LMFDB - Embedded newform 324.5.k.a.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,5,Mod(17,324)]

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, 11]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("324.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	324.k (of order $18$, 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:	$33.4918680392$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			17.3
Character	$\chi$	$=$	324.17
Dual form			324.5.k.a.305.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-26.8634 - 4.73675i) q^{5} +(65.2588 - 54.7587i) q^{7} +O(q^{10})$	$q+(-26.8634 - 4.73675i) q^{5} +(65.2588 - 54.7587i) q^{7} +(12.8354 - 2.26323i) q^{11} +(100.626 - 36.6250i) q^{13} +(-200.213 - 115.593i) q^{17} +(252.750 + 437.776i) q^{19} +(-294.915 + 351.466i) q^{23} +(111.899 + 40.7278i) q^{25} +(462.641 - 1271.10i) q^{29} +(-598.047 - 501.821i) q^{31} +(-2012.45 + 1161.89i) q^{35} +(-434.747 + 753.004i) q^{37} +(-614.297 - 1687.77i) q^{41} +(-451.587 - 2561.08i) q^{43} +(-228.689 - 272.541i) q^{47} +(843.274 - 4782.45i) q^{49} -1806.38i q^{53} -355.523 q^{55} +(-3269.88 - 576.568i) q^{59} +(-496.129 + 416.302i) q^{61} +(-2876.65 + 507.232i) q^{65} +(77.3876 - 28.1668i) q^{67} +(7307.81 + 4219.17i) q^{71} +(-4502.96 - 7799.36i) q^{73} +(713.691 - 850.544i) q^{77} +(-4575.32 - 1665.28i) q^{79} +(-4293.04 + 11795.0i) q^{83} +(4830.87 + 4053.59i) q^{85} +(-5504.23 + 3177.87i) q^{89} +(4561.23 - 7900.27i) q^{91} +(-4716.10 - 12957.4i) q^{95} +(1755.90 + 9958.19i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 9 q^{5}+O(q^{10}) $ 72 * q - 9 * q^5	$ 72 q - 9 q^{5} - 18 q^{11} + 1278 q^{23} + 441 q^{25} - 1854 q^{29} - 1665 q^{31} + 2673 q^{35} + 5472 q^{41} + 1260 q^{43} - 5103 q^{47} - 5904 q^{49} + 10944 q^{59} + 8352 q^{61} - 8757 q^{65} + 378 q^{67} + 19764 q^{71} + 6111 q^{73} + 5679 q^{77} - 5652 q^{79} + 20061 q^{83} + 26100 q^{85} - 15633 q^{89} - 6039 q^{91} - 48024 q^{95} - 37530 q^{97}+O(q^{100}) $ 72 * q - 9 * q^5 - 18 * q^11 + 1278 * q^23 + 441 * q^25 - 1854 * q^29 - 1665 * q^31 + 2673 * q^35 + 5472 * q^41 + 1260 * q^43 - 5103 * q^47 - 5904 * q^49 + 10944 * q^59 + 8352 * q^61 - 8757 * q^65 + 378 * q^67 + 19764 * q^71 + 6111 * q^73 + 5679 * q^77 - 5652 * q^79 + 20061 * q^83 + 26100 * q^85 - 15633 * q^89 - 6039 * q^91 - 48024 * q^95 - 37530 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{11}{18}\right)$

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
$5$	−26.8634	−	4.73675i	−1.07454	−	0.189470i	−0.391738	−	0.920077i	$-0.628126\pi$
$5$	−26.8634	−	4.73675i	−1.07454	−	0.189470i	−0.682798	+	0.730607i	$0.739237\pi$
$6$		0			0
$7$	65.2588	−	54.7587i	1.33181	−	1.11752i	0.348162	−	0.937434i	$-0.386806\pi$
$7$	65.2588	−	54.7587i	1.33181	−	1.11752i	0.983650	−	0.180089i	$-0.0576387\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	12.8354	−	2.26323i	0.106078	−	0.0187043i	−0.120357	−	0.992731i	$-0.538404\pi$
$11$	12.8354	−	2.26323i	0.106078	−	0.0187043i	0.226435	+	0.974026i	$0.427293\pi$
$12$		0			0
$13$	100.626	−	36.6250i	0.595423	−	0.216716i	−0.0266901	−	0.999644i	$-0.508497\pi$
$13$	100.626	−	36.6250i	0.595423	−	0.216716i	0.622113	+	0.782928i	$0.286275\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−200.213	−	115.593i	−0.692779	−	0.399976i	0.111873	−	0.993722i	$-0.464315\pi$
$17$	−200.213	−	115.593i	−0.692779	−	0.399976i	−0.804652	+	0.593746i	$0.797648\pi$
$18$		0			0
$19$	252.750	+	437.776i	0.700139	+	1.21268i	0.968417	+	0.249335i	$0.0802121\pi$
$19$	252.750	+	437.776i	0.700139	+	1.21268i	−0.268278	+	0.963342i	$0.586455\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−294.915	+	351.466i	−0.557495	+	0.664397i	−0.969014	−	0.247004i	$-0.920554\pi$
$23$	−294.915	+	351.466i	−0.557495	+	0.664397i	0.411519	+	0.911401i	$0.364998\pi$
$24$		0			0
$25$	111.899	+	40.7278i	0.179038	+	0.0651644i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	462.641	−	1271.10i	0.550109	−	1.51141i	−0.283454	−	0.958986i	$-0.591480\pi$
$29$	462.641	−	1271.10i	0.550109	−	1.51141i	0.833562	−	0.552425i	$-0.186298\pi$
$30$		0			0
$31$	−598.047	−	501.821i	−0.622317	−	0.522186i	0.276214	−	0.961096i	$-0.410920\pi$
$31$	−598.047	−	501.821i	−0.622317	−	0.522186i	−0.898531	+	0.438910i	$0.855365\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2012.45	+	1161.89i	−1.64282	+	0.948482i
$36$		0			0
$37$	−434.747	+	753.004i	−0.317565	+	0.550039i	−0.979979	−	0.199099i	$-0.936199\pi$
$37$	−434.747	+	753.004i	−0.317565	+	0.550039i	0.662414	+	0.749138i	$0.269532\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−614.297	−	1687.77i	−0.365436	−	1.00403i	−0.977076	−	0.212890i	$-0.931712\pi$
$41$	−614.297	−	1687.77i	−0.365436	−	1.00403i	0.611641	−	0.791136i	$-0.290510\pi$
$42$		0			0
$43$	−451.587	−	2561.08i	−0.244233	−	1.38512i	−0.822266	−	0.569103i	$-0.807291\pi$
$43$	−451.587	−	2561.08i	−0.244233	−	1.38512i	0.578033	−	0.816013i	$-0.303820\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−228.689	−	272.541i	−0.103526	−	0.123378i	0.711794	−	0.702389i	$-0.247883\pi$
$47$	−228.689	−	272.541i	−0.103526	−	0.123378i	−0.815320	+	0.579011i	$0.803439\pi$
$48$		0			0
$49$	843.274	−	4782.45i	0.351218	−	1.99186i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	1806.38i		−	0.643068i	−0.946898	−	0.321534i	$-0.895802\pi$
$53$		−	1806.38i		−	0.643068i	0.946898	−	0.321534i	$-0.104198\pi$
$54$		0			0
$55$	−355.523			−0.117528
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3269.88	−	576.568i	−0.939351	−	0.165633i	−0.317048	−	0.948409i	$-0.602692\pi$
$59$	−3269.88	−	576.568i	−0.939351	−	0.165633i	−0.622303	+	0.782777i	$0.713803\pi$
$60$		0			0
$61$	−496.129	+	416.302i	−0.133332	+	0.111879i	−0.707015	−	0.707199i	$-0.749959\pi$
$61$	−496.129	+	416.302i	−0.133332	+	0.111879i	0.573683	+	0.819078i	$0.305514\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2876.65	+	507.232i	−0.680865	+	0.120055i
$66$		0			0
$67$	77.3876	−	28.1668i	0.0172394	−	0.00627462i	−0.333386	−	0.942790i	$-0.608191\pi$
$67$	77.3876	−	28.1668i	0.0172394	−	0.00627462i	0.350625	+	0.936516i	$0.385969\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	7307.81	+	4219.17i	1.44968	+	0.836970i	0.998462	−	0.0554456i	$-0.0176579\pi$
$71$	7307.81	+	4219.17i	1.44968	+	0.836970i	0.451214	+	0.892416i	$0.350991\pi$
$72$		0			0
$73$	−4502.96	−	7799.36i	−0.844992	−	1.46357i	−0.885629	−	0.464394i	$-0.846272\pi$
$73$	−4502.96	−	7799.36i	−0.844992	−	1.46357i	0.0406371	−	0.999174i	$-0.487061\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	713.691	−	850.544i	0.120373	−	0.143455i
$78$		0			0
$79$	−4575.32	−	1665.28i	−0.733107	−	0.266829i	−0.0516274	−	0.998666i	$-0.516441\pi$
$79$	−4575.32	−	1665.28i	−0.733107	−	0.266829i	−0.681479	+	0.731837i	$0.738663\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4293.04	+	11795.0i	−0.623174	+	1.71216i	0.0759092	+	0.997115i	$0.475814\pi$
$83$	−4293.04	+	11795.0i	−0.623174	+	1.71216i	−0.699083	+	0.715041i	$0.746408\pi$
$84$		0			0
$85$	4830.87	+	4053.59i	0.668633	+	0.561050i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5504.23	+	3177.87i	−0.694891	+	0.401196i	−0.805442	−	0.592675i	$-0.798072\pi$
$89$	−5504.23	+	3177.87i	−0.694891	+	0.401196i	0.110551	+	0.993870i	$0.464739\pi$
$90$		0			0
$91$	4561.23	−	7900.27i	0.550806	−	0.954024i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4716.10	−	12957.4i	−0.522560	−	1.43572i
$96$		0			0
$97$	1755.90	+	9958.19i	0.186619	+	1.05837i	0.923858	+	0.382736i	$0.125018\pi$
$97$	1755.90	+	9958.19i	0.186619	+	1.05837i	−0.737239	+	0.675632i	$0.763871\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9718.55	−	11582.1i	−0.952705	−	1.13539i	−0.990694	−	0.136112i	$-0.956539\pi$
$101$	−9718.55	−	11582.1i	−0.952705	−	1.13539i	0.0379884	−	0.999278i	$-0.487905\pi$
$102$		0			0
$103$	2796.51	−	15859.8i	0.263597	−	1.49494i	−0.509402	−	0.860529i	$-0.670133\pi$
$103$	2796.51	−	15859.8i	0.263597	−	1.49494i	0.772999	−	0.634407i	$-0.218756\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	21225.3i		−	1.85390i	−0.375190	−	0.926948i	$-0.622423\pi$
$107$		−	21225.3i		−	1.85390i	0.375190	−	0.926948i	$-0.377577\pi$
$108$		0			0
$109$	−14761.1			−1.24241			−0.621205	−	0.783648i	$-0.713357\pi$
$109$	−14761.1			−1.24241			−0.621205	+	0.783648i	$0.713357\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3332.45	−	587.601i	−0.260980	−	0.0460178i	0.0416272	−	0.999133i	$-0.486746\pi$
$113$	−3332.45	−	587.601i	−0.260980	−	0.0460178i	−0.302607	+	0.953115i	$0.597857\pi$
$114$		0			0
$115$	9587.23	−	8044.64i	0.724932	−	0.608291i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−19395.4	+	3419.93i	−1.36963	+	0.241504i
$120$		0			0
$121$	−13598.4	+	4949.42i	−0.928790	+	0.338052i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11951.5	+	6900.20i	0.764896	+	0.441613i
$126$		0			0
$127$	2355.54	+	4079.91i	0.146044	+	0.252955i	0.929762	−	0.368161i	$-0.120013\pi$
$127$	2355.54	+	4079.91i	0.146044	+	0.252955i	−0.783718	+	0.621117i	$0.786679\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	10758.1	−	12821.0i	0.626891	−	0.747100i	−0.355348	−	0.934734i	$-0.615638\pi$
$131$	10758.1	−	12821.0i	0.626891	−	0.747100i	0.982239	+	0.187634i	$0.0600820\pi$
$132$		0			0
$133$	40466.2	+	14728.5i	2.28765	+	0.832636i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−767.514	+	2108.73i	−0.0408926	+	0.112352i	−0.958458	−	0.285233i	$-0.907929\pi$
$137$	−767.514	+	2108.73i	−0.0408926	+	0.112352i	0.917566	+	0.397584i	$0.130151\pi$
$138$		0			0
$139$	−2719.82	−	2282.20i	−0.140770	−	0.118120i	0.569683	−	0.821864i	$-0.307066\pi$
$139$	−2719.82	−	2282.20i	−0.140770	−	0.118120i	−0.710454	+	0.703744i	$0.751510\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1208.69	−	697.837i	0.0591075	−	0.0341257i
$144$		0			0
$145$	−18449.0	+	31954.6i	−0.877479	+	1.51984i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11427.7	+	31397.2i	0.514736	+	1.41423i	0.876249	+	0.481858i	$0.160038\pi$
$149$	11427.7	+	31397.2i	0.514736	+	1.41423i	−0.361513	+	0.932367i	$0.617740\pi$
$150$		0			0
$151$	2323.52	+	13177.3i	0.101904	+	0.577927i	0.992412	+	0.122959i	$0.0392383\pi$
$151$	2323.52	+	13177.3i	0.101904	+	0.577927i	−0.890508	+	0.454968i	$0.849651\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	13688.6	+	16313.4i	0.569764	+	0.679019i
$156$		0			0
$157$	3452.54	−	19580.3i	0.140068	−	0.794366i	−0.831127	−	0.556082i	$-0.812304\pi$
$157$	3452.54	−	19580.3i	0.140068	−	0.794366i	0.971195	−	0.238284i	$-0.0765849\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			39085.4i			1.50787i
$162$		0			0
$163$	−7104.46			−0.267397			−0.133698	−	0.991022i	$-0.542685\pi$
$163$	−7104.46			−0.267397			−0.133698	+	0.991022i	$0.542685\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	17679.4	+	3117.35i	0.633919	+	0.111777i	0.481368	−	0.876519i	$-0.340140\pi$
$167$	17679.4	+	3117.35i	0.633919	+	0.111777i	0.152551	+	0.988296i	$0.451251\pi$
$168$		0			0
$169$	−13094.7	+	10987.8i	−0.458482	+	0.384712i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	21158.4	−	3730.80i	0.706953	−	0.124655i	0.191400	−	0.981512i	$-0.438697\pi$
$173$	21158.4	−	3730.80i	0.706953	−	0.124655i	0.515554	+	0.856857i	$0.327586\pi$
$174$		0			0
$175$	9532.57	−	3469.57i	0.311268	−	0.113292i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	30928.3	+	17856.5i	0.965274	+	0.557301i	0.897792	−	0.440419i	$-0.145170\pi$
$179$	30928.3	+	17856.5i	0.965274	+	0.557301i	0.0674816	+	0.997721i	$0.478504\pi$
$180$		0			0
$181$	3407.07	+	5901.22i	0.103998	+	0.180129i	0.913328	−	0.407224i	$-0.133503\pi$
$181$	3407.07	+	5901.22i	0.103998	+	0.180129i	−0.809331	+	0.587353i	$0.800170\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	15245.6	−	18169.0i	0.445451	−	0.530868i
$186$		0			0
$187$	−2831.43	−	1030.56i	−0.0809696	−	0.0294705i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8403.46	+	23088.3i	−0.230352	+	0.632886i	−0.999984	−	0.00560103i	$-0.998217\pi$
$191$	−8403.46	+	23088.3i	−0.230352	+	0.632886i	0.769633	+	0.638487i	$0.220439\pi$
$192$		0			0
$193$	10632.4	+	8921.65i	0.285442	+	0.239514i	0.774254	−	0.632875i	$-0.218125\pi$
$193$	10632.4	+	8921.65i	0.285442	+	0.239514i	−0.488812	+	0.872389i	$0.662570\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	58910.9	−	34012.2i	1.51797	−	0.876400i	0.518193	−	0.855264i	$-0.326605\pi$
$197$	58910.9	−	34012.2i	1.51797	−	0.876400i	0.999777	−	0.0211363i	$-0.00672839\pi$
$198$		0			0
$199$	−20434.4	+	35393.5i	−0.516008	+	0.893753i	0.483819	+	0.875168i	$0.339249\pi$
$199$	−20434.4	+	35393.5i	−0.516008	+	0.893753i	−0.999827	+	0.0185845i	$0.994084\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−39412.1	−	108284.i	−0.956396	−	2.62768i
$204$		0			0
$205$	8507.60	+	48249.0i	0.202441	+	1.14810i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4234.93	+	5047.00i	0.0969514	+	0.115542i
$210$		0			0
$211$	12341.3	−	69991.0i	0.277202	−	1.57209i	−0.454677	−	0.890656i	$-0.650245\pi$
$211$	12341.3	−	69991.0i	0.277202	−	1.57209i	0.731879	−	0.681434i	$-0.238644\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			70938.4i			1.53463i
$216$		0			0
$217$	−66506.9			−1.41237
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−24380.3	−	4298.91i	−0.499178	−	0.0880185i
$222$		0			0
$223$	−28933.9	+	24278.4i	−0.581831	+	0.488214i	−0.885548	−	0.464548i	$-0.846217\pi$
$223$	−28933.9	+	24278.4i	−0.581831	+	0.488214i	0.303717	+	0.952762i	$0.401772\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−18048.0	+	3182.34i	−0.350248	+	0.0617582i	−0.346005	−	0.938233i	$-0.612462\pi$
$227$	−18048.0	+	3182.34i	−0.350248	+	0.0617582i	−0.00424364	+	0.999991i	$0.501351\pi$
$228$		0			0
$229$	34821.6	−	12674.0i	0.664014	−	0.241681i	0.0120457	−	0.999927i	$-0.496166\pi$
$229$	34821.6	−	12674.0i	0.664014	−	0.241681i	0.651969	+	0.758246i	$0.273943\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	61518.1	+	35517.5i	1.13316	+	0.654230i	0.944728	−	0.327856i	$-0.106326\pi$
$233$	61518.1	+	35517.5i	1.13316	+	0.654230i	0.188433	+	0.982086i	$0.439659\pi$
$234$		0			0
$235$	4852.41	+	8404.63i	0.0878662	+	0.152189i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	20774.2	−	24757.8i	0.363688	−	0.433427i	−0.552907	−	0.833243i	$-0.686482\pi$
$239$	20774.2	−	24757.8i	0.363688	−	0.433427i	0.916595	+	0.399816i	$0.130926\pi$
$240$		0			0
$241$	32367.0	+	11780.6i	0.557273	+	0.202831i	0.605275	−	0.796016i	$-0.293063\pi$
$241$	32367.0	+	11780.6i	0.557273	+	0.202831i	−0.0480017	+	0.998847i	$0.515285\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−45306.5	+	124479.i	−0.754793	+	2.07378i
$246$		0			0
$247$	41466.9	+	34794.9i	0.679685	+	0.570324i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	78128.6	−	45107.6i	1.24012	−	0.715982i	0.270999	−	0.962580i	$-0.412646\pi$
$251$	78128.6	−	45107.6i	1.24012	−	0.715982i	0.969118	+	0.246598i	$0.0793128\pi$
$252$		0			0
$253$	−2989.90	+	5178.66i	−0.0467107	+	0.0809052i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8379.78	−	23023.3i	−0.126872	−	0.348578i	0.859952	−	0.510375i	$-0.170493\pi$
$257$	−8379.78	−	23023.3i	−0.126872	−	0.348578i	−0.986824	+	0.161797i	$0.948271\pi$
$258$		0			0
$259$	12862.4	+	72946.3i	0.191744	+	1.08744i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−77000.3	−	91765.4i	−1.11322	−	1.32668i	−0.939757	−	0.341843i	$-0.888949\pi$
$263$	−77000.3	−	91765.4i	−1.11322	−	1.32668i	−0.173462	−	0.984840i	$-0.555496\pi$
$264$		0			0
$265$	−8556.35	+	48525.5i	−0.121842	+	0.691000i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			100139.i			1.38388i	0.721957	+	0.691938i	$0.243243\pi$
$269$			100139.i			1.38388i	−0.721957	+	0.691938i	$0.756757\pi$
$270$		0			0
$271$	−17954.2			−0.244471			−0.122235	−	0.992501i	$-0.539006\pi$
$271$	−17954.2			−0.244471			−0.122235	+	0.992501i	$0.539006\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1528.44	+	269.505i	0.0202108	+	0.00356370i
$276$		0			0
$277$	6267.43	−	5259.00i	0.0816827	−	0.0685399i	−0.601032	−	0.799225i	$-0.705244\pi$
$277$	6267.43	−	5259.00i	0.0816827	−	0.0685399i	0.682715	+	0.730685i	$0.260799\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4651.41	+	820.169i	−0.0589077	+	0.0103870i	−0.203024	−	0.979174i	$-0.565077\pi$
$281$	−4651.41	+	820.169i	−0.0589077	+	0.0103870i	0.144117	+	0.989561i	$0.453966\pi$
$282$		0			0
$283$	139860.	−	50904.8i	1.74630	−	0.635602i	0.746739	−	0.665117i	$-0.231619\pi$
$283$	139860.	−	50904.8i	1.74630	−	0.635602i	0.999564	+	0.0295151i	$0.00939631\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−132508.	−	76503.6i	−1.60871	−	0.928792i
$288$		0			0
$289$	−15037.0	−	26044.8i	−0.180038	−	0.311835i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	21937.2	−	26143.7i	0.255532	−	0.304532i	−0.622993	−	0.782228i	$-0.714083\pi$
$293$	21937.2	−	26143.7i	0.255532	−	0.304532i	0.878525	+	0.477696i	$0.158528\pi$
$294$		0			0
$295$	85109.1	+	30977.2i	0.977985	+	0.355957i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−16803.8	+	46168.1i	−0.187960	+	0.516415i
$300$		0			0
$301$	−169711.	−	142405.i	−1.87317	−	1.57178i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	15299.6	−	8833.25i	0.164468	−	0.0949557i
$306$		0			0
$307$	15537.3	−	26911.4i	0.164854	−	0.285536i	−0.771749	−	0.635927i	$-0.780618\pi$
$307$	15537.3	−	26911.4i	0.164854	−	0.285536i	0.936603	+	0.350391i	$0.113951\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−15790.1	−	43382.8i	−0.163254	−	0.448536i	0.830911	−	0.556405i	$-0.187820\pi$
$311$	−15790.1	−	43382.8i	−0.163254	−	0.448536i	−0.994165	+	0.107869i	$0.965597\pi$
$312$		0			0
$313$	−10783.4	−	61155.9i	−0.110070	−	0.624237i	−0.989074	−	0.147422i	$-0.952902\pi$
$313$	−10783.4	−	61155.9i	−0.110070	−	0.624237i	0.879004	−	0.476815i	$-0.158209\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−37079.6	−	44189.8i	−0.368992	−	0.439748i	0.549316	−	0.835615i	$-0.314888\pi$
$317$	−37079.6	−	44189.8i	−0.368992	−	0.439748i	−0.918308	+	0.395867i	$0.870444\pi$
$318$		0			0
$319$	3061.40	−	17362.1i	0.0300843	−	0.170616i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	116865.i		−	1.12016i
$324$		0			0
$325$	12751.6			0.120725
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−29848.0	−	5263.00i	−0.275755	−	0.0486230i
$330$		0			0
$331$	153771.	−	129029.i	1.40352	−	1.17769i	0.444006	−	0.896024i	$-0.353557\pi$
$331$	153771.	−	129029.i	1.40352	−	1.17769i	0.959512	−	0.281668i	$-0.0908877\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2212.31	+	390.091i	−0.0197132	+	0.00347597i
$336$		0			0
$337$	−129281.	+	47054.6i	−1.13835	+	0.414326i	−0.841318	−	0.540541i	$-0.818220\pi$
$337$	−129281.	+	47054.6i	−1.13835	+	0.414326i	−0.297033	+	0.954867i	$0.595997\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8811.90	−	5087.55i	−0.0757811	−	0.0437522i
$342$		0			0
$343$	−104579.	−	181137.i	−0.888911	−	1.53964i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−63689.4	+	75902.0i	−0.528942	+	0.630368i	−0.962671	−	0.270675i	$-0.912753\pi$
$347$	−63689.4	+	75902.0i	−0.528942	+	0.630368i	0.433729	+	0.901043i	$0.357198\pi$
$348$		0			0
$349$	−59048.7	−	21492.0i	−0.484796	−	0.176451i	0.0880471	−	0.996116i	$-0.471937\pi$
$349$	−59048.7	−	21492.0i	−0.484796	−	0.176451i	−0.572843	+	0.819665i	$0.694160\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−16363.2	+	44957.4i	−0.131316	+	0.360788i	−0.987873	−	0.155265i	$-0.950377\pi$
$353$	−16363.2	+	44957.4i	−0.131316	+	0.360788i	0.856557	+	0.516053i	$0.172599\pi$
$354$		0			0
$355$	−176328.	−	147957.i	−1.39915	−	1.17403i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−84648.7	+	48871.9i	−0.656797	+	0.379202i	−0.791055	−	0.611744i	$-0.790468\pi$
$359$	−84648.7	+	48871.9i	−0.656797	+	0.379202i	0.134258	+	0.990946i	$0.457135\pi$
$360$		0			0
$361$	−62604.9	+	108435.i	−0.480390	+	0.832060i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	84021.3	+	230847.i	0.630672	+	1.73276i
$366$		0			0
$367$	1042.91	+	5914.63i	0.00774308	+	0.0439132i	0.988434	−	0.151648i	$-0.0484581\pi$
$367$	1042.91	+	5914.63i	0.00774308	+	0.0439132i	−0.980691	+	0.195562i	$0.937347\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−98914.8	−	117882.i	−0.718644	−	0.856446i
$372$		0			0
$373$	−4182.98	+	23722.8i	−0.0300654	+	0.170510i	−0.996143	−	0.0877414i	$-0.972035\pi$
$373$	−4182.98	+	23722.8i	−0.0300654	+	0.170510i	0.966078	+	0.258251i	$0.0831462\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	144850.i		−	1.01915i
$378$		0			0
$379$	−132967.			−0.925689			−0.462844	−	0.886440i	$-0.653171\pi$
$379$	−132967.			−0.925689			−0.462844	+	0.886440i	$0.653171\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	43325.4	+	7639.43i	0.295355	+	0.0520791i	0.319362	−	0.947633i	$-0.396531\pi$
$383$	43325.4	+	7639.43i	0.295355	+	0.0520791i	−0.0240071	+	0.999712i	$0.507642\pi$
$384$		0			0
$385$	−23201.0	+	19467.9i	−0.156526	+	0.131341i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	58930.3	−	10391.0i	0.389439	−	0.0686686i	0.0244994	−	0.999700i	$-0.492201\pi$
$389$	58930.3	−	10391.0i	0.389439	−	0.0686686i	0.364939	+	0.931031i	$0.381090\pi$
$390$		0			0
$391$	99672.9	−	36278.0i	0.651964	−	0.237296i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	115021.	+	66407.2i	0.737194	+	0.425619i
$396$		0			0
$397$	88828.3	+	153855.i	0.563599	+	0.976182i	0.997179	+	0.0750668i	$0.0239170\pi$
$397$	88828.3	+	153855.i	0.563599	+	0.976182i	−0.433579	+	0.901115i	$0.642750\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	107489.	−	128100.i	0.668459	−	0.796639i	−0.320114	−	0.947379i	$-0.603721\pi$
$401$	107489.	−	128100.i	0.668459	−	0.796639i	0.988573	+	0.150740i	$0.0481657\pi$
$402$		0			0
$403$	−78558.5	−	28593.0i	−0.483708	−	0.176055i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3875.93	+	10649.0i	−0.0233984	+	0.0642867i
$408$		0			0
$409$	153961.	+	129189.i	0.920376	+	0.772287i	0.974064	−	0.226271i	$-0.0726535\pi$
$409$	153961.	+	129189.i	0.920376	+	0.772287i	−0.0536889	+	0.998558i	$0.517098\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−244961.	+	141428.i	−1.43614	+	0.829155i
$414$		0			0
$415$	171196.	−	296520.i	0.994025	−	1.72170i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−81421.9	−	223705.i	−0.463781	−	1.27423i	−0.922620	−	0.385710i	$-0.873957\pi$
$419$	−81421.9	−	223705.i	−0.463781	−	1.27423i	0.458839	−	0.888520i	$-0.348266\pi$
$420$		0			0
$421$	−43202.1	−	245011.i	−0.243748	−	1.38236i	−0.823382	−	0.567487i	$-0.807916\pi$
$421$	−43202.1	−	245011.i	−0.243748	−	1.38236i	0.579634	−	0.814877i	$-0.303195\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−17695.7	−	21088.9i	−0.0979694	−	0.116755i
$426$		0			0
$427$	−9580.68	+	54334.7i	−0.0525461	+	0.298004i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			46314.3i			0.249322i	0.992199	+	0.124661i	$0.0397844\pi$
$431$			46314.3i			0.249322i	−0.992199	+	0.124661i	$0.960216\pi$
$432$		0			0
$433$	180059.			0.960369			0.480184	−	0.877168i	$-0.340570\pi$
$433$	180059.			0.960369			0.480184	+	0.877168i	$0.340570\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−228403.	−	40273.7i	−1.19602	−	0.210891i
$438$		0			0
$439$	−188675.	+	158317.i	−0.979005	+	0.821483i	−0.983939	−	0.178505i	$-0.942874\pi$
$439$	−188675.	+	158317.i	−0.979005	+	0.821483i	0.00493404	+	0.999988i	$0.498429\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	188942.	−	33315.6i	0.962767	−	0.169762i	0.329894	−	0.944018i	$-0.392987\pi$
$443$	188942.	−	33315.6i	0.962767	−	0.169762i	0.632873	+	0.774256i	$0.281876\pi$
$444$		0			0
$445$	162915.	−	59296.3i	0.822701	−	0.299439i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−12120.0	−	6997.51i	−0.0601190	−	0.0347097i	0.469639	−	0.882858i	$-0.344384\pi$
$449$	−12120.0	−	6997.51i	−0.0601190	−	0.0347097i	−0.529758	+	0.848149i	$0.677717\pi$
$450$		0			0
$451$	−11704.5	−	20272.9i	−0.0575442	−	0.0996694i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−159952.	+	190623.i	−0.772620	+	0.920773i
$456$		0			0
$457$	180110.	+	65554.6i	0.862392	+	0.313885i	0.735082	−	0.677978i	$-0.237143\pi$
$457$	180110.	+	65554.6i	0.862392	+	0.313885i	0.127310	+	0.991863i	$0.459366\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−65887.5	+	181024.i	−0.310028	+	0.851796i	0.682621	+	0.730772i	$0.260840\pi$
$461$	−65887.5	+	181024.i	−0.310028	+	0.851796i	−0.992650	+	0.121023i	$0.961382\pi$
$462$		0			0
$463$	180090.	+	151114.i	0.840095	+	0.704923i	0.957585	−	0.288151i	$-0.0930404\pi$
$463$	180090.	+	151114.i	0.840095	+	0.704923i	−0.117490	+	0.993074i	$0.537485\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	66079.7	−	38151.1i	0.302994	−	0.174934i	−0.340793	−	0.940138i	$-0.610696\pi$
$467$	66079.7	−	38151.1i	0.302994	−	0.174934i	0.643787	+	0.765205i	$0.277362\pi$
$468$		0			0
$469$	3507.85	−	6075.77i	0.0159476	−	0.0276220i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−11592.6	−	31850.4i	−0.0518154	−	0.142362i
$474$		0			0
$475$	10452.8	+	59280.5i	0.0463280	+	0.262739i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−152747.	−	182037.i	−0.665737	−	0.793395i	0.322460	−	0.946583i	$-0.395490\pi$
$479$	−152747.	−	182037.i	−0.665737	−	0.793395i	−0.988197	+	0.153189i	$0.951046\pi$
$480$		0			0
$481$	−16168.2	+	91694.7i	−0.0698832	+	0.396327i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	275828.i		−	1.17261i
$486$		0			0
$487$	281593.			1.18731			0.593654	−	0.804720i	$-0.297685\pi$
$487$	281593.			1.18731			0.593654	+	0.804720i	$0.297685\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	39942.1	+	7042.87i	0.165679	+	0.0292137i	0.255872	−	0.966711i	$-0.417637\pi$
$491$	39942.1	+	7042.87i	0.165679	+	0.0292137i	−0.0901931	+	0.995924i	$0.528748\pi$
$492$		0			0
$493$	−239557.	+	201012.i	−0.985632	+	0.827044i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	707935.	−	124828.i	2.86603	−	0.505358i
$498$		0			0
$499$	−130143.	+	47368.3i	−0.522662	+	0.190233i	−0.589859	−	0.807506i	$-0.700817\pi$
$499$	−130143.	+	47368.3i	−0.522662	+	0.190233i	0.0671970	+	0.997740i	$0.478594\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	337356.	+	194773.i	1.33338	+	0.769825i	0.985816	−	0.167833i	$-0.0536768\pi$
$503$	337356.	+	194773.i	1.33338	+	0.769825i	0.347560	+	0.937658i	$0.387010\pi$
$504$		0			0
$505$	206212.	+	357169.i	0.808595	+	1.40053i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5930.47	+	7067.66i	−0.0228904	+	0.0272797i	−0.777368	−	0.629046i	$-0.783446\pi$
$509$	−5930.47	+	7067.66i	−0.0228904	+	0.0272797i	0.754478	+	0.656326i	$0.227890\pi$
$510$		0			0
$511$	−720940.	−	262401.i	−2.76094	−	1.00490i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−150247.	+	412801.i	−0.566490	+	1.55642i
$516$		0			0
$517$	−3552.13	−	2980.60i	−0.0132895	−	0.0111512i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−254302.	+	146821.i	−0.936858	+	0.540895i	−0.888974	−	0.457957i	$-0.848581\pi$
$521$	−254302.	+	146821.i	−0.936858	+	0.540895i	−0.0478843	+	0.998853i	$0.515248\pi$
$522$		0			0
$523$	−136185.	+	235879.i	−0.497880	+	0.862354i	−0.999997	−	0.00244613i	$-0.999221\pi$
$523$	−136185.	+	235879.i	−0.497880	+	0.862354i	0.502117	+	0.864800i	$0.332555\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	61729.8	+	169601.i	0.222266	+	0.610672i
$528$		0			0
$529$	12040.4	+	68284.3i	0.0430257	+	0.244011i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−123629.	−	147335.i	−0.435177	−	0.518624i
$534$		0			0
$535$	−100539.	+	570183.i	−0.351257	+	1.99208i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	63293.1i		−	0.217861i
$540$		0			0
$541$	−47565.3			−0.162516			−0.0812579	−	0.996693i	$-0.525894\pi$
$541$	−47565.3			−0.162516			−0.0812579	+	0.996693i	$0.525894\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	396533.	+	69919.4i	1.33502	+	0.235399i
$546$		0			0
$547$	433454.	−	363711.i	1.44867	−	1.21558i	0.515120	−	0.857118i	$-0.327747\pi$
$547$	433454.	−	363711.i	1.44867	−	1.21558i	0.933546	−	0.358457i	$-0.116697\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	673389.	−	118737.i	2.21801	−	0.391094i
$552$		0			0
$553$	−389768.	+	141864.i	−1.27455	+	0.463898i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−485600.	−	280361.i	−1.56519	−	0.903666i	−0.996717	−	0.0809672i	$-0.974199\pi$
$557$	−485600.	−	280361.i	−1.56519	−	0.903666i	−0.568478	−	0.822698i	$-0.692468\pi$
$558$		0			0
$559$	−139241.	−	241173.i	−0.445599	−	0.771800i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−59896.6	+	71382.0i	−0.188967	+	0.225202i	−0.852207	−	0.523205i	$-0.824736\pi$
$563$	−59896.6	+	71382.0i	−0.188967	+	0.225202i	0.663240	+	0.748407i	$0.269181\pi$
$564$		0			0
$565$	86737.7	+	31569.9i	0.271713	+	0.0988956i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	211430.	−	580900.i	0.653044	−	1.79422i	0.0468588	−	0.998902i	$-0.485079\pi$
$569$	211430.	−	580900.i	0.653044	−	1.79422i	0.606186	−	0.795323i	$-0.292699\pi$
$570$		0			0
$571$	354836.	+	297743.i	1.08832	+	0.913208i	0.996585	−	0.0825758i	$-0.0263147\pi$
$571$	354836.	+	297743.i	1.08832	+	0.913208i	0.0917339	+	0.995784i	$0.470759\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−47315.0	+	27317.3i	−0.143108	+	0.0826233i
$576$		0			0
$577$	7019.69	−	12158.5i	0.0210846	−	0.0365197i	−0.855291	−	0.518149i	$-0.826621\pi$
$577$	7019.69	−	12158.5i	0.0210846	−	0.0365197i	0.876375	+	0.481629i	$0.159955\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	365722.	+	1.00481e6i	1.08342	+	2.97668i
$582$		0			0
$583$	−4088.24	−	23185.6i	−0.0120282	−	0.0682151i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−41989.5	−	50041.1i	−0.121861	−	0.145228i	0.701665	−	0.712507i	$-0.252440\pi$
$587$	−41989.5	−	50041.1i	−0.121861	−	0.145228i	−0.823526	+	0.567279i	$0.807996\pi$
$588$		0			0
$589$	68528.8	−	388646.i	0.197534	−	1.12027i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			169695.i			0.482569i	0.970454	+	0.241285i	$0.0775688\pi$
$593$			169695.i			0.482569i	−0.970454	+	0.241285i	$0.922431\pi$
$594$		0			0
$595$	537226.			1.51748
$596$		0			0
$597$		0			0
$598$		0			0
$599$	353915.	+	62404.8i	0.986383	+	0.173926i	0.643495	−	0.765451i	$-0.277484\pi$
$599$	353915.	+	62404.8i	0.986383	+	0.173926i	0.342888	+	0.939376i	$0.388595\pi$
$600$		0			0
$601$	119233.	−	100048.i	0.330102	−	0.276988i	−0.462640	−	0.886546i	$-0.653098\pi$
$601$	119233.	−	100048.i	0.330102	−	0.276988i	0.792741	+	0.609558i	$0.208653\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	388744.	−	68546.1i	1.06207	−	0.187272i
$606$		0			0
$607$	−550382.	+	200323.i	−1.49378	+	0.543691i	−0.954442	−	0.298398i	$-0.903548\pi$
$607$	−550382.	+	200323.i	−1.49378	+	0.543691i	−0.539338	+	0.842089i	$0.681326\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−32994.0	−	19049.1i	−0.0883797	−	0.0510260i
$612$		0			0
$613$	134825.	+	233523.i	0.358797	+	0.621454i	0.987760	−	0.155981i	$-0.0498538\pi$
$613$	134825.	+	233523.i	0.358797	+	0.621454i	−0.628963	+	0.777435i	$0.716520\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−324359.	+	386556.i	−0.852031	+	1.01541i	0.147621	+	0.989044i	$0.452838\pi$
$617$	−324359.	+	386556.i	−0.852031	+	1.01541i	−0.999652	+	0.0263669i	$0.991606\pi$
$618$		0			0
$619$	260218.	+	94711.4i	0.679134	+	0.247184i	0.658476	−	0.752602i	$-0.271202\pi$
$619$	260218.	+	94711.4i	0.679134	+	0.247184i	0.0206582	+	0.999787i	$0.493424\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−185184.	+	508788.i	−0.477119	+	1.31087i
$624$		0			0
$625$	−345386.	−	289814.i	−0.884189	−	0.741923i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	174084.	−	100508.i	0.440005	−	0.254037i
$630$		0			0
$631$	201748.	−	349438.i	0.506700	−	0.877631i	−0.493269	−	0.869877i	$-0.664198\pi$
$631$	201748.	−	349438.i	0.506700	−	0.877631i	0.999970	−	0.00775442i	$-0.00246833\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−43952.3	−	120758.i	−0.109002	−	0.299480i
$636$		0			0
$637$	−90301.6	−	512126.i	−0.222544	−	1.26211i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−146534.	−	174633.i	−0.356634	−	0.425020i	0.557661	−	0.830069i	$-0.311699\pi$
$641$	−146534.	−	174633.i	−0.356634	−	0.425020i	−0.914295	+	0.405049i	$0.867254\pi$
$642$		0			0
$643$	−21894.5	+	124170.i	−0.0529557	+	0.300327i	−0.999770	−	0.0214542i	$-0.993170\pi$
$643$	−21894.5	+	124170.i	−0.0529557	+	0.300327i	0.946814	+	0.321781i	$0.104282\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	88320.7i		−	0.210986i	−0.994420	−	0.105493i	$-0.966358\pi$
$647$		−	88320.7i		−	0.210986i	0.994420	−	0.105493i	$-0.0336421\pi$
$648$		0			0
$649$	−43275.1			−0.102742
$650$		0			0
$651$		0			0
$652$		0			0
$653$	624814.	+	110172.i	1.46529	+	0.258370i	0.848684	−	0.528900i	$-0.177395\pi$
$653$	624814.	+	110172.i	1.46529	+	0.258370i	0.616608	+	0.787271i	$0.288506\pi$
$654$		0			0
$655$	−349728.	+	293457.i	−0.815170	+	0.684009i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−63931.3	+	11272.8i	−0.147212	+	0.0259574i	−0.246768	−	0.969074i	$-0.579369\pi$
$659$	−63931.3	+	11272.8i	−0.147212	+	0.0259574i	0.0995565	+	0.995032i	$0.468258\pi$
$660$		0			0
$661$	−463801.	+	168810.i	−1.06152	+	0.386362i	−0.813000	−	0.582264i	$-0.802167\pi$
$661$	−463801.	+	168810.i	−1.06152	+	0.386362i	−0.248522	+	0.968626i	$0.579945\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.01730e6	−	587336.i	−2.30040	−	1.32814i
$666$		0			0
$667$	310308.	+	537468.i	0.697494	+	1.20810i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−5425.83	+	6466.25i	−0.0120509	+	0.0143618i
$672$		0			0
$673$	211186.	+	76865.4i	0.466267	+	0.169707i	0.564461	−	0.825460i	$-0.309084\pi$
$673$	211186.	+	76865.4i	0.466267	+	0.169707i	−0.0981936	+	0.995167i	$0.531306\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1249.59	−	3433.23i	0.00272641	−	0.00749075i	−0.938322	−	0.345763i	$-0.887620\pi$
$677$	1249.59	−	3433.23i	0.00272641	−	0.00749075i	0.941048	+	0.338272i	$0.109842\pi$
$678$		0			0
$679$	659885.	+	553709.i	1.43129	+	1.20100i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	534916.	−	308834.i	1.14668	−	0.662038i	0.198607	−	0.980079i	$-0.436358\pi$
$683$	534916.	−	308834.i	1.14668	−	0.662038i	0.948077	+	0.318041i	$0.103025\pi$
$684$		0			0
$685$	30606.5	−	53012.1i	0.0652278	−	0.112978i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−66158.7	−	181769.i	−0.139363	−	0.382897i
$690$		0			0
$691$	70343.2	+	398936.i	0.147322	+	0.835502i	0.965474	+	0.260500i	$0.0838875\pi$
$691$	70343.2	+	398936.i	0.147322	+	0.835502i	−0.818152	+	0.575002i	$0.805001\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	62253.5	+	74190.8i	0.128883	+	0.153596i
$696$		0			0
$697$	−72103.9	+	408922.i	−0.148420	+	0.841734i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			327328.i			0.666111i	0.942907	+	0.333056i	$0.108080\pi$
$701$			327328.i			0.666111i	−0.942907	+	0.333056i	$0.891920\pi$
$702$		0			0
$703$	−439530.			−0.889360
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.26844e6	−	223660.i	−2.53765	−	0.447456i
$708$		0			0
$709$	319485.	−	268079.i	0.635561	−	0.533299i	−0.267090	−	0.963672i	$-0.586062\pi$
$709$	319485.	−	268079.i	0.635561	−	0.533299i	0.902652	+	0.430372i	$0.141618\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	352746.	−	62198.7i	0.693878	−	0.122349i
$714$		0			0
$715$	−35775.0	+	13021.0i	−0.0699789	+	0.0254703i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−17170.6	−	9913.42i	−0.0332144	−	0.0191763i	0.483301	−	0.875454i	$-0.339438\pi$
$719$	−17170.6	−	9913.42i	−0.0332144	−	0.0191763i	−0.516515	+	0.856278i	$0.672771\pi$
$720$		0			0
$721$	−685963.	−	1.18812e6i	−1.31956	−	2.28555i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	103538.	−	123392.i	0.196981	−	0.234752i
$726$		0			0
$727$	−834237.	−	303637.i	−1.57841	−	0.574495i	−0.603555	−	0.797321i	$-0.706250\pi$
$727$	−834237.	−	303637.i	−1.57841	−	0.574495i	−0.974858	+	0.222826i	$0.928472\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−205629.	+	564962.i	−0.384814	+	1.05727i
$732$		0			0
$733$	298436.	+	250417.i	0.555447	+	0.466076i	0.876781	−	0.480890i	$-0.159687\pi$
$733$	298436.	+	250417.i	0.555447	+	0.466076i	−0.321333	+	0.946966i	$0.604131\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	929.552	−	536.677i	0.00171135	−	0.000988048i
$738$		0			0
$739$	417334.	−	722844.i	0.764179	−	1.32360i	−0.176500	−	0.984301i	$-0.556478\pi$
$739$	417334.	−	722844.i	0.764179	−	1.32360i	0.940679	−	0.339297i	$-0.110189\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	48455.3	+	133130.i	0.0877735	+	0.241156i	0.975811	−	0.218615i	$-0.0701538\pi$
$743$	48455.3	+	133130.i	0.0877735	+	0.241156i	−0.888038	+	0.459771i	$0.847932\pi$
$744$		0			0
$745$	−158265.	−	897566.i	−0.285150	−	1.61716i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.16227e6	−	1.38513e6i	−2.07177	−	2.46904i
$750$		0			0
$751$	81581.4	−	462671.i	0.144648	−	0.820338i	−0.823002	−	0.568039i	$-0.807702\pi$
$751$	81581.4	−	462671.i	0.144648	−	0.820338i	0.967649	−	0.252299i	$-0.0811866\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	364994.i		−	0.640312i
$756$		0			0
$757$	916889.			1.60002			0.800009	−	0.599988i	$-0.204828\pi$
$757$	916889.			1.60002			0.800009	+	0.599988i	$0.204828\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−745611.	−	131471.i	−1.28749	−	0.227019i	−0.512331	−	0.858788i	$-0.671218\pi$
$761$	−745611.	−	131471.i	−1.28749	−	0.227019i	−0.775157	+	0.631769i	$0.782329\pi$
$762$		0			0
$763$	−963290.	+	808296.i	−1.65466	+	1.38842i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−350153.	+	61741.5i	−0.595206	+	0.104951i
$768$		0			0
$769$	960494.	−	349591.i	1.62421	−	0.591164i	0.640032	−	0.768349i	$-0.278921\pi$
$769$	960494.	−	349591.i	1.62421	−	0.591164i	0.984178	+	0.177185i	$0.0566990\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−390743.	−	225596.i	−0.653932	−	0.377548i	0.136029	−	0.990705i	$-0.456566\pi$
$773$	−390743.	−	225596.i	−0.653932	−	0.377548i	−0.789961	+	0.613157i	$0.789899\pi$
$774$		0			0
$775$	−46482.6	−	80510.2i	−0.0773903	−	0.134044i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	583601.	−	695508.i	0.961703	−	1.14611i
$780$		0			0
$781$	103348.	+	37615.4i	0.169433	+	0.0616686i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−185494.	+	509641.i	−0.301017	+	0.827037i
$786$		0			0
$787$	−164988.	−	138441.i	−0.266381	−	0.223520i	0.499807	−	0.866137i	$-0.333404\pi$
$787$	−164988.	−	138441.i	−0.266381	−	0.223520i	−0.766188	+	0.642617i	$0.777849\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−249648.	+	144134.i	−0.399002	+	0.230364i
$792$		0			0
$793$	−34676.7	+	60061.7i	−0.0551431	+	0.0955106i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−241962.	−	664784.i	−0.380917	−	1.04656i	−0.970971	−	0.239197i	$-0.923116\pi$
$797$	−241962.	−	664784.i	−0.380917	−	1.04656i	0.590054	−	0.807363i	$-0.299106\pi$
$798$		0			0
$799$	14282.7	+	81001.2i	0.0223726	+	0.126881i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−75448.9	−	89916.5i	−0.117010	−	0.139447i
$804$		0			0
$805$	185138.	−	1.04997e6i	0.285695	−	1.62026i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			724268.i			1.10663i	0.832972	+	0.553315i	$0.186637\pi$
$809$			724268.i			1.10663i	−0.832972	+	0.553315i	$0.813363\pi$
$810$		0			0
$811$	−251299.			−0.382076			−0.191038	−	0.981583i	$-0.561185\pi$
$811$	−251299.			−0.382076			−0.191038	+	0.981583i	$0.561185\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	190850.	+	33652.0i	0.287327	+	0.0506636i
$816$		0			0
$817$	1.00704e6	−	845008.i	1.50870	−	1.26595i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.01486e6	−	178947.i	1.50563	−	0.265483i	0.640862	−	0.767656i	$-0.278577\pi$
$821$	1.01486e6	−	178947.i	1.50563	−	0.265483i	0.864767	+	0.502173i	$0.167466\pi$
$822$		0			0
$823$	151530.	−	55152.5i	0.223717	−	0.0814264i	−0.227730	−	0.973724i	$-0.573130\pi$
$823$	151530.	−	55152.5i	0.223717	−	0.0814264i	0.451447	+	0.892298i	$0.350908\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	442766.	+	255631.i	0.647387	+	0.373769i	0.787454	−	0.616373i	$-0.211399\pi$
$827$	442766.	+	255631.i	0.647387	+	0.373769i	−0.140068	+	0.990142i	$0.544732\pi$
$828$		0			0
$829$	284418.	+	492627.i	0.413855	+	0.716818i	0.995308	−	0.0967622i	$-0.0308486\pi$
$829$	284418.	+	492627.i	0.413855	+	0.716818i	−0.581452	+	0.813581i	$0.697515\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−721653.	+	860032.i	−1.04001	+	1.23944i
$834$		0			0
$835$	−460162.	−	167485.i	−0.659991	−	0.240217i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−290412.	+	797902.i	−0.412564	+	1.13351i	0.543258	+	0.839566i	$0.317190\pi$
$839$	−290412.	+	797902.i	−0.412564	+	1.13351i	−0.955822	+	0.293945i	$0.905032\pi$
$840$		0			0
$841$	−859842.	−	721493.i	−1.21570	−	1.02009i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	403815.	−	233143.i	0.565547	−	0.326519i
$846$		0			0
$847$	−616393.	+	1.06762e6i	−0.859193	+	1.48817i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−136442.	−	374871.i	−0.188403	−	0.517634i
$852$		0			0
$853$	98343.6	+	557735.i	0.135160	+	0.766531i	0.974748	+	0.223307i	$0.0716853\pi$
$853$	98343.6	+	557735.i	0.135160	+	0.766531i	−0.839588	+	0.543223i	$0.817204\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	123165.	+	146783.i	0.167698	+	0.199854i	0.843348	−	0.537368i	$-0.180581\pi$
$857$	123165.	+	146783.i	0.167698	+	0.199854i	−0.675650	+	0.737222i	$0.736137\pi$
$858$		0			0
$859$	−62045.6	+	351878.i	−0.0840861	+	0.476876i	0.913464	+	0.406920i	$0.133397\pi$
$859$	−62045.6	+	351878.i	−0.0840861	+	0.476876i	−0.997550	+	0.0699565i	$0.977714\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			1.36365e6i			1.83098i	0.402346	+	0.915488i	$0.368195\pi$
$863$			1.36365e6i			1.83098i	−0.402346	+	0.915488i	$0.631805\pi$
$864$		0			0
$865$	−586059.			−0.783266
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−62494.9	−	11019.5i	−0.0827571	−	0.0145923i
$870$		0			0
$871$	6755.63	−	5668.65i	0.00890491	−	0.00747211i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.15779e6	−	204149.i	1.51221	−	0.266644i
$876$		0			0
$877$	−342169.	+	124539.i	−0.444878	+	0.161922i	−0.554739	−	0.832025i	$-0.687182\pi$
$877$	−342169.	+	124539.i	−0.444878	+	0.161922i	0.109861	+	0.993947i	$0.464960\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	510409.	+	294685.i	0.657607	+	0.379670i	0.791365	−	0.611345i	$-0.209371\pi$
$881$	510409.	+	294685.i	0.657607	+	0.379670i	−0.133758	+	0.991014i	$0.542704\pi$
$882$		0			0
$883$	−295952.	−	512604.i	−0.379577	−	0.657447i	0.611424	−	0.791303i	$-0.290597\pi$
$883$	−295952.	−	512604.i	−0.379577	−	0.657447i	−0.991001	+	0.133857i	$0.957264\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	266358.	−	317433.i	0.338546	−	0.403464i	−0.569732	−	0.821831i	$-0.692953\pi$
$887$	266358.	−	317433.i	0.338546	−	0.403464i	0.908278	+	0.418367i	$0.137397\pi$
$888$		0			0
$889$	377130.	+	137264.i	0.477186	+	0.173682i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	61510.8	−	168999.i	0.0771344	−	0.211925i
$894$		0			0
$895$	−746259.	−	626186.i	−0.931630	−	0.781731i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−914544.	+	528012.i	−1.13158	+	0.653318i
$900$		0			0
$901$	−208805.	+	361661.i	−0.257212	+	0.445504i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−63573.0	−	174665.i	−0.0776203	−	0.213260i
$906$		0			0
$907$	−85195.0	−	483165.i	−0.103562	−	0.587328i	−0.991785	−	0.127916i	$-0.959171\pi$
$907$	−85195.0	−	483165.i	−0.103562	−	0.587328i	0.888223	−	0.459412i	$-0.151940\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−372483.	−	443908.i	−0.448817	−	0.534879i	0.493436	−	0.869782i	$-0.335741\pi$
$911$	−372483.	−	443908.i	−0.448817	−	0.534879i	−0.942253	+	0.334903i	$0.891296\pi$
$912$		0			0
$913$	−28408.0	+	161110.i	−0.0340800	+	0.193277i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	1.42578e6i		−	1.69556i
$918$		0			0
$919$	−873291.			−1.03402			−0.517009	−	0.855980i	$-0.672954\pi$
$919$	−873291.			−1.03402			−0.517009	+	0.855980i	$0.672954\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	889886.	+	156911.i	1.04455	+	0.184183i
$924$		0			0
$925$	−79315.7	+	66553.8i	−0.0926992	+	0.0777838i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−820093.	+	144605.i	−0.950236	+	0.167552i	−0.627221	−	0.778841i	$-0.715808\pi$
$929$	−820093.	+	144605.i	−0.950236	+	0.167552i	−0.323015	+	0.946394i	$0.604697\pi$
$930$		0			0
$931$	2.30678e6	−	839599.i	2.66138	−	0.968663i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	71180.3	+	41096.0i	0.0814211	+	0.0470085i
$936$		0			0
$937$	611448.	+	1.05906e6i	0.696434	+	1.20626i	0.969695	+	0.244320i	$0.0785646\pi$
$937$	611448.	+	1.05906e6i	0.696434	+	1.20626i	−0.273260	+	0.961940i	$0.588102\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−315935.	+	376517.i	−0.356795	+	0.425211i	−0.914348	−	0.404930i	$-0.867296\pi$
$941$	−315935.	+	376517.i	−0.356795	+	0.425211i	0.557553	+	0.830141i	$0.311740\pi$
$942$		0			0
$943$	774359.	+	281843.i	0.870801	+	0.316945i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−36318.3	+	99783.6i	−0.0404972	+	0.111265i	−0.958293	−	0.285788i	$-0.907745\pi$
$947$	−36318.3	+	99783.6i	−0.0404972	+	0.111265i	0.917796	+	0.397053i	$0.129967\pi$
$948$		0			0
$949$	−738768.	−	619900.i	−0.820306	−	0.688318i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−549318.	+	317149.i	−0.604837	+	0.349203i	−0.770942	−	0.636905i	$-0.780214\pi$
$953$	−549318.	+	317149.i	−0.604837	+	0.349203i	0.166105	+	0.986108i	$0.446881\pi$
$954$		0			0
$955$	335109.	−	580426.i	0.367434	−	0.636414i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	65384.0	+	179641.i	0.0710942	+	0.195330i
$960$		0			0
$961$	−54531.9	−	309266.i	−0.0590478	−	0.334877i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−243363.	−	290029.i	−0.261337	−	0.311449i
$966$		0			0
$967$	68466.6	−	388293.i	0.0732193	−	0.415247i	−0.926063	−	0.377369i	$-0.876829\pi$
$967$	68466.6	−	388293.i	0.0732193	−	0.415247i	0.999282	−	0.0378785i	$-0.0120600\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	1.67881e6i		−	1.78058i	−0.455392	−	0.890291i	$-0.650501\pi$
$971$		−	1.67881e6i		−	1.78058i	0.455392	−	0.890291i	$-0.349499\pi$
$972$		0			0
$973$	−302463.			−0.319482
$974$		0			0
$975$		0			0
$976$		0			0
$977$	485549.	+	85615.4i	0.508679	+	0.0896938i	0.422097	−	0.906551i	$-0.361294\pi$
$977$	485549.	+	85615.4i	0.508679	+	0.0896938i	0.0865824	+	0.996245i	$0.472405\pi$
$978$		0			0
$979$	−63456.7	+	53246.5i	−0.0662083	+	0.0555553i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.19508e6	+	210724.i	−1.23677	+	0.218076i	−0.753531	−	0.657413i	$-0.771651\pi$
$983$	−1.19508e6	+	210724.i	−1.23677	+	0.218076i	−0.483239	+	0.875489i	$0.660540\pi$
$984$		0			0
$985$	−1.74365e6	+	634638.i	−1.79717	+	0.654115i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.03331e6	+	596583.i	1.05643	+	0.609928i
$990$		0			0
$991$	−105754.	−	183172.i	−0.107684	−	0.186514i	0.807148	−	0.590350i	$-0.201010\pi$
$991$	−105754.	−	183172.i	−0.107684	−	0.186514i	−0.914832	+	0.403835i	$0.867677\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	716589.	−	853998.i	0.723809	−	0.862602i
$996$		0			0
$997$	776096.	+	282476.i	0.780773	+	0.284178i	0.701495	−	0.712674i	$-0.252516\pi$
$997$	776096.	+	282476.i	0.780773	+	0.284178i	0.0792781	+	0.996853i	$0.474738\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.5.k.a.17.3		72
3.2	odd	2		108.5.k.a.77.6	✓	72
27.7	even	9		108.5.k.a.101.6	yes	72
27.20	odd	18	inner	324.5.k.a.305.3		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.5.k.a.77.6	✓	72	3.2	odd	2
108.5.k.a.101.6	yes	72	27.7	even	9
324.5.k.a.17.3		72	1.1	even	1	trivial
324.5.k.a.305.3		72	27.20	odd	18	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	324.k (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-26.8634 - 4.73675i) q^{5} +(65.2588 - 54.7587i) q^{7} +O(q^{10})\)	\(q+(-26.8634 - 4.73675i) q^{5} +(65.2588 - 54.7587i) q^{7} +(12.8354 - 2.26323i) q^{11} +(100.626 - 36.6250i) q^{13} +(-200.213 - 115.593i) q^{17} +(252.750 + 437.776i) q^{19} +(-294.915 + 351.466i) q^{23} +(111.899 + 40.7278i) q^{25} +(462.641 - 1271.10i) q^{29} +(-598.047 - 501.821i) q^{31} +(-2012.45 + 1161.89i) q^{35} +(-434.747 + 753.004i) q^{37} +(-614.297 - 1687.77i) q^{41} +(-451.587 - 2561.08i) q^{43} +(-228.689 - 272.541i) q^{47} +(843.274 - 4782.45i) q^{49} -1806.38i q^{53} -355.523 q^{55} +(-3269.88 - 576.568i) q^{59} +(-496.129 + 416.302i) q^{61} +(-2876.65 + 507.232i) q^{65} +(77.3876 - 28.1668i) q^{67} +(7307.81 + 4219.17i) q^{71} +(-4502.96 - 7799.36i) q^{73} +(713.691 - 850.544i) q^{77} +(-4575.32 - 1665.28i) q^{79} +(-4293.04 + 11795.0i) q^{83} +(4830.87 + 4053.59i) q^{85} +(-5504.23 + 3177.87i) q^{89} +(4561.23 - 7900.27i) q^{91} +(-4716.10 - 12957.4i) q^{95} +(1755.90 + 9958.19i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 9 q^{5}+O(q^{10}) \) 72 * q - 9 * q^5	\( 72 q - 9 q^{5} - 18 q^{11} + 1278 q^{23} + 441 q^{25} - 1854 q^{29} - 1665 q^{31} + 2673 q^{35} + 5472 q^{41} + 1260 q^{43} - 5103 q^{47} - 5904 q^{49} + 10944 q^{59} + 8352 q^{61} - 8757 q^{65} + 378 q^{67} + 19764 q^{71} + 6111 q^{73} + 5679 q^{77} - 5652 q^{79} + 20061 q^{83} + 26100 q^{85} - 15633 q^{89} - 6039 q^{91} - 48024 q^{95} - 37530 q^{97}+O(q^{100}) \) 72 * q - 9 * q^5 - 18 * q^11 + 1278 * q^23 + 441 * q^25 - 1854 * q^29 - 1665 * q^31 + 2673 * q^35 + 5472 * q^41 + 1260 * q^43 - 5103 * q^47 - 5904 * q^49 + 10944 * q^59 + 8352 * q^61 - 8757 * q^65 + 378 * q^67 + 19764 * q^71 + 6111 * q^73 + 5679 * q^77 - 5652 * q^79 + 20061 * q^83 + 26100 * q^85 - 15633 * q^89 - 6039 * q^91 - 48024 * q^95 - 37530 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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