LMFDB - Embedded newform 630.6.a.j.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)

$f(q)$

$=$

$q+4.00000 q^{2} +16.0000 q^{4} -25.0000 q^{5} +49.0000 q^{7} +64.0000 q^{8} +O(q^{10})$

\(q+4.00000 q^{2} +16.0000 q^{4} -25.0000 q^{5} +49.0000 q^{7} +64.0000 q^{8} -100.000 q^{10} -555.000 q^{11} -241.000 q^{13} +196.000 q^{14} +256.000 q^{16} +1491.00 q^{17} -2038.00 q^{19} -400.000 q^{20} -2220.00 q^{22} +1230.00 q^{23} +625.000 q^{25} -964.000 q^{26} +784.000 q^{28} +5001.00 q^{29} +5696.00 q^{31} +1024.00 q^{32} +5964.00 q^{34} -1225.00 q^{35} -5602.00 q^{37} -8152.00 q^{38} -1600.00 q^{40} +2424.00 q^{41} +602.000 q^{43} -8880.00 q^{44} +4920.00 q^{46} +23163.0 q^{47} +2401.00 q^{49} +2500.00 q^{50} -3856.00 q^{52} +25296.0 q^{53} +13875.0 q^{55} +3136.00 q^{56} +20004.0 q^{58} -5724.00 q^{59} -36112.0 q^{61} +22784.0 q^{62} +4096.00 q^{64} +6025.00 q^{65} +66104.0 q^{67} +23856.0 q^{68} -4900.00 q^{70} -16080.0 q^{71} -80482.0 q^{73} -22408.0 q^{74} -32608.0 q^{76} -27195.0 q^{77} -64147.0 q^{79} -6400.00 q^{80} +9696.00 q^{82} +106284. q^{83} -37275.0 q^{85} +2408.00 q^{86} -35520.0 q^{88} +71676.0 q^{89} -11809.0 q^{91} +19680.0 q^{92} +92652.0 q^{94} +50950.0 q^{95} +151025. q^{97} +9604.00 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
$11$	−555.000	−1.38297	−0.691483	−	0.722393i	$-0.743042\pi$
$11$	−555.000	−1.38297	−0.691483	+	0.722393i	$0.743042\pi$
$12$	0	0
$13$	−241.000	−0.395511	−0.197756	−	0.980251i	$-0.563365\pi$
$13$	−241.000	−0.395511	−0.197756	+	0.980251i	$0.563365\pi$
$14$	196.000	0.267261
$15$	0	0
$16$	256.000	0.250000
$17$	1491.00	1.25128	0.625641	−	0.780111i	$-0.284837\pi$
$17$	1491.00	1.25128	0.625641	+	0.780111i	$0.284837\pi$
$18$	0	0
$19$	−2038.00	−1.29515	−0.647575	−	0.762002i	$-0.724217\pi$
$19$	−2038.00	−1.29515	−0.647575	+	0.762002i	$0.724217\pi$
$20$	−400.000	−0.223607
$21$	0	0
$22$	−2220.00	−0.977904
$23$	1230.00	0.484826	0.242413	−	0.970173i	$-0.422061\pi$
$23$	1230.00	0.484826	0.242413	+	0.970173i	$0.422061\pi$
$24$	0	0
$25$	625.000	0.200000
$26$	−964.000	−0.279669
$27$	0	0
$28$	784.000	0.188982
$29$	5001.00	1.10424	0.552118	−	0.833766i	$-0.313820\pi$
$29$	5001.00	1.10424	0.552118	+	0.833766i	$0.313820\pi$
$30$	0	0
$31$	5696.00	1.06455	0.532275	−	0.846572i	$-0.321337\pi$
$31$	5696.00	1.06455	0.532275	+	0.846572i	$0.321337\pi$
$32$	1024.00	0.176777
$33$	0	0
$34$	5964.00	0.884790
$35$	−1225.00	−0.169031
$36$	0	0
$37$	−5602.00	−0.672727	−0.336363	−	0.941732i	$-0.609197\pi$
$37$	−5602.00	−0.672727	−0.336363	+	0.941732i	$0.609197\pi$
$38$	−8152.00	−0.915810
$39$	0	0
$40$	−1600.00	−0.158114
$41$	2424.00	0.225202	0.112601	−	0.993640i	$-0.464082\pi$
$41$	2424.00	0.225202	0.112601	+	0.993640i	$0.464082\pi$
$42$	0	0
$43$	602.000	0.0496507	0.0248253	−	0.999692i	$-0.492097\pi$
$43$	602.000	0.0496507	0.0248253	+	0.999692i	$0.492097\pi$
$44$	−8880.00	−0.691483
$45$	0	0
$46$	4920.00	0.342823
$47$	23163.0	1.52950	0.764751	−	0.644326i	$-0.222862\pi$
$47$	23163.0	1.52950	0.764751	+	0.644326i	$0.222862\pi$
$48$	0	0
$49$	2401.00	0.142857
$50$	2500.00	0.141421
$51$	0	0
$52$	−3856.00	−0.197756
$53$	25296.0	1.23698	0.618489	−	0.785793i	$-0.287745\pi$
$53$	25296.0	1.23698	0.618489	+	0.785793i	$0.287745\pi$
$54$	0	0
$55$	13875.0	0.618481
$56$	3136.00	0.133631
$57$	0	0
$58$	20004.0	0.780813
$59$	−5724.00	−0.214077	−0.107038	−	0.994255i	$-0.534137\pi$
$59$	−5724.00	−0.214077	−0.107038	+	0.994255i	$0.534137\pi$
$60$	0	0
$61$	−36112.0	−1.24259	−0.621294	−	0.783578i	$-0.713393\pi$
$61$	−36112.0	−1.24259	−0.621294	+	0.783578i	$0.713393\pi$
$62$	22784.0	0.752750
$63$	0	0
$64$	4096.00	0.125000
$65$	6025.00	0.176878
$66$	0	0
$67$	66104.0	1.79904	0.899520	−	0.436880i	$-0.143917\pi$
$67$	66104.0	1.79904	0.899520	+	0.436880i	$0.143917\pi$
$68$	23856.0	0.625641
$69$	0	0
$70$	−4900.00	−0.119523
$71$	−16080.0	−0.378565	−0.189282	−	0.981923i	$-0.560616\pi$
$71$	−16080.0	−0.378565	−0.189282	+	0.981923i	$0.560616\pi$
$72$	0	0
$73$	−80482.0	−1.76763	−0.883816	−	0.467836i	$-0.845034\pi$
$73$	−80482.0	−1.76763	−0.883816	+	0.467836i	$0.845034\pi$
$74$	−22408.0	−0.475690
$75$	0	0
$76$	−32608.0	−0.647575
$77$	−27195.0	−0.522712
$78$	0	0
$79$	−64147.0	−1.15640	−0.578201	−	0.815895i	$-0.696245\pi$
$79$	−64147.0	−1.15640	−0.578201	+	0.815895i	$0.696245\pi$
$80$	−6400.00	−0.111803
$81$	0	0
$82$	9696.00	0.159242
$83$	106284.	1.69345	0.846726	−	0.532030i	$-0.178571\pi$
$83$	106284.	1.69345	0.846726	+	0.532030i	$0.178571\pi$
$84$	0	0
$85$	−37275.0	−0.559591
$86$	2408.00	0.0351083
$87$	0	0
$88$	−35520.0	−0.488952
$89$	71676.0	0.959177	0.479588	−	0.877494i	$-0.340786\pi$
$89$	71676.0	0.959177	0.479588	+	0.877494i	$0.340786\pi$
$90$	0	0
$91$	−11809.0	−0.149489
$92$	19680.0	0.242413
$93$	0	0
$94$	92652.0	1.08152
$95$	50950.0	0.579209
$96$	0	0
$97$	151025.	1.62974	0.814872	−	0.579641i	$-0.196807\pi$
$97$	151025.	1.62974	0.814872	+	0.579641i	$0.196807\pi$
$98$	9604.00	0.101015
$99$	0	0
$100$	10000.0	0.100000
$101$	57150.0	0.557459	0.278729	−	0.960370i	$-0.410087\pi$
$101$	57150.0	0.557459	0.278729	+	0.960370i	$0.410087\pi$
$102$	0	0
$103$	115889.	1.07634	0.538170	−	0.842837i	$-0.319116\pi$
$103$	115889.	1.07634	0.538170	+	0.842837i	$0.319116\pi$
$104$	−15424.0	−0.139834
$105$	0	0
$106$	101184.	0.874676
$107$	137862.	1.16409	0.582043	−	0.813158i	$-0.302253\pi$
$107$	137862.	1.16409	0.582043	+	0.813158i	$0.302253\pi$
$108$	0	0
$109$	88397.0	0.712642	0.356321	−	0.934364i	$-0.384031\pi$
$109$	88397.0	0.712642	0.356321	+	0.934364i	$0.384031\pi$
$110$	55500.0	0.437332
$111$	0	0
$112$	12544.0	0.0944911
$113$	−205554.	−1.51436	−0.757181	−	0.653205i	$-0.773424\pi$
$113$	−205554.	−1.51436	−0.757181	+	0.653205i	$0.773424\pi$
$114$	0	0
$115$	−30750.0	−0.216821
$116$	80016.0	0.552118
$117$	0	0
$118$	−22896.0	−0.151375
$119$	73059.0	0.472940
$120$	0	0
$121$	146974.	0.912593
$122$	−144448.	−0.878642
$123$	0	0
$124$	91136.0	0.532275
$125$	−15625.0	−0.0894427
$126$	0	0
$127$	250916.	1.38044	0.690222	−	0.723597i	$-0.257513\pi$
$127$	250916.	1.38044	0.690222	+	0.723597i	$0.257513\pi$
$128$	16384.0	0.0883883
$129$	0	0
$130$	24100.0	0.125072
$131$	52122.0	0.265365	0.132682	−	0.991159i	$-0.457641\pi$
$131$	52122.0	0.265365	0.132682	+	0.991159i	$0.457641\pi$
$132$	0	0
$133$	−99862.0	−0.489521
$134$	264416.	1.27211
$135$	0	0
$136$	95424.0	0.442395
$137$	135468.	0.616645	0.308323	−	0.951282i	$-0.400232\pi$
$137$	135468.	0.616645	0.308323	+	0.951282i	$0.400232\pi$
$138$	0	0
$139$	−349486.	−1.53424	−0.767119	−	0.641505i	$-0.778310\pi$
$139$	−349486.	−1.53424	−0.767119	+	0.641505i	$0.778310\pi$
$140$	−19600.0	−0.0845154
$141$	0	0
$142$	−64320.0	−0.267686
$143$	133755.	0.546978
$144$	0	0
$145$	−125025.	−0.493829
$146$	−321928.	−1.24990
$147$	0	0
$148$	−89632.0	−0.336363
$149$	−176082.	−0.649754	−0.324877	−	0.945756i	$-0.605323\pi$
$149$	−176082.	−0.649754	−0.324877	+	0.945756i	$0.605323\pi$
$150$	0	0
$151$	383333.	1.36815	0.684075	−	0.729411i	$-0.260206\pi$
$151$	383333.	1.36815	0.684075	+	0.729411i	$0.260206\pi$
$152$	−130432.	−0.457905
$153$	0	0
$154$	−108780.	−0.369613
$155$	−142400.	−0.476081
$156$	0	0
$157$	345914.	1.12000	0.560001	−	0.828492i	$-0.310801\pi$
$157$	345914.	1.12000	0.560001	+	0.828492i	$0.310801\pi$
$158$	−256588.	−0.817699
$159$	0	0
$160$	−25600.0	−0.0790569
$161$	60270.0	0.183247
$162$	0	0
$163$	91586.0	0.269998	0.134999	−	0.990846i	$-0.456897\pi$
$163$	91586.0	0.269998	0.134999	+	0.990846i	$0.456897\pi$
$164$	38784.0	0.112601
$165$	0	0
$166$	425136.	1.19745
$167$	−38097.0	−0.105706	−0.0528530	−	0.998602i	$-0.516831\pi$
$167$	−38097.0	−0.105706	−0.0528530	+	0.998602i	$0.516831\pi$
$168$	0	0
$169$	−313212.	−0.843571
$170$	−149100.	−0.395690
$171$	0	0
$172$	9632.00	0.0248253
$173$	541443.	1.37543	0.687713	−	0.725982i	$-0.258615\pi$
$173$	541443.	1.37543	0.687713	+	0.725982i	$0.258615\pi$
$174$	0	0
$175$	30625.0	0.0755929
$176$	−142080.	−0.345741
$177$	0	0
$178$	286704.	0.678241
$179$	−166188.	−0.387674	−0.193837	−	0.981034i	$-0.562093\pi$
$179$	−166188.	−0.387674	−0.193837	+	0.981034i	$0.562093\pi$
$180$	0	0
$181$	−197320.	−0.447687	−0.223844	−	0.974625i	$-0.571860\pi$
$181$	−197320.	−0.447687	−0.223844	+	0.974625i	$0.571860\pi$
$182$	−47236.0	−0.105705
$183$	0	0
$184$	78720.0	0.171412
$185$	140050.	0.300853
$186$	0	0
$187$	−827505.	−1.73048
$188$	370608.	0.764751
$189$	0	0
$190$	203800.	0.409562
$191$	337221.	0.668854	0.334427	−	0.942422i	$-0.391457\pi$
$191$	337221.	0.668854	0.334427	+	0.942422i	$0.391457\pi$
$192$	0	0
$193$	260516.	0.503432	0.251716	−	0.967801i	$-0.419005\pi$
$193$	260516.	0.503432	0.251716	+	0.967801i	$0.419005\pi$
$194$	604100.	1.15240
$195$	0	0
$196$	38416.0	0.0714286
$197$	409212.	0.751247	0.375624	−	0.926772i	$-0.377429\pi$
$197$	409212.	0.751247	0.375624	+	0.926772i	$0.377429\pi$
$198$	0	0
$199$	300980.	0.538772	0.269386	−	0.963032i	$-0.413179\pi$
$199$	300980.	0.538772	0.269386	+	0.963032i	$0.413179\pi$
$200$	40000.0	0.0707107
$201$	0	0
$202$	228600.	0.394183
$203$	245049.	0.417362
$204$	0	0
$205$	−60600.0	−0.100714
$206$	463556.	0.761087
$207$	0	0
$208$	−61696.0	−0.0988778
$209$	1.13109e6	1.79115
$210$	0	0
$211$	−1.22618e6	−1.89604	−0.948021	−	0.318209i	$-0.896919\pi$
$211$	−1.22618e6	−1.89604	−0.948021	+	0.318209i	$0.896919\pi$
$212$	404736.	0.618489
$213$	0	0
$214$	551448.	0.823133
$215$	−15050.0	−0.0222045
$216$	0	0
$217$	279104.	0.402362
$218$	353588.	0.503914
$219$	0	0
$220$	222000.	0.309240
$221$	−359331.	−0.494896
$222$	0	0
$223$	621257.	0.836583	0.418292	−	0.908313i	$-0.362629\pi$
$223$	621257.	0.836583	0.418292	+	0.908313i	$0.362629\pi$
$224$	50176.0	0.0668153
$225$	0	0
$226$	−822216.	−1.07082
$227$	−1.29768e6	−1.67148	−0.835742	−	0.549123i	$-0.814962\pi$
$227$	−1.29768e6	−1.67148	−0.835742	+	0.549123i	$0.814962\pi$
$228$	0	0
$229$	−124264.	−0.156587	−0.0782937	−	0.996930i	$-0.524947\pi$
$229$	−124264.	−0.156587	−0.0782937	+	0.996930i	$0.524947\pi$
$230$	−123000.	−0.153315
$231$	0	0
$232$	320064.	0.390406
$233$	−1.08742e6	−1.31222	−0.656109	−	0.754666i	$-0.727799\pi$
$233$	−1.08742e6	−1.31222	−0.656109	+	0.754666i	$0.727799\pi$
$234$	0	0
$235$	−579075.	−0.684014
$236$	−91584.0	−0.107038
$237$	0	0
$238$	292236.	0.334419
$239$	545631.	0.617880	0.308940	−	0.951081i	$-0.400026\pi$
$239$	545631.	0.617880	0.308940	+	0.951081i	$0.400026\pi$
$240$	0	0
$241$	811310.	0.899796	0.449898	−	0.893080i	$-0.351460\pi$
$241$	811310.	0.899796	0.449898	+	0.893080i	$0.351460\pi$
$242$	587896.	0.645301
$243$	0	0
$244$	−577792.	−0.621294
$245$	−60025.0	−0.0638877
$246$	0	0
$247$	491158.	0.512246
$248$	364544.	0.376375
$249$	0	0
$250$	−62500.0	−0.0632456
$251$	897738.	0.899426	0.449713	−	0.893173i	$-0.351526\pi$
$251$	897738.	0.899426	0.449713	+	0.893173i	$0.351526\pi$
$252$	0	0
$253$	−682650.	−0.670497
$254$	1.00366e6	0.976122
$255$	0	0
$256$	65536.0	0.0625000
$257$	594678.	0.561628	0.280814	−	0.959762i	$-0.409396\pi$
$257$	594678.	0.561628	0.280814	+	0.959762i	$0.409396\pi$
$258$	0	0
$259$	−274498.	−0.254267
$260$	96400.0	0.0884390
$261$	0	0
$262$	208488.	0.187641
$263$	−1.02837e6	−0.916769	−0.458385	−	0.888754i	$-0.651572\pi$
$263$	−1.02837e6	−0.916769	−0.458385	+	0.888754i	$0.651572\pi$
$264$	0	0
$265$	−632400.	−0.553194
$266$	−399448.	−0.346143
$267$	0	0
$268$	1.05766e6	0.899520
$269$	1.24390e6	1.04811	0.524053	−	0.851685i	$-0.324419\pi$
$269$	1.24390e6	1.04811	0.524053	+	0.851685i	$0.324419\pi$
$270$	0	0
$271$	737624.	0.610115	0.305058	−	0.952334i	$-0.401324\pi$
$271$	737624.	0.610115	0.305058	+	0.952334i	$0.401324\pi$
$272$	381696.	0.312821
$273$	0	0
$274$	541872.	0.436034
$275$	−346875.	−0.276593
$276$	0	0
$277$	−2.20063e6	−1.72325	−0.861624	−	0.507548i	$-0.830552\pi$
$277$	−2.20063e6	−1.72325	−0.861624	+	0.507548i	$0.830552\pi$
$278$	−1.39794e6	−1.08487
$279$	0	0
$280$	−78400.0	−0.0597614
$281$	−173979.	−0.131441	−0.0657205	−	0.997838i	$-0.520935\pi$
$281$	−173979.	−0.131441	−0.0657205	+	0.997838i	$0.520935\pi$
$282$	0	0
$283$	−551053.	−0.409004	−0.204502	−	0.978866i	$-0.565557\pi$
$283$	−551053.	−0.409004	−0.204502	+	0.978866i	$0.565557\pi$
$284$	−257280.	−0.189282
$285$	0	0
$286$	535020.	0.386772
$287$	118776.	0.0851185
$288$	0	0
$289$	803224.	0.565708
$290$	−500100.	−0.349190
$291$	0	0
$292$	−1.28771e6	−0.883816
$293$	1.67512e6	1.13993	0.569963	−	0.821670i	$-0.306958\pi$
$293$	1.67512e6	1.13993	0.569963	+	0.821670i	$0.306958\pi$
$294$	0	0
$295$	143100.	0.0957381
$296$	−358528.	−0.237845
$297$	0	0
$298$	−704328.	−0.459446
$299$	−296430.	−0.191754
$300$	0	0
$301$	29498.0	0.0187662
$302$	1.53333e6	0.967428
$303$	0	0
$304$	−521728.	−0.323788
$305$	902800.	0.555702
$306$	0	0
$307$	2.33060e6	1.41131	0.705655	−	0.708556i	$-0.250653\pi$
$307$	2.33060e6	1.41131	0.705655	+	0.708556i	$0.250653\pi$
$308$	−435120.	−0.261356
$309$	0	0
$310$	−569600.	−0.336640
$311$	−706266.	−0.414064	−0.207032	−	0.978334i	$-0.566380\pi$
$311$	−706266.	−0.414064	−0.207032	+	0.978334i	$0.566380\pi$
$312$	0	0
$313$	−183565.	−0.105908	−0.0529540	−	0.998597i	$-0.516864\pi$
$313$	−183565.	−0.105908	−0.0529540	+	0.998597i	$0.516864\pi$
$314$	1.38366e6	0.791961
$315$	0	0
$316$	−1.02635e6	−0.578201
$317$	−2.70665e6	−1.51281	−0.756405	−	0.654103i	$-0.773046\pi$
$317$	−2.70665e6	−1.51281	−0.756405	+	0.654103i	$0.773046\pi$
$318$	0	0
$319$	−2.77556e6	−1.52712
$320$	−102400.	−0.0559017
$321$	0	0
$322$	241080.	0.129575
$323$	−3.03866e6	−1.62060
$324$	0	0
$325$	−150625.	−0.0791022
$326$	366344.	0.190917
$327$	0	0
$328$	155136.	0.0796211
$329$	1.13499e6	0.578098
$330$	0	0
$331$	−2.14337e6	−1.07529	−0.537647	−	0.843170i	$-0.680687\pi$
$331$	−2.14337e6	−1.07529	−0.537647	+	0.843170i	$0.680687\pi$
$332$	1.70054e6	0.846726
$333$	0	0
$334$	−152388.	−0.0747454
$335$	−1.65260e6	−0.804555
$336$	0	0
$337$	655346.	0.314337	0.157169	−	0.987572i	$-0.449763\pi$
$337$	655346.	0.314337	0.157169	+	0.987572i	$0.449763\pi$
$338$	−1.25285e6	−0.596495
$339$	0	0
$340$	−596400.	−0.279795
$341$	−3.16128e6	−1.47223
$342$	0	0
$343$	117649.	0.0539949
$344$	38528.0	0.0175542
$345$	0	0
$346$	2.16577e6	0.972574
$347$	4.22275e6	1.88266	0.941329	−	0.337491i	$-0.109578\pi$
$347$	4.22275e6	1.88266	0.941329	+	0.337491i	$0.109578\pi$
$348$	0	0
$349$	3.01710e6	1.32595	0.662974	−	0.748643i	$-0.269294\pi$
$349$	3.01710e6	1.32595	0.662974	+	0.748643i	$0.269294\pi$
$350$	122500.	0.0534522
$351$	0	0
$352$	−568320.	−0.244476
$353$	−2.25258e6	−0.962150	−0.481075	−	0.876679i	$-0.659754\pi$
$353$	−2.25258e6	−0.962150	−0.481075	+	0.876679i	$0.659754\pi$
$354$	0	0
$355$	402000.	0.169299
$356$	1.14682e6	0.479588
$357$	0	0
$358$	−664752.	−0.274127
$359$	1.83950e6	0.753294	0.376647	−	0.926357i	$-0.377077\pi$
$359$	1.83950e6	0.753294	0.376647	+	0.926357i	$0.377077\pi$
$360$	0	0
$361$	1.67735e6	0.677414
$362$	−789280.	−0.316563
$363$	0	0
$364$	−188944.	−0.0747446
$365$	2.01205e6	0.790509
$366$	0	0
$367$	−1.68832e6	−0.654320	−0.327160	−	0.944969i	$-0.606092\pi$
$367$	−1.68832e6	−0.654320	−0.327160	+	0.944969i	$0.606092\pi$
$368$	314880.	0.121206
$369$	0	0
$370$	560200.	0.212735
$371$	1.23950e6	0.467534
$372$	0	0
$373$	1.81212e6	0.674394	0.337197	−	0.941434i	$-0.390521\pi$
$373$	1.81212e6	0.674394	0.337197	+	0.941434i	$0.390521\pi$
$374$	−3.31002e6	−1.22363
$375$	0	0
$376$	1.48243e6	0.540761
$377$	−1.20524e6	−0.436738
$378$	0	0
$379$	−4.76708e6	−1.70472	−0.852362	−	0.522952i	$-0.824831\pi$
$379$	−4.76708e6	−1.70472	−0.852362	+	0.522952i	$0.824831\pi$
$380$	815200.	0.289604
$381$	0	0
$382$	1.34888e6	0.472951
$383$	69996.0	0.0243824	0.0121912	−	0.999926i	$-0.496119\pi$
$383$	69996.0	0.0243824	0.0121912	+	0.999926i	$0.496119\pi$
$384$	0	0
$385$	679875.	0.233764
$386$	1.04206e6	0.355980
$387$	0	0
$388$	2.41640e6	0.814872
$389$	−3.98895e6	−1.33655	−0.668275	−	0.743915i	$-0.732967\pi$
$389$	−3.98895e6	−1.33655	−0.668275	+	0.743915i	$0.732967\pi$
$390$	0	0
$391$	1.83393e6	0.606654
$392$	153664.	0.0505076
$393$	0	0
$394$	1.63685e6	0.531212
$395$	1.60367e6	0.517158
$396$	0	0
$397$	−3.05904e6	−0.974110	−0.487055	−	0.873371i	$-0.661929\pi$
$397$	−3.05904e6	−0.974110	−0.487055	+	0.873371i	$0.661929\pi$
$398$	1.20392e6	0.380969
$399$	0	0
$400$	160000.	0.0500000
$401$	−4.30794e6	−1.33785	−0.668927	−	0.743329i	$-0.733246\pi$
$401$	−4.30794e6	−1.33785	−0.668927	+	0.743329i	$0.733246\pi$
$402$	0	0
$403$	−1.37274e6	−0.421041
$404$	914400.	0.278729
$405$	0	0
$406$	980196.	0.295119
$407$	3.10911e6	0.930358
$408$	0	0
$409$	−239206.	−0.0707072	−0.0353536	−	0.999375i	$-0.511256\pi$
$409$	−239206.	−0.0707072	−0.0353536	+	0.999375i	$0.511256\pi$
$410$	−242400.	−0.0712152
$411$	0	0
$412$	1.85422e6	0.538170
$413$	−280476.	−0.0809134
$414$	0	0
$415$	−2.65710e6	−0.757334
$416$	−246784.	−0.0699171
$417$	0	0
$418$	4.52436e6	1.26653
$419$	−4.63462e6	−1.28967	−0.644835	−	0.764322i	$-0.723074\pi$
$419$	−4.63462e6	−1.28967	−0.644835	+	0.764322i	$0.723074\pi$
$420$	0	0
$421$	−2.10108e6	−0.577745	−0.288873	−	0.957368i	$-0.593280\pi$
$421$	−2.10108e6	−0.577745	−0.288873	+	0.957368i	$0.593280\pi$
$422$	−4.90472e6	−1.34070
$423$	0	0
$424$	1.61894e6	0.437338
$425$	931875.	0.250256
$426$	0	0
$427$	−1.76949e6	−0.469654
$428$	2.20579e6	0.582043
$429$	0	0
$430$	−60200.0	−0.0157009
$431$	−1.65484e6	−0.429104	−0.214552	−	0.976713i	$-0.568829\pi$
$431$	−1.65484e6	−0.429104	−0.214552	+	0.976713i	$0.568829\pi$
$432$	0	0
$433$	−1.84031e6	−0.471705	−0.235852	−	0.971789i	$-0.575788\pi$
$433$	−1.84031e6	−0.471705	−0.235852	+	0.971789i	$0.575788\pi$
$434$	1.11642e6	0.284513
$435$	0	0
$436$	1.41435e6	0.356321
$437$	−2.50674e6	−0.627922
$438$	0	0
$439$	5.83684e6	1.44549	0.722747	−	0.691113i	$-0.242879\pi$
$439$	5.83684e6	1.44549	0.722747	+	0.691113i	$0.242879\pi$
$440$	888000.	0.218666
$441$	0	0
$442$	−1.43732e6	−0.349944
$443$	−1.19704e6	−0.289801	−0.144901	−	0.989446i	$-0.546286\pi$
$443$	−1.19704e6	−0.289801	−0.144901	+	0.989446i	$0.546286\pi$
$444$	0	0
$445$	−1.79190e6	−0.428957
$446$	2.48503e6	0.591554
$447$	0	0
$448$	200704.	0.0472456
$449$	3.42570e6	0.801924	0.400962	−	0.916095i	$-0.368676\pi$
$449$	3.42570e6	0.801924	0.400962	+	0.916095i	$0.368676\pi$
$450$	0	0
$451$	−1.34532e6	−0.311447
$452$	−3.28886e6	−0.757181
$453$	0	0
$454$	−5.19071e6	−1.18192
$455$	295225.	0.0668536
$456$	0	0
$457$	5.29742e6	1.18652	0.593258	−	0.805012i	$-0.297841\pi$
$457$	5.29742e6	1.18652	0.593258	+	0.805012i	$0.297841\pi$
$458$	−497056.	−0.110724
$459$	0	0
$460$	−492000.	−0.108410
$461$	−8.87731e6	−1.94549	−0.972745	−	0.231876i	$-0.925514\pi$
$461$	−8.87731e6	−1.94549	−0.972745	+	0.231876i	$0.925514\pi$
$462$	0	0
$463$	−2.17475e6	−0.471473	−0.235737	−	0.971817i	$-0.575750\pi$
$463$	−2.17475e6	−0.471473	−0.235737	+	0.971817i	$0.575750\pi$
$464$	1.28026e6	0.276059
$465$	0	0
$466$	−4.34966e6	−0.927878
$467$	378969.	0.0804103	0.0402051	−	0.999191i	$-0.487199\pi$
$467$	378969.	0.0804103	0.0402051	+	0.999191i	$0.487199\pi$
$468$	0	0
$469$	3.23910e6	0.679973
$470$	−2.31630e6	−0.483671
$471$	0	0
$472$	−366336.	−0.0756876
$473$	−334110.	−0.0686652
$474$	0	0
$475$	−1.27375e6	−0.259030
$476$	1.16894e6	0.236470
$477$	0	0
$478$	2.18252e6	0.436907
$479$	−1.88489e6	−0.375360	−0.187680	−	0.982230i	$-0.560097\pi$
$479$	−1.88489e6	−0.375360	−0.187680	+	0.982230i	$0.560097\pi$
$480$	0	0
$481$	1.35008e6	0.266071
$482$	3.24524e6	0.636252
$483$	0	0
$484$	2.35158e6	0.456296
$485$	−3.77562e6	−0.728844
$486$	0	0
$487$	3.67689e6	0.702518	0.351259	−	0.936278i	$-0.385754\pi$
$487$	3.67689e6	0.702518	0.351259	+	0.936278i	$0.385754\pi$
$488$	−2.31117e6	−0.439321
$489$	0	0
$490$	−240100.	−0.0451754
$491$	−9.54015e6	−1.78588	−0.892939	−	0.450178i	$-0.851360\pi$
$491$	−9.54015e6	−1.78588	−0.892939	+	0.450178i	$0.851360\pi$
$492$	0	0
$493$	7.45649e6	1.38171
$494$	1.96463e6	0.362213
$495$	0	0
$496$	1.45818e6	0.266137
$497$	−787920.	−0.143084
$498$	0	0
$499$	4.78243e6	0.859800	0.429900	−	0.902877i	$-0.358549\pi$
$499$	4.78243e6	0.859800	0.429900	+	0.902877i	$0.358549\pi$
$500$	−250000.	−0.0447214
$501$	0	0
$502$	3.59095e6	0.635990
$503$	1.08395e7	1.91024	0.955120	−	0.296220i	$-0.0957260\pi$
$503$	1.08395e7	1.91024	0.955120	+	0.296220i	$0.0957260\pi$
$504$	0	0
$505$	−1.42875e6	−0.249303
$506$	−2.73060e6	−0.474113
$507$	0	0
$508$	4.01466e6	0.690222
$509$	7.64177e6	1.30737	0.653687	−	0.756765i	$-0.273221\pi$
$509$	7.64177e6	1.30737	0.653687	+	0.756765i	$0.273221\pi$
$510$	0	0
$511$	−3.94362e6	−0.668102
$512$	262144.	0.0441942
$513$	0	0
$514$	2.37871e6	0.397131
$515$	−2.89723e6	−0.481354
$516$	0	0
$517$	−1.28555e7	−2.11525
$518$	−1.09799e6	−0.179794
$519$	0	0
$520$	385600.	0.0625358
$521$	−6.44011e6	−1.03944	−0.519719	−	0.854337i	$-0.673963\pi$
$521$	−6.44011e6	−1.03944	−0.519719	+	0.854337i	$0.673963\pi$
$522$	0	0
$523$	−4.77929e6	−0.764028	−0.382014	−	0.924157i	$-0.624769\pi$
$523$	−4.77929e6	−0.764028	−0.382014	+	0.924157i	$0.624769\pi$
$524$	833952.	0.132682
$525$	0	0
$526$	−4.11348e6	−0.648254
$527$	8.49274e6	1.33205
$528$	0	0
$529$	−4.92344e6	−0.764944
$530$	−2.52960e6	−0.391167
$531$	0	0
$532$	−1.59779e6	−0.244760
$533$	−584184.	−0.0890700
$534$	0	0
$535$	−3.44655e6	−0.520595
$536$	4.23066e6	0.636057
$537$	0	0
$538$	4.97561e6	0.741123
$539$	−1.33256e6	−0.197566
$540$	0	0
$541$	−2.05678e6	−0.302130	−0.151065	−	0.988524i	$-0.548270\pi$
$541$	−2.05678e6	−0.302130	−0.151065	+	0.988524i	$0.548270\pi$
$542$	2.95050e6	0.431417
$543$	0	0
$544$	1.52678e6	0.221198
$545$	−2.20992e6	−0.318703
$546$	0	0
$547$	−1.20189e7	−1.71750	−0.858751	−	0.512393i	$-0.828759\pi$
$547$	−1.20189e7	−1.71750	−0.858751	+	0.512393i	$0.828759\pi$
$548$	2.16749e6	0.308323
$549$	0	0
$550$	−1.38750e6	−0.195581
$551$	−1.01920e7	−1.43015
$552$	0	0
$553$	−3.14320e6	−0.437079
$554$	−8.80252e6	−1.21852
$555$	0	0
$556$	−5.59178e6	−0.767119
$557$	−8.69942e6	−1.18810	−0.594049	−	0.804429i	$-0.702472\pi$
$557$	−8.69942e6	−1.18810	−0.594049	+	0.804429i	$0.702472\pi$
$558$	0	0
$559$	−145082.	−0.0196374
$560$	−313600.	−0.0422577
$561$	0	0
$562$	−695916.	−0.0929429
$563$	7.35942e6	0.978527	0.489263	−	0.872136i	$-0.337266\pi$
$563$	7.35942e6	0.978527	0.489263	+	0.872136i	$0.337266\pi$
$564$	0	0
$565$	5.13885e6	0.677243
$566$	−2.20421e6	−0.289209
$567$	0	0
$568$	−1.02912e6	−0.133843
$569$	7.50029e6	0.971175	0.485588	−	0.874188i	$-0.338606\pi$
$569$	7.50029e6	0.971175	0.485588	+	0.874188i	$0.338606\pi$
$570$	0	0
$571$	−2.22879e6	−0.286074	−0.143037	−	0.989717i	$-0.545687\pi$
$571$	−2.22879e6	−0.286074	−0.143037	+	0.989717i	$0.545687\pi$
$572$	2.14008e6	0.273489
$573$	0	0
$574$	475104.	0.0601879
$575$	768750.	0.0969651
$576$	0	0
$577$	−5.10946e6	−0.638903	−0.319452	−	0.947603i	$-0.603499\pi$
$577$	−5.10946e6	−0.638903	−0.319452	+	0.947603i	$0.603499\pi$
$578$	3.21290e6	0.400016
$579$	0	0
$580$	−2.00040e6	−0.246915
$581$	5.20792e6	0.640064
$582$	0	0
$583$	−1.40393e7	−1.71070
$584$	−5.15085e6	−0.624952
$585$	0	0
$586$	6.70048e6	0.806049
$587$	−1.10646e7	−1.32537	−0.662687	−	0.748896i	$-0.730584\pi$
$587$	−1.10646e7	−1.32537	−0.662687	+	0.748896i	$0.730584\pi$
$588$	0	0
$589$	−1.16084e7	−1.37875
$590$	572400.	0.0676970
$591$	0	0
$592$	−1.43411e6	−0.168182
$593$	−9.10043e6	−1.06274	−0.531368	−	0.847141i	$-0.678322\pi$
$593$	−9.10043e6	−1.06274	−0.531368	+	0.847141i	$0.678322\pi$
$594$	0	0
$595$	−1.82648e6	−0.211505
$596$	−2.81731e6	−0.324877
$597$	0	0
$598$	−1.18572e6	−0.135590
$599$	1.28615e7	1.46462	0.732309	−	0.680973i	$-0.238443\pi$
$599$	1.28615e7	1.46462	0.732309	+	0.680973i	$0.238443\pi$
$600$	0	0
$601$	1.58163e6	0.178615	0.0893074	−	0.996004i	$-0.471535\pi$
$601$	1.58163e6	0.178615	0.0893074	+	0.996004i	$0.471535\pi$
$602$	117992.	0.0132697
$603$	0	0
$604$	6.13333e6	0.684075
$605$	−3.67435e6	−0.408124
$606$	0	0
$607$	−688297.	−0.0758236	−0.0379118	−	0.999281i	$-0.512071\pi$
$607$	−688297.	−0.0758236	−0.0379118	+	0.999281i	$0.512071\pi$
$608$	−2.08691e6	−0.228952
$609$	0	0
$610$	3.61120e6	0.392941
$611$	−5.58228e6	−0.604935
$612$	0	0
$613$	−6.02150e6	−0.647223	−0.323611	−	0.946190i	$-0.604897\pi$
$613$	−6.02150e6	−0.647223	−0.323611	+	0.946190i	$0.604897\pi$
$614$	9.32241e6	0.997947
$615$	0	0
$616$	−1.74048e6	−0.184807
$617$	−3.36137e6	−0.355471	−0.177735	−	0.984078i	$-0.556877\pi$
$617$	−3.36137e6	−0.355471	−0.177735	+	0.984078i	$0.556877\pi$
$618$	0	0
$619$	1.31769e7	1.38225	0.691126	−	0.722734i	$-0.257115\pi$
$619$	1.31769e7	1.38225	0.691126	+	0.722734i	$0.257115\pi$
$620$	−2.27840e6	−0.238040
$621$	0	0
$622$	−2.82506e6	−0.292787
$623$	3.51212e6	0.362535
$624$	0	0
$625$	390625.	0.0400000
$626$	−734260.	−0.0748883
$627$	0	0
$628$	5.53462e6	0.560001
$629$	−8.35258e6	−0.841771
$630$	0	0
$631$	1.26264e6	0.126243	0.0631213	−	0.998006i	$-0.479895\pi$
$631$	1.26264e6	0.126243	0.0631213	+	0.998006i	$0.479895\pi$
$632$	−4.10541e6	−0.408850
$633$	0	0
$634$	−1.08266e7	−1.06972
$635$	−6.27290e6	−0.617354
$636$	0	0
$637$	−578641.	−0.0565016
$638$	−1.11022e7	−1.07984
$639$	0	0
$640$	−409600.	−0.0395285
$641$	1.58859e7	1.52710	0.763550	−	0.645749i	$-0.223455\pi$
$641$	1.58859e7	1.52710	0.763550	+	0.645749i	$0.223455\pi$
$642$	0	0
$643$	1.80880e6	0.172529	0.0862647	−	0.996272i	$-0.472507\pi$
$643$	1.80880e6	0.172529	0.0862647	+	0.996272i	$0.472507\pi$
$644$	964320.	0.0916234
$645$	0	0
$646$	−1.21546e7	−1.14594
$647$	−95712.0	−0.00898888	−0.00449444	−	0.999990i	$-0.501431\pi$
$647$	−95712.0	−0.00898888	−0.00449444	+	0.999990i	$0.501431\pi$
$648$	0	0
$649$	3.17682e6	0.296061
$650$	−602500.	−0.0559337
$651$	0	0
$652$	1.46538e6	0.134999
$653$	−3.06736e6	−0.281502	−0.140751	−	0.990045i	$-0.544952\pi$
$653$	−3.06736e6	−0.281502	−0.140751	+	0.990045i	$0.544952\pi$
$654$	0	0
$655$	−1.30305e6	−0.118675
$656$	620544.	0.0563006
$657$	0	0
$658$	4.53995e6	0.408777
$659$	1.32961e6	0.119264	0.0596321	−	0.998220i	$-0.481007\pi$
$659$	1.32961e6	0.119264	0.0596321	+	0.998220i	$0.481007\pi$
$660$	0	0
$661$	−7.37188e6	−0.656258	−0.328129	−	0.944633i	$-0.606418\pi$
$661$	−7.37188e6	−0.656258	−0.328129	+	0.944633i	$0.606418\pi$
$662$	−8.57349e6	−0.760348
$663$	0	0
$664$	6.80218e6	0.598725
$665$	2.49655e6	0.218920
$666$	0	0
$667$	6.15123e6	0.535362
$668$	−609552.	−0.0528530
$669$	0	0
$670$	−6.61040e6	−0.568906
$671$	2.00422e7	1.71846
$672$	0	0
$673$	8.48476e6	0.722108	0.361054	−	0.932545i	$-0.382417\pi$
$673$	8.48476e6	0.722108	0.361054	+	0.932545i	$0.382417\pi$
$674$	2.62138e6	0.222270
$675$	0	0
$676$	−5.01139e6	−0.421785
$677$	4.35891e6	0.365516	0.182758	−	0.983158i	$-0.441497\pi$
$677$	4.35891e6	0.365516	0.182758	+	0.983158i	$0.441497\pi$
$678$	0	0
$679$	7.40022e6	0.615985
$680$	−2.38560e6	−0.197845
$681$	0	0
$682$	−1.26451e7	−1.04103
$683$	1.58732e7	1.30200	0.651001	−	0.759077i	$-0.274349\pi$
$683$	1.58732e7	1.30200	0.651001	+	0.759077i	$0.274349\pi$
$684$	0	0
$685$	−3.38670e6	−0.275772
$686$	470596.	0.0381802
$687$	0	0
$688$	154112.	0.0124127
$689$	−6.09634e6	−0.489239
$690$	0	0
$691$	−554956.	−0.0442144	−0.0221072	−	0.999756i	$-0.507038\pi$
$691$	−554956.	−0.0442144	−0.0221072	+	0.999756i	$0.507038\pi$
$692$	8.66309e6	0.687713
$693$	0	0
$694$	1.68910e7	1.33124
$695$	8.73715e6	0.686132
$696$	0	0
$697$	3.61418e6	0.281792
$698$	1.20684e7	0.937587
$699$	0	0
$700$	490000.	0.0377964
$701$	7.74720e6	0.595456	0.297728	−	0.954651i	$-0.403771\pi$
$701$	7.74720e6	0.595456	0.297728	+	0.954651i	$0.403771\pi$
$702$	0	0
$703$	1.14169e7	0.871282
$704$	−2.27328e6	−0.172871
$705$	0	0
$706$	−9.01031e6	−0.680343
$707$	2.80035e6	0.210700
$708$	0	0
$709$	−1.89055e7	−1.41245	−0.706225	−	0.707987i	$-0.749603\pi$
$709$	−1.89055e7	−1.41245	−0.706225	+	0.707987i	$0.749603\pi$
$710$	1.60800e6	0.119713
$711$	0	0
$712$	4.58726e6	0.339120
$713$	7.00608e6	0.516121
$714$	0	0
$715$	−3.34388e6	−0.244616
$716$	−2.65901e6	−0.193837
$717$	0	0
$718$	7.35802e6	0.532659
$719$	1.83928e7	1.32686	0.663430	−	0.748238i	$-0.269100\pi$
$719$	1.83928e7	1.32686	0.663430	+	0.748238i	$0.269100\pi$
$720$	0	0
$721$	5.67856e6	0.406818
$722$	6.70938e6	0.479004
$723$	0	0
$724$	−3.15712e6	−0.223844
$725$	3.12562e6	0.220847
$726$	0	0
$727$	−1.34259e7	−0.942123	−0.471061	−	0.882100i	$-0.656129\pi$
$727$	−1.34259e7	−0.942123	−0.471061	+	0.882100i	$0.656129\pi$
$728$	−755776.	−0.0528524
$729$	0	0
$730$	8.04820e6	0.558974
$731$	897582.	0.0621270
$732$	0	0
$733$	1.08473e7	0.745697	0.372848	−	0.927892i	$-0.378381\pi$
$733$	1.08473e7	0.745697	0.372848	+	0.927892i	$0.378381\pi$
$734$	−6.75329e6	−0.462674
$735$	0	0
$736$	1.25952e6	0.0857059
$737$	−3.66877e7	−2.48801
$738$	0	0
$739$	2.64323e7	1.78043	0.890214	−	0.455542i	$-0.150555\pi$
$739$	2.64323e7	1.78043	0.890214	+	0.455542i	$0.150555\pi$
$740$	2.24080e6	0.150426
$741$	0	0
$742$	4.95802e6	0.330596
$743$	−2.03120e7	−1.34984	−0.674918	−	0.737893i	$-0.735821\pi$
$743$	−2.03120e7	−1.34984	−0.674918	+	0.737893i	$0.735821\pi$
$744$	0	0
$745$	4.40205e6	0.290579
$746$	7.24846e6	0.476869
$747$	0	0
$748$	−1.32401e7	−0.865240
$749$	6.75524e6	0.439983
$750$	0	0
$751$	−3.95388e6	−0.255813	−0.127907	−	0.991786i	$-0.540826\pi$
$751$	−3.95388e6	−0.255813	−0.127907	+	0.991786i	$0.540826\pi$
$752$	5.92973e6	0.382376
$753$	0	0
$754$	−4.82096e6	−0.308820
$755$	−9.58332e6	−0.611855
$756$	0	0
$757$	−2.62165e7	−1.66278	−0.831391	−	0.555688i	$-0.812455\pi$
$757$	−2.62165e7	−1.66278	−0.831391	+	0.555688i	$0.812455\pi$
$758$	−1.90683e7	−1.20542
$759$	0	0
$760$	3.26080e6	0.204781
$761$	−1.14329e7	−0.715638	−0.357819	−	0.933791i	$-0.616479\pi$
$761$	−1.14329e7	−0.715638	−0.357819	+	0.933791i	$0.616479\pi$
$762$	0	0
$763$	4.33145e6	0.269353
$764$	5.39554e6	0.334427
$765$	0	0
$766$	279984.	0.0172410
$767$	1.37948e6	0.0846697
$768$	0	0
$769$	2.37076e7	1.44568	0.722840	−	0.691015i	$-0.242836\pi$
$769$	2.37076e7	1.44568	0.722840	+	0.691015i	$0.242836\pi$
$770$	2.71950e6	0.165296
$771$	0	0
$772$	4.16826e6	0.251716
$773$	1.24180e7	0.747484	0.373742	−	0.927533i	$-0.378075\pi$
$773$	1.24180e7	0.747484	0.373742	+	0.927533i	$0.378075\pi$
$774$	0	0
$775$	3.56000e6	0.212910
$776$	9.66560e6	0.576202
$777$	0	0
$778$	−1.59558e7	−0.945083
$779$	−4.94011e6	−0.291671
$780$	0	0
$781$	8.92440e6	0.523542
$782$	7.33572e6	0.428969
$783$	0	0
$784$	614656.	0.0357143
$785$	−8.64785e6	−0.500880
$786$	0	0
$787$	3.06553e7	1.76428	0.882142	−	0.470984i	$-0.156101\pi$
$787$	3.06553e7	1.76428	0.882142	+	0.470984i	$0.156101\pi$
$788$	6.54739e6	0.375624
$789$	0	0
$790$	6.41470e6	0.365686
$791$	−1.00721e7	−0.572375
$792$	0	0
$793$	8.70299e6	0.491457
$794$	−1.22361e7	−0.688800
$795$	0	0
$796$	4.81568e6	0.269386
$797$	1.51870e7	0.846886	0.423443	−	0.905923i	$-0.360821\pi$
$797$	1.51870e7	0.846886	0.423443	+	0.905923i	$0.360821\pi$
$798$	0	0
$799$	3.45360e7	1.91384
$800$	640000.	0.0353553
$801$	0	0
$802$	−1.72317e7	−0.946005
$803$	4.46675e7	2.44457
$804$	0	0
$805$	−1.50675e6	−0.0819505
$806$	−5.49094e6	−0.297721
$807$	0	0
$808$	3.65760e6	0.197091
$809$	−539721.	−0.0289933	−0.0144967	−	0.999895i	$-0.504615\pi$
$809$	−539721.	−0.0289933	−0.0144967	+	0.999895i	$0.504615\pi$
$810$	0	0
$811$	1.39772e7	0.746221	0.373111	−	0.927787i	$-0.378291\pi$
$811$	1.39772e7	0.746221	0.373111	+	0.927787i	$0.378291\pi$
$812$	3.92078e6	0.208681
$813$	0	0
$814$	1.24364e7	0.657862
$815$	−2.28965e6	−0.120747
$816$	0	0
$817$	−1.22688e6	−0.0643051
$818$	−956824.	−0.0499976
$819$	0	0
$820$	−969600.	−0.0503568
$821$	1.78137e7	0.922350	0.461175	−	0.887309i	$-0.347428\pi$
$821$	1.78137e7	0.922350	0.461175	+	0.887309i	$0.347428\pi$
$822$	0	0
$823$	1.91010e7	0.983005	0.491502	−	0.870876i	$-0.336448\pi$
$823$	1.91010e7	0.983005	0.491502	+	0.870876i	$0.336448\pi$
$824$	7.41690e6	0.380543
$825$	0	0
$826$	−1.12190e6	−0.0572144
$827$	−3.19225e6	−0.162305	−0.0811526	−	0.996702i	$-0.525860\pi$
$827$	−3.19225e6	−0.162305	−0.0811526	+	0.996702i	$0.525860\pi$
$828$	0	0
$829$	8.56842e6	0.433026	0.216513	−	0.976280i	$-0.430532\pi$
$829$	8.56842e6	0.433026	0.216513	+	0.976280i	$0.430532\pi$
$830$	−1.06284e7	−0.535516
$831$	0	0
$832$	−987136.	−0.0494389
$833$	3.57989e6	0.178755
$834$	0	0
$835$	952425.	0.0472732
$836$	1.80974e7	0.895574
$837$	0	0
$838$	−1.85385e7	−0.911935
$839$	−3.56751e7	−1.74969	−0.874843	−	0.484407i	$-0.839036\pi$
$839$	−3.56751e7	−1.74969	−0.874843	+	0.484407i	$0.839036\pi$
$840$	0	0
$841$	4.49885e6	0.219337
$842$	−8.40430e6	−0.408528
$843$	0	0
$844$	−1.96189e7	−0.948021
$845$	7.83030e6	0.377256
$846$	0	0
$847$	7.20173e6	0.344928
$848$	6.47578e6	0.309245
$849$	0	0
$850$	3.72750e6	0.176958
$851$	−6.89046e6	−0.326155
$852$	0	0
$853$	3.06355e7	1.44163	0.720814	−	0.693129i	$-0.243768\pi$
$853$	3.06355e7	1.44163	0.720814	+	0.693129i	$0.243768\pi$
$854$	−7.07795e6	−0.332095
$855$	0	0
$856$	8.82317e6	0.411567
$857$	4.46188e6	0.207523	0.103761	−	0.994602i	$-0.466912\pi$
$857$	4.46188e6	0.207523	0.103761	+	0.994602i	$0.466912\pi$
$858$	0	0
$859$	2.63974e7	1.22061	0.610307	−	0.792165i	$-0.291046\pi$
$859$	2.63974e7	1.22061	0.610307	+	0.792165i	$0.291046\pi$
$860$	−240800.	−0.0111022
$861$	0	0
$862$	−6.61936e6	−0.303422
$863$	2.17530e7	0.994244	0.497122	−	0.867681i	$-0.334390\pi$
$863$	2.17530e7	0.994244	0.497122	+	0.867681i	$0.334390\pi$
$864$	0	0
$865$	−1.35361e7	−0.615110
$866$	−7.36122e6	−0.333546
$867$	0	0
$868$	4.46566e6	0.201181
$869$	3.56016e7	1.59926
$870$	0	0
$871$	−1.59311e7	−0.711540
$872$	5.65741e6	0.251957
$873$	0	0
$874$	−1.00270e7	−0.444008
$875$	−765625.	−0.0338062
$876$	0	0
$877$	−1.58383e7	−0.695361	−0.347680	−	0.937613i	$-0.613031\pi$
$877$	−1.58383e7	−0.695361	−0.347680	+	0.937613i	$0.613031\pi$
$878$	2.33474e7	1.02212
$879$	0	0
$880$	3.55200e6	0.154620
$881$	−1.97427e7	−0.856974	−0.428487	−	0.903548i	$-0.640953\pi$
$881$	−1.97427e7	−0.856974	−0.428487	+	0.903548i	$0.640953\pi$
$882$	0	0
$883$	−1.72899e7	−0.746263	−0.373131	−	0.927779i	$-0.621716\pi$
$883$	−1.72899e7	−0.746263	−0.373131	+	0.927779i	$0.621716\pi$
$884$	−5.74930e6	−0.247448
$885$	0	0
$886$	−4.78817e6	−0.204920
$887$	4.44693e7	1.89780	0.948901	−	0.315574i	$-0.102197\pi$
$887$	4.44693e7	1.89780	0.948901	+	0.315574i	$0.102197\pi$
$888$	0	0
$889$	1.22949e7	0.521759
$890$	−7.16760e6	−0.303318
$891$	0	0
$892$	9.94011e6	0.418292
$893$	−4.72062e7	−1.98094
$894$	0	0
$895$	4.15470e6	0.173373
$896$	802816.	0.0334077
$897$	0	0
$898$	1.37028e7	0.567046
$899$	2.84857e7	1.17551
$900$	0	0
$901$	3.77163e7	1.54781
$902$	−5.38128e6	−0.220226
$903$	0	0
$904$	−1.31555e7	−0.535408
$905$	4.93300e6	0.200212
$906$	0	0
$907$	2.56887e6	0.103687	0.0518434	−	0.998655i	$-0.483490\pi$
$907$	2.56887e6	0.103687	0.0518434	+	0.998655i	$0.483490\pi$
$908$	−2.07628e7	−0.835742
$909$	0	0
$910$	1.18090e6	0.0472726
$911$	−1.12692e7	−0.449882	−0.224941	−	0.974372i	$-0.572219\pi$
$911$	−1.12692e7	−0.449882	−0.224941	+	0.974372i	$0.572219\pi$
$912$	0	0
$913$	−5.89876e7	−2.34198
$914$	2.11897e7	0.838994
$915$	0	0
$916$	−1.98822e6	−0.0782937
$917$	2.55398e6	0.100298
$918$	0	0
$919$	3.18378e7	1.24353	0.621763	−	0.783205i	$-0.286417\pi$
$919$	3.18378e7	1.24353	0.621763	+	0.783205i	$0.286417\pi$
$920$	−1.96800e6	−0.0766577
$921$	0	0
$922$	−3.55092e7	−1.37567
$923$	3.87528e6	0.149727
$924$	0	0
$925$	−3.50125e6	−0.134545
$926$	−8.69901e6	−0.333382
$927$	0	0
$928$	5.12102e6	0.195203
$929$	−1.88558e7	−0.716813	−0.358407	−	0.933566i	$-0.616680\pi$
$929$	−1.88558e7	−0.716813	−0.358407	+	0.933566i	$0.616680\pi$
$930$	0	0
$931$	−4.89324e6	−0.185021
$932$	−1.73987e7	−0.656109
$933$	0	0
$934$	1.51588e6	0.0568586
$935$	2.06876e7	0.773894
$936$	0	0
$937$	1.12946e7	0.420265	0.210132	−	0.977673i	$-0.432610\pi$
$937$	1.12946e7	0.420265	0.210132	+	0.977673i	$0.432610\pi$
$938$	1.29564e7	0.480814
$939$	0	0
$940$	−9.26520e6	−0.342007
$941$	2.91941e7	1.07478	0.537392	−	0.843333i	$-0.319410\pi$
$941$	2.91941e7	1.07478	0.537392	+	0.843333i	$0.319410\pi$
$942$	0	0
$943$	2.98152e6	0.109184
$944$	−1.46534e6	−0.0535192
$945$	0	0
$946$	−1.33644e6	−0.0485536
$947$	−1.05892e7	−0.383697	−0.191848	−	0.981425i	$-0.561448\pi$
$947$	−1.05892e7	−0.383697	−0.191848	+	0.981425i	$0.561448\pi$
$948$	0	0
$949$	1.93962e7	0.699118
$950$	−5.09500e6	−0.183162
$951$	0	0
$952$	4.67578e6	0.167210
$953$	3.90317e7	1.39215	0.696074	−	0.717970i	$-0.254929\pi$
$953$	3.90317e7	1.39215	0.696074	+	0.717970i	$0.254929\pi$
$954$	0	0
$955$	−8.43052e6	−0.299121
$956$	8.73010e6	0.308940
$957$	0	0
$958$	−7.53958e6	−0.265420
$959$	6.63793e6	0.233070
$960$	0	0
$961$	3.81526e6	0.133265
$962$	5.40033e6	0.188141
$963$	0	0
$964$	1.29810e7	0.449898
$965$	−6.51290e6	−0.225142
$966$	0	0
$967$	−3.43395e7	−1.18094	−0.590470	−	0.807059i	$-0.701058\pi$
$967$	−3.43395e7	−1.18094	−0.590470	+	0.807059i	$0.701058\pi$
$968$	9.40634e6	0.322650
$969$	0	0
$970$	−1.51025e7	−0.515370
$971$	1.81464e7	0.617651	0.308826	−	0.951119i	$-0.400064\pi$
$971$	1.81464e7	0.617651	0.308826	+	0.951119i	$0.400064\pi$
$972$	0	0
$973$	−1.71248e7	−0.579888
$974$	1.47075e7	0.496756
$975$	0	0
$976$	−9.24467e6	−0.310647
$977$	1.05223e7	0.352675	0.176338	−	0.984330i	$-0.443575\pi$
$977$	1.05223e7	0.352675	0.176338	+	0.984330i	$0.443575\pi$
$978$	0	0
$979$	−3.97802e7	−1.32651
$980$	−960400.	−0.0319438
$981$	0	0
$982$	−3.81606e7	−1.26281
$983$	7.91353e6	0.261208	0.130604	−	0.991435i	$-0.458308\pi$
$983$	7.91353e6	0.261208	0.130604	+	0.991435i	$0.458308\pi$
$984$	0	0
$985$	−1.02303e7	−0.335968
$986$	2.98260e7	0.977017
$987$	0	0
$988$	7.85853e6	0.256123
$989$	740460.	0.0240719
$990$	0	0
$991$	4.01556e7	1.29886	0.649429	−	0.760422i	$-0.275008\pi$
$991$	4.01556e7	1.29886	0.649429	+	0.760422i	$0.275008\pi$
$992$	5.83270e6	0.188187
$993$	0	0
$994$	−3.15168e6	−0.101176
$995$	−7.52450e6	−0.240946
$996$	0	0
$997$	−4.93478e7	−1.57228	−0.786140	−	0.618048i	$-0.787924\pi$
$997$	−4.93478e7	−1.57228	−0.786140	+	0.618048i	$0.787924\pi$
$998$	1.91297e7	0.607970
$999$	0	0

Twists

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

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