LMFDB - Embedded newform 2450.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2450,2,Mod(1,2450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2450, 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("2450.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2450 = 2 \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2450.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:	$19.5633484952$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 350)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2450.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} +3.00000 q^{6} -1.00000 q^{8} +6.00000 q^{9} +O(q^{10})$

$q-1.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} +3.00000 q^{6} -1.00000 q^{8} +6.00000 q^{9} -5.00000 q^{11} -3.00000 q^{12} -6.00000 q^{13} +1.00000 q^{16} -1.00000 q^{17} -6.00000 q^{18} +3.00000 q^{19} +5.00000 q^{22} +3.00000 q^{24} +6.00000 q^{26} -9.00000 q^{27} -6.00000 q^{29} +4.00000 q^{31} -1.00000 q^{32} +15.0000 q^{33} +1.00000 q^{34} +6.00000 q^{36} -8.00000 q^{37} -3.00000 q^{38} +18.0000 q^{39} -11.0000 q^{41} +8.00000 q^{43} -5.00000 q^{44} +2.00000 q^{47} -3.00000 q^{48} +3.00000 q^{51} -6.00000 q^{52} -4.00000 q^{53} +9.00000 q^{54} -9.00000 q^{57} +6.00000 q^{58} -4.00000 q^{59} +2.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} -15.0000 q^{66} -9.00000 q^{67} -1.00000 q^{68} -10.0000 q^{71} -6.00000 q^{72} -7.00000 q^{73} +8.00000 q^{74} +3.00000 q^{76} -18.0000 q^{78} -2.00000 q^{79} +9.00000 q^{81} +11.0000 q^{82} +11.0000 q^{83} -8.00000 q^{86} +18.0000 q^{87} +5.00000 q^{88} +11.0000 q^{89} -12.0000 q^{93} -2.00000 q^{94} +3.00000 q^{96} -10.0000 q^{97} -30.0000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.00000	−1.73205	−0.866025	−	0.500000i	$-0.833333\pi$
$3$	−3.00000	−1.73205	−0.866025	+	0.500000i	$0.833333\pi$
$4$	1.00000	0.500000
$5$	0	0
$5$	0	0
$6$	3.00000	1.22474
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	6.00000	2.00000
$10$	0	0
$11$	−5.00000	−1.50756	−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000	−1.50756	−0.753778	+	0.657129i	$0.771771\pi$
$12$	−3.00000	−0.866025
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	0	0
$15$	0	0
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536	−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000	−0.242536	−0.121268	+	0.992620i	$0.538696\pi$
$18$	−6.00000	−1.41421
$19$	3.00000	0.688247	0.344124	−	0.938924i	$-0.388176\pi$
$19$	3.00000	0.688247	0.344124	+	0.938924i	$0.388176\pi$
$20$	0	0
$21$	0	0
$22$	5.00000	1.06600
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	3.00000	0.612372
$25$	0	0
$26$	6.00000	1.17670
$27$	−9.00000	−1.73205
$28$	0	0
$29$	−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
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.00000	−0.176777
$33$	15.0000	2.61116
$34$	1.00000	0.171499
$35$	0	0
$36$	6.00000	1.00000
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	−3.00000	−0.486664
$39$	18.0000	2.88231
$40$	0	0
$41$	−11.0000	−1.71791	−0.858956	−	0.512050i	$-0.828886\pi$
$41$	−11.0000	−1.71791	−0.858956	+	0.512050i	$0.828886\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	−5.00000	−0.753778
$45$	0	0
$46$	0	0
$47$	2.00000	0.291730	0.145865	−	0.989305i	$-0.453403\pi$
$47$	2.00000	0.291730	0.145865	+	0.989305i	$0.453403\pi$
$48$	−3.00000	−0.433013
$49$	0	0
$50$	0	0
$51$	3.00000	0.420084
$52$	−6.00000	−0.832050
$53$	−4.00000	−0.549442	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000	−0.549442	−0.274721	+	0.961524i	$0.588586\pi$
$54$	9.00000	1.22474
$55$	0	0
$56$	0	0
$57$	−9.00000	−1.19208
$58$	6.00000	0.787839
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−4.00000	−0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	0	0
$66$	−15.0000	−1.84637
$67$	−9.00000	−1.09952	−0.549762	−	0.835321i	$-0.685282\pi$
$67$	−9.00000	−1.09952	−0.549762	+	0.835321i	$0.685282\pi$
$68$	−1.00000	−0.121268
$69$	0	0
$70$	0	0
$71$	−10.0000	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$71$	−10.0000	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$72$	−6.00000	−0.707107
$73$	−7.00000	−0.819288	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000	−0.819288	−0.409644	+	0.912245i	$0.634347\pi$
$74$	8.00000	0.929981
$75$	0	0
$76$	3.00000	0.344124
$77$	0	0
$78$	−18.0000	−2.03810
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	0	0
$81$	9.00000	1.00000
$82$	11.0000	1.21475
$83$	11.0000	1.20741	0.603703	−	0.797209i	$-0.293691\pi$
$83$	11.0000	1.20741	0.603703	+	0.797209i	$0.293691\pi$
$84$	0	0
$85$	0	0
$86$	−8.00000	−0.862662
$87$	18.0000	1.92980
$88$	5.00000	0.533002
$89$	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
$91$	0	0
$92$	0	0
$93$	−12.0000	−1.24434
$94$	−2.00000	−0.206284
$95$	0	0
$96$	3.00000	0.306186
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	0	0
$99$	−30.0000	−3.01511
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	−3.00000	−0.297044
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	6.00000	0.588348
$105$	0	0
$106$	4.00000	0.388514
$107$	−3.00000	−0.290021	−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000	−0.290021	−0.145010	+	0.989430i	$0.546322\pi$
$108$	−9.00000	−0.866025
$109$	−18.0000	−1.72409	−0.862044	−	0.506834i	$-0.830816\pi$
$109$	−18.0000	−1.72409	−0.862044	+	0.506834i	$0.830816\pi$
$110$	0	0
$111$	24.0000	2.27798
$112$	0	0
$113$	1.00000	0.0940721	0.0470360	−	0.998893i	$-0.485022\pi$
$113$	1.00000	0.0940721	0.0470360	+	0.998893i	$0.485022\pi$
$114$	9.00000	0.842927
$115$	0	0
$116$	−6.00000	−0.557086
$117$	−36.0000	−3.32820
$118$	4.00000	0.368230
$119$	0	0
$120$	0	0
$121$	14.0000	1.27273
$122$	−2.00000	−0.181071
$123$	33.0000	2.97551
$124$	4.00000	0.359211
$125$	0	0
$126$	0	0
$127$	14.0000	1.24230	0.621150	−	0.783692i	$-0.286666\pi$
$127$	14.0000	1.24230	0.621150	+	0.783692i	$0.286666\pi$
$128$	−1.00000	−0.0883883
$129$	−24.0000	−2.11308
$130$	0	0
$131$	−8.00000	−0.698963	−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000	−0.698963	−0.349482	+	0.936943i	$0.613642\pi$
$132$	15.0000	1.30558
$133$	0	0
$134$	9.00000	0.777482
$135$	0	0
$136$	1.00000	0.0857493
$137$	3.00000	0.256307	0.128154	−	0.991754i	$-0.459095\pi$
$137$	3.00000	0.256307	0.128154	+	0.991754i	$0.459095\pi$
$138$	0	0
$139$	11.0000	0.933008	0.466504	−	0.884519i	$-0.345513\pi$
$139$	11.0000	0.933008	0.466504	+	0.884519i	$0.345513\pi$
$140$	0	0
$141$	−6.00000	−0.505291
$142$	10.0000	0.839181
$143$	30.0000	2.50873
$144$	6.00000	0.500000
$145$	0	0
$146$	7.00000	0.579324
$147$	0	0
$148$	−8.00000	−0.657596
$149$	12.0000	0.983078	0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000	0.983078	0.491539	+	0.870855i	$0.336434\pi$
$150$	0	0
$151$	8.00000	0.651031	0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000	0.651031	0.325515	+	0.945537i	$0.394462\pi$
$152$	−3.00000	−0.243332
$153$	−6.00000	−0.485071
$154$	0	0
$155$	0	0
$156$	18.0000	1.44115
$157$	4.00000	0.319235	0.159617	−	0.987179i	$-0.448974\pi$
$157$	4.00000	0.319235	0.159617	+	0.987179i	$0.448974\pi$
$158$	2.00000	0.159111
$159$	12.0000	0.951662
$160$	0	0
$161$	0	0
$162$	−9.00000	−0.707107
$163$	19.0000	1.48819	0.744097	−	0.668071i	$-0.232880\pi$
$163$	19.0000	1.48819	0.744097	+	0.668071i	$0.232880\pi$
$164$	−11.0000	−0.858956
$165$	0	0
$166$	−11.0000	−0.853766
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	0	0
$171$	18.0000	1.37649
$172$	8.00000	0.609994
$173$	2.00000	0.152057	0.0760286	−	0.997106i	$-0.475776\pi$
$173$	2.00000	0.152057	0.0760286	+	0.997106i	$0.475776\pi$
$174$	−18.0000	−1.36458
$175$	0	0
$176$	−5.00000	−0.376889
$177$	12.0000	0.901975
$178$	−11.0000	−0.824485
$179$	3.00000	0.224231	0.112115	−	0.993695i	$-0.464237\pi$
$179$	3.00000	0.224231	0.112115	+	0.993695i	$0.464237\pi$
$180$	0	0
$181$	−10.0000	−0.743294	−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000	−0.743294	−0.371647	+	0.928374i	$0.621207\pi$
$182$	0	0
$183$	−6.00000	−0.443533
$184$	0	0
$185$	0	0
$186$	12.0000	0.879883
$187$	5.00000	0.365636
$188$	2.00000	0.145865
$189$	0	0
$190$	0	0
$191$	−6.00000	−0.434145	−0.217072	−	0.976156i	$-0.569651\pi$
$191$	−6.00000	−0.434145	−0.217072	+	0.976156i	$0.569651\pi$
$192$	−3.00000	−0.216506
$193$	19.0000	1.36765	0.683825	−	0.729646i	$-0.260315\pi$
$193$	19.0000	1.36765	0.683825	+	0.729646i	$0.260315\pi$
$194$	10.0000	0.717958
$195$	0	0
$196$	0	0
$197$	22.0000	1.56744	0.783718	−	0.621117i	$-0.213321\pi$
$197$	22.0000	1.56744	0.783718	+	0.621117i	$0.213321\pi$
$198$	30.0000	2.13201
$199$	10.0000	0.708881	0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000	0.708881	0.354441	+	0.935079i	$0.384671\pi$
$200$	0	0
$201$	27.0000	1.90443
$202$	0	0
$203$	0	0
$204$	3.00000	0.210042
$205$	0	0
$206$	−4.00000	−0.278693
$207$	0	0
$208$	−6.00000	−0.416025
$209$	−15.0000	−1.03757
$210$	0	0
$211$	1.00000	0.0688428	0.0344214	−	0.999407i	$-0.489041\pi$
$211$	1.00000	0.0688428	0.0344214	+	0.999407i	$0.489041\pi$
$212$	−4.00000	−0.274721
$213$	30.0000	2.05557
$214$	3.00000	0.205076
$215$	0	0
$216$	9.00000	0.612372
$217$	0	0
$218$	18.0000	1.21911
$219$	21.0000	1.41905
$220$	0	0
$221$	6.00000	0.403604
$222$	−24.0000	−1.61077
$223$	22.0000	1.47323	0.736614	−	0.676313i	$-0.236423\pi$
$223$	22.0000	1.47323	0.736614	+	0.676313i	$0.236423\pi$
$224$	0	0
$225$	0	0
$226$	−1.00000	−0.0665190
$227$	−28.0000	−1.85843	−0.929213	−	0.369546i	$-0.879513\pi$
$227$	−28.0000	−1.85843	−0.929213	+	0.369546i	$0.879513\pi$
$228$	−9.00000	−0.596040
$229$	14.0000	0.925146	0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000	0.925146	0.462573	+	0.886581i	$0.346926\pi$
$230$	0	0
$231$	0	0
$232$	6.00000	0.393919
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	36.0000	2.35339
$235$	0	0
$236$	−4.00000	−0.260378
$237$	6.00000	0.389742
$238$	0	0
$239$	4.00000	0.258738	0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000	0.258738	0.129369	+	0.991596i	$0.458705\pi$
$240$	0	0
$241$	5.00000	0.322078	0.161039	−	0.986948i	$-0.448515\pi$
$241$	5.00000	0.322078	0.161039	+	0.986948i	$0.448515\pi$
$242$	−14.0000	−0.899954
$243$	0	0
$244$	2.00000	0.128037
$245$	0	0
$246$	−33.0000	−2.10400
$247$	−18.0000	−1.14531
$248$	−4.00000	−0.254000
$249$	−33.0000	−2.09129
$250$	0	0
$251$	−27.0000	−1.70422	−0.852112	−	0.523359i	$-0.824679\pi$
$251$	−27.0000	−1.70422	−0.852112	+	0.523359i	$0.824679\pi$
$252$	0	0
$253$	0	0
$254$	−14.0000	−0.878438
$255$	0	0
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	24.0000	1.49417
$259$	0	0
$260$	0	0
$261$	−36.0000	−2.22834
$262$	8.00000	0.494242
$263$	10.0000	0.616626	0.308313	−	0.951285i	$-0.400236\pi$
$263$	10.0000	0.616626	0.308313	+	0.951285i	$0.400236\pi$
$264$	−15.0000	−0.923186
$265$	0	0
$266$	0	0
$267$	−33.0000	−2.01957
$268$	−9.00000	−0.549762
$269$	−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
$271$	6.00000	0.364474	0.182237	−	0.983255i	$-0.441666\pi$
$271$	6.00000	0.364474	0.182237	+	0.983255i	$0.441666\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	−3.00000	−0.181237
$275$	0	0
$276$	0	0
$277$	30.0000	1.80253	0.901263	−	0.433273i	$-0.142641\pi$
$277$	30.0000	1.80253	0.901263	+	0.433273i	$0.142641\pi$
$278$	−11.0000	−0.659736
$279$	24.0000	1.43684
$280$	0	0
$281$	14.0000	0.835170	0.417585	−	0.908638i	$-0.362877\pi$
$281$	14.0000	0.835170	0.417585	+	0.908638i	$0.362877\pi$
$282$	6.00000	0.357295
$283$	−13.0000	−0.772770	−0.386385	−	0.922338i	$-0.626276\pi$
$283$	−13.0000	−0.772770	−0.386385	+	0.922338i	$0.626276\pi$
$284$	−10.0000	−0.593391
$285$	0	0
$286$	−30.0000	−1.77394
$287$	0	0
$288$	−6.00000	−0.353553
$289$	−16.0000	−0.941176
$290$	0	0
$291$	30.0000	1.75863
$292$	−7.00000	−0.409644
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	0	0
$295$	0	0
$296$	8.00000	0.464991
$297$	45.0000	2.61116
$298$	−12.0000	−0.695141
$299$	0	0
$300$	0	0
$301$	0	0
$302$	−8.00000	−0.460348
$303$	0	0
$304$	3.00000	0.172062
$305$	0	0
$306$	6.00000	0.342997
$307$	13.0000	0.741949	0.370975	−	0.928643i	$-0.379024\pi$
$307$	13.0000	0.741949	0.370975	+	0.928643i	$0.379024\pi$
$308$	0	0
$309$	−12.0000	−0.682656
$310$	0	0
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	−18.0000	−1.01905
$313$	−10.0000	−0.565233	−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000	−0.565233	−0.282617	+	0.959233i	$0.591202\pi$
$314$	−4.00000	−0.225733
$315$	0	0
$316$	−2.00000	−0.112509
$317$	−4.00000	−0.224662	−0.112331	−	0.993671i	$-0.535832\pi$
$317$	−4.00000	−0.224662	−0.112331	+	0.993671i	$0.535832\pi$
$318$	−12.0000	−0.672927
$319$	30.0000	1.67968
$320$	0	0
$321$	9.00000	0.502331
$322$	0	0
$323$	−3.00000	−0.166924
$324$	9.00000	0.500000
$325$	0	0
$326$	−19.0000	−1.05231
$327$	54.0000	2.98621
$328$	11.0000	0.607373
$329$	0	0
$330$	0	0
$331$	−17.0000	−0.934405	−0.467202	−	0.884150i	$-0.654738\pi$
$331$	−17.0000	−0.934405	−0.467202	+	0.884150i	$0.654738\pi$
$332$	11.0000	0.603703
$333$	−48.0000	−2.63038
$334$	−12.0000	−0.656611
$335$	0	0
$336$	0	0
$337$	29.0000	1.57973	0.789865	−	0.613280i	$-0.210150\pi$
$337$	29.0000	1.57973	0.789865	+	0.613280i	$0.210150\pi$
$338$	−23.0000	−1.25104
$339$	−3.00000	−0.162938
$340$	0	0
$341$	−20.0000	−1.08306
$342$	−18.0000	−0.973329
$343$	0	0
$344$	−8.00000	−0.431331
$345$	0	0
$346$	−2.00000	−0.107521
$347$	−19.0000	−1.01997	−0.509987	−	0.860182i	$-0.670350\pi$
$347$	−19.0000	−1.01997	−0.509987	+	0.860182i	$0.670350\pi$
$348$	18.0000	0.964901
$349$	8.00000	0.428230	0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000	0.428230	0.214115	+	0.976808i	$0.431313\pi$
$350$	0	0
$351$	54.0000	2.88231
$352$	5.00000	0.266501
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	−12.0000	−0.637793
$355$	0	0
$356$	11.0000	0.582999
$357$	0	0
$358$	−3.00000	−0.158555
$359$	26.0000	1.37223	0.686114	−	0.727494i	$-0.259315\pi$
$359$	26.0000	1.37223	0.686114	+	0.727494i	$0.259315\pi$
$360$	0	0
$361$	−10.0000	−0.526316
$362$	10.0000	0.525588
$363$	−42.0000	−2.20443
$364$	0	0
$365$	0	0
$366$	6.00000	0.313625
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	0	0
$369$	−66.0000	−3.43582
$370$	0	0
$371$	0	0
$372$	−12.0000	−0.622171
$373$	4.00000	0.207112	0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000	0.207112	0.103556	+	0.994624i	$0.466978\pi$
$374$	−5.00000	−0.258544
$375$	0	0
$376$	−2.00000	−0.103142
$377$	36.0000	1.85409
$378$	0	0
$379$	9.00000	0.462299	0.231149	−	0.972918i	$-0.425751\pi$
$379$	9.00000	0.462299	0.231149	+	0.972918i	$0.425751\pi$
$380$	0	0
$381$	−42.0000	−2.15173
$382$	6.00000	0.306987
$383$	−6.00000	−0.306586	−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000	−0.306586	−0.153293	+	0.988181i	$0.548988\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	−19.0000	−0.967075
$387$	48.0000	2.43998
$388$	−10.0000	−0.507673
$389$	8.00000	0.405616	0.202808	−	0.979219i	$-0.434993\pi$
$389$	8.00000	0.405616	0.202808	+	0.979219i	$0.434993\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	24.0000	1.21064
$394$	−22.0000	−1.10834
$395$	0	0
$396$	−30.0000	−1.50756
$397$	10.0000	0.501886	0.250943	−	0.968002i	$-0.419259\pi$
$397$	10.0000	0.501886	0.250943	+	0.968002i	$0.419259\pi$
$398$	−10.0000	−0.501255
$399$	0	0
$400$	0	0
$401$	37.0000	1.84769	0.923846	−	0.382765i	$-0.125028\pi$
$401$	37.0000	1.84769	0.923846	+	0.382765i	$0.125028\pi$
$402$	−27.0000	−1.34664
$403$	−24.0000	−1.19553
$404$	0	0
$405$	0	0
$406$	0	0
$407$	40.0000	1.98273
$408$	−3.00000	−0.148522
$409$	21.0000	1.03838	0.519192	−	0.854658i	$-0.326233\pi$
$409$	21.0000	1.03838	0.519192	+	0.854658i	$0.326233\pi$
$410$	0	0
$411$	−9.00000	−0.443937
$412$	4.00000	0.197066
$413$	0	0
$414$	0	0
$415$	0	0
$416$	6.00000	0.294174
$417$	−33.0000	−1.61602
$418$	15.0000	0.733674
$419$	39.0000	1.90527	0.952637	−	0.304109i	$-0.0983586\pi$
$419$	39.0000	1.90527	0.952637	+	0.304109i	$0.0983586\pi$
$420$	0	0
$421$	20.0000	0.974740	0.487370	−	0.873195i	$-0.337956\pi$
$421$	20.0000	0.974740	0.487370	+	0.873195i	$0.337956\pi$
$422$	−1.00000	−0.0486792
$423$	12.0000	0.583460
$424$	4.00000	0.194257
$425$	0	0
$426$	−30.0000	−1.45350
$427$	0	0
$428$	−3.00000	−0.145010
$429$	−90.0000	−4.34524
$430$	0	0
$431$	−36.0000	−1.73406	−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000	−1.73406	−0.867029	+	0.498257i	$0.833974\pi$
$432$	−9.00000	−0.433013
$433$	−1.00000	−0.0480569	−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000	−0.0480569	−0.0240285	+	0.999711i	$0.507649\pi$
$434$	0	0
$435$	0	0
$436$	−18.0000	−0.862044
$437$	0	0
$438$	−21.0000	−1.00342
$439$	−28.0000	−1.33637	−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000	−1.33637	−0.668184	+	0.743996i	$0.732928\pi$
$440$	0	0
$441$	0	0
$442$	−6.00000	−0.285391
$443$	−37.0000	−1.75792	−0.878962	−	0.476893i	$-0.841763\pi$
$443$	−37.0000	−1.75792	−0.878962	+	0.476893i	$0.841763\pi$
$444$	24.0000	1.13899
$445$	0	0
$446$	−22.0000	−1.04173
$447$	−36.0000	−1.70274
$448$	0	0
$449$	33.0000	1.55737	0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000	1.55737	0.778683	+	0.627417i	$0.215888\pi$
$450$	0	0
$451$	55.0000	2.58985
$452$	1.00000	0.0470360
$453$	−24.0000	−1.12762
$454$	28.0000	1.31411
$455$	0	0
$456$	9.00000	0.421464
$457$	−25.0000	−1.16945	−0.584725	−	0.811231i	$-0.698798\pi$
$457$	−25.0000	−1.16945	−0.584725	+	0.811231i	$0.698798\pi$
$458$	−14.0000	−0.654177
$459$	9.00000	0.420084
$460$	0	0
$461$	38.0000	1.76984	0.884918	−	0.465746i	$-0.154214\pi$
$461$	38.0000	1.76984	0.884918	+	0.465746i	$0.154214\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	−6.00000	−0.278543
$465$	0	0
$466$	6.00000	0.277945
$467$	−4.00000	−0.185098	−0.0925490	−	0.995708i	$-0.529501\pi$
$467$	−4.00000	−0.185098	−0.0925490	+	0.995708i	$0.529501\pi$
$468$	−36.0000	−1.66410
$469$	0	0
$470$	0	0
$471$	−12.0000	−0.552931
$472$	4.00000	0.184115
$473$	−40.0000	−1.83920
$474$	−6.00000	−0.275589
$475$	0	0
$476$	0	0
$477$	−24.0000	−1.09888
$478$	−4.00000	−0.182956
$479$	6.00000	0.274147	0.137073	−	0.990561i	$-0.456230\pi$
$479$	6.00000	0.274147	0.137073	+	0.990561i	$0.456230\pi$
$480$	0	0
$481$	48.0000	2.18861
$482$	−5.00000	−0.227744
$483$	0	0
$484$	14.0000	0.636364
$485$	0	0
$486$	0	0
$487$	34.0000	1.54069	0.770344	−	0.637629i	$-0.220085\pi$
$487$	34.0000	1.54069	0.770344	+	0.637629i	$0.220085\pi$
$488$	−2.00000	−0.0905357
$489$	−57.0000	−2.57763
$490$	0	0
$491$	−12.0000	−0.541552	−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000	−0.541552	−0.270776	+	0.962642i	$0.587280\pi$
$492$	33.0000	1.48775
$493$	6.00000	0.270226
$494$	18.0000	0.809858
$495$	0	0
$496$	4.00000	0.179605
$497$	0	0
$498$	33.0000	1.47877
$499$	36.0000	1.61158	0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000	1.61158	0.805791	+	0.592200i	$0.201741\pi$
$500$	0	0
$501$	−36.0000	−1.60836
$502$	27.0000	1.20507
$503$	−30.0000	−1.33763	−0.668817	−	0.743427i	$-0.733199\pi$
$503$	−30.0000	−1.33763	−0.668817	+	0.743427i	$0.733199\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−69.0000	−3.06440
$508$	14.0000	0.621150
$509$	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
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−27.0000	−1.19208
$514$	−2.00000	−0.0882162
$515$	0	0
$516$	−24.0000	−1.05654
$517$	−10.0000	−0.439799
$518$	0	0
$519$	−6.00000	−0.263371
$520$	0	0
$521$	−11.0000	−0.481919	−0.240959	−	0.970535i	$-0.577462\pi$
$521$	−11.0000	−0.481919	−0.240959	+	0.970535i	$0.577462\pi$
$522$	36.0000	1.57568
$523$	13.0000	0.568450	0.284225	−	0.958758i	$-0.408264\pi$
$523$	13.0000	0.568450	0.284225	+	0.958758i	$0.408264\pi$
$524$	−8.00000	−0.349482
$525$	0	0
$526$	−10.0000	−0.436021
$527$	−4.00000	−0.174243
$528$	15.0000	0.652791
$529$	−23.0000	−1.00000
$530$	0	0
$531$	−24.0000	−1.04151
$532$	0	0
$533$	66.0000	2.85878
$534$	33.0000	1.42805
$535$	0	0
$536$	9.00000	0.388741
$537$	−9.00000	−0.388379
$538$	18.0000	0.776035
$539$	0	0
$540$	0	0
$541$	−42.0000	−1.80572	−0.902861	−	0.429934i	$-0.858537\pi$
$541$	−42.0000	−1.80572	−0.902861	+	0.429934i	$0.858537\pi$
$542$	−6.00000	−0.257722
$543$	30.0000	1.28742
$544$	1.00000	0.0428746
$545$	0	0
$546$	0	0
$547$	−27.0000	−1.15444	−0.577218	−	0.816590i	$-0.695862\pi$
$547$	−27.0000	−1.15444	−0.577218	+	0.816590i	$0.695862\pi$
$548$	3.00000	0.128154
$549$	12.0000	0.512148
$550$	0	0
$551$	−18.0000	−0.766826
$552$	0	0
$553$	0	0
$554$	−30.0000	−1.27458
$555$	0	0
$556$	11.0000	0.466504
$557$	−4.00000	−0.169485	−0.0847427	−	0.996403i	$-0.527007\pi$
$557$	−4.00000	−0.169485	−0.0847427	+	0.996403i	$0.527007\pi$
$558$	−24.0000	−1.01600
$559$	−48.0000	−2.03018
$560$	0	0
$561$	−15.0000	−0.633300
$562$	−14.0000	−0.590554
$563$	20.0000	0.842900	0.421450	−	0.906852i	$-0.361521\pi$
$563$	20.0000	0.842900	0.421450	+	0.906852i	$0.361521\pi$
$564$	−6.00000	−0.252646
$565$	0	0
$566$	13.0000	0.546431
$567$	0	0
$568$	10.0000	0.419591
$569$	21.0000	0.880366	0.440183	−	0.897908i	$-0.354914\pi$
$569$	21.0000	0.880366	0.440183	+	0.897908i	$0.354914\pi$
$570$	0	0
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	30.0000	1.25436
$573$	18.0000	0.751961
$574$	0	0
$575$	0	0
$576$	6.00000	0.250000
$577$	13.0000	0.541197	0.270599	−	0.962692i	$-0.412778\pi$
$577$	13.0000	0.541197	0.270599	+	0.962692i	$0.412778\pi$
$578$	16.0000	0.665512
$579$	−57.0000	−2.36884
$580$	0	0
$581$	0	0
$582$	−30.0000	−1.24354
$583$	20.0000	0.828315
$584$	7.00000	0.289662
$585$	0	0
$586$	14.0000	0.578335
$587$	−13.0000	−0.536567	−0.268284	−	0.963340i	$-0.586456\pi$
$587$	−13.0000	−0.536567	−0.268284	+	0.963340i	$0.586456\pi$
$588$	0	0
$589$	12.0000	0.494451
$590$	0	0
$591$	−66.0000	−2.71488
$592$	−8.00000	−0.328798
$593$	−39.0000	−1.60154	−0.800769	−	0.598973i	$-0.795576\pi$
$593$	−39.0000	−1.60154	−0.800769	+	0.598973i	$0.795576\pi$
$594$	−45.0000	−1.84637
$595$	0	0
$596$	12.0000	0.491539
$597$	−30.0000	−1.22782
$598$	0	0
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	0	0
$601$	−21.0000	−0.856608	−0.428304	−	0.903635i	$-0.640889\pi$
$601$	−21.0000	−0.856608	−0.428304	+	0.903635i	$0.640889\pi$
$602$	0	0
$603$	−54.0000	−2.19905
$604$	8.00000	0.325515
$605$	0	0
$606$	0	0
$607$	28.0000	1.13648	0.568242	−	0.822861i	$-0.307624\pi$
$607$	28.0000	1.13648	0.568242	+	0.822861i	$0.307624\pi$
$608$	−3.00000	−0.121666
$609$	0	0
$610$	0	0
$611$	−12.0000	−0.485468
$612$	−6.00000	−0.242536
$613$	−18.0000	−0.727013	−0.363507	−	0.931592i	$-0.618421\pi$
$613$	−18.0000	−0.727013	−0.363507	+	0.931592i	$0.618421\pi$
$614$	−13.0000	−0.524637
$615$	0	0
$616$	0	0
$617$	−14.0000	−0.563619	−0.281809	−	0.959470i	$-0.590935\pi$
$617$	−14.0000	−0.563619	−0.281809	+	0.959470i	$0.590935\pi$
$618$	12.0000	0.482711
$619$	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
$622$	6.00000	0.240578
$623$	0	0
$624$	18.0000	0.720577
$625$	0	0
$626$	10.0000	0.399680
$627$	45.0000	1.79713
$628$	4.00000	0.159617
$629$	8.00000	0.318981
$630$	0	0
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	2.00000	0.0795557
$633$	−3.00000	−0.119239
$634$	4.00000	0.158860
$635$	0	0
$636$	12.0000	0.475831
$637$	0	0
$638$	−30.0000	−1.18771
$639$	−60.0000	−2.37356
$640$	0	0
$641$	2.00000	0.0789953	0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000	0.0789953	0.0394976	+	0.999220i	$0.487424\pi$
$642$	−9.00000	−0.355202
$643$	16.0000	0.630978	0.315489	−	0.948929i	$-0.397831\pi$
$643$	16.0000	0.630978	0.315489	+	0.948929i	$0.397831\pi$
$644$	0	0
$645$	0	0
$646$	3.00000	0.118033
$647$	−8.00000	−0.314512	−0.157256	−	0.987558i	$-0.550265\pi$
$647$	−8.00000	−0.314512	−0.157256	+	0.987558i	$0.550265\pi$
$648$	−9.00000	−0.353553
$649$	20.0000	0.785069
$650$	0	0
$651$	0	0
$652$	19.0000	0.744097
$653$	28.0000	1.09572	0.547862	−	0.836569i	$-0.315442\pi$
$653$	28.0000	1.09572	0.547862	+	0.836569i	$0.315442\pi$
$654$	−54.0000	−2.11157
$655$	0	0
$656$	−11.0000	−0.429478
$657$	−42.0000	−1.63858
$658$	0	0
$659$	1.00000	0.0389545	0.0194772	−	0.999810i	$-0.493800\pi$
$659$	1.00000	0.0389545	0.0194772	+	0.999810i	$0.493800\pi$
$660$	0	0
$661$	50.0000	1.94477	0.972387	−	0.233373i	$-0.0749763\pi$
$661$	50.0000	1.94477	0.972387	+	0.233373i	$0.0749763\pi$
$662$	17.0000	0.660724
$663$	−18.0000	−0.699062
$664$	−11.0000	−0.426883
$665$	0	0
$666$	48.0000	1.85996
$667$	0	0
$668$	12.0000	0.464294
$669$	−66.0000	−2.55171
$670$	0	0
$671$	−10.0000	−0.386046
$672$	0	0
$673$	−34.0000	−1.31060	−0.655302	−	0.755367i	$-0.727459\pi$
$673$	−34.0000	−1.31060	−0.655302	+	0.755367i	$0.727459\pi$
$674$	−29.0000	−1.11704
$675$	0	0
$676$	23.0000	0.884615
$677$	−48.0000	−1.84479	−0.922395	−	0.386248i	$-0.873771\pi$
$677$	−48.0000	−1.84479	−0.922395	+	0.386248i	$0.873771\pi$
$678$	3.00000	0.115214
$679$	0	0
$680$	0	0
$681$	84.0000	3.21889
$682$	20.0000	0.765840
$683$	13.0000	0.497431	0.248716	−	0.968577i	$-0.419992\pi$
$683$	13.0000	0.497431	0.248716	+	0.968577i	$0.419992\pi$
$684$	18.0000	0.688247
$685$	0	0
$686$	0	0
$687$	−42.0000	−1.60240
$688$	8.00000	0.304997
$689$	24.0000	0.914327
$690$	0	0
$691$	−49.0000	−1.86405	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−49.0000	−1.86405	−0.932024	+	0.362397i	$0.881959\pi$
$692$	2.00000	0.0760286
$693$	0	0
$694$	19.0000	0.721230
$695$	0	0
$696$	−18.0000	−0.682288
$697$	11.0000	0.416655
$698$	−8.00000	−0.302804
$699$	18.0000	0.680823
$700$	0	0
$701$	−32.0000	−1.20862	−0.604312	−	0.796748i	$-0.706552\pi$
$701$	−32.0000	−1.20862	−0.604312	+	0.796748i	$0.706552\pi$
$702$	−54.0000	−2.03810
$703$	−24.0000	−0.905177
$704$	−5.00000	−0.188445
$705$	0	0
$706$	18.0000	0.677439
$707$	0	0
$708$	12.0000	0.450988
$709$	4.00000	0.150223	0.0751116	−	0.997175i	$-0.476069\pi$
$709$	4.00000	0.150223	0.0751116	+	0.997175i	$0.476069\pi$
$710$	0	0
$711$	−12.0000	−0.450035
$712$	−11.0000	−0.412242
$713$	0	0
$714$	0	0
$715$	0	0
$716$	3.00000	0.112115
$717$	−12.0000	−0.448148
$718$	−26.0000	−0.970311
$719$	48.0000	1.79010	0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000	1.79010	0.895049	+	0.445968i	$0.147140\pi$
$720$	0	0
$721$	0	0
$722$	10.0000	0.372161
$723$	−15.0000	−0.557856
$724$	−10.0000	−0.371647
$725$	0	0
$726$	42.0000	1.55877
$727$	6.00000	0.222528	0.111264	−	0.993791i	$-0.464510\pi$
$727$	6.00000	0.222528	0.111264	+	0.993791i	$0.464510\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	0	0
$731$	−8.00000	−0.295891
$732$	−6.00000	−0.221766
$733$	40.0000	1.47743	0.738717	−	0.674016i	$-0.235432\pi$
$733$	40.0000	1.47743	0.738717	+	0.674016i	$0.235432\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	0	0
$737$	45.0000	1.65760
$738$	66.0000	2.42949
$739$	4.00000	0.147142	0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000	0.147142	0.0735712	+	0.997290i	$0.476560\pi$
$740$	0	0
$741$	54.0000	1.98374
$742$	0	0
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	12.0000	0.439941
$745$	0	0
$746$	−4.00000	−0.146450
$747$	66.0000	2.41481
$748$	5.00000	0.182818
$749$	0	0
$750$	0	0
$751$	50.0000	1.82453	0.912263	−	0.409605i	$-0.134333\pi$
$751$	50.0000	1.82453	0.912263	+	0.409605i	$0.134333\pi$
$752$	2.00000	0.0729325
$753$	81.0000	2.95180
$754$	−36.0000	−1.31104
$755$	0	0
$756$	0	0
$757$	2.00000	0.0726912	0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000	0.0726912	0.0363456	+	0.999339i	$0.488428\pi$
$758$	−9.00000	−0.326895
$759$	0	0
$760$	0	0
$761$	−27.0000	−0.978749	−0.489375	−	0.872074i	$-0.662775\pi$
$761$	−27.0000	−0.978749	−0.489375	+	0.872074i	$0.662775\pi$
$762$	42.0000	1.52150
$763$	0	0
$764$	−6.00000	−0.217072
$765$	0	0
$766$	6.00000	0.216789
$767$	24.0000	0.866590
$768$	−3.00000	−0.108253
$769$	−19.0000	−0.685158	−0.342579	−	0.939489i	$-0.611300\pi$
$769$	−19.0000	−0.685158	−0.342579	+	0.939489i	$0.611300\pi$
$770$	0	0
$771$	−6.00000	−0.216085
$772$	19.0000	0.683825
$773$	36.0000	1.29483	0.647415	−	0.762138i	$-0.275850\pi$
$773$	36.0000	1.29483	0.647415	+	0.762138i	$0.275850\pi$
$774$	−48.0000	−1.72532
$775$	0	0
$776$	10.0000	0.358979
$777$	0	0
$778$	−8.00000	−0.286814
$779$	−33.0000	−1.18235
$780$	0	0
$781$	50.0000	1.78914
$782$	0	0
$783$	54.0000	1.92980
$784$	0	0
$785$	0	0
$786$	−24.0000	−0.856052
$787$	52.0000	1.85360	0.926800	−	0.375555i	$-0.122548\pi$
$787$	52.0000	1.85360	0.926800	+	0.375555i	$0.122548\pi$
$788$	22.0000	0.783718
$789$	−30.0000	−1.06803
$790$	0	0
$791$	0	0
$792$	30.0000	1.06600
$793$	−12.0000	−0.426132
$794$	−10.0000	−0.354887
$795$	0	0
$796$	10.0000	0.354441
$797$	42.0000	1.48772	0.743858	−	0.668338i	$-0.232994\pi$
$797$	42.0000	1.48772	0.743858	+	0.668338i	$0.232994\pi$
$798$	0	0
$799$	−2.00000	−0.0707549
$800$	0	0
$801$	66.0000	2.33200
$802$	−37.0000	−1.30652
$803$	35.0000	1.23512
$804$	27.0000	0.952217
$805$	0	0
$806$	24.0000	0.845364
$807$	54.0000	1.90089
$808$	0	0
$809$	6.00000	0.210949	0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000	0.210949	0.105474	+	0.994422i	$0.466364\pi$
$810$	0	0
$811$	28.0000	0.983213	0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000	0.983213	0.491606	+	0.870817i	$0.336410\pi$
$812$	0	0
$813$	−18.0000	−0.631288
$814$	−40.0000	−1.40200
$815$	0	0
$816$	3.00000	0.105021
$817$	24.0000	0.839654
$818$	−21.0000	−0.734248
$819$	0	0
$820$	0	0
$821$	−24.0000	−0.837606	−0.418803	−	0.908077i	$-0.637550\pi$
$821$	−24.0000	−0.837606	−0.418803	+	0.908077i	$0.637550\pi$
$822$	9.00000	0.313911
$823$	−10.0000	−0.348578	−0.174289	−	0.984695i	$-0.555763\pi$
$823$	−10.0000	−0.348578	−0.174289	+	0.984695i	$0.555763\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	0	0
$827$	−41.0000	−1.42571	−0.712855	−	0.701312i	$-0.752598\pi$
$827$	−41.0000	−1.42571	−0.712855	+	0.701312i	$0.752598\pi$
$828$	0	0
$829$	4.00000	0.138926	0.0694629	−	0.997585i	$-0.477871\pi$
$829$	4.00000	0.138926	0.0694629	+	0.997585i	$0.477871\pi$
$830$	0	0
$831$	−90.0000	−3.12207
$832$	−6.00000	−0.208013
$833$	0	0
$834$	33.0000	1.14270
$835$	0	0
$836$	−15.0000	−0.518786
$837$	−36.0000	−1.24434
$838$	−39.0000	−1.34723
$839$	−2.00000	−0.0690477	−0.0345238	−	0.999404i	$-0.510991\pi$
$839$	−2.00000	−0.0690477	−0.0345238	+	0.999404i	$0.510991\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−20.0000	−0.689246
$843$	−42.0000	−1.44656
$844$	1.00000	0.0344214
$845$	0	0
$846$	−12.0000	−0.412568
$847$	0	0
$848$	−4.00000	−0.137361
$849$	39.0000	1.33848
$850$	0	0
$851$	0	0
$852$	30.0000	1.02778
$853$	−34.0000	−1.16414	−0.582069	−	0.813139i	$-0.697757\pi$
$853$	−34.0000	−1.16414	−0.582069	+	0.813139i	$0.697757\pi$
$854$	0	0
$855$	0	0
$856$	3.00000	0.102538
$857$	3.00000	0.102478	0.0512390	−	0.998686i	$-0.483683\pi$
$857$	3.00000	0.102478	0.0512390	+	0.998686i	$0.483683\pi$
$858$	90.0000	3.07255
$859$	51.0000	1.74010	0.870049	−	0.492966i	$-0.164087\pi$
$859$	51.0000	1.74010	0.870049	+	0.492966i	$0.164087\pi$
$860$	0	0
$861$	0	0
$862$	36.0000	1.22616
$863$	−4.00000	−0.136162	−0.0680808	−	0.997680i	$-0.521688\pi$
$863$	−4.00000	−0.136162	−0.0680808	+	0.997680i	$0.521688\pi$
$864$	9.00000	0.306186
$865$	0	0
$866$	1.00000	0.0339814
$867$	48.0000	1.63017
$868$	0	0
$869$	10.0000	0.339227
$870$	0	0
$871$	54.0000	1.82972
$872$	18.0000	0.609557
$873$	−60.0000	−2.03069
$874$	0	0
$875$	0	0
$876$	21.0000	0.709524
$877$	−32.0000	−1.08056	−0.540282	−	0.841484i	$-0.681682\pi$
$877$	−32.0000	−1.08056	−0.540282	+	0.841484i	$0.681682\pi$
$878$	28.0000	0.944954
$879$	42.0000	1.41662
$880$	0	0
$881$	−26.0000	−0.875962	−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000	−0.875962	−0.437981	+	0.898984i	$0.644306\pi$
$882$	0	0
$883$	−15.0000	−0.504790	−0.252395	−	0.967624i	$-0.581218\pi$
$883$	−15.0000	−0.504790	−0.252395	+	0.967624i	$0.581218\pi$
$884$	6.00000	0.201802
$885$	0	0
$886$	37.0000	1.24304
$887$	−34.0000	−1.14161	−0.570804	−	0.821086i	$-0.693368\pi$
$887$	−34.0000	−1.14161	−0.570804	+	0.821086i	$0.693368\pi$
$888$	−24.0000	−0.805387
$889$	0	0
$890$	0	0
$891$	−45.0000	−1.50756
$892$	22.0000	0.736614
$893$	6.00000	0.200782
$894$	36.0000	1.20402
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−33.0000	−1.10122
$899$	−24.0000	−0.800445
$900$	0	0
$901$	4.00000	0.133259
$902$	−55.0000	−1.83130
$903$	0	0
$904$	−1.00000	−0.0332595
$905$	0	0
$906$	24.0000	0.797347
$907$	4.00000	0.132818	0.0664089	−	0.997792i	$-0.478846\pi$
$907$	4.00000	0.132818	0.0664089	+	0.997792i	$0.478846\pi$
$908$	−28.0000	−0.929213
$909$	0	0
$910$	0	0
$911$	−12.0000	−0.397578	−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000	−0.397578	−0.198789	+	0.980042i	$0.563701\pi$
$912$	−9.00000	−0.298020
$913$	−55.0000	−1.82023
$914$	25.0000	0.826927
$915$	0	0
$916$	14.0000	0.462573
$917$	0	0
$918$	−9.00000	−0.297044
$919$	−34.0000	−1.12156	−0.560778	−	0.827966i	$-0.689498\pi$
$919$	−34.0000	−1.12156	−0.560778	+	0.827966i	$0.689498\pi$
$920$	0	0
$921$	−39.0000	−1.28509
$922$	−38.0000	−1.25146
$923$	60.0000	1.97492
$924$	0	0
$925$	0	0
$926$	8.00000	0.262896
$927$	24.0000	0.788263
$928$	6.00000	0.196960
$929$	−46.0000	−1.50921	−0.754606	−	0.656179i	$-0.772172\pi$
$929$	−46.0000	−1.50921	−0.754606	+	0.656179i	$0.772172\pi$
$930$	0	0
$931$	0	0
$932$	−6.00000	−0.196537
$933$	18.0000	0.589294
$934$	4.00000	0.130884
$935$	0	0
$936$	36.0000	1.17670
$937$	−7.00000	−0.228680	−0.114340	−	0.993442i	$-0.536475\pi$
$937$	−7.00000	−0.228680	−0.114340	+	0.993442i	$0.536475\pi$
$938$	0	0
$939$	30.0000	0.979013
$940$	0	0
$941$	−56.0000	−1.82555	−0.912774	−	0.408465i	$-0.866064\pi$
$941$	−56.0000	−1.82555	−0.912774	+	0.408465i	$0.866064\pi$
$942$	12.0000	0.390981
$943$	0	0
$944$	−4.00000	−0.130189
$945$	0	0
$946$	40.0000	1.30051
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	6.00000	0.194871
$949$	42.0000	1.36338
$950$	0	0
$951$	12.0000	0.389127
$952$	0	0
$953$	−9.00000	−0.291539	−0.145769	−	0.989319i	$-0.546566\pi$
$953$	−9.00000	−0.291539	−0.145769	+	0.989319i	$0.546566\pi$
$954$	24.0000	0.777029
$955$	0	0
$956$	4.00000	0.129369
$957$	−90.0000	−2.90929
$958$	−6.00000	−0.193851
$959$	0	0
$960$	0	0
$961$	−15.0000	−0.483871
$962$	−48.0000	−1.54758
$963$	−18.0000	−0.580042
$964$	5.00000	0.161039
$965$	0	0
$966$	0	0
$967$	2.00000	0.0643157	0.0321578	−	0.999483i	$-0.489762\pi$
$967$	2.00000	0.0643157	0.0321578	+	0.999483i	$0.489762\pi$
$968$	−14.0000	−0.449977
$969$	9.00000	0.289122
$970$	0	0
$971$	51.0000	1.63667	0.818334	−	0.574743i	$-0.194898\pi$
$971$	51.0000	1.63667	0.818334	+	0.574743i	$0.194898\pi$
$972$	0	0
$973$	0	0
$974$	−34.0000	−1.08943
$975$	0	0
$976$	2.00000	0.0640184
$977$	−21.0000	−0.671850	−0.335925	−	0.941889i	$-0.609049\pi$
$977$	−21.0000	−0.671850	−0.335925	+	0.941889i	$0.609049\pi$
$978$	57.0000	1.82266
$979$	−55.0000	−1.75781
$980$	0	0
$981$	−108.000	−3.44817
$982$	12.0000	0.382935
$983$	−4.00000	−0.127580	−0.0637901	−	0.997963i	$-0.520319\pi$
$983$	−4.00000	−0.127580	−0.0637901	+	0.997963i	$0.520319\pi$
$984$	−33.0000	−1.05200
$985$	0	0
$986$	−6.00000	−0.191079
$987$	0	0
$988$	−18.0000	−0.572656
$989$	0	0
$990$	0	0
$991$	4.00000	0.127064	0.0635321	−	0.997980i	$-0.479763\pi$
$991$	4.00000	0.127064	0.0635321	+	0.997980i	$0.479763\pi$
$992$	−4.00000	−0.127000
$993$	51.0000	1.61844
$994$	0	0
$995$	0	0
$996$	−33.0000	−1.04565
$997$	−58.0000	−1.83688	−0.918439	−	0.395562i	$-0.870550\pi$
$997$	−58.0000	−1.83688	−0.918439	+	0.395562i	$0.870550\pi$
$998$	−36.0000	−1.13956
$999$	72.0000	2.27798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2450.2.a.a.1.1		1
5.2	odd	4		2450.2.c.r.99.1		2
5.3	odd	4		2450.2.c.r.99.2		2
5.4	even	2		2450.2.a.bg.1.1		1
7.6	odd	2		350.2.a.c.1.1	✓	1
21.20	even	2		3150.2.a.bq.1.1		1
28.27	even	2		2800.2.a.b.1.1		1
35.13	even	4		350.2.c.a.99.2		2
35.27	even	4		350.2.c.a.99.1		2
35.34	odd	2		350.2.a.d.1.1	yes	1
105.62	odd	4		3150.2.g.v.2899.2		2
105.83	odd	4		3150.2.g.v.2899.1		2
105.104	even	2		3150.2.a.j.1.1		1
140.27	odd	4		2800.2.g.a.449.2		2
140.83	odd	4		2800.2.g.a.449.1		2
140.139	even	2		2800.2.a.bg.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.a.c.1.1	✓	1	7.6	odd	2
350.2.a.d.1.1	yes	1	35.34	odd	2
350.2.c.a.99.1		2	35.27	even	4
350.2.c.a.99.2		2	35.13	even	4
2450.2.a.a.1.1		1	1.1	even	1	trivial
2450.2.a.bg.1.1		1	5.4	even	2
2450.2.c.r.99.1		2	5.2	odd	4
2450.2.c.r.99.2		2	5.3	odd	4
2800.2.a.b.1.1		1	28.27	even	2
2800.2.a.bg.1.1		1	140.139	even	2
2800.2.g.a.449.1		2	140.83	odd	4
2800.2.g.a.449.2		2	140.27	odd	4
3150.2.a.j.1.1		1	105.104	even	2
3150.2.a.bq.1.1		1	21.20	even	2
3150.2.g.v.2899.1		2	105.83	odd	4
3150.2.g.v.2899.2		2	105.62	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2450.a (trivial)

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Modular forms

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