LMFDB - Embedded newform 325.4.b.f.274.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,4,Mod(274,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("325.274");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	325.b (of order $2$, degree $1$, 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:	$19.1756207519$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9x^{2} + 16 $ x^4 + 9*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.4
Root			$2.56155i$ of defining polynomial
Character	$\chi$	$=$	325.274
Dual form			325.4.b.f.274.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.56155i q^{2} -8.24621i q^{3} +1.43845 q^{4} +21.1231 q^{6} +24.8769i q^{7} +24.1771i q^{8} -41.0000 q^{9} +O(q^{10})$	\(q+2.56155i q^{2} -8.24621i q^{3} +1.43845 q^{4} +21.1231 q^{6} +24.8769i q^{7} +24.1771i q^{8} -41.0000 q^{9} -38.8769 q^{11} -11.8617i q^{12} +13.0000i q^{13} -63.7235 q^{14} -50.4233 q^{16} -79.9697i q^{17} -105.024i q^{18} -128.354 q^{19} +205.140 q^{21} -99.5852i q^{22} +101.939i q^{23} +199.369 q^{24} -33.3002 q^{26} +115.447i q^{27} +35.7841i q^{28} -117.723 q^{29} -298.756 q^{31} +64.2547i q^{32} +320.587i q^{33} +204.847 q^{34} -58.9763 q^{36} +254.216i q^{37} -328.786i q^{38} +107.201 q^{39} +219.633 q^{41} +525.477i q^{42} +104.462i q^{43} -55.9224 q^{44} -261.123 q^{46} +308.816i q^{47} +415.801i q^{48} -275.860 q^{49} -659.447 q^{51} +18.6998i q^{52} +0.0909300i q^{53} -295.723 q^{54} -601.451 q^{56} +1058.44i q^{57} -301.555i q^{58} +349.710 q^{59} +442.000 q^{61} -765.278i q^{62} -1019.95i q^{63} -567.978 q^{64} -821.201 q^{66} +228.074i q^{67} -115.032i q^{68} +840.614 q^{69} +964.328 q^{71} -991.260i q^{72} -662.682i q^{73} -651.187 q^{74} -184.631 q^{76} -967.136i q^{77} +274.600i q^{78} +65.2614 q^{79} -155.000 q^{81} +562.600i q^{82} +92.4185i q^{83} +295.083 q^{84} -267.585 q^{86} +970.773i q^{87} -939.930i q^{88} +178.614 q^{89} -323.400 q^{91} +146.634i q^{92} +2463.60i q^{93} -791.049 q^{94} +529.858 q^{96} -1707.46i q^{97} -706.630i q^{98} +1593.95 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 14 q^{4} + 68 q^{6} - 164 q^{9}+O(q^{10}) $ 4 * q + 14 * q^4 + 68 * q^6 - 164 * q^9	$ 4 q + 14 q^{4} + 68 q^{6} - 164 q^{9} - 172 q^{11} - 24 q^{14} - 78 q^{16} - 332 q^{19} - 136 q^{21} + 748 q^{24} - 26 q^{26} - 240 q^{29} - 156 q^{31} + 572 q^{34} - 574 q^{36} - 144 q^{41} - 636 q^{44} - 1028 q^{46} - 2060 q^{49} - 2176 q^{51} - 952 q^{54} + 200 q^{56} - 36 q^{59} + 1768 q^{61} - 1538 q^{64} - 2856 q^{66} + 4352 q^{69} + 1268 q^{71} - 972 q^{74} - 788 q^{76} + 360 q^{79} - 620 q^{81} - 2448 q^{84} - 724 q^{86} + 1704 q^{89} - 1508 q^{91} - 1416 q^{94} + 4148 q^{96} + 7052 q^{99}+O(q^{100}) $ 4 * q + 14 * q^4 + 68 * q^6 - 164 * q^9 - 172 * q^11 - 24 * q^14 - 78 * q^16 - 332 * q^19 - 136 * q^21 + 748 * q^24 - 26 * q^26 - 240 * q^29 - 156 * q^31 + 572 * q^34 - 574 * q^36 - 144 * q^41 - 636 * q^44 - 1028 * q^46 - 2060 * q^49 - 2176 * q^51 - 952 * q^54 + 200 * q^56 - 36 * q^59 + 1768 * q^61 - 1538 * q^64 - 2856 * q^66 + 4352 * q^69 + 1268 * q^71 - 972 * q^74 - 788 * q^76 + 360 * q^79 - 620 * q^81 - 2448 * q^84 - 724 * q^86 + 1704 * q^89 - 1508 * q^91 - 1416 * q^94 + 4148 * q^96 + 7052 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$1$

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 $

$2$	2.56155i	0.905646i	0.891601	+	0.452823i	$0.149583\pi$
$2$	2.56155i	0.905646i	−0.891601	+	0.452823i	$0.850417\pi$
$3$	− 8.24621i	− 1.58698i	−0.608581	−	0.793492i	$-0.708261\pi$
$3$	− 8.24621i	− 1.58698i	0.608581	−	0.793492i	$-0.291739\pi$
$4$	1.43845	0.179806
$5$	0	0
$5$	0	0
$6$	21.1231	1.43725
$7$	24.8769i	1.34323i	0.740902	+	0.671613i	$0.234398\pi$
$7$	24.8769i	1.34323i	−0.740902	+	0.671613i	$0.765602\pi$
$8$	24.1771i	1.06849i
$9$	−41.0000	−1.51852
$10$	0	0
$11$	−38.8769	−1.06562	−0.532810	−	0.846235i	$-0.678864\pi$
$11$	−38.8769	−1.06562	−0.532810	+	0.846235i	$0.678864\pi$
$12$	− 11.8617i	− 0.285349i
$13$	13.0000i	0.277350i
$13$	13.0000i	0.277350i
$14$	−63.7235	−1.21649
$15$	0	0
$16$	−50.4233	−0.787864
$17$	− 79.9697i	− 1.14091i	−0.821328	−	0.570456i	$-0.806767\pi$
$17$	− 79.9697i	− 1.14091i	0.821328	−	0.570456i	$-0.193233\pi$
$18$	− 105.024i	− 1.37524i
$19$	−128.354	−1.54981	−0.774907	−	0.632075i	$-0.782203\pi$
$19$	−128.354	−1.54981	−0.774907	+	0.632075i	$0.782203\pi$
$20$	0	0
$21$	205.140	2.13168
$22$	− 99.5852i	− 0.965075i
$23$	101.939i	0.924167i	0.886837	+	0.462083i	$0.152898\pi$
$23$	101.939i	0.924167i	−0.886837	+	0.462083i	$0.847102\pi$
$24$	199.369	1.69567
$25$	0	0
$26$	−33.3002	−0.251181
$27$	115.447i	0.822881i
$28$	35.7841i	0.241520i
$29$	−117.723	−0.753817	−0.376909	−	0.926250i	$-0.623013\pi$
$29$	−117.723	−0.753817	−0.376909	+	0.926250i	$0.623013\pi$
$30$	0	0
$31$	−298.756	−1.73091	−0.865453	−	0.500990i	$-0.832969\pi$
$31$	−298.756	−1.73091	−0.865453	+	0.500990i	$0.832969\pi$
$32$	64.2547i	0.354961i
$33$	320.587i	1.69112i
$34$	204.847	1.03326
$35$	0	0
$36$	−58.9763	−0.273039
$37$	254.216i	1.12954i	0.825250	+	0.564768i	$0.191034\pi$
$37$	254.216i	1.12954i	−0.825250	+	0.564768i	$0.808966\pi$
$38$	− 328.786i	− 1.40358i
$39$	107.201	0.440150
$40$	0	0
$41$	219.633	0.836606	0.418303	−	0.908308i	$-0.362625\pi$
$41$	219.633	0.836606	0.418303	+	0.908308i	$0.362625\pi$
$42$	525.477i	1.93055i
$43$	104.462i	0.370473i	0.982694	+	0.185236i	$0.0593051\pi$
$43$	104.462i	0.370473i	−0.982694	+	0.185236i	$0.940695\pi$
$44$	−55.9224	−0.191605
$45$	0	0
$46$	−261.123	−0.836967
$47$	308.816i	0.958415i	0.877702	+	0.479207i	$0.159076\pi$
$47$	308.816i	0.958415i	−0.877702	+	0.479207i	$0.840924\pi$
$48$	415.801i	1.25033i
$49$	−275.860	−0.804256
$50$	0	0
$51$	−659.447	−1.81061
$52$	18.6998i	0.0498692i
$53$	0.0909300i	0 0.000235664i	1.00000		0.000117832i	$3.75071e-5\pi$
$53$	0.0909300i	0 0.000235664i	−1.00000		0.000117832i	$0.999962\pi$
$54$	−295.723	−0.745238
$55$	0	0
$56$	−601.451	−1.43522
$57$	1058.44i	2.45953i
$58$	− 301.555i	− 0.682691i
$59$	349.710	0.771668	0.385834	−	0.922568i	$-0.373914\pi$
$59$	349.710	0.771668	0.385834	+	0.922568i	$0.373914\pi$
$60$	0	0
$61$	442.000	0.927743	0.463871	−	0.885903i	$-0.346460\pi$
$61$	442.000	0.927743	0.463871	+	0.885903i	$0.346460\pi$
$62$	− 765.278i	− 1.56759i
$63$	− 1019.95i	− 2.03971i
$64$	−567.978	−1.10933
$65$	0	0
$66$	−821.201	−1.53156
$67$	228.074i	0.415876i	0.978142	+	0.207938i	$0.0666752\pi$
$67$	228.074i	0.415876i	−0.978142	+	0.207938i	$0.933325\pi$
$68$	− 115.032i	− 0.205143i
$69$	840.614	1.46664
$70$	0	0
$71$	964.328	1.61190	0.805948	−	0.591986i	$-0.201656\pi$
$71$	964.328	1.61190	0.805948	+	0.591986i	$0.201656\pi$
$72$	− 991.260i	− 1.62252i
$73$	− 662.682i	− 1.06248i	−0.847221	−	0.531240i	$-0.821726\pi$
$73$	− 662.682i	− 1.06248i	0.847221	−	0.531240i	$-0.178274\pi$
$74$	−651.187	−1.02296
$75$	0	0
$76$	−184.631	−0.278666
$77$	− 967.136i	− 1.43137i
$78$	274.600i	0.398620i
$79$	65.2614	0.0929428	0.0464714	−	0.998920i	$-0.485202\pi$
$79$	65.2614	0.0929428	0.0464714	+	0.998920i	$0.485202\pi$
$80$	0	0
$81$	−155.000	−0.212620
$82$	562.600i	0.757669i
$83$	92.4185i	0.122220i	0.998131	+	0.0611099i	$0.0194640\pi$
$83$	92.4185i	0.122220i	−0.998131	+	0.0611099i	$0.980536\pi$
$84$	295.083	0.383288
$85$	0	0
$86$	−267.585	−0.335517
$87$	970.773i	1.19630i
$88$	− 939.930i	− 1.13860i
$89$	178.614	0.212730	0.106365	−	0.994327i	$-0.466079\pi$
$89$	178.614	0.212730	0.106365	+	0.994327i	$0.466079\pi$
$90$	0	0
$91$	−323.400	−0.372544
$92$	146.634i	0.166171i
$93$	2463.60i	2.74692i
$94$	−791.049	−0.867984
$95$	0	0
$96$	529.858	0.563317
$97$	− 1707.46i	− 1.78728i	−0.448785	−	0.893640i	$-0.648143\pi$
$97$	− 1707.46i	− 1.78728i	0.448785	−	0.893640i	$-0.351857\pi$
$98$	− 706.630i	− 0.728371i
$99$	1593.95	1.61816
$100$	0	0
$101$	−1364.04	−1.34383	−0.671915	−	0.740628i	$-0.734528\pi$
$101$	−1364.04	−1.34383	−0.671915	+	0.740628i	$0.734528\pi$
$102$	− 1689.21i	− 1.63977i
$103$	− 355.167i	− 0.339763i	−0.985464	−	0.169882i	$-0.945661\pi$
$103$	− 355.167i	− 0.339763i	0.985464	−	0.169882i	$-0.0543385\pi$
$104$	−314.302	−0.296345
$105$	0	0
$106$	−0.232922	−0.000213428 0
$107$	325.905i	0.294453i	0.989103	+	0.147226i	$0.0470346\pi$
$107$	325.905i	0.294453i	−0.989103	+	0.147226i	$0.952965\pi$
$108$	166.064i	0.147959i
$109$	−1738.93	−1.52807	−0.764034	−	0.645176i	$-0.776784\pi$
$109$	−1738.93	−1.52807	−0.764034	+	0.645176i	$0.776784\pi$
$110$	0	0
$111$	2096.32	1.79256
$112$	− 1254.37i	− 1.05828i
$113$	1628.89i	1.35605i	0.735040	+	0.678024i	$0.237164\pi$
$113$	1628.89i	1.35605i	−0.735040	+	0.678024i	$0.762836\pi$
$114$	−2711.24	−2.22746
$115$	0	0
$116$	−169.339	−0.135541
$117$	− 533.000i	− 0.421161i
$118$	895.801i	0.698857i
$119$	1989.40	1.53250
$120$	0	0
$121$	180.413	0.135547
$122$	1132.21i	0.840206i
$123$	− 1811.14i	− 1.32768i
$124$	−429.744	−0.311227
$125$	0	0
$126$	2612.66	1.84726
$127$	165.333i	0.115519i	0.998331	+	0.0577596i	$0.0183957\pi$
$127$	165.333i	0.115519i	−0.998331	+	0.0577596i	$0.981604\pi$
$128$	− 940.868i	− 0.649702i
$129$	861.417	0.587934
$130$	0	0
$131$	−1867.49	−1.24552	−0.622760	−	0.782413i	$-0.713989\pi$
$131$	−1867.49	−1.24552	−0.622760	+	0.782413i	$0.713989\pi$
$132$	461.148i	0.304074i
$133$	− 3193.05i	− 2.08175i
$134$	−584.223	−0.376636
$135$	0	0
$136$	1933.43	1.21905
$137$	1740.80i	1.08560i	0.839864	+	0.542798i	$0.182635\pi$
$137$	1740.80i	1.08560i	−0.839864	+	0.542798i	$0.817365\pi$
$138$	2153.28i	1.32825i
$139$	985.511	0.601367	0.300683	−	0.953724i	$-0.402785\pi$
$139$	985.511	0.601367	0.300683	+	0.953724i	$0.402785\pi$
$140$	0	0
$141$	2546.56	1.52099
$142$	2470.18i	1.45981i
$143$	− 505.400i	− 0.295550i
$144$	2067.35	1.19639
$145$	0	0
$146$	1697.49	0.962230
$147$	2274.80i	1.27634i
$148$	365.676i	0.203097i
$149$	2496.90	1.37285	0.686423	−	0.727202i	$-0.259180\pi$
$149$	2496.90	1.37285	0.686423	+	0.727202i	$0.259180\pi$
$150$	0	0
$151$	357.710	0.192782	0.0963909	−	0.995344i	$-0.469270\pi$
$151$	357.710	0.192782	0.0963909	+	0.995344i	$0.469270\pi$
$152$	− 3103.23i	− 1.65595i
$153$	3278.76i	1.73250i
$154$	2477.37	1.29631
$155$	0	0
$156$	154.203	0.0791416
$157$	− 3218.32i	− 1.63599i	−0.575228	−	0.817993i	$-0.695087\pi$
$157$	− 3218.32i	− 1.63599i	0.575228	−	0.817993i	$-0.304913\pi$
$158$	167.170i	0.0841732i
$159$	0.749828	0.000373995 0
$160$	0	0
$161$	−2535.94	−1.24136
$162$	− 397.041i	− 0.192558i
$163$	2901.51i	1.39425i	0.716948	+	0.697127i	$0.245539\pi$
$163$	2901.51i	1.39425i	−0.716948	+	0.697127i	$0.754461\pi$
$164$	315.930	0.150427
$165$	0	0
$166$	−236.735	−0.110688
$167$	531.036i	0.246065i	0.992403	+	0.123032i	$0.0392619\pi$
$167$	531.036i	0.246065i	−0.992403	+	0.123032i	$0.960738\pi$
$168$	4959.69i	2.27767i
$169$	−169.000	−0.0769231
$170$	0	0
$171$	5262.52	2.35342
$172$	150.263i	0.0666132i
$173$	− 809.826i	− 0.355895i	−0.984040	−	0.177948i	$-0.943054\pi$
$173$	− 809.826i	− 0.355895i	0.984040	−	0.177948i	$-0.0569458\pi$
$174$	−2486.69	−1.08342
$175$	0	0
$176$	1960.30	0.839564
$177$	− 2883.78i	− 1.22462i
$178$	457.528i	0.192658i
$179$	1831.87	0.764919	0.382459	−	0.923972i	$-0.375077\pi$
$179$	1831.87	0.764919	0.382459	+	0.923972i	$0.375077\pi$
$180$	0	0
$181$	1046.76	0.429863	0.214931	−	0.976629i	$-0.431047\pi$
$181$	1046.76	0.429863	0.214931	+	0.976629i	$0.431047\pi$
$182$	− 828.405i	− 0.337393i
$183$	− 3644.83i	− 1.47231i
$184$	−2464.60	−0.987459
$185$	0	0
$186$	−6310.65	−2.48774
$187$	3108.97i	1.21578i
$188$	444.216i	0.172329i
$189$	−2871.96	−1.10531
$190$	0	0
$191$	759.973	0.287904	0.143952	−	0.989585i	$-0.454019\pi$
$191$	759.973	0.287904	0.143952	+	0.989585i	$0.454019\pi$
$192$	4683.67i	1.76049i
$193$	411.618i	0.153518i	0.997050	+	0.0767588i	$0.0244571\pi$
$193$	411.618i	0.153518i	−0.997050	+	0.0767588i	$0.975543\pi$
$194$	4373.74	1.61864
$195$	0	0
$196$	−396.810	−0.144610
$197$	− 805.204i	− 0.291210i	−0.989343	−	0.145605i	$-0.953487\pi$
$197$	− 805.204i	− 0.291210i	0.989343	−	0.145605i	$-0.0465129\pi$
$198$	4082.99i	1.46548i
$199$	−2932.02	−1.04445	−0.522225	−	0.852808i	$-0.674898\pi$
$199$	−2932.02	−1.04445	−0.522225	+	0.852808i	$0.674898\pi$
$200$	0	0
$201$	1880.75	0.659988
$202$	− 3494.05i	− 1.21703i
$203$	− 2928.59i	− 1.01255i
$204$	−948.580	−0.325558
$205$	0	0
$206$	909.778	0.307705
$207$	− 4179.51i	− 1.40336i
$208$	− 655.503i	− 0.218514i
$209$	4990.01	1.65151
$210$	0	0
$211$	−3922.57	−1.27982	−0.639908	−	0.768452i	$-0.721027\pi$
$211$	−3922.57	−1.27982	−0.639908	+	0.768452i	$0.721027\pi$
$212$	0.130798i	0 4.23738e-5i
$213$	− 7952.05i	− 2.55805i
$214$	−834.824	−0.266670
$215$	0	0
$216$	−2791.17	−0.879237
$217$	− 7432.11i	− 2.32500i
$218$	− 4454.37i	− 1.38389i
$219$	−5464.61	−1.68614
$220$	0	0
$221$	1039.61	0.316432
$222$	5369.83i	1.62342i
$223$	− 6115.27i	− 1.83636i	−0.396162	−	0.918181i	$-0.629658\pi$
$223$	− 6115.27i	− 1.83636i	0.396162	−	0.918181i	$-0.370342\pi$
$224$	−1598.46	−0.476792
$225$	0	0
$226$	−4172.50	−1.22810
$227$	4216.13i	1.23275i	0.787452	+	0.616376i	$0.211400\pi$
$227$	4216.13i	1.23275i	−0.787452	+	0.616376i	$0.788600\pi$
$228$	1522.50i	0.442238i
$229$	299.451	0.0864116	0.0432058	−	0.999066i	$-0.486243\pi$
$229$	299.451	0.0864116	0.0432058	+	0.999066i	$0.486243\pi$
$230$	0	0
$231$	−7975.21	−2.27156
$232$	− 2846.21i	− 0.805443i
$233$	− 1223.17i	− 0.343916i	−0.985104	−	0.171958i	$-0.944991\pi$
$233$	− 1223.17i	− 0.343916i	0.985104	−	0.171958i	$-0.0550093\pi$
$234$	1365.31	0.381423
$235$	0	0
$236$	503.040	0.138750
$237$	− 538.159i	− 0.147499i
$238$	5095.95i	1.38790i
$239$	48.7253	0.0131874	0.00659368	−	0.999978i	$-0.497901\pi$
$239$	48.7253	0.0131874	0.00659368	+	0.999978i	$0.497901\pi$
$240$	0	0
$241$	−4499.83	−1.20274	−0.601368	−	0.798972i	$-0.705378\pi$
$241$	−4499.83	−1.20274	−0.601368	+	0.798972i	$0.705378\pi$
$242$	462.137i	0.122757i
$243$	4395.23i	1.16031i
$244$	635.794	0.166814
$245$	0	0
$246$	4639.32	1.20241
$247$	− 1668.60i	− 0.429841i
$248$	− 7223.04i	− 1.84945i
$249$	762.103	0.193961
$250$	0	0
$251$	−110.288	−0.0277343	−0.0138671	−	0.999904i	$-0.504414\pi$
$251$	−110.288	−0.0277343	−0.0138671	+	0.999904i	$0.504414\pi$
$252$	− 1467.15i	− 0.366753i
$253$	− 3963.09i	− 0.984811i
$254$	−423.510	−0.104620
$255$	0	0
$256$	−2133.74	−0.520933
$257$	7453.76i	1.80916i	0.426308	+	0.904578i	$0.359814\pi$
$257$	7453.76i	1.80916i	−0.426308	+	0.904578i	$0.640186\pi$
$258$	2206.56i	0.532460i
$259$	−6324.10	−1.51722
$260$	0	0
$261$	4826.66	1.14469
$262$	− 4783.67i	− 1.12800i
$263$	225.156i	0.0527897i	0.999652	+	0.0263948i	$0.00840271\pi$
$263$	225.156i	0.0527897i	−0.999652	+	0.0263948i	$0.991597\pi$
$264$	−7750.86	−1.80694
$265$	0	0
$266$	8179.17	1.88533
$267$	− 1472.89i	− 0.337600i
$268$	328.072i	0.0747769i
$269$	2742.09	0.621517	0.310758	−	0.950489i	$-0.399417\pi$
$269$	2742.09	0.621517	0.310758	+	0.950489i	$0.399417\pi$
$270$	0	0
$271$	6749.69	1.51297	0.756484	−	0.654012i	$-0.226916\pi$
$271$	6749.69	1.51297	0.756484	+	0.654012i	$0.226916\pi$
$272$	4032.34i	0.898883i
$273$	2666.82i	0.591221i
$274$	−4459.15	−0.983164
$275$	0	0
$276$	1209.18	0.263710
$277$	1511.65i	0.327893i	0.986469	+	0.163946i	$0.0524224\pi$
$277$	1511.65i	0.327893i	−0.986469	+	0.163946i	$0.947578\pi$
$278$	2524.44i	0.544625i
$279$	12249.0	2.62841
$280$	0	0
$281$	−5593.69	−1.18751	−0.593757	−	0.804645i	$-0.702356\pi$
$281$	−5593.69	−1.18751	−0.593757	+	0.804645i	$0.702356\pi$
$282$	6523.16i	1.37748i
$283$	3221.02i	0.676572i	0.941043	+	0.338286i	$0.109847\pi$
$283$	3221.02i	0.676572i	−0.941043	+	0.338286i	$0.890153\pi$
$284$	1387.13	0.289828
$285$	0	0
$286$	1294.61	0.267664
$287$	5463.78i	1.12375i
$288$	− 2634.44i	− 0.539014i
$289$	−1482.15	−0.301679
$290$	0	0
$291$	−14080.1	−2.83638
$292$	− 953.233i	− 0.191040i
$293$	− 7809.84i	− 1.55719i	−0.627528	−	0.778594i	$-0.715933\pi$
$293$	− 7809.84i	− 1.55719i	0.627528	−	0.778594i	$-0.284067\pi$
$294$	−5827.02	−1.15591
$295$	0	0
$296$	−6146.20	−1.20689
$297$	− 4488.22i	− 0.876878i
$298$	6395.94i	1.24331i
$299$	−1325.21	−0.256318
$300$	0	0
$301$	−2598.69	−0.497628
$302$	916.294i	0.174592i
$303$	11248.1i	2.13264i
$304$	6472.04	1.22104
$305$	0	0
$306$	−8398.71	−1.56903
$307$	8581.07i	1.59527i	0.603141	+	0.797634i	$0.293916\pi$
$307$	8581.07i	1.59527i	−0.603141	+	0.797634i	$0.706084\pi$
$308$	− 1391.17i	− 0.257369i
$309$	−2928.78	−0.539199
$310$	0	0
$311$	9251.84	1.68689	0.843447	−	0.537213i	$-0.180523\pi$
$311$	9251.84	1.68689	0.843447	+	0.537213i	$0.180523\pi$
$312$	2591.80i	0.470294i
$313$	− 4386.17i	− 0.792081i	−0.918233	−	0.396040i	$-0.870384\pi$
$313$	− 4386.17i	− 0.792081i	0.918233	−	0.396040i	$-0.129616\pi$
$314$	8243.89	1.48162
$315$	0	0
$316$	93.8750	0.0167117
$317$	− 587.686i	− 0.104125i	−0.998644	−	0.0520626i	$-0.983420\pi$
$317$	− 587.686i	− 0.104125i	0.998644	−	0.0520626i	$-0.0165796\pi$
$318$	1.92072i	0 0.000338707i
$319$	4576.72	0.803283
$320$	0	0
$321$	2687.48	0.467292
$322$	− 6495.93i	− 1.12424i
$323$	10264.4i	1.76820i
$324$	−222.959	−0.0382303
$325$	0	0
$326$	−7432.36	−1.26270
$327$	14339.6i	2.42502i
$328$	5310.07i	0.893902i
$329$	−7682.39	−1.28737
$330$	0	0
$331$	−6559.71	−1.08929	−0.544644	−	0.838668i	$-0.683335\pi$
$331$	−6559.71	−1.08929	−0.544644	+	0.838668i	$0.683335\pi$
$332$	132.939i	0.0219759i
$333$	− 10422.9i	− 1.71522i
$334$	−1360.28	−0.222847
$335$	0	0
$336$	−10343.8	−1.67947
$337$	3316.98i	0.536165i	0.963396	+	0.268083i	$0.0863900\pi$
$337$	3316.98i	0.536165i	−0.963396	+	0.268083i	$0.913610\pi$
$338$	− 432.902i	− 0.0696651i
$339$	13432.2	2.15203
$340$	0	0
$341$	11614.7	1.84449
$342$	13480.2i	2.13137i
$343$	1670.24i	0.262928i
$344$	−2525.59	−0.395845
$345$	0	0
$346$	2074.41	0.322315
$347$	− 3729.06i	− 0.576906i	−0.957494	−	0.288453i	$-0.906859\pi$
$347$	− 3729.06i	− 0.576906i	0.957494	−	0.288453i	$-0.0931408\pi$
$348$	1396.41i	0.215101i
$349$	−3748.22	−0.574892	−0.287446	−	0.957797i	$-0.592806\pi$
$349$	−3748.22	−0.574892	−0.287446	+	0.957797i	$0.592806\pi$
$350$	0	0
$351$	−1500.81	−0.228226
$352$	− 2498.02i	− 0.378253i
$353$	3353.90i	0.505694i	0.967506	+	0.252847i	$0.0813670\pi$
$353$	3353.90i	0.505694i	−0.967506	+	0.252847i	$0.918633\pi$
$354$	7386.97	1.10908
$355$	0	0
$356$	256.926	0.0382502
$357$	− 16405.0i	− 2.43206i
$358$	4692.44i	0.692746i
$359$	1041.87	0.153169	0.0765843	−	0.997063i	$-0.475599\pi$
$359$	1041.87	0.153169	0.0765843	+	0.997063i	$0.475599\pi$
$360$	0	0
$361$	9615.79	1.40192
$362$	2681.33i	0.389303i
$363$	− 1487.72i	− 0.215111i
$364$	−465.193	−0.0669856
$365$	0	0
$366$	9336.41	1.33339
$367$	1099.95i	0.156449i	0.996936	+	0.0782247i	$0.0249252\pi$
$367$	1099.95i	0.156449i	−0.996936	+	0.0782247i	$0.975075\pi$
$368$	− 5140.12i	− 0.728117i
$369$	−9004.93	−1.27040
$370$	0	0
$371$	−2.26206	−0.000316550 0
$372$	3543.76i	0.493913i
$373$	− 2967.14i	− 0.411884i	−0.978564	−	0.205942i	$-0.933974\pi$
$373$	− 2967.14i	− 0.411884i	0.978564	−	0.205942i	$-0.0660259\pi$
$374$	−7963.80	−1.10106
$375$	0	0
$376$	−7466.28	−1.02405
$377$	− 1530.41i	− 0.209071i
$378$	− 7356.68i	− 1.00102i
$379$	9221.67	1.24983	0.624915	−	0.780693i	$-0.285134\pi$
$379$	9221.67	1.24983	0.624915	+	0.780693i	$0.285134\pi$
$380$	0	0
$381$	1363.37	0.183327
$382$	1946.71i	0.260739i
$383$	11048.0i	1.47395i	0.675918	+	0.736976i	$0.263747\pi$
$383$	11048.0i	1.47395i	−0.675918	+	0.736976i	$0.736253\pi$
$384$	−7758.60	−1.03107
$385$	0	0
$386$	−1054.38	−0.139032
$387$	− 4282.95i	− 0.562570i
$388$	− 2456.09i	− 0.321363i
$389$	201.382	0.0262480	0.0131240	−	0.999914i	$-0.495822\pi$
$389$	201.382	0.0262480	0.0131240	+	0.999914i	$0.495822\pi$
$390$	0	0
$391$	8152.06	1.05439
$392$	− 6669.49i	− 0.859337i
$393$	15399.7i	1.97662i
$394$	2062.57	0.263733
$395$	0	0
$396$	2292.82	0.290955
$397$	− 4354.09i	− 0.550443i	−0.961381	−	0.275221i	$-0.911249\pi$
$397$	− 4354.09i	− 0.550443i	0.961381	−	0.275221i	$-0.0887511\pi$
$398$	− 7510.53i	− 0.945902i
$399$	−26330.6	−3.30370
$400$	0	0
$401$	4241.31	0.528182	0.264091	−	0.964498i	$-0.414928\pi$
$401$	4241.31	0.528182	0.264091	+	0.964498i	$0.414928\pi$
$402$	4817.63i	0.597715i
$403$	− 3883.82i	− 0.480067i
$404$	−1962.10	−0.241629
$405$	0	0
$406$	7501.75	0.917009
$407$	− 9883.12i	− 1.20366i
$408$	− 15943.5i	− 1.93461i
$409$	1622.25	0.196124	0.0980622	−	0.995180i	$-0.468736\pi$
$409$	1622.25	0.196124	0.0980622	+	0.995180i	$0.468736\pi$
$410$	0	0
$411$	14355.0	1.72282
$412$	− 510.889i	− 0.0610914i
$413$	8699.70i	1.03652i
$414$	10706.0	1.27095
$415$	0	0
$416$	−835.311	−0.0984483
$417$	− 8126.73i	− 0.954359i
$418$	12782.2i	1.49569i
$419$	6344.39	0.739723	0.369861	−	0.929087i	$-0.379405\pi$
$419$	6344.39	0.739723	0.369861	+	0.929087i	$0.379405\pi$
$420$	0	0
$421$	−7050.55	−0.816206	−0.408103	−	0.912936i	$-0.633810\pi$
$421$	−7050.55	−0.816206	−0.408103	+	0.912936i	$0.633810\pi$
$422$	− 10047.9i	− 1.15906i
$423$	− 12661.5i	− 1.45537i
$424$	−2.19842	−0.000251804 0
$425$	0	0
$426$	20369.6	2.31669
$427$	10995.6i	1.24617i
$428$	468.798i	0.0529444i
$429$	−4167.63	−0.469033
$430$	0	0
$431$	−2749.74	−0.307309	−0.153655	−	0.988125i	$-0.549104\pi$
$431$	−2749.74	−0.307309	−0.153655	+	0.988125i	$0.549104\pi$
$432$	− 5821.22i	− 0.648318i
$433$	12718.7i	1.41160i	0.708413	+	0.705798i	$0.249411\pi$
$433$	12718.7i	1.41160i	−0.708413	+	0.705798i	$0.750589\pi$
$434$	19037.7	2.10562
$435$	0	0
$436$	−2501.36	−0.274756
$437$	− 13084.3i	− 1.43229i
$438$	− 13997.9i	− 1.52704i
$439$	−17656.7	−1.91961	−0.959807	−	0.280660i	$-0.909447\pi$
$439$	−17656.7	−1.91961	−0.959807	+	0.280660i	$0.909447\pi$
$440$	0	0
$441$	11310.3	1.22128
$442$	2663.01i	0.286575i
$443$	− 18355.7i	− 1.96864i	−0.176397	−	0.984319i	$-0.556444\pi$
$443$	− 18355.7i	− 1.96864i	0.176397	−	0.984319i	$-0.443556\pi$
$444$	3015.44	0.322312
$445$	0	0
$446$	15664.6	1.66309
$447$	− 20590.0i	− 2.17869i
$448$	− 14129.5i	− 1.49008i
$449$	2675.78	0.281242	0.140621	−	0.990063i	$-0.455090\pi$
$449$	2675.78	0.281242	0.140621	+	0.990063i	$0.455090\pi$
$450$	0	0
$451$	−8538.63	−0.891504
$452$	2343.08i	0.243825i
$453$	− 2949.75i	− 0.305942i
$454$	−10799.9	−1.11644
$455$	0	0
$456$	−25589.9	−2.62797
$457$	6114.51i	0.625875i	0.949774	+	0.312937i	$0.101313\pi$
$457$	6114.51i	0.625875i	−0.949774	+	0.312937i	$0.898687\pi$
$458$	767.059i	0.0782583i
$459$	9232.26	0.938834
$460$	0	0
$461$	−13983.6	−1.41275	−0.706377	−	0.707836i	$-0.749671\pi$
$461$	−13983.6	−1.41275	−0.706377	+	0.707836i	$0.749671\pi$
$462$	− 20428.9i	− 2.05723i
$463$	5068.98i	0.508802i	0.967099	+	0.254401i	$0.0818783\pi$
$463$	5068.98i	0.508802i	−0.967099	+	0.254401i	$0.918122\pi$
$464$	5936.01	0.593905
$465$	0	0
$466$	3133.21	0.311466
$467$	2449.21i	0.242689i	0.992610	+	0.121345i	$0.0387206\pi$
$467$	2449.21i	0.242689i	−0.992610	+	0.121345i	$0.961279\pi$
$468$	− 766.692i	− 0.0757273i
$469$	−5673.77	−0.558615
$470$	0	0
$471$	−26538.9	−2.59628
$472$	8454.97i	0.824516i
$473$	− 4061.16i	− 0.394783i
$474$	1378.52	0.133582
$475$	0	0
$476$	2861.64	0.275553
$477$	− 3.72813i	0 0.000357860i
$478$	124.813i	0.0119431i
$479$	14106.1	1.34556	0.672780	−	0.739842i	$-0.265100\pi$
$479$	14106.1	1.34556	0.672780	+	0.739842i	$0.265100\pi$
$480$	0	0
$481$	−3304.81	−0.313277
$482$	− 11526.6i	− 1.08925i
$483$	20911.9i	1.97003i
$484$	259.514	0.0243721
$485$	0	0
$486$	−11258.6	−1.05083
$487$	11324.4i	1.05371i	0.849955	+	0.526855i	$0.176629\pi$
$487$	11324.4i	1.05371i	−0.849955	+	0.526855i	$0.823371\pi$
$488$	10686.3i	0.991280i
$489$	23926.4	2.21266
$490$	0	0
$491$	−11824.8	−1.08686	−0.543430	−	0.839455i	$-0.682875\pi$
$491$	−11824.8	−1.08686	−0.543430	+	0.839455i	$0.682875\pi$
$492$	− 2605.22i	− 0.238725i
$493$	9414.31i	0.860039i
$494$	4274.22	0.389284
$495$	0	0
$496$	15064.2	1.36372
$497$	23989.5i	2.16514i
$498$	1952.17i	0.175660i
$499$	−11462.3	−1.02830	−0.514150	−	0.857700i	$-0.671892\pi$
$499$	−11462.3	−1.02830	−0.514150	+	0.857700i	$0.671892\pi$
$500$	0	0
$501$	4379.03	0.390501
$502$	− 282.508i	− 0.0251174i
$503$	13165.2i	1.16701i	0.812109	+	0.583506i	$0.198320\pi$
$503$	13165.2i	1.16701i	−0.812109	+	0.583506i	$0.801680\pi$
$504$	24659.5	2.17941
$505$	0	0
$506$	10151.7	0.891890
$507$	1393.61i	0.122076i
$508$	237.823i	0.0207710i
$509$	−8849.94	−0.770661	−0.385331	−	0.922779i	$-0.625913\pi$
$509$	−8849.94	−0.770661	−0.385331	+	0.922779i	$0.625913\pi$
$510$	0	0
$511$	16485.5	1.42715
$512$	− 12992.6i	− 1.12148i
$513$	− 14818.1i	− 1.27531i
$514$	−19093.2	−1.63845
$515$	0	0
$516$	1239.10	0.105714
$517$	− 12005.8i	− 1.02131i
$518$	− 16199.5i	− 1.37407i
$519$	−6677.99	−0.564800
$520$	0	0
$521$	20509.2	1.72461	0.862306	−	0.506387i	$-0.169019\pi$
$521$	20509.2	1.72461	0.862306	+	0.506387i	$0.169019\pi$
$522$	12363.8i	1.03668i
$523$	− 434.056i	− 0.0362906i	−0.999835	−	0.0181453i	$-0.994224\pi$
$523$	− 434.056i	− 0.0362906i	0.999835	−	0.0181453i	$-0.00577614\pi$
$524$	−2686.28	−0.223952
$525$	0	0
$526$	−576.748	−0.0478087
$527$	23891.4i	1.97481i
$528$	− 16165.1i	− 1.33237i
$529$	1775.36	0.145916
$530$	0	0
$531$	−14338.1	−1.17179
$532$	− 4593.04i	− 0.374311i
$533$	2855.22i	0.232033i
$534$	3772.88	0.305746
$535$	0	0
$536$	−5514.16	−0.444357
$537$	− 15106.0i	− 1.21391i
$538$	7024.00i	0.562874i
$539$	10724.6	0.857032
$540$	0	0
$541$	−5500.16	−0.437099	−0.218549	−	0.975826i	$-0.570132\pi$
$541$	−5500.16	−0.437099	−0.218549	+	0.975826i	$0.570132\pi$
$542$	17289.7i	1.37021i
$543$	− 8631.82i	− 0.682185i
$544$	5138.43	0.404979
$545$	0	0
$546$	−6831.20	−0.535437
$547$	8536.10i	0.667235i	0.942709	+	0.333617i	$0.108269\pi$
$547$	8536.10i	0.667235i	−0.942709	+	0.333617i	$0.891731\pi$
$548$	2504.05i	0.195196i
$549$	−18122.0	−1.40879
$550$	0	0
$551$	15110.3	1.16828
$552$	20323.6i	1.56708i
$553$	1623.50i	0.124843i
$554$	−3872.18	−0.296955
$555$	0	0
$556$	1417.61	0.108129
$557$	− 4701.29i	− 0.357630i	−0.983883	−	0.178815i	$-0.942774\pi$
$557$	− 4701.29i	− 0.357630i	0.983883	−	0.178815i	$-0.0572264\pi$
$558$	31376.4i	2.38041i
$559$	−1358.01	−0.102751
$560$	0	0
$561$	25637.2	1.92942
$562$	− 14328.5i	− 1.07547i
$563$	− 14613.9i	− 1.09396i	−0.837145	−	0.546981i	$-0.815777\pi$
$563$	− 14613.9i	− 1.09396i	0.837145	−	0.546981i	$-0.184223\pi$
$564$	3663.10	0.273483
$565$	0	0
$566$	−8250.82	−0.612735
$567$	− 3855.92i	− 0.285597i
$568$	23314.6i	1.72229i
$569$	10789.3	0.794921	0.397461	−	0.917619i	$-0.369892\pi$
$569$	10789.3	0.794921	0.397461	+	0.917619i	$0.369892\pi$
$570$	0	0
$571$	−1553.39	−0.113848	−0.0569240	−	0.998379i	$-0.518129\pi$
$571$	−1553.39	−0.113848	−0.0569240	+	0.998379i	$0.518129\pi$
$572$	− 726.991i	− 0.0531416i
$573$	− 6266.90i	− 0.456900i
$574$	−13995.8	−1.01772
$575$	0	0
$576$	23287.1	1.68454
$577$	11828.6i	0.853431i	0.904386	+	0.426715i	$0.140329\pi$
$577$	11828.6i	0.853431i	−0.904386	+	0.426715i	$0.859671\pi$
$578$	− 3796.61i	− 0.273215i
$579$	3394.29	0.243630
$580$	0	0
$581$	−2299.09	−0.164169
$582$	− 36066.8i	− 2.56876i
$583$	− 3.53507i	0 0.000251128i
$584$	16021.7	1.13525
$585$	0	0
$586$	20005.3	1.41026
$587$	2823.97i	0.198565i	0.995059	+	0.0992825i	$0.0316548\pi$
$587$	2823.97i	0.198565i	−0.995059	+	0.0992825i	$0.968345\pi$
$588$	3272.18i	0.229494i
$589$	38346.5	2.68258
$590$	0	0
$591$	−6639.89	−0.462146
$592$	− 12818.4i	− 0.889921i
$593$	− 2016.22i	− 0.139623i	−0.997560	−	0.0698115i	$-0.977760\pi$
$593$	− 2016.22i	− 0.139623i	0.997560	−	0.0698115i	$-0.0222398\pi$
$594$	11496.8	0.794141
$595$	0	0
$596$	3591.66	0.246846
$597$	24178.1i	1.65753i
$598$	− 3394.60i	− 0.232133i
$599$	−9247.60	−0.630796	−0.315398	−	0.948960i	$-0.602138\pi$
$599$	−9247.60	−0.630796	−0.315398	+	0.948960i	$0.602138\pi$
$600$	0	0
$601$	8105.84	0.550156	0.275078	−	0.961422i	$-0.411296\pi$
$601$	8105.84	0.550156	0.275078	+	0.961422i	$0.411296\pi$
$602$	− 6656.69i	− 0.450675i
$603$	− 9351.03i	− 0.631515i
$604$	514.547	0.0346633
$605$	0	0
$606$	−28812.7	−1.93141
$607$	11059.6i	0.739534i	0.929124	+	0.369767i	$0.120563\pi$
$607$	11059.6i	0.739534i	−0.929124	+	0.369767i	$0.879437\pi$
$608$	− 8247.36i	− 0.550123i
$609$	−24149.8	−1.60690
$610$	0	0
$611$	−4014.61	−0.265816
$612$	4716.32i	0.311513i
$613$	12579.3i	0.828831i	0.910088	+	0.414416i	$0.136014\pi$
$613$	12579.3i	0.828831i	−0.910088	+	0.414416i	$0.863986\pi$
$614$	−21980.9	−1.44475
$615$	0	0
$616$	23382.5	1.52940
$617$	16915.6i	1.10372i	0.833935	+	0.551862i	$0.186083\pi$
$617$	16915.6i	1.10372i	−0.833935	+	0.551862i	$0.813917\pi$
$618$	− 7502.22i	− 0.488323i
$619$	−10313.7	−0.669697	−0.334849	−	0.942272i	$-0.608685\pi$
$619$	−10313.7	−0.669697	−0.334849	+	0.942272i	$0.608685\pi$
$620$	0	0
$621$	−11768.6	−0.760479
$622$	23699.1i	1.52773i
$623$	4443.35i	0.285745i
$624$	−5405.41	−0.346778
$625$	0	0
$626$	11235.4	0.717344
$627$	− 41148.7i	− 2.62093i
$628$	− 4629.38i	− 0.294160i
$629$	20329.6	1.28870
$630$	0	0
$631$	−20558.9	−1.29705	−0.648524	−	0.761194i	$-0.724613\pi$
$631$	−20558.9	−1.29705	−0.648524	+	0.761194i	$0.724613\pi$
$632$	1577.83i	0.0993080i
$633$	32346.4i	2.03105i
$634$	1505.39	0.0943006
$635$	0	0
$636$	1.07859	6.72465e−5 0
$637$	− 3586.18i	− 0.223061i
$638$	11723.5i	0.727490i
$639$	−39537.4	−2.44769
$640$	0	0
$641$	−5651.22	−0.348221	−0.174111	−	0.984726i	$-0.555705\pi$
$641$	−5651.22	−0.348221	−0.174111	+	0.984726i	$0.555705\pi$
$642$	6884.13i	0.423201i
$643$	− 2197.26i	− 0.134761i	−0.997727	−	0.0673805i	$-0.978536\pi$
$643$	− 2197.26i	− 0.134761i	0.997727	−	0.0673805i	$-0.0214641\pi$
$644$	−3647.81	−0.223205
$645$	0	0
$646$	−26292.9	−1.60136
$647$	23529.6i	1.42974i	0.699255	+	0.714872i	$0.253515\pi$
$647$	23529.6i	1.42974i	−0.699255	+	0.714872i	$0.746485\pi$
$648$	− 3747.45i	− 0.227182i
$649$	−13595.6	−0.822305
$650$	0	0
$651$	−61286.8	−3.68974
$652$	4173.66i	0.250695i
$653$	− 26577.6i	− 1.59275i	−0.604806	−	0.796373i	$-0.706749\pi$
$653$	− 26577.6i	− 1.59275i	0.604806	−	0.796373i	$-0.293251\pi$
$654$	−36731.6	−2.19621
$655$	0	0
$656$	−11074.6	−0.659132
$657$	27170.0i	1.61340i
$658$	− 19678.8i	− 1.16590i
$659$	454.595	0.0268718	0.0134359	−	0.999910i	$-0.495723\pi$
$659$	454.595	0.0268718	0.0134359	+	0.999910i	$0.495723\pi$
$660$	0	0
$661$	−21367.3	−1.25732	−0.628662	−	0.777679i	$-0.716397\pi$
$661$	−21367.3	−1.25732	−0.628662	+	0.777679i	$0.716397\pi$
$662$	− 16803.0i	− 0.986508i
$663$	− 8572.81i	− 0.502173i
$664$	−2234.41	−0.130590
$665$	0	0
$666$	26698.7	1.55338
$667$	− 12000.7i	− 0.696653i
$668$	763.867i	0.0442439i
$669$	−50427.8	−2.91428
$670$	0	0
$671$	−17183.6	−0.988622
$672$	13181.2i	0.756662i
$673$	18710.7i	1.07169i	0.844318	+	0.535843i	$0.180006\pi$
$673$	18710.7i	1.07169i	−0.844318	+	0.535843i	$0.819994\pi$
$674$	−8496.63	−0.485576
$675$	0	0
$676$	−243.098	−0.0138312
$677$	− 29181.5i	− 1.65662i	−0.560267	−	0.828312i	$-0.689301\pi$
$677$	− 29181.5i	− 1.65662i	0.560267	−	0.828312i	$-0.310699\pi$
$678$	34407.3i	1.94897i
$679$	42476.3	2.40072
$680$	0	0
$681$	34767.1	1.95636
$682$	29751.6i	1.67045i
$683$	− 21953.8i	− 1.22992i	−0.788557	−	0.614961i	$-0.789172\pi$
$683$	− 21953.8i	− 1.22992i	0.788557	−	0.614961i	$-0.210828\pi$
$684$	7569.86	0.423159
$685$	0	0
$686$	−4278.40	−0.238120
$687$	− 2469.33i	− 0.137134i
$688$	− 5267.32i	− 0.291882i
$689$	−1.18209	−6.53614e−5 0
$690$	0	0
$691$	2242.59	0.123462	0.0617309	−	0.998093i	$-0.480338\pi$
$691$	2242.59	0.123462	0.0617309	+	0.998093i	$0.480338\pi$
$692$	− 1164.89i	− 0.0639921i
$693$	39652.6i	2.17356i
$694$	9552.18	0.522472
$695$	0	0
$696$	−23470.4	−1.27823
$697$	− 17563.9i	− 0.954493i
$698$	− 9601.25i	− 0.520649i
$699$	−10086.5	−0.545788
$700$	0	0
$701$	16013.4	0.862794	0.431397	−	0.902162i	$-0.358021\pi$
$701$	16013.4	0.862794	0.431397	+	0.902162i	$0.358021\pi$
$702$	− 3844.41i	− 0.206692i
$703$	− 32629.7i	− 1.75057i
$704$	22081.2	1.18213
$705$	0	0
$706$	−8591.19	−0.457980
$707$	− 33933.0i	− 1.80507i
$708$	− 4148.17i	− 0.220195i
$709$	34333.3	1.81864	0.909318	−	0.416102i	$-0.136604\pi$
$709$	34333.3	1.81864	0.909318	+	0.416102i	$0.136604\pi$
$710$	0	0
$711$	−2675.72	−0.141135
$712$	4318.36i	0.227300i
$713$	− 30455.0i	− 1.59965i
$714$	42022.3	2.20258
$715$	0	0
$716$	2635.05	0.137537
$717$	− 401.799i	− 0.0209281i
$718$	2668.79i	0.138717i
$719$	4359.43	0.226119	0.113059	−	0.993588i	$-0.463935\pi$
$719$	4359.43	0.226119	0.113059	+	0.993588i	$0.463935\pi$
$720$	0	0
$721$	8835.44	0.456379
$722$	24631.4i	1.26965i
$723$	37106.5i	1.90872i
$724$	1505.71	0.0772919
$725$	0	0
$726$	3810.88	0.194814
$727$	− 9626.47i	− 0.491095i	−0.969385	−	0.245547i	$-0.921032\pi$
$727$	− 9626.47i	− 0.491095i	0.969385	−	0.245547i	$-0.0789677\pi$
$728$	− 7818.86i	− 0.398058i
$729$	32059.0	1.62877
$730$	0	0
$731$	8353.80	0.422677
$732$	− 5242.89i	− 0.264731i
$733$	11224.3i	0.565590i	0.959180	+	0.282795i	$0.0912617\pi$
$733$	11224.3i	0.565590i	−0.959180	+	0.282795i	$0.908738\pi$
$734$	−2817.58	−0.141688
$735$	0	0
$736$	−6550.09	−0.328043
$737$	− 8866.81i	− 0.443165i
$738$	− 23066.6i	− 1.15053i
$739$	−20190.6	−1.00504	−0.502519	−	0.864566i	$-0.667593\pi$
$739$	−20190.6	−1.00504	−0.502519	+	0.864566i	$0.667593\pi$
$740$	0	0
$741$	−13759.7	−0.682151
$742$	− 5.79437i	0 0.000286682i
$743$	19756.1i	0.975479i	0.872989	+	0.487739i	$0.162178\pi$
$743$	19756.1i	0.975479i	−0.872989	+	0.487739i	$0.837822\pi$
$744$	−59562.7	−2.93505
$745$	0	0
$746$	7600.49	0.373021
$747$	− 3789.16i	− 0.185593i
$748$	4472.09i	0.218604i
$749$	−8107.51	−0.395517
$750$	0	0
$751$	17597.3	0.855040	0.427520	−	0.904006i	$-0.359387\pi$
$751$	17597.3	0.855040	0.427520	+	0.904006i	$0.359387\pi$
$752$	− 15571.5i	− 0.755100i
$753$	909.456i	0.0440138i
$754$	3920.21	0.189345
$755$	0	0
$756$	−4131.17	−0.198742
$757$	29920.3i	1.43655i	0.695757	+	0.718277i	$0.255069\pi$
$757$	29920.3i	1.43655i	−0.695757	+	0.718277i	$0.744931\pi$
$758$	23621.8i	1.13190i
$759$	−32680.4	−1.56288
$760$	0	0
$761$	13040.7	0.621190	0.310595	−	0.950542i	$-0.399472\pi$
$761$	13040.7	0.621190	0.310595	+	0.950542i	$0.399472\pi$
$762$	3492.35i	0.166030i
$763$	− 43259.2i	− 2.05254i
$764$	1093.18	0.0517669
$765$	0	0
$766$	−28299.9	−1.33488
$767$	4546.23i	0.214022i
$768$	17595.3i	0.826712i
$769$	−23856.2	−1.11869	−0.559347	−	0.828934i	$-0.688948\pi$
$769$	−23856.2	−1.11869	−0.559347	+	0.828934i	$0.688948\pi$
$770$	0	0
$771$	61465.3	2.87110
$772$	592.090i	0.0276034i
$773$	20701.3i	0.963224i	0.876384	+	0.481612i	$0.159949\pi$
$773$	20701.3i	0.963224i	−0.876384	+	0.481612i	$0.840051\pi$
$774$	10971.0	0.509489
$775$	0	0
$776$	41281.4	1.90968
$777$	52149.9i	2.40781i
$778$	515.851i	0.0237714i
$779$	−28190.8	−1.29658
$780$	0	0
$781$	−37490.1	−1.71767
$782$	20881.9i	0.954906i
$783$	− 13590.8i	− 0.620302i
$784$	13909.8	0.633644
$785$	0	0
$786$	−39447.2	−1.79012
$787$	− 4082.21i	− 0.184899i	−0.995717	−	0.0924493i	$-0.970530\pi$
$787$	− 4082.21i	− 0.184899i	0.995717	−	0.0924493i	$-0.0294696\pi$
$788$	− 1158.24i	− 0.0523613i
$789$	1856.68	0.0837764
$790$	0	0
$791$	−40521.8	−1.82148
$792$	38537.1i	1.72899i
$793$	5746.00i	0.257310i
$794$	11153.2	0.498506
$795$	0	0
$796$	−4217.56	−0.187798
$797$	17269.3i	0.767514i	0.923434	+	0.383757i	$0.125370\pi$
$797$	17269.3i	0.767514i	−0.923434	+	0.383757i	$0.874630\pi$
$798$	− 67447.2i	− 2.99199i
$799$	24695.9	1.09347
$800$	0	0
$801$	−7323.16	−0.323035
$802$	10864.3i	0.478346i
$803$	25763.0i	1.13220i
$804$	2705.35	0.118670
$805$	0	0
$806$	9948.62	0.434771
$807$	− 22611.8i	− 0.986337i
$808$	− 32978.5i	− 1.43586i
$809$	35166.8	1.52831	0.764153	−	0.645034i	$-0.223157\pi$
$809$	35166.8	1.52831	0.764153	+	0.645034i	$0.223157\pi$
$810$	0	0
$811$	−40718.1	−1.76302	−0.881509	−	0.472167i	$-0.843472\pi$
$811$	−40718.1	−1.76302	−0.881509	+	0.472167i	$0.843472\pi$
$812$	− 4212.63i	− 0.182062i
$813$	− 55659.3i	− 2.40106i
$814$	25316.1	1.09009
$815$	0	0
$816$	33251.5	1.42651
$817$	− 13408.1i	− 0.574164i
$818$	4155.47i	0.177619i
$819$	13259.4	0.565715
$820$	0	0
$821$	−30057.8	−1.27774	−0.638870	−	0.769314i	$-0.720598\pi$
$821$	−30057.8	−1.27774	−0.638870	+	0.769314i	$0.720598\pi$
$822$	36771.1i	1.56027i
$823$	− 4548.10i	− 0.192633i	−0.995351	−	0.0963163i	$-0.969294\pi$
$823$	− 4548.10i	− 0.192633i	0.995351	−	0.0963163i	$-0.0307060\pi$
$824$	8586.89	0.363032
$825$	0	0
$826$	−22284.7	−0.938724
$827$	9335.94i	0.392554i	0.980548	+	0.196277i	$0.0628852\pi$
$827$	9335.94i	0.392554i	−0.980548	+	0.196277i	$0.937115\pi$
$828$	− 6012.01i	− 0.252333i
$829$	22765.0	0.953751	0.476876	−	0.878971i	$-0.341769\pi$
$829$	22765.0	0.953751	0.476876	+	0.878971i	$0.341769\pi$
$830$	0	0
$831$	12465.4	0.520361
$832$	− 7383.72i	− 0.307673i
$833$	22060.4i	0.917585i
$834$	20817.1	0.864312
$835$	0	0
$836$	7177.87	0.296952
$837$	− 34490.4i	− 1.42433i
$838$	16251.5i	0.669927i
$839$	−28521.3	−1.17362	−0.586808	−	0.809726i	$-0.699616\pi$
$839$	−28521.3	−1.17362	−0.586808	+	0.809726i	$0.699616\pi$
$840$	0	0
$841$	−10530.2	−0.431760
$842$	− 18060.3i	− 0.739193i
$843$	46126.7i	1.88456i
$844$	−5642.41	−0.230118
$845$	0	0
$846$	32433.0	1.31805
$847$	4488.11i	0.182070i
$848$	− 4.58499i	0 0.000185671i
$849$	26561.2	1.07371
$850$	0	0
$851$	−25914.6	−1.04388
$852$	− 11438.6i	− 0.459953i
$853$	− 5037.10i	− 0.202189i	−0.994877	−	0.101094i	$-0.967766\pi$
$853$	− 5037.10i	− 0.202189i	0.994877	−	0.101094i	$-0.0322344\pi$
$854$	−28165.8	−1.12859
$855$	0	0
$856$	−7879.44	−0.314619
$857$	− 27178.6i	− 1.08332i	−0.840599	−	0.541658i	$-0.817797\pi$
$857$	− 27178.6i	− 1.08332i	0.840599	−	0.541658i	$-0.182203\pi$
$858$	− 10675.6i	− 0.424778i
$859$	−21916.5	−0.870525	−0.435262	−	0.900304i	$-0.643344\pi$
$859$	−21916.5	−0.870525	−0.435262	+	0.900304i	$0.643344\pi$
$860$	0	0
$861$	45055.4	1.78337
$862$	− 7043.60i	− 0.278313i
$863$	− 38533.9i	− 1.51994i	−0.649957	−	0.759971i	$-0.725213\pi$
$863$	− 38533.9i	− 1.51994i	0.649957	−	0.759971i	$-0.274787\pi$
$864$	−7418.01	−0.292090
$865$	0	0
$866$	−32579.6	−1.27841
$867$	12222.1i	0.478761i
$868$	− 10690.7i	− 0.418048i
$869$	−2537.16	−0.0990417
$870$	0	0
$871$	−2964.96	−0.115343
$872$	− 42042.3i	− 1.63272i
$873$	70005.8i	2.71402i
$874$	33516.2	1.29714
$875$	0	0
$876$	−7860.56	−0.303178
$877$	4812.41i	0.185295i	0.995699	+	0.0926475i	$0.0295330\pi$
$877$	4812.41i	0.185295i	−0.995699	+	0.0926475i	$0.970467\pi$
$878$	− 45228.7i	− 1.73849i
$879$	−64401.6	−2.47123
$880$	0	0
$881$	−18910.3	−0.723160	−0.361580	−	0.932341i	$-0.617763\pi$
$881$	−18910.3	−0.723160	−0.361580	+	0.932341i	$0.617763\pi$
$882$	28971.8i	1.10605i
$883$	35174.6i	1.34057i	0.742106	+	0.670283i	$0.233827\pi$
$883$	35174.6i	1.34057i	−0.742106	+	0.670283i	$0.766173\pi$
$884$	1495.42	0.0568963
$885$	0	0
$886$	47019.2	1.78289
$887$	38502.7i	1.45749i	0.684785	+	0.728745i	$0.259896\pi$
$887$	38502.7i	1.45749i	−0.684785	+	0.728745i	$0.740104\pi$
$888$	50682.9i	1.91532i
$889$	−4112.98	−0.155168
$890$	0	0
$891$	6025.92	0.226572
$892$	− 8796.49i	− 0.330189i
$893$	− 39637.9i	− 1.48536i
$894$	52742.3	1.97312
$895$	0	0
$896$	23405.9	0.872696
$897$	10928.0i	0.406772i
$898$	6854.14i	0.254706i
$899$	35170.6	1.30479
$900$	0	0
$901$	7.27164	0.000268872 0
$902$	− 21872.2i	− 0.807387i
$903$	21429.4i	0.789728i
$904$	−39381.9	−1.44892
$905$	0	0
$906$	7555.95	0.277075
$907$	− 52947.3i	− 1.93835i	−0.246368	−	0.969176i	$-0.579237\pi$
$907$	− 52947.3i	− 1.93835i	0.246368	−	0.969176i	$-0.420763\pi$
$908$	6064.69i	0.221656i
$909$	55925.5	2.04063
$910$	0	0
$911$	11565.8	0.420627	0.210314	−	0.977634i	$-0.432551\pi$
$911$	11565.8	0.420627	0.210314	+	0.977634i	$0.432551\pi$
$912$	− 53369.8i	− 1.93778i
$913$	− 3592.94i	− 0.130240i
$914$	−15662.6	−0.566821
$915$	0	0
$916$	430.744	0.0155373
$917$	− 46457.3i	− 1.67302i
$918$	23648.9i	0.850251i
$919$	31800.9	1.14148	0.570738	−	0.821132i	$-0.306657\pi$
$919$	31800.9	1.14148	0.570738	+	0.821132i	$0.306657\pi$
$920$	0	0
$921$	70761.3	2.53167
$922$	− 35819.6i	− 1.27945i
$923$	12536.3i	0.447060i
$924$	−11471.9	−0.408440
$925$	0	0
$926$	−12984.5	−0.460794
$927$	14561.8i	0.515937i
$928$	− 7564.29i	− 0.267575i
$929$	−39306.1	−1.38815	−0.694075	−	0.719903i	$-0.744186\pi$
$929$	−39306.1	−1.38815	−0.694075	+	0.719903i	$0.744186\pi$
$930$	0	0
$931$	35407.8	1.24645
$932$	− 1759.46i	− 0.0618380i
$933$	− 76292.6i	− 2.67707i
$934$	−6273.78	−0.219791
$935$	0	0
$936$	12886.4	0.450005
$937$	2554.39i	0.0890589i	0.999008	+	0.0445294i	$0.0141789\pi$
$937$	2554.39i	0.0890589i	−0.999008	+	0.0445294i	$0.985821\pi$
$938$	− 14533.7i	− 0.505907i
$939$	−36169.3	−1.25702
$940$	0	0
$941$	17871.8	0.619133	0.309567	−	0.950878i	$-0.399816\pi$
$941$	17871.8	0.619133	0.309567	+	0.950878i	$0.399816\pi$
$942$	− 67980.9i	− 2.35131i
$943$	22389.2i	0.773163i
$944$	−17633.5	−0.607969
$945$	0	0
$946$	10402.9	0.357534
$947$	13013.0i	0.446532i	0.974758	+	0.223266i	$0.0716719\pi$
$947$	13013.0i	0.446532i	−0.974758	+	0.223266i	$0.928328\pi$
$948$	− 774.113i	− 0.0265211i
$949$	8614.86	0.294679
$950$	0	0
$951$	−4846.18	−0.165245
$952$	48097.8i	1.63746i
$953$	11984.0i	0.407345i	0.979039	+	0.203672i	$0.0652877\pi$
$953$	11984.0i	0.407345i	−0.979039	+	0.203672i	$0.934712\pi$
$954$	9.54980	0.000324094 0
$955$	0	0
$956$	70.0888	0.00237117
$957$	− 37740.6i	− 1.27480i
$958$	36133.5i	1.21860i
$959$	−43305.7	−1.45820
$960$	0	0
$961$	59463.9	1.99604
$962$	− 8465.44i	− 0.283718i
$963$	− 13362.1i	− 0.447132i
$964$	−6472.77	−0.216259
$965$	0	0
$966$	−53566.8	−1.78415
$967$	34643.6i	1.15208i	0.817421	+	0.576041i	$0.195403\pi$
$967$	34643.6i	1.15208i	−0.817421	+	0.576041i	$0.804597\pi$
$968$	4361.86i	0.144830i
$969$	84642.8	2.80611
$970$	0	0
$971$	11097.6	0.366776	0.183388	−	0.983041i	$-0.441294\pi$
$971$	11097.6	0.366776	0.183388	+	0.983041i	$0.441294\pi$
$972$	6322.31i	0.208630i
$973$	24516.5i	0.807771i
$974$	−29008.0	−0.954288
$975$	0	0
$976$	−22287.1	−0.730935
$977$	6609.39i	0.216431i	0.994127	+	0.108215i	$0.0345136\pi$
$977$	6609.39i	0.216431i	−0.994127	+	0.108215i	$0.965486\pi$
$978$	61288.8i	2.00389i
$979$	−6943.94	−0.226690
$980$	0	0
$981$	71296.2	2.32040
$982$	− 30290.0i	− 0.984309i
$983$	− 30211.3i	− 0.980254i	−0.871651	−	0.490127i	$-0.836950\pi$
$983$	− 30211.3i	− 0.980254i	0.871651	−	0.490127i	$-0.163050\pi$
$984$	43788.0	1.41861
$985$	0	0
$986$	−24115.3	−0.778891
$987$	63350.6i	2.04303i
$988$	− 2400.20i	− 0.0772880i
$989$	−10648.8	−0.342378
$990$	0	0
$991$	36910.1	1.18313	0.591567	−	0.806256i	$-0.298509\pi$
$991$	36910.1	1.18313	0.591567	+	0.806256i	$0.298509\pi$
$992$	− 19196.5i	− 0.614403i
$993$	54092.7i	1.72868i
$994$	−61450.3	−1.96085
$995$	0	0
$996$	1096.24	0.0348753
$997$	− 42912.3i	− 1.36313i	−0.731755	−	0.681567i	$-0.761299\pi$
$997$	− 42912.3i	− 1.36313i	0.731755	−	0.681567i	$-0.238701\pi$
$998$	− 29361.2i	− 0.931275i
$999$	−29348.5	−0.929473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.4.b.f.274.4		4
5.2	odd	4		325.4.a.g.1.1		2
5.3	odd	4		65.4.a.c.1.2	✓	2
5.4	even	2	inner	325.4.b.f.274.1		4
15.8	even	4		585.4.a.h.1.1		2
20.3	even	4		1040.4.a.k.1.1		2
65.38	odd	4		845.4.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.a.c.1.2	✓	2	5.3	odd	4
325.4.a.g.1.1		2	5.2	odd	4
325.4.b.f.274.1		4	5.4	even	2	inner
325.4.b.f.274.4		4	1.1	even	1	trivial
585.4.a.h.1.1		2	15.8	even	4
845.4.a.d.1.1		2	65.38	odd	4
1040.4.a.k.1.1		2	20.3	even	4

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	325.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.56155i q^{2} -8.24621i q^{3} +1.43845 q^{4} +21.1231 q^{6} +24.8769i q^{7} +24.1771i q^{8} -41.0000 q^{9} +O(q^{10})\)	\(q+2.56155i q^{2} -8.24621i q^{3} +1.43845 q^{4} +21.1231 q^{6} +24.8769i q^{7} +24.1771i q^{8} -41.0000 q^{9} -38.8769 q^{11} -11.8617i q^{12} +13.0000i q^{13} -63.7235 q^{14} -50.4233 q^{16} -79.9697i q^{17} -105.024i q^{18} -128.354 q^{19} +205.140 q^{21} -99.5852i q^{22} +101.939i q^{23} +199.369 q^{24} -33.3002 q^{26} +115.447i q^{27} +35.7841i q^{28} -117.723 q^{29} -298.756 q^{31} +64.2547i q^{32} +320.587i q^{33} +204.847 q^{34} -58.9763 q^{36} +254.216i q^{37} -328.786i q^{38} +107.201 q^{39} +219.633 q^{41} +525.477i q^{42} +104.462i q^{43} -55.9224 q^{44} -261.123 q^{46} +308.816i q^{47} +415.801i q^{48} -275.860 q^{49} -659.447 q^{51} +18.6998i q^{52} +0.0909300i q^{53} -295.723 q^{54} -601.451 q^{56} +1058.44i q^{57} -301.555i q^{58} +349.710 q^{59} +442.000 q^{61} -765.278i q^{62} -1019.95i q^{63} -567.978 q^{64} -821.201 q^{66} +228.074i q^{67} -115.032i q^{68} +840.614 q^{69} +964.328 q^{71} -991.260i q^{72} -662.682i q^{73} -651.187 q^{74} -184.631 q^{76} -967.136i q^{77} +274.600i q^{78} +65.2614 q^{79} -155.000 q^{81} +562.600i q^{82} +92.4185i q^{83} +295.083 q^{84} -267.585 q^{86} +970.773i q^{87} -939.930i q^{88} +178.614 q^{89} -323.400 q^{91} +146.634i q^{92} +2463.60i q^{93} -791.049 q^{94} +529.858 q^{96} -1707.46i q^{97} -706.630i q^{98} +1593.95 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 14 q^{4} + 68 q^{6} - 164 q^{9}+O(q^{10}) \) 4 * q + 14 * q^4 + 68 * q^6 - 164 * q^9	\( 4 q + 14 q^{4} + 68 q^{6} - 164 q^{9} - 172 q^{11} - 24 q^{14} - 78 q^{16} - 332 q^{19} - 136 q^{21} + 748 q^{24} - 26 q^{26} - 240 q^{29} - 156 q^{31} + 572 q^{34} - 574 q^{36} - 144 q^{41} - 636 q^{44} - 1028 q^{46} - 2060 q^{49} - 2176 q^{51} - 952 q^{54} + 200 q^{56} - 36 q^{59} + 1768 q^{61} - 1538 q^{64} - 2856 q^{66} + 4352 q^{69} + 1268 q^{71} - 972 q^{74} - 788 q^{76} + 360 q^{79} - 620 q^{81} - 2448 q^{84} - 724 q^{86} + 1704 q^{89} - 1508 q^{91} - 1416 q^{94} + 4148 q^{96} + 7052 q^{99}+O(q^{100}) \) 4 * q + 14 * q^4 + 68 * q^6 - 164 * q^9 - 172 * q^11 - 24 * q^14 - 78 * q^16 - 332 * q^19 - 136 * q^21 + 748 * q^24 - 26 * q^26 - 240 * q^29 - 156 * q^31 + 572 * q^34 - 574 * q^36 - 144 * q^41 - 636 * q^44 - 1028 * q^46 - 2060 * q^49 - 2176 * q^51 - 952 * q^54 + 200 * q^56 - 36 * q^59 + 1768 * q^61 - 1538 * q^64 - 2856 * q^66 + 4352 * q^69 + 1268 * q^71 - 972 * q^74 - 788 * q^76 + 360 * q^79 - 620 * q^81 - 2448 * q^84 - 724 * q^86 + 1704 * q^89 - 1508 * q^91 - 1416 * q^94 + 4148 * q^96 + 7052 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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