LMFDB - Embedded newform 147.10.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,10,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, 10, names="a")

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

chi := DirichletCharacter("147.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
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:	$75.7102679161$
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)

$f(q)$

$=$

$q-36.0000 q^{2} +81.0000 q^{3} +784.000 q^{4} +1314.00 q^{5} -2916.00 q^{6} -9792.00 q^{8} +6561.00 q^{9} +O(q^{10})$

\(q-36.0000 q^{2} +81.0000 q^{3} +784.000 q^{4} +1314.00 q^{5} -2916.00 q^{6} -9792.00 q^{8} +6561.00 q^{9} -47304.0 q^{10} +1476.00 q^{11} +63504.0 q^{12} +151522. q^{13} +106434. q^{15} -48896.0 q^{16} -108162. q^{17} -236196. q^{18} -593084. q^{19} +1.03018e6 q^{20} -53136.0 q^{22} -969480. q^{23} -793152. q^{24} -226529. q^{25} -5.45479e6 q^{26} +531441. q^{27} -6.64252e6 q^{29} -3.83162e6 q^{30} -7.07060e6 q^{31} +6.77376e6 q^{32} +119556. q^{33} +3.89383e6 q^{34} +5.14382e6 q^{36} -7.47241e6 q^{37} +2.13510e7 q^{38} +1.22733e7 q^{39} -1.28667e7 q^{40} +4.35015e6 q^{41} -4.35872e6 q^{43} +1.15718e6 q^{44} +8.62115e6 q^{45} +3.49013e7 q^{46} -2.83092e7 q^{47} -3.96058e6 q^{48} +8.15504e6 q^{50} -8.76112e6 q^{51} +1.18793e8 q^{52} +1.61117e7 q^{53} -1.91319e7 q^{54} +1.93946e6 q^{55} -4.80398e7 q^{57} +2.39131e8 q^{58} +8.60760e7 q^{59} +8.34443e7 q^{60} -3.22139e7 q^{61} +2.54542e8 q^{62} -2.18821e8 q^{64} +1.99100e8 q^{65} -4.30402e6 q^{66} +9.95315e7 q^{67} -8.47990e7 q^{68} -7.85279e7 q^{69} -4.41705e7 q^{71} -6.42453e7 q^{72} +2.35606e7 q^{73} +2.69007e8 q^{74} -1.83488e7 q^{75} -4.64978e8 q^{76} -4.41838e8 q^{78} -4.01755e8 q^{79} -6.42493e7 q^{80} +4.30467e7 q^{81} -1.56605e8 q^{82} +7.44529e8 q^{83} -1.42125e8 q^{85} +1.56914e8 q^{86} -5.38044e8 q^{87} -1.44530e7 q^{88} -7.69871e8 q^{89} -3.10362e8 q^{90} -7.60072e8 q^{92} -5.72719e8 q^{93} +1.01913e9 q^{94} -7.79312e8 q^{95} +5.48675e8 q^{96} -9.07131e8 q^{97} +9.68404e6 q^{99} +O(q^{100})\)

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 $

$2$	−36.0000	−1.59099	−0.795495	−	0.605960i	$-0.792789\pi$
$2$	−36.0000	−1.59099	−0.795495	+	0.605960i	$0.792789\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	784.000	1.53125
$5$	1314.00	0.940222	0.470111	−	0.882607i	$-0.344214\pi$
$5$	1314.00	0.940222	0.470111	+	0.882607i	$0.344214\pi$
$6$	−2916.00	−0.918559
$7$	0	0
$7$	0	0
$8$	−9792.00	−0.845214
$9$	6561.00	0.333333
$10$	−47304.0	−1.49588
$11$	1476.00	0.0303962	0.0151981	−	0.999885i	$-0.495162\pi$
$11$	1476.00	0.0303962	0.0151981	+	0.999885i	$0.495162\pi$
$12$	63504.0	0.884068
$13$	151522.	1.47140	0.735700	−	0.677308i	$-0.236853\pi$
$13$	151522.	1.47140	0.735700	+	0.677308i	$0.236853\pi$
$14$	0	0
$15$	106434.	0.542837
$16$	−48896.0	−0.186523
$17$	−108162.	−0.314090	−0.157045	−	0.987591i	$-0.550197\pi$
$17$	−108162.	−0.314090	−0.157045	+	0.987591i	$0.550197\pi$
$18$	−236196.	−0.530330
$19$	−593084.	−1.04406	−0.522029	−	0.852927i	$-0.674825\pi$
$19$	−593084.	−1.04406	−0.522029	+	0.852927i	$0.674825\pi$
$20$	1.03018e6	1.43971
$21$	0	0
$22$	−53136.0	−0.0483601
$23$	−969480.	−0.722376	−0.361188	−	0.932493i	$-0.617629\pi$
$23$	−969480.	−0.722376	−0.361188	+	0.932493i	$0.617629\pi$
$24$	−793152.	−0.487984
$25$	−226529.	−0.115983
$26$	−5.45479e6	−2.34098
$27$	531441.	0.192450
$28$	0	0
$29$	−6.64252e6	−1.74398	−0.871991	−	0.489522i	$-0.837171\pi$
$29$	−6.64252e6	−1.74398	−0.871991	+	0.489522i	$0.837171\pi$
$30$	−3.83162e6	−0.863649
$31$	−7.07060e6	−1.37508	−0.687541	−	0.726145i	$-0.741310\pi$
$31$	−7.07060e6	−1.37508	−0.687541	+	0.726145i	$0.741310\pi$
$32$	6.77376e6	1.14197
$33$	119556.	0.0175493
$34$	3.89383e6	0.499715
$35$	0	0
$36$	5.14382e6	0.510417
$37$	−7.47241e6	−0.655470	−0.327735	−	0.944770i	$-0.606285\pi$
$37$	−7.47241e6	−0.655470	−0.327735	+	0.944770i	$0.606285\pi$
$38$	2.13510e7	1.66109
$39$	1.22733e7	0.849513
$40$	−1.28667e7	−0.794688
$41$	4.35015e6	0.240423	0.120212	−	0.992748i	$-0.461643\pi$
$41$	4.35015e6	0.240423	0.120212	+	0.992748i	$0.461643\pi$
$42$	0	0
$43$	−4.35872e6	−0.194424	−0.0972121	−	0.995264i	$-0.530993\pi$
$43$	−4.35872e6	−0.194424	−0.0972121	+	0.995264i	$0.530993\pi$
$44$	1.15718e6	0.0465442
$45$	8.62115e6	0.313407
$46$	3.49013e7	1.14929
$47$	−2.83092e7	−0.846229	−0.423115	−	0.906076i	$-0.639063\pi$
$47$	−2.83092e7	−0.846229	−0.423115	+	0.906076i	$0.639063\pi$
$48$	−3.96058e6	−0.107689
$49$	0	0
$50$	8.15504e6	0.184528
$51$	−8.76112e6	−0.181340
$52$	1.18793e8	2.25308
$53$	1.61117e7	0.280479	0.140239	−	0.990118i	$-0.455213\pi$
$53$	1.61117e7	0.280479	0.140239	+	0.990118i	$0.455213\pi$
$54$	−1.91319e7	−0.306186
$55$	1.93946e6	0.0285792
$56$	0	0
$57$	−4.80398e7	−0.602788
$58$	2.39131e8	2.77466
$59$	8.60760e7	0.924800	0.462400	−	0.886671i	$-0.346988\pi$
$59$	8.60760e7	0.924800	0.462400	+	0.886671i	$0.346988\pi$
$60$	8.34443e7	0.831220
$61$	−3.22139e7	−0.297892	−0.148946	−	0.988845i	$-0.547588\pi$
$61$	−3.22139e7	−0.297892	−0.148946	+	0.988845i	$0.547588\pi$
$62$	2.54542e8	2.18774
$63$	0	0
$64$	−2.18821e8	−1.63034
$65$	1.99100e8	1.38344
$66$	−4.30402e6	−0.0279207
$67$	9.95315e7	0.603426	0.301713	−	0.953399i	$-0.402442\pi$
$67$	9.95315e7	0.603426	0.301713	+	0.953399i	$0.402442\pi$
$68$	−8.47990e7	−0.480951
$69$	−7.85279e7	−0.417064
$70$	0	0
$71$	−4.41705e7	−0.206286	−0.103143	−	0.994667i	$-0.532890\pi$
$71$	−4.41705e7	−0.206286	−0.103143	+	0.994667i	$0.532890\pi$
$72$	−6.42453e7	−0.281738
$73$	2.35606e7	0.0971033	0.0485517	−	0.998821i	$-0.484539\pi$
$73$	2.35606e7	0.0971033	0.0485517	+	0.998821i	$0.484539\pi$
$74$	2.69007e8	1.04285
$75$	−1.83488e7	−0.0669627
$76$	−4.64978e8	−1.59872
$77$	0	0
$78$	−4.41838e8	−1.35157
$79$	−4.01755e8	−1.16048	−0.580242	−	0.814444i	$-0.697042\pi$
$79$	−4.01755e8	−1.16048	−0.580242	+	0.814444i	$0.697042\pi$
$80$	−6.42493e7	−0.175373
$81$	4.30467e7	0.111111
$82$	−1.56605e8	−0.382511
$83$	7.44529e8	1.72199	0.860994	−	0.508615i	$-0.169842\pi$
$83$	7.44529e8	1.72199	0.860994	+	0.508615i	$0.169842\pi$
$84$	0	0
$85$	−1.42125e8	−0.295315
$86$	1.56914e8	0.309327
$87$	−5.38044e8	−1.00689
$88$	−1.44530e7	−0.0256913
$89$	−7.69871e8	−1.30066	−0.650329	−	0.759653i	$-0.725369\pi$
$89$	−7.69871e8	−1.30066	−0.650329	+	0.759653i	$0.725369\pi$
$90$	−3.10362e8	−0.498628
$91$	0	0
$92$	−7.60072e8	−1.10614
$93$	−5.72719e8	−0.793904
$94$	1.01913e9	1.34634
$95$	−7.79312e8	−0.981647
$96$	5.48675e8	0.659317
$97$	−9.07131e8	−1.04039	−0.520196	−	0.854047i	$-0.674141\pi$
$97$	−9.07131e8	−1.04039	−0.520196	+	0.854047i	$0.674141\pi$
$98$	0	0
$99$	9.68404e6	0.0101321
$100$	−1.77599e8	−0.177599
$101$	4.21902e8	0.403427	0.201714	−	0.979445i	$-0.435349\pi$
$101$	4.21902e8	0.403427	0.201714	+	0.979445i	$0.435349\pi$
$102$	3.15400e8	0.288510
$103$	−5.79043e8	−0.506924	−0.253462	−	0.967345i	$-0.581569\pi$
$103$	−5.79043e8	−0.506924	−0.253462	+	0.967345i	$0.581569\pi$
$104$	−1.48370e9	−1.24365
$105$	0	0
$106$	−5.80022e8	−0.446239
$107$	1.39714e9	1.03042	0.515208	−	0.857065i	$-0.327715\pi$
$107$	1.39714e9	1.03042	0.515208	+	0.857065i	$0.327715\pi$
$108$	4.16650e8	0.294689
$109$	−2.68530e9	−1.82211	−0.911054	−	0.412286i	$-0.864730\pi$
$109$	−2.68530e9	−1.82211	−0.911054	+	0.412286i	$0.864730\pi$
$110$	−6.98207e7	−0.0454692
$111$	−6.05265e8	−0.378436
$112$	0	0
$113$	4.54749e8	0.262373	0.131186	−	0.991358i	$-0.458121\pi$
$113$	4.54749e8	0.262373	0.131186	+	0.991358i	$0.458121\pi$
$114$	1.72943e9	0.959029
$115$	−1.27390e9	−0.679194
$116$	−5.20774e9	−2.67047
$117$	9.94136e8	0.490467
$118$	−3.09873e9	−1.47135
$119$	0	0
$120$	−1.04220e9	−0.458813
$121$	−2.35577e9	−0.999076
$122$	1.15970e9	0.473944
$123$	3.52362e8	0.138809
$124$	−5.54335e9	−2.10559
$125$	−2.86407e9	−1.04927
$126$	0	0
$127$	−8.38650e7	−0.0286064	−0.0143032	−	0.999898i	$-0.504553\pi$
$127$	−8.38650e7	−0.0286064	−0.0143032	+	0.999898i	$0.504553\pi$
$128$	4.40938e9	1.45189
$129$	−3.53056e8	−0.112251
$130$	−7.16760e9	−2.20104
$131$	3.73601e9	1.10838	0.554188	−	0.832391i	$-0.313029\pi$
$131$	3.73601e9	1.10838	0.554188	+	0.832391i	$0.313029\pi$
$132$	9.37319e7	0.0268723
$133$	0	0
$134$	−3.58313e9	−0.960044
$135$	6.98313e8	0.180946
$136$	1.05912e9	0.265473
$137$	6.43598e9	1.56089	0.780444	−	0.625225i	$-0.214993\pi$
$137$	6.43598e9	1.56089	0.780444	+	0.625225i	$0.214993\pi$
$138$	2.82700e9	0.663545
$139$	−1.81833e9	−0.413148	−0.206574	−	0.978431i	$-0.566231\pi$
$139$	−1.81833e9	−0.413148	−0.206574	+	0.978431i	$0.566231\pi$
$140$	0	0
$141$	−2.29305e9	−0.488571
$142$	1.59014e9	0.328199
$143$	2.23646e8	0.0447250
$144$	−3.20807e8	−0.0621745
$145$	−8.72827e9	−1.63973
$146$	−8.48183e8	−0.154490
$147$	0	0
$148$	−5.85837e9	−1.00369
$149$	−8.30199e9	−1.37989	−0.689944	−	0.723863i	$-0.742365\pi$
$149$	−8.30199e9	−1.37989	−0.689944	+	0.723863i	$0.742365\pi$
$150$	6.60559e8	0.106537
$151$	3.84057e9	0.601173	0.300587	−	0.953755i	$-0.402818\pi$
$151$	3.84057e9	0.601173	0.300587	+	0.953755i	$0.402818\pi$
$152$	5.80748e9	0.882453
$153$	−7.09651e8	−0.104697
$154$	0	0
$155$	−9.29077e9	−1.29288
$156$	9.62225e9	1.30082
$157$	2.17912e9	0.286242	0.143121	−	0.989705i	$-0.454286\pi$
$157$	2.17912e9	0.286242	0.143121	+	0.989705i	$0.454286\pi$
$158$	1.44632e10	1.84632
$159$	1.30505e9	0.161935
$160$	8.90072e9	1.07371
$161$	0	0
$162$	−1.54968e9	−0.176777
$163$	−1.54147e10	−1.71038	−0.855188	−	0.518317i	$-0.826559\pi$
$163$	−1.54147e10	−1.71038	−0.855188	+	0.518317i	$0.826559\pi$
$164$	3.41052e9	0.368148
$165$	1.57097e8	0.0165002
$166$	−2.68030e10	−2.73967
$167$	5.65506e9	0.562617	0.281309	−	0.959617i	$-0.409232\pi$
$167$	5.65506e9	0.562617	0.281309	+	0.959617i	$0.409232\pi$
$168$	0	0
$169$	1.23544e10	1.16502
$170$	5.11650e9	0.469843
$171$	−3.89122e9	−0.348020
$172$	−3.41723e9	−0.297712
$173$	−7.69892e7	−0.00653465	−0.00326733	−	0.999995i	$-0.501040\pi$
$173$	−7.69892e7	−0.00653465	−0.00326733	+	0.999995i	$0.501040\pi$
$174$	1.93696e10	1.60195
$175$	0	0
$176$	−7.21705e7	−0.00566960
$177$	6.97215e9	0.533934
$178$	2.77154e10	2.06933
$179$	2.32247e10	1.69087	0.845436	−	0.534077i	$-0.179341\pi$
$179$	2.32247e10	1.69087	0.845436	+	0.534077i	$0.179341\pi$
$180$	6.75898e9	0.479905
$181$	1.23532e10	0.855513	0.427756	−	0.903894i	$-0.359304\pi$
$181$	1.23532e10	0.855513	0.427756	+	0.903894i	$0.359304\pi$
$182$	0	0
$183$	−2.60933e9	−0.171988
$184$	9.49315e9	0.610562
$185$	−9.81875e9	−0.616287
$186$	2.06179e10	1.26309
$187$	−1.59647e8	−0.00954715
$188$	−2.21945e10	−1.29579
$189$	0	0
$190$	2.80552e10	1.56179
$191$	−4.20433e9	−0.228584	−0.114292	−	0.993447i	$-0.536460\pi$
$191$	−4.20433e9	−0.228584	−0.114292	+	0.993447i	$0.536460\pi$
$192$	−1.77245e10	−0.941278
$193$	−4.38611e9	−0.227547	−0.113774	−	0.993507i	$-0.536294\pi$
$193$	−4.38611e9	−0.227547	−0.113774	+	0.993507i	$0.536294\pi$
$194$	3.26567e10	1.65525
$195$	1.61271e10	0.798731
$196$	0	0
$197$	−3.36694e10	−1.59271	−0.796356	−	0.604828i	$-0.793242\pi$
$197$	−3.36694e10	−1.59271	−0.796356	+	0.604828i	$0.793242\pi$
$198$	−3.48625e8	−0.0161200
$199$	−1.02732e10	−0.464374	−0.232187	−	0.972671i	$-0.574588\pi$
$199$	−1.02732e10	−0.464374	−0.232187	+	0.972671i	$0.574588\pi$
$200$	2.21817e9	0.0980303
$201$	8.06205e9	0.348388
$202$	−1.51885e10	−0.641849
$203$	0	0
$204$	−6.86872e9	−0.277677
$205$	5.71610e9	0.226051
$206$	2.08455e10	0.806512
$207$	−6.36076e9	−0.240792
$208$	−7.40882e9	−0.274450
$209$	−8.75392e8	−0.0317354
$210$	0	0
$211$	7.96696e9	0.276708	0.138354	−	0.990383i	$-0.455819\pi$
$211$	7.96696e9	0.276708	0.138354	+	0.990383i	$0.455819\pi$
$212$	1.26316e10	0.429483
$213$	−3.57781e9	−0.119099
$214$	−5.02970e10	−1.63938
$215$	−5.72735e9	−0.182802
$216$	−5.20387e9	−0.162661
$217$	0	0
$218$	9.66710e10	2.89896
$219$	1.90841e9	0.0560626
$220$	1.52054e9	0.0437619
$221$	−1.63889e10	−0.462152
$222$	2.17895e10	0.602088
$223$	−6.96581e9	−0.188625	−0.0943126	−	0.995543i	$-0.530065\pi$
$223$	−6.96581e9	−0.188625	−0.0943126	+	0.995543i	$0.530065\pi$
$224$	0	0
$225$	−1.48626e9	−0.0386609
$226$	−1.63709e10	−0.417432
$227$	−3.35697e10	−0.839133	−0.419567	−	0.907725i	$-0.637818\pi$
$227$	−3.35697e10	−0.839133	−0.419567	+	0.907725i	$0.637818\pi$
$228$	−3.76632e10	−0.923019
$229$	−2.93198e10	−0.704534	−0.352267	−	0.935900i	$-0.614589\pi$
$229$	−2.93198e10	−0.704534	−0.352267	+	0.935900i	$0.614589\pi$
$230$	4.58603e10	1.08059
$231$	0	0
$232$	6.50436e10	1.47404
$233$	−8.20079e10	−1.82286	−0.911431	−	0.411453i	$-0.865022\pi$
$233$	−8.20079e10	−1.82286	−0.911431	+	0.411453i	$0.865022\pi$
$234$	−3.57889e10	−0.780327
$235$	−3.71984e10	−0.795643
$236$	6.74836e10	1.41610
$237$	−3.25421e10	−0.670006
$238$	0	0
$239$	6.26609e10	1.24224	0.621121	−	0.783715i	$-0.286677\pi$
$239$	6.26609e10	1.24224	0.621121	+	0.783715i	$0.286677\pi$
$240$	−5.20420e9	−0.101252
$241$	−7.75548e10	−1.48092	−0.740460	−	0.672100i	$-0.765392\pi$
$241$	−7.75548e10	−1.48092	−0.740460	+	0.672100i	$0.765392\pi$
$242$	8.48077e10	1.58952
$243$	3.48678e9	0.0641500
$244$	−2.52557e10	−0.456148
$245$	0	0
$246$	−1.26850e10	−0.220843
$247$	−8.98653e10	−1.53623
$248$	6.92353e10	1.16224
$249$	6.03068e10	0.994190
$250$	1.03106e11	1.66938
$251$	5.81901e10	0.925374	0.462687	−	0.886522i	$-0.346885\pi$
$251$	5.81901e10	0.925374	0.462687	+	0.886522i	$0.346885\pi$
$252$	0	0
$253$	−1.43095e9	−0.0219575
$254$	3.01914e9	0.0455126
$255$	−1.15121e10	−0.170500
$256$	−4.67014e10	−0.679595
$257$	7.41485e9	0.106024	0.0530119	−	0.998594i	$-0.483118\pi$
$257$	7.41485e9	0.106024	0.0530119	+	0.998594i	$0.483118\pi$
$258$	1.27100e10	0.178590
$259$	0	0
$260$	1.56094e11	2.11840
$261$	−4.35816e10	−0.581327
$262$	−1.34496e11	−1.76342
$263$	−1.05271e11	−1.35677	−0.678387	−	0.734705i	$-0.737321\pi$
$263$	−1.05271e11	−1.35677	−0.678387	+	0.734705i	$0.737321\pi$
$264$	−1.17069e9	−0.0148329
$265$	2.11708e10	0.263712
$266$	0	0
$267$	−6.23596e10	−0.750935
$268$	7.80327e10	0.923995
$269$	−4.67239e10	−0.544069	−0.272034	−	0.962288i	$-0.587696\pi$
$269$	−4.67239e10	−0.544069	−0.272034	+	0.962288i	$0.587696\pi$
$270$	−2.51393e10	−0.287883
$271$	−2.86868e10	−0.323087	−0.161544	−	0.986866i	$-0.551647\pi$
$271$	−2.86868e10	−0.323087	−0.161544	+	0.986866i	$0.551647\pi$
$272$	5.28869e9	0.0585852
$273$	0	0
$274$	−2.31695e11	−2.48336
$275$	−3.34357e8	−0.00352544
$276$	−6.15659e10	−0.638630
$277$	8.50676e10	0.868171	0.434085	−	0.900872i	$-0.357072\pi$
$277$	8.50676e10	0.868171	0.434085	+	0.900872i	$0.357072\pi$
$278$	6.54598e10	0.657314
$279$	−4.63902e10	−0.458361
$280$	0	0
$281$	−7.87257e8	−0.00753248	−0.00376624	−	0.999993i	$-0.501199\pi$
$281$	−7.87257e8	−0.00753248	−0.00376624	+	0.999993i	$0.501199\pi$
$282$	8.25498e10	0.777311
$283$	−2.48961e10	−0.230724	−0.115362	−	0.993324i	$-0.536803\pi$
$283$	−2.48961e10	−0.230724	−0.115362	+	0.993324i	$0.536803\pi$
$284$	−3.46297e10	−0.315875
$285$	−6.31243e10	−0.566754
$286$	−8.05127e9	−0.0711570
$287$	0	0
$288$	4.44426e10	0.380657
$289$	−1.06889e11	−0.901347
$290$	3.14218e11	2.60879
$291$	−7.34776e10	−0.600671
$292$	1.84715e10	0.148689
$293$	−1.57074e11	−1.24509	−0.622543	−	0.782586i	$-0.713900\pi$
$293$	−1.57074e11	−1.24509	−0.622543	+	0.782586i	$0.713900\pi$
$294$	0	0
$295$	1.13104e11	0.869517
$296$	7.31698e10	0.554012
$297$	7.84407e8	0.00584975
$298$	2.98871e11	2.19539
$299$	−1.46898e11	−1.06290
$300$	−1.43855e10	−0.102537
$301$	0	0
$302$	−1.38261e11	−0.956461
$303$	3.41741e10	0.232919
$304$	2.89994e10	0.194741
$305$	−4.23291e10	−0.280085
$306$	2.55474e10	0.166572
$307$	2.45737e11	1.57887	0.789437	−	0.613831i	$-0.210372\pi$
$307$	2.45737e11	1.57887	0.789437	+	0.613831i	$0.210372\pi$
$308$	0	0
$309$	−4.69025e10	−0.292673
$310$	3.34468e11	2.05696
$311$	1.61050e11	0.976201	0.488101	−	0.872787i	$-0.337690\pi$
$311$	1.61050e11	0.976201	0.488101	+	0.872787i	$0.337690\pi$
$312$	−1.20180e11	−0.718020
$313$	2.44646e11	1.44075	0.720374	−	0.693586i	$-0.243970\pi$
$313$	2.44646e11	1.44075	0.720374	+	0.693586i	$0.243970\pi$
$314$	−7.84484e10	−0.455408
$315$	0	0
$316$	−3.14976e11	−1.77699
$317$	1.12832e11	0.627575	0.313787	−	0.949493i	$-0.398402\pi$
$317$	1.12832e11	0.627575	0.313787	+	0.949493i	$0.398402\pi$
$318$	−4.69817e10	−0.257636
$319$	−9.80436e9	−0.0530104
$320$	−2.87530e11	−1.53288
$321$	1.13168e11	0.594911
$322$	0	0
$323$	6.41492e10	0.327929
$324$	3.37486e10	0.170139
$325$	−3.43241e10	−0.170657
$326$	5.54930e11	2.72119
$327$	−2.17510e11	−1.05200
$328$	−4.25967e10	−0.203209
$329$	0	0
$330$	−5.65548e9	−0.0262516
$331$	2.87348e11	1.31578	0.657889	−	0.753115i	$-0.271450\pi$
$331$	2.87348e11	1.31578	0.657889	+	0.753115i	$0.271450\pi$
$332$	5.83711e11	2.63679
$333$	−4.90265e10	−0.218490
$334$	−2.03582e11	−0.895119
$335$	1.30784e11	0.567354
$336$	0	0
$337$	−2.52635e10	−0.106699	−0.0533494	−	0.998576i	$-0.516990\pi$
$337$	−2.52635e10	−0.106699	−0.0533494	+	0.998576i	$0.516990\pi$
$338$	−4.44759e11	−1.85353
$339$	3.68346e10	0.151481
$340$	−1.11426e11	−0.452200
$341$	−1.04362e10	−0.0417973
$342$	1.40084e11	0.553696
$343$	0	0
$344$	4.26805e10	0.164330
$345$	−1.03186e11	−0.392133
$346$	2.77161e9	0.0103966
$347$	9.04803e10	0.335020	0.167510	−	0.985870i	$-0.446427\pi$
$347$	9.04803e10	0.335020	0.167510	+	0.985870i	$0.446427\pi$
$348$	−4.21827e11	−1.54180
$349$	1.53822e10	0.0555016	0.0277508	−	0.999615i	$-0.491166\pi$
$349$	1.53822e10	0.0555016	0.0277508	+	0.999615i	$0.491166\pi$
$350$	0	0
$351$	8.05250e10	0.283171
$352$	9.99807e9	0.0347116
$353$	1.46875e11	0.503457	0.251728	−	0.967798i	$-0.419001\pi$
$353$	1.46875e11	0.503457	0.251728	+	0.967798i	$0.419001\pi$
$354$	−2.50998e11	−0.849483
$355$	−5.80400e10	−0.193955
$356$	−6.03579e11	−1.99163
$357$	0	0
$358$	−8.36088e11	−2.69016
$359$	−4.42246e11	−1.40520	−0.702602	−	0.711583i	$-0.747979\pi$
$359$	−4.42246e11	−1.40520	−0.702602	+	0.711583i	$0.747979\pi$
$360$	−8.44183e10	−0.264896
$361$	2.90609e10	0.0900590
$362$	−4.44716e11	−1.36111
$363$	−1.90817e11	−0.576817
$364$	0	0
$365$	3.09587e10	0.0912987
$366$	9.39358e10	0.273632
$367$	−1.48110e11	−0.426175	−0.213088	−	0.977033i	$-0.568352\pi$
$367$	−1.48110e11	−0.426175	−0.213088	+	0.977033i	$0.568352\pi$
$368$	4.74037e10	0.134740
$369$	2.85413e10	0.0801412
$370$	3.53475e11	0.980507
$371$	0	0
$372$	−4.49011e11	−1.21567
$373$	7.63489e10	0.204227	0.102114	−	0.994773i	$-0.467440\pi$
$373$	7.63489e10	0.204227	0.102114	+	0.994773i	$0.467440\pi$
$374$	5.74730e9	0.0151894
$375$	−2.31989e11	−0.605797
$376$	2.77204e11	0.715244
$377$	−1.00649e12	−2.56609
$378$	0	0
$379$	−2.70192e11	−0.672660	−0.336330	−	0.941744i	$-0.609186\pi$
$379$	−2.70192e11	−0.672660	−0.336330	+	0.941744i	$0.609186\pi$
$380$	−6.10981e11	−1.50315
$381$	−6.79306e9	−0.0165159
$382$	1.51356e11	0.363676
$383$	6.61033e11	1.56974	0.784872	−	0.619658i	$-0.212729\pi$
$383$	6.61033e11	1.56974	0.784872	+	0.619658i	$0.212729\pi$
$384$	3.57160e11	0.838246
$385$	0	0
$386$	1.57900e11	0.362026
$387$	−2.85975e10	−0.0648081
$388$	−7.11191e11	−1.59310
$389$	−3.09861e11	−0.686109	−0.343054	−	0.939316i	$-0.611462\pi$
$389$	−3.09861e11	−0.686109	−0.343054	+	0.939316i	$0.611462\pi$
$390$	−5.80575e11	−1.27077
$391$	1.04861e11	0.226891
$392$	0	0
$393$	3.02617e11	0.639921
$394$	1.21210e12	2.53399
$395$	−5.27906e11	−1.09111
$396$	7.59228e9	0.0155147
$397$	6.50589e11	1.31447	0.657233	−	0.753688i	$-0.271727\pi$
$397$	6.50589e11	1.31447	0.657233	+	0.753688i	$0.271727\pi$
$398$	3.69836e11	0.738814
$399$	0	0
$400$	1.10764e10	0.0216335
$401$	2.76701e10	0.0534393	0.0267196	−	0.999643i	$-0.491494\pi$
$401$	2.76701e10	0.0534393	0.0267196	+	0.999643i	$0.491494\pi$
$402$	−2.90234e11	−0.554282
$403$	−1.07135e12	−2.02330
$404$	3.30771e11	0.617748
$405$	5.65634e10	0.104469
$406$	0	0
$407$	−1.10293e10	−0.0199238
$408$	8.57889e10	0.153271
$409$	−2.08505e11	−0.368436	−0.184218	−	0.982885i	$-0.558975\pi$
$409$	−2.08505e11	−0.368436	−0.184218	+	0.982885i	$0.558975\pi$
$410$	−2.05779e11	−0.359646
$411$	5.21314e11	0.901180
$412$	−4.53969e11	−0.776228
$413$	0	0
$414$	2.28987e11	0.383098
$415$	9.78311e11	1.61905
$416$	1.02637e12	1.68029
$417$	−1.47285e11	−0.238531
$418$	3.15141e10	0.0504907
$419$	−4.50465e11	−0.714000	−0.357000	−	0.934104i	$-0.616200\pi$
$419$	−4.50465e11	−0.714000	−0.357000	+	0.934104i	$0.616200\pi$
$420$	0	0
$421$	8.60883e11	1.33559	0.667797	−	0.744343i	$-0.267237\pi$
$421$	8.60883e11	1.33559	0.667797	+	0.744343i	$0.267237\pi$
$422$	−2.86810e11	−0.440239
$423$	−1.85737e11	−0.282076
$424$	−1.57766e11	−0.237065
$425$	2.45018e10	0.0364291
$426$	1.28801e11	0.189486
$427$	0	0
$428$	1.09536e12	1.57782
$429$	1.81154e10	0.0258220
$430$	2.06185e11	0.290836
$431$	−3.02405e10	−0.0422125	−0.0211063	−	0.999777i	$-0.506719\pi$
$431$	−3.02405e10	−0.0422125	−0.0211063	+	0.999777i	$0.506719\pi$
$432$	−2.59853e10	−0.0358965
$433$	−1.03636e12	−1.41682	−0.708410	−	0.705802i	$-0.750587\pi$
$433$	−1.03636e12	−1.41682	−0.708410	+	0.705802i	$0.750587\pi$
$434$	0	0
$435$	−7.06990e11	−0.946699
$436$	−2.10528e12	−2.79010
$437$	5.74983e11	0.754204
$438$	−6.87028e10	−0.0891951
$439$	5.90670e11	0.759022	0.379511	−	0.925187i	$-0.376092\pi$
$439$	5.90670e11	0.759022	0.379511	+	0.925187i	$0.376092\pi$
$440$	−1.89912e10	−0.0241555
$441$	0	0
$442$	5.90001e11	0.735280
$443$	1.27097e12	1.56790	0.783948	−	0.620827i	$-0.213203\pi$
$443$	1.27097e12	1.56790	0.783948	+	0.620827i	$0.213203\pi$
$444$	−4.74528e11	−0.579480
$445$	−1.01161e12	−1.22291
$446$	2.50769e11	0.300101
$447$	−6.72461e11	−0.796679
$448$	0	0
$449$	−9.34644e11	−1.08527	−0.542635	−	0.839969i	$-0.682573\pi$
$449$	−9.34644e11	−1.08527	−0.542635	+	0.839969i	$0.682573\pi$
$450$	5.35052e10	0.0615092
$451$	6.42082e9	0.00730796
$452$	3.56523e11	0.401758
$453$	3.11086e11	0.347087
$454$	1.20851e12	1.33505
$455$	0	0
$456$	4.70406e11	0.509484
$457$	−4.52481e11	−0.485263	−0.242632	−	0.970119i	$-0.578011\pi$
$457$	−4.52481e11	−0.485263	−0.242632	+	0.970119i	$0.578011\pi$
$458$	1.05551e12	1.12091
$459$	−5.74817e10	−0.0604467
$460$	−9.98735e11	−1.04002
$461$	8.56467e11	0.883195	0.441597	−	0.897213i	$-0.354412\pi$
$461$	8.56467e11	0.883195	0.441597	+	0.897213i	$0.354412\pi$
$462$	0	0
$463$	9.21380e11	0.931803	0.465902	−	0.884836i	$-0.345730\pi$
$463$	9.21380e11	0.931803	0.465902	+	0.884836i	$0.345730\pi$
$464$	3.24793e11	0.325294
$465$	−7.52552e11	−0.746446
$466$	2.95228e12	2.90016
$467$	−8.65382e10	−0.0841941	−0.0420971	−	0.999114i	$-0.513404\pi$
$467$	−8.65382e10	−0.0841941	−0.0420971	+	0.999114i	$0.513404\pi$
$468$	7.79403e11	0.751027
$469$	0	0
$470$	1.33914e12	1.26586
$471$	1.76509e11	0.165262
$472$	−8.42856e11	−0.781654
$473$	−6.43346e9	−0.00590976
$474$	1.17152e12	1.06597
$475$	1.34351e11	0.121093
$476$	0	0
$477$	1.05709e11	0.0934930
$478$	−2.25579e12	−1.97640
$479$	−7.63707e11	−0.662852	−0.331426	−	0.943481i	$-0.607530\pi$
$479$	−7.63707e11	−0.662852	−0.331426	+	0.943481i	$0.607530\pi$
$480$	7.20958e11	0.619904
$481$	−1.13223e12	−0.964458
$482$	2.79197e12	2.35613
$483$	0	0
$484$	−1.84692e12	−1.52984
$485$	−1.19197e12	−0.978200
$486$	−1.25524e11	−0.102062
$487$	−5.25531e11	−0.423368	−0.211684	−	0.977338i	$-0.567895\pi$
$487$	−5.25531e11	−0.423368	−0.211684	+	0.977338i	$0.567895\pi$
$488$	3.15439e11	0.251783
$489$	−1.24859e12	−0.987487
$490$	0	0
$491$	2.37265e12	1.84233	0.921163	−	0.389177i	$-0.127241\pi$
$491$	2.37265e12	1.84233	0.921163	+	0.389177i	$0.127241\pi$
$492$	2.76252e11	0.212551
$493$	7.18468e11	0.547768
$494$	3.23515e12	2.44412
$495$	1.27248e10	0.00952639
$496$	3.45724e11	0.256485
$497$	0	0
$498$	−2.17105e12	−1.58175
$499$	−1.33387e11	−0.0963080	−0.0481540	−	0.998840i	$-0.515334\pi$
$499$	−1.33387e11	−0.0963080	−0.0481540	+	0.998840i	$0.515334\pi$
$500$	−2.24543e12	−1.60670
$501$	4.58060e11	0.324827
$502$	−2.09484e12	−1.47226
$503$	6.58632e11	0.458762	0.229381	−	0.973337i	$-0.426330\pi$
$503$	6.58632e11	0.458762	0.229381	+	0.973337i	$0.426330\pi$
$504$	0	0
$505$	5.54379e11	0.379311
$506$	5.15143e10	0.0349342
$507$	1.00071e12	0.672623
$508$	−6.57501e10	−0.0438036
$509$	1.01965e12	0.673322	0.336661	−	0.941626i	$-0.390702\pi$
$509$	1.01965e12	0.673322	0.336661	+	0.941626i	$0.390702\pi$
$510$	4.14436e11	0.271264
$511$	0	0
$512$	−5.76350e11	−0.370656
$513$	−3.15189e11	−0.200929
$514$	−2.66935e11	−0.168683
$515$	−7.60862e11	−0.476621
$516$	−2.76796e11	−0.171884
$517$	−4.17845e10	−0.0257221
$518$	0	0
$519$	−6.23613e9	−0.00377278
$520$	−1.94959e12	−1.16930
$521$	5.57535e11	0.331514	0.165757	−	0.986167i	$-0.446993\pi$
$521$	5.57535e11	0.331514	0.165757	+	0.986167i	$0.446993\pi$
$522$	1.56894e12	0.924886
$523$	−2.12050e12	−1.23931	−0.619657	−	0.784873i	$-0.712728\pi$
$523$	−2.12050e12	−1.23931	−0.619657	+	0.784873i	$0.712728\pi$
$524$	2.92903e12	1.69720
$525$	0	0
$526$	3.78975e12	2.15861
$527$	7.64770e11	0.431900
$528$	−5.84581e9	−0.00327335
$529$	−8.61261e11	−0.478172
$530$	−7.62148e11	−0.419564
$531$	5.64744e11	0.308267
$532$	0	0
$533$	6.59143e11	0.353759
$534$	2.24494e12	1.19473
$535$	1.83584e12	0.968820
$536$	−9.74612e11	−0.510024
$537$	1.88120e12	0.976225
$538$	1.68206e12	0.865608
$539$	0	0
$540$	5.47478e11	0.277073
$541$	1.92746e12	0.967379	0.483690	−	0.875240i	$-0.339296\pi$
$541$	1.92746e12	0.967379	0.483690	+	0.875240i	$0.339296\pi$
$542$	1.03272e12	0.514029
$543$	1.00061e12	0.493931
$544$	−7.32663e11	−0.358682
$545$	−3.52849e12	−1.71319
$546$	0	0
$547$	−2.32751e12	−1.11160	−0.555799	−	0.831317i	$-0.687588\pi$
$547$	−2.32751e12	−1.11160	−0.555799	+	0.831317i	$0.687588\pi$
$548$	5.04581e12	2.39011
$549$	−2.11356e11	−0.0992974
$550$	1.20368e10	0.00560894
$551$	3.93957e12	1.82082
$552$	7.68945e11	0.352508
$553$	0	0
$554$	−3.06243e12	−1.38125
$555$	−7.95318e11	−0.355814
$556$	−1.42557e12	−0.632633
$557$	4.94739e11	0.217785	0.108892	−	0.994054i	$-0.465270\pi$
$557$	4.94739e11	0.217785	0.108892	+	0.994054i	$0.465270\pi$
$558$	1.67005e12	0.729247
$559$	−6.60441e11	−0.286076
$560$	0	0
$561$	−1.29314e10	−0.00551205
$562$	2.83413e10	0.0119841
$563$	−1.14083e12	−0.478557	−0.239279	−	0.970951i	$-0.576911\pi$
$563$	−1.14083e12	−0.478557	−0.239279	+	0.970951i	$0.576911\pi$
$564$	−1.79775e12	−0.748124
$565$	5.97540e11	0.246688
$566$	8.96260e11	0.367079
$567$	0	0
$568$	4.32517e11	0.174356
$569$	−1.64398e10	−0.00657495	−0.00328747	−	0.999995i	$-0.501046\pi$
$569$	−1.64398e10	−0.00657495	−0.00328747	+	0.999995i	$0.501046\pi$
$570$	2.27247e12	0.901700
$571$	−3.67652e12	−1.44735	−0.723676	−	0.690139i	$-0.757549\pi$
$571$	−3.67652e12	−1.44735	−0.723676	+	0.690139i	$0.757549\pi$
$572$	1.75339e11	0.0684851
$573$	−3.40551e11	−0.131973
$574$	0	0
$575$	2.19615e11	0.0837833
$576$	−1.43568e12	−0.543447
$577$	2.29045e12	0.860260	0.430130	−	0.902767i	$-0.358468\pi$
$577$	2.29045e12	0.860260	0.430130	+	0.902767i	$0.358468\pi$
$578$	3.84800e12	1.43403
$579$	−3.55275e11	−0.131375
$580$	−6.84297e12	−2.51084
$581$	0	0
$582$	2.64519e12	0.955661
$583$	2.37809e10	0.00852549
$584$	−2.30706e11	−0.0820730
$585$	1.30629e12	0.461147
$586$	5.65465e12	1.98092
$587$	−4.68750e12	−1.62956	−0.814780	−	0.579771i	$-0.803142\pi$
$587$	−4.68750e12	−1.62956	−0.814780	+	0.579771i	$0.803142\pi$
$588$	0	0
$589$	4.19346e12	1.43567
$590$	−4.07174e12	−1.38339
$591$	−2.72722e12	−0.919553
$592$	3.65371e11	0.122261
$593$	2.33770e12	0.776323	0.388162	−	0.921591i	$-0.373110\pi$
$593$	2.33770e12	0.776323	0.388162	+	0.921591i	$0.373110\pi$
$594$	−2.82386e10	−0.00930690
$595$	0	0
$596$	−6.50876e12	−2.11295
$597$	−8.32131e11	−0.268106
$598$	5.28831e12	1.69107
$599$	−4.66995e12	−1.48215	−0.741075	−	0.671423i	$-0.765684\pi$
$599$	−4.66995e12	−1.48215	−0.741075	+	0.671423i	$0.765684\pi$
$600$	1.79672e11	0.0565978
$601$	3.96517e12	1.23973	0.619864	−	0.784709i	$-0.287188\pi$
$601$	3.96517e12	1.23973	0.619864	+	0.784709i	$0.287188\pi$
$602$	0	0
$603$	6.53026e11	0.201142
$604$	3.01101e12	0.920546
$605$	−3.09548e12	−0.939353
$606$	−1.23027e12	−0.370572
$607$	−6.24743e12	−1.86790	−0.933948	−	0.357409i	$-0.883660\pi$
$607$	−6.24743e12	−1.86790	−0.933948	+	0.357409i	$0.883660\pi$
$608$	−4.01741e12	−1.19228
$609$	0	0
$610$	1.52385e12	0.445612
$611$	−4.28947e12	−1.24514
$612$	−5.56366e11	−0.160317
$613$	−3.73193e12	−1.06748	−0.533742	−	0.845647i	$-0.679215\pi$
$613$	−3.73193e12	−1.06748	−0.533742	+	0.845647i	$0.679215\pi$
$614$	−8.84653e12	−2.51197
$615$	4.63004e11	0.130511
$616$	0	0
$617$	−6.05181e12	−1.68113	−0.840567	−	0.541708i	$-0.817778\pi$
$617$	−6.05181e12	−1.68113	−0.840567	+	0.541708i	$0.817778\pi$
$618$	1.68849e12	0.465640
$619$	−4.69849e12	−1.28632	−0.643162	−	0.765730i	$-0.722378\pi$
$619$	−4.69849e12	−1.28632	−0.643162	+	0.765730i	$0.722378\pi$
$620$	−7.28396e12	−1.97973
$621$	−5.15221e11	−0.139021
$622$	−5.79780e12	−1.55313
$623$	0	0
$624$	−6.00114e11	−0.158454
$625$	−3.32094e12	−0.870565
$626$	−8.80724e12	−2.29222
$627$	−7.09068e10	−0.0183225
$628$	1.70843e12	0.438308
$629$	8.08231e11	0.205877
$630$	0	0
$631$	2.16875e12	0.544600	0.272300	−	0.962212i	$-0.412216\pi$
$631$	2.16875e12	0.544600	0.272300	+	0.962212i	$0.412216\pi$
$632$	3.93398e12	0.980857
$633$	6.45323e11	0.159757
$634$	−4.06195e12	−0.998466
$635$	−1.10199e11	−0.0268964
$636$	1.02316e12	0.247962
$637$	0	0
$638$	3.52957e11	0.0843391
$639$	−2.89803e11	−0.0687620
$640$	5.79392e12	1.36509
$641$	3.56446e12	0.833936	0.416968	−	0.908921i	$-0.363093\pi$
$641$	3.56446e12	0.833936	0.416968	+	0.908921i	$0.363093\pi$
$642$	−4.07406e12	−0.946497
$643$	5.37917e12	1.24098	0.620491	−	0.784213i	$-0.286933\pi$
$643$	5.37917e12	1.24098	0.620491	+	0.784213i	$0.286933\pi$
$644$	0	0
$645$	−4.63916e11	−0.105541
$646$	−2.30937e12	−0.521732
$647$	−6.01827e12	−1.35021	−0.675107	−	0.737720i	$-0.735903\pi$
$647$	−6.01827e12	−1.35021	−0.675107	+	0.737720i	$0.735903\pi$
$648$	−4.21513e11	−0.0939126
$649$	1.27048e11	0.0281104
$650$	1.23567e12	0.271514
$651$	0	0
$652$	−1.20852e13	−2.61901
$653$	−3.68383e11	−0.0792849	−0.0396424	−	0.999214i	$-0.512622\pi$
$653$	−3.68383e11	−0.0792849	−0.0396424	+	0.999214i	$0.512622\pi$
$654$	7.83035e12	1.67371
$655$	4.90912e12	1.04212
$656$	−2.12705e11	−0.0448446
$657$	1.54581e11	0.0323678
$658$	0	0
$659$	−5.24810e12	−1.08397	−0.541985	−	0.840388i	$-0.682327\pi$
$659$	−5.24810e12	−1.08397	−0.541985	+	0.840388i	$0.682327\pi$
$660$	1.23164e11	0.0252659
$661$	−1.55039e11	−0.0315888	−0.0157944	−	0.999875i	$-0.505028\pi$
$661$	−1.55039e11	−0.0315888	−0.0157944	+	0.999875i	$0.505028\pi$
$662$	−1.03445e13	−2.09339
$663$	−1.32750e12	−0.266824
$664$	−7.29043e12	−1.45545
$665$	0	0
$666$	1.76495e12	0.347616
$667$	6.43979e12	1.25981
$668$	4.43357e12	0.861508
$669$	−5.64230e11	−0.108903
$670$	−4.70824e12	−0.902655
$671$	−4.75477e10	−0.00905479
$672$	0	0
$673$	5.89588e11	0.110785	0.0553925	−	0.998465i	$-0.482359\pi$
$673$	5.89588e11	0.110785	0.0553925	+	0.998465i	$0.482359\pi$
$674$	9.09487e11	0.169757
$675$	−1.20387e11	−0.0223209
$676$	9.68586e12	1.78393
$677$	−3.32980e12	−0.609214	−0.304607	−	0.952478i	$-0.598525\pi$
$677$	−3.32980e12	−0.609214	−0.304607	+	0.952478i	$0.598525\pi$
$678$	−1.32605e12	−0.241005
$679$	0	0
$680$	1.39169e12	0.249604
$681$	−2.71914e12	−0.484474
$682$	3.75703e11	0.0664991
$683$	2.28928e12	0.402536	0.201268	−	0.979536i	$-0.435494\pi$
$683$	2.28928e12	0.402536	0.201268	+	0.979536i	$0.435494\pi$
$684$	−3.05072e12	−0.532905
$685$	8.45687e12	1.46758
$686$	0	0
$687$	−2.37491e12	−0.406763
$688$	2.13124e11	0.0362647
$689$	2.44128e12	0.412697
$690$	3.71468e12	0.623880
$691$	9.46129e12	1.57870	0.789349	−	0.613945i	$-0.210418\pi$
$691$	9.46129e12	1.57870	0.789349	+	0.613945i	$0.210418\pi$
$692$	−6.03596e10	−0.0100062
$693$	0	0
$694$	−3.25729e12	−0.533014
$695$	−2.38928e12	−0.388451
$696$	5.26853e12	0.851036
$697$	−4.70521e11	−0.0755147
$698$	−5.53761e11	−0.0883024
$699$	−6.64264e12	−1.05243
$700$	0	0
$701$	8.22209e12	1.28603	0.643015	−	0.765854i	$-0.277683\pi$
$701$	8.22209e12	1.28603	0.643015	+	0.765854i	$0.277683\pi$
$702$	−2.89890e12	−0.450522
$703$	4.43177e12	0.684349
$704$	−3.22979e11	−0.0495562
$705$	−3.01307e12	−0.459365
$706$	−5.28751e12	−0.800995
$707$	0	0
$708$	5.46617e12	0.817586
$709$	7.61957e12	1.13246	0.566230	−	0.824247i	$-0.308401\pi$
$709$	7.61957e12	1.13246	0.566230	+	0.824247i	$0.308401\pi$
$710$	2.08944e12	0.308580
$711$	−2.63591e12	−0.386828
$712$	7.53858e12	1.09933
$713$	6.85481e12	0.993327
$714$	0	0
$715$	2.93871e11	0.0420514
$716$	1.82081e13	2.58915
$717$	5.07554e12	0.717209
$718$	1.59209e13	2.23567
$719$	−7.94823e12	−1.10915	−0.554575	−	0.832134i	$-0.687119\pi$
$719$	−7.94823e12	−1.10915	−0.554575	+	0.832134i	$0.687119\pi$
$720$	−4.21540e11	−0.0584578
$721$	0	0
$722$	−1.04619e12	−0.143283
$723$	−6.28194e12	−0.855010
$724$	9.68492e12	1.31000
$725$	1.50472e12	0.202272
$726$	6.86942e12	0.917710
$727$	5.75787e12	0.764464	0.382232	−	0.924066i	$-0.375156\pi$
$727$	5.75787e12	0.764464	0.382232	+	0.924066i	$0.375156\pi$
$728$	0	0
$729$	2.82430e11	0.0370370
$730$	−1.11451e12	−0.145255
$731$	4.71447e11	0.0610668
$732$	−2.04571e12	−0.263357
$733$	−1.07808e13	−1.37938	−0.689690	−	0.724105i	$-0.742253\pi$
$733$	−1.07808e13	−1.37938	−0.689690	+	0.724105i	$0.742253\pi$
$734$	5.33198e12	0.678041
$735$	0	0
$736$	−6.56702e12	−0.824933
$737$	1.46908e11	0.0183418
$738$	−1.02749e12	−0.127504
$739$	7.37756e12	0.909940	0.454970	−	0.890507i	$-0.349650\pi$
$739$	7.37756e12	0.909940	0.454970	+	0.890507i	$0.349650\pi$
$740$	−7.69790e12	−0.943690
$741$	−7.27909e12	−0.886942
$742$	0	0
$743$	−1.02899e13	−1.23869	−0.619346	−	0.785118i	$-0.712602\pi$
$743$	−1.02899e13	−1.23869	−0.619346	+	0.785118i	$0.712602\pi$
$744$	5.60806e12	0.671018
$745$	−1.09088e13	−1.29740
$746$	−2.74856e12	−0.324923
$747$	4.88485e12	0.573996
$748$	−1.25163e11	−0.0146191
$749$	0	0
$750$	8.35161e12	0.963817
$751$	−7.56555e12	−0.867882	−0.433941	−	0.900941i	$-0.642877\pi$
$751$	−7.56555e12	−0.867882	−0.433941	+	0.900941i	$0.642877\pi$
$752$	1.38421e12	0.157842
$753$	4.71340e12	0.534265
$754$	3.62336e13	4.08263
$755$	5.04651e12	0.565236
$756$	0	0
$757$	−6.88713e12	−0.762267	−0.381133	−	0.924520i	$-0.624466\pi$
$757$	−6.88713e12	−0.762267	−0.381133	+	0.924520i	$0.624466\pi$
$758$	9.72690e12	1.07020
$759$	−1.15907e11	−0.0126772
$760$	7.63103e12	0.829701
$761$	−4.30641e12	−0.465462	−0.232731	−	0.972541i	$-0.574766\pi$
$761$	−4.30641e12	−0.465462	−0.232731	+	0.972541i	$0.574766\pi$
$762$	2.44550e11	0.0262767
$763$	0	0
$764$	−3.29619e12	−0.350020
$765$	−9.32481e11	−0.0984382
$766$	−2.37972e13	−2.49745
$767$	1.30424e13	1.36075
$768$	−3.78281e12	−0.392364
$769$	−2.16296e12	−0.223039	−0.111519	−	0.993762i	$-0.535572\pi$
$769$	−2.16296e12	−0.223039	−0.111519	+	0.993762i	$0.535572\pi$
$770$	0	0
$771$	6.00603e11	0.0612129
$772$	−3.43871e12	−0.348432
$773$	8.15447e12	0.821463	0.410731	−	0.911756i	$-0.365273\pi$
$773$	8.15447e12	0.821463	0.410731	+	0.911756i	$0.365273\pi$
$774$	1.02951e12	0.103109
$775$	1.60170e12	0.159486
$776$	8.88263e12	0.879354
$777$	0	0
$778$	1.11550e13	1.09159
$779$	−2.58000e12	−0.251016
$780$	1.26436e13	1.22306
$781$	−6.51956e10	−0.00627031
$782$	−3.77499e12	−0.360982
$783$	−3.53011e12	−0.335630
$784$	0	0
$785$	2.86337e12	0.269131
$786$	−1.08942e13	−1.01811
$787$	2.25199e12	0.209257	0.104629	−	0.994511i	$-0.466635\pi$
$787$	2.25199e12	0.209257	0.104629	+	0.994511i	$0.466635\pi$
$788$	−2.63968e13	−2.43884
$789$	−8.52694e12	−0.783334
$790$	1.90046e13	1.73595
$791$	0	0
$792$	−9.48261e10	−0.00856376
$793$	−4.88112e12	−0.438319
$794$	−2.34212e13	−2.09130
$795$	1.71483e12	0.152254
$796$	−8.05420e12	−0.711072
$797$	1.16128e13	1.01947	0.509737	−	0.860331i	$-0.329743\pi$
$797$	1.16128e13	1.01947	0.509737	+	0.860331i	$0.329743\pi$
$798$	0	0
$799$	3.06198e12	0.265792
$800$	−1.53445e12	−0.132449
$801$	−5.05112e12	−0.433553
$802$	−9.96122e11	−0.0850214
$803$	3.47755e10	0.00295157
$804$	6.32065e12	0.533469
$805$	0	0
$806$	3.85687e13	3.21904
$807$	−3.78464e12	−0.314118
$808$	−4.13126e12	−0.340982
$809$	2.31768e12	0.190233	0.0951165	−	0.995466i	$-0.469678\pi$
$809$	2.31768e12	0.190233	0.0951165	+	0.995466i	$0.469678\pi$
$810$	−2.03628e12	−0.166209
$811$	9.18815e12	0.745821	0.372910	−	0.927867i	$-0.378360\pi$
$811$	9.18815e12	0.745821	0.372910	+	0.927867i	$0.378360\pi$
$812$	0	0
$813$	−2.32363e12	−0.186535
$814$	3.97054e11	0.0316986
$815$	−2.02550e13	−1.60813
$816$	4.28384e11	0.0338242
$817$	2.58508e12	0.202990
$818$	7.50620e12	0.586179
$819$	0	0
$820$	4.48142e12	0.346141
$821$	−1.92679e13	−1.48010	−0.740048	−	0.672554i	$-0.765197\pi$
$821$	−1.92679e13	−1.48010	−0.740048	+	0.672554i	$0.765197\pi$
$822$	−1.87673e13	−1.43377
$823$	−1.04990e13	−0.797713	−0.398857	−	0.917013i	$-0.630593\pi$
$823$	−1.04990e13	−0.797713	−0.398857	+	0.917013i	$0.630593\pi$
$824$	5.66999e12	0.428459
$825$	−2.70829e10	−0.00203541
$826$	0	0
$827$	−8.10053e12	−0.602197	−0.301098	−	0.953593i	$-0.597353\pi$
$827$	−8.10053e12	−0.602197	−0.301098	+	0.953593i	$0.597353\pi$
$828$	−4.98683e12	−0.368713
$829$	1.52452e13	1.12108	0.560542	−	0.828126i	$-0.310593\pi$
$829$	1.52452e13	1.12108	0.560542	+	0.828126i	$0.310593\pi$
$830$	−3.52192e13	−2.57589
$831$	6.89048e12	0.501239
$832$	−3.31561e13	−2.39888
$833$	0	0
$834$	5.30224e12	0.379501
$835$	7.43075e12	0.528985
$836$	−6.86307e11	−0.0485949
$837$	−3.75761e12	−0.264635
$838$	1.62168e13	1.13597
$839$	−2.72258e13	−1.89694	−0.948468	−	0.316874i	$-0.897367\pi$
$839$	−2.72258e13	−1.89694	−0.948468	+	0.316874i	$0.897367\pi$
$840$	0	0
$841$	2.96160e13	2.04147
$842$	−3.09918e13	−2.12492
$843$	−6.37678e10	−0.00434888
$844$	6.24609e12	0.423709
$845$	1.62337e13	1.09537
$846$	6.68653e12	0.448781
$847$	0	0
$848$	−7.87798e11	−0.0523159
$849$	−2.01658e12	−0.133208
$850$	−8.82066e11	−0.0579583
$851$	7.24435e12	0.473496
$852$	−2.80500e12	−0.182371
$853$	−5.38234e12	−0.348097	−0.174048	−	0.984737i	$-0.555685\pi$
$853$	−5.38234e12	−0.348097	−0.174048	+	0.984737i	$0.555685\pi$
$854$	0	0
$855$	−5.11307e12	−0.327216
$856$	−1.36808e13	−0.870922
$857$	−2.13114e12	−0.134958	−0.0674791	−	0.997721i	$-0.521496\pi$
$857$	−2.13114e12	−0.134958	−0.0674791	+	0.997721i	$0.521496\pi$
$858$	−6.52153e11	−0.0410825
$859$	−1.07650e13	−0.674598	−0.337299	−	0.941398i	$-0.609513\pi$
$859$	−1.07650e13	−0.674598	−0.337299	+	0.941398i	$0.609513\pi$
$860$	−4.49024e12	−0.279916
$861$	0	0
$862$	1.08866e12	0.0671597
$863$	2.36698e13	1.45260	0.726299	−	0.687379i	$-0.241239\pi$
$863$	2.36698e13	1.45260	0.726299	+	0.687379i	$0.241239\pi$
$864$	3.59985e12	0.219772
$865$	−1.01164e11	−0.00614402
$866$	3.73089e13	2.25415
$867$	−8.65800e12	−0.520393
$868$	0	0
$869$	−5.92990e11	−0.0352743
$870$	2.54516e13	1.50619
$871$	1.50812e13	0.887880
$872$	2.62945e13	1.54007
$873$	−5.95169e12	−0.346797
$874$	−2.06994e13	−1.19993
$875$	0	0
$876$	1.49619e12	0.0858459
$877$	−9.91806e12	−0.566146	−0.283073	−	0.959098i	$-0.591354\pi$
$877$	−9.91806e12	−0.566146	−0.283073	+	0.959098i	$0.591354\pi$
$878$	−2.12641e13	−1.20760
$879$	−1.27230e13	−0.718851
$880$	−9.48320e10	−0.00533069
$881$	−1.28992e13	−0.721391	−0.360696	−	0.932684i	$-0.617461\pi$
$881$	−1.28992e13	−0.721391	−0.360696	+	0.932684i	$0.617461\pi$
$882$	0	0
$883$	1.00956e13	0.558866	0.279433	−	0.960165i	$-0.409854\pi$
$883$	1.00956e13	0.558866	0.279433	+	0.960165i	$0.409854\pi$
$884$	−1.28489e13	−0.707671
$885$	9.16141e12	0.502016
$886$	−4.57548e13	−2.49451
$887$	2.22403e12	0.120638	0.0603190	−	0.998179i	$-0.480788\pi$
$887$	2.22403e12	0.120638	0.0603190	+	0.998179i	$0.480788\pi$
$888$	5.92676e12	0.319859
$889$	0	0
$890$	3.64180e13	1.94563
$891$	6.35370e10	0.00337736
$892$	−5.46119e12	−0.288832
$893$	1.67898e13	0.883513
$894$	2.42086e13	1.26751
$895$	3.05172e13	1.58979
$896$	0	0
$897$	−1.18987e13	−0.613668
$898$	3.36472e13	1.72665
$899$	4.69666e13	2.39812
$900$	−1.16523e12	−0.0591996
$901$	−1.74267e12	−0.0880957
$902$	−2.31150e11	−0.0116269
$903$	0	0
$904$	−4.45290e12	−0.221761
$905$	1.62321e13	0.804372
$906$	−1.11991e13	−0.552213
$907$	−6.35542e12	−0.311825	−0.155913	−	0.987771i	$-0.549832\pi$
$907$	−6.35542e12	−0.311825	−0.155913	+	0.987771i	$0.549832\pi$
$908$	−2.63186e13	−1.28492
$909$	2.76810e12	0.134476
$910$	0	0
$911$	−1.91432e13	−0.920837	−0.460418	−	0.887702i	$-0.652301\pi$
$911$	−1.91432e13	−0.920837	−0.460418	+	0.887702i	$0.652301\pi$
$912$	2.34895e12	0.112434
$913$	1.09892e12	0.0523419
$914$	1.62893e13	0.772049
$915$	−3.42866e12	−0.161707
$916$	−2.29867e13	−1.07882
$917$	0	0
$918$	2.06934e12	0.0961701
$919$	2.86053e13	1.32290	0.661449	−	0.749991i	$-0.269942\pi$
$919$	2.86053e13	1.32290	0.661449	+	0.749991i	$0.269942\pi$
$920$	1.24740e13	0.574064
$921$	1.99047e13	0.911564
$922$	−3.08328e13	−1.40515
$923$	−6.69280e12	−0.303529
$924$	0	0
$925$	1.69272e12	0.0760233
$926$	−3.31697e13	−1.48249
$927$	−3.79910e12	−0.168975
$928$	−4.49948e13	−1.99158
$929$	1.18899e13	0.523728	0.261864	−	0.965105i	$-0.415663\pi$
$929$	1.18899e13	0.523728	0.261864	+	0.965105i	$0.415663\pi$
$930$	2.70919e13	1.18759
$931$	0	0
$932$	−6.42942e13	−2.79126
$933$	1.30451e13	0.563610
$934$	3.11537e12	0.133952
$935$	−2.09776e11	−0.00897644
$936$	−9.73458e12	−0.414549
$937$	3.45871e13	1.46584	0.732920	−	0.680315i	$-0.238157\pi$
$937$	3.45871e13	1.46584	0.732920	+	0.680315i	$0.238157\pi$
$938$	0	0
$939$	1.98163e13	0.831816
$940$	−2.91635e13	−1.21833
$941$	−2.59742e13	−1.07991	−0.539956	−	0.841693i	$-0.681559\pi$
$941$	−2.59742e13	−1.07991	−0.539956	+	0.841693i	$0.681559\pi$
$942$	−6.35432e12	−0.262930
$943$	−4.21738e12	−0.173676
$944$	−4.20877e12	−0.172497
$945$	0	0
$946$	2.31605e11	0.00940237
$947$	2.43739e13	0.984804	0.492402	−	0.870368i	$-0.336119\pi$
$947$	2.43739e13	0.984804	0.492402	+	0.870368i	$0.336119\pi$
$948$	−2.55130e13	−1.02595
$949$	3.56995e12	0.142878
$950$	−4.83663e12	−0.192658
$951$	9.13939e12	0.362331
$952$	0	0
$953$	−2.34891e13	−0.922461	−0.461230	−	0.887280i	$-0.652592\pi$
$953$	−2.34891e13	−0.922461	−0.461230	+	0.887280i	$0.652592\pi$
$954$	−3.80552e12	−0.148746
$955$	−5.52449e12	−0.214920
$956$	4.91262e13	1.90218
$957$	−7.94153e11	−0.0306056
$958$	2.74934e13	1.05459
$959$	0	0
$960$	−2.32900e13	−0.885010
$961$	2.35538e13	0.890851
$962$	4.07604e13	1.53444
$963$	9.16663e12	0.343472
$964$	−6.08029e13	−2.26766
$965$	−5.76335e12	−0.213945
$966$	0	0
$967$	4.68639e12	0.172353	0.0861766	−	0.996280i	$-0.472535\pi$
$967$	4.68639e12	0.172353	0.0861766	+	0.996280i	$0.472535\pi$
$968$	2.30677e13	0.844433
$969$	5.19608e12	0.189330
$970$	4.29109e13	1.55631
$971$	4.63936e13	1.67483	0.837416	−	0.546566i	$-0.184065\pi$
$971$	4.63936e13	1.67483	0.837416	+	0.546566i	$0.184065\pi$
$972$	2.73364e12	0.0982297
$973$	0	0
$974$	1.89191e13	0.673574
$975$	−2.78025e12	−0.0985289
$976$	1.57513e12	0.0555639
$977$	2.53890e13	0.891496	0.445748	−	0.895159i	$-0.352938\pi$
$977$	2.53890e13	0.891496	0.445748	+	0.895159i	$0.352938\pi$
$978$	4.49494e13	1.57108
$979$	−1.13633e12	−0.0395350
$980$	0	0
$981$	−1.76183e13	−0.607370
$982$	−8.54153e13	−2.93112
$983$	8.90780e12	0.304284	0.152142	−	0.988359i	$-0.451383\pi$
$983$	8.90780e12	0.304284	0.152142	+	0.988359i	$0.451383\pi$
$984$	−3.45033e12	−0.117323
$985$	−4.42416e13	−1.49750
$986$	−2.58649e13	−0.871493
$987$	0	0
$988$	−7.04544e13	−2.35235
$989$	4.22569e12	0.140448
$990$	−4.58094e11	−0.0151564
$991$	3.90840e13	1.28727	0.643633	−	0.765335i	$-0.277427\pi$
$991$	3.90840e13	1.28727	0.643633	+	0.765335i	$0.277427\pi$
$992$	−4.78945e13	−1.57030
$993$	2.32752e13	0.759665
$994$	0	0
$995$	−1.34990e13	−0.436614
$996$	4.72806e13	1.52235
$997$	1.94045e12	0.0621975	0.0310988	−	0.999516i	$-0.490099\pi$
$997$	1.94045e12	0.0621975	0.0310988	+	0.999516i	$0.490099\pi$
$998$	4.80195e12	0.153225
$999$	−3.97115e12	−0.126145

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.10.a.a.1.1		1
7.6	odd	2		3.10.a.a.1.1	✓	1
21.20	even	2		9.10.a.c.1.1		1
28.27	even	2		48.10.a.e.1.1		1
35.13	even	4		75.10.b.a.49.2		2
35.27	even	4		75.10.b.a.49.1		2
35.34	odd	2		75.10.a.d.1.1		1
56.13	odd	2		192.10.a.m.1.1		1
56.27	even	2		192.10.a.f.1.1		1
63.13	odd	6		81.10.c.e.55.1		2
63.20	even	6		81.10.c.a.28.1		2
63.34	odd	6		81.10.c.e.28.1		2
63.41	even	6		81.10.c.a.55.1		2
77.76	even	2		363.10.a.b.1.1		1
84.83	odd	2		144.10.a.l.1.1		1
105.62	odd	4		225.10.b.a.199.2		2
105.83	odd	4		225.10.b.a.199.1		2
105.104	even	2		225.10.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.10.a.a.1.1	✓	1	7.6	odd	2
9.10.a.c.1.1		1	21.20	even	2
48.10.a.e.1.1		1	28.27	even	2
75.10.a.d.1.1		1	35.34	odd	2
75.10.b.a.49.1		2	35.27	even	4
75.10.b.a.49.2		2	35.13	even	4
81.10.c.a.28.1		2	63.20	even	6
81.10.c.a.55.1		2	63.41	even	6
81.10.c.e.28.1		2	63.34	odd	6
81.10.c.e.55.1		2	63.13	odd	6
144.10.a.l.1.1		1	84.83	odd	2
147.10.a.a.1.1		1	1.1	even	1	trivial
192.10.a.f.1.1		1	56.27	even	2
192.10.a.m.1.1		1	56.13	odd	2
225.10.a.a.1.1		1	105.104	even	2
225.10.b.a.199.1		2	105.83	odd	4
225.10.b.a.199.2		2	105.62	odd	4
363.10.a.b.1.1		1	77.76	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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more