LMFDB - Embedded newform 4025.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4025,2,Mod(1,4025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4025, 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("4025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4025 = 5^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4025.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:	$32.1397868136$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{7} -3.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{2} -1.00000 q^{4} +1.00000 q^{7} -3.00000 q^{8} -3.00000 q^{9} -4.00000 q^{11} +2.00000 q^{13} +1.00000 q^{14} -1.00000 q^{16} -6.00000 q^{17} -3.00000 q^{18} +4.00000 q^{19} -4.00000 q^{22} -1.00000 q^{23} +2.00000 q^{26} -1.00000 q^{28} -2.00000 q^{29} +4.00000 q^{31} +5.00000 q^{32} -6.00000 q^{34} +3.00000 q^{36} +10.0000 q^{37} +4.00000 q^{38} +10.0000 q^{41} -12.0000 q^{43} +4.00000 q^{44} -1.00000 q^{46} +12.0000 q^{47} +1.00000 q^{49} -2.00000 q^{52} -14.0000 q^{53} -3.00000 q^{56} -2.00000 q^{58} +8.00000 q^{59} +10.0000 q^{61} +4.00000 q^{62} -3.00000 q^{63} +7.00000 q^{64} +4.00000 q^{67} +6.00000 q^{68} +8.00000 q^{71} +9.00000 q^{72} +6.00000 q^{73} +10.0000 q^{74} -4.00000 q^{76} -4.00000 q^{77} +9.00000 q^{81} +10.0000 q^{82} -12.0000 q^{83} -12.0000 q^{86} +12.0000 q^{88} -2.00000 q^{89} +2.00000 q^{91} +1.00000 q^{92} +12.0000 q^{94} +2.00000 q^{97} +1.00000 q^{98} +12.0000 q^{99} +O(q^{100})$

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	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.00000	−1.06066
$9$	−3.00000	−1.00000
$10$	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
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	1.00000	0.267261
$15$	0	0
$16$	−1.00000	−0.250000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	−3.00000	−0.707107
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	0	0
$21$	0	0
$22$	−4.00000	−0.852803
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0	0
$25$	0	0
$26$	2.00000	0.392232
$27$	0	0
$28$	−1.00000	−0.188982
$29$	−2.00000	−0.371391	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000	−0.371391	−0.185695	+	0.982607i	$0.559454\pi$
$30$	0	0
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	−6.00000	−1.02899
$35$	0	0
$36$	3.00000	0.500000
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	4.00000	0.648886
$39$	0	0
$40$	0	0
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	0	0
$43$	−12.0000	−1.82998	−0.914991	−	0.403473i	$-0.867803\pi$
$43$	−12.0000	−1.82998	−0.914991	+	0.403473i	$0.867803\pi$
$44$	4.00000	0.603023
$45$	0	0
$46$	−1.00000	−0.147442
$47$	12.0000	1.75038	0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000	1.75038	0.875190	+	0.483779i	$0.160736\pi$
$48$	0	0
$49$	1.00000	0.142857
$50$	0	0
$51$	0	0
$52$	−2.00000	−0.277350
$53$	−14.0000	−1.92305	−0.961524	−	0.274721i	$-0.911414\pi$
$53$	−14.0000	−1.92305	−0.961524	+	0.274721i	$0.911414\pi$
$54$	0	0
$55$	0	0
$56$	−3.00000	−0.400892
$57$	0	0
$58$	−2.00000	−0.262613
$59$	8.00000	1.04151	0.520756	−	0.853706i	$-0.325650\pi$
$59$	8.00000	1.04151	0.520756	+	0.853706i	$0.325650\pi$
$60$	0	0
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	4.00000	0.508001
$63$	−3.00000	−0.377964
$64$	7.00000	0.875000
$65$	0	0
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	0	0
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	9.00000	1.06066
$73$	6.00000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	6.00000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	10.0000	1.16248
$75$	0	0
$76$	−4.00000	−0.458831
$77$	−4.00000	−0.455842
$78$	0	0
$79$	0	0		−	1.00000i	$-0.5\pi$
$79$	0	0			1.00000i	$0.5\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	10.0000	1.10432
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	0	0
$86$	−12.0000	−1.29399
$87$	0	0
$88$	12.0000	1.27920
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	0	0
$91$	2.00000	0.209657
$92$	1.00000	0.104257
$93$	0	0
$94$	12.0000	1.23771
$95$	0	0
$96$	0	0
$97$	2.00000	0.203069	0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000	0.203069	0.101535	+	0.994832i	$0.467625\pi$
$98$	1.00000	0.101015
$99$	12.0000	1.20605
$100$	0	0
$101$	−2.00000	−0.199007	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000	−0.199007	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	0	0
$103$	8.00000	0.788263	0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000	0.788263	0.394132	+	0.919054i	$0.371045\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	−14.0000	−1.35980
$107$	−12.0000	−1.16008	−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000	−1.16008	−0.580042	+	0.814587i	$0.696964\pi$
$108$	0	0
$109$	−10.0000	−0.957826	−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000	−0.957826	−0.478913	+	0.877862i	$0.658969\pi$
$110$	0	0
$111$	0	0
$112$	−1.00000	−0.0944911
$113$	6.00000	0.564433	0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000	0.564433	0.282216	+	0.959351i	$0.408930\pi$
$114$	0	0
$115$	0	0
$116$	2.00000	0.185695
$117$	−6.00000	−0.554700
$118$	8.00000	0.736460
$119$	−6.00000	−0.550019
$120$	0	0
$121$	5.00000	0.454545
$122$	10.0000	0.905357
$123$	0	0
$124$	−4.00000	−0.359211
$125$	0	0
$126$	−3.00000	−0.267261
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	−3.00000	−0.265165
$129$	0	0
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	4.00000	0.346844
$134$	4.00000	0.345547
$135$	0	0
$136$	18.0000	1.54349
$137$	6.00000	0.512615	0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000	0.512615	0.256307	+	0.966595i	$0.417494\pi$
$138$	0	0
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	0	0
$141$	0	0
$142$	8.00000	0.671345
$143$	−8.00000	−0.668994
$144$	3.00000	0.250000
$145$	0	0
$146$	6.00000	0.496564
$147$	0	0
$148$	−10.0000	−0.821995
$149$	22.0000	1.80231	0.901155	−	0.433497i	$-0.142720\pi$
$149$	22.0000	1.80231	0.901155	+	0.433497i	$0.142720\pi$
$150$	0	0
$151$	0	0		−	1.00000i	$-0.5\pi$
$151$	0	0			1.00000i	$0.5\pi$
$152$	−12.0000	−0.973329
$153$	18.0000	1.45521
$154$	−4.00000	−0.322329
$155$	0	0
$156$	0	0
$157$	22.0000	1.75579	0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000	1.75579	0.877896	+	0.478852i	$0.158947\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−1.00000	−0.0788110
$162$	9.00000	0.707107
$163$	12.0000	0.939913	0.469956	−	0.882690i	$-0.344270\pi$
$163$	12.0000	0.939913	0.469956	+	0.882690i	$0.344270\pi$
$164$	−10.0000	−0.780869
$165$	0	0
$166$	−12.0000	−0.931381
$167$	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
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−12.0000	−0.917663
$172$	12.0000	0.914991
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	0	0
$176$	4.00000	0.301511
$177$	0	0
$178$	−2.00000	−0.149906
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	0	0
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	2.00000	0.148250
$183$	0	0
$184$	3.00000	0.221163
$185$	0	0
$186$	0	0
$187$	24.0000	1.75505
$188$	−12.0000	−0.875190
$189$	0	0
$190$	0	0
$191$	−24.0000	−1.73658	−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000	−1.73658	−0.868290	+	0.496058i	$0.834780\pi$
$192$	0	0
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	2.00000	0.143592
$195$	0	0
$196$	−1.00000	−0.0714286
$197$	−22.0000	−1.56744	−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000	−1.56744	−0.783718	+	0.621117i	$0.786679\pi$
$198$	12.0000	0.852803
$199$	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
$202$	−2.00000	−0.140720
$203$	−2.00000	−0.140372
$204$	0	0
$205$	0	0
$206$	8.00000	0.557386
$207$	3.00000	0.208514
$208$	−2.00000	−0.138675
$209$	−16.0000	−1.10674
$210$	0	0
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	14.0000	0.961524
$213$	0	0
$214$	−12.0000	−0.820303
$215$	0	0
$216$	0	0
$217$	4.00000	0.271538
$218$	−10.0000	−0.677285
$219$	0	0
$220$	0	0
$221$	−12.0000	−0.807207
$222$	0	0
$223$	4.00000	0.267860	0.133930	−	0.990991i	$-0.457240\pi$
$223$	4.00000	0.267860	0.133930	+	0.990991i	$0.457240\pi$
$224$	5.00000	0.334077
$225$	0	0
$226$	6.00000	0.399114
$227$	−4.00000	−0.265489	−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000	−0.265489	−0.132745	+	0.991150i	$0.542379\pi$
$228$	0	0
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	0	0
$231$	0	0
$232$	6.00000	0.393919
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	−6.00000	−0.392232
$235$	0	0
$236$	−8.00000	−0.520756
$237$	0	0
$238$	−6.00000	−0.388922
$239$	−8.00000	−0.517477	−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000	−0.517477	−0.258738	+	0.965947i	$0.583307\pi$
$240$	0	0
$241$	6.00000	0.386494	0.193247	−	0.981150i	$-0.438098\pi$
$241$	6.00000	0.386494	0.193247	+	0.981150i	$0.438098\pi$
$242$	5.00000	0.321412
$243$	0	0
$244$	−10.0000	−0.640184
$245$	0	0
$246$	0	0
$247$	8.00000	0.509028
$248$	−12.0000	−0.762001
$249$	0	0
$250$	0	0
$251$	−20.0000	−1.26239	−0.631194	−	0.775625i	$-0.717435\pi$
$251$	−20.0000	−1.26239	−0.631194	+	0.775625i	$0.717435\pi$
$252$	3.00000	0.188982
$253$	4.00000	0.251478
$254$	−8.00000	−0.501965
$255$	0	0
$256$	−17.0000	−1.06250
$257$	−10.0000	−0.623783	−0.311891	−	0.950118i	$-0.600963\pi$
$257$	−10.0000	−0.623783	−0.311891	+	0.950118i	$0.600963\pi$
$258$	0	0
$259$	10.0000	0.621370
$260$	0	0
$261$	6.00000	0.371391
$262$	0	0
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	0	0
$266$	4.00000	0.245256
$267$	0	0
$268$	−4.00000	−0.244339
$269$	30.0000	1.82913	0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000	1.82913	0.914566	+	0.404436i	$0.132532\pi$
$270$	0	0
$271$	28.0000	1.70088	0.850439	−	0.526073i	$-0.176336\pi$
$271$	28.0000	1.70088	0.850439	+	0.526073i	$0.176336\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	6.00000	0.362473
$275$	0	0
$276$	0	0
$277$	−6.00000	−0.360505	−0.180253	−	0.983620i	$-0.557691\pi$
$277$	−6.00000	−0.360505	−0.180253	+	0.983620i	$0.557691\pi$
$278$	8.00000	0.479808
$279$	−12.0000	−0.718421
$280$	0	0
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	0	0
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	−8.00000	−0.474713
$285$	0	0
$286$	−8.00000	−0.473050
$287$	10.0000	0.590281
$288$	−15.0000	−0.883883
$289$	19.0000	1.11765
$290$	0	0
$291$	0	0
$292$	−6.00000	−0.351123
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	0	0
$296$	−30.0000	−1.74371
$297$	0	0
$298$	22.0000	1.27443
$299$	−2.00000	−0.115663
$300$	0	0
$301$	−12.0000	−0.691669
$302$	0	0
$303$	0	0
$304$	−4.00000	−0.229416
$305$	0	0
$306$	18.0000	1.02899
$307$	−16.0000	−0.913168	−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000	−0.913168	−0.456584	+	0.889680i	$0.650927\pi$
$308$	4.00000	0.227921
$309$	0	0
$310$	0	0
$311$	28.0000	1.58773	0.793867	−	0.608091i	$-0.208065\pi$
$311$	28.0000	1.58773	0.793867	+	0.608091i	$0.208065\pi$
$312$	0	0
$313$	18.0000	1.01742	0.508710	−	0.860938i	$-0.330123\pi$
$313$	18.0000	1.01742	0.508710	+	0.860938i	$0.330123\pi$
$314$	22.0000	1.24153
$315$	0	0
$316$	0	0
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	0	0
$319$	8.00000	0.447914
$320$	0	0
$321$	0	0
$322$	−1.00000	−0.0557278
$323$	−24.0000	−1.33540
$324$	−9.00000	−0.500000
$325$	0	0
$326$	12.0000	0.664619
$327$	0	0
$328$	−30.0000	−1.65647
$329$	12.0000	0.661581
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	12.0000	0.658586
$333$	−30.0000	−1.64399
$334$	12.0000	0.656611
$335$	0	0
$336$	0	0
$337$	14.0000	0.762629	0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000	0.762629	0.381314	+	0.924445i	$0.375472\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	0	0
$341$	−16.0000	−0.866449
$342$	−12.0000	−0.648886
$343$	1.00000	0.0539949
$344$	36.0000	1.94099
$345$	0	0
$346$	−6.00000	−0.322562
$347$	−36.0000	−1.93258	−0.966291	−	0.257454i	$-0.917117\pi$
$347$	−36.0000	−1.93258	−0.966291	+	0.257454i	$0.917117\pi$
$348$	0	0
$349$	−34.0000	−1.81998	−0.909989	−	0.414632i	$-0.863910\pi$
$349$	−34.0000	−1.81998	−0.909989	+	0.414632i	$0.863910\pi$
$350$	0	0
$351$	0	0
$352$	−20.0000	−1.06600
$353$	14.0000	0.745145	0.372572	−	0.928003i	$-0.378476\pi$
$353$	14.0000	0.745145	0.372572	+	0.928003i	$0.378476\pi$
$354$	0	0
$355$	0	0
$356$	2.00000	0.106000
$357$	0	0
$358$	12.0000	0.634220
$359$	24.0000	1.26667	0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000	1.26667	0.633336	+	0.773877i	$0.281685\pi$
$360$	0	0
$361$	−3.00000	−0.157895
$362$	10.0000	0.525588
$363$	0	0
$364$	−2.00000	−0.104828
$365$	0	0
$366$	0	0
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	1.00000	0.0521286
$369$	−30.0000	−1.56174
$370$	0	0
$371$	−14.0000	−0.726844
$372$	0	0
$373$	−14.0000	−0.724893	−0.362446	−	0.932005i	$-0.618058\pi$
$373$	−14.0000	−0.724893	−0.362446	+	0.932005i	$0.618058\pi$
$374$	24.0000	1.24101
$375$	0	0
$376$	−36.0000	−1.85656
$377$	−4.00000	−0.206010
$378$	0	0
$379$	12.0000	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$379$	12.0000	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$380$	0	0
$381$	0	0
$382$	−24.0000	−1.22795
$383$	−8.00000	−0.408781	−0.204390	−	0.978889i	$-0.565521\pi$
$383$	−8.00000	−0.408781	−0.204390	+	0.978889i	$0.565521\pi$
$384$	0	0
$385$	0	0
$386$	14.0000	0.712581
$387$	36.0000	1.82998
$388$	−2.00000	−0.101535
$389$	−2.00000	−0.101404	−0.0507020	−	0.998714i	$-0.516146\pi$
$389$	−2.00000	−0.101404	−0.0507020	+	0.998714i	$0.516146\pi$
$390$	0	0
$391$	6.00000	0.303433
$392$	−3.00000	−0.151523
$393$	0	0
$394$	−22.0000	−1.10834
$395$	0	0
$396$	−12.0000	−0.603023
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	8.00000	0.401004
$399$	0	0
$400$	0	0
$401$	26.0000	1.29838	0.649189	−	0.760627i	$-0.275108\pi$
$401$	26.0000	1.29838	0.649189	+	0.760627i	$0.275108\pi$
$402$	0	0
$403$	8.00000	0.398508
$404$	2.00000	0.0995037
$405$	0	0
$406$	−2.00000	−0.0992583
$407$	−40.0000	−1.98273
$408$	0	0
$409$	−14.0000	−0.692255	−0.346128	−	0.938187i	$-0.612504\pi$
$409$	−14.0000	−0.692255	−0.346128	+	0.938187i	$0.612504\pi$
$410$	0	0
$411$	0	0
$412$	−8.00000	−0.394132
$413$	8.00000	0.393654
$414$	3.00000	0.147442
$415$	0	0
$416$	10.0000	0.490290
$417$	0	0
$418$	−16.0000	−0.782586
$419$	36.0000	1.75872	0.879358	−	0.476162i	$-0.157972\pi$
$419$	36.0000	1.75872	0.879358	+	0.476162i	$0.157972\pi$
$420$	0	0
$421$	22.0000	1.07221	0.536107	−	0.844150i	$-0.319894\pi$
$421$	22.0000	1.07221	0.536107	+	0.844150i	$0.319894\pi$
$422$	12.0000	0.584151
$423$	−36.0000	−1.75038
$424$	42.0000	2.03970
$425$	0	0
$426$	0	0
$427$	10.0000	0.483934
$428$	12.0000	0.580042
$429$	0	0
$430$	0	0
$431$	−8.00000	−0.385346	−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000	−0.385346	−0.192673	+	0.981263i	$0.561716\pi$
$432$	0	0
$433$	34.0000	1.63394	0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000	1.63394	0.816968	+	0.576683i	$0.195653\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	10.0000	0.478913
$437$	−4.00000	−0.191346
$438$	0	0
$439$	−4.00000	−0.190910	−0.0954548	−	0.995434i	$-0.530431\pi$
$439$	−4.00000	−0.190910	−0.0954548	+	0.995434i	$0.530431\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	−12.0000	−0.570782
$443$	20.0000	0.950229	0.475114	−	0.879924i	$-0.342407\pi$
$443$	20.0000	0.950229	0.475114	+	0.879924i	$0.342407\pi$
$444$	0	0
$445$	0	0
$446$	4.00000	0.189405
$447$	0	0
$448$	7.00000	0.330719
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	0	0
$451$	−40.0000	−1.88353
$452$	−6.00000	−0.282216
$453$	0	0
$454$	−4.00000	−0.187729
$455$	0	0
$456$	0	0
$457$	−34.0000	−1.59045	−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000	−1.59045	−0.795226	+	0.606313i	$0.792648\pi$
$458$	−22.0000	−1.02799
$459$	0	0
$460$	0	0
$461$	−2.00000	−0.0931493	−0.0465746	−	0.998915i	$-0.514831\pi$
$461$	−2.00000	−0.0931493	−0.0465746	+	0.998915i	$0.514831\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	2.00000	0.0928477
$465$	0	0
$466$	−10.0000	−0.463241
$467$	12.0000	0.555294	0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000	0.555294	0.277647	+	0.960683i	$0.410445\pi$
$468$	6.00000	0.277350
$469$	4.00000	0.184703
$470$	0	0
$471$	0	0
$472$	−24.0000	−1.10469
$473$	48.0000	2.20704
$474$	0	0
$475$	0	0
$476$	6.00000	0.275010
$477$	42.0000	1.92305
$478$	−8.00000	−0.365911
$479$	0	0		−	1.00000i	$-0.5\pi$
$479$	0	0			1.00000i	$0.5\pi$
$480$	0	0
$481$	20.0000	0.911922
$482$	6.00000	0.273293
$483$	0	0
$484$	−5.00000	−0.227273
$485$	0	0
$486$	0	0
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	−30.0000	−1.35804
$489$	0	0
$490$	0	0
$491$	12.0000	0.541552	0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000	0.541552	0.270776	+	0.962642i	$0.412720\pi$
$492$	0	0
$493$	12.0000	0.540453
$494$	8.00000	0.359937
$495$	0	0
$496$	−4.00000	−0.179605
$497$	8.00000	0.358849
$498$	0	0
$499$	28.0000	1.25345	0.626726	−	0.779240i	$-0.284395\pi$
$499$	28.0000	1.25345	0.626726	+	0.779240i	$0.284395\pi$
$500$	0	0
$501$	0	0
$502$	−20.0000	−0.892644
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	9.00000	0.400892
$505$	0	0
$506$	4.00000	0.177822
$507$	0	0
$508$	8.00000	0.354943
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	0	0
$511$	6.00000	0.265424
$512$	−11.0000	−0.486136
$513$	0	0
$514$	−10.0000	−0.441081
$515$	0	0
$516$	0	0
$517$	−48.0000	−2.11104
$518$	10.0000	0.439375
$519$	0	0
$520$	0	0
$521$	−42.0000	−1.84005	−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000	−1.84005	−0.920027	+	0.391856i	$0.871833\pi$
$522$	6.00000	0.262613
$523$	−44.0000	−1.92399	−0.961993	−	0.273075i	$-0.911959\pi$
$523$	−44.0000	−1.92399	−0.961993	+	0.273075i	$0.911959\pi$
$524$	0	0
$525$	0	0
$526$	−16.0000	−0.697633
$527$	−24.0000	−1.04546
$528$	0	0
$529$	1.00000	0.0434783
$530$	0	0
$531$	−24.0000	−1.04151
$532$	−4.00000	−0.173422
$533$	20.0000	0.866296
$534$	0	0
$535$	0	0
$536$	−12.0000	−0.518321
$537$	0	0
$538$	30.0000	1.29339
$539$	−4.00000	−0.172292
$540$	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
$543$	0	0
$544$	−30.0000	−1.28624
$545$	0	0
$546$	0	0
$547$	36.0000	1.53925	0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000	1.53925	0.769624	+	0.638497i	$0.220443\pi$
$548$	−6.00000	−0.256307
$549$	−30.0000	−1.28037
$550$	0	0
$551$	−8.00000	−0.340811
$552$	0	0
$553$	0	0
$554$	−6.00000	−0.254916
$555$	0	0
$556$	−8.00000	−0.339276
$557$	−38.0000	−1.61011	−0.805056	−	0.593199i	$-0.797865\pi$
$557$	−38.0000	−1.61011	−0.805056	+	0.593199i	$0.797865\pi$
$558$	−12.0000	−0.508001
$559$	−24.0000	−1.01509
$560$	0	0
$561$	0	0
$562$	18.0000	0.759284
$563$	44.0000	1.85438	0.927189	−	0.374593i	$-0.122217\pi$
$563$	44.0000	1.85438	0.927189	+	0.374593i	$0.122217\pi$
$564$	0	0
$565$	0	0
$566$	4.00000	0.168133
$567$	9.00000	0.377964
$568$	−24.0000	−1.00702
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	0	0
$571$	20.0000	0.836974	0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000	0.836974	0.418487	+	0.908223i	$0.362561\pi$
$572$	8.00000	0.334497
$573$	0	0
$574$	10.0000	0.417392
$575$	0	0
$576$	−21.0000	−0.875000
$577$	−2.00000	−0.0832611	−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000	−0.0832611	−0.0416305	+	0.999133i	$0.513255\pi$
$578$	19.0000	0.790296
$579$	0	0
$580$	0	0
$581$	−12.0000	−0.497844
$582$	0	0
$583$	56.0000	2.31928
$584$	−18.0000	−0.744845
$585$	0	0
$586$	6.00000	0.247858
$587$	−32.0000	−1.32078	−0.660391	−	0.750922i	$-0.729609\pi$
$587$	−32.0000	−1.32078	−0.660391	+	0.750922i	$0.729609\pi$
$588$	0	0
$589$	16.0000	0.659269
$590$	0	0
$591$	0	0
$592$	−10.0000	−0.410997
$593$	−26.0000	−1.06769	−0.533846	−	0.845582i	$-0.679254\pi$
$593$	−26.0000	−1.06769	−0.533846	+	0.845582i	$0.679254\pi$
$594$	0	0
$595$	0	0
$596$	−22.0000	−0.901155
$597$	0	0
$598$	−2.00000	−0.0817861
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	−30.0000	−1.22373	−0.611863	−	0.790964i	$-0.709580\pi$
$601$	−30.0000	−1.22373	−0.611863	+	0.790964i	$0.709580\pi$
$602$	−12.0000	−0.489083
$603$	−12.0000	−0.488678
$604$	0	0
$605$	0	0
$606$	0	0
$607$	−20.0000	−0.811775	−0.405887	−	0.913923i	$-0.633038\pi$
$607$	−20.0000	−0.811775	−0.405887	+	0.913923i	$0.633038\pi$
$608$	20.0000	0.811107
$609$	0	0
$610$	0	0
$611$	24.0000	0.970936
$612$	−18.0000	−0.727607
$613$	−22.0000	−0.888572	−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000	−0.888572	−0.444286	+	0.895885i	$0.646543\pi$
$614$	−16.0000	−0.645707
$615$	0	0
$616$	12.0000	0.483494
$617$	38.0000	1.52982	0.764911	−	0.644136i	$-0.222783\pi$
$617$	38.0000	1.52982	0.764911	+	0.644136i	$0.222783\pi$
$618$	0	0
$619$	−12.0000	−0.482321	−0.241160	−	0.970485i	$-0.577528\pi$
$619$	−12.0000	−0.482321	−0.241160	+	0.970485i	$0.577528\pi$
$620$	0	0
$621$	0	0
$622$	28.0000	1.12270
$623$	−2.00000	−0.0801283
$624$	0	0
$625$	0	0
$626$	18.0000	0.719425
$627$	0	0
$628$	−22.0000	−0.877896
$629$	−60.0000	−2.39236
$630$	0	0
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	0	0
$633$	0	0
$634$	18.0000	0.714871
$635$	0	0
$636$	0	0
$637$	2.00000	0.0792429
$638$	8.00000	0.316723
$639$	−24.0000	−0.949425
$640$	0	0
$641$	26.0000	1.02694	0.513469	−	0.858108i	$-0.328360\pi$
$641$	26.0000	1.02694	0.513469	+	0.858108i	$0.328360\pi$
$642$	0	0
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	1.00000	0.0394055
$645$	0	0
$646$	−24.0000	−0.944267
$647$	−4.00000	−0.157256	−0.0786281	−	0.996904i	$-0.525054\pi$
$647$	−4.00000	−0.157256	−0.0786281	+	0.996904i	$0.525054\pi$
$648$	−27.0000	−1.06066
$649$	−32.0000	−1.25611
$650$	0	0
$651$	0	0
$652$	−12.0000	−0.469956
$653$	18.0000	0.704394	0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000	0.704394	0.352197	+	0.935926i	$0.385435\pi$
$654$	0	0
$655$	0	0
$656$	−10.0000	−0.390434
$657$	−18.0000	−0.702247
$658$	12.0000	0.467809
$659$	−36.0000	−1.40236	−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000	−1.40236	−0.701180	+	0.712984i	$0.747343\pi$
$660$	0	0
$661$	−14.0000	−0.544537	−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000	−0.544537	−0.272268	+	0.962221i	$0.587774\pi$
$662$	20.0000	0.777322
$663$	0	0
$664$	36.0000	1.39707
$665$	0	0
$666$	−30.0000	−1.16248
$667$	2.00000	0.0774403
$668$	−12.0000	−0.464294
$669$	0	0
$670$	0	0
$671$	−40.0000	−1.54418
$672$	0	0
$673$	−34.0000	−1.31060	−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000	−1.31060	−0.655302	+	0.755367i	$0.727459\pi$
$674$	14.0000	0.539260
$675$	0	0
$676$	9.00000	0.346154
$677$	30.0000	1.15299	0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000	1.15299	0.576497	+	0.817099i	$0.304419\pi$
$678$	0	0
$679$	2.00000	0.0767530
$680$	0	0
$681$	0	0
$682$	−16.0000	−0.612672
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	12.0000	0.458831
$685$	0	0
$686$	1.00000	0.0381802
$687$	0	0
$688$	12.0000	0.457496
$689$	−28.0000	−1.06672
$690$	0	0
$691$	40.0000	1.52167	0.760836	−	0.648944i	$-0.224789\pi$
$691$	40.0000	1.52167	0.760836	+	0.648944i	$0.224789\pi$
$692$	6.00000	0.228086
$693$	12.0000	0.455842
$694$	−36.0000	−1.36654
$695$	0	0
$696$	0	0
$697$	−60.0000	−2.27266
$698$	−34.0000	−1.28692
$699$	0	0
$700$	0	0
$701$	−42.0000	−1.58632	−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000	−1.58632	−0.793159	+	0.609015i	$0.791565\pi$
$702$	0	0
$703$	40.0000	1.50863
$704$	−28.0000	−1.05529
$705$	0	0
$706$	14.0000	0.526897
$707$	−2.00000	−0.0752177
$708$	0	0
$709$	−18.0000	−0.676004	−0.338002	−	0.941145i	$-0.609751\pi$
$709$	−18.0000	−0.676004	−0.338002	+	0.941145i	$0.609751\pi$
$710$	0	0
$711$	0	0
$712$	6.00000	0.224860
$713$	−4.00000	−0.149801
$714$	0	0
$715$	0	0
$716$	−12.0000	−0.448461
$717$	0	0
$718$	24.0000	0.895672
$719$	20.0000	0.745874	0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000	0.745874	0.372937	+	0.927857i	$0.378351\pi$
$720$	0	0
$721$	8.00000	0.297936
$722$	−3.00000	−0.111648
$723$	0	0
$724$	−10.0000	−0.371647
$725$	0	0
$726$	0	0
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	−6.00000	−0.222375
$729$	−27.0000	−1.00000
$730$	0	0
$731$	72.0000	2.66302
$732$	0	0
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	−8.00000	−0.295285
$735$	0	0
$736$	−5.00000	−0.184302
$737$	−16.0000	−0.589368
$738$	−30.0000	−1.10432
$739$	20.0000	0.735712	0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000	0.735712	0.367856	+	0.929883i	$0.380092\pi$
$740$	0	0
$741$	0	0
$742$	−14.0000	−0.513956
$743$	−16.0000	−0.586983	−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000	−0.586983	−0.293492	+	0.955962i	$0.594817\pi$
$744$	0	0
$745$	0	0
$746$	−14.0000	−0.512576
$747$	36.0000	1.31717
$748$	−24.0000	−0.877527
$749$	−12.0000	−0.438470
$750$	0	0
$751$	32.0000	1.16770	0.583848	−	0.811863i	$-0.301546\pi$
$751$	32.0000	1.16770	0.583848	+	0.811863i	$0.301546\pi$
$752$	−12.0000	−0.437595
$753$	0	0
$754$	−4.00000	−0.145671
$755$	0	0
$756$	0	0
$757$	26.0000	0.944986	0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000	0.944986	0.472493	+	0.881334i	$0.343354\pi$
$758$	12.0000	0.435860
$759$	0	0
$760$	0	0
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	0	0
$763$	−10.0000	−0.362024
$764$	24.0000	0.868290
$765$	0	0
$766$	−8.00000	−0.289052
$767$	16.0000	0.577727
$768$	0	0
$769$	−10.0000	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$770$	0	0
$771$	0	0
$772$	−14.0000	−0.503871
$773$	46.0000	1.65451	0.827253	−	0.561830i	$-0.189903\pi$
$773$	46.0000	1.65451	0.827253	+	0.561830i	$0.189903\pi$
$774$	36.0000	1.29399
$775$	0	0
$776$	−6.00000	−0.215387
$777$	0	0
$778$	−2.00000	−0.0717035
$779$	40.0000	1.43315
$780$	0	0
$781$	−32.0000	−1.14505
$782$	6.00000	0.214560
$783$	0	0
$784$	−1.00000	−0.0357143
$785$	0	0
$786$	0	0
$787$	4.00000	0.142585	0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000	0.142585	0.0712923	+	0.997455i	$0.477288\pi$
$788$	22.0000	0.783718
$789$	0	0
$790$	0	0
$791$	6.00000	0.213335
$792$	−36.0000	−1.27920
$793$	20.0000	0.710221
$794$	2.00000	0.0709773
$795$	0	0
$796$	−8.00000	−0.283552
$797$	−2.00000	−0.0708436	−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000	−0.0708436	−0.0354218	+	0.999372i	$0.511277\pi$
$798$	0	0
$799$	−72.0000	−2.54718
$800$	0	0
$801$	6.00000	0.212000
$802$	26.0000	0.918092
$803$	−24.0000	−0.846942
$804$	0	0
$805$	0	0
$806$	8.00000	0.281788
$807$	0	0
$808$	6.00000	0.211079
$809$	42.0000	1.47664	0.738321	−	0.674450i	$-0.235619\pi$
$809$	42.0000	1.47664	0.738321	+	0.674450i	$0.235619\pi$
$810$	0	0
$811$	24.0000	0.842754	0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000	0.842754	0.421377	+	0.906886i	$0.361547\pi$
$812$	2.00000	0.0701862
$813$	0	0
$814$	−40.0000	−1.40200
$815$	0	0
$816$	0	0
$817$	−48.0000	−1.67931
$818$	−14.0000	−0.489499
$819$	−6.00000	−0.209657
$820$	0	0
$821$	22.0000	0.767805	0.383903	−	0.923374i	$-0.374580\pi$
$821$	22.0000	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$822$	0	0
$823$	−8.00000	−0.278862	−0.139431	−	0.990232i	$-0.544527\pi$
$823$	−8.00000	−0.278862	−0.139431	+	0.990232i	$0.544527\pi$
$824$	−24.0000	−0.836080
$825$	0	0
$826$	8.00000	0.278356
$827$	−28.0000	−0.973655	−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000	−0.973655	−0.486828	+	0.873498i	$0.661846\pi$
$828$	−3.00000	−0.104257
$829$	30.0000	1.04194	0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000	1.04194	0.520972	+	0.853574i	$0.325570\pi$
$830$	0	0
$831$	0	0
$832$	14.0000	0.485363
$833$	−6.00000	−0.207888
$834$	0	0
$835$	0	0
$836$	16.0000	0.553372
$837$	0	0
$838$	36.0000	1.24360
$839$	−48.0000	−1.65714	−0.828572	−	0.559883i	$-0.810846\pi$
$839$	−48.0000	−1.65714	−0.828572	+	0.559883i	$0.810846\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	22.0000	0.758170
$843$	0	0
$844$	−12.0000	−0.413057
$845$	0	0
$846$	−36.0000	−1.23771
$847$	5.00000	0.171802
$848$	14.0000	0.480762
$849$	0	0
$850$	0	0
$851$	−10.0000	−0.342796
$852$	0	0
$853$	−22.0000	−0.753266	−0.376633	−	0.926363i	$-0.622918\pi$
$853$	−22.0000	−0.753266	−0.376633	+	0.926363i	$0.622918\pi$
$854$	10.0000	0.342193
$855$	0	0
$856$	36.0000	1.23045
$857$	14.0000	0.478231	0.239115	−	0.970991i	$-0.423143\pi$
$857$	14.0000	0.478231	0.239115	+	0.970991i	$0.423143\pi$
$858$	0	0
$859$	40.0000	1.36478	0.682391	−	0.730987i	$-0.260940\pi$
$859$	40.0000	1.36478	0.682391	+	0.730987i	$0.260940\pi$
$860$	0	0
$861$	0	0
$862$	−8.00000	−0.272481
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	0	0
$866$	34.0000	1.15537
$867$	0	0
$868$	−4.00000	−0.135769
$869$	0	0
$870$	0	0
$871$	8.00000	0.271070
$872$	30.0000	1.01593
$873$	−6.00000	−0.203069
$874$	−4.00000	−0.135302
$875$	0	0
$876$	0	0
$877$	50.0000	1.68838	0.844190	−	0.536044i	$-0.180082\pi$
$877$	50.0000	1.68838	0.844190	+	0.536044i	$0.180082\pi$
$878$	−4.00000	−0.134993
$879$	0	0
$880$	0	0
$881$	−2.00000	−0.0673817	−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000	−0.0673817	−0.0336909	+	0.999432i	$0.510726\pi$
$882$	−3.00000	−0.101015
$883$	20.0000	0.673054	0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000	0.673054	0.336527	+	0.941674i	$0.390748\pi$
$884$	12.0000	0.403604
$885$	0	0
$886$	20.0000	0.671913
$887$	−4.00000	−0.134307	−0.0671534	−	0.997743i	$-0.521392\pi$
$887$	−4.00000	−0.134307	−0.0671534	+	0.997743i	$0.521392\pi$
$888$	0	0
$889$	−8.00000	−0.268311
$890$	0	0
$891$	−36.0000	−1.20605
$892$	−4.00000	−0.133930
$893$	48.0000	1.60626
$894$	0	0
$895$	0	0
$896$	−3.00000	−0.100223
$897$	0	0
$898$	18.0000	0.600668
$899$	−8.00000	−0.266815
$900$	0	0
$901$	84.0000	2.79845
$902$	−40.0000	−1.33185
$903$	0	0
$904$	−18.0000	−0.598671
$905$	0	0
$906$	0	0
$907$	4.00000	0.132818	0.0664089	−	0.997792i	$-0.478846\pi$
$907$	4.00000	0.132818	0.0664089	+	0.997792i	$0.478846\pi$
$908$	4.00000	0.132745
$909$	6.00000	0.199007
$910$	0	0
$911$	−16.0000	−0.530104	−0.265052	−	0.964234i	$-0.585389\pi$
$911$	−16.0000	−0.530104	−0.265052	+	0.964234i	$0.585389\pi$
$912$	0	0
$913$	48.0000	1.58857
$914$	−34.0000	−1.12462
$915$	0	0
$916$	22.0000	0.726900
$917$	0	0
$918$	0	0
$919$	−40.0000	−1.31948	−0.659739	−	0.751495i	$-0.729333\pi$
$919$	−40.0000	−1.31948	−0.659739	+	0.751495i	$0.729333\pi$
$920$	0	0
$921$	0	0
$922$	−2.00000	−0.0658665
$923$	16.0000	0.526646
$924$	0	0
$925$	0	0
$926$	−8.00000	−0.262896
$927$	−24.0000	−0.788263
$928$	−10.0000	−0.328266
$929$	−30.0000	−0.984268	−0.492134	−	0.870519i	$-0.663783\pi$
$929$	−30.0000	−0.984268	−0.492134	+	0.870519i	$0.663783\pi$
$930$	0	0
$931$	4.00000	0.131095
$932$	10.0000	0.327561
$933$	0	0
$934$	12.0000	0.392652
$935$	0	0
$936$	18.0000	0.588348
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	4.00000	0.130605
$939$	0	0
$940$	0	0
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	0	0
$943$	−10.0000	−0.325645
$944$	−8.00000	−0.260378
$945$	0	0
$946$	48.0000	1.56061
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	0	0
$949$	12.0000	0.389536
$950$	0	0
$951$	0	0
$952$	18.0000	0.583383
$953$	46.0000	1.49009	0.745043	−	0.667016i	$-0.232429\pi$
$953$	46.0000	1.49009	0.745043	+	0.667016i	$0.232429\pi$
$954$	42.0000	1.35980
$955$	0	0
$956$	8.00000	0.258738
$957$	0	0
$958$	0	0
$959$	6.00000	0.193750
$960$	0	0
$961$	−15.0000	−0.483871
$962$	20.0000	0.644826
$963$	36.0000	1.16008
$964$	−6.00000	−0.193247
$965$	0	0
$966$	0	0
$967$	40.0000	1.28631	0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000	1.28631	0.643157	+	0.765735i	$0.277624\pi$
$968$	−15.0000	−0.482118
$969$	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
$974$	−8.00000	−0.256337
$975$	0	0
$976$	−10.0000	−0.320092
$977$	−18.0000	−0.575871	−0.287936	−	0.957650i	$-0.592969\pi$
$977$	−18.0000	−0.575871	−0.287936	+	0.957650i	$0.592969\pi$
$978$	0	0
$979$	8.00000	0.255681
$980$	0	0
$981$	30.0000	0.957826
$982$	12.0000	0.382935
$983$	48.0000	1.53096	0.765481	−	0.643458i	$-0.222501\pi$
$983$	48.0000	1.53096	0.765481	+	0.643458i	$0.222501\pi$
$984$	0	0
$985$	0	0
$986$	12.0000	0.382158
$987$	0	0
$988$	−8.00000	−0.254514
$989$	12.0000	0.381578
$990$	0	0
$991$	−16.0000	−0.508257	−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000	−0.508257	−0.254128	+	0.967170i	$0.581789\pi$
$992$	20.0000	0.635001
$993$	0	0
$994$	8.00000	0.253745
$995$	0	0
$996$	0	0
$997$	−62.0000	−1.96356	−0.981780	−	0.190022i	$-0.939144\pi$
$997$	−62.0000	−1.96356	−0.981780	+	0.190022i	$0.939144\pi$
$998$	28.0000	0.886325
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4025.2.a.f.1.1		1
5.4	even	2		805.2.a.a.1.1	✓	1
15.14	odd	2		7245.2.a.q.1.1		1
35.34	odd	2		5635.2.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.a.1.1	✓	1	5.4	even	2
4025.2.a.f.1.1		1	1.1	even	1	trivial
5635.2.a.b.1.1		1	35.34	odd	2
7245.2.a.q.1.1		1	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4025.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more