LMFDB - Embedded newform 630.4.a.p.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,4,Mod(1,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [1,2,0,4,-5,0,7,8,0,-10,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$37.1712033036$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	630.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} +7.00000 q^{7} +8.00000 q^{8} -10.0000 q^{10} -24.0000 q^{11} +74.0000 q^{13} +14.0000 q^{14} +16.0000 q^{16} -24.0000 q^{17} -34.0000 q^{19} -20.0000 q^{20} -48.0000 q^{22} +168.000 q^{23} +25.0000 q^{25} +148.000 q^{26} +28.0000 q^{28} -162.000 q^{29} +128.000 q^{31} +32.0000 q^{32} -48.0000 q^{34} -35.0000 q^{35} +380.000 q^{37} -68.0000 q^{38} -40.0000 q^{40} +126.000 q^{41} -34.0000 q^{43} -96.0000 q^{44} +336.000 q^{46} +294.000 q^{47} +49.0000 q^{49} +50.0000 q^{50} +296.000 q^{52} +318.000 q^{53} +120.000 q^{55} +56.0000 q^{56} -324.000 q^{58} +444.000 q^{59} -592.000 q^{61} +256.000 q^{62} +64.0000 q^{64} -370.000 q^{65} +110.000 q^{67} -96.0000 q^{68} -70.0000 q^{70} -198.000 q^{71} +866.000 q^{73} +760.000 q^{74} -136.000 q^{76} -168.000 q^{77} +776.000 q^{79} -80.0000 q^{80} +252.000 q^{82} -576.000 q^{83} +120.000 q^{85} -68.0000 q^{86} -192.000 q^{88} -354.000 q^{89} +518.000 q^{91} +672.000 q^{92} +588.000 q^{94} +170.000 q^{95} +614.000 q^{97} +98.0000 q^{98} +O(q^{100})\)

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
$11$	−24.0000	−0.657843	−0.328921	−	0.944357i	$-0.606685\pi$
$11$	−24.0000	−0.657843	−0.328921	+	0.944357i	$0.606685\pi$
$12$	0	0
$13$	74.0000	1.57876	0.789381	−	0.613904i	$-0.210402\pi$
$13$	74.0000	1.57876	0.789381	+	0.613904i	$0.210402\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	−24.0000	−0.342403	−0.171202	−	0.985236i	$-0.554765\pi$
$17$	−24.0000	−0.342403	−0.171202	+	0.985236i	$0.554765\pi$
$18$	0	0
$19$	−34.0000	−0.410533	−0.205267	−	0.978706i	$-0.565806\pi$
$19$	−34.0000	−0.410533	−0.205267	+	0.978706i	$0.565806\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	−48.0000	−0.465165
$23$	168.000	1.52306	0.761531	−	0.648129i	$-0.224448\pi$
$23$	168.000	1.52306	0.761531	+	0.648129i	$0.224448\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	148.000	1.11635
$27$	0	0
$28$	28.0000	0.188982
$29$	−162.000	−1.03733	−0.518666	−	0.854977i	$-0.673571\pi$
$29$	−162.000	−1.03733	−0.518666	+	0.854977i	$0.673571\pi$
$30$	0	0
$31$	128.000	0.741596	0.370798	−	0.928714i	$-0.379084\pi$
$31$	128.000	0.741596	0.370798	+	0.928714i	$0.379084\pi$
$32$	32.0000	0.176777
$33$	0	0
$34$	−48.0000	−0.242116
$35$	−35.0000	−0.169031
$36$	0	0
$37$	380.000	1.68842	0.844211	−	0.536011i	$-0.180069\pi$
$37$	380.000	1.68842	0.844211	+	0.536011i	$0.180069\pi$
$38$	−68.0000	−0.290291
$39$	0	0
$40$	−40.0000	−0.158114
$41$	126.000	0.479949	0.239974	−	0.970779i	$-0.422861\pi$
$41$	126.000	0.479949	0.239974	+	0.970779i	$0.422861\pi$
$42$	0	0
$43$	−34.0000	−0.120580	−0.0602901	−	0.998181i	$-0.519203\pi$
$43$	−34.0000	−0.120580	−0.0602901	+	0.998181i	$0.519203\pi$
$44$	−96.0000	−0.328921
$45$	0	0
$46$	336.000	1.07697
$47$	294.000	0.912432	0.456216	−	0.889869i	$-0.349204\pi$
$47$	294.000	0.912432	0.456216	+	0.889869i	$0.349204\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	50.0000	0.141421
$51$	0	0
$52$	296.000	0.789381
$53$	318.000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	318.000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	120.000	0.294196
$56$	56.0000	0.133631
$57$	0	0
$58$	−324.000	−0.733505
$59$	444.000	0.979727	0.489863	−	0.871799i	$-0.337047\pi$
$59$	444.000	0.979727	0.489863	+	0.871799i	$0.337047\pi$
$60$	0	0
$61$	−592.000	−1.24259	−0.621294	−	0.783578i	$-0.713393\pi$
$61$	−592.000	−1.24259	−0.621294	+	0.783578i	$0.713393\pi$
$62$	256.000	0.524388
$63$	0	0
$64$	64.0000	0.125000
$65$	−370.000	−0.706044
$66$	0	0
$67$	110.000	0.200577	0.100288	−	0.994958i	$-0.468023\pi$
$67$	110.000	0.200577	0.100288	+	0.994958i	$0.468023\pi$
$68$	−96.0000	−0.171202
$69$	0	0
$70$	−70.0000	−0.119523
$71$	−198.000	−0.330962	−0.165481	−	0.986213i	$-0.552918\pi$
$71$	−198.000	−0.330962	−0.165481	+	0.986213i	$0.552918\pi$
$72$	0	0
$73$	866.000	1.38846	0.694230	−	0.719753i	$-0.255745\pi$
$73$	866.000	1.38846	0.694230	+	0.719753i	$0.255745\pi$
$74$	760.000	1.19389
$75$	0	0
$76$	−136.000	−0.205267
$77$	−168.000	−0.248641
$78$	0	0
$79$	776.000	1.10515	0.552575	−	0.833463i	$-0.313645\pi$
$79$	776.000	1.10515	0.552575	+	0.833463i	$0.313645\pi$
$80$	−80.0000	−0.111803
$81$	0	0
$82$	252.000	0.339375
$83$	−576.000	−0.761738	−0.380869	−	0.924629i	$-0.624375\pi$
$83$	−576.000	−0.761738	−0.380869	+	0.924629i	$0.624375\pi$
$84$	0	0
$85$	120.000	0.153127
$86$	−68.0000	−0.0852631
$87$	0	0
$88$	−192.000	−0.232583
$89$	−354.000	−0.421617	−0.210809	−	0.977527i	$-0.567610\pi$
$89$	−354.000	−0.421617	−0.210809	+	0.977527i	$0.567610\pi$
$90$	0	0
$91$	518.000	0.596716
$92$	672.000	0.761531
$93$	0	0
$94$	588.000	0.645187
$95$	170.000	0.183596
$96$	0	0
$97$	614.000	0.642704	0.321352	−	0.946960i	$-0.395863\pi$
$97$	614.000	0.642704	0.321352	+	0.946960i	$0.395863\pi$
$98$	98.0000	0.101015
$99$	0	0
$100$	100.000	0.100000
$101$	606.000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	606.000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	0	0
$103$	1928.00	1.84438	0.922192	−	0.386733i	$-0.126397\pi$
$103$	1928.00	1.84438	0.922192	+	0.386733i	$0.126397\pi$
$104$	592.000	0.558177
$105$	0	0
$106$	636.000	0.582772
$107$	−948.000	−0.856510	−0.428255	−	0.903658i	$-0.640872\pi$
$107$	−948.000	−0.856510	−0.428255	+	0.903658i	$0.640872\pi$
$108$	0	0
$109$	−34.0000	−0.0298772	−0.0149386	−	0.999888i	$-0.504755\pi$
$109$	−34.0000	−0.0298772	−0.0149386	+	0.999888i	$0.504755\pi$
$110$	240.000	0.208028
$111$	0	0
$112$	112.000	0.0944911
$113$	−2358.00	−1.96303	−0.981513	−	0.191395i	$-0.938699\pi$
$113$	−2358.00	−1.96303	−0.981513	+	0.191395i	$0.938699\pi$
$114$	0	0
$115$	−840.000	−0.681134
$116$	−648.000	−0.518666
$117$	0	0
$118$	888.000	0.692771
$119$	−168.000	−0.129416
$120$	0	0
$121$	−755.000	−0.567243
$122$	−1184.00	−0.878642
$123$	0	0
$124$	512.000	0.370798
$125$	−125.000	−0.0894427
$126$	0	0
$127$	128.000	0.0894344	0.0447172	−	0.999000i	$-0.485761\pi$
$127$	128.000	0.0894344	0.0447172	+	0.999000i	$0.485761\pi$
$128$	128.000	0.0883883
$129$	0	0
$130$	−740.000	−0.499248
$131$	−1020.00	−0.680289	−0.340144	−	0.940373i	$-0.610476\pi$
$131$	−1020.00	−0.680289	−0.340144	+	0.940373i	$0.610476\pi$
$132$	0	0
$133$	−238.000	−0.155167
$134$	220.000	0.141829
$135$	0	0
$136$	−192.000	−0.121058
$137$	−1914.00	−1.19361	−0.596803	−	0.802388i	$-0.703563\pi$
$137$	−1914.00	−1.19361	−0.596803	+	0.802388i	$0.703563\pi$
$138$	0	0
$139$	218.000	0.133025	0.0665127	−	0.997786i	$-0.478813\pi$
$139$	218.000	0.133025	0.0665127	+	0.997786i	$0.478813\pi$
$140$	−140.000	−0.0845154
$141$	0	0
$142$	−396.000	−0.234025
$143$	−1776.00	−1.03858
$144$	0	0
$145$	810.000	0.463909
$146$	1732.00	0.981790
$147$	0	0
$148$	1520.00	0.844211
$149$	1626.00	0.894007	0.447004	−	0.894532i	$-0.352491\pi$
$149$	1626.00	0.894007	0.447004	+	0.894532i	$0.352491\pi$
$150$	0	0
$151$	272.000	0.146590	0.0732949	−	0.997310i	$-0.476649\pi$
$151$	272.000	0.146590	0.0732949	+	0.997310i	$0.476649\pi$
$152$	−272.000	−0.145145
$153$	0	0
$154$	−336.000	−0.175816
$155$	−640.000	−0.331652
$156$	0	0
$157$	2774.00	1.41012	0.705061	−	0.709146i	$-0.250919\pi$
$157$	2774.00	1.41012	0.705061	+	0.709146i	$0.250919\pi$
$158$	1552.00	0.781459
$159$	0	0
$160$	−160.000	−0.0790569
$161$	1176.00	0.575663
$162$	0	0
$163$	−3418.00	−1.64244	−0.821222	−	0.570609i	$-0.806707\pi$
$163$	−3418.00	−1.64244	−0.821222	+	0.570609i	$0.806707\pi$
$164$	504.000	0.239974
$165$	0	0
$166$	−1152.00	−0.538630
$167$	1026.00	0.475415	0.237707	−	0.971337i	$-0.423604\pi$
$167$	1026.00	0.475415	0.237707	+	0.971337i	$0.423604\pi$
$168$	0	0
$169$	3279.00	1.49249
$170$	240.000	0.108277
$171$	0	0
$172$	−136.000	−0.0602901
$173$	2850.00	1.25249	0.626247	−	0.779625i	$-0.284590\pi$
$173$	2850.00	1.25249	0.626247	+	0.779625i	$0.284590\pi$
$174$	0	0
$175$	175.000	0.0755929
$176$	−384.000	−0.164461
$177$	0	0
$178$	−708.000	−0.298128
$179$	−2796.00	−1.16750	−0.583751	−	0.811933i	$-0.698416\pi$
$179$	−2796.00	−1.16750	−0.583751	+	0.811933i	$0.698416\pi$
$180$	0	0
$181$	488.000	0.200402	0.100201	−	0.994967i	$-0.468051\pi$
$181$	488.000	0.200402	0.100201	+	0.994967i	$0.468051\pi$
$182$	1036.00	0.421942
$183$	0	0
$184$	1344.00	0.538484
$185$	−1900.00	−0.755085
$186$	0	0
$187$	576.000	0.225248
$188$	1176.00	0.456216
$189$	0	0
$190$	340.000	0.129822
$191$	−2334.00	−0.884201	−0.442100	−	0.896966i	$-0.645766\pi$
$191$	−2334.00	−0.884201	−0.442100	+	0.896966i	$0.645766\pi$
$192$	0	0
$193$	−1762.00	−0.657158	−0.328579	−	0.944476i	$-0.606570\pi$
$193$	−1762.00	−0.657158	−0.328579	+	0.944476i	$0.606570\pi$
$194$	1228.00	0.454460
$195$	0	0
$196$	196.000	0.0714286
$197$	−4770.00	−1.72512	−0.862559	−	0.505956i	$-0.831140\pi$
$197$	−4770.00	−1.72512	−0.862559	+	0.505956i	$0.831140\pi$
$198$	0	0
$199$	92.0000	0.0327724	0.0163862	−	0.999866i	$-0.494784\pi$
$199$	92.0000	0.0327724	0.0163862	+	0.999866i	$0.494784\pi$
$200$	200.000	0.0707107
$201$	0	0
$202$	1212.00	0.422159
$203$	−1134.00	−0.392075
$204$	0	0
$205$	−630.000	−0.214640
$206$	3856.00	1.30418
$207$	0	0
$208$	1184.00	0.394691
$209$	816.000	0.270067
$210$	0	0
$211$	−5632.00	−1.83755	−0.918775	−	0.394783i	$-0.870820\pi$
$211$	−5632.00	−1.83755	−0.918775	+	0.394783i	$0.870820\pi$
$212$	1272.00	0.412082
$213$	0	0
$214$	−1896.00	−0.605644
$215$	170.000	0.0539251
$216$	0	0
$217$	896.000	0.280297
$218$	−68.0000	−0.0211263
$219$	0	0
$220$	480.000	0.147098
$221$	−1776.00	−0.540573
$222$	0	0
$223$	−1384.00	−0.415603	−0.207802	−	0.978171i	$-0.566631\pi$
$223$	−1384.00	−0.415603	−0.207802	+	0.978171i	$0.566631\pi$
$224$	224.000	0.0668153
$225$	0	0
$226$	−4716.00	−1.38807
$227$	−1428.00	−0.417532	−0.208766	−	0.977966i	$-0.566945\pi$
$227$	−1428.00	−0.417532	−0.208766	+	0.977966i	$0.566945\pi$
$228$	0	0
$229$	−2212.00	−0.638310	−0.319155	−	0.947702i	$-0.603399\pi$
$229$	−2212.00	−0.638310	−0.319155	+	0.947702i	$0.603399\pi$
$230$	−1680.00	−0.481634
$231$	0	0
$232$	−1296.00	−0.366752
$233$	1986.00	0.558400	0.279200	−	0.960233i	$-0.409931\pi$
$233$	1986.00	0.558400	0.279200	+	0.960233i	$0.409931\pi$
$234$	0	0
$235$	−1470.00	−0.408052
$236$	1776.00	0.489863
$237$	0	0
$238$	−336.000	−0.0915111
$239$	1062.00	0.287427	0.143714	−	0.989619i	$-0.454096\pi$
$239$	1062.00	0.287427	0.143714	+	0.989619i	$0.454096\pi$
$240$	0	0
$241$	−2158.00	−0.576801	−0.288400	−	0.957510i	$-0.593123\pi$
$241$	−2158.00	−0.576801	−0.288400	+	0.957510i	$0.593123\pi$
$242$	−1510.00	−0.401101
$243$	0	0
$244$	−2368.00	−0.621294
$245$	−245.000	−0.0638877
$246$	0	0
$247$	−2516.00	−0.648135
$248$	1024.00	0.262194
$249$	0	0
$250$	−250.000	−0.0632456
$251$	6444.00	1.62048	0.810242	−	0.586095i	$-0.199335\pi$
$251$	6444.00	1.62048	0.810242	+	0.586095i	$0.199335\pi$
$252$	0	0
$253$	−4032.00	−1.00194
$254$	256.000	0.0632396
$255$	0	0
$256$	256.000	0.0625000
$257$	−7716.00	−1.87280	−0.936402	−	0.350928i	$-0.885866\pi$
$257$	−7716.00	−1.87280	−0.936402	+	0.350928i	$0.885866\pi$
$258$	0	0
$259$	2660.00	0.638164
$260$	−1480.00	−0.353022
$261$	0	0
$262$	−2040.00	−0.481037
$263$	7716.00	1.80908	0.904542	−	0.426385i	$-0.140213\pi$
$263$	7716.00	1.80908	0.904542	+	0.426385i	$0.140213\pi$
$264$	0	0
$265$	−1590.00	−0.368577
$266$	−476.000	−0.109720
$267$	0	0
$268$	440.000	0.100288
$269$	−474.000	−0.107436	−0.0537180	−	0.998556i	$-0.517107\pi$
$269$	−474.000	−0.107436	−0.0537180	+	0.998556i	$0.517107\pi$
$270$	0	0
$271$	−3040.00	−0.681427	−0.340714	−	0.940167i	$-0.610669\pi$
$271$	−3040.00	−0.681427	−0.340714	+	0.940167i	$0.610669\pi$
$272$	−384.000	−0.0856008
$273$	0	0
$274$	−3828.00	−0.844007
$275$	−600.000	−0.131569
$276$	0	0
$277$	4736.00	1.02729	0.513644	−	0.858004i	$-0.328295\pi$
$277$	4736.00	1.02729	0.513644	+	0.858004i	$0.328295\pi$
$278$	436.000	0.0940631
$279$	0	0
$280$	−280.000	−0.0597614
$281$	−432.000	−0.0917116	−0.0458558	−	0.998948i	$-0.514601\pi$
$281$	−432.000	−0.0917116	−0.0458558	+	0.998948i	$0.514601\pi$
$282$	0	0
$283$	6428.00	1.35019	0.675097	−	0.737729i	$-0.264102\pi$
$283$	6428.00	1.35019	0.675097	+	0.737729i	$0.264102\pi$
$284$	−792.000	−0.165481
$285$	0	0
$286$	−3552.00	−0.734385
$287$	882.000	0.181404
$288$	0	0
$289$	−4337.00	−0.882760
$290$	1620.00	0.328033
$291$	0	0
$292$	3464.00	0.694230
$293$	−3546.00	−0.707029	−0.353515	−	0.935429i	$-0.615014\pi$
$293$	−3546.00	−0.707029	−0.353515	+	0.935429i	$0.615014\pi$
$294$	0	0
$295$	−2220.00	−0.438147
$296$	3040.00	0.596947
$297$	0	0
$298$	3252.00	0.632159
$299$	12432.0	2.40455
$300$	0	0
$301$	−238.000	−0.0455751
$302$	544.000	0.103655
$303$	0	0
$304$	−544.000	−0.102633
$305$	2960.00	0.555702
$306$	0	0
$307$	−4156.00	−0.772624	−0.386312	−	0.922368i	$-0.626251\pi$
$307$	−4156.00	−0.772624	−0.386312	+	0.922368i	$0.626251\pi$
$308$	−672.000	−0.124321
$309$	0	0
$310$	−1280.00	−0.234513
$311$	−6180.00	−1.12680	−0.563401	−	0.826183i	$-0.690508\pi$
$311$	−6180.00	−1.12680	−0.563401	+	0.826183i	$0.690508\pi$
$312$	0	0
$313$	−8422.00	−1.52089	−0.760447	−	0.649400i	$-0.775020\pi$
$313$	−8422.00	−1.52089	−0.760447	+	0.649400i	$0.775020\pi$
$314$	5548.00	0.997107
$315$	0	0
$316$	3104.00	0.552575
$317$	1338.00	0.237065	0.118532	−	0.992950i	$-0.462181\pi$
$317$	1338.00	0.237065	0.118532	+	0.992950i	$0.462181\pi$
$318$	0	0
$319$	3888.00	0.682402
$320$	−320.000	−0.0559017
$321$	0	0
$322$	2352.00	0.407055
$323$	816.000	0.140568
$324$	0	0
$325$	1850.00	0.315752
$326$	−6836.00	−1.16138
$327$	0	0
$328$	1008.00	0.169687
$329$	2058.00	0.344867
$330$	0	0
$331$	−3760.00	−0.624376	−0.312188	−	0.950020i	$-0.601062\pi$
$331$	−3760.00	−0.624376	−0.312188	+	0.950020i	$0.601062\pi$
$332$	−2304.00	−0.380869
$333$	0	0
$334$	2052.00	0.336169
$335$	−550.000	−0.0897006
$336$	0	0
$337$	3710.00	0.599693	0.299847	−	0.953987i	$-0.403065\pi$
$337$	3710.00	0.599693	0.299847	+	0.953987i	$0.403065\pi$
$338$	6558.00	1.05535
$339$	0	0
$340$	480.000	0.0765637
$341$	−3072.00	−0.487854
$342$	0	0
$343$	343.000	0.0539949
$344$	−272.000	−0.0426316
$345$	0	0
$346$	5700.00	0.885647
$347$	−8484.00	−1.31252	−0.656261	−	0.754534i	$-0.727863\pi$
$347$	−8484.00	−1.31252	−0.656261	+	0.754534i	$0.727863\pi$
$348$	0	0
$349$	−9484.00	−1.45463	−0.727316	−	0.686302i	$-0.759233\pi$
$349$	−9484.00	−1.45463	−0.727316	+	0.686302i	$0.759233\pi$
$350$	350.000	0.0534522
$351$	0	0
$352$	−768.000	−0.116291
$353$	−7260.00	−1.09465	−0.547324	−	0.836921i	$-0.684353\pi$
$353$	−7260.00	−1.09465	−0.547324	+	0.836921i	$0.684353\pi$
$354$	0	0
$355$	990.000	0.148011
$356$	−1416.00	−0.210809
$357$	0	0
$358$	−5592.00	−0.825549
$359$	8646.00	1.27108	0.635541	−	0.772067i	$-0.280777\pi$
$359$	8646.00	1.27108	0.635541	+	0.772067i	$0.280777\pi$
$360$	0	0
$361$	−5703.00	−0.831462
$362$	976.000	0.141706
$363$	0	0
$364$	2072.00	0.298358
$365$	−4330.00	−0.620939
$366$	0	0
$367$	−4696.00	−0.667927	−0.333963	−	0.942586i	$-0.608386\pi$
$367$	−4696.00	−0.667927	−0.333963	+	0.942586i	$0.608386\pi$
$368$	2688.00	0.380765
$369$	0	0
$370$	−3800.00	−0.533926
$371$	2226.00	0.311504
$372$	0	0
$373$	−2212.00	−0.307059	−0.153530	−	0.988144i	$-0.549064\pi$
$373$	−2212.00	−0.307059	−0.153530	+	0.988144i	$0.549064\pi$
$374$	1152.00	0.159274
$375$	0	0
$376$	2352.00	0.322593
$377$	−11988.0	−1.63770
$378$	0	0
$379$	1280.00	0.173481	0.0867403	−	0.996231i	$-0.472355\pi$
$379$	1280.00	0.173481	0.0867403	+	0.996231i	$0.472355\pi$
$380$	680.000	0.0917981
$381$	0	0
$382$	−4668.00	−0.625224
$383$	12390.0	1.65300	0.826501	−	0.562936i	$-0.190328\pi$
$383$	12390.0	1.65300	0.826501	+	0.562936i	$0.190328\pi$
$384$	0	0
$385$	840.000	0.111196
$386$	−3524.00	−0.464681
$387$	0	0
$388$	2456.00	0.321352
$389$	8346.00	1.08781	0.543906	−	0.839146i	$-0.316945\pi$
$389$	8346.00	1.08781	0.543906	+	0.839146i	$0.316945\pi$
$390$	0	0
$391$	−4032.00	−0.521501
$392$	392.000	0.0505076
$393$	0	0
$394$	−9540.00	−1.21984
$395$	−3880.00	−0.494238
$396$	0	0
$397$	3602.00	0.455363	0.227682	−	0.973736i	$-0.426885\pi$
$397$	3602.00	0.455363	0.227682	+	0.973736i	$0.426885\pi$
$398$	184.000	0.0231736
$399$	0	0
$400$	400.000	0.0500000
$401$	−2784.00	−0.346699	−0.173350	−	0.984860i	$-0.555459\pi$
$401$	−2784.00	−0.346699	−0.173350	+	0.984860i	$0.555459\pi$
$402$	0	0
$403$	9472.00	1.17080
$404$	2424.00	0.298511
$405$	0	0
$406$	−2268.00	−0.277239
$407$	−9120.00	−1.11072
$408$	0	0
$409$	14690.0	1.77597	0.887987	−	0.459868i	$-0.152103\pi$
$409$	14690.0	1.77597	0.887987	+	0.459868i	$0.152103\pi$
$410$	−1260.00	−0.151773
$411$	0	0
$412$	7712.00	0.922192
$413$	3108.00	0.370302
$414$	0	0
$415$	2880.00	0.340659
$416$	2368.00	0.279088
$417$	0	0
$418$	1632.00	0.190966
$419$	5076.00	0.591835	0.295917	−	0.955214i	$-0.404375\pi$
$419$	5076.00	0.591835	0.295917	+	0.955214i	$0.404375\pi$
$420$	0	0
$421$	−5362.00	−0.620731	−0.310366	−	0.950617i	$-0.600451\pi$
$421$	−5362.00	−0.620731	−0.310366	+	0.950617i	$0.600451\pi$
$422$	−11264.0	−1.29934
$423$	0	0
$424$	2544.00	0.291386
$425$	−600.000	−0.0684806
$426$	0	0
$427$	−4144.00	−0.469654
$428$	−3792.00	−0.428255
$429$	0	0
$430$	340.000	0.0381308
$431$	4746.00	0.530410	0.265205	−	0.964192i	$-0.414560\pi$
$431$	4746.00	0.530410	0.265205	+	0.964192i	$0.414560\pi$
$432$	0	0
$433$	−1186.00	−0.131629	−0.0658147	−	0.997832i	$-0.520965\pi$
$433$	−1186.00	−0.131629	−0.0658147	+	0.997832i	$0.520965\pi$
$434$	1792.00	0.198200
$435$	0	0
$436$	−136.000	−0.0149386
$437$	−5712.00	−0.625268
$438$	0	0
$439$	17120.0	1.86126	0.930630	−	0.365962i	$-0.119260\pi$
$439$	17120.0	1.86126	0.930630	+	0.365962i	$0.119260\pi$
$440$	960.000	0.104014
$441$	0	0
$442$	−3552.00	−0.382243
$443$	4164.00	0.446586	0.223293	−	0.974751i	$-0.428319\pi$
$443$	4164.00	0.446586	0.223293	+	0.974751i	$0.428319\pi$
$444$	0	0
$445$	1770.00	0.188553
$446$	−2768.00	−0.293876
$447$	0	0
$448$	448.000	0.0472456
$449$	−7380.00	−0.775688	−0.387844	−	0.921725i	$-0.626780\pi$
$449$	−7380.00	−0.775688	−0.387844	+	0.921725i	$0.626780\pi$
$450$	0	0
$451$	−3024.00	−0.315731
$452$	−9432.00	−0.981513
$453$	0	0
$454$	−2856.00	−0.295239
$455$	−2590.00	−0.266860
$456$	0	0
$457$	−19366.0	−1.98228	−0.991141	−	0.132811i	$-0.957600\pi$
$457$	−19366.0	−1.98228	−0.991141	+	0.132811i	$0.957600\pi$
$458$	−4424.00	−0.451354
$459$	0	0
$460$	−3360.00	−0.340567
$461$	1494.00	0.150938	0.0754691	−	0.997148i	$-0.475955\pi$
$461$	1494.00	0.150938	0.0754691	+	0.997148i	$0.475955\pi$
$462$	0	0
$463$	−5452.00	−0.547248	−0.273624	−	0.961837i	$-0.588222\pi$
$463$	−5452.00	−0.547248	−0.273624	+	0.961837i	$0.588222\pi$
$464$	−2592.00	−0.259333
$465$	0	0
$466$	3972.00	0.394848
$467$	11400.0	1.12961	0.564806	−	0.825224i	$-0.308951\pi$
$467$	11400.0	1.12961	0.564806	+	0.825224i	$0.308951\pi$
$468$	0	0
$469$	770.000	0.0758109
$470$	−2940.00	−0.288536
$471$	0	0
$472$	3552.00	0.346386
$473$	816.000	0.0793229
$474$	0	0
$475$	−850.000	−0.0821067
$476$	−672.000	−0.0647081
$477$	0	0
$478$	2124.00	0.203242
$479$	6780.00	0.646735	0.323368	−	0.946273i	$-0.395185\pi$
$479$	6780.00	0.646735	0.323368	+	0.946273i	$0.395185\pi$
$480$	0	0
$481$	28120.0	2.66562
$482$	−4316.00	−0.407860
$483$	0	0
$484$	−3020.00	−0.283621
$485$	−3070.00	−0.287426
$486$	0	0
$487$	3008.00	0.279888	0.139944	−	0.990159i	$-0.455308\pi$
$487$	3008.00	0.279888	0.139944	+	0.990159i	$0.455308\pi$
$488$	−4736.00	−0.439321
$489$	0	0
$490$	−490.000	−0.0451754
$491$	−2556.00	−0.234930	−0.117465	−	0.993077i	$-0.537477\pi$
$491$	−2556.00	−0.234930	−0.117465	+	0.993077i	$0.537477\pi$
$492$	0	0
$493$	3888.00	0.355186
$494$	−5032.00	−0.458300
$495$	0	0
$496$	2048.00	0.185399
$497$	−1386.00	−0.125092
$498$	0	0
$499$	−4264.00	−0.382531	−0.191265	−	0.981538i	$-0.561259\pi$
$499$	−4264.00	−0.382531	−0.191265	+	0.981538i	$0.561259\pi$
$500$	−500.000	−0.0447214
$501$	0	0
$502$	12888.0	1.14586
$503$	9450.00	0.837683	0.418842	−	0.908059i	$-0.362436\pi$
$503$	9450.00	0.837683	0.418842	+	0.908059i	$0.362436\pi$
$504$	0	0
$505$	−3030.00	−0.266996
$506$	−8064.00	−0.708475
$507$	0	0
$508$	512.000	0.0447172
$509$	−9246.00	−0.805151	−0.402575	−	0.915387i	$-0.631885\pi$
$509$	−9246.00	−0.805151	−0.402575	+	0.915387i	$0.631885\pi$
$510$	0	0
$511$	6062.00	0.524789
$512$	512.000	0.0441942
$513$	0	0
$514$	−15432.0	−1.32427
$515$	−9640.00	−0.824833
$516$	0	0
$517$	−7056.00	−0.600237
$518$	5320.00	0.451250
$519$	0	0
$520$	−2960.00	−0.249624
$521$	5718.00	0.480826	0.240413	−	0.970671i	$-0.422717\pi$
$521$	5718.00	0.480826	0.240413	+	0.970671i	$0.422717\pi$
$522$	0	0
$523$	3872.00	0.323730	0.161865	−	0.986813i	$-0.448249\pi$
$523$	3872.00	0.323730	0.161865	+	0.986813i	$0.448249\pi$
$524$	−4080.00	−0.340144
$525$	0	0
$526$	15432.0	1.27922
$527$	−3072.00	−0.253925
$528$	0	0
$529$	16057.0	1.31972
$530$	−3180.00	−0.260623
$531$	0	0
$532$	−952.000	−0.0775835
$533$	9324.00	0.757725
$534$	0	0
$535$	4740.00	0.383043
$536$	880.000	0.0709146
$537$	0	0
$538$	−948.000	−0.0759687
$539$	−1176.00	−0.0939776
$540$	0	0
$541$	−22822.0	−1.81367	−0.906834	−	0.421488i	$-0.861508\pi$
$541$	−22822.0	−1.81367	−0.906834	+	0.421488i	$0.861508\pi$
$542$	−6080.00	−0.481842
$543$	0	0
$544$	−768.000	−0.0605289
$545$	170.000	0.0133615
$546$	0	0
$547$	20918.0	1.63508	0.817540	−	0.575871i	$-0.195337\pi$
$547$	20918.0	1.63508	0.817540	+	0.575871i	$0.195337\pi$
$548$	−7656.00	−0.596803
$549$	0	0
$550$	−1200.00	−0.0930330
$551$	5508.00	0.425860
$552$	0	0
$553$	5432.00	0.417707
$554$	9472.00	0.726402
$555$	0	0
$556$	872.000	0.0665127
$557$	−5334.00	−0.405761	−0.202880	−	0.979204i	$-0.565030\pi$
$557$	−5334.00	−0.405761	−0.202880	+	0.979204i	$0.565030\pi$
$558$	0	0
$559$	−2516.00	−0.190368
$560$	−560.000	−0.0422577
$561$	0	0
$562$	−864.000	−0.0648499
$563$	19308.0	1.44536	0.722678	−	0.691185i	$-0.242911\pi$
$563$	19308.0	1.44536	0.722678	+	0.691185i	$0.242911\pi$
$564$	0	0
$565$	11790.0	0.877892
$566$	12856.0	0.954731
$567$	0	0
$568$	−1584.00	−0.117013
$569$	18744.0	1.38100	0.690500	−	0.723332i	$-0.257390\pi$
$569$	18744.0	1.38100	0.690500	+	0.723332i	$0.257390\pi$
$570$	0	0
$571$	23276.0	1.70590	0.852951	−	0.521991i	$-0.174810\pi$
$571$	23276.0	1.70590	0.852951	+	0.521991i	$0.174810\pi$
$572$	−7104.00	−0.519289
$573$	0	0
$574$	1764.00	0.128272
$575$	4200.00	0.304612
$576$	0	0
$577$	15698.0	1.13261	0.566305	−	0.824196i	$-0.308372\pi$
$577$	15698.0	1.13261	0.566305	+	0.824196i	$0.308372\pi$
$578$	−8674.00	−0.624206
$579$	0	0
$580$	3240.00	0.231955
$581$	−4032.00	−0.287910
$582$	0	0
$583$	−7632.00	−0.542170
$584$	6928.00	0.490895
$585$	0	0
$586$	−7092.00	−0.499945
$587$	−16164.0	−1.13656	−0.568279	−	0.822836i	$-0.692391\pi$
$587$	−16164.0	−1.13656	−0.568279	+	0.822836i	$0.692391\pi$
$588$	0	0
$589$	−4352.00	−0.304450
$590$	−4440.00	−0.309817
$591$	0	0
$592$	6080.00	0.422106
$593$	4416.00	0.305807	0.152903	−	0.988241i	$-0.451138\pi$
$593$	4416.00	0.305807	0.152903	+	0.988241i	$0.451138\pi$
$594$	0	0
$595$	840.000	0.0578767
$596$	6504.00	0.447004
$597$	0	0
$598$	24864.0	1.70028
$599$	17274.0	1.17829	0.589146	−	0.808027i	$-0.299464\pi$
$599$	17274.0	1.17829	0.589146	+	0.808027i	$0.299464\pi$
$600$	0	0
$601$	17930.0	1.21694	0.608469	−	0.793578i	$-0.291784\pi$
$601$	17930.0	1.21694	0.608469	+	0.793578i	$0.291784\pi$
$602$	−476.000	−0.0322264
$603$	0	0
$604$	1088.00	0.0732949
$605$	3775.00	0.253679
$606$	0	0
$607$	14456.0	0.966641	0.483320	−	0.875444i	$-0.339431\pi$
$607$	14456.0	0.966641	0.483320	+	0.875444i	$0.339431\pi$
$608$	−1088.00	−0.0725727
$609$	0	0
$610$	5920.00	0.392941
$611$	21756.0	1.44051
$612$	0	0
$613$	−556.000	−0.0366340	−0.0183170	−	0.999832i	$-0.505831\pi$
$613$	−556.000	−0.0366340	−0.0183170	+	0.999832i	$0.505831\pi$
$614$	−8312.00	−0.546327
$615$	0	0
$616$	−1344.00	−0.0879080
$617$	−8118.00	−0.529689	−0.264845	−	0.964291i	$-0.585321\pi$
$617$	−8118.00	−0.529689	−0.264845	+	0.964291i	$0.585321\pi$
$618$	0	0
$619$	23006.0	1.49384	0.746922	−	0.664912i	$-0.231531\pi$
$619$	23006.0	1.49384	0.746922	+	0.664912i	$0.231531\pi$
$620$	−2560.00	−0.165826
$621$	0	0
$622$	−12360.0	−0.796770
$623$	−2478.00	−0.159356
$624$	0	0
$625$	625.000	0.0400000
$626$	−16844.0	−1.07543
$627$	0	0
$628$	11096.0	0.705061
$629$	−9120.00	−0.578121
$630$	0	0
$631$	−10312.0	−0.650577	−0.325289	−	0.945615i	$-0.605461\pi$
$631$	−10312.0	−0.650577	−0.325289	+	0.945615i	$0.605461\pi$
$632$	6208.00	0.390729
$633$	0	0
$634$	2676.00	0.167630
$635$	−640.000	−0.0399963
$636$	0	0
$637$	3626.00	0.225537
$638$	7776.00	0.482531
$639$	0	0
$640$	−640.000	−0.0395285
$641$	27876.0	1.71768	0.858842	−	0.512240i	$-0.171184\pi$
$641$	27876.0	1.71768	0.858842	+	0.512240i	$0.171184\pi$
$642$	0	0
$643$	−29536.0	−1.81149	−0.905743	−	0.423826i	$-0.860687\pi$
$643$	−29536.0	−1.81149	−0.905743	+	0.423826i	$0.860687\pi$
$644$	4704.00	0.287832
$645$	0	0
$646$	1632.00	0.0993966
$647$	−11994.0	−0.728799	−0.364399	−	0.931243i	$-0.618726\pi$
$647$	−11994.0	−0.728799	−0.364399	+	0.931243i	$0.618726\pi$
$648$	0	0
$649$	−10656.0	−0.644506
$650$	3700.00	0.223271
$651$	0	0
$652$	−13672.0	−0.821222
$653$	−15798.0	−0.946744	−0.473372	−	0.880863i	$-0.656963\pi$
$653$	−15798.0	−0.946744	−0.473372	+	0.880863i	$0.656963\pi$
$654$	0	0
$655$	5100.00	0.304234
$656$	2016.00	0.119987
$657$	0	0
$658$	4116.00	0.243858
$659$	23256.0	1.37470	0.687348	−	0.726328i	$-0.258775\pi$
$659$	23256.0	1.37470	0.687348	+	0.726328i	$0.258775\pi$
$660$	0	0
$661$	7328.00	0.431204	0.215602	−	0.976481i	$-0.430829\pi$
$661$	7328.00	0.431204	0.215602	+	0.976481i	$0.430829\pi$
$662$	−7520.00	−0.441500
$663$	0	0
$664$	−4608.00	−0.269315
$665$	1190.00	0.0693928
$666$	0	0
$667$	−27216.0	−1.57992
$668$	4104.00	0.237707
$669$	0	0
$670$	−1100.00	−0.0634279
$671$	14208.0	0.817427
$672$	0	0
$673$	−9898.00	−0.566924	−0.283462	−	0.958983i	$-0.591483\pi$
$673$	−9898.00	−0.566924	−0.283462	+	0.958983i	$0.591483\pi$
$674$	7420.00	0.424047
$675$	0	0
$676$	13116.0	0.746245
$677$	5514.00	0.313028	0.156514	−	0.987676i	$-0.449974\pi$
$677$	5514.00	0.313028	0.156514	+	0.987676i	$0.449974\pi$
$678$	0	0
$679$	4298.00	0.242919
$680$	960.000	0.0541387
$681$	0	0
$682$	−6144.00	−0.344965
$683$	−8196.00	−0.459167	−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−8196.00	−0.459167	−0.229584	+	0.973289i	$0.573736\pi$
$684$	0	0
$685$	9570.00	0.533797
$686$	686.000	0.0381802
$687$	0	0
$688$	−544.000	−0.0301451
$689$	23532.0	1.30116
$690$	0	0
$691$	−1978.00	−0.108895	−0.0544477	−	0.998517i	$-0.517340\pi$
$691$	−1978.00	−0.108895	−0.0544477	+	0.998517i	$0.517340\pi$
$692$	11400.0	0.626247
$693$	0	0
$694$	−16968.0	−0.928093
$695$	−1090.00	−0.0594907
$696$	0	0
$697$	−3024.00	−0.164336
$698$	−18968.0	−1.02858
$699$	0	0
$700$	700.000	0.0377964
$701$	−28602.0	−1.54106	−0.770530	−	0.637404i	$-0.780008\pi$
$701$	−28602.0	−1.54106	−0.770530	+	0.637404i	$0.780008\pi$
$702$	0	0
$703$	−12920.0	−0.693154
$704$	−1536.00	−0.0822304
$705$	0	0
$706$	−14520.0	−0.774033
$707$	4242.00	0.225653
$708$	0	0
$709$	15122.0	0.801014	0.400507	−	0.916294i	$-0.368834\pi$
$709$	15122.0	0.801014	0.400507	+	0.916294i	$0.368834\pi$
$710$	1980.00	0.104659
$711$	0	0
$712$	−2832.00	−0.149064
$713$	21504.0	1.12950
$714$	0	0
$715$	8880.00	0.464466
$716$	−11184.0	−0.583751
$717$	0	0
$718$	17292.0	0.898791
$719$	32460.0	1.68366	0.841832	−	0.539740i	$-0.181478\pi$
$719$	32460.0	1.68366	0.841832	+	0.539740i	$0.181478\pi$
$720$	0	0
$721$	13496.0	0.697111
$722$	−11406.0	−0.587933
$723$	0	0
$724$	1952.00	0.100201
$725$	−4050.00	−0.207467
$726$	0	0
$727$	−17224.0	−0.878683	−0.439342	−	0.898320i	$-0.644788\pi$
$727$	−17224.0	−0.878683	−0.439342	+	0.898320i	$0.644788\pi$
$728$	4144.00	0.210971
$729$	0	0
$730$	−8660.00	−0.439070
$731$	816.000	0.0412871
$732$	0	0
$733$	9218.00	0.464495	0.232247	−	0.972657i	$-0.425392\pi$
$733$	9218.00	0.464495	0.232247	+	0.972657i	$0.425392\pi$
$734$	−9392.00	−0.472296
$735$	0	0
$736$	5376.00	0.269242
$737$	−2640.00	−0.131948
$738$	0	0
$739$	−5128.00	−0.255259	−0.127630	−	0.991822i	$-0.540737\pi$
$739$	−5128.00	−0.255259	−0.127630	+	0.991822i	$0.540737\pi$
$740$	−7600.00	−0.377543
$741$	0	0
$742$	4452.00	0.220267
$743$	2520.00	0.124428	0.0622139	−	0.998063i	$-0.480184\pi$
$743$	2520.00	0.124428	0.0622139	+	0.998063i	$0.480184\pi$
$744$	0	0
$745$	−8130.00	−0.399812
$746$	−4424.00	−0.217124
$747$	0	0
$748$	2304.00	0.112624
$749$	−6636.00	−0.323731
$750$	0	0
$751$	4520.00	0.219623	0.109812	−	0.993952i	$-0.464975\pi$
$751$	4520.00	0.219623	0.109812	+	0.993952i	$0.464975\pi$
$752$	4704.00	0.228108
$753$	0	0
$754$	−23976.0	−1.15803
$755$	−1360.00	−0.0655569
$756$	0	0
$757$	−37420.0	−1.79664	−0.898318	−	0.439346i	$-0.855210\pi$
$757$	−37420.0	−1.79664	−0.898318	+	0.439346i	$0.855210\pi$
$758$	2560.00	0.122669
$759$	0	0
$760$	1360.00	0.0649110
$761$	6162.00	0.293525	0.146762	−	0.989172i	$-0.453115\pi$
$761$	6162.00	0.293525	0.146762	+	0.989172i	$0.453115\pi$
$762$	0	0
$763$	−238.000	−0.0112925
$764$	−9336.00	−0.442100
$765$	0	0
$766$	24780.0	1.16885
$767$	32856.0	1.54676
$768$	0	0
$769$	15806.0	0.741195	0.370597	−	0.928794i	$-0.379153\pi$
$769$	15806.0	0.741195	0.370597	+	0.928794i	$0.379153\pi$
$770$	1680.00	0.0786273
$771$	0	0
$772$	−7048.00	−0.328579
$773$	−36978.0	−1.72058	−0.860289	−	0.509807i	$-0.829717\pi$
$773$	−36978.0	−1.72058	−0.860289	+	0.509807i	$0.829717\pi$
$774$	0	0
$775$	3200.00	0.148319
$776$	4912.00	0.227230
$777$	0	0
$778$	16692.0	0.769199
$779$	−4284.00	−0.197035
$780$	0	0
$781$	4752.00	0.217721
$782$	−8064.00	−0.368757
$783$	0	0
$784$	784.000	0.0357143
$785$	−13870.0	−0.630626
$786$	0	0
$787$	16436.0	0.744447	0.372224	−	0.928143i	$-0.378595\pi$
$787$	16436.0	0.744447	0.372224	+	0.928143i	$0.378595\pi$
$788$	−19080.0	−0.862559
$789$	0	0
$790$	−7760.00	−0.349479
$791$	−16506.0	−0.741954
$792$	0	0
$793$	−43808.0	−1.96175
$794$	7204.00	0.321990
$795$	0	0
$796$	368.000	0.0163862
$797$	−33750.0	−1.49998	−0.749991	−	0.661448i	$-0.769942\pi$
$797$	−33750.0	−1.49998	−0.749991	+	0.661448i	$0.769942\pi$
$798$	0	0
$799$	−7056.00	−0.312420
$800$	800.000	0.0353553
$801$	0	0
$802$	−5568.00	−0.245153
$803$	−20784.0	−0.913389
$804$	0	0
$805$	−5880.00	−0.257444
$806$	18944.0	0.827883
$807$	0	0
$808$	4848.00	0.211079
$809$	−4272.00	−0.185656	−0.0928279	−	0.995682i	$-0.529591\pi$
$809$	−4272.00	−0.185656	−0.0928279	+	0.995682i	$0.529591\pi$
$810$	0	0
$811$	−27430.0	−1.18767	−0.593833	−	0.804588i	$-0.702386\pi$
$811$	−27430.0	−1.18767	−0.593833	+	0.804588i	$0.702386\pi$
$812$	−4536.00	−0.196037
$813$	0	0
$814$	−18240.0	−0.785395
$815$	17090.0	0.734523
$816$	0	0
$817$	1156.00	0.0495022
$818$	29380.0	1.25580
$819$	0	0
$820$	−2520.00	−0.107320
$821$	−19722.0	−0.838371	−0.419185	−	0.907901i	$-0.637684\pi$
$821$	−19722.0	−0.838371	−0.419185	+	0.907901i	$0.637684\pi$
$822$	0	0
$823$	−12292.0	−0.520622	−0.260311	−	0.965525i	$-0.583825\pi$
$823$	−12292.0	−0.520622	−0.260311	+	0.965525i	$0.583825\pi$
$824$	15424.0	0.652088
$825$	0	0
$826$	6216.00	0.261843
$827$	40212.0	1.69082	0.845410	−	0.534118i	$-0.179356\pi$
$827$	40212.0	1.69082	0.845410	+	0.534118i	$0.179356\pi$
$828$	0	0
$829$	−3940.00	−0.165069	−0.0825343	−	0.996588i	$-0.526301\pi$
$829$	−3940.00	−0.165069	−0.0825343	+	0.996588i	$0.526301\pi$
$830$	5760.00	0.240883
$831$	0	0
$832$	4736.00	0.197345
$833$	−1176.00	−0.0489147
$834$	0	0
$835$	−5130.00	−0.212612
$836$	3264.00	0.135033
$837$	0	0
$838$	10152.0	0.418490
$839$	−288.000	−0.0118509	−0.00592543	−	0.999982i	$-0.501886\pi$
$839$	−288.000	−0.0118509	−0.00592543	+	0.999982i	$0.501886\pi$
$840$	0	0
$841$	1855.00	0.0760589
$842$	−10724.0	−0.438923
$843$	0	0
$844$	−22528.0	−0.918775
$845$	−16395.0	−0.667462
$846$	0	0
$847$	−5285.00	−0.214398
$848$	5088.00	0.206041
$849$	0	0
$850$	−1200.00	−0.0484231
$851$	63840.0	2.57157
$852$	0	0
$853$	−13966.0	−0.560594	−0.280297	−	0.959913i	$-0.590433\pi$
$853$	−13966.0	−0.560594	−0.280297	+	0.959913i	$0.590433\pi$
$854$	−8288.00	−0.332095
$855$	0	0
$856$	−7584.00	−0.302822
$857$	−36708.0	−1.46315	−0.731576	−	0.681760i	$-0.761215\pi$
$857$	−36708.0	−1.46315	−0.731576	+	0.681760i	$0.761215\pi$
$858$	0	0
$859$	−19906.0	−0.790668	−0.395334	−	0.918537i	$-0.629371\pi$
$859$	−19906.0	−0.790668	−0.395334	+	0.918537i	$0.629371\pi$
$860$	680.000	0.0269626
$861$	0	0
$862$	9492.00	0.375057
$863$	5244.00	0.206846	0.103423	−	0.994637i	$-0.467021\pi$
$863$	5244.00	0.206846	0.103423	+	0.994637i	$0.467021\pi$
$864$	0	0
$865$	−14250.0	−0.560132
$866$	−2372.00	−0.0930760
$867$	0	0
$868$	3584.00	0.140148
$869$	−18624.0	−0.727015
$870$	0	0
$871$	8140.00	0.316663
$872$	−272.000	−0.0105632
$873$	0	0
$874$	−11424.0	−0.442131
$875$	−875.000	−0.0338062
$876$	0	0
$877$	−26656.0	−1.02635	−0.513175	−	0.858284i	$-0.671531\pi$
$877$	−26656.0	−1.02635	−0.513175	+	0.858284i	$0.671531\pi$
$878$	34240.0	1.31611
$879$	0	0
$880$	1920.00	0.0735491
$881$	−34182.0	−1.30717	−0.653587	−	0.756851i	$-0.726737\pi$
$881$	−34182.0	−1.30717	−0.653587	+	0.756851i	$0.726737\pi$
$882$	0	0
$883$	−7522.00	−0.286677	−0.143338	−	0.989674i	$-0.545784\pi$
$883$	−7522.00	−0.286677	−0.143338	+	0.989674i	$0.545784\pi$
$884$	−7104.00	−0.270287
$885$	0	0
$886$	8328.00	0.315784
$887$	−33294.0	−1.26032	−0.630160	−	0.776466i	$-0.717011\pi$
$887$	−33294.0	−1.26032	−0.630160	+	0.776466i	$0.717011\pi$
$888$	0	0
$889$	896.000	0.0338030
$890$	3540.00	0.133327
$891$	0	0
$892$	−5536.00	−0.207802
$893$	−9996.00	−0.374584
$894$	0	0
$895$	13980.0	0.522123
$896$	896.000	0.0334077
$897$	0	0
$898$	−14760.0	−0.548494
$899$	−20736.0	−0.769282
$900$	0	0
$901$	−7632.00	−0.282196
$902$	−6048.00	−0.223255
$903$	0	0
$904$	−18864.0	−0.694035
$905$	−2440.00	−0.0896225
$906$	0	0
$907$	−30274.0	−1.10830	−0.554152	−	0.832416i	$-0.686957\pi$
$907$	−30274.0	−1.10830	−0.554152	+	0.832416i	$0.686957\pi$
$908$	−5712.00	−0.208766
$909$	0	0
$910$	−5180.00	−0.188698
$911$	9954.00	0.362010	0.181005	−	0.983482i	$-0.442065\pi$
$911$	9954.00	0.362010	0.181005	+	0.983482i	$0.442065\pi$
$912$	0	0
$913$	13824.0	0.501104
$914$	−38732.0	−1.40169
$915$	0	0
$916$	−8848.00	−0.319155
$917$	−7140.00	−0.257125
$918$	0	0
$919$	−43000.0	−1.54346	−0.771730	−	0.635951i	$-0.780608\pi$
$919$	−43000.0	−1.54346	−0.771730	+	0.635951i	$0.780608\pi$
$920$	−6720.00	−0.240817
$921$	0	0
$922$	2988.00	0.106729
$923$	−14652.0	−0.522510
$924$	0	0
$925$	9500.00	0.337684
$926$	−10904.0	−0.386963
$927$	0	0
$928$	−5184.00	−0.183376
$929$	−18534.0	−0.654554	−0.327277	−	0.944928i	$-0.606131\pi$
$929$	−18534.0	−0.654554	−0.327277	+	0.944928i	$0.606131\pi$
$930$	0	0
$931$	−1666.00	−0.0586476
$932$	7944.00	0.279200
$933$	0	0
$934$	22800.0	0.798757
$935$	−2880.00	−0.100734
$936$	0	0
$937$	−6586.00	−0.229621	−0.114811	−	0.993387i	$-0.536626\pi$
$937$	−6586.00	−0.229621	−0.114811	+	0.993387i	$0.536626\pi$
$938$	1540.00	0.0536064
$939$	0	0
$940$	−5880.00	−0.204026
$941$	−13650.0	−0.472877	−0.236439	−	0.971646i	$-0.575980\pi$
$941$	−13650.0	−0.472877	−0.236439	+	0.971646i	$0.575980\pi$
$942$	0	0
$943$	21168.0	0.730991
$944$	7104.00	0.244932
$945$	0	0
$946$	1632.00	0.0560897
$947$	35484.0	1.21761	0.608804	−	0.793321i	$-0.291650\pi$
$947$	35484.0	1.21761	0.608804	+	0.793321i	$0.291650\pi$
$948$	0	0
$949$	64084.0	2.19205
$950$	−1700.00	−0.0580582
$951$	0	0
$952$	−1344.00	−0.0457556
$953$	45666.0	1.55222	0.776111	−	0.630597i	$-0.217190\pi$
$953$	45666.0	1.55222	0.776111	+	0.630597i	$0.217190\pi$
$954$	0	0
$955$	11670.0	0.395427
$956$	4248.00	0.143714
$957$	0	0
$958$	13560.0	0.457311
$959$	−13398.0	−0.451141
$960$	0	0
$961$	−13407.0	−0.450035
$962$	56240.0	1.88488
$963$	0	0
$964$	−8632.00	−0.288400
$965$	8810.00	0.293890
$966$	0	0
$967$	35912.0	1.19426	0.597131	−	0.802143i	$-0.296307\pi$
$967$	35912.0	1.19426	0.597131	+	0.802143i	$0.296307\pi$
$968$	−6040.00	−0.200551
$969$	0	0
$970$	−6140.00	−0.203241
$971$	−34284.0	−1.13309	−0.566543	−	0.824032i	$-0.691719\pi$
$971$	−34284.0	−1.13309	−0.566543	+	0.824032i	$0.691719\pi$
$972$	0	0
$973$	1526.00	0.0502788
$974$	6016.00	0.197911
$975$	0	0
$976$	−9472.00	−0.310647
$977$	38370.0	1.25646	0.628232	−	0.778026i	$-0.283779\pi$
$977$	38370.0	1.25646	0.628232	+	0.778026i	$0.283779\pi$
$978$	0	0
$979$	8496.00	0.277358
$980$	−980.000	−0.0319438
$981$	0	0
$982$	−5112.00	−0.166121
$983$	2118.00	0.0687220	0.0343610	−	0.999409i	$-0.489060\pi$
$983$	2118.00	0.0687220	0.0343610	+	0.999409i	$0.489060\pi$
$984$	0	0
$985$	23850.0	0.771497
$986$	7776.00	0.251154
$987$	0	0
$988$	−10064.0	−0.324067
$989$	−5712.00	−0.183651
$990$	0	0
$991$	−35656.0	−1.14294	−0.571468	−	0.820624i	$-0.693626\pi$
$991$	−35656.0	−1.14294	−0.571468	+	0.820624i	$0.693626\pi$
$992$	4096.00	0.131097
$993$	0	0
$994$	−2772.00	−0.0884532
$995$	−460.000	−0.0146563
$996$	0	0
$997$	−45718.0	−1.45226	−0.726130	−	0.687557i	$-0.758683\pi$
$997$	−45718.0	−1.45226	−0.726130	+	0.687557i	$0.758683\pi$
$998$	−8528.00	−0.270490
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.a.p.1.1	yes	1
3.2	odd	2		630.4.a.i.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.4.a.i.1.1	✓	1	3.2	odd	2
630.4.a.p.1.1	yes	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 $\F_{q}$
Belyi maps

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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