LMFDB - Embedded newform 9025.2.a.g.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)

$f(q)$

$=$

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

$q+2.00000 q^{3} -2.00000 q^{4} +4.00000 q^{7} +1.00000 q^{9} +3.00000 q^{11} -4.00000 q^{12} -2.00000 q^{13} +4.00000 q^{16} -6.00000 q^{17} +8.00000 q^{21} -4.00000 q^{27} -8.00000 q^{28} -3.00000 q^{29} -7.00000 q^{31} +6.00000 q^{33} -2.00000 q^{36} -8.00000 q^{37} -4.00000 q^{39} -6.00000 q^{41} +4.00000 q^{43} -6.00000 q^{44} -6.00000 q^{47} +8.00000 q^{48} +9.00000 q^{49} -12.0000 q^{51} +4.00000 q^{52} +6.00000 q^{53} -15.0000 q^{59} +5.00000 q^{61} +4.00000 q^{63} -8.00000 q^{64} -2.00000 q^{67} +12.0000 q^{68} -3.00000 q^{71} -8.00000 q^{73} +12.0000 q^{77} +5.00000 q^{79} -11.0000 q^{81} -12.0000 q^{83} -16.0000 q^{84} -6.00000 q^{87} -15.0000 q^{89} -8.00000 q^{91} -14.0000 q^{93} -8.00000 q^{97} +3.00000 q^{99} +O(q^{100})$

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 $

$2$	0	0		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	−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
$9$	1.00000	0.333333
$10$	0	0
$11$	3.00000	0.904534	0.452267	−	0.891883i	$-0.350615\pi$
$11$	3.00000	0.904534	0.452267	+	0.891883i	$0.350615\pi$
$12$	−4.00000	−1.15470
$13$	−2.00000	−0.554700	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	0	0
$16$	4.00000	1.00000
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	0	0
$19$	0	0
$19$	0	0
$20$	0	0
$21$	8.00000	1.74574
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−4.00000	−0.769800
$28$	−8.00000	−1.51186
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	0	0
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0	0
$33$	6.00000	1.04447
$34$	0	0
$35$	0	0
$36$	−2.00000	−0.333333
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	0	0
$39$	−4.00000	−0.640513
$40$	0	0
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−6.00000	−0.904534
$45$	0	0
$46$	0	0
$47$	−6.00000	−0.875190	−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000	−0.875190	−0.437595	+	0.899172i	$0.644170\pi$
$48$	8.00000	1.15470
$49$	9.00000	1.28571
$50$	0	0
$51$	−12.0000	−1.68034
$52$	4.00000	0.554700
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	0	0
$58$	0	0
$59$	−15.0000	−1.95283	−0.976417	−	0.215894i	$-0.930733\pi$
$59$	−15.0000	−1.95283	−0.976417	+	0.215894i	$0.930733\pi$
$60$	0	0
$61$	5.00000	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$62$	0	0
$63$	4.00000	0.503953
$64$	−8.00000	−1.00000
$65$	0	0
$66$	0	0
$67$	−2.00000	−0.244339	−0.122169	−	0.992509i	$-0.538985\pi$
$67$	−2.00000	−0.244339	−0.122169	+	0.992509i	$0.538985\pi$
$68$	12.0000	1.45521
$69$	0	0
$70$	0	0
$71$	−3.00000	−0.356034	−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000	−0.356034	−0.178017	+	0.984027i	$0.556968\pi$
$72$	0	0
$73$	−8.00000	−0.936329	−0.468165	−	0.883641i	$-0.655085\pi$
$73$	−8.00000	−0.936329	−0.468165	+	0.883641i	$0.655085\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	12.0000	1.36753
$78$	0	0
$79$	5.00000	0.562544	0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000	0.562544	0.281272	+	0.959628i	$0.409244\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	−16.0000	−1.74574
$85$	0	0
$86$	0	0
$87$	−6.00000	−0.643268
$88$	0	0
$89$	−15.0000	−1.59000	−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000	−1.59000	−0.794998	+	0.606612i	$0.792528\pi$
$90$	0	0
$91$	−8.00000	−0.838628
$92$	0	0
$93$	−14.0000	−1.45173
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	0	0
$99$	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
$106$	0	0
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	8.00000	0.769800
$109$	11.0000	1.05361	0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000	1.05361	0.526804	+	0.849987i	$0.323390\pi$
$110$	0	0
$111$	−16.0000	−1.51865
$112$	16.0000	1.51186
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	0	0
$115$	0	0
$116$	6.00000	0.557086
$117$	−2.00000	−0.184900
$118$	0	0
$119$	−24.0000	−2.20008
$120$	0	0
$121$	−2.00000	−0.181818
$122$	0	0
$123$	−12.0000	−1.08200
$124$	14.0000	1.25724
$125$	0	0
$126$	0	0
$127$	−2.00000	−0.177471	−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000	−0.177471	−0.0887357	+	0.996055i	$0.528283\pi$
$128$	0	0
$129$	8.00000	0.704361
$130$	0	0
$131$	12.0000	1.04844	0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000	1.04844	0.524222	+	0.851581i	$0.324356\pi$
$132$	−12.0000	−1.04447
$133$	0	0
$134$	0	0
$135$	0	0
$136$	0	0
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	0	0
$139$	−16.0000	−1.35710	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000	−1.35710	−0.678551	+	0.734553i	$0.737392\pi$
$140$	0	0
$141$	−12.0000	−1.01058
$142$	0	0
$143$	−6.00000	−0.501745
$144$	4.00000	0.333333
$145$	0	0
$146$	0	0
$147$	18.0000	1.48461
$148$	16.0000	1.31519
$149$	3.00000	0.245770	0.122885	−	0.992421i	$-0.460785\pi$
$149$	3.00000	0.245770	0.122885	+	0.992421i	$0.460785\pi$
$150$	0	0
$151$	17.0000	1.38344	0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000	1.38344	0.691720	+	0.722166i	$0.256853\pi$
$152$	0	0
$153$	−6.00000	−0.485071
$154$	0	0
$155$	0	0
$156$	8.00000	0.640513
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	0	0
$159$	12.0000	0.951662
$160$	0	0
$161$	0	0
$162$	0	0
$163$	10.0000	0.783260	0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000	0.783260	0.391630	+	0.920123i	$0.371911\pi$
$164$	12.0000	0.937043
$165$	0	0
$166$	0	0
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	0	0
$172$	−8.00000	−0.609994
$173$	0	0		−	1.00000i	$-0.5\pi$
$173$	0	0			1.00000i	$0.5\pi$
$174$	0	0
$175$	0	0
$176$	12.0000	0.904534
$177$	−30.0000	−2.25494
$178$	0	0
$179$	−9.00000	−0.672692	−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000	−0.672692	−0.336346	+	0.941739i	$0.609191\pi$
$180$	0	0
$181$	2.00000	0.148659	0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000	0.148659	0.0743294	+	0.997234i	$0.476318\pi$
$182$	0	0
$183$	10.0000	0.739221
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−18.0000	−1.31629
$188$	12.0000	0.875190
$189$	−16.0000	−1.16383
$190$	0	0
$191$	−15.0000	−1.08536	−0.542681	−	0.839939i	$-0.682591\pi$
$191$	−15.0000	−1.08536	−0.542681	+	0.839939i	$0.682591\pi$
$192$	−16.0000	−1.15470
$193$	16.0000	1.15171	0.575853	−	0.817554i	$-0.304670\pi$
$193$	16.0000	1.15171	0.575853	+	0.817554i	$0.304670\pi$
$194$	0	0
$195$	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	$0.278427\pi$
$198$	0	0
$199$	−19.0000	−1.34687	−0.673437	−	0.739244i	$-0.735183\pi$
$199$	−19.0000	−1.34687	−0.673437	+	0.739244i	$0.735183\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	0	0
$203$	−12.0000	−0.842235
$204$	24.0000	1.68034
$205$	0	0
$206$	0	0
$207$	0	0
$208$	−8.00000	−0.554700
$209$	0	0
$210$	0	0
$211$	−7.00000	−0.481900	−0.240950	−	0.970538i	$-0.577459\pi$
$211$	−7.00000	−0.481900	−0.240950	+	0.970538i	$0.577459\pi$
$212$	−12.0000	−0.824163
$213$	−6.00000	−0.411113
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−28.0000	−1.90076
$218$	0	0
$219$	−16.0000	−1.08118
$220$	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	$0.457240\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	24.0000	1.59294	0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000	1.59294	0.796468	+	0.604681i	$0.206699\pi$
$228$	0	0
$229$	−7.00000	−0.462573	−0.231287	−	0.972886i	$-0.574293\pi$
$229$	−7.00000	−0.462573	−0.231287	+	0.972886i	$0.574293\pi$
$230$	0	0
$231$	24.0000	1.57908
$232$	0	0
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	0	0
$235$	0	0
$236$	30.0000	1.95283
$237$	10.0000	0.649570
$238$	0	0
$239$	−3.00000	−0.194054	−0.0970269	−	0.995282i	$-0.530933\pi$
$239$	−3.00000	−0.194054	−0.0970269	+	0.995282i	$0.530933\pi$
$240$	0	0
$241$	5.00000	0.322078	0.161039	−	0.986948i	$-0.448515\pi$
$241$	5.00000	0.322078	0.161039	+	0.986948i	$0.448515\pi$
$242$	0	0
$243$	−10.0000	−0.641500
$244$	−10.0000	−0.640184
$245$	0	0
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−24.0000	−1.52094
$250$	0	0
$251$	−15.0000	−0.946792	−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000	−0.946792	−0.473396	+	0.880850i	$0.656972\pi$
$252$	−8.00000	−0.503953
$253$	0	0
$254$	0	0
$255$	0	0
$256$	16.0000	1.00000
$257$	18.0000	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$257$	18.0000	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$258$	0	0
$259$	−32.0000	−1.98838
$260$	0	0
$261$	−3.00000	−0.185695
$262$	0	0
$263$	18.0000	1.10993	0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000	1.10993	0.554964	+	0.831875i	$0.312732\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−30.0000	−1.83597
$268$	4.00000	0.244339
$269$	−21.0000	−1.28039	−0.640196	−	0.768211i	$-0.721147\pi$
$269$	−21.0000	−1.28039	−0.640196	+	0.768211i	$0.721147\pi$
$270$	0	0
$271$	11.0000	0.668202	0.334101	−	0.942537i	$-0.391567\pi$
$271$	11.0000	0.668202	0.334101	+	0.942537i	$0.391567\pi$
$272$	−24.0000	−1.45521
$273$	−16.0000	−0.968364
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−8.00000	−0.480673	−0.240337	−	0.970690i	$-0.577258\pi$
$277$	−8.00000	−0.480673	−0.240337	+	0.970690i	$0.577258\pi$
$278$	0	0
$279$	−7.00000	−0.419079
$280$	0	0
$281$	6.00000	0.357930	0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000	0.357930	0.178965	+	0.983855i	$0.442725\pi$
$282$	0	0
$283$	−14.0000	−0.832214	−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000	−0.832214	−0.416107	+	0.909316i	$0.636606\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	0	0
$287$	−24.0000	−1.41668
$288$	0	0
$289$	19.0000	1.11765
$290$	0	0
$291$	−16.0000	−0.937937
$292$	16.0000	0.936329
$293$	−24.0000	−1.40209	−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000	−1.40209	−0.701047	+	0.713115i	$0.747284\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−12.0000	−0.696311
$298$	0	0
$299$	0	0
$300$	0	0
$301$	16.0000	0.922225
$302$	0	0
$303$	30.0000	1.72345
$304$	0	0
$305$	0	0
$306$	0	0
$307$	34.0000	1.94048	0.970241	−	0.242140i	$-0.0778494\pi$
$307$	34.0000	1.94048	0.970241	+	0.242140i	$0.0778494\pi$
$308$	−24.0000	−1.36753
$309$	32.0000	1.82042
$310$	0	0
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	0	0
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	0	0
$315$	0	0
$316$	−10.0000	−0.562544
$317$	−24.0000	−1.34797	−0.673987	−	0.738743i	$-0.735420\pi$
$317$	−24.0000	−1.34797	−0.673987	+	0.738743i	$0.735420\pi$
$318$	0	0
$319$	−9.00000	−0.503903
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	22.0000	1.22222
$325$	0	0
$326$	0	0
$327$	22.0000	1.21660
$328$	0	0
$329$	−24.0000	−1.32316
$330$	0	0
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	24.0000	1.31717
$333$	−8.00000	−0.438397
$334$	0	0
$335$	0	0
$336$	32.0000	1.74574
$337$	16.0000	0.871576	0.435788	−	0.900049i	$-0.356470\pi$
$337$	16.0000	0.871576	0.435788	+	0.900049i	$0.356470\pi$
$338$	0	0
$339$	−12.0000	−0.651751
$340$	0	0
$341$	−21.0000	−1.13721
$342$	0	0
$343$	8.00000	0.431959
$344$	0	0
$345$	0	0
$346$	0	0
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	12.0000	0.643268
$349$	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
$351$	8.00000	0.427008
$352$	0	0
$353$	−12.0000	−0.638696	−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000	−0.638696	−0.319348	+	0.947638i	$0.603464\pi$
$354$	0	0
$355$	0	0
$356$	30.0000	1.59000
$357$	−48.0000	−2.54043
$358$	0	0
$359$	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
$361$	0	0
$362$	0	0
$363$	−4.00000	−0.209946
$364$	16.0000	0.838628
$365$	0	0
$366$	0	0
$367$	4.00000	0.208798	0.104399	−	0.994535i	$-0.466708\pi$
$367$	4.00000	0.208798	0.104399	+	0.994535i	$0.466708\pi$
$368$	0	0
$369$	−6.00000	−0.312348
$370$	0	0
$371$	24.0000	1.24602
$372$	28.0000	1.45173
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	6.00000	0.309016
$378$	0	0
$379$	−37.0000	−1.90056	−0.950281	−	0.311393i	$-0.899204\pi$
$379$	−37.0000	−1.90056	−0.950281	+	0.311393i	$0.899204\pi$
$380$	0	0
$381$	−4.00000	−0.204926
$382$	0	0
$383$	−30.0000	−1.53293	−0.766464	−	0.642287i	$-0.777986\pi$
$383$	−30.0000	−1.53293	−0.766464	+	0.642287i	$0.777986\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	4.00000	0.203331
$388$	16.0000	0.812277
$389$	15.0000	0.760530	0.380265	−	0.924878i	$-0.375833\pi$
$389$	15.0000	0.760530	0.380265	+	0.924878i	$0.375833\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	24.0000	1.21064
$394$	0	0
$395$	0	0
$396$	−6.00000	−0.301511
$397$	−8.00000	−0.401508	−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000	−0.401508	−0.200754	+	0.979642i	$0.564339\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−33.0000	−1.64794	−0.823971	−	0.566632i	$-0.808246\pi$
$401$	−33.0000	−1.64794	−0.823971	+	0.566632i	$0.808246\pi$
$402$	0	0
$403$	14.0000	0.697390
$404$	−30.0000	−1.49256
$405$	0	0
$406$	0	0
$407$	−24.0000	−1.18964
$408$	0	0
$409$	23.0000	1.13728	0.568638	−	0.822588i	$-0.307470\pi$
$409$	23.0000	1.13728	0.568638	+	0.822588i	$0.307470\pi$
$410$	0	0
$411$	24.0000	1.18383
$412$	−32.0000	−1.57653
$413$	−60.0000	−2.95241
$414$	0	0
$415$	0	0
$416$	0	0
$417$	−32.0000	−1.56705
$418$	0	0
$419$	−3.00000	−0.146560	−0.0732798	−	0.997311i	$-0.523347\pi$
$419$	−3.00000	−0.146560	−0.0732798	+	0.997311i	$0.523347\pi$
$420$	0	0
$421$	−19.0000	−0.926003	−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000	−0.926003	−0.463002	+	0.886357i	$0.653228\pi$
$422$	0	0
$423$	−6.00000	−0.291730
$424$	0	0
$425$	0	0
$426$	0	0
$427$	20.0000	0.967868
$428$	0	0
$429$	−12.0000	−0.579365
$430$	0	0
$431$	−15.0000	−0.722525	−0.361262	−	0.932464i	$-0.617654\pi$
$431$	−15.0000	−0.722525	−0.361262	+	0.932464i	$0.617654\pi$
$432$	−16.0000	−0.769800
$433$	−8.00000	−0.384455	−0.192228	−	0.981350i	$-0.561571\pi$
$433$	−8.00000	−0.384455	−0.192228	+	0.981350i	$0.561571\pi$
$434$	0	0
$435$	0	0
$436$	−22.0000	−1.05361
$437$	0	0
$438$	0	0
$439$	−13.0000	−0.620456	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	−13.0000	−0.620456	−0.310228	+	0.950662i	$0.600405\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	0	0
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	32.0000	1.51865
$445$	0	0
$446$	0	0
$447$	6.00000	0.283790
$448$	−32.0000	−1.51186
$449$	−9.00000	−0.424736	−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000	−0.424736	−0.212368	+	0.977190i	$0.568118\pi$
$450$	0	0
$451$	−18.0000	−0.847587
$452$	12.0000	0.564433
$453$	34.0000	1.59746
$454$	0	0
$455$	0	0
$456$	0	0
$457$	22.0000	1.02912	0.514558	−	0.857455i	$-0.327956\pi$
$457$	22.0000	1.02912	0.514558	+	0.857455i	$0.327956\pi$
$458$	0	0
$459$	24.0000	1.12022
$460$	0	0
$461$	−9.00000	−0.419172	−0.209586	−	0.977790i	$-0.567212\pi$
$461$	−9.00000	−0.419172	−0.209586	+	0.977790i	$0.567212\pi$
$462$	0	0
$463$	16.0000	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$464$	−12.0000	−0.557086
$465$	0	0
$466$	0	0
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	4.00000	0.184900
$469$	−8.00000	−0.369406
$470$	0	0
$471$	−4.00000	−0.184310
$472$	0	0
$473$	12.0000	0.551761
$474$	0	0
$475$	0	0
$476$	48.0000	2.20008
$477$	6.00000	0.274721
$478$	0	0
$479$	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
$481$	16.0000	0.729537
$482$	0	0
$483$	0	0
$484$	4.00000	0.181818
$485$	0	0
$486$	0	0
$487$	−2.00000	−0.0906287	−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000	−0.0906287	−0.0453143	+	0.998973i	$0.514429\pi$
$488$	0	0
$489$	20.0000	0.904431
$490$	0	0
$491$	−15.0000	−0.676941	−0.338470	−	0.940977i	$-0.609909\pi$
$491$	−15.0000	−0.676941	−0.338470	+	0.940977i	$0.609909\pi$
$492$	24.0000	1.08200
$493$	18.0000	0.810679
$494$	0	0
$495$	0	0
$496$	−28.0000	−1.25724
$497$	−12.0000	−0.538274
$498$	0	0
$499$	20.0000	0.895323	0.447661	−	0.894203i	$-0.352257\pi$
$499$	20.0000	0.895323	0.447661	+	0.894203i	$0.352257\pi$
$500$	0	0
$501$	0	0
$502$	0	0
$503$	42.0000	1.87269	0.936344	−	0.351085i	$-0.114187\pi$
$503$	42.0000	1.87269	0.936344	+	0.351085i	$0.114187\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−18.0000	−0.799408
$508$	4.00000	0.177471
$509$	−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
$511$	−32.0000	−1.41560
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	−16.0000	−0.704361
$517$	−18.0000	−0.791639
$518$	0	0
$519$	0	0
$520$	0	0
$521$	−45.0000	−1.97149	−0.985743	−	0.168259i	$-0.946186\pi$
$521$	−45.0000	−1.97149	−0.985743	+	0.168259i	$0.946186\pi$
$522$	0	0
$523$	−26.0000	−1.13690	−0.568450	−	0.822718i	$-0.692457\pi$
$523$	−26.0000	−1.13690	−0.568450	+	0.822718i	$0.692457\pi$
$524$	−24.0000	−1.04844
$525$	0	0
$526$	0	0
$527$	42.0000	1.82955
$528$	24.0000	1.04447
$529$	−23.0000	−1.00000
$530$	0	0
$531$	−15.0000	−0.650945
$532$	0	0
$533$	12.0000	0.519778
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−18.0000	−0.776757
$538$	0	0
$539$	27.0000	1.16297
$540$	0	0
$541$	−37.0000	−1.59075	−0.795377	−	0.606115i	$-0.792727\pi$
$541$	−37.0000	−1.59075	−0.795377	+	0.606115i	$0.792727\pi$
$542$	0	0
$543$	4.00000	0.171656
$544$	0	0
$545$	0	0
$546$	0	0
$547$	4.00000	0.171028	0.0855138	−	0.996337i	$-0.472747\pi$
$547$	4.00000	0.171028	0.0855138	+	0.996337i	$0.472747\pi$
$548$	−24.0000	−1.02523
$549$	5.00000	0.213395
$550$	0	0
$551$	0	0
$552$	0	0
$553$	20.0000	0.850487
$554$	0	0
$555$	0	0
$556$	32.0000	1.35710
$557$	−12.0000	−0.508456	−0.254228	−	0.967144i	$-0.581821\pi$
$557$	−12.0000	−0.508456	−0.254228	+	0.967144i	$0.581821\pi$
$558$	0	0
$559$	−8.00000	−0.338364
$560$	0	0
$561$	−36.0000	−1.51992
$562$	0	0
$563$	−6.00000	−0.252870	−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000	−0.252870	−0.126435	+	0.991975i	$0.540353\pi$
$564$	24.0000	1.01058
$565$	0	0
$566$	0	0
$567$	−44.0000	−1.84783
$568$	0	0
$569$	39.0000	1.63497	0.817483	−	0.575953i	$-0.195369\pi$
$569$	39.0000	1.63497	0.817483	+	0.575953i	$0.195369\pi$
$570$	0	0
$571$	−7.00000	−0.292941	−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000	−0.292941	−0.146470	+	0.989215i	$0.546791\pi$
$572$	12.0000	0.501745
$573$	−30.0000	−1.25327
$574$	0	0
$575$	0	0
$576$	−8.00000	−0.333333
$577$	16.0000	0.666089	0.333044	−	0.942911i	$-0.391924\pi$
$577$	16.0000	0.666089	0.333044	+	0.942911i	$0.391924\pi$
$578$	0	0
$579$	32.0000	1.32987
$580$	0	0
$581$	−48.0000	−1.99138
$582$	0	0
$583$	18.0000	0.745484
$584$	0	0
$585$	0	0
$586$	0	0
$587$	36.0000	1.48588	0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000	1.48588	0.742940	+	0.669359i	$0.233431\pi$
$588$	−36.0000	−1.48461
$589$	0	0
$590$	0	0
$591$	36.0000	1.48084
$592$	−32.0000	−1.31519
$593$	−12.0000	−0.492781	−0.246390	−	0.969171i	$-0.579245\pi$
$593$	−12.0000	−0.492781	−0.246390	+	0.969171i	$0.579245\pi$
$594$	0	0
$595$	0	0
$596$	−6.00000	−0.245770
$597$	−38.0000	−1.55524
$598$	0	0
$599$	0	0		−	1.00000i	$-0.5\pi$
$599$	0	0			1.00000i	$0.5\pi$
$600$	0	0
$601$	−31.0000	−1.26452	−0.632258	−	0.774758i	$-0.717872\pi$
$601$	−31.0000	−1.26452	−0.632258	+	0.774758i	$0.717872\pi$
$602$	0	0
$603$	−2.00000	−0.0814463
$604$	−34.0000	−1.38344
$605$	0	0
$606$	0	0
$607$	−2.00000	−0.0811775	−0.0405887	−	0.999176i	$-0.512923\pi$
$607$	−2.00000	−0.0811775	−0.0405887	+	0.999176i	$0.512923\pi$
$608$	0	0
$609$	−24.0000	−0.972529
$610$	0	0
$611$	12.0000	0.485468
$612$	12.0000	0.485071
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−36.0000	−1.44931	−0.724653	−	0.689114i	$-0.758000\pi$
$617$	−36.0000	−1.44931	−0.724653	+	0.689114i	$0.758000\pi$
$618$	0	0
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	−60.0000	−2.40385
$624$	−16.0000	−0.640513
$625$	0	0
$626$	0	0
$627$	0	0
$628$	4.00000	0.159617
$629$	48.0000	1.91389
$630$	0	0
$631$	−19.0000	−0.756378	−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000	−0.756378	−0.378189	+	0.925728i	$0.623453\pi$
$632$	0	0
$633$	−14.0000	−0.556450
$634$	0	0
$635$	0	0
$636$	−24.0000	−0.951662
$637$	−18.0000	−0.713186
$638$	0	0
$639$	−3.00000	−0.118678
$640$	0	0
$641$	9.00000	0.355479	0.177739	−	0.984078i	$-0.443122\pi$
$641$	9.00000	0.355479	0.177739	+	0.984078i	$0.443122\pi$
$642$	0	0
$643$	34.0000	1.34083	0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000	1.34083	0.670415	+	0.741987i	$0.266116\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−18.0000	−0.707653	−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000	−0.707653	−0.353827	+	0.935311i	$0.615120\pi$
$648$	0	0
$649$	−45.0000	−1.76640
$650$	0	0
$651$	−56.0000	−2.19481
$652$	−20.0000	−0.783260
$653$	−24.0000	−0.939193	−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000	−0.939193	−0.469596	+	0.882881i	$0.655601\pi$
$654$	0	0
$655$	0	0
$656$	−24.0000	−0.937043
$657$	−8.00000	−0.312110
$658$	0	0
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	0	0
$661$	5.00000	0.194477	0.0972387	−	0.995261i	$-0.468999\pi$
$661$	5.00000	0.194477	0.0972387	+	0.995261i	$0.468999\pi$
$662$	0	0
$663$	24.0000	0.932083
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	8.00000	0.309298
$670$	0	0
$671$	15.0000	0.579069
$672$	0	0
$673$	4.00000	0.154189	0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000	0.154189	0.0770943	+	0.997024i	$0.475436\pi$
$674$	0	0
$675$	0	0
$676$	18.0000	0.692308
$677$	−48.0000	−1.84479	−0.922395	−	0.386248i	$-0.873771\pi$
$677$	−48.0000	−1.84479	−0.922395	+	0.386248i	$0.873771\pi$
$678$	0	0
$679$	−32.0000	−1.22805
$680$	0	0
$681$	48.0000	1.83936
$682$	0	0
$683$	18.0000	0.688751	0.344375	−	0.938832i	$-0.388091\pi$
$683$	18.0000	0.688751	0.344375	+	0.938832i	$0.388091\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−14.0000	−0.534133
$688$	16.0000	0.609994
$689$	−12.0000	−0.457164
$690$	0	0
$691$	−37.0000	−1.40755	−0.703773	−	0.710425i	$-0.748503\pi$
$691$	−37.0000	−1.40755	−0.703773	+	0.710425i	$0.748503\pi$
$692$	0	0
$693$	12.0000	0.455842
$694$	0	0
$695$	0	0
$696$	0	0
$697$	36.0000	1.36360
$698$	0	0
$699$	−12.0000	−0.453882
$700$	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
$704$	−24.0000	−0.904534
$705$	0	0
$706$	0	0
$707$	60.0000	2.25653
$708$	60.0000	2.25494
$709$	−31.0000	−1.16423	−0.582115	−	0.813107i	$-0.697775\pi$
$709$	−31.0000	−1.16423	−0.582115	+	0.813107i	$0.697775\pi$
$710$	0	0
$711$	5.00000	0.187515
$712$	0	0
$713$	0	0
$714$	0	0
$715$	0	0
$716$	18.0000	0.672692
$717$	−6.00000	−0.224074
$718$	0	0
$719$	15.0000	0.559406	0.279703	−	0.960087i	$-0.409764\pi$
$719$	15.0000	0.559406	0.279703	+	0.960087i	$0.409764\pi$
$720$	0	0
$721$	64.0000	2.38348
$722$	0	0
$723$	10.0000	0.371904
$724$	−4.00000	−0.148659
$725$	0	0
$726$	0	0
$727$	−14.0000	−0.519231	−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000	−0.519231	−0.259616	+	0.965712i	$0.583596\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	−24.0000	−0.887672
$732$	−20.0000	−0.739221
$733$	−32.0000	−1.18195	−0.590973	−	0.806691i	$-0.701256\pi$
$733$	−32.0000	−1.18195	−0.590973	+	0.806691i	$0.701256\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	−6.00000	−0.221013
$738$	0	0
$739$	35.0000	1.28750	0.643748	−	0.765238i	$-0.277379\pi$
$739$	35.0000	1.28750	0.643748	+	0.765238i	$0.277379\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−12.0000	−0.439057
$748$	36.0000	1.31629
$749$	0	0
$750$	0	0
$751$	−7.00000	−0.255434	−0.127717	−	0.991811i	$-0.540765\pi$
$751$	−7.00000	−0.255434	−0.127717	+	0.991811i	$0.540765\pi$
$752$	−24.0000	−0.875190
$753$	−30.0000	−1.09326
$754$	0	0
$755$	0	0
$756$	32.0000	1.16383
$757$	10.0000	0.363456	0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000	0.363456	0.181728	+	0.983349i	$0.441831\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	0	0
$763$	44.0000	1.59291
$764$	30.0000	1.08536
$765$	0	0
$766$	0	0
$767$	30.0000	1.08324
$768$	32.0000	1.15470
$769$	29.0000	1.04577	0.522883	−	0.852404i	$-0.324856\pi$
$769$	29.0000	1.04577	0.522883	+	0.852404i	$0.324856\pi$
$770$	0	0
$771$	36.0000	1.29651
$772$	−32.0000	−1.15171
$773$	−30.0000	−1.07903	−0.539513	−	0.841978i	$-0.681391\pi$
$773$	−30.0000	−1.07903	−0.539513	+	0.841978i	$0.681391\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	−64.0000	−2.29599
$778$	0	0
$779$	0	0
$780$	0	0
$781$	−9.00000	−0.322045
$782$	0	0
$783$	12.0000	0.428845
$784$	36.0000	1.28571
$785$	0	0
$786$	0	0
$787$	34.0000	1.21197	0.605985	−	0.795476i	$-0.292779\pi$
$787$	34.0000	1.21197	0.605985	+	0.795476i	$0.292779\pi$
$788$	−36.0000	−1.28245
$789$	36.0000	1.28163
$790$	0	0
$791$	−24.0000	−0.853342
$792$	0	0
$793$	−10.0000	−0.355110
$794$	0	0
$795$	0	0
$796$	38.0000	1.34687
$797$	30.0000	1.06265	0.531327	−	0.847167i	$-0.321693\pi$
$797$	30.0000	1.06265	0.531327	+	0.847167i	$0.321693\pi$
$798$	0	0
$799$	36.0000	1.27359
$800$	0	0
$801$	−15.0000	−0.529999
$802$	0	0
$803$	−24.0000	−0.846942
$804$	8.00000	0.282138
$805$	0	0
$806$	0	0
$807$	−42.0000	−1.47847
$808$	0	0
$809$	−27.0000	−0.949269	−0.474635	−	0.880183i	$-0.657420\pi$
$809$	−27.0000	−0.949269	−0.474635	+	0.880183i	$0.657420\pi$
$810$	0	0
$811$	−43.0000	−1.50993	−0.754967	−	0.655763i	$-0.772347\pi$
$811$	−43.0000	−1.50993	−0.754967	+	0.655763i	$0.772347\pi$
$812$	24.0000	0.842235
$813$	22.0000	0.771574
$814$	0	0
$815$	0	0
$816$	−48.0000	−1.68034
$817$	0	0
$818$	0	0
$819$	−8.00000	−0.279543
$820$	0	0
$821$	−3.00000	−0.104701	−0.0523504	−	0.998629i	$-0.516671\pi$
$821$	−3.00000	−0.104701	−0.0523504	+	0.998629i	$0.516671\pi$
$822$	0	0
$823$	22.0000	0.766872	0.383436	−	0.923567i	$-0.374741\pi$
$823$	22.0000	0.766872	0.383436	+	0.923567i	$0.374741\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	42.0000	1.46048	0.730242	−	0.683189i	$-0.239408\pi$
$827$	42.0000	1.46048	0.730242	+	0.683189i	$0.239408\pi$
$828$	0	0
$829$	26.0000	0.903017	0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000	0.903017	0.451509	+	0.892267i	$0.350886\pi$
$830$	0	0
$831$	−16.0000	−0.555034
$832$	16.0000	0.554700
$833$	−54.0000	−1.87099
$834$	0	0
$835$	0	0
$836$	0	0
$837$	28.0000	0.967822
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	−20.0000	−0.689655
$842$	0	0
$843$	12.0000	0.413302
$844$	14.0000	0.481900
$845$	0	0
$846$	0	0
$847$	−8.00000	−0.274883
$848$	24.0000	0.824163
$849$	−28.0000	−0.960958
$850$	0	0
$851$	0	0
$852$	12.0000	0.411113
$853$	−14.0000	−0.479351	−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000	−0.479351	−0.239675	+	0.970853i	$0.577041\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−36.0000	−1.22974	−0.614868	−	0.788630i	$-0.710791\pi$
$857$	−36.0000	−1.22974	−0.614868	+	0.788630i	$0.710791\pi$
$858$	0	0
$859$	−7.00000	−0.238837	−0.119418	−	0.992844i	$-0.538103\pi$
$859$	−7.00000	−0.238837	−0.119418	+	0.992844i	$0.538103\pi$
$860$	0	0
$861$	−48.0000	−1.63584
$862$	0	0
$863$	−18.0000	−0.612727	−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000	−0.612727	−0.306364	+	0.951915i	$0.599112\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	38.0000	1.29055
$868$	56.0000	1.90076
$869$	15.0000	0.508840
$870$	0	0
$871$	4.00000	0.135535
$872$	0	0
$873$	−8.00000	−0.270759
$874$	0	0
$875$	0	0
$876$	32.0000	1.08118
$877$	52.0000	1.75592	0.877958	−	0.478738i	$-0.158906\pi$
$877$	52.0000	1.75592	0.877958	+	0.478738i	$0.158906\pi$
$878$	0	0
$879$	−48.0000	−1.61900
$880$	0	0
$881$	9.00000	0.303218	0.151609	−	0.988441i	$-0.451555\pi$
$881$	9.00000	0.303218	0.151609	+	0.988441i	$0.451555\pi$
$882$	0	0
$883$	−8.00000	−0.269221	−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000	−0.269221	−0.134611	+	0.990899i	$0.542978\pi$
$884$	−24.0000	−0.807207
$885$	0	0
$886$	0	0
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	0	0
$889$	−8.00000	−0.268311
$890$	0	0
$891$	−33.0000	−1.10554
$892$	−8.00000	−0.267860
$893$	0	0
$894$	0	0
$895$	0	0
$896$	0	0
$897$	0	0
$898$	0	0
$899$	21.0000	0.700389
$900$	0	0
$901$	−36.0000	−1.19933
$902$	0	0
$903$	32.0000	1.06489
$904$	0	0
$905$	0	0
$906$	0	0
$907$	−8.00000	−0.265636	−0.132818	−	0.991140i	$-0.542403\pi$
$907$	−8.00000	−0.265636	−0.132818	+	0.991140i	$0.542403\pi$
$908$	−48.0000	−1.59294
$909$	15.0000	0.497519
$910$	0	0
$911$	21.0000	0.695761	0.347881	−	0.937539i	$-0.386901\pi$
$911$	21.0000	0.695761	0.347881	+	0.937539i	$0.386901\pi$
$912$	0	0
$913$	−36.0000	−1.19143
$914$	0	0
$915$	0	0
$916$	14.0000	0.462573
$917$	48.0000	1.58510
$918$	0	0
$919$	8.00000	0.263896	0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000	0.263896	0.131948	+	0.991257i	$0.457877\pi$
$920$	0	0
$921$	68.0000	2.24068
$922$	0	0
$923$	6.00000	0.197492
$924$	−48.0000	−1.57908
$925$	0	0
$926$	0	0
$927$	16.0000	0.525509
$928$	0	0
$929$	27.0000	0.885841	0.442921	−	0.896561i	$-0.353942\pi$
$929$	27.0000	0.885841	0.442921	+	0.896561i	$0.353942\pi$
$930$	0	0
$931$	0	0
$932$	12.0000	0.393073
$933$	48.0000	1.57145
$934$	0	0
$935$	0	0
$936$	0	0
$937$	46.0000	1.50275	0.751377	−	0.659873i	$-0.229390\pi$
$937$	46.0000	1.50275	0.751377	+	0.659873i	$0.229390\pi$
$938$	0	0
$939$	20.0000	0.652675
$940$	0	0
$941$	−9.00000	−0.293392	−0.146696	−	0.989182i	$-0.546864\pi$
$941$	−9.00000	−0.293392	−0.146696	+	0.989182i	$0.546864\pi$
$942$	0	0
$943$	0	0
$944$	−60.0000	−1.95283
$945$	0	0
$946$	0	0
$947$	18.0000	0.584921	0.292461	−	0.956278i	$-0.405526\pi$
$947$	18.0000	0.584921	0.292461	+	0.956278i	$0.405526\pi$
$948$	−20.0000	−0.649570
$949$	16.0000	0.519382
$950$	0	0
$951$	−48.0000	−1.55651
$952$	0	0
$953$	12.0000	0.388718	0.194359	−	0.980930i	$-0.437737\pi$
$953$	12.0000	0.388718	0.194359	+	0.980930i	$0.437737\pi$
$954$	0	0
$955$	0	0
$956$	6.00000	0.194054
$957$	−18.0000	−0.581857
$958$	0	0
$959$	48.0000	1.55000
$960$	0	0
$961$	18.0000	0.580645
$962$	0	0
$963$	0	0
$964$	−10.0000	−0.322078
$965$	0	0
$966$	0	0
$967$	16.0000	0.514525	0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000	0.514525	0.257263	+	0.966342i	$0.417179\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	20.0000	0.641500
$973$	−64.0000	−2.05175
$974$	0	0
$975$	0	0
$976$	20.0000	0.640184
$977$	12.0000	0.383914	0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000	0.383914	0.191957	+	0.981403i	$0.438517\pi$
$978$	0	0
$979$	−45.0000	−1.43821
$980$	0	0
$981$	11.0000	0.351203
$982$	0	0
$983$	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
$986$	0	0
$987$	−48.0000	−1.52786
$988$	0	0
$989$	0	0
$990$	0	0
$991$	8.00000	0.254128	0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000	0.254128	0.127064	+	0.991894i	$0.459445\pi$
$992$	0	0
$993$	−8.00000	−0.253872
$994$	0	0
$995$	0	0
$996$	48.0000	1.52094
$997$	22.0000	0.696747	0.348373	−	0.937356i	$-0.386734\pi$
$997$	22.0000	0.696747	0.348373	+	0.937356i	$0.386734\pi$
$998$	0	0
$999$	32.0000	1.01244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.g.1.1		1
5.4	even	2		1805.2.a.a.1.1		1
19.7	even	3		475.2.e.b.201.1		2
19.11	even	3		475.2.e.b.26.1		2
19.18	odd	2		9025.2.a.e.1.1		1
95.7	odd	12		475.2.j.a.49.2		4
95.49	even	6		95.2.e.a.26.1	yes	2
95.64	even	6		95.2.e.a.11.1	✓	2
95.68	odd	12		475.2.j.a.349.2		4
95.83	odd	12		475.2.j.a.49.1		4
95.87	odd	12		475.2.j.a.349.1		4
95.94	odd	2		1805.2.a.b.1.1		1
285.239	odd	6		855.2.k.b.406.1		2
285.254	odd	6		855.2.k.b.676.1		2
380.159	odd	6		1520.2.q.c.961.1		2
380.239	odd	6		1520.2.q.c.881.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.a.11.1	✓	2	95.64	even	6
95.2.e.a.26.1	yes	2	95.49	even	6
475.2.e.b.26.1		2	19.11	even	3
475.2.e.b.201.1		2	19.7	even	3
475.2.j.a.49.1		4	95.83	odd	12
475.2.j.a.49.2		4	95.7	odd	12
475.2.j.a.349.1		4	95.87	odd	12
475.2.j.a.349.2		4	95.68	odd	12
855.2.k.b.406.1		2	285.239	odd	6
855.2.k.b.676.1		2	285.254	odd	6
1520.2.q.c.881.1		2	380.239	odd	6
1520.2.q.c.961.1		2	380.159	odd	6
1805.2.a.a.1.1		1	5.4	even	2
1805.2.a.b.1.1		1	95.94	odd	2
9025.2.a.e.1.1		1	19.18	odd	2
9025.2.a.g.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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

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