LMFDB - Embedded newform 54.9.d.a.35.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,9,Mod(17,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("54.17");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	54.d (of order $6$, degree $2$, not 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:	$21.9984449433$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 150208 x^{14} - 1927740 x^{13} + 8702363206 x^{12} + 239206241152 x^{11} + \cdots + 81\!\cdots\!61 $ x^16 - 4x^15 - 150208x^14 - 1927740x^13 + 8702363206x^12 + 239206241152x^11 - 241960304158448x^10 - 9458863275320348x^9 + 3259352971808015407x^8 + 150983052056025751536x^7 - 18744835998632687401792x^6 - 866018994869774202180460x^5 + 35643731791394373752805382x^4 + 1485002234815673954960734644x^3 + 16292568366453217677347743656x^2 + 62373298381917691066182105696*x + 81301302751102601946916438161
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{28}\cdot 3^{36} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.8
Root			$-147.309 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	54.35
Dual form			54.9.d.a.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(9.79796 + 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(719.139 - 415.195i) q^{5} +(1343.41 - 2326.85i) q^{7} +1448.15i q^{8} +9394.80 q^{10} +(-21366.9 - 12336.2i) q^{11} +(-4848.77 - 8398.31i) q^{13} +(26325.3 - 15198.9i) q^{14} +(-8192.00 + 14189.0i) q^{16} -42669.1i q^{17} +101194. q^{19} +(92049.8 + 53145.0i) q^{20} +(-139568. - 241739. i) q^{22} +(396990. - 229203. i) q^{23} +(149462. - 258875. i) q^{25} -109715. i q^{26} +343913. q^{28} +(-577159. - 333223. i) q^{29} +(709545. + 1.22897e6i) q^{31} +(-160530. + 92681.9i) q^{32} +(241373. - 418071. i) q^{34} -2.23111e6i q^{35} +1.62583e6 q^{37} +(991496. + 572441. i) q^{38} +(601267. + 1.04142e6i) q^{40} +(-1.99920e6 + 1.15424e6i) q^{41} +(812997. - 1.40815e6i) q^{43} -3.15806e6i q^{44} +5.18626e6 q^{46} +(3.38272e6 + 1.95301e6i) q^{47} +(-727099. - 1.25937e6i) q^{49} +(2.92884e6 - 1.69097e6i) q^{50} +(620642. - 1.07498e6i) q^{52} -6.96433e6i q^{53} -2.04877e7 q^{55} +(3.36964e6 + 1.94547e6i) q^{56} +(-3.76999e6 - 6.52981e6i) q^{58} +(-5.94959e6 + 3.43500e6i) q^{59} +(1.26576e6 - 2.19236e6i) q^{61} +1.60552e7i q^{62} -2.09715e6 q^{64} +(-6.97388e6 - 4.02637e6i) q^{65} +(1.58375e7 + 2.74313e7i) q^{67} +(4.72993e6 - 2.73083e6i) q^{68} +(1.26211e7 - 2.18603e7i) q^{70} +1.75496e7i q^{71} -2.86971e7 q^{73} +(1.59299e7 + 9.19711e6i) q^{74} +(6.47643e6 + 1.12175e7i) q^{76} +(-5.74089e7 + 3.31451e7i) q^{77} +(-3.40323e7 + 5.89457e7i) q^{79} +1.36051e7i q^{80} -2.61174e7 q^{82} +(-4.73759e7 - 2.73525e7i) q^{83} +(-1.77160e7 - 3.06851e7i) q^{85} +(1.59314e7 - 9.19801e6i) q^{86} +(1.78647e7 - 3.09425e7i) q^{88} +7.04968e6i q^{89} -2.60555e7 q^{91} +(5.08148e7 + 2.93379e7i) q^{92} +(2.20958e7 + 3.82711e7i) q^{94} +(7.27727e7 - 4.20153e7i) q^{95} +(5.14341e7 - 8.90865e7i) q^{97} -1.64524e7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7} - 45756 q^{11} - 3370 q^{13} + 94464 q^{14} - 131072 q^{16} + 362180 q^{19} + 112896 q^{20} - 61824 q^{22} - 1311138 q^{23} + 963394 q^{25} - 472576 q^{28} + 2851290 q^{29}+ \cdots - 89415484 q^{97}+O(q^{100}) $ 16 * q + 1024 * q^4 + 882 * q^5 - 1846 * q^7 - 45756 * q^11 - 3370 * q^13 + 94464 * q^14 - 131072 * q^16 + 362180 * q^19 + 112896 * q^20 - 61824 * q^22 - 1311138 * q^23 + 963394 * q^25 - 472576 * q^28 + 2851290 * q^29 + 542438 * q^31 + 220416 * q^34 + 3343328 * q^37 + 1314432 * q^38 - 9218592 * q^41 + 339512 * q^43 + 7417344 * q^46 + 34980606 * q^47 - 2364654 * q^49 - 27744768 * q^50 + 431360 * q^52 - 4584276 * q^55 + 12091392 * q^56 - 7852800 * q^58 - 93924216 * q^59 - 841954 * q^61 - 33554432 * q^64 + 126568134 * q^65 + 29946644 * q^67 + 5476608 * q^68 - 34359552 * q^70 - 7547764 * q^73 - 35124480 * q^74 + 23179520 * q^76 - 9309294 * q^77 + 33813002 * q^79 - 137346048 * q^82 - 114200226 * q^83 - 125696772 * q^85 + 171379584 * q^86 + 7913472 * q^88 + 268578316 * q^91 - 167825664 * q^92 - 11832576 * q^94 + 143949240 * q^95 - 89415484 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	9.79796	+	5.65685i	0.612372	+	0.353553i
$2$	9.79796	+	5.65685i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	64.0000	+	110.851i	0.250000	+	0.433013i
$5$	719.139	−	415.195i	1.15062	−	0.664312i	0.201584	−	0.979471i	$-0.435391\pi$
$5$	719.139	−	415.195i	1.15062	−	0.664312i	0.949039	+	0.315159i	$0.102058\pi$
$6$		0			0
$7$	1343.41	−	2326.85i	0.559521	−	0.969119i	−0.438015	−	0.898967i	$-0.644318\pi$
$7$	1343.41	−	2326.85i	0.559521	−	0.969119i	0.997536	−	0.0701513i	$-0.0223482\pi$
$8$			1448.15i			0.353553i
$9$		0			0
$10$	9394.80			0.939480
$11$	−21366.9	−	12336.2i	−1.45939	−	0.842577i	−0.460405	−	0.887709i	$-0.652296\pi$
$11$	−21366.9	−	12336.2i	−1.45939	−	0.842577i	−0.998981	+	0.0451321i	$0.985629\pi$
$12$		0			0
$13$	−4848.77	−	8398.31i	−0.169769	−	0.294048i	0.768570	−	0.639766i	$-0.220969\pi$
$13$	−4848.77	−	8398.31i	−0.169769	−	0.294048i	−0.938339	+	0.345718i	$0.887635\pi$
$14$	26325.3	−	15198.9i	0.685270	−	0.395641i
$15$		0			0
$16$	−8192.00	+	14189.0i	−0.125000	+	0.216506i
$17$		−	42669.1i		−	0.510879i	−0.966825	−	0.255440i	$-0.917780\pi$
$17$		−	42669.1i		−	0.510879i	0.966825	−	0.255440i	$-0.0822202\pi$
$18$		0			0
$19$	101194.			0.776499			0.388250	−	0.921554i	$-0.373080\pi$
$19$	101194.			0.776499			0.388250	+	0.921554i	$0.373080\pi$
$20$	92049.8	+	53145.0i	0.575311	+	0.332156i
$21$		0			0
$22$	−139568.	−	241739.i	−0.595792	−	1.03194i
$23$	396990.	−	229203.i	1.41863	−	0.819046i	0.422450	−	0.906386i	$-0.361170\pi$
$23$	396990.	−	229203.i	1.41863	−	0.819046i	0.996179	+	0.0873406i	$0.0278369\pi$
$24$		0			0
$25$	149462.	−	258875.i	0.382622	−	0.662721i
$26$		−	109715.i		−	0.240089i
$27$		0			0
$28$	343913.			0.559521
$29$	−577159.	−	333223.i	−0.816025	−	0.471132i	0.0330188	−	0.999455i	$-0.489488\pi$
$29$	−577159.	−	333223.i	−0.816025	−	0.471132i	−0.849044	+	0.528322i	$0.822821\pi$
$30$		0			0
$31$	709545.	+	1.22897e6i	0.768305	+	1.33074i	0.938482	+	0.345329i	$0.112233\pi$
$31$	709545.	+	1.22897e6i	0.768305	+	1.33074i	−0.170177	+	0.985413i	$0.554434\pi$
$32$	−160530.	+	92681.9i	−0.153093	+	0.0883883i
$33$		0			0
$34$	241373.	−	418071.i	0.180623	−	0.312848i
$35$		−	2.23111e6i		−	1.48679i
$36$		0			0
$37$	1.62583e6			0.867500			0.433750	−	0.901033i	$-0.357190\pi$
$37$	1.62583e6			0.867500			0.433750	+	0.901033i	$0.357190\pi$
$38$	991496.	+	572441.i	0.475507	+	0.274534i
$39$		0			0
$40$	601267.	+	1.04142e6i	0.234870	+	0.406807i
$41$	−1.99920e6	+	1.15424e6i	−0.707491	+	0.408470i	−0.810131	−	0.586249i	$-0.800604\pi$
$41$	−1.99920e6	+	1.15424e6i	−0.707491	+	0.408470i	0.102641	+	0.994719i	$0.467271\pi$
$42$		0			0
$43$	812997.	−	1.40815e6i	0.237802	−	0.411885i	−0.722281	−	0.691599i	$-0.756906\pi$
$43$	812997.	−	1.40815e6i	0.237802	−	0.411885i	0.960083	+	0.279714i	$0.0902398\pi$
$44$		−	3.15806e6i		−	0.842577i
$45$		0			0
$46$	5.18626e6			1.15831
$47$	3.38272e6	+	1.95301e6i	0.693226	+	0.400234i	0.804819	−	0.593520i	$-0.202262\pi$
$47$	3.38272e6	+	1.95301e6i	0.693226	+	0.400234i	−0.111594	+	0.993754i	$0.535595\pi$
$48$		0			0
$49$	−727099.	−	1.25937e6i	−0.126127	−	0.218459i
$50$	2.92884e6	−	1.69097e6i	0.468614	−	0.270555i
$51$		0			0
$52$	620642.	−	1.07498e6i	0.0848844	−	0.147024i
$53$		−	6.96433e6i		−	0.882624i	−0.897354	−	0.441312i	$-0.854513\pi$
$53$		−	6.96433e6i		−	0.882624i	0.897354	−	0.441312i	$-0.145487\pi$
$54$		0			0
$55$	−2.04877e7			−2.23894
$56$	3.36964e6	+	1.94547e6i	0.342635	+	0.197821i
$57$		0			0
$58$	−3.76999e6	−	6.52981e6i	−0.333141	−	0.577017i
$59$	−5.94959e6	+	3.43500e6i	−0.490997	+	0.283477i	−0.724988	−	0.688761i	$-0.758155\pi$
$59$	−5.94959e6	+	3.43500e6i	−0.490997	+	0.283477i	0.233991	+	0.972239i	$0.424821\pi$
$60$		0			0
$61$	1.26576e6	−	2.19236e6i	0.0914182	−	0.158341i	−0.816690	−	0.577077i	$-0.804193\pi$
$61$	1.26576e6	−	2.19236e6i	0.0914182	−	0.158341i	0.908108	+	0.418736i	$0.137527\pi$
$62$			1.60552e7i			1.08655i
$63$		0			0
$64$	−2.09715e6			−0.125000
$65$	−6.97388e6	−	4.02637e6i	−0.390680	−	0.225559i
$66$		0			0
$67$	1.58375e7	+	2.74313e7i	0.785936	+	1.36128i	0.928439	+	0.371486i	$0.121152\pi$
$67$	1.58375e7	+	2.74313e7i	0.785936	+	1.36128i	−0.142503	+	0.989794i	$0.545515\pi$
$68$	4.72993e6	−	2.73083e6i	0.221217	−	0.127720i
$69$		0			0
$70$	1.26211e7	−	2.18603e7i	0.525659	−	0.910467i
$71$			1.75496e7i			0.690612i	0.938490	+	0.345306i	$0.112225\pi$
$71$			1.75496e7i			0.690612i	−0.938490	+	0.345306i	$0.887775\pi$
$72$		0			0
$73$	−2.86971e7			−1.01052			−0.505261	−	0.862966i	$-0.668604\pi$
$73$	−2.86971e7			−1.01052			−0.505261	+	0.862966i	$0.668604\pi$
$74$	1.59299e7	+	9.19711e6i	0.531233	+	0.306707i
$75$		0			0
$76$	6.47643e6	+	1.12175e7i	0.194125	+	0.336234i
$77$	−5.74089e7	+	3.31451e7i	−1.63311	+	0.942879i
$78$		0			0
$79$	−3.40323e7	+	5.89457e7i	−0.873741	+	1.51336i	−0.0156441	+	0.999878i	$0.504980\pi$
$79$	−3.40323e7	+	5.89457e7i	−0.873741	+	1.51336i	−0.858097	+	0.513487i	$0.828353\pi$
$80$			1.36051e7i			0.332156i
$81$		0			0
$82$	−2.61174e7			−0.577664
$83$	−4.73759e7	−	2.73525e7i	−0.998263	−	0.576347i	−0.0905288	−	0.995894i	$-0.528856\pi$
$83$	−4.73759e7	−	2.73525e7i	−0.998263	−	0.576347i	−0.907734	+	0.419547i	$0.862189\pi$
$84$		0			0
$85$	−1.77160e7	−	3.06851e7i	−0.339383	−	0.587829i
$86$	1.59314e7	−	9.19801e6i	0.291247	−	0.168151i
$87$		0			0
$88$	1.78647e7	−	3.09425e7i	0.297896	−	0.515971i
$89$			7.04968e6i			0.112359i	0.998421	+	0.0561797i	$0.0178920\pi$
$89$			7.04968e6i			0.112359i	−0.998421	+	0.0561797i	$0.982108\pi$
$90$		0			0
$91$	−2.60555e7			−0.379957
$92$	5.08148e7	+	2.93379e7i	0.709314	+	0.409523i
$93$		0			0
$94$	2.20958e7	+	3.82711e7i	0.283008	+	0.490185i
$95$	7.27727e7	−	4.20153e7i	0.893458	−	0.515838i
$96$		0			0
$97$	5.14341e7	−	8.90865e7i	0.580984	−	1.00629i	−0.414379	−	0.910104i	$-0.636001\pi$
$97$	5.14341e7	−	8.90865e7i	0.580984	−	1.00629i	0.995363	−	0.0961894i	$-0.0306655\pi$
$98$		−	1.64524e7i		−	0.178371i
$99$		0			0
$100$	3.82622e7			0.382622
$101$	8.11338e7	+	4.68426e7i	0.779680	+	0.450148i	0.836317	−	0.548246i	$-0.184704\pi$
$101$	8.11338e7	+	4.68426e7i	0.779680	+	0.450148i	−0.0566370	+	0.998395i	$0.518038\pi$
$102$		0			0
$103$	4.68590e7	+	8.11622e7i	0.416336	+	0.721116i	0.995568	−	0.0940475i	$-0.0299806\pi$
$103$	4.68590e7	+	8.11622e7i	0.416336	+	0.721116i	−0.579231	+	0.815163i	$0.696647\pi$
$104$	1.21621e7	−	7.02177e6i	0.103962	−	0.0600224i
$105$		0			0
$106$	3.93962e7	−	6.82362e7i	0.312055	−	0.540495i
$107$		−	1.34556e8i		−	1.02652i	−0.858232	−	0.513262i	$-0.828437\pi$
$107$		−	1.34556e8i		−	1.02652i	0.858232	−	0.513262i	$-0.171563\pi$
$108$		0			0
$109$	−5.31868e7			−0.376788			−0.188394	−	0.982093i	$-0.560328\pi$
$109$	−5.31868e7			−0.376788			−0.188394	+	0.982093i	$0.560328\pi$
$110$	−2.00737e8	−	1.15896e8i	−1.37106	−	0.791584i
$111$		0			0
$112$	2.20104e7	+	3.81232e7i	0.139880	+	0.242280i
$113$	1.14368e8	−	6.60307e7i	0.701443	−	0.404978i	−0.106442	−	0.994319i	$-0.533946\pi$
$113$	1.14368e8	−	6.60307e7i	0.701443	−	0.404978i	0.807885	+	0.589341i	$0.200612\pi$
$114$		0			0
$115$	1.90328e8	−	3.29657e8i	1.08820	−	1.88483i
$116$		−	8.53051e7i		−	0.471132i
$117$		0			0
$118$	−7.77251e7			−0.400897
$119$	−9.92849e7	−	5.73222e7i	−0.495103	−	0.285848i
$120$		0			0
$121$	1.97183e8	+	3.41530e8i	0.919872	+	1.59326i
$122$	2.48038e7	−	1.43205e7i	0.111964	−	0.0646424i
$123$		0			0
$124$	−9.08218e7	+	1.57308e8i	−0.384152	+	0.665371i
$125$			7.61481e7i			0.311903i
$126$		0			0
$127$	5.72307e7			0.219996			0.109998	−	0.993932i	$-0.464916\pi$
$127$	5.72307e7			0.219996			0.109998	+	0.993932i	$0.464916\pi$
$128$	−2.05478e7	−	1.18633e7i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−4.55532e7	−	7.89004e7i	−0.159494	−	0.276252i
$131$	9.79607e7	−	5.65576e7i	0.332634	−	0.192046i	−0.324376	−	0.945928i	$-0.605154\pi$
$131$	9.79607e7	−	5.65576e7i	0.332634	−	0.192046i	0.657010	+	0.753882i	$0.271821\pi$
$132$		0			0
$133$	1.35945e8	−	2.35464e8i	0.434468	−	0.752520i
$134$			3.58361e8i			1.11148i
$135$		0			0
$136$	6.17915e7			0.180623
$137$	1.19042e8	+	6.87289e7i	0.337923	+	0.195100i	0.659353	−	0.751833i	$-0.270830\pi$
$137$	1.19042e8	+	6.87289e7i	0.337923	+	0.195100i	−0.321430	+	0.946933i	$0.604164\pi$
$138$		0			0
$139$	−9.70841e7	−	1.68155e8i	−0.260069	−	0.450453i	0.706191	−	0.708022i	$-0.250412\pi$
$139$	−9.70841e7	−	1.68155e8i	−0.260069	−	0.450453i	−0.966260	+	0.257568i	$0.917079\pi$
$140$	2.47321e8	−	1.42791e8i	0.643798	−	0.371697i
$141$		0			0
$142$	−9.92757e7	+	1.71950e8i	−0.244168	+	0.422912i
$143$			2.39261e8i			0.572173i
$144$		0			0
$145$	−5.53410e8			−1.25192
$146$	−2.81173e8	−	1.62335e8i	−0.618816	−	0.357274i
$147$		0			0
$148$	1.04053e8	+	1.80226e8i	0.216875	+	0.375638i
$149$	−6.70921e8	+	3.87357e8i	−1.36121	+	0.785897i	−0.989786	−	0.142564i	$-0.954465\pi$
$149$	−6.70921e8	+	3.87357e8i	−1.36121	+	0.785897i	−0.371429	+	0.928461i	$0.621132\pi$
$150$		0			0
$151$	−3.48071e8	+	6.02877e8i	−0.669515	+	1.15963i	0.308525	+	0.951216i	$0.400165\pi$
$151$	−3.48071e8	+	6.02877e8i	−0.669515	+	1.15963i	−0.978040	+	0.208418i	$0.933169\pi$
$152$			1.46545e8i			0.274534i
$153$		0			0
$154$	−7.49987e8			−1.33343
$155$	1.02052e9	+	5.89200e8i	1.76806	+	1.02079i
$156$		0			0
$157$	−4.99364e6	−	8.64924e6i	−0.00821900	−	0.0142357i	0.861887	−	0.507101i	$-0.169283\pi$
$157$	−4.99364e6	−	8.64924e6i	−0.00821900	−	0.0142357i	−0.870106	+	0.492865i	$0.835950\pi$
$158$	−6.66894e8	+	3.85032e8i	−1.07011	+	0.617829i
$159$		0			0
$160$	−7.69622e7	+	1.33302e8i	−0.117435	+	0.203403i
$161$		−	1.23165e9i		−	1.83309i
$162$		0			0
$163$	1.22877e9			1.74068			0.870340	−	0.492451i	$-0.163899\pi$
$163$	1.22877e9			1.74068			0.870340	+	0.492451i	$0.163899\pi$
$164$	−2.55898e8	−	1.47743e8i	−0.353745	−	0.204235i
$165$		0			0
$166$	−3.09458e8	−	5.35997e8i	−0.407539	−	0.705878i
$167$	−7.41092e8	+	4.27870e8i	−0.952809	+	0.550105i	−0.893953	−	0.448162i	$-0.852079\pi$
$167$	−7.41092e8	+	4.27870e8i	−0.952809	+	0.550105i	−0.0588569	+	0.998266i	$0.518746\pi$
$168$		0			0
$169$	3.60844e8	−	6.25001e8i	0.442357	−	0.766185i
$170$		−	4.00868e8i		−	0.479961i
$171$		0			0
$172$	2.08127e8			0.237802
$173$	3.96513e8	+	2.28927e8i	0.442663	+	0.255572i	0.704727	−	0.709479i	$-0.251070\pi$
$173$	3.96513e8	+	2.28927e8i	0.442663	+	0.255572i	−0.262064	+	0.965051i	$0.584403\pi$
$174$		0			0
$175$	−4.01577e8	−	6.95551e8i	−0.428170	−	0.741612i
$176$	3.50075e8	−	2.02116e8i	0.364846	−	0.210644i
$177$		0			0
$178$	−3.98790e7	+	6.90725e7i	−0.0397250	+	0.0688058i
$179$			1.46762e9i			1.42956i	0.699350	+	0.714779i	$0.253473\pi$
$179$			1.46762e9i			1.42956i	−0.699350	+	0.714779i	$0.746527\pi$
$180$		0			0
$181$	−1.59274e9			−1.48399			−0.741993	−	0.670408i	$-0.766119\pi$
$181$	−1.59274e9			−1.48399			−0.741993	+	0.670408i	$0.766119\pi$
$182$	−2.55291e8	−	1.47392e8i	−0.232675	−	0.134335i
$183$		0			0
$184$	3.31921e8	+	5.74904e8i	0.289576	+	0.501561i
$185$	1.16920e9	−	6.75039e8i	0.998165	−	0.576291i
$186$		0			0
$187$	−5.26374e8	+	9.11706e8i	−0.430455	+	0.745570i
$188$			4.99972e8i			0.400234i
$189$		0			0
$190$	9.50699e8			0.729505
$191$	1.60894e8	+	9.28923e7i	0.120895	+	0.0697985i	0.559228	−	0.829014i	$-0.311098\pi$
$191$	1.60894e8	+	9.28923e7i	0.120895	+	0.0697985i	−0.438333	+	0.898813i	$0.644431\pi$
$192$		0			0
$193$	−5.85324e8	−	1.01381e9i	−0.421859	−	0.730681i	0.574262	−	0.818671i	$-0.305289\pi$
$193$	−5.85324e8	−	1.01381e9i	−0.421859	−	0.730681i	−0.996121	+	0.0879903i	$0.971956\pi$
$194$	1.00790e9	−	5.81910e8i	0.711557	−	0.410818i
$195$		0			0
$196$	9.30687e7	−	1.61200e8i	0.0630637	−	0.109230i
$197$		−	1.90415e9i		−	1.26426i	−0.774864	−	0.632128i	$-0.782182\pi$
$197$		−	1.90415e9i		−	1.26426i	0.774864	−	0.632128i	$-0.217818\pi$
$198$		0			0
$199$	1.59363e9			1.01619			0.508096	−	0.861300i	$-0.330349\pi$
$199$	1.59363e9			1.01619			0.508096	+	0.861300i	$0.330349\pi$
$200$	3.74891e8	+	2.16444e8i	0.234307	+	0.135277i
$201$		0			0
$202$	5.29964e8	+	9.17924e8i	0.318303	+	0.551317i
$203$	−1.55072e9	+	8.95310e8i	−0.913166	+	0.527217i
$204$		0			0
$205$	−9.58469e8	+	1.66012e9i	−0.542703	+	0.939990i
$206$			1.06030e9i			0.588788i
$207$		0			0
$208$	1.58884e8			0.0848844
$209$	−2.16220e9	−	1.24835e9i	−1.13321	−	0.654260i
$210$		0			0
$211$	4.36444e8	+	7.55944e8i	0.220191	+	0.381382i	0.954866	−	0.297038i	$-0.0959987\pi$
$211$	4.36444e8	+	7.55944e8i	0.220191	+	0.381382i	−0.734675	+	0.678419i	$0.762665\pi$
$212$	7.72004e8	−	4.45717e8i	0.382187	−	0.220656i
$213$		0			0
$214$	7.61166e8	−	1.31838e9i	0.362931	−	0.628615i
$215$		−	1.35021e9i		−	0.631899i
$216$		0			0
$217$	3.81284e9			1.71953
$218$	−5.21122e8	−	3.00870e8i	−0.230735	−	0.133215i
$219$		0			0
$220$	−1.31121e9	−	2.27108e9i	−0.559734	−	0.969488i
$221$	−3.58349e8	+	2.06893e8i	−0.150223	+	0.0867314i
$222$		0			0
$223$	1.69943e8	−	2.94349e8i	0.0687199	−	0.119026i	−0.829618	−	0.558331i	$-0.811442\pi$
$223$	1.69943e8	−	2.94349e8i	0.0687199	−	0.119026i	0.898338	+	0.439305i	$0.144775\pi$
$224$			4.98039e8i			0.197821i
$225$		0			0
$226$	1.49410e9			0.572726
$227$	7.86249e8	+	4.53941e8i	0.296113	+	0.170961i	0.640695	−	0.767795i	$-0.278646\pi$
$227$	7.86249e8	+	4.53941e8i	0.296113	+	0.170961i	−0.344583	+	0.938756i	$0.611980\pi$
$228$		0			0
$229$	1.91967e7	+	3.32497e7i	0.00698047	+	0.0120905i	0.869495	−	0.493943i	$-0.164445\pi$
$229$	1.91967e7	+	3.32497e7i	0.00698047	+	0.0120905i	−0.862514	+	0.506033i	$0.831111\pi$
$230$	3.72964e9	−	2.15331e9i	1.33277	−	0.769477i
$231$		0			0
$232$	4.82558e8	−	8.35816e8i	0.166570	−	0.288508i
$233$		−	3.39626e9i		−	1.15233i	−0.817334	−	0.576165i	$-0.804549\pi$
$233$		−	3.39626e9i		−	1.15233i	0.817334	−	0.576165i	$-0.195451\pi$
$234$		0			0
$235$	3.24353e9			1.06352
$236$	−7.61547e8	−	4.39680e8i	−0.245499	−	0.141739i
$237$		0			0
$238$	−6.48526e8	−	1.12328e9i	−0.202125	−	0.350090i
$239$	2.60050e8	−	1.50140e8i	0.0797012	−	0.0460155i	−0.459620	−	0.888116i	$-0.652014\pi$
$239$	2.60050e8	−	1.50140e8i	0.0797012	−	0.0460155i	0.539321	+	0.842100i	$0.318681\pi$
$240$		0			0
$241$	−2.67282e9	+	4.62946e9i	−0.792321	+	1.37234i	0.132205	+	0.991222i	$0.457794\pi$
$241$	−2.67282e9	+	4.62946e9i	−0.792321	+	1.37234i	−0.924526	+	0.381119i	$0.875539\pi$
$242$			4.46173e9i			1.30089i
$243$		0			0
$244$	3.24035e8			0.0914182
$245$	−1.04577e9	−	6.03776e8i	−0.290250	−	0.167576i
$246$		0			0
$247$	−4.90667e8	−	8.49860e8i	−0.131825	−	0.228328i
$248$	−1.77974e9	+	1.02753e9i	−0.470489	+	0.271637i
$249$		0			0
$250$	−4.30759e8	+	7.46096e8i	−0.110274	+	0.191001i
$251$			2.15800e8i			0.0543696i	0.999630	+	0.0271848i	$0.00865425\pi$
$251$			2.15800e8i			0.0543696i	−0.999630	+	0.0271848i	$0.991346\pi$
$252$		0			0
$253$	−1.13099e10			−2.76044
$254$	5.60744e8	+	3.23746e8i	0.134719	+	0.0777802i
$255$		0			0
$256$	−1.34218e8	−	2.32472e8i	−0.0312500	−	0.0541266i
$257$	−1.30255e9	+	7.52028e8i	−0.298581	+	0.172386i	−0.641805	−	0.766868i	$-0.721814\pi$
$257$	−1.30255e9	+	7.52028e8i	−0.298581	+	0.172386i	0.343224	+	0.939254i	$0.388481\pi$
$258$		0			0
$259$	2.18416e9	−	3.78308e9i	0.485384	−	0.840710i
$260$		−	1.03075e9i		−	0.225559i
$261$		0			0
$262$	1.27975e9			0.271595
$263$	4.86114e9	+	2.80658e9i	1.01605	+	0.586616i	0.912957	−	0.408055i	$-0.133793\pi$
$263$	4.86114e9	+	2.80658e9i	1.01605	+	0.586616i	0.103092	+	0.994672i	$0.467126\pi$
$264$		0			0
$265$	−2.89156e9	−	5.00832e9i	−0.586338	−	1.01557i
$266$	2.66397e9	−	1.53804e9i	0.532112	−	0.307215i
$267$		0			0
$268$	−2.02720e9	+	3.51121e9i	−0.392968	+	0.680640i
$269$			5.36842e9i			1.02527i	0.858607	+	0.512634i	$0.171330\pi$
$269$			5.36842e9i			1.02527i	−0.858607	+	0.512634i	$0.828670\pi$
$270$		0			0
$271$	−3.34972e9			−0.621056			−0.310528	−	0.950564i	$-0.600506\pi$
$271$	−3.34972e9			−0.621056			−0.310528	+	0.950564i	$0.600506\pi$
$272$	6.05431e8	+	3.49546e8i	0.110609	+	0.0638599i
$273$		0			0
$274$	7.77578e8	+	1.34681e9i	0.137956	+	0.238948i
$275$	−6.38706e9	+	3.68757e9i	−1.11679	+	0.644777i
$276$		0			0
$277$	4.05893e8	−	7.03028e8i	0.0689434	−	0.119413i	−0.829493	−	0.558517i	$-0.811371\pi$
$277$	4.05893e8	−	7.03028e8i	0.0689434	−	0.119413i	0.898436	+	0.439104i	$0.144704\pi$
$278$		−	2.19676e9i		−	0.367793i
$279$		0			0
$280$	3.23099e9			0.525659
$281$	9.24159e8	+	5.33564e8i	0.148225	+	0.0855778i	0.572278	−	0.820060i	$-0.306060\pi$
$281$	9.24159e8	+	5.33564e8i	0.148225	+	0.0855778i	−0.424053	+	0.905637i	$0.639393\pi$
$282$		0			0
$283$	4.18292e9	+	7.24503e9i	0.652130	+	1.12952i	0.982605	+	0.185707i	$0.0594577\pi$
$283$	4.18292e9	+	7.24503e9i	0.652130	+	1.12952i	−0.330475	+	0.943815i	$0.607209\pi$
$284$	−1.94540e9	+	1.12318e9i	−0.299044	+	0.172653i
$285$		0			0
$286$	−1.35346e9	+	2.34427e9i	−0.202294	+	0.350383i
$287$			6.20246e9i			0.914190i
$288$		0			0
$289$	5.15510e9			0.739002
$290$	−5.42229e9	−	3.13056e9i	−0.766639	−	0.442619i
$291$		0			0
$292$	−1.83661e9	−	3.18111e9i	−0.252631	−	0.437569i
$293$	1.17267e9	−	6.77039e8i	0.159112	−	0.0918636i	−0.418330	−	0.908295i	$-0.637384\pi$
$293$	1.17267e9	−	6.77039e8i	0.159112	−	0.0918636i	0.577442	+	0.816432i	$0.304051\pi$
$294$		0			0
$295$	−2.85239e9	+	4.94048e9i	−0.376635	+	0.652351i
$296$			2.35446e9i			0.306707i
$297$		0			0
$298$	−8.76488e9			−1.11143
$299$	−3.84983e9	−	2.22270e9i	−0.481678	−	0.278097i
$300$		0			0
$301$	−2.18438e9	−	3.78345e9i	−0.266110	−	0.460916i
$302$	−6.82078e9	+	3.93798e9i	−0.819985	+	0.473419i
$303$		0			0
$304$	−8.28983e8	+	1.43584e9i	−0.0970624	+	0.168117i
$305$		−	2.10215e9i		−	0.242921i
$306$		0			0
$307$	3.34624e9			0.376707			0.188354	−	0.982101i	$-0.439685\pi$
$307$	3.34624e9			0.376707			0.188354	+	0.982101i	$0.439685\pi$
$308$	−7.34834e9	−	4.24257e9i	−0.816557	−	0.471439i
$309$		0			0
$310$	6.66603e9	+	1.15459e10i	0.721806	+	1.25021i
$311$	7.07501e9	−	4.08476e9i	0.756285	−	0.436641i	−0.0716755	−	0.997428i	$-0.522835\pi$
$311$	7.07501e9	−	4.08476e9i	0.756285	−	0.436641i	0.827960	+	0.560787i	$0.189501\pi$
$312$		0			0
$313$	6.49273e9	−	1.12457e10i	0.676472	−	1.17168i	−0.299564	−	0.954076i	$-0.596841\pi$
$313$	6.49273e9	−	1.12457e10i	0.676472	−	1.17168i	0.976036	−	0.217608i	$-0.0698255\pi$
$314$		−	1.12993e8i		−	0.0116234i
$315$		0			0
$316$	−8.71227e9			−0.873741
$317$	2.27583e9	+	1.31395e9i	0.225374	+	0.130120i	0.608436	−	0.793603i	$-0.291797\pi$
$317$	2.27583e9	+	1.31395e9i	0.225374	+	0.130120i	−0.383062	+	0.923723i	$0.625131\pi$
$318$		0			0
$319$	8.22139e9	+	1.42399e10i	0.793930	+	1.37513i
$320$	−1.50814e9	+	8.70728e8i	−0.143828	+	0.0830391i
$321$		0			0
$322$	6.96727e9	−	1.20677e10i	0.648096	−	1.12254i
$323$		−	4.31787e9i		−	0.396697i
$324$		0			0
$325$	−2.89882e9			−0.259829
$326$	1.20394e10	+	6.95095e9i	1.06594	+	0.615423i
$327$		0			0
$328$	−1.67152e9	−	2.89515e9i	−0.144416	−	0.250136i
$329$	9.08876e9	−	5.24740e9i	0.775749	−	0.447879i
$330$		0			0
$331$	5.38121e9	−	9.32053e9i	0.448299	−	0.776477i	−0.549976	−	0.835180i	$-0.685363\pi$
$331$	5.38121e9	−	9.32053e9i	0.448299	−	0.776477i	0.998275	+	0.0587032i	$0.0186965\pi$
$332$		−	7.00223e9i		−	0.576347i
$333$		0			0
$334$	−9.68158e9			−0.777966
$335$	2.27787e10	+	1.31513e10i	1.80863	+	1.04421i
$336$		0			0
$337$	−6.49324e9	−	1.12466e10i	−0.503433	−	0.871972i	−0.999992	−	0.00396864i	$-0.998737\pi$
$337$	−6.49324e9	−	1.12466e10i	−0.503433	−	0.871972i	0.496559	−	0.868003i	$-0.334597\pi$
$338$	7.07107e9	−	4.08249e9i	0.541775	−	0.312794i
$339$		0			0
$340$	2.26765e9	−	3.92769e9i	0.169692	−	0.293915i
$341$		−	3.50123e10i		−	2.58942i
$342$		0			0
$343$	1.15818e10			0.836758
$344$	2.03922e9	+	1.17735e9i	0.145623	+	0.0840757i
$345$		0			0
$346$	2.59001e9	+	4.48603e9i	0.180716	+	0.313010i
$347$	−2.11272e9	+	1.21978e9i	−0.145722	+	0.0841324i	−0.571088	−	0.820889i	$-0.693479\pi$
$347$	−2.11272e9	+	1.21978e9i	−0.145722	+	0.0841324i	0.425366	+	0.905021i	$0.360145\pi$
$348$		0			0
$349$	1.08992e10	−	1.88779e10i	0.734669	−	1.27248i	−0.220200	−	0.975455i	$-0.570671\pi$
$349$	1.08992e10	−	1.88779e10i	0.734669	−	1.27248i	0.954869	−	0.297029i	$-0.0959957\pi$
$350$		−	9.08664e9i		−	0.605524i
$351$		0			0
$352$	4.57336e9			0.297896
$353$	−1.22820e10	−	7.09100e9i	−0.790987	−	0.456677i	0.0493227	−	0.998783i	$-0.484294\pi$
$353$	−1.22820e10	−	7.09100e9i	−0.790987	−	0.456677i	−0.840310	+	0.542106i	$0.817627\pi$
$354$		0			0
$355$	7.28652e9	+	1.26206e10i	0.458782	+	0.794634i
$356$	−7.81466e8	+	4.51180e8i	−0.0486530	+	0.0280898i
$357$		0			0
$358$	−8.30212e9	+	1.43797e10i	−0.505425	+	0.875422i
$359$			1.62366e10i			0.977499i	0.872424	+	0.488750i	$0.162547\pi$
$359$			1.62366e10i			0.977499i	−0.872424	+	0.488750i	$0.837453\pi$
$360$		0			0
$361$	−6.74331e9			−0.397049
$362$	−1.56056e10	−	9.00988e9i	−0.908752	−	0.524668i
$363$		0			0
$364$	−1.66755e9	−	2.88829e9i	−0.0949892	−	0.164526i
$365$	−2.06372e10	+	1.19149e10i	−1.16273	+	0.671303i
$366$		0			0
$367$	4.72220e9	−	8.17909e9i	0.260303	−	0.450859i	−0.706019	−	0.708193i	$-0.749511\pi$
$367$	4.72220e9	−	8.17909e9i	0.260303	−	0.450859i	0.966323	+	0.257334i	$0.0828440\pi$
$368$			7.51051e9i			0.409523i
$369$		0			0
$370$	1.52744e10			0.814998
$371$	−1.62050e10	−	9.35595e9i	−0.855367	−	0.493847i
$372$		0			0
$373$	6.87407e9	+	1.19062e10i	0.355123	+	0.615091i	0.987139	−	0.159864i	$-0.0511056\pi$
$373$	6.87407e9	+	1.19062e10i	0.355123	+	0.615091i	−0.632016	+	0.774955i	$0.717772\pi$
$374$	−1.03148e10	+	5.95524e9i	−0.527198	+	0.304378i
$375$		0			0
$376$	−2.82827e9	+	4.89870e9i	−0.141504	+	0.245092i
$377$			6.46288e9i			0.319934i
$378$		0			0
$379$	−8.10058e9			−0.392608			−0.196304	−	0.980543i	$-0.562894\pi$
$379$	−8.10058e9			−0.392608			−0.196304	+	0.980543i	$0.562894\pi$
$380$	9.31490e9	+	5.37796e9i	0.446729	+	0.257919i
$381$		0			0
$382$	1.05096e9	+	1.82031e9i	0.0493550	+	0.0854854i
$383$	3.26313e10	−	1.88397e10i	1.51649	−	0.875544i	0.516675	−	0.856182i	$-0.327170\pi$
$383$	3.26313e10	−	1.88397e10i	1.51649	−	0.875544i	0.999813	−	0.0193625i	$-0.00616365\pi$
$384$		0			0
$385$	−2.75233e10	+	4.76718e10i	−1.25273	+	2.16980i
$386$		−	1.32444e10i		−	0.596599i
$387$		0			0
$388$	1.31671e10			0.580984
$389$	7.44708e9	+	4.29957e9i	0.325228	+	0.187770i	0.653720	−	0.756736i	$-0.273207\pi$
$389$	7.44708e9	+	4.29957e9i	0.325228	+	0.187770i	−0.328493	+	0.944507i	$0.606541\pi$
$390$		0			0
$391$	−9.77988e9	−	1.69392e10i	−0.418433	−	0.724748i
$392$	1.82377e9	−	1.05295e9i	0.0772369	−	0.0445928i
$393$		0			0
$394$	1.07715e10	−	1.86567e10i	0.446982	−	0.774196i
$395$			5.65202e10i			2.32175i
$396$		0			0
$397$	−7.53858e9			−0.303478			−0.151739	−	0.988421i	$-0.548487\pi$
$397$	−7.53858e9			−0.303478			−0.151739	+	0.988421i	$0.548487\pi$
$398$	1.56144e10	+	9.01495e9i	0.622289	+	0.359278i
$399$		0			0
$400$	2.44878e9	+	4.24141e9i	0.0956555	+	0.165680i
$401$	2.42910e9	−	1.40244e9i	0.0939436	−	0.0542384i	−0.452292	−	0.891870i	$-0.649394\pi$
$401$	2.42910e9	−	1.40244e9i	0.0939436	−	0.0542384i	0.546236	+	0.837631i	$0.316060\pi$
$402$		0			0
$403$	6.88084e9	−	1.19180e10i	0.260868	−	0.451837i
$404$			1.19917e10i			0.450148i
$405$		0			0
$406$	−2.02585e10			−0.745597
$407$	−3.47390e10	−	2.00566e10i	−1.26602	−	0.730935i
$408$		0			0
$409$	4.31779e9	+	7.47864e9i	0.154301	+	0.267257i	0.932804	−	0.360383i	$-0.117354\pi$
$409$	4.31779e9	+	7.47864e9i	0.154301	+	0.267257i	−0.778503	+	0.627641i	$0.784021\pi$
$410$	−1.87821e10	+	1.08438e10i	−0.664673	+	0.383749i
$411$		0			0
$412$	−5.99795e9	+	1.03888e10i	−0.208168	+	0.360558i
$413$			1.84584e10i			0.634446i
$414$		0			0
$415$	−4.54265e10			−1.53150
$416$	1.55674e9	+	8.98786e8i	0.0519809	+	0.0300112i
$417$		0			0
$418$	−1.41234e10	−	2.44625e10i	−0.462632	−	0.801302i
$419$	−2.20697e10	+	1.27420e10i	−0.716046	+	0.413409i	−0.813296	−	0.581851i	$-0.802329\pi$
$419$	−2.20697e10	+	1.27420e10i	−0.716046	+	0.413409i	0.0972497	+	0.995260i	$0.468995\pi$
$420$		0			0
$421$	7.22114e7	−	1.25074e8i	0.00229867	−	0.00398142i	−0.864874	−	0.501989i	$-0.832602\pi$
$421$	7.22114e7	−	1.25074e8i	0.00229867	−	0.00398142i	0.867172	+	0.498008i	$0.165935\pi$
$422$			9.87561e9i			0.311397i
$423$		0			0
$424$	1.00854e10			0.312055
$425$	−1.10460e10	−	6.37740e9i	−0.338570	−	0.195474i
$426$		0			0
$427$	−3.40087e9	−	5.89049e9i	−0.102301	−	0.177190i
$428$	1.49157e10	−	8.61161e9i	0.444498	−	0.256631i
$429$		0			0
$430$	7.63794e9	−	1.32293e10i	0.223410	−	0.386957i
$431$		−	6.31640e9i		−	0.183046i	−0.995803	−	0.0915231i	$-0.970826\pi$
$431$		−	6.31640e9i		−	0.183046i	0.995803	−	0.0915231i	$-0.0291735\pi$
$432$		0			0
$433$	−3.96241e10			−1.12722			−0.563609	−	0.826042i	$-0.690587\pi$
$433$	−3.96241e10			−1.12722			−0.563609	+	0.826042i	$0.690587\pi$
$434$	3.73581e10	+	2.15687e10i	1.05299	+	0.607946i
$435$		0			0
$436$	−3.40395e9	−	5.89582e9i	−0.0941971	−	0.163154i
$437$	4.01731e10	−	2.31940e10i	1.10156	−	0.635988i
$438$		0			0
$439$	−1.57438e10	+	2.72691e10i	−0.423889	+	0.734196i	−0.996316	−	0.0857589i	$-0.972669\pi$
$439$	−1.57438e10	+	2.72691e10i	−0.423889	+	0.734196i	0.572427	+	0.819955i	$0.306002\pi$
$440$		−	2.96693e10i		−	0.791584i
$441$		0			0
$442$	−4.68145e9			−0.122657
$443$	−3.86111e10	−	2.22921e10i	−1.00253	−	0.578810i	−0.0935330	−	0.995616i	$-0.529816\pi$
$443$	−3.86111e10	−	2.22921e10i	−1.00253	−	0.578810i	−0.908995	+	0.416806i	$0.863149\pi$
$444$		0			0
$445$	2.92699e9	+	5.06970e9i	0.0746417	+	0.129283i
$446$	3.33018e9	−	1.92268e9i	0.0841644	−	0.0485923i
$447$		0			0
$448$	−2.81733e9	+	4.87977e9i	−0.0699401	+	0.121140i
$449$			2.35548e10i			0.579553i	0.957094	+	0.289777i	$0.0935810\pi$
$449$			2.35548e10i			0.579553i	−0.957094	+	0.289777i	$0.906419\pi$
$450$		0			0
$451$	5.69555e10			1.37667
$452$	1.46392e10	+	8.45192e9i	0.350722	+	0.202489i
$453$		0			0
$454$	5.13576e9	+	8.89540e9i	0.120887	+	0.209383i
$455$	−1.87376e10	+	1.08181e10i	−0.437187	+	0.252410i
$456$		0			0
$457$	−2.05058e10	+	3.55170e10i	−0.470122	+	0.814276i	−0.999416	−	0.0341626i	$-0.989124\pi$
$457$	−2.05058e10	+	3.55170e10i	−0.470122	+	0.814276i	0.529294	+	0.848439i	$0.322457\pi$
$458$			4.34372e8i			0.00987188i
$459$		0			0
$460$	4.87239e10			1.08820
$461$	3.37174e9	+	1.94668e9i	0.0746536	+	0.0431013i	0.536862	−	0.843670i	$-0.319610\pi$
$461$	3.37174e9	+	1.94668e9i	0.0746536	+	0.0431013i	−0.462209	+	0.886771i	$0.652943\pi$
$462$		0			0
$463$	−2.67932e10	−	4.64073e10i	−0.583044	−	1.00986i	−0.995116	−	0.0987107i	$-0.968528\pi$
$463$	−2.67932e10	−	4.64073e10i	−0.583044	−	1.00986i	0.412072	−	0.911151i	$-0.364805\pi$
$464$	9.45617e9	−	5.45952e9i	0.204006	−	0.117783i
$465$		0			0
$466$	1.92121e10	−	3.32764e10i	0.407410	−	0.705655i
$467$		−	4.53162e10i		−	0.952766i	−0.879238	−	0.476383i	$-0.841948\pi$
$467$		−	4.53162e10i		−	0.952766i	0.879238	−	0.476383i	$-0.158052\pi$
$468$		0			0
$469$	8.51049e10			1.75899
$470$	3.17800e10	+	1.83482e10i	0.651272	+	0.376012i
$471$		0			0
$472$	−4.97441e9	−	8.61593e9i	−0.100224	−	0.173594i
$473$	−3.47424e10	+	2.00585e10i	−0.694089	+	0.400733i
$474$		0			0
$475$	1.51247e10	−	2.61967e10i	0.297106	−	0.514602i
$476$		−	1.46745e10i		−	0.285848i
$477$		0			0
$478$	3.39728e9			0.0650758
$479$	−4.92416e9	−	2.84297e9i	−0.0935385	−	0.0540045i	0.452501	−	0.891764i	$-0.350532\pi$
$479$	−4.92416e9	−	2.84297e9i	−0.0935385	−	0.0540045i	−0.546040	+	0.837759i	$0.683865\pi$
$480$		0			0
$481$	−7.88329e9	−	1.36543e10i	−0.147274	−	0.255087i
$482$	−5.23763e10	+	3.02395e10i	−0.970392	+	0.560256i
$483$		0			0
$484$	−2.52394e10	+	4.37159e10i	−0.459936	+	0.796632i
$485$		−	8.54208e10i		−	1.54382i
$486$		0			0
$487$	3.64760e10			0.648472			0.324236	−	0.945976i	$-0.394893\pi$
$487$	3.64760e10			0.648472			0.324236	+	0.945976i	$0.394893\pi$
$488$	3.17488e9	+	1.83302e9i	0.0559820	+	0.0323212i
$489$		0			0
$490$	−6.83095e9	−	1.18316e10i	−0.118494	−	0.205238i
$491$	5.07409e10	−	2.92952e10i	0.873035	−	0.504047i	0.00467962	−	0.999989i	$-0.498510\pi$
$491$	5.07409e10	−	2.92952e10i	0.873035	−	0.504047i	0.868356	+	0.495942i	$0.165177\pi$
$492$		0			0
$493$	−1.42183e10	+	2.46269e10i	−0.240692	+	0.416890i
$494$		−	1.11025e10i		−	0.186429i
$495$		0			0
$496$	−2.32504e10			−0.384152
$497$	4.08354e10	+	2.35763e10i	0.669285	+	0.386412i
$498$		0			0
$499$	3.18425e10	+	5.51528e10i	0.513576	+	0.889541i	0.999876	+	0.0157483i	$0.00501306\pi$
$499$	3.18425e10	+	5.51528e10i	0.513576	+	0.889541i	−0.486300	+	0.873792i	$0.661654\pi$
$500$	−8.44112e9	+	4.87348e9i	−0.135058	+	0.0779757i
$501$		0			0
$502$	−1.22075e9	+	2.11440e9i	−0.0192225	+	0.0332944i
$503$		−	1.09134e10i		−	0.170486i	−0.996360	−	0.0852430i	$-0.972833\pi$
$503$		−	1.09134e10i		−	0.170486i	0.996360	−	0.0852430i	$-0.0271667\pi$
$504$		0			0
$505$	7.77953e10			1.19616
$506$	−1.10814e11	−	6.39786e10i	−1.69041	−	0.975961i
$507$		0			0
$508$	3.66277e9	+	6.34410e9i	0.0549989	+	0.0952609i
$509$	9.71431e9	−	5.60856e9i	0.144724	−	0.0835565i	−0.425889	−	0.904775i	$-0.640039\pi$
$509$	9.71431e9	−	5.60856e9i	0.144724	−	0.0835565i	0.570614	+	0.821219i	$0.306705\pi$
$510$		0			0
$511$	−3.85519e10	+	6.67739e10i	−0.565409	+	0.979316i
$512$		−	3.03700e9i		−	0.0441942i
$513$		0			0
$514$	−1.70165e10			−0.243790
$515$	6.73963e10	+	3.89113e10i	0.958092	+	0.553155i
$516$		0			0
$517$	−4.81854e10	−	8.34596e10i	−0.674456	−	1.16819i
$518$	4.28006e10	−	2.47110e10i	0.594472	−	0.343218i
$519$		0			0
$520$	5.83081e9	−	1.00993e10i	0.0797472	−	0.138126i
$521$			1.03375e11i			1.40302i	0.712658	+	0.701511i	$0.247491\pi$
$521$			1.03375e11i			1.40302i	−0.712658	+	0.701511i	$0.752509\pi$
$522$		0			0
$523$	−6.50405e10			−0.869314			−0.434657	−	0.900596i	$-0.643130\pi$
$523$	−6.50405e10			−0.869314			−0.434657	+	0.900596i	$0.643130\pi$
$524$	1.25390e10	+	7.23938e9i	0.166317	+	0.0960232i
$525$		0			0
$526$	3.17528e10	+	5.49975e10i	0.414800	+	0.718456i
$527$	5.24390e10	−	3.02757e10i	0.679849	−	0.392511i
$528$		0			0
$529$	6.59121e10	−	1.14163e11i	0.841671	−	1.45782i
$530$		−	6.54284e10i		−	0.829207i
$531$		0			0
$532$	3.48020e10			0.434468
$533$	1.93873e10	+	1.11933e10i	0.240220	+	0.138691i
$534$		0			0
$535$	−5.58672e10	−	9.67648e10i	−0.681933	−	1.18114i
$536$	−3.97248e10	+	2.29351e10i	−0.481285	+	0.277870i
$537$		0			0
$538$	−3.03684e10	+	5.25995e10i	−0.362487	+	0.627845i
$539$			3.58785e10i			0.425088i
$540$		0			0
$541$	9.26356e10			1.08141			0.540703	−	0.841214i	$-0.318158\pi$
$541$	9.26356e10			1.08141			0.540703	+	0.841214i	$0.318158\pi$
$542$	−3.28204e10	−	1.89489e10i	−0.380318	−	0.219577i
$543$		0			0
$544$	3.95466e9	+	6.84967e9i	0.0451558	+	0.0782121i
$545$	−3.82487e10	+	2.20829e10i	−0.433541	+	0.250305i
$546$		0			0
$547$	−6.17442e9	+	1.06944e10i	−0.0689679	+	0.119456i	−0.898447	−	0.439081i	$-0.855304\pi$
$547$	−6.17442e9	+	1.06944e10i	−0.0689679	+	0.119456i	0.829479	+	0.558537i	$0.188637\pi$
$548$			1.75946e10i			0.195100i
$549$		0			0
$550$	−8.34402e10			−0.911852
$551$	−5.84051e10	−	3.37202e10i	−0.633643	−	0.365834i
$552$		0			0
$553$	9.14387e10	+	1.58376e11i	0.977753	+	1.69352i
$554$	7.95385e9	−	4.59216e9i	0.0844381	−	0.0487503i
$555$		0			0
$556$	1.24268e10	−	2.15238e10i	0.130035	−	0.225227i
$557$			1.17871e9i			0.0122458i	0.999981	+	0.00612290i	$0.00194899\pi$
$557$			1.17871e9i			0.0122458i	−0.999981	+	0.00612290i	$0.998051\pi$
$558$		0			0
$559$	−1.57681e10			−0.161485
$560$	3.16571e10	+	1.82772e10i	0.321899	+	0.185848i
$561$		0			0
$562$	6.03658e9	+	1.04557e10i	0.0605126	+	0.104811i
$563$	4.60975e10	−	2.66144e10i	0.458822	−	0.264901i	−0.252727	−	0.967538i	$-0.581327\pi$
$563$	4.60975e10	−	2.66144e10i	0.458822	−	0.264901i	0.711549	+	0.702637i	$0.247994\pi$
$564$		0			0
$565$	5.48312e10	−	9.49705e10i	0.538064	−	0.931955i
$566$			9.46487e10i			0.922251i
$567$		0			0
$568$	−2.54146e10			−0.244168
$569$	7.89230e9	+	4.55662e9i	0.0752930	+	0.0434704i	0.537174	−	0.843472i	$-0.319492\pi$
$569$	7.89230e9	+	4.55662e9i	0.0752930	+	0.0434704i	−0.461881	+	0.886942i	$0.652825\pi$
$570$		0			0
$571$	−8.93207e10	−	1.54708e11i	−0.840248	−	1.45535i	−0.889685	−	0.456575i	$-0.849076\pi$
$571$	−8.93207e10	−	1.54708e11i	−0.840248	−	1.45535i	0.0494367	−	0.998777i	$-0.484257\pi$
$572$	−2.65224e10	+	1.53127e10i	−0.247758	+	0.143043i
$573$		0			0
$574$	−3.50864e10	+	6.07715e10i	−0.323215	+	0.559825i
$575$		−	1.37028e11i		−	1.25354i
$576$		0			0
$577$	−1.57035e11			−1.41675			−0.708374	−	0.705837i	$-0.750571\pi$
$577$	−1.57035e11			−1.41675			−0.708374	+	0.705837i	$0.750571\pi$
$578$	5.05095e10	+	2.91617e10i	0.452545	+	0.261277i
$579$		0			0
$580$	−3.54183e10	−	6.13462e10i	−0.312979	−	0.542096i
$581$	−1.27290e11	+	7.34911e10i	−1.11710	+	0.644957i
$582$		0			0
$583$	−8.59131e10	+	1.48806e11i	−0.743679	+	1.28809i
$584$		−	4.15578e10i		−	0.357274i
$585$		0			0
$586$	1.53197e10			0.129915
$587$	−7.02172e10	−	4.05399e10i	−0.591413	−	0.341452i	0.174243	−	0.984703i	$-0.444252\pi$
$587$	−7.02172e10	−	4.05399e10i	−0.591413	−	0.341452i	−0.765656	+	0.643250i	$0.777586\pi$
$588$		0			0
$589$	7.18018e10	+	1.24364e11i	0.596588	+	1.03332i
$590$	−5.58952e10	+	3.22711e10i	−0.461282	+	0.266321i
$591$		0			0
$592$	−1.33188e10	+	2.30689e10i	−0.108437	+	0.187819i
$593$			2.32095e11i			1.87693i	0.345379	+	0.938463i	$0.387750\pi$
$593$			2.32095e11i			1.87693i	−0.345379	+	0.938463i	$0.612250\pi$
$594$		0			0
$595$	−9.51995e10			−0.759569
$596$	−8.58779e10	−	4.95816e10i	−0.680607	−	0.392949i
$597$		0			0
$598$	−2.51470e10	−	4.35558e10i	−0.196644	−	0.340598i
$599$	6.67859e9	−	3.85589e9i	0.0518773	−	0.0299514i	−0.473837	−	0.880613i	$-0.657131\pi$
$599$	6.67859e9	−	3.85589e9i	0.0518773	−	0.0299514i	0.525714	+	0.850661i	$0.323798\pi$
$600$		0			0
$601$	8.64971e10	−	1.49817e11i	0.662985	−	1.14832i	−0.316842	−	0.948478i	$-0.602623\pi$
$601$	8.64971e10	−	1.49817e11i	0.662985	−	1.14832i	0.979827	−	0.199846i	$-0.0640441\pi$
$602$		−	4.94268e10i		−	0.376337i
$603$		0			0
$604$	−8.91062e10			−0.669515
$605$	2.83604e11	+	1.63739e11i	2.11685	+	1.22216i
$606$		0			0
$607$	6.33224e10	+	1.09678e11i	0.466448	+	0.807911i	0.999266	−	0.0383189i	$-0.0122003\pi$
$607$	6.33224e10	+	1.09678e11i	0.466448	+	0.807911i	−0.532818	+	0.846230i	$0.678867\pi$
$608$	−1.62447e10	+	9.37887e9i	−0.118877	+	0.0686335i
$609$		0			0
$610$	1.18916e10	−	2.05968e10i	0.0858855	−	0.148758i
$611$		−	3.78789e10i		−	0.271789i
$612$		0			0
$613$	−1.90947e11			−1.35230			−0.676148	−	0.736765i	$-0.736352\pi$
$613$	−1.90947e11			−1.35230			−0.676148	+	0.736765i	$0.736352\pi$
$614$	3.27863e10	+	1.89292e10i	0.230685	+	0.133186i
$615$		0			0
$616$	−4.79992e10	−	8.31370e10i	−0.333358	−	0.577393i
$617$	−3.94255e10	+	2.27623e10i	−0.272043	+	0.157064i	−0.629816	−	0.776745i	$-0.716870\pi$
$617$	−3.94255e10	+	2.27623e10i	−0.272043	+	0.157064i	0.357773	+	0.933809i	$0.383536\pi$
$618$		0			0
$619$	2.52527e10	−	4.37390e10i	0.172007	−	0.297925i	−0.767114	−	0.641510i	$-0.778308\pi$
$619$	2.52527e10	−	4.37390e10i	0.172007	−	0.297925i	0.939121	+	0.343585i	$0.111642\pi$
$620$			1.50835e11i			1.02079i
$621$		0			0
$622$	9.24275e10			0.617504
$623$	1.64036e10	+	9.47061e9i	0.108890	+	0.0628674i
$624$		0			0
$625$	8.99998e10	+	1.55884e11i	0.589823	+	1.02160i
$626$	1.27231e11	−	7.34569e10i	0.828506	−	0.478338i
$627$		0			0
$628$	6.39186e8	−	1.10710e9i	0.00410950	−	0.00711786i
$629$		−	6.93730e10i		−	0.443188i
$630$		0			0
$631$	7.46120e10			0.470642			0.235321	−	0.971918i	$-0.424386\pi$
$631$	7.46120e10			0.470642			0.235321	+	0.971918i	$0.424386\pi$
$632$	−8.53625e10	−	4.92840e10i	−0.535055	−	0.308914i
$633$		0			0
$634$	1.48657e10	+	2.57481e10i	0.0920085	+	0.159363i
$635$	4.11568e10	−	2.37619e10i	0.253132	−	0.146146i
$636$		0			0
$637$	−7.05107e9	+	1.22128e10i	−0.0428250	+	0.0741751i
$638$			1.86029e11i			1.12279i
$639$		0			0
$640$	−1.97023e10			−0.117435
$641$	−2.44739e11	−	1.41300e11i	−1.44968	−	0.836972i	−0.451215	−	0.892415i	$-0.649009\pi$
$641$	−2.44739e11	−	1.41300e11i	−1.44968	−	0.836972i	−0.998462	+	0.0554435i	$0.982343\pi$
$642$		0			0
$643$	8.57408e10	+	1.48507e11i	0.501584	+	0.868769i	0.999998	+	0.00183012i	$0.000582545\pi$
$643$	8.57408e10	+	1.48507e11i	0.501584	+	0.868769i	−0.498414	+	0.866939i	$0.666084\pi$
$644$	1.36530e11	−	7.88257e10i	0.793752	−	0.458273i
$645$		0			0
$646$	2.44256e10	−	4.23063e10i	0.140254	−	0.242927i
$647$			6.51359e10i			0.371709i	0.982577	+	0.185855i	$0.0595053\pi$
$647$			6.51359e10i			0.371709i	−0.982577	+	0.185855i	$0.940495\pi$
$648$		0			0
$649$	1.69499e11			0.955406
$650$	−2.84025e10	−	1.63982e10i	−0.159112	−	0.0918635i
$651$		0			0
$652$	7.86411e10	+	1.36210e11i	0.435170	+	0.753737i
$653$	−2.27135e10	+	1.31137e10i	−0.124920	+	0.0721226i	−0.561158	−	0.827709i	$-0.689644\pi$
$653$	−2.27135e10	+	1.31137e10i	−0.124920	+	0.0721226i	0.436238	+	0.899831i	$0.356311\pi$
$654$		0			0
$655$	4.69649e10	−	8.13456e10i	0.255158	−	0.441946i
$656$		−	3.78221e10i		−	0.204235i
$657$		0			0
$658$	1.18735e11			0.633396
$659$	−2.34946e11	−	1.35646e11i	−1.24574	−	0.719228i	−0.275483	−	0.961306i	$-0.588838\pi$
$659$	−2.34946e11	−	1.35646e11i	−1.24574	−	0.719228i	−0.970257	+	0.242078i	$0.922171\pi$
$660$		0			0
$661$	−1.12700e11	−	1.95203e11i	−0.590364	−	1.02254i	−0.994183	−	0.107702i	$-0.965651\pi$
$661$	−1.12700e11	−	1.95203e11i	−0.590364	−	1.02254i	0.403819	−	0.914839i	$-0.367682\pi$
$662$	1.05450e11	−	6.08815e10i	0.549052	−	0.316995i
$663$		0			0
$664$	3.96106e10	−	6.86076e10i	0.203769	−	0.352939i
$665$		−	2.25775e11i		−	1.15449i
$666$		0			0
$667$	−3.05502e11			−1.54352
$668$	−9.48597e10	−	5.47673e10i	−0.476405	−	0.275052i
$669$		0			0
$670$	1.48790e11	+	2.57712e11i	0.738370	+	1.27890i
$671$	−5.40907e10	+	3.12293e10i	−0.266829	+	0.154054i
$672$		0			0
$673$	−7.58538e10	+	1.31383e11i	−0.369757	+	0.640439i	−0.989527	−	0.144345i	$-0.953893\pi$
$673$	−7.58538e10	+	1.31383e11i	−0.369757	+	0.640439i	0.619770	+	0.784784i	$0.287226\pi$
$674$		−	1.46925e11i		−	0.711962i
$675$		0			0
$676$	9.23761e10			0.442357
$677$	2.20192e11	+	1.27128e11i	1.04821	+	0.605183i	0.922147	−	0.386839i	$-0.126433\pi$
$677$	2.20192e11	+	1.27128e11i	1.04821	+	0.605183i	0.126061	+	0.992023i	$0.459767\pi$
$678$		0			0
$679$	−1.38194e11	−	2.39359e11i	−0.650145	−	1.12608i
$680$	4.44367e10	−	2.56555e10i	0.207829	−	0.119990i
$681$		0			0
$682$	1.98059e11	−	3.43049e11i	0.915499	−	1.58569i
$683$		−	2.98251e11i		−	1.37056i	−0.728279	−	0.685281i	$-0.759679\pi$
$683$		−	2.98251e11i		−	1.37056i	0.728279	−	0.685281i	$-0.240321\pi$
$684$		0			0
$685$	1.14144e11			0.518429
$686$	1.13478e11	+	6.55166e10i	0.512408	+	0.295839i
$687$		0			0
$688$	1.33201e10	+	2.30712e10i	0.0594505	+	0.102971i
$689$	−5.84886e10	+	3.37684e10i	−0.259534	+	0.149842i
$690$		0			0
$691$	1.50423e11	−	2.60541e11i	0.659785	−	1.14278i	−0.320886	−	0.947118i	$-0.603981\pi$
$691$	1.50423e11	−	2.60541e11i	0.659785	−	1.14278i	0.980671	−	0.195663i	$-0.0626860\pi$
$692$			5.86053e10i			0.255572i
$693$		0			0
$694$	−2.76005e10			−0.118981
$695$	−1.39634e11	−	8.06177e10i	−0.598483	−	0.345534i
$696$		0			0
$697$	4.92504e10	+	8.53041e10i	0.208679	+	0.361442i
$698$	2.13579e11	−	1.23310e11i	0.899782	−	0.519489i
$699$		0			0
$700$	5.14018e10	−	8.90305e10i	0.214085	−	0.370806i
$701$		−	2.33302e11i		−	0.966156i	−0.875577	−	0.483078i	$-0.839519\pi$
$701$		−	2.33302e11i		−	0.966156i	0.875577	−	0.483078i	$-0.160481\pi$
$702$		0			0
$703$	1.64525e11			0.673613
$704$	4.48096e10	+	2.58708e10i	0.182423	+	0.105322i
$705$		0			0
$706$	−8.02255e10	−	1.38955e11i	−0.322919	−	0.559312i
$707$	2.17992e11	−	1.25858e11i	0.872494	−	0.503735i
$708$		0			0
$709$	−1.36103e11	+	2.35737e11i	−0.538620	+	0.932918i	0.460358	+	0.887733i	$0.347721\pi$
$709$	−1.36103e11	+	2.35737e11i	−0.538620	+	0.932918i	−0.998979	+	0.0451845i	$0.985612\pi$
$710$			1.64875e11i			0.648816i
$711$		0			0
$712$	−1.02090e10			−0.0397250
$713$	5.63365e11	+	3.25259e11i	2.17988	+	1.25855i
$714$		0			0
$715$	9.93400e10	+	1.72062e11i	0.380102	+	0.658356i
$716$	−1.62688e11	+	9.39278e10i	−0.619017	+	0.357390i
$717$		0			0
$718$	−9.18479e10	+	1.59085e11i	−0.345598	+	0.598594i
$719$			4.94299e11i			1.84958i	0.380473	+	0.924792i	$0.375761\pi$
$719$			4.94299e11i			1.84958i	−0.380473	+	0.924792i	$0.624239\pi$
$720$		0			0
$721$	2.51803e11			0.931796
$722$	−6.60706e10	−	3.81459e10i	−0.243142	−	0.140378i
$723$		0			0
$724$	−1.01935e11	−	1.76557e11i	−0.370996	−	0.642585i
$725$	−1.72526e11	+	9.96081e10i	−0.624458	+	0.360531i
$726$		0			0
$727$	7.37697e10	−	1.27773e11i	0.264083	−	0.457405i	−0.703240	−	0.710952i	$-0.748264\pi$
$727$	7.37697e10	−	1.27773e11i	0.264083	−	0.457405i	0.967323	+	0.253548i	$0.0815974\pi$
$728$		−	3.77324e10i		−	0.134335i
$729$		0			0
$730$	−2.69603e11			−0.949365
$731$	−6.00847e10	−	3.46899e10i	−0.210423	−	0.121488i
$732$		0			0
$733$	2.03374e10	+	3.52254e10i	0.0704497	+	0.122022i	0.899098	−	0.437746i	$-0.144223\pi$
$733$	2.03374e10	+	3.52254e10i	0.0704497	+	0.122022i	−0.828649	+	0.559769i	$0.810890\pi$
$734$	9.25358e10	−	5.34256e10i	0.318805	−	0.184062i
$735$		0			0
$736$	−4.24859e10	+	7.35877e10i	−0.144788	+	0.250780i
$737$		−	7.81495e11i		−	2.64884i
$738$		0			0
$739$	−4.39058e11			−1.47212			−0.736062	−	0.676915i	$-0.763317\pi$
$739$	−4.39058e11			−1.47212			−0.736062	+	0.676915i	$0.763317\pi$
$740$	1.49658e11	+	8.64049e10i	0.499082	+	0.288145i
$741$		0			0
$742$	−1.05850e11	−	1.83338e11i	−0.349202	−	0.604836i
$743$	−2.39798e11	+	1.38447e11i	−0.786846	+	0.454286i	−0.838851	−	0.544361i	$-0.816772\pi$
$743$	−2.39798e11	+	1.38447e11i	−0.786846	+	0.454286i	0.0520049	+	0.998647i	$0.483439\pi$
$744$		0			0
$745$	−3.21657e11	+	5.57127e11i	−1.04416	+	1.80854i
$746$			1.55543e11i			0.502220i
$747$		0			0
$748$	−1.34752e11			−0.430455
$749$	−3.13093e11	−	1.80764e11i	−0.994824	−	0.574362i
$750$		0			0
$751$	−2.18499e10	−	3.78451e10i	−0.0686893	−	0.118973i	0.829635	−	0.558306i	$-0.188548\pi$
$751$	−2.18499e10	−	3.78451e10i	−0.0686893	−	0.118973i	−0.898325	+	0.439332i	$0.855215\pi$
$752$	−5.54225e10	+	3.19982e10i	−0.173306	+	0.100059i
$753$		0			0
$754$	−3.65596e10	+	6.33231e10i	−0.113114	+	0.195919i
$755$			5.78070e11i			1.77907i
$756$		0			0
$757$	−2.44223e11			−0.743708			−0.371854	−	0.928291i	$-0.621278\pi$
$757$	−2.44223e11			−0.743708			−0.371854	+	0.928291i	$0.621278\pi$
$758$	−7.93691e10	−	4.58238e10i	−0.240422	−	0.138808i
$759$		0			0
$760$	6.08447e10	+	1.05386e11i	0.182376	+	0.315885i
$761$	−3.60019e11	+	2.07857e11i	−1.07346	+	0.619764i	−0.929125	−	0.369765i	$-0.879438\pi$
$761$	−3.60019e11	+	2.07857e11i	−1.07346	+	0.619764i	−0.144337	+	0.989529i	$0.546105\pi$
$762$		0			0
$763$	−7.14516e10	+	1.23758e11i	−0.210821	+	0.365153i
$764$			2.37804e10i			0.0697985i
$765$		0			0
$766$	4.26293e11			1.23821
$767$	5.76964e10	+	3.33110e10i	0.166712	+	0.0962512i
$768$		0			0
$769$	−5.75903e10	−	9.97493e10i	−0.164681	−	0.285236i	0.771861	−	0.635792i	$-0.219326\pi$
$769$	−5.75903e10	−	9.97493e10i	−0.164681	−	0.285236i	−0.936542	+	0.350555i	$0.885993\pi$
$770$	−5.39345e11	+	3.11391e11i	−1.53428	+	0.885815i
$771$		0			0
$772$	7.49215e10	−	1.29768e11i	0.210929	−	0.365340i
$773$			1.78665e11i			0.500406i	0.968193	+	0.250203i	$0.0804973\pi$
$773$			1.78665e11i			0.500406i	−0.968193	+	0.250203i	$0.919503\pi$
$774$		0			0
$775$	4.24199e11			1.17588
$776$	1.29011e11	+	7.44845e10i	0.355779	+	0.205409i
$777$		0			0
$778$	4.86441e10	+	8.42541e10i	0.132774	+	0.229971i
$779$	−2.02307e11	+	1.16802e11i	−0.549366	+	0.317177i
$780$		0			0
$781$	2.16495e11	−	3.74981e11i	0.581894	−	1.00787i
$782$		−	2.21293e11i		−	0.591754i
$783$		0			0
$784$	2.38256e10			0.0630637
$785$	−7.18225e9	−	4.14667e9i	−0.0189139	−	0.0109200i
$786$		0			0
$787$	2.61255e11	+	4.52507e11i	0.681029	+	1.17958i	0.974667	+	0.223660i	$0.0718005\pi$
$787$	2.61255e11	+	4.52507e11i	0.681029	+	1.17958i	−0.293638	+	0.955917i	$0.594866\pi$
$788$	2.11077e11	−	1.21865e11i	0.547439	−	0.316064i
$789$		0			0
$790$	−3.19727e11	+	5.53783e11i	−0.820862	+	1.42178i
$791$		−	3.54825e11i		−	0.906376i
$792$		0			0
$793$	−2.45495e10			−0.0620798
$794$	−7.38627e10	−	4.26446e10i	−0.185842	−	0.107296i
$795$		0			0
$796$	1.01993e11	+	1.76656e11i	0.254048	+	0.440024i
$797$	−1.67664e11	+	9.68008e10i	−0.415534	+	0.239908i	−0.693165	−	0.720779i	$-0.743784\pi$
$797$	−1.67664e11	+	9.68008e10i	−0.415534	+	0.239908i	0.277631	+	0.960688i	$0.410451\pi$
$798$		0			0
$799$	8.33335e10	−	1.44338e11i	0.204471	−	0.354155i
$800$			5.54096e10i			0.135277i
$801$		0			0
$802$	3.17336e10			0.0767047
$803$	6.13166e11	+	3.54012e11i	1.47474	+	0.851443i
$804$		0			0
$805$	−5.11376e11	−	8.85729e11i	−1.21775	−	2.10920i
$806$	1.34836e11	−	7.78478e10i	0.319497	−	0.184462i
$807$		0			0
$808$	−6.78354e10	+	1.17494e11i	−0.159151	+	0.275658i
$809$			4.05968e11i			0.947760i	0.880590	+	0.473880i	$0.157147\pi$
$809$			4.05968e11i			0.947760i	−0.880590	+	0.473880i	$0.842853\pi$
$810$		0			0
$811$	−3.49637e11			−0.808229			−0.404115	−	0.914708i	$-0.632420\pi$
$811$	−3.49637e11			−0.808229			−0.404115	+	0.914708i	$0.632420\pi$
$812$	−1.98492e11	−	1.14600e11i	−0.456583	−	0.263608i
$813$		0			0
$814$	−2.26914e11	−	3.93027e11i	−0.516849	−	0.895209i
$815$	8.83654e11	−	5.10178e11i	2.00287	−	1.15636i
$816$		0			0
$817$	8.22706e10	−	1.42497e11i	0.184653	−	0.319828i
$818$			9.77005e10i			0.218215i
$819$		0			0
$820$	−2.45368e11			−0.542703
$821$	1.48992e11	+	8.60206e10i	0.327937	+	0.189334i	0.654925	−	0.755694i	$-0.272700\pi$
$821$	1.48992e11	+	8.60206e10i	0.327937	+	0.189334i	−0.326988	+	0.945029i	$0.606034\pi$
$822$		0			0
$823$	−1.51520e11	−	2.62440e11i	−0.330271	−	0.572046i	0.652294	−	0.757966i	$-0.273807\pi$
$823$	−1.51520e11	−	2.62440e11i	−0.330271	−	0.572046i	−0.982565	+	0.185920i	$0.940473\pi$
$824$	−1.17535e11	+	6.78591e10i	−0.254953	+	0.147197i
$825$		0			0
$826$	−1.04417e11	+	1.80855e11i	−0.224311	+	0.388517i
$827$			7.71110e11i			1.64852i	0.566211	+	0.824260i	$0.308409\pi$
$827$			7.71110e11i			1.64852i	−0.566211	+	0.824260i	$0.691591\pi$
$828$		0			0
$829$	1.56682e11			0.331742			0.165871	−	0.986147i	$-0.446956\pi$
$829$	1.56682e11			0.331742			0.165871	+	0.986147i	$0.446956\pi$
$830$	−4.45087e11	−	2.56971e11i	−0.937847	−	0.541466i
$831$		0			0
$832$	1.01686e10	+	1.76125e10i	0.0212211	+	0.0367560i
$833$	−5.37364e10	+	3.10247e10i	−0.111606	+	0.0644359i
$834$		0			0
$835$	−3.55299e11	+	6.15396e11i	−0.730883	+	1.26593i
$836$		−	3.19577e11i		−	0.654260i
$837$		0			0
$838$	−2.88318e11			−0.584649
$839$	−4.22447e11	−	2.43900e11i	−0.852559	−	0.492225i	0.00895468	−	0.999960i	$-0.497150\pi$
$839$	−4.22447e11	−	2.43900e11i	−0.852559	−	0.492225i	−0.861513	+	0.507735i	$0.830483\pi$
$840$		0			0
$841$	−2.80482e10	−	4.85809e10i	−0.0560688	−	0.0971140i
$842$	1.41505e9	−	8.16978e8i	0.00281529	−	0.00162541i
$843$		0			0
$844$	−5.58649e10	+	9.67608e10i	−0.110095	+	0.190691i
$845$		−	5.99283e11i		−	1.17545i
$846$		0			0
$847$	1.05959e12			2.05875
$848$	9.88166e10	+	5.70518e10i	0.191094	+	0.110328i
$849$		0			0
$850$	−7.21521e10	−	1.24971e11i	−0.138221	−	0.239405i
$851$	6.45441e11	−	3.72645e11i	1.23066	−	0.710522i
$852$		0			0
$853$	−5.07020e10	+	8.78185e10i	−0.0957699	+	0.165878i	−0.909930	−	0.414763i	$-0.863865\pi$
$853$	−5.07020e10	+	8.78185e10i	−0.0957699	+	0.165878i	0.814160	+	0.580641i	$0.197198\pi$
$854$		−	7.69530e10i		−	0.144675i
$855$		0			0
$856$	1.94859e11			0.362931
$857$	−2.37864e11	−	1.37331e11i	−0.440967	−	0.254592i	0.263041	−	0.964785i	$-0.415275\pi$
$857$	−2.37864e11	−	1.37331e11i	−0.440967	−	0.254592i	−0.704008	+	0.710192i	$0.748608\pi$
$858$		0			0
$859$	−2.10607e11	−	3.64783e11i	−0.386813	−	0.669980i	0.605206	−	0.796069i	$-0.293091\pi$
$859$	−2.10607e11	−	3.64783e11i	−0.386813	−	0.669980i	−0.992019	+	0.126089i	$0.959757\pi$
$860$	1.49673e11	−	8.64135e10i	0.273620	−	0.157975i
$861$		0			0
$862$	3.57310e10	−	6.18879e10i	0.0647166	−	0.112092i
$863$			8.61056e11i			1.55235i	0.630520	+	0.776173i	$0.282842\pi$
$863$			8.61056e11i			1.55235i	−0.630520	+	0.776173i	$0.717158\pi$
$864$		0			0
$865$	3.80198e11			0.679117
$866$	−3.88235e11	−	2.24148e11i	−0.690277	−	0.398532i
$867$		0			0
$868$	2.44022e11	+	4.22658e11i	0.429882	+	0.744578i
$869$	1.45433e12	−	8.39656e11i	2.55025	−	1.47239i
$870$		0			0
$871$	1.53585e11	−	2.66016e11i	0.266855	−	0.462206i
$872$		−	7.70227e10i		−	0.133215i
$873$		0			0
$874$	5.24819e11			0.899423
$875$	1.77186e11	+	1.02298e11i	0.302271	+	0.174516i
$876$		0			0
$877$	−3.14825e11	−	5.45294e11i	−0.532196	−	0.921790i	−0.999293	−	0.0375845i	$-0.988034\pi$
$877$	−3.14825e11	−	5.45294e11i	−0.532196	−	0.921790i	0.467098	−	0.884206i	$-0.345300\pi$
$878$	−3.08514e11	+	1.78121e11i	−0.519155	+	0.299734i
$879$		0			0
$880$	1.67835e11	−	2.90699e11i	0.279867	−	0.484744i
$881$		−	8.26944e11i		−	1.37269i	−0.727276	−	0.686345i	$-0.759214\pi$
$881$		−	8.26944e11i		−	1.37269i	0.727276	−	0.686345i	$-0.240786\pi$
$882$		0			0
$883$	1.00813e12			1.65834			0.829168	−	0.558999i	$-0.188815\pi$
$883$	1.00813e12			1.65834			0.829168	+	0.558999i	$0.188815\pi$
$884$	−4.58687e10	−	2.64823e10i	−0.0751116	−	0.0433657i
$885$		0			0
$886$	−2.52206e11	−	4.36834e11i	−0.409281	−	0.708895i
$887$	−8.45160e11	+	4.87954e11i	−1.36535	+	0.788286i	−0.990330	−	0.138730i	$-0.955698\pi$
$887$	−8.45160e11	+	4.87954e11i	−1.36535	+	0.788286i	−0.375022	+	0.927016i	$0.622365\pi$
$888$		0			0
$889$	7.68843e10	−	1.33167e11i	0.123092	−	0.213202i
$890$			6.62303e10i			0.105559i
$891$		0			0
$892$	4.35053e10			0.0687199
$893$	3.42312e11	+	1.97634e11i	0.538289	+	0.310781i
$894$		0			0
$895$	6.09349e11	+	1.05542e12i	0.949673	+	1.64488i
$896$	−5.52083e10	+	3.18745e10i	−0.0856588	+	0.0494551i
$897$		0			0
$898$	−1.33246e11	+	2.30789e11i	−0.204903	+	0.354902i
$899$		−	9.45747e11i		−	1.44789i
$900$		0			0
$901$	−2.97162e11			−0.450914
$902$	5.58048e11	+	3.22189e11i	0.843034	+	0.486726i
$903$		0			0
$904$	9.56226e10	+	1.65623e11i	0.143181	+	0.247998i
$905$	−1.14540e12	+	6.61297e11i	−1.70751	+	0.985830i
$906$		0			0
$907$	2.98209e11	−	5.16514e11i	0.440648	−	0.763225i	−0.557089	−	0.830453i	$-0.688082\pi$
$907$	2.98209e11	−	5.16514e11i	0.440648	−	0.763225i	0.997738	+	0.0672273i	$0.0214153\pi$
$908$			1.16209e11i			0.170961i
$909$		0			0
$910$	−2.44786e11			−0.356962
$911$	−1.16083e12	−	6.70203e11i	−1.68536	−	0.973045i	−0.957989	−	0.286804i	$-0.907407\pi$
$911$	−1.16083e12	−	6.70203e11i	−1.68536	−	0.973045i	−0.727374	−	0.686241i	$-0.759259\pi$
$912$		0			0
$913$	6.74849e11	+	1.16887e12i	0.971234	+	1.68223i
$914$	−4.01829e11	+	2.31996e11i	−0.575780	+	0.332427i
$915$		0			0
$916$	−2.45718e9	+	4.25596e9i	−0.00349024	+	0.00604527i
$917$		−	3.03920e11i		−	0.429816i
$918$		0			0
$919$	−3.60905e11			−0.505977			−0.252988	−	0.967469i	$-0.581413\pi$
$919$	−3.60905e11			−0.505977			−0.252988	+	0.967469i	$0.581413\pi$
$920$	4.77394e11	+	2.75624e11i	0.666386	+	0.384738i
$921$		0			0
$922$	2.20241e10	+	3.81469e10i	0.0304772	+	0.0527880i
$923$	1.47387e11	−	8.50941e10i	0.203073	−	0.117244i
$924$		0			0
$925$	2.43000e11	−	4.20888e11i	0.331924	−	0.574910i
$926$		−	6.06262e11i		−	0.824549i
$927$		0			0
$928$	1.23535e11			0.166570
$929$	−8.27772e10	−	4.77914e10i	−0.111134	−	0.0641634i	0.443403	−	0.896323i	$-0.353771\pi$
$929$	−8.27772e10	−	4.77914e10i	−0.111134	−	0.0641634i	−0.554537	+	0.832159i	$0.687105\pi$
$930$		0			0
$931$	−7.35782e10	−	1.27441e11i	−0.0979378	−	0.169633i
$932$	3.76479e11	−	2.17360e11i	0.498973	−	0.288082i
$933$		0			0
$934$	2.56347e11	−	4.44006e11i	0.336854	−	0.583448i
$935$			8.74192e11i			1.14383i
$936$		0			0
$937$	−1.26218e12			−1.63743			−0.818714	−	0.574201i	$-0.805313\pi$
$937$	−1.26218e12			−1.63743			−0.818714	+	0.574201i	$0.805313\pi$
$938$	8.33855e11	+	4.81426e11i	1.07716	+	0.621897i
$939$		0			0
$940$	2.07586e11	+	3.59549e11i	0.265880	+	0.460519i
$941$	5.84641e11	−	3.37543e11i	0.745643	−	0.430497i	−0.0784743	−	0.996916i	$-0.525005\pi$
$941$	5.84641e11	−	3.37543e11i	0.745643	−	0.430497i	0.824118	+	0.566419i	$0.191672\pi$
$942$		0			0
$943$	−5.29109e11	+	9.16443e11i	−0.669111	+	1.15893i
$944$		−	1.12558e11i		−	0.141739i
$945$		0			0
$946$	−4.53873e11			−0.566722
$947$	−4.41361e11	−	2.54820e11i	−0.548775	−	0.316835i	0.199853	−	0.979826i	$-0.435954\pi$
$947$	−4.41361e11	−	2.54820e11i	−0.548775	−	0.316835i	−0.748628	+	0.662991i	$0.769287\pi$
$948$		0			0
$949$	1.39145e11	+	2.41007e11i	0.171555	+	0.297142i
$950$	2.96381e11	−	1.71116e11i	0.363879	−	0.210085i
$951$		0			0
$952$	8.30113e10	−	1.43780e11i	0.101062	−	0.175045i
$953$			1.54025e12i			1.86732i	0.358160	+	0.933660i	$0.383404\pi$
$953$			1.54025e12i			1.86732i	−0.358160	+	0.933660i	$0.616596\pi$
$954$		0			0
$955$	1.54274e11			0.185472
$956$	3.32864e10	+	1.92179e10i	0.0398506	+	0.0230078i
$957$		0			0
$958$	−3.21645e10	−	5.57106e10i	−0.0381869	−	0.0661417i
$959$	3.19844e11	−	1.84662e11i	0.378150	−	0.218325i
$960$		0			0
$961$	−5.80464e11	+	1.00539e12i	−0.680584	+	1.17881i
$962$		−	1.78379e11i		−	0.208277i
$963$		0			0
$964$	−6.84242e11			−0.792321
$965$	−8.41859e11	−	4.86048e11i	−0.970801	−	0.560492i
$966$		0			0
$967$	−4.00962e11	−	6.94486e11i	−0.458561	−	0.794251i	0.540324	−	0.841457i	$-0.318302\pi$
$967$	−4.00962e11	−	6.94486e11i	−0.458561	−	0.794251i	−0.998885	+	0.0472059i	$0.984968\pi$
$968$	−4.94589e11	+	2.85551e11i	−0.563304	+	0.325224i
$969$		0			0
$970$	4.83213e11	−	8.36949e11i	0.545823	−	0.945393i
$971$			5.82235e11i			0.654970i	0.944856	+	0.327485i	$0.106201\pi$
$971$			5.82235e11i			0.654970i	−0.944856	+	0.327485i	$0.893799\pi$
$972$		0			0
$973$	−5.21695e11			−0.582057
$974$	3.57390e11	+	2.06339e11i	0.397106	+	0.229269i
$975$		0			0
$976$	2.07382e10	+	3.59197e10i	0.0228545	+	0.0395852i
$977$	−1.00625e12	+	5.80962e11i	−1.10441	+	0.637631i	−0.937375	−	0.348321i	$-0.886752\pi$
$977$	−1.00625e12	+	5.80962e11i	−1.10441	+	0.637631i	−0.167033	+	0.985951i	$0.553419\pi$
$978$		0			0
$979$	8.69660e10	−	1.50630e11i	0.0946714	−	0.163976i
$980$		−	1.54567e11i		−	0.167576i
$981$		0			0
$982$	6.62876e11			0.712830
$983$	1.19414e12	+	6.89439e11i	1.27892	+	0.738383i	0.976649	−	0.214840i	$-0.0689230\pi$
$983$	1.19414e12	+	6.89439e11i	1.27892	+	0.738383i	0.302268	+	0.953223i	$0.402256\pi$
$984$		0			0
$985$	−7.90592e11	−	1.36935e12i	−0.839861	−	1.45468i
$986$	−2.78621e11	+	1.60862e11i	−0.294786	+	0.170195i
$987$		0			0
$988$	6.28054e10	−	1.08782e11i	0.0659127	−	0.114164i
$989$		−	7.45364e11i		−	0.779082i
$990$		0			0
$991$	−8.57390e11			−0.888963			−0.444482	−	0.895788i	$-0.646612\pi$
$991$	−8.57390e11			−0.888963			−0.444482	+	0.895788i	$0.646612\pi$
$992$	−2.27806e11	−	1.31524e11i	−0.235244	−	0.135818i
$993$		0			0
$994$	2.66736e11	+	4.62000e11i	0.273235	+	0.473256i
$995$	1.14604e12	−	6.61669e11i	1.16925	−	0.675070i
$996$		0			0
$997$	7.94454e11	−	1.37603e12i	0.804060	−	1.39267i	−0.112865	−	0.993610i	$-0.536003\pi$
$997$	7.94454e11	−	1.37603e12i	0.804060	−	1.39267i	0.916924	−	0.399062i	$-0.130664\pi$
$998$			7.20514e11i			0.726307i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.9.d.a.35.8		16
3.2	odd	2		18.9.d.a.11.1	yes	16
4.3	odd	2		432.9.q.c.305.7		16
9.2	odd	6		162.9.b.c.161.10		16
9.4	even	3		18.9.d.a.5.1	✓	16
9.5	odd	6	inner	54.9.d.a.17.8		16
9.7	even	3		162.9.b.c.161.7		16
12.11	even	2		144.9.q.b.65.8		16
36.23	even	6		432.9.q.c.17.7		16
36.31	odd	6		144.9.q.b.113.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.9.d.a.5.1	✓	16	9.4	even	3
18.9.d.a.11.1	yes	16	3.2	odd	2
54.9.d.a.17.8		16	9.5	odd	6	inner
54.9.d.a.35.8		16	1.1	even	1	trivial
144.9.q.b.65.8		16	12.11	even	2
144.9.q.b.113.8		16	36.31	odd	6
162.9.b.c.161.7		16	9.7	even	3
162.9.b.c.161.10		16	9.2	odd	6
432.9.q.c.17.7		16	36.23	even	6
432.9.q.c.305.7		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(9.79796 + 5.65685i) q^{2} +(64.0000 + 110.851i) q^{4} +(719.139 - 415.195i) q^{5} +(1343.41 - 2326.85i) q^{7} +1448.15i q^{8} +9394.80 q^{10} +(-21366.9 - 12336.2i) q^{11} +(-4848.77 - 8398.31i) q^{13} +(26325.3 - 15198.9i) q^{14} +(-8192.00 + 14189.0i) q^{16} -42669.1i q^{17} +101194. q^{19} +(92049.8 + 53145.0i) q^{20} +(-139568. - 241739. i) q^{22} +(396990. - 229203. i) q^{23} +(149462. - 258875. i) q^{25} -109715. i q^{26} +343913. q^{28} +(-577159. - 333223. i) q^{29} +(709545. + 1.22897e6i) q^{31} +(-160530. + 92681.9i) q^{32} +(241373. - 418071. i) q^{34} -2.23111e6i q^{35} +1.62583e6 q^{37} +(991496. + 572441. i) q^{38} +(601267. + 1.04142e6i) q^{40} +(-1.99920e6 + 1.15424e6i) q^{41} +(812997. - 1.40815e6i) q^{43} -3.15806e6i q^{44} +5.18626e6 q^{46} +(3.38272e6 + 1.95301e6i) q^{47} +(-727099. - 1.25937e6i) q^{49} +(2.92884e6 - 1.69097e6i) q^{50} +(620642. - 1.07498e6i) q^{52} -6.96433e6i q^{53} -2.04877e7 q^{55} +(3.36964e6 + 1.94547e6i) q^{56} +(-3.76999e6 - 6.52981e6i) q^{58} +(-5.94959e6 + 3.43500e6i) q^{59} +(1.26576e6 - 2.19236e6i) q^{61} +1.60552e7i q^{62} -2.09715e6 q^{64} +(-6.97388e6 - 4.02637e6i) q^{65} +(1.58375e7 + 2.74313e7i) q^{67} +(4.72993e6 - 2.73083e6i) q^{68} +(1.26211e7 - 2.18603e7i) q^{70} +1.75496e7i q^{71} -2.86971e7 q^{73} +(1.59299e7 + 9.19711e6i) q^{74} +(6.47643e6 + 1.12175e7i) q^{76} +(-5.74089e7 + 3.31451e7i) q^{77} +(-3.40323e7 + 5.89457e7i) q^{79} +1.36051e7i q^{80} -2.61174e7 q^{82} +(-4.73759e7 - 2.73525e7i) q^{83} +(-1.77160e7 - 3.06851e7i) q^{85} +(1.59314e7 - 9.19801e6i) q^{86} +(1.78647e7 - 3.09425e7i) q^{88} +7.04968e6i q^{89} -2.60555e7 q^{91} +(5.08148e7 + 2.93379e7i) q^{92} +(2.20958e7 + 3.82711e7i) q^{94} +(7.27727e7 - 4.20153e7i) q^{95} +(5.14341e7 - 8.90865e7i) q^{97} -1.64524e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7} - 45756 q^{11} - 3370 q^{13} + 94464 q^{14} - 131072 q^{16} + 362180 q^{19} + 112896 q^{20} - 61824 q^{22} - 1311138 q^{23} + 963394 q^{25} - 472576 q^{28} + 2851290 q^{29}+ \cdots - 89415484 q^{97}+O(q^{100}) \) 16 * q + 1024 * q^4 + 882 * q^5 - 1846 * q^7 - 45756 * q^11 - 3370 * q^13 + 94464 * q^14 - 131072 * q^16 + 362180 * q^19 + 112896 * q^20 - 61824 * q^22 - 1311138 * q^23 + 963394 * q^25 - 472576 * q^28 + 2851290 * q^29 + 542438 * q^31 + 220416 * q^34 + 3343328 * q^37 + 1314432 * q^38 - 9218592 * q^41 + 339512 * q^43 + 7417344 * q^46 + 34980606 * q^47 - 2364654 * q^49 - 27744768 * q^50 + 431360 * q^52 - 4584276 * q^55 + 12091392 * q^56 - 7852800 * q^58 - 93924216 * q^59 - 841954 * q^61 - 33554432 * q^64 + 126568134 * q^65 + 29946644 * q^67 + 5476608 * q^68 - 34359552 * q^70 - 7547764 * q^73 - 35124480 * q^74 + 23179520 * q^76 - 9309294 * q^77 + 33813002 * q^79 - 137346048 * q^82 - 114200226 * q^83 - 125696772 * q^85 + 171379584 * q^86 + 7913472 * q^88 + 268578316 * q^91 - 167825664 * q^92 - 11832576 * q^94 + 143949240 * q^95 - 89415484 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more