LMFDB - Embedded newform 630.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,4,Mod(1,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("630.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	630.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:	$37.1712033036$
Analytic rank:	$1$
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	$\chi$	$=$	630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q-2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} -7.00000 q^{7} -8.00000 q^{8} +10.0000 q^{10} +1.00000 q^{11} +7.00000 q^{13} +14.0000 q^{14} +16.0000 q^{16} +51.0000 q^{17} +30.0000 q^{19} -20.0000 q^{20} -2.00000 q^{22} +50.0000 q^{23} +25.0000 q^{25} -14.0000 q^{26} -28.0000 q^{28} -79.0000 q^{29} -212.000 q^{31} -32.0000 q^{32} -102.000 q^{34} +35.0000 q^{35} -190.000 q^{37} -60.0000 q^{38} +40.0000 q^{40} +308.000 q^{41} +422.000 q^{43} +4.00000 q^{44} -100.000 q^{46} -121.000 q^{47} +49.0000 q^{49} -50.0000 q^{50} +28.0000 q^{52} -664.000 q^{53} -5.00000 q^{55} +56.0000 q^{56} +158.000 q^{58} -628.000 q^{59} -684.000 q^{61} +424.000 q^{62} +64.0000 q^{64} -35.0000 q^{65} +1056.00 q^{67} +204.000 q^{68} -70.0000 q^{70} -744.000 q^{71} +726.000 q^{73} +380.000 q^{74} +120.000 q^{76} -7.00000 q^{77} -407.000 q^{79} -80.0000 q^{80} -616.000 q^{82} -644.000 q^{83} -255.000 q^{85} -844.000 q^{86} -8.00000 q^{88} +880.000 q^{89} -49.0000 q^{91} +200.000 q^{92} +242.000 q^{94} -150.000 q^{95} -1351.00 q^{97} -98.0000 q^{98} +O(q^{100})\)

Coefficient data

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

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

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

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	0	0
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	0	0
$10$	10.0000	0.316228
$11$	1.00000	0.0274101	0.0137051	−	0.999906i	$-0.495637\pi$
$11$	1.00000	0.0274101	0.0137051	+	0.999906i	$0.495637\pi$
$12$	0	0
$13$	7.00000	0.149342	0.0746712	−	0.997208i	$-0.476209\pi$
$13$	7.00000	0.149342	0.0746712	+	0.997208i	$0.476209\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	51.0000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	51.0000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	0	0
$19$	30.0000	0.362235	0.181118	−	0.983461i	$-0.442029\pi$
$19$	30.0000	0.362235	0.181118	+	0.983461i	$0.442029\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	−2.00000	−0.0193819
$23$	50.0000	0.453292	0.226646	−	0.973977i	$-0.427224\pi$
$23$	50.0000	0.453292	0.226646	+	0.973977i	$0.427224\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	−14.0000	−0.105601
$27$	0	0
$28$	−28.0000	−0.188982
$29$	−79.0000	−0.505860	−0.252930	−	0.967485i	$-0.581394\pi$
$29$	−79.0000	−0.505860	−0.252930	+	0.967485i	$0.581394\pi$
$30$	0	0
$31$	−212.000	−1.22827	−0.614134	−	0.789202i	$-0.710495\pi$
$31$	−212.000	−1.22827	−0.614134	+	0.789202i	$0.710495\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	−102.000	−0.514496
$35$	35.0000	0.169031
$36$	0	0
$37$	−190.000	−0.844211	−0.422106	−	0.906547i	$-0.638709\pi$
$37$	−190.000	−0.844211	−0.422106	+	0.906547i	$0.638709\pi$
$38$	−60.0000	−0.256139
$39$	0	0
$40$	40.0000	0.158114
$41$	308.000	1.17321	0.586604	−	0.809874i	$-0.300465\pi$
$41$	308.000	1.17321	0.586604	+	0.809874i	$0.300465\pi$
$42$	0	0
$43$	422.000	1.49661	0.748307	−	0.663353i	$-0.230867\pi$
$43$	422.000	1.49661	0.748307	+	0.663353i	$0.230867\pi$
$44$	4.00000	0.0137051
$45$	0	0
$46$	−100.000	−0.320526
$47$	−121.000	−0.375525	−0.187762	−	0.982214i	$-0.560123\pi$
$47$	−121.000	−0.375525	−0.187762	+	0.982214i	$0.560123\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	−50.0000	−0.141421
$51$	0	0
$52$	28.0000	0.0746712
$53$	−664.000	−1.72089	−0.860447	−	0.509539i	$-0.829816\pi$
$53$	−664.000	−1.72089	−0.860447	+	0.509539i	$0.829816\pi$
$54$	0	0
$55$	−5.00000	−0.0122582
$56$	56.0000	0.133631
$57$	0	0
$58$	158.000	0.357697
$59$	−628.000	−1.38574	−0.692870	−	0.721063i	$-0.743654\pi$
$59$	−628.000	−1.38574	−0.692870	+	0.721063i	$0.743654\pi$
$60$	0	0
$61$	−684.000	−1.43569	−0.717846	−	0.696202i	$-0.754872\pi$
$61$	−684.000	−1.43569	−0.717846	+	0.696202i	$0.754872\pi$
$62$	424.000	0.868517
$63$	0	0
$64$	64.0000	0.125000
$65$	−35.0000	−0.0667879
$66$	0	0
$67$	1056.00	1.92554	0.962768	−	0.270328i	$-0.0871323\pi$
$67$	1056.00	1.92554	0.962768	+	0.270328i	$0.0871323\pi$
$68$	204.000	0.363803
$69$	0	0
$70$	−70.0000	−0.119523
$71$	−744.000	−1.24361	−0.621807	−	0.783171i	$-0.713601\pi$
$71$	−744.000	−1.24361	−0.621807	+	0.783171i	$0.713601\pi$
$72$	0	0
$73$	726.000	1.16400	0.581999	−	0.813189i	$-0.302271\pi$
$73$	726.000	1.16400	0.581999	+	0.813189i	$0.302271\pi$
$74$	380.000	0.596947
$75$	0	0
$76$	120.000	0.181118
$77$	−7.00000	−0.0103601
$78$	0	0
$79$	−407.000	−0.579634	−0.289817	−	0.957082i	$-0.593594\pi$
$79$	−407.000	−0.579634	−0.289817	+	0.957082i	$0.593594\pi$
$80$	−80.0000	−0.111803
$81$	0	0
$82$	−616.000	−0.829583
$83$	−644.000	−0.851665	−0.425832	−	0.904802i	$-0.640019\pi$
$83$	−644.000	−0.851665	−0.425832	+	0.904802i	$0.640019\pi$
$84$	0	0
$85$	−255.000	−0.325396
$86$	−844.000	−1.05827
$87$	0	0
$88$	−8.00000	−0.00969094
$89$	880.000	1.04809	0.524044	−	0.851691i	$-0.324423\pi$
$89$	880.000	1.04809	0.524044	+	0.851691i	$0.324423\pi$
$90$	0	0
$91$	−49.0000	−0.0564461
$92$	200.000	0.226646
$93$	0	0
$94$	242.000	0.265536
$95$	−150.000	−0.161997
$96$	0	0
$97$	−1351.00	−1.41416	−0.707079	−	0.707135i	$-0.749987\pi$
$97$	−1351.00	−1.41416	−0.707079	+	0.707135i	$0.749987\pi$
$98$	−98.0000	−0.101015
$99$	0	0
$100$	100.000	0.100000
$101$	−54.0000	−0.0532000	−0.0266000	−	0.999646i	$-0.508468\pi$
$101$	−54.0000	−0.0532000	−0.0266000	+	0.999646i	$0.508468\pi$
$102$	0	0
$103$	−1027.00	−0.982459	−0.491230	−	0.871030i	$-0.663452\pi$
$103$	−1027.00	−0.982459	−0.491230	+	0.871030i	$0.663452\pi$
$104$	−56.0000	−0.0528005
$105$	0	0
$106$	1328.00	1.21686
$107$	−314.000	−0.283697	−0.141848	−	0.989888i	$-0.545305\pi$
$107$	−314.000	−0.283697	−0.141848	+	0.989888i	$0.545305\pi$
$108$	0	0
$109$	−1611.00	−1.41565	−0.707825	−	0.706388i	$-0.750323\pi$
$109$	−1611.00	−1.41565	−0.707825	+	0.706388i	$0.750323\pi$
$110$	10.0000	0.00866784
$111$	0	0
$112$	−112.000	−0.0944911
$113$	−366.000	−0.304694	−0.152347	−	0.988327i	$-0.548683\pi$
$113$	−366.000	−0.304694	−0.152347	+	0.988327i	$0.548683\pi$
$114$	0	0
$115$	−250.000	−0.202718
$116$	−316.000	−0.252930
$117$	0	0
$118$	1256.00	0.979866
$119$	−357.000	−0.275010
$120$	0	0
$121$	−1330.00	−0.999249
$122$	1368.00	1.01519
$123$	0	0
$124$	−848.000	−0.614134
$125$	−125.000	−0.0894427
$126$	0	0
$127$	604.000	0.422018	0.211009	−	0.977484i	$-0.432325\pi$
$127$	604.000	0.422018	0.211009	+	0.977484i	$0.432325\pi$
$128$	−128.000	−0.0883883
$129$	0	0
$130$	70.0000	0.0472262
$131$	−2914.00	−1.94349	−0.971746	−	0.236030i	$-0.924153\pi$
$131$	−2914.00	−1.94349	−0.971746	+	0.236030i	$0.924153\pi$
$132$	0	0
$133$	−210.000	−0.136912
$134$	−2112.00	−1.36156
$135$	0	0
$136$	−408.000	−0.257248
$137$	−2568.00	−1.60145	−0.800726	−	0.599030i	$-0.795553\pi$
$137$	−2568.00	−1.60145	−0.800726	+	0.599030i	$0.795553\pi$
$138$	0	0
$139$	1274.00	0.777405	0.388702	−	0.921363i	$-0.372923\pi$
$139$	1274.00	0.777405	0.388702	+	0.921363i	$0.372923\pi$
$140$	140.000	0.0845154
$141$	0	0
$142$	1488.00	0.879368
$143$	7.00000	0.00409349
$144$	0	0
$145$	395.000	0.226227
$146$	−1452.00	−0.823071
$147$	0	0
$148$	−760.000	−0.422106
$149$	−594.000	−0.326593	−0.163297	−	0.986577i	$-0.552213\pi$
$149$	−594.000	−0.326593	−0.163297	+	0.986577i	$0.552213\pi$
$150$	0	0
$151$	−1527.00	−0.822950	−0.411475	−	0.911421i	$-0.634986\pi$
$151$	−1527.00	−0.822950	−0.411475	+	0.911421i	$0.634986\pi$
$152$	−240.000	−0.128070
$153$	0	0
$154$	14.0000	0.00732566
$155$	1060.00	0.549298
$156$	0	0
$157$	530.000	0.269418	0.134709	−	0.990885i	$-0.456990\pi$
$157$	530.000	0.269418	0.134709	+	0.990885i	$0.456990\pi$
$158$	814.000	0.409863
$159$	0	0
$160$	160.000	0.0790569
$161$	−350.000	−0.171328
$162$	0	0
$163$	−3662.00	−1.75969	−0.879847	−	0.475258i	$-0.842355\pi$
$163$	−3662.00	−1.75969	−0.879847	+	0.475258i	$0.842355\pi$
$164$	1232.00	0.586604
$165$	0	0
$166$	1288.00	0.602218
$167$	315.000	0.145961	0.0729803	−	0.997333i	$-0.476749\pi$
$167$	315.000	0.145961	0.0729803	+	0.997333i	$0.476749\pi$
$168$	0	0
$169$	−2148.00	−0.977697
$170$	510.000	0.230089
$171$	0	0
$172$	1688.00	0.748307
$173$	1251.00	0.549779	0.274890	−	0.961476i	$-0.411359\pi$
$173$	1251.00	0.549779	0.274890	+	0.961476i	$0.411359\pi$
$174$	0	0
$175$	−175.000	−0.0755929
$176$	16.0000	0.00685253
$177$	0	0
$178$	−1760.00	−0.741110
$179$	148.000	0.0617991	0.0308996	−	0.999522i	$-0.490163\pi$
$179$	148.000	0.0617991	0.0308996	+	0.999522i	$0.490163\pi$
$180$	0	0
$181$	−1344.00	−0.551927	−0.275963	−	0.961168i	$-0.588997\pi$
$181$	−1344.00	−0.551927	−0.275963	+	0.961168i	$0.588997\pi$
$182$	98.0000	0.0399134
$183$	0	0
$184$	−400.000	−0.160263
$185$	950.000	0.377543
$186$	0	0
$187$	51.0000	0.0199438
$188$	−484.000	−0.187762
$189$	0	0
$190$	300.000	0.114549
$191$	561.000	0.212526	0.106263	−	0.994338i	$-0.466111\pi$
$191$	561.000	0.212526	0.106263	+	0.994338i	$0.466111\pi$
$192$	0	0
$193$	3016.00	1.12485	0.562426	−	0.826848i	$-0.309868\pi$
$193$	3016.00	1.12485	0.562426	+	0.826848i	$0.309868\pi$
$194$	2702.00	0.999960
$195$	0	0
$196$	196.000	0.0714286
$197$	3232.00	1.16889	0.584443	−	0.811435i	$-0.301313\pi$
$197$	3232.00	1.16889	0.584443	+	0.811435i	$0.301313\pi$
$198$	0	0
$199$	−1164.00	−0.414642	−0.207321	−	0.978273i	$-0.566474\pi$
$199$	−1164.00	−0.414642	−0.207321	+	0.978273i	$0.566474\pi$
$200$	−200.000	−0.0707107
$201$	0	0
$202$	108.000	0.0376181
$203$	553.000	0.191197
$204$	0	0
$205$	−1540.00	−0.524674
$206$	2054.00	0.694704
$207$	0	0
$208$	112.000	0.0373356
$209$	30.0000	0.00992892
$210$	0	0
$211$	569.000	0.185647	0.0928236	−	0.995683i	$-0.470411\pi$
$211$	569.000	0.185647	0.0928236	+	0.995683i	$0.470411\pi$
$212$	−2656.00	−0.860447
$213$	0	0
$214$	628.000	0.200604
$215$	−2110.00	−0.669306
$216$	0	0
$217$	1484.00	0.464242
$218$	3222.00	1.00102
$219$	0	0
$220$	−20.0000	−0.00612909
$221$	357.000	0.108663
$222$	0	0
$223$	693.000	0.208102	0.104051	−	0.994572i	$-0.466820\pi$
$223$	693.000	0.208102	0.104051	+	0.994572i	$0.466820\pi$
$224$	224.000	0.0668153
$225$	0	0
$226$	732.000	0.215451
$227$	4279.00	1.25113	0.625567	−	0.780171i	$-0.284868\pi$
$227$	4279.00	1.25113	0.625567	+	0.780171i	$0.284868\pi$
$228$	0	0
$229$	−3316.00	−0.956888	−0.478444	−	0.878118i	$-0.658799\pi$
$229$	−3316.00	−0.956888	−0.478444	+	0.878118i	$0.658799\pi$
$230$	500.000	0.143344
$231$	0	0
$232$	632.000	0.178848
$233$	−3912.00	−1.09993	−0.549965	−	0.835188i	$-0.685359\pi$
$233$	−3912.00	−1.09993	−0.549965	+	0.835188i	$0.685359\pi$
$234$	0	0
$235$	605.000	0.167940
$236$	−2512.00	−0.692870
$237$	0	0
$238$	714.000	0.194461
$239$	5451.00	1.47530	0.737648	−	0.675185i	$-0.235936\pi$
$239$	5451.00	1.47530	0.737648	+	0.675185i	$0.235936\pi$
$240$	0	0
$241$	250.000	0.0668212	0.0334106	−	0.999442i	$-0.489363\pi$
$241$	250.000	0.0668212	0.0334106	+	0.999442i	$0.489363\pi$
$242$	2660.00	0.706576
$243$	0	0
$244$	−2736.00	−0.717846
$245$	−245.000	−0.0638877
$246$	0	0
$247$	210.000	0.0540971
$248$	1696.00	0.434258
$249$	0	0
$250$	250.000	0.0632456
$251$	−910.000	−0.228839	−0.114420	−	0.993432i	$-0.536501\pi$
$251$	−910.000	−0.228839	−0.114420	+	0.993432i	$0.536501\pi$
$252$	0	0
$253$	50.0000	0.0124248
$254$	−1208.00	−0.298412
$255$	0	0
$256$	256.000	0.0625000
$257$	6494.00	1.57620	0.788102	−	0.615544i	$-0.211064\pi$
$257$	6494.00	1.57620	0.788102	+	0.615544i	$0.211064\pi$
$258$	0	0
$259$	1330.00	0.319082
$260$	−140.000	−0.0333940
$261$	0	0
$262$	5828.00	1.37426
$263$	−1434.00	−0.336214	−0.168107	−	0.985769i	$-0.553765\pi$
$263$	−1434.00	−0.336214	−0.168107	+	0.985769i	$0.553765\pi$
$264$	0	0
$265$	3320.00	0.769607
$266$	420.000	0.0968115
$267$	0	0
$268$	4224.00	0.962768
$269$	5014.00	1.13646	0.568232	−	0.822868i	$-0.307627\pi$
$269$	5014.00	1.13646	0.568232	+	0.822868i	$0.307627\pi$
$270$	0	0
$271$	5420.00	1.21491	0.607457	−	0.794353i	$-0.292190\pi$
$271$	5420.00	1.21491	0.607457	+	0.794353i	$0.292190\pi$
$272$	816.000	0.181902
$273$	0	0
$274$	5136.00	1.13240
$275$	25.0000	0.00548202
$276$	0	0
$277$	3674.00	0.796929	0.398464	−	0.917184i	$-0.369543\pi$
$277$	3674.00	0.796929	0.398464	+	0.917184i	$0.369543\pi$
$278$	−2548.00	−0.549708
$279$	0	0
$280$	−280.000	−0.0597614
$281$	−7331.00	−1.55634	−0.778169	−	0.628055i	$-0.783851\pi$
$281$	−7331.00	−1.55634	−0.778169	+	0.628055i	$0.783851\pi$
$282$	0	0
$283$	271.000	0.0569232	0.0284616	−	0.999595i	$-0.490939\pi$
$283$	271.000	0.0569232	0.0284616	+	0.999595i	$0.490939\pi$
$284$	−2976.00	−0.621807
$285$	0	0
$286$	−14.0000	−0.00289454
$287$	−2156.00	−0.443431
$288$	0	0
$289$	−2312.00	−0.470588
$290$	−790.000	−0.159967
$291$	0	0
$292$	2904.00	0.581999
$293$	−4305.00	−0.858364	−0.429182	−	0.903218i	$-0.641198\pi$
$293$	−4305.00	−0.858364	−0.429182	+	0.903218i	$0.641198\pi$
$294$	0	0
$295$	3140.00	0.619722
$296$	1520.00	0.298474
$297$	0	0
$298$	1188.00	0.230936
$299$	350.000	0.0676957
$300$	0	0
$301$	−2954.00	−0.565667
$302$	3054.00	0.581914
$303$	0	0
$304$	480.000	0.0905588
$305$	3420.00	0.642061
$306$	0	0
$307$	2639.00	0.490605	0.245302	−	0.969447i	$-0.421113\pi$
$307$	2639.00	0.490605	0.245302	+	0.969447i	$0.421113\pi$
$308$	−28.0000	−0.00518003
$309$	0	0
$310$	−2120.00	−0.388413
$311$	8514.00	1.55236	0.776181	−	0.630510i	$-0.217154\pi$
$311$	8514.00	1.55236	0.776181	+	0.630510i	$0.217154\pi$
$312$	0	0
$313$	219.000	0.0395483	0.0197741	−	0.999804i	$-0.493705\pi$
$313$	219.000	0.0395483	0.0197741	+	0.999804i	$0.493705\pi$
$314$	−1060.00	−0.190507
$315$	0	0
$316$	−1628.00	−0.289817
$317$	4026.00	0.713321	0.356660	−	0.934234i	$-0.383915\pi$
$317$	4026.00	0.713321	0.356660	+	0.934234i	$0.383915\pi$
$318$	0	0
$319$	−79.0000	−0.0138657
$320$	−320.000	−0.0559017
$321$	0	0
$322$	700.000	0.121147
$323$	1530.00	0.263565
$324$	0	0
$325$	175.000	0.0298685
$326$	7324.00	1.24429
$327$	0	0
$328$	−2464.00	−0.414792
$329$	847.000	0.141935
$330$	0	0
$331$	−7036.00	−1.16838	−0.584190	−	0.811617i	$-0.698588\pi$
$331$	−7036.00	−1.16838	−0.584190	+	0.811617i	$0.698588\pi$
$332$	−2576.00	−0.425832
$333$	0	0
$334$	−630.000	−0.103210
$335$	−5280.00	−0.861126
$336$	0	0
$337$	10362.0	1.67494	0.837469	−	0.546485i	$-0.184034\pi$
$337$	10362.0	1.67494	0.837469	+	0.546485i	$0.184034\pi$
$338$	4296.00	0.691336
$339$	0	0
$340$	−1020.00	−0.162698
$341$	−212.000	−0.0336670
$342$	0	0
$343$	−343.000	−0.0539949
$344$	−3376.00	−0.529133
$345$	0	0
$346$	−2502.00	−0.388752
$347$	8422.00	1.30293	0.651465	−	0.758679i	$-0.274155\pi$
$347$	8422.00	1.30293	0.651465	+	0.758679i	$0.274155\pi$
$348$	0	0
$349$	−7350.00	−1.12733	−0.563663	−	0.826005i	$-0.690608\pi$
$349$	−7350.00	−1.12733	−0.563663	+	0.826005i	$0.690608\pi$
$350$	350.000	0.0534522
$351$	0	0
$352$	−32.0000	−0.00484547
$353$	−3057.00	−0.460928	−0.230464	−	0.973081i	$-0.574024\pi$
$353$	−3057.00	−0.460928	−0.230464	+	0.973081i	$0.574024\pi$
$354$	0	0
$355$	3720.00	0.556161
$356$	3520.00	0.524044
$357$	0	0
$358$	−296.000	−0.0436986
$359$	−8392.00	−1.23374	−0.616870	−	0.787065i	$-0.711600\pi$
$359$	−8392.00	−1.23374	−0.616870	+	0.787065i	$0.711600\pi$
$360$	0	0
$361$	−5959.00	−0.868786
$362$	2688.00	0.390271
$363$	0	0
$364$	−196.000	−0.0282231
$365$	−3630.00	−0.520556
$366$	0	0
$367$	8377.00	1.19149	0.595744	−	0.803175i	$-0.296857\pi$
$367$	8377.00	1.19149	0.595744	+	0.803175i	$0.296857\pi$
$368$	800.000	0.113323
$369$	0	0
$370$	−1900.00	−0.266963
$371$	4648.00	0.650437
$372$	0	0
$373$	−1968.00	−0.273188	−0.136594	−	0.990627i	$-0.543616\pi$
$373$	−1968.00	−0.273188	−0.136594	+	0.990627i	$0.543616\pi$
$374$	−102.000	−0.0141024
$375$	0	0
$376$	968.000	0.132768
$377$	−553.000	−0.0755463
$378$	0	0
$379$	1052.00	0.142579	0.0712897	−	0.997456i	$-0.477289\pi$
$379$	1052.00	0.142579	0.0712897	+	0.997456i	$0.477289\pi$
$380$	−600.000	−0.0809983
$381$	0	0
$382$	−1122.00	−0.150279
$383$	2308.00	0.307920	0.153960	−	0.988077i	$-0.450797\pi$
$383$	2308.00	0.307920	0.153960	+	0.988077i	$0.450797\pi$
$384$	0	0
$385$	35.0000	0.00463316
$386$	−6032.00	−0.795390
$387$	0	0
$388$	−5404.00	−0.707079
$389$	−2281.00	−0.297304	−0.148652	−	0.988890i	$-0.547493\pi$
$389$	−2281.00	−0.297304	−0.148652	+	0.988890i	$0.547493\pi$
$390$	0	0
$391$	2550.00	0.329819
$392$	−392.000	−0.0505076
$393$	0	0
$394$	−6464.00	−0.826527
$395$	2035.00	0.259220
$396$	0	0
$397$	−14635.0	−1.85015	−0.925075	−	0.379784i	$-0.875998\pi$
$397$	−14635.0	−1.85015	−0.925075	+	0.379784i	$0.875998\pi$
$398$	2328.00	0.293196
$399$	0	0
$400$	400.000	0.0500000
$401$	−5641.00	−0.702489	−0.351245	−	0.936284i	$-0.614241\pi$
$401$	−5641.00	−0.702489	−0.351245	+	0.936284i	$0.614241\pi$
$402$	0	0
$403$	−1484.00	−0.183433
$404$	−216.000	−0.0266000
$405$	0	0
$406$	−1106.00	−0.135197
$407$	−190.000	−0.0231399
$408$	0	0
$409$	6410.00	0.774949	0.387474	−	0.921880i	$-0.373348\pi$
$409$	6410.00	0.774949	0.387474	+	0.921880i	$0.373348\pi$
$410$	3080.00	0.371001
$411$	0	0
$412$	−4108.00	−0.491230
$413$	4396.00	0.523760
$414$	0	0
$415$	3220.00	0.380876
$416$	−224.000	−0.0264002
$417$	0	0
$418$	−60.0000	−0.00702080
$419$	−4816.00	−0.561520	−0.280760	−	0.959778i	$-0.590587\pi$
$419$	−4816.00	−0.561520	−0.280760	+	0.959778i	$0.590587\pi$
$420$	0	0
$421$	15325.0	1.77410	0.887048	−	0.461676i	$-0.152752\pi$
$421$	15325.0	1.77410	0.887048	+	0.461676i	$0.152752\pi$
$422$	−1138.00	−0.131272
$423$	0	0
$424$	5312.00	0.608428
$425$	1275.00	0.145521
$426$	0	0
$427$	4788.00	0.542641
$428$	−1256.00	−0.141848
$429$	0	0
$430$	4220.00	0.473271
$431$	−1875.00	−0.209549	−0.104774	−	0.994496i	$-0.533412\pi$
$431$	−1875.00	−0.209549	−0.104774	+	0.994496i	$0.533412\pi$
$432$	0	0
$433$	−13874.0	−1.53982	−0.769910	−	0.638153i	$-0.779699\pi$
$433$	−13874.0	−1.53982	−0.769910	+	0.638153i	$0.779699\pi$
$434$	−2968.00	−0.328269
$435$	0	0
$436$	−6444.00	−0.707825
$437$	1500.00	0.164198
$438$	0	0
$439$	−3442.00	−0.374209	−0.187104	−	0.982340i	$-0.559910\pi$
$439$	−3442.00	−0.374209	−0.187104	+	0.982340i	$0.559910\pi$
$440$	40.0000	0.00433392
$441$	0	0
$442$	−714.000	−0.0768360
$443$	−16750.0	−1.79643	−0.898213	−	0.439561i	$-0.855134\pi$
$443$	−16750.0	−1.79643	−0.898213	+	0.439561i	$0.855134\pi$
$444$	0	0
$445$	−4400.00	−0.468719
$446$	−1386.00	−0.147150
$447$	0	0
$448$	−448.000	−0.0472456
$449$	−695.000	−0.0730492	−0.0365246	−	0.999333i	$-0.511629\pi$
$449$	−695.000	−0.0730492	−0.0365246	+	0.999333i	$0.511629\pi$
$450$	0	0
$451$	308.000	0.0321578
$452$	−1464.00	−0.152347
$453$	0	0
$454$	−8558.00	−0.884685
$455$	245.000	0.0252435
$456$	0	0
$457$	5760.00	0.589587	0.294794	−	0.955561i	$-0.404749\pi$
$457$	5760.00	0.589587	0.294794	+	0.955561i	$0.404749\pi$
$458$	6632.00	0.676622
$459$	0	0
$460$	−1000.00	−0.101359
$461$	−13440.0	−1.35784	−0.678919	−	0.734213i	$-0.737551\pi$
$461$	−13440.0	−1.35784	−0.678919	+	0.734213i	$0.737551\pi$
$462$	0	0
$463$	−7348.00	−0.737561	−0.368780	−	0.929517i	$-0.620225\pi$
$463$	−7348.00	−0.737561	−0.368780	+	0.929517i	$0.620225\pi$
$464$	−1264.00	−0.126465
$465$	0	0
$466$	7824.00	0.777768
$467$	17925.0	1.77617	0.888084	−	0.459682i	$-0.152037\pi$
$467$	17925.0	1.77617	0.888084	+	0.459682i	$0.152037\pi$
$468$	0	0
$469$	−7392.00	−0.727784
$470$	−1210.00	−0.118751
$471$	0	0
$472$	5024.00	0.489933
$473$	422.000	0.0410224
$474$	0	0
$475$	750.000	0.0724471
$476$	−1428.00	−0.137505
$477$	0	0
$478$	−10902.0	−1.04319
$479$	−12346.0	−1.17767	−0.588834	−	0.808254i	$-0.700413\pi$
$479$	−12346.0	−1.17767	−0.588834	+	0.808254i	$0.700413\pi$
$480$	0	0
$481$	−1330.00	−0.126076
$482$	−500.000	−0.0472497
$483$	0	0
$484$	−5320.00	−0.499624
$485$	6755.00	0.632430
$486$	0	0
$487$	15014.0	1.39702	0.698511	−	0.715600i	$-0.253847\pi$
$487$	15014.0	1.39702	0.698511	+	0.715600i	$0.253847\pi$
$488$	5472.00	0.507594
$489$	0	0
$490$	490.000	0.0451754
$491$	4723.00	0.434106	0.217053	−	0.976160i	$-0.430356\pi$
$491$	4723.00	0.434106	0.217053	+	0.976160i	$0.430356\pi$
$492$	0	0
$493$	−4029.00	−0.368067
$494$	−420.000	−0.0382524
$495$	0	0
$496$	−3392.00	−0.307067
$497$	5208.00	0.470042
$498$	0	0
$499$	11227.0	1.00719	0.503597	−	0.863939i	$-0.332010\pi$
$499$	11227.0	1.00719	0.503597	+	0.863939i	$0.332010\pi$
$500$	−500.000	−0.0447214
$501$	0	0
$502$	1820.00	0.161814
$503$	4557.00	0.403949	0.201975	−	0.979391i	$-0.435264\pi$
$503$	4557.00	0.403949	0.201975	+	0.979391i	$0.435264\pi$
$504$	0	0
$505$	270.000	0.0237918
$506$	−100.000	−0.00878566
$507$	0	0
$508$	2416.00	0.211009
$509$	14110.0	1.22871	0.614356	−	0.789029i	$-0.289416\pi$
$509$	14110.0	1.22871	0.614356	+	0.789029i	$0.289416\pi$
$510$	0	0
$511$	−5082.00	−0.439950
$512$	−512.000	−0.0441942
$513$	0	0
$514$	−12988.0	−1.11454
$515$	5135.00	0.439369
$516$	0	0
$517$	−121.000	−0.0102932
$518$	−2660.00	−0.225625
$519$	0	0
$520$	280.000	0.0236131
$521$	−1902.00	−0.159939	−0.0799694	−	0.996797i	$-0.525482\pi$
$521$	−1902.00	−0.159939	−0.0799694	+	0.996797i	$0.525482\pi$
$522$	0	0
$523$	−1972.00	−0.164875	−0.0824374	−	0.996596i	$-0.526270\pi$
$523$	−1972.00	−0.164875	−0.0824374	+	0.996596i	$0.526270\pi$
$524$	−11656.0	−0.971746
$525$	0	0
$526$	2868.00	0.237739
$527$	−10812.0	−0.893697
$528$	0	0
$529$	−9667.00	−0.794526
$530$	−6640.00	−0.544195
$531$	0	0
$532$	−840.000	−0.0684561
$533$	2156.00	0.175210
$534$	0	0
$535$	1570.00	0.126873
$536$	−8448.00	−0.680780
$537$	0	0
$538$	−10028.0	−0.803602
$539$	49.0000	0.00391573
$540$	0	0
$541$	−25033.0	−1.98938	−0.994688	−	0.102933i	$-0.967177\pi$
$541$	−25033.0	−1.98938	−0.994688	+	0.102933i	$0.967177\pi$
$542$	−10840.0	−0.859074
$543$	0	0
$544$	−1632.00	−0.128624
$545$	8055.00	0.633098
$546$	0	0
$547$	−236.000	−0.0184472	−0.00922361	−	0.999957i	$-0.502936\pi$
$547$	−236.000	−0.0184472	−0.00922361	+	0.999957i	$0.502936\pi$
$548$	−10272.0	−0.800726
$549$	0	0
$550$	−50.0000	−0.00387638
$551$	−2370.00	−0.183240
$552$	0	0
$553$	2849.00	0.219081
$554$	−7348.00	−0.563514
$555$	0	0
$556$	5096.00	0.388702
$557$	−15504.0	−1.17940	−0.589700	−	0.807623i	$-0.700754\pi$
$557$	−15504.0	−1.17940	−0.589700	+	0.807623i	$0.700754\pi$
$558$	0	0
$559$	2954.00	0.223508
$560$	560.000	0.0422577
$561$	0	0
$562$	14662.0	1.10050
$563$	8948.00	0.669828	0.334914	−	0.942249i	$-0.391293\pi$
$563$	8948.00	0.669828	0.334914	+	0.942249i	$0.391293\pi$
$564$	0	0
$565$	1830.00	0.136263
$566$	−542.000	−0.0402508
$567$	0	0
$568$	5952.00	0.439684
$569$	−13866.0	−1.02160	−0.510802	−	0.859698i	$-0.670652\pi$
$569$	−13866.0	−1.02160	−0.510802	+	0.859698i	$0.670652\pi$
$570$	0	0
$571$	9988.00	0.732022	0.366011	−	0.930610i	$-0.380723\pi$
$571$	9988.00	0.732022	0.366011	+	0.930610i	$0.380723\pi$
$572$	28.0000	0.00204675
$573$	0	0
$574$	4312.00	0.313553
$575$	1250.00	0.0906584
$576$	0	0
$577$	−2585.00	−0.186508	−0.0932539	−	0.995642i	$-0.529727\pi$
$577$	−2585.00	−0.186508	−0.0932539	+	0.995642i	$0.529727\pi$
$578$	4624.00	0.332756
$579$	0	0
$580$	1580.00	0.113114
$581$	4508.00	0.321899
$582$	0	0
$583$	−664.000	−0.0471699
$584$	−5808.00	−0.411536
$585$	0	0
$586$	8610.00	0.606955
$587$	−19656.0	−1.38210	−0.691048	−	0.722809i	$-0.742851\pi$
$587$	−19656.0	−1.38210	−0.691048	+	0.722809i	$0.742851\pi$
$588$	0	0
$589$	−6360.00	−0.444922
$590$	−6280.00	−0.438209
$591$	0	0
$592$	−3040.00	−0.211053
$593$	−21247.0	−1.47135	−0.735674	−	0.677335i	$-0.763135\pi$
$593$	−21247.0	−1.47135	−0.735674	+	0.677335i	$0.763135\pi$
$594$	0	0
$595$	1785.00	0.122988
$596$	−2376.00	−0.163297
$597$	0	0
$598$	−700.000	−0.0478681
$599$	9325.00	0.636075	0.318038	−	0.948078i	$-0.396976\pi$
$599$	9325.00	0.636075	0.318038	+	0.948078i	$0.396976\pi$
$600$	0	0
$601$	5362.00	0.363928	0.181964	−	0.983305i	$-0.441755\pi$
$601$	5362.00	0.363928	0.181964	+	0.983305i	$0.441755\pi$
$602$	5908.00	0.399987
$603$	0	0
$604$	−6108.00	−0.411475
$605$	6650.00	0.446878
$606$	0	0
$607$	15731.0	1.05190	0.525949	−	0.850516i	$-0.323710\pi$
$607$	15731.0	1.05190	0.525949	+	0.850516i	$0.323710\pi$
$608$	−960.000	−0.0640348
$609$	0	0
$610$	−6840.00	−0.454006
$611$	−847.000	−0.0560818
$612$	0	0
$613$	−13742.0	−0.905439	−0.452720	−	0.891653i	$-0.649546\pi$
$613$	−13742.0	−0.905439	−0.452720	+	0.891653i	$0.649546\pi$
$614$	−5278.00	−0.346910
$615$	0	0
$616$	56.0000	0.00366283
$617$	−18286.0	−1.19314	−0.596569	−	0.802561i	$-0.703470\pi$
$617$	−18286.0	−1.19314	−0.596569	+	0.802561i	$0.703470\pi$
$618$	0	0
$619$	24722.0	1.60527	0.802634	−	0.596472i	$-0.203431\pi$
$619$	24722.0	1.60527	0.802634	+	0.596472i	$0.203431\pi$
$620$	4240.00	0.274649
$621$	0	0
$622$	−17028.0	−1.09769
$623$	−6160.00	−0.396140
$624$	0	0
$625$	625.000	0.0400000
$626$	−438.000	−0.0279649
$627$	0	0
$628$	2120.00	0.134709
$629$	−9690.00	−0.614254
$630$	0	0
$631$	−22181.0	−1.39938	−0.699692	−	0.714444i	$-0.746680\pi$
$631$	−22181.0	−1.39938	−0.699692	+	0.714444i	$0.746680\pi$
$632$	3256.00	0.204932
$633$	0	0
$634$	−8052.00	−0.504394
$635$	−3020.00	−0.188732
$636$	0	0
$637$	343.000	0.0213346
$638$	158.000	0.00980451
$639$	0	0
$640$	640.000	0.0395285
$641$	23598.0	1.45408	0.727040	−	0.686595i	$-0.240896\pi$
$641$	23598.0	1.45408	0.727040	+	0.686595i	$0.240896\pi$
$642$	0	0
$643$	13349.0	0.818714	0.409357	−	0.912374i	$-0.365753\pi$
$643$	13349.0	0.818714	0.409357	+	0.912374i	$0.365753\pi$
$644$	−1400.00	−0.0856642
$645$	0	0
$646$	−3060.00	−0.186369
$647$	24488.0	1.48798	0.743990	−	0.668191i	$-0.232931\pi$
$647$	24488.0	1.48798	0.743990	+	0.668191i	$0.232931\pi$
$648$	0	0
$649$	−628.000	−0.0379833
$650$	−350.000	−0.0211202
$651$	0	0
$652$	−14648.0	−0.879847
$653$	−21622.0	−1.29576	−0.647882	−	0.761740i	$-0.724345\pi$
$653$	−21622.0	−1.29576	−0.647882	+	0.761740i	$0.724345\pi$
$654$	0	0
$655$	14570.0	0.869156
$656$	4928.00	0.293302
$657$	0	0
$658$	−1694.00	−0.100363
$659$	2973.00	0.175738	0.0878692	−	0.996132i	$-0.471994\pi$
$659$	2973.00	0.175738	0.0878692	+	0.996132i	$0.471994\pi$
$660$	0	0
$661$	18912.0	1.11285	0.556423	−	0.830899i	$-0.312173\pi$
$661$	18912.0	1.11285	0.556423	+	0.830899i	$0.312173\pi$
$662$	14072.0	0.826169
$663$	0	0
$664$	5152.00	0.301109
$665$	1050.00	0.0612290
$666$	0	0
$667$	−3950.00	−0.229302
$668$	1260.00	0.0729803
$669$	0	0
$670$	10560.0	0.608908
$671$	−684.000	−0.0393525
$672$	0	0
$673$	688.000	0.0394063	0.0197032	−	0.999806i	$-0.493728\pi$
$673$	688.000	0.0394063	0.0197032	+	0.999806i	$0.493728\pi$
$674$	−20724.0	−1.18436
$675$	0	0
$676$	−8592.00	−0.488848
$677$	−12791.0	−0.726142	−0.363071	−	0.931761i	$-0.618272\pi$
$677$	−12791.0	−0.726142	−0.363071	+	0.931761i	$0.618272\pi$
$678$	0	0
$679$	9457.00	0.534501
$680$	2040.00	0.115045
$681$	0	0
$682$	424.000	0.0238062
$683$	7652.00	0.428691	0.214345	−	0.976758i	$-0.431238\pi$
$683$	7652.00	0.428691	0.214345	+	0.976758i	$0.431238\pi$
$684$	0	0
$685$	12840.0	0.716192
$686$	686.000	0.0381802
$687$	0	0
$688$	6752.00	0.374153
$689$	−4648.00	−0.257002
$690$	0	0
$691$	−2532.00	−0.139395	−0.0696974	−	0.997568i	$-0.522203\pi$
$691$	−2532.00	−0.139395	−0.0696974	+	0.997568i	$0.522203\pi$
$692$	5004.00	0.274890
$693$	0	0
$694$	−16844.0	−0.921311
$695$	−6370.00	−0.347666
$696$	0	0
$697$	15708.0	0.853634
$698$	14700.0	0.797139
$699$	0	0
$700$	−700.000	−0.0377964
$701$	2133.00	0.114925	0.0574624	−	0.998348i	$-0.481699\pi$
$701$	2133.00	0.114925	0.0574624	+	0.998348i	$0.481699\pi$
$702$	0	0
$703$	−5700.00	−0.305803
$704$	64.0000	0.00342627
$705$	0	0
$706$	6114.00	0.325926
$707$	378.000	0.0201077
$708$	0	0
$709$	−19153.0	−1.01454	−0.507268	−	0.861788i	$-0.669345\pi$
$709$	−19153.0	−1.01454	−0.507268	+	0.861788i	$0.669345\pi$
$710$	−7440.00	−0.393265
$711$	0	0
$712$	−7040.00	−0.370555
$713$	−10600.0	−0.556765
$714$	0	0
$715$	−35.0000	−0.00183067
$716$	592.000	0.0308996
$717$	0	0
$718$	16784.0	0.872386
$719$	21334.0	1.10657	0.553285	−	0.832992i	$-0.313374\pi$
$719$	21334.0	1.10657	0.553285	+	0.832992i	$0.313374\pi$
$720$	0	0
$721$	7189.00	0.371335
$722$	11918.0	0.614324
$723$	0	0
$724$	−5376.00	−0.275963
$725$	−1975.00	−0.101172
$726$	0	0
$727$	11480.0	0.585653	0.292826	−	0.956166i	$-0.405404\pi$
$727$	11480.0	0.585653	0.292826	+	0.956166i	$0.405404\pi$
$728$	392.000	0.0199567
$729$	0	0
$730$	7260.00	0.368089
$731$	21522.0	1.08895
$732$	0	0
$733$	19763.0	0.995857	0.497928	−	0.867218i	$-0.334094\pi$
$733$	19763.0	0.995857	0.497928	+	0.867218i	$0.334094\pi$
$734$	−16754.0	−0.842509
$735$	0	0
$736$	−1600.00	−0.0801315
$737$	1056.00	0.0527792
$738$	0	0
$739$	−40153.0	−1.99872	−0.999359	−	0.0358110i	$-0.988599\pi$
$739$	−40153.0	−1.99872	−0.999359	+	0.0358110i	$0.988599\pi$
$740$	3800.00	0.188771
$741$	0	0
$742$	−9296.00	−0.459928
$743$	30896.0	1.52552	0.762762	−	0.646679i	$-0.223843\pi$
$743$	30896.0	1.52552	0.762762	+	0.646679i	$0.223843\pi$
$744$	0	0
$745$	2970.00	0.146057
$746$	3936.00	0.193173
$747$	0	0
$748$	204.000	0.00997190
$749$	2198.00	0.107227
$750$	0	0
$751$	11969.0	0.581565	0.290782	−	0.956789i	$-0.406084\pi$
$751$	11969.0	0.581565	0.290782	+	0.956789i	$0.406084\pi$
$752$	−1936.00	−0.0938812
$753$	0	0
$754$	1106.00	0.0534193
$755$	7635.00	0.368035
$756$	0	0
$757$	−10456.0	−0.502021	−0.251010	−	0.967984i	$-0.580763\pi$
$757$	−10456.0	−0.502021	−0.251010	+	0.967984i	$0.580763\pi$
$758$	−2104.00	−0.100819
$759$	0	0
$760$	1200.00	0.0572744
$761$	28782.0	1.37102	0.685510	−	0.728063i	$-0.259579\pi$
$761$	28782.0	1.37102	0.685510	+	0.728063i	$0.259579\pi$
$762$	0	0
$763$	11277.0	0.535065
$764$	2244.00	0.106263
$765$	0	0
$766$	−4616.00	−0.217732
$767$	−4396.00	−0.206950
$768$	0	0
$769$	−14630.0	−0.686048	−0.343024	−	0.939327i	$-0.611451\pi$
$769$	−14630.0	−0.686048	−0.343024	+	0.939327i	$0.611451\pi$
$770$	−70.0000	−0.00327614
$771$	0	0
$772$	12064.0	0.562426
$773$	−24351.0	−1.13305	−0.566523	−	0.824046i	$-0.691712\pi$
$773$	−24351.0	−1.13305	−0.566523	+	0.824046i	$0.691712\pi$
$774$	0	0
$775$	−5300.00	−0.245654
$776$	10808.0	0.499980
$777$	0	0
$778$	4562.00	0.210226
$779$	9240.00	0.424977
$780$	0	0
$781$	−744.000	−0.0340876
$782$	−5100.00	−0.233217
$783$	0	0
$784$	784.000	0.0357143
$785$	−2650.00	−0.120487
$786$	0	0
$787$	2329.00	0.105489	0.0527445	−	0.998608i	$-0.483203\pi$
$787$	2329.00	0.105489	0.0527445	+	0.998608i	$0.483203\pi$
$788$	12928.0	0.584443
$789$	0	0
$790$	−4070.00	−0.183296
$791$	2562.00	0.115163
$792$	0	0
$793$	−4788.00	−0.214410
$794$	29270.0	1.30825
$795$	0	0
$796$	−4656.00	−0.207321
$797$	11067.0	0.491861	0.245931	−	0.969287i	$-0.420906\pi$
$797$	11067.0	0.491861	0.245931	+	0.969287i	$0.420906\pi$
$798$	0	0
$799$	−6171.00	−0.273234
$800$	−800.000	−0.0353553
$801$	0	0
$802$	11282.0	0.496735
$803$	726.000	0.0319053
$804$	0	0
$805$	1750.00	0.0766204
$806$	2968.00	0.129706
$807$	0	0
$808$	432.000	0.0188090
$809$	3879.00	0.168576	0.0842882	−	0.996441i	$-0.473138\pi$
$809$	3879.00	0.168576	0.0842882	+	0.996441i	$0.473138\pi$
$810$	0	0
$811$	7518.00	0.325515	0.162758	−	0.986666i	$-0.447961\pi$
$811$	7518.00	0.325515	0.162758	+	0.986666i	$0.447961\pi$
$812$	2212.00	0.0955985
$813$	0	0
$814$	380.000	0.0163624
$815$	18310.0	0.786959
$816$	0	0
$817$	12660.0	0.542126
$818$	−12820.0	−0.547972
$819$	0	0
$820$	−6160.00	−0.262337
$821$	−39801.0	−1.69192	−0.845959	−	0.533248i	$-0.820971\pi$
$821$	−39801.0	−1.69192	−0.845959	+	0.533248i	$0.820971\pi$
$822$	0	0
$823$	−3564.00	−0.150952	−0.0754758	−	0.997148i	$-0.524048\pi$
$823$	−3564.00	−0.150952	−0.0754758	+	0.997148i	$0.524048\pi$
$824$	8216.00	0.347352
$825$	0	0
$826$	−8792.00	−0.370354
$827$	−10838.0	−0.455712	−0.227856	−	0.973695i	$-0.573172\pi$
$827$	−10838.0	−0.455712	−0.227856	+	0.973695i	$0.573172\pi$
$828$	0	0
$829$	41956.0	1.75777	0.878885	−	0.477033i	$-0.158288\pi$
$829$	41956.0	1.75777	0.878885	+	0.477033i	$0.158288\pi$
$830$	−6440.00	−0.269320
$831$	0	0
$832$	448.000	0.0186678
$833$	2499.00	0.103944
$834$	0	0
$835$	−1575.00	−0.0652756
$836$	120.000	0.00496446
$837$	0	0
$838$	9632.00	0.397055
$839$	28714.0	1.18155	0.590773	−	0.806838i	$-0.298823\pi$
$839$	28714.0	1.18155	0.590773	+	0.806838i	$0.298823\pi$
$840$	0	0
$841$	−18148.0	−0.744106
$842$	−30650.0	−1.25448
$843$	0	0
$844$	2276.00	0.0928236
$845$	10740.0	0.437239
$846$	0	0
$847$	9310.00	0.377681
$848$	−10624.0	−0.430224
$849$	0	0
$850$	−2550.00	−0.102899
$851$	−9500.00	−0.382674
$852$	0	0
$853$	15442.0	0.619841	0.309920	−	0.950763i	$-0.399698\pi$
$853$	15442.0	0.619841	0.309920	+	0.950763i	$0.399698\pi$
$854$	−9576.00	−0.383705
$855$	0	0
$856$	2512.00	0.100302
$857$	17978.0	0.716589	0.358295	−	0.933609i	$-0.383358\pi$
$857$	17978.0	0.716589	0.358295	+	0.933609i	$0.383358\pi$
$858$	0	0
$859$	19308.0	0.766916	0.383458	−	0.923558i	$-0.374733\pi$
$859$	19308.0	0.766916	0.383458	+	0.923558i	$0.374733\pi$
$860$	−8440.00	−0.334653
$861$	0	0
$862$	3750.00	0.148173
$863$	−17464.0	−0.688855	−0.344427	−	0.938813i	$-0.611927\pi$
$863$	−17464.0	−0.688855	−0.344427	+	0.938813i	$0.611927\pi$
$864$	0	0
$865$	−6255.00	−0.245869
$866$	27748.0	1.08882
$867$	0	0
$868$	5936.00	0.232121
$869$	−407.000	−0.0158878
$870$	0	0
$871$	7392.00	0.287564
$872$	12888.0	0.500508
$873$	0	0
$874$	−3000.00	−0.116106
$875$	875.000	0.0338062
$876$	0	0
$877$	−23962.0	−0.922622	−0.461311	−	0.887239i	$-0.652621\pi$
$877$	−23962.0	−0.922622	−0.461311	+	0.887239i	$0.652621\pi$
$878$	6884.00	0.264606
$879$	0	0
$880$	−80.0000	−0.00306454
$881$	35168.0	1.34488	0.672440	−	0.740151i	$-0.265246\pi$
$881$	35168.0	1.34488	0.672440	+	0.740151i	$0.265246\pi$
$882$	0	0
$883$	−37896.0	−1.44428	−0.722142	−	0.691745i	$-0.756842\pi$
$883$	−37896.0	−1.44428	−0.722142	+	0.691745i	$0.756842\pi$
$884$	1428.00	0.0543313
$885$	0	0
$886$	33500.0	1.27026
$887$	−30368.0	−1.14956	−0.574779	−	0.818309i	$-0.694912\pi$
$887$	−30368.0	−1.14956	−0.574779	+	0.818309i	$0.694912\pi$
$888$	0	0
$889$	−4228.00	−0.159508
$890$	8800.00	0.331434
$891$	0	0
$892$	2772.00	0.104051
$893$	−3630.00	−0.136028
$894$	0	0
$895$	−740.000	−0.0276374
$896$	896.000	0.0334077
$897$	0	0
$898$	1390.00	0.0516536
$899$	16748.0	0.621332
$900$	0	0
$901$	−33864.0	−1.25213
$902$	−616.000	−0.0227390
$903$	0	0
$904$	2928.00	0.107725
$905$	6720.00	0.246829
$906$	0	0
$907$	−33874.0	−1.24010	−0.620048	−	0.784564i	$-0.712887\pi$
$907$	−33874.0	−1.24010	−0.620048	+	0.784564i	$0.712887\pi$
$908$	17116.0	0.625567
$909$	0	0
$910$	−490.000	−0.0178498
$911$	−24880.0	−0.904842	−0.452421	−	0.891804i	$-0.649440\pi$
$911$	−24880.0	−0.904842	−0.452421	+	0.891804i	$0.649440\pi$
$912$	0	0
$913$	−644.000	−0.0233442
$914$	−11520.0	−0.416901
$915$	0	0
$916$	−13264.0	−0.478444
$917$	20398.0	0.734571
$918$	0	0
$919$	−25299.0	−0.908092	−0.454046	−	0.890978i	$-0.650020\pi$
$919$	−25299.0	−0.908092	−0.454046	+	0.890978i	$0.650020\pi$
$920$	2000.00	0.0716718
$921$	0	0
$922$	26880.0	0.960136
$923$	−5208.00	−0.185724
$924$	0	0
$925$	−4750.00	−0.168842
$926$	14696.0	0.521534
$927$	0	0
$928$	2528.00	0.0894242
$929$	−6792.00	−0.239869	−0.119934	−	0.992782i	$-0.538268\pi$
$929$	−6792.00	−0.239869	−0.119934	+	0.992782i	$0.538268\pi$
$930$	0	0
$931$	1470.00	0.0517479
$932$	−15648.0	−0.549965
$933$	0	0
$934$	−35850.0	−1.25594
$935$	−255.000	−0.00891914
$936$	0	0
$937$	−43575.0	−1.51925	−0.759623	−	0.650364i	$-0.774616\pi$
$937$	−43575.0	−1.51925	−0.759623	+	0.650364i	$0.774616\pi$
$938$	14784.0	0.514621
$939$	0	0
$940$	2420.00	0.0839699
$941$	−45372.0	−1.57182	−0.785911	−	0.618339i	$-0.787806\pi$
$941$	−45372.0	−1.57182	−0.785911	+	0.618339i	$0.787806\pi$
$942$	0	0
$943$	15400.0	0.531806
$944$	−10048.0	−0.346435
$945$	0	0
$946$	−844.000	−0.0290072
$947$	39152.0	1.34347	0.671737	−	0.740790i	$-0.265549\pi$
$947$	39152.0	1.34347	0.671737	+	0.740790i	$0.265549\pi$
$948$	0	0
$949$	5082.00	0.173834
$950$	−1500.00	−0.0512278
$951$	0	0
$952$	2856.00	0.0972306
$953$	18632.0	0.633316	0.316658	−	0.948540i	$-0.397439\pi$
$953$	18632.0	0.633316	0.316658	+	0.948540i	$0.397439\pi$
$954$	0	0
$955$	−2805.00	−0.0950447
$956$	21804.0	0.737648
$957$	0	0
$958$	24692.0	0.832737
$959$	17976.0	0.605292
$960$	0	0
$961$	15153.0	0.508644
$962$	2660.00	0.0891495
$963$	0	0
$964$	1000.00	0.0334106
$965$	−15080.0	−0.503049
$966$	0	0
$967$	48862.0	1.62492	0.812459	−	0.583018i	$-0.198128\pi$
$967$	48862.0	1.62492	0.812459	+	0.583018i	$0.198128\pi$
$968$	10640.0	0.353288
$969$	0	0
$970$	−13510.0	−0.447196
$971$	−19896.0	−0.657562	−0.328781	−	0.944406i	$-0.606638\pi$
$971$	−19896.0	−0.657562	−0.328781	+	0.944406i	$0.606638\pi$
$972$	0	0
$973$	−8918.00	−0.293831
$974$	−30028.0	−0.987843
$975$	0	0
$976$	−10944.0	−0.358923
$977$	−5130.00	−0.167987	−0.0839935	−	0.996466i	$-0.526767\pi$
$977$	−5130.00	−0.167987	−0.0839935	+	0.996466i	$0.526767\pi$
$978$	0	0
$979$	880.000	0.0287282
$980$	−980.000	−0.0319438
$981$	0	0
$982$	−9446.00	−0.306959
$983$	11573.0	0.375505	0.187752	−	0.982216i	$-0.439880\pi$
$983$	11573.0	0.375505	0.187752	+	0.982216i	$0.439880\pi$
$984$	0	0
$985$	−16160.0	−0.522742
$986$	8058.00	0.260263
$987$	0	0
$988$	840.000	0.0270485
$989$	21100.0	0.678403
$990$	0	0
$991$	34600.0	1.10909	0.554544	−	0.832155i	$-0.312893\pi$
$991$	34600.0	1.10909	0.554544	+	0.832155i	$0.312893\pi$
$992$	6784.00	0.217129
$993$	0	0
$994$	−10416.0	−0.332370
$995$	5820.00	0.185434
$996$	0	0
$997$	−15199.0	−0.482806	−0.241403	−	0.970425i	$-0.577607\pi$
$997$	−15199.0	−0.482806	−0.241403	+	0.970425i	$0.577607\pi$
$998$	−22454.0	−0.712193
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.a.b.1.1		1
3.2	odd	2		70.4.a.e.1.1	✓	1
12.11	even	2		560.4.a.f.1.1		1
15.2	even	4		350.4.c.k.99.2		2
15.8	even	4		350.4.c.k.99.1		2
15.14	odd	2		350.4.a.c.1.1		1
21.2	odd	6		490.4.e.c.361.1		2
21.5	even	6		490.4.e.g.361.1		2
21.11	odd	6		490.4.e.c.471.1		2
21.17	even	6		490.4.e.g.471.1		2
21.20	even	2		490.4.a.j.1.1		1
24.5	odd	2		2240.4.a.h.1.1		1
24.11	even	2		2240.4.a.bc.1.1		1
105.104	even	2		2450.4.a.r.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.4.a.e.1.1	✓	1	3.2	odd	2
350.4.a.c.1.1		1	15.14	odd	2
350.4.c.k.99.1		2	15.8	even	4
350.4.c.k.99.2		2	15.2	even	4
490.4.a.j.1.1		1	21.20	even	2
490.4.e.c.361.1		2	21.2	odd	6
490.4.e.c.471.1		2	21.11	odd	6
490.4.e.g.361.1		2	21.5	even	6
490.4.e.g.471.1		2	21.17	even	6
560.4.a.f.1.1		1	12.11	even	2
630.4.a.b.1.1		1	1.1	even	1	trivial
2240.4.a.h.1.1		1	24.5	odd	2
2240.4.a.bc.1.1		1	24.11	even	2
2450.4.a.r.1.1		1	105.104	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	630.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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