LMFDB - Embedded newform 9150.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9150,2,Mod(1,9150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9150, 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("9150.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$9150 = 2 \cdot 3 \cdot 5^{2} \cdot 61$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	9150.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:	$73.0631178495$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 366)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9150.1

$q$ -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^{6} +3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{11} +1.00000 q^{12} +5.00000 q^{13} -3.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} -1.00000 q^{18} -8.00000 q^{19} +3.00000 q^{21} +1.00000 q^{22} -5.00000 q^{23} -1.00000 q^{24} -5.00000 q^{26} +1.00000 q^{27} +3.00000 q^{28} -4.00000 q^{31} -1.00000 q^{32} -1.00000 q^{33} +2.00000 q^{34} +1.00000 q^{36} -4.00000 q^{37} +8.00000 q^{38} +5.00000 q^{39} +3.00000 q^{41} -3.00000 q^{42} -4.00000 q^{43} -1.00000 q^{44} +5.00000 q^{46} -2.00000 q^{47} +1.00000 q^{48} +2.00000 q^{49} -2.00000 q^{51} +5.00000 q^{52} -1.00000 q^{54} -3.00000 q^{56} -8.00000 q^{57} -7.00000 q^{59} +1.00000 q^{61} +4.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} +1.00000 q^{66} +13.0000 q^{67} -2.00000 q^{68} -5.00000 q^{69} -16.0000 q^{71} -1.00000 q^{72} -9.00000 q^{73} +4.00000 q^{74} -8.00000 q^{76} -3.00000 q^{77} -5.00000 q^{78} -1.00000 q^{79} +1.00000 q^{81} -3.00000 q^{82} -14.0000 q^{83} +3.00000 q^{84} +4.00000 q^{86} +1.00000 q^{88} -4.00000 q^{89} +15.0000 q^{91} -5.00000 q^{92} -4.00000 q^{93} +2.00000 q^{94} -1.00000 q^{96} -14.0000 q^{97} -2.00000 q^{98} -1.00000 q^{99} +O(q^{100})

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
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	3.00000	1.13389	0.566947	−	0.823754i	$-0.308125\pi$
$7$	3.00000	1.13389	0.566947	+	0.823754i	$0.308125\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0	0
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	1.00000	0.288675
$13$	5.00000	1.38675	0.693375	−	0.720577i	$-0.256123\pi$
$13$	5.00000	1.38675	0.693375	+	0.720577i	$0.256123\pi$
$14$	−3.00000	−0.801784
$15$	0	0
$16$	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
$19$	−8.00000	−1.83533	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000	−1.83533	−0.917663	+	0.397360i	$0.869927\pi$
$20$	0	0
$21$	3.00000	0.654654
$22$	1.00000	0.213201
$23$	−5.00000	−1.04257	−0.521286	−	0.853382i	$-0.674548\pi$
$23$	−5.00000	−1.04257	−0.521286	+	0.853382i	$0.674548\pi$
$24$	−1.00000	−0.204124
$25$	0	0
$26$	−5.00000	−0.980581
$27$	1.00000	0.192450
$28$	3.00000	0.566947
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	2.00000	0.342997
$35$	0	0
$36$	1.00000	0.166667
$37$	−4.00000	−0.657596	−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000	−0.657596	−0.328798	+	0.944400i	$0.606644\pi$
$38$	8.00000	1.29777
$39$	5.00000	0.800641
$40$	0	0
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	−3.00000	−0.462910
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−1.00000	−0.150756
$45$	0	0
$46$	5.00000	0.737210
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	1.00000	0.144338
$49$	2.00000	0.285714
$50$	0	0
$51$	−2.00000	−0.280056
$52$	5.00000	0.693375
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−3.00000	−0.400892
$57$	−8.00000	−1.05963
$58$	0	0
$59$	−7.00000	−0.911322	−0.455661	−	0.890153i	$-0.650597\pi$
$59$	−7.00000	−0.911322	−0.455661	+	0.890153i	$0.650597\pi$
$60$	0	0
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	4.00000	0.508001
$63$	3.00000	0.377964
$64$	1.00000	0.125000
$65$	0	0
$66$	1.00000	0.123091
$67$	13.0000	1.58820	0.794101	−	0.607785i	$-0.207942\pi$
$67$	13.0000	1.58820	0.794101	+	0.607785i	$0.207942\pi$
$68$	−2.00000	−0.242536
$69$	−5.00000	−0.601929
$70$	0	0
$71$	−16.0000	−1.89885	−0.949425	−	0.313993i	$-0.898333\pi$
$71$	−16.0000	−1.89885	−0.949425	+	0.313993i	$0.898333\pi$
$72$	−1.00000	−0.117851
$73$	−9.00000	−1.05337	−0.526685	−	0.850060i	$-0.676565\pi$
$73$	−9.00000	−1.05337	−0.526685	+	0.850060i	$0.676565\pi$
$74$	4.00000	0.464991
$75$	0	0
$76$	−8.00000	−0.917663
$77$	−3.00000	−0.341882
$78$	−5.00000	−0.566139
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	−3.00000	−0.331295
$83$	−14.0000	−1.53670	−0.768350	−	0.640030i	$-0.778922\pi$
$83$	−14.0000	−1.53670	−0.768350	+	0.640030i	$0.778922\pi$
$84$	3.00000	0.327327
$85$	0	0
$86$	4.00000	0.431331
$87$	0	0
$88$	1.00000	0.106600
$89$	−4.00000	−0.423999	−0.212000	−	0.977270i	$-0.567998\pi$
$89$	−4.00000	−0.423999	−0.212000	+	0.977270i	$0.567998\pi$
$90$	0	0
$91$	15.0000	1.57243
$92$	−5.00000	−0.521286
$93$	−4.00000	−0.414781
$94$	2.00000	0.206284
$95$	0	0
$96$	−1.00000	−0.102062
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	−2.00000	−0.202031
$99$	−1.00000	−0.100504
$100$	0	0
$101$	−8.00000	−0.796030	−0.398015	−	0.917379i	$-0.630301\pi$
$101$	−8.00000	−0.796030	−0.398015	+	0.917379i	$0.630301\pi$
$102$	2.00000	0.198030
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	−5.00000	−0.490290
$105$	0	0
$106$	0	0
$107$	2.00000	0.193347	0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000	0.193347	0.0966736	+	0.995316i	$0.469180\pi$
$108$	1.00000	0.0962250
$109$	−15.0000	−1.43674	−0.718370	−	0.695662i	$-0.755111\pi$
$109$	−15.0000	−1.43674	−0.718370	+	0.695662i	$0.755111\pi$
$110$	0	0
$111$	−4.00000	−0.379663
$112$	3.00000	0.283473
$113$	−11.0000	−1.03479	−0.517396	−	0.855746i	$-0.673099\pi$
$113$	−11.0000	−1.03479	−0.517396	+	0.855746i	$0.673099\pi$
$114$	8.00000	0.749269
$115$	0	0
$116$	0	0
$117$	5.00000	0.462250
$118$	7.00000	0.644402
$119$	−6.00000	−0.550019
$120$	0	0
$121$	−10.0000	−0.909091
$122$	−1.00000	−0.0905357
$123$	3.00000	0.270501
$124$	−4.00000	−0.359211
$125$	0	0
$126$	−3.00000	−0.267261
$127$	22.0000	1.95218	0.976092	−	0.217357i	$-0.0697436\pi$
$127$	22.0000	1.95218	0.976092	+	0.217357i	$0.0697436\pi$
$128$	−1.00000	−0.0883883
$129$	−4.00000	−0.352180
$130$	0	0
$131$	10.0000	0.873704	0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000	0.873704	0.436852	+	0.899533i	$0.356093\pi$
$132$	−1.00000	−0.0870388
$133$	−24.0000	−2.08106
$134$	−13.0000	−1.12303
$135$	0	0
$136$	2.00000	0.171499
$137$	−15.0000	−1.28154	−0.640768	−	0.767734i	$-0.721384\pi$
$137$	−15.0000	−1.28154	−0.640768	+	0.767734i	$0.721384\pi$
$138$	5.00000	0.425628
$139$	−5.00000	−0.424094	−0.212047	−	0.977259i	$-0.568013\pi$
$139$	−5.00000	−0.424094	−0.212047	+	0.977259i	$0.568013\pi$
$140$	0	0
$141$	−2.00000	−0.168430
$142$	16.0000	1.34269
$143$	−5.00000	−0.418121
$144$	1.00000	0.0833333
$145$	0	0
$146$	9.00000	0.744845
$147$	2.00000	0.164957
$148$	−4.00000	−0.328798
$149$	−21.0000	−1.72039	−0.860194	−	0.509968i	$-0.829657\pi$
$149$	−21.0000	−1.72039	−0.860194	+	0.509968i	$0.829657\pi$
$150$	0	0
$151$	−9.00000	−0.732410	−0.366205	−	0.930534i	$-0.619343\pi$
$151$	−9.00000	−0.732410	−0.366205	+	0.930534i	$0.619343\pi$
$152$	8.00000	0.648886
$153$	−2.00000	−0.161690
$154$	3.00000	0.241747
$155$	0	0
$156$	5.00000	0.400320
$157$	−6.00000	−0.478852	−0.239426	−	0.970915i	$-0.576959\pi$
$157$	−6.00000	−0.478852	−0.239426	+	0.970915i	$0.576959\pi$
$158$	1.00000	0.0795557
$159$	0	0
$160$	0	0
$161$	−15.0000	−1.18217
$162$	−1.00000	−0.0785674
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	3.00000	0.234261
$165$	0	0
$166$	14.0000	1.08661
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	−3.00000	−0.231455
$169$	12.0000	0.923077
$170$	0	0
$171$	−8.00000	−0.611775
$172$	−4.00000	−0.304997
$173$	22.0000	1.67263	0.836315	−	0.548250i	$-0.184706\pi$
$173$	22.0000	1.67263	0.836315	+	0.548250i	$0.184706\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	−7.00000	−0.526152
$178$	4.00000	0.299813
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	26.0000	1.93256	0.966282	−	0.257485i	$-0.0828937\pi$
$181$	26.0000	1.93256	0.966282	+	0.257485i	$0.0828937\pi$
$182$	−15.0000	−1.11187
$183$	1.00000	0.0739221
$184$	5.00000	0.368605
$185$	0	0
$186$	4.00000	0.293294
$187$	2.00000	0.146254
$188$	−2.00000	−0.145865
$189$	3.00000	0.218218
$190$	0	0
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	1.00000	0.0721688
$193$	18.0000	1.29567	0.647834	−	0.761781i	$-0.275675\pi$
$193$	18.0000	1.29567	0.647834	+	0.761781i	$0.275675\pi$
$194$	14.0000	1.00514
$195$	0	0
$196$	2.00000	0.142857
$197$	−21.0000	−1.49619	−0.748094	−	0.663593i	$-0.769031\pi$
$197$	−21.0000	−1.49619	−0.748094	+	0.663593i	$0.769031\pi$
$198$	1.00000	0.0710669
$199$	18.0000	1.27599	0.637993	−	0.770042i	$-0.279765\pi$
$199$	18.0000	1.27599	0.637993	+	0.770042i	$0.279765\pi$
$200$	0	0
$201$	13.0000	0.916949
$202$	8.00000	0.562878
$203$	0	0
$204$	−2.00000	−0.140028
$205$	0	0
$206$	−14.0000	−0.975426
$207$	−5.00000	−0.347524
$208$	5.00000	0.346688
$209$	8.00000	0.553372
$210$	0	0
$211$	20.0000	1.37686	0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000	1.37686	0.688428	+	0.725304i	$0.258301\pi$
$212$	0	0
$213$	−16.0000	−1.09630
$214$	−2.00000	−0.136717
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	−12.0000	−0.814613
$218$	15.0000	1.01593
$219$	−9.00000	−0.608164
$220$	0	0
$221$	−10.0000	−0.672673
$222$	4.00000	0.268462
$223$	21.0000	1.40626	0.703132	−	0.711059i	$-0.251784\pi$
$223$	21.0000	1.40626	0.703132	+	0.711059i	$0.251784\pi$
$224$	−3.00000	−0.200446
$225$	0	0
$226$	11.0000	0.731709
$227$	15.0000	0.995585	0.497792	−	0.867296i	$-0.334144\pi$
$227$	15.0000	0.995585	0.497792	+	0.867296i	$0.334144\pi$
$228$	−8.00000	−0.529813
$229$	−17.0000	−1.12339	−0.561696	−	0.827344i	$-0.689851\pi$
$229$	−17.0000	−1.12339	−0.561696	+	0.827344i	$0.689851\pi$
$230$	0	0
$231$	−3.00000	−0.197386
$232$	0	0
$233$	0	0		−	1.00000i	$-0.5\pi$
$233$	0	0			1.00000i	$0.5\pi$
$234$	−5.00000	−0.326860
$235$	0	0
$236$	−7.00000	−0.455661
$237$	−1.00000	−0.0649570
$238$	6.00000	0.388922
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	25.0000	1.61039	0.805196	−	0.593009i	$-0.202060\pi$
$241$	25.0000	1.61039	0.805196	+	0.593009i	$0.202060\pi$
$242$	10.0000	0.642824
$243$	1.00000	0.0641500
$244$	1.00000	0.0640184
$245$	0	0
$246$	−3.00000	−0.191273
$247$	−40.0000	−2.54514
$248$	4.00000	0.254000
$249$	−14.0000	−0.887214
$250$	0	0
$251$	8.00000	0.504956	0.252478	−	0.967603i	$-0.418755\pi$
$251$	8.00000	0.504956	0.252478	+	0.967603i	$0.418755\pi$
$252$	3.00000	0.188982
$253$	5.00000	0.314347
$254$	−22.0000	−1.38040
$255$	0	0
$256$	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	$0.310261\pi$
$258$	4.00000	0.249029
$259$	−12.0000	−0.745644
$260$	0	0
$261$	0	0
$262$	−10.0000	−0.617802
$263$	−24.0000	−1.47990	−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000	−1.47990	−0.739952	+	0.672660i	$0.765152\pi$
$264$	1.00000	0.0615457
$265$	0	0
$266$	24.0000	1.47153
$267$	−4.00000	−0.244796
$268$	13.0000	0.794101
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	−2.00000	−0.121268
$273$	15.0000	0.907841
$274$	15.0000	0.906183
$275$	0	0
$276$	−5.00000	−0.300965
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	5.00000	0.299880
$279$	−4.00000	−0.239474
$280$	0	0
$281$	24.0000	1.43172	0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000	1.43172	0.715860	+	0.698244i	$0.246035\pi$
$282$	2.00000	0.119098
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−16.0000	−0.949425
$285$	0	0
$286$	5.00000	0.295656
$287$	9.00000	0.531253
$288$	−1.00000	−0.0589256
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−14.0000	−0.820695
$292$	−9.00000	−0.526685
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−2.00000	−0.116642
$295$	0	0
$296$	4.00000	0.232495
$297$	−1.00000	−0.0580259
$298$	21.0000	1.21650
$299$	−25.0000	−1.44579
$300$	0	0
$301$	−12.0000	−0.691669
$302$	9.00000	0.517892
$303$	−8.00000	−0.459588
$304$	−8.00000	−0.458831
$305$	0	0
$306$	2.00000	0.114332
$307$	−19.0000	−1.08439	−0.542194	−	0.840254i	$-0.682406\pi$
$307$	−19.0000	−1.08439	−0.542194	+	0.840254i	$0.682406\pi$
$308$	−3.00000	−0.170941
$309$	14.0000	0.796432
$310$	0	0
$311$	35.0000	1.98467	0.992334	−	0.123585i	$-0.0394392\pi$
$311$	35.0000	1.98467	0.992334	+	0.123585i	$0.0394392\pi$
$312$	−5.00000	−0.283069
$313$	8.00000	0.452187	0.226093	−	0.974106i	$-0.427405\pi$
$313$	8.00000	0.452187	0.226093	+	0.974106i	$0.427405\pi$
$314$	6.00000	0.338600
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	−10.0000	−0.561656	−0.280828	−	0.959758i	$-0.590609\pi$
$317$	−10.0000	−0.561656	−0.280828	+	0.959758i	$0.590609\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	2.00000	0.111629
$322$	15.0000	0.835917
$323$	16.0000	0.890264
$324$	1.00000	0.0555556
$325$	0	0
$326$	−4.00000	−0.221540
$327$	−15.0000	−0.829502
$328$	−3.00000	−0.165647
$329$	−6.00000	−0.330791
$330$	0	0
$331$	9.00000	0.494685	0.247342	−	0.968928i	$-0.420443\pi$
$331$	9.00000	0.494685	0.247342	+	0.968928i	$0.420443\pi$
$332$	−14.0000	−0.768350
$333$	−4.00000	−0.219199
$334$	−18.0000	−0.984916
$335$	0	0
$336$	3.00000	0.163663
$337$	16.0000	0.871576	0.435788	−	0.900049i	$-0.356470\pi$
$337$	16.0000	0.871576	0.435788	+	0.900049i	$0.356470\pi$
$338$	−12.0000	−0.652714
$339$	−11.0000	−0.597438
$340$	0	0
$341$	4.00000	0.216612
$342$	8.00000	0.432590
$343$	−15.0000	−0.809924
$344$	4.00000	0.215666
$345$	0	0
$346$	−22.0000	−1.18273
$347$	4.00000	0.214731	0.107366	−	0.994220i	$-0.465758\pi$
$347$	4.00000	0.214731	0.107366	+	0.994220i	$0.465758\pi$
$348$	0	0
$349$	−22.0000	−1.17763	−0.588817	−	0.808267i	$-0.700406\pi$
$349$	−22.0000	−1.17763	−0.588817	+	0.808267i	$0.700406\pi$
$350$	0	0
$351$	5.00000	0.266880
$352$	1.00000	0.0533002
$353$	−25.0000	−1.33062	−0.665308	−	0.746569i	$-0.731700\pi$
$353$	−25.0000	−1.33062	−0.665308	+	0.746569i	$0.731700\pi$
$354$	7.00000	0.372046
$355$	0	0
$356$	−4.00000	−0.212000
$357$	−6.00000	−0.317554
$358$	0	0
$359$	36.0000	1.90001	0.950004	−	0.312239i	$-0.101079\pi$
$359$	36.0000	1.90001	0.950004	+	0.312239i	$0.101079\pi$
$360$	0	0
$361$	45.0000	2.36842
$362$	−26.0000	−1.36653
$363$	−10.0000	−0.524864
$364$	15.0000	0.786214
$365$	0	0
$366$	−1.00000	−0.0522708
$367$	−36.0000	−1.87918	−0.939592	−	0.342296i	$-0.888796\pi$
$367$	−36.0000	−1.87918	−0.939592	+	0.342296i	$0.888796\pi$
$368$	−5.00000	−0.260643
$369$	3.00000	0.156174
$370$	0	0
$371$	0	0
$372$	−4.00000	−0.207390
$373$	−4.00000	−0.207112	−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000	−0.207112	−0.103556	+	0.994624i	$0.533022\pi$
$374$	−2.00000	−0.103418
$375$	0	0
$376$	2.00000	0.103142
$377$	0	0
$378$	−3.00000	−0.154303
$379$	0	0		−	1.00000i	$-0.5\pi$
$379$	0	0			1.00000i	$0.5\pi$
$380$	0	0
$381$	22.0000	1.12709
$382$	15.0000	0.767467
$383$	−7.00000	−0.357683	−0.178842	−	0.983878i	$-0.557235\pi$
$383$	−7.00000	−0.357683	−0.178842	+	0.983878i	$0.557235\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−18.0000	−0.916176
$387$	−4.00000	−0.203331
$388$	−14.0000	−0.710742
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	0	0
$391$	10.0000	0.505722
$392$	−2.00000	−0.101015
$393$	10.0000	0.504433
$394$	21.0000	1.05796
$395$	0	0
$396$	−1.00000	−0.0502519
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	−18.0000	−0.902258
$399$	−24.0000	−1.20150
$400$	0	0
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	−13.0000	−0.648381
$403$	−20.0000	−0.996271
$404$	−8.00000	−0.398015
$405$	0	0
$406$	0	0
$407$	4.00000	0.198273
$408$	2.00000	0.0990148
$409$	−20.0000	−0.988936	−0.494468	−	0.869196i	$-0.664637\pi$
$409$	−20.0000	−0.988936	−0.494468	+	0.869196i	$0.664637\pi$
$410$	0	0
$411$	−15.0000	−0.739895
$412$	14.0000	0.689730
$413$	−21.0000	−1.03334
$414$	5.00000	0.245737
$415$	0	0
$416$	−5.00000	−0.245145
$417$	−5.00000	−0.244851
$418$	−8.00000	−0.391293
$419$	4.00000	0.195413	0.0977064	−	0.995215i	$-0.468849\pi$
$419$	4.00000	0.195413	0.0977064	+	0.995215i	$0.468849\pi$
$420$	0	0
$421$	2.00000	0.0974740	0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000	0.0974740	0.0487370	+	0.998812i	$0.484480\pi$
$422$	−20.0000	−0.973585
$423$	−2.00000	−0.0972433
$424$	0	0
$425$	0	0
$426$	16.0000	0.775203
$427$	3.00000	0.145180
$428$	2.00000	0.0966736
$429$	−5.00000	−0.241402
$430$	0	0
$431$	−2.00000	−0.0963366	−0.0481683	−	0.998839i	$-0.515338\pi$
$431$	−2.00000	−0.0963366	−0.0481683	+	0.998839i	$0.515338\pi$
$432$	1.00000	0.0481125
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	12.0000	0.576018
$435$	0	0
$436$	−15.0000	−0.718370
$437$	40.0000	1.91346
$438$	9.00000	0.430037
$439$	−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
$441$	2.00000	0.0952381
$442$	10.0000	0.475651
$443$	16.0000	0.760183	0.380091	−	0.924949i	$-0.375893\pi$
$443$	16.0000	0.760183	0.380091	+	0.924949i	$0.375893\pi$
$444$	−4.00000	−0.189832
$445$	0	0
$446$	−21.0000	−0.994379
$447$	−21.0000	−0.993266
$448$	3.00000	0.141737
$449$	−17.0000	−0.802280	−0.401140	−	0.916017i	$-0.631386\pi$
$449$	−17.0000	−0.802280	−0.401140	+	0.916017i	$0.631386\pi$
$450$	0	0
$451$	−3.00000	−0.141264
$452$	−11.0000	−0.517396
$453$	−9.00000	−0.422857
$454$	−15.0000	−0.703985
$455$	0	0
$456$	8.00000	0.374634
$457$	−8.00000	−0.374224	−0.187112	−	0.982339i	$-0.559913\pi$
$457$	−8.00000	−0.374224	−0.187112	+	0.982339i	$0.559913\pi$
$458$	17.0000	0.794358
$459$	−2.00000	−0.0933520
$460$	0	0
$461$	−6.00000	−0.279448	−0.139724	−	0.990190i	$-0.544622\pi$
$461$	−6.00000	−0.279448	−0.139724	+	0.990190i	$0.544622\pi$
$462$	3.00000	0.139573
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	25.0000	1.15686	0.578431	−	0.815731i	$-0.303665\pi$
$467$	25.0000	1.15686	0.578431	+	0.815731i	$0.303665\pi$
$468$	5.00000	0.231125
$469$	39.0000	1.80085
$470$	0	0
$471$	−6.00000	−0.276465
$472$	7.00000	0.322201
$473$	4.00000	0.183920
$474$	1.00000	0.0459315
$475$	0	0
$476$	−6.00000	−0.275010
$477$	0	0
$478$	12.0000	0.548867
$479$	−36.0000	−1.64488	−0.822441	−	0.568850i	$-0.807388\pi$
$479$	−36.0000	−1.64488	−0.822441	+	0.568850i	$0.807388\pi$
$480$	0	0
$481$	−20.0000	−0.911922
$482$	−25.0000	−1.13872
$483$	−15.0000	−0.682524
$484$	−10.0000	−0.454545
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	16.0000	0.725029	0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000	0.725029	0.362515	+	0.931978i	$0.381918\pi$
$488$	−1.00000	−0.0452679
$489$	4.00000	0.180886
$490$	0	0
$491$	28.0000	1.26362	0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000	1.26362	0.631811	+	0.775122i	$0.282312\pi$
$492$	3.00000	0.135250
$493$	0	0
$494$	40.0000	1.79969
$495$	0	0
$496$	−4.00000	−0.179605
$497$	−48.0000	−2.15309
$498$	14.0000	0.627355
$499$	−5.00000	−0.223831	−0.111915	−	0.993718i	$-0.535699\pi$
$499$	−5.00000	−0.223831	−0.111915	+	0.993718i	$0.535699\pi$
$500$	0	0
$501$	18.0000	0.804181
$502$	−8.00000	−0.357057
$503$	10.0000	0.445878	0.222939	−	0.974832i	$-0.428435\pi$
$503$	10.0000	0.445878	0.222939	+	0.974832i	$0.428435\pi$
$504$	−3.00000	−0.133631
$505$	0	0
$506$	−5.00000	−0.222277
$507$	12.0000	0.532939
$508$	22.0000	0.976092
$509$	−10.0000	−0.443242	−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000	−0.443242	−0.221621	+	0.975133i	$0.571135\pi$
$510$	0	0
$511$	−27.0000	−1.19441
$512$	−1.00000	−0.0441942
$513$	−8.00000	−0.353209
$514$	−18.0000	−0.793946
$515$	0	0
$516$	−4.00000	−0.176090
$517$	2.00000	0.0879599
$518$	12.0000	0.527250
$519$	22.0000	0.965693
$520$	0	0
$521$	−22.0000	−0.963837	−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000	−0.963837	−0.481919	+	0.876216i	$0.660060\pi$
$522$	0	0
$523$	−5.00000	−0.218635	−0.109317	−	0.994007i	$-0.534866\pi$
$523$	−5.00000	−0.218635	−0.109317	+	0.994007i	$0.534866\pi$
$524$	10.0000	0.436852
$525$	0	0
$526$	24.0000	1.04645
$527$	8.00000	0.348485
$528$	−1.00000	−0.0435194
$529$	2.00000	0.0869565
$530$	0	0
$531$	−7.00000	−0.303774
$532$	−24.0000	−1.04053
$533$	15.0000	0.649722
$534$	4.00000	0.173097
$535$	0	0
$536$	−13.0000	−0.561514
$537$	0	0
$538$	18.0000	0.776035
$539$	−2.00000	−0.0861461
$540$	0	0
$541$	−40.0000	−1.71973	−0.859867	−	0.510518i	$-0.829454\pi$
$541$	−40.0000	−1.71973	−0.859867	+	0.510518i	$0.829454\pi$
$542$	−8.00000	−0.343629
$543$	26.0000	1.11577
$544$	2.00000	0.0857493
$545$	0	0
$546$	−15.0000	−0.641941
$547$	35.0000	1.49649	0.748246	−	0.663421i	$-0.230896\pi$
$547$	35.0000	1.49649	0.748246	+	0.663421i	$0.230896\pi$
$548$	−15.0000	−0.640768
$549$	1.00000	0.0426790
$550$	0	0
$551$	0	0
$552$	5.00000	0.212814
$553$	−3.00000	−0.127573
$554$	22.0000	0.934690
$555$	0	0
$556$	−5.00000	−0.212047
$557$	12.0000	0.508456	0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000	0.508456	0.254228	+	0.967144i	$0.418179\pi$
$558$	4.00000	0.169334
$559$	−20.0000	−0.845910
$560$	0	0
$561$	2.00000	0.0844401
$562$	−24.0000	−1.01238
$563$	−6.00000	−0.252870	−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000	−0.252870	−0.126435	+	0.991975i	$0.540353\pi$
$564$	−2.00000	−0.0842152
$565$	0	0
$566$	−14.0000	−0.588464
$567$	3.00000	0.125988
$568$	16.0000	0.671345
$569$	−17.0000	−0.712677	−0.356339	−	0.934357i	$-0.615975\pi$
$569$	−17.0000	−0.712677	−0.356339	+	0.934357i	$0.615975\pi$
$570$	0	0
$571$	−2.00000	−0.0836974	−0.0418487	−	0.999124i	$-0.513325\pi$
$571$	−2.00000	−0.0836974	−0.0418487	+	0.999124i	$0.513325\pi$
$572$	−5.00000	−0.209061
$573$	−15.0000	−0.626634
$574$	−9.00000	−0.375653
$575$	0	0
$576$	1.00000	0.0416667
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	13.0000	0.540729
$579$	18.0000	0.748054
$580$	0	0
$581$	−42.0000	−1.74245
$582$	14.0000	0.580319
$583$	0	0
$584$	9.00000	0.372423
$585$	0	0
$586$	−6.00000	−0.247858
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	2.00000	0.0824786
$589$	32.0000	1.31854
$590$	0	0
$591$	−21.0000	−0.863825
$592$	−4.00000	−0.164399
$593$	6.00000	0.246390	0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000	0.246390	0.123195	+	0.992382i	$0.460686\pi$
$594$	1.00000	0.0410305
$595$	0	0
$596$	−21.0000	−0.860194
$597$	18.0000	0.736691
$598$	25.0000	1.02233
$599$	39.0000	1.59350	0.796748	−	0.604311i	$-0.206552\pi$
$599$	39.0000	1.59350	0.796748	+	0.604311i	$0.206552\pi$
$600$	0	0
$601$	−3.00000	−0.122373	−0.0611863	−	0.998126i	$-0.519488\pi$
$601$	−3.00000	−0.122373	−0.0611863	+	0.998126i	$0.519488\pi$
$602$	12.0000	0.489083
$603$	13.0000	0.529401
$604$	−9.00000	−0.366205
$605$	0	0
$606$	8.00000	0.324978
$607$	4.00000	0.162355	0.0811775	−	0.996700i	$-0.474132\pi$
$607$	4.00000	0.162355	0.0811775	+	0.996700i	$0.474132\pi$
$608$	8.00000	0.324443
$609$	0	0
$610$	0	0
$611$	−10.0000	−0.404557
$612$	−2.00000	−0.0808452
$613$	38.0000	1.53481	0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000	1.53481	0.767403	+	0.641165i	$0.221549\pi$
$614$	19.0000	0.766778
$615$	0	0
$616$	3.00000	0.120873
$617$	−10.0000	−0.402585	−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000	−0.402585	−0.201292	+	0.979531i	$0.564514\pi$
$618$	−14.0000	−0.563163
$619$	−14.0000	−0.562708	−0.281354	−	0.959604i	$-0.590783\pi$
$619$	−14.0000	−0.562708	−0.281354	+	0.959604i	$0.590783\pi$
$620$	0	0
$621$	−5.00000	−0.200643
$622$	−35.0000	−1.40337
$623$	−12.0000	−0.480770
$624$	5.00000	0.200160
$625$	0	0
$626$	−8.00000	−0.319744
$627$	8.00000	0.319489
$628$	−6.00000	−0.239426
$629$	8.00000	0.318981
$630$	0	0
$631$	25.0000	0.995234	0.497617	−	0.867397i	$-0.334208\pi$
$631$	25.0000	0.995234	0.497617	+	0.867397i	$0.334208\pi$
$632$	1.00000	0.0397779
$633$	20.0000	0.794929
$634$	10.0000	0.397151
$635$	0	0
$636$	0	0
$637$	10.0000	0.396214
$638$	0	0
$639$	−16.0000	−0.632950
$640$	0	0
$641$	−44.0000	−1.73790	−0.868948	−	0.494904i	$-0.835203\pi$
$641$	−44.0000	−1.73790	−0.868948	+	0.494904i	$0.835203\pi$
$642$	−2.00000	−0.0789337
$643$	8.00000	0.315489	0.157745	−	0.987480i	$-0.449578\pi$
$643$	8.00000	0.315489	0.157745	+	0.987480i	$0.449578\pi$
$644$	−15.0000	−0.591083
$645$	0	0
$646$	−16.0000	−0.629512
$647$	3.00000	0.117942	0.0589711	−	0.998260i	$-0.481218\pi$
$647$	3.00000	0.117942	0.0589711	+	0.998260i	$0.481218\pi$
$648$	−1.00000	−0.0392837
$649$	7.00000	0.274774
$650$	0	0
$651$	−12.0000	−0.470317
$652$	4.00000	0.156652
$653$	14.0000	0.547862	0.273931	−	0.961749i	$-0.411676\pi$
$653$	14.0000	0.547862	0.273931	+	0.961749i	$0.411676\pi$
$654$	15.0000	0.586546
$655$	0	0
$656$	3.00000	0.117130
$657$	−9.00000	−0.351123
$658$	6.00000	0.233904
$659$	6.00000	0.233727	0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000	0.233727	0.116863	+	0.993148i	$0.462716\pi$
$660$	0	0
$661$	32.0000	1.24466	0.622328	−	0.782757i	$-0.286187\pi$
$661$	32.0000	1.24466	0.622328	+	0.782757i	$0.286187\pi$
$662$	−9.00000	−0.349795
$663$	−10.0000	−0.388368
$664$	14.0000	0.543305
$665$	0	0
$666$	4.00000	0.154997
$667$	0	0
$668$	18.0000	0.696441
$669$	21.0000	0.811907
$670$	0	0
$671$	−1.00000	−0.0386046
$672$	−3.00000	−0.115728
$673$	14.0000	0.539660	0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000	0.539660	0.269830	+	0.962908i	$0.413032\pi$
$674$	−16.0000	−0.616297
$675$	0	0
$676$	12.0000	0.461538
$677$	−30.0000	−1.15299	−0.576497	−	0.817099i	$-0.695581\pi$
$677$	−30.0000	−1.15299	−0.576497	+	0.817099i	$0.695581\pi$
$678$	11.0000	0.422452
$679$	−42.0000	−1.61181
$680$	0	0
$681$	15.0000	0.574801
$682$	−4.00000	−0.153168
$683$	−48.0000	−1.83667	−0.918334	−	0.395805i	$-0.870466\pi$
$683$	−48.0000	−1.83667	−0.918334	+	0.395805i	$0.870466\pi$
$684$	−8.00000	−0.305888
$685$	0	0
$686$	15.0000	0.572703
$687$	−17.0000	−0.648590
$688$	−4.00000	−0.152499
$689$	0	0
$690$	0	0
$691$	−24.0000	−0.913003	−0.456502	−	0.889723i	$-0.650898\pi$
$691$	−24.0000	−0.913003	−0.456502	+	0.889723i	$0.650898\pi$
$692$	22.0000	0.836315
$693$	−3.00000	−0.113961
$694$	−4.00000	−0.151838
$695$	0	0
$696$	0	0
$697$	−6.00000	−0.227266
$698$	22.0000	0.832712
$699$	0	0
$700$	0	0
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	−5.00000	−0.188713
$703$	32.0000	1.20690
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	25.0000	0.940887
$707$	−24.0000	−0.902613
$708$	−7.00000	−0.263076
$709$	−14.0000	−0.525781	−0.262891	−	0.964826i	$-0.584676\pi$
$709$	−14.0000	−0.525781	−0.262891	+	0.964826i	$0.584676\pi$
$710$	0	0
$711$	−1.00000	−0.0375029
$712$	4.00000	0.149906
$713$	20.0000	0.749006
$714$	6.00000	0.224544
$715$	0	0
$716$	0	0
$717$	−12.0000	−0.448148
$718$	−36.0000	−1.34351
$719$	−20.0000	−0.745874	−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000	−0.745874	−0.372937	+	0.927857i	$0.621649\pi$
$720$	0	0
$721$	42.0000	1.56416
$722$	−45.0000	−1.67473
$723$	25.0000	0.929760
$724$	26.0000	0.966282
$725$	0	0
$726$	10.0000	0.371135
$727$	−34.0000	−1.26099	−0.630495	−	0.776193i	$-0.717148\pi$
$727$	−34.0000	−1.26099	−0.630495	+	0.776193i	$0.717148\pi$
$728$	−15.0000	−0.555937
$729$	1.00000	0.0370370
$730$	0	0
$731$	8.00000	0.295891
$732$	1.00000	0.0369611
$733$	1.00000	0.0369358	0.0184679	−	0.999829i	$-0.494121\pi$
$733$	1.00000	0.0369358	0.0184679	+	0.999829i	$0.494121\pi$
$734$	36.0000	1.32878
$735$	0	0
$736$	5.00000	0.184302
$737$	−13.0000	−0.478861
$738$	−3.00000	−0.110432
$739$	19.0000	0.698926	0.349463	−	0.936950i	$-0.386364\pi$
$739$	19.0000	0.698926	0.349463	+	0.936950i	$0.386364\pi$
$740$	0	0
$741$	−40.0000	−1.46944
$742$	0	0
$743$	31.0000	1.13728	0.568640	−	0.822587i	$-0.307470\pi$
$743$	31.0000	1.13728	0.568640	+	0.822587i	$0.307470\pi$
$744$	4.00000	0.146647
$745$	0	0
$746$	4.00000	0.146450
$747$	−14.0000	−0.512233
$748$	2.00000	0.0731272
$749$	6.00000	0.219235
$750$	0	0
$751$	−12.0000	−0.437886	−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000	−0.437886	−0.218943	+	0.975738i	$0.570261\pi$
$752$	−2.00000	−0.0729325
$753$	8.00000	0.291536
$754$	0	0
$755$	0	0
$756$	3.00000	0.109109
$757$	23.0000	0.835949	0.417975	−	0.908459i	$-0.362740\pi$
$757$	23.0000	0.835949	0.417975	+	0.908459i	$0.362740\pi$
$758$	0	0
$759$	5.00000	0.181489
$760$	0	0
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	−22.0000	−0.796976
$763$	−45.0000	−1.62911
$764$	−15.0000	−0.542681
$765$	0	0
$766$	7.00000	0.252920
$767$	−35.0000	−1.26378
$768$	1.00000	0.0360844
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	0	0
$771$	18.0000	0.648254
$772$	18.0000	0.647834
$773$	−18.0000	−0.647415	−0.323708	−	0.946157i	$-0.604929\pi$
$773$	−18.0000	−0.647415	−0.323708	+	0.946157i	$0.604929\pi$
$774$	4.00000	0.143777
$775$	0	0
$776$	14.0000	0.502571
$777$	−12.0000	−0.430498
$778$	−18.0000	−0.645331
$779$	−24.0000	−0.859889
$780$	0	0
$781$	16.0000	0.572525
$782$	−10.0000	−0.357599
$783$	0	0
$784$	2.00000	0.0714286
$785$	0	0
$786$	−10.0000	−0.356688
$787$	32.0000	1.14068	0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000	1.14068	0.570338	+	0.821410i	$0.306812\pi$
$788$	−21.0000	−0.748094
$789$	−24.0000	−0.854423
$790$	0	0
$791$	−33.0000	−1.17334
$792$	1.00000	0.0355335
$793$	5.00000	0.177555
$794$	−2.00000	−0.0709773
$795$	0	0
$796$	18.0000	0.637993
$797$	−29.0000	−1.02723	−0.513616	−	0.858020i	$-0.671695\pi$
$797$	−29.0000	−1.02723	−0.513616	+	0.858020i	$0.671695\pi$
$798$	24.0000	0.849591
$799$	4.00000	0.141510
$800$	0	0
$801$	−4.00000	−0.141333
$802$	−6.00000	−0.211867
$803$	9.00000	0.317603
$804$	13.0000	0.458475
$805$	0	0
$806$	20.0000	0.704470
$807$	−18.0000	−0.633630
$808$	8.00000	0.281439
$809$	23.0000	0.808637	0.404318	−	0.914618i	$-0.367509\pi$
$809$	23.0000	0.808637	0.404318	+	0.914618i	$0.367509\pi$
$810$	0	0
$811$	−7.00000	−0.245803	−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000	−0.245803	−0.122902	+	0.992419i	$0.539220\pi$
$812$	0	0
$813$	8.00000	0.280572
$814$	−4.00000	−0.140200
$815$	0	0
$816$	−2.00000	−0.0700140
$817$	32.0000	1.11954
$818$	20.0000	0.699284
$819$	15.0000	0.524142
$820$	0	0
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	15.0000	0.523185
$823$	−40.0000	−1.39431	−0.697156	−	0.716919i	$-0.745552\pi$
$823$	−40.0000	−1.39431	−0.697156	+	0.716919i	$0.745552\pi$
$824$	−14.0000	−0.487713
$825$	0	0
$826$	21.0000	0.730683
$827$	48.0000	1.66912	0.834562	−	0.550914i	$-0.185721\pi$
$827$	48.0000	1.66912	0.834562	+	0.550914i	$0.185721\pi$
$828$	−5.00000	−0.173762
$829$	−7.00000	−0.243120	−0.121560	−	0.992584i	$-0.538790\pi$
$829$	−7.00000	−0.243120	−0.121560	+	0.992584i	$0.538790\pi$
$830$	0	0
$831$	−22.0000	−0.763172
$832$	5.00000	0.173344
$833$	−4.00000	−0.138592
$834$	5.00000	0.173136
$835$	0	0
$836$	8.00000	0.276686
$837$	−4.00000	−0.138260
$838$	−4.00000	−0.138178
$839$	20.0000	0.690477	0.345238	−	0.938515i	$-0.387798\pi$
$839$	20.0000	0.690477	0.345238	+	0.938515i	$0.387798\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	−2.00000	−0.0689246
$843$	24.0000	0.826604
$844$	20.0000	0.688428
$845$	0	0
$846$	2.00000	0.0687614
$847$	−30.0000	−1.03081
$848$	0	0
$849$	14.0000	0.480479
$850$	0	0
$851$	20.0000	0.685591
$852$	−16.0000	−0.548151
$853$	−39.0000	−1.33533	−0.667667	−	0.744460i	$-0.732707\pi$
$853$	−39.0000	−1.33533	−0.667667	+	0.744460i	$0.732707\pi$
$854$	−3.00000	−0.102658
$855$	0	0
$856$	−2.00000	−0.0683586
$857$	53.0000	1.81045	0.905223	−	0.424937i	$-0.139704\pi$
$857$	53.0000	1.81045	0.905223	+	0.424937i	$0.139704\pi$
$858$	5.00000	0.170697
$859$	−14.0000	−0.477674	−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000	−0.477674	−0.238837	+	0.971060i	$0.576766\pi$
$860$	0	0
$861$	9.00000	0.306719
$862$	2.00000	0.0681203
$863$	56.0000	1.90626	0.953131	−	0.302558i	$-0.0978405\pi$
$863$	56.0000	1.90626	0.953131	+	0.302558i	$0.0978405\pi$
$864$	−1.00000	−0.0340207
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	−13.0000	−0.441503
$868$	−12.0000	−0.407307
$869$	1.00000	0.0339227
$870$	0	0
$871$	65.0000	2.20244
$872$	15.0000	0.507964
$873$	−14.0000	−0.473828
$874$	−40.0000	−1.35302
$875$	0	0
$876$	−9.00000	−0.304082
$877$	40.0000	1.35070	0.675352	−	0.737496i	$-0.263992\pi$
$877$	40.0000	1.35070	0.675352	+	0.737496i	$0.263992\pi$
$878$	12.0000	0.404980
$879$	6.00000	0.202375
$880$	0	0
$881$	−35.0000	−1.17918	−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000	−1.17918	−0.589590	+	0.807703i	$0.700711\pi$
$882$	−2.00000	−0.0673435
$883$	−15.0000	−0.504790	−0.252395	−	0.967624i	$-0.581218\pi$
$883$	−15.0000	−0.504790	−0.252395	+	0.967624i	$0.581218\pi$
$884$	−10.0000	−0.336336
$885$	0	0
$886$	−16.0000	−0.537531
$887$	−32.0000	−1.07445	−0.537227	−	0.843437i	$-0.680528\pi$
$887$	−32.0000	−1.07445	−0.537227	+	0.843437i	$0.680528\pi$
$888$	4.00000	0.134231
$889$	66.0000	2.21357
$890$	0	0
$891$	−1.00000	−0.0335013
$892$	21.0000	0.703132
$893$	16.0000	0.535420
$894$	21.0000	0.702345
$895$	0	0
$896$	−3.00000	−0.100223
$897$	−25.0000	−0.834726
$898$	17.0000	0.567297
$899$	0	0
$900$	0	0
$901$	0	0
$902$	3.00000	0.0998891
$903$	−12.0000	−0.399335
$904$	11.0000	0.365855
$905$	0	0
$906$	9.00000	0.299005
$907$	−28.0000	−0.929725	−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000	−0.929725	−0.464862	+	0.885383i	$0.653896\pi$
$908$	15.0000	0.497792
$909$	−8.00000	−0.265343
$910$	0	0
$911$	12.0000	0.397578	0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000	0.397578	0.198789	+	0.980042i	$0.436299\pi$
$912$	−8.00000	−0.264906
$913$	14.0000	0.463332
$914$	8.00000	0.264616
$915$	0	0
$916$	−17.0000	−0.561696
$917$	30.0000	0.990687
$918$	2.00000	0.0660098
$919$	−52.0000	−1.71532	−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000	−1.71532	−0.857661	+	0.514216i	$0.828083\pi$
$920$	0	0
$921$	−19.0000	−0.626071
$922$	6.00000	0.197599
$923$	−80.0000	−2.63323
$924$	−3.00000	−0.0986928
$925$	0	0
$926$	8.00000	0.262896
$927$	14.0000	0.459820
$928$	0	0
$929$	43.0000	1.41078	0.705392	−	0.708817i	$-0.250771\pi$
$929$	43.0000	1.41078	0.705392	+	0.708817i	$0.250771\pi$
$930$	0	0
$931$	−16.0000	−0.524379
$932$	0	0
$933$	35.0000	1.14585
$934$	−25.0000	−0.818025
$935$	0	0
$936$	−5.00000	−0.163430
$937$	41.0000	1.33941	0.669706	−	0.742627i	$-0.266420\pi$
$937$	41.0000	1.33941	0.669706	+	0.742627i	$0.266420\pi$
$938$	−39.0000	−1.27340
$939$	8.00000	0.261070
$940$	0	0
$941$	40.0000	1.30396	0.651981	−	0.758235i	$-0.273938\pi$
$941$	40.0000	1.30396	0.651981	+	0.758235i	$0.273938\pi$
$942$	6.00000	0.195491
$943$	−15.0000	−0.488467
$944$	−7.00000	−0.227831
$945$	0	0
$946$	−4.00000	−0.130051
$947$	−35.0000	−1.13735	−0.568674	−	0.822563i	$-0.692543\pi$
$947$	−35.0000	−1.13735	−0.568674	+	0.822563i	$0.692543\pi$
$948$	−1.00000	−0.0324785
$949$	−45.0000	−1.46076
$950$	0	0
$951$	−10.0000	−0.324272
$952$	6.00000	0.194461
$953$	−50.0000	−1.61966	−0.809829	−	0.586665i	$-0.800440\pi$
$953$	−50.0000	−1.61966	−0.809829	+	0.586665i	$0.800440\pi$
$954$	0	0
$955$	0	0
$956$	−12.0000	−0.388108
$957$	0	0
$958$	36.0000	1.16311
$959$	−45.0000	−1.45313
$960$	0	0
$961$	−15.0000	−0.483871
$962$	20.0000	0.644826
$963$	2.00000	0.0644491
$964$	25.0000	0.805196
$965$	0	0
$966$	15.0000	0.482617
$967$	−18.0000	−0.578841	−0.289420	−	0.957202i	$-0.593463\pi$
$967$	−18.0000	−0.578841	−0.289420	+	0.957202i	$0.593463\pi$
$968$	10.0000	0.321412
$969$	16.0000	0.513994
$970$	0	0
$971$	−14.0000	−0.449281	−0.224641	−	0.974442i	$-0.572121\pi$
$971$	−14.0000	−0.449281	−0.224641	+	0.974442i	$0.572121\pi$
$972$	1.00000	0.0320750
$973$	−15.0000	−0.480878
$974$	−16.0000	−0.512673
$975$	0	0
$976$	1.00000	0.0320092
$977$	30.0000	0.959785	0.479893	−	0.877327i	$-0.340676\pi$
$977$	30.0000	0.959785	0.479893	+	0.877327i	$0.340676\pi$
$978$	−4.00000	−0.127906
$979$	4.00000	0.127841
$980$	0	0
$981$	−15.0000	−0.478913
$982$	−28.0000	−0.893516
$983$	4.00000	0.127580	0.0637901	−	0.997963i	$-0.479681\pi$
$983$	4.00000	0.127580	0.0637901	+	0.997963i	$0.479681\pi$
$984$	−3.00000	−0.0956365
$985$	0	0
$986$	0	0
$987$	−6.00000	−0.190982
$988$	−40.0000	−1.27257
$989$	20.0000	0.635963
$990$	0	0
$991$	40.0000	1.27064	0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000	1.27064	0.635321	+	0.772248i	$0.280868\pi$
$992$	4.00000	0.127000
$993$	9.00000	0.285606
$994$	48.0000	1.52247
$995$	0	0
$996$	−14.0000	−0.443607
$997$	−2.00000	−0.0633406	−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000	−0.0633406	−0.0316703	+	0.999498i	$0.510083\pi$
$998$	5.00000	0.158272
$999$	−4.00000	−0.126554

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9150.2.a.n.1.1		1
5.4	even	2		366.2.a.d.1.1	✓	1
15.14	odd	2		1098.2.a.e.1.1		1
20.19	odd	2		2928.2.a.h.1.1		1
60.59	even	2		8784.2.a.z.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
366.2.a.d.1.1	✓	1	5.4	even	2
1098.2.a.e.1.1		1	15.14	odd	2
2928.2.a.h.1.1		1	20.19	odd	2
8784.2.a.z.1.1		1	60.59	even	2
9150.2.a.n.1.1		1	1.1	even	1	trivial

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Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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Modular forms

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Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	9150.2.a.n.1.1

Level	$9150$
Weight	$2$
Character	9150.1
Self dual	yes
Analytic conductor	$73.063$
Analytic rank	$1$
Dimension	$1$
CM	no
Inner twists	$1$