LMFDB - Embedded newform 630.6.a.i.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,6,Mod(1,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [1,4,0,16,-25,0,-49,64,0,-100,187] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$101.041806482$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	630.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+4.00000 q^{2} +16.0000 q^{4} -25.0000 q^{5} -49.0000 q^{7} +64.0000 q^{8} -100.000 q^{10} +187.000 q^{11} +627.000 q^{13} -196.000 q^{14} +256.000 q^{16} -1813.00 q^{17} +258.000 q^{19} -400.000 q^{20} +748.000 q^{22} -2970.00 q^{23} +625.000 q^{25} +2508.00 q^{26} -784.000 q^{28} -1299.00 q^{29} +1916.00 q^{31} +1024.00 q^{32} -7252.00 q^{34} +1225.00 q^{35} +6578.00 q^{37} +1032.00 q^{38} -1600.00 q^{40} -6676.00 q^{41} +3178.00 q^{43} +2992.00 q^{44} -11880.0 q^{46} +22001.0 q^{47} +2401.00 q^{49} +2500.00 q^{50} +10032.0 q^{52} -26168.0 q^{53} -4675.00 q^{55} -3136.00 q^{56} -5196.00 q^{58} -3932.00 q^{59} -48740.0 q^{61} +7664.00 q^{62} +4096.00 q^{64} -15675.0 q^{65} -44832.0 q^{67} -29008.0 q^{68} +4900.00 q^{70} -63736.0 q^{71} +60470.0 q^{73} +26312.0 q^{74} +4128.00 q^{76} -9163.00 q^{77} -43721.0 q^{79} -6400.00 q^{80} -26704.0 q^{82} -97276.0 q^{83} +45325.0 q^{85} +12712.0 q^{86} +11968.0 q^{88} -45560.0 q^{89} -30723.0 q^{91} -47520.0 q^{92} +88004.0 q^{94} -6450.00 q^{95} -57295.0 q^{97} +9604.00 q^{98} +O(q^{100})\)

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
$11$	187.000	0.465972	0.232986	−	0.972480i	$-0.425150\pi$
$11$	187.000	0.465972	0.232986	+	0.972480i	$0.425150\pi$
$12$	0	0
$13$	627.000	1.02899	0.514493	−	0.857495i	$-0.327980\pi$
$13$	627.000	1.02899	0.514493	+	0.857495i	$0.327980\pi$
$14$	−196.000	−0.267261
$15$	0	0
$16$	256.000	0.250000
$17$	−1813.00	−1.52151	−0.760756	−	0.649038i	$-0.775172\pi$
$17$	−1813.00	−1.52151	−0.760756	+	0.649038i	$0.775172\pi$
$18$	0	0
$19$	258.000	0.163959	0.0819796	−	0.996634i	$-0.473876\pi$
$19$	258.000	0.163959	0.0819796	+	0.996634i	$0.473876\pi$
$20$	−400.000	−0.223607
$21$	0	0
$22$	748.000	0.329492
$23$	−2970.00	−1.17068	−0.585338	−	0.810789i	$-0.699038\pi$
$23$	−2970.00	−1.17068	−0.585338	+	0.810789i	$0.699038\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	2508.00	0.727602
$27$	0	0
$28$	−784.000	−0.188982
$29$	−1299.00	−0.286823	−0.143412	−	0.989663i	$-0.545807\pi$
$29$	−1299.00	−0.286823	−0.143412	+	0.989663i	$0.545807\pi$
$30$	0	0
$31$	1916.00	0.358089	0.179045	−	0.983841i	$-0.442699\pi$
$31$	1916.00	0.358089	0.179045	+	0.983841i	$0.442699\pi$
$32$	1024.00	0.176777
$33$	0	0
$34$	−7252.00	−1.07587
$35$	1225.00	0.169031
$36$	0	0
$37$	6578.00	0.789932	0.394966	−	0.918696i	$-0.370756\pi$
$37$	6578.00	0.789932	0.394966	+	0.918696i	$0.370756\pi$
$38$	1032.00	0.115937
$39$	0	0
$40$	−1600.00	−0.158114
$41$	−6676.00	−0.620236	−0.310118	−	0.950698i	$-0.600368\pi$
$41$	−6676.00	−0.620236	−0.310118	+	0.950698i	$0.600368\pi$
$42$	0	0
$43$	3178.00	0.262109	0.131055	−	0.991375i	$-0.458164\pi$
$43$	3178.00	0.262109	0.131055	+	0.991375i	$0.458164\pi$
$44$	2992.00	0.232986
$45$	0	0
$46$	−11880.0	−0.827793
$47$	22001.0	1.45277	0.726387	−	0.687286i	$-0.241198\pi$
$47$	22001.0	1.45277	0.726387	+	0.687286i	$0.241198\pi$
$48$	0	0
$49$	2401.00	0.142857
$50$	2500.00	0.141421
$51$	0	0
$52$	10032.0	0.514493
$53$	−26168.0	−1.27962	−0.639810	−	0.768533i	$-0.720987\pi$
$53$	−26168.0	−1.27962	−0.639810	+	0.768533i	$0.720987\pi$
$54$	0	0
$55$	−4675.00	−0.208389
$56$	−3136.00	−0.133631
$57$	0	0
$58$	−5196.00	−0.202815
$59$	−3932.00	−0.147056	−0.0735281	−	0.997293i	$-0.523426\pi$
$59$	−3932.00	−0.147056	−0.0735281	+	0.997293i	$0.523426\pi$
$60$	0	0
$61$	−48740.0	−1.67711	−0.838554	−	0.544819i	$-0.816598\pi$
$61$	−48740.0	−1.67711	−0.838554	+	0.544819i	$0.816598\pi$
$62$	7664.00	0.253207
$63$	0	0
$64$	4096.00	0.125000
$65$	−15675.0	−0.460176
$66$	0	0
$67$	−44832.0	−1.22012	−0.610058	−	0.792357i	$-0.708854\pi$
$67$	−44832.0	−1.22012	−0.610058	+	0.792357i	$0.708854\pi$
$68$	−29008.0	−0.760756
$69$	0	0
$70$	4900.00	0.119523
$71$	−63736.0	−1.50051	−0.750255	−	0.661148i	$-0.770069\pi$
$71$	−63736.0	−1.50051	−0.750255	+	0.661148i	$0.770069\pi$
$72$	0	0
$73$	60470.0	1.32811	0.664053	−	0.747685i	$-0.268835\pi$
$73$	60470.0	1.32811	0.664053	+	0.747685i	$0.268835\pi$
$74$	26312.0	0.558566
$75$	0	0
$76$	4128.00	0.0819796
$77$	−9163.00	−0.176121
$78$	0	0
$79$	−43721.0	−0.788174	−0.394087	−	0.919073i	$-0.628939\pi$
$79$	−43721.0	−0.788174	−0.394087	+	0.919073i	$0.628939\pi$
$80$	−6400.00	−0.111803
$81$	0	0
$82$	−26704.0	−0.438573
$83$	−97276.0	−1.54992	−0.774962	−	0.632008i	$-0.782231\pi$
$83$	−97276.0	−1.54992	−0.774962	+	0.632008i	$0.782231\pi$
$84$	0	0
$85$	45325.0	0.680441
$86$	12712.0	0.185339
$87$	0	0
$88$	11968.0	0.164746
$89$	−45560.0	−0.609689	−0.304845	−	0.952402i	$-0.598605\pi$
$89$	−45560.0	−0.609689	−0.304845	+	0.952402i	$0.598605\pi$
$90$	0	0
$91$	−30723.0	−0.388920
$92$	−47520.0	−0.585338
$93$	0	0
$94$	88004.0	1.02727
$95$	−6450.00	−0.0733248
$96$	0	0
$97$	−57295.0	−0.618283	−0.309142	−	0.951016i	$-0.600042\pi$
$97$	−57295.0	−0.618283	−0.309142	+	0.951016i	$0.600042\pi$
$98$	9604.00	0.101015
$99$	0	0
$100$	10000.0	0.100000
$101$	44970.0	0.438651	0.219326	−	0.975652i	$-0.429614\pi$
$101$	44970.0	0.438651	0.219326	+	0.975652i	$0.429614\pi$
$102$	0	0
$103$	−101405.	−0.941817	−0.470908	−	0.882182i	$-0.656074\pi$
$103$	−101405.	−0.941817	−0.470908	+	0.882182i	$0.656074\pi$
$104$	40128.0	0.363801
$105$	0	0
$106$	−104672.	−0.904828
$107$	166002.	1.40170	0.700848	−	0.713311i	$-0.252805\pi$
$107$	166002.	1.40170	0.700848	+	0.713311i	$0.252805\pi$
$108$	0	0
$109$	8289.00	0.0668245	0.0334123	−	0.999442i	$-0.489363\pi$
$109$	8289.00	0.0668245	0.0334123	+	0.999442i	$0.489363\pi$
$110$	−18700.0	−0.147353
$111$	0	0
$112$	−12544.0	−0.0944911
$113$	−263206.	−1.93910	−0.969549	−	0.244898i	$-0.921245\pi$
$113$	−263206.	−1.93910	−0.969549	+	0.244898i	$0.921245\pi$
$114$	0	0
$115$	74250.0	0.523542
$116$	−20784.0	−0.143412
$117$	0	0
$118$	−15728.0	−0.103984
$119$	88837.0	0.575078
$120$	0	0
$121$	−126082.	−0.782870
$122$	−194960.	−1.18589
$123$	0	0
$124$	30656.0	0.179045
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	30052.0	0.165335	0.0826674	−	0.996577i	$-0.473656\pi$
$127$	30052.0	0.165335	0.0826674	+	0.996577i	$0.473656\pi$
$128$	16384.0	0.0883883
$129$	0	0
$130$	−62700.0	−0.325394
$131$	120050.	0.611201	0.305600	−	0.952160i	$-0.401143\pi$
$131$	120050.	0.611201	0.305600	+	0.952160i	$0.401143\pi$
$132$	0	0
$133$	−12642.0	−0.0619707
$134$	−179328.	−0.862752
$135$	0	0
$136$	−116032.	−0.537936
$137$	−31776.0	−0.144643	−0.0723216	−	0.997381i	$-0.523041\pi$
$137$	−31776.0	−0.144643	−0.0723216	+	0.997381i	$0.523041\pi$
$138$	0	0
$139$	−200162.	−0.878708	−0.439354	−	0.898314i	$-0.644793\pi$
$139$	−200162.	−0.878708	−0.439354	+	0.898314i	$0.644793\pi$
$140$	19600.0	0.0845154
$141$	0	0
$142$	−254944.	−1.06102
$143$	117249.	0.479478
$144$	0	0
$145$	32475.0	0.128271
$146$	241880.	0.939113
$147$	0	0
$148$	105248.	0.394966
$149$	−309642.	−1.14260	−0.571300	−	0.820741i	$-0.693561\pi$
$149$	−309642.	−1.14260	−0.571300	+	0.820741i	$0.693561\pi$
$150$	0	0
$151$	−208657.	−0.744716	−0.372358	−	0.928089i	$-0.621451\pi$
$151$	−208657.	−0.744716	−0.372358	+	0.928089i	$0.621451\pi$
$152$	16512.0	0.0579683
$153$	0	0
$154$	−36652.0	−0.124536
$155$	−47900.0	−0.160142
$156$	0	0
$157$	36010.0	0.116593	0.0582967	−	0.998299i	$-0.481433\pi$
$157$	36010.0	0.116593	0.0582967	+	0.998299i	$0.481433\pi$
$158$	−174884.	−0.557324
$159$	0	0
$160$	−25600.0	−0.0790569
$161$	145530.	0.442474
$162$	0	0
$163$	175670.	0.517879	0.258940	−	0.965893i	$-0.416627\pi$
$163$	175670.	0.517879	0.258940	+	0.965893i	$0.416627\pi$
$164$	−106816.	−0.310118
$165$	0	0
$166$	−389104.	−1.09596
$167$	157413.	0.436767	0.218383	−	0.975863i	$-0.429922\pi$
$167$	157413.	0.436767	0.218383	+	0.975863i	$0.429922\pi$
$168$	0	0
$169$	21836.0	0.0588107
$170$	181300.	0.481144
$171$	0	0
$172$	50848.0	0.131055
$173$	23471.0	0.0596233	0.0298117	−	0.999556i	$-0.490509\pi$
$173$	23471.0	0.0596233	0.0298117	+	0.999556i	$0.490509\pi$
$174$	0	0
$175$	−30625.0	−0.0755929
$176$	47872.0	0.116493
$177$	0	0
$178$	−182240.	−0.431116
$179$	−612228.	−1.42817	−0.714086	−	0.700058i	$-0.753158\pi$
$179$	−612228.	−1.42817	−0.714086	+	0.700058i	$0.753158\pi$
$180$	0	0
$181$	528832.	1.19983	0.599917	−	0.800062i	$-0.295200\pi$
$181$	528832.	1.19983	0.599917	+	0.800062i	$0.295200\pi$
$182$	−122892.	−0.275008
$183$	0	0
$184$	−190080.	−0.413897
$185$	−164450.	−0.353268
$186$	0	0
$187$	−339031.	−0.708982
$188$	352016.	0.726387
$189$	0	0
$190$	−25800.0	−0.0518484
$191$	−540369.	−1.07178	−0.535892	−	0.844287i	$-0.680024\pi$
$191$	−540369.	−1.07178	−0.535892	+	0.844287i	$0.680024\pi$
$192$	0	0
$193$	960320.	1.85576	0.927882	−	0.372874i	$-0.121628\pi$
$193$	960320.	1.85576	0.927882	+	0.372874i	$0.121628\pi$
$194$	−229180.	−0.437192
$195$	0	0
$196$	38416.0	0.0714286
$197$	−761944.	−1.39881	−0.699403	−	0.714728i	$-0.746551\pi$
$197$	−761944.	−1.39881	−0.699403	+	0.714728i	$0.746551\pi$
$198$	0	0
$199$	125084.	0.223908	0.111954	−	0.993713i	$-0.464289\pi$
$199$	125084.	0.223908	0.111954	+	0.993713i	$0.464289\pi$
$200$	40000.0	0.0707107
$201$	0	0
$202$	179880.	0.310173
$203$	63651.0	0.108409
$204$	0	0
$205$	166900.	0.277378
$206$	−405620.	−0.665965
$207$	0	0
$208$	160512.	0.257246
$209$	48246.0	0.0764004
$210$	0	0
$211$	627547.	0.970376	0.485188	−	0.874410i	$-0.338751\pi$
$211$	627547.	0.970376	0.485188	+	0.874410i	$0.338751\pi$
$212$	−418688.	−0.639810
$213$	0	0
$214$	664008.	0.991149
$215$	−79450.0	−0.117219
$216$	0	0
$217$	−93884.0	−0.135345
$218$	33156.0	0.0472521
$219$	0	0
$220$	−74800.0	−0.104195
$221$	−1.13675e6	−1.56561
$222$	0	0
$223$	−1.22110e6	−1.64433	−0.822166	−	0.569248i	$-0.807234\pi$
$223$	−1.22110e6	−1.64433	−0.822166	+	0.569248i	$0.807234\pi$
$224$	−50176.0	−0.0668153
$225$	0	0
$226$	−1.05282e6	−1.37115
$227$	−390547.	−0.503047	−0.251524	−	0.967851i	$-0.580932\pi$
$227$	−390547.	−0.503047	−0.251524	+	0.967851i	$0.580932\pi$
$228$	0	0
$229$	−712124.	−0.897360	−0.448680	−	0.893692i	$-0.648106\pi$
$229$	−712124.	−0.897360	−0.448680	+	0.893692i	$0.648106\pi$
$230$	297000.	0.370200
$231$	0	0
$232$	−83136.0	−0.101407
$233$	−561576.	−0.677671	−0.338835	−	0.940846i	$-0.610033\pi$
$233$	−561576.	−0.677671	−0.338835	+	0.940846i	$0.610033\pi$
$234$	0	0
$235$	−550025.	−0.649700
$236$	−62912.0	−0.0735281
$237$	0	0
$238$	355348.	0.406641
$239$	1.36084e6	1.54103	0.770515	−	0.637421i	$-0.219999\pi$
$239$	1.36084e6	1.54103	0.770515	+	0.637421i	$0.219999\pi$
$240$	0	0
$241$	530050.	0.587860	0.293930	−	0.955827i	$-0.405037\pi$
$241$	530050.	0.587860	0.293930	+	0.955827i	$0.405037\pi$
$242$	−504328.	−0.553573
$243$	0	0
$244$	−779840.	−0.838554
$245$	−60025.0	−0.0638877
$246$	0	0
$247$	161766.	0.168712
$248$	122624.	0.126604
$249$	0	0
$250$	−62500.0	−0.0632456
$251$	−990330.	−0.992192	−0.496096	−	0.868268i	$-0.665234\pi$
$251$	−990330.	−0.992192	−0.496096	+	0.868268i	$0.665234\pi$
$252$	0	0
$253$	−555390.	−0.545503
$254$	120208.	0.116909
$255$	0	0
$256$	65536.0	0.0625000
$257$	1.81643e6	1.71548	0.857740	−	0.514083i	$-0.171868\pi$
$257$	1.81643e6	1.71548	0.857740	+	0.514083i	$0.171868\pi$
$258$	0	0
$259$	−322322.	−0.298566
$260$	−250800.	−0.230088
$261$	0	0
$262$	480200.	0.432184
$263$	1.95847e6	1.74594	0.872968	−	0.487777i	$-0.162192\pi$
$263$	1.95847e6	1.74594	0.872968	+	0.487777i	$0.162192\pi$
$264$	0	0
$265$	654200.	0.572263
$266$	−50568.0	−0.0438199
$267$	0	0
$268$	−717312.	−0.610058
$269$	−218034.	−0.183715	−0.0918573	−	0.995772i	$-0.529280\pi$
$269$	−218034.	−0.183715	−0.0918573	+	0.995772i	$0.529280\pi$
$270$	0	0
$271$	1.26265e6	1.04438	0.522192	−	0.852828i	$-0.325114\pi$
$271$	1.26265e6	1.04438	0.522192	+	0.852828i	$0.325114\pi$
$272$	−464128.	−0.380378
$273$	0	0
$274$	−127104.	−0.102278
$275$	116875.	0.0931944
$276$	0	0
$277$	−1.10264e6	−0.863443	−0.431721	−	0.902007i	$-0.642094\pi$
$277$	−1.10264e6	−0.863443	−0.431721	+	0.902007i	$0.642094\pi$
$278$	−800648.	−0.621340
$279$	0	0
$280$	78400.0	0.0597614
$281$	998213.	0.754149	0.377075	−	0.926183i	$-0.376930\pi$
$281$	998213.	0.754149	0.377075	+	0.926183i	$0.376930\pi$
$282$	0	0
$283$	−386371.	−0.286773	−0.143387	−	0.989667i	$-0.545799\pi$
$283$	−386371.	−0.286773	−0.143387	+	0.989667i	$0.545799\pi$
$284$	−1.01978e6	−0.750255
$285$	0	0
$286$	468996.	0.339042
$287$	327124.	0.234427
$288$	0	0
$289$	1.86711e6	1.31500
$290$	129900.	0.0907014
$291$	0	0
$292$	967520.	0.664053
$293$	783571.	0.533224	0.266612	−	0.963804i	$-0.414096\pi$
$293$	783571.	0.533224	0.266612	+	0.963804i	$0.414096\pi$
$294$	0	0
$295$	98300.0	0.0657656
$296$	420992.	0.279283
$297$	0	0
$298$	−1.23857e6	−0.807940
$299$	−1.86219e6	−1.20461
$300$	0	0
$301$	−155722.	−0.0990681
$302$	−834628.	−0.526594
$303$	0	0
$304$	66048.0	0.0409898
$305$	1.21850e6	0.750025
$306$	0	0
$307$	2.81773e6	1.70629	0.853147	−	0.521670i	$-0.174691\pi$
$307$	2.81773e6	1.70629	0.853147	+	0.521670i	$0.174691\pi$
$308$	−146608.	−0.0880604
$309$	0	0
$310$	−191600.	−0.113238
$311$	847398.	0.496806	0.248403	−	0.968657i	$-0.420094\pi$
$311$	847398.	0.496806	0.248403	+	0.968657i	$0.420094\pi$
$312$	0	0
$313$	364955.	0.210561	0.105281	−	0.994443i	$-0.466426\pi$
$313$	364955.	0.210561	0.105281	+	0.994443i	$0.466426\pi$
$314$	144040.	0.0824440
$315$	0	0
$316$	−699536.	−0.394087
$317$	−1.93744e6	−1.08288	−0.541439	−	0.840740i	$-0.682120\pi$
$317$	−1.93744e6	−1.08288	−0.541439	+	0.840740i	$0.682120\pi$
$318$	0	0
$319$	−242913.	−0.133652
$320$	−102400.	−0.0559017
$321$	0	0
$322$	582120.	0.312876
$323$	−467754.	−0.249466
$324$	0	0
$325$	391875.	0.205797
$326$	702680.	0.366196
$327$	0	0
$328$	−427264.	−0.219286
$329$	−1.07805e6	−0.549097
$330$	0	0
$331$	−61460.0	−0.0308335	−0.0154167	−	0.999881i	$-0.504907\pi$
$331$	−61460.0	−0.0308335	−0.0154167	+	0.999881i	$0.504907\pi$
$332$	−1.55642e6	−0.774962
$333$	0	0
$334$	629652.	0.308841
$335$	1.12080e6	0.545652
$336$	0	0
$337$	−3.74116e6	−1.79445	−0.897225	−	0.441574i	$-0.854420\pi$
$337$	−3.74116e6	−1.79445	−0.897225	+	0.441574i	$0.854420\pi$
$338$	87344.0	0.0415854
$339$	0	0
$340$	725200.	0.340221
$341$	358292.	0.166860
$342$	0	0
$343$	−117649.	−0.0539949
$344$	203392.	0.0926697
$345$	0	0
$346$	93884.0	0.0421601
$347$	−211334.	−0.0942206	−0.0471103	−	0.998890i	$-0.515001\pi$
$347$	−211334.	−0.0942206	−0.0471103	+	0.998890i	$0.515001\pi$
$348$	0	0
$349$	3.39558e6	1.49228	0.746140	−	0.665789i	$-0.231905\pi$
$349$	3.39558e6	1.49228	0.746140	+	0.665789i	$0.231905\pi$
$350$	−122500.	−0.0534522
$351$	0	0
$352$	191488.	0.0823730
$353$	3.88094e6	1.65768	0.828838	−	0.559489i	$-0.189003\pi$
$353$	3.88094e6	1.65768	0.828838	+	0.559489i	$0.189003\pi$
$354$	0	0
$355$	1.59340e6	0.671049
$356$	−728960.	−0.304845
$357$	0	0
$358$	−2.44891e6	−1.00987
$359$	−3.24210e6	−1.32767	−0.663836	−	0.747878i	$-0.731073\pi$
$359$	−3.24210e6	−1.32767	−0.663836	+	0.747878i	$0.731073\pi$
$360$	0	0
$361$	−2.40954e6	−0.973117
$362$	2.11533e6	0.848411
$363$	0	0
$364$	−491568.	−0.194460
$365$	−1.51175e6	−0.593947
$366$	0	0
$367$	1.44430e6	0.559749	0.279874	−	0.960037i	$-0.409707\pi$
$367$	1.44430e6	0.559749	0.279874	+	0.960037i	$0.409707\pi$
$368$	−760320.	−0.292669
$369$	0	0
$370$	−657800.	−0.249798
$371$	1.28223e6	0.483651
$372$	0	0
$373$	3.43542e6	1.27852	0.639260	−	0.768991i	$-0.279241\pi$
$373$	3.43542e6	1.27852	0.639260	+	0.768991i	$0.279241\pi$
$374$	−1.35612e6	−0.501326
$375$	0	0
$376$	1.40806e6	0.513633
$377$	−814473.	−0.295137
$378$	0	0
$379$	−1.68635e6	−0.603044	−0.301522	−	0.953459i	$-0.597495\pi$
$379$	−1.68635e6	−0.603044	−0.301522	+	0.953459i	$0.597495\pi$
$380$	−103200.	−0.0366624
$381$	0	0
$382$	−2.16148e6	−0.757865
$383$	−2.64354e6	−0.920850	−0.460425	−	0.887699i	$-0.652303\pi$
$383$	−2.64354e6	−0.920850	−0.460425	+	0.887699i	$0.652303\pi$
$384$	0	0
$385$	229075.	0.0787637
$386$	3.84128e6	1.31222
$387$	0	0
$388$	−916720.	−0.309142
$389$	452099.	0.151481	0.0757407	−	0.997128i	$-0.475868\pi$
$389$	452099.	0.151481	0.0757407	+	0.997128i	$0.475868\pi$
$390$	0	0
$391$	5.38461e6	1.78120
$392$	153664.	0.0505076
$393$	0	0
$394$	−3.04778e6	−0.989105
$395$	1.09302e6	0.352482
$396$	0	0
$397$	−1.95530e6	−0.622641	−0.311321	−	0.950305i	$-0.600771\pi$
$397$	−1.95530e6	−0.622641	−0.311321	+	0.950305i	$0.600771\pi$
$398$	500336.	0.158327
$399$	0	0
$400$	160000.	0.0500000
$401$	4.76737e6	1.48053	0.740266	−	0.672314i	$-0.234700\pi$
$401$	4.76737e6	1.48053	0.740266	+	0.672314i	$0.234700\pi$
$402$	0	0
$403$	1.20133e6	0.368469
$404$	719520.	0.219326
$405$	0	0
$406$	254604.	0.0766567
$407$	1.23009e6	0.368086
$408$	0	0
$409$	−4.13199e6	−1.22138	−0.610690	−	0.791870i	$-0.709108\pi$
$409$	−4.13199e6	−1.22138	−0.610690	+	0.791870i	$0.709108\pi$
$410$	667600.	0.196136
$411$	0	0
$412$	−1.62248e6	−0.470908
$413$	192668.	0.0555820
$414$	0	0
$415$	2.43190e6	0.693147
$416$	642048.	0.181901
$417$	0	0
$418$	192984.	0.0540232
$419$	−190512.	−0.0530136	−0.0265068	−	0.999649i	$-0.508438\pi$
$419$	−190512.	−0.0530136	−0.0265068	+	0.999649i	$0.508438\pi$
$420$	0	0
$421$	−5.19186e6	−1.42764	−0.713818	−	0.700332i	$-0.753035\pi$
$421$	−5.19186e6	−1.42764	−0.713818	+	0.700332i	$0.753035\pi$
$422$	2.51019e6	0.686160
$423$	0	0
$424$	−1.67475e6	−0.452414
$425$	−1.13312e6	−0.304302
$426$	0	0
$427$	2.38826e6	0.633887
$428$	2.65603e6	0.700848
$429$	0	0
$430$	−317800.	−0.0828863
$431$	4.21781e6	1.09369	0.546845	−	0.837234i	$-0.315829\pi$
$431$	4.21781e6	1.09369	0.546845	+	0.837234i	$0.315829\pi$
$432$	0	0
$433$	−4.86027e6	−1.24578	−0.622890	−	0.782310i	$-0.714041\pi$
$433$	−4.86027e6	−1.24578	−0.622890	+	0.782310i	$0.714041\pi$
$434$	−375536.	−0.0957034
$435$	0	0
$436$	132624.	0.0334123
$437$	−766260.	−0.191943
$438$	0	0
$439$	−2.03113e6	−0.503011	−0.251505	−	0.967856i	$-0.580926\pi$
$439$	−2.03113e6	−0.503011	−0.251505	+	0.967856i	$0.580926\pi$
$440$	−299200.	−0.0736767
$441$	0	0
$442$	−4.54700e6	−1.10706
$443$	−2.84199e6	−0.688038	−0.344019	−	0.938963i	$-0.611789\pi$
$443$	−2.84199e6	−0.688038	−0.344019	+	0.938963i	$0.611789\pi$
$444$	0	0
$445$	1.13900e6	0.272661
$446$	−4.88440e6	−1.16272
$447$	0	0
$448$	−200704.	−0.0472456
$449$	4.59682e6	1.07607	0.538037	−	0.842921i	$-0.319166\pi$
$449$	4.59682e6	1.07607	0.538037	+	0.842921i	$0.319166\pi$
$450$	0	0
$451$	−1.24841e6	−0.289012
$452$	−4.21130e6	−0.969549
$453$	0	0
$454$	−1.56219e6	−0.355708
$455$	768075.	0.173930
$456$	0	0
$457$	4.93367e6	1.10504	0.552522	−	0.833498i	$-0.313665\pi$
$457$	4.93367e6	1.10504	0.552522	+	0.833498i	$0.313665\pi$
$458$	−2.84850e6	−0.634530
$459$	0	0
$460$	1.18800e6	0.261771
$461$	4.75667e6	1.04244	0.521220	−	0.853422i	$-0.325477\pi$
$461$	4.75667e6	1.04244	0.521220	+	0.853422i	$0.325477\pi$
$462$	0	0
$463$	4.08619e6	0.885862	0.442931	−	0.896556i	$-0.353939\pi$
$463$	4.08619e6	0.885862	0.442931	+	0.896556i	$0.353939\pi$
$464$	−332544.	−0.0717058
$465$	0	0
$466$	−2.24630e6	−0.479186
$467$	4.15932e6	0.882531	0.441266	−	0.897377i	$-0.354530\pi$
$467$	4.15932e6	0.882531	0.441266	+	0.897377i	$0.354530\pi$
$468$	0	0
$469$	2.19677e6	0.461160
$470$	−2.20010e6	−0.459407
$471$	0	0
$472$	−251648.	−0.0519922
$473$	594286.	0.122136
$474$	0	0
$475$	161250.	0.0327918
$476$	1.42139e6	0.287539
$477$	0	0
$478$	5.44335e6	1.08967
$479$	3.36040e6	0.669195	0.334597	−	0.942361i	$-0.391400\pi$
$479$	3.36040e6	0.669195	0.334597	+	0.942361i	$0.391400\pi$
$480$	0	0
$481$	4.12441e6	0.812828
$482$	2.12020e6	0.415680
$483$	0	0
$484$	−2.01731e6	−0.391435
$485$	1.43238e6	0.276505
$486$	0	0
$487$	7.05243e6	1.34746	0.673730	−	0.738977i	$-0.264691\pi$
$487$	7.05243e6	1.34746	0.673730	+	0.738977i	$0.264691\pi$
$488$	−3.11936e6	−0.592947
$489$	0	0
$490$	−240100.	−0.0451754
$491$	83937.0	0.0157127	0.00785633	−	0.999969i	$-0.497499\pi$
$491$	83937.0	0.0157127	0.00785633	+	0.999969i	$0.497499\pi$
$492$	0	0
$493$	2.35509e6	0.436405
$494$	647064.	0.119297
$495$	0	0
$496$	490496.	0.0895223
$497$	3.12306e6	0.567140
$498$	0	0
$499$	−7.10526e6	−1.27741	−0.638703	−	0.769454i	$-0.720529\pi$
$499$	−7.10526e6	−1.27741	−0.638703	+	0.769454i	$0.720529\pi$
$500$	−250000.	−0.0447214
$501$	0	0
$502$	−3.96132e6	−0.701586
$503$	−2.89147e6	−0.509564	−0.254782	−	0.966999i	$-0.582004\pi$
$503$	−2.89147e6	−0.509564	−0.254782	+	0.966999i	$0.582004\pi$
$504$	0	0
$505$	−1.12425e6	−0.196171
$506$	−2.22156e6	−0.385729
$507$	0	0
$508$	480832.	0.0826674
$509$	−1.03548e6	−0.177153	−0.0885764	−	0.996069i	$-0.528232\pi$
$509$	−1.03548e6	−0.177153	−0.0885764	+	0.996069i	$0.528232\pi$
$510$	0	0
$511$	−2.96303e6	−0.501977
$512$	262144.	0.0441942
$513$	0	0
$514$	7.26572e6	1.21303
$515$	2.53513e6	0.421193
$516$	0	0
$517$	4.11419e6	0.676952
$518$	−1.28929e6	−0.211118
$519$	0	0
$520$	−1.00320e6	−0.162697
$521$	7.49715e6	1.21005	0.605023	−	0.796208i	$-0.293164\pi$
$521$	7.49715e6	1.21005	0.605023	+	0.796208i	$0.293164\pi$
$522$	0	0
$523$	3.53223e6	0.564670	0.282335	−	0.959316i	$-0.408891\pi$
$523$	3.53223e6	0.564670	0.282335	+	0.959316i	$0.408891\pi$
$524$	1.92080e6	0.305600
$525$	0	0
$526$	7.83390e6	1.23456
$527$	−3.47371e6	−0.544837
$528$	0	0
$529$	2.38456e6	0.370483
$530$	2.61680e6	0.404651
$531$	0	0
$532$	−202272.	−0.0309854
$533$	−4.18585e6	−0.638213
$534$	0	0
$535$	−4.15005e6	−0.626858
$536$	−2.86925e6	−0.431376
$537$	0	0
$538$	−872136.	−0.129906
$539$	448987.	0.0665674
$540$	0	0
$541$	−4.99188e6	−0.733281	−0.366641	−	0.930363i	$-0.619492\pi$
$541$	−4.99188e6	−0.733281	−0.366641	+	0.930363i	$0.619492\pi$
$542$	5.05061e6	0.738491
$543$	0	0
$544$	−1.85651e6	−0.268968
$545$	−207225.	−0.0298848
$546$	0	0
$547$	5.12634e6	0.732553	0.366277	−	0.930506i	$-0.380632\pi$
$547$	5.12634e6	0.732553	0.366277	+	0.930506i	$0.380632\pi$
$548$	−508416.	−0.0723216
$549$	0	0
$550$	467500.	0.0658984
$551$	−335142.	−0.0470273
$552$	0	0
$553$	2.14233e6	0.297902
$554$	−4.41055e6	−0.610546
$555$	0	0
$556$	−3.20259e6	−0.439354
$557$	−8.86866e6	−1.21121	−0.605606	−	0.795765i	$-0.707069\pi$
$557$	−8.86866e6	−1.21121	−0.605606	+	0.795765i	$0.707069\pi$
$558$	0	0
$559$	1.99261e6	0.269707
$560$	313600.	0.0422577
$561$	0	0
$562$	3.99285e6	0.533264
$563$	−9.07277e6	−1.20634	−0.603169	−	0.797613i	$-0.706096\pi$
$563$	−9.07277e6	−1.20634	−0.603169	+	0.797613i	$0.706096\pi$
$564$	0	0
$565$	6.58015e6	0.867191
$566$	−1.54548e6	−0.202779
$567$	0	0
$568$	−4.07910e6	−0.530510
$569$	−2.08310e6	−0.269730	−0.134865	−	0.990864i	$-0.543060\pi$
$569$	−2.08310e6	−0.269730	−0.134865	+	0.990864i	$0.543060\pi$
$570$	0	0
$571$	−5.46368e6	−0.701286	−0.350643	−	0.936509i	$-0.614037\pi$
$571$	−5.46368e6	−0.701286	−0.350643	+	0.936509i	$0.614037\pi$
$572$	1.87598e6	0.239739
$573$	0	0
$574$	1.30850e6	0.165765
$575$	−1.85625e6	−0.234135
$576$	0	0
$577$	7.66246e6	0.958140	0.479070	−	0.877777i	$-0.340974\pi$
$577$	7.66246e6	0.958140	0.479070	+	0.877777i	$0.340974\pi$
$578$	7.46845e6	0.929845
$579$	0	0
$580$	519600.	0.0641356
$581$	4.76652e6	0.585816
$582$	0	0
$583$	−4.89342e6	−0.596267
$584$	3.87008e6	0.469556
$585$	0	0
$586$	3.13428e6	0.377046
$587$	1.57465e7	1.88620	0.943100	−	0.332510i	$-0.107896\pi$
$587$	1.57465e7	1.88620	0.943100	+	0.332510i	$0.107896\pi$
$588$	0	0
$589$	494328.	0.0587120
$590$	393200.	0.0465033
$591$	0	0
$592$	1.68397e6	0.197483
$593$	1.62409e7	1.89658	0.948292	−	0.317398i	$-0.102809\pi$
$593$	1.62409e7	1.89658	0.948292	+	0.317398i	$0.102809\pi$
$594$	0	0
$595$	−2.22093e6	−0.257183
$596$	−4.95427e6	−0.571300
$597$	0	0
$598$	−7.44876e6	−0.851787
$599$	1.90793e6	0.217268	0.108634	−	0.994082i	$-0.465352\pi$
$599$	1.90793e6	0.217268	0.108634	+	0.994082i	$0.465352\pi$
$600$	0	0
$601$	3.52970e6	0.398613	0.199306	−	0.979937i	$-0.436131\pi$
$601$	3.52970e6	0.398613	0.199306	+	0.979937i	$0.436131\pi$
$602$	−622888.	−0.0700517
$603$	0	0
$604$	−3.33851e6	−0.372358
$605$	3.15205e6	0.350110
$606$	0	0
$607$	3.37799e6	0.372123	0.186061	−	0.982538i	$-0.440428\pi$
$607$	3.37799e6	0.372123	0.186061	+	0.982538i	$0.440428\pi$
$608$	264192.	0.0289842
$609$	0	0
$610$	4.87400e6	0.530348
$611$	1.37946e7	1.49488
$612$	0	0
$613$	1.20412e6	0.129425	0.0647127	−	0.997904i	$-0.479387\pi$
$613$	1.20412e6	0.129425	0.0647127	+	0.997904i	$0.479387\pi$
$614$	1.12709e7	1.20653
$615$	0	0
$616$	−586432.	−0.0622681
$617$	5.47330e6	0.578810	0.289405	−	0.957207i	$-0.406543\pi$
$617$	5.47330e6	0.578810	0.289405	+	0.957207i	$0.406543\pi$
$618$	0	0
$619$	3.22662e6	0.338471	0.169236	−	0.985576i	$-0.445870\pi$
$619$	3.22662e6	0.338471	0.169236	+	0.985576i	$0.445870\pi$
$620$	−766400.	−0.0800712
$621$	0	0
$622$	3.38959e6	0.351295
$623$	2.23244e6	0.230441
$624$	0	0
$625$	390625.	0.0400000
$626$	1.45982e6	0.148889
$627$	0	0
$628$	576160.	0.0582967
$629$	−1.19259e7	−1.20189
$630$	0	0
$631$	1.36282e7	1.36259	0.681297	−	0.732007i	$-0.261416\pi$
$631$	1.36282e7	1.36259	0.681297	+	0.732007i	$0.261416\pi$
$632$	−2.79814e6	−0.278662
$633$	0	0
$634$	−7.74975e6	−0.765711
$635$	−751300.	−0.0739399
$636$	0	0
$637$	1.50543e6	0.146998
$638$	−971652.	−0.0945059
$639$	0	0
$640$	−409600.	−0.0395285
$641$	1.92472e7	1.85021	0.925106	−	0.379710i	$-0.123976\pi$
$641$	1.92472e7	1.85021	0.925106	+	0.379710i	$0.123976\pi$
$642$	0	0
$643$	−1.28399e7	−1.22472	−0.612358	−	0.790580i	$-0.709779\pi$
$643$	−1.28399e7	−1.22472	−0.612358	+	0.790580i	$0.709779\pi$
$644$	2.32848e6	0.221237
$645$	0	0
$646$	−1.87102e6	−0.176399
$647$	−2.00233e7	−1.88050	−0.940251	−	0.340481i	$-0.889410\pi$
$647$	−2.00233e7	−1.88050	−0.940251	+	0.340481i	$0.889410\pi$
$648$	0	0
$649$	−735284.	−0.0685241
$650$	1.56750e6	0.145520
$651$	0	0
$652$	2.81072e6	0.258940
$653$	7.23655e6	0.664124	0.332062	−	0.943258i	$-0.392256\pi$
$653$	7.23655e6	0.664124	0.332062	+	0.943258i	$0.392256\pi$
$654$	0	0
$655$	−3.00125e6	−0.273337
$656$	−1.70906e6	−0.155059
$657$	0	0
$658$	−4.31220e6	−0.388270
$659$	−1.42474e7	−1.27798	−0.638989	−	0.769216i	$-0.720647\pi$
$659$	−1.42474e7	−1.27798	−0.638989	+	0.769216i	$0.720647\pi$
$660$	0	0
$661$	1.49265e7	1.32878	0.664391	−	0.747385i	$-0.268691\pi$
$661$	1.49265e7	1.32878	0.664391	+	0.747385i	$0.268691\pi$
$662$	−245840.	−0.0218026
$663$	0	0
$664$	−6.22566e6	−0.547981
$665$	316050.	0.0277142
$666$	0	0
$667$	3.85803e6	0.335777
$668$	2.51861e6	0.218383
$669$	0	0
$670$	4.48320e6	0.385835
$671$	−9.11438e6	−0.781485
$672$	0	0
$673$	−1.55062e7	−1.31967	−0.659837	−	0.751409i	$-0.729375\pi$
$673$	−1.55062e7	−1.31967	−0.659837	+	0.751409i	$0.729375\pi$
$674$	−1.49646e7	−1.26887
$675$	0	0
$676$	349376.	0.0294053
$677$	7.80065e6	0.654122	0.327061	−	0.945003i	$-0.393942\pi$
$677$	7.80065e6	0.654122	0.327061	+	0.945003i	$0.393942\pi$
$678$	0	0
$679$	2.80745e6	0.233689
$680$	2.90080e6	0.240572
$681$	0	0
$682$	1.43317e6	0.117988
$683$	−1.58547e7	−1.30049	−0.650243	−	0.759727i	$-0.725333\pi$
$683$	−1.58547e7	−1.30049	−0.650243	+	0.759727i	$0.725333\pi$
$684$	0	0
$685$	794400.	0.0646864
$686$	−470596.	−0.0381802
$687$	0	0
$688$	813568.	0.0655274
$689$	−1.64073e7	−1.31671
$690$	0	0
$691$	2.03656e7	1.62257	0.811284	−	0.584652i	$-0.198769\pi$
$691$	2.03656e7	1.62257	0.811284	+	0.584652i	$0.198769\pi$
$692$	375536.	0.0298117
$693$	0	0
$694$	−845336.	−0.0666240
$695$	5.00405e6	0.392970
$696$	0	0
$697$	1.21036e7	0.943696
$698$	1.35823e7	1.05520
$699$	0	0
$700$	−490000.	−0.0377964
$701$	−2.48036e7	−1.90643	−0.953213	−	0.302300i	$-0.902246\pi$
$701$	−2.48036e7	−1.90643	−0.953213	+	0.302300i	$0.902246\pi$
$702$	0	0
$703$	1.69712e6	0.129517
$704$	765952.	0.0582465
$705$	0	0
$706$	1.55237e7	1.17215
$707$	−2.20353e6	−0.165795
$708$	0	0
$709$	1.81917e7	1.35912	0.679560	−	0.733620i	$-0.262171\pi$
$709$	1.81917e7	1.35912	0.679560	+	0.733620i	$0.262171\pi$
$710$	6.37360e6	0.474503
$711$	0	0
$712$	−2.91584e6	−0.215558
$713$	−5.69052e6	−0.419207
$714$	0	0
$715$	−2.93122e6	−0.214429
$716$	−9.79565e6	−0.714086
$717$	0	0
$718$	−1.29684e7	−0.938806
$719$	1.66202e7	1.19899	0.599493	−	0.800380i	$-0.295369\pi$
$719$	1.66202e7	1.19899	0.599493	+	0.800380i	$0.295369\pi$
$720$	0	0
$721$	4.96884e6	0.355973
$722$	−9.63814e6	−0.688098
$723$	0	0
$724$	8.46131e6	0.599917
$725$	−811875.	−0.0573646
$726$	0	0
$727$	−1.57591e7	−1.10585	−0.552925	−	0.833231i	$-0.686489\pi$
$727$	−1.57591e7	−1.10585	−0.552925	+	0.833231i	$0.686489\pi$
$728$	−1.96627e6	−0.137504
$729$	0	0
$730$	−6.04700e6	−0.419984
$731$	−5.76171e6	−0.398803
$732$	0	0
$733$	−2.15238e6	−0.147965	−0.0739827	−	0.997260i	$-0.523571\pi$
$733$	−2.15238e6	−0.147965	−0.0739827	+	0.997260i	$0.523571\pi$
$734$	5.77721e6	0.395802
$735$	0	0
$736$	−3.04128e6	−0.206948
$737$	−8.38358e6	−0.568540
$738$	0	0
$739$	−2.27267e7	−1.53083	−0.765413	−	0.643540i	$-0.777465\pi$
$739$	−2.27267e7	−1.53083	−0.765413	+	0.643540i	$0.777465\pi$
$740$	−2.63120e6	−0.176634
$741$	0	0
$742$	5.12893e6	0.341993
$743$	−1.21153e7	−0.805123	−0.402561	−	0.915393i	$-0.631880\pi$
$743$	−1.21153e7	−0.805123	−0.402561	+	0.915393i	$0.631880\pi$
$744$	0	0
$745$	7.74105e6	0.510986
$746$	1.37417e7	0.904050
$747$	0	0
$748$	−5.42450e6	−0.354491
$749$	−8.13410e6	−0.529791
$750$	0	0
$751$	−2.07590e7	−1.34310	−0.671549	−	0.740961i	$-0.734371\pi$
$751$	−2.07590e7	−1.34310	−0.671549	+	0.740961i	$0.734371\pi$
$752$	5.63226e6	0.363193
$753$	0	0
$754$	−3.25789e6	−0.208693
$755$	5.21642e6	0.333047
$756$	0	0
$757$	−1.86222e7	−1.18111	−0.590556	−	0.806997i	$-0.701091\pi$
$757$	−1.86222e7	−1.18111	−0.590556	+	0.806997i	$0.701091\pi$
$758$	−6.74539e6	−0.426417
$759$	0	0
$760$	−412800.	−0.0259242
$761$	−2.65336e7	−1.66087	−0.830434	−	0.557117i	$-0.811907\pi$
$761$	−2.65336e7	−1.66087	−0.830434	+	0.557117i	$0.811907\pi$
$762$	0	0
$763$	−406161.	−0.0252573
$764$	−8.64590e6	−0.535892
$765$	0	0
$766$	−1.05742e7	−0.651139
$767$	−2.46536e6	−0.151319
$768$	0	0
$769$	−2.01595e7	−1.22931	−0.614657	−	0.788794i	$-0.710706\pi$
$769$	−2.01595e7	−1.22931	−0.614657	+	0.788794i	$0.710706\pi$
$770$	916300.	0.0556943
$771$	0	0
$772$	1.53651e7	0.927882
$773$	5.86488e6	0.353029	0.176514	−	0.984298i	$-0.443518\pi$
$773$	5.86488e6	0.353029	0.176514	+	0.984298i	$0.443518\pi$
$774$	0	0
$775$	1.19750e6	0.0716178
$776$	−3.66688e6	−0.218596
$777$	0	0
$778$	1.80840e6	0.107114
$779$	−1.72241e6	−0.101693
$780$	0	0
$781$	−1.19186e7	−0.699196
$782$	2.15384e7	1.25950
$783$	0	0
$784$	614656.	0.0357143
$785$	−900250.	−0.0521422
$786$	0	0
$787$	−1.63347e6	−0.0940100	−0.0470050	−	0.998895i	$-0.514968\pi$
$787$	−1.63347e6	−0.0940100	−0.0470050	+	0.998895i	$0.514968\pi$
$788$	−1.21911e7	−0.699403
$789$	0	0
$790$	4.37210e6	0.249243
$791$	1.28971e7	0.732910
$792$	0	0
$793$	−3.05600e7	−1.72572
$794$	−7.82121e6	−0.440274
$795$	0	0
$796$	2.00134e6	0.111954
$797$	−2.07673e7	−1.15807	−0.579034	−	0.815303i	$-0.696570\pi$
$797$	−2.07673e7	−1.15807	−0.579034	+	0.815303i	$0.696570\pi$
$798$	0	0
$799$	−3.98878e7	−2.21041
$800$	640000.	0.0353553
$801$	0	0
$802$	1.90695e7	1.04689
$803$	1.13079e7	0.618860
$804$	0	0
$805$	−3.63825e6	−0.197880
$806$	4.80533e6	0.260547
$807$	0	0
$808$	2.87808e6	0.155087
$809$	−3.53936e6	−0.190131	−0.0950656	−	0.995471i	$-0.530306\pi$
$809$	−3.53936e6	−0.190131	−0.0950656	+	0.995471i	$0.530306\pi$
$810$	0	0
$811$	−2.11480e7	−1.12906	−0.564530	−	0.825412i	$-0.690943\pi$
$811$	−2.11480e7	−1.12906	−0.564530	+	0.825412i	$0.690943\pi$
$812$	1.01842e6	0.0542045
$813$	0	0
$814$	4.92034e6	0.260276
$815$	−4.39175e6	−0.231603
$816$	0	0
$817$	819924.	0.0429753
$818$	−1.65280e7	−0.863646
$819$	0	0
$820$	2.67040e6	0.138689
$821$	−265389.	−0.0137412	−0.00687061	−	0.999976i	$-0.502187\pi$
$821$	−265389.	−0.0137412	−0.00687061	+	0.999976i	$0.502187\pi$
$822$	0	0
$823$	3.09261e7	1.59157	0.795785	−	0.605579i	$-0.207058\pi$
$823$	3.09261e7	1.59157	0.795785	+	0.605579i	$0.207058\pi$
$824$	−6.48992e6	−0.332982
$825$	0	0
$826$	770672.	0.0393024
$827$	2.84152e7	1.44473	0.722367	−	0.691510i	$-0.243054\pi$
$827$	2.84152e7	1.44473	0.722367	+	0.691510i	$0.243054\pi$
$828$	0	0
$829$	−3.33547e7	−1.68566	−0.842832	−	0.538177i	$-0.819113\pi$
$829$	−3.33547e7	−1.68566	−0.842832	+	0.538177i	$0.819113\pi$
$830$	9.72760e6	0.490129
$831$	0	0
$832$	2.56819e6	0.128623
$833$	−4.35301e6	−0.217359
$834$	0	0
$835$	−3.93532e6	−0.195328
$836$	771936.	0.0382002
$837$	0	0
$838$	−762048.	−0.0374863
$839$	5.66205e6	0.277695	0.138848	−	0.990314i	$-0.455660\pi$
$839$	5.66205e6	0.277695	0.138848	+	0.990314i	$0.455660\pi$
$840$	0	0
$841$	−1.88237e7	−0.917732
$842$	−2.07674e7	−1.00949
$843$	0	0
$844$	1.00408e7	0.485188
$845$	−545900.	−0.0263009
$846$	0	0
$847$	6.17802e6	0.295897
$848$	−6.69901e6	−0.319905
$849$	0	0
$850$	−4.53250e6	−0.215174
$851$	−1.95367e7	−0.924754
$852$	0	0
$853$	2.19983e7	1.03518	0.517592	−	0.855628i	$-0.326829\pi$
$853$	2.19983e7	1.03518	0.517592	+	0.855628i	$0.326829\pi$
$854$	9.55304e6	0.448226
$855$	0	0
$856$	1.06241e7	0.495574
$857$	2.17568e7	1.01191	0.505956	−	0.862559i	$-0.331140\pi$
$857$	2.17568e7	1.01191	0.505956	+	0.862559i	$0.331140\pi$
$858$	0	0
$859$	−4.09384e7	−1.89299	−0.946494	−	0.322721i	$-0.895402\pi$
$859$	−4.09384e7	−1.89299	−0.946494	+	0.322721i	$0.895402\pi$
$860$	−1.27120e6	−0.0586095
$861$	0	0
$862$	1.68712e7	0.773355
$863$	−5.65597e6	−0.258512	−0.129256	−	0.991611i	$-0.541259\pi$
$863$	−5.65597e6	−0.258512	−0.129256	+	0.991611i	$0.541259\pi$
$864$	0	0
$865$	−586775.	−0.0266644
$866$	−1.94411e7	−0.880899
$867$	0	0
$868$	−1.50214e6	−0.0676725
$869$	−8.17583e6	−0.367267
$870$	0	0
$871$	−2.81097e7	−1.25548
$872$	530496.	0.0236260
$873$	0	0
$874$	−3.06504e6	−0.135724
$875$	765625.	0.0338062
$876$	0	0
$877$	2.61067e7	1.14618	0.573089	−	0.819493i	$-0.305745\pi$
$877$	2.61067e7	1.14618	0.573089	+	0.819493i	$0.305745\pi$
$878$	−8.12454e6	−0.355682
$879$	0	0
$880$	−1.19680e6	−0.0520973
$881$	−1.44294e6	−0.0626339	−0.0313170	−	0.999510i	$-0.509970\pi$
$881$	−1.44294e6	−0.0626339	−0.0313170	+	0.999510i	$0.509970\pi$
$882$	0	0
$883$	−1.52432e7	−0.657921	−0.328960	−	0.944344i	$-0.606698\pi$
$883$	−1.52432e7	−0.657921	−0.328960	+	0.944344i	$0.606698\pi$
$884$	−1.81880e7	−0.782807
$885$	0	0
$886$	−1.13679e7	−0.486517
$887$	3.31500e7	1.41473	0.707366	−	0.706847i	$-0.249883\pi$
$887$	3.31500e7	1.41473	0.707366	+	0.706847i	$0.249883\pi$
$888$	0	0
$889$	−1.47255e6	−0.0624907
$890$	4.55600e6	0.192801
$891$	0	0
$892$	−1.95376e7	−0.822166
$893$	5.67626e6	0.238195
$894$	0	0
$895$	1.53057e7	0.638698
$896$	−802816.	−0.0334077
$897$	0	0
$898$	1.83873e7	0.760899
$899$	−2.48888e6	−0.102708
$900$	0	0
$901$	4.74426e7	1.94696
$902$	−4.99365e6	−0.204363
$903$	0	0
$904$	−1.68452e7	−0.685575
$905$	−1.32208e7	−0.536582
$906$	0	0
$907$	1.16963e7	0.472096	0.236048	−	0.971741i	$-0.424148\pi$
$907$	1.16963e7	0.472096	0.236048	+	0.971741i	$0.424148\pi$
$908$	−6.24875e6	−0.251524
$909$	0	0
$910$	3.07230e6	0.122987
$911$	−2.89321e7	−1.15501	−0.577503	−	0.816389i	$-0.695973\pi$
$911$	−2.89321e7	−1.15501	−0.577503	+	0.816389i	$0.695973\pi$
$912$	0	0
$913$	−1.81906e7	−0.722221
$914$	1.97347e7	0.781384
$915$	0	0
$916$	−1.13940e7	−0.448680
$917$	−5.88245e6	−0.231012
$918$	0	0
$919$	−4.57838e7	−1.78823	−0.894115	−	0.447838i	$-0.852194\pi$
$919$	−4.57838e7	−1.78823	−0.894115	+	0.447838i	$0.852194\pi$
$920$	4.75200e6	0.185100
$921$	0	0
$922$	1.90267e7	0.737116
$923$	−3.99625e7	−1.54400
$924$	0	0
$925$	4.11125e6	0.157986
$926$	1.63448e7	0.626399
$927$	0	0
$928$	−1.33018e6	−0.0507036
$929$	−2.46947e7	−0.938782	−0.469391	−	0.882990i	$-0.655526\pi$
$929$	−2.46947e7	−0.938782	−0.469391	+	0.882990i	$0.655526\pi$
$930$	0	0
$931$	619458.	0.0234227
$932$	−8.98522e6	−0.338835
$933$	0	0
$934$	1.66373e7	0.624044
$935$	8.47578e6	0.317067
$936$	0	0
$937$	−1.98926e7	−0.740187	−0.370094	−	0.928994i	$-0.620674\pi$
$937$	−1.98926e7	−0.740187	−0.370094	+	0.928994i	$0.620674\pi$
$938$	8.78707e6	0.326090
$939$	0	0
$940$	−8.80040e6	−0.324850
$941$	3.73454e7	1.37488	0.687438	−	0.726243i	$-0.258735\pi$
$941$	3.73454e7	1.37488	0.687438	+	0.726243i	$0.258735\pi$
$942$	0	0
$943$	1.98277e7	0.726095
$944$	−1.00659e6	−0.0367641
$945$	0	0
$946$	2.37714e6	0.0863630
$947$	−5.10396e7	−1.84941	−0.924703	−	0.380689i	$-0.875687\pi$
$947$	−5.10396e7	−1.84941	−0.924703	+	0.380689i	$0.875687\pi$
$948$	0	0
$949$	3.79147e7	1.36660
$950$	645000.	0.0231873
$951$	0	0
$952$	5.68557e6	0.203321
$953$	−254832.	−0.00908912	−0.00454456	−	0.999990i	$-0.501447\pi$
$953$	−254832.	−0.00908912	−0.00454456	+	0.999990i	$0.501447\pi$
$954$	0	0
$955$	1.35092e7	0.479316
$956$	2.17734e7	0.770515
$957$	0	0
$958$	1.34416e7	0.473192
$959$	1.55702e6	0.0546700
$960$	0	0
$961$	−2.49581e7	−0.871772
$962$	1.64976e7	0.574756
$963$	0	0
$964$	8.48080e6	0.293930
$965$	−2.40080e7	−0.829923
$966$	0	0
$967$	1.17012e7	0.402405	0.201203	−	0.979550i	$-0.435515\pi$
$967$	1.17012e7	0.402405	0.201203	+	0.979550i	$0.435515\pi$
$968$	−8.06925e6	−0.276786
$969$	0	0
$970$	5.72950e6	0.195518
$971$	−3.59080e7	−1.22220	−0.611101	−	0.791553i	$-0.709273\pi$
$971$	−3.59080e7	−1.22220	−0.611101	+	0.791553i	$0.709273\pi$
$972$	0	0
$973$	9.80794e6	0.332120
$974$	2.82097e7	0.952799
$975$	0	0
$976$	−1.24774e7	−0.419277
$977$	5.50592e7	1.84541	0.922706	−	0.385504i	$-0.125972\pi$
$977$	5.50592e7	1.84541	0.922706	+	0.385504i	$0.125972\pi$
$978$	0	0
$979$	−8.51972e6	−0.284098
$980$	−960400.	−0.0319438
$981$	0	0
$982$	335748.	0.0111105
$983$	1.81317e7	0.598488	0.299244	−	0.954177i	$-0.403266\pi$
$983$	1.81317e7	0.598488	0.299244	+	0.954177i	$0.403266\pi$
$984$	0	0
$985$	1.90486e7	0.625565
$986$	9.42035e6	0.308585
$987$	0	0
$988$	2.58826e6	0.0843558
$989$	−9.43866e6	−0.306845
$990$	0	0
$991$	−2.02908e7	−0.656318	−0.328159	−	0.944623i	$-0.606428\pi$
$991$	−2.02908e7	−0.656318	−0.328159	+	0.944623i	$0.606428\pi$
$992$	1.96198e6	0.0633018
$993$	0	0
$994$	1.24923e7	0.401028
$995$	−3.12710e6	−0.100135
$996$	0	0
$997$	4.75390e7	1.51465	0.757325	−	0.653038i	$-0.226506\pi$
$997$	4.75390e7	1.51465	0.757325	+	0.653038i	$0.226506\pi$
$998$	−2.84211e7	−0.903262
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.6.a.b.1.1	✓	1	3.2	odd	2
350.6.a.l.1.1		1	15.14	odd	2
350.6.c.g.99.1		2	15.2	even	4
350.6.c.g.99.2		2	15.8	even	4
490.6.a.g.1.1		1	21.20	even	2
560.6.a.e.1.1		1	12.11	even	2
630.6.a.i.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 $\F_{q}$
Belyi maps

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

Related objects

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