LMFDB - Embedded newform 2175.4.a.c.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2175,4,Mod(1,2175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2175.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2175, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 2175 = 3 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2175.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,2,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$128.329154262$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 435)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2175.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+2.00000 q^{2} +3.00000 q^{3} -4.00000 q^{4} +6.00000 q^{6} -29.0000 q^{7} -24.0000 q^{8} +9.00000 q^{9} -15.0000 q^{11} -12.0000 q^{12} -3.00000 q^{13} -58.0000 q^{14} -16.0000 q^{16} -121.000 q^{17} +18.0000 q^{18} -40.0000 q^{19} -87.0000 q^{21} -30.0000 q^{22} +116.000 q^{23} -72.0000 q^{24} -6.00000 q^{26} +27.0000 q^{27} +116.000 q^{28} +29.0000 q^{29} -116.000 q^{31} +160.000 q^{32} -45.0000 q^{33} -242.000 q^{34} -36.0000 q^{36} -36.0000 q^{37} -80.0000 q^{38} -9.00000 q^{39} -170.000 q^{41} -174.000 q^{42} -230.000 q^{43} +60.0000 q^{44} +232.000 q^{46} -231.000 q^{47} -48.0000 q^{48} +498.000 q^{49} -363.000 q^{51} +12.0000 q^{52} -456.000 q^{53} +54.0000 q^{54} +696.000 q^{56} -120.000 q^{57} +58.0000 q^{58} +576.000 q^{59} +342.000 q^{61} -232.000 q^{62} -261.000 q^{63} +448.000 q^{64} -90.0000 q^{66} +269.000 q^{67} +484.000 q^{68} +348.000 q^{69} +302.000 q^{71} -216.000 q^{72} +372.000 q^{73} -72.0000 q^{74} +160.000 q^{76} +435.000 q^{77} -18.0000 q^{78} -348.000 q^{79} +81.0000 q^{81} -340.000 q^{82} +512.000 q^{83} +348.000 q^{84} -460.000 q^{86} +87.0000 q^{87} +360.000 q^{88} +1525.00 q^{89} +87.0000 q^{91} -464.000 q^{92} -348.000 q^{93} -462.000 q^{94} +480.000 q^{96} +560.000 q^{97} +996.000 q^{98} -135.000 q^{99} +O(q^{100})\)

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107	0.353553	−	0.935414i	$-0.384973\pi$
$2$	2.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−4.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	6.00000	0.408248
$7$	−29.0000	−1.56585	−0.782926	−	0.622114i	$-0.786274\pi$
$7$	−29.0000	−1.56585	−0.782926	+	0.622114i	$0.786274\pi$
$8$	−24.0000	−1.06066
$9$	9.00000	0.333333
$10$	0	0
$11$	−15.0000	−0.411152	−0.205576	−	0.978641i	$-0.565907\pi$
$11$	−15.0000	−0.411152	−0.205576	+	0.978641i	$0.565907\pi$
$12$	−12.0000	−0.288675
$13$	−3.00000	−0.0640039	−0.0320019	−	0.999488i	$-0.510188\pi$
$13$	−3.00000	−0.0640039	−0.0320019	+	0.999488i	$0.510188\pi$
$14$	−58.0000	−1.10723
$15$	0	0
$16$	−16.0000	−0.250000
$17$	−121.000	−1.72628	−0.863141	−	0.504962i	$-0.831506\pi$
$17$	−121.000	−1.72628	−0.863141	+	0.504962i	$0.831506\pi$
$18$	18.0000	0.235702
$19$	−40.0000	−0.482980	−0.241490	−	0.970403i	$-0.577636\pi$
$19$	−40.0000	−0.482980	−0.241490	+	0.970403i	$0.577636\pi$
$20$	0	0
$21$	−87.0000	−0.904046
$22$	−30.0000	−0.290728
$23$	116.000	1.05164	0.525819	−	0.850597i	$-0.323759\pi$
$23$	116.000	1.05164	0.525819	+	0.850597i	$0.323759\pi$
$24$	−72.0000	−0.612372
$25$	0	0
$26$	−6.00000	−0.0452576
$27$	27.0000	0.192450
$28$	116.000	0.782926
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	0	0
$31$	−116.000	−0.672071	−0.336036	−	0.941849i	$-0.609086\pi$
$31$	−116.000	−0.672071	−0.336036	+	0.941849i	$0.609086\pi$
$32$	160.000	0.883883
$33$	−45.0000	−0.237379
$34$	−242.000	−1.22067
$35$	0	0
$36$	−36.0000	−0.166667
$37$	−36.0000	−0.159956	−0.0799779	−	0.996797i	$-0.525485\pi$
$37$	−36.0000	−0.159956	−0.0799779	+	0.996797i	$0.525485\pi$
$38$	−80.0000	−0.341519
$39$	−9.00000	−0.0369527
$40$	0	0
$41$	−170.000	−0.647550	−0.323775	−	0.946134i	$-0.604952\pi$
$41$	−170.000	−0.647550	−0.323775	+	0.946134i	$0.604952\pi$
$42$	−174.000	−0.639257
$43$	−230.000	−0.815690	−0.407845	−	0.913051i	$-0.633720\pi$
$43$	−230.000	−0.815690	−0.407845	+	0.913051i	$0.633720\pi$
$44$	60.0000	0.205576
$45$	0	0
$46$	232.000	0.743620
$47$	−231.000	−0.716911	−0.358455	−	0.933547i	$-0.616697\pi$
$47$	−231.000	−0.716911	−0.358455	+	0.933547i	$0.616697\pi$
$48$	−48.0000	−0.144338
$49$	498.000	1.45190
$50$	0	0
$51$	−363.000	−0.996670
$52$	12.0000	0.0320019
$53$	−456.000	−1.18182	−0.590910	−	0.806738i	$-0.701231\pi$
$53$	−456.000	−1.18182	−0.590910	+	0.806738i	$0.701231\pi$
$54$	54.0000	0.136083
$55$	0	0
$56$	696.000	1.66084
$57$	−120.000	−0.278849
$58$	58.0000	0.131306
$59$	576.000	1.27100	0.635498	−	0.772102i	$-0.280795\pi$
$59$	576.000	1.27100	0.635498	+	0.772102i	$0.280795\pi$
$60$	0	0
$61$	342.000	0.717846	0.358923	−	0.933367i	$-0.383144\pi$
$61$	342.000	0.717846	0.358923	+	0.933367i	$0.383144\pi$
$62$	−232.000	−0.475226
$63$	−261.000	−0.521951
$64$	448.000	0.875000
$65$	0	0
$66$	−90.0000	−0.167852
$67$	269.000	0.490501	0.245251	−	0.969460i	$-0.421130\pi$
$67$	269.000	0.490501	0.245251	+	0.969460i	$0.421130\pi$
$68$	484.000	0.863141
$69$	348.000	0.607163
$70$	0	0
$71$	302.000	0.504800	0.252400	−	0.967623i	$-0.418780\pi$
$71$	302.000	0.504800	0.252400	+	0.967623i	$0.418780\pi$
$72$	−216.000	−0.353553
$73$	372.000	0.596429	0.298214	−	0.954499i	$-0.403609\pi$
$73$	372.000	0.596429	0.298214	+	0.954499i	$0.403609\pi$
$74$	−72.0000	−0.113106
$75$	0	0
$76$	160.000	0.241490
$77$	435.000	0.643803
$78$	−18.0000	−0.0261295
$79$	−348.000	−0.495608	−0.247804	−	0.968810i	$-0.579709\pi$
$79$	−348.000	−0.495608	−0.247804	+	0.968810i	$0.579709\pi$
$80$	0	0
$81$	81.0000	0.111111
$82$	−340.000	−0.457887
$83$	512.000	0.677100	0.338550	−	0.940948i	$-0.390064\pi$
$83$	512.000	0.677100	0.338550	+	0.940948i	$0.390064\pi$
$84$	348.000	0.452023
$85$	0	0
$86$	−460.000	−0.576780
$87$	87.0000	0.107211
$88$	360.000	0.436092
$89$	1525.00	1.81629	0.908144	−	0.418657i	$-0.137499\pi$
$89$	1525.00	1.81629	0.908144	+	0.418657i	$0.137499\pi$
$90$	0	0
$91$	87.0000	0.100221
$92$	−464.000	−0.525819
$93$	−348.000	−0.388021
$94$	−462.000	−0.506933
$95$	0	0
$96$	480.000	0.510310
$97$	560.000	0.586179	0.293090	−	0.956085i	$-0.405317\pi$
$97$	560.000	0.586179	0.293090	+	0.956085i	$0.405317\pi$
$98$	996.000	1.02664
$99$	−135.000	−0.137051
$100$	0	0
$101$	1447.00	1.42556	0.712782	−	0.701386i	$-0.247435\pi$
$101$	1447.00	1.42556	0.712782	+	0.701386i	$0.247435\pi$
$102$	−726.000	−0.704752
$103$	−556.000	−0.531886	−0.265943	−	0.963989i	$-0.585683\pi$
$103$	−556.000	−0.531886	−0.265943	+	0.963989i	$0.585683\pi$
$104$	72.0000	0.0678864
$105$	0	0
$106$	−912.000	−0.835672
$107$	−1558.00	−1.40764	−0.703820	−	0.710378i	$-0.748524\pi$
$107$	−1558.00	−1.40764	−0.703820	+	0.710378i	$0.748524\pi$
$108$	−108.000	−0.0962250
$109$	−881.000	−0.774170	−0.387085	−	0.922044i	$-0.626518\pi$
$109$	−881.000	−0.774170	−0.387085	+	0.922044i	$0.626518\pi$
$110$	0	0
$111$	−108.000	−0.0923505
$112$	464.000	0.391463
$113$	−313.000	−0.260571	−0.130286	−	0.991476i	$-0.541589\pi$
$113$	−313.000	−0.260571	−0.130286	+	0.991476i	$0.541589\pi$
$114$	−240.000	−0.197176
$115$	0	0
$116$	−116.000	−0.0928477
$117$	−27.0000	−0.0213346
$118$	1152.00	0.898730
$119$	3509.00	2.70311
$120$	0	0
$121$	−1106.00	−0.830954
$122$	684.000	0.507594
$123$	−510.000	−0.373863
$124$	464.000	0.336036
$125$	0	0
$126$	−522.000	−0.369075
$127$	494.000	0.345161	0.172580	−	0.984995i	$-0.444790\pi$
$127$	494.000	0.345161	0.172580	+	0.984995i	$0.444790\pi$
$128$	−384.000	−0.265165
$129$	−690.000	−0.470939
$130$	0	0
$131$	−2007.00	−1.33857	−0.669284	−	0.743007i	$-0.733399\pi$
$131$	−2007.00	−1.33857	−0.669284	+	0.743007i	$0.733399\pi$
$132$	180.000	0.118689
$133$	1160.00	0.756276
$134$	538.000	0.346837
$135$	0	0
$136$	2904.00	1.83100
$137$	−918.000	−0.572482	−0.286241	−	0.958158i	$-0.592406\pi$
$137$	−918.000	−0.572482	−0.286241	+	0.958158i	$0.592406\pi$
$138$	696.000	0.429329
$139$	1619.00	0.987927	0.493963	−	0.869483i	$-0.335548\pi$
$139$	1619.00	0.987927	0.493963	+	0.869483i	$0.335548\pi$
$140$	0	0
$141$	−693.000	−0.413909
$142$	604.000	0.356948
$143$	45.0000	0.0263153
$144$	−144.000	−0.0833333
$145$	0	0
$146$	744.000	0.421739
$147$	1494.00	0.838252
$148$	144.000	0.0799779
$149$	3046.00	1.67475	0.837376	−	0.546627i	$-0.184089\pi$
$149$	3046.00	1.67475	0.837376	+	0.546627i	$0.184089\pi$
$150$	0	0
$151$	1576.00	0.849358	0.424679	−	0.905344i	$-0.360387\pi$
$151$	1576.00	0.849358	0.424679	+	0.905344i	$0.360387\pi$
$152$	960.000	0.512278
$153$	−1089.00	−0.575428
$154$	870.000	0.455238
$155$	0	0
$156$	36.0000	0.0184763
$157$	3544.00	1.80154	0.900771	−	0.434295i	$-0.143002\pi$
$157$	3544.00	1.80154	0.900771	+	0.434295i	$0.143002\pi$
$158$	−696.000	−0.350448
$159$	−1368.00	−0.682324
$160$	0	0
$161$	−3364.00	−1.64671
$162$	162.000	0.0785674
$163$	768.000	0.369045	0.184523	−	0.982828i	$-0.440926\pi$
$163$	768.000	0.369045	0.184523	+	0.982828i	$0.440926\pi$
$164$	680.000	0.323775
$165$	0	0
$166$	1024.00	0.478782
$167$	1624.00	0.752508	0.376254	−	0.926516i	$-0.377212\pi$
$167$	1624.00	0.752508	0.376254	+	0.926516i	$0.377212\pi$
$168$	2088.00	0.958885
$169$	−2188.00	−0.995904
$170$	0	0
$171$	−360.000	−0.160993
$172$	920.000	0.407845
$173$	−1700.00	−0.747102	−0.373551	−	0.927610i	$-0.621860\pi$
$173$	−1700.00	−0.747102	−0.373551	+	0.927610i	$0.621860\pi$
$174$	174.000	0.0758098
$175$	0	0
$176$	240.000	0.102788
$177$	1728.00	0.733810
$178$	3050.00	1.28431
$179$	3870.00	1.61596	0.807982	−	0.589208i	$-0.200560\pi$
$179$	3870.00	1.61596	0.807982	+	0.589208i	$0.200560\pi$
$180$	0	0
$181$	1757.00	0.721529	0.360765	−	0.932657i	$-0.382516\pi$
$181$	1757.00	0.721529	0.360765	+	0.932657i	$0.382516\pi$
$182$	174.000	0.0708667
$183$	1026.00	0.414449
$184$	−2784.00	−1.11543
$185$	0	0
$186$	−696.000	−0.274372
$187$	1815.00	0.709764
$188$	924.000	0.358455
$189$	−783.000	−0.301349
$190$	0	0
$191$	−2048.00	−0.775854	−0.387927	−	0.921690i	$-0.626809\pi$
$191$	−2048.00	−0.775854	−0.387927	+	0.921690i	$0.626809\pi$
$192$	1344.00	0.505181
$193$	2398.00	0.894362	0.447181	−	0.894444i	$-0.352428\pi$
$193$	2398.00	0.894362	0.447181	+	0.894444i	$0.352428\pi$
$194$	1120.00	0.414491
$195$	0	0
$196$	−1992.00	−0.725948
$197$	−3966.00	−1.43434	−0.717172	−	0.696896i	$-0.754564\pi$
$197$	−3966.00	−1.43434	−0.717172	+	0.696896i	$0.754564\pi$
$198$	−270.000	−0.0969094
$199$	641.000	0.228338	0.114169	−	0.993461i	$-0.463579\pi$
$199$	641.000	0.228338	0.114169	+	0.993461i	$0.463579\pi$
$200$	0	0
$201$	807.000	0.283191
$202$	2894.00	1.00803
$203$	−841.000	−0.290772
$204$	1452.00	0.498335
$205$	0	0
$206$	−1112.00	−0.376101
$207$	1044.00	0.350546
$208$	48.0000	0.0160010
$209$	600.000	0.198578
$210$	0	0
$211$	5438.00	1.77425	0.887126	−	0.461526i	$-0.152698\pi$
$211$	5438.00	1.77425	0.887126	+	0.461526i	$0.152698\pi$
$212$	1824.00	0.590910
$213$	906.000	0.291446
$214$	−3116.00	−0.995352
$215$	0	0
$216$	−648.000	−0.204124
$217$	3364.00	1.05236
$218$	−1762.00	−0.547421
$219$	1116.00	0.344348
$220$	0	0
$221$	363.000	0.110489
$222$	−216.000	−0.0653017
$223$	−2799.00	−0.840515	−0.420258	−	0.907405i	$-0.638060\pi$
$223$	−2799.00	−0.840515	−0.420258	+	0.907405i	$0.638060\pi$
$224$	−4640.00	−1.38403
$225$	0	0
$226$	−626.000	−0.184252
$227$	−1492.00	−0.436245	−0.218122	−	0.975921i	$-0.569993\pi$
$227$	−1492.00	−0.436245	−0.218122	+	0.975921i	$0.569993\pi$
$228$	480.000	0.139424
$229$	4622.00	1.33376	0.666879	−	0.745166i	$-0.267630\pi$
$229$	4622.00	1.33376	0.666879	+	0.745166i	$0.267630\pi$
$230$	0	0
$231$	1305.00	0.371700
$232$	−696.000	−0.196960
$233$	−4170.00	−1.17247	−0.586236	−	0.810141i	$-0.699391\pi$
$233$	−4170.00	−1.17247	−0.586236	+	0.810141i	$0.699391\pi$
$234$	−54.0000	−0.0150859
$235$	0	0
$236$	−2304.00	−0.635498
$237$	−1044.00	−0.286140
$238$	7018.00	1.91138
$239$	1686.00	0.456311	0.228155	−	0.973625i	$-0.426731\pi$
$239$	1686.00	0.456311	0.228155	+	0.973625i	$0.426731\pi$
$240$	0	0
$241$	−3925.00	−1.04909	−0.524547	−	0.851382i	$-0.675765\pi$
$241$	−3925.00	−1.04909	−0.524547	+	0.851382i	$0.675765\pi$
$242$	−2212.00	−0.587573
$243$	243.000	0.0641500
$244$	−1368.00	−0.358923
$245$	0	0
$246$	−1020.00	−0.264361
$247$	120.000	0.0309126
$248$	2784.00	0.712839
$249$	1536.00	0.390924
$250$	0	0
$251$	−5775.00	−1.45225	−0.726125	−	0.687563i	$-0.758681\pi$
$251$	−5775.00	−1.45225	−0.726125	+	0.687563i	$0.758681\pi$
$252$	1044.00	0.260975
$253$	−1740.00	−0.432383
$254$	988.000	0.244065
$255$	0	0
$256$	−4352.00	−1.06250
$257$	3146.00	0.763588	0.381794	−	0.924247i	$-0.375306\pi$
$257$	3146.00	0.763588	0.381794	+	0.924247i	$0.375306\pi$
$258$	−1380.00	−0.333004
$259$	1044.00	0.250467
$260$	0	0
$261$	261.000	0.0618984
$262$	−4014.00	−0.946510
$263$	5768.00	1.35236	0.676179	−	0.736737i	$-0.263635\pi$
$263$	5768.00	1.35236	0.676179	+	0.736737i	$0.263635\pi$
$264$	1080.00	0.251778
$265$	0	0
$266$	2320.00	0.534768
$267$	4575.00	1.04863
$268$	−1076.00	−0.245251
$269$	−7341.00	−1.66390	−0.831949	−	0.554852i	$-0.812775\pi$
$269$	−7341.00	−1.66390	−0.831949	+	0.554852i	$0.812775\pi$
$270$	0	0
$271$	−14.0000	−0.00313815	−0.00156908	−	0.999999i	$-0.500499\pi$
$271$	−14.0000	−0.00313815	−0.00156908	+	0.999999i	$0.500499\pi$
$272$	1936.00	0.431571
$273$	261.000	0.0578624
$274$	−1836.00	−0.404806
$275$	0	0
$276$	−1392.00	−0.303582
$277$	−3721.00	−0.807124	−0.403562	−	0.914952i	$-0.632228\pi$
$277$	−3721.00	−0.807124	−0.403562	+	0.914952i	$0.632228\pi$
$278$	3238.00	0.698570
$279$	−1044.00	−0.224024
$280$	0	0
$281$	924.000	0.196161	0.0980805	−	0.995178i	$-0.468730\pi$
$281$	924.000	0.196161	0.0980805	+	0.995178i	$0.468730\pi$
$282$	−1386.00	−0.292678
$283$	−1940.00	−0.407495	−0.203747	−	0.979023i	$-0.565312\pi$
$283$	−1940.00	−0.407495	−0.203747	+	0.979023i	$0.565312\pi$
$284$	−1208.00	−0.252400
$285$	0	0
$286$	90.0000	0.0186077
$287$	4930.00	1.01397
$288$	1440.00	0.294628
$289$	9728.00	1.98005
$290$	0	0
$291$	1680.00	0.338431
$292$	−1488.00	−0.298214
$293$	−5267.00	−1.05018	−0.525088	−	0.851048i	$-0.675968\pi$
$293$	−5267.00	−1.05018	−0.525088	+	0.851048i	$0.675968\pi$
$294$	2988.00	0.592734
$295$	0	0
$296$	864.000	0.169659
$297$	−405.000	−0.0791262
$298$	6092.00	1.18423
$299$	−348.000	−0.0673089
$300$	0	0
$301$	6670.00	1.27725
$302$	3152.00	0.600587
$303$	4341.00	0.823049
$304$	640.000	0.120745
$305$	0	0
$306$	−2178.00	−0.406889
$307$	−6856.00	−1.27457	−0.637284	−	0.770629i	$-0.719942\pi$
$307$	−6856.00	−1.27457	−0.637284	+	0.770629i	$0.719942\pi$
$308$	−1740.00	−0.321902
$309$	−1668.00	−0.307085
$310$	0	0
$311$	−2447.00	−0.446163	−0.223081	−	0.974800i	$-0.571612\pi$
$311$	−2447.00	−0.446163	−0.223081	+	0.974800i	$0.571612\pi$
$312$	216.000	0.0391942
$313$	−511.000	−0.0922793	−0.0461397	−	0.998935i	$-0.514692\pi$
$313$	−511.000	−0.0922793	−0.0461397	+	0.998935i	$0.514692\pi$
$314$	7088.00	1.27388
$315$	0	0
$316$	1392.00	0.247804
$317$	−7167.00	−1.26984	−0.634919	−	0.772578i	$-0.718967\pi$
$317$	−7167.00	−1.26984	−0.634919	+	0.772578i	$0.718967\pi$
$318$	−2736.00	−0.482476
$319$	−435.000	−0.0763490
$320$	0	0
$321$	−4674.00	−0.812702
$322$	−6728.00	−1.16440
$323$	4840.00	0.833761
$324$	−324.000	−0.0555556
$325$	0	0
$326$	1536.00	0.260955
$327$	−2643.00	−0.446967
$328$	4080.00	0.686830
$329$	6699.00	1.12258
$330$	0	0
$331$	−8962.00	−1.48821	−0.744103	−	0.668065i	$-0.767123\pi$
$331$	−8962.00	−1.48821	−0.744103	+	0.668065i	$0.767123\pi$
$332$	−2048.00	−0.338550
$333$	−324.000	−0.0533186
$334$	3248.00	0.532104
$335$	0	0
$336$	1392.00	0.226011
$337$	−2706.00	−0.437404	−0.218702	−	0.975792i	$-0.570182\pi$
$337$	−2706.00	−0.437404	−0.218702	+	0.975792i	$0.570182\pi$
$338$	−4376.00	−0.704210
$339$	−939.000	−0.150441
$340$	0	0
$341$	1740.00	0.276323
$342$	−720.000	−0.113840
$343$	−4495.00	−0.707601
$344$	5520.00	0.865170
$345$	0	0
$346$	−3400.00	−0.528281
$347$	−2232.00	−0.345303	−0.172651	−	0.984983i	$-0.555233\pi$
$347$	−2232.00	−0.345303	−0.172651	+	0.984983i	$0.555233\pi$
$348$	−348.000	−0.0536056
$349$	9742.00	1.49420	0.747102	−	0.664709i	$-0.231445\pi$
$349$	9742.00	1.49420	0.747102	+	0.664709i	$0.231445\pi$
$350$	0	0
$351$	−81.0000	−0.0123176
$352$	−2400.00	−0.363410
$353$	2694.00	0.406196	0.203098	−	0.979158i	$-0.434899\pi$
$353$	2694.00	0.406196	0.203098	+	0.979158i	$0.434899\pi$
$354$	3456.00	0.518882
$355$	0	0
$356$	−6100.00	−0.908144
$357$	10527.0	1.56064
$358$	7740.00	1.14266
$359$	−960.000	−0.141133	−0.0705667	−	0.997507i	$-0.522481\pi$
$359$	−960.000	−0.141133	−0.0705667	+	0.997507i	$0.522481\pi$
$360$	0	0
$361$	−5259.00	−0.766730
$362$	3514.00	0.510198
$363$	−3318.00	−0.479752
$364$	−348.000	−0.0501103
$365$	0	0
$366$	2052.00	0.293059
$367$	4632.00	0.658824	0.329412	−	0.944186i	$-0.393149\pi$
$367$	4632.00	0.658824	0.329412	+	0.944186i	$0.393149\pi$
$368$	−1856.00	−0.262909
$369$	−1530.00	−0.215850
$370$	0	0
$371$	13224.0	1.85055
$372$	1392.00	0.194010
$373$	6682.00	0.927563	0.463781	−	0.885950i	$-0.346492\pi$
$373$	6682.00	0.927563	0.463781	+	0.885950i	$0.346492\pi$
$374$	3630.00	0.501879
$375$	0	0
$376$	5544.00	0.760399
$377$	−87.0000	−0.0118852
$378$	−1566.00	−0.213086
$379$	11270.0	1.52744	0.763722	−	0.645546i	$-0.223370\pi$
$379$	11270.0	1.52744	0.763722	+	0.645546i	$0.223370\pi$
$380$	0	0
$381$	1482.00	0.199279
$382$	−4096.00	−0.548611
$383$	−1016.00	−0.135549	−0.0677744	−	0.997701i	$-0.521590\pi$
$383$	−1016.00	−0.135549	−0.0677744	+	0.997701i	$0.521590\pi$
$384$	−1152.00	−0.153093
$385$	0	0
$386$	4796.00	0.632409
$387$	−2070.00	−0.271897
$388$	−2240.00	−0.293090
$389$	−3727.00	−0.485775	−0.242887	−	0.970054i	$-0.578095\pi$
$389$	−3727.00	−0.485775	−0.242887	+	0.970054i	$0.578095\pi$
$390$	0	0
$391$	−14036.0	−1.81542
$392$	−11952.0	−1.53997
$393$	−6021.00	−0.772823
$394$	−7932.00	−1.01423
$395$	0	0
$396$	540.000	0.0685253
$397$	−1990.00	−0.251575	−0.125787	−	0.992057i	$-0.540146\pi$
$397$	−1990.00	−0.251575	−0.125787	+	0.992057i	$0.540146\pi$
$398$	1282.00	0.161459
$399$	3480.00	0.436636
$400$	0	0
$401$	6696.00	0.833871	0.416936	−	0.908936i	$-0.363104\pi$
$401$	6696.00	0.833871	0.416936	+	0.908936i	$0.363104\pi$
$402$	1614.00	0.200246
$403$	348.000	0.0430152
$404$	−5788.00	−0.712782
$405$	0	0
$406$	−1682.00	−0.205607
$407$	540.000	0.0657661
$408$	8712.00	1.05713
$409$	252.000	0.0304660	0.0152330	−	0.999884i	$-0.495151\pi$
$409$	252.000	0.0304660	0.0152330	+	0.999884i	$0.495151\pi$
$410$	0	0
$411$	−2754.00	−0.330523
$412$	2224.00	0.265943
$413$	−16704.0	−1.99019
$414$	2088.00	0.247873
$415$	0	0
$416$	−480.000	−0.0565720
$417$	4857.00	0.570380
$418$	1200.00	0.140416
$419$	7418.00	0.864900	0.432450	−	0.901658i	$-0.357649\pi$
$419$	7418.00	0.864900	0.432450	+	0.901658i	$0.357649\pi$
$420$	0	0
$421$	11268.0	1.30444	0.652219	−	0.758030i	$-0.273838\pi$
$421$	11268.0	1.30444	0.652219	+	0.758030i	$0.273838\pi$
$422$	10876.0	1.25459
$423$	−2079.00	−0.238970
$424$	10944.0	1.25351
$425$	0	0
$426$	1812.00	0.206084
$427$	−9918.00	−1.12404
$428$	6232.00	0.703820
$429$	135.000	0.0151932
$430$	0	0
$431$	−11600.0	−1.29641	−0.648205	−	0.761466i	$-0.724480\pi$
$431$	−11600.0	−1.29641	−0.648205	+	0.761466i	$0.724480\pi$
$432$	−432.000	−0.0481125
$433$	−1072.00	−0.118977	−0.0594885	−	0.998229i	$-0.518947\pi$
$433$	−1072.00	−0.118977	−0.0594885	+	0.998229i	$0.518947\pi$
$434$	6728.00	0.744134
$435$	0	0
$436$	3524.00	0.387085
$437$	−4640.00	−0.507921
$438$	2232.00	0.243491
$439$	−12339.0	−1.34148	−0.670738	−	0.741694i	$-0.734023\pi$
$439$	−12339.0	−1.34148	−0.670738	+	0.741694i	$0.734023\pi$
$440$	0	0
$441$	4482.00	0.483965
$442$	726.000	0.0781274
$443$	15263.0	1.63695	0.818473	−	0.574545i	$-0.194821\pi$
$443$	15263.0	1.63695	0.818473	+	0.574545i	$0.194821\pi$
$444$	432.000	0.0461753
$445$	0	0
$446$	−5598.00	−0.594334
$447$	9138.00	0.966918
$448$	−12992.0	−1.37012
$449$	11019.0	1.15817	0.579085	−	0.815267i	$-0.303410\pi$
$449$	11019.0	1.15817	0.579085	+	0.815267i	$0.303410\pi$
$450$	0	0
$451$	2550.00	0.266241
$452$	1252.00	0.130286
$453$	4728.00	0.490377
$454$	−2984.00	−0.308471
$455$	0	0
$456$	2880.00	0.295764
$457$	6769.00	0.692868	0.346434	−	0.938074i	$-0.387393\pi$
$457$	6769.00	0.692868	0.346434	+	0.938074i	$0.387393\pi$
$458$	9244.00	0.943109
$459$	−3267.00	−0.332223
$460$	0	0
$461$	−5514.00	−0.557077	−0.278539	−	0.960425i	$-0.589850\pi$
$461$	−5514.00	−0.557077	−0.278539	+	0.960425i	$0.589850\pi$
$462$	2610.00	0.262832
$463$	14205.0	1.42584	0.712918	−	0.701247i	$-0.247373\pi$
$463$	14205.0	1.42584	0.712918	+	0.701247i	$0.247373\pi$
$464$	−464.000	−0.0464238
$465$	0	0
$466$	−8340.00	−0.829062
$467$	9660.00	0.957198	0.478599	−	0.878034i	$-0.341145\pi$
$467$	9660.00	0.957198	0.478599	+	0.878034i	$0.341145\pi$
$468$	108.000	0.0106673
$469$	−7801.00	−0.768053
$470$	0	0
$471$	10632.0	1.04012
$472$	−13824.0	−1.34810
$473$	3450.00	0.335372
$474$	−2088.00	−0.202331
$475$	0	0
$476$	−14036.0	−1.35155
$477$	−4104.00	−0.393940
$478$	3372.00	0.322660
$479$	−7656.00	−0.730296	−0.365148	−	0.930950i	$-0.618982\pi$
$479$	−7656.00	−0.730296	−0.365148	+	0.930950i	$0.618982\pi$
$480$	0	0
$481$	108.000	0.0102378
$482$	−7850.00	−0.741821
$483$	−10092.0	−0.950729
$484$	4424.00	0.415477
$485$	0	0
$486$	486.000	0.0453609
$487$	15968.0	1.48579	0.742894	−	0.669409i	$-0.233452\pi$
$487$	15968.0	1.48579	0.742894	+	0.669409i	$0.233452\pi$
$488$	−8208.00	−0.761391
$489$	2304.00	0.213068
$490$	0	0
$491$	4236.00	0.389344	0.194672	−	0.980868i	$-0.437636\pi$
$491$	4236.00	0.389344	0.194672	+	0.980868i	$0.437636\pi$
$492$	2040.00	0.186932
$493$	−3509.00	−0.320563
$494$	240.000	0.0218585
$495$	0	0
$496$	1856.00	0.168018
$497$	−8758.00	−0.790443
$498$	3072.00	0.276425
$499$	−16941.0	−1.51981	−0.759903	−	0.650036i	$-0.774754\pi$
$499$	−16941.0	−1.51981	−0.759903	+	0.650036i	$0.774754\pi$
$500$	0	0
$501$	4872.00	0.434461
$502$	−11550.0	−1.02690
$503$	1857.00	0.164611	0.0823057	−	0.996607i	$-0.473772\pi$
$503$	1857.00	0.164611	0.0823057	+	0.996607i	$0.473772\pi$
$504$	6264.00	0.553613
$505$	0	0
$506$	−3480.00	−0.305741
$507$	−6564.00	−0.574985
$508$	−1976.00	−0.172580
$509$	−3096.00	−0.269603	−0.134801	−	0.990873i	$-0.543040\pi$
$509$	−3096.00	−0.269603	−0.134801	+	0.990873i	$0.543040\pi$
$510$	0	0
$511$	−10788.0	−0.933920
$512$	−5632.00	−0.486136
$513$	−1080.00	−0.0929496
$514$	6292.00	0.539938
$515$	0	0
$516$	2760.00	0.235469
$517$	3465.00	0.294759
$518$	2088.00	0.177107
$519$	−5100.00	−0.431339
$520$	0	0
$521$	7530.00	0.633196	0.316598	−	0.948560i	$-0.397459\pi$
$521$	7530.00	0.633196	0.316598	+	0.948560i	$0.397459\pi$
$522$	522.000	0.0437688
$523$	5767.00	0.482167	0.241083	−	0.970504i	$-0.422497\pi$
$523$	5767.00	0.482167	0.241083	+	0.970504i	$0.422497\pi$
$524$	8028.00	0.669284
$525$	0	0
$526$	11536.0	0.956261
$527$	14036.0	1.16019
$528$	720.000	0.0593447
$529$	1289.00	0.105942
$530$	0	0
$531$	5184.00	0.423666
$532$	−4640.00	−0.378138
$533$	510.000	0.0414457
$534$	9150.00	0.741497
$535$	0	0
$536$	−6456.00	−0.520255
$537$	11610.0	0.932977
$538$	−14682.0	−1.17655
$539$	−7470.00	−0.596949
$540$	0	0
$541$	−21122.0	−1.67857	−0.839284	−	0.543693i	$-0.817026\pi$
$541$	−21122.0	−1.67857	−0.839284	+	0.543693i	$0.817026\pi$
$542$	−28.0000	−0.00221901
$543$	5271.00	0.416575
$544$	−19360.0	−1.52583
$545$	0	0
$546$	522.000	0.0409149
$547$	−17857.0	−1.39581	−0.697907	−	0.716188i	$-0.745885\pi$
$547$	−17857.0	−1.39581	−0.697907	+	0.716188i	$0.745885\pi$
$548$	3672.00	0.286241
$549$	3078.00	0.239282
$550$	0	0
$551$	−1160.00	−0.0896872
$552$	−8352.00	−0.643994
$553$	10092.0	0.776050
$554$	−7442.00	−0.570723
$555$	0	0
$556$	−6476.00	−0.493963
$557$	−6040.00	−0.459467	−0.229733	−	0.973254i	$-0.573785\pi$
$557$	−6040.00	−0.459467	−0.229733	+	0.973254i	$0.573785\pi$
$558$	−2088.00	−0.158409
$559$	690.000	0.0522073
$560$	0	0
$561$	5445.00	0.409783
$562$	1848.00	0.138707
$563$	15371.0	1.15064	0.575320	−	0.817928i	$-0.304877\pi$
$563$	15371.0	1.15064	0.575320	+	0.817928i	$0.304877\pi$
$564$	2772.00	0.206954
$565$	0	0
$566$	−3880.00	−0.288142
$567$	−2349.00	−0.173984
$568$	−7248.00	−0.535421
$569$	17901.0	1.31889	0.659445	−	0.751752i	$-0.270791\pi$
$569$	17901.0	1.31889	0.659445	+	0.751752i	$0.270791\pi$
$570$	0	0
$571$	−10056.0	−0.737006	−0.368503	−	0.929627i	$-0.620130\pi$
$571$	−10056.0	−0.737006	−0.368503	+	0.929627i	$0.620130\pi$
$572$	−180.000	−0.0131577
$573$	−6144.00	−0.447939
$574$	9860.00	0.716983
$575$	0	0
$576$	4032.00	0.291667
$577$	−3068.00	−0.221356	−0.110678	−	0.993856i	$-0.535302\pi$
$577$	−3068.00	−0.221356	−0.110678	+	0.993856i	$0.535302\pi$
$578$	19456.0	1.40011
$579$	7194.00	0.516360
$580$	0	0
$581$	−14848.0	−1.06024
$582$	3360.00	0.239307
$583$	6840.00	0.485907
$584$	−8928.00	−0.632608
$585$	0	0
$586$	−10534.0	−0.742586
$587$	2984.00	0.209817	0.104909	−	0.994482i	$-0.466545\pi$
$587$	2984.00	0.209817	0.104909	+	0.994482i	$0.466545\pi$
$588$	−5976.00	−0.419126
$589$	4640.00	0.324597
$590$	0	0
$591$	−11898.0	−0.828119
$592$	576.000	0.0399889
$593$	−5952.00	−0.412174	−0.206087	−	0.978534i	$-0.566073\pi$
$593$	−5952.00	−0.412174	−0.206087	+	0.978534i	$0.566073\pi$
$594$	−810.000	−0.0559507
$595$	0	0
$596$	−12184.0	−0.837376
$597$	1923.00	0.131831
$598$	−696.000	−0.0475946
$599$	−12999.0	−0.886686	−0.443343	−	0.896352i	$-0.646208\pi$
$599$	−12999.0	−0.886686	−0.443343	+	0.896352i	$0.646208\pi$
$600$	0	0
$601$	23398.0	1.58806	0.794030	−	0.607878i	$-0.207979\pi$
$601$	23398.0	1.58806	0.794030	+	0.607878i	$0.207979\pi$
$602$	13340.0	0.903153
$603$	2421.00	0.163500
$604$	−6304.00	−0.424679
$605$	0	0
$606$	8682.00	0.581984
$607$	−26116.0	−1.74632	−0.873160	−	0.487434i	$-0.837933\pi$
$607$	−26116.0	−1.74632	−0.873160	+	0.487434i	$0.837933\pi$
$608$	−6400.00	−0.426898
$609$	−2523.00	−0.167877
$610$	0	0
$611$	693.000	0.0458851
$612$	4356.00	0.287714
$613$	24185.0	1.59351	0.796756	−	0.604301i	$-0.206548\pi$
$613$	24185.0	1.59351	0.796756	+	0.604301i	$0.206548\pi$
$614$	−13712.0	−0.901256
$615$	0	0
$616$	−10440.0	−0.682856
$617$	−2214.00	−0.144461	−0.0722304	−	0.997388i	$-0.523012\pi$
$617$	−2214.00	−0.144461	−0.0722304	+	0.997388i	$0.523012\pi$
$618$	−3336.00	−0.217142
$619$	−19586.0	−1.27177	−0.635887	−	0.771782i	$-0.719365\pi$
$619$	−19586.0	−1.27177	−0.635887	+	0.771782i	$0.719365\pi$
$620$	0	0
$621$	3132.00	0.202388
$622$	−4894.00	−0.315485
$623$	−44225.0	−2.84404
$624$	144.000	0.00923816
$625$	0	0
$626$	−1022.00	−0.0652513
$627$	1800.00	0.114649
$628$	−14176.0	−0.900771
$629$	4356.00	0.276129
$630$	0	0
$631$	4377.00	0.276142	0.138071	−	0.990422i	$-0.455910\pi$
$631$	4377.00	0.276142	0.138071	+	0.990422i	$0.455910\pi$
$632$	8352.00	0.525672
$633$	16314.0	1.02437
$634$	−14334.0	−0.897911
$635$	0	0
$636$	5472.00	0.341162
$637$	−1494.00	−0.0929269
$638$	−870.000	−0.0539869
$639$	2718.00	0.168267
$640$	0	0
$641$	−24015.0	−1.47977	−0.739887	−	0.672731i	$-0.765121\pi$
$641$	−24015.0	−1.47977	−0.739887	+	0.672731i	$0.765121\pi$
$642$	−9348.00	−0.574667
$643$	19465.0	1.19382	0.596909	−	0.802309i	$-0.296395\pi$
$643$	19465.0	1.19382	0.596909	+	0.802309i	$0.296395\pi$
$644$	13456.0	0.823355
$645$	0	0
$646$	9680.00	0.589558
$647$	19954.0	1.21248	0.606239	−	0.795283i	$-0.292678\pi$
$647$	19954.0	1.21248	0.606239	+	0.795283i	$0.292678\pi$
$648$	−1944.00	−0.117851
$649$	−8640.00	−0.522573
$650$	0	0
$651$	10092.0	0.607583
$652$	−3072.00	−0.184523
$653$	22597.0	1.35419	0.677097	−	0.735894i	$-0.263238\pi$
$653$	22597.0	1.35419	0.677097	+	0.735894i	$0.263238\pi$
$654$	−5286.00	−0.316053
$655$	0	0
$656$	2720.00	0.161887
$657$	3348.00	0.198810
$658$	13398.0	0.793782
$659$	7467.00	0.441385	0.220693	−	0.975343i	$-0.429168\pi$
$659$	7467.00	0.441385	0.220693	+	0.975343i	$0.429168\pi$
$660$	0	0
$661$	16601.0	0.976859	0.488430	−	0.872603i	$-0.337570\pi$
$661$	16601.0	0.976859	0.488430	+	0.872603i	$0.337570\pi$
$662$	−17924.0	−1.05232
$663$	1089.00	0.0637907
$664$	−12288.0	−0.718173
$665$	0	0
$666$	−648.000	−0.0377019
$667$	3364.00	0.195284
$668$	−6496.00	−0.376254
$669$	−8397.00	−0.485272
$670$	0	0
$671$	−5130.00	−0.295144
$672$	−13920.0	−0.799071
$673$	−23571.0	−1.35007	−0.675034	−	0.737787i	$-0.735871\pi$
$673$	−23571.0	−1.35007	−0.675034	+	0.737787i	$0.735871\pi$
$674$	−5412.00	−0.309291
$675$	0	0
$676$	8752.00	0.497952
$677$	16963.0	0.962985	0.481493	−	0.876450i	$-0.340095\pi$
$677$	16963.0	0.962985	0.481493	+	0.876450i	$0.340095\pi$
$678$	−1878.00	−0.106378
$679$	−16240.0	−0.917870
$680$	0	0
$681$	−4476.00	−0.251866
$682$	3480.00	0.195390
$683$	−6144.00	−0.344207	−0.172104	−	0.985079i	$-0.555056\pi$
$683$	−6144.00	−0.344207	−0.172104	+	0.985079i	$0.555056\pi$
$684$	1440.00	0.0804967
$685$	0	0
$686$	−8990.00	−0.500350
$687$	13866.0	0.770045
$688$	3680.00	0.203923
$689$	1368.00	0.0756410
$690$	0	0
$691$	18461.0	1.01634	0.508169	−	0.861257i	$-0.330323\pi$
$691$	18461.0	1.01634	0.508169	+	0.861257i	$0.330323\pi$
$692$	6800.00	0.373551
$693$	3915.00	0.214601
$694$	−4464.00	−0.244166
$695$	0	0
$696$	−2088.00	−0.113715
$697$	20570.0	1.11785
$698$	19484.0	1.05656
$699$	−12510.0	−0.676927
$700$	0	0
$701$	−7550.00	−0.406790	−0.203395	−	0.979097i	$-0.565198\pi$
$701$	−7550.00	−0.406790	−0.203395	+	0.979097i	$0.565198\pi$
$702$	−162.000	−0.00870982
$703$	1440.00	0.0772555
$704$	−6720.00	−0.359758
$705$	0	0
$706$	5388.00	0.287224
$707$	−41963.0	−2.23222
$708$	−6912.00	−0.366905
$709$	29126.0	1.54281	0.771403	−	0.636347i	$-0.219555\pi$
$709$	29126.0	1.54281	0.771403	+	0.636347i	$0.219555\pi$
$710$	0	0
$711$	−3132.00	−0.165203
$712$	−36600.0	−1.92646
$713$	−13456.0	−0.706776
$714$	21054.0	1.10354
$715$	0	0
$716$	−15480.0	−0.807982
$717$	5058.00	0.263451
$718$	−1920.00	−0.0997963
$719$	−31670.0	−1.64269	−0.821343	−	0.570434i	$-0.806775\pi$
$719$	−31670.0	−1.64269	−0.821343	+	0.570434i	$0.806775\pi$
$720$	0	0
$721$	16124.0	0.832856
$722$	−10518.0	−0.542160
$723$	−11775.0	−0.605694
$724$	−7028.00	−0.360765
$725$	0	0
$726$	−6636.00	−0.339236
$727$	−21080.0	−1.07540	−0.537699	−	0.843137i	$-0.680706\pi$
$727$	−21080.0	−1.07540	−0.537699	+	0.843137i	$0.680706\pi$
$728$	−2088.00	−0.106300
$729$	729.000	0.0370370
$730$	0	0
$731$	27830.0	1.40811
$732$	−4104.00	−0.207224
$733$	31730.0	1.59887	0.799437	−	0.600750i	$-0.205131\pi$
$733$	31730.0	1.59887	0.799437	+	0.600750i	$0.205131\pi$
$734$	9264.00	0.465859
$735$	0	0
$736$	18560.0	0.929525
$737$	−4035.00	−0.201670
$738$	−3060.00	−0.152629
$739$	−35010.0	−1.74271	−0.871356	−	0.490652i	$-0.836759\pi$
$739$	−35010.0	−1.74271	−0.871356	+	0.490652i	$0.836759\pi$
$740$	0	0
$741$	360.000	0.0178474
$742$	26448.0	1.30854
$743$	36625.0	1.80840	0.904200	−	0.427110i	$-0.140468\pi$
$743$	36625.0	1.80840	0.904200	+	0.427110i	$0.140468\pi$
$744$	8352.00	0.411558
$745$	0	0
$746$	13364.0	0.655886
$747$	4608.00	0.225700
$748$	−7260.00	−0.354882
$749$	45182.0	2.20416
$750$	0	0
$751$	8420.00	0.409121	0.204561	−	0.978854i	$-0.434423\pi$
$751$	8420.00	0.409121	0.204561	+	0.978854i	$0.434423\pi$
$752$	3696.00	0.179228
$753$	−17325.0	−0.838457
$754$	−174.000	−0.00840412
$755$	0	0
$756$	3132.00	0.150674
$757$	14404.0	0.691575	0.345788	−	0.938313i	$-0.387612\pi$
$757$	14404.0	0.691575	0.345788	+	0.938313i	$0.387612\pi$
$758$	22540.0	1.08007
$759$	−5220.00	−0.249636
$760$	0	0
$761$	7208.00	0.343351	0.171675	−	0.985154i	$-0.445082\pi$
$761$	7208.00	0.343351	0.171675	+	0.985154i	$0.445082\pi$
$762$	2964.00	0.140911
$763$	25549.0	1.21224
$764$	8192.00	0.387927
$765$	0	0
$766$	−2032.00	−0.0958474
$767$	−1728.00	−0.0813487
$768$	−13056.0	−0.613435
$769$	−31638.0	−1.48361	−0.741805	−	0.670616i	$-0.766030\pi$
$769$	−31638.0	−1.48361	−0.741805	+	0.670616i	$0.766030\pi$
$770$	0	0
$771$	9438.00	0.440858
$772$	−9592.00	−0.447181
$773$	930.000	0.0432727	0.0216363	−	0.999766i	$-0.493112\pi$
$773$	930.000	0.0432727	0.0216363	+	0.999766i	$0.493112\pi$
$774$	−4140.00	−0.192260
$775$	0	0
$776$	−13440.0	−0.621737
$777$	3132.00	0.144607
$778$	−7454.00	−0.343495
$779$	6800.00	0.312754
$780$	0	0
$781$	−4530.00	−0.207549
$782$	−28072.0	−1.28370
$783$	783.000	0.0357371
$784$	−7968.00	−0.362974
$785$	0	0
$786$	−12042.0	−0.546468
$787$	−7188.00	−0.325571	−0.162786	−	0.986661i	$-0.552048\pi$
$787$	−7188.00	−0.325571	−0.162786	+	0.986661i	$0.552048\pi$
$788$	15864.0	0.717172
$789$	17304.0	0.780784
$790$	0	0
$791$	9077.00	0.408016
$792$	3240.00	0.145364
$793$	−1026.00	−0.0459449
$794$	−3980.00	−0.177890
$795$	0	0
$796$	−2564.00	−0.114169
$797$	31986.0	1.42158	0.710792	−	0.703402i	$-0.248337\pi$
$797$	31986.0	1.42158	0.710792	+	0.703402i	$0.248337\pi$
$798$	6960.00	0.308749
$799$	27951.0	1.23759
$800$	0	0
$801$	13725.0	0.605430
$802$	13392.0	0.589636
$803$	−5580.00	−0.245223
$804$	−3228.00	−0.141596
$805$	0	0
$806$	696.000	0.0304163
$807$	−22023.0	−0.960652
$808$	−34728.0	−1.51204
$809$	8235.00	0.357883	0.178941	−	0.983860i	$-0.442733\pi$
$809$	8235.00	0.357883	0.178941	+	0.983860i	$0.442733\pi$
$810$	0	0
$811$	−9031.00	−0.391025	−0.195513	−	0.980701i	$-0.562637\pi$
$811$	−9031.00	−0.391025	−0.195513	+	0.980701i	$0.562637\pi$
$812$	3364.00	0.145386
$813$	−42.0000	−0.00181181
$814$	1080.00	0.0465037
$815$	0	0
$816$	5808.00	0.249167
$817$	9200.00	0.393962
$818$	504.000	0.0215427
$819$	783.000	0.0334069
$820$	0	0
$821$	41318.0	1.75640	0.878202	−	0.478289i	$-0.158743\pi$
$821$	41318.0	1.75640	0.878202	+	0.478289i	$0.158743\pi$
$822$	−5508.00	−0.233715
$823$	−31150.0	−1.31934	−0.659672	−	0.751553i	$-0.729305\pi$
$823$	−31150.0	−1.31934	−0.659672	+	0.751553i	$0.729305\pi$
$824$	13344.0	0.564151
$825$	0	0
$826$	−33408.0	−1.40728
$827$	−7584.00	−0.318889	−0.159445	−	0.987207i	$-0.550970\pi$
$827$	−7584.00	−0.318889	−0.159445	+	0.987207i	$0.550970\pi$
$828$	−4176.00	−0.175273
$829$	−28316.0	−1.18632	−0.593158	−	0.805086i	$-0.702119\pi$
$829$	−28316.0	−1.18632	−0.593158	+	0.805086i	$0.702119\pi$
$830$	0	0
$831$	−11163.0	−0.465993
$832$	−1344.00	−0.0560034
$833$	−60258.0	−2.50638
$834$	9714.00	0.403319
$835$	0	0
$836$	−2400.00	−0.0992892
$837$	−3132.00	−0.129340
$838$	14836.0	0.611577
$839$	−26615.0	−1.09518	−0.547588	−	0.836748i	$-0.684454\pi$
$839$	−26615.0	−1.09518	−0.547588	+	0.836748i	$0.684454\pi$
$840$	0	0
$841$	841.000	0.0344828
$842$	22536.0	0.922377
$843$	2772.00	0.113254
$844$	−21752.0	−0.887126
$845$	0	0
$846$	−4158.00	−0.168978
$847$	32074.0	1.30115
$848$	7296.00	0.295455
$849$	−5820.00	−0.235267
$850$	0	0
$851$	−4176.00	−0.168216
$852$	−3624.00	−0.145723
$853$	−33538.0	−1.34621	−0.673106	−	0.739546i	$-0.735040\pi$
$853$	−33538.0	−1.34621	−0.673106	+	0.739546i	$0.735040\pi$
$854$	−19836.0	−0.794817
$855$	0	0
$856$	37392.0	1.49303
$857$	26394.0	1.05204	0.526022	−	0.850471i	$-0.323683\pi$
$857$	26394.0	1.05204	0.526022	+	0.850471i	$0.323683\pi$
$858$	270.000	0.0107432
$859$	−12076.0	−0.479660	−0.239830	−	0.970815i	$-0.577092\pi$
$859$	−12076.0	−0.479660	−0.239830	+	0.970815i	$0.577092\pi$
$860$	0	0
$861$	14790.0	0.585414
$862$	−23200.0	−0.916700
$863$	2450.00	0.0966384	0.0483192	−	0.998832i	$-0.484614\pi$
$863$	2450.00	0.0966384	0.0483192	+	0.998832i	$0.484614\pi$
$864$	4320.00	0.170103
$865$	0	0
$866$	−2144.00	−0.0841294
$867$	29184.0	1.14318
$868$	−13456.0	−0.526182
$869$	5220.00	0.203770
$870$	0	0
$871$	−807.000	−0.0313940
$872$	21144.0	0.821131
$873$	5040.00	0.195393
$874$	−9280.00	−0.359154
$875$	0	0
$876$	−4464.00	−0.172174
$877$	15566.0	0.599346	0.299673	−	0.954042i	$-0.403122\pi$
$877$	15566.0	0.599346	0.299673	+	0.954042i	$0.403122\pi$
$878$	−24678.0	−0.948567
$879$	−15801.0	−0.606319
$880$	0	0
$881$	34497.0	1.31922	0.659610	−	0.751608i	$-0.270721\pi$
$881$	34497.0	1.31922	0.659610	+	0.751608i	$0.270721\pi$
$882$	8964.00	0.342215
$883$	−17044.0	−0.649577	−0.324788	−	0.945787i	$-0.605293\pi$
$883$	−17044.0	−0.649577	−0.324788	+	0.945787i	$0.605293\pi$
$884$	−1452.00	−0.0552444
$885$	0	0
$886$	30526.0	1.15750
$887$	16903.0	0.639850	0.319925	−	0.947443i	$-0.396342\pi$
$887$	16903.0	0.639850	0.319925	+	0.947443i	$0.396342\pi$
$888$	2592.00	0.0979525
$889$	−14326.0	−0.540471
$890$	0	0
$891$	−1215.00	−0.0456835
$892$	11196.0	0.420258
$893$	9240.00	0.346254
$894$	18276.0	0.683715
$895$	0	0
$896$	11136.0	0.415209
$897$	−1044.00	−0.0388608
$898$	22038.0	0.818951
$899$	−3364.00	−0.124801
$900$	0	0
$901$	55176.0	2.04015
$902$	5100.00	0.188261
$903$	20010.0	0.737421
$904$	7512.00	0.276378
$905$	0	0
$906$	9456.00	0.346749
$907$	−40504.0	−1.48282	−0.741408	−	0.671055i	$-0.765841\pi$
$907$	−40504.0	−1.48282	−0.741408	+	0.671055i	$0.765841\pi$
$908$	5968.00	0.218122
$909$	13023.0	0.475188
$910$	0	0
$911$	−14783.0	−0.537632	−0.268816	−	0.963192i	$-0.586632\pi$
$911$	−14783.0	−0.537632	−0.268816	+	0.963192i	$0.586632\pi$
$912$	1920.00	0.0697122
$913$	−7680.00	−0.278391
$914$	13538.0	0.489931
$915$	0	0
$916$	−18488.0	−0.666879
$917$	58203.0	2.09600
$918$	−6534.00	−0.234917
$919$	42241.0	1.51622	0.758108	−	0.652129i	$-0.226124\pi$
$919$	42241.0	1.51622	0.758108	+	0.652129i	$0.226124\pi$
$920$	0	0
$921$	−20568.0	−0.735873
$922$	−11028.0	−0.393913
$923$	−906.000	−0.0323092
$924$	−5220.00	−0.185850
$925$	0	0
$926$	28410.0	1.00822
$927$	−5004.00	−0.177295
$928$	4640.00	0.164133
$929$	28686.0	1.01309	0.506543	−	0.862215i	$-0.330923\pi$
$929$	28686.0	1.01309	0.506543	+	0.862215i	$0.330923\pi$
$930$	0	0
$931$	−19920.0	−0.701237
$932$	16680.0	0.586236
$933$	−7341.00	−0.257592
$934$	19320.0	0.676841
$935$	0	0
$936$	648.000	0.0226288
$937$	53063.0	1.85005	0.925023	−	0.379912i	$-0.124046\pi$
$937$	53063.0	1.85005	0.925023	+	0.379912i	$0.124046\pi$
$938$	−15602.0	−0.543095
$939$	−1533.00	−0.0532775
$940$	0	0
$941$	−16542.0	−0.573065	−0.286532	−	0.958071i	$-0.592503\pi$
$941$	−16542.0	−0.573065	−0.286532	+	0.958071i	$0.592503\pi$
$942$	21264.0	0.735476
$943$	−19720.0	−0.680988
$944$	−9216.00	−0.317749
$945$	0	0
$946$	6900.00	0.237144
$947$	−30839.0	−1.05822	−0.529109	−	0.848554i	$-0.677474\pi$
$947$	−30839.0	−1.05822	−0.529109	+	0.848554i	$0.677474\pi$
$948$	4176.00	0.143070
$949$	−1116.00	−0.0381738
$950$	0	0
$951$	−21501.0	−0.733142
$952$	−84216.0	−2.86708
$953$	−46314.0	−1.57425	−0.787124	−	0.616795i	$-0.788431\pi$
$953$	−46314.0	−1.57425	−0.787124	+	0.616795i	$0.788431\pi$
$954$	−8208.00	−0.278557
$955$	0	0
$956$	−6744.00	−0.228155
$957$	−1305.00	−0.0440801
$958$	−15312.0	−0.516397
$959$	26622.0	0.896423
$960$	0	0
$961$	−16335.0	−0.548320
$962$	216.000	0.00723921
$963$	−14022.0	−0.469214
$964$	15700.0	0.524547
$965$	0	0
$966$	−20184.0	−0.672267
$967$	12904.0	0.429126	0.214563	−	0.976710i	$-0.431167\pi$
$967$	12904.0	0.429126	0.214563	+	0.976710i	$0.431167\pi$
$968$	26544.0	0.881360
$969$	14520.0	0.481372
$970$	0	0
$971$	−900.000	−0.0297450	−0.0148725	−	0.999889i	$-0.504734\pi$
$971$	−900.000	−0.0297450	−0.0148725	+	0.999889i	$0.504734\pi$
$972$	−972.000	−0.0320750
$973$	−46951.0	−1.54695
$974$	31936.0	1.05061
$975$	0	0
$976$	−5472.00	−0.179462
$977$	20376.0	0.667232	0.333616	−	0.942709i	$-0.391731\pi$
$977$	20376.0	0.667232	0.333616	+	0.942709i	$0.391731\pi$
$978$	4608.00	0.150662
$979$	−22875.0	−0.746770
$980$	0	0
$981$	−7929.00	−0.258057
$982$	8472.00	0.275308
$983$	−13456.0	−0.436602	−0.218301	−	0.975881i	$-0.570051\pi$
$983$	−13456.0	−0.436602	−0.218301	+	0.975881i	$0.570051\pi$
$984$	12240.0	0.396542
$985$	0	0
$986$	−7018.00	−0.226672
$987$	20097.0	0.648120
$988$	−480.000	−0.0154563
$989$	−26680.0	−0.857811
$990$	0	0
$991$	−27245.0	−0.873326	−0.436663	−	0.899625i	$-0.643840\pi$
$991$	−27245.0	−0.873326	−0.436663	+	0.899625i	$0.643840\pi$
$992$	−18560.0	−0.594033
$993$	−26886.0	−0.859216
$994$	−17516.0	−0.558927
$995$	0	0
$996$	−6144.00	−0.195462
$997$	1552.00	0.0493002	0.0246501	−	0.999696i	$-0.492153\pi$
$997$	1552.00	0.0493002	0.0246501	+	0.999696i	$0.492153\pi$
$998$	−33882.0	−1.07467
$999$	−972.000	−0.0307835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2175.4.a.c.1.1		1
5.4	even	2		435.4.a.a.1.1	✓	1
15.14	odd	2		1305.4.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.a.1.1	✓	1	5.4	even	2
1305.4.a.d.1.1		1	15.14	odd	2
2175.4.a.c.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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2175 = 3 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2175.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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