LMFDB - Embedded newform 3150.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3150,2,Mod(1,3150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3150, 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("3150.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3150.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:	$25.1528766367$
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	$\chi$	$=$	3150.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})$

$q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{7} -1.00000 q^{8} -4.00000 q^{11} -3.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +7.00000 q^{17} -6.00000 q^{19} +4.00000 q^{22} +9.00000 q^{23} +3.00000 q^{26} -1.00000 q^{28} -3.00000 q^{29} -7.00000 q^{31} -1.00000 q^{32} -7.00000 q^{34} -10.0000 q^{37} +6.00000 q^{38} +1.00000 q^{41} +13.0000 q^{43} -4.00000 q^{44} -9.00000 q^{46} -2.00000 q^{47} +1.00000 q^{49} -3.00000 q^{52} -1.00000 q^{53} +1.00000 q^{56} +3.00000 q^{58} +11.0000 q^{59} +13.0000 q^{61} +7.00000 q^{62} +1.00000 q^{64} +7.00000 q^{68} -8.00000 q^{71} +8.00000 q^{73} +10.0000 q^{74} -6.00000 q^{76} +4.00000 q^{77} +4.00000 q^{79} -1.00000 q^{82} +7.00000 q^{83} -13.0000 q^{86} +4.00000 q^{88} +14.0000 q^{89} +3.00000 q^{91} +9.00000 q^{92} +2.00000 q^{94} +8.00000 q^{97} -1.00000 q^{98} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	0	0
$10$	0	0
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	0	0
$13$	−3.00000	−0.832050	−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000	−0.832050	−0.416025	+	0.909353i	$0.636577\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	7.00000	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$18$	0	0
$19$	−6.00000	−1.37649	−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000	−1.37649	−0.688247	+	0.725476i	$0.741620\pi$
$20$	0	0
$21$	0	0
$22$	4.00000	0.852803
$23$	9.00000	1.87663	0.938315	−	0.345782i	$-0.112386\pi$
$23$	9.00000	1.87663	0.938315	+	0.345782i	$0.112386\pi$
$24$	0	0
$25$	0	0
$26$	3.00000	0.588348
$27$	0	0
$28$	−1.00000	−0.188982
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−7.00000	−1.20049
$35$	0	0
$36$	0	0
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	6.00000	0.973329
$39$	0	0
$40$	0	0
$41$	1.00000	0.156174	0.0780869	−	0.996947i	$-0.475119\pi$
$41$	1.00000	0.156174	0.0780869	+	0.996947i	$0.475119\pi$
$42$	0	0
$43$	13.0000	1.98248	0.991241	−	0.132068i	$-0.0421616\pi$
$43$	13.0000	1.98248	0.991241	+	0.132068i	$0.0421616\pi$
$44$	−4.00000	−0.603023
$45$	0	0
$46$	−9.00000	−1.32698
$47$	−2.00000	−0.291730	−0.145865	−	0.989305i	$-0.546597\pi$
$47$	−2.00000	−0.291730	−0.145865	+	0.989305i	$0.546597\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	−3.00000	−0.416025
$53$	−1.00000	−0.137361	−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000	−0.137361	−0.0686803	+	0.997639i	$0.521879\pi$
$54$	0	0
$55$	0	0
$56$	1.00000	0.133631
$57$	0	0
$58$	3.00000	0.393919
$59$	11.0000	1.43208	0.716039	−	0.698060i	$-0.245953\pi$
$59$	11.0000	1.43208	0.716039	+	0.698060i	$0.245953\pi$
$60$	0	0
$61$	13.0000	1.66448	0.832240	−	0.554416i	$-0.187058\pi$
$61$	13.0000	1.66448	0.832240	+	0.554416i	$0.187058\pi$
$62$	7.00000	0.889001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	0	0
$67$	0	0		−	1.00000i	$-0.5\pi$
$67$	0	0			1.00000i	$0.5\pi$
$68$	7.00000	0.848875
$69$	0	0
$70$	0	0
$71$	−8.00000	−0.949425	−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000	−0.949425	−0.474713	+	0.880141i	$0.657448\pi$
$72$	0	0
$73$	8.00000	0.936329	0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000	0.936329	0.468165	+	0.883641i	$0.344915\pi$
$74$	10.0000	1.16248
$75$	0	0
$76$	−6.00000	−0.688247
$77$	4.00000	0.455842
$78$	0	0
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	0	0
$81$	0	0
$82$	−1.00000	−0.110432
$83$	7.00000	0.768350	0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000	0.768350	0.384175	+	0.923260i	$0.374486\pi$
$84$	0	0
$85$	0	0
$86$	−13.0000	−1.40183
$87$	0	0
$88$	4.00000	0.426401
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	0	0
$91$	3.00000	0.314485
$92$	9.00000	0.938315
$93$	0	0
$94$	2.00000	0.206284
$95$	0	0
$96$	0	0
$97$	8.00000	0.812277	0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000	0.812277	0.406138	+	0.913812i	$0.366875\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	0	0
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	0	0
$103$	−11.0000	−1.08386	−0.541931	−	0.840423i	$-0.682307\pi$
$103$	−11.0000	−1.08386	−0.541931	+	0.840423i	$0.682307\pi$
$104$	3.00000	0.294174
$105$	0	0
$106$	1.00000	0.0971286
$107$	−6.00000	−0.580042	−0.290021	−	0.957020i	$-0.593662\pi$
$107$	−6.00000	−0.580042	−0.290021	+	0.957020i	$0.593662\pi$
$108$	0	0
$109$	−6.00000	−0.574696	−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000	−0.574696	−0.287348	+	0.957826i	$0.592774\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	16.0000	1.50515	0.752577	−	0.658505i	$-0.228811\pi$
$113$	16.0000	1.50515	0.752577	+	0.658505i	$0.228811\pi$
$114$	0	0
$115$	0	0
$116$	−3.00000	−0.278543
$117$	0	0
$118$	−11.0000	−1.01263
$119$	−7.00000	−0.641689
$120$	0	0
$121$	5.00000	0.454545
$122$	−13.0000	−1.17696
$123$	0	0
$124$	−7.00000	−0.628619
$125$	0	0
$126$	0	0
$127$	−14.0000	−1.24230	−0.621150	−	0.783692i	$-0.713334\pi$
$127$	−14.0000	−1.24230	−0.621150	+	0.783692i	$0.713334\pi$
$128$	−1.00000	−0.0883883
$129$	0	0
$130$	0	0
$131$	−20.0000	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$132$	0	0
$133$	6.00000	0.520266
$134$	0	0
$135$	0	0
$136$	−7.00000	−0.600245
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	0	0
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	0	0
$141$	0	0
$142$	8.00000	0.671345
$143$	12.0000	1.00349
$144$	0	0
$145$	0	0
$146$	−8.00000	−0.662085
$147$	0	0
$148$	−10.0000	−0.821995
$149$	9.00000	0.737309	0.368654	−	0.929567i	$-0.379819\pi$
$149$	9.00000	0.737309	0.368654	+	0.929567i	$0.379819\pi$
$150$	0	0
$151$	2.00000	0.162758	0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000	0.162758	0.0813788	+	0.996683i	$0.474068\pi$
$152$	6.00000	0.486664
$153$	0	0
$154$	−4.00000	−0.322329
$155$	0	0
$156$	0	0
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	−4.00000	−0.318223
$159$	0	0
$160$	0	0
$161$	−9.00000	−0.709299
$162$	0	0
$163$	11.0000	0.861586	0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000	0.861586	0.430793	+	0.902451i	$0.358234\pi$
$164$	1.00000	0.0780869
$165$	0	0
$166$	−7.00000	−0.543305
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	0	0
$171$	0	0
$172$	13.0000	0.991241
$173$	10.0000	0.760286	0.380143	−	0.924928i	$-0.375875\pi$
$173$	10.0000	0.760286	0.380143	+	0.924928i	$0.375875\pi$
$174$	0	0
$175$	0	0
$176$	−4.00000	−0.301511
$177$	0	0
$178$	−14.0000	−1.04934
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	−3.00000	−0.222375
$183$	0	0
$184$	−9.00000	−0.663489
$185$	0	0
$186$	0	0
$187$	−28.0000	−2.04756
$188$	−2.00000	−0.145865
$189$	0	0
$190$	0	0
$191$	21.0000	1.51951	0.759753	−	0.650211i	$-0.225320\pi$
$191$	21.0000	1.51951	0.759753	+	0.650211i	$0.225320\pi$
$192$	0	0
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−8.00000	−0.574367
$195$	0	0
$196$	1.00000	0.0714286
$197$	−5.00000	−0.356235	−0.178118	−	0.984009i	$-0.557001\pi$
$197$	−5.00000	−0.356235	−0.178118	+	0.984009i	$0.557001\pi$
$198$	0	0
$199$	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
$201$	0	0
$202$	−6.00000	−0.422159
$203$	3.00000	0.210559
$204$	0	0
$205$	0	0
$206$	11.0000	0.766406
$207$	0	0
$208$	−3.00000	−0.208013
$209$	24.0000	1.66011
$210$	0	0
$211$	13.0000	0.894957	0.447478	−	0.894295i	$-0.352322\pi$
$211$	13.0000	0.894957	0.447478	+	0.894295i	$0.352322\pi$
$212$	−1.00000	−0.0686803
$213$	0	0
$214$	6.00000	0.410152
$215$	0	0
$216$	0	0
$217$	7.00000	0.475191
$218$	6.00000	0.406371
$219$	0	0
$220$	0	0
$221$	−21.0000	−1.41261
$222$	0	0
$223$	13.0000	0.870544	0.435272	−	0.900299i	$-0.356652\pi$
$223$	13.0000	0.870544	0.435272	+	0.900299i	$0.356652\pi$
$224$	1.00000	0.0668153
$225$	0	0
$226$	−16.0000	−1.06430
$227$	−11.0000	−0.730096	−0.365048	−	0.930989i	$-0.618947\pi$
$227$	−11.0000	−0.730096	−0.365048	+	0.930989i	$0.618947\pi$
$228$	0	0
$229$	22.0000	1.45380	0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000	1.45380	0.726900	+	0.686743i	$0.240960\pi$
$230$	0	0
$231$	0	0
$232$	3.00000	0.196960
$233$	18.0000	1.17922	0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000	1.17922	0.589610	+	0.807688i	$0.299282\pi$
$234$	0	0
$235$	0	0
$236$	11.0000	0.716039
$237$	0	0
$238$	7.00000	0.453743
$239$	8.00000	0.517477	0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000	0.517477	0.258738	+	0.965947i	$0.416693\pi$
$240$	0	0
$241$	22.0000	1.41714	0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000	1.41714	0.708572	+	0.705638i	$0.249340\pi$
$242$	−5.00000	−0.321412
$243$	0	0
$244$	13.0000	0.832240
$245$	0	0
$246$	0	0
$247$	18.0000	1.14531
$248$	7.00000	0.444500
$249$	0	0
$250$	0	0
$251$	−21.0000	−1.32551	−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000	−1.32551	−0.662754	+	0.748837i	$0.730613\pi$
$252$	0	0
$253$	−36.0000	−2.26330
$254$	14.0000	0.878438
$255$	0	0
$256$	1.00000	0.0625000
$257$	−17.0000	−1.06043	−0.530215	−	0.847863i	$-0.677889\pi$
$257$	−17.0000	−1.06043	−0.530215	+	0.847863i	$0.677889\pi$
$258$	0	0
$259$	10.0000	0.621370
$260$	0	0
$261$	0	0
$262$	20.0000	1.23560
$263$	13.0000	0.801614	0.400807	−	0.916162i	$-0.368730\pi$
$263$	13.0000	0.801614	0.400807	+	0.916162i	$0.368730\pi$
$264$	0	0
$265$	0	0
$266$	−6.00000	−0.367884
$267$	0	0
$268$	0	0
$269$	−6.00000	−0.365826	−0.182913	−	0.983129i	$-0.558553\pi$
$269$	−6.00000	−0.365826	−0.182913	+	0.983129i	$0.558553\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	7.00000	0.424437
$273$	0	0
$274$	−12.0000	−0.724947
$275$	0	0
$276$	0	0
$277$	12.0000	0.721010	0.360505	−	0.932757i	$-0.382604\pi$
$277$	12.0000	0.721010	0.360505	+	0.932757i	$0.382604\pi$
$278$	8.00000	0.479808
$279$	0	0
$280$	0	0
$281$	−32.0000	−1.90896	−0.954480	−	0.298275i	$-0.903589\pi$
$281$	−32.0000	−1.90896	−0.954480	+	0.298275i	$0.903589\pi$
$282$	0	0
$283$	14.0000	0.832214	0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000	0.832214	0.416107	+	0.909316i	$0.363394\pi$
$284$	−8.00000	−0.474713
$285$	0	0
$286$	−12.0000	−0.709575
$287$	−1.00000	−0.0590281
$288$	0	0
$289$	32.0000	1.88235
$290$	0	0
$291$	0	0
$292$	8.00000	0.468165
$293$	−28.0000	−1.63578	−0.817889	−	0.575376i	$-0.804856\pi$
$293$	−28.0000	−1.63578	−0.817889	+	0.575376i	$0.804856\pi$
$294$	0	0
$295$	0	0
$296$	10.0000	0.581238
$297$	0	0
$298$	−9.00000	−0.521356
$299$	−27.0000	−1.56145
$300$	0	0
$301$	−13.0000	−0.749308
$302$	−2.00000	−0.115087
$303$	0	0
$304$	−6.00000	−0.344124
$305$	0	0
$306$	0	0
$307$	−2.00000	−0.114146	−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000	−0.114146	−0.0570730	+	0.998370i	$0.518177\pi$
$308$	4.00000	0.227921
$309$	0	0
$310$	0	0
$311$	30.0000	1.70114	0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000	1.70114	0.850572	+	0.525859i	$0.176256\pi$
$312$	0	0
$313$	−16.0000	−0.904373	−0.452187	−	0.891923i	$-0.649356\pi$
$313$	−16.0000	−0.904373	−0.452187	+	0.891923i	$0.649356\pi$
$314$	2.00000	0.112867
$315$	0	0
$316$	4.00000	0.225018
$317$	11.0000	0.617822	0.308911	−	0.951091i	$-0.400036\pi$
$317$	11.0000	0.617822	0.308911	+	0.951091i	$0.400036\pi$
$318$	0	0
$319$	12.0000	0.671871
$320$	0	0
$321$	0	0
$322$	9.00000	0.501550
$323$	−42.0000	−2.33694
$324$	0	0
$325$	0	0
$326$	−11.0000	−0.609234
$327$	0	0
$328$	−1.00000	−0.0552158
$329$	2.00000	0.110264
$330$	0	0
$331$	−5.00000	−0.274825	−0.137412	−	0.990514i	$-0.543879\pi$
$331$	−5.00000	−0.274825	−0.137412	+	0.990514i	$0.543879\pi$
$332$	7.00000	0.384175
$333$	0	0
$334$	−12.0000	−0.656611
$335$	0	0
$336$	0	0
$337$	−5.00000	−0.272367	−0.136184	−	0.990684i	$-0.543484\pi$
$337$	−5.00000	−0.272367	−0.136184	+	0.990684i	$0.543484\pi$
$338$	4.00000	0.217571
$339$	0	0
$340$	0	0
$341$	28.0000	1.51629
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−13.0000	−0.700913
$345$	0	0
$346$	−10.0000	−0.537603
$347$	32.0000	1.71785	0.858925	−	0.512101i	$-0.171133\pi$
$347$	32.0000	1.71785	0.858925	+	0.512101i	$0.171133\pi$
$348$	0	0
$349$	19.0000	1.01705	0.508523	−	0.861048i	$-0.330192\pi$
$349$	19.0000	1.01705	0.508523	+	0.861048i	$0.330192\pi$
$350$	0	0
$351$	0	0
$352$	4.00000	0.213201
$353$	30.0000	1.59674	0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000	1.59674	0.798369	+	0.602168i	$0.205696\pi$
$354$	0	0
$355$	0	0
$356$	14.0000	0.741999
$357$	0	0
$358$	−6.00000	−0.317110
$359$	−11.0000	−0.580558	−0.290279	−	0.956942i	$-0.593748\pi$
$359$	−11.0000	−0.580558	−0.290279	+	0.956942i	$0.593748\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	2.00000	0.105118
$363$	0	0
$364$	3.00000	0.157243
$365$	0	0
$366$	0	0
$367$	−17.0000	−0.887393	−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000	−0.887393	−0.443696	+	0.896177i	$0.646333\pi$
$368$	9.00000	0.469157
$369$	0	0
$370$	0	0
$371$	1.00000	0.0519174
$372$	0	0
$373$	14.0000	0.724893	0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000	0.724893	0.362446	+	0.932005i	$0.381942\pi$
$374$	28.0000	1.44785
$375$	0	0
$376$	2.00000	0.103142
$377$	9.00000	0.463524
$378$	0	0
$379$	−15.0000	−0.770498	−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000	−0.770498	−0.385249	+	0.922813i	$0.625884\pi$
$380$	0	0
$381$	0	0
$382$	−21.0000	−1.07445
$383$	0	0		−	1.00000i	$-0.5\pi$
$383$	0	0			1.00000i	$0.5\pi$
$384$	0	0
$385$	0	0
$386$	−14.0000	−0.712581
$387$	0	0
$388$	8.00000	0.406138
$389$	−26.0000	−1.31825	−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000	−1.31825	−0.659126	+	0.752032i	$0.729074\pi$
$390$	0	0
$391$	63.0000	3.18605
$392$	−1.00000	−0.0505076
$393$	0	0
$394$	5.00000	0.251896
$395$	0	0
$396$	0	0
$397$	19.0000	0.953583	0.476791	−	0.879017i	$-0.341800\pi$
$397$	19.0000	0.953583	0.476791	+	0.879017i	$0.341800\pi$
$398$	−8.00000	−0.401004
$399$	0	0
$400$	0	0
$401$	−4.00000	−0.199750	−0.0998752	−	0.995000i	$-0.531844\pi$
$401$	−4.00000	−0.199750	−0.0998752	+	0.995000i	$0.531844\pi$
$402$	0	0
$403$	21.0000	1.04608
$404$	6.00000	0.298511
$405$	0	0
$406$	−3.00000	−0.148888
$407$	40.0000	1.98273
$408$	0	0
$409$	0	0		−	1.00000i	$-0.5\pi$
$409$	0	0			1.00000i	$0.5\pi$
$410$	0	0
$411$	0	0
$412$	−11.0000	−0.541931
$413$	−11.0000	−0.541275
$414$	0	0
$415$	0	0
$416$	3.00000	0.147087
$417$	0	0
$418$	−24.0000	−1.17388
$419$	9.00000	0.439679	0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000	0.439679	0.219839	+	0.975536i	$0.429447\pi$
$420$	0	0
$421$	8.00000	0.389896	0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000	0.389896	0.194948	+	0.980814i	$0.437546\pi$
$422$	−13.0000	−0.632830
$423$	0	0
$424$	1.00000	0.0485643
$425$	0	0
$426$	0	0
$427$	−13.0000	−0.629114
$428$	−6.00000	−0.290021
$429$	0	0
$430$	0	0
$431$	21.0000	1.01153	0.505767	−	0.862670i	$-0.331209\pi$
$431$	21.0000	1.01153	0.505767	+	0.862670i	$0.331209\pi$
$432$	0	0
$433$	2.00000	0.0961139	0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000	0.0961139	0.0480569	+	0.998845i	$0.484697\pi$
$434$	−7.00000	−0.336011
$435$	0	0
$436$	−6.00000	−0.287348
$437$	−54.0000	−2.58317
$438$	0	0
$439$	−35.0000	−1.67046	−0.835229	−	0.549902i	$-0.814665\pi$
$439$	−35.0000	−1.67046	−0.835229	+	0.549902i	$0.814665\pi$
$440$	0	0
$441$	0	0
$442$	21.0000	0.998868
$443$	2.00000	0.0950229	0.0475114	−	0.998871i	$-0.484871\pi$
$443$	2.00000	0.0950229	0.0475114	+	0.998871i	$0.484871\pi$
$444$	0	0
$445$	0	0
$446$	−13.0000	−0.615568
$447$	0	0
$448$	−1.00000	−0.0472456
$449$	−30.0000	−1.41579	−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000	−1.41579	−0.707894	+	0.706319i	$0.750354\pi$
$450$	0	0
$451$	−4.00000	−0.188353
$452$	16.0000	0.752577
$453$	0	0
$454$	11.0000	0.516256
$455$	0	0
$456$	0	0
$457$	−17.0000	−0.795226	−0.397613	−	0.917553i	$-0.630161\pi$
$457$	−17.0000	−0.795226	−0.397613	+	0.917553i	$0.630161\pi$
$458$	−22.0000	−1.02799
$459$	0	0
$460$	0	0
$461$	14.0000	0.652045	0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000	0.652045	0.326023	+	0.945362i	$0.394291\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	−18.0000	−0.833834
$467$	−5.00000	−0.231372	−0.115686	−	0.993286i	$-0.536907\pi$
$467$	−5.00000	−0.231372	−0.115686	+	0.993286i	$0.536907\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	0	0
$472$	−11.0000	−0.506316
$473$	−52.0000	−2.39096
$474$	0	0
$475$	0	0
$476$	−7.00000	−0.320844
$477$	0	0
$478$	−8.00000	−0.365911
$479$	30.0000	1.37073	0.685367	−	0.728197i	$-0.259642\pi$
$479$	30.0000	1.37073	0.685367	+	0.728197i	$0.259642\pi$
$480$	0	0
$481$	30.0000	1.36788
$482$	−22.0000	−1.00207
$483$	0	0
$484$	5.00000	0.227273
$485$	0	0
$486$	0	0
$487$	−4.00000	−0.181257	−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000	−0.181257	−0.0906287	+	0.995885i	$0.528888\pi$
$488$	−13.0000	−0.588482
$489$	0	0
$490$	0	0
$491$	−6.00000	−0.270776	−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000	−0.270776	−0.135388	+	0.990793i	$0.543228\pi$
$492$	0	0
$493$	−21.0000	−0.945792
$494$	−18.0000	−0.809858
$495$	0	0
$496$	−7.00000	−0.314309
$497$	8.00000	0.358849
$498$	0	0
$499$	−21.0000	−0.940089	−0.470045	−	0.882643i	$-0.655762\pi$
$499$	−21.0000	−0.940089	−0.470045	+	0.882643i	$0.655762\pi$
$500$	0	0
$501$	0	0
$502$	21.0000	0.937276
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	0	0
$506$	36.0000	1.60040
$507$	0	0
$508$	−14.0000	−0.621150
$509$	26.0000	1.15243	0.576215	−	0.817298i	$-0.304529\pi$
$509$	26.0000	1.15243	0.576215	+	0.817298i	$0.304529\pi$
$510$	0	0
$511$	−8.00000	−0.353899
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	17.0000	0.749838
$515$	0	0
$516$	0	0
$517$	8.00000	0.351840
$518$	−10.0000	−0.439375
$519$	0	0
$520$	0	0
$521$	43.0000	1.88386	0.941932	−	0.335803i	$-0.109008\pi$
$521$	43.0000	1.88386	0.941932	+	0.335803i	$0.109008\pi$
$522$	0	0
$523$	−14.0000	−0.612177	−0.306089	−	0.952003i	$-0.599020\pi$
$523$	−14.0000	−0.612177	−0.306089	+	0.952003i	$0.599020\pi$
$524$	−20.0000	−0.873704
$525$	0	0
$526$	−13.0000	−0.566827
$527$	−49.0000	−2.13447
$528$	0	0
$529$	58.0000	2.52174
$530$	0	0
$531$	0	0
$532$	6.00000	0.260133
$533$	−3.00000	−0.129944
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	6.00000	0.258678
$539$	−4.00000	−0.172292
$540$	0	0
$541$	−42.0000	−1.80572	−0.902861	−	0.429934i	$-0.858537\pi$
$541$	−42.0000	−1.80572	−0.902861	+	0.429934i	$0.858537\pi$
$542$	0	0
$543$	0	0
$544$	−7.00000	−0.300123
$545$	0	0
$546$	0	0
$547$	−9.00000	−0.384812	−0.192406	−	0.981315i	$-0.561629\pi$
$547$	−9.00000	−0.384812	−0.192406	+	0.981315i	$0.561629\pi$
$548$	12.0000	0.512615
$549$	0	0
$550$	0	0
$551$	18.0000	0.766826
$552$	0	0
$553$	−4.00000	−0.170097
$554$	−12.0000	−0.509831
$555$	0	0
$556$	−8.00000	−0.339276
$557$	2.00000	0.0847427	0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000	0.0847427	0.0423714	+	0.999102i	$0.486509\pi$
$558$	0	0
$559$	−39.0000	−1.64952
$560$	0	0
$561$	0	0
$562$	32.0000	1.34984
$563$	19.0000	0.800755	0.400377	−	0.916350i	$-0.368879\pi$
$563$	19.0000	0.800755	0.400377	+	0.916350i	$0.368879\pi$
$564$	0	0
$565$	0	0
$566$	−14.0000	−0.588464
$567$	0	0
$568$	8.00000	0.335673
$569$	−24.0000	−1.00613	−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000	−1.00613	−0.503066	+	0.864248i	$0.667795\pi$
$570$	0	0
$571$	−39.0000	−1.63210	−0.816050	−	0.577982i	$-0.803840\pi$
$571$	−39.0000	−1.63210	−0.816050	+	0.577982i	$0.803840\pi$
$572$	12.0000	0.501745
$573$	0	0
$574$	1.00000	0.0417392
$575$	0	0
$576$	0	0
$577$	46.0000	1.91501	0.957503	−	0.288425i	$-0.0931316\pi$
$577$	46.0000	1.91501	0.957503	+	0.288425i	$0.0931316\pi$
$578$	−32.0000	−1.33102
$579$	0	0
$580$	0	0
$581$	−7.00000	−0.290409
$582$	0	0
$583$	4.00000	0.165663
$584$	−8.00000	−0.331042
$585$	0	0
$586$	28.0000	1.15667
$587$	7.00000	0.288921	0.144460	−	0.989511i	$-0.453855\pi$
$587$	7.00000	0.288921	0.144460	+	0.989511i	$0.453855\pi$
$588$	0	0
$589$	42.0000	1.73058
$590$	0	0
$591$	0	0
$592$	−10.0000	−0.410997
$593$	18.0000	0.739171	0.369586	−	0.929197i	$-0.379500\pi$
$593$	18.0000	0.739171	0.369586	+	0.929197i	$0.379500\pi$
$594$	0	0
$595$	0	0
$596$	9.00000	0.368654
$597$	0	0
$598$	27.0000	1.10411
$599$	21.0000	0.858037	0.429018	−	0.903296i	$-0.358860\pi$
$599$	21.0000	0.858037	0.429018	+	0.903296i	$0.358860\pi$
$600$	0	0
$601$	30.0000	1.22373	0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000	1.22373	0.611863	+	0.790964i	$0.290420\pi$
$602$	13.0000	0.529840
$603$	0	0
$604$	2.00000	0.0813788
$605$	0	0
$606$	0	0
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	6.00000	0.243332
$609$	0	0
$610$	0	0
$611$	6.00000	0.242734
$612$	0	0
$613$	42.0000	1.69636	0.848182	−	0.529705i	$-0.177697\pi$
$613$	42.0000	1.69636	0.848182	+	0.529705i	$0.177697\pi$
$614$	2.00000	0.0807134
$615$	0	0
$616$	−4.00000	−0.161165
$617$	−26.0000	−1.04672	−0.523360	−	0.852111i	$-0.675322\pi$
$617$	−26.0000	−1.04672	−0.523360	+	0.852111i	$0.675322\pi$
$618$	0	0
$619$	14.0000	0.562708	0.281354	−	0.959604i	$-0.409217\pi$
$619$	14.0000	0.562708	0.281354	+	0.959604i	$0.409217\pi$
$620$	0	0
$621$	0	0
$622$	−30.0000	−1.20289
$623$	−14.0000	−0.560898
$624$	0	0
$625$	0	0
$626$	16.0000	0.639489
$627$	0	0
$628$	−2.00000	−0.0798087
$629$	−70.0000	−2.79108
$630$	0	0
$631$	−22.0000	−0.875806	−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000	−0.875806	−0.437903	+	0.899022i	$0.644279\pi$
$632$	−4.00000	−0.159111
$633$	0	0
$634$	−11.0000	−0.436866
$635$	0	0
$636$	0	0
$637$	−3.00000	−0.118864
$638$	−12.0000	−0.475085
$639$	0	0
$640$	0	0
$641$	−14.0000	−0.552967	−0.276483	−	0.961019i	$-0.589169\pi$
$641$	−14.0000	−0.552967	−0.276483	+	0.961019i	$0.589169\pi$
$642$	0	0
$643$	−8.00000	−0.315489	−0.157745	−	0.987480i	$-0.550422\pi$
$643$	−8.00000	−0.315489	−0.157745	+	0.987480i	$0.550422\pi$
$644$	−9.00000	−0.354650
$645$	0	0
$646$	42.0000	1.65247
$647$	−28.0000	−1.10079	−0.550397	−	0.834903i	$-0.685524\pi$
$647$	−28.0000	−1.10079	−0.550397	+	0.834903i	$0.685524\pi$
$648$	0	0
$649$	−44.0000	−1.72715
$650$	0	0
$651$	0	0
$652$	11.0000	0.430793
$653$	−14.0000	−0.547862	−0.273931	−	0.961749i	$-0.588324\pi$
$653$	−14.0000	−0.547862	−0.273931	+	0.961749i	$0.588324\pi$
$654$	0	0
$655$	0	0
$656$	1.00000	0.0390434
$657$	0	0
$658$	−2.00000	−0.0779681
$659$	−16.0000	−0.623272	−0.311636	−	0.950202i	$-0.600877\pi$
$659$	−16.0000	−0.623272	−0.311636	+	0.950202i	$0.600877\pi$
$660$	0	0
$661$	−2.00000	−0.0777910	−0.0388955	−	0.999243i	$-0.512384\pi$
$661$	−2.00000	−0.0777910	−0.0388955	+	0.999243i	$0.512384\pi$
$662$	5.00000	0.194331
$663$	0	0
$664$	−7.00000	−0.271653
$665$	0	0
$666$	0	0
$667$	−27.0000	−1.04544
$668$	12.0000	0.464294
$669$	0	0
$670$	0	0
$671$	−52.0000	−2.00744
$672$	0	0
$673$	31.0000	1.19496	0.597481	−	0.801883i	$-0.296168\pi$
$673$	31.0000	1.19496	0.597481	+	0.801883i	$0.296168\pi$
$674$	5.00000	0.192593
$675$	0	0
$676$	−4.00000	−0.153846
$677$	18.0000	0.691796	0.345898	−	0.938272i	$-0.387574\pi$
$677$	18.0000	0.691796	0.345898	+	0.938272i	$0.387574\pi$
$678$	0	0
$679$	−8.00000	−0.307012
$680$	0	0
$681$	0	0
$682$	−28.0000	−1.07218
$683$	−38.0000	−1.45403	−0.727015	−	0.686622i	$-0.759093\pi$
$683$	−38.0000	−1.45403	−0.727015	+	0.686622i	$0.759093\pi$
$684$	0	0
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	13.0000	0.495620
$689$	3.00000	0.114291
$690$	0	0
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	10.0000	0.380143
$693$	0	0
$694$	−32.0000	−1.21470
$695$	0	0
$696$	0	0
$697$	7.00000	0.265144
$698$	−19.0000	−0.719161
$699$	0	0
$700$	0	0
$701$	−7.00000	−0.264386	−0.132193	−	0.991224i	$-0.542202\pi$
$701$	−7.00000	−0.264386	−0.132193	+	0.991224i	$0.542202\pi$
$702$	0	0
$703$	60.0000	2.26294
$704$	−4.00000	−0.150756
$705$	0	0
$706$	−30.0000	−1.12906
$707$	−6.00000	−0.225653
$708$	0	0
$709$	28.0000	1.05156	0.525781	−	0.850620i	$-0.323773\pi$
$709$	28.0000	1.05156	0.525781	+	0.850620i	$0.323773\pi$
$710$	0	0
$711$	0	0
$712$	−14.0000	−0.524672
$713$	−63.0000	−2.35937
$714$	0	0
$715$	0	0
$716$	6.00000	0.224231
$717$	0	0
$718$	11.0000	0.410516
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	11.0000	0.409661
$722$	−17.0000	−0.632674
$723$	0	0
$724$	−2.00000	−0.0743294
$725$	0	0
$726$	0	0
$727$	−3.00000	−0.111264	−0.0556319	−	0.998451i	$-0.517717\pi$
$727$	−3.00000	−0.111264	−0.0556319	+	0.998451i	$0.517717\pi$
$728$	−3.00000	−0.111187
$729$	0	0
$730$	0	0
$731$	91.0000	3.36576
$732$	0	0
$733$	−41.0000	−1.51437	−0.757185	−	0.653201i	$-0.773426\pi$
$733$	−41.0000	−1.51437	−0.757185	+	0.653201i	$0.773426\pi$
$734$	17.0000	0.627481
$735$	0	0
$736$	−9.00000	−0.331744
$737$	0	0
$738$	0	0
$739$	−47.0000	−1.72892	−0.864461	−	0.502699i	$-0.832340\pi$
$739$	−47.0000	−1.72892	−0.864461	+	0.502699i	$0.832340\pi$
$740$	0	0
$741$	0	0
$742$	−1.00000	−0.0367112
$743$	−45.0000	−1.65089	−0.825445	−	0.564483i	$-0.809076\pi$
$743$	−45.0000	−1.65089	−0.825445	+	0.564483i	$0.809076\pi$
$744$	0	0
$745$	0	0
$746$	−14.0000	−0.512576
$747$	0	0
$748$	−28.0000	−1.02378
$749$	6.00000	0.219235
$750$	0	0
$751$	−10.0000	−0.364905	−0.182453	−	0.983215i	$-0.558404\pi$
$751$	−10.0000	−0.364905	−0.182453	+	0.983215i	$0.558404\pi$
$752$	−2.00000	−0.0729325
$753$	0	0
$754$	−9.00000	−0.327761
$755$	0	0
$756$	0	0
$757$	−20.0000	−0.726912	−0.363456	−	0.931611i	$-0.618403\pi$
$757$	−20.0000	−0.726912	−0.363456	+	0.931611i	$0.618403\pi$
$758$	15.0000	0.544825
$759$	0	0
$760$	0	0
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	0	0
$763$	6.00000	0.217215
$764$	21.0000	0.759753
$765$	0	0
$766$	0	0
$767$	−33.0000	−1.19156
$768$	0	0
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	0	0
$771$	0	0
$772$	14.0000	0.503871
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	0	0
$775$	0	0
$776$	−8.00000	−0.287183
$777$	0	0
$778$	26.0000	0.932145
$779$	−6.00000	−0.214972
$780$	0	0
$781$	32.0000	1.14505
$782$	−63.0000	−2.25288
$783$	0	0
$784$	1.00000	0.0357143
$785$	0	0
$786$	0	0
$787$	22.0000	0.784215	0.392108	−	0.919919i	$-0.371746\pi$
$787$	22.0000	0.784215	0.392108	+	0.919919i	$0.371746\pi$
$788$	−5.00000	−0.178118
$789$	0	0
$790$	0	0
$791$	−16.0000	−0.568895
$792$	0	0
$793$	−39.0000	−1.38493
$794$	−19.0000	−0.674285
$795$	0	0
$796$	8.00000	0.283552
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	0	0
$799$	−14.0000	−0.495284
$800$	0	0
$801$	0	0
$802$	4.00000	0.141245
$803$	−32.0000	−1.12926
$804$	0	0
$805$	0	0
$806$	−21.0000	−0.739693
$807$	0	0
$808$	−6.00000	−0.211079
$809$	−18.0000	−0.632846	−0.316423	−	0.948618i	$-0.602482\pi$
$809$	−18.0000	−0.632846	−0.316423	+	0.948618i	$0.602482\pi$
$810$	0	0
$811$	−40.0000	−1.40459	−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000	−1.40459	−0.702295	+	0.711886i	$0.747841\pi$
$812$	3.00000	0.105279
$813$	0	0
$814$	−40.0000	−1.40200
$815$	0	0
$816$	0	0
$817$	−78.0000	−2.72887
$818$	0	0
$819$	0	0
$820$	0	0
$821$	18.0000	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$822$	0	0
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	11.0000	0.383203
$825$	0	0
$826$	11.0000	0.382739
$827$	34.0000	1.18230	0.591148	−	0.806563i	$-0.298675\pi$
$827$	34.0000	1.18230	0.591148	+	0.806563i	$0.298675\pi$
$828$	0	0
$829$	−25.0000	−0.868286	−0.434143	−	0.900844i	$-0.642949\pi$
$829$	−25.0000	−0.868286	−0.434143	+	0.900844i	$0.642949\pi$
$830$	0	0
$831$	0	0
$832$	−3.00000	−0.104006
$833$	7.00000	0.242536
$834$	0	0
$835$	0	0
$836$	24.0000	0.830057
$837$	0	0
$838$	−9.00000	−0.310900
$839$	−32.0000	−1.10476	−0.552381	−	0.833592i	$-0.686281\pi$
$839$	−32.0000	−1.10476	−0.552381	+	0.833592i	$0.686281\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	−8.00000	−0.275698
$843$	0	0
$844$	13.0000	0.447478
$845$	0	0
$846$	0	0
$847$	−5.00000	−0.171802
$848$	−1.00000	−0.0343401
$849$	0	0
$850$	0	0
$851$	−90.0000	−3.08516
$852$	0	0
$853$	−13.0000	−0.445112	−0.222556	−	0.974920i	$-0.571440\pi$
$853$	−13.0000	−0.445112	−0.222556	+	0.974920i	$0.571440\pi$
$854$	13.0000	0.444851
$855$	0	0
$856$	6.00000	0.205076
$857$	−6.00000	−0.204956	−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000	−0.204956	−0.102478	+	0.994735i	$0.532677\pi$
$858$	0	0
$859$	36.0000	1.22830	0.614152	−	0.789188i	$-0.289498\pi$
$859$	36.0000	1.22830	0.614152	+	0.789188i	$0.289498\pi$
$860$	0	0
$861$	0	0
$862$	−21.0000	−0.715263
$863$	−28.0000	−0.953131	−0.476566	−	0.879139i	$-0.658119\pi$
$863$	−28.0000	−0.953131	−0.476566	+	0.879139i	$0.658119\pi$
$864$	0	0
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	0	0
$868$	7.00000	0.237595
$869$	−16.0000	−0.542763
$870$	0	0
$871$	0	0
$872$	6.00000	0.203186
$873$	0	0
$874$	54.0000	1.82658
$875$	0	0
$876$	0	0
$877$	8.00000	0.270141	0.135070	−	0.990836i	$-0.456874\pi$
$877$	8.00000	0.270141	0.135070	+	0.990836i	$0.456874\pi$
$878$	35.0000	1.18119
$879$	0	0
$880$	0	0
$881$	13.0000	0.437981	0.218991	−	0.975727i	$-0.429724\pi$
$881$	13.0000	0.437981	0.218991	+	0.975727i	$0.429724\pi$
$882$	0	0
$883$	−21.0000	−0.706706	−0.353353	−	0.935490i	$-0.614959\pi$
$883$	−21.0000	−0.706706	−0.353353	+	0.935490i	$0.614959\pi$
$884$	−21.0000	−0.706306
$885$	0	0
$886$	−2.00000	−0.0671913
$887$	−38.0000	−1.27592	−0.637958	−	0.770072i	$-0.720220\pi$
$887$	−38.0000	−1.27592	−0.637958	+	0.770072i	$0.720220\pi$
$888$	0	0
$889$	14.0000	0.469545
$890$	0	0
$891$	0	0
$892$	13.0000	0.435272
$893$	12.0000	0.401565
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	0	0
$898$	30.0000	1.00111
$899$	21.0000	0.700389
$900$	0	0
$901$	−7.00000	−0.233204
$902$	4.00000	0.133185
$903$	0	0
$904$	−16.0000	−0.532152
$905$	0	0
$906$	0	0
$907$	47.0000	1.56061	0.780305	−	0.625400i	$-0.215064\pi$
$907$	47.0000	1.56061	0.780305	+	0.625400i	$0.215064\pi$
$908$	−11.0000	−0.365048
$909$	0	0
$910$	0	0
$911$	−21.0000	−0.695761	−0.347881	−	0.937539i	$-0.613099\pi$
$911$	−21.0000	−0.695761	−0.347881	+	0.937539i	$0.613099\pi$
$912$	0	0
$913$	−28.0000	−0.926665
$914$	17.0000	0.562310
$915$	0	0
$916$	22.0000	0.726900
$917$	20.0000	0.660458
$918$	0	0
$919$	−10.0000	−0.329870	−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000	−0.329870	−0.164935	+	0.986304i	$0.552741\pi$
$920$	0	0
$921$	0	0
$922$	−14.0000	−0.461065
$923$	24.0000	0.789970
$924$	0	0
$925$	0	0
$926$	16.0000	0.525793
$927$	0	0
$928$	3.00000	0.0984798
$929$	−31.0000	−1.01708	−0.508539	−	0.861039i	$-0.669814\pi$
$929$	−31.0000	−1.01708	−0.508539	+	0.861039i	$0.669814\pi$
$930$	0	0
$931$	−6.00000	−0.196642
$932$	18.0000	0.589610
$933$	0	0
$934$	5.00000	0.163605
$935$	0	0
$936$	0	0
$937$	38.0000	1.24141	0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000	1.24141	0.620703	+	0.784046i	$0.286847\pi$
$938$	0	0
$939$	0	0
$940$	0	0
$941$	40.0000	1.30396	0.651981	−	0.758235i	$-0.273938\pi$
$941$	40.0000	1.30396	0.651981	+	0.758235i	$0.273938\pi$
$942$	0	0
$943$	9.00000	0.293080
$944$	11.0000	0.358020
$945$	0	0
$946$	52.0000	1.69067
$947$	−2.00000	−0.0649913	−0.0324956	−	0.999472i	$-0.510346\pi$
$947$	−2.00000	−0.0649913	−0.0324956	+	0.999472i	$0.510346\pi$
$948$	0	0
$949$	−24.0000	−0.779073
$950$	0	0
$951$	0	0
$952$	7.00000	0.226871
$953$	−12.0000	−0.388718	−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000	−0.388718	−0.194359	+	0.980930i	$0.562263\pi$
$954$	0	0
$955$	0	0
$956$	8.00000	0.258738
$957$	0	0
$958$	−30.0000	−0.969256
$959$	−12.0000	−0.387500
$960$	0	0
$961$	18.0000	0.580645
$962$	−30.0000	−0.967239
$963$	0	0
$964$	22.0000	0.708572
$965$	0	0
$966$	0	0
$967$	−26.0000	−0.836104	−0.418052	−	0.908423i	$-0.637287\pi$
$967$	−26.0000	−0.836104	−0.418052	+	0.908423i	$0.637287\pi$
$968$	−5.00000	−0.160706
$969$	0	0
$970$	0	0
$971$	36.0000	1.15529	0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000	1.15529	0.577647	+	0.816286i	$0.303971\pi$
$972$	0	0
$973$	8.00000	0.256468
$974$	4.00000	0.128168
$975$	0	0
$976$	13.0000	0.416120
$977$	−30.0000	−0.959785	−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000	−0.959785	−0.479893	+	0.877327i	$0.659324\pi$
$978$	0	0
$979$	−56.0000	−1.78977
$980$	0	0
$981$	0	0
$982$	6.00000	0.191468
$983$	4.00000	0.127580	0.0637901	−	0.997963i	$-0.479681\pi$
$983$	4.00000	0.127580	0.0637901	+	0.997963i	$0.479681\pi$
$984$	0	0
$985$	0	0
$986$	21.0000	0.668776
$987$	0	0
$988$	18.0000	0.572656
$989$	117.000	3.72038
$990$	0	0
$991$	−26.0000	−0.825917	−0.412959	−	0.910750i	$-0.635505\pi$
$991$	−26.0000	−0.825917	−0.412959	+	0.910750i	$0.635505\pi$
$992$	7.00000	0.222250
$993$	0	0
$994$	−8.00000	−0.253745
$995$	0	0
$996$	0	0
$997$	14.0000	0.443384	0.221692	−	0.975117i	$-0.428842\pi$
$997$	14.0000	0.443384	0.221692	+	0.975117i	$0.428842\pi$
$998$	21.0000	0.664743
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3150.2.a.b.1.1	✓	1
3.2	odd	2		3150.2.a.bf.1.1	yes	1
5.2	odd	4		3150.2.g.d.2899.1		2
5.3	odd	4		3150.2.g.d.2899.2		2
5.4	even	2		3150.2.a.bi.1.1	yes	1
15.2	even	4		3150.2.g.u.2899.2		2
15.8	even	4		3150.2.g.u.2899.1		2
15.14	odd	2		3150.2.a.u.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3150.2.a.b.1.1	✓	1	1.1	even	1	trivial
3150.2.a.u.1.1	yes	1	15.14	odd	2
3150.2.a.bf.1.1	yes	1	3.2	odd	2
3150.2.a.bi.1.1	yes	1	5.4	even	2
3150.2.g.d.2899.1		2	5.2	odd	4
3150.2.g.d.2899.2		2	5.3	odd	4
3150.2.g.u.2899.1		2	15.8	even	4
3150.2.g.u.2899.2		2	15.2	even	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:	\( N \)	\(=\)	\( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3150.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more