LMFDB - Embedded newform 126.12.g.b.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,12,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, 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:	$96.8112407505$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 1516x^{4} + 1461x^{3} + 2295252x^{2} - 40905x + 729 $ x^6 - x^5 + 1516x^4 + 1461x^3 + 2295252x^2 - 40905x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.3
Root			$0.00891079 + 0.0154339i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.12.g.b.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(16.0000 - 27.7128i) q^{2} +(-512.000 - 886.810i) q^{4} +(1098.21 - 1902.16i) q^{5} +(39703.5 + 20023.9i) q^{7} -32768.0 q^{8} +(-35142.9 - 60869.3i) q^{10} +(206569. + 357788. i) q^{11} +1.89569e6 q^{13} +(1.19018e6 - 779913. i) q^{14} +(-524288. + 908093. i) q^{16} +(-4.55417e6 - 7.88805e6i) q^{17} +(-1.24340e6 + 2.15364e6i) q^{19} -2.24914e6 q^{20} +1.32204e7 q^{22} +(-2.95467e7 + 5.11765e7i) q^{23} +(2.20019e7 + 3.81084e7i) q^{25} +(3.03310e7 - 5.25349e7i) q^{26} +(-2.57079e6 - 4.54617e7i) q^{28} +7.92564e7 q^{29} +(5.46551e7 + 9.46654e7i) q^{31} +(1.67772e7 + 2.90590e7i) q^{32} -2.91467e8 q^{34} +(8.16918e7 - 5.35320e7i) q^{35} +(-3.38292e8 + 5.85938e8i) q^{37} +(3.97889e7 + 6.89163e7i) q^{38} +(-3.59863e7 + 6.23301e7i) q^{40} -2.52468e8 q^{41} -1.75201e9 q^{43} +(2.11526e8 - 3.66374e8i) q^{44} +(9.45496e8 + 1.63765e9i) q^{46} +(1.29188e9 - 2.23760e9i) q^{47} +(1.17541e9 + 1.59004e9i) q^{49} +1.40812e9 q^{50} +(-9.70593e8 - 1.68112e9i) q^{52} +(2.44697e9 + 4.23828e9i) q^{53} +9.07428e8 q^{55} +(-1.30100e9 - 6.56144e8i) q^{56} +(1.26810e9 - 2.19642e9i) q^{58} +(-1.46530e9 - 2.53797e9i) q^{59} +(-5.72843e8 + 9.92193e8i) q^{61} +3.49793e9 q^{62} +1.07374e9 q^{64} +(2.08187e9 - 3.60591e9i) q^{65} +(5.82061e9 + 1.00816e10i) q^{67} +(-4.66347e9 + 8.07736e9i) q^{68} +(-1.76455e8 - 3.12042e9i) q^{70} -5.24957e9 q^{71} +(8.75111e9 + 1.51574e10i) q^{73} +(1.08253e10 + 1.87500e10i) q^{74} +2.54649e9 q^{76} +(1.03720e9 + 1.83417e10i) q^{77} +(2.12040e10 - 3.67263e10i) q^{79} +(1.15156e9 + 1.99456e9i) q^{80} +(-4.03949e9 + 6.99661e9i) q^{82} +8.46684e9 q^{83} -2.00058e10 q^{85} +(-2.80322e10 + 4.85531e10i) q^{86} +(-6.76885e9 - 1.17240e10i) q^{88} +(-9.36269e9 + 1.62167e10i) q^{89} +(7.52655e10 + 3.79591e10i) q^{91} +6.05117e10 q^{92} +(-4.13402e10 - 7.16034e10i) q^{94} +(2.73104e9 + 4.73031e9i) q^{95} +1.03324e11 q^{97} +(6.28711e10 - 7.13333e9i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 96 q^{2} - 3072 q^{4} - 1045 q^{5} + 45731 q^{7} - 196608 q^{8} + 33440 q^{10} - 181565 q^{11} + 1186364 q^{13} + 703808 q^{14} - 3145728 q^{16} + 701848 q^{17} - 7893102 q^{19} + 2140160 q^{20} - 11620160 q^{22}+ \cdots - 30564771552 q^{98}+O(q^{100}) $ 6 * q + 96 * q^2 - 3072 * q^4 - 1045 * q^5 + 45731 * q^7 - 196608 * q^8 + 33440 * q^10 - 181565 * q^11 + 1186364 * q^13 + 703808 * q^14 - 3145728 * q^16 + 701848 * q^17 - 7893102 * q^19 + 2140160 * q^20 - 11620160 * q^22 - 59247728 * q^23 + 124585550 * q^25 + 18981824 * q^26 - 24306688 * q^28 + 30040070 * q^29 - 299540305 * q^31 + 100663296 * q^32 + 44918272 * q^34 + 181163920 * q^35 - 352325094 * q^37 + 252579264 * q^38 + 34242560 * q^40 - 1199954472 * q^41 - 4298844576 * q^43 - 185922560 * q^44 + 1895927296 * q^46 + 1179123942 * q^47 + 3621837009 * q^49 + 7973475200 * q^50 - 607418368 * q^52 + 67875849 * q^53 + 1874846050 * q^55 - 1498513408 * q^56 + 480641120 * q^58 + 2911039823 * q^59 - 10148733466 * q^61 - 19170579520 * q^62 + 6442450944 * q^64 + 2404013040 * q^65 - 5535975380 * q^67 + 718692352 * q^68 - 11741350880 * q^70 + 20558197876 * q^71 + 29230853572 * q^73 + 11274403008 * q^74 + 16165072896 * q^76 - 34001756425 * q^77 + 58886709107 * q^79 - 1095761920 * q^80 - 19199271552 * q^82 - 26001713726 * q^83 - 93104330000 * q^85 - 68781513216 * q^86 + 5949521920 * q^88 + 32237877702 * q^89 + 67979059274 * q^91 + 121339346944 * q^92 - 37731966144 * q^94 + 37720110280 * q^95 + 175446876934 * q^97 - 30564771552 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	16.0000	−	27.7128i	0.353553	−	0.612372i
$2$	16.0000	−	27.7128i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−512.000	−	886.810i	−0.250000	−	0.433013i
$5$	1098.21	−	1902.16i	0.157164	−	0.272216i	−0.776681	−	0.629894i	$-0.783098\pi$
$5$	1098.21	−	1902.16i	0.157164	−	0.272216i	0.933845	+	0.357678i	$0.116432\pi$
$6$		0			0
$7$	39703.5	+	20023.9i	0.892873	+	0.450308i
$7$	39703.5	+	20023.9i	0.892873	+	0.450308i
$8$	−32768.0			−0.353553
$9$		0			0
$10$	−35142.9	−	60869.3i	−0.111132	−	0.192485i
$11$	206569.	+	357788.i	0.386727	+	0.669831i	0.992007	−	0.126181i	$-0.0402721\pi$
$11$	206569.	+	357788.i	0.386727	+	0.669831i	−0.605280	+	0.796013i	$0.706939\pi$
$12$		0			0
$13$	1.89569e6			1.41605			0.708025	−	0.706187i	$-0.249586\pi$
$13$	1.89569e6			1.41605			0.708025	+	0.706187i	$0.249586\pi$
$14$	1.19018e6	−	779913.i	0.591435	−	0.387563i
$15$		0			0
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	−4.55417e6	−	7.88805e6i	−0.777929	−	1.34741i	−0.933134	−	0.359530i	$-0.882937\pi$
$17$	−4.55417e6	−	7.88805e6i	−0.777929	−	1.34741i	0.155205	−	0.987882i	$-0.450396\pi$
$18$		0			0
$19$	−1.24340e6	+	2.15364e6i	−0.115204	+	0.199539i	−0.917861	−	0.396902i	$-0.870085\pi$
$19$	−1.24340e6	+	2.15364e6i	−0.115204	+	0.199539i	0.802657	+	0.596440i	$0.203419\pi$
$20$	−2.24914e6			−0.157164
$21$		0			0
$22$	1.32204e7			0.546915
$23$	−2.95467e7	+	5.11765e7i	−0.957208	+	1.65793i	−0.227977	+	0.973667i	$0.573211\pi$
$23$	−2.95467e7	+	5.11765e7i	−0.957208	+	1.65793i	−0.729232	+	0.684267i	$0.760122\pi$
$24$		0			0
$25$	2.20019e7	+	3.81084e7i	0.450599	+	0.780461i
$26$	3.03310e7	−	5.25349e7i	0.500649	−	0.867150i
$27$		0			0
$28$	−2.57079e6	−	4.54617e7i	−0.0282291	−	0.499202i
$29$	7.92564e7			0.717539			0.358769	−	0.933426i	$-0.383196\pi$
$29$	7.92564e7			0.717539			0.358769	+	0.933426i	$0.383196\pi$
$30$		0			0
$31$	5.46551e7	+	9.46654e7i	0.342879	+	0.593884i	0.984966	−	0.172747i	$-0.0552645\pi$
$31$	5.46551e7	+	9.46654e7i	0.342879	+	0.593884i	−0.642087	+	0.766632i	$0.721931\pi$
$32$	1.67772e7	+	2.90590e7i	0.0883883	+	0.153093i
$33$		0			0
$34$	−2.91467e8			−1.10016
$35$	8.16918e7	−	5.35320e7i	0.262908	−	0.172282i
$36$		0			0
$37$	−3.38292e8	+	5.85938e8i	−0.802014	+	1.38913i	0.116275	+	0.993217i	$0.462905\pi$
$37$	−3.38292e8	+	5.85938e8i	−0.802014	+	1.38913i	−0.918289	+	0.395912i	$0.870429\pi$
$38$	3.97889e7	+	6.89163e7i	0.0814614	+	0.141095i
$39$		0			0
$40$	−3.59863e7	+	6.23301e7i	−0.0555658	+	0.0962427i
$41$	−2.52468e8			−0.340327			−0.170163	−	0.985416i	$-0.554430\pi$
$41$	−2.52468e8			−0.340327			−0.170163	+	0.985416i	$0.554430\pi$
$42$		0			0
$43$	−1.75201e9			−1.81744			−0.908720	−	0.417407i	$-0.862939\pi$
$43$	−1.75201e9			−1.81744			−0.908720	+	0.417407i	$0.862939\pi$
$44$	2.11526e8	−	3.66374e8i	0.193364	−	0.334916i
$45$		0			0
$46$	9.45496e8	+	1.63765e9i	0.676849	+	1.17234i
$47$	1.29188e9	−	2.23760e9i	0.821646	−	1.42313i	−0.0828105	−	0.996565i	$-0.526390\pi$
$47$	1.29188e9	−	2.23760e9i	0.821646	−	1.42313i	0.904456	−	0.426567i	$-0.140277\pi$
$48$		0			0
$49$	1.17541e9	+	1.59004e9i	0.594445	+	0.804136i
$50$	1.40812e9			0.637243
$51$		0			0
$52$	−9.70593e8	−	1.68112e9i	−0.354013	−	0.613168i
$53$	2.44697e9	+	4.23828e9i	0.803732	+	1.39210i	0.917144	+	0.398557i	$0.130489\pi$
$53$	2.44697e9	+	4.23828e9i	0.803732	+	1.39210i	−0.113412	+	0.993548i	$0.536178\pi$
$54$		0			0
$55$	9.07428e8			0.243118
$56$	−1.30100e9	−	6.56144e8i	−0.315678	−	0.159208i
$57$		0			0
$58$	1.26810e9	−	2.19642e9i	0.253688	−	0.439401i
$59$	−1.46530e9	−	2.53797e9i	−0.266833	−	0.462168i	0.701209	−	0.712955i	$-0.252644\pi$
$59$	−1.46530e9	−	2.53797e9i	−0.266833	−	0.462168i	−0.968042	+	0.250787i	$0.919310\pi$
$60$		0			0
$61$	−5.72843e8	+	9.92193e8i	−0.0868403	+	0.150412i	−0.906174	−	0.422905i	$-0.861010\pi$
$61$	−5.72843e8	+	9.92193e8i	−0.0868403	+	0.150412i	0.819334	+	0.573317i	$0.194344\pi$
$62$	3.49793e9			0.484905
$63$		0			0
$64$	1.07374e9			0.125000
$65$	2.08187e9	−	3.60591e9i	0.222552	−	0.385471i
$66$		0			0
$67$	5.82061e9	+	1.00816e10i	0.526692	+	0.912258i	0.999516	+	0.0311008i	$0.00990130\pi$
$67$	5.82061e9	+	1.00816e10i	0.526692	+	0.912258i	−0.472824	+	0.881157i	$0.656765\pi$
$68$	−4.66347e9	+	8.07736e9i	−0.388964	+	0.673706i
$69$		0			0
$70$	−1.76455e8	−	3.12042e9i	−0.0125486	−	0.221909i
$71$	−5.24957e9			−0.345305			−0.172653	−	0.984983i	$-0.555234\pi$
$71$	−5.24957e9			−0.345305			−0.172653	+	0.984983i	$0.555234\pi$
$72$		0			0
$73$	8.75111e9	+	1.51574e10i	0.494069	+	0.855752i	0.999977	−	0.00683535i	$-0.00217578\pi$
$73$	8.75111e9	+	1.51574e10i	0.494069	+	0.855752i	−0.505908	+	0.862587i	$0.668842\pi$
$74$	1.08253e10	+	1.87500e10i	0.567109	+	0.982262i
$75$		0			0
$76$	2.54649e9			0.115204
$77$	1.03720e9	+	1.83417e10i	0.0436679	+	0.772221i
$78$		0			0
$79$	2.12040e10	−	3.67263e10i	0.775297	−	1.34285i	−0.159331	−	0.987225i	$-0.550934\pi$
$79$	2.12040e10	−	3.67263e10i	0.775297	−	1.34285i	0.934627	−	0.355628i	$-0.115733\pi$
$80$	1.15156e9	+	1.99456e9i	0.0392909	+	0.0680539i
$81$		0			0
$82$	−4.03949e9	+	6.99661e9i	−0.120324	+	0.208407i
$83$	8.46684e9			0.235935			0.117967	−	0.993017i	$-0.462362\pi$
$83$	8.46684e9			0.235935			0.117967	+	0.993017i	$0.462362\pi$
$84$		0			0
$85$	−2.00058e10			−0.489049
$86$	−2.80322e10	+	4.85531e10i	−0.642562	+	1.11295i
$87$		0			0
$88$	−6.76885e9	−	1.17240e10i	−0.136729	−	0.236821i
$89$	−9.36269e9	+	1.62167e10i	−0.177728	+	0.307834i	−0.941102	−	0.338123i	$-0.890208\pi$
$89$	−9.36269e9	+	1.62167e10i	−0.177728	+	0.307834i	0.763374	+	0.645957i	$0.223541\pi$
$90$		0			0
$91$	7.52655e10	+	3.79591e10i	1.26435	+	0.637659i
$92$	6.05117e10			0.957208
$93$		0			0
$94$	−4.13402e10	−	7.16034e10i	−0.580991	−	1.00631i
$95$	2.73104e9	+	4.73031e9i	0.0362117	+	0.0627205i
$96$		0			0
$97$	1.03324e11			1.22168			0.610839	−	0.791755i	$-0.290832\pi$
$97$	1.03324e11			1.22168			0.610839	+	0.791755i	$0.290832\pi$
$98$	6.28711e10	−	7.13333e9i	0.702599	−	0.0797167i
$99$		0			0
$100$	2.25300e10	−	3.90230e10i	0.225300	−	0.390230i
$101$	−3.13221e10	−	5.42515e10i	−0.296540	−	0.513623i	0.678802	−	0.734322i	$-0.262500\pi$
$101$	−3.13221e10	−	5.42515e10i	−0.296540	−	0.513623i	−0.975342	+	0.220699i	$0.929166\pi$
$102$		0			0
$103$	−2.71368e10	+	4.70024e10i	−0.230651	+	0.399499i	−0.958000	−	0.286769i	$-0.907419\pi$
$103$	−2.71368e10	+	4.70024e10i	−0.230651	+	0.399499i	0.727349	+	0.686268i	$0.240752\pi$
$104$	−6.21179e10			−0.500649
$105$		0			0
$106$	1.56606e11			1.13665
$107$	−3.82438e10	+	6.62402e10i	−0.263603	+	0.456573i	−0.967197	−	0.254029i	$-0.918244\pi$
$107$	−3.82438e10	+	6.62402e10i	−0.263603	+	0.456573i	0.703594	+	0.710602i	$0.251577\pi$
$108$		0			0
$109$	8.25991e10	+	1.43066e11i	0.514197	+	0.890615i	0.999864	+	0.0164715i	$0.00524329\pi$
$109$	8.25991e10	+	1.43066e11i	0.514197	+	0.890615i	−0.485667	+	0.874144i	$0.661423\pi$
$110$	1.45188e10	−	2.51474e10i	0.0859552	−	0.148879i
$111$		0			0
$112$	−3.89997e10	+	2.55562e10i	−0.209104	+	0.137024i
$113$	1.20455e11			0.615025			0.307513	−	0.951544i	$-0.400503\pi$
$113$	1.20455e11			0.615025			0.307513	+	0.951544i	$0.400503\pi$
$114$		0			0
$115$	6.48973e10	+	1.12406e11i	0.300877	+	0.521134i
$116$	−4.05793e10	−	7.02854e10i	−0.179385	−	0.310703i
$117$		0			0
$118$	−9.37789e10			−0.377359
$119$	−2.28668e10	−	4.04375e11i	−0.0878410	−	1.55338i
$120$		0			0
$121$	5.73145e10	−	9.92717e10i	0.200884	−	0.347941i
$122$	1.83310e10	+	3.17502e10i	0.0614054	+	0.106357i
$123$		0			0
$124$	5.59668e10	−	9.69374e10i	0.171440	−	0.296942i
$125$	2.03899e11			0.597599
$126$		0			0
$127$	5.61600e9			0.0150837			0.00754183	−	0.999972i	$-0.497599\pi$
$127$	5.61600e9			0.0150837			0.00754183	+	0.999972i	$0.497599\pi$
$128$	1.71799e10	−	2.97564e10i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−6.66200e10	−	1.15389e11i	−0.157368	−	0.272569i
$131$	3.24628e11	−	5.62272e11i	0.735180	−	1.27337i	−0.219464	−	0.975621i	$-0.570431\pi$
$131$	3.24628e11	−	5.62272e11i	0.735180	−	1.27337i	0.954644	−	0.297749i	$-0.0962358\pi$
$132$		0			0
$133$	−9.24916e10	+	6.06091e10i	−0.192716	+	0.126286i
$134$	3.72519e11			0.744855
$135$		0			0
$136$	1.49231e11	+	2.58476e11i	0.275039	+	0.476382i
$137$	4.90376e10	+	8.49356e10i	0.0868093	+	0.150358i	0.906161	−	0.422933i	$-0.139000\pi$
$137$	4.90376e10	+	8.49356e10i	0.0868093	+	0.150358i	−0.819351	+	0.573292i	$0.805666\pi$
$138$		0			0
$139$	1.01778e12			1.66369			0.831846	−	0.555007i	$-0.187284\pi$
$139$	1.01778e12			1.66369			0.831846	+	0.555007i	$0.187284\pi$
$140$	−8.92989e10	−	4.50367e10i	−0.140327	−	0.0707721i
$141$		0			0
$142$	−8.39931e10	+	1.45480e11i	−0.122084	+	0.211455i
$143$	3.91590e11	+	6.78254e11i	0.547625	+	0.948515i
$144$		0			0
$145$	8.70406e10	−	1.50759e11i	0.112771	−	0.195325i
$146$	5.60071e11			0.698719
$147$		0			0
$148$	6.92821e11			0.802014
$149$	2.04842e11	−	3.54797e11i	0.228505	−	0.395782i	−0.728861	−	0.684662i	$-0.759950\pi$
$149$	2.04842e11	−	3.54797e11i	0.228505	−	0.395782i	0.957365	+	0.288881i	$0.0932831\pi$
$150$		0			0
$151$	1.75347e11	+	3.03711e11i	0.181772	+	0.314838i	0.942484	−	0.334252i	$-0.108484\pi$
$151$	1.75347e11	+	3.03711e11i	0.181772	+	0.314838i	−0.760712	+	0.649089i	$0.775150\pi$
$152$	4.07438e10	−	7.05703e10i	0.0407307	−	0.0705476i
$153$		0			0
$154$	5.24896e11	+	2.64724e11i	0.488326	+	0.246280i
$155$	2.40092e11			0.215553
$156$		0			0
$157$	−2.34655e11	−	4.06435e11i	−0.196328	−	0.340050i	0.751007	−	0.660294i	$-0.229568\pi$
$157$	−2.34655e11	−	4.06435e11i	−0.196328	−	0.340050i	−0.947335	+	0.320244i	$0.896235\pi$
$158$	−6.78527e11	−	1.17524e12i	−0.548218	−	0.949541i
$159$		0			0
$160$	7.37000e10			0.0555658
$161$	−2.19786e12	+	1.44024e12i	−1.60125	+	1.04929i
$162$		0			0
$163$	1.04916e12	−	1.81719e12i	0.714182	−	1.23700i	−0.249092	−	0.968480i	$-0.580132\pi$
$163$	1.04916e12	−	1.81719e12i	0.714182	−	1.23700i	0.963274	−	0.268520i	$-0.0865345\pi$
$164$	1.29264e11	+	2.23892e11i	0.0850816	+	0.147366i
$165$		0			0
$166$	1.35469e11	−	2.34640e11i	0.0834155	−	0.144480i
$167$	1.60121e12			0.953912			0.476956	−	0.878927i	$-0.341740\pi$
$167$	1.60121e12			0.953912			0.476956	+	0.878927i	$0.341740\pi$
$168$		0			0
$169$	1.80148e12			1.00520
$170$	−3.20093e11	+	5.54417e11i	−0.172905	+	0.299480i
$171$		0			0
$172$	8.97029e11	+	1.55370e12i	0.454360	+	0.786974i
$173$	−1.50220e12	+	2.60189e12i	−0.737012	+	1.27654i	0.216823	+	0.976211i	$0.430430\pi$
$173$	−1.50220e12	+	2.60189e12i	−0.737012	+	1.27654i	−0.953835	+	0.300331i	$0.902903\pi$
$174$		0			0
$175$	1.10473e11	+	1.95360e12i	0.0508801	+	0.899761i
$176$	−4.33206e11			−0.193364
$177$		0			0
$178$	2.99606e11	+	5.18933e11i	0.125673	+	0.217671i
$179$	7.74326e11	+	1.34117e12i	0.314943	+	0.545497i	0.979425	−	0.201807i	$-0.0646812\pi$
$179$	7.74326e11	+	1.34117e12i	0.314943	+	0.545497i	−0.664482	+	0.747304i	$0.731348\pi$
$180$		0			0
$181$	−2.86403e12			−1.09584			−0.547918	−	0.836532i	$-0.684579\pi$
$181$	−2.86403e12			−1.09584			−0.547918	+	0.836532i	$0.684579\pi$
$182$	2.25620e12	−	1.47847e12i	0.837501	−	0.548809i
$183$		0			0
$184$	9.68188e11	−	1.67695e12i	0.338424	−	0.586168i
$185$	7.43034e11	+	1.28697e12i	0.252095	+	0.436641i
$186$		0			0
$187$	1.88150e12	−	3.25885e12i	0.601693	−	1.04216i
$188$	−2.64577e12			−0.821646
$189$		0			0
$190$	1.74787e11			0.0512111
$191$	−2.43222e12	+	4.21273e12i	−0.692340	+	1.19917i	0.278729	+	0.960370i	$0.410087\pi$
$191$	−2.43222e12	+	4.21273e12i	−0.692340	+	1.19917i	−0.971069	+	0.238798i	$0.923247\pi$
$192$		0			0
$193$	1.58703e12	+	2.74881e12i	0.426598	+	0.738890i	0.996568	−	0.0827756i	$-0.0263785\pi$
$193$	1.58703e12	+	2.74881e12i	0.426598	+	0.738890i	−0.569970	+	0.821666i	$0.693045\pi$
$194$	1.65319e12	−	2.86340e12i	0.431929	−	0.748122i
$195$		0			0
$196$	8.08252e11	−	1.85647e12i	0.199590	−	0.458436i
$197$	6.68041e12			1.60413			0.802064	−	0.597238i	$-0.203735\pi$
$197$	6.68041e12			1.60413			0.802064	+	0.597238i	$0.203735\pi$
$198$		0			0
$199$	6.07895e11	+	1.05291e12i	0.138082	+	0.239165i	0.926771	−	0.375628i	$-0.122573\pi$
$199$	6.07895e11	+	1.05291e12i	0.138082	+	0.239165i	−0.788689	+	0.614793i	$0.789240\pi$
$200$	−7.20959e11	−	1.24874e12i	−0.159311	−	0.275934i
$201$		0			0
$202$	−2.00462e12			−0.419371
$203$	3.14676e12	+	1.58702e12i	0.640671	+	0.323114i
$204$		0			0
$205$	−2.77265e11	+	4.80236e11i	−0.0534870	+	0.0926422i
$206$	8.68379e11	+	1.50408e12i	0.163095	+	0.282488i
$207$		0			0
$208$	−9.93887e11	+	1.72146e12i	−0.177006	+	0.306584i
$209$	−1.02739e12			−0.178210
$210$		0			0
$211$	−5.96917e12			−0.982563			−0.491282	−	0.871001i	$-0.663471\pi$
$211$	−5.96917e12			−0.982563			−0.491282	+	0.871001i	$0.663471\pi$
$212$	2.50570e12	−	4.33999e12i	0.401866	−	0.696052i
$213$		0			0
$214$	1.22380e12	+	2.11969e12i	0.186395	+	0.322846i
$215$	−1.92408e12	+	3.33261e12i	−0.285636	+	0.494735i
$216$		0			0
$217$	2.74427e11	+	4.85296e12i	0.0387167	+	0.684665i
$218$	5.28634e12			0.727184
$219$		0			0
$220$	−4.64603e11	−	8.04716e11i	−0.0607795	−	0.105273i
$221$	−8.63328e12	−	1.49533e13i	−1.10159	−	1.90800i
$222$		0			0
$223$	−7.21084e12			−0.875607			−0.437804	−	0.899071i	$-0.644243\pi$
$223$	−7.21084e12			−0.875607			−0.437804	+	0.899071i	$0.644243\pi$
$224$	8.42396e10	+	1.48969e12i	0.00998050	+	0.176495i
$225$		0			0
$226$	1.92728e12	−	3.33814e12i	0.217444	−	0.376625i
$227$	−2.76893e12	−	4.79593e12i	−0.304909	−	0.528118i	0.672332	−	0.740250i	$-0.265293\pi$
$227$	−2.76893e12	−	4.79593e12i	−0.304909	−	0.528118i	−0.977241	+	0.212132i	$0.931959\pi$
$228$		0			0
$229$	−3.76757e12	+	6.52561e12i	−0.395335	+	0.684741i	−0.993144	−	0.116898i	$-0.962705\pi$
$229$	−3.76757e12	+	6.52561e12i	−0.395335	+	0.684741i	0.597809	+	0.801639i	$0.296038\pi$
$230$	4.15343e12			0.425504
$231$		0			0
$232$	−2.59707e12			−0.253688
$233$	−3.13160e11	+	5.42409e11i	−0.0298751	+	0.0517451i	−0.880576	−	0.473904i	$-0.842844\pi$
$233$	−3.13160e11	+	5.42409e11i	−0.0298751	+	0.0517451i	0.850701	+	0.525649i	$0.176178\pi$
$234$		0			0
$235$	−2.83753e12	−	4.91474e12i	−0.258266	−	0.447329i
$236$	−1.50046e12	+	2.59888e12i	−0.133416	+	0.231084i
$237$		0			0
$238$	−1.15723e13	−	5.83630e12i	−0.982301	−	0.495410i
$239$	−1.71468e13			−1.42231			−0.711154	−	0.703037i	$-0.751827\pi$
$239$	−1.71468e13			−1.42231			−0.711154	+	0.703037i	$0.751827\pi$
$240$		0			0
$241$	1.60918e12	+	2.78718e12i	0.127500	+	0.220837i	0.922707	−	0.385501i	$-0.125971\pi$
$241$	1.60918e12	+	2.78718e12i	0.127500	+	0.220837i	−0.795207	+	0.606338i	$0.792638\pi$
$242$	−1.83407e12	−	3.17669e12i	−0.142046	−	0.246032i
$243$		0			0
$244$	1.17318e12			0.0868403
$245$	4.31537e12	−	4.89621e11i	0.312324	−	0.0354361i
$246$		0			0
$247$	−2.35710e12	+	4.08262e12i	−0.163134	+	0.282557i
$248$	−1.79094e12	−	3.10200e12i	−0.121226	−	0.209970i
$249$		0			0
$250$	3.26238e12	−	5.65061e12i	0.211283	−	0.365953i
$251$	−1.76163e13			−1.11611			−0.558057	−	0.829803i	$-0.688453\pi$
$251$	−1.76163e13			−1.11611			−0.558057	+	0.829803i	$0.688453\pi$
$252$		0			0
$253$	−2.44137e13			−1.48071
$254$	8.98561e10	−	1.55635e11i	0.00533288	−	0.00923682i
$255$		0			0
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−6.40081e12	+	1.10865e13i	−0.356125	+	0.616827i	−0.987310	−	0.158805i	$-0.949236\pi$
$257$	−6.40081e12	+	1.10865e13i	−0.356125	+	0.616827i	0.631184	+	0.775633i	$0.282569\pi$
$258$		0			0
$259$	−2.51642e13	+	1.64899e13i	−1.34163	+	0.879162i
$260$	−4.26368e12			−0.222552
$261$		0			0
$262$	−1.03881e13	−	1.79927e13i	−0.519851	−	0.900408i
$263$	−7.22781e12	−	1.25189e13i	−0.354201	−	0.613495i	0.632780	−	0.774332i	$-0.281914\pi$
$263$	−7.22781e12	−	1.25189e13i	−0.354201	−	0.613495i	−0.986981	+	0.160837i	$0.948581\pi$
$264$		0			0
$265$	1.07492e13			0.505270
$266$	1.99783e11	+	3.53295e12i	0.00919833	+	0.162663i
$267$		0			0
$268$	5.96030e12	−	1.03235e13i	0.263346	−	0.456129i
$269$	2.42568e12	+	4.20141e12i	0.105002	+	0.181868i	0.913739	−	0.406302i	$-0.133182\pi$
$269$	2.42568e12	+	4.20141e12i	0.105002	+	0.181868i	−0.808737	+	0.588170i	$0.799848\pi$
$270$		0			0
$271$	2.06716e13	−	3.58043e13i	0.859100	−	1.48800i	−0.0136892	−	0.999906i	$-0.504358\pi$
$271$	2.06716e13	−	3.58043e13i	0.859100	−	1.48800i	0.872789	−	0.488098i	$-0.162309\pi$
$272$	9.55078e12			0.388964
$273$		0			0
$274$	3.13841e12			0.122767
$275$	−9.08981e12	+	1.57440e13i	−0.348518	+	0.603651i
$276$		0			0
$277$	1.64215e12	+	2.84429e12i	0.0605026	+	0.104794i	0.894690	−	0.446687i	$-0.147396\pi$
$277$	1.64215e12	+	2.84429e12i	0.0605026	+	0.104794i	−0.834188	+	0.551481i	$0.814063\pi$
$278$	1.62845e13	−	2.82056e13i	0.588204	−	1.01880i
$279$		0			0
$280$	−2.67688e12	+	1.75414e12i	−0.0929521	+	0.0609108i
$281$	2.08840e13			0.711097			0.355549	−	0.934658i	$-0.384294\pi$
$281$	2.08840e13			0.711097			0.355549	+	0.934658i	$0.384294\pi$
$282$		0			0
$283$	−7.45841e12	−	1.29183e13i	−0.244242	−	0.423040i	0.717676	−	0.696377i	$-0.245206\pi$
$283$	−7.45841e12	−	1.29183e13i	−0.244242	−	0.423040i	−0.961918	+	0.273337i	$0.911873\pi$
$284$	2.68778e12	+	4.65537e12i	0.0863263	+	0.149521i
$285$		0			0
$286$	2.50618e13			0.774459
$287$	−1.00239e13	−	5.05541e12i	−0.303868	−	0.153252i
$288$		0			0
$289$	−2.43449e13	+	4.21666e13i	−0.710346	+	1.23036i
$290$	−2.78530e12	−	4.82428e12i	−0.0797412	−	0.138116i
$291$		0			0
$292$	8.96114e12	−	1.55211e13i	0.247034	−	0.427876i
$293$	−6.23932e13			−1.68797			−0.843986	−	0.536366i	$-0.819797\pi$
$293$	−6.23932e13			−1.68797			−0.843986	+	0.536366i	$0.819797\pi$
$294$		0			0
$295$	−6.43684e12			−0.167746
$296$	1.10851e13	−	1.92000e13i	0.283555	−	0.491131i
$297$		0			0
$298$	−6.55495e12	−	1.13535e13i	−0.161577	−	0.279860i
$299$	−5.60114e13	+	9.70146e13i	−1.35546	+	2.34772i
$300$		0			0
$301$	−6.95609e13	−	3.50821e13i	−1.62274	−	0.818408i
$302$	1.12222e13			0.257064
$303$		0			0
$304$	−1.30380e12	−	2.25825e12i	−0.0288009	−	0.0498847i
$305$	1.25821e12	+	2.17928e12i	0.0272963	+	0.0472786i
$306$		0			0
$307$	3.87055e13			0.810050			0.405025	−	0.914306i	$-0.367263\pi$
$307$	3.87055e13			0.810050			0.405025	+	0.914306i	$0.367263\pi$
$308$	1.57346e13	−	1.03108e13i	0.323465	−	0.211964i
$309$		0			0
$310$	3.84147e12	−	6.65363e12i	0.0762094	−	0.131999i
$311$	2.53578e13	+	4.39210e13i	0.494231	+	0.856033i	0.999978	−	0.00664890i	$-0.00211643\pi$
$311$	2.53578e13	+	4.39210e13i	0.494231	+	0.856033i	−0.505747	+	0.862682i	$0.668783\pi$
$312$		0			0
$313$	−7.29975e12	+	1.26435e13i	−0.137345	+	0.237889i	−0.926491	−	0.376317i	$-0.877190\pi$
$313$	−7.29975e12	+	1.26435e13i	−0.137345	+	0.237889i	0.789146	+	0.614206i	$0.210524\pi$
$314$	−1.50179e13			−0.277650
$315$		0			0
$316$	−4.34257e13			−0.775297
$317$	1.62473e13	−	2.81412e13i	0.285073	−	0.493761i	−0.687554	−	0.726133i	$-0.741315\pi$
$317$	1.62473e13	−	2.81412e13i	0.285073	−	0.493761i	0.972627	+	0.232372i	$0.0746488\pi$
$318$		0			0
$319$	1.63719e13	+	2.83570e13i	0.277492	+	0.480630i
$320$	1.17920e12	−	2.04243e12i	0.0196455	−	0.0340269i
$321$		0			0
$322$	4.74740e12	+	8.39529e13i	0.0764274	+	1.35154i
$323$	2.26506e13			0.358481
$324$		0			0
$325$	4.17088e13	+	7.22417e13i	0.638071	+	1.10517i
$326$	−3.35730e13	−	5.81502e13i	−0.505003	−	0.874691i
$327$		0			0
$328$	8.27288e12			0.120324
$329$	9.60979e13	−	6.29722e13i	1.37447	−	0.900683i
$330$		0			0
$331$	4.44555e13	−	7.69992e13i	0.614995	−	1.06520i	−0.375391	−	0.926867i	$-0.622491\pi$
$331$	4.44555e13	−	7.69992e13i	0.614995	−	1.06520i	0.990385	−	0.138336i	$-0.0441753\pi$
$332$	−4.33502e12	−	7.50848e12i	−0.0589837	−	0.102163i
$333$		0			0
$334$	2.56194e13	−	4.43741e13i	0.337259	−	0.584149i
$335$	2.55691e13			0.331108
$336$		0			0
$337$	1.66318e13			0.208437			0.104219	−	0.994554i	$-0.466766\pi$
$337$	1.66318e13			0.208437			0.104219	+	0.994554i	$0.466766\pi$
$338$	2.88236e13	−	4.99240e13i	0.355391	−	0.615556i
$339$		0			0
$340$	1.02430e13	+	1.77414e13i	0.122262	+	0.211764i
$341$	−2.25801e13	+	3.91098e13i	−0.265202	+	0.459343i
$342$		0			0
$343$	1.48292e13	+	8.66665e13i	0.168655	+	0.985675i
$344$	5.74098e13			0.642562
$345$		0			0
$346$	4.80704e13	+	8.32604e13i	0.521146	+	0.902651i
$347$	−3.13085e13	−	5.42279e13i	−0.334080	−	0.578643i	0.649228	−	0.760594i	$-0.275092\pi$
$347$	−3.13085e13	−	5.42279e13i	−0.334080	−	0.578643i	−0.983308	+	0.181951i	$0.941759\pi$
$348$		0			0
$349$	−6.87125e13			−0.710389			−0.355194	−	0.934792i	$-0.615585\pi$
$349$	−6.87125e13			−0.710389			−0.355194	+	0.934792i	$0.615585\pi$
$350$	5.59074e13	+	2.81961e13i	0.568978	+	0.286956i
$351$		0			0
$352$	−6.93130e12	+	1.20054e13i	−0.0683644	+	0.118411i
$353$	8.42583e13	+	1.45940e14i	0.818186	+	1.41714i	0.907018	+	0.421093i	$0.138353\pi$
$353$	8.42583e13	+	1.45940e14i	0.818186	+	1.41714i	−0.0888317	+	0.996047i	$0.528313\pi$
$354$		0			0
$355$	−5.76516e12	+	9.98555e12i	−0.0542694	+	0.0939974i
$356$	1.91748e13			0.177728
$357$		0			0
$358$	4.95569e13			0.445397
$359$	1.41556e13	−	2.45182e13i	0.125288	−	0.217005i	−0.796558	−	0.604563i	$-0.793348\pi$
$359$	1.41556e13	−	2.45182e13i	0.125288	−	0.217005i	0.921845	+	0.387558i	$0.126681\pi$
$360$		0			0
$361$	5.51530e13	+	9.55279e13i	0.473456	+	0.820050i
$362$	−4.58245e13	+	7.93703e13i	−0.387436	+	0.671059i
$363$		0			0
$364$	−4.87342e12	−	8.61813e13i	−0.0399739	−	0.706896i
$365$	3.84424e13			0.310599
$366$		0			0
$367$	−9.23617e13	−	1.59975e14i	−0.724150	−	1.25427i	−0.959323	−	0.282312i	$-0.908899\pi$
$367$	−9.23617e13	−	1.59975e14i	−0.724150	−	1.25427i	0.235172	−	0.971954i	$-0.424435\pi$
$368$	−3.09820e13	−	5.36624e13i	−0.239302	−	0.414483i
$369$		0			0
$370$	4.75542e13			0.356516
$371$	1.22864e13	+	2.17272e14i	0.0907546	+	1.60490i
$372$		0			0
$373$	6.80240e12	−	1.17821e13i	0.0487825	−	0.0844937i	−0.840603	−	0.541652i	$-0.817799\pi$
$373$	6.80240e12	−	1.17821e13i	0.0487825	−	0.0844937i	0.889386	+	0.457158i	$0.151133\pi$
$374$	−6.02079e13	−	1.04283e14i	−0.425461	−	0.736920i
$375$		0			0
$376$	−4.23324e13	+	7.33218e13i	−0.290496	+	0.503153i
$377$	1.50246e14			1.01607
$378$		0			0
$379$	−1.45859e14			−0.958113			−0.479057	−	0.877784i	$-0.659021\pi$
$379$	−1.45859e14			−0.958113			−0.479057	+	0.877784i	$0.659021\pi$
$380$	2.79659e12	−	4.84384e12i	0.0181059	−	0.0313603i
$381$		0			0
$382$	7.78310e13	+	1.34807e14i	0.489558	+	0.847940i
$383$	−8.99451e13	+	1.55789e14i	−0.557679	+	0.965928i	0.440011	+	0.897992i	$0.354975\pi$
$383$	−8.99451e13	+	1.55789e14i	−0.557679	+	0.965928i	−0.997690	+	0.0679355i	$0.978359\pi$
$384$		0			0
$385$	3.60281e13	+	1.81703e13i	0.217074	+	0.109478i
$386$	1.01570e14			0.603301
$387$		0			0
$388$	−5.29019e13	−	9.16288e13i	−0.305420	−	0.529002i
$389$	−1.28981e14	−	2.23401e14i	−0.734180	−	1.27164i	−0.955082	−	0.296340i	$-0.904234\pi$
$389$	−1.28981e14	−	2.23401e14i	−0.734180	−	1.27164i	0.220903	−	0.975296i	$-0.429100\pi$
$390$		0			0
$391$	5.38243e14			2.97856
$392$	−3.85159e13	−	5.21024e13i	−0.210168	−	0.284305i
$393$		0			0
$394$	1.06887e14	−	1.85133e14i	0.567145	−	0.982324i
$395$	−4.65730e13	−	8.06668e13i	−0.243697	−	0.422096i
$396$		0			0
$397$	1.42077e14	−	2.46084e14i	0.723061	−	1.25238i	−0.236706	−	0.971581i	$-0.576068\pi$
$397$	1.42077e14	−	2.46084e14i	0.723061	−	1.25238i	0.959767	−	0.280797i	$-0.0905989\pi$
$398$	3.89053e13			0.195277
$399$		0			0
$400$	−4.61414e13			−0.225300
$401$	−5.22923e13	+	9.05729e13i	−0.251851	+	0.436218i	−0.964035	−	0.265774i	$-0.914373\pi$
$401$	−5.22923e13	+	9.05729e13i	−0.251851	+	0.436218i	0.712185	+	0.701992i	$0.247706\pi$
$402$		0			0
$403$	1.03609e14	+	1.79456e14i	0.485534	+	0.840970i
$404$	−3.20738e13	+	5.55535e13i	−0.148270	+	0.256811i
$405$		0			0
$406$	9.43291e13	−	6.18132e13i	0.424377	−	0.278092i
$407$	−2.79522e14			−1.24064
$408$		0			0
$409$	−2.25545e13	−	3.90656e13i	−0.0974441	−	0.168778i	0.813182	−	0.582010i	$-0.197733\pi$
$409$	−2.25545e13	−	3.90656e13i	−0.0974441	−	0.168778i	−0.910626	+	0.413231i	$0.864400\pi$
$410$	8.87247e12	+	1.53676e13i	0.0378210	+	0.0655079i
$411$		0			0
$412$	5.55763e13			0.230651
$413$	−7.35736e12	−	1.30107e14i	−0.0301298	−	0.532814i
$414$		0			0
$415$	9.29841e12	−	1.61053e13i	0.0370804	−	0.0642251i
$416$	3.18044e13	+	5.50868e13i	0.125162	+	0.216788i
$417$		0			0
$418$	−1.64383e13	+	2.84719e13i	−0.0630067	+	0.109131i
$419$	1.89082e14			0.715276			0.357638	−	0.933860i	$-0.383582\pi$
$419$	1.89082e14			0.715276			0.357638	+	0.933860i	$0.383582\pi$
$420$		0			0
$421$	2.40145e14			0.884955			0.442478	−	0.896780i	$-0.354100\pi$
$421$	2.40145e14			0.884955			0.442478	+	0.896780i	$0.354100\pi$
$422$	−9.55067e13	+	1.65423e14i	−0.347389	+	0.601695i
$423$		0			0
$424$	−8.01823e13	−	1.38880e14i	−0.284162	−	0.492183i
$425$	2.00401e14	−	3.47104e14i	0.701068	−	1.21429i
$426$		0			0
$427$	−4.26115e13	+	2.79230e13i	−0.145269	+	0.0951938i
$428$	7.83233e13			0.263603
$429$		0			0
$430$	6.15707e13	+	1.06644e14i	0.201975	+	0.349831i
$431$	−2.70880e13	−	4.69177e13i	−0.0877306	−	0.151954i	0.818821	−	0.574049i	$-0.194628\pi$
$431$	−2.70880e13	−	4.69177e13i	−0.0877306	−	0.151954i	−0.906552	+	0.422095i	$0.861295\pi$
$432$		0			0
$433$	−3.19018e14			−1.00724			−0.503619	−	0.863926i	$-0.667999\pi$
$433$	−3.19018e14			−1.00724			−0.503619	+	0.863926i	$0.667999\pi$
$434$	1.38880e14	+	7.00422e13i	0.432958	+	0.218357i
$435$		0			0
$436$	8.45815e13	−	1.46499e14i	0.257098	−	0.445308i
$437$	−7.34769e13	−	1.27266e14i	−0.220548	−	0.382000i
$438$		0			0
$439$	2.34219e14	−	4.05680e14i	0.685596	−	1.18749i	−0.287653	−	0.957735i	$-0.592875\pi$
$439$	2.34219e14	−	4.05680e14i	0.685596	−	1.18749i	0.973249	−	0.229752i	$-0.0737916\pi$
$440$	−2.97346e13			−0.0859552
$441$		0			0
$442$	−5.52530e14			−1.55788
$443$	2.19487e13	−	3.80163e13i	0.0611208	−	0.105864i	−0.833846	−	0.551997i	$-0.813866\pi$
$443$	2.19487e13	−	3.80163e13i	0.0611208	−	0.105864i	0.894967	+	0.446133i	$0.147199\pi$
$444$		0			0
$445$	2.05645e13	+	3.56188e13i	0.0558648	+	0.0967606i
$446$	−1.15374e14	+	1.99833e14i	−0.309574	+	0.536198i
$447$		0			0
$448$	4.26313e13	+	2.15005e13i	0.111609	+	0.0562885i
$449$	−2.17474e14			−0.562409			−0.281204	−	0.959648i	$-0.590734\pi$
$449$	−2.17474e14			−0.562409			−0.281204	+	0.959648i	$0.590734\pi$
$450$		0			0
$451$	−5.21521e13	−	9.03301e13i	−0.131614	−	0.227961i
$452$	−6.16729e13	−	1.06821e14i	−0.153756	−	0.266314i
$453$		0			0
$454$	−1.77212e14			−0.431207
$455$	1.54862e14	−	1.01480e14i	0.372291	−	0.243960i
$456$		0			0
$457$	−4.03290e14	+	6.98518e14i	−0.946407	+	1.63923i	−0.193498	+	0.981101i	$0.561983\pi$
$457$	−4.03290e14	+	6.98518e14i	−0.946407	+	1.63923i	−0.752909	+	0.658125i	$0.771350\pi$
$458$	1.20562e14	+	2.08820e14i	0.279544	+	0.484185i
$459$		0			0
$460$	6.64549e13	−	1.15103e14i	0.150438	−	0.260567i
$461$	7.25880e14			1.62371			0.811857	−	0.583856i	$-0.198457\pi$
$461$	7.25880e14			1.62371			0.811857	+	0.583856i	$0.198457\pi$
$462$		0			0
$463$	−1.15814e14			−0.252968			−0.126484	−	0.991969i	$-0.540369\pi$
$463$	−1.15814e14			−0.252968			−0.126484	+	0.991969i	$0.540369\pi$
$464$	−4.15532e13	+	7.19722e13i	−0.0896924	+	0.155352i
$465$		0			0
$466$	1.00211e13	+	1.73571e13i	0.0211249	+	0.0365893i
$467$	3.43718e13	−	5.95337e13i	0.0716076	−	0.124028i	−0.827998	−	0.560730i	$-0.810520\pi$
$467$	3.43718e13	−	5.95337e13i	0.0716076	−	0.124028i	0.899606	+	0.436702i	$0.143854\pi$
$468$		0			0
$469$	2.92257e13	+	5.16826e14i	0.0594722	+	1.05170i
$470$	−1.81602e14			−0.365243
$471$		0			0
$472$	4.80148e13	+	8.31641e13i	0.0943396	+	0.163401i
$473$	−3.61910e14	−	6.26847e14i	−0.702854	−	1.21738i
$474$		0			0
$475$	−1.09429e14			−0.207643
$476$	−3.46896e14	+	2.27319e14i	−0.650671	+	0.426380i
$477$		0			0
$478$	−2.74348e14	+	4.75185e14i	−0.502862	+	0.870982i
$479$	−5.74784e12	−	9.95556e12i	−0.0104150	−	0.0180393i	0.860771	−	0.508993i	$-0.169982\pi$
$479$	−5.74784e12	−	9.95556e12i	−0.0104150	−	0.0180393i	−0.871186	+	0.490953i	$0.836649\pi$
$480$		0			0
$481$	−6.41296e14	+	1.11076e15i	−1.13569	+	1.96708i
$482$	1.02988e14			0.180313
$483$		0			0
$484$	−1.17380e14			−0.200884
$485$	1.13472e14	−	1.96539e14i	0.192004	−	0.332560i
$486$		0			0
$487$	−3.39579e14	−	5.88168e14i	−0.561735	−	0.972954i	−0.997345	−	0.0728186i	$-0.976801\pi$
$487$	−3.39579e14	−	5.88168e14i	−0.561735	−	0.972954i	0.435610	−	0.900136i	$-0.356533\pi$
$488$	1.87709e13	−	3.25122e13i	0.0307027	−	0.0531786i
$489$		0			0
$490$	5.54772e13	−	1.27425e14i	0.0887230	−	0.203787i
$491$	9.19715e13			0.145447			0.0727235	−	0.997352i	$-0.476831\pi$
$491$	9.19715e13			0.145447			0.0727235	+	0.997352i	$0.476831\pi$
$492$		0			0
$493$	−3.60947e14	−	6.25178e14i	−0.558194	−	0.966821i
$494$	7.54273e13	+	1.30644e14i	0.115353	+	0.199798i
$495$		0			0
$496$	−1.14620e14			−0.171440
$497$	−2.08426e14	−	1.05117e14i	−0.308314	−	0.155494i
$498$		0			0
$499$	5.10323e14	−	8.83905e14i	0.738400	−	1.27895i	−0.214815	−	0.976655i	$-0.568915\pi$
$499$	5.10323e14	−	8.83905e14i	0.738400	−	1.27895i	0.953215	−	0.302292i	$-0.0977518\pi$
$500$	−1.04396e14	−	1.80820e14i	−0.149400	−	0.258768i
$501$		0			0
$502$	−2.81860e14	+	4.88196e14i	−0.394606	+	0.683477i
$503$	1.64199e14			0.227377			0.113689	−	0.993516i	$-0.463733\pi$
$503$	1.64199e14			0.227377			0.113689	+	0.993516i	$0.463733\pi$
$504$		0			0
$505$	−1.37594e14			−0.186421
$506$	−3.90620e14	+	6.76573e14i	−0.523512	+	0.906749i
$507$		0			0
$508$	−2.87539e12	−	4.98033e12i	−0.00377092	−	0.00653142i
$509$	−4.17114e14	+	7.22463e14i	−0.541137	+	0.937276i	0.457702	+	0.889105i	$0.348673\pi$
$509$	−4.17114e14	+	7.22463e14i	−0.541137	+	0.937276i	−0.998839	+	0.0481709i	$0.984661\pi$
$510$		0			0
$511$	4.39400e13	+	7.77032e14i	0.0557885	+	0.986561i
$512$	−3.51844e13			−0.0441942
$513$		0			0
$514$	2.04826e14	+	3.54769e14i	0.251819	+	0.436163i
$515$	5.96042e13	+	1.03237e14i	0.0724998	+	0.125573i
$516$		0			0
$517$	1.06745e15			1.27101
$518$	5.43548e13	+	9.61208e14i	0.0640360	+	1.13241i
$519$		0			0
$520$	−6.82188e13	+	1.18159e14i	−0.0786839	+	0.136285i
$521$	2.31769e14	+	4.01435e14i	0.264513	+	0.458150i	0.967436	−	0.253116i	$-0.0814554\pi$
$521$	2.31769e14	+	4.01435e14i	0.264513	+	0.458150i	−0.702923	+	0.711266i	$0.748122\pi$
$522$		0			0
$523$	5.66164e13	−	9.80626e13i	0.0632679	−	0.109583i	−0.832656	−	0.553790i	$-0.813181\pi$
$523$	5.66164e13	−	9.80626e13i	0.0632679	−	0.109583i	0.895924	+	0.444207i	$0.146514\pi$
$524$	−6.64838e14			−0.735180
$525$		0			0
$526$	−4.62580e14			−0.500916
$527$	4.97817e14	−	8.62244e14i	0.533471	−	0.924000i
$528$		0			0
$529$	−1.26962e15	−	2.19904e15i	−1.33250	−	2.30795i
$530$	1.71987e14	−	2.97890e14i	0.178640	−	0.309413i
$531$		0			0
$532$	1.01104e14	+	5.09906e13i	0.102862	+	0.0518772i
$533$	−4.78602e14			−0.481919
$534$		0			0
$535$	8.39998e13	+	1.45492e14i	0.0828576	+	0.143514i
$536$	−1.90730e14	−	3.30353e14i	−0.186214	−	0.322532i
$537$		0			0
$538$	1.55244e14			0.148495
$539$	−3.26093e14	+	7.49000e14i	−0.308748	+	0.709159i
$540$		0			0
$541$	1.17921e14	−	2.04245e14i	0.109397	−	0.189481i	−0.806129	−	0.591740i	$-0.798441\pi$
$541$	1.17921e14	−	2.04245e14i	0.109397	−	0.189481i	0.915526	+	0.402258i	$0.131775\pi$
$542$	−6.61492e14	−	1.14574e15i	−0.607475	−	1.05218i
$543$		0			0
$544$	1.52812e14	−	2.64679e14i	0.137520	−	0.238191i
$545$	3.62846e14			0.323252
$546$		0			0
$547$	3.36340e14			0.293662			0.146831	−	0.989162i	$-0.453093\pi$
$547$	3.36340e14			0.293662			0.146831	+	0.989162i	$0.453093\pi$
$548$	5.02145e13	−	8.69741e13i	0.0434046	−	0.0751790i
$549$		0			0
$550$	2.90874e14	+	5.03809e14i	0.246439	+	0.426846i
$551$	−9.85476e13	+	1.70689e14i	−0.0826632	+	0.143177i
$552$		0			0
$553$	1.57728e15	−	1.03358e15i	1.29694	−	0.849875i
$554$	1.05098e14			0.0855636
$555$		0			0
$556$	−5.21104e14	−	9.02578e14i	−0.415923	−	0.720399i
$557$	6.00397e14	+	1.03992e15i	0.474498	+	0.821855i	0.999574	−	0.0292007i	$-0.00929620\pi$
$557$	6.00397e14	+	1.03992e15i	0.474498	+	0.821855i	−0.525075	+	0.851056i	$0.675963\pi$
$558$		0			0
$559$	−3.32127e15			−2.57359
$560$	5.78208e12	+	1.02250e14i	0.00443659	+	0.0784565i
$561$		0			0
$562$	3.34144e14	−	5.78754e14i	0.251411	−	0.435456i
$563$	9.61397e13	+	1.66519e14i	0.0716319	+	0.124070i	0.899617	−	0.436681i	$-0.143846\pi$
$563$	9.61397e13	+	1.66519e14i	0.0716319	+	0.124070i	−0.827985	+	0.560751i	$0.810513\pi$
$564$		0			0
$565$	1.32285e14	−	2.29125e14i	0.0966597	−	0.167420i
$566$	−4.77338e14			−0.345411
$567$		0			0
$568$	1.72018e14			0.122084
$569$	1.79609e14	−	3.11093e14i	0.126244	−	0.218661i	−0.795974	−	0.605330i	$-0.793041\pi$
$569$	1.79609e14	−	3.11093e14i	0.126244	−	0.218661i	0.922219	+	0.386669i	$0.126374\pi$
$570$		0			0
$571$	5.64553e13	+	9.77834e13i	0.0389230	+	0.0674166i	0.884831	−	0.465913i	$-0.154274\pi$
$571$	5.64553e13	+	9.77834e13i	0.0389230	+	0.0674166i	−0.845908	+	0.533329i	$0.820941\pi$
$572$	4.00988e14	−	6.94532e14i	0.273813	−	0.474257i
$573$		0			0
$574$	−3.00482e14	+	1.96904e14i	−0.201281	+	0.131898i
$575$	−2.60034e15			−1.72527
$576$		0			0
$577$	−2.03777e14	−	3.52952e14i	−0.132644	−	0.229746i	0.792051	−	0.610455i	$-0.209013\pi$
$577$	−2.03777e14	−	3.52952e14i	−0.132644	−	0.229746i	−0.924695	+	0.380709i	$0.875680\pi$
$578$	7.79037e14	+	1.34933e15i	0.502291	+	0.869993i
$579$		0			0
$580$	−1.78259e14			−0.112771
$581$	3.36163e14	+	1.69539e14i	0.210660	+	0.106243i
$582$		0			0
$583$	−1.01093e15	+	1.75099e15i	−0.621650	+	1.07673i
$584$	−2.86756e14	−	4.96677e14i	−0.174680	−	0.302554i
$585$		0			0
$586$	−9.98291e14	+	1.72909e15i	−0.596788	+	1.03367i
$587$	−8.47437e14			−0.501878			−0.250939	−	0.968003i	$-0.580739\pi$
$587$	−8.47437e14			−0.501878			−0.250939	+	0.968003i	$0.580739\pi$
$588$		0			0
$589$	−2.71833e14			−0.158004
$590$	−1.02989e14	+	1.78383e14i	−0.0593071	+	0.102723i
$591$		0			0
$592$	−3.54725e14	−	6.14401e14i	−0.200503	−	0.347282i
$593$	1.12009e15	−	1.94006e15i	0.627267	−	1.08646i	−0.360830	−	0.932631i	$-0.617507\pi$
$593$	1.12009e15	−	1.94006e15i	0.627267	−	1.08646i	0.988098	−	0.153827i	$-0.0491600\pi$
$594$		0			0
$595$	−7.94301e14	−	4.00595e14i	−0.436658	−	0.220223i
$596$	−4.19517e14			−0.228505
$597$		0			0
$598$	1.79237e15	+	3.10447e15i	0.958452	+	1.66009i
$599$	2.49488e14	+	4.32127e14i	0.132191	+	0.228962i	0.924521	−	0.381131i	$-0.124465\pi$
$599$	2.49488e14	+	4.32127e14i	0.132191	+	0.228962i	−0.792330	+	0.610093i	$0.791132\pi$
$600$		0			0
$601$	3.23660e15			1.68375			0.841877	−	0.539669i	$-0.181451\pi$
$601$	3.23660e15			1.68375			0.841877	+	0.539669i	$0.181451\pi$
$602$	−2.08520e15	+	1.36642e15i	−1.07490	+	0.704372i
$603$		0			0
$604$	1.79556e14	−	3.11000e14i	0.0908858	−	0.157419i
$605$	−1.25887e14	−	2.18043e14i	−0.0631433	−	0.109367i
$606$		0			0
$607$	1.08736e15	−	1.88337e15i	0.535595	−	0.927677i	−0.463540	−	0.886076i	$-0.653421\pi$
$607$	1.08736e15	−	1.88337e15i	0.535595	−	0.927677i	0.999134	−	0.0416011i	$-0.0132459\pi$
$608$	−8.34433e13			−0.0407307
$609$		0			0
$610$	8.05254e13			0.0386028
$611$	2.44901e15	−	4.24180e15i	1.16349	−	2.01523i
$612$		0			0
$613$	−1.58056e15	−	2.73760e15i	−0.737526	−	1.27743i	−0.953606	−	0.301057i	$-0.902661\pi$
$613$	−1.58056e15	−	2.73760e15i	−0.737526	−	1.27743i	0.216080	−	0.976376i	$-0.430673\pi$
$614$	6.19288e14	−	1.07264e15i	0.286396	−	0.496052i
$615$		0			0
$616$	−3.39869e13	−	6.01022e14i	−0.0154389	−	0.273021i
$617$	−2.27574e14			−0.102460			−0.0512300	−	0.998687i	$-0.516314\pi$
$617$	−2.27574e14			−0.102460			−0.0512300	+	0.998687i	$0.516314\pi$
$618$		0			0
$619$	1.60371e15	+	2.77772e15i	0.709298	+	1.22854i	0.965118	+	0.261815i	$0.0843211\pi$
$619$	1.60371e15	+	2.77772e15i	0.709298	+	1.22854i	−0.255820	+	0.966724i	$0.582346\pi$
$620$	−1.22927e14	−	2.12916e14i	−0.0538882	−	0.0933371i
$621$		0			0
$622$	1.62290e15			0.698948
$623$	−6.96453e14	+	4.56381e14i	−0.297309	+	0.194824i
$624$		0			0
$625$	−8.50387e14	+	1.47291e15i	−0.356678	+	0.617785i
$626$	2.33592e14	+	4.04593e14i	0.0971179	+	0.168213i
$627$		0			0
$628$	−2.40287e14	+	4.16190e14i	−0.0981641	+	0.170025i
$629$	6.16255e15			2.49564
$630$		0			0
$631$	2.60523e15			1.03678			0.518389	−	0.855145i	$-0.326532\pi$
$631$	2.60523e15			1.03678			0.518389	+	0.855145i	$0.326532\pi$
$632$	−6.94811e14	+	1.20345e15i	−0.274109	+	0.474770i
$633$		0			0
$634$	−5.19915e14	−	9.00519e14i	−0.201577	−	0.349142i
$635$	6.16758e12	−	1.06826e13i	0.00237061	−	0.00410601i
$636$		0			0
$637$	2.22822e15	+	3.01422e15i	0.841764	+	1.13870i
$638$	1.04780e15			0.392433
$639$		0			0
$640$	−3.77344e13	−	6.53579e13i	−0.0138914	−	0.0240607i
$641$	−9.64829e14	−	1.67113e15i	−0.352153	−	0.609947i	0.634473	−	0.772945i	$-0.281217\pi$
$641$	−9.64829e14	−	1.67113e15i	−0.352153	−	0.609947i	−0.986626	+	0.162998i	$0.947884\pi$
$642$		0			0
$643$	−2.92728e15			−1.05028			−0.525139	−	0.851016i	$-0.675987\pi$
$643$	−2.92728e15			−1.05028			−0.525139	+	0.851016i	$0.675987\pi$
$644$	2.40253e15	+	1.21168e15i	0.854666	+	0.431039i
$645$		0			0
$646$	3.62410e14	−	6.27713e14i	0.126742	−	0.219524i
$647$	−2.34714e15	−	4.06536e15i	−0.813888	−	1.40970i	−0.910123	−	0.414337i	$-0.864013\pi$
$647$	−2.34714e15	−	4.06536e15i	−0.813888	−	1.40970i	0.0962350	−	0.995359i	$-0.469320\pi$
$648$		0			0
$649$	6.05369e14	−	1.04853e15i	0.206383	−	0.357466i
$650$	2.66936e15			0.902369
$651$		0			0
$652$	−2.14867e15			−0.714182
$653$	−1.46511e15	+	2.53765e15i	−0.482891	+	0.836391i	−0.999807	−	0.0196446i	$-0.993747\pi$
$653$	−1.46511e15	+	2.53765e15i	−0.482891	+	0.836391i	0.516916	+	0.856036i	$0.327080\pi$
$654$		0			0
$655$	−7.13023e14	−	1.23499e15i	−0.231087	−	0.400255i
$656$	1.32366e14	−	2.29265e14i	0.0425408	−	0.0736829i
$657$		0			0
$658$	−2.07572e14	−	3.67070e15i	−0.0656035	−	1.16013i
$659$	−9.39749e13			−0.0294538			−0.0147269	−	0.999892i	$-0.504688\pi$
$659$	−9.39749e13			−0.0294538			−0.0147269	+	0.999892i	$0.504688\pi$
$660$		0			0
$661$	1.81950e15	+	3.15147e15i	0.560847	+	0.971416i	0.997423	+	0.0717483i	$0.0228578\pi$
$661$	1.81950e15	+	3.15147e15i	0.560847	+	0.971416i	−0.436576	+	0.899668i	$0.643809\pi$
$662$	−1.42258e15	−	2.46397e15i	−0.434867	−	0.753212i
$663$		0			0
$664$	−2.77441e14			−0.0834155
$665$	1.37128e13	+	2.42496e14i	0.00408890	+	0.0723079i
$666$		0			0
$667$	−2.34177e15	+	4.05606e15i	−0.686834	+	1.18963i
$668$	−8.19821e14	−	1.41997e15i	−0.238478	−	0.413056i
$669$		0			0
$670$	4.09106e14	−	7.08592e14i	0.117064	−	0.202761i
$671$	−4.73326e14			−0.134334
$672$		0			0
$673$	5.20155e15			1.45228			0.726140	−	0.687547i	$-0.241313\pi$
$673$	5.20155e15			1.45228			0.726140	+	0.687547i	$0.241313\pi$
$674$	2.66109e14	−	4.60914e14i	0.0736936	−	0.127641i
$675$		0			0
$676$	−9.22356e14	−	1.59757e15i	−0.251300	−	0.435264i
$677$	−1.10820e15	+	1.91946e15i	−0.299489	+	0.518730i	−0.976019	−	0.217685i	$-0.930149\pi$
$677$	−1.10820e15	+	1.91946e15i	−0.299489	+	0.518730i	0.676530	+	0.736415i	$0.263483\pi$
$678$		0			0
$679$	4.10233e15	+	2.06895e15i	1.09080	+	0.550132i
$680$	6.55550e14			0.172905
$681$		0			0
$682$	7.22562e14	+	1.25151e15i	0.187526	+	0.324804i
$683$	2.53825e15	+	4.39637e15i	0.653461	+	1.13183i	0.982277	+	0.187434i	$0.0600171\pi$
$683$	2.53825e15	+	4.39637e15i	0.653461	+	1.13183i	−0.328816	+	0.944394i	$0.606650\pi$
$684$		0			0
$685$	2.15415e14			0.0545731
$686$	2.63904e15	+	9.75707e14i	0.663229	+	0.245209i
$687$		0			0
$688$	9.18558e14	−	1.59099e15i	0.227180	−	0.393487i
$689$	4.63869e15	+	8.03445e15i	1.13812	+	1.97129i
$690$		0			0
$691$	1.06653e15	−	1.84729e15i	0.257540	−	0.446073i	−0.708042	−	0.706170i	$-0.750421\pi$
$691$	1.06653e15	−	1.84729e15i	0.257540	−	0.446073i	0.965582	+	0.260097i	$0.0837547\pi$
$692$	3.07651e15			0.737012
$693$		0			0
$694$	−2.00375e15			−0.472460
$695$	1.11774e15	−	1.93599e15i	0.261472	−	0.452883i
$696$		0			0
$697$	1.14978e15	+	1.99148e15i	0.264750	+	0.458560i
$698$	−1.09940e15	+	1.90422e15i	−0.251160	+	0.435023i
$699$		0			0
$700$	1.67591e15	−	1.09821e15i	0.376888	−	0.246972i
$701$	−7.19614e15			−1.60565			−0.802825	−	0.596215i	$-0.796670\pi$
$701$	−7.19614e15			−1.60565			−0.802825	+	0.596215i	$0.796670\pi$
$702$		0			0
$703$	−8.41265e14	−	1.45711e15i	−0.184790	−	0.320066i
$704$	2.21802e14	+	3.84171e14i	0.0483409	+	0.0837289i
$705$		0			0
$706$	5.39253e15			1.15709
$707$	−1.57271e14	−	2.78117e15i	−0.0334843	−	0.592134i
$708$		0			0
$709$	1.78025e15	−	3.08348e15i	0.373187	−	0.646378i	−0.616867	−	0.787067i	$-0.711598\pi$
$709$	1.78025e15	−	3.08348e15i	0.373187	−	0.646378i	0.990054	+	0.140689i	$0.0449318\pi$
$710$	1.84485e14	+	3.19537e14i	0.0383743	+	0.0664662i
$711$		0			0
$712$	3.06797e14	−	5.31387e14i	0.0628363	−	0.108836i
$713$	−6.45952e15			−1.31283
$714$		0			0
$715$	1.72020e15			0.344267
$716$	7.92910e14	−	1.37336e15i	0.157472	−	0.272749i
$717$		0			0
$718$	−4.52979e14	−	7.84583e14i	−0.0885919	−	0.153446i
$719$	2.36049e15	−	4.08849e15i	0.458135	−	0.793513i	−0.540727	−	0.841198i	$-0.681851\pi$
$719$	2.36049e15	−	4.08849e15i	0.458135	−	0.793513i	0.998862	+	0.0476846i	$0.0151842\pi$
$720$		0			0
$721$	−2.01860e15	+	1.32277e15i	−0.385839	+	0.252838i
$722$	3.52979e15			0.669568
$723$		0			0
$724$	1.46638e15	+	2.53985e15i	0.273959	+	0.474511i
$725$	1.74379e15	+	3.02034e15i	0.323322	+	0.560011i
$726$		0			0
$727$	−3.86491e15			−0.705829			−0.352915	−	0.935656i	$-0.614809\pi$
$727$	−3.86491e15			−0.705829			−0.352915	+	0.935656i	$0.614809\pi$
$728$	−2.46630e15	−	1.24384e15i	−0.447016	−	0.225447i
$729$		0			0
$730$	6.15078e14	−	1.06535e15i	0.109813	−	0.190202i
$731$	7.97894e15	+	1.38199e16i	1.41384	+	2.44884i
$732$		0			0
$733$	3.55474e15	−	6.15699e15i	0.620492	−	1.07472i	−0.368902	−	0.929468i	$-0.620266\pi$
$733$	3.55474e15	−	6.15699e15i	0.620492	−	1.07472i	0.989394	−	0.145256i	$-0.0464004\pi$
$734$	−5.91115e15			−1.02410
$735$		0			0
$736$	−1.98285e15			−0.338424
$737$	−2.40471e15	+	4.16508e15i	−0.407373	+	0.705590i
$738$		0			0
$739$	2.49707e15	+	4.32505e15i	0.416760	+	0.721849i	0.995611	−	0.0935840i	$-0.0298324\pi$
$739$	2.49707e15	+	4.32505e15i	0.416760	+	0.721849i	−0.578852	+	0.815433i	$0.696499\pi$
$740$	7.60867e14	−	1.31786e15i	0.126047	−	0.218321i
$741$		0			0
$742$	6.21781e15	+	3.13587e15i	1.01488	+	0.511842i
$743$	−7.94563e15			−1.28733			−0.643665	−	0.765307i	$-0.722587\pi$
$743$	−7.94563e15			−1.28733			−0.643665	+	0.765307i	$0.722587\pi$
$744$		0			0
$745$	−4.49922e14	−	7.79287e14i	−0.0718253	−	0.124405i
$746$	−2.17677e14	−	3.77027e14i	−0.0344944	−	0.0597461i
$747$		0			0
$748$	−3.85331e15			−0.601693
$749$	−2.84480e15	+	1.86418e15i	−0.440963	+	0.288960i
$750$		0			0
$751$	1.62485e15	−	2.81433e15i	0.248196	−	0.429888i	−0.714830	−	0.699299i	$-0.753496\pi$
$751$	1.62485e15	−	2.81433e15i	0.248196	−	0.429888i	0.963025	+	0.269411i	$0.0868291\pi$
$752$	1.35464e15	+	2.34630e15i	0.205411	+	0.355783i
$753$		0			0
$754$	2.40393e15	−	4.16373e15i	0.359235	−	0.622214i
$755$	7.70277e14			0.114272
$756$		0			0
$757$	−6.67369e15			−0.975750			−0.487875	−	0.872914i	$-0.662228\pi$
$757$	−6.67369e15			−0.975750			−0.487875	+	0.872914i	$0.662228\pi$
$758$	−2.33374e15	+	4.04216e15i	−0.338744	+	0.586722i
$759$		0			0
$760$	−8.94909e13	−	1.55003e14i	−0.0128028	−	0.0221751i
$761$	2.34409e15	−	4.06008e15i	0.332934	−	0.576658i	−0.650152	−	0.759804i	$-0.725295\pi$
$761$	2.34409e15	−	4.06008e15i	0.332934	−	0.576658i	0.983086	+	0.183146i	$0.0586281\pi$
$762$		0			0
$763$	4.14736e14	+	7.33417e15i	0.0580613	+	1.02675i
$764$	4.98119e15			0.692340
$765$		0			0
$766$	2.87824e15	+	4.98526e15i	0.394338	+	0.683014i
$767$	−2.77775e15	−	4.81120e15i	−0.377849	−	0.654453i
$768$		0			0
$769$	−5.61692e15			−0.753189			−0.376594	−	0.926378i	$-0.622905\pi$
$769$	−5.61692e15			−0.753189			−0.376594	+	0.926378i	$0.622905\pi$
$770$	1.08000e15	−	7.07715e14i	0.143788	−	0.0942235i
$771$		0			0
$772$	1.62512e15	−	2.81478e15i	0.213299	−	0.369445i
$773$	−4.01315e15	−	6.95098e15i	−0.522996	−	0.905856i	−0.999642	−	0.0267602i	$-0.991481\pi$
$773$	−4.01315e15	−	6.95098e15i	−0.522996	−	0.905856i	0.476646	−	0.879095i	$-0.341852\pi$
$774$		0			0
$775$	−2.40503e15	+	4.16564e15i	−0.309002	+	0.535208i
$776$	−3.38572e15			−0.431929
$777$		0			0
$778$	−8.25477e15			−1.03829
$779$	3.13920e14	−	5.43725e14i	0.0392069	−	0.0679083i
$780$		0			0
$781$	−1.08440e15	−	1.87823e15i	−0.133539	−	0.231296i
$782$	8.61189e15	−	1.49162e16i	1.05308	−	1.82399i
$783$		0			0
$784$	−2.06016e15	+	2.33745e14i	−0.248406	+	0.0281841i
$785$	−1.03081e15			−0.123423
$786$		0			0
$787$	−1.21637e15	−	2.10681e15i	−0.143616	−	0.248751i	0.785240	−	0.619192i	$-0.212540\pi$
$787$	−1.21637e15	−	2.10681e15i	−0.143616	−	0.248751i	−0.928856	+	0.370441i	$0.879206\pi$
$788$	−3.42037e15	−	5.92426e15i	−0.401032	−	0.694608i
$789$		0			0
$790$	−2.98067e15			−0.344640
$791$	4.78248e15	+	2.41198e15i	0.549140	+	0.276951i
$792$		0			0
$793$	−1.08593e15	+	1.88089e15i	−0.122970	+	0.212991i
$794$	−4.54645e15	−	7.87469e15i	−0.511281	−	0.885565i
$795$		0			0
$796$	6.22485e14	−	1.07818e15i	0.0690410	−	0.119582i
$797$	9.46059e14			0.104207			0.0521036	−	0.998642i	$-0.483407\pi$
$797$	9.46059e14			0.104207			0.0521036	+	0.998642i	$0.483407\pi$
$798$		0			0
$799$	−2.35338e16			−2.55673
$800$	−7.38262e14	+	1.27871e15i	−0.0796554	+	0.137967i
$801$		0			0
$802$	1.67335e15	+	2.89833e15i	0.178085	+	0.308453i
$803$	−3.61541e15	+	6.26208e15i	−0.382140	+	0.661885i
$804$		0			0
$805$	3.25854e14	+	5.76239e15i	0.0339740	+	0.600794i
$806$	6.63098e15			0.686649
$807$		0			0
$808$	1.02636e15	+	1.77771e15i	0.104843	+	0.181593i
$809$	4.85762e15	+	8.41364e15i	0.492841	+	0.853625i	0.999966	−	0.00824739i	$-0.00262525\pi$
$809$	4.85762e15	+	8.41364e15i	0.492841	+	0.853625i	−0.507125	+	0.861872i	$0.669292\pi$
$810$		0			0
$811$	−1.45341e16			−1.45470			−0.727348	−	0.686269i	$-0.759247\pi$
$811$	−1.45341e16			−1.45470			−0.727348	+	0.686269i	$0.759247\pi$
$812$	−2.03752e14	−	3.60313e15i	−0.0202555	−	0.358197i
$813$		0			0
$814$	−4.47235e15	+	7.74634e15i	−0.438633	+	0.759735i
$815$	−2.30440e15	−	3.99134e15i	−0.224487	−	0.388823i
$816$		0			0
$817$	2.17845e15	−	3.77319e15i	0.209376	−	0.362650i
$818$	−1.44349e15			−0.137807
$819$		0			0
$820$	5.67838e14			0.0534870
$821$	−2.89155e15	+	5.00832e15i	−0.270548	+	0.468602i	−0.969002	−	0.247052i	$-0.920538\pi$
$821$	−2.89155e15	+	5.00832e15i	−0.270548	+	0.468602i	0.698455	+	0.715654i	$0.253871\pi$
$822$		0			0
$823$	−4.96010e15	−	8.59114e15i	−0.457922	−	0.793143i	0.540929	−	0.841068i	$-0.318073\pi$
$823$	−4.96010e15	−	8.59114e15i	−0.457922	−	0.793143i	−0.998851	+	0.0479246i	$0.984739\pi$
$824$	8.89220e14	−	1.54017e15i	0.0815473	−	0.141244i
$825$		0			0
$826$	−3.72335e15	−	1.87782e15i	−0.336933	−	0.169928i
$827$	−3.66176e15			−0.329162			−0.164581	−	0.986364i	$-0.552627\pi$
$827$	−3.66176e15			−0.329162			−0.164581	+	0.986364i	$0.552627\pi$
$828$		0			0
$829$	−5.78989e15	−	1.00284e16i	−0.513594	−	0.889571i	−0.999876	−	0.0157691i	$-0.994980\pi$
$829$	−5.78989e15	−	1.00284e16i	−0.513594	−	0.889571i	0.486281	−	0.873802i	$-0.338353\pi$
$830$	−2.97549e14	−	5.15370e14i	−0.0262198	−	0.0454140i
$831$		0			0
$832$	2.03548e15			0.177006
$833$	7.18929e15	−	1.65130e16i	0.621067	−	1.42652i
$834$		0			0
$835$	1.75847e15	−	3.04577e15i	0.149920	−	0.259670i
$836$	5.26025e14	+	9.11101e14i	0.0445524	+	0.0771671i
$837$		0			0
$838$	3.02532e15	−	5.24000e15i	0.252888	−	0.438015i
$839$	−1.53723e16			−1.27658			−0.638292	−	0.769794i	$-0.720359\pi$
$839$	−1.53723e16			−1.27658			−0.638292	+	0.769794i	$0.720359\pi$
$840$		0			0
$841$	−5.91893e15			−0.485138
$842$	3.84231e15	−	6.65508e15i	0.312879	−	0.541922i
$843$		0			0
$844$	3.05622e15	+	5.29352e15i	0.245641	+	0.425462i
$845$	1.97841e15	−	3.42670e15i	0.157981	−	0.273631i
$846$		0			0
$847$	4.26340e15	−	2.79377e15i	0.336045	−	0.220208i
$848$	−5.13167e15			−0.401866
$849$		0			0
$850$	−6.41282e15	−	1.11073e16i	−0.495730	−	0.858629i
$851$	−1.99908e16	−	3.46251e16i	−1.53539	−	2.65937i
$852$		0			0
$853$	1.35790e16			1.02955			0.514777	−	0.857324i	$-0.327875\pi$
$853$	1.35790e16			1.02955			0.514777	+	0.857324i	$0.327875\pi$
$854$	9.20411e13	+	1.62765e15i	0.00693368	+	0.122615i
$855$		0			0
$856$	1.25317e15	−	2.17056e15i	0.0931977	−	0.161423i
$857$	1.26143e16	+	2.18486e16i	0.932111	+	1.61446i	0.779707	+	0.626145i	$0.215368\pi$
$857$	1.26143e16	+	2.18486e16i	0.932111	+	1.61446i	0.152404	+	0.988318i	$0.451298\pi$
$858$		0			0
$859$	8.73719e15	−	1.51333e16i	0.637396	−	1.10400i	−0.348606	−	0.937269i	$-0.613345\pi$
$859$	8.73719e15	−	1.51333e16i	0.637396	−	1.10400i	0.986002	−	0.166733i	$-0.0533219\pi$
$860$	3.94052e15			0.285636
$861$		0			0
$862$	−1.73363e15			−0.124070
$863$	−8.58667e15	+	1.48725e16i	−0.610612	+	1.05761i	0.380526	+	0.924770i	$0.375743\pi$
$863$	−8.58667e15	+	1.48725e16i	−0.610612	+	1.05761i	−0.991137	+	0.132840i	$0.957590\pi$
$864$		0			0
$865$	3.29948e15	+	5.71487e15i	0.231663	+	0.401252i
$866$	−5.10430e15	+	8.84090e15i	−0.356113	+	0.616805i
$867$		0			0
$868$	4.16315e15	−	2.72808e15i	0.286789	−	0.187931i
$869$	1.75203e16			1.19931
$870$		0			0
$871$	1.10341e16	+	1.91116e16i	0.745823	+	1.29180i
$872$	−2.70661e15	−	4.68798e15i	−0.181796	−	0.314880i
$873$		0			0
$874$	−4.70252e15			−0.311902
$875$	8.09550e15	+	4.08285e15i	0.533580	+	0.269104i
$876$		0			0
$877$	−1.42352e16	+	2.46561e16i	−0.926543	+	1.60482i	−0.137483	+	0.990504i	$0.543901\pi$
$877$	−1.42352e16	+	2.46561e16i	−0.926543	+	1.60482i	−0.789060	+	0.614316i	$0.789432\pi$
$878$	−7.49502e15	−	1.29818e16i	−0.484789	−	0.839680i
$879$		0			0
$880$	−4.75753e14	+	8.24029e14i	−0.0303898	+	0.0526366i
$881$	−1.93122e16			−1.22593			−0.612963	−	0.790112i	$-0.710023\pi$
$881$	−1.93122e16			−1.22593			−0.612963	+	0.790112i	$0.710023\pi$
$882$		0			0
$883$	−9.08204e15			−0.569376			−0.284688	−	0.958620i	$-0.591890\pi$
$883$	−9.08204e15			−0.569376			−0.284688	+	0.958620i	$0.591890\pi$
$884$	−8.84048e15	+	1.53122e16i	−0.550793	+	0.954002i
$885$		0			0
$886$	−7.02360e14	−	1.21652e15i	−0.0432189	−	0.0748574i
$887$	−8.94539e15	+	1.54939e16i	−0.547040	+	0.947502i	0.451435	+	0.892304i	$0.350912\pi$
$887$	−8.94539e15	+	1.54939e16i	−0.547040	+	0.947502i	−0.998475	+	0.0551978i	$0.982421\pi$
$888$		0			0
$889$	2.22975e14	+	1.12454e14i	0.0134678	+	0.00679230i
$890$	1.31613e15			0.0790047
$891$		0			0
$892$	3.69195e15	+	6.39465e15i	0.218902	+	0.379149i
$893$	3.21266e15	+	5.56448e15i	0.189313	+	0.327900i
$894$		0			0
$895$	3.40150e15			0.197991
$896$	1.27794e15	−	8.37426e14i	0.0739293	−	0.0484454i
$897$		0			0
$898$	−3.47958e15	+	6.02681e15i	−0.198841	+	0.344403i
$899$	4.33177e15	+	7.50284e15i	0.246029	+	0.426135i
$900$		0			0
$901$	2.22878e16	−	3.86036e16i	1.25049	−	2.16592i
$902$	−3.33773e15			−0.186130
$903$		0			0
$904$	−3.94707e15			−0.217444
$905$	−3.14532e15	+	5.44785e15i	−0.172226	+	0.298303i
$906$		0			0
$907$	−5.99693e15	−	1.03870e16i	−0.324406	−	0.561888i	0.656986	−	0.753903i	$-0.271831\pi$
$907$	−5.99693e15	−	1.03870e16i	−0.324406	−	0.561888i	−0.981392	+	0.192015i	$0.938498\pi$
$908$	−2.83539e15	+	4.91104e15i	−0.152455	+	0.264059i
$909$		0			0
$910$	−3.34504e14	−	5.91535e15i	−0.0177694	−	0.314234i
$911$	−1.64716e16			−0.869728			−0.434864	−	0.900496i	$-0.643204\pi$
$911$	−1.64716e16			−0.869728			−0.434864	+	0.900496i	$0.643204\pi$
$912$		0			0
$913$	1.74898e15	+	3.02933e15i	0.0912424	+	0.158037i
$914$	1.29053e16	+	2.23526e16i	0.669211	+	1.15911i
$915$		0			0
$916$	7.71597e15			0.395335
$917$	2.41478e16	−	1.58239e16i	1.22983	−	0.805900i
$918$		0			0
$919$	−1.18247e16	+	2.04810e16i	−0.595053	+	1.03066i	0.398487	+	0.917174i	$0.369535\pi$
$919$	−1.18247e16	+	2.04810e16i	−0.595053	+	1.03066i	−0.993539	+	0.113487i	$0.963798\pi$
$920$	−2.12656e15	−	3.68330e15i	−0.106376	−	0.184249i
$921$		0			0
$922$	1.16141e16	−	2.01162e16i	0.574070	−	0.994318i
$923$	−9.95155e15			−0.488969
$924$		0			0
$925$	−2.97723e16			−1.44555
$926$	−1.85302e15	+	3.20953e15i	−0.0894376	+	0.154911i
$927$		0			0
$928$	1.32970e15	+	2.30311e15i	0.0634221	+	0.109850i
$929$	9.67202e15	−	1.67524e16i	0.458596	−	0.794312i	−0.540291	−	0.841479i	$-0.681686\pi$
$929$	9.67202e15	−	1.67524e16i	0.458596	−	0.794312i	0.998887	+	0.0471661i	$0.0150190\pi$
$930$		0			0
$931$	−4.88588e15	+	5.54350e14i	−0.228939	+	0.0259753i
$932$	6.41352e14			0.0298751
$933$		0			0
$934$	−1.09990e15	−	1.90508e15i	−0.0506342	−	0.0877010i
$935$	−4.13258e15	−	7.15783e15i	−0.189129	−	0.327580i
$936$		0			0
$937$	3.88518e15			0.175729			0.0878644	−	0.996132i	$-0.471996\pi$
$937$	3.88518e15			0.175729			0.0878644	+	0.996132i	$0.471996\pi$
$938$	1.47903e16	+	7.45929e15i	0.665061	+	0.335414i
$939$		0			0
$940$	−2.90563e15	+	5.03270e15i	−0.129133	+	0.223665i
$941$	5.26866e15	+	9.12558e15i	0.232786	+	0.403197i	0.958627	−	0.284665i	$-0.0918825\pi$
$941$	5.26866e15	+	9.12558e15i	0.232786	+	0.403197i	−0.725841	+	0.687863i	$0.758549\pi$
$942$		0			0
$943$	7.45962e15	−	1.29204e16i	0.325763	−	0.564239i
$944$	3.07295e15			0.133416
$945$		0			0
$946$	−2.31623e16			−0.993985
$947$	−1.22564e16	+	2.12286e16i	−0.522922	+	0.905727i	0.476722	+	0.879054i	$0.341825\pi$
$947$	−1.22564e16	+	2.12286e16i	−0.522922	+	0.905727i	−0.999644	+	0.0266732i	$0.991509\pi$
$948$		0			0
$949$	1.65894e16	+	2.87337e16i	0.699626	+	1.21179i
$950$	−1.75086e15	+	3.03258e15i	−0.0734128	+	0.127155i
$951$		0			0
$952$	7.49299e14	+	1.32506e16i	0.0310565	+	0.549201i
$953$	2.70879e16			1.11626			0.558129	−	0.829754i	$-0.311519\pi$
$953$	2.70879e16			1.11626			0.558129	+	0.829754i	$0.311519\pi$
$954$		0			0
$955$	5.34220e15	+	9.25296e15i	0.217621	+	0.376931i
$956$	8.77914e15	+	1.52059e16i	0.355577	+	0.615877i
$957$		0			0
$958$	−3.67862e14			−0.0147290
$959$	2.46221e14	+	4.35417e15i	0.00980220	+	0.173342i
$960$		0			0
$961$	6.72988e15	−	1.16565e16i	0.264867	−	0.458764i
$962$	2.05215e16	+	3.55442e16i	0.803055	+	1.39093i
$963$		0			0
$964$	1.64780e15	−	2.85407e15i	0.0637501	−	0.110418i
$965$	6.97159e15			0.268183
$966$		0			0
$967$	4.76683e16			1.81294			0.906472	−	0.422266i	$-0.138765\pi$
$967$	4.76683e16			1.81294			0.906472	+	0.422266i	$0.138765\pi$
$968$	−1.87808e15	+	3.25293e15i	−0.0710232	+	0.123016i
$969$		0			0
$970$	−3.63111e15	−	6.28926e15i	−0.135767	−	0.235155i
$971$	1.06577e16	−	1.84598e16i	0.396241	−	0.686310i	−0.597017	−	0.802228i	$-0.703648\pi$
$971$	1.06577e16	−	1.84598e16i	0.396241	−	0.686310i	0.993259	+	0.115918i	$0.0369810\pi$
$972$		0			0
$973$	4.04095e16	+	2.03800e16i	1.48547	+	0.749174i
$974$	−2.17331e16			−0.794414
$975$		0			0
$976$	−6.00669e14	−	1.04039e15i	−0.0217101	−	0.0376030i
$977$	3.78564e15	+	6.55692e15i	0.136056	+	0.235657i	0.926001	−	0.377522i	$-0.123224\pi$
$977$	3.78564e15	+	6.55692e15i	0.136056	+	0.235657i	−0.789944	+	0.613179i	$0.789890\pi$
$978$		0			0
$979$	−7.73616e15			−0.274929
$980$	−2.64367e15	−	3.57623e15i	−0.0934252	−	0.126381i
$981$		0			0
$982$	1.47154e15	−	2.54879e15i	0.0514233	−	0.0890678i
$983$	−1.86896e16	−	3.23714e16i	−0.649466	−	1.12491i	−0.983251	−	0.182259i	$-0.941659\pi$
$983$	−1.86896e16	−	3.23714e16i	−0.649466	−	1.12491i	0.333785	−	0.942649i	$-0.391674\pi$
$984$		0			0
$985$	7.33653e15	−	1.27072e16i	0.252111	−	0.436669i
$986$	−2.31006e16			−0.789406
$987$		0			0
$988$	4.82735e15			0.163134
$989$	5.17662e16	−	8.96616e16i	1.73967	−	3.01319i
$990$		0			0
$991$	5.88130e15	+	1.01867e16i	0.195465	+	0.338555i	0.947053	−	0.321078i	$-0.104045\pi$
$991$	5.88130e15	+	1.01867e16i	0.195465	+	0.338555i	−0.751588	+	0.659633i	$0.770712\pi$
$992$	−1.83392e15	+	3.17644e15i	−0.0606131	+	0.104985i
$993$		0			0
$994$	−6.24791e15	+	4.09421e15i	−0.204225	+	0.133827i
$995$	2.67040e15			0.0868059
$996$		0			0
$997$	1.43321e16	+	2.48239e16i	0.460771	+	0.798080i	0.999000	−	0.0447196i	$-0.0142395\pi$
$997$	1.43321e16	+	2.48239e16i	0.460771	+	0.798080i	−0.538228	+	0.842799i	$0.680906\pi$
$998$	−1.63303e16	−	2.82850e16i	−0.522128	−	0.904352i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.12.g.b.37.3		6
3.2	odd	2		42.12.e.a.37.1	yes	6
7.4	even	3	inner	126.12.g.b.109.3		6
21.11	odd	6		42.12.e.a.25.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.e.a.25.1	✓	6	21.11	odd	6
42.12.e.a.37.1	yes	6	3.2	odd	2
126.12.g.b.37.3		6	1.1	even	1	trivial
126.12.g.b.109.3		6	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(16.0000 - 27.7128i) q^{2} +(-512.000 - 886.810i) q^{4} +(1098.21 - 1902.16i) q^{5} +(39703.5 + 20023.9i) q^{7} -32768.0 q^{8} +(-35142.9 - 60869.3i) q^{10} +(206569. + 357788. i) q^{11} +1.89569e6 q^{13} +(1.19018e6 - 779913. i) q^{14} +(-524288. + 908093. i) q^{16} +(-4.55417e6 - 7.88805e6i) q^{17} +(-1.24340e6 + 2.15364e6i) q^{19} -2.24914e6 q^{20} +1.32204e7 q^{22} +(-2.95467e7 + 5.11765e7i) q^{23} +(2.20019e7 + 3.81084e7i) q^{25} +(3.03310e7 - 5.25349e7i) q^{26} +(-2.57079e6 - 4.54617e7i) q^{28} +7.92564e7 q^{29} +(5.46551e7 + 9.46654e7i) q^{31} +(1.67772e7 + 2.90590e7i) q^{32} -2.91467e8 q^{34} +(8.16918e7 - 5.35320e7i) q^{35} +(-3.38292e8 + 5.85938e8i) q^{37} +(3.97889e7 + 6.89163e7i) q^{38} +(-3.59863e7 + 6.23301e7i) q^{40} -2.52468e8 q^{41} -1.75201e9 q^{43} +(2.11526e8 - 3.66374e8i) q^{44} +(9.45496e8 + 1.63765e9i) q^{46} +(1.29188e9 - 2.23760e9i) q^{47} +(1.17541e9 + 1.59004e9i) q^{49} +1.40812e9 q^{50} +(-9.70593e8 - 1.68112e9i) q^{52} +(2.44697e9 + 4.23828e9i) q^{53} +9.07428e8 q^{55} +(-1.30100e9 - 6.56144e8i) q^{56} +(1.26810e9 - 2.19642e9i) q^{58} +(-1.46530e9 - 2.53797e9i) q^{59} +(-5.72843e8 + 9.92193e8i) q^{61} +3.49793e9 q^{62} +1.07374e9 q^{64} +(2.08187e9 - 3.60591e9i) q^{65} +(5.82061e9 + 1.00816e10i) q^{67} +(-4.66347e9 + 8.07736e9i) q^{68} +(-1.76455e8 - 3.12042e9i) q^{70} -5.24957e9 q^{71} +(8.75111e9 + 1.51574e10i) q^{73} +(1.08253e10 + 1.87500e10i) q^{74} +2.54649e9 q^{76} +(1.03720e9 + 1.83417e10i) q^{77} +(2.12040e10 - 3.67263e10i) q^{79} +(1.15156e9 + 1.99456e9i) q^{80} +(-4.03949e9 + 6.99661e9i) q^{82} +8.46684e9 q^{83} -2.00058e10 q^{85} +(-2.80322e10 + 4.85531e10i) q^{86} +(-6.76885e9 - 1.17240e10i) q^{88} +(-9.36269e9 + 1.62167e10i) q^{89} +(7.52655e10 + 3.79591e10i) q^{91} +6.05117e10 q^{92} +(-4.13402e10 - 7.16034e10i) q^{94} +(2.73104e9 + 4.73031e9i) q^{95} +1.03324e11 q^{97} +(6.28711e10 - 7.13333e9i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 96 q^{2} - 3072 q^{4} - 1045 q^{5} + 45731 q^{7} - 196608 q^{8} + 33440 q^{10} - 181565 q^{11} + 1186364 q^{13} + 703808 q^{14} - 3145728 q^{16} + 701848 q^{17} - 7893102 q^{19} + 2140160 q^{20} - 11620160 q^{22}+ \cdots - 30564771552 q^{98}+O(q^{100}) \) 6 * q + 96 * q^2 - 3072 * q^4 - 1045 * q^5 + 45731 * q^7 - 196608 * q^8 + 33440 * q^10 - 181565 * q^11 + 1186364 * q^13 + 703808 * q^14 - 3145728 * q^16 + 701848 * q^17 - 7893102 * q^19 + 2140160 * q^20 - 11620160 * q^22 - 59247728 * q^23 + 124585550 * q^25 + 18981824 * q^26 - 24306688 * q^28 + 30040070 * q^29 - 299540305 * q^31 + 100663296 * q^32 + 44918272 * q^34 + 181163920 * q^35 - 352325094 * q^37 + 252579264 * q^38 + 34242560 * q^40 - 1199954472 * q^41 - 4298844576 * q^43 - 185922560 * q^44 + 1895927296 * q^46 + 1179123942 * q^47 + 3621837009 * q^49 + 7973475200 * q^50 - 607418368 * q^52 + 67875849 * q^53 + 1874846050 * q^55 - 1498513408 * q^56 + 480641120 * q^58 + 2911039823 * q^59 - 10148733466 * q^61 - 19170579520 * q^62 + 6442450944 * q^64 + 2404013040 * q^65 - 5535975380 * q^67 + 718692352 * q^68 - 11741350880 * q^70 + 20558197876 * q^71 + 29230853572 * q^73 + 11274403008 * q^74 + 16165072896 * q^76 - 34001756425 * q^77 + 58886709107 * q^79 - 1095761920 * q^80 - 19199271552 * q^82 - 26001713726 * q^83 - 93104330000 * q^85 - 68781513216 * q^86 + 5949521920 * q^88 + 32237877702 * q^89 + 67979059274 * q^91 + 121339346944 * q^92 - 37731966144 * q^94 + 37720110280 * q^95 + 175446876934 * q^97 - 30564771552 * q^98

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