LMFDB - Embedded newform 126.10.g.f.37.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [126,10,Mod(37,126)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(126, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("126.37"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,48,0,-768,733] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$64.8945153566$
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} + 1116x^{4} - 3085x^{3} + 1245325x^{2} - 2341500x + 4410000 $ x^6 - x^5 + 1116x^4 - 3085x^3 + 1245325x^2 - 2341500x + 4410000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$0.943118 - 1.63353i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.10.g.f.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.00000 - 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(-859.469 + 1488.64i) q^{5} +(1802.93 + 6091.23i) q^{7} -4096.00 q^{8} +(13751.5 + 23818.3i) q^{10} +(-35661.7 - 61767.9i) q^{11} +156547. q^{13} +(98826.0 + 23747.7i) q^{14} +(-32768.0 + 56755.8i) q^{16} +(255856. + 443155. i) q^{17} +(97247.0 - 168437. i) q^{19} +440048. q^{20} -1.14118e6 q^{22} +(-54078.1 + 93666.0i) q^{23} +(-500810. - 867429. i) q^{25} +(1.25237e6 - 2.16918e6i) q^{26} +(1.11966e6 - 1.17939e6i) q^{28} -4.21769e6 q^{29} +(-1.58367e6 - 2.74299e6i) q^{31} +(524288. + 908093. i) q^{32} +8.18738e6 q^{34} +(-1.06172e7 - 2.55130e6i) q^{35} +(-7.20686e6 + 1.24827e7i) q^{37} +(-1.55595e6 - 2.69499e6i) q^{38} +(3.52038e6 - 6.09748e6i) q^{40} -7.69007e6 q^{41} -3.64544e7 q^{43} +(-9.12940e6 + 1.58126e7i) q^{44} +(865249. + 1.49866e6i) q^{46} +(9.11895e6 - 1.57945e7i) q^{47} +(-3.38525e7 + 2.19641e7i) q^{49} -1.60259e7 q^{50} +(-2.00380e7 - 3.47068e7i) q^{52} +(2.26037e7 + 3.91507e7i) q^{53} +1.22601e8 q^{55} +(-7.38481e6 - 2.49497e7i) q^{56} +(-3.37415e7 + 5.84420e7i) q^{58} +(-4.89074e7 - 8.47100e7i) q^{59} +(-5.73352e7 + 9.93075e7i) q^{61} -5.06773e7 q^{62} +1.67772e7 q^{64} +(-1.34547e8 + 2.33042e8i) q^{65} +(-1.00808e8 - 1.74605e8i) q^{67} +(6.54991e7 - 1.13448e8i) q^{68} +(-1.20290e8 + 1.26706e8i) q^{70} -2.08831e7 q^{71} +(-4.42392e6 - 7.66245e6i) q^{73} +(1.15310e8 + 1.99722e8i) q^{74} -4.97905e7 q^{76} +(3.11947e8 - 3.28587e8i) q^{77} +(-1.92244e7 + 3.32976e7i) q^{79} +(-5.63261e7 - 9.75597e7i) q^{80} +(-6.15205e7 + 1.06557e8i) q^{82} -5.55300e8 q^{83} -8.79600e8 q^{85} +(-2.91635e8 + 5.05127e8i) q^{86} +(1.46070e8 + 2.53001e8i) q^{88} +(-8.24594e7 + 1.42824e8i) q^{89} +(2.82243e8 + 9.53562e8i) q^{91} +2.76880e7 q^{92} +(-1.45903e8 - 2.52712e8i) q^{94} +(1.67162e8 + 2.89532e8i) q^{95} +1.57025e8 q^{97} +(3.35242e7 + 6.44787e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 48 q^{2} - 768 q^{4} + 733 q^{5} + 5012 q^{7} - 24576 q^{8} - 11728 q^{10} - 7339 q^{11} + 197036 q^{13} + 142576 q^{14} - 196608 q^{16} + 306665 q^{17} - 377991 q^{19} - 375296 q^{20} - 234848 q^{22}+ \cdots + 2185885296 q^{98}+O(q^{100}) $ 6 * q + 48 * q^2 - 768 * q^4 + 733 * q^5 + 5012 * q^7 - 24576 * q^8 - 11728 * q^10 - 7339 * q^11 + 197036 * q^13 + 142576 * q^14 - 196608 * q^16 + 306665 * q^17 - 377991 * q^19 - 375296 * q^20 - 234848 * q^22 + 2267255 * q^23 - 142612 * q^25 + 1576288 * q^26 + 998144 * q^28 + 13085956 * q^29 - 6654517 * q^31 + 3145728 * q^32 + 9813280 * q^34 - 22864807 * q^35 - 22287969 * q^37 + 6047856 * q^38 - 3002368 * q^40 - 68096196 * q^41 - 125648280 * q^43 - 1878784 * q^44 - 36276080 * q^46 + 52703019 * q^47 + 57596070 * q^49 - 4563584 * q^50 - 25220608 * q^52 + 12091125 * q^53 + 377435398 * q^55 - 20529152 * q^56 + 104687648 * q^58 + 12949897 * q^59 - 160252153 * q^61 - 212944544 * q^62 + 100663296 * q^64 - 334191270 * q^65 - 480890225 * q^67 + 78506240 * q^68 - 349171760 * q^70 + 74421440 * q^71 + 251382283 * q^73 + 356607504 * q^74 + 193531392 * q^76 + 527045155 * q^77 + 286494785 * q^79 + 48037888 * q^80 - 544769568 * q^82 - 2295182344 * q^83 - 2389185074 * q^85 - 1005186240 * q^86 + 30060544 * q^88 + 901243845 * q^89 + 1026798920 * q^91 - 1160834560 * q^92 - 843248304 * q^94 + 887366177 * q^95 + 629707876 * q^97 + 2185885296 * 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 $

$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	−859.469	+	1488.64i	−0.614986	+	1.06519i	0.375401	+	0.926862i	$0.377505\pi$
$5$	−859.469	+	1488.64i	−0.614986	+	1.06519i	−0.990387	+	0.138324i	$0.955828\pi$
$6$		0			0
$7$	1802.93	+	6091.23i	0.283817	+	0.958878i
$7$	1802.93	+	6091.23i	0.283817	+	0.958878i
$8$	−4096.00			−0.353553
$9$		0			0
$10$	13751.5	+	23818.3i	0.434861	+	0.753201i
$11$	−35661.7	−	61767.9i	−0.734404	−	1.27203i	−0.954984	−	0.296657i	$-0.904128\pi$
$11$	−35661.7	−	61767.9i	−0.734404	−	1.27203i	0.220580	−	0.975369i	$-0.429205\pi$
$12$		0			0
$13$	156547.			1.52019			0.760097	−	0.649809i	$-0.225151\pi$
$13$	156547.			1.52019			0.760097	+	0.649809i	$0.225151\pi$
$14$	98826.0	+	23747.7i	0.687535	+	0.165213i
$15$		0			0
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	255856.	+	443155.i	0.742976	+	1.28687i	0.951134	+	0.308778i	$0.0999199\pi$
$17$	255856.	+	443155.i	0.742976	+	1.28687i	−0.208158	+	0.978095i	$0.566747\pi$
$18$		0			0
$19$	97247.0	−	168437.i	0.171193	−	0.296514i	−0.767644	−	0.640876i	$-0.778571\pi$
$19$	97247.0	−	168437.i	0.171193	−	0.296514i	0.938837	+	0.344362i	$0.111905\pi$
$20$	440048.			0.614986
$21$		0			0
$22$	−1.14118e6			−1.03860
$23$	−54078.1	+	93666.0i	−0.0402945	+	0.0697922i	−0.885469	−	0.464698i	$-0.846163\pi$
$23$	−54078.1	+	93666.0i	−0.0402945	+	0.0697922i	0.845175	+	0.534490i	$0.179496\pi$
$24$		0			0
$25$	−500810.	−	867429.i	−0.256415	−	0.444124i
$26$	1.25237e6	−	2.16918e6i	0.537470	−	0.930925i
$27$		0			0
$28$	1.11966e6	−	1.17939e6i	0.344252	−	0.362616i
$29$	−4.21769e6			−1.10735			−0.553674	−	0.832734i	$-0.686774\pi$
$29$	−4.21769e6			−1.10735			−0.553674	+	0.832734i	$0.686774\pi$
$30$		0			0
$31$	−1.58367e6	−	2.74299e6i	−0.307990	−	0.533454i	0.669933	−	0.742422i	$-0.266323\pi$
$31$	−1.58367e6	−	2.74299e6i	−0.307990	−	0.533454i	−0.977922	+	0.208968i	$0.932990\pi$
$32$	524288.	+	908093.i	0.0883883	+	0.153093i
$33$		0			0
$34$	8.18738e6			1.05073
$35$	−1.06172e7	−	2.55130e6i	−1.19593	−	0.287379i
$36$		0			0
$37$	−7.20686e6	+	1.24827e7i	−0.632177	+	1.09496i	0.354929	+	0.934893i	$0.384505\pi$
$37$	−7.20686e6	+	1.24827e7i	−0.632177	+	1.09496i	−0.987106	+	0.160069i	$0.948828\pi$
$38$	−1.55595e6	−	2.69499e6i	−0.121051	−	0.209667i
$39$		0			0
$40$	3.52038e6	−	6.09748e6i	0.217430	−	0.376600i
$41$	−7.69007e6			−0.425014			−0.212507	−	0.977160i	$-0.568163\pi$
$41$	−7.69007e6			−0.425014			−0.212507	+	0.977160i	$0.568163\pi$
$42$		0			0
$43$	−3.64544e7			−1.62608			−0.813040	−	0.582208i	$-0.802189\pi$
$43$	−3.64544e7			−1.62608			−0.813040	+	0.582208i	$0.802189\pi$
$44$	−9.12940e6	+	1.58126e7i	−0.367202	+	0.636013i
$45$		0			0
$46$	865249.	+	1.49866e6i	0.0284925	+	0.0493505i
$47$	9.11895e6	−	1.57945e7i	0.272587	−	0.472134i	−0.696937	−	0.717132i	$-0.745454\pi$
$47$	9.11895e6	−	1.57945e7i	0.272587	−	0.472134i	0.969523	+	0.244999i	$0.0787876\pi$
$48$		0			0
$49$	−3.38525e7	+	2.19641e7i	−0.838896	+	0.544292i
$50$	−1.60259e7			−0.362625
$51$		0			0
$52$	−2.00380e7	−	3.47068e7i	−0.380049	−	0.658264i
$53$	2.26037e7	+	3.91507e7i	0.393494	+	0.681551i	0.992908	−	0.118888i	$-0.0379330\pi$
$53$	2.26037e7	+	3.91507e7i	0.393494	+	0.681551i	−0.599414	+	0.800439i	$0.704600\pi$
$54$		0			0
$55$	1.22601e8			1.80659
$56$	−7.38481e6	−	2.49497e7i	−0.100344	−	0.339015i
$57$		0			0
$58$	−3.37415e7	+	5.84420e7i	−0.391506	+	0.678109i
$59$	−4.89074e7	−	8.47100e7i	−0.525461	−	0.910124i	−0.999560	−	0.0296532i	$-0.990560\pi$
$59$	−4.89074e7	−	8.47100e7i	−0.525461	−	0.910124i	0.474100	−	0.880471i	$-0.342774\pi$
$60$		0			0
$61$	−5.73352e7	+	9.93075e7i	−0.530197	+	0.918328i	0.469182	+	0.883101i	$0.344549\pi$
$61$	−5.73352e7	+	9.93075e7i	−0.530197	+	0.918328i	−0.999379	+	0.0352269i	$0.988785\pi$
$62$	−5.06773e7			−0.435563
$63$		0			0
$64$	1.67772e7			0.125000
$65$	−1.34547e8	+	2.33042e8i	−0.934898	+	1.61929i
$66$		0			0
$67$	−1.00808e8	−	1.74605e8i	−0.611166	−	1.05857i	−0.991044	−	0.133534i	$-0.957367\pi$
$67$	−1.00808e8	−	1.74605e8i	−0.611166	−	1.05857i	0.379878	−	0.925036i	$-0.375966\pi$
$68$	6.54991e7	−	1.13448e8i	0.371488	−	0.643436i
$69$		0			0
$70$	−1.20290e8	+	1.26706e8i	−0.598807	+	0.630750i
$71$	−2.08831e7			−0.0975288			−0.0487644	−	0.998810i	$-0.515528\pi$
$71$	−2.08831e7			−0.0975288			−0.0487644	+	0.998810i	$0.515528\pi$
$72$		0			0
$73$	−4.42392e6	−	7.66245e6i	−0.0182328	−	0.0315802i	0.856765	−	0.515707i	$-0.172471\pi$
$73$	−4.42392e6	−	7.66245e6i	−0.0182328	−	0.0315802i	−0.874998	+	0.484127i	$0.839137\pi$
$74$	1.15310e8	+	1.99722e8i	0.447016	+	0.774255i
$75$		0			0
$76$	−4.97905e7			−0.171193
$77$	3.11947e8	−	3.28587e8i	1.01128	−	1.06523i
$78$		0			0
$79$	−1.92244e7	+	3.32976e7i	−0.0555304	+	0.0961814i	−0.892454	−	0.451138i	$-0.851018\pi$
$79$	−1.92244e7	+	3.32976e7i	−0.0555304	+	0.0961814i	0.836924	+	0.547319i	$0.184352\pi$
$80$	−5.63261e7	−	9.75597e7i	−0.153746	−	0.266297i
$81$		0			0
$82$	−6.15205e7	+	1.06557e8i	−0.150265	+	0.260267i
$83$	−5.55300e8			−1.28433			−0.642164	−	0.766567i	$-0.721963\pi$
$83$	−5.55300e8			−1.28433			−0.642164	+	0.766567i	$0.721963\pi$
$84$		0			0
$85$	−8.79600e8			−1.82768
$86$	−2.91635e8	+	5.05127e8i	−0.574906	+	0.995767i
$87$		0			0
$88$	1.46070e8	+	2.53001e8i	0.259651	+	0.449729i
$89$	−8.24594e7	+	1.42824e8i	−0.139311	+	0.241294i	−0.927236	−	0.374478i	$-0.877822\pi$
$89$	−8.24594e7	+	1.42824e8i	−0.139311	+	0.241294i	0.787925	+	0.615771i	$0.211155\pi$
$90$		0			0
$91$	2.82243e8	+	9.53562e8i	0.431457	+	1.45768i
$92$	2.76880e7			0.0402945
$93$		0			0
$94$	−1.45903e8	−	2.52712e8i	−0.192748	−	0.333849i
$95$	1.67162e8	+	2.89532e8i	0.210562	+	0.364704i
$96$		0			0
$97$	1.57025e8			0.180093			0.0900466	−	0.995938i	$-0.471298\pi$
$97$	1.57025e8			0.180093			0.0900466	+	0.995938i	$0.471298\pi$
$98$	3.35242e7	+	6.44787e8i	0.0367148	+	0.706153i
$99$		0			0
$100$	−1.28207e8	+	2.22062e8i	−0.128207	+	0.222062i
$101$	8.13868e7	+	1.40966e8i	0.0778230	+	0.134793i	0.902310	−	0.431087i	$-0.141870\pi$
$101$	8.13868e7	+	1.40966e8i	0.0778230	+	0.134793i	−0.824487	+	0.565880i	$0.808536\pi$
$102$		0			0
$103$	−6.77028e8	+	1.17265e9i	−0.592705	+	1.02660i	0.401161	+	0.916008i	$0.368607\pi$
$103$	−6.77028e8	+	1.17265e9i	−0.592705	+	1.02660i	−0.993866	+	0.110588i	$0.964727\pi$
$104$	−6.41216e8			−0.537470
$105$		0			0
$106$	7.23318e8			0.556484
$107$	4.39302e6	−	7.60893e6i	0.00323993	−	0.00561173i	−0.864401	−	0.502803i	$-0.832302\pi$
$107$	4.39302e6	−	7.60893e6i	0.00323993	−	0.00561173i	0.867641	+	0.497192i	$0.165635\pi$
$108$		0			0
$109$	−3.61434e8	−	6.26023e8i	−0.245251	−	0.424787i	0.716951	−	0.697123i	$-0.245537\pi$
$109$	−3.61434e8	−	6.26023e8i	−0.245251	−	0.424787i	−0.962202	+	0.272337i	$0.912204\pi$
$110$	9.80804e8	−	1.69880e9i	0.638727	−	1.10631i
$111$		0			0
$112$	−4.04791e8	−	9.72704e7i	−0.243080	−	0.0584117i
$113$	2.94124e9			1.69698			0.848492	−	0.529209i	$-0.177511\pi$
$113$	2.94124e9			1.69698			0.848492	+	0.529209i	$0.177511\pi$
$114$		0			0
$115$	−9.29568e7	−	1.61006e8i	−0.0495611	−	0.0858424i
$116$	5.39864e8	+	9.35073e8i	0.276837	+	0.479495i
$117$		0			0
$118$	−1.56504e9			−0.743113
$119$	−2.23807e9	+	2.35745e9i	−1.02309	+	1.07766i
$120$		0			0
$121$	−1.36454e9	+	2.36346e9i	−0.578699	+	1.00234i
$122$	9.17364e8	+	1.58892e9i	0.374906	+	0.649356i
$123$		0			0
$124$	−4.05418e8	+	7.02205e8i	−0.153995	+	0.266727i
$125$	−1.63558e9			−0.599205
$126$		0			0
$127$	−6.47761e8			−0.220952			−0.110476	−	0.993879i	$-0.535238\pi$
$127$	−6.47761e8			−0.220952			−0.110476	+	0.993879i	$0.535238\pi$
$128$	1.34218e8	−	2.32472e8i	0.0441942	−	0.0765466i
$129$		0			0
$130$	2.15275e9	+	3.72868e9i	0.661073	+	1.14501i
$131$	−1.47377e9	+	2.55264e9i	−0.437228	+	0.757301i	−0.997475	−	0.0710247i	$-0.977373\pi$
$131$	−1.47377e9	+	2.55264e9i	−0.437228	+	0.757301i	0.560246	+	0.828326i	$0.310706\pi$
$132$		0			0
$133$	1.20132e9	+	2.88674e8i	0.332909	+	0.0799972i
$134$	−3.22586e9			−0.864319
$135$		0			0
$136$	−1.04799e9	−	1.81516e9i	−0.262682	−	0.454978i
$137$	−3.85668e9	−	6.67997e9i	−0.935344	−	1.62006i	−0.774019	−	0.633162i	$-0.781757\pi$
$137$	−3.85668e9	−	6.67997e9i	−0.935344	−	1.62006i	−0.161325	−	0.986901i	$-0.551577\pi$
$138$		0			0
$139$	−5.40626e9			−1.22837			−0.614187	−	0.789161i	$-0.710516\pi$
$139$	−5.40626e9			−1.22837			−0.614187	+	0.789161i	$0.710516\pi$
$140$	7.93377e8	+	2.68043e9i	0.174543	+	0.589697i
$141$		0			0
$142$	−1.67065e8	+	2.89365e8i	−0.0344816	+	0.0597239i
$143$	−5.58273e9	−	9.66957e9i	−1.11644	−	1.93373i
$144$		0			0
$145$	3.62497e9	−	6.27864e9i	0.681003	−	1.17953i
$146$	−1.41565e8			−0.0257851
$147$		0			0
$148$	3.68991e9			0.632177
$149$	1.55301e7	−	2.68989e7i	0.00258129	−	0.00447092i	−0.864732	−	0.502234i	$-0.832512\pi$
$149$	1.55301e7	−	2.68989e7i	0.00258129	−	0.00447092i	0.867313	+	0.497763i	$0.165845\pi$
$150$		0			0
$151$	−4.08350e9	−	7.07283e9i	−0.639199	−	1.10713i	−0.985609	−	0.169043i	$-0.945932\pi$
$151$	−4.08350e9	−	7.07283e9i	−0.639199	−	1.10713i	0.346409	−	0.938083i	$-0.387401\pi$
$152$	−3.98324e8	+	6.89917e8i	−0.0605257	+	0.104834i
$153$		0			0
$154$	−2.05746e9	−	6.95116e9i	−0.294774	−	0.995896i
$155$	5.44445e9			0.757637
$156$		0			0
$157$	−7.72057e7	−	1.33724e8i	−0.0101415	−	0.0175655i	0.860910	−	0.508757i	$-0.169895\pi$
$157$	−7.72057e7	−	1.33724e8i	−0.0101415	−	0.0175655i	−0.871052	+	0.491192i	$0.836562\pi$
$158$	3.07590e8	+	5.32762e8i	0.0392659	+	0.0680105i
$159$		0			0
$160$	−1.80244e9			−0.217430
$161$	−6.68040e8	−	1.60528e8i	−0.0783585	−	0.0188294i
$162$		0			0
$163$	−5.72335e9	+	9.91314e9i	−0.635048	+	1.09994i	0.351457	+	0.936204i	$0.385686\pi$
$163$	−5.72335e9	+	9.91314e9i	−0.635048	+	1.09994i	−0.986505	+	0.163731i	$0.947647\pi$
$164$	9.84329e8	+	1.70491e9i	0.106253	+	0.184036i
$165$		0			0
$166$	−4.44240e9	+	7.69446e9i	−0.454079	+	0.786487i
$167$	1.71056e10			1.70182			0.850911	−	0.525310i	$-0.176051\pi$
$167$	1.71056e10			1.70182			0.850911	+	0.525310i	$0.176051\pi$
$168$		0			0
$169$	1.39024e10			1.31099
$170$	−7.03680e9	+	1.21881e10i	−0.646182	+	1.11922i
$171$		0			0
$172$	4.66616e9	+	8.08203e9i	0.406520	+	0.704113i
$173$	−9.09679e8	+	1.57561e9i	−0.0772113	+	0.133734i	−0.902046	−	0.431640i	$-0.857935\pi$
$173$	−9.09679e8	+	1.57561e9i	−0.0772113	+	0.133734i	0.824834	+	0.565374i	$0.191268\pi$
$174$		0			0
$175$	4.38078e9	−	4.61447e9i	0.353086	−	0.371921i
$176$	4.67425e9			0.367202
$177$		0			0
$178$	1.31935e9	+	2.28518e9i	0.0985077	+	0.170620i
$179$	−1.18157e9	−	2.04654e9i	−0.0860241	−	0.148998i	0.819803	−	0.572646i	$-0.194083\pi$
$179$	−1.18157e9	−	2.04654e9i	−0.0860241	−	0.148998i	−0.905827	+	0.423647i	$0.860750\pi$
$180$		0			0
$181$	1.65554e10			1.14653			0.573265	−	0.819370i	$-0.305677\pi$
$181$	1.65554e10			1.14653			0.573265	+	0.819370i	$0.305677\pi$
$182$	1.54709e10	+	3.71762e9i	1.04519	+	0.251156i
$183$		0			0
$184$	2.21504e8	−	3.83656e8i	0.0142463	−	0.0246753i
$185$	−1.23881e10	−	2.14569e10i	−0.777559	−	1.34677i
$186$		0			0
$187$	1.82485e10	−	3.16073e10i	1.09129	−	1.89017i
$188$	−4.66890e9			−0.272587
$189$		0			0
$190$	5.34917e9			0.297780
$191$	−1.68265e9	+	2.91443e9i	−0.0914835	+	0.158454i	−0.908136	−	0.418676i	$-0.862494\pi$
$191$	−1.68265e9	+	2.91443e9i	−0.0914835	+	0.158454i	0.816652	+	0.577130i	$0.195828\pi$
$192$		0			0
$193$	2.36192e9	+	4.09097e9i	0.122534	+	0.212236i	0.920766	−	0.390114i	$-0.127564\pi$
$193$	2.36192e9	+	4.09097e9i	0.122534	+	0.212236i	−0.798232	+	0.602350i	$0.794231\pi$
$194$	1.25620e9	−	2.17581e9i	0.0636725	−	0.110284i
$195$		0			0
$196$	9.20262e9	+	4.69377e9i	0.445409	+	0.227180i
$197$	1.66982e10			0.789897			0.394949	−	0.918703i	$-0.370762\pi$
$197$	1.66982e10			0.789897			0.394949	+	0.918703i	$0.370762\pi$
$198$		0			0
$199$	−1.30913e10	−	2.26748e10i	−0.591759	−	1.02496i	−0.993996	−	0.109421i	$-0.965100\pi$
$199$	−1.30913e10	−	2.26748e10i	−0.591759	−	1.02496i	0.402237	−	0.915536i	$-0.368233\pi$
$200$	2.05132e9	+	3.55299e9i	0.0906564	+	0.157021i
$201$		0			0
$202$	2.60438e9			0.110058
$203$	−7.60421e9	−	2.56909e10i	−0.314284	−	1.06181i
$204$		0			0
$205$	6.60937e9	−	1.14478e10i	0.261377	−	0.452719i
$206$	1.08324e10	+	1.87623e10i	0.419106	+	0.725913i
$207$		0			0
$208$	−5.12973e9	+	8.88495e9i	−0.190024	+	0.329132i
$209$	−1.38720e10			−0.502898
$210$		0			0
$211$	−3.90431e10			−1.35604			−0.678021	−	0.735042i	$-0.737162\pi$
$211$	−3.90431e10			−1.35604			−0.678021	+	0.735042i	$0.737162\pi$
$212$	5.78654e9	−	1.00226e10i	0.196747	−	0.340775i
$213$		0			0
$214$	−7.02883e7	−	1.21743e8i	−0.00229098	−	0.00396809i
$215$	3.13314e10	−	5.42676e10i	1.00002	−	1.73208i
$216$		0			0
$217$	1.38529e10	−	1.45919e10i	0.424104	−	0.446728i
$218$	−1.15659e10			−0.346837
$219$		0			0
$220$	−1.56929e10	−	2.71808e10i	−0.451648	−	0.782278i
$221$	4.00534e10	+	6.93745e10i	1.12947	+	1.95630i
$222$		0			0
$223$	4.53210e10			1.22723			0.613617	−	0.789603i	$-0.289714\pi$
$223$	4.53210e10			1.22723			0.613617	+	0.789603i	$0.289714\pi$
$224$	−4.58615e9	+	4.83079e9i	−0.121712	+	0.128204i
$225$		0			0
$226$	2.35299e10	−	4.07550e10i	0.599974	−	1.03919i
$227$	3.75422e9	+	6.50249e9i	0.0938432	+	0.162541i	0.909125	−	0.416523i	$-0.136751\pi$
$227$	3.75422e9	+	6.50249e9i	0.0938432	+	0.162541i	−0.815282	+	0.579064i	$0.803418\pi$
$228$		0			0
$229$	−2.09237e10	+	3.62409e10i	−0.502781	+	0.870842i	0.497214	+	0.867628i	$0.334356\pi$
$229$	−2.09237e10	+	3.62409e10i	−0.502781	+	0.870842i	−0.999995	+	0.00321410i	$0.998977\pi$
$230$	−2.97462e9			−0.0700900
$231$		0			0
$232$	1.72757e10			0.391506
$233$	1.52461e10	−	2.64070e10i	0.338888	−	0.586971i	−0.645336	−	0.763899i	$-0.723283\pi$
$233$	1.52461e10	−	2.64070e10i	0.338888	−	0.586971i	0.984224	+	0.176928i	$0.0566158\pi$
$234$		0			0
$235$	1.56749e10	+	2.71497e10i	0.335274	+	0.580711i
$236$	−1.25203e10	+	2.16858e10i	−0.262730	+	0.455062i
$237$		0			0
$238$	1.47613e10	+	4.98712e10i	0.298214	+	1.00752i
$239$	−4.29290e10			−0.851060			−0.425530	−	0.904944i	$-0.639912\pi$
$239$	−4.29290e10			−0.851060			−0.425530	+	0.904944i	$0.639912\pi$
$240$		0			0
$241$	4.20533e9	+	7.28385e9i	0.0803015	+	0.139086i	0.903379	−	0.428842i	$-0.141078\pi$
$241$	4.20533e9	+	7.28385e9i	0.0803015	+	0.139086i	−0.823078	+	0.567928i	$0.807745\pi$
$242$	2.18327e10	+	3.78153e10i	0.409202	+	0.708759i
$243$		0			0
$244$	2.93556e10			0.530197
$245$	−3.60163e9	−	6.92718e10i	−0.0638633	−	1.22831i
$246$		0			0
$247$	1.52237e10	−	2.63682e10i	0.260246	−	0.450760i
$248$	6.48670e9	+	1.12353e10i	0.108891	+	0.188604i
$249$		0			0
$250$	−1.30846e10	+	2.26632e10i	−0.211851	+	0.366937i
$251$	−8.14744e10			−1.29566			−0.647828	−	0.761787i	$-0.724322\pi$
$251$	−8.14744e10			−1.29566			−0.647828	+	0.761787i	$0.724322\pi$
$252$		0			0
$253$	7.71407e9			0.118370
$254$	−5.18209e9	+	8.97564e9i	−0.0781184	+	0.135305i
$255$		0			0
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	1.90519e10	−	3.29988e10i	0.272420	−	0.471845i	−0.697061	−	0.717012i	$-0.745509\pi$
$257$	1.90519e10	−	3.29988e10i	0.272420	−	0.471845i	0.969481	+	0.245167i	$0.0788428\pi$
$258$		0			0
$259$	−8.90281e10	−	2.13933e10i	−1.22936	−	0.295412i
$260$	6.88881e10			0.934898
$261$		0			0
$262$	2.35803e10	+	4.08422e10i	0.309167	+	0.535493i
$263$	−2.83241e10	−	4.90588e10i	−0.365053	−	0.632290i	0.623732	−	0.781638i	$-0.285616\pi$
$263$	−2.83241e10	−	4.90588e10i	−0.365053	−	0.632290i	−0.988785	+	0.149349i	$0.952282\pi$
$264$		0			0
$265$	−7.77086e10			−0.967972
$266$	1.36105e10	−	1.43365e10i	0.166689	−	0.175581i
$267$		0			0
$268$	−2.58069e10	+	4.46988e10i	−0.305583	+	0.529285i
$269$	7.10675e10	+	1.23092e11i	0.827534	+	1.43333i	0.899967	+	0.435957i	$0.143590\pi$
$269$	7.10675e10	+	1.23092e11i	0.827534	+	1.43333i	−0.0724338	+	0.997373i	$0.523077\pi$
$270$		0			0
$271$	1.86332e10	−	3.22737e10i	0.209859	−	0.363486i	−0.741811	−	0.670609i	$-0.766033\pi$
$271$	1.86332e10	−	3.22737e10i	0.209859	−	0.363486i	0.951670	+	0.307123i	$0.0993663\pi$
$272$	−3.35355e10			−0.371488
$273$		0			0
$274$	−1.23414e11			−1.32278
$275$	−3.57195e10	+	6.18680e10i	−0.376624	+	0.652333i
$276$		0			0
$277$	−7.86972e10	−	1.36308e11i	−0.803157	−	1.39111i	−0.917528	−	0.397671i	$-0.869819\pi$
$277$	−7.86972e10	−	1.36308e11i	−0.803157	−	1.39111i	0.114371	−	0.993438i	$-0.463515\pi$
$278$	−4.32501e10	+	7.49114e10i	−0.434296	+	0.752222i
$279$		0			0
$280$	4.34882e10	+	1.04501e10i	0.422824	+	0.101604i
$281$	−9.66888e10			−0.925119			−0.462560	−	0.886588i	$-0.653069\pi$
$281$	−9.66888e10			−0.925119			−0.462560	+	0.886588i	$0.653069\pi$
$282$		0			0
$283$	9.95631e10	+	1.72448e11i	0.922698	+	1.59816i	0.795223	+	0.606318i	$0.207354\pi$
$283$	9.95631e10	+	1.72448e11i	0.922698	+	1.59816i	0.127475	+	0.991842i	$0.459313\pi$
$284$	2.67304e9	+	4.62984e9i	0.0243822	+	0.0422312i
$285$		0			0
$286$	−1.78647e11			−1.57888
$287$	−1.38647e10	−	4.68420e10i	−0.120626	−	0.407536i
$288$		0			0
$289$	−7.16304e10	+	1.24067e11i	−0.604028	+	1.04621i
$290$	−5.79996e10	−	1.00458e11i	−0.481542	−	0.834055i
$291$		0			0
$292$	−1.13252e9	+	1.96159e9i	−0.00911641	+	0.0157901i
$293$	−7.28364e10			−0.577357			−0.288679	−	0.957426i	$-0.593216\pi$
$293$	−7.28364e10			−0.577357			−0.288679	+	0.957426i	$0.593216\pi$
$294$		0			0
$295$	1.68137e11			1.29260
$296$	2.95193e10	−	5.11289e10i	0.223508	−	0.387128i
$297$		0			0
$298$	−2.48482e8	−	4.30383e8i	−0.00182524	−	0.00316142i
$299$	−8.46575e9	+	1.46631e10i	−0.0612555	+	0.106098i
$300$		0			0
$301$	−6.57248e10	−	2.22052e11i	−0.461509	−	1.55921i
$302$	−1.30672e11			−0.903965
$303$		0			0
$304$	6.37318e9	+	1.10387e10i	0.0427982	+	0.0741286i
$305$	−9.85557e10	−	1.70703e11i	−0.652127	−	1.12952i
$306$		0			0
$307$	−1.17824e11			−0.757027			−0.378514	−	0.925596i	$-0.623565\pi$
$307$	−1.17824e11			−0.757027			−0.378514	+	0.925596i	$0.623565\pi$
$308$	−1.12778e11	−	2.71002e10i	−0.714077	−	0.171591i
$309$		0			0
$310$	4.35556e10	−	7.54404e10i	0.267865	−	0.463956i
$311$	9.06944e10	+	1.57087e11i	0.549742	+	0.952180i	0.998292	+	0.0584227i	$0.0186071\pi$
$311$	9.06944e10	+	1.57087e11i	0.549742	+	0.952180i	−0.448550	+	0.893758i	$0.648060\pi$
$312$		0			0
$313$	−1.42218e11	+	2.46328e11i	−0.837537	+	1.45066i	0.0544112	+	0.998519i	$0.482672\pi$
$313$	−1.42218e11	+	2.46328e11i	−0.837537	+	1.45066i	−0.891948	+	0.452138i	$0.850662\pi$
$314$	−2.47058e9			−0.0143422
$315$		0			0
$316$	9.84288e9			0.0555304
$317$	−5.08743e10	+	8.81169e10i	−0.282964	+	0.490109i	−0.972114	−	0.234511i	$-0.924651\pi$
$317$	−5.08743e10	+	8.81169e10i	−0.282964	+	0.490109i	0.689149	+	0.724620i	$0.257984\pi$
$318$		0			0
$319$	1.50410e11	+	2.60518e11i	0.813241	+	1.40857i
$320$	−1.44195e10	+	2.49753e10i	−0.0768732	+	0.133148i
$321$		0			0
$322$	−7.56867e9	+	7.97240e9i	−0.0392345	+	0.0413274i
$323$	9.95248e10			0.508768
$324$		0			0
$325$	−7.84003e10	−	1.35793e11i	−0.389801	−	0.675154i
$326$	9.15737e10	+	1.58610e11i	0.449047	+	0.777772i
$327$		0			0
$328$	3.14985e10			0.150265
$329$	1.12649e11	+	2.70692e10i	0.530084	+	0.127378i
$330$		0			0
$331$	−1.51983e11	+	2.63242e11i	−0.695935	+	1.20540i	0.273929	+	0.961750i	$0.411677\pi$
$331$	−1.51983e11	+	2.63242e11i	−0.695935	+	1.20540i	−0.969864	+	0.243645i	$0.921657\pi$
$332$	7.10784e10	+	1.23111e11i	0.321082	+	0.556130i
$333$		0			0
$334$	1.36845e11	−	2.37022e11i	0.601685	−	1.04215i
$335$	3.46566e11			1.50343
$336$		0			0
$337$	−1.72473e10			−0.0728427			−0.0364213	−	0.999337i	$-0.511596\pi$
$337$	−1.72473e10			−0.0728427			−0.0364213	+	0.999337i	$0.511596\pi$
$338$	1.11219e11	−	1.92638e11i	0.463506	−	0.802816i
$339$		0			0
$340$	1.12589e11	+	1.95010e11i	0.456920	+	0.791408i
$341$	−1.12953e11	+	1.95639e11i	−0.452378	+	0.783541i
$342$		0			0
$343$	−1.94822e11	−	1.66603e11i	−0.760003	−	0.649920i
$344$	1.49317e11			0.574906
$345$		0			0
$346$	1.45549e10	+	2.52098e10i	0.0545966	+	0.0945642i
$347$	1.58417e11	+	2.74386e11i	0.586569	+	1.01597i	0.994678	+	0.103034i	$0.0328551\pi$
$347$	1.58417e11	+	2.74386e11i	0.586569	+	1.01597i	−0.408109	+	0.912933i	$0.633812\pi$
$348$		0			0
$349$	9.59821e10			0.346318			0.173159	−	0.984894i	$-0.444602\pi$
$349$	9.59821e10			0.346318			0.173159	+	0.984894i	$0.444602\pi$
$350$	−2.88937e10	−	9.76176e10i	−0.102919	−	0.347714i
$351$		0			0
$352$	3.73940e10	−	6.47684e10i	0.129826	−	0.224864i
$353$	−1.31095e11	−	2.27063e11i	−0.449365	−	0.778324i	0.548979	−	0.835836i	$-0.315017\pi$
$353$	−1.31095e11	−	2.27063e11i	−0.449365	−	0.778324i	−0.998345	+	0.0575122i	$0.981683\pi$
$354$		0			0
$355$	1.79484e10	−	3.10875e10i	0.0599788	−	0.103886i
$356$	4.22192e10			0.139311
$357$		0			0
$358$	−3.78102e10			−0.121656
$359$	−5.42664e10	+	9.39922e10i	−0.172427	+	0.298653i	−0.939268	−	0.343185i	$-0.888494\pi$
$359$	−5.42664e10	+	9.39922e10i	−0.172427	+	0.298653i	0.766841	+	0.641838i	$0.221828\pi$
$360$		0			0
$361$	1.42430e11	+	2.46696e11i	0.441386	+	0.764503i
$362$	1.32443e11	−	2.29398e11i	0.405360	−	0.702104i
$363$		0			0
$364$	1.75280e11	−	1.84630e11i	0.523331	−	0.551247i
$365$	1.52089e10			0.0448517
$366$		0			0
$367$	−1.06268e11	−	1.84061e11i	−0.305777	−	0.529621i	0.671657	−	0.740862i	$-0.265583\pi$
$367$	−1.06268e11	−	1.84061e11i	−0.305777	−	0.529621i	−0.977434	+	0.211241i	$0.932249\pi$
$368$	−3.54406e9	−	6.13849e9i	−0.0100736	−	0.0174480i
$369$		0			0
$370$	−3.96421e11			−1.09963
$371$	−1.97723e11	+	2.08270e11i	−0.541844	+	0.570748i
$372$		0			0
$373$	1.58915e11	−	2.75249e11i	0.425085	−	0.736269i	−0.571343	−	0.820711i	$-0.693577\pi$
$373$	1.58915e11	−	2.75249e11i	0.425085	−	0.736269i	0.996428	+	0.0844421i	$0.0269108\pi$
$374$	−2.91976e11	−	5.05718e11i	−0.771659	−	1.33655i
$375$		0			0
$376$	−3.73512e10	+	6.46942e10i	−0.0963739	+	0.166924i
$377$	−6.60266e11			−1.68338
$378$		0			0
$379$	6.09315e11			1.51693			0.758465	−	0.651714i	$-0.225950\pi$
$379$	6.09315e11			1.51693			0.758465	+	0.651714i	$0.225950\pi$
$380$	4.27934e10	−	7.41203e10i	0.105281	−	0.182352i
$381$		0			0
$382$	2.69224e10	+	4.66309e10i	0.0646886	+	0.112044i
$383$	1.70032e11	−	2.94503e11i	0.403771	−	0.699352i	−0.590407	−	0.807106i	$-0.701033\pi$
$383$	1.70032e11	−	2.94503e11i	0.403771	−	0.699352i	0.994178	+	0.107754i	$0.0343659\pi$
$384$		0			0
$385$	2.21040e11	+	7.46788e11i	0.512742	+	1.73230i
$386$	7.55816e10			0.173290
$387$		0			0
$388$	−2.00993e10	−	3.48129e10i	−0.0450233	−	0.0779826i
$389$	3.77442e11	+	6.53749e11i	0.835751	+	1.44756i	0.893417	+	0.449227i	$0.148301\pi$
$389$	3.77442e11	+	6.53749e11i	0.835751	+	1.44756i	−0.0576663	+	0.998336i	$0.518366\pi$
$390$		0			0
$391$	−5.53447e10			−0.119751
$392$	1.38660e11	−	8.99651e10i	0.296595	−	0.192436i
$393$		0			0
$394$	1.33585e11	−	2.31376e11i	0.279271	−	0.483711i
$395$	−3.30455e10	−	5.72365e10i	−0.0683008	−	0.118300i
$396$		0			0
$397$	1.34694e11	−	2.33297e11i	0.272140	−	0.471360i	−0.697270	−	0.716809i	$-0.745602\pi$
$397$	1.34694e11	−	2.33297e11i	0.272140	−	0.471360i	0.969409	+	0.245449i	$0.0789354\pi$
$398$	−4.18923e11			−0.836874
$399$		0			0
$400$	6.56422e10			0.128207
$401$	−1.78083e11	+	3.08449e11i	−0.343932	+	0.595708i	−0.985159	−	0.171643i	$-0.945092\pi$
$401$	−1.78083e11	+	3.08449e11i	−0.343932	+	0.595708i	0.641227	+	0.767351i	$0.278426\pi$
$402$		0			0
$403$	−2.47918e11	−	4.29406e11i	−0.468204	−	0.810953i
$404$	2.08350e10	−	3.60873e10i	0.0389115	−	0.0673967i
$405$		0			0
$406$	−4.16817e11	−	1.00160e11i	−0.761340	−	0.182948i
$407$	1.02804e12			1.85709
$408$		0			0
$409$	4.37201e10	+	7.57254e10i	0.0772549	+	0.133809i	0.902065	−	0.431601i	$-0.142051\pi$
$409$	4.37201e10	+	7.57254e10i	0.0772549	+	0.133809i	−0.824810	+	0.565410i	$0.808718\pi$
$410$	−1.05750e11	−	1.83164e11i	−0.184822	−	0.320121i
$411$		0			0
$412$	3.46638e11			0.592705
$413$	4.27811e11	−	4.50632e11i	0.723564	−	0.762162i
$414$		0			0
$415$	4.77263e11	−	8.26643e11i	0.789843	−	1.36805i
$416$	8.20756e10	+	1.42159e11i	0.134368	+	0.232731i
$417$		0			0
$418$	−1.10976e11	+	1.92216e11i	−0.177801	+	0.307961i
$419$	−4.46048e9			−0.00706999			−0.00353499	−	0.999994i	$-0.501125\pi$
$419$	−4.46048e9			−0.00706999			−0.00353499	+	0.999994i	$0.501125\pi$
$420$		0			0
$421$	−9.34684e10			−0.145009			−0.0725046	−	0.997368i	$-0.523099\pi$
$421$	−9.34684e10			−0.145009			−0.0725046	+	0.997368i	$0.523099\pi$
$422$	−3.12345e11	+	5.40997e11i	−0.479434	+	0.830403i
$423$		0			0
$424$	−9.25846e10	−	1.60361e11i	−0.139121	−	0.240965i
$425$	2.56270e11	−	4.43873e11i	0.381020	−	0.659947i
$426$		0			0
$427$	−7.08276e11	−	1.70197e11i	−1.03104	−	0.247757i
$428$	−2.24923e9			−0.00323993
$429$		0			0
$430$	−5.01303e11	−	8.68282e11i	−0.707118	−	1.22476i
$431$	−2.49562e11	−	4.32254e11i	−0.348362	−	0.603381i	0.637597	−	0.770370i	$-0.279929\pi$
$431$	−2.49562e11	−	4.32254e11i	−0.348362	−	0.603381i	−0.985959	+	0.166990i	$0.946595\pi$
$432$		0			0
$433$	1.04168e12			1.42410			0.712049	−	0.702130i	$-0.247768\pi$
$433$	1.04168e12			1.42410			0.712049	+	0.702130i	$0.247768\pi$
$434$	−9.13678e10	−	3.08687e11i	−0.123620	−	0.417652i
$435$		0			0
$436$	−9.25272e10	+	1.60262e11i	−0.122625	+	0.212393i
$437$	1.05179e10	+	1.82175e10i	0.0137963	+	0.0238958i
$438$		0			0
$439$	1.00140e11	−	1.73447e11i	0.128681	−	0.222883i	−0.794485	−	0.607284i	$-0.792259\pi$
$439$	1.00140e11	−	1.73447e11i	0.128681	−	0.222883i	0.923166	+	0.384402i	$0.125592\pi$
$440$	−5.02172e11			−0.638727
$441$		0			0
$442$	1.28171e12			1.59731
$443$	1.13051e11	−	1.95810e11i	0.139463	−	0.241556i	−0.787831	−	0.615892i	$-0.788796\pi$
$443$	1.13051e11	−	1.95810e11i	0.139463	−	0.241556i	0.927293	+	0.374335i	$0.122129\pi$
$444$		0			0
$445$	−1.41743e11	−	2.45505e11i	−0.171349	−	0.296784i
$446$	3.62568e11	−	6.27986e11i	0.433893	−	0.751525i
$447$		0			0
$448$	3.02482e10	+	1.02194e11i	0.0354771	+	0.119860i
$449$	1.20089e12			1.39443			0.697213	−	0.716864i	$-0.254423\pi$
$449$	1.20089e12			1.39443			0.697213	+	0.716864i	$0.254423\pi$
$450$		0			0
$451$	2.74241e11	+	4.74999e11i	0.312132	+	0.540628i
$452$	−3.76479e11	−	6.52080e11i	−0.424246	−	0.734815i
$453$		0			0
$454$	1.20135e11			0.132714
$455$	−1.66209e12	−	3.99397e11i	−1.81804	−	0.436872i
$456$		0			0
$457$	−1.64864e11	+	2.85552e11i	−0.176808	+	0.306241i	−0.940786	−	0.339002i	$-0.889911\pi$
$457$	−1.64864e11	+	2.85552e11i	−0.176808	+	0.306241i	0.763977	+	0.645243i	$0.223244\pi$
$458$	3.34779e11	+	5.79855e11i	0.355520	+	0.615778i
$459$		0			0
$460$	−2.37969e10	+	4.12175e10i	−0.0247806	+	0.0429212i
$461$	−1.38928e12			−1.43263			−0.716317	−	0.697775i	$-0.754173\pi$
$461$	−1.38928e12			−1.43263			−0.716317	+	0.697775i	$0.754173\pi$
$462$		0			0
$463$	−6.88123e7			−6.95908e−5			−3.47954e−5	−	1.00000i	$-0.500011\pi$
$463$	−6.88123e7			−6.95908e−5			−3.47954e−5		1.00000i	$0.500011\pi$
$464$	1.38205e11	−	2.39379e11i	0.138418	−	0.239748i
$465$		0			0
$466$	−2.43937e11	−	4.22512e11i	−0.239630	−	0.415052i
$467$	−5.39451e11	+	9.34356e11i	−0.524839	+	0.909048i	0.474743	+	0.880125i	$0.342541\pi$
$467$	−5.39451e11	+	9.34356e11i	−0.524839	+	0.909048i	−0.999582	+	0.0289230i	$0.990792\pi$
$468$		0			0
$469$	8.81808e11	−	9.28846e11i	0.841581	−	0.886474i
$470$	5.01597e11			0.474149
$471$		0			0
$472$	2.00325e11	+	3.46972e11i	0.185778	+	0.321778i
$473$	1.30003e12	+	2.25171e12i	1.19420	+	2.06842i
$474$		0			0
$475$	−1.94809e11			−0.175585
$476$	8.09126e11	+	1.94431e11i	0.722412	+	0.173594i
$477$		0			0
$478$	−3.43432e11	+	5.94841e11i	−0.300895	+	0.521165i
$479$	−3.11905e11	−	5.40235e11i	−0.270715	−	0.468892i	0.698330	−	0.715776i	$-0.253927\pi$
$479$	−3.11905e11	−	5.40235e11i	−0.270715	−	0.468892i	−0.969045	+	0.246884i	$0.920593\pi$
$480$		0			0
$481$	−1.12821e12	+	1.95412e12i	−0.961032	+	1.66456i
$482$	1.34571e11			0.113563
$483$		0			0
$484$	6.98646e11			0.578699
$485$	−1.34958e11	+	2.33755e11i	−0.110755	+	0.191833i
$486$		0			0
$487$	7.48463e11	+	1.29638e12i	0.602962	+	1.04436i	0.992370	+	0.123295i	$0.0393462\pi$
$487$	7.48463e11	+	1.29638e12i	0.602962	+	1.04436i	−0.389408	+	0.921065i	$0.627321\pi$
$488$	2.34845e11	−	4.06764e11i	0.187453	−	0.324678i
$489$		0			0
$490$	−9.88671e11	−	5.04268e11i	−0.774764	−	0.395166i
$491$	−6.91050e11			−0.536590			−0.268295	−	0.963337i	$-0.586460\pi$
$491$	−6.91050e11			−0.536590			−0.268295	+	0.963337i	$0.586460\pi$
$492$		0			0
$493$	−1.07912e12	−	1.86909e12i	−0.822733	−	1.42501i
$494$	−2.43579e11	−	4.21892e11i	−0.184022	−	0.318735i
$495$		0			0
$496$	2.07574e11			0.153995
$497$	−3.76508e10	−	1.27204e11i	−0.0276803	−	0.0935182i
$498$		0			0
$499$	−6.87459e11	+	1.19071e12i	−0.496357	+	0.859716i	−0.999991	−	0.00420123i	$-0.998663\pi$
$499$	−6.87459e11	+	1.19071e12i	−0.496357	+	0.859716i	0.503634	+	0.863917i	$0.331996\pi$
$500$	2.09354e11	+	3.62611e11i	0.149801	+	0.259464i
$501$		0			0
$502$	−6.51796e11	+	1.12894e12i	−0.458084	+	0.793424i
$503$	2.02197e12			1.40837			0.704187	−	0.710015i	$-0.251312\pi$
$503$	2.02197e12			1.40837			0.704187	+	0.710015i	$0.251312\pi$
$504$		0			0
$505$	−2.79798e11			−0.191440
$506$	6.17126e10	−	1.06889e11i	0.0418501	−	0.0724864i
$507$		0			0
$508$	8.29134e10	+	1.43610e11i	0.0552380	+	0.0956751i
$509$	−5.74038e11	+	9.94263e11i	−0.379062	+	0.656555i	−0.990926	−	0.134408i	$-0.957087\pi$
$509$	−5.74038e11	+	9.94263e11i	−0.379062	+	0.656555i	0.611864	+	0.790963i	$0.290420\pi$
$510$		0			0
$511$	3.86977e10	−	4.07620e10i	0.0251068	−	0.0264461i
$512$	−6.87195e10			−0.0441942
$513$		0			0
$514$	−3.04830e11	−	5.27981e11i	−0.192630	−	0.333645i
$515$	−1.16377e12	−	2.01571e12i	−0.729011	−	1.26268i
$516$		0			0
$517$	−1.30079e12			−0.800755
$518$	−1.00866e12	+	1.06246e12i	−0.615546	+	0.648381i
$519$		0			0
$520$	5.51105e11	−	9.54542e11i	0.330536	−	0.572506i
$521$	−6.50321e11	−	1.12639e12i	−0.386686	−	0.669759i	0.605316	−	0.795985i	$-0.293047\pi$
$521$	−6.50321e11	−	1.12639e12i	−0.386686	−	0.669759i	−0.992002	+	0.126226i	$0.959714\pi$
$522$		0			0
$523$	1.12086e12	−	1.94139e12i	0.655079	−	1.13463i	−0.326794	−	0.945095i	$-0.605968\pi$
$523$	1.12086e12	−	1.94139e12i	0.655079	−	1.13463i	0.981874	−	0.189535i	$-0.0606982\pi$
$524$	7.54569e11			0.437228
$525$		0			0
$526$	−9.06371e11			−0.516262
$527$	8.10380e11	−	1.40362e12i	0.457658	−	0.792687i
$528$		0			0
$529$	8.94727e11	+	1.54971e12i	0.496753	+	0.860401i
$530$	−6.21669e11	+	1.07676e12i	−0.342230	+	0.592759i
$531$		0			0
$532$	−8.97689e10	−	3.03285e11i	−0.0485874	−	0.164153i
$533$	−1.20386e12			−0.646104
$534$		0			0
$535$	7.55132e9	+	1.30793e10i	0.00398502	+	0.00690227i
$536$	4.12910e11	+	7.15182e11i	0.216080	+	0.374261i
$537$		0			0
$538$	2.27416e12			1.17031
$539$	2.56392e12	+	1.30772e12i	1.30844	+	0.667367i
$540$		0			0
$541$	5.81162e10	−	1.00660e11i	0.0291682	−	0.0505208i	−0.851073	−	0.525048i	$-0.824047\pi$
$541$	5.81162e10	−	1.00660e11i	0.0291682	−	0.0505208i	0.880241	+	0.474527i	$0.157381\pi$
$542$	−2.98132e11	−	5.16380e11i	−0.148392	−	0.257023i
$543$		0			0
$544$	−2.68284e11	+	4.64682e11i	−0.131341	+	0.227489i
$545$	1.24257e12			0.603303
$546$		0			0
$547$	1.58473e12			0.756854			0.378427	−	0.925631i	$-0.376465\pi$
$547$	1.58473e12			0.756854			0.378427	+	0.925631i	$0.376465\pi$
$548$	−9.87311e11	+	1.71007e12i	−0.467672	+	0.810032i
$549$		0			0
$550$	5.71512e11	+	9.89888e11i	0.266314	+	0.461269i
$551$	−4.10158e11	+	7.10414e11i	−0.189570	+	0.328344i
$552$		0			0
$553$	−2.37484e11	−	5.70667e10i	−0.107987	−	0.0259490i
$554$	−2.51831e12			−1.13584
$555$		0			0
$556$	6.92002e11	+	1.19858e12i	0.307093	+	0.531901i
$557$	7.55286e11	+	1.30819e12i	0.332478	+	0.575869i	0.982997	−	0.183621i	$-0.0587820\pi$
$557$	7.55286e11	+	1.30819e12i	0.332478	+	0.575869i	−0.650519	+	0.759490i	$0.725449\pi$
$558$		0			0
$559$	−5.70682e12			−2.47196
$560$	4.92706e11	−	5.18989e11i	0.211710	−	0.223004i
$561$		0			0
$562$	−7.73510e11	+	1.33976e12i	−0.327079	+	0.566517i
$563$	−3.03012e11	−	5.24832e11i	−0.127108	−	0.220157i	0.795447	−	0.606023i	$-0.207236\pi$
$563$	−3.03012e11	−	5.24832e11i	−0.127108	−	0.220157i	−0.922555	+	0.385866i	$0.873903\pi$
$564$		0			0
$565$	−2.52790e12	+	4.37846e12i	−1.04362	+	1.80760i
$566$	3.18602e12			1.30489
$567$		0			0
$568$	8.55372e10			0.0344816
$569$	−1.60132e11	+	2.77356e11i	−0.0640431	+	0.110926i	−0.896269	−	0.443511i	$-0.853733\pi$
$569$	−1.60132e11	+	2.77356e11i	−0.0640431	+	0.110926i	0.832226	+	0.554436i	$0.187066\pi$
$570$		0			0
$571$	1.52614e12	+	2.64335e12i	0.600802	+	1.04062i	0.992700	+	0.120611i	$0.0384853\pi$
$571$	1.52614e12	+	2.64335e12i	0.600802	+	1.04062i	−0.391898	+	0.920009i	$0.628181\pi$
$572$	−1.42918e12	+	2.47541e12i	−0.558219	+	0.966863i
$573$		0			0
$574$	−7.59979e11	−	1.82621e11i	−0.292212	−	0.0702178i
$575$	1.08331e11			0.0413285
$576$		0			0
$577$	−1.41483e12	−	2.45055e12i	−0.531389	−	0.920392i	−0.999329	−	0.0366320i	$-0.988337\pi$
$577$	−1.41483e12	−	2.45055e12i	−0.531389	−	0.920392i	0.467940	−	0.883760i	$-0.344996\pi$
$578$	1.14609e12	+	1.98508e12i	0.427112	+	0.739780i
$579$		0			0
$580$	−1.85599e12			−0.681003
$581$	−1.00117e12	−	3.38246e12i	−0.364514	−	1.23151i
$582$		0			0
$583$	1.61217e12	−	2.79236e12i	0.577967	−	1.00107i
$584$	1.81204e10	+	3.13854e10i	0.00644628	+	0.0111653i
$585$		0			0
$586$	−5.82692e11	+	1.00925e12i	−0.204127	+	0.353558i
$587$	2.10206e12			0.730756			0.365378	−	0.930859i	$-0.380940\pi$
$587$	2.10206e12			0.730756			0.365378	+	0.930859i	$0.380940\pi$
$588$		0			0
$589$	−6.16027e11			−0.210902
$590$	1.34510e12	−	2.32978e12i	0.457004	−	0.791554i
$591$		0			0
$592$	−4.72309e11	−	8.18063e11i	−0.158044	−	0.273741i
$593$	−2.96534e12	+	5.13612e12i	−0.984756	+	1.70565i	−0.341742	+	0.939794i	$0.611017\pi$
$593$	−2.96534e12	+	5.13612e12i	−0.984756	+	1.70565i	−0.643014	+	0.765854i	$0.722316\pi$
$594$		0			0
$595$	−1.58586e12	−	5.35784e12i	−0.518726	−	1.75252i
$596$	−7.95141e9			−0.00258129
$597$		0			0
$598$	1.35452e11	+	2.34610e11i	0.0433142	+	0.0750224i
$599$	−1.57607e12	−	2.72984e12i	−0.500213	−	0.866395i	−1.00000		0.000246421i	$-0.999922\pi$
$599$	−1.57607e12	−	2.72984e12i	−0.500213	−	0.866395i	0.499787	−	0.866149i	$-0.333412\pi$
$600$		0			0
$601$	6.20966e12			1.94148			0.970740	−	0.240132i	$-0.0771909\pi$
$601$	6.20966e12			1.94148			0.970740	+	0.240132i	$0.0771909\pi$
$602$	−3.60264e12	−	8.65706e11i	−1.11799	−	0.268650i
$603$		0			0
$604$	−1.04538e12	+	1.81064e12i	−0.319600	+	0.553563i
$605$	−2.34556e12	−	4.06264e12i	−0.711784	−	1.23285i
$606$		0			0
$607$	−2.27519e12	+	3.94075e12i	−0.680251	+	1.17823i	0.294653	+	0.955604i	$0.404796\pi$
$607$	−2.27519e12	+	3.94075e12i	−0.680251	+	1.17823i	−0.974904	+	0.222625i	$0.928537\pi$
$608$	2.03942e11			0.0605257
$609$		0			0
$610$	−3.15378e12			−0.922247
$611$	1.42754e12	−	2.47258e12i	0.414385	−	0.717735i
$612$		0			0
$613$	3.48631e11	+	6.03847e11i	0.0997227	+	0.172725i	0.911570	−	0.411145i	$-0.134871\pi$
$613$	3.48631e11	+	6.03847e11i	0.0997227	+	0.172725i	−0.811847	+	0.583870i	$0.801538\pi$
$614$	−9.42593e11	+	1.63262e12i	−0.267650	+	0.463583i
$615$		0			0
$616$	−1.27773e12	+	1.34589e12i	−0.357542	+	0.376615i
$617$	−3.02922e12			−0.841488			−0.420744	−	0.907179i	$-0.638231\pi$
$617$	−3.02922e12			−0.841488			−0.420744	+	0.907179i	$0.638231\pi$
$618$		0			0
$619$	−1.58193e12	−	2.73998e12i	−0.433090	−	0.750135i	0.564047	−	0.825743i	$-0.309244\pi$
$619$	−1.58193e12	−	2.73998e12i	−0.433090	−	0.750135i	−0.997138	+	0.0756079i	$0.975910\pi$
$620$	−6.96889e11	−	1.20705e12i	−0.189409	−	0.328066i
$621$		0			0
$622$	2.90222e12			0.777452
$623$	−1.01864e12	−	2.44777e11i	−0.270910	−	0.0650991i
$624$		0			0
$625$	2.38387e12	−	4.12899e12i	0.624918	−	1.08239i
$626$	2.27548e12	+	3.94125e12i	0.592228	+	1.02577i
$627$		0			0
$628$	−1.97647e10	+	3.42334e10i	−0.00507074	+	0.00878277i
$629$	−7.37567e12			−1.87877
$630$		0			0
$631$	6.97874e12			1.75245			0.876223	−	0.481906i	$-0.160055\pi$
$631$	6.97874e12			1.75245			0.876223	+	0.481906i	$0.160055\pi$
$632$	7.87431e10	−	1.36387e11i	0.0196329	−	0.0340053i
$633$		0			0
$634$	8.13989e11	+	1.40987e12i	0.200086	+	0.346559i
$635$	5.56730e11	−	9.64285e11i	0.135882	−	0.235355i
$636$		0			0
$637$	−5.29950e12	+	3.43842e12i	−1.27529	+	0.827430i
$638$	4.81312e12			1.15010
$639$		0			0
$640$	2.30712e11	+	3.99605e11i	0.0543576	+	0.0941501i
$641$	−1.49724e12	−	2.59330e12i	−0.350293	−	0.606725i	0.636008	−	0.771682i	$-0.280585\pi$
$641$	−1.49724e12	−	2.59330e12i	−0.350293	−	0.606725i	−0.986301	+	0.164958i	$0.947251\pi$
$642$		0			0
$643$	1.46030e12			0.336894			0.168447	−	0.985711i	$-0.446125\pi$
$643$	1.46030e12			0.336894			0.168447	+	0.985711i	$0.446125\pi$
$644$	4.99195e10	+	1.68654e11i	0.0114363	+	0.0386375i
$645$		0			0
$646$	7.96199e11	−	1.37906e12i	0.179877	−	0.311556i
$647$	2.07950e12	+	3.60181e12i	0.466542	+	0.808074i	0.999270	−	0.0382124i	$-0.0121663\pi$
$647$	2.07950e12	+	3.60181e12i	0.466542	+	0.808074i	−0.532728	+	0.846287i	$0.678833\pi$
$648$		0			0
$649$	−3.48824e12	+	6.04181e12i	−0.771801	+	1.33680i
$650$	−2.50881e12			−0.551261
$651$		0			0
$652$	2.93036e12			0.635048
$653$	7.92472e11	−	1.37260e12i	0.170559	−	0.295417i	−0.768056	−	0.640382i	$-0.778776\pi$
$653$	7.92472e11	−	1.37260e12i	0.170559	−	0.295417i	0.938615	+	0.344965i	$0.112109\pi$
$654$		0			0
$655$	−2.53331e12	−	4.38783e12i	−0.537778	−	0.931459i
$656$	2.51988e11	−	4.36456e11i	0.0531267	−	0.0920182i
$657$		0			0
$658$	1.27627e12	−	1.34435e12i	0.265416	−	0.279574i
$659$	3.00036e12			0.619711			0.309855	−	0.950784i	$-0.399719\pi$
$659$	3.00036e12			0.619711			0.309855	+	0.950784i	$0.399719\pi$
$660$		0			0
$661$	−3.44920e12	−	5.97419e12i	−0.702768	−	1.21723i	−0.967491	−	0.252905i	$-0.918614\pi$
$661$	−3.44920e12	−	5.97419e12i	−0.702768	−	1.21723i	0.264723	−	0.964325i	$-0.414719\pi$
$662$	2.43173e12	+	4.21187e12i	0.492100	+	0.852343i
$663$		0			0
$664$	2.27451e12			0.454079
$665$	−1.46223e12	+	1.54023e12i	−0.289946	+	0.305413i
$666$		0			0
$667$	2.28085e11	−	3.95054e11i	0.0446200	−	0.0772841i
$668$	−2.18952e12	−	3.79235e12i	−0.425455	−	0.736910i
$669$		0			0
$670$	2.77253e12	−	4.80216e12i	0.531544	−	0.920661i
$671$	8.17869e12			1.55752
$672$		0			0
$673$	−4.53756e12			−0.852618			−0.426309	−	0.904578i	$-0.640186\pi$
$673$	−4.53756e12			−0.852618			−0.426309	+	0.904578i	$0.640186\pi$
$674$	−1.37978e11	+	2.38985e11i	−0.0257538	+	0.0446069i
$675$		0			0
$676$	−1.77951e12	−	3.08220e12i	−0.327748	−	0.567676i
$677$	5.21397e12	−	9.03085e12i	0.953936	−	1.65227i	0.217151	−	0.976138i	$-0.430324\pi$
$677$	5.21397e12	−	9.03085e12i	0.953936	−	1.65227i	0.736785	−	0.676127i	$-0.236343\pi$
$678$		0			0
$679$	2.83106e11	+	9.56477e11i	0.0511135	+	0.172687i
$680$	3.60284e12			0.646182
$681$		0			0
$682$	1.80724e12	+	3.13023e12i	0.319879	+	0.554047i
$683$	2.01247e12	+	3.48569e12i	0.353863	+	0.612909i	0.986923	−	0.161194i	$-0.0515346\pi$
$683$	2.01247e12	+	3.48569e12i	0.353863	+	0.612909i	−0.633060	+	0.774103i	$0.718201\pi$
$684$		0			0
$685$	1.32588e13			2.30089
$686$	−3.86710e12	+	1.36671e12i	−0.666695	+	0.235623i
$687$		0			0
$688$	1.19454e12	−	2.06900e12i	0.203260	−	0.352057i
$689$	3.53853e12	+	6.12892e12i	0.598187	+	1.03609i
$690$		0			0
$691$	−2.02863e12	+	3.51369e12i	−0.338494	+	0.586289i	−0.984150	−	0.177339i	$-0.943251\pi$
$691$	−2.02863e12	+	3.51369e12i	−0.338494	+	0.586289i	0.645655	+	0.763629i	$0.276584\pi$
$692$	4.65756e11			0.0772113
$693$		0			0
$694$	5.06934e12			0.829534
$695$	4.64651e12	−	8.04800e12i	0.755432	−	1.30845i
$696$		0			0
$697$	−1.96755e12	−	3.40789e12i	−0.315775	−	0.546938i
$698$	7.67856e11	−	1.32997e12i	0.122442	−	0.212076i
$699$		0			0
$700$	−1.58378e12	−	3.80578e11i	−0.249318	−	0.0599105i
$701$	−2.14575e11			−0.0335621			−0.0167810	−	0.999859i	$-0.505342\pi$
$701$	−2.14575e11			−0.0335621			−0.0167810	+	0.999859i	$0.505342\pi$
$702$		0			0
$703$	1.40169e12	+	2.42780e12i	0.216448	+	0.374899i
$704$	−5.98304e11	−	1.03629e12i	−0.0918005	−	0.159003i
$705$		0			0
$706$	−4.19504e12			−0.635499
$707$	−7.11922e11	+	7.49898e11i	−0.107163	+	0.112879i
$708$		0			0
$709$	4.27735e12	−	7.40859e12i	0.635721	−	1.10110i	−0.350640	−	0.936510i	$-0.614036\pi$
$709$	4.27735e12	−	7.40859e12i	0.635721	−	1.10110i	0.986362	−	0.164592i	$-0.0526306\pi$
$710$	−2.87174e11	−	4.97400e11i	−0.0424114	−	0.0734587i
$711$		0			0
$712$	3.37754e11	−	5.85007e11i	0.0492539	−	0.0853102i
$713$	3.42566e11			0.0496412
$714$		0			0
$715$	1.91927e13			2.74637
$716$	−3.02481e11	+	5.23913e11i	−0.0430121	+	0.0744991i
$717$		0			0
$718$	8.68263e11	+	1.50388e12i	0.121925	+	0.211180i
$719$	−3.24741e12	+	5.62468e12i	−0.453166	+	0.784906i	−0.998581	−	0.0532602i	$-0.983039\pi$
$719$	−3.24741e12	+	5.62468e12i	−0.453166	+	0.784906i	0.545415	+	0.838166i	$0.316372\pi$
$720$		0			0
$721$	−8.36349e12	−	2.00973e12i	−1.15260	−	0.276967i
$722$	4.55776e12			0.624214
$723$		0			0
$724$	−2.11909e12	−	3.67037e12i	−0.286633	−	0.496462i
$725$	2.11226e12	+	3.65855e12i	0.283940	+	0.491799i
$726$		0			0
$727$	5.36028e12			0.711677			0.355838	−	0.934548i	$-0.384195\pi$
$727$	5.36028e12			0.711677			0.355838	+	0.934548i	$0.384195\pi$
$728$	−1.15607e12	−	3.90579e12i	−0.152543	−	0.515368i
$729$		0			0
$730$	1.21671e11	−	2.10740e11i	0.0158575	−	0.0274660i
$731$	−9.32707e12	−	1.61550e13i	−1.20814	−	2.09256i
$732$		0			0
$733$	−1.73332e12	+	3.00220e12i	−0.221774	+	0.384124i	−0.955347	−	0.295487i	$-0.904518\pi$
$733$	−1.73332e12	+	3.00220e12i	−0.221774	+	0.384124i	0.733573	+	0.679611i	$0.237851\pi$
$734$	−3.40057e12			−0.432434
$735$		0			0
$736$	−1.13410e11			−0.0142463
$737$	−7.18999e12	+	1.24534e13i	−0.897686	+	1.55484i
$738$		0			0
$739$	2.12046e12	+	3.67275e12i	0.261536	+	0.452993i	0.966650	−	0.256100i	$-0.0824378\pi$
$739$	2.12046e12	+	3.67275e12i	0.261536	+	0.452993i	−0.705115	+	0.709093i	$0.749104\pi$
$740$	−3.17136e12	+	5.49297e12i	−0.388780	+	0.673386i
$741$		0			0
$742$	1.30409e12	+	4.40589e12i	0.157940	+	0.533600i
$743$	7.87489e12			0.947970			0.473985	−	0.880533i	$-0.342815\pi$
$743$	7.87489e12			0.947970			0.473985	+	0.880533i	$0.342815\pi$
$744$		0			0
$745$	2.66953e10	+	4.62376e10i	0.00317491	+	0.00549910i
$746$	−2.54264e12	−	4.40399e12i	−0.300581	−	0.520621i
$747$		0			0
$748$	−9.34324e12			−1.09129
$749$	5.42680e10	+	1.30405e10i	0.00630051	+	0.00151400i
$750$		0			0
$751$	5.52671e12	−	9.57254e12i	0.633997	−	1.09811i	−0.352730	−	0.935725i	$-0.614747\pi$
$751$	5.52671e12	−	9.57254e12i	0.633997	−	1.09811i	0.986727	−	0.162389i	$-0.0519200\pi$
$752$	5.97619e11	+	1.03511e12i	0.0681466	+	0.118033i
$753$		0			0
$754$	−5.28213e12	+	9.14892e12i	−0.595166	+	1.03086i
$755$	1.40386e13			1.57239
$756$		0			0
$757$	−3.02707e12			−0.335035			−0.167518	−	0.985869i	$-0.553575\pi$
$757$	−3.02707e12			−0.335035			−0.167518	+	0.985869i	$0.553575\pi$
$758$	4.87452e12	−	8.44291e12i	0.536315	−	0.928926i
$759$		0			0
$760$	−6.84694e11	−	1.18592e12i	−0.0744449	−	0.128942i
$761$	−6.58247e12	+	1.14012e13i	−0.711472	+	1.23231i	0.252832	+	0.967510i	$0.418638\pi$
$761$	−6.58247e12	+	1.14012e13i	−0.711472	+	1.23231i	−0.964304	+	0.264796i	$0.914695\pi$
$762$		0			0
$763$	3.16160e12	−	3.33025e12i	0.337712	−	0.355727i
$764$	8.61515e11			0.0914835
$765$		0			0
$766$	−2.72051e12	−	4.71205e12i	−0.285509	−	0.494516i
$767$	−7.65629e12	−	1.32611e13i	−0.798802	−	1.38357i
$768$		0			0
$769$	−5.52244e12			−0.569460			−0.284730	−	0.958608i	$-0.591904\pi$
$769$	−5.52244e12			−0.569460			−0.284730	+	0.958608i	$0.591904\pi$
$770$	1.21161e13	+	2.91147e12i	1.24210	+	0.298473i
$771$		0			0
$772$	6.04652e11	−	1.04729e12i	0.0612672	−	0.106118i
$773$	−9.92941e11	−	1.71982e12i	−0.100027	−	0.173251i	0.811669	−	0.584118i	$-0.198559\pi$
$773$	−9.92941e11	−	1.71982e12i	−0.100027	−	0.173251i	−0.911695	+	0.410867i	$0.865226\pi$
$774$		0			0
$775$	−1.58623e12	+	2.74744e12i	−0.157946	+	0.273571i
$776$	−6.43176e11			−0.0636725
$777$		0			0
$778$	1.20781e13			1.18193
$779$	−7.47836e11	+	1.29529e12i	−0.0727592	+	0.126023i
$780$		0			0
$781$	7.44728e11	+	1.28991e12i	0.0716255	+	0.124059i
$782$	−4.42758e11	+	7.66879e11i	−0.0423385	+	0.0733325i
$783$		0			0
$784$	−1.37315e11	−	2.64105e12i	−0.0129806	−	0.249663i
$785$	2.65424e11			0.0249474
$786$		0			0
$787$	−7.05480e12	−	1.22193e13i	−0.655538	−	1.13543i	−0.981759	−	0.190132i	$-0.939108\pi$
$787$	−7.05480e12	−	1.22193e13i	−0.655538	−	1.13543i	0.326220	−	0.945294i	$-0.394225\pi$
$788$	−2.13736e12	−	3.70202e12i	−0.197474	−	0.342036i
$789$		0			0
$790$	−1.05746e12			−0.0965919
$791$	5.30286e12	+	1.79158e13i	0.481632	+	1.62720i
$792$		0			0
$793$	−8.97565e12	+	1.55463e13i	−0.806003	+	1.39604i
$794$	−2.15511e12	−	3.73276e12i	−0.192432	−	0.333302i
$795$		0			0
$796$	−3.35138e12	+	5.80476e12i	−0.295880	+	0.512478i
$797$	9.54651e12			0.838074			0.419037	−	0.907969i	$-0.362368\pi$
$797$	9.54651e12			0.838074			0.419037	+	0.907969i	$0.362368\pi$
$798$		0			0
$799$	9.33254e12			0.810101
$800$	5.25138e11	−	9.09565e11i	0.0453282	−	0.0785107i
$801$		0			0
$802$	2.84933e12	+	4.93518e12i	0.243197	+	0.421229i
$803$	−3.15529e11	+	5.46512e11i	−0.0267805	+	0.0463852i
$804$		0			0
$805$	8.13129e11	−	8.56504e11i	0.0682461	−	0.0718866i
$806$	−7.93337e12			−0.662141
$807$		0			0
$808$	−3.33360e11	−	5.77397e11i	−0.0275146	−	0.0476566i
$809$	9.23775e12	+	1.60003e13i	0.758225	+	1.31328i	0.943755	+	0.330645i	$0.107266\pi$
$809$	9.23775e12	+	1.60003e13i	0.758225	+	1.31328i	−0.185531	+	0.982639i	$0.559400\pi$
$810$		0			0
$811$	−1.08163e13			−0.877981			−0.438991	−	0.898492i	$-0.644664\pi$
$811$	−1.08163e13			−0.877981			−0.438991	+	0.898492i	$0.644664\pi$
$812$	−4.72240e12	+	4.97431e12i	−0.381207	+	0.401542i
$813$		0			0
$814$	8.22429e12	−	1.42449e13i	0.656582	−	1.13723i
$815$	−9.83809e12	−	1.70401e13i	−0.781091	−	1.35289i
$816$		0			0
$817$	−3.54508e12	+	6.14026e12i	−0.278373	+	0.482156i
$818$	1.39904e12			0.109255
$819$		0			0
$820$	−3.38400e12			−0.261377
$821$	−4.49231e12	+	7.78092e12i	−0.345085	+	0.597704i	−0.985369	−	0.170434i	$-0.945483\pi$
$821$	−4.49231e12	+	7.78092e12i	−0.345085	+	0.597704i	0.640284	+	0.768138i	$0.278817\pi$
$822$		0			0
$823$	1.04734e13	+	1.81404e13i	0.795770	+	1.37831i	0.922349	+	0.386357i	$0.126267\pi$
$823$	1.04734e13	+	1.81404e13i	0.795770	+	1.37831i	−0.126579	+	0.991957i	$0.540400\pi$
$824$	2.77310e12	−	4.80316e12i	0.209553	−	0.362956i
$825$		0			0
$826$	−2.82165e12	−	9.53299e12i	−0.210908	−	0.712556i
$827$	7.58139e12			0.563604			0.281802	−	0.959473i	$-0.409068\pi$
$827$	7.58139e12			0.563604			0.281802	+	0.959473i	$0.409068\pi$
$828$		0			0
$829$	6.64524e12	+	1.15099e13i	0.488670	+	0.846401i	0.999915	−	0.0130340i	$-0.00414896\pi$
$829$	6.64524e12	+	1.15099e13i	0.488670	+	0.846401i	−0.511245	+	0.859435i	$0.670816\pi$
$830$	−7.63620e12	−	1.32263e13i	−0.558504	−	0.967357i
$831$		0			0
$832$	2.62642e12			0.190024
$833$	−1.83949e13	−	9.38225e12i	−1.32371	−	0.675156i
$834$		0			0
$835$	−1.47017e13	+	2.54641e13i	−1.04660	+	1.81276i
$836$	1.77561e12	+	3.07545e12i	0.125725	+	0.217761i
$837$		0			0
$838$	−3.56838e10	+	6.18062e10i	−0.00249962	+	0.00432946i
$839$	−6.44356e12			−0.448949			−0.224474	−	0.974480i	$-0.572067\pi$
$839$	−6.44356e12			−0.448949			−0.224474	+	0.974480i	$0.572067\pi$
$840$		0			0
$841$	3.28177e12			0.226218
$842$	−7.47748e11	+	1.29514e12i	−0.0512685	+	0.0887996i
$843$		0			0
$844$	4.99752e12	+	8.65596e12i	0.339011	+	0.587184i
$845$	−1.19487e13	+	2.06957e13i	−0.806242	+	1.39645i
$846$		0			0
$847$	−1.68565e13	−	4.05059e12i	−1.12536	−	0.270422i
$848$	−2.96271e12			−0.196747
$849$		0			0
$850$	−4.10033e12	−	7.10197e12i	−0.269422	−	0.466653i
$851$	−7.79466e11	−	1.35008e12i	−0.0509465	−	0.0882419i
$852$		0			0
$853$	−1.11447e13			−0.720769			−0.360384	−	0.932804i	$-0.617354\pi$
$853$	−1.11447e13			−0.720769			−0.360384	+	0.932804i	$0.617354\pi$
$854$	−8.02453e12	+	8.45259e12i	−0.516249	+	0.543787i
$855$		0			0
$856$	−1.79938e10	+	3.11662e10i	−0.00114549	+	0.00198405i
$857$	2.95516e12	+	5.11849e12i	0.187140	+	0.324137i	0.944296	−	0.329098i	$-0.106745\pi$
$857$	2.95516e12	+	5.11849e12i	0.187140	+	0.324137i	−0.757155	+	0.653235i	$0.773411\pi$
$858$		0			0
$859$	8.90380e12	−	1.54218e13i	0.557964	−	0.966422i	−0.439702	−	0.898144i	$-0.644916\pi$
$859$	8.90380e12	−	1.54218e13i	0.557964	−	0.966422i	0.997666	−	0.0682787i	$-0.0217507\pi$
$860$	−1.60417e13			−1.00002
$861$		0			0
$862$	−7.98598e12			−0.492658
$863$	7.15238e12	−	1.23883e13i	0.438937	−	0.760261i	−0.558671	−	0.829389i	$-0.688689\pi$
$863$	7.15238e12	−	1.23883e13i	0.438937	−	0.760261i	0.997608	+	0.0691286i	$0.0220219\pi$
$864$		0			0
$865$	−1.56368e12	−	2.70838e12i	−0.0949677	−	0.164489i
$866$	8.33346e12	−	1.44340e13i	0.503494	−	0.872078i
$867$		0			0
$868$	−5.00823e12	−	1.20347e12i	−0.299465	−	0.0719607i
$869$	2.74230e12			0.163127
$870$		0			0
$871$	−1.57812e13	−	2.73338e13i	−0.929091	−	1.60923i
$872$	1.48043e12	+	2.56419e12i	0.0867092	+	0.150185i
$873$		0			0
$874$	3.36572e11			0.0195108
$875$	−2.94883e12	−	9.96267e12i	−0.170065	−	0.574565i
$876$		0			0
$877$	−3.01728e12	+	5.22608e12i	−0.172233	+	0.298317i	−0.939200	−	0.343370i	$-0.888432\pi$
$877$	−3.01728e12	+	5.22608e12i	−0.172233	+	0.298317i	0.766967	+	0.641687i	$0.221765\pi$
$878$	−1.60223e12	−	2.77515e12i	−0.0909914	−	0.157602i
$879$		0			0
$880$	−4.01737e12	+	6.95830e12i	−0.225824	+	0.391139i
$881$	−1.54875e12			−0.0866142			−0.0433071	−	0.999062i	$-0.513789\pi$
$881$	−1.54875e12			−0.0866142			−0.0433071	+	0.999062i	$0.513789\pi$
$882$		0			0
$883$	−2.01052e13			−1.11297			−0.556487	−	0.830857i	$-0.687851\pi$
$883$	−2.01052e13			−1.11297			−0.556487	+	0.830857i	$0.687851\pi$
$884$	1.02537e13	−	1.77599e13i	0.564734	−	0.978149i
$885$		0			0
$886$	−1.80882e12	−	3.13296e12i	−0.0986150	−	0.170806i
$887$	−1.07813e13	+	1.86737e13i	−0.584809	+	1.01292i	0.410091	+	0.912045i	$0.365497\pi$
$887$	−1.07813e13	+	1.86737e13i	−0.584809	+	1.01292i	−0.994899	+	0.100873i	$0.967836\pi$
$888$		0			0
$889$	−1.16787e12	−	3.94566e12i	−0.0627099	−	0.211866i
$890$	−4.53576e12			−0.242323
$891$		0			0
$892$	−5.80109e12	−	1.00478e13i	−0.306809	−	0.531408i
$893$	−1.77358e12	−	3.07193e12i	−0.0933296	−	0.161652i
$894$		0			0
$895$	4.06208e12			0.211614
$896$	1.65802e12	+	3.98419e11i	0.0859419	+	0.0206516i
$897$		0			0
$898$	9.60713e12	−	1.66400e13i	0.493004	−	0.853908i
$899$	6.67941e12	+	1.15691e13i	0.341051	+	0.590718i
$900$		0			0
$901$	−1.15666e13	+	2.00339e13i	−0.584713	+	1.01275i
$902$	8.77571e12			0.441421
$903$		0			0
$904$	−1.20473e13			−0.599974
$905$	−1.42288e13	+	2.46451e13i	−0.705100	+	1.22127i
$906$		0			0
$907$	1.10527e12	+	1.91438e12i	0.0542295	+	0.0939283i	0.891866	−	0.452300i	$-0.149396\pi$
$907$	1.10527e12	+	1.91438e12i	0.0542295	+	0.0939283i	−0.837636	+	0.546228i	$0.816063\pi$
$908$	9.61079e11	−	1.66464e12i	0.0469216	−	0.0812706i
$909$		0			0
$910$	−1.88310e13	+	1.98355e13i	−0.910303	+	0.958862i
$911$	−7.06459e11			−0.0339824			−0.0169912	−	0.999856i	$-0.505409\pi$
$911$	−7.06459e11			−0.0339824			−0.0169912	+	0.999856i	$0.505409\pi$
$912$		0			0
$913$	1.98029e13	+	3.42997e13i	0.943216	+	1.63370i
$914$	2.63782e12	+	4.56884e12i	0.125022	+	0.216545i
$915$		0			0
$916$	1.07129e13			0.502781
$917$	−1.82058e13	−	4.37481e12i	−0.850253	−	0.204314i
$918$		0			0
$919$	−8.29830e12	+	1.43731e13i	−0.383768	+	0.664706i	−0.991597	−	0.129362i	$-0.958707\pi$
$919$	−8.29830e12	+	1.43731e13i	−0.383768	+	0.664706i	0.607829	+	0.794068i	$0.292041\pi$
$920$	3.80751e11	+	6.59480e11i	0.0175225	+	0.0303499i
$921$		0			0
$922$	−1.11142e13	+	1.92504e13i	−0.506513	+	0.877305i
$923$	−3.26919e12			−0.148263
$924$		0			0
$925$	1.44371e13			0.648398
$926$	−5.50499e8	+	9.53492e8i	−2.46041e−5	+	4.26155e-5i
$927$		0			0
$928$	−2.21128e12	−	3.83006e12i	−0.0978766	−	0.169527i
$929$	8.93907e12	−	1.54829e13i	0.393751	−	0.681996i	−0.599190	−	0.800607i	$-0.704511\pi$
$929$	8.93907e12	−	1.54829e13i	0.393751	−	0.681996i	0.992941	+	0.118610i	$0.0378440\pi$
$930$		0			0
$931$	4.07516e11	+	7.83795e12i	0.0177775	+	0.341923i
$932$	−7.80599e12			−0.338888
$933$		0			0
$934$	8.63121e12	+	1.49497e13i	0.371117	+	0.642794i
$935$	3.13680e13	+	5.43311e13i	1.34226	+	2.32485i
$936$		0			0
$937$	4.36868e13			1.85149			0.925747	−	0.378143i	$-0.123437\pi$
$937$	4.36868e13			1.85149			0.925747	+	0.378143i	$0.123437\pi$
$938$	−5.81601e12	−	1.96495e13i	−0.245308	−	0.828777i
$939$		0			0
$940$	4.01277e12	−	6.95033e12i	0.167637	−	0.290356i
$941$	3.20352e12	+	5.54866e12i	0.133191	+	0.230693i	0.924905	−	0.380199i	$-0.124144\pi$
$941$	3.20352e12	+	5.54866e12i	0.133191	+	0.230693i	−0.791714	+	0.610892i	$0.790811\pi$
$942$		0			0
$943$	4.15864e11	−	7.20298e11i	0.0171257	−	0.0296626i
$944$	6.41039e12			0.262730
$945$		0			0
$946$	4.16009e13			1.68885
$947$	−5.20865e12	+	9.02164e12i	−0.210451	+	0.364511i	−0.951856	−	0.306547i	$-0.900826\pi$
$947$	−5.20865e12	+	9.02164e12i	−0.210451	+	0.364511i	0.741405	+	0.671058i	$0.234160\pi$
$948$		0			0
$949$	−6.92550e11	−	1.19953e12i	−0.0277175	−	0.0480080i
$950$	−1.55847e12	+	2.69936e12i	−0.0620788	+	0.107524i
$951$		0			0
$952$	9.16713e12	−	9.65613e12i	0.361715	−	0.381010i
$953$	−6.40900e12			−0.251694			−0.125847	−	0.992050i	$-0.540165\pi$
$953$	−6.40900e12			−0.251694			−0.125847	+	0.992050i	$0.540165\pi$
$954$		0			0
$955$	−2.89236e12	−	5.00972e12i	−0.112522	−	0.194894i
$956$	5.49491e12	+	9.51746e12i	0.212765	+	0.368520i
$957$		0			0
$958$	−9.98096e12			−0.382849
$959$	3.37359e13	−	3.55355e13i	1.28798	−	1.35668i
$960$		0			0
$961$	8.20382e12	−	1.42094e13i	0.310285	−	0.537429i
$962$	1.80514e13	+	3.12659e13i	0.679552	+	1.17702i
$963$		0			0
$964$	1.07657e12	−	1.86467e12i	0.0401507	−	0.0695431i
$965$	−8.12000e12			−0.301428
$966$		0			0
$967$	1.24456e12			0.0457718			0.0228859	−	0.999738i	$-0.492715\pi$
$967$	1.24456e12			0.0457718			0.0228859	+	0.999738i	$0.492715\pi$
$968$	5.58917e12	−	9.68072e12i	0.204601	−	0.354380i
$969$		0			0
$970$	2.15933e12	+	3.74008e12i	0.0783154	+	0.135646i
$971$	1.88913e13	−	3.27208e13i	0.681988	−	1.18124i	−0.292386	−	0.956300i	$-0.594449\pi$
$971$	1.88913e13	−	3.27208e13i	0.681988	−	1.18124i	0.974373	−	0.224937i	$-0.0722175\pi$
$972$		0			0
$973$	−9.74713e12	−	3.29308e13i	−0.348633	−	1.17786i
$974$	2.39508e13			0.852717
$975$		0			0
$976$	−3.75752e12	−	6.50822e12i	−0.132549	−	0.229582i
$977$	−6.39041e12	−	1.10685e13i	−0.224390	−	0.388655i	0.731746	−	0.681577i	$-0.238706\pi$
$977$	−6.39041e12	−	1.10685e13i	−0.224390	−	0.388655i	−0.956136	+	0.292922i	$0.905372\pi$
$978$		0			0
$979$	1.17626e13			0.409242
$980$	−1.48967e13	+	9.66527e12i	−0.515909	+	0.334732i
$981$		0			0
$982$	−5.52840e12	+	9.57547e12i	−0.189713	+	0.328593i
$983$	−1.14746e13	−	1.98746e13i	−0.391964	−	0.678902i	0.600744	−	0.799441i	$-0.294871\pi$
$983$	−1.14746e13	−	1.98746e13i	−0.391964	−	0.678902i	−0.992709	+	0.120539i	$0.961538\pi$
$984$		0			0
$985$	−1.43515e13	+	2.48576e13i	−0.485776	+	0.841388i
$986$	−3.45319e13			−1.16352
$987$		0			0
$988$	−7.79454e12			−0.260246
$989$	1.97138e12	−	3.41454e12i	0.0655221	−	0.113488i
$990$		0			0
$991$	−1.37595e13	−	2.38322e13i	−0.453182	−	0.784934i	0.545400	−	0.838176i	$-0.316378\pi$
$991$	−1.37595e13	−	2.38322e13i	−0.453182	−	0.784934i	−0.998582	+	0.0532423i	$0.983044\pi$
$992$	1.66059e12	−	2.87623e12i	0.0544454	−	0.0943022i
$993$		0			0
$994$	−2.06379e12	−	4.95925e11i	−0.0670544	−	0.0161130i
$995$	4.50063e13			1.45569
$996$		0			0
$997$	−1.41861e13	−	2.45711e13i	−0.454712	−	0.787583i	0.543960	−	0.839111i	$-0.316924\pi$
$997$	−1.41861e13	−	2.45711e13i	−0.454712	−	0.787583i	−0.998672	+	0.0515277i	$0.983591\pi$
$998$	1.09993e13	+	1.90514e13i	0.350978	+	0.607911i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.10.g.f.37.1		6
3.2	odd	2		14.10.c.a.9.2	✓	6
7.4	even	3	inner	126.10.g.f.109.1		6
12.11	even	2		112.10.i.b.65.2		6
21.2	odd	6		98.10.a.j.1.2		3
21.5	even	6		98.10.a.i.1.2		3
21.11	odd	6		14.10.c.a.11.2	yes	6
21.17	even	6		98.10.c.k.67.2		6
21.20	even	2		98.10.c.k.79.2		6
84.11	even	6		112.10.i.b.81.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.c.a.9.2	✓	6	3.2	odd	2
14.10.c.a.11.2	yes	6	21.11	odd	6
98.10.a.i.1.2		3	21.5	even	6
98.10.a.j.1.2		3	21.2	odd	6
98.10.c.k.67.2		6	21.17	even	6
98.10.c.k.79.2		6	21.20	even	2
112.10.i.b.65.2		6	12.11	even	2
112.10.i.b.81.2		6	84.11	even	6
126.10.g.f.37.1		6	1.1	even	1	trivial
126.10.g.f.109.1		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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 - 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(-859.469 + 1488.64i) q^{5} +(1802.93 + 6091.23i) q^{7} -4096.00 q^{8} +(13751.5 + 23818.3i) q^{10} +(-35661.7 - 61767.9i) q^{11} +156547. q^{13} +(98826.0 + 23747.7i) q^{14} +(-32768.0 + 56755.8i) q^{16} +(255856. + 443155. i) q^{17} +(97247.0 - 168437. i) q^{19} +440048. q^{20} -1.14118e6 q^{22} +(-54078.1 + 93666.0i) q^{23} +(-500810. - 867429. i) q^{25} +(1.25237e6 - 2.16918e6i) q^{26} +(1.11966e6 - 1.17939e6i) q^{28} -4.21769e6 q^{29} +(-1.58367e6 - 2.74299e6i) q^{31} +(524288. + 908093. i) q^{32} +8.18738e6 q^{34} +(-1.06172e7 - 2.55130e6i) q^{35} +(-7.20686e6 + 1.24827e7i) q^{37} +(-1.55595e6 - 2.69499e6i) q^{38} +(3.52038e6 - 6.09748e6i) q^{40} -7.69007e6 q^{41} -3.64544e7 q^{43} +(-9.12940e6 + 1.58126e7i) q^{44} +(865249. + 1.49866e6i) q^{46} +(9.11895e6 - 1.57945e7i) q^{47} +(-3.38525e7 + 2.19641e7i) q^{49} -1.60259e7 q^{50} +(-2.00380e7 - 3.47068e7i) q^{52} +(2.26037e7 + 3.91507e7i) q^{53} +1.22601e8 q^{55} +(-7.38481e6 - 2.49497e7i) q^{56} +(-3.37415e7 + 5.84420e7i) q^{58} +(-4.89074e7 - 8.47100e7i) q^{59} +(-5.73352e7 + 9.93075e7i) q^{61} -5.06773e7 q^{62} +1.67772e7 q^{64} +(-1.34547e8 + 2.33042e8i) q^{65} +(-1.00808e8 - 1.74605e8i) q^{67} +(6.54991e7 - 1.13448e8i) q^{68} +(-1.20290e8 + 1.26706e8i) q^{70} -2.08831e7 q^{71} +(-4.42392e6 - 7.66245e6i) q^{73} +(1.15310e8 + 1.99722e8i) q^{74} -4.97905e7 q^{76} +(3.11947e8 - 3.28587e8i) q^{77} +(-1.92244e7 + 3.32976e7i) q^{79} +(-5.63261e7 - 9.75597e7i) q^{80} +(-6.15205e7 + 1.06557e8i) q^{82} -5.55300e8 q^{83} -8.79600e8 q^{85} +(-2.91635e8 + 5.05127e8i) q^{86} +(1.46070e8 + 2.53001e8i) q^{88} +(-8.24594e7 + 1.42824e8i) q^{89} +(2.82243e8 + 9.53562e8i) q^{91} +2.76880e7 q^{92} +(-1.45903e8 - 2.52712e8i) q^{94} +(1.67162e8 + 2.89532e8i) q^{95} +1.57025e8 q^{97} +(3.35242e7 + 6.44787e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 48 q^{2} - 768 q^{4} + 733 q^{5} + 5012 q^{7} - 24576 q^{8} - 11728 q^{10} - 7339 q^{11} + 197036 q^{13} + 142576 q^{14} - 196608 q^{16} + 306665 q^{17} - 377991 q^{19} - 375296 q^{20} - 234848 q^{22}+ \cdots + 2185885296 q^{98}+O(q^{100}) \) 6 * q + 48 * q^2 - 768 * q^4 + 733 * q^5 + 5012 * q^7 - 24576 * q^8 - 11728 * q^10 - 7339 * q^11 + 197036 * q^13 + 142576 * q^14 - 196608 * q^16 + 306665 * q^17 - 377991 * q^19 - 375296 * q^20 - 234848 * q^22 + 2267255 * q^23 - 142612 * q^25 + 1576288 * q^26 + 998144 * q^28 + 13085956 * q^29 - 6654517 * q^31 + 3145728 * q^32 + 9813280 * q^34 - 22864807 * q^35 - 22287969 * q^37 + 6047856 * q^38 - 3002368 * q^40 - 68096196 * q^41 - 125648280 * q^43 - 1878784 * q^44 - 36276080 * q^46 + 52703019 * q^47 + 57596070 * q^49 - 4563584 * q^50 - 25220608 * q^52 + 12091125 * q^53 + 377435398 * q^55 - 20529152 * q^56 + 104687648 * q^58 + 12949897 * q^59 - 160252153 * q^61 - 212944544 * q^62 + 100663296 * q^64 - 334191270 * q^65 - 480890225 * q^67 + 78506240 * q^68 - 349171760 * q^70 + 74421440 * q^71 + 251382283 * q^73 + 356607504 * q^74 + 193531392 * q^76 + 527045155 * q^77 + 286494785 * q^79 + 48037888 * q^80 - 544769568 * q^82 - 2295182344 * q^83 - 2389185074 * q^85 - 1005186240 * q^86 + 30060544 * q^88 + 901243845 * q^89 + 1026798920 * q^91 - 1160834560 * q^92 - 843248304 * q^94 + 887366177 * q^95 + 629707876 * q^97 + 2185885296 * q^98

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