LMFDB - Embedded newform 1155.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,4,Mod(1,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1155.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1155.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:	$68.1472060566$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1155.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} -5.00000 q^{5} +9.00000 q^{6} +7.00000 q^{7} +21.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-3.00000 q^{2} -3.00000 q^{3} +1.00000 q^{4} -5.00000 q^{5} +9.00000 q^{6} +7.00000 q^{7} +21.0000 q^{8} +9.00000 q^{9} +15.0000 q^{10} -11.0000 q^{11} -3.00000 q^{12} -82.0000 q^{13} -21.0000 q^{14} +15.0000 q^{15} -71.0000 q^{16} +54.0000 q^{17} -27.0000 q^{18} +80.0000 q^{19} -5.00000 q^{20} -21.0000 q^{21} +33.0000 q^{22} +48.0000 q^{23} -63.0000 q^{24} +25.0000 q^{25} +246.000 q^{26} -27.0000 q^{27} +7.00000 q^{28} -234.000 q^{29} -45.0000 q^{30} -28.0000 q^{31} +45.0000 q^{32} +33.0000 q^{33} -162.000 q^{34} -35.0000 q^{35} +9.00000 q^{36} -82.0000 q^{37} -240.000 q^{38} +246.000 q^{39} -105.000 q^{40} +270.000 q^{41} +63.0000 q^{42} -28.0000 q^{43} -11.0000 q^{44} -45.0000 q^{45} -144.000 q^{46} -300.000 q^{47} +213.000 q^{48} +49.0000 q^{49} -75.0000 q^{50} -162.000 q^{51} -82.0000 q^{52} +582.000 q^{53} +81.0000 q^{54} +55.0000 q^{55} +147.000 q^{56} -240.000 q^{57} +702.000 q^{58} -684.000 q^{59} +15.0000 q^{60} +758.000 q^{61} +84.0000 q^{62} +63.0000 q^{63} +433.000 q^{64} +410.000 q^{65} -99.0000 q^{66} +524.000 q^{67} +54.0000 q^{68} -144.000 q^{69} +105.000 q^{70} +552.000 q^{71} +189.000 q^{72} +110.000 q^{73} +246.000 q^{74} -75.0000 q^{75} +80.0000 q^{76} -77.0000 q^{77} -738.000 q^{78} +944.000 q^{79} +355.000 q^{80} +81.0000 q^{81} -810.000 q^{82} +1368.00 q^{83} -21.0000 q^{84} -270.000 q^{85} +84.0000 q^{86} +702.000 q^{87} -231.000 q^{88} +42.0000 q^{89} +135.000 q^{90} -574.000 q^{91} +48.0000 q^{92} +84.0000 q^{93} +900.000 q^{94} -400.000 q^{95} -135.000 q^{96} +1658.00 q^{97} -147.000 q^{98} -99.0000 q^{99} +O(q^{100})\)

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	$-0.677932\pi$
$2$	−3.00000	−1.06066	−0.530330	+	0.847791i	$0.677932\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	1.00000	0.125000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	9.00000	0.612372
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	21.0000	0.928078
$9$	9.00000	0.333333
$10$	15.0000	0.474342
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−3.00000	−0.0721688
$13$	−82.0000	−1.74944	−0.874720	−	0.484629i	$-0.838954\pi$
$13$	−82.0000	−1.74944	−0.874720	+	0.484629i	$0.838954\pi$
$14$	−21.0000	−0.400892
$15$	15.0000	0.258199
$16$	−71.0000	−1.10938
$17$	54.0000	0.770407	0.385204	−	0.922832i	$-0.374131\pi$
$17$	54.0000	0.770407	0.385204	+	0.922832i	$0.374131\pi$
$18$	−27.0000	−0.353553
$19$	80.0000	0.965961	0.482980	−	0.875631i	$-0.339554\pi$
$19$	80.0000	0.965961	0.482980	+	0.875631i	$0.339554\pi$
$20$	−5.00000	−0.0559017
$21$	−21.0000	−0.218218
$22$	33.0000	0.319801
$23$	48.0000	0.435161	0.217580	−	0.976042i	$-0.430184\pi$
$23$	48.0000	0.435161	0.217580	+	0.976042i	$0.430184\pi$
$24$	−63.0000	−0.535826
$25$	25.0000	0.200000
$26$	246.000	1.85556
$27$	−27.0000	−0.192450
$28$	7.00000	0.0472456
$29$	−234.000	−1.49837	−0.749185	−	0.662361i	$-0.769554\pi$
$29$	−234.000	−1.49837	−0.749185	+	0.662361i	$0.769554\pi$
$30$	−45.0000	−0.273861
$31$	−28.0000	−0.162224	−0.0811121	−	0.996705i	$-0.525847\pi$
$31$	−28.0000	−0.162224	−0.0811121	+	0.996705i	$0.525847\pi$
$32$	45.0000	0.248592
$33$	33.0000	0.174078
$34$	−162.000	−0.817140
$35$	−35.0000	−0.169031
$36$	9.00000	0.0416667
$37$	−82.0000	−0.364344	−0.182172	−	0.983267i	$-0.558313\pi$
$37$	−82.0000	−0.364344	−0.182172	+	0.983267i	$0.558313\pi$
$38$	−240.000	−1.02456
$39$	246.000	1.01004
$40$	−105.000	−0.415049
$41$	270.000	1.02846	0.514231	−	0.857652i	$-0.328078\pi$
$41$	270.000	1.02846	0.514231	+	0.857652i	$0.328078\pi$
$42$	63.0000	0.231455
$43$	−28.0000	−0.0993014	−0.0496507	−	0.998767i	$-0.515811\pi$
$43$	−28.0000	−0.0993014	−0.0496507	+	0.998767i	$0.515811\pi$
$44$	−11.0000	−0.0376889
$45$	−45.0000	−0.149071
$46$	−144.000	−0.461557
$47$	−300.000	−0.931053	−0.465527	−	0.885034i	$-0.654135\pi$
$47$	−300.000	−0.931053	−0.465527	+	0.885034i	$0.654135\pi$
$48$	213.000	0.640498
$49$	49.0000	0.142857
$50$	−75.0000	−0.212132
$51$	−162.000	−0.444795
$52$	−82.0000	−0.218680
$53$	582.000	1.50837	0.754187	−	0.656659i	$-0.228031\pi$
$53$	582.000	1.50837	0.754187	+	0.656659i	$0.228031\pi$
$54$	81.0000	0.204124
$55$	55.0000	0.134840
$56$	147.000	0.350780
$57$	−240.000	−0.557698
$58$	702.000	1.58926
$59$	−684.000	−1.50931	−0.754654	−	0.656123i	$-0.772195\pi$
$59$	−684.000	−1.50931	−0.754654	+	0.656123i	$0.772195\pi$
$60$	15.0000	0.0322749
$61$	758.000	1.59102	0.795508	−	0.605943i	$-0.207204\pi$
$61$	758.000	1.59102	0.795508	+	0.605943i	$0.207204\pi$
$62$	84.0000	0.172065
$63$	63.0000	0.125988
$64$	433.000	0.845703
$65$	410.000	0.782373
$66$	−99.0000	−0.184637
$67$	524.000	0.955474	0.477737	−	0.878503i	$-0.341457\pi$
$67$	524.000	0.955474	0.477737	+	0.878503i	$0.341457\pi$
$68$	54.0000	0.0963009
$69$	−144.000	−0.251240
$70$	105.000	0.179284
$71$	552.000	0.922681	0.461340	−	0.887223i	$-0.347369\pi$
$71$	552.000	0.922681	0.461340	+	0.887223i	$0.347369\pi$
$72$	189.000	0.309359
$73$	110.000	0.176363	0.0881817	−	0.996104i	$-0.471894\pi$
$73$	110.000	0.176363	0.0881817	+	0.996104i	$0.471894\pi$
$74$	246.000	0.386445
$75$	−75.0000	−0.115470
$76$	80.0000	0.120745
$77$	−77.0000	−0.113961
$78$	−738.000	−1.07131
$79$	944.000	1.34441	0.672204	−	0.740366i	$-0.265348\pi$
$79$	944.000	1.34441	0.672204	+	0.740366i	$0.265348\pi$
$80$	355.000	0.496128
$81$	81.0000	0.111111
$82$	−810.000	−1.09085
$83$	1368.00	1.80913	0.904563	−	0.426339i	$-0.140197\pi$
$83$	1368.00	1.80913	0.904563	+	0.426339i	$0.140197\pi$
$84$	−21.0000	−0.0272772
$85$	−270.000	−0.344537
$86$	84.0000	0.105325
$87$	702.000	0.865084
$88$	−231.000	−0.279826
$89$	42.0000	0.0500224	0.0250112	−	0.999687i	$-0.492038\pi$
$89$	42.0000	0.0500224	0.0250112	+	0.999687i	$0.492038\pi$
$90$	135.000	0.158114
$91$	−574.000	−0.661226
$92$	48.0000	0.0543951
$93$	84.0000	0.0936602
$94$	900.000	0.987531
$95$	−400.000	−0.431991
$96$	−135.000	−0.143525
$97$	1658.00	1.73551	0.867755	−	0.496993i	$-0.165563\pi$
$97$	1658.00	1.73551	0.867755	+	0.496993i	$0.165563\pi$
$98$	−147.000	−0.151523
$99$	−99.0000	−0.100504
$100$	25.0000	0.0250000
$101$	−1194.00	−1.17631	−0.588156	−	0.808748i	$-0.700146\pi$
$101$	−1194.00	−1.17631	−0.588156	+	0.808748i	$0.700146\pi$
$102$	486.000	0.471776
$103$	−484.000	−0.463009	−0.231505	−	0.972834i	$-0.574365\pi$
$103$	−484.000	−0.463009	−0.231505	+	0.972834i	$0.574365\pi$
$104$	−1722.00	−1.62362
$105$	105.000	0.0975900
$106$	−1746.00	−1.59987
$107$	−1884.00	−1.70218	−0.851090	−	0.525021i	$-0.824058\pi$
$107$	−1884.00	−1.70218	−0.851090	+	0.525021i	$0.824058\pi$
$108$	−27.0000	−0.0240563
$109$	−394.000	−0.346223	−0.173112	−	0.984902i	$-0.555382\pi$
$109$	−394.000	−0.346223	−0.173112	+	0.984902i	$0.555382\pi$
$110$	−165.000	−0.143019
$111$	246.000	0.210354
$112$	−497.000	−0.419304
$113$	−1422.00	−1.18381	−0.591905	−	0.806008i	$-0.701624\pi$
$113$	−1422.00	−1.18381	−0.591905	+	0.806008i	$0.701624\pi$
$114$	720.000	0.591528
$115$	−240.000	−0.194610
$116$	−234.000	−0.187296
$117$	−738.000	−0.583146
$118$	2052.00	1.60086
$119$	378.000	0.291187
$120$	315.000	0.239629
$121$	121.000	0.0909091
$122$	−2274.00	−1.68753
$123$	−810.000	−0.593782
$124$	−28.0000	−0.0202780
$125$	−125.000	−0.0894427
$126$	−189.000	−0.133631
$127$	824.000	0.575734	0.287867	−	0.957670i	$-0.407054\pi$
$127$	824.000	0.575734	0.287867	+	0.957670i	$0.407054\pi$
$128$	−1659.00	−1.14560
$129$	84.0000	0.0573317
$130$	−1230.00	−0.829832
$131$	−1896.00	−1.26454	−0.632268	−	0.774750i	$-0.717876\pi$
$131$	−1896.00	−1.26454	−0.632268	+	0.774750i	$0.717876\pi$
$132$	33.0000	0.0217597
$133$	560.000	0.365099
$134$	−1572.00	−1.01343
$135$	135.000	0.0860663
$136$	1134.00	0.714998
$137$	2874.00	1.79228	0.896140	−	0.443771i	$-0.146360\pi$
$137$	2874.00	1.79228	0.896140	+	0.443771i	$0.146360\pi$
$138$	432.000	0.266480
$139$	−1024.00	−0.624853	−0.312426	−	0.949942i	$-0.601142\pi$
$139$	−1024.00	−0.624853	−0.312426	+	0.949942i	$0.601142\pi$
$140$	−35.0000	−0.0211289
$141$	900.000	0.537544
$142$	−1656.00	−0.978651
$143$	902.000	0.527476
$144$	−639.000	−0.369792
$145$	1170.00	0.670091
$146$	−330.000	−0.187062
$147$	−147.000	−0.0824786
$148$	−82.0000	−0.0455430
$149$	−3570.00	−1.96286	−0.981429	−	0.191827i	$-0.938559\pi$
$149$	−3570.00	−1.96286	−0.981429	+	0.191827i	$0.938559\pi$
$150$	225.000	0.122474
$151$	−1888.00	−1.01751	−0.508753	−	0.860913i	$-0.669893\pi$
$151$	−1888.00	−1.01751	−0.508753	+	0.860913i	$0.669893\pi$
$152$	1680.00	0.896487
$153$	486.000	0.256802
$154$	231.000	0.120873
$155$	140.000	0.0725488
$156$	246.000	0.126255
$157$	1202.00	0.611019	0.305510	−	0.952189i	$-0.401173\pi$
$157$	1202.00	0.611019	0.305510	+	0.952189i	$0.401173\pi$
$158$	−2832.00	−1.42596
$159$	−1746.00	−0.870860
$160$	−225.000	−0.111174
$161$	336.000	0.164475
$162$	−243.000	−0.117851
$163$	−3052.00	−1.46657	−0.733286	−	0.679921i	$-0.762014\pi$
$163$	−3052.00	−1.46657	−0.733286	+	0.679921i	$0.762014\pi$
$164$	270.000	0.128558
$165$	−165.000	−0.0778499
$166$	−4104.00	−1.91887
$167$	1392.00	0.645007	0.322504	−	0.946568i	$-0.395476\pi$
$167$	1392.00	0.645007	0.322504	+	0.946568i	$0.395476\pi$
$168$	−441.000	−0.202523
$169$	4527.00	2.06054
$170$	810.000	0.365436
$171$	720.000	0.321987
$172$	−28.0000	−0.0124127
$173$	−1122.00	−0.493087	−0.246544	−	0.969132i	$-0.579295\pi$
$173$	−1122.00	−0.493087	−0.246544	+	0.969132i	$0.579295\pi$
$174$	−2106.00	−0.917560
$175$	175.000	0.0755929
$176$	781.000	0.334489
$177$	2052.00	0.871400
$178$	−126.000	−0.0530567
$179$	−84.0000	−0.0350752	−0.0175376	−	0.999846i	$-0.505583\pi$
$179$	−84.0000	−0.0350752	−0.0175376	+	0.999846i	$0.505583\pi$
$180$	−45.0000	−0.0186339
$181$	3122.00	1.28208	0.641040	−	0.767508i	$-0.278503\pi$
$181$	3122.00	1.28208	0.641040	+	0.767508i	$0.278503\pi$
$182$	1722.00	0.701336
$183$	−2274.00	−0.918573
$184$	1008.00	0.403863
$185$	410.000	0.162939
$186$	−252.000	−0.0993416
$187$	−594.000	−0.232287
$188$	−300.000	−0.116382
$189$	−189.000	−0.0727393
$190$	1200.00	0.458196
$191$	−3720.00	−1.40927	−0.704633	−	0.709572i	$-0.748888\pi$
$191$	−3720.00	−1.40927	−0.704633	+	0.709572i	$0.748888\pi$
$192$	−1299.00	−0.488267
$193$	−3670.00	−1.36877	−0.684384	−	0.729121i	$-0.739929\pi$
$193$	−3670.00	−1.36877	−0.684384	+	0.729121i	$0.739929\pi$
$194$	−4974.00	−1.84079
$195$	−1230.00	−0.451703
$196$	49.0000	0.0178571
$197$	3294.00	1.19131	0.595654	−	0.803241i	$-0.296893\pi$
$197$	3294.00	1.19131	0.595654	+	0.803241i	$0.296893\pi$
$198$	297.000	0.106600
$199$	−1132.00	−0.403243	−0.201621	−	0.979464i	$-0.564621\pi$
$199$	−1132.00	−0.403243	−0.201621	+	0.979464i	$0.564621\pi$
$200$	525.000	0.185616
$201$	−1572.00	−0.551643
$202$	3582.00	1.24767
$203$	−1638.00	−0.566330
$204$	−162.000	−0.0555994
$205$	−1350.00	−0.459942
$206$	1452.00	0.491095
$207$	432.000	0.145054
$208$	5822.00	1.94078
$209$	−880.000	−0.291248
$210$	−315.000	−0.103510
$211$	−1348.00	−0.439811	−0.219906	−	0.975521i	$-0.570575\pi$
$211$	−1348.00	−0.439811	−0.219906	+	0.975521i	$0.570575\pi$
$212$	582.000	0.188547
$213$	−1656.00	−0.532710
$214$	5652.00	1.80543
$215$	140.000	0.0444089
$216$	−567.000	−0.178609
$217$	−196.000	−0.0613150
$218$	1182.00	0.367225
$219$	−330.000	−0.101823
$220$	55.0000	0.0168550
$221$	−4428.00	−1.34778
$222$	−738.000	−0.223114
$223$	−2692.00	−0.808384	−0.404192	−	0.914674i	$-0.632447\pi$
$223$	−2692.00	−0.808384	−0.404192	+	0.914674i	$0.632447\pi$
$224$	315.000	0.0939590
$225$	225.000	0.0666667
$226$	4266.00	1.25562
$227$	1680.00	0.491214	0.245607	−	0.969370i	$-0.421013\pi$
$227$	1680.00	0.491214	0.245607	+	0.969370i	$0.421013\pi$
$228$	−240.000	−0.0697122
$229$	1922.00	0.554626	0.277313	−	0.960780i	$-0.410556\pi$
$229$	1922.00	0.554626	0.277313	+	0.960780i	$0.410556\pi$
$230$	720.000	0.206415
$231$	231.000	0.0657952
$232$	−4914.00	−1.39060
$233$	−6390.00	−1.79666	−0.898332	−	0.439317i	$-0.855221\pi$
$233$	−6390.00	−1.79666	−0.898332	+	0.439317i	$0.855221\pi$
$234$	2214.00	0.618520
$235$	1500.00	0.416380
$236$	−684.000	−0.188664
$237$	−2832.00	−0.776195
$238$	−1134.00	−0.308850
$239$	−336.000	−0.0909374	−0.0454687	−	0.998966i	$-0.514478\pi$
$239$	−336.000	−0.0909374	−0.0454687	+	0.998966i	$0.514478\pi$
$240$	−1065.00	−0.286439
$241$	−5242.00	−1.40111	−0.700554	−	0.713600i	$-0.747064\pi$
$241$	−5242.00	−1.40111	−0.700554	+	0.713600i	$0.747064\pi$
$242$	−363.000	−0.0964237
$243$	−243.000	−0.0641500
$244$	758.000	0.198877
$245$	−245.000	−0.0638877
$246$	2430.00	0.629801
$247$	−6560.00	−1.68989
$248$	−588.000	−0.150557
$249$	−4104.00	−1.04450
$250$	375.000	0.0948683
$251$	−5484.00	−1.37907	−0.689536	−	0.724252i	$-0.742185\pi$
$251$	−5484.00	−1.37907	−0.689536	+	0.724252i	$0.742185\pi$
$252$	63.0000	0.0157485
$253$	−528.000	−0.131206
$254$	−2472.00	−0.610658
$255$	810.000	0.198918
$256$	1513.00	0.369385
$257$	2154.00	0.522813	0.261406	−	0.965229i	$-0.415814\pi$
$257$	2154.00	0.522813	0.261406	+	0.965229i	$0.415814\pi$
$258$	−252.000	−0.0608094
$259$	−574.000	−0.137709
$260$	410.000	0.0977966
$261$	−2106.00	−0.499456
$262$	5688.00	1.34124
$263$	4104.00	0.962219	0.481109	−	0.876661i	$-0.340234\pi$
$263$	4104.00	0.962219	0.481109	+	0.876661i	$0.340234\pi$
$264$	693.000	0.161558
$265$	−2910.00	−0.674566
$266$	−1680.00	−0.387246
$267$	−126.000	−0.0288804
$268$	524.000	0.119434
$269$	−1158.00	−0.262470	−0.131235	−	0.991351i	$-0.541894\pi$
$269$	−1158.00	−0.262470	−0.131235	+	0.991351i	$0.541894\pi$
$270$	−405.000	−0.0912871
$271$	−1528.00	−0.342507	−0.171253	−	0.985227i	$-0.554782\pi$
$271$	−1528.00	−0.342507	−0.171253	+	0.985227i	$0.554782\pi$
$272$	−3834.00	−0.854671
$273$	1722.00	0.381759
$274$	−8622.00	−1.90100
$275$	−275.000	−0.0603023
$276$	−144.000	−0.0314050
$277$	494.000	0.107154	0.0535769	−	0.998564i	$-0.482938\pi$
$277$	494.000	0.107154	0.0535769	+	0.998564i	$0.482938\pi$
$278$	3072.00	0.662757
$279$	−252.000	−0.0540747
$280$	−735.000	−0.156874
$281$	−4206.00	−0.892914	−0.446457	−	0.894805i	$-0.647314\pi$
$281$	−4206.00	−0.892914	−0.446457	+	0.894805i	$0.647314\pi$
$282$	−2700.00	−0.570151
$283$	4760.00	0.999833	0.499916	−	0.866074i	$-0.333364\pi$
$283$	4760.00	0.999833	0.499916	+	0.866074i	$0.333364\pi$
$284$	552.000	0.115335
$285$	1200.00	0.249410
$286$	−2706.00	−0.559472
$287$	1890.00	0.388722
$288$	405.000	0.0828641
$289$	−1997.00	−0.406473
$290$	−3510.00	−0.710739
$291$	−4974.00	−1.00200
$292$	110.000	0.0220454
$293$	1398.00	0.278744	0.139372	−	0.990240i	$-0.455492\pi$
$293$	1398.00	0.278744	0.139372	+	0.990240i	$0.455492\pi$
$294$	441.000	0.0874818
$295$	3420.00	0.674983
$296$	−1722.00	−0.338139
$297$	297.000	0.0580259
$298$	10710.0	2.08192
$299$	−3936.00	−0.761287
$300$	−75.0000	−0.0144338
$301$	−196.000	−0.0375324
$302$	5664.00	1.07923
$303$	3582.00	0.679144
$304$	−5680.00	−1.07161
$305$	−3790.00	−0.711524
$306$	−1458.00	−0.272380
$307$	−3040.00	−0.565153	−0.282576	−	0.959245i	$-0.591189\pi$
$307$	−3040.00	−0.565153	−0.282576	+	0.959245i	$0.591189\pi$
$308$	−77.0000	−0.0142451
$309$	1452.00	0.267318
$310$	−420.000	−0.0769497
$311$	−8388.00	−1.52939	−0.764694	−	0.644393i	$-0.777110\pi$
$311$	−8388.00	−1.52939	−0.764694	+	0.644393i	$0.777110\pi$
$312$	5166.00	0.937395
$313$	6458.00	1.16622	0.583111	−	0.812392i	$-0.301835\pi$
$313$	6458.00	1.16622	0.583111	+	0.812392i	$0.301835\pi$
$314$	−3606.00	−0.648084
$315$	−315.000	−0.0563436
$316$	944.000	0.168051
$317$	−6834.00	−1.21084	−0.605419	−	0.795907i	$-0.706994\pi$
$317$	−6834.00	−1.21084	−0.605419	+	0.795907i	$0.706994\pi$
$318$	5238.00	0.923687
$319$	2574.00	0.451775
$320$	−2165.00	−0.378210
$321$	5652.00	0.982754
$322$	−1008.00	−0.174452
$323$	4320.00	0.744183
$324$	81.0000	0.0138889
$325$	−2050.00	−0.349888
$326$	9156.00	1.55553
$327$	1182.00	0.199892
$328$	5670.00	0.954492
$329$	−2100.00	−0.351905
$330$	495.000	0.0825723
$331$	9260.00	1.53769	0.768845	−	0.639435i	$-0.220832\pi$
$331$	9260.00	1.53769	0.768845	+	0.639435i	$0.220832\pi$
$332$	1368.00	0.226141
$333$	−738.000	−0.121448
$334$	−4176.00	−0.684133
$335$	−2620.00	−0.427301
$336$	1491.00	0.242085
$337$	5330.00	0.861554	0.430777	−	0.902458i	$-0.358240\pi$
$337$	5330.00	0.861554	0.430777	+	0.902458i	$0.358240\pi$
$338$	−13581.0	−2.18553
$339$	4266.00	0.683473
$340$	−270.000	−0.0430671
$341$	308.000	0.0489124
$342$	−2160.00	−0.341519
$343$	343.000	0.0539949
$344$	−588.000	−0.0921594
$345$	720.000	0.112358
$346$	3366.00	0.522998
$347$	4308.00	0.666471	0.333236	−	0.942844i	$-0.391860\pi$
$347$	4308.00	0.666471	0.333236	+	0.942844i	$0.391860\pi$
$348$	702.000	0.108135
$349$	−4690.00	−0.719341	−0.359670	−	0.933079i	$-0.617111\pi$
$349$	−4690.00	−0.719341	−0.359670	+	0.933079i	$0.617111\pi$
$350$	−525.000	−0.0801784
$351$	2214.00	0.336680
$352$	−495.000	−0.0749534
$353$	−9414.00	−1.41942	−0.709712	−	0.704492i	$-0.751175\pi$
$353$	−9414.00	−1.41942	−0.709712	+	0.704492i	$0.751175\pi$
$354$	−6156.00	−0.924259
$355$	−2760.00	−0.412635
$356$	42.0000	0.00625280
$357$	−1134.00	−0.168117
$358$	252.000	0.0372028
$359$	2880.00	0.423400	0.211700	−	0.977335i	$-0.432100\pi$
$359$	2880.00	0.423400	0.211700	+	0.977335i	$0.432100\pi$
$360$	−945.000	−0.138350
$361$	−459.000	−0.0669194
$362$	−9366.00	−1.35985
$363$	−363.000	−0.0524864
$364$	−574.000	−0.0826532
$365$	−550.000	−0.0788721
$366$	6822.00	0.974294
$367$	2972.00	0.422717	0.211358	−	0.977409i	$-0.432211\pi$
$367$	2972.00	0.422717	0.211358	+	0.977409i	$0.432211\pi$
$368$	−3408.00	−0.482756
$369$	2430.00	0.342820
$370$	−1230.00	−0.172823
$371$	4074.00	0.570112
$372$	84.0000	0.0117075
$373$	2414.00	0.335100	0.167550	−	0.985864i	$-0.446414\pi$
$373$	2414.00	0.335100	0.167550	+	0.985864i	$0.446414\pi$
$374$	1782.00	0.246377
$375$	375.000	0.0516398
$376$	−6300.00	−0.864090
$377$	19188.0	2.62131
$378$	567.000	0.0771517
$379$	13172.0	1.78522	0.892612	−	0.450825i	$-0.148870\pi$
$379$	13172.0	1.78522	0.892612	+	0.450825i	$0.148870\pi$
$380$	−400.000	−0.0539989
$381$	−2472.00	−0.332400
$382$	11160.0	1.49475
$383$	2172.00	0.289775	0.144888	−	0.989448i	$-0.453718\pi$
$383$	2172.00	0.289775	0.144888	+	0.989448i	$0.453718\pi$
$384$	4977.00	0.661410
$385$	385.000	0.0509647
$386$	11010.0	1.45180
$387$	−252.000	−0.0331005
$388$	1658.00	0.216939
$389$	−12666.0	−1.65088	−0.825439	−	0.564491i	$-0.809072\pi$
$389$	−12666.0	−1.65088	−0.825439	+	0.564491i	$0.809072\pi$
$390$	3690.00	0.479104
$391$	2592.00	0.335251
$392$	1029.00	0.132583
$393$	5688.00	0.730081
$394$	−9882.00	−1.26357
$395$	−4720.00	−0.601238
$396$	−99.0000	−0.0125630
$397$	−6334.00	−0.800741	−0.400371	−	0.916353i	$-0.631119\pi$
$397$	−6334.00	−0.800741	−0.400371	+	0.916353i	$0.631119\pi$
$398$	3396.00	0.427704
$399$	−1680.00	−0.210790
$400$	−1775.00	−0.221875
$401$	−14910.0	−1.85678	−0.928391	−	0.371604i	$-0.878808\pi$
$401$	−14910.0	−1.85678	−0.928391	+	0.371604i	$0.878808\pi$
$402$	4716.00	0.585106
$403$	2296.00	0.283801
$404$	−1194.00	−0.147039
$405$	−405.000	−0.0496904
$406$	4914.00	0.600684
$407$	902.000	0.109854
$408$	−3402.00	−0.412804
$409$	10550.0	1.27546	0.637731	−	0.770259i	$-0.279873\pi$
$409$	10550.0	1.27546	0.637731	+	0.770259i	$0.279873\pi$
$410$	4050.00	0.487842
$411$	−8622.00	−1.03477
$412$	−484.000	−0.0578761
$413$	−4788.00	−0.570465
$414$	−1296.00	−0.153852
$415$	−6840.00	−0.809066
$416$	−3690.00	−0.434897
$417$	3072.00	0.360759
$418$	2640.00	0.308915
$419$	3540.00	0.412745	0.206373	−	0.978473i	$-0.433834\pi$
$419$	3540.00	0.412745	0.206373	+	0.978473i	$0.433834\pi$
$420$	105.000	0.0121988
$421$	−14146.0	−1.63761	−0.818805	−	0.574072i	$-0.805363\pi$
$421$	−14146.0	−1.63761	−0.818805	+	0.574072i	$0.805363\pi$
$422$	4044.00	0.466490
$423$	−2700.00	−0.310351
$424$	12222.0	1.39989
$425$	1350.00	0.154081
$426$	4968.00	0.565024
$427$	5306.00	0.601347
$428$	−1884.00	−0.212772
$429$	−2706.00	−0.304538
$430$	−420.000	−0.0471028
$431$	−12024.0	−1.34380	−0.671898	−	0.740644i	$-0.734520\pi$
$431$	−12024.0	−1.34380	−0.671898	+	0.740644i	$0.734520\pi$
$432$	1917.00	0.213499
$433$	698.000	0.0774682	0.0387341	−	0.999250i	$-0.487667\pi$
$433$	698.000	0.0774682	0.0387341	+	0.999250i	$0.487667\pi$
$434$	588.000	0.0650343
$435$	−3510.00	−0.386877
$436$	−394.000	−0.0432779
$437$	3840.00	0.420348
$438$	990.000	0.108000
$439$	−2896.00	−0.314849	−0.157424	−	0.987531i	$-0.550319\pi$
$439$	−2896.00	−0.314849	−0.157424	+	0.987531i	$0.550319\pi$
$440$	1155.00	0.125142
$441$	441.000	0.0476190
$442$	13284.0	1.42954
$443$	−3588.00	−0.384810	−0.192405	−	0.981316i	$-0.561629\pi$
$443$	−3588.00	−0.384810	−0.192405	+	0.981316i	$0.561629\pi$
$444$	246.000	0.0262942
$445$	−210.000	−0.0223707
$446$	8076.00	0.857421
$447$	10710.0	1.13326
$448$	3031.00	0.319646
$449$	4626.00	0.486224	0.243112	−	0.969998i	$-0.421832\pi$
$449$	4626.00	0.486224	0.243112	+	0.969998i	$0.421832\pi$
$450$	−675.000	−0.0707107
$451$	−2970.00	−0.310093
$452$	−1422.00	−0.147976
$453$	5664.00	0.587457
$454$	−5040.00	−0.521011
$455$	2870.00	0.295709
$456$	−5040.00	−0.517587
$457$	17426.0	1.78371	0.891853	−	0.452325i	$-0.149405\pi$
$457$	17426.0	1.78371	0.891853	+	0.452325i	$0.149405\pi$
$458$	−5766.00	−0.588270
$459$	−1458.00	−0.148265
$460$	−240.000	−0.0243262
$461$	3390.00	0.342490	0.171245	−	0.985228i	$-0.445221\pi$
$461$	3390.00	0.342490	0.171245	+	0.985228i	$0.445221\pi$
$462$	−693.000	−0.0697863
$463$	−6208.00	−0.623132	−0.311566	−	0.950224i	$-0.600854\pi$
$463$	−6208.00	−0.623132	−0.311566	+	0.950224i	$0.600854\pi$
$464$	16614.0	1.66225
$465$	−420.000	−0.0418861
$466$	19170.0	1.90565
$467$	2676.00	0.265162	0.132581	−	0.991172i	$-0.457674\pi$
$467$	2676.00	0.265162	0.132581	+	0.991172i	$0.457674\pi$
$468$	−738.000	−0.0728933
$469$	3668.00	0.361135
$470$	−4500.00	−0.441637
$471$	−3606.00	−0.352772
$472$	−14364.0	−1.40076
$473$	308.000	0.0299405
$474$	8496.00	0.823279
$475$	2000.00	0.193192
$476$	378.000	0.0363983
$477$	5238.00	0.502791
$478$	1008.00	0.0964537
$479$	−12480.0	−1.19045	−0.595225	−	0.803559i	$-0.702937\pi$
$479$	−12480.0	−1.19045	−0.595225	+	0.803559i	$0.702937\pi$
$480$	675.000	0.0641862
$481$	6724.00	0.637397
$482$	15726.0	1.48610
$483$	−1008.00	−0.0949598
$484$	121.000	0.0113636
$485$	−8290.00	−0.776143
$486$	729.000	0.0680414
$487$	14048.0	1.30714	0.653568	−	0.756867i	$-0.273271\pi$
$487$	14048.0	1.30714	0.653568	+	0.756867i	$0.273271\pi$
$488$	15918.0	1.47659
$489$	9156.00	0.846725
$490$	735.000	0.0677631
$491$	−10692.0	−0.982736	−0.491368	−	0.870952i	$-0.663503\pi$
$491$	−10692.0	−0.982736	−0.491368	+	0.870952i	$0.663503\pi$
$492$	−810.000	−0.0742228
$493$	−12636.0	−1.15435
$494$	19680.0	1.79240
$495$	495.000	0.0449467
$496$	1988.00	0.179967
$497$	3864.00	0.348741
$498$	12312.0	1.10786
$499$	−21724.0	−1.94890	−0.974449	−	0.224610i	$-0.927889\pi$
$499$	−21724.0	−1.94890	−0.974449	+	0.224610i	$0.927889\pi$
$500$	−125.000	−0.0111803
$501$	−4176.00	−0.372395
$502$	16452.0	1.46273
$503$	16272.0	1.44241	0.721205	−	0.692721i	$-0.243588\pi$
$503$	16272.0	1.44241	0.721205	+	0.692721i	$0.243588\pi$
$504$	1323.00	0.116927
$505$	5970.00	0.526062
$506$	1584.00	0.139165
$507$	−13581.0	−1.18965
$508$	824.000	0.0719667
$509$	−20646.0	−1.79787	−0.898937	−	0.438078i	$-0.855659\pi$
$509$	−20646.0	−1.79787	−0.898937	+	0.438078i	$0.855659\pi$
$510$	−2430.00	−0.210985
$511$	770.000	0.0666591
$512$	8733.00	0.753804
$513$	−2160.00	−0.185899
$514$	−6462.00	−0.554526
$515$	2420.00	0.207064
$516$	84.0000	0.00716646
$517$	3300.00	0.280723
$518$	1722.00	0.146062
$519$	3366.00	0.284684
$520$	8610.00	0.726103
$521$	17082.0	1.43642	0.718211	−	0.695825i	$-0.244961\pi$
$521$	17082.0	1.43642	0.718211	+	0.695825i	$0.244961\pi$
$522$	6318.00	0.529754
$523$	13736.0	1.14844	0.574219	−	0.818702i	$-0.305306\pi$
$523$	13736.0	1.14844	0.574219	+	0.818702i	$0.305306\pi$
$524$	−1896.00	−0.158067
$525$	−525.000	−0.0436436
$526$	−12312.0	−1.02059
$527$	−1512.00	−0.124979
$528$	−2343.00	−0.193117
$529$	−9863.00	−0.810635
$530$	8730.00	0.715485
$531$	−6156.00	−0.503103
$532$	560.000	0.0456374
$533$	−22140.0	−1.79923
$534$	378.000	0.0306323
$535$	9420.00	0.761238
$536$	11004.0	0.886754
$537$	252.000	0.0202507
$538$	3474.00	0.278392
$539$	−539.000	−0.0430730
$540$	135.000	0.0107583
$541$	7622.00	0.605722	0.302861	−	0.953035i	$-0.402058\pi$
$541$	7622.00	0.605722	0.302861	+	0.953035i	$0.402058\pi$
$542$	4584.00	0.363284
$543$	−9366.00	−0.740209
$544$	2430.00	0.191517
$545$	1970.00	0.154836
$546$	−5166.00	−0.404916
$547$	−15532.0	−1.21408	−0.607039	−	0.794672i	$-0.707643\pi$
$547$	−15532.0	−1.21408	−0.607039	+	0.794672i	$0.707643\pi$
$548$	2874.00	0.224035
$549$	6822.00	0.530339
$550$	825.000	0.0639602
$551$	−18720.0	−1.44737
$552$	−3024.00	−0.233170
$553$	6608.00	0.508139
$554$	−1482.00	−0.113654
$555$	−1230.00	−0.0940731
$556$	−1024.00	−0.0781066
$557$	−15498.0	−1.17894	−0.589472	−	0.807789i	$-0.700664\pi$
$557$	−15498.0	−1.17894	−0.589472	+	0.807789i	$0.700664\pi$
$558$	756.000	0.0573549
$559$	2296.00	0.173722
$560$	2485.00	0.187519
$561$	1782.00	0.134111
$562$	12618.0	0.947079
$563$	−11424.0	−0.855176	−0.427588	−	0.903974i	$-0.640637\pi$
$563$	−11424.0	−0.855176	−0.427588	+	0.903974i	$0.640637\pi$
$564$	900.000	0.0671930
$565$	7110.00	0.529416
$566$	−14280.0	−1.06048
$567$	567.000	0.0419961
$568$	11592.0	0.856320
$569$	1026.00	0.0755925	0.0377963	−	0.999285i	$-0.487966\pi$
$569$	1026.00	0.0755925	0.0377963	+	0.999285i	$0.487966\pi$
$570$	−3600.00	−0.264539
$571$	−7828.00	−0.573716	−0.286858	−	0.957973i	$-0.592611\pi$
$571$	−7828.00	−0.573716	−0.286858	+	0.957973i	$0.592611\pi$
$572$	902.000	0.0659345
$573$	11160.0	0.813640
$574$	−5670.00	−0.412302
$575$	1200.00	0.0870321
$576$	3897.00	0.281901
$577$	−7630.00	−0.550504	−0.275252	−	0.961372i	$-0.588761\pi$
$577$	−7630.00	−0.550504	−0.275252	+	0.961372i	$0.588761\pi$
$578$	5991.00	0.431129
$579$	11010.0	0.790259
$580$	1170.00	0.0837614
$581$	9576.00	0.683786
$582$	14922.0	1.06278
$583$	−6402.00	−0.454792
$584$	2310.00	0.163679
$585$	3690.00	0.260791
$586$	−4194.00	−0.295653
$587$	10500.0	0.738299	0.369149	−	0.929370i	$-0.379649\pi$
$587$	10500.0	0.738299	0.369149	+	0.929370i	$0.379649\pi$
$588$	−147.000	−0.0103098
$589$	−2240.00	−0.156702
$590$	−10260.0	−0.715928
$591$	−9882.00	−0.687802
$592$	5822.00	0.404194
$593$	−13482.0	−0.933625	−0.466812	−	0.884356i	$-0.654598\pi$
$593$	−13482.0	−0.933625	−0.466812	+	0.884356i	$0.654598\pi$
$594$	−891.000	−0.0615457
$595$	−1890.00	−0.130223
$596$	−3570.00	−0.245357
$597$	3396.00	0.232812
$598$	11808.0	0.807467
$599$	22872.0	1.56014	0.780071	−	0.625691i	$-0.215183\pi$
$599$	22872.0	1.56014	0.780071	+	0.625691i	$0.215183\pi$
$600$	−1575.00	−0.107165
$601$	−17194.0	−1.16698	−0.583492	−	0.812119i	$-0.698314\pi$
$601$	−17194.0	−1.16698	−0.583492	+	0.812119i	$0.698314\pi$
$602$	588.000	0.0398091
$603$	4716.00	0.318491
$604$	−1888.00	−0.127188
$605$	−605.000	−0.0406558
$606$	−10746.0	−0.720341
$607$	15680.0	1.04849	0.524243	−	0.851568i	$-0.324348\pi$
$607$	15680.0	1.04849	0.524243	+	0.851568i	$0.324348\pi$
$608$	3600.00	0.240130
$609$	4914.00	0.326971
$610$	11370.0	0.754685
$611$	24600.0	1.62882
$612$	486.000	0.0321003
$613$	−21922.0	−1.44441	−0.722203	−	0.691681i	$-0.756870\pi$
$613$	−21922.0	−1.44441	−0.722203	+	0.691681i	$0.756870\pi$
$614$	9120.00	0.599435
$615$	4050.00	0.265548
$616$	−1617.00	−0.105764
$617$	14634.0	0.954850	0.477425	−	0.878672i	$-0.341570\pi$
$617$	14634.0	0.954850	0.477425	+	0.878672i	$0.341570\pi$
$618$	−4356.00	−0.283534
$619$	11468.0	0.744649	0.372325	−	0.928103i	$-0.378561\pi$
$619$	11468.0	0.744649	0.372325	+	0.928103i	$0.378561\pi$
$620$	140.000	0.00906861
$621$	−1296.00	−0.0837467
$622$	25164.0	1.62216
$623$	294.000	0.0189067
$624$	−17466.0	−1.12051
$625$	625.000	0.0400000
$626$	−19374.0	−1.23697
$627$	2640.00	0.168152
$628$	1202.00	0.0763774
$629$	−4428.00	−0.280693
$630$	945.000	0.0597614
$631$	−6160.00	−0.388630	−0.194315	−	0.980939i	$-0.562248\pi$
$631$	−6160.00	−0.388630	−0.194315	+	0.980939i	$0.562248\pi$
$632$	19824.0	1.24772
$633$	4044.00	0.253925
$634$	20502.0	1.28429
$635$	−4120.00	−0.257476
$636$	−1746.00	−0.108858
$637$	−4018.00	−0.249920
$638$	−7722.00	−0.479180
$639$	4968.00	0.307560
$640$	8295.00	0.512326
$641$	25170.0	1.55094	0.775472	−	0.631382i	$-0.217512\pi$
$641$	25170.0	1.55094	0.775472	+	0.631382i	$0.217512\pi$
$642$	−16956.0	−1.04237
$643$	−11860.0	−0.727392	−0.363696	−	0.931518i	$-0.618485\pi$
$643$	−11860.0	−0.727392	−0.363696	+	0.931518i	$0.618485\pi$
$644$	336.000	0.0205594
$645$	−420.000	−0.0256395
$646$	−12960.0	−0.789326
$647$	−7356.00	−0.446977	−0.223489	−	0.974707i	$-0.571745\pi$
$647$	−7356.00	−0.446977	−0.223489	+	0.974707i	$0.571745\pi$
$648$	1701.00	0.103120
$649$	7524.00	0.455074
$650$	6150.00	0.371112
$651$	588.000	0.0354002
$652$	−3052.00	−0.183321
$653$	−24858.0	−1.48969	−0.744846	−	0.667237i	$-0.767477\pi$
$653$	−24858.0	−1.48969	−0.744846	+	0.667237i	$0.767477\pi$
$654$	−3546.00	−0.212018
$655$	9480.00	0.565518
$656$	−19170.0	−1.14095
$657$	990.000	0.0587878
$658$	6300.00	0.373252
$659$	5676.00	0.335517	0.167758	−	0.985828i	$-0.446347\pi$
$659$	5676.00	0.335517	0.167758	+	0.985828i	$0.446347\pi$
$660$	−165.000	−0.00973124
$661$	−10942.0	−0.643865	−0.321932	−	0.946763i	$-0.604332\pi$
$661$	−10942.0	−0.643865	−0.321932	+	0.946763i	$0.604332\pi$
$662$	−27780.0	−1.63097
$663$	13284.0	0.778141
$664$	28728.0	1.67901
$665$	−2800.00	−0.163277
$666$	2214.00	0.128815
$667$	−11232.0	−0.652031
$668$	1392.00	0.0806259
$669$	8076.00	0.466721
$670$	7860.00	0.453221
$671$	−8338.00	−0.479709
$672$	−945.000	−0.0542473
$673$	−7678.00	−0.439770	−0.219885	−	0.975526i	$-0.570568\pi$
$673$	−7678.00	−0.439770	−0.219885	+	0.975526i	$0.570568\pi$
$674$	−15990.0	−0.913816
$675$	−675.000	−0.0384900
$676$	4527.00	0.257567
$677$	−28698.0	−1.62918	−0.814589	−	0.580038i	$-0.803038\pi$
$677$	−28698.0	−1.62918	−0.814589	+	0.580038i	$0.803038\pi$
$678$	−12798.0	−0.724932
$679$	11606.0	0.655961
$680$	−5670.00	−0.319757
$681$	−5040.00	−0.283602
$682$	−924.000	−0.0518795
$683$	−16452.0	−0.921696	−0.460848	−	0.887479i	$-0.652455\pi$
$683$	−16452.0	−0.921696	−0.460848	+	0.887479i	$0.652455\pi$
$684$	720.000	0.0402484
$685$	−14370.0	−0.801532
$686$	−1029.00	−0.0572703
$687$	−5766.00	−0.320213
$688$	1988.00	0.110162
$689$	−47724.0	−2.63881
$690$	−2160.00	−0.119174
$691$	5756.00	0.316886	0.158443	−	0.987368i	$-0.449353\pi$
$691$	5756.00	0.316886	0.158443	+	0.987368i	$0.449353\pi$
$692$	−1122.00	−0.0616359
$693$	−693.000	−0.0379869
$694$	−12924.0	−0.706900
$695$	5120.00	0.279443
$696$	14742.0	0.802865
$697$	14580.0	0.792334
$698$	14070.0	0.762976
$699$	19170.0	1.03730
$700$	175.000	0.00944911
$701$	−9402.00	−0.506574	−0.253287	−	0.967391i	$-0.581512\pi$
$701$	−9402.00	−0.506574	−0.253287	+	0.967391i	$0.581512\pi$
$702$	−6642.00	−0.357103
$703$	−6560.00	−0.351942
$704$	−4763.00	−0.254989
$705$	−4500.00	−0.240397
$706$	28242.0	1.50553
$707$	−8358.00	−0.444604
$708$	2052.00	0.108925
$709$	2534.00	0.134226	0.0671131	−	0.997745i	$-0.478621\pi$
$709$	2534.00	0.134226	0.0671131	+	0.997745i	$0.478621\pi$
$710$	8280.00	0.437666
$711$	8496.00	0.448136
$712$	882.000	0.0464246
$713$	−1344.00	−0.0705935
$714$	3402.00	0.178315
$715$	−4510.00	−0.235894
$716$	−84.0000	−0.00438440
$717$	1008.00	0.0525027
$718$	−8640.00	−0.449083
$719$	6036.00	0.313080	0.156540	−	0.987672i	$-0.449966\pi$
$719$	6036.00	0.313080	0.156540	+	0.987672i	$0.449966\pi$
$720$	3195.00	0.165376
$721$	−3388.00	−0.175001
$722$	1377.00	0.0709787
$723$	15726.0	0.808930
$724$	3122.00	0.160260
$725$	−5850.00	−0.299674
$726$	1089.00	0.0556702
$727$	−18268.0	−0.931943	−0.465972	−	0.884800i	$-0.654295\pi$
$727$	−18268.0	−0.931943	−0.465972	+	0.884800i	$0.654295\pi$
$728$	−12054.0	−0.613669
$729$	729.000	0.0370370
$730$	1650.00	0.0836565
$731$	−1512.00	−0.0765025
$732$	−2274.00	−0.114822
$733$	−610.000	−0.0307379	−0.0153689	−	0.999882i	$-0.504892\pi$
$733$	−610.000	−0.0307379	−0.0153689	+	0.999882i	$0.504892\pi$
$734$	−8916.00	−0.448359
$735$	735.000	0.0368856
$736$	2160.00	0.108178
$737$	−5764.00	−0.288086
$738$	−7290.00	−0.363616
$739$	8756.00	0.435852	0.217926	−	0.975965i	$-0.430071\pi$
$739$	8756.00	0.435852	0.217926	+	0.975965i	$0.430071\pi$
$740$	410.000	0.0203674
$741$	19680.0	0.975658
$742$	−12222.0	−0.604695
$743$	−26112.0	−1.28931	−0.644654	−	0.764474i	$-0.722999\pi$
$743$	−26112.0	−1.28931	−0.644654	+	0.764474i	$0.722999\pi$
$744$	1764.00	0.0869239
$745$	17850.0	0.877817
$746$	−7242.00	−0.355427
$747$	12312.0	0.603042
$748$	−594.000	−0.0290358
$749$	−13188.0	−0.643363
$750$	−1125.00	−0.0547723
$751$	−22648.0	−1.10045	−0.550225	−	0.835017i	$-0.685458\pi$
$751$	−22648.0	−1.10045	−0.550225	+	0.835017i	$0.685458\pi$
$752$	21300.0	1.03289
$753$	16452.0	0.796207
$754$	−57564.0	−2.78031
$755$	9440.00	0.455042
$756$	−189.000	−0.00909241
$757$	−24802.0	−1.19081	−0.595406	−	0.803425i	$-0.703009\pi$
$757$	−24802.0	−1.19081	−0.595406	+	0.803425i	$0.703009\pi$
$758$	−39516.0	−1.89352
$759$	1584.00	0.0757517
$760$	−8400.00	−0.400921
$761$	8118.00	0.386698	0.193349	−	0.981130i	$-0.438065\pi$
$761$	8118.00	0.386698	0.193349	+	0.981130i	$0.438065\pi$
$762$	7416.00	0.352563
$763$	−2758.00	−0.130860
$764$	−3720.00	−0.176158
$765$	−2430.00	−0.114846
$766$	−6516.00	−0.307353
$767$	56088.0	2.64044
$768$	−4539.00	−0.213264
$769$	5918.00	0.277514	0.138757	−	0.990326i	$-0.455689\pi$
$769$	5918.00	0.277514	0.138757	+	0.990326i	$0.455689\pi$
$770$	−1155.00	−0.0540562
$771$	−6462.00	−0.301846
$772$	−3670.00	−0.171096
$773$	27930.0	1.29958	0.649788	−	0.760115i	$-0.274858\pi$
$773$	27930.0	1.29958	0.649788	+	0.760115i	$0.274858\pi$
$774$	756.000	0.0351083
$775$	−700.000	−0.0324448
$776$	34818.0	1.61069
$777$	1722.00	0.0795063
$778$	37998.0	1.75102
$779$	21600.0	0.993454
$780$	−1230.00	−0.0564629
$781$	−6072.00	−0.278199
$782$	−7776.00	−0.355587
$783$	6318.00	0.288361
$784$	−3479.00	−0.158482
$785$	−6010.00	−0.273256
$786$	−17064.0	−0.774367
$787$	30872.0	1.39831	0.699154	−	0.714971i	$-0.253560\pi$
$787$	30872.0	1.39831	0.699154	+	0.714971i	$0.253560\pi$
$788$	3294.00	0.148914
$789$	−12312.0	−0.555537
$790$	14160.0	0.637709
$791$	−9954.00	−0.447438
$792$	−2079.00	−0.0932753
$793$	−62156.0	−2.78338
$794$	19002.0	0.849315
$795$	8730.00	0.389461
$796$	−1132.00	−0.0504054
$797$	4386.00	0.194931	0.0974656	−	0.995239i	$-0.468926\pi$
$797$	4386.00	0.194931	0.0974656	+	0.995239i	$0.468926\pi$
$798$	5040.00	0.223577
$799$	−16200.0	−0.717290
$800$	1125.00	0.0497184
$801$	378.000	0.0166741
$802$	44730.0	1.96942
$803$	−1210.00	−0.0531756
$804$	−1572.00	−0.0689554
$805$	−1680.00	−0.0735556
$806$	−6888.00	−0.301017
$807$	3474.00	0.151537
$808$	−25074.0	−1.09171
$809$	20346.0	0.884212	0.442106	−	0.896963i	$-0.354232\pi$
$809$	20346.0	0.884212	0.442106	+	0.896963i	$0.354232\pi$
$810$	1215.00	0.0527046
$811$	4016.00	0.173885	0.0869426	−	0.996213i	$-0.472290\pi$
$811$	4016.00	0.173885	0.0869426	+	0.996213i	$0.472290\pi$
$812$	−1638.00	−0.0707913
$813$	4584.00	0.197746
$814$	−2706.00	−0.116518
$815$	15260.0	0.655871
$816$	11502.0	0.493444
$817$	−2240.00	−0.0959213
$818$	−31650.0	−1.35283
$819$	−5166.00	−0.220409
$820$	−1350.00	−0.0574927
$821$	8910.00	0.378759	0.189380	−	0.981904i	$-0.439352\pi$
$821$	8910.00	0.378759	0.189380	+	0.981904i	$0.439352\pi$
$822$	25866.0	1.09754
$823$	−41488.0	−1.75721	−0.878603	−	0.477553i	$-0.841524\pi$
$823$	−41488.0	−1.75721	−0.878603	+	0.477553i	$0.841524\pi$
$824$	−10164.0	−0.429708
$825$	825.000	0.0348155
$826$	14364.0	0.605070
$827$	19116.0	0.803783	0.401891	−	0.915687i	$-0.368353\pi$
$827$	19116.0	0.803783	0.401891	+	0.915687i	$0.368353\pi$
$828$	432.000	0.0181317
$829$	−23494.0	−0.984295	−0.492147	−	0.870512i	$-0.663788\pi$
$829$	−23494.0	−0.984295	−0.492147	+	0.870512i	$0.663788\pi$
$830$	20520.0	0.858144
$831$	−1482.00	−0.0618652
$832$	−35506.0	−1.47951
$833$	2646.00	0.110058
$834$	−9216.00	−0.382643
$835$	−6960.00	−0.288456
$836$	−880.000	−0.0364060
$837$	756.000	0.0312201
$838$	−10620.0	−0.437783
$839$	−7188.00	−0.295777	−0.147889	−	0.989004i	$-0.547248\pi$
$839$	−7188.00	−0.295777	−0.147889	+	0.989004i	$0.547248\pi$
$840$	2205.00	0.0905711
$841$	30367.0	1.24511
$842$	42438.0	1.73695
$843$	12618.0	0.515524
$844$	−1348.00	−0.0549764
$845$	−22635.0	−0.921500
$846$	8100.00	0.329177
$847$	847.000	0.0343604
$848$	−41322.0	−1.67335
$849$	−14280.0	−0.577254
$850$	−4050.00	−0.163428
$851$	−3936.00	−0.158548
$852$	−1656.00	−0.0665888
$853$	23942.0	0.961030	0.480515	−	0.876987i	$-0.340450\pi$
$853$	23942.0	0.961030	0.480515	+	0.876987i	$0.340450\pi$
$854$	−15918.0	−0.637825
$855$	−3600.00	−0.143997
$856$	−39564.0	−1.57975
$857$	−21258.0	−0.847327	−0.423664	−	0.905820i	$-0.639256\pi$
$857$	−21258.0	−0.847327	−0.423664	+	0.905820i	$0.639256\pi$
$858$	8118.00	0.323012
$859$	−33292.0	−1.32236	−0.661181	−	0.750227i	$-0.729944\pi$
$859$	−33292.0	−1.32236	−0.661181	+	0.750227i	$0.729944\pi$
$860$	140.000	0.00555112
$861$	−5670.00	−0.224429
$862$	36072.0	1.42531
$863$	22344.0	0.881343	0.440671	−	0.897669i	$-0.354740\pi$
$863$	22344.0	0.881343	0.440671	+	0.897669i	$0.354740\pi$
$864$	−1215.00	−0.0478416
$865$	5610.00	0.220515
$866$	−2094.00	−0.0821675
$867$	5991.00	0.234677
$868$	−196.000	−0.00766437
$869$	−10384.0	−0.405355
$870$	10530.0	0.410345
$871$	−42968.0	−1.67154
$872$	−8274.00	−0.321322
$873$	14922.0	0.578503
$874$	−11520.0	−0.445846
$875$	−875.000	−0.0338062
$876$	−330.000	−0.0127279
$877$	−7402.00	−0.285003	−0.142502	−	0.989795i	$-0.545515\pi$
$877$	−7402.00	−0.285003	−0.142502	+	0.989795i	$0.545515\pi$
$878$	8688.00	0.333947
$879$	−4194.00	−0.160933
$880$	−3905.00	−0.149588
$881$	−7062.00	−0.270062	−0.135031	−	0.990841i	$-0.543113\pi$
$881$	−7062.00	−0.270062	−0.135031	+	0.990841i	$0.543113\pi$
$882$	−1323.00	−0.0505076
$883$	−24604.0	−0.937702	−0.468851	−	0.883277i	$-0.655332\pi$
$883$	−24604.0	−0.937702	−0.468851	+	0.883277i	$0.655332\pi$
$884$	−4428.00	−0.168473
$885$	−10260.0	−0.389702
$886$	10764.0	0.408153
$887$	13464.0	0.509670	0.254835	−	0.966985i	$-0.417979\pi$
$887$	13464.0	0.509670	0.254835	+	0.966985i	$0.417979\pi$
$888$	5166.00	0.195225
$889$	5768.00	0.217607
$890$	630.000	0.0237277
$891$	−891.000	−0.0335013
$892$	−2692.00	−0.101048
$893$	−24000.0	−0.899361
$894$	−32130.0	−1.20200
$895$	420.000	0.0156861
$896$	−11613.0	−0.432995
$897$	11808.0	0.439529
$898$	−13878.0	−0.515718
$899$	6552.00	0.243072
$900$	225.000	0.00833333
$901$	31428.0	1.16206
$902$	8910.00	0.328903
$903$	588.000	0.0216693
$904$	−29862.0	−1.09867
$905$	−15610.0	−0.573363
$906$	−16992.0	−0.623092
$907$	−2092.00	−0.0765862	−0.0382931	−	0.999267i	$-0.512192\pi$
$907$	−2092.00	−0.0765862	−0.0382931	+	0.999267i	$0.512192\pi$
$908$	1680.00	0.0614017
$909$	−10746.0	−0.392104
$910$	−8610.00	−0.313647
$911$	30888.0	1.12334	0.561671	−	0.827360i	$-0.310159\pi$
$911$	30888.0	1.12334	0.561671	+	0.827360i	$0.310159\pi$
$912$	17040.0	0.618696
$913$	−15048.0	−0.545472
$914$	−52278.0	−1.89191
$915$	11370.0	0.410798
$916$	1922.00	0.0693282
$917$	−13272.0	−0.477950
$918$	4374.00	0.157259
$919$	−28960.0	−1.03950	−0.519751	−	0.854318i	$-0.673975\pi$
$919$	−28960.0	−1.03950	−0.519751	+	0.854318i	$0.673975\pi$
$920$	−5040.00	−0.180613
$921$	9120.00	0.326291
$922$	−10170.0	−0.363266
$923$	−45264.0	−1.61417
$924$	231.000	0.00822440
$925$	−2050.00	−0.0728687
$926$	18624.0	0.660932
$927$	−4356.00	−0.154336
$928$	−10530.0	−0.372483
$929$	34914.0	1.23304	0.616518	−	0.787341i	$-0.288543\pi$
$929$	34914.0	1.23304	0.616518	+	0.787341i	$0.288543\pi$
$930$	1260.00	0.0444269
$931$	3920.00	0.137994
$932$	−6390.00	−0.224583
$933$	25164.0	0.882993
$934$	−8028.00	−0.281246
$935$	2970.00	0.103882
$936$	−15498.0	−0.541205
$937$	37694.0	1.31420	0.657102	−	0.753802i	$-0.271782\pi$
$937$	37694.0	1.31420	0.657102	+	0.753802i	$0.271782\pi$
$938$	−11004.0	−0.383042
$939$	−19374.0	−0.673319
$940$	1500.00	0.0520475
$941$	12294.0	0.425901	0.212951	−	0.977063i	$-0.431693\pi$
$941$	12294.0	0.425901	0.212951	+	0.977063i	$0.431693\pi$
$942$	10818.0	0.374171
$943$	12960.0	0.447546
$944$	48564.0	1.67439
$945$	945.000	0.0325300
$946$	−924.000	−0.0317567
$947$	−30900.0	−1.06031	−0.530156	−	0.847900i	$-0.677867\pi$
$947$	−30900.0	−1.06031	−0.530156	+	0.847900i	$0.677867\pi$
$948$	−2832.00	−0.0970244
$949$	−9020.00	−0.308537
$950$	−6000.00	−0.204911
$951$	20502.0	0.699078
$952$	7938.00	0.270244
$953$	50562.0	1.71864	0.859320	−	0.511438i	$-0.170887\pi$
$953$	50562.0	1.71864	0.859320	+	0.511438i	$0.170887\pi$
$954$	−15714.0	−0.533291
$955$	18600.0	0.630243
$956$	−336.000	−0.0113672
$957$	−7722.00	−0.260833
$958$	37440.0	1.26266
$959$	20118.0	0.677418
$960$	6495.00	0.218360
$961$	−29007.0	−0.973683
$962$	−20172.0	−0.676062
$963$	−16956.0	−0.567393
$964$	−5242.00	−0.175138
$965$	18350.0	0.612132
$966$	3024.00	0.100720
$967$	−1384.00	−0.0460253	−0.0230126	−	0.999735i	$-0.507326\pi$
$967$	−1384.00	−0.0460253	−0.0230126	+	0.999735i	$0.507326\pi$
$968$	2541.00	0.0843707
$969$	−12960.0	−0.429654
$970$	24870.0	0.823224
$971$	−9060.00	−0.299433	−0.149716	−	0.988729i	$-0.547836\pi$
$971$	−9060.00	−0.299433	−0.149716	+	0.988729i	$0.547836\pi$
$972$	−243.000	−0.00801875
$973$	−7168.00	−0.236172
$974$	−42144.0	−1.38643
$975$	6150.00	0.202008
$976$	−53818.0	−1.76503
$977$	−12126.0	−0.397078	−0.198539	−	0.980093i	$-0.563620\pi$
$977$	−12126.0	−0.397078	−0.198539	+	0.980093i	$0.563620\pi$
$978$	−27468.0	−0.898088
$979$	−462.000	−0.0150823
$980$	−245.000	−0.00798596
$981$	−3546.00	−0.115408
$982$	32076.0	1.04235
$983$	−8196.00	−0.265933	−0.132966	−	0.991121i	$-0.542450\pi$
$983$	−8196.00	−0.265933	−0.132966	+	0.991121i	$0.542450\pi$
$984$	−17010.0	−0.551076
$985$	−16470.0	−0.532769
$986$	37908.0	1.22438
$987$	6300.00	0.203172
$988$	−6560.00	−0.211236
$989$	−1344.00	−0.0432120
$990$	−1485.00	−0.0476731
$991$	−25936.0	−0.831366	−0.415683	−	0.909509i	$-0.636458\pi$
$991$	−25936.0	−0.831366	−0.415683	+	0.909509i	$0.636458\pi$
$992$	−1260.00	−0.0403277
$993$	−27780.0	−0.887786
$994$	−11592.0	−0.369895
$995$	5660.00	0.180336
$996$	−4104.00	−0.130562
$997$	−8818.00	−0.280109	−0.140055	−	0.990144i	$-0.544728\pi$
$997$	−8818.00	−0.280109	−0.140055	+	0.990144i	$0.544728\pi$
$998$	65172.0	2.06712
$999$	2214.00	0.0701180

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.4.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.4.a.a.1.1	✓	1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1155.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more