LMFDB - Embedded newform 1617.2.c.a.538.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(538,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1617.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.c (of order $2$, degree $1$, 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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			538.7
Character	$\chi$	$=$	1617.538
Dual form			1617.2.c.a.538.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.72615i q^{2} -1.00000i q^{3} -0.979587 q^{4} -1.65517i q^{5} -1.72615 q^{6} -1.76138i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.72615i q^{2} -1.00000i q^{3} -0.979587 q^{4} -1.65517i q^{5} -1.72615 q^{6} -1.76138i q^{8} -1.00000 q^{9} -2.85707 q^{10} +(-2.71972 - 1.89819i) q^{11} +0.979587i q^{12} -2.97508 q^{13} -1.65517 q^{15} -4.99958 q^{16} +1.49538 q^{17} +1.72615i q^{18} +5.51610 q^{19} +1.62139i q^{20} +(-3.27656 + 4.69464i) q^{22} -8.62843 q^{23} -1.76138 q^{24} +2.26040 q^{25} +5.13544i q^{26} +1.00000i q^{27} -8.02774i q^{29} +2.85707i q^{30} +8.86643i q^{31} +5.10725i q^{32} +(-1.89819 + 2.71972i) q^{33} -2.58126i q^{34} +0.979587 q^{36} +8.22774 q^{37} -9.52160i q^{38} +2.97508i q^{39} -2.91540 q^{40} -8.12983 q^{41} -5.03560i q^{43} +(2.66420 + 1.85944i) q^{44} +1.65517i q^{45} +14.8939i q^{46} +7.36847i q^{47} +4.99958i q^{48} -3.90179i q^{50} -1.49538i q^{51} +2.91435 q^{52} -1.26049 q^{53} +1.72615 q^{54} +(-3.14184 + 4.50161i) q^{55} -5.51610i q^{57} -13.8571 q^{58} -4.96848i q^{59} +1.62139 q^{60} +3.65902 q^{61} +15.3048 q^{62} -1.18329 q^{64} +4.92428i q^{65} +(4.69464 + 3.27656i) q^{66} -10.7360 q^{67} -1.46486 q^{68} +8.62843i q^{69} -1.05369 q^{71} +1.76138i q^{72} -9.85074 q^{73} -14.2023i q^{74} -2.26040i q^{75} -5.40350 q^{76} +5.13544 q^{78} -3.93938i q^{79} +8.27518i q^{80} +1.00000 q^{81} +14.0333i q^{82} +10.2146 q^{83} -2.47512i q^{85} -8.69219 q^{86} -8.02774 q^{87} +(-3.34344 + 4.79047i) q^{88} +5.16502i q^{89} +2.85707 q^{90} +8.45230 q^{92} +8.86643 q^{93} +12.7191 q^{94} -9.13010i q^{95} +5.10725 q^{96} -3.35986i q^{97} +(2.71972 + 1.89819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 24 q^{4} - 32 q^{9}+O(q^{10}) $ 32 * q - 24 * q^4 - 32 * q^9	$ 32 q - 24 q^{4} - 32 q^{9} - 4 q^{11} + 8 q^{15} + 40 q^{16} + 8 q^{22} - 48 q^{23} + 24 q^{36} + 64 q^{37} + 56 q^{44} - 72 q^{53} - 24 q^{58} + 8 q^{64} - 40 q^{67} + 72 q^{71} - 48 q^{78} + 32 q^{81} - 128 q^{86} - 48 q^{88} - 16 q^{92} - 32 q^{93} + 4 q^{99}+O(q^{100}) $ 32 * q - 24 * q^4 - 32 * q^9 - 4 * q^11 + 8 * q^15 + 40 * q^16 + 8 * q^22 - 48 * q^23 + 24 * q^36 + 64 * q^37 + 56 * q^44 - 72 * q^53 - 24 * q^58 + 8 * q^64 - 40 * q^67 + 72 * q^71 - 48 * q^78 + 32 * q^81 - 128 * q^86 - 48 * q^88 - 16 * q^92 - 32 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1617\mathbb{Z}\right)^\times$.

$n$	$199$	$442$	$1079$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.72615i		−	1.22057i	−0.792182	−	0.610286i	$-0.791055\pi$
$2$		−	1.72615i		−	1.22057i	0.792182	−	0.610286i	$-0.208945\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−0.979587			−0.489794
$5$		−	1.65517i		−	0.740216i	−0.928989	−	0.370108i	$-0.879321\pi$
$5$		−	1.65517i		−	0.740216i	0.928989	−	0.370108i	$-0.120679\pi$
$6$	−1.72615			−0.704697
$7$		0			0
$7$		0			0
$8$		−	1.76138i		−	0.622743i
$9$	−1.00000			−0.333333
$10$	−2.85707			−0.903486
$11$	−2.71972	−	1.89819i	−0.820026	−	0.572326i
$11$	−2.71972	−	1.89819i	−0.820026	−	0.572326i
$12$			0.979587i			0.282783i
$13$	−2.97508			−0.825140			−0.412570	−	0.910926i	$-0.635369\pi$
$13$	−2.97508			−0.825140			−0.412570	+	0.910926i	$0.635369\pi$
$14$		0			0
$15$	−1.65517			−0.427364
$16$	−4.99958			−1.24990
$17$	1.49538			0.362684			0.181342	−	0.983420i	$-0.441956\pi$
$17$	1.49538			0.362684			0.181342	+	0.983420i	$0.441956\pi$
$18$			1.72615i			0.406857i
$19$	5.51610			1.26548			0.632740	−	0.774364i	$-0.281930\pi$
$19$	5.51610			1.26548			0.632740	+	0.774364i	$0.281930\pi$
$20$			1.62139i			0.362553i
$21$		0			0
$22$	−3.27656	+	4.69464i	−0.698565	+	1.00090i
$23$	−8.62843			−1.79915			−0.899576	−	0.436764i	$-0.856124\pi$
$23$	−8.62843			−1.79915			−0.899576	+	0.436764i	$0.856124\pi$
$24$	−1.76138			−0.359541
$25$	2.26040			0.452080
$26$			5.13544i			1.00714i
$27$			1.00000i			0.192450i
$28$		0			0
$29$		−	8.02774i		−	1.49071i	−0.666665	−	0.745357i	$-0.732279\pi$
$29$		−	8.02774i		−	1.49071i	0.666665	−	0.745357i	$-0.267721\pi$
$30$			2.85707i			0.521628i
$31$			8.86643i			1.59246i	0.604996	+	0.796229i	$0.293175\pi$
$31$			8.86643i			1.59246i	−0.604996	+	0.796229i	$0.706825\pi$
$32$			5.10725i			0.902844i
$33$	−1.89819	+	2.71972i	−0.330433	+	0.473442i
$34$		−	2.58126i		−	0.442682i
$35$		0			0
$36$	0.979587			0.163265
$37$	8.22774			1.35263			0.676316	−	0.736611i	$-0.263575\pi$
$37$	8.22774			1.35263			0.676316	+	0.736611i	$0.263575\pi$
$38$		−	9.52160i		−	1.54461i
$39$			2.97508i			0.476395i
$40$	−2.91540			−0.460964
$41$	−8.12983			−1.26967			−0.634833	−	0.772649i	$-0.718931\pi$
$41$	−8.12983			−1.26967			−0.634833	+	0.772649i	$0.718931\pi$
$42$		0			0
$43$		−	5.03560i		−	0.767922i	−0.923349	−	0.383961i	$-0.874560\pi$
$43$		−	5.03560i		−	0.767922i	0.923349	−	0.383961i	$-0.125440\pi$
$44$	2.66420	+	1.85944i	0.401644	+	0.280322i
$45$			1.65517i			0.246739i
$46$			14.8939i			2.19599i
$47$			7.36847i			1.07480i	0.843327	+	0.537401i	$0.180594\pi$
$47$			7.36847i			1.07480i	−0.843327	+	0.537401i	$0.819406\pi$
$48$			4.99958i			0.721628i
$49$		0			0
$50$		−	3.90179i		−	0.551796i
$51$		−	1.49538i		−	0.209396i
$52$	2.91435			0.404148
$53$	−1.26049			−0.173142			−0.0865708	−	0.996246i	$-0.527591\pi$
$53$	−1.26049			−0.173142			−0.0865708	+	0.996246i	$0.527591\pi$
$54$	1.72615			0.234899
$55$	−3.14184	+	4.50161i	−0.423645	+	0.606996i
$56$		0			0
$57$		−	5.51610i		−	0.730625i
$58$	−13.8571			−1.81952
$59$		−	4.96848i		−	0.646841i	−0.946255	−	0.323421i	$-0.895167\pi$
$59$		−	4.96848i		−	0.646841i	0.946255	−	0.323421i	$-0.104833\pi$
$60$	1.62139			0.209320
$61$	3.65902			0.468489			0.234244	−	0.972178i	$-0.424738\pi$
$61$	3.65902			0.468489			0.234244	+	0.972178i	$0.424738\pi$
$62$	15.3048			1.94371
$63$		0			0
$64$	−1.18329			−0.147911
$65$			4.92428i			0.610782i
$66$	4.69464	+	3.27656i	0.577870	+	0.403317i
$67$	−10.7360			−1.31161			−0.655804	−	0.754931i	$-0.727670\pi$
$67$	−10.7360			−1.31161			−0.655804	+	0.754931i	$0.727670\pi$
$68$	−1.46486			−0.177640
$69$			8.62843i			1.03874i
$70$		0			0
$71$	−1.05369			−0.125050			−0.0625250	−	0.998043i	$-0.519915\pi$
$71$	−1.05369			−0.125050			−0.0625250	+	0.998043i	$0.519915\pi$
$72$			1.76138i			0.207581i
$73$	−9.85074			−1.15294			−0.576471	−	0.817118i	$-0.695571\pi$
$73$	−9.85074			−1.15294			−0.576471	+	0.817118i	$0.695571\pi$
$74$		−	14.2023i		−	1.65098i
$75$		−	2.26040i		−	0.261009i
$76$	−5.40350			−0.619824
$77$		0			0
$78$	5.13544			0.581474
$79$		−	3.93938i		−	0.443215i	−0.975136	−	0.221608i	$-0.928870\pi$
$79$		−	3.93938i		−	0.443215i	0.975136	−	0.221608i	$-0.0711304\pi$
$80$			8.27518i			0.925193i
$81$	1.00000			0.111111
$82$			14.0333i			1.54972i
$83$	10.2146			1.12120			0.560600	−	0.828087i	$-0.310571\pi$
$83$	10.2146			1.12120			0.560600	+	0.828087i	$0.310571\pi$
$84$		0			0
$85$		−	2.47512i		−	0.268465i
$86$	−8.69219			−0.937303
$87$	−8.02774			−0.860664
$88$	−3.34344	+	4.79047i	−0.356412	+	0.510665i
$89$			5.16502i			0.547491i	0.961802	+	0.273746i	$0.0882627\pi$
$89$			5.16502i			0.547491i	−0.961802	+	0.273746i	$0.911737\pi$
$90$	2.85707			0.301162
$91$		0			0
$92$	8.45230			0.881213
$93$	8.86643			0.919406
$94$	12.7191			1.31187
$95$		−	9.13010i		−	0.936728i
$96$	5.10725			0.521257
$97$		−	3.35986i		−	0.341142i	−0.985345	−	0.170571i	$-0.945439\pi$
$97$		−	3.35986i		−	0.341142i	0.985345	−	0.170571i	$-0.0545613\pi$
$98$		0			0
$99$	2.71972	+	1.89819i	0.273342	+	0.190775i
$100$	−2.21426			−0.221426
$101$	8.34007			0.829868			0.414934	−	0.909852i	$-0.363805\pi$
$101$	8.34007			0.829868			0.414934	+	0.909852i	$0.363805\pi$
$102$	−2.58126			−0.255582
$103$		−	4.17978i		−	0.411846i	−0.978568	−	0.205923i	$-0.933980\pi$
$103$		−	4.17978i		−	0.411846i	0.978568	−	0.205923i	$-0.0660196\pi$
$104$			5.24026i			0.513850i
$105$		0			0
$106$			2.17579i			0.211332i
$107$		−	2.85751i		−	0.276246i	−0.990415	−	0.138123i	$-0.955893\pi$
$107$		−	2.85751i		−	0.276246i	0.990415	−	0.138123i	$-0.0441070\pi$
$108$		−	0.979587i		−	0.0942608i
$109$		−	8.20464i		−	0.785862i	−0.919568	−	0.392931i	$-0.871461\pi$
$109$		−	8.20464i		−	0.785862i	0.919568	−	0.392931i	$-0.128539\pi$
$110$	7.77044	+	5.42328i	0.740882	+	0.517089i
$111$		−	8.22774i		−	0.780943i
$112$		0			0
$113$	−2.03684			−0.191609			−0.0958047	−	0.995400i	$-0.530542\pi$
$113$	−2.03684			−0.191609			−0.0958047	+	0.995400i	$0.530542\pi$
$114$	−9.52160			−0.891780
$115$			14.2815i			1.33176i
$116$			7.86388i			0.730143i
$117$	2.97508			0.275047
$118$	−8.57633			−0.789515
$119$		0			0
$120$			2.91540i			0.266138i
$121$	3.79373	+	10.3251i	0.344885	+	0.938645i
$122$		−	6.31600i		−	0.571824i
$123$			8.12983i			0.733042i
$124$		−	8.68544i		−	0.779976i
$125$		−	12.0172i		−	1.07485i
$126$		0			0
$127$			14.2795i			1.26710i	0.773703	+	0.633549i	$0.218402\pi$
$127$			14.2795i			1.26710i	−0.773703	+	0.633549i	$0.781598\pi$
$128$			12.2570i			1.08338i
$129$	−5.03560			−0.443360
$130$	8.50004			0.745502
$131$	0.600371			0.0524547			0.0262273	−	0.999656i	$-0.491651\pi$
$131$	0.600371			0.0524547			0.0262273	+	0.999656i	$0.491651\pi$
$132$	1.85944	−	2.66420i	0.161844	−	0.231889i
$133$		0			0
$134$			18.5319i			1.60091i
$135$	1.65517			0.142455
$136$		−	2.63395i		−	0.225859i
$137$	−14.2959			−1.22138			−0.610689	−	0.791871i	$-0.709107\pi$
$137$	−14.2959			−1.22138			−0.610689	+	0.791871i	$0.709107\pi$
$138$	14.8939			1.26786
$139$	−1.20134			−0.101896			−0.0509482	−	0.998701i	$-0.516224\pi$
$139$	−1.20134			−0.101896			−0.0509482	+	0.998701i	$0.516224\pi$
$140$		0			0
$141$	7.36847			0.620537
$142$			1.81882i			0.152632i
$143$	8.09139	+	5.64728i	0.676636	+	0.472249i
$144$	4.99958			0.416632
$145$	−13.2873			−1.10345
$146$			17.0038i			1.40725i
$147$		0			0
$148$	−8.05979			−0.662511
$149$		−	17.4030i		−	1.42571i	−0.701311	−	0.712856i	$-0.747401\pi$
$149$		−	17.4030i		−	1.42571i	0.701311	−	0.712856i	$-0.252599\pi$
$150$	−3.90179			−0.318580
$151$		−	8.11527i		−	0.660411i	−0.943909	−	0.330206i	$-0.892882\pi$
$151$		−	8.11527i		−	0.660411i	0.943909	−	0.330206i	$-0.107118\pi$
$152$		−	9.71596i		−	0.788069i
$153$	−1.49538			−0.120895
$154$		0			0
$155$	14.6755			1.17876
$156$		−	2.91435i		−	0.233335i
$157$			8.07999i			0.644854i	0.946594	+	0.322427i	$0.104499\pi$
$157$			8.07999i			0.644854i	−0.946594	+	0.322427i	$0.895501\pi$
$158$	−6.79996			−0.540976
$159$			1.26049i			0.0999634i
$160$	8.45339			0.668299
$161$		0			0
$162$		−	1.72615i		−	0.135619i
$163$	12.7329			0.997314			0.498657	−	0.866799i	$-0.333827\pi$
$163$	12.7329			0.997314			0.498657	+	0.866799i	$0.333827\pi$
$164$	7.96388			0.621875
$165$	4.50161	+	3.14184i	0.350450	+	0.244592i
$166$		−	17.6319i		−	1.36850i
$167$	19.0316			1.47271			0.736356	−	0.676594i	$-0.236545\pi$
$167$	19.0316			1.47271			0.736356	+	0.676594i	$0.236545\pi$
$168$		0			0
$169$	−4.14888			−0.319144
$170$	−4.27243			−0.327680
$171$	−5.51610			−0.421827
$172$			4.93281i			0.376123i
$173$	2.83906			0.215849			0.107925	−	0.994159i	$-0.465579\pi$
$173$	2.83906			0.215849			0.107925	+	0.994159i	$0.465579\pi$
$174$			13.8571i			1.05050i
$175$		0			0
$176$	13.5975	+	9.49017i	1.02495	+	0.715348i
$177$	−4.96848			−0.373454
$178$	8.91560			0.668252
$179$	−2.95795			−0.221088			−0.110544	−	0.993871i	$-0.535259\pi$
$179$	−2.95795			−0.221088			−0.110544	+	0.993871i	$0.535259\pi$
$180$		−	1.62139i		−	0.120851i
$181$		−	16.1267i		−	1.19869i	−0.800492	−	0.599343i	$-0.795429\pi$
$181$		−	16.1267i		−	1.19869i	0.800492	−	0.599343i	$-0.204571\pi$
$182$		0			0
$183$		−	3.65902i		−	0.270482i
$184$			15.1980i			1.12041i
$185$		−	13.6183i		−	1.00124i
$186$		−	15.3048i		−	1.12220i
$187$	−4.06703	−	2.83853i	−0.297410	−	0.207574i
$188$		−	7.21806i		−	0.526431i
$189$		0			0
$190$	−15.7599			−1.14334
$191$	15.1230			1.09426			0.547130	−	0.837048i	$-0.315720\pi$
$191$	15.1230			1.09426			0.547130	+	0.837048i	$0.315720\pi$
$192$			1.18329i			0.0853965i
$193$			6.38692i			0.459741i	0.973221	+	0.229870i	$0.0738302\pi$
$193$			6.38692i			0.459741i	−0.973221	+	0.229870i	$0.926170\pi$
$194$	−5.79962			−0.416388
$195$	4.92428			0.352635
$196$		0			0
$197$		−	22.4207i		−	1.59741i	−0.601721	−	0.798706i	$-0.705518\pi$
$197$		−	22.4207i		−	1.59741i	0.601721	−	0.798706i	$-0.294482\pi$
$198$	3.27656	−	4.69464i	0.232855	−	0.333633i
$199$		−	24.1852i		−	1.71444i	−0.514947	−	0.857222i	$-0.672189\pi$
$199$		−	24.1852i		−	1.71444i	0.514947	−	0.857222i	$-0.327811\pi$
$200$		−	3.98143i		−	0.281530i
$201$			10.7360i			0.757258i
$202$		−	14.3962i		−	1.01291i
$203$		0			0
$204$			1.46486i			0.102561i
$205$			13.4563i			0.939827i
$206$	−7.21492			−0.502687
$207$	8.62843			0.599717
$208$	14.8742			1.03134
$209$	−15.0022	−	10.4706i	−1.03773	−	0.724267i
$210$		0			0
$211$		−	3.05467i		−	0.210292i	−0.994457	−	0.105146i	$-0.966469\pi$
$211$		−	3.05467i		−	0.210292i	0.994457	−	0.105146i	$-0.0335311\pi$
$212$	1.23476			0.0848037
$213$			1.05369i			0.0721976i
$214$	−4.93249			−0.337178
$215$	−8.33479			−0.568428
$216$	1.76138			0.119847
$217$		0			0
$218$	−14.1624			−0.959200
$219$			9.85074i			0.665651i
$220$	3.07770	−	4.40972i	0.207499	−	0.297303i
$221$	−4.44890			−0.299265
$222$	−14.2023			−0.953196
$223$		−	9.90928i		−	0.663575i	−0.943354	−	0.331787i	$-0.892348\pi$
$223$		−	9.90928i		−	0.663575i	0.943354	−	0.331787i	$-0.107652\pi$
$224$		0			0
$225$	−2.26040			−0.150693
$226$			3.51588i			0.233873i
$227$	−13.2910			−0.882155			−0.441077	−	0.897469i	$-0.645404\pi$
$227$	−13.2910			−0.882155			−0.441077	+	0.897469i	$0.645404\pi$
$228$			5.40350i			0.357855i
$229$		−	8.61205i		−	0.569100i	−0.958661	−	0.284550i	$-0.908156\pi$
$229$		−	8.61205i		−	0.569100i	0.958661	−	0.284550i	$-0.0918442\pi$
$230$	24.6521			1.62551
$231$		0			0
$232$	−14.1399			−0.928332
$233$			0.409541i			0.0268299i	0.999910	+	0.0134150i	$0.00427024\pi$
$233$			0.409541i			0.0268299i	−0.999910	+	0.0134150i	$0.995730\pi$
$234$		−	5.13544i		−	0.335714i
$235$	12.1961			0.795586
$236$			4.86706i			0.316819i
$237$	−3.93938			−0.255891
$238$		0			0
$239$		−	0.631535i		−	0.0408506i	−0.999791	−	0.0204253i	$-0.993498\pi$
$239$		−	0.631535i		−	0.0408506i	0.999791	−	0.0204253i	$-0.00650203\pi$
$240$	8.27518			0.534160
$241$	5.94639			0.383041			0.191520	−	0.981489i	$-0.438658\pi$
$241$	5.94639			0.383041			0.191520	+	0.981489i	$0.438658\pi$
$242$	17.8226	−	6.54855i	1.14568	−	0.420957i
$243$		−	1.00000i		−	0.0641500i
$244$	−3.58433			−0.229463
$245$		0			0
$246$	14.0333			0.894730
$247$	−16.4109			−1.04420
$248$	15.6172			0.991692
$249$		−	10.2146i		−	0.647325i
$250$	−20.7435			−1.31193
$251$		−	0.396714i		−	0.0250404i	−0.999922	−	0.0125202i	$-0.996015\pi$
$251$		−	0.396714i		−	0.0250404i	0.999922	−	0.0125202i	$-0.00398540\pi$
$252$		0			0
$253$	23.4669	+	16.3784i	1.47535	+	1.02970i
$254$	24.6485			1.54658
$255$	−2.47512			−0.154998
$256$	18.7909			1.17443
$257$			18.0469i			1.12573i	0.826548	+	0.562866i	$0.190301\pi$
$257$			18.0469i			1.12573i	−0.826548	+	0.562866i	$0.809699\pi$
$258$			8.69219i			0.541152i
$259$		0			0
$260$		−	4.82376i		−	0.299157i
$261$			8.02774i			0.496905i
$262$		−	1.03633i		−	0.0640246i
$263$		−	0.559813i		−	0.0345195i	−0.999851	−	0.0172598i	$-0.994506\pi$
$263$		−	0.559813i		−	0.0345195i	0.999851	−	0.0172598i	$-0.00549423\pi$
$264$	4.79047	+	3.34344i	0.294833	+	0.205775i
$265$			2.08633i			0.128162i
$266$		0			0
$267$	5.16502			0.316094
$268$	10.5168			0.642418
$269$			1.68255i			0.102587i	0.998684	+	0.0512934i	$0.0163344\pi$
$269$			1.68255i			0.102587i	−0.998684	+	0.0512934i	$0.983666\pi$
$270$		−	2.85707i		−	0.173876i
$271$	−27.4237			−1.66587			−0.832936	−	0.553369i	$-0.813342\pi$
$271$	−27.4237			−1.66587			−0.832936	+	0.553369i	$0.813342\pi$
$272$	−7.47630			−0.453317
$273$		0			0
$274$			24.6768i			1.49078i
$275$	−6.14765	−	4.29067i	−0.370717	−	0.258737i
$276$		−	8.45230i		−	0.508769i
$277$		−	4.05068i		−	0.243382i	−0.992568	−	0.121691i	$-0.961168\pi$
$277$		−	4.05068i		−	0.243382i	0.992568	−	0.121691i	$-0.0388317\pi$
$278$			2.07369i			0.124372i
$279$		−	8.86643i		−	0.530819i
$280$		0			0
$281$		−	1.37565i		−	0.0820646i	−0.999158	−	0.0410323i	$-0.986935\pi$
$281$		−	1.37565i		−	0.0820646i	0.999158	−	0.0410323i	$-0.0130647\pi$
$282$		−	12.7191i		−	0.757410i
$283$	−14.8869			−0.884937			−0.442469	−	0.896784i	$-0.645897\pi$
$283$	−14.8869			−0.884937			−0.442469	+	0.896784i	$0.645897\pi$
$284$	1.03218			0.0612487
$285$	−9.13010			−0.540820
$286$	9.74804	−	13.9669i	0.576414	−	0.825882i
$287$		0			0
$288$		−	5.10725i		−	0.300948i
$289$	−14.7638			−0.868460
$290$			22.9359i			1.34684i
$291$	−3.35986			−0.196959
$292$	9.64966			0.564704
$293$	−23.7041			−1.38481			−0.692403	−	0.721511i	$-0.743448\pi$
$293$	−23.7041			−1.38481			−0.692403	+	0.721511i	$0.743448\pi$
$294$		0			0
$295$	−8.22370			−0.478802
$296$		−	14.4922i		−	0.842342i
$297$	1.89819	−	2.71972i	0.110144	−	0.157814i
$298$	−30.0402			−1.74018
$299$	25.6703			1.48455
$300$			2.21426i			0.127840i
$301$		0			0
$302$	−14.0082			−0.806079
$303$		−	8.34007i		−	0.479124i
$304$	−27.5782			−1.58172
$305$		−	6.05631i		−	0.346783i
$306$			2.58126i			0.147561i
$307$	−29.9744			−1.71073			−0.855364	−	0.518028i	$-0.826666\pi$
$307$	−29.9744			−1.71073			−0.855364	+	0.518028i	$0.826666\pi$
$308$		0			0
$309$	−4.17978			−0.237779
$310$		−	25.3320i		−	1.43876i
$311$		−	9.19535i		−	0.521420i	−0.965417	−	0.260710i	$-0.916043\pi$
$311$		−	9.19535i		−	0.521420i	0.965417	−	0.260710i	$-0.0839567\pi$
$312$	5.24026			0.296671
$313$		−	18.6771i		−	1.05569i	−0.849341	−	0.527845i	$-0.823000\pi$
$313$		−	18.6771i		−	1.05569i	0.849341	−	0.527845i	$-0.177000\pi$
$314$	13.9473			0.787090
$315$		0			0
$316$			3.85897i			0.217084i
$317$	9.44657			0.530572			0.265286	−	0.964170i	$-0.414534\pi$
$317$	9.44657			0.530572			0.265286	+	0.964170i	$0.414534\pi$
$318$	2.17579			0.122012
$319$	−15.2382	+	21.8332i	−0.853175	+	1.22242i
$320$			1.95855i			0.109486i
$321$	−2.85751			−0.159491
$322$		0			0
$323$	8.24869			0.458969
$324$	−0.979587			−0.0544215
$325$	−6.72488			−0.373029
$326$		−	21.9788i		−	1.21729i
$327$	−8.20464			−0.453718
$328$			14.3197i			0.790676i
$329$		0			0
$330$	5.42328	−	7.77044i	0.298542	−	0.427749i
$331$	24.7954			1.36288			0.681438	−	0.731876i	$-0.261355\pi$
$331$	24.7954			1.36288			0.681438	+	0.731876i	$0.261355\pi$
$332$	−10.0061			−0.549157
$333$	−8.22774			−0.450877
$334$		−	32.8514i		−	1.79755i
$335$			17.7699i			0.970874i
$336$		0			0
$337$		−	19.2924i		−	1.05093i	−0.850816	−	0.525463i	$-0.823892\pi$
$337$		−	19.2924i		−	1.05093i	0.850816	−	0.525463i	$-0.176108\pi$
$338$			7.16158i			0.389538i
$339$			2.03684i			0.110626i
$340$			2.42460i			0.131492i
$341$	16.8302	−	24.1142i	0.911405	−	1.30586i
$342$			9.52160i			0.514869i
$343$		0			0
$344$	−8.86962			−0.478218
$345$	14.2815			0.768893
$346$		−	4.90063i		−	0.263460i
$347$			34.5555i			1.85504i	0.373779	+	0.927518i	$0.378062\pi$
$347$			34.5555i			1.85504i	−0.373779	+	0.927518i	$0.621938\pi$
$348$	7.86388			0.421548
$349$	13.4656			0.720796			0.360398	−	0.932799i	$-0.382641\pi$
$349$	13.4656			0.720796			0.360398	+	0.932799i	$0.382641\pi$
$350$		0			0
$351$		−	2.97508i		−	0.158798i
$352$	9.69455	−	13.8903i	0.516721	−	0.740355i
$353$		−	7.75709i		−	0.412868i	−0.978461	−	0.206434i	$-0.933814\pi$
$353$		−	7.75709i		−	0.412868i	0.978461	−	0.206434i	$-0.0661859\pi$
$354$			8.57633i			0.455827i
$355$			1.74404i			0.0925640i
$356$		−	5.05959i		−	0.268158i
$357$		0			0
$358$			5.10586i			0.269853i
$359$		−	21.0656i		−	1.11180i	−0.831249	−	0.555900i	$-0.812374\pi$
$359$		−	21.0656i		−	1.11180i	0.831249	−	0.555900i	$-0.187626\pi$
$360$	2.91540			0.153655
$361$	11.4273			0.601439
$362$	−27.8370			−1.46308
$363$	10.3251	−	3.79373i	0.541927	−	0.199119i
$364$		0			0
$365$			16.3047i			0.853426i
$366$	−6.31600			−0.330143
$367$			22.6887i			1.18434i	0.805812	+	0.592171i	$0.201729\pi$
$367$			22.6887i			1.18434i	−0.805812	+	0.592171i	$0.798271\pi$
$368$	43.1386			2.24875
$369$	8.12983			0.423222
$370$	−23.5073			−1.22208
$371$		0			0
$372$	−8.68544			−0.450319
$373$		−	30.4487i		−	1.57657i	−0.615308	−	0.788287i	$-0.710968\pi$
$373$		−	30.4487i		−	1.57657i	0.615308	−	0.788287i	$-0.289032\pi$
$374$	−4.89972	+	7.02029i	−0.253358	+	0.363010i
$375$	−12.0172			−0.620567
$376$	12.9787			0.669326
$377$			23.8832i			1.23005i
$378$		0			0
$379$	−11.7721			−0.604695			−0.302347	−	0.953198i	$-0.597770\pi$
$379$	−11.7721			−0.604695			−0.302347	+	0.953198i	$0.597770\pi$
$380$			8.94373i			0.458804i
$381$	14.2795			0.731559
$382$		−	26.1045i		−	1.33562i
$383$		−	22.1439i		−	1.13150i	−0.824577	−	0.565750i	$-0.808587\pi$
$383$		−	22.1439i		−	1.13150i	0.824577	−	0.565750i	$-0.191413\pi$
$384$	12.2570			0.625489
$385$		0			0
$386$	11.0248			0.561146
$387$			5.03560i			0.255974i
$388$			3.29128i			0.167089i
$389$	2.78137			0.141021			0.0705105	−	0.997511i	$-0.477537\pi$
$389$	2.78137			0.141021			0.0705105	+	0.997511i	$0.477537\pi$
$390$		−	8.50004i		−	0.430416i
$391$	−12.9028			−0.652524
$392$		0			0
$393$		−	0.600371i		−	0.0302847i
$394$	−38.7015			−1.94976
$395$	−6.52037			−0.328075
$396$	−2.66420	−	1.85944i	−0.133881	−	0.0934406i
$397$		−	3.12729i		−	0.156954i	−0.996916	−	0.0784770i	$-0.974994\pi$
$397$		−	3.12729i		−	0.156954i	0.996916	−	0.0784770i	$-0.0250057\pi$
$398$	−41.7472			−2.09260
$399$		0			0
$400$	−11.3011			−0.565053
$401$	8.68284			0.433600			0.216800	−	0.976216i	$-0.430438\pi$
$401$	8.68284			0.433600			0.216800	+	0.976216i	$0.430438\pi$
$402$	18.5319			0.924287
$403$		−	26.3784i		−	1.31400i
$404$	−8.16982			−0.406464
$405$		−	1.65517i		−	0.0822462i
$406$		0			0
$407$	−22.3771	−	15.6178i	−1.10919	−	0.774147i
$408$	−2.63395			−0.130400
$409$	24.9765			1.23501			0.617503	−	0.786568i	$-0.288144\pi$
$409$	24.9765			1.23501			0.617503	+	0.786568i	$0.288144\pi$
$410$	23.2275			1.14713
$411$			14.2959i			0.705163i
$412$			4.09446i			0.201720i
$413$		0			0
$414$		−	14.8939i		−	0.731998i
$415$		−	16.9070i		−	0.829930i
$416$		−	15.1945i		−	0.744972i
$417$			1.20134i			0.0588300i
$418$	−18.0738	+	25.8961i	−0.884020	+	1.26662i
$419$		−	5.05059i		−	0.246738i	−0.992361	−	0.123369i	$-0.960630\pi$
$419$		−	5.05059i		−	0.246738i	0.992361	−	0.123369i	$-0.0393698\pi$
$420$		0			0
$421$	−26.8136			−1.30682			−0.653408	−	0.757006i	$-0.726661\pi$
$421$	−26.8136			−1.30682			−0.653408	+	0.757006i	$0.726661\pi$
$422$	−5.27282			−0.256677
$423$		−	7.36847i		−	0.358267i
$424$			2.22021i			0.107823i
$425$	3.38017			0.163962
$426$	1.81882			0.0881223
$427$		0			0
$428$			2.79918i			0.135304i
$429$	5.64728	−	8.09139i	0.272653	−	0.390656i
$430$			14.3871i			0.693807i
$431$			4.51622i			0.217539i	0.994067	+	0.108769i	$0.0346910\pi$
$431$			4.51622i			0.217539i	−0.994067	+	0.108769i	$0.965309\pi$
$432$		−	4.99958i		−	0.240543i
$433$		−	0.625010i		−	0.0300361i	−0.999887	−	0.0150180i	$-0.995219\pi$
$433$		−	0.625010i		−	0.0300361i	0.999887	−	0.0150180i	$-0.00478057\pi$
$434$		0			0
$435$			13.2873i			0.637078i
$436$			8.03716i			0.384910i
$437$	−47.5953			−2.27679
$438$	17.0038			0.812475
$439$	21.6268			1.03219			0.516096	−	0.856531i	$-0.327385\pi$
$439$	21.6268			1.03219			0.516096	+	0.856531i	$0.327385\pi$
$440$	7.92905	+	5.53398i	0.378003	+	0.263822i
$441$		0			0
$442$			7.67945i			0.365274i
$443$	−22.5595			−1.07183			−0.535917	−	0.844270i	$-0.680034\pi$
$443$	−22.5595			−1.07183			−0.535917	+	0.844270i	$0.680034\pi$
$444$			8.05979i			0.382501i
$445$	8.54901			0.405262
$446$	−17.1049			−0.809940
$447$	−17.4030			−0.823135
$448$		0			0
$449$	−1.18995			−0.0561571			−0.0280785	−	0.999606i	$-0.508939\pi$
$449$	−1.18995			−0.0561571			−0.0280785	+	0.999606i	$0.508939\pi$
$450$			3.90179i			0.183932i
$451$	22.1109	+	15.4320i	1.04116	+	0.726664i
$452$	1.99526			0.0938490
$453$	−8.11527			−0.381289
$454$			22.9422i			1.07673i
$455$		0			0
$456$	−9.71596			−0.454992
$457$		−	7.29080i		−	0.341049i	−0.985353	−	0.170525i	$-0.945454\pi$
$457$		−	7.29080i		−	0.341049i	0.985353	−	0.170525i	$-0.0545463\pi$
$458$	−14.8657			−0.694627
$459$			1.49538i			0.0697986i
$460$		−	13.9900i		−	0.652288i
$461$	−9.97446			−0.464557			−0.232279	−	0.972649i	$-0.574618\pi$
$461$	−9.97446			−0.464557			−0.232279	+	0.972649i	$0.574618\pi$
$462$		0			0
$463$	10.9915			0.510818			0.255409	−	0.966833i	$-0.417790\pi$
$463$	10.9915			0.510818			0.255409	+	0.966833i	$0.417790\pi$
$464$			40.1354i			1.86324i
$465$		−	14.6755i		−	0.680559i
$466$	0.706929			0.0327478
$467$			25.0594i			1.15961i	0.814755	+	0.579806i	$0.196872\pi$
$467$			25.0594i			1.15961i	−0.814755	+	0.579806i	$0.803128\pi$
$468$	−2.91435			−0.134716
$469$		0			0
$470$		−	21.0523i		−	0.971069i
$471$	8.07999			0.372306
$472$	−8.75140			−0.402816
$473$	−9.55854	+	13.6954i	−0.439502	+	0.629716i
$474$			6.79996i			0.312333i
$475$	12.4686			0.572098
$476$		0			0
$477$	1.26049			0.0577139
$478$	−1.09012			−0.0498611
$479$	24.4049			1.11509			0.557544	−	0.830147i	$-0.311744\pi$
$479$	24.4049			1.11509			0.557544	+	0.830147i	$0.311744\pi$
$480$		−	8.45339i		−	0.385843i
$481$	−24.4782			−1.11611
$482$		−	10.2644i		−	0.467528i
$483$		0			0
$484$	−3.71629	−	10.1143i	−0.168922	−	0.459742i
$485$	−5.56116			−0.252519
$486$	−1.72615			−0.0782997
$487$	−7.69485			−0.348687			−0.174343	−	0.984685i	$-0.555780\pi$
$487$	−7.69485			−0.348687			−0.174343	+	0.984685i	$0.555780\pi$
$488$		−	6.44493i		−	0.291748i
$489$		−	12.7329i		−	0.575800i
$490$		0			0
$491$		−	12.2135i		−	0.551190i	−0.961274	−	0.275595i	$-0.911125\pi$
$491$		−	12.2135i		−	0.551190i	0.961274	−	0.275595i	$-0.0888748\pi$
$492$		−	7.96388i		−	0.359039i
$493$		−	12.0046i		−	0.540659i
$494$			28.3276i			1.27452i
$495$	3.14184	−	4.50161i	0.141215	−	0.202332i
$496$		−	44.3284i		−	1.99041i
$497$		0			0
$498$	−17.6319			−0.790106
$499$	25.4962			1.14137			0.570683	−	0.821170i	$-0.306678\pi$
$499$	25.4962			1.14137			0.570683	+	0.821170i	$0.306678\pi$
$500$			11.7719i			0.526456i
$501$		−	19.0316i		−	0.850271i
$502$	−0.684787			−0.0305635
$503$	−13.6574			−0.608953			−0.304477	−	0.952520i	$-0.598482\pi$
$503$	−13.6574			−0.608953			−0.304477	+	0.952520i	$0.598482\pi$
$504$		0			0
$505$		−	13.8043i		−	0.614281i
$506$	28.2716	−	40.5073i	1.25682	−	1.80077i
$507$			4.14888i			0.184258i
$508$		−	13.9880i		−	0.620616i
$509$		−	27.6327i		−	1.22480i	−0.790548	−	0.612400i	$-0.790204\pi$
$509$		−	27.6327i		−	1.22480i	0.790548	−	0.612400i	$-0.209796\pi$
$510$			4.27243i			0.189186i
$511$		0			0
$512$		−	7.92178i		−	0.350097i
$513$			5.51610i			0.243542i
$514$	31.1515			1.37404
$515$	−6.91826			−0.304855
$516$	4.93281			0.217155
$517$	13.9868	−	20.0402i	0.615138	−	0.881366i
$518$		0			0
$519$		−	2.83906i		−	0.124621i
$520$	8.67354			0.380360
$521$		−	35.9253i		−	1.57391i	−0.617008	−	0.786957i	$-0.711655\pi$
$521$		−	35.9253i		−	1.57391i	0.617008	−	0.786957i	$-0.288345\pi$
$522$	13.8571			0.606508
$523$	−42.0050			−1.83675			−0.918375	−	0.395711i	$-0.870498\pi$
$523$	−42.0050			−1.83675			−0.918375	+	0.395711i	$0.870498\pi$
$524$	−0.588116			−0.0256920
$525$		0			0
$526$	−0.966320			−0.0421335
$527$			13.2587i			0.577559i
$528$	9.49017	−	13.5975i	0.413007	−	0.591753i
$529$	51.4498			2.23695
$530$	3.60132			0.156431
$531$			4.96848i			0.215614i
$532$		0			0
$533$	24.1869			1.04765
$534$		−	8.91560i		−	0.385816i
$535$	−4.72968			−0.204482
$536$			18.9102i			0.816795i
$537$			2.95795i			0.127645i
$538$	2.90433			0.125214
$539$		0			0
$540$	−1.62139			−0.0697734
$541$		−	2.67907i		−	0.115182i	−0.998340	−	0.0575911i	$-0.981658\pi$
$541$		−	2.67907i		−	0.115182i	0.998340	−	0.0575911i	$-0.0183420\pi$
$542$			47.3374i			2.03332i
$543$	−16.1267			−0.692061
$544$			7.63731i			0.327447i
$545$	−13.5801			−0.581708
$546$		0			0
$547$		−	29.7261i		−	1.27100i	−0.772103	−	0.635498i	$-0.780795\pi$
$547$		−	29.7261i		−	1.27100i	0.772103	−	0.635498i	$-0.219205\pi$
$548$	14.0040			0.598223
$549$	−3.65902			−0.156163
$550$	−7.40634	+	10.6118i	−0.315807	+	0.452487i
$551$		−	44.2818i		−	1.88647i
$552$	15.1980			0.646869
$553$		0			0
$554$	−6.99208			−0.297065
$555$	−13.6183			−0.578066
$556$	1.17682			0.0499083
$557$		−	23.9029i		−	1.01280i	−0.862299	−	0.506400i	$-0.830976\pi$
$557$		−	23.9029i		−	1.01280i	0.862299	−	0.506400i	$-0.169024\pi$
$558$	−15.3048			−0.647902
$559$			14.9813i			0.633643i
$560$		0			0
$561$	−2.83853	+	4.06703i	−0.119843	+	0.171710i
$562$	−2.37458			−0.100166
$563$	−5.17398			−0.218057			−0.109029	−	0.994039i	$-0.534774\pi$
$563$	−5.17398			−0.218057			−0.109029	+	0.994039i	$0.534774\pi$
$564$	−7.21806			−0.303935
$565$			3.37132i			0.141832i
$566$			25.6971i			1.08013i
$567$		0			0
$568$			1.85595i			0.0778740i
$569$			9.35983i			0.392384i	0.980565	+	0.196192i	$0.0628576\pi$
$569$			9.35983i			0.392384i	−0.980565	+	0.196192i	$0.937142\pi$
$570$			15.7599i			0.660110i
$571$		−	0.861521i		−	0.0360535i	−0.999838	−	0.0180268i	$-0.994262\pi$
$571$		−	0.861521i		−	0.0360535i	0.999838	−	0.0180268i	$-0.00573841\pi$
$572$	−7.92622	−	5.53200i	−0.331412	−	0.231305i
$573$		−	15.1230i		−	0.631771i
$574$		0			0
$575$	−19.5037			−0.813361
$576$	1.18329			0.0493037
$577$			9.24447i			0.384852i	0.981311	+	0.192426i	$0.0616356\pi$
$577$			9.24447i			0.384852i	−0.981311	+	0.192426i	$0.938364\pi$
$578$			25.4845i			1.06002i
$579$	6.38692			0.265431
$580$	13.0161			0.540463
$581$		0			0
$582$			5.79962i			0.240402i
$583$	3.42818	+	2.39265i	0.141981	+	0.0990936i
$584$			17.3509i			0.717987i
$585$		−	4.92428i		−	0.203594i
$586$			40.9167i			1.69025i
$587$			9.19283i			0.379429i	0.981839	+	0.189714i	$0.0607562\pi$
$587$			9.19283i			0.379429i	−0.981839	+	0.189714i	$0.939244\pi$
$588$		0			0
$589$			48.9081i			2.01522i
$590$			14.1953i			0.584412i
$591$	−22.4207			−0.922266
$592$	−41.1353			−1.69065
$593$	−36.3457			−1.49254			−0.746269	−	0.665645i	$-0.768157\pi$
$593$	−36.3457			−1.49254			−0.746269	+	0.665645i	$0.768157\pi$
$594$	−4.69464	−	3.27656i	−0.192623	−	0.134439i
$595$		0			0
$596$			17.0478i			0.698304i
$597$	−24.1852			−0.989834
$598$		−	44.3107i		−	1.81200i
$599$	10.6629			0.435675			0.217837	−	0.975985i	$-0.430100\pi$
$599$	10.6629			0.435675			0.217837	+	0.975985i	$0.430100\pi$
$600$	−3.98143			−0.162541
$601$	27.8885			1.13760			0.568798	−	0.822477i	$-0.307408\pi$
$601$	27.8885			1.13760			0.568798	+	0.822477i	$0.307408\pi$
$602$		0			0
$603$	10.7360			0.437203
$604$			7.94962i			0.323465i
$605$	17.0898	−	6.27929i	0.694800	−	0.255289i
$606$	−14.3962			−0.584805
$607$	48.7384			1.97823			0.989116	−	0.147137i	$-0.0470057\pi$
$607$	48.7384			1.97823			0.989116	+	0.147137i	$0.0470057\pi$
$608$			28.1721i			1.14253i
$609$		0			0
$610$	−10.4541			−0.423273
$611$		−	21.9218i		−	0.886862i
$612$	1.46486			0.0592135
$613$			15.4361i			0.623459i	0.950171	+	0.311729i	$0.100908\pi$
$613$			15.4361i			0.623459i	−0.950171	+	0.311729i	$0.899092\pi$
$614$			51.7402i			2.08806i
$615$	13.4563			0.542610
$616$		0			0
$617$	40.0745			1.61334			0.806669	−	0.591004i	$-0.201268\pi$
$617$	40.0745			1.61334			0.806669	+	0.591004i	$0.201268\pi$
$618$			7.21492i			0.290227i
$619$		−	12.5532i		−	0.504555i	−0.967655	−	0.252278i	$-0.918820\pi$
$619$		−	12.5532i		−	0.504555i	0.967655	−	0.252278i	$-0.0811796\pi$
$620$	−14.3759			−0.577351
$621$		−	8.62843i		−	0.346247i
$622$	−15.8725			−0.636430
$623$		0			0
$624$		−	14.8742i		−	0.595444i
$625$	−8.58859			−0.343543
$626$	−32.2394			−1.28854
$627$	−10.4706	+	15.0022i	−0.418156	+	0.599131i
$628$		−	7.91506i		−	0.315845i
$629$	12.3036			0.490578
$630$		0			0
$631$	29.4070			1.17067			0.585337	−	0.810790i	$-0.300962\pi$
$631$	29.4070			1.17067			0.585337	+	0.810790i	$0.300962\pi$
$632$	−6.93877			−0.276009
$633$	−3.05467			−0.121412
$634$		−	16.3062i		−	0.647601i
$635$	23.6350			0.937926
$636$		−	1.23476i		−	0.0489614i
$637$		0			0
$638$	37.6873	+	26.3034i	1.49206	+	1.04136i
$639$	1.05369			0.0416833
$640$	20.2875			0.801935
$641$	46.9868			1.85587			0.927933	−	0.372747i	$-0.121584\pi$
$641$	46.9868			1.85587			0.927933	+	0.372747i	$0.121584\pi$
$642$			4.93249i			0.194670i
$643$			43.4205i			1.71234i	0.516697	+	0.856168i	$0.327161\pi$
$643$			43.4205i			1.71234i	−0.516697	+	0.856168i	$0.672839\pi$
$644$		0			0
$645$			8.33479i			0.328182i
$646$		−	14.2385i		−	0.560205i
$647$			36.6322i			1.44016i	0.693890	+	0.720081i	$0.255895\pi$
$647$			36.6322i			1.44016i	−0.693890	+	0.720081i	$0.744105\pi$
$648$		−	1.76138i		−	0.0691937i
$649$	−9.43113	+	13.5129i	−0.370204	+	0.530426i
$650$			11.6081i			0.455309i
$651$		0			0
$652$	−12.4729			−0.488478
$653$	−18.0899			−0.707911			−0.353956	−	0.935262i	$-0.615164\pi$
$653$	−18.0899			−0.707911			−0.353956	+	0.935262i	$0.615164\pi$
$654$			14.1624i			0.553795i
$655$		−	0.993718i		−	0.0388278i
$656$	40.6458			1.58695
$657$	9.85074			0.384314
$658$		0			0
$659$			42.0600i			1.63842i	0.573490	+	0.819212i	$0.305589\pi$
$659$			42.0600i			1.63842i	−0.573490	+	0.819212i	$0.694411\pi$
$660$	−4.40972	−	3.07770i	−0.171648	−	0.119799i
$661$		−	7.77476i		−	0.302403i	−0.988503	−	0.151201i	$-0.951686\pi$
$661$		−	7.77476i		−	0.302403i	0.988503	−	0.151201i	$-0.0483142\pi$
$662$		−	42.8005i		−	1.66349i
$663$			4.44890i			0.172781i
$664$		−	17.9919i		−	0.698219i
$665$		0			0
$666$			14.2023i			0.550328i
$667$			69.2668i			2.68202i
$668$	−18.6432			−0.721326
$669$	−9.90928			−0.383115
$670$	30.6735			1.18502
$671$	−9.95149	−	6.94551i	−0.384173	−	0.268129i
$672$		0			0
$673$		−	29.5062i		−	1.13738i	−0.822552	−	0.568690i	$-0.807450\pi$
$673$		−	29.5062i		−	1.13738i	0.822552	−	0.568690i	$-0.192550\pi$
$674$	−33.3016			−1.28273
$675$			2.26040i			0.0870029i
$676$	4.06419			0.156315
$677$	36.2027			1.39138			0.695692	−	0.718340i	$-0.255098\pi$
$677$	36.2027			1.39138			0.695692	+	0.718340i	$0.255098\pi$
$678$	3.51588			0.135027
$679$		0			0
$680$	−4.35964			−0.167184
$681$			13.2910i			0.509312i
$682$	−41.6247	−	29.0514i	−1.59389	−	1.11244i
$683$	16.6378			0.636627			0.318313	−	0.947986i	$-0.396884\pi$
$683$	16.6378			0.636627			0.318313	+	0.947986i	$0.396884\pi$
$684$	5.40350			0.206608
$685$			23.6621i			0.904084i
$686$		0			0
$687$	−8.61205			−0.328570
$688$			25.1759i			0.959822i
$689$	3.75006			0.142866
$690$		−	24.6521i		−	0.938488i
$691$			29.3939i			1.11820i	0.829101	+	0.559099i	$0.188853\pi$
$691$			29.3939i			1.11820i	−0.829101	+	0.559099i	$0.811147\pi$
$692$	−2.78110			−0.105722
$693$		0			0
$694$	59.6479			2.26420
$695$			1.98843i			0.0754254i
$696$			14.1399i			0.535973i
$697$	−12.1572			−0.460488
$698$		−	23.2436i		−	0.879783i
$699$	0.409541			0.0154903
$700$		0			0
$701$			2.65658i			0.100338i	0.998741	+	0.0501688i	$0.0159759\pi$
$701$			2.65658i			0.100338i	−0.998741	+	0.0501688i	$0.984024\pi$
$702$	−5.13544			−0.193825
$703$	45.3850			1.71173
$704$	3.21821	+	2.24611i	0.121291	+	0.0846534i
$705$		−	12.1961i		−	0.459332i
$706$	−13.3899			−0.503935
$707$		0			0
$708$	4.86706			0.182915
$709$	−20.0152			−0.751688			−0.375844	−	0.926683i	$-0.622647\pi$
$709$	−20.0152			−0.751688			−0.375844	+	0.926683i	$0.622647\pi$
$710$	3.01047			0.112981
$711$			3.93938i			0.147738i
$712$	9.09759			0.340946
$713$		−	76.5033i		−	2.86507i
$714$		0			0
$715$	9.34723	−	13.3927i	0.349567	−	0.500857i
$716$	2.89757			0.108287
$717$	−0.631535			−0.0235851
$718$	−36.3624			−1.35703
$719$			7.47626i			0.278817i	0.990235	+	0.139409i	$0.0445202\pi$
$719$			7.47626i			0.278817i	−0.990235	+	0.139409i	$0.955480\pi$
$720$		−	8.27518i		−	0.308398i
$721$		0			0
$722$		−	19.7253i		−	0.734098i
$723$		−	5.94639i		−	0.221149i
$724$			15.7975i			0.587109i
$725$		−	18.1459i		−	0.673922i
$726$	−6.54855	−	17.8226i	−0.243039	−	0.661460i
$727$		−	36.4649i		−	1.35241i	−0.736714	−	0.676204i	$-0.763624\pi$
$727$		−	36.4649i		−	1.35241i	0.736714	−	0.676204i	$-0.236376\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	28.1443			1.04167
$731$		−	7.53016i		−	0.278513i
$732$			3.58433i			0.132480i
$733$	−17.1342			−0.632866			−0.316433	−	0.948615i	$-0.602485\pi$
$733$	−17.1342			−0.632866			−0.316433	+	0.948615i	$0.602485\pi$
$734$	39.1641			1.44557
$735$		0			0
$736$		−	44.0676i		−	1.62435i
$737$	29.1988	+	20.3790i	1.07555	+	0.750668i
$738$		−	14.0333i		−	0.516573i
$739$			8.40661i			0.309242i	0.987974	+	0.154621i	$0.0494157\pi$
$739$			8.40661i			0.309242i	−0.987974	+	0.154621i	$0.950584\pi$
$740$			13.3404i			0.490401i
$741$			16.4109i			0.602868i
$742$		0			0
$743$			27.0887i			0.993790i	0.867811	+	0.496895i	$0.165527\pi$
$743$			27.0887i			0.993790i	−0.867811	+	0.496895i	$0.834473\pi$
$744$		−	15.6172i		−	0.572554i
$745$	−28.8050			−1.05533
$746$	−52.5589			−1.92432
$747$	−10.2146			−0.373733
$748$	3.98401	+	2.78059i	0.145670	+	0.101668i
$749$		0			0
$750$			20.7435i			0.757446i
$751$	40.6037			1.48165			0.740825	−	0.671698i	$-0.234435\pi$
$751$	40.6037			1.48165			0.740825	+	0.671698i	$0.234435\pi$
$752$		−	36.8393i		−	1.34339i
$753$	−0.396714			−0.0144571
$754$	41.2260			1.50136
$755$	−13.4322			−0.488847
$756$		0			0
$757$	27.7043			1.00693			0.503465	−	0.864016i	$-0.332058\pi$
$757$	27.7043			1.00693			0.503465	+	0.864016i	$0.332058\pi$
$758$			20.3205i			0.738073i
$759$	16.3784	−	23.4669i	0.594499	−	0.851794i
$760$	−16.0816			−0.583341
$761$	13.3759			0.484875			0.242438	−	0.970167i	$-0.422053\pi$
$761$	13.3759			0.484875			0.242438	+	0.970167i	$0.422053\pi$
$762$		−	24.6485i		−	0.892920i
$763$		0			0
$764$	−14.8143			−0.535961
$765$			2.47512i			0.0894882i
$766$	−38.2237			−1.38108
$767$			14.7816i			0.533734i
$768$		−	18.7909i		−	0.678058i
$769$	32.4856			1.17146			0.585731	−	0.810506i	$-0.300808\pi$
$769$	32.4856			1.17146			0.585731	+	0.810506i	$0.300808\pi$
$770$		0			0
$771$	18.0469			0.649941
$772$		−	6.25655i		−	0.225178i
$773$			25.5373i			0.918513i	0.888304	+	0.459256i	$0.151884\pi$
$773$			25.5373i			0.918513i	−0.888304	+	0.459256i	$0.848116\pi$
$774$	8.69219			0.312434
$775$			20.0417i			0.719918i
$776$	−5.91801			−0.212444
$777$		0			0
$778$		−	4.80105i		−	0.172126i
$779$	−44.8449			−1.60674
$780$	−4.82376			−0.172718
$781$	2.86574	+	2.00010i	0.102544	+	0.0715694i
$782$			22.2722i			0.796452i
$783$	8.02774			0.286888
$784$		0			0
$785$	13.3738			0.477331
$786$	−1.03633			−0.0369646
$787$	45.1113			1.60804			0.804021	−	0.594601i	$-0.202690\pi$
$787$	45.1113			1.60804			0.804021	+	0.594601i	$0.202690\pi$
$788$			21.9631i			0.782402i
$789$	−0.559813			−0.0199299
$790$			11.2551i			0.400439i
$791$		0			0
$792$	3.34344	−	4.79047i	0.118804	−	0.170222i
$793$	−10.8859			−0.386569
$794$	−5.39816			−0.191573
$795$	2.08633			0.0739945
$796$			23.6915i			0.839724i
$797$			6.70198i			0.237396i	0.992930	+	0.118698i	$0.0378721\pi$
$797$			6.70198i			0.237396i	−0.992930	+	0.118698i	$0.962128\pi$
$798$		0			0
$799$			11.0187i			0.389814i
$800$			11.5444i			0.408158i
$801$		−	5.16502i		−	0.182497i
$802$		−	14.9879i		−	0.529240i
$803$	26.7912	+	18.6986i	0.945442	+	0.659859i
$804$		−	10.5168i		−	0.370900i
$805$		0			0
$806$	−45.5330			−1.60383
$807$	1.68255			0.0592285
$808$		−	14.6901i		−	0.516794i
$809$			15.0320i			0.528496i	0.964455	+	0.264248i	$0.0851237\pi$
$809$			15.0320i			0.528496i	−0.964455	+	0.264248i	$0.914876\pi$
$810$	−2.85707			−0.100387
$811$	38.8505			1.36423			0.682113	−	0.731247i	$-0.261061\pi$
$811$	38.8505			1.36423			0.682113	+	0.731247i	$0.261061\pi$
$812$		0			0
$813$			27.4237i			0.961792i
$814$	−26.9587	+	38.6263i	−0.944902	+	1.35385i
$815$		−	21.0751i		−	0.738228i
$816$			7.47630i			0.261723i
$817$		−	27.7769i		−	0.971789i
$818$		−	43.1131i		−	1.50741i
$819$		0			0
$820$		−	13.1816i		−	0.460322i
$821$		−	26.3684i		−	0.920265i	−0.887850	−	0.460133i	$-0.847802\pi$
$821$		−	26.3684i		−	0.920265i	0.887850	−	0.460133i	$-0.152198\pi$
$822$	24.6768			0.860701
$823$	27.8060			0.969258			0.484629	−	0.874720i	$-0.338955\pi$
$823$	27.8060			0.969258			0.484629	+	0.874720i	$0.338955\pi$
$824$	−7.36220			−0.256474
$825$	−4.29067	+	6.14765i	−0.149382	+	0.214034i
$826$		0			0
$827$			6.14673i			0.213743i	0.994273	+	0.106871i	$0.0340833\pi$
$827$			6.14673i			0.213743i	−0.994273	+	0.106871i	$0.965917\pi$
$828$	−8.45230			−0.293738
$829$			45.8251i			1.59157i	0.605578	+	0.795786i	$0.292942\pi$
$829$			45.8251i			1.59157i	−0.605578	+	0.795786i	$0.707058\pi$
$830$	−29.1839			−1.01299
$831$	−4.05068			−0.140517
$832$	3.52038			0.122047
$833$		0			0
$834$	2.07369			0.0718062
$835$		−	31.5007i		−	1.09013i
$836$	14.6960	+	10.2569i	0.508272	+	0.354742i
$837$	−8.86643			−0.306469
$838$	−8.71807			−0.301161
$839$			16.5099i			0.569984i	0.958530	+	0.284992i	$0.0919909\pi$
$839$			16.5099i			0.569984i	−0.958530	+	0.284992i	$0.908009\pi$
$840$		0			0
$841$	−35.4447			−1.22223
$842$			46.2843i			1.59506i
$843$	−1.37565			−0.0473800
$844$			2.99232i			0.103000i
$845$			6.86711i			0.236236i
$846$	−12.7191			−0.437291
$847$		0			0
$848$	6.30193			0.216409
$849$			14.8869i			0.510919i
$850$		−	5.83467i		−	0.200128i
$851$	−70.9925			−2.43359
$852$		−	1.03218i		−	0.0353619i
$853$	31.2895			1.07133			0.535666	−	0.844430i	$-0.320060\pi$
$853$	31.2895			1.07133			0.535666	+	0.844430i	$0.320060\pi$
$854$		0			0
$855$			9.13010i			0.312243i
$856$	−5.03318			−0.172030
$857$	−4.40856			−0.150594			−0.0752968	−	0.997161i	$-0.523990\pi$
$857$	−4.40856			−0.150594			−0.0752968	+	0.997161i	$0.523990\pi$
$858$	−13.9669	−	9.74804i	−0.476823	−	0.332793i
$859$			33.4479i			1.14123i	0.821218	+	0.570614i	$0.193295\pi$
$859$			33.4479i			1.14123i	−0.821218	+	0.570614i	$0.806705\pi$
$860$	8.16466			0.278412
$861$		0			0
$862$	7.79567			0.265522
$863$	3.49755			0.119058			0.0595290	−	0.998227i	$-0.481040\pi$
$863$	3.49755			0.119058			0.0595290	+	0.998227i	$0.481040\pi$
$864$	−5.10725			−0.173752
$865$		−	4.69913i		−	0.159775i
$866$	−1.07886			−0.0366611
$867$			14.7638i			0.501406i
$868$		0			0
$869$	−7.47771	+	10.7140i	−0.253664	+	0.363448i
$870$	22.9359			0.777599
$871$	31.9404			1.08226
$872$	−14.4515			−0.489390
$873$			3.35986i			0.113714i
$874$			82.1565i			2.77898i
$875$		0			0
$876$		−	9.64966i		−	0.326032i
$877$		−	2.75380i		−	0.0929893i	−0.998919	−	0.0464946i	$-0.985195\pi$
$877$		−	2.75380i		−	0.0929893i	0.998919	−	0.0464946i	$-0.0148050\pi$
$878$		−	37.3311i		−	1.25986i
$879$			23.7041i			0.799519i
$880$	15.7079	−	22.5062i	0.529512	−	0.758682i
$881$			1.11529i			0.0375752i	0.999823	+	0.0187876i	$0.00598063\pi$
$881$			1.11529i			0.0375752i	−0.999823	+	0.0187876i	$0.994019\pi$
$882$		0			0
$883$	17.3039			0.582323			0.291161	−	0.956674i	$-0.405958\pi$
$883$	17.3039			0.582323			0.291161	+	0.956674i	$0.405958\pi$
$884$	4.35808			0.146578
$885$			8.22370i			0.276437i
$886$			38.9411i			1.30825i
$887$	−38.5876			−1.29564			−0.647822	−	0.761792i	$-0.724320\pi$
$887$	−38.5876			−1.29564			−0.647822	+	0.761792i	$0.724320\pi$
$888$	−14.4922			−0.486327
$889$		0			0
$890$		−	14.7569i		−	0.494651i
$891$	−2.71972	−	1.89819i	−0.0911140	−	0.0635918i
$892$			9.70701i			0.325015i
$893$			40.6452i			1.36014i
$894$			30.0402i			1.00469i
$895$			4.89592i			0.163653i
$896$		0			0
$897$		−	25.6703i		−	0.857106i
$898$			2.05402i			0.0685437i
$899$	71.1774			2.37390
$900$	2.21426			0.0738087
$901$	−1.88492			−0.0627957
$902$	26.6379	−	38.1666i	0.886945	−	1.27081i
$903$		0			0
$904$			3.58765i			0.119323i
$905$	−26.6924			−0.887286
$906$			14.0082i			0.465390i
$907$	−28.8033			−0.956397			−0.478198	−	0.878252i	$-0.658710\pi$
$907$	−28.8033			−0.956397			−0.478198	+	0.878252i	$0.658710\pi$
$908$	13.0197			0.432074
$909$	−8.34007			−0.276623
$910$		0			0
$911$	−30.2528			−1.00232			−0.501161	−	0.865354i	$-0.667093\pi$
$911$	−30.2528			−1.00232			−0.501161	+	0.865354i	$0.667093\pi$
$912$			27.5782i			0.913205i
$913$	−27.7809	−	19.3893i	−0.919413	−	0.641692i
$914$	−12.5850			−0.416275
$915$	−6.05631			−0.200215
$916$			8.43625i			0.278742i
$917$		0			0
$918$	2.58126			0.0851941
$919$		−	28.9258i		−	0.954175i	−0.878856	−	0.477087i	$-0.841692\pi$
$919$		−	28.9258i		−	0.954175i	0.878856	−	0.477087i	$-0.158308\pi$
$920$	25.1553			0.829345
$921$			29.9744i			0.987689i
$922$			17.2174i			0.567025i
$923$	3.13481			0.103184
$924$		0			0
$925$	18.5980			0.611498
$926$		−	18.9729i		−	0.623490i
$927$			4.17978i			0.137282i
$928$	40.9997			1.34588
$929$			12.0571i			0.395580i	0.980244	+	0.197790i	$0.0633764\pi$
$929$			12.0571i			0.395580i	−0.980244	+	0.197790i	$0.936624\pi$
$930$	−25.3320			−0.830671
$931$		0			0
$932$		−	0.401181i		−	0.0131411i
$933$	−9.19535			−0.301042
$934$	43.2563			1.41539
$935$	−4.69826	+	6.73163i	−0.153649	+	0.220148i
$936$		−	5.24026i		−	0.171283i
$937$	−32.2826			−1.05463			−0.527314	−	0.849671i	$-0.676801\pi$
$937$	−32.2826			−1.05463			−0.527314	+	0.849671i	$0.676801\pi$
$938$		0			0
$939$	−18.6771			−0.609503
$940$	−11.9471			−0.389673
$941$	0.248101			0.00808785			0.00404393	−	0.999992i	$-0.498713\pi$
$941$	0.248101			0.00808785			0.00404393	+	0.999992i	$0.498713\pi$
$942$		−	13.9473i		−	0.454426i
$943$	70.1477			2.28432
$944$			24.8403i			0.808484i
$945$		0			0
$946$	23.6403	+	16.4994i	0.768613	+	0.536443i
$947$	38.9155			1.26458			0.632292	−	0.774730i	$-0.282114\pi$
$947$	38.9155			1.26458			0.632292	+	0.774730i	$0.282114\pi$
$948$	3.85897			0.125334
$949$	29.3068			0.951338
$950$		−	21.5226i		−	0.698286i
$951$		−	9.44657i		−	0.306326i
$952$		0			0
$953$		−	2.04695i		−	0.0663073i	−0.999450	−	0.0331537i	$-0.989445\pi$
$953$		−	2.04695i		−	0.0663073i	0.999450	−	0.0331537i	$-0.0105551\pi$
$954$		−	2.17579i		−	0.0704439i
$955$		−	25.0311i		−	0.809989i
$956$			0.618644i			0.0200084i
$957$	21.8332	+	15.2382i	0.705767	+	0.492581i
$958$		−	42.1265i		−	1.36105i
$959$		0			0
$960$	1.95855			0.0632119
$961$	−47.6135			−1.53592
$962$			42.2530i			1.36229i
$963$			2.85751i			0.0920821i
$964$	−5.82501			−0.187611
$965$	10.5715			0.340308
$966$		0			0
$967$			21.7478i			0.699361i	0.936869	+	0.349681i	$0.113710\pi$
$967$			21.7478i			0.699361i	−0.936869	+	0.349681i	$0.886290\pi$
$968$	18.1864	−	6.68222i	0.584535	−	0.214775i
$969$		−	8.24869i		−	0.264986i
$970$			9.59938i			0.308217i
$971$		−	1.59405i		−	0.0511554i	−0.999673	−	0.0255777i	$-0.991857\pi$
$971$		−	1.59405i		−	0.0511554i	0.999673	−	0.0255777i	$-0.00814252\pi$
$972$			0.979587i			0.0314203i
$973$		0			0
$974$			13.2824i			0.425597i
$975$			6.72488i			0.215369i
$976$	−18.2936			−0.585562
$977$	−17.5824			−0.562509			−0.281255	−	0.959633i	$-0.590751\pi$
$977$	−17.5824			−0.562509			−0.281255	+	0.959633i	$0.590751\pi$
$978$	−21.9788			−0.702804
$979$	9.80421	−	14.0474i	0.313344	−	0.448957i
$980$		0			0
$981$			8.20464i			0.261954i
$982$	−21.0824			−0.672766
$983$			13.3934i			0.427184i	0.976923	+	0.213592i	$0.0685163\pi$
$983$			13.3934i			0.427184i	−0.976923	+	0.213592i	$0.931484\pi$
$984$	14.3197			0.456497
$985$	−37.1102			−1.18243
$986$	−20.7217			−0.659912
$987$		0			0
$988$	16.0759			0.511441
$989$			43.4493i			1.38161i
$990$	−7.77044	−	5.42328i	−0.246961	−	0.172363i
$991$	−12.7819			−0.406031			−0.203016	−	0.979175i	$-0.565074\pi$
$991$	−12.7819			−0.406031			−0.203016	+	0.979175i	$0.565074\pi$
$992$	−45.2831			−1.43774
$993$		−	24.7954i		−	0.786857i
$994$		0			0
$995$	−40.0307			−1.26906
$996$			10.0061i			0.317056i
$997$	−49.6900			−1.57370			−0.786849	−	0.617145i	$-0.788289\pi$
$997$	−49.6900			−1.57370			−0.786849	+	0.617145i	$0.788289\pi$
$998$		−	44.0102i		−	1.39312i
$999$			8.22774i			0.260314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.c.a.538.7		32
7.4	even	3		231.2.p.a.208.13	yes	32
7.5	odd	6		231.2.p.a.10.4	✓	32
7.6	odd	2	inner	1617.2.c.a.538.8		32
11.10	odd	2	inner	1617.2.c.a.538.25		32
21.5	even	6		693.2.bg.b.10.13		32
21.11	odd	6		693.2.bg.b.208.4		32
77.32	odd	6		231.2.p.a.208.4	yes	32
77.54	even	6		231.2.p.a.10.13	yes	32
77.76	even	2	inner	1617.2.c.a.538.26		32
231.32	even	6		693.2.bg.b.208.13		32
231.131	odd	6		693.2.bg.b.10.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.4	✓	32	7.5	odd	6
231.2.p.a.10.13	yes	32	77.54	even	6
231.2.p.a.208.4	yes	32	77.32	odd	6
231.2.p.a.208.13	yes	32	7.4	even	3
693.2.bg.b.10.4		32	231.131	odd	6
693.2.bg.b.10.13		32	21.5	even	6
693.2.bg.b.208.4		32	21.11	odd	6
693.2.bg.b.208.13		32	231.32	even	6
1617.2.c.a.538.7		32	1.1	even	1	trivial
1617.2.c.a.538.8		32	7.6	odd	2	inner
1617.2.c.a.538.25		32	11.10	odd	2	inner
1617.2.c.a.538.26		32	77.76	even	2	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.72615i q^{2} -1.00000i q^{3} -0.979587 q^{4} -1.65517i q^{5} -1.72615 q^{6} -1.76138i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.72615i q^{2} -1.00000i q^{3} -0.979587 q^{4} -1.65517i q^{5} -1.72615 q^{6} -1.76138i q^{8} -1.00000 q^{9} -2.85707 q^{10} +(-2.71972 - 1.89819i) q^{11} +0.979587i q^{12} -2.97508 q^{13} -1.65517 q^{15} -4.99958 q^{16} +1.49538 q^{17} +1.72615i q^{18} +5.51610 q^{19} +1.62139i q^{20} +(-3.27656 + 4.69464i) q^{22} -8.62843 q^{23} -1.76138 q^{24} +2.26040 q^{25} +5.13544i q^{26} +1.00000i q^{27} -8.02774i q^{29} +2.85707i q^{30} +8.86643i q^{31} +5.10725i q^{32} +(-1.89819 + 2.71972i) q^{33} -2.58126i q^{34} +0.979587 q^{36} +8.22774 q^{37} -9.52160i q^{38} +2.97508i q^{39} -2.91540 q^{40} -8.12983 q^{41} -5.03560i q^{43} +(2.66420 + 1.85944i) q^{44} +1.65517i q^{45} +14.8939i q^{46} +7.36847i q^{47} +4.99958i q^{48} -3.90179i q^{50} -1.49538i q^{51} +2.91435 q^{52} -1.26049 q^{53} +1.72615 q^{54} +(-3.14184 + 4.50161i) q^{55} -5.51610i q^{57} -13.8571 q^{58} -4.96848i q^{59} +1.62139 q^{60} +3.65902 q^{61} +15.3048 q^{62} -1.18329 q^{64} +4.92428i q^{65} +(4.69464 + 3.27656i) q^{66} -10.7360 q^{67} -1.46486 q^{68} +8.62843i q^{69} -1.05369 q^{71} +1.76138i q^{72} -9.85074 q^{73} -14.2023i q^{74} -2.26040i q^{75} -5.40350 q^{76} +5.13544 q^{78} -3.93938i q^{79} +8.27518i q^{80} +1.00000 q^{81} +14.0333i q^{82} +10.2146 q^{83} -2.47512i q^{85} -8.69219 q^{86} -8.02774 q^{87} +(-3.34344 + 4.79047i) q^{88} +5.16502i q^{89} +2.85707 q^{90} +8.45230 q^{92} +8.86643 q^{93} +12.7191 q^{94} -9.13010i q^{95} +5.10725 q^{96} -3.35986i q^{97} +(2.71972 + 1.89819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 24 q^{4} - 32 q^{9}+O(q^{10}) \) 32 * q - 24 * q^4 - 32 * q^9	\( 32 q - 24 q^{4} - 32 q^{9} - 4 q^{11} + 8 q^{15} + 40 q^{16} + 8 q^{22} - 48 q^{23} + 24 q^{36} + 64 q^{37} + 56 q^{44} - 72 q^{53} - 24 q^{58} + 8 q^{64} - 40 q^{67} + 72 q^{71} - 48 q^{78} + 32 q^{81} - 128 q^{86} - 48 q^{88} - 16 q^{92} - 32 q^{93} + 4 q^{99}+O(q^{100}) \) 32 * q - 24 * q^4 - 32 * q^9 - 4 * q^11 + 8 * q^15 + 40 * q^16 + 8 * q^22 - 48 * q^23 + 24 * q^36 + 64 * q^37 + 56 * q^44 - 72 * q^53 - 24 * q^58 + 8 * q^64 - 40 * q^67 + 72 * q^71 - 48 * q^78 + 32 * q^81 - 128 * q^86 - 48 * q^88 - 16 * q^92 - 32 * q^93 + 4 * q^99

Introduction

L-functions

Modular forms

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Database

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