q^{62} +(7.26375e10 + 8.79159e8i) q^{63} -8.58993e9 q^{64} +1.24804e10i q^{65} +(-3.51419e8 + 5.80718e10i) q^{66} -5.88864e10 q^{67} +8.00581e10i q^{68} +(-8.47310e10 - 5.12747e8i) q^{69} -1.10936e10 q^{70} -1.03143e11i q^{71} +(5.96108e8 - 4.92514e10i) q^{72} -1.32650e11 q^{73} +5.01112e9i q^{74} +(1.06282e9 - 1.75631e11i) q^{75} +1.23440e11 q^{76} +2.40613e11i q^{77} +(-2.29583e11 - 1.38932e9i) q^{78} +1.57563e11 q^{79} +7.52197e9i q^{80} +(2.82347e11 + 6.83570e9i) q^{81} +1.45644e11 q^{82} +3.02225e11i q^{83} +(1.23495e9 - 2.04074e11i) q^{84} +7.01046e10 q^{85} -2.75587e11i q^{86} +(1.32169e11 + 7.99819e8i) q^{87} +1.63146e11 q^{88} +5.40489e10i q^{89} +(-4.31280e10 - 5.21995e8i) q^{90} -9.51247e11 q^{91} +2.38042e11i q^{92} +(1.05477e9 - 1.74300e11i) q^{93} -1.38549e11 q^{94} -1.08093e11i q^{95} +(-1.38371e11 - 8.37346e8i) q^{96} -1.33559e11 q^{97} -2.19167e11i q^{98} +(-1.13217e10 + 9.35414e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 780 q^{3} - 8192 q^{4} - 9984 q^{6} + 153080 q^{7} - 1530972 q^{9}+O(q^{10}) \) 4 * q + 780 * q^3 - 8192 * q^4 - 9984 * q^6 + 153080 * q^7 - 1530972 * q^9	\( 4 q + 780 q^{3} - 8192 q^{4} - 9984 q^{6} + 153080 q^{7} - 1530972 q^{9} + 1641984 q^{10} - 1597440 q^{12} + 7253000 q^{13} - 17613792 q^{15} + 16777216 q^{16} + 42600960 q^{18} - 120268072 q^{19} + 163232328 q^{21} - 159244800 q^{22} + 20447232 q^{24} + 435605764 q^{25} - 784941300 q^{27} - 313507840 q^{28} + 571258368 q^{30} + 2731727672 q^{31} - 2567489760 q^{33} - 3097810944 q^{34} + 3135430656 q^{36} - 15280120 q^{37} - 2508657000 q^{39} - 3362783232 q^{40} + 20958988800 q^{42} + 1629119960 q^{43} - 15576677568 q^{45} - 29905849344 q^{46} + 3271557120 q^{48} + 72937649100 q^{49} - 63012636288 q^{51} - 14854144000 q^{52} + 38602586880 q^{54} + 6285799872 q^{55} - 424311000 q^{57} - 62351992320 q^{58} + 36073046016 q^{60} + 45477065096 q^{61} + 45447449400 q^{63} - 34359738368 q^{64} - 673085952 q^{66} - 213433609960 q^{67} + 95560926912 q^{69} + 293322353664 q^{70} - 87246766080 q^{72} - 254383625080 q^{73} - 15705158772 q^{75} + 246309011456 q^{76} - 645782208000 q^{78} + 308580159032 q^{79} + 219015659268 q^{81} + 234603709440 q^{82} - 334299807744 q^{84} - 18844054272 q^{85} + 1341091294560 q^{87} + 326133350400 q^{88} - 432622121472 q^{90} - 3323734346000 q^{91} + 871044956040 q^{93} + 775668172800 q^{94} - 41875931136 q^{96} + 1276228475720 q^{97} - 23456841408 q^{99}+O(q^{100}) \) 4 * q + 780 * q^3 - 8192 * q^4 - 9984 * q^6 + 153080 * q^7 - 1530972 * q^9 + 1641984 * q^10 - 1597440 * q^12 + 7253000 * q^13 - 17613792 * q^15 + 16777216 * q^16 + 42600960 * q^18 - 120268072 * q^19 + 163232328 * q^21 - 159244800 * q^22 + 20447232 * q^24 + 435605764 * q^25 - 784941300 * q^27 - 313507840 * q^28 + 571258368 * q^30 + 2731727672 * q^31 - 2567489760 * q^33 - 3097810944 * q^34 + 3135430656 * q^36 - 15280120 * q^37 - 2508657000 * q^39 - 3362783232 * q^40 + 20958988800 * q^42 + 1629119960 * q^43 - 15576677568 * q^45 - 29905849344 * q^46 + 3271557120 * q^48 + 72937649100 * q^49 - 63012636288 * q^51 - 14854144000 * q^52 + 38602586880 * q^54 + 6285799872 * q^55 - 424311000 * q^57 - 62351992320 * q^58 + 36073046016 * q^60 + 45477065096 * q^61 + 45447449400 * q^63 - 34359738368 * q^64 - 673085952 * q^66 - 213433609960 * q^67 + 95560926912 * q^69 + 293322353664 * q^70 - 87246766080 * q^72 - 254383625080 * q^73 - 15705158772 * q^75 + 246309011456 * q^76 - 645782208000 * q^78 + 308580159032 * q^79 + 219015659268 * q^81 + 234603709440 * q^82 - 334299807744 * q^84 - 18844054272 * q^85 + 1341091294560 * q^87 + 326133350400 * q^88 - 432622121472 * q^90 - 3323734346000 * q^91 + 871044956040 * q^93 + 775668172800 * q^94 - 41875931136 * q^96 + 1276228475720 * q^97 - 23456841408 * q^99

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