LMFDB - Embedded newform 630.4.a.o.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)

$f(q)$

$=$

\(q+2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} +7.00000 q^{7} +8.00000 q^{8} -10.0000 q^{10} -60.0000 q^{11} +38.0000 q^{13} +14.0000 q^{14} +16.0000 q^{16} -42.0000 q^{17} -52.0000 q^{19} -20.0000 q^{20} -120.000 q^{22} -120.000 q^{23} +25.0000 q^{25} +76.0000 q^{26} +28.0000 q^{28} +234.000 q^{29} -304.000 q^{31} +32.0000 q^{32} -84.0000 q^{34} -35.0000 q^{35} -106.000 q^{37} -104.000 q^{38} -40.0000 q^{40} +54.0000 q^{41} -196.000 q^{43} -240.000 q^{44} -240.000 q^{46} -336.000 q^{47} +49.0000 q^{49} +50.0000 q^{50} +152.000 q^{52} -438.000 q^{53} +300.000 q^{55} +56.0000 q^{56} +468.000 q^{58} +444.000 q^{59} +38.0000 q^{61} -608.000 q^{62} +64.0000 q^{64} -190.000 q^{65} -988.000 q^{67} -168.000 q^{68} -70.0000 q^{70} +720.000 q^{71} +146.000 q^{73} -212.000 q^{74} -208.000 q^{76} -420.000 q^{77} -808.000 q^{79} -80.0000 q^{80} +108.000 q^{82} -612.000 q^{83} +210.000 q^{85} -392.000 q^{86} -480.000 q^{88} -1146.00 q^{89} +266.000 q^{91} -480.000 q^{92} -672.000 q^{94} +260.000 q^{95} -70.0000 q^{97} +98.0000 q^{98} +O(q^{100})\)

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
$11$	−60.0000	−1.64461	−0.822304	−	0.569049i	$-0.807311\pi$
$11$	−60.0000	−1.64461	−0.822304	+	0.569049i	$0.807311\pi$
$12$	0	0
$13$	38.0000	0.810716	0.405358	−	0.914158i	$-0.367147\pi$
$13$	38.0000	0.810716	0.405358	+	0.914158i	$0.367147\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	−42.0000	−0.599206	−0.299603	−	0.954064i	$-0.596854\pi$
$17$	−42.0000	−0.599206	−0.299603	+	0.954064i	$0.596854\pi$
$18$	0	0
$19$	−52.0000	−0.627875	−0.313937	−	0.949444i	$-0.601648\pi$
$19$	−52.0000	−0.627875	−0.313937	+	0.949444i	$0.601648\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	−120.000	−1.16291
$23$	−120.000	−1.08790	−0.543951	−	0.839117i	$-0.683072\pi$
$23$	−120.000	−1.08790	−0.543951	+	0.839117i	$0.683072\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	76.0000	0.573263
$27$	0	0
$28$	28.0000	0.188982
$29$	234.000	1.49837	0.749185	−	0.662361i	$-0.230446\pi$
$29$	234.000	1.49837	0.749185	+	0.662361i	$0.230446\pi$
$30$	0	0
$31$	−304.000	−1.76129	−0.880645	−	0.473776i	$-0.842891\pi$
$31$	−304.000	−1.76129	−0.880645	+	0.473776i	$0.842891\pi$
$32$	32.0000	0.176777
$33$	0	0
$34$	−84.0000	−0.423702
$35$	−35.0000	−0.169031
$36$	0	0
$37$	−106.000	−0.470981	−0.235490	−	0.971877i	$-0.575670\pi$
$37$	−106.000	−0.470981	−0.235490	+	0.971877i	$0.575670\pi$
$38$	−104.000	−0.443974
$39$	0	0
$40$	−40.0000	−0.158114
$41$	54.0000	0.205692	0.102846	−	0.994697i	$-0.467205\pi$
$41$	54.0000	0.205692	0.102846	+	0.994697i	$0.467205\pi$
$42$	0	0
$43$	−196.000	−0.695110	−0.347555	−	0.937660i	$-0.612988\pi$
$43$	−196.000	−0.695110	−0.347555	+	0.937660i	$0.612988\pi$
$44$	−240.000	−0.822304
$45$	0	0
$46$	−240.000	−0.769262
$47$	−336.000	−1.04278	−0.521390	−	0.853319i	$-0.674586\pi$
$47$	−336.000	−1.04278	−0.521390	+	0.853319i	$0.674586\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	50.0000	0.141421
$51$	0	0
$52$	152.000	0.405358
$53$	−438.000	−1.13517	−0.567584	−	0.823315i	$-0.692122\pi$
$53$	−438.000	−1.13517	−0.567584	+	0.823315i	$0.692122\pi$
$54$	0	0
$55$	300.000	0.735491
$56$	56.0000	0.133631
$57$	0	0
$58$	468.000	1.05951
$59$	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
$61$	38.0000	0.0797607	0.0398803	−	0.999204i	$-0.487302\pi$
$61$	38.0000	0.0797607	0.0398803	+	0.999204i	$0.487302\pi$
$62$	−608.000	−1.24542
$63$	0	0
$64$	64.0000	0.125000
$65$	−190.000	−0.362563
$66$	0	0
$67$	−988.000	−1.80154	−0.900772	−	0.434293i	$-0.856998\pi$
$67$	−988.000	−1.80154	−0.900772	+	0.434293i	$0.856998\pi$
$68$	−168.000	−0.299603
$69$	0	0
$70$	−70.0000	−0.119523
$71$	720.000	1.20350	0.601748	−	0.798686i	$-0.294471\pi$
$71$	720.000	1.20350	0.601748	+	0.798686i	$0.294471\pi$
$72$	0	0
$73$	146.000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	146.000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−212.000	−0.333034
$75$	0	0
$76$	−208.000	−0.313937
$77$	−420.000	−0.621603
$78$	0	0
$79$	−808.000	−1.15072	−0.575361	−	0.817899i	$-0.695139\pi$
$79$	−808.000	−1.15072	−0.575361	+	0.817899i	$0.695139\pi$
$80$	−80.0000	−0.111803
$81$	0	0
$82$	108.000	0.145446
$83$	−612.000	−0.809346	−0.404673	−	0.914461i	$-0.632615\pi$
$83$	−612.000	−0.809346	−0.404673	+	0.914461i	$0.632615\pi$
$84$	0	0
$85$	210.000	0.267973
$86$	−392.000	−0.491517
$87$	0	0
$88$	−480.000	−0.581456
$89$	−1146.00	−1.36490	−0.682448	−	0.730934i	$-0.739085\pi$
$89$	−1146.00	−1.36490	−0.682448	+	0.730934i	$0.739085\pi$
$90$	0	0
$91$	266.000	0.306422
$92$	−480.000	−0.543951
$93$	0	0
$94$	−672.000	−0.737356
$95$	260.000	0.280794
$96$	0	0
$97$	−70.0000	−0.0732724	−0.0366362	−	0.999329i	$-0.511664\pi$
$97$	−70.0000	−0.0732724	−0.0366362	+	0.999329i	$0.511664\pi$
$98$	98.0000	0.101015
$99$	0	0
$100$	100.000	0.100000
$101$	−1950.00	−1.92111	−0.960556	−	0.278088i	$-0.910299\pi$
$101$	−1950.00	−1.92111	−0.960556	+	0.278088i	$0.910299\pi$
$102$	0	0
$103$	488.000	0.466836	0.233418	−	0.972377i	$-0.425009\pi$
$103$	488.000	0.466836	0.233418	+	0.972377i	$0.425009\pi$
$104$	304.000	0.286631
$105$	0	0
$106$	−876.000	−0.802685
$107$	996.000	0.899878	0.449939	−	0.893059i	$-0.351446\pi$
$107$	996.000	0.899878	0.449939	+	0.893059i	$0.351446\pi$
$108$	0	0
$109$	758.000	0.666085	0.333042	−	0.942912i	$-0.391925\pi$
$109$	758.000	0.666085	0.333042	+	0.942912i	$0.391925\pi$
$110$	600.000	0.520071
$111$	0	0
$112$	112.000	0.0944911
$113$	1422.00	1.18381	0.591905	−	0.806008i	$-0.298376\pi$
$113$	1422.00	1.18381	0.591905	+	0.806008i	$0.298376\pi$
$114$	0	0
$115$	600.000	0.486524
$116$	936.000	0.749185
$117$	0	0
$118$	888.000	0.692771
$119$	−294.000	−0.226478
$120$	0	0
$121$	2269.00	1.70473
$122$	76.0000	0.0563993
$123$	0	0
$124$	−1216.00	−0.880645
$125$	−125.000	−0.0894427
$126$	0	0
$127$	848.000	0.592503	0.296251	−	0.955110i	$-0.404263\pi$
$127$	848.000	0.592503	0.296251	+	0.955110i	$0.404263\pi$
$128$	128.000	0.0883883
$129$	0	0
$130$	−380.000	−0.256371
$131$	−588.000	−0.392166	−0.196083	−	0.980587i	$-0.562822\pi$
$131$	−588.000	−0.392166	−0.196083	+	0.980587i	$0.562822\pi$
$132$	0	0
$133$	−364.000	−0.237314
$134$	−1976.00	−1.27388
$135$	0	0
$136$	−336.000	−0.211851
$137$	1254.00	0.782018	0.391009	−	0.920387i	$-0.372126\pi$
$137$	1254.00	0.782018	0.391009	+	0.920387i	$0.372126\pi$
$138$	0	0
$139$	−1564.00	−0.954365	−0.477183	−	0.878804i	$-0.658342\pi$
$139$	−1564.00	−0.954365	−0.477183	+	0.878804i	$0.658342\pi$
$140$	−140.000	−0.0845154
$141$	0	0
$142$	1440.00	0.851001
$143$	−2280.00	−1.33331
$144$	0	0
$145$	−1170.00	−0.670091
$146$	292.000	0.165521
$147$	0	0
$148$	−424.000	−0.235490
$149$	−1038.00	−0.570713	−0.285357	−	0.958421i	$-0.592112\pi$
$149$	−1038.00	−0.570713	−0.285357	+	0.958421i	$0.592112\pi$
$150$	0	0
$151$	3008.00	1.62111	0.810555	−	0.585663i	$-0.199166\pi$
$151$	3008.00	1.62111	0.810555	+	0.585663i	$0.199166\pi$
$152$	−416.000	−0.221987
$153$	0	0
$154$	−840.000	−0.439540
$155$	1520.00	0.787673
$156$	0	0
$157$	3062.00	1.55652	0.778262	−	0.627940i	$-0.216102\pi$
$157$	3062.00	1.55652	0.778262	+	0.627940i	$0.216102\pi$
$158$	−1616.00	−0.813684
$159$	0	0
$160$	−160.000	−0.0790569
$161$	−840.000	−0.411188
$162$	0	0
$163$	−988.000	−0.474762	−0.237381	−	0.971417i	$-0.576289\pi$
$163$	−988.000	−0.474762	−0.237381	+	0.971417i	$0.576289\pi$
$164$	216.000	0.102846
$165$	0	0
$166$	−1224.00	−0.572294
$167$	−1656.00	−0.767336	−0.383668	−	0.923471i	$-0.625339\pi$
$167$	−1656.00	−0.767336	−0.383668	+	0.923471i	$0.625339\pi$
$168$	0	0
$169$	−753.000	−0.342740
$170$	420.000	0.189485
$171$	0	0
$172$	−784.000	−0.347555
$173$	3066.00	1.34742	0.673710	−	0.738996i	$-0.264700\pi$
$173$	3066.00	1.34742	0.673710	+	0.738996i	$0.264700\pi$
$174$	0	0
$175$	175.000	0.0755929
$176$	−960.000	−0.411152
$177$	0	0
$178$	−2292.00	−0.965127
$179$	2028.00	0.846815	0.423407	−	0.905939i	$-0.360834\pi$
$179$	2028.00	0.846815	0.423407	+	0.905939i	$0.360834\pi$
$180$	0	0
$181$	−4210.00	−1.72888	−0.864439	−	0.502738i	$-0.832326\pi$
$181$	−4210.00	−1.72888	−0.864439	+	0.502738i	$0.832326\pi$
$182$	532.000	0.216673
$183$	0	0
$184$	−960.000	−0.384631
$185$	530.000	0.210629
$186$	0	0
$187$	2520.00	0.985458
$188$	−1344.00	−0.521390
$189$	0	0
$190$	520.000	0.198551
$191$	2616.00	0.991032	0.495516	−	0.868599i	$-0.334979\pi$
$191$	2616.00	0.991032	0.495516	+	0.868599i	$0.334979\pi$
$192$	0	0
$193$	722.000	0.269278	0.134639	−	0.990895i	$-0.457012\pi$
$193$	722.000	0.269278	0.134639	+	0.990895i	$0.457012\pi$
$194$	−140.000	−0.0518114
$195$	0	0
$196$	196.000	0.0714286
$197$	−2934.00	−1.06111	−0.530555	−	0.847650i	$-0.678017\pi$
$197$	−2934.00	−1.06111	−0.530555	+	0.847650i	$0.678017\pi$
$198$	0	0
$199$	−520.000	−0.185235	−0.0926176	−	0.995702i	$-0.529523\pi$
$199$	−520.000	−0.185235	−0.0926176	+	0.995702i	$0.529523\pi$
$200$	200.000	0.0707107
$201$	0	0
$202$	−3900.00	−1.35843
$203$	1638.00	0.566330
$204$	0	0
$205$	−270.000	−0.0919884
$206$	976.000	0.330103
$207$	0	0
$208$	608.000	0.202679
$209$	3120.00	1.03261
$210$	0	0
$211$	3476.00	1.13411	0.567056	−	0.823679i	$-0.308082\pi$
$211$	3476.00	1.13411	0.567056	+	0.823679i	$0.308082\pi$
$212$	−1752.00	−0.567584
$213$	0	0
$214$	1992.00	0.636310
$215$	980.000	0.310863
$216$	0	0
$217$	−2128.00	−0.665705
$218$	1516.00	0.470993
$219$	0	0
$220$	1200.00	0.367745
$221$	−1596.00	−0.485785
$222$	0	0
$223$	−1456.00	−0.437224	−0.218612	−	0.975812i	$-0.570153\pi$
$223$	−1456.00	−0.437224	−0.218612	+	0.975812i	$0.570153\pi$
$224$	224.000	0.0668153
$225$	0	0
$226$	2844.00	0.837080
$227$	3324.00	0.971901	0.485951	−	0.873986i	$-0.338473\pi$
$227$	3324.00	0.971901	0.485951	+	0.873986i	$0.338473\pi$
$228$	0	0
$229$	1694.00	0.488833	0.244416	−	0.969670i	$-0.421404\pi$
$229$	1694.00	0.488833	0.244416	+	0.969670i	$0.421404\pi$
$230$	1200.00	0.344025
$231$	0	0
$232$	1872.00	0.529754
$233$	6198.00	1.74268	0.871340	−	0.490680i	$-0.163251\pi$
$233$	6198.00	1.74268	0.871340	+	0.490680i	$0.163251\pi$
$234$	0	0
$235$	1680.00	0.466345
$236$	1776.00	0.489863
$237$	0	0
$238$	−588.000	−0.160144
$239$	−936.000	−0.253326	−0.126663	−	0.991946i	$-0.540427\pi$
$239$	−936.000	−0.253326	−0.126663	+	0.991946i	$0.540427\pi$
$240$	0	0
$241$	1730.00	0.462403	0.231201	−	0.972906i	$-0.425734\pi$
$241$	1730.00	0.462403	0.231201	+	0.972906i	$0.425734\pi$
$242$	4538.00	1.20543
$243$	0	0
$244$	152.000	0.0398803
$245$	−245.000	−0.0638877
$246$	0	0
$247$	−1976.00	−0.509028
$248$	−2432.00	−0.622710
$249$	0	0
$250$	−250.000	−0.0632456
$251$	3708.00	0.932458	0.466229	−	0.884664i	$-0.345612\pi$
$251$	3708.00	0.932458	0.466229	+	0.884664i	$0.345612\pi$
$252$	0	0
$253$	7200.00	1.78917
$254$	1696.00	0.418963
$255$	0	0
$256$	256.000	0.0625000
$257$	−4746.00	−1.15194	−0.575968	−	0.817473i	$-0.695375\pi$
$257$	−4746.00	−1.15194	−0.575968	+	0.817473i	$0.695375\pi$
$258$	0	0
$259$	−742.000	−0.178014
$260$	−760.000	−0.181282
$261$	0	0
$262$	−1176.00	−0.277304
$263$	−4200.00	−0.984727	−0.492363	−	0.870390i	$-0.663867\pi$
$263$	−4200.00	−0.984727	−0.492363	+	0.870390i	$0.663867\pi$
$264$	0	0
$265$	2190.00	0.507663
$266$	−728.000	−0.167807
$267$	0	0
$268$	−3952.00	−0.900772
$269$	−8502.00	−1.92705	−0.963524	−	0.267621i	$-0.913763\pi$
$269$	−8502.00	−1.92705	−0.963524	+	0.267621i	$0.913763\pi$
$270$	0	0
$271$	−4336.00	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−4336.00	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−672.000	−0.149801
$273$	0	0
$274$	2508.00	0.552970
$275$	−1500.00	−0.328921
$276$	0	0
$277$	3350.00	0.726650	0.363325	−	0.931663i	$-0.381641\pi$
$277$	3350.00	0.726650	0.363325	+	0.931663i	$0.381641\pi$
$278$	−3128.00	−0.674838
$279$	0	0
$280$	−280.000	−0.0597614
$281$	8406.00	1.78455	0.892277	−	0.451488i	$-0.149106\pi$
$281$	8406.00	1.78455	0.892277	+	0.451488i	$0.149106\pi$
$282$	0	0
$283$	6284.00	1.31995	0.659974	−	0.751289i	$-0.270567\pi$
$283$	6284.00	1.31995	0.659974	+	0.751289i	$0.270567\pi$
$284$	2880.00	0.601748
$285$	0	0
$286$	−4560.00	−0.942792
$287$	378.000	0.0777444
$288$	0	0
$289$	−3149.00	−0.640953
$290$	−2340.00	−0.473826
$291$	0	0
$292$	584.000	0.117041
$293$	−3582.00	−0.714207	−0.357104	−	0.934065i	$-0.616236\pi$
$293$	−3582.00	−0.714207	−0.357104	+	0.934065i	$0.616236\pi$
$294$	0	0
$295$	−2220.00	−0.438147
$296$	−848.000	−0.166517
$297$	0	0
$298$	−2076.00	−0.403555
$299$	−4560.00	−0.881979
$300$	0	0
$301$	−1372.00	−0.262727
$302$	6016.00	1.14630
$303$	0	0
$304$	−832.000	−0.156969
$305$	−190.000	−0.0356701
$306$	0	0
$307$	8804.00	1.63671	0.818356	−	0.574711i	$-0.194886\pi$
$307$	8804.00	1.63671	0.818356	+	0.574711i	$0.194886\pi$
$308$	−1680.00	−0.310802
$309$	0	0
$310$	3040.00	0.556969
$311$	2424.00	0.441969	0.220985	−	0.975277i	$-0.429073\pi$
$311$	2424.00	0.441969	0.220985	+	0.975277i	$0.429073\pi$
$312$	0	0
$313$	−9070.00	−1.63791	−0.818956	−	0.573856i	$-0.805447\pi$
$313$	−9070.00	−1.63791	−0.818956	+	0.573856i	$0.805447\pi$
$314$	6124.00	1.10063
$315$	0	0
$316$	−3232.00	−0.575361
$317$	6738.00	1.19383	0.596914	−	0.802305i	$-0.296393\pi$
$317$	6738.00	1.19383	0.596914	+	0.802305i	$0.296393\pi$
$318$	0	0
$319$	−14040.0	−2.46423
$320$	−320.000	−0.0559017
$321$	0	0
$322$	−1680.00	−0.290754
$323$	2184.00	0.376226
$324$	0	0
$325$	950.000	0.162143
$326$	−1976.00	−0.335707
$327$	0	0
$328$	432.000	0.0727232
$329$	−2352.00	−0.394134
$330$	0	0
$331$	7868.00	1.30654	0.653269	−	0.757125i	$-0.273397\pi$
$331$	7868.00	1.30654	0.653269	+	0.757125i	$0.273397\pi$
$332$	−2448.00	−0.404673
$333$	0	0
$334$	−3312.00	−0.542589
$335$	4940.00	0.805675
$336$	0	0
$337$	9218.00	1.49002	0.745010	−	0.667054i	$-0.232445\pi$
$337$	9218.00	1.49002	0.745010	+	0.667054i	$0.232445\pi$
$338$	−1506.00	−0.242354
$339$	0	0
$340$	840.000	0.133986
$341$	18240.0	2.89663
$342$	0	0
$343$	343.000	0.0539949
$344$	−1568.00	−0.245758
$345$	0	0
$346$	6132.00	0.952770
$347$	−1212.00	−0.187503	−0.0937515	−	0.995596i	$-0.529886\pi$
$347$	−1212.00	−0.187503	−0.0937515	+	0.995596i	$0.529886\pi$
$348$	0	0
$349$	10118.0	1.55187	0.775937	−	0.630810i	$-0.217277\pi$
$349$	10118.0	1.55187	0.775937	+	0.630810i	$0.217277\pi$
$350$	350.000	0.0534522
$351$	0	0
$352$	−1920.00	−0.290728
$353$	−1194.00	−0.180029	−0.0900145	−	0.995940i	$-0.528691\pi$
$353$	−1194.00	−0.180029	−0.0900145	+	0.995940i	$0.528691\pi$
$354$	0	0
$355$	−3600.00	−0.538220
$356$	−4584.00	−0.682448
$357$	0	0
$358$	4056.00	0.598788
$359$	−2064.00	−0.303437	−0.151718	−	0.988424i	$-0.548481\pi$
$359$	−2064.00	−0.303437	−0.151718	+	0.988424i	$0.548481\pi$
$360$	0	0
$361$	−4155.00	−0.605773
$362$	−8420.00	−1.22250
$363$	0	0
$364$	1064.00	0.153211
$365$	−730.000	−0.104685
$366$	0	0
$367$	−7504.00	−1.06732	−0.533659	−	0.845700i	$-0.679183\pi$
$367$	−7504.00	−1.06732	−0.533659	+	0.845700i	$0.679183\pi$
$368$	−1920.00	−0.271975
$369$	0	0
$370$	1060.00	0.148937
$371$	−3066.00	−0.429053
$372$	0	0
$373$	902.000	0.125211	0.0626056	−	0.998038i	$-0.480059\pi$
$373$	902.000	0.125211	0.0626056	+	0.998038i	$0.480059\pi$
$374$	5040.00	0.696824
$375$	0	0
$376$	−2688.00	−0.368678
$377$	8892.00	1.21475
$378$	0	0
$379$	−12004.0	−1.62692	−0.813462	−	0.581618i	$-0.802420\pi$
$379$	−12004.0	−1.62692	−0.813462	+	0.581618i	$0.802420\pi$
$380$	1040.00	0.140397
$381$	0	0
$382$	5232.00	0.700765
$383$	−10848.0	−1.44728	−0.723638	−	0.690179i	$-0.757532\pi$
$383$	−10848.0	−1.44728	−0.723638	+	0.690179i	$0.757532\pi$
$384$	0	0
$385$	2100.00	0.277989
$386$	1444.00	0.190408
$387$	0	0
$388$	−280.000	−0.0366362
$389$	5538.00	0.721819	0.360910	−	0.932601i	$-0.382466\pi$
$389$	5538.00	0.721819	0.360910	+	0.932601i	$0.382466\pi$
$390$	0	0
$391$	5040.00	0.651877
$392$	392.000	0.0505076
$393$	0	0
$394$	−5868.00	−0.750319
$395$	4040.00	0.514619
$396$	0	0
$397$	11270.0	1.42475	0.712374	−	0.701800i	$-0.247620\pi$
$397$	11270.0	1.42475	0.712374	+	0.701800i	$0.247620\pi$
$398$	−1040.00	−0.130981
$399$	0	0
$400$	400.000	0.0500000
$401$	−2802.00	−0.348941	−0.174470	−	0.984662i	$-0.555821\pi$
$401$	−2802.00	−0.348941	−0.174470	+	0.984662i	$0.555821\pi$
$402$	0	0
$403$	−11552.0	−1.42791
$404$	−7800.00	−0.960556
$405$	0	0
$406$	3276.00	0.400456
$407$	6360.00	0.774579
$408$	0	0
$409$	4106.00	0.496403	0.248201	−	0.968708i	$-0.420161\pi$
$409$	4106.00	0.496403	0.248201	+	0.968708i	$0.420161\pi$
$410$	−540.000	−0.0650456
$411$	0	0
$412$	1952.00	0.233418
$413$	3108.00	0.370302
$414$	0	0
$415$	3060.00	0.361951
$416$	1216.00	0.143316
$417$	0	0
$418$	6240.00	0.730164
$419$	−4284.00	−0.499492	−0.249746	−	0.968311i	$-0.580347\pi$
$419$	−4284.00	−0.499492	−0.249746	+	0.968311i	$0.580347\pi$
$420$	0	0
$421$	1550.00	0.179436	0.0897178	−	0.995967i	$-0.471403\pi$
$421$	1550.00	0.179436	0.0897178	+	0.995967i	$0.471403\pi$
$422$	6952.00	0.801939
$423$	0	0
$424$	−3504.00	−0.401343
$425$	−1050.00	−0.119841
$426$	0	0
$427$	266.000	0.0301467
$428$	3984.00	0.449939
$429$	0	0
$430$	1960.00	0.219813
$431$	−16584.0	−1.85342	−0.926709	−	0.375780i	$-0.877375\pi$
$431$	−16584.0	−1.85342	−0.926709	+	0.375780i	$0.877375\pi$
$432$	0	0
$433$	−8422.00	−0.934724	−0.467362	−	0.884066i	$-0.654796\pi$
$433$	−8422.00	−0.934724	−0.467362	+	0.884066i	$0.654796\pi$
$434$	−4256.00	−0.470725
$435$	0	0
$436$	3032.00	0.333042
$437$	6240.00	0.683066
$438$	0	0
$439$	−2968.00	−0.322676	−0.161338	−	0.986899i	$-0.551581\pi$
$439$	−2968.00	−0.322676	−0.161338	+	0.986899i	$0.551581\pi$
$440$	2400.00	0.260035
$441$	0	0
$442$	−3192.00	−0.343502
$443$	2436.00	0.261259	0.130630	−	0.991431i	$-0.458300\pi$
$443$	2436.00	0.261259	0.130630	+	0.991431i	$0.458300\pi$
$444$	0	0
$445$	5730.00	0.610400
$446$	−2912.00	−0.309164
$447$	0	0
$448$	448.000	0.0472456
$449$	−7362.00	−0.773796	−0.386898	−	0.922123i	$-0.626453\pi$
$449$	−7362.00	−0.773796	−0.386898	+	0.922123i	$0.626453\pi$
$450$	0	0
$451$	−3240.00	−0.338283
$452$	5688.00	0.591905
$453$	0	0
$454$	6648.00	0.687238
$455$	−1330.00	−0.137036
$456$	0	0
$457$	9290.00	0.950914	0.475457	−	0.879739i	$-0.342283\pi$
$457$	9290.00	0.950914	0.475457	+	0.879739i	$0.342283\pi$
$458$	3388.00	0.345657
$459$	0	0
$460$	2400.00	0.243262
$461$	−11862.0	−1.19841	−0.599207	−	0.800594i	$-0.704517\pi$
$461$	−11862.0	−1.19841	−0.599207	+	0.800594i	$0.704517\pi$
$462$	0	0
$463$	−13264.0	−1.33138	−0.665692	−	0.746227i	$-0.731863\pi$
$463$	−13264.0	−1.33138	−0.665692	+	0.746227i	$0.731863\pi$
$464$	3744.00	0.374592
$465$	0	0
$466$	12396.0	1.23226
$467$	−14628.0	−1.44947	−0.724736	−	0.689027i	$-0.758038\pi$
$467$	−14628.0	−1.44947	−0.724736	+	0.689027i	$0.758038\pi$
$468$	0	0
$469$	−6916.00	−0.680919
$470$	3360.00	0.329756
$471$	0	0
$472$	3552.00	0.346386
$473$	11760.0	1.14318
$474$	0	0
$475$	−1300.00	−0.125575
$476$	−1176.00	−0.113239
$477$	0	0
$478$	−1872.00	−0.179128
$479$	−4416.00	−0.421236	−0.210618	−	0.977568i	$-0.567548\pi$
$479$	−4416.00	−0.421236	−0.210618	+	0.977568i	$0.567548\pi$
$480$	0	0
$481$	−4028.00	−0.381832
$482$	3460.00	0.326968
$483$	0	0
$484$	9076.00	0.852367
$485$	350.000	0.0327684
$486$	0	0
$487$	−232.000	−0.0215871	−0.0107936	−	0.999942i	$-0.503436\pi$
$487$	−232.000	−0.0215871	−0.0107936	+	0.999942i	$0.503436\pi$
$488$	304.000	0.0281997
$489$	0	0
$490$	−490.000	−0.0451754
$491$	17892.0	1.64451	0.822255	−	0.569119i	$-0.192716\pi$
$491$	17892.0	1.64451	0.822255	+	0.569119i	$0.192716\pi$
$492$	0	0
$493$	−9828.00	−0.897831
$494$	−3952.00	−0.359937
$495$	0	0
$496$	−4864.00	−0.440323
$497$	5040.00	0.454879
$498$	0	0
$499$	−6316.00	−0.566619	−0.283310	−	0.959029i	$-0.591432\pi$
$499$	−6316.00	−0.566619	−0.283310	+	0.959029i	$0.591432\pi$
$500$	−500.000	−0.0447214
$501$	0	0
$502$	7416.00	0.659347
$503$	12600.0	1.11691	0.558455	−	0.829534i	$-0.311394\pi$
$503$	12600.0	1.11691	0.558455	+	0.829534i	$0.311394\pi$
$504$	0	0
$505$	9750.00	0.859147
$506$	14400.0	1.26513
$507$	0	0
$508$	3392.00	0.296251
$509$	−17094.0	−1.48856	−0.744281	−	0.667866i	$-0.767208\pi$
$509$	−17094.0	−1.48856	−0.744281	+	0.667866i	$0.767208\pi$
$510$	0	0
$511$	1022.00	0.0884748
$512$	512.000	0.0441942
$513$	0	0
$514$	−9492.00	−0.814541
$515$	−2440.00	−0.208775
$516$	0	0
$517$	20160.0	1.71496
$518$	−1484.00	−0.125875
$519$	0	0
$520$	−1520.00	−0.128185
$521$	−14586.0	−1.22653	−0.613267	−	0.789876i	$-0.710145\pi$
$521$	−14586.0	−1.22653	−0.613267	+	0.789876i	$0.710145\pi$
$522$	0	0
$523$	−16324.0	−1.36482	−0.682408	−	0.730972i	$-0.739067\pi$
$523$	−16324.0	−1.36482	−0.682408	+	0.730972i	$0.739067\pi$
$524$	−2352.00	−0.196083
$525$	0	0
$526$	−8400.00	−0.696307
$527$	12768.0	1.05538
$528$	0	0
$529$	2233.00	0.183529
$530$	4380.00	0.358972
$531$	0	0
$532$	−1456.00	−0.118657
$533$	2052.00	0.166758
$534$	0	0
$535$	−4980.00	−0.402438
$536$	−7904.00	−0.636942
$537$	0	0
$538$	−17004.0	−1.36263
$539$	−2940.00	−0.234944
$540$	0	0
$541$	−7162.00	−0.569165	−0.284583	−	0.958652i	$-0.591855\pi$
$541$	−7162.00	−0.569165	−0.284583	+	0.958652i	$0.591855\pi$
$542$	−8672.00	−0.687259
$543$	0	0
$544$	−1344.00	−0.105926
$545$	−3790.00	−0.297882
$546$	0	0
$547$	9956.00	0.778223	0.389111	−	0.921191i	$-0.372782\pi$
$547$	9956.00	0.778223	0.389111	+	0.921191i	$0.372782\pi$
$548$	5016.00	0.391009
$549$	0	0
$550$	−3000.00	−0.232583
$551$	−12168.0	−0.940788
$552$	0	0
$553$	−5656.00	−0.434932
$554$	6700.00	0.513819
$555$	0	0
$556$	−6256.00	−0.477183
$557$	−15342.0	−1.16708	−0.583538	−	0.812086i	$-0.698332\pi$
$557$	−15342.0	−1.16708	−0.583538	+	0.812086i	$0.698332\pi$
$558$	0	0
$559$	−7448.00	−0.563536
$560$	−560.000	−0.0422577
$561$	0	0
$562$	16812.0	1.26187
$563$	−3300.00	−0.247031	−0.123515	−	0.992343i	$-0.539417\pi$
$563$	−3300.00	−0.247031	−0.123515	+	0.992343i	$0.539417\pi$
$564$	0	0
$565$	−7110.00	−0.529416
$566$	12568.0	0.933344
$567$	0	0
$568$	5760.00	0.425500
$569$	−2154.00	−0.158700	−0.0793501	−	0.996847i	$-0.525284\pi$
$569$	−2154.00	−0.158700	−0.0793501	+	0.996847i	$0.525284\pi$
$570$	0	0
$571$	−1348.00	−0.0987952	−0.0493976	−	0.998779i	$-0.515730\pi$
$571$	−1348.00	−0.0987952	−0.0493976	+	0.998779i	$0.515730\pi$
$572$	−9120.00	−0.666654
$573$	0	0
$574$	756.000	0.0549736
$575$	−3000.00	−0.217580
$576$	0	0
$577$	−16486.0	−1.18946	−0.594732	−	0.803924i	$-0.702742\pi$
$577$	−16486.0	−1.18946	−0.594732	+	0.803924i	$0.702742\pi$
$578$	−6298.00	−0.453222
$579$	0	0
$580$	−4680.00	−0.335046
$581$	−4284.00	−0.305904
$582$	0	0
$583$	26280.0	1.86691
$584$	1168.00	0.0827606
$585$	0	0
$586$	−7164.00	−0.505021
$587$	−9756.00	−0.685985	−0.342993	−	0.939338i	$-0.611441\pi$
$587$	−9756.00	−0.685985	−0.342993	+	0.939338i	$0.611441\pi$
$588$	0	0
$589$	15808.0	1.10587
$590$	−4440.00	−0.309817
$591$	0	0
$592$	−1696.00	−0.117745
$593$	−8202.00	−0.567986	−0.283993	−	0.958826i	$-0.591659\pi$
$593$	−8202.00	−0.567986	−0.283993	+	0.958826i	$0.591659\pi$
$594$	0	0
$595$	1470.00	0.101284
$596$	−4152.00	−0.285357
$597$	0	0
$598$	−9120.00	−0.623653
$599$	−20544.0	−1.40134	−0.700672	−	0.713484i	$-0.747116\pi$
$599$	−20544.0	−1.40134	−0.700672	+	0.713484i	$0.747116\pi$
$600$	0	0
$601$	−5254.00	−0.356598	−0.178299	−	0.983976i	$-0.557059\pi$
$601$	−5254.00	−0.356598	−0.178299	+	0.983976i	$0.557059\pi$
$602$	−2744.00	−0.185776
$603$	0	0
$604$	12032.0	0.810555
$605$	−11345.0	−0.762380
$606$	0	0
$607$	−19456.0	−1.30098	−0.650490	−	0.759515i	$-0.725436\pi$
$607$	−19456.0	−1.30098	−0.650490	+	0.759515i	$0.725436\pi$
$608$	−1664.00	−0.110994
$609$	0	0
$610$	−380.000	−0.0252225
$611$	−12768.0	−0.845398
$612$	0	0
$613$	3926.00	0.258678	0.129339	−	0.991600i	$-0.458714\pi$
$613$	3926.00	0.258678	0.129339	+	0.991600i	$0.458714\pi$
$614$	17608.0	1.15733
$615$	0	0
$616$	−3360.00	−0.219770
$617$	−22122.0	−1.44343	−0.721717	−	0.692189i	$-0.756647\pi$
$617$	−22122.0	−1.44343	−0.721717	+	0.692189i	$0.756647\pi$
$618$	0	0
$619$	−12796.0	−0.830880	−0.415440	−	0.909621i	$-0.636372\pi$
$619$	−12796.0	−0.830880	−0.415440	+	0.909621i	$0.636372\pi$
$620$	6080.00	0.393837
$621$	0	0
$622$	4848.00	0.312519
$623$	−8022.00	−0.515882
$624$	0	0
$625$	625.000	0.0400000
$626$	−18140.0	−1.15818
$627$	0	0
$628$	12248.0	0.778262
$629$	4452.00	0.282214
$630$	0	0
$631$	−16576.0	−1.04577	−0.522884	−	0.852404i	$-0.675144\pi$
$631$	−16576.0	−1.04577	−0.522884	+	0.852404i	$0.675144\pi$
$632$	−6464.00	−0.406842
$633$	0	0
$634$	13476.0	0.844165
$635$	−4240.00	−0.264975
$636$	0	0
$637$	1862.00	0.115817
$638$	−28080.0	−1.74247
$639$	0	0
$640$	−640.000	−0.0395285
$641$	−11202.0	−0.690253	−0.345127	−	0.938556i	$-0.612164\pi$
$641$	−11202.0	−0.690253	−0.345127	+	0.938556i	$0.612164\pi$
$642$	0	0
$643$	4052.00	0.248515	0.124258	−	0.992250i	$-0.460345\pi$
$643$	4052.00	0.248515	0.124258	+	0.992250i	$0.460345\pi$
$644$	−3360.00	−0.205594
$645$	0	0
$646$	4368.00	0.266032
$647$	17544.0	1.06604	0.533018	−	0.846104i	$-0.321058\pi$
$647$	17544.0	1.06604	0.533018	+	0.846104i	$0.321058\pi$
$648$	0	0
$649$	−26640.0	−1.61127
$650$	1900.00	0.114653
$651$	0	0
$652$	−3952.00	−0.237381
$653$	12066.0	0.723092	0.361546	−	0.932354i	$-0.382249\pi$
$653$	12066.0	0.723092	0.361546	+	0.932354i	$0.382249\pi$
$654$	0	0
$655$	2940.00	0.175382
$656$	864.000	0.0514231
$657$	0	0
$658$	−4704.00	−0.278695
$659$	7596.00	0.449011	0.224505	−	0.974473i	$-0.427923\pi$
$659$	7596.00	0.449011	0.224505	+	0.974473i	$0.427923\pi$
$660$	0	0
$661$	11630.0	0.684349	0.342174	−	0.939636i	$-0.388837\pi$
$661$	11630.0	0.684349	0.342174	+	0.939636i	$0.388837\pi$
$662$	15736.0	0.923863
$663$	0	0
$664$	−4896.00	−0.286147
$665$	1820.00	0.106130
$666$	0	0
$667$	−28080.0	−1.63008
$668$	−6624.00	−0.383668
$669$	0	0
$670$	9880.00	0.569698
$671$	−2280.00	−0.131175
$672$	0	0
$673$	7778.00	0.445498	0.222749	−	0.974876i	$-0.428497\pi$
$673$	7778.00	0.445498	0.222749	+	0.974876i	$0.428497\pi$
$674$	18436.0	1.05360
$675$	0	0
$676$	−3012.00	−0.171370
$677$	28914.0	1.64144	0.820720	−	0.571330i	$-0.193572\pi$
$677$	28914.0	1.64144	0.820720	+	0.571330i	$0.193572\pi$
$678$	0	0
$679$	−490.000	−0.0276944
$680$	1680.00	0.0947427
$681$	0	0
$682$	36480.0	2.04823
$683$	−25404.0	−1.42322	−0.711608	−	0.702576i	$-0.752033\pi$
$683$	−25404.0	−1.42322	−0.711608	+	0.702576i	$0.752033\pi$
$684$	0	0
$685$	−6270.00	−0.349729
$686$	686.000	0.0381802
$687$	0	0
$688$	−3136.00	−0.173777
$689$	−16644.0	−0.920299
$690$	0	0
$691$	1244.00	0.0684862	0.0342431	−	0.999414i	$-0.489098\pi$
$691$	1244.00	0.0684862	0.0342431	+	0.999414i	$0.489098\pi$
$692$	12264.0	0.673710
$693$	0	0
$694$	−2424.00	−0.132585
$695$	7820.00	0.426805
$696$	0	0
$697$	−2268.00	−0.123252
$698$	20236.0	1.09734
$699$	0	0
$700$	700.000	0.0377964
$701$	−3798.00	−0.204634	−0.102317	−	0.994752i	$-0.532626\pi$
$701$	−3798.00	−0.204634	−0.102317	+	0.994752i	$0.532626\pi$
$702$	0	0
$703$	5512.00	0.295717
$704$	−3840.00	−0.205576
$705$	0	0
$706$	−2388.00	−0.127300
$707$	−13650.0	−0.726112
$708$	0	0
$709$	−15154.0	−0.802709	−0.401354	−	0.915923i	$-0.631460\pi$
$709$	−15154.0	−0.802709	−0.401354	+	0.915923i	$0.631460\pi$
$710$	−7200.00	−0.380579
$711$	0	0
$712$	−9168.00	−0.482564
$713$	36480.0	1.91611
$714$	0	0
$715$	11400.0	0.596274
$716$	8112.00	0.423407
$717$	0	0
$718$	−4128.00	−0.214562
$719$	10032.0	0.520348	0.260174	−	0.965562i	$-0.416220\pi$
$719$	10032.0	0.520348	0.260174	+	0.965562i	$0.416220\pi$
$720$	0	0
$721$	3416.00	0.176447
$722$	−8310.00	−0.428347
$723$	0	0
$724$	−16840.0	−0.864439
$725$	5850.00	0.299674
$726$	0	0
$727$	17768.0	0.906436	0.453218	−	0.891400i	$-0.350276\pi$
$727$	17768.0	0.906436	0.453218	+	0.891400i	$0.350276\pi$
$728$	2128.00	0.108336
$729$	0	0
$730$	−1460.00	−0.0740233
$731$	8232.00	0.416514
$732$	0	0
$733$	9830.00	0.495333	0.247667	−	0.968845i	$-0.420336\pi$
$733$	9830.00	0.495333	0.247667	+	0.968845i	$0.420336\pi$
$734$	−15008.0	−0.754708
$735$	0	0
$736$	−3840.00	−0.192316
$737$	59280.0	2.96283
$738$	0	0
$739$	−33244.0	−1.65480	−0.827402	−	0.561610i	$-0.810182\pi$
$739$	−33244.0	−1.65480	−0.827402	+	0.561610i	$0.810182\pi$
$740$	2120.00	0.105315
$741$	0	0
$742$	−6132.00	−0.303387
$743$	−3672.00	−0.181309	−0.0906545	−	0.995882i	$-0.528896\pi$
$743$	−3672.00	−0.181309	−0.0906545	+	0.995882i	$0.528896\pi$
$744$	0	0
$745$	5190.00	0.255231
$746$	1804.00	0.0885377
$747$	0	0
$748$	10080.0	0.492729
$749$	6972.00	0.340122
$750$	0	0
$751$	−6280.00	−0.305140	−0.152570	−	0.988293i	$-0.548755\pi$
$751$	−6280.00	−0.305140	−0.152570	+	0.988293i	$0.548755\pi$
$752$	−5376.00	−0.260695
$753$	0	0
$754$	17784.0	0.858959
$755$	−15040.0	−0.724982
$756$	0	0
$757$	−826.000	−0.0396585	−0.0198292	−	0.999803i	$-0.506312\pi$
$757$	−826.000	−0.0396585	−0.0198292	+	0.999803i	$0.506312\pi$
$758$	−24008.0	−1.15041
$759$	0	0
$760$	2080.00	0.0992757
$761$	−16842.0	−0.802263	−0.401131	−	0.916021i	$-0.631383\pi$
$761$	−16842.0	−0.802263	−0.401131	+	0.916021i	$0.631383\pi$
$762$	0	0
$763$	5306.00	0.251756
$764$	10464.0	0.495516
$765$	0	0
$766$	−21696.0	−1.02338
$767$	16872.0	0.794280
$768$	0	0
$769$	−21454.0	−1.00605	−0.503024	−	0.864272i	$-0.667779\pi$
$769$	−21454.0	−1.00605	−0.503024	+	0.864272i	$0.667779\pi$
$770$	4200.00	0.196568
$771$	0	0
$772$	2888.00	0.134639
$773$	−13182.0	−0.613355	−0.306678	−	0.951813i	$-0.599217\pi$
$773$	−13182.0	−0.613355	−0.306678	+	0.951813i	$0.599217\pi$
$774$	0	0
$775$	−7600.00	−0.352258
$776$	−560.000	−0.0259057
$777$	0	0
$778$	11076.0	0.510403
$779$	−2808.00	−0.129149
$780$	0	0
$781$	−43200.0	−1.97928
$782$	10080.0	0.460946
$783$	0	0
$784$	784.000	0.0357143
$785$	−15310.0	−0.696099
$786$	0	0
$787$	24356.0	1.10317	0.551587	−	0.834117i	$-0.314023\pi$
$787$	24356.0	1.10317	0.551587	+	0.834117i	$0.314023\pi$
$788$	−11736.0	−0.530555
$789$	0	0
$790$	8080.00	0.363891
$791$	9954.00	0.447438
$792$	0	0
$793$	1444.00	0.0646632
$794$	22540.0	1.00745
$795$	0	0
$796$	−2080.00	−0.0926176
$797$	13194.0	0.586393	0.293197	−	0.956052i	$-0.405281\pi$
$797$	13194.0	0.586393	0.293197	+	0.956052i	$0.405281\pi$
$798$	0	0
$799$	14112.0	0.624839
$800$	800.000	0.0353553
$801$	0	0
$802$	−5604.00	−0.246738
$803$	−8760.00	−0.384973
$804$	0	0
$805$	4200.00	0.183889
$806$	−23104.0	−1.00968
$807$	0	0
$808$	−15600.0	−0.679215
$809$	−29274.0	−1.27221	−0.636106	−	0.771602i	$-0.719456\pi$
$809$	−29274.0	−1.27221	−0.636106	+	0.771602i	$0.719456\pi$
$810$	0	0
$811$	9812.00	0.424841	0.212420	−	0.977178i	$-0.431865\pi$
$811$	9812.00	0.424841	0.212420	+	0.977178i	$0.431865\pi$
$812$	6552.00	0.283165
$813$	0	0
$814$	12720.0	0.547710
$815$	4940.00	0.212320
$816$	0	0
$817$	10192.0	0.436442
$818$	8212.00	0.351010
$819$	0	0
$820$	−1080.00	−0.0459942
$821$	41154.0	1.74943	0.874717	−	0.484635i	$-0.161048\pi$
$821$	41154.0	1.74943	0.874717	+	0.484635i	$0.161048\pi$
$822$	0	0
$823$	37640.0	1.59423	0.797113	−	0.603830i	$-0.206360\pi$
$823$	37640.0	1.59423	0.797113	+	0.603830i	$0.206360\pi$
$824$	3904.00	0.165051
$825$	0	0
$826$	6216.00	0.261843
$827$	13572.0	0.570671	0.285335	−	0.958428i	$-0.407895\pi$
$827$	13572.0	0.570671	0.285335	+	0.958428i	$0.407895\pi$
$828$	0	0
$829$	13574.0	0.568691	0.284345	−	0.958722i	$-0.408224\pi$
$829$	13574.0	0.568691	0.284345	+	0.958722i	$0.408224\pi$
$830$	6120.00	0.255938
$831$	0	0
$832$	2432.00	0.101339
$833$	−2058.00	−0.0856008
$834$	0	0
$835$	8280.00	0.343163
$836$	12480.0	0.516304
$837$	0	0
$838$	−8568.00	−0.353194
$839$	5112.00	0.210353	0.105176	−	0.994454i	$-0.466459\pi$
$839$	5112.00	0.210353	0.105176	+	0.994454i	$0.466459\pi$
$840$	0	0
$841$	30367.0	1.24511
$842$	3100.00	0.126880
$843$	0	0
$844$	13904.0	0.567056
$845$	3765.00	0.153278
$846$	0	0
$847$	15883.0	0.644329
$848$	−7008.00	−0.283792
$849$	0	0
$850$	−2100.00	−0.0847405
$851$	12720.0	0.512381
$852$	0	0
$853$	20702.0	0.830977	0.415488	−	0.909599i	$-0.363611\pi$
$853$	20702.0	0.830977	0.415488	+	0.909599i	$0.363611\pi$
$854$	532.000	0.0213169
$855$	0	0
$856$	7968.00	0.318155
$857$	5646.00	0.225045	0.112523	−	0.993649i	$-0.464107\pi$
$857$	5646.00	0.225045	0.112523	+	0.993649i	$0.464107\pi$
$858$	0	0
$859$	20756.0	0.824430	0.412215	−	0.911087i	$-0.364755\pi$
$859$	20756.0	0.824430	0.412215	+	0.911087i	$0.364755\pi$
$860$	3920.00	0.155431
$861$	0	0
$862$	−33168.0	−1.31056
$863$	24432.0	0.963702	0.481851	−	0.876253i	$-0.339965\pi$
$863$	24432.0	0.963702	0.481851	+	0.876253i	$0.339965\pi$
$864$	0	0
$865$	−15330.0	−0.602585
$866$	−16844.0	−0.660950
$867$	0	0
$868$	−8512.00	−0.332853
$869$	48480.0	1.89249
$870$	0	0
$871$	−37544.0	−1.46054
$872$	6064.00	0.235497
$873$	0	0
$874$	12480.0	0.483000
$875$	−875.000	−0.0338062
$876$	0	0
$877$	43166.0	1.66204	0.831022	−	0.556240i	$-0.187756\pi$
$877$	43166.0	1.66204	0.831022	+	0.556240i	$0.187756\pi$
$878$	−5936.00	−0.228167
$879$	0	0
$880$	4800.00	0.183873
$881$	1854.00	0.0708999	0.0354500	−	0.999371i	$-0.488714\pi$
$881$	1854.00	0.0708999	0.0354500	+	0.999371i	$0.488714\pi$
$882$	0	0
$883$	−23740.0	−0.904773	−0.452387	−	0.891822i	$-0.649427\pi$
$883$	−23740.0	−0.904773	−0.452387	+	0.891822i	$0.649427\pi$
$884$	−6384.00	−0.242893
$885$	0	0
$886$	4872.00	0.184738
$887$	−32088.0	−1.21467	−0.607333	−	0.794447i	$-0.707761\pi$
$887$	−32088.0	−1.21467	−0.607333	+	0.794447i	$0.707761\pi$
$888$	0	0
$889$	5936.00	0.223945
$890$	11460.0	0.431618
$891$	0	0
$892$	−5824.00	−0.218612
$893$	17472.0	0.654735
$894$	0	0
$895$	−10140.0	−0.378707
$896$	896.000	0.0334077
$897$	0	0
$898$	−14724.0	−0.547156
$899$	−71136.0	−2.63906
$900$	0	0
$901$	18396.0	0.680199
$902$	−6480.00	−0.239202
$903$	0	0
$904$	11376.0	0.418540
$905$	21050.0	0.773178
$906$	0	0
$907$	4268.00	0.156248	0.0781238	−	0.996944i	$-0.475107\pi$
$907$	4268.00	0.156248	0.0781238	+	0.996944i	$0.475107\pi$
$908$	13296.0	0.485951
$909$	0	0
$910$	−2660.00	−0.0968991
$911$	19512.0	0.709617	0.354809	−	0.934939i	$-0.384546\pi$
$911$	19512.0	0.709617	0.354809	+	0.934939i	$0.384546\pi$
$912$	0	0
$913$	36720.0	1.33106
$914$	18580.0	0.672398
$915$	0	0
$916$	6776.00	0.244416
$917$	−4116.00	−0.148225
$918$	0	0
$919$	−6496.00	−0.233170	−0.116585	−	0.993181i	$-0.537195\pi$
$919$	−6496.00	−0.233170	−0.116585	+	0.993181i	$0.537195\pi$
$920$	4800.00	0.172012
$921$	0	0
$922$	−23724.0	−0.847406
$923$	27360.0	0.975694
$924$	0	0
$925$	−2650.00	−0.0941962
$926$	−26528.0	−0.941430
$927$	0	0
$928$	7488.00	0.264877
$929$	16926.0	0.597765	0.298883	−	0.954290i	$-0.403386\pi$
$929$	16926.0	0.597765	0.298883	+	0.954290i	$0.403386\pi$
$930$	0	0
$931$	−2548.00	−0.0896964
$932$	24792.0	0.871340
$933$	0	0
$934$	−29256.0	−1.02493
$935$	−12600.0	−0.440710
$936$	0	0
$937$	−14686.0	−0.512029	−0.256014	−	0.966673i	$-0.582409\pi$
$937$	−14686.0	−0.512029	−0.256014	+	0.966673i	$0.582409\pi$
$938$	−13832.0	−0.481483
$939$	0	0
$940$	6720.00	0.233173
$941$	33834.0	1.17211	0.586056	−	0.810271i	$-0.300680\pi$
$941$	33834.0	1.17211	0.586056	+	0.810271i	$0.300680\pi$
$942$	0	0
$943$	−6480.00	−0.223773
$944$	7104.00	0.244932
$945$	0	0
$946$	23520.0	0.808352
$947$	−17508.0	−0.600775	−0.300387	−	0.953817i	$-0.597116\pi$
$947$	−17508.0	−0.600775	−0.300387	+	0.953817i	$0.597116\pi$
$948$	0	0
$949$	5548.00	0.189774
$950$	−2600.00	−0.0887949
$951$	0	0
$952$	−2352.00	−0.0800722
$953$	12582.0	0.427672	0.213836	−	0.976870i	$-0.431404\pi$
$953$	12582.0	0.427672	0.213836	+	0.976870i	$0.431404\pi$
$954$	0	0
$955$	−13080.0	−0.443203
$956$	−3744.00	−0.126663
$957$	0	0
$958$	−8832.00	−0.297859
$959$	8778.00	0.295575
$960$	0	0
$961$	62625.0	2.10214
$962$	−8056.00	−0.269996
$963$	0	0
$964$	6920.00	0.231201
$965$	−3610.00	−0.120425
$966$	0	0
$967$	−19096.0	−0.635042	−0.317521	−	0.948251i	$-0.602850\pi$
$967$	−19096.0	−0.635042	−0.317521	+	0.948251i	$0.602850\pi$
$968$	18152.0	0.602714
$969$	0	0
$970$	700.000	0.0231708
$971$	−50484.0	−1.66850	−0.834248	−	0.551390i	$-0.814098\pi$
$971$	−50484.0	−1.66850	−0.834248	+	0.551390i	$0.814098\pi$
$972$	0	0
$973$	−10948.0	−0.360716
$974$	−464.000	−0.0152644
$975$	0	0
$976$	608.000	0.0199402
$977$	−26898.0	−0.880802	−0.440401	−	0.897801i	$-0.645164\pi$
$977$	−26898.0	−0.880802	−0.440401	+	0.897801i	$0.645164\pi$
$978$	0	0
$979$	68760.0	2.24472
$980$	−980.000	−0.0319438
$981$	0	0
$982$	35784.0	1.16284
$983$	13368.0	0.433747	0.216873	−	0.976200i	$-0.430414\pi$
$983$	13368.0	0.433747	0.216873	+	0.976200i	$0.430414\pi$
$984$	0	0
$985$	14670.0	0.474543
$986$	−19656.0	−0.634863
$987$	0	0
$988$	−7904.00	−0.254514
$989$	23520.0	0.756211
$990$	0	0
$991$	−44296.0	−1.41989	−0.709944	−	0.704258i	$-0.751280\pi$
$991$	−44296.0	−1.41989	−0.709944	+	0.704258i	$0.751280\pi$
$992$	−9728.00	−0.311355
$993$	0	0
$994$	10080.0	0.321648
$995$	2600.00	0.0828397
$996$	0	0
$997$	−4354.00	−0.138307	−0.0691537	−	0.997606i	$-0.522030\pi$
$997$	−4354.00	−0.138307	−0.0691537	+	0.997606i	$0.522030\pi$
$998$	−12632.0	−0.400660
$999$	0	0

Twists

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

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