LMFDB - Embedded newform 2450.4.a.bq.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2450,4,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, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2450.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2450 = 2 \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
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:	$144.554679514$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
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)

$f(q)$

$=$

$q+2.00000 q^{2} +10.0000 q^{3} +4.00000 q^{4} +20.0000 q^{6} +8.00000 q^{8} +73.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} +10.0000 q^{3} +4.00000 q^{4} +20.0000 q^{6} +8.00000 q^{8} +73.0000 q^{9} +53.0000 q^{11} +40.0000 q^{12} +25.0000 q^{13} +16.0000 q^{16} +14.0000 q^{17} +146.000 q^{18} +95.0000 q^{19} +106.000 q^{22} -1.00000 q^{23} +80.0000 q^{24} +50.0000 q^{26} +460.000 q^{27} -206.000 q^{29} -108.000 q^{31} +32.0000 q^{32} +530.000 q^{33} +28.0000 q^{34} +292.000 q^{36} +57.0000 q^{37} +190.000 q^{38} +250.000 q^{39} -243.000 q^{41} -434.000 q^{43} +212.000 q^{44} -2.00000 q^{46} -231.000 q^{47} +160.000 q^{48} +140.000 q^{51} +100.000 q^{52} -263.000 q^{53} +920.000 q^{54} +950.000 q^{57} -412.000 q^{58} -24.0000 q^{59} -116.000 q^{61} -216.000 q^{62} +64.0000 q^{64} +1060.00 q^{66} +204.000 q^{67} +56.0000 q^{68} -10.0000 q^{69} +484.000 q^{71} +584.000 q^{72} -692.000 q^{73} +114.000 q^{74} +380.000 q^{76} +500.000 q^{78} +466.000 q^{79} +2629.00 q^{81} -486.000 q^{82} +228.000 q^{83} -868.000 q^{86} -2060.00 q^{87} +424.000 q^{88} +362.000 q^{89} -4.00000 q^{92} -1080.00 q^{93} -462.000 q^{94} +320.000 q^{96} +854.000 q^{97} +3869.00 q^{99} +O(q^{100})\)

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	0.707107
$2$	2.00000	0.707107
$3$	10.0000	1.92450	0.962250	−	0.272166i	$-0.0877398\pi$
$3$	10.0000	1.92450	0.962250	+	0.272166i	$0.0877398\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	20.0000	1.36083
$7$	0	0
$7$	0	0
$8$	8.00000	0.353553
$9$	73.0000	2.70370
$10$	0	0
$11$	53.0000	1.45274	0.726368	−	0.687306i	$-0.241207\pi$
$11$	53.0000	1.45274	0.726368	+	0.687306i	$0.241207\pi$
$12$	40.0000	0.962250
$13$	25.0000	0.533366	0.266683	−	0.963784i	$-0.414072\pi$
$13$	25.0000	0.533366	0.266683	+	0.963784i	$0.414072\pi$
$14$	0	0
$15$	0	0
$16$	16.0000	0.250000
$17$	14.0000	0.199735	0.0998676	−	0.995001i	$-0.468158\pi$
$17$	14.0000	0.199735	0.0998676	+	0.995001i	$0.468158\pi$
$18$	146.000	1.91181
$19$	95.0000	1.14708	0.573539	−	0.819178i	$-0.305570\pi$
$19$	95.0000	1.14708	0.573539	+	0.819178i	$0.305570\pi$
$20$	0	0
$21$	0	0
$22$	106.000	1.02724
$23$	−1.00000	−0.00906584	−0.00453292	−	0.999990i	$-0.501443\pi$
$23$	−1.00000	−0.00906584	−0.00453292	+	0.999990i	$0.501443\pi$
$24$	80.0000	0.680414
$25$	0	0
$26$	50.0000	0.377146
$27$	460.000	3.27878
$28$	0	0
$29$	−206.000	−1.31908	−0.659539	−	0.751671i	$-0.729248\pi$
$29$	−206.000	−1.31908	−0.659539	+	0.751671i	$0.729248\pi$
$30$	0	0
$31$	−108.000	−0.625722	−0.312861	−	0.949799i	$-0.601287\pi$
$31$	−108.000	−0.625722	−0.312861	+	0.949799i	$0.601287\pi$
$32$	32.0000	0.176777
$33$	530.000	2.79579
$34$	28.0000	0.141234
$35$	0	0
$36$	292.000	1.35185
$37$	57.0000	0.253263	0.126632	−	0.991950i	$-0.459583\pi$
$37$	57.0000	0.253263	0.126632	+	0.991950i	$0.459583\pi$
$38$	190.000	0.811107
$39$	250.000	1.02646
$40$	0	0
$41$	−243.000	−0.925615	−0.462808	−	0.886459i	$-0.653158\pi$
$41$	−243.000	−0.925615	−0.462808	+	0.886459i	$0.653158\pi$
$42$	0	0
$43$	−434.000	−1.53917	−0.769586	−	0.638543i	$-0.779537\pi$
$43$	−434.000	−1.53917	−0.769586	+	0.638543i	$0.779537\pi$
$44$	212.000	0.726368
$45$	0	0
$46$	−2.00000	−0.00641052
$47$	−231.000	−0.716911	−0.358455	−	0.933547i	$-0.616697\pi$
$47$	−231.000	−0.716911	−0.358455	+	0.933547i	$0.616697\pi$
$48$	160.000	0.481125
$49$	0	0
$50$	0	0
$51$	140.000	0.384391
$52$	100.000	0.266683
$53$	−263.000	−0.681619	−0.340810	−	0.940132i	$-0.610701\pi$
$53$	−263.000	−0.681619	−0.340810	+	0.940132i	$0.610701\pi$
$54$	920.000	2.31845
$55$	0	0
$56$	0	0
$57$	950.000	2.20755
$58$	−412.000	−0.932728
$59$	−24.0000	−0.0529582	−0.0264791	−	0.999649i	$-0.508430\pi$
$59$	−24.0000	−0.0529582	−0.0264791	+	0.999649i	$0.508430\pi$
$60$	0	0
$61$	−116.000	−0.243480	−0.121740	−	0.992562i	$-0.538847\pi$
$61$	−116.000	−0.243480	−0.121740	+	0.992562i	$0.538847\pi$
$62$	−216.000	−0.442452
$63$	0	0
$64$	64.0000	0.125000
$65$	0	0
$66$	1060.00	1.97692
$67$	204.000	0.371979	0.185989	−	0.982552i	$-0.440451\pi$
$67$	204.000	0.371979	0.185989	+	0.982552i	$0.440451\pi$
$68$	56.0000	0.0998676
$69$	−10.0000	−0.0174472
$70$	0	0
$71$	484.000	0.809017	0.404509	−	0.914534i	$-0.367443\pi$
$71$	484.000	0.809017	0.404509	+	0.914534i	$0.367443\pi$
$72$	584.000	0.955904
$73$	−692.000	−1.10949	−0.554743	−	0.832022i	$-0.687183\pi$
$73$	−692.000	−1.10949	−0.554743	+	0.832022i	$0.687183\pi$
$74$	114.000	0.179084
$75$	0	0
$76$	380.000	0.573539
$77$	0	0
$78$	500.000	0.725819
$79$	466.000	0.663659	0.331830	−	0.943339i	$-0.392334\pi$
$79$	466.000	0.663659	0.331830	+	0.943339i	$0.392334\pi$
$80$	0	0
$81$	2629.00	3.60631
$82$	−486.000	−0.654509
$83$	228.000	0.301521	0.150761	−	0.988570i	$-0.451828\pi$
$83$	228.000	0.301521	0.150761	+	0.988570i	$0.451828\pi$
$84$	0	0
$85$	0	0
$86$	−868.000	−1.08836
$87$	−2060.00	−2.53857
$88$	424.000	0.513620
$89$	362.000	0.431145	0.215573	−	0.976488i	$-0.430838\pi$
$89$	362.000	0.431145	0.215573	+	0.976488i	$0.430838\pi$
$90$	0	0
$91$	0	0
$92$	−4.00000	−0.00453292
$93$	−1080.00	−1.20420
$94$	−462.000	−0.506933
$95$	0	0
$96$	320.000	0.340207
$97$	854.000	0.893923	0.446962	−	0.894553i	$-0.352506\pi$
$97$	854.000	0.893923	0.446962	+	0.894553i	$0.352506\pi$
$98$	0	0
$99$	3869.00	3.92777
$100$	0	0
$101$	−780.000	−0.768445	−0.384222	−	0.923241i	$-0.625530\pi$
$101$	−780.000	−0.768445	−0.384222	+	0.923241i	$0.625530\pi$
$102$	280.000	0.271805
$103$	−1076.00	−1.02933	−0.514667	−	0.857390i	$-0.672084\pi$
$103$	−1076.00	−1.02933	−0.514667	+	0.857390i	$0.672084\pi$
$104$	200.000	0.188573
$105$	0	0
$106$	−526.000	−0.481978
$107$	−852.000	−0.769775	−0.384888	−	0.922963i	$-0.625760\pi$
$107$	−852.000	−0.769775	−0.384888	+	0.922963i	$0.625760\pi$
$108$	1840.00	1.63939
$109$	−1972.00	−1.73287	−0.866437	−	0.499286i	$-0.833596\pi$
$109$	−1972.00	−1.73287	−0.866437	+	0.499286i	$0.833596\pi$
$110$	0	0
$111$	570.000	0.487405
$112$	0	0
$113$	−2148.00	−1.78820	−0.894101	−	0.447865i	$-0.852184\pi$
$113$	−2148.00	−1.78820	−0.894101	+	0.447865i	$0.852184\pi$
$114$	1900.00	1.56098
$115$	0	0
$116$	−824.000	−0.659539
$117$	1825.00	1.44206
$118$	−48.0000	−0.0374471
$119$	0	0
$120$	0	0
$121$	1478.00	1.11044
$122$	−232.000	−0.172166
$123$	−2430.00	−1.78135
$124$	−432.000	−0.312861
$125$	0	0
$126$	0	0
$127$	2449.00	1.71113	0.855565	−	0.517695i	$-0.173210\pi$
$127$	2449.00	1.71113	0.855565	+	0.517695i	$0.173210\pi$
$128$	128.000	0.0883883
$129$	−4340.00	−2.96214
$130$	0	0
$131$	1771.00	1.18117	0.590584	−	0.806976i	$-0.298897\pi$
$131$	1771.00	1.18117	0.590584	+	0.806976i	$0.298897\pi$
$132$	2120.00	1.39790
$133$	0	0
$134$	408.000	0.263029
$135$	0	0
$136$	112.000	0.0706171
$137$	764.000	0.476445	0.238222	−	0.971211i	$-0.423435\pi$
$137$	764.000	0.476445	0.238222	+	0.971211i	$0.423435\pi$
$138$	−20.0000	−0.0123371
$139$	2356.00	1.43765	0.718825	−	0.695191i	$-0.244680\pi$
$139$	2356.00	1.43765	0.718825	+	0.695191i	$0.244680\pi$
$140$	0	0
$141$	−2310.00	−1.37970
$142$	968.000	0.572062
$143$	1325.00	0.774840
$144$	1168.00	0.675926
$145$	0	0
$146$	−1384.00	−0.784525
$147$	0	0
$148$	228.000	0.126632
$149$	2018.00	1.10954	0.554768	−	0.832005i	$-0.312807\pi$
$149$	2018.00	1.10954	0.554768	+	0.832005i	$0.312807\pi$
$150$	0	0
$151$	−1766.00	−0.951755	−0.475878	−	0.879512i	$-0.657869\pi$
$151$	−1766.00	−0.951755	−0.475878	+	0.879512i	$0.657869\pi$
$152$	760.000	0.405554
$153$	1022.00	0.540025
$154$	0	0
$155$	0	0
$156$	1000.00	0.513231
$157$	753.000	0.382777	0.191388	−	0.981514i	$-0.438701\pi$
$157$	753.000	0.382777	0.191388	+	0.981514i	$0.438701\pi$
$158$	932.000	0.469278
$159$	−2630.00	−1.31178
$160$	0	0
$161$	0	0
$162$	5258.00	2.55005
$163$	484.000	0.232575	0.116288	−	0.993216i	$-0.462901\pi$
$163$	484.000	0.232575	0.116288	+	0.993216i	$0.462901\pi$
$164$	−972.000	−0.462808
$165$	0	0
$166$	456.000	0.213208
$167$	−1565.00	−0.725170	−0.362585	−	0.931951i	$-0.618106\pi$
$167$	−1565.00	−0.725170	−0.362585	+	0.931951i	$0.618106\pi$
$168$	0	0
$169$	−1572.00	−0.715521
$170$	0	0
$171$	6935.00	3.10136
$172$	−1736.00	−0.769586
$173$	−777.000	−0.341469	−0.170735	−	0.985317i	$-0.554614\pi$
$173$	−777.000	−0.341469	−0.170735	+	0.985317i	$0.554614\pi$
$174$	−4120.00	−1.79504
$175$	0	0
$176$	848.000	0.363184
$177$	−240.000	−0.101918
$178$	724.000	0.304866
$179$	2347.00	0.980017	0.490008	−	0.871718i	$-0.336994\pi$
$179$	2347.00	0.980017	0.490008	+	0.871718i	$0.336994\pi$
$180$	0	0
$181$	2454.00	1.00776	0.503880	−	0.863774i	$-0.331906\pi$
$181$	2454.00	1.00776	0.503880	+	0.863774i	$0.331906\pi$
$182$	0	0
$183$	−1160.00	−0.468577
$184$	−8.00000	−0.00320526
$185$	0	0
$186$	−2160.00	−0.851499
$187$	742.000	0.290163
$188$	−924.000	−0.358455
$189$	0	0
$190$	0	0
$191$	−460.000	−0.174264	−0.0871320	−	0.996197i	$-0.527770\pi$
$191$	−460.000	−0.174264	−0.0871320	+	0.996197i	$0.527770\pi$
$192$	640.000	0.240563
$193$	2260.00	0.842893	0.421447	−	0.906853i	$-0.361523\pi$
$193$	2260.00	0.842893	0.421447	+	0.906853i	$0.361523\pi$
$194$	1708.00	0.632099
$195$	0	0
$196$	0	0
$197$	−2745.00	−0.992757	−0.496379	−	0.868106i	$-0.665337\pi$
$197$	−2745.00	−0.992757	−0.496379	+	0.868106i	$0.665337\pi$
$198$	7738.00	2.77735
$199$	348.000	0.123965	0.0619826	−	0.998077i	$-0.480258\pi$
$199$	348.000	0.123965	0.0619826	+	0.998077i	$0.480258\pi$
$200$	0	0
$201$	2040.00	0.715873
$202$	−1560.00	−0.543372
$203$	0	0
$204$	560.000	0.192195
$205$	0	0
$206$	−2152.00	−0.727849
$207$	−73.0000	−0.0245114
$208$	400.000	0.133341
$209$	5035.00	1.66640
$210$	0	0
$211$	2601.00	0.848627	0.424313	−	0.905515i	$-0.360516\pi$
$211$	2601.00	0.848627	0.424313	+	0.905515i	$0.360516\pi$
$212$	−1052.00	−0.340810
$213$	4840.00	1.55695
$214$	−1704.00	−0.544313
$215$	0	0
$216$	3680.00	1.15922
$217$	0	0
$218$	−3944.00	−1.22533
$219$	−6920.00	−2.13521
$220$	0	0
$221$	350.000	0.106532
$222$	1140.00	0.344648
$223$	1904.00	0.571755	0.285877	−	0.958266i	$-0.407715\pi$
$223$	1904.00	0.571755	0.285877	+	0.958266i	$0.407715\pi$
$224$	0	0
$225$	0	0
$226$	−4296.00	−1.26445
$227$	−5048.00	−1.47598	−0.737990	−	0.674811i	$-0.764225\pi$
$227$	−5048.00	−1.47598	−0.737990	+	0.674811i	$0.764225\pi$
$228$	3800.00	1.10378
$229$	1036.00	0.298955	0.149478	−	0.988765i	$-0.452241\pi$
$229$	1036.00	0.298955	0.149478	+	0.988765i	$0.452241\pi$
$230$	0	0
$231$	0	0
$232$	−1648.00	−0.466364
$233$	−2594.00	−0.729350	−0.364675	−	0.931135i	$-0.618820\pi$
$233$	−2594.00	−0.729350	−0.364675	+	0.931135i	$0.618820\pi$
$234$	3650.00	1.01969
$235$	0	0
$236$	−96.0000	−0.0264791
$237$	4660.00	1.27721
$238$	0	0
$239$	−5910.00	−1.59952	−0.799762	−	0.600318i	$-0.795041\pi$
$239$	−5910.00	−1.59952	−0.799762	+	0.600318i	$0.795041\pi$
$240$	0	0
$241$	2969.00	0.793569	0.396784	−	0.917912i	$-0.370126\pi$
$241$	2969.00	0.793569	0.396784	+	0.917912i	$0.370126\pi$
$242$	2956.00	0.785202
$243$	13870.0	3.66157
$244$	−464.000	−0.121740
$245$	0	0
$246$	−4860.00	−1.25960
$247$	2375.00	0.611812
$248$	−864.000	−0.221226
$249$	2280.00	0.580278
$250$	0	0
$251$	6225.00	1.56541	0.782706	−	0.622391i	$-0.213839\pi$
$251$	6225.00	1.56541	0.782706	+	0.622391i	$0.213839\pi$
$252$	0	0
$253$	−53.0000	−0.0131703
$254$	4898.00	1.20995
$255$	0	0
$256$	256.000	0.0625000
$257$	4732.00	1.14854	0.574269	−	0.818667i	$-0.305287\pi$
$257$	4732.00	1.14854	0.574269	+	0.818667i	$0.305287\pi$
$258$	−8680.00	−2.09455
$259$	0	0
$260$	0	0
$261$	−15038.0	−3.56639
$262$	3542.00	0.835212
$263$	−1400.00	−0.328242	−0.164121	−	0.986440i	$-0.552479\pi$
$263$	−1400.00	−0.328242	−0.164121	+	0.986440i	$0.552479\pi$
$264$	4240.00	0.988462
$265$	0	0
$266$	0	0
$267$	3620.00	0.829739
$268$	816.000	0.185989
$269$	6780.00	1.53674	0.768372	−	0.640004i	$-0.221067\pi$
$269$	6780.00	1.53674	0.768372	+	0.640004i	$0.221067\pi$
$270$	0	0
$271$	2216.00	0.496725	0.248362	−	0.968667i	$-0.420108\pi$
$271$	2216.00	0.496725	0.248362	+	0.968667i	$0.420108\pi$
$272$	224.000	0.0499338
$273$	0	0
$274$	1528.00	0.336897
$275$	0	0
$276$	−40.0000	−0.00872361
$277$	1046.00	0.226888	0.113444	−	0.993544i	$-0.463812\pi$
$277$	1046.00	0.226888	0.113444	+	0.993544i	$0.463812\pi$
$278$	4712.00	1.01657
$279$	−7884.00	−1.69177
$280$	0	0
$281$	3669.00	0.778912	0.389456	−	0.921045i	$-0.372663\pi$
$281$	3669.00	0.778912	0.389456	+	0.921045i	$0.372663\pi$
$282$	−4620.00	−0.975592
$283$	−2882.00	−0.605361	−0.302680	−	0.953092i	$-0.597881\pi$
$283$	−2882.00	−0.605361	−0.302680	+	0.953092i	$0.597881\pi$
$284$	1936.00	0.404509
$285$	0	0
$286$	2650.00	0.547894
$287$	0	0
$288$	2336.00	0.477952
$289$	−4717.00	−0.960106
$290$	0	0
$291$	8540.00	1.72036
$292$	−2768.00	−0.554743
$293$	2697.00	0.537749	0.268874	−	0.963175i	$-0.413348\pi$
$293$	2697.00	0.537749	0.268874	+	0.963175i	$0.413348\pi$
$294$	0	0
$295$	0	0
$296$	456.000	0.0895421
$297$	24380.0	4.76320
$298$	4036.00	0.784561
$299$	−25.0000	−0.00483541
$300$	0	0
$301$	0	0
$302$	−3532.00	−0.672993
$303$	−7800.00	−1.47887
$304$	1520.00	0.286770
$305$	0	0
$306$	2044.00	0.381855
$307$	−8146.00	−1.51439	−0.757193	−	0.653191i	$-0.773430\pi$
$307$	−8146.00	−1.51439	−0.757193	+	0.653191i	$0.773430\pi$
$308$	0	0
$309$	−10760.0	−1.98095
$310$	0	0
$311$	4604.00	0.839450	0.419725	−	0.907651i	$-0.362127\pi$
$311$	4604.00	0.839450	0.419725	+	0.907651i	$0.362127\pi$
$312$	2000.00	0.362909
$313$	−9984.00	−1.80297	−0.901484	−	0.432812i	$-0.857521\pi$
$313$	−9984.00	−1.80297	−0.901484	+	0.432812i	$0.857521\pi$
$314$	1506.00	0.270664
$315$	0	0
$316$	1864.00	0.331830
$317$	−9754.00	−1.72820	−0.864100	−	0.503321i	$-0.832111\pi$
$317$	−9754.00	−1.72820	−0.864100	+	0.503321i	$0.832111\pi$
$318$	−5260.00	−0.927567
$319$	−10918.0	−1.91627
$320$	0	0
$321$	−8520.00	−1.48143
$322$	0	0
$323$	1330.00	0.229112
$324$	10516.0	1.80316
$325$	0	0
$326$	968.000	0.164456
$327$	−19720.0	−3.33492
$328$	−1944.00	−0.327254
$329$	0	0
$330$	0	0
$331$	6615.00	1.09847	0.549235	−	0.835668i	$-0.314919\pi$
$331$	6615.00	1.09847	0.549235	+	0.835668i	$0.314919\pi$
$332$	912.000	0.150761
$333$	4161.00	0.684749
$334$	−3130.00	−0.512772
$335$	0	0
$336$	0	0
$337$	−6390.00	−1.03289	−0.516447	−	0.856319i	$-0.672746\pi$
$337$	−6390.00	−1.03289	−0.516447	+	0.856319i	$0.672746\pi$
$338$	−3144.00	−0.505950
$339$	−21480.0	−3.44140
$340$	0	0
$341$	−5724.00	−0.909009
$342$	13870.0	2.19299
$343$	0	0
$344$	−3472.00	−0.544179
$345$	0	0
$346$	−1554.00	−0.241455
$347$	−3704.00	−0.573029	−0.286515	−	0.958076i	$-0.592497\pi$
$347$	−3704.00	−0.573029	−0.286515	+	0.958076i	$0.592497\pi$
$348$	−8240.00	−1.26928
$349$	−5702.00	−0.874559	−0.437279	−	0.899326i	$-0.644058\pi$
$349$	−5702.00	−0.874559	−0.437279	+	0.899326i	$0.644058\pi$
$350$	0	0
$351$	11500.0	1.74879
$352$	1696.00	0.256810
$353$	388.000	0.0585019	0.0292509	−	0.999572i	$-0.490688\pi$
$353$	388.000	0.0585019	0.0292509	+	0.999572i	$0.490688\pi$
$354$	−480.000	−0.0720670
$355$	0	0
$356$	1448.00	0.215573
$357$	0	0
$358$	4694.00	0.692977
$359$	−12846.0	−1.88854	−0.944270	−	0.329172i	$-0.893231\pi$
$359$	−12846.0	−1.88854	−0.944270	+	0.329172i	$0.893231\pi$
$360$	0	0
$361$	2166.00	0.315789
$362$	4908.00	0.712593
$363$	14780.0	2.13705
$364$	0	0
$365$	0	0
$366$	−2320.00	−0.331334
$367$	11389.0	1.61989	0.809947	−	0.586503i	$-0.199496\pi$
$367$	11389.0	1.61989	0.809947	+	0.586503i	$0.199496\pi$
$368$	−16.0000	−0.00226646
$369$	−17739.0	−2.50259
$370$	0	0
$371$	0	0
$372$	−4320.00	−0.602101
$373$	−902.000	−0.125211	−0.0626056	−	0.998038i	$-0.519941\pi$
$373$	−902.000	−0.125211	−0.0626056	+	0.998038i	$0.519941\pi$
$374$	1484.00	0.205176
$375$	0	0
$376$	−1848.00	−0.253466
$377$	−5150.00	−0.703550
$378$	0	0
$379$	3529.00	0.478292	0.239146	−	0.970984i	$-0.423133\pi$
$379$	3529.00	0.478292	0.239146	+	0.970984i	$0.423133\pi$
$380$	0	0
$381$	24490.0	3.29307
$382$	−920.000	−0.123223
$383$	−1643.00	−0.219199	−0.109600	−	0.993976i	$-0.534957\pi$
$383$	−1643.00	−0.219199	−0.109600	+	0.993976i	$0.534957\pi$
$384$	1280.00	0.170103
$385$	0	0
$386$	4520.00	0.596015
$387$	−31682.0	−4.16146
$388$	3416.00	0.446962
$389$	−1184.00	−0.154322	−0.0771609	−	0.997019i	$-0.524586\pi$
$389$	−1184.00	−0.154322	−0.0771609	+	0.997019i	$0.524586\pi$
$390$	0	0
$391$	−14.0000	−0.00181077
$392$	0	0
$393$	17710.0	2.27316
$394$	−5490.00	−0.701985
$395$	0	0
$396$	15476.0	1.96388
$397$	−11382.0	−1.43891	−0.719454	−	0.694540i	$-0.755608\pi$
$397$	−11382.0	−1.43891	−0.719454	+	0.694540i	$0.755608\pi$
$398$	696.000	0.0876566
$399$	0	0
$400$	0	0
$401$	−1475.00	−0.183686	−0.0918429	−	0.995774i	$-0.529276\pi$
$401$	−1475.00	−0.183686	−0.0918429	+	0.995774i	$0.529276\pi$
$402$	4080.00	0.506199
$403$	−2700.00	−0.333738
$404$	−3120.00	−0.384222
$405$	0	0
$406$	0	0
$407$	3021.00	0.367925
$408$	1120.00	0.135903
$409$	5366.00	0.648733	0.324366	−	0.945932i	$-0.394849\pi$
$409$	5366.00	0.648733	0.324366	+	0.945932i	$0.394849\pi$
$410$	0	0
$411$	7640.00	0.916918
$412$	−4304.00	−0.514667
$413$	0	0
$414$	−146.000	−0.0173321
$415$	0	0
$416$	800.000	0.0942866
$417$	23560.0	2.76676
$418$	10070.0	1.17832
$419$	−13265.0	−1.54663	−0.773315	−	0.634022i	$-0.781403\pi$
$419$	−13265.0	−1.54663	−0.773315	+	0.634022i	$0.781403\pi$
$420$	0	0
$421$	−12170.0	−1.40886	−0.704429	−	0.709774i	$-0.748797\pi$
$421$	−12170.0	−1.40886	−0.704429	+	0.709774i	$0.748797\pi$
$422$	5202.00	0.600070
$423$	−16863.0	−1.93831
$424$	−2104.00	−0.240989
$425$	0	0
$426$	9680.00	1.10093
$427$	0	0
$428$	−3408.00	−0.384888
$429$	13250.0	1.49118
$430$	0	0
$431$	3312.00	0.370147	0.185074	−	0.982725i	$-0.440748\pi$
$431$	3312.00	0.370147	0.185074	+	0.982725i	$0.440748\pi$
$432$	7360.00	0.819695
$433$	−8504.00	−0.943825	−0.471912	−	0.881645i	$-0.656436\pi$
$433$	−8504.00	−0.943825	−0.471912	+	0.881645i	$0.656436\pi$
$434$	0	0
$435$	0	0
$436$	−7888.00	−0.866437
$437$	−95.0000	−0.0103992
$438$	−13840.0	−1.50982
$439$	−9898.00	−1.07610	−0.538048	−	0.842914i	$-0.680838\pi$
$439$	−9898.00	−1.07610	−0.538048	+	0.842914i	$0.680838\pi$
$440$	0	0
$441$	0	0
$442$	700.000	0.0753294
$443$	−1680.00	−0.180179	−0.0900894	−	0.995934i	$-0.528715\pi$
$443$	−1680.00	−0.180179	−0.0900894	+	0.995934i	$0.528715\pi$
$444$	2280.00	0.243703
$445$	0	0
$446$	3808.00	0.404292
$447$	20180.0	2.13530
$448$	0	0
$449$	−5875.00	−0.617502	−0.308751	−	0.951143i	$-0.599911\pi$
$449$	−5875.00	−0.617502	−0.308751	+	0.951143i	$0.599911\pi$
$450$	0	0
$451$	−12879.0	−1.34467
$452$	−8592.00	−0.894101
$453$	−17660.0	−1.83165
$454$	−10096.0	−1.04368
$455$	0	0
$456$	7600.00	0.780488
$457$	6950.00	0.711395	0.355697	−	0.934601i	$-0.384243\pi$
$457$	6950.00	0.711395	0.355697	+	0.934601i	$0.384243\pi$
$458$	2072.00	0.211393
$459$	6440.00	0.654888
$460$	0	0
$461$	13402.0	1.35400	0.676999	−	0.735984i	$-0.263280\pi$
$461$	13402.0	1.35400	0.676999	+	0.735984i	$0.263280\pi$
$462$	0	0
$463$	−4551.00	−0.456810	−0.228405	−	0.973566i	$-0.573351\pi$
$463$	−4551.00	−0.456810	−0.228405	+	0.973566i	$0.573351\pi$
$464$	−3296.00	−0.329769
$465$	0	0
$466$	−5188.00	−0.515728
$467$	−2238.00	−0.221761	−0.110880	−	0.993834i	$-0.535367\pi$
$467$	−2238.00	−0.221761	−0.110880	+	0.993834i	$0.535367\pi$
$468$	7300.00	0.721031
$469$	0	0
$470$	0	0
$471$	7530.00	0.736654
$472$	−192.000	−0.0187236
$473$	−23002.0	−2.23601
$474$	9320.00	0.903126
$475$	0	0
$476$	0	0
$477$	−19199.0	−1.84290
$478$	−11820.0	−1.13103
$479$	15616.0	1.48959	0.744795	−	0.667294i	$-0.232547\pi$
$479$	15616.0	1.48959	0.744795	+	0.667294i	$0.232547\pi$
$480$	0	0
$481$	1425.00	0.135082
$482$	5938.00	0.561138
$483$	0	0
$484$	5912.00	0.555222
$485$	0	0
$486$	27740.0	2.58912
$487$	−9064.00	−0.843386	−0.421693	−	0.906739i	$-0.638564\pi$
$487$	−9064.00	−0.843386	−0.421693	+	0.906739i	$0.638564\pi$
$488$	−928.000	−0.0860832
$489$	4840.00	0.447592
$490$	0	0
$491$	5124.00	0.470963	0.235482	−	0.971879i	$-0.424333\pi$
$491$	5124.00	0.470963	0.235482	+	0.971879i	$0.424333\pi$
$492$	−9720.00	−0.890674
$493$	−2884.00	−0.263466
$494$	4750.00	0.432617
$495$	0	0
$496$	−1728.00	−0.156430
$497$	0	0
$498$	4560.00	0.410318
$499$	5556.00	0.498438	0.249219	−	0.968447i	$-0.419826\pi$
$499$	5556.00	0.498438	0.249219	+	0.968447i	$0.419826\pi$
$500$	0	0
$501$	−15650.0	−1.39559
$502$	12450.0	1.10691
$503$	−7280.00	−0.645326	−0.322663	−	0.946514i	$-0.604578\pi$
$503$	−7280.00	−0.645326	−0.322663	+	0.946514i	$0.604578\pi$
$504$	0	0
$505$	0	0
$506$	−106.000	−0.00931280
$507$	−15720.0	−1.37702
$508$	9796.00	0.855565
$509$	19866.0	1.72995	0.864975	−	0.501814i	$-0.167334\pi$
$509$	19866.0	1.72995	0.864975	+	0.501814i	$0.167334\pi$
$510$	0	0
$511$	0	0
$512$	512.000	0.0441942
$513$	43700.0	3.76102
$514$	9464.00	0.812138
$515$	0	0
$516$	−17360.0	−1.48107
$517$	−12243.0	−1.04148
$518$	0	0
$519$	−7770.00	−0.657158
$520$	0	0
$521$	327.000	0.0274974	0.0137487	−	0.999905i	$-0.495624\pi$
$521$	327.000	0.0274974	0.0137487	+	0.999905i	$0.495624\pi$
$522$	−30076.0	−2.52182
$523$	−1148.00	−0.0959819	−0.0479910	−	0.998848i	$-0.515282\pi$
$523$	−1148.00	−0.0959819	−0.0479910	+	0.998848i	$0.515282\pi$
$524$	7084.00	0.590584
$525$	0	0
$526$	−2800.00	−0.232102
$527$	−1512.00	−0.124979
$528$	8480.00	0.698948
$529$	−12166.0	−0.999918
$530$	0	0
$531$	−1752.00	−0.143183
$532$	0	0
$533$	−6075.00	−0.493691
$534$	7240.00	0.586714
$535$	0	0
$536$	1632.00	0.131514
$537$	23470.0	1.88604
$538$	13560.0	1.08664
$539$	0	0
$540$	0	0
$541$	−15016.0	−1.19332	−0.596662	−	0.802493i	$-0.703507\pi$
$541$	−15016.0	−1.19332	−0.596662	+	0.802493i	$0.703507\pi$
$542$	4432.00	0.351237
$543$	24540.0	1.93943
$544$	448.000	0.0353085
$545$	0	0
$546$	0	0
$547$	22188.0	1.73435	0.867176	−	0.498002i	$-0.165933\pi$
$547$	22188.0	1.73435	0.867176	+	0.498002i	$0.165933\pi$
$548$	3056.00	0.238222
$549$	−8468.00	−0.658298
$550$	0	0
$551$	−19570.0	−1.51309
$552$	−80.0000	−0.00616853
$553$	0	0
$554$	2092.00	0.160434
$555$	0	0
$556$	9424.00	0.718825
$557$	2991.00	0.227527	0.113764	−	0.993508i	$-0.463709\pi$
$557$	2991.00	0.227527	0.113764	+	0.993508i	$0.463709\pi$
$558$	−15768.0	−1.19626
$559$	−10850.0	−0.820941
$560$	0	0
$561$	7420.00	0.558418
$562$	7338.00	0.550774
$563$	4274.00	0.319942	0.159971	−	0.987122i	$-0.448860\pi$
$563$	4274.00	0.319942	0.159971	+	0.987122i	$0.448860\pi$
$564$	−9240.00	−0.689848
$565$	0	0
$566$	−5764.00	−0.428055
$567$	0	0
$568$	3872.00	0.286031
$569$	845.000	0.0622570	0.0311285	−	0.999515i	$-0.490090\pi$
$569$	845.000	0.0622570	0.0311285	+	0.999515i	$0.490090\pi$
$570$	0	0
$571$	−20108.0	−1.47372	−0.736860	−	0.676046i	$-0.763692\pi$
$571$	−20108.0	−1.47372	−0.736860	+	0.676046i	$0.763692\pi$
$572$	5300.00	0.387420
$573$	−4600.00	−0.335371
$574$	0	0
$575$	0	0
$576$	4672.00	0.337963
$577$	22828.0	1.64704	0.823520	−	0.567287i	$-0.192007\pi$
$577$	22828.0	1.64704	0.823520	+	0.567287i	$0.192007\pi$
$578$	−9434.00	−0.678897
$579$	22600.0	1.62215
$580$	0	0
$581$	0	0
$582$	17080.0	1.21648
$583$	−13939.0	−0.990213
$584$	−5536.00	−0.392263
$585$	0	0
$586$	5394.00	0.380246
$587$	16452.0	1.15681	0.578404	−	0.815750i	$-0.303676\pi$
$587$	16452.0	1.15681	0.578404	+	0.815750i	$0.303676\pi$
$588$	0	0
$589$	−10260.0	−0.717752
$590$	0	0
$591$	−27450.0	−1.91056
$592$	912.000	0.0633158
$593$	25188.0	1.74426	0.872131	−	0.489273i	$-0.162738\pi$
$593$	25188.0	1.74426	0.872131	+	0.489273i	$0.162738\pi$
$594$	48760.0	3.36809
$595$	0	0
$596$	8072.00	0.554768
$597$	3480.00	0.238571
$598$	−50.0000	−0.00341915
$599$	26382.0	1.79956	0.899782	−	0.436339i	$-0.143725\pi$
$599$	26382.0	1.79956	0.899782	+	0.436339i	$0.143725\pi$
$600$	0	0
$601$	−9538.00	−0.647360	−0.323680	−	0.946167i	$-0.604920\pi$
$601$	−9538.00	−0.647360	−0.323680	+	0.946167i	$0.604920\pi$
$602$	0	0
$603$	14892.0	1.00572
$604$	−7064.00	−0.475878
$605$	0	0
$606$	−15600.0	−1.04572
$607$	20191.0	1.35013	0.675064	−	0.737759i	$-0.264116\pi$
$607$	20191.0	1.35013	0.675064	+	0.737759i	$0.264116\pi$
$608$	3040.00	0.202777
$609$	0	0
$610$	0	0
$611$	−5775.00	−0.382376
$612$	4088.00	0.270012
$613$	−18675.0	−1.23047	−0.615233	−	0.788345i	$-0.710938\pi$
$613$	−18675.0	−1.23047	−0.615233	+	0.788345i	$0.710938\pi$
$614$	−16292.0	−1.07083
$615$	0	0
$616$	0	0
$617$	−12602.0	−0.822265	−0.411132	−	0.911576i	$-0.634867\pi$
$617$	−12602.0	−0.822265	−0.411132	+	0.911576i	$0.634867\pi$
$618$	−21520.0	−1.40075
$619$	−3521.00	−0.228628	−0.114314	−	0.993445i	$-0.536467\pi$
$619$	−3521.00	−0.228628	−0.114314	+	0.993445i	$0.536467\pi$
$620$	0	0
$621$	−460.000	−0.0297249
$622$	9208.00	0.593581
$623$	0	0
$624$	4000.00	0.256616
$625$	0	0
$626$	−19968.0	−1.27489
$627$	50350.0	3.20699
$628$	3012.00	0.191388
$629$	798.000	0.0505856
$630$	0	0
$631$	−13048.0	−0.823190	−0.411595	−	0.911367i	$-0.635028\pi$
$631$	−13048.0	−0.823190	−0.411595	+	0.911367i	$0.635028\pi$
$632$	3728.00	0.234639
$633$	26010.0	1.63318
$634$	−19508.0	−1.22202
$635$	0	0
$636$	−10520.0	−0.655889
$637$	0	0
$638$	−21836.0	−1.35501
$639$	35332.0	2.18734
$640$	0	0
$641$	7555.00	0.465530	0.232765	−	0.972533i	$-0.425223\pi$
$641$	7555.00	0.465530	0.232765	+	0.972533i	$0.425223\pi$
$642$	−17040.0	−1.04753
$643$	31802.0	1.95046	0.975232	−	0.221184i	$-0.0709922\pi$
$643$	31802.0	1.95046	0.975232	+	0.221184i	$0.0709922\pi$
$644$	0	0
$645$	0	0
$646$	2660.00	0.162007
$647$	−831.000	−0.0504946	−0.0252473	−	0.999681i	$-0.508037\pi$
$647$	−831.000	−0.0504946	−0.0252473	+	0.999681i	$0.508037\pi$
$648$	21032.0	1.27502
$649$	−1272.00	−0.0769343
$650$	0	0
$651$	0	0
$652$	1936.00	0.116288
$653$	−26441.0	−1.58456	−0.792279	−	0.610159i	$-0.791106\pi$
$653$	−26441.0	−1.58456	−0.792279	+	0.610159i	$0.791106\pi$
$654$	−39440.0	−2.35814
$655$	0	0
$656$	−3888.00	−0.231404
$657$	−50516.0	−2.99972
$658$	0	0
$659$	19536.0	1.15480	0.577401	−	0.816461i	$-0.304067\pi$
$659$	19536.0	1.15480	0.577401	+	0.816461i	$0.304067\pi$
$660$	0	0
$661$	−9356.00	−0.550539	−0.275269	−	0.961367i	$-0.588767\pi$
$661$	−9356.00	−0.550539	−0.275269	+	0.961367i	$0.588767\pi$
$662$	13230.0	0.776735
$663$	3500.00	0.205021
$664$	1824.00	0.106604
$665$	0	0
$666$	8322.00	0.484191
$667$	206.000	0.0119585
$668$	−6260.00	−0.362585
$669$	19040.0	1.10034
$670$	0	0
$671$	−6148.00	−0.353712
$672$	0	0
$673$	−24774.0	−1.41897	−0.709486	−	0.704720i	$-0.751073\pi$
$673$	−24774.0	−1.41897	−0.709486	+	0.704720i	$0.751073\pi$
$674$	−12780.0	−0.730367
$675$	0	0
$676$	−6288.00	−0.357761
$677$	−10391.0	−0.589894	−0.294947	−	0.955514i	$-0.595302\pi$
$677$	−10391.0	−0.589894	−0.294947	+	0.955514i	$0.595302\pi$
$678$	−42960.0	−2.43343
$679$	0	0
$680$	0	0
$681$	−50480.0	−2.84053
$682$	−11448.0	−0.642766
$683$	−15492.0	−0.867913	−0.433957	−	0.900934i	$-0.642883\pi$
$683$	−15492.0	−0.867913	−0.433957	+	0.900934i	$0.642883\pi$
$684$	27740.0	1.55068
$685$	0	0
$686$	0	0
$687$	10360.0	0.575340
$688$	−6944.00	−0.384793
$689$	−6575.00	−0.363552
$690$	0	0
$691$	17064.0	0.939429	0.469714	−	0.882818i	$-0.344357\pi$
$691$	17064.0	0.939429	0.469714	+	0.882818i	$0.344357\pi$
$692$	−3108.00	−0.170735
$693$	0	0
$694$	−7408.00	−0.405193
$695$	0	0
$696$	−16480.0	−0.897518
$697$	−3402.00	−0.184878
$698$	−11404.0	−0.618407
$699$	−25940.0	−1.40364
$700$	0	0
$701$	−24174.0	−1.30248	−0.651241	−	0.758871i	$-0.725751\pi$
$701$	−24174.0	−1.30248	−0.651241	+	0.758871i	$0.725751\pi$
$702$	23000.0	1.23658
$703$	5415.00	0.290513
$704$	3392.00	0.181592
$705$	0	0
$706$	776.000	0.0413671
$707$	0	0
$708$	−960.000	−0.0509591
$709$	7078.00	0.374922	0.187461	−	0.982272i	$-0.439974\pi$
$709$	7078.00	0.374922	0.187461	+	0.982272i	$0.439974\pi$
$710$	0	0
$711$	34018.0	1.79434
$712$	2896.00	0.152433
$713$	108.000	0.00567270
$714$	0	0
$715$	0	0
$716$	9388.00	0.490008
$717$	−59100.0	−3.07828
$718$	−25692.0	−1.33540
$719$	−31844.0	−1.65171	−0.825856	−	0.563881i	$-0.809308\pi$
$719$	−31844.0	−1.65171	−0.825856	+	0.563881i	$0.809308\pi$
$720$	0	0
$721$	0	0
$722$	4332.00	0.223297
$723$	29690.0	1.52722
$724$	9816.00	0.503880
$725$	0	0
$726$	29560.0	1.51112
$727$	12143.0	0.619476	0.309738	−	0.950822i	$-0.399759\pi$
$727$	12143.0	0.619476	0.309738	+	0.950822i	$0.399759\pi$
$728$	0	0
$729$	67717.0	3.44038
$730$	0	0
$731$	−6076.00	−0.307427
$732$	−4640.00	−0.234289
$733$	−2333.00	−0.117560	−0.0587799	−	0.998271i	$-0.518721\pi$
$733$	−2333.00	−0.117560	−0.0587799	+	0.998271i	$0.518721\pi$
$734$	22778.0	1.14544
$735$	0	0
$736$	−32.0000	−0.00160263
$737$	10812.0	0.540387
$738$	−35478.0	−1.76960
$739$	15749.0	0.783946	0.391973	−	0.919977i	$-0.371793\pi$
$739$	15749.0	0.783946	0.391973	+	0.919977i	$0.371793\pi$
$740$	0	0
$741$	23750.0	1.17743
$742$	0	0
$743$	31797.0	1.57001	0.785006	−	0.619488i	$-0.212660\pi$
$743$	31797.0	1.57001	0.785006	+	0.619488i	$0.212660\pi$
$744$	−8640.00	−0.425750
$745$	0	0
$746$	−1804.00	−0.0885377
$747$	16644.0	0.815224
$748$	2968.00	0.145081
$749$	0	0
$750$	0	0
$751$	2638.00	0.128178	0.0640892	−	0.997944i	$-0.479586\pi$
$751$	2638.00	0.128178	0.0640892	+	0.997944i	$0.479586\pi$
$752$	−3696.00	−0.179228
$753$	62250.0	3.01264
$754$	−10300.0	−0.497485
$755$	0	0
$756$	0	0
$757$	5054.00	0.242656	0.121328	−	0.992612i	$-0.461285\pi$
$757$	5054.00	0.242656	0.121328	+	0.992612i	$0.461285\pi$
$758$	7058.00	0.338203
$759$	−530.000	−0.0253462
$760$	0	0
$761$	−21301.0	−1.01467	−0.507333	−	0.861750i	$-0.669369\pi$
$761$	−21301.0	−1.01467	−0.507333	+	0.861750i	$0.669369\pi$
$762$	48980.0	2.32855
$763$	0	0
$764$	−1840.00	−0.0871320
$765$	0	0
$766$	−3286.00	−0.154997
$767$	−600.000	−0.0282461
$768$	2560.00	0.120281
$769$	12041.0	0.564642	0.282321	−	0.959320i	$-0.408896\pi$
$769$	12041.0	0.564642	0.282321	+	0.959320i	$0.408896\pi$
$770$	0	0
$771$	47320.0	2.21036
$772$	9040.00	0.421447
$773$	−11285.0	−0.525088	−0.262544	−	0.964920i	$-0.584562\pi$
$773$	−11285.0	−0.525088	−0.262544	+	0.964920i	$0.584562\pi$
$774$	−63364.0	−2.94260
$775$	0	0
$776$	6832.00	0.316050
$777$	0	0
$778$	−2368.00	−0.109122
$779$	−23085.0	−1.06175
$780$	0	0
$781$	25652.0	1.17529
$782$	−28.0000	−0.00128041
$783$	−94760.0	−4.32496
$784$	0	0
$785$	0	0
$786$	35420.0	1.60737
$787$	−8326.00	−0.377115	−0.188558	−	0.982062i	$-0.560381\pi$
$787$	−8326.00	−0.377115	−0.188558	+	0.982062i	$0.560381\pi$
$788$	−10980.0	−0.496379
$789$	−14000.0	−0.631702
$790$	0	0
$791$	0	0
$792$	30952.0	1.38868
$793$	−2900.00	−0.129864
$794$	−22764.0	−1.01746
$795$	0	0
$796$	1392.00	0.0619826
$797$	4794.00	0.213064	0.106532	−	0.994309i	$-0.466025\pi$
$797$	4794.00	0.213064	0.106532	+	0.994309i	$0.466025\pi$
$798$	0	0
$799$	−3234.00	−0.143192
$800$	0	0
$801$	26426.0	1.16569
$802$	−2950.00	−0.129885
$803$	−36676.0	−1.61179
$804$	8160.00	0.357937
$805$	0	0
$806$	−5400.00	−0.235989
$807$	67800.0	2.95746
$808$	−6240.00	−0.271686
$809$	11375.0	0.494343	0.247172	−	0.968972i	$-0.420499\pi$
$809$	11375.0	0.494343	0.247172	+	0.968972i	$0.420499\pi$
$810$	0	0
$811$	23063.0	0.998584	0.499292	−	0.866434i	$-0.333594\pi$
$811$	23063.0	0.998584	0.499292	+	0.866434i	$0.333594\pi$
$812$	0	0
$813$	22160.0	0.955947
$814$	6042.00	0.260162
$815$	0	0
$816$	2240.00	0.0960977
$817$	−41230.0	−1.76555
$818$	10732.0	0.458723
$819$	0	0
$820$	0	0
$821$	−22058.0	−0.937673	−0.468836	−	0.883285i	$-0.655327\pi$
$821$	−22058.0	−0.937673	−0.468836	+	0.883285i	$0.655327\pi$
$822$	15280.0	0.648359
$823$	2148.00	0.0909776	0.0454888	−	0.998965i	$-0.485515\pi$
$823$	2148.00	0.0909776	0.0454888	+	0.998965i	$0.485515\pi$
$824$	−8608.00	−0.363925
$825$	0	0
$826$	0	0
$827$	24506.0	1.03042	0.515210	−	0.857064i	$-0.327714\pi$
$827$	24506.0	1.03042	0.515210	+	0.857064i	$0.327714\pi$
$828$	−292.000	−0.0122557
$829$	−32766.0	−1.37275	−0.686375	−	0.727248i	$-0.740799\pi$
$829$	−32766.0	−1.37275	−0.686375	+	0.727248i	$0.740799\pi$
$830$	0	0
$831$	10460.0	0.436647
$832$	1600.00	0.0666707
$833$	0	0
$834$	47120.0	1.95639
$835$	0	0
$836$	20140.0	0.833202
$837$	−49680.0	−2.05160
$838$	−26530.0	−1.09363
$839$	−13694.0	−0.563492	−0.281746	−	0.959489i	$-0.590913\pi$
$839$	−13694.0	−0.563492	−0.281746	+	0.959489i	$0.590913\pi$
$840$	0	0
$841$	18047.0	0.739965
$842$	−24340.0	−0.996214
$843$	36690.0	1.49902
$844$	10404.0	0.424313
$845$	0	0
$846$	−33726.0	−1.37060
$847$	0	0
$848$	−4208.00	−0.170405
$849$	−28820.0	−1.16502
$850$	0	0
$851$	−57.0000	−0.00229605
$852$	19360.0	0.778477
$853$	14179.0	0.569144	0.284572	−	0.958655i	$-0.408149\pi$
$853$	14179.0	0.569144	0.284572	+	0.958655i	$0.408149\pi$
$854$	0	0
$855$	0	0
$856$	−6816.00	−0.272157
$857$	8054.00	0.321026	0.160513	−	0.987034i	$-0.448685\pi$
$857$	8054.00	0.321026	0.160513	+	0.987034i	$0.448685\pi$
$858$	26500.0	1.05442
$859$	26888.0	1.06799	0.533997	−	0.845486i	$-0.320689\pi$
$859$	26888.0	1.06799	0.533997	+	0.845486i	$0.320689\pi$
$860$	0	0
$861$	0	0
$862$	6624.00	0.261734
$863$	−37133.0	−1.46468	−0.732342	−	0.680937i	$-0.761573\pi$
$863$	−37133.0	−1.46468	−0.732342	+	0.680937i	$0.761573\pi$
$864$	14720.0	0.579612
$865$	0	0
$866$	−17008.0	−0.667385
$867$	−47170.0	−1.84772
$868$	0	0
$869$	24698.0	0.964122
$870$	0	0
$871$	5100.00	0.198401
$872$	−15776.0	−0.612664
$873$	62342.0	2.41690
$874$	−190.000	−0.00735337
$875$	0	0
$876$	−27680.0	−1.06760
$877$	16747.0	0.644819	0.322409	−	0.946600i	$-0.395507\pi$
$877$	16747.0	0.644819	0.322409	+	0.946600i	$0.395507\pi$
$878$	−19796.0	−0.760914
$879$	26970.0	1.03490
$880$	0	0
$881$	49015.0	1.87441	0.937206	−	0.348776i	$-0.113403\pi$
$881$	49015.0	1.87441	0.937206	+	0.348776i	$0.113403\pi$
$882$	0	0
$883$	−22712.0	−0.865594	−0.432797	−	0.901491i	$-0.642473\pi$
$883$	−22712.0	−0.865594	−0.432797	+	0.901491i	$0.642473\pi$
$884$	1400.00	0.0532659
$885$	0	0
$886$	−3360.00	−0.127406
$887$	28448.0	1.07688	0.538439	−	0.842665i	$-0.319014\pi$
$887$	28448.0	1.07688	0.538439	+	0.842665i	$0.319014\pi$
$888$	4560.00	0.172324
$889$	0	0
$890$	0	0
$891$	139337.	5.23902
$892$	7616.00	0.285877
$893$	−21945.0	−0.822353
$894$	40360.0	1.50989
$895$	0	0
$896$	0	0
$897$	−250.000	−0.00930575
$898$	−11750.0	−0.436640
$899$	22248.0	0.825375
$900$	0	0
$901$	−3682.00	−0.136143
$902$	−25758.0	−0.950829
$903$	0	0
$904$	−17184.0	−0.632225
$905$	0	0
$906$	−35320.0	−1.29517
$907$	39230.0	1.43618	0.718088	−	0.695953i	$-0.245018\pi$
$907$	39230.0	1.43618	0.718088	+	0.695953i	$0.245018\pi$
$908$	−20192.0	−0.737990
$909$	−56940.0	−2.07765
$910$	0	0
$911$	40982.0	1.49044	0.745222	−	0.666817i	$-0.232344\pi$
$911$	40982.0	1.49044	0.745222	+	0.666817i	$0.232344\pi$
$912$	15200.0	0.551888
$913$	12084.0	0.438031
$914$	13900.0	0.503032
$915$	0	0
$916$	4144.00	0.149478
$917$	0	0
$918$	12880.0	0.463076
$919$	43330.0	1.55530	0.777652	−	0.628695i	$-0.216410\pi$
$919$	43330.0	1.55530	0.777652	+	0.628695i	$0.216410\pi$
$920$	0	0
$921$	−81460.0	−2.91444
$922$	26804.0	0.957422
$923$	12100.0	0.431502
$924$	0	0
$925$	0	0
$926$	−9102.00	−0.323013
$927$	−78548.0	−2.78301
$928$	−6592.00	−0.233182
$929$	−42049.0	−1.48502	−0.742510	−	0.669835i	$-0.766365\pi$
$929$	−42049.0	−1.48502	−0.742510	+	0.669835i	$0.766365\pi$
$930$	0	0
$931$	0	0
$932$	−10376.0	−0.364675
$933$	46040.0	1.61552
$934$	−4476.00	−0.156809
$935$	0	0
$936$	14600.0	0.509846
$937$	19642.0	0.684820	0.342410	−	0.939551i	$-0.388757\pi$
$937$	19642.0	0.684820	0.342410	+	0.939551i	$0.388757\pi$
$938$	0	0
$939$	−99840.0	−3.46981
$940$	0	0
$941$	14088.0	0.488051	0.244025	−	0.969769i	$-0.421532\pi$
$941$	14088.0	0.488051	0.244025	+	0.969769i	$0.421532\pi$
$942$	15060.0	0.520893
$943$	243.000	0.00839148
$944$	−384.000	−0.0132396
$945$	0	0
$946$	−46004.0	−1.58110
$947$	8966.00	0.307662	0.153831	−	0.988097i	$-0.450839\pi$
$947$	8966.00	0.307662	0.153831	+	0.988097i	$0.450839\pi$
$948$	18640.0	0.638607
$949$	−17300.0	−0.591762
$950$	0	0
$951$	−97540.0	−3.32592
$952$	0	0
$953$	−23132.0	−0.786274	−0.393137	−	0.919480i	$-0.628610\pi$
$953$	−23132.0	−0.786274	−0.393137	+	0.919480i	$0.628610\pi$
$954$	−38398.0	−1.30312
$955$	0	0
$956$	−23640.0	−0.799762
$957$	−109180.	−3.68787
$958$	31232.0	1.05330
$959$	0	0
$960$	0	0
$961$	−18127.0	−0.608472
$962$	2850.00	0.0955173
$963$	−62196.0	−2.08124
$964$	11876.0	0.396784
$965$	0	0
$966$	0	0
$967$	−30856.0	−1.02612	−0.513062	−	0.858352i	$-0.671489\pi$
$967$	−30856.0	−1.02612	−0.513062	+	0.858352i	$0.671489\pi$
$968$	11824.0	0.392601
$969$	13300.0	0.440926
$970$	0	0
$971$	−5677.00	−0.187625	−0.0938124	−	0.995590i	$-0.529905\pi$
$971$	−5677.00	−0.187625	−0.0938124	+	0.995590i	$0.529905\pi$
$972$	55480.0	1.83078
$973$	0	0
$974$	−18128.0	−0.596364
$975$	0	0
$976$	−1856.00	−0.0608700
$977$	32238.0	1.05567	0.527833	−	0.849348i	$-0.323005\pi$
$977$	32238.0	1.05567	0.527833	+	0.849348i	$0.323005\pi$
$978$	9680.00	0.316495
$979$	19186.0	0.626340
$980$	0	0
$981$	−143956.	−4.68518
$982$	10248.0	0.333021
$983$	−44613.0	−1.44754	−0.723771	−	0.690040i	$-0.757593\pi$
$983$	−44613.0	−1.44754	−0.723771	+	0.690040i	$0.757593\pi$
$984$	−19440.0	−0.629801
$985$	0	0
$986$	−5768.00	−0.186299
$987$	0	0
$988$	9500.00	0.305906
$989$	434.000	0.0139539
$990$	0	0
$991$	35812.0	1.14794	0.573969	−	0.818877i	$-0.305403\pi$
$991$	35812.0	1.14794	0.573969	+	0.818877i	$0.305403\pi$
$992$	−3456.00	−0.110613
$993$	66150.0	2.11400
$994$	0	0
$995$	0	0
$996$	9120.00	0.290139
$997$	2086.00	0.0662631	0.0331315	−	0.999451i	$-0.489452\pi$
$997$	2086.00	0.0662631	0.0331315	+	0.999451i	$0.489452\pi$
$998$	11112.0	0.352449
$999$	26220.0	0.830394

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2450.4.a.bq.1.1		1
5.4	even	2		490.4.a.a.1.1		1
7.3	odd	6		350.4.e.d.51.1		2
7.5	odd	6		350.4.e.d.151.1		2
7.6	odd	2		2450.4.a.v.1.1		1
35.3	even	12		350.4.j.a.149.2		4
35.4	even	6		490.4.e.s.471.1		2
35.9	even	6		490.4.e.s.361.1		2
35.12	even	12		350.4.j.a.249.2		4
35.17	even	12		350.4.j.a.149.1		4
35.19	odd	6		70.4.e.b.11.1	✓	2
35.24	odd	6		70.4.e.b.51.1	yes	2
35.33	even	12		350.4.j.a.249.1		4
35.34	odd	2		490.4.a.h.1.1		1
105.59	even	6		630.4.k.c.541.1		2
105.89	even	6		630.4.k.c.361.1		2
140.19	even	6		560.4.q.g.81.1		2
140.59	even	6		560.4.q.g.401.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.e.b.11.1	✓	2	35.19	odd	6
70.4.e.b.51.1	yes	2	35.24	odd	6
350.4.e.d.51.1		2	7.3	odd	6
350.4.e.d.151.1		2	7.5	odd	6
350.4.j.a.149.1		4	35.17	even	12
350.4.j.a.149.2		4	35.3	even	12
350.4.j.a.249.1		4	35.33	even	12
350.4.j.a.249.2		4	35.12	even	12
490.4.a.a.1.1		1	5.4	even	2
490.4.a.h.1.1		1	35.34	odd	2
490.4.e.s.361.1		2	35.9	even	6
490.4.e.s.471.1		2	35.4	even	6
560.4.q.g.81.1		2	140.19	even	6
560.4.q.g.401.1		2	140.59	even	6
630.4.k.c.361.1		2	105.89	even	6
630.4.k.c.541.1		2	105.59	even	6
2450.4.a.v.1.1		1	7.6	odd	2
2450.4.a.bq.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:	\( N \)	\(=\)	\( 2450 = 2 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2450.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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