LMFDB - Embedded newform 153.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,4,Mod(1,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("153.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	153.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:	$9.02729223088$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	153.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -7.00000 q^{4} -16.0000 q^{5} +34.0000 q^{7} -15.0000 q^{8} +O(q^{10})$

$q+1.00000 q^{2} -7.00000 q^{4} -16.0000 q^{5} +34.0000 q^{7} -15.0000 q^{8} -16.0000 q^{10} +48.0000 q^{11} +58.0000 q^{13} +34.0000 q^{14} +41.0000 q^{16} +17.0000 q^{17} +20.0000 q^{19} +112.000 q^{20} +48.0000 q^{22} -58.0000 q^{23} +131.000 q^{25} +58.0000 q^{26} -238.000 q^{28} -218.000 q^{31} +161.000 q^{32} +17.0000 q^{34} -544.000 q^{35} +184.000 q^{37} +20.0000 q^{38} +240.000 q^{40} +138.000 q^{41} +148.000 q^{43} -336.000 q^{44} -58.0000 q^{46} +516.000 q^{47} +813.000 q^{49} +131.000 q^{50} -406.000 q^{52} +162.000 q^{53} -768.000 q^{55} -510.000 q^{56} +180.000 q^{59} +152.000 q^{61} -218.000 q^{62} -167.000 q^{64} -928.000 q^{65} -956.000 q^{67} -119.000 q^{68} -544.000 q^{70} +538.000 q^{71} -462.000 q^{73} +184.000 q^{74} -140.000 q^{76} +1632.00 q^{77} +390.000 q^{79} -656.000 q^{80} +138.000 q^{82} -1268.00 q^{83} -272.000 q^{85} +148.000 q^{86} -720.000 q^{88} +770.000 q^{89} +1972.00 q^{91} +406.000 q^{92} +516.000 q^{94} -320.000 q^{95} +494.000 q^{97} +813.000 q^{98} +O(q^{100})$

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 $

$2$	1.00000	0.353553	0.176777	−	0.984251i	$-0.443433\pi$
$2$	1.00000	0.353553	0.176777	+	0.984251i	$0.443433\pi$
$3$	0	0
$3$	0	0
$4$	−7.00000	−0.875000
$5$	−16.0000	−1.43108	−0.715542	−	0.698570i	$-0.753820\pi$
$5$	−16.0000	−1.43108	−0.715542	+	0.698570i	$0.753820\pi$
$6$	0	0
$7$	34.0000	1.83583	0.917914	−	0.396780i	$-0.129872\pi$
$7$	34.0000	1.83583	0.917914	+	0.396780i	$0.129872\pi$
$8$	−15.0000	−0.662913
$9$	0	0
$10$	−16.0000	−0.505964
$11$	48.0000	1.31569	0.657843	−	0.753155i	$-0.271469\pi$
$11$	48.0000	1.31569	0.657843	+	0.753155i	$0.271469\pi$
$12$	0	0
$13$	58.0000	1.23741	0.618704	−	0.785624i	$-0.287658\pi$
$13$	58.0000	1.23741	0.618704	+	0.785624i	$0.287658\pi$
$14$	34.0000	0.649063
$15$	0	0
$16$	41.0000	0.640625
$17$	17.0000	0.242536
$17$	17.0000	0.242536
$18$	0	0
$19$	20.0000	0.241490	0.120745	−	0.992684i	$-0.461472\pi$
$19$	20.0000	0.241490	0.120745	+	0.992684i	$0.461472\pi$
$20$	112.000	1.25220
$21$	0	0
$22$	48.0000	0.465165
$23$	−58.0000	−0.525819	−0.262909	−	0.964821i	$-0.584682\pi$
$23$	−58.0000	−0.525819	−0.262909	+	0.964821i	$0.584682\pi$
$24$	0	0
$25$	131.000	1.04800
$26$	58.0000	0.437490
$27$	0	0
$28$	−238.000	−1.60635
$29$	0	0		−	1.00000i	$-0.5\pi$
$29$	0	0			1.00000i	$0.5\pi$
$30$	0	0
$31$	−218.000	−1.26303	−0.631515	−	0.775363i	$-0.717567\pi$
$31$	−218.000	−1.26303	−0.631515	+	0.775363i	$0.717567\pi$
$32$	161.000	0.889408
$33$	0	0
$34$	17.0000	0.0857493
$35$	−544.000	−2.62722
$36$	0	0
$37$	184.000	0.817552	0.408776	−	0.912635i	$-0.365956\pi$
$37$	184.000	0.817552	0.408776	+	0.912635i	$0.365956\pi$
$38$	20.0000	0.0853797
$39$	0	0
$40$	240.000	0.948683
$41$	138.000	0.525658	0.262829	−	0.964842i	$-0.415344\pi$
$41$	138.000	0.525658	0.262829	+	0.964842i	$0.415344\pi$
$42$	0	0
$43$	148.000	0.524879	0.262439	−	0.964948i	$-0.415473\pi$
$43$	148.000	0.524879	0.262439	+	0.964948i	$0.415473\pi$
$44$	−336.000	−1.15123
$45$	0	0
$46$	−58.0000	−0.185905
$47$	516.000	1.60141	0.800706	−	0.599058i	$-0.204458\pi$
$47$	516.000	1.60141	0.800706	+	0.599058i	$0.204458\pi$
$48$	0	0
$49$	813.000	2.37026
$50$	131.000	0.370524
$51$	0	0
$52$	−406.000	−1.08273
$53$	162.000	0.419857	0.209928	−	0.977717i	$-0.432677\pi$
$53$	162.000	0.419857	0.209928	+	0.977717i	$0.432677\pi$
$54$	0	0
$55$	−768.000	−1.88286
$56$	−510.000	−1.21699
$57$	0	0
$58$	0	0
$59$	180.000	0.397187	0.198593	−	0.980082i	$-0.436363\pi$
$59$	180.000	0.397187	0.198593	+	0.980082i	$0.436363\pi$
$60$	0	0
$61$	152.000	0.319043	0.159521	−	0.987194i	$-0.449005\pi$
$61$	152.000	0.319043	0.159521	+	0.987194i	$0.449005\pi$
$62$	−218.000	−0.446549
$63$	0	0
$64$	−167.000	−0.326172
$65$	−928.000	−1.77083
$66$	0	0
$67$	−956.000	−1.74319	−0.871597	−	0.490223i	$-0.836915\pi$
$67$	−956.000	−1.74319	−0.871597	+	0.490223i	$0.836915\pi$
$68$	−119.000	−0.212219
$69$	0	0
$70$	−544.000	−0.928863
$71$	538.000	0.899280	0.449640	−	0.893210i	$-0.351552\pi$
$71$	538.000	0.899280	0.449640	+	0.893210i	$0.351552\pi$
$72$	0	0
$73$	−462.000	−0.740726	−0.370363	−	0.928887i	$-0.620767\pi$
$73$	−462.000	−0.740726	−0.370363	+	0.928887i	$0.620767\pi$
$74$	184.000	0.289048
$75$	0	0
$76$	−140.000	−0.211304
$77$	1632.00	2.41537
$78$	0	0
$79$	390.000	0.555423	0.277712	−	0.960665i	$-0.410424\pi$
$79$	390.000	0.555423	0.277712	+	0.960665i	$0.410424\pi$
$80$	−656.000	−0.916788
$81$	0	0
$82$	138.000	0.185848
$83$	−1268.00	−1.67688	−0.838440	−	0.544994i	$-0.816532\pi$
$83$	−1268.00	−1.67688	−0.838440	+	0.544994i	$0.816532\pi$
$84$	0	0
$85$	−272.000	−0.347089
$86$	148.000	0.185573
$87$	0	0
$88$	−720.000	−0.872185
$89$	770.000	0.917077	0.458538	−	0.888675i	$-0.348373\pi$
$89$	770.000	0.917077	0.458538	+	0.888675i	$0.348373\pi$
$90$	0	0
$91$	1972.00	2.27167
$92$	406.000	0.460092
$93$	0	0
$94$	516.000	0.566184
$95$	−320.000	−0.345593
$96$	0	0
$97$	494.000	0.517094	0.258547	−	0.965999i	$-0.416756\pi$
$97$	494.000	0.517094	0.258547	+	0.965999i	$0.416756\pi$
$98$	813.000	0.838014
$99$	0	0
$100$	−917.000	−0.917000
$101$	−1022.00	−1.00686	−0.503430	−	0.864036i	$-0.667929\pi$
$101$	−1022.00	−1.00686	−0.503430	+	0.864036i	$0.667929\pi$
$102$	0	0
$103$	−1732.00	−1.65688	−0.828442	−	0.560075i	$-0.810772\pi$
$103$	−1732.00	−1.65688	−0.828442	+	0.560075i	$0.810772\pi$
$104$	−870.000	−0.820293
$105$	0	0
$106$	162.000	0.148442
$107$	256.000	0.231294	0.115647	−	0.993290i	$-0.463106\pi$
$107$	256.000	0.231294	0.115647	+	0.993290i	$0.463106\pi$
$108$	0	0
$109$	−60.0000	−0.0527244	−0.0263622	−	0.999652i	$-0.508392\pi$
$109$	−60.0000	−0.0527244	−0.0263622	+	0.999652i	$0.508392\pi$
$110$	−768.000	−0.665690
$111$	0	0
$112$	1394.00	1.17608
$113$	−1018.00	−0.847481	−0.423741	−	0.905784i	$-0.639283\pi$
$113$	−1018.00	−0.847481	−0.423741	+	0.905784i	$0.639283\pi$
$114$	0	0
$115$	928.000	0.752491
$116$	0	0
$117$	0	0
$118$	180.000	0.140427
$119$	578.000	0.445254
$120$	0	0
$121$	973.000	0.731029
$122$	152.000	0.112799
$123$	0	0
$124$	1526.00	1.10515
$125$	−96.0000	−0.0686920
$126$	0	0
$127$	824.000	0.575734	0.287867	−	0.957670i	$-0.407054\pi$
$127$	824.000	0.575734	0.287867	+	0.957670i	$0.407054\pi$
$128$	−1455.00	−1.00473
$129$	0	0
$130$	−928.000	−0.626084
$131$	1808.00	1.20584	0.602922	−	0.797800i	$-0.294003\pi$
$131$	1808.00	1.20584	0.602922	+	0.797800i	$0.294003\pi$
$132$	0	0
$133$	680.000	0.443334
$134$	−956.000	−0.616312
$135$	0	0
$136$	−255.000	−0.160780
$137$	246.000	0.153410	0.0767051	−	0.997054i	$-0.475560\pi$
$137$	246.000	0.153410	0.0767051	+	0.997054i	$0.475560\pi$
$138$	0	0
$139$	−440.000	−0.268491	−0.134246	−	0.990948i	$-0.542861\pi$
$139$	−440.000	−0.268491	−0.134246	+	0.990948i	$0.542861\pi$
$140$	3808.00	2.29882
$141$	0	0
$142$	538.000	0.317943
$143$	2784.00	1.62804
$144$	0	0
$145$	0	0
$146$	−462.000	−0.261886
$147$	0	0
$148$	−1288.00	−0.715358
$149$	−290.000	−0.159448	−0.0797239	−	0.996817i	$-0.525404\pi$
$149$	−290.000	−0.159448	−0.0797239	+	0.996817i	$0.525404\pi$
$150$	0	0
$151$	392.000	0.211262	0.105631	−	0.994405i	$-0.466314\pi$
$151$	392.000	0.211262	0.105631	+	0.994405i	$0.466314\pi$
$152$	−300.000	−0.160087
$153$	0	0
$154$	1632.00	0.853963
$155$	3488.00	1.80750
$156$	0	0
$157$	−2786.00	−1.41622	−0.708111	−	0.706101i	$-0.750453\pi$
$157$	−2786.00	−1.41622	−0.708111	+	0.706101i	$0.750453\pi$
$158$	390.000	0.196372
$159$	0	0
$160$	−2576.00	−1.27282
$161$	−1972.00	−0.965313
$162$	0	0
$163$	468.000	0.224887	0.112444	−	0.993658i	$-0.464132\pi$
$163$	468.000	0.224887	0.112444	+	0.993658i	$0.464132\pi$
$164$	−966.000	−0.459951
$165$	0	0
$166$	−1268.00	−0.592867
$167$	1006.00	0.466147	0.233074	−	0.972459i	$-0.425122\pi$
$167$	1006.00	0.466147	0.233074	+	0.972459i	$0.425122\pi$
$168$	0	0
$169$	1167.00	0.531179
$170$	−272.000	−0.122714
$171$	0	0
$172$	−1036.00	−0.459269
$173$	−3808.00	−1.67351	−0.836754	−	0.547579i	$-0.815550\pi$
$173$	−3808.00	−1.67351	−0.836754	+	0.547579i	$0.815550\pi$
$174$	0	0
$175$	4454.00	1.92395
$176$	1968.00	0.842861
$177$	0	0
$178$	770.000	0.324236
$179$	−1740.00	−0.726557	−0.363279	−	0.931681i	$-0.618343\pi$
$179$	−1740.00	−0.726557	−0.363279	+	0.931681i	$0.618343\pi$
$180$	0	0
$181$	712.000	0.292390	0.146195	−	0.989256i	$-0.453297\pi$
$181$	712.000	0.292390	0.146195	+	0.989256i	$0.453297\pi$
$182$	1972.00	0.803156
$183$	0	0
$184$	870.000	0.348572
$185$	−2944.00	−1.16998
$186$	0	0
$187$	816.000	0.319101
$188$	−3612.00	−1.40123
$189$	0	0
$190$	−320.000	−0.122185
$191$	988.000	0.374289	0.187144	−	0.982332i	$-0.440077\pi$
$191$	988.000	0.374289	0.187144	+	0.982332i	$0.440077\pi$
$192$	0	0
$193$	2318.00	0.864525	0.432262	−	0.901748i	$-0.357715\pi$
$193$	2318.00	0.864525	0.432262	+	0.901748i	$0.357715\pi$
$194$	494.000	0.182820
$195$	0	0
$196$	−5691.00	−2.07398
$197$	1356.00	0.490411	0.245206	−	0.969471i	$-0.421145\pi$
$197$	1356.00	0.490411	0.245206	+	0.969471i	$0.421145\pi$
$198$	0	0
$199$	3490.00	1.24321	0.621607	−	0.783329i	$-0.286480\pi$
$199$	3490.00	1.24321	0.621607	+	0.783329i	$0.286480\pi$
$200$	−1965.00	−0.694732
$201$	0	0
$202$	−1022.00	−0.355979
$203$	0	0
$204$	0	0
$205$	−2208.00	−0.752261
$206$	−1732.00	−0.585797
$207$	0	0
$208$	2378.00	0.792715
$209$	960.000	0.317725
$210$	0	0
$211$	−2968.00	−0.968368	−0.484184	−	0.874966i	$-0.660883\pi$
$211$	−2968.00	−0.968368	−0.484184	+	0.874966i	$0.660883\pi$
$212$	−1134.00	−0.367375
$213$	0	0
$214$	256.000	0.0817748
$215$	−2368.00	−0.751145
$216$	0	0
$217$	−7412.00	−2.31871
$218$	−60.0000	−0.0186409
$219$	0	0
$220$	5376.00	1.64750
$221$	986.000	0.300116
$222$	0	0
$223$	−732.000	−0.219813	−0.109907	−	0.993942i	$-0.535055\pi$
$223$	−732.000	−0.219813	−0.109907	+	0.993942i	$0.535055\pi$
$224$	5474.00	1.63280
$225$	0	0
$226$	−1018.00	−0.299630
$227$	−5484.00	−1.60346	−0.801731	−	0.597685i	$-0.796087\pi$
$227$	−5484.00	−1.60346	−0.801731	+	0.597685i	$0.796087\pi$
$228$	0	0
$229$	−3930.00	−1.13407	−0.567034	−	0.823694i	$-0.691909\pi$
$229$	−3930.00	−1.13407	−0.567034	+	0.823694i	$0.691909\pi$
$230$	928.000	0.266046
$231$	0	0
$232$	0	0
$233$	4302.00	1.20959	0.604793	−	0.796383i	$-0.293256\pi$
$233$	4302.00	1.20959	0.604793	+	0.796383i	$0.293256\pi$
$234$	0	0
$235$	−8256.00	−2.29175
$236$	−1260.00	−0.347538
$237$	0	0
$238$	578.000	0.157421
$239$	2140.00	0.579184	0.289592	−	0.957150i	$-0.406480\pi$
$239$	2140.00	0.579184	0.289592	+	0.957150i	$0.406480\pi$
$240$	0	0
$241$	−1098.00	−0.293479	−0.146739	−	0.989175i	$-0.546878\pi$
$241$	−1098.00	−0.293479	−0.146739	+	0.989175i	$0.546878\pi$
$242$	973.000	0.258458
$243$	0	0
$244$	−1064.00	−0.279162
$245$	−13008.0	−3.39204
$246$	0	0
$247$	1160.00	0.298822
$248$	3270.00	0.837279
$249$	0	0
$250$	−96.0000	−0.0242863
$251$	−4452.00	−1.11955	−0.559776	−	0.828644i	$-0.689113\pi$
$251$	−4452.00	−1.11955	−0.559776	+	0.828644i	$0.689113\pi$
$252$	0	0
$253$	−2784.00	−0.691813
$254$	824.000	0.203553
$255$	0	0
$256$	−119.000	−0.0290527
$257$	6126.00	1.48688	0.743442	−	0.668800i	$-0.233192\pi$
$257$	6126.00	1.48688	0.743442	+	0.668800i	$0.233192\pi$
$258$	0	0
$259$	6256.00	1.50088
$260$	6496.00	1.54948
$261$	0	0
$262$	1808.00	0.426331
$263$	1732.00	0.406082	0.203041	−	0.979170i	$-0.434917\pi$
$263$	1732.00	0.406082	0.203041	+	0.979170i	$0.434917\pi$
$264$	0	0
$265$	−2592.00	−0.600850
$266$	680.000	0.156742
$267$	0	0
$268$	6692.00	1.52529
$269$	−7960.00	−1.80420	−0.902100	−	0.431527i	$-0.857975\pi$
$269$	−7960.00	−1.80420	−0.902100	+	0.431527i	$0.857975\pi$
$270$	0	0
$271$	−5968.00	−1.33775	−0.668875	−	0.743375i	$-0.733224\pi$
$271$	−5968.00	−1.33775	−0.668875	+	0.743375i	$0.733224\pi$
$272$	697.000	0.155374
$273$	0	0
$274$	246.000	0.0542387
$275$	6288.00	1.37884
$276$	0	0
$277$	−5716.00	−1.23986	−0.619930	−	0.784657i	$-0.712839\pi$
$277$	−5716.00	−1.23986	−0.619930	+	0.784657i	$0.712839\pi$
$278$	−440.000	−0.0949261
$279$	0	0
$280$	8160.00	1.74162
$281$	3858.00	0.819036	0.409518	−	0.912302i	$-0.365697\pi$
$281$	3858.00	0.819036	0.409518	+	0.912302i	$0.365697\pi$
$282$	0	0
$283$	6848.00	1.43841	0.719207	−	0.694796i	$-0.244505\pi$
$283$	6848.00	1.43841	0.719207	+	0.694796i	$0.244505\pi$
$284$	−3766.00	−0.786870
$285$	0	0
$286$	2784.00	0.575599
$287$	4692.00	0.965017
$288$	0	0
$289$	289.000	0.0588235
$290$	0	0
$291$	0	0
$292$	3234.00	0.648135
$293$	1542.00	0.307456	0.153728	−	0.988113i	$-0.450872\pi$
$293$	1542.00	0.307456	0.153728	+	0.988113i	$0.450872\pi$
$294$	0	0
$295$	−2880.00	−0.568407
$296$	−2760.00	−0.541965
$297$	0	0
$298$	−290.000	−0.0563733
$299$	−3364.00	−0.650653
$300$	0	0
$301$	5032.00	0.963587
$302$	392.000	0.0746923
$303$	0	0
$304$	820.000	0.154705
$305$	−2432.00	−0.456577
$306$	0	0
$307$	2124.00	0.394863	0.197432	−	0.980317i	$-0.436740\pi$
$307$	2124.00	0.394863	0.197432	+	0.980317i	$0.436740\pi$
$308$	−11424.0	−2.11345
$309$	0	0
$310$	3488.00	0.639049
$311$	−2482.00	−0.452544	−0.226272	−	0.974064i	$-0.572654\pi$
$311$	−2482.00	−0.452544	−0.226272	+	0.974064i	$0.572654\pi$
$312$	0	0
$313$	−1762.00	−0.318192	−0.159096	−	0.987263i	$-0.550858\pi$
$313$	−1762.00	−0.318192	−0.159096	+	0.987263i	$0.550858\pi$
$314$	−2786.00	−0.500710
$315$	0	0
$316$	−2730.00	−0.485995
$317$	4516.00	0.800138	0.400069	−	0.916485i	$-0.368986\pi$
$317$	4516.00	0.800138	0.400069	+	0.916485i	$0.368986\pi$
$318$	0	0
$319$	0	0
$320$	2672.00	0.466779
$321$	0	0
$322$	−1972.00	−0.341290
$323$	340.000	0.0585700
$324$	0	0
$325$	7598.00	1.29680
$326$	468.000	0.0795096
$327$	0	0
$328$	−2070.00	−0.348465
$329$	17544.0	2.93991
$330$	0	0
$331$	−7508.00	−1.24676	−0.623379	−	0.781920i	$-0.714241\pi$
$331$	−7508.00	−1.24676	−0.623379	+	0.781920i	$0.714241\pi$
$332$	8876.00	1.46727
$333$	0	0
$334$	1006.00	0.164808
$335$	15296.0	2.49466
$336$	0	0
$337$	3274.00	0.529217	0.264609	−	0.964356i	$-0.414757\pi$
$337$	3274.00	0.529217	0.264609	+	0.964356i	$0.414757\pi$
$338$	1167.00	0.187800
$339$	0	0
$340$	1904.00	0.303703
$341$	−10464.0	−1.66175
$342$	0	0
$343$	15980.0	2.51557
$344$	−2220.00	−0.347949
$345$	0	0
$346$	−3808.00	−0.591674
$347$	−11684.0	−1.80758	−0.903790	−	0.427977i	$-0.859226\pi$
$347$	−11684.0	−1.80758	−0.903790	+	0.427977i	$0.859226\pi$
$348$	0	0
$349$	10770.0	1.65188	0.825938	−	0.563761i	$-0.190646\pi$
$349$	10770.0	1.65188	0.825938	+	0.563761i	$0.190646\pi$
$350$	4454.00	0.680218
$351$	0	0
$352$	7728.00	1.17018
$353$	−8238.00	−1.24211	−0.621055	−	0.783767i	$-0.713295\pi$
$353$	−8238.00	−1.24211	−0.621055	+	0.783767i	$0.713295\pi$
$354$	0	0
$355$	−8608.00	−1.28694
$356$	−5390.00	−0.802442
$357$	0	0
$358$	−1740.00	−0.256877
$359$	−9600.00	−1.41133	−0.705667	−	0.708544i	$-0.749352\pi$
$359$	−9600.00	−1.41133	−0.705667	+	0.708544i	$0.749352\pi$
$360$	0	0
$361$	−6459.00	−0.941682
$362$	712.000	0.103375
$363$	0	0
$364$	−13804.0	−1.98771
$365$	7392.00	1.06004
$366$	0	0
$367$	11494.0	1.63483	0.817414	−	0.576051i	$-0.195407\pi$
$367$	11494.0	1.63483	0.817414	+	0.576051i	$0.195407\pi$
$368$	−2378.00	−0.336853
$369$	0	0
$370$	−2944.00	−0.413652
$371$	5508.00	0.770785
$372$	0	0
$373$	−7182.00	−0.996970	−0.498485	−	0.866898i	$-0.666110\pi$
$373$	−7182.00	−0.996970	−0.498485	+	0.866898i	$0.666110\pi$
$374$	816.000	0.112819
$375$	0	0
$376$	−7740.00	−1.06160
$377$	0	0
$378$	0	0
$379$	5380.00	0.729161	0.364581	−	0.931172i	$-0.381212\pi$
$379$	5380.00	0.729161	0.364581	+	0.931172i	$0.381212\pi$
$380$	2240.00	0.302394
$381$	0	0
$382$	988.000	0.132331
$383$	4812.00	0.641989	0.320994	−	0.947081i	$-0.395983\pi$
$383$	4812.00	0.641989	0.320994	+	0.947081i	$0.395983\pi$
$384$	0	0
$385$	−26112.0	−3.45660
$386$	2318.00	0.305656
$387$	0	0
$388$	−3458.00	−0.452457
$389$	−8010.00	−1.04402	−0.522009	−	0.852940i	$-0.674817\pi$
$389$	−8010.00	−1.04402	−0.522009	+	0.852940i	$0.674817\pi$
$390$	0	0
$391$	−986.000	−0.127530
$392$	−12195.0	−1.57128
$393$	0	0
$394$	1356.00	0.173387
$395$	−6240.00	−0.794857
$396$	0	0
$397$	2304.00	0.291271	0.145635	−	0.989338i	$-0.453477\pi$
$397$	2304.00	0.291271	0.145635	+	0.989338i	$0.453477\pi$
$398$	3490.00	0.439542
$399$	0	0
$400$	5371.00	0.671375
$401$	3218.00	0.400746	0.200373	−	0.979720i	$-0.435785\pi$
$401$	3218.00	0.400746	0.200373	+	0.979720i	$0.435785\pi$
$402$	0	0
$403$	−12644.0	−1.56288
$404$	7154.00	0.881002
$405$	0	0
$406$	0	0
$407$	8832.00	1.07564
$408$	0	0
$409$	−2890.00	−0.349392	−0.174696	−	0.984622i	$-0.555894\pi$
$409$	−2890.00	−0.349392	−0.174696	+	0.984622i	$0.555894\pi$
$410$	−2208.00	−0.265964
$411$	0	0
$412$	12124.0	1.44977
$413$	6120.00	0.729166
$414$	0	0
$415$	20288.0	2.39976
$416$	9338.00	1.10056
$417$	0	0
$418$	960.000	0.112333
$419$	−8540.00	−0.995719	−0.497860	−	0.867258i	$-0.665880\pi$
$419$	−8540.00	−0.995719	−0.497860	+	0.867258i	$0.665880\pi$
$420$	0	0
$421$	10162.0	1.17640	0.588201	−	0.808714i	$-0.299836\pi$
$421$	10162.0	1.17640	0.588201	+	0.808714i	$0.299836\pi$
$422$	−2968.00	−0.342370
$423$	0	0
$424$	−2430.00	−0.278328
$425$	2227.00	0.254177
$426$	0	0
$427$	5168.00	0.585707
$428$	−1792.00	−0.202382
$429$	0	0
$430$	−2368.00	−0.265570
$431$	3918.00	0.437873	0.218937	−	0.975739i	$-0.429741\pi$
$431$	3918.00	0.437873	0.218937	+	0.975739i	$0.429741\pi$
$432$	0	0
$433$	−15442.0	−1.71385	−0.856923	−	0.515445i	$-0.827627\pi$
$433$	−15442.0	−1.71385	−0.856923	+	0.515445i	$0.827627\pi$
$434$	−7412.00	−0.819787
$435$	0	0
$436$	420.000	0.0461338
$437$	−1160.00	−0.126980
$438$	0	0
$439$	7930.00	0.862137	0.431069	−	0.902319i	$-0.358137\pi$
$439$	7930.00	0.862137	0.431069	+	0.902319i	$0.358137\pi$
$440$	11520.0	1.24817
$441$	0	0
$442$	986.000	0.106107
$443$	−9748.00	−1.04547	−0.522733	−	0.852496i	$-0.675088\pi$
$443$	−9748.00	−1.04547	−0.522733	+	0.852496i	$0.675088\pi$
$444$	0	0
$445$	−12320.0	−1.31241
$446$	−732.000	−0.0777157
$447$	0	0
$448$	−5678.00	−0.598795
$449$	2330.00	0.244899	0.122449	−	0.992475i	$-0.460925\pi$
$449$	2330.00	0.244899	0.122449	+	0.992475i	$0.460925\pi$
$450$	0	0
$451$	6624.00	0.691601
$452$	7126.00	0.741546
$453$	0	0
$454$	−5484.00	−0.566909
$455$	−31552.0	−3.25095
$456$	0	0
$457$	7014.00	0.717945	0.358973	−	0.933348i	$-0.383127\pi$
$457$	7014.00	0.717945	0.358973	+	0.933348i	$0.383127\pi$
$458$	−3930.00	−0.400954
$459$	0	0
$460$	−6496.00	−0.658429
$461$	2618.00	0.264495	0.132248	−	0.991217i	$-0.457781\pi$
$461$	2618.00	0.264495	0.132248	+	0.991217i	$0.457781\pi$
$462$	0	0
$463$	4388.00	0.440448	0.220224	−	0.975449i	$-0.429321\pi$
$463$	4388.00	0.440448	0.220224	+	0.975449i	$0.429321\pi$
$464$	0	0
$465$	0	0
$466$	4302.00	0.427653
$467$	−19044.0	−1.88705	−0.943524	−	0.331305i	$-0.892511\pi$
$467$	−19044.0	−1.88705	−0.943524	+	0.331305i	$0.892511\pi$
$468$	0	0
$469$	−32504.0	−3.20020
$470$	−8256.00	−0.810257
$471$	0	0
$472$	−2700.00	−0.263300
$473$	7104.00	0.690576
$474$	0	0
$475$	2620.00	0.253082
$476$	−4046.00	−0.389597
$477$	0	0
$478$	2140.00	0.204773
$479$	7530.00	0.718277	0.359138	−	0.933284i	$-0.383071\pi$
$479$	7530.00	0.718277	0.359138	+	0.933284i	$0.383071\pi$
$480$	0	0
$481$	10672.0	1.01165
$482$	−1098.00	−0.103760
$483$	0	0
$484$	−6811.00	−0.639651
$485$	−7904.00	−0.740004
$486$	0	0
$487$	854.000	0.0794629	0.0397315	−	0.999210i	$-0.487350\pi$
$487$	854.000	0.0794629	0.0397315	+	0.999210i	$0.487350\pi$
$488$	−2280.00	−0.211497
$489$	0	0
$490$	−13008.0	−1.19927
$491$	−9572.00	−0.879793	−0.439896	−	0.898049i	$-0.644985\pi$
$491$	−9572.00	−0.879793	−0.439896	+	0.898049i	$0.644985\pi$
$492$	0	0
$493$	0	0
$494$	1160.00	0.105650
$495$	0	0
$496$	−8938.00	−0.809129
$497$	18292.0	1.65092
$498$	0	0
$499$	7520.00	0.674632	0.337316	−	0.941391i	$-0.390481\pi$
$499$	7520.00	0.674632	0.337316	+	0.941391i	$0.390481\pi$
$500$	672.000	0.0601055
$501$	0	0
$502$	−4452.00	−0.395822
$503$	10662.0	0.945119	0.472560	−	0.881299i	$-0.343330\pi$
$503$	10662.0	0.945119	0.472560	+	0.881299i	$0.343330\pi$
$504$	0	0
$505$	16352.0	1.44090
$506$	−2784.00	−0.244593
$507$	0	0
$508$	−5768.00	−0.503767
$509$	−370.000	−0.0322200	−0.0161100	−	0.999870i	$-0.505128\pi$
$509$	−370.000	−0.0322200	−0.0161100	+	0.999870i	$0.505128\pi$
$510$	0	0
$511$	−15708.0	−1.35985
$512$	11521.0	0.994455
$513$	0	0
$514$	6126.00	0.525693
$515$	27712.0	2.37114
$516$	0	0
$517$	24768.0	2.10695
$518$	6256.00	0.530643
$519$	0	0
$520$	13920.0	1.17391
$521$	−12662.0	−1.06475	−0.532373	−	0.846510i	$-0.678699\pi$
$521$	−12662.0	−1.06475	−0.532373	+	0.846510i	$0.678699\pi$
$522$	0	0
$523$	−11412.0	−0.954134	−0.477067	−	0.878867i	$-0.658300\pi$
$523$	−11412.0	−0.954134	−0.477067	+	0.878867i	$0.658300\pi$
$524$	−12656.0	−1.05511
$525$	0	0
$526$	1732.00	0.143572
$527$	−3706.00	−0.306330
$528$	0	0
$529$	−8803.00	−0.723514
$530$	−2592.00	−0.212433
$531$	0	0
$532$	−4760.00	−0.387918
$533$	8004.00	0.650454
$534$	0	0
$535$	−4096.00	−0.331001
$536$	14340.0	1.15559
$537$	0	0
$538$	−7960.00	−0.637881
$539$	39024.0	3.11852
$540$	0	0
$541$	−3408.00	−0.270834	−0.135417	−	0.990789i	$-0.543237\pi$
$541$	−3408.00	−0.270834	−0.135417	+	0.990789i	$0.543237\pi$
$542$	−5968.00	−0.472966
$543$	0	0
$544$	2737.00	0.215713
$545$	960.000	0.0754530
$546$	0	0
$547$	12664.0	0.989897	0.494948	−	0.868922i	$-0.335187\pi$
$547$	12664.0	0.989897	0.494948	+	0.868922i	$0.335187\pi$
$548$	−1722.00	−0.134234
$549$	0	0
$550$	6288.00	0.487493
$551$	0	0
$552$	0	0
$553$	13260.0	1.01966
$554$	−5716.00	−0.438357
$555$	0	0
$556$	3080.00	0.234930
$557$	25506.0	1.94026	0.970129	−	0.242589i	$-0.0779966\pi$
$557$	25506.0	1.94026	0.970129	+	0.242589i	$0.0779966\pi$
$558$	0	0
$559$	8584.00	0.649489
$560$	−22304.0	−1.68306
$561$	0	0
$562$	3858.00	0.289573
$563$	−4508.00	−0.337459	−0.168730	−	0.985662i	$-0.553966\pi$
$563$	−4508.00	−0.337459	−0.168730	+	0.985662i	$0.553966\pi$
$564$	0	0
$565$	16288.0	1.21282
$566$	6848.00	0.508556
$567$	0	0
$568$	−8070.00	−0.596144
$569$	5270.00	0.388277	0.194139	−	0.980974i	$-0.437809\pi$
$569$	5270.00	0.388277	0.194139	+	0.980974i	$0.437809\pi$
$570$	0	0
$571$	23332.0	1.71001	0.855003	−	0.518622i	$-0.173555\pi$
$571$	23332.0	1.71001	0.855003	+	0.518622i	$0.173555\pi$
$572$	−19488.0	−1.42454
$573$	0	0
$574$	4692.00	0.341185
$575$	−7598.00	−0.551058
$576$	0	0
$577$	−18686.0	−1.34819	−0.674097	−	0.738643i	$-0.735467\pi$
$577$	−18686.0	−1.34819	−0.674097	+	0.738643i	$0.735467\pi$
$578$	289.000	0.0207973
$579$	0	0
$580$	0	0
$581$	−43112.0	−3.07846
$582$	0	0
$583$	7776.00	0.552400
$584$	6930.00	0.491037
$585$	0	0
$586$	1542.00	0.108702
$587$	2276.00	0.160035	0.0800175	−	0.996793i	$-0.474502\pi$
$587$	2276.00	0.160035	0.0800175	+	0.996793i	$0.474502\pi$
$588$	0	0
$589$	−4360.00	−0.305010
$590$	−2880.00	−0.200962
$591$	0	0
$592$	7544.00	0.523744
$593$	−17778.0	−1.23112	−0.615561	−	0.788089i	$-0.711070\pi$
$593$	−17778.0	−1.23112	−0.615561	+	0.788089i	$0.711070\pi$
$594$	0	0
$595$	−9248.00	−0.637195
$596$	2030.00	0.139517
$597$	0	0
$598$	−3364.00	−0.230040
$599$	22320.0	1.52249	0.761244	−	0.648465i	$-0.224589\pi$
$599$	22320.0	1.52249	0.761244	+	0.648465i	$0.224589\pi$
$600$	0	0
$601$	−6278.00	−0.426098	−0.213049	−	0.977042i	$-0.568339\pi$
$601$	−6278.00	−0.426098	−0.213049	+	0.977042i	$0.568339\pi$
$602$	5032.00	0.340679
$603$	0	0
$604$	−2744.00	−0.184854
$605$	−15568.0	−1.04616
$606$	0	0
$607$	614.000	0.0410568	0.0205284	−	0.999789i	$-0.493465\pi$
$607$	614.000	0.0410568	0.0205284	+	0.999789i	$0.493465\pi$
$608$	3220.00	0.214783
$609$	0	0
$610$	−2432.00	−0.161424
$611$	29928.0	1.98160
$612$	0	0
$613$	14518.0	0.956569	0.478284	−	0.878205i	$-0.341259\pi$
$613$	14518.0	0.956569	0.478284	+	0.878205i	$0.341259\pi$
$614$	2124.00	0.139605
$615$	0	0
$616$	−24480.0	−1.60118
$617$	−13794.0	−0.900041	−0.450021	−	0.893018i	$-0.648583\pi$
$617$	−13794.0	−0.900041	−0.450021	+	0.893018i	$0.648583\pi$
$618$	0	0
$619$	−25260.0	−1.64020	−0.820101	−	0.572219i	$-0.806083\pi$
$619$	−25260.0	−1.64020	−0.820101	+	0.572219i	$0.806083\pi$
$620$	−24416.0	−1.58156
$621$	0	0
$622$	−2482.00	−0.159999
$623$	26180.0	1.68359
$624$	0	0
$625$	−14839.0	−0.949696
$626$	−1762.00	−0.112498
$627$	0	0
$628$	19502.0	1.23920
$629$	3128.00	0.198285
$630$	0	0
$631$	−8948.00	−0.564523	−0.282262	−	0.959337i	$-0.591085\pi$
$631$	−8948.00	−0.564523	−0.282262	+	0.959337i	$0.591085\pi$
$632$	−5850.00	−0.368197
$633$	0	0
$634$	4516.00	0.282892
$635$	−13184.0	−0.823923
$636$	0	0
$637$	47154.0	2.93298
$638$	0	0
$639$	0	0
$640$	23280.0	1.43785
$641$	−17982.0	−1.10803	−0.554014	−	0.832507i	$-0.686905\pi$
$641$	−17982.0	−1.10803	−0.554014	+	0.832507i	$0.686905\pi$
$642$	0	0
$643$	18188.0	1.11550	0.557749	−	0.830010i	$-0.311665\pi$
$643$	18188.0	1.11550	0.557749	+	0.830010i	$0.311665\pi$
$644$	13804.0	0.844649
$645$	0	0
$646$	340.000	0.0207076
$647$	−15524.0	−0.943294	−0.471647	−	0.881787i	$-0.656340\pi$
$647$	−15524.0	−0.943294	−0.471647	+	0.881787i	$0.656340\pi$
$648$	0	0
$649$	8640.00	0.522573
$650$	7598.00	0.458489
$651$	0	0
$652$	−3276.00	−0.196776
$653$	3912.00	0.234439	0.117219	−	0.993106i	$-0.462602\pi$
$653$	3912.00	0.234439	0.117219	+	0.993106i	$0.462602\pi$
$654$	0	0
$655$	−28928.0	−1.72566
$656$	5658.00	0.336750
$657$	0	0
$658$	17544.0	1.03942
$659$	18980.0	1.12194	0.560968	−	0.827837i	$-0.310429\pi$
$659$	18980.0	1.12194	0.560968	+	0.827837i	$0.310429\pi$
$660$	0	0
$661$	−6958.00	−0.409432	−0.204716	−	0.978821i	$-0.565627\pi$
$661$	−6958.00	−0.409432	−0.204716	+	0.978821i	$0.565627\pi$
$662$	−7508.00	−0.440796
$663$	0	0
$664$	19020.0	1.11163
$665$	−10880.0	−0.634449
$666$	0	0
$667$	0	0
$668$	−7042.00	−0.407879
$669$	0	0
$670$	15296.0	0.881994
$671$	7296.00	0.419760
$672$	0	0
$673$	−2242.00	−0.128414	−0.0642071	−	0.997937i	$-0.520452\pi$
$673$	−2242.00	−0.128414	−0.0642071	+	0.997937i	$0.520452\pi$
$674$	3274.00	0.187106
$675$	0	0
$676$	−8169.00	−0.464782
$677$	24636.0	1.39858	0.699290	−	0.714838i	$-0.253500\pi$
$677$	24636.0	1.39858	0.699290	+	0.714838i	$0.253500\pi$
$678$	0	0
$679$	16796.0	0.949295
$680$	4080.00	0.230089
$681$	0	0
$682$	−10464.0	−0.587518
$683$	26092.0	1.46176	0.730880	−	0.682506i	$-0.239110\pi$
$683$	26092.0	1.46176	0.730880	+	0.682506i	$0.239110\pi$
$684$	0	0
$685$	−3936.00	−0.219543
$686$	15980.0	0.889387
$687$	0	0
$688$	6068.00	0.336250
$689$	9396.00	0.519534
$690$	0	0
$691$	−12128.0	−0.667686	−0.333843	−	0.942629i	$-0.608345\pi$
$691$	−12128.0	−0.667686	−0.333843	+	0.942629i	$0.608345\pi$
$692$	26656.0	1.46432
$693$	0	0
$694$	−11684.0	−0.639076
$695$	7040.00	0.384234
$696$	0	0
$697$	2346.00	0.127491
$698$	10770.0	0.584027
$699$	0	0
$700$	−31178.0	−1.68345
$701$	−11742.0	−0.632652	−0.316326	−	0.948651i	$-0.602449\pi$
$701$	−11742.0	−0.632652	−0.316326	+	0.948651i	$0.602449\pi$
$702$	0	0
$703$	3680.00	0.197431
$704$	−8016.00	−0.429140
$705$	0	0
$706$	−8238.00	−0.439152
$707$	−34748.0	−1.84842
$708$	0	0
$709$	5540.00	0.293454	0.146727	−	0.989177i	$-0.453126\pi$
$709$	5540.00	0.293454	0.146727	+	0.989177i	$0.453126\pi$
$710$	−8608.00	−0.455003
$711$	0	0
$712$	−11550.0	−0.607942
$713$	12644.0	0.664126
$714$	0	0
$715$	−44544.0	−2.32986
$716$	12180.0	0.635737
$717$	0	0
$718$	−9600.00	−0.498982
$719$	−30550.0	−1.58459	−0.792297	−	0.610136i	$-0.791115\pi$
$719$	−30550.0	−1.58459	−0.792297	+	0.610136i	$0.791115\pi$
$720$	0	0
$721$	−58888.0	−3.04175
$722$	−6459.00	−0.332935
$723$	0	0
$724$	−4984.00	−0.255841
$725$	0	0
$726$	0	0
$727$	22744.0	1.16029	0.580143	−	0.814514i	$-0.302997\pi$
$727$	22744.0	1.16029	0.580143	+	0.814514i	$0.302997\pi$
$728$	−29580.0	−1.50592
$729$	0	0
$730$	7392.00	0.374781
$731$	2516.00	0.127302
$732$	0	0
$733$	−13742.0	−0.692459	−0.346229	−	0.938150i	$-0.612538\pi$
$733$	−13742.0	−0.692459	−0.346229	+	0.938150i	$0.612538\pi$
$734$	11494.0	0.577999
$735$	0	0
$736$	−9338.00	−0.467667
$737$	−45888.0	−2.29350
$738$	0	0
$739$	10900.0	0.542575	0.271288	−	0.962498i	$-0.412551\pi$
$739$	10900.0	0.542575	0.271288	+	0.962498i	$0.412551\pi$
$740$	20608.0	1.02374
$741$	0	0
$742$	5508.00	0.272514
$743$	−21258.0	−1.04964	−0.524819	−	0.851214i	$-0.675867\pi$
$743$	−21258.0	−1.04964	−0.524819	+	0.851214i	$0.675867\pi$
$744$	0	0
$745$	4640.00	0.228183
$746$	−7182.00	−0.352482
$747$	0	0
$748$	−5712.00	−0.279213
$749$	8704.00	0.424616
$750$	0	0
$751$	1202.00	0.0584043	0.0292021	−	0.999574i	$-0.490703\pi$
$751$	1202.00	0.0584043	0.0292021	+	0.999574i	$0.490703\pi$
$752$	21156.0	1.02590
$753$	0	0
$754$	0	0
$755$	−6272.00	−0.302333
$756$	0	0
$757$	21814.0	1.04735	0.523675	−	0.851918i	$-0.324561\pi$
$757$	21814.0	1.04735	0.523675	+	0.851918i	$0.324561\pi$
$758$	5380.00	0.257797
$759$	0	0
$760$	4800.00	0.229098
$761$	−17402.0	−0.828938	−0.414469	−	0.910063i	$-0.636033\pi$
$761$	−17402.0	−0.828938	−0.414469	+	0.910063i	$0.636033\pi$
$762$	0	0
$763$	−2040.00	−0.0967929
$764$	−6916.00	−0.327503
$765$	0	0
$766$	4812.00	0.226977
$767$	10440.0	0.491482
$768$	0	0
$769$	−14870.0	−0.697303	−0.348651	−	0.937252i	$-0.613360\pi$
$769$	−14870.0	−0.697303	−0.348651	+	0.937252i	$0.613360\pi$
$770$	−26112.0	−1.22209
$771$	0	0
$772$	−16226.0	−0.756459
$773$	8702.00	0.404902	0.202451	−	0.979292i	$-0.435109\pi$
$773$	8702.00	0.404902	0.202451	+	0.979292i	$0.435109\pi$
$774$	0	0
$775$	−28558.0	−1.32366
$776$	−7410.00	−0.342788
$777$	0	0
$778$	−8010.00	−0.369116
$779$	2760.00	0.126941
$780$	0	0
$781$	25824.0	1.18317
$782$	−986.000	−0.0450886
$783$	0	0
$784$	33333.0	1.51845
$785$	44576.0	2.02673
$786$	0	0
$787$	−25136.0	−1.13850	−0.569251	−	0.822164i	$-0.692767\pi$
$787$	−25136.0	−1.13850	−0.569251	+	0.822164i	$0.692767\pi$
$788$	−9492.00	−0.429110
$789$	0	0
$790$	−6240.00	−0.281024
$791$	−34612.0	−1.55583
$792$	0	0
$793$	8816.00	0.394786
$794$	2304.00	0.102980
$795$	0	0
$796$	−24430.0	−1.08781
$797$	−31054.0	−1.38016	−0.690081	−	0.723732i	$-0.742425\pi$
$797$	−31054.0	−1.38016	−0.690081	+	0.723732i	$0.742425\pi$
$798$	0	0
$799$	8772.00	0.388399
$800$	21091.0	0.932099
$801$	0	0
$802$	3218.00	0.141685
$803$	−22176.0	−0.974563
$804$	0	0
$805$	31552.0	1.38144
$806$	−12644.0	−0.552563
$807$	0	0
$808$	15330.0	0.667460
$809$	−11990.0	−0.521070	−0.260535	−	0.965464i	$-0.583899\pi$
$809$	−11990.0	−0.521070	−0.260535	+	0.965464i	$0.583899\pi$
$810$	0	0
$811$	−6788.00	−0.293907	−0.146954	−	0.989143i	$-0.546947\pi$
$811$	−6788.00	−0.293907	−0.146954	+	0.989143i	$0.546947\pi$
$812$	0	0
$813$	0	0
$814$	8832.00	0.380297
$815$	−7488.00	−0.321832
$816$	0	0
$817$	2960.00	0.126753
$818$	−2890.00	−0.123529
$819$	0	0
$820$	15456.0	0.658228
$821$	−15372.0	−0.653455	−0.326727	−	0.945119i	$-0.605946\pi$
$821$	−15372.0	−0.653455	−0.326727	+	0.945119i	$0.605946\pi$
$822$	0	0
$823$	2078.00	0.0880128	0.0440064	−	0.999031i	$-0.485988\pi$
$823$	2078.00	0.0880128	0.0440064	+	0.999031i	$0.485988\pi$
$824$	25980.0	1.09837
$825$	0	0
$826$	6120.00	0.257799
$827$	26976.0	1.13428	0.567139	−	0.823622i	$-0.308050\pi$
$827$	26976.0	1.13428	0.567139	+	0.823622i	$0.308050\pi$
$828$	0	0
$829$	−4930.00	−0.206545	−0.103273	−	0.994653i	$-0.532931\pi$
$829$	−4930.00	−0.206545	−0.103273	+	0.994653i	$0.532931\pi$
$830$	20288.0	0.848442
$831$	0	0
$832$	−9686.00	−0.403608
$833$	13821.0	0.574873
$834$	0	0
$835$	−16096.0	−0.667096
$836$	−6720.00	−0.278010
$837$	0	0
$838$	−8540.00	−0.352040
$839$	−36590.0	−1.50563	−0.752817	−	0.658230i	$-0.771306\pi$
$839$	−36590.0	−1.50563	−0.752817	+	0.658230i	$0.771306\pi$
$840$	0	0
$841$	−24389.0	−1.00000
$842$	10162.0	0.415921
$843$	0	0
$844$	20776.0	0.847322
$845$	−18672.0	−0.760161
$846$	0	0
$847$	33082.0	1.34204
$848$	6642.00	0.268971
$849$	0	0
$850$	2227.00	0.0898653
$851$	−10672.0	−0.429884
$852$	0	0
$853$	−21772.0	−0.873926	−0.436963	−	0.899479i	$-0.643946\pi$
$853$	−21772.0	−0.873926	−0.436963	+	0.899479i	$0.643946\pi$
$854$	5168.00	0.207079
$855$	0	0
$856$	−3840.00	−0.153328
$857$	30506.0	1.21595	0.607973	−	0.793958i	$-0.291983\pi$
$857$	30506.0	1.21595	0.607973	+	0.793958i	$0.291983\pi$
$858$	0	0
$859$	−13220.0	−0.525100	−0.262550	−	0.964918i	$-0.584563\pi$
$859$	−13220.0	−0.525100	−0.262550	+	0.964918i	$0.584563\pi$
$860$	16576.0	0.657252
$861$	0	0
$862$	3918.00	0.154812
$863$	40592.0	1.60112	0.800561	−	0.599252i	$-0.204535\pi$
$863$	40592.0	1.60112	0.800561	+	0.599252i	$0.204535\pi$
$864$	0	0
$865$	60928.0	2.39493
$866$	−15442.0	−0.605936
$867$	0	0
$868$	51884.0	2.02887
$869$	18720.0	0.730762
$870$	0	0
$871$	−55448.0	−2.15704
$872$	900.000	0.0349517
$873$	0	0
$874$	−1160.00	−0.0448943
$875$	−3264.00	−0.126107
$876$	0	0
$877$	24684.0	0.950421	0.475211	−	0.879872i	$-0.342372\pi$
$877$	24684.0	0.950421	0.475211	+	0.879872i	$0.342372\pi$
$878$	7930.00	0.304812
$879$	0	0
$880$	−31488.0	−1.20620
$881$	1558.00	0.0595804	0.0297902	−	0.999556i	$-0.490516\pi$
$881$	1558.00	0.0595804	0.0297902	+	0.999556i	$0.490516\pi$
$882$	0	0
$883$	21948.0	0.836477	0.418238	−	0.908337i	$-0.362648\pi$
$883$	21948.0	0.836477	0.418238	+	0.908337i	$0.362648\pi$
$884$	−6902.00	−0.262601
$885$	0	0
$886$	−9748.00	−0.369628
$887$	36786.0	1.39251	0.696253	−	0.717796i	$-0.254849\pi$
$887$	36786.0	1.39251	0.696253	+	0.717796i	$0.254849\pi$
$888$	0	0
$889$	28016.0	1.05695
$890$	−12320.0	−0.464008
$891$	0	0
$892$	5124.00	0.192337
$893$	10320.0	0.386725
$894$	0	0
$895$	27840.0	1.03976
$896$	−49470.0	−1.84451
$897$	0	0
$898$	2330.00	0.0865848
$899$	0	0
$900$	0	0
$901$	2754.00	0.101830
$902$	6624.00	0.244518
$903$	0	0
$904$	15270.0	0.561806
$905$	−11392.0	−0.418434
$906$	0	0
$907$	−51736.0	−1.89401	−0.947004	−	0.321221i	$-0.895907\pi$
$907$	−51736.0	−1.89401	−0.947004	+	0.321221i	$0.895907\pi$
$908$	38388.0	1.40303
$909$	0	0
$910$	−31552.0	−1.14938
$911$	18538.0	0.674195	0.337097	−	0.941470i	$-0.390555\pi$
$911$	18538.0	0.674195	0.337097	+	0.941470i	$0.390555\pi$
$912$	0	0
$913$	−60864.0	−2.20625
$914$	7014.00	0.253832
$915$	0	0
$916$	27510.0	0.992310
$917$	61472.0	2.21372
$918$	0	0
$919$	−20640.0	−0.740860	−0.370430	−	0.928860i	$-0.620790\pi$
$919$	−20640.0	−0.740860	−0.370430	+	0.928860i	$0.620790\pi$
$920$	−13920.0	−0.498836
$921$	0	0
$922$	2618.00	0.0935133
$923$	31204.0	1.11278
$924$	0	0
$925$	24104.0	0.856794
$926$	4388.00	0.155722
$927$	0	0
$928$	0	0
$929$	−51150.0	−1.80643	−0.903217	−	0.429184i	$-0.858801\pi$
$929$	−51150.0	−1.80643	−0.903217	+	0.429184i	$0.858801\pi$
$930$	0	0
$931$	16260.0	0.572395
$932$	−30114.0	−1.05839
$933$	0	0
$934$	−19044.0	−0.667172
$935$	−13056.0	−0.456660
$936$	0	0
$937$	34534.0	1.20403	0.602015	−	0.798485i	$-0.294365\pi$
$937$	34534.0	1.20403	0.602015	+	0.798485i	$0.294365\pi$
$938$	−32504.0	−1.13144
$939$	0	0
$940$	57792.0	2.00528
$941$	49188.0	1.70402	0.852010	−	0.523525i	$-0.175383\pi$
$941$	49188.0	1.70402	0.852010	+	0.523525i	$0.175383\pi$
$942$	0	0
$943$	−8004.00	−0.276401
$944$	7380.00	0.254448
$945$	0	0
$946$	7104.00	0.244155
$947$	−13064.0	−0.448282	−0.224141	−	0.974557i	$-0.571958\pi$
$947$	−13064.0	−0.448282	−0.224141	+	0.974557i	$0.571958\pi$
$948$	0	0
$949$	−26796.0	−0.916581
$950$	2620.00	0.0894779
$951$	0	0
$952$	−8670.00	−0.295164
$953$	15802.0	0.537122	0.268561	−	0.963263i	$-0.413452\pi$
$953$	15802.0	0.537122	0.268561	+	0.963263i	$0.413452\pi$
$954$	0	0
$955$	−15808.0	−0.535639
$956$	−14980.0	−0.506786
$957$	0	0
$958$	7530.00	0.253949
$959$	8364.00	0.281635
$960$	0	0
$961$	17733.0	0.595247
$962$	10672.0	0.357671
$963$	0	0
$964$	7686.00	0.256794
$965$	−37088.0	−1.23721
$966$	0	0
$967$	−24756.0	−0.823267	−0.411634	−	0.911349i	$-0.635042\pi$
$967$	−24756.0	−0.823267	−0.411634	+	0.911349i	$0.635042\pi$
$968$	−14595.0	−0.484609
$969$	0	0
$970$	−7904.00	−0.261631
$971$	−7332.00	−0.242322	−0.121161	−	0.992633i	$-0.538662\pi$
$971$	−7332.00	−0.242322	−0.121161	+	0.992633i	$0.538662\pi$
$972$	0	0
$973$	−14960.0	−0.492904
$974$	854.000	0.0280944
$975$	0	0
$976$	6232.00	0.204387
$977$	−2754.00	−0.0901825	−0.0450912	−	0.998983i	$-0.514358\pi$
$977$	−2754.00	−0.0901825	−0.0450912	+	0.998983i	$0.514358\pi$
$978$	0	0
$979$	36960.0	1.20659
$980$	91056.0	2.96804
$981$	0	0
$982$	−9572.00	−0.311054
$983$	−26598.0	−0.863016	−0.431508	−	0.902109i	$-0.642018\pi$
$983$	−26598.0	−0.863016	−0.431508	+	0.902109i	$0.642018\pi$
$984$	0	0
$985$	−21696.0	−0.701819
$986$	0	0
$987$	0	0
$988$	−8120.00	−0.261469
$989$	−8584.00	−0.275991
$990$	0	0
$991$	11922.0	0.382154	0.191077	−	0.981575i	$-0.438802\pi$
$991$	11922.0	0.382154	0.191077	+	0.981575i	$0.438802\pi$
$992$	−35098.0	−1.12335
$993$	0	0
$994$	18292.0	0.583689
$995$	−55840.0	−1.77914
$996$	0	0
$997$	−2456.00	−0.0780163	−0.0390082	−	0.999239i	$-0.512420\pi$
$997$	−2456.00	−0.0780163	−0.0390082	+	0.999239i	$0.512420\pi$
$998$	7520.00	0.238518
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.4.a.b.1.1		1
3.2	odd	2		51.4.a.a.1.1	✓	1
4.3	odd	2		2448.4.a.b.1.1		1
12.11	even	2		816.4.a.j.1.1		1
15.14	odd	2		1275.4.a.f.1.1		1
21.20	even	2		2499.4.a.e.1.1		1
51.50	odd	2		867.4.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.4.a.a.1.1	✓	1	3.2	odd	2
153.4.a.b.1.1		1	1.1	even	1	trivial
816.4.a.j.1.1		1	12.11	even	2
867.4.a.d.1.1		1	51.50	odd	2
1275.4.a.f.1.1		1	15.14	odd	2
2448.4.a.b.1.1		1	4.3	odd	2
2499.4.a.e.1.1		1	21.20	even	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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	153.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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