LMFDB - Embedded newform 54.9.d.a.17.6

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			17.6
Root			$-2.97990 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	54.17
Dual form			54.9.d.a.35.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(69.6596 + 40.2180i) q^{5} +(370.849 + 642.329i) q^{7} -1448.15i q^{8} +O(q^{10})$	\(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(69.6596 + 40.2180i) q^{5} +(370.849 + 642.329i) q^{7} -1448.15i q^{8} +910.029 q^{10} +(19777.4 - 11418.5i) q^{11} +(-6499.12 + 11256.8i) q^{13} +(7267.12 + 4195.67i) q^{14} +(-8192.00 - 14189.0i) q^{16} -105666. i q^{17} +118278. q^{19} +(8916.42 - 5147.90i) q^{20} +(129186. - 223756. i) q^{22} +(77410.8 + 44693.1i) q^{23} +(-192078. - 332688. i) q^{25} +147058. i q^{26} +94937.3 q^{28} +(952037. - 549659. i) q^{29} +(226348. - 392047. i) q^{31} +(-160530. - 92681.9i) q^{32} +(-597737. - 1.03531e6i) q^{34} +59659.1i q^{35} -2.12547e6 q^{37} +(1.15889e6 - 669084. i) q^{38} +(58241.8 - 100878. i) q^{40} +(1.45174e6 + 838161. i) q^{41} +(-569118. - 985742. i) q^{43} -2.92314e6i q^{44} +1.01129e6 q^{46} +(3.10681e6 - 1.79372e6i) q^{47} +(2.60734e6 - 4.51605e6i) q^{49} +(-3.76394e6 - 2.17311e6i) q^{50} +(831887. + 1.44087e6i) q^{52} +1.16039e7i q^{53} +1.83692e6 q^{55} +(930192. - 537046. i) q^{56} +(6.21868e6 - 1.07711e7i) q^{58} +(-5.34715e6 - 3.08718e6i) q^{59} +(1.10379e7 + 1.91182e7i) q^{61} -5.12168e6i q^{62} -2.09715e6 q^{64} +(-905451. + 522763. i) q^{65} +(-1.84669e7 + 3.19855e7i) q^{67} +(-1.17132e7 - 6.76262e6i) q^{68} +(337483. + 584538. i) q^{70} +1.51775e7i q^{71} -4.91641e7 q^{73} +(-2.08253e7 + 1.20235e7i) q^{74} +(7.56982e6 - 1.31113e7i) q^{76} +(1.46689e7 + 8.46908e6i) q^{77} +(3.15777e7 + 5.46942e7i) q^{79} -1.31786e6i q^{80} +1.89654e7 q^{82} +(-4.45835e7 + 2.57403e7i) q^{83} +(4.24967e6 - 7.36064e6i) q^{85} +(-1.11524e7 - 6.43884e6i) q^{86} +(-1.65358e7 - 2.86408e7i) q^{88} +5.17343e7i q^{89} -9.64076e6 q^{91} +(9.90858e6 - 5.72072e6i) q^{92} +(2.02936e7 - 3.51495e7i) q^{94} +(8.23923e6 + 4.75692e6i) q^{95} +(-4.54739e6 - 7.87630e6i) q^{97} -5.89974e7i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7}+O(q^{10}) $ 16 * q + 1024 * q^4 + 882 * q^5 - 1846 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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
$5$	69.6596	+	40.2180i	0.111455	+	0.0643487i	0.554691	−	0.832056i	$-0.312836\pi$
$5$	69.6596	+	40.2180i	0.111455	+	0.0643487i	−0.443236	+	0.896405i	$0.646170\pi$
$6$		0			0
$7$	370.849	+	642.329i	0.154456	+	0.267526i	0.932861	−	0.360237i	$-0.117304\pi$
$7$	370.849	+	642.329i	0.154456	+	0.267526i	−0.778405	+	0.627763i	$0.783971\pi$
$8$		−	1448.15i		−	0.353553i
$9$		0			0
$10$	910.029			0.0910029
$11$	19777.4	−	11418.5i	1.35083	−	0.779900i	0.362461	−	0.931999i	$-0.381937\pi$
$11$	19777.4	−	11418.5i	1.35083	−	0.779900i	0.988365	+	0.152099i	$0.0486034\pi$
$12$		0			0
$13$	−6499.12	+	11256.8i	−0.227552	+	0.394132i	−0.957082	−	0.289817i	$-0.906406\pi$
$13$	−6499.12	+	11256.8i	−0.227552	+	0.394132i	0.729530	+	0.683949i	$0.239739\pi$
$14$	7267.12	+	4195.67i	0.189169	+	0.109217i
$15$		0			0
$16$	−8192.00	−	14189.0i	−0.125000	−	0.216506i
$17$		−	105666.i		−	1.26514i	−0.774502	−	0.632571i	$-0.782000\pi$
$17$		−	105666.i		−	1.26514i	0.774502	−	0.632571i	$-0.218000\pi$
$18$		0			0
$19$	118278.			0.907594			0.453797	−	0.891105i	$-0.350069\pi$
$19$	118278.			0.907594			0.453797	+	0.891105i	$0.350069\pi$
$20$	8916.42	−	5147.90i	0.0557276	−	0.0321744i
$21$		0			0
$22$	129186.	−	223756.i	0.551472	−	0.955178i
$23$	77410.8	+	44693.1i	0.276624	+	0.159709i	0.631894	−	0.775055i	$-0.282278\pi$
$23$	77410.8	+	44693.1i	0.276624	+	0.159709i	−0.355270	+	0.934764i	$0.615611\pi$
$24$		0			0
$25$	−192078.	−	332688.i	−0.491718	−	0.851681i
$26$			147058.i			0.321807i
$27$		0			0
$28$	94937.3			0.154456
$29$	952037.	−	549659.i	1.34605	−	0.777143i	0.358364	−	0.933582i	$-0.383335\pi$
$29$	952037.	−	549659.i	1.34605	−	0.777143i	0.987688	+	0.156439i	$0.0500014\pi$
$30$		0			0
$31$	226348.	−	392047.i	0.245093	−	0.424513i	−0.717065	−	0.697007i	$-0.754515\pi$
$31$	226348.	−	392047.i	0.245093	−	0.424513i	0.962158	+	0.272493i	$0.0878482\pi$
$32$	−160530.	−	92681.9i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−597737.	−	1.03531e6i	−0.447295	−	0.774738i
$35$			59659.1i			0.0397562i
$36$		0			0
$37$	−2.12547e6			−1.13409			−0.567046	−	0.823686i	$-0.691914\pi$
$37$	−2.12547e6			−1.13409			−0.567046	+	0.823686i	$0.691914\pi$
$38$	1.15889e6	−	669084.i	0.555785	−	0.320883i
$39$		0			0
$40$	58241.8	−	100878.i	0.0227507	−	0.0394054i
$41$	1.45174e6	+	838161.i	0.513751	+	0.296614i	0.734374	−	0.678745i	$-0.237476\pi$
$41$	1.45174e6	+	838161.i	0.513751	+	0.296614i	−0.220623	+	0.975359i	$0.570809\pi$
$42$		0			0
$43$	−569118.	−	985742.i	−0.166467	−	0.288330i	0.770708	−	0.637188i	$-0.219903\pi$
$43$	−569118.	−	985742.i	−0.166467	−	0.288330i	−0.937175	+	0.348859i	$0.886569\pi$
$44$		−	2.92314e6i		−	0.779900i
$45$		0			0
$46$	1.01129e6			0.225863
$47$	3.10681e6	−	1.79372e6i	0.636683	−	0.367589i	−0.146653	−	0.989188i	$-0.546850\pi$
$47$	3.10681e6	−	1.79372e6i	0.636683	−	0.367589i	0.783336	+	0.621599i	$0.213517\pi$
$48$		0			0
$49$	2.60734e6	−	4.51605e6i	0.452287	−	0.783384i
$50$	−3.76394e6	−	2.17311e6i	−0.602230	−	0.347697i
$51$		0			0
$52$	831887.	+	1.44087e6i	0.113776	+	0.197066i
$53$			1.16039e7i			1.47062i	0.677730	+	0.735311i	$0.262964\pi$
$53$			1.16039e7i			1.47062i	−0.677730	+	0.735311i	$0.737036\pi$
$54$		0			0
$55$	1.83692e6			0.200742
$56$	930192.	−	537046.i	0.0945846	−	0.0546084i
$57$		0			0
$58$	6.21868e6	−	1.07711e7i	0.549523	−	0.951802i
$59$	−5.34715e6	−	3.08718e6i	−0.441280	−	0.254773i	0.262860	−	0.964834i	$-0.415334\pi$
$59$	−5.34715e6	−	3.08718e6i	−0.441280	−	0.254773i	−0.704141	+	0.710061i	$0.748668\pi$
$60$		0			0
$61$	1.10379e7	+	1.91182e7i	0.797198	+	1.38079i	0.921434	+	0.388534i	$0.127018\pi$
$61$	1.10379e7	+	1.91182e7i	0.797198	+	1.38079i	−0.124237	+	0.992253i	$0.539648\pi$
$62$		−	5.12168e6i		−	0.346614i
$63$		0			0
$64$	−2.09715e6			−0.125000
$65$	−905451.	+	522763.i	−0.0507238	+	0.0292854i
$66$		0			0
$67$	−1.84669e7	+	3.19855e7i	−0.916418	+	1.58728i	−0.111607	+	0.993752i	$0.535600\pi$
$67$	−1.84669e7	+	3.19855e7i	−0.916418	+	1.58728i	−0.804811	+	0.593531i	$0.797733\pi$
$68$	−1.17132e7	−	6.76262e6i	−0.547823	−	0.316286i
$69$		0			0
$70$	337483.	+	584538.i	0.0140559	+	0.0243456i
$71$			1.51775e7i			0.597267i	0.954368	+	0.298633i	$0.0965307\pi$
$71$			1.51775e7i			0.597267i	−0.954368	+	0.298633i	$0.903469\pi$
$72$		0			0
$73$	−4.91641e7			−1.73124			−0.865618	−	0.500704i	$-0.833074\pi$
$73$	−4.91641e7			−1.73124			−0.865618	+	0.500704i	$0.833074\pi$
$74$	−2.08253e7	+	1.20235e7i	−0.694487	+	0.400962i
$75$		0			0
$76$	7.56982e6	−	1.31113e7i	0.226898	−	0.393000i
$77$	1.46689e7	+	8.46908e6i	0.417286	+	0.240920i
$78$		0			0
$79$	3.15777e7	+	5.46942e7i	0.810722	+	1.40421i	0.912359	+	0.409391i	$0.134259\pi$
$79$	3.15777e7	+	5.46942e7i	0.810722	+	1.40421i	−0.101637	+	0.994822i	$0.532408\pi$
$80$		−	1.31786e6i		−	0.0321744i
$81$		0			0
$82$	1.89654e7			0.419476
$83$	−4.45835e7	+	2.57403e7i	−0.939425	+	0.542377i	−0.889780	−	0.456390i	$-0.849142\pi$
$83$	−4.45835e7	+	2.57403e7i	−0.939425	+	0.542377i	−0.0496450	+	0.998767i	$0.515809\pi$
$84$		0			0
$85$	4.24967e6	−	7.36064e6i	0.0814103	−	0.141007i
$86$	−1.11524e7	−	6.43884e6i	−0.203880	−	0.117710i
$87$		0			0
$88$	−1.65358e7	−	2.86408e7i	−0.275736	−	0.477589i
$89$			5.17343e7i			0.824553i	0.911059	+	0.412277i	$0.135266\pi$
$89$			5.17343e7i			0.824553i	−0.911059	+	0.412277i	$0.864734\pi$
$90$		0			0
$91$	−9.64076e6			−0.140587
$92$	9.90858e6	−	5.72072e6i	0.138312	−	0.0798545i
$93$		0			0
$94$	2.02936e7	−	3.51495e7i	0.259925	−	0.450203i
$95$	8.23923e6	+	4.75692e6i	0.101156	+	0.0584025i
$96$		0			0
$97$	−4.54739e6	−	7.87630e6i	−0.0513659	−	0.0889684i	0.839199	−	0.543824i	$-0.183024\pi$
$97$	−4.54739e6	−	7.87630e6i	−0.0513659	−	0.0889684i	−0.890565	+	0.454856i	$0.849691\pi$
$98$		−	5.89974e7i		−	0.639630i
$99$		0			0
$100$	−4.91718e7			−0.491718
$101$	9.46459e7	−	5.46438e7i	0.909528	−	0.525117i	0.0292491	−	0.999572i	$-0.490688\pi$
$101$	9.46459e7	−	5.46438e7i	0.909528	−	0.525117i	0.880279	+	0.474456i	$0.157355\pi$
$102$		0			0
$103$	9.55744e7	−	1.65540e8i	0.849166	−	1.47080i	−0.0327875	−	0.999462i	$-0.510438\pi$
$103$	9.55744e7	−	1.65540e8i	0.849166	−	1.47080i	0.881954	−	0.471336i	$-0.156228\pi$
$104$	1.63016e7	+	9.41173e6i	0.139347	+	0.0804519i
$105$		0			0
$106$	6.56416e7	+	1.13695e8i	0.519943	+	0.900568i
$107$		−	1.73989e8i		−	1.32736i	−0.748019	−	0.663678i	$-0.768995\pi$
$107$		−	1.73989e8i		−	1.32736i	0.748019	−	0.663678i	$-0.231005\pi$
$108$		0			0
$109$	−1.00364e8			−0.711002			−0.355501	−	0.934676i	$-0.615690\pi$
$109$	−1.00364e8			−0.711002			−0.355501	+	0.934676i	$0.615690\pi$
$110$	1.79980e7	−	1.03912e7i	0.122929	−	0.0709731i
$111$		0			0
$112$	6.07599e6	−	1.05239e7i	0.0386140	−	0.0668814i
$113$	1.26056e8	+	7.27784e7i	0.773124	+	0.446364i	0.833988	−	0.551783i	$-0.186052\pi$
$113$	1.26056e8	+	7.27784e7i	0.773124	+	0.446364i	−0.0608637	+	0.998146i	$0.519386\pi$
$114$		0			0
$115$	3.59493e6	+	6.22661e6i	0.0205542	+	0.0356008i
$116$		−	1.40713e8i		−	0.777143i
$117$		0			0
$118$	−6.98549e7			−0.360304
$119$	6.78723e7	−	3.91861e7i	0.338458	−	0.195409i
$120$		0			0
$121$	1.53585e8	−	2.66018e8i	0.716487	−	1.24099i
$122$	2.16297e8	+	1.24879e8i	0.976364	+	0.563704i
$123$		0			0
$124$	−2.89726e7	−	5.01820e7i	−0.122546	−	0.212257i
$125$		−	6.23202e7i		−	0.255263i
$126$		0			0
$127$	−1.57730e8			−0.606315			−0.303157	−	0.952941i	$-0.598041\pi$
$127$	−1.57730e8			−0.606315			−0.303157	+	0.952941i	$0.598041\pi$
$128$	−2.05478e7	+	1.18633e7i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−5.91438e6	+	1.02440e7i	−0.0207079	+	0.0358671i
$131$	−2.71215e8	−	1.56586e8i	−0.920934	−	0.531701i	−0.0370008	−	0.999315i	$-0.511780\pi$
$131$	−2.71215e8	−	1.56586e8i	−0.920934	−	0.531701i	−0.883933	+	0.467614i	$0.845114\pi$
$132$		0			0
$133$	4.38634e7	+	7.59737e7i	0.140183	+	0.242804i
$134$			4.17857e8i			1.29601i
$135$		0			0
$136$	−1.53021e8			−0.447295
$137$	−8.44998e7	+	4.87860e7i	−0.239869	+	0.138488i	−0.615116	−	0.788436i	$-0.710891\pi$
$137$	−8.44998e7	+	4.87860e7i	−0.239869	+	0.138488i	0.375248	+	0.926925i	$0.377558\pi$
$138$		0			0
$139$	4.51078e7	−	7.81290e7i	0.120835	−	0.209292i	−0.799262	−	0.600982i	$-0.794776\pi$
$139$	4.51078e7	−	7.81290e7i	0.120835	−	0.209292i	0.920097	+	0.391690i	$0.128110\pi$
$140$	6.61329e6	+	3.81818e6i	0.0172149	+	0.00993905i
$141$		0			0
$142$	8.58572e7	+	1.48709e8i	0.211166	+	0.365750i
$143$			2.96841e8i			0.709872i
$144$		0			0
$145$	8.84246e7			0.200033
$146$	−4.81708e8	+	2.78114e8i	−1.06016	+	0.612085i
$147$		0			0
$148$	−1.36030e8	+	2.35611e8i	−0.283523	+	0.491076i
$149$	−5.31181e8	−	3.06678e8i	−1.07770	−	0.622210i	−0.147425	−	0.989073i	$-0.547098\pi$
$149$	−5.31181e8	−	3.06678e8i	−1.07770	−	0.622210i	−0.930275	+	0.366863i	$0.880432\pi$
$150$		0			0
$151$	7.34431e7	+	1.27207e8i	0.141268	+	0.244683i	0.927974	−	0.372644i	$-0.121549\pi$
$151$	7.34431e7	+	1.27207e8i	0.141268	+	0.244683i	−0.786706	+	0.617327i	$0.788215\pi$
$152$		−	1.71286e8i		−	0.320883i
$153$		0			0
$154$	1.91633e8			0.340713
$155$	3.15347e7	−	1.82065e7i	0.0546338	−	0.0315428i
$156$		0			0
$157$	−2.79253e8	+	4.83681e8i	−0.459621	+	0.796086i	−0.998941	−	0.0460145i	$-0.985348\pi$
$157$	−2.79253e8	+	4.83681e8i	−0.459621	+	0.796086i	0.539320	+	0.842101i	$0.318681\pi$
$158$	6.18794e8	+	3.57261e8i	0.992928	+	0.573267i
$159$		0			0
$160$	−7.45495e6	−	1.29124e7i	−0.0113754	−	0.0197027i
$161$			6.62976e7i			0.0986720i
$162$		0			0
$163$	−2.70277e6			−0.00382876			−0.00191438	−	0.999998i	$-0.500609\pi$
$163$	−2.70277e6			−0.00382876			−0.00191438	+	0.999998i	$0.500609\pi$
$164$	1.85822e8	−	1.07285e8i	0.256876	−	0.148307i
$165$		0			0
$166$	−2.91218e8	+	5.04405e8i	−0.383519	+	0.664274i
$167$	−6.54080e8	−	3.77633e8i	−0.840940	−	0.485517i	0.0166436	−	0.999861i	$-0.494702\pi$
$167$	−6.54080e8	−	3.77633e8i	−0.840940	−	0.485517i	−0.857584	+	0.514344i	$0.828035\pi$
$168$		0			0
$169$	3.23388e8	+	5.60125e8i	0.396440	+	0.686654i
$170$		−	9.61591e7i		−	0.115132i
$171$		0			0
$172$	−1.45694e8			−0.166467
$173$	8.12759e8	−	4.69247e8i	0.907355	−	0.523862i	0.0277761	−	0.999614i	$-0.491157\pi$
$173$	8.12759e8	−	4.69247e8i	0.907355	−	0.523862i	0.879579	+	0.475752i	$0.157824\pi$
$174$		0			0
$175$	1.42463e8	−	2.46754e8i	0.151898	−	0.263095i
$176$	−3.24034e8	−	1.87081e8i	−0.337706	−	0.194975i
$177$		0			0
$178$	2.92653e8	+	5.06891e8i	0.291524	+	0.504934i
$179$			9.19557e8i			0.895708i	0.894107	+	0.447854i	$0.147812\pi$
$179$			9.19557e8i			0.895708i	−0.894107	+	0.447854i	$0.852188\pi$
$180$		0			0
$181$	1.65808e9			1.54487			0.772435	−	0.635094i	$-0.219039\pi$
$181$	1.65808e9			1.54487			0.772435	+	0.635094i	$0.219039\pi$
$182$	−9.44598e7	+	5.45364e7i	−0.0860917	+	0.0497051i
$183$		0			0
$184$	6.47226e7	−	1.12103e8i	0.0564657	−	0.0978014i
$185$	−1.48059e8	−	8.54821e7i	−0.126401	−	0.0729774i
$186$		0			0
$187$	−1.20655e9	−	2.08980e9i	−0.986684	−	1.70899i
$188$		−	4.59192e8i		−	0.367589i
$189$		0			0
$190$	1.07637e8			0.0825936
$191$	−8.35643e8	+	4.82459e8i	−0.627895	+	0.362516i	−0.779937	−	0.625859i	$-0.784749\pi$
$191$	−8.35643e8	+	4.82459e8i	−0.627895	+	0.362516i	0.152041	+	0.988374i	$0.451415\pi$
$192$		0			0
$193$	−3.96992e8	+	6.87610e8i	−0.286123	+	0.495579i	−0.972881	−	0.231307i	$-0.925700\pi$
$193$	−3.96992e8	+	6.87610e8i	−0.286123	+	0.495579i	0.686758	+	0.726886i	$0.259033\pi$
$194$	−8.91102e7	−	5.14478e7i	−0.0629101	−	0.0363212i
$195$		0			0
$196$	−3.33740e8	−	5.78054e8i	−0.226143	−	0.391692i
$197$			1.07092e9i			0.711038i	0.934669	+	0.355519i	$0.115696\pi$
$197$			1.07092e9i			0.711038i	−0.934669	+	0.355519i	$0.884304\pi$
$198$		0			0
$199$	−1.01385e9			−0.646486			−0.323243	−	0.946316i	$-0.604773\pi$
$199$	−1.01385e9			−0.646486			−0.323243	+	0.946316i	$0.604773\pi$
$200$	−4.81784e8	+	2.78158e8i	−0.301115	+	0.173849i
$201$		0			0
$202$	6.18224e8	−	1.07080e9i	0.371313	−	0.643134i
$203$	7.06123e8	+	4.07680e8i	0.415811	+	0.240069i
$204$		0			0
$205$	6.74183e7	+	1.16772e8i	0.0381735	+	0.0661185i
$206$		−	2.16260e9i		−	1.20090i
$207$		0			0
$208$	2.12963e8			0.113776
$209$	2.33925e9	−	1.35056e9i	1.22600	−	0.707832i
$210$		0			0
$211$	−3.50549e8	+	6.07168e8i	−0.176856	+	0.306323i	−0.940802	−	0.338957i	$-0.889926\pi$
$211$	−3.50549e8	+	6.07168e8i	−0.176856	+	0.306323i	0.763946	+	0.645280i	$0.223259\pi$
$212$	1.28631e9	+	7.42650e8i	0.636798	+	0.367655i
$213$		0			0
$214$	−9.84231e8	−	1.70474e9i	−0.469291	−	0.812836i
$215$		−	9.15551e7i		−	0.0428478i
$216$		0			0
$217$	3.35764e8			0.151424
$218$	−9.83360e8	+	5.67743e8i	−0.435398	+	0.251377i
$219$		0			0
$220$	1.17563e8	−	2.03625e8i	0.0501856	−	0.0869240i
$221$	1.18946e9	+	6.86736e8i	0.498633	+	0.287886i
$222$		0			0
$223$	−1.37390e9	−	2.37966e9i	−0.555566	−	0.962268i	−0.997859	−	0.0653978i	$-0.979168\pi$
$223$	−1.37390e9	−	2.37966e9i	−0.555566	−	0.962268i	0.442293	−	0.896870i	$-0.354165\pi$
$224$		−	1.37484e8i		−	0.0546084i
$225$		0			0
$226$	1.64679e9			0.631253
$227$	2.22472e9	−	1.28445e9i	0.837862	−	0.483740i	−0.0186746	−	0.999826i	$-0.505945\pi$
$227$	2.22472e9	−	1.28445e9i	0.837862	−	0.483740i	0.856537	+	0.516085i	$0.172611\pi$
$228$		0			0
$229$	−1.26517e9	+	2.19134e9i	−0.460053	+	0.796835i	−0.998963	−	0.0455283i	$-0.985503\pi$
$229$	−1.26517e9	+	2.19134e9i	−0.460053	+	0.796835i	0.538910	+	0.842363i	$0.318836\pi$
$230$	7.04460e7	+	4.06720e7i	0.0251736	+	0.0145340i
$231$		0			0
$232$	−7.95991e8	−	1.37870e9i	−0.274762	−	0.475901i
$233$		−	1.19788e9i		−	0.406434i	−0.979134	−	0.203217i	$-0.934860\pi$
$233$		−	1.19788e9i		−	0.406434i	0.979134	−	0.203217i	$-0.0651397\pi$
$234$		0			0
$235$	2.88559e8			0.0946156
$236$	−6.84436e8	+	3.95159e8i	−0.220640	+	0.127387i
$237$		0			0
$238$	4.43340e8	−	7.67887e8i	0.138175	−	0.239326i
$239$	−1.41385e9	−	8.16289e8i	−0.433324	−	0.250180i	0.267438	−	0.963575i	$-0.413823\pi$
$239$	−1.41385e9	−	8.16289e8i	−0.433324	−	0.250180i	−0.700762	+	0.713395i	$0.747156\pi$
$240$		0			0
$241$	1.78726e9	+	3.09563e9i	0.529810	+	0.917659i	0.999395	+	0.0347712i	$0.0110702\pi$
$241$	1.78726e9	+	3.09563e9i	0.529810	+	0.917659i	−0.469585	+	0.882887i	$0.655596\pi$
$242$		−	3.47524e9i		−	1.01327i
$243$		0			0
$244$	2.82570e9			0.797198
$245$	3.63253e8	−	2.09724e8i	0.100819	−	0.0582082i
$246$		0			0
$247$	−7.68706e8	+	1.33144e9i	−0.206525	+	0.357712i
$248$	−5.67745e8	−	3.27788e8i	−0.150088	−	0.0866534i
$249$		0			0
$250$	−3.52536e8	−	6.10610e8i	−0.0902492	−	0.156316i
$251$			2.65229e9i			0.668230i	0.942532	+	0.334115i	$0.108437\pi$
$251$			2.65229e9i			0.668230i	−0.942532	+	0.334115i	$0.891563\pi$
$252$		0			0
$253$	2.04132e9			0.498228
$254$	−1.54543e9	+	8.92253e8i	−0.371290	+	0.214365i
$255$		0			0
$256$	−1.34218e8	+	2.32472e8i	−0.0312500	+	0.0541266i
$257$	2.52067e9	+	1.45531e9i	0.577807	+	0.333597i	0.760261	−	0.649617i	$-0.225071\pi$
$257$	2.52067e9	+	1.45531e9i	0.577807	+	0.333597i	−0.182454	+	0.983214i	$0.558404\pi$
$258$		0			0
$259$	−7.88228e8	−	1.36525e9i	−0.175167	−	0.303399i
$260$			1.33827e8i			0.0292854i
$261$		0			0
$262$	−3.54314e9			−0.751939
$263$	−7.19663e9	+	4.15498e9i	−1.50420	+	0.868452i	−0.504215	+	0.863578i	$0.668218\pi$
$263$	−7.19663e9	+	4.15498e9i	−1.50420	+	0.868452i	−0.999988	+	0.00487337i	$0.998449\pi$
$264$		0			0
$265$	−4.66686e8	+	8.08323e8i	−0.0946326	+	0.163909i
$266$	8.59544e8	+	4.96258e8i	0.171689	+	0.0991245i
$267$		0			0
$268$	2.36376e9	+	4.09415e9i	0.458209	+	0.793642i
$269$			3.91667e9i			0.748010i	0.927427	+	0.374005i	$0.122016\pi$
$269$			3.91667e9i			0.748010i	−0.927427	+	0.374005i	$0.877984\pi$
$270$		0			0
$271$	4.26666e9			0.791063			0.395532	−	0.918452i	$-0.370560\pi$
$271$	4.26666e9			0.791063			0.395532	+	0.918452i	$0.370560\pi$
$272$	−1.49929e9	+	8.65616e8i	−0.273911	+	0.158143i
$273$		0			0
$274$	−5.51950e8	+	9.56006e8i	−0.0979259	+	0.169613i
$275$	−7.59760e9	−	4.38648e9i	−1.32845	−	0.766982i
$276$		0			0
$277$	6.34405e8	+	1.09882e9i	0.107758	+	0.186642i	0.914861	−	0.403768i	$-0.132300\pi$
$277$	6.34405e8	+	1.09882e9i	0.107758	+	0.186642i	−0.807104	+	0.590409i	$0.798966\pi$
$278$		−	1.02067e9i		−	0.170886i
$279$		0			0
$280$	8.63956e7			0.0140559
$281$	5.43672e8	−	3.13889e8i	0.0871990	−	0.0503444i	−0.455766	−	0.890099i	$-0.650635\pi$
$281$	5.43672e8	−	3.13889e8i	0.0871990	−	0.0503444i	0.542965	+	0.839755i	$0.317301\pi$
$282$		0			0
$283$	−7.75733e8	+	1.34361e9i	−0.120939	+	0.209473i	−0.920138	−	0.391594i	$-0.871924\pi$
$283$	−7.75733e8	+	1.34361e9i	−0.120939	+	0.209473i	0.799199	+	0.601066i	$0.205257\pi$
$284$	1.68245e9	+	9.71363e8i	0.258624	+	0.149317i
$285$		0			0
$286$	1.67919e9	+	2.90844e9i	0.250978	+	0.434706i
$287$			1.24332e9i			0.183255i
$288$		0			0
$289$	−4.18954e9			−0.600586
$290$	8.66381e8	−	5.00205e8i	0.122495	−	0.0707223i
$291$		0			0
$292$	−3.14650e9	+	5.44990e9i	−0.432809	+	0.749648i
$293$	4.21204e9	+	2.43182e9i	0.571507	+	0.329960i	0.757751	−	0.652544i	$-0.226298\pi$
$293$	4.21204e9	+	2.43182e9i	0.571507	+	0.329960i	−0.186244	+	0.982504i	$0.559631\pi$
$294$		0			0
$295$	−2.48320e8	−	4.30103e8i	−0.0327887	−	0.0567917i
$296$			3.07801e9i			0.400962i
$297$		0			0
$298$	−6.93933e9			−0.879938
$299$	−1.00620e9	+	5.80932e8i	−0.125893	+	0.0726843i
$300$		0			0
$301$	4.22114e8	−	7.31122e8i	0.0514237	−	0.0890685i
$302$	1.43919e9	+	8.30914e8i	0.173017	+	0.0998915i
$303$		0			0
$304$	−9.68937e8	−	1.67825e9i	−0.113449	−	0.196500i
$305$			1.77568e9i			0.205195i
$306$		0			0
$307$	−1.51737e10			−1.70820			−0.854101	−	0.520108i	$-0.825892\pi$
$307$	−1.51737e10			−1.70820			−0.854101	+	0.520108i	$0.825892\pi$
$308$	1.87762e9	−	1.08404e9i	0.208643	−	0.120460i
$309$		0			0
$310$	2.05984e8	−	3.56774e8i	0.0223042	−	0.0386319i
$311$	−1.31231e10	−	7.57662e9i	−1.40280	−	0.809905i	−0.408118	−	0.912929i	$-0.633815\pi$
$311$	−1.31231e10	−	7.57662e9i	−1.40280	−	0.809905i	−0.994679	+	0.103024i	$0.967148\pi$
$312$		0			0
$313$	5.67865e9	+	9.83571e9i	0.591654	+	1.02477i	0.994010	+	0.109291i	$0.0348581\pi$
$313$	5.67865e9	+	9.83571e9i	0.591654	+	1.02477i	−0.402356	+	0.915483i	$0.631809\pi$
$314$			6.31878e9i			0.650002i
$315$		0			0
$316$	8.08389e9			0.810722
$317$	1.44463e10	−	8.34059e9i	1.43061	−	0.825961i	0.433440	−	0.901183i	$-0.357300\pi$
$317$	1.44463e10	−	8.34059e9i	1.43061	−	0.825961i	0.997167	+	0.0752213i	$0.0239663\pi$
$318$		0			0
$319$	1.25526e10	−	2.17417e10i	1.21219	−	2.09957i
$320$	−1.46087e8	−	8.43432e7i	−0.0139319	−	0.00804359i
$321$		0			0
$322$	3.75036e8	+	6.49581e8i	0.0348858	+	0.0604240i
$323$		−	1.24980e10i		−	1.14824i
$324$		0			0
$325$	4.99334e9			0.447566
$326$	−2.64816e7	+	1.52892e7i	−0.00234463	+	0.00135367i
$327$		0			0
$328$	1.21379e9	−	2.10234e9i	0.104869	−	0.181638i
$329$	2.30431e9	+	1.33040e9i	0.196679	+	0.113553i
$330$		0			0
$331$	−1.60334e9	−	2.77707e9i	−0.133571	−	0.231353i	0.791479	−	0.611196i	$-0.209311\pi$
$331$	−1.60334e9	−	2.77707e9i	−0.133571	−	0.231353i	−0.925051	+	0.379843i	$0.875978\pi$
$332$			6.58952e9i			0.542377i
$333$		0			0
$334$	−8.54487e9			−0.686625
$335$	−2.57279e9	+	1.48540e9i	−0.204279	+	0.117941i
$336$		0			0
$337$	8.82134e9	−	1.52790e10i	0.683935	−	1.18461i	−0.289835	−	0.957077i	$-0.593600\pi$
$337$	8.82134e9	−	1.52790e10i	0.683935	−	1.18461i	0.973770	−	0.227534i	$-0.0730662\pi$
$338$	6.33709e9	+	3.65872e9i	0.485538	+	0.280325i
$339$		0			0
$340$	−5.43958e8	−	9.42163e8i	−0.0407052	−	0.0705034i
$341$		−	1.03383e10i		−	0.764592i
$342$		0			0
$343$	8.14346e9			0.588345
$344$	−1.42751e9	+	8.24171e8i	−0.101940	+	0.0588550i
$345$		0			0
$346$	5.30892e9	−	9.19532e9i	0.370426	−	0.641597i
$347$	7.55287e9	+	4.36065e9i	0.520948	+	0.300769i	0.737322	−	0.675541i	$-0.236090\pi$
$347$	7.55287e9	+	4.36065e9i	0.520948	+	0.300769i	−0.216375	+	0.976310i	$0.569423\pi$
$348$		0			0
$349$	−5.08867e9	−	8.81384e9i	−0.343007	−	0.594105i	0.641983	−	0.766719i	$-0.278112\pi$
$349$	−5.08867e9	−	8.81384e9i	−0.343007	−	0.594105i	−0.984990	+	0.172614i	$0.944779\pi$
$350$		−	3.22358e9i		−	0.214816i
$351$		0			0
$352$	−4.23316e9			−0.275736
$353$	1.37900e10	−	7.96168e9i	0.888109	−	0.512750i	0.0147858	−	0.999891i	$-0.495293\pi$
$353$	1.37900e10	−	7.96168e9i	0.888109	−	0.512750i	0.873324	+	0.487141i	$0.161960\pi$
$354$		0			0
$355$	−6.10410e8	+	1.05726e9i	−0.0384333	+	0.0665685i
$356$	5.73481e9	+	3.31100e9i	0.357042	+	0.206138i
$357$		0			0
$358$	5.20180e9	+	9.00978e9i	0.316681	+	0.548507i
$359$		−	5.57548e9i		−	0.335664i	−0.985816	−	0.167832i	$-0.946323\pi$
$359$		−	5.57548e9i		−	0.335664i	0.985816	−	0.167832i	$-0.0536766\pi$
$360$		0			0
$361$	−2.99376e9			−0.176274
$362$	1.62458e10	−	9.37953e9i	0.946036	−	0.546194i
$363$		0			0
$364$	−6.17009e8	+	1.06869e9i	−0.0351468	+	0.0608760i
$365$	−3.42475e9	−	1.97728e9i	−0.192955	−	0.111403i
$366$		0			0
$367$	2.34540e9	+	4.06235e9i	0.129286	+	0.223930i	0.923400	−	0.383839i	$-0.125398\pi$
$367$	2.34540e9	+	4.06235e9i	0.129286	+	0.223930i	−0.794114	+	0.607769i	$0.792065\pi$
$368$		−	1.46450e9i		−	0.0798545i
$369$		0			0
$370$	−1.93424e9			−0.103206
$371$	−7.45353e9	+	4.30330e9i	−0.393429	+	0.227146i
$372$		0			0
$373$	−9.98911e9	+	1.73016e10i	−0.516049	+	0.893824i	0.483777	+	0.875191i	$0.339265\pi$
$373$	−9.98911e9	+	1.73016e10i	−0.516049	+	0.893824i	−0.999826	+	0.0186325i	$0.994069\pi$
$374$	−2.36434e10	−	1.36505e10i	−1.20844	−	0.697691i
$375$		0			0
$376$	−2.59758e9	−	4.49914e9i	−0.129962	−	0.225101i
$377$			1.42892e10i			0.707363i
$378$		0			0
$379$	−3.40327e10			−1.64945			−0.824726	−	0.565532i	$-0.808671\pi$
$379$	−3.40327e10			−1.64945			−0.824726	+	0.565532i	$0.808671\pi$
$380$	1.05462e9	−	6.08886e8i	0.0505781	−	0.0292013i
$381$		0			0
$382$	−5.45840e9	+	9.45422e9i	−0.256337	+	0.443989i
$383$	1.39611e10	+	8.06046e9i	0.648822	+	0.374597i	0.788005	−	0.615669i	$-0.211114\pi$
$383$	1.39611e10	+	8.06046e9i	0.648822	+	0.374597i	−0.139183	+	0.990267i	$0.544448\pi$
$384$		0			0
$385$	6.81218e8	+	1.17990e9i	0.0310058	+	0.0537037i
$386$			8.98290e9i			0.404639i
$387$		0			0
$388$	−1.16413e9			−0.0513659
$389$	−2.29807e10	+	1.32679e10i	−1.00361	+	0.579435i	−0.909315	−	0.416109i	$-0.863393\pi$
$389$	−2.29807e10	+	1.32679e10i	−1.00361	+	0.579435i	−0.0942959	+	0.995544i	$0.530060\pi$
$390$		0			0
$391$	4.72254e9	−	8.17969e9i	0.202055	−	0.349969i
$392$	−6.53994e9	−	3.77584e9i	−0.276968	−	0.159908i
$393$		0			0
$394$	6.05804e9	+	1.04928e10i	0.251390	+	0.435420i
$395$			5.07996e9i			0.208676i
$396$		0			0
$397$	2.50944e10			1.01022			0.505108	−	0.863056i	$-0.331452\pi$
$397$	2.50944e10			1.01022			0.505108	+	0.863056i	$0.331452\pi$
$398$	−9.93361e9	+	5.73518e9i	−0.395890	+	0.228567i
$399$		0			0
$400$	−3.14700e9	+	5.45076e9i	−0.122930	+	0.212920i
$401$	6.71173e9	+	3.87502e9i	0.259572	+	0.149864i	0.624139	−	0.781313i	$-0.285450\pi$
$401$	6.71173e9	+	3.87502e9i	0.259572	+	0.149864i	−0.364567	+	0.931177i	$0.618783\pi$
$402$		0			0
$403$	2.94213e9	+	5.09592e9i	0.111543	+	0.193198i
$404$		−	1.39888e10i		−	0.525117i
$405$		0			0
$406$	9.22475e9			0.339509
$407$	−4.20364e10	+	2.42697e10i	−1.53196	+	0.884478i
$408$		0			0
$409$	−1.37487e10	+	2.38135e10i	−0.491326	+	0.851001i	−0.999950	−	0.00998745i	$-0.996821\pi$
$409$	−1.37487e10	+	2.38135e10i	−0.491326	+	0.851001i	0.508624	+	0.860988i	$0.330154\pi$
$410$	1.32112e9	+	7.62751e8i	0.0467528	+	0.0269928i
$411$		0			0
$412$	−1.22335e10	−	2.11891e10i	−0.424583	−	0.735399i
$413$		−	4.57951e9i		−	0.157405i
$414$		0			0
$415$	−4.14089e9			−0.139605
$416$	2.08660e9	−	1.20470e9i	0.0696733	−	0.0402259i
$417$		0			0
$418$	1.52799e10	−	2.64656e10i	0.500513	−	0.866914i
$419$	3.00646e10	+	1.73578e10i	0.975439	+	0.563170i	0.900890	−	0.434048i	$-0.142915\pi$
$419$	3.00646e10	+	1.73578e10i	0.975439	+	0.563170i	0.0745486	+	0.997217i	$0.476248\pi$
$420$		0			0
$421$	2.79802e10	+	4.84631e10i	0.890681	+	1.54271i	0.839060	+	0.544039i	$0.183106\pi$
$421$	2.79802e10	+	4.84631e10i	0.890681	+	1.54271i	0.0516215	+	0.998667i	$0.483561\pi$
$422$			7.93201e9i			0.250111i
$423$		0			0
$424$	1.68043e10			0.519943
$425$	−3.51538e10	+	2.02961e10i	−1.07750	+	0.622094i
$426$		0			0
$427$	−8.18676e9	+	1.41799e10i	−0.246264	+	0.426541i
$428$	−1.92869e10	−	1.11353e10i	−0.574762	−	0.331839i
$429$		0			0
$430$	−5.17914e8	−	8.97053e8i	−0.0151490	−	0.0262388i
$431$		−	1.05381e9i		−	0.0305390i	−0.999883	−	0.0152695i	$-0.995139\pi$
$431$		−	1.05381e9i		−	0.0305390i	0.999883	−	0.0152695i	$-0.00486062\pi$
$432$		0			0
$433$	−1.08239e10			−0.307916			−0.153958	−	0.988077i	$-0.549202\pi$
$433$	−1.08239e10			−0.307916			−0.153958	+	0.988077i	$0.549202\pi$
$434$	3.28980e9	−	1.89937e9i	0.0927280	−	0.0535366i
$435$		0			0
$436$	−6.42328e9	+	1.11254e10i	−0.177750	+	0.307873i
$437$	9.15603e9	+	5.28624e9i	0.251062	+	0.144951i
$438$		0			0
$439$	−9.63567e9	−	1.66895e10i	−0.259432	−	0.449350i	0.706658	−	0.707556i	$-0.250202\pi$
$439$	−9.63567e9	−	1.66895e10i	−0.259432	−	0.449350i	−0.966090	+	0.258206i	$0.916869\pi$
$440$		−	2.66014e9i		−	0.0709731i
$441$		0			0
$442$	1.55391e10			0.407132
$443$	3.47005e10	−	2.00344e10i	0.900993	−	0.520189i	0.0234707	−	0.999725i	$-0.492528\pi$
$443$	3.47005e10	−	2.00344e10i	0.900993	−	0.520189i	0.877522	+	0.479536i	$0.159195\pi$
$444$		0			0
$445$	−2.08065e9	+	3.60379e9i	−0.0530590	+	0.0919008i
$446$	−2.69228e10	−	1.55439e10i	−0.680426	−	0.392844i
$447$		0			0
$448$	−7.77726e8	−	1.34706e9i	−0.0193070	−	0.0334407i
$449$		−	2.89578e10i		−	0.712493i	−0.934392	−	0.356247i	$-0.884056\pi$
$449$		−	2.89578e10i		−	0.712493i	0.934392	−	0.356247i	$-0.115944\pi$
$450$		0			0
$451$	3.82822e10			0.925318
$452$	1.61352e10	−	9.31563e9i	0.386562	−	0.223182i
$453$		0			0
$454$	1.45318e10	−	2.51699e10i	0.342056	−	0.592458i
$455$	−6.71571e8	−	3.87732e8i	−0.0156692	−	0.00904661i
$456$		0			0
$457$	−2.76429e9	−	4.78789e9i	−0.0633752	−	0.109769i	0.832597	−	0.553879i	$-0.186853\pi$
$457$	−2.76429e9	−	4.78789e9i	−0.0633752	−	0.109769i	−0.895972	+	0.444110i	$0.853520\pi$
$458$			2.86276e10i			0.650613i
$459$		0			0
$460$	9.20303e8			0.0205542
$461$	4.96113e10	−	2.86431e10i	1.09844	−	0.634186i	0.162631	−	0.986687i	$-0.448002\pi$
$461$	4.96113e10	−	2.86431e10i	1.09844	−	0.634186i	0.935811	+	0.352501i	$0.114669\pi$
$462$		0			0
$463$	−4.30725e10	+	7.46037e10i	−0.937294	+	1.62344i	−0.166802	+	0.985990i	$0.553344\pi$
$463$	−4.30725e10	+	7.46037e10i	−0.937294	+	1.62344i	−0.770492	+	0.637450i	$0.779989\pi$
$464$	−1.55982e10	−	9.00561e9i	−0.336513	−	0.194286i
$465$		0			0
$466$	−6.77624e9	−	1.17368e10i	−0.143696	−	0.248889i
$467$		−	1.73366e10i		−	0.364498i	−0.983252	−	0.182249i	$-0.941662\pi$
$467$		−	1.73366e10i		−	0.364498i	0.983252	−	0.182249i	$-0.0583377\pi$
$468$		0			0
$469$	−2.73936e10			−0.566185
$470$	2.82729e9	−	1.63233e9i	0.0579400	−	0.0334517i
$471$		0			0
$472$	−4.47071e9	+	7.74351e9i	−0.0900760	+	0.156016i
$473$	−2.25114e10	−	1.29970e10i	−0.449736	−	0.259655i
$474$		0			0
$475$	−2.27186e10	−	3.93498e10i	−0.446281	−	0.772981i
$476$		−	1.00316e10i		−	0.195409i
$477$		0			0
$478$	−1.84705e10			−0.353808
$479$	−1.41007e10	+	8.14105e9i	−0.267855	+	0.154646i	−0.627912	−	0.778284i	$-0.716090\pi$
$479$	−1.41007e10	+	8.14105e9i	−0.267855	+	0.154646i	0.360058	+	0.932930i	$0.382757\pi$
$480$		0			0
$481$	1.38137e10	−	2.39260e10i	0.258065	−	0.446982i
$482$	3.50231e10	+	2.02206e10i	0.648883	+	0.374633i
$483$		0			0
$484$	−1.96589e10	−	3.40503e10i	−0.358244	−	0.620496i
$485$		−	7.31547e8i		−	0.0132213i
$486$		0			0
$487$	8.59101e10			1.52731			0.763657	−	0.645622i	$-0.223402\pi$
$487$	8.59101e10			1.52731			0.763657	+	0.645622i	$0.223402\pi$
$488$	2.76860e10	−	1.59845e10i	0.488182	−	0.281852i
$489$		0			0
$490$	2.37276e9	−	4.10974e9i	0.0411594	−	0.0712901i
$491$	9.42747e10	+	5.44295e10i	1.62207	+	0.936502i	0.986366	+	0.164569i	$0.0526233\pi$
$491$	9.42747e10	+	5.44295e10i	1.62207	+	0.936502i	0.635704	+	0.771933i	$0.280710\pi$
$492$		0			0
$493$	−5.80802e10	−	1.00598e11i	−0.983197	−	1.70295i
$494$			1.73938e10i			0.292070i
$495$		0			0
$496$	−7.41699e9			−0.122546
$497$	−9.74898e9	+	5.62857e9i	−0.159784	+	0.0922514i
$498$		0			0
$499$	1.01210e10	−	1.75301e10i	0.163238	−	0.282737i	−0.772790	−	0.634662i	$-0.781139\pi$
$499$	1.01210e10	−	1.75301e10i	0.163238	−	0.282737i	0.936028	+	0.351925i	$0.114473\pi$
$500$	−6.90827e9	−	3.98849e9i	−0.110532	−	0.0638158i
$501$		0			0
$502$	1.50036e10	+	2.59870e10i	0.236255	+	0.409206i
$503$			8.95990e9i			0.139969i	0.997548	+	0.0699844i	$0.0222949\pi$
$503$			8.95990e9i			0.139969i	−0.997548	+	0.0699844i	$0.977705\pi$
$504$		0			0
$505$	8.79066e9			0.135162
$506$	2.00007e10	−	1.15474e10i	0.305101	−	0.176150i
$507$		0			0
$508$	−1.00947e10	+	1.74845e10i	−0.151579	+	0.262542i
$509$	−7.49283e10	−	4.32599e10i	−1.11628	−	0.644487i	−0.175835	−	0.984420i	$-0.556262\pi$
$509$	−7.49283e10	−	4.32599e10i	−1.11628	−	0.644487i	−0.940450	+	0.339933i	$0.889596\pi$
$510$		0			0
$511$	−1.82324e10	−	3.15795e10i	−0.267400	−	0.463150i
$512$			3.03700e9i			0.0441942i
$513$		0			0
$514$	3.29298e10			0.471777
$515$	1.33153e10	−	7.68761e9i	0.189288	−	0.109286i
$516$		0			0
$517$	4.09632e10	−	7.09503e10i	0.573365	−	0.993098i
$518$	−1.54461e10	−	8.91778e9i	−0.214535	−	0.123862i
$519$		0			0
$520$	7.57041e8	+	1.31123e9i	0.0103540	+	0.0179336i
$521$			7.83590e10i			1.06350i	0.846901	+	0.531750i	$0.178466\pi$
$521$			7.83590e10i			1.06350i	−0.846901	+	0.531750i	$0.821534\pi$
$522$		0			0
$523$	−9.36222e9			−0.125133			−0.0625665	−	0.998041i	$-0.519929\pi$
$523$	−9.36222e9			−0.125133			−0.0625665	+	0.998041i	$0.519929\pi$
$524$	−3.47155e10	+	2.00430e10i	−0.460467	+	0.265851i
$525$		0			0
$526$	−4.70082e10	+	8.14206e10i	−0.614088	+	1.06363i
$527$	−4.14260e10	−	2.39173e10i	−0.537070	−	0.310078i
$528$		0			0
$529$	−3.51605e10	−	6.08998e10i	−0.448986	−	0.777667i
$530$			1.05599e10i			0.133831i
$531$		0			0
$532$	1.12290e10			0.140183
$533$	−1.88700e10	+	1.08946e10i	−0.233810	+	0.134990i
$534$		0			0
$535$	6.99749e9	−	1.21200e10i	0.0854136	−	0.147941i
$536$	4.63200e10	+	2.67429e10i	0.561189	+	0.324003i
$537$		0			0
$538$	2.21560e10	+	3.83754e10i	0.264462	+	0.458061i
$539$		−	1.19088e11i		−	1.41095i
$540$		0			0
$541$	2.87519e10			0.335642			0.167821	−	0.985817i	$-0.446327\pi$
$541$	2.87519e10			0.335642			0.167821	+	0.985817i	$0.446327\pi$
$542$	4.18046e10	−	2.41359e10i	0.484425	−	0.279683i
$543$		0			0
$544$	−9.79332e9	+	1.69625e10i	−0.111824	+	0.193685i
$545$	−6.99129e9	−	4.03642e9i	−0.0792449	−	0.0457521i
$546$		0			0
$547$	7.14292e10	+	1.23719e11i	0.797860	+	1.38193i	0.921007	+	0.389545i	$0.127368\pi$
$547$	7.14292e10	+	1.23719e11i	0.797860	+	1.38193i	−0.123147	+	0.992388i	$0.539299\pi$
$548$			1.24892e10i			0.138488i
$549$		0			0
$550$	−9.92547e10			−1.08468
$551$	1.12605e11	−	6.50128e10i	1.22167	−	0.705330i
$552$		0			0
$553$	−2.34211e10	+	4.05665e10i	−0.250442	+	0.433778i
$554$	1.24318e10	+	7.17747e9i	0.131975	+	0.0761961i
$555$		0			0
$556$	−5.77380e9	−	1.00005e10i	−0.0604174	−	0.104646i
$557$			1.20526e10i			0.125216i	0.998038	+	0.0626080i	$0.0199418\pi$
$557$			1.20526e10i			0.125216i	−0.998038	+	0.0626080i	$0.980058\pi$
$558$		0			0
$559$	1.47951e10			0.151520
$560$	8.46501e8	−	4.88728e8i	0.00860747	−	0.00496952i
$561$		0			0
$562$	3.55125e9	−	6.15094e9i	0.0355988	−	0.0616590i
$563$	−7.41550e10	−	4.28134e10i	−0.738086	−	0.426134i	0.0832869	−	0.996526i	$-0.473458\pi$
$563$	−7.41550e10	−	4.28134e10i	−0.738086	−	0.426134i	−0.821373	+	0.570391i	$0.806792\pi$
$564$		0			0
$565$	5.85400e9	+	1.01394e10i	0.0574459	+	0.0994992i
$566$			1.75528e10i			0.171034i
$567$		0			0
$568$	2.19794e10			0.211166
$569$	−6.77244e10	+	3.91007e10i	−0.646095	+	0.373023i	−0.786958	−	0.617006i	$-0.788345\pi$
$569$	−6.77244e10	+	3.91007e10i	−0.646095	+	0.373023i	0.140864	+	0.990029i	$0.455012\pi$
$570$		0			0
$571$	−1.68244e10	+	2.91408e10i	−0.158269	+	0.274130i	−0.934245	−	0.356633i	$-0.883925\pi$
$571$	−1.68244e10	+	2.91408e10i	−0.158269	+	0.274130i	0.775975	+	0.630763i	$0.217258\pi$
$572$	3.29052e10	+	1.89978e10i	0.307383	+	0.177468i
$573$		0			0
$574$	7.03330e9	+	1.21820e10i	0.0647906	+	0.112221i
$575$		−	3.43382e10i		−	0.314128i
$576$		0			0
$577$	−5.68149e10			−0.512577			−0.256288	−	0.966600i	$-0.582500\pi$
$577$	−5.68149e10			−0.512577			−0.256288	+	0.966600i	$0.582500\pi$
$578$	−4.10490e10	+	2.36996e10i	−0.367782	+	0.212339i
$579$		0			0
$580$	5.65917e9	−	9.80198e9i	0.0500082	−	0.0866167i
$581$	−3.30675e10	−	1.90915e10i	−0.290200	−	0.167547i
$582$		0			0
$583$	1.32499e11	+	2.29496e11i	1.14694	+	1.98655i
$584$			7.11972e10i			0.612085i
$585$		0			0
$586$	5.50258e10			0.466634
$587$	−1.52093e11	+	8.78111e10i	−1.28103	+	0.739600i	−0.977036	−	0.213075i	$-0.931652\pi$
$587$	−1.52093e11	+	8.78111e10i	−1.28103	+	0.739600i	−0.303990	+	0.952675i	$0.598319\pi$
$588$		0			0
$589$	2.67722e10	−	4.63707e10i	0.222445	−	0.385286i
$590$	−4.86606e9	−	2.80942e9i	−0.0401578	−	0.0231851i
$591$		0			0
$592$	1.74119e10	+	3.01582e10i	0.141761	+	0.245538i
$593$		−	1.42615e10i		−	0.115331i	−0.998336	−	0.0576655i	$-0.981634\pi$
$593$		−	1.42615e10i		−	0.115331i	0.998336	−	0.0576655i	$-0.0183657\pi$
$594$		0			0
$595$	6.30394e9			0.0502972
$596$	−6.79912e10	+	3.92548e10i	−0.538850	+	0.311105i
$597$		0			0
$598$	−6.57250e9	+	1.13839e10i	−0.0513956	+	0.0890197i
$599$	1.21666e11	+	7.02441e10i	0.945068	+	0.545635i	0.891545	−	0.452931i	$-0.149622\pi$
$599$	1.21666e11	+	7.02441e10i	0.945068	+	0.545635i	0.0535228	+	0.998567i	$0.482955\pi$
$600$		0			0
$601$	−7.75136e10	−	1.34257e11i	−0.594128	−	1.02906i	−0.993669	−	0.112344i	$-0.964164\pi$
$601$	−7.75136e10	−	1.34257e11i	−0.594128	−	1.02906i	0.399542	−	0.916715i	$-0.369169\pi$
$602$		−	9.55134e9i		−	0.0727241i
$603$		0			0
$604$	1.88014e10			0.141268
$605$	2.13974e10	−	1.23538e10i	0.159713	−	0.0922101i
$606$		0			0
$607$	5.96405e10	−	1.03300e11i	0.439325	−	0.760934i	−0.558312	−	0.829631i	$-0.688551\pi$
$607$	5.96405e10	−	1.03300e11i	0.439325	−	0.760934i	0.997638	+	0.0686970i	$0.0218842\pi$
$608$	−1.89872e10	−	1.09623e10i	−0.138946	−	0.0802207i
$609$		0			0
$610$	1.00448e10	+	1.73981e10i	0.0725473	+	0.125656i
$611$			4.66303e10i			0.334583i
$612$		0			0
$613$	−1.07532e11			−0.761546			−0.380773	−	0.924669i	$-0.624342\pi$
$613$	−1.07532e11			−0.761546			−0.380773	+	0.924669i	$0.624342\pi$
$614$	−1.48672e11	+	8.58356e10i	−1.04606	+	0.603940i
$615$		0			0
$616$	1.22645e10	−	2.12428e10i	0.0851782	−	0.147533i
$617$	−1.08306e11	−	6.25304e10i	−0.747328	−	0.431470i	0.0773997	−	0.997000i	$-0.475338\pi$
$617$	−1.08306e11	−	6.25304e10i	−0.747328	−	0.431470i	−0.824728	+	0.565530i	$0.808672\pi$
$618$		0			0
$619$	3.18581e10	+	5.51798e10i	0.216998	+	0.375852i	0.953889	−	0.300160i	$-0.0970400\pi$
$619$	3.18581e10	+	5.51798e10i	0.216998	+	0.375852i	−0.736890	+	0.676012i	$0.763707\pi$
$620$		−	4.66088e9i		−	0.0315428i
$621$		0			0
$622$	−1.71439e11			−1.14538
$623$	−3.32304e10	+	1.91856e10i	−0.220589	+	0.127357i
$624$		0			0
$625$	−7.25239e10	+	1.25615e11i	−0.475293	+	0.823231i
$626$	1.11278e11	+	6.42466e10i	0.724625	+	0.418362i
$627$		0			0
$628$	3.57444e10	+	6.19111e10i	0.229810	+	0.398043i
$629$			2.24590e11i			1.43479i
$630$		0			0
$631$	−8.53724e10			−0.538518			−0.269259	−	0.963068i	$-0.586779\pi$
$631$	−8.53724e10			−0.538518			−0.269259	+	0.963068i	$0.586779\pi$
$632$	7.92056e10	−	4.57294e10i	0.496464	−	0.286634i
$633$		0			0
$634$	9.43630e10	−	1.63441e11i	0.584043	−	1.01159i
$635$	−1.09874e10	−	6.34356e9i	−0.0675770	−	0.0390156i
$636$		0			0
$637$	3.38909e10	+	5.87007e10i	0.205838	+	0.356521i
$638$		−	2.84032e11i		−	1.71429i
$639$		0			0
$640$	−1.90847e9			−0.0113754
$641$	3.48018e10	−	2.00929e10i	0.206144	−	0.119017i	−0.393374	−	0.919378i	$-0.628692\pi$
$641$	3.48018e10	−	2.00929e10i	0.206144	−	0.119017i	0.599518	+	0.800361i	$0.295359\pi$
$642$		0			0
$643$	−2.65057e10	+	4.59092e10i	−0.155058	+	0.268569i	−0.933080	−	0.359668i	$-0.882890\pi$
$643$	−2.65057e10	+	4.59092e10i	−0.155058	+	0.268569i	0.778022	+	0.628237i	$0.216223\pi$
$644$	7.34917e9	+	4.24304e9i	0.0427263	+	0.0246680i
$645$		0			0
$646$	−7.06994e10	−	1.22455e11i	−0.405962	−	0.703148i
$647$		−	8.40520e10i		−	0.479657i	−0.970815	−	0.239829i	$-0.922909\pi$
$647$		−	8.40520e10i		−	0.479657i	0.970815	−	0.239829i	$-0.0770912\pi$
$648$		0			0
$649$	−1.41004e11			−0.794791
$650$	4.89245e10	−	2.82466e10i	0.274077	−	0.158239i
$651$		0			0
$652$	−1.72977e8	+	2.99605e8i	−0.000957190	+	0.00165790i
$653$	−5.79412e10	−	3.34523e10i	−0.318665	−	0.183981i	0.332132	−	0.943233i	$-0.392232\pi$
$653$	−5.79412e10	−	3.34523e10i	−0.318665	−	0.183981i	−0.650797	+	0.759251i	$0.725565\pi$
$654$		0			0
$655$	−1.25951e10	−	2.18154e10i	−0.0684286	−	0.118522i
$656$		−	2.74649e10i		−	0.148307i
$657$		0			0
$658$	3.01034e10			0.160588
$659$	1.98528e11	−	1.14620e11i	1.05264	−	0.607741i	0.129251	−	0.991612i	$-0.458743\pi$
$659$	1.98528e11	−	1.14620e11i	1.05264	−	0.607741i	0.923387	+	0.383871i	$0.125409\pi$
$660$		0			0
$661$	1.62836e11	−	2.82040e11i	0.852989	−	1.47742i	−0.0255089	−	0.999675i	$-0.508121\pi$
$661$	1.62836e11	−	2.82040e11i	0.852989	−	1.47742i	0.878498	−	0.477746i	$-0.158546\pi$
$662$	−3.14189e10	−	1.81397e10i	−0.163591	−	0.0944493i
$663$		0			0
$664$	3.72760e10	+	6.45639e10i	0.191759	+	0.332137i
$665$			7.05639e9i			0.0360825i
$666$		0			0
$667$	9.82639e10			0.496467
$668$	−8.37223e10	+	4.83371e10i	−0.420470	+	0.242758i
$669$		0			0
$670$	−1.68054e10	+	2.91078e10i	−0.0833967	+	0.144447i
$671$	4.36602e11	+	2.52072e11i	2.15375	+	1.24347i
$672$		0			0
$673$	−1.20089e10	−	2.08001e10i	−0.0585389	−	0.101392i	0.835271	−	0.549839i	$-0.185311\pi$
$673$	−1.20089e10	−	2.08001e10i	−0.0585389	−	0.101392i	−0.893810	+	0.448446i	$0.851977\pi$
$674$		−	1.99604e11i		−	0.967230i
$675$		0			0
$676$	8.27874e10			0.396440
$677$	2.50617e11	−	1.44694e11i	1.19304	−	0.688804i	0.234048	−	0.972225i	$-0.424803\pi$
$677$	2.50617e11	−	1.44694e11i	1.19304	−	0.688804i	0.958995	+	0.283421i	$0.0914695\pi$
$678$		0			0
$679$	3.37279e9	−	5.84184e9i	0.0158675	−	0.0274834i
$680$	−1.06594e10	−	6.15418e9i	−0.0498534	−	0.0287829i
$681$		0			0
$682$	−5.84820e10	−	1.01294e11i	−0.270324	−	0.468215i
$683$			1.04015e11i			0.477982i	0.971022	+	0.238991i	$0.0768166\pi$
$683$			1.04015e11i			0.477982i	−0.971022	+	0.238991i	$0.923183\pi$
$684$		0			0
$685$	−7.84829e9			−0.0356462
$686$	7.97893e10	−	4.60664e10i	0.360287	−	0.208012i
$687$		0			0
$688$	−9.32443e9	+	1.61504e10i	−0.0416168	+	0.0720824i
$689$	−1.30623e11	−	7.54152e10i	−0.579619	−	0.334643i
$690$		0			0
$691$	−5.51122e10	−	9.54571e10i	−0.241733	−	0.418694i	0.719475	−	0.694518i	$-0.244382\pi$
$691$	−5.51122e10	−	9.54571e10i	−0.241733	−	0.418694i	−0.961208	+	0.275825i	$0.911049\pi$
$692$		−	1.20127e11i		−	0.523862i
$693$		0			0
$694$	9.86703e10			0.425352
$695$	6.28438e9	−	3.62829e9i	0.0269354	−	0.0155511i
$696$		0			0
$697$	8.85651e10	−	1.53399e11i	0.375259	−	0.649968i
$698$	−9.97172e10	−	5.75718e10i	−0.420096	−	0.242542i
$699$		0			0
$700$	−1.82353e10	−	3.15845e10i	−0.0759488	−	0.131547i
$701$		−	7.57816e10i		−	0.313828i	−0.987612	−	0.156914i	$-0.949845\pi$
$701$		−	7.57816e10i		−	0.313828i	0.987612	−	0.156914i	$-0.0501546\pi$
$702$		0			0
$703$	−2.51397e11			−1.02929
$704$	−4.14763e10	+	2.39464e10i	−0.168853	+	0.0974875i
$705$		0			0
$706$	9.00761e10	−	1.56016e11i	0.362569	−	0.627988i
$707$	7.01986e10	+	4.05292e10i	0.280964	+	0.162215i
$708$		0			0
$709$	1.71004e11	+	2.96187e11i	0.676737	+	1.17214i	0.975958	+	0.217959i	$0.0699400\pi$
$709$	1.71004e11	+	2.96187e11i	0.676737	+	1.17214i	−0.299221	+	0.954184i	$0.596727\pi$
$710$			1.38120e10i			0.0543530i
$711$		0			0
$712$	7.49193e10			0.291524
$713$	3.50436e10	−	2.02324e10i	0.135597	−	0.0782871i
$714$		0			0
$715$	−1.19383e10	+	2.06778e10i	−0.0456793	+	0.0791189i
$716$	1.01934e11	+	5.88516e10i	0.387853	+	0.223927i
$717$		0			0
$718$	−3.15397e10	−	5.46283e10i	−0.118675	−	0.205551i
$719$		−	8.86727e10i		−	0.331799i	−0.986143	−	0.165899i	$-0.946947\pi$
$719$		−	8.86727e10i		−	0.331799i	0.986143	−	0.165899i	$-0.0530527\pi$
$720$		0			0
$721$	1.41775e11			0.524635
$722$	−2.93327e10	+	1.69353e10i	−0.107945	+	0.0623223i
$723$		0			0
$724$	1.06117e11	−	1.83801e11i	0.386218	−	0.668948i
$725$	−3.65730e11	−	2.11154e11i	−1.32376	−	0.764271i
$726$		0			0
$727$	−6.21757e10	−	1.07691e11i	−0.222578	−	0.385517i	0.733012	−	0.680216i	$-0.238114\pi$
$727$	−6.21757e10	−	1.07691e11i	−0.222578	−	0.385517i	−0.955590	+	0.294699i	$0.904781\pi$
$728$			1.39613e10i			0.0497051i
$729$		0			0
$730$	−4.47407e10			−0.157548
$731$	−1.04159e11	+	6.01364e10i	−0.364778	+	0.210605i
$732$		0			0
$733$	−1.20019e11	+	2.07878e11i	−0.415750	+	0.720101i	−0.995507	−	0.0946891i	$-0.969814\pi$
$733$	−1.20019e11	+	2.07878e11i	−0.415750	+	0.720101i	0.579757	+	0.814790i	$0.303148\pi$
$734$	4.59602e10	+	2.65351e10i	0.158343	+	0.0914191i
$735$		0			0
$736$	−8.28449e9	−	1.43492e10i	−0.0282328	−	0.0489007i
$737$			8.43456e11i			2.85886i
$738$		0			0
$739$	9.80470e10			0.328743			0.164372	−	0.986398i	$-0.447440\pi$
$739$	9.80470e10			0.328743			0.164372	+	0.986398i	$0.447440\pi$
$740$	−1.89516e10	+	1.09417e10i	−0.0632003	+	0.0364887i
$741$		0			0
$742$	−4.86862e10	+	8.43270e10i	−0.160617	+	0.278196i
$743$	−3.60334e11	−	2.08039e11i	−1.18236	−	0.682636i	−0.225801	−	0.974173i	$-0.572500\pi$
$743$	−3.60334e11	−	2.08039e11i	−1.18236	−	0.682636i	−0.956560	+	0.291537i	$0.905833\pi$
$744$		0			0
$745$	−2.46679e10	−	4.27261e10i	−0.0800769	−	0.138697i
$746$			2.26028e11i			0.729804i
$747$		0			0
$748$	−3.08876e11			−0.986684
$749$	1.11758e11	−	6.45237e10i	0.355101	−	0.205018i
$750$		0			0
$751$	−1.91821e11	+	3.32243e11i	−0.603025	+	1.04447i	0.389335	+	0.921096i	$0.372705\pi$
$751$	−1.91821e11	+	3.32243e11i	−0.603025	+	1.04447i	−0.992360	+	0.123374i	$0.960629\pi$
$752$	−5.09020e10	−	2.93883e10i	−0.159171	−	0.0918973i
$753$		0			0
$754$	8.08318e10	+	1.40005e11i	0.250090	+	0.433169i
$755$			1.18149e10i			0.0363616i
$756$		0			0
$757$	2.00507e11			0.610584			0.305292	−	0.952259i	$-0.401246\pi$
$757$	2.00507e11			0.610584			0.305292	+	0.952259i	$0.401246\pi$
$758$	−3.33451e11	+	1.92518e11i	−1.01008	+	0.583170i
$759$		0			0
$760$	6.88876e9	−	1.19317e10i	0.0206484	−	0.0357641i
$761$	1.41971e11	+	8.19667e10i	0.423311	+	0.244399i	0.696493	−	0.717564i	$-0.254743\pi$
$761$	1.41971e11	+	8.19667e10i	0.423311	+	0.244399i	−0.273182	+	0.961962i	$0.588076\pi$
$762$		0			0
$763$	−3.72198e10	−	6.44665e10i	−0.109818	−	0.190211i
$764$			1.23509e11i			0.362516i
$765$		0			0
$766$	1.82387e11			0.529761
$767$	6.95036e10	−	4.01279e10i	0.200829	−	0.115948i
$768$		0			0
$769$	−3.02003e11	+	5.23085e11i	−0.863588	+	1.49578i	0.00485515	+	0.999988i	$0.498455\pi$
$769$	−3.02003e11	+	5.23085e11i	−0.863588	+	1.49578i	−0.868443	+	0.495789i	$0.834879\pi$
$770$	1.33491e10	+	7.70711e9i	0.0379742	+	0.0219244i
$771$		0			0
$772$	5.08150e10	+	8.80141e10i	0.143061	+	0.247790i
$773$		−	5.78731e11i		−	1.62091i	−0.585801	−	0.810455i	$-0.699220\pi$
$773$		−	5.78731e11i		−	1.62091i	0.585801	−	0.810455i	$-0.300780\pi$
$774$		0			0
$775$	−1.73906e11			−0.482067
$776$	−1.14061e10	+	6.58532e9i	−0.0314551	+	0.0181606i
$777$		0			0
$778$	−1.50109e11	+	2.59997e11i	−0.409722	+	0.709660i
$779$	1.71709e11	+	9.91364e10i	0.466277	+	0.269205i
$780$		0			0
$781$	1.73305e11	+	3.00173e11i	0.465808	+	0.806803i
$782$		−	1.06859e11i		−	0.285749i
$783$		0			0
$784$	−8.54374e10			−0.226143
$785$	−3.89053e10	+	2.24620e10i	−0.102454	+	0.0591520i
$786$		0			0
$787$	1.88724e11	−	3.26880e11i	0.491958	−	0.852096i	−0.507999	−	0.861358i	$-0.669615\pi$
$787$	1.88724e11	−	3.26880e11i	0.491958	−	0.852096i	0.999957	+	0.00926121i	$0.00294798\pi$
$788$	1.18713e11	+	6.85390e10i	0.307888	+	0.177759i
$789$		0			0
$790$	2.87366e10	+	4.97733e10i	0.0737780	+	0.127787i
$791$			1.07959e11i			0.275774i
$792$		0			0
$793$	−2.86946e11			−0.725616
$794$	2.45874e11	−	1.41955e11i	0.618629	−	0.357166i
$795$		0			0
$796$	−6.48861e10	+	1.12386e11i	−0.161622	+	0.279937i
$797$	−2.07081e11	−	1.19558e11i	−0.513224	−	0.296310i	0.220934	−	0.975289i	$-0.429090\pi$
$797$	−2.07081e11	−	1.19558e11i	−0.513224	−	0.296310i	−0.734158	+	0.678979i	$0.762423\pi$
$798$		0			0
$799$	−1.89535e11	−	3.28284e11i	−0.465053	−	0.805495i
$800$			7.12084e10i			0.173849i
$801$		0			0
$802$	8.76817e10			0.211939
$803$	−9.72340e11	+	5.61381e11i	−2.33860	+	1.35019i
$804$		0			0
$805$	−2.66635e9	+	4.61826e9i	−0.00634942	+	0.0109975i
$806$	5.76538e10	+	3.32864e10i	0.136612	+	0.0788727i
$807$		0			0
$808$	−7.91327e10	−	1.37062e11i	−0.185657	−	0.321567i
$809$			2.09694e11i			0.489544i	0.969581	+	0.244772i	$0.0787131\pi$
$809$			2.09694e11i			0.489544i	−0.969581	+	0.244772i	$0.921287\pi$
$810$		0			0
$811$	7.14392e11			1.65140			0.825702	−	0.564107i	$-0.190779\pi$
$811$	7.14392e11			1.65140			0.825702	+	0.564107i	$0.190779\pi$
$812$	9.03838e10	−	5.21831e10i	0.207906	−	0.120034i
$813$		0			0
$814$	−2.74580e11	+	4.75587e11i	−0.625420	+	1.08326i
$815$	−1.88273e8	−	1.08700e8i	−0.000426735	−	0.000246376i
$816$		0			0
$817$	−6.73144e10	−	1.16592e11i	−0.151085	−	0.261686i
$818$			3.11098e11i			0.694839i
$819$		0			0
$820$	1.72591e10			0.0381735
$821$	5.95004e11	−	3.43526e11i	1.30963	−	0.756113i	0.327592	−	0.944819i	$-0.393763\pi$
$821$	5.95004e11	−	3.43526e11i	1.30963	−	0.756113i	0.982033	+	0.188707i	$0.0604296\pi$
$822$		0			0
$823$	−4.54624e10	+	7.87432e10i	−0.0990953	+	0.171638i	−0.911310	−	0.411720i	$-0.864928\pi$
$823$	−4.54624e10	+	7.87432e10i	−0.0990953	+	0.171638i	0.812215	+	0.583358i	$0.198262\pi$
$824$	−2.39727e11	−	1.38406e11i	−0.520006	−	0.300226i
$825$		0			0
$826$	−2.59056e10	−	4.48698e10i	−0.0556511	−	0.0963905i
$827$		−	3.03065e11i		−	0.647908i	−0.946073	−	0.323954i	$-0.894988\pi$
$827$		−	3.03065e11i		−	0.647908i	0.946073	−	0.323954i	$-0.105012\pi$
$828$		0			0
$829$	7.06427e11			1.49572			0.747858	−	0.663859i	$-0.231082\pi$
$829$	7.06427e11			1.49572			0.747858	+	0.663859i	$0.231082\pi$
$830$	−4.05723e10	+	2.34244e10i	−0.0854904	+	0.0493579i
$831$		0			0
$832$	1.36296e10	−	2.36072e10i	0.0284440	−	0.0492665i
$833$	−4.77193e11	−	2.75507e11i	−0.991092	−	0.572207i
$834$		0			0
$835$	−3.03753e10	−	5.26115e10i	−0.0624848	−	0.108227i
$836$		−	3.45745e11i		−	0.707832i
$837$		0			0
$838$	3.92763e11			0.796442
$839$	−7.75197e10	+	4.47560e10i	−0.156446	+	0.0903241i	−0.576179	−	0.817323i	$-0.695457\pi$
$839$	−7.75197e10	+	4.47560e10i	−0.156446	+	0.0903241i	0.419733	+	0.907648i	$0.362124\pi$
$840$		0			0
$841$	3.54126e11	−	6.13364e11i	0.707903	−	1.22612i
$842$	5.48298e11	+	3.16560e11i	1.09086	+	0.629807i
$843$		0			0
$844$	4.48702e10	+	7.77175e10i	0.0884278	+	0.153161i
$845$			5.20241e10i			0.102042i
$846$		0			0
$847$	2.27828e11			0.442663
$848$	1.64647e11	−	9.50592e10i	0.318399	−	0.183828i
$849$		0			0
$850$	−2.29624e11	+	3.97720e11i	−0.439887	+	0.761906i
$851$	−1.64534e11	−	9.49940e10i	−0.313717	−	0.181125i
$852$		0			0
$853$	−4.25979e11	−	7.37818e11i	−0.804623	−	1.39365i	−0.916545	−	0.399931i	$-0.869034\pi$
$853$	−4.25979e11	−	7.37818e11i	−0.804623	−	1.39365i	0.111922	−	0.993717i	$-0.464299\pi$
$854$			1.85245e11i			0.348270i
$855$		0			0
$856$	−2.51963e11			−0.469291
$857$	9.19638e10	−	5.30953e10i	0.170488	−	0.0984313i	−0.412328	−	0.911035i	$-0.635284\pi$
$857$	9.19638e10	−	5.30953e10i	0.170488	−	0.0984313i	0.582816	+	0.812604i	$0.301951\pi$
$858$		0			0
$859$	1.80076e11	−	3.11901e11i	0.330737	−	0.572854i	−0.651919	−	0.758288i	$-0.726036\pi$
$859$	1.80076e11	−	3.11901e11i	0.330737	−	0.572854i	0.982657	+	0.185435i	$0.0593693\pi$
$860$	−1.01490e10	−	5.85953e9i	−0.0185536	−	0.0107120i
$861$		0			0
$862$	−5.96127e9	−	1.03252e10i	−0.0107972	−	0.0187013i
$863$		−	1.03087e12i		−	1.85849i	−0.369462	−	0.929246i	$-0.620458\pi$
$863$		−	1.03087e12i		−	1.85849i	0.369462	−	0.929246i	$-0.379542\pi$
$864$		0			0
$865$	7.54886e10			0.134839
$866$	−1.06052e11	+	6.12292e10i	−0.188559	+	0.108865i
$867$		0			0
$868$	2.14889e10	−	3.72199e10i	0.0378561	−	0.0655686i
$869$	1.24905e12	+	7.21141e11i	2.19029	+	1.26456i
$870$		0			0
$871$	−2.40037e11	−	4.15756e11i	−0.417066	−	0.722380i
$872$			1.45342e11i			0.251377i
$873$		0			0
$874$	1.19614e11			0.204992
$875$	4.00300e10	−	2.31113e10i	0.0682895	−	0.0394269i
$876$		0			0
$877$	−1.55982e11	+	2.70169e11i	−0.263679	+	0.456706i	−0.967217	−	0.253952i	$-0.918269\pi$
$877$	−1.55982e11	+	2.70169e11i	−0.263679	+	0.456706i	0.703537	+	0.710658i	$0.251603\pi$
$878$	−1.88820e11	−	1.09015e11i	−0.317738	−	0.183446i
$879$		0			0
$880$	−1.50480e10	−	2.60639e10i	−0.0250928	−	0.0434620i
$881$		−	7.28854e10i		−	0.120987i	−0.998169	−	0.0604933i	$-0.980733\pi$
$881$		−	7.28854e10i		−	0.120987i	0.998169	−	0.0604933i	$-0.0192674\pi$
$882$		0			0
$883$	−1.07132e12			−1.76228			−0.881142	−	0.472852i	$-0.843224\pi$
$883$	−1.07132e12			−1.76228			−0.881142	+	0.472852i	$0.843224\pi$
$884$	1.52251e11	−	8.79022e10i	0.249317	−	0.143943i
$885$		0			0
$886$	2.26663e11	−	3.92592e11i	0.367829	−	0.637098i
$887$	3.56195e11	+	2.05649e11i	0.575432	+	0.332226i	0.759316	−	0.650722i	$-0.225534\pi$
$887$	3.56195e11	+	2.05649e11i	0.575432	+	0.332226i	−0.183884	+	0.982948i	$0.558867\pi$
$888$		0			0
$889$	−5.84938e10	−	1.01314e11i	−0.0936489	−	0.162205i
$890$			4.70797e10i			0.0750367i
$891$		0			0
$892$	−3.51718e11			−0.555566
$893$	3.67469e11	−	2.12158e11i	0.577849	−	0.333621i
$894$		0			0
$895$	−3.69827e10	+	6.40559e10i	−0.0576377	+	0.0998314i
$896$	−1.52403e10	−	8.79897e9i	−0.0236461	−	0.0136521i
$897$		0			0
$898$	−1.63810e11	−	2.83728e11i	−0.251904	−	0.436311i
$899$		−	4.97658e11i		−	0.761889i
$900$		0			0
$901$	1.22614e12			1.86055
$902$	3.75088e11	−	2.16557e11i	0.566639	−	0.327149i
$903$		0			0
$904$	1.05394e11	−	1.82548e11i	0.157813	−	0.273341i
$905$	1.15501e11	+	6.66847e10i	0.172184	+	0.0994104i
$906$		0			0
$907$	−7.64334e10	−	1.32387e11i	−0.112942	−	0.195621i	0.804013	−	0.594611i	$-0.202694\pi$
$907$	−7.64334e10	−	1.32387e11i	−0.112942	−	0.195621i	−0.916955	+	0.398991i	$0.869361\pi$
$908$		−	3.28818e11i		−	0.483740i
$909$		0			0
$910$	−8.77337e9			−0.0127938
$911$	−7.19623e11	+	4.15475e11i	−1.04480	+	0.603213i	−0.921188	−	0.389118i	$-0.872780\pi$
$911$	−7.19623e11	+	4.15475e11i	−1.04480	+	0.603213i	−0.123608	+	0.992331i	$0.539447\pi$
$912$		0			0
$913$	−5.87832e11	+	1.01816e12i	−0.846000	+	1.46531i
$914$	−5.41688e10	−	3.12744e10i	−0.0776184	−	0.0448130i
$915$		0			0
$916$	1.61942e11	+	2.80492e11i	0.230026	+	0.398417i
$917$		−	2.32279e11i		−	0.328498i
$918$		0			0
$919$	−4.99778e11			−0.700673			−0.350336	−	0.936624i	$-0.613933\pi$
$919$	−4.99778e11			−0.700673			−0.350336	+	0.936624i	$0.613933\pi$
$920$	9.01709e9	−	5.20602e9i	0.0125868	−	0.00726699i
$921$		0			0
$922$	3.24060e11	−	5.61288e11i	0.448437	−	0.776716i
$923$	−1.70851e11	−	9.86407e10i	−0.235402	−	0.135909i
$924$		0			0
$925$	4.08255e11	+	7.07119e11i	0.557654	+	0.965885i
$926$			9.74619e11i			1.32553i
$927$		0			0
$928$	−2.03774e11			−0.274762
$929$	3.65549e11	−	2.11050e11i	0.490775	−	0.283349i	−0.234121	−	0.972207i	$-0.575221\pi$
$929$	3.65549e11	−	2.11050e11i	0.490775	−	0.283349i	0.724896	+	0.688858i	$0.241888\pi$
$930$		0			0
$931$	3.08393e11	−	5.34152e11i	0.410493	−	0.710994i
$932$	−1.32787e11	−	7.66644e10i	−0.175991	−	0.101609i
$933$		0			0
$934$	−9.80704e10	−	1.69863e11i	−0.128870	−	0.223209i
$935$		−	1.94100e11i		−	0.253968i
$936$		0			0
$937$	−1.46649e12			−1.90248			−0.951240	−	0.308452i	$-0.900189\pi$
$937$	−1.46649e12			−1.90248			−0.951240	+	0.308452i	$0.900189\pi$
$938$	−2.68402e11	+	1.54962e11i	−0.346716	+	0.200177i
$939$		0			0
$940$	1.84678e10	−	3.19871e10i	0.0236539	−	0.0409697i
$941$	−1.80375e11	−	1.04140e11i	−0.230048	−	0.132818i	0.380546	−	0.924762i	$-0.375736\pi$
$941$	−1.80375e11	−	1.04140e11i	−0.230048	−	0.132818i	−0.610594	+	0.791944i	$0.709069\pi$
$942$		0			0
$943$	7.49201e10	+	1.29765e11i	0.0947440	+	0.164101i
$944$			1.01161e11i			0.127387i
$945$		0			0
$946$	−2.94088e11			−0.367208
$947$	−3.88417e11	+	2.24252e11i	−0.482945	+	0.278828i	−0.721643	−	0.692265i	$-0.756613\pi$
$947$	−3.88417e11	+	2.24252e11i	−0.482945	+	0.278828i	0.238698	+	0.971094i	$0.423279\pi$
$948$		0			0
$949$	3.19523e11	−	5.53430e11i	0.393947	−	0.682336i
$950$	−4.45193e11	−	2.57032e11i	−0.546580	−	0.315568i
$951$		0			0
$952$	−5.67475e10	−	9.82896e10i	−0.0690874	−	0.119663i
$953$			1.57158e12i			1.90531i	0.304053	+	0.952655i	$0.401660\pi$
$953$			1.57158e12i			1.90531i	−0.304053	+	0.952655i	$0.598340\pi$
$954$		0			0
$955$	−7.76140e10			−0.0933097
$956$	−1.80973e11	+	1.04485e11i	−0.216662	+	0.125090i
$957$		0			0
$958$	−9.21055e10	+	1.59531e11i	−0.109351	+	0.189402i
$959$	−6.26733e10	−	3.61844e10i	−0.0740982	−	0.0427806i
$960$		0			0
$961$	3.23978e11	+	5.61147e11i	0.379859	+	0.657935i
$962$		−	3.12568e11i		−	0.364959i
$963$		0			0
$964$	4.57540e11			0.529810
$965$	−5.53086e10	+	3.19324e10i	−0.0637798	+	0.0368233i
$966$		0			0
$967$	−4.92009e10	+	8.52185e10i	−0.0562688	+	0.0974604i	−0.892788	−	0.450478i	$-0.851254\pi$
$967$	−4.92009e10	+	8.52185e10i	−0.0562688	+	0.0974604i	0.836519	+	0.547938i	$0.184587\pi$
$968$	−3.85235e11	−	2.22415e11i	−0.438757	−	0.253316i
$969$		0			0
$970$	−4.13825e9	−	7.16766e9i	−0.00467444	−	0.00809638i
$971$		−	2.12176e11i		−	0.238682i	−0.992853	−	0.119341i	$-0.961922\pi$
$971$		−	2.12176e11i		−	0.238682i	0.992853	−	0.119341i	$-0.0380781\pi$
$972$		0			0
$973$	6.69127e10			0.0746547
$974$	8.41744e11	−	4.85981e11i	0.935286	−	0.539987i
$975$		0			0
$976$	1.80844e11	−	3.13232e11i	0.199299	−	0.345197i
$977$	9.53074e11	+	5.50257e11i	1.04604	+	0.603931i	0.921538	−	0.388288i	$-0.126933\pi$
$977$	9.53074e11	+	5.50257e11i	1.04604	+	0.603931i	0.124502	+	0.992219i	$0.460267\pi$
$978$		0			0
$979$	5.90729e11	+	1.02317e12i	0.643069	+	1.11383i
$980$		−	5.36894e10i		−	0.0582082i
$981$		0			0
$982$	1.23160e12			1.32441
$983$	−6.07234e11	+	3.50586e11i	−0.650342	+	0.375475i	−0.788587	−	0.614923i	$-0.789187\pi$
$983$	−6.07234e11	+	3.50586e11i	−0.650342	+	0.375475i	0.138245	+	0.990398i	$0.455854\pi$
$984$		0			0
$985$	−4.30703e10	+	7.45999e10i	−0.0457544	+	0.0792489i
$986$	−1.13814e12	−	6.57103e11i	−1.20417	−	0.695225i
$987$		0			0
$988$	9.83944e10	+	1.70424e11i	0.103262	+	0.178856i
$989$		−	1.01743e11i		−	0.106345i
$990$		0			0
$991$	1.38686e12			1.43793			0.718963	−	0.695048i	$-0.244617\pi$
$991$	1.38686e12			1.43793			0.718963	+	0.695048i	$0.244617\pi$
$992$	−7.26713e10	+	4.19568e10i	−0.0750441	+	0.0433267i
$993$		0			0
$994$	−6.36800e10	+	1.10297e11i	−0.0652316	+	0.112984i
$995$	−7.06240e10	−	4.07748e10i	−0.0720543	−	0.0416006i
$996$		0			0
$997$	3.17360e11	+	5.49684e11i	0.321197	+	0.556330i	0.980735	−	0.195341i	$-0.0625814\pi$
$997$	3.17360e11	+	5.49684e11i	0.321197	+	0.556330i	−0.659538	+	0.751671i	$0.729248\pi$
$998$		−	2.29013e11i		−	0.230854i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.9.d.a.17.6		16
3.2	odd	2		18.9.d.a.5.2	✓	16
4.3	odd	2		432.9.q.c.17.4		16
9.2	odd	6	inner	54.9.d.a.35.6		16
9.4	even	3		162.9.b.c.161.13		16
9.5	odd	6		162.9.b.c.161.4		16
9.7	even	3		18.9.d.a.11.2	yes	16
12.11	even	2		144.9.q.b.113.6		16
36.7	odd	6		144.9.q.b.65.6		16
36.11	even	6		432.9.q.c.305.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.9.d.a.5.2	✓	16	3.2	odd	2
18.9.d.a.11.2	yes	16	9.7	even	3
54.9.d.a.17.6		16	1.1	even	1	trivial
54.9.d.a.35.6		16	9.2	odd	6	inner
144.9.q.b.65.6		16	36.7	odd	6
144.9.q.b.113.6		16	12.11	even	2
162.9.b.c.161.4		16	9.5	odd	6
162.9.b.c.161.13		16	9.4	even	3
432.9.q.c.17.4		16	4.3	odd	2
432.9.q.c.305.4		16	36.11	even	6

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)

\(f(q)\)	\(=\)	\(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(69.6596 + 40.2180i) q^{5} +(370.849 + 642.329i) q^{7} -1448.15i q^{8} +O(q^{10})\)	\(q+(9.79796 - 5.65685i) q^{2} +(64.0000 - 110.851i) q^{4} +(69.6596 + 40.2180i) q^{5} +(370.849 + 642.329i) q^{7} -1448.15i q^{8} +910.029 q^{10} +(19777.4 - 11418.5i) q^{11} +(-6499.12 + 11256.8i) q^{13} +(7267.12 + 4195.67i) q^{14} +(-8192.00 - 14189.0i) q^{16} -105666. i q^{17} +118278. q^{19} +(8916.42 - 5147.90i) q^{20} +(129186. - 223756. i) q^{22} +(77410.8 + 44693.1i) q^{23} +(-192078. - 332688. i) q^{25} +147058. i q^{26} +94937.3 q^{28} +(952037. - 549659. i) q^{29} +(226348. - 392047. i) q^{31} +(-160530. - 92681.9i) q^{32} +(-597737. - 1.03531e6i) q^{34} +59659.1i q^{35} -2.12547e6 q^{37} +(1.15889e6 - 669084. i) q^{38} +(58241.8 - 100878. i) q^{40} +(1.45174e6 + 838161. i) q^{41} +(-569118. - 985742. i) q^{43} -2.92314e6i q^{44} +1.01129e6 q^{46} +(3.10681e6 - 1.79372e6i) q^{47} +(2.60734e6 - 4.51605e6i) q^{49} +(-3.76394e6 - 2.17311e6i) q^{50} +(831887. + 1.44087e6i) q^{52} +1.16039e7i q^{53} +1.83692e6 q^{55} +(930192. - 537046. i) q^{56} +(6.21868e6 - 1.07711e7i) q^{58} +(-5.34715e6 - 3.08718e6i) q^{59} +(1.10379e7 + 1.91182e7i) q^{61} -5.12168e6i q^{62} -2.09715e6 q^{64} +(-905451. + 522763. i) q^{65} +(-1.84669e7 + 3.19855e7i) q^{67} +(-1.17132e7 - 6.76262e6i) q^{68} +(337483. + 584538. i) q^{70} +1.51775e7i q^{71} -4.91641e7 q^{73} +(-2.08253e7 + 1.20235e7i) q^{74} +(7.56982e6 - 1.31113e7i) q^{76} +(1.46689e7 + 8.46908e6i) q^{77} +(3.15777e7 + 5.46942e7i) q^{79} -1.31786e6i q^{80} +1.89654e7 q^{82} +(-4.45835e7 + 2.57403e7i) q^{83} +(4.24967e6 - 7.36064e6i) q^{85} +(-1.11524e7 - 6.43884e6i) q^{86} +(-1.65358e7 - 2.86408e7i) q^{88} +5.17343e7i q^{89} -9.64076e6 q^{91} +(9.90858e6 - 5.72072e6i) q^{92} +(2.02936e7 - 3.51495e7i) q^{94} +(8.23923e6 + 4.75692e6i) q^{95} +(-4.54739e6 - 7.87630e6i) q^{97} -5.89974e7i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7}+O(q^{10}) \) 16 * q + 1024 * q^4 + 882 * q^5 - 1846 * q^7	\( 16 q + 1024 q^{4} + 882 q^{5} - 1846 q^{7} - 45756 q^{11} - 3370 q^{13} + 94464 q^{14} - 131072 q^{16} + 362180 q^{19} + 112896 q^{20} - 61824 q^{22} - 1311138 q^{23} + 963394 q^{25} - 472576 q^{28} + 2851290 q^{29} + 542438 q^{31} + 220416 q^{34} + 3343328 q^{37} + 1314432 q^{38} - 9218592 q^{41} + 339512 q^{43} + 7417344 q^{46} + 34980606 q^{47} - 2364654 q^{49} - 27744768 q^{50} + 431360 q^{52} - 4584276 q^{55} + 12091392 q^{56} - 7852800 q^{58} - 93924216 q^{59} - 841954 q^{61} - 33554432 q^{64} + 126568134 q^{65} + 29946644 q^{67} + 5476608 q^{68} - 34359552 q^{70} - 7547764 q^{73} - 35124480 q^{74} + 23179520 q^{76} - 9309294 q^{77} + 33813002 q^{79} - 137346048 q^{82} - 114200226 q^{83} - 125696772 q^{85} + 171379584 q^{86} + 7913472 q^{88} + 268578316 q^{91} - 167825664 q^{92} - 11832576 q^{94} + 143949240 q^{95} - 89415484 q^{97}+O(q^{100}) \) 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

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