LMFDB - Embedded newform 1815.4.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1815,4,Mod(1,1815)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1815, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1815.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1815 = 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1815.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:	$107.088466660$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1815.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-3.00000 q^{3} -8.00000 q^{4} -5.00000 q^{5} -2.00000 q^{7} +9.00000 q^{9} +O(q^{10})$

$q-3.00000 q^{3} -8.00000 q^{4} -5.00000 q^{5} -2.00000 q^{7} +9.00000 q^{9} +24.0000 q^{12} +22.0000 q^{13} +15.0000 q^{15} +64.0000 q^{16} -72.0000 q^{17} -122.000 q^{19} +40.0000 q^{20} +6.00000 q^{21} +72.0000 q^{23} +25.0000 q^{25} -27.0000 q^{27} +16.0000 q^{28} -96.0000 q^{29} -112.000 q^{31} +10.0000 q^{35} -72.0000 q^{36} +266.000 q^{37} -66.0000 q^{39} +96.0000 q^{41} +382.000 q^{43} -45.0000 q^{45} +360.000 q^{47} -192.000 q^{48} -339.000 q^{49} +216.000 q^{51} -176.000 q^{52} +318.000 q^{53} +366.000 q^{57} +660.000 q^{59} -120.000 q^{60} +430.000 q^{61} -18.0000 q^{63} -512.000 q^{64} -110.000 q^{65} +380.000 q^{67} +576.000 q^{68} -216.000 q^{69} +168.000 q^{71} -218.000 q^{73} -75.0000 q^{75} +976.000 q^{76} +706.000 q^{79} -320.000 q^{80} +81.0000 q^{81} -1068.00 q^{83} -48.0000 q^{84} +360.000 q^{85} +288.000 q^{87} -6.00000 q^{89} -44.0000 q^{91} -576.000 q^{92} +336.000 q^{93} +610.000 q^{95} +686.000 q^{97} +O(q^{100})$

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 $

$2$	0	0		−	1.00000i	$-0.5\pi$
$2$	0	0			1.00000i	$0.5\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−8.00000	−1.00000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	0	0
$7$	−2.00000	−0.107990	−0.0539949	−	0.998541i	$-0.517195\pi$
$7$	−2.00000	−0.107990	−0.0539949	+	0.998541i	$0.517195\pi$
$8$	0	0
$9$	9.00000	0.333333
$10$	0	0
$11$	0	0
$11$	0	0
$12$	24.0000	0.577350
$13$	22.0000	0.469362	0.234681	−	0.972072i	$-0.424595\pi$
$13$	22.0000	0.469362	0.234681	+	0.972072i	$0.424595\pi$
$14$	0	0
$15$	15.0000	0.258199
$16$	64.0000	1.00000
$17$	−72.0000	−1.02721	−0.513605	−	0.858027i	$-0.671690\pi$
$17$	−72.0000	−1.02721	−0.513605	+	0.858027i	$0.671690\pi$
$18$	0	0
$19$	−122.000	−1.47309	−0.736545	−	0.676388i	$-0.763544\pi$
$19$	−122.000	−1.47309	−0.736545	+	0.676388i	$0.763544\pi$
$20$	40.0000	0.447214
$21$	6.00000	0.0623480
$22$	0	0
$23$	72.0000	0.652741	0.326370	−	0.945242i	$-0.394174\pi$
$23$	72.0000	0.652741	0.326370	+	0.945242i	$0.394174\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	0	0
$27$	−27.0000	−0.192450
$28$	16.0000	0.107990
$29$	−96.0000	−0.614716	−0.307358	−	0.951594i	$-0.599445\pi$
$29$	−96.0000	−0.614716	−0.307358	+	0.951594i	$0.599445\pi$
$30$	0	0
$31$	−112.000	−0.648897	−0.324448	−	0.945903i	$-0.605179\pi$
$31$	−112.000	−0.648897	−0.324448	+	0.945903i	$0.605179\pi$
$32$	0	0
$33$	0	0
$34$	0	0
$35$	10.0000	0.0482945
$36$	−72.0000	−0.333333
$37$	266.000	1.18190	0.590948	−	0.806710i	$-0.298754\pi$
$37$	266.000	1.18190	0.590948	+	0.806710i	$0.298754\pi$
$38$	0	0
$39$	−66.0000	−0.270986
$40$	0	0
$41$	96.0000	0.365675	0.182838	−	0.983143i	$-0.441472\pi$
$41$	96.0000	0.365675	0.182838	+	0.983143i	$0.441472\pi$
$42$	0	0
$43$	382.000	1.35475	0.677377	−	0.735636i	$-0.263116\pi$
$43$	382.000	1.35475	0.677377	+	0.735636i	$0.263116\pi$
$44$	0	0
$45$	−45.0000	−0.149071
$46$	0	0
$47$	360.000	1.11726	0.558632	−	0.829416i	$-0.311326\pi$
$47$	360.000	1.11726	0.558632	+	0.829416i	$0.311326\pi$
$48$	−192.000	−0.577350
$49$	−339.000	−0.988338
$50$	0	0
$51$	216.000	0.593060
$52$	−176.000	−0.469362
$53$	318.000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	318.000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	366.000	0.850489
$58$	0	0
$59$	660.000	1.45635	0.728175	−	0.685391i	$-0.240369\pi$
$59$	660.000	1.45635	0.728175	+	0.685391i	$0.240369\pi$
$60$	−120.000	−0.258199
$61$	430.000	0.902555	0.451278	−	0.892384i	$-0.350968\pi$
$61$	430.000	0.902555	0.451278	+	0.892384i	$0.350968\pi$
$62$	0	0
$63$	−18.0000	−0.0359966
$64$	−512.000	−1.00000
$65$	−110.000	−0.209905
$66$	0	0
$67$	380.000	0.692901	0.346451	−	0.938068i	$-0.387387\pi$
$67$	380.000	0.692901	0.346451	+	0.938068i	$0.387387\pi$
$68$	576.000	1.02721
$69$	−216.000	−0.376860
$70$	0	0
$71$	168.000	0.280816	0.140408	−	0.990094i	$-0.455159\pi$
$71$	168.000	0.280816	0.140408	+	0.990094i	$0.455159\pi$
$72$	0	0
$73$	−218.000	−0.349520	−0.174760	−	0.984611i	$-0.555915\pi$
$73$	−218.000	−0.349520	−0.174760	+	0.984611i	$0.555915\pi$
$74$	0	0
$75$	−75.0000	−0.115470
$76$	976.000	1.47309
$77$	0	0
$78$	0	0
$79$	706.000	1.00546	0.502729	−	0.864444i	$-0.332329\pi$
$79$	706.000	1.00546	0.502729	+	0.864444i	$0.332329\pi$
$80$	−320.000	−0.447214
$81$	81.0000	0.111111
$82$	0	0
$83$	−1068.00	−1.41239	−0.706194	−	0.708018i	$-0.749589\pi$
$83$	−1068.00	−1.41239	−0.706194	+	0.708018i	$0.749589\pi$
$84$	−48.0000	−0.0623480
$85$	360.000	0.459382
$86$	0	0
$87$	288.000	0.354906
$88$	0	0
$89$	−6.00000	−0.00714605	−0.00357303	−	0.999994i	$-0.501137\pi$
$89$	−6.00000	−0.00714605	−0.00357303	+	0.999994i	$0.501137\pi$
$90$	0	0
$91$	−44.0000	−0.0506863
$92$	−576.000	−0.652741
$93$	336.000	0.374641
$94$	0	0
$95$	610.000	0.658786
$96$	0	0
$97$	686.000	0.718070	0.359035	−	0.933324i	$-0.383106\pi$
$97$	686.000	0.718070	0.359035	+	0.933324i	$0.383106\pi$
$98$	0	0
$99$	0	0
$100$	−200.000	−0.200000
$101$	960.000	0.945778	0.472889	−	0.881122i	$-0.343211\pi$
$101$	960.000	0.945778	0.472889	+	0.881122i	$0.343211\pi$
$102$	0	0
$103$	−844.000	−0.807396	−0.403698	−	0.914892i	$-0.632275\pi$
$103$	−844.000	−0.807396	−0.403698	+	0.914892i	$0.632275\pi$
$104$	0	0
$105$	−30.0000	−0.0278829
$106$	0	0
$107$	−2172.00	−1.96238	−0.981192	−	0.193033i	$-0.938168\pi$
$107$	−2172.00	−1.96238	−0.981192	+	0.193033i	$0.938168\pi$
$108$	216.000	0.192450
$109$	−614.000	−0.539546	−0.269773	−	0.962924i	$-0.586949\pi$
$109$	−614.000	−0.539546	−0.269773	+	0.962924i	$0.586949\pi$
$110$	0	0
$111$	−798.000	−0.682368
$112$	−128.000	−0.107990
$113$	1254.00	1.04395	0.521975	−	0.852961i	$-0.325195\pi$
$113$	1254.00	1.04395	0.521975	+	0.852961i	$0.325195\pi$
$114$	0	0
$115$	−360.000	−0.291915
$116$	768.000	0.614716
$117$	198.000	0.156454
$118$	0	0
$119$	144.000	0.110928
$120$	0	0
$121$	0	0
$122$	0	0
$123$	−288.000	−0.211123
$124$	896.000	0.648897
$125$	−125.000	−0.0894427
$126$	0	0
$127$	−1394.00	−0.973996	−0.486998	−	0.873403i	$-0.661908\pi$
$127$	−1394.00	−0.973996	−0.486998	+	0.873403i	$0.661908\pi$
$128$	0	0
$129$	−1146.00	−0.782168
$130$	0	0
$131$	252.000	0.168071	0.0840357	−	0.996463i	$-0.473219\pi$
$131$	252.000	0.168071	0.0840357	+	0.996463i	$0.473219\pi$
$132$	0	0
$133$	244.000	0.159079
$134$	0	0
$135$	135.000	0.0860663
$136$	0	0
$137$	−1050.00	−0.654800	−0.327400	−	0.944886i	$-0.606172\pi$
$137$	−1050.00	−0.654800	−0.327400	+	0.944886i	$0.606172\pi$
$138$	0	0
$139$	−1874.00	−1.14353	−0.571765	−	0.820418i	$-0.693741\pi$
$139$	−1874.00	−1.14353	−0.571765	+	0.820418i	$0.693741\pi$
$140$	−80.0000	−0.0482945
$141$	−1080.00	−0.645053
$142$	0	0
$143$	0	0
$144$	576.000	0.333333
$145$	480.000	0.274909
$146$	0	0
$147$	1017.00	0.570617
$148$	−2128.00	−1.18190
$149$	−1476.00	−0.811534	−0.405767	−	0.913976i	$-0.632996\pi$
$149$	−1476.00	−0.811534	−0.405767	+	0.913976i	$0.632996\pi$
$150$	0	0
$151$	−1478.00	−0.796543	−0.398271	−	0.917268i	$-0.630390\pi$
$151$	−1478.00	−0.796543	−0.398271	+	0.917268i	$0.630390\pi$
$152$	0	0
$153$	−648.000	−0.342403
$154$	0	0
$155$	560.000	0.290195
$156$	528.000	0.270986
$157$	854.000	0.434119	0.217059	−	0.976158i	$-0.430354\pi$
$157$	854.000	0.434119	0.217059	+	0.976158i	$0.430354\pi$
$158$	0	0
$159$	−954.000	−0.475831
$160$	0	0
$161$	−144.000	−0.0704894
$162$	0	0
$163$	1544.00	0.741935	0.370968	−	0.928646i	$-0.379026\pi$
$163$	1544.00	0.741935	0.370968	+	0.928646i	$0.379026\pi$
$164$	−768.000	−0.365675
$165$	0	0
$166$	0	0
$167$	−240.000	−0.111208	−0.0556041	−	0.998453i	$-0.517708\pi$
$167$	−240.000	−0.111208	−0.0556041	+	0.998453i	$0.517708\pi$
$168$	0	0
$169$	−1713.00	−0.779700
$170$	0	0
$171$	−1098.00	−0.491030
$172$	−3056.00	−1.35475
$173$	−2532.00	−1.11274	−0.556371	−	0.830934i	$-0.687807\pi$
$173$	−2532.00	−1.11274	−0.556371	+	0.830934i	$0.687807\pi$
$174$	0	0
$175$	−50.0000	−0.0215980
$176$	0	0
$177$	−1980.00	−0.840824
$178$	0	0
$179$	1092.00	0.455977	0.227989	−	0.973664i	$-0.426785\pi$
$179$	1092.00	0.455977	0.227989	+	0.973664i	$0.426785\pi$
$180$	360.000	0.149071
$181$	−2290.00	−0.940411	−0.470205	−	0.882557i	$-0.655820\pi$
$181$	−2290.00	−0.940411	−0.470205	+	0.882557i	$0.655820\pi$
$182$	0	0
$183$	−1290.00	−0.521090
$184$	0	0
$185$	−1330.00	−0.528560
$186$	0	0
$187$	0	0
$188$	−2880.00	−1.11726
$189$	54.0000	0.0207827
$190$	0	0
$191$	−4392.00	−1.66384	−0.831921	−	0.554894i	$-0.812759\pi$
$191$	−4392.00	−1.66384	−0.831921	+	0.554894i	$0.812759\pi$
$192$	1536.00	0.577350
$193$	5074.00	1.89241	0.946203	−	0.323572i	$-0.104884\pi$
$193$	5074.00	1.89241	0.946203	+	0.323572i	$0.104884\pi$
$194$	0	0
$195$	330.000	0.121189
$196$	2712.00	0.988338
$197$	−1692.00	−0.611929	−0.305964	−	0.952043i	$-0.598979\pi$
$197$	−1692.00	−0.611929	−0.305964	+	0.952043i	$0.598979\pi$
$198$	0	0
$199$	4664.00	1.66142	0.830709	−	0.556707i	$-0.187935\pi$
$199$	4664.00	1.66142	0.830709	+	0.556707i	$0.187935\pi$
$200$	0	0
$201$	−1140.00	−0.400047
$202$	0	0
$203$	192.000	0.0663830
$204$	−1728.00	−0.593060
$205$	−480.000	−0.163535
$206$	0	0
$207$	648.000	0.217580
$208$	1408.00	0.469362
$209$	0	0
$210$	0	0
$211$	1870.00	0.610124	0.305062	−	0.952333i	$-0.401323\pi$
$211$	1870.00	0.610124	0.305062	+	0.952333i	$0.401323\pi$
$212$	−2544.00	−0.824163
$213$	−504.000	−0.162129
$214$	0	0
$215$	−1910.00	−0.605865
$216$	0	0
$217$	224.000	0.0700742
$218$	0	0
$219$	654.000	0.201796
$220$	0	0
$221$	−1584.00	−0.482133
$222$	0	0
$223$	2300.00	0.690670	0.345335	−	0.938479i	$-0.387765\pi$
$223$	2300.00	0.690670	0.345335	+	0.938479i	$0.387765\pi$
$224$	0	0
$225$	225.000	0.0666667
$226$	0	0
$227$	1332.00	0.389462	0.194731	−	0.980857i	$-0.437617\pi$
$227$	1332.00	0.389462	0.194731	+	0.980857i	$0.437617\pi$
$228$	−2928.00	−0.850489
$229$	−6022.00	−1.73775	−0.868875	−	0.495031i	$-0.835157\pi$
$229$	−6022.00	−1.73775	−0.868875	+	0.495031i	$0.835157\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	4716.00	1.32599	0.662994	−	0.748624i	$-0.269285\pi$
$233$	4716.00	1.32599	0.662994	+	0.748624i	$0.269285\pi$
$234$	0	0
$235$	−1800.00	−0.499656
$236$	−5280.00	−1.45635
$237$	−2118.00	−0.580502
$238$	0	0
$239$	6420.00	1.73755	0.868777	−	0.495204i	$-0.164907\pi$
$239$	6420.00	1.73755	0.868777	+	0.495204i	$0.164907\pi$
$240$	960.000	0.258199
$241$	−3302.00	−0.882575	−0.441287	−	0.897366i	$-0.645478\pi$
$241$	−3302.00	−0.882575	−0.441287	+	0.897366i	$0.645478\pi$
$242$	0	0
$243$	−243.000	−0.0641500
$244$	−3440.00	−0.902555
$245$	1695.00	0.441998
$246$	0	0
$247$	−2684.00	−0.691412
$248$	0	0
$249$	3204.00	0.815443
$250$	0	0
$251$	732.000	0.184077	0.0920387	−	0.995755i	$-0.470662\pi$
$251$	732.000	0.184077	0.0920387	+	0.995755i	$0.470662\pi$
$252$	144.000	0.0359966
$253$	0	0
$254$	0	0
$255$	−1080.00	−0.265224
$256$	4096.00	1.00000
$257$	−3438.00	−0.834461	−0.417231	−	0.908801i	$-0.636999\pi$
$257$	−3438.00	−0.834461	−0.417231	+	0.908801i	$0.636999\pi$
$258$	0	0
$259$	−532.000	−0.127633
$260$	880.000	0.209905
$261$	−864.000	−0.204905
$262$	0	0
$263$	696.000	0.163183	0.0815916	−	0.996666i	$-0.474000\pi$
$263$	696.000	0.163183	0.0815916	+	0.996666i	$0.474000\pi$
$264$	0	0
$265$	−1590.00	−0.368577
$266$	0	0
$267$	18.0000	0.00412578
$268$	−3040.00	−0.692901
$269$	−7338.00	−1.66322	−0.831609	−	0.555361i	$-0.812580\pi$
$269$	−7338.00	−1.66322	−0.831609	+	0.555361i	$0.812580\pi$
$270$	0	0
$271$	−5114.00	−1.14632	−0.573161	−	0.819443i	$-0.694283\pi$
$271$	−5114.00	−1.14632	−0.573161	+	0.819443i	$0.694283\pi$
$272$	−4608.00	−1.02721
$273$	132.000	0.0292637
$274$	0	0
$275$	0	0
$276$	1728.00	0.376860
$277$	−986.000	−0.213874	−0.106937	−	0.994266i	$-0.534104\pi$
$277$	−986.000	−0.213874	−0.106937	+	0.994266i	$0.534104\pi$
$278$	0	0
$279$	−1008.00	−0.216299
$280$	0	0
$281$	−3312.00	−0.703122	−0.351561	−	0.936165i	$-0.614349\pi$
$281$	−3312.00	−0.703122	−0.351561	+	0.936165i	$0.614349\pi$
$282$	0	0
$283$	−4298.00	−0.902790	−0.451395	−	0.892324i	$-0.649073\pi$
$283$	−4298.00	−0.902790	−0.451395	+	0.892324i	$0.649073\pi$
$284$	−1344.00	−0.280816
$285$	−1830.00	−0.380350
$286$	0	0
$287$	−192.000	−0.0394892
$288$	0	0
$289$	271.000	0.0551598
$290$	0	0
$291$	−2058.00	−0.414578
$292$	1744.00	0.349520
$293$	−2736.00	−0.545525	−0.272763	−	0.962081i	$-0.587937\pi$
$293$	−2736.00	−0.545525	−0.272763	+	0.962081i	$0.587937\pi$
$294$	0	0
$295$	−3300.00	−0.651300
$296$	0	0
$297$	0	0
$298$	0	0
$299$	1584.00	0.306372
$300$	600.000	0.115470
$301$	−764.000	−0.146300
$302$	0	0
$303$	−2880.00	−0.546045
$304$	−7808.00	−1.47309
$305$	−2150.00	−0.403635
$306$	0	0
$307$	250.000	0.0464764	0.0232382	−	0.999730i	$-0.492602\pi$
$307$	250.000	0.0464764	0.0232382	+	0.999730i	$0.492602\pi$
$308$	0	0
$309$	2532.00	0.466150
$310$	0	0
$311$	7248.00	1.32153	0.660766	−	0.750592i	$-0.270232\pi$
$311$	7248.00	1.32153	0.660766	+	0.750592i	$0.270232\pi$
$312$	0	0
$313$	−7786.00	−1.40604	−0.703020	−	0.711170i	$-0.748166\pi$
$313$	−7786.00	−1.40604	−0.703020	+	0.711170i	$0.748166\pi$
$314$	0	0
$315$	90.0000	0.0160982
$316$	−5648.00	−1.00546
$317$	−4230.00	−0.749465	−0.374733	−	0.927133i	$-0.622265\pi$
$317$	−4230.00	−0.749465	−0.374733	+	0.927133i	$0.622265\pi$
$318$	0	0
$319$	0	0
$320$	2560.00	0.447214
$321$	6516.00	1.13298
$322$	0	0
$323$	8784.00	1.51317
$324$	−648.000	−0.111111
$325$	550.000	0.0938723
$326$	0	0
$327$	1842.00	0.311507
$328$	0	0
$329$	−720.000	−0.120653
$330$	0	0
$331$	7736.00	1.28462	0.642310	−	0.766445i	$-0.277976\pi$
$331$	7736.00	1.28462	0.642310	+	0.766445i	$0.277976\pi$
$332$	8544.00	1.41239
$333$	2394.00	0.393965
$334$	0	0
$335$	−1900.00	−0.309875
$336$	384.000	0.0623480
$337$	2014.00	0.325548	0.162774	−	0.986663i	$-0.447956\pi$
$337$	2014.00	0.325548	0.162774	+	0.986663i	$0.447956\pi$
$338$	0	0
$339$	−3762.00	−0.602725
$340$	−2880.00	−0.459382
$341$	0	0
$342$	0	0
$343$	1364.00	0.214720
$344$	0	0
$345$	1080.00	0.168537
$346$	0	0
$347$	−7692.00	−1.18999	−0.594997	−	0.803728i	$-0.702847\pi$
$347$	−7692.00	−1.18999	−0.594997	+	0.803728i	$0.702847\pi$
$348$	−2304.00	−0.354906
$349$	1750.00	0.268411	0.134205	−	0.990954i	$-0.457152\pi$
$349$	1750.00	0.268411	0.134205	+	0.990954i	$0.457152\pi$
$350$	0	0
$351$	−594.000	−0.0903287
$352$	0	0
$353$	8034.00	1.21135	0.605675	−	0.795712i	$-0.292903\pi$
$353$	8034.00	1.21135	0.605675	+	0.795712i	$0.292903\pi$
$354$	0	0
$355$	−840.000	−0.125585
$356$	48.0000	0.00714605
$357$	−432.000	−0.0640444
$358$	0	0
$359$	−2304.00	−0.338720	−0.169360	−	0.985554i	$-0.554170\pi$
$359$	−2304.00	−0.338720	−0.169360	+	0.985554i	$0.554170\pi$
$360$	0	0
$361$	8025.00	1.17000
$362$	0	0
$363$	0	0
$364$	352.000	0.0506863
$365$	1090.00	0.156310
$366$	0	0
$367$	−2356.00	−0.335101	−0.167551	−	0.985863i	$-0.553586\pi$
$367$	−2356.00	−0.335101	−0.167551	+	0.985863i	$0.553586\pi$
$368$	4608.00	0.652741
$369$	864.000	0.121892
$370$	0	0
$371$	−636.000	−0.0890013
$372$	−2688.00	−0.374641
$373$	8602.00	1.19409	0.597044	−	0.802209i	$-0.296342\pi$
$373$	8602.00	1.19409	0.597044	+	0.802209i	$0.296342\pi$
$374$	0	0
$375$	375.000	0.0516398
$376$	0	0
$377$	−2112.00	−0.288524
$378$	0	0
$379$	−12016.0	−1.62855	−0.814275	−	0.580479i	$-0.802865\pi$
$379$	−12016.0	−1.62855	−0.814275	+	0.580479i	$0.802865\pi$
$380$	−4880.00	−0.658786
$381$	4182.00	0.562337
$382$	0	0
$383$	1728.00	0.230540	0.115270	−	0.993334i	$-0.463227\pi$
$383$	1728.00	0.230540	0.115270	+	0.993334i	$0.463227\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	3438.00	0.451585
$388$	−5488.00	−0.718070
$389$	8010.00	1.04402	0.522009	−	0.852940i	$-0.325183\pi$
$389$	8010.00	1.04402	0.522009	+	0.852940i	$0.325183\pi$
$390$	0	0
$391$	−5184.00	−0.670502
$392$	0	0
$393$	−756.000	−0.0970360
$394$	0	0
$395$	−3530.00	−0.449655
$396$	0	0
$397$	−10150.0	−1.28316	−0.641579	−	0.767057i	$-0.721720\pi$
$397$	−10150.0	−1.28316	−0.641579	+	0.767057i	$0.721720\pi$
$398$	0	0
$399$	−732.000	−0.0918442
$400$	1600.00	0.200000
$401$	11862.0	1.47721	0.738604	−	0.674140i	$-0.235486\pi$
$401$	11862.0	1.47721	0.738604	+	0.674140i	$0.235486\pi$
$402$	0	0
$403$	−2464.00	−0.304567
$404$	−7680.00	−0.945778
$405$	−405.000	−0.0496904
$406$	0	0
$407$	0	0
$408$	0	0
$409$	682.000	0.0824517	0.0412258	−	0.999150i	$-0.486874\pi$
$409$	682.000	0.0824517	0.0412258	+	0.999150i	$0.486874\pi$
$410$	0	0
$411$	3150.00	0.378049
$412$	6752.00	0.807396
$413$	−1320.00	−0.157271
$414$	0	0
$415$	5340.00	0.631639
$416$	0	0
$417$	5622.00	0.660217
$418$	0	0
$419$	10836.0	1.26342	0.631710	−	0.775205i	$-0.282353\pi$
$419$	10836.0	1.26342	0.631710	+	0.775205i	$0.282353\pi$
$420$	240.000	0.0278829
$421$	12350.0	1.42970	0.714848	−	0.699280i	$-0.246496\pi$
$421$	12350.0	1.42970	0.714848	+	0.699280i	$0.246496\pi$
$422$	0	0
$423$	3240.00	0.372421
$424$	0	0
$425$	−1800.00	−0.205442
$426$	0	0
$427$	−860.000	−0.0974668
$428$	17376.0	1.96238
$429$	0	0
$430$	0	0
$431$	5940.00	0.663851	0.331925	−	0.943306i	$-0.392302\pi$
$431$	5940.00	0.663851	0.331925	+	0.943306i	$0.392302\pi$
$432$	−1728.00	−0.192450
$433$	−12898.0	−1.43150	−0.715749	−	0.698358i	$-0.753914\pi$
$433$	−12898.0	−1.43150	−0.715749	+	0.698358i	$0.753914\pi$
$434$	0	0
$435$	−1440.00	−0.158719
$436$	4912.00	0.539546
$437$	−8784.00	−0.961546
$438$	0	0
$439$	−11450.0	−1.24483	−0.622413	−	0.782689i	$-0.713848\pi$
$439$	−11450.0	−1.24483	−0.622413	+	0.782689i	$0.713848\pi$
$440$	0	0
$441$	−3051.00	−0.329446
$442$	0	0
$443$	2100.00	0.225224	0.112612	−	0.993639i	$-0.464078\pi$
$443$	2100.00	0.225224	0.112612	+	0.993639i	$0.464078\pi$
$444$	6384.00	0.682368
$445$	30.0000	0.00319581
$446$	0	0
$447$	4428.00	0.468540
$448$	1024.00	0.107990
$449$	−11934.0	−1.25434	−0.627172	−	0.778881i	$-0.715788\pi$
$449$	−11934.0	−1.25434	−0.627172	+	0.778881i	$0.715788\pi$
$450$	0	0
$451$	0	0
$452$	−10032.0	−1.04395
$453$	4434.00	0.459884
$454$	0	0
$455$	220.000	0.0226676
$456$	0	0
$457$	−578.000	−0.0591635	−0.0295817	−	0.999562i	$-0.509418\pi$
$457$	−578.000	−0.0591635	−0.0295817	+	0.999562i	$0.509418\pi$
$458$	0	0
$459$	1944.00	0.197687
$460$	2880.00	0.291915
$461$	324.000	0.0327336	0.0163668	−	0.999866i	$-0.494790\pi$
$461$	324.000	0.0327336	0.0163668	+	0.999866i	$0.494790\pi$
$462$	0	0
$463$	−11788.0	−1.18323	−0.591614	−	0.806221i	$-0.701509\pi$
$463$	−11788.0	−1.18323	−0.591614	+	0.806221i	$0.701509\pi$
$464$	−6144.00	−0.614716
$465$	−1680.00	−0.167544
$466$	0	0
$467$	−14484.0	−1.43520	−0.717601	−	0.696454i	$-0.754760\pi$
$467$	−14484.0	−1.43520	−0.717601	+	0.696454i	$0.754760\pi$
$468$	−1584.00	−0.156454
$469$	−760.000	−0.0748263
$470$	0	0
$471$	−2562.00	−0.250638
$472$	0	0
$473$	0	0
$474$	0	0
$475$	−3050.00	−0.294618
$476$	−1152.00	−0.110928
$477$	2862.00	0.274721
$478$	0	0
$479$	3084.00	0.294179	0.147089	−	0.989123i	$-0.453010\pi$
$479$	3084.00	0.294179	0.147089	+	0.989123i	$0.453010\pi$
$480$	0	0
$481$	5852.00	0.554736
$482$	0	0
$483$	432.000	0.0406971
$484$	0	0
$485$	−3430.00	−0.321130
$486$	0	0
$487$	−5584.00	−0.519579	−0.259790	−	0.965665i	$-0.583653\pi$
$487$	−5584.00	−0.519579	−0.259790	+	0.965665i	$0.583653\pi$
$488$	0	0
$489$	−4632.00	−0.428356
$490$	0	0
$491$	10752.0	0.988250	0.494125	−	0.869391i	$-0.335488\pi$
$491$	10752.0	0.988250	0.494125	+	0.869391i	$0.335488\pi$
$492$	2304.00	0.211123
$493$	6912.00	0.631442
$494$	0	0
$495$	0	0
$496$	−7168.00	−0.648897
$497$	−336.000	−0.0303253
$498$	0	0
$499$	−13372.0	−1.19963	−0.599813	−	0.800141i	$-0.704758\pi$
$499$	−13372.0	−1.19963	−0.599813	+	0.800141i	$0.704758\pi$
$500$	1000.00	0.0894427
$501$	720.000	0.0642060
$502$	0	0
$503$	−9072.00	−0.804176	−0.402088	−	0.915601i	$-0.631715\pi$
$503$	−9072.00	−0.804176	−0.402088	+	0.915601i	$0.631715\pi$
$504$	0	0
$505$	−4800.00	−0.422965
$506$	0	0
$507$	5139.00	0.450160
$508$	11152.0	0.973996
$509$	−14586.0	−1.27016	−0.635082	−	0.772445i	$-0.719034\pi$
$509$	−14586.0	−1.27016	−0.635082	+	0.772445i	$0.719034\pi$
$510$	0	0
$511$	436.000	0.0377446
$512$	0	0
$513$	3294.00	0.283496
$514$	0	0
$515$	4220.00	0.361078
$516$	9168.00	0.782168
$517$	0	0
$518$	0	0
$519$	7596.00	0.642442
$520$	0	0
$521$	2718.00	0.228556	0.114278	−	0.993449i	$-0.463545\pi$
$521$	2718.00	0.228556	0.114278	+	0.993449i	$0.463545\pi$
$522$	0	0
$523$	2086.00	0.174406	0.0872031	−	0.996191i	$-0.472207\pi$
$523$	2086.00	0.174406	0.0872031	+	0.996191i	$0.472207\pi$
$524$	−2016.00	−0.168071
$525$	150.000	0.0124696
$526$	0	0
$527$	8064.00	0.666553
$528$	0	0
$529$	−6983.00	−0.573929
$530$	0	0
$531$	5940.00	0.485450
$532$	−1952.00	−0.159079
$533$	2112.00	0.171634
$534$	0	0
$535$	10860.0	0.877605
$536$	0	0
$537$	−3276.00	−0.263259
$538$	0	0
$539$	0	0
$540$	−1080.00	−0.0860663
$541$	−13838.0	−1.09971	−0.549854	−	0.835261i	$-0.685317\pi$
$541$	−13838.0	−1.09971	−0.549854	+	0.835261i	$0.685317\pi$
$542$	0	0
$543$	6870.00	0.542946
$544$	0	0
$545$	3070.00	0.241292
$546$	0	0
$547$	−23546.0	−1.84050	−0.920251	−	0.391329i	$-0.872015\pi$
$547$	−23546.0	−1.84050	−0.920251	+	0.391329i	$0.872015\pi$
$548$	8400.00	0.654800
$549$	3870.00	0.300852
$550$	0	0
$551$	11712.0	0.905532
$552$	0	0
$553$	−1412.00	−0.108579
$554$	0	0
$555$	3990.00	0.305164
$556$	14992.0	1.14353
$557$	−15624.0	−1.18853	−0.594264	−	0.804270i	$-0.702557\pi$
$557$	−15624.0	−1.18853	−0.594264	+	0.804270i	$0.702557\pi$
$558$	0	0
$559$	8404.00	0.635870
$560$	640.000	0.0482945
$561$	0	0
$562$	0	0
$563$	−2400.00	−0.179659	−0.0898294	−	0.995957i	$-0.528632\pi$
$563$	−2400.00	−0.179659	−0.0898294	+	0.995957i	$0.528632\pi$
$564$	8640.00	0.645053
$565$	−6270.00	−0.466869
$566$	0	0
$567$	−162.000	−0.0119989
$568$	0	0
$569$	18300.0	1.34829	0.674144	−	0.738600i	$-0.264513\pi$
$569$	18300.0	1.34829	0.674144	+	0.738600i	$0.264513\pi$
$570$	0	0
$571$	−25454.0	−1.86553	−0.932764	−	0.360487i	$-0.882611\pi$
$571$	−25454.0	−1.86553	−0.932764	+	0.360487i	$0.882611\pi$
$572$	0	0
$573$	13176.0	0.960620
$574$	0	0
$575$	1800.00	0.130548
$576$	−4608.00	−0.333333
$577$	19802.0	1.42871	0.714357	−	0.699781i	$-0.246719\pi$
$577$	19802.0	1.42871	0.714357	+	0.699781i	$0.246719\pi$
$578$	0	0
$579$	−15222.0	−1.09258
$580$	−3840.00	−0.274909
$581$	2136.00	0.152524
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−990.000	−0.0699683
$586$	0	0
$587$	18396.0	1.29350	0.646750	−	0.762702i	$-0.276128\pi$
$587$	18396.0	1.29350	0.646750	+	0.762702i	$0.276128\pi$
$588$	−8136.00	−0.570617
$589$	13664.0	0.955883
$590$	0	0
$591$	5076.00	0.353297
$592$	17024.0	1.18190
$593$	−15012.0	−1.03958	−0.519788	−	0.854295i	$-0.673989\pi$
$593$	−15012.0	−1.03958	−0.519788	+	0.854295i	$0.673989\pi$
$594$	0	0
$595$	−720.000	−0.0496086
$596$	11808.0	0.811534
$597$	−13992.0	−0.959220
$598$	0	0
$599$	15408.0	1.05101	0.525504	−	0.850791i	$-0.323877\pi$
$599$	15408.0	1.05101	0.525504	+	0.850791i	$0.323877\pi$
$600$	0	0
$601$	1558.00	0.105744	0.0528720	−	0.998601i	$-0.483162\pi$
$601$	1558.00	0.105744	0.0528720	+	0.998601i	$0.483162\pi$
$602$	0	0
$603$	3420.00	0.230967
$604$	11824.0	0.796543
$605$	0	0
$606$	0	0
$607$	−22970.0	−1.53595	−0.767977	−	0.640478i	$-0.778736\pi$
$607$	−22970.0	−1.53595	−0.767977	+	0.640478i	$0.778736\pi$
$608$	0	0
$609$	−576.000	−0.0383263
$610$	0	0
$611$	7920.00	0.524401
$612$	5184.00	0.342403
$613$	11482.0	0.756531	0.378266	−	0.925697i	$-0.376521\pi$
$613$	11482.0	0.756531	0.378266	+	0.925697i	$0.376521\pi$
$614$	0	0
$615$	1440.00	0.0944169
$616$	0	0
$617$	246.000	0.0160512	0.00802560	−	0.999968i	$-0.497445\pi$
$617$	246.000	0.0160512	0.00802560	+	0.999968i	$0.497445\pi$
$618$	0	0
$619$	11648.0	0.756337	0.378169	−	0.925737i	$-0.376554\pi$
$619$	11648.0	0.756337	0.378169	+	0.925737i	$0.376554\pi$
$620$	−4480.00	−0.290195
$621$	−1944.00	−0.125620
$622$	0	0
$623$	12.0000	0.000771701 0
$624$	−4224.00	−0.270986
$625$	625.000	0.0400000
$626$	0	0
$627$	0	0
$628$	−6832.00	−0.434119
$629$	−19152.0	−1.21405
$630$	0	0
$631$	−22024.0	−1.38948	−0.694740	−	0.719261i	$-0.744480\pi$
$631$	−22024.0	−1.38948	−0.694740	+	0.719261i	$0.744480\pi$
$632$	0	0
$633$	−5610.00	−0.352255
$634$	0	0
$635$	6970.00	0.435584
$636$	7632.00	0.475831
$637$	−7458.00	−0.463888
$638$	0	0
$639$	1512.00	0.0936053
$640$	0	0
$641$	2322.00	0.143079	0.0715394	−	0.997438i	$-0.477209\pi$
$641$	2322.00	0.143079	0.0715394	+	0.997438i	$0.477209\pi$
$642$	0	0
$643$	14024.0	0.860113	0.430056	−	0.902802i	$-0.358494\pi$
$643$	14024.0	0.860113	0.430056	+	0.902802i	$0.358494\pi$
$644$	1152.00	0.0704894
$645$	5730.00	0.349796
$646$	0	0
$647$	−7152.00	−0.434581	−0.217291	−	0.976107i	$-0.569722\pi$
$647$	−7152.00	−0.434581	−0.217291	+	0.976107i	$0.569722\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	−672.000	−0.0404574
$652$	−12352.0	−0.741935
$653$	−3138.00	−0.188054	−0.0940271	−	0.995570i	$-0.529974\pi$
$653$	−3138.00	−0.188054	−0.0940271	+	0.995570i	$0.529974\pi$
$654$	0	0
$655$	−1260.00	−0.0751638
$656$	6144.00	0.365675
$657$	−1962.00	−0.116507
$658$	0	0
$659$	15876.0	0.938454	0.469227	−	0.883078i	$-0.344533\pi$
$659$	15876.0	0.938454	0.469227	+	0.883078i	$0.344533\pi$
$660$	0	0
$661$	−20554.0	−1.20947	−0.604734	−	0.796428i	$-0.706720\pi$
$661$	−20554.0	−1.20947	−0.604734	+	0.796428i	$0.706720\pi$
$662$	0	0
$663$	4752.00	0.278360
$664$	0	0
$665$	−1220.00	−0.0711422
$666$	0	0
$667$	−6912.00	−0.401250
$668$	1920.00	0.111208
$669$	−6900.00	−0.398758
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−27806.0	−1.59263	−0.796317	−	0.604880i	$-0.793221\pi$
$673$	−27806.0	−1.59263	−0.796317	+	0.604880i	$0.793221\pi$
$674$	0	0
$675$	−675.000	−0.0384900
$676$	13704.0	0.779700
$677$	−20820.0	−1.18195	−0.590973	−	0.806691i	$-0.701256\pi$
$677$	−20820.0	−1.18195	−0.590973	+	0.806691i	$0.701256\pi$
$678$	0	0
$679$	−1372.00	−0.0775442
$680$	0	0
$681$	−3996.00	−0.224856
$682$	0	0
$683$	−7020.00	−0.393284	−0.196642	−	0.980475i	$-0.563004\pi$
$683$	−7020.00	−0.393284	−0.196642	+	0.980475i	$0.563004\pi$
$684$	8784.00	0.491030
$685$	5250.00	0.292835
$686$	0	0
$687$	18066.0	1.00329
$688$	24448.0	1.35475
$689$	6996.00	0.386831
$690$	0	0
$691$	12536.0	0.690147	0.345074	−	0.938576i	$-0.387854\pi$
$691$	12536.0	0.690147	0.345074	+	0.938576i	$0.387854\pi$
$692$	20256.0	1.11274
$693$	0	0
$694$	0	0
$695$	9370.00	0.511402
$696$	0	0
$697$	−6912.00	−0.375625
$698$	0	0
$699$	−14148.0	−0.765560
$700$	400.000	0.0215980
$701$	33276.0	1.79289	0.896446	−	0.443153i	$-0.146140\pi$
$701$	33276.0	1.79289	0.896446	+	0.443153i	$0.146140\pi$
$702$	0	0
$703$	−32452.0	−1.74104
$704$	0	0
$705$	5400.00	0.288476
$706$	0	0
$707$	−1920.00	−0.102134
$708$	15840.0	0.840824
$709$	9818.00	0.520060	0.260030	−	0.965601i	$-0.416267\pi$
$709$	9818.00	0.520060	0.260030	+	0.965601i	$0.416267\pi$
$710$	0	0
$711$	6354.00	0.335153
$712$	0	0
$713$	−8064.00	−0.423561
$714$	0	0
$715$	0	0
$716$	−8736.00	−0.455977
$717$	−19260.0	−1.00318
$718$	0	0
$719$	3216.00	0.166810	0.0834051	−	0.996516i	$-0.473420\pi$
$719$	3216.00	0.166810	0.0834051	+	0.996516i	$0.473420\pi$
$720$	−2880.00	−0.149071
$721$	1688.00	0.0871906
$722$	0	0
$723$	9906.00	0.509555
$724$	18320.0	0.940411
$725$	−2400.00	−0.122943
$726$	0	0
$727$	−10960.0	−0.559125	−0.279563	−	0.960127i	$-0.590189\pi$
$727$	−10960.0	−0.559125	−0.279563	+	0.960127i	$0.590189\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	0	0
$731$	−27504.0	−1.39162
$732$	10320.0	0.521090
$733$	−14618.0	−0.736600	−0.368300	−	0.929707i	$-0.620060\pi$
$733$	−14618.0	−0.736600	−0.368300	+	0.929707i	$0.620060\pi$
$734$	0	0
$735$	−5085.00	−0.255188
$736$	0	0
$737$	0	0
$738$	0	0
$739$	−36518.0	−1.81778	−0.908888	−	0.417040i	$-0.863067\pi$
$739$	−36518.0	−1.81778	−0.908888	+	0.417040i	$0.863067\pi$
$740$	10640.0	0.528560
$741$	8052.00	0.399187
$742$	0	0
$743$	37452.0	1.84923	0.924617	−	0.380899i	$-0.124385\pi$
$743$	37452.0	1.84923	0.924617	+	0.380899i	$0.124385\pi$
$744$	0	0
$745$	7380.00	0.362929
$746$	0	0
$747$	−9612.00	−0.470796
$748$	0	0
$749$	4344.00	0.211918
$750$	0	0
$751$	−10648.0	−0.517378	−0.258689	−	0.965961i	$-0.583291\pi$
$751$	−10648.0	−0.517378	−0.258689	+	0.965961i	$0.583291\pi$
$752$	23040.0	1.11726
$753$	−2196.00	−0.106277
$754$	0	0
$755$	7390.00	0.356225
$756$	−432.000	−0.0207827
$757$	−1258.00	−0.0604000	−0.0302000	−	0.999544i	$-0.509614\pi$
$757$	−1258.00	−0.0604000	−0.0302000	+	0.999544i	$0.509614\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	−1740.00	−0.0828843	−0.0414421	−	0.999141i	$-0.513195\pi$
$761$	−1740.00	−0.0828843	−0.0414421	+	0.999141i	$0.513195\pi$
$762$	0	0
$763$	1228.00	0.0582655
$764$	35136.0	1.66384
$765$	3240.00	0.153127
$766$	0	0
$767$	14520.0	0.683555
$768$	−12288.0	−0.577350
$769$	10774.0	0.505228	0.252614	−	0.967567i	$-0.418710\pi$
$769$	10774.0	0.505228	0.252614	+	0.967567i	$0.418710\pi$
$770$	0	0
$771$	10314.0	0.481776
$772$	−40592.0	−1.89241
$773$	−19146.0	−0.890859	−0.445429	−	0.895317i	$-0.646949\pi$
$773$	−19146.0	−0.890859	−0.445429	+	0.895317i	$0.646949\pi$
$774$	0	0
$775$	−2800.00	−0.129779
$776$	0	0
$777$	1596.00	0.0736888
$778$	0	0
$779$	−11712.0	−0.538673
$780$	−2640.00	−0.121189
$781$	0	0
$782$	0	0
$783$	2592.00	0.118302
$784$	−21696.0	−0.988338
$785$	−4270.00	−0.194144
$786$	0	0
$787$	30670.0	1.38916	0.694579	−	0.719416i	$-0.255591\pi$
$787$	30670.0	1.38916	0.694579	+	0.719416i	$0.255591\pi$
$788$	13536.0	0.611929
$789$	−2088.00	−0.0942139
$790$	0	0
$791$	−2508.00	−0.112736
$792$	0	0
$793$	9460.00	0.423625
$794$	0	0
$795$	4770.00	0.212798
$796$	−37312.0	−1.66142
$797$	11970.0	0.531994	0.265997	−	0.963974i	$-0.414299\pi$
$797$	11970.0	0.531994	0.265997	+	0.963974i	$0.414299\pi$
$798$	0	0
$799$	−25920.0	−1.14766
$800$	0	0
$801$	−54.0000	−0.00238202
$802$	0	0
$803$	0	0
$804$	9120.00	0.400047
$805$	720.000	0.0315238
$806$	0	0
$807$	22014.0	0.960260
$808$	0	0
$809$	19932.0	0.866220	0.433110	−	0.901341i	$-0.357416\pi$
$809$	19932.0	0.866220	0.433110	+	0.901341i	$0.357416\pi$
$810$	0	0
$811$	31462.0	1.36224	0.681122	−	0.732170i	$-0.261492\pi$
$811$	31462.0	1.36224	0.681122	+	0.732170i	$0.261492\pi$
$812$	−1536.00	−0.0663830
$813$	15342.0	0.661830
$814$	0	0
$815$	−7720.00	−0.331803
$816$	13824.0	0.593060
$817$	−46604.0	−1.99568
$818$	0	0
$819$	−396.000	−0.0168954
$820$	3840.00	0.163535
$821$	39720.0	1.68847	0.844237	−	0.535970i	$-0.180054\pi$
$821$	39720.0	1.68847	0.844237	+	0.535970i	$0.180054\pi$
$822$	0	0
$823$	−28492.0	−1.20677	−0.603383	−	0.797451i	$-0.706181\pi$
$823$	−28492.0	−1.20677	−0.603383	+	0.797451i	$0.706181\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	18324.0	0.770481	0.385241	−	0.922816i	$-0.374118\pi$
$827$	18324.0	0.770481	0.385241	+	0.922816i	$0.374118\pi$
$828$	−5184.00	−0.217580
$829$	21626.0	0.906034	0.453017	−	0.891502i	$-0.350348\pi$
$829$	21626.0	0.906034	0.453017	+	0.891502i	$0.350348\pi$
$830$	0	0
$831$	2958.00	0.123480
$832$	−11264.0	−0.469362
$833$	24408.0	1.01523
$834$	0	0
$835$	1200.00	0.0497338
$836$	0	0
$837$	3024.00	0.124880
$838$	0	0
$839$	−36960.0	−1.52086	−0.760430	−	0.649420i	$-0.775012\pi$
$839$	−36960.0	−1.52086	−0.760430	+	0.649420i	$0.775012\pi$
$840$	0	0
$841$	−15173.0	−0.622125
$842$	0	0
$843$	9936.00	0.405948
$844$	−14960.0	−0.610124
$845$	8565.00	0.348692
$846$	0	0
$847$	0	0
$848$	20352.0	0.824163
$849$	12894.0	0.521226
$850$	0	0
$851$	19152.0	0.771471
$852$	4032.00	0.162129
$853$	−31502.0	−1.26449	−0.632244	−	0.774769i	$-0.717866\pi$
$853$	−31502.0	−1.26449	−0.632244	+	0.774769i	$0.717866\pi$
$854$	0	0
$855$	5490.00	0.219595
$856$	0	0
$857$	−5640.00	−0.224806	−0.112403	−	0.993663i	$-0.535855\pi$
$857$	−5640.00	−0.224806	−0.112403	+	0.993663i	$0.535855\pi$
$858$	0	0
$859$	−2056.00	−0.0816645	−0.0408323	−	0.999166i	$-0.513001\pi$
$859$	−2056.00	−0.0816645	−0.0408323	+	0.999166i	$0.513001\pi$
$860$	15280.0	0.605865
$861$	576.000	0.0227991
$862$	0	0
$863$	18336.0	0.723250	0.361625	−	0.932324i	$-0.382222\pi$
$863$	18336.0	0.723250	0.361625	+	0.932324i	$0.382222\pi$
$864$	0	0
$865$	12660.0	0.497633
$866$	0	0
$867$	−813.000	−0.0318465
$868$	−1792.00	−0.0700742
$869$	0	0
$870$	0	0
$871$	8360.00	0.325221
$872$	0	0
$873$	6174.00	0.239357
$874$	0	0
$875$	250.000	0.00965891
$876$	−5232.00	−0.201796
$877$	51346.0	1.97700	0.988501	−	0.151213i	$-0.0483178\pi$
$877$	51346.0	1.97700	0.988501	+	0.151213i	$0.0483178\pi$
$878$	0	0
$879$	8208.00	0.314959
$880$	0	0
$881$	32910.0	1.25853	0.629266	−	0.777190i	$-0.283356\pi$
$881$	32910.0	1.25853	0.629266	+	0.777190i	$0.283356\pi$
$882$	0	0
$883$	15356.0	0.585244	0.292622	−	0.956228i	$-0.405472\pi$
$883$	15356.0	0.585244	0.292622	+	0.956228i	$0.405472\pi$
$884$	12672.0	0.482133
$885$	9900.00	0.376028
$886$	0	0
$887$	−18372.0	−0.695458	−0.347729	−	0.937595i	$-0.613047\pi$
$887$	−18372.0	−0.695458	−0.347729	+	0.937595i	$0.613047\pi$
$888$	0	0
$889$	2788.00	0.105182
$890$	0	0
$891$	0	0
$892$	−18400.0	−0.690670
$893$	−43920.0	−1.64583
$894$	0	0
$895$	−5460.00	−0.203919
$896$	0	0
$897$	−4752.00	−0.176884
$898$	0	0
$899$	10752.0	0.398887
$900$	−1800.00	−0.0666667
$901$	−22896.0	−0.846589
$902$	0	0
$903$	2292.00	0.0844662
$904$	0	0
$905$	11450.0	0.420565
$906$	0	0
$907$	7640.00	0.279694	0.139847	−	0.990173i	$-0.455339\pi$
$907$	7640.00	0.279694	0.139847	+	0.990173i	$0.455339\pi$
$908$	−10656.0	−0.389462
$909$	8640.00	0.315259
$910$	0	0
$911$	−53040.0	−1.92897	−0.964486	−	0.264134i	$-0.914914\pi$
$911$	−53040.0	−1.92897	−0.964486	+	0.264134i	$0.914914\pi$
$912$	23424.0	0.850489
$913$	0	0
$914$	0	0
$915$	6450.00	0.233039
$916$	48176.0	1.73775
$917$	−504.000	−0.0181500
$918$	0	0
$919$	11302.0	0.405679	0.202839	−	0.979212i	$-0.434983\pi$
$919$	11302.0	0.405679	0.202839	+	0.979212i	$0.434983\pi$
$920$	0	0
$921$	−750.000	−0.0268332
$922$	0	0
$923$	3696.00	0.131804
$924$	0	0
$925$	6650.00	0.236379
$926$	0	0
$927$	−7596.00	−0.269132
$928$	0	0
$929$	19254.0	0.679982	0.339991	−	0.940429i	$-0.389576\pi$
$929$	19254.0	0.679982	0.339991	+	0.940429i	$0.389576\pi$
$930$	0	0
$931$	41358.0	1.45591
$932$	−37728.0	−1.32599
$933$	−21744.0	−0.762987
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−22214.0	−0.774493	−0.387246	−	0.921976i	$-0.626574\pi$
$937$	−22214.0	−0.774493	−0.387246	+	0.921976i	$0.626574\pi$
$938$	0	0
$939$	23358.0	0.811778
$940$	14400.0	0.499656
$941$	−41736.0	−1.44586	−0.722930	−	0.690921i	$-0.757205\pi$
$941$	−41736.0	−1.44586	−0.722930	+	0.690921i	$0.757205\pi$
$942$	0	0
$943$	6912.00	0.238691
$944$	42240.0	1.45635
$945$	−270.000	−0.00929429
$946$	0	0
$947$	42732.0	1.46632	0.733159	−	0.680057i	$-0.238045\pi$
$947$	42732.0	1.46632	0.733159	+	0.680057i	$0.238045\pi$
$948$	16944.0	0.580502
$949$	−4796.00	−0.164051
$950$	0	0
$951$	12690.0	0.432704
$952$	0	0
$953$	25056.0	0.851672	0.425836	−	0.904800i	$-0.359980\pi$
$953$	25056.0	0.851672	0.425836	+	0.904800i	$0.359980\pi$
$954$	0	0
$955$	21960.0	0.744093
$956$	−51360.0	−1.73755
$957$	0	0
$958$	0	0
$959$	2100.00	0.0707117
$960$	−7680.00	−0.258199
$961$	−17247.0	−0.578933
$962$	0	0
$963$	−19548.0	−0.654128
$964$	26416.0	0.882575
$965$	−25370.0	−0.846310
$966$	0	0
$967$	14326.0	0.476415	0.238207	−	0.971214i	$-0.423440\pi$
$967$	14326.0	0.476415	0.238207	+	0.971214i	$0.423440\pi$
$968$	0	0
$969$	−26352.0	−0.873631
$970$	0	0
$971$	45924.0	1.51779	0.758894	−	0.651215i	$-0.225740\pi$
$971$	45924.0	1.51779	0.758894	+	0.651215i	$0.225740\pi$
$972$	1944.00	0.0641500
$973$	3748.00	0.123490
$974$	0	0
$975$	−1650.00	−0.0541972
$976$	27520.0	0.902555
$977$	−38946.0	−1.27533	−0.637663	−	0.770316i	$-0.720099\pi$
$977$	−38946.0	−1.27533	−0.637663	+	0.770316i	$0.720099\pi$
$978$	0	0
$979$	0	0
$980$	−13560.0	−0.441998
$981$	−5526.00	−0.179849
$982$	0	0
$983$	21000.0	0.681379	0.340690	−	0.940176i	$-0.389339\pi$
$983$	21000.0	0.681379	0.340690	+	0.940176i	$0.389339\pi$
$984$	0	0
$985$	8460.00	0.273663
$986$	0	0
$987$	2160.00	0.0696591
$988$	21472.0	0.691412
$989$	27504.0	0.884304
$990$	0	0
$991$	7760.00	0.248743	0.124372	−	0.992236i	$-0.460309\pi$
$991$	7760.00	0.248743	0.124372	+	0.992236i	$0.460309\pi$
$992$	0	0
$993$	−23208.0	−0.741675
$994$	0	0
$995$	−23320.0	−0.743009
$996$	−25632.0	−0.815443
$997$	−21350.0	−0.678196	−0.339098	−	0.940751i	$-0.610122\pi$
$997$	−21350.0	−0.678196	−0.339098	+	0.940751i	$0.610122\pi$
$998$	0	0
$999$	−7182.00	−0.227456

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1815.4.a.f.1.1		1
11.10	odd	2		165.4.a.a.1.1	✓	1
33.32	even	2		495.4.a.c.1.1		1
55.32	even	4		825.4.c.g.199.2		2
55.43	even	4		825.4.c.g.199.1		2
55.54	odd	2		825.4.a.e.1.1		1
165.164	even	2		2475.4.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.4.a.a.1.1	✓	1	11.10	odd	2
495.4.a.c.1.1		1	33.32	even	2
825.4.a.e.1.1		1	55.54	odd	2
825.4.c.g.199.1		2	55.43	even	4
825.4.c.g.199.2		2	55.32	even	4
1815.4.a.f.1.1		1	1.1	even	1	trivial
2475.4.a.f.1.1		1	165.164	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:	\( N \)	\(=\)	\( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1815.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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