LMFDB - Embedded newform 1170.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,4,Mod(1,1170)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("1170.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1170.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:	$69.0322347067$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1170.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} +5.00000 q^{7} +8.00000 q^{8} +O(q^{10})$

\(q+2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} +5.00000 q^{7} +8.00000 q^{8} -10.0000 q^{10} +35.0000 q^{11} -13.0000 q^{13} +10.0000 q^{14} +16.0000 q^{16} -23.0000 q^{17} -30.0000 q^{19} -20.0000 q^{20} +70.0000 q^{22} -63.0000 q^{23} +25.0000 q^{25} -26.0000 q^{26} +20.0000 q^{28} +190.000 q^{29} +330.000 q^{31} +32.0000 q^{32} -46.0000 q^{34} -25.0000 q^{35} +43.0000 q^{37} -60.0000 q^{38} -40.0000 q^{40} +473.000 q^{41} -232.000 q^{43} +140.000 q^{44} -126.000 q^{46} -270.000 q^{47} -318.000 q^{49} +50.0000 q^{50} -52.0000 q^{52} +193.000 q^{53} -175.000 q^{55} +40.0000 q^{56} +380.000 q^{58} +200.000 q^{59} -679.000 q^{61} +660.000 q^{62} +64.0000 q^{64} +65.0000 q^{65} -12.0000 q^{67} -92.0000 q^{68} -50.0000 q^{70} +899.000 q^{71} +154.000 q^{73} +86.0000 q^{74} -120.000 q^{76} +175.000 q^{77} +215.000 q^{79} -80.0000 q^{80} +946.000 q^{82} +1308.00 q^{83} +115.000 q^{85} -464.000 q^{86} +280.000 q^{88} +1019.00 q^{89} -65.0000 q^{91} -252.000 q^{92} -540.000 q^{94} +150.000 q^{95} -427.000 q^{97} -636.000 q^{98} +O(q^{100})\)

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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	0	0
$3$	0	0
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	0	0
$7$	5.00000	0.269975	0.134987	−	0.990847i	$-0.456901\pi$
$7$	5.00000	0.269975	0.134987	+	0.990847i	$0.456901\pi$
$8$	8.00000	0.353553
$9$	0	0
$10$	−10.0000	−0.316228
$11$	35.0000	0.959354	0.479677	−	0.877445i	$-0.340754\pi$
$11$	35.0000	0.959354	0.479677	+	0.877445i	$0.340754\pi$
$12$	0	0
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	10.0000	0.190901
$15$	0	0
$16$	16.0000	0.250000
$17$	−23.0000	−0.328136	−0.164068	−	0.986449i	$-0.552462\pi$
$17$	−23.0000	−0.328136	−0.164068	+	0.986449i	$0.552462\pi$
$18$	0	0
$19$	−30.0000	−0.362235	−0.181118	−	0.983461i	$-0.557971\pi$
$19$	−30.0000	−0.362235	−0.181118	+	0.983461i	$0.557971\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	70.0000	0.678366
$23$	−63.0000	−0.571148	−0.285574	−	0.958357i	$-0.592184\pi$
$23$	−63.0000	−0.571148	−0.285574	+	0.958357i	$0.592184\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	−26.0000	−0.196116
$27$	0	0
$28$	20.0000	0.134987
$29$	190.000	1.21662	0.608312	−	0.793698i	$-0.291847\pi$
$29$	190.000	1.21662	0.608312	+	0.793698i	$0.291847\pi$
$30$	0	0
$31$	330.000	1.91193	0.955964	−	0.293485i	$-0.0948150\pi$
$31$	330.000	1.91193	0.955964	+	0.293485i	$0.0948150\pi$
$32$	32.0000	0.176777
$33$	0	0
$34$	−46.0000	−0.232027
$35$	−25.0000	−0.120736
$36$	0	0
$37$	43.0000	0.191058	0.0955291	−	0.995427i	$-0.469546\pi$
$37$	43.0000	0.191058	0.0955291	+	0.995427i	$0.469546\pi$
$38$	−60.0000	−0.256139
$39$	0	0
$40$	−40.0000	−0.158114
$41$	473.000	1.80171	0.900856	−	0.434118i	$-0.142940\pi$
$41$	473.000	1.80171	0.900856	+	0.434118i	$0.142940\pi$
$42$	0	0
$43$	−232.000	−0.822783	−0.411391	−	0.911459i	$-0.634957\pi$
$43$	−232.000	−0.822783	−0.411391	+	0.911459i	$0.634957\pi$
$44$	140.000	0.479677
$45$	0	0
$46$	−126.000	−0.403863
$47$	−270.000	−0.837948	−0.418974	−	0.907998i	$-0.637610\pi$
$47$	−270.000	−0.837948	−0.418974	+	0.907998i	$0.637610\pi$
$48$	0	0
$49$	−318.000	−0.927114
$50$	50.0000	0.141421
$51$	0	0
$52$	−52.0000	−0.138675
$53$	193.000	0.500200	0.250100	−	0.968220i	$-0.419537\pi$
$53$	193.000	0.500200	0.250100	+	0.968220i	$0.419537\pi$
$54$	0	0
$55$	−175.000	−0.429036
$56$	40.0000	0.0954504
$57$	0	0
$58$	380.000	0.860284
$59$	200.000	0.441318	0.220659	−	0.975351i	$-0.429179\pi$
$59$	200.000	0.441318	0.220659	+	0.975351i	$0.429179\pi$
$60$	0	0
$61$	−679.000	−1.42520	−0.712599	−	0.701572i	$-0.752482\pi$
$61$	−679.000	−1.42520	−0.712599	+	0.701572i	$0.752482\pi$
$62$	660.000	1.35194
$63$	0	0
$64$	64.0000	0.125000
$65$	65.0000	0.124035
$66$	0	0
$67$	−12.0000	−0.0218811	−0.0109405	−	0.999940i	$-0.503483\pi$
$67$	−12.0000	−0.0218811	−0.0109405	+	0.999940i	$0.503483\pi$
$68$	−92.0000	−0.164068
$69$	0	0
$70$	−50.0000	−0.0853735
$71$	899.000	1.50270	0.751350	−	0.659904i	$-0.229403\pi$
$71$	899.000	1.50270	0.751350	+	0.659904i	$0.229403\pi$
$72$	0	0
$73$	154.000	0.246909	0.123454	−	0.992350i	$-0.460603\pi$
$73$	154.000	0.246909	0.123454	+	0.992350i	$0.460603\pi$
$74$	86.0000	0.135099
$75$	0	0
$76$	−120.000	−0.181118
$77$	175.000	0.259001
$78$	0	0
$79$	215.000	0.306195	0.153097	−	0.988211i	$-0.451075\pi$
$79$	215.000	0.306195	0.153097	+	0.988211i	$0.451075\pi$
$80$	−80.0000	−0.111803
$81$	0	0
$82$	946.000	1.27400
$83$	1308.00	1.72978	0.864889	−	0.501962i	$-0.167388\pi$
$83$	1308.00	1.72978	0.864889	+	0.501962i	$0.167388\pi$
$84$	0	0
$85$	115.000	0.146747
$86$	−464.000	−0.581795
$87$	0	0
$88$	280.000	0.339183
$89$	1019.00	1.21364	0.606819	−	0.794840i	$-0.292445\pi$
$89$	1019.00	1.21364	0.606819	+	0.794840i	$0.292445\pi$
$90$	0	0
$91$	−65.0000	−0.0748775
$92$	−252.000	−0.285574
$93$	0	0
$94$	−540.000	−0.592519
$95$	150.000	0.161997
$96$	0	0
$97$	−427.000	−0.446962	−0.223481	−	0.974708i	$-0.571742\pi$
$97$	−427.000	−0.446962	−0.223481	+	0.974708i	$0.571742\pi$
$98$	−636.000	−0.655568
$99$	0	0
$100$	100.000	0.100000
$101$	1144.00	1.12705	0.563526	−	0.826098i	$-0.309444\pi$
$101$	1144.00	1.12705	0.563526	+	0.826098i	$0.309444\pi$
$102$	0	0
$103$	696.000	0.665815	0.332907	−	0.942960i	$-0.391970\pi$
$103$	696.000	0.665815	0.332907	+	0.942960i	$0.391970\pi$
$104$	−104.000	−0.0980581
$105$	0	0
$106$	386.000	0.353695
$107$	1353.00	1.22242	0.611212	−	0.791467i	$-0.290682\pi$
$107$	1353.00	1.22242	0.611212	+	0.791467i	$0.290682\pi$
$108$	0	0
$109$	504.000	0.442885	0.221442	−	0.975173i	$-0.428924\pi$
$109$	504.000	0.442885	0.221442	+	0.975173i	$0.428924\pi$
$110$	−350.000	−0.303374
$111$	0	0
$112$	80.0000	0.0674937
$113$	−1790.00	−1.49017	−0.745084	−	0.666970i	$-0.767591\pi$
$113$	−1790.00	−1.49017	−0.745084	+	0.666970i	$0.767591\pi$
$114$	0	0
$115$	315.000	0.255425
$116$	760.000	0.608312
$117$	0	0
$118$	400.000	0.312059
$119$	−115.000	−0.0885885
$120$	0	0
$121$	−106.000	−0.0796394
$122$	−1358.00	−1.00777
$123$	0	0
$124$	1320.00	0.955964
$125$	−125.000	−0.0894427
$126$	0	0
$127$	1306.00	0.912510	0.456255	−	0.889849i	$-0.349191\pi$
$127$	1306.00	0.912510	0.456255	+	0.889849i	$0.349191\pi$
$128$	128.000	0.0883883
$129$	0	0
$130$	130.000	0.0877058
$131$	1718.00	1.14582	0.572910	−	0.819618i	$-0.305815\pi$
$131$	1718.00	1.14582	0.572910	+	0.819618i	$0.305815\pi$
$132$	0	0
$133$	−150.000	−0.0977944
$134$	−24.0000	−0.0154723
$135$	0	0
$136$	−184.000	−0.116014
$137$	438.000	0.273145	0.136573	−	0.990630i	$-0.456391\pi$
$137$	438.000	0.273145	0.136573	+	0.990630i	$0.456391\pi$
$138$	0	0
$139$	721.000	0.439960	0.219980	−	0.975504i	$-0.429401\pi$
$139$	721.000	0.439960	0.219980	+	0.975504i	$0.429401\pi$
$140$	−100.000	−0.0603682
$141$	0	0
$142$	1798.00	1.06257
$143$	−455.000	−0.266077
$144$	0	0
$145$	−950.000	−0.544091
$146$	308.000	0.174591
$147$	0	0
$148$	172.000	0.0955291
$149$	−29.0000	−0.0159448	−0.00797239	−	0.999968i	$-0.502538\pi$
$149$	−29.0000	−0.0159448	−0.00797239	+	0.999968i	$0.502538\pi$
$150$	0	0
$151$	−816.000	−0.439769	−0.219885	−	0.975526i	$-0.570568\pi$
$151$	−816.000	−0.439769	−0.219885	+	0.975526i	$0.570568\pi$
$152$	−240.000	−0.128070
$153$	0	0
$154$	350.000	0.183142
$155$	−1650.00	−0.855040
$156$	0	0
$157$	−1298.00	−0.659820	−0.329910	−	0.944012i	$-0.607018\pi$
$157$	−1298.00	−0.659820	−0.329910	+	0.944012i	$0.607018\pi$
$158$	430.000	0.216512
$159$	0	0
$160$	−160.000	−0.0790569
$161$	−315.000	−0.154196
$162$	0	0
$163$	3113.00	1.49588	0.747942	−	0.663764i	$-0.231042\pi$
$163$	3113.00	1.49588	0.747942	+	0.663764i	$0.231042\pi$
$164$	1892.00	0.900856
$165$	0	0
$166$	2616.00	1.22314
$167$	172.000	0.0796992	0.0398496	−	0.999206i	$-0.487312\pi$
$167$	172.000	0.0796992	0.0398496	+	0.999206i	$0.487312\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	230.000	0.103766
$171$	0	0
$172$	−928.000	−0.411391
$173$	1982.00	0.871033	0.435516	−	0.900181i	$-0.356566\pi$
$173$	1982.00	0.871033	0.435516	+	0.900181i	$0.356566\pi$
$174$	0	0
$175$	125.000	0.0539949
$176$	560.000	0.239839
$177$	0	0
$178$	2038.00	0.858172
$179$	−2990.00	−1.24851	−0.624254	−	0.781221i	$-0.714597\pi$
$179$	−2990.00	−1.24851	−0.624254	+	0.781221i	$0.714597\pi$
$180$	0	0
$181$	1885.00	0.774094	0.387047	−	0.922060i	$-0.373495\pi$
$181$	1885.00	0.774094	0.387047	+	0.922060i	$0.373495\pi$
$182$	−130.000	−0.0529464
$183$	0	0
$184$	−504.000	−0.201931
$185$	−215.000	−0.0854439
$186$	0	0
$187$	−805.000	−0.314799
$188$	−1080.00	−0.418974
$189$	0	0
$190$	300.000	0.114549
$191$	516.000	0.195479	0.0977394	−	0.995212i	$-0.468839\pi$
$191$	516.000	0.195479	0.0977394	+	0.995212i	$0.468839\pi$
$192$	0	0
$193$	−2713.00	−1.01184	−0.505922	−	0.862579i	$-0.668848\pi$
$193$	−2713.00	−1.01184	−0.505922	+	0.862579i	$0.668848\pi$
$194$	−854.000	−0.316050
$195$	0	0
$196$	−1272.00	−0.463557
$197$	−1116.00	−0.403613	−0.201806	−	0.979425i	$-0.564681\pi$
$197$	−1116.00	−0.403613	−0.201806	+	0.979425i	$0.564681\pi$
$198$	0	0
$199$	−1164.00	−0.414642	−0.207321	−	0.978273i	$-0.566474\pi$
$199$	−1164.00	−0.414642	−0.207321	+	0.978273i	$0.566474\pi$
$200$	200.000	0.0707107
$201$	0	0
$202$	2288.00	0.796946
$203$	950.000	0.328458
$204$	0	0
$205$	−2365.00	−0.805750
$206$	1392.00	0.470802
$207$	0	0
$208$	−208.000	−0.0693375
$209$	−1050.00	−0.347512
$210$	0	0
$211$	−3572.00	−1.16543	−0.582717	−	0.812675i	$-0.698010\pi$
$211$	−3572.00	−1.16543	−0.582717	+	0.812675i	$0.698010\pi$
$212$	772.000	0.250100
$213$	0	0
$214$	2706.00	0.864385
$215$	1160.00	0.367960
$216$	0	0
$217$	1650.00	0.516172
$218$	1008.00	0.313167
$219$	0	0
$220$	−700.000	−0.214518
$221$	299.000	0.0910087
$222$	0	0
$223$	5248.00	1.57593	0.787964	−	0.615721i	$-0.211135\pi$
$223$	5248.00	1.57593	0.787964	+	0.615721i	$0.211135\pi$
$224$	160.000	0.0477252
$225$	0	0
$226$	−3580.00	−1.05371
$227$	−5810.00	−1.69878	−0.849390	−	0.527765i	$-0.823030\pi$
$227$	−5810.00	−1.69878	−0.849390	+	0.527765i	$0.823030\pi$
$228$	0	0
$229$	5278.00	1.52306	0.761529	−	0.648131i	$-0.224449\pi$
$229$	5278.00	1.52306	0.761529	+	0.648131i	$0.224449\pi$
$230$	630.000	0.180613
$231$	0	0
$232$	1520.00	0.430142
$233$	5091.00	1.43143	0.715714	−	0.698394i	$-0.246102\pi$
$233$	5091.00	1.43143	0.715714	+	0.698394i	$0.246102\pi$
$234$	0	0
$235$	1350.00	0.374742
$236$	800.000	0.220659
$237$	0	0
$238$	−230.000	−0.0626415
$239$	−4549.00	−1.23117	−0.615587	−	0.788069i	$-0.711081\pi$
$239$	−4549.00	−1.23117	−0.615587	+	0.788069i	$0.711081\pi$
$240$	0	0
$241$	−4534.00	−1.21187	−0.605935	−	0.795514i	$-0.707201\pi$
$241$	−4534.00	−1.21187	−0.605935	+	0.795514i	$0.707201\pi$
$242$	−212.000	−0.0563135
$243$	0	0
$244$	−2716.00	−0.712599
$245$	1590.00	0.414618
$246$	0	0
$247$	390.000	0.100466
$248$	2640.00	0.675968
$249$	0	0
$250$	−250.000	−0.0632456
$251$	6144.00	1.54504	0.772522	−	0.634988i	$-0.218995\pi$
$251$	6144.00	1.54504	0.772522	+	0.634988i	$0.218995\pi$
$252$	0	0
$253$	−2205.00	−0.547933
$254$	2612.00	0.645242
$255$	0	0
$256$	256.000	0.0625000
$257$	282.000	0.0684462	0.0342231	−	0.999414i	$-0.489104\pi$
$257$	282.000	0.0684462	0.0342231	+	0.999414i	$0.489104\pi$
$258$	0	0
$259$	215.000	0.0515809
$260$	260.000	0.0620174
$261$	0	0
$262$	3436.00	0.810217
$263$	−1736.00	−0.407020	−0.203510	−	0.979073i	$-0.565235\pi$
$263$	−1736.00	−0.407020	−0.203510	+	0.979073i	$0.565235\pi$
$264$	0	0
$265$	−965.000	−0.223696
$266$	−300.000	−0.0691511
$267$	0	0
$268$	−48.0000	−0.0109405
$269$	−6636.00	−1.50410	−0.752052	−	0.659104i	$-0.770936\pi$
$269$	−6636.00	−1.50410	−0.752052	+	0.659104i	$0.770936\pi$
$270$	0	0
$271$	106.000	0.0237603	0.0118802	−	0.999929i	$-0.496218\pi$
$271$	106.000	0.0237603	0.0118802	+	0.999929i	$0.496218\pi$
$272$	−368.000	−0.0820341
$273$	0	0
$274$	876.000	0.193143
$275$	875.000	0.191871
$276$	0	0
$277$	−4366.00	−0.947031	−0.473515	−	0.880786i	$-0.657015\pi$
$277$	−4366.00	−0.947031	−0.473515	+	0.880786i	$0.657015\pi$
$278$	1442.00	0.311099
$279$	0	0
$280$	−200.000	−0.0426867
$281$	4266.00	0.905652	0.452826	−	0.891599i	$-0.350416\pi$
$281$	4266.00	0.905652	0.452826	+	0.891599i	$0.350416\pi$
$282$	0	0
$283$	−3076.00	−0.646110	−0.323055	−	0.946380i	$-0.604710\pi$
$283$	−3076.00	−0.646110	−0.323055	+	0.946380i	$0.604710\pi$
$284$	3596.00	0.751350
$285$	0	0
$286$	−910.000	−0.188145
$287$	2365.00	0.486417
$288$	0	0
$289$	−4384.00	−0.892326
$290$	−1900.00	−0.384730
$291$	0	0
$292$	616.000	0.123454
$293$	−7048.00	−1.40529	−0.702643	−	0.711543i	$-0.747997\pi$
$293$	−7048.00	−1.40529	−0.702643	+	0.711543i	$0.747997\pi$
$294$	0	0
$295$	−1000.00	−0.197364
$296$	344.000	0.0675493
$297$	0	0
$298$	−58.0000	−0.0112747
$299$	819.000	0.158408
$300$	0	0
$301$	−1160.00	−0.222131
$302$	−1632.00	−0.310964
$303$	0	0
$304$	−480.000	−0.0905588
$305$	3395.00	0.637368
$306$	0	0
$307$	−4263.00	−0.792516	−0.396258	−	0.918139i	$-0.629691\pi$
$307$	−4263.00	−0.792516	−0.396258	+	0.918139i	$0.629691\pi$
$308$	700.000	0.129501
$309$	0	0
$310$	−3300.00	−0.604605
$311$	−444.000	−0.0809548	−0.0404774	−	0.999180i	$-0.512888\pi$
$311$	−444.000	−0.0809548	−0.0404774	+	0.999180i	$0.512888\pi$
$312$	0	0
$313$	−4242.00	−0.766045	−0.383022	−	0.923739i	$-0.625117\pi$
$313$	−4242.00	−0.766045	−0.383022	+	0.923739i	$0.625117\pi$
$314$	−2596.00	−0.466563
$315$	0	0
$316$	860.000	0.153097
$317$	2736.00	0.484760	0.242380	−	0.970181i	$-0.422072\pi$
$317$	2736.00	0.484760	0.242380	+	0.970181i	$0.422072\pi$
$318$	0	0
$319$	6650.00	1.16717
$320$	−320.000	−0.0559017
$321$	0	0
$322$	−630.000	−0.109033
$323$	690.000	0.118863
$324$	0	0
$325$	−325.000	−0.0554700
$326$	6226.00	1.05775
$327$	0	0
$328$	3784.00	0.637001
$329$	−1350.00	−0.226225
$330$	0	0
$331$	6148.00	1.02092	0.510460	−	0.859901i	$-0.329475\pi$
$331$	6148.00	1.02092	0.510460	+	0.859901i	$0.329475\pi$
$332$	5232.00	0.864889
$333$	0	0
$334$	344.000	0.0563558
$335$	60.0000	0.00978552
$336$	0	0
$337$	4016.00	0.649156	0.324578	−	0.945859i	$-0.394778\pi$
$337$	4016.00	0.649156	0.324578	+	0.945859i	$0.394778\pi$
$338$	338.000	0.0543928
$339$	0	0
$340$	460.000	0.0733735
$341$	11550.0	1.83422
$342$	0	0
$343$	−3305.00	−0.520272
$344$	−1856.00	−0.290898
$345$	0	0
$346$	3964.00	0.615913
$347$	−7299.00	−1.12920	−0.564598	−	0.825366i	$-0.690969\pi$
$347$	−7299.00	−1.12920	−0.564598	+	0.825366i	$0.690969\pi$
$348$	0	0
$349$	116.000	0.0177918	0.00889590	−	0.999960i	$-0.497168\pi$
$349$	116.000	0.0177918	0.00889590	+	0.999960i	$0.497168\pi$
$350$	250.000	0.0381802
$351$	0	0
$352$	1120.00	0.169591
$353$	6878.00	1.03705	0.518525	−	0.855062i	$-0.326481\pi$
$353$	6878.00	1.03705	0.518525	+	0.855062i	$0.326481\pi$
$354$	0	0
$355$	−4495.00	−0.672028
$356$	4076.00	0.606819
$357$	0	0
$358$	−5980.00	−0.882829
$359$	−4656.00	−0.684497	−0.342248	−	0.939610i	$-0.611188\pi$
$359$	−4656.00	−0.684497	−0.342248	+	0.939610i	$0.611188\pi$
$360$	0	0
$361$	−5959.00	−0.868786
$362$	3770.00	0.547367
$363$	0	0
$364$	−260.000	−0.0374387
$365$	−770.000	−0.110421
$366$	0	0
$367$	−5640.00	−0.802195	−0.401098	−	0.916035i	$-0.631371\pi$
$367$	−5640.00	−0.802195	−0.401098	+	0.916035i	$0.631371\pi$
$368$	−1008.00	−0.142787
$369$	0	0
$370$	−430.000	−0.0604179
$371$	965.000	0.135041
$372$	0	0
$373$	−4160.00	−0.577471	−0.288735	−	0.957409i	$-0.593235\pi$
$373$	−4160.00	−0.577471	−0.288735	+	0.957409i	$0.593235\pi$
$374$	−1610.00	−0.222597
$375$	0	0
$376$	−2160.00	−0.296259
$377$	−2470.00	−0.337431
$378$	0	0
$379$	−7854.00	−1.06447	−0.532233	−	0.846598i	$-0.678647\pi$
$379$	−7854.00	−1.06447	−0.532233	+	0.846598i	$0.678647\pi$
$380$	600.000	0.0809983
$381$	0	0
$382$	1032.00	0.138224
$383$	−1206.00	−0.160897	−0.0804487	−	0.996759i	$-0.525635\pi$
$383$	−1206.00	−0.160897	−0.0804487	+	0.996759i	$0.525635\pi$
$384$	0	0
$385$	−875.000	−0.115829
$386$	−5426.00	−0.715482
$387$	0	0
$388$	−1708.00	−0.223481
$389$	952.000	0.124083	0.0620415	−	0.998074i	$-0.480239\pi$
$389$	952.000	0.124083	0.0620415	+	0.998074i	$0.480239\pi$
$390$	0	0
$391$	1449.00	0.187415
$392$	−2544.00	−0.327784
$393$	0	0
$394$	−2232.00	−0.285397
$395$	−1075.00	−0.136934
$396$	0	0
$397$	5747.00	0.726533	0.363267	−	0.931685i	$-0.381661\pi$
$397$	5747.00	0.726533	0.363267	+	0.931685i	$0.381661\pi$
$398$	−2328.00	−0.293196
$399$	0	0
$400$	400.000	0.0500000
$401$	−11958.0	−1.48916	−0.744581	−	0.667532i	$-0.767351\pi$
$401$	−11958.0	−1.48916	−0.744581	+	0.667532i	$0.767351\pi$
$402$	0	0
$403$	−4290.00	−0.530273
$404$	4576.00	0.563526
$405$	0	0
$406$	1900.00	0.232255
$407$	1505.00	0.183293
$408$	0	0
$409$	14878.0	1.79870	0.899352	−	0.437226i	$-0.144039\pi$
$409$	14878.0	1.79870	0.899352	+	0.437226i	$0.144039\pi$
$410$	−4730.00	−0.569751
$411$	0	0
$412$	2784.00	0.332907
$413$	1000.00	0.119145
$414$	0	0
$415$	−6540.00	−0.773581
$416$	−416.000	−0.0490290
$417$	0	0
$418$	−2100.00	−0.245728
$419$	−3178.00	−0.370538	−0.185269	−	0.982688i	$-0.559316\pi$
$419$	−3178.00	−0.370538	−0.185269	+	0.982688i	$0.559316\pi$
$420$	0	0
$421$	−4412.00	−0.510755	−0.255377	−	0.966841i	$-0.582200\pi$
$421$	−4412.00	−0.510755	−0.255377	+	0.966841i	$0.582200\pi$
$422$	−7144.00	−0.824086
$423$	0	0
$424$	1544.00	0.176847
$425$	−575.000	−0.0656273
$426$	0	0
$427$	−3395.00	−0.384767
$428$	5412.00	0.611212
$429$	0	0
$430$	2320.00	0.260187
$431$	−9216.00	−1.02997	−0.514987	−	0.857198i	$-0.672203\pi$
$431$	−9216.00	−1.02997	−0.514987	+	0.857198i	$0.672203\pi$
$432$	0	0
$433$	2536.00	0.281460	0.140730	−	0.990048i	$-0.455055\pi$
$433$	2536.00	0.281460	0.140730	+	0.990048i	$0.455055\pi$
$434$	3300.00	0.364989
$435$	0	0
$436$	2016.00	0.221442
$437$	1890.00	0.206890
$438$	0	0
$439$	−1811.00	−0.196889	−0.0984445	−	0.995143i	$-0.531387\pi$
$439$	−1811.00	−0.196889	−0.0984445	+	0.995143i	$0.531387\pi$
$440$	−1400.00	−0.151687
$441$	0	0
$442$	598.000	0.0643528
$443$	−14743.0	−1.58118	−0.790588	−	0.612348i	$-0.790225\pi$
$443$	−14743.0	−1.58118	−0.790588	+	0.612348i	$0.790225\pi$
$444$	0	0
$445$	−5095.00	−0.542755
$446$	10496.0	1.11435
$447$	0	0
$448$	320.000	0.0337468
$449$	−999.000	−0.105002	−0.0525008	−	0.998621i	$-0.516719\pi$
$449$	−999.000	−0.105002	−0.0525008	+	0.998621i	$0.516719\pi$
$450$	0	0
$451$	16555.0	1.72848
$452$	−7160.00	−0.745084
$453$	0	0
$454$	−11620.0	−1.20122
$455$	325.000	0.0334862
$456$	0	0
$457$	18497.0	1.89333	0.946666	−	0.322215i	$-0.104427\pi$
$457$	18497.0	1.89333	0.946666	+	0.322215i	$0.104427\pi$
$458$	10556.0	1.07696
$459$	0	0
$460$	1260.00	0.127713
$461$	−3951.00	−0.399168	−0.199584	−	0.979881i	$-0.563959\pi$
$461$	−3951.00	−0.399168	−0.199584	+	0.979881i	$0.563959\pi$
$462$	0	0
$463$	−947.000	−0.0950558	−0.0475279	−	0.998870i	$-0.515134\pi$
$463$	−947.000	−0.0950558	−0.0475279	+	0.998870i	$0.515134\pi$
$464$	3040.00	0.304156
$465$	0	0
$466$	10182.0	1.01217
$467$	−4159.00	−0.412110	−0.206055	−	0.978540i	$-0.566063\pi$
$467$	−4159.00	−0.412110	−0.206055	+	0.978540i	$0.566063\pi$
$468$	0	0
$469$	−60.0000	−0.00590734
$470$	2700.00	0.264982
$471$	0	0
$472$	1600.00	0.156030
$473$	−8120.00	−0.789340
$474$	0	0
$475$	−750.000	−0.0724471
$476$	−460.000	−0.0442943
$477$	0	0
$478$	−9098.00	−0.870571
$479$	−14135.0	−1.34832	−0.674159	−	0.738586i	$-0.735494\pi$
$479$	−14135.0	−1.34832	−0.674159	+	0.738586i	$0.735494\pi$
$480$	0	0
$481$	−559.000	−0.0529900
$482$	−9068.00	−0.856921
$483$	0	0
$484$	−424.000	−0.0398197
$485$	2135.00	0.199887
$486$	0	0
$487$	−7609.00	−0.708001	−0.354001	−	0.935245i	$-0.615179\pi$
$487$	−7609.00	−0.708001	−0.354001	+	0.935245i	$0.615179\pi$
$488$	−5432.00	−0.503883
$489$	0	0
$490$	3180.00	0.293179
$491$	13320.0	1.22428	0.612142	−	0.790748i	$-0.290308\pi$
$491$	13320.0	1.22428	0.612142	+	0.790748i	$0.290308\pi$
$492$	0	0
$493$	−4370.00	−0.399219
$494$	780.000	0.0710402
$495$	0	0
$496$	5280.00	0.477982
$497$	4495.00	0.405691
$498$	0	0
$499$	−3010.00	−0.270032	−0.135016	−	0.990843i	$-0.543109\pi$
$499$	−3010.00	−0.270032	−0.135016	+	0.990843i	$0.543109\pi$
$500$	−500.000	−0.0447214
$501$	0	0
$502$	12288.0	1.09251
$503$	−16252.0	−1.44064	−0.720319	−	0.693643i	$-0.756005\pi$
$503$	−16252.0	−1.44064	−0.720319	+	0.693643i	$0.756005\pi$
$504$	0	0
$505$	−5720.00	−0.504033
$506$	−4410.00	−0.387447
$507$	0	0
$508$	5224.00	0.456255
$509$	−15873.0	−1.38224	−0.691118	−	0.722742i	$-0.742882\pi$
$509$	−15873.0	−1.38224	−0.691118	+	0.722742i	$0.742882\pi$
$510$	0	0
$511$	770.000	0.0666591
$512$	512.000	0.0441942
$513$	0	0
$514$	564.000	0.0483988
$515$	−3480.00	−0.297761
$516$	0	0
$517$	−9450.00	−0.803889
$518$	430.000	0.0364732
$519$	0	0
$520$	520.000	0.0438529
$521$	7910.00	0.665150	0.332575	−	0.943077i	$-0.392082\pi$
$521$	7910.00	0.665150	0.332575	+	0.943077i	$0.392082\pi$
$522$	0	0
$523$	−7020.00	−0.586928	−0.293464	−	0.955970i	$-0.594808\pi$
$523$	−7020.00	−0.586928	−0.293464	+	0.955970i	$0.594808\pi$
$524$	6872.00	0.572910
$525$	0	0
$526$	−3472.00	−0.287807
$527$	−7590.00	−0.627373
$528$	0	0
$529$	−8198.00	−0.673790
$530$	−1930.00	−0.158177
$531$	0	0
$532$	−600.000	−0.0488972
$533$	−6149.00	−0.499705
$534$	0	0
$535$	−6765.00	−0.546685
$536$	−96.0000	−0.00773614
$537$	0	0
$538$	−13272.0	−1.06356
$539$	−11130.0	−0.889430
$540$	0	0
$541$	7018.00	0.557722	0.278861	−	0.960332i	$-0.410043\pi$
$541$	7018.00	0.557722	0.278861	+	0.960332i	$0.410043\pi$
$542$	212.000	0.0168011
$543$	0	0
$544$	−736.000	−0.0580069
$545$	−2520.00	−0.198064
$546$	0	0
$547$	21136.0	1.65212	0.826060	−	0.563582i	$-0.190577\pi$
$547$	21136.0	1.65212	0.826060	+	0.563582i	$0.190577\pi$
$548$	1752.00	0.136573
$549$	0	0
$550$	1750.00	0.135673
$551$	−5700.00	−0.440704
$552$	0	0
$553$	1075.00	0.0826648
$554$	−8732.00	−0.669652
$555$	0	0
$556$	2884.00	0.219980
$557$	−13070.0	−0.994244	−0.497122	−	0.867681i	$-0.665610\pi$
$557$	−13070.0	−0.994244	−0.497122	+	0.867681i	$0.665610\pi$
$558$	0	0
$559$	3016.00	0.228199
$560$	−400.000	−0.0301841
$561$	0	0
$562$	8532.00	0.640393
$563$	15669.0	1.17295	0.586474	−	0.809968i	$-0.300516\pi$
$563$	15669.0	1.17295	0.586474	+	0.809968i	$0.300516\pi$
$564$	0	0
$565$	8950.00	0.666424
$566$	−6152.00	−0.456869
$567$	0	0
$568$	7192.00	0.531285
$569$	1404.00	0.103442	0.0517212	−	0.998662i	$-0.483529\pi$
$569$	1404.00	0.103442	0.0517212	+	0.998662i	$0.483529\pi$
$570$	0	0
$571$	8791.00	0.644294	0.322147	−	0.946690i	$-0.395595\pi$
$571$	8791.00	0.644294	0.322147	+	0.946690i	$0.395595\pi$
$572$	−1820.00	−0.133039
$573$	0	0
$574$	4730.00	0.343948
$575$	−1575.00	−0.114230
$576$	0	0
$577$	−8511.00	−0.614069	−0.307034	−	0.951698i	$-0.599337\pi$
$577$	−8511.00	−0.614069	−0.307034	+	0.951698i	$0.599337\pi$
$578$	−8768.00	−0.630970
$579$	0	0
$580$	−3800.00	−0.272046
$581$	6540.00	0.466996
$582$	0	0
$583$	6755.00	0.479869
$584$	1232.00	0.0872954
$585$	0	0
$586$	−14096.0	−0.993687
$587$	10494.0	0.737877	0.368938	−	0.929454i	$-0.379721\pi$
$587$	10494.0	0.737877	0.368938	+	0.929454i	$0.379721\pi$
$588$	0	0
$589$	−9900.00	−0.692568
$590$	−2000.00	−0.139557
$591$	0	0
$592$	688.000	0.0477646
$593$	22052.0	1.52709	0.763547	−	0.645752i	$-0.223456\pi$
$593$	22052.0	1.52709	0.763547	+	0.645752i	$0.223456\pi$
$594$	0	0
$595$	575.000	0.0396180
$596$	−116.000	−0.00797239
$597$	0	0
$598$	1638.00	0.112011
$599$	6384.00	0.435464	0.217732	−	0.976009i	$-0.430134\pi$
$599$	6384.00	0.435464	0.217732	+	0.976009i	$0.430134\pi$
$600$	0	0
$601$	10627.0	0.721272	0.360636	−	0.932707i	$-0.382560\pi$
$601$	10627.0	0.721272	0.360636	+	0.932707i	$0.382560\pi$
$602$	−2320.00	−0.157070
$603$	0	0
$604$	−3264.00	−0.219885
$605$	530.000	0.0356158
$606$	0	0
$607$	12668.0	0.847081	0.423541	−	0.905877i	$-0.360787\pi$
$607$	12668.0	0.847081	0.423541	+	0.905877i	$0.360787\pi$
$608$	−960.000	−0.0640348
$609$	0	0
$610$	6790.00	0.450687
$611$	3510.00	0.232405
$612$	0	0
$613$	−11491.0	−0.757124	−0.378562	−	0.925576i	$-0.623581\pi$
$613$	−11491.0	−0.757124	−0.378562	+	0.925576i	$0.623581\pi$
$614$	−8526.00	−0.560393
$615$	0	0
$616$	1400.00	0.0915708
$617$	23250.0	1.51703	0.758517	−	0.651653i	$-0.225924\pi$
$617$	23250.0	1.51703	0.758517	+	0.651653i	$0.225924\pi$
$618$	0	0
$619$	−20050.0	−1.30190	−0.650951	−	0.759120i	$-0.725630\pi$
$619$	−20050.0	−1.30190	−0.650951	+	0.759120i	$0.725630\pi$
$620$	−6600.00	−0.427520
$621$	0	0
$622$	−888.000	−0.0572437
$623$	5095.00	0.327651
$624$	0	0
$625$	625.000	0.0400000
$626$	−8484.00	−0.541675
$627$	0	0
$628$	−5192.00	−0.329910
$629$	−989.000	−0.0626932
$630$	0	0
$631$	−48.0000	−0.00302829	−0.00151414	−	0.999999i	$-0.500482\pi$
$631$	−48.0000	−0.00302829	−0.00151414	+	0.999999i	$0.500482\pi$
$632$	1720.00	0.108256
$633$	0	0
$634$	5472.00	0.342777
$635$	−6530.00	−0.408087
$636$	0	0
$637$	4134.00	0.257135
$638$	13300.0	0.825317
$639$	0	0
$640$	−640.000	−0.0395285
$641$	−912.000	−0.0561963	−0.0280982	−	0.999605i	$-0.508945\pi$
$641$	−912.000	−0.0561963	−0.0280982	+	0.999605i	$0.508945\pi$
$642$	0	0
$643$	13877.0	0.851097	0.425549	−	0.904936i	$-0.360081\pi$
$643$	13877.0	0.851097	0.425549	+	0.904936i	$0.360081\pi$
$644$	−1260.00	−0.0770978
$645$	0	0
$646$	1380.00	0.0840486
$647$	15987.0	0.971428	0.485714	−	0.874118i	$-0.338560\pi$
$647$	15987.0	0.971428	0.485714	+	0.874118i	$0.338560\pi$
$648$	0	0
$649$	7000.00	0.423381
$650$	−650.000	−0.0392232
$651$	0	0
$652$	12452.0	0.747942
$653$	−10542.0	−0.631762	−0.315881	−	0.948799i	$-0.602300\pi$
$653$	−10542.0	−0.631762	−0.315881	+	0.948799i	$0.602300\pi$
$654$	0	0
$655$	−8590.00	−0.512426
$656$	7568.00	0.450428
$657$	0	0
$658$	−2700.00	−0.159965
$659$	−22820.0	−1.34892	−0.674462	−	0.738310i	$-0.735624\pi$
$659$	−22820.0	−1.34892	−0.674462	+	0.738310i	$0.735624\pi$
$660$	0	0
$661$	6360.00	0.374244	0.187122	−	0.982337i	$-0.440084\pi$
$661$	6360.00	0.374244	0.187122	+	0.982337i	$0.440084\pi$
$662$	12296.0	0.721900
$663$	0	0
$664$	10464.0	0.611569
$665$	750.000	0.0437350
$666$	0	0
$667$	−11970.0	−0.694873
$668$	688.000	0.0398496
$669$	0	0
$670$	120.000	0.00691941
$671$	−23765.0	−1.36727
$672$	0	0
$673$	−32554.0	−1.86458	−0.932292	−	0.361708i	$-0.882194\pi$
$673$	−32554.0	−1.86458	−0.932292	+	0.361708i	$0.882194\pi$
$674$	8032.00	0.459022
$675$	0	0
$676$	676.000	0.0384615
$677$	7065.00	0.401078	0.200539	−	0.979686i	$-0.435731\pi$
$677$	7065.00	0.401078	0.200539	+	0.979686i	$0.435731\pi$
$678$	0	0
$679$	−2135.00	−0.120668
$680$	920.000	0.0518829
$681$	0	0
$682$	23100.0	1.29699
$683$	−8236.00	−0.461408	−0.230704	−	0.973024i	$-0.574103\pi$
$683$	−8236.00	−0.461408	−0.230704	+	0.973024i	$0.574103\pi$
$684$	0	0
$685$	−2190.00	−0.122154
$686$	−6610.00	−0.367888
$687$	0	0
$688$	−3712.00	−0.205696
$689$	−2509.00	−0.138730
$690$	0	0
$691$	23242.0	1.27955	0.639774	−	0.768563i	$-0.279028\pi$
$691$	23242.0	1.27955	0.639774	+	0.768563i	$0.279028\pi$
$692$	7928.00	0.435516
$693$	0	0
$694$	−14598.0	−0.798462
$695$	−3605.00	−0.196756
$696$	0	0
$697$	−10879.0	−0.591207
$698$	232.000	0.0125807
$699$	0	0
$700$	500.000	0.0269975
$701$	17308.0	0.932545	0.466273	−	0.884641i	$-0.345597\pi$
$701$	17308.0	0.932545	0.466273	+	0.884641i	$0.345597\pi$
$702$	0	0
$703$	−1290.00	−0.0692081
$704$	2240.00	0.119919
$705$	0	0
$706$	13756.0	0.733306
$707$	5720.00	0.304275
$708$	0	0
$709$	−4252.00	−0.225229	−0.112614	−	0.993639i	$-0.535922\pi$
$709$	−4252.00	−0.225229	−0.112614	+	0.993639i	$0.535922\pi$
$710$	−8990.00	−0.475195
$711$	0	0
$712$	8152.00	0.429086
$713$	−20790.0	−1.09199
$714$	0	0
$715$	2275.00	0.118993
$716$	−11960.0	−0.624254
$717$	0	0
$718$	−9312.00	−0.484012
$719$	35424.0	1.83740	0.918701	−	0.394953i	$-0.129239\pi$
$719$	35424.0	1.83740	0.918701	+	0.394953i	$0.129239\pi$
$720$	0	0
$721$	3480.00	0.179753
$722$	−11918.0	−0.614324
$723$	0	0
$724$	7540.00	0.387047
$725$	4750.00	0.243325
$726$	0	0
$727$	3754.00	0.191511	0.0957553	−	0.995405i	$-0.469473\pi$
$727$	3754.00	0.191511	0.0957553	+	0.995405i	$0.469473\pi$
$728$	−520.000	−0.0264732
$729$	0	0
$730$	−1540.00	−0.0780794
$731$	5336.00	0.269985
$732$	0	0
$733$	−35425.0	−1.78506	−0.892532	−	0.450984i	$-0.851073\pi$
$733$	−35425.0	−1.78506	−0.892532	+	0.450984i	$0.851073\pi$
$734$	−11280.0	−0.567238
$735$	0	0
$736$	−2016.00	−0.100966
$737$	−420.000	−0.0209917
$738$	0	0
$739$	−7170.00	−0.356905	−0.178452	−	0.983949i	$-0.557109\pi$
$739$	−7170.00	−0.356905	−0.178452	+	0.983949i	$0.557109\pi$
$740$	−860.000	−0.0427219
$741$	0	0
$742$	1930.00	0.0954886
$743$	−35946.0	−1.77487	−0.887437	−	0.460930i	$-0.847516\pi$
$743$	−35946.0	−1.77487	−0.887437	+	0.460930i	$0.847516\pi$
$744$	0	0
$745$	145.000	0.00713072
$746$	−8320.00	−0.408334
$747$	0	0
$748$	−3220.00	−0.157400
$749$	6765.00	0.330024
$750$	0	0
$751$	−20791.0	−1.01022	−0.505109	−	0.863055i	$-0.668548\pi$
$751$	−20791.0	−1.01022	−0.505109	+	0.863055i	$0.668548\pi$
$752$	−4320.00	−0.209487
$753$	0	0
$754$	−4940.00	−0.238600
$755$	4080.00	0.196671
$756$	0	0
$757$	−10536.0	−0.505862	−0.252931	−	0.967484i	$-0.581395\pi$
$757$	−10536.0	−0.505862	−0.252931	+	0.967484i	$0.581395\pi$
$758$	−15708.0	−0.752692
$759$	0	0
$760$	1200.00	0.0572744
$761$	−6778.00	−0.322868	−0.161434	−	0.986884i	$-0.551612\pi$
$761$	−6778.00	−0.322868	−0.161434	+	0.986884i	$0.551612\pi$
$762$	0	0
$763$	2520.00	0.119568
$764$	2064.00	0.0977394
$765$	0	0
$766$	−2412.00	−0.113772
$767$	−2600.00	−0.122400
$768$	0	0
$769$	33436.0	1.56792	0.783962	−	0.620809i	$-0.213196\pi$
$769$	33436.0	1.56792	0.783962	+	0.620809i	$0.213196\pi$
$770$	−1750.00	−0.0819034
$771$	0	0
$772$	−10852.0	−0.505922
$773$	13972.0	0.650114	0.325057	−	0.945694i	$-0.394617\pi$
$773$	13972.0	0.650114	0.325057	+	0.945694i	$0.394617\pi$
$774$	0	0
$775$	8250.00	0.382385
$776$	−3416.00	−0.158025
$777$	0	0
$778$	1904.00	0.0877400
$779$	−14190.0	−0.652644
$780$	0	0
$781$	31465.0	1.44162
$782$	2898.00	0.132522
$783$	0	0
$784$	−5088.00	−0.231778
$785$	6490.00	0.295080
$786$	0	0
$787$	−38132.0	−1.72714	−0.863570	−	0.504229i	$-0.831777\pi$
$787$	−38132.0	−1.72714	−0.863570	+	0.504229i	$0.831777\pi$
$788$	−4464.00	−0.201806
$789$	0	0
$790$	−2150.00	−0.0968273
$791$	−8950.00	−0.402308
$792$	0	0
$793$	8827.00	0.395279
$794$	11494.0	0.513737
$795$	0	0
$796$	−4656.00	−0.207321
$797$	6259.00	0.278175	0.139087	−	0.990280i	$-0.455583\pi$
$797$	6259.00	0.278175	0.139087	+	0.990280i	$0.455583\pi$
$798$	0	0
$799$	6210.00	0.274961
$800$	800.000	0.0353553
$801$	0	0
$802$	−23916.0	−1.05300
$803$	5390.00	0.236873
$804$	0	0
$805$	1575.00	0.0689583
$806$	−8580.00	−0.374960
$807$	0	0
$808$	9152.00	0.398473
$809$	2026.00	0.0880474	0.0440237	−	0.999030i	$-0.485982\pi$
$809$	2026.00	0.0880474	0.0440237	+	0.999030i	$0.485982\pi$
$810$	0	0
$811$	−5888.00	−0.254939	−0.127470	−	0.991842i	$-0.540686\pi$
$811$	−5888.00	−0.254939	−0.127470	+	0.991842i	$0.540686\pi$
$812$	3800.00	0.164229
$813$	0	0
$814$	3010.00	0.129607
$815$	−15565.0	−0.668979
$816$	0	0
$817$	6960.00	0.298041
$818$	29756.0	1.27188
$819$	0	0
$820$	−9460.00	−0.402875
$821$	31957.0	1.35847	0.679237	−	0.733919i	$-0.262311\pi$
$821$	31957.0	1.35847	0.679237	+	0.733919i	$0.262311\pi$
$822$	0	0
$823$	−40972.0	−1.73535	−0.867676	−	0.497131i	$-0.834387\pi$
$823$	−40972.0	−1.73535	−0.867676	+	0.497131i	$0.834387\pi$
$824$	5568.00	0.235401
$825$	0	0
$826$	2000.00	0.0842481
$827$	20934.0	0.880226	0.440113	−	0.897943i	$-0.354938\pi$
$827$	20934.0	0.880226	0.440113	+	0.897943i	$0.354938\pi$
$828$	0	0
$829$	−21994.0	−0.921451	−0.460726	−	0.887543i	$-0.652411\pi$
$829$	−21994.0	−0.921451	−0.460726	+	0.887543i	$0.652411\pi$
$830$	−13080.0	−0.547004
$831$	0	0
$832$	−832.000	−0.0346688
$833$	7314.00	0.304220
$834$	0	0
$835$	−860.000	−0.0356425
$836$	−4200.00	−0.173756
$837$	0	0
$838$	−6356.00	−0.262010
$839$	−19925.0	−0.819890	−0.409945	−	0.912110i	$-0.634452\pi$
$839$	−19925.0	−0.819890	−0.409945	+	0.912110i	$0.634452\pi$
$840$	0	0
$841$	11711.0	0.480175
$842$	−8824.00	−0.361158
$843$	0	0
$844$	−14288.0	−0.582717
$845$	−845.000	−0.0344010
$846$	0	0
$847$	−530.000	−0.0215006
$848$	3088.00	0.125050
$849$	0	0
$850$	−1150.00	−0.0464055
$851$	−2709.00	−0.109123
$852$	0	0
$853$	29821.0	1.19701	0.598506	−	0.801118i	$-0.295761\pi$
$853$	29821.0	1.19701	0.598506	+	0.801118i	$0.295761\pi$
$854$	−6790.00	−0.272071
$855$	0	0
$856$	10824.0	0.432192
$857$	−469.000	−0.0186940	−0.00934699	−	0.999956i	$-0.502975\pi$
$857$	−469.000	−0.0186940	−0.00934699	+	0.999956i	$0.502975\pi$
$858$	0	0
$859$	−26595.0	−1.05636	−0.528178	−	0.849134i	$-0.677125\pi$
$859$	−26595.0	−1.05636	−0.528178	+	0.849134i	$0.677125\pi$
$860$	4640.00	0.183980
$861$	0	0
$862$	−18432.0	−0.728302
$863$	−174.000	−0.00686330	−0.00343165	−	0.999994i	$-0.501092\pi$
$863$	−174.000	−0.00686330	−0.00343165	+	0.999994i	$0.501092\pi$
$864$	0	0
$865$	−9910.00	−0.389538
$866$	5072.00	0.199023
$867$	0	0
$868$	6600.00	0.258086
$869$	7525.00	0.293749
$870$	0	0
$871$	156.000	0.00606872
$872$	4032.00	0.156583
$873$	0	0
$874$	3780.00	0.146293
$875$	−625.000	−0.0241473
$876$	0	0
$877$	−18398.0	−0.708388	−0.354194	−	0.935172i	$-0.615245\pi$
$877$	−18398.0	−0.708388	−0.354194	+	0.935172i	$0.615245\pi$
$878$	−3622.00	−0.139222
$879$	0	0
$880$	−2800.00	−0.107259
$881$	17946.0	0.686284	0.343142	−	0.939284i	$-0.388509\pi$
$881$	17946.0	0.686284	0.343142	+	0.939284i	$0.388509\pi$
$882$	0	0
$883$	−27544.0	−1.04975	−0.524875	−	0.851179i	$-0.675888\pi$
$883$	−27544.0	−1.04975	−0.524875	+	0.851179i	$0.675888\pi$
$884$	1196.00	0.0455043
$885$	0	0
$886$	−29486.0	−1.11806
$887$	10967.0	0.415147	0.207574	−	0.978219i	$-0.433443\pi$
$887$	10967.0	0.415147	0.207574	+	0.978219i	$0.433443\pi$
$888$	0	0
$889$	6530.00	0.246355
$890$	−10190.0	−0.383786
$891$	0	0
$892$	20992.0	0.787964
$893$	8100.00	0.303534
$894$	0	0
$895$	14950.0	0.558350
$896$	640.000	0.0238626
$897$	0	0
$898$	−1998.00	−0.0742474
$899$	62700.0	2.32610
$900$	0	0
$901$	−4439.00	−0.164134
$902$	33110.0	1.22222
$903$	0	0
$904$	−14320.0	−0.526854
$905$	−9425.00	−0.346185
$906$	0	0
$907$	−23414.0	−0.857166	−0.428583	−	0.903503i	$-0.640987\pi$
$907$	−23414.0	−0.857166	−0.428583	+	0.903503i	$0.640987\pi$
$908$	−23240.0	−0.849390
$909$	0	0
$910$	650.000	0.0236783
$911$	14000.0	0.509156	0.254578	−	0.967052i	$-0.418064\pi$
$911$	14000.0	0.509156	0.254578	+	0.967052i	$0.418064\pi$
$912$	0	0
$913$	45780.0	1.65947
$914$	36994.0	1.33879
$915$	0	0
$916$	21112.0	0.761529
$917$	8590.00	0.309342
$918$	0	0
$919$	7471.00	0.268167	0.134084	−	0.990970i	$-0.457191\pi$
$919$	7471.00	0.268167	0.134084	+	0.990970i	$0.457191\pi$
$920$	2520.00	0.0903065
$921$	0	0
$922$	−7902.00	−0.282254
$923$	−11687.0	−0.416774
$924$	0	0
$925$	1075.00	0.0382117
$926$	−1894.00	−0.0672146
$927$	0	0
$928$	6080.00	0.215071
$929$	−15861.0	−0.560153	−0.280077	−	0.959978i	$-0.590360\pi$
$929$	−15861.0	−0.560153	−0.280077	+	0.959978i	$0.590360\pi$
$930$	0	0
$931$	9540.00	0.335833
$932$	20364.0	0.715714
$933$	0	0
$934$	−8318.00	−0.291406
$935$	4025.00	0.140782
$936$	0	0
$937$	−7494.00	−0.261279	−0.130639	−	0.991430i	$-0.541703\pi$
$937$	−7494.00	−0.261279	−0.130639	+	0.991430i	$0.541703\pi$
$938$	−120.000	−0.00417712
$939$	0	0
$940$	5400.00	0.187371
$941$	29995.0	1.03912	0.519558	−	0.854435i	$-0.326096\pi$
$941$	29995.0	1.03912	0.519558	+	0.854435i	$0.326096\pi$
$942$	0	0
$943$	−29799.0	−1.02904
$944$	3200.00	0.110330
$945$	0	0
$946$	−16240.0	−0.558148
$947$	20792.0	0.713463	0.356731	−	0.934207i	$-0.383891\pi$
$947$	20792.0	0.713463	0.356731	+	0.934207i	$0.383891\pi$
$948$	0	0
$949$	−2002.00	−0.0684802
$950$	−1500.00	−0.0512278
$951$	0	0
$952$	−920.000	−0.0313208
$953$	−32895.0	−1.11813	−0.559063	−	0.829125i	$-0.688839\pi$
$953$	−32895.0	−1.11813	−0.559063	+	0.829125i	$0.688839\pi$
$954$	0	0
$955$	−2580.00	−0.0874208
$956$	−18196.0	−0.615587
$957$	0	0
$958$	−28270.0	−0.953405
$959$	2190.00	0.0737422
$960$	0	0
$961$	79109.0	2.65547
$962$	−1118.00	−0.0374696
$963$	0	0
$964$	−18136.0	−0.605935
$965$	13565.0	0.452511
$966$	0	0
$967$	−37304.0	−1.24055	−0.620277	−	0.784383i	$-0.712980\pi$
$967$	−37304.0	−1.24055	−0.620277	+	0.784383i	$0.712980\pi$
$968$	−848.000	−0.0281568
$969$	0	0
$970$	4270.00	0.141342
$971$	26248.0	0.867496	0.433748	−	0.901034i	$-0.357191\pi$
$971$	26248.0	0.867496	0.433748	+	0.901034i	$0.357191\pi$
$972$	0	0
$973$	3605.00	0.118778
$974$	−15218.0	−0.500633
$975$	0	0
$976$	−10864.0	−0.356299
$977$	18804.0	0.615756	0.307878	−	0.951426i	$-0.400381\pi$
$977$	18804.0	0.615756	0.307878	+	0.951426i	$0.400381\pi$
$978$	0	0
$979$	35665.0	1.16431
$980$	6360.00	0.207309
$981$	0	0
$982$	26640.0	0.865699
$983$	−26228.0	−0.851010	−0.425505	−	0.904956i	$-0.639904\pi$
$983$	−26228.0	−0.851010	−0.425505	+	0.904956i	$0.639904\pi$
$984$	0	0
$985$	5580.00	0.180501
$986$	−8740.00	−0.282290
$987$	0	0
$988$	1560.00	0.0502330
$989$	14616.0	0.469931
$990$	0	0
$991$	23757.0	0.761520	0.380760	−	0.924674i	$-0.375662\pi$
$991$	23757.0	0.761520	0.380760	+	0.924674i	$0.375662\pi$
$992$	10560.0	0.337984
$993$	0	0
$994$	8990.00	0.286867
$995$	5820.00	0.185434
$996$	0	0
$997$	38356.0	1.21840	0.609201	−	0.793016i	$-0.291490\pi$
$997$	38356.0	1.21840	0.609201	+	0.793016i	$0.291490\pi$
$998$	−6020.00	−0.190942
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.4.a.j.1.1		1
3.2	odd	2		390.4.a.b.1.1	✓	1
15.14	odd	2		1950.4.a.p.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.4.a.b.1.1	✓	1	3.2	odd	2
1170.4.a.j.1.1		1	1.1	even	1	trivial
1950.4.a.p.1.1		1	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1170.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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