LMFDB - Embedded newform 2890.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2890,2,Mod(1,2890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2890, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2890.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2890 = 2 \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2890.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:	$23.0767661842$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 170)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2890.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{10} +6.00000 q^{11} -1.00000 q^{12} -5.00000 q^{13} +1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{18} -3.00000 q^{19} -1.00000 q^{20} +6.00000 q^{22} +2.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} -5.00000 q^{26} +5.00000 q^{27} +1.00000 q^{29} +1.00000 q^{30} +7.00000 q^{31} +1.00000 q^{32} -6.00000 q^{33} -2.00000 q^{36} +10.0000 q^{37} -3.00000 q^{38} +5.00000 q^{39} -1.00000 q^{40} -12.0000 q^{41} +4.00000 q^{43} +6.00000 q^{44} +2.00000 q^{45} +2.00000 q^{46} +7.00000 q^{47} -1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} -5.00000 q^{52} +1.00000 q^{53} +5.00000 q^{54} -6.00000 q^{55} +3.00000 q^{57} +1.00000 q^{58} +9.00000 q^{59} +1.00000 q^{60} +3.00000 q^{61} +7.00000 q^{62} +1.00000 q^{64} +5.00000 q^{65} -6.00000 q^{66} +10.0000 q^{67} -2.00000 q^{69} -9.00000 q^{71} -2.00000 q^{72} +7.00000 q^{73} +10.0000 q^{74} -1.00000 q^{75} -3.00000 q^{76} +5.00000 q^{78} +8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} -12.0000 q^{82} -2.00000 q^{83} +4.00000 q^{86} -1.00000 q^{87} +6.00000 q^{88} -1.00000 q^{89} +2.00000 q^{90} +2.00000 q^{92} -7.00000 q^{93} +7.00000 q^{94} +3.00000 q^{95} -1.00000 q^{96} +1.00000 q^{97} -7.00000 q^{98} -12.0000 q^{99} +O(q^{100})\)

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	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	−2.00000	−0.666667
$10$	−1.00000	−0.316228
$11$	6.00000	1.80907	0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000	1.80907	0.904534	+	0.426401i	$0.140219\pi$
$12$	−1.00000	−0.288675
$13$	−5.00000	−1.38675	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000	−1.38675	−0.693375	+	0.720577i	$0.743877\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	−2.00000	−0.471405
$19$	−3.00000	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	6.00000	1.27920
$23$	2.00000	0.417029	0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000	0.417029	0.208514	+	0.978019i	$0.433137\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−5.00000	−0.980581
$27$	5.00000	0.962250
$28$	0	0
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	1.00000	0.182574
$31$	7.00000	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$32$	1.00000	0.176777
$33$	−6.00000	−1.04447
$34$	0	0
$35$	0	0
$36$	−2.00000	−0.333333
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	−3.00000	−0.486664
$39$	5.00000	0.800641
$40$	−1.00000	−0.158114
$41$	−12.0000	−1.87409	−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−12.0000	−1.87409	−0.937043	+	0.349215i	$0.886448\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	6.00000	0.904534
$45$	2.00000	0.298142
$46$	2.00000	0.294884
$47$	7.00000	1.02105	0.510527	−	0.859861i	$-0.329450\pi$
$47$	7.00000	1.02105	0.510527	+	0.859861i	$0.329450\pi$
$48$	−1.00000	−0.144338
$49$	−7.00000	−1.00000
$50$	1.00000	0.141421
$51$	0	0
$52$	−5.00000	−0.693375
$53$	1.00000	0.137361	0.0686803	−	0.997639i	$-0.478121\pi$
$53$	1.00000	0.137361	0.0686803	+	0.997639i	$0.478121\pi$
$54$	5.00000	0.680414
$55$	−6.00000	−0.809040
$56$	0	0
$57$	3.00000	0.397360
$58$	1.00000	0.131306
$59$	9.00000	1.17170	0.585850	−	0.810419i	$-0.300761\pi$
$59$	9.00000	1.17170	0.585850	+	0.810419i	$0.300761\pi$
$60$	1.00000	0.129099
$61$	3.00000	0.384111	0.192055	−	0.981384i	$-0.438485\pi$
$61$	3.00000	0.384111	0.192055	+	0.981384i	$0.438485\pi$
$62$	7.00000	0.889001
$63$	0	0
$64$	1.00000	0.125000
$65$	5.00000	0.620174
$66$	−6.00000	−0.738549
$67$	10.0000	1.22169	0.610847	−	0.791748i	$-0.290829\pi$
$67$	10.0000	1.22169	0.610847	+	0.791748i	$0.290829\pi$
$68$	0	0
$69$	−2.00000	−0.240772
$70$	0	0
$71$	−9.00000	−1.06810	−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000	−1.06810	−0.534052	+	0.845452i	$0.679331\pi$
$72$	−2.00000	−0.235702
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	10.0000	1.16248
$75$	−1.00000	−0.115470
$76$	−3.00000	−0.344124
$77$	0	0
$78$	5.00000	0.566139
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−12.0000	−1.32518
$83$	−2.00000	−0.219529	−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000	−0.219529	−0.109764	+	0.993958i	$0.535010\pi$
$84$	0	0
$85$	0	0
$86$	4.00000	0.431331
$87$	−1.00000	−0.107211
$88$	6.00000	0.639602
$89$	−1.00000	−0.106000	−0.0529999	−	0.998595i	$-0.516878\pi$
$89$	−1.00000	−0.106000	−0.0529999	+	0.998595i	$0.516878\pi$
$90$	2.00000	0.210819
$91$	0	0
$92$	2.00000	0.208514
$93$	−7.00000	−0.725866
$94$	7.00000	0.721995
$95$	3.00000	0.307794
$96$	−1.00000	−0.102062
$97$	1.00000	0.101535	0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000	0.101535	0.0507673	+	0.998711i	$0.483833\pi$
$98$	−7.00000	−0.707107
$99$	−12.0000	−1.20605
$100$	1.00000	0.100000
$101$	−6.00000	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$102$	0	0
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−5.00000	−0.490290
$105$	0	0
$106$	1.00000	0.0971286
$107$	8.00000	0.773389	0.386695	−	0.922208i	$-0.373617\pi$
$107$	8.00000	0.773389	0.386695	+	0.922208i	$0.373617\pi$
$108$	5.00000	0.481125
$109$	−17.0000	−1.62830	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	−17.0000	−1.62830	−0.814152	+	0.580651i	$0.802798\pi$
$110$	−6.00000	−0.572078
$111$	−10.0000	−0.949158
$112$	0	0
$113$	17.0000	1.59923	0.799613	−	0.600516i	$-0.205038\pi$
$113$	17.0000	1.59923	0.799613	+	0.600516i	$0.205038\pi$
$114$	3.00000	0.280976
$115$	−2.00000	−0.186501
$116$	1.00000	0.0928477
$117$	10.0000	0.924500
$118$	9.00000	0.828517
$119$	0	0
$120$	1.00000	0.0912871
$121$	25.0000	2.27273
$122$	3.00000	0.271607
$123$	12.0000	1.08200
$124$	7.00000	0.628619
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	9.00000	0.798621	0.399310	−	0.916816i	$-0.369250\pi$
$127$	9.00000	0.798621	0.399310	+	0.916816i	$0.369250\pi$
$128$	1.00000	0.0883883
$129$	−4.00000	−0.352180
$130$	5.00000	0.438529
$131$	8.00000	0.698963	0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000	0.698963	0.349482	+	0.936943i	$0.386358\pi$
$132$	−6.00000	−0.522233
$133$	0	0
$134$	10.0000	0.863868
$135$	−5.00000	−0.430331
$136$	0	0
$137$	−4.00000	−0.341743	−0.170872	−	0.985293i	$-0.554658\pi$
$137$	−4.00000	−0.341743	−0.170872	+	0.985293i	$0.554658\pi$
$138$	−2.00000	−0.170251
$139$	−10.0000	−0.848189	−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000	−0.848189	−0.424094	+	0.905618i	$0.639408\pi$
$140$	0	0
$141$	−7.00000	−0.589506
$142$	−9.00000	−0.755263
$143$	−30.0000	−2.50873
$144$	−2.00000	−0.166667
$145$	−1.00000	−0.0830455
$146$	7.00000	0.579324
$147$	7.00000	0.577350
$148$	10.0000	0.821995
$149$	6.00000	0.491539	0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000	0.491539	0.245770	+	0.969328i	$0.420959\pi$
$150$	−1.00000	−0.0816497
$151$	6.00000	0.488273	0.244137	−	0.969741i	$-0.421495\pi$
$151$	6.00000	0.488273	0.244137	+	0.969741i	$0.421495\pi$
$152$	−3.00000	−0.243332
$153$	0	0
$154$	0	0
$155$	−7.00000	−0.562254
$156$	5.00000	0.400320
$157$	14.0000	1.11732	0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000	1.11732	0.558661	+	0.829396i	$0.311315\pi$
$158$	8.00000	0.636446
$159$	−1.00000	−0.0793052
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	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	$0.449930\pi$
$164$	−12.0000	−0.937043
$165$	6.00000	0.467099
$166$	−2.00000	−0.155230
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	0	0
$169$	12.0000	0.923077
$170$	0	0
$171$	6.00000	0.458831
$172$	4.00000	0.304997
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	−1.00000	−0.0758098
$175$	0	0
$176$	6.00000	0.452267
$177$	−9.00000	−0.676481
$178$	−1.00000	−0.0749532
$179$	16.0000	1.19590	0.597948	−	0.801535i	$-0.295983\pi$
$179$	16.0000	1.19590	0.597948	+	0.801535i	$0.295983\pi$
$180$	2.00000	0.149071
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	0	0
$183$	−3.00000	−0.221766
$184$	2.00000	0.147442
$185$	−10.0000	−0.735215
$186$	−7.00000	−0.513265
$187$	0	0
$188$	7.00000	0.510527
$189$	0	0
$190$	3.00000	0.217643
$191$	−14.0000	−1.01300	−0.506502	−	0.862239i	$-0.669062\pi$
$191$	−14.0000	−1.01300	−0.506502	+	0.862239i	$0.669062\pi$
$192$	−1.00000	−0.0721688
$193$	6.00000	0.431889	0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000	0.431889	0.215945	+	0.976406i	$0.430717\pi$
$194$	1.00000	0.0717958
$195$	−5.00000	−0.358057
$196$	−7.00000	−0.500000
$197$	6.00000	0.427482	0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000	0.427482	0.213741	+	0.976890i	$0.431435\pi$
$198$	−12.0000	−0.852803
$199$	13.0000	0.921546	0.460773	−	0.887518i	$-0.347572\pi$
$199$	13.0000	0.921546	0.460773	+	0.887518i	$0.347572\pi$
$200$	1.00000	0.0707107
$201$	−10.0000	−0.705346
$202$	−6.00000	−0.422159
$203$	0	0
$204$	0	0
$205$	12.0000	0.838116
$206$	8.00000	0.557386
$207$	−4.00000	−0.278019
$208$	−5.00000	−0.346688
$209$	−18.0000	−1.24509
$210$	0	0
$211$	10.0000	0.688428	0.344214	−	0.938891i	$-0.388145\pi$
$211$	10.0000	0.688428	0.344214	+	0.938891i	$0.388145\pi$
$212$	1.00000	0.0686803
$213$	9.00000	0.616670
$214$	8.00000	0.546869
$215$	−4.00000	−0.272798
$216$	5.00000	0.340207
$217$	0	0
$218$	−17.0000	−1.15139
$219$	−7.00000	−0.473016
$220$	−6.00000	−0.404520
$221$	0	0
$222$	−10.0000	−0.671156
$223$	−19.0000	−1.27233	−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000	−1.27233	−0.636167	+	0.771551i	$0.719481\pi$
$224$	0	0
$225$	−2.00000	−0.133333
$226$	17.0000	1.13082
$227$	−7.00000	−0.464606	−0.232303	−	0.972643i	$-0.574626\pi$
$227$	−7.00000	−0.464606	−0.232303	+	0.972643i	$0.574626\pi$
$228$	3.00000	0.198680
$229$	−20.0000	−1.32164	−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000	−1.32164	−0.660819	+	0.750546i	$0.729791\pi$
$230$	−2.00000	−0.131876
$231$	0	0
$232$	1.00000	0.0656532
$233$	13.0000	0.851658	0.425829	−	0.904804i	$-0.359982\pi$
$233$	13.0000	0.851658	0.425829	+	0.904804i	$0.359982\pi$
$234$	10.0000	0.653720
$235$	−7.00000	−0.456630
$236$	9.00000	0.585850
$237$	−8.00000	−0.519656
$238$	0	0
$239$	−28.0000	−1.81117	−0.905585	−	0.424165i	$-0.860568\pi$
$239$	−28.0000	−1.81117	−0.905585	+	0.424165i	$0.860568\pi$
$240$	1.00000	0.0645497
$241$	8.00000	0.515325	0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000	0.515325	0.257663	+	0.966235i	$0.417048\pi$
$242$	25.0000	1.60706
$243$	−16.0000	−1.02640
$244$	3.00000	0.192055
$245$	7.00000	0.447214
$246$	12.0000	0.765092
$247$	15.0000	0.954427
$248$	7.00000	0.444500
$249$	2.00000	0.126745
$250$	−1.00000	−0.0632456
$251$	16.0000	1.00991	0.504956	−	0.863145i	$-0.331509\pi$
$251$	16.0000	1.00991	0.504956	+	0.863145i	$0.331509\pi$
$252$	0	0
$253$	12.0000	0.754434
$254$	9.00000	0.564710
$255$	0	0
$256$	1.00000	0.0625000
$257$	−20.0000	−1.24757	−0.623783	−	0.781598i	$-0.714405\pi$
$257$	−20.0000	−1.24757	−0.623783	+	0.781598i	$0.714405\pi$
$258$	−4.00000	−0.249029
$259$	0	0
$260$	5.00000	0.310087
$261$	−2.00000	−0.123797
$262$	8.00000	0.494242
$263$	−17.0000	−1.04826	−0.524132	−	0.851637i	$-0.675610\pi$
$263$	−17.0000	−1.04826	−0.524132	+	0.851637i	$0.675610\pi$
$264$	−6.00000	−0.369274
$265$	−1.00000	−0.0614295
$266$	0	0
$267$	1.00000	0.0611990
$268$	10.0000	0.610847
$269$	3.00000	0.182913	0.0914566	−	0.995809i	$-0.470848\pi$
$269$	3.00000	0.182913	0.0914566	+	0.995809i	$0.470848\pi$
$270$	−5.00000	−0.304290
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	0	0
$273$	0	0
$274$	−4.00000	−0.241649
$275$	6.00000	0.361814
$276$	−2.00000	−0.120386
$277$	−26.0000	−1.56219	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000	−1.56219	−0.781094	+	0.624413i	$0.785338\pi$
$278$	−10.0000	−0.599760
$279$	−14.0000	−0.838158
$280$	0	0
$281$	−25.0000	−1.49137	−0.745687	−	0.666296i	$-0.767879\pi$
$281$	−25.0000	−1.49137	−0.745687	+	0.666296i	$0.767879\pi$
$282$	−7.00000	−0.416844
$283$	−11.0000	−0.653882	−0.326941	−	0.945045i	$-0.606018\pi$
$283$	−11.0000	−0.653882	−0.326941	+	0.945045i	$0.606018\pi$
$284$	−9.00000	−0.534052
$285$	−3.00000	−0.177705
$286$	−30.0000	−1.77394
$287$	0	0
$288$	−2.00000	−0.117851
$289$	0	0
$290$	−1.00000	−0.0587220
$291$	−1.00000	−0.0586210
$292$	7.00000	0.409644
$293$	−15.0000	−0.876309	−0.438155	−	0.898900i	$-0.644368\pi$
$293$	−15.0000	−0.876309	−0.438155	+	0.898900i	$0.644368\pi$
$294$	7.00000	0.408248
$295$	−9.00000	−0.524000
$296$	10.0000	0.581238
$297$	30.0000	1.74078
$298$	6.00000	0.347571
$299$	−10.0000	−0.578315
$300$	−1.00000	−0.0577350
$301$	0	0
$302$	6.00000	0.345261
$303$	6.00000	0.344691
$304$	−3.00000	−0.172062
$305$	−3.00000	−0.171780
$306$	0	0
$307$	−22.0000	−1.25561	−0.627803	−	0.778372i	$-0.716046\pi$
$307$	−22.0000	−1.25561	−0.627803	+	0.778372i	$0.716046\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	−7.00000	−0.397573
$311$	32.0000	1.81455	0.907277	−	0.420534i	$-0.138157\pi$
$311$	32.0000	1.81455	0.907277	+	0.420534i	$0.138157\pi$
$312$	5.00000	0.283069
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	14.0000	0.790066
$315$	0	0
$316$	8.00000	0.450035
$317$	20.0000	1.12331	0.561656	−	0.827371i	$-0.310164\pi$
$317$	20.0000	1.12331	0.561656	+	0.827371i	$0.310164\pi$
$318$	−1.00000	−0.0560772
$319$	6.00000	0.335936
$320$	−1.00000	−0.0559017
$321$	−8.00000	−0.446516
$322$	0	0
$323$	0	0
$324$	1.00000	0.0555556
$325$	−5.00000	−0.277350
$326$	4.00000	0.221540
$327$	17.0000	0.940102
$328$	−12.0000	−0.662589
$329$	0	0
$330$	6.00000	0.330289
$331$	−17.0000	−0.934405	−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000	−0.934405	−0.467202	+	0.884150i	$0.654738\pi$
$332$	−2.00000	−0.109764
$333$	−20.0000	−1.09599
$334$	18.0000	0.984916
$335$	−10.0000	−0.546358
$336$	0	0
$337$	7.00000	0.381314	0.190657	−	0.981657i	$-0.438938\pi$
$337$	7.00000	0.381314	0.190657	+	0.981657i	$0.438938\pi$
$338$	12.0000	0.652714
$339$	−17.0000	−0.923313
$340$	0	0
$341$	42.0000	2.27443
$342$	6.00000	0.324443
$343$	0	0
$344$	4.00000	0.215666
$345$	2.00000	0.107676
$346$	−6.00000	−0.322562
$347$	−9.00000	−0.483145	−0.241573	−	0.970383i	$-0.577663\pi$
$347$	−9.00000	−0.483145	−0.241573	+	0.970383i	$0.577663\pi$
$348$	−1.00000	−0.0536056
$349$	−8.00000	−0.428230	−0.214115	−	0.976808i	$-0.568687\pi$
$349$	−8.00000	−0.428230	−0.214115	+	0.976808i	$0.568687\pi$
$350$	0	0
$351$	−25.0000	−1.33440
$352$	6.00000	0.319801
$353$	−34.0000	−1.80964	−0.904819	−	0.425797i	$-0.859994\pi$
$353$	−34.0000	−1.80964	−0.904819	+	0.425797i	$0.859994\pi$
$354$	−9.00000	−0.478345
$355$	9.00000	0.477670
$356$	−1.00000	−0.0529999
$357$	0	0
$358$	16.0000	0.845626
$359$	32.0000	1.68890	0.844448	−	0.535638i	$-0.179929\pi$
$359$	32.0000	1.68890	0.844448	+	0.535638i	$0.179929\pi$
$360$	2.00000	0.105409
$361$	−10.0000	−0.526316
$362$	10.0000	0.525588
$363$	−25.0000	−1.31216
$364$	0	0
$365$	−7.00000	−0.366397
$366$	−3.00000	−0.156813
$367$	−22.0000	−1.14839	−0.574195	−	0.818718i	$-0.694685\pi$
$367$	−22.0000	−1.14839	−0.574195	+	0.818718i	$0.694685\pi$
$368$	2.00000	0.104257
$369$	24.0000	1.24939
$370$	−10.0000	−0.519875
$371$	0	0
$372$	−7.00000	−0.362933
$373$	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
$376$	7.00000	0.360997
$377$	−5.00000	−0.257513
$378$	0	0
$379$	−16.0000	−0.821865	−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000	−0.821865	−0.410932	+	0.911666i	$0.634797\pi$
$380$	3.00000	0.153897
$381$	−9.00000	−0.461084
$382$	−14.0000	−0.716302
$383$	21.0000	1.07305	0.536525	−	0.843884i	$-0.319737\pi$
$383$	21.0000	1.07305	0.536525	+	0.843884i	$0.319737\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	6.00000	0.305392
$387$	−8.00000	−0.406663
$388$	1.00000	0.0507673
$389$	20.0000	1.01404	0.507020	−	0.861934i	$-0.330747\pi$
$389$	20.0000	1.01404	0.507020	+	0.861934i	$0.330747\pi$
$390$	−5.00000	−0.253185
$391$	0	0
$392$	−7.00000	−0.353553
$393$	−8.00000	−0.403547
$394$	6.00000	0.302276
$395$	−8.00000	−0.402524
$396$	−12.0000	−0.603023
$397$	−32.0000	−1.60603	−0.803017	−	0.595956i	$-0.796773\pi$
$397$	−32.0000	−1.60603	−0.803017	+	0.595956i	$0.796773\pi$
$398$	13.0000	0.651631
$399$	0	0
$400$	1.00000	0.0500000
$401$	4.00000	0.199750	0.0998752	−	0.995000i	$-0.468156\pi$
$401$	4.00000	0.199750	0.0998752	+	0.995000i	$0.468156\pi$
$402$	−10.0000	−0.498755
$403$	−35.0000	−1.74347
$404$	−6.00000	−0.298511
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	60.0000	2.97409
$408$	0	0
$409$	−19.0000	−0.939490	−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000	−0.939490	−0.469745	+	0.882802i	$0.655654\pi$
$410$	12.0000	0.592638
$411$	4.00000	0.197305
$412$	8.00000	0.394132
$413$	0	0
$414$	−4.00000	−0.196589
$415$	2.00000	0.0981761
$416$	−5.00000	−0.245145
$417$	10.0000	0.489702
$418$	−18.0000	−0.880409
$419$	−30.0000	−1.46560	−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000	−1.46560	−0.732798	+	0.680446i	$0.761786\pi$
$420$	0	0
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	10.0000	0.486792
$423$	−14.0000	−0.680703
$424$	1.00000	0.0485643
$425$	0	0
$426$	9.00000	0.436051
$427$	0	0
$428$	8.00000	0.386695
$429$	30.0000	1.44841
$430$	−4.00000	−0.192897
$431$	16.0000	0.770693	0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000	0.770693	0.385346	+	0.922772i	$0.374082\pi$
$432$	5.00000	0.240563
$433$	28.0000	1.34559	0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000	1.34559	0.672797	+	0.739827i	$0.265093\pi$
$434$	0	0
$435$	1.00000	0.0479463
$436$	−17.0000	−0.814152
$437$	−6.00000	−0.287019
$438$	−7.00000	−0.334473
$439$	8.00000	0.381819	0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000	0.381819	0.190910	+	0.981608i	$0.438856\pi$
$440$	−6.00000	−0.286039
$441$	14.0000	0.666667
$442$	0	0
$443$	−12.0000	−0.570137	−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000	−0.570137	−0.285069	+	0.958507i	$0.592016\pi$
$444$	−10.0000	−0.474579
$445$	1.00000	0.0474045
$446$	−19.0000	−0.899676
$447$	−6.00000	−0.283790
$448$	0	0
$449$	30.0000	1.41579	0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000	1.41579	0.707894	+	0.706319i	$0.249646\pi$
$450$	−2.00000	−0.0942809
$451$	−72.0000	−3.39035
$452$	17.0000	0.799613
$453$	−6.00000	−0.281905
$454$	−7.00000	−0.328526
$455$	0	0
$456$	3.00000	0.140488
$457$	24.0000	1.12267	0.561336	−	0.827588i	$-0.310287\pi$
$457$	24.0000	1.12267	0.561336	+	0.827588i	$0.310287\pi$
$458$	−20.0000	−0.934539
$459$	0	0
$460$	−2.00000	−0.0932505
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	−17.0000	−0.790057	−0.395029	−	0.918669i	$-0.629265\pi$
$463$	−17.0000	−0.790057	−0.395029	+	0.918669i	$0.629265\pi$
$464$	1.00000	0.0464238
$465$	7.00000	0.324617
$466$	13.0000	0.602213
$467$	22.0000	1.01804	0.509019	−	0.860755i	$-0.330008\pi$
$467$	22.0000	1.01804	0.509019	+	0.860755i	$0.330008\pi$
$468$	10.0000	0.462250
$469$	0	0
$470$	−7.00000	−0.322886
$471$	−14.0000	−0.645086
$472$	9.00000	0.414259
$473$	24.0000	1.10352
$474$	−8.00000	−0.367452
$475$	−3.00000	−0.137649
$476$	0	0
$477$	−2.00000	−0.0915737
$478$	−28.0000	−1.28069
$479$	−23.0000	−1.05090	−0.525448	−	0.850825i	$-0.676102\pi$
$479$	−23.0000	−1.05090	−0.525448	+	0.850825i	$0.676102\pi$
$480$	1.00000	0.0456435
$481$	−50.0000	−2.27980
$482$	8.00000	0.364390
$483$	0	0
$484$	25.0000	1.13636
$485$	−1.00000	−0.0454077
$486$	−16.0000	−0.725775
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	3.00000	0.135804
$489$	−4.00000	−0.180886
$490$	7.00000	0.316228
$491$	−37.0000	−1.66979	−0.834893	−	0.550412i	$-0.814471\pi$
$491$	−37.0000	−1.66979	−0.834893	+	0.550412i	$0.814471\pi$
$492$	12.0000	0.541002
$493$	0	0
$494$	15.0000	0.674882
$495$	12.0000	0.539360
$496$	7.00000	0.314309
$497$	0	0
$498$	2.00000	0.0896221
$499$	−16.0000	−0.716258	−0.358129	−	0.933672i	$-0.616585\pi$
$499$	−16.0000	−0.716258	−0.358129	+	0.933672i	$0.616585\pi$
$500$	−1.00000	−0.0447214
$501$	−18.0000	−0.804181
$502$	16.0000	0.714115
$503$	32.0000	1.42681	0.713405	−	0.700752i	$-0.247152\pi$
$503$	32.0000	1.42681	0.713405	+	0.700752i	$0.247152\pi$
$504$	0	0
$505$	6.00000	0.266996
$506$	12.0000	0.533465
$507$	−12.0000	−0.532939
$508$	9.00000	0.399310
$509$	−4.00000	−0.177297	−0.0886484	−	0.996063i	$-0.528255\pi$
$509$	−4.00000	−0.177297	−0.0886484	+	0.996063i	$0.528255\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	−15.0000	−0.662266
$514$	−20.0000	−0.882162
$515$	−8.00000	−0.352522
$516$	−4.00000	−0.176090
$517$	42.0000	1.84716
$518$	0	0
$519$	6.00000	0.263371
$520$	5.00000	0.219265
$521$	16.0000	0.700973	0.350486	−	0.936568i	$-0.386016\pi$
$521$	16.0000	0.700973	0.350486	+	0.936568i	$0.386016\pi$
$522$	−2.00000	−0.0875376
$523$	6.00000	0.262362	0.131181	−	0.991358i	$-0.458123\pi$
$523$	6.00000	0.262362	0.131181	+	0.991358i	$0.458123\pi$
$524$	8.00000	0.349482
$525$	0	0
$526$	−17.0000	−0.741235
$527$	0	0
$528$	−6.00000	−0.261116
$529$	−19.0000	−0.826087
$530$	−1.00000	−0.0434372
$531$	−18.0000	−0.781133
$532$	0	0
$533$	60.0000	2.59889
$534$	1.00000	0.0432742
$535$	−8.00000	−0.345870
$536$	10.0000	0.431934
$537$	−16.0000	−0.690451
$538$	3.00000	0.129339
$539$	−42.0000	−1.80907
$540$	−5.00000	−0.215166
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	−16.0000	−0.687259
$543$	−10.0000	−0.429141
$544$	0	0
$545$	17.0000	0.728200
$546$	0	0
$547$	−29.0000	−1.23995	−0.619975	−	0.784621i	$-0.712857\pi$
$547$	−29.0000	−1.23995	−0.619975	+	0.784621i	$0.712857\pi$
$548$	−4.00000	−0.170872
$549$	−6.00000	−0.256074
$550$	6.00000	0.255841
$551$	−3.00000	−0.127804
$552$	−2.00000	−0.0851257
$553$	0	0
$554$	−26.0000	−1.10463
$555$	10.0000	0.424476
$556$	−10.0000	−0.424094
$557$	39.0000	1.65248	0.826242	−	0.563316i	$-0.190475\pi$
$557$	39.0000	1.65248	0.826242	+	0.563316i	$0.190475\pi$
$558$	−14.0000	−0.592667
$559$	−20.0000	−0.845910
$560$	0	0
$561$	0	0
$562$	−25.0000	−1.05456
$563$	6.00000	0.252870	0.126435	−	0.991975i	$-0.459647\pi$
$563$	6.00000	0.252870	0.126435	+	0.991975i	$0.459647\pi$
$564$	−7.00000	−0.294753
$565$	−17.0000	−0.715195
$566$	−11.0000	−0.462364
$567$	0	0
$568$	−9.00000	−0.377632
$569$	−1.00000	−0.0419222	−0.0209611	−	0.999780i	$-0.506673\pi$
$569$	−1.00000	−0.0419222	−0.0209611	+	0.999780i	$0.506673\pi$
$570$	−3.00000	−0.125656
$571$	−40.0000	−1.67395	−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000	−1.67395	−0.836974	+	0.547243i	$0.815677\pi$
$572$	−30.0000	−1.25436
$573$	14.0000	0.584858
$574$	0	0
$575$	2.00000	0.0834058
$576$	−2.00000	−0.0833333
$577$	24.0000	0.999133	0.499567	−	0.866276i	$-0.333493\pi$
$577$	24.0000	0.999133	0.499567	+	0.866276i	$0.333493\pi$
$578$	0	0
$579$	−6.00000	−0.249351
$580$	−1.00000	−0.0415227
$581$	0	0
$582$	−1.00000	−0.0414513
$583$	6.00000	0.248495
$584$	7.00000	0.289662
$585$	−10.0000	−0.413449
$586$	−15.0000	−0.619644
$587$	26.0000	1.07313	0.536567	−	0.843857i	$-0.319721\pi$
$587$	26.0000	1.07313	0.536567	+	0.843857i	$0.319721\pi$
$588$	7.00000	0.288675
$589$	−21.0000	−0.865290
$590$	−9.00000	−0.370524
$591$	−6.00000	−0.246807
$592$	10.0000	0.410997
$593$	−18.0000	−0.739171	−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000	−0.739171	−0.369586	+	0.929197i	$0.620500\pi$
$594$	30.0000	1.23091
$595$	0	0
$596$	6.00000	0.245770
$597$	−13.0000	−0.532055
$598$	−10.0000	−0.408930
$599$	38.0000	1.55264	0.776319	−	0.630340i	$-0.217085\pi$
$599$	38.0000	1.55264	0.776319	+	0.630340i	$0.217085\pi$
$600$	−1.00000	−0.0408248
$601$	−28.0000	−1.14214	−0.571072	−	0.820900i	$-0.693472\pi$
$601$	−28.0000	−1.14214	−0.571072	+	0.820900i	$0.693472\pi$
$602$	0	0
$603$	−20.0000	−0.814463
$604$	6.00000	0.244137
$605$	−25.0000	−1.01639
$606$	6.00000	0.243733
$607$	−16.0000	−0.649420	−0.324710	−	0.945814i	$-0.605267\pi$
$607$	−16.0000	−0.649420	−0.324710	+	0.945814i	$0.605267\pi$
$608$	−3.00000	−0.121666
$609$	0	0
$610$	−3.00000	−0.121466
$611$	−35.0000	−1.41595
$612$	0	0
$613$	−17.0000	−0.686624	−0.343312	−	0.939222i	$-0.611549\pi$
$613$	−17.0000	−0.686624	−0.343312	+	0.939222i	$0.611549\pi$
$614$	−22.0000	−0.887848
$615$	−12.0000	−0.483887
$616$	0	0
$617$	25.0000	1.00646	0.503231	−	0.864152i	$-0.332144\pi$
$617$	25.0000	1.00646	0.503231	+	0.864152i	$0.332144\pi$
$618$	−8.00000	−0.321807
$619$	18.0000	0.723481	0.361741	−	0.932279i	$-0.382183\pi$
$619$	18.0000	0.723481	0.361741	+	0.932279i	$0.382183\pi$
$620$	−7.00000	−0.281127
$621$	10.0000	0.401286
$622$	32.0000	1.28308
$623$	0	0
$624$	5.00000	0.200160
$625$	1.00000	0.0400000
$626$	22.0000	0.879297
$627$	18.0000	0.718851
$628$	14.0000	0.558661
$629$	0	0
$630$	0	0
$631$	20.0000	0.796187	0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000	0.796187	0.398094	+	0.917345i	$0.369672\pi$
$632$	8.00000	0.318223
$633$	−10.0000	−0.397464
$634$	20.0000	0.794301
$635$	−9.00000	−0.357154
$636$	−1.00000	−0.0396526
$637$	35.0000	1.38675
$638$	6.00000	0.237542
$639$	18.0000	0.712069
$640$	−1.00000	−0.0395285
$641$	−30.0000	−1.18493	−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000	−1.18493	−0.592464	+	0.805597i	$0.701845\pi$
$642$	−8.00000	−0.315735
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	0	0
$645$	4.00000	0.157500
$646$	0	0
$647$	−3.00000	−0.117942	−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000	−0.117942	−0.0589711	+	0.998260i	$0.518782\pi$
$648$	1.00000	0.0392837
$649$	54.0000	2.11969
$650$	−5.00000	−0.196116
$651$	0	0
$652$	4.00000	0.156652
$653$	−16.0000	−0.626128	−0.313064	−	0.949732i	$-0.601356\pi$
$653$	−16.0000	−0.626128	−0.313064	+	0.949732i	$0.601356\pi$
$654$	17.0000	0.664753
$655$	−8.00000	−0.312586
$656$	−12.0000	−0.468521
$657$	−14.0000	−0.546192
$658$	0	0
$659$	−33.0000	−1.28550	−0.642749	−	0.766077i	$-0.722206\pi$
$659$	−33.0000	−1.28550	−0.642749	+	0.766077i	$0.722206\pi$
$660$	6.00000	0.233550
$661$	−4.00000	−0.155582	−0.0777910	−	0.996970i	$-0.524787\pi$
$661$	−4.00000	−0.155582	−0.0777910	+	0.996970i	$0.524787\pi$
$662$	−17.0000	−0.660724
$663$	0	0
$664$	−2.00000	−0.0776151
$665$	0	0
$666$	−20.0000	−0.774984
$667$	2.00000	0.0774403
$668$	18.0000	0.696441
$669$	19.0000	0.734582
$670$	−10.0000	−0.386334
$671$	18.0000	0.694882
$672$	0	0
$673$	−41.0000	−1.58043	−0.790217	−	0.612827i	$-0.790032\pi$
$673$	−41.0000	−1.58043	−0.790217	+	0.612827i	$0.790032\pi$
$674$	7.00000	0.269630
$675$	5.00000	0.192450
$676$	12.0000	0.461538
$677$	−12.0000	−0.461197	−0.230599	−	0.973049i	$-0.574068\pi$
$677$	−12.0000	−0.461197	−0.230599	+	0.973049i	$0.574068\pi$
$678$	−17.0000	−0.652881
$679$	0	0
$680$	0	0
$681$	7.00000	0.268241
$682$	42.0000	1.60826
$683$	7.00000	0.267848	0.133924	−	0.990992i	$-0.457242\pi$
$683$	7.00000	0.267848	0.133924	+	0.990992i	$0.457242\pi$
$684$	6.00000	0.229416
$685$	4.00000	0.152832
$686$	0	0
$687$	20.0000	0.763048
$688$	4.00000	0.152499
$689$	−5.00000	−0.190485
$690$	2.00000	0.0761387
$691$	−18.0000	−0.684752	−0.342376	−	0.939563i	$-0.611232\pi$
$691$	−18.0000	−0.684752	−0.342376	+	0.939563i	$0.611232\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−9.00000	−0.341635
$695$	10.0000	0.379322
$696$	−1.00000	−0.0379049
$697$	0	0
$698$	−8.00000	−0.302804
$699$	−13.0000	−0.491705
$700$	0	0
$701$	−16.0000	−0.604312	−0.302156	−	0.953259i	$-0.597706\pi$
$701$	−16.0000	−0.604312	−0.302156	+	0.953259i	$0.597706\pi$
$702$	−25.0000	−0.943564
$703$	−30.0000	−1.13147
$704$	6.00000	0.226134
$705$	7.00000	0.263635
$706$	−34.0000	−1.27961
$707$	0	0
$708$	−9.00000	−0.338241
$709$	−3.00000	−0.112667	−0.0563337	−	0.998412i	$-0.517941\pi$
$709$	−3.00000	−0.112667	−0.0563337	+	0.998412i	$0.517941\pi$
$710$	9.00000	0.337764
$711$	−16.0000	−0.600047
$712$	−1.00000	−0.0374766
$713$	14.0000	0.524304
$714$	0	0
$715$	30.0000	1.12194
$716$	16.0000	0.597948
$717$	28.0000	1.04568
$718$	32.0000	1.19423
$719$	7.00000	0.261056	0.130528	−	0.991445i	$-0.458333\pi$
$719$	7.00000	0.261056	0.130528	+	0.991445i	$0.458333\pi$
$720$	2.00000	0.0745356
$721$	0	0
$722$	−10.0000	−0.372161
$723$	−8.00000	−0.297523
$724$	10.0000	0.371647
$725$	1.00000	0.0371391
$726$	−25.0000	−0.927837
$727$	−13.0000	−0.482143	−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000	−0.482143	−0.241072	+	0.970507i	$0.577499\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	−7.00000	−0.259082
$731$	0	0
$732$	−3.00000	−0.110883
$733$	14.0000	0.517102	0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000	0.517102	0.258551	+	0.965998i	$0.416755\pi$
$734$	−22.0000	−0.812035
$735$	−7.00000	−0.258199
$736$	2.00000	0.0737210
$737$	60.0000	2.21013
$738$	24.0000	0.883452
$739$	−9.00000	−0.331070	−0.165535	−	0.986204i	$-0.552935\pi$
$739$	−9.00000	−0.331070	−0.165535	+	0.986204i	$0.552935\pi$
$740$	−10.0000	−0.367607
$741$	−15.0000	−0.551039
$742$	0	0
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	−7.00000	−0.256632
$745$	−6.00000	−0.219823
$746$	6.00000	0.219676
$747$	4.00000	0.146352
$748$	0	0
$749$	0	0
$750$	1.00000	0.0365148
$751$	−43.0000	−1.56909	−0.784546	−	0.620070i	$-0.787104\pi$
$751$	−43.0000	−1.56909	−0.784546	+	0.620070i	$0.787104\pi$
$752$	7.00000	0.255264
$753$	−16.0000	−0.583072
$754$	−5.00000	−0.182089
$755$	−6.00000	−0.218362
$756$	0	0
$757$	15.0000	0.545184	0.272592	−	0.962130i	$-0.412119\pi$
$757$	15.0000	0.545184	0.272592	+	0.962130i	$0.412119\pi$
$758$	−16.0000	−0.581146
$759$	−12.0000	−0.435572
$760$	3.00000	0.108821
$761$	−26.0000	−0.942499	−0.471250	−	0.882000i	$-0.656197\pi$
$761$	−26.0000	−0.942499	−0.471250	+	0.882000i	$0.656197\pi$
$762$	−9.00000	−0.326036
$763$	0	0
$764$	−14.0000	−0.506502
$765$	0	0
$766$	21.0000	0.758761
$767$	−45.0000	−1.62486
$768$	−1.00000	−0.0360844
$769$	25.0000	0.901523	0.450762	−	0.892644i	$-0.351152\pi$
$769$	25.0000	0.901523	0.450762	+	0.892644i	$0.351152\pi$
$770$	0	0
$771$	20.0000	0.720282
$772$	6.00000	0.215945
$773$	−30.0000	−1.07903	−0.539513	−	0.841978i	$-0.681391\pi$
$773$	−30.0000	−1.07903	−0.539513	+	0.841978i	$0.681391\pi$
$774$	−8.00000	−0.287554
$775$	7.00000	0.251447
$776$	1.00000	0.0358979
$777$	0	0
$778$	20.0000	0.717035
$779$	36.0000	1.28983
$780$	−5.00000	−0.179029
$781$	−54.0000	−1.93227
$782$	0	0
$783$	5.00000	0.178685
$784$	−7.00000	−0.250000
$785$	−14.0000	−0.499681
$786$	−8.00000	−0.285351
$787$	27.0000	0.962446	0.481223	−	0.876598i	$-0.340193\pi$
$787$	27.0000	0.962446	0.481223	+	0.876598i	$0.340193\pi$
$788$	6.00000	0.213741
$789$	17.0000	0.605216
$790$	−8.00000	−0.284627
$791$	0	0
$792$	−12.0000	−0.426401
$793$	−15.0000	−0.532666
$794$	−32.0000	−1.13564
$795$	1.00000	0.0354663
$796$	13.0000	0.460773
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	0	0
$799$	0	0
$800$	1.00000	0.0353553
$801$	2.00000	0.0706665
$802$	4.00000	0.141245
$803$	42.0000	1.48215
$804$	−10.0000	−0.352673
$805$	0	0
$806$	−35.0000	−1.23282
$807$	−3.00000	−0.105605
$808$	−6.00000	−0.211079
$809$	0	0		−	1.00000i	$-0.5\pi$
$809$	0	0			1.00000i	$0.5\pi$
$810$	−1.00000	−0.0351364
$811$	−20.0000	−0.702295	−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000	−0.702295	−0.351147	+	0.936320i	$0.614208\pi$
$812$	0	0
$813$	16.0000	0.561144
$814$	60.0000	2.10300
$815$	−4.00000	−0.140114
$816$	0	0
$817$	−12.0000	−0.419827
$818$	−19.0000	−0.664319
$819$	0	0
$820$	12.0000	0.419058
$821$	−17.0000	−0.593304	−0.296652	−	0.954986i	$-0.595870\pi$
$821$	−17.0000	−0.593304	−0.296652	+	0.954986i	$0.595870\pi$
$822$	4.00000	0.139516
$823$	50.0000	1.74289	0.871445	−	0.490493i	$-0.163183\pi$
$823$	50.0000	1.74289	0.871445	+	0.490493i	$0.163183\pi$
$824$	8.00000	0.278693
$825$	−6.00000	−0.208893
$826$	0	0
$827$	−20.0000	−0.695468	−0.347734	−	0.937593i	$-0.613049\pi$
$827$	−20.0000	−0.695468	−0.347734	+	0.937593i	$0.613049\pi$
$828$	−4.00000	−0.139010
$829$	−20.0000	−0.694629	−0.347314	−	0.937749i	$-0.612906\pi$
$829$	−20.0000	−0.694629	−0.347314	+	0.937749i	$0.612906\pi$
$830$	2.00000	0.0694210
$831$	26.0000	0.901930
$832$	−5.00000	−0.173344
$833$	0	0
$834$	10.0000	0.346272
$835$	−18.0000	−0.622916
$836$	−18.0000	−0.622543
$837$	35.0000	1.20978
$838$	−30.0000	−1.03633
$839$	5.00000	0.172619	0.0863096	−	0.996268i	$-0.472493\pi$
$839$	5.00000	0.172619	0.0863096	+	0.996268i	$0.472493\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	−2.00000	−0.0689246
$843$	25.0000	0.861046
$844$	10.0000	0.344214
$845$	−12.0000	−0.412813
$846$	−14.0000	−0.481330
$847$	0	0
$848$	1.00000	0.0343401
$849$	11.0000	0.377519
$850$	0	0
$851$	20.0000	0.685591
$852$	9.00000	0.308335
$853$	44.0000	1.50653	0.753266	−	0.657716i	$-0.228477\pi$
$853$	44.0000	1.50653	0.753266	+	0.657716i	$0.228477\pi$
$854$	0	0
$855$	−6.00000	−0.205196
$856$	8.00000	0.273434
$857$	−31.0000	−1.05894	−0.529470	−	0.848329i	$-0.677609\pi$
$857$	−31.0000	−1.05894	−0.529470	+	0.848329i	$0.677609\pi$
$858$	30.0000	1.02418
$859$	53.0000	1.80834	0.904168	−	0.427176i	$-0.140492\pi$
$859$	53.0000	1.80834	0.904168	+	0.427176i	$0.140492\pi$
$860$	−4.00000	−0.136399
$861$	0	0
$862$	16.0000	0.544962
$863$	36.0000	1.22545	0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000	1.22545	0.612727	+	0.790295i	$0.290072\pi$
$864$	5.00000	0.170103
$865$	6.00000	0.204006
$866$	28.0000	0.951479
$867$	0	0
$868$	0	0
$869$	48.0000	1.62829
$870$	1.00000	0.0339032
$871$	−50.0000	−1.69419
$872$	−17.0000	−0.575693
$873$	−2.00000	−0.0676897
$874$	−6.00000	−0.202953
$875$	0	0
$876$	−7.00000	−0.236508
$877$	18.0000	0.607817	0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000	0.607817	0.303908	+	0.952701i	$0.401708\pi$
$878$	8.00000	0.269987
$879$	15.0000	0.505937
$880$	−6.00000	−0.202260
$881$	30.0000	1.01073	0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000	1.01073	0.505363	+	0.862907i	$0.331359\pi$
$882$	14.0000	0.471405
$883$	−12.0000	−0.403832	−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000	−0.403832	−0.201916	+	0.979403i	$0.564717\pi$
$884$	0	0
$885$	9.00000	0.302532
$886$	−12.0000	−0.403148
$887$	−28.0000	−0.940148	−0.470074	−	0.882627i	$-0.655773\pi$
$887$	−28.0000	−0.940148	−0.470074	+	0.882627i	$0.655773\pi$
$888$	−10.0000	−0.335578
$889$	0	0
$890$	1.00000	0.0335201
$891$	6.00000	0.201008
$892$	−19.0000	−0.636167
$893$	−21.0000	−0.702738
$894$	−6.00000	−0.200670
$895$	−16.0000	−0.534821
$896$	0	0
$897$	10.0000	0.333890
$898$	30.0000	1.00111
$899$	7.00000	0.233463
$900$	−2.00000	−0.0666667
$901$	0	0
$902$	−72.0000	−2.39734
$903$	0	0
$904$	17.0000	0.565412
$905$	−10.0000	−0.332411
$906$	−6.00000	−0.199337
$907$	1.00000	0.0332045	0.0166022	−	0.999862i	$-0.494715\pi$
$907$	1.00000	0.0332045	0.0166022	+	0.999862i	$0.494715\pi$
$908$	−7.00000	−0.232303
$909$	12.0000	0.398015
$910$	0	0
$911$	48.0000	1.59031	0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000	1.59031	0.795155	+	0.606406i	$0.207389\pi$
$912$	3.00000	0.0993399
$913$	−12.0000	−0.397142
$914$	24.0000	0.793849
$915$	3.00000	0.0991769
$916$	−20.0000	−0.660819
$917$	0	0
$918$	0	0
$919$	16.0000	0.527791	0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000	0.527791	0.263896	+	0.964551i	$0.414993\pi$
$920$	−2.00000	−0.0659380
$921$	22.0000	0.724925
$922$	18.0000	0.592798
$923$	45.0000	1.48119
$924$	0	0
$925$	10.0000	0.328798
$926$	−17.0000	−0.558655
$927$	−16.0000	−0.525509
$928$	1.00000	0.0328266
$929$	44.0000	1.44359	0.721797	−	0.692105i	$-0.243317\pi$
$929$	44.0000	1.44359	0.721797	+	0.692105i	$0.243317\pi$
$930$	7.00000	0.229539
$931$	21.0000	0.688247
$932$	13.0000	0.425829
$933$	−32.0000	−1.04763
$934$	22.0000	0.719862
$935$	0	0
$936$	10.0000	0.326860
$937$	−30.0000	−0.980057	−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000	−0.980057	−0.490029	+	0.871706i	$0.663014\pi$
$938$	0	0
$939$	−22.0000	−0.717943
$940$	−7.00000	−0.228315
$941$	29.0000	0.945373	0.472686	−	0.881231i	$-0.343284\pi$
$941$	29.0000	0.945373	0.472686	+	0.881231i	$0.343284\pi$
$942$	−14.0000	−0.456145
$943$	−24.0000	−0.781548
$944$	9.00000	0.292925
$945$	0	0
$946$	24.0000	0.780307
$947$	−27.0000	−0.877382	−0.438691	−	0.898638i	$-0.644558\pi$
$947$	−27.0000	−0.877382	−0.438691	+	0.898638i	$0.644558\pi$
$948$	−8.00000	−0.259828
$949$	−35.0000	−1.13615
$950$	−3.00000	−0.0973329
$951$	−20.0000	−0.648544
$952$	0	0
$953$	−22.0000	−0.712650	−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000	−0.712650	−0.356325	+	0.934362i	$0.615970\pi$
$954$	−2.00000	−0.0647524
$955$	14.0000	0.453029
$956$	−28.0000	−0.905585
$957$	−6.00000	−0.193952
$958$	−23.0000	−0.743096
$959$	0	0
$960$	1.00000	0.0322749
$961$	18.0000	0.580645
$962$	−50.0000	−1.61206
$963$	−16.0000	−0.515593
$964$	8.00000	0.257663
$965$	−6.00000	−0.193147
$966$	0	0
$967$	−8.00000	−0.257263	−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000	−0.257263	−0.128631	+	0.991692i	$0.541058\pi$
$968$	25.0000	0.803530
$969$	0	0
$970$	−1.00000	−0.0321081
$971$	9.00000	0.288824	0.144412	−	0.989518i	$-0.453871\pi$
$971$	9.00000	0.288824	0.144412	+	0.989518i	$0.453871\pi$
$972$	−16.0000	−0.513200
$973$	0	0
$974$	−8.00000	−0.256337
$975$	5.00000	0.160128
$976$	3.00000	0.0960277
$977$	10.0000	0.319928	0.159964	−	0.987123i	$-0.448862\pi$
$977$	10.0000	0.319928	0.159964	+	0.987123i	$0.448862\pi$
$978$	−4.00000	−0.127906
$979$	−6.00000	−0.191761
$980$	7.00000	0.223607
$981$	34.0000	1.08554
$982$	−37.0000	−1.18072
$983$	12.0000	0.382741	0.191370	−	0.981518i	$-0.438707\pi$
$983$	12.0000	0.382741	0.191370	+	0.981518i	$0.438707\pi$
$984$	12.0000	0.382546
$985$	−6.00000	−0.191176
$986$	0	0
$987$	0	0
$988$	15.0000	0.477214
$989$	8.00000	0.254385
$990$	12.0000	0.381385
$991$	39.0000	1.23888	0.619438	−	0.785046i	$-0.287361\pi$
$991$	39.0000	1.23888	0.619438	+	0.785046i	$0.287361\pi$
$992$	7.00000	0.222250
$993$	17.0000	0.539479
$994$	0	0
$995$	−13.0000	−0.412128
$996$	2.00000	0.0633724
$997$	0	0		−	1.00000i	$-0.5\pi$
$997$	0	0			1.00000i	$0.5\pi$
$998$	−16.0000	−0.506471
$999$	50.0000	1.58193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2890.2.a.m.1.1		1
17.4	even	4		170.2.b.a.101.2	yes	2
17.13	even	4		170.2.b.a.101.1	✓	2
17.16	even	2		2890.2.a.q.1.1		1
51.38	odd	4		1530.2.c.d.271.1		2
51.47	odd	4		1530.2.c.d.271.2		2
68.47	odd	4		1360.2.c.b.1121.2		2
68.55	odd	4		1360.2.c.b.1121.1		2
85.4	even	4		850.2.b.j.101.1		2
85.13	odd	4		850.2.d.g.849.2		2
85.38	odd	4		850.2.d.b.849.2		2
85.47	odd	4		850.2.d.b.849.1		2
85.64	even	4		850.2.b.j.101.2		2
85.72	odd	4		850.2.d.g.849.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.b.a.101.1	✓	2	17.13	even	4
170.2.b.a.101.2	yes	2	17.4	even	4
850.2.b.j.101.1		2	85.4	even	4
850.2.b.j.101.2		2	85.64	even	4
850.2.d.b.849.1		2	85.47	odd	4
850.2.d.b.849.2		2	85.38	odd	4
850.2.d.g.849.1		2	85.72	odd	4
850.2.d.g.849.2		2	85.13	odd	4
1360.2.c.b.1121.1		2	68.55	odd	4
1360.2.c.b.1121.2		2	68.47	odd	4
1530.2.c.d.271.1		2	51.38	odd	4
1530.2.c.d.271.2		2	51.47	odd	4
2890.2.a.m.1.1		1	1.1	even	1	trivial
2890.2.a.q.1.1		1	17.16	even	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:	\( N \)	\(=\)	\( 2890 = 2 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2890.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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