LMFDB - Embedded newform 585.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,4,Mod(1,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, 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("585.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	585.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:	$34.5161173534$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	585.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+3.00000 q^{2} +1.00000 q^{4} +5.00000 q^{5} +2.00000 q^{7} -21.0000 q^{8} +O(q^{10})$

\(q+3.00000 q^{2} +1.00000 q^{4} +5.00000 q^{5} +2.00000 q^{7} -21.0000 q^{8} +15.0000 q^{10} -24.0000 q^{11} +13.0000 q^{13} +6.00000 q^{14} -71.0000 q^{16} -24.0000 q^{17} -70.0000 q^{19} +5.00000 q^{20} -72.0000 q^{22} -90.0000 q^{23} +25.0000 q^{25} +39.0000 q^{26} +2.00000 q^{28} +120.000 q^{29} -196.000 q^{31} -45.0000 q^{32} -72.0000 q^{34} +10.0000 q^{35} -214.000 q^{37} -210.000 q^{38} -105.000 q^{40} +54.0000 q^{41} -196.000 q^{43} -24.0000 q^{44} -270.000 q^{46} -120.000 q^{47} -339.000 q^{49} +75.0000 q^{50} +13.0000 q^{52} -18.0000 q^{53} -120.000 q^{55} -42.0000 q^{56} +360.000 q^{58} +312.000 q^{59} -322.000 q^{61} -588.000 q^{62} +433.000 q^{64} +65.0000 q^{65} -376.000 q^{67} -24.0000 q^{68} +30.0000 q^{70} -240.000 q^{71} +1136.00 q^{73} -642.000 q^{74} -70.0000 q^{76} -48.0000 q^{77} -808.000 q^{79} -355.000 q^{80} +162.000 q^{82} -1092.00 q^{83} -120.000 q^{85} -588.000 q^{86} +504.000 q^{88} +618.000 q^{89} +26.0000 q^{91} -90.0000 q^{92} -360.000 q^{94} -350.000 q^{95} -880.000 q^{97} -1017.00 q^{98} +O(q^{100})\)

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 $

$2$	3.00000	1.06066	0.530330	−	0.847791i	$-0.322068\pi$
$2$	3.00000	1.06066	0.530330	+	0.847791i	$0.322068\pi$
$3$	0	0
$3$	0	0
$4$	1.00000	0.125000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0	0
$7$	2.00000	0.107990	0.0539949	−	0.998541i	$-0.482805\pi$
$7$	2.00000	0.107990	0.0539949	+	0.998541i	$0.482805\pi$
$8$	−21.0000	−0.928078
$9$	0	0
$10$	15.0000	0.474342
$11$	−24.0000	−0.657843	−0.328921	−	0.944357i	$-0.606685\pi$
$11$	−24.0000	−0.657843	−0.328921	+	0.944357i	$0.606685\pi$
$12$	0	0
$13$	13.0000	0.277350
$13$	13.0000	0.277350
$14$	6.00000	0.114541
$15$	0	0
$16$	−71.0000	−1.10938
$17$	−24.0000	−0.342403	−0.171202	−	0.985236i	$-0.554765\pi$
$17$	−24.0000	−0.342403	−0.171202	+	0.985236i	$0.554765\pi$
$18$	0	0
$19$	−70.0000	−0.845216	−0.422608	−	0.906313i	$-0.638885\pi$
$19$	−70.0000	−0.845216	−0.422608	+	0.906313i	$0.638885\pi$
$20$	5.00000	0.0559017
$21$	0	0
$22$	−72.0000	−0.697748
$23$	−90.0000	−0.815926	−0.407963	−	0.912998i	$-0.633761\pi$
$23$	−90.0000	−0.815926	−0.407963	+	0.912998i	$0.633761\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	39.0000	0.294174
$27$	0	0
$28$	2.00000	0.0134987
$29$	120.000	0.768395	0.384197	−	0.923251i	$-0.374478\pi$
$29$	120.000	0.768395	0.384197	+	0.923251i	$0.374478\pi$
$30$	0	0
$31$	−196.000	−1.13557	−0.567785	−	0.823177i	$-0.692199\pi$
$31$	−196.000	−1.13557	−0.567785	+	0.823177i	$0.692199\pi$
$32$	−45.0000	−0.248592
$33$	0	0
$34$	−72.0000	−0.363173
$35$	10.0000	0.0482945
$36$	0	0
$37$	−214.000	−0.950848	−0.475424	−	0.879757i	$-0.657705\pi$
$37$	−214.000	−0.950848	−0.475424	+	0.879757i	$0.657705\pi$
$38$	−210.000	−0.896487
$39$	0	0
$40$	−105.000	−0.415049
$41$	54.0000	0.205692	0.102846	−	0.994697i	$-0.467205\pi$
$41$	54.0000	0.205692	0.102846	+	0.994697i	$0.467205\pi$
$42$	0	0
$43$	−196.000	−0.695110	−0.347555	−	0.937660i	$-0.612988\pi$
$43$	−196.000	−0.695110	−0.347555	+	0.937660i	$0.612988\pi$
$44$	−24.0000	−0.0822304
$45$	0	0
$46$	−270.000	−0.865420
$47$	−120.000	−0.372421	−0.186211	−	0.982510i	$-0.559621\pi$
$47$	−120.000	−0.372421	−0.186211	+	0.982510i	$0.559621\pi$
$48$	0	0
$49$	−339.000	−0.988338
$50$	75.0000	0.212132
$51$	0	0
$52$	13.0000	0.0346688
$53$	−18.0000	−0.0466508	−0.0233254	−	0.999728i	$-0.507425\pi$
$53$	−18.0000	−0.0466508	−0.0233254	+	0.999728i	$0.507425\pi$
$54$	0	0
$55$	−120.000	−0.294196
$56$	−42.0000	−0.100223
$57$	0	0
$58$	360.000	0.815005
$59$	312.000	0.688457	0.344228	−	0.938886i	$-0.388141\pi$
$59$	312.000	0.688457	0.344228	+	0.938886i	$0.388141\pi$
$60$	0	0
$61$	−322.000	−0.675867	−0.337933	−	0.941170i	$-0.609728\pi$
$61$	−322.000	−0.675867	−0.337933	+	0.941170i	$0.609728\pi$
$62$	−588.000	−1.20445
$63$	0	0
$64$	433.000	0.845703
$65$	65.0000	0.124035
$66$	0	0
$67$	−376.000	−0.685608	−0.342804	−	0.939407i	$-0.611377\pi$
$67$	−376.000	−0.685608	−0.342804	+	0.939407i	$0.611377\pi$
$68$	−24.0000	−0.0428004
$69$	0	0
$70$	30.0000	0.0512241
$71$	−240.000	−0.401166	−0.200583	−	0.979677i	$-0.564284\pi$
$71$	−240.000	−0.401166	−0.200583	+	0.979677i	$0.564284\pi$
$72$	0	0
$73$	1136.00	1.82135	0.910676	−	0.413121i	$-0.135561\pi$
$73$	1136.00	1.82135	0.910676	+	0.413121i	$0.135561\pi$
$74$	−642.000	−1.00853
$75$	0	0
$76$	−70.0000	−0.105652
$77$	−48.0000	−0.0710404
$78$	0	0
$79$	−808.000	−1.15072	−0.575361	−	0.817899i	$-0.695139\pi$
$79$	−808.000	−1.15072	−0.575361	+	0.817899i	$0.695139\pi$
$80$	−355.000	−0.496128
$81$	0	0
$82$	162.000	0.218170
$83$	−1092.00	−1.44413	−0.722064	−	0.691827i	$-0.756806\pi$
$83$	−1092.00	−1.44413	−0.722064	+	0.691827i	$0.756806\pi$
$84$	0	0
$85$	−120.000	−0.153127
$86$	−588.000	−0.737275
$87$	0	0
$88$	504.000	0.610529
$89$	618.000	0.736043	0.368022	−	0.929817i	$-0.380035\pi$
$89$	618.000	0.736043	0.368022	+	0.929817i	$0.380035\pi$
$90$	0	0
$91$	26.0000	0.0299510
$92$	−90.0000	−0.101991
$93$	0	0
$94$	−360.000	−0.395012
$95$	−350.000	−0.377992
$96$	0	0
$97$	−880.000	−0.921139	−0.460569	−	0.887624i	$-0.652355\pi$
$97$	−880.000	−0.921139	−0.460569	+	0.887624i	$0.652355\pi$
$98$	−1017.00	−1.04829
$99$	0	0
$100$	25.0000	0.0250000
$101$	228.000	0.224622	0.112311	−	0.993673i	$-0.464175\pi$
$101$	228.000	0.224622	0.112311	+	0.993673i	$0.464175\pi$
$102$	0	0
$103$	560.000	0.535713	0.267857	−	0.963459i	$-0.413685\pi$
$103$	560.000	0.535713	0.267857	+	0.963459i	$0.413685\pi$
$104$	−273.000	−0.257402
$105$	0	0
$106$	−54.0000	−0.0494806
$107$	996.000	0.899878	0.449939	−	0.893059i	$-0.351446\pi$
$107$	996.000	0.899878	0.449939	+	0.893059i	$0.351446\pi$
$108$	0	0
$109$	−88.0000	−0.0773291	−0.0386645	−	0.999252i	$-0.512310\pi$
$109$	−88.0000	−0.0773291	−0.0386645	+	0.999252i	$0.512310\pi$
$110$	−360.000	−0.312042
$111$	0	0
$112$	−142.000	−0.119801
$113$	708.000	0.589407	0.294704	−	0.955589i	$-0.404779\pi$
$113$	708.000	0.589407	0.294704	+	0.955589i	$0.404779\pi$
$114$	0	0
$115$	−450.000	−0.364893
$116$	120.000	0.0960493
$117$	0	0
$118$	936.000	0.730219
$119$	−48.0000	−0.0369761
$120$	0	0
$121$	−755.000	−0.567243
$122$	−966.000	−0.716865
$123$	0	0
$124$	−196.000	−0.141946
$125$	125.000	0.0894427
$126$	0	0
$127$	−2032.00	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−2032.00	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	1659.00	1.14560
$129$	0	0
$130$	195.000	0.131559
$131$	1146.00	0.764324	0.382162	−	0.924095i	$-0.375180\pi$
$131$	1146.00	0.764324	0.382162	+	0.924095i	$0.375180\pi$
$132$	0	0
$133$	−140.000	−0.0912747
$134$	−1128.00	−0.727197
$135$	0	0
$136$	504.000	0.317777
$137$	558.000	0.347979	0.173990	−	0.984747i	$-0.444334\pi$
$137$	558.000	0.347979	0.173990	+	0.984747i	$0.444334\pi$
$138$	0	0
$139$	128.000	0.0781066	0.0390533	−	0.999237i	$-0.487566\pi$
$139$	128.000	0.0781066	0.0390533	+	0.999237i	$0.487566\pi$
$140$	10.0000	0.00603682
$141$	0	0
$142$	−720.000	−0.425500
$143$	−312.000	−0.182453
$144$	0	0
$145$	600.000	0.343636
$146$	3408.00	1.93184
$147$	0	0
$148$	−214.000	−0.118856
$149$	2994.00	1.64616	0.823081	−	0.567924i	$-0.192253\pi$
$149$	2994.00	1.64616	0.823081	+	0.567924i	$0.192253\pi$
$150$	0	0
$151$	2324.00	1.25248	0.626240	−	0.779630i	$-0.284593\pi$
$151$	2324.00	1.25248	0.626240	+	0.779630i	$0.284593\pi$
$152$	1470.00	0.784426
$153$	0	0
$154$	−144.000	−0.0753497
$155$	−980.000	−0.507842
$156$	0	0
$157$	−2086.00	−1.06039	−0.530194	−	0.847876i	$-0.677881\pi$
$157$	−2086.00	−1.06039	−0.530194	+	0.847876i	$0.677881\pi$
$158$	−2424.00	−1.22053
$159$	0	0
$160$	−225.000	−0.111174
$161$	−180.000	−0.0881117
$162$	0	0
$163$	1604.00	0.770767	0.385383	−	0.922757i	$-0.374069\pi$
$163$	1604.00	0.770767	0.385383	+	0.922757i	$0.374069\pi$
$164$	54.0000	0.0257115
$165$	0	0
$166$	−3276.00	−1.53173
$167$	2556.00	1.18437	0.592183	−	0.805803i	$-0.298266\pi$
$167$	2556.00	1.18437	0.592183	+	0.805803i	$0.298266\pi$
$168$	0	0
$169$	169.000	0.0769231
$170$	−360.000	−0.162416
$171$	0	0
$172$	−196.000	−0.0868887
$173$	1422.00	0.624929	0.312464	−	0.949929i	$-0.398846\pi$
$173$	1422.00	0.624929	0.312464	+	0.949929i	$0.398846\pi$
$174$	0	0
$175$	50.0000	0.0215980
$176$	1704.00	0.729795
$177$	0	0
$178$	1854.00	0.780692
$179$	294.000	0.122763	0.0613815	−	0.998114i	$-0.480449\pi$
$179$	294.000	0.122763	0.0613815	+	0.998114i	$0.480449\pi$
$180$	0	0
$181$	−1150.00	−0.472259	−0.236129	−	0.971722i	$-0.575879\pi$
$181$	−1150.00	−0.472259	−0.236129	+	0.971722i	$0.575879\pi$
$182$	78.0000	0.0317678
$183$	0	0
$184$	1890.00	0.757243
$185$	−1070.00	−0.425232
$186$	0	0
$187$	576.000	0.225248
$188$	−120.000	−0.0465527
$189$	0	0
$190$	−1050.00	−0.400921
$191$	1512.00	0.572798	0.286399	−	0.958110i	$-0.407542\pi$
$191$	1512.00	0.572798	0.286399	+	0.958110i	$0.407542\pi$
$192$	0	0
$193$	−3796.00	−1.41576	−0.707881	−	0.706332i	$-0.750349\pi$
$193$	−3796.00	−1.41576	−0.707881	+	0.706332i	$0.750349\pi$
$194$	−2640.00	−0.977015
$195$	0	0
$196$	−339.000	−0.123542
$197$	−606.000	−0.219166	−0.109583	−	0.993978i	$-0.534952\pi$
$197$	−606.000	−0.219166	−0.109583	+	0.993978i	$0.534952\pi$
$198$	0	0
$199$	3152.00	1.12281	0.561405	−	0.827541i	$-0.310261\pi$
$199$	3152.00	1.12281	0.561405	+	0.827541i	$0.310261\pi$
$200$	−525.000	−0.185616
$201$	0	0
$202$	684.000	0.238248
$203$	240.000	0.0829788
$204$	0	0
$205$	270.000	0.0919884
$206$	1680.00	0.568209
$207$	0	0
$208$	−923.000	−0.307685
$209$	1680.00	0.556019
$210$	0	0
$211$	−1420.00	−0.463303	−0.231651	−	0.972799i	$-0.574413\pi$
$211$	−1420.00	−0.463303	−0.231651	+	0.972799i	$0.574413\pi$
$212$	−18.0000	−0.00583134
$213$	0	0
$214$	2988.00	0.954465
$215$	−980.000	−0.310863
$216$	0	0
$217$	−392.000	−0.122630
$218$	−264.000	−0.0820199
$219$	0	0
$220$	−120.000	−0.0367745
$221$	−312.000	−0.0949656
$222$	0	0
$223$	4142.00	1.24381	0.621903	−	0.783094i	$-0.286360\pi$
$223$	4142.00	1.24381	0.621903	+	0.783094i	$0.286360\pi$
$224$	−90.0000	−0.0268454
$225$	0	0
$226$	2124.00	0.625161
$227$	−5580.00	−1.63153	−0.815766	−	0.578383i	$-0.803684\pi$
$227$	−5580.00	−1.63153	−0.815766	+	0.578383i	$0.803684\pi$
$228$	0	0
$229$	3080.00	0.888787	0.444393	−	0.895832i	$-0.353419\pi$
$229$	3080.00	0.888787	0.444393	+	0.895832i	$0.353419\pi$
$230$	−1350.00	−0.387028
$231$	0	0
$232$	−2520.00	−0.713130
$233$	3312.00	0.931229	0.465614	−	0.884988i	$-0.345833\pi$
$233$	3312.00	0.931229	0.465614	+	0.884988i	$0.345833\pi$
$234$	0	0
$235$	−600.000	−0.166552
$236$	312.000	0.0860571
$237$	0	0
$238$	−144.000	−0.0392190
$239$	−5784.00	−1.56542	−0.782711	−	0.622385i	$-0.786164\pi$
$239$	−5784.00	−1.56542	−0.782711	+	0.622385i	$0.786164\pi$
$240$	0	0
$241$	6050.00	1.61707	0.808537	−	0.588446i	$-0.200260\pi$
$241$	6050.00	1.61707	0.808537	+	0.588446i	$0.200260\pi$
$242$	−2265.00	−0.601652
$243$	0	0
$244$	−322.000	−0.0844834
$245$	−1695.00	−0.441998
$246$	0	0
$247$	−910.000	−0.234421
$248$	4116.00	1.05390
$249$	0	0
$250$	375.000	0.0948683
$251$	−4938.00	−1.24177	−0.620884	−	0.783902i	$-0.713226\pi$
$251$	−4938.00	−1.24177	−0.620884	+	0.783902i	$0.713226\pi$
$252$	0	0
$253$	2160.00	0.536751
$254$	−6096.00	−1.50589
$255$	0	0
$256$	1513.00	0.369385
$257$	108.000	0.0262134	0.0131067	−	0.999914i	$-0.495828\pi$
$257$	108.000	0.0262134	0.0131067	+	0.999914i	$0.495828\pi$
$258$	0	0
$259$	−428.000	−0.102682
$260$	65.0000	0.0155043
$261$	0	0
$262$	3438.00	0.810688
$263$	1578.00	0.369976	0.184988	−	0.982741i	$-0.440775\pi$
$263$	1578.00	0.369976	0.184988	+	0.982741i	$0.440775\pi$
$264$	0	0
$265$	−90.0000	−0.0208629
$266$	−420.000	−0.0968115
$267$	0	0
$268$	−376.000	−0.0857010
$269$	−1428.00	−0.323668	−0.161834	−	0.986818i	$-0.551741\pi$
$269$	−1428.00	−0.323668	−0.161834	+	0.986818i	$0.551741\pi$
$270$	0	0
$271$	−5092.00	−1.14139	−0.570696	−	0.821162i	$-0.693326\pi$
$271$	−5092.00	−1.14139	−0.570696	+	0.821162i	$0.693326\pi$
$272$	1704.00	0.379854
$273$	0	0
$274$	1674.00	0.369088
$275$	−600.000	−0.131569
$276$	0	0
$277$	−4750.00	−1.03032	−0.515162	−	0.857093i	$-0.672268\pi$
$277$	−4750.00	−1.03032	−0.515162	+	0.857093i	$0.672268\pi$
$278$	384.000	0.0828446
$279$	0	0
$280$	−210.000	−0.0448211
$281$	330.000	0.0700575	0.0350287	−	0.999386i	$-0.488848\pi$
$281$	330.000	0.0700575	0.0350287	+	0.999386i	$0.488848\pi$
$282$	0	0
$283$	956.000	0.200807	0.100403	−	0.994947i	$-0.467987\pi$
$283$	956.000	0.200807	0.100403	+	0.994947i	$0.467987\pi$
$284$	−240.000	−0.0501457
$285$	0	0
$286$	−936.000	−0.193520
$287$	108.000	0.0222127
$288$	0	0
$289$	−4337.00	−0.882760
$290$	1800.00	0.364482
$291$	0	0
$292$	1136.00	0.227669
$293$	8898.00	1.77415	0.887076	−	0.461623i	$-0.152733\pi$
$293$	8898.00	1.77415	0.887076	+	0.461623i	$0.152733\pi$
$294$	0	0
$295$	1560.00	0.307887
$296$	4494.00	0.882461
$297$	0	0
$298$	8982.00	1.74602
$299$	−1170.00	−0.226297
$300$	0	0
$301$	−392.000	−0.0750648
$302$	6972.00	1.32846
$303$	0	0
$304$	4970.00	0.937661
$305$	−1610.00	−0.302257
$306$	0	0
$307$	848.000	0.157648	0.0788240	−	0.996889i	$-0.474883\pi$
$307$	848.000	0.157648	0.0788240	+	0.996889i	$0.474883\pi$
$308$	−48.0000	−0.00888004
$309$	0	0
$310$	−2940.00	−0.538648
$311$	1920.00	0.350075	0.175037	−	0.984562i	$-0.443995\pi$
$311$	1920.00	0.350075	0.175037	+	0.984562i	$0.443995\pi$
$312$	0	0
$313$	7022.00	1.26807	0.634037	−	0.773303i	$-0.281397\pi$
$313$	7022.00	1.26807	0.634037	+	0.773303i	$0.281397\pi$
$314$	−6258.00	−1.12471
$315$	0	0
$316$	−808.000	−0.143840
$317$	−7482.00	−1.32565	−0.662825	−	0.748774i	$-0.730643\pi$
$317$	−7482.00	−1.32565	−0.662825	+	0.748774i	$0.730643\pi$
$318$	0	0
$319$	−2880.00	−0.505483
$320$	2165.00	0.378210
$321$	0	0
$322$	−540.000	−0.0934566
$323$	1680.00	0.289405
$324$	0	0
$325$	325.000	0.0554700
$326$	4812.00	0.817522
$327$	0	0
$328$	−1134.00	−0.190898
$329$	−240.000	−0.0402177
$330$	0	0
$331$	5474.00	0.908998	0.454499	−	0.890747i	$-0.349818\pi$
$331$	5474.00	0.908998	0.454499	+	0.890747i	$0.349818\pi$
$332$	−1092.00	−0.180516
$333$	0	0
$334$	7668.00	1.25621
$335$	−1880.00	−0.306613
$336$	0	0
$337$	−6514.00	−1.05294	−0.526469	−	0.850194i	$-0.676484\pi$
$337$	−6514.00	−1.05294	−0.526469	+	0.850194i	$0.676484\pi$
$338$	507.000	0.0815892
$339$	0	0
$340$	−120.000	−0.0191409
$341$	4704.00	0.747026
$342$	0	0
$343$	−1364.00	−0.214720
$344$	4116.00	0.645116
$345$	0	0
$346$	4266.00	0.662837
$347$	−9336.00	−1.44433	−0.722165	−	0.691720i	$-0.756853\pi$
$347$	−9336.00	−1.44433	−0.722165	+	0.691720i	$0.756853\pi$
$348$	0	0
$349$	−6424.00	−0.985298	−0.492649	−	0.870228i	$-0.663971\pi$
$349$	−6424.00	−0.985298	−0.492649	+	0.870228i	$0.663971\pi$
$350$	150.000	0.0229081
$351$	0	0
$352$	1080.00	0.163535
$353$	−8034.00	−1.21135	−0.605675	−	0.795712i	$-0.707097\pi$
$353$	−8034.00	−1.21135	−0.605675	+	0.795712i	$0.707097\pi$
$354$	0	0
$355$	−1200.00	−0.179407
$356$	618.000	0.0920054
$357$	0	0
$358$	882.000	0.130210
$359$	−9216.00	−1.35488	−0.677440	−	0.735578i	$-0.736911\pi$
$359$	−9216.00	−1.35488	−0.677440	+	0.735578i	$0.736911\pi$
$360$	0	0
$361$	−1959.00	−0.285610
$362$	−3450.00	−0.500906
$363$	0	0
$364$	26.0000	0.00374387
$365$	5680.00	0.814534
$366$	0	0
$367$	10712.0	1.52360	0.761801	−	0.647811i	$-0.224315\pi$
$367$	10712.0	1.52360	0.761801	+	0.647811i	$0.224315\pi$
$368$	6390.00	0.905168
$369$	0	0
$370$	−3210.00	−0.451027
$371$	−36.0000	−0.00503781
$372$	0	0
$373$	−5038.00	−0.699351	−0.349675	−	0.936871i	$-0.613708\pi$
$373$	−5038.00	−0.699351	−0.349675	+	0.936871i	$0.613708\pi$
$374$	1728.00	0.238911
$375$	0	0
$376$	2520.00	0.345636
$377$	1560.00	0.213114
$378$	0	0
$379$	−6226.00	−0.843821	−0.421910	−	0.906637i	$-0.638640\pi$
$379$	−6226.00	−0.843821	−0.421910	+	0.906637i	$0.638640\pi$
$380$	−350.000	−0.0472490
$381$	0	0
$382$	4536.00	0.607544
$383$	5388.00	0.718835	0.359418	−	0.933177i	$-0.382975\pi$
$383$	5388.00	0.718835	0.359418	+	0.933177i	$0.382975\pi$
$384$	0	0
$385$	−240.000	−0.0317702
$386$	−11388.0	−1.50164
$387$	0	0
$388$	−880.000	−0.115142
$389$	13452.0	1.75333	0.876663	−	0.481106i	$-0.159765\pi$
$389$	13452.0	1.75333	0.876663	+	0.481106i	$0.159765\pi$
$390$	0	0
$391$	2160.00	0.279376
$392$	7119.00	0.917255
$393$	0	0
$394$	−1818.00	−0.232461
$395$	−4040.00	−0.514619
$396$	0	0
$397$	−4174.00	−0.527675	−0.263838	−	0.964567i	$-0.584988\pi$
$397$	−4174.00	−0.527675	−0.263838	+	0.964567i	$0.584988\pi$
$398$	9456.00	1.19092
$399$	0	0
$400$	−1775.00	−0.221875
$401$	−5562.00	−0.692651	−0.346325	−	0.938114i	$-0.612571\pi$
$401$	−5562.00	−0.692651	−0.346325	+	0.938114i	$0.612571\pi$
$402$	0	0
$403$	−2548.00	−0.314950
$404$	228.000	0.0280778
$405$	0	0
$406$	720.000	0.0880123
$407$	5136.00	0.625509
$408$	0	0
$409$	−8674.00	−1.04866	−0.524330	−	0.851515i	$-0.675684\pi$
$409$	−8674.00	−1.04866	−0.524330	+	0.851515i	$0.675684\pi$
$410$	810.000	0.0975684
$411$	0	0
$412$	560.000	0.0669641
$413$	624.000	0.0743463
$414$	0	0
$415$	−5460.00	−0.645833
$416$	−585.000	−0.0689471
$417$	0	0
$418$	5040.00	0.589748
$419$	7434.00	0.866765	0.433383	−	0.901210i	$-0.357320\pi$
$419$	7434.00	0.866765	0.433383	+	0.901210i	$0.357320\pi$
$420$	0	0
$421$	8660.00	1.00252	0.501262	−	0.865296i	$-0.332869\pi$
$421$	8660.00	1.00252	0.501262	+	0.865296i	$0.332869\pi$
$422$	−4260.00	−0.491407
$423$	0	0
$424$	378.000	0.0432955
$425$	−600.000	−0.0684806
$426$	0	0
$427$	−644.000	−0.0729868
$428$	996.000	0.112485
$429$	0	0
$430$	−2940.00	−0.329720
$431$	−11640.0	−1.30088	−0.650440	−	0.759558i	$-0.725415\pi$
$431$	−11640.0	−1.30088	−0.650440	+	0.759558i	$0.725415\pi$
$432$	0	0
$433$	2702.00	0.299884	0.149942	−	0.988695i	$-0.452091\pi$
$433$	2702.00	0.299884	0.149942	+	0.988695i	$0.452091\pi$
$434$	−1176.00	−0.130069
$435$	0	0
$436$	−88.0000	−0.00966614
$437$	6300.00	0.689634
$438$	0	0
$439$	−3832.00	−0.416609	−0.208305	−	0.978064i	$-0.566795\pi$
$439$	−3832.00	−0.416609	−0.208305	+	0.978064i	$0.566795\pi$
$440$	2520.00	0.273037
$441$	0	0
$442$	−936.000	−0.100726
$443$	11832.0	1.26897	0.634487	−	0.772934i	$-0.281211\pi$
$443$	11832.0	1.26897	0.634487	+	0.772934i	$0.281211\pi$
$444$	0	0
$445$	3090.00	0.329169
$446$	12426.0	1.31926
$447$	0	0
$448$	866.000	0.0913274
$449$	−1518.00	−0.159552	−0.0797760	−	0.996813i	$-0.525421\pi$
$449$	−1518.00	−0.159552	−0.0797760	+	0.996813i	$0.525421\pi$
$450$	0	0
$451$	−1296.00	−0.135313
$452$	708.000	0.0736759
$453$	0	0
$454$	−16740.0	−1.73050
$455$	130.000	0.0133945
$456$	0	0
$457$	5384.00	0.551100	0.275550	−	0.961287i	$-0.411140\pi$
$457$	5384.00	0.551100	0.275550	+	0.961287i	$0.411140\pi$
$458$	9240.00	0.942701
$459$	0	0
$460$	−450.000	−0.0456116
$461$	6678.00	0.674676	0.337338	−	0.941384i	$-0.390474\pi$
$461$	6678.00	0.674676	0.337338	+	0.941384i	$0.390474\pi$
$462$	0	0
$463$	−3058.00	−0.306949	−0.153474	−	0.988153i	$-0.549046\pi$
$463$	−3058.00	−0.306949	−0.153474	+	0.988153i	$0.549046\pi$
$464$	−8520.00	−0.852438
$465$	0	0
$466$	9936.00	0.987717
$467$	2556.00	0.253271	0.126636	−	0.991949i	$-0.459582\pi$
$467$	2556.00	0.253271	0.126636	+	0.991949i	$0.459582\pi$
$468$	0	0
$469$	−752.000	−0.0740387
$470$	−1800.00	−0.176655
$471$	0	0
$472$	−6552.00	−0.638941
$473$	4704.00	0.457273
$474$	0	0
$475$	−1750.00	−0.169043
$476$	−48.0000	−0.00462201
$477$	0	0
$478$	−17352.0	−1.66038
$479$	−10104.0	−0.963807	−0.481903	−	0.876224i	$-0.660054\pi$
$479$	−10104.0	−0.963807	−0.481903	+	0.876224i	$0.660054\pi$
$480$	0	0
$481$	−2782.00	−0.263718
$482$	18150.0	1.71517
$483$	0	0
$484$	−755.000	−0.0709053
$485$	−4400.00	−0.411946
$486$	0	0
$487$	4034.00	0.375355	0.187678	−	0.982231i	$-0.439904\pi$
$487$	4034.00	0.375355	0.187678	+	0.982231i	$0.439904\pi$
$488$	6762.00	0.627257
$489$	0	0
$490$	−5085.00	−0.468810
$491$	−15678.0	−1.44101	−0.720507	−	0.693447i	$-0.756091\pi$
$491$	−15678.0	−1.44101	−0.720507	+	0.693447i	$0.756091\pi$
$492$	0	0
$493$	−2880.00	−0.263101
$494$	−2730.00	−0.248641
$495$	0	0
$496$	13916.0	1.25977
$497$	−480.000	−0.0433218
$498$	0	0
$499$	−20986.0	−1.88269	−0.941345	−	0.337445i	$-0.890437\pi$
$499$	−20986.0	−1.88269	−0.941345	+	0.337445i	$0.890437\pi$
$500$	125.000	0.0111803
$501$	0	0
$502$	−14814.0	−1.31709
$503$	−9366.00	−0.830237	−0.415119	−	0.909767i	$-0.636260\pi$
$503$	−9366.00	−0.830237	−0.415119	+	0.909767i	$0.636260\pi$
$504$	0	0
$505$	1140.00	0.100454
$506$	6480.00	0.569311
$507$	0	0
$508$	−2032.00	−0.177471
$509$	−16650.0	−1.44990	−0.724949	−	0.688802i	$-0.758137\pi$
$509$	−16650.0	−1.44990	−0.724949	+	0.688802i	$0.758137\pi$
$510$	0	0
$511$	2272.00	0.196688
$512$	−8733.00	−0.753804
$513$	0	0
$514$	324.000	0.0278036
$515$	2800.00	0.239578
$516$	0	0
$517$	2880.00	0.244995
$518$	−1284.00	−0.108911
$519$	0	0
$520$	−1365.00	−0.115114
$521$	−17838.0	−1.49999	−0.749997	−	0.661441i	$-0.769945\pi$
$521$	−17838.0	−1.49999	−0.749997	+	0.661441i	$0.769945\pi$
$522$	0	0
$523$	−12868.0	−1.07587	−0.537933	−	0.842987i	$-0.680795\pi$
$523$	−12868.0	−1.07587	−0.537933	+	0.842987i	$0.680795\pi$
$524$	1146.00	0.0955405
$525$	0	0
$526$	4734.00	0.392419
$527$	4704.00	0.388823
$528$	0	0
$529$	−4067.00	−0.334265
$530$	−270.000	−0.0221284
$531$	0	0
$532$	−140.000	−0.0114093
$533$	702.000	0.0570488
$534$	0	0
$535$	4980.00	0.402438
$536$	7896.00	0.636297
$537$	0	0
$538$	−4284.00	−0.343302
$539$	8136.00	0.650171
$540$	0	0
$541$	−10420.0	−0.828079	−0.414040	−	0.910259i	$-0.635882\pi$
$541$	−10420.0	−0.828079	−0.414040	+	0.910259i	$0.635882\pi$
$542$	−15276.0	−1.21063
$543$	0	0
$544$	1080.00	0.0851188
$545$	−440.000	−0.0345826
$546$	0	0
$547$	23708.0	1.85316	0.926582	−	0.376092i	$-0.122732\pi$
$547$	23708.0	1.85316	0.926582	+	0.376092i	$0.122732\pi$
$548$	558.000	0.0434974
$549$	0	0
$550$	−1800.00	−0.139550
$551$	−8400.00	−0.649459
$552$	0	0
$553$	−1616.00	−0.124266
$554$	−14250.0	−1.09282
$555$	0	0
$556$	128.000	0.00976333
$557$	−15186.0	−1.15521	−0.577605	−	0.816317i	$-0.696012\pi$
$557$	−15186.0	−1.15521	−0.577605	+	0.816317i	$0.696012\pi$
$558$	0	0
$559$	−2548.00	−0.192789
$560$	−710.000	−0.0535767
$561$	0	0
$562$	990.000	0.0743072
$563$	−9984.00	−0.747381	−0.373690	−	0.927553i	$-0.621908\pi$
$563$	−9984.00	−0.747381	−0.373690	+	0.927553i	$0.621908\pi$
$564$	0	0
$565$	3540.00	0.263591
$566$	2868.00	0.212988
$567$	0	0
$568$	5040.00	0.372313
$569$	−16206.0	−1.19401	−0.597004	−	0.802238i	$-0.703642\pi$
$569$	−16206.0	−1.19401	−0.597004	+	0.802238i	$0.703642\pi$
$570$	0	0
$571$	−14344.0	−1.05127	−0.525637	−	0.850709i	$-0.676173\pi$
$571$	−14344.0	−1.05127	−0.525637	+	0.850709i	$0.676173\pi$
$572$	−312.000	−0.0228066
$573$	0	0
$574$	324.000	0.0235601
$575$	−2250.00	−0.163185
$576$	0	0
$577$	11828.0	0.853390	0.426695	−	0.904396i	$-0.359678\pi$
$577$	11828.0	0.853390	0.426695	+	0.904396i	$0.359678\pi$
$578$	−13011.0	−0.936308
$579$	0	0
$580$	600.000	0.0429546
$581$	−2184.00	−0.155951
$582$	0	0
$583$	432.000	0.0306889
$584$	−23856.0	−1.69036
$585$	0	0
$586$	26694.0	1.88177
$587$	−3156.00	−0.221912	−0.110956	−	0.993825i	$-0.535391\pi$
$587$	−3156.00	−0.221912	−0.110956	+	0.993825i	$0.535391\pi$
$588$	0	0
$589$	13720.0	0.959801
$590$	4680.00	0.326564
$591$	0	0
$592$	15194.0	1.05485
$593$	−2502.00	−0.173263	−0.0866314	−	0.996240i	$-0.527610\pi$
$593$	−2502.00	−0.173263	−0.0866314	+	0.996240i	$0.527610\pi$
$594$	0	0
$595$	−240.000	−0.0165362
$596$	2994.00	0.205770
$597$	0	0
$598$	−3510.00	−0.240024
$599$	−9960.00	−0.679390	−0.339695	−	0.940536i	$-0.610324\pi$
$599$	−9960.00	−0.679390	−0.339695	+	0.940536i	$0.610324\pi$
$600$	0	0
$601$	−25738.0	−1.74688	−0.873440	−	0.486932i	$-0.838116\pi$
$601$	−25738.0	−1.74688	−0.873440	+	0.486932i	$0.838116\pi$
$602$	−1176.00	−0.0796182
$603$	0	0
$604$	2324.00	0.156560
$605$	−3775.00	−0.253679
$606$	0	0
$607$	−2392.00	−0.159948	−0.0799739	−	0.996797i	$-0.525484\pi$
$607$	−2392.00	−0.159948	−0.0799739	+	0.996797i	$0.525484\pi$
$608$	3150.00	0.210114
$609$	0	0
$610$	−4830.00	−0.320592
$611$	−1560.00	−0.103291
$612$	0	0
$613$	1874.00	0.123475	0.0617375	−	0.998092i	$-0.480336\pi$
$613$	1874.00	0.123475	0.0617375	+	0.998092i	$0.480336\pi$
$614$	2544.00	0.167211
$615$	0	0
$616$	1008.00	0.0659310
$617$	3246.00	0.211797	0.105899	−	0.994377i	$-0.466228\pi$
$617$	3246.00	0.211797	0.105899	+	0.994377i	$0.466228\pi$
$618$	0	0
$619$	13286.0	0.862697	0.431348	−	0.902185i	$-0.358038\pi$
$619$	13286.0	0.862697	0.431348	+	0.902185i	$0.358038\pi$
$620$	−980.000	−0.0634802
$621$	0	0
$622$	5760.00	0.371310
$623$	1236.00	0.0794852
$624$	0	0
$625$	625.000	0.0400000
$626$	21066.0	1.34499
$627$	0	0
$628$	−2086.00	−0.132549
$629$	5136.00	0.325573
$630$	0	0
$631$	4520.00	0.285164	0.142582	−	0.989783i	$-0.454460\pi$
$631$	4520.00	0.285164	0.142582	+	0.989783i	$0.454460\pi$
$632$	16968.0	1.06796
$633$	0	0
$634$	−22446.0	−1.40606
$635$	−10160.0	−0.634941
$636$	0	0
$637$	−4407.00	−0.274116
$638$	−8640.00	−0.536146
$639$	0	0
$640$	8295.00	0.512326
$641$	3798.00	0.234028	0.117014	−	0.993130i	$-0.462668\pi$
$641$	3798.00	0.234028	0.117014	+	0.993130i	$0.462668\pi$
$642$	0	0
$643$	−14920.0	−0.915066	−0.457533	−	0.889193i	$-0.651267\pi$
$643$	−14920.0	−0.915066	−0.457533	+	0.889193i	$0.651267\pi$
$644$	−180.000	−0.0110140
$645$	0	0
$646$	5040.00	0.306960
$647$	−28974.0	−1.76056	−0.880282	−	0.474450i	$-0.842647\pi$
$647$	−28974.0	−1.76056	−0.880282	+	0.474450i	$0.842647\pi$
$648$	0	0
$649$	−7488.00	−0.452896
$650$	975.000	0.0588348
$651$	0	0
$652$	1604.00	0.0963458
$653$	19602.0	1.17471	0.587355	−	0.809329i	$-0.300169\pi$
$653$	19602.0	1.17471	0.587355	+	0.809329i	$0.300169\pi$
$654$	0	0
$655$	5730.00	0.341816
$656$	−3834.00	−0.228190
$657$	0	0
$658$	−720.000	−0.0426573
$659$	−4662.00	−0.275578	−0.137789	−	0.990462i	$-0.544000\pi$
$659$	−4662.00	−0.275578	−0.137789	+	0.990462i	$0.544000\pi$
$660$	0	0
$661$	−19780.0	−1.16392	−0.581961	−	0.813216i	$-0.697714\pi$
$661$	−19780.0	−1.16392	−0.581961	+	0.813216i	$0.697714\pi$
$662$	16422.0	0.964138
$663$	0	0
$664$	22932.0	1.34026
$665$	−700.000	−0.0408193
$666$	0	0
$667$	−10800.0	−0.626953
$668$	2556.00	0.148046
$669$	0	0
$670$	−5640.00	−0.325212
$671$	7728.00	0.444614
$672$	0	0
$673$	8858.00	0.507356	0.253678	−	0.967289i	$-0.418360\pi$
$673$	8858.00	0.507356	0.253678	+	0.967289i	$0.418360\pi$
$674$	−19542.0	−1.11681
$675$	0	0
$676$	169.000	0.00961538
$677$	27906.0	1.58422	0.792108	−	0.610381i	$-0.208983\pi$
$677$	27906.0	1.58422	0.792108	+	0.610381i	$0.208983\pi$
$678$	0	0
$679$	−1760.00	−0.0994736
$680$	2520.00	0.142114
$681$	0	0
$682$	14112.0	0.792341
$683$	17436.0	0.976823	0.488411	−	0.872613i	$-0.337577\pi$
$683$	17436.0	0.976823	0.488411	+	0.872613i	$0.337577\pi$
$684$	0	0
$685$	2790.00	0.155621
$686$	−4092.00	−0.227745
$687$	0	0
$688$	13916.0	0.771137
$689$	−234.000	−0.0129386
$690$	0	0
$691$	−26134.0	−1.43876	−0.719381	−	0.694616i	$-0.755574\pi$
$691$	−26134.0	−1.43876	−0.719381	+	0.694616i	$0.755574\pi$
$692$	1422.00	0.0781161
$693$	0	0
$694$	−28008.0	−1.53194
$695$	640.000	0.0349303
$696$	0	0
$697$	−1296.00	−0.0704297
$698$	−19272.0	−1.04507
$699$	0	0
$700$	50.0000	0.00269975
$701$	5724.00	0.308406	0.154203	−	0.988039i	$-0.450719\pi$
$701$	5724.00	0.308406	0.154203	+	0.988039i	$0.450719\pi$
$702$	0	0
$703$	14980.0	0.803672
$704$	−10392.0	−0.556340
$705$	0	0
$706$	−24102.0	−1.28483
$707$	456.000	0.0242569
$708$	0	0
$709$	−21184.0	−1.12212	−0.561059	−	0.827776i	$-0.689606\pi$
$709$	−21184.0	−1.12212	−0.561059	+	0.827776i	$0.689606\pi$
$710$	−3600.00	−0.190290
$711$	0	0
$712$	−12978.0	−0.683105
$713$	17640.0	0.926540
$714$	0	0
$715$	−1560.00	−0.0815954
$716$	294.000	0.0153454
$717$	0	0
$718$	−27648.0	−1.43707
$719$	−14244.0	−0.738820	−0.369410	−	0.929267i	$-0.620440\pi$
$719$	−14244.0	−0.738820	−0.369410	+	0.929267i	$0.620440\pi$
$720$	0	0
$721$	1120.00	0.0578516
$722$	−5877.00	−0.302935
$723$	0	0
$724$	−1150.00	−0.0590323
$725$	3000.00	0.153679
$726$	0	0
$727$	−2644.00	−0.134884	−0.0674419	−	0.997723i	$-0.521484\pi$
$727$	−2644.00	−0.134884	−0.0674419	+	0.997723i	$0.521484\pi$
$728$	−546.000	−0.0277968
$729$	0	0
$730$	17040.0	0.863943
$731$	4704.00	0.238008
$732$	0	0
$733$	−6190.00	−0.311914	−0.155957	−	0.987764i	$-0.549846\pi$
$733$	−6190.00	−0.311914	−0.155957	+	0.987764i	$0.549846\pi$
$734$	32136.0	1.61602
$735$	0	0
$736$	4050.00	0.202833
$737$	9024.00	0.451022
$738$	0	0
$739$	−19402.0	−0.965784	−0.482892	−	0.875680i	$-0.660414\pi$
$739$	−19402.0	−0.965784	−0.482892	+	0.875680i	$0.660414\pi$
$740$	−1070.00	−0.0531540
$741$	0	0
$742$	−108.000	−0.00534340
$743$	30276.0	1.49491	0.747455	−	0.664312i	$-0.231275\pi$
$743$	30276.0	1.49491	0.747455	+	0.664312i	$0.231275\pi$
$744$	0	0
$745$	14970.0	0.736186
$746$	−15114.0	−0.741773
$747$	0	0
$748$	576.000	0.0281559
$749$	1992.00	0.0971777
$750$	0	0
$751$	−11392.0	−0.553529	−0.276764	−	0.960938i	$-0.589262\pi$
$751$	−11392.0	−0.553529	−0.276764	+	0.960938i	$0.589262\pi$
$752$	8520.00	0.413155
$753$	0	0
$754$	4680.00	0.226042
$755$	11620.0	0.560126
$756$	0	0
$757$	33734.0	1.61966	0.809830	−	0.586664i	$-0.199559\pi$
$757$	33734.0	1.61966	0.809830	+	0.586664i	$0.199559\pi$
$758$	−18678.0	−0.895007
$759$	0	0
$760$	7350.00	0.350806
$761$	18150.0	0.864569	0.432284	−	0.901737i	$-0.357708\pi$
$761$	18150.0	0.864569	0.432284	+	0.901737i	$0.357708\pi$
$762$	0	0
$763$	−176.000	−0.00835076
$764$	1512.00	0.0715998
$765$	0	0
$766$	16164.0	0.762440
$767$	4056.00	0.190944
$768$	0	0
$769$	21530.0	1.00961	0.504806	−	0.863233i	$-0.331564\pi$
$769$	21530.0	1.00961	0.504806	+	0.863233i	$0.331564\pi$
$770$	−720.000	−0.0336974
$771$	0	0
$772$	−3796.00	−0.176970
$773$	10290.0	0.478791	0.239396	−	0.970922i	$-0.423051\pi$
$773$	10290.0	0.478791	0.239396	+	0.970922i	$0.423051\pi$
$774$	0	0
$775$	−4900.00	−0.227114
$776$	18480.0	0.854888
$777$	0	0
$778$	40356.0	1.85968
$779$	−3780.00	−0.173854
$780$	0	0
$781$	5760.00	0.263904
$782$	6480.00	0.296323
$783$	0	0
$784$	24069.0	1.09644
$785$	−10430.0	−0.474220
$786$	0	0
$787$	1676.00	0.0759123	0.0379561	−	0.999279i	$-0.487915\pi$
$787$	1676.00	0.0759123	0.0379561	+	0.999279i	$0.487915\pi$
$788$	−606.000	−0.0273958
$789$	0	0
$790$	−12120.0	−0.545836
$791$	1416.00	0.0636500
$792$	0	0
$793$	−4186.00	−0.187452
$794$	−12522.0	−0.559684
$795$	0	0
$796$	3152.00	0.140351
$797$	31398.0	1.39545	0.697725	−	0.716365i	$-0.254196\pi$
$797$	31398.0	1.39545	0.697725	+	0.716365i	$0.254196\pi$
$798$	0	0
$799$	2880.00	0.127518
$800$	−1125.00	−0.0497184
$801$	0	0
$802$	−16686.0	−0.734667
$803$	−27264.0	−1.19816
$804$	0	0
$805$	−900.000	−0.0394048
$806$	−7644.00	−0.334055
$807$	0	0
$808$	−4788.00	−0.208467
$809$	19230.0	0.835712	0.417856	−	0.908513i	$-0.362782\pi$
$809$	19230.0	0.835712	0.417856	+	0.908513i	$0.362782\pi$
$810$	0	0
$811$	−7342.00	−0.317895	−0.158947	−	0.987287i	$-0.550810\pi$
$811$	−7342.00	−0.317895	−0.158947	+	0.987287i	$0.550810\pi$
$812$	240.000	0.0103724
$813$	0	0
$814$	15408.0	0.663452
$815$	8020.00	0.344697
$816$	0	0
$817$	13720.0	0.587518
$818$	−26022.0	−1.11227
$819$	0	0
$820$	270.000	0.0114985
$821$	23322.0	0.991405	0.495702	−	0.868492i	$-0.334911\pi$
$821$	23322.0	0.991405	0.495702	+	0.868492i	$0.334911\pi$
$822$	0	0
$823$	24320.0	1.03006	0.515032	−	0.857171i	$-0.327780\pi$
$823$	24320.0	1.03006	0.515032	+	0.857171i	$0.327780\pi$
$824$	−11760.0	−0.497183
$825$	0	0
$826$	1872.00	0.0788562
$827$	−1548.00	−0.0650898	−0.0325449	−	0.999470i	$-0.510361\pi$
$827$	−1548.00	−0.0650898	−0.0325449	+	0.999470i	$0.510361\pi$
$828$	0	0
$829$	−22426.0	−0.939550	−0.469775	−	0.882786i	$-0.655665\pi$
$829$	−22426.0	−0.939550	−0.469775	+	0.882786i	$0.655665\pi$
$830$	−16380.0	−0.685010
$831$	0	0
$832$	5629.00	0.234556
$833$	8136.00	0.338410
$834$	0	0
$835$	12780.0	0.529665
$836$	1680.00	0.0695024
$837$	0	0
$838$	22302.0	0.919343
$839$	28728.0	1.18212	0.591061	−	0.806627i	$-0.298709\pi$
$839$	28728.0	1.18212	0.591061	+	0.806627i	$0.298709\pi$
$840$	0	0
$841$	−9989.00	−0.409570
$842$	25980.0	1.06334
$843$	0	0
$844$	−1420.00	−0.0579128
$845$	845.000	0.0344010
$846$	0	0
$847$	−1510.00	−0.0612565
$848$	1278.00	0.0517532
$849$	0	0
$850$	−1800.00	−0.0726347
$851$	19260.0	0.775822
$852$	0	0
$853$	25490.0	1.02317	0.511583	−	0.859234i	$-0.329059\pi$
$853$	25490.0	1.02317	0.511583	+	0.859234i	$0.329059\pi$
$854$	−1932.00	−0.0774141
$855$	0	0
$856$	−20916.0	−0.835157
$857$	20652.0	0.823173	0.411586	−	0.911371i	$-0.364975\pi$
$857$	20652.0	0.823173	0.411586	+	0.911371i	$0.364975\pi$
$858$	0	0
$859$	39404.0	1.56513	0.782565	−	0.622569i	$-0.213911\pi$
$859$	39404.0	1.56513	0.782565	+	0.622569i	$0.213911\pi$
$860$	−980.000	−0.0388578
$861$	0	0
$862$	−34920.0	−1.37979
$863$	30852.0	1.21693	0.608467	−	0.793579i	$-0.291785\pi$
$863$	30852.0	1.21693	0.608467	+	0.793579i	$0.291785\pi$
$864$	0	0
$865$	7110.00	0.279477
$866$	8106.00	0.318075
$867$	0	0
$868$	−392.000	−0.0153287
$869$	19392.0	0.756995
$870$	0	0
$871$	−4888.00	−0.190153
$872$	1848.00	0.0717674
$873$	0	0
$874$	18900.0	0.731467
$875$	250.000	0.00965891
$876$	0	0
$877$	40790.0	1.57056	0.785280	−	0.619141i	$-0.212519\pi$
$877$	40790.0	1.57056	0.785280	+	0.619141i	$0.212519\pi$
$878$	−11496.0	−0.441881
$879$	0	0
$880$	8520.00	0.326374
$881$	−31278.0	−1.19612	−0.598060	−	0.801451i	$-0.704062\pi$
$881$	−31278.0	−1.19612	−0.598060	+	0.801451i	$0.704062\pi$
$882$	0	0
$883$	39548.0	1.50724	0.753622	−	0.657308i	$-0.228305\pi$
$883$	39548.0	1.50724	0.753622	+	0.657308i	$0.228305\pi$
$884$	−312.000	−0.0118707
$885$	0	0
$886$	35496.0	1.34595
$887$	−44514.0	−1.68504	−0.842522	−	0.538662i	$-0.818930\pi$
$887$	−44514.0	−1.68504	−0.842522	+	0.538662i	$0.818930\pi$
$888$	0	0
$889$	−4064.00	−0.153321
$890$	9270.00	0.349136
$891$	0	0
$892$	4142.00	0.155476
$893$	8400.00	0.314776
$894$	0	0
$895$	1470.00	0.0549013
$896$	3318.00	0.123713
$897$	0	0
$898$	−4554.00	−0.169230
$899$	−23520.0	−0.872565
$900$	0	0
$901$	432.000	0.0159734
$902$	−3888.00	−0.143521
$903$	0	0
$904$	−14868.0	−0.547016
$905$	−5750.00	−0.211201
$906$	0	0
$907$	31484.0	1.15260	0.576300	−	0.817238i	$-0.304496\pi$
$907$	31484.0	1.15260	0.576300	+	0.817238i	$0.304496\pi$
$908$	−5580.00	−0.203941
$909$	0	0
$910$	390.000	0.0142070
$911$	43620.0	1.58638	0.793192	−	0.608972i	$-0.208418\pi$
$911$	43620.0	1.58638	0.793192	+	0.608972i	$0.208418\pi$
$912$	0	0
$913$	26208.0	0.950009
$914$	16152.0	0.584530
$915$	0	0
$916$	3080.00	0.111098
$917$	2292.00	0.0825393
$918$	0	0
$919$	−52072.0	−1.86909	−0.934547	−	0.355841i	$-0.884195\pi$
$919$	−52072.0	−1.86909	−0.934547	+	0.355841i	$0.884195\pi$
$920$	9450.00	0.338649
$921$	0	0
$922$	20034.0	0.715602
$923$	−3120.00	−0.111263
$924$	0	0
$925$	−5350.00	−0.190170
$926$	−9174.00	−0.325568
$927$	0	0
$928$	−5400.00	−0.191017
$929$	40770.0	1.43985	0.719925	−	0.694052i	$-0.244176\pi$
$929$	40770.0	1.43985	0.719925	+	0.694052i	$0.244176\pi$
$930$	0	0
$931$	23730.0	0.835359
$932$	3312.00	0.116404
$933$	0	0
$934$	7668.00	0.268635
$935$	2880.00	0.100734
$936$	0	0
$937$	−14038.0	−0.489436	−0.244718	−	0.969594i	$-0.578695\pi$
$937$	−14038.0	−0.489436	−0.244718	+	0.969594i	$0.578695\pi$
$938$	−2256.00	−0.0785299
$939$	0	0
$940$	−600.000	−0.0208190
$941$	7554.00	0.261693	0.130847	−	0.991403i	$-0.458230\pi$
$941$	7554.00	0.261693	0.130847	+	0.991403i	$0.458230\pi$
$942$	0	0
$943$	−4860.00	−0.167830
$944$	−22152.0	−0.763757
$945$	0	0
$946$	14112.0	0.485011
$947$	−9060.00	−0.310887	−0.155444	−	0.987845i	$-0.549681\pi$
$947$	−9060.00	−0.310887	−0.155444	+	0.987845i	$0.549681\pi$
$948$	0	0
$949$	14768.0	0.505152
$950$	−5250.00	−0.179297
$951$	0	0
$952$	1008.00	0.0343167
$953$	−48840.0	−1.66011	−0.830054	−	0.557683i	$-0.811690\pi$
$953$	−48840.0	−1.66011	−0.830054	+	0.557683i	$0.811690\pi$
$954$	0	0
$955$	7560.00	0.256163
$956$	−5784.00	−0.195678
$957$	0	0
$958$	−30312.0	−1.02227
$959$	1116.00	0.0375782
$960$	0	0
$961$	8625.00	0.289517
$962$	−8346.00	−0.279715
$963$	0	0
$964$	6050.00	0.202134
$965$	−18980.0	−0.633148
$966$	0	0
$967$	28946.0	0.962607	0.481303	−	0.876554i	$-0.340164\pi$
$967$	28946.0	0.962607	0.481303	+	0.876554i	$0.340164\pi$
$968$	15855.0	0.526445
$969$	0	0
$970$	−13200.0	−0.436934
$971$	−10410.0	−0.344050	−0.172025	−	0.985093i	$-0.555031\pi$
$971$	−10410.0	−0.344050	−0.172025	+	0.985093i	$0.555031\pi$
$972$	0	0
$973$	256.000	0.00843472
$974$	12102.0	0.398124
$975$	0	0
$976$	22862.0	0.749790
$977$	−24966.0	−0.817536	−0.408768	−	0.912638i	$-0.634042\pi$
$977$	−24966.0	−0.817536	−0.408768	+	0.912638i	$0.634042\pi$
$978$	0	0
$979$	−14832.0	−0.484201
$980$	−1695.00	−0.0552498
$981$	0	0
$982$	−47034.0	−1.52843
$983$	−44508.0	−1.44414	−0.722068	−	0.691823i	$-0.756808\pi$
$983$	−44508.0	−1.44414	−0.722068	+	0.691823i	$0.756808\pi$
$984$	0	0
$985$	−3030.00	−0.0980140
$986$	−8640.00	−0.279061
$987$	0	0
$988$	−910.000	−0.0293026
$989$	17640.0	0.567158
$990$	0	0
$991$	−12544.0	−0.402092	−0.201046	−	0.979582i	$-0.564434\pi$
$991$	−12544.0	−0.402092	−0.201046	+	0.979582i	$0.564434\pi$
$992$	8820.00	0.282294
$993$	0	0
$994$	−1440.00	−0.0459497
$995$	15760.0	0.502136
$996$	0	0
$997$	−45862.0	−1.45683	−0.728417	−	0.685134i	$-0.759744\pi$
$997$	−45862.0	−1.45683	−0.728417	+	0.685134i	$0.759744\pi$
$998$	−62958.0	−1.99689
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.4.a.d.1.1		1
3.2	odd	2		195.4.a.b.1.1	✓	1
15.14	odd	2		975.4.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.4.a.b.1.1	✓	1	3.2	odd	2
585.4.a.d.1.1		1	1.1	even	1	trivial
975.4.a.h.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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	585.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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