LMFDB - Embedded newform 8025.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8025,2,Mod(1,8025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8025, 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("8025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8025 = 3 \cdot 5^{2} \cdot 107 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8025.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:	$64.0799476221$
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	$\chi$	$=$	8025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q-2.00000 q^{2} -1.00000 q^{3} +2.00000 q^{4} +2.00000 q^{6} +1.00000 q^{7} +1.00000 q^{9} -2.00000 q^{11} -2.00000 q^{12} +1.00000 q^{13} -2.00000 q^{14} -4.00000 q^{16} -2.00000 q^{17} -2.00000 q^{18} -5.00000 q^{19} -1.00000 q^{21} +4.00000 q^{22} -6.00000 q^{23} -2.00000 q^{26} -1.00000 q^{27} +2.00000 q^{28} -6.00000 q^{29} -7.00000 q^{31} +8.00000 q^{32} +2.00000 q^{33} +4.00000 q^{34} +2.00000 q^{36} -6.00000 q^{37} +10.0000 q^{38} -1.00000 q^{39} +2.00000 q^{42} +5.00000 q^{43} -4.00000 q^{44} +12.0000 q^{46} -6.00000 q^{47} +4.00000 q^{48} -6.00000 q^{49} +2.00000 q^{51} +2.00000 q^{52} -12.0000 q^{53} +2.00000 q^{54} +5.00000 q^{57} +12.0000 q^{58} -10.0000 q^{59} -1.00000 q^{61} +14.0000 q^{62} +1.00000 q^{63} -8.00000 q^{64} -4.00000 q^{66} +9.00000 q^{67} -4.00000 q^{68} +6.00000 q^{69} -12.0000 q^{71} +2.00000 q^{73} +12.0000 q^{74} -10.0000 q^{76} -2.00000 q^{77} +2.00000 q^{78} -8.00000 q^{79} +1.00000 q^{81} +18.0000 q^{83} -2.00000 q^{84} -10.0000 q^{86} +6.00000 q^{87} +12.0000 q^{89} +1.00000 q^{91} -12.0000 q^{92} +7.00000 q^{93} +12.0000 q^{94} -8.00000 q^{96} +5.00000 q^{97} +12.0000 q^{98} -2.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.00000	−1.41421	−0.707107	−	0.707107i	$-0.750000\pi$
$2$	−2.00000	−1.41421	−0.707107	+	0.707107i	$0.750000\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.00000	1.00000
$5$	0	0
$5$	0	0
$6$	2.00000	0.816497
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	0	0
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	−2.00000	−0.577350
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	−2.00000	−0.534522
$15$	0	0
$16$	−4.00000	−1.00000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−2.00000	−0.471405
$19$	−5.00000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	4.00000	0.852803
$23$	−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
$26$	−2.00000	−0.392232
$27$	−1.00000	−0.192450
$28$	2.00000	0.377964
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	0	0
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	8.00000	1.41421
$33$	2.00000	0.348155
$34$	4.00000	0.685994
$35$	0	0
$36$	2.00000	0.333333
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	10.0000	1.62221
$39$	−1.00000	−0.160128
$40$	0	0
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	2.00000	0.308607
$43$	5.00000	0.762493	0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000	0.762493	0.381246	+	0.924473i	$0.375495\pi$
$44$	−4.00000	−0.603023
$45$	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	$0.644170\pi$
$48$	4.00000	0.577350
$49$	−6.00000	−0.857143
$50$	0	0
$51$	2.00000	0.280056
$52$	2.00000	0.277350
$53$	−12.0000	−1.64833	−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000	−1.64833	−0.824163	+	0.566352i	$0.808354\pi$
$54$	2.00000	0.272166
$55$	0	0
$56$	0	0
$57$	5.00000	0.662266
$58$	12.0000	1.57568
$59$	−10.0000	−1.30189	−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000	−1.30189	−0.650945	+	0.759125i	$0.725627\pi$
$60$	0	0
$61$	−1.00000	−0.128037	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000	−0.128037	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	14.0000	1.77800
$63$	1.00000	0.125988
$64$	−8.00000	−1.00000
$65$	0	0
$66$	−4.00000	−0.492366
$67$	9.00000	1.09952	0.549762	−	0.835321i	$-0.314718\pi$
$67$	9.00000	1.09952	0.549762	+	0.835321i	$0.314718\pi$
$68$	−4.00000	−0.485071
$69$	6.00000	0.722315
$70$	0	0
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	0	0
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	12.0000	1.39497
$75$	0	0
$76$	−10.0000	−1.14708
$77$	−2.00000	−0.227921
$78$	2.00000	0.226455
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	0	0
$83$	18.0000	1.97576	0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000	1.97576	0.987878	+	0.155230i	$0.0496119\pi$
$84$	−2.00000	−0.218218
$85$	0	0
$86$	−10.0000	−1.07833
$87$	6.00000	0.643268
$88$	0	0
$89$	12.0000	1.27200	0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000	1.27200	0.635999	+	0.771690i	$0.280588\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	−12.0000	−1.25109
$93$	7.00000	0.725866
$94$	12.0000	1.23771
$95$	0	0
$96$	−8.00000	−0.816497
$97$	5.00000	0.507673	0.253837	−	0.967247i	$-0.418307\pi$
$97$	5.00000	0.507673	0.253837	+	0.967247i	$0.418307\pi$
$98$	12.0000	1.21218
$99$	−2.00000	−0.201008
$100$	0	0
$101$	4.00000	0.398015	0.199007	−	0.979998i	$-0.436228\pi$
$101$	4.00000	0.398015	0.199007	+	0.979998i	$0.436228\pi$
$102$	−4.00000	−0.396059
$103$	20.0000	1.97066	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	20.0000	1.97066	0.985329	+	0.170664i	$0.0545913\pi$
$104$	0	0
$105$	0	0
$106$	24.0000	2.33109
$107$	−1.00000	−0.0966736
$107$	−1.00000	−0.0966736
$108$	−2.00000	−0.192450
$109$	1.00000	0.0957826	0.0478913	−	0.998853i	$-0.484750\pi$
$109$	1.00000	0.0957826	0.0478913	+	0.998853i	$0.484750\pi$
$110$	0	0
$111$	6.00000	0.569495
$112$	−4.00000	−0.377964
$113$	16.0000	1.50515	0.752577	−	0.658505i	$-0.228811\pi$
$113$	16.0000	1.50515	0.752577	+	0.658505i	$0.228811\pi$
$114$	−10.0000	−0.936586
$115$	0	0
$116$	−12.0000	−1.11417
$117$	1.00000	0.0924500
$118$	20.0000	1.84115
$119$	−2.00000	−0.183340
$120$	0	0
$121$	−7.00000	−0.636364
$122$	2.00000	0.181071
$123$	0	0
$124$	−14.0000	−1.25724
$125$	0	0
$126$	−2.00000	−0.178174
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	0	0
$129$	−5.00000	−0.440225
$130$	0	0
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	4.00000	0.348155
$133$	−5.00000	−0.433555
$134$	−18.0000	−1.55496
$135$	0	0
$136$	0	0
$137$	−14.0000	−1.19610	−0.598050	−	0.801459i	$-0.704058\pi$
$137$	−14.0000	−1.19610	−0.598050	+	0.801459i	$0.704058\pi$
$138$	−12.0000	−1.02151
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	6.00000	0.505291
$142$	24.0000	2.01404
$143$	−2.00000	−0.167248
$144$	−4.00000	−0.333333
$145$	0	0
$146$	−4.00000	−0.331042
$147$	6.00000	0.494872
$148$	−12.0000	−0.986394
$149$	2.00000	0.163846	0.0819232	−	0.996639i	$-0.473894\pi$
$149$	2.00000	0.163846	0.0819232	+	0.996639i	$0.473894\pi$
$150$	0	0
$151$	23.0000	1.87171	0.935857	−	0.352381i	$-0.114628\pi$
$151$	23.0000	1.87171	0.935857	+	0.352381i	$0.114628\pi$
$152$	0	0
$153$	−2.00000	−0.161690
$154$	4.00000	0.322329
$155$	0	0
$156$	−2.00000	−0.160128
$157$	−17.0000	−1.35675	−0.678374	−	0.734717i	$-0.737315\pi$
$157$	−17.0000	−1.35675	−0.678374	+	0.734717i	$0.737315\pi$
$158$	16.0000	1.27289
$159$	12.0000	0.951662
$160$	0	0
$161$	−6.00000	−0.472866
$162$	−2.00000	−0.157135
$163$	11.0000	0.861586	0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000	0.861586	0.430793	+	0.902451i	$0.358234\pi$
$164$	0	0
$165$	0	0
$166$	−36.0000	−2.79414
$167$	−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
$169$	−12.0000	−0.923077
$170$	0	0
$171$	−5.00000	−0.382360
$172$	10.0000	0.762493
$173$	−22.0000	−1.67263	−0.836315	−	0.548250i	$-0.815294\pi$
$173$	−22.0000	−1.67263	−0.836315	+	0.548250i	$0.815294\pi$
$174$	−12.0000	−0.909718
$175$	0	0
$176$	8.00000	0.603023
$177$	10.0000	0.751646
$178$	−24.0000	−1.79888
$179$	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
$181$	5.00000	0.371647	0.185824	−	0.982583i	$-0.440505\pi$
$181$	5.00000	0.371647	0.185824	+	0.982583i	$0.440505\pi$
$182$	−2.00000	−0.148250
$183$	1.00000	0.0739221
$184$	0	0
$185$	0	0
$186$	−14.0000	−1.02653
$187$	4.00000	0.292509
$188$	−12.0000	−0.875190
$189$	−1.00000	−0.0727393
$190$	0	0
$191$	10.0000	0.723575	0.361787	−	0.932261i	$-0.382167\pi$
$191$	10.0000	0.723575	0.361787	+	0.932261i	$0.382167\pi$
$192$	8.00000	0.577350
$193$	−13.0000	−0.935760	−0.467880	−	0.883792i	$-0.654982\pi$
$193$	−13.0000	−0.935760	−0.467880	+	0.883792i	$0.654982\pi$
$194$	−10.0000	−0.717958
$195$	0	0
$196$	−12.0000	−0.857143
$197$	14.0000	0.997459	0.498729	−	0.866758i	$-0.333800\pi$
$197$	14.0000	0.997459	0.498729	+	0.866758i	$0.333800\pi$
$198$	4.00000	0.284268
$199$	11.0000	0.779769	0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000	0.779769	0.389885	+	0.920864i	$0.372515\pi$
$200$	0	0
$201$	−9.00000	−0.634811
$202$	−8.00000	−0.562878
$203$	−6.00000	−0.421117
$204$	4.00000	0.280056
$205$	0	0
$206$	−40.0000	−2.78693
$207$	−6.00000	−0.417029
$208$	−4.00000	−0.277350
$209$	10.0000	0.691714
$210$	0	0
$211$	7.00000	0.481900	0.240950	−	0.970538i	$-0.422541\pi$
$211$	7.00000	0.481900	0.240950	+	0.970538i	$0.422541\pi$
$212$	−24.0000	−1.64833
$213$	12.0000	0.822226
$214$	2.00000	0.136717
$215$	0	0
$216$	0	0
$217$	−7.00000	−0.475191
$218$	−2.00000	−0.135457
$219$	−2.00000	−0.135147
$220$	0	0
$221$	−2.00000	−0.134535
$222$	−12.0000	−0.805387
$223$	29.0000	1.94198	0.970992	−	0.239113i	$-0.0768565\pi$
$223$	29.0000	1.94198	0.970992	+	0.239113i	$0.0768565\pi$
$224$	8.00000	0.534522
$225$	0	0
$226$	−32.0000	−2.12861
$227$	−16.0000	−1.06196	−0.530979	−	0.847385i	$-0.678176\pi$
$227$	−16.0000	−1.06196	−0.530979	+	0.847385i	$0.678176\pi$
$228$	10.0000	0.662266
$229$	5.00000	0.330409	0.165205	−	0.986259i	$-0.447172\pi$
$229$	5.00000	0.330409	0.165205	+	0.986259i	$0.447172\pi$
$230$	0	0
$231$	2.00000	0.131590
$232$	0	0
$233$	28.0000	1.83434	0.917170	−	0.398495i	$-0.130467\pi$
$233$	28.0000	1.83434	0.917170	+	0.398495i	$0.130467\pi$
$234$	−2.00000	−0.130744
$235$	0	0
$236$	−20.0000	−1.30189
$237$	8.00000	0.519656
$238$	4.00000	0.259281
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	0	0
$241$	25.0000	1.61039	0.805196	−	0.593009i	$-0.202060\pi$
$241$	25.0000	1.61039	0.805196	+	0.593009i	$0.202060\pi$
$242$	14.0000	0.899954
$243$	−1.00000	−0.0641500
$244$	−2.00000	−0.128037
$245$	0	0
$246$	0	0
$247$	−5.00000	−0.318142
$248$	0	0
$249$	−18.0000	−1.14070
$250$	0	0
$251$	−28.0000	−1.76734	−0.883672	−	0.468106i	$-0.844936\pi$
$251$	−28.0000	−1.76734	−0.883672	+	0.468106i	$0.844936\pi$
$252$	2.00000	0.125988
$253$	12.0000	0.754434
$254$	−32.0000	−2.00786
$255$	0	0
$256$	16.0000	1.00000
$257$	−16.0000	−0.998053	−0.499026	−	0.866587i	$-0.666309\pi$
$257$	−16.0000	−0.998053	−0.499026	+	0.866587i	$0.666309\pi$
$258$	10.0000	0.622573
$259$	−6.00000	−0.372822
$260$	0	0
$261$	−6.00000	−0.371391
$262$	8.00000	0.494242
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	0	0
$265$	0	0
$266$	10.0000	0.613139
$267$	−12.0000	−0.734388
$268$	18.0000	1.09952
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	8.00000	0.485071
$273$	−1.00000	−0.0605228
$274$	28.0000	1.69154
$275$	0	0
$276$	12.0000	0.722315
$277$	−7.00000	−0.420589	−0.210295	−	0.977638i	$-0.567442\pi$
$277$	−7.00000	−0.420589	−0.210295	+	0.977638i	$0.567442\pi$
$278$	−8.00000	−0.479808
$279$	−7.00000	−0.419079
$280$	0	0
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	−12.0000	−0.714590
$283$	23.0000	1.36721	0.683604	−	0.729853i	$-0.260412\pi$
$283$	23.0000	1.36721	0.683604	+	0.729853i	$0.260412\pi$
$284$	−24.0000	−1.42414
$285$	0	0
$286$	4.00000	0.236525
$287$	0	0
$288$	8.00000	0.471405
$289$	−13.0000	−0.764706
$290$	0	0
$291$	−5.00000	−0.293105
$292$	4.00000	0.234082
$293$	10.0000	0.584206	0.292103	−	0.956387i	$-0.405645\pi$
$293$	10.0000	0.584206	0.292103	+	0.956387i	$0.405645\pi$
$294$	−12.0000	−0.699854
$295$	0	0
$296$	0	0
$297$	2.00000	0.116052
$298$	−4.00000	−0.231714
$299$	−6.00000	−0.346989
$300$	0	0
$301$	5.00000	0.288195
$302$	−46.0000	−2.64700
$303$	−4.00000	−0.229794
$304$	20.0000	1.14708
$305$	0	0
$306$	4.00000	0.228665
$307$	−21.0000	−1.19853	−0.599267	−	0.800549i	$-0.704541\pi$
$307$	−21.0000	−1.19853	−0.599267	+	0.800549i	$0.704541\pi$
$308$	−4.00000	−0.227921
$309$	−20.0000	−1.13776
$310$	0	0
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	0	0
$313$	−21.0000	−1.18699	−0.593495	−	0.804838i	$-0.702252\pi$
$313$	−21.0000	−1.18699	−0.593495	+	0.804838i	$0.702252\pi$
$314$	34.0000	1.91873
$315$	0	0
$316$	−16.0000	−0.900070
$317$	−4.00000	−0.224662	−0.112331	−	0.993671i	$-0.535832\pi$
$317$	−4.00000	−0.224662	−0.112331	+	0.993671i	$0.535832\pi$
$318$	−24.0000	−1.34585
$319$	12.0000	0.671871
$320$	0	0
$321$	1.00000	0.0558146
$322$	12.0000	0.668734
$323$	10.0000	0.556415
$324$	2.00000	0.111111
$325$	0	0
$326$	−22.0000	−1.21847
$327$	−1.00000	−0.0553001
$328$	0	0
$329$	−6.00000	−0.330791
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	36.0000	1.97576
$333$	−6.00000	−0.328798
$334$	24.0000	1.31322
$335$	0	0
$336$	4.00000	0.218218
$337$	−7.00000	−0.381314	−0.190657	−	0.981657i	$-0.561062\pi$
$337$	−7.00000	−0.381314	−0.190657	+	0.981657i	$0.561062\pi$
$338$	24.0000	1.30543
$339$	−16.0000	−0.869001
$340$	0	0
$341$	14.0000	0.758143
$342$	10.0000	0.540738
$343$	−13.0000	−0.701934
$344$	0	0
$345$	0	0
$346$	44.0000	2.36545
$347$	−22.0000	−1.18102	−0.590511	−	0.807030i	$-0.701074\pi$
$347$	−22.0000	−1.18102	−0.590511	+	0.807030i	$0.701074\pi$
$348$	12.0000	0.643268
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	−16.0000	−0.852803
$353$	−30.0000	−1.59674	−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000	−1.59674	−0.798369	+	0.602168i	$0.794304\pi$
$354$	−20.0000	−1.06299
$355$	0	0
$356$	24.0000	1.27200
$357$	2.00000	0.105851
$358$	−12.0000	−0.634220
$359$	28.0000	1.47778	0.738892	−	0.673824i	$-0.235349\pi$
$359$	28.0000	1.47778	0.738892	+	0.673824i	$0.235349\pi$
$360$	0	0
$361$	6.00000	0.315789
$362$	−10.0000	−0.525588
$363$	7.00000	0.367405
$364$	2.00000	0.104828
$365$	0	0
$366$	−2.00000	−0.104542
$367$	−33.0000	−1.72259	−0.861293	−	0.508109i	$-0.830345\pi$
$367$	−33.0000	−1.72259	−0.861293	+	0.508109i	$0.830345\pi$
$368$	24.0000	1.25109
$369$	0	0
$370$	0	0
$371$	−12.0000	−0.623009
$372$	14.0000	0.725866
$373$	27.0000	1.39801	0.699004	−	0.715118i	$-0.253627\pi$
$373$	27.0000	1.39801	0.699004	+	0.715118i	$0.253627\pi$
$374$	−8.00000	−0.413670
$375$	0	0
$376$	0	0
$377$	−6.00000	−0.309016
$378$	2.00000	0.102869
$379$	−19.0000	−0.975964	−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000	−0.975964	−0.487982	+	0.872854i	$0.662267\pi$
$380$	0	0
$381$	−16.0000	−0.819705
$382$	−20.0000	−1.02329
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	0	0
$385$	0	0
$386$	26.0000	1.32337
$387$	5.00000	0.254164
$388$	10.0000	0.507673
$389$	16.0000	0.811232	0.405616	−	0.914044i	$-0.367057\pi$
$389$	16.0000	0.811232	0.405616	+	0.914044i	$0.367057\pi$
$390$	0	0
$391$	12.0000	0.606866
$392$	0	0
$393$	4.00000	0.201773
$394$	−28.0000	−1.41062
$395$	0	0
$396$	−4.00000	−0.201008
$397$	7.00000	0.351320	0.175660	−	0.984451i	$-0.443794\pi$
$397$	7.00000	0.351320	0.175660	+	0.984451i	$0.443794\pi$
$398$	−22.0000	−1.10276
$399$	5.00000	0.250313
$400$	0	0
$401$	−36.0000	−1.79775	−0.898877	−	0.438201i	$-0.855616\pi$
$401$	−36.0000	−1.79775	−0.898877	+	0.438201i	$0.855616\pi$
$402$	18.0000	0.897758
$403$	−7.00000	−0.348695
$404$	8.00000	0.398015
$405$	0	0
$406$	12.0000	0.595550
$407$	12.0000	0.594818
$408$	0	0
$409$	33.0000	1.63174	0.815872	−	0.578232i	$-0.196257\pi$
$409$	33.0000	1.63174	0.815872	+	0.578232i	$0.196257\pi$
$410$	0	0
$411$	14.0000	0.690569
$412$	40.0000	1.97066
$413$	−10.0000	−0.492068
$414$	12.0000	0.589768
$415$	0	0
$416$	8.00000	0.392232
$417$	−4.00000	−0.195881
$418$	−20.0000	−0.978232
$419$	20.0000	0.977064	0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000	0.977064	0.488532	+	0.872546i	$0.337533\pi$
$420$	0	0
$421$	−2.00000	−0.0974740	−0.0487370	−	0.998812i	$-0.515520\pi$
$421$	−2.00000	−0.0974740	−0.0487370	+	0.998812i	$0.515520\pi$
$422$	−14.0000	−0.681509
$423$	−6.00000	−0.291730
$424$	0	0
$425$	0	0
$426$	−24.0000	−1.16280
$427$	−1.00000	−0.0483934
$428$	−2.00000	−0.0966736
$429$	2.00000	0.0965609
$430$	0	0
$431$	−2.00000	−0.0963366	−0.0481683	−	0.998839i	$-0.515338\pi$
$431$	−2.00000	−0.0963366	−0.0481683	+	0.998839i	$0.515338\pi$
$432$	4.00000	0.192450
$433$	39.0000	1.87422	0.937110	−	0.349034i	$-0.113490\pi$
$433$	39.0000	1.87422	0.937110	+	0.349034i	$0.113490\pi$
$434$	14.0000	0.672022
$435$	0	0
$436$	2.00000	0.0957826
$437$	30.0000	1.43509
$438$	4.00000	0.191127
$439$	−3.00000	−0.143182	−0.0715911	−	0.997434i	$-0.522808\pi$
$439$	−3.00000	−0.143182	−0.0715911	+	0.997434i	$0.522808\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	4.00000	0.190261
$443$	4.00000	0.190046	0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000	0.190046	0.0950229	+	0.995475i	$0.469708\pi$
$444$	12.0000	0.569495
$445$	0	0
$446$	−58.0000	−2.74638
$447$	−2.00000	−0.0945968
$448$	−8.00000	−0.377964
$449$	−4.00000	−0.188772	−0.0943858	−	0.995536i	$-0.530089\pi$
$449$	−4.00000	−0.188772	−0.0943858	+	0.995536i	$0.530089\pi$
$450$	0	0
$451$	0	0
$452$	32.0000	1.50515
$453$	−23.0000	−1.08063
$454$	32.0000	1.50183
$455$	0	0
$456$	0	0
$457$	6.00000	0.280668	0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000	0.280668	0.140334	+	0.990104i	$0.455182\pi$
$458$	−10.0000	−0.467269
$459$	2.00000	0.0933520
$460$	0	0
$461$	16.0000	0.745194	0.372597	−	0.927993i	$-0.378467\pi$
$461$	16.0000	0.745194	0.372597	+	0.927993i	$0.378467\pi$
$462$	−4.00000	−0.186097
$463$	−40.0000	−1.85896	−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000	−1.85896	−0.929479	+	0.368875i	$0.879743\pi$
$464$	24.0000	1.11417
$465$	0	0
$466$	−56.0000	−2.59415
$467$	−18.0000	−0.832941	−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000	−0.832941	−0.416470	+	0.909149i	$0.636733\pi$
$468$	2.00000	0.0924500
$469$	9.00000	0.415581
$470$	0	0
$471$	17.0000	0.783319
$472$	0	0
$473$	−10.0000	−0.459800
$474$	−16.0000	−0.734904
$475$	0	0
$476$	−4.00000	−0.183340
$477$	−12.0000	−0.549442
$478$	−24.0000	−1.09773
$479$	−18.0000	−0.822441	−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000	−0.822441	−0.411220	+	0.911536i	$0.634897\pi$
$480$	0	0
$481$	−6.00000	−0.273576
$482$	−50.0000	−2.27744
$483$	6.00000	0.273009
$484$	−14.0000	−0.636364
$485$	0	0
$486$	2.00000	0.0907218
$487$	−25.0000	−1.13286	−0.566429	−	0.824110i	$-0.691675\pi$
$487$	−25.0000	−1.13286	−0.566429	+	0.824110i	$0.691675\pi$
$488$	0	0
$489$	−11.0000	−0.497437
$490$	0	0
$491$	36.0000	1.62466	0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000	1.62466	0.812329	+	0.583200i	$0.198200\pi$
$492$	0	0
$493$	12.0000	0.540453
$494$	10.0000	0.449921
$495$	0	0
$496$	28.0000	1.25724
$497$	−12.0000	−0.538274
$498$	36.0000	1.61320
$499$	−41.0000	−1.83541	−0.917706	−	0.397260i	$-0.869961\pi$
$499$	−41.0000	−1.83541	−0.917706	+	0.397260i	$0.869961\pi$
$500$	0	0
$501$	12.0000	0.536120
$502$	56.0000	2.49940
$503$	36.0000	1.60516	0.802580	−	0.596544i	$-0.203460\pi$
$503$	36.0000	1.60516	0.802580	+	0.596544i	$0.203460\pi$
$504$	0	0
$505$	0	0
$506$	−24.0000	−1.06693
$507$	12.0000	0.532939
$508$	32.0000	1.41977
$509$	14.0000	0.620539	0.310270	−	0.950649i	$-0.399581\pi$
$509$	14.0000	0.620539	0.310270	+	0.950649i	$0.399581\pi$
$510$	0	0
$511$	2.00000	0.0884748
$512$	−32.0000	−1.41421
$513$	5.00000	0.220755
$514$	32.0000	1.41146
$515$	0	0
$516$	−10.0000	−0.440225
$517$	12.0000	0.527759
$518$	12.0000	0.527250
$519$	22.0000	0.965693
$520$	0	0
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	12.0000	0.525226
$523$	11.0000	0.480996	0.240498	−	0.970650i	$-0.422689\pi$
$523$	11.0000	0.480996	0.240498	+	0.970650i	$0.422689\pi$
$524$	−8.00000	−0.349482
$525$	0	0
$526$	−16.0000	−0.697633
$527$	14.0000	0.609850
$528$	−8.00000	−0.348155
$529$	13.0000	0.565217
$530$	0	0
$531$	−10.0000	−0.433963
$532$	−10.0000	−0.433555
$533$	0	0
$534$	24.0000	1.03858
$535$	0	0
$536$	0	0
$537$	−6.00000	−0.258919
$538$	36.0000	1.55207
$539$	12.0000	0.516877
$540$	0	0
$541$	17.0000	0.730887	0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000	0.730887	0.365444	+	0.930834i	$0.380917\pi$
$542$	−16.0000	−0.687259
$543$	−5.00000	−0.214571
$544$	−16.0000	−0.685994
$545$	0	0
$546$	2.00000	0.0855921
$547$	−8.00000	−0.342055	−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000	−0.342055	−0.171028	+	0.985266i	$0.554709\pi$
$548$	−28.0000	−1.19610
$549$	−1.00000	−0.0426790
$550$	0	0
$551$	30.0000	1.27804
$552$	0	0
$553$	−8.00000	−0.340195
$554$	14.0000	0.594803
$555$	0	0
$556$	8.00000	0.339276
$557$	42.0000	1.77960	0.889799	−	0.456354i	$-0.150845\pi$
$557$	42.0000	1.77960	0.889799	+	0.456354i	$0.150845\pi$
$558$	14.0000	0.592667
$559$	5.00000	0.211477
$560$	0	0
$561$	−4.00000	−0.168880
$562$	36.0000	1.51857
$563$	−6.00000	−0.252870	−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000	−0.252870	−0.126435	+	0.991975i	$0.540353\pi$
$564$	12.0000	0.505291
$565$	0	0
$566$	−46.0000	−1.93352
$567$	1.00000	0.0419961
$568$	0	0
$569$	−14.0000	−0.586911	−0.293455	−	0.955973i	$-0.594805\pi$
$569$	−14.0000	−0.586911	−0.293455	+	0.955973i	$0.594805\pi$
$570$	0	0
$571$	−29.0000	−1.21361	−0.606806	−	0.794850i	$-0.707550\pi$
$571$	−29.0000	−1.21361	−0.606806	+	0.794850i	$0.707550\pi$
$572$	−4.00000	−0.167248
$573$	−10.0000	−0.417756
$574$	0	0
$575$	0	0
$576$	−8.00000	−0.333333
$577$	27.0000	1.12402	0.562012	−	0.827129i	$-0.310027\pi$
$577$	27.0000	1.12402	0.562012	+	0.827129i	$0.310027\pi$
$578$	26.0000	1.08146
$579$	13.0000	0.540262
$580$	0	0
$581$	18.0000	0.746766
$582$	10.0000	0.414513
$583$	24.0000	0.993978
$584$	0	0
$585$	0	0
$586$	−20.0000	−0.826192
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	12.0000	0.494872
$589$	35.0000	1.44215
$590$	0	0
$591$	−14.0000	−0.575883
$592$	24.0000	0.986394
$593$	−24.0000	−0.985562	−0.492781	−	0.870153i	$-0.664020\pi$
$593$	−24.0000	−0.985562	−0.492781	+	0.870153i	$0.664020\pi$
$594$	−4.00000	−0.164122
$595$	0	0
$596$	4.00000	0.163846
$597$	−11.0000	−0.450200
$598$	12.0000	0.490716
$599$	−16.0000	−0.653742	−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000	−0.653742	−0.326871	+	0.945069i	$0.605994\pi$
$600$	0	0
$601$	15.0000	0.611863	0.305931	−	0.952054i	$-0.401032\pi$
$601$	15.0000	0.611863	0.305931	+	0.952054i	$0.401032\pi$
$602$	−10.0000	−0.407570
$603$	9.00000	0.366508
$604$	46.0000	1.87171
$605$	0	0
$606$	8.00000	0.324978
$607$	40.0000	1.62355	0.811775	−	0.583970i	$-0.198502\pi$
$607$	40.0000	1.62355	0.811775	+	0.583970i	$0.198502\pi$
$608$	−40.0000	−1.62221
$609$	6.00000	0.243132
$610$	0	0
$611$	−6.00000	−0.242734
$612$	−4.00000	−0.161690
$613$	−14.0000	−0.565455	−0.282727	−	0.959200i	$-0.591239\pi$
$613$	−14.0000	−0.565455	−0.282727	+	0.959200i	$0.591239\pi$
$614$	42.0000	1.69498
$615$	0	0
$616$	0	0
$617$	−32.0000	−1.28827	−0.644136	−	0.764911i	$-0.722783\pi$
$617$	−32.0000	−1.28827	−0.644136	+	0.764911i	$0.722783\pi$
$618$	40.0000	1.60904
$619$	19.0000	0.763674	0.381837	−	0.924230i	$-0.375291\pi$
$619$	19.0000	0.763674	0.381837	+	0.924230i	$0.375291\pi$
$620$	0	0
$621$	6.00000	0.240772
$622$	12.0000	0.481156
$623$	12.0000	0.480770
$624$	4.00000	0.160128
$625$	0	0
$626$	42.0000	1.67866
$627$	−10.0000	−0.399362
$628$	−34.0000	−1.35675
$629$	12.0000	0.478471
$630$	0	0
$631$	−3.00000	−0.119428	−0.0597141	−	0.998216i	$-0.519019\pi$
$631$	−3.00000	−0.119428	−0.0597141	+	0.998216i	$0.519019\pi$
$632$	0	0
$633$	−7.00000	−0.278225
$634$	8.00000	0.317721
$635$	0	0
$636$	24.0000	0.951662
$637$	−6.00000	−0.237729
$638$	−24.0000	−0.950169
$639$	−12.0000	−0.474713
$640$	0	0
$641$	−24.0000	−0.947943	−0.473972	−	0.880540i	$-0.657180\pi$
$641$	−24.0000	−0.947943	−0.473972	+	0.880540i	$0.657180\pi$
$642$	−2.00000	−0.0789337
$643$	36.0000	1.41970	0.709851	−	0.704352i	$-0.248762\pi$
$643$	36.0000	1.41970	0.709851	+	0.704352i	$0.248762\pi$
$644$	−12.0000	−0.472866
$645$	0	0
$646$	−20.0000	−0.786889
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	0	0
$649$	20.0000	0.785069
$650$	0	0
$651$	7.00000	0.274352
$652$	22.0000	0.861586
$653$	−38.0000	−1.48705	−0.743527	−	0.668705i	$-0.766849\pi$
$653$	−38.0000	−1.48705	−0.743527	+	0.668705i	$0.766849\pi$
$654$	2.00000	0.0782062
$655$	0	0
$656$	0	0
$657$	2.00000	0.0780274
$658$	12.0000	0.467809
$659$	20.0000	0.779089	0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000	0.779089	0.389545	+	0.921008i	$0.372632\pi$
$660$	0	0
$661$	2.00000	0.0777910	0.0388955	−	0.999243i	$-0.487616\pi$
$661$	2.00000	0.0777910	0.0388955	+	0.999243i	$0.487616\pi$
$662$	−40.0000	−1.55464
$663$	2.00000	0.0776736
$664$	0	0
$665$	0	0
$666$	12.0000	0.464991
$667$	36.0000	1.39393
$668$	−24.0000	−0.928588
$669$	−29.0000	−1.12120
$670$	0	0
$671$	2.00000	0.0772091
$672$	−8.00000	−0.308607
$673$	−10.0000	−0.385472	−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000	−0.385472	−0.192736	+	0.981251i	$0.561736\pi$
$674$	14.0000	0.539260
$675$	0	0
$676$	−24.0000	−0.923077
$677$	22.0000	0.845529	0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000	0.845529	0.422764	+	0.906240i	$0.361060\pi$
$678$	32.0000	1.22895
$679$	5.00000	0.191882
$680$	0	0
$681$	16.0000	0.613121
$682$	−28.0000	−1.07218
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	−10.0000	−0.382360
$685$	0	0
$686$	26.0000	0.992685
$687$	−5.00000	−0.190762
$688$	−20.0000	−0.762493
$689$	−12.0000	−0.457164
$690$	0	0
$691$	40.0000	1.52167	0.760836	−	0.648944i	$-0.224789\pi$
$691$	40.0000	1.52167	0.760836	+	0.648944i	$0.224789\pi$
$692$	−44.0000	−1.67263
$693$	−2.00000	−0.0759737
$694$	44.0000	1.67022
$695$	0	0
$696$	0	0
$697$	0	0
$698$	−4.00000	−0.151402
$699$	−28.0000	−1.05906
$700$	0	0
$701$	30.0000	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$702$	2.00000	0.0754851
$703$	30.0000	1.13147
$704$	16.0000	0.603023
$705$	0	0
$706$	60.0000	2.25813
$707$	4.00000	0.150435
$708$	20.0000	0.751646
$709$	−19.0000	−0.713560	−0.356780	−	0.934188i	$-0.616125\pi$
$709$	−19.0000	−0.713560	−0.356780	+	0.934188i	$0.616125\pi$
$710$	0	0
$711$	−8.00000	−0.300023
$712$	0	0
$713$	42.0000	1.57291
$714$	−4.00000	−0.149696
$715$	0	0
$716$	12.0000	0.448461
$717$	−12.0000	−0.448148
$718$	−56.0000	−2.08990
$719$	−18.0000	−0.671287	−0.335643	−	0.941989i	$-0.608954\pi$
$719$	−18.0000	−0.671287	−0.335643	+	0.941989i	$0.608954\pi$
$720$	0	0
$721$	20.0000	0.744839
$722$	−12.0000	−0.446594
$723$	−25.0000	−0.929760
$724$	10.0000	0.371647
$725$	0	0
$726$	−14.0000	−0.519589
$727$	−3.00000	−0.111264	−0.0556319	−	0.998451i	$-0.517717\pi$
$727$	−3.00000	−0.111264	−0.0556319	+	0.998451i	$0.517717\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	0	0
$731$	−10.0000	−0.369863
$732$	2.00000	0.0739221
$733$	−18.0000	−0.664845	−0.332423	−	0.943131i	$-0.607866\pi$
$733$	−18.0000	−0.664845	−0.332423	+	0.943131i	$0.607866\pi$
$734$	66.0000	2.43610
$735$	0	0
$736$	−48.0000	−1.76930
$737$	−18.0000	−0.663039
$738$	0	0
$739$	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
$741$	5.00000	0.183680
$742$	24.0000	0.881068
$743$	32.0000	1.17397	0.586983	−	0.809599i	$-0.300316\pi$
$743$	32.0000	1.17397	0.586983	+	0.809599i	$0.300316\pi$
$744$	0	0
$745$	0	0
$746$	−54.0000	−1.97708
$747$	18.0000	0.658586
$748$	8.00000	0.292509
$749$	−1.00000	−0.0365392
$750$	0	0
$751$	40.0000	1.45962	0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000	1.45962	0.729810	+	0.683650i	$0.239608\pi$
$752$	24.0000	0.875190
$753$	28.0000	1.02038
$754$	12.0000	0.437014
$755$	0	0
$756$	−2.00000	−0.0727393
$757$	21.0000	0.763258	0.381629	−	0.924316i	$-0.375363\pi$
$757$	21.0000	0.763258	0.381629	+	0.924316i	$0.375363\pi$
$758$	38.0000	1.38022
$759$	−12.0000	−0.435572
$760$	0	0
$761$	−44.0000	−1.59500	−0.797499	−	0.603320i	$-0.793844\pi$
$761$	−44.0000	−1.59500	−0.797499	+	0.603320i	$0.793844\pi$
$762$	32.0000	1.15924
$763$	1.00000	0.0362024
$764$	20.0000	0.723575
$765$	0	0
$766$	−72.0000	−2.60147
$767$	−10.0000	−0.361079
$768$	−16.0000	−0.577350
$769$	15.0000	0.540914	0.270457	−	0.962732i	$-0.412825\pi$
$769$	15.0000	0.540914	0.270457	+	0.962732i	$0.412825\pi$
$770$	0	0
$771$	16.0000	0.576226
$772$	−26.0000	−0.935760
$773$	0	0		−	1.00000i	$-0.5\pi$
$773$	0	0			1.00000i	$0.5\pi$
$774$	−10.0000	−0.359443
$775$	0	0
$776$	0	0
$777$	6.00000	0.215249
$778$	−32.0000	−1.14726
$779$	0	0
$780$	0	0
$781$	24.0000	0.858788
$782$	−24.0000	−0.858238
$783$	6.00000	0.214423
$784$	24.0000	0.857143
$785$	0	0
$786$	−8.00000	−0.285351
$787$	51.0000	1.81795	0.908977	−	0.416847i	$-0.136865\pi$
$787$	51.0000	1.81795	0.908977	+	0.416847i	$0.136865\pi$
$788$	28.0000	0.997459
$789$	−8.00000	−0.284808
$790$	0	0
$791$	16.0000	0.568895
$792$	0	0
$793$	−1.00000	−0.0355110
$794$	−14.0000	−0.496841
$795$	0	0
$796$	22.0000	0.779769
$797$	20.0000	0.708436	0.354218	−	0.935163i	$-0.384747\pi$
$797$	20.0000	0.708436	0.354218	+	0.935163i	$0.384747\pi$
$798$	−10.0000	−0.353996
$799$	12.0000	0.424529
$800$	0	0
$801$	12.0000	0.423999
$802$	72.0000	2.54241
$803$	−4.00000	−0.141157
$804$	−18.0000	−0.634811
$805$	0	0
$806$	14.0000	0.493129
$807$	18.0000	0.633630
$808$	0	0
$809$	36.0000	1.26569	0.632846	−	0.774277i	$-0.281886\pi$
$809$	36.0000	1.26569	0.632846	+	0.774277i	$0.281886\pi$
$810$	0	0
$811$	−5.00000	−0.175574	−0.0877869	−	0.996139i	$-0.527979\pi$
$811$	−5.00000	−0.175574	−0.0877869	+	0.996139i	$0.527979\pi$
$812$	−12.0000	−0.421117
$813$	−8.00000	−0.280572
$814$	−24.0000	−0.841200
$815$	0	0
$816$	−8.00000	−0.280056
$817$	−25.0000	−0.874639
$818$	−66.0000	−2.30764
$819$	1.00000	0.0349428
$820$	0	0
$821$	−42.0000	−1.46581	−0.732905	−	0.680331i	$-0.761836\pi$
$821$	−42.0000	−1.46581	−0.732905	+	0.680331i	$0.761836\pi$
$822$	−28.0000	−0.976612
$823$	37.0000	1.28974	0.644869	−	0.764293i	$-0.276912\pi$
$823$	37.0000	1.28974	0.644869	+	0.764293i	$0.276912\pi$
$824$	0	0
$825$	0	0
$826$	20.0000	0.695889
$827$	−48.0000	−1.66912	−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000	−1.66912	−0.834562	+	0.550914i	$0.814279\pi$
$828$	−12.0000	−0.417029
$829$	−30.0000	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$830$	0	0
$831$	7.00000	0.242827
$832$	−8.00000	−0.277350
$833$	12.0000	0.415775
$834$	8.00000	0.277017
$835$	0	0
$836$	20.0000	0.691714
$837$	7.00000	0.241955
$838$	−40.0000	−1.38178
$839$	−10.0000	−0.345238	−0.172619	−	0.984989i	$-0.555223\pi$
$839$	−10.0000	−0.345238	−0.172619	+	0.984989i	$0.555223\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	4.00000	0.137849
$843$	18.0000	0.619953
$844$	14.0000	0.481900
$845$	0	0
$846$	12.0000	0.412568
$847$	−7.00000	−0.240523
$848$	48.0000	1.64833
$849$	−23.0000	−0.789358
$850$	0	0
$851$	36.0000	1.23406
$852$	24.0000	0.822226
$853$	−57.0000	−1.95164	−0.975821	−	0.218569i	$-0.929861\pi$
$853$	−57.0000	−1.95164	−0.975821	+	0.218569i	$0.929861\pi$
$854$	2.00000	0.0684386
$855$	0	0
$856$	0	0
$857$	−56.0000	−1.91292	−0.956462	−	0.291858i	$-0.905727\pi$
$857$	−56.0000	−1.91292	−0.956462	+	0.291858i	$0.905727\pi$
$858$	−4.00000	−0.136558
$859$	−24.0000	−0.818869	−0.409435	−	0.912339i	$-0.634274\pi$
$859$	−24.0000	−0.818869	−0.409435	+	0.912339i	$0.634274\pi$
$860$	0	0
$861$	0	0
$862$	4.00000	0.136241
$863$	12.0000	0.408485	0.204242	−	0.978920i	$-0.434527\pi$
$863$	12.0000	0.408485	0.204242	+	0.978920i	$0.434527\pi$
$864$	−8.00000	−0.272166
$865$	0	0
$866$	−78.0000	−2.65055
$867$	13.0000	0.441503
$868$	−14.0000	−0.475191
$869$	16.0000	0.542763
$870$	0	0
$871$	9.00000	0.304953
$872$	0	0
$873$	5.00000	0.169224
$874$	−60.0000	−2.02953
$875$	0	0
$876$	−4.00000	−0.135147
$877$	−33.0000	−1.11433	−0.557165	−	0.830402i	$-0.688111\pi$
$877$	−33.0000	−1.11433	−0.557165	+	0.830402i	$0.688111\pi$
$878$	6.00000	0.202490
$879$	−10.0000	−0.337292
$880$	0	0
$881$	−40.0000	−1.34763	−0.673817	−	0.738898i	$-0.735346\pi$
$881$	−40.0000	−1.34763	−0.673817	+	0.738898i	$0.735346\pi$
$882$	12.0000	0.404061
$883$	1.00000	0.0336527	0.0168263	−	0.999858i	$-0.494644\pi$
$883$	1.00000	0.0336527	0.0168263	+	0.999858i	$0.494644\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	−8.00000	−0.268765
$887$	34.0000	1.14161	0.570804	−	0.821086i	$-0.306632\pi$
$887$	34.0000	1.14161	0.570804	+	0.821086i	$0.306632\pi$
$888$	0	0
$889$	16.0000	0.536623
$890$	0	0
$891$	−2.00000	−0.0670025
$892$	58.0000	1.94198
$893$	30.0000	1.00391
$894$	4.00000	0.133780
$895$	0	0
$896$	0	0
$897$	6.00000	0.200334
$898$	8.00000	0.266963
$899$	42.0000	1.40078
$900$	0	0
$901$	24.0000	0.799556
$902$	0	0
$903$	−5.00000	−0.166390
$904$	0	0
$905$	0	0
$906$	46.0000	1.52825
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	−32.0000	−1.06196
$909$	4.00000	0.132672
$910$	0	0
$911$	2.00000	0.0662630	0.0331315	−	0.999451i	$-0.489452\pi$
$911$	2.00000	0.0662630	0.0331315	+	0.999451i	$0.489452\pi$
$912$	−20.0000	−0.662266
$913$	−36.0000	−1.19143
$914$	−12.0000	−0.396925
$915$	0	0
$916$	10.0000	0.330409
$917$	−4.00000	−0.132092
$918$	−4.00000	−0.132020
$919$	11.0000	0.362857	0.181428	−	0.983404i	$-0.441928\pi$
$919$	11.0000	0.362857	0.181428	+	0.983404i	$0.441928\pi$
$920$	0	0
$921$	21.0000	0.691974
$922$	−32.0000	−1.05386
$923$	−12.0000	−0.394985
$924$	4.00000	0.131590
$925$	0	0
$926$	80.0000	2.62896
$927$	20.0000	0.656886
$928$	−48.0000	−1.57568
$929$	−34.0000	−1.11550	−0.557752	−	0.830008i	$-0.688336\pi$
$929$	−34.0000	−1.11550	−0.557752	+	0.830008i	$0.688336\pi$
$930$	0	0
$931$	30.0000	0.983210
$932$	56.0000	1.83434
$933$	6.00000	0.196431
$934$	36.0000	1.17796
$935$	0	0
$936$	0	0
$937$	−17.0000	−0.555366	−0.277683	−	0.960673i	$-0.589566\pi$
$937$	−17.0000	−0.555366	−0.277683	+	0.960673i	$0.589566\pi$
$938$	−18.0000	−0.587721
$939$	21.0000	0.685309
$940$	0	0
$941$	14.0000	0.456387	0.228193	−	0.973616i	$-0.426718\pi$
$941$	14.0000	0.456387	0.228193	+	0.973616i	$0.426718\pi$
$942$	−34.0000	−1.10778
$943$	0	0
$944$	40.0000	1.30189
$945$	0	0
$946$	20.0000	0.650256
$947$	10.0000	0.324956	0.162478	−	0.986712i	$-0.448051\pi$
$947$	10.0000	0.324956	0.162478	+	0.986712i	$0.448051\pi$
$948$	16.0000	0.519656
$949$	2.00000	0.0649227
$950$	0	0
$951$	4.00000	0.129709
$952$	0	0
$953$	36.0000	1.16615	0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000	1.16615	0.583077	+	0.812417i	$0.301849\pi$
$954$	24.0000	0.777029
$955$	0	0
$956$	24.0000	0.776215
$957$	−12.0000	−0.387905
$958$	36.0000	1.16311
$959$	−14.0000	−0.452084
$960$	0	0
$961$	18.0000	0.580645
$962$	12.0000	0.386896
$963$	−1.00000	−0.0322245
$964$	50.0000	1.61039
$965$	0	0
$966$	−12.0000	−0.386094
$967$	56.0000	1.80084	0.900419	−	0.435023i	$-0.143260\pi$
$967$	56.0000	1.80084	0.900419	+	0.435023i	$0.143260\pi$
$968$	0	0
$969$	−10.0000	−0.321246
$970$	0	0
$971$	10.0000	0.320915	0.160458	−	0.987043i	$-0.448703\pi$
$971$	10.0000	0.320915	0.160458	+	0.987043i	$0.448703\pi$
$972$	−2.00000	−0.0641500
$973$	4.00000	0.128234
$974$	50.0000	1.60210
$975$	0	0
$976$	4.00000	0.128037
$977$	58.0000	1.85558	0.927792	−	0.373097i	$-0.121704\pi$
$977$	58.0000	1.85558	0.927792	+	0.373097i	$0.121704\pi$
$978$	22.0000	0.703482
$979$	−24.0000	−0.767043
$980$	0	0
$981$	1.00000	0.0319275
$982$	−72.0000	−2.29761
$983$	0	0		−	1.00000i	$-0.5\pi$
$983$	0	0			1.00000i	$0.5\pi$
$984$	0	0
$985$	0	0
$986$	−24.0000	−0.764316
$987$	6.00000	0.190982
$988$	−10.0000	−0.318142
$989$	−30.0000	−0.953945
$990$	0	0
$991$	−43.0000	−1.36594	−0.682970	−	0.730446i	$-0.739312\pi$
$991$	−43.0000	−1.36594	−0.682970	+	0.730446i	$0.739312\pi$
$992$	−56.0000	−1.77800
$993$	−20.0000	−0.634681
$994$	24.0000	0.761234
$995$	0	0
$996$	−36.0000	−1.14070
$997$	2.00000	0.0633406	0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000	0.0633406	0.0316703	+	0.999498i	$0.489917\pi$
$998$	82.0000	2.59566
$999$	6.00000	0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8025.2.a.b.1.1	✓	1
5.4	even	2		8025.2.a.p.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8025.2.a.b.1.1	✓	1	1.1	even	1	trivial
8025.2.a.p.1.1	yes	1	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8025.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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