LMFDB - Embedded newform 147.14.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,14,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, 14, names="a")

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

chi := DirichletCharacter("147.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 14 $
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:	$157.629465559$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 3)
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)

$f(q)$

$=$

\(q-12.0000 q^{2} +729.000 q^{3} -8048.00 q^{4} +30210.0 q^{5} -8748.00 q^{6} +194880. q^{8} +531441. q^{9} -362520. q^{10} -1.11829e7 q^{11} -5.86699e6 q^{12} -8.04961e6 q^{13} +2.20231e7 q^{15} +6.35907e7 q^{16} +1.17495e8 q^{17} -6.37729e6 q^{18} +2.14061e8 q^{19} -2.43130e8 q^{20} +1.34195e8 q^{22} +8.30556e8 q^{23} +1.42068e8 q^{24} -3.08059e8 q^{25} +9.65954e7 q^{26} +3.87420e8 q^{27} -1.25240e9 q^{29} -2.64277e8 q^{30} -6.15935e9 q^{31} -2.35954e9 q^{32} -8.15234e9 q^{33} -1.40994e9 q^{34} -4.27704e9 q^{36} -5.49819e9 q^{37} -2.56874e9 q^{38} -5.86817e9 q^{39} +5.88732e9 q^{40} +4.67869e9 q^{41} +7.11501e9 q^{43} +9.00000e10 q^{44} +1.60548e10 q^{45} -9.96667e9 q^{46} +2.95288e10 q^{47} +4.63576e10 q^{48} +3.69671e9 q^{50} +8.56536e10 q^{51} +6.47833e10 q^{52} -2.04125e11 q^{53} -4.64905e9 q^{54} -3.37836e11 q^{55} +1.56051e11 q^{57} +1.50288e10 q^{58} +2.99098e10 q^{59} -1.77242e11 q^{60} +1.34392e11 q^{61} +7.39122e10 q^{62} -4.92620e11 q^{64} -2.43179e11 q^{65} +9.78281e10 q^{66} +3.48519e11 q^{67} -9.45597e11 q^{68} +6.05475e11 q^{69} +1.31434e12 q^{71} +1.03567e11 q^{72} +1.17888e12 q^{73} +6.59783e10 q^{74} -2.24575e11 q^{75} -1.72277e12 q^{76} +7.04180e10 q^{78} -1.07242e12 q^{79} +1.92107e12 q^{80} +2.82430e11 q^{81} -5.61443e10 q^{82} -1.12403e12 q^{83} +3.54951e12 q^{85} -8.53802e10 q^{86} -9.13000e11 q^{87} -2.17933e12 q^{88} -2.23561e12 q^{89} -1.92658e11 q^{90} -6.68431e12 q^{92} -4.49017e12 q^{93} -3.54345e11 q^{94} +6.46679e12 q^{95} -1.72011e12 q^{96} +1.42153e13 q^{97} -5.94306e12 q^{99} +O(q^{100})\)

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 $

$2$	−12.0000	−0.132583	−0.0662913	−	0.997800i	$-0.521117\pi$
$2$	−12.0000	−0.132583	−0.0662913	+	0.997800i	$0.521117\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−8048.00	−0.982422
$5$	30210.0	0.864661	0.432330	−	0.901715i	$-0.357691\pi$
$5$	30210.0	0.864661	0.432330	+	0.901715i	$0.357691\pi$
$6$	−8748.00	−0.0765466
$7$	0	0
$7$	0	0
$8$	194880.	0.262834
$9$	531441.	0.333333
$10$	−362520.	−0.114639
$11$	−1.11829e7	−1.90328	−0.951639	−	0.307218i	$-0.900602\pi$
$11$	−1.11829e7	−1.90328	−0.951639	+	0.307218i	$0.900602\pi$
$12$	−5.86699e6	−0.567202
$13$	−8.04961e6	−0.462534	−0.231267	−	0.972890i	$-0.574287\pi$
$13$	−8.04961e6	−0.462534	−0.231267	+	0.972890i	$0.574287\pi$
$14$	0	0
$15$	2.20231e7	0.499212
$16$	6.35907e7	0.947575
$17$	1.17495e8	1.18059	0.590296	−	0.807187i	$-0.299011\pi$
$17$	1.17495e8	1.18059	0.590296	+	0.807187i	$0.299011\pi$
$18$	−6.37729e6	−0.0441942
$19$	2.14061e8	1.04385	0.521927	−	0.852990i	$-0.325213\pi$
$19$	2.14061e8	1.04385	0.521927	+	0.852990i	$0.325213\pi$
$20$	−2.43130e8	−0.849462
$21$	0	0
$22$	1.34195e8	0.252341
$23$	8.30556e8	1.16987	0.584935	−	0.811080i	$-0.301120\pi$
$23$	8.30556e8	1.16987	0.584935	+	0.811080i	$0.301120\pi$
$24$	1.42068e8	0.151748
$25$	−3.08059e8	−0.252362
$26$	9.65954e7	0.0613239
$27$	3.87420e8	0.192450
$28$	0	0
$29$	−1.25240e9	−0.390981	−0.195491	−	0.980706i	$-0.562630\pi$
$29$	−1.25240e9	−0.390981	−0.195491	+	0.980706i	$0.562630\pi$
$30$	−2.64277e8	−0.0661868
$31$	−6.15935e9	−1.24648	−0.623238	−	0.782032i	$-0.714183\pi$
$31$	−6.15935e9	−1.24648	−0.623238	+	0.782032i	$0.714183\pi$
$32$	−2.35954e9	−0.388466
$33$	−8.15234e9	−1.09886
$34$	−1.40994e9	−0.156526
$35$	0	0
$36$	−4.27704e9	−0.327474
$37$	−5.49819e9	−0.352297	−0.176148	−	0.984364i	$-0.556364\pi$
$37$	−5.49819e9	−0.352297	−0.176148	+	0.984364i	$0.556364\pi$
$38$	−2.56874e9	−0.138397
$39$	−5.86817e9	−0.267044
$40$	5.88732e9	0.227263
$41$	4.67869e9	0.153826	0.0769129	−	0.997038i	$-0.475494\pi$
$41$	4.67869e9	0.153826	0.0769129	+	0.997038i	$0.475494\pi$
$42$	0	0
$43$	7.11501e9	0.171645	0.0858224	−	0.996310i	$-0.472648\pi$
$43$	7.11501e9	0.171645	0.0858224	+	0.996310i	$0.472648\pi$
$44$	9.00000e10	1.86982
$45$	1.60548e10	0.288220
$46$	−9.96667e9	−0.155104
$47$	2.95288e10	0.399585	0.199793	−	0.979838i	$-0.435973\pi$
$47$	2.95288e10	0.399585	0.199793	+	0.979838i	$0.435973\pi$
$48$	4.63576e10	0.547082
$49$	0	0
$50$	3.69671e9	0.0334588
$51$	8.56536e10	0.681615
$52$	6.47833e10	0.454403
$53$	−2.04125e11	−1.26504	−0.632518	−	0.774545i	$-0.717979\pi$
$53$	−2.04125e11	−1.26504	−0.632518	+	0.774545i	$0.717979\pi$
$54$	−4.64905e9	−0.0255155
$55$	−3.37836e11	−1.64569
$56$	0	0
$57$	1.56051e11	0.602670
$58$	1.50288e10	0.0518373
$59$	2.99098e10	0.0923157	0.0461579	−	0.998934i	$-0.485302\pi$
$59$	2.99098e10	0.0923157	0.0461579	+	0.998934i	$0.485302\pi$
$60$	−1.77242e11	−0.490437
$61$	1.34392e11	0.333987	0.166993	−	0.985958i	$-0.446594\pi$
$61$	1.34392e11	0.333987	0.166993	+	0.985958i	$0.446594\pi$
$62$	7.39122e10	0.165261
$63$	0	0
$64$	−4.92620e11	−0.896071
$65$	−2.43179e11	−0.399935
$66$	9.78281e10	0.145689
$67$	3.48519e11	0.470695	0.235348	−	0.971911i	$-0.424377\pi$
$67$	3.48519e11	0.470695	0.235348	+	0.971911i	$0.424377\pi$
$68$	−9.45597e11	−1.15984
$69$	6.05475e11	0.675425
$70$	0	0
$71$	1.31434e12	1.21766	0.608831	−	0.793300i	$-0.291639\pi$
$71$	1.31434e12	1.21766	0.608831	+	0.793300i	$0.291639\pi$
$72$	1.03567e11	0.0876115
$73$	1.17888e12	0.911737	0.455868	−	0.890047i	$-0.349329\pi$
$73$	1.17888e12	0.911737	0.455868	+	0.890047i	$0.349329\pi$
$74$	6.59783e10	0.0467084
$75$	−2.24575e11	−0.145701
$76$	−1.72277e12	−1.02551
$77$	0	0
$78$	7.04180e10	0.0354054
$79$	−1.07242e12	−0.496351	−0.248176	−	0.968715i	$-0.579831\pi$
$79$	−1.07242e12	−0.496351	−0.248176	+	0.968715i	$0.579831\pi$
$80$	1.92107e12	0.819330
$81$	2.82430e11	0.111111
$82$	−5.61443e10	−0.0203946
$83$	−1.12403e12	−0.377371	−0.188685	−	0.982038i	$-0.560423\pi$
$83$	−1.12403e12	−0.377371	−0.188685	+	0.982038i	$0.560423\pi$
$84$	0	0
$85$	3.54951e12	1.02081
$86$	−8.53802e10	−0.0227571
$87$	−9.13000e11	−0.225733
$88$	−2.17933e12	−0.500247
$89$	−2.23561e12	−0.476827	−0.238414	−	0.971164i	$-0.576627\pi$
$89$	−2.23561e12	−0.476827	−0.238414	+	0.971164i	$0.576627\pi$
$90$	−1.92658e11	−0.0382130
$91$	0	0
$92$	−6.68431e12	−1.14931
$93$	−4.49017e12	−0.719653
$94$	−3.54345e11	−0.0529780
$95$	6.46679e12	0.902580
$96$	−1.72011e12	−0.224281
$97$	1.42153e13	1.73276	0.866380	−	0.499385i	$-0.166441\pi$
$97$	1.42153e13	1.73276	0.866380	+	0.499385i	$0.166441\pi$
$98$	0	0
$99$	−5.94306e12	−0.634426
$100$	2.47926e12	0.247926
$101$	−1.70194e13	−1.59535	−0.797675	−	0.603088i	$-0.793937\pi$
$101$	−1.70194e13	−1.59535	−0.797675	+	0.603088i	$0.793937\pi$
$102$	−1.02784e12	−0.0903703
$103$	−1.09904e13	−0.906928	−0.453464	−	0.891275i	$-0.649812\pi$
$103$	−1.09904e13	−0.906928	−0.453464	+	0.891275i	$0.649812\pi$
$104$	−1.56871e12	−0.121570
$105$	0	0
$106$	2.44950e12	0.167722
$107$	−1.96403e13	−1.26519	−0.632593	−	0.774485i	$-0.718009\pi$
$107$	−1.96403e13	−1.26519	−0.632593	+	0.774485i	$0.718009\pi$
$108$	−3.11796e12	−0.189067
$109$	−9.82099e12	−0.560897	−0.280448	−	0.959869i	$-0.590483\pi$
$109$	−9.82099e12	−0.560897	−0.280448	+	0.959869i	$0.590483\pi$
$110$	4.05403e12	0.218190
$111$	−4.00818e12	−0.203399
$112$	0	0
$113$	−1.70267e13	−0.769344	−0.384672	−	0.923053i	$-0.625685\pi$
$113$	−1.70267e13	−0.769344	−0.384672	+	0.923053i	$0.625685\pi$
$114$	−1.87261e12	−0.0799035
$115$	2.50911e13	1.01154
$116$	1.00793e13	0.384109
$117$	−4.27789e12	−0.154178
$118$	−3.58918e11	−0.0122395
$119$	0	0
$120$	4.29186e12	0.131210
$121$	9.05347e13	2.62247
$122$	−1.61270e12	−0.0442808
$123$	3.41076e12	0.0888113
$124$	4.95705e13	1.22457
$125$	−4.61839e13	−1.08287
$126$	0	0
$127$	−4.49347e13	−0.950292	−0.475146	−	0.879907i	$-0.657605\pi$
$127$	−4.49347e13	−0.950292	−0.475146	+	0.879907i	$0.657605\pi$
$128$	2.52408e13	0.507270
$129$	5.18685e12	0.0990992
$130$	2.91815e12	0.0530243
$131$	1.20182e12	0.0207768	0.0103884	−	0.999946i	$-0.496693\pi$
$131$	1.20182e12	0.0207768	0.0103884	+	0.999946i	$0.496693\pi$
$132$	6.56100e13	1.07954
$133$	0	0
$134$	−4.18223e12	−0.0624060
$135$	1.17040e13	0.166404
$136$	2.28974e13	0.310300
$137$	1.71562e13	0.221685	0.110842	−	0.993838i	$-0.464645\pi$
$137$	1.71562e13	0.221685	0.110842	+	0.993838i	$0.464645\pi$
$138$	−7.26570e12	−0.0895495
$139$	−1.05644e14	−1.24236	−0.621182	−	0.783666i	$-0.713347\pi$
$139$	−1.05644e14	−1.24236	−0.621182	+	0.783666i	$0.713347\pi$
$140$	0	0
$141$	2.15265e13	0.230701
$142$	−1.57720e13	−0.161441
$143$	9.00181e13	0.880330
$144$	3.37947e13	0.315858
$145$	−3.78350e13	−0.338066
$146$	−1.41465e13	−0.120880
$147$	0	0
$148$	4.42494e13	0.346104
$149$	−8.53533e13	−0.639012	−0.319506	−	0.947584i	$-0.603517\pi$
$149$	−8.53533e13	−0.639012	−0.319506	+	0.947584i	$0.603517\pi$
$150$	2.69490e12	0.0193174
$151$	−6.16414e13	−0.423177	−0.211589	−	0.977359i	$-0.567864\pi$
$151$	−6.16414e13	−0.423177	−0.211589	+	0.977359i	$0.567864\pi$
$152$	4.17163e13	0.274361
$153$	6.24415e13	0.393531
$154$	0	0
$155$	−1.86074e14	−1.07778
$156$	4.72270e13	0.262350
$157$	1.18021e14	0.628942	0.314471	−	0.949267i	$-0.398173\pi$
$157$	1.18021e14	0.628942	0.314471	+	0.949267i	$0.398173\pi$
$158$	1.28690e13	0.0658075
$159$	−1.48807e14	−0.730369
$160$	−7.12818e13	−0.335892
$161$	0	0
$162$	−3.38915e12	−0.0147314
$163$	1.54710e14	0.646099	0.323050	−	0.946382i	$-0.395292\pi$
$163$	1.54710e14	0.646099	0.323050	+	0.946382i	$0.395292\pi$
$164$	−3.76541e13	−0.151122
$165$	−2.46282e14	−0.950139
$166$	1.34883e13	0.0500328
$167$	−3.76012e14	−1.34136	−0.670679	−	0.741748i	$-0.733997\pi$
$167$	−3.76012e14	−1.34136	−0.670679	+	0.741748i	$0.733997\pi$
$168$	0	0
$169$	−2.38079e14	−0.786063
$170$	−4.25942e13	−0.135342
$171$	1.13761e14	0.347951
$172$	−5.72616e13	−0.168628
$173$	−3.73562e14	−1.05941	−0.529704	−	0.848182i	$-0.677697\pi$
$173$	−3.73562e14	−1.05941	−0.529704	+	0.848182i	$0.677697\pi$
$174$	1.09560e13	0.0299283
$175$	0	0
$176$	−7.11128e14	−1.80350
$177$	2.18043e13	0.0532985
$178$	2.68273e13	0.0632190
$179$	4.23349e13	0.0961952	0.0480976	−	0.998843i	$-0.484684\pi$
$179$	4.23349e13	0.0961952	0.0480976	+	0.998843i	$0.484684\pi$
$180$	−1.29209e14	−0.283154
$181$	3.10447e14	0.656261	0.328130	−	0.944632i	$-0.393581\pi$
$181$	3.10447e14	0.656261	0.328130	+	0.944632i	$0.393581\pi$
$182$	0	0
$183$	9.79718e13	0.192827
$184$	1.61859e14	0.307482
$185$	−1.66100e14	−0.304617
$186$	5.38820e13	0.0954134
$187$	−1.31393e15	−2.24700
$188$	−2.37648e14	−0.392561
$189$	0	0
$190$	−7.76015e13	−0.119666
$191$	−8.62273e14	−1.28507	−0.642537	−	0.766255i	$-0.722118\pi$
$191$	−8.62273e14	−1.28507	−0.642537	+	0.766255i	$0.722118\pi$
$192$	−3.59120e14	−0.517347
$193$	−9.37837e14	−1.30618	−0.653092	−	0.757278i	$-0.726529\pi$
$193$	−9.37837e14	−1.30618	−0.653092	+	0.757278i	$0.726529\pi$
$194$	−1.70583e14	−0.229734
$195$	−1.77277e14	−0.230902
$196$	0	0
$197$	−6.71715e14	−0.818756	−0.409378	−	0.912365i	$-0.634254\pi$
$197$	−6.71715e14	−0.818756	−0.409378	+	0.912365i	$0.634254\pi$
$198$	7.13167e13	0.0841138
$199$	4.36451e13	0.0498185	0.0249093	−	0.999690i	$-0.492070\pi$
$199$	4.36451e13	0.0498185	0.0249093	+	0.999690i	$0.492070\pi$
$200$	−6.00345e13	−0.0663294
$201$	2.54070e14	0.271756
$202$	2.04233e14	0.211515
$203$	0	0
$204$	−6.89340e14	−0.669634
$205$	1.41343e14	0.133007
$206$	1.31885e14	0.120243
$207$	4.41391e14	0.389957
$208$	−5.11880e14	−0.438285
$209$	−2.39383e15	−1.98675
$210$	0	0
$211$	−1.62162e15	−1.26507	−0.632534	−	0.774533i	$-0.717985\pi$
$211$	−1.62162e15	−1.26507	−0.632534	+	0.774533i	$0.717985\pi$
$212$	1.64280e15	1.24280
$213$	9.58151e14	0.703018
$214$	2.35684e14	0.167742
$215$	2.14945e14	0.148415
$216$	7.55005e13	0.0505825
$217$	0	0
$218$	1.17852e14	0.0743651
$219$	8.59401e14	0.526392
$220$	2.71890e15	1.61676
$221$	−9.45786e14	−0.546064
$222$	4.80982e13	0.0269671
$223$	−1.47333e15	−0.802266	−0.401133	−	0.916020i	$-0.631383\pi$
$223$	−1.47333e15	−0.802266	−0.401133	+	0.916020i	$0.631383\pi$
$224$	0	0
$225$	−1.63715e14	−0.0841207
$226$	2.04320e14	0.102002
$227$	3.74889e15	1.81859	0.909294	−	0.416153i	$-0.136622\pi$
$227$	3.74889e15	1.81859	0.909294	+	0.416153i	$0.136622\pi$
$228$	−1.25590e15	−0.592076
$229$	1.47993e13	0.00678126	0.00339063	−	0.999994i	$-0.498921\pi$
$229$	1.47993e13	0.00678126	0.00339063	+	0.999994i	$0.498921\pi$
$230$	−3.01093e14	−0.134113
$231$	0	0
$232$	−2.44068e14	−0.102763
$233$	3.63053e15	1.48647	0.743236	−	0.669030i	$-0.233290\pi$
$233$	3.63053e15	1.48647	0.743236	+	0.669030i	$0.233290\pi$
$234$	5.13347e13	0.0204413
$235$	8.92064e14	0.345506
$236$	−2.40714e14	−0.0906930
$237$	−7.81795e14	−0.286569
$238$	0	0
$239$	−4.33900e15	−1.50592	−0.752962	−	0.658063i	$-0.771376\pi$
$239$	−4.33900e15	−1.50592	−0.752962	+	0.658063i	$0.771376\pi$
$240$	1.40046e15	0.473041
$241$	−3.02372e15	−0.994103	−0.497051	−	0.867721i	$-0.665584\pi$
$241$	−3.02372e15	−0.994103	−0.497051	+	0.867721i	$0.665584\pi$
$242$	−1.08642e15	−0.347693
$243$	2.05891e14	0.0641500
$244$	−1.08159e15	−0.328116
$245$	0	0
$246$	−4.09292e13	−0.0117748
$247$	−1.72311e15	−0.482818
$248$	−1.20033e15	−0.327617
$249$	−8.19414e14	−0.217875
$250$	5.54207e14	0.143569
$251$	1.75146e15	0.442099	0.221050	−	0.975263i	$-0.429052\pi$
$251$	1.75146e15	0.442099	0.221050	+	0.975263i	$0.429052\pi$
$252$	0	0
$253$	−9.28803e15	−2.22659
$254$	5.39216e14	0.125992
$255$	2.58759e15	0.589366
$256$	3.73265e15	0.828816
$257$	−4.87604e15	−1.05561	−0.527803	−	0.849367i	$-0.676984\pi$
$257$	−4.87604e15	−1.05561	−0.527803	+	0.849367i	$0.676984\pi$
$258$	−6.22421e13	−0.0131388
$259$	0	0
$260$	1.95710e15	0.392904
$261$	−6.65577e14	−0.130327
$262$	−1.44219e13	−0.00275463
$263$	4.67882e15	0.871815	0.435907	−	0.899992i	$-0.356428\pi$
$263$	4.67882e15	0.871815	0.435907	+	0.899992i	$0.356428\pi$
$264$	−1.58873e15	−0.288818
$265$	−6.16662e15	−1.09383
$266$	0	0
$267$	−1.62976e15	−0.275296
$268$	−2.80488e15	−0.462422
$269$	1.80262e15	0.290078	0.145039	−	0.989426i	$-0.453669\pi$
$269$	1.80262e15	0.290078	0.145039	+	0.989426i	$0.453669\pi$
$270$	−1.40448e14	−0.0220623
$271$	−6.10016e15	−0.935494	−0.467747	−	0.883862i	$-0.654934\pi$
$271$	−6.10016e15	−0.935494	−0.467747	+	0.883862i	$0.654934\pi$
$272$	7.47156e15	1.11870
$273$	0	0
$274$	−2.05874e14	−0.0293915
$275$	3.44500e15	0.480315
$276$	−4.87286e15	−0.663552
$277$	−1.07023e16	−1.42351	−0.711754	−	0.702428i	$-0.752099\pi$
$277$	−1.07023e16	−1.42351	−0.711754	+	0.702428i	$0.752099\pi$
$278$	1.26773e15	0.164716
$279$	−3.27333e15	−0.415492
$280$	0	0
$281$	−2.45460e15	−0.297433	−0.148717	−	0.988880i	$-0.547514\pi$
$281$	−2.45460e15	−0.297433	−0.148717	+	0.988880i	$0.547514\pi$
$282$	−2.58318e14	−0.0305869
$283$	−4.01155e15	−0.464195	−0.232098	−	0.972692i	$-0.574559\pi$
$283$	−4.01155e15	−0.464195	−0.232098	+	0.972692i	$0.574559\pi$
$284$	−1.05778e16	−1.19626
$285$	4.71429e15	0.521105
$286$	−1.08022e15	−0.116716
$287$	0	0
$288$	−1.25396e15	−0.129489
$289$	3.90041e15	0.393799
$290$	4.54020e14	0.0448217
$291$	1.03629e16	1.00041
$292$	−9.48759e15	−0.895710
$293$	−2.08187e15	−0.192227	−0.0961133	−	0.995370i	$-0.530641\pi$
$293$	−2.08187e15	−0.192227	−0.0961133	+	0.995370i	$0.530641\pi$
$294$	0	0
$295$	9.03576e14	0.0798218
$296$	−1.07149e15	−0.0925957
$297$	−4.33249e15	−0.366286
$298$	1.02424e15	0.0847219
$299$	−6.68565e15	−0.541104
$300$	1.80738e15	0.143140
$301$	0	0
$302$	7.39697e14	0.0561059
$303$	−1.24072e16	−0.921075
$304$	1.36123e16	0.989130
$305$	4.05998e15	0.288785
$306$	−7.49298e14	−0.0521753
$307$	1.32352e16	0.902260	0.451130	−	0.892458i	$-0.351021\pi$
$307$	1.32352e16	0.902260	0.451130	+	0.892458i	$0.351021\pi$
$308$	0	0
$309$	−8.01202e15	−0.523615
$310$	2.23289e15	0.142895
$311$	8.09301e15	0.507187	0.253593	−	0.967311i	$-0.418388\pi$
$311$	8.09301e15	0.507187	0.253593	+	0.967311i	$0.418388\pi$
$312$	−1.14359e15	−0.0701883
$313$	1.48181e16	0.890748	0.445374	−	0.895345i	$-0.353071\pi$
$313$	1.48181e16	0.890748	0.445374	+	0.895345i	$0.353071\pi$
$314$	−1.41625e15	−0.0833868
$315$	0	0
$316$	8.63084e15	0.487626
$317$	−2.43171e16	−1.34594	−0.672970	−	0.739670i	$-0.734982\pi$
$317$	−2.43171e16	−1.34594	−0.672970	+	0.739670i	$0.734982\pi$
$318$	1.78569e15	0.0968342
$319$	1.40055e16	0.744147
$320$	−1.48821e16	−0.774797
$321$	−1.43178e16	−0.730455
$322$	0	0
$323$	2.51511e16	1.23237
$324$	−2.27299e15	−0.109158
$325$	2.47976e15	0.116726
$326$	−1.85652e15	−0.0856615
$327$	−7.15950e15	−0.323834
$328$	9.11783e14	0.0404307
$329$	0	0
$330$	2.95539e15	0.125972
$331$	1.16232e16	0.485783	0.242892	−	0.970053i	$-0.421904\pi$
$331$	1.16232e16	0.485783	0.242892	+	0.970053i	$0.421904\pi$
$332$	9.04615e15	0.370737
$333$	−2.92196e15	−0.117432
$334$	4.51214e15	0.177841
$335$	1.05288e16	0.406992
$336$	0	0
$337$	4.62652e16	1.72052	0.860262	−	0.509853i	$-0.170300\pi$
$337$	4.62652e16	1.72052	0.860262	+	0.509853i	$0.170300\pi$
$338$	2.85695e15	0.104218
$339$	−1.24125e16	−0.444181
$340$	−2.85665e16	−1.00287
$341$	6.88795e16	2.37239
$342$	−1.36513e15	−0.0461323
$343$	0	0
$344$	1.38657e15	0.0451142
$345$	1.82914e16	0.584013
$346$	4.48275e15	0.140459
$347$	4.79404e15	0.147421	0.0737106	−	0.997280i	$-0.476516\pi$
$347$	4.79404e15	0.147421	0.0737106	+	0.997280i	$0.476516\pi$
$348$	7.34782e15	0.221765
$349$	−3.76900e16	−1.11651	−0.558253	−	0.829671i	$-0.688528\pi$
$349$	−3.76900e16	−1.11651	−0.558253	+	0.829671i	$0.688528\pi$
$350$	0	0
$351$	−3.11859e15	−0.0890146
$352$	2.63866e16	0.739360
$353$	−4.80179e16	−1.32089	−0.660446	−	0.750873i	$-0.729633\pi$
$353$	−4.80179e16	−1.32089	−0.660446	+	0.750873i	$0.729633\pi$
$354$	−2.61651e14	−0.00706645
$355$	3.97061e16	1.05286
$356$	1.79922e16	0.468446
$357$	0	0
$358$	−5.08018e14	−0.0127538
$359$	4.06616e16	1.00247	0.501234	−	0.865312i	$-0.332880\pi$
$359$	4.06616e16	1.00247	0.501234	+	0.865312i	$0.332880\pi$
$360$	3.12877e15	0.0757542
$361$	3.76929e15	0.0896320
$362$	−3.72536e15	−0.0870087
$363$	6.59998e16	1.51408
$364$	0	0
$365$	3.56138e16	0.788343
$366$	−1.17566e15	−0.0255656
$367$	−2.96733e16	−0.633923	−0.316961	−	0.948438i	$-0.602663\pi$
$367$	−2.96733e16	−0.633923	−0.316961	+	0.948438i	$0.602663\pi$
$368$	5.28156e16	1.10854
$369$	2.48645e15	0.0512752
$370$	1.99320e15	0.0403869
$371$	0	0
$372$	3.61369e16	0.707003
$373$	−9.01346e16	−1.73294	−0.866471	−	0.499227i	$-0.833617\pi$
$373$	−9.01346e16	−1.73294	−0.866471	+	0.499227i	$0.833617\pi$
$374$	1.57672e16	0.297912
$375$	−3.36681e16	−0.625194
$376$	5.75457e15	0.105025
$377$	1.00813e16	0.180842
$378$	0	0
$379$	−1.54841e16	−0.268369	−0.134184	−	0.990956i	$-0.542841\pi$
$379$	−1.54841e16	−0.268369	−0.134184	+	0.990956i	$0.542841\pi$
$380$	−5.20448e16	−0.886714
$381$	−3.27574e16	−0.548652
$382$	1.03473e16	0.170378
$383$	−9.37088e15	−0.151701	−0.0758505	−	0.997119i	$-0.524167\pi$
$383$	−9.37088e15	−0.151701	−0.0758505	+	0.997119i	$0.524167\pi$
$384$	1.84006e16	0.292872
$385$	0	0
$386$	1.12540e16	0.173177
$387$	3.78121e15	0.0572150
$388$	−1.14404e17	−1.70230
$389$	2.95806e16	0.432847	0.216423	−	0.976300i	$-0.430561\pi$
$389$	2.95806e16	0.432847	0.216423	+	0.976300i	$0.430561\pi$
$390$	2.12733e15	0.0306136
$391$	9.75858e16	1.38114
$392$	0	0
$393$	8.76130e14	0.0119955
$394$	8.06058e15	0.108553
$395$	−3.23978e16	−0.429175
$396$	4.78297e16	0.623274
$397$	−1.80617e16	−0.231538	−0.115769	−	0.993276i	$-0.536933\pi$
$397$	−1.80617e16	−0.231538	−0.115769	+	0.993276i	$0.536933\pi$
$398$	−5.23742e14	−0.00660507
$399$	0	0
$400$	−1.95897e16	−0.239132
$401$	−1.20412e17	−1.44621	−0.723107	−	0.690736i	$-0.757287\pi$
$401$	−1.20412e17	−1.44621	−0.723107	+	0.690736i	$0.757287\pi$
$402$	−3.04884e15	−0.0360301
$403$	4.95804e16	0.576537
$404$	1.36972e17	1.56731
$405$	8.53220e15	0.0960734
$406$	0	0
$407$	6.14858e16	0.670519
$408$	1.66922e16	0.179152
$409$	1.77522e16	0.187521	0.0937606	−	0.995595i	$-0.470111\pi$
$409$	1.77522e16	0.187521	0.0937606	+	0.995595i	$0.470111\pi$
$410$	−1.69612e15	−0.0176344
$411$	1.25068e16	0.127990
$412$	8.84510e16	0.890986
$413$	0	0
$414$	−5.29670e15	−0.0517015
$415$	−3.39568e16	−0.326298
$416$	1.89934e16	0.179679
$417$	−7.70145e16	−0.717279
$418$	2.87259e16	0.263408
$419$	−1.75670e17	−1.58602	−0.793008	−	0.609212i	$-0.791486\pi$
$419$	−1.75670e17	−1.58602	−0.793008	+	0.609212i	$0.791486\pi$
$420$	0	0
$421$	1.84473e17	1.61473	0.807365	−	0.590052i	$-0.200893\pi$
$421$	1.84473e17	1.61473	0.807365	+	0.590052i	$0.200893\pi$
$422$	1.94595e16	0.167726
$423$	1.56928e16	0.133195
$424$	−3.97799e16	−0.332495
$425$	−3.61953e16	−0.297937
$426$	−1.14978e16	−0.0932079
$427$	0	0
$428$	1.58065e17	1.24295
$429$	6.56232e16	0.508259
$430$	−2.57933e15	−0.0196772
$431$	8.05532e16	0.605314	0.302657	−	0.953100i	$-0.402126\pi$
$431$	8.05532e16	0.605314	0.302657	+	0.953100i	$0.402126\pi$
$432$	2.46363e16	0.182361
$433$	1.97092e17	1.43714	0.718568	−	0.695457i	$-0.244798\pi$
$433$	1.97092e17	1.43714	0.718568	+	0.695457i	$0.244798\pi$
$434$	0	0
$435$	−2.75817e16	−0.195183
$436$	7.90393e16	0.551037
$437$	1.77790e17	1.22117
$438$	−1.03128e16	−0.0697903
$439$	−9.89007e16	−0.659447	−0.329724	−	0.944078i	$-0.606956\pi$
$439$	−9.89007e16	−0.659447	−0.329724	+	0.944078i	$0.606956\pi$
$440$	−6.58374e16	−0.432544
$441$	0	0
$442$	1.13494e16	0.0723985
$443$	−1.25104e17	−0.786404	−0.393202	−	0.919452i	$-0.628633\pi$
$443$	−1.25104e17	−0.786404	−0.393202	+	0.919452i	$0.628633\pi$
$444$	3.22578e16	0.199823
$445$	−6.75378e16	−0.412294
$446$	1.76800e16	0.106366
$447$	−6.22225e16	−0.368934
$448$	0	0
$449$	−1.80095e17	−1.03729	−0.518645	−	0.854990i	$-0.673563\pi$
$449$	−1.80095e17	−1.03729	−0.518645	+	0.854990i	$0.673563\pi$
$450$	1.96458e15	0.0111529
$451$	−5.23213e16	−0.292773
$452$	1.37031e17	0.755820
$453$	−4.49366e16	−0.244322
$454$	−4.49867e16	−0.241113
$455$	0	0
$456$	3.04112e16	0.158402
$457$	−9.43597e16	−0.484542	−0.242271	−	0.970209i	$-0.577892\pi$
$457$	−9.43597e16	−0.484542	−0.242271	+	0.970209i	$0.577892\pi$
$458$	−1.77592e14	−0.000899076 0
$459$	4.55198e16	0.227205
$460$	−2.01933e17	−0.993760
$461$	−8.00500e16	−0.388423	−0.194212	−	0.980960i	$-0.562215\pi$
$461$	−8.00500e16	−0.388423	−0.194212	+	0.980960i	$0.562215\pi$
$462$	0	0
$463$	2.14174e17	1.01039	0.505196	−	0.863004i	$-0.331420\pi$
$463$	2.14174e17	1.01039	0.505196	+	0.863004i	$0.331420\pi$
$464$	−7.96410e16	−0.370484
$465$	−1.35648e17	−0.622256
$466$	−4.35663e16	−0.197080
$467$	1.80681e17	0.806031	0.403015	−	0.915193i	$-0.367962\pi$
$467$	1.80681e17	0.806031	0.403015	+	0.915193i	$0.367962\pi$
$468$	3.44285e16	0.151468
$469$	0	0
$470$	−1.07048e16	−0.0458080
$471$	8.60372e16	0.363120
$472$	5.82883e15	0.0242638
$473$	−7.95665e16	−0.326688
$474$	9.38154e15	0.0379940
$475$	−6.59435e16	−0.263429
$476$	0	0
$477$	−1.08480e17	−0.421679
$478$	5.20680e16	0.199659
$479$	2.66712e17	1.00893	0.504466	−	0.863431i	$-0.331689\pi$
$479$	2.66712e17	1.00893	0.504466	+	0.863431i	$0.331689\pi$
$480$	−5.19645e16	−0.193927
$481$	4.42583e16	0.162949
$482$	3.62847e16	0.131801
$483$	0	0
$484$	−7.28623e17	−2.57637
$485$	4.29443e17	1.49825
$486$	−2.47069e15	−0.00850517
$487$	−2.63552e17	−0.895216	−0.447608	−	0.894230i	$-0.647724\pi$
$487$	−2.63552e17	−0.895216	−0.447608	+	0.894230i	$0.647724\pi$
$488$	2.61903e16	0.0877833
$489$	1.12784e17	0.373026
$490$	0	0
$491$	4.11733e17	1.32613	0.663065	−	0.748562i	$-0.269255\pi$
$491$	4.11733e17	1.32613	0.663065	+	0.748562i	$0.269255\pi$
$492$	−2.74498e16	−0.0872502
$493$	−1.47150e17	−0.461590
$494$	2.06773e16	0.0640132
$495$	−1.79540e17	−0.548563
$496$	−3.91677e17	−1.18113
$497$	0	0
$498$	9.83297e15	0.0288864
$499$	3.99658e17	1.15887	0.579435	−	0.815018i	$-0.303273\pi$
$499$	3.99658e17	1.15887	0.579435	+	0.815018i	$0.303273\pi$
$500$	3.71688e17	1.06383
$501$	−2.74113e17	−0.774433
$502$	−2.10175e16	−0.0586146
$503$	2.83581e17	0.780702	0.390351	−	0.920666i	$-0.372354\pi$
$503$	2.83581e17	0.780702	0.390351	+	0.920666i	$0.372354\pi$
$504$	0	0
$505$	−5.14157e17	−1.37944
$506$	1.11456e17	0.295207
$507$	−1.73559e17	−0.453834
$508$	3.61634e17	0.933588
$509$	−6.40327e17	−1.63206	−0.816030	−	0.578009i	$-0.803830\pi$
$509$	−6.40327e17	−1.63206	−0.816030	+	0.578009i	$0.803830\pi$
$510$	−3.10511e16	−0.0781396
$511$	0	0
$512$	−2.51565e17	−0.617156
$513$	8.29318e16	0.200890
$514$	5.85124e16	0.139955
$515$	−3.32021e17	−0.784185
$516$	−4.17437e16	−0.0973572
$517$	−3.30218e17	−0.760522
$518$	0	0
$519$	−2.72327e17	−0.611650
$520$	−4.73907e16	−0.105117
$521$	4.01348e17	0.879175	0.439588	−	0.898200i	$-0.355125\pi$
$521$	4.01348e17	0.879175	0.439588	+	0.898200i	$0.355125\pi$
$522$	7.98692e15	0.0172791
$523$	5.05985e17	1.08113	0.540564	−	0.841303i	$-0.318211\pi$
$523$	5.05985e17	1.08113	0.540564	+	0.841303i	$0.318211\pi$
$524$	−9.67228e15	−0.0204115
$525$	0	0
$526$	−5.61459e16	−0.115587
$527$	−7.23691e17	−1.47158
$528$	−5.18413e17	−1.04125
$529$	1.85786e17	0.368597
$530$	7.39994e16	0.145022
$531$	1.58953e16	0.0307719
$532$	0	0
$533$	−3.76616e16	−0.0711496
$534$	1.95571e16	0.0364995
$535$	−5.93334e17	−1.09396
$536$	6.79193e16	0.123715
$537$	3.08621e16	0.0555383
$538$	−2.16314e16	−0.0384592
$539$	0	0
$540$	−9.41936e16	−0.163479
$541$	−1.69124e17	−0.290017	−0.145009	−	0.989430i	$-0.546321\pi$
$541$	−1.69124e17	−0.290017	−0.145009	+	0.989430i	$0.546321\pi$
$542$	7.32020e16	0.124030
$543$	2.26316e17	0.378892
$544$	−2.77234e17	−0.458620
$545$	−2.96692e17	−0.484986
$546$	0	0
$547$	−4.32104e17	−0.689717	−0.344858	−	0.938655i	$-0.612073\pi$
$547$	−4.32104e17	−0.689717	−0.344858	+	0.938655i	$0.612073\pi$
$548$	−1.38073e17	−0.217788
$549$	7.14214e16	0.111329
$550$	−4.13399e16	−0.0636814
$551$	−2.68091e17	−0.408128
$552$	1.17995e17	0.177525
$553$	0	0
$554$	1.28428e17	0.188732
$555$	−1.21087e17	−0.175871
$556$	8.50224e17	1.22053
$557$	1.36804e18	1.94107	0.970534	−	0.240966i	$-0.0774642\pi$
$557$	1.36804e18	1.94107	0.970534	+	0.240966i	$0.0774642\pi$
$558$	3.92800e16	0.0550870
$559$	−5.72731e16	−0.0793915
$560$	0	0
$561$	−9.57856e17	−1.29730
$562$	2.94552e16	0.0394345
$563$	9.52405e17	1.26043	0.630213	−	0.776422i	$-0.282968\pi$
$563$	9.52405e17	1.26043	0.630213	+	0.776422i	$0.282968\pi$
$564$	−1.73245e17	−0.226645
$565$	−5.14377e17	−0.665221
$566$	4.81386e16	0.0615442
$567$	0	0
$568$	2.56138e17	0.320044
$569$	1.53632e17	0.189780	0.0948902	−	0.995488i	$-0.469750\pi$
$569$	1.53632e17	0.189780	0.0948902	+	0.995488i	$0.469750\pi$
$570$	−5.65715e16	−0.0690894
$571$	−1.27956e18	−1.54500	−0.772498	−	0.635017i	$-0.780993\pi$
$571$	−1.27956e18	−1.54500	−0.772498	+	0.635017i	$0.780993\pi$
$572$	−7.24466e17	−0.864856
$573$	−6.28597e17	−0.741938
$574$	0	0
$575$	−2.55860e17	−0.295231
$576$	−2.61799e17	−0.298690
$577$	−3.56770e17	−0.402481	−0.201241	−	0.979542i	$-0.564497\pi$
$577$	−3.56770e17	−0.402481	−0.201241	+	0.979542i	$0.564497\pi$
$578$	−4.68049e16	−0.0522108
$579$	−6.83683e17	−0.754126
$580$	3.04496e17	0.332124
$581$	0	0
$582$	−1.24355e17	−0.132637
$583$	2.28271e18	2.40772
$584$	2.29739e17	0.239636
$585$	−1.29235e17	−0.133312
$586$	2.49824e16	0.0254859
$587$	−1.28968e18	−1.30118	−0.650588	−	0.759431i	$-0.725477\pi$
$587$	−1.28968e18	−1.30118	−0.650588	+	0.759431i	$0.725477\pi$
$588$	0	0
$589$	−1.31848e18	−1.30114
$590$	−1.08429e16	−0.0105830
$591$	−4.89680e17	−0.472709
$592$	−3.49634e17	−0.333827
$593$	1.88640e18	1.78147	0.890735	−	0.454523i	$-0.150190\pi$
$593$	1.88640e18	1.78147	0.890735	+	0.454523i	$0.150190\pi$
$594$	5.19899e16	0.0485631
$595$	0	0
$596$	6.86923e17	0.627780
$597$	3.18173e16	0.0287627
$598$	8.02278e16	0.0717410
$599$	−1.44668e18	−1.27967	−0.639834	−	0.768513i	$-0.720997\pi$
$599$	−1.44668e18	−1.27967	−0.639834	+	0.768513i	$0.720997\pi$
$600$	−4.37652e16	−0.0382953
$601$	4.44358e16	0.0384635	0.0192317	−	0.999815i	$-0.493878\pi$
$601$	4.44358e16	0.0384635	0.0192317	+	0.999815i	$0.493878\pi$
$602$	0	0
$603$	1.85217e17	0.156898
$604$	4.96090e17	0.415739
$605$	2.73505e18	2.26755
$606$	1.48886e17	0.122118
$607$	−2.98050e16	−0.0241860	−0.0120930	−	0.999927i	$-0.503849\pi$
$607$	−2.98050e16	−0.0241860	−0.0120930	+	0.999927i	$0.503849\pi$
$608$	−5.05087e17	−0.405502
$609$	0	0
$610$	−4.87198e16	−0.0382879
$611$	−2.37695e17	−0.184822
$612$	−5.02529e17	−0.386613
$613$	−8.84082e17	−0.672976	−0.336488	−	0.941688i	$-0.609239\pi$
$613$	−8.84082e17	−0.672976	−0.336488	+	0.941688i	$0.609239\pi$
$614$	−1.58823e17	−0.119624
$615$	1.03039e17	0.0767917
$616$	0	0
$617$	1.43684e18	1.04846	0.524232	−	0.851575i	$-0.324352\pi$
$617$	1.43684e18	1.04846	0.524232	+	0.851575i	$0.324352\pi$
$618$	9.61443e16	0.0694222
$619$	−1.68862e18	−1.20654	−0.603272	−	0.797535i	$-0.706137\pi$
$619$	−1.68862e18	−1.20654	−0.603272	+	0.797535i	$0.706137\pi$
$620$	1.49752e18	1.05883
$621$	3.21774e17	0.225142
$622$	−9.71162e16	−0.0672441
$623$	0	0
$624$	−3.73161e17	−0.253044
$625$	−1.01917e18	−0.683951
$626$	−1.77817e17	−0.118098
$627$	−1.74510e18	−1.14705
$628$	−9.49831e17	−0.617887
$629$	−6.46008e17	−0.415919
$630$	0	0
$631$	−3.53490e17	−0.222939	−0.111470	−	0.993768i	$-0.535556\pi$
$631$	−3.53490e17	−0.222939	−0.111470	+	0.993768i	$0.535556\pi$
$632$	−2.08993e17	−0.130458
$633$	−1.18216e18	−0.730387
$634$	2.91805e17	0.178448
$635$	−1.35748e18	−0.821680
$636$	1.19760e18	0.717531
$637$	0	0
$638$	−1.68066e17	−0.0986608
$639$	6.98492e17	0.405888
$640$	7.62526e17	0.438616
$641$	1.61802e18	0.921313	0.460656	−	0.887579i	$-0.347614\pi$
$641$	1.61802e18	0.921313	0.460656	+	0.887579i	$0.347614\pi$
$642$	1.71814e17	0.0968456
$643$	1.96065e18	1.09403	0.547015	−	0.837123i	$-0.315764\pi$
$643$	1.96065e18	1.09403	0.547015	+	0.837123i	$0.315764\pi$
$644$	0	0
$645$	1.56695e17	0.0856872
$646$	−3.01813e17	−0.163390
$647$	5.96114e17	0.319486	0.159743	−	0.987159i	$-0.448933\pi$
$647$	5.96114e17	0.319486	0.159743	+	0.987159i	$0.448933\pi$
$648$	5.50399e16	0.0292038
$649$	−3.34479e17	−0.175703
$650$	−2.97571e16	−0.0154758
$651$	0	0
$652$	−1.24511e18	−0.634742
$653$	−2.58318e18	−1.30382	−0.651912	−	0.758295i	$-0.726033\pi$
$653$	−2.58318e18	−1.30382	−0.651912	+	0.758295i	$0.726033\pi$
$654$	8.59140e16	0.0429347
$655$	3.63071e16	0.0179648
$656$	2.97521e17	0.145761
$657$	6.26503e17	0.303912
$658$	0	0
$659$	2.64137e18	1.25624	0.628121	−	0.778116i	$-0.283824\pi$
$659$	2.64137e18	1.25624	0.628121	+	0.778116i	$0.283824\pi$
$660$	1.98208e18	0.933438
$661$	−4.12451e18	−1.92337	−0.961685	−	0.274156i	$-0.911602\pi$
$661$	−4.12451e18	−1.92337	−0.961685	+	0.274156i	$0.911602\pi$
$662$	−1.39478e17	−0.0644064
$663$	−6.89478e17	−0.315270
$664$	−2.19050e17	−0.0991861
$665$	0	0
$666$	3.50636e16	0.0155695
$667$	−1.04019e18	−0.457398
$668$	3.02614e18	1.31778
$669$	−1.07406e18	−0.463189
$670$	−1.26345e17	−0.0539600
$671$	−1.50289e18	−0.635670
$672$	0	0
$673$	2.79726e18	1.16047	0.580236	−	0.814449i	$-0.302961\pi$
$673$	2.79726e18	1.16047	0.580236	+	0.814449i	$0.302961\pi$
$674$	−5.55183e17	−0.228111
$675$	−1.19348e17	−0.0485671
$676$	1.91606e18	0.772245
$677$	4.25553e18	1.69874	0.849372	−	0.527795i	$-0.176981\pi$
$677$	4.25553e18	1.69874	0.849372	+	0.527795i	$0.176981\pi$
$678$	1.48950e17	0.0588906
$679$	0	0
$680$	6.91729e17	0.268305
$681$	2.73294e18	1.04996
$682$	−8.26553e17	−0.314538
$683$	1.60893e18	0.606461	0.303230	−	0.952917i	$-0.401935\pi$
$683$	1.60893e18	0.606461	0.303230	+	0.952917i	$0.401935\pi$
$684$	−9.15548e17	−0.341835
$685$	5.18287e17	0.191682
$686$	0	0
$687$	1.07887e16	0.00391516
$688$	4.52448e17	0.162646
$689$	1.64313e18	0.585122
$690$	−2.19497e17	−0.0774300
$691$	3.06331e18	1.07049	0.535247	−	0.844696i	$-0.320218\pi$
$691$	3.06331e18	1.07049	0.535247	+	0.844696i	$0.320218\pi$
$692$	3.00643e18	1.04079
$693$	0	0
$694$	−5.75285e16	−0.0195455
$695$	−3.19151e18	−1.07422
$696$	−1.77925e17	−0.0593305
$697$	5.49721e17	0.181606
$698$	4.52280e17	0.148029
$699$	2.64666e18	0.858214
$700$	0	0
$701$	2.99144e18	0.952166	0.476083	−	0.879400i	$-0.342056\pi$
$701$	2.99144e18	0.952166	0.476083	+	0.879400i	$0.342056\pi$
$702$	3.74230e16	0.0118018
$703$	−1.17695e18	−0.367747
$704$	5.50893e18	1.70547
$705$	6.50315e17	0.199478
$706$	5.76215e17	0.175127
$707$	0	0
$708$	−1.75481e17	−0.0523616
$709$	−5.31694e18	−1.57203	−0.786015	−	0.618207i	$-0.787859\pi$
$709$	−5.31694e18	−1.57203	−0.786015	+	0.618207i	$0.787859\pi$
$710$	−4.76473e17	−0.139591
$711$	−5.69928e17	−0.165450
$712$	−4.35676e17	−0.125327
$713$	−5.11568e18	−1.45822
$714$	0	0
$715$	2.71945e18	0.761187
$716$	−3.40711e17	−0.0945043
$717$	−3.16313e18	−0.869446
$718$	−4.87939e17	−0.132910
$719$	4.03153e18	1.08826	0.544129	−	0.839001i	$-0.316860\pi$
$719$	4.03153e18	1.08826	0.544129	+	0.839001i	$0.316860\pi$
$720$	1.02094e18	0.273110
$721$	0	0
$722$	−4.52315e16	−0.0118836
$723$	−2.20429e18	−0.573945
$724$	−2.49848e18	−0.644725
$725$	3.85813e17	0.0986688
$726$	−7.91998e17	−0.200741
$727$	4.77643e18	1.19986	0.599928	−	0.800054i	$-0.295196\pi$
$727$	4.77643e18	1.19986	0.599928	+	0.800054i	$0.295196\pi$
$728$	0	0
$729$	1.50095e17	0.0370370
$730$	−4.27366e17	−0.104520
$731$	8.35976e17	0.202643
$732$	−7.88477e17	−0.189438
$733$	−1.71668e18	−0.408803	−0.204401	−	0.978887i	$-0.565525\pi$
$733$	−1.71668e18	−0.408803	−0.204401	+	0.978887i	$0.565525\pi$
$734$	3.56080e17	0.0840471
$735$	0	0
$736$	−1.95973e18	−0.454455
$737$	−3.89745e18	−0.895864
$738$	−2.98374e16	−0.00679820
$739$	−8.69723e17	−0.196423	−0.0982114	−	0.995166i	$-0.531312\pi$
$739$	−8.69723e17	−0.196423	−0.0982114	+	0.995166i	$0.531312\pi$
$740$	1.33678e18	0.299263
$741$	−1.25615e18	−0.278755
$742$	0	0
$743$	2.40272e18	0.523933	0.261966	−	0.965077i	$-0.415629\pi$
$743$	2.40272e18	0.523933	0.261966	+	0.965077i	$0.415629\pi$
$744$	−8.75044e17	−0.189150
$745$	−2.57852e18	−0.552529
$746$	1.08161e18	0.229758
$747$	−5.97353e17	−0.125790
$748$	1.05745e19	2.20750
$749$	0	0
$750$	4.04017e17	0.0828898
$751$	9.37175e18	1.90617	0.953084	−	0.302706i	$-0.0978899\pi$
$751$	9.37175e18	1.90617	0.953084	+	0.302706i	$0.0978899\pi$
$752$	1.87775e18	0.378637
$753$	1.27681e18	0.255246
$754$	−1.20976e17	−0.0239765
$755$	−1.86219e18	−0.365905
$756$	0	0
$757$	3.09120e18	0.597040	0.298520	−	0.954403i	$-0.403507\pi$
$757$	3.09120e18	0.597040	0.298520	+	0.954403i	$0.403507\pi$
$758$	1.85810e17	0.0355810
$759$	−6.77097e18	−1.28552
$760$	1.26025e18	0.237229
$761$	7.97787e18	1.48897	0.744486	−	0.667638i	$-0.232694\pi$
$761$	7.97787e18	1.48897	0.744486	+	0.667638i	$0.232694\pi$
$762$	3.93088e17	0.0727416
$763$	0	0
$764$	6.93957e18	1.26248
$765$	1.88636e18	0.340271
$766$	1.12451e17	0.0201129
$767$	−2.40763e17	−0.0426991
$768$	2.72110e18	0.478517
$769$	−7.37344e18	−1.28573	−0.642863	−	0.765981i	$-0.722254\pi$
$769$	−7.37344e18	−1.28573	−0.642863	+	0.765981i	$0.722254\pi$
$770$	0	0
$771$	−3.55463e18	−0.609454
$772$	7.54771e18	1.28322
$773$	1.67335e18	0.282111	0.141056	−	0.990002i	$-0.454950\pi$
$773$	1.67335e18	0.282111	0.141056	+	0.990002i	$0.454950\pi$
$774$	−4.53745e16	−0.00758570
$775$	1.89744e18	0.314563
$776$	2.77027e18	0.455429
$777$	0	0
$778$	−3.54967e17	−0.0573879
$779$	1.00153e18	0.160572
$780$	1.42673e18	0.226844
$781$	−1.46981e19	−2.31755
$782$	−1.17103e18	−0.183115
$783$	−4.85206e17	−0.0752444
$784$	0	0
$785$	3.56541e18	0.543822
$786$	−1.05136e16	−0.00159039
$787$	3.75359e18	0.563133	0.281566	−	0.959542i	$-0.409146\pi$
$787$	3.75359e18	0.563133	0.281566	+	0.959542i	$0.409146\pi$
$788$	5.40596e18	0.804363
$789$	3.41086e18	0.503342
$790$	3.88774e17	0.0569012
$791$	0	0
$792$	−1.15818e18	−0.166749
$793$	−1.08180e18	−0.154480
$794$	2.16741e17	0.0306978
$795$	−4.49546e18	−0.631522
$796$	−3.51256e17	−0.0489428
$797$	−3.38853e18	−0.468309	−0.234154	−	0.972199i	$-0.575232\pi$
$797$	−3.38853e18	−0.468309	−0.234154	+	0.972199i	$0.575232\pi$
$798$	0	0
$799$	3.46947e18	0.471747
$800$	7.26879e17	0.0980341
$801$	−1.18810e18	−0.158942
$802$	1.44495e18	0.191743
$803$	−1.31833e19	−1.73529
$804$	−2.04476e18	−0.266979
$805$	0	0
$806$	−5.94965e17	−0.0764387
$807$	1.31411e18	0.167476
$808$	−3.31674e18	−0.419313
$809$	−3.13119e18	−0.392685	−0.196343	−	0.980535i	$-0.562906\pi$
$809$	−3.13119e18	−0.392685	−0.196343	+	0.980535i	$0.562906\pi$
$810$	−1.02386e17	−0.0127377
$811$	−1.04731e19	−1.29253	−0.646264	−	0.763114i	$-0.723669\pi$
$811$	−1.04731e19	−1.29253	−0.646264	+	0.763114i	$0.723669\pi$
$812$	0	0
$813$	−4.44702e18	−0.540108
$814$	−7.37829e17	−0.0888991
$815$	4.67379e18	0.558657
$816$	5.44677e18	0.645881
$817$	1.52305e18	0.179172
$818$	−2.13026e17	−0.0248620
$819$	0	0
$820$	−1.13753e18	−0.130669
$821$	−6.85162e18	−0.780841	−0.390421	−	0.920637i	$-0.627670\pi$
$821$	−6.85162e18	−0.780841	−0.390421	+	0.920637i	$0.627670\pi$
$822$	−1.50082e17	−0.0169692
$823$	3.06934e17	0.0344308	0.0172154	−	0.999852i	$-0.494520\pi$
$823$	3.06934e17	0.0344308	0.0172154	+	0.999852i	$0.494520\pi$
$824$	−2.14181e18	−0.238372
$825$	2.51140e18	0.277310
$826$	0	0
$827$	7.75365e18	0.842792	0.421396	−	0.906877i	$-0.361540\pi$
$827$	7.75365e18	0.842792	0.421396	+	0.906877i	$0.361540\pi$
$828$	−3.55232e18	−0.383102
$829$	−2.34336e18	−0.250747	−0.125373	−	0.992110i	$-0.540013\pi$
$829$	−2.34336e18	−0.250747	−0.125373	+	0.992110i	$0.540013\pi$
$830$	4.07482e17	0.0432614
$831$	−7.80200e18	−0.821863
$832$	3.96540e18	0.414463
$833$	0	0
$834$	9.24174e17	0.0950987
$835$	−1.13593e19	−1.15982
$836$	1.92655e19	1.95182
$837$	−2.38626e18	−0.239884
$838$	2.10804e18	0.210278
$839$	1.63297e19	1.61632	0.808158	−	0.588965i	$-0.200465\pi$
$839$	1.63297e19	1.61632	0.808158	+	0.588965i	$0.200465\pi$
$840$	0	0
$841$	−8.69212e18	−0.847134
$842$	−2.21368e18	−0.214085
$843$	−1.78940e18	−0.171723
$844$	1.30508e19	1.24283
$845$	−7.19236e18	−0.679677
$846$	−1.88314e17	−0.0176593
$847$	0	0
$848$	−1.29804e19	−1.19872
$849$	−2.92442e18	−0.268003
$850$	4.34343e17	0.0395012
$851$	−4.56655e18	−0.412142
$852$	−7.71120e18	−0.690660
$853$	−1.93794e19	−1.72255	−0.861276	−	0.508137i	$-0.830334\pi$
$853$	−1.93794e19	−1.72255	−0.861276	+	0.508137i	$0.830334\pi$
$854$	0	0
$855$	3.43672e18	0.300860
$856$	−3.82751e18	−0.332534
$857$	−1.20537e19	−1.03931	−0.519656	−	0.854376i	$-0.673940\pi$
$857$	−1.20537e19	−1.03931	−0.519656	+	0.854376i	$0.673940\pi$
$858$	−7.87478e17	−0.0673862
$859$	1.00612e19	0.854465	0.427232	−	0.904142i	$-0.359489\pi$
$859$	1.00612e19	0.854465	0.427232	+	0.904142i	$0.359489\pi$
$860$	−1.72987e18	−0.145806
$861$	0	0
$862$	−9.66639e17	−0.0802541
$863$	8.01407e18	0.660363	0.330182	−	0.943917i	$-0.392890\pi$
$863$	8.01407e18	0.660363	0.330182	+	0.943917i	$0.392890\pi$
$864$	−9.14136e17	−0.0747604
$865$	−1.12853e19	−0.916029
$866$	−2.36510e18	−0.190539
$867$	2.84340e18	0.227360
$868$	0	0
$869$	1.19928e19	0.944694
$870$	3.30981e17	0.0258778
$871$	−2.80544e18	−0.217712
$872$	−1.91391e18	−0.147423
$873$	7.55457e18	0.577587
$874$	−2.13348e18	−0.161906
$875$	0	0
$876$	−6.91646e18	−0.517139
$877$	8.87791e17	0.0658891	0.0329445	−	0.999457i	$-0.489512\pi$
$877$	8.87791e17	0.0658891	0.0329445	+	0.999457i	$0.489512\pi$
$878$	1.18681e18	0.0874312
$879$	−1.51768e18	−0.110982
$880$	−2.14832e19	−1.55941
$881$	−3.78774e18	−0.272921	−0.136460	−	0.990646i	$-0.543573\pi$
$881$	−3.78774e18	−0.272921	−0.136460	+	0.990646i	$0.543573\pi$
$882$	0	0
$883$	−2.75428e19	−1.95553	−0.977763	−	0.209712i	$-0.932747\pi$
$883$	−2.75428e19	−1.95553	−0.977763	+	0.209712i	$0.932747\pi$
$884$	7.61169e18	0.536465
$885$	6.58707e17	0.0460851
$886$	1.50124e18	0.104263
$887$	2.84165e19	1.95914	0.979572	−	0.201092i	$-0.0644489\pi$
$887$	2.84165e19	1.95914	0.979572	+	0.201092i	$0.0644489\pi$
$888$	−7.81114e17	−0.0534602
$889$	0	0
$890$	8.10454e17	0.0546630
$891$	−3.15838e18	−0.211475
$892$	1.18574e19	0.788164
$893$	6.32097e18	0.417109
$894$	7.46670e17	0.0489142
$895$	1.27894e18	0.0831762
$896$	0	0
$897$	−4.87384e18	−0.312407
$898$	2.16114e18	0.137527
$899$	7.71397e18	0.487349
$900$	1.31758e18	0.0826420
$901$	−2.39836e19	−1.49349
$902$	6.27856e17	0.0388166
$903$	0	0
$904$	−3.31816e18	−0.202210
$905$	9.37860e18	0.567443
$906$	5.39239e17	0.0323928
$907$	7.51023e18	0.447926	0.223963	−	0.974598i	$-0.428101\pi$
$907$	7.51023e18	0.447926	0.223963	+	0.974598i	$0.428101\pi$
$908$	−3.01711e19	−1.78662
$909$	−9.04482e18	−0.531783
$910$	0	0
$911$	−2.34028e19	−1.35643	−0.678216	−	0.734863i	$-0.737247\pi$
$911$	−2.34028e19	−1.35643	−0.678216	+	0.734863i	$0.737247\pi$
$912$	9.92337e18	0.571074
$913$	1.25699e19	0.718242
$914$	1.13232e18	0.0642418
$915$	2.95973e18	0.166730
$916$	−1.19105e17	−0.00666206
$917$	0	0
$918$	−5.46238e17	−0.0301234
$919$	2.20881e19	1.20950	0.604752	−	0.796414i	$-0.293272\pi$
$919$	2.20881e19	1.20950	0.604752	+	0.796414i	$0.293272\pi$
$920$	4.88975e18	0.265868
$921$	9.64848e18	0.520920
$922$	9.60600e17	0.0514982
$923$	−1.05799e19	−0.563210
$924$	0	0
$925$	1.69377e18	0.0889063
$926$	−2.57009e18	−0.133960
$927$	−5.84077e18	−0.302309
$928$	2.95509e18	0.151883
$929$	1.05632e19	0.539132	0.269566	−	0.962982i	$-0.413120\pi$
$929$	1.05632e19	0.539132	0.269566	+	0.962982i	$0.413120\pi$
$930$	1.62778e18	0.0825002
$931$	0	0
$932$	−2.92185e19	−1.46034
$933$	5.89981e18	0.292824
$934$	−2.16817e18	−0.106866
$935$	−3.96939e19	−1.94289
$936$	−8.33676e17	−0.0405233
$937$	1.72833e19	0.834294	0.417147	−	0.908839i	$-0.363030\pi$
$937$	1.72833e19	0.834294	0.417147	+	0.908839i	$0.363030\pi$
$938$	0	0
$939$	1.08024e19	0.514273
$940$	−7.17933e18	−0.339432
$941$	−2.14038e19	−1.00498	−0.502490	−	0.864583i	$-0.667583\pi$
$941$	−2.14038e19	−1.00498	−0.502490	+	0.864583i	$0.667583\pi$
$942$	−1.03245e18	−0.0481434
$943$	3.88591e18	0.179956
$944$	1.90199e18	0.0874760
$945$	0	0
$946$	9.54799e17	0.0433131
$947$	−5.91308e17	−0.0266403	−0.0133202	−	0.999911i	$-0.504240\pi$
$947$	−5.91308e17	−0.0266403	−0.0133202	+	0.999911i	$0.504240\pi$
$948$	6.29188e18	0.281531
$949$	−9.48950e18	−0.421709
$950$	7.91322e17	0.0349261
$951$	−1.77271e19	−0.777079
$952$	0	0
$953$	−2.39396e19	−1.03517	−0.517587	−	0.855631i	$-0.673170\pi$
$953$	−2.39396e19	−1.03517	−0.517587	+	0.855631i	$0.673170\pi$
$954$	1.30177e18	0.0559073
$955$	−2.60493e19	−1.11115
$956$	3.49203e19	1.47945
$957$	1.02100e19	0.429633
$958$	−3.20055e18	−0.133767
$959$	0	0
$960$	−1.08490e19	−0.447329
$961$	1.35201e19	0.553702
$962$	−5.31100e17	−0.0216042
$963$	−1.04377e19	−0.421729
$964$	2.43349e19	0.976628
$965$	−2.83320e19	−1.12941
$966$	0	0
$967$	1.99045e18	0.0782853	0.0391427	−	0.999234i	$-0.487537\pi$
$967$	1.99045e18	0.0782853	0.0391427	+	0.999234i	$0.487537\pi$
$968$	1.76434e19	0.689275
$969$	1.83351e19	0.711507
$970$	−5.15332e18	−0.198642
$971$	−4.12385e19	−1.57898	−0.789492	−	0.613761i	$-0.789656\pi$
$971$	−4.12385e19	−1.57898	−0.789492	+	0.613761i	$0.789656\pi$
$972$	−1.65701e18	−0.0630224
$973$	0	0
$974$	3.16262e18	0.118690
$975$	1.80774e18	0.0673917
$976$	8.54608e18	0.316478
$977$	−1.25374e19	−0.461202	−0.230601	−	0.973048i	$-0.574069\pi$
$977$	−1.25374e19	−0.461202	−0.230601	+	0.973048i	$0.574069\pi$
$978$	−1.35340e18	−0.0494567
$979$	2.50006e19	0.907535
$980$	0	0
$981$	−5.21928e18	−0.186966
$982$	−4.94080e18	−0.175822
$983$	1.83966e19	0.650340	0.325170	−	0.945656i	$-0.394578\pi$
$983$	1.83966e19	0.650340	0.325170	+	0.945656i	$0.394578\pi$
$984$	6.64690e17	0.0233427
$985$	−2.02925e19	−0.707946
$986$	1.76580e18	0.0611987
$987$	0	0
$988$	1.38676e19	0.474331
$989$	5.90941e18	0.200802
$990$	2.15448e18	0.0727299
$991$	−3.43064e19	−1.15053	−0.575263	−	0.817969i	$-0.695100\pi$
$991$	−3.43064e19	−1.15053	−0.575263	+	0.817969i	$0.695100\pi$
$992$	1.45333e19	0.484214
$993$	8.47329e18	0.280467
$994$	0	0
$995$	1.31852e18	0.0430761
$996$	6.59465e18	0.214045
$997$	5.72458e19	1.84597	0.922985	−	0.384835i	$-0.125742\pi$
$997$	5.72458e19	1.84597	0.922985	+	0.384835i	$0.125742\pi$
$998$	−4.79589e18	−0.153646
$999$	−2.13011e18	−0.0677995

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.14.a.a.1.1		1
7.6	odd	2		3.14.a.a.1.1	✓	1
21.20	even	2		9.14.a.a.1.1		1
28.27	even	2		48.14.a.c.1.1		1
35.13	even	4		75.14.b.b.49.2		2
35.27	even	4		75.14.b.b.49.1		2
35.34	odd	2		75.14.a.a.1.1		1
56.13	odd	2		192.14.a.j.1.1		1
56.27	even	2		192.14.a.e.1.1		1
84.83	odd	2		144.14.a.k.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.14.a.a.1.1	✓	1	7.6	odd	2
9.14.a.a.1.1		1	21.20	even	2
48.14.a.c.1.1		1	28.27	even	2
75.14.a.a.1.1		1	35.34	odd	2
75.14.b.b.49.1		2	35.27	even	4
75.14.b.b.49.2		2	35.13	even	4
144.14.a.k.1.1		1	84.83	odd	2
147.14.a.a.1.1		1	1.1	even	1	trivial
192.14.a.e.1.1		1	56.27	even	2
192.14.a.j.1.1		1	56.13	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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