LMFDB - Embedded newform 490.6.a.m.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:	$1$
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	$\chi$	$=$	490.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q+4.00000 q^{2} +17.0000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +68.0000 q^{6} +64.0000 q^{8} +46.0000 q^{9} -100.000 q^{10} -715.000 q^{11} +272.000 q^{12} -331.000 q^{13} -425.000 q^{15} +256.000 q^{16} +1699.00 q^{17} +184.000 q^{18} +1718.00 q^{19} -400.000 q^{20} -2860.00 q^{22} -3950.00 q^{23} +1088.00 q^{24} +625.000 q^{25} -1324.00 q^{26} -3349.00 q^{27} +4579.00 q^{29} -1700.00 q^{30} -6756.00 q^{31} +1024.00 q^{32} -12155.0 q^{33} +6796.00 q^{34} +736.000 q^{36} -16518.0 q^{37} +6872.00 q^{38} -5627.00 q^{39} -1600.00 q^{40} -18876.0 q^{41} +2258.00 q^{43} -11440.0 q^{44} -1150.00 q^{45} -15800.0 q^{46} +537.000 q^{47} +4352.00 q^{48} +2500.00 q^{50} +28883.0 q^{51} -5296.00 q^{52} -10984.0 q^{53} -13396.0 q^{54} +17875.0 q^{55} +29206.0 q^{57} +18316.0 q^{58} +25956.0 q^{59} -6800.00 q^{60} -39188.0 q^{61} -27024.0 q^{62} +4096.00 q^{64} +8275.00 q^{65} -48620.0 q^{66} +4416.00 q^{67} +27184.0 q^{68} -67150.0 q^{69} -31880.0 q^{71} +2944.00 q^{72} +5018.00 q^{73} -66072.0 q^{74} +10625.0 q^{75} +27488.0 q^{76} -22508.0 q^{78} -27977.0 q^{79} -6400.00 q^{80} -68111.0 q^{81} -75504.0 q^{82} -37644.0 q^{83} -42475.0 q^{85} +9032.00 q^{86} +77843.0 q^{87} -45760.0 q^{88} +17216.0 q^{89} -4600.00 q^{90} -63200.0 q^{92} -114852. q^{93} +2148.00 q^{94} -42950.0 q^{95} +17408.0 q^{96} +63175.0 q^{97} -32890.0 q^{99} +O(q^{100})\)

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
$3$	17.0000	1.09055	0.545275	−	0.838257i	$-0.316425\pi$
$3$	17.0000	1.09055	0.545275	+	0.838257i	$0.316425\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	68.0000	0.771136
$7$	0	0
$7$	0	0
$8$	64.0000	0.353553
$9$	46.0000	0.189300
$10$	−100.000	−0.316228
$11$	−715.000	−1.78166	−0.890829	−	0.454339i	$-0.849876\pi$
$11$	−715.000	−1.78166	−0.890829	+	0.454339i	$0.849876\pi$
$12$	272.000	0.545275
$13$	−331.000	−0.543212	−0.271606	−	0.962408i	$-0.587555\pi$
$13$	−331.000	−0.543212	−0.271606	+	0.962408i	$0.587555\pi$
$14$	0	0
$15$	−425.000	−0.487709
$16$	256.000	0.250000
$17$	1699.00	1.42584	0.712920	−	0.701245i	$-0.247372\pi$
$17$	1699.00	1.42584	0.712920	+	0.701245i	$0.247372\pi$
$18$	184.000	0.133856
$19$	1718.00	1.09179	0.545895	−	0.837854i	$-0.316190\pi$
$19$	1718.00	1.09179	0.545895	+	0.837854i	$0.316190\pi$
$20$	−400.000	−0.223607
$21$	0	0
$22$	−2860.00	−1.25982
$23$	−3950.00	−1.55696	−0.778480	−	0.627669i	$-0.784009\pi$
$23$	−3950.00	−1.55696	−0.778480	+	0.627669i	$0.784009\pi$
$24$	1088.00	0.385568
$25$	625.000	0.200000
$26$	−1324.00	−0.384109
$27$	−3349.00	−0.884109
$28$	0	0
$29$	4579.00	1.01106	0.505529	−	0.862810i	$-0.331298\pi$
$29$	4579.00	1.01106	0.505529	+	0.862810i	$0.331298\pi$
$30$	−1700.00	−0.344862
$31$	−6756.00	−1.26266	−0.631329	−	0.775516i	$-0.717490\pi$
$31$	−6756.00	−1.26266	−0.631329	+	0.775516i	$0.717490\pi$
$32$	1024.00	0.176777
$33$	−12155.0	−1.94299
$34$	6796.00	1.00822
$35$	0	0
$36$	736.000	0.0946502
$37$	−16518.0	−1.98360	−0.991798	−	0.127816i	$-0.959203\pi$
$37$	−16518.0	−1.98360	−0.991798	+	0.127816i	$0.959203\pi$
$38$	6872.00	0.772012
$39$	−5627.00	−0.592400
$40$	−1600.00	−0.158114
$41$	−18876.0	−1.75368	−0.876840	−	0.480782i	$-0.840353\pi$
$41$	−18876.0	−1.75368	−0.876840	+	0.480782i	$0.840353\pi$
$42$	0	0
$43$	2258.00	0.186231	0.0931157	−	0.995655i	$-0.470317\pi$
$43$	2258.00	0.186231	0.0931157	+	0.995655i	$0.470317\pi$
$44$	−11440.0	−0.890829
$45$	−1150.00	−0.0846577
$46$	−15800.0	−1.10094
$47$	537.000	0.0354593	0.0177296	−	0.999843i	$-0.494356\pi$
$47$	537.000	0.0354593	0.0177296	+	0.999843i	$0.494356\pi$
$48$	4352.00	0.272638
$49$	0	0
$50$	2500.00	0.141421
$51$	28883.0	1.55495
$52$	−5296.00	−0.271606
$53$	−10984.0	−0.537119	−0.268560	−	0.963263i	$-0.586548\pi$
$53$	−10984.0	−0.537119	−0.268560	+	0.963263i	$0.586548\pi$
$54$	−13396.0	−0.625159
$55$	17875.0	0.796782
$56$	0	0
$57$	29206.0	1.19065
$58$	18316.0	0.714925
$59$	25956.0	0.970751	0.485375	−	0.874306i	$-0.338683\pi$
$59$	25956.0	0.970751	0.485375	+	0.874306i	$0.338683\pi$
$60$	−6800.00	−0.243855
$61$	−39188.0	−1.34843	−0.674215	−	0.738535i	$-0.735518\pi$
$61$	−39188.0	−1.34843	−0.674215	+	0.738535i	$0.735518\pi$
$62$	−27024.0	−0.892833
$63$	0	0
$64$	4096.00	0.125000
$65$	8275.00	0.242932
$66$	−48620.0	−1.37390
$67$	4416.00	0.120183	0.0600914	−	0.998193i	$-0.480861\pi$
$67$	4416.00	0.120183	0.0600914	+	0.998193i	$0.480861\pi$
$68$	27184.0	0.712920
$69$	−67150.0	−1.69794
$70$	0	0
$71$	−31880.0	−0.750538	−0.375269	−	0.926916i	$-0.622450\pi$
$71$	−31880.0	−0.750538	−0.375269	+	0.926916i	$0.622450\pi$
$72$	2944.00	0.0669278
$73$	5018.00	0.110211	0.0551053	−	0.998481i	$-0.482451\pi$
$73$	5018.00	0.110211	0.0551053	+	0.998481i	$0.482451\pi$
$74$	−66072.0	−1.40261
$75$	10625.0	0.218110
$76$	27488.0	0.545895
$77$	0	0
$78$	−22508.0	−0.418890
$79$	−27977.0	−0.504352	−0.252176	−	0.967681i	$-0.581146\pi$
$79$	−27977.0	−0.504352	−0.252176	+	0.967681i	$0.581146\pi$
$80$	−6400.00	−0.111803
$81$	−68111.0	−1.15347
$82$	−75504.0	−1.24004
$83$	−37644.0	−0.599792	−0.299896	−	0.953972i	$-0.596952\pi$
$83$	−37644.0	−0.599792	−0.299896	+	0.953972i	$0.596952\pi$
$84$	0	0
$85$	−42475.0	−0.637655
$86$	9032.00	0.131685
$87$	77843.0	1.10261
$88$	−45760.0	−0.629911
$89$	17216.0	0.230387	0.115193	−	0.993343i	$-0.463251\pi$
$89$	17216.0	0.230387	0.115193	+	0.993343i	$0.463251\pi$
$90$	−4600.00	−0.0598620
$91$	0	0
$92$	−63200.0	−0.778480
$93$	−114852.	−1.37699
$94$	2148.00	0.0250735
$95$	−42950.0	−0.488263
$96$	17408.0	0.192784
$97$	63175.0	0.681736	0.340868	−	0.940111i	$-0.389279\pi$
$97$	63175.0	0.681736	0.340868	+	0.940111i	$0.389279\pi$
$98$	0	0
$99$	−32890.0	−0.337269
$100$	10000.0	0.100000
$101$	29250.0	0.285314	0.142657	−	0.989772i	$-0.454435\pi$
$101$	29250.0	0.285314	0.142657	+	0.989772i	$0.454435\pi$
$102$	115532.	1.09952
$103$	149189.	1.38562	0.692809	−	0.721121i	$-0.256373\pi$
$103$	149189.	1.38562	0.692809	+	0.721121i	$0.256373\pi$
$104$	−21184.0	−0.192055
$105$	0	0
$106$	−43936.0	−0.379801
$107$	83742.0	0.707105	0.353552	−	0.935415i	$-0.384974\pi$
$107$	83742.0	0.707105	0.353552	+	0.935415i	$0.384974\pi$
$108$	−53584.0	−0.442054
$109$	105377.	0.849532	0.424766	−	0.905303i	$-0.360356\pi$
$109$	105377.	0.849532	0.424766	+	0.905303i	$0.360356\pi$
$110$	71500.0	0.563410
$111$	−280806.	−2.16321
$112$	0	0
$113$	−122754.	−0.904356	−0.452178	−	0.891928i	$-0.649353\pi$
$113$	−122754.	−0.904356	−0.452178	+	0.891928i	$0.649353\pi$
$114$	116824.	0.841918
$115$	98750.0	0.696294
$116$	73264.0	0.505529
$117$	−15226.0	−0.102830
$118$	103824.	0.686424
$119$	0	0
$120$	−27200.0	−0.172431
$121$	350174.	2.17431
$122$	−156752.	−0.953484
$123$	−320892.	−1.91248
$124$	−108096.	−0.631329
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	−219196.	−1.20593	−0.602967	−	0.797766i	$-0.706015\pi$
$127$	−219196.	−1.20593	−0.602967	+	0.797766i	$0.706015\pi$
$128$	16384.0	0.0883883
$129$	38386.0	0.203095
$130$	33100.0	0.171779
$131$	96682.0	0.492229	0.246115	−	0.969241i	$-0.420846\pi$
$131$	96682.0	0.492229	0.246115	+	0.969241i	$0.420846\pi$
$132$	−194480.	−0.971494
$133$	0	0
$134$	17664.0	0.0849820
$135$	83725.0	0.395385
$136$	108736.	0.504111
$137$	187288.	0.852528	0.426264	−	0.904599i	$-0.359830\pi$
$137$	187288.	0.852528	0.426264	+	0.904599i	$0.359830\pi$
$138$	−268600.	−1.20063
$139$	−176894.	−0.776562	−0.388281	−	0.921541i	$-0.626931\pi$
$139$	−176894.	−0.776562	−0.388281	+	0.921541i	$0.626931\pi$
$140$	0	0
$141$	9129.00	0.0386701
$142$	−127520.	−0.530710
$143$	236665.	0.967819
$144$	11776.0	0.0473251
$145$	−114475.	−0.452158
$146$	20072.0	0.0779307
$147$	0	0
$148$	−264288.	−0.991798
$149$	−199078.	−0.734611	−0.367306	−	0.930100i	$-0.619720\pi$
$149$	−199078.	−0.734611	−0.367306	+	0.930100i	$0.619720\pi$
$150$	42500.0	0.154227
$151$	471583.	1.68312	0.841561	−	0.540162i	$-0.181637\pi$
$151$	471583.	1.68312	0.841561	+	0.540162i	$0.181637\pi$
$152$	109952.	0.386006
$153$	78154.0	0.269912
$154$	0	0
$155$	168900.	0.564677
$156$	−90032.0	−0.296200
$157$	72054.0	0.233297	0.116648	−	0.993173i	$-0.462785\pi$
$157$	72054.0	0.233297	0.116648	+	0.993173i	$0.462785\pi$
$158$	−111908.	−0.356630
$159$	−186728.	−0.585756
$160$	−25600.0	−0.0790569
$161$	0	0
$162$	−272444.	−0.815623
$163$	385334.	1.13597	0.567987	−	0.823038i	$-0.307722\pi$
$163$	385334.	1.13597	0.567987	+	0.823038i	$0.307722\pi$
$164$	−302016.	−0.876840
$165$	303875.	0.868931
$166$	−150576.	−0.424117
$167$	542957.	1.50652	0.753259	−	0.657724i	$-0.228481\pi$
$167$	542957.	1.50652	0.753259	+	0.657724i	$0.228481\pi$
$168$	0	0
$169$	−261732.	−0.704920
$170$	−169900.	−0.450890
$171$	79028.0	0.206676
$172$	36128.0	0.0931157
$173$	−370953.	−0.942331	−0.471166	−	0.882045i	$-0.656167\pi$
$173$	−370953.	−0.942331	−0.471166	+	0.882045i	$0.656167\pi$
$174$	311372.	0.779662
$175$	0	0
$176$	−183040.	−0.445414
$177$	441252.	1.05865
$178$	68864.0	0.162908
$179$	−754172.	−1.75929	−0.879646	−	0.475629i	$-0.842220\pi$
$179$	−754172.	−1.75929	−0.879646	+	0.475629i	$0.842220\pi$
$180$	−18400.0	−0.0423289
$181$	−303840.	−0.689364	−0.344682	−	0.938720i	$-0.612013\pi$
$181$	−303840.	−0.689364	−0.344682	+	0.938720i	$0.612013\pi$
$182$	0	0
$183$	−666196.	−1.47053
$184$	−252800.	−0.550469
$185$	412950.	0.887091
$186$	−459408.	−0.973680
$187$	−1.21478e6	−2.54036
$188$	8592.00	0.0177296
$189$	0	0
$190$	−171800.	−0.345254
$191$	−186271.	−0.369455	−0.184728	−	0.982790i	$-0.559140\pi$
$191$	−186271.	−0.369455	−0.184728	+	0.982790i	$0.559140\pi$
$192$	69632.0	0.136319
$193$	92504.0	0.178759	0.0893794	−	0.995998i	$-0.471512\pi$
$193$	92504.0	0.178759	0.0893794	+	0.995998i	$0.471512\pi$
$194$	252700.	0.482060
$195$	140675.	0.264930
$196$	0	0
$197$	−736368.	−1.35185	−0.675926	−	0.736969i	$-0.736256\pi$
$197$	−736368.	−1.35185	−0.675926	+	0.736969i	$0.736256\pi$
$198$	−131560.	−0.238485
$199$	481620.	0.862128	0.431064	−	0.902321i	$-0.358138\pi$
$199$	481620.	0.862128	0.431064	+	0.902321i	$0.358138\pi$
$200$	40000.0	0.0707107
$201$	75072.0	0.131065
$202$	117000.	0.201747
$203$	0	0
$204$	462128.	0.777476
$205$	471900.	0.784269
$206$	596756.	0.979780
$207$	−181700.	−0.294733
$208$	−84736.0	−0.135803
$209$	−1.22837e6	−1.94520
$210$	0	0
$211$	189531.	0.293072	0.146536	−	0.989205i	$-0.453188\pi$
$211$	189531.	0.293072	0.146536	+	0.989205i	$0.453188\pi$
$212$	−175744.	−0.268560
$213$	−541960.	−0.818499
$214$	334968.	0.499999
$215$	−56450.0	−0.0832852
$216$	−214336.	−0.312580
$217$	0	0
$218$	421508.	0.600710
$219$	85306.0	0.120190
$220$	286000.	0.398391
$221$	−562369.	−0.774534
$222$	−1.12322e6	−1.52962
$223$	22597.0	0.0304291	0.0152145	−	0.999884i	$-0.495157\pi$
$223$	22597.0	0.0304291	0.0152145	+	0.999884i	$0.495157\pi$
$224$	0	0
$225$	28750.0	0.0378601
$226$	−491016.	−0.639476
$227$	998117.	1.28563	0.642816	−	0.766020i	$-0.277766\pi$
$227$	998117.	1.28563	0.642816	+	0.766020i	$0.277766\pi$
$228$	467296.	0.595326
$229$	854644.	1.07695	0.538476	−	0.842641i	$-0.319000\pi$
$229$	854644.	1.07695	0.538476	+	0.842641i	$0.319000\pi$
$230$	395000.	0.492354
$231$	0	0
$232$	293056.	0.357463
$233$	1.25818e6	1.51829	0.759144	−	0.650922i	$-0.225618\pi$
$233$	1.25818e6	1.51829	0.759144	+	0.650922i	$0.225618\pi$
$234$	−60904.0	−0.0727120
$235$	−13425.0	−0.0158579
$236$	415296.	0.485375
$237$	−475609.	−0.550021
$238$	0	0
$239$	−706581.	−0.800142	−0.400071	−	0.916484i	$-0.631015\pi$
$239$	−706581.	−0.800142	−0.400071	+	0.916484i	$0.631015\pi$
$240$	−108800.	−0.121927
$241$	−616330.	−0.683551	−0.341775	−	0.939782i	$-0.611028\pi$
$241$	−616330.	−0.683551	−0.341775	+	0.939782i	$0.611028\pi$
$242$	1.40070e6	1.53747
$243$	−344080.	−0.373804
$244$	−627008.	−0.674215
$245$	0	0
$246$	−1.28357e6	−1.35233
$247$	−568658.	−0.593074
$248$	−432384.	−0.446417
$249$	−639948.	−0.654103
$250$	−62500.0	−0.0632456
$251$	−190842.	−0.191201	−0.0956004	−	0.995420i	$-0.530477\pi$
$251$	−190842.	−0.191201	−0.0956004	+	0.995420i	$0.530477\pi$
$252$	0	0
$253$	2.82425e6	2.77397
$254$	−876784.	−0.852724
$255$	−722075.	−0.695395
$256$	65536.0	0.0625000
$257$	1.13094e6	1.06809	0.534045	−	0.845456i	$-0.320671\pi$
$257$	1.13094e6	1.06809	0.534045	+	0.845456i	$0.320671\pi$
$258$	153544.	0.143610
$259$	0	0
$260$	132400.	0.121466
$261$	210634.	0.191394
$262$	386728.	0.348059
$263$	−1.67377e6	−1.49213	−0.746065	−	0.665874i	$-0.768059\pi$
$263$	−1.67377e6	−1.49213	−0.746065	+	0.665874i	$0.768059\pi$
$264$	−777920.	−0.686950
$265$	274600.	0.240207
$266$	0	0
$267$	292672.	0.251248
$268$	70656.0	0.0600914
$269$	630942.	0.531629	0.265815	−	0.964024i	$-0.414359\pi$
$269$	630942.	0.531629	0.265815	+	0.964024i	$0.414359\pi$
$270$	334900.	0.279580
$271$	372476.	0.308088	0.154044	−	0.988064i	$-0.450770\pi$
$271$	372476.	0.308088	0.154044	+	0.988064i	$0.450770\pi$
$272$	434944.	0.356460
$273$	0	0
$274$	749152.	0.602828
$275$	−446875.	−0.356332
$276$	−1.07440e6	−0.848972
$277$	867010.	0.678930	0.339465	−	0.940619i	$-0.389754\pi$
$277$	867010.	0.678930	0.339465	+	0.940619i	$0.389754\pi$
$278$	−707576.	−0.549112
$279$	−310776.	−0.239021
$280$	0	0
$281$	−1.94498e6	−1.46943	−0.734716	−	0.678375i	$-0.762685\pi$
$281$	−1.94498e6	−1.46943	−0.734716	+	0.678375i	$0.762685\pi$
$282$	36516.0	0.0273439
$283$	−1.18501e6	−0.879543	−0.439771	−	0.898110i	$-0.644941\pi$
$283$	−1.18501e6	−0.879543	−0.439771	+	0.898110i	$0.644941\pi$
$284$	−510080.	−0.375269
$285$	−730150.	−0.532476
$286$	946660.	0.684351
$287$	0	0
$288$	47104.0	0.0334639
$289$	1.46674e6	1.03302
$290$	−457900.	−0.319724
$291$	1.07398e6	0.743467
$292$	80288.0	0.0551053
$293$	−33669.0	−0.0229119	−0.0114560	−	0.999934i	$-0.503647\pi$
$293$	−33669.0	−0.0229119	−0.0114560	+	0.999934i	$0.503647\pi$
$294$	0	0
$295$	−648900.	−0.434133
$296$	−1.05715e6	−0.701307
$297$	2.39454e6	1.57518
$298$	−796312.	−0.519449
$299$	1.30745e6	0.845760
$300$	170000.	0.109055
$301$	0	0
$302$	1.88633e6	1.19015
$303$	497250.	0.311149
$304$	439808.	0.272948
$305$	979700.	0.603036
$306$	312616.	0.190857
$307$	27043.0	0.0163760	0.00818802	−	0.999966i	$-0.497394\pi$
$307$	27043.0	0.0163760	0.00818802	+	0.999966i	$0.497394\pi$
$308$	0	0
$309$	2.53621e6	1.51109
$310$	675600.	0.399287
$311$	−2.14919e6	−1.26001	−0.630004	−	0.776592i	$-0.716947\pi$
$311$	−2.14919e6	−1.26001	−0.630004	+	0.776592i	$0.716947\pi$
$312$	−360128.	−0.209445
$313$	2.67052e6	1.54076	0.770381	−	0.637583i	$-0.220066\pi$
$313$	2.67052e6	1.54076	0.770381	+	0.637583i	$0.220066\pi$
$314$	288216.	0.164966
$315$	0	0
$316$	−447632.	−0.252176
$317$	−250514.	−0.140018	−0.0700090	−	0.997546i	$-0.522303\pi$
$317$	−250514.	−0.140018	−0.0700090	+	0.997546i	$0.522303\pi$
$318$	−746912.	−0.414192
$319$	−3.27398e6	−1.80136
$320$	−102400.	−0.0559017
$321$	1.42361e6	0.771134
$322$	0	0
$323$	2.91888e6	1.55672
$324$	−1.08978e6	−0.576733
$325$	−206875.	−0.108642
$326$	1.54134e6	0.803255
$327$	1.79141e6	0.926457
$328$	−1.20806e6	−0.620019
$329$	0	0
$330$	1.21550e6	0.614427
$331$	1.05899e6	0.531277	0.265639	−	0.964073i	$-0.414417\pi$
$331$	1.05899e6	0.531277	0.265639	+	0.964073i	$0.414417\pi$
$332$	−602304.	−0.299896
$333$	−759828.	−0.375495
$334$	2.17183e6	1.06527
$335$	−110400.	−0.0537473
$336$	0	0
$337$	−2.85025e6	−1.36712	−0.683562	−	0.729893i	$-0.739570\pi$
$337$	−2.85025e6	−1.36712	−0.683562	+	0.729893i	$0.739570\pi$
$338$	−1.04693e6	−0.498454
$339$	−2.08682e6	−0.986246
$340$	−679600.	−0.318828
$341$	4.83054e6	2.24962
$342$	316112.	0.146142
$343$	0	0
$344$	144512.	0.0658427
$345$	1.67875e6	0.759344
$346$	−1.48381e6	−0.666329
$347$	1.89141e6	0.843259	0.421630	−	0.906768i	$-0.361458\pi$
$347$	1.89141e6	0.843259	0.421630	+	0.906768i	$0.361458\pi$
$348$	1.24549e6	0.551304
$349$	1.04232e6	0.458075	0.229038	−	0.973418i	$-0.426442\pi$
$349$	1.04232e6	0.458075	0.229038	+	0.973418i	$0.426442\pi$
$350$	0	0
$351$	1.10852e6	0.480259
$352$	−732160.	−0.314956
$353$	2.30309e6	0.983725	0.491862	−	0.870673i	$-0.336316\pi$
$353$	2.30309e6	0.983725	0.491862	+	0.870673i	$0.336316\pi$
$354$	1.76501e6	0.748581
$355$	797000.	0.335651
$356$	275456.	0.115193
$357$	0	0
$358$	−3.01669e6	−1.24401
$359$	−1.67594e6	−0.686315	−0.343157	−	0.939278i	$-0.611496\pi$
$359$	−1.67594e6	−0.686315	−0.343157	+	0.939278i	$0.611496\pi$
$360$	−73600.0	−0.0299310
$361$	475425.	0.192006
$362$	−1.21536e6	−0.487454
$363$	5.95296e6	2.37119
$364$	0	0
$365$	−125450.	−0.0492877
$366$	−2.66478e6	−1.03982
$367$	−94663.0	−0.0366872	−0.0183436	−	0.999832i	$-0.505839\pi$
$367$	−94663.0	−0.0366872	−0.0183436	+	0.999832i	$0.505839\pi$
$368$	−1.01120e6	−0.389240
$369$	−868296.	−0.331972
$370$	1.65180e6	0.627268
$371$	0	0
$372$	−1.83763e6	−0.688496
$373$	−953536.	−0.354867	−0.177433	−	0.984133i	$-0.556779\pi$
$373$	−953536.	−0.354867	−0.177433	+	0.984133i	$0.556779\pi$
$374$	−4.85914e6	−1.79631
$375$	−265625.	−0.0975418
$376$	34368.0	0.0125367
$377$	−1.51565e6	−0.549219
$378$	0	0
$379$	3.88824e6	1.39045	0.695225	−	0.718792i	$-0.255305\pi$
$379$	3.88824e6	1.39045	0.695225	+	0.718792i	$0.255305\pi$
$380$	−687200.	−0.244132
$381$	−3.72633e6	−1.31513
$382$	−745084.	−0.261244
$383$	−2.93636e6	−1.02285	−0.511425	−	0.859328i	$-0.670882\pi$
$383$	−2.93636e6	−1.02285	−0.511425	+	0.859328i	$0.670882\pi$
$384$	278528.	0.0963920
$385$	0	0
$386$	370016.	0.126402
$387$	103868.	0.0352537
$388$	1.01080e6	0.340868
$389$	1.70377e6	0.570871	0.285435	−	0.958398i	$-0.407862\pi$
$389$	1.70377e6	0.570871	0.285435	+	0.958398i	$0.407862\pi$
$390$	562700.	0.187333
$391$	−6.71105e6	−2.21998
$392$	0	0
$393$	1.64359e6	0.536801
$394$	−2.94547e6	−0.955904
$395$	699425.	0.225553
$396$	−526240.	−0.168634
$397$	−1.19110e6	−0.379292	−0.189646	−	0.981853i	$-0.560734\pi$
$397$	−1.19110e6	−0.379292	−0.189646	+	0.981853i	$0.560734\pi$
$398$	1.92648e6	0.609617
$399$	0	0
$400$	160000.	0.0500000
$401$	−3.38330e6	−1.05070	−0.525351	−	0.850885i	$-0.676066\pi$
$401$	−3.38330e6	−1.05070	−0.525351	+	0.850885i	$0.676066\pi$
$402$	300288.	0.0926772
$403$	2.23624e6	0.685891
$404$	468000.	0.142657
$405$	1.70278e6	0.515846
$406$	0	0
$407$	1.18104e7	3.53409
$408$	1.84851e6	0.549758
$409$	1.33185e6	0.393682	0.196841	−	0.980435i	$-0.436932\pi$
$409$	1.33185e6	0.393682	0.196841	+	0.980435i	$0.436932\pi$
$410$	1.88760e6	0.554562
$411$	3.18390e6	0.929725
$412$	2.38702e6	0.692809
$413$	0	0
$414$	−726800.	−0.208408
$415$	941100.	0.268235
$416$	−338944.	−0.0960273
$417$	−3.00720e6	−0.846880
$418$	−4.91348e6	−1.37546
$419$	−5.82786e6	−1.62171	−0.810856	−	0.585246i	$-0.800998\pi$
$419$	−5.82786e6	−1.62171	−0.810856	+	0.585246i	$0.800998\pi$
$420$	0	0
$421$	2.47430e6	0.680374	0.340187	−	0.940358i	$-0.389510\pi$
$421$	2.47430e6	0.680374	0.340187	+	0.940358i	$0.389510\pi$
$422$	758124.	0.207233
$423$	24702.0	0.00671245
$424$	−702976.	−0.189900
$425$	1.06188e6	0.285168
$426$	−2.16784e6	−0.578766
$427$	0	0
$428$	1.33987e6	0.353552
$429$	4.02331e6	1.05546
$430$	−225800.	−0.0588915
$431$	4.61851e6	1.19759	0.598796	−	0.800902i	$-0.295646\pi$
$431$	4.61851e6	1.19759	0.598796	+	0.800902i	$0.295646\pi$
$432$	−857344.	−0.221027
$433$	−58606.0	−0.0150218	−0.00751091	−	0.999972i	$-0.502391\pi$
$433$	−58606.0	−0.0150218	−0.00751091	+	0.999972i	$0.502391\pi$
$434$	0	0
$435$	−1.94608e6	−0.493102
$436$	1.68603e6	0.424766
$437$	−6.78610e6	−1.69987
$438$	341224.	0.0849874
$439$	−7.04298e6	−1.74419	−0.872097	−	0.489332i	$-0.837241\pi$
$439$	−7.04298e6	−1.74419	−0.872097	+	0.489332i	$0.837241\pi$
$440$	1.14400e6	0.281705
$441$	0	0
$442$	−2.24948e6	−0.547678
$443$	1.46894e6	0.355627	0.177813	−	0.984064i	$-0.443098\pi$
$443$	1.46894e6	0.355627	0.177813	+	0.984064i	$0.443098\pi$
$444$	−4.49290e6	−1.08161
$445$	−430400.	−0.103032
$446$	90388.0	0.0215166
$447$	−3.38433e6	−0.801131
$448$	0	0
$449$	−7.48414e6	−1.75197	−0.875983	−	0.482341i	$-0.839787\pi$
$449$	−7.48414e6	−1.75197	−0.875983	+	0.482341i	$0.839787\pi$
$450$	115000.	0.0267711
$451$	1.34963e7	3.12446
$452$	−1.96406e6	−0.452178
$453$	8.01691e6	1.83553
$454$	3.99247e6	0.909079
$455$	0	0
$456$	1.86918e6	0.420959
$457$	170320.	0.0381483	0.0190741	−	0.999818i	$-0.493928\pi$
$457$	170320.	0.0381483	0.0190741	+	0.999818i	$0.493928\pi$
$458$	3.41858e6	0.761520
$459$	−5.68995e6	−1.26060
$460$	1.58000e6	0.348147
$461$	4.28685e6	0.939476	0.469738	−	0.882806i	$-0.344348\pi$
$461$	4.28685e6	0.939476	0.469738	+	0.882806i	$0.344348\pi$
$462$	0	0
$463$	3.38317e6	0.733452	0.366726	−	0.930329i	$-0.380479\pi$
$463$	3.38317e6	0.733452	0.366726	+	0.930329i	$0.380479\pi$
$464$	1.17222e6	0.252764
$465$	2.87130e6	0.615809
$466$	5.03274e6	1.07359
$467$	−5.18029e6	−1.09916	−0.549581	−	0.835440i	$-0.685213\pi$
$467$	−5.18029e6	−1.09916	−0.549581	+	0.835440i	$0.685213\pi$
$468$	−243616.	−0.0514152
$469$	0	0
$470$	−53700.0	−0.0112132
$471$	1.22492e6	0.254422
$472$	1.66118e6	0.343212
$473$	−1.61447e6	−0.331801
$474$	−1.90244e6	−0.388924
$475$	1.07375e6	0.218358
$476$	0	0
$477$	−505264.	−0.101677
$478$	−2.82632e6	−0.565786
$479$	8.76779e6	1.74603	0.873014	−	0.487695i	$-0.162162\pi$
$479$	8.76779e6	1.74603	0.873014	+	0.487695i	$0.162162\pi$
$480$	−435200.	−0.0862156
$481$	5.46746e6	1.07751
$482$	−2.46532e6	−0.483343
$483$	0	0
$484$	5.60278e6	1.08715
$485$	−1.57938e6	−0.304881
$486$	−1.37632e6	−0.264319
$487$	270154.	0.0516166	0.0258083	−	0.999667i	$-0.491784\pi$
$487$	270154.	0.0516166	0.0258083	+	0.999667i	$0.491784\pi$
$488$	−2.50803e6	−0.476742
$489$	6.55068e6	1.23884
$490$	0	0
$491$	4.85550e6	0.908930	0.454465	−	0.890765i	$-0.349830\pi$
$491$	4.85550e6	0.908930	0.454465	+	0.890765i	$0.349830\pi$
$492$	−5.13427e6	−0.956238
$493$	7.77972e6	1.44161
$494$	−2.27463e6	−0.419367
$495$	822250.	0.150831
$496$	−1.72954e6	−0.315664
$497$	0	0
$498$	−2.55979e6	−0.462521
$499$	−2.98576e6	−0.536789	−0.268394	−	0.963309i	$-0.586493\pi$
$499$	−2.98576e6	−0.536789	−0.268394	+	0.963309i	$0.586493\pi$
$500$	−250000.	−0.0447214
$501$	9.23027e6	1.64293
$502$	−763368.	−0.135199
$503$	8.28783e6	1.46057	0.730283	−	0.683145i	$-0.239388\pi$
$503$	8.28783e6	1.46057	0.730283	+	0.683145i	$0.239388\pi$
$504$	0	0
$505$	−731250.	−0.127596
$506$	1.12970e7	1.96149
$507$	−4.44944e6	−0.768751
$508$	−3.50714e6	−0.602967
$509$	−6.24307e6	−1.06808	−0.534040	−	0.845459i	$-0.679327\pi$
$509$	−6.24307e6	−1.06808	−0.534040	+	0.845459i	$0.679327\pi$
$510$	−2.88830e6	−0.491719
$511$	0	0
$512$	262144.	0.0441942
$513$	−5.75358e6	−0.965261
$514$	4.52377e6	0.755253
$515$	−3.72972e6	−0.619668
$516$	614176.	0.101547
$517$	−383955.	−0.0631763
$518$	0	0
$519$	−6.30620e6	−1.02766
$520$	529600.	0.0858894
$521$	−7.49509e6	−1.20971	−0.604856	−	0.796335i	$-0.706770\pi$
$521$	−7.49509e6	−1.20971	−0.604856	+	0.796335i	$0.706770\pi$
$522$	842536.	0.135336
$523$	−3.80957e6	−0.609007	−0.304503	−	0.952511i	$-0.598490\pi$
$523$	−3.80957e6	−0.609007	−0.304503	+	0.952511i	$0.598490\pi$
$524$	1.54691e6	0.246115
$525$	0	0
$526$	−6.69508e6	−1.05509
$527$	−1.14784e7	−1.80035
$528$	−3.11168e6	−0.485747
$529$	9.16616e6	1.42413
$530$	1.09840e6	0.169852
$531$	1.19398e6	0.183764
$532$	0	0
$533$	6.24796e6	0.952621
$534$	1.17069e6	0.177659
$535$	−2.09355e6	−0.316227
$536$	282624.	0.0424910
$537$	−1.28209e7	−1.91860
$538$	2.52377e6	0.375919
$539$	0	0
$540$	1.33960e6	0.197693
$541$	7.67156e6	1.12691	0.563457	−	0.826145i	$-0.309471\pi$
$541$	7.67156e6	1.12691	0.563457	+	0.826145i	$0.309471\pi$
$542$	1.48990e6	0.217851
$543$	−5.16528e6	−0.751786
$544$	1.73978e6	0.252055
$545$	−2.63442e6	−0.379922
$546$	0	0
$547$	−9.53845e6	−1.36304	−0.681522	−	0.731798i	$-0.738681\pi$
$547$	−9.53845e6	−1.36304	−0.681522	+	0.731798i	$0.738681\pi$
$548$	2.99661e6	0.426264
$549$	−1.80265e6	−0.255258
$550$	−1.78750e6	−0.251964
$551$	7.86672e6	1.10386
$552$	−4.29760e6	−0.600314
$553$	0	0
$554$	3.46804e6	0.480076
$555$	7.02015e6	0.967417
$556$	−2.83030e6	−0.388281
$557$	−7.45022e6	−1.01749	−0.508746	−	0.860916i	$-0.669891\pi$
$557$	−7.45022e6	−1.01749	−0.508746	+	0.860916i	$0.669891\pi$
$558$	−1.24310e6	−0.169014
$559$	−747398.	−0.101163
$560$	0	0
$561$	−2.06513e7	−2.77039
$562$	−7.77992e6	−1.03905
$563$	−3.36698e6	−0.447682	−0.223841	−	0.974626i	$-0.571860\pi$
$563$	−3.36698e6	−0.447682	−0.223841	+	0.974626i	$0.571860\pi$
$564$	146064.	0.0193351
$565$	3.06885e6	0.404440
$566$	−4.74005e6	−0.621931
$567$	0	0
$568$	−2.04032e6	−0.265355
$569$	−4.05501e6	−0.525063	−0.262532	−	0.964923i	$-0.584557\pi$
$569$	−4.05501e6	−0.525063	−0.262532	+	0.964923i	$0.584557\pi$
$570$	−2.92060e6	−0.376517
$571$	7.31585e6	0.939020	0.469510	−	0.882927i	$-0.344431\pi$
$571$	7.31585e6	0.939020	0.469510	+	0.882927i	$0.344431\pi$
$572$	3.78664e6	0.483909
$573$	−3.16661e6	−0.402910
$574$	0	0
$575$	−2.46875e6	−0.311392
$576$	188416.	0.0236626
$577$	9.76895e6	1.22154	0.610771	−	0.791807i	$-0.290860\pi$
$577$	9.76895e6	1.22154	0.610771	+	0.791807i	$0.290860\pi$
$578$	5.86698e6	0.730457
$579$	1.57257e6	0.194945
$580$	−1.83160e6	−0.226079
$581$	0	0
$582$	4.29590e6	0.525711
$583$	7.85356e6	0.956963
$584$	321152.	0.0389653
$585$	380650.	0.0459871
$586$	−134676.	−0.0162012
$587$	−3.75689e6	−0.450021	−0.225011	−	0.974356i	$-0.572242\pi$
$587$	−3.75689e6	−0.450021	−0.225011	+	0.974356i	$0.572242\pi$
$588$	0	0
$589$	−1.16068e7	−1.37856
$590$	−2.59560e6	−0.306978
$591$	−1.25183e7	−1.47426
$592$	−4.22861e6	−0.495899
$593$	−2.89048e6	−0.337546	−0.168773	−	0.985655i	$-0.553980\pi$
$593$	−2.89048e6	−0.337546	−0.168773	+	0.985655i	$0.553980\pi$
$594$	9.57814e6	1.11382
$595$	0	0
$596$	−3.18525e6	−0.367306
$597$	8.18754e6	0.940194
$598$	5.22980e6	0.598043
$599$	1.32233e7	1.50582	0.752910	−	0.658124i	$-0.228650\pi$
$599$	1.32233e7	1.50582	0.752910	+	0.658124i	$0.228650\pi$
$600$	680000.	0.0771136
$601$	−3.47399e6	−0.392321	−0.196161	−	0.980572i	$-0.562847\pi$
$601$	−3.47399e6	−0.392321	−0.196161	+	0.980572i	$0.562847\pi$
$602$	0	0
$603$	203136.	0.0227506
$604$	7.54533e6	0.841561
$605$	−8.75435e6	−0.972379
$606$	1.98900e6	0.220015
$607$	−6.45088e6	−0.710636	−0.355318	−	0.934746i	$-0.615627\pi$
$607$	−6.45088e6	−0.710636	−0.355318	+	0.934746i	$0.615627\pi$
$608$	1.75923e6	0.193003
$609$	0	0
$610$	3.91880e6	0.426411
$611$	−177747.	−0.0192619
$612$	1.25046e6	0.134956
$613$	8.43820e6	0.906982	0.453491	−	0.891261i	$-0.350178\pi$
$613$	8.43820e6	0.906982	0.453491	+	0.891261i	$0.350178\pi$
$614$	108172.	0.0115796
$615$	8.02230e6	0.855285
$616$	0	0
$617$	9.45501e6	0.999882	0.499941	−	0.866059i	$-0.333355\pi$
$617$	9.45501e6	0.999882	0.499941	+	0.866059i	$0.333355\pi$
$618$	1.01449e7	1.06850
$619$	−1.43145e6	−0.150158	−0.0750790	−	0.997178i	$-0.523921\pi$
$619$	−1.43145e6	−0.150158	−0.0750790	+	0.997178i	$0.523921\pi$
$620$	2.70240e6	0.282339
$621$	1.32286e7	1.37652
$622$	−8.59674e6	−0.890960
$623$	0	0
$624$	−1.44051e6	−0.148100
$625$	390625.	0.0400000
$626$	1.06821e7	1.08948
$627$	−2.08823e7	−2.12134
$628$	1.15286e6	0.116648
$629$	−2.80641e7	−2.82829
$630$	0	0
$631$	−1.01813e7	−1.01795	−0.508977	−	0.860780i	$-0.669976\pi$
$631$	−1.01813e7	−1.01795	−0.508977	+	0.860780i	$0.669976\pi$
$632$	−1.79053e6	−0.178315
$633$	3.22203e6	0.319610
$634$	−1.00206e6	−0.0990077
$635$	5.47990e6	0.539310
$636$	−2.98765e6	−0.292878
$637$	0	0
$638$	−1.30959e7	−1.27375
$639$	−1.46648e6	−0.142077
$640$	−409600.	−0.0395285
$641$	−1.76908e7	−1.70060	−0.850300	−	0.526298i	$-0.823580\pi$
$641$	−1.76908e7	−1.70060	−0.850300	+	0.526298i	$0.823580\pi$
$642$	5.69446e6	0.545274
$643$	−1.82748e7	−1.74311	−0.871556	−	0.490296i	$-0.836889\pi$
$643$	−1.82748e7	−1.74311	−0.871556	+	0.490296i	$0.836889\pi$
$644$	0	0
$645$	−959650.	−0.0908267
$646$	1.16755e7	1.10077
$647$	−1.52897e6	−0.143594	−0.0717972	−	0.997419i	$-0.522873\pi$
$647$	−1.52897e6	−0.143594	−0.0717972	+	0.997419i	$0.522873\pi$
$648$	−4.35910e6	−0.407812
$649$	−1.85585e7	−1.72955
$650$	−827500.	−0.0768218
$651$	0	0
$652$	6.16534e6	0.567987
$653$	−9.10088e6	−0.835219	−0.417610	−	0.908627i	$-0.637132\pi$
$653$	−9.10088e6	−0.835219	−0.417610	+	0.908627i	$0.637132\pi$
$654$	7.16564e6	0.655104
$655$	−2.41705e6	−0.220132
$656$	−4.83226e6	−0.438420
$657$	230828.	0.0208629
$658$	0	0
$659$	−430119.	−0.0385811	−0.0192906	−	0.999814i	$-0.506141\pi$
$659$	−430119.	−0.0385811	−0.0192906	+	0.999814i	$0.506141\pi$
$660$	4.86200e6	0.434465
$661$	−7.65248e6	−0.681238	−0.340619	−	0.940202i	$-0.610637\pi$
$661$	−7.65248e6	−0.681238	−0.340619	+	0.940202i	$0.610637\pi$
$662$	4.23595e6	0.375670
$663$	−9.56027e6	−0.844669
$664$	−2.40922e6	−0.212058
$665$	0	0
$666$	−3.03931e6	−0.265515
$667$	−1.80870e7	−1.57418
$668$	8.68731e6	0.753259
$669$	384149.	0.0331844
$670$	−441600.	−0.0380051
$671$	2.80194e7	2.40244
$672$	0	0
$673$	−2.18404e7	−1.85876	−0.929378	−	0.369128i	$-0.879656\pi$
$673$	−2.18404e7	−1.85876	−0.929378	+	0.369128i	$0.879656\pi$
$674$	−1.14010e7	−0.966702
$675$	−2.09312e6	−0.176822
$676$	−4.18771e6	−0.352460
$677$	−1.39504e7	−1.16981	−0.584905	−	0.811102i	$-0.698868\pi$
$677$	−1.39504e7	−1.16981	−0.584905	+	0.811102i	$0.698868\pi$
$678$	−8.34727e6	−0.697381
$679$	0	0
$680$	−2.71840e6	−0.225445
$681$	1.69680e7	1.40205
$682$	1.93222e7	1.59072
$683$	2.29121e7	1.87937	0.939686	−	0.342040i	$-0.111118\pi$
$683$	2.29121e7	1.87937	0.939686	+	0.342040i	$0.111118\pi$
$684$	1.26445e6	0.103338
$685$	−4.68220e6	−0.381262
$686$	0	0
$687$	1.45289e7	1.17447
$688$	578048.	0.0465578
$689$	3.63570e6	0.291770
$690$	6.71500e6	0.536937
$691$	1.69127e7	1.34747	0.673734	−	0.738974i	$-0.264690\pi$
$691$	1.69127e7	1.34747	0.673734	+	0.738974i	$0.264690\pi$
$692$	−5.93525e6	−0.471166
$693$	0	0
$694$	7.56562e6	0.596274
$695$	4.42235e6	0.347289
$696$	4.98195e6	0.389831
$697$	−3.20703e7	−2.50047
$698$	4.16927e6	0.323908
$699$	2.13891e7	1.65577
$700$	0	0
$701$	−1.90087e7	−1.46102	−0.730510	−	0.682902i	$-0.760718\pi$
$701$	−1.90087e7	−1.46102	−0.730510	+	0.682902i	$0.760718\pi$
$702$	4.43408e6	0.339594
$703$	−2.83779e7	−2.16567
$704$	−2.92864e6	−0.222707
$705$	−228225.	−0.0172938
$706$	9.21235e6	0.695598
$707$	0	0
$708$	7.06003e6	0.529326
$709$	1.66079e7	1.24079	0.620396	−	0.784289i	$-0.286972\pi$
$709$	1.66079e7	1.24079	0.620396	+	0.784289i	$0.286972\pi$
$710$	3.18800e6	0.237341
$711$	−1.28694e6	−0.0954740
$712$	1.10182e6	0.0814540
$713$	2.66862e7	1.96591
$714$	0	0
$715$	−5.91662e6	−0.432822
$716$	−1.20668e7	−0.879646
$717$	−1.20119e7	−0.872596
$718$	−6.70378e6	−0.485298
$719$	−5.93610e6	−0.428232	−0.214116	−	0.976808i	$-0.568687\pi$
$719$	−5.93610e6	−0.428232	−0.214116	+	0.976808i	$0.568687\pi$
$720$	−294400.	−0.0211644
$721$	0	0
$722$	1.90170e6	0.135768
$723$	−1.04776e7	−0.745447
$724$	−4.86144e6	−0.344682
$725$	2.86188e6	0.202211
$726$	2.38118e7	1.67668
$727$	−1.73276e7	−1.21591	−0.607957	−	0.793970i	$-0.708011\pi$
$727$	−1.73276e7	−1.21591	−0.607957	+	0.793970i	$0.708011\pi$
$728$	0	0
$729$	1.07016e7	0.745814
$730$	−501800.	−0.0348517
$731$	3.83634e6	0.265536
$732$	−1.06591e7	−0.735266
$733$	−1.39829e7	−0.961255	−0.480627	−	0.876925i	$-0.659591\pi$
$733$	−1.39829e7	−0.961255	−0.480627	+	0.876925i	$0.659591\pi$
$734$	−378652.	−0.0259418
$735$	0	0
$736$	−4.04480e6	−0.275234
$737$	−3.15744e6	−0.214125
$738$	−3.47318e6	−0.234740
$739$	−1.14263e7	−0.769649	−0.384824	−	0.922990i	$-0.625738\pi$
$739$	−1.14263e7	−0.769649	−0.384824	+	0.922990i	$0.625738\pi$
$740$	6.60720e6	0.443545
$741$	−9.66719e6	−0.646777
$742$	0	0
$743$	1.23126e7	0.818236	0.409118	−	0.912481i	$-0.365836\pi$
$743$	1.23126e7	0.818236	0.409118	+	0.912481i	$0.365836\pi$
$744$	−7.35053e6	−0.486840
$745$	4.97695e6	0.328528
$746$	−3.81414e6	−0.250929
$747$	−1.73162e6	−0.113541
$748$	−1.94366e7	−1.27018
$749$	0	0
$750$	−1.06250e6	−0.0689725
$751$	−1.43093e7	−0.925806	−0.462903	−	0.886409i	$-0.653192\pi$
$751$	−1.43093e7	−0.925806	−0.462903	+	0.886409i	$0.653192\pi$
$752$	137472.	0.00886481
$753$	−3.24431e6	−0.208514
$754$	−6.06260e6	−0.388356
$755$	−1.17896e7	−0.752715
$756$	0	0
$757$	−5.34505e6	−0.339010	−0.169505	−	0.985529i	$-0.554217\pi$
$757$	−5.34505e6	−0.339010	−0.169505	+	0.985529i	$0.554217\pi$
$758$	1.55530e7	0.983197
$759$	4.80122e7	3.02515
$760$	−2.74880e6	−0.172627
$761$	−6.22568e6	−0.389695	−0.194848	−	0.980834i	$-0.562421\pi$
$761$	−6.22568e6	−0.389695	−0.194848	+	0.980834i	$0.562421\pi$
$762$	−1.49053e7	−0.929938
$763$	0	0
$764$	−2.98034e6	−0.184728
$765$	−1.95385e6	−0.120708
$766$	−1.17454e7	−0.723264
$767$	−8.59144e6	−0.527324
$768$	1.11411e6	0.0681594
$769$	−1.57888e7	−0.962793	−0.481397	−	0.876503i	$-0.659870\pi$
$769$	−1.57888e7	−0.962793	−0.481397	+	0.876503i	$0.659870\pi$
$770$	0	0
$771$	1.92260e7	1.16481
$772$	1.48006e6	0.0893794
$773$	2.50453e7	1.50757	0.753785	−	0.657121i	$-0.228226\pi$
$773$	2.50453e7	1.50757	0.753785	+	0.657121i	$0.228226\pi$
$774$	415472.	0.0249281
$775$	−4.22250e6	−0.252531
$776$	4.04320e6	0.241030
$777$	0	0
$778$	6.81509e6	0.403667
$779$	−3.24290e7	−1.91465
$780$	2.25080e6	0.132465
$781$	2.27942e7	1.33720
$782$	−2.68442e7	−1.56976
$783$	−1.53351e7	−0.893884
$784$	0	0
$785$	−1.80135e6	−0.104334
$786$	6.57438e6	0.379576
$787$	1.28020e6	0.0736784	0.0368392	−	0.999321i	$-0.488271\pi$
$787$	1.28020e6	0.0736784	0.0368392	+	0.999321i	$0.488271\pi$
$788$	−1.17819e7	−0.675926
$789$	−2.84541e7	−1.62724
$790$	2.79770e6	0.159490
$791$	0	0
$792$	−2.10496e6	−0.119242
$793$	1.29712e7	0.732484
$794$	−4.76442e6	−0.268200
$795$	4.66820e6	0.261958
$796$	7.70592e6	0.431064
$797$	1.13798e7	0.634584	0.317292	−	0.948328i	$-0.397226\pi$
$797$	1.13798e7	0.634584	0.317292	+	0.948328i	$0.397226\pi$
$798$	0	0
$799$	912363.	0.0505593
$800$	640000.	0.0353553
$801$	791936.	0.0436123
$802$	−1.35332e7	−0.742959
$803$	−3.58787e6	−0.196358
$804$	1.20115e6	0.0655327
$805$	0	0
$806$	8.94494e6	0.484998
$807$	1.07260e7	0.579768
$808$	1.87200e6	0.100874
$809$	−1.70542e7	−0.916138	−0.458069	−	0.888917i	$-0.651459\pi$
$809$	−1.70542e7	−0.916138	−0.458069	+	0.888917i	$0.651459\pi$
$810$	6.81110e6	0.364758
$811$	2.21494e7	1.18252	0.591262	−	0.806480i	$-0.298630\pi$
$811$	2.21494e7	1.18252	0.591262	+	0.806480i	$0.298630\pi$
$812$	0	0
$813$	6.33209e6	0.335986
$814$	4.72415e7	2.49898
$815$	−9.63335e6	−0.508023
$816$	7.39405e6	0.388738
$817$	3.87924e6	0.203326
$818$	5.32738e6	0.278375
$819$	0	0
$820$	7.55040e6	0.392135
$821$	−1.01068e7	−0.523307	−0.261654	−	0.965162i	$-0.584268\pi$
$821$	−1.01068e7	−0.523307	−0.261654	+	0.965162i	$0.584268\pi$
$822$	1.27356e7	0.657415
$823$	−1.83993e7	−0.946895	−0.473447	−	0.880822i	$-0.656991\pi$
$823$	−1.83993e7	−0.946895	−0.473447	+	0.880822i	$0.656991\pi$
$824$	9.54810e6	0.489890
$825$	−7.59688e6	−0.388598
$826$	0	0
$827$	−2.48056e7	−1.26121	−0.630604	−	0.776105i	$-0.717193\pi$
$827$	−2.48056e7	−1.26121	−0.630604	+	0.776105i	$0.717193\pi$
$828$	−2.90720e6	−0.147367
$829$	1.19708e6	0.0604976	0.0302488	−	0.999542i	$-0.490370\pi$
$829$	1.19708e6	0.0604976	0.0302488	+	0.999542i	$0.490370\pi$
$830$	3.76440e6	0.189671
$831$	1.47392e7	0.740407
$832$	−1.35578e6	−0.0679015
$833$	0	0
$834$	−1.20288e7	−0.598835
$835$	−1.35739e7	−0.673735
$836$	−1.96539e7	−0.972598
$837$	2.26258e7	1.11633
$838$	−2.33114e7	−1.14672
$839$	3.17171e7	1.55557	0.777783	−	0.628533i	$-0.216344\pi$
$839$	3.17171e7	1.55557	0.777783	+	0.628533i	$0.216344\pi$
$840$	0	0
$841$	456092.	0.0222363
$842$	9.89722e6	0.481097
$843$	−3.30647e7	−1.60249
$844$	3.03250e6	0.146536
$845$	6.54330e6	0.315250
$846$	98808.0	0.00474642
$847$	0	0
$848$	−2.81190e6	−0.134280
$849$	−2.01452e7	−0.959186
$850$	4.24750e6	0.201644
$851$	6.52461e7	3.08838
$852$	−8.67136e6	−0.409250
$853$	−3.18237e7	−1.49754	−0.748769	−	0.662831i	$-0.769355\pi$
$853$	−3.18237e7	−1.49754	−0.748769	+	0.662831i	$0.769355\pi$
$854$	0	0
$855$	−1.97570e6	−0.0924285
$856$	5.35949e6	0.249999
$857$	−2.27853e7	−1.05975	−0.529874	−	0.848076i	$-0.677761\pi$
$857$	−2.27853e7	−1.05975	−0.529874	+	0.848076i	$0.677761\pi$
$858$	1.60932e7	0.746319
$859$	1.85966e7	0.859907	0.429953	−	0.902851i	$-0.358530\pi$
$859$	1.85966e7	0.859907	0.429953	+	0.902851i	$0.358530\pi$
$860$	−903200.	−0.0416426
$861$	0	0
$862$	1.84740e7	0.846825
$863$	−2.77046e7	−1.26627	−0.633133	−	0.774043i	$-0.718231\pi$
$863$	−2.77046e7	−1.26627	−0.633133	+	0.774043i	$0.718231\pi$
$864$	−3.42938e6	−0.156290
$865$	9.27382e6	0.421423
$866$	−234424.	−0.0106220
$867$	2.49346e7	1.12656
$868$	0	0
$869$	2.00036e7	0.898582
$870$	−7.78430e6	−0.348676
$871$	−1.46170e6	−0.0652847
$872$	6.74413e6	0.300355
$873$	2.90605e6	0.129053
$874$	−2.71444e7	−1.20199
$875$	0	0
$876$	1.36490e6	0.0600951
$877$	−2.41150e7	−1.05874	−0.529370	−	0.848391i	$-0.677572\pi$
$877$	−2.41150e7	−1.05874	−0.529370	+	0.848391i	$0.677572\pi$
$878$	−2.81719e7	−1.23333
$879$	−572373.	−0.0249866
$880$	4.57600e6	0.199195
$881$	1.26207e7	0.547827	0.273914	−	0.961754i	$-0.411682\pi$
$881$	1.26207e7	0.547827	0.273914	+	0.961754i	$0.411682\pi$
$882$	0	0
$883$	−6.01876e6	−0.259780	−0.129890	−	0.991528i	$-0.541462\pi$
$883$	−6.01876e6	−0.259780	−0.129890	+	0.991528i	$0.541462\pi$
$884$	−8.99790e6	−0.387267
$885$	−1.10313e7	−0.473444
$886$	5.87575e6	0.251466
$887$	−2.36901e7	−1.01102	−0.505509	−	0.862821i	$-0.668695\pi$
$887$	−2.36901e7	−1.01102	−0.505509	+	0.862821i	$0.668695\pi$
$888$	−1.79716e7	−0.764811
$889$	0	0
$890$	−1.72160e6	−0.0728546
$891$	4.86994e7	2.05508
$892$	361552.	0.0152145
$893$	922566.	0.0387141
$894$	−1.35373e7	−0.566485
$895$	1.88543e7	0.786779
$896$	0	0
$897$	2.22266e7	0.922344
$898$	−2.99365e7	−1.23883
$899$	−3.09357e7	−1.27662
$900$	460000.	0.0189300
$901$	−1.86618e7	−0.765847
$902$	5.39854e7	2.20933
$903$	0	0
$904$	−7.85626e6	−0.319738
$905$	7.59600e6	0.308293
$906$	3.20676e7	1.29792
$907$	−1.10583e7	−0.446346	−0.223173	−	0.974779i	$-0.571641\pi$
$907$	−1.10583e7	−0.446346	−0.223173	+	0.974779i	$0.571641\pi$
$908$	1.59699e7	0.642816
$909$	1.34550e6	0.0540100
$910$	0	0
$911$	3.07573e6	0.122787	0.0613934	−	0.998114i	$-0.480446\pi$
$911$	3.07573e6	0.122787	0.0613934	+	0.998114i	$0.480446\pi$
$912$	7.47674e6	0.297663
$913$	2.69155e7	1.06862
$914$	681280.	0.0269749
$915$	1.66549e7	0.657642
$916$	1.36743e7	0.538476
$917$	0	0
$918$	−2.27598e7	−0.891378
$919$	−1.89018e7	−0.738270	−0.369135	−	0.929376i	$-0.620346\pi$
$919$	−1.89018e7	−0.738270	−0.369135	+	0.929376i	$0.620346\pi$
$920$	6.32000e6	0.246177
$921$	459731.	0.0178589
$922$	1.71474e7	0.664310
$923$	1.05523e7	0.407701
$924$	0	0
$925$	−1.03238e7	−0.396719
$926$	1.35327e7	0.518629
$927$	6.86269e6	0.262298
$928$	4.68890e6	0.178731
$929$	1.81458e7	0.689821	0.344911	−	0.938636i	$-0.387909\pi$
$929$	1.81458e7	0.689821	0.344911	+	0.938636i	$0.387909\pi$
$930$	1.14852e7	0.435443
$931$	0	0
$932$	2.01309e7	0.759144
$933$	−3.65362e7	−1.37410
$934$	−2.07212e7	−0.777225
$935$	3.03696e7	1.13608
$936$	−974464.	−0.0363560
$937$	2.17350e7	0.808744	0.404372	−	0.914595i	$-0.367490\pi$
$937$	2.17350e7	0.808744	0.404372	+	0.914595i	$0.367490\pi$
$938$	0	0
$939$	4.53989e7	1.68028
$940$	−214800.	−0.00792893
$941$	−1.86808e7	−0.687735	−0.343868	−	0.939018i	$-0.611737\pi$
$941$	−1.86808e7	−0.687735	−0.343868	+	0.939018i	$0.611737\pi$
$942$	4.89967e6	0.179904
$943$	7.45602e7	2.73041
$944$	6.64474e6	0.242688
$945$	0	0
$946$	−6.45788e6	−0.234618
$947$	−2.24778e6	−0.0814476	−0.0407238	−	0.999170i	$-0.512966\pi$
$947$	−2.24778e6	−0.0814476	−0.0407238	+	0.999170i	$0.512966\pi$
$948$	−7.60974e6	−0.275010
$949$	−1.66096e6	−0.0598678
$950$	4.29500e6	0.154402
$951$	−4.25874e6	−0.152697
$952$	0	0
$953$	−3.73293e7	−1.33143	−0.665714	−	0.746207i	$-0.731873\pi$
$953$	−3.73293e7	−1.33143	−0.665714	+	0.746207i	$0.731873\pi$
$954$	−2.02106e6	−0.0718964
$955$	4.65678e6	0.165225
$956$	−1.13053e7	−0.400071
$957$	−5.56577e7	−1.96447
$958$	3.50711e7	1.23463
$959$	0	0
$960$	−1.74080e6	−0.0609636
$961$	1.70144e7	0.594303
$962$	2.18698e7	0.761917
$963$	3.85213e6	0.133855
$964$	−9.86128e6	−0.341775
$965$	−2.31260e6	−0.0799433
$966$	0	0
$967$	2.61870e7	0.900573	0.450287	−	0.892884i	$-0.351322\pi$
$967$	2.61870e7	0.900573	0.450287	+	0.892884i	$0.351322\pi$
$968$	2.24111e7	0.768733
$969$	4.96210e7	1.69768
$970$	−6.31750e6	−0.215584
$971$	3.91957e7	1.33410	0.667052	−	0.745011i	$-0.267556\pi$
$971$	3.91957e7	1.33410	0.667052	+	0.745011i	$0.267556\pi$
$972$	−5.50528e6	−0.186902
$973$	0	0
$974$	1.08062e6	0.0364984
$975$	−3.51688e6	−0.118480
$976$	−1.00321e7	−0.337108
$977$	3.03935e6	0.101870	0.0509348	−	0.998702i	$-0.483780\pi$
$977$	3.03935e6	0.101870	0.0509348	+	0.998702i	$0.483780\pi$
$978$	2.62027e7	0.875990
$979$	−1.23094e7	−0.410470
$980$	0	0
$981$	4.84734e6	0.160817
$982$	1.94220e7	0.642711
$983$	1.59937e7	0.527915	0.263957	−	0.964534i	$-0.414972\pi$
$983$	1.59937e7	0.527915	0.263957	+	0.964534i	$0.414972\pi$
$984$	−2.05371e7	−0.676163
$985$	1.84092e7	0.604567
$986$	3.11189e7	1.01937
$987$	0	0
$988$	−9.09853e6	−0.296537
$989$	−8.91910e6	−0.289955
$990$	3.28900e6	0.106654
$991$	3.63186e6	0.117475	0.0587375	−	0.998273i	$-0.481293\pi$
$991$	3.63186e6	0.117475	0.0587375	+	0.998273i	$0.481293\pi$
$992$	−6.91814e6	−0.223208
$993$	1.80028e7	0.579384
$994$	0	0
$995$	−1.20405e7	−0.385555
$996$	−1.02392e7	−0.327052
$997$	4.33287e7	1.38051	0.690253	−	0.723568i	$-0.257499\pi$
$997$	4.33287e7	1.38051	0.690253	+	0.723568i	$0.257499\pi$
$998$	−1.19430e7	−0.379567
$999$	5.53188e7	1.75371

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.e.1.1	✓	1	7.6	odd	2
350.6.a.e.1.1		1	35.34	odd	2
350.6.c.a.99.1		2	35.13	even	4
350.6.c.a.99.2		2	35.27	even	4
490.6.a.m.1.1		1	1.1	even	1	trivial
560.6.a.h.1.1		1	28.27	even	2
630.6.a.b.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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