LMFDB - Embedded newform 1850.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1850,2,Mod(1,1850)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1850, 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("1850.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1850 = 2 \cdot 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1850.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:	$14.7723243739$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1850.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +4.00000 q^{7} -1.00000 q^{8} -2.00000 q^{9} +3.00000 q^{11} -1.00000 q^{12} +6.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} +3.00000 q^{17} +2.00000 q^{18} -3.00000 q^{19} -4.00000 q^{21} -3.00000 q^{22} +2.00000 q^{23} +1.00000 q^{24} -6.00000 q^{26} +5.00000 q^{27} +4.00000 q^{28} -1.00000 q^{32} -3.00000 q^{33} -3.00000 q^{34} -2.00000 q^{36} -1.00000 q^{37} +3.00000 q^{38} -6.00000 q^{39} -3.00000 q^{41} +4.00000 q^{42} -4.00000 q^{43} +3.00000 q^{44} -2.00000 q^{46} +4.00000 q^{47} -1.00000 q^{48} +9.00000 q^{49} -3.00000 q^{51} +6.00000 q^{52} -2.00000 q^{53} -5.00000 q^{54} -4.00000 q^{56} +3.00000 q^{57} -12.0000 q^{59} +12.0000 q^{61} -8.00000 q^{63} +1.00000 q^{64} +3.00000 q^{66} +9.00000 q^{67} +3.00000 q^{68} -2.00000 q^{69} -2.00000 q^{71} +2.00000 q^{72} -9.00000 q^{73} +1.00000 q^{74} -3.00000 q^{76} +12.0000 q^{77} +6.00000 q^{78} -2.00000 q^{79} +1.00000 q^{81} +3.00000 q^{82} -7.00000 q^{83} -4.00000 q^{84} +4.00000 q^{86} -3.00000 q^{88} -3.00000 q^{89} +24.0000 q^{91} +2.00000 q^{92} -4.00000 q^{94} +1.00000 q^{96} +2.00000 q^{97} -9.00000 q^{98} -6.00000 q^{99} +O(q^{100})\)

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
$5$	0	0
$5$	0	0
$6$	1.00000	0.408248
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	−1.00000	−0.353553
$9$	−2.00000	−0.666667
$10$	0	0
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	−1.00000	−0.288675
$13$	6.00000	1.66410	0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000	1.66410	0.832050	+	0.554700i	$0.187167\pi$
$14$	−4.00000	−1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	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	$0.611824\pi$
$20$	0	0
$21$	−4.00000	−0.872872
$22$	−3.00000	−0.639602
$23$	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
$25$	0	0
$26$	−6.00000	−1.17670
$27$	5.00000	0.962250
$28$	4.00000	0.755929
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−1.00000	−0.176777
$33$	−3.00000	−0.522233
$34$	−3.00000	−0.514496
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	3.00000	0.486664
$39$	−6.00000	−0.960769
$40$	0	0
$41$	−3.00000	−0.468521	−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000	−0.468521	−0.234261	+	0.972174i	$0.575267\pi$
$42$	4.00000	0.617213
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	3.00000	0.452267
$45$	0	0
$46$	−2.00000	−0.294884
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	−1.00000	−0.144338
$49$	9.00000	1.28571
$50$	0	0
$51$	−3.00000	−0.420084
$52$	6.00000	0.832050
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	−5.00000	−0.680414
$55$	0	0
$56$	−4.00000	−0.534522
$57$	3.00000	0.397360
$58$	0	0
$59$	−12.0000	−1.56227	−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000	−1.56227	−0.781133	+	0.624364i	$0.785358\pi$
$60$	0	0
$61$	12.0000	1.53644	0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000	1.53644	0.768221	+	0.640184i	$0.221142\pi$
$62$	0	0
$63$	−8.00000	−1.00791
$64$	1.00000	0.125000
$65$	0	0
$66$	3.00000	0.369274
$67$	9.00000	1.09952	0.549762	−	0.835321i	$-0.314718\pi$
$67$	9.00000	1.09952	0.549762	+	0.835321i	$0.314718\pi$
$68$	3.00000	0.363803
$69$	−2.00000	−0.240772
$70$	0	0
$71$	−2.00000	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$72$	2.00000	0.235702
$73$	−9.00000	−1.05337	−0.526685	−	0.850060i	$-0.676565\pi$
$73$	−9.00000	−1.05337	−0.526685	+	0.850060i	$0.676565\pi$
$74$	1.00000	0.116248
$75$	0	0
$76$	−3.00000	−0.344124
$77$	12.0000	1.36753
$78$	6.00000	0.679366
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	3.00000	0.331295
$83$	−7.00000	−0.768350	−0.384175	−	0.923260i	$-0.625514\pi$
$83$	−7.00000	−0.768350	−0.384175	+	0.923260i	$0.625514\pi$
$84$	−4.00000	−0.436436
$85$	0	0
$86$	4.00000	0.431331
$87$	0	0
$88$	−3.00000	−0.319801
$89$	−3.00000	−0.317999	−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000	−0.317999	−0.159000	+	0.987279i	$0.550827\pi$
$90$	0	0
$91$	24.0000	2.51588
$92$	2.00000	0.208514
$93$	0	0
$94$	−4.00000	−0.412568
$95$	0	0
$96$	1.00000	0.102062
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	−9.00000	−0.909137
$99$	−6.00000	−0.603023
$100$	0	0
$101$	−10.0000	−0.995037	−0.497519	−	0.867453i	$-0.665755\pi$
$101$	−10.0000	−0.995037	−0.497519	+	0.867453i	$0.665755\pi$
$102$	3.00000	0.297044
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	2.00000	0.194257
$107$	−1.00000	−0.0966736	−0.0483368	−	0.998831i	$-0.515392\pi$
$107$	−1.00000	−0.0966736	−0.0483368	+	0.998831i	$0.515392\pi$
$108$	5.00000	0.481125
$109$	18.0000	1.72409	0.862044	−	0.506834i	$-0.169184\pi$
$109$	18.0000	1.72409	0.862044	+	0.506834i	$0.169184\pi$
$110$	0	0
$111$	1.00000	0.0949158
$112$	4.00000	0.377964
$113$	5.00000	0.470360	0.235180	−	0.971952i	$-0.424432\pi$
$113$	5.00000	0.470360	0.235180	+	0.971952i	$0.424432\pi$
$114$	−3.00000	−0.280976
$115$	0	0
$116$	0	0
$117$	−12.0000	−1.10940
$118$	12.0000	1.10469
$119$	12.0000	1.10004
$120$	0	0
$121$	−2.00000	−0.181818
$122$	−12.0000	−1.08643
$123$	3.00000	0.270501
$124$	0	0
$125$	0	0
$126$	8.00000	0.712697
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	4.00000	0.352180
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	−3.00000	−0.261116
$133$	−12.0000	−1.04053
$134$	−9.00000	−0.777482
$135$	0	0
$136$	−3.00000	−0.257248
$137$	−7.00000	−0.598050	−0.299025	−	0.954245i	$-0.596661\pi$
$137$	−7.00000	−0.598050	−0.299025	+	0.954245i	$0.596661\pi$
$138$	2.00000	0.170251
$139$	3.00000	0.254457	0.127228	−	0.991873i	$-0.459392\pi$
$139$	3.00000	0.254457	0.127228	+	0.991873i	$0.459392\pi$
$140$	0	0
$141$	−4.00000	−0.336861
$142$	2.00000	0.167836
$143$	18.0000	1.50524
$144$	−2.00000	−0.166667
$145$	0	0
$146$	9.00000	0.744845
$147$	−9.00000	−0.742307
$148$	−1.00000	−0.0821995
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	0	0
$151$	22.0000	1.79033	0.895167	−	0.445730i	$-0.147056\pi$
$151$	22.0000	1.79033	0.895167	+	0.445730i	$0.147056\pi$
$152$	3.00000	0.243332
$153$	−6.00000	−0.485071
$154$	−12.0000	−0.966988
$155$	0	0
$156$	−6.00000	−0.480384
$157$	24.0000	1.91541	0.957704	−	0.287754i	$-0.0929087\pi$
$157$	24.0000	1.91541	0.957704	+	0.287754i	$0.0929087\pi$
$158$	2.00000	0.159111
$159$	2.00000	0.158610
$160$	0	0
$161$	8.00000	0.630488
$162$	−1.00000	−0.0785674
$163$	−17.0000	−1.33154	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	−17.0000	−1.33154	−0.665771	+	0.746156i	$0.731897\pi$
$164$	−3.00000	−0.234261
$165$	0	0
$166$	7.00000	0.543305
$167$	−18.0000	−1.39288	−0.696441	−	0.717614i	$-0.745234\pi$
$167$	−18.0000	−1.39288	−0.696441	+	0.717614i	$0.745234\pi$
$168$	4.00000	0.308607
$169$	23.0000	1.76923
$170$	0	0
$171$	6.00000	0.458831
$172$	−4.00000	−0.304997
$173$	24.0000	1.82469	0.912343	−	0.409426i	$-0.134271\pi$
$173$	24.0000	1.82469	0.912343	+	0.409426i	$0.134271\pi$
$174$	0	0
$175$	0	0
$176$	3.00000	0.226134
$177$	12.0000	0.901975
$178$	3.00000	0.224860
$179$	21.0000	1.56961	0.784807	−	0.619740i	$-0.212762\pi$
$179$	21.0000	1.56961	0.784807	+	0.619740i	$0.212762\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	−24.0000	−1.77900
$183$	−12.0000	−0.887066
$184$	−2.00000	−0.147442
$185$	0	0
$186$	0	0
$187$	9.00000	0.658145
$188$	4.00000	0.291730
$189$	20.0000	1.45479
$190$	0	0
$191$	6.00000	0.434145	0.217072	−	0.976156i	$-0.430349\pi$
$191$	6.00000	0.434145	0.217072	+	0.976156i	$0.430349\pi$
$192$	−1.00000	−0.0721688
$193$	11.0000	0.791797	0.395899	−	0.918294i	$-0.370433\pi$
$193$	11.0000	0.791797	0.395899	+	0.918294i	$0.370433\pi$
$194$	−2.00000	−0.143592
$195$	0	0
$196$	9.00000	0.642857
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	6.00000	0.426401
$199$	8.00000	0.567105	0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000	0.567105	0.283552	+	0.958957i	$0.408487\pi$
$200$	0	0
$201$	−9.00000	−0.634811
$202$	10.0000	0.703598
$203$	0	0
$204$	−3.00000	−0.210042
$205$	0	0
$206$	−14.0000	−0.975426
$207$	−4.00000	−0.278019
$208$	6.00000	0.416025
$209$	−9.00000	−0.622543
$210$	0	0
$211$	9.00000	0.619586	0.309793	−	0.950804i	$-0.399740\pi$
$211$	9.00000	0.619586	0.309793	+	0.950804i	$0.399740\pi$
$212$	−2.00000	−0.137361
$213$	2.00000	0.137038
$214$	1.00000	0.0683586
$215$	0	0
$216$	−5.00000	−0.340207
$217$	0	0
$218$	−18.0000	−1.21911
$219$	9.00000	0.608164
$220$	0	0
$221$	18.0000	1.21081
$222$	−1.00000	−0.0671156
$223$	8.00000	0.535720	0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000	0.535720	0.267860	+	0.963458i	$0.413684\pi$
$224$	−4.00000	−0.267261
$225$	0	0
$226$	−5.00000	−0.332595
$227$	28.0000	1.85843	0.929213	−	0.369546i	$-0.120487\pi$
$227$	28.0000	1.85843	0.929213	+	0.369546i	$0.120487\pi$
$228$	3.00000	0.198680
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	0	0
$231$	−12.0000	−0.789542
$232$	0	0
$233$	−26.0000	−1.70332	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000	−1.70332	−0.851658	+	0.524097i	$0.824403\pi$
$234$	12.0000	0.784465
$235$	0	0
$236$	−12.0000	−0.781133
$237$	2.00000	0.129914
$238$	−12.0000	−0.777844
$239$	−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
$241$	−21.0000	−1.35273	−0.676364	−	0.736567i	$-0.736446\pi$
$241$	−21.0000	−1.35273	−0.676364	+	0.736567i	$0.736446\pi$
$242$	2.00000	0.128565
$243$	−16.0000	−1.02640
$244$	12.0000	0.768221
$245$	0	0
$246$	−3.00000	−0.191273
$247$	−18.0000	−1.14531
$248$	0	0
$249$	7.00000	0.443607
$250$	0	0
$251$	−9.00000	−0.568075	−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000	−0.568075	−0.284037	+	0.958813i	$0.591674\pi$
$252$	−8.00000	−0.503953
$253$	6.00000	0.377217
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	−22.0000	−1.37232	−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000	−1.37232	−0.686161	+	0.727450i	$0.740706\pi$
$258$	−4.00000	−0.249029
$259$	−4.00000	−0.248548
$260$	0	0
$261$	0	0
$262$	−12.0000	−0.741362
$263$	26.0000	1.60323	0.801614	−	0.597841i	$-0.203975\pi$
$263$	26.0000	1.60323	0.801614	+	0.597841i	$0.203975\pi$
$264$	3.00000	0.184637
$265$	0	0
$266$	12.0000	0.735767
$267$	3.00000	0.183597
$268$	9.00000	0.549762
$269$	−28.0000	−1.70719	−0.853595	−	0.520937i	$-0.825583\pi$
$269$	−28.0000	−1.70719	−0.853595	+	0.520937i	$0.825583\pi$
$270$	0	0
$271$	−28.0000	−1.70088	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000	−1.70088	−0.850439	+	0.526073i	$0.823664\pi$
$272$	3.00000	0.181902
$273$	−24.0000	−1.45255
$274$	7.00000	0.422885
$275$	0	0
$276$	−2.00000	−0.120386
$277$	28.0000	1.68236	0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000	1.68236	0.841178	+	0.540758i	$0.181862\pi$
$278$	−3.00000	−0.179928
$279$	0	0
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	4.00000	0.238197
$283$	7.00000	0.416107	0.208053	−	0.978117i	$-0.433287\pi$
$283$	7.00000	0.416107	0.208053	+	0.978117i	$0.433287\pi$
$284$	−2.00000	−0.118678
$285$	0	0
$286$	−18.0000	−1.06436
$287$	−12.0000	−0.708338
$288$	2.00000	0.117851
$289$	−8.00000	−0.470588
$290$	0	0
$291$	−2.00000	−0.117242
$292$	−9.00000	−0.526685
$293$	12.0000	0.701047	0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000	0.701047	0.350524	+	0.936554i	$0.386004\pi$
$294$	9.00000	0.524891
$295$	0	0
$296$	1.00000	0.0581238
$297$	15.0000	0.870388
$298$	18.0000	1.04271
$299$	12.0000	0.693978
$300$	0	0
$301$	−16.0000	−0.922225
$302$	−22.0000	−1.26596
$303$	10.0000	0.574485
$304$	−3.00000	−0.172062
$305$	0	0
$306$	6.00000	0.342997
$307$	−29.0000	−1.65512	−0.827559	−	0.561379i	$-0.810271\pi$
$307$	−29.0000	−1.65512	−0.827559	+	0.561379i	$0.810271\pi$
$308$	12.0000	0.683763
$309$	−14.0000	−0.796432
$310$	0	0
$311$	28.0000	1.58773	0.793867	−	0.608091i	$-0.208065\pi$
$311$	28.0000	1.58773	0.793867	+	0.608091i	$0.208065\pi$
$312$	6.00000	0.339683
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	−24.0000	−1.35440
$315$	0	0
$316$	−2.00000	−0.112509
$317$	−18.0000	−1.01098	−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000	−1.01098	−0.505490	+	0.862832i	$0.668688\pi$
$318$	−2.00000	−0.112154
$319$	0	0
$320$	0	0
$321$	1.00000	0.0558146
$322$	−8.00000	−0.445823
$323$	−9.00000	−0.500773
$324$	1.00000	0.0555556
$325$	0	0
$326$	17.0000	0.941543
$327$	−18.0000	−0.995402
$328$	3.00000	0.165647
$329$	16.0000	0.882109
$330$	0	0
$331$	−3.00000	−0.164895	−0.0824475	−	0.996595i	$-0.526274\pi$
$331$	−3.00000	−0.164895	−0.0824475	+	0.996595i	$0.526274\pi$
$332$	−7.00000	−0.384175
$333$	2.00000	0.109599
$334$	18.0000	0.984916
$335$	0	0
$336$	−4.00000	−0.218218
$337$	−9.00000	−0.490261	−0.245131	−	0.969490i	$-0.578831\pi$
$337$	−9.00000	−0.490261	−0.245131	+	0.969490i	$0.578831\pi$
$338$	−23.0000	−1.25104
$339$	−5.00000	−0.271563
$340$	0	0
$341$	0	0
$342$	−6.00000	−0.324443
$343$	8.00000	0.431959
$344$	4.00000	0.215666
$345$	0	0
$346$	−24.0000	−1.29025
$347$	−31.0000	−1.66417	−0.832084	−	0.554650i	$-0.812852\pi$
$347$	−31.0000	−1.66417	−0.832084	+	0.554650i	$0.812852\pi$
$348$	0	0
$349$	−16.0000	−0.856460	−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000	−0.856460	−0.428230	+	0.903670i	$0.640863\pi$
$350$	0	0
$351$	30.0000	1.60128
$352$	−3.00000	−0.159901
$353$	−14.0000	−0.745145	−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000	−0.745145	−0.372572	+	0.928003i	$0.621524\pi$
$354$	−12.0000	−0.637793
$355$	0	0
$356$	−3.00000	−0.159000
$357$	−12.0000	−0.635107
$358$	−21.0000	−1.10988
$359$	34.0000	1.79445	0.897226	−	0.441572i	$-0.145579\pi$
$359$	34.0000	1.79445	0.897226	+	0.441572i	$0.145579\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	10.0000	0.525588
$363$	2.00000	0.104973
$364$	24.0000	1.25794
$365$	0	0
$366$	12.0000	0.627250
$367$	−2.00000	−0.104399	−0.0521996	−	0.998637i	$-0.516623\pi$
$367$	−2.00000	−0.104399	−0.0521996	+	0.998637i	$0.516623\pi$
$368$	2.00000	0.104257
$369$	6.00000	0.312348
$370$	0	0
$371$	−8.00000	−0.415339
$372$	0	0
$373$	28.0000	1.44979	0.724893	−	0.688862i	$-0.241889\pi$
$373$	28.0000	1.44979	0.724893	+	0.688862i	$0.241889\pi$
$374$	−9.00000	−0.465379
$375$	0	0
$376$	−4.00000	−0.206284
$377$	0	0
$378$	−20.0000	−1.02869
$379$	1.00000	0.0513665	0.0256833	−	0.999670i	$-0.491824\pi$
$379$	1.00000	0.0513665	0.0256833	+	0.999670i	$0.491824\pi$
$380$	0	0
$381$	−8.00000	−0.409852
$382$	−6.00000	−0.306987
$383$	24.0000	1.22634	0.613171	−	0.789950i	$-0.289894\pi$
$383$	24.0000	1.22634	0.613171	+	0.789950i	$0.289894\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−11.0000	−0.559885
$387$	8.00000	0.406663
$388$	2.00000	0.101535
$389$	−12.0000	−0.608424	−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000	−0.608424	−0.304212	+	0.952604i	$0.598393\pi$
$390$	0	0
$391$	6.00000	0.303433
$392$	−9.00000	−0.454569
$393$	−12.0000	−0.605320
$394$	−12.0000	−0.604551
$395$	0	0
$396$	−6.00000	−0.301511
$397$	−30.0000	−1.50566	−0.752828	−	0.658217i	$-0.771311\pi$
$397$	−30.0000	−1.50566	−0.752828	+	0.658217i	$0.771311\pi$
$398$	−8.00000	−0.401004
$399$	12.0000	0.600751
$400$	0	0
$401$	−5.00000	−0.249688	−0.124844	−	0.992176i	$-0.539843\pi$
$401$	−5.00000	−0.249688	−0.124844	+	0.992176i	$0.539843\pi$
$402$	9.00000	0.448879
$403$	0	0
$404$	−10.0000	−0.497519
$405$	0	0
$406$	0	0
$407$	−3.00000	−0.148704
$408$	3.00000	0.148522
$409$	15.0000	0.741702	0.370851	−	0.928692i	$-0.379066\pi$
$409$	15.0000	0.741702	0.370851	+	0.928692i	$0.379066\pi$
$410$	0	0
$411$	7.00000	0.345285
$412$	14.0000	0.689730
$413$	−48.0000	−2.36193
$414$	4.00000	0.196589
$415$	0	0
$416$	−6.00000	−0.294174
$417$	−3.00000	−0.146911
$418$	9.00000	0.440204
$419$	27.0000	1.31904	0.659518	−	0.751689i	$-0.270760\pi$
$419$	27.0000	1.31904	0.659518	+	0.751689i	$0.270760\pi$
$420$	0	0
$421$	−32.0000	−1.55958	−0.779792	−	0.626038i	$-0.784675\pi$
$421$	−32.0000	−1.55958	−0.779792	+	0.626038i	$0.784675\pi$
$422$	−9.00000	−0.438113
$423$	−8.00000	−0.388973
$424$	2.00000	0.0971286
$425$	0	0
$426$	−2.00000	−0.0969003
$427$	48.0000	2.32288
$428$	−1.00000	−0.0483368
$429$	−18.0000	−0.869048
$430$	0	0
$431$	2.00000	0.0963366	0.0481683	−	0.998839i	$-0.484662\pi$
$431$	2.00000	0.0963366	0.0481683	+	0.998839i	$0.484662\pi$
$432$	5.00000	0.240563
$433$	5.00000	0.240285	0.120142	−	0.992757i	$-0.461665\pi$
$433$	5.00000	0.240285	0.120142	+	0.992757i	$0.461665\pi$
$434$	0	0
$435$	0	0
$436$	18.0000	0.862044
$437$	−6.00000	−0.287019
$438$	−9.00000	−0.430037
$439$	16.0000	0.763638	0.381819	−	0.924237i	$-0.375298\pi$
$439$	16.0000	0.763638	0.381819	+	0.924237i	$0.375298\pi$
$440$	0	0
$441$	−18.0000	−0.857143
$442$	−18.0000	−0.856173
$443$	5.00000	0.237557	0.118779	−	0.992921i	$-0.462102\pi$
$443$	5.00000	0.237557	0.118779	+	0.992921i	$0.462102\pi$
$444$	1.00000	0.0474579
$445$	0	0
$446$	−8.00000	−0.378811
$447$	18.0000	0.851371
$448$	4.00000	0.188982
$449$	−37.0000	−1.74614	−0.873069	−	0.487597i	$-0.837874\pi$
$449$	−37.0000	−1.74614	−0.873069	+	0.487597i	$0.837874\pi$
$450$	0	0
$451$	−9.00000	−0.423793
$452$	5.00000	0.235180
$453$	−22.0000	−1.03365
$454$	−28.0000	−1.31411
$455$	0	0
$456$	−3.00000	−0.140488
$457$	−33.0000	−1.54367	−0.771837	−	0.635820i	$-0.780662\pi$
$457$	−33.0000	−1.54367	−0.771837	+	0.635820i	$0.780662\pi$
$458$	0	0
$459$	15.0000	0.700140
$460$	0	0
$461$	20.0000	0.931493	0.465746	−	0.884918i	$-0.345786\pi$
$461$	20.0000	0.931493	0.465746	+	0.884918i	$0.345786\pi$
$462$	12.0000	0.558291
$463$	6.00000	0.278844	0.139422	−	0.990233i	$-0.455476\pi$
$463$	6.00000	0.278844	0.139422	+	0.990233i	$0.455476\pi$
$464$	0	0
$465$	0	0
$466$	26.0000	1.20443
$467$	−28.0000	−1.29569	−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000	−1.29569	−0.647843	+	0.761774i	$0.724329\pi$
$468$	−12.0000	−0.554700
$469$	36.0000	1.66233
$470$	0	0
$471$	−24.0000	−1.10586
$472$	12.0000	0.552345
$473$	−12.0000	−0.551761
$474$	−2.00000	−0.0918630
$475$	0	0
$476$	12.0000	0.550019
$477$	4.00000	0.183147
$478$	12.0000	0.548867
$479$	16.0000	0.731059	0.365529	−	0.930800i	$-0.380888\pi$
$479$	16.0000	0.731059	0.365529	+	0.930800i	$0.380888\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	21.0000	0.956524
$483$	−8.00000	−0.364013
$484$	−2.00000	−0.0909091
$485$	0	0
$486$	16.0000	0.725775
$487$	28.0000	1.26880	0.634401	−	0.773004i	$-0.281247\pi$
$487$	28.0000	1.26880	0.634401	+	0.773004i	$0.281247\pi$
$488$	−12.0000	−0.543214
$489$	17.0000	0.768767
$490$	0	0
$491$	−20.0000	−0.902587	−0.451294	−	0.892375i	$-0.649037\pi$
$491$	−20.0000	−0.902587	−0.451294	+	0.892375i	$0.649037\pi$
$492$	3.00000	0.135250
$493$	0	0
$494$	18.0000	0.809858
$495$	0	0
$496$	0	0
$497$	−8.00000	−0.358849
$498$	−7.00000	−0.313678
$499$	−16.0000	−0.716258	−0.358129	−	0.933672i	$-0.616585\pi$
$499$	−16.0000	−0.716258	−0.358129	+	0.933672i	$0.616585\pi$
$500$	0	0
$501$	18.0000	0.804181
$502$	9.00000	0.401690
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	8.00000	0.356348
$505$	0	0
$506$	−6.00000	−0.266733
$507$	−23.0000	−1.02147
$508$	8.00000	0.354943
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	−36.0000	−1.59255
$512$	−1.00000	−0.0441942
$513$	−15.0000	−0.662266
$514$	22.0000	0.970378
$515$	0	0
$516$	4.00000	0.176090
$517$	12.0000	0.527759
$518$	4.00000	0.175750
$519$	−24.0000	−1.05348
$520$	0	0
$521$	−11.0000	−0.481919	−0.240959	−	0.970535i	$-0.577462\pi$
$521$	−11.0000	−0.481919	−0.240959	+	0.970535i	$0.577462\pi$
$522$	0	0
$523$	37.0000	1.61790	0.808949	−	0.587879i	$-0.200037\pi$
$523$	37.0000	1.61790	0.808949	+	0.587879i	$0.200037\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	−26.0000	−1.13365
$527$	0	0
$528$	−3.00000	−0.130558
$529$	−19.0000	−0.826087
$530$	0	0
$531$	24.0000	1.04151
$532$	−12.0000	−0.520266
$533$	−18.0000	−0.779667
$534$	−3.00000	−0.129823
$535$	0	0
$536$	−9.00000	−0.388741
$537$	−21.0000	−0.906217
$538$	28.0000	1.20717
$539$	27.0000	1.16297
$540$	0	0
$541$	−2.00000	−0.0859867	−0.0429934	−	0.999075i	$-0.513689\pi$
$541$	−2.00000	−0.0859867	−0.0429934	+	0.999075i	$0.513689\pi$
$542$	28.0000	1.20270
$543$	10.0000	0.429141
$544$	−3.00000	−0.128624
$545$	0	0
$546$	24.0000	1.02711
$547$	5.00000	0.213785	0.106892	−	0.994271i	$-0.465910\pi$
$547$	5.00000	0.213785	0.106892	+	0.994271i	$0.465910\pi$
$548$	−7.00000	−0.299025
$549$	−24.0000	−1.02430
$550$	0	0
$551$	0	0
$552$	2.00000	0.0851257
$553$	−8.00000	−0.340195
$554$	−28.0000	−1.18961
$555$	0	0
$556$	3.00000	0.127228
$557$	32.0000	1.35588	0.677942	−	0.735116i	$-0.262872\pi$
$557$	32.0000	1.35588	0.677942	+	0.735116i	$0.262872\pi$
$558$	0	0
$559$	−24.0000	−1.01509
$560$	0	0
$561$	−9.00000	−0.379980
$562$	6.00000	0.253095
$563$	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
$565$	0	0
$566$	−7.00000	−0.294232
$567$	4.00000	0.167984
$568$	2.00000	0.0839181
$569$	19.0000	0.796521	0.398261	−	0.917272i	$-0.369614\pi$
$569$	19.0000	0.796521	0.398261	+	0.917272i	$0.369614\pi$
$570$	0	0
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	18.0000	0.752618
$573$	−6.00000	−0.250654
$574$	12.0000	0.500870
$575$	0	0
$576$	−2.00000	−0.0833333
$577$	−15.0000	−0.624458	−0.312229	−	0.950007i	$-0.601076\pi$
$577$	−15.0000	−0.624458	−0.312229	+	0.950007i	$0.601076\pi$
$578$	8.00000	0.332756
$579$	−11.0000	−0.457144
$580$	0	0
$581$	−28.0000	−1.16164
$582$	2.00000	0.0829027
$583$	−6.00000	−0.248495
$584$	9.00000	0.372423
$585$	0	0
$586$	−12.0000	−0.495715
$587$	−13.0000	−0.536567	−0.268284	−	0.963340i	$-0.586456\pi$
$587$	−13.0000	−0.536567	−0.268284	+	0.963340i	$0.586456\pi$
$588$	−9.00000	−0.371154
$589$	0	0
$590$	0	0
$591$	−12.0000	−0.493614
$592$	−1.00000	−0.0410997
$593$	−9.00000	−0.369586	−0.184793	−	0.982777i	$-0.559161\pi$
$593$	−9.00000	−0.369586	−0.184793	+	0.982777i	$0.559161\pi$
$594$	−15.0000	−0.615457
$595$	0	0
$596$	−18.0000	−0.737309
$597$	−8.00000	−0.327418
$598$	−12.0000	−0.490716
$599$	−36.0000	−1.47092	−0.735460	−	0.677568i	$-0.763034\pi$
$599$	−36.0000	−1.47092	−0.735460	+	0.677568i	$0.763034\pi$
$600$	0	0
$601$	−33.0000	−1.34610	−0.673049	−	0.739598i	$-0.735016\pi$
$601$	−33.0000	−1.34610	−0.673049	+	0.739598i	$0.735016\pi$
$602$	16.0000	0.652111
$603$	−18.0000	−0.733017
$604$	22.0000	0.895167
$605$	0	0
$606$	−10.0000	−0.406222
$607$	−26.0000	−1.05531	−0.527654	−	0.849460i	$-0.676928\pi$
$607$	−26.0000	−1.05531	−0.527654	+	0.849460i	$0.676928\pi$
$608$	3.00000	0.121666
$609$	0	0
$610$	0	0
$611$	24.0000	0.970936
$612$	−6.00000	−0.242536
$613$	−46.0000	−1.85792	−0.928961	−	0.370177i	$-0.879297\pi$
$613$	−46.0000	−1.85792	−0.928961	+	0.370177i	$0.879297\pi$
$614$	29.0000	1.17034
$615$	0	0
$616$	−12.0000	−0.483494
$617$	−42.0000	−1.69086	−0.845428	−	0.534089i	$-0.820655\pi$
$617$	−42.0000	−1.69086	−0.845428	+	0.534089i	$0.820655\pi$
$618$	14.0000	0.563163
$619$	−16.0000	−0.643094	−0.321547	−	0.946894i	$-0.604203\pi$
$619$	−16.0000	−0.643094	−0.321547	+	0.946894i	$0.604203\pi$
$620$	0	0
$621$	10.0000	0.401286
$622$	−28.0000	−1.12270
$623$	−12.0000	−0.480770
$624$	−6.00000	−0.240192
$625$	0	0
$626$	10.0000	0.399680
$627$	9.00000	0.359425
$628$	24.0000	0.957704
$629$	−3.00000	−0.119618
$630$	0	0
$631$	22.0000	0.875806	0.437903	−	0.899022i	$-0.355721\pi$
$631$	22.0000	0.875806	0.437903	+	0.899022i	$0.355721\pi$
$632$	2.00000	0.0795557
$633$	−9.00000	−0.357718
$634$	18.0000	0.714871
$635$	0	0
$636$	2.00000	0.0793052
$637$	54.0000	2.13956
$638$	0	0
$639$	4.00000	0.158238
$640$	0	0
$641$	−6.00000	−0.236986	−0.118493	−	0.992955i	$-0.537806\pi$
$641$	−6.00000	−0.236986	−0.118493	+	0.992955i	$0.537806\pi$
$642$	−1.00000	−0.0394669
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	8.00000	0.315244
$645$	0	0
$646$	9.00000	0.354100
$647$	42.0000	1.65119	0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000	1.65119	0.825595	+	0.564263i	$0.190840\pi$
$648$	−1.00000	−0.0392837
$649$	−36.0000	−1.41312
$650$	0	0
$651$	0	0
$652$	−17.0000	−0.665771
$653$	36.0000	1.40879	0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000	1.40879	0.704394	+	0.709809i	$0.251219\pi$
$654$	18.0000	0.703856
$655$	0	0
$656$	−3.00000	−0.117130
$657$	18.0000	0.702247
$658$	−16.0000	−0.623745
$659$	9.00000	0.350590	0.175295	−	0.984516i	$-0.443912\pi$
$659$	9.00000	0.350590	0.175295	+	0.984516i	$0.443912\pi$
$660$	0	0
$661$	−16.0000	−0.622328	−0.311164	−	0.950356i	$-0.600719\pi$
$661$	−16.0000	−0.622328	−0.311164	+	0.950356i	$0.600719\pi$
$662$	3.00000	0.116598
$663$	−18.0000	−0.699062
$664$	7.00000	0.271653
$665$	0	0
$666$	−2.00000	−0.0774984
$667$	0	0
$668$	−18.0000	−0.696441
$669$	−8.00000	−0.309298
$670$	0	0
$671$	36.0000	1.38976
$672$	4.00000	0.154303
$673$	−34.0000	−1.31060	−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000	−1.31060	−0.655302	+	0.755367i	$0.727459\pi$
$674$	9.00000	0.346667
$675$	0	0
$676$	23.0000	0.884615
$677$	−8.00000	−0.307465	−0.153732	−	0.988113i	$-0.549129\pi$
$677$	−8.00000	−0.307465	−0.153732	+	0.988113i	$0.549129\pi$
$678$	5.00000	0.192024
$679$	8.00000	0.307012
$680$	0	0
$681$	−28.0000	−1.07296
$682$	0	0
$683$	17.0000	0.650487	0.325243	−	0.945630i	$-0.394554\pi$
$683$	17.0000	0.650487	0.325243	+	0.945630i	$0.394554\pi$
$684$	6.00000	0.229416
$685$	0	0
$686$	−8.00000	−0.305441
$687$	0	0
$688$	−4.00000	−0.152499
$689$	−12.0000	−0.457164
$690$	0	0
$691$	−1.00000	−0.0380418	−0.0190209	−	0.999819i	$-0.506055\pi$
$691$	−1.00000	−0.0380418	−0.0190209	+	0.999819i	$0.506055\pi$
$692$	24.0000	0.912343
$693$	−24.0000	−0.911685
$694$	31.0000	1.17674
$695$	0	0
$696$	0	0
$697$	−9.00000	−0.340899
$698$	16.0000	0.605609
$699$	26.0000	0.983410
$700$	0	0
$701$	−10.0000	−0.377695	−0.188847	−	0.982006i	$-0.560475\pi$
$701$	−10.0000	−0.377695	−0.188847	+	0.982006i	$0.560475\pi$
$702$	−30.0000	−1.13228
$703$	3.00000	0.113147
$704$	3.00000	0.113067
$705$	0	0
$706$	14.0000	0.526897
$707$	−40.0000	−1.50435
$708$	12.0000	0.450988
$709$	32.0000	1.20179	0.600893	−	0.799330i	$-0.294812\pi$
$709$	32.0000	1.20179	0.600893	+	0.799330i	$0.294812\pi$
$710$	0	0
$711$	4.00000	0.150012
$712$	3.00000	0.112430
$713$	0	0
$714$	12.0000	0.449089
$715$	0	0
$716$	21.0000	0.784807
$717$	12.0000	0.448148
$718$	−34.0000	−1.26887
$719$	−36.0000	−1.34257	−0.671287	−	0.741198i	$-0.734258\pi$
$719$	−36.0000	−1.34257	−0.671287	+	0.741198i	$0.734258\pi$
$720$	0	0
$721$	56.0000	2.08555
$722$	10.0000	0.372161
$723$	21.0000	0.780998
$724$	−10.0000	−0.371647
$725$	0	0
$726$	−2.00000	−0.0742270
$727$	−44.0000	−1.63187	−0.815935	−	0.578144i	$-0.803777\pi$
$727$	−44.0000	−1.63187	−0.815935	+	0.578144i	$0.803777\pi$
$728$	−24.0000	−0.889499
$729$	13.0000	0.481481
$730$	0	0
$731$	−12.0000	−0.443836
$732$	−12.0000	−0.443533
$733$	40.0000	1.47743	0.738717	−	0.674016i	$-0.235432\pi$
$733$	40.0000	1.47743	0.738717	+	0.674016i	$0.235432\pi$
$734$	2.00000	0.0738213
$735$	0	0
$736$	−2.00000	−0.0737210
$737$	27.0000	0.994558
$738$	−6.00000	−0.220863
$739$	−12.0000	−0.441427	−0.220714	−	0.975339i	$-0.570839\pi$
$739$	−12.0000	−0.441427	−0.220714	+	0.975339i	$0.570839\pi$
$740$	0	0
$741$	18.0000	0.661247
$742$	8.00000	0.293689
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	0	0
$745$	0	0
$746$	−28.0000	−1.02515
$747$	14.0000	0.512233
$748$	9.00000	0.329073
$749$	−4.00000	−0.146157
$750$	0	0
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	4.00000	0.145865
$753$	9.00000	0.327978
$754$	0	0
$755$	0	0
$756$	20.0000	0.727393
$757$	16.0000	0.581530	0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000	0.581530	0.290765	+	0.956795i	$0.406090\pi$
$758$	−1.00000	−0.0363216
$759$	−6.00000	−0.217786
$760$	0	0
$761$	45.0000	1.63125	0.815624	−	0.578582i	$-0.196394\pi$
$761$	45.0000	1.63125	0.815624	+	0.578582i	$0.196394\pi$
$762$	8.00000	0.289809
$763$	72.0000	2.60658
$764$	6.00000	0.217072
$765$	0	0
$766$	−24.0000	−0.867155
$767$	−72.0000	−2.59977
$768$	−1.00000	−0.0360844
$769$	23.0000	0.829401	0.414701	−	0.909958i	$-0.363886\pi$
$769$	23.0000	0.829401	0.414701	+	0.909958i	$0.363886\pi$
$770$	0	0
$771$	22.0000	0.792311
$772$	11.0000	0.395899
$773$	46.0000	1.65451	0.827253	−	0.561830i	$-0.189903\pi$
$773$	46.0000	1.65451	0.827253	+	0.561830i	$0.189903\pi$
$774$	−8.00000	−0.287554
$775$	0	0
$776$	−2.00000	−0.0717958
$777$	4.00000	0.143499
$778$	12.0000	0.430221
$779$	9.00000	0.322458
$780$	0	0
$781$	−6.00000	−0.214697
$782$	−6.00000	−0.214560
$783$	0	0
$784$	9.00000	0.321429
$785$	0	0
$786$	12.0000	0.428026
$787$	32.0000	1.14068	0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000	1.14068	0.570338	+	0.821410i	$0.306812\pi$
$788$	12.0000	0.427482
$789$	−26.0000	−0.925625
$790$	0	0
$791$	20.0000	0.711118
$792$	6.00000	0.213201
$793$	72.0000	2.55679
$794$	30.0000	1.06466
$795$	0	0
$796$	8.00000	0.283552
$797$	16.0000	0.566749	0.283375	−	0.959009i	$-0.408546\pi$
$797$	16.0000	0.566749	0.283375	+	0.959009i	$0.408546\pi$
$798$	−12.0000	−0.424795
$799$	12.0000	0.424529
$800$	0	0
$801$	6.00000	0.212000
$802$	5.00000	0.176556
$803$	−27.0000	−0.952809
$804$	−9.00000	−0.317406
$805$	0	0
$806$	0	0
$807$	28.0000	0.985647
$808$	10.0000	0.351799
$809$	−38.0000	−1.33601	−0.668004	−	0.744157i	$-0.732851\pi$
$809$	−38.0000	−1.33601	−0.668004	+	0.744157i	$0.732851\pi$
$810$	0	0
$811$	20.0000	0.702295	0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000	0.702295	0.351147	+	0.936320i	$0.385792\pi$
$812$	0	0
$813$	28.0000	0.982003
$814$	3.00000	0.105150
$815$	0	0
$816$	−3.00000	−0.105021
$817$	12.0000	0.419827
$818$	−15.0000	−0.524463
$819$	−48.0000	−1.67726
$820$	0	0
$821$	−4.00000	−0.139601	−0.0698005	−	0.997561i	$-0.522236\pi$
$821$	−4.00000	−0.139601	−0.0698005	+	0.997561i	$0.522236\pi$
$822$	−7.00000	−0.244153
$823$	42.0000	1.46403	0.732014	−	0.681290i	$-0.238581\pi$
$823$	42.0000	1.46403	0.732014	+	0.681290i	$0.238581\pi$
$824$	−14.0000	−0.487713
$825$	0	0
$826$	48.0000	1.67013
$827$	7.00000	0.243414	0.121707	−	0.992566i	$-0.461163\pi$
$827$	7.00000	0.243414	0.121707	+	0.992566i	$0.461163\pi$
$828$	−4.00000	−0.139010
$829$	6.00000	0.208389	0.104194	−	0.994557i	$-0.466774\pi$
$829$	6.00000	0.208389	0.104194	+	0.994557i	$0.466774\pi$
$830$	0	0
$831$	−28.0000	−0.971309
$832$	6.00000	0.208013
$833$	27.0000	0.935495
$834$	3.00000	0.103882
$835$	0	0
$836$	−9.00000	−0.311272
$837$	0	0
$838$	−27.0000	−0.932700
$839$	−42.0000	−1.45000	−0.725001	−	0.688748i	$-0.758161\pi$
$839$	−42.0000	−1.45000	−0.725001	+	0.688748i	$0.758161\pi$
$840$	0	0
$841$	−29.0000	−1.00000
$842$	32.0000	1.10279
$843$	6.00000	0.206651
$844$	9.00000	0.309793
$845$	0	0
$846$	8.00000	0.275046
$847$	−8.00000	−0.274883
$848$	−2.00000	−0.0686803
$849$	−7.00000	−0.240239
$850$	0	0
$851$	−2.00000	−0.0685591
$852$	2.00000	0.0685189
$853$	40.0000	1.36957	0.684787	−	0.728743i	$-0.259895\pi$
$853$	40.0000	1.36957	0.684787	+	0.728743i	$0.259895\pi$
$854$	−48.0000	−1.64253
$855$	0	0
$856$	1.00000	0.0341793
$857$	3.00000	0.102478	0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000	0.102478	0.0512390	+	0.998686i	$0.483683\pi$
$858$	18.0000	0.614510
$859$	9.00000	0.307076	0.153538	−	0.988143i	$-0.450933\pi$
$859$	9.00000	0.307076	0.153538	+	0.988143i	$0.450933\pi$
$860$	0	0
$861$	12.0000	0.408959
$862$	−2.00000	−0.0681203
$863$	6.00000	0.204242	0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000	0.204242	0.102121	+	0.994772i	$0.467437\pi$
$864$	−5.00000	−0.170103
$865$	0	0
$866$	−5.00000	−0.169907
$867$	8.00000	0.271694
$868$	0	0
$869$	−6.00000	−0.203536
$870$	0	0
$871$	54.0000	1.82972
$872$	−18.0000	−0.609557
$873$	−4.00000	−0.135379
$874$	6.00000	0.202953
$875$	0	0
$876$	9.00000	0.304082
$877$	26.0000	0.877958	0.438979	−	0.898497i	$-0.355340\pi$
$877$	26.0000	0.877958	0.438979	+	0.898497i	$0.355340\pi$
$878$	−16.0000	−0.539974
$879$	−12.0000	−0.404750
$880$	0	0
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	18.0000	0.606092
$883$	−7.00000	−0.235569	−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000	−0.235569	−0.117784	+	0.993039i	$0.537579\pi$
$884$	18.0000	0.605406
$885$	0	0
$886$	−5.00000	−0.167978
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	−1.00000	−0.0335578
$889$	32.0000	1.07325
$890$	0	0
$891$	3.00000	0.100504
$892$	8.00000	0.267860
$893$	−12.0000	−0.401565
$894$	−18.0000	−0.602010
$895$	0	0
$896$	−4.00000	−0.133631
$897$	−12.0000	−0.400668
$898$	37.0000	1.23471
$899$	0	0
$900$	0	0
$901$	−6.00000	−0.199889
$902$	9.00000	0.299667
$903$	16.0000	0.532447
$904$	−5.00000	−0.166298
$905$	0	0
$906$	22.0000	0.730901
$907$	36.0000	1.19536	0.597680	−	0.801735i	$-0.296089\pi$
$907$	36.0000	1.19536	0.597680	+	0.801735i	$0.296089\pi$
$908$	28.0000	0.929213
$909$	20.0000	0.663358
$910$	0	0
$911$	18.0000	0.596367	0.298183	−	0.954509i	$-0.403619\pi$
$911$	18.0000	0.596367	0.298183	+	0.954509i	$0.403619\pi$
$912$	3.00000	0.0993399
$913$	−21.0000	−0.694999
$914$	33.0000	1.09154
$915$	0	0
$916$	0	0
$917$	48.0000	1.58510
$918$	−15.0000	−0.495074
$919$	−34.0000	−1.12156	−0.560778	−	0.827966i	$-0.689498\pi$
$919$	−34.0000	−1.12156	−0.560778	+	0.827966i	$0.689498\pi$
$920$	0	0
$921$	29.0000	0.955582
$922$	−20.0000	−0.658665
$923$	−12.0000	−0.394985
$924$	−12.0000	−0.394771
$925$	0	0
$926$	−6.00000	−0.197172
$927$	−28.0000	−0.919641
$928$	0	0
$929$	−54.0000	−1.77168	−0.885841	−	0.463988i	$-0.846418\pi$
$929$	−54.0000	−1.77168	−0.885841	+	0.463988i	$0.846418\pi$
$930$	0	0
$931$	−27.0000	−0.884889
$932$	−26.0000	−0.851658
$933$	−28.0000	−0.916679
$934$	28.0000	0.916188
$935$	0	0
$936$	12.0000	0.392232
$937$	7.00000	0.228680	0.114340	−	0.993442i	$-0.463525\pi$
$937$	7.00000	0.228680	0.114340	+	0.993442i	$0.463525\pi$
$938$	−36.0000	−1.17544
$939$	10.0000	0.326338
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	24.0000	0.781962
$943$	−6.00000	−0.195387
$944$	−12.0000	−0.390567
$945$	0	0
$946$	12.0000	0.390154
$947$	−24.0000	−0.779895	−0.389948	−	0.920837i	$-0.627507\pi$
$947$	−24.0000	−0.779895	−0.389948	+	0.920837i	$0.627507\pi$
$948$	2.00000	0.0649570
$949$	−54.0000	−1.75291
$950$	0	0
$951$	18.0000	0.583690
$952$	−12.0000	−0.388922
$953$	33.0000	1.06897	0.534487	−	0.845176i	$-0.320505\pi$
$953$	33.0000	1.06897	0.534487	+	0.845176i	$0.320505\pi$
$954$	−4.00000	−0.129505
$955$	0	0
$956$	−12.0000	−0.388108
$957$	0	0
$958$	−16.0000	−0.516937
$959$	−28.0000	−0.904167
$960$	0	0
$961$	−31.0000	−1.00000
$962$	6.00000	0.193448
$963$	2.00000	0.0644491
$964$	−21.0000	−0.676364
$965$	0	0
$966$	8.00000	0.257396
$967$	−48.0000	−1.54358	−0.771788	−	0.635880i	$-0.780637\pi$
$967$	−48.0000	−1.54358	−0.771788	+	0.635880i	$0.780637\pi$
$968$	2.00000	0.0642824
$969$	9.00000	0.289122
$970$	0	0
$971$	3.00000	0.0962746	0.0481373	−	0.998841i	$-0.484672\pi$
$971$	3.00000	0.0962746	0.0481373	+	0.998841i	$0.484672\pi$
$972$	−16.0000	−0.513200
$973$	12.0000	0.384702
$974$	−28.0000	−0.897178
$975$	0	0
$976$	12.0000	0.384111
$977$	23.0000	0.735835	0.367918	−	0.929858i	$-0.380071\pi$
$977$	23.0000	0.735835	0.367918	+	0.929858i	$0.380071\pi$
$978$	−17.0000	−0.543600
$979$	−9.00000	−0.287641
$980$	0	0
$981$	−36.0000	−1.14939
$982$	20.0000	0.638226
$983$	18.0000	0.574111	0.287055	−	0.957914i	$-0.407324\pi$
$983$	18.0000	0.574111	0.287055	+	0.957914i	$0.407324\pi$
$984$	−3.00000	−0.0956365
$985$	0	0
$986$	0	0
$987$	−16.0000	−0.509286
$988$	−18.0000	−0.572656
$989$	−8.00000	−0.254385
$990$	0	0
$991$	−12.0000	−0.381193	−0.190596	−	0.981669i	$-0.561042\pi$
$991$	−12.0000	−0.381193	−0.190596	+	0.981669i	$0.561042\pi$
$992$	0	0
$993$	3.00000	0.0952021
$994$	8.00000	0.253745
$995$	0	0
$996$	7.00000	0.221803
$997$	−18.0000	−0.570066	−0.285033	−	0.958518i	$-0.592005\pi$
$997$	−18.0000	−0.570066	−0.285033	+	0.958518i	$0.592005\pi$
$998$	16.0000	0.506471
$999$	−5.00000	−0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1850.2.a.c.1.1	✓	1
5.2	odd	4		1850.2.b.e.149.1		2
5.3	odd	4		1850.2.b.e.149.2		2
5.4	even	2		1850.2.a.m.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1850.2.a.c.1.1	✓	1	1.1	even	1	trivial
1850.2.a.m.1.1	yes	1	5.4	even	2
1850.2.b.e.149.1		2	5.2	odd	4
1850.2.b.e.149.2		2	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1850 = 2 \cdot 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1850.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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