LMFDB - Embedded newform 630.6.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,6,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, 6, names="a")

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

chi := DirichletCharacter("630.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
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:	$101.041806482$
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	$\chi$	$=$	630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q-4.00000 q^{2} +16.0000 q^{4} +25.0000 q^{5} +49.0000 q^{7} -64.0000 q^{8} -100.000 q^{10} +267.000 q^{11} -1087.00 q^{13} -196.000 q^{14} +256.000 q^{16} +513.000 q^{17} -802.000 q^{19} +400.000 q^{20} -1068.00 q^{22} +1290.00 q^{23} +625.000 q^{25} +4348.00 q^{26} +784.000 q^{28} -1779.00 q^{29} -2584.00 q^{31} -1024.00 q^{32} -2052.00 q^{34} +1225.00 q^{35} +13862.0 q^{37} +3208.00 q^{38} -1600.00 q^{40} +11904.0 q^{41} -598.000 q^{43} +4272.00 q^{44} -5160.00 q^{46} +17019.0 q^{47} +2401.00 q^{49} -2500.00 q^{50} -17392.0 q^{52} -27852.0 q^{53} +6675.00 q^{55} -3136.00 q^{56} +7116.00 q^{58} -30912.0 q^{59} -1780.00 q^{61} +10336.0 q^{62} +4096.00 q^{64} -27175.0 q^{65} +25052.0 q^{67} +8208.00 q^{68} -4900.00 q^{70} +51984.0 q^{71} +47690.0 q^{73} -55448.0 q^{74} -12832.0 q^{76} +13083.0 q^{77} -102121. q^{79} +6400.00 q^{80} -47616.0 q^{82} +83676.0 q^{83} +12825.0 q^{85} +2392.00 q^{86} -17088.0 q^{88} +32400.0 q^{89} -53263.0 q^{91} +20640.0 q^{92} -68076.0 q^{94} -20050.0 q^{95} -148645. q^{97} -9604.00 q^{98} +O(q^{100})\)

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 $

$2$	−4.00000	−0.707107
$2$	−4.00000	−0.707107
$3$	0	0
$3$	0	0
$4$	16.0000	0.500000
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	0	0
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	−64.0000	−0.353553
$9$	0	0
$10$	−100.000	−0.316228
$11$	267.000	0.665318	0.332659	−	0.943047i	$-0.392054\pi$
$11$	267.000	0.665318	0.332659	+	0.943047i	$0.392054\pi$
$12$	0	0
$13$	−1087.00	−1.78390	−0.891951	−	0.452131i	$-0.850664\pi$
$13$	−1087.00	−1.78390	−0.891951	+	0.452131i	$0.850664\pi$
$14$	−196.000	−0.267261
$15$	0	0
$16$	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	$0.430940\pi$
$18$	0	0
$19$	−802.000	−0.509672	−0.254836	−	0.966984i	$-0.582021\pi$
$19$	−802.000	−0.509672	−0.254836	+	0.966984i	$0.582021\pi$
$20$	400.000	0.223607
$21$	0	0
$22$	−1068.00	−0.470451
$23$	1290.00	0.508476	0.254238	−	0.967142i	$-0.418175\pi$
$23$	1290.00	0.508476	0.254238	+	0.967142i	$0.418175\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	4348.00	1.26141
$27$	0	0
$28$	784.000	0.188982
$29$	−1779.00	−0.392809	−0.196404	−	0.980523i	$-0.562926\pi$
$29$	−1779.00	−0.392809	−0.196404	+	0.980523i	$0.562926\pi$
$30$	0	0
$31$	−2584.00	−0.482935	−0.241467	−	0.970409i	$-0.577629\pi$
$31$	−2584.00	−0.482935	−0.241467	+	0.970409i	$0.577629\pi$
$32$	−1024.00	−0.176777
$33$	0	0
$34$	−2052.00	−0.304425
$35$	1225.00	0.169031
$36$	0	0
$37$	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
$39$	0	0
$40$	−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
$45$	0	0
$46$	−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	$0.310070\pi$
$48$	0	0
$49$	2401.00	0.142857
$50$	−2500.00	−0.141421
$51$	0	0
$52$	−17392.0	−0.891951
$53$	−27852.0	−1.36197	−0.680984	−	0.732299i	$-0.738448\pi$
$53$	−27852.0	−1.36197	−0.680984	+	0.732299i	$0.738448\pi$
$54$	0	0
$55$	6675.00	0.297539
$56$	−3136.00	−0.133631
$57$	0	0
$58$	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	$0.696187\pi$
$60$	0	0
$61$	−1780.00	−0.0612485	−0.0306242	−	0.999531i	$-0.509750\pi$
$61$	−1780.00	−0.0612485	−0.0306242	+	0.999531i	$0.509750\pi$
$62$	10336.0	0.341486
$63$	0	0
$64$	4096.00	0.125000
$65$	−27175.0	−0.797786
$66$	0	0
$67$	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
$69$	0	0
$70$	−4900.00	−0.119523
$71$	51984.0	1.22384	0.611919	−	0.790921i	$-0.290398\pi$
$71$	51984.0	1.22384	0.611919	+	0.790921i	$0.290398\pi$
$72$	0	0
$73$	47690.0	1.04742	0.523709	−	0.851897i	$-0.324548\pi$
$73$	47690.0	1.04742	0.523709	+	0.851897i	$0.324548\pi$
$74$	−55448.0	−1.17708
$75$	0	0
$76$	−12832.0	−0.254836
$77$	13083.0	0.251467
$78$	0	0
$79$	−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
$81$	0	0
$82$	−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
$87$	0	0
$88$	−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	$0.430441\pi$
$90$	0	0
$91$	−53263.0	−0.674252
$92$	20640.0	0.254238
$93$	0	0
$94$	−68076.0	−0.794647
$95$	−20050.0	−0.227932
$96$	0	0
$97$	−148645.	−1.60406	−0.802031	−	0.597283i	$-0.796247\pi$
$97$	−148645.	−1.60406	−0.802031	+	0.597283i	$0.796247\pi$
$98$	−9604.00	−0.101015
$99$	0	0
$100$	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	$0.435426\pi$
$102$	0	0
$103$	108785.	1.01036	0.505180	−	0.863014i	$-0.331426\pi$
$103$	108785.	1.01036	0.505180	+	0.863014i	$0.331426\pi$
$104$	69568.0	0.630705
$105$	0	0
$106$	111408.	0.963056
$107$	106098.	0.895876	0.447938	−	0.894065i	$-0.352159\pi$
$107$	106098.	0.895876	0.447938	+	0.894065i	$0.352159\pi$
$108$	0	0
$109$	−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
$111$	0	0
$112$	12544.0	0.0944911
$113$	−192834.	−1.42065	−0.710326	−	0.703873i	$-0.751452\pi$
$113$	−192834.	−1.42065	−0.710326	+	0.703873i	$0.751452\pi$
$114$	0	0
$115$	32250.0	0.227397
$116$	−28464.0	−0.196404
$117$	0	0
$118$	123648.	0.817489
$119$	25137.0	0.162722
$120$	0	0
$121$	−89762.0	−0.557351
$122$	7120.00	0.0433092
$123$	0	0
$124$	−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
$129$	0	0
$130$	108700.	0.564120
$131$	276810.	1.40930	0.704650	−	0.709555i	$-0.251104\pi$
$131$	276810.	1.40930	0.704650	+	0.709555i	$0.251104\pi$
$132$	0	0
$133$	−39298.0	−0.192638
$134$	−100208.	−0.482104
$135$	0	0
$136$	−32832.0	−0.152212
$137$	−237744.	−1.08220	−0.541101	−	0.840958i	$-0.681992\pi$
$137$	−237744.	−1.08220	−0.541101	+	0.840958i	$0.681992\pi$
$138$	0	0
$139$	160478.	0.704496	0.352248	−	0.935907i	$-0.385417\pi$
$139$	160478.	0.704496	0.352248	+	0.935907i	$0.385417\pi$
$140$	19600.0	0.0845154
$141$	0	0
$142$	−207936.	−0.865384
$143$	−290229.	−1.18686
$144$	0	0
$145$	−44475.0	−0.175669
$146$	−190760.	−0.740637
$147$	0	0
$148$	221792.	0.832322
$149$	99678.0	0.367819	0.183909	−	0.982943i	$-0.441125\pi$
$149$	99678.0	0.367819	0.183909	+	0.982943i	$0.441125\pi$
$150$	0	0
$151$	−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
$153$	0	0
$154$	−52332.0	−0.177814
$155$	−64600.0	−0.215975
$156$	0	0
$157$	581150.	1.88165	0.940826	−	0.338891i	$-0.110052\pi$
$157$	581150.	1.88165	0.940826	+	0.338891i	$0.110052\pi$
$158$	408484.	1.30176
$159$	0	0
$160$	−25600.0	−0.0790569
$161$	63210.0	0.192186
$162$	0	0
$163$	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
$165$	0	0
$166$	−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
$171$	0	0
$172$	−9568.00	−0.0246604
$173$	262509.	0.666851	0.333426	−	0.942776i	$-0.391795\pi$
$173$	262509.	0.666851	0.333426	+	0.942776i	$0.391795\pi$
$174$	0	0
$175$	30625.0	0.0755929
$176$	68352.0	0.166330
$177$	0	0
$178$	−129600.	−0.306588
$179$	111012.	0.258963	0.129481	−	0.991582i	$-0.458669\pi$
$179$	111012.	0.258963	0.129481	+	0.991582i	$0.458669\pi$
$180$	0	0
$181$	112772.	0.255861	0.127931	−	0.991783i	$-0.459166\pi$
$181$	112772.	0.255861	0.127931	+	0.991783i	$0.459166\pi$
$182$	213052.	0.476768
$183$	0	0
$184$	−82560.0	−0.179773
$185$	346550.	0.744452
$186$	0	0
$187$	136971.	0.286434
$188$	272304.	0.561900
$189$	0	0
$190$	80200.0	0.161172
$191$	731991.	1.45185	0.725926	−	0.687773i	$-0.241411\pi$
$191$	731991.	1.45185	0.725926	+	0.687773i	$0.241411\pi$
$192$	0	0
$193$	−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
$195$	0	0
$196$	38416.0	0.0714286
$197$	−121356.	−0.222790	−0.111395	−	0.993776i	$-0.535532\pi$
$197$	−121356.	−0.222790	−0.111395	+	0.993776i	$0.535532\pi$
$198$	0	0
$199$	648584.	1.16100	0.580502	−	0.814259i	$-0.302856\pi$
$199$	648584.	1.16100	0.580502	+	0.814259i	$0.302856\pi$
$200$	−40000.0	−0.0707107
$201$	0	0
$202$	−165240.	−0.284929
$203$	−87171.0	−0.148468
$204$	0	0
$205$	297600.	0.494593
$206$	−435140.	−0.714432
$207$	0	0
$208$	−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
$213$	0	0
$214$	−424392.	−0.633480
$215$	−14950.0	−0.0220569
$216$	0	0
$217$	−126616.	−0.182532
$218$	496444.	0.707504
$219$	0	0
$220$	106800.	0.148770
$221$	−557631.	−0.768009
$222$	0	0
$223$	−1.10096e6	−1.48255	−0.741274	−	0.671202i	$-0.765778\pi$
$223$	−1.10096e6	−1.48255	−0.741274	+	0.671202i	$0.765778\pi$
$224$	−50176.0	−0.0668153
$225$	0	0
$226$	771336.	1.00455
$227$	695127.	0.895364	0.447682	−	0.894193i	$-0.352250\pi$
$227$	695127.	0.895364	0.447682	+	0.894193i	$0.352250\pi$
$228$	0	0
$229$	463736.	0.584362	0.292181	−	0.956363i	$-0.405619\pi$
$229$	463736.	0.584362	0.292181	+	0.956363i	$0.405619\pi$
$230$	−129000.	−0.160794
$231$	0	0
$232$	113856.	0.138879
$233$	1.57654e6	1.90245	0.951227	−	0.308492i	$-0.0998244\pi$
$233$	1.57654e6	1.90245	0.951227	+	0.308492i	$0.0998244\pi$
$234$	0	0
$235$	425475.	0.502579
$236$	−494592.	−0.578052
$237$	0	0
$238$	−100548.	−0.115062
$239$	512037.	0.579838	0.289919	−	0.957051i	$-0.406372\pi$
$239$	512037.	0.579838	0.289919	+	0.957051i	$0.406372\pi$
$240$	0	0
$241$	989330.	1.09723	0.548616	−	0.836074i	$-0.315155\pi$
$241$	989330.	1.09723	0.548616	+	0.836074i	$0.315155\pi$
$242$	359048.	0.394107
$243$	0	0
$244$	−28480.0	−0.0306242
$245$	60025.0	0.0638877
$246$	0	0
$247$	871774.	0.909204
$248$	165376.	0.170743
$249$	0	0
$250$	−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
$255$	0	0
$256$	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	$0.717861\pi$
$258$	0	0
$259$	679238.	0.629177
$260$	−434800.	−0.398893
$261$	0	0
$262$	−1.10724e6	−0.996526
$263$	1.65619e6	1.47645	0.738227	−	0.674553i	$-0.235663\pi$
$263$	1.65619e6	1.47645	0.738227	+	0.674553i	$0.235663\pi$
$264$	0	0
$265$	−696300.	−0.609090
$266$	157192.	0.136215
$267$	0	0
$268$	400832.	0.340899
$269$	750606.	0.632457	0.316229	−	0.948683i	$-0.397583\pi$
$269$	750606.	0.632457	0.316229	+	0.948683i	$0.397583\pi$
$270$	0	0
$271$	−557908.	−0.461466	−0.230733	−	0.973017i	$-0.574112\pi$
$271$	−557908.	−0.461466	−0.230733	+	0.973017i	$0.574112\pi$
$272$	131328.	0.107630
$273$	0	0
$274$	950976.	0.765232
$275$	166875.	0.133064
$276$	0	0
$277$	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
$279$	0	0
$280$	−78400.0	−0.0597614
$281$	1.09893e6	0.830243	0.415122	−	0.909766i	$-0.363739\pi$
$281$	1.09893e6	0.830243	0.415122	+	0.909766i	$0.363739\pi$
$282$	0	0
$283$	−320569.	−0.237933	−0.118967	−	0.992898i	$-0.537958\pi$
$283$	−320569.	−0.237933	−0.118967	+	0.992898i	$0.537958\pi$
$284$	831744.	0.611919
$285$	0	0
$286$	1.16092e6	0.839239
$287$	583296.	0.418008
$288$	0	0
$289$	−1.15669e6	−0.814651
$290$	177900.	0.124217
$291$	0	0
$292$	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
$297$	0	0
$298$	−398712.	−0.260087
$299$	−1.40223e6	−0.907071
$300$	0	0
$301$	−29302.0	−0.0186415
$302$	824068.	0.519931
$303$	0	0
$304$	−205312.	−0.127418
$305$	−44500.0	−0.0273912
$306$	0	0
$307$	995087.	0.602581	0.301290	−	0.953532i	$-0.402583\pi$
$307$	995087.	0.602581	0.301290	+	0.953532i	$0.402583\pi$
$308$	209328.	0.125733
$309$	0	0
$310$	258400.	0.152717
$311$	−1.34398e6	−0.787939	−0.393969	−	0.919124i	$-0.628898\pi$
$311$	−1.34398e6	−0.787939	−0.393969	+	0.919124i	$0.628898\pi$
$312$	0	0
$313$	1.91971e6	1.10758	0.553788	−	0.832658i	$-0.313182\pi$
$313$	1.91971e6	1.10758	0.553788	+	0.832658i	$0.313182\pi$
$314$	−2.32460e6	−1.33053
$315$	0	0
$316$	−1.63394e6	−0.920486
$317$	1.91366e6	1.06959	0.534794	−	0.844983i	$-0.320389\pi$
$317$	1.91366e6	1.06959	0.534794	+	0.844983i	$0.320389\pi$
$318$	0	0
$319$	−474993.	−0.261343
$320$	102400.	0.0559017
$321$	0	0
$322$	−252840.	−0.135896
$323$	−411426.	−0.219425
$324$	0	0
$325$	−679375.	−0.356781
$326$	−1.38644e6	−0.722532
$327$	0	0
$328$	−761856.	−0.391010
$329$	833931.	0.424757
$330$	0	0
$331$	−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
$333$	0	0
$334$	−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
$339$	0	0
$340$	205200.	0.0962676
$341$	−689928.	−0.321305
$342$	0	0
$343$	117649.	0.0539949
$344$	38272.0	0.0174375
$345$	0	0
$346$	−1.05004e6	−0.471535
$347$	−856386.	−0.381809	−0.190904	−	0.981609i	$-0.561142\pi$
$347$	−856386.	−0.381809	−0.190904	+	0.981609i	$0.561142\pi$
$348$	0	0
$349$	−347602.	−0.152763	−0.0763816	−	0.997079i	$-0.524337\pi$
$349$	−347602.	−0.152763	−0.0763816	+	0.997079i	$0.524337\pi$
$350$	−122500.	−0.0534522
$351$	0	0
$352$	−273408.	−0.117613
$353$	2.21860e6	0.947640	0.473820	−	0.880622i	$-0.342875\pi$
$353$	2.21860e6	0.947640	0.473820	+	0.880622i	$0.342875\pi$
$354$	0	0
$355$	1.29960e6	0.547317
$356$	518400.	0.216790
$357$	0	0
$358$	−444048.	−0.183114
$359$	−2.94338e6	−1.20534	−0.602672	−	0.797989i	$-0.705897\pi$
$359$	−2.94338e6	−1.20534	−0.602672	+	0.797989i	$0.705897\pi$
$360$	0	0
$361$	−1.83290e6	−0.740235
$362$	−451088.	−0.180921
$363$	0	0
$364$	−852208.	−0.337126
$365$	1.19225e6	0.468420
$366$	0	0
$367$	2.33000e6	0.903005	0.451503	−	0.892270i	$-0.350888\pi$
$367$	2.33000e6	0.903005	0.451503	+	0.892270i	$0.350888\pi$
$368$	330240.	0.127119
$369$	0	0
$370$	−1.38620e6	−0.526407
$371$	−1.36475e6	−0.514775
$372$	0	0
$373$	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
$375$	0	0
$376$	−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
$381$	0	0
$382$	−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	$0.707635\pi$
$384$	0	0
$385$	327075.	0.112459
$386$	744160.	0.254213
$387$	0	0
$388$	−2.37832e6	−0.802031
$389$	3.60598e6	1.20823	0.604114	−	0.796898i	$-0.293527\pi$
$389$	3.60598e6	1.20823	0.604114	+	0.796898i	$0.293527\pi$
$390$	0	0
$391$	661770.	0.218910
$392$	−153664.	−0.0505076
$393$	0	0
$394$	485424.	0.157536
$395$	−2.55302e6	−0.823308
$396$	0	0
$397$	4.74380e6	1.51060	0.755302	−	0.655377i	$-0.227490\pi$
$397$	4.74380e6	1.51060	0.755302	+	0.655377i	$0.227490\pi$
$398$	−2.59434e6	−0.820953
$399$	0	0
$400$	160000.	0.0500000
$401$	−5.26539e6	−1.63520	−0.817598	−	0.575789i	$-0.804695\pi$
$401$	−5.26539e6	−1.63520	−0.817598	+	0.575789i	$0.804695\pi$
$402$	0	0
$403$	2.80881e6	0.861508
$404$	660960.	0.201475
$405$	0	0
$406$	348684.	0.104983
$407$	3.70115e6	1.10752
$408$	0	0
$409$	1.37015e6	0.405004	0.202502	−	0.979282i	$-0.435093\pi$
$409$	1.37015e6	0.405004	0.202502	+	0.979282i	$0.435093\pi$
$410$	−1.19040e6	−0.349730
$411$	0	0
$412$	1.74056e6	0.505180
$413$	−1.51469e6	−0.436966
$414$	0	0
$415$	2.09190e6	0.596239
$416$	1.11309e6	0.315352
$417$	0	0
$418$	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
$423$	0	0
$424$	1.78253e6	0.481528
$425$	320625.	0.0861043
$426$	0	0
$427$	−87220.0	−0.0231498
$428$	1.69757e6	0.447938
$429$	0	0
$430$	59800.0	0.0155966
$431$	−7.66771e6	−1.98826	−0.994128	−	0.108207i	$-0.965489\pi$
$431$	−7.66771e6	−1.98826	−0.994128	+	0.108207i	$0.965489\pi$
$432$	0	0
$433$	−5.00285e6	−1.28232	−0.641161	−	0.767406i	$-0.721547\pi$
$433$	−5.00285e6	−1.28232	−0.641161	+	0.767406i	$0.721547\pi$
$434$	506464.	0.129070
$435$	0	0
$436$	−1.98578e6	−0.500281
$437$	−1.03458e6	−0.259156
$438$	0	0
$439$	1.86363e6	0.461527	0.230764	−	0.973010i	$-0.425878\pi$
$439$	1.86363e6	0.461527	0.230764	+	0.973010i	$0.425878\pi$
$440$	−427200.	−0.105196
$441$	0	0
$442$	2.23052e6	0.543064
$443$	−2.60747e6	−0.631263	−0.315632	−	0.948882i	$-0.602216\pi$
$443$	−2.60747e6	−0.631263	−0.315632	+	0.948882i	$0.602216\pi$
$444$	0	0
$445$	810000.	0.193903
$446$	4.40384e6	1.04832
$447$	0	0
$448$	200704.	0.0472456
$449$	4.78007e6	1.11897	0.559484	−	0.828841i	$-0.310999\pi$
$449$	4.78007e6	1.11897	0.559484	+	0.828841i	$0.310999\pi$
$450$	0	0
$451$	3.17837e6	0.735805
$452$	−3.08534e6	−0.710326
$453$	0	0
$454$	−2.78051e6	−0.633118
$455$	−1.33157e6	−0.301535
$456$	0	0
$457$	−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
$459$	0	0
$460$	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
$465$	0	0
$466$	−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	$0.318633\pi$
$468$	0	0
$469$	1.22755e6	0.257695
$470$	−1.70190e6	−0.355377
$471$	0	0
$472$	1.97837e6	0.408745
$473$	−159666.	−0.0328140
$474$	0	0
$475$	−501250.	−0.101934
$476$	402192.	0.0813610
$477$	0	0
$478$	−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	$0.620758\pi$
$480$	0	0
$481$	−1.50680e7	−2.96956
$482$	−3.95732e6	−0.775860
$483$	0	0
$484$	−1.43619e6	−0.278676
$485$	−3.71612e6	−0.717358
$486$	0	0
$487$	−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
$489$	0	0
$490$	−240100.	−0.0451754
$491$	7.83774e6	1.46719	0.733596	−	0.679586i	$-0.237840\pi$
$491$	7.83774e6	1.46719	0.733596	+	0.679586i	$0.237840\pi$
$492$	0	0
$493$	−912627.	−0.169113
$494$	−3.48710e6	−0.642905
$495$	0	0
$496$	−661504.	−0.120734
$497$	2.54722e6	0.462567
$498$	0	0
$499$	−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
$501$	0	0
$502$	−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
$507$	0	0
$508$	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	$0.668863\pi$
$510$	0	0
$511$	2.33681e6	0.395887
$512$	−262144.	−0.0441942
$513$	0	0
$514$	5.35548e6	0.894109
$515$	2.71963e6	0.451847
$516$	0	0
$517$	4.54407e6	0.747685
$518$	−2.71695e6	−0.444895
$519$	0	0
$520$	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	$0.537617\pi$
$522$	0	0
$523$	−2.90691e6	−0.464705	−0.232352	−	0.972632i	$-0.574642\pi$
$523$	−2.90691e6	−0.464705	−0.232352	+	0.972632i	$0.574642\pi$
$524$	4.42896e6	0.704650
$525$	0	0
$526$	−6.62474e6	−1.04401
$527$	−1.32559e6	−0.207914
$528$	0	0
$529$	−4.77224e6	−0.741453
$530$	2.78520e6	0.430692
$531$	0	0
$532$	−628768.	−0.0963189
$533$	−1.29396e7	−1.97290
$534$	0	0
$535$	2.65245e6	0.400648
$536$	−1.60333e6	−0.241052
$537$	0	0
$538$	−3.00242e6	−0.447215
$539$	641067.	0.0950455
$540$	0	0
$541$	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
$543$	0	0
$544$	−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
$549$	0	0
$550$	−667500.	−0.0940902
$551$	1.42676e6	0.200203
$552$	0	0
$553$	−5.00393e6	−0.695822
$554$	−7.09023e6	−0.981490
$555$	0	0
$556$	2.56765e6	0.352248
$557$	1.39920e7	1.91091	0.955457	−	0.295131i	$-0.0953633\pi$
$557$	1.39920e7	1.91091	0.955457	+	0.295131i	$0.0953633\pi$
$558$	0	0
$559$	650026.	0.0879835
$560$	313600.	0.0422577
$561$	0	0
$562$	−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	$0.389288\pi$
$564$	0	0
$565$	−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	$-0.319640\pi$
$569$	8.29102e6	1.07356	0.536781	+	0.843721i	$0.319640\pi$
$570$	0	0
$571$	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
$573$	0	0
$574$	−2.33318e6	−0.295576
$575$	806250.	0.101695
$576$	0	0
$577$	1.14818e7	1.43572	0.717861	−	0.696186i	$-0.245121\pi$
$577$	1.14818e7	1.43572	0.717861	+	0.696186i	$0.245121\pi$
$578$	4.62675e6	0.576045
$579$	0	0
$580$	−711600.	−0.0878347
$581$	4.10012e6	0.503914
$582$	0	0
$583$	−7.43648e6	−0.906142
$584$	−3.05216e6	−0.370318
$585$	0	0
$586$	−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
$591$	0	0
$592$	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	$0.447617\pi$
$594$	0	0
$595$	628425.	0.0727715
$596$	1.59485e6	0.183909
$597$	0	0
$598$	5.60892e6	0.641396
$599$	−7.74415e6	−0.881874	−0.440937	−	0.897538i	$-0.645354\pi$
$599$	−7.74415e6	−0.881874	−0.440937	+	0.897538i	$0.645354\pi$
$600$	0	0
$601$	2.88868e6	0.326222	0.163111	−	0.986608i	$-0.447847\pi$
$601$	2.88868e6	0.326222	0.163111	+	0.986608i	$0.447847\pi$
$602$	117208.	0.0131815
$603$	0	0
$604$	−3.29627e6	−0.367647
$605$	−2.24405e6	−0.249255
$606$	0	0
$607$	1.22095e7	1.34501	0.672504	−	0.740093i	$-0.265219\pi$
$607$	1.22095e7	1.34501	0.672504	+	0.740093i	$0.265219\pi$
$608$	821248.	0.0900980
$609$	0	0
$610$	178000.	0.0193685
$611$	−1.84997e7	−2.00475
$612$	0	0
$613$	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
$615$	0	0
$616$	−837312.	−0.0889069
$617$	−1.53927e7	−1.62780	−0.813899	−	0.581006i	$-0.802659\pi$
$617$	−1.53927e7	−1.62780	−0.813899	+	0.581006i	$0.802659\pi$
$618$	0	0
$619$	−1.40843e7	−1.47744	−0.738720	−	0.674013i	$-0.764569\pi$
$619$	−1.40843e7	−1.47744	−0.738720	+	0.674013i	$0.764569\pi$
$620$	−1.03360e6	−0.107987
$621$	0	0
$622$	5.37593e6	0.557157
$623$	1.58760e6	0.163878
$624$	0	0
$625$	390625.	0.0400000
$626$	−7.67882e6	−0.783175
$627$	0	0
$628$	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
$633$	0	0
$634$	−7.65463e6	−0.756312
$635$	2.48120e6	0.244190
$636$	0	0
$637$	−2.60989e6	−0.254843
$638$	1.89997e6	0.184797
$639$	0	0
$640$	−409600.	−0.0395285
$641$	−4.04157e6	−0.388513	−0.194256	−	0.980951i	$-0.562229\pi$
$641$	−4.04157e6	−0.388513	−0.194256	+	0.980951i	$0.562229\pi$
$642$	0	0
$643$	−1.71035e7	−1.63139	−0.815693	−	0.578485i	$-0.803644\pi$
$643$	−1.71035e7	−1.63139	−0.815693	+	0.578485i	$0.803644\pi$
$644$	1.01136e6	0.0960929
$645$	0	0
$646$	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	$0.363818\pi$
$648$	0	0
$649$	−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	$-0.641330\pi$
$653$	−9.36125e6	−0.859115	−0.429557	+	0.903040i	$0.641330\pi$
$654$	0	0
$655$	6.92025e6	0.630258
$656$	3.04742e6	0.276486
$657$	0	0
$658$	−3.33572e6	−0.300348
$659$	366111.	0.0328397	0.0164199	−	0.999865i	$-0.494773\pi$
$659$	366111.	0.0328397	0.0164199	+	0.999865i	$0.494773\pi$
$660$	0	0
$661$	2.05164e7	1.82640	0.913202	−	0.407508i	$-0.133602\pi$
$661$	2.05164e7	1.82640	0.913202	+	0.407508i	$0.133602\pi$
$662$	9.02776e6	0.800636
$663$	0	0
$664$	−5.35526e6	−0.471369
$665$	−982450.	−0.0861502
$666$	0	0
$667$	−2.29491e6	−0.199734
$668$	7.18219e6	0.622753
$669$	0	0
$670$	−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
$675$	0	0
$676$	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	$0.670076\pi$
$678$	0	0
$679$	−7.28360e6	−0.606278
$680$	−820800.	−0.0680715
$681$	0	0
$682$	2.75971e6	0.227197
$683$	1.15232e7	0.945197	0.472599	−	0.881278i	$-0.343316\pi$
$683$	1.15232e7	0.945197	0.472599	+	0.881278i	$0.343316\pi$
$684$	0	0
$685$	−5.94360e6	−0.483975
$686$	−470596.	−0.0381802
$687$	0	0
$688$	−153088.	−0.0123302
$689$	3.02751e7	2.42962
$690$	0	0
$691$	−1.71185e7	−1.36386	−0.681931	−	0.731417i	$-0.738859\pi$
$691$	−1.71185e7	−1.36386	−0.681931	+	0.731417i	$0.738859\pi$
$692$	4.20014e6	0.333426
$693$	0	0
$694$	3.42554e6	0.269980
$695$	4.01195e6	0.315060
$696$	0	0
$697$	6.10675e6	0.476133
$698$	1.39041e6	0.108020
$699$	0	0
$700$	490000.	0.0377964
$701$	−9.72758e6	−0.747669	−0.373835	−	0.927495i	$-0.621957\pi$
$701$	−9.72758e6	−0.747669	−0.373835	+	0.927495i	$0.621957\pi$
$702$	0	0
$703$	−1.11173e7	−0.848422
$704$	1.09363e6	0.0831648
$705$	0	0
$706$	−8.87442e6	−0.670082
$707$	2.02419e6	0.152301
$708$	0	0
$709$	−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
$711$	0	0
$712$	−2.07360e6	−0.153294
$713$	−3.33336e6	−0.245560
$714$	0	0
$715$	−7.25572e6	−0.530781
$716$	1.77619e6	0.129481
$717$	0	0
$718$	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	$0.531940\pi$
$720$	0	0
$721$	5.33046e6	0.381880
$722$	7.33158e6	0.523425
$723$	0	0
$724$	1.80435e6	0.127931
$725$	−1.11188e6	−0.0785617
$726$	0	0
$727$	1.16385e7	0.816700	0.408350	−	0.912825i	$-0.366104\pi$
$727$	1.16385e7	0.816700	0.408350	+	0.912825i	$0.366104\pi$
$728$	3.40883e6	0.238384
$729$	0	0
$730$	−4.76900e6	−0.331223
$731$	−306774.	−0.0212337
$732$	0	0
$733$	−1.32013e7	−0.907522	−0.453761	−	0.891123i	$-0.649918\pi$
$733$	−1.32013e7	−0.907522	−0.453761	+	0.891123i	$0.649918\pi$
$734$	−9.31999e6	−0.638521
$735$	0	0
$736$	−1.32096e6	−0.0898866
$737$	6.68888e6	0.453612
$738$	0	0
$739$	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
$741$	0	0
$742$	5.45899e6	0.364001
$743$	7.61596e6	0.506119	0.253059	−	0.967451i	$-0.418563\pi$
$743$	7.61596e6	0.506119	0.253059	+	0.967451i	$0.418563\pi$
$744$	0	0
$745$	2.49195e6	0.164493
$746$	−6.76986e6	−0.445382
$747$	0	0
$748$	2.19154e6	0.143217
$749$	5.19880e6	0.338609
$750$	0	0
$751$	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
$753$	0	0
$754$	−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
$759$	0	0
$760$	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	$0.303086\pi$
$762$	0	0
$763$	−6.08144e6	−0.378177
$764$	1.17119e7	0.725926
$765$	0	0
$766$	1.39409e7	0.858456
$767$	3.36013e7	2.06238
$768$	0	0
$769$	−1.48414e7	−0.905024	−0.452512	−	0.891758i	$-0.649472\pi$
$769$	−1.48414e7	−0.905024	−0.452512	+	0.891758i	$0.649472\pi$
$770$	−1.30830e6	−0.0795208
$771$	0	0
$772$	−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	$0.537742\pi$
$774$	0	0
$775$	−1.61500e6	−0.0965869
$776$	9.51328e6	0.567121
$777$	0	0
$778$	−1.44239e7	−0.854347
$779$	−9.54701e6	−0.563668
$780$	0	0
$781$	1.38797e7	0.814242
$782$	−2.64708e6	−0.154793
$783$	0	0
$784$	614656.	0.0357143
$785$	1.45288e7	0.841500
$786$	0	0
$787$	1.17824e7	0.678105	0.339053	−	0.940767i	$-0.389893\pi$
$787$	1.17824e7	0.678105	0.339053	+	0.940767i	$0.389893\pi$
$788$	−1.94170e6	−0.111395
$789$	0	0
$790$	1.02121e7	0.582167
$791$	−9.44887e6	−0.536956
$792$	0	0
$793$	1.93486e6	0.109261
$794$	−1.89752e7	−1.06816
$795$	0	0
$796$	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
$801$	0	0
$802$	2.10616e7	1.15626
$803$	1.27332e7	0.696867
$804$	0	0
$805$	1.58025e6	0.0859481
$806$	−1.12352e7	−0.609178
$807$	0	0
$808$	−2.64384e6	−0.142465
$809$	7.12264e6	0.382622	0.191311	−	0.981529i	$-0.438726\pi$
$809$	7.12264e6	0.382622	0.191311	+	0.981529i	$0.438726\pi$
$810$	0	0
$811$	−3.03045e7	−1.61791	−0.808956	−	0.587869i	$-0.799967\pi$
$811$	−3.03045e7	−1.61791	−0.808956	+	0.587869i	$0.799967\pi$
$812$	−1.39474e6	−0.0742338
$813$	0	0
$814$	−1.48046e7	−0.783134
$815$	8.66525e6	0.456969
$816$	0	0
$817$	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	$-0.760728\pi$
$821$	−2.82181e7	−1.46106	−0.730532	+	0.682878i	$0.760728\pi$
$822$	0	0
$823$	−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
$825$	0	0
$826$	6.05875e6	0.308982
$827$	−4.44481e6	−0.225990	−0.112995	−	0.993596i	$-0.536044\pi$
$827$	−4.44481e6	−0.225990	−0.112995	+	0.993596i	$0.536044\pi$
$828$	0	0
$829$	−2.80386e6	−0.141700	−0.0708501	−	0.997487i	$-0.522571\pi$
$829$	−2.80386e6	−0.141700	−0.0708501	+	0.997487i	$0.522571\pi$
$830$	−8.36760e6	−0.421605
$831$	0	0
$832$	−4.45235e6	−0.222988
$833$	1.23171e6	0.0615031
$834$	0	0
$835$	1.12222e7	0.557007
$836$	−3.42614e6	−0.169547
$837$	0	0
$838$	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
$843$	0	0
$844$	−2.39637e6	−0.115797
$845$	2.02569e7	0.975958
$846$	0	0
$847$	−4.39834e6	−0.210659
$848$	−7.13011e6	−0.340492
$849$	0	0
$850$	−1.28250e6	−0.0608850
$851$	1.78820e7	0.846431
$852$	0	0
$853$	1.18392e7	0.557121	0.278560	−	0.960419i	$-0.410143\pi$
$853$	1.18392e7	0.557121	0.278560	+	0.960419i	$0.410143\pi$
$854$	348880.	0.0163693
$855$	0	0
$856$	−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	$0.477828\pi$
$858$	0	0
$859$	2.80980e7	1.29925	0.649626	−	0.760254i	$-0.274926\pi$
$859$	2.80980e7	1.29925	0.649626	+	0.760254i	$0.274926\pi$
$860$	−239200.	−0.0110285
$861$	0	0
$862$	3.06708e7	1.40591
$863$	−1.15833e7	−0.529424	−0.264712	−	0.964328i	$-0.585277\pi$
$863$	−1.15833e7	−0.529424	−0.264712	+	0.964328i	$0.585277\pi$
$864$	0	0
$865$	6.56272e6	0.298225
$866$	2.00114e7	0.906739
$867$	0	0
$868$	−2.02586e6	−0.0912661
$869$	−2.72663e7	−1.22483
$870$	0	0
$871$	−2.72315e7	−1.21626
$872$	7.94310e6	0.353752
$873$	0	0
$874$	4.13832e6	0.183251
$875$	765625.	0.0338062
$876$	0	0
$877$	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
$879$	0	0
$880$	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
$885$	0	0
$886$	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	$0.621305\pi$
$888$	0	0
$889$	4.86315e6	0.206378
$890$	−3.24000e6	−0.137110
$891$	0	0
$892$	−1.76153e7	−0.741274
$893$	−1.36492e7	−0.572769
$894$	0	0
$895$	2.77530e6	0.115812
$896$	−802816.	−0.0334077
$897$	0	0
$898$	−1.91203e7	−0.791230
$899$	4.59694e6	0.189701
$900$	0	0
$901$	−1.42881e7	−0.586357
$902$	−1.27135e7	−0.520293
$903$	0	0
$904$	1.23414e7	0.502276
$905$	2.81930e6	0.114425
$906$	0	0
$907$	−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
$909$	0	0
$910$	5.32630e6	0.213217
$911$	4.91214e7	1.96099	0.980494	−	0.196548i	$-0.0629732\pi$
$911$	4.91214e7	1.96099	0.980494	+	0.196548i	$0.0629732\pi$
$912$	0	0
$913$	2.23415e7	0.887024
$914$	3.18703e7	1.26189
$915$	0	0
$916$	7.41978e6	0.292181
$917$	1.35637e7	0.532665
$918$	0	0
$919$	−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
$921$	0	0
$922$	7.10659e6	0.275318
$923$	−5.65066e7	−2.18321
$924$	0	0
$925$	8.66375e6	0.332929
$926$	3.99419e6	0.153074
$927$	0	0
$928$	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	$0.253247\pi$
$930$	0	0
$931$	−1.92560e6	−0.0728102
$932$	2.52246e7	0.951227
$933$	0	0
$934$	−2.03391e7	−0.762896
$935$	3.42428e6	0.128097
$936$	0	0
$937$	1.71904e7	0.639641	0.319820	−	0.947478i	$-0.396377\pi$
$937$	1.71904e7	0.639641	0.319820	+	0.947478i	$0.396377\pi$
$938$	−4.91019e6	−0.182218
$939$	0	0
$940$	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	$0.452341\pi$
$942$	0	0
$943$	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	$-0.607777\pi$
$947$	−1.83337e7	−0.664317	−0.332158	+	0.943224i	$0.607777\pi$
$948$	0	0
$949$	−5.18390e7	−1.86849
$950$	2.00500e6	0.0720784
$951$	0	0
$952$	−1.60877e6	−0.0575309
$953$	−6.03035e6	−0.215085	−0.107542	−	0.994200i	$-0.534298\pi$
$953$	−6.03035e6	−0.215085	−0.107542	+	0.994200i	$0.534298\pi$
$954$	0	0
$955$	1.82998e7	0.649288
$956$	8.19259e6	0.289919
$957$	0	0
$958$	1.48774e7	0.523738
$959$	−1.16495e7	−0.409034
$960$	0	0
$961$	−2.19521e7	−0.766774
$962$	6.02720e7	2.09980
$963$	0	0
$964$	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
$969$	0	0
$970$	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	$0.486566\pi$
$972$	0	0
$973$	7.86342e6	0.266274
$974$	3.64814e7	1.23218
$975$	0	0
$976$	−455680.	−0.0153121
$977$	2.09758e6	0.0703044	0.0351522	−	0.999382i	$-0.488808\pi$
$977$	2.09758e6	0.0703044	0.0351522	+	0.999382i	$0.488808\pi$
$978$	0	0
$979$	8.65080e6	0.288469
$980$	960400.	0.0319438
$981$	0	0
$982$	−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	$0.237073\pi$
$984$	0	0
$985$	−3.03390e6	−0.0996347
$986$	3.65051e6	0.119581
$987$	0	0
$988$	1.39484e7	0.454602
$989$	−771420.	−0.0250784
$990$	0	0
$991$	−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
$993$	0	0
$994$	−1.01889e7	−0.327084
$995$	1.62146e7	0.519217
$996$	0	0
$997$	−2.00678e7	−0.639385	−0.319692	−	0.947521i	$-0.603580\pi$
$997$	−2.00678e7	−0.639385	−0.319692	+	0.947521i	$0.603580\pi$
$998$	384412.	0.0122172
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.6.a.e.1.1		1
3.2	odd	2		70.6.a.f.1.1	✓	1
12.11	even	2		560.6.a.f.1.1		1
15.2	even	4		350.6.c.b.99.2		2
15.8	even	4		350.6.c.b.99.1		2
15.14	odd	2		350.6.a.d.1.1		1
21.20	even	2		490.6.a.l.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.f.1.1	✓	1	3.2	odd	2
350.6.a.d.1.1		1	15.14	odd	2
350.6.c.b.99.1		2	15.8	even	4
350.6.c.b.99.2		2	15.2	even	4
490.6.a.l.1.1		1	21.20	even	2
560.6.a.f.1.1		1	12.11	even	2
630.6.a.e.1.1		1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	630.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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