LMFDB - Embedded newform 630.6.a.b.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)

$f(q)$

$=$

\(q-4.00000 q^{2} +16.0000 q^{4} -25.0000 q^{5} -49.0000 q^{7} -64.0000 q^{8} +100.000 q^{10} +715.000 q^{11} +331.000 q^{13} +196.000 q^{14} +256.000 q^{16} +1699.00 q^{17} -1718.00 q^{19} -400.000 q^{20} -2860.00 q^{22} +3950.00 q^{23} +625.000 q^{25} -1324.00 q^{26} -784.000 q^{28} -4579.00 q^{29} +6756.00 q^{31} -1024.00 q^{32} -6796.00 q^{34} +1225.00 q^{35} -16518.0 q^{37} +6872.00 q^{38} +1600.00 q^{40} -18876.0 q^{41} +2258.00 q^{43} +11440.0 q^{44} -15800.0 q^{46} +537.000 q^{47} +2401.00 q^{49} -2500.00 q^{50} +5296.00 q^{52} +10984.0 q^{53} -17875.0 q^{55} +3136.00 q^{56} +18316.0 q^{58} +25956.0 q^{59} +39188.0 q^{61} -27024.0 q^{62} +4096.00 q^{64} -8275.00 q^{65} +4416.00 q^{67} +27184.0 q^{68} -4900.00 q^{70} +31880.0 q^{71} -5018.00 q^{73} +66072.0 q^{74} -27488.0 q^{76} -35035.0 q^{77} -27977.0 q^{79} -6400.00 q^{80} +75504.0 q^{82} -37644.0 q^{83} -42475.0 q^{85} -9032.00 q^{86} -45760.0 q^{88} +17216.0 q^{89} -16219.0 q^{91} +63200.0 q^{92} -2148.00 q^{94} +42950.0 q^{95} -63175.0 q^{97} -9604.00 q^{98} +O(q^{100})\)

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
$11$	715.000	1.78166	0.890829	−	0.454339i	$-0.150124\pi$
$11$	715.000	1.78166	0.890829	+	0.454339i	$0.150124\pi$
$12$	0	0
$13$	331.000	0.543212	0.271606	−	0.962408i	$-0.412445\pi$
$13$	331.000	0.543212	0.271606	+	0.962408i	$0.412445\pi$
$14$	196.000	0.267261
$15$	0	0
$16$	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	$0.247372\pi$
$18$	0	0
$19$	−1718.00	−1.09179	−0.545895	−	0.837854i	$-0.683810\pi$
$19$	−1718.00	−1.09179	−0.545895	+	0.837854i	$0.683810\pi$
$20$	−400.000	−0.223607
$21$	0	0
$22$	−2860.00	−1.25982
$23$	3950.00	1.55696	0.778480	−	0.627669i	$-0.215991\pi$
$23$	3950.00	1.55696	0.778480	+	0.627669i	$0.215991\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	−1324.00	−0.384109
$27$	0	0
$28$	−784.000	−0.188982
$29$	−4579.00	−1.01106	−0.505529	−	0.862810i	$-0.668702\pi$
$29$	−4579.00	−1.01106	−0.505529	+	0.862810i	$0.668702\pi$
$30$	0	0
$31$	6756.00	1.26266	0.631329	−	0.775516i	$-0.282510\pi$
$31$	6756.00	1.26266	0.631329	+	0.775516i	$0.282510\pi$
$32$	−1024.00	−0.176777
$33$	0	0
$34$	−6796.00	−1.00822
$35$	1225.00	0.169031
$36$	0	0
$37$	−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
$39$	0	0
$40$	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
$45$	0	0
$46$	−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	$0.494356\pi$
$48$	0	0
$49$	2401.00	0.142857
$50$	−2500.00	−0.141421
$51$	0	0
$52$	5296.00	0.271606
$53$	10984.0	0.537119	0.268560	−	0.963263i	$-0.413452\pi$
$53$	10984.0	0.537119	0.268560	+	0.963263i	$0.413452\pi$
$54$	0	0
$55$	−17875.0	−0.796782
$56$	3136.00	0.133631
$57$	0	0
$58$	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	$0.338683\pi$
$60$	0	0
$61$	39188.0	1.34843	0.674215	−	0.738535i	$-0.264482\pi$
$61$	39188.0	1.34843	0.674215	+	0.738535i	$0.264482\pi$
$62$	−27024.0	−0.892833
$63$	0	0
$64$	4096.00	0.125000
$65$	−8275.00	−0.242932
$66$	0	0
$67$	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
$69$	0	0
$70$	−4900.00	−0.119523
$71$	31880.0	0.750538	0.375269	−	0.926916i	$-0.377550\pi$
$71$	31880.0	0.750538	0.375269	+	0.926916i	$0.377550\pi$
$72$	0	0
$73$	−5018.00	−0.110211	−0.0551053	−	0.998481i	$-0.517549\pi$
$73$	−5018.00	−0.110211	−0.0551053	+	0.998481i	$0.517549\pi$
$74$	66072.0	1.40261
$75$	0	0
$76$	−27488.0	−0.545895
$77$	−35035.0	−0.673403
$78$	0	0
$79$	−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
$81$	0	0
$82$	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
$87$	0	0
$88$	−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	$0.463251\pi$
$90$	0	0
$91$	−16219.0	−0.205315
$92$	63200.0	0.778480
$93$	0	0
$94$	−2148.00	−0.0250735
$95$	42950.0	0.488263
$96$	0	0
$97$	−63175.0	−0.681736	−0.340868	−	0.940111i	$-0.610721\pi$
$97$	−63175.0	−0.681736	−0.340868	+	0.940111i	$0.610721\pi$
$98$	−9604.00	−0.101015
$99$	0	0
$100$	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	$0.454435\pi$
$102$	0	0
$103$	−149189.	−1.38562	−0.692809	−	0.721121i	$-0.743627\pi$
$103$	−149189.	−1.38562	−0.692809	+	0.721121i	$0.743627\pi$
$104$	−21184.0	−0.192055
$105$	0	0
$106$	−43936.0	−0.379801
$107$	−83742.0	−0.707105	−0.353552	−	0.935415i	$-0.615026\pi$
$107$	−83742.0	−0.707105	−0.353552	+	0.935415i	$0.615026\pi$
$108$	0	0
$109$	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
$111$	0	0
$112$	−12544.0	−0.0944911
$113$	122754.	0.904356	0.452178	−	0.891928i	$-0.350647\pi$
$113$	122754.	0.904356	0.452178	+	0.891928i	$0.350647\pi$
$114$	0	0
$115$	−98750.0	−0.696294
$116$	−73264.0	−0.505529
$117$	0	0
$118$	−103824.	−0.686424
$119$	−83251.0	−0.538917
$120$	0	0
$121$	350174.	2.17431
$122$	−156752.	−0.953484
$123$	0	0
$124$	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
$129$	0	0
$130$	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	$0.420846\pi$
$132$	0	0
$133$	84182.0	0.412658
$134$	−17664.0	−0.0849820
$135$	0	0
$136$	−108736.	−0.504111
$137$	−187288.	−0.852528	−0.426264	−	0.904599i	$-0.640170\pi$
$137$	−187288.	−0.852528	−0.426264	+	0.904599i	$0.640170\pi$
$138$	0	0
$139$	176894.	0.776562	0.388281	−	0.921541i	$-0.373069\pi$
$139$	176894.	0.776562	0.388281	+	0.921541i	$0.373069\pi$
$140$	19600.0	0.0845154
$141$	0	0
$142$	−127520.	−0.530710
$143$	236665.	0.967819
$144$	0	0
$145$	114475.	0.452158
$146$	20072.0	0.0779307
$147$	0	0
$148$	−264288.	−0.991798
$149$	199078.	0.734611	0.367306	−	0.930100i	$-0.380280\pi$
$149$	199078.	0.734611	0.367306	+	0.930100i	$0.380280\pi$
$150$	0	0
$151$	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
$153$	0	0
$154$	140140.	0.476168
$155$	−168900.	−0.564677
$156$	0	0
$157$	−72054.0	−0.233297	−0.116648	−	0.993173i	$-0.537215\pi$
$157$	−72054.0	−0.233297	−0.116648	+	0.993173i	$0.537215\pi$
$158$	111908.	0.356630
$159$	0	0
$160$	25600.0	0.0790569
$161$	−193550.	−0.588476
$162$	0	0
$163$	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
$165$	0	0
$166$	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
$171$	0	0
$172$	36128.0	0.0931157
$173$	−370953.	−0.942331	−0.471166	−	0.882045i	$-0.656167\pi$
$173$	−370953.	−0.942331	−0.471166	+	0.882045i	$0.656167\pi$
$174$	0	0
$175$	−30625.0	−0.0755929
$176$	183040.	0.445414
$177$	0	0
$178$	−68864.0	−0.162908
$179$	754172.	1.75929	0.879646	−	0.475629i	$-0.157780\pi$
$179$	754172.	1.75929	0.879646	+	0.475629i	$0.157780\pi$
$180$	0	0
$181$	303840.	0.689364	0.344682	−	0.938720i	$-0.387987\pi$
$181$	303840.	0.689364	0.344682	+	0.938720i	$0.387987\pi$
$182$	64876.0	0.145180
$183$	0	0
$184$	−252800.	−0.550469
$185$	412950.	0.887091
$186$	0	0
$187$	1.21478e6	2.54036
$188$	8592.00	0.0177296
$189$	0	0
$190$	−171800.	−0.345254
$191$	186271.	0.369455	0.184728	−	0.982790i	$-0.440860\pi$
$191$	186271.	0.369455	0.184728	+	0.982790i	$0.440860\pi$
$192$	0	0
$193$	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
$195$	0	0
$196$	38416.0	0.0714286
$197$	736368.	1.35185	0.675926	−	0.736969i	$-0.263744\pi$
$197$	736368.	1.35185	0.675926	+	0.736969i	$0.263744\pi$
$198$	0	0
$199$	−481620.	−0.862128	−0.431064	−	0.902321i	$-0.641862\pi$
$199$	−481620.	−0.862128	−0.431064	+	0.902321i	$0.641862\pi$
$200$	−40000.0	−0.0707107
$201$	0	0
$202$	−117000.	−0.201747
$203$	224371.	0.382144
$204$	0	0
$205$	471900.	0.784269
$206$	596756.	0.979780
$207$	0	0
$208$	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
$213$	0	0
$214$	334968.	0.499999
$215$	−56450.0	−0.0832852
$216$	0	0
$217$	−331044.	−0.477240
$218$	−421508.	−0.600710
$219$	0	0
$220$	−286000.	−0.398391
$221$	562369.	0.774534
$222$	0	0
$223$	−22597.0	−0.0304291	−0.0152145	−	0.999884i	$-0.504843\pi$
$223$	−22597.0	−0.0304291	−0.0152145	+	0.999884i	$0.504843\pi$
$224$	50176.0	0.0668153
$225$	0	0
$226$	−491016.	−0.639476
$227$	998117.	1.28563	0.642816	−	0.766020i	$-0.277766\pi$
$227$	998117.	1.28563	0.642816	+	0.766020i	$0.277766\pi$
$228$	0	0
$229$	−854644.	−1.07695	−0.538476	−	0.842641i	$-0.681000\pi$
$229$	−854644.	−1.07695	−0.538476	+	0.842641i	$0.681000\pi$
$230$	395000.	0.492354
$231$	0	0
$232$	293056.	0.357463
$233$	−1.25818e6	−1.51829	−0.759144	−	0.650922i	$-0.774382\pi$
$233$	−1.25818e6	−1.51829	−0.759144	+	0.650922i	$0.774382\pi$
$234$	0	0
$235$	−13425.0	−0.0158579
$236$	415296.	0.485375
$237$	0	0
$238$	333004.	0.381072
$239$	706581.	0.800142	0.400071	−	0.916484i	$-0.368985\pi$
$239$	706581.	0.800142	0.400071	+	0.916484i	$0.368985\pi$
$240$	0	0
$241$	616330.	0.683551	0.341775	−	0.939782i	$-0.388972\pi$
$241$	616330.	0.683551	0.341775	+	0.939782i	$0.388972\pi$
$242$	−1.40070e6	−1.53747
$243$	0	0
$244$	627008.	0.674215
$245$	−60025.0	−0.0638877
$246$	0	0
$247$	−568658.	−0.593074
$248$	−432384.	−0.446417
$249$	0	0
$250$	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
$255$	0	0
$256$	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	$0.320671\pi$
$258$	0	0
$259$	809382.	0.749729
$260$	−132400.	−0.121466
$261$	0	0
$262$	−386728.	−0.348059
$263$	1.67377e6	1.49213	0.746065	−	0.665874i	$-0.231941\pi$
$263$	1.67377e6	1.49213	0.746065	+	0.665874i	$0.231941\pi$
$264$	0	0
$265$	−274600.	−0.240207
$266$	−336728.	−0.291793
$267$	0	0
$268$	70656.0	0.0600914
$269$	630942.	0.531629	0.265815	−	0.964024i	$-0.414359\pi$
$269$	630942.	0.531629	0.265815	+	0.964024i	$0.414359\pi$
$270$	0	0
$271$	−372476.	−0.308088	−0.154044	−	0.988064i	$-0.549230\pi$
$271$	−372476.	−0.308088	−0.154044	+	0.988064i	$0.549230\pi$
$272$	434944.	0.356460
$273$	0	0
$274$	749152.	0.602828
$275$	446875.	0.356332
$276$	0	0
$277$	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
$279$	0	0
$280$	−78400.0	−0.0597614
$281$	1.94498e6	1.46943	0.734716	−	0.678375i	$-0.237315\pi$
$281$	1.94498e6	1.46943	0.734716	+	0.678375i	$0.237315\pi$
$282$	0	0
$283$	1.18501e6	0.879543	0.439771	−	0.898110i	$-0.355059\pi$
$283$	1.18501e6	0.879543	0.439771	+	0.898110i	$0.355059\pi$
$284$	510080.	0.375269
$285$	0	0
$286$	−946660.	−0.684351
$287$	924924.	0.662829
$288$	0	0
$289$	1.46674e6	1.03302
$290$	−457900.	−0.319724
$291$	0	0
$292$	−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
$297$	0	0
$298$	−796312.	−0.519449
$299$	1.30745e6	0.845760
$300$	0	0
$301$	−110642.	−0.0703888
$302$	−1.88633e6	−1.19015
$303$	0	0
$304$	−439808.	−0.272948
$305$	−979700.	−0.603036
$306$	0	0
$307$	−27043.0	−0.0163760	−0.00818802	−	0.999966i	$-0.502606\pi$
$307$	−27043.0	−0.0163760	−0.00818802	+	0.999966i	$0.502606\pi$
$308$	−560560.	−0.336702
$309$	0	0
$310$	675600.	0.399287
$311$	−2.14919e6	−1.26001	−0.630004	−	0.776592i	$-0.716947\pi$
$311$	−2.14919e6	−1.26001	−0.630004	+	0.776592i	$0.716947\pi$
$312$	0	0
$313$	−2.67052e6	−1.54076	−0.770381	−	0.637583i	$-0.779934\pi$
$313$	−2.67052e6	−1.54076	−0.770381	+	0.637583i	$0.779934\pi$
$314$	288216.	0.164966
$315$	0	0
$316$	−447632.	−0.252176
$317$	250514.	0.140018	0.0700090	−	0.997546i	$-0.477697\pi$
$317$	250514.	0.140018	0.0700090	+	0.997546i	$0.477697\pi$
$318$	0	0
$319$	−3.27398e6	−1.80136
$320$	−102400.	−0.0559017
$321$	0	0
$322$	774200.	0.416115
$323$	−2.91888e6	−1.55672
$324$	0	0
$325$	206875.	0.108642
$326$	−1.54134e6	−0.803255
$327$	0	0
$328$	1.20806e6	0.620019
$329$	−26313.0	−0.0134023
$330$	0	0
$331$	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
$333$	0	0
$334$	−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
$339$	0	0
$340$	−679600.	−0.318828
$341$	4.83054e6	2.24962
$342$	0	0
$343$	−117649.	−0.0539949
$344$	−144512.	−0.0658427
$345$	0	0
$346$	1.48381e6	0.666329
$347$	−1.89141e6	−0.843259	−0.421630	−	0.906768i	$-0.638542\pi$
$347$	−1.89141e6	−0.843259	−0.421630	+	0.906768i	$0.638542\pi$
$348$	0	0
$349$	−1.04232e6	−0.458075	−0.229038	−	0.973418i	$-0.573558\pi$
$349$	−1.04232e6	−0.458075	−0.229038	+	0.973418i	$0.573558\pi$
$350$	122500.	0.0534522
$351$	0	0
$352$	−732160.	−0.314956
$353$	2.30309e6	0.983725	0.491862	−	0.870673i	$-0.336316\pi$
$353$	2.30309e6	0.983725	0.491862	+	0.870673i	$0.336316\pi$
$354$	0	0
$355$	−797000.	−0.335651
$356$	275456.	0.115193
$357$	0	0
$358$	−3.01669e6	−1.24401
$359$	1.67594e6	0.686315	0.343157	−	0.939278i	$-0.388504\pi$
$359$	1.67594e6	0.686315	0.343157	+	0.939278i	$0.388504\pi$
$360$	0	0
$361$	475425.	0.192006
$362$	−1.21536e6	−0.487454
$363$	0	0
$364$	−259504.	−0.102657
$365$	125450.	0.0492877
$366$	0	0
$367$	94663.0	0.0366872	0.0183436	−	0.999832i	$-0.494161\pi$
$367$	94663.0	0.0366872	0.0183436	+	0.999832i	$0.494161\pi$
$368$	1.01120e6	0.389240
$369$	0	0
$370$	−1.65180e6	−0.627268
$371$	−538216.	−0.203012
$372$	0	0
$373$	−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
$375$	0	0
$376$	−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
$381$	0	0
$382$	−745084.	−0.261244
$383$	−2.93636e6	−1.02285	−0.511425	−	0.859328i	$-0.670882\pi$
$383$	−2.93636e6	−1.02285	−0.511425	+	0.859328i	$0.670882\pi$
$384$	0	0
$385$	875875.	0.301155
$386$	−370016.	−0.126402
$387$	0	0
$388$	−1.01080e6	−0.340868
$389$	−1.70377e6	−0.570871	−0.285435	−	0.958398i	$-0.592138\pi$
$389$	−1.70377e6	−0.570871	−0.285435	+	0.958398i	$0.592138\pi$
$390$	0	0
$391$	6.71105e6	2.21998
$392$	−153664.	−0.0505076
$393$	0	0
$394$	−2.94547e6	−0.955904
$395$	699425.	0.225553
$396$	0	0
$397$	1.19110e6	0.379292	0.189646	−	0.981853i	$-0.439266\pi$
$397$	1.19110e6	0.379292	0.189646	+	0.981853i	$0.439266\pi$
$398$	1.92648e6	0.609617
$399$	0	0
$400$	160000.	0.0500000
$401$	3.38330e6	1.05070	0.525351	−	0.850885i	$-0.323934\pi$
$401$	3.38330e6	1.05070	0.525351	+	0.850885i	$0.323934\pi$
$402$	0	0
$403$	2.23624e6	0.685891
$404$	468000.	0.142657
$405$	0	0
$406$	−897484.	−0.270216
$407$	−1.18104e7	−3.53409
$408$	0	0
$409$	−1.33185e6	−0.393682	−0.196841	−	0.980435i	$-0.563068\pi$
$409$	−1.33185e6	−0.393682	−0.196841	+	0.980435i	$0.563068\pi$
$410$	−1.88760e6	−0.554562
$411$	0	0
$412$	−2.38702e6	−0.692809
$413$	−1.27184e6	−0.366909
$414$	0	0
$415$	941100.	0.268235
$416$	−338944.	−0.0960273
$417$	0	0
$418$	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
$423$	0	0
$424$	−702976.	−0.189900
$425$	1.06188e6	0.285168
$426$	0	0
$427$	−1.92021e6	−0.509659
$428$	−1.33987e6	−0.353552
$429$	0	0
$430$	225800.	0.0588915
$431$	−4.61851e6	−1.19759	−0.598796	−	0.800902i	$-0.704354\pi$
$431$	−4.61851e6	−1.19759	−0.598796	+	0.800902i	$0.704354\pi$
$432$	0	0
$433$	58606.0	0.0150218	0.00751091	−	0.999972i	$-0.497609\pi$
$433$	58606.0	0.0150218	0.00751091	+	0.999972i	$0.497609\pi$
$434$	1.32418e6	0.337459
$435$	0	0
$436$	1.68603e6	0.424766
$437$	−6.78610e6	−1.69987
$438$	0	0
$439$	7.04298e6	1.74419	0.872097	−	0.489332i	$-0.162759\pi$
$439$	7.04298e6	1.74419	0.872097	+	0.489332i	$0.162759\pi$
$440$	1.14400e6	0.281705
$441$	0	0
$442$	−2.24948e6	−0.547678
$443$	−1.46894e6	−0.355627	−0.177813	−	0.984064i	$-0.556902\pi$
$443$	−1.46894e6	−0.355627	−0.177813	+	0.984064i	$0.556902\pi$
$444$	0	0
$445$	−430400.	−0.103032
$446$	90388.0	0.0215166
$447$	0	0
$448$	−200704.	−0.0472456
$449$	7.48414e6	1.75197	0.875983	−	0.482341i	$-0.160213\pi$
$449$	7.48414e6	1.75197	0.875983	+	0.482341i	$0.160213\pi$
$450$	0	0
$451$	−1.34963e7	−3.12446
$452$	1.96406e6	0.452178
$453$	0	0
$454$	−3.99247e6	−0.909079
$455$	405475.	0.0918196
$456$	0	0
$457$	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
$459$	0	0
$460$	−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
$465$	0	0
$466$	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	$0.685213\pi$
$468$	0	0
$469$	−216384.	−0.0454248
$470$	53700.0	0.0112132
$471$	0	0
$472$	−1.66118e6	−0.343212
$473$	1.61447e6	0.331801
$474$	0	0
$475$	−1.07375e6	−0.218358
$476$	−1.33202e6	−0.269459
$477$	0	0
$478$	−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	$0.162162\pi$
$480$	0	0
$481$	−5.46746e6	−1.07751
$482$	−2.46532e6	−0.483343
$483$	0	0
$484$	5.60278e6	1.08715
$485$	1.57938e6	0.304881
$486$	0	0
$487$	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
$489$	0	0
$490$	240100.	0.0451754
$491$	−4.85550e6	−0.908930	−0.454465	−	0.890765i	$-0.650170\pi$
$491$	−4.85550e6	−0.908930	−0.454465	+	0.890765i	$0.650170\pi$
$492$	0	0
$493$	−7.77972e6	−1.44161
$494$	2.27463e6	0.419367
$495$	0	0
$496$	1.72954e6	0.315664
$497$	−1.56212e6	−0.283677
$498$	0	0
$499$	−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
$501$	0	0
$502$	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
$507$	0	0
$508$	−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	$0.679327\pi$
$510$	0	0
$511$	245882.	0.0416557
$512$	−262144.	−0.0441942
$513$	0	0
$514$	−4.52377e6	−0.755253
$515$	3.72972e6	0.619668
$516$	0	0
$517$	383955.	0.0631763
$518$	−3.23753e6	−0.530138
$519$	0	0
$520$	529600.	0.0858894
$521$	−7.49509e6	−1.20971	−0.604856	−	0.796335i	$-0.706770\pi$
$521$	−7.49509e6	−1.20971	−0.604856	+	0.796335i	$0.706770\pi$
$522$	0	0
$523$	3.80957e6	0.609007	0.304503	−	0.952511i	$-0.401510\pi$
$523$	3.80957e6	0.609007	0.304503	+	0.952511i	$0.401510\pi$
$524$	1.54691e6	0.246115
$525$	0	0
$526$	−6.69508e6	−1.05509
$527$	1.14784e7	1.80035
$528$	0	0
$529$	9.16616e6	1.42413
$530$	1.09840e6	0.169852
$531$	0	0
$532$	1.34691e6	0.206329
$533$	−6.24796e6	−0.952621
$534$	0	0
$535$	2.09355e6	0.316227
$536$	−282624.	−0.0424910
$537$	0	0
$538$	−2.52377e6	−0.375919
$539$	1.71672e6	0.254523
$540$	0	0
$541$	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
$543$	0	0
$544$	−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
$549$	0	0
$550$	−1.78750e6	−0.251964
$551$	7.86672e6	1.10386
$552$	0	0
$553$	1.37087e6	0.190627
$554$	−3.46804e6	−0.480076
$555$	0	0
$556$	2.83030e6	0.388281
$557$	7.45022e6	1.01749	0.508746	−	0.860916i	$-0.330109\pi$
$557$	7.45022e6	1.01749	0.508746	+	0.860916i	$0.330109\pi$
$558$	0	0
$559$	747398.	0.101163
$560$	313600.	0.0422577
$561$	0	0
$562$	−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	$0.571860\pi$
$564$	0	0
$565$	−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	$-0.415443\pi$
$569$	4.05501e6	0.525063	0.262532	+	0.964923i	$0.415443\pi$
$570$	0	0
$571$	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
$573$	0	0
$574$	−3.69970e6	−0.468691
$575$	2.46875e6	0.311392
$576$	0	0
$577$	−9.76895e6	−1.22154	−0.610771	−	0.791807i	$-0.709140\pi$
$577$	−9.76895e6	−1.22154	−0.610771	+	0.791807i	$0.709140\pi$
$578$	−5.86698e6	−0.730457
$579$	0	0
$580$	1.83160e6	0.226079
$581$	1.84456e6	0.226700
$582$	0	0
$583$	7.85356e6	0.956963
$584$	321152.	0.0389653
$585$	0	0
$586$	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
$591$	0	0
$592$	−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	$0.553980\pi$
$594$	0	0
$595$	2.08128e6	0.241011
$596$	3.18525e6	0.367306
$597$	0	0
$598$	−5.22980e6	−0.598043
$599$	−1.32233e7	−1.50582	−0.752910	−	0.658124i	$-0.771350\pi$
$599$	−1.32233e7	−1.50582	−0.752910	+	0.658124i	$0.771350\pi$
$600$	0	0
$601$	3.47399e6	0.392321	0.196161	−	0.980572i	$-0.437153\pi$
$601$	3.47399e6	0.392321	0.196161	+	0.980572i	$0.437153\pi$
$602$	442568.	0.0497724
$603$	0	0
$604$	7.54533e6	0.841561
$605$	−8.75435e6	−0.972379
$606$	0	0
$607$	6.45088e6	0.710636	0.355318	−	0.934746i	$-0.384373\pi$
$607$	6.45088e6	0.710636	0.355318	+	0.934746i	$0.384373\pi$
$608$	1.75923e6	0.193003
$609$	0	0
$610$	3.91880e6	0.426411
$611$	177747.	0.0192619
$612$	0	0
$613$	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
$615$	0	0
$616$	2.24224e6	0.238084
$617$	−9.45501e6	−0.999882	−0.499941	−	0.866059i	$-0.666645\pi$
$617$	−9.45501e6	−0.999882	−0.499941	+	0.866059i	$0.666645\pi$
$618$	0	0
$619$	1.43145e6	0.150158	0.0750790	−	0.997178i	$-0.476079\pi$
$619$	1.43145e6	0.150158	0.0750790	+	0.997178i	$0.476079\pi$
$620$	−2.70240e6	−0.282339
$621$	0	0
$622$	8.59674e6	0.890960
$623$	−843584.	−0.0870780
$624$	0	0
$625$	390625.	0.0400000
$626$	1.06821e7	1.08948
$627$	0	0
$628$	−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
$633$	0	0
$634$	−1.00206e6	−0.0990077
$635$	5.47990e6	0.539310
$636$	0	0
$637$	794731.	0.0776018
$638$	1.30959e7	1.27375
$639$	0	0
$640$	409600.	0.0395285
$641$	1.76908e7	1.70060	0.850300	−	0.526298i	$-0.176420\pi$
$641$	1.76908e7	1.70060	0.850300	+	0.526298i	$0.176420\pi$
$642$	0	0
$643$	1.82748e7	1.74311	0.871556	−	0.490296i	$-0.163111\pi$
$643$	1.82748e7	1.74311	0.871556	+	0.490296i	$0.163111\pi$
$644$	−3.09680e6	−0.294238
$645$	0	0
$646$	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	$0.522873\pi$
$648$	0	0
$649$	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	$-0.362868\pi$
$653$	9.10088e6	0.835219	0.417610	+	0.908627i	$0.362868\pi$
$654$	0	0
$655$	−2.41705e6	−0.220132
$656$	−4.83226e6	−0.438420
$657$	0	0
$658$	105252.	0.00947689
$659$	430119.	0.0385811	0.0192906	−	0.999814i	$-0.493859\pi$
$659$	430119.	0.0385811	0.0192906	+	0.999814i	$0.493859\pi$
$660$	0	0
$661$	7.65248e6	0.681238	0.340619	−	0.940202i	$-0.389363\pi$
$661$	7.65248e6	0.681238	0.340619	+	0.940202i	$0.389363\pi$
$662$	−4.23595e6	−0.375670
$663$	0	0
$664$	2.40922e6	0.212058
$665$	−2.10455e6	−0.184546
$666$	0	0
$667$	−1.80870e7	−1.57418
$668$	8.68731e6	0.753259
$669$	0	0
$670$	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
$675$	0	0
$676$	−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	$0.698868\pi$
$678$	0	0
$679$	3.09558e6	0.257672
$680$	2.71840e6	0.225445
$681$	0	0
$682$	−1.93222e7	−1.59072
$683$	−2.29121e7	−1.87937	−0.939686	−	0.342040i	$-0.888882\pi$
$683$	−2.29121e7	−1.87937	−0.939686	+	0.342040i	$0.888882\pi$
$684$	0	0
$685$	4.68220e6	0.381262
$686$	470596.	0.0381802
$687$	0	0
$688$	578048.	0.0465578
$689$	3.63570e6	0.291770
$690$	0	0
$691$	−1.69127e7	−1.34747	−0.673734	−	0.738974i	$-0.735310\pi$
$691$	−1.69127e7	−1.34747	−0.673734	+	0.738974i	$0.735310\pi$
$692$	−5.93525e6	−0.471166
$693$	0	0
$694$	7.56562e6	0.596274
$695$	−4.42235e6	−0.347289
$696$	0	0
$697$	−3.20703e7	−2.50047
$698$	4.16927e6	0.323908
$699$	0	0
$700$	−490000.	−0.0377964
$701$	1.90087e7	1.46102	0.730510	−	0.682902i	$-0.239282\pi$
$701$	1.90087e7	1.46102	0.730510	+	0.682902i	$0.239282\pi$
$702$	0	0
$703$	2.83779e7	2.16567
$704$	2.92864e6	0.222707
$705$	0	0
$706$	−9.21235e6	−0.695598
$707$	−1.43325e6	−0.107838
$708$	0	0
$709$	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
$711$	0	0
$712$	−1.10182e6	−0.0814540
$713$	2.66862e7	1.96591
$714$	0	0
$715$	−5.91662e6	−0.432822
$716$	1.20668e7	0.879646
$717$	0	0
$718$	−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	$0.568687\pi$
$720$	0	0
$721$	7.31026e6	0.523715
$722$	−1.90170e6	−0.135768
$723$	0	0
$724$	4.86144e6	0.344682
$725$	−2.86188e6	−0.202211
$726$	0	0
$727$	1.73276e7	1.21591	0.607957	−	0.793970i	$-0.291989\pi$
$727$	1.73276e7	1.21591	0.607957	+	0.793970i	$0.291989\pi$
$728$	1.03802e6	0.0725898
$729$	0	0
$730$	−501800.	−0.0348517
$731$	3.83634e6	0.265536
$732$	0	0
$733$	1.39829e7	0.961255	0.480627	−	0.876925i	$-0.340409\pi$
$733$	1.39829e7	0.961255	0.480627	+	0.876925i	$0.340409\pi$
$734$	−378652.	−0.0259418
$735$	0	0
$736$	−4.04480e6	−0.275234
$737$	3.15744e6	0.214125
$738$	0	0
$739$	−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
$741$	0	0
$742$	2.15286e6	0.143551
$743$	−1.23126e7	−0.818236	−0.409118	−	0.912481i	$-0.634164\pi$
$743$	−1.23126e7	−0.818236	−0.409118	+	0.912481i	$0.634164\pi$
$744$	0	0
$745$	−4.97695e6	−0.328528
$746$	3.81414e6	0.250929
$747$	0	0
$748$	1.94366e7	1.27018
$749$	4.10336e6	0.267261
$750$	0	0
$751$	−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
$753$	0	0
$754$	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
$759$	0	0
$760$	−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	$0.562421\pi$
$762$	0	0
$763$	−5.16347e6	−0.321093
$764$	2.98034e6	0.184728
$765$	0	0
$766$	1.17454e7	0.723264
$767$	8.59144e6	0.527324
$768$	0	0
$769$	1.57888e7	0.962793	0.481397	−	0.876503i	$-0.340130\pi$
$769$	1.57888e7	0.962793	0.481397	+	0.876503i	$0.340130\pi$
$770$	−3.50350e6	−0.212949
$771$	0	0
$772$	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	$0.228226\pi$
$774$	0	0
$775$	4.22250e6	0.252531
$776$	4.04320e6	0.241030
$777$	0	0
$778$	6.81509e6	0.403667
$779$	3.24290e7	1.91465
$780$	0	0
$781$	2.27942e7	1.33720
$782$	−2.68442e7	−1.56976
$783$	0	0
$784$	614656.	0.0357143
$785$	1.80135e6	0.104334
$786$	0	0
$787$	−1.28020e6	−0.0736784	−0.0368392	−	0.999321i	$-0.511729\pi$
$787$	−1.28020e6	−0.0736784	−0.0368392	+	0.999321i	$0.511729\pi$
$788$	1.17819e7	0.675926
$789$	0	0
$790$	−2.79770e6	−0.159490
$791$	−6.01495e6	−0.341815
$792$	0	0
$793$	1.29712e7	0.732484
$794$	−4.76442e6	−0.268200
$795$	0	0
$796$	−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
$801$	0	0
$802$	−1.35332e7	−0.742959
$803$	−3.58787e6	−0.196358
$804$	0	0
$805$	4.83875e6	0.263174
$806$	−8.94494e6	−0.484998
$807$	0	0
$808$	−1.87200e6	−0.100874
$809$	1.70542e7	0.916138	0.458069	−	0.888917i	$-0.348541\pi$
$809$	1.70542e7	0.916138	0.458069	+	0.888917i	$0.348541\pi$
$810$	0	0
$811$	−2.21494e7	−1.18252	−0.591262	−	0.806480i	$-0.701370\pi$
$811$	−2.21494e7	−1.18252	−0.591262	+	0.806480i	$0.701370\pi$
$812$	3.58994e6	0.191072
$813$	0	0
$814$	4.72415e7	2.49898
$815$	−9.63335e6	−0.508023
$816$	0	0
$817$	−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	$-0.415732\pi$
$821$	1.01068e7	0.523307	0.261654	+	0.965162i	$0.415732\pi$
$822$	0	0
$823$	−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
$825$	0	0
$826$	5.08738e6	0.259444
$827$	2.48056e7	1.26121	0.630604	−	0.776105i	$-0.282807\pi$
$827$	2.48056e7	1.26121	0.630604	+	0.776105i	$0.282807\pi$
$828$	0	0
$829$	−1.19708e6	−0.0604976	−0.0302488	−	0.999542i	$-0.509630\pi$
$829$	−1.19708e6	−0.0604976	−0.0302488	+	0.999542i	$0.509630\pi$
$830$	−3.76440e6	−0.189671
$831$	0	0
$832$	1.35578e6	0.0679015
$833$	4.07930e6	0.203692
$834$	0	0
$835$	−1.35739e7	−0.673735
$836$	−1.96539e7	−0.972598
$837$	0	0
$838$	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
$843$	0	0
$844$	3.03250e6	0.146536
$845$	6.54330e6	0.315250
$846$	0	0
$847$	−1.71585e7	−0.821810
$848$	2.81190e6	0.134280
$849$	0	0
$850$	−4.24750e6	−0.201644
$851$	−6.52461e7	−3.08838
$852$	0	0
$853$	3.18237e7	1.49754	0.748769	−	0.662831i	$-0.230645\pi$
$853$	3.18237e7	1.49754	0.748769	+	0.662831i	$0.230645\pi$
$854$	7.68085e6	0.360383
$855$	0	0
$856$	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	$0.677761\pi$
$858$	0	0
$859$	−1.85966e7	−0.859907	−0.429953	−	0.902851i	$-0.641470\pi$
$859$	−1.85966e7	−0.859907	−0.429953	+	0.902851i	$0.641470\pi$
$860$	−903200.	−0.0416426
$861$	0	0
$862$	1.84740e7	0.846825
$863$	2.77046e7	1.26627	0.633133	−	0.774043i	$-0.281769\pi$
$863$	2.77046e7	1.26627	0.633133	+	0.774043i	$0.281769\pi$
$864$	0	0
$865$	9.27382e6	0.421423
$866$	−234424.	−0.0106220
$867$	0	0
$868$	−5.29670e6	−0.238620
$869$	−2.00036e7	−0.898582
$870$	0	0
$871$	1.46170e6	0.0652847
$872$	−6.74413e6	−0.300355
$873$	0	0
$874$	2.71444e7	1.20199
$875$	765625.	0.0338062
$876$	0	0
$877$	−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
$879$	0	0
$880$	−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
$885$	0	0
$886$	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	$0.668695\pi$
$888$	0	0
$889$	1.07406e7	0.455800
$890$	1.72160e6	0.0728546
$891$	0	0
$892$	−361552.	−0.0152145
$893$	−922566.	−0.0387141
$894$	0	0
$895$	−1.88543e7	−0.786779
$896$	802816.	0.0334077
$897$	0	0
$898$	−2.99365e7	−1.23883
$899$	−3.09357e7	−1.27662
$900$	0	0
$901$	1.86618e7	0.765847
$902$	5.39854e7	2.20933
$903$	0	0
$904$	−7.85626e6	−0.319738
$905$	−7.59600e6	−0.308293
$906$	0	0
$907$	−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
$909$	0	0
$910$	−1.62190e6	−0.0649263
$911$	−3.07573e6	−0.122787	−0.0613934	−	0.998114i	$-0.519554\pi$
$911$	−3.07573e6	−0.122787	−0.0613934	+	0.998114i	$0.519554\pi$
$912$	0	0
$913$	−2.69155e7	−1.06862
$914$	−681280.	−0.0269749
$915$	0	0
$916$	−1.36743e7	−0.538476
$917$	−4.73742e6	−0.186045
$918$	0	0
$919$	−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
$921$	0	0
$922$	−1.71474e7	−0.664310
$923$	1.05523e7	0.407701
$924$	0	0
$925$	−1.03238e7	−0.396719
$926$	−1.35327e7	−0.518629
$927$	0	0
$928$	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	$0.387909\pi$
$930$	0	0
$931$	−4.12492e6	−0.155970
$932$	−2.01309e7	−0.759144
$933$	0	0
$934$	2.07212e7	0.777225
$935$	−3.03696e7	−1.13608
$936$	0	0
$937$	−2.17350e7	−0.808744	−0.404372	−	0.914595i	$-0.632510\pi$
$937$	−2.17350e7	−0.808744	−0.404372	+	0.914595i	$0.632510\pi$
$938$	865536.	0.0321202
$939$	0	0
$940$	−214800.	−0.00792893
$941$	−1.86808e7	−0.687735	−0.343868	−	0.939018i	$-0.611737\pi$
$941$	−1.86808e7	−0.687735	−0.343868	+	0.939018i	$0.611737\pi$
$942$	0	0
$943$	−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	$-0.487034\pi$
$947$	2.24778e6	0.0814476	0.0407238	+	0.999170i	$0.487034\pi$
$948$	0	0
$949$	−1.66096e6	−0.0598678
$950$	4.29500e6	0.154402
$951$	0	0
$952$	5.32806e6	0.190536
$953$	3.73293e7	1.33143	0.665714	−	0.746207i	$-0.268127\pi$
$953$	3.73293e7	1.33143	0.665714	+	0.746207i	$0.268127\pi$
$954$	0	0
$955$	−4.65678e6	−0.165225
$956$	1.13053e7	0.400071
$957$	0	0
$958$	−3.50711e7	−1.23463
$959$	9.17711e6	0.322225
$960$	0	0
$961$	1.70144e7	0.594303
$962$	2.18698e7	0.761917
$963$	0	0
$964$	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
$969$	0	0
$970$	−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	$0.267556\pi$
$972$	0	0
$973$	−8.66781e6	−0.293513
$974$	−1.08062e6	−0.0364984
$975$	0	0
$976$	1.00321e7	0.337108
$977$	−3.03935e6	−0.101870	−0.0509348	−	0.998702i	$-0.516220\pi$
$977$	−3.03935e6	−0.101870	−0.0509348	+	0.998702i	$0.516220\pi$
$978$	0	0
$979$	1.23094e7	0.410470
$980$	−960400.	−0.0319438
$981$	0	0
$982$	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	$0.414972\pi$
$984$	0	0
$985$	−1.84092e7	−0.604567
$986$	3.11189e7	1.01937
$987$	0	0
$988$	−9.09853e6	−0.296537
$989$	8.91910e6	0.289955
$990$	0	0
$991$	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
$993$	0	0
$994$	6.24848e6	0.200590
$995$	1.20405e7	0.385555
$996$	0	0
$997$	−4.33287e7	−1.38051	−0.690253	−	0.723568i	$-0.742501\pi$
$997$	−4.33287e7	−1.38051	−0.690253	+	0.723568i	$0.742501\pi$
$998$	1.19430e7	0.379567
$999$	0	0

Twists

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

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