LMFDB - Embedded newform 324.4.i.a.73.4

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			73.4
Character	$\chi$	$=$	324.73
Dual form			324.4.i.a.253.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.54095 + 5.48851i) q^{5} +(11.9650 - 4.35489i) q^{7} +O(q^{10})$	$q+(-6.54095 + 5.48851i) q^{5} +(11.9650 - 4.35489i) q^{7} +(7.56521 + 6.34796i) q^{11} +(-6.10231 - 34.6079i) q^{13} +(44.7027 + 77.4273i) q^{17} +(-1.00444 + 1.73974i) q^{19} +(-33.9901 - 12.3714i) q^{23} +(-9.04572 + 51.3009i) q^{25} +(-40.5831 + 230.158i) q^{29} +(113.063 + 41.1517i) q^{31} +(-54.3604 + 94.1550i) q^{35} +(98.7263 + 170.999i) q^{37} +(4.40922 + 25.0059i) q^{41} +(410.543 + 344.487i) q^{43} +(17.7125 - 6.44681i) q^{47} +(-138.558 + 116.264i) q^{49} -366.433 q^{53} -84.3245 q^{55} +(122.347 - 102.661i) q^{59} +(385.626 - 140.356i) q^{61} +(229.861 + 192.876i) q^{65} +(152.450 + 864.586i) q^{67} +(-69.1038 - 119.691i) q^{71} +(554.236 - 959.964i) q^{73} +(118.162 + 43.0075i) q^{77} +(-48.8286 + 276.921i) q^{79} +(-168.981 + 958.337i) q^{83} +(-717.359 - 261.097i) q^{85} +(-530.757 + 919.298i) q^{89} +(-223.728 - 387.508i) q^{91} +(-2.97859 - 16.8924i) q^{95} +(-158.761 - 133.216i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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
$5$	−6.54095	+	5.48851i	−0.585040	+	0.490907i	−0.886598	−	0.462541i	$-0.846938\pi$
$5$	−6.54095	+	5.48851i	−0.585040	+	0.490907i	0.301558	+	0.953448i	$0.402493\pi$
$6$		0			0
$7$	11.9650	−	4.35489i	0.646048	−	0.235142i	0.00184654	−	0.999998i	$-0.499412\pi$
$7$	11.9650	−	4.35489i	0.646048	−	0.235142i	0.644201	+	0.764856i	$0.277190\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	7.56521	+	6.34796i	0.207363	+	0.173998i	0.740555	−	0.671996i	$-0.234563\pi$
$11$	7.56521	+	6.34796i	0.207363	+	0.173998i	−0.533191	+	0.845995i	$0.679007\pi$
$12$		0			0
$13$	−6.10231	−	34.6079i	−0.130191	−	0.738347i	−0.978089	−	0.208188i	$-0.933243\pi$
$13$	−6.10231	−	34.6079i	−0.130191	−	0.738347i	0.847898	−	0.530159i	$-0.177868\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	44.7027	+	77.4273i	0.637764	+	1.10464i	0.985922	+	0.167204i	$0.0534740\pi$
$17$	44.7027	+	77.4273i	0.637764	+	1.10464i	−0.348158	+	0.937436i	$0.613193\pi$
$18$		0			0
$19$	−1.00444	+	1.73974i	−0.0121281	+	0.0210065i	−0.872026	−	0.489460i	$-0.837194\pi$
$19$	−1.00444	+	1.73974i	−0.0121281	+	0.0210065i	0.859898	+	0.510466i	$0.170527\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−33.9901	−	12.3714i	−0.308149	−	0.112157i	0.183317	−	0.983054i	$-0.441317\pi$
$23$	−33.9901	−	12.3714i	−0.308149	−	0.112157i	−0.491466	+	0.870897i	$0.663539\pi$
$24$		0			0
$25$	−9.04572	+	51.3009i	−0.0723658	+	0.410407i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−40.5831	+	230.158i	−0.259865	+	1.47377i	0.523404	+	0.852085i	$0.324662\pi$
$29$	−40.5831	+	230.158i	−0.259865	+	1.47377i	−0.783269	+	0.621683i	$0.786449\pi$
$30$		0			0
$31$	113.063	+	41.1517i	0.655057	+	0.238421i	0.648101	−	0.761554i	$-0.275563\pi$
$31$	113.063	+	41.1517i	0.655057	+	0.238421i	0.00695640	+	0.999976i	$0.497786\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−54.3604	+	94.1550i	−0.262531	+	0.454717i
$36$		0			0
$37$	98.7263	+	170.999i	0.438662	+	0.759785i	0.997587	−	0.0694333i	$-0.0221191\pi$
$37$	98.7263	+	170.999i	0.438662	+	0.759785i	−0.558924	+	0.829219i	$0.688786\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.40922	+	25.0059i	0.0167952	+	0.0952504i	0.992053	−	0.125820i	$-0.0401561\pi$
$41$	4.40922	+	25.0059i	0.0167952	+	0.0952504i	−0.975258	+	0.221070i	$0.929045\pi$
$42$		0			0
$43$	410.543	+	344.487i	1.45598	+	1.22171i	0.928065	+	0.372419i	$0.121471\pi$
$43$	410.543	+	344.487i	1.45598	+	1.22171i	0.527918	+	0.849296i	$0.322973\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	17.7125	−	6.44681i	0.0549708	−	0.0200077i	−0.314388	−	0.949294i	$-0.601799\pi$
$47$	17.7125	−	6.44681i	0.0549708	−	0.0200077i	0.369359	+	0.929287i	$0.379577\pi$
$48$		0			0
$49$	−138.558	+	116.264i	−0.403959	+	0.338962i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−366.433			−0.949687			−0.474844	−	0.880070i	$-0.657495\pi$
$53$	−366.433			−0.949687			−0.474844	+	0.880070i	$0.657495\pi$
$54$		0			0
$55$	−84.3245			−0.206733
$56$		0			0
$57$		0			0
$58$		0			0
$59$	122.347	−	102.661i	0.269969	−	0.226531i	−0.497745	−	0.867323i	$-0.665839\pi$
$59$	122.347	−	102.661i	0.269969	−	0.226531i	0.767714	+	0.640793i	$0.221394\pi$
$60$		0			0
$61$	385.626	−	140.356i	0.809415	−	0.294603i	0.0960331	−	0.995378i	$-0.469385\pi$
$61$	385.626	−	140.356i	0.809415	−	0.294603i	0.713382	+	0.700775i	$0.247162\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	229.861	+	192.876i	0.438627	+	0.368051i
$66$		0			0
$67$	152.450	+	864.586i	0.277981	+	1.57651i	0.729332	+	0.684160i	$0.239831\pi$
$67$	152.450	+	864.586i	0.277981	+	1.57651i	−0.451351	+	0.892346i	$0.649058\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−69.1038	−	119.691i	−0.115509	−	0.200067i	0.802474	−	0.596687i	$-0.203516\pi$
$71$	−69.1038	−	119.691i	−0.115509	−	0.200067i	−0.917983	+	0.396620i	$0.870183\pi$
$72$		0			0
$73$	554.236	−	959.964i	0.888608	−	1.53911i	0.0470856	−	0.998891i	$-0.485007\pi$
$73$	554.236	−	959.964i	0.888608	−	1.53911i	0.841522	−	0.540223i	$-0.181660\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	118.162	+	43.0075i	0.174881	+	0.0636515i
$78$		0			0
$79$	−48.8286	+	276.921i	−0.0695399	+	0.394380i	0.930094	+	0.367322i	$0.119725\pi$
$79$	−48.8286	+	276.921i	−0.0695399	+	0.394380i	−0.999634	+	0.0270585i	$0.991386\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−168.981	+	958.337i	−0.223470	+	1.26736i	0.642118	+	0.766606i	$0.278056\pi$
$83$	−168.981	+	958.337i	−0.223470	+	1.26736i	−0.865588	+	0.500757i	$0.833055\pi$
$84$		0			0
$85$	−717.359	−	261.097i	−0.915394	−	0.333176i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−530.757	+	919.298i	−0.632136	+	1.09489i	0.354978	+	0.934875i	$0.384488\pi$
$89$	−530.757	+	919.298i	−0.632136	+	1.09489i	−0.987114	+	0.160017i	$0.948845\pi$
$90$		0			0
$91$	−223.728	−	387.508i	−0.257726	−	0.446394i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.97859	−	16.8924i	−0.00321681	−	0.0182434i
$96$		0			0
$97$	−158.761	−	133.216i	−0.166183	−	0.139444i	0.555904	−	0.831247i	$-0.312372\pi$
$97$	−158.761	−	133.216i	−0.166183	−	0.139444i	−0.722087	+	0.691803i	$0.756817\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1263.16	−	459.753i	1.24445	−	0.452942i	0.365927	−	0.930644i	$-0.380752\pi$
$101$	1263.16	−	459.753i	1.24445	−	0.452942i	0.878522	+	0.477701i	$0.158530\pi$
$102$		0			0
$103$	−725.221	+	608.533i	−0.693768	+	0.582141i	−0.919993	−	0.391934i	$-0.871806\pi$
$103$	−725.221	+	608.533i	−0.693768	+	0.582141i	0.226225	+	0.974075i	$0.427362\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1007.69			−0.910439			−0.455219	−	0.890379i	$-0.650439\pi$
$107$	−1007.69			−0.910439			−0.455219	+	0.890379i	$0.650439\pi$
$108$		0			0
$109$	−542.749			−0.476935			−0.238467	−	0.971151i	$-0.576645\pi$
$109$	−542.749			−0.476935			−0.238467	+	0.971151i	$0.576645\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1544.12	−	1295.67i	1.28548	−	1.07864i	0.293013	−	0.956109i	$-0.405342\pi$
$113$	1544.12	−	1295.67i	1.28548	−	1.07864i	0.992464	−	0.122535i	$-0.0391023\pi$
$114$		0			0
$115$	290.228	−	105.634i	0.235339	−	0.0856562i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	872.054	+	731.740i	0.671774	+	0.563685i
$120$		0			0
$121$	−214.190	−	1214.73i	−0.160924	−	0.912646i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−756.060	−	1309.53i	−0.540993	−	0.937027i
$126$		0			0
$127$	731.061	−	1266.24i	0.510797	−	0.884726i	−0.489125	−	0.872214i	$-0.662684\pi$
$127$	731.061	−	1266.24i	0.510797	−	0.884726i	0.999922	−	0.0125122i	$-0.00398286\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1594.59	−	580.385i	−1.06351	−	0.387087i	−0.249766	−	0.968306i	$-0.580354\pi$
$131$	−1594.59	−	580.385i	−1.06351	−	0.387087i	−0.813747	+	0.581219i	$0.802576\pi$
$132$		0			0
$133$	−4.44170	+	25.1901i	−0.00289582	+	0.0164230i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	323.495	−	1834.63i	0.201737	−	1.14411i	−0.700755	−	0.713402i	$-0.747153\pi$
$137$	323.495	−	1834.63i	0.201737	−	1.14411i	0.902492	−	0.430707i	$-0.141736\pi$
$138$		0			0
$139$	−999.280	−	363.708i	−0.609768	−	0.221938i	0.0186335	−	0.999826i	$-0.494068\pi$
$139$	−999.280	−	363.708i	−0.609768	−	0.221938i	−0.628402	+	0.777889i	$0.716291\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	173.525	−	300.554i	0.101475	−	0.175759i
$144$		0			0
$145$	−997.772	−	1728.19i	−0.571452	−	0.989783i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−578.529	−	3281.00i	−0.318087	−	1.80396i	−0.554365	−	0.832274i	$-0.687039\pi$
$149$	−578.529	−	3281.00i	−0.318087	−	1.80396i	0.236278	−	0.971685i	$-0.424072\pi$
$150$		0			0
$151$	1959.73	+	1644.41i	1.05616	+	0.886224i	0.993728	−	0.111825i	$-0.0356696\pi$
$151$	1959.73	+	1644.41i	1.05616	+	0.886224i	0.0624329	+	0.998049i	$0.480114\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−965.403	+	351.378i	−0.500278	+	0.182086i
$156$		0			0
$157$	−2145.49	+	1800.28i	−1.09063	+	0.915144i	−0.996759	−	0.0804405i	$-0.974367\pi$
$157$	−2145.49	+	1800.28i	−1.09063	+	0.915144i	−0.0938671	+	0.995585i	$0.529923\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−460.567			−0.225452
$162$		0			0
$163$	−1529.32			−0.734879			−0.367440	−	0.930047i	$-0.619766\pi$
$163$	−1529.32			−0.734879			−0.367440	+	0.930047i	$0.619766\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2951.09	−	2476.26i	1.36744	−	1.14742i	0.393831	−	0.919183i	$-0.371150\pi$
$167$	2951.09	−	2476.26i	1.36744	−	1.14742i	0.973607	−	0.228233i	$-0.0732948\pi$
$168$		0			0
$169$	904.034	−	329.041i	0.411486	−	0.149769i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1403.86	+	1177.98i	0.616956	+	0.517688i	0.896845	−	0.442345i	$-0.145853\pi$
$173$	1403.86	+	1177.98i	0.616956	+	0.517688i	−0.279889	+	0.960032i	$0.590298\pi$
$174$		0			0
$175$	115.178	+	653.206i	0.0497522	+	0.282159i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	191.456	+	331.612i	0.0799448	+	0.138469i	0.903226	−	0.429165i	$-0.141192\pi$
$179$	191.456	+	331.612i	0.0799448	+	0.138469i	−0.823281	+	0.567634i	$0.807859\pi$
$180$		0			0
$181$	150.411	−	260.519i	0.0617677	−	0.106985i	−0.833488	−	0.552538i	$-0.813660\pi$
$181$	150.411	−	260.519i	0.0617677	−	0.106985i	0.895256	+	0.445553i	$0.146993\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1584.29	−	576.636i	−0.629619	−	0.229163i
$186$		0			0
$187$	−153.321	+	869.525i	−0.0599568	+	0.340032i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−566.341	+	3211.88i	−0.214550	+	1.21677i	0.667136	+	0.744936i	$0.267520\pi$
$191$	−566.341	+	3211.88i	−0.214550	+	1.21677i	−0.881686	+	0.471836i	$0.843591\pi$
$192$		0			0
$193$	−1782.33	−	648.714i	−0.664739	−	0.241945i	−0.0124579	−	0.999922i	$-0.503966\pi$
$193$	−1782.33	−	648.714i	−0.664739	−	0.241945i	−0.652281	+	0.757977i	$0.726188\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	486.365	−	842.409i	0.175899	−	0.304666i	−0.764573	−	0.644537i	$-0.777050\pi$
$197$	486.365	−	842.409i	0.175899	−	0.304666i	0.940472	+	0.339871i	$0.110384\pi$
$198$		0			0
$199$	−1402.61	−	2429.40i	−0.499641	−	0.865403i	0.500359	−	0.865818i	$-0.333201\pi$
$199$	−1402.61	−	2429.40i	−0.499641	−	0.865403i	−1.00000		0.000414695i	$0.999868\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	516.738	+	2930.57i	0.178660	+	1.01323i
$204$		0			0
$205$	−166.086	−	139.362i	−0.0565850	−	0.0474804i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−18.6426	+	6.78534i	−0.00617002	+	0.00224570i
$210$		0			0
$211$	−6.10520	+	5.12287i	−0.00199194	+	0.00167144i	−0.643783	−	0.765208i	$-0.722636\pi$
$211$	−6.10520	+	5.12287i	−0.00199194	+	0.00167144i	0.641791	+	0.766880i	$0.278192\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4576.06			−1.45156
$216$		0			0
$217$	1532.01			0.479261
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2406.81	−	2019.55i	0.732577	−	0.614705i
$222$		0			0
$223$	3121.71	−	1136.21i	0.937422	−	0.341194i	0.172275	−	0.985049i	$-0.444888\pi$
$223$	3121.71	−	1136.21i	0.937422	−	0.341194i	0.765147	+	0.643855i	$0.222666\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2498.72	+	2096.68i	0.730599	+	0.613046i	0.930295	−	0.366812i	$-0.119551\pi$
$227$	2498.72	+	2096.68i	0.730599	+	0.613046i	−0.199696	+	0.979858i	$0.563995\pi$
$228$		0			0
$229$	0.498021	+	2.82442i	0.000143712	+	0.000815033i	0.984880	−	0.173241i	$-0.0554238\pi$
$229$	0.498021	+	2.82442i	0.000143712	+	0.000815033i	−0.984736	+	0.174056i	$0.944313\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	419.561	+	726.702i	0.117967	+	0.204325i	0.918962	−	0.394346i	$-0.129029\pi$
$233$	419.561	+	726.702i	0.117967	+	0.204325i	−0.800995	+	0.598671i	$0.795696\pi$
$234$		0			0
$235$	−80.4729	+	139.383i	−0.0223382	+	0.0386909i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−928.725	−	338.028i	−0.251356	−	0.0914863i	0.213269	−	0.976993i	$-0.431589\pi$
$239$	−928.725	−	338.028i	−0.251356	−	0.0914863i	−0.464626	+	0.885507i	$0.653811\pi$
$240$		0			0
$241$	157.896	−	895.472i	0.0422032	−	0.239346i	−0.956408	−	0.292034i	$-0.905668\pi$
$241$	157.896	−	895.472i	0.0422032	−	0.239346i	0.998611	+	0.0526883i	$0.0167790\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	268.185	−	1520.95i	0.0699335	−	0.396612i
$246$		0			0
$247$	66.3381	+	24.1451i	0.0170890	+	0.00621990i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2208.59	+	3825.39i	−0.555398	+	0.961977i	0.442475	+	0.896781i	$0.354101\pi$
$251$	−2208.59	+	3825.39i	−0.555398	+	0.961977i	−0.997872	+	0.0651964i	$0.979233\pi$
$252$		0			0
$253$	−178.609	−	309.360i	−0.0443837	−	0.0768748i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1181.55	+	6700.91i	0.286782	+	1.62642i	0.698848	+	0.715270i	$0.253696\pi$
$257$	1181.55	+	6700.91i	0.286782	+	1.62642i	−0.412066	+	0.911154i	$0.635193\pi$
$258$		0			0
$259$	1925.94	+	1616.06i	0.462054	+	0.387710i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−817.417	+	297.515i	−0.191650	+	0.0697551i	−0.436062	−	0.899916i	$-0.643627\pi$
$263$	−817.417	+	297.515i	−0.191650	+	0.0697551i	0.244412	+	0.969671i	$0.421405\pi$
$264$		0			0
$265$	2396.82	−	2011.17i	0.555605	−	0.466208i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4222.12			0.956977			0.478489	−	0.878094i	$-0.341185\pi$
$269$	4222.12			0.956977			0.478489	+	0.878094i	$0.341185\pi$
$270$		0			0
$271$	7100.72			1.59165			0.795826	−	0.605525i	$-0.207037\pi$
$271$	7100.72			1.59165			0.795826	+	0.605525i	$0.207037\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−394.089	+	330.680i	−0.0864162	+	0.0725118i
$276$		0			0
$277$	−6209.30	+	2260.00i	−1.34686	+	0.490218i	−0.911967	−	0.410263i	$-0.865437\pi$
$277$	−6209.30	+	2260.00i	−1.34686	+	0.490218i	−0.434895	+	0.900481i	$0.643215\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1603.24	−	1345.28i	−0.340360	−	0.285596i	0.456546	−	0.889700i	$-0.349087\pi$
$281$	−1603.24	−	1345.28i	−0.340360	−	0.285596i	−0.796905	+	0.604104i	$0.793531\pi$
$282$		0			0
$283$	1511.14	+	8570.09i	0.317413	+	1.80014i	0.558359	+	0.829599i	$0.311431\pi$
$283$	1511.14	+	8570.09i	0.317413	+	1.80014i	−0.240946	+	0.970538i	$0.577458\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	161.654	+	279.993i	0.0332479	+	0.0575870i
$288$		0			0
$289$	−1540.16	+	2667.64i	−0.313487	+	0.542975i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7336.53	−	2670.28i	−1.46282	−	0.532421i	−0.516676	−	0.856181i	$-0.672831\pi$
$293$	−7336.53	−	2670.28i	−1.46282	−	0.532421i	−0.946139	+	0.323760i	$0.895053\pi$
$294$		0			0
$295$	−236.807	+	1343.00i	−0.0467371	+	0.265059i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−220.730	+	1251.82i	−0.0426928	+	0.242123i
$300$		0			0
$301$	6412.34	+	2333.90i	1.22791	+	0.446923i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1752.01	+	3034.58i	−0.328918	+	0.569703i
$306$		0			0
$307$	2400.44	+	4157.68i	0.446255	+	0.772936i	0.998139	−	0.0609852i	$-0.0194242\pi$
$307$	2400.44	+	4157.68i	0.446255	+	0.772936i	−0.551884	+	0.833921i	$0.686091\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1262.48	+	7159.88i	0.230189	+	1.30546i	0.852513	+	0.522705i	$0.175077\pi$
$311$	1262.48	+	7159.88i	0.230189	+	1.30546i	−0.622325	+	0.782759i	$0.713812\pi$
$312$		0			0
$313$	22.5342	+	18.9084i	0.00406935	+	0.00341459i	0.644820	−	0.764334i	$-0.276932\pi$
$313$	22.5342	+	18.9084i	0.00406935	+	0.00341459i	−0.640751	+	0.767749i	$0.721377\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3605.13	−	1312.16i	0.638752	−	0.232487i	−0.00228399	−	0.999997i	$-0.500727\pi$
$317$	3605.13	−	1312.16i	0.638752	−	0.232487i	0.641036	+	0.767511i	$0.278505\pi$
$318$		0			0
$319$	−1768.05	+	1483.57i	−0.310320	+	0.260389i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−179.604			−0.0309395
$324$		0			0
$325$	1830.62			0.312444
$326$		0			0
$327$		0			0
$328$		0			0
$329$	183.854	−	154.272i	0.0308091	−	0.0258519i
$330$		0			0
$331$	2593.45	−	943.938i	0.430661	−	0.156748i	−0.117589	−	0.993062i	$-0.537516\pi$
$331$	2593.45	−	943.938i	0.430661	−	0.156748i	0.548250	+	0.836315i	$0.315294\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5742.45	−	4818.49i	−0.936548	−	0.785857i
$336$		0			0
$337$	−1738.35	−	9858.65i	−0.280990	−	1.59358i	−0.719266	−	0.694735i	$-0.755522\pi$
$337$	−1738.35	−	9858.65i	−0.280990	−	1.59358i	0.438275	−	0.898841i	$-0.355590\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	594.118	+	1029.04i	0.0943499	+	0.163419i
$342$		0			0
$343$	−3335.21	+	5776.75i	−0.525027	+	0.909374i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−376.101	−	136.890i	−0.0581849	−	0.0211776i	0.312764	−	0.949831i	$-0.398745\pi$
$347$	−376.101	−	136.890i	−0.0581849	−	0.0211776i	−0.370949	+	0.928653i	$0.620967\pi$
$348$		0			0
$349$	−124.917	+	708.438i	−0.0191594	+	0.108659i	−0.992888	−	0.119054i	$-0.962014\pi$
$349$	−124.917	+	708.438i	−0.0191594	+	0.108659i	0.973728	+	0.227713i	$0.0731248\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	27.6907	−	157.042i	0.00417515	−	0.0236784i	−0.982649	−	0.185475i	$-0.940618\pi$
$353$	27.6907	−	157.042i	0.00417515	−	0.0236784i	0.986824	+	0.161796i	$0.0517288\pi$
$354$		0			0
$355$	1108.93	+	403.618i	0.165791	+	0.0603431i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4825.04	−	8357.21i	0.709348	−	1.22863i	−0.255752	−	0.966743i	$-0.582323\pi$
$359$	4825.04	−	8357.21i	0.709348	−	1.22863i	0.965099	−	0.261884i	$-0.0843438\pi$
$360$		0			0
$361$	3427.48	+	5936.57i	0.499706	+	0.865516i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1643.54	+	9321.00i	0.235691	+	1.33667i
$366$		0			0
$367$	−6305.46	−	5290.91i	−0.896845	−	0.752543i	0.0727258	−	0.997352i	$-0.476830\pi$
$367$	−6305.46	−	5290.91i	−0.896845	−	0.752543i	−0.969571	+	0.244809i	$0.921275\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4384.36	+	1595.78i	−0.613543	+	0.223311i
$372$		0			0
$373$	5136.29	−	4309.86i	0.712995	−	0.598274i	−0.212443	−	0.977174i	$-0.568142\pi$
$373$	5136.29	−	4309.86i	0.712995	−	0.598274i	0.925438	+	0.378899i	$0.123697\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8212.94			1.12198
$378$		0			0
$379$	−7620.82			−1.03286			−0.516432	−	0.856328i	$-0.672740\pi$
$379$	−7620.82			−1.03286			−0.516432	+	0.856328i	$0.672740\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8850.82	−	7426.72i	1.18082	−	0.990829i	0.180851	−	0.983510i	$-0.442115\pi$
$383$	8850.82	−	7426.72i	1.18082	−	0.990829i	0.999973	−	0.00731893i	$-0.00232971\pi$
$384$		0			0
$385$	−1008.94	+	367.224i	−0.133559	+	0.0486116i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−596.696	−	500.687i	−0.0777729	−	0.0652592i	0.603072	−	0.797686i	$-0.293943\pi$
$389$	−596.696	−	500.687i	−0.0777729	−	0.0652592i	−0.680845	+	0.732427i	$0.738387\pi$
$390$		0			0
$391$	−561.566	−	3184.80i	−0.0726333	−	0.411924i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1200.50	−	2079.32i	−0.152920	−	0.264866i
$396$		0			0
$397$	420.795	−	728.838i	0.0531967	−	0.0921394i	−0.838201	−	0.545362i	$-0.816392\pi$
$397$	420.795	−	728.838i	0.0531967	−	0.0921394i	0.891398	+	0.453222i	$0.149726\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14884.6	−	5417.54i	−1.85362	−	0.674661i	−0.983252	−	0.182252i	$-0.941661\pi$
$401$	−14884.6	−	5417.54i	−1.85362	−	0.674661i	−0.870364	−	0.492409i	$-0.836117\pi$
$402$		0			0
$403$	734.227	−	4164.01i	0.0907555	−	0.514700i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−338.610	+	1920.35i	−0.0412390	+	0.233878i
$408$		0			0
$409$	4496.30	+	1636.52i	0.543588	+	0.197850i	0.599196	−	0.800603i	$-0.295487\pi$
$409$	4496.30	+	1636.52i	0.543588	+	0.197850i	−0.0556071	+	0.998453i	$0.517709\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1016.79	−	1761.14i	0.121146	−	0.209831i
$414$		0			0
$415$	−4154.55	−	7195.88i	−0.491418	−	0.851161i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1644.96	+	9329.01i	0.191793	+	1.08771i	0.916912	+	0.399090i	$0.130674\pi$
$419$	1644.96	+	9329.01i	0.191793	+	1.08771i	−0.725119	+	0.688624i	$0.758215\pi$
$420$		0			0
$421$	−7997.87	−	6711.01i	−0.925873	−	0.776900i	0.0491989	−	0.998789i	$-0.484333\pi$
$421$	−7997.87	−	6711.01i	−0.925873	−	0.776900i	−0.975072	+	0.221889i	$0.928778\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4376.46	+	1592.90i	−0.499504	+	0.181805i
$426$		0			0
$427$	4002.77	−	3358.72i	0.453647	−	0.380655i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	8608.62			0.962094			0.481047	−	0.876695i	$-0.340257\pi$
$431$	8608.62			0.962094			0.481047	+	0.876695i	$0.340257\pi$
$432$		0			0
$433$	−4458.02			−0.494778			−0.247389	−	0.968916i	$-0.579573\pi$
$433$	−4458.02			−0.494778			−0.247389	+	0.968916i	$0.579573\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	55.6640	−	46.7076i	0.00609330	−	0.00511288i
$438$		0			0
$439$	−621.671	+	226.270i	−0.0675871	+	0.0245997i	−0.375592	−	0.926785i	$-0.622561\pi$
$439$	−621.671	+	226.270i	−0.0675871	+	0.0245997i	0.308005	+	0.951385i	$0.400339\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12445.6	−	10443.1i	−1.33478	−	1.12001i	−0.982934	−	0.183957i	$-0.941109\pi$
$443$	−12445.6	−	10443.1i	−1.33478	−	1.12001i	−0.351847	−	0.936057i	$-0.614446\pi$
$444$		0			0
$445$	−1573.92	−	8926.14i	−0.167665	−	0.950876i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	6286.72	+	10888.9i	0.660777	+	1.14450i	0.980412	+	0.196959i	$0.0631064\pi$
$449$	6286.72	+	10888.9i	0.660777	+	1.14450i	−0.319635	+	0.947541i	$0.603560\pi$
$450$		0			0
$451$	−125.380	+	217.164i	−0.0130907	+	0.0226738i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3590.23	+	1306.74i	0.369918	+	0.134639i
$456$		0			0
$457$	344.908	−	1956.07i	0.0353044	−	0.200221i	−0.962054	−	0.272859i	$-0.912031\pi$
$457$	344.908	−	1956.07i	0.0353044	−	0.200221i	0.997358	+	0.0726379i	$0.0231418\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2257.12	−	12800.8i	0.228036	−	1.29326i	−0.628759	−	0.777600i	$-0.716437\pi$
$461$	2257.12	−	12800.8i	0.228036	−	1.29326i	0.856795	−	0.515657i	$-0.172452\pi$
$462$		0			0
$463$	−11058.6	−	4024.98i	−1.11001	−	0.404010i	−0.279013	−	0.960287i	$-0.590007\pi$
$463$	−11058.6	−	4024.98i	−1.11001	−	0.404010i	−0.830997	+	0.556277i	$0.812229\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8253.92	−	14296.2i	0.817871	−	1.41659i	−0.0893763	−	0.995998i	$-0.528487\pi$
$467$	8253.92	−	14296.2i	0.817871	−	1.41659i	0.907248	−	0.420597i	$-0.138179\pi$
$468$		0			0
$469$	5589.23	+	9680.84i	0.550292	+	0.953133i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	919.056	+	5212.23i	0.0893409	+	0.506677i
$474$		0			0
$475$	−80.1642	−	67.2657i	−0.00774355	−	0.00649761i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8477.76	−	3085.65i	0.808682	−	0.294336i	0.0956026	−	0.995420i	$-0.469522\pi$
$479$	8477.76	−	3085.65i	0.808682	−	0.294336i	0.713079	+	0.701083i	$0.247300\pi$
$480$		0			0
$481$	5315.46	−	4460.20i	0.503876	−	0.422802i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1769.61			0.165678
$486$		0			0
$487$	−14156.8			−1.31726			−0.658632	−	0.752465i	$-0.728865\pi$
$487$	−14156.8			−1.31726			−0.658632	+	0.752465i	$0.728865\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3325.98	−	2790.83i	0.305702	−	0.256514i	−0.477011	−	0.878897i	$-0.658280\pi$
$491$	3325.98	−	2790.83i	0.305702	−	0.256514i	0.782713	+	0.622383i	$0.213835\pi$
$492$		0			0
$493$	−19634.7	+	7146.44i	−1.79372	+	0.652859i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1348.07	−	1131.16i	−0.121668	−	0.102092i
$498$		0			0
$499$	1245.95	+	7066.16i	0.111777	+	0.633917i	0.988296	+	0.152550i	$0.0487485\pi$
$499$	1245.95	+	7066.16i	0.111777	+	0.633917i	−0.876519	+	0.481367i	$0.840140\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−8090.46	−	14013.1i	−0.717168	−	1.24217i	−0.962117	−	0.272636i	$-0.912105\pi$
$503$	−8090.46	−	14013.1i	−0.717168	−	1.24217i	0.244949	−	0.969536i	$-0.421229\pi$
$504$		0			0
$505$	−5738.92	+	9940.10i	−0.505700	+	0.875898i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16489.7	−	6001.77i	−1.43594	−	0.522640i	−0.497313	−	0.867571i	$-0.665680\pi$
$509$	−16489.7	−	6001.77i	−1.43594	−	0.522640i	−0.938628	+	0.344931i	$0.887902\pi$
$510$		0			0
$511$	2450.87	−	13899.6i	0.212172	−	1.20329i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1403.70	−	7960.76i	0.120105	−	0.681152i
$516$		0			0
$517$	174.923	+	63.6666i	0.0148802	+	0.00541597i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−525.762	+	910.646i	−0.0442112	+	0.0765761i	−0.887284	−	0.461223i	$-0.847411\pi$
$521$	−525.762	+	910.646i	−0.0442112	+	0.0765761i	0.843073	+	0.537799i	$0.180744\pi$
$522$		0			0
$523$	5220.14	+	9041.55i	0.436445	+	0.755946i	0.997412	−	0.0718925i	$-0.0229039\pi$
$523$	5220.14	+	9041.55i	0.436445	+	0.755946i	−0.560967	+	0.827838i	$0.689571\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1867.97	+	10593.8i	0.154402	+	0.875659i
$528$		0			0
$529$	−8318.18	−	6979.79i	−0.683668	−	0.573665i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	838.496	−	305.188i	0.0681413	−	0.0248014i
$534$		0			0
$535$	6591.24	−	5530.71i	0.532643	−	0.446941i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1786.26			−0.142745
$540$		0			0
$541$	19911.0			1.58233			0.791165	−	0.611603i	$-0.209475\pi$
$541$	19911.0			1.58233			0.791165	+	0.611603i	$0.209475\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3550.09	−	2978.88i	0.279026	−	0.234131i
$546$		0			0
$547$	181.433	−	66.0364i	0.0141820	−	0.00516181i	−0.334919	−	0.942247i	$-0.608709\pi$
$547$	181.433	−	66.0364i	0.0141820	−	0.00516181i	0.349101	+	0.937085i	$0.386487\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−359.651	−	301.783i	−0.0278070	−	0.0233329i
$552$		0			0
$553$	621.728	+	3525.99i	0.0478093	+	0.271140i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	5088.83	+	8814.12i	0.387111	+	0.670496i	0.992060	−	0.125769i	$-0.0401397\pi$
$557$	5088.83	+	8814.12i	0.387111	+	0.670496i	−0.604949	+	0.796264i	$0.706806\pi$
$558$		0			0
$559$	9416.71	−	16310.2i	0.712494	−	1.23408i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−10169.9	−	3701.53i	−0.761295	−	0.277089i	−0.0679443	−	0.997689i	$-0.521644\pi$
$563$	−10169.9	−	3701.53i	−0.761295	−	0.277089i	−0.693351	+	0.720600i	$0.743866\pi$
$564$		0			0
$565$	−2988.72	+	16949.9i	−0.222542	+	1.26210i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2827.77	−	16037.1i	0.208341	−	1.18156i	−0.683753	−	0.729713i	$-0.739654\pi$
$569$	2827.77	−	16037.1i	0.208341	−	1.18156i	0.892095	−	0.451849i	$-0.149235\pi$
$570$		0			0
$571$	13023.1	+	4740.01i	0.954464	+	0.347396i	0.771862	−	0.635791i	$-0.219326\pi$
$571$	13023.1	+	4740.01i	0.954464	+	0.347396i	0.182602	+	0.983187i	$0.441548\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	942.129	−	1631.82i	0.0683296	−	0.118350i
$576$		0			0
$577$	8766.90	+	15184.7i	0.632532	+	1.09558i	0.987032	+	0.160521i	$0.0513175\pi$
$577$	8766.90	+	15184.7i	0.632532	+	1.09558i	−0.354501	+	0.935056i	$0.615349\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2151.61	+	12202.4i	0.153638	+	0.871324i
$582$		0			0
$583$	−2772.14	−	2326.10i	−0.196930	−	0.165244i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−17793.1	+	6476.17i	−1.25111	+	0.455367i	−0.880777	−	0.473532i	$-0.842979\pi$
$587$	−17793.1	+	6476.17i	−1.25111	+	0.455367i	−0.370333	+	0.928899i	$0.620757\pi$
$588$		0			0
$589$	−185.158	+	155.366i	−0.0129530	+	0.0108689i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−8252.04			−0.571451			−0.285726	−	0.958311i	$-0.592235\pi$
$593$	−8252.04			−0.571451			−0.285726	+	0.958311i	$0.592235\pi$
$594$		0			0
$595$	−9720.22			−0.669732
$596$		0			0
$597$		0			0
$598$		0			0
$599$	12055.4	−	10115.7i	0.822320	−	0.690008i	−0.131194	−	0.991357i	$-0.541881\pi$
$599$	12055.4	−	10115.7i	0.822320	−	0.690008i	0.953514	+	0.301348i	$0.0974367\pi$
$600$		0			0
$601$	3323.58	−	1209.69i	0.225577	−	0.0821033i	−0.226759	−	0.973951i	$-0.572813\pi$
$601$	3323.58	−	1209.69i	0.225577	−	0.0821033i	0.452336	+	0.891848i	$0.350591\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	8068.07	+	6769.92i	0.542171	+	0.454936i
$606$		0			0
$607$	−202.364	−	1147.67i	−0.0135317	−	0.0767419i	0.977294	−	0.211887i	$-0.0679610\pi$
$607$	−202.364	−	1147.67i	−0.0135317	−	0.0767419i	−0.990826	+	0.135145i	$0.956850\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−331.198	−	573.651i	−0.0219293	−	0.0379827i
$612$		0			0
$613$	−1701.46	+	2947.01i	−0.112107	+	0.194174i	−0.916619	−	0.399761i	$-0.869093\pi$
$613$	−1701.46	+	2947.01i	−0.112107	+	0.194174i	0.804513	+	0.593935i	$0.202426\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	6455.20	+	2349.50i	0.421194	+	0.153302i	0.543917	−	0.839139i	$-0.316941\pi$
$617$	6455.20	+	2349.50i	0.421194	+	0.153302i	−0.122723	+	0.992441i	$0.539163\pi$
$618$		0			0
$619$	1533.49	−	8696.87i	0.0995739	−	0.564712i	−0.893676	−	0.448714i	$-0.851882\pi$
$619$	1533.49	−	8696.87i	0.0995739	−	0.564712i	0.993249	−	0.115998i	$-0.0370066\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−2347.05	+	13310.8i	−0.150935	+	0.855994i
$624$		0			0
$625$	6013.91	+	2188.88i	0.384890	+	0.140089i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−8826.66	+	15288.2i	−0.559526	+	0.969128i
$630$		0			0
$631$	−14372.3	−	24893.6i	−0.906739	−	1.57052i	−0.818566	−	0.574413i	$-0.805230\pi$
$631$	−14372.3	−	24893.6i	−0.906739	−	1.57052i	−0.0881735	−	0.996105i	$-0.528103\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2167.91	+	12294.8i	0.135482	+	0.768354i
$636$		0			0
$637$	4869.17	+	4085.72i	0.302863	+	0.254132i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−383.429	+	139.557i	−0.0236264	+	0.00859932i	−0.353806	−	0.935319i	$-0.615113\pi$
$641$	−383.429	+	139.557i	−0.0236264	+	0.00859932i	0.330180	+	0.943918i	$0.392891\pi$
$642$		0			0
$643$	−19820.7	+	16631.6i	−1.21563	+	1.02004i	−0.216593	+	0.976262i	$0.569494\pi$
$643$	−19820.7	+	16631.6i	−1.21563	+	1.02004i	−0.999041	+	0.0437759i	$0.986061\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	17713.1			1.07631			0.538156	−	0.842845i	$-0.319121\pi$
$647$	17713.1			1.07631			0.538156	+	0.842845i	$0.319121\pi$
$648$		0			0
$649$	1577.26			0.0953976
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15919.4	+	13357.9i	−0.954017	+	0.800516i	−0.979970	−	0.199147i	$-0.936183\pi$
$653$	−15919.4	+	13357.9i	−0.954017	+	0.800516i	0.0259520	+	0.999663i	$0.491738\pi$
$654$		0			0
$655$	13615.6	−	4955.67i	0.812222	−	0.295625i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	17125.5	+	14370.0i	1.01232	+	0.849434i	0.988643	−	0.150286i	$-0.0480194\pi$
$659$	17125.5	+	14370.0i	1.01232	+	0.849434i	0.0236732	+	0.999720i	$0.492464\pi$
$660$		0			0
$661$	−651.001	−	3692.01i	−0.0383071	−	0.217251i	0.959645	−	0.281214i	$-0.0907370\pi$
$661$	−651.001	−	3692.01i	−0.0383071	−	0.217251i	−0.997952	+	0.0639633i	$0.979626\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−109.203	−	189.146i	−0.00636800	−	0.0110297i
$666$		0			0
$667$	4226.80	−	7321.03i	0.245371	−	0.424995i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3808.32	+	1386.11i	0.219104	+	0.0797472i
$672$		0			0
$673$	−1678.26	+	9517.90i	−0.0961252	+	0.545153i	0.898271	+	0.439441i	$0.144823\pi$
$673$	−1678.26	+	9517.90i	−0.0961252	+	0.545153i	−0.994397	+	0.105712i	$0.966288\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2125.75	+	12055.7i	−0.120678	+	0.684400i	0.863103	+	0.505028i	$0.168518\pi$
$677$	−2125.75	+	12055.7i	−0.120678	+	0.684400i	−0.983781	+	0.179372i	$0.942593\pi$
$678$		0			0
$679$	−2479.72	−	902.543i	−0.140151	−	0.0510109i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−9922.08	+	17185.5i	−0.555868	+	0.962791i	0.441968	+	0.897031i	$0.354281\pi$
$683$	−9922.08	+	17185.5i	−0.555868	+	0.962791i	−0.997835	+	0.0657604i	$0.979053\pi$
$684$		0			0
$685$	7953.41	+	13775.7i	0.443627	+	0.768384i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2236.09	+	12681.5i	0.123640	+	0.701199i
$690$		0			0
$691$	22107.7	+	18550.5i	1.21710	+	1.02127i	0.998971	+	0.0453479i	$0.0144396\pi$
$691$	22107.7	+	18550.5i	1.21710	+	1.02127i	0.218129	+	0.975920i	$0.430005\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8532.45	−	3105.56i	0.465690	−	0.169497i
$696$		0			0
$697$	−1739.04	+	1459.22i	−0.0945060	+	0.0793000i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−12315.2			−0.663538			−0.331769	−	0.943361i	$-0.607645\pi$
$701$	−12315.2			−0.663538			−0.331769	+	0.943361i	$0.607645\pi$
$702$		0			0
$703$	−396.658			−0.0212806
$704$		0			0
$705$		0			0
$706$		0			0
$707$	13111.5	−	11001.9i	0.697467	−	0.585245i
$708$		0			0
$709$	18496.8	−	6732.27i	0.979776	−	0.356609i	0.198023	−	0.980197i	$-0.436548\pi$
$709$	18496.8	−	6732.27i	0.979776	−	0.356609i	0.781753	+	0.623588i	$0.214326\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3333.94	−	2797.50i	−0.175115	−	0.146939i
$714$		0			0
$715$	514.574	+	2918.30i	0.0269147	+	0.152641i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3523.96	−	6103.67i	−0.182784	−	0.316590i	0.760044	−	0.649872i	$-0.225177\pi$
$719$	−3523.96	−	6103.67i	−0.182784	−	0.316590i	−0.942827	+	0.333281i	$0.891844\pi$
$720$		0			0
$721$	−6027.15	+	10439.3i	−0.311322	+	0.539225i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−11440.2	−	4163.89i	−0.586039	−	0.213301i
$726$		0			0
$727$	−598.760	+	3395.73i	−0.0305458	+	0.173234i	−0.996264	−	0.0863584i	$-0.972477\pi$
$727$	−598.760	+	3395.73i	−0.0305458	+	0.173234i	0.965718	+	0.259592i	$0.0835881\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8320.29	+	47186.7i	−0.420981	+	2.38750i
$732$		0			0
$733$	708.598	+	257.909i	0.0357062	+	0.0129960i	0.359812	−	0.933025i	$-0.382841\pi$
$733$	708.598	+	257.909i	0.0357062	+	0.0129960i	−0.324105	+	0.946021i	$0.605063\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4335.04	+	7508.52i	−0.216667	+	0.375278i
$738$		0			0
$739$	−9360.22	−	16212.4i	−0.465929	−	0.807012i	0.533314	−	0.845917i	$-0.320946\pi$
$739$	−9360.22	−	16212.4i	−0.465929	−	0.807012i	−0.999243	+	0.0389052i	$0.987613\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−4145.09	−	23508.0i	−0.204668	−	1.16073i	−0.897961	−	0.440076i	$-0.854952\pi$
$743$	−4145.09	−	23508.0i	−0.204668	−	1.16073i	0.693292	−	0.720656i	$-0.256159\pi$
$744$		0			0
$745$	21791.9	+	18285.6i	1.07167	+	0.899238i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−12057.0	+	4388.38i	−0.588187	+	0.214082i
$750$		0			0
$751$	2631.87	−	2208.40i	0.127880	−	0.107304i	−0.576604	−	0.817024i	$-0.695623\pi$
$751$	2631.87	−	2208.40i	0.127880	−	0.107304i	0.704485	+	0.709719i	$0.251178\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−21843.8			−1.05295
$756$		0			0
$757$	16653.4			0.799573			0.399786	−	0.916608i	$-0.369084\pi$
$757$	16653.4			0.799573			0.399786	+	0.916608i	$0.369084\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	15257.9	−	12802.9i	0.726806	−	0.609862i	−0.202453	−	0.979292i	$-0.564891\pi$
$761$	15257.9	−	12802.9i	0.726806	−	0.609862i	0.929259	+	0.369430i	$0.120447\pi$
$762$		0			0
$763$	−6493.97	+	2363.61i	−0.308123	+	0.112147i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4299.48	−	3607.69i	−0.202406	−	0.169839i
$768$		0			0
$769$	3628.05	+	20575.7i	0.170131	+	0.964861i	0.943615	+	0.331045i	$0.107401\pi$
$769$	3628.05	+	20575.7i	0.170131	+	0.964861i	−0.773484	+	0.633816i	$0.781488\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	8425.94	+	14594.1i	0.392057	+	0.679062i	0.992721	−	0.120439i	$-0.0384304\pi$
$773$	8425.94	+	14594.1i	0.392057	+	0.679062i	−0.600664	+	0.799502i	$0.705097\pi$
$774$		0			0
$775$	−3133.86	+	5428.00i	−0.145254	+	0.251586i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−47.9325	−	17.4460i	−0.00220457	−	0.000802398i
$780$		0			0
$781$	237.011	−	1344.16i	0.0108591	−	0.0615848i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4152.68	−	23551.0i	0.188810	−	1.07079i
$786$		0			0
$787$	−11260.1	−	4098.33i	−0.510010	−	0.185628i	0.0741808	−	0.997245i	$-0.476366\pi$
$787$	−11260.1	−	4098.33i	−0.510010	−	0.185628i	−0.584191	+	0.811616i	$0.698588\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	12832.9	−	22227.2i	0.576845	−	0.999125i
$792$		0			0
$793$	−7210.65	−	12489.2i	−0.322898	−	0.559275i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7532.17	−	42717.0i	−0.334759	−	1.89851i	−0.429598	−	0.903020i	$-0.641345\pi$
$797$	−7532.17	−	42717.0i	−0.334759	−	1.89851i	0.0948385	−	0.995493i	$-0.469767\pi$
$798$		0			0
$799$	1290.95	+	1083.24i	0.0571598	+	0.0479627i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	10286.7	−	3744.06i	0.452068	−	0.164539i
$804$		0			0
$805$	3012.55	−	2527.83i	0.131899	−	0.110676i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5452.36			0.236953			0.118476	−	0.992957i	$-0.462199\pi$
$809$	5452.36			0.236953			0.118476	+	0.992957i	$0.462199\pi$
$810$		0			0
$811$	17403.7			0.753548			0.376774	−	0.926305i	$-0.377033\pi$
$811$	17403.7			0.753548			0.376774	+	0.926305i	$0.377033\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10003.2	−	8393.67i	0.429934	−	0.360758i
$816$		0			0
$817$	−1011.68	+	368.222i	−0.0433222	+	0.0157680i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	31338.9	+	26296.5i	1.33220	+	1.11785i	0.983558	+	0.180591i	$0.0578009\pi$
$821$	31338.9	+	26296.5i	1.33220	+	1.11785i	0.348640	+	0.937257i	$0.386644\pi$
$822$		0			0
$823$	1104.56	+	6264.27i	0.0467831	+	0.265320i	0.999223	−	0.0394053i	$-0.0125463\pi$
$823$	1104.56	+	6264.27i	0.0467831	+	0.265320i	−0.952440	+	0.304726i	$0.901435\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−9552.52	−	16545.5i	−0.401661	−	0.695698i	0.592265	−	0.805743i	$-0.298234\pi$
$827$	−9552.52	−	16545.5i	−0.401661	−	0.695698i	−0.993927	+	0.110045i	$0.964900\pi$
$828$		0			0
$829$	11338.5	−	19638.8i	0.475033	−	0.822781i	−0.524558	−	0.851374i	$-0.675770\pi$
$829$	11338.5	−	19638.8i	0.475033	−	0.822781i	0.999591	+	0.0285937i	$0.00910290\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−15195.9	−	5530.86i	−0.632061	−	0.230051i
$834$		0			0
$835$	−5711.96	+	32394.1i	−0.236731	+	1.34257i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	409.589	−	2322.89i	0.0168541	−	0.0955842i	−0.975220	−	0.221236i	$-0.928991\pi$
$839$	409.589	−	2322.89i	0.0168541	−	0.0955842i	0.992074	+	0.125651i	$0.0401021\pi$
$840$		0			0
$841$	−28407.6	−	10339.5i	−1.16477	−	0.423941i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4107.29	+	7114.04i	−0.167213	+	0.289622i
$846$		0			0
$847$	−7852.80	−	13601.5i	−0.318566	−	0.551773i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1240.22	−	7033.66i	−0.0499581	−	0.283327i
$852$		0			0
$853$	−18056.3	−	15151.1i	−0.724780	−	0.608163i	0.203923	−	0.978987i	$-0.434631\pi$
$853$	−18056.3	−	15151.1i	−0.724780	−	0.608163i	−0.928703	+	0.370824i	$0.879075\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	15096.0	−	5494.49i	0.601714	−	0.219006i	−0.0231598	−	0.999732i	$-0.507373\pi$
$857$	15096.0	−	5494.49i	0.601714	−	0.219006i	0.624874	+	0.780726i	$0.285150\pi$
$858$		0			0
$859$	−22951.6	+	19258.7i	−0.911639	+	0.764956i	−0.972430	−	0.233194i	$-0.925082\pi$
$859$	−22951.6	+	19258.7i	−0.911639	+	0.764956i	0.0607910	+	0.998151i	$0.480638\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−34109.9			−1.34544			−0.672719	−	0.739898i	$-0.734874\pi$
$863$	−34109.9			−1.34544			−0.672719	+	0.739898i	$0.734874\pi$
$864$		0			0
$865$	−15647.9			−0.615081
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2127.28	+	1785.00i	−0.0830416	+	0.0696801i
$870$		0			0
$871$	28991.2	−	10551.9i	1.12782	−	0.410492i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−14749.1	−	12376.0i	−0.569841	−	0.478154i
$876$		0			0
$877$	−2513.11	−	14252.6i	−0.0967638	−	0.548775i	−0.994193	−	0.107615i	$-0.965678\pi$
$877$	−2513.11	−	14252.6i	−0.0967638	−	0.548775i	0.897429	−	0.441159i	$-0.145433\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	3372.51	+	5841.37i	0.128970	+	0.223383i	0.923278	−	0.384133i	$-0.125499\pi$
$881$	3372.51	+	5841.37i	0.128970	+	0.223383i	−0.794308	+	0.607516i	$0.792166\pi$
$882$		0			0
$883$	−7289.54	+	12625.9i	−0.277817	+	0.481193i	−0.970842	−	0.239720i	$-0.922944\pi$
$883$	−7289.54	+	12625.9i	−0.277817	+	0.481193i	0.693025	+	0.720914i	$0.256278\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	11377.1	+	4140.92i	0.430671	+	0.156751i	0.548254	−	0.836312i	$-0.315293\pi$
$887$	11377.1	+	4140.92i	0.430671	+	0.156751i	−0.117584	+	0.993063i	$0.537515\pi$
$888$		0			0
$889$	3232.81	−	18334.2i	0.121963	−	0.691685i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−6.57531	+	37.2905i	−0.000246399	+	0.00139740i
$894$		0			0
$895$	−3072.36	−	1118.25i	−0.114746	−	0.0417642i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−14059.8	+	24352.4i	−0.521604	+	0.903445i
$900$		0			0
$901$	−16380.5	−	28371.9i	−0.605677	−	1.04906i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	446.033	+	2529.58i	0.0163830	+	0.0929127i
$906$		0			0
$907$	15986.2	+	13414.0i	0.585239	+	0.491073i	0.886663	−	0.462417i	$-0.153018\pi$
$907$	15986.2	+	13414.0i	0.585239	+	0.491073i	−0.301424	+	0.953490i	$0.597462\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	40925.5	−	14895.7i	1.48839	−	0.541729i	0.535365	−	0.844621i	$-0.320174\pi$
$911$	40925.5	−	14895.7i	1.48839	−	0.541729i	0.953025	+	0.302892i	$0.0979520\pi$
$912$		0			0
$913$	−7361.86	+	6177.33i	−0.266859	+	0.223921i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−21606.8			−0.778101
$918$		0			0
$919$	241.628			0.00867310			0.00433655	−	0.999991i	$-0.498620\pi$
$919$	241.628			0.00867310			0.00433655	+	0.999991i	$0.498620\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3720.57	+	3121.93i	−0.132681	+	0.111332i
$924$		0			0
$925$	−9665.44	+	3517.93i	−0.343565	+	0.125048i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	248.263	+	208.317i	0.00876775	+	0.00735702i	0.647161	−	0.762353i	$-0.275956\pi$
$929$	248.263	+	208.317i	0.00876775	+	0.00735702i	−0.638393	+	0.769710i	$0.720401\pi$
$930$		0			0
$931$	−63.0958	−	357.834i	−0.00222114	−	0.0125967i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3769.53	−	6529.02i	−0.131847	−	0.228366i
$936$		0			0
$937$	15521.6	−	26884.2i	0.541162	−	0.937320i	−0.457675	−	0.889119i	$-0.651318\pi$
$937$	15521.6	−	26884.2i	0.541162	−	0.937320i	0.998838	−	0.0482011i	$-0.0153488\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	41340.5	+	15046.7i	1.43216	+	0.521263i	0.937550	−	0.347852i	$-0.113089\pi$
$941$	41340.5	+	15046.7i	1.43216	+	0.521263i	0.494610	+	0.869115i	$0.335311\pi$
$942$		0			0
$943$	159.488	−	904.503i	0.00550758	−	0.0312351i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3654.72	+	20726.9i	−0.125409	+	0.711230i	0.855655	+	0.517546i	$0.173155\pi$
$947$	−3654.72	+	20726.9i	−0.125409	+	0.711230i	−0.981064	+	0.193683i	$0.937957\pi$
$948$		0			0
$949$	−36604.5	−	13322.9i	−1.25209	−	0.455723i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	12519.2	−	21684.0i	0.425538	−	0.737054i	−0.570932	−	0.820997i	$-0.693418\pi$
$953$	12519.2	−	21684.0i	0.425538	−	0.737054i	0.996471	+	0.0839433i	$0.0267515\pi$
$954$		0			0
$955$	−13924.0	−	24117.1i	−0.471802	−	0.817185i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4119.01	−	23360.1i	−0.138696	−	0.786586i
$960$		0			0
$961$	−11731.4	−	9843.79i	−0.393789	−	0.330428i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	15218.6	−	5539.11i	0.507672	−	0.184777i
$966$		0			0
$967$	−16449.7	+	13802.9i	−0.547038	+	0.459019i	−0.873936	−	0.486040i	$-0.838441\pi$
$967$	−16449.7	+	13802.9i	−0.547038	+	0.459019i	0.326899	+	0.945059i	$0.393996\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2611.91			0.0863236			0.0431618	−	0.999068i	$-0.486257\pi$
$971$	2611.91			0.0863236			0.0431618	+	0.999068i	$0.486257\pi$
$972$		0			0
$973$	−13540.3			−0.446126
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−5137.13	+	4310.56i	−0.168220	+	0.141154i	−0.723011	−	0.690836i	$-0.757243\pi$
$977$	−5137.13	+	4310.56i	−0.168220	+	0.141154i	0.554791	+	0.831990i	$0.312798\pi$
$978$		0			0
$979$	−9850.95	+	3585.45i	−0.321591	+	0.117050i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−7814.81	−	6557.41i	−0.253564	−	0.212766i	0.507141	−	0.861863i	$-0.330702\pi$
$983$	−7814.81	−	6557.41i	−0.253564	−	0.212766i	−0.760705	+	0.649097i	$0.775147\pi$
$984$		0			0
$985$	1442.28	+	8179.57i	0.0466546	+	0.264592i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9692.64	−	16788.1i	−0.311636	−	0.539769i
$990$		0			0
$991$	16979.4	−	29409.2i	0.544268	−	0.942699i	−0.454385	−	0.890805i	$-0.650141\pi$
$991$	16979.4	−	29409.2i	0.544268	−	0.942699i	0.998653	−	0.0518937i	$-0.0165257\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	22508.2	+	8192.30i	0.717143	+	0.261019i
$996$		0			0
$997$	5475.70	−	31054.3i	0.173939	−	0.986457i	−0.765422	−	0.643528i	$-0.777470\pi$
$997$	5475.70	−	31054.3i	0.173939	−	0.986457i	0.939361	−	0.342929i	$-0.111419\pi$
$998$		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.73.4		54
3.2	odd	2		108.4.i.a.25.5	yes	54
27.13	even	9	inner	324.4.i.a.253.4		54
27.14	odd	18		108.4.i.a.13.5	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.4.i.a.13.5	✓	54	27.14	odd	18
108.4.i.a.25.5	yes	54	3.2	odd	2
324.4.i.a.73.4		54	1.1	even	1	trivial
324.4.i.a.253.4		54	27.13	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)

\(f(q)\)	\(=\)	\(q+(-6.54095 + 5.48851i) q^{5} +(11.9650 - 4.35489i) q^{7} +O(q^{10})\)	\(q+(-6.54095 + 5.48851i) q^{5} +(11.9650 - 4.35489i) q^{7} +(7.56521 + 6.34796i) q^{11} +(-6.10231 - 34.6079i) q^{13} +(44.7027 + 77.4273i) q^{17} +(-1.00444 + 1.73974i) q^{19} +(-33.9901 - 12.3714i) q^{23} +(-9.04572 + 51.3009i) q^{25} +(-40.5831 + 230.158i) q^{29} +(113.063 + 41.1517i) q^{31} +(-54.3604 + 94.1550i) q^{35} +(98.7263 + 170.999i) q^{37} +(4.40922 + 25.0059i) q^{41} +(410.543 + 344.487i) q^{43} +(17.7125 - 6.44681i) q^{47} +(-138.558 + 116.264i) q^{49} -366.433 q^{53} -84.3245 q^{55} +(122.347 - 102.661i) q^{59} +(385.626 - 140.356i) q^{61} +(229.861 + 192.876i) q^{65} +(152.450 + 864.586i) q^{67} +(-69.1038 - 119.691i) q^{71} +(554.236 - 959.964i) q^{73} +(118.162 + 43.0075i) q^{77} +(-48.8286 + 276.921i) q^{79} +(-168.981 + 958.337i) q^{83} +(-717.359 - 261.097i) q^{85} +(-530.757 + 919.298i) q^{89} +(-223.728 - 387.508i) q^{91} +(-2.97859 - 16.8924i) q^{95} +(-158.761 - 133.216i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 12 q^{5}+O(q^{10}) \) 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

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Database

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