LMFDB - Embedded newform 9025.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9025, 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("9025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$9025 = 5^{2} \cdot 19^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	9025.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:	$72.0649878242$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9025.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

f(q)

=

q+2.00000 q^{2} +2.00000 q^{4} +4.00000 q^{7} -3.00000 q^{9} -1.00000 q^{11} -2.00000 q^{13} +8.00000 q^{14} -4.00000 q^{16} +2.00000 q^{17} -6.00000 q^{18} -2.00000 q^{22} -6.00000 q^{23} -4.00000 q^{26} +8.00000 q^{28} -9.00000 q^{29} +7.00000 q^{31} -8.00000 q^{32} +4.00000 q^{34} -6.00000 q^{36} +2.00000 q^{37} -2.00000 q^{41} -2.00000 q^{43} -2.00000 q^{44} -12.0000 q^{46} -6.00000 q^{47} +9.00000 q^{49} -4.00000 q^{52} +4.00000 q^{53} -18.0000 q^{58} -9.00000 q^{59} -7.00000 q^{61} +14.0000 q^{62} -12.0000 q^{63} -8.00000 q^{64} -10.0000 q^{67} +4.00000 q^{68} -1.00000 q^{71} -10.0000 q^{73} +4.00000 q^{74} -4.00000 q^{77} -1.00000 q^{79} +9.00000 q^{81} -4.00000 q^{82} +6.00000 q^{83} -4.00000 q^{86} +11.0000 q^{89} -8.00000 q^{91} -12.0000 q^{92} -12.0000 q^{94} -6.00000 q^{97} +18.0000 q^{98} +3.00000 q^{99} +O(q^{100})

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	2.00000	1.41421	0.707107	−	0.707107i	$-0.250000\pi$
$2$	2.00000	1.41421	0.707107	+	0.707107i	$0.250000\pi$
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	2.00000	1.00000
$5$	0	0
$5$	0	0
$6$	0	0
$7$	4.00000	1.51186	0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000	1.51186	0.755929	+	0.654654i	$0.227186\pi$
$8$	0	0
$9$	−3.00000	−1.00000
$10$	0	0
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	0	0
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	8.00000	2.13809
$15$	0	0
$16$	−4.00000	−1.00000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	−6.00000	−1.41421
$19$	0	0
$19$	0	0
$20$	0	0
$21$	0	0
$22$	−2.00000	−0.426401
$23$	−6.00000	−1.25109	−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000	−1.25109	−0.625543	+	0.780189i	$0.715123\pi$
$24$	0	0
$25$	0	0
$26$	−4.00000	−0.784465
$27$	0	0
$28$	8.00000	1.51186
$29$	−9.00000	−1.67126	−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000	−1.67126	−0.835629	+	0.549294i	$0.814897\pi$
$30$	0	0
$31$	7.00000	1.25724	0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000	1.25724	0.628619	+	0.777714i	$0.283621\pi$
$32$	−8.00000	−1.41421
$33$	0	0
$34$	4.00000	0.685994
$35$	0	0
$36$	−6.00000	−1.00000
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	0	0
$39$	0	0
$40$	0	0
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	0	0
$43$	−2.00000	−0.304997	−0.152499	−	0.988304i	$-0.548732\pi$
$43$	−2.00000	−0.304997	−0.152499	+	0.988304i	$0.548732\pi$
$44$	−2.00000	−0.301511
$45$	0	0
$46$	−12.0000	−1.76930
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	0	0
$51$	0	0
$52$	−4.00000	−0.554700
$53$	4.00000	0.549442	0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000	0.549442	0.274721	+	0.961524i	$0.411414\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	−18.0000	−2.36352
$59$	−9.00000	−1.17170	−0.585850	−	0.810419i	$-0.699239\pi$
$59$	−9.00000	−1.17170	−0.585850	+	0.810419i	$0.699239\pi$
$60$	0	0
$61$	−7.00000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	14.0000	1.77800
$63$	−12.0000	−1.51186
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	−10.0000	−1.22169	−0.610847	−	0.791748i	$-0.709171\pi$
$67$	−10.0000	−1.22169	−0.610847	+	0.791748i	$0.709171\pi$
$68$	4.00000	0.485071
$69$	0	0
$70$	0	0
$71$	−1.00000	−0.118678	−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000	−0.118678	−0.0593391	+	0.998238i	$0.518899\pi$
$72$	0	0
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	4.00000	0.464991
$75$	0	0
$76$	0	0
$77$	−4.00000	−0.455842
$78$	0	0
$79$	−1.00000	−0.112509	−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000	−0.112509	−0.0562544	+	0.998416i	$0.517916\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	−4.00000	−0.441726
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0	0
$85$	0	0
$86$	−4.00000	−0.431331
$87$	0	0
$88$	0	0
$89$	11.0000	1.16600	0.582999	−	0.812473i	$-0.301879\pi$
$89$	11.0000	1.16600	0.582999	+	0.812473i	$0.301879\pi$
$90$	0	0
$91$	−8.00000	−0.838628
$92$	−12.0000	−1.25109
$93$	0	0
$94$	−12.0000	−1.23771
$95$	0	0
$96$	0	0
$97$	−6.00000	−0.609208	−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000	−0.609208	−0.304604	+	0.952479i	$0.598524\pi$
$98$	18.0000	1.81827
$99$	3.00000	0.301511
$100$	0	0
$101$	15.0000	1.49256	0.746278	−	0.665635i	$-0.231839\pi$
$101$	15.0000	1.49256	0.746278	+	0.665635i	$0.231839\pi$
$102$	0	0
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	0	0
$105$	0	0
$106$	8.00000	0.777029
$107$	−10.0000	−0.966736	−0.483368	−	0.875417i	$-0.660587\pi$
$107$	−10.0000	−0.966736	−0.483368	+	0.875417i	$0.660587\pi$
$108$	0	0
$109$	−15.0000	−1.43674	−0.718370	−	0.695662i	$-0.755111\pi$
$109$	−15.0000	−1.43674	−0.718370	+	0.695662i	$0.755111\pi$
$110$	0	0
$111$	0	0
$112$	−16.0000	−1.51186
$113$	−12.0000	−1.12887	−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000	−1.12887	−0.564433	+	0.825479i	$0.690905\pi$
$114$	0	0
$115$	0	0
$116$	−18.0000	−1.67126
$117$	6.00000	0.554700
$118$	−18.0000	−1.65703
$119$	8.00000	0.733359
$120$	0	0
$121$	−10.0000	−0.909091
$122$	−14.0000	−1.26750
$123$	0	0
$124$	14.0000	1.25724
$125$	0	0
$126$	−24.0000	−2.13809
$127$	−6.00000	−0.532414	−0.266207	−	0.963916i	$-0.585770\pi$
$127$	−6.00000	−0.532414	−0.266207	+	0.963916i	$0.585770\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	0	0
$133$	0	0
$134$	−20.0000	−1.72774
$135$	0	0
$136$	0	0
$137$	−12.0000	−1.02523	−0.512615	−	0.858619i	$-0.671323\pi$
$137$	−12.0000	−1.02523	−0.512615	+	0.858619i	$0.671323\pi$
$138$	0	0
$139$	20.0000	1.69638	0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000	1.69638	0.848189	+	0.529694i	$0.177693\pi$
$140$	0	0
$141$	0	0
$142$	−2.00000	−0.167836
$143$	2.00000	0.167248
$144$	12.0000	1.00000
$145$	0	0
$146$	−20.0000	−1.65521
$147$	0	0
$148$	4.00000	0.328798
$149$	−1.00000	−0.0819232	−0.0409616	−	0.999161i	$-0.513042\pi$
$149$	−1.00000	−0.0819232	−0.0409616	+	0.999161i	$0.513042\pi$
$150$	0	0
$151$	−9.00000	−0.732410	−0.366205	−	0.930534i	$-0.619343\pi$
$151$	−9.00000	−0.732410	−0.366205	+	0.930534i	$0.619343\pi$
$152$	0	0
$153$	−6.00000	−0.485071
$154$	−8.00000	−0.644658
$155$	0	0
$156$	0	0
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	−2.00000	−0.159111
$159$	0	0
$160$	0	0
$161$	−24.0000	−1.89146
$162$	18.0000	1.41421
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	−4.00000	−0.312348
$165$	0	0
$166$	12.0000	0.931381
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	0	0
$172$	−4.00000	−0.304997
$173$	−24.0000	−1.82469	−0.912343	−	0.409426i	$-0.865729\pi$
$173$	−24.0000	−1.82469	−0.912343	+	0.409426i	$0.865729\pi$
$174$	0	0
$175$	0	0
$176$	4.00000	0.301511
$177$	0	0
$178$	22.0000	1.64897
$179$	−15.0000	−1.12115	−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000	−1.12115	−0.560576	+	0.828103i	$0.689420\pi$
$180$	0	0
$181$	6.00000	0.445976	0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000	0.445976	0.222988	+	0.974821i	$0.428419\pi$
$182$	−16.0000	−1.18600
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−2.00000	−0.146254
$188$	−12.0000	−0.875190
$189$	0	0
$190$	0	0
$191$	−3.00000	−0.217072	−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000	−0.217072	−0.108536	+	0.994092i	$0.534616\pi$
$192$	0	0
$193$	16.0000	1.15171	0.575853	−	0.817554i	$-0.304670\pi$
$193$	16.0000	1.15171	0.575853	+	0.817554i	$0.304670\pi$
$194$	−12.0000	−0.861550
$195$	0	0
$196$	18.0000	1.28571
$197$	18.0000	1.28245	0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000	1.28245	0.641223	+	0.767354i	$0.278427\pi$
$198$	6.00000	0.426401
$199$	13.0000	0.921546	0.460773	−	0.887518i	$-0.347572\pi$
$199$	13.0000	0.921546	0.460773	+	0.887518i	$0.347572\pi$
$200$	0	0
$201$	0	0
$202$	30.0000	2.11079
$203$	−36.0000	−2.52670
$204$	0	0
$205$	0	0
$206$	32.0000	2.22955
$207$	18.0000	1.25109
$208$	8.00000	0.554700
$209$	0	0
$210$	0	0
$211$	−5.00000	−0.344214	−0.172107	−	0.985078i	$-0.555058\pi$
$211$	−5.00000	−0.344214	−0.172107	+	0.985078i	$0.555058\pi$
$212$	8.00000	0.549442
$213$	0	0
$214$	−20.0000	−1.36717
$215$	0	0
$216$	0	0
$217$	28.0000	1.90076
$218$	−30.0000	−2.03186
$219$	0	0
$220$	0	0
$221$	−4.00000	−0.269069
$222$	0	0
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	−32.0000	−2.13809
$225$	0	0
$226$	−24.0000	−1.59646
$227$	14.0000	0.929213	0.464606	−	0.885517i	$-0.346196\pi$
$227$	14.0000	0.929213	0.464606	+	0.885517i	$0.346196\pi$
$228$	0	0
$229$	17.0000	1.12339	0.561696	−	0.827344i	$-0.310149\pi$
$229$	17.0000	1.12339	0.561696	+	0.827344i	$0.310149\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	8.00000	0.524097	0.262049	−	0.965055i	$-0.415602\pi$
$233$	8.00000	0.524097	0.262049	+	0.965055i	$0.415602\pi$
$234$	12.0000	0.784465
$235$	0	0
$236$	−18.0000	−1.17170
$237$	0	0
$238$	16.0000	1.03713
$239$	−19.0000	−1.22901	−0.614504	−	0.788914i	$-0.710644\pi$
$239$	−19.0000	−1.22901	−0.614504	+	0.788914i	$0.710644\pi$
$240$	0	0
$241$	−1.00000	−0.0644157	−0.0322078	−	0.999481i	$-0.510254\pi$
$241$	−1.00000	−0.0644157	−0.0322078	+	0.999481i	$0.510254\pi$
$242$	−20.0000	−1.28565
$243$	0	0
$244$	−14.0000	−0.896258
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	0	0
$250$	0	0
$251$	13.0000	0.820553	0.410276	−	0.911961i	$-0.365432\pi$
$251$	13.0000	0.820553	0.410276	+	0.911961i	$0.365432\pi$
$252$	−24.0000	−1.51186
$253$	6.00000	0.377217
$254$	−12.0000	−0.752947
$255$	0	0
$256$	16.0000	1.00000
$257$	−6.00000	−0.374270	−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000	−0.374270	−0.187135	+	0.982334i	$0.559920\pi$
$258$	0	0
$259$	8.00000	0.497096
$260$	0	0
$261$	27.0000	1.67126
$262$	24.0000	1.48272
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	−20.0000	−1.22169
$269$	−3.00000	−0.182913	−0.0914566	−	0.995809i	$-0.529152\pi$
$269$	−3.00000	−0.182913	−0.0914566	+	0.995809i	$0.529152\pi$
$270$	0	0
$271$	3.00000	0.182237	0.0911185	−	0.995840i	$-0.470956\pi$
$271$	3.00000	0.182237	0.0911185	+	0.995840i	$0.470956\pi$
$272$	−8.00000	−0.485071
$273$	0	0
$274$	−24.0000	−1.44989
$275$	0	0
$276$	0	0
$277$	28.0000	1.68236	0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000	1.68236	0.841178	+	0.540758i	$0.181862\pi$
$278$	40.0000	2.39904
$279$	−21.0000	−1.25724
$280$	0	0
$281$	−10.0000	−0.596550	−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000	−0.596550	−0.298275	+	0.954480i	$0.596411\pi$
$282$	0	0
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	−2.00000	−0.118678
$285$	0	0
$286$	4.00000	0.236525
$287$	−8.00000	−0.472225
$288$	24.0000	1.41421
$289$	−13.0000	−0.764706
$290$	0	0
$291$	0	0
$292$	−20.0000	−1.17041
$293$	4.00000	0.233682	0.116841	−	0.993151i	$-0.462723\pi$
$293$	4.00000	0.233682	0.116841	+	0.993151i	$0.462723\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	0	0
$298$	−2.00000	−0.115857
$299$	12.0000	0.693978
$300$	0	0
$301$	−8.00000	−0.461112
$302$	−18.0000	−1.03578
$303$	0	0
$304$	0	0
$305$	0	0
$306$	−12.0000	−0.685994
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	−8.00000	−0.455842
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	−30.0000	−1.69570	−0.847850	−	0.530236i	$-0.822103\pi$
$313$	−30.0000	−1.69570	−0.847850	+	0.530236i	$0.822103\pi$
$314$	−8.00000	−0.451466
$315$	0	0
$316$	−2.00000	−0.112509
$317$	−2.00000	−0.112331	−0.0561656	−	0.998421i	$-0.517887\pi$
$317$	−2.00000	−0.112331	−0.0561656	+	0.998421i	$0.517887\pi$
$318$	0	0
$319$	9.00000	0.503903
$320$	0	0
$321$	0	0
$322$	−48.0000	−2.67494
$323$	0	0
$324$	18.0000	1.00000
$325$	0	0
$326$	−8.00000	−0.443079
$327$	0	0
$328$	0	0
$329$	−24.0000	−1.32316
$330$	0	0
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	12.0000	0.658586
$333$	−6.00000	−0.328798
$334$	−24.0000	−1.31322
$335$	0	0
$336$	0	0
$337$	34.0000	1.85210	0.926049	−	0.377403i	$-0.123183\pi$
$337$	34.0000	1.85210	0.926049	+	0.377403i	$0.123183\pi$
$338$	−18.0000	−0.979071
$339$	0	0
$340$	0	0
$341$	−7.00000	−0.379071
$342$	0	0
$343$	8.00000	0.431959
$344$	0	0
$345$	0	0
$346$	−48.0000	−2.58050
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	0	0
$351$	0	0
$352$	8.00000	0.426401
$353$	8.00000	0.425797	0.212899	−	0.977074i	$-0.431710\pi$
$353$	8.00000	0.425797	0.212899	+	0.977074i	$0.431710\pi$
$354$	0	0
$355$	0	0
$356$	22.0000	1.16600
$357$	0	0
$358$	−30.0000	−1.58555
$359$	−20.0000	−1.05556	−0.527780	−	0.849381i	$-0.676975\pi$
$359$	−20.0000	−1.05556	−0.527780	+	0.849381i	$0.676975\pi$
$360$	0	0
$361$	0	0
$362$	12.0000	0.630706
$363$	0	0
$364$	−16.0000	−0.838628
$365$	0	0
$366$	0	0
$367$	16.0000	0.835193	0.417597	−	0.908633i	$-0.362873\pi$
$367$	16.0000	0.835193	0.417597	+	0.908633i	$0.362873\pi$
$368$	24.0000	1.25109
$369$	6.00000	0.312348
$370$	0	0
$371$	16.0000	0.830679
$372$	0	0
$373$	−12.0000	−0.621336	−0.310668	−	0.950518i	$-0.600553\pi$
$373$	−12.0000	−0.621336	−0.310668	+	0.950518i	$0.600553\pi$
$374$	−4.00000	−0.206835
$375$	0	0
$376$	0	0
$377$	18.0000	0.927047
$378$	0	0
$379$	29.0000	1.48963	0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000	1.48963	0.744815	+	0.667271i	$0.232538\pi$
$380$	0	0
$381$	0	0
$382$	−6.00000	−0.306987
$383$	6.00000	0.306586	0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000	0.306586	0.153293	+	0.988181i	$0.451012\pi$
$384$	0	0
$385$	0	0
$386$	32.0000	1.62876
$387$	6.00000	0.304997
$388$	−12.0000	−0.609208
$389$	−33.0000	−1.67317	−0.836583	−	0.547840i	$-0.815450\pi$
$389$	−33.0000	−1.67317	−0.836583	+	0.547840i	$0.815450\pi$
$390$	0	0
$391$	−12.0000	−0.606866
$392$	0	0
$393$	0	0
$394$	36.0000	1.81365
$395$	0	0
$396$	6.00000	0.301511
$397$	8.00000	0.401508	0.200754	−	0.979642i	$-0.435661\pi$
$397$	8.00000	0.401508	0.200754	+	0.979642i	$0.435661\pi$
$398$	26.0000	1.30326
$399$	0	0
$400$	0	0
$401$	−3.00000	−0.149813	−0.0749064	−	0.997191i	$-0.523866\pi$
$401$	−3.00000	−0.149813	−0.0749064	+	0.997191i	$0.523866\pi$
$402$	0	0
$403$	−14.0000	−0.697390
$404$	30.0000	1.49256
$405$	0	0
$406$	−72.0000	−3.57330
$407$	−2.00000	−0.0991363
$408$	0	0
$409$	5.00000	0.247234	0.123617	−	0.992330i	$-0.460551\pi$
$409$	5.00000	0.247234	0.123617	+	0.992330i	$0.460551\pi$
$410$	0	0
$411$	0	0
$412$	32.0000	1.57653
$413$	−36.0000	−1.77144
$414$	36.0000	1.76930
$415$	0	0
$416$	16.0000	0.784465
$417$	0	0
$418$	0	0
$419$	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
$421$	15.0000	0.731055	0.365528	−	0.930800i	$-0.380889\pi$
$421$	15.0000	0.731055	0.365528	+	0.930800i	$0.380889\pi$
$422$	−10.0000	−0.486792
$423$	18.0000	0.875190
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−28.0000	−1.35501
$428$	−20.0000	−0.966736
$429$	0	0
$430$	0	0
$431$	−21.0000	−1.01153	−0.505767	−	0.862670i	$-0.668791\pi$
$431$	−21.0000	−1.01153	−0.505767	+	0.862670i	$0.668791\pi$
$432$	0	0
$433$	−4.00000	−0.192228	−0.0961139	−	0.995370i	$-0.530641\pi$
$433$	−4.00000	−0.192228	−0.0961139	+	0.995370i	$0.530641\pi$
$434$	56.0000	2.68809
$435$	0	0
$436$	−30.0000	−1.43674
$437$	0	0
$438$	0	0
$439$	13.0000	0.620456	0.310228	−	0.950662i	$-0.399595\pi$
$439$	13.0000	0.620456	0.310228	+	0.950662i	$0.399595\pi$
$440$	0	0
$441$	−27.0000	−1.28571
$442$	−8.00000	−0.380521
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	0	0
$445$	0	0
$446$	−4.00000	−0.189405
$447$	0	0
$448$	−32.0000	−1.51186
$449$	−31.0000	−1.46298	−0.731490	−	0.681852i	$-0.761175\pi$
$449$	−31.0000	−1.46298	−0.731490	+	0.681852i	$0.761175\pi$
$450$	0	0
$451$	2.00000	0.0941763
$452$	−24.0000	−1.12887
$453$	0	0
$454$	28.0000	1.31411
$455$	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	$0.792648\pi$
$458$	34.0000	1.58872
$459$	0	0
$460$	0	0
$461$	−25.0000	−1.16437	−0.582183	−	0.813058i	$-0.697801\pi$
$461$	−25.0000	−1.16437	−0.582183	+	0.813058i	$0.697801\pi$
$462$	0	0
$463$	4.00000	0.185896	0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000	0.185896	0.0929479	+	0.995671i	$0.470371\pi$
$464$	36.0000	1.67126
$465$	0	0
$466$	16.0000	0.741186
$467$	−10.0000	−0.462745	−0.231372	−	0.972865i	$-0.574322\pi$
$467$	−10.0000	−0.462745	−0.231372	+	0.972865i	$0.574322\pi$
$468$	12.0000	0.554700
$469$	−40.0000	−1.84703
$470$	0	0
$471$	0	0
$472$	0	0
$473$	2.00000	0.0919601
$474$	0	0
$475$	0	0
$476$	16.0000	0.733359
$477$	−12.0000	−0.549442
$478$	−38.0000	−1.73808
$479$	15.0000	0.685367	0.342684	−	0.939451i	$-0.388664\pi$
$479$	15.0000	0.685367	0.342684	+	0.939451i	$0.388664\pi$
$480$	0	0
$481$	−4.00000	−0.182384
$482$	−2.00000	−0.0910975
$483$	0	0
$484$	−20.0000	−0.909091
$485$	0	0
$486$	0	0
$487$	−38.0000	−1.72194	−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000	−1.72194	−0.860972	+	0.508652i	$0.830144\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	13.0000	0.586682	0.293341	−	0.956008i	$-0.405233\pi$
$491$	13.0000	0.586682	0.293341	+	0.956008i	$0.405233\pi$
$492$	0	0
$493$	−18.0000	−0.810679
$494$	0	0
$495$	0	0
$496$	−28.0000	−1.25724
$497$	−4.00000	−0.179425
$498$	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
$502$	26.0000	1.16044
$503$	26.0000	1.15928	0.579641	−	0.814872i	$-0.303193\pi$
$503$	26.0000	1.15928	0.579641	+	0.814872i	$0.303193\pi$
$504$	0	0
$505$	0	0
$506$	12.0000	0.533465
$507$	0	0
$508$	−12.0000	−0.532414
$509$	−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
$511$	−40.0000	−1.76950
$512$	32.0000	1.41421
$513$	0	0
$514$	−12.0000	−0.529297
$515$	0	0
$516$	0	0
$517$	6.00000	0.263880
$518$	16.0000	0.703000
$519$	0	0
$520$	0	0
$521$	−15.0000	−0.657162	−0.328581	−	0.944476i	$-0.606570\pi$
$521$	−15.0000	−0.657162	−0.328581	+	0.944476i	$0.606570\pi$
$522$	54.0000	2.36352
$523$	16.0000	0.699631	0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000	0.699631	0.349816	+	0.936819i	$0.386244\pi$
$524$	24.0000	1.04844
$525$	0	0
$526$	0	0
$527$	14.0000	0.609850
$528$	0	0
$529$	13.0000	0.565217
$530$	0	0
$531$	27.0000	1.17170
$532$	0	0
$533$	4.00000	0.173259
$534$	0	0
$535$	0	0
$536$	0	0
$537$	0	0
$538$	−6.00000	−0.258678
$539$	−9.00000	−0.387657
$540$	0	0
$541$	23.0000	0.988847	0.494424	−	0.869221i	$-0.335379\pi$
$541$	23.0000	0.988847	0.494424	+	0.869221i	$0.335379\pi$
$542$	6.00000	0.257722
$543$	0	0
$544$	−16.0000	−0.685994
$545$	0	0
$546$	0	0
$547$	22.0000	0.940652	0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000	0.940652	0.470326	+	0.882493i	$0.344136\pi$
$548$	−24.0000	−1.02523
$549$	21.0000	0.896258
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−4.00000	−0.170097
$554$	56.0000	2.37921
$555$	0	0
$556$	40.0000	1.69638
$557$	−14.0000	−0.593199	−0.296600	−	0.955002i	$-0.595853\pi$
$557$	−14.0000	−0.593199	−0.296600	+	0.955002i	$0.595853\pi$
$558$	−42.0000	−1.77800
$559$	4.00000	0.169182
$560$	0	0
$561$	0	0
$562$	−20.0000	−0.843649
$563$	−24.0000	−1.01148	−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000	−1.01148	−0.505740	+	0.862686i	$0.668780\pi$
$564$	0	0
$565$	0	0
$566$	−28.0000	−1.17693
$567$	36.0000	1.51186
$568$	0	0
$569$	−15.0000	−0.628833	−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000	−0.628833	−0.314416	+	0.949285i	$0.601809\pi$
$570$	0	0
$571$	13.0000	0.544033	0.272017	−	0.962293i	$-0.412309\pi$
$571$	13.0000	0.544033	0.272017	+	0.962293i	$0.412309\pi$
$572$	4.00000	0.167248
$573$	0	0
$574$	−16.0000	−0.667827
$575$	0	0
$576$	24.0000	1.00000
$577$	−6.00000	−0.249783	−0.124892	−	0.992170i	$-0.539858\pi$
$577$	−6.00000	−0.249783	−0.124892	+	0.992170i	$0.539858\pi$
$578$	−26.0000	−1.08146
$579$	0	0
$580$	0	0
$581$	24.0000	0.995688
$582$	0	0
$583$	−4.00000	−0.165663
$584$	0	0
$585$	0	0
$586$	8.00000	0.330477
$587$	24.0000	0.990586	0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000	0.990586	0.495293	+	0.868726i	$0.335061\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	−8.00000	−0.328798
$593$	32.0000	1.31408	0.657041	−	0.753855i	$-0.271808\pi$
$593$	32.0000	1.31408	0.657041	+	0.753855i	$0.271808\pi$
$594$	0	0
$595$	0	0
$596$	−2.00000	−0.0819232
$597$	0	0
$598$	24.0000	0.981433
$599$	12.0000	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$600$	0	0
$601$	−17.0000	−0.693444	−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000	−0.693444	−0.346722	+	0.937968i	$0.612705\pi$
$602$	−16.0000	−0.652111
$603$	30.0000	1.22169
$604$	−18.0000	−0.732410
$605$	0	0
$606$	0	0
$607$	−14.0000	−0.568242	−0.284121	−	0.958788i	$-0.591702\pi$
$607$	−14.0000	−0.568242	−0.284121	+	0.958788i	$0.591702\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	12.0000	0.485468
$612$	−12.0000	−0.485071
$613$	−24.0000	−0.969351	−0.484675	−	0.874694i	$-0.661062\pi$
$613$	−24.0000	−0.969351	−0.484675	+	0.874694i	$0.661062\pi$
$614$	32.0000	1.29141
$615$	0	0
$616$	0	0
$617$	−18.0000	−0.724653	−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000	−0.724653	−0.362326	+	0.932051i	$0.618017\pi$
$618$	0	0
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	44.0000	1.76282
$624$	0	0
$625$	0	0
$626$	−60.0000	−2.39808
$627$	0	0
$628$	−8.00000	−0.319235
$629$	4.00000	0.159490
$630$	0	0
$631$	1.00000	0.0398094	0.0199047	−	0.999802i	$-0.493664\pi$
$631$	1.00000	0.0398094	0.0199047	+	0.999802i	$0.493664\pi$
$632$	0	0
$633$	0	0
$634$	−4.00000	−0.158860
$635$	0	0
$636$	0	0
$637$	−18.0000	−0.713186
$638$	18.0000	0.712627
$639$	3.00000	0.118678
$640$	0	0
$641$	−21.0000	−0.829450	−0.414725	−	0.909947i	$-0.636122\pi$
$641$	−21.0000	−0.829450	−0.414725	+	0.909947i	$0.636122\pi$
$642$	0	0
$643$	46.0000	1.81406	0.907031	−	0.421063i	$-0.138343\pi$
$643$	46.0000	1.81406	0.907031	+	0.421063i	$0.138343\pi$
$644$	−48.0000	−1.89146
$645$	0	0
$646$	0	0
$647$	6.00000	0.235884	0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000	0.235884	0.117942	+	0.993020i	$0.462370\pi$
$648$	0	0
$649$	9.00000	0.353281
$650$	0	0
$651$	0	0
$652$	−8.00000	−0.313304
$653$	−10.0000	−0.391330	−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000	−0.391330	−0.195665	+	0.980671i	$0.562687\pi$
$654$	0	0
$655$	0	0
$656$	8.00000	0.312348
$657$	30.0000	1.17041
$658$	−48.0000	−1.87123
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	0	0
$661$	15.0000	0.583432	0.291716	−	0.956505i	$-0.405774\pi$
$661$	15.0000	0.583432	0.291716	+	0.956505i	$0.405774\pi$
$662$	−40.0000	−1.55464
$663$	0	0
$664$	0	0
$665$	0	0
$666$	−12.0000	−0.464991
$667$	54.0000	2.09089
$668$	−24.0000	−0.928588
$669$	0	0
$670$	0	0
$671$	7.00000	0.270232
$672$	0	0
$673$	−20.0000	−0.770943	−0.385472	−	0.922720i	$-0.625961\pi$
$673$	−20.0000	−0.770943	−0.385472	+	0.922720i	$0.625961\pi$
$674$	68.0000	2.61926
$675$	0	0
$676$	−18.0000	−0.692308
$677$	0	0		−	1.00000i	$-0.5\pi$
$677$	0	0			1.00000i	$0.5\pi$
$678$	0	0
$679$	−24.0000	−0.921035
$680$	0	0
$681$	0	0
$682$	−14.0000	−0.536088
$683$	30.0000	1.14792	0.573959	−	0.818884i	$-0.305407\pi$
$683$	30.0000	1.14792	0.573959	+	0.818884i	$0.305407\pi$
$684$	0	0
$685$	0	0
$686$	16.0000	0.610883
$687$	0	0
$688$	8.00000	0.304997
$689$	−8.00000	−0.304776
$690$	0	0
$691$	3.00000	0.114125	0.0570627	−	0.998371i	$-0.481827\pi$
$691$	3.00000	0.114125	0.0570627	+	0.998371i	$0.481827\pi$
$692$	−48.0000	−1.82469
$693$	12.0000	0.455842
$694$	24.0000	0.911028
$695$	0	0
$696$	0	0
$697$	−4.00000	−0.151511
$698$	28.0000	1.05982
$699$	0	0
$700$	0	0
$701$	6.00000	0.226617	0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000	0.226617	0.113308	+	0.993560i	$0.463855\pi$
$702$	0	0
$703$	0	0
$704$	8.00000	0.301511
$705$	0	0
$706$	16.0000	0.602168
$707$	60.0000	2.25653
$708$	0	0
$709$	25.0000	0.938895	0.469447	−	0.882960i	$-0.344453\pi$
$709$	25.0000	0.938895	0.469447	+	0.882960i	$0.344453\pi$
$710$	0	0
$711$	3.00000	0.112509
$712$	0	0
$713$	−42.0000	−1.57291
$714$	0	0
$715$	0	0
$716$	−30.0000	−1.12115
$717$	0	0
$718$	−40.0000	−1.49279
$719$	−21.0000	−0.783168	−0.391584	−	0.920142i	$-0.628073\pi$
$719$	−21.0000	−0.783168	−0.391584	+	0.920142i	$0.628073\pi$
$720$	0	0
$721$	64.0000	2.38348
$722$	0	0
$723$	0	0
$724$	12.0000	0.445976
$725$	0	0
$726$	0	0
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	−4.00000	−0.147945
$732$	0	0
$733$	6.00000	0.221615	0.110808	−	0.993842i	$-0.464656\pi$
$733$	6.00000	0.221615	0.110808	+	0.993842i	$0.464656\pi$
$734$	32.0000	1.18114
$735$	0	0
$736$	48.0000	1.76930
$737$	10.0000	0.368355
$738$	12.0000	0.441726
$739$	−29.0000	−1.06678	−0.533391	−	0.845869i	$-0.679083\pi$
$739$	−29.0000	−1.06678	−0.533391	+	0.845869i	$0.679083\pi$
$740$	0	0
$741$	0	0
$742$	32.0000	1.17476
$743$	50.0000	1.83432	0.917161	−	0.398517i	$-0.130475\pi$
$743$	50.0000	1.83432	0.917161	+	0.398517i	$0.130475\pi$
$744$	0	0
$745$	0	0
$746$	−24.0000	−0.878702
$747$	−18.0000	−0.658586
$748$	−4.00000	−0.146254
$749$	−40.0000	−1.46157
$750$	0	0
$751$	−41.0000	−1.49611	−0.748056	−	0.663636i	$-0.769012\pi$
$751$	−41.0000	−1.49611	−0.748056	+	0.663636i	$0.769012\pi$
$752$	24.0000	0.875190
$753$	0	0
$754$	36.0000	1.31104
$755$	0	0
$756$	0	0
$757$	−26.0000	−0.944986	−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000	−0.944986	−0.472493	+	0.881334i	$0.656646\pi$
$758$	58.0000	2.10665
$759$	0	0
$760$	0	0
$761$	−18.0000	−0.652499	−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000	−0.652499	−0.326250	+	0.945284i	$0.605785\pi$
$762$	0	0
$763$	−60.0000	−2.17215
$764$	−6.00000	−0.217072
$765$	0	0
$766$	12.0000	0.433578
$767$	18.0000	0.649942
$768$	0	0
$769$	5.00000	0.180305	0.0901523	−	0.995928i	$-0.471265\pi$
$769$	5.00000	0.180305	0.0901523	+	0.995928i	$0.471265\pi$
$770$	0	0
$771$	0	0
$772$	32.0000	1.15171
$773$	34.0000	1.22290	0.611448	−	0.791285i	$-0.290588\pi$
$773$	34.0000	1.22290	0.611448	+	0.791285i	$0.290588\pi$
$774$	12.0000	0.431331
$775$	0	0
$776$	0	0
$777$	0	0
$778$	−66.0000	−2.36621
$779$	0	0
$780$	0	0
$781$	1.00000	0.0357828
$782$	−24.0000	−0.858238
$783$	0	0
$784$	−36.0000	−1.28571
$785$	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	$0.371746\pi$
$788$	36.0000	1.28245
$789$	0	0
$790$	0	0
$791$	−48.0000	−1.70668
$792$	0	0
$793$	14.0000	0.497155
$794$	16.0000	0.567819
$795$	0	0
$796$	26.0000	0.921546
$797$	24.0000	0.850124	0.425062	−	0.905164i	$-0.360252\pi$
$797$	24.0000	0.850124	0.425062	+	0.905164i	$0.360252\pi$
$798$	0	0
$799$	−12.0000	−0.424529
$800$	0	0
$801$	−33.0000	−1.16600
$802$	−6.00000	−0.211867
$803$	10.0000	0.352892
$804$	0	0
$805$	0	0
$806$	−28.0000	−0.986258
$807$	0	0
$808$	0	0
$809$	−43.0000	−1.51180	−0.755900	−	0.654687i	$-0.772800\pi$
$809$	−43.0000	−1.51180	−0.755900	+	0.654687i	$0.772800\pi$
$810$	0	0
$811$	−9.00000	−0.316033	−0.158016	−	0.987436i	$-0.550510\pi$
$811$	−9.00000	−0.316033	−0.158016	+	0.987436i	$0.550510\pi$
$812$	−72.0000	−2.52670
$813$	0	0
$814$	−4.00000	−0.140200
$815$	0	0
$816$	0	0
$817$	0	0
$818$	10.0000	0.349642
$819$	24.0000	0.838628
$820$	0	0
$821$	21.0000	0.732905	0.366453	−	0.930437i	$-0.380572\pi$
$821$	21.0000	0.732905	0.366453	+	0.930437i	$0.380572\pi$
$822$	0	0
$823$	30.0000	1.04573	0.522867	−	0.852414i	$-0.324862\pi$
$823$	30.0000	1.04573	0.522867	+	0.852414i	$0.324862\pi$
$824$	0	0
$825$	0	0
$826$	−72.0000	−2.50520
$827$	6.00000	0.208640	0.104320	−	0.994544i	$-0.466733\pi$
$827$	6.00000	0.208640	0.104320	+	0.994544i	$0.466733\pi$
$828$	36.0000	1.25109
$829$	−2.00000	−0.0694629	−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000	−0.0694629	−0.0347314	+	0.999397i	$0.511058\pi$
$830$	0	0
$831$	0	0
$832$	16.0000	0.554700
$833$	18.0000	0.623663
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	18.0000	0.621800
$839$	−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
$841$	52.0000	1.79310
$842$	30.0000	1.03387
$843$	0	0
$844$	−10.0000	−0.344214
$845$	0	0
$846$	36.0000	1.23771
$847$	−40.0000	−1.37442
$848$	−16.0000	−0.549442
$849$	0	0
$850$	0	0
$851$	−12.0000	−0.411355
$852$	0	0
$853$	16.0000	0.547830	0.273915	−	0.961754i	$-0.411681\pi$
$853$	16.0000	0.547830	0.273915	+	0.961754i	$0.411681\pi$
$854$	−56.0000	−1.91628
$855$	0	0
$856$	0	0
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	0	0
$859$	1.00000	0.0341196	0.0170598	−	0.999854i	$-0.494569\pi$
$859$	1.00000	0.0341196	0.0170598	+	0.999854i	$0.494569\pi$
$860$	0	0
$861$	0	0
$862$	−42.0000	−1.43053
$863$	20.0000	0.680808	0.340404	−	0.940279i	$-0.389436\pi$
$863$	20.0000	0.680808	0.340404	+	0.940279i	$0.389436\pi$
$864$	0	0
$865$	0	0
$866$	−8.00000	−0.271851
$867$	0	0
$868$	56.0000	1.90076
$869$	1.00000	0.0339227
$870$	0	0
$871$	20.0000	0.677674
$872$	0	0
$873$	18.0000	0.609208
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−58.0000	−1.95852	−0.979260	−	0.202606i	$-0.935059\pi$
$877$	−58.0000	−1.95852	−0.979260	+	0.202606i	$0.935059\pi$
$878$	26.0000	0.877457
$879$	0	0
$880$	0	0
$881$	37.0000	1.24656	0.623281	−	0.781998i	$-0.285799\pi$
$881$	37.0000	1.24656	0.623281	+	0.781998i	$0.285799\pi$
$882$	−54.0000	−1.81827
$883$	8.00000	0.269221	0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000	0.269221	0.134611	+	0.990899i	$0.457022\pi$
$884$	−8.00000	−0.269069
$885$	0	0
$886$	−8.00000	−0.268765
$887$	−16.0000	−0.537227	−0.268614	−	0.963248i	$-0.586566\pi$
$887$	−16.0000	−0.537227	−0.268614	+	0.963248i	$0.586566\pi$
$888$	0	0
$889$	−24.0000	−0.804934
$890$	0	0
$891$	−9.00000	−0.301511
$892$	−4.00000	−0.133930
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−62.0000	−2.06897
$899$	−63.0000	−2.10117
$900$	0	0
$901$	8.00000	0.266519
$902$	4.00000	0.133185
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	12.0000	0.398453	0.199227	−	0.979953i	$-0.436157\pi$
$907$	12.0000	0.398453	0.199227	+	0.979953i	$0.436157\pi$
$908$	28.0000	0.929213
$909$	−45.0000	−1.49256
$910$	0	0
$911$	−41.0000	−1.35839	−0.679195	−	0.733958i	$-0.737671\pi$
$911$	−41.0000	−1.35839	−0.679195	+	0.733958i	$0.737671\pi$
$912$	0	0
$913$	−6.00000	−0.198571
$914$	−68.0000	−2.24924
$915$	0	0
$916$	34.0000	1.12339
$917$	48.0000	1.58510
$918$	0	0
$919$	16.0000	0.527791	0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000	0.527791	0.263896	+	0.964551i	$0.414993\pi$
$920$	0	0
$921$	0	0
$922$	−50.0000	−1.64666
$923$	2.00000	0.0658308
$924$	0	0
$925$	0	0
$926$	8.00000	0.262896
$927$	−48.0000	−1.57653
$928$	72.0000	2.36352
$929$	51.0000	1.67326	0.836628	−	0.547772i	$-0.184524\pi$
$929$	51.0000	1.67326	0.836628	+	0.547772i	$0.184524\pi$
$930$	0	0
$931$	0	0
$932$	16.0000	0.524097
$933$	0	0
$934$	−20.0000	−0.654420
$935$	0	0
$936$	0	0
$937$	56.0000	1.82944	0.914720	−	0.404088i	$-0.132411\pi$
$937$	56.0000	1.82944	0.914720	+	0.404088i	$0.132411\pi$
$938$	−80.0000	−2.61209
$939$	0	0
$940$	0	0
$941$	−35.0000	−1.14097	−0.570484	−	0.821309i	$-0.693244\pi$
$941$	−35.0000	−1.14097	−0.570484	+	0.821309i	$0.693244\pi$
$942$	0	0
$943$	12.0000	0.390774
$944$	36.0000	1.17170
$945$	0	0
$946$	4.00000	0.130051
$947$	42.0000	1.36482	0.682408	−	0.730971i	$-0.260933\pi$
$947$	42.0000	1.36482	0.682408	+	0.730971i	$0.260933\pi$
$948$	0	0
$949$	20.0000	0.649227
$950$	0	0
$951$	0	0
$952$	0	0
$953$	−24.0000	−0.777436	−0.388718	−	0.921357i	$-0.627082\pi$
$953$	−24.0000	−0.777436	−0.388718	+	0.921357i	$0.627082\pi$
$954$	−24.0000	−0.777029
$955$	0	0
$956$	−38.0000	−1.22901
$957$	0	0
$958$	30.0000	0.969256
$959$	−48.0000	−1.55000
$960$	0	0
$961$	18.0000	0.580645
$962$	−8.00000	−0.257930
$963$	30.0000	0.966736
$964$	−2.00000	−0.0644157
$965$	0	0
$966$	0	0
$967$	−22.0000	−0.707472	−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000	−0.707472	−0.353736	+	0.935345i	$0.615089\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−36.0000	−1.15529	−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000	−1.15529	−0.577647	+	0.816286i	$0.696029\pi$
$972$	0	0
$973$	80.0000	2.56468
$974$	−76.0000	−2.43520
$975$	0	0
$976$	28.0000	0.896258
$977$	−44.0000	−1.40768	−0.703842	−	0.710356i	$-0.748534\pi$
$977$	−44.0000	−1.40768	−0.703842	+	0.710356i	$0.748534\pi$
$978$	0	0
$979$	−11.0000	−0.351562
$980$	0	0
$981$	45.0000	1.43674
$982$	26.0000	0.829693
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	0	0
$985$	0	0
$986$	−36.0000	−1.14647
$987$	0	0
$988$	0	0
$989$	12.0000	0.381578
$990$	0	0
$991$	−44.0000	−1.39771	−0.698853	−	0.715265i	$-0.746306\pi$
$991$	−44.0000	−1.39771	−0.698853	+	0.715265i	$0.746306\pi$
$992$	−56.0000	−1.77800
$993$	0	0
$994$	−8.00000	−0.253745
$995$	0	0
$996$	0	0
$997$	−26.0000	−0.823428	−0.411714	−	0.911313i	$-0.635070\pi$
$997$	−26.0000	−0.823428	−0.411714	+	0.911313i	$0.635070\pi$
$998$	56.0000	1.77265
$999$	0	0

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.j.1.1		1
5.2	odd	4		1805.2.b.a.1084.2		2
5.3	odd	4		1805.2.b.a.1084.1		2
5.4	even	2		9025.2.a.a.1.1		1
19.8	odd	6		475.2.e.c.26.1		2
19.12	odd	6		475.2.e.c.201.1		2
19.18	odd	2		9025.2.a.b.1.1		1
95.8	even	12		95.2.i.a.64.2	yes	4
95.12	even	12		95.2.i.a.49.2	yes	4
95.18	even	4		1805.2.b.b.1084.2		2
95.27	even	12		95.2.i.a.64.1	yes	4
95.37	even	4		1805.2.b.b.1084.1		2
95.69	odd	6		475.2.e.a.201.1		2
95.84	odd	6		475.2.e.a.26.1		2
95.88	even	12		95.2.i.a.49.1	✓	4
95.94	odd	2		9025.2.a.i.1.1		1
285.8	odd	12		855.2.be.a.64.1		4
285.107	odd	12		855.2.be.a.334.1		4
285.122	odd	12		855.2.be.a.64.2		4
285.278	odd	12		855.2.be.a.334.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.i.a.49.1	✓	4	95.88	even	12
95.2.i.a.49.2	yes	4	95.12	even	12
95.2.i.a.64.1	yes	4	95.27	even	12
95.2.i.a.64.2	yes	4	95.8	even	12
475.2.e.a.26.1		2	95.84	odd	6
475.2.e.a.201.1		2	95.69	odd	6
475.2.e.c.26.1		2	19.8	odd	6
475.2.e.c.201.1		2	19.12	odd	6
855.2.be.a.64.1		4	285.8	odd	12
855.2.be.a.64.2		4	285.122	odd	12
855.2.be.a.334.1		4	285.107	odd	12
855.2.be.a.334.2		4	285.278	odd	12
1805.2.b.a.1084.1		2	5.3	odd	4
1805.2.b.a.1084.2		2	5.2	odd	4
1805.2.b.b.1084.1		2	95.37	even	4
1805.2.b.b.1084.2		2	95.18	even	4
9025.2.a.a.1.1		1	5.4	even	2
9025.2.a.b.1.1		1	19.18	odd	2
9025.2.a.i.1.1		1	95.94	odd	2
9025.2.a.j.1.1		1	1.1	even	1	trivial

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 $\F_{q}$

Introduction

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Modular forms

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

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

Label	9025.2.a.j.1.1

Level	$9025$
Weight	$2$
Character	9025.1
Self dual	yes
Analytic conductor	$72.065$
Analytic rank	$1$
Dimension	$1$
CM	no
Inner twists	$1$