LMFDB - Embedded newform 490.6.a.l.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,6,Mod(1,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("490.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	490.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:	$78.5880717084$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	490.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+4.00000 q^{2} +11.0000 q^{3} +16.0000 q^{4} +25.0000 q^{5} +44.0000 q^{6} +64.0000 q^{8} -122.000 q^{9} +100.000 q^{10} -267.000 q^{11} +176.000 q^{12} +1087.00 q^{13} +275.000 q^{15} +256.000 q^{16} +513.000 q^{17} -488.000 q^{18} +802.000 q^{19} +400.000 q^{20} -1068.00 q^{22} -1290.00 q^{23} +704.000 q^{24} +625.000 q^{25} +4348.00 q^{26} -4015.00 q^{27} +1779.00 q^{29} +1100.00 q^{30} +2584.00 q^{31} +1024.00 q^{32} -2937.00 q^{33} +2052.00 q^{34} -1952.00 q^{36} +13862.0 q^{37} +3208.00 q^{38} +11957.0 q^{39} +1600.00 q^{40} +11904.0 q^{41} -598.000 q^{43} -4272.00 q^{44} -3050.00 q^{45} -5160.00 q^{46} +17019.0 q^{47} +2816.00 q^{48} +2500.00 q^{50} +5643.00 q^{51} +17392.0 q^{52} +27852.0 q^{53} -16060.0 q^{54} -6675.00 q^{55} +8822.00 q^{57} +7116.00 q^{58} -30912.0 q^{59} +4400.00 q^{60} +1780.00 q^{61} +10336.0 q^{62} +4096.00 q^{64} +27175.0 q^{65} -11748.0 q^{66} +25052.0 q^{67} +8208.00 q^{68} -14190.0 q^{69} -51984.0 q^{71} -7808.00 q^{72} -47690.0 q^{73} +55448.0 q^{74} +6875.00 q^{75} +12832.0 q^{76} +47828.0 q^{78} -102121. q^{79} +6400.00 q^{80} -14519.0 q^{81} +47616.0 q^{82} +83676.0 q^{83} +12825.0 q^{85} -2392.00 q^{86} +19569.0 q^{87} -17088.0 q^{88} +32400.0 q^{89} -12200.0 q^{90} -20640.0 q^{92} +28424.0 q^{93} +68076.0 q^{94} +20050.0 q^{95} +11264.0 q^{96} +148645. q^{97} +32574.0 q^{99} +O(q^{100})\)

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 $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	11.0000	0.705650	0.352825	−	0.935689i	$-0.385221\pi$
$3$	11.0000	0.705650	0.352825	+	0.935689i	$0.385221\pi$
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	44.0000	0.498970
$7$	0	0
$7$	0	0
$8$	64.0000	0.353553
$9$	−122.000	−0.502058
$10$	100.000	0.316228
$11$	−267.000	−0.665318	−0.332659	−	0.943047i	$-0.607946\pi$
$11$	−267.000	−0.665318	−0.332659	+	0.943047i	$0.607946\pi$
$12$	176.000	0.352825
$13$	1087.00	1.78390	0.891951	−	0.452131i	$-0.149336\pi$
$13$	1087.00	1.78390	0.891951	+	0.452131i	$0.149336\pi$
$14$	0	0
$15$	275.000	0.315576
$16$	256.000	0.250000
$17$	513.000	0.430522	0.215261	−	0.976557i	$-0.430940\pi$
$17$	513.000	0.430522	0.215261	+	0.976557i	$0.430940\pi$
$18$	−488.000	−0.355008
$19$	802.000	0.509672	0.254836	−	0.966984i	$-0.417979\pi$
$19$	802.000	0.509672	0.254836	+	0.966984i	$0.417979\pi$
$20$	400.000	0.223607
$21$	0	0
$22$	−1068.00	−0.470451
$23$	−1290.00	−0.508476	−0.254238	−	0.967142i	$-0.581825\pi$
$23$	−1290.00	−0.508476	−0.254238	+	0.967142i	$0.581825\pi$
$24$	704.000	0.249485
$25$	625.000	0.200000
$26$	4348.00	1.26141
$27$	−4015.00	−1.05993
$28$	0	0
$29$	1779.00	0.392809	0.196404	−	0.980523i	$-0.437074\pi$
$29$	1779.00	0.392809	0.196404	+	0.980523i	$0.437074\pi$
$30$	1100.00	0.223146
$31$	2584.00	0.482935	0.241467	−	0.970409i	$-0.422371\pi$
$31$	2584.00	0.482935	0.241467	+	0.970409i	$0.422371\pi$
$32$	1024.00	0.176777
$33$	−2937.00	−0.469482
$34$	2052.00	0.304425
$35$	0	0
$36$	−1952.00	−0.251029
$37$	13862.0	1.66464	0.832322	−	0.554292i	$-0.187011\pi$
$37$	13862.0	1.66464	0.832322	+	0.554292i	$0.187011\pi$
$38$	3208.00	0.360392
$39$	11957.0	1.25881
$40$	1600.00	0.158114
$41$	11904.0	1.10594	0.552972	−	0.833200i	$-0.313494\pi$
$41$	11904.0	1.10594	0.552972	+	0.833200i	$0.313494\pi$
$42$	0	0
$43$	−598.000	−0.0493208	−0.0246604	−	0.999696i	$-0.507850\pi$
$43$	−598.000	−0.0493208	−0.0246604	+	0.999696i	$0.507850\pi$
$44$	−4272.00	−0.332659
$45$	−3050.00	−0.224527
$46$	−5160.00	−0.359547
$47$	17019.0	1.12380	0.561900	−	0.827205i	$-0.310070\pi$
$47$	17019.0	1.12380	0.561900	+	0.827205i	$0.310070\pi$
$48$	2816.00	0.176413
$49$	0	0
$50$	2500.00	0.141421
$51$	5643.00	0.303798
$52$	17392.0	0.891951
$53$	27852.0	1.36197	0.680984	−	0.732299i	$-0.261552\pi$
$53$	27852.0	1.36197	0.680984	+	0.732299i	$0.261552\pi$
$54$	−16060.0	−0.749482
$55$	−6675.00	−0.297539
$56$	0	0
$57$	8822.00	0.359650
$58$	7116.00	0.277758
$59$	−30912.0	−1.15610	−0.578052	−	0.816000i	$-0.696187\pi$
$59$	−30912.0	−1.15610	−0.578052	+	0.816000i	$0.696187\pi$
$60$	4400.00	0.157788
$61$	1780.00	0.0612485	0.0306242	−	0.999531i	$-0.490250\pi$
$61$	1780.00	0.0612485	0.0306242	+	0.999531i	$0.490250\pi$
$62$	10336.0	0.341486
$63$	0	0
$64$	4096.00	0.125000
$65$	27175.0	0.797786
$66$	−11748.0	−0.331974
$67$	25052.0	0.681797	0.340899	−	0.940100i	$-0.389269\pi$
$67$	25052.0	0.681797	0.340899	+	0.940100i	$0.389269\pi$
$68$	8208.00	0.215261
$69$	−14190.0	−0.358806
$70$	0	0
$71$	−51984.0	−1.22384	−0.611919	−	0.790921i	$-0.709602\pi$
$71$	−51984.0	−1.22384	−0.611919	+	0.790921i	$0.709602\pi$
$72$	−7808.00	−0.177504
$73$	−47690.0	−1.04742	−0.523709	−	0.851897i	$-0.675452\pi$
$73$	−47690.0	−1.04742	−0.523709	+	0.851897i	$0.675452\pi$
$74$	55448.0	1.17708
$75$	6875.00	0.141130
$76$	12832.0	0.254836
$77$	0	0
$78$	47828.0	0.890114
$79$	−102121.	−1.84097	−0.920486	−	0.390775i	$-0.872207\pi$
$79$	−102121.	−1.84097	−0.920486	+	0.390775i	$0.872207\pi$
$80$	6400.00	0.111803
$81$	−14519.0	−0.245881
$82$	47616.0	0.782021
$83$	83676.0	1.33323	0.666616	−	0.745401i	$-0.267742\pi$
$83$	83676.0	1.33323	0.666616	+	0.745401i	$0.267742\pi$
$84$	0	0
$85$	12825.0	0.192535
$86$	−2392.00	−0.0348751
$87$	19569.0	0.277185
$88$	−17088.0	−0.235226
$89$	32400.0	0.433581	0.216790	−	0.976218i	$-0.430441\pi$
$89$	32400.0	0.433581	0.216790	+	0.976218i	$0.430441\pi$
$90$	−12200.0	−0.158765
$91$	0	0
$92$	−20640.0	−0.254238
$93$	28424.0	0.340783
$94$	68076.0	0.794647
$95$	20050.0	0.227932
$96$	11264.0	0.124743
$97$	148645.	1.60406	0.802031	−	0.597283i	$-0.203753\pi$
$97$	148645.	1.60406	0.802031	+	0.597283i	$0.203753\pi$
$98$	0	0
$99$	32574.0	0.334028
$100$	10000.0	0.100000
$101$	41310.0	0.402951	0.201475	−	0.979494i	$-0.435426\pi$
$101$	41310.0	0.402951	0.201475	+	0.979494i	$0.435426\pi$
$102$	22572.0	0.214817
$103$	−108785.	−1.01036	−0.505180	−	0.863014i	$-0.668574\pi$
$103$	−108785.	−1.01036	−0.505180	+	0.863014i	$0.668574\pi$
$104$	69568.0	0.630705
$105$	0	0
$106$	111408.	0.963056
$107$	−106098.	−0.895876	−0.447938	−	0.894065i	$-0.647841\pi$
$107$	−106098.	−0.895876	−0.447938	+	0.894065i	$0.647841\pi$
$108$	−64240.0	−0.529964
$109$	−124111.	−1.00056	−0.500281	−	0.865863i	$-0.666770\pi$
$109$	−124111.	−1.00056	−0.500281	+	0.865863i	$0.666770\pi$
$110$	−26700.0	−0.210392
$111$	152482.	1.17466
$112$	0	0
$113$	192834.	1.42065	0.710326	−	0.703873i	$-0.248548\pi$
$113$	192834.	1.42065	0.710326	+	0.703873i	$0.248548\pi$
$114$	35288.0	0.254311
$115$	−32250.0	−0.227397
$116$	28464.0	0.196404
$117$	−132614.	−0.895622
$118$	−123648.	−0.817489
$119$	0	0
$120$	17600.0	0.111573
$121$	−89762.0	−0.557351
$122$	7120.00	0.0433092
$123$	130944.	0.780410
$124$	41344.0	0.241467
$125$	15625.0	0.0894427
$126$	0	0
$127$	99248.0	0.546025	0.273012	−	0.962010i	$-0.411980\pi$
$127$	99248.0	0.546025	0.273012	+	0.962010i	$0.411980\pi$
$128$	16384.0	0.0883883
$129$	−6578.00	−0.0348032
$130$	108700.	0.564120
$131$	276810.	1.40930	0.704650	−	0.709555i	$-0.251104\pi$
$131$	276810.	1.40930	0.704650	+	0.709555i	$0.251104\pi$
$132$	−46992.0	−0.234741
$133$	0	0
$134$	100208.	0.482104
$135$	−100375.	−0.474014
$136$	32832.0	0.152212
$137$	237744.	1.08220	0.541101	−	0.840958i	$-0.318008\pi$
$137$	237744.	1.08220	0.541101	+	0.840958i	$0.318008\pi$
$138$	−56760.0	−0.253714
$139$	−160478.	−0.704496	−0.352248	−	0.935907i	$-0.614583\pi$
$139$	−160478.	−0.704496	−0.352248	+	0.935907i	$0.614583\pi$
$140$	0	0
$141$	187209.	0.793011
$142$	−207936.	−0.865384
$143$	−290229.	−1.18686
$144$	−31232.0	−0.125514
$145$	44475.0	0.175669
$146$	−190760.	−0.740637
$147$	0	0
$148$	221792.	0.832322
$149$	−99678.0	−0.367819	−0.183909	−	0.982943i	$-0.558875\pi$
$149$	−99678.0	−0.367819	−0.183909	+	0.982943i	$0.558875\pi$
$150$	27500.0	0.0997940
$151$	−206017.	−0.735293	−0.367647	−	0.929966i	$-0.619836\pi$
$151$	−206017.	−0.735293	−0.367647	+	0.929966i	$0.619836\pi$
$152$	51328.0	0.180196
$153$	−62586.0	−0.216147
$154$	0	0
$155$	64600.0	0.215975
$156$	191312.	0.629406
$157$	−581150.	−1.88165	−0.940826	−	0.338891i	$-0.889948\pi$
$157$	−581150.	−1.88165	−0.940826	+	0.338891i	$0.889948\pi$
$158$	−408484.	−1.30176
$159$	306372.	0.961073
$160$	25600.0	0.0790569
$161$	0	0
$162$	−58076.0	−0.173864
$163$	346610.	1.02181	0.510907	−	0.859636i	$-0.329310\pi$
$163$	346610.	1.02181	0.510907	+	0.859636i	$0.329310\pi$
$164$	190464.	0.552972
$165$	−73425.0	−0.209959
$166$	334704.	0.942737
$167$	448887.	1.24551	0.622753	−	0.782418i	$-0.286014\pi$
$167$	448887.	1.24551	0.622753	+	0.782418i	$0.286014\pi$
$168$	0	0
$169$	810276.	2.18231
$170$	51300.0	0.136143
$171$	−97844.0	−0.255884
$172$	−9568.00	−0.0246604
$173$	262509.	0.666851	0.333426	−	0.942776i	$-0.391795\pi$
$173$	262509.	0.666851	0.333426	+	0.942776i	$0.391795\pi$
$174$	78276.0	0.196000
$175$	0	0
$176$	−68352.0	−0.166330
$177$	−340032.	−0.815805
$178$	129600.	0.306588
$179$	−111012.	−0.258963	−0.129481	−	0.991582i	$-0.541331\pi$
$179$	−111012.	−0.258963	−0.129481	+	0.991582i	$0.541331\pi$
$180$	−48800.0	−0.112263
$181$	−112772.	−0.255861	−0.127931	−	0.991783i	$-0.540834\pi$
$181$	−112772.	−0.255861	−0.127931	+	0.991783i	$0.540834\pi$
$182$	0	0
$183$	19580.0	0.0432200
$184$	−82560.0	−0.179773
$185$	346550.	0.744452
$186$	113696.	0.240970
$187$	−136971.	−0.286434
$188$	272304.	0.561900
$189$	0	0
$190$	80200.0	0.161172
$191$	−731991.	−1.45185	−0.725926	−	0.687773i	$-0.758589\pi$
$191$	−731991.	−1.45185	−0.725926	+	0.687773i	$0.758589\pi$
$192$	45056.0	0.0882063
$193$	−186040.	−0.359512	−0.179756	−	0.983711i	$-0.557531\pi$
$193$	−186040.	−0.359512	−0.179756	+	0.983711i	$0.557531\pi$
$194$	594580.	1.13424
$195$	298925.	0.562958
$196$	0	0
$197$	121356.	0.222790	0.111395	−	0.993776i	$-0.464468\pi$
$197$	121356.	0.222790	0.111395	+	0.993776i	$0.464468\pi$
$198$	130296.	0.236194
$199$	−648584.	−1.16100	−0.580502	−	0.814259i	$-0.697144\pi$
$199$	−648584.	−1.16100	−0.580502	+	0.814259i	$0.697144\pi$
$200$	40000.0	0.0707107
$201$	275572.	0.481111
$202$	165240.	0.284929
$203$	0	0
$204$	90288.0	0.151899
$205$	297600.	0.494593
$206$	−435140.	−0.714432
$207$	157380.	0.255284
$208$	278272.	0.445976
$209$	−214134.	−0.339094
$210$	0	0
$211$	−149773.	−0.231594	−0.115797	−	0.993273i	$-0.536942\pi$
$211$	−149773.	−0.231594	−0.115797	+	0.993273i	$0.536942\pi$
$212$	445632.	0.680984
$213$	−571824.	−0.863601
$214$	−424392.	−0.633480
$215$	−14950.0	−0.0220569
$216$	−256960.	−0.374741
$217$	0	0
$218$	−496444.	−0.707504
$219$	−524590.	−0.739111
$220$	−106800.	−0.148770
$221$	557631.	0.768009
$222$	609928.	0.830608
$223$	1.10096e6	1.48255	0.741274	−	0.671202i	$-0.234222\pi$
$223$	1.10096e6	1.48255	0.741274	+	0.671202i	$0.234222\pi$
$224$	0	0
$225$	−76250.0	−0.100412
$226$	771336.	1.00455
$227$	695127.	0.895364	0.447682	−	0.894193i	$-0.352250\pi$
$227$	695127.	0.895364	0.447682	+	0.894193i	$0.352250\pi$
$228$	141152.	0.179825
$229$	−463736.	−0.584362	−0.292181	−	0.956363i	$-0.594381\pi$
$229$	−463736.	−0.584362	−0.292181	+	0.956363i	$0.594381\pi$
$230$	−129000.	−0.160794
$231$	0	0
$232$	113856.	0.138879
$233$	−1.57654e6	−1.90245	−0.951227	−	0.308492i	$-0.900176\pi$
$233$	−1.57654e6	−1.90245	−0.951227	+	0.308492i	$0.900176\pi$
$234$	−530456.	−0.633300
$235$	425475.	0.502579
$236$	−494592.	−0.578052
$237$	−1.12333e6	−1.29908
$238$	0	0
$239$	−512037.	−0.579838	−0.289919	−	0.957051i	$-0.593628\pi$
$239$	−512037.	−0.579838	−0.289919	+	0.957051i	$0.593628\pi$
$240$	70400.0	0.0788941
$241$	−989330.	−1.09723	−0.548616	−	0.836074i	$-0.684845\pi$
$241$	−989330.	−1.09723	−0.548616	+	0.836074i	$0.684845\pi$
$242$	−359048.	−0.394107
$243$	815936.	0.886422
$244$	28480.0	0.0306242
$245$	0	0
$246$	523776.	0.551833
$247$	871774.	0.909204
$248$	165376.	0.170743
$249$	920436.	0.940795
$250$	62500.0	0.0632456
$251$	61230.0	0.0613451	0.0306726	−	0.999529i	$-0.490235\pi$
$251$	61230.0	0.0613451	0.0306726	+	0.999529i	$0.490235\pi$
$252$	0	0
$253$	344430.	0.338298
$254$	396992.	0.386098
$255$	141075.	0.135863
$256$	65536.0	0.0625000
$257$	−1.33887e6	−1.26446	−0.632231	−	0.774780i	$-0.717861\pi$
$257$	−1.33887e6	−1.26446	−0.632231	+	0.774780i	$0.717861\pi$
$258$	−26312.0	−0.0246096
$259$	0	0
$260$	434800.	0.398893
$261$	−217038.	−0.197213
$262$	1.10724e6	0.996526
$263$	−1.65619e6	−1.47645	−0.738227	−	0.674553i	$-0.764337\pi$
$263$	−1.65619e6	−1.47645	−0.738227	+	0.674553i	$0.764337\pi$
$264$	−187968.	−0.165987
$265$	696300.	0.609090
$266$	0	0
$267$	356400.	0.305956
$268$	400832.	0.340899
$269$	750606.	0.632457	0.316229	−	0.948683i	$-0.397583\pi$
$269$	750606.	0.632457	0.316229	+	0.948683i	$0.397583\pi$
$270$	−401500.	−0.335178
$271$	557908.	0.461466	0.230733	−	0.973017i	$-0.425888\pi$
$271$	557908.	0.461466	0.230733	+	0.973017i	$0.425888\pi$
$272$	131328.	0.107630
$273$	0	0
$274$	950976.	0.765232
$275$	−166875.	−0.133064
$276$	−227040.	−0.179403
$277$	1.77256e6	1.38804	0.694018	−	0.719957i	$-0.255839\pi$
$277$	1.77256e6	1.38804	0.694018	+	0.719957i	$0.255839\pi$
$278$	−641912.	−0.498154
$279$	−315248.	−0.242461
$280$	0	0
$281$	−1.09893e6	−0.830243	−0.415122	−	0.909766i	$-0.636261\pi$
$281$	−1.09893e6	−0.830243	−0.415122	+	0.909766i	$0.636261\pi$
$282$	748836.	0.560743
$283$	320569.	0.237933	0.118967	−	0.992898i	$-0.462042\pi$
$283$	320569.	0.237933	0.118967	+	0.992898i	$0.462042\pi$
$284$	−831744.	−0.611919
$285$	220550.	0.160840
$286$	−1.16092e6	−0.839239
$287$	0	0
$288$	−124928.	−0.0887521
$289$	−1.15669e6	−0.814651
$290$	177900.	0.124217
$291$	1.63510e6	1.13191
$292$	−763040.	−0.523709
$293$	1.62337e6	1.10471	0.552355	−	0.833609i	$-0.313729\pi$
$293$	1.62337e6	1.10471	0.552355	+	0.833609i	$0.313729\pi$
$294$	0	0
$295$	−772800.	−0.517026
$296$	887168.	0.588541
$297$	1.07200e6	0.705189
$298$	−398712.	−0.260087
$299$	−1.40223e6	−0.907071
$300$	110000.	0.0705650
$301$	0	0
$302$	−824068.	−0.519931
$303$	454410.	0.284342
$304$	205312.	0.127418
$305$	44500.0	0.0273912
$306$	−250344.	−0.152839
$307$	−995087.	−0.602581	−0.301290	−	0.953532i	$-0.597417\pi$
$307$	−995087.	−0.602581	−0.301290	+	0.953532i	$0.597417\pi$
$308$	0	0
$309$	−1.19664e6	−0.712961
$310$	258400.	0.152717
$311$	−1.34398e6	−0.787939	−0.393969	−	0.919124i	$-0.628898\pi$
$311$	−1.34398e6	−0.787939	−0.393969	+	0.919124i	$0.628898\pi$
$312$	765248.	0.445057
$313$	−1.91971e6	−1.10758	−0.553788	−	0.832658i	$-0.686818\pi$
$313$	−1.91971e6	−1.10758	−0.553788	+	0.832658i	$0.686818\pi$
$314$	−2.32460e6	−1.33053
$315$	0	0
$316$	−1.63394e6	−0.920486
$317$	−1.91366e6	−1.06959	−0.534794	−	0.844983i	$-0.679611\pi$
$317$	−1.91366e6	−1.06959	−0.534794	+	0.844983i	$0.679611\pi$
$318$	1.22549e6	0.679581
$319$	−474993.	−0.261343
$320$	102400.	0.0559017
$321$	−1.16708e6	−0.632175
$322$	0	0
$323$	411426.	0.219425
$324$	−232304.	−0.122940
$325$	679375.	0.356781
$326$	1.38644e6	0.722532
$327$	−1.36522e6	−0.706047
$328$	761856.	0.391010
$329$	0	0
$330$	−293700.	−0.148463
$331$	−2.25694e6	−1.13227	−0.566135	−	0.824313i	$-0.691562\pi$
$331$	−2.25694e6	−1.13227	−0.566135	+	0.824313i	$0.691562\pi$
$332$	1.33882e6	0.666616
$333$	−1.69116e6	−0.835748
$334$	1.79555e6	0.880706
$335$	626300.	0.304909
$336$	0	0
$337$	−1.45016e6	−0.695571	−0.347786	−	0.937574i	$-0.613066\pi$
$337$	−1.45016e6	−0.695571	−0.347786	+	0.937574i	$0.613066\pi$
$338$	3.24110e6	1.54313
$339$	2.12117e6	1.00248
$340$	205200.	0.0962676
$341$	−689928.	−0.321305
$342$	−391376.	−0.180938
$343$	0	0
$344$	−38272.0	−0.0174375
$345$	−354750.	−0.160463
$346$	1.05004e6	0.471535
$347$	856386.	0.381809	0.190904	−	0.981609i	$-0.438858\pi$
$347$	856386.	0.381809	0.190904	+	0.981609i	$0.438858\pi$
$348$	313104.	0.138593
$349$	347602.	0.152763	0.0763816	−	0.997079i	$-0.475663\pi$
$349$	347602.	0.152763	0.0763816	+	0.997079i	$0.475663\pi$
$350$	0	0
$351$	−4.36430e6	−1.89081
$352$	−273408.	−0.117613
$353$	2.21860e6	0.947640	0.473820	−	0.880622i	$-0.342875\pi$
$353$	2.21860e6	0.947640	0.473820	+	0.880622i	$0.342875\pi$
$354$	−1.36013e6	−0.576862
$355$	−1.29960e6	−0.547317
$356$	518400.	0.216790
$357$	0	0
$358$	−444048.	−0.183114
$359$	2.94338e6	1.20534	0.602672	−	0.797989i	$-0.294103\pi$
$359$	2.94338e6	1.20534	0.602672	+	0.797989i	$0.294103\pi$
$360$	−195200.	−0.0793823
$361$	−1.83290e6	−0.740235
$362$	−451088.	−0.180921
$363$	−987382.	−0.393295
$364$	0	0
$365$	−1.19225e6	−0.468420
$366$	78320.0	0.0305612
$367$	−2.33000e6	−0.903005	−0.451503	−	0.892270i	$-0.649112\pi$
$367$	−2.33000e6	−0.903005	−0.451503	+	0.892270i	$0.649112\pi$
$368$	−330240.	−0.127119
$369$	−1.45229e6	−0.555248
$370$	1.38620e6	0.526407
$371$	0	0
$372$	454784.	0.170391
$373$	1.69246e6	0.629865	0.314932	−	0.949114i	$-0.398018\pi$
$373$	1.69246e6	0.629865	0.314932	+	0.949114i	$0.398018\pi$
$374$	−547884.	−0.202539
$375$	171875.	0.0631153
$376$	1.08922e6	0.397324
$377$	1.93377e6	0.700732
$378$	0	0
$379$	−1.50075e6	−0.536673	−0.268337	−	0.963325i	$-0.586474\pi$
$379$	−1.50075e6	−0.536673	−0.268337	+	0.963325i	$0.586474\pi$
$380$	320800.	0.113966
$381$	1.09173e6	0.385303
$382$	−2.92796e6	−1.02661
$383$	−3.48522e6	−1.21404	−0.607020	−	0.794686i	$-0.707635\pi$
$383$	−3.48522e6	−1.21404	−0.607020	+	0.794686i	$0.707635\pi$
$384$	180224.	0.0623713
$385$	0	0
$386$	−744160.	−0.254213
$387$	72956.0	0.0247619
$388$	2.37832e6	0.802031
$389$	−3.60598e6	−1.20823	−0.604114	−	0.796898i	$-0.706473\pi$
$389$	−3.60598e6	−1.20823	−0.604114	+	0.796898i	$0.706473\pi$
$390$	1.19570e6	0.398071
$391$	−661770.	−0.218910
$392$	0	0
$393$	3.04491e6	0.994473
$394$	485424.	0.157536
$395$	−2.55302e6	−0.823308
$396$	521184.	0.167014
$397$	−4.74380e6	−1.51060	−0.755302	−	0.655377i	$-0.772510\pi$
$397$	−4.74380e6	−1.51060	−0.755302	+	0.655377i	$0.772510\pi$
$398$	−2.59434e6	−0.820953
$399$	0	0
$400$	160000.	0.0500000
$401$	5.26539e6	1.63520	0.817598	−	0.575789i	$-0.195305\pi$
$401$	5.26539e6	1.63520	0.817598	+	0.575789i	$0.195305\pi$
$402$	1.10229e6	0.340197
$403$	2.80881e6	0.861508
$404$	660960.	0.201475
$405$	−362975.	−0.109961
$406$	0	0
$407$	−3.70115e6	−1.10752
$408$	361152.	0.107409
$409$	−1.37015e6	−0.405004	−0.202502	−	0.979282i	$-0.564907\pi$
$409$	−1.37015e6	−0.405004	−0.202502	+	0.979282i	$0.564907\pi$
$410$	1.19040e6	0.349730
$411$	2.61518e6	0.763656
$412$	−1.74056e6	−0.505180
$413$	0	0
$414$	629520.	0.180513
$415$	2.09190e6	0.596239
$416$	1.11309e6	0.315352
$417$	−1.76526e6	−0.497128
$418$	−856536.	−0.239776
$419$	−6.16429e6	−1.71533	−0.857666	−	0.514207i	$-0.828086\pi$
$419$	−6.16429e6	−1.71533	−0.857666	+	0.514207i	$0.828086\pi$
$420$	0	0
$421$	2.45358e6	0.674677	0.337338	−	0.941383i	$-0.390473\pi$
$421$	2.45358e6	0.674677	0.337338	+	0.941383i	$0.390473\pi$
$422$	−599092.	−0.163762
$423$	−2.07632e6	−0.564213
$424$	1.78253e6	0.481528
$425$	320625.	0.0861043
$426$	−2.28730e6	−0.610658
$427$	0	0
$428$	−1.69757e6	−0.447938
$429$	−3.19252e6	−0.837510
$430$	−59800.0	−0.0155966
$431$	7.66771e6	1.98826	0.994128	−	0.108207i	$-0.0345111\pi$
$431$	7.66771e6	1.98826	0.994128	+	0.108207i	$0.0345111\pi$
$432$	−1.02784e6	−0.264982
$433$	5.00285e6	1.28232	0.641161	−	0.767406i	$-0.278453\pi$
$433$	5.00285e6	1.28232	0.641161	+	0.767406i	$0.278453\pi$
$434$	0	0
$435$	489225.	0.123961
$436$	−1.98578e6	−0.500281
$437$	−1.03458e6	−0.259156
$438$	−2.09836e6	−0.522630
$439$	−1.86363e6	−0.461527	−0.230764	−	0.973010i	$-0.574122\pi$
$439$	−1.86363e6	−0.461527	−0.230764	+	0.973010i	$0.574122\pi$
$440$	−427200.	−0.105196
$441$	0	0
$442$	2.23052e6	0.543064
$443$	2.60747e6	0.631263	0.315632	−	0.948882i	$-0.397784\pi$
$443$	2.60747e6	0.631263	0.315632	+	0.948882i	$0.397784\pi$
$444$	2.43971e6	0.587329
$445$	810000.	0.193903
$446$	4.40384e6	1.04832
$447$	−1.09646e6	−0.259551
$448$	0	0
$449$	−4.78007e6	−1.11897	−0.559484	−	0.828841i	$-0.689001\pi$
$449$	−4.78007e6	−1.11897	−0.559484	+	0.828841i	$0.689001\pi$
$450$	−305000.	−0.0710017
$451$	−3.17837e6	−0.735805
$452$	3.08534e6	0.710326
$453$	−2.26619e6	−0.518860
$454$	2.78051e6	0.633118
$455$	0	0
$456$	564608.	0.127155
$457$	−7.96757e6	−1.78458	−0.892289	−	0.451465i	$-0.850902\pi$
$457$	−7.96757e6	−1.78458	−0.892289	+	0.451465i	$0.850902\pi$
$458$	−1.85494e6	−0.413206
$459$	−2.05969e6	−0.456322
$460$	−516000.	−0.113699
$461$	−1.77665e6	−0.389358	−0.194679	−	0.980867i	$-0.562367\pi$
$461$	−1.77665e6	−0.389358	−0.194679	+	0.980867i	$0.562367\pi$
$462$	0	0
$463$	−998548.	−0.216479	−0.108240	−	0.994125i	$-0.534521\pi$
$463$	−998548.	−0.216479	−0.108240	+	0.994125i	$0.534521\pi$
$464$	455424.	0.0982021
$465$	710600.	0.152403
$466$	−6.30614e6	−1.34524
$467$	5.08478e6	1.07890	0.539449	−	0.842019i	$-0.318633\pi$
$467$	5.08478e6	1.07890	0.539449	+	0.842019i	$0.318633\pi$
$468$	−2.12182e6	−0.447811
$469$	0	0
$470$	1.70190e6	0.355377
$471$	−6.39265e6	−1.32779
$472$	−1.97837e6	−0.408745
$473$	159666.	0.0328140
$474$	−4.49332e6	−0.918590
$475$	501250.	0.101934
$476$	0	0
$477$	−3.39794e6	−0.683786
$478$	−2.04815e6	−0.410007
$479$	−3.71936e6	−0.740678	−0.370339	−	0.928897i	$-0.620758\pi$
$479$	−3.71936e6	−0.740678	−0.370339	+	0.928897i	$0.620758\pi$
$480$	281600.	0.0557866
$481$	1.50680e7	2.96956
$482$	−3.95732e6	−0.775860
$483$	0	0
$484$	−1.43619e6	−0.278676
$485$	3.71612e6	0.717358
$486$	3.26374e6	0.626795
$487$	−9.12035e6	−1.74256	−0.871282	−	0.490782i	$-0.836711\pi$
$487$	−9.12035e6	−1.74256	−0.871282	+	0.490782i	$0.836711\pi$
$488$	113920.	0.0216546
$489$	3.81271e6	0.721044
$490$	0	0
$491$	−7.83774e6	−1.46719	−0.733596	−	0.679586i	$-0.762160\pi$
$491$	−7.83774e6	−1.46719	−0.733596	+	0.679586i	$0.762160\pi$
$492$	2.09510e6	0.390205
$493$	912627.	0.169113
$494$	3.48710e6	0.642905
$495$	814350.	0.149382
$496$	661504.	0.120734
$497$	0	0
$498$	3.68174e6	0.665243
$499$	−96103.0	−0.0172777	−0.00863884	−	0.999963i	$-0.502750\pi$
$499$	−96103.0	−0.0172777	−0.00863884	+	0.999963i	$0.502750\pi$
$500$	250000.	0.0447214
$501$	4.93776e6	0.878892
$502$	244920.	0.0433775
$503$	2.37577e6	0.418682	0.209341	−	0.977843i	$-0.432868\pi$
$503$	2.37577e6	0.418682	0.209341	+	0.977843i	$0.432868\pi$
$504$	0	0
$505$	1.03275e6	0.180205
$506$	1.37772e6	0.239213
$507$	8.91304e6	1.53995
$508$	1.58797e6	0.273012
$509$	−5.91484e6	−1.01193	−0.505963	−	0.862555i	$-0.668863\pi$
$509$	−5.91484e6	−1.01193	−0.505963	+	0.862555i	$0.668863\pi$
$510$	564300.	0.0960693
$511$	0	0
$512$	262144.	0.0441942
$513$	−3.22003e6	−0.540215
$514$	−5.35548e6	−0.894109
$515$	−2.71963e6	−0.451847
$516$	−105248.	−0.0174016
$517$	−4.54407e6	−0.747685
$518$	0	0
$519$	2.88760e6	0.470564
$520$	1.73920e6	0.282060
$521$	−1.46099e6	−0.235806	−0.117903	−	0.993025i	$-0.537617\pi$
$521$	−1.46099e6	−0.235806	−0.117903	+	0.993025i	$0.537617\pi$
$522$	−868152.	−0.139450
$523$	2.90691e6	0.464705	0.232352	−	0.972632i	$-0.425358\pi$
$523$	2.90691e6	0.464705	0.232352	+	0.972632i	$0.425358\pi$
$524$	4.42896e6	0.704650
$525$	0	0
$526$	−6.62474e6	−1.04401
$527$	1.32559e6	0.207914
$528$	−751872.	−0.117371
$529$	−4.77224e6	−0.741453
$530$	2.78520e6	0.430692
$531$	3.77126e6	0.580431
$532$	0	0
$533$	1.29396e7	1.97290
$534$	1.42560e6	0.216344
$535$	−2.65245e6	−0.400648
$536$	1.60333e6	0.241052
$537$	−1.22113e6	−0.182737
$538$	3.00242e6	0.447215
$539$	0	0
$540$	−1.60600e6	−0.237007
$541$	5.28092e6	0.775741	0.387870	−	0.921714i	$-0.373211\pi$
$541$	5.28092e6	0.775741	0.387870	+	0.921714i	$0.373211\pi$
$542$	2.23163e6	0.326305
$543$	−1.24049e6	−0.180549
$544$	525312.	0.0761062
$545$	−3.10278e6	−0.447465
$546$	0	0
$547$	1.31999e7	1.88626	0.943132	−	0.332419i	$-0.107865\pi$
$547$	1.31999e7	1.88626	0.943132	+	0.332419i	$0.107865\pi$
$548$	3.80390e6	0.541101
$549$	−217160.	−0.0307503
$550$	−667500.	−0.0940902
$551$	1.42676e6	0.200203
$552$	−908160.	−0.126857
$553$	0	0
$554$	7.09023e6	0.981490
$555$	3.81205e6	0.525323
$556$	−2.56765e6	−0.352248
$557$	−1.39920e7	−1.91091	−0.955457	−	0.295131i	$-0.904637\pi$
$557$	−1.39920e7	−1.91091	−0.955457	+	0.295131i	$0.904637\pi$
$558$	−1.26099e6	−0.171446
$559$	−650026.	−0.0879835
$560$	0	0
$561$	−1.50668e6	−0.202122
$562$	−4.39573e6	−0.587071
$563$	5.12689e6	0.681684	0.340842	−	0.940121i	$-0.389288\pi$
$563$	5.12689e6	0.681684	0.340842	+	0.940121i	$0.389288\pi$
$564$	2.99534e6	0.396505
$565$	4.82085e6	0.635335
$566$	1.28228e6	0.168244
$567$	0	0
$568$	−3.32698e6	−0.432692
$569$	−8.29102e6	−1.07356	−0.536781	−	0.843721i	$-0.680360\pi$
$569$	−8.29102e6	−1.07356	−0.536781	+	0.843721i	$0.680360\pi$
$570$	882200.	0.113731
$571$	6.21372e6	0.797556	0.398778	−	0.917048i	$-0.369434\pi$
$571$	6.21372e6	0.797556	0.398778	+	0.917048i	$0.369434\pi$
$572$	−4.64366e6	−0.593432
$573$	−8.05190e6	−1.02450
$574$	0	0
$575$	−806250.	−0.101695
$576$	−499712.	−0.0627572
$577$	−1.14818e7	−1.43572	−0.717861	−	0.696186i	$-0.754879\pi$
$577$	−1.14818e7	−1.43572	−0.717861	+	0.696186i	$0.754879\pi$
$578$	−4.62675e6	−0.576045
$579$	−2.04644e6	−0.253690
$580$	711600.	0.0878347
$581$	0	0
$582$	6.54038e6	0.800379
$583$	−7.43648e6	−0.906142
$584$	−3.05216e6	−0.370318
$585$	−3.31535e6	−0.400534
$586$	6.49348e6	0.781148
$587$	−641856.	−0.0768851	−0.0384426	−	0.999261i	$-0.512240\pi$
$587$	−641856.	−0.0768851	−0.0384426	+	0.999261i	$0.512240\pi$
$588$	0	0
$589$	2.07237e6	0.246138
$590$	−3.09120e6	−0.365592
$591$	1.33492e6	0.157212
$592$	3.54867e6	0.416161
$593$	2.80572e6	0.327648	0.163824	−	0.986490i	$-0.447617\pi$
$593$	2.80572e6	0.327648	0.163824	+	0.986490i	$0.447617\pi$
$594$	4.28802e6	0.498644
$595$	0	0
$596$	−1.59485e6	−0.183909
$597$	−7.13442e6	−0.819263
$598$	−5.60892e6	−0.641396
$599$	7.74415e6	0.881874	0.440937	−	0.897538i	$-0.354646\pi$
$599$	7.74415e6	0.881874	0.440937	+	0.897538i	$0.354646\pi$
$600$	440000.	0.0498970
$601$	−2.88868e6	−0.326222	−0.163111	−	0.986608i	$-0.552153\pi$
$601$	−2.88868e6	−0.326222	−0.163111	+	0.986608i	$0.552153\pi$
$602$	0	0
$603$	−3.05634e6	−0.342302
$604$	−3.29627e6	−0.367647
$605$	−2.24405e6	−0.249255
$606$	1.81764e6	0.201060
$607$	−1.22095e7	−1.34501	−0.672504	−	0.740093i	$-0.734781\pi$
$607$	−1.22095e7	−1.34501	−0.672504	+	0.740093i	$0.734781\pi$
$608$	821248.	0.0900980
$609$	0	0
$610$	178000.	0.0193685
$611$	1.84997e7	2.00475
$612$	−1.00138e6	−0.108073
$613$	1.51667e7	1.63019	0.815096	−	0.579326i	$-0.196684\pi$
$613$	1.51667e7	1.63019	0.815096	+	0.579326i	$0.196684\pi$
$614$	−3.98035e6	−0.426089
$615$	3.27360e6	0.349010
$616$	0	0
$617$	1.53927e7	1.62780	0.813899	−	0.581006i	$-0.197341\pi$
$617$	1.53927e7	1.62780	0.813899	+	0.581006i	$0.197341\pi$
$618$	−4.78654e6	−0.504139
$619$	1.40843e7	1.47744	0.738720	−	0.674013i	$-0.235431\pi$
$619$	1.40843e7	1.47744	0.738720	+	0.674013i	$0.235431\pi$
$620$	1.03360e6	0.107987
$621$	5.17935e6	0.538947
$622$	−5.37593e6	−0.557157
$623$	0	0
$624$	3.06099e6	0.314703
$625$	390625.	0.0400000
$626$	−7.67882e6	−0.783175
$627$	−2.35547e6	−0.239282
$628$	−9.29840e6	−0.940826
$629$	7.11121e6	0.716666
$630$	0	0
$631$	1.56178e7	1.56152	0.780760	−	0.624831i	$-0.214832\pi$
$631$	1.56178e7	1.56152	0.780760	+	0.624831i	$0.214832\pi$
$632$	−6.53574e6	−0.650882
$633$	−1.64750e6	−0.163424
$634$	−7.65463e6	−0.756312
$635$	2.48120e6	0.244190
$636$	4.90195e6	0.480536
$637$	0	0
$638$	−1.89997e6	−0.184797
$639$	6.34205e6	0.614437
$640$	409600.	0.0395285
$641$	4.04157e6	0.388513	0.194256	−	0.980951i	$-0.437771\pi$
$641$	4.04157e6	0.388513	0.194256	+	0.980951i	$0.437771\pi$
$642$	−4.66831e6	−0.447015
$643$	1.71035e7	1.63139	0.815693	−	0.578485i	$-0.196356\pi$
$643$	1.71035e7	1.63139	0.815693	+	0.578485i	$0.196356\pi$
$644$	0	0
$645$	−164450.	−0.0155645
$646$	1.64570e6	0.155157
$647$	8.83546e6	0.829790	0.414895	−	0.909869i	$-0.363818\pi$
$647$	8.83546e6	0.829790	0.414895	+	0.909869i	$0.363818\pi$
$648$	−929216.	−0.0869319
$649$	8.25350e6	0.769178
$650$	2.71750e6	0.252282
$651$	0	0
$652$	5.54576e6	0.510907
$653$	9.36125e6	0.859115	0.429557	−	0.903040i	$-0.358670\pi$
$653$	9.36125e6	0.859115	0.429557	+	0.903040i	$0.358670\pi$
$654$	−5.46088e6	−0.499251
$655$	6.92025e6	0.630258
$656$	3.04742e6	0.276486
$657$	5.81818e6	0.525864
$658$	0	0
$659$	−366111.	−0.0328397	−0.0164199	−	0.999865i	$-0.505227\pi$
$659$	−366111.	−0.0328397	−0.0164199	+	0.999865i	$0.505227\pi$
$660$	−1.17480e6	−0.104979
$661$	−2.05164e7	−1.82640	−0.913202	−	0.407508i	$-0.866398\pi$
$661$	−2.05164e7	−1.82640	−0.913202	+	0.407508i	$0.866398\pi$
$662$	−9.02776e6	−0.800636
$663$	6.13394e6	0.541946
$664$	5.35526e6	0.471369
$665$	0	0
$666$	−6.76466e6	−0.590963
$667$	−2.29491e6	−0.199734
$668$	7.18219e6	0.622753
$669$	1.21105e7	1.04616
$670$	2.50520e6	0.215603
$671$	−475260.	−0.0407498
$672$	0	0
$673$	7.48189e6	0.636757	0.318378	−	0.947964i	$-0.396862\pi$
$673$	7.48189e6	0.636757	0.318378	+	0.947964i	$0.396862\pi$
$674$	−5.80065e6	−0.491843
$675$	−2.50938e6	−0.211985
$676$	1.29644e7	1.09115
$677$	−1.21459e7	−1.01849	−0.509247	−	0.860621i	$-0.670076\pi$
$677$	−1.21459e7	−1.01849	−0.509247	+	0.860621i	$0.670076\pi$
$678$	8.48470e6	0.708863
$679$	0	0
$680$	820800.	0.0680715
$681$	7.64640e6	0.631814
$682$	−2.75971e6	−0.227197
$683$	−1.15232e7	−0.945197	−0.472599	−	0.881278i	$-0.656684\pi$
$683$	−1.15232e7	−0.945197	−0.472599	+	0.881278i	$0.656684\pi$
$684$	−1.56550e6	−0.127942
$685$	5.94360e6	0.483975
$686$	0	0
$687$	−5.10110e6	−0.412355
$688$	−153088.	−0.0123302
$689$	3.02751e7	2.42962
$690$	−1.41900e6	−0.113464
$691$	1.71185e7	1.36386	0.681931	−	0.731417i	$-0.261141\pi$
$691$	1.71185e7	1.36386	0.681931	+	0.731417i	$0.261141\pi$
$692$	4.20014e6	0.333426
$693$	0	0
$694$	3.42554e6	0.269980
$695$	−4.01195e6	−0.315060
$696$	1.25242e6	0.0979999
$697$	6.10675e6	0.476133
$698$	1.39041e6	0.108020
$699$	−1.73419e7	−1.34247
$700$	0	0
$701$	9.72758e6	0.747669	0.373835	−	0.927495i	$-0.378043\pi$
$701$	9.72758e6	0.747669	0.373835	+	0.927495i	$0.378043\pi$
$702$	−1.74572e7	−1.33700
$703$	1.11173e7	0.848422
$704$	−1.09363e6	−0.0831648
$705$	4.68022e6	0.354645
$706$	8.87442e6	0.670082
$707$	0	0
$708$	−5.44051e6	−0.407903
$709$	−673813.	−0.0503412	−0.0251706	−	0.999683i	$-0.508013\pi$
$709$	−673813.	−0.0503412	−0.0251706	+	0.999683i	$0.508013\pi$
$710$	−5.19840e6	−0.387011
$711$	1.24588e7	0.924274
$712$	2.07360e6	0.153294
$713$	−3.33336e6	−0.245560
$714$	0	0
$715$	−7.25572e6	−0.530781
$716$	−1.77619e6	−0.129481
$717$	−5.63241e6	−0.409163
$718$	1.17735e7	0.852307
$719$	−2.77719e6	−0.200347	−0.100174	−	0.994970i	$-0.531940\pi$
$719$	−2.77719e6	−0.200347	−0.100174	+	0.994970i	$0.531940\pi$
$720$	−780800.	−0.0561317
$721$	0	0
$722$	−7.33158e6	−0.523425
$723$	−1.08826e7	−0.774262
$724$	−1.80435e6	−0.127931
$725$	1.11188e6	0.0785617
$726$	−3.94953e6	−0.278102
$727$	−1.16385e7	−0.816700	−0.408350	−	0.912825i	$-0.633896\pi$
$727$	−1.16385e7	−0.816700	−0.408350	+	0.912825i	$0.633896\pi$
$728$	0	0
$729$	1.25034e7	0.871384
$730$	−4.76900e6	−0.331223
$731$	−306774.	−0.0212337
$732$	313280.	0.0216100
$733$	1.32013e7	0.907522	0.453761	−	0.891123i	$-0.350082\pi$
$733$	1.32013e7	0.907522	0.453761	+	0.891123i	$0.350082\pi$
$734$	−9.31999e6	−0.638521
$735$	0	0
$736$	−1.32096e6	−0.0898866
$737$	−6.68888e6	−0.453612
$738$	−5.80915e6	−0.392619
$739$	3.25476e6	0.219234	0.109617	−	0.993974i	$-0.465038\pi$
$739$	3.25476e6	0.219234	0.109617	+	0.993974i	$0.465038\pi$
$740$	5.54480e6	0.372226
$741$	9.58951e6	0.641580
$742$	0	0
$743$	−7.61596e6	−0.506119	−0.253059	−	0.967451i	$-0.581437\pi$
$743$	−7.61596e6	−0.506119	−0.253059	+	0.967451i	$0.581437\pi$
$744$	1.81914e6	0.120485
$745$	−2.49195e6	−0.164493
$746$	6.76986e6	0.445382
$747$	−1.02085e7	−0.669359
$748$	−2.19154e6	−0.143217
$749$	0	0
$750$	687500.	0.0446292
$751$	655199.	0.0423910	0.0211955	−	0.999775i	$-0.493253\pi$
$751$	655199.	0.0423910	0.0211955	+	0.999775i	$0.493253\pi$
$752$	4.35686e6	0.280950
$753$	673530.	0.0432882
$754$	7.73509e6	0.495493
$755$	−5.15042e6	−0.328833
$756$	0	0
$757$	1.85111e7	1.17406	0.587032	−	0.809564i	$-0.300296\pi$
$757$	1.85111e7	1.17406	0.587032	+	0.809564i	$0.300296\pi$
$758$	−6.00299e6	−0.379485
$759$	3.78873e6	0.238720
$760$	1.28320e6	0.0805861
$761$	1.85291e7	1.15983	0.579914	−	0.814678i	$-0.303086\pi$
$761$	1.85291e7	1.15983	0.579914	+	0.814678i	$0.303086\pi$
$762$	4.36691e6	0.272450
$763$	0	0
$764$	−1.17119e7	−0.725926
$765$	−1.56465e6	−0.0966637
$766$	−1.39409e7	−0.858456
$767$	−3.36013e7	−2.06238
$768$	720896.	0.0441031
$769$	1.48414e7	0.905024	0.452512	−	0.891758i	$-0.350528\pi$
$769$	1.48414e7	0.905024	0.452512	+	0.891758i	$0.350528\pi$
$770$	0	0
$771$	−1.47276e7	−0.892268
$772$	−2.97664e6	−0.179756
$773$	−3.93042e6	−0.236586	−0.118293	−	0.992979i	$-0.537742\pi$
$773$	−3.93042e6	−0.236586	−0.118293	+	0.992979i	$0.537742\pi$
$774$	291824.	0.0175093
$775$	1.61500e6	0.0965869
$776$	9.51328e6	0.567121
$777$	0	0
$778$	−1.44239e7	−0.854347
$779$	9.54701e6	0.563668
$780$	4.78280e6	0.281479
$781$	1.38797e7	0.814242
$782$	−2.64708e6	−0.154793
$783$	−7.14269e6	−0.416349
$784$	0	0
$785$	−1.45288e7	−0.841500
$786$	1.21796e7	0.703199
$787$	−1.17824e7	−0.678105	−0.339053	−	0.940767i	$-0.610107\pi$
$787$	−1.17824e7	−0.678105	−0.339053	+	0.940767i	$0.610107\pi$
$788$	1.94170e6	0.111395
$789$	−1.82180e7	−1.04186
$790$	−1.02121e7	−0.582167
$791$	0	0
$792$	2.08474e6	0.118097
$793$	1.93486e6	0.109261
$794$	−1.89752e7	−1.06816
$795$	7.65930e6	0.429805
$796$	−1.03773e7	−0.580502
$797$	5.40952e6	0.301657	0.150828	−	0.988560i	$-0.451806\pi$
$797$	5.40952e6	0.301657	0.150828	+	0.988560i	$0.451806\pi$
$798$	0	0
$799$	8.73075e6	0.483821
$800$	640000.	0.0353553
$801$	−3.95280e6	−0.217683
$802$	2.10616e7	1.15626
$803$	1.27332e7	0.696867
$804$	4.40915e6	0.240555
$805$	0	0
$806$	1.12352e7	0.609178
$807$	8.25667e6	0.446294
$808$	2.64384e6	0.142465
$809$	−7.12264e6	−0.382622	−0.191311	−	0.981529i	$-0.561274\pi$
$809$	−7.12264e6	−0.382622	−0.191311	+	0.981529i	$0.561274\pi$
$810$	−1.45190e6	−0.0777543
$811$	3.03045e7	1.61791	0.808956	−	0.587869i	$-0.200033\pi$
$811$	3.03045e7	1.61791	0.808956	+	0.587869i	$0.200033\pi$
$812$	0	0
$813$	6.13699e6	0.325633
$814$	−1.48046e7	−0.783134
$815$	8.66525e6	0.456969
$816$	1.44461e6	0.0759494
$817$	−479596.	−0.0251374
$818$	−5.48060e6	−0.286381
$819$	0	0
$820$	4.76160e6	0.247297
$821$	2.82181e7	1.46106	0.730532	−	0.682878i	$-0.239272\pi$
$821$	2.82181e7	1.46106	0.730532	+	0.682878i	$0.239272\pi$
$822$	1.04607e7	0.539986
$823$	−2.64534e7	−1.36139	−0.680694	−	0.732567i	$-0.738322\pi$
$823$	−2.64534e7	−1.36139	−0.680694	+	0.732567i	$0.738322\pi$
$824$	−6.96224e6	−0.357216
$825$	−1.83563e6	−0.0938964
$826$	0	0
$827$	4.44481e6	0.225990	0.112995	−	0.993596i	$-0.463956\pi$
$827$	4.44481e6	0.225990	0.112995	+	0.993596i	$0.463956\pi$
$828$	2.51808e6	0.127642
$829$	2.80386e6	0.141700	0.0708501	−	0.997487i	$-0.477429\pi$
$829$	2.80386e6	0.141700	0.0708501	+	0.997487i	$0.477429\pi$
$830$	8.36760e6	0.421605
$831$	1.94981e7	0.979469
$832$	4.45235e6	0.222988
$833$	0	0
$834$	−7.06103e6	−0.351522
$835$	1.12222e7	0.557007
$836$	−3.42614e6	−0.169547
$837$	−1.03748e7	−0.511876
$838$	−2.46572e7	−1.21292
$839$	−2.59804e7	−1.27421	−0.637104	−	0.770778i	$-0.719868\pi$
$839$	−2.59804e7	−1.27421	−0.637104	+	0.770778i	$0.719868\pi$
$840$	0	0
$841$	−1.73463e7	−0.845701
$842$	9.81434e6	0.477069
$843$	−1.20883e7	−0.585862
$844$	−2.39637e6	−0.115797
$845$	2.02569e7	0.975958
$846$	−8.30527e6	−0.398959
$847$	0	0
$848$	7.13011e6	0.340492
$849$	3.52626e6	0.167898
$850$	1.28250e6	0.0608850
$851$	−1.78820e7	−0.846431
$852$	−9.14918e6	−0.431801
$853$	−1.18392e7	−0.557121	−0.278560	−	0.960419i	$-0.589857\pi$
$853$	−1.18392e7	−0.557121	−0.278560	+	0.960419i	$0.589857\pi$
$854$	0	0
$855$	−2.44610e6	−0.114435
$856$	−6.79027e6	−0.316740
$857$	2.99283e6	0.139197	0.0695985	−	0.997575i	$-0.477828\pi$
$857$	2.99283e6	0.139197	0.0695985	+	0.997575i	$0.477828\pi$
$858$	−1.27701e7	−0.592209
$859$	−2.80980e7	−1.29925	−0.649626	−	0.760254i	$-0.725074\pi$
$859$	−2.80980e7	−1.29925	−0.649626	+	0.760254i	$0.725074\pi$
$860$	−239200.	−0.0110285
$861$	0	0
$862$	3.06708e7	1.40591
$863$	1.15833e7	0.529424	0.264712	−	0.964328i	$-0.414723\pi$
$863$	1.15833e7	0.529424	0.264712	+	0.964328i	$0.414723\pi$
$864$	−4.11136e6	−0.187370
$865$	6.56272e6	0.298225
$866$	2.00114e7	0.906739
$867$	−1.27236e7	−0.574859
$868$	0	0
$869$	2.72663e7	1.22483
$870$	1.95690e6	0.0876538
$871$	2.72315e7	1.21626
$872$	−7.94310e6	−0.353752
$873$	−1.81347e7	−0.805331
$874$	−4.13832e6	−0.183251
$875$	0	0
$876$	−8.39344e6	−0.369556
$877$	4.12538e7	1.81119	0.905596	−	0.424141i	$-0.139424\pi$
$877$	4.12538e7	1.81119	0.905596	+	0.424141i	$0.139424\pi$
$878$	−7.45450e6	−0.326349
$879$	1.78571e7	0.779539
$880$	−1.70880e6	−0.0743849
$881$	1.32541e7	0.575321	0.287661	−	0.957732i	$-0.407123\pi$
$881$	1.32541e7	0.575321	0.287661	+	0.957732i	$0.407123\pi$
$882$	0	0
$883$	−3.19208e7	−1.37776	−0.688878	−	0.724877i	$-0.741897\pi$
$883$	−3.19208e7	−1.37776	−0.688878	+	0.724877i	$0.741897\pi$
$884$	8.92210e6	0.384004
$885$	−8.50080e6	−0.364839
$886$	1.04299e7	0.446371
$887$	−1.74303e7	−0.743866	−0.371933	−	0.928260i	$-0.621305\pi$
$887$	−1.74303e7	−0.743866	−0.371933	+	0.928260i	$0.621305\pi$
$888$	9.75885e6	0.415304
$889$	0	0
$890$	3.24000e6	0.137110
$891$	3.87657e6	0.163589
$892$	1.76153e7	0.741274
$893$	1.36492e7	0.572769
$894$	−4.38583e6	−0.183530
$895$	−2.77530e6	−0.115812
$896$	0	0
$897$	−1.54245e7	−0.640075
$898$	−1.91203e7	−0.791230
$899$	4.59694e6	0.189701
$900$	−1.22000e6	−0.0502058
$901$	1.42881e7	0.586357
$902$	−1.27135e7	−0.520293
$903$	0	0
$904$	1.23414e7	0.502276
$905$	−2.81930e6	−0.114425
$906$	−9.06475e6	−0.366889
$907$	−3.15066e7	−1.27170	−0.635848	−	0.771815i	$-0.719349\pi$
$907$	−3.15066e7	−1.27170	−0.635848	+	0.771815i	$0.719349\pi$
$908$	1.11220e7	0.447682
$909$	−5.03982e6	−0.202304
$910$	0	0
$911$	−4.91214e7	−1.96099	−0.980494	−	0.196548i	$-0.937027\pi$
$911$	−4.91214e7	−1.96099	−0.980494	+	0.196548i	$0.937027\pi$
$912$	2.25843e6	0.0899125
$913$	−2.23415e7	−0.887024
$914$	−3.18703e7	−1.26189
$915$	489500.	0.0193286
$916$	−7.41978e6	−0.292181
$917$	0	0
$918$	−8.23878e6	−0.322668
$919$	−4.51238e7	−1.76245	−0.881226	−	0.472696i	$-0.843281\pi$
$919$	−4.51238e7	−1.76245	−0.881226	+	0.472696i	$0.843281\pi$
$920$	−2.06400e6	−0.0803971
$921$	−1.09460e7	−0.425211
$922$	−7.10659e6	−0.275318
$923$	−5.65066e7	−2.18321
$924$	0	0
$925$	8.66375e6	0.332929
$926$	−3.99419e6	−0.153074
$927$	1.32718e7	0.507259
$928$	1.82170e6	0.0694394
$929$	3.68196e7	1.39972	0.699858	−	0.714282i	$-0.253247\pi$
$929$	3.68196e7	1.39972	0.699858	+	0.714282i	$0.253247\pi$
$930$	2.84240e6	0.107765
$931$	0	0
$932$	−2.52246e7	−0.951227
$933$	−1.47838e7	−0.556009
$934$	2.03391e7	0.762896
$935$	−3.42428e6	−0.128097
$936$	−8.48730e6	−0.316650
$937$	−1.71904e7	−0.639641	−0.319820	−	0.947478i	$-0.603623\pi$
$937$	−1.71904e7	−0.639641	−0.319820	+	0.947478i	$0.603623\pi$
$938$	0	0
$939$	−2.11168e7	−0.781562
$940$	6.80760e6	0.251290
$941$	8.10352e6	0.298332	0.149166	−	0.988812i	$-0.452341\pi$
$941$	8.10352e6	0.298332	0.149166	+	0.988812i	$0.452341\pi$
$942$	−2.55706e7	−0.938888
$943$	−1.53562e7	−0.562346
$944$	−7.91347e6	−0.289026
$945$	0	0
$946$	638664.	0.0232030
$947$	1.83337e7	0.664317	0.332158	−	0.943224i	$-0.392223\pi$
$947$	1.83337e7	0.664317	0.332158	+	0.943224i	$0.392223\pi$
$948$	−1.79733e7	−0.649541
$949$	−5.18390e7	−1.86849
$950$	2.00500e6	0.0720784
$951$	−2.10502e7	−0.754755
$952$	0	0
$953$	6.03035e6	0.215085	0.107542	−	0.994200i	$-0.465702\pi$
$953$	6.03035e6	0.215085	0.107542	+	0.994200i	$0.465702\pi$
$954$	−1.35918e7	−0.483510
$955$	−1.82998e7	−0.649288
$956$	−8.19259e6	−0.289919
$957$	−5.22492e6	−0.184417
$958$	−1.48774e7	−0.523738
$959$	0	0
$960$	1.12640e6	0.0394471
$961$	−2.19521e7	−0.766774
$962$	6.02720e7	2.09980
$963$	1.29440e7	0.449781
$964$	−1.58293e7	−0.548616
$965$	−4.65100e6	−0.160779
$966$	0	0
$967$	−3.09228e7	−1.06344	−0.531720	−	0.846920i	$-0.678454\pi$
$967$	−3.09228e7	−1.06344	−0.531720	+	0.846920i	$0.678454\pi$
$968$	−5.74477e6	−0.197053
$969$	4.52569e6	0.154837
$970$	1.48645e7	0.507249
$971$	2.47924e6	0.0843859	0.0421929	−	0.999109i	$-0.486566\pi$
$971$	2.47924e6	0.0843859	0.0421929	+	0.999109i	$0.486566\pi$
$972$	1.30550e7	0.443211
$973$	0	0
$974$	−3.64814e7	−1.23218
$975$	7.47312e6	0.251762
$976$	455680.	0.0153121
$977$	−2.09758e6	−0.0703044	−0.0351522	−	0.999382i	$-0.511192\pi$
$977$	−2.09758e6	−0.0703044	−0.0351522	+	0.999382i	$0.511192\pi$
$978$	1.52508e7	0.509855
$979$	−8.65080e6	−0.288469
$980$	0	0
$981$	1.51415e7	0.502340
$982$	−3.13509e7	−1.03746
$983$	4.45491e7	1.47047	0.735233	−	0.677814i	$-0.237073\pi$
$983$	4.45491e7	1.47047	0.735233	+	0.677814i	$0.237073\pi$
$984$	8.38042e6	0.275917
$985$	3.03390e6	0.0996347
$986$	3.65051e6	0.119581
$987$	0	0
$988$	1.39484e7	0.454602
$989$	771420.	0.0250784
$990$	3.25740e6	0.105629
$991$	−1.95104e7	−0.631075	−0.315538	−	0.948913i	$-0.602185\pi$
$991$	−1.95104e7	−0.631075	−0.315538	+	0.948913i	$0.602185\pi$
$992$	2.64602e6	0.0853716
$993$	−2.48263e7	−0.798987
$994$	0	0
$995$	−1.62146e7	−0.519217
$996$	1.47270e7	0.470398
$997$	2.00678e7	0.639385	0.319692	−	0.947521i	$-0.396420\pi$
$997$	2.00678e7	0.639385	0.319692	+	0.947521i	$0.396420\pi$
$998$	−384412.	−0.0122172
$999$	−5.56559e7	−1.76440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.6.a.l.1.1		1
7.6	odd	2		70.6.a.f.1.1	✓	1
21.20	even	2		630.6.a.e.1.1		1
28.27	even	2		560.6.a.f.1.1		1
35.13	even	4		350.6.c.b.99.1		2
35.27	even	4		350.6.c.b.99.2		2
35.34	odd	2		350.6.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.f.1.1	✓	1	7.6	odd	2
350.6.a.d.1.1		1	35.34	odd	2
350.6.c.b.99.1		2	35.13	even	4
350.6.c.b.99.2		2	35.27	even	4
490.6.a.l.1.1		1	1.1	even	1	trivial
560.6.a.f.1.1		1	28.27	even	2
630.6.a.e.1.1		1	21.20	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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	490.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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