LMFDB - Embedded newform 324.4.i.a.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,4,Mod(37,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("324.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	324.i (of order $9$, degree $6$, 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:	$19.1166188419$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			37.6
Character	$\chi$	$=$	324.37
Dual form			324.4.i.a.289.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.80495 - 1.74886i) q^{5} +(5.74341 + 32.5725i) q^{7} +O(q^{10})$	$q+(4.80495 - 1.74886i) q^{5} +(5.74341 + 32.5725i) q^{7} +(-28.2317 - 10.2755i) q^{11} +(7.59849 + 6.37589i) q^{13} +(-44.7319 + 77.4779i) q^{17} +(-29.6509 - 51.3568i) q^{19} +(17.0562 - 96.7304i) q^{23} +(-75.7266 + 63.5421i) q^{25} +(-108.085 + 90.6938i) q^{29} +(4.10141 - 23.2603i) q^{31} +(84.5615 + 146.465i) q^{35} +(-114.087 + 197.604i) q^{37} +(357.814 + 300.241i) q^{41} +(-10.1135 - 3.68102i) q^{43} +(66.0561 + 374.623i) q^{47} +(-705.667 + 256.842i) q^{49} +202.984 q^{53} -153.622 q^{55} +(-766.955 + 279.149i) q^{59} +(-109.702 - 622.151i) q^{61} +(47.6609 + 17.3471i) q^{65} +(-466.269 - 391.246i) q^{67} +(-140.376 + 243.138i) q^{71} +(608.806 + 1054.48i) q^{73} +(172.552 - 978.592i) q^{77} +(278.680 - 233.841i) q^{79} +(-453.825 + 380.804i) q^{83} +(-79.4366 + 450.507i) q^{85} +(359.138 + 622.046i) q^{89} +(-164.037 + 284.121i) q^{91} +(-232.286 - 194.911i) q^{95} +(776.386 + 282.581i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 12 q^{5}+O(q^{10}) $ 54 * q - 12 * q^5	$ 54 q - 12 q^{5} + 87 q^{11} - 204 q^{17} - 96 q^{23} - 216 q^{25} - 318 q^{29} - 54 q^{31} - 6 q^{35} - 867 q^{41} - 513 q^{43} + 1548 q^{47} + 594 q^{49} + 1068 q^{53} + 1218 q^{59} - 54 q^{61} - 96 q^{65} - 2997 q^{67} + 120 q^{71} - 216 q^{73} - 3480 q^{77} + 2808 q^{79} - 4464 q^{83} + 2160 q^{85} - 4029 q^{89} + 270 q^{91} + 1650 q^{95} - 3483 q^{97}+O(q^{100}) $ 54 * q - 12 * q^5 + 87 * q^11 - 204 * q^17 - 96 * q^23 - 216 * q^25 - 318 * q^29 - 54 * q^31 - 6 * q^35 - 867 * q^41 - 513 * q^43 + 1548 * q^47 + 594 * q^49 + 1068 * q^53 + 1218 * q^59 - 54 * q^61 - 96 * q^65 - 2997 * q^67 + 120 * q^71 - 216 * q^73 - 3480 * q^77 + 2808 * q^79 - 4464 * q^83 + 2160 * q^85 - 4029 * q^89 + 270 * q^91 + 1650 * q^95 - 3483 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	4.80495	−	1.74886i	0.429767	−	0.156423i	−0.118074	−	0.993005i	$-0.537672\pi$
$5$	4.80495	−	1.74886i	0.429767	−	0.156423i	0.547841	+	0.836582i	$0.315450\pi$
$6$		0			0
$7$	5.74341	+	32.5725i	0.310115	+	1.75875i	0.598392	+	0.801203i	$0.295806\pi$
$7$	5.74341	+	32.5725i	0.310115	+	1.75875i	−0.288277	+	0.957547i	$0.593082\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−28.2317	−	10.2755i	−0.773833	−	0.281652i	−0.0752344	−	0.997166i	$-0.523971\pi$
$11$	−28.2317	−	10.2755i	−0.773833	−	0.281652i	−0.698599	+	0.715514i	$0.746193\pi$
$12$		0			0
$13$	7.59849	+	6.37589i	0.162111	+	0.136027i	0.720235	−	0.693731i	$-0.244034\pi$
$13$	7.59849	+	6.37589i	0.162111	+	0.136027i	−0.558124	+	0.829758i	$0.688479\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−44.7319	+	77.4779i	−0.638181	+	1.10536i	0.347650	+	0.937624i	$0.386980\pi$
$17$	−44.7319	+	77.4779i	−0.638181	+	1.10536i	−0.985832	+	0.167738i	$0.946354\pi$
$18$		0			0
$19$	−29.6509	−	51.3568i	−0.358020	−	0.620108i	0.629610	−	0.776911i	$-0.283215\pi$
$19$	−29.6509	−	51.3568i	−0.358020	−	0.620108i	−0.987630	+	0.156803i	$0.949881\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	17.0562	−	96.7304i	0.154629	−	0.876943i	−0.804496	−	0.593958i	$-0.797564\pi$
$23$	17.0562	−	96.7304i	0.154629	−	0.876943i	0.959124	−	0.282984i	$-0.0913245\pi$
$24$		0			0
$25$	−75.7266	+	63.5421i	−0.605812	+	0.508337i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−108.085	+	90.6938i	−0.692097	+	0.580738i	−0.919513	−	0.393059i	$-0.871417\pi$
$29$	−108.085	+	90.6938i	−0.692097	+	0.580738i	0.227416	+	0.973798i	$0.426972\pi$
$30$		0			0
$31$	4.10141	−	23.2603i	0.0237624	−	0.134764i	−0.970619	−	0.240623i	$-0.922648\pi$
$31$	4.10141	−	23.2603i	0.0237624	−	0.134764i	0.994381	+	0.105859i	$0.0337594\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	84.5615	+	146.465i	0.408386	+	0.707345i
$36$		0			0
$37$	−114.087	+	197.604i	−0.506912	+	0.877997i	0.493056	+	0.869998i	$0.335880\pi$
$37$	−114.087	+	197.604i	−0.506912	+	0.877997i	−0.999968	+	0.00799976i	$0.997454\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	357.814	+	300.241i	1.36295	+	1.14365i	0.975058	+	0.221951i	$0.0712424\pi$
$41$	357.814	+	300.241i	1.36295	+	1.14365i	0.387896	+	0.921703i	$0.373202\pi$
$42$		0			0
$43$	−10.1135	−	3.68102i	−0.0358673	−	0.0130546i	0.324024	−	0.946049i	$-0.394964\pi$
$43$	−10.1135	−	3.68102i	−0.0358673	−	0.0130546i	−0.359892	+	0.932994i	$0.617186\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	66.0561	+	374.623i	0.205006	+	1.16265i	0.897430	+	0.441156i	$0.145431\pi$
$47$	66.0561	+	374.623i	0.205006	+	1.16265i	−0.692424	+	0.721490i	$0.743457\pi$
$48$		0			0
$49$	−705.667	+	256.842i	−2.05734	+	0.748810i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	202.984			0.526076			0.263038	−	0.964786i	$-0.415276\pi$
$53$	202.984			0.526076			0.263038	+	0.964786i	$0.415276\pi$
$54$		0			0
$55$	−153.622			−0.376625
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−766.955	+	279.149i	−1.69236	+	0.615967i	−0.994919	−	0.100678i	$-0.967899\pi$
$59$	−766.955	+	279.149i	−1.69236	+	0.615967i	−0.697437	+	0.716646i	$0.745676\pi$
$60$		0			0
$61$	−109.702	−	622.151i	−0.230261	−	1.30587i	−0.852368	−	0.522942i	$-0.824835\pi$
$61$	−109.702	−	622.151i	−0.230261	−	1.30587i	0.622108	−	0.782932i	$-0.286277\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	47.6609	+	17.3471i	0.0909477	+	0.0331023i
$66$		0			0
$67$	−466.269	−	391.246i	−0.850206	−	0.713408i	0.109629	−	0.993973i	$-0.465034\pi$
$67$	−466.269	−	391.246i	−0.850206	−	0.713408i	−0.959835	+	0.280565i	$0.909478\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−140.376	+	243.138i	−0.234642	+	0.406411i	−0.959168	−	0.282835i	$-0.908725\pi$
$71$	−140.376	+	243.138i	−0.234642	+	0.406411i	0.724527	+	0.689247i	$0.242058\pi$
$72$		0			0
$73$	608.806	+	1054.48i	0.976101	+	1.69066i	0.676252	+	0.736671i	$0.263603\pi$
$73$	608.806	+	1054.48i	0.976101	+	1.69066i	0.299849	+	0.953987i	$0.403064\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	172.552	−	978.592i	0.255379	−	1.44832i
$78$		0			0
$79$	278.680	−	233.841i	0.396886	−	0.333027i	−0.422402	−	0.906408i	$-0.638813\pi$
$79$	278.680	−	233.841i	0.396886	−	0.333027i	0.819289	+	0.573381i	$0.194369\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−453.825	+	380.804i	−0.600166	+	0.503599i	−0.891499	−	0.453023i	$-0.850346\pi$
$83$	−453.825	+	380.804i	−0.600166	+	0.503599i	0.291333	+	0.956622i	$0.405901\pi$
$84$		0			0
$85$	−79.4366	+	450.507i	−0.101366	+	0.574875i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	359.138	+	622.046i	0.427737	+	0.740862i	0.996672	−	0.0815204i	$-0.0259776\pi$
$89$	359.138	+	622.046i	0.427737	+	0.740862i	−0.568935	+	0.822383i	$0.692644\pi$
$90$		0			0
$91$	−164.037	+	284.121i	−0.188965	+	0.327297i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−232.286	−	194.911i	−0.250864	−	0.210500i
$96$		0			0
$97$	776.386	+	282.581i	0.812681	+	0.295792i	0.714731	−	0.699400i	$-0.246549\pi$
$97$	776.386	+	282.581i	0.812681	+	0.295792i	0.0979501	+	0.995191i	$0.468771\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−171.883	−	974.796i	−0.169336	−	0.960355i	−0.944480	−	0.328569i	$-0.893434\pi$
$101$	−171.883	−	974.796i	−0.169336	−	0.960355i	0.775143	−	0.631785i	$-0.217678\pi$
$102$		0			0
$103$	645.975	−	235.116i	0.617959	−	0.224919i	−0.0140232	−	0.999902i	$-0.504464\pi$
$103$	645.975	−	235.116i	0.617959	−	0.224919i	0.631982	+	0.774983i	$0.282242\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1298.75			1.17341			0.586706	−	0.809800i	$-0.300424\pi$
$107$	1298.75			1.17341			0.586706	+	0.809800i	$0.300424\pi$
$108$		0			0
$109$	576.373			0.506482			0.253241	−	0.967403i	$-0.418503\pi$
$109$	576.373			0.506482			0.253241	+	0.967403i	$0.418503\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1844.78	−	671.443i	1.53577	−	0.558974i	0.570743	−	0.821129i	$-0.306655\pi$
$113$	1844.78	−	671.443i	1.53577	−	0.558974i	0.965026	+	0.262155i	$0.0844331\pi$
$114$		0			0
$115$	−87.2136	−	494.613i	−0.0707193	−	0.401069i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2780.57	−	1012.04i	−2.14197	−	0.779612i
$120$		0			0
$121$	−328.164	−	275.362i	−0.246555	−	0.206884i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−572.318	+	991.284i	−0.409518	+	0.709305i
$126$		0			0
$127$	−245.983	−	426.055i	−0.171870	−	0.297687i	0.767204	−	0.641403i	$-0.221647\pi$
$127$	−245.983	−	426.055i	−0.171870	−	0.297687i	−0.939073	+	0.343716i	$0.888314\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	377.965	−	2143.55i	0.252084	−	1.42964i	−0.551365	−	0.834264i	$-0.685893\pi$
$131$	377.965	−	2143.55i	0.252084	−	1.42964i	0.803449	−	0.595374i	$-0.202996\pi$
$132$		0			0
$133$	1502.52	−	1260.77i	0.979588	−	0.821972i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1065.12	+	893.740i	−0.664228	+	0.557353i	−0.911351	−	0.411631i	$-0.864959\pi$
$137$	−1065.12	+	893.740i	−0.664228	+	0.557353i	0.247123	+	0.968984i	$0.420515\pi$
$138$		0			0
$139$	191.282	−	1084.82i	0.116722	−	0.661963i	−0.869161	−	0.494529i	$-0.835341\pi$
$139$	191.282	−	1084.82i	0.116722	−	0.661963i	0.985883	−	0.167435i	$-0.0535483\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−149.003	−	258.080i	−0.0871344	−	0.150921i
$144$		0			0
$145$	−360.730	+	624.803i	−0.206600	+	0.357842i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1499.38	−	1258.13i	−0.824388	−	0.691744i	0.129607	−	0.991565i	$-0.458628\pi$
$149$	−1499.38	−	1258.13i	−0.824388	−	0.691744i	−0.953995	+	0.299821i	$0.903073\pi$
$150$		0			0
$151$	617.466	+	224.739i	0.332773	+	0.121119i	0.503002	−	0.864285i	$-0.332229\pi$
$151$	617.466	+	224.739i	0.332773	+	0.121119i	−0.170230	+	0.985404i	$0.554451\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−20.9718	−	118.937i	−0.0108677	−	0.0616339i
$156$		0			0
$157$	−1247.25	+	453.962i	−0.634022	+	0.230765i	−0.638981	−	0.769222i	$-0.720644\pi$
$157$	−1247.25	+	453.962i	−0.634022	+	0.230765i	0.00495878	+	0.999988i	$0.498422\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	3248.71			1.59028
$162$		0			0
$163$	2562.11			1.23116			0.615582	−	0.788073i	$-0.288921\pi$
$163$	2562.11			1.23116			0.615582	+	0.788073i	$0.288921\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3356.67	−	1221.73i	1.55537	−	0.566109i	0.585703	−	0.810526i	$-0.300819\pi$
$167$	3356.67	−	1221.73i	1.55537	−	0.566109i	0.969670	+	0.244417i	$0.0785965\pi$
$168$		0			0
$169$	−364.420	−	2066.73i	−0.165872	−	0.940705i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2140.09	+	778.930i	0.940510	+	0.342318i	0.766367	−	0.642403i	$-0.222062\pi$
$173$	2140.09	+	778.930i	0.940510	+	0.342318i	0.174143	+	0.984720i	$0.444285\pi$
$174$		0			0
$175$	−2504.66	−	2101.66i	−1.08191	−	0.907830i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−577.965	+	1001.07i	−0.241336	+	0.418006i	−0.961095	−	0.276218i	$-0.910919\pi$
$179$	−577.965	+	1001.07i	−0.241336	+	0.418006i	0.719759	+	0.694224i	$0.244252\pi$
$180$		0			0
$181$	1786.92	+	3095.03i	0.733815	+	1.27100i	0.955241	+	0.295827i	$0.0955952\pi$
$181$	1786.92	+	3095.03i	0.733815	+	1.27100i	−0.221427	+	0.975177i	$0.571071\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−202.599	+	1149.00i	−0.0805157	+	0.456627i
$186$		0			0
$187$	2058.98	−	1727.69i	0.805174	−	0.675621i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	615.799	−	516.717i	0.233286	−	0.195750i	−0.518649	−	0.854987i	$-0.673565\pi$
$191$	615.799	−	516.717i	0.233286	−	0.195750i	0.751935	+	0.659237i	$0.229120\pi$
$192$		0			0
$193$	−155.121	+	879.737i	−0.0578543	+	0.328108i	−0.999974	−	0.00716788i	$-0.997718\pi$
$193$	−155.121	+	879.737i	−0.0578543	+	0.328108i	0.942120	+	0.335276i	$0.108829\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1162.98	−	2014.35i	−0.420605	−	0.728509i	0.575394	−	0.817876i	$-0.304849\pi$
$197$	−1162.98	−	2014.35i	−0.420605	−	0.728509i	−0.995999	+	0.0893676i	$0.971515\pi$
$198$		0			0
$199$	158.416	−	274.384i	0.0564311	−	0.0977415i	−0.836430	−	0.548074i	$-0.815361\pi$
$199$	158.416	−	274.384i	0.0564311	−	0.0977415i	0.892861	+	0.450333i	$0.148695\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−3574.90	−	2999.70i	−1.23600	−	1.03713i
$204$		0			0
$205$	2244.35	+	816.878i	0.764646	+	0.278309i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	309.377	+	1754.56i	0.102393	+	0.580697i
$210$		0			0
$211$	−3958.48	+	1440.77i	−1.29153	+	0.470079i	−0.894229	−	0.447609i	$-0.852276\pi$
$211$	−3958.48	+	1440.77i	−1.29153	+	0.470079i	−0.397302	+	0.917688i	$0.630054\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−55.0324			−0.0174567
$216$		0			0
$217$	781.202			0.244384
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−833.886	+	303.510i	−0.253816	+	0.0923813i
$222$		0			0
$223$	−92.7029	−	525.744i	−0.0278379	−	0.157876i	0.967720	−	0.252028i	$-0.0810974\pi$
$223$	−92.7029	−	525.744i	−0.0278379	−	0.157876i	−0.995558	+	0.0941513i	$0.969986\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5420.84	−	1973.03i	−1.58500	−	0.576891i	−0.608713	−	0.793391i	$-0.708314\pi$
$227$	−5420.84	−	1973.03i	−1.58500	−	0.576891i	−0.976283	+	0.216500i	$0.930536\pi$
$228$		0			0
$229$	1142.36	+	958.554i	0.329647	+	0.276607i	0.792556	−	0.609799i	$-0.208750\pi$
$229$	1142.36	+	958.554i	0.329647	+	0.276607i	−0.462909	+	0.886406i	$0.653194\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−225.811	+	391.116i	−0.0634908	+	0.109969i	−0.896024	−	0.444007i	$-0.853557\pi$
$233$	−225.811	+	391.116i	−0.0634908	+	0.109969i	0.832533	+	0.553976i	$0.186890\pi$
$234$		0			0
$235$	972.558	+	1684.52i	0.269969	+	0.467600i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−537.820	+	3050.13i	−0.145559	+	0.825508i	0.821357	+	0.570414i	$0.193217\pi$
$239$	−537.820	+	3050.13i	−0.145559	+	0.825508i	−0.966916	+	0.255093i	$0.917894\pi$
$240$		0			0
$241$	427.852	−	359.010i	0.114358	−	0.0959580i	−0.583815	−	0.811886i	$-0.698441\pi$
$241$	427.852	−	359.010i	0.114358	−	0.0959580i	0.698174	+	0.715928i	$0.253996\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2941.51	+	2468.22i	−0.767046	+	0.643628i
$246$		0			0
$247$	102.143	−	579.285i	0.0263127	−	0.149227i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	315.189	+	545.923i	0.0792612	+	0.137284i	0.902931	−	0.429785i	$-0.141411\pi$
$251$	315.189	+	545.923i	0.0792612	+	0.137284i	−0.823670	+	0.567069i	$0.808077\pi$
$252$		0			0
$253$	−1475.48	+	2555.60i	−0.366650	+	0.635056i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1711.18	+	1435.85i	0.415333	+	0.348506i	0.826384	−	0.563106i	$-0.190394\pi$
$257$	1711.18	+	1435.85i	0.415333	+	0.348506i	−0.411051	+	0.911612i	$0.634838\pi$
$258$		0			0
$259$	−7091.71	−	2581.17i	−1.70138	−	0.619251i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−115.370	−	654.298i	−0.0270496	−	0.153406i	0.968291	−	0.249824i	$-0.0803726\pi$
$263$	−115.370	−	654.298i	−0.0270496	−	0.153406i	−0.995341	+	0.0964178i	$0.969262\pi$
$264$		0			0
$265$	975.328	−	354.990i	0.226090	−	0.0822901i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6952.64			1.57587			0.787936	−	0.615757i	$-0.211150\pi$
$269$	6952.64			1.57587			0.787936	+	0.615757i	$0.211150\pi$
$270$		0			0
$271$	−8783.48			−1.96885			−0.984426	−	0.175802i	$-0.943748\pi$
$271$	−8783.48			−1.96885			−0.984426	+	0.175802i	$0.943748\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2790.81	−	1015.77i	0.611972	−	0.222740i
$276$		0			0
$277$	1226.41	+	6955.33i	0.266021	+	1.50868i	0.766111	+	0.642709i	$0.222189\pi$
$277$	1226.41	+	6955.33i	0.266021	+	1.50868i	−0.500089	+	0.865974i	$0.666699\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6216.63	+	2262.67i	1.31976	+	0.480354i	0.903382	−	0.428837i	$-0.141077\pi$
$281$	6216.63	+	2262.67i	1.31976	+	0.480354i	0.416379	+	0.909191i	$0.363299\pi$
$282$		0			0
$283$	4086.69	+	3429.14i	0.858405	+	0.720288i	0.961624	−	0.274371i	$-0.0884696\pi$
$283$	4086.69	+	3429.14i	0.858405	+	0.720288i	−0.103218	+	0.994659i	$0.532914\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−7724.54	+	13379.3i	−1.58873	+	2.75176i
$288$		0			0
$289$	−1545.39	−	2676.69i	−0.314551	−	0.544818i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	50.5304	−	286.572i	0.0100751	−	0.0571390i	−0.979356	−	0.202145i	$-0.935209\pi$
$293$	50.5304	−	286.572i	0.0100751	−	0.0571390i	0.989431	+	0.145006i	$0.0463200\pi$
$294$		0			0
$295$	−3196.99	+	2682.59i	−0.630968	+	0.529445i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	746.344	−	626.257i	0.144355	−	0.121128i
$300$		0			0
$301$	61.8139	−	350.564i	0.0118369	−	0.0671302i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1615.17	−	2797.55i	−0.303227	−	0.525204i
$306$		0			0
$307$	572.764	−	992.056i	0.106480	−	0.184429i	−0.807862	−	0.589372i	$-0.799375\pi$
$307$	572.764	−	992.056i	0.106480	−	0.184429i	0.914342	+	0.404943i	$0.132709\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7195.48	+	6037.72i	1.31196	+	1.10086i	0.987945	+	0.154808i	$0.0494759\pi$
$311$	7195.48	+	6037.72i	1.31196	+	1.10086i	0.324011	+	0.946053i	$0.394969\pi$
$312$		0			0
$313$	−2912.59	−	1060.10i	−0.525972	−	0.191438i	0.0653667	−	0.997861i	$-0.479178\pi$
$313$	−2912.59	−	1060.10i	−0.525972	−	0.191438i	−0.591339	+	0.806423i	$0.701401\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−116.213	−	659.077i	−0.0205905	−	0.116774i	0.972780	−	0.231730i	$-0.0744385\pi$
$317$	−116.213	−	659.077i	−0.0205905	−	0.116774i	−0.993371	+	0.114956i	$0.963327\pi$
$318$		0			0
$319$	3983.33	−	1449.81i	0.699134	−	0.254464i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	5305.36			0.913926
$324$		0			0
$325$	−980.545			−0.167356
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−11823.0	+	4303.23i	−1.98123	+	0.721109i
$330$		0			0
$331$	50.4286	+	285.995i	0.00837404	+	0.0474915i	0.988708	−	0.149852i	$-0.0478797\pi$
$331$	50.4286	+	285.995i	0.00837404	+	0.0474915i	−0.980334	+	0.197343i	$0.936769\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2924.63	−	1064.48i	−0.476984	−	0.173608i
$336$		0			0
$337$	−6338.56	−	5318.68i	−1.02458	−	0.859724i	−0.0343831	−	0.999409i	$-0.510947\pi$
$337$	−6338.56	−	5318.68i	−1.02458	−	0.859724i	−0.990196	+	0.139685i	$0.955391\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−354.800	+	614.532i	−0.0563446	+	0.0975917i
$342$		0			0
$343$	−6746.56	−	11685.4i	−1.06204	−	1.83951i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	698.081	−	3959.02i	0.107997	−	0.612482i	−0.881984	−	0.471280i	$-0.843792\pi$
$347$	698.081	−	3959.02i	0.107997	−	0.612482i	0.989981	−	0.141202i	$-0.0450967\pi$
$348$		0			0
$349$	−6291.10	+	5278.86i	−0.964914	+	0.809659i	−0.981745	−	0.190200i	$-0.939086\pi$
$349$	−6291.10	+	5278.86i	−0.964914	+	0.809659i	0.0168317	+	0.999858i	$0.494642\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3542.55	−	2972.56i	0.534139	−	0.448196i	−0.335389	−	0.942080i	$-0.608868\pi$
$353$	3542.55	−	2972.56i	0.534139	−	0.448196i	0.869528	+	0.493884i	$0.164423\pi$
$354$		0			0
$355$	−249.285	+	1413.76i	−0.0372694	+	0.211366i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−6159.42	−	10668.4i	−0.905521	−	1.56841i	−0.820217	−	0.572053i	$-0.806147\pi$
$359$	−6159.42	−	10668.4i	−0.905521	−	1.56841i	−0.0853041	−	0.996355i	$-0.527186\pi$
$360$		0			0
$361$	1671.15	−	2894.52i	0.243644	−	0.422004i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4769.42	+	4002.02i	0.683953	+	0.573905i
$366$		0			0
$367$	8080.39	+	2941.02i	1.14930	+	0.418311i	0.845263	−	0.534350i	$-0.179444\pi$
$367$	8080.39	+	2941.02i	1.14930	+	0.418311i	0.304036	+	0.952661i	$0.401666\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1165.82	+	6611.70i	0.163144	+	0.925236i
$372$		0			0
$373$	−2385.97	+	868.421i	−0.331208	+	0.120550i	−0.502271	−	0.864710i	$-0.667502\pi$
$373$	−2385.97	+	868.421i	−0.331208	+	0.120550i	0.171063	+	0.985260i	$0.445280\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−1399.53			−0.191193
$378$		0			0
$379$	11211.7			1.51955			0.759774	−	0.650187i	$-0.225309\pi$
$379$	11211.7			1.51955			0.759774	+	0.650187i	$0.225309\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−7480.47	+	2722.67i	−0.998001	+	0.363243i	−0.788813	−	0.614633i	$-0.789304\pi$
$383$	−7480.47	+	2722.67i	−0.998001	+	0.363243i	−0.209188	+	0.977876i	$0.567082\pi$
$384$		0			0
$385$	−882.314	−	5003.85i	−0.116797	−	0.662389i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	12432.6	+	4525.09i	1.62045	+	0.589797i	0.983469	−	0.181078i	$-0.0579586\pi$
$389$	12432.6	+	4525.09i	1.62045	+	0.589797i	0.636986	+	0.770875i	$0.280181\pi$
$390$		0			0
$391$	6731.52	+	5648.41i	0.870659	+	0.730569i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	930.091	−	1610.96i	0.118476	−	0.205206i
$396$		0			0
$397$	6065.99	+	10506.6i	0.766859	+	1.32824i	0.939258	+	0.343212i	$0.111515\pi$
$397$	6065.99	+	10506.6i	0.766859	+	1.32824i	−0.172399	+	0.985027i	$0.555152\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−533.798	+	3027.32i	−0.0664753	+	0.377000i	0.933362	+	0.358938i	$0.116861\pi$
$401$	−533.798	+	3027.32i	−0.0664753	+	0.377000i	−0.999837	+	0.0180626i	$0.994250\pi$
$402$		0			0
$403$	179.469	−	150.593i	0.0221837	−	0.0186143i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5251.33	−	4406.39i	0.639555	−	0.536651i
$408$		0			0
$409$	−1787.94	+	10139.9i	−0.216156	+	1.22588i	0.662733	+	0.748856i	$0.269396\pi$
$409$	−1787.94	+	10139.9i	−0.216156	+	1.22588i	−0.878889	+	0.477026i	$0.841715\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−13497.5	−	23378.4i	−1.60816	−	2.78541i
$414$		0			0
$415$	−1514.63	+	2623.42i	−0.179157	+	0.310310i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3312.78	−	2779.75i	−0.386252	−	0.324104i	0.428899	−	0.903353i	$-0.358902\pi$
$419$	−3312.78	−	2779.75i	−0.386252	−	0.324104i	−0.815151	+	0.579248i	$0.803346\pi$
$420$		0			0
$421$	−5518.54	−	2008.58i	−0.638853	−	0.232523i	0.00222710	−	0.999998i	$-0.499291\pi$
$421$	−5518.54	−	2008.58i	−0.638853	−	0.232523i	−0.641080	+	0.767474i	$0.721513\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1535.72	−	8709.50i	−0.175278	−	0.994054i
$426$		0			0
$427$	19635.0	−	7146.54i	2.22530	−	0.809942i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	187.346			0.0209377			0.0104688	−	0.999945i	$-0.496668\pi$
$431$	187.346			0.0209377			0.0104688	+	0.999945i	$0.496668\pi$
$432$		0			0
$433$	−313.829			−0.0348307			−0.0174153	−	0.999848i	$-0.505544\pi$
$433$	−313.829			−0.0348307			−0.0174153	+	0.999848i	$0.505544\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5473.49	+	1992.19i	−0.599159	+	0.218076i
$438$		0			0
$439$	2543.97	+	14427.5i	0.276576	+	1.56854i	0.733911	+	0.679246i	$0.237693\pi$
$439$	2543.97	+	14427.5i	0.276576	+	1.56854i	−0.457335	+	0.889295i	$0.651196\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3295.46	+	1199.45i	0.353436	+	0.128640i	0.512636	−	0.858606i	$-0.328669\pi$
$443$	3295.46	+	1199.45i	0.353436	+	0.128640i	−0.159200	+	0.987246i	$0.550891\pi$
$444$		0			0
$445$	2813.51	+	2360.82i	0.299715	+	0.251491i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	905.931	−	1569.12i	0.0952194	−	0.164925i	−0.814481	−	0.580191i	$-0.802978\pi$
$449$	905.931	−	1569.12i	0.0952194	−	0.164925i	0.909700	+	0.415266i	$0.136311\pi$
$450$		0			0
$451$	−7016.55	−	12153.0i	−0.732586	−	1.26888i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−291.304	+	1652.07i	−0.0300143	+	0.170220i
$456$		0			0
$457$	11433.8	−	9594.07i	1.17035	−	0.982039i	0.170354	−	0.985383i	$-0.445509\pi$
$457$	11433.8	−	9594.07i	1.17035	−	0.982039i	0.999994	+	0.00334372i	$0.00106434\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6096.59	−	5115.65i	0.615936	−	0.516832i	−0.280587	−	0.959829i	$-0.590529\pi$
$461$	6096.59	−	5115.65i	0.615936	−	0.516832i	0.896523	+	0.442997i	$0.146085\pi$
$462$		0			0
$463$	2533.18	−	14366.4i	0.254270	−	1.44204i	−0.543669	−	0.839300i	$-0.682965\pi$
$463$	2533.18	−	14366.4i	0.254270	−	1.44204i	0.797939	−	0.602738i	$-0.205924\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4109.70	−	7118.22i	−0.407226	−	0.705336i	0.587352	−	0.809332i	$-0.300170\pi$
$467$	−4109.70	−	7118.22i	−0.407226	−	0.705336i	−0.994578	+	0.103996i	$0.966837\pi$
$468$		0			0
$469$	10065.9	−	17434.6i	0.991044	−	1.71654i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	247.697	+	207.842i	0.0240785	+	0.0202042i
$474$		0			0
$475$	5508.68	+	2004.99i	0.532117	+	0.193675i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−729.906	−	4139.50i	−0.0696247	−	0.394861i	−0.999627	−	0.0273078i	$-0.991307\pi$
$479$	−729.906	−	4139.50i	−0.0696247	−	0.394861i	0.930002	−	0.367554i	$-0.119805\pi$
$480$		0			0
$481$	−2126.79	+	774.088i	−0.201607	+	0.0733791i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4224.69			0.395532
$486$		0			0
$487$	−13008.8			−1.21044			−0.605219	−	0.796059i	$-0.706914\pi$
$487$	−13008.8			−1.21044			−0.605219	+	0.796059i	$0.706914\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13256.1	−	4824.83i	1.21841	−	0.443465i	0.348797	−	0.937198i	$-0.386590\pi$
$491$	13256.1	−	4824.83i	1.21841	−	0.443465i	0.869614	+	0.493733i	$0.164368\pi$
$492$		0			0
$493$	−2191.93	−	12431.1i	−0.200243	−	1.13563i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8725.86	−	3175.95i	−0.787542	−	0.286642i
$498$		0			0
$499$	7229.72	+	6066.46i	0.648591	+	0.544232i	0.906643	−	0.421899i	$-0.138636\pi$
$499$	7229.72	+	6066.46i	0.648591	+	0.544232i	−0.258052	+	0.966131i	$0.583081\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4547.85	+	7877.10i	−0.403138	+	0.698256i	−0.994103	−	0.108442i	$-0.965414\pi$
$503$	−4547.85	+	7877.10i	−0.403138	+	0.698256i	0.590965	+	0.806697i	$0.298747\pi$
$504$		0			0
$505$	−2530.67	−	4383.24i	−0.222996	−	0.386241i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1245.45	+	7063.30i	−0.108455	+	0.615079i	0.881329	+	0.472503i	$0.156650\pi$
$509$	−1245.45	+	7063.30i	−0.108455	+	0.615079i	−0.989784	+	0.142576i	$0.954462\pi$
$510$		0			0
$511$	−30850.6	+	25886.7i	−2.67074	+	2.24102i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2692.69	−	2259.43i	0.230396	−	0.193325i
$516$		0			0
$517$	1984.56	−	11255.0i	0.168822	−	0.957435i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4043.78	−	7004.04i	−0.340041	−	0.588968i	0.644399	−	0.764689i	$-0.277108\pi$
$521$	−4043.78	−	7004.04i	−0.340041	−	0.588968i	−0.984440	+	0.175721i	$0.943774\pi$
$522$		0			0
$523$	7678.53	−	13299.6i	0.641986	−	1.11195i	−0.343003	−	0.939334i	$-0.611444\pi$
$523$	7678.53	−	13299.6i	0.641986	−	1.11195i	0.984989	−	0.172618i	$-0.0552226\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1618.69	+	1358.25i	0.133798	+	0.112270i
$528$		0			0
$529$	2367.38	+	861.657i	0.194574	+	0.0708192i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	804.538	+	4562.76i	0.0653816	+	0.370798i
$534$		0			0
$535$	6240.43	−	2271.33i	0.504294	−	0.183548i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	22561.3			1.80294
$540$		0			0
$541$	2309.43			0.183531			0.0917654	−	0.995781i	$-0.470749\pi$
$541$	2309.43			0.183531			0.0917654	+	0.995781i	$0.470749\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2769.44	−	1007.99i	0.217669	−	0.0792252i
$546$		0			0
$547$	2461.77	+	13961.4i	0.192427	+	1.09131i	0.916035	+	0.401098i	$0.131371\pi$
$547$	2461.77	+	13961.4i	0.192427	+	1.09131i	−0.723608	+	0.690212i	$0.757517\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7862.54	+	2861.73i	0.607905	+	0.221259i
$552$		0			0
$553$	9217.36	+	7734.28i	0.708792	+	0.594747i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11430.0	+	19797.4i	−0.869489	+	1.50600i	−0.00697005	+	0.999976i	$0.502219\pi$
$557$	−11430.0	+	19797.4i	−0.869489	+	1.50600i	−0.862519	+	0.506024i	$0.831115\pi$
$558$		0			0
$559$	−53.3776	−	92.4528i	−0.00403870	−	0.00699524i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1033.46	+	5861.04i	−0.0773626	+	0.438745i	0.921382	+	0.388658i	$0.127061\pi$
$563$	−1033.46	+	5861.04i	−0.0773626	+	0.438745i	−0.998745	+	0.0500875i	$0.984050\pi$
$564$		0			0
$565$	7689.79	−	6452.50i	0.572587	−	0.480458i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8500.63	−	7132.88i	0.626301	−	0.525529i	−0.273476	−	0.961879i	$-0.588174\pi$
$569$	8500.63	−	7132.88i	0.626301	−	0.525529i	0.899777	+	0.436350i	$0.143729\pi$
$570$		0			0
$571$	−1804.91	+	10236.2i	−0.132282	+	0.750211i	0.844431	+	0.535664i	$0.179939\pi$
$571$	−1804.91	+	10236.2i	−0.132282	+	0.750211i	−0.976714	+	0.214547i	$0.931173\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4854.85	+	8408.85i	0.352106	+	0.609866i
$576$		0			0
$577$	−10062.0	+	17427.8i	−0.725971	+	1.25742i	0.232602	+	0.972572i	$0.425276\pi$
$577$	−10062.0	+	17427.8i	−0.725971	+	1.25742i	−0.958573	+	0.284846i	$0.908057\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−15010.3	−	12595.1i	−1.07183	−	0.899368i
$582$		0			0
$583$	−5730.58	−	2085.76i	−0.407095	−	0.148170i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2679.51	−	15196.3i	−0.188408	−	1.06851i	−0.921498	−	0.388382i	$-0.873034\pi$
$587$	−2679.51	−	15196.3i	−0.188408	−	1.06851i	0.733091	−	0.680131i	$-0.238077\pi$
$588$		0			0
$589$	−1316.18	+	479.052i	−0.0920754	+	0.0335127i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−8549.53			−0.592052			−0.296026	−	0.955180i	$-0.595662\pi$
$593$	−8549.53			−0.592052			−0.296026	+	0.955180i	$0.595662\pi$
$594$		0			0
$595$	−15130.4			−1.04250
$596$		0			0
$597$		0			0
$598$		0			0
$599$	15101.5	−	5496.51i	1.03010	−	0.374927i	0.228983	−	0.973430i	$-0.426460\pi$
$599$	15101.5	−	5496.51i	1.03010	−	0.374927i	0.801120	+	0.598504i	$0.204238\pi$
$600$		0			0
$601$	−1363.83	−	7734.68i	−0.0925656	−	0.524966i	−0.995466	−	0.0951161i	$-0.969678\pi$
$601$	−1363.83	−	7734.68i	−0.0925656	−	0.524966i	0.902901	−	0.429849i	$-0.141433\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2058.38	−	749.189i	−0.138322	−	0.0503453i
$606$		0			0
$607$	1421.95	+	1193.16i	0.0950829	+	0.0797840i	0.689090	−	0.724676i	$-0.258010\pi$
$607$	1421.95	+	1193.16i	0.0950829	+	0.0797840i	−0.594007	+	0.804460i	$0.702455\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1886.63	+	3267.74i	−0.124918	+	0.216364i
$612$		0			0
$613$	−3861.72	−	6688.70i	−0.254443	−	0.440708i	0.710301	−	0.703898i	$-0.248559\pi$
$613$	−3861.72	−	6688.70i	−0.254443	−	0.440708i	−0.964744	+	0.263190i	$0.915225\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−3164.80	+	17948.4i	−0.206499	+	1.17111i	0.688564	+	0.725175i	$0.258241\pi$
$617$	−3164.80	+	17948.4i	−0.206499	+	1.17111i	−0.895063	+	0.445939i	$0.852870\pi$
$618$		0			0
$619$	1605.52	−	1347.19i	0.104251	−	0.0874770i	−0.589172	−	0.808007i	$-0.700546\pi$
$619$	1605.52	−	1347.19i	0.104251	−	0.0874770i	0.693423	+	0.720530i	$0.256102\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−18198.9	+	15270.7i	−1.17034	+	0.982035i
$624$		0			0
$625$	1129.38	−	6405.05i	0.0722806	−	0.409923i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−10206.6	−	17678.4i	−0.647004	−	1.12064i
$630$		0			0
$631$	−9208.35	+	15949.3i	−0.580948	+	1.00623i	0.414419	+	0.910086i	$0.363985\pi$
$631$	−9208.35	+	15949.3i	−0.580948	+	1.00623i	−0.995367	+	0.0961459i	$0.969348\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1927.04	−	1616.98i	−0.120429	−	0.101052i
$636$		0			0
$637$	−6999.60	−	2547.65i	−0.435376	−	0.158464i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4147.90	+	23523.9i	0.255589	+	1.44951i	0.794557	+	0.607189i	$0.207703\pi$
$641$	4147.90	+	23523.9i	0.255589	+	1.44951i	−0.538969	+	0.842326i	$0.681186\pi$
$642$		0			0
$643$	−3014.06	+	1097.03i	−0.184857	+	0.0672824i	−0.432790	−	0.901495i	$-0.642471\pi$
$643$	−3014.06	+	1097.03i	−0.184857	+	0.0672824i	0.247933	+	0.968777i	$0.420249\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8439.89			0.512838			0.256419	−	0.966566i	$-0.417457\pi$
$647$	8439.89			0.512838			0.256419	+	0.966566i	$0.417457\pi$
$648$		0			0
$649$	24520.8			1.48309
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−26279.5	+	9564.97i	−1.57488	+	0.573210i	−0.974083	−	0.226191i	$-0.927373\pi$
$653$	−26279.5	+	9564.97i	−1.57488	+	0.573210i	−0.600798	+	0.799401i	$0.705151\pi$
$654$		0			0
$655$	−1932.66	−	10960.6i	−0.115290	−	0.653844i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	4419.19	+	1608.45i	0.261225	+	0.0950781i	0.469313	−	0.883032i	$-0.344502\pi$
$659$	4419.19	+	1608.45i	0.261225	+	0.0950781i	−0.208088	+	0.978110i	$0.566724\pi$
$660$		0			0
$661$	−24298.4	−	20388.8i	−1.42980	−	1.19975i	−0.945829	−	0.324664i	$-0.894749\pi$
$661$	−24298.4	−	20388.8i	−1.42980	−	1.19975i	−0.483973	−	0.875083i	$-0.660807\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5014.64	−	8685.61i	0.292420	−	0.506486i
$666$		0			0
$667$	6929.33	+	12002.0i	0.402256	+	0.696728i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3295.83	+	18691.6i	−0.189619	+	1.07538i
$672$		0			0
$673$	1397.36	−	1172.52i	0.0800358	−	0.0671580i	−0.601892	−	0.798577i	$-0.705586\pi$
$673$	1397.36	−	1172.52i	0.0800358	−	0.0671580i	0.681928	+	0.731419i	$0.261142\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7383.95	+	6195.87i	−0.419185	+	0.351738i	−0.827853	−	0.560945i	$-0.810438\pi$
$677$	−7383.95	+	6195.87i	−0.419185	+	0.351738i	0.408668	+	0.912683i	$0.365993\pi$
$678$		0			0
$679$	−4745.28	+	26911.8i	−0.268199	+	1.52103i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3985.79	−	6903.58i	−0.223297	−	0.386762i	0.732510	−	0.680756i	$-0.238349\pi$
$683$	−3985.79	−	6903.58i	−0.223297	−	0.386762i	−0.955807	+	0.293994i	$0.905015\pi$
$684$		0			0
$685$	−3554.81	+	6157.11i	−0.198281	+	0.343432i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1542.37	+	1294.20i	0.0852826	+	0.0715606i
$690$		0			0
$691$	18824.4	+	6851.54i	1.03635	+	0.377199i	0.803494	−	0.595313i	$-0.202972\pi$
$691$	18824.4	+	6851.54i	1.03635	+	0.377199i	0.232853	+	0.972512i	$0.425194\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−978.087	−	5547.01i	−0.0533827	−	0.302748i
$696$		0			0
$697$	−39267.8	+	14292.3i	−2.13396	+	0.776699i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	14959.1			0.805987			0.402993	−	0.915203i	$-0.367970\pi$
$701$	14959.1			0.805987			0.402993	+	0.915203i	$0.367970\pi$
$702$		0			0
$703$	13531.1			0.725938
$704$		0			0
$705$		0			0
$706$		0			0
$707$	30764.4	−	11197.3i	1.63651	−	0.595641i
$708$		0			0
$709$	−1068.39	−	6059.12i	−0.0565925	−	0.320952i	0.943349	−	0.331803i	$-0.107657\pi$
$709$	−1068.39	−	6059.12i	−0.0565925	−	0.320952i	−0.999941	+	0.0108511i	$0.996546\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2180.02	−	793.463i	−0.114506	−	0.0416766i
$714$		0			0
$715$	−1167.29	−	979.477i	−0.0610550	−	0.0512313i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−10762.6	+	18641.4i	−0.558244	+	0.966908i	0.439399	+	0.898292i	$0.355191\pi$
$719$	−10762.6	+	18641.4i	−0.558244	+	0.966908i	−0.997643	+	0.0686155i	$0.978142\pi$
$720$		0			0
$721$	11368.4	+	19690.7i	0.587214	+	1.01708i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2422.00	−	13735.9i	0.124070	−	0.703637i
$726$		0			0
$727$	9630.04	−	8080.56i	0.491277	−	0.412230i	−0.363207	−	0.931709i	$-0.618318\pi$
$727$	9630.04	−	8080.56i	0.491277	−	0.412230i	0.854484	+	0.519478i	$0.173874\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	737.594	−	618.915i	0.0373200	−	0.0313152i
$732$		0			0
$733$	−644.806	+	3656.88i	−0.0324918	+	0.184270i	−0.996734	−	0.0807515i	$-0.974268\pi$
$733$	−644.806	+	3656.88i	−0.0324918	+	0.184270i	0.964242	+	0.265022i	$0.0853791\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	9143.30	+	15836.7i	0.456985	+	0.791521i
$738$		0			0
$739$	−2061.21	+	3570.13i	−0.102602	+	0.177712i	−0.912756	−	0.408505i	$-0.866050\pi$
$739$	−2061.21	+	3570.13i	−0.102602	+	0.177712i	0.810154	+	0.586217i	$0.199384\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−7603.08	−	6379.74i	−0.375411	−	0.315007i	0.435487	−	0.900195i	$-0.356576\pi$
$743$	−7603.08	−	6379.74i	−0.375411	−	0.315007i	−0.810898	+	0.585188i	$0.801021\pi$
$744$		0			0
$745$	−9404.72	−	3423.04i	−0.462500	−	0.168336i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	7459.27	+	42303.6i	0.363893	+	2.06374i
$750$		0			0
$751$	−10461.9	+	3807.83i	−0.508337	+	0.185020i	−0.583440	−	0.812156i	$-0.698294\pi$
$751$	−10461.9	+	3807.83i	−0.508337	+	0.185020i	0.0751030	+	0.997176i	$0.476071\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3359.93			0.161961
$756$		0			0
$757$	−32325.4			−1.55203			−0.776015	−	0.630715i	$-0.782762\pi$
$757$	−32325.4			−1.55203			−0.776015	+	0.630715i	$0.782762\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−13060.1	+	4753.49i	−0.622114	+	0.226431i	−0.633795	−	0.773501i	$-0.718504\pi$
$761$	−13060.1	+	4753.49i	−0.622114	+	0.226431i	0.0116814	+	0.999932i	$0.496282\pi$
$762$		0			0
$763$	3310.35	+	18773.9i	0.157068	+	0.890775i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7607.52	−	2768.91i	−0.358138	−	0.130351i
$768$		0			0
$769$	−7019.28	−	5889.88i	−0.329157	−	0.276196i	0.463199	−	0.886254i	$-0.346701\pi$
$769$	−7019.28	−	5889.88i	−0.329157	−	0.276196i	−0.792356	+	0.610059i	$0.791146\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1545.03	−	2676.06i	0.0718897	−	0.124517i	−0.827840	−	0.560965i	$-0.810430\pi$
$773$	1545.03	−	2676.06i	0.0718897	−	0.124517i	0.899729	+	0.436448i	$0.143764\pi$
$774$		0			0
$775$	1167.42	+	2022.03i	0.0541097	+	0.0937207i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4809.95	−	27278.6i	0.221225	−	1.25463i
$780$		0			0
$781$	6461.41	−	5421.76i	0.296040	−	0.248407i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5199.06	+	4362.53i	−0.236385	+	0.198351i
$786$		0			0
$787$	3688.64	−	20919.3i	0.167072	−	0.947512i	−0.779830	−	0.625991i	$-0.784695\pi$
$787$	3688.64	−	20919.3i	0.167072	−	0.947512i	0.946902	−	0.321521i	$-0.104194\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	32465.9	+	56232.6i	1.45936	+	2.52769i
$792$		0			0
$793$	3133.20	−	5426.86i	0.140307	−	0.243018i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	16702.1	+	14014.7i	0.742307	+	0.622870i	0.933456	−	0.358691i	$-0.116777\pi$
$797$	16702.1	+	14014.7i	0.742307	+	0.622870i	−0.191149	+	0.981561i	$0.561221\pi$
$798$		0			0
$799$	−31979.8	−	11639.7i	−1.41598	−	0.515373i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6352.29	−	36025.6i	−0.279162	−	1.58321i
$804$		0			0
$805$	15609.9	−	5681.54i	0.683449	−	0.248755i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−17728.5			−0.770460			−0.385230	−	0.922821i	$-0.625878\pi$
$809$	−17728.5			−0.770460			−0.385230	+	0.922821i	$0.625878\pi$
$810$		0			0
$811$	3211.20			0.139039			0.0695194	−	0.997581i	$-0.477853\pi$
$811$	3211.20			0.139039			0.0695194	+	0.997581i	$0.477853\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	12310.8	−	4480.76i	0.529114	−	0.192582i
$816$		0			0
$817$	110.829	+	628.543i	0.00474592	+	0.0269155i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−11961.2	−	4353.53i	−0.508465	−	0.185066i	0.0750324	−	0.997181i	$-0.476094\pi$
$821$	−11961.2	−	4353.53i	−0.508465	−	0.185066i	−0.583497	+	0.812115i	$0.698316\pi$
$822$		0			0
$823$	−31351.4	−	26306.9i	−1.32787	−	1.11422i	−0.984570	−	0.174994i	$-0.944009\pi$
$823$	−31351.4	−	26306.9i	−1.32787	−	1.11422i	−0.343304	−	0.939224i	$-0.611546\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−14546.9	+	25195.9i	−0.611662	+	1.05943i	0.379298	+	0.925274i	$0.376165\pi$
$827$	−14546.9	+	25195.9i	−0.611662	+	1.05943i	−0.990960	+	0.134155i	$0.957168\pi$
$828$		0			0
$829$	−4034.95	−	6988.75i	−0.169047	−	0.292798i	0.769038	−	0.639203i	$-0.220736\pi$
$829$	−4034.95	−	6988.75i	−0.169047	−	0.292798i	−0.938085	+	0.346405i	$0.887402\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	11666.3	−	66162.7i	0.485249	−	2.75198i
$834$		0			0
$835$	13992.0	−	11740.7i	0.579896	−	0.486591i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−32834.5	+	27551.4i	−1.35110	+	1.13371i	−0.372475	+	0.928042i	$0.621491\pi$
$839$	−32834.5	+	27551.4i	−1.35110	+	1.13371i	−0.978623	+	0.205664i	$0.934065\pi$
$840$		0			0
$841$	−778.180	+	4413.28i	−0.0319070	+	0.180954i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−5365.43	−	9293.20i	−0.218434	−	0.378338i
$846$		0			0
$847$	7084.46	−	12270.7i	0.287397	−	0.497786i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	17168.4	+	14406.0i	0.691570	+	0.580296i
$852$		0			0
$853$	25788.2	+	9386.15i	1.03514	+	0.376759i	0.803035	−	0.595932i	$-0.203217\pi$
$853$	25788.2	+	9386.15i	1.03514	+	0.376759i	0.232103	+	0.972691i	$0.425439\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3298.00	−	18703.9i	−0.131456	−	0.745522i	−0.977263	−	0.212033i	$-0.931992\pi$
$857$	−3298.00	−	18703.9i	−0.131456	−	0.745522i	0.845807	−	0.533489i	$-0.179119\pi$
$858$		0			0
$859$	12590.2	−	4582.47i	0.500085	−	0.182016i	−0.0796470	−	0.996823i	$-0.525379\pi$
$859$	12590.2	−	4582.47i	0.500085	−	0.182016i	0.579732	+	0.814807i	$0.303157\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3158.44			0.124582			0.0622912	−	0.998058i	$-0.480159\pi$
$863$	3158.44			0.124582			0.0622912	+	0.998058i	$0.480159\pi$
$864$		0			0
$865$	11645.3			0.457747
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−10270.4	+	3738.13i	−0.400921	+	0.145923i
$870$		0			0
$871$	−1048.40	−	5945.76i	−0.0407849	−	0.231302i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−35575.7	−	12948.5i	−1.37449	−	0.500273i
$876$		0			0
$877$	5090.44	+	4271.38i	0.196000	+	0.164463i	0.735506	−	0.677518i	$-0.236945\pi$
$877$	5090.44	+	4271.38i	0.196000	+	0.164463i	−0.539506	+	0.841982i	$0.681389\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	20849.2	−	36111.8i	0.797305	−	1.38097i	−0.124060	−	0.992275i	$-0.539592\pi$
$881$	20849.2	−	36111.8i	0.797305	−	1.38097i	0.921365	−	0.388698i	$-0.127075\pi$
$882$		0			0
$883$	8379.42	+	14513.6i	0.319354	+	0.553138i	0.980353	−	0.197249i	$-0.0632006\pi$
$883$	8379.42	+	14513.6i	0.319354	+	0.553138i	−0.660999	+	0.750387i	$0.729867\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	4201.60	−	23828.5i	0.159049	−	0.902009i	−0.795942	−	0.605373i	$-0.793024\pi$
$887$	4201.60	−	23828.5i	0.159049	−	0.902009i	0.954991	−	0.296636i	$-0.0958649\pi$
$888$		0			0
$889$	12464.9	−	10459.3i	0.470257	−	0.394593i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	17280.8	−	14500.3i	0.647570	−	0.543376i
$894$		0			0
$895$	−1026.37	+	5820.84i	−0.0383328	+	0.217396i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1666.26	+	2886.05i	0.0618164	+	0.107069i
$900$		0			0
$901$	−9079.87	+	15726.8i	−0.335732	+	0.581504i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	13998.8	+	11746.4i	0.514183	+	0.431451i
$906$		0			0
$907$	17284.4	+	6291.01i	0.632766	+	0.230308i	0.638435	−	0.769676i	$-0.279582\pi$
$907$	17284.4	+	6291.01i	0.632766	+	0.230308i	−0.00566855	+	0.999984i	$0.501804\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−397.004	−	2251.52i	−0.0144383	−	0.0818839i	0.976737	−	0.214440i	$-0.0687926\pi$
$911$	−397.004	−	2251.52i	−0.0144383	−	0.0818839i	−0.991176	+	0.132556i	$0.957682\pi$
$912$		0			0
$913$	16725.2	−	6087.47i	0.606268	−	0.220664i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	71991.5			2.59255
$918$		0			0
$919$	4568.58			0.163986			0.0819932	−	0.996633i	$-0.473871\pi$
$919$	4568.58			0.163986			0.0819932	+	0.996633i	$0.473871\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2616.87	+	952.462i	−0.0933209	+	0.0339660i
$924$		0			0
$925$	−3916.78	−	22213.2i	−0.139225	−	0.789584i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−27954.9	−	10174.8i	−0.987268	−	0.359336i	−0.202606	−	0.979260i	$-0.564941\pi$
$929$	−27954.9	−	10174.8i	−0.987268	−	0.359336i	−0.784662	+	0.619924i	$0.787163\pi$
$930$		0			0
$931$	34114.2	+	28625.2i	1.20091	+	1.00768i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	6871.80	−	11902.3i	0.240355	−	0.416307i
$936$		0			0
$937$	19606.1	+	33958.8i	0.683568	+	1.18397i	0.973885	+	0.227044i	$0.0729060\pi$
$937$	19606.1	+	33958.8i	0.683568	+	1.18397i	−0.290317	+	0.956931i	$0.593761\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3310.43	−	18774.4i	0.114683	−	0.650400i	−0.872223	−	0.489108i	$-0.837323\pi$
$941$	3310.43	−	18774.4i	0.114683	−	0.650400i	0.986907	−	0.161293i	$-0.0515663\pi$
$942$		0			0
$943$	35145.4	−	29490.5i	1.21367	−	1.01839i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4780.70	−	4011.49i	0.164046	−	0.137651i	−0.557069	−	0.830466i	$-0.688074\pi$
$947$	4780.70	−	4011.49i	0.164046	−	0.137651i	0.721115	+	0.692815i	$0.243630\pi$
$948$		0			0
$949$	−2097.26	+	11894.2i	−0.0717387	+	0.406850i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	2401.20	+	4159.01i	0.0816187	+	0.141368i	0.903945	−	0.427648i	$-0.140658\pi$
$953$	2401.20	+	4159.01i	0.0816187	+	0.141368i	−0.822327	+	0.569016i	$0.807324\pi$
$954$		0			0
$955$	2055.22	−	3559.74i	0.0696390	−	0.120618i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−35228.8	−	29560.5i	−1.18623	−	0.995367i
$960$		0			0
$961$	27470.2	+	9998.32i	0.922096	+	0.335616i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	793.184	+	4498.37i	0.0264596	+	0.150060i
$966$		0			0
$967$	−41151.1	+	14977.8i	−1.36849	+	0.498089i	−0.918668	−	0.395030i	$-0.870734\pi$
$967$	−41151.1	+	14977.8i	−1.36849	+	0.498089i	−0.449820	+	0.893119i	$0.648512\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−54379.6			−1.79725			−0.898623	−	0.438723i	$-0.855431\pi$
$971$	−54379.6			−1.79725			−0.898623	+	0.438723i	$0.855431\pi$
$972$		0			0
$973$	36433.8			1.20043
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11761.8	+	4280.96i	−0.385153	+	0.140184i	−0.527337	−	0.849656i	$-0.676810\pi$
$977$	−11761.8	+	4280.96i	−0.385153	+	0.140184i	0.142184	+	0.989840i	$0.454587\pi$
$978$		0			0
$979$	−3747.25	−	21251.7i	−0.122332	−	0.693777i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	4043.60	+	1471.75i	0.131201	+	0.0477534i	0.406786	−	0.913523i	$-0.366649\pi$
$983$	4043.60	+	1471.75i	0.131201	+	0.0477534i	−0.275585	+	0.961277i	$0.588872\pi$
$984$		0			0
$985$	−9110.88	−	7644.93i	−0.294717	−	0.247297i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−528.564	+	915.500i	−0.0169943	+	0.0294350i
$990$		0			0
$991$	4071.74	+	7052.46i	0.130518	+	0.226063i	0.923876	−	0.382691i	$-0.125003\pi$
$991$	4071.74	+	7052.46i	0.130518	+	0.226063i	−0.793359	+	0.608755i	$0.791669\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	281.320	−	1595.45i	0.00896326	−	0.0508332i
$996$		0			0
$997$	−1755.63	+	1473.15i	−0.0557687	+	0.0467955i	−0.670246	−	0.742139i	$-0.733811\pi$
$997$	−1755.63	+	1473.15i	−0.0557687	+	0.0467955i	0.614477	+	0.788935i	$0.289367\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.4.i.a.37.6		54
3.2	odd	2		108.4.i.a.49.9	✓	54
27.11	odd	18		108.4.i.a.97.9	yes	54
27.16	even	9	inner	324.4.i.a.289.6		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.49.9	✓	54	3.2	odd	2
108.4.i.a.97.9	yes	54	27.11	odd	18
324.4.i.a.37.6		54	1.1	even	1	trivial
324.4.i.a.289.6		54	27.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	324.i (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.80495 - 1.74886i) q^{5} +(5.74341 + 32.5725i) q^{7} +O(q^{10})\)	\(q+(4.80495 - 1.74886i) q^{5} +(5.74341 + 32.5725i) q^{7} +(-28.2317 - 10.2755i) q^{11} +(7.59849 + 6.37589i) q^{13} +(-44.7319 + 77.4779i) q^{17} +(-29.6509 - 51.3568i) q^{19} +(17.0562 - 96.7304i) q^{23} +(-75.7266 + 63.5421i) q^{25} +(-108.085 + 90.6938i) q^{29} +(4.10141 - 23.2603i) q^{31} +(84.5615 + 146.465i) q^{35} +(-114.087 + 197.604i) q^{37} +(357.814 + 300.241i) q^{41} +(-10.1135 - 3.68102i) q^{43} +(66.0561 + 374.623i) q^{47} +(-705.667 + 256.842i) q^{49} +202.984 q^{53} -153.622 q^{55} +(-766.955 + 279.149i) q^{59} +(-109.702 - 622.151i) q^{61} +(47.6609 + 17.3471i) q^{65} +(-466.269 - 391.246i) q^{67} +(-140.376 + 243.138i) q^{71} +(608.806 + 1054.48i) q^{73} +(172.552 - 978.592i) q^{77} +(278.680 - 233.841i) q^{79} +(-453.825 + 380.804i) q^{83} +(-79.4366 + 450.507i) q^{85} +(359.138 + 622.046i) q^{89} +(-164.037 + 284.121i) q^{91} +(-232.286 - 194.911i) q^{95} +(776.386 + 282.581i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 12 q^{5}+O(q^{10}) \) 54 * q - 12 * q^5	\( 54 q - 12 q^{5} + 87 q^{11} - 204 q^{17} - 96 q^{23} - 216 q^{25} - 318 q^{29} - 54 q^{31} - 6 q^{35} - 867 q^{41} - 513 q^{43} + 1548 q^{47} + 594 q^{49} + 1068 q^{53} + 1218 q^{59} - 54 q^{61} - 96 q^{65} - 2997 q^{67} + 120 q^{71} - 216 q^{73} - 3480 q^{77} + 2808 q^{79} - 4464 q^{83} + 2160 q^{85} - 4029 q^{89} + 270 q^{91} + 1650 q^{95} - 3483 q^{97}+O(q^{100}) \) 54 * q - 12 * q^5 + 87 * q^11 - 204 * q^17 - 96 * q^23 - 216 * q^25 - 318 * q^29 - 54 * q^31 - 6 * q^35 - 867 * q^41 - 513 * q^43 + 1548 * q^47 + 594 * q^49 + 1068 * q^53 + 1218 * q^59 - 54 * q^61 - 96 * q^65 - 2997 * q^67 + 120 * q^71 - 216 * q^73 - 3480 * q^77 + 2808 * q^79 - 4464 * q^83 + 2160 * q^85 - 4029 * q^89 + 270 * q^91 + 1650 * q^95 - 3483 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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