LMFDB - Embedded newform 12.14.b.a.11.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,14,Mod(11,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("12.11");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	12.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.8677114742$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.16
Character	$\chi$	$=$	12.11
Dual form			12.14.b.a.11.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(26.1905 + 86.6375i) q^{2} +(-919.540 + 865.314i) q^{3} +(-6820.12 + 4538.16i) q^{4} +34796.6i q^{5} +(-99051.9 - 57003.7i) q^{6} +298175. i q^{7} +(-571797. - 472022. i) q^{8} +(96786.4 - 1.59138e6i) q^{9} +O(q^{10})$	\(q+(26.1905 + 86.6375i) q^{2} +(-919.540 + 865.314i) q^{3} +(-6820.12 + 4538.16i) q^{4} +34796.6i q^{5} +(-99051.9 - 57003.7i) q^{6} +298175. i q^{7} +(-571797. - 472022. i) q^{8} +(96786.4 - 1.59138e6i) q^{9} +(-3.01469e6 + 911338. i) q^{10} -2.90289e6 q^{11} +(2.34444e6 - 1.00746e7i) q^{12} +2.73529e7 q^{13} +(-2.58331e7 + 7.80934e6i) q^{14} +(-3.01099e7 - 3.19968e7i) q^{15} +(2.59191e7 - 6.19015e7i) q^{16} -2.14781e7i q^{17} +(1.40408e8 - 3.32937e7i) q^{18} -2.70019e7i q^{19} +(-1.57912e8 - 2.37317e8i) q^{20} +(-2.58015e8 - 2.74184e8i) q^{21} +(-7.60280e7 - 2.51499e8i) q^{22} -1.21010e9 q^{23} +(9.34237e8 - 6.07408e7i) q^{24} +9.90321e6 q^{25} +(7.16386e8 + 2.36979e9i) q^{26} +(1.28805e9 + 1.54709e9i) q^{27} +(-1.35316e9 - 2.03359e9i) q^{28} +1.45524e9i q^{29} +(1.98353e9 - 3.44666e9i) q^{30} +8.52012e9i q^{31} +(6.04183e9 + 6.24340e8i) q^{32} +(2.66932e9 - 2.51191e9i) q^{33} +(1.86081e9 - 5.62521e8i) q^{34} -1.03755e10 q^{35} +(6.56185e9 + 1.12926e10i) q^{36} -2.62979e10 q^{37} +(2.33938e9 - 7.07193e8i) q^{38} +(-2.51521e10 + 2.36689e10i) q^{39} +(1.64247e10 - 1.98966e10i) q^{40} -2.12707e10i q^{41} +(1.69971e10 - 2.95348e10i) q^{42} -2.09825e10i q^{43} +(1.97980e10 - 1.31738e10i) q^{44} +(5.53746e10 + 3.36783e9i) q^{45} +(-3.16931e10 - 1.04840e11i) q^{46} -2.83548e10 q^{47} +(2.97305e10 + 7.93491e10i) q^{48} +7.98078e9 q^{49} +(2.59370e8 + 8.57989e8i) q^{50} +(1.85853e10 + 1.97500e10i) q^{51} +(-1.86550e11 + 1.24132e11i) q^{52} +1.84057e10i q^{53} +(-1.00302e11 + 1.52112e11i) q^{54} -1.01011e11i q^{55} +(1.40745e11 - 1.70495e11i) q^{56} +(2.33651e10 + 2.48294e10i) q^{57} +(-1.26079e11 + 3.81135e10i) q^{58} +4.65889e11 q^{59} +(3.50560e11 + 8.15786e10i) q^{60} -4.08856e11 q^{61} +(-7.38162e11 + 2.23146e11i) q^{62} +(4.74510e11 + 2.88593e10i) q^{63} +(1.04147e11 + 5.39801e11i) q^{64} +9.51787e11i q^{65} +(2.87537e11 + 1.65475e11i) q^{66} -1.14344e12i q^{67} +(9.74709e10 + 1.46483e11i) q^{68} +(1.11274e12 - 1.04712e12i) q^{69} +(-2.71738e11 - 8.98904e11i) q^{70} -9.35998e11 q^{71} +(-8.06509e11 + 8.64262e11i) q^{72} +5.16147e11 q^{73} +(-6.88753e11 - 2.27838e12i) q^{74} +(-9.10640e9 + 8.56938e9i) q^{75} +(1.22539e11 + 1.84156e11i) q^{76} -8.65568e11i q^{77} +(-2.70936e12 - 1.55922e12i) q^{78} +2.03157e12i q^{79} +(2.15396e12 + 9.01897e11i) q^{80} +(-2.52313e12 - 3.08048e11i) q^{81} +(1.84284e12 - 5.57091e11i) q^{82} -1.79895e12 q^{83} +(3.00398e12 + 6.99054e11i) q^{84} +7.47363e11 q^{85} +(1.81787e12 - 5.49541e11i) q^{86} +(-1.25924e12 - 1.33815e12i) q^{87} +(1.65986e12 + 1.37023e12i) q^{88} +6.29425e12i q^{89} +(1.15851e12 + 4.88572e12i) q^{90} +8.15595e12i q^{91} +(8.25302e12 - 5.49162e12i) q^{92} +(-7.37258e12 - 7.83459e12i) q^{93} +(-7.42627e11 - 2.45659e12i) q^{94} +9.39573e11 q^{95} +(-6.09596e12 + 4.65397e12i) q^{96} +3.83919e12 q^{97} +(2.09020e11 + 6.91435e11i) q^{98} +(-2.80960e11 + 4.61961e12i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8376 q^{4} - 135720 q^{6} - 327240 q^{9}+O(q^{10}) $ 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9	$ 24 q - 8376 q^{4} - 135720 q^{6} - 327240 q^{9} + 4403568 q^{10} - 139896 q^{12} - 17520048 q^{13} + 41046816 q^{16} - 102153744 q^{18} + 340864272 q^{21} + 401914896 q^{22} + 14766624 q^{24} - 3043252488 q^{25} + 3306349488 q^{28} + 3523891248 q^{30} - 10577805696 q^{33} + 5461322688 q^{34} + 16126437096 q^{36} - 29352930672 q^{37} - 5243368896 q^{40} + 35399300688 q^{42} + 36221734656 q^{45} + 1675946784 q^{46} + 27878547744 q^{48} - 165718477944 q^{49} - 6459860112 q^{52} - 10955701656 q^{54} + 590611321584 q^{57} - 440462601456 q^{58} - 208761511104 q^{60} + 555426186192 q^{61} - 741528997248 q^{64} + 263546293968 q^{66} - 122266973952 q^{69} - 885399371232 q^{70} + 625428177984 q^{72} + 365028975600 q^{73} + 1427271642000 q^{76} + 1481181276240 q^{78} - 2327652239400 q^{81} + 874644720480 q^{82} - 6757787638224 q^{84} - 3308476422144 q^{85} + 11607512359104 q^{88} + 4426488729648 q^{90} - 3971016902448 q^{93} - 3078833939904 q^{94} - 6470779487616 q^{96} - 4159752429648 q^{97}+O(q^{100}) $ 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9 + 4403568 * q^10 - 139896 * q^12 - 17520048 * q^13 + 41046816 * q^16 - 102153744 * q^18 + 340864272 * q^21 + 401914896 * q^22 + 14766624 * q^24 - 3043252488 * q^25 + 3306349488 * q^28 + 3523891248 * q^30 - 10577805696 * q^33 + 5461322688 * q^34 + 16126437096 * q^36 - 29352930672 * q^37 - 5243368896 * q^40 + 35399300688 * q^42 + 36221734656 * q^45 + 1675946784 * q^46 + 27878547744 * q^48 - 165718477944 * q^49 - 6459860112 * q^52 - 10955701656 * q^54 + 590611321584 * q^57 - 440462601456 * q^58 - 208761511104 * q^60 + 555426186192 * q^61 - 741528997248 * q^64 + 263546293968 * q^66 - 122266973952 * q^69 - 885399371232 * q^70 + 625428177984 * q^72 + 365028975600 * q^73 + 1427271642000 * q^76 + 1481181276240 * q^78 - 2327652239400 * q^81 + 874644720480 * q^82 - 6757787638224 * q^84 - 3308476422144 * q^85 + 11607512359104 * q^88 + 4426488729648 * q^90 - 3971016902448 * q^93 - 3078833939904 * q^94 - 6470779487616 * q^96 - 4159752429648 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	26.1905	+	86.6375i	0.289367	+	0.957218i
$2$	26.1905	+	86.6375i	0.289367	+	0.957218i
$3$	−919.540	+	865.314i	−0.728254	+	0.685308i
$3$	−919.540	+	865.314i	−0.728254	+	0.685308i
$4$	−6820.12	+	4538.16i	−0.832534	+	0.553974i
$5$			34796.6i			0.995935i	0.867196	+	0.497968i	$0.165920\pi$
$5$			34796.6i			0.995935i	−0.867196	+	0.497968i	$0.834080\pi$
$6$	−99051.9	−	57003.7i	−0.866721	−	0.498793i
$7$			298175.i			0.957930i	0.877834	+	0.478965i	$0.158988\pi$
$7$			298175.i			0.957930i	−0.877834	+	0.478965i	$0.841012\pi$
$8$	−571797.	−	472022.i	−0.771182	−	0.636615i
$9$	96786.4	−	1.59138e6i	0.0607069	−	0.998156i
$10$	−3.01469e6	+	911338.i	−0.953328	+	0.288190i
$11$	−2.90289e6			−0.494058			−0.247029	−	0.969008i	$-0.579454\pi$
$11$	−2.90289e6			−0.494058			−0.247029	+	0.969008i	$0.579454\pi$
$12$	2.34444e6	−	1.00746e7i	0.226653	−	0.973976i
$13$	2.73529e7			1.57171			0.785854	−	0.618412i	$-0.212224\pi$
$13$	2.73529e7			1.57171			0.785854	+	0.618412i	$0.212224\pi$
$14$	−2.58331e7	+	7.80934e6i	−0.916948	+	0.277193i
$15$	−3.01099e7	−	3.19968e7i	−0.682522	−	0.725294i
$16$	2.59191e7	−	6.19015e7i	0.386225	−	0.922404i
$17$		−	2.14781e7i		−	0.215813i	−0.994161	−	0.107906i	$-0.965585\pi$
$17$		−	2.14781e7i		−	0.215813i	0.994161	−	0.107906i	$-0.0344147\pi$
$18$	1.40408e8	−	3.32937e7i	0.973019	−	0.230723i
$19$		−	2.70019e7i		−	0.131673i	−0.997830	−	0.0658364i	$-0.979028\pi$
$19$		−	2.70019e7i		−	0.131673i	0.997830	−	0.0658364i	$-0.0209715\pi$
$20$	−1.57912e8	−	2.37317e8i	−0.551722	−	0.829150i
$21$	−2.58015e8	−	2.74184e8i	−0.656477	−	0.697616i
$22$	−7.60280e7	−	2.51499e8i	−0.142964	−	0.472921i
$23$	−1.21010e9			−1.70447			−0.852237	−	0.523156i	$-0.824754\pi$
$23$	−1.21010e9			−1.70447			−0.852237	+	0.523156i	$0.824754\pi$
$24$	9.34237e8	−	6.07408e7i	0.997893	−	0.0648794i
$25$	9.90321e6			0.00811271
$26$	7.16386e8	+	2.36979e9i	0.454800	+	1.50447i
$27$	1.28805e9	+	1.54709e9i	0.639834	+	0.768513i
$28$	−1.35316e9	−	2.03359e9i	−0.530668	−	0.797509i
$29$			1.45524e9i			0.454306i	0.973859	+	0.227153i	$0.0729418\pi$
$29$			1.45524e9i			0.454306i	−0.973859	+	0.227153i	$0.927058\pi$
$30$	1.98353e9	−	3.44666e9i	0.496765	−	0.863198i
$31$			8.52012e9i			1.72423i	0.506715	+	0.862114i	$0.330860\pi$
$31$			8.52012e9i			1.72423i	−0.506715	+	0.862114i	$0.669140\pi$
$32$	6.04183e9	+	6.24340e8i	0.994703	+	0.102789i
$33$	2.66932e9	−	2.51191e9i	0.359800	−	0.338582i
$34$	1.86081e9	−	5.62521e8i	0.206580	−	0.0624491i
$35$	−1.03755e10			−0.954036
$36$	6.56185e9	+	1.12926e10i	0.502412	+	0.864628i
$37$	−2.62979e10			−1.68504			−0.842518	−	0.538669i	$-0.818928\pi$
$37$	−2.62979e10			−1.68504			−0.842518	+	0.538669i	$0.818928\pi$
$38$	2.33938e9	−	7.07193e8i	0.126040	−	0.0381017i
$39$	−2.51521e10	+	2.36689e10i	−1.14460	+	1.07710i
$40$	1.64247e10	−	1.98966e10i	0.634027	−	0.768047i
$41$		−	2.12707e10i		−	0.699338i	−0.936873	−	0.349669i	$-0.886294\pi$
$41$		−	2.12707e10i		−	0.699338i	0.936873	−	0.349669i	$-0.113706\pi$
$42$	1.69971e10	−	2.95348e10i	0.477808	−	0.830258i
$43$		−	2.09825e10i		−	0.506188i	−0.967442	−	0.253094i	$-0.918552\pi$
$43$		−	2.09825e10i		−	0.506188i	0.967442	−	0.253094i	$-0.0814481\pi$
$44$	1.97980e10	−	1.31738e10i	0.411320	−	0.273695i
$45$	5.53746e10	+	3.36783e9i	0.994099	+	0.0604601i
$46$	−3.16931e10	−	1.04840e11i	−0.493218	−	1.63155i
$47$	−2.83548e10			−0.383699			−0.191850	−	0.981424i	$-0.561449\pi$
$47$	−2.83548e10			−0.383699			−0.191850	+	0.981424i	$0.561449\pi$
$48$	2.97305e10	+	7.93491e10i	0.350861	+	0.936428i
$49$	7.98078e9			0.0823703
$50$	2.59370e8	+	8.57989e8i	0.00234755	+	0.00776563i
$51$	1.85853e10	+	1.97500e10i	0.147898	+	0.157167i
$52$	−1.86550e11	+	1.24132e11i	−1.30850	+	0.870686i
$53$			1.84057e10i			0.114067i	0.998372	+	0.0570333i	$0.0181641\pi$
$53$			1.84057e10i			0.114067i	−0.998372	+	0.0570333i	$0.981836\pi$
$54$	−1.00302e11	+	1.52112e11i	−0.550489	+	0.834843i
$55$		−	1.01011e11i		−	0.492050i
$56$	1.40745e11	−	1.70495e11i	0.609833	−	0.738738i
$57$	2.33651e10	+	2.48294e10i	0.0902364	+	0.0958912i
$58$	−1.26079e11	+	3.81135e10i	−0.434870	+	0.131461i
$59$	4.65889e11			1.43795			0.718976	−	0.695035i	$-0.244611\pi$
$59$	4.65889e11			1.43795			0.718976	+	0.695035i	$0.244611\pi$
$60$	3.50560e11	+	8.15786e10i	0.970017	+	0.225732i
$61$	−4.08856e11			−1.01608			−0.508038	−	0.861335i	$-0.669629\pi$
$61$	−4.08856e11			−1.01608			−0.508038	+	0.861335i	$0.669629\pi$
$62$	−7.38162e11	+	2.23146e11i	−1.65046	+	0.498934i
$63$	4.74510e11	+	2.88593e10i	0.956163	+	0.0581529i
$64$	1.04147e11	+	5.39801e11i	0.189443	+	0.981892i
$65$			9.51787e11i			1.56532i
$66$	2.87537e11	+	1.65475e11i	0.428211	+	0.246432i
$67$		−	1.14344e12i		−	1.54429i	−0.635449	−	0.772143i	$-0.719185\pi$
$67$		−	1.14344e12i		−	1.54429i	0.635449	−	0.772143i	$-0.280815\pi$
$68$	9.74709e10	+	1.46483e11i	0.119555	+	0.179672i
$69$	1.11274e12	−	1.04712e12i	1.24129	−	1.16809i
$70$	−2.71738e11	−	8.98904e11i	−0.276066	−	0.913221i
$71$	−9.35998e11			−0.867153			−0.433576	−	0.901117i	$-0.642749\pi$
$71$	−9.35998e11			−0.867153			−0.433576	+	0.901117i	$0.642749\pi$
$72$	−8.06509e11	+	8.64262e11i	−0.682257	+	0.731112i
$73$	5.16147e11			0.399185			0.199593	−	0.979879i	$-0.436038\pi$
$73$	5.16147e11			0.399185			0.199593	+	0.979879i	$0.436038\pi$
$74$	−6.88753e11	−	2.27838e12i	−0.487593	−	1.61295i
$75$	−9.10640e9	+	8.56938e9i	−0.00590811	+	0.00555970i
$76$	1.22539e11	+	1.84156e11i	0.0729433	+	0.109622i
$77$		−	8.65568e11i		−	0.473273i
$78$	−2.70936e12	−	1.55922e12i	−1.36223	−	0.783957i
$79$			2.03157e12i			0.940278i	0.882592	+	0.470139i	$0.155796\pi$
$79$			2.03157e12i			0.940278i	−0.882592	+	0.470139i	$0.844204\pi$
$80$	2.15396e12	+	9.01897e11i	0.918655	+	0.384655i
$81$	−2.52313e12	−	3.08048e11i	−0.992629	−	0.121190i
$82$	1.84284e12	−	5.57091e11i	0.669420	−	0.202365i
$83$	−1.79895e12			−0.603965			−0.301983	−	0.953313i	$-0.597649\pi$
$83$	−1.79895e12			−0.603965			−0.301983	+	0.953313i	$0.597649\pi$
$84$	3.00398e12	+	6.99054e11i	0.933000	+	0.217118i
$85$	7.47363e11			0.214936
$86$	1.81787e12	−	5.49541e11i	0.484532	−	0.146474i
$87$	−1.25924e12	−	1.33815e12i	−0.311339	−	0.330850i
$88$	1.65986e12	+	1.37023e12i	0.381009	+	0.314525i
$89$			6.29425e12i			1.34248i	0.741238	+	0.671242i	$0.234239\pi$
$89$			6.29425e12i			1.34248i	−0.741238	+	0.671242i	$0.765761\pi$
$90$	1.15851e12	+	4.88572e12i	0.229785	+	0.969064i
$91$			8.15595e12i			1.50559i
$92$	8.25302e12	−	5.49162e12i	1.41903	−	0.944234i
$93$	−7.37258e12	−	7.83459e12i	−1.18163	−	1.25567i
$94$	−7.42627e11	−	2.45659e12i	−0.111030	−	0.367284i
$95$	9.39573e11			0.131138
$96$	−6.09596e12	+	4.65397e12i	−0.794838	+	0.606821i
$97$	3.83919e12			0.467975			0.233988	−	0.972240i	$-0.424822\pi$
$97$	3.83919e12			0.467975			0.233988	+	0.972240i	$0.424822\pi$
$98$	2.09020e11	+	6.91435e11i	0.0238352	+	0.0788464i
$99$	−2.80960e11	+	4.61961e12i	−0.0299927	+	0.493147i
$100$	−6.75410e10	+	4.49423e10i	−0.00675410	+	0.00449423i
$101$			4.88295e12i			0.457713i	0.973460	+	0.228856i	$0.0734986\pi$
$101$			4.88295e12i			0.457713i	−0.973460	+	0.228856i	$0.926501\pi$
$102$	−1.22433e12	+	2.12744e12i	−0.107646	+	0.187050i
$103$		−	1.33906e12i		−	0.110499i	−0.998473	−	0.0552495i	$-0.982405\pi$
$103$		−	1.33906e12i		−	0.110499i	0.998473	−	0.0552495i	$-0.0175954\pi$
$104$	−1.56403e13	−	1.29112e13i	−1.21207	−	1.00057i
$105$	9.54065e12	−	8.97803e12i	0.694780	−	0.653808i
$106$	−1.59462e12	+	4.82053e11i	−0.109187	+	0.0330070i
$107$	−1.47421e13			−0.949655			−0.474827	−	0.880079i	$-0.657489\pi$
$107$	−1.47421e13			−0.949655			−0.474827	+	0.880079i	$0.657489\pi$
$108$	−1.58056e13	−	4.70599e12i	−0.958420	−	0.285362i
$109$	5.70963e12			0.326089			0.163044	−	0.986619i	$-0.447869\pi$
$109$	5.70963e12			0.326089			0.163044	+	0.986619i	$0.447869\pi$
$110$	8.75130e12	−	2.64551e12i	0.470999	−	0.142383i
$111$	2.41819e13	−	2.27559e13i	1.22713	−	1.15477i
$112$	1.84575e13	+	7.72844e12i	0.883599	+	0.369977i
$113$			3.20124e13i			1.44646i	0.690605	+	0.723232i	$0.257344\pi$
$113$			3.20124e13i			1.44646i	−0.690605	+	0.723232i	$0.742656\pi$
$114$	−1.53921e12	+	2.67459e12i	−0.0656774	+	0.114124i
$115$		−	4.21073e13i		−	1.69755i
$116$	−6.60412e12	−	9.92493e12i	−0.251674	−	0.378225i
$117$	2.64739e12	−	4.35290e13i	0.0954135	−	1.56881i
$118$	1.22018e13	+	4.03634e13i	0.416095	+	1.37643i
$119$	6.40422e12			0.206734
$120$	2.11357e12	+	3.25082e13i	0.0646157	+	0.993837i
$121$	−2.60959e13			−0.755907
$122$	−1.07081e13	−	3.54222e13i	−0.294018	−	0.972606i
$123$	1.84059e13	+	1.95593e13i	0.479262	+	0.509296i
$124$	−3.86656e13	−	5.81082e13i	−0.955177	−	1.43548i
$125$			4.28209e13i			1.00402i
$126$	9.92735e12	+	4.18662e13i	0.221017	+	0.932084i
$127$			2.60554e13i			0.551029i	0.961297	+	0.275514i	$0.0888482\pi$
$127$			2.60554e13i			0.551029i	−0.961297	+	0.275514i	$0.911152\pi$
$128$	−4.40393e13	+	2.31607e13i	−0.885067	+	0.465465i
$129$	1.81564e13	+	1.92942e13i	0.346894	+	0.368633i
$130$	−8.24605e13	+	2.49278e13i	−1.49835	+	0.452951i
$131$	6.09012e13			1.05284			0.526420	−	0.850225i	$-0.323534\pi$
$131$	6.09012e13			1.05284			0.526420	+	0.850225i	$0.323534\pi$
$132$	−6.80566e12	+	2.92453e13i	−0.111980	+	0.481200i
$133$	8.05129e12			0.126133
$134$	9.90649e13	−	2.99473e13i	1.47822	−	0.446865i
$135$	−5.38334e13	+	4.48196e13i	−0.765390	+	0.637233i
$136$	−1.01381e13	+	1.22811e13i	−0.137390	+	0.166431i
$137$		−	4.56611e13i		−	0.590014i	−0.955495	−	0.295007i	$-0.904678\pi$
$137$		−	4.56611e13i		−	0.590014i	0.955495	−	0.295007i	$-0.0953220\pi$
$138$	1.19863e14	+	6.89802e13i	1.47730	+	0.850179i
$139$		−	3.19184e13i		−	0.375357i	−0.982230	−	0.187679i	$-0.939904\pi$
$139$		−	3.19184e13i		−	0.375357i	0.982230	−	0.187679i	$-0.0600963\pi$
$140$	7.07618e13	−	4.70854e13i	0.794268	−	0.528511i
$141$	2.60734e13	−	2.45358e13i	0.279431	−	0.262952i
$142$	−2.45142e13	−	8.10925e13i	−0.250925	−	0.830055i
$143$	−7.94025e13			−0.776515
$144$	−9.60004e13	−	4.72385e13i	−0.897257	−	0.441509i
$145$	−5.06374e13			−0.452459
$146$	1.35181e13	+	4.47177e13i	0.115511	+	0.382107i
$147$	−7.33865e12	+	6.90588e12i	−0.0599865	+	0.0564490i
$148$	1.79354e14	−	1.19344e14i	1.40285	−	0.933466i
$149$			3.86994e13i			0.289730i	0.989451	+	0.144865i	$0.0462748\pi$
$149$			3.86994e13i			0.289730i	−0.989451	+	0.144865i	$0.953725\pi$
$150$	−9.80931e11	−	5.64519e11i	−0.00703146	−	0.00404656i
$151$			1.29650e14i			0.890065i	0.895514	+	0.445033i	$0.146808\pi$
$151$			1.29650e14i			0.890065i	−0.895514	+	0.445033i	$0.853192\pi$
$152$	−1.27455e13	+	1.54396e13i	−0.0838249	+	0.101544i
$153$	−3.41798e13	−	2.07879e12i	−0.215415	−	0.0131013i
$154$	7.49907e13	−	2.26697e13i	0.453026	−	0.136949i
$155$	−2.96471e14			−1.71722
$156$	6.41274e13	−	2.75569e14i	0.356233	−	1.53081i
$157$	−1.43864e14			−0.766663			−0.383332	−	0.923611i	$-0.625223\pi$
$157$	−1.43864e14			−0.766663			−0.383332	+	0.923611i	$0.625223\pi$
$158$	−1.76011e14	+	5.32079e13i	−0.900052	+	0.272085i
$159$	−1.59267e13	−	1.69247e13i	−0.0781707	−	0.0830694i
$160$	−2.17249e13	+	2.10235e14i	−0.102371	+	0.990660i
$161$		−	3.60821e14i		−	1.63277i
$162$	−3.93935e13	−	2.26666e14i	−0.171229	−	0.985231i
$163$		−	3.25680e13i		−	0.136010i	−0.997685	−	0.0680052i	$-0.978337\pi$
$163$		−	3.25680e13i		−	0.136010i	0.997685	−	0.0680052i	$-0.0216634\pi$
$164$	9.65299e13	+	1.45069e14i	0.387415	+	0.582223i
$165$	8.74058e13	+	9.28833e13i	0.337206	+	0.358337i
$166$	−4.71154e13	−	1.55857e14i	−0.174767	−	0.578127i
$167$	3.83736e14			1.36891			0.684456	−	0.729054i	$-0.260040\pi$
$167$	3.83736e14			1.36891			0.684456	+	0.729054i	$0.260040\pi$
$168$	1.81114e13	+	2.78566e14i	0.0621500	+	0.955912i
$169$	4.45307e14			1.47027
$170$	1.95738e13	+	6.47497e13i	0.0621952	+	0.205740i
$171$	−4.29704e13	−	2.61342e12i	−0.131430	−	0.00799345i
$172$	9.52217e13	+	1.43103e14i	0.280415	+	0.421418i
$173$			5.03657e14i			1.42835i	0.699966	+	0.714176i	$0.253198\pi$
$173$			5.03657e14i			1.42835i	−0.699966	+	0.714176i	$0.746802\pi$
$174$	8.29543e13	−	1.44145e14i	0.226605	−	0.393757i
$175$			2.95289e12i			0.00777140i
$176$	−7.52404e13	+	1.79693e14i	−0.190818	+	0.455721i
$177$	−4.28404e14	+	4.03140e14i	−1.04719	+	0.985439i
$178$	−5.45319e14	+	1.64850e14i	−1.28505	+	0.388470i
$179$	4.65674e14			1.05812			0.529062	−	0.848583i	$-0.322544\pi$
$179$	4.65674e14			1.05812			0.529062	+	0.848583i	$0.322544\pi$
$180$	−3.92945e14	+	2.28330e14i	−0.861114	+	0.500370i
$181$	1.76681e14			0.373491			0.186745	−	0.982408i	$-0.440206\pi$
$181$	1.76681e14			0.373491			0.186745	+	0.982408i	$0.440206\pi$
$182$	−7.06612e14	+	2.13608e14i	−1.44117	+	0.435666i
$183$	3.75959e14	−	3.53788e14i	0.739961	−	0.696324i
$184$	6.91931e14	+	5.71193e14i	1.31446	+	1.08509i
$185$		−	9.15075e14i		−	1.67819i
$186$	4.85678e14	−	8.43933e14i	0.860032	−	1.49442i
$187$			6.23485e13i			0.106624i
$188$	1.93383e14	−	1.28679e14i	0.319443	−	0.212560i
$189$	−4.61304e14	+	3.84063e14i	−0.736182	+	0.612916i
$190$	2.46079e13	+	8.14023e13i	0.0379469	+	0.125527i
$191$	1.60442e14			0.239113			0.119556	−	0.992827i	$-0.461853\pi$
$191$	1.60442e14			0.239113			0.119556	+	0.992827i	$0.461853\pi$
$192$	−5.62865e14	−	4.06249e14i	−0.810860	−	0.585240i
$193$	−1.59681e14			−0.222398			−0.111199	−	0.993798i	$-0.535469\pi$
$193$	−1.59681e14			−0.222398			−0.111199	+	0.993798i	$0.535469\pi$
$194$	1.00550e14	+	3.32618e14i	0.135416	+	0.447954i
$195$	−8.23595e14	−	8.75207e14i	−1.07273	−	1.13995i
$196$	−5.44299e13	+	3.62180e13i	−0.0685761	+	0.0456310i
$197$		−	8.26072e14i		−	1.00690i	−0.864024	−	0.503451i	$-0.832063\pi$
$197$		−	8.26072e14i		−	1.00690i	0.864024	−	0.503451i	$-0.167937\pi$
$198$	−4.07590e14	+	9.66480e13i	−0.480728	+	0.113991i
$199$		−	6.23241e14i		−	0.711396i	−0.934601	−	0.355698i	$-0.884243\pi$
$199$		−	6.23241e14i		−	0.711396i	0.934601	−	0.355698i	$-0.115757\pi$
$200$	−5.66262e12	−	4.67453e12i	−0.00625637	−	0.00516467i
$201$	9.89435e14	+	1.05144e15i	1.05831	+	1.12463i
$202$	−4.23046e14	+	1.27887e14i	−0.438131	+	0.132447i
$203$	−4.33917e14			−0.435193
$204$	−2.16382e14	−	5.03542e13i	−0.210196	−	0.0489147i
$205$	7.40148e14			0.696496
$206$	1.16013e14	−	3.50707e13i	0.105772	−	0.0319747i
$207$	−1.17121e14	+	1.92573e15i	−0.103473	+	1.70133i
$208$	7.08964e14	−	1.69319e15i	0.607034	−	1.44975i
$209$			7.83836e13i			0.0650540i
$210$	1.02771e15	+	5.91439e14i	0.826884	+	0.475866i
$211$		−	3.21468e14i		−	0.250785i	−0.992107	−	0.125393i	$-0.959981\pi$
$211$		−	3.21468e14i		−	0.250785i	0.992107	−	0.125393i	$-0.0400191\pi$
$212$	−8.35277e13	−	1.25529e14i	−0.0631899	−	0.0949642i
$213$	8.60688e14	−	8.09932e14i	0.631507	−	0.594267i
$214$	−3.86103e14	−	1.27722e15i	−0.274798	−	0.909027i
$215$	7.30117e14			0.504130
$216$	−6.24034e12	−	1.49261e15i	−0.00418080	−	0.999991i
$217$	−2.54048e15			−1.65169
$218$	1.49538e14	+	4.94668e14i	0.0943592	+	0.312138i
$219$	−4.74618e14	+	4.46629e14i	−0.290708	+	0.273565i
$220$	4.58401e14	+	6.88904e14i	0.272583	+	0.409648i
$221$		−	5.87488e14i		−	0.339195i
$222$	2.60485e15	+	1.49908e15i	1.46046	+	0.840483i
$223$			2.73142e15i			1.48733i	0.668555	+	0.743663i	$0.266913\pi$
$223$			2.73142e15i			1.48733i	−0.668555	+	0.743663i	$0.733087\pi$
$224$	−1.86162e14	+	1.80152e15i	−0.0984646	+	0.952856i
$225$	9.58496e11	−	1.57598e13i	0.000492497	−	0.00809774i
$226$	−2.77347e15	+	8.38419e14i	−1.38458	+	0.418559i
$227$	−3.15817e15			−1.53203			−0.766015	−	0.642823i	$-0.777763\pi$
$227$	−3.15817e15			−1.53203			−0.766015	+	0.642823i	$0.777763\pi$
$228$	−2.72032e14	−	6.33045e13i	−0.128246	−	0.0298441i
$229$	−2.30523e15			−1.05629			−0.528145	−	0.849154i	$-0.677112\pi$
$229$	−2.30523e15			−1.05629			−0.528145	+	0.849154i	$0.677112\pi$
$230$	3.64807e15	−	1.10281e15i	1.62492	−	0.491213i
$231$	7.48988e14	+	7.95925e14i	0.324338	+	0.344663i
$232$	6.86906e14	−	8.32103e14i	0.289218	−	0.350353i
$233$			3.03338e15i			1.24198i	0.783820	+	0.620988i	$0.213268\pi$
$233$			3.03338e15i			1.24198i	−0.783820	+	0.620988i	$0.786732\pi$
$234$	3.84058e15	−	9.10681e14i	1.52930	−	0.362630i
$235$		−	9.86651e14i		−	0.382140i
$236$	−3.17742e15	+	2.11428e15i	−1.19714	+	0.796588i
$237$	−1.75795e15	−	1.86811e15i	−0.644380	−	0.684761i
$238$	1.67730e14	+	5.54846e14i	0.0598218	+	0.197889i
$239$	1.08831e15			0.377718			0.188859	−	0.982004i	$-0.439521\pi$
$239$	1.08831e15			0.377718			0.188859	+	0.982004i	$0.439521\pi$
$240$	−2.76108e15	+	1.03452e15i	−0.932621	+	0.349435i
$241$	3.53567e15			1.16241			0.581207	−	0.813756i	$-0.302581\pi$
$241$	3.53567e15			1.16241			0.581207	+	0.813756i	$0.302581\pi$
$242$	−6.83465e14	−	2.26089e15i	−0.218734	−	0.723568i
$243$	2.58668e15	−	1.90004e15i	0.805938	−	0.592000i
$244$	2.78844e15	−	1.85545e15i	0.845917	−	0.562880i
$245$			2.77704e14i			0.0820355i
$246$	−1.21251e15	+	2.10691e15i	−0.348825	+	0.606131i
$247$		−	7.38581e14i		−	0.206951i
$248$	4.02168e15	−	4.87177e15i	1.09767	−	1.32969i
$249$	1.65421e15	−	1.55666e15i	0.439840	−	0.413902i
$250$	−3.70989e15	+	1.12150e15i	−0.961062	+	0.290528i
$251$	−9.04544e14			−0.228323			−0.114162	−	0.993462i	$-0.536418\pi$
$251$	−9.04544e14			−0.228323			−0.114162	+	0.993462i	$0.536418\pi$
$252$	−3.36718e15	+	1.95658e15i	−0.828253	+	0.481275i
$253$	3.51279e15			0.842109
$254$	−2.25738e15	+	6.82405e14i	−0.527455	+	0.159449i
$255$	−6.87231e14	+	6.46704e14i	−0.156528	+	0.147297i
$256$	−3.16000e15	−	3.20887e15i	−0.701660	−	0.712512i
$257$			7.98520e14i			0.172870i	0.996257	+	0.0864352i	$0.0275475\pi$
$257$			7.98520e14i			0.172870i	−0.996257	+	0.0864352i	$0.972452\pi$
$258$	−1.19608e15	+	2.07835e15i	−0.252483	+	0.438724i
$259$		−	7.84136e15i		−	1.61415i
$260$	−4.31936e15	−	6.49130e15i	−0.867147	−	1.30318i
$261$	2.31585e15	+	1.40848e14i	0.453468	+	0.0275795i
$262$	1.59503e15	+	5.27632e15i	0.304657	+	1.00780i
$263$	5.17370e15			0.964025			0.482013	−	0.876164i	$-0.339906\pi$
$263$	5.17370e15			0.964025			0.482013	+	0.876164i	$0.339906\pi$
$264$	−2.71199e15	+	1.76324e14i	−0.493017	+	0.0320542i
$265$	−6.40453e14			−0.113603
$266$	2.10867e14	+	6.97544e14i	0.0364988	+	0.120737i
$267$	−5.44651e15	−	5.78782e15i	−0.920015	−	0.977669i
$268$	5.18911e15	+	7.79840e15i	0.855494	+	1.28567i
$269$			2.85579e15i			0.459553i	0.973243	+	0.229777i	$0.0737996\pi$
$269$			2.85579e15i			0.459553i	−0.973243	+	0.229777i	$0.926200\pi$
$270$	−5.29298e15	−	3.49015e15i	−0.831449	−	0.548251i
$271$			7.33665e15i			1.12512i	0.826758	+	0.562558i	$0.190183\pi$
$271$			7.33665e15i			1.12512i	−0.826758	+	0.562558i	$0.809817\pi$
$272$	−1.32953e15	−	5.56693e14i	−0.199067	−	0.0833524i
$273$	−7.05746e15	−	7.49973e15i	−1.03179	−	1.09645i
$274$	3.95596e15	−	1.19589e15i	0.564772	−	0.170730i
$275$	−2.87479e13			−0.00400815
$276$	−2.83701e15	+	1.21912e16i	−0.386324	+	1.66012i
$277$	−5.55757e15			−0.739207			−0.369604	−	0.929189i	$-0.620507\pi$
$277$	−5.55757e15			−0.739207			−0.369604	+	0.929189i	$0.620507\pi$
$278$	2.76533e15	−	8.35958e14i	0.359299	−	0.108616i
$279$	1.35588e16	+	8.24631e14i	1.72105	+	0.104672i
$280$	5.93265e15	+	4.89744e15i	0.735735	+	0.607354i
$281$			1.35955e16i			1.64742i	0.567012	+	0.823709i	$0.308099\pi$
$281$			1.35955e16i			1.64742i	−0.567012	+	0.823709i	$0.691901\pi$
$282$	2.80860e15	+	1.61633e15i	0.332561	+	0.191386i
$283$		−	1.16124e15i		−	0.134372i	−0.997740	−	0.0671862i	$-0.978598\pi$
$283$		−	1.16124e15i		−	0.134372i	0.997740	−	0.0671862i	$-0.0214022\pi$
$284$	6.38362e15	−	4.24771e15i	0.721934	−	0.480380i
$285$	−8.63976e14	+	8.13026e14i	−0.0955015	+	0.0898696i
$286$	−2.07959e15	−	6.87923e15i	−0.224698	−	0.743294i
$287$	6.34240e15			0.669917
$288$	1.57833e15	−	9.55443e15i	0.162985	−	0.986629i
$289$	9.44327e15			0.953425
$290$	−1.32622e15	−	4.38710e15i	−0.130927	−	0.433102i
$291$	−3.53029e15	+	3.32210e15i	−0.340805	+	0.320707i
$292$	−3.52018e15	+	2.34235e15i	−0.332335	+	0.221138i
$293$		−	3.24993e15i		−	0.300078i	−0.988680	−	0.150039i	$-0.952060\pi$
$293$		−	3.24993e15i		−	0.300078i	0.988680	−	0.150039i	$-0.0479399\pi$
$294$	−7.90511e14	−	4.54934e14i	−0.0713921	−	0.0410857i
$295$			1.62113e16i			1.43211i
$296$	1.50370e16	+	1.24132e16i	1.29947	+	1.07272i
$297$	−3.73906e15	−	4.49103e15i	−0.316115	−	0.379690i
$298$	−3.35282e15	+	1.01356e15i	−0.277335	+	0.0838383i
$299$	−3.30998e16			−2.67894
$300$	2.32175e13	−	9.97705e13i	0.00183877	−	0.00790158i
$301$	6.25644e15			0.484892
$302$	−1.12325e16	+	3.39559e15i	−0.851987	+	0.257555i
$303$	−4.22528e15	−	4.49007e15i	−0.313674	−	0.333331i
$304$	−1.67146e15	−	6.99867e14i	−0.121456	−	0.0508554i
$305$		−	1.42268e16i		−	1.01195i
$306$	−7.15085e14	−	3.01570e15i	−0.0497930	−	0.209990i
$307$		−	2.46339e15i		−	0.167932i	−0.996469	−	0.0839662i	$-0.973241\pi$
$307$		−	2.46339e15i		−	0.167932i	0.996469	−	0.0839662i	$-0.0267588\pi$
$308$	3.92808e15	+	5.90328e15i	0.262181	+	0.394016i
$309$	1.15871e15	+	1.23132e15i	0.0757258	+	0.0804713i
$310$	−7.76471e15	−	2.56855e16i	−0.496906	−	1.64375i
$311$	2.10185e15			0.131723			0.0658613	−	0.997829i	$-0.479021\pi$
$311$	2.10185e15			0.131723			0.0658613	+	0.997829i	$0.479021\pi$
$312$	2.55541e16	−	1.66144e15i	1.56840	−	0.101972i
$313$	−1.58177e16			−0.950834			−0.475417	−	0.879761i	$-0.657703\pi$
$313$	−1.58177e16			−0.950834			−0.475417	+	0.879761i	$0.657703\pi$
$314$	−3.76787e15	−	1.24640e16i	−0.221847	−	0.733864i
$315$	−1.00420e15	+	1.65113e16i	−0.0579166	+	0.952277i
$316$	−9.21960e15	−	1.38556e16i	−0.520890	−	0.782814i
$317$			6.98368e15i			0.386544i	0.981145	+	0.193272i	$0.0619100\pi$
$317$			6.98368e15i			0.386544i	−0.981145	+	0.193272i	$0.938090\pi$
$318$	1.04919e15	−	1.82311e15i	0.0568955	−	0.0988639i
$319$		−	4.22441e15i		−	0.224454i
$320$	−1.87832e16	+	3.62396e15i	−0.977901	+	0.188672i
$321$	1.35560e16	−	1.27566e16i	0.691590	−	0.650806i
$322$	3.12607e16	−	9.45008e15i	1.56291	−	0.472468i
$323$	−5.79949e14			−0.0284167
$324$	1.86060e16	−	9.34943e15i	0.893534	−	0.448996i
$325$	2.70882e14			0.0127508
$326$	2.82161e15	−	8.52972e14i	0.130192	−	0.0393569i
$327$	−5.25023e15	+	4.94062e15i	−0.237475	+	0.223471i
$328$	−1.00402e16	+	1.21625e16i	−0.445209	+	0.539317i
$329$		−	8.45470e15i		−	0.367557i
$330$	−5.75797e15	+	1.00053e16i	−0.245431	+	0.426470i
$331$		−	3.48464e16i		−	1.45639i	−0.685372	−	0.728193i	$-0.740361\pi$
$331$		−	3.48464e16i		−	1.45639i	0.685372	−	0.728193i	$-0.259639\pi$
$332$	1.22691e16	−	8.16393e15i	0.502822	−	0.334581i
$333$	−2.54527e15	+	4.18499e16i	−0.102293	+	1.68193i
$334$	1.00502e16	+	3.32460e16i	0.396118	+	1.31035i
$335$	3.97878e16			1.53801
$336$	−2.36599e16	+	8.86490e15i	−0.897032	+	0.336100i
$337$	−2.97827e16			−1.10757			−0.553783	−	0.832661i	$-0.686816\pi$
$337$	−2.97827e16			−1.10757			−0.553783	+	0.832661i	$0.686816\pi$
$338$	1.16628e16	+	3.85803e16i	0.425446	+	1.40737i
$339$	−2.77007e16	−	2.94367e16i	−0.991273	−	1.05339i
$340$	−5.09710e15	+	3.39165e15i	−0.178941	+	0.119069i
$341$		−	2.47329e16i		−	0.851868i
$342$	−8.98995e14	−	3.79129e15i	−0.0303800	−	0.128120i
$343$			3.12695e16i			1.03683i
$344$	−9.90417e15	+	1.19977e16i	−0.322247	+	0.390363i
$345$	3.64360e16	+	3.87194e16i	1.16334	+	1.23624i
$346$	−4.36356e16	+	1.31910e16i	−1.36724	+	0.413317i
$347$	4.04507e16			1.24390			0.621948	−	0.783058i	$-0.286341\pi$
$347$	4.04507e16			1.24390			0.621948	+	0.783058i	$0.286341\pi$
$348$	1.46609e16	+	3.41174e15i	0.442483	+	0.102970i
$349$	−1.36925e15			−0.0405619			−0.0202810	−	0.999794i	$-0.506456\pi$
$349$	−1.36925e15			−0.0405619			−0.0202810	+	0.999794i	$0.506456\pi$
$350$	−2.55831e14	+	7.73375e13i	−0.00743893	+	0.00224878i
$351$	3.52318e16	+	4.23175e16i	1.00563	+	1.20788i
$352$	−1.75388e16	−	1.81239e15i	−0.491441	−	0.0507837i
$353$		−	3.58837e16i		−	0.987101i	−0.869717	−	0.493551i	$-0.835699\pi$
$353$		−	3.58837e16i		−	0.987101i	0.869717	−	0.493551i	$-0.164301\pi$
$354$	−4.61471e16	−	2.65574e16i	−1.24630	−	0.717239i
$355$		−	3.25695e16i		−	0.863628i
$356$	−2.85643e16	−	4.29276e16i	−0.743702	−	1.11766i
$357$	−5.88894e15	+	5.54166e15i	−0.150555	+	0.141676i
$358$	1.21962e16	+	4.03448e16i	0.306186	+	1.01286i
$359$	−1.64845e16			−0.406407			−0.203204	−	0.979136i	$-0.565135\pi$
$359$	−1.64845e16			−0.406407			−0.203204	+	0.979136i	$0.565135\pi$
$360$	−3.00733e16	−	2.80637e16i	−0.728141	−	0.679484i
$361$	4.13239e16			0.982662
$362$	4.62737e15	+	1.53072e16i	0.108076	+	0.357512i
$363$	2.39963e16	−	2.25812e16i	0.550492	−	0.518029i
$364$	−3.70130e16	−	5.56246e16i	−0.834056	−	1.25345i
$365$			1.79601e16i			0.397563i
$366$	4.04979e16	+	2.33063e16i	0.880654	+	0.506811i
$367$		−	1.65164e16i		−	0.352847i	−0.984314	−	0.176424i	$-0.943547\pi$
$367$		−	1.65164e16i		−	0.352847i	0.984314	−	0.176424i	$-0.0564528\pi$
$368$	−3.13648e16	+	7.49070e16i	−0.658311	+	1.57221i
$369$	−3.38499e16	−	2.05872e15i	−0.698049	−	0.0424547i
$370$	7.92798e16	−	2.39662e16i	1.60639	−	0.485611i
$371$	−5.48810e15			−0.109268
$372$	8.58364e16	+	1.99749e16i	1.67936	+	0.390802i
$373$	4.34646e15			0.0835657			0.0417828	−	0.999127i	$-0.486696\pi$
$373$	4.34646e15			0.0835657			0.0417828	+	0.999127i	$0.486696\pi$
$374$	−5.40172e15	+	1.63294e15i	−0.102063	+	0.0308535i
$375$	−3.70535e16	−	3.93755e16i	−0.688059	−	0.731178i
$376$	1.62132e16	+	1.33841e16i	0.295902	+	0.244269i
$377$			3.98051e16i			0.714037i
$378$	−4.53560e16	−	2.99074e16i	−0.799721	−	0.527330i
$379$			3.83312e15i			0.0664351i	0.999448	+	0.0332176i	$0.0105754\pi$
$379$			3.83312e15i			0.0664351i	−0.999448	+	0.0332176i	$0.989425\pi$
$380$	−6.40800e15	+	4.26393e15i	−0.109177	+	0.0726468i
$381$	−2.25461e16	−	2.39590e16i	−0.377624	−	0.401289i
$382$	4.20206e15	+	1.39003e16i	0.0691912	+	0.228883i
$383$	−3.39768e16			−0.550034			−0.275017	−	0.961439i	$-0.588684\pi$
$383$	−3.39768e16			−0.550034			−0.275017	+	0.961439i	$0.588684\pi$
$384$	2.04547e16	−	5.94050e16i	0.325567	−	0.945519i
$385$	3.01188e16			0.471349
$386$	−4.18212e15	−	1.38344e16i	−0.0643546	−	0.212884i
$387$	−3.33911e16	−	2.03082e15i	−0.505254	−	0.0307291i
$388$	−2.61837e16	+	1.74228e16i	−0.389605	+	0.259246i
$389$		−	1.30017e17i		−	1.90252i	−0.308392	−	0.951259i	$-0.599791\pi$
$389$		−	1.30017e17i		−	1.90252i	0.308392	−	0.951259i	$-0.400209\pi$
$390$	5.42554e16	−	9.42763e16i	0.780770	−	1.35670i
$391$			2.59906e16i			0.367847i
$392$	−4.56338e15	−	3.76710e15i	−0.0635225	−	0.0524382i
$393$	−5.60011e16	+	5.26986e16i	−0.766734	+	0.721519i
$394$	7.15688e16	−	2.16352e16i	0.963826	−	0.291364i
$395$	−7.06918e16			−0.936457
$396$	−1.90483e16	−	3.27813e16i	−0.248221	−	0.427177i
$397$	2.81477e16			0.360831			0.180416	−	0.983590i	$-0.442256\pi$
$397$	2.81477e16			0.360831			0.180416	+	0.983590i	$0.442256\pi$
$398$	5.39961e16	−	1.63230e16i	0.680961	−	0.205854i
$399$	−7.40349e15	+	6.96689e15i	−0.0918571	+	0.0864401i
$400$	2.56683e14	−	6.13023e14i	0.00313333	−	0.00748320i
$401$			2.80629e16i			0.337050i	0.985697	+	0.168525i	$0.0539004\pi$
$401$			2.80629e16i			0.337050i	−0.985697	+	0.168525i	$0.946100\pi$
$402$	−6.51804e16	+	1.13260e17i	−0.770278	+	1.33846i
$403$			2.33050e17i			2.70998i
$404$	−2.21596e16	−	3.33023e16i	−0.253561	−	0.381061i
$405$	1.07190e16	−	8.77962e16i	0.120697	−	0.988595i
$406$	−1.13645e16	−	3.75935e16i	−0.125930	−	0.416575i
$407$	7.63397e16			0.832505
$408$	−1.30459e15	−	2.00656e16i	−0.0140018	−	0.215358i
$409$	−6.70558e16			−0.708328			−0.354164	−	0.935183i	$-0.615235\pi$
$409$	−6.70558e16			−0.708328			−0.354164	+	0.935183i	$0.615235\pi$
$410$	1.93848e16	+	6.41246e16i	0.201543	+	0.666699i
$411$	3.95112e16	+	4.19872e16i	0.404341	+	0.429680i
$412$	6.07687e15	+	9.13255e15i	0.0612136	+	0.0919942i
$413$			1.38916e17i			1.37746i
$414$	−1.69908e17	+	4.02887e16i	−1.65849	+	0.393262i
$415$		−	6.25973e16i		−	0.601511i
$416$	1.65262e17	+	1.70775e16i	1.56338	+	0.161554i
$417$	2.76194e16	+	2.93502e16i	0.257235	+	0.273355i
$418$	−6.79096e15	+	2.05290e15i	−0.0622709	+	0.0188245i
$419$	−8.15129e16			−0.735928			−0.367964	−	0.929840i	$-0.619945\pi$
$419$	−8.15129e16			−0.735928			−0.367964	+	0.929840i	$0.619945\pi$
$420$	−2.43247e16	+	1.04528e17i	−0.216235	+	0.929208i
$421$	1.51619e16			0.132715			0.0663575	−	0.997796i	$-0.478862\pi$
$421$	1.51619e16			0.132715			0.0663575	+	0.997796i	$0.478862\pi$
$422$	2.78512e16	−	8.41941e15i	0.240056	−	0.0725689i
$423$	−2.74436e15	+	4.51234e16i	−0.0232932	+	0.382992i
$424$	8.68787e15	−	1.05243e16i	0.0726165	−	0.0879660i
$425$		−	2.12702e14i		−	0.00175083i
$426$	9.27123e16	+	5.33554e16i	0.751580	+	0.432529i
$427$		−	1.21910e17i		−	0.973329i
$428$	1.00543e17	−	6.69021e16i	0.790620	−	0.526084i
$429$	7.30138e16	−	6.87081e16i	0.565500	−	0.532152i
$430$	1.91221e16	+	6.32556e16i	0.145878	+	0.482563i
$431$	1.96291e16			0.147502			0.0737512	−	0.997277i	$-0.476503\pi$
$431$	1.96291e16			0.147502			0.0737512	+	0.997277i	$0.476503\pi$
$432$	1.29152e17	−	3.96328e16i	0.956000	−	0.293366i
$433$	−1.83373e16			−0.133710			−0.0668550	−	0.997763i	$-0.521296\pi$
$433$	−1.83373e16			−0.133710			−0.0668550	+	0.997763i	$0.521296\pi$
$434$	−6.65365e16	−	2.20101e17i	−0.477944	−	1.58103i
$435$	4.65632e16	−	4.38173e16i	0.329505	−	0.310074i
$436$	−3.89403e16	+	2.59112e16i	−0.271480	+	0.180645i
$437$			3.26750e16i			0.224433i
$438$	−5.11253e16	−	2.94223e16i	−0.345982	−	0.199111i
$439$		−	1.56559e17i		−	1.04390i	−0.852976	−	0.521950i	$-0.825205\pi$
$439$		−	1.56559e17i		−	1.04390i	0.852976	−	0.521950i	$-0.174795\pi$
$440$	−4.76791e16	+	5.77575e16i	−0.313246	+	0.379460i
$441$	7.72431e14	−	1.27005e16i	0.00500045	−	0.0822184i
$442$	5.08985e16	−	1.53866e16i	0.324684	−	0.0981517i
$443$	2.30283e17			1.44756			0.723780	−	0.690030i	$-0.242403\pi$
$443$	2.30283e17			1.44756			0.723780	+	0.690030i	$0.242403\pi$
$444$	−6.16538e16	+	2.64939e17i	−0.381919	+	1.64118i
$445$	−2.19018e17			−1.33703
$446$	−2.36643e17	+	7.15371e16i	−1.42370	+	0.430383i
$447$	−3.34872e16	−	3.55857e16i	−0.198554	−	0.210997i
$448$	−1.60955e17	+	3.10540e16i	−0.940584	+	0.181473i
$449$		−	2.31569e16i		−	0.133376i	−0.997774	−	0.0666882i	$-0.978757\pi$
$449$		−	2.31569e16i		−	0.133376i	0.997774	−	0.0666882i	$-0.0212433\pi$
$450$	1.39049e15	−	3.29715e14i	0.00789382	−	0.00187179i
$451$			6.17466e16i			0.345514i
$452$	−1.45277e17	−	2.18328e17i	−0.801304	−	1.20423i
$453$	−1.12188e17	−	1.19218e17i	−0.609968	−	0.648193i
$454$	−8.27139e16	−	2.73616e17i	−0.443318	−	1.46649i
$455$	−2.83799e17			−1.49947
$456$	−1.64012e15	−	2.52262e16i	−0.00854286	−	0.131395i
$457$	2.79911e17			1.43736			0.718678	−	0.695343i	$-0.244748\pi$
$457$	2.79911e17			1.43736			0.718678	+	0.695343i	$0.244748\pi$
$458$	−6.03750e16	−	1.99719e17i	−0.305655	−	1.01110i
$459$	3.32285e16	−	2.76648e16i	0.165855	−	0.138084i
$460$	1.91090e17	+	2.87177e17i	0.940396	+	1.41326i
$461$			3.44894e17i			1.67351i	0.547574	+	0.836757i	$0.315551\pi$
$461$			3.44894e17i			1.67351i	−0.547574	+	0.836757i	$0.684449\pi$
$462$	−4.93406e16	+	8.57362e16i	−0.236065	+	0.410196i
$463$		−	2.58612e17i		−	1.22003i	−0.792388	−	0.610017i	$-0.791163\pi$
$463$		−	2.58612e17i		−	1.22003i	0.792388	−	0.610017i	$-0.208837\pi$
$464$	9.00817e16	+	3.77187e16i	0.419054	+	0.175465i
$465$	2.72617e17	−	2.56540e17i	1.25057	−	1.17682i
$466$	−2.62804e17	+	7.94456e16i	−1.18884	+	0.359386i
$467$	2.18680e17			0.975551			0.487776	−	0.872969i	$-0.337808\pi$
$467$	2.18680e17			0.975551			0.487776	+	0.872969i	$0.337808\pi$
$468$	1.79486e17	+	3.08887e17i	0.789645	+	1.35894i
$469$	3.40945e17			1.47932
$470$	8.54810e16	−	2.58409e16i	0.365791	−	0.110579i
$471$	1.32289e17	−	1.24488e17i	0.558325	−	0.525400i
$472$	−2.66394e17	−	2.19910e17i	−1.10892	−	0.915421i
$473$			6.09098e16i			0.250086i
$474$	1.15807e17	−	2.01231e17i	0.469004	−	0.814959i
$475$		−	2.67406e14i		−	0.00106822i
$476$	−4.36775e16	+	2.90634e16i	−0.172113	+	0.114525i
$477$	2.92904e16	+	1.78142e15i	0.113856	+	0.00692462i
$478$	2.85035e16	+	9.42889e16i	0.109299	+	0.361559i
$479$	−2.78594e17			−1.05388			−0.526940	−	0.849903i	$-0.676661\pi$
$479$	−2.78594e17			−1.05388			−0.526940	+	0.849903i	$0.676661\pi$
$480$	−1.61942e17	−	2.12118e17i	−0.604355	−	0.791608i
$481$	−7.19323e17			−2.64838
$482$	9.26009e16	+	3.06322e17i	0.336364	+	1.11268i
$483$	3.12224e17	+	3.31790e17i	1.11895	+	1.18907i
$484$	1.77977e17	−	1.18427e17i	0.629318	−	0.418753i
$485$			1.33590e17i			0.466073i
$486$	2.32361e17	+	1.74341e17i	0.799884	+	0.600154i
$487$			3.42010e17i			1.16172i	0.814005	+	0.580858i	$0.197283\pi$
$487$			3.42010e17i			1.16172i	−0.814005	+	0.580858i	$0.802717\pi$
$488$	2.33782e17	+	1.92989e17i	0.783579	+	0.646849i
$489$	2.81816e16	+	2.99476e16i	0.0932089	+	0.0990500i
$490$	−2.40596e16	+	7.27319e15i	−0.0785259	+	0.0237383i
$491$	1.32470e17			0.426666			0.213333	−	0.976979i	$-0.431568\pi$
$491$	1.32470e17			0.426666			0.213333	+	0.976979i	$0.431568\pi$
$492$	−2.14293e17	−	4.98680e16i	−0.681138	−	0.158507i
$493$	3.12558e16			0.0980451
$494$	6.39888e16	−	1.93438e16i	0.198098	−	0.0598848i
$495$	−1.60746e17	−	9.77644e15i	−0.491142	−	0.0298708i
$496$	5.27408e17	+	2.20834e17i	1.59043	+	0.665940i
$497$		−	2.79091e17i		−	0.830672i
$498$	1.78190e17	+	1.02547e17i	0.523470	+	0.301254i
$499$		−	6.42956e15i		−	0.0186435i	−0.999957	−	0.00932175i	$-0.997033\pi$
$499$		−	6.42956e15i		−	0.0186435i	0.999957	−	0.00932175i	$-0.00296725\pi$
$500$	−1.94328e17	−	2.92043e17i	−0.556198	−	0.835877i
$501$	−3.52861e17	+	3.32052e17i	−0.996916	+	0.938126i
$502$	−2.36904e16	−	7.83674e16i	−0.0660692	−	0.218555i
$503$	−2.53043e17			−0.696630			−0.348315	−	0.937378i	$-0.613246\pi$
$503$	−2.53043e17			−0.696630			−0.348315	+	0.937378i	$0.613246\pi$
$504$	−2.57701e17	−	2.40481e17i	−0.700354	−	0.653554i
$505$	−1.69910e17			−0.455852
$506$	9.20015e16	+	3.04339e17i	0.243678	+	0.806082i
$507$	−4.09478e17	+	3.85331e17i	−1.07073	+	1.00759i
$508$	−1.18244e17	−	1.77701e17i	−0.305256	−	0.458750i
$509$		−	2.89062e17i		−	0.736758i	−0.929676	−	0.368379i	$-0.879913\pi$
$509$		−	2.89062e17i		−	0.736758i	0.929676	−	0.368379i	$-0.120087\pi$
$510$	−7.40277e16	−	4.26025e16i	−0.186289	−	0.107208i
$511$			1.53902e17i			0.382391i
$512$	1.95247e17	−	3.57816e17i	0.478993	−	0.877819i
$513$	4.17744e16	−	3.47797e16i	0.101192	−	0.0842487i
$514$	−6.91818e16	+	2.09136e16i	−0.165475	+	0.0500229i
$515$	4.65947e16			0.110050
$516$	−2.11389e17	−	4.91922e16i	−0.493014	−	0.114729i
$517$	8.23110e16			0.189570
$518$	6.79356e17	−	2.05369e17i	1.54509	−	0.467080i
$519$	−4.35821e17	−	4.63133e17i	−0.978860	−	1.04020i
$520$	4.49264e17	−	5.44229e17i	0.996506	−	1.20715i
$521$		−	1.68996e17i		−	0.370195i	−0.982720	−	0.185097i	$-0.940740\pi$
$521$		−	1.68996e17i		−	0.370195i	0.982720	−	0.185097i	$-0.0592600\pi$
$522$	4.84505e16	+	2.04328e17i	0.104819	+	0.442049i
$523$			6.18450e17i			1.32143i	0.750638	+	0.660714i	$0.229746\pi$
$523$			6.18450e17i			1.32143i	−0.750638	+	0.660714i	$0.770254\pi$
$524$	−4.15353e17	+	2.76379e17i	−0.876524	+	0.583246i
$525$	−2.55517e15	−	2.71530e15i	−0.00532580	−	0.00565955i
$526$	1.35502e17	+	4.48236e17i	0.278957	+	0.922783i
$527$	1.82996e17			0.372110
$528$	−8.63045e16	−	2.30342e17i	−0.173346	−	0.462650i
$529$	9.60306e17			1.90523
$530$	−1.67738e16	−	5.54873e16i	−0.0328729	−	0.108743i
$531$	4.50917e16	−	7.41407e17i	0.0872935	−	1.43530i
$532$	−5.49108e16	+	3.65380e16i	−0.105010	+	0.0698746i
$533$		−	5.81817e17i		−	1.09916i
$534$	3.58796e17	−	6.23458e17i	0.669621	−	1.16356i
$535$		−	5.12975e17i		−	0.945795i
$536$	−5.39729e17	+	6.53816e17i	−0.983115	+	1.19092i
$537$	−4.28206e17	+	4.02954e17i	−0.770583	+	0.725141i
$538$	−2.47418e17	+	7.47944e16i	−0.439893	+	0.132979i
$539$	−2.31673e16			−0.0406957
$540$	1.63752e17	−	5.49979e17i	0.284202	−	0.954524i
$541$	7.67513e17			1.31614			0.658072	−	0.752955i	$-0.271372\pi$
$541$	7.67513e17			1.31614			0.658072	+	0.752955i	$0.271372\pi$
$542$	−6.35629e17	+	1.92150e17i	−1.07698	+	0.325571i
$543$	−1.62466e17	+	1.52885e17i	−0.271996	+	0.255956i
$544$	1.34096e16	−	1.29767e17i	0.0221832	−	0.214670i
$545$			1.98675e17i			0.324763i
$546$	4.64920e17	−	8.07862e17i	0.750975	−	1.30492i
$547$			2.37613e17i			0.379273i	0.981854	+	0.189637i	$0.0607310\pi$
$547$			2.37613e17i			0.379273i	−0.981854	+	0.189637i	$0.939269\pi$
$548$	2.07217e17	+	3.11414e17i	0.326853	+	0.491207i
$549$	−3.95717e16	+	6.50646e17i	−0.0616828	+	1.01420i
$550$	−7.52921e14	−	2.49065e15i	−0.00115982	−	0.00383667i
$551$	3.92943e16			0.0598198
$552$	−1.13052e18	+	7.35024e16i	−1.70088	+	0.110585i
$553$	−6.05764e17			−0.900721
$554$	−1.45555e17	−	4.81494e17i	−0.213902	−	0.707583i
$555$	7.91827e17	+	8.41448e17i	1.15007	+	1.22215i
$556$	1.44851e17	+	2.17687e17i	0.207938	+	0.312498i
$557$		−	2.86105e17i		−	0.405944i	−0.979185	−	0.202972i	$-0.934940\pi$
$557$		−	2.86105e17i		−	0.405944i	0.979185	−	0.202972i	$-0.0650600\pi$
$558$	2.83666e17	+	1.19629e18i	0.397819	+	1.67771i
$559$		−	5.73932e17i		−	0.795579i
$560$	−2.68923e17	+	6.42256e17i	−0.368473	+	0.880007i
$561$	−5.39510e16	−	5.73319e16i	−0.0730703	−	0.0776494i
$562$	−1.17788e18	+	3.56073e17i	−1.57694	+	0.476708i
$563$	8.97023e17			1.18713			0.593566	−	0.804785i	$-0.297720\pi$
$563$	8.97023e17			1.18713			0.593566	+	0.804785i	$0.297720\pi$
$564$	−6.64764e16	+	2.85663e17i	−0.0869667	+	0.373714i
$565$	−1.11392e18			−1.44059
$566$	1.00607e17	−	3.04134e16i	0.128624	−	0.0388829i
$567$	9.18523e16	−	7.52334e17i	0.116091	−	0.950869i
$568$	5.35201e17	+	4.41811e17i	0.668732	+	0.552043i
$569$			1.21954e17i			0.150650i	0.997159	+	0.0753248i	$0.0239994\pi$
$569$			1.21954e17i			0.150650i	−0.997159	+	0.0753248i	$0.976001\pi$
$570$	−9.30665e16	−	5.35592e16i	−0.113660	−	0.0654105i
$571$		−	6.30914e17i		−	0.761790i	−0.924618	−	0.380895i	$-0.875616\pi$
$571$		−	6.30914e17i		−	0.761790i	0.924618	−	0.380895i	$-0.124384\pi$
$572$	5.41534e17	−	3.60341e17i	0.646475	−	0.430169i
$573$	−1.47533e17	+	1.38833e17i	−0.174135	+	0.163866i
$574$	1.66110e17	+	5.49489e17i	0.193852	+	0.641257i
$575$	−1.19839e16			−0.0138279
$576$	8.69109e17	−	1.13493e17i	0.991581	−	0.129486i
$577$	−1.08717e16			−0.0122646			−0.00613229	−	0.999981i	$-0.501952\pi$
$577$	−1.08717e16			−0.0122646			−0.00613229	+	0.999981i	$0.501952\pi$
$578$	2.47324e17	+	8.18141e17i	0.275889	+	0.912636i
$579$	1.46833e17	−	1.38174e17i	0.161962	−	0.152411i
$580$	3.45353e17	−	2.29801e17i	0.376688	−	0.250651i
$581$		−	5.36402e17i		−	0.578557i
$582$	−3.80279e17	−	2.18848e17i	−0.405604	−	0.233423i
$583$		−	5.34296e16i		−	0.0563555i
$584$	−2.95131e17	−	2.43632e17i	−0.307844	−	0.254127i
$585$	1.51466e18	+	9.21201e16i	1.56243	+	0.0950257i
$586$	2.81565e17	−	8.51171e16i	0.287240	−	0.0868325i
$587$	−2.76652e17			−0.279117			−0.139558	−	0.990214i	$-0.544568\pi$
$587$	−2.76652e17			−0.279117			−0.139558	+	0.990214i	$0.544568\pi$
$588$	1.87105e16	−	8.04029e16i	0.0186695	−	0.0802267i
$589$	2.30059e17			0.227034
$590$	−1.40451e18	+	4.24582e17i	−1.37084	+	0.414404i
$591$	7.14812e17	+	7.59607e17i	0.690038	+	0.733281i
$592$	−6.81618e17	+	1.62788e18i	−0.650803	+	1.55428i
$593$			1.51250e18i			1.42837i	0.699957	+	0.714185i	$0.253202\pi$
$593$			1.51250e18i			1.42837i	−0.699957	+	0.714185i	$0.746798\pi$
$594$	2.91164e17	−	4.41565e17i	0.271973	−	0.412461i
$595$			2.22845e17i			0.205893i
$596$	−1.75624e17	−	2.63935e17i	−0.160503	−	0.241210i
$597$	5.39299e17	+	5.73095e17i	0.487525	+	0.518076i
$598$	−8.66899e17	−	2.86768e18i	−0.775195	−	2.56433i
$599$	9.45670e17			0.836499			0.418249	−	0.908332i	$-0.362644\pi$
$599$	9.45670e17			0.836499			0.418249	+	0.908332i	$0.362644\pi$
$600$	9.25194e15	−	6.01528e14i	0.00809561	−	0.000526348i
$601$	−4.68443e17			−0.405483			−0.202741	−	0.979232i	$-0.564985\pi$
$601$	−4.68443e17			−0.405483			−0.202741	+	0.979232i	$0.564985\pi$
$602$	1.63859e17	+	5.42043e17i	0.140312	+	0.464148i
$603$	−1.81965e18	−	1.10670e17i	−1.54144	−	0.0937487i
$604$	−5.88371e17	−	8.84227e17i	−0.493073	−	0.741009i
$605$		−	9.08049e17i		−	0.752834i
$606$	2.78346e17	−	4.83665e17i	0.228304	−	0.396709i
$607$			6.64963e16i			0.0539599i	0.999636	+	0.0269799i	$0.00858903\pi$
$607$			6.64963e16i			0.0539599i	−0.999636	+	0.0269799i	$0.991411\pi$
$608$	1.68584e16	−	1.63141e17i	0.0135345	−	0.130975i
$609$	3.99004e17	−	3.75474e17i	0.316931	−	0.298241i
$610$	1.23257e18	−	3.72606e17i	0.968653	−	0.292823i
$611$	−7.75588e17			−0.603064
$612$	2.42544e17	−	1.40936e17i	0.186598	−	0.108427i
$613$	7.73724e17			0.588969			0.294485	−	0.955656i	$-0.404852\pi$
$613$	7.73724e17			0.588969			0.294485	+	0.955656i	$0.404852\pi$
$614$	2.13422e17	−	6.45174e16i	0.160748	−	0.0485940i
$615$	−6.80596e17	+	6.40460e17i	−0.507226	+	0.477314i
$616$	−4.08567e17	+	4.94929e17i	−0.301293	+	0.364979i
$617$		−	1.93689e18i		−	1.41335i	−0.707536	−	0.706677i	$-0.750193\pi$
$617$		−	1.93689e18i		−	1.41335i	0.707536	−	0.706677i	$-0.249807\pi$
$618$	−7.63315e16	+	1.32636e17i	−0.0551161	+	0.0957719i
$619$		−	1.69210e17i		−	0.120903i	−0.998171	−	0.0604514i	$-0.980746\pi$
$619$		−	1.69210e17i		−	0.120903i	0.998171	−	0.0604514i	$-0.0192540\pi$
$620$	2.02196e18	−	1.34543e18i	1.42964	−	0.951295i
$621$	−1.55867e18	−	1.87214e18i	−1.09058	−	1.30991i
$622$	5.50486e16	+	1.82099e17i	0.0381161	+	0.126087i
$623$	−1.87679e18			−1.28601
$624$	8.13217e17	+	2.17043e18i	0.551451	+	1.47179i
$625$	−1.47793e18			−0.991821
$626$	−4.14273e17	−	1.37040e18i	−0.275140	−	0.910156i
$627$	−6.78264e16	−	7.20769e16i	−0.0445820	−	0.0473758i
$628$	9.81170e17	−	6.52878e17i	0.638273	−	0.424712i
$629$			5.64827e17i			0.363652i
$630$	−1.45680e18	+	3.45438e17i	−0.928296	+	0.220118i
$631$		−	7.81811e16i		−	0.0493073i	−0.999696	−	0.0246536i	$-0.992152\pi$
$631$		−	7.81811e16i		−	0.0493073i	0.999696	−	0.0246536i	$-0.00784830\pi$
$632$	9.58947e17	−	1.16165e18i	0.598595	−	0.725126i
$633$	2.78171e17	+	2.95603e17i	0.171865	+	0.182635i
$634$	−6.05049e17	+	1.82906e17i	−0.370007	+	0.111853i
$635$	−9.06640e17			−0.548789
$636$	1.85429e17	+	4.31510e16i	0.111098	+	0.0258535i
$637$	2.18298e17			0.129462
$638$	3.65992e17	−	1.10639e17i	0.214851	−	0.0649494i
$639$	−9.05919e16	+	1.48953e18i	−0.0526422	+	0.865554i
$640$	−8.05912e17	−	1.53242e18i	−0.463573	−	0.881469i
$641$			2.70376e18i			1.53954i	0.638321	+	0.769770i	$0.279629\pi$
$641$			2.70376e18i			1.53954i	−0.638321	+	0.769770i	$0.720371\pi$
$642$	1.46024e18	+	8.40356e17i	0.823086	+	0.473681i
$643$			1.54472e18i			0.861940i	0.902366	+	0.430970i	$0.141829\pi$
$643$			1.54472e18i			0.861940i	−0.902366	+	0.430970i	$0.858171\pi$
$644$	1.63746e18	+	2.46084e18i	0.904510	+	1.35933i
$645$	−6.71372e17	+	6.31781e17i	−0.367135	+	0.345484i
$646$	−1.51891e16	−	5.02454e16i	−0.00822284	−	0.0272010i
$647$	6.55549e17			0.351340			0.175670	−	0.984449i	$-0.443791\pi$
$647$	6.55549e17			0.351340			0.175670	+	0.984449i	$0.443791\pi$
$648$	1.29731e18	+	1.36711e18i	0.688346	+	0.725382i
$649$	−1.35242e18			−0.710431
$650$	7.09452e15	+	2.34685e16i	0.00368966	+	0.0122053i
$651$	2.33608e18	−	2.19832e18i	1.20285	−	1.13191i
$652$	1.47799e17	+	2.22118e17i	0.0753462	+	0.113233i
$653$			8.77808e17i			0.443061i	0.975153	+	0.221531i	$0.0711053\pi$
$653$			8.77808e17i			0.443061i	−0.975153	+	0.221531i	$0.928895\pi$
$654$	−5.65549e17	−	3.25470e17i	−0.282628	−	0.162651i
$655$			2.11915e18i			1.04856i
$656$	−1.31669e18	−	5.51319e17i	−0.645073	−	0.270102i
$657$	4.99560e16	−	8.21387e17i	0.0242333	−	0.398449i
$658$	7.32494e17	−	2.21433e17i	0.351832	−	0.106359i
$659$	9.21545e17			0.438290			0.219145	−	0.975692i	$-0.429673\pi$
$659$	9.21545e17			0.438290			0.219145	+	0.975692i	$0.429673\pi$
$660$	−1.01764e18	−	2.36814e17i	−0.479245	−	0.111525i
$661$	3.84526e18			1.79315			0.896574	−	0.442895i	$-0.146048\pi$
$661$	3.84526e18			1.79315			0.896574	+	0.442895i	$0.146048\pi$
$662$	3.01901e18	−	9.12645e17i	1.39408	−	0.421429i
$663$	5.08362e17	+	5.40219e17i	0.232453	+	0.247020i
$664$	1.02864e18	+	8.49144e17i	0.465767	+	0.384494i
$665$			2.80157e17i			0.125621i
$666$	−3.69244e18	+	8.75554e17i	−1.63957	+	0.388777i
$667$		−	1.76099e18i		−	0.774353i
$668$	−2.61713e18	+	1.74146e18i	−1.13967	+	0.758342i
$669$	−2.36353e18	−	2.51165e18i	−1.01928	−	1.08315i
$670$	1.04206e18	+	3.44712e18i	0.445048	+	1.47221i
$671$	1.18686e18			0.502000
$672$	−1.38770e18	−	1.81766e18i	−0.581292	−	0.761399i
$673$	−4.22782e17			−0.175396			−0.0876978	−	0.996147i	$-0.527951\pi$
$673$	−4.22782e17			−0.175396			−0.0876978	+	0.996147i	$0.527951\pi$
$674$	−7.80022e17	−	2.58030e18i	−0.320492	−	1.06018i
$675$	1.27558e16	+	1.53212e16i	0.00519078	+	0.00623472i
$676$	−3.03705e18	+	2.02087e18i	−1.22405	+	0.814490i
$677$			2.49241e18i			0.994933i	0.867483	+	0.497466i	$0.165736\pi$
$677$			2.49241e18i			0.994933i	−0.867483	+	0.497466i	$0.834264\pi$
$678$	1.82482e18	−	3.17088e18i	0.721486	−	1.25368i
$679$			1.14475e18i			0.448287i
$680$	−4.27340e17	−	3.52771e17i	−0.165754	−	0.136831i
$681$	2.90406e18	−	2.73281e18i	1.11571	−	1.04991i
$682$	2.14280e18	−	6.47768e17i	0.815424	−	0.246502i
$683$	−2.65244e18			−0.999797			−0.499898	−	0.866084i	$-0.666629\pi$
$683$	−2.65244e18			−0.999797			−0.499898	+	0.866084i	$0.666629\pi$
$684$	3.04923e17	−	1.77182e17i	0.113848	−	0.0661540i
$685$	1.58885e18			0.587616
$686$	−2.70911e18	+	8.18964e17i	−0.992477	+	0.300025i
$687$	2.11975e18	−	1.99474e18i	0.769247	−	0.723883i
$688$	−1.29885e18	−	5.43847e17i	−0.466910	−	0.195502i
$689$			5.03449e17i			0.179279i
$690$	−2.40027e18	+	4.17081e18i	−0.846723	+	1.47130i
$691$		−	4.17082e18i		−	1.45752i	−0.684770	−	0.728759i	$-0.740098\pi$
$691$		−	4.17082e18i		−	1.45752i	0.684770	−	0.728759i	$-0.259902\pi$
$692$	−2.28567e18	−	3.43500e18i	−0.791270	−	1.18915i
$693$	−1.37745e18	−	8.37752e16i	−0.472400	−	0.0287309i
$694$	1.05942e18	+	3.50455e18i	0.359942	+	1.19068i
$695$	1.11065e18			0.373831
$696$	8.83926e16	+	1.35954e18i	0.0294751	+	0.453349i
$697$	−4.56854e17			−0.150926
$698$	−3.58614e16	−	1.18629e17i	−0.0117373	−	0.0388266i
$699$	−2.62482e18	−	2.78931e18i	−0.851135	−	0.904473i
$700$	−1.34007e16	−	2.01390e16i	−0.00430516	−	0.00646996i
$701$			5.87570e18i			1.87022i	0.354357	+	0.935110i	$0.384700\pi$
$701$			5.87570e18i			1.87022i	−0.354357	+	0.935110i	$0.615300\pi$
$702$	−2.74354e18	+	4.16071e18i	−0.865208	+	1.31213i
$703$			7.10092e17i			0.221873i
$704$	−3.02328e17	−	1.56698e18i	−0.0935956	−	0.485112i
$705$	8.53763e17	+	9.07265e17i	0.261883	+	0.278295i
$706$	3.10888e18	−	9.39812e17i	0.944872	−	0.285634i
$707$	−1.45597e18			−0.438457
$708$	1.09225e18	−	4.69362e18i	0.325916	−	1.40053i
$709$	−1.18393e18			−0.350047			−0.175024	−	0.984564i	$-0.556000\pi$
$709$	−1.18393e18			−0.350047			−0.175024	+	0.984564i	$0.556000\pi$
$710$	2.82174e18	−	8.53011e17i	0.826681	−	0.249905i
$711$	3.23301e18	+	1.96629e17i	0.938544	+	0.0570814i
$712$	2.97102e18	−	3.59903e18i	0.854646	−	1.03530i
$713$		−	1.03102e19i		−	2.93890i
$714$	−6.34350e17	−	3.65064e17i	−0.179180	−	0.103117i
$715$		−	2.76293e18i		−	0.773359i
$716$	−3.17595e18	+	2.11330e18i	−0.880925	+	0.586174i
$717$	−1.00075e18	+	9.41734e17i	−0.275075	+	0.258853i
$718$	−4.31737e17	−	1.42817e18i	−0.117601	−	0.389021i
$719$	6.28015e18			1.69524			0.847622	−	0.530600i	$-0.178033\pi$
$719$	6.28015e18			1.69524			0.847622	+	0.530600i	$0.178033\pi$
$720$	1.64374e18	−	3.34048e18i	0.439715	−	0.893610i
$721$	3.99274e17			0.105850
$722$	1.08229e18	+	3.58020e18i	0.284350	+	0.940622i
$723$	−3.25119e18	+	3.05946e18i	−0.846532	+	0.796611i
$724$	−1.20499e18	+	8.01807e17i	−0.310944	+	0.206904i
$725$			1.44116e16i			0.00368565i
$726$	2.58485e18	+	1.48757e18i	0.655160	+	0.377041i
$727$		−	1.44096e18i		−	0.361976i	−0.983485	−	0.180988i	$-0.942071\pi$
$727$		−	1.44096e18i		−	0.361976i	0.983485	−	0.180988i	$-0.0579294\pi$
$728$	3.84979e18	−	4.66355e18i	0.958479	−	1.16108i
$729$	−7.34427e17	+	3.98545e18i	−0.181226	+	0.983442i
$730$	−1.55602e18	+	4.70384e17i	−0.380554	+	0.115041i
$731$	−4.50663e17			−0.109242
$732$	−9.58539e17	+	4.11904e18i	−0.230297	+	0.989633i
$733$	2.39471e18			0.570265			0.285133	−	0.958488i	$-0.407962\pi$
$733$	2.39471e18			0.570265			0.285133	+	0.958488i	$0.407962\pi$
$734$	1.43094e18	−	4.32573e17i	0.337752	−	0.102102i
$735$	−2.40301e17	−	2.55360e17i	−0.0562196	−	0.0597427i
$736$	−7.31122e18	−	7.55514e17i	−1.69545	−	0.175201i
$737$			3.31928e18i			0.762966i
$738$	−7.08182e17	−	2.98659e18i	−0.161354	−	0.680470i
$739$			5.19008e18i			1.17215i	0.810255	+	0.586077i	$0.199329\pi$
$739$			5.19008e18i			1.17215i	−0.810255	+	0.586077i	$0.800671\pi$
$740$	4.15275e18	+	6.24092e18i	0.929672	+	1.39715i
$741$	6.39105e17	+	6.79155e17i	0.141825	+	0.150713i
$742$	−1.43736e17	−	4.75476e17i	−0.0316184	−	0.104593i
$743$	−6.27546e18			−1.36842			−0.684208	−	0.729287i	$-0.739852\pi$
$743$	−6.27546e18			−1.36842			−0.684208	+	0.729287i	$0.739852\pi$
$744$	5.17518e17	+	7.95981e18i	0.111867	+	1.72059i
$745$	−1.34661e18			−0.288553
$746$	1.13836e17	+	3.76566e17i	0.0241811	+	0.0799906i
$747$	−1.74114e17	+	2.86282e18i	−0.0366649	+	0.602852i
$748$	−2.82947e17	−	4.25224e17i	−0.0590670	−	0.0887682i
$749$		−	4.39573e18i		−	0.909703i
$750$	2.44095e18	−	4.24149e18i	0.500795	−	0.870201i
$751$			6.00920e18i			1.22224i	0.791537	+	0.611121i	$0.209281\pi$
$751$			6.00920e18i			1.22224i	−0.791537	+	0.611121i	$0.790719\pi$
$752$	−7.34933e17	+	1.75521e18i	−0.148194	+	0.353926i
$753$	8.31764e17	−	7.82714e17i	0.166277	−	0.156472i
$754$	−3.44862e18	+	1.04252e18i	−0.683489	+	0.206618i
$755$	−4.51137e18			−0.886447
$756$	1.40321e18	−	4.71282e18i	0.273357	−	0.918099i
$757$	−3.70513e18			−0.715616			−0.357808	−	0.933795i	$-0.616476\pi$
$757$	−3.70513e18			−0.715616			−0.357808	+	0.933795i	$0.616476\pi$
$758$	−3.32092e17	+	1.00391e17i	−0.0635929	+	0.0192241i
$759$	−3.23015e18	+	3.03966e18i	−0.613269	+	0.577104i
$760$	−5.37245e17	−	4.43499e17i	−0.101131	−	0.0834842i
$761$		−	1.12740e18i		−	0.210415i	−0.994450	−	0.105207i	$-0.966449\pi$
$761$		−	1.12740e18i		−	0.210415i	0.994450	−	0.105207i	$-0.0335507\pi$
$762$	1.48526e18	−	2.58084e18i	0.274849	−	0.477588i
$763$			1.70247e18i			0.312370i
$764$	−1.09424e18	+	7.28113e17i	−0.199069	+	0.132462i
$765$	7.23346e16	−	1.18934e18i	0.0130481	−	0.214539i
$766$	−8.89868e17	−	2.94366e18i	−0.159162	−	0.526503i
$767$	1.27434e19			2.26004
$768$	5.68242e18	+	2.16296e17i	0.999276	+	0.0380365i
$769$	−6.01394e18			−1.04867			−0.524334	−	0.851513i	$-0.675686\pi$
$769$	−6.01394e18			−1.04867			−0.524334	+	0.851513i	$0.675686\pi$
$770$	7.88826e17	+	2.60942e18i	0.136393	+	0.451184i
$771$	−6.90970e17	−	7.34271e17i	−0.118469	−	0.125893i
$772$	1.08904e18	−	7.24658e17i	0.185154	−	0.123203i
$773$		−	1.76652e18i		−	0.297818i	−0.988851	−	0.148909i	$-0.952424\pi$
$773$		−	1.76652e18i		−	0.297818i	0.988851	−	0.148909i	$-0.0475762\pi$
$774$	−6.98585e17	−	2.94611e18i	−0.116789	−	0.492530i
$775$			8.43765e16i			0.0139881i
$776$	−2.19523e18	−	1.81218e18i	−0.360894	−	0.297920i
$777$	6.78524e18	+	7.21045e18i	1.10619	+	1.17551i
$778$	1.12644e19	−	3.40522e18i	1.82113	−	0.550526i
$779$	−5.74350e17			−0.0920839
$780$	9.58884e18	+	2.23141e18i	1.52458	+	0.354785i
$781$	2.71710e18			0.428424
$782$	−2.25176e18	+	6.80707e17i	−0.352110	+	0.106443i
$783$	−2.25139e18	+	1.87442e18i	−0.349140	+	0.290680i
$784$	2.06855e17	−	4.94022e17i	0.0318135	−	0.0759788i
$785$		−	5.00597e18i		−	0.763547i
$786$	−6.03237e18	−	3.47159e18i	−0.912518	−	0.525148i
$787$		−	1.09902e19i		−	1.64881i	−0.565999	−	0.824406i	$-0.691509\pi$
$787$		−	1.09902e19i		−	1.64881i	0.565999	−	0.824406i	$-0.308491\pi$
$788$	3.74884e18	+	5.63391e18i	0.557798	+	0.838281i
$789$	−4.75742e18	+	4.47687e18i	−0.702055	+	0.660654i
$790$	−1.85145e18	−	6.12456e18i	−0.270979	−	0.896393i
$791$	−9.54528e18			−1.38561
$792$	2.34121e18	−	2.50886e18i	0.337075	−	0.361212i
$793$	−1.11834e19			−1.59697
$794$	7.37201e17	+	2.43864e18i	0.104413	+	0.345394i
$795$	5.88923e17	−	5.54193e17i	0.0827317	−	0.0778529i
$796$	2.82837e18	+	4.25058e18i	0.394095	+	0.592261i
$797$		−	8.33450e18i		−	1.15186i	−0.817498	−	0.575931i	$-0.804640\pi$
$797$		−	8.33450e18i		−	1.15186i	0.817498	−	0.575931i	$-0.195360\pi$
$798$	−7.97495e17	−	4.58953e17i	−0.109322	−	0.0629144i
$799$			6.09007e17i			0.0828073i
$800$	5.98335e16	+	6.18297e15i	0.00806973	+	0.000833896i
$801$	1.00166e19	+	6.09198e17i	1.34001	+	0.0814981i
$802$	−2.43130e18	+	7.34981e17i	−0.322630	+	0.0975310i
$803$	−1.49832e18			−0.197221
$804$	−1.15197e19	−	2.68073e18i	−1.50410	−	0.350017i
$805$	1.25553e19			1.62613
$806$	−2.01909e19	+	6.10369e18i	−2.59404	+	0.784178i
$807$	−2.47115e18	−	2.62601e18i	−0.314935	−	0.334671i
$808$	2.30486e18	−	2.79205e18i	0.291387	−	0.352980i
$809$			1.47952e19i			1.85547i	0.373234	+	0.927737i	$0.378249\pi$
$809$			1.47952e19i			1.85547i	−0.373234	+	0.927737i	$0.621751\pi$
$810$	7.88718e18	−	1.37076e18i	0.981227	−	0.170533i
$811$		−	1.52874e19i		−	1.88668i	−0.331830	−	0.943339i	$-0.607666\pi$
$811$		−	1.52874e19i		−	1.88668i	0.331830	−	0.943339i	$-0.392334\pi$
$812$	2.95936e18	−	1.96918e18i	0.362313	−	0.241086i
$813$	−6.34851e18	−	6.74635e18i	−0.771051	−	0.819371i
$814$	1.99937e18	+	6.61389e18i	0.240899	+	0.796889i
$815$	1.13325e18			0.135458
$816$	1.70427e18	−	6.38555e17i	0.202093	−	0.0757203i
$817$	−5.66567e17			−0.0666511
$818$	−1.75622e18	−	5.80955e18i	−0.204967	−	0.678025i
$819$	1.29792e19	+	7.89385e17i	1.50281	+	0.0913995i
$820$	−5.04790e18	+	3.35891e18i	−0.579856	+	0.385841i
$821$		−	1.31539e19i		−	1.49907i	−0.661963	−	0.749537i	$-0.730276\pi$
$821$		−	1.31539e19i		−	1.49907i	0.661963	−	0.749537i	$-0.269724\pi$
$822$	−2.60285e18	+	4.52281e18i	−0.294295	+	0.511378i
$823$			1.12185e19i			1.25845i	0.777221	+	0.629227i	$0.216629\pi$
$823$			1.12185e19i			1.25845i	−0.777221	+	0.629227i	$0.783371\pi$
$824$	−6.32066e17	+	7.65671e17i	−0.0703453	+	0.0852148i
$825$	2.64349e16	−	2.48760e16i	0.00291895	−	0.00274681i
$826$	−1.20354e19	+	3.63828e18i	−1.31853	+	0.398590i
$827$	2.34762e18			0.255177			0.127589	−	0.991827i	$-0.459276\pi$
$827$	2.34762e18			0.255177			0.127589	+	0.991827i	$0.459276\pi$
$828$	−7.94049e18	−	1.36652e19i	−0.856348	−	1.47374i
$829$	7.94710e18			0.850363			0.425181	−	0.905108i	$-0.360210\pi$
$829$	7.94710e18			0.850363			0.425181	+	0.905108i	$0.360210\pi$
$830$	5.42328e18	−	1.63945e18i	0.575777	−	0.174057i
$831$	5.11041e18	−	4.80904e18i	0.538331	−	0.506585i
$832$	2.84873e18	+	1.47651e19i	0.297748	+	1.54325i
$833$		−	1.71412e17i		−	0.0177766i
$834$	−1.81947e18	+	3.16158e18i	−0.187225	+	0.325330i
$835$			1.33527e19i			1.36335i
$836$	−3.55717e17	−	5.34585e17i	−0.0360382	−	0.0541597i
$837$	−1.31814e19	+	1.09743e19i	−1.32509	+	1.10322i
$838$	−2.13486e18	−	7.06207e18i	−0.212953	−	0.704444i
$839$	9.84278e18			0.974238			0.487119	−	0.873336i	$-0.338048\pi$
$839$	9.84278e18			0.974238			0.487119	+	0.873336i	$0.338048\pi$
$840$	−9.69314e18	+	6.30213e17i	−0.952026	+	0.0618973i
$841$	8.14290e18			0.793606
$842$	3.97098e17	+	1.31359e18i	0.0384033	+	0.127037i
$843$	−1.17644e19	−	1.25016e19i	−1.12899	−	1.19974i
$844$	1.45887e18	+	2.19245e18i	0.138929	+	0.208787i
$845$			1.54952e19i			1.46429i
$846$	−3.98126e18	+	9.44039e17i	−0.373347	+	0.0885284i
$847$		−	7.78116e18i		−	0.724106i
$848$	1.13934e18	+	4.77059e17i	0.105215	+	0.0440554i
$849$	1.00484e18	+	1.06781e18i	0.0920865	+	0.0978572i
$850$	1.84280e16	−	5.57076e15i	0.00167592	−	0.000506631i
$851$	3.18230e19			2.87210
$852$	−2.19440e18	+	9.42977e18i	−0.196543	+	0.844586i
$853$	1.17852e19			1.04754			0.523769	−	0.851860i	$-0.324525\pi$
$853$	1.17852e19			1.04754			0.523769	+	0.851860i	$0.324525\pi$
$854$	1.05620e19	−	3.19289e18i	0.931688	−	0.281649i
$855$	9.09379e16	−	1.49522e18i	0.00796096	−	0.130896i
$856$	8.42950e18	+	6.95860e18i	0.732356	+	0.604564i
$857$		−	6.53005e18i		−	0.563042i	−0.959555	−	0.281521i	$-0.909161\pi$
$857$		−	6.53005e18i		−	0.563042i	0.959555	−	0.281521i	$-0.0908389\pi$
$858$	7.86496e18	+	4.52624e18i	0.673022	+	0.387320i
$859$			1.58512e19i			1.34619i	0.739555	+	0.673096i	$0.235036\pi$
$859$			1.58512e19i			1.34619i	−0.739555	+	0.673096i	$0.764964\pi$
$860$	−4.97949e18	+	3.31339e18i	−0.419705	+	0.279275i
$861$	−5.83209e18	+	5.48816e18i	−0.487870	+	0.459099i
$862$	5.14097e17	+	1.70062e18i	0.0426823	+	0.141192i
$863$	−1.59290e19			−1.31256			−0.656280	−	0.754518i	$-0.727871\pi$
$863$	−1.59290e19			−1.31256			−0.656280	+	0.754518i	$0.727871\pi$
$864$	6.81625e18	+	1.01514e19i	0.557450	+	0.830211i
$865$	−1.75255e19			−1.42255
$866$	−4.80263e17	−	1.58870e18i	−0.0386912	−	0.127990i
$867$	−8.68347e18	+	8.17139e18i	−0.694335	+	0.653389i
$868$	1.73264e19	−	1.15291e19i	1.37509	−	0.914993i
$869$		−	5.89743e18i		−	0.464552i
$870$	5.01573e18	+	2.88652e18i	0.392156	+	0.225683i
$871$		−	3.12765e19i		−	2.42717i
$872$	−3.26475e18	−	2.69507e18i	−0.251474	−	0.207593i
$873$	3.71581e17	−	6.10961e18i	0.0284093	−	0.467112i
$874$	−2.83088e18	+	8.55774e17i	−0.214831	+	0.0649434i
$875$	−1.27681e19			−0.961776
$876$	1.21008e18	−	5.19995e18i	0.0904766	−	0.388797i
$877$	−1.47065e18			−0.109147			−0.0545736	−	0.998510i	$-0.517380\pi$
$877$	−1.47065e18			−0.109147			−0.0545736	+	0.998510i	$0.517380\pi$
$878$	1.35639e19	−	4.10036e18i	0.999241	−	0.302070i
$879$	2.81221e18	+	2.98844e18i	0.205646	+	0.218533i
$880$	−6.25270e18	−	2.61811e18i	−0.453869	−	0.190042i
$881$			1.29169e19i			0.930711i	0.885124	+	0.465356i	$0.154074\pi$
$881$			1.29169e19i			0.930711i	−0.885124	+	0.465356i	$0.845926\pi$
$882$	1.12057e18	−	2.65710e17i	0.0801479	−	0.0190047i
$883$			1.71359e19i			1.21664i	0.793691	+	0.608321i	$0.208157\pi$
$883$			1.71359e19i			1.21664i	−0.793691	+	0.608321i	$0.791843\pi$
$884$	2.66611e18	+	4.00674e18i	0.187905	+	0.282391i
$885$	−1.40279e19	−	1.49070e19i	−0.981433	−	1.04294i
$886$	6.03121e18	+	1.99511e19i	0.418876	+	1.38563i
$887$	−1.35972e19			−0.937445			−0.468722	−	0.883346i	$-0.655286\pi$
$887$	−1.35972e19			−0.937445			−0.468722	+	0.883346i	$0.655286\pi$
$888$	−2.45684e19	+	1.59735e18i	−1.68149	+	0.109324i
$889$	−7.76908e18			−0.527847
$890$	−5.73620e18	−	1.89752e19i	−0.386891	−	1.27983i
$891$	7.32437e18	+	8.94230e17i	0.490416	+	0.0598748i
$892$	−1.23956e19	−	1.86286e19i	−0.823940	−	1.23825i
$893$			7.65635e17i			0.0505228i
$894$	2.20601e18	−	3.83325e18i	0.144515	−	0.251115i
$895$			1.62038e19i			1.05382i
$896$	−6.90593e18	−	1.31314e19i	−0.445882	−	0.847832i
$897$	3.04366e19	−	2.86417e19i	1.95094	−	1.83589i
$898$	2.00626e18	−	6.06490e17i	0.127670	−	0.0385947i
$899$	−1.23988e19			−0.783327
$900$	6.49833e16	+	1.11833e17i	0.00407592	+	0.00701448i
$901$	3.95318e17			0.0246170
$902$	−5.34957e18	+	1.61717e18i	−0.330732	+	0.0999801i
$903$	−5.75305e18	+	5.41379e18i	−0.353125	+	0.332300i
$904$	1.51105e19	−	1.83046e19i	0.920841	−	1.11549i
$905$			6.14790e18i			0.371973i
$906$	7.39052e18	−	1.28421e19i	0.443958	−	0.771438i
$907$			8.03995e18i			0.479519i	0.970832	+	0.239760i	$0.0770686\pi$
$907$			8.03995e18i			0.479519i	−0.970832	+	0.239760i	$0.922931\pi$
$908$	2.15391e19	−	1.43323e19i	1.27547	−	0.848705i
$909$	7.77063e18	+	4.72603e17i	0.456869	+	0.0277863i
$910$	−7.43283e18	−	2.45876e19i	−0.433896	−	1.43532i
$911$	−8.21326e18			−0.476043			−0.238021	−	0.971260i	$-0.576499\pi$
$911$	−8.21326e18			−0.476043			−0.238021	+	0.971260i	$0.576499\pi$
$912$	2.14258e18	−	8.02782e17i	0.123302	−	0.0461988i
$913$	5.22216e18			0.298394
$914$	7.33100e18	+	2.42508e19i	0.415923	+	1.37586i
$915$	1.23106e19	+	1.30821e19i	0.693494	+	0.736953i
$916$	1.57219e19	−	1.04615e19i	0.879397	−	0.585157i
$917$			1.81592e19i			1.00855i
$918$	3.26708e18	+	2.15429e18i	0.180170	+	0.118803i
$919$		−	3.12387e19i		−	1.71057i	−0.518155	−	0.855287i	$-0.673381\pi$
$919$		−	3.12387e19i		−	1.71057i	0.518155	−	0.855287i	$-0.326619\pi$
$920$	−1.98756e19	+	2.40768e19i	−1.08068	+	1.30912i
$921$	2.13161e18	+	2.26519e18i	0.115085	+	0.122297i
$922$	−2.98807e19	+	9.03293e18i	−1.60192	+	0.484259i
$923$	−2.56023e19			−1.36291
$924$	−8.72022e18	−	2.02928e18i	−0.460956	−	0.107269i
$925$	−2.60433e17			−0.0136702
$926$	2.24055e19	−	6.77317e18i	1.16784	−	0.353037i
$927$	−2.13096e18	−	1.29603e17i	−0.110295	−	0.00670805i
$928$	−9.08566e17	+	8.79233e18i	−0.0466976	+	0.451900i
$929$		−	1.41463e19i		−	0.722004i	−0.932565	−	0.361002i	$-0.882435\pi$
$929$		−	1.41463e19i		−	0.722004i	0.932565	−	0.361002i	$-0.117565\pi$
$930$	2.93660e19	+	1.68999e19i	1.48835	+	0.856536i
$931$		−	2.15496e17i		−	0.0108459i
$932$	−1.37659e19	−	2.06880e19i	−0.688022	−	1.03399i
$933$	−1.93274e18	+	1.81876e18i	−0.0959274	+	0.0902705i
$934$	5.72734e18	+	1.89459e19i	0.282292	+	0.933816i
$935$	−2.16951e18			−0.106191
$936$	−2.20604e19	+	2.36401e19i	−1.07231	+	1.14910i
$937$	−1.56573e19			−0.755807			−0.377903	−	0.925845i	$-0.623355\pi$
$937$	−1.56573e19			−0.755807			−0.377903	+	0.925845i	$0.623355\pi$
$938$	8.92952e18	+	2.95387e19i	0.428065	+	1.41603i
$939$	1.45450e19	−	1.36873e19i	0.692448	−	0.651614i
$940$	4.47757e18	+	6.72907e18i	0.211696	+	0.318144i
$941$			1.26838e19i			0.595546i	0.954637	+	0.297773i	$0.0962439\pi$
$941$			1.26838e19i			0.595546i	−0.954637	+	0.297773i	$0.903756\pi$
$942$	1.42500e19	+	8.20079e18i	0.664484	+	0.382406i
$943$			2.57397e19i			1.19200i
$944$	1.20754e19	−	2.88392e19i	0.555373	−	1.32637i
$945$	−1.33641e19	−	1.60518e19i	−0.610425	−	0.733190i
$946$	−5.27707e18	+	1.59526e18i	−0.239387	+	0.0723666i
$947$	4.18947e19			1.88749			0.943745	−	0.330674i	$-0.107276\pi$
$947$	4.18947e19			1.88749			0.943745	+	0.330674i	$0.107276\pi$
$948$	2.04672e19	+	4.76291e18i	0.915808	+	0.213117i
$949$	1.41181e19			0.627403
$950$	2.31673e16	−	7.00348e15i	0.00102252	−	0.000309108i
$951$	−6.04308e18	−	6.42178e18i	−0.264902	−	0.281502i
$952$	−3.66191e18	−	3.02293e18i	−0.159429	−	0.131610i
$953$			3.26523e19i			1.41192i	0.708253	+	0.705959i	$0.249484\pi$
$953$			3.26523e19i			1.41192i	−0.708253	+	0.705959i	$0.750516\pi$
$954$	6.12793e17	+	2.58431e18i	0.0263178	+	0.110989i
$955$			5.58284e18i			0.238141i
$956$	−7.42244e18	+	4.93894e18i	−0.314463	+	0.209246i
$957$	3.65544e18	+	3.88451e18i	0.153820	+	0.163459i
$958$	−7.29651e18	−	2.41367e19i	−0.304958	−	1.00879i
$959$	1.36150e19			0.565192
$960$	1.41361e19	−	1.95857e19i	0.582861	−	0.807564i
$961$	−4.81748e19			−1.97296
$962$	−1.88394e19	−	6.23204e19i	−0.766354	−	2.53508i
$963$	−1.42684e18	+	2.34604e19i	−0.0576506	+	0.947903i
$964$	−2.41137e19	+	1.60454e19i	−0.967749	+	0.643947i
$965$		−	5.55635e18i		−	0.221494i
$966$	−2.05682e19	+	3.57400e19i	−0.814412	+	1.41515i
$967$		−	3.94723e19i		−	1.55246i	−0.630449	−	0.776231i	$-0.717129\pi$
$967$		−	3.94723e19i		−	1.55246i	0.630449	−	0.776231i	$-0.282871\pi$
$968$	1.49216e19	+	1.23179e19i	0.582941	+	0.481222i
$969$	5.33287e17	−	5.01838e17i	0.0206946	−	0.0194742i
$970$	−1.15739e19	+	3.49880e18i	−0.446134	+	0.134866i
$971$	3.57946e19			1.37054			0.685271	−	0.728288i	$-0.259684\pi$
$971$	3.57946e19			1.37054			0.685271	+	0.728288i	$0.259684\pi$
$972$	−9.01879e18	+	2.46972e19i	−0.343019	+	0.939329i
$973$	9.51726e18			0.359566
$974$	−2.96309e19	+	8.95740e18i	−1.11202	+	0.336162i
$975$	−2.49087e17	+	2.34398e17i	−0.00928582	+	0.00873823i
$976$	−1.05972e19	+	2.53088e19i	−0.392434	+	0.937233i
$977$		−	2.54739e19i		−	0.937087i	−0.883440	−	0.468544i	$-0.844779\pi$
$977$		−	2.54739e19i		−	0.937087i	0.883440	−	0.468544i	$-0.155221\pi$
$978$	−1.85650e18	+	3.22592e18i	−0.0678410	+	0.117883i
$979$		−	1.82715e19i		−	0.663265i
$980$	−1.26026e18	−	1.89397e18i	−0.0454456	−	0.0682974i
$981$	5.52614e17	−	9.08620e18i	0.0197958	−	0.325487i
$982$	3.46946e18	+	1.14769e19i	0.123463	+	0.408413i
$983$	−3.21919e19			−1.13802			−0.569009	−	0.822331i	$-0.692673\pi$
$983$	−3.21919e19			−1.13802			−0.569009	+	0.822331i	$0.692673\pi$
$984$	−1.29200e18	−	1.98719e19i	−0.0453727	−	0.697865i
$985$	2.87445e19			1.00281
$986$	8.18605e17	+	2.70793e18i	0.0283710	+	0.0938506i
$987$	7.31597e18	+	7.77444e18i	0.251890	+	0.267675i
$988$	3.35180e18	+	5.03721e18i	0.114646	+	0.172294i
$989$			2.53909e19i			0.862783i
$990$	−3.36302e18	−	1.41827e19i	−0.113527	−	0.478774i
$991$		−	5.24100e18i		−	0.175766i	−0.996131	−	0.0878830i	$-0.971990\pi$
$991$		−	5.24100e18i		−	0.175766i	0.996131	−	0.0878830i	$-0.0280102\pi$
$992$	−5.31945e18	+	5.14771e19i	−0.177231	+	1.71509i
$993$	3.01531e19	+	3.20427e19i	0.998072	+	1.06062i
$994$	2.41798e19	−	7.30953e18i	0.795134	−	0.240369i
$995$	2.16866e19			0.708504
$996$	−4.21754e18	+	1.81237e19i	−0.136891	+	0.588248i
$997$	1.79147e19			0.577684			0.288842	−	0.957377i	$-0.406730\pi$
$997$	1.79147e19			0.577684			0.288842	+	0.957377i	$0.406730\pi$
$998$	5.57041e17	−	1.68393e17i	0.0178459	−	0.00539481i
$999$	−3.38729e19	−	4.06852e19i	−1.07814	−	1.29497i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.14.b.a.11.16	yes	24
3.2	odd	2	inner	12.14.b.a.11.9	✓	24
4.3	odd	2	inner	12.14.b.a.11.10	yes	24
12.11	even	2	inner	12.14.b.a.11.15	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.14.b.a.11.9	✓	24	3.2	odd	2	inner
12.14.b.a.11.10	yes	24	4.3	odd	2	inner
12.14.b.a.11.15	yes	24	12.11	even	2	inner
12.14.b.a.11.16	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	12.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(26.1905 + 86.6375i) q^{2} +(-919.540 + 865.314i) q^{3} +(-6820.12 + 4538.16i) q^{4} +34796.6i q^{5} +(-99051.9 - 57003.7i) q^{6} +298175. i q^{7} +(-571797. - 472022. i) q^{8} +(96786.4 - 1.59138e6i) q^{9} +O(q^{10})\)	\(q+(26.1905 + 86.6375i) q^{2} +(-919.540 + 865.314i) q^{3} +(-6820.12 + 4538.16i) q^{4} +34796.6i q^{5} +(-99051.9 - 57003.7i) q^{6} +298175. i q^{7} +(-571797. - 472022. i) q^{8} +(96786.4 - 1.59138e6i) q^{9} +(-3.01469e6 + 911338. i) q^{10} -2.90289e6 q^{11} +(2.34444e6 - 1.00746e7i) q^{12} +2.73529e7 q^{13} +(-2.58331e7 + 7.80934e6i) q^{14} +(-3.01099e7 - 3.19968e7i) q^{15} +(2.59191e7 - 6.19015e7i) q^{16} -2.14781e7i q^{17} +(1.40408e8 - 3.32937e7i) q^{18} -2.70019e7i q^{19} +(-1.57912e8 - 2.37317e8i) q^{20} +(-2.58015e8 - 2.74184e8i) q^{21} +(-7.60280e7 - 2.51499e8i) q^{22} -1.21010e9 q^{23} +(9.34237e8 - 6.07408e7i) q^{24} +9.90321e6 q^{25} +(7.16386e8 + 2.36979e9i) q^{26} +(1.28805e9 + 1.54709e9i) q^{27} +(-1.35316e9 - 2.03359e9i) q^{28} +1.45524e9i q^{29} +(1.98353e9 - 3.44666e9i) q^{30} +8.52012e9i q^{31} +(6.04183e9 + 6.24340e8i) q^{32} +(2.66932e9 - 2.51191e9i) q^{33} +(1.86081e9 - 5.62521e8i) q^{34} -1.03755e10 q^{35} +(6.56185e9 + 1.12926e10i) q^{36} -2.62979e10 q^{37} +(2.33938e9 - 7.07193e8i) q^{38} +(-2.51521e10 + 2.36689e10i) q^{39} +(1.64247e10 - 1.98966e10i) q^{40} -2.12707e10i q^{41} +(1.69971e10 - 2.95348e10i) q^{42} -2.09825e10i q^{43} +(1.97980e10 - 1.31738e10i) q^{44} +(5.53746e10 + 3.36783e9i) q^{45} +(-3.16931e10 - 1.04840e11i) q^{46} -2.83548e10 q^{47} +(2.97305e10 + 7.93491e10i) q^{48} +7.98078e9 q^{49} +(2.59370e8 + 8.57989e8i) q^{50} +(1.85853e10 + 1.97500e10i) q^{51} +(-1.86550e11 + 1.24132e11i) q^{52} +1.84057e10i q^{53} +(-1.00302e11 + 1.52112e11i) q^{54} -1.01011e11i q^{55} +(1.40745e11 - 1.70495e11i) q^{56} +(2.33651e10 + 2.48294e10i) q^{57} +(-1.26079e11 + 3.81135e10i) q^{58} +4.65889e11 q^{59} +(3.50560e11 + 8.15786e10i) q^{60} -4.08856e11 q^{61} +(-7.38162e11 + 2.23146e11i) q^{62} +(4.74510e11 + 2.88593e10i) q^{63} +(1.04147e11 + 5.39801e11i) q^{64} +9.51787e11i q^{65} +(2.87537e11 + 1.65475e11i) q^{66} -1.14344e12i q^{67} +(9.74709e10 + 1.46483e11i) q^{68} +(1.11274e12 - 1.04712e12i) q^{69} +(-2.71738e11 - 8.98904e11i) q^{70} -9.35998e11 q^{71} +(-8.06509e11 + 8.64262e11i) q^{72} +5.16147e11 q^{73} +(-6.88753e11 - 2.27838e12i) q^{74} +(-9.10640e9 + 8.56938e9i) q^{75} +(1.22539e11 + 1.84156e11i) q^{76} -8.65568e11i q^{77} +(-2.70936e12 - 1.55922e12i) q^{78} +2.03157e12i q^{79} +(2.15396e12 + 9.01897e11i) q^{80} +(-2.52313e12 - 3.08048e11i) q^{81} +(1.84284e12 - 5.57091e11i) q^{82} -1.79895e12 q^{83} +(3.00398e12 + 6.99054e11i) q^{84} +7.47363e11 q^{85} +(1.81787e12 - 5.49541e11i) q^{86} +(-1.25924e12 - 1.33815e12i) q^{87} +(1.65986e12 + 1.37023e12i) q^{88} +6.29425e12i q^{89} +(1.15851e12 + 4.88572e12i) q^{90} +8.15595e12i q^{91} +(8.25302e12 - 5.49162e12i) q^{92} +(-7.37258e12 - 7.83459e12i) q^{93} +(-7.42627e11 - 2.45659e12i) q^{94} +9.39573e11 q^{95} +(-6.09596e12 + 4.65397e12i) q^{96} +3.83919e12 q^{97} +(2.09020e11 + 6.91435e11i) q^{98} +(-2.80960e11 + 4.61961e12i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8376 q^{4} - 135720 q^{6} - 327240 q^{9}+O(q^{10}) \) 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9	\( 24 q - 8376 q^{4} - 135720 q^{6} - 327240 q^{9} + 4403568 q^{10} - 139896 q^{12} - 17520048 q^{13} + 41046816 q^{16} - 102153744 q^{18} + 340864272 q^{21} + 401914896 q^{22} + 14766624 q^{24} - 3043252488 q^{25} + 3306349488 q^{28} + 3523891248 q^{30} - 10577805696 q^{33} + 5461322688 q^{34} + 16126437096 q^{36} - 29352930672 q^{37} - 5243368896 q^{40} + 35399300688 q^{42} + 36221734656 q^{45} + 1675946784 q^{46} + 27878547744 q^{48} - 165718477944 q^{49} - 6459860112 q^{52} - 10955701656 q^{54} + 590611321584 q^{57} - 440462601456 q^{58} - 208761511104 q^{60} + 555426186192 q^{61} - 741528997248 q^{64} + 263546293968 q^{66} - 122266973952 q^{69} - 885399371232 q^{70} + 625428177984 q^{72} + 365028975600 q^{73} + 1427271642000 q^{76} + 1481181276240 q^{78} - 2327652239400 q^{81} + 874644720480 q^{82} - 6757787638224 q^{84} - 3308476422144 q^{85} + 11607512359104 q^{88} + 4426488729648 q^{90} - 3971016902448 q^{93} - 3078833939904 q^{94} - 6470779487616 q^{96} - 4159752429648 q^{97}+O(q^{100}) \) 24 * q - 8376 * q^4 - 135720 * q^6 - 327240 * q^9 + 4403568 * q^10 - 139896 * q^12 - 17520048 * q^13 + 41046816 * q^16 - 102153744 * q^18 + 340864272 * q^21 + 401914896 * q^22 + 14766624 * q^24 - 3043252488 * q^25 + 3306349488 * q^28 + 3523891248 * q^30 - 10577805696 * q^33 + 5461322688 * q^34 + 16126437096 * q^36 - 29352930672 * q^37 - 5243368896 * q^40 + 35399300688 * q^42 + 36221734656 * q^45 + 1675946784 * q^46 + 27878547744 * q^48 - 165718477944 * q^49 - 6459860112 * q^52 - 10955701656 * q^54 + 590611321584 * q^57 - 440462601456 * q^58 - 208761511104 * q^60 + 555426186192 * q^61 - 741528997248 * q^64 + 263546293968 * q^66 - 122266973952 * q^69 - 885399371232 * q^70 + 625428177984 * q^72 + 365028975600 * q^73 + 1427271642000 * q^76 + 1481181276240 * q^78 - 2327652239400 * q^81 + 874644720480 * q^82 - 6757787638224 * q^84 - 3308476422144 * q^85 + 11607512359104 * q^88 + 4426488729648 * q^90 - 3971016902448 * q^93 - 3078833939904 * q^94 - 6470779487616 * q^96 - 4159752429648 * q^97

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