LMFDB - Embedded newform 630.4.a.v.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:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
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)

$f(q)$

$=$

$q+2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} +7.00000 q^{7} +8.00000 q^{8} +O(q^{10})$

\(q+2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} +7.00000 q^{7} +8.00000 q^{8} +10.0000 q^{10} -12.0000 q^{11} +2.00000 q^{13} +14.0000 q^{14} +16.0000 q^{16} +18.0000 q^{17} +56.0000 q^{19} +20.0000 q^{20} -24.0000 q^{22} +156.000 q^{23} +25.0000 q^{25} +4.00000 q^{26} +28.0000 q^{28} +186.000 q^{29} -52.0000 q^{31} +32.0000 q^{32} +36.0000 q^{34} +35.0000 q^{35} -178.000 q^{37} +112.000 q^{38} +40.0000 q^{40} +138.000 q^{41} -412.000 q^{43} -48.0000 q^{44} +312.000 q^{46} +456.000 q^{47} +49.0000 q^{49} +50.0000 q^{50} +8.00000 q^{52} +198.000 q^{53} -60.0000 q^{55} +56.0000 q^{56} +372.000 q^{58} -348.000 q^{59} +110.000 q^{61} -104.000 q^{62} +64.0000 q^{64} +10.0000 q^{65} -196.000 q^{67} +72.0000 q^{68} +70.0000 q^{70} +936.000 q^{71} +542.000 q^{73} -356.000 q^{74} +224.000 q^{76} -84.0000 q^{77} +992.000 q^{79} +80.0000 q^{80} +276.000 q^{82} +276.000 q^{83} +90.0000 q^{85} -824.000 q^{86} -96.0000 q^{88} -630.000 q^{89} +14.0000 q^{91} +624.000 q^{92} +912.000 q^{94} +280.000 q^{95} +110.000 q^{97} +98.0000 q^{98} +O(q^{100})\)

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
$3$	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
$11$	−12.0000	−0.328921	−0.164461	−	0.986384i	$-0.552588\pi$
$11$	−12.0000	−0.328921	−0.164461	+	0.986384i	$0.552588\pi$
$12$	0	0
$13$	2.00000	0.0426692	0.0213346	−	0.999772i	$-0.493208\pi$
$13$	2.00000	0.0426692	0.0213346	+	0.999772i	$0.493208\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	18.0000	0.256802	0.128401	−	0.991722i	$-0.459015\pi$
$17$	18.0000	0.256802	0.128401	+	0.991722i	$0.459015\pi$
$18$	0	0
$19$	56.0000	0.676173	0.338086	−	0.941115i	$-0.390220\pi$
$19$	56.0000	0.676173	0.338086	+	0.941115i	$0.390220\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−24.0000	−0.232583
$23$	156.000	1.41427	0.707136	−	0.707078i	$-0.249987\pi$
$23$	156.000	1.41427	0.707136	+	0.707078i	$0.249987\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	4.00000	0.0301717
$27$	0	0
$28$	28.0000	0.188982
$29$	186.000	1.19101	0.595506	−	0.803351i	$-0.296952\pi$
$29$	186.000	1.19101	0.595506	+	0.803351i	$0.296952\pi$
$30$	0	0
$31$	−52.0000	−0.301273	−0.150637	−	0.988589i	$-0.548132\pi$
$31$	−52.0000	−0.301273	−0.150637	+	0.988589i	$0.548132\pi$
$32$	32.0000	0.176777
$33$	0	0
$34$	36.0000	0.181587
$35$	35.0000	0.169031
$36$	0	0
$37$	−178.000	−0.790892	−0.395446	−	0.918489i	$-0.629410\pi$
$37$	−178.000	−0.790892	−0.395446	+	0.918489i	$0.629410\pi$
$38$	112.000	0.478126
$39$	0	0
$40$	40.0000	0.158114
$41$	138.000	0.525658	0.262829	−	0.964842i	$-0.415344\pi$
$41$	138.000	0.525658	0.262829	+	0.964842i	$0.415344\pi$
$42$	0	0
$43$	−412.000	−1.46115	−0.730575	−	0.682833i	$-0.760748\pi$
$43$	−412.000	−1.46115	−0.730575	+	0.682833i	$0.760748\pi$
$44$	−48.0000	−0.164461
$45$	0	0
$46$	312.000	1.00004
$47$	456.000	1.41520	0.707600	−	0.706613i	$-0.249778\pi$
$47$	456.000	1.41520	0.707600	+	0.706613i	$0.249778\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	50.0000	0.141421
$51$	0	0
$52$	8.00000	0.0213346
$53$	198.000	0.513158	0.256579	−	0.966523i	$-0.417405\pi$
$53$	198.000	0.513158	0.256579	+	0.966523i	$0.417405\pi$
$54$	0	0
$55$	−60.0000	−0.147098
$56$	56.0000	0.133631
$57$	0	0
$58$	372.000	0.842172
$59$	−348.000	−0.767894	−0.383947	−	0.923355i	$-0.625435\pi$
$59$	−348.000	−0.767894	−0.383947	+	0.923355i	$0.625435\pi$
$60$	0	0
$61$	110.000	0.230886	0.115443	−	0.993314i	$-0.463171\pi$
$61$	110.000	0.230886	0.115443	+	0.993314i	$0.463171\pi$
$62$	−104.000	−0.213032
$63$	0	0
$64$	64.0000	0.125000
$65$	10.0000	0.0190823
$66$	0	0
$67$	−196.000	−0.357391	−0.178696	−	0.983904i	$-0.557188\pi$
$67$	−196.000	−0.357391	−0.178696	+	0.983904i	$0.557188\pi$
$68$	72.0000	0.128401
$69$	0	0
$70$	70.0000	0.119523
$71$	936.000	1.56455	0.782273	−	0.622936i	$-0.214060\pi$
$71$	936.000	1.56455	0.782273	+	0.622936i	$0.214060\pi$
$72$	0	0
$73$	542.000	0.868990	0.434495	−	0.900674i	$-0.356927\pi$
$73$	542.000	0.868990	0.434495	+	0.900674i	$0.356927\pi$
$74$	−356.000	−0.559245
$75$	0	0
$76$	224.000	0.338086
$77$	−84.0000	−0.124321
$78$	0	0
$79$	992.000	1.41277	0.706384	−	0.707829i	$-0.250325\pi$
$79$	992.000	1.41277	0.706384	+	0.707829i	$0.250325\pi$
$80$	80.0000	0.111803
$81$	0	0
$82$	276.000	0.371696
$83$	276.000	0.364999	0.182500	−	0.983206i	$-0.441581\pi$
$83$	276.000	0.364999	0.182500	+	0.983206i	$0.441581\pi$
$84$	0	0
$85$	90.0000	0.114846
$86$	−824.000	−1.03319
$87$	0	0
$88$	−96.0000	−0.116291
$89$	−630.000	−0.750336	−0.375168	−	0.926957i	$-0.622415\pi$
$89$	−630.000	−0.750336	−0.375168	+	0.926957i	$0.622415\pi$
$90$	0	0
$91$	14.0000	0.0161275
$92$	624.000	0.707136
$93$	0	0
$94$	912.000	1.00070
$95$	280.000	0.302394
$96$	0	0
$97$	110.000	0.115142	0.0575712	−	0.998341i	$-0.481664\pi$
$97$	110.000	0.115142	0.0575712	+	0.998341i	$0.481664\pi$
$98$	98.0000	0.101015
$99$	0	0
$100$	100.000	0.100000
$101$	−570.000	−0.561556	−0.280778	−	0.959773i	$-0.590592\pi$
$101$	−570.000	−0.561556	−0.280778	+	0.959773i	$0.590592\pi$
$102$	0	0
$103$	−304.000	−0.290816	−0.145408	−	0.989372i	$-0.546449\pi$
$103$	−304.000	−0.290816	−0.145408	+	0.989372i	$0.546449\pi$
$104$	16.0000	0.0150859
$105$	0	0
$106$	396.000	0.362858
$107$	−216.000	−0.195154	−0.0975771	−	0.995228i	$-0.531109\pi$
$107$	−216.000	−0.195154	−0.0975771	+	0.995228i	$0.531109\pi$
$108$	0	0
$109$	614.000	0.539546	0.269773	−	0.962924i	$-0.413051\pi$
$109$	614.000	0.539546	0.269773	+	0.962924i	$0.413051\pi$
$110$	−120.000	−0.104014
$111$	0	0
$112$	112.000	0.0944911
$113$	498.000	0.414583	0.207292	−	0.978279i	$-0.433535\pi$
$113$	498.000	0.414583	0.207292	+	0.978279i	$0.433535\pi$
$114$	0	0
$115$	780.000	0.632482
$116$	744.000	0.595506
$117$	0	0
$118$	−696.000	−0.542983
$119$	126.000	0.0970622
$120$	0	0
$121$	−1187.00	−0.891811
$122$	220.000	0.163261
$123$	0	0
$124$	−208.000	−0.150637
$125$	125.000	0.0894427
$126$	0	0
$127$	−1888.00	−1.31916	−0.659578	−	0.751636i	$-0.729265\pi$
$127$	−1888.00	−1.31916	−0.659578	+	0.751636i	$0.729265\pi$
$128$	128.000	0.0883883
$129$	0	0
$130$	20.0000	0.0134932
$131$	2892.00	1.92882	0.964409	−	0.264414i	$-0.0851786\pi$
$131$	2892.00	1.92882	0.964409	+	0.264414i	$0.0851786\pi$
$132$	0	0
$133$	392.000	0.255569
$134$	−392.000	−0.252714
$135$	0	0
$136$	144.000	0.0907934
$137$	−822.000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−822.000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	−376.000	−0.229438	−0.114719	−	0.993398i	$-0.536597\pi$
$139$	−376.000	−0.229438	−0.114719	+	0.993398i	$0.536597\pi$
$140$	140.000	0.0845154
$141$	0	0
$142$	1872.00	1.10630
$143$	−24.0000	−0.0140348
$144$	0	0
$145$	930.000	0.532637
$146$	1084.00	0.614469
$147$	0	0
$148$	−712.000	−0.395446
$149$	−3390.00	−1.86389	−0.931945	−	0.362600i	$-0.881889\pi$
$149$	−3390.00	−1.86389	−0.931945	+	0.362600i	$0.881889\pi$
$150$	0	0
$151$	−2968.00	−1.59955	−0.799776	−	0.600298i	$-0.795049\pi$
$151$	−2968.00	−1.59955	−0.799776	+	0.600298i	$0.795049\pi$
$152$	448.000	0.239063
$153$	0	0
$154$	−168.000	−0.0879080
$155$	−260.000	−0.134734
$156$	0	0
$157$	1874.00	0.952621	0.476310	−	0.879277i	$-0.341974\pi$
$157$	1874.00	0.952621	0.476310	+	0.879277i	$0.341974\pi$
$158$	1984.00	0.998978
$159$	0	0
$160$	160.000	0.0790569
$161$	1092.00	0.534544
$162$	0	0
$163$	452.000	0.217199	0.108599	−	0.994086i	$-0.465363\pi$
$163$	452.000	0.217199	0.108599	+	0.994086i	$0.465363\pi$
$164$	552.000	0.262829
$165$	0	0
$166$	552.000	0.258093
$167$	1416.00	0.656128	0.328064	−	0.944656i	$-0.393604\pi$
$167$	1416.00	0.656128	0.328064	+	0.944656i	$0.393604\pi$
$168$	0	0
$169$	−2193.00	−0.998179
$170$	180.000	0.0812081
$171$	0	0
$172$	−1648.00	−0.730575
$173$	−426.000	−0.187215	−0.0936075	−	0.995609i	$-0.529840\pi$
$173$	−426.000	−0.187215	−0.0936075	+	0.995609i	$0.529840\pi$
$174$	0	0
$175$	175.000	0.0755929
$176$	−192.000	−0.0822304
$177$	0	0
$178$	−1260.00	−0.530567
$179$	−2700.00	−1.12742	−0.563708	−	0.825974i	$-0.690626\pi$
$179$	−2700.00	−1.12742	−0.563708	+	0.825974i	$0.690626\pi$
$180$	0	0
$181$	−1978.00	−0.812285	−0.406142	−	0.913810i	$-0.633126\pi$
$181$	−1978.00	−0.812285	−0.406142	+	0.913810i	$0.633126\pi$
$182$	28.0000	0.0114038
$183$	0	0
$184$	1248.00	0.500021
$185$	−890.000	−0.353698
$186$	0	0
$187$	−216.000	−0.0844678
$188$	1824.00	0.707600
$189$	0	0
$190$	560.000	0.213825
$191$	2328.00	0.881928	0.440964	−	0.897525i	$-0.354637\pi$
$191$	2328.00	0.881928	0.440964	+	0.897525i	$0.354637\pi$
$192$	0	0
$193$	−3166.00	−1.18080	−0.590398	−	0.807112i	$-0.701029\pi$
$193$	−3166.00	−1.18080	−0.590398	+	0.807112i	$0.701029\pi$
$194$	220.000	0.0814179
$195$	0	0
$196$	196.000	0.0714286
$197$	414.000	0.149727	0.0748637	−	0.997194i	$-0.476148\pi$
$197$	414.000	0.149727	0.0748637	+	0.997194i	$0.476148\pi$
$198$	0	0
$199$	−1636.00	−0.582779	−0.291389	−	0.956605i	$-0.594118\pi$
$199$	−1636.00	−0.582779	−0.291389	+	0.956605i	$0.594118\pi$
$200$	200.000	0.0707107
$201$	0	0
$202$	−1140.00	−0.397080
$203$	1302.00	0.450160
$204$	0	0
$205$	690.000	0.235081
$206$	−608.000	−0.205638
$207$	0	0
$208$	32.0000	0.0106673
$209$	−672.000	−0.222408
$210$	0	0
$211$	−2860.00	−0.933130	−0.466565	−	0.884487i	$-0.654509\pi$
$211$	−2860.00	−0.933130	−0.466565	+	0.884487i	$0.654509\pi$
$212$	792.000	0.256579
$213$	0	0
$214$	−432.000	−0.137995
$215$	−2060.00	−0.653446
$216$	0	0
$217$	−364.000	−0.113871
$218$	1228.00	0.381517
$219$	0	0
$220$	−240.000	−0.0735491
$221$	36.0000	0.0109576
$222$	0	0
$223$	−1096.00	−0.329119	−0.164560	−	0.986367i	$-0.552620\pi$
$223$	−1096.00	−0.329119	−0.164560	+	0.986367i	$0.552620\pi$
$224$	224.000	0.0668153
$225$	0	0
$226$	996.000	0.293155
$227$	−6276.00	−1.83503	−0.917517	−	0.397696i	$-0.869810\pi$
$227$	−6276.00	−1.83503	−0.917517	+	0.397696i	$0.869810\pi$
$228$	0	0
$229$	−754.000	−0.217580	−0.108790	−	0.994065i	$-0.534698\pi$
$229$	−754.000	−0.217580	−0.108790	+	0.994065i	$0.534698\pi$
$230$	1560.00	0.447232
$231$	0	0
$232$	1488.00	0.421086
$233$	−3870.00	−1.08812	−0.544060	−	0.839046i	$-0.683114\pi$
$233$	−3870.00	−1.08812	−0.544060	+	0.839046i	$0.683114\pi$
$234$	0	0
$235$	2280.00	0.632897
$236$	−1392.00	−0.383947
$237$	0	0
$238$	252.000	0.0686333
$239$	−744.000	−0.201361	−0.100681	−	0.994919i	$-0.532102\pi$
$239$	−744.000	−0.201361	−0.100681	+	0.994919i	$0.532102\pi$
$240$	0	0
$241$	5474.00	1.46312	0.731559	−	0.681778i	$-0.238793\pi$
$241$	5474.00	1.46312	0.731559	+	0.681778i	$0.238793\pi$
$242$	−2374.00	−0.630605
$243$	0	0
$244$	440.000	0.115443
$245$	245.000	0.0638877
$246$	0	0
$247$	112.000	0.0288518
$248$	−416.000	−0.106516
$249$	0	0
$250$	250.000	0.0632456
$251$	−1980.00	−0.497914	−0.248957	−	0.968514i	$-0.580088\pi$
$251$	−1980.00	−0.497914	−0.248957	+	0.968514i	$0.580088\pi$
$252$	0	0
$253$	−1872.00	−0.465184
$254$	−3776.00	−0.932785
$255$	0	0
$256$	256.000	0.0625000
$257$	210.000	0.0509706	0.0254853	−	0.999675i	$-0.491887\pi$
$257$	210.000	0.0509706	0.0254853	+	0.999675i	$0.491887\pi$
$258$	0	0
$259$	−1246.00	−0.298929
$260$	40.0000	0.00954113
$261$	0	0
$262$	5784.00	1.36388
$263$	1428.00	0.334807	0.167404	−	0.985888i	$-0.446462\pi$
$263$	1428.00	0.334807	0.167404	+	0.985888i	$0.446462\pi$
$264$	0	0
$265$	990.000	0.229491
$266$	784.000	0.180715
$267$	0	0
$268$	−784.000	−0.178696
$269$	−4122.00	−0.934285	−0.467143	−	0.884182i	$-0.654717\pi$
$269$	−4122.00	−0.934285	−0.467143	+	0.884182i	$0.654717\pi$
$270$	0	0
$271$	5780.00	1.29561	0.647804	−	0.761807i	$-0.275687\pi$
$271$	5780.00	1.29561	0.647804	+	0.761807i	$0.275687\pi$
$272$	288.000	0.0642006
$273$	0	0
$274$	−1644.00	−0.362473
$275$	−300.000	−0.0657843
$276$	0	0
$277$	4574.00	0.992148	0.496074	−	0.868280i	$-0.334774\pi$
$277$	4574.00	0.992148	0.496074	+	0.868280i	$0.334774\pi$
$278$	−752.000	−0.162237
$279$	0	0
$280$	280.000	0.0597614
$281$	−3450.00	−0.732419	−0.366210	−	0.930532i	$-0.619345\pi$
$281$	−3450.00	−0.732419	−0.366210	+	0.930532i	$0.619345\pi$
$282$	0	0
$283$	−700.000	−0.147034	−0.0735171	−	0.997294i	$-0.523422\pi$
$283$	−700.000	−0.147034	−0.0735171	+	0.997294i	$0.523422\pi$
$284$	3744.00	0.782273
$285$	0	0
$286$	−48.0000	−0.00992412
$287$	966.000	0.198680
$288$	0	0
$289$	−4589.00	−0.934053
$290$	1860.00	0.376631
$291$	0	0
$292$	2168.00	0.434495
$293$	−7170.00	−1.42961	−0.714805	−	0.699324i	$-0.753485\pi$
$293$	−7170.00	−1.42961	−0.714805	+	0.699324i	$0.753485\pi$
$294$	0	0
$295$	−1740.00	−0.343413
$296$	−1424.00	−0.279623
$297$	0	0
$298$	−6780.00	−1.31797
$299$	312.000	0.0603459
$300$	0	0
$301$	−2884.00	−0.552262
$302$	−5936.00	−1.13105
$303$	0	0
$304$	896.000	0.169043
$305$	550.000	0.103255
$306$	0	0
$307$	6644.00	1.23516	0.617578	−	0.786509i	$-0.288114\pi$
$307$	6644.00	1.23516	0.617578	+	0.786509i	$0.288114\pi$
$308$	−336.000	−0.0621603
$309$	0	0
$310$	−520.000	−0.0952710
$311$	5376.00	0.980209	0.490104	−	0.871664i	$-0.336959\pi$
$311$	5376.00	0.980209	0.490104	+	0.871664i	$0.336959\pi$
$312$	0	0
$313$	2126.00	0.383925	0.191963	−	0.981402i	$-0.438515\pi$
$313$	2126.00	0.383925	0.191963	+	0.981402i	$0.438515\pi$
$314$	3748.00	0.673605
$315$	0	0
$316$	3968.00	0.706384
$317$	−1074.00	−0.190290	−0.0951449	−	0.995463i	$-0.530331\pi$
$317$	−1074.00	−0.190290	−0.0951449	+	0.995463i	$0.530331\pi$
$318$	0	0
$319$	−2232.00	−0.391749
$320$	320.000	0.0559017
$321$	0	0
$322$	2184.00	0.377980
$323$	1008.00	0.173643
$324$	0	0
$325$	50.0000	0.00853385
$326$	904.000	0.153583
$327$	0	0
$328$	1104.00	0.185848
$329$	3192.00	0.534896
$330$	0	0
$331$	−2788.00	−0.462968	−0.231484	−	0.972839i	$-0.574358\pi$
$331$	−2788.00	−0.462968	−0.231484	+	0.972839i	$0.574358\pi$
$332$	1104.00	0.182500
$333$	0	0
$334$	2832.00	0.463953
$335$	−980.000	−0.159830
$336$	0	0
$337$	−6334.00	−1.02384	−0.511921	−	0.859032i	$-0.671066\pi$
$337$	−6334.00	−1.02384	−0.511921	+	0.859032i	$0.671066\pi$
$338$	−4386.00	−0.705819
$339$	0	0
$340$	360.000	0.0574228
$341$	624.000	0.0990953
$342$	0	0
$343$	343.000	0.0539949
$344$	−3296.00	−0.516594
$345$	0	0
$346$	−852.000	−0.132381
$347$	7032.00	1.08789	0.543945	−	0.839121i	$-0.316930\pi$
$347$	7032.00	1.08789	0.543945	+	0.839121i	$0.316930\pi$
$348$	0	0
$349$	−1474.00	−0.226079	−0.113039	−	0.993591i	$-0.536059\pi$
$349$	−1474.00	−0.226079	−0.113039	+	0.993591i	$0.536059\pi$
$350$	350.000	0.0534522
$351$	0	0
$352$	−384.000	−0.0581456
$353$	−7950.00	−1.19868	−0.599342	−	0.800493i	$-0.704571\pi$
$353$	−7950.00	−1.19868	−0.599342	+	0.800493i	$0.704571\pi$
$354$	0	0
$355$	4680.00	0.699686
$356$	−2520.00	−0.375168
$357$	0	0
$358$	−5400.00	−0.797204
$359$	−6624.00	−0.973820	−0.486910	−	0.873452i	$-0.661876\pi$
$359$	−6624.00	−0.973820	−0.486910	+	0.873452i	$0.661876\pi$
$360$	0	0
$361$	−3723.00	−0.542790
$362$	−3956.00	−0.574372
$363$	0	0
$364$	56.0000	0.00806373
$365$	2710.00	0.388624
$366$	0	0
$367$	1784.00	0.253744	0.126872	−	0.991919i	$-0.459506\pi$
$367$	1784.00	0.253744	0.126872	+	0.991919i	$0.459506\pi$
$368$	2496.00	0.353568
$369$	0	0
$370$	−1780.00	−0.250102
$371$	1386.00	0.193956
$372$	0	0
$373$	−1978.00	−0.274576	−0.137288	−	0.990531i	$-0.543839\pi$
$373$	−1978.00	−0.274576	−0.137288	+	0.990531i	$0.543839\pi$
$374$	−432.000	−0.0597278
$375$	0	0
$376$	3648.00	0.500349
$377$	372.000	0.0508196
$378$	0	0
$379$	−10780.0	−1.46103	−0.730516	−	0.682895i	$-0.760721\pi$
$379$	−10780.0	−1.46103	−0.730516	+	0.682895i	$0.760721\pi$
$380$	1120.00	0.151197
$381$	0	0
$382$	4656.00	0.623617
$383$	5880.00	0.784475	0.392238	−	0.919864i	$-0.371701\pi$
$383$	5880.00	0.784475	0.392238	+	0.919864i	$0.371701\pi$
$384$	0	0
$385$	−420.000	−0.0555979
$386$	−6332.00	−0.834949
$387$	0	0
$388$	440.000	0.0575712
$389$	−6438.00	−0.839125	−0.419562	−	0.907726i	$-0.637816\pi$
$389$	−6438.00	−0.839125	−0.419562	+	0.907726i	$0.637816\pi$
$390$	0	0
$391$	2808.00	0.363188
$392$	392.000	0.0505076
$393$	0	0
$394$	828.000	0.105873
$395$	4960.00	0.631809
$396$	0	0
$397$	2954.00	0.373443	0.186722	−	0.982413i	$-0.440214\pi$
$397$	2954.00	0.373443	0.186722	+	0.982413i	$0.440214\pi$
$398$	−3272.00	−0.412087
$399$	0	0
$400$	400.000	0.0500000
$401$	5574.00	0.694145	0.347073	−	0.937838i	$-0.387176\pi$
$401$	5574.00	0.694145	0.347073	+	0.937838i	$0.387176\pi$
$402$	0	0
$403$	−104.000	−0.0128551
$404$	−2280.00	−0.280778
$405$	0	0
$406$	2604.00	0.318311
$407$	2136.00	0.260141
$408$	0	0
$409$	−15406.0	−1.86254	−0.931269	−	0.364333i	$-0.881297\pi$
$409$	−15406.0	−1.86254	−0.931269	+	0.364333i	$0.881297\pi$
$410$	1380.00	0.166228
$411$	0	0
$412$	−1216.00	−0.145408
$413$	−2436.00	−0.290237
$414$	0	0
$415$	1380.00	0.163233
$416$	64.0000	0.00754293
$417$	0	0
$418$	−1344.00	−0.157266
$419$	−2940.00	−0.342789	−0.171394	−	0.985203i	$-0.554827\pi$
$419$	−2940.00	−0.342789	−0.171394	+	0.985203i	$0.554827\pi$
$420$	0	0
$421$	254.000	0.0294043	0.0147021	−	0.999892i	$-0.495320\pi$
$421$	254.000	0.0294043	0.0147021	+	0.999892i	$0.495320\pi$
$422$	−5720.00	−0.659823
$423$	0	0
$424$	1584.00	0.181429
$425$	450.000	0.0513605
$426$	0	0
$427$	770.000	0.0872668
$428$	−864.000	−0.0975771
$429$	0	0
$430$	−4120.00	−0.462056
$431$	13248.0	1.48059	0.740294	−	0.672283i	$-0.234686\pi$
$431$	13248.0	1.48059	0.740294	+	0.672283i	$0.234686\pi$
$432$	0	0
$433$	16598.0	1.84215	0.921073	−	0.389391i	$-0.127314\pi$
$433$	16598.0	1.84215	0.921073	+	0.389391i	$0.127314\pi$
$434$	−728.000	−0.0805187
$435$	0	0
$436$	2456.00	0.269773
$437$	8736.00	0.956292
$438$	0	0
$439$	−6532.00	−0.710149	−0.355074	−	0.934838i	$-0.615544\pi$
$439$	−6532.00	−0.710149	−0.355074	+	0.934838i	$0.615544\pi$
$440$	−480.000	−0.0520071
$441$	0	0
$442$	72.0000	0.00774817
$443$	−12216.0	−1.31016	−0.655079	−	0.755561i	$-0.727365\pi$
$443$	−12216.0	−1.31016	−0.655079	+	0.755561i	$0.727365\pi$
$444$	0	0
$445$	−3150.00	−0.335560
$446$	−2192.00	−0.232722
$447$	0	0
$448$	448.000	0.0472456
$449$	−306.000	−0.0321627	−0.0160813	−	0.999871i	$-0.505119\pi$
$449$	−306.000	−0.0321627	−0.0160813	+	0.999871i	$0.505119\pi$
$450$	0	0
$451$	−1656.00	−0.172900
$452$	1992.00	0.207292
$453$	0	0
$454$	−12552.0	−1.29757
$455$	70.0000	0.00721242
$456$	0	0
$457$	−6046.00	−0.618862	−0.309431	−	0.950922i	$-0.600139\pi$
$457$	−6046.00	−0.618862	−0.309431	+	0.950922i	$0.600139\pi$
$458$	−1508.00	−0.153852
$459$	0	0
$460$	3120.00	0.316241
$461$	−7122.00	−0.719533	−0.359766	−	0.933042i	$-0.617144\pi$
$461$	−7122.00	−0.719533	−0.359766	+	0.933042i	$0.617144\pi$
$462$	0	0
$463$	−11248.0	−1.12903	−0.564513	−	0.825424i	$-0.690936\pi$
$463$	−11248.0	−1.12903	−0.564513	+	0.825424i	$0.690936\pi$
$464$	2976.00	0.297753
$465$	0	0
$466$	−7740.00	−0.769418
$467$	18252.0	1.80857	0.904285	−	0.426930i	$-0.140405\pi$
$467$	18252.0	1.80857	0.904285	+	0.426930i	$0.140405\pi$
$468$	0	0
$469$	−1372.00	−0.135081
$470$	4560.00	0.447526
$471$	0	0
$472$	−2784.00	−0.271491
$473$	4944.00	0.480603
$474$	0	0
$475$	1400.00	0.135235
$476$	504.000	0.0485311
$477$	0	0
$478$	−1488.00	−0.142384
$479$	18168.0	1.73302	0.866511	−	0.499159i	$-0.166358\pi$
$479$	18168.0	1.73302	0.866511	+	0.499159i	$0.166358\pi$
$480$	0	0
$481$	−356.000	−0.0337468
$482$	10948.0	1.03458
$483$	0	0
$484$	−4748.00	−0.445905
$485$	550.000	0.0514932
$486$	0	0
$487$	19856.0	1.84756	0.923780	−	0.382925i	$-0.125083\pi$
$487$	19856.0	1.84756	0.923780	+	0.382925i	$0.125083\pi$
$488$	880.000	0.0816306
$489$	0	0
$490$	490.000	0.0451754
$491$	−11220.0	−1.03127	−0.515633	−	0.856810i	$-0.672443\pi$
$491$	−11220.0	−1.03127	−0.515633	+	0.856810i	$0.672443\pi$
$492$	0	0
$493$	3348.00	0.305855
$494$	224.000	0.0204013
$495$	0	0
$496$	−832.000	−0.0753184
$497$	6552.00	0.591343
$498$	0	0
$499$	−9268.00	−0.831448	−0.415724	−	0.909491i	$-0.636472\pi$
$499$	−9268.00	−0.831448	−0.415724	+	0.909491i	$0.636472\pi$
$500$	500.000	0.0447214
$501$	0	0
$502$	−3960.00	−0.352079
$503$	−18576.0	−1.64665	−0.823323	−	0.567573i	$-0.807882\pi$
$503$	−18576.0	−1.64665	−0.823323	+	0.567573i	$0.807882\pi$
$504$	0	0
$505$	−2850.00	−0.251135
$506$	−3744.00	−0.328935
$507$	0	0
$508$	−7552.00	−0.659578
$509$	11190.0	0.974436	0.487218	−	0.873280i	$-0.338012\pi$
$509$	11190.0	0.974436	0.487218	+	0.873280i	$0.338012\pi$
$510$	0	0
$511$	3794.00	0.328448
$512$	512.000	0.0441942
$513$	0	0
$514$	420.000	0.0360416
$515$	−1520.00	−0.130057
$516$	0	0
$517$	−5472.00	−0.465490
$518$	−2492.00	−0.211375
$519$	0	0
$520$	80.0000	0.00674660
$521$	306.000	0.0257315	0.0128657	−	0.999917i	$-0.495905\pi$
$521$	306.000	0.0257315	0.0128657	+	0.999917i	$0.495905\pi$
$522$	0	0
$523$	17444.0	1.45846	0.729228	−	0.684270i	$-0.239879\pi$
$523$	17444.0	1.45846	0.729228	+	0.684270i	$0.239879\pi$
$524$	11568.0	0.964409
$525$	0	0
$526$	2856.00	0.236744
$527$	−936.000	−0.0773677
$528$	0	0
$529$	12169.0	1.00016
$530$	1980.00	0.162275
$531$	0	0
$532$	1568.00	0.127785
$533$	276.000	0.0224294
$534$	0	0
$535$	−1080.00	−0.0872756
$536$	−1568.00	−0.126357
$537$	0	0
$538$	−8244.00	−0.660640
$539$	−588.000	−0.0469888
$540$	0	0
$541$	−538.000	−0.0427549	−0.0213775	−	0.999771i	$-0.506805\pi$
$541$	−538.000	−0.0427549	−0.0213775	+	0.999771i	$0.506805\pi$
$542$	11560.0	0.916134
$543$	0	0
$544$	576.000	0.0453967
$545$	3070.00	0.241292
$546$	0	0
$547$	19820.0	1.54925	0.774627	−	0.632418i	$-0.217938\pi$
$547$	19820.0	1.54925	0.774627	+	0.632418i	$0.217938\pi$
$548$	−3288.00	−0.256307
$549$	0	0
$550$	−600.000	−0.0465165
$551$	10416.0	0.805329
$552$	0	0
$553$	6944.00	0.533976
$554$	9148.00	0.701555
$555$	0	0
$556$	−1504.00	−0.114719
$557$	16686.0	1.26932	0.634658	−	0.772794i	$-0.281141\pi$
$557$	16686.0	1.26932	0.634658	+	0.772794i	$0.281141\pi$
$558$	0	0
$559$	−824.000	−0.0623461
$560$	560.000	0.0422577
$561$	0	0
$562$	−6900.00	−0.517898
$563$	16788.0	1.25671	0.628357	−	0.777925i	$-0.283728\pi$
$563$	16788.0	1.25671	0.628357	+	0.777925i	$0.283728\pi$
$564$	0	0
$565$	2490.00	0.185407
$566$	−1400.00	−0.103969
$567$	0	0
$568$	7488.00	0.553151
$569$	−15906.0	−1.17191	−0.585953	−	0.810345i	$-0.699280\pi$
$569$	−15906.0	−1.17191	−0.585953	+	0.810345i	$0.699280\pi$
$570$	0	0
$571$	17084.0	1.25209	0.626045	−	0.779787i	$-0.284673\pi$
$571$	17084.0	1.25209	0.626045	+	0.779787i	$0.284673\pi$
$572$	−96.0000	−0.00701742
$573$	0	0
$574$	1932.00	0.140488
$575$	3900.00	0.282854
$576$	0	0
$577$	25382.0	1.83131	0.915656	−	0.401964i	$-0.131672\pi$
$577$	25382.0	1.83131	0.915656	+	0.401964i	$0.131672\pi$
$578$	−9178.00	−0.660475
$579$	0	0
$580$	3720.00	0.266318
$581$	1932.00	0.137957
$582$	0	0
$583$	−2376.00	−0.168789
$584$	4336.00	0.307235
$585$	0	0
$586$	−14340.0	−1.01089
$587$	−13764.0	−0.967804	−0.483902	−	0.875122i	$-0.660781\pi$
$587$	−13764.0	−0.967804	−0.483902	+	0.875122i	$0.660781\pi$
$588$	0	0
$589$	−2912.00	−0.203713
$590$	−3480.00	−0.242829
$591$	0	0
$592$	−2848.00	−0.197723
$593$	13266.0	0.918667	0.459333	−	0.888264i	$-0.348088\pi$
$593$	13266.0	0.918667	0.459333	+	0.888264i	$0.348088\pi$
$594$	0	0
$595$	630.000	0.0434075
$596$	−13560.0	−0.931945
$597$	0	0
$598$	624.000	0.0426710
$599$	−9600.00	−0.654834	−0.327417	−	0.944880i	$-0.606178\pi$
$599$	−9600.00	−0.654834	−0.327417	+	0.944880i	$0.606178\pi$
$600$	0	0
$601$	−19582.0	−1.32906	−0.664531	−	0.747261i	$-0.731369\pi$
$601$	−19582.0	−1.32906	−0.664531	+	0.747261i	$0.731369\pi$
$602$	−5768.00	−0.390509
$603$	0	0
$604$	−11872.0	−0.799776
$605$	−5935.00	−0.398830
$606$	0	0
$607$	3944.00	0.263727	0.131863	−	0.991268i	$-0.457904\pi$
$607$	3944.00	0.263727	0.131863	+	0.991268i	$0.457904\pi$
$608$	1792.00	0.119532
$609$	0	0
$610$	1100.00	0.0730126
$611$	912.000	0.0603855
$612$	0	0
$613$	20846.0	1.37351	0.686755	−	0.726889i	$-0.259034\pi$
$613$	20846.0	1.37351	0.686755	+	0.726889i	$0.259034\pi$
$614$	13288.0	0.873388
$615$	0	0
$616$	−672.000	−0.0439540
$617$	−15342.0	−1.00105	−0.500523	−	0.865723i	$-0.666859\pi$
$617$	−15342.0	−1.00105	−0.500523	+	0.865723i	$0.666859\pi$
$618$	0	0
$619$	−5128.00	−0.332975	−0.166488	−	0.986044i	$-0.553243\pi$
$619$	−5128.00	−0.332975	−0.166488	+	0.986044i	$0.553243\pi$
$620$	−1040.00	−0.0673668
$621$	0	0
$622$	10752.0	0.693112
$623$	−4410.00	−0.283600
$624$	0	0
$625$	625.000	0.0400000
$626$	4252.00	0.271476
$627$	0	0
$628$	7496.00	0.476310
$629$	−3204.00	−0.203103
$630$	0	0
$631$	31016.0	1.95678	0.978389	−	0.206771i	$-0.0662954\pi$
$631$	31016.0	1.95678	0.978389	+	0.206771i	$0.0662954\pi$
$632$	7936.00	0.499489
$633$	0	0
$634$	−2148.00	−0.134555
$635$	−9440.00	−0.589945
$636$	0	0
$637$	98.0000	0.00609561
$638$	−4464.00	−0.277009
$639$	0	0
$640$	640.000	0.0395285
$641$	−15474.0	−0.953489	−0.476744	−	0.879042i	$-0.658183\pi$
$641$	−15474.0	−0.953489	−0.476744	+	0.879042i	$0.658183\pi$
$642$	0	0
$643$	24644.0	1.51145	0.755727	−	0.654887i	$-0.227284\pi$
$643$	24644.0	1.51145	0.755727	+	0.654887i	$0.227284\pi$
$644$	4368.00	0.267272
$645$	0	0
$646$	2016.00	0.122784
$647$	16632.0	1.01062	0.505310	−	0.862938i	$-0.331378\pi$
$647$	16632.0	1.01062	0.505310	+	0.862938i	$0.331378\pi$
$648$	0	0
$649$	4176.00	0.252577
$650$	100.000	0.00603434
$651$	0	0
$652$	1808.00	0.108599
$653$	10542.0	0.631762	0.315881	−	0.948799i	$-0.397700\pi$
$653$	10542.0	0.631762	0.315881	+	0.948799i	$0.397700\pi$
$654$	0	0
$655$	14460.0	0.862594
$656$	2208.00	0.131415
$657$	0	0
$658$	6384.00	0.378228
$659$	−15276.0	−0.902987	−0.451494	−	0.892274i	$-0.649109\pi$
$659$	−15276.0	−0.902987	−0.451494	+	0.892274i	$0.649109\pi$
$660$	0	0
$661$	1478.00	0.0869706	0.0434853	−	0.999054i	$-0.486154\pi$
$661$	1478.00	0.0869706	0.0434853	+	0.999054i	$0.486154\pi$
$662$	−5576.00	−0.327368
$663$	0	0
$664$	2208.00	0.129047
$665$	1960.00	0.114294
$666$	0	0
$667$	29016.0	1.68441
$668$	5664.00	0.328064
$669$	0	0
$670$	−1960.00	−0.113017
$671$	−1320.00	−0.0759434
$672$	0	0
$673$	−19366.0	−1.10922	−0.554610	−	0.832111i	$-0.687132\pi$
$673$	−19366.0	−1.10922	−0.554610	+	0.832111i	$0.687132\pi$
$674$	−12668.0	−0.723966
$675$	0	0
$676$	−8772.00	−0.499090
$677$	21390.0	1.21430	0.607152	−	0.794585i	$-0.292312\pi$
$677$	21390.0	1.21430	0.607152	+	0.794585i	$0.292312\pi$
$678$	0	0
$679$	770.000	0.0435197
$680$	720.000	0.0406040
$681$	0	0
$682$	1248.00	0.0700710
$683$	21672.0	1.21414	0.607069	−	0.794649i	$-0.292345\pi$
$683$	21672.0	1.21414	0.607069	+	0.794649i	$0.292345\pi$
$684$	0	0
$685$	−4110.00	−0.229248
$686$	686.000	0.0381802
$687$	0	0
$688$	−6592.00	−0.365287
$689$	396.000	0.0218961
$690$	0	0
$691$	−5992.00	−0.329879	−0.164940	−	0.986304i	$-0.552743\pi$
$691$	−5992.00	−0.329879	−0.164940	+	0.986304i	$0.552743\pi$
$692$	−1704.00	−0.0936075
$693$	0	0
$694$	14064.0	0.769254
$695$	−1880.00	−0.102608
$696$	0	0
$697$	2484.00	0.134990
$698$	−2948.00	−0.159862
$699$	0	0
$700$	700.000	0.0377964
$701$	−17766.0	−0.957222	−0.478611	−	0.878027i	$-0.658860\pi$
$701$	−17766.0	−0.957222	−0.478611	+	0.878027i	$0.658860\pi$
$702$	0	0
$703$	−9968.00	−0.534780
$704$	−768.000	−0.0411152
$705$	0	0
$706$	−15900.0	−0.847598
$707$	−3990.00	−0.212248
$708$	0	0
$709$	−24514.0	−1.29851	−0.649254	−	0.760571i	$-0.724919\pi$
$709$	−24514.0	−1.29851	−0.649254	+	0.760571i	$0.724919\pi$
$710$	9360.00	0.494753
$711$	0	0
$712$	−5040.00	−0.265284
$713$	−8112.00	−0.426082
$714$	0	0
$715$	−120.000	−0.00627657
$716$	−10800.0	−0.563708
$717$	0	0
$718$	−13248.0	−0.688595
$719$	13176.0	0.683424	0.341712	−	0.939805i	$-0.388993\pi$
$719$	13176.0	0.683424	0.341712	+	0.939805i	$0.388993\pi$
$720$	0	0
$721$	−2128.00	−0.109918
$722$	−7446.00	−0.383811
$723$	0	0
$724$	−7912.00	−0.406142
$725$	4650.00	0.238202
$726$	0	0
$727$	20792.0	1.06071	0.530353	−	0.847777i	$-0.322060\pi$
$727$	20792.0	1.06071	0.530353	+	0.847777i	$0.322060\pi$
$728$	112.000	0.00570192
$729$	0	0
$730$	5420.00	0.274799
$731$	−7416.00	−0.375227
$732$	0	0
$733$	−21742.0	−1.09558	−0.547789	−	0.836616i	$-0.684530\pi$
$733$	−21742.0	−1.09558	−0.547789	+	0.836616i	$0.684530\pi$
$734$	3568.00	0.179424
$735$	0	0
$736$	4992.00	0.250010
$737$	2352.00	0.117554
$738$	0	0
$739$	39044.0	1.94351	0.971757	−	0.235984i	$-0.0758313\pi$
$739$	39044.0	1.94351	0.971757	+	0.235984i	$0.0758313\pi$
$740$	−3560.00	−0.176849
$741$	0	0
$742$	2772.00	0.137147
$743$	31116.0	1.53639	0.768193	−	0.640218i	$-0.221156\pi$
$743$	31116.0	1.53639	0.768193	+	0.640218i	$0.221156\pi$
$744$	0	0
$745$	−16950.0	−0.833557
$746$	−3956.00	−0.194155
$747$	0	0
$748$	−864.000	−0.0422339
$749$	−1512.00	−0.0737614
$750$	0	0
$751$	−29320.0	−1.42464	−0.712318	−	0.701857i	$-0.752355\pi$
$751$	−29320.0	−1.42464	−0.712318	+	0.701857i	$0.752355\pi$
$752$	7296.00	0.353800
$753$	0	0
$754$	744.000	0.0359349
$755$	−14840.0	−0.715342
$756$	0	0
$757$	−2266.00	−0.108797	−0.0543984	−	0.998519i	$-0.517324\pi$
$757$	−2266.00	−0.108797	−0.0543984	+	0.998519i	$0.517324\pi$
$758$	−21560.0	−1.03311
$759$	0	0
$760$	2240.00	0.106912
$761$	29946.0	1.42647	0.713234	−	0.700926i	$-0.247230\pi$
$761$	29946.0	1.42647	0.713234	+	0.700926i	$0.247230\pi$
$762$	0	0
$763$	4298.00	0.203929
$764$	9312.00	0.440964
$765$	0	0
$766$	11760.0	0.554708
$767$	−696.000	−0.0327655
$768$	0	0
$769$	−23110.0	−1.08370	−0.541852	−	0.840474i	$-0.682277\pi$
$769$	−23110.0	−1.08370	−0.541852	+	0.840474i	$0.682277\pi$
$770$	−840.000	−0.0393136
$771$	0	0
$772$	−12664.0	−0.590398
$773$	31950.0	1.48663	0.743313	−	0.668944i	$-0.233253\pi$
$773$	31950.0	1.48663	0.743313	+	0.668944i	$0.233253\pi$
$774$	0	0
$775$	−1300.00	−0.0602547
$776$	880.000	0.0407090
$777$	0	0
$778$	−12876.0	−0.593351
$779$	7728.00	0.355436
$780$	0	0
$781$	−11232.0	−0.514613
$782$	5616.00	0.256813
$783$	0	0
$784$	784.000	0.0357143
$785$	9370.00	0.426025
$786$	0	0
$787$	6284.00	0.284626	0.142313	−	0.989822i	$-0.454546\pi$
$787$	6284.00	0.284626	0.142313	+	0.989822i	$0.454546\pi$
$788$	1656.00	0.0748637
$789$	0	0
$790$	9920.00	0.446757
$791$	3486.00	0.156698
$792$	0	0
$793$	220.000	0.00985174
$794$	5908.00	0.264064
$795$	0	0
$796$	−6544.00	−0.291389
$797$	−5946.00	−0.264264	−0.132132	−	0.991232i	$-0.542182\pi$
$797$	−5946.00	−0.264264	−0.132132	+	0.991232i	$0.542182\pi$
$798$	0	0
$799$	8208.00	0.363427
$800$	800.000	0.0353553
$801$	0	0
$802$	11148.0	0.490835
$803$	−6504.00	−0.285830
$804$	0	0
$805$	5460.00	0.239056
$806$	−208.000	−0.00908993
$807$	0	0
$808$	−4560.00	−0.198540
$809$	−27090.0	−1.17730	−0.588649	−	0.808389i	$-0.700340\pi$
$809$	−27090.0	−1.17730	−0.588649	+	0.808389i	$0.700340\pi$
$810$	0	0
$811$	−20104.0	−0.870465	−0.435232	−	0.900318i	$-0.643334\pi$
$811$	−20104.0	−0.870465	−0.435232	+	0.900318i	$0.643334\pi$
$812$	5208.00	0.225080
$813$	0	0
$814$	4272.00	0.183948
$815$	2260.00	0.0971342
$816$	0	0
$817$	−23072.0	−0.987989
$818$	−30812.0	−1.31701
$819$	0	0
$820$	2760.00	0.117541
$821$	−7302.00	−0.310404	−0.155202	−	0.987883i	$-0.549603\pi$
$821$	−7302.00	−0.310404	−0.155202	+	0.987883i	$0.549603\pi$
$822$	0	0
$823$	−24136.0	−1.02227	−0.511135	−	0.859500i	$-0.670775\pi$
$823$	−24136.0	−1.02227	−0.511135	+	0.859500i	$0.670775\pi$
$824$	−2432.00	−0.102819
$825$	0	0
$826$	−4872.00	−0.205228
$827$	−22680.0	−0.953641	−0.476820	−	0.879001i	$-0.658211\pi$
$827$	−22680.0	−0.953641	−0.476820	+	0.879001i	$0.658211\pi$
$828$	0	0
$829$	−20338.0	−0.852072	−0.426036	−	0.904706i	$-0.640090\pi$
$829$	−20338.0	−0.852072	−0.426036	+	0.904706i	$0.640090\pi$
$830$	2760.00	0.115423
$831$	0	0
$832$	128.000	0.00533366
$833$	882.000	0.0366861
$834$	0	0
$835$	7080.00	0.293429
$836$	−2688.00	−0.111204
$837$	0	0
$838$	−5880.00	−0.242388
$839$	−6600.00	−0.271582	−0.135791	−	0.990738i	$-0.543358\pi$
$839$	−6600.00	−0.271582	−0.135791	+	0.990738i	$0.543358\pi$
$840$	0	0
$841$	10207.0	0.418508
$842$	508.000	0.0207920
$843$	0	0
$844$	−11440.0	−0.466565
$845$	−10965.0	−0.446399
$846$	0	0
$847$	−8309.00	−0.337073
$848$	3168.00	0.128290
$849$	0	0
$850$	900.000	0.0363173
$851$	−27768.0	−1.11854
$852$	0	0
$853$	−40174.0	−1.61258	−0.806290	−	0.591520i	$-0.798528\pi$
$853$	−40174.0	−1.61258	−0.806290	+	0.591520i	$0.798528\pi$
$854$	1540.00	0.0617069
$855$	0	0
$856$	−1728.00	−0.0689975
$857$	20778.0	0.828195	0.414097	−	0.910233i	$-0.364097\pi$
$857$	20778.0	0.828195	0.414097	+	0.910233i	$0.364097\pi$
$858$	0	0
$859$	7400.00	0.293929	0.146964	−	0.989142i	$-0.453050\pi$
$859$	7400.00	0.293929	0.146964	+	0.989142i	$0.453050\pi$
$860$	−8240.00	−0.326723
$861$	0	0
$862$	26496.0	1.04693
$863$	−684.000	−0.0269799	−0.0134899	−	0.999909i	$-0.504294\pi$
$863$	−684.000	−0.0269799	−0.0134899	+	0.999909i	$0.504294\pi$
$864$	0	0
$865$	−2130.00	−0.0837251
$866$	33196.0	1.30259
$867$	0	0
$868$	−1456.00	−0.0569353
$869$	−11904.0	−0.464690
$870$	0	0
$871$	−392.000	−0.0152496
$872$	4912.00	0.190758
$873$	0	0
$874$	17472.0	0.676200
$875$	875.000	0.0338062
$876$	0	0
$877$	−9754.00	−0.375563	−0.187782	−	0.982211i	$-0.560130\pi$
$877$	−9754.00	−0.375563	−0.187782	+	0.982211i	$0.560130\pi$
$878$	−13064.0	−0.502151
$879$	0	0
$880$	−960.000	−0.0367745
$881$	−14310.0	−0.547237	−0.273619	−	0.961838i	$-0.588221\pi$
$881$	−14310.0	−0.547237	−0.273619	+	0.961838i	$0.588221\pi$
$882$	0	0
$883$	−14092.0	−0.537071	−0.268535	−	0.963270i	$-0.586540\pi$
$883$	−14092.0	−0.537071	−0.268535	+	0.963270i	$0.586540\pi$
$884$	144.000	0.00547878
$885$	0	0
$886$	−24432.0	−0.926421
$887$	−45600.0	−1.72615	−0.863077	−	0.505073i	$-0.831466\pi$
$887$	−45600.0	−1.72615	−0.863077	+	0.505073i	$0.831466\pi$
$888$	0	0
$889$	−13216.0	−0.498594
$890$	−6300.00	−0.237277
$891$	0	0
$892$	−4384.00	−0.164560
$893$	25536.0	0.956920
$894$	0	0
$895$	−13500.0	−0.504196
$896$	896.000	0.0334077
$897$	0	0
$898$	−612.000	−0.0227424
$899$	−9672.00	−0.358820
$900$	0	0
$901$	3564.00	0.131780
$902$	−3312.00	−0.122259
$903$	0	0
$904$	3984.00	0.146577
$905$	−9890.00	−0.363265
$906$	0	0
$907$	8012.00	0.293312	0.146656	−	0.989188i	$-0.453149\pi$
$907$	8012.00	0.293312	0.146656	+	0.989188i	$0.453149\pi$
$908$	−25104.0	−0.917517
$909$	0	0
$910$	140.000	0.00509995
$911$	−2136.00	−0.0776826	−0.0388413	−	0.999245i	$-0.512367\pi$
$911$	−2136.00	−0.0776826	−0.0388413	+	0.999245i	$0.512367\pi$
$912$	0	0
$913$	−3312.00	−0.120056
$914$	−12092.0	−0.437602
$915$	0	0
$916$	−3016.00	−0.108790
$917$	20244.0	0.729025
$918$	0	0
$919$	−15280.0	−0.548466	−0.274233	−	0.961663i	$-0.588424\pi$
$919$	−15280.0	−0.548466	−0.274233	+	0.961663i	$0.588424\pi$
$920$	6240.00	0.223616
$921$	0	0
$922$	−14244.0	−0.508787
$923$	1872.00	0.0667580
$924$	0	0
$925$	−4450.00	−0.158178
$926$	−22496.0	−0.798342
$927$	0	0
$928$	5952.00	0.210543
$929$	−20910.0	−0.738466	−0.369233	−	0.929337i	$-0.620380\pi$
$929$	−20910.0	−0.738466	−0.369233	+	0.929337i	$0.620380\pi$
$930$	0	0
$931$	2744.00	0.0965961
$932$	−15480.0	−0.544060
$933$	0	0
$934$	36504.0	1.27885
$935$	−1080.00	−0.0377752
$936$	0	0
$937$	−38122.0	−1.32913	−0.664563	−	0.747232i	$-0.731382\pi$
$937$	−38122.0	−1.32913	−0.664563	+	0.747232i	$0.731382\pi$
$938$	−2744.00	−0.0955168
$939$	0	0
$940$	9120.00	0.316449
$941$	−42810.0	−1.48307	−0.741534	−	0.670916i	$-0.765901\pi$
$941$	−42810.0	−1.48307	−0.741534	+	0.670916i	$0.765901\pi$
$942$	0	0
$943$	21528.0	0.743423
$944$	−5568.00	−0.191973
$945$	0	0
$946$	9888.00	0.339838
$947$	−39864.0	−1.36790	−0.683952	−	0.729527i	$-0.739740\pi$
$947$	−39864.0	−1.36790	−0.683952	+	0.729527i	$0.739740\pi$
$948$	0	0
$949$	1084.00	0.0370792
$950$	2800.00	0.0956253
$951$	0	0
$952$	1008.00	0.0343167
$953$	23850.0	0.810679	0.405340	−	0.914166i	$-0.367153\pi$
$953$	23850.0	0.810679	0.405340	+	0.914166i	$0.367153\pi$
$954$	0	0
$955$	11640.0	0.394410
$956$	−2976.00	−0.100681
$957$	0	0
$958$	36336.0	1.22543
$959$	−5754.00	−0.193750
$960$	0	0
$961$	−27087.0	−0.909234
$962$	−712.000	−0.0238626
$963$	0	0
$964$	21896.0	0.731559
$965$	−15830.0	−0.528068
$966$	0	0
$967$	−12832.0	−0.426731	−0.213366	−	0.976972i	$-0.568443\pi$
$967$	−12832.0	−0.426731	−0.213366	+	0.976972i	$0.568443\pi$
$968$	−9496.00	−0.315303
$969$	0	0
$970$	1100.00	0.0364112
$971$	15804.0	0.522322	0.261161	−	0.965295i	$-0.415895\pi$
$971$	15804.0	0.522322	0.261161	+	0.965295i	$0.415895\pi$
$972$	0	0
$973$	−2632.00	−0.0867195
$974$	39712.0	1.30642
$975$	0	0
$976$	1760.00	0.0577215
$977$	33114.0	1.08435	0.542175	−	0.840265i	$-0.317601\pi$
$977$	33114.0	1.08435	0.542175	+	0.840265i	$0.317601\pi$
$978$	0	0
$979$	7560.00	0.246801
$980$	980.000	0.0319438
$981$	0	0
$982$	−22440.0	−0.729215
$983$	58632.0	1.90241	0.951206	−	0.308558i	$-0.0998462\pi$
$983$	58632.0	1.90241	0.951206	+	0.308558i	$0.0998462\pi$
$984$	0	0
$985$	2070.00	0.0669601
$986$	6696.00	0.216272
$987$	0	0
$988$	448.000	0.0144259
$989$	−64272.0	−2.06646
$990$	0	0
$991$	55784.0	1.78813	0.894065	−	0.447937i	$-0.147841\pi$
$991$	55784.0	1.78813	0.894065	+	0.447937i	$0.147841\pi$
$992$	−1664.00	−0.0532581
$993$	0	0
$994$	13104.0	0.418142
$995$	−8180.00	−0.260627
$996$	0	0
$997$	−23326.0	−0.740965	−0.370482	−	0.928840i	$-0.620808\pi$
$997$	−23326.0	−0.740965	−0.370482	+	0.928840i	$0.620808\pi$
$998$	−18536.0	−0.587923
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.4.a.v.1.1		1
3.2	odd	2		210.4.a.a.1.1	✓	1
12.11	even	2		1680.4.a.n.1.1		1
15.2	even	4		1050.4.g.o.799.1		2
15.8	even	4		1050.4.g.o.799.2		2
15.14	odd	2		1050.4.a.t.1.1		1
21.20	even	2		1470.4.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.a.a.1.1	✓	1	3.2	odd	2
630.4.a.v.1.1		1	1.1	even	1	trivial
1050.4.a.t.1.1		1	15.14	odd	2
1050.4.g.o.799.1		2	15.2	even	4
1050.4.g.o.799.2		2	15.8	even	4
1470.4.a.n.1.1		1	21.20	even	2
1680.4.a.n.1.1		1	12.11	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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