LMFDB - Embedded newform 3630.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3630,2,Mod(1,3630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3630, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3630.a (trivial)

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:	yes
Analytic conductor:	$28.9856959337$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	3630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -4.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} -2.00000 q^{13} +4.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} +4.00000 q^{21} -4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} -4.00000 q^{28} -6.00000 q^{29} -1.00000 q^{30} -1.00000 q^{32} +2.00000 q^{34} +4.00000 q^{35} +1.00000 q^{36} -10.0000 q^{37} +4.00000 q^{38} +2.00000 q^{39} +1.00000 q^{40} +6.00000 q^{41} -4.00000 q^{42} +12.0000 q^{43} -1.00000 q^{45} +4.00000 q^{46} -4.00000 q^{47} -1.00000 q^{48} +9.00000 q^{49} -1.00000 q^{50} +2.00000 q^{51} -2.00000 q^{52} -6.00000 q^{53} +1.00000 q^{54} +4.00000 q^{56} +4.00000 q^{57} +6.00000 q^{58} -4.00000 q^{59} +1.00000 q^{60} -10.0000 q^{61} -4.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} -12.0000 q^{67} -2.00000 q^{68} +4.00000 q^{69} -4.00000 q^{70} -4.00000 q^{71} -1.00000 q^{72} -10.0000 q^{73} +10.0000 q^{74} -1.00000 q^{75} -4.00000 q^{76} -2.00000 q^{78} -4.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -4.00000 q^{83} +4.00000 q^{84} +2.00000 q^{85} -12.0000 q^{86} +6.00000 q^{87} +10.0000 q^{89} +1.00000 q^{90} +8.00000 q^{91} -4.00000 q^{92} +4.00000 q^{94} +4.00000 q^{95} +1.00000 q^{96} +18.0000 q^{97} -9.00000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	4.00000	1.06904
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−1.00000	−0.235702
$19$	−4.00000	−0.917663	−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000	−0.917663	−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.00000	−0.223607
$21$	4.00000	0.872872
$22$	0	0
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	2.00000	0.392232
$27$	−1.00000	−0.192450
$28$	−4.00000	−0.755929
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	−1.00000	−0.182574
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	2.00000	0.342997
$35$	4.00000	0.676123
$36$	1.00000	0.166667
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	4.00000	0.648886
$39$	2.00000	0.320256
$40$	1.00000	0.158114
$41$	6.00000	0.937043	0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000	0.937043	0.468521	+	0.883452i	$0.344787\pi$
$42$	−4.00000	−0.617213
$43$	12.0000	1.82998	0.914991	−	0.403473i	$-0.132197\pi$
$43$	12.0000	1.82998	0.914991	+	0.403473i	$0.132197\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	4.00000	0.589768
$47$	−4.00000	−0.583460	−0.291730	−	0.956501i	$-0.594231\pi$
$47$	−4.00000	−0.583460	−0.291730	+	0.956501i	$0.594231\pi$
$48$	−1.00000	−0.144338
$49$	9.00000	1.28571
$50$	−1.00000	−0.141421
$51$	2.00000	0.280056
$52$	−2.00000	−0.277350
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	4.00000	0.534522
$57$	4.00000	0.529813
$58$	6.00000	0.787839
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	1.00000	0.129099
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	0	0
$63$	−4.00000	−0.503953
$64$	1.00000	0.125000
$65$	2.00000	0.248069
$66$	0	0
$67$	−12.0000	−1.46603	−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000	−1.46603	−0.733017	+	0.680211i	$0.761888\pi$
$68$	−2.00000	−0.242536
$69$	4.00000	0.481543
$70$	−4.00000	−0.478091
$71$	−4.00000	−0.474713	−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000	−0.474713	−0.237356	+	0.971423i	$0.576281\pi$
$72$	−1.00000	−0.117851
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	10.0000	1.16248
$75$	−1.00000	−0.115470
$76$	−4.00000	−0.458831
$77$	0	0
$78$	−2.00000	−0.226455
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	4.00000	0.436436
$85$	2.00000	0.216930
$86$	−12.0000	−1.29399
$87$	6.00000	0.643268
$88$	0	0
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	1.00000	0.105409
$91$	8.00000	0.838628
$92$	−4.00000	−0.417029
$93$	0	0
$94$	4.00000	0.412568
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	18.0000	1.82762	0.913812	−	0.406138i	$-0.133125\pi$
$97$	18.0000	1.82762	0.913812	+	0.406138i	$0.133125\pi$
$98$	−9.00000	−0.909137
$99$	0	0
$100$	1.00000	0.100000
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	−2.00000	−0.198030
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	2.00000	0.196116
$105$	−4.00000	−0.390360
$106$	6.00000	0.582772
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	−1.00000	−0.0962250
$109$	−2.00000	−0.191565	−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000	−0.191565	−0.0957826	+	0.995402i	$0.530535\pi$
$110$	0	0
$111$	10.0000	0.949158
$112$	−4.00000	−0.377964
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	−4.00000	−0.374634
$115$	4.00000	0.373002
$116$	−6.00000	−0.557086
$117$	−2.00000	−0.184900
$118$	4.00000	0.368230
$119$	8.00000	0.733359
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	10.0000	0.905357
$123$	−6.00000	−0.541002
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	4.00000	0.356348
$127$	−4.00000	−0.354943	−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000	−0.354943	−0.177471	+	0.984126i	$0.556792\pi$
$128$	−1.00000	−0.0883883
$129$	−12.0000	−1.05654
$130$	−2.00000	−0.175412
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	16.0000	1.38738
$134$	12.0000	1.03664
$135$	1.00000	0.0860663
$136$	2.00000	0.171499
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	−4.00000	−0.340503
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	4.00000	0.338062
$141$	4.00000	0.336861
$142$	4.00000	0.335673
$143$	0	0
$144$	1.00000	0.0833333
$145$	6.00000	0.498273
$146$	10.0000	0.827606
$147$	−9.00000	−0.742307
$148$	−10.0000	−0.821995
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	1.00000	0.0816497
$151$	−12.0000	−0.976546	−0.488273	−	0.872691i	$-0.662373\pi$
$151$	−12.0000	−0.976546	−0.488273	+	0.872691i	$0.662373\pi$
$152$	4.00000	0.324443
$153$	−2.00000	−0.161690
$154$	0	0
$155$	0	0
$156$	2.00000	0.160128
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	4.00000	0.318223
$159$	6.00000	0.475831
$160$	1.00000	0.0790569
$161$	16.0000	1.26098
$162$	−1.00000	−0.0785674
$163$	−20.0000	−1.56652	−0.783260	−	0.621694i	$-0.786445\pi$
$163$	−20.0000	−1.56652	−0.783260	+	0.621694i	$0.786445\pi$
$164$	6.00000	0.468521
$165$	0	0
$166$	4.00000	0.310460
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	−4.00000	−0.308607
$169$	−9.00000	−0.692308
$170$	−2.00000	−0.153393
$171$	−4.00000	−0.305888
$172$	12.0000	0.914991
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	−6.00000	−0.454859
$175$	−4.00000	−0.302372
$176$	0	0
$177$	4.00000	0.300658
$178$	−10.0000	−0.749532
$179$	4.00000	0.298974	0.149487	−	0.988764i	$-0.452238\pi$
$179$	4.00000	0.298974	0.149487	+	0.988764i	$0.452238\pi$
$180$	−1.00000	−0.0745356
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	−8.00000	−0.592999
$183$	10.0000	0.739221
$184$	4.00000	0.294884
$185$	10.0000	0.735215
$186$	0	0
$187$	0	0
$188$	−4.00000	−0.291730
$189$	4.00000	0.290957
$190$	−4.00000	−0.290191
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	−1.00000	−0.0721688
$193$	22.0000	1.58359	0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000	1.58359	0.791797	+	0.610784i	$0.209146\pi$
$194$	−18.0000	−1.29232
$195$	−2.00000	−0.143223
$196$	9.00000	0.642857
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	−1.00000	−0.0707107
$201$	12.0000	0.846415
$202$	−18.0000	−1.26648
$203$	24.0000	1.68447
$204$	2.00000	0.140028
$205$	−6.00000	−0.419058
$206$	16.0000	1.11477
$207$	−4.00000	−0.278019
$208$	−2.00000	−0.138675
$209$	0	0
$210$	4.00000	0.276026
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	−6.00000	−0.412082
$213$	4.00000	0.274075
$214$	−12.0000	−0.820303
$215$	−12.0000	−0.818393
$216$	1.00000	0.0680414
$217$	0	0
$218$	2.00000	0.135457
$219$	10.0000	0.675737
$220$	0	0
$221$	4.00000	0.269069
$222$	−10.0000	−0.671156
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	4.00000	0.267261
$225$	1.00000	0.0666667
$226$	−18.0000	−1.19734
$227$	−28.0000	−1.85843	−0.929213	−	0.369546i	$-0.879513\pi$
$227$	−28.0000	−1.85843	−0.929213	+	0.369546i	$0.879513\pi$
$228$	4.00000	0.264906
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	−4.00000	−0.263752
$231$	0	0
$232$	6.00000	0.393919
$233$	22.0000	1.44127	0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000	1.44127	0.720634	+	0.693316i	$0.243851\pi$
$234$	2.00000	0.130744
$235$	4.00000	0.260931
$236$	−4.00000	−0.260378
$237$	4.00000	0.259828
$238$	−8.00000	−0.518563
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	1.00000	0.0645497
$241$	6.00000	0.386494	0.193247	−	0.981150i	$-0.438098\pi$
$241$	6.00000	0.386494	0.193247	+	0.981150i	$0.438098\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−10.0000	−0.640184
$245$	−9.00000	−0.574989
$246$	6.00000	0.382546
$247$	8.00000	0.509028
$248$	0	0
$249$	4.00000	0.253490
$250$	1.00000	0.0632456
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	−4.00000	−0.251976
$253$	0	0
$254$	4.00000	0.250982
$255$	−2.00000	−0.125245
$256$	1.00000	0.0625000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	12.0000	0.747087
$259$	40.0000	2.48548
$260$	2.00000	0.124035
$261$	−6.00000	−0.371391
$262$	−12.0000	−0.741362
$263$	24.0000	1.47990	0.739952	−	0.672660i	$-0.234848\pi$
$263$	24.0000	1.47990	0.739952	+	0.672660i	$0.234848\pi$
$264$	0	0
$265$	6.00000	0.368577
$266$	−16.0000	−0.981023
$267$	−10.0000	−0.611990
$268$	−12.0000	−0.733017
$269$	18.0000	1.09748	0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000	1.09748	0.548740	+	0.835993i	$0.315108\pi$
$270$	−1.00000	−0.0608581
$271$	20.0000	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	−2.00000	−0.121268
$273$	−8.00000	−0.484182
$274$	−2.00000	−0.120824
$275$	0	0
$276$	4.00000	0.240772
$277$	−18.0000	−1.08152	−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000	−1.08152	−0.540758	+	0.841178i	$0.681862\pi$
$278$	−4.00000	−0.239904
$279$	0	0
$280$	−4.00000	−0.239046
$281$	22.0000	1.31241	0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000	1.31241	0.656205	+	0.754583i	$0.272161\pi$
$282$	−4.00000	−0.238197
$283$	12.0000	0.713326	0.356663	−	0.934233i	$-0.383914\pi$
$283$	12.0000	0.713326	0.356663	+	0.934233i	$0.383914\pi$
$284$	−4.00000	−0.237356
$285$	−4.00000	−0.236940
$286$	0	0
$287$	−24.0000	−1.41668
$288$	−1.00000	−0.0589256
$289$	−13.0000	−0.764706
$290$	−6.00000	−0.352332
$291$	−18.0000	−1.05518
$292$	−10.0000	−0.585206
$293$	10.0000	0.584206	0.292103	−	0.956387i	$-0.405645\pi$
$293$	10.0000	0.584206	0.292103	+	0.956387i	$0.405645\pi$
$294$	9.00000	0.524891
$295$	4.00000	0.232889
$296$	10.0000	0.581238
$297$	0	0
$298$	6.00000	0.347571
$299$	8.00000	0.462652
$300$	−1.00000	−0.0577350
$301$	−48.0000	−2.76667
$302$	12.0000	0.690522
$303$	−18.0000	−1.03407
$304$	−4.00000	−0.229416
$305$	10.0000	0.572598
$306$	2.00000	0.114332
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	0	0
$309$	16.0000	0.910208
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	−2.00000	−0.113228
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	10.0000	0.564333
$315$	4.00000	0.225374
$316$	−4.00000	−0.225018
$317$	26.0000	1.46031	0.730153	−	0.683284i	$-0.239449\pi$
$317$	26.0000	1.46031	0.730153	+	0.683284i	$0.239449\pi$
$318$	−6.00000	−0.336463
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−12.0000	−0.669775
$322$	−16.0000	−0.891645
$323$	8.00000	0.445132
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	20.0000	1.10770
$327$	2.00000	0.110600
$328$	−6.00000	−0.331295
$329$	16.0000	0.882109
$330$	0	0
$331$	−28.0000	−1.53902	−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000	−1.53902	−0.769510	+	0.638635i	$0.779499\pi$
$332$	−4.00000	−0.219529
$333$	−10.0000	−0.547997
$334$	16.0000	0.875481
$335$	12.0000	0.655630
$336$	4.00000	0.218218
$337$	−2.00000	−0.108947	−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000	−0.108947	−0.0544735	+	0.998515i	$0.517348\pi$
$338$	9.00000	0.489535
$339$	−18.0000	−0.977626
$340$	2.00000	0.108465
$341$	0	0
$342$	4.00000	0.216295
$343$	−8.00000	−0.431959
$344$	−12.0000	−0.646997
$345$	−4.00000	−0.215353
$346$	6.00000	0.322562
$347$	−28.0000	−1.50312	−0.751559	−	0.659665i	$-0.770698\pi$
$347$	−28.0000	−1.50312	−0.751559	+	0.659665i	$0.770698\pi$
$348$	6.00000	0.321634
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	4.00000	0.213809
$351$	2.00000	0.106752
$352$	0	0
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	−4.00000	−0.212598
$355$	4.00000	0.212298
$356$	10.0000	0.529999
$357$	−8.00000	−0.423405
$358$	−4.00000	−0.211407
$359$	16.0000	0.844448	0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000	0.844448	0.422224	+	0.906492i	$0.361250\pi$
$360$	1.00000	0.0527046
$361$	−3.00000	−0.157895
$362$	−14.0000	−0.735824
$363$	0	0
$364$	8.00000	0.419314
$365$	10.0000	0.523424
$366$	−10.0000	−0.522708
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	−4.00000	−0.208514
$369$	6.00000	0.312348
$370$	−10.0000	−0.519875
$371$	24.0000	1.24602
$372$	0	0
$373$	6.00000	0.310668	0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000	0.310668	0.155334	+	0.987862i	$0.450355\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	4.00000	0.206284
$377$	12.0000	0.618031
$378$	−4.00000	−0.205738
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	4.00000	0.205196
$381$	4.00000	0.204926
$382$	−12.0000	−0.613973
$383$	20.0000	1.02195	0.510976	−	0.859595i	$-0.329284\pi$
$383$	20.0000	1.02195	0.510976	+	0.859595i	$0.329284\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−22.0000	−1.11977
$387$	12.0000	0.609994
$388$	18.0000	0.913812
$389$	26.0000	1.31825	0.659126	−	0.752032i	$-0.270926\pi$
$389$	26.0000	1.31825	0.659126	+	0.752032i	$0.270926\pi$
$390$	2.00000	0.101274
$391$	8.00000	0.404577
$392$	−9.00000	−0.454569
$393$	−12.0000	−0.605320
$394$	−18.0000	−0.906827
$395$	4.00000	0.201262
$396$	0	0
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	0	0
$399$	−16.0000	−0.801002
$400$	1.00000	0.0500000
$401$	−22.0000	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$401$	−22.0000	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$402$	−12.0000	−0.598506
$403$	0	0
$404$	18.0000	0.895533
$405$	−1.00000	−0.0496904
$406$	−24.0000	−1.19110
$407$	0	0
$408$	−2.00000	−0.0990148
$409$	−2.00000	−0.0988936	−0.0494468	−	0.998777i	$-0.515746\pi$
$409$	−2.00000	−0.0988936	−0.0494468	+	0.998777i	$0.515746\pi$
$410$	6.00000	0.296319
$411$	−2.00000	−0.0986527
$412$	−16.0000	−0.788263
$413$	16.0000	0.787309
$414$	4.00000	0.196589
$415$	4.00000	0.196352
$416$	2.00000	0.0980581
$417$	−4.00000	−0.195881
$418$	0	0
$419$	−28.0000	−1.36789	−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000	−1.36789	−0.683945	+	0.729534i	$0.739737\pi$
$420$	−4.00000	−0.195180
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	12.0000	0.584151
$423$	−4.00000	−0.194487
$424$	6.00000	0.291386
$425$	−2.00000	−0.0970143
$426$	−4.00000	−0.193801
$427$	40.0000	1.93574
$428$	12.0000	0.580042
$429$	0	0
$430$	12.0000	0.578691
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	−1.00000	−0.0481125
$433$	34.0000	1.63394	0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000	1.63394	0.816968	+	0.576683i	$0.195653\pi$
$434$	0	0
$435$	−6.00000	−0.287678
$436$	−2.00000	−0.0957826
$437$	16.0000	0.765384
$438$	−10.0000	−0.477818
$439$	−12.0000	−0.572729	−0.286364	−	0.958121i	$-0.592447\pi$
$439$	−12.0000	−0.572729	−0.286364	+	0.958121i	$0.592447\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	−4.00000	−0.190261
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	10.0000	0.474579
$445$	−10.0000	−0.474045
$446$	0	0
$447$	6.00000	0.283790
$448$	−4.00000	−0.188982
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	18.0000	0.846649
$453$	12.0000	0.563809
$454$	28.0000	1.31411
$455$	−8.00000	−0.375046
$456$	−4.00000	−0.187317
$457$	−34.0000	−1.59045	−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000	−1.59045	−0.795226	+	0.606313i	$0.792648\pi$
$458$	2.00000	0.0934539
$459$	2.00000	0.0933520
$460$	4.00000	0.186501
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	0	0
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	−22.0000	−1.01913
$467$	−20.0000	−0.925490	−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000	−0.925490	−0.462745	+	0.886492i	$0.653135\pi$
$468$	−2.00000	−0.0924500
$469$	48.0000	2.21643
$470$	−4.00000	−0.184506
$471$	10.0000	0.460776
$472$	4.00000	0.184115
$473$	0	0
$474$	−4.00000	−0.183726
$475$	−4.00000	−0.183533
$476$	8.00000	0.366679
$477$	−6.00000	−0.274721
$478$	24.0000	1.09773
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	−1.00000	−0.0456435
$481$	20.0000	0.911922
$482$	−6.00000	−0.273293
$483$	−16.0000	−0.728025
$484$	0	0
$485$	−18.0000	−0.817338
$486$	1.00000	0.0453609
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	10.0000	0.452679
$489$	20.0000	0.904431
$490$	9.00000	0.406579
$491$	−36.0000	−1.62466	−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000	−1.62466	−0.812329	+	0.583200i	$0.801800\pi$
$492$	−6.00000	−0.270501
$493$	12.0000	0.540453
$494$	−8.00000	−0.359937
$495$	0	0
$496$	0	0
$497$	16.0000	0.717698
$498$	−4.00000	−0.179244
$499$	12.0000	0.537194	0.268597	−	0.963253i	$-0.413440\pi$
$499$	12.0000	0.537194	0.268597	+	0.963253i	$0.413440\pi$
$500$	−1.00000	−0.0447214
$501$	16.0000	0.714827
$502$	−12.0000	−0.535586
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	4.00000	0.178174
$505$	−18.0000	−0.800989
$506$	0	0
$507$	9.00000	0.399704
$508$	−4.00000	−0.177471
$509$	34.0000	1.50702	0.753512	−	0.657434i	$-0.228358\pi$
$509$	34.0000	1.50702	0.753512	+	0.657434i	$0.228358\pi$
$510$	2.00000	0.0885615
$511$	40.0000	1.76950
$512$	−1.00000	−0.0441942
$513$	4.00000	0.176604
$514$	−18.0000	−0.793946
$515$	16.0000	0.705044
$516$	−12.0000	−0.528271
$517$	0	0
$518$	−40.0000	−1.75750
$519$	6.00000	0.263371
$520$	−2.00000	−0.0877058
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	6.00000	0.262613
$523$	28.0000	1.22435	0.612177	−	0.790721i	$-0.290294\pi$
$523$	28.0000	1.22435	0.612177	+	0.790721i	$0.290294\pi$
$524$	12.0000	0.524222
$525$	4.00000	0.174574
$526$	−24.0000	−1.04645
$527$	0	0
$528$	0	0
$529$	−7.00000	−0.304348
$530$	−6.00000	−0.260623
$531$	−4.00000	−0.173585
$532$	16.0000	0.693688
$533$	−12.0000	−0.519778
$534$	10.0000	0.432742
$535$	−12.0000	−0.518805
$536$	12.0000	0.518321
$537$	−4.00000	−0.172613
$538$	−18.0000	−0.776035
$539$	0	0
$540$	1.00000	0.0430331
$541$	−2.00000	−0.0859867	−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000	−0.0859867	−0.0429934	+	0.999075i	$0.513689\pi$
$542$	−20.0000	−0.859074
$543$	−14.0000	−0.600798
$544$	2.00000	0.0857493
$545$	2.00000	0.0856706
$546$	8.00000	0.342368
$547$	−4.00000	−0.171028	−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000	−0.171028	−0.0855138	+	0.996337i	$0.527253\pi$
$548$	2.00000	0.0854358
$549$	−10.0000	−0.426790
$550$	0	0
$551$	24.0000	1.02243
$552$	−4.00000	−0.170251
$553$	16.0000	0.680389
$554$	18.0000	0.764747
$555$	−10.0000	−0.424476
$556$	4.00000	0.169638
$557$	−30.0000	−1.27114	−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000	−1.27114	−0.635570	+	0.772043i	$0.719235\pi$
$558$	0	0
$559$	−24.0000	−1.01509
$560$	4.00000	0.169031
$561$	0	0
$562$	−22.0000	−0.928014
$563$	4.00000	0.168580	0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000	0.168580	0.0842900	+	0.996441i	$0.473138\pi$
$564$	4.00000	0.168430
$565$	−18.0000	−0.757266
$566$	−12.0000	−0.504398
$567$	−4.00000	−0.167984
$568$	4.00000	0.167836
$569$	22.0000	0.922288	0.461144	−	0.887325i	$-0.347439\pi$
$569$	22.0000	0.922288	0.461144	+	0.887325i	$0.347439\pi$
$570$	4.00000	0.167542
$571$	−44.0000	−1.84134	−0.920671	−	0.390339i	$-0.872358\pi$
$571$	−44.0000	−1.84134	−0.920671	+	0.390339i	$0.872358\pi$
$572$	0	0
$573$	−12.0000	−0.501307
$574$	24.0000	1.00174
$575$	−4.00000	−0.166812
$576$	1.00000	0.0416667
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	13.0000	0.540729
$579$	−22.0000	−0.914289
$580$	6.00000	0.249136
$581$	16.0000	0.663792
$582$	18.0000	0.746124
$583$	0	0
$584$	10.0000	0.413803
$585$	2.00000	0.0826898
$586$	−10.0000	−0.413096
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	−9.00000	−0.371154
$589$	0	0
$590$	−4.00000	−0.164677
$591$	−18.0000	−0.740421
$592$	−10.0000	−0.410997
$593$	−2.00000	−0.0821302	−0.0410651	−	0.999156i	$-0.513075\pi$
$593$	−2.00000	−0.0821302	−0.0410651	+	0.999156i	$0.513075\pi$
$594$	0	0
$595$	−8.00000	−0.327968
$596$	−6.00000	−0.245770
$597$	0	0
$598$	−8.00000	−0.327144
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	1.00000	0.0408248
$601$	−10.0000	−0.407909	−0.203954	−	0.978980i	$-0.565379\pi$
$601$	−10.0000	−0.407909	−0.203954	+	0.978980i	$0.565379\pi$
$602$	48.0000	1.95633
$603$	−12.0000	−0.488678
$604$	−12.0000	−0.488273
$605$	0	0
$606$	18.0000	0.731200
$607$	−20.0000	−0.811775	−0.405887	−	0.913923i	$-0.633038\pi$
$607$	−20.0000	−0.811775	−0.405887	+	0.913923i	$0.633038\pi$
$608$	4.00000	0.162221
$609$	−24.0000	−0.972529
$610$	−10.0000	−0.404888
$611$	8.00000	0.323645
$612$	−2.00000	−0.0808452
$613$	14.0000	0.565455	0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000	0.565455	0.282727	+	0.959200i	$0.408761\pi$
$614$	−28.0000	−1.12999
$615$	6.00000	0.241943
$616$	0	0
$617$	−6.00000	−0.241551	−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000	−0.241551	−0.120775	+	0.992680i	$0.538538\pi$
$618$	−16.0000	−0.643614
$619$	−36.0000	−1.44696	−0.723481	−	0.690344i	$-0.757459\pi$
$619$	−36.0000	−1.44696	−0.723481	+	0.690344i	$0.757459\pi$
$620$	0	0
$621$	4.00000	0.160514
$622$	−12.0000	−0.481156
$623$	−40.0000	−1.60257
$624$	2.00000	0.0800641
$625$	1.00000	0.0400000
$626$	6.00000	0.239808
$627$	0	0
$628$	−10.0000	−0.399043
$629$	20.0000	0.797452
$630$	−4.00000	−0.159364
$631$	24.0000	0.955425	0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000	0.955425	0.477712	+	0.878516i	$0.341466\pi$
$632$	4.00000	0.159111
$633$	12.0000	0.476957
$634$	−26.0000	−1.03259
$635$	4.00000	0.158735
$636$	6.00000	0.237915
$637$	−18.0000	−0.713186
$638$	0	0
$639$	−4.00000	−0.158238
$640$	1.00000	0.0395285
$641$	26.0000	1.02694	0.513469	−	0.858108i	$-0.328360\pi$
$641$	26.0000	1.02694	0.513469	+	0.858108i	$0.328360\pi$
$642$	12.0000	0.473602
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	16.0000	0.630488
$645$	12.0000	0.472500
$646$	−8.00000	−0.314756
$647$	−36.0000	−1.41531	−0.707653	−	0.706560i	$-0.750246\pi$
$647$	−36.0000	−1.41531	−0.707653	+	0.706560i	$0.750246\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	2.00000	0.0784465
$651$	0	0
$652$	−20.0000	−0.783260
$653$	26.0000	1.01746	0.508729	−	0.860927i	$-0.330115\pi$
$653$	26.0000	1.01746	0.508729	+	0.860927i	$0.330115\pi$
$654$	−2.00000	−0.0782062
$655$	−12.0000	−0.468879
$656$	6.00000	0.234261
$657$	−10.0000	−0.390137
$658$	−16.0000	−0.623745
$659$	−28.0000	−1.09073	−0.545363	−	0.838200i	$-0.683608\pi$
$659$	−28.0000	−1.09073	−0.545363	+	0.838200i	$0.683608\pi$
$660$	0	0
$661$	−34.0000	−1.32245	−0.661223	−	0.750189i	$-0.729962\pi$
$661$	−34.0000	−1.32245	−0.661223	+	0.750189i	$0.729962\pi$
$662$	28.0000	1.08825
$663$	−4.00000	−0.155347
$664$	4.00000	0.155230
$665$	−16.0000	−0.620453
$666$	10.0000	0.387492
$667$	24.0000	0.929284
$668$	−16.0000	−0.619059
$669$	0	0
$670$	−12.0000	−0.463600
$671$	0	0
$672$	−4.00000	−0.154303
$673$	−26.0000	−1.00223	−0.501113	−	0.865382i	$-0.667076\pi$
$673$	−26.0000	−1.00223	−0.501113	+	0.865382i	$0.667076\pi$
$674$	2.00000	0.0770371
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	−30.0000	−1.15299	−0.576497	−	0.817099i	$-0.695581\pi$
$677$	−30.0000	−1.15299	−0.576497	+	0.817099i	$0.695581\pi$
$678$	18.0000	0.691286
$679$	−72.0000	−2.76311
$680$	−2.00000	−0.0766965
$681$	28.0000	1.07296
$682$	0	0
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	−4.00000	−0.152944
$685$	−2.00000	−0.0764161
$686$	8.00000	0.305441
$687$	2.00000	0.0763048
$688$	12.0000	0.457496
$689$	12.0000	0.457164
$690$	4.00000	0.152277
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	28.0000	1.06287
$695$	−4.00000	−0.151729
$696$	−6.00000	−0.227429
$697$	−12.0000	−0.454532
$698$	2.00000	0.0757011
$699$	−22.0000	−0.832116
$700$	−4.00000	−0.151186
$701$	18.0000	0.679851	0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000	0.679851	0.339925	+	0.940452i	$0.389598\pi$
$702$	−2.00000	−0.0754851
$703$	40.0000	1.50863
$704$	0	0
$705$	−4.00000	−0.150649
$706$	30.0000	1.12906
$707$	−72.0000	−2.70784
$708$	4.00000	0.150329
$709$	−34.0000	−1.27690	−0.638448	−	0.769665i	$-0.720423\pi$
$709$	−34.0000	−1.27690	−0.638448	+	0.769665i	$0.720423\pi$
$710$	−4.00000	−0.150117
$711$	−4.00000	−0.150012
$712$	−10.0000	−0.374766
$713$	0	0
$714$	8.00000	0.299392
$715$	0	0
$716$	4.00000	0.149487
$717$	24.0000	0.896296
$718$	−16.0000	−0.597115
$719$	20.0000	0.745874	0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000	0.745874	0.372937	+	0.927857i	$0.378351\pi$
$720$	−1.00000	−0.0372678
$721$	64.0000	2.38348
$722$	3.00000	0.111648
$723$	−6.00000	−0.223142
$724$	14.0000	0.520306
$725$	−6.00000	−0.222834
$726$	0	0
$727$	16.0000	0.593407	0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000	0.593407	0.296704	+	0.954970i	$0.404113\pi$
$728$	−8.00000	−0.296500
$729$	1.00000	0.0370370
$730$	−10.0000	−0.370117
$731$	−24.0000	−0.887672
$732$	10.0000	0.369611
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	−16.0000	−0.590571
$735$	9.00000	0.331970
$736$	4.00000	0.147442
$737$	0	0
$738$	−6.00000	−0.220863
$739$	36.0000	1.32428	0.662141	−	0.749380i	$-0.269648\pi$
$739$	36.0000	1.32428	0.662141	+	0.749380i	$0.269648\pi$
$740$	10.0000	0.367607
$741$	−8.00000	−0.293887
$742$	−24.0000	−0.881068
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	0	0
$745$	6.00000	0.219823
$746$	−6.00000	−0.219676
$747$	−4.00000	−0.146352
$748$	0	0
$749$	−48.0000	−1.75388
$750$	−1.00000	−0.0365148
$751$	−32.0000	−1.16770	−0.583848	−	0.811863i	$-0.698454\pi$
$751$	−32.0000	−1.16770	−0.583848	+	0.811863i	$0.698454\pi$
$752$	−4.00000	−0.145865
$753$	−12.0000	−0.437304
$754$	−12.0000	−0.437014
$755$	12.0000	0.436725
$756$	4.00000	0.145479
$757$	22.0000	0.799604	0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000	0.799604	0.399802	+	0.916602i	$0.369079\pi$
$758$	−20.0000	−0.726433
$759$	0	0
$760$	−4.00000	−0.145095
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	−4.00000	−0.144905
$763$	8.00000	0.289619
$764$	12.0000	0.434145
$765$	2.00000	0.0723102
$766$	−20.0000	−0.722629
$767$	8.00000	0.288863
$768$	−1.00000	−0.0360844
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	0	0
$771$	−18.0000	−0.648254
$772$	22.0000	0.791797
$773$	10.0000	0.359675	0.179838	−	0.983696i	$-0.442443\pi$
$773$	10.0000	0.359675	0.179838	+	0.983696i	$0.442443\pi$
$774$	−12.0000	−0.431331
$775$	0	0
$776$	−18.0000	−0.646162
$777$	−40.0000	−1.43499
$778$	−26.0000	−0.932145
$779$	−24.0000	−0.859889
$780$	−2.00000	−0.0716115
$781$	0	0
$782$	−8.00000	−0.286079
$783$	6.00000	0.214423
$784$	9.00000	0.321429
$785$	10.0000	0.356915
$786$	12.0000	0.428026
$787$	36.0000	1.28326	0.641631	−	0.767014i	$-0.278258\pi$
$787$	36.0000	1.28326	0.641631	+	0.767014i	$0.278258\pi$
$788$	18.0000	0.641223
$789$	−24.0000	−0.854423
$790$	−4.00000	−0.142314
$791$	−72.0000	−2.56003
$792$	0	0
$793$	20.0000	0.710221
$794$	−22.0000	−0.780751
$795$	−6.00000	−0.212798
$796$	0	0
$797$	−30.0000	−1.06265	−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000	−1.06265	−0.531327	+	0.847167i	$0.678307\pi$
$798$	16.0000	0.566394
$799$	8.00000	0.283020
$800$	−1.00000	−0.0353553
$801$	10.0000	0.353333
$802$	22.0000	0.776847
$803$	0	0
$804$	12.0000	0.423207
$805$	−16.0000	−0.563926
$806$	0	0
$807$	−18.0000	−0.633630
$808$	−18.0000	−0.633238
$809$	22.0000	0.773479	0.386739	−	0.922189i	$-0.373601\pi$
$809$	22.0000	0.773479	0.386739	+	0.922189i	$0.373601\pi$
$810$	1.00000	0.0351364
$811$	−52.0000	−1.82597	−0.912983	−	0.407997i	$-0.866228\pi$
$811$	−52.0000	−1.82597	−0.912983	+	0.407997i	$0.866228\pi$
$812$	24.0000	0.842235
$813$	−20.0000	−0.701431
$814$	0	0
$815$	20.0000	0.700569
$816$	2.00000	0.0700140
$817$	−48.0000	−1.67931
$818$	2.00000	0.0699284
$819$	8.00000	0.279543
$820$	−6.00000	−0.209529
$821$	2.00000	0.0698005	0.0349002	−	0.999391i	$-0.488889\pi$
$821$	2.00000	0.0698005	0.0349002	+	0.999391i	$0.488889\pi$
$822$	2.00000	0.0697580
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	16.0000	0.557386
$825$	0	0
$826$	−16.0000	−0.556711
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	−4.00000	−0.139010
$829$	46.0000	1.59765	0.798823	−	0.601566i	$-0.205456\pi$
$829$	46.0000	1.59765	0.798823	+	0.601566i	$0.205456\pi$
$830$	−4.00000	−0.138842
$831$	18.0000	0.624413
$832$	−2.00000	−0.0693375
$833$	−18.0000	−0.623663
$834$	4.00000	0.138509
$835$	16.0000	0.553703
$836$	0	0
$837$	0	0
$838$	28.0000	0.967244
$839$	36.0000	1.24286	0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000	1.24286	0.621429	+	0.783470i	$0.286552\pi$
$840$	4.00000	0.138013
$841$	7.00000	0.241379
$842$	−22.0000	−0.758170
$843$	−22.0000	−0.757720
$844$	−12.0000	−0.413057
$845$	9.00000	0.309609
$846$	4.00000	0.137523
$847$	0	0
$848$	−6.00000	−0.206041
$849$	−12.0000	−0.411839
$850$	2.00000	0.0685994
$851$	40.0000	1.37118
$852$	4.00000	0.137038
$853$	−18.0000	−0.616308	−0.308154	−	0.951336i	$-0.599711\pi$
$853$	−18.0000	−0.616308	−0.308154	+	0.951336i	$0.599711\pi$
$854$	−40.0000	−1.36877
$855$	4.00000	0.136797
$856$	−12.0000	−0.410152
$857$	38.0000	1.29806	0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000	1.29806	0.649028	+	0.760765i	$0.275176\pi$
$858$	0	0
$859$	−44.0000	−1.50126	−0.750630	−	0.660722i	$-0.770250\pi$
$859$	−44.0000	−1.50126	−0.750630	+	0.660722i	$0.770250\pi$
$860$	−12.0000	−0.409197
$861$	24.0000	0.817918
$862$	0	0
$863$	−36.0000	−1.22545	−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000	−1.22545	−0.612727	+	0.790295i	$0.709928\pi$
$864$	1.00000	0.0340207
$865$	6.00000	0.204006
$866$	−34.0000	−1.15537
$867$	13.0000	0.441503
$868$	0	0
$869$	0	0
$870$	6.00000	0.203419
$871$	24.0000	0.813209
$872$	2.00000	0.0677285
$873$	18.0000	0.609208
$874$	−16.0000	−0.541208
$875$	4.00000	0.135225
$876$	10.0000	0.337869
$877$	14.0000	0.472746	0.236373	−	0.971662i	$-0.424041\pi$
$877$	14.0000	0.472746	0.236373	+	0.971662i	$0.424041\pi$
$878$	12.0000	0.404980
$879$	−10.0000	−0.337292
$880$	0	0
$881$	18.0000	0.606435	0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000	0.606435	0.303218	+	0.952921i	$0.401939\pi$
$882$	−9.00000	−0.303046
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	4.00000	0.134535
$885$	−4.00000	−0.134459
$886$	−12.0000	−0.403148
$887$	−48.0000	−1.61168	−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000	−1.61168	−0.805841	+	0.592132i	$0.798286\pi$
$888$	−10.0000	−0.335578
$889$	16.0000	0.536623
$890$	10.0000	0.335201
$891$	0	0
$892$	0	0
$893$	16.0000	0.535420
$894$	−6.00000	−0.200670
$895$	−4.00000	−0.133705
$896$	4.00000	0.133631
$897$	−8.00000	−0.267112
$898$	6.00000	0.200223
$899$	0	0
$900$	1.00000	0.0333333
$901$	12.0000	0.399778
$902$	0	0
$903$	48.0000	1.59734
$904$	−18.0000	−0.598671
$905$	−14.0000	−0.465376
$906$	−12.0000	−0.398673
$907$	−52.0000	−1.72663	−0.863316	−	0.504664i	$-0.831616\pi$
$907$	−52.0000	−1.72663	−0.863316	+	0.504664i	$0.831616\pi$
$908$	−28.0000	−0.929213
$909$	18.0000	0.597022
$910$	8.00000	0.265197
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	4.00000	0.132453
$913$	0	0
$914$	34.0000	1.12462
$915$	−10.0000	−0.330590
$916$	−2.00000	−0.0660819
$917$	−48.0000	−1.58510
$918$	−2.00000	−0.0660098
$919$	12.0000	0.395843	0.197922	−	0.980218i	$-0.436581\pi$
$919$	12.0000	0.395843	0.197922	+	0.980218i	$0.436581\pi$
$920$	−4.00000	−0.131876
$921$	−28.0000	−0.922631
$922$	30.0000	0.987997
$923$	8.00000	0.263323
$924$	0	0
$925$	−10.0000	−0.328798
$926$	−24.0000	−0.788689
$927$	−16.0000	−0.525509
$928$	6.00000	0.196960
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	0	0
$931$	−36.0000	−1.17985
$932$	22.0000	0.720634
$933$	−12.0000	−0.392862
$934$	20.0000	0.654420
$935$	0	0
$936$	2.00000	0.0653720
$937$	22.0000	0.718709	0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000	0.718709	0.359354	+	0.933201i	$0.382997\pi$
$938$	−48.0000	−1.56726
$939$	6.00000	0.195803
$940$	4.00000	0.130466
$941$	−22.0000	−0.717180	−0.358590	−	0.933495i	$-0.616742\pi$
$941$	−22.0000	−0.717180	−0.358590	+	0.933495i	$0.616742\pi$
$942$	−10.0000	−0.325818
$943$	−24.0000	−0.781548
$944$	−4.00000	−0.130189
$945$	−4.00000	−0.130120
$946$	0	0
$947$	−52.0000	−1.68977	−0.844886	−	0.534946i	$-0.820332\pi$
$947$	−52.0000	−1.68977	−0.844886	+	0.534946i	$0.820332\pi$
$948$	4.00000	0.129914
$949$	20.0000	0.649227
$950$	4.00000	0.129777
$951$	−26.0000	−0.843108
$952$	−8.00000	−0.259281
$953$	6.00000	0.194359	0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000	0.194359	0.0971795	+	0.995267i	$0.469018\pi$
$954$	6.00000	0.194257
$955$	−12.0000	−0.388311
$956$	−24.0000	−0.776215
$957$	0	0
$958$	0	0
$959$	−8.00000	−0.258333
$960$	1.00000	0.0322749
$961$	−31.0000	−1.00000
$962$	−20.0000	−0.644826
$963$	12.0000	0.386695
$964$	6.00000	0.193247
$965$	−22.0000	−0.708205
$966$	16.0000	0.514792
$967$	−12.0000	−0.385894	−0.192947	−	0.981209i	$-0.561805\pi$
$967$	−12.0000	−0.385894	−0.192947	+	0.981209i	$0.561805\pi$
$968$	0	0
$969$	−8.00000	−0.256997
$970$	18.0000	0.577945
$971$	−4.00000	−0.128366	−0.0641831	−	0.997938i	$-0.520444\pi$
$971$	−4.00000	−0.128366	−0.0641831	+	0.997938i	$0.520444\pi$
$972$	−1.00000	−0.0320750
$973$	−16.0000	−0.512936
$974$	32.0000	1.02535
$975$	2.00000	0.0640513
$976$	−10.0000	−0.320092
$977$	−38.0000	−1.21573	−0.607864	−	0.794041i	$-0.707973\pi$
$977$	−38.0000	−1.21573	−0.607864	+	0.794041i	$0.707973\pi$
$978$	−20.0000	−0.639529
$979$	0	0
$980$	−9.00000	−0.287494
$981$	−2.00000	−0.0638551
$982$	36.0000	1.14881
$983$	28.0000	0.893061	0.446531	−	0.894768i	$-0.352659\pi$
$983$	28.0000	0.893061	0.446531	+	0.894768i	$0.352659\pi$
$984$	6.00000	0.191273
$985$	−18.0000	−0.573528
$986$	−12.0000	−0.382158
$987$	−16.0000	−0.509286
$988$	8.00000	0.254514
$989$	−48.0000	−1.52631
$990$	0	0
$991$	0	0		−	1.00000i	$-0.5\pi$
$991$	0	0			1.00000i	$0.5\pi$
$992$	0	0
$993$	28.0000	0.888553
$994$	−16.0000	−0.507489
$995$	0	0
$996$	4.00000	0.126745
$997$	38.0000	1.20347	0.601736	−	0.798695i	$-0.294476\pi$
$997$	38.0000	1.20347	0.601736	+	0.798695i	$0.294476\pi$
$998$	−12.0000	−0.379853
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.a.1.1		1
11.10	odd	2		330.2.a.c.1.1	✓	1
33.32	even	2		990.2.a.g.1.1		1
44.43	even	2		2640.2.a.j.1.1		1
55.32	even	4		1650.2.c.a.199.2		2
55.43	even	4		1650.2.c.a.199.1		2
55.54	odd	2		1650.2.a.e.1.1		1
132.131	odd	2		7920.2.a.t.1.1		1
165.32	odd	4		4950.2.c.y.199.1		2
165.98	odd	4		4950.2.c.y.199.2		2
165.164	even	2		4950.2.a.x.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.a.c.1.1	✓	1	11.10	odd	2
990.2.a.g.1.1		1	33.32	even	2
1650.2.a.e.1.1		1	55.54	odd	2
1650.2.c.a.199.1		2	55.43	even	4
1650.2.c.a.199.2		2	55.32	even	4
2640.2.a.j.1.1		1	44.43	even	2
3630.2.a.a.1.1		1	1.1	even	1	trivial
4950.2.a.x.1.1		1	165.164	even	2
4950.2.c.y.199.1		2	165.32	odd	4
4950.2.c.y.199.2		2	165.98	odd	4
7920.2.a.t.1.1		1	132.131	odd	2

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:	\( N \)	\(=\)	\( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3630.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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