LMFDB - Embedded newform 147.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(1,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("147.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.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:	$8.67328077084$
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	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{2} -3.00000 q^{3} -7.00000 q^{4} +12.0000 q^{5} +3.00000 q^{6} +15.0000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q-1.00000 q^{2} -3.00000 q^{3} -7.00000 q^{4} +12.0000 q^{5} +3.00000 q^{6} +15.0000 q^{8} +9.00000 q^{9} -12.0000 q^{10} +20.0000 q^{11} +21.0000 q^{12} -84.0000 q^{13} -36.0000 q^{15} +41.0000 q^{16} -96.0000 q^{17} -9.00000 q^{18} +12.0000 q^{19} -84.0000 q^{20} -20.0000 q^{22} -176.000 q^{23} -45.0000 q^{24} +19.0000 q^{25} +84.0000 q^{26} -27.0000 q^{27} +58.0000 q^{29} +36.0000 q^{30} -264.000 q^{31} -161.000 q^{32} -60.0000 q^{33} +96.0000 q^{34} -63.0000 q^{36} +258.000 q^{37} -12.0000 q^{38} +252.000 q^{39} +180.000 q^{40} +156.000 q^{43} -140.000 q^{44} +108.000 q^{45} +176.000 q^{46} -408.000 q^{47} -123.000 q^{48} -19.0000 q^{50} +288.000 q^{51} +588.000 q^{52} -722.000 q^{53} +27.0000 q^{54} +240.000 q^{55} -36.0000 q^{57} -58.0000 q^{58} +492.000 q^{59} +252.000 q^{60} -492.000 q^{61} +264.000 q^{62} -167.000 q^{64} -1008.00 q^{65} +60.0000 q^{66} +412.000 q^{67} +672.000 q^{68} +528.000 q^{69} +296.000 q^{71} +135.000 q^{72} +240.000 q^{73} -258.000 q^{74} -57.0000 q^{75} -84.0000 q^{76} -252.000 q^{78} +776.000 q^{79} +492.000 q^{80} +81.0000 q^{81} +924.000 q^{83} -1152.00 q^{85} -156.000 q^{86} -174.000 q^{87} +300.000 q^{88} -744.000 q^{89} -108.000 q^{90} +1232.00 q^{92} +792.000 q^{93} +408.000 q^{94} +144.000 q^{95} +483.000 q^{96} -168.000 q^{97} +180.000 q^{99} +O(q^{100})\)

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 $

$2$	−1.00000	−0.353553	−0.176777	−	0.984251i	$-0.556567\pi$
$2$	−1.00000	−0.353553	−0.176777	+	0.984251i	$0.556567\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−7.00000	−0.875000
$5$	12.0000	1.07331	0.536656	−	0.843801i	$-0.319687\pi$
$5$	12.0000	1.07331	0.536656	+	0.843801i	$0.319687\pi$
$6$	3.00000	0.204124
$7$	0	0
$7$	0	0
$8$	15.0000	0.662913
$9$	9.00000	0.333333
$10$	−12.0000	−0.379473
$11$	20.0000	0.548202	0.274101	−	0.961701i	$-0.411620\pi$
$11$	20.0000	0.548202	0.274101	+	0.961701i	$0.411620\pi$
$12$	21.0000	0.505181
$13$	−84.0000	−1.79211	−0.896054	−	0.443945i	$-0.853579\pi$
$13$	−84.0000	−1.79211	−0.896054	+	0.443945i	$0.853579\pi$
$14$	0	0
$15$	−36.0000	−0.619677
$16$	41.0000	0.640625
$17$	−96.0000	−1.36961	−0.684806	−	0.728725i	$-0.740113\pi$
$17$	−96.0000	−1.36961	−0.684806	+	0.728725i	$0.740113\pi$
$18$	−9.00000	−0.117851
$19$	12.0000	0.144894	0.0724471	−	0.997372i	$-0.476919\pi$
$19$	12.0000	0.144894	0.0724471	+	0.997372i	$0.476919\pi$
$20$	−84.0000	−0.939149
$21$	0	0
$22$	−20.0000	−0.193819
$23$	−176.000	−1.59559	−0.797794	−	0.602930i	$-0.794000\pi$
$23$	−176.000	−1.59559	−0.797794	+	0.602930i	$0.794000\pi$
$24$	−45.0000	−0.382733
$25$	19.0000	0.152000
$26$	84.0000	0.633606
$27$	−27.0000	−0.192450
$28$	0	0
$29$	58.0000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	58.0000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	36.0000	0.219089
$31$	−264.000	−1.52954	−0.764771	−	0.644302i	$-0.777148\pi$
$31$	−264.000	−1.52954	−0.764771	+	0.644302i	$0.777148\pi$
$32$	−161.000	−0.889408
$33$	−60.0000	−0.316505
$34$	96.0000	0.484231
$35$	0	0
$36$	−63.0000	−0.291667
$37$	258.000	1.14635	0.573175	−	0.819433i	$-0.305712\pi$
$37$	258.000	1.14635	0.573175	+	0.819433i	$0.305712\pi$
$38$	−12.0000	−0.0512278
$39$	252.000	1.03467
$40$	180.000	0.711512
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	0	0
$43$	156.000	0.553251	0.276625	−	0.960978i	$-0.410784\pi$
$43$	156.000	0.553251	0.276625	+	0.960978i	$0.410784\pi$
$44$	−140.000	−0.479677
$45$	108.000	0.357771
$46$	176.000	0.564126
$47$	−408.000	−1.26623	−0.633116	−	0.774057i	$-0.718224\pi$
$47$	−408.000	−1.26623	−0.633116	+	0.774057i	$0.718224\pi$
$48$	−123.000	−0.369865
$49$	0	0
$50$	−19.0000	−0.0537401
$51$	288.000	0.790746
$52$	588.000	1.56809
$53$	−722.000	−1.87121	−0.935607	−	0.353044i	$-0.885147\pi$
$53$	−722.000	−1.87121	−0.935607	+	0.353044i	$0.885147\pi$
$54$	27.0000	0.0680414
$55$	240.000	0.588393
$56$	0	0
$57$	−36.0000	−0.0836547
$58$	−58.0000	−0.131306
$59$	492.000	1.08564	0.542822	−	0.839848i	$-0.317356\pi$
$59$	492.000	1.08564	0.542822	+	0.839848i	$0.317356\pi$
$60$	252.000	0.542218
$61$	−492.000	−1.03269	−0.516345	−	0.856380i	$-0.672708\pi$
$61$	−492.000	−1.03269	−0.516345	+	0.856380i	$0.672708\pi$
$62$	264.000	0.540775
$63$	0	0
$64$	−167.000	−0.326172
$65$	−1008.00	−1.92349
$66$	60.0000	0.111901
$67$	412.000	0.751251	0.375625	−	0.926772i	$-0.377428\pi$
$67$	412.000	0.751251	0.375625	+	0.926772i	$0.377428\pi$
$68$	672.000	1.19841
$69$	528.000	0.921213
$70$	0	0
$71$	296.000	0.494771	0.247385	−	0.968917i	$-0.420429\pi$
$71$	296.000	0.494771	0.247385	+	0.968917i	$0.420429\pi$
$72$	135.000	0.220971
$73$	240.000	0.384793	0.192396	−	0.981317i	$-0.438374\pi$
$73$	240.000	0.384793	0.192396	+	0.981317i	$0.438374\pi$
$74$	−258.000	−0.405296
$75$	−57.0000	−0.0877572
$76$	−84.0000	−0.126782
$77$	0	0
$78$	−252.000	−0.365813
$79$	776.000	1.10515	0.552575	−	0.833463i	$-0.313645\pi$
$79$	776.000	1.10515	0.552575	+	0.833463i	$0.313645\pi$
$80$	492.000	0.687591
$81$	81.0000	0.111111
$82$	0	0
$83$	924.000	1.22195	0.610977	−	0.791648i	$-0.290777\pi$
$83$	924.000	1.22195	0.610977	+	0.791648i	$0.290777\pi$
$84$	0	0
$85$	−1152.00	−1.47002
$86$	−156.000	−0.195604
$87$	−174.000	−0.214423
$88$	300.000	0.363410
$89$	−744.000	−0.886111	−0.443055	−	0.896494i	$-0.646105\pi$
$89$	−744.000	−0.886111	−0.443055	+	0.896494i	$0.646105\pi$
$90$	−108.000	−0.126491
$91$	0	0
$92$	1232.00	1.39614
$93$	792.000	0.883081
$94$	408.000	0.447681
$95$	144.000	0.155517
$96$	483.000	0.513500
$97$	−168.000	−0.175854	−0.0879269	−	0.996127i	$-0.528024\pi$
$97$	−168.000	−0.175854	−0.0879269	+	0.996127i	$0.528024\pi$
$98$	0	0
$99$	180.000	0.182734
$100$	−133.000	−0.133000
$101$	−1524.00	−1.50142	−0.750711	−	0.660630i	$-0.770289\pi$
$101$	−1524.00	−1.50142	−0.750711	+	0.660630i	$0.770289\pi$
$102$	−288.000	−0.279571
$103$	−408.000	−0.390305	−0.195153	−	0.980773i	$-0.562520\pi$
$103$	−408.000	−0.390305	−0.195153	+	0.980773i	$0.562520\pi$
$104$	−1260.00	−1.18801
$105$	0	0
$106$	722.000	0.661574
$107$	−820.000	−0.740863	−0.370432	−	0.928860i	$-0.620790\pi$
$107$	−820.000	−0.740863	−0.370432	+	0.928860i	$0.620790\pi$
$108$	189.000	0.168394
$109$	−918.000	−0.806683	−0.403342	−	0.915050i	$-0.632151\pi$
$109$	−918.000	−0.806683	−0.403342	+	0.915050i	$0.632151\pi$
$110$	−240.000	−0.208028
$111$	−774.000	−0.661845
$112$	0	0
$113$	−110.000	−0.0915746	−0.0457873	−	0.998951i	$-0.514580\pi$
$113$	−110.000	−0.0915746	−0.0457873	+	0.998951i	$0.514580\pi$
$114$	36.0000	0.0295764
$115$	−2112.00	−1.71257
$116$	−406.000	−0.324967
$117$	−756.000	−0.597369
$118$	−492.000	−0.383833
$119$	0	0
$120$	−540.000	−0.410792
$121$	−931.000	−0.699474
$122$	492.000	0.365111
$123$	0	0
$124$	1848.00	1.33835
$125$	−1272.00	−0.910169
$126$	0	0
$127$	16.0000	0.0111793	0.00558965	−	0.999984i	$-0.498221\pi$
$127$	16.0000	0.0111793	0.00558965	+	0.999984i	$0.498221\pi$
$128$	1455.00	1.00473
$129$	−468.000	−0.319419
$130$	1008.00	0.680057
$131$	1692.00	1.12848	0.564239	−	0.825611i	$-0.309169\pi$
$131$	1692.00	1.12848	0.564239	+	0.825611i	$0.309169\pi$
$132$	420.000	0.276942
$133$	0	0
$134$	−412.000	−0.265607
$135$	−324.000	−0.206559
$136$	−1440.00	−0.907934
$137$	1126.00	0.702195	0.351097	−	0.936339i	$-0.385809\pi$
$137$	1126.00	0.702195	0.351097	+	0.936339i	$0.385809\pi$
$138$	−528.000	−0.325698
$139$	1092.00	0.666347	0.333173	−	0.942866i	$-0.391881\pi$
$139$	1092.00	0.666347	0.333173	+	0.942866i	$0.391881\pi$
$140$	0	0
$141$	1224.00	0.731060
$142$	−296.000	−0.174928
$143$	−1680.00	−0.982438
$144$	369.000	0.213542
$145$	696.000	0.398618
$146$	−240.000	−0.136045
$147$	0	0
$148$	−1806.00	−1.00306
$149$	1070.00	0.588307	0.294154	−	0.955758i	$-0.404962\pi$
$149$	1070.00	0.588307	0.294154	+	0.955758i	$0.404962\pi$
$150$	57.0000	0.0310269
$151$	−120.000	−0.0646719	−0.0323360	−	0.999477i	$-0.510295\pi$
$151$	−120.000	−0.0646719	−0.0323360	+	0.999477i	$0.510295\pi$
$152$	180.000	0.0960522
$153$	−864.000	−0.456538
$154$	0	0
$155$	−3168.00	−1.64168
$156$	−1764.00	−0.905340
$157$	1836.00	0.933304	0.466652	−	0.884441i	$-0.345460\pi$
$157$	1836.00	0.933304	0.466652	+	0.884441i	$0.345460\pi$
$158$	−776.000	−0.390729
$159$	2166.00	1.08035
$160$	−1932.00	−0.954613
$161$	0	0
$162$	−81.0000	−0.0392837
$163$	916.000	0.440164	0.220082	−	0.975481i	$-0.429368\pi$
$163$	916.000	0.440164	0.220082	+	0.975481i	$0.429368\pi$
$164$	0	0
$165$	−720.000	−0.339709
$166$	−924.000	−0.432026
$167$	504.000	0.233537	0.116769	−	0.993159i	$-0.462746\pi$
$167$	504.000	0.233537	0.116769	+	0.993159i	$0.462746\pi$
$168$	0	0
$169$	4859.00	2.21165
$170$	1152.00	0.519732
$171$	108.000	0.0482980
$172$	−1092.00	−0.484094
$173$	−1836.00	−0.806870	−0.403435	−	0.915008i	$-0.632184\pi$
$173$	−1836.00	−0.806870	−0.403435	+	0.915008i	$0.632184\pi$
$174$	174.000	0.0758098
$175$	0	0
$176$	820.000	0.351192
$177$	−1476.00	−0.626796
$178$	744.000	0.313287
$179$	2372.00	0.990456	0.495228	−	0.868763i	$-0.335085\pi$
$179$	2372.00	0.990456	0.495228	+	0.868763i	$0.335085\pi$
$180$	−756.000	−0.313050
$181$	−1092.00	−0.448440	−0.224220	−	0.974539i	$-0.571983\pi$
$181$	−1092.00	−0.448440	−0.224220	+	0.974539i	$0.571983\pi$
$182$	0	0
$183$	1476.00	0.596224
$184$	−2640.00	−1.05774
$185$	3096.00	1.23039
$186$	−792.000	−0.312216
$187$	−1920.00	−0.750825
$188$	2856.00	1.10795
$189$	0	0
$190$	−144.000	−0.0549835
$191$	2512.00	0.951633	0.475817	−	0.879545i	$-0.342153\pi$
$191$	2512.00	0.951633	0.475817	+	0.879545i	$0.342153\pi$
$192$	501.000	0.188315
$193$	−2430.00	−0.906297	−0.453148	−	0.891435i	$-0.649699\pi$
$193$	−2430.00	−0.906297	−0.453148	+	0.891435i	$0.649699\pi$
$194$	168.000	0.0621737
$195$	3024.00	1.11053
$196$	0	0
$197$	−1762.00	−0.637245	−0.318623	−	0.947882i	$-0.603220\pi$
$197$	−1762.00	−0.637245	−0.318623	+	0.947882i	$0.603220\pi$
$198$	−180.000	−0.0646063
$199$	3096.00	1.10286	0.551431	−	0.834220i	$-0.314082\pi$
$199$	3096.00	1.10286	0.551431	+	0.834220i	$0.314082\pi$
$200$	285.000	0.100763
$201$	−1236.00	−0.433735
$202$	1524.00	0.530833
$203$	0	0
$204$	−2016.00	−0.691903
$205$	0	0
$206$	408.000	0.137994
$207$	−1584.00	−0.531863
$208$	−3444.00	−1.14807
$209$	240.000	0.0794313
$210$	0	0
$211$	156.000	0.0508980	0.0254490	−	0.999676i	$-0.491898\pi$
$211$	156.000	0.0508980	0.0254490	+	0.999676i	$0.491898\pi$
$212$	5054.00	1.63731
$213$	−888.000	−0.285656
$214$	820.000	0.261935
$215$	1872.00	0.593811
$216$	−405.000	−0.127578
$217$	0	0
$218$	918.000	0.285206
$219$	−720.000	−0.222160
$220$	−1680.00	−0.514844
$221$	8064.00	2.45449
$222$	774.000	0.233998
$223$	5040.00	1.51347	0.756734	−	0.653723i	$-0.226794\pi$
$223$	5040.00	1.51347	0.756734	+	0.653723i	$0.226794\pi$
$224$	0	0
$225$	171.000	0.0506667
$226$	110.000	0.0323765
$227$	2172.00	0.635069	0.317535	−	0.948247i	$-0.397145\pi$
$227$	2172.00	0.635069	0.317535	+	0.948247i	$0.397145\pi$
$228$	252.000	0.0731978
$229$	2700.00	0.779131	0.389566	−	0.920999i	$-0.372625\pi$
$229$	2700.00	0.779131	0.389566	+	0.920999i	$0.372625\pi$
$230$	2112.00	0.605483
$231$	0	0
$232$	870.000	0.246200
$233$	−3802.00	−1.06900	−0.534501	−	0.845168i	$-0.679500\pi$
$233$	−3802.00	−1.06900	−0.534501	+	0.845168i	$0.679500\pi$
$234$	756.000	0.211202
$235$	−4896.00	−1.35906
$236$	−3444.00	−0.949938
$237$	−2328.00	−0.638058
$238$	0	0
$239$	−4408.00	−1.19301	−0.596506	−	0.802609i	$-0.703445\pi$
$239$	−4408.00	−1.19301	−0.596506	+	0.802609i	$0.703445\pi$
$240$	−1476.00	−0.396981
$241$	3096.00	0.827514	0.413757	−	0.910387i	$-0.364216\pi$
$241$	3096.00	0.827514	0.413757	+	0.910387i	$0.364216\pi$
$242$	931.000	0.247301
$243$	−243.000	−0.0641500
$244$	3444.00	0.903605
$245$	0	0
$246$	0	0
$247$	−1008.00	−0.259666
$248$	−3960.00	−1.01395
$249$	−2772.00	−0.705495
$250$	1272.00	0.321793
$251$	−924.000	−0.232360	−0.116180	−	0.993228i	$-0.537065\pi$
$251$	−924.000	−0.232360	−0.116180	+	0.993228i	$0.537065\pi$
$252$	0	0
$253$	−3520.00	−0.874706
$254$	−16.0000	−0.00395248
$255$	3456.00	0.848718
$256$	−119.000	−0.0290527
$257$	−2760.00	−0.669899	−0.334950	−	0.942236i	$-0.608719\pi$
$257$	−2760.00	−0.669899	−0.334950	+	0.942236i	$0.608719\pi$
$258$	468.000	0.112932
$259$	0	0
$260$	7056.00	1.68306
$261$	522.000	0.123797
$262$	−1692.00	−0.398978
$263$	−2360.00	−0.553323	−0.276661	−	0.960967i	$-0.589228\pi$
$263$	−2360.00	−0.553323	−0.276661	+	0.960967i	$0.589228\pi$
$264$	−900.000	−0.209815
$265$	−8664.00	−2.00840
$266$	0	0
$267$	2232.00	0.511596
$268$	−2884.00	−0.657345
$269$	4020.00	0.911166	0.455583	−	0.890193i	$-0.349431\pi$
$269$	4020.00	0.911166	0.455583	+	0.890193i	$0.349431\pi$
$270$	324.000	0.0730297
$271$	4800.00	1.07594	0.537969	−	0.842965i	$-0.319192\pi$
$271$	4800.00	1.07594	0.537969	+	0.842965i	$0.319192\pi$
$272$	−3936.00	−0.877408
$273$	0	0
$274$	−1126.00	−0.248263
$275$	380.000	0.0833268
$276$	−3696.00	−0.806062
$277$	6446.00	1.39820	0.699102	−	0.715022i	$-0.253583\pi$
$277$	6446.00	1.39820	0.699102	+	0.715022i	$0.253583\pi$
$278$	−1092.00	−0.235589
$279$	−2376.00	−0.509847
$280$	0	0
$281$	−2602.00	−0.552393	−0.276196	−	0.961101i	$-0.589074\pi$
$281$	−2602.00	−0.552393	−0.276196	+	0.961101i	$0.589074\pi$
$282$	−1224.00	−0.258469
$283$	−6900.00	−1.44934	−0.724669	−	0.689098i	$-0.758007\pi$
$283$	−6900.00	−1.44934	−0.724669	+	0.689098i	$0.758007\pi$
$284$	−2072.00	−0.432925
$285$	−432.000	−0.0897876
$286$	1680.00	0.347344
$287$	0	0
$288$	−1449.00	−0.296469
$289$	4303.00	0.875840
$290$	−696.000	−0.140933
$291$	504.000	0.101529
$292$	−1680.00	−0.336694
$293$	−4452.00	−0.887674	−0.443837	−	0.896107i	$-0.646383\pi$
$293$	−4452.00	−0.887674	−0.443837	+	0.896107i	$0.646383\pi$
$294$	0	0
$295$	5904.00	1.16523
$296$	3870.00	0.759930
$297$	−540.000	−0.105502
$298$	−1070.00	−0.207998
$299$	14784.0	2.85947
$300$	399.000	0.0767876
$301$	0	0
$302$	120.000	0.0228650
$303$	4572.00	0.866847
$304$	492.000	0.0928228
$305$	−5904.00	−1.10840
$306$	864.000	0.161410
$307$	−2436.00	−0.452866	−0.226433	−	0.974027i	$-0.572706\pi$
$307$	−2436.00	−0.452866	−0.226433	+	0.974027i	$0.572706\pi$
$308$	0	0
$309$	1224.00	0.225343
$310$	3168.00	0.580420
$311$	−7488.00	−1.36529	−0.682646	−	0.730750i	$-0.739171\pi$
$311$	−7488.00	−1.36529	−0.682646	+	0.730750i	$0.739171\pi$
$312$	3780.00	0.685899
$313$	−1752.00	−0.316386	−0.158193	−	0.987408i	$-0.550567\pi$
$313$	−1752.00	−0.316386	−0.158193	+	0.987408i	$0.550567\pi$
$314$	−1836.00	−0.329973
$315$	0	0
$316$	−5432.00	−0.967006
$317$	−1562.00	−0.276753	−0.138376	−	0.990380i	$-0.544188\pi$
$317$	−1562.00	−0.276753	−0.138376	+	0.990380i	$0.544188\pi$
$318$	−2166.00	−0.381960
$319$	1160.00	0.203597
$320$	−2004.00	−0.350084
$321$	2460.00	0.427738
$322$	0	0
$323$	−1152.00	−0.198449
$324$	−567.000	−0.0972222
$325$	−1596.00	−0.272400
$326$	−916.000	−0.155621
$327$	2754.00	0.465739
$328$	0	0
$329$	0	0
$330$	720.000	0.120105
$331$	−7092.00	−1.17768	−0.588839	−	0.808250i	$-0.700415\pi$
$331$	−7092.00	−1.17768	−0.588839	+	0.808250i	$0.700415\pi$
$332$	−6468.00	−1.06921
$333$	2322.00	0.382117
$334$	−504.000	−0.0825678
$335$	4944.00	0.806327
$336$	0	0
$337$	366.000	0.0591611	0.0295805	−	0.999562i	$-0.490583\pi$
$337$	366.000	0.0591611	0.0295805	+	0.999562i	$0.490583\pi$
$338$	−4859.00	−0.781937
$339$	330.000	0.0528706
$340$	8064.00	1.28627
$341$	−5280.00	−0.838499
$342$	−108.000	−0.0170759
$343$	0	0
$344$	2340.00	0.366757
$345$	6336.00	0.988750
$346$	1836.00	0.285272
$347$	−6364.00	−0.984546	−0.492273	−	0.870441i	$-0.663834\pi$
$347$	−6364.00	−0.984546	−0.492273	+	0.870441i	$0.663834\pi$
$348$	1218.00	0.187620
$349$	−10500.0	−1.61046	−0.805232	−	0.592960i	$-0.797959\pi$
$349$	−10500.0	−1.61046	−0.805232	+	0.592960i	$0.797959\pi$
$350$	0	0
$351$	2268.00	0.344891
$352$	−3220.00	−0.487576
$353$	408.000	0.0615174	0.0307587	−	0.999527i	$-0.490208\pi$
$353$	408.000	0.0615174	0.0307587	+	0.999527i	$0.490208\pi$
$354$	1476.00	0.221606
$355$	3552.00	0.531044
$356$	5208.00	0.775347
$357$	0	0
$358$	−2372.00	−0.350179
$359$	−11936.0	−1.75476	−0.877379	−	0.479798i	$-0.840710\pi$
$359$	−11936.0	−1.75476	−0.877379	+	0.479798i	$0.840710\pi$
$360$	1620.00	0.237171
$361$	−6715.00	−0.979006
$362$	1092.00	0.158548
$363$	2793.00	0.403842
$364$	0	0
$365$	2880.00	0.413003
$366$	−1476.00	−0.210797
$367$	−2448.00	−0.348187	−0.174093	−	0.984729i	$-0.555699\pi$
$367$	−2448.00	−0.348187	−0.174093	+	0.984729i	$0.555699\pi$
$368$	−7216.00	−1.02217
$369$	0	0
$370$	−3096.00	−0.435009
$371$	0	0
$372$	−5544.00	−0.772696
$373$	11374.0	1.57888	0.789442	−	0.613826i	$-0.210370\pi$
$373$	11374.0	1.57888	0.789442	+	0.613826i	$0.210370\pi$
$374$	1920.00	0.265457
$375$	3816.00	0.525486
$376$	−6120.00	−0.839401
$377$	−4872.00	−0.665572
$378$	0	0
$379$	−5892.00	−0.798553	−0.399277	−	0.916830i	$-0.630739\pi$
$379$	−5892.00	−0.798553	−0.399277	+	0.916830i	$0.630739\pi$
$380$	−1008.00	−0.136077
$381$	−48.0000	−0.00645437
$382$	−2512.00	−0.336453
$383$	−10488.0	−1.39925	−0.699624	−	0.714511i	$-0.746649\pi$
$383$	−10488.0	−1.39925	−0.699624	+	0.714511i	$0.746649\pi$
$384$	−4365.00	−0.580079
$385$	0	0
$386$	2430.00	0.320424
$387$	1404.00	0.184417
$388$	1176.00	0.153872
$389$	4514.00	0.588352	0.294176	−	0.955751i	$-0.404955\pi$
$389$	4514.00	0.588352	0.294176	+	0.955751i	$0.404955\pi$
$390$	−3024.00	−0.392631
$391$	16896.0	2.18534
$392$	0	0
$393$	−5076.00	−0.651528
$394$	1762.00	0.225300
$395$	9312.00	1.18617
$396$	−1260.00	−0.159892
$397$	−6036.00	−0.763068	−0.381534	−	0.924355i	$-0.624604\pi$
$397$	−6036.00	−0.763068	−0.381534	+	0.924355i	$0.624604\pi$
$398$	−3096.00	−0.389921
$399$	0	0
$400$	779.000	0.0973750
$401$	−6770.00	−0.843086	−0.421543	−	0.906808i	$-0.638511\pi$
$401$	−6770.00	−0.843086	−0.421543	+	0.906808i	$0.638511\pi$
$402$	1236.00	0.153348
$403$	22176.0	2.74110
$404$	10668.0	1.31374
$405$	972.000	0.119257
$406$	0	0
$407$	5160.00	0.628432
$408$	4320.00	0.524196
$409$	12504.0	1.51169	0.755847	−	0.654748i	$-0.227225\pi$
$409$	12504.0	1.51169	0.755847	+	0.654748i	$0.227225\pi$
$410$	0	0
$411$	−3378.00	−0.405412
$412$	2856.00	0.341517
$413$	0	0
$414$	1584.00	0.188042
$415$	11088.0	1.31154
$416$	13524.0	1.59392
$417$	−3276.00	−0.384716
$418$	−240.000	−0.0280832
$419$	9492.00	1.10672	0.553359	−	0.832943i	$-0.313346\pi$
$419$	9492.00	1.10672	0.553359	+	0.832943i	$0.313346\pi$
$420$	0	0
$421$	5182.00	0.599894	0.299947	−	0.953956i	$-0.403031\pi$
$421$	5182.00	0.599894	0.299947	+	0.953956i	$0.403031\pi$
$422$	−156.000	−0.0179952
$423$	−3672.00	−0.422077
$424$	−10830.0	−1.24045
$425$	−1824.00	−0.208181
$426$	888.000	0.100995
$427$	0	0
$428$	5740.00	0.648256
$429$	5040.00	0.567211
$430$	−1872.00	−0.209944
$431$	−5720.00	−0.639264	−0.319632	−	0.947542i	$-0.603559\pi$
$431$	−5720.00	−0.639264	−0.319632	+	0.947542i	$0.603559\pi$
$432$	−1107.00	−0.123288
$433$	13608.0	1.51030	0.755149	−	0.655554i	$-0.227565\pi$
$433$	13608.0	1.51030	0.755149	+	0.655554i	$0.227565\pi$
$434$	0	0
$435$	−2088.00	−0.230142
$436$	6426.00	0.705848
$437$	−2112.00	−0.231191
$438$	720.000	0.0785455
$439$	12864.0	1.39855	0.699277	−	0.714851i	$-0.253505\pi$
$439$	12864.0	1.39855	0.699277	+	0.714851i	$0.253505\pi$
$440$	3600.00	0.390053
$441$	0	0
$442$	−8064.00	−0.867795
$443$	−13252.0	−1.42127	−0.710634	−	0.703562i	$-0.751592\pi$
$443$	−13252.0	−1.42127	−0.710634	+	0.703562i	$0.751592\pi$
$444$	5418.00	0.579115
$445$	−8928.00	−0.951074
$446$	−5040.00	−0.535092
$447$	−3210.00	−0.339659
$448$	0	0
$449$	226.000	0.0237541	0.0118771	−	0.999929i	$-0.496219\pi$
$449$	226.000	0.0237541	0.0118771	+	0.999929i	$0.496219\pi$
$450$	−171.000	−0.0179134
$451$	0	0
$452$	770.000	0.0801278
$453$	360.000	0.0373384
$454$	−2172.00	−0.224531
$455$	0	0
$456$	−540.000	−0.0554557
$457$	−11334.0	−1.16014	−0.580068	−	0.814568i	$-0.696974\pi$
$457$	−11334.0	−1.16014	−0.580068	+	0.814568i	$0.696974\pi$
$458$	−2700.00	−0.275464
$459$	2592.00	0.263582
$460$	14784.0	1.49849
$461$	−1596.00	−0.161243	−0.0806216	−	0.996745i	$-0.525691\pi$
$461$	−1596.00	−0.161243	−0.0806216	+	0.996745i	$0.525691\pi$
$462$	0	0
$463$	12728.0	1.27758	0.638791	−	0.769380i	$-0.279435\pi$
$463$	12728.0	1.27758	0.638791	+	0.769380i	$0.279435\pi$
$464$	2378.00	0.237922
$465$	9504.00	0.947822
$466$	3802.00	0.377949
$467$	−3012.00	−0.298456	−0.149228	−	0.988803i	$-0.547679\pi$
$467$	−3012.00	−0.298456	−0.149228	+	0.988803i	$0.547679\pi$
$468$	5292.00	0.522698
$469$	0	0
$470$	4896.00	0.480501
$471$	−5508.00	−0.538843
$472$	7380.00	0.719687
$473$	3120.00	0.303293
$474$	2328.00	0.225588
$475$	228.000	0.0220239
$476$	0	0
$477$	−6498.00	−0.623738
$478$	4408.00	0.421793
$479$	−4296.00	−0.409790	−0.204895	−	0.978784i	$-0.565685\pi$
$479$	−4296.00	−0.409790	−0.204895	+	0.978784i	$0.565685\pi$
$480$	5796.00	0.551146
$481$	−21672.0	−2.05438
$482$	−3096.00	−0.292570
$483$	0	0
$484$	6517.00	0.612040
$485$	−2016.00	−0.188746
$486$	243.000	0.0226805
$487$	−8184.00	−0.761504	−0.380752	−	0.924677i	$-0.624335\pi$
$487$	−8184.00	−0.761504	−0.380752	+	0.924677i	$0.624335\pi$
$488$	−7380.00	−0.684584
$489$	−2748.00	−0.254129
$490$	0	0
$491$	−12164.0	−1.11803	−0.559016	−	0.829157i	$-0.688821\pi$
$491$	−12164.0	−1.11803	−0.559016	+	0.829157i	$0.688821\pi$
$492$	0	0
$493$	−5568.00	−0.508661
$494$	1008.00	0.0918058
$495$	2160.00	0.196131
$496$	−10824.0	−0.979863
$497$	0	0
$498$	2772.00	0.249430
$499$	972.000	0.0871998	0.0435999	−	0.999049i	$-0.486117\pi$
$499$	972.000	0.0871998	0.0435999	+	0.999049i	$0.486117\pi$
$500$	8904.00	0.796398
$501$	−1512.00	−0.134833
$502$	924.000	0.0821517
$503$	7728.00	0.685039	0.342519	−	0.939511i	$-0.388720\pi$
$503$	7728.00	0.685039	0.342519	+	0.939511i	$0.388720\pi$
$504$	0	0
$505$	−18288.0	−1.61150
$506$	3520.00	0.309255
$507$	−14577.0	−1.27690
$508$	−112.000	−0.00978188
$509$	11604.0	1.01049	0.505244	−	0.862977i	$-0.331403\pi$
$509$	11604.0	1.01049	0.505244	+	0.862977i	$0.331403\pi$
$510$	−3456.00	−0.300067
$511$	0	0
$512$	−11521.0	−0.994455
$513$	−324.000	−0.0278849
$514$	2760.00	0.236845
$515$	−4896.00	−0.418919
$516$	3276.00	0.279492
$517$	−8160.00	−0.694152
$518$	0	0
$519$	5508.00	0.465847
$520$	−15120.0	−1.27511
$521$	−10848.0	−0.912206	−0.456103	−	0.889927i	$-0.650755\pi$
$521$	−10848.0	−0.912206	−0.456103	+	0.889927i	$0.650755\pi$
$522$	−522.000	−0.0437688
$523$	−18132.0	−1.51598	−0.757989	−	0.652267i	$-0.773818\pi$
$523$	−18132.0	−1.51598	−0.757989	+	0.652267i	$0.773818\pi$
$524$	−11844.0	−0.987419
$525$	0	0
$526$	2360.00	0.195629
$527$	25344.0	2.09488
$528$	−2460.00	−0.202761
$529$	18809.0	1.54590
$530$	8664.00	0.710076
$531$	4428.00	0.361881
$532$	0	0
$533$	0	0
$534$	−2232.00	−0.180877
$535$	−9840.00	−0.795178
$536$	6180.00	0.498014
$537$	−7116.00	−0.571840
$538$	−4020.00	−0.322146
$539$	0	0
$540$	2268.00	0.180739
$541$	6950.00	0.552318	0.276159	−	0.961112i	$-0.410938\pi$
$541$	6950.00	0.552318	0.276159	+	0.961112i	$0.410938\pi$
$542$	−4800.00	−0.380402
$543$	3276.00	0.258907
$544$	15456.0	1.21814
$545$	−11016.0	−0.865823
$546$	0	0
$547$	17012.0	1.32976	0.664882	−	0.746949i	$-0.268482\pi$
$547$	17012.0	1.32976	0.664882	+	0.746949i	$0.268482\pi$
$548$	−7882.00	−0.614420
$549$	−4428.00	−0.344230
$550$	−380.000	−0.0294605
$551$	696.000	0.0538123
$552$	7920.00	0.610684
$553$	0	0
$554$	−6446.00	−0.494340
$555$	−9288.00	−0.710367
$556$	−7644.00	−0.583054
$557$	3926.00	0.298653	0.149327	−	0.988788i	$-0.452289\pi$
$557$	3926.00	0.298653	0.149327	+	0.988788i	$0.452289\pi$
$558$	2376.00	0.180258
$559$	−13104.0	−0.991485
$560$	0	0
$561$	5760.00	0.433489
$562$	2602.00	0.195300
$563$	−18828.0	−1.40942	−0.704712	−	0.709494i	$-0.748924\pi$
$563$	−18828.0	−1.40942	−0.704712	+	0.709494i	$0.748924\pi$
$564$	−8568.00	−0.639677
$565$	−1320.00	−0.0982882
$566$	6900.00	0.512418
$567$	0	0
$568$	4440.00	0.327990
$569$	11990.0	0.883387	0.441693	−	0.897166i	$-0.354378\pi$
$569$	11990.0	0.883387	0.441693	+	0.897166i	$0.354378\pi$
$570$	432.000	0.0317447
$571$	−15716.0	−1.15183	−0.575914	−	0.817510i	$-0.695354\pi$
$571$	−15716.0	−1.15183	−0.575914	+	0.817510i	$0.695354\pi$
$572$	11760.0	0.859633
$573$	−7536.00	−0.549426
$574$	0	0
$575$	−3344.00	−0.242529
$576$	−1503.00	−0.108724
$577$	−13872.0	−1.00086	−0.500432	−	0.865776i	$-0.666826\pi$
$577$	−13872.0	−1.00086	−0.500432	+	0.865776i	$0.666826\pi$
$578$	−4303.00	−0.309656
$579$	7290.00	0.523251
$580$	−4872.00	−0.348791
$581$	0	0
$582$	−504.000	−0.0358960
$583$	−14440.0	−1.02580
$584$	3600.00	0.255084
$585$	−9072.00	−0.641164
$586$	4452.00	0.313840
$587$	8820.00	0.620171	0.310085	−	0.950709i	$-0.399642\pi$
$587$	8820.00	0.620171	0.310085	+	0.950709i	$0.399642\pi$
$588$	0	0
$589$	−3168.00	−0.221622
$590$	−5904.00	−0.411973
$591$	5286.00	0.367914
$592$	10578.0	0.734380
$593$	−16872.0	−1.16838	−0.584191	−	0.811617i	$-0.698588\pi$
$593$	−16872.0	−1.16838	−0.584191	+	0.811617i	$0.698588\pi$
$594$	540.000	0.0373005
$595$	0	0
$596$	−7490.00	−0.514769
$597$	−9288.00	−0.636738
$598$	−14784.0	−1.01097
$599$	−6056.00	−0.413091	−0.206545	−	0.978437i	$-0.566222\pi$
$599$	−6056.00	−0.413091	−0.206545	+	0.978437i	$0.566222\pi$
$600$	−855.000	−0.0581754
$601$	10752.0	0.729756	0.364878	−	0.931055i	$-0.381111\pi$
$601$	10752.0	0.729756	0.364878	+	0.931055i	$0.381111\pi$
$602$	0	0
$603$	3708.00	0.250417
$604$	840.000	0.0565879
$605$	−11172.0	−0.750754
$606$	−4572.00	−0.306477
$607$	20256.0	1.35447	0.677237	−	0.735765i	$-0.263177\pi$
$607$	20256.0	1.35447	0.677237	+	0.735765i	$0.263177\pi$
$608$	−1932.00	−0.128870
$609$	0	0
$610$	5904.00	0.391879
$611$	34272.0	2.26923
$612$	6048.00	0.399470
$613$	−28190.0	−1.85740	−0.928698	−	0.370838i	$-0.879071\pi$
$613$	−28190.0	−1.85740	−0.928698	+	0.370838i	$0.879071\pi$
$614$	2436.00	0.160112
$615$	0	0
$616$	0	0
$617$	29318.0	1.91296	0.956482	−	0.291793i	$-0.0942518\pi$
$617$	29318.0	1.91296	0.956482	+	0.291793i	$0.0942518\pi$
$618$	−1224.00	−0.0796707
$619$	24348.0	1.58098	0.790492	−	0.612473i	$-0.209825\pi$
$619$	24348.0	1.58098	0.790492	+	0.612473i	$0.209825\pi$
$620$	22176.0	1.43647
$621$	4752.00	0.307071
$622$	7488.00	0.482703
$623$	0	0
$624$	10332.0	0.662838
$625$	−17639.0	−1.12890
$626$	1752.00	0.111859
$627$	−720.000	−0.0458597
$628$	−12852.0	−0.816641
$629$	−24768.0	−1.57006
$630$	0	0
$631$	−25184.0	−1.58884	−0.794421	−	0.607368i	$-0.792226\pi$
$631$	−25184.0	−1.58884	−0.794421	+	0.607368i	$0.792226\pi$
$632$	11640.0	0.732618
$633$	−468.000	−0.0293860
$634$	1562.00	0.0978469
$635$	192.000	0.0119989
$636$	−15162.0	−0.945303
$637$	0	0
$638$	−1160.00	−0.0719825
$639$	2664.00	0.164924
$640$	17460.0	1.07839
$641$	32318.0	1.99140	0.995698	−	0.0926628i	$-0.0295379\pi$
$641$	32318.0	1.99140	0.995698	+	0.0926628i	$0.0295379\pi$
$642$	−2460.00	−0.151228
$643$	−3948.00	−0.242137	−0.121068	−	0.992644i	$-0.538632\pi$
$643$	−3948.00	−0.242137	−0.121068	+	0.992644i	$0.538632\pi$
$644$	0	0
$645$	−5616.00	−0.342837
$646$	1152.00	0.0701623
$647$	13848.0	0.841454	0.420727	−	0.907187i	$-0.361775\pi$
$647$	13848.0	0.841454	0.420727	+	0.907187i	$0.361775\pi$
$648$	1215.00	0.0736570
$649$	9840.00	0.595152
$650$	1596.00	0.0963081
$651$	0	0
$652$	−6412.00	−0.385143
$653$	−3158.00	−0.189253	−0.0946264	−	0.995513i	$-0.530166\pi$
$653$	−3158.00	−0.189253	−0.0946264	+	0.995513i	$0.530166\pi$
$654$	−2754.00	−0.164663
$655$	20304.0	1.21121
$656$	0	0
$657$	2160.00	0.128264
$658$	0	0
$659$	−24596.0	−1.45391	−0.726953	−	0.686687i	$-0.759064\pi$
$659$	−24596.0	−1.45391	−0.726953	+	0.686687i	$0.759064\pi$
$660$	5040.00	0.297245
$661$	−15468.0	−0.910190	−0.455095	−	0.890443i	$-0.650395\pi$
$661$	−15468.0	−0.910190	−0.455095	+	0.890443i	$0.650395\pi$
$662$	7092.00	0.416372
$663$	−24192.0	−1.41710
$664$	13860.0	0.810049
$665$	0	0
$666$	−2322.00	−0.135099
$667$	−10208.0	−0.592587
$668$	−3528.00	−0.204345
$669$	−15120.0	−0.873801
$670$	−4944.00	−0.285080
$671$	−9840.00	−0.566124
$672$	0	0
$673$	13470.0	0.771516	0.385758	−	0.922600i	$-0.373940\pi$
$673$	13470.0	0.771516	0.385758	+	0.922600i	$0.373940\pi$
$674$	−366.000	−0.0209166
$675$	−513.000	−0.0292524
$676$	−34013.0	−1.93520
$677$	−9564.00	−0.542946	−0.271473	−	0.962446i	$-0.587511\pi$
$677$	−9564.00	−0.542946	−0.271473	+	0.962446i	$0.587511\pi$
$678$	−330.000	−0.0186926
$679$	0	0
$680$	−17280.0	−0.974497
$681$	−6516.00	−0.366657
$682$	5280.00	0.296454
$683$	13852.0	0.776035	0.388018	−	0.921652i	$-0.373160\pi$
$683$	13852.0	0.776035	0.388018	+	0.921652i	$0.373160\pi$
$684$	−756.000	−0.0422608
$685$	13512.0	0.753674
$686$	0	0
$687$	−8100.00	−0.449832
$688$	6396.00	0.354426
$689$	60648.0	3.35342
$690$	−6336.00	−0.349576
$691$	−324.000	−0.0178373	−0.00891863	−	0.999960i	$-0.502839\pi$
$691$	−324.000	−0.0178373	−0.00891863	+	0.999960i	$0.502839\pi$
$692$	12852.0	0.706011
$693$	0	0
$694$	6364.00	0.348090
$695$	13104.0	0.715199
$696$	−2610.00	−0.142143
$697$	0	0
$698$	10500.0	0.569385
$699$	11406.0	0.617188
$700$	0	0
$701$	24922.0	1.34278	0.671392	−	0.741103i	$-0.265697\pi$
$701$	24922.0	1.34278	0.671392	+	0.741103i	$0.265697\pi$
$702$	−2268.00	−0.121938
$703$	3096.00	0.166099
$704$	−3340.00	−0.178808
$705$	14688.0	0.784655
$706$	−408.000	−0.0217497
$707$	0	0
$708$	10332.0	0.548447
$709$	−17886.0	−0.947423	−0.473711	−	0.880680i	$-0.657086\pi$
$709$	−17886.0	−0.947423	−0.473711	+	0.880680i	$0.657086\pi$
$710$	−3552.00	−0.187752
$711$	6984.00	0.368383
$712$	−11160.0	−0.587414
$713$	46464.0	2.44052
$714$	0	0
$715$	−20160.0	−1.05446
$716$	−16604.0	−0.866649
$717$	13224.0	0.688786
$718$	11936.0	0.620401
$719$	−6792.00	−0.352293	−0.176147	−	0.984364i	$-0.556363\pi$
$719$	−6792.00	−0.352293	−0.176147	+	0.984364i	$0.556363\pi$
$720$	4428.00	0.229197
$721$	0	0
$722$	6715.00	0.346131
$723$	−9288.00	−0.477765
$724$	7644.00	0.392385
$725$	1102.00	0.0564514
$726$	−2793.00	−0.142780
$727$	1512.00	0.0771348	0.0385674	−	0.999256i	$-0.487721\pi$
$727$	1512.00	0.0771348	0.0385674	+	0.999256i	$0.487721\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−2880.00	−0.146019
$731$	−14976.0	−0.757739
$732$	−10332.0	−0.521696
$733$	−11244.0	−0.566585	−0.283292	−	0.959034i	$-0.591427\pi$
$733$	−11244.0	−0.566585	−0.283292	+	0.959034i	$0.591427\pi$
$734$	2448.00	0.123103
$735$	0	0
$736$	28336.0	1.41913
$737$	8240.00	0.411838
$738$	0	0
$739$	−1996.00	−0.0993559	−0.0496780	−	0.998765i	$-0.515820\pi$
$739$	−1996.00	−0.0993559	−0.0496780	+	0.998765i	$0.515820\pi$
$740$	−21672.0	−1.07659
$741$	3024.00	0.149918
$742$	0	0
$743$	−656.000	−0.0323907	−0.0161954	−	0.999869i	$-0.505155\pi$
$743$	−656.000	−0.0323907	−0.0161954	+	0.999869i	$0.505155\pi$
$744$	11880.0	0.585406
$745$	12840.0	0.631438
$746$	−11374.0	−0.558219
$747$	8316.00	0.407318
$748$	13440.0	0.656972
$749$	0	0
$750$	−3816.00	−0.185787
$751$	1056.00	0.0513102	0.0256551	−	0.999671i	$-0.491833\pi$
$751$	1056.00	0.0513102	0.0256551	+	0.999671i	$0.491833\pi$
$752$	−16728.0	−0.811180
$753$	2772.00	0.134153
$754$	4872.00	0.235315
$755$	−1440.00	−0.0694132
$756$	0	0
$757$	−18702.0	−0.897934	−0.448967	−	0.893548i	$-0.648208\pi$
$757$	−18702.0	−0.897934	−0.448967	+	0.893548i	$0.648208\pi$
$758$	5892.00	0.282331
$759$	10560.0	0.505011
$760$	2160.00	0.103094
$761$	17904.0	0.852851	0.426425	−	0.904523i	$-0.359773\pi$
$761$	17904.0	0.852851	0.426425	+	0.904523i	$0.359773\pi$
$762$	48.0000	0.00228196
$763$	0	0
$764$	−17584.0	−0.832679
$765$	−10368.0	−0.490008
$766$	10488.0	0.494709
$767$	−41328.0	−1.94559
$768$	357.000	0.0167736
$769$	−7560.00	−0.354513	−0.177257	−	0.984165i	$-0.556722\pi$
$769$	−7560.00	−0.354513	−0.177257	+	0.984165i	$0.556722\pi$
$770$	0	0
$771$	8280.00	0.386766
$772$	17010.0	0.793009
$773$	−14292.0	−0.665003	−0.332502	−	0.943103i	$-0.607893\pi$
$773$	−14292.0	−0.665003	−0.332502	+	0.943103i	$0.607893\pi$
$774$	−1404.00	−0.0652012
$775$	−5016.00	−0.232490
$776$	−2520.00	−0.116576
$777$	0	0
$778$	−4514.00	−0.208014
$779$	0	0
$780$	−21168.0	−0.971713
$781$	5920.00	0.271235
$782$	−16896.0	−0.772634
$783$	−1566.00	−0.0714742
$784$	0	0
$785$	22032.0	1.00173
$786$	5076.00	0.230350
$787$	26364.0	1.19412	0.597062	−	0.802195i	$-0.296335\pi$
$787$	26364.0	1.19412	0.597062	+	0.802195i	$0.296335\pi$
$788$	12334.0	0.557590
$789$	7080.00	0.319461
$790$	−9312.00	−0.419375
$791$	0	0
$792$	2700.00	0.121137
$793$	41328.0	1.85069
$794$	6036.00	0.269785
$795$	25992.0	1.15955
$796$	−21672.0	−0.965005
$797$	17220.0	0.765325	0.382662	−	0.923888i	$-0.375007\pi$
$797$	17220.0	0.765325	0.382662	+	0.923888i	$0.375007\pi$
$798$	0	0
$799$	39168.0	1.73425
$800$	−3059.00	−0.135190
$801$	−6696.00	−0.295370
$802$	6770.00	0.298076
$803$	4800.00	0.210944
$804$	8652.00	0.379518
$805$	0	0
$806$	−22176.0	−0.969127
$807$	−12060.0	−0.526062
$808$	−22860.0	−0.995312
$809$	16442.0	0.714549	0.357274	−	0.933999i	$-0.383706\pi$
$809$	16442.0	0.714549	0.357274	+	0.933999i	$0.383706\pi$
$810$	−972.000	−0.0421637
$811$	−31332.0	−1.35662	−0.678308	−	0.734778i	$-0.737286\pi$
$811$	−31332.0	−1.35662	−0.678308	+	0.734778i	$0.737286\pi$
$812$	0	0
$813$	−14400.0	−0.621193
$814$	−5160.00	−0.222184
$815$	10992.0	0.472433
$816$	11808.0	0.506572
$817$	1872.00	0.0801628
$818$	−12504.0	−0.534465
$819$	0	0
$820$	0	0
$821$	−25810.0	−1.09717	−0.548584	−	0.836095i	$-0.684833\pi$
$821$	−25810.0	−1.09717	−0.548584	+	0.836095i	$0.684833\pi$
$822$	3378.00	0.143335
$823$	12368.0	0.523841	0.261921	−	0.965089i	$-0.415644\pi$
$823$	12368.0	0.523841	0.261921	+	0.965089i	$0.415644\pi$
$824$	−6120.00	−0.258738
$825$	−1140.00	−0.0481087
$826$	0	0
$827$	6316.00	0.265573	0.132786	−	0.991145i	$-0.457608\pi$
$827$	6316.00	0.265573	0.132786	+	0.991145i	$0.457608\pi$
$828$	11088.0	0.465380
$829$	−23868.0	−0.999964	−0.499982	−	0.866036i	$-0.666660\pi$
$829$	−23868.0	−0.999964	−0.499982	+	0.866036i	$0.666660\pi$
$830$	−11088.0	−0.463699
$831$	−19338.0	−0.807254
$832$	14028.0	0.584535
$833$	0	0
$834$	3276.00	0.136018
$835$	6048.00	0.250658
$836$	−1680.00	−0.0695024
$837$	7128.00	0.294360
$838$	−9492.00	−0.391284
$839$	−48216.0	−1.98403	−0.992015	−	0.126120i	$-0.959748\pi$
$839$	−48216.0	−1.98403	−0.992015	+	0.126120i	$0.959748\pi$
$840$	0	0
$841$	−21025.0	−0.862069
$842$	−5182.00	−0.212094
$843$	7806.00	0.318924
$844$	−1092.00	−0.0445358
$845$	58308.0	2.37379
$846$	3672.00	0.149227
$847$	0	0
$848$	−29602.0	−1.19875
$849$	20700.0	0.836775
$850$	1824.00	0.0736032
$851$	−45408.0	−1.82910
$852$	6216.00	0.249949
$853$	−27300.0	−1.09582	−0.547910	−	0.836537i	$-0.684576\pi$
$853$	−27300.0	−1.09582	−0.547910	+	0.836537i	$0.684576\pi$
$854$	0	0
$855$	1296.00	0.0518389
$856$	−12300.0	−0.491128
$857$	8640.00	0.344384	0.172192	−	0.985063i	$-0.444915\pi$
$857$	8640.00	0.344384	0.172192	+	0.985063i	$0.444915\pi$
$858$	−5040.00	−0.200539
$859$	24372.0	0.968058	0.484029	−	0.875052i	$-0.339173\pi$
$859$	24372.0	0.968058	0.484029	+	0.875052i	$0.339173\pi$
$860$	−13104.0	−0.519585
$861$	0	0
$862$	5720.00	0.226014
$863$	2176.00	0.0858307	0.0429154	−	0.999079i	$-0.486335\pi$
$863$	2176.00	0.0858307	0.0429154	+	0.999079i	$0.486335\pi$
$864$	4347.00	0.171167
$865$	−22032.0	−0.866024
$866$	−13608.0	−0.533971
$867$	−12909.0	−0.505666
$868$	0	0
$869$	15520.0	0.605846
$870$	2088.00	0.0813676
$871$	−34608.0	−1.34632
$872$	−13770.0	−0.534760
$873$	−1512.00	−0.0586179
$874$	2112.00	0.0817385
$875$	0	0
$876$	5040.00	0.194390
$877$	−27574.0	−1.06170	−0.530848	−	0.847467i	$-0.678127\pi$
$877$	−27574.0	−1.06170	−0.530848	+	0.847467i	$0.678127\pi$
$878$	−12864.0	−0.494464
$879$	13356.0	0.512499
$880$	9840.00	0.376939
$881$	16968.0	0.648884	0.324442	−	0.945906i	$-0.394824\pi$
$881$	16968.0	0.648884	0.324442	+	0.945906i	$0.394824\pi$
$882$	0	0
$883$	−1860.00	−0.0708879	−0.0354439	−	0.999372i	$-0.511285\pi$
$883$	−1860.00	−0.0708879	−0.0354439	+	0.999372i	$0.511285\pi$
$884$	−56448.0	−2.14768
$885$	−17712.0	−0.672748
$886$	13252.0	0.502494
$887$	2280.00	0.0863077	0.0431538	−	0.999068i	$-0.486259\pi$
$887$	2280.00	0.0863077	0.0431538	+	0.999068i	$0.486259\pi$
$888$	−11610.0	−0.438746
$889$	0	0
$890$	8928.00	0.336255
$891$	1620.00	0.0609114
$892$	−35280.0	−1.32428
$893$	−4896.00	−0.183470
$894$	3210.00	0.120088
$895$	28464.0	1.06307
$896$	0	0
$897$	−44352.0	−1.65091
$898$	−226.000	−0.00839835
$899$	−15312.0	−0.568058
$900$	−1197.00	−0.0443333
$901$	69312.0	2.56284
$902$	0	0
$903$	0	0
$904$	−1650.00	−0.0607060
$905$	−13104.0	−0.481317
$906$	−360.000	−0.0132011
$907$	36084.0	1.32100	0.660501	−	0.750825i	$-0.270344\pi$
$907$	36084.0	1.32100	0.660501	+	0.750825i	$0.270344\pi$
$908$	−15204.0	−0.555686
$909$	−13716.0	−0.500474
$910$	0	0
$911$	24152.0	0.878366	0.439183	−	0.898398i	$-0.355268\pi$
$911$	24152.0	0.878366	0.439183	+	0.898398i	$0.355268\pi$
$912$	−1476.00	−0.0535913
$913$	18480.0	0.669878
$914$	11334.0	0.410170
$915$	17712.0	0.639935
$916$	−18900.0	−0.681740
$917$	0	0
$918$	−2592.00	−0.0931904
$919$	36336.0	1.30426	0.652130	−	0.758108i	$-0.273876\pi$
$919$	36336.0	1.30426	0.652130	+	0.758108i	$0.273876\pi$
$920$	−31680.0	−1.13528
$921$	7308.00	0.261462
$922$	1596.00	0.0570081
$923$	−24864.0	−0.886683
$924$	0	0
$925$	4902.00	0.174245
$926$	−12728.0	−0.451693
$927$	−3672.00	−0.130102
$928$	−9338.00	−0.330318
$929$	432.000	0.0152567	0.00762834	−	0.999971i	$-0.497572\pi$
$929$	432.000	0.0152567	0.00762834	+	0.999971i	$0.497572\pi$
$930$	−9504.00	−0.335106
$931$	0	0
$932$	26614.0	0.935376
$933$	22464.0	0.788251
$934$	3012.00	0.105520
$935$	−23040.0	−0.805870
$936$	−11340.0	−0.396004
$937$	22176.0	0.773168	0.386584	−	0.922254i	$-0.373655\pi$
$937$	22176.0	0.773168	0.386584	+	0.922254i	$0.373655\pi$
$938$	0	0
$939$	5256.00	0.182666
$940$	34272.0	1.18918
$941$	−43524.0	−1.50780	−0.753901	−	0.656988i	$-0.771830\pi$
$941$	−43524.0	−1.50780	−0.753901	+	0.656988i	$0.771830\pi$
$942$	5508.00	0.190510
$943$	0	0
$944$	20172.0	0.695490
$945$	0	0
$946$	−3120.00	−0.107230
$947$	1868.00	0.0640991	0.0320495	−	0.999486i	$-0.489797\pi$
$947$	1868.00	0.0640991	0.0320495	+	0.999486i	$0.489797\pi$
$948$	16296.0	0.558301
$949$	−20160.0	−0.689590
$950$	−228.000	−0.00778663
$951$	4686.00	0.159783
$952$	0	0
$953$	−9238.00	−0.314006	−0.157003	−	0.987598i	$-0.550183\pi$
$953$	−9238.00	−0.314006	−0.157003	+	0.987598i	$0.550183\pi$
$954$	6498.00	0.220525
$955$	30144.0	1.02140
$956$	30856.0	1.04389
$957$	−3480.00	−0.117547
$958$	4296.00	0.144883
$959$	0	0
$960$	6012.00	0.202121
$961$	39905.0	1.33950
$962$	21672.0	0.726334
$963$	−7380.00	−0.246954
$964$	−21672.0	−0.724075
$965$	−29160.0	−0.972739
$966$	0	0
$967$	−30616.0	−1.01814	−0.509071	−	0.860724i	$-0.670011\pi$
$967$	−30616.0	−1.01814	−0.509071	+	0.860724i	$0.670011\pi$
$968$	−13965.0	−0.463690
$969$	3456.00	0.114575
$970$	2016.00	0.0667318
$971$	−27540.0	−0.910196	−0.455098	−	0.890441i	$-0.650396\pi$
$971$	−27540.0	−0.910196	−0.455098	+	0.890441i	$0.650396\pi$
$972$	1701.00	0.0561313
$973$	0	0
$974$	8184.00	0.269232
$975$	4788.00	0.157270
$976$	−20172.0	−0.661568
$977$	−16402.0	−0.537100	−0.268550	−	0.963266i	$-0.586544\pi$
$977$	−16402.0	−0.537100	−0.268550	+	0.963266i	$0.586544\pi$
$978$	2748.00	0.0898480
$979$	−14880.0	−0.485768
$980$	0	0
$981$	−8262.00	−0.268894
$982$	12164.0	0.395284
$983$	55176.0	1.79028	0.895138	−	0.445789i	$-0.147077\pi$
$983$	55176.0	1.79028	0.895138	+	0.445789i	$0.147077\pi$
$984$	0	0
$985$	−21144.0	−0.683963
$986$	5568.00	0.179839
$987$	0	0
$988$	7056.00	0.227208
$989$	−27456.0	−0.882760
$990$	−2160.00	−0.0693427
$991$	27096.0	0.868550	0.434275	−	0.900780i	$-0.357005\pi$
$991$	27096.0	0.868550	0.434275	+	0.900780i	$0.357005\pi$
$992$	42504.0	1.36039
$993$	21276.0	0.679933
$994$	0	0
$995$	37152.0	1.18372
$996$	19404.0	0.617309
$997$	−16812.0	−0.534044	−0.267022	−	0.963691i	$-0.586040\pi$
$997$	−16812.0	−0.534044	−0.267022	+	0.963691i	$0.586040\pi$
$998$	−972.000	−0.0308298
$999$	−6966.00	−0.220615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.a.d.1.1	✓	1
3.2	odd	2		441.4.a.g.1.1		1
4.3	odd	2		2352.4.a.bi.1.1		1
7.2	even	3		147.4.e.f.67.1		2
7.3	odd	6		147.4.e.e.79.1		2
7.4	even	3		147.4.e.f.79.1		2
7.5	odd	6		147.4.e.e.67.1		2
7.6	odd	2		147.4.a.e.1.1	yes	1
21.2	odd	6		441.4.e.g.361.1		2
21.5	even	6		441.4.e.f.361.1		2
21.11	odd	6		441.4.e.g.226.1		2
21.17	even	6		441.4.e.f.226.1		2
21.20	even	2		441.4.a.h.1.1		1
28.27	even	2		2352.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.4.a.d.1.1	✓	1	1.1	even	1	trivial
147.4.a.e.1.1	yes	1	7.6	odd	2
147.4.e.e.67.1		2	7.5	odd	6
147.4.e.e.79.1		2	7.3	odd	6
147.4.e.f.67.1		2	7.2	even	3
147.4.e.f.79.1		2	7.4	even	3
441.4.a.g.1.1		1	3.2	odd	2
441.4.a.h.1.1		1	21.20	even	2
441.4.e.f.226.1		2	21.17	even	6
441.4.e.f.361.1		2	21.5	even	6
441.4.e.g.226.1		2	21.11	odd	6
441.4.e.g.361.1		2	21.2	odd	6
2352.4.a.b.1.1		1	28.27	even	2
2352.4.a.bi.1.1		1	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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