LMFDB - Embedded newform 147.10.a.c.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:	$0$
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)

$f(q)$

$=$

$q+18.0000 q^{2} -81.0000 q^{3} -188.000 q^{4} +1530.00 q^{5} -1458.00 q^{6} -12600.0 q^{8} +6561.00 q^{9} +O(q^{10})$

\(q+18.0000 q^{2} -81.0000 q^{3} -188.000 q^{4} +1530.00 q^{5} -1458.00 q^{6} -12600.0 q^{8} +6561.00 q^{9} +27540.0 q^{10} +21132.0 q^{11} +15228.0 q^{12} -31214.0 q^{13} -123930. q^{15} -130544. q^{16} +279342. q^{17} +118098. q^{18} -144020. q^{19} -287640. q^{20} +380376. q^{22} -1.76350e6 q^{23} +1.02060e6 q^{24} +387775. q^{25} -561852. q^{26} -531441. q^{27} +4.69251e6 q^{29} -2.23074e6 q^{30} +369088. q^{31} +4.10141e6 q^{32} -1.71169e6 q^{33} +5.02816e6 q^{34} -1.23347e6 q^{36} +9.34708e6 q^{37} -2.59236e6 q^{38} +2.52833e6 q^{39} -1.92780e7 q^{40} +7.22684e6 q^{41} -2.31475e7 q^{43} -3.97282e6 q^{44} +1.00383e7 q^{45} -3.17429e7 q^{46} -2.29719e7 q^{47} +1.05741e7 q^{48} +6.97995e6 q^{50} -2.26267e7 q^{51} +5.86823e6 q^{52} +7.84772e7 q^{53} -9.56594e6 q^{54} +3.23320e7 q^{55} +1.16656e7 q^{57} +8.44652e7 q^{58} +2.03107e7 q^{59} +2.32988e7 q^{60} +1.79340e8 q^{61} +6.64358e6 q^{62} +1.40664e8 q^{64} -4.77574e7 q^{65} -3.08105e7 q^{66} +2.74528e8 q^{67} -5.25163e7 q^{68} +1.42843e8 q^{69} -3.63426e7 q^{71} -8.26686e7 q^{72} +2.47090e8 q^{73} +1.68247e8 q^{74} -3.14098e7 q^{75} +2.70758e7 q^{76} +4.55100e7 q^{78} +1.91875e8 q^{79} -1.99732e8 q^{80} +4.30467e7 q^{81} +1.30083e8 q^{82} +2.76159e8 q^{83} +4.27393e8 q^{85} -4.16655e8 q^{86} -3.80093e8 q^{87} -2.66263e8 q^{88} +6.78997e8 q^{89} +1.80690e8 q^{90} +3.31537e8 q^{92} -2.98961e7 q^{93} -4.13494e8 q^{94} -2.20351e8 q^{95} -3.32214e8 q^{96} +5.67658e8 q^{97} +1.38647e8 q^{99} +O(q^{100})\)

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 $

$2$	18.0000	0.795495	0.397748	−	0.917495i	$-0.369792\pi$
$2$	18.0000	0.795495	0.397748	+	0.917495i	$0.369792\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−188.000	−0.367188
$5$	1530.00	1.09478	0.547389	−	0.836878i	$-0.315622\pi$
$5$	1530.00	1.09478	0.547389	+	0.836878i	$0.315622\pi$
$6$	−1458.00	−0.459279
$7$	0	0
$7$	0	0
$8$	−12600.0	−1.08759
$9$	6561.00	0.333333
$10$	27540.0	0.870891
$11$	21132.0	0.435185	0.217592	−	0.976040i	$-0.430180\pi$
$11$	21132.0	0.435185	0.217592	+	0.976040i	$0.430180\pi$
$12$	15228.0	0.211996
$13$	−31214.0	−0.303113	−0.151556	−	0.988449i	$-0.548429\pi$
$13$	−31214.0	−0.303113	−0.151556	+	0.988449i	$0.548429\pi$
$14$	0	0
$15$	−123930.	−0.632071
$16$	−130544.	−0.497986
$17$	279342.	0.811178	0.405589	−	0.914056i	$-0.367066\pi$
$17$	279342.	0.811178	0.405589	+	0.914056i	$0.367066\pi$
$18$	118098.	0.265165
$19$	−144020.	−0.253531	−0.126766	−	0.991933i	$-0.540460\pi$
$19$	−144020.	−0.253531	−0.126766	+	0.991933i	$0.540460\pi$
$20$	−287640.	−0.401989
$21$	0	0
$22$	380376.	0.346187
$23$	−1.76350e6	−1.31401	−0.657006	−	0.753885i	$-0.728177\pi$
$23$	−1.76350e6	−1.31401	−0.657006	+	0.753885i	$0.728177\pi$
$24$	1.02060e6	0.627921
$25$	387775.	0.198541
$26$	−561852.	−0.241125
$27$	−531441.	−0.192450
$28$	0	0
$29$	4.69251e6	1.23201	0.616005	−	0.787742i	$-0.288750\pi$
$29$	4.69251e6	1.23201	0.616005	+	0.787742i	$0.288750\pi$
$30$	−2.23074e6	−0.502809
$31$	369088.	0.0717798	0.0358899	−	0.999356i	$-0.488573\pi$
$31$	369088.	0.0717798	0.0358899	+	0.999356i	$0.488573\pi$
$32$	4.10141e6	0.691446
$33$	−1.71169e6	−0.251254
$34$	5.02816e6	0.645288
$35$	0	0
$36$	−1.23347e6	−0.122396
$37$	9.34708e6	0.819914	0.409957	−	0.912105i	$-0.365544\pi$
$37$	9.34708e6	0.819914	0.409957	+	0.912105i	$0.365544\pi$
$38$	−2.59236e6	−0.201683
$39$	2.52833e6	0.175002
$40$	−1.92780e7	−1.19067
$41$	7.22684e6	0.399412	0.199706	−	0.979856i	$-0.436001\pi$
$41$	7.22684e6	0.399412	0.199706	+	0.979856i	$0.436001\pi$
$42$	0	0
$43$	−2.31475e7	−1.03251	−0.516257	−	0.856434i	$-0.672675\pi$
$43$	−2.31475e7	−1.03251	−0.516257	+	0.856434i	$0.672675\pi$
$44$	−3.97282e6	−0.159794
$45$	1.00383e7	0.364926
$46$	−3.17429e7	−1.04529
$47$	−2.29719e7	−0.686683	−0.343342	−	0.939211i	$-0.611559\pi$
$47$	−2.29719e7	−0.686683	−0.343342	+	0.939211i	$0.611559\pi$
$48$	1.05741e7	0.287512
$49$	0	0
$50$	6.97995e6	0.157938
$51$	−2.26267e7	−0.468334
$52$	5.86823e6	0.111299
$53$	7.84772e7	1.36616	0.683081	−	0.730343i	$-0.260640\pi$
$53$	7.84772e7	1.36616	0.683081	+	0.730343i	$0.260640\pi$
$54$	−9.56594e6	−0.153093
$55$	3.23320e7	0.476431
$56$	0	0
$57$	1.16656e7	0.146376
$58$	8.44652e7	0.980058
$59$	2.03107e7	0.218218	0.109109	−	0.994030i	$-0.465200\pi$
$59$	2.03107e7	0.218218	0.109109	+	0.994030i	$0.465200\pi$
$60$	2.32988e7	0.232089
$61$	1.79340e8	1.65841	0.829207	−	0.558942i	$-0.188793\pi$
$61$	1.79340e8	1.65841	0.829207	+	0.558942i	$0.188793\pi$
$62$	6.64358e6	0.0571005
$63$	0	0
$64$	1.40664e8	1.04803
$65$	−4.77574e7	−0.331842
$66$	−3.08105e7	−0.199871
$67$	2.74528e8	1.66437	0.832186	−	0.554496i	$-0.187089\pi$
$67$	2.74528e8	1.66437	0.832186	+	0.554496i	$0.187089\pi$
$68$	−5.25163e7	−0.297854
$69$	1.42843e8	0.758645
$70$	0	0
$71$	−3.63426e7	−0.169728	−0.0848641	−	0.996393i	$-0.527046\pi$
$71$	−3.63426e7	−0.169728	−0.0848641	+	0.996393i	$0.527046\pi$
$72$	−8.26686e7	−0.362530
$73$	2.47090e8	1.01836	0.509180	−	0.860660i	$-0.329949\pi$
$73$	2.47090e8	1.01836	0.509180	+	0.860660i	$0.329949\pi$
$74$	1.68247e8	0.652237
$75$	−3.14098e7	−0.114628
$76$	2.70758e7	0.0930935
$77$	0	0
$78$	4.55100e7	0.139213
$79$	1.91875e8	0.554238	0.277119	−	0.960836i	$-0.410620\pi$
$79$	1.91875e8	0.554238	0.277119	+	0.960836i	$0.410620\pi$
$80$	−1.99732e8	−0.545184
$81$	4.30467e7	0.111111
$82$	1.30083e8	0.317730
$83$	2.76159e8	0.638717	0.319358	−	0.947634i	$-0.396533\pi$
$83$	2.76159e8	0.638717	0.319358	+	0.947634i	$0.396533\pi$
$84$	0	0
$85$	4.27393e8	0.888060
$86$	−4.16655e8	−0.821359
$87$	−3.80093e8	−0.711301
$88$	−2.66263e8	−0.473303
$89$	6.78997e8	1.14713	0.573566	−	0.819160i	$-0.305560\pi$
$89$	6.78997e8	1.14713	0.573566	+	0.819160i	$0.305560\pi$
$90$	1.80690e8	0.290297
$91$	0	0
$92$	3.31537e8	0.482489
$93$	−2.98961e7	−0.0414421
$94$	−4.13494e8	−0.546253
$95$	−2.20351e8	−0.277561
$96$	−3.32214e8	−0.399206
$97$	5.67658e8	0.651049	0.325524	−	0.945534i	$-0.394459\pi$
$97$	5.67658e8	0.651049	0.325524	+	0.945534i	$0.394459\pi$
$98$	0	0
$99$	1.38647e8	0.145062
$100$	−7.29017e7	−0.0729017
$101$	−1.62282e9	−1.55176	−0.775881	−	0.630879i	$-0.782694\pi$
$101$	−1.62282e9	−1.55176	−0.775881	+	0.630879i	$0.782694\pi$
$102$	−4.07281e8	−0.372557
$103$	1.75103e9	1.53294	0.766470	−	0.642280i	$-0.222011\pi$
$103$	1.75103e9	1.53294	0.766470	+	0.642280i	$0.222011\pi$
$104$	3.93296e8	0.329663
$105$	0	0
$106$	1.41259e9	1.08677
$107$	−1.54296e9	−1.13796	−0.568980	−	0.822352i	$-0.692662\pi$
$107$	−1.54296e9	−1.13796	−0.568980	+	0.822352i	$0.692662\pi$
$108$	9.99109e7	0.0706653
$109$	4.57665e8	0.310548	0.155274	−	0.987871i	$-0.450374\pi$
$109$	4.57665e8	0.310548	0.155274	+	0.987871i	$0.450374\pi$
$110$	5.81975e8	0.378998
$111$	−7.57113e8	−0.473377
$112$	0	0
$113$	3.26794e9	1.88548	0.942739	−	0.333531i	$-0.108240\pi$
$113$	3.26794e9	1.88548	0.942739	+	0.333531i	$0.108240\pi$
$114$	2.09981e8	0.116442
$115$	−2.69815e9	−1.43855
$116$	−8.82192e8	−0.452379
$117$	−2.04795e8	−0.101038
$118$	3.65592e8	0.173591
$119$	0	0
$120$	1.56152e9	0.687435
$121$	−1.91139e9	−0.810614
$122$	3.22812e9	1.31926
$123$	−5.85374e8	−0.230601
$124$	−6.93885e7	−0.0263566
$125$	−2.39499e9	−0.877421
$126$	0	0
$127$	9.28879e8	0.316842	0.158421	−	0.987372i	$-0.449360\pi$
$127$	9.28879e8	0.316842	0.158421	+	0.987372i	$0.449360\pi$
$128$	4.32029e8	0.142255
$129$	1.87495e9	0.596122
$130$	−8.59634e8	−0.263978
$131$	9.88659e8	0.293309	0.146655	−	0.989188i	$-0.453149\pi$
$131$	9.88659e8	0.293309	0.146655	+	0.989188i	$0.453149\pi$
$132$	3.21798e8	0.0922573
$133$	0	0
$134$	4.94151e9	1.32400
$135$	−8.13105e8	−0.210690
$136$	−3.51971e9	−0.882230
$137$	−5.73253e7	−0.0139028	−0.00695142	−	0.999976i	$-0.502213\pi$
$137$	−5.73253e7	−0.0139028	−0.00695142	+	0.999976i	$0.502213\pi$
$138$	2.57118e9	0.603498
$139$	4.65052e9	1.05666	0.528330	−	0.849039i	$-0.322818\pi$
$139$	4.65052e9	1.05666	0.528330	+	0.849039i	$0.322818\pi$
$140$	0	0
$141$	1.86072e9	0.396457
$142$	−6.54168e8	−0.135018
$143$	−6.59614e8	−0.131910
$144$	−8.56499e8	−0.165995
$145$	7.17954e9	1.34878
$146$	4.44761e9	0.810101
$147$	0	0
$148$	−1.75725e9	−0.301062
$149$	−1.40236e9	−0.233089	−0.116545	−	0.993185i	$-0.537182\pi$
$149$	−1.40236e9	−0.233089	−0.116545	+	0.993185i	$0.537182\pi$
$150$	−5.65376e8	−0.0911857
$151$	1.01548e10	1.58955	0.794773	−	0.606907i	$-0.207590\pi$
$151$	1.01548e10	1.58955	0.794773	+	0.606907i	$0.207590\pi$
$152$	1.81465e9	0.275738
$153$	1.83276e9	0.270393
$154$	0	0
$155$	5.64705e8	0.0785830
$156$	−4.75327e8	−0.0642587
$157$	−9.36605e9	−1.23029	−0.615146	−	0.788413i	$-0.710903\pi$
$157$	−9.36605e9	−1.23029	−0.615146	+	0.788413i	$0.710903\pi$
$158$	3.45375e9	0.440893
$159$	−6.35665e9	−0.788754
$160$	6.27515e9	0.756980
$161$	0	0
$162$	7.74841e8	0.0883883
$163$	−7.34780e8	−0.0815292	−0.0407646	−	0.999169i	$-0.512979\pi$
$163$	−7.34780e8	−0.0815292	−0.0407646	+	0.999169i	$0.512979\pi$
$164$	−1.35865e9	−0.146659
$165$	−2.61889e9	−0.275068
$166$	4.97087e9	0.508096
$167$	−1.55584e9	−0.154789	−0.0773947	−	0.997001i	$-0.524660\pi$
$167$	−1.55584e9	−0.154789	−0.0773947	+	0.997001i	$0.524660\pi$
$168$	0	0
$169$	−9.63019e9	−0.908123
$170$	7.69308e9	0.706448
$171$	−9.44915e8	−0.0845104
$172$	4.35173e9	0.379126
$173$	−1.90448e10	−1.61648	−0.808238	−	0.588856i	$-0.799579\pi$
$173$	−1.90448e10	−1.61648	−0.808238	+	0.588856i	$0.799579\pi$
$174$	−6.84168e9	−0.565837
$175$	0	0
$176$	−2.75866e9	−0.216716
$177$	−1.64516e9	−0.125988
$178$	1.22220e10	0.912537
$179$	4.32852e9	0.315138	0.157569	−	0.987508i	$-0.449634\pi$
$179$	4.32852e9	0.315138	0.157569	+	0.987508i	$0.449634\pi$
$180$	−1.88721e9	−0.133996
$181$	9.56757e8	0.0662595	0.0331298	−	0.999451i	$-0.489453\pi$
$181$	9.56757e8	0.0662595	0.0331298	+	0.999451i	$0.489453\pi$
$182$	0	0
$183$	−1.45265e10	−0.957485
$184$	2.22200e10	1.42911
$185$	1.43010e10	0.897624
$186$	−5.38130e8	−0.0329670
$187$	5.90306e9	0.353012
$188$	4.31871e9	0.252141
$189$	0	0
$190$	−3.96631e9	−0.220798
$191$	−1.76438e10	−0.959274	−0.479637	−	0.877467i	$-0.659232\pi$
$191$	−1.76438e10	−0.959274	−0.479637	+	0.877467i	$0.659232\pi$
$192$	−1.13938e10	−0.605079
$193$	1.30993e10	0.679581	0.339790	−	0.940501i	$-0.389644\pi$
$193$	1.30993e10	0.679581	0.339790	+	0.940501i	$0.389644\pi$
$194$	1.02178e10	0.517906
$195$	3.86835e9	0.191589
$196$	0	0
$197$	4.74589e9	0.224502	0.112251	−	0.993680i	$-0.464194\pi$
$197$	4.74589e9	0.224502	0.112251	+	0.993680i	$0.464194\pi$
$198$	2.49565e9	0.115396
$199$	1.92102e10	0.868348	0.434174	−	0.900829i	$-0.357040\pi$
$199$	1.92102e10	0.868348	0.434174	+	0.900829i	$0.357040\pi$
$200$	−4.88596e9	−0.215931
$201$	−2.22368e10	−0.960926
$202$	−2.92108e10	−1.23442
$203$	0	0
$204$	4.25382e9	0.171966
$205$	1.10571e10	0.437268
$206$	3.15185e10	1.21945
$207$	−1.15703e10	−0.438004
$208$	4.07480e9	0.150946
$209$	−3.04343e9	−0.110333
$210$	0	0
$211$	−1.81273e10	−0.629597	−0.314798	−	0.949159i	$-0.601937\pi$
$211$	−1.81273e10	−0.629597	−0.314798	+	0.949159i	$0.601937\pi$
$212$	−1.47537e10	−0.501637
$213$	2.94375e9	0.0979926
$214$	−2.77732e10	−0.905241
$215$	−3.54156e10	−1.13037
$216$	6.69616e9	0.209307
$217$	0	0
$218$	8.23797e9	0.247039
$219$	−2.00143e10	−0.587951
$220$	−6.07841e9	−0.174939
$221$	−8.71938e9	−0.245878
$222$	−1.36280e10	−0.376569
$223$	−3.91081e9	−0.105900	−0.0529499	−	0.998597i	$-0.516862\pi$
$223$	−3.91081e9	−0.105900	−0.0529499	+	0.998597i	$0.516862\pi$
$224$	0	0
$225$	2.54419e9	0.0661803
$226$	5.88230e10	1.49989
$227$	3.58126e10	0.895199	0.447599	−	0.894234i	$-0.352279\pi$
$227$	3.58126e10	0.895199	0.447599	+	0.894234i	$0.352279\pi$
$228$	−2.19314e9	−0.0537476
$229$	−5.30445e9	−0.127462	−0.0637310	−	0.997967i	$-0.520300\pi$
$229$	−5.30445e9	−0.127462	−0.0637310	+	0.997967i	$0.520300\pi$
$230$	−4.85667e10	−1.14436
$231$	0	0
$232$	−5.91256e10	−1.33992
$233$	−2.54172e10	−0.564970	−0.282485	−	0.959272i	$-0.591159\pi$
$233$	−2.54172e10	−0.564970	−0.282485	+	0.959272i	$0.591159\pi$
$234$	−3.68631e9	−0.0803749
$235$	−3.51470e10	−0.751766
$236$	−3.81840e9	−0.0801268
$237$	−1.55419e10	−0.319989
$238$	0	0
$239$	−6.33494e10	−1.25589	−0.627946	−	0.778257i	$-0.716104\pi$
$239$	−6.33494e10	−1.25589	−0.627946	+	0.778257i	$0.716104\pi$
$240$	1.61783e10	0.314762
$241$	−1.01929e11	−1.94635	−0.973173	−	0.230073i	$-0.926103\pi$
$241$	−1.01929e11	−1.94635	−0.973173	+	0.230073i	$0.926103\pi$
$242$	−3.44050e10	−0.644840
$243$	−3.48678e9	−0.0641500
$244$	−3.37159e10	−0.608949
$245$	0	0
$246$	−1.05367e10	−0.183442
$247$	4.49544e9	0.0768486
$248$	−4.65051e9	−0.0780671
$249$	−2.23689e10	−0.368763
$250$	−4.31097e10	−0.697984
$251$	−9.64745e10	−1.53420	−0.767098	−	0.641530i	$-0.778300\pi$
$251$	−9.64745e10	−1.53420	−0.767098	+	0.641530i	$0.778300\pi$
$252$	0	0
$253$	−3.72662e10	−0.571838
$254$	1.67198e10	0.252046
$255$	−3.46189e10	−0.512722
$256$	−6.42434e10	−0.934864
$257$	7.99591e9	0.114332	0.0571661	−	0.998365i	$-0.481794\pi$
$257$	7.99591e9	0.114332	0.0571661	+	0.998365i	$0.481794\pi$
$258$	3.37490e10	0.474212
$259$	0	0
$260$	8.97839e9	0.121848
$261$	3.07876e10	0.410670
$262$	1.77959e10	0.233326
$263$	1.06269e11	1.36964	0.684821	−	0.728712i	$-0.259881\pi$
$263$	1.06269e11	1.36964	0.684821	+	0.728712i	$0.259881\pi$
$264$	2.15673e10	0.273262
$265$	1.20070e11	1.49564
$266$	0	0
$267$	−5.49988e10	−0.662296
$268$	−5.16113e10	−0.611137
$269$	1.00886e11	1.17475	0.587377	−	0.809313i	$-0.300160\pi$
$269$	1.00886e11	1.17475	0.587377	+	0.809313i	$0.300160\pi$
$270$	−1.46359e10	−0.167603
$271$	2.86345e10	0.322498	0.161249	−	0.986914i	$-0.448448\pi$
$271$	2.86345e10	0.322498	0.161249	+	0.986914i	$0.448448\pi$
$272$	−3.64664e10	−0.403955
$273$	0	0
$274$	−1.03186e9	−0.0110596
$275$	8.19446e9	0.0864019
$276$	−2.68545e10	−0.278565
$277$	4.12251e10	0.420729	0.210365	−	0.977623i	$-0.432535\pi$
$277$	4.12251e10	0.420729	0.210365	+	0.977623i	$0.432535\pi$
$278$	8.37094e10	0.840568
$279$	2.42159e9	0.0239266
$280$	0	0
$281$	1.21800e11	1.16538	0.582692	−	0.812693i	$-0.301999\pi$
$281$	1.21800e11	1.16538	0.582692	+	0.812693i	$0.301999\pi$
$282$	3.34930e10	0.315379
$283$	−2.32820e10	−0.215765	−0.107883	−	0.994164i	$-0.534407\pi$
$283$	−2.32820e10	−0.215765	−0.107883	+	0.994164i	$0.534407\pi$
$284$	6.83242e9	0.0623221
$285$	1.78484e10	0.160250
$286$	−1.18731e10	−0.104934
$287$	0	0
$288$	2.69093e10	0.230482
$289$	−4.05559e10	−0.341990
$290$	1.29232e11	1.07295
$291$	−4.59803e10	−0.375883
$292$	−4.64528e10	−0.373929
$293$	9.12801e10	0.723555	0.361778	−	0.932264i	$-0.382170\pi$
$293$	9.12801e10	0.723555	0.361778	+	0.932264i	$0.382170\pi$
$294$	0	0
$295$	3.10753e10	0.238900
$296$	−1.17773e11	−0.891731
$297$	−1.12304e10	−0.0837513
$298$	−2.52425e10	−0.185421
$299$	5.50458e10	0.398294
$300$	5.90504e9	0.0420898
$301$	0	0
$302$	1.82786e11	1.26448
$303$	1.31449e11	0.895910
$304$	1.88009e10	0.126255
$305$	2.74390e11	1.81560
$306$	3.29897e10	0.215096
$307$	4.39070e10	0.282105	0.141053	−	0.990002i	$-0.454951\pi$
$307$	4.39070e10	0.282105	0.141053	+	0.990002i	$0.454951\pi$
$308$	0	0
$309$	−1.41833e11	−0.885043
$310$	1.01647e10	0.0625124
$311$	7.64835e10	0.463603	0.231801	−	0.972763i	$-0.425538\pi$
$311$	7.64835e10	0.463603	0.231801	+	0.972763i	$0.425538\pi$
$312$	−3.18570e10	−0.190331
$313$	−2.68488e11	−1.58116	−0.790580	−	0.612359i	$-0.790221\pi$
$313$	−2.68488e11	−1.58116	−0.790580	+	0.612359i	$0.790221\pi$
$314$	−1.68589e11	−0.978691
$315$	0	0
$316$	−3.60725e10	−0.203509
$317$	1.52056e11	0.845738	0.422869	−	0.906191i	$-0.361023\pi$
$317$	1.52056e11	0.845738	0.422869	+	0.906191i	$0.361023\pi$
$318$	−1.14420e11	−0.627450
$319$	9.91621e10	0.536152
$320$	2.15216e11	1.14736
$321$	1.24980e11	0.657001
$322$	0	0
$323$	−4.02308e10	−0.205659
$324$	−8.09278e9	−0.0407986
$325$	−1.21040e10	−0.0601803
$326$	−1.32260e10	−0.0648561
$327$	−3.70709e10	−0.179295
$328$	−9.10582e10	−0.434397
$329$	0	0
$330$	−4.71400e10	−0.218815
$331$	−2.63057e11	−1.20455	−0.602274	−	0.798289i	$-0.705739\pi$
$331$	−2.63057e11	−1.20455	−0.602274	+	0.798289i	$0.705739\pi$
$332$	−5.19179e10	−0.234529
$333$	6.13262e10	0.273305
$334$	−2.80051e10	−0.123134
$335$	4.20028e11	1.82212
$336$	0	0
$337$	2.97183e11	1.25513	0.627566	−	0.778564i	$-0.284051\pi$
$337$	2.97183e11	1.25513	0.627566	+	0.778564i	$0.284051\pi$
$338$	−1.73343e11	−0.722407
$339$	−2.64703e11	−1.08858
$340$	−8.03499e10	−0.326085
$341$	7.79957e9	0.0312375
$342$	−1.70085e10	−0.0672276
$343$	0	0
$344$	2.91658e11	1.12295
$345$	2.18550e11	0.830549
$346$	−3.42807e11	−1.28590
$347$	1.40219e11	0.519186	0.259593	−	0.965718i	$-0.416412\pi$
$347$	1.40219e11	0.519186	0.259593	+	0.965718i	$0.416412\pi$
$348$	7.14575e10	0.261181
$349$	3.14891e11	1.13618	0.568088	−	0.822968i	$-0.307683\pi$
$349$	3.14891e11	1.13618	0.568088	+	0.822968i	$0.307683\pi$
$350$	0	0
$351$	1.65884e10	0.0583341
$352$	8.66710e10	0.300907
$353$	5.31195e11	1.82082	0.910411	−	0.413704i	$-0.135765\pi$
$353$	5.31195e11	1.82082	0.910411	+	0.413704i	$0.135765\pi$
$354$	−2.96129e10	−0.100223
$355$	−5.56043e10	−0.185815
$356$	−1.27652e11	−0.421212
$357$	0	0
$358$	7.79133e10	0.250691
$359$	−4.97684e11	−1.58135	−0.790676	−	0.612235i	$-0.790271\pi$
$359$	−4.97684e11	−1.58135	−0.790676	+	0.612235i	$0.790271\pi$
$360$	−1.26483e11	−0.396891
$361$	−3.01946e11	−0.935722
$362$	1.72216e10	0.0527091
$363$	1.54822e11	0.468008
$364$	0	0
$365$	3.78047e11	1.11488
$366$	−2.61478e11	−0.761675
$367$	−2.77743e11	−0.799183	−0.399591	−	0.916693i	$-0.630848\pi$
$367$	−2.77743e11	−0.799183	−0.399591	+	0.916693i	$0.630848\pi$
$368$	2.30214e11	0.654359
$369$	4.74153e10	0.133137
$370$	2.57419e11	0.714056
$371$	0	0
$372$	5.62047e9	0.0152170
$373$	2.55319e11	0.682957	0.341478	−	0.939890i	$-0.389072\pi$
$373$	2.55319e11	0.682957	0.341478	+	0.939890i	$0.389072\pi$
$374$	1.06255e11	0.280819
$375$	1.93994e11	0.506579
$376$	2.89446e11	0.746830
$377$	−1.46472e11	−0.373438
$378$	0	0
$379$	8.12103e10	0.202178	0.101089	−	0.994877i	$-0.467767\pi$
$379$	8.12103e10	0.202178	0.101089	+	0.994877i	$0.467767\pi$
$380$	4.14259e10	0.101917
$381$	−7.52392e10	−0.182929
$382$	−3.17589e11	−0.763097
$383$	4.13123e11	0.981036	0.490518	−	0.871431i	$-0.336808\pi$
$383$	4.13123e11	0.981036	0.490518	+	0.871431i	$0.336808\pi$
$384$	−3.49943e10	−0.0821310
$385$	0	0
$386$	2.35788e11	0.540603
$387$	−1.51871e11	−0.344171
$388$	−1.06720e11	−0.239057
$389$	2.53052e11	0.560321	0.280160	−	0.959953i	$-0.409612\pi$
$389$	2.53052e11	0.560321	0.280160	+	0.959953i	$0.409612\pi$
$390$	6.96303e10	0.152408
$391$	−4.92618e11	−1.06590
$392$	0	0
$393$	−8.00814e10	−0.169342
$394$	8.54259e10	0.178590
$395$	2.93568e11	0.606768
$396$	−2.60656e10	−0.0532648
$397$	6.53562e10	0.132047	0.0660236	−	0.997818i	$-0.478969\pi$
$397$	6.53562e10	0.132047	0.0660236	+	0.997818i	$0.478969\pi$
$398$	3.45784e11	0.690766
$399$	0	0
$400$	−5.06217e10	−0.0988705
$401$	−2.40886e11	−0.465225	−0.232612	−	0.972570i	$-0.574727\pi$
$401$	−2.40886e11	−0.465225	−0.232612	+	0.972570i	$0.574727\pi$
$402$	−4.00262e11	−0.764412
$403$	−1.15207e10	−0.0217574
$404$	3.05091e11	0.569788
$405$	6.58615e10	0.121642
$406$	0	0
$407$	1.97522e11	0.356814
$408$	2.85096e11	0.509356
$409$	3.78340e11	0.668540	0.334270	−	0.942477i	$-0.391510\pi$
$409$	3.78340e11	0.668540	0.334270	+	0.942477i	$0.391510\pi$
$410$	1.99027e11	0.347844
$411$	4.64335e9	0.00802681
$412$	−3.29193e11	−0.562876
$413$	0	0
$414$	−2.08265e11	−0.348430
$415$	4.22524e11	0.699253
$416$	−1.28021e11	−0.209586
$417$	−3.76693e11	−0.610063
$418$	−5.47818e10	−0.0877693
$419$	−9.68766e11	−1.53552	−0.767760	−	0.640737i	$-0.778629\pi$
$419$	−9.68766e11	−1.53552	−0.767760	+	0.640737i	$0.778629\pi$
$420$	0	0
$421$	−1.43789e11	−0.223077	−0.111539	−	0.993760i	$-0.535578\pi$
$421$	−1.43789e11	−0.223077	−0.111539	+	0.993760i	$0.535578\pi$
$422$	−3.26292e11	−0.500841
$423$	−1.50719e11	−0.228894
$424$	−9.88812e11	−1.48582
$425$	1.08322e11	0.161052
$426$	5.29876e10	0.0779527
$427$	0	0
$428$	2.90076e11	0.417845
$429$	5.34288e10	0.0761583
$430$	−6.37481e11	−0.899207
$431$	2.06890e11	0.288796	0.144398	−	0.989520i	$-0.453875\pi$
$431$	2.06890e11	0.288796	0.144398	+	0.989520i	$0.453875\pi$
$432$	6.93764e10	0.0958374
$433$	4.81883e10	0.0658789	0.0329394	−	0.999457i	$-0.489513\pi$
$433$	4.81883e10	0.0658789	0.0329394	+	0.999457i	$0.489513\pi$
$434$	0	0
$435$	−5.81543e11	−0.778718
$436$	−8.60411e10	−0.114029
$437$	2.53979e11	0.333143
$438$	−3.60257e11	−0.467712
$439$	−4.37941e11	−0.562763	−0.281381	−	0.959596i	$-0.590793\pi$
$439$	−4.37941e11	−0.562763	−0.281381	+	0.959596i	$0.590793\pi$
$440$	−4.07383e11	−0.518162
$441$	0	0
$442$	−1.56949e11	−0.195595
$443$	7.58665e11	0.935908	0.467954	−	0.883753i	$-0.344991\pi$
$443$	7.58665e11	0.935908	0.467954	+	0.883753i	$0.344991\pi$
$444$	1.42337e11	0.173818
$445$	1.03887e12	1.25585
$446$	−7.03946e10	−0.0842427
$447$	1.13591e11	0.134574
$448$	0	0
$449$	−1.37280e11	−0.159403	−0.0797017	−	0.996819i	$-0.525397\pi$
$449$	−1.37280e11	−0.159403	−0.0797017	+	0.996819i	$0.525397\pi$
$450$	4.57955e10	0.0526461
$451$	1.52718e11	0.173818
$452$	−6.14373e11	−0.692324
$453$	−8.22535e11	−0.917725
$454$	6.44627e11	0.712126
$455$	0	0
$456$	−1.46987e11	−0.159198
$457$	1.31091e11	0.140589	0.0702944	−	0.997526i	$-0.477606\pi$
$457$	1.31091e11	0.140589	0.0702944	+	0.997526i	$0.477606\pi$
$458$	−9.54800e10	−0.101395
$459$	−1.48454e11	−0.156111
$460$	5.07252e11	0.528218
$461$	8.03508e11	0.828583	0.414291	−	0.910144i	$-0.364029\pi$
$461$	8.03508e11	0.828583	0.414291	+	0.910144i	$0.364029\pi$
$462$	0	0
$463$	−1.78582e12	−1.80602	−0.903009	−	0.429621i	$-0.858647\pi$
$463$	−1.78582e12	−1.80602	−0.903009	+	0.429621i	$0.858647\pi$
$464$	−6.12579e11	−0.613524
$465$	−4.57411e10	−0.0453699
$466$	−4.57509e11	−0.449431
$467$	−6.44366e11	−0.626912	−0.313456	−	0.949603i	$-0.601487\pi$
$467$	−6.44366e11	−0.626912	−0.313456	+	0.949603i	$0.601487\pi$
$468$	3.85015e10	0.0370997
$469$	0	0
$470$	−6.32646e11	−0.598026
$471$	7.58650e11	0.710309
$472$	−2.55914e11	−0.237332
$473$	−4.89152e11	−0.449334
$474$	−2.79753e11	−0.254550
$475$	−5.58474e10	−0.0503363
$476$	0	0
$477$	5.14889e11	0.455387
$478$	−1.14029e12	−0.999056
$479$	1.87701e12	1.62913	0.814565	−	0.580073i	$-0.196976\pi$
$479$	1.87701e12	1.62913	0.814565	+	0.580073i	$0.196976\pi$
$480$	−5.08287e11	−0.437043
$481$	−2.91760e11	−0.248526
$482$	−1.83472e12	−1.54831
$483$	0	0
$484$	3.59341e11	0.297647
$485$	8.68516e11	0.712755
$486$	−6.27621e10	−0.0510310
$487$	1.49355e12	1.20321	0.601603	−	0.798795i	$-0.294529\pi$
$487$	1.49355e12	1.20321	0.601603	+	0.798795i	$0.294529\pi$
$488$	−2.25968e12	−1.80368
$489$	5.95172e10	0.0470709
$490$	0	0
$491$	−7.47313e11	−0.580278	−0.290139	−	0.956985i	$-0.593702\pi$
$491$	−7.47313e11	−0.580278	−0.290139	+	0.956985i	$0.593702\pi$
$492$	1.10050e11	0.0846736
$493$	1.31082e12	0.999379
$494$	8.09179e10	0.0611327
$495$	2.12130e11	0.158810
$496$	−4.81822e10	−0.0357453
$497$	0	0
$498$	−4.02640e11	−0.293349
$499$	1.01300e12	0.731402	0.365701	−	0.930732i	$-0.380829\pi$
$499$	1.01300e12	0.731402	0.365701	+	0.930732i	$0.380829\pi$
$500$	4.50257e11	0.322178
$501$	1.26023e11	0.0893677
$502$	−1.73654e12	−1.22044
$503$	−2.03399e11	−0.141675	−0.0708373	−	0.997488i	$-0.522567\pi$
$503$	−2.03399e11	−0.141675	−0.0708373	+	0.997488i	$0.522567\pi$
$504$	0	0
$505$	−2.48292e12	−1.69884
$506$	−6.70792e11	−0.454894
$507$	7.80045e11	0.524305
$508$	−1.74629e11	−0.116340
$509$	−5.93699e11	−0.392045	−0.196023	−	0.980599i	$-0.562803\pi$
$509$	−5.93699e11	−0.392045	−0.196023	+	0.980599i	$0.562803\pi$
$510$	−6.23139e11	−0.407868
$511$	0	0
$512$	−1.37758e12	−0.885935
$513$	7.65381e10	0.0487921
$514$	1.43926e11	0.0909508
$515$	2.67907e12	1.67823
$516$	−3.52490e11	−0.218888
$517$	−4.85442e11	−0.298834
$518$	0	0
$519$	1.54263e12	0.933273
$520$	6.01743e11	0.360908
$521$	1.74950e12	1.04027	0.520133	−	0.854085i	$-0.325882\pi$
$521$	1.74950e12	1.04027	0.520133	+	0.854085i	$0.325882\pi$
$522$	5.54176e11	0.326686
$523$	−3.20555e11	−0.187346	−0.0936731	−	0.995603i	$-0.529861\pi$
$523$	−3.20555e11	−0.187346	−0.0936731	+	0.995603i	$0.529861\pi$
$524$	−1.85868e11	−0.107699
$525$	0	0
$526$	1.91285e12	1.08954
$527$	1.03102e11	0.0582262
$528$	2.23451e11	0.125121
$529$	1.30877e12	0.726627
$530$	2.16126e12	1.18978
$531$	1.33258e11	0.0727392
$532$	0	0
$533$	−2.25579e11	−0.121067
$534$	−9.89978e11	−0.526854
$535$	−2.36072e12	−1.24581
$536$	−3.45906e12	−1.81016
$537$	−3.50610e11	−0.181945
$538$	1.81595e12	0.934512
$539$	0	0
$540$	1.52864e11	0.0773628
$541$	3.50229e11	0.175778	0.0878889	−	0.996130i	$-0.471988\pi$
$541$	3.50229e11	0.175778	0.0878889	+	0.996130i	$0.471988\pi$
$542$	5.15421e11	0.256546
$543$	−7.74974e10	−0.0382549
$544$	1.14570e12	0.560885
$545$	7.00228e11	0.339981
$546$	0	0
$547$	−2.46037e12	−1.17505	−0.587527	−	0.809205i	$-0.699898\pi$
$547$	−2.46037e12	−1.17505	−0.587527	+	0.809205i	$0.699898\pi$
$548$	1.07772e10	0.00510495
$549$	1.17665e12	0.552804
$550$	1.47500e11	0.0687323
$551$	−6.75815e11	−0.312353
$552$	−1.79982e12	−0.825095
$553$	0	0
$554$	7.42051e11	0.334688
$555$	−1.15838e12	−0.518244
$556$	−8.74299e11	−0.387992
$557$	1.04356e12	0.459376	0.229688	−	0.973264i	$-0.426229\pi$
$557$	1.04356e12	0.459376	0.229688	+	0.973264i	$0.426229\pi$
$558$	4.35886e10	0.0190335
$559$	7.22525e11	0.312968
$560$	0	0
$561$	−4.78147e11	−0.203812
$562$	2.19240e12	0.927057
$563$	−3.81849e12	−1.60179	−0.800893	−	0.598808i	$-0.795641\pi$
$563$	−3.81849e12	−1.60179	−0.800893	+	0.598808i	$0.795641\pi$
$564$	−3.49816e11	−0.145574
$565$	4.99995e12	2.06418
$566$	−4.19076e11	−0.171640
$567$	0	0
$568$	4.57917e11	0.184595
$569$	4.84062e11	0.193596	0.0967979	−	0.995304i	$-0.469140\pi$
$569$	4.84062e11	0.193596	0.0967979	+	0.995304i	$0.469140\pi$
$570$	3.21271e11	0.127478
$571$	1.77044e10	0.00696978	0.00348489	−	0.999994i	$-0.498891\pi$
$571$	1.77044e10	0.00696978	0.00348489	+	0.999994i	$0.498891\pi$
$572$	1.24007e11	0.0484357
$573$	1.42915e12	0.553837
$574$	0	0
$575$	−6.83840e11	−0.260885
$576$	9.22896e11	0.349343
$577$	7.46985e11	0.280557	0.140278	−	0.990112i	$-0.455200\pi$
$577$	7.46985e11	0.280557	0.140278	+	0.990112i	$0.455200\pi$
$578$	−7.30007e11	−0.272052
$579$	−1.06105e12	−0.392356
$580$	−1.34975e12	−0.495255
$581$	0	0
$582$	−8.27645e11	−0.299013
$583$	1.65838e12	0.594532
$584$	−3.11333e12	−1.10756
$585$	−3.13336e11	−0.110614
$586$	1.64304e12	0.575585
$587$	4.33948e12	1.50857	0.754286	−	0.656546i	$-0.227983\pi$
$587$	4.33948e12	1.50857	0.754286	+	0.656546i	$0.227983\pi$
$588$	0	0
$589$	−5.31561e10	−0.0181984
$590$	5.59356e11	0.190044
$591$	−3.84417e11	−0.129616
$592$	−1.22020e12	−0.408305
$593$	−1.90120e12	−0.631366	−0.315683	−	0.948865i	$-0.602234\pi$
$593$	−1.90120e12	−0.631366	−0.315683	+	0.948865i	$0.602234\pi$
$594$	−2.02147e11	−0.0666238
$595$	0	0
$596$	2.63644e11	0.0855874
$597$	−1.55603e12	−0.501341
$598$	9.90824e11	0.316841
$599$	−5.49649e12	−1.74447	−0.872237	−	0.489083i	$-0.837332\pi$
$599$	−5.49649e12	−1.74447	−0.872237	+	0.489083i	$0.837332\pi$
$600$	3.95763e11	0.124668
$601$	−4.77698e12	−1.49355	−0.746773	−	0.665079i	$-0.768398\pi$
$601$	−4.77698e12	−1.49355	−0.746773	+	0.665079i	$0.768398\pi$
$602$	0	0
$603$	1.80118e12	0.554791
$604$	−1.90909e12	−0.583661
$605$	−2.92442e12	−0.887443
$606$	2.36608e12	0.712692
$607$	−8.25000e11	−0.246663	−0.123332	−	0.992366i	$-0.539358\pi$
$607$	−8.25000e11	−0.246663	−0.123332	+	0.992366i	$0.539358\pi$
$608$	−5.90685e11	−0.175303
$609$	0	0
$610$	4.93902e12	1.44430
$611$	7.17045e11	0.208142
$612$	−3.44559e11	−0.0992848
$613$	−1.46985e12	−0.420438	−0.210219	−	0.977654i	$-0.567418\pi$
$613$	−1.46985e12	−0.420438	−0.210219	+	0.977654i	$0.567418\pi$
$614$	7.90326e11	0.224413
$615$	−8.95622e11	−0.252457
$616$	0	0
$617$	5.17373e12	1.43721	0.718606	−	0.695418i	$-0.244781\pi$
$617$	5.17373e12	1.43721	0.718606	+	0.695418i	$0.244781\pi$
$618$	−2.55300e12	−0.704048
$619$	4.80274e12	1.31487	0.657433	−	0.753513i	$-0.271642\pi$
$619$	4.80274e12	1.31487	0.657433	+	0.753513i	$0.271642\pi$
$620$	−1.06164e11	−0.0288547
$621$	9.37194e11	0.252882
$622$	1.37670e12	0.368794
$623$	0	0
$624$	−3.30059e11	−0.0871487
$625$	−4.42170e12	−1.15912
$626$	−4.83279e12	−1.25780
$627$	2.46518e11	0.0637007
$628$	1.76082e12	0.451748
$629$	2.61103e12	0.665096
$630$	0	0
$631$	5.93992e12	1.49159	0.745794	−	0.666177i	$-0.232071\pi$
$631$	5.93992e12	1.49159	0.745794	+	0.666177i	$0.232071\pi$
$632$	−2.41762e12	−0.602784
$633$	1.46831e12	0.363498
$634$	2.73700e12	0.672780
$635$	1.42119e12	0.346872
$636$	1.19505e12	0.289620
$637$	0	0
$638$	1.78492e12	0.426506
$639$	−2.38444e11	−0.0565761
$640$	6.61004e11	0.155738
$641$	6.47738e12	1.51544	0.757720	−	0.652580i	$-0.226313\pi$
$641$	6.47738e12	1.51544	0.757720	+	0.652580i	$0.226313\pi$
$642$	2.24963e12	0.522641
$643$	1.74519e12	0.402619	0.201309	−	0.979528i	$-0.435480\pi$
$643$	1.74519e12	0.402619	0.201309	+	0.979528i	$0.435480\pi$
$644$	0	0
$645$	2.86867e12	0.652621
$646$	−7.24155e11	−0.163601
$647$	−4.97244e12	−1.11558	−0.557790	−	0.829982i	$-0.688350\pi$
$647$	−4.97244e12	−1.11558	−0.557790	+	0.829982i	$0.688350\pi$
$648$	−5.42389e11	−0.120843
$649$	4.29205e11	0.0949650
$650$	−2.17872e11	−0.0478731
$651$	0	0
$652$	1.38139e11	0.0299365
$653$	−1.45057e12	−0.312198	−0.156099	−	0.987741i	$-0.549892\pi$
$653$	−1.45057e12	−0.312198	−0.156099	+	0.987741i	$0.549892\pi$
$654$	−6.67276e11	−0.142628
$655$	1.51265e12	0.321109
$656$	−9.43420e11	−0.198901
$657$	1.62115e12	0.339453
$658$	0	0
$659$	−3.05175e12	−0.630325	−0.315162	−	0.949038i	$-0.602059\pi$
$659$	−3.05175e12	−0.630325	−0.315162	+	0.949038i	$0.602059\pi$
$660$	4.92351e11	0.101001
$661$	1.88315e12	0.383688	0.191844	−	0.981425i	$-0.438553\pi$
$661$	1.88315e12	0.383688	0.191844	+	0.981425i	$0.438553\pi$
$662$	−4.73503e12	−0.958213
$663$	7.06270e11	0.141958
$664$	−3.47961e12	−0.694662
$665$	0	0
$666$	1.10387e12	0.217412
$667$	−8.27522e12	−1.61888
$668$	2.92498e11	0.0568367
$669$	3.16776e11	0.0611412
$670$	7.56051e12	1.44949
$671$	3.78981e12	0.721716
$672$	0	0
$673$	7.84359e12	1.47383	0.736914	−	0.675986i	$-0.236282\pi$
$673$	7.84359e12	1.47383	0.736914	+	0.675986i	$0.236282\pi$
$674$	5.34929e12	0.998451
$675$	−2.06080e11	−0.0382092
$676$	1.81047e12	0.333451
$677$	−2.32420e12	−0.425230	−0.212615	−	0.977136i	$-0.568198\pi$
$677$	−2.32420e12	−0.425230	−0.212615	+	0.977136i	$0.568198\pi$
$678$	−4.76466e12	−0.865961
$679$	0	0
$680$	−5.38516e12	−0.965846
$681$	−2.90082e12	−0.516843
$682$	1.40392e11	0.0248493
$683$	−6.89265e12	−1.21197	−0.605986	−	0.795475i	$-0.707221\pi$
$683$	−6.89265e12	−1.21197	−0.605986	+	0.795475i	$0.707221\pi$
$684$	1.77644e11	0.0310312
$685$	−8.77077e10	−0.0152205
$686$	0	0
$687$	4.29660e11	0.0735902
$688$	3.02176e12	0.514177
$689$	−2.44959e12	−0.414101
$690$	3.93390e12	0.660697
$691$	−1.11430e13	−1.85931	−0.929654	−	0.368434i	$-0.879894\pi$
$691$	−1.11430e13	−1.85931	−0.929654	+	0.368434i	$0.879894\pi$
$692$	3.58043e12	0.593550
$693$	0	0
$694$	2.52393e12	0.413010
$695$	7.11530e12	1.15681
$696$	4.78918e12	0.773605
$697$	2.01876e12	0.323994
$698$	5.66803e12	0.903822
$699$	2.05879e12	0.326186
$700$	0	0
$701$	−5.78015e12	−0.904082	−0.452041	−	0.891997i	$-0.649304\pi$
$701$	−5.78015e12	−0.904082	−0.452041	+	0.891997i	$0.649304\pi$
$702$	2.98591e11	0.0464045
$703$	−1.34617e12	−0.207874
$704$	2.97251e12	0.456085
$705$	2.84691e12	0.434032
$706$	9.56151e12	1.44846
$707$	0	0
$708$	3.09291e11	0.0462612
$709$	−3.39902e12	−0.505180	−0.252590	−	0.967573i	$-0.581282\pi$
$709$	−3.39902e12	−0.505180	−0.252590	+	0.967573i	$0.581282\pi$
$710$	−1.00088e12	−0.147815
$711$	1.25889e12	0.184746
$712$	−8.55537e12	−1.24761
$713$	−6.50885e11	−0.0943195
$714$	0	0
$715$	−1.00921e12	−0.144412
$716$	−8.13761e11	−0.115715
$717$	5.13130e12	0.725089
$718$	−8.95831e12	−1.25796
$719$	−2.71272e11	−0.0378551	−0.0189276	−	0.999821i	$-0.506025\pi$
$719$	−2.71272e11	−0.0378551	−0.0189276	+	0.999821i	$0.506025\pi$
$720$	−1.31044e12	−0.181728
$721$	0	0
$722$	−5.43503e12	−0.744362
$723$	8.25623e12	1.12372
$724$	−1.79870e11	−0.0243297
$725$	1.81964e12	0.244604
$726$	2.78680e12	0.372298
$727$	2.13863e12	0.283943	0.141972	−	0.989871i	$-0.454656\pi$
$727$	2.13863e12	0.283943	0.141972	+	0.989871i	$0.454656\pi$
$728$	0	0
$729$	2.82430e11	0.0370370
$730$	6.80485e12	0.886881
$731$	−6.46606e12	−0.837552
$732$	2.73099e12	0.351577
$733$	−4.60033e12	−0.588601	−0.294301	−	0.955713i	$-0.595087\pi$
$733$	−4.60033e12	−0.588601	−0.294301	+	0.955713i	$0.595087\pi$
$734$	−4.99938e12	−0.635746
$735$	0	0
$736$	−7.23282e12	−0.908568
$737$	5.80133e12	0.724309
$738$	8.53475e11	0.105910
$739$	8.60245e12	1.06102	0.530508	−	0.847680i	$-0.322001\pi$
$739$	8.60245e12	1.06102	0.530508	+	0.847680i	$0.322001\pi$
$740$	−2.68859e12	−0.329596
$741$	−3.64131e11	−0.0443686
$742$	0	0
$743$	1.31407e12	0.158187	0.0790934	−	0.996867i	$-0.474797\pi$
$743$	1.31407e12	0.158187	0.0790934	+	0.996867i	$0.474797\pi$
$744$	3.76691e11	0.0450720
$745$	−2.14561e12	−0.255181
$746$	4.59574e12	0.543289
$747$	1.81188e12	0.212906
$748$	−1.10977e12	−0.129622
$749$	0	0
$750$	3.49189e12	0.402981
$751$	−7.95810e12	−0.912913	−0.456457	−	0.889746i	$-0.650882\pi$
$751$	−7.95810e12	−0.912913	−0.456457	+	0.889746i	$0.650882\pi$
$752$	2.99884e12	0.341958
$753$	7.81443e12	0.885768
$754$	−2.63650e12	−0.297068
$755$	1.55368e13	1.74020
$756$	0	0
$757$	−6.95936e12	−0.770261	−0.385131	−	0.922862i	$-0.625844\pi$
$757$	−6.95936e12	−0.770261	−0.385131	+	0.922862i	$0.625844\pi$
$758$	1.46179e12	0.160832
$759$	3.01856e12	0.330151
$760$	2.77642e12	0.301873
$761$	1.38632e13	1.49841	0.749207	−	0.662336i	$-0.230435\pi$
$761$	1.38632e13	1.49841	0.749207	+	0.662336i	$0.230435\pi$
$762$	−1.35431e12	−0.145519
$763$	0	0
$764$	3.31704e12	0.352233
$765$	2.80413e12	0.296020
$766$	7.43621e12	0.780409
$767$	−6.33977e11	−0.0661446
$768$	5.20371e12	0.539744
$769$	−1.35604e13	−1.39832	−0.699158	−	0.714967i	$-0.746442\pi$
$769$	−1.35604e13	−1.39832	−0.699158	+	0.714967i	$0.746442\pi$
$770$	0	0
$771$	−6.47669e11	−0.0660098
$772$	−2.46267e12	−0.249534
$773$	−4.96740e12	−0.500405	−0.250203	−	0.968194i	$-0.580497\pi$
$773$	−4.96740e12	−0.500405	−0.250203	+	0.968194i	$0.580497\pi$
$774$	−2.73367e12	−0.273786
$775$	1.43123e11	0.0142512
$776$	−7.15248e12	−0.708075
$777$	0	0
$778$	4.55494e12	0.445732
$779$	−1.04081e12	−0.101263
$780$	−7.27250e11	−0.0703490
$781$	−7.67993e11	−0.0738631
$782$	−8.86713e12	−0.847916
$783$	−2.49379e12	−0.237100
$784$	0	0
$785$	−1.43301e13	−1.34690
$786$	−1.44146e12	−0.134711
$787$	5.25809e12	0.488587	0.244293	−	0.969701i	$-0.421444\pi$
$787$	5.25809e12	0.488587	0.244293	+	0.969701i	$0.421444\pi$
$788$	−8.92227e11	−0.0824342
$789$	−8.60781e12	−0.790763
$790$	5.28423e12	0.482681
$791$	0	0
$792$	−1.74695e12	−0.157768
$793$	−5.59792e12	−0.502686
$794$	1.17641e12	0.105043
$795$	−9.72568e12	−0.863511
$796$	−3.61152e12	−0.318846
$797$	−1.61816e13	−1.42056	−0.710281	−	0.703918i	$-0.751432\pi$
$797$	−1.61816e13	−1.42056	−0.710281	+	0.703918i	$0.751432\pi$
$798$	0	0
$799$	−6.41701e12	−0.557022
$800$	1.59042e12	0.137280
$801$	4.45490e12	0.382377
$802$	−4.33596e12	−0.370084
$803$	5.22150e12	0.443175
$804$	4.18052e12	0.352840
$805$	0	0
$806$	−2.07373e11	−0.0173079
$807$	−8.17180e12	−0.678245
$808$	2.04476e13	1.68768
$809$	−1.39276e13	−1.14317	−0.571583	−	0.820544i	$-0.693671\pi$
$809$	−1.39276e13	−1.14317	−0.571583	+	0.820544i	$0.693671\pi$
$810$	1.18551e12	0.0967657
$811$	−1.38190e13	−1.12171	−0.560857	−	0.827913i	$-0.689528\pi$
$811$	−1.38190e13	−1.12171	−0.560857	+	0.827913i	$0.689528\pi$
$812$	0	0
$813$	−2.31939e12	−0.186194
$814$	3.55540e12	0.283844
$815$	−1.12421e12	−0.0892564
$816$	2.95378e12	0.233224
$817$	3.33370e12	0.261774
$818$	6.81012e12	0.531820
$819$	0	0
$820$	−2.07873e12	−0.160559
$821$	3.48578e12	0.267766	0.133883	−	0.990997i	$-0.457255\pi$
$821$	3.48578e12	0.267766	0.133883	+	0.990997i	$0.457255\pi$
$822$	8.35803e10	0.00638529
$823$	−1.21472e13	−0.922948	−0.461474	−	0.887154i	$-0.652679\pi$
$823$	−1.21472e13	−0.922948	−0.461474	+	0.887154i	$0.652679\pi$
$824$	−2.20629e13	−1.66721
$825$	−6.63751e11	−0.0498842
$826$	0	0
$827$	−1.70702e13	−1.26901	−0.634504	−	0.772919i	$-0.718796\pi$
$827$	−1.70702e13	−1.26901	−0.634504	+	0.772919i	$0.718796\pi$
$828$	2.17522e12	0.160830
$829$	−5.58071e12	−0.410387	−0.205194	−	0.978721i	$-0.565782\pi$
$829$	−5.58071e12	−0.410387	−0.205194	+	0.978721i	$0.565782\pi$
$830$	7.60543e12	0.556253
$831$	−3.33923e12	−0.242908
$832$	−4.39068e12	−0.317671
$833$	0	0
$834$	−6.78047e12	−0.485302
$835$	−2.38044e12	−0.169460
$836$	5.72165e11	0.0405129
$837$	−1.96148e11	−0.0138140
$838$	−1.74378e13	−1.22150
$839$	−1.28642e13	−0.896304	−0.448152	−	0.893957i	$-0.647918\pi$
$839$	−1.28642e13	−0.896304	−0.448152	+	0.893957i	$0.647918\pi$
$840$	0	0
$841$	7.51250e12	0.517849
$842$	−2.58819e12	−0.177457
$843$	−9.86580e12	−0.672835
$844$	3.40793e12	0.231180
$845$	−1.47342e13	−0.994193
$846$	−2.71293e12	−0.182084
$847$	0	0
$848$	−1.02447e13	−0.680329
$849$	1.88584e12	0.124572
$850$	1.94979e12	0.128116
$851$	−1.64835e13	−1.07738
$852$	−5.53426e11	−0.0359817
$853$	−1.03465e13	−0.669147	−0.334574	−	0.942370i	$-0.608592\pi$
$853$	−1.03465e13	−0.669147	−0.334574	+	0.942370i	$0.608592\pi$
$854$	0	0
$855$	−1.44572e12	−0.0925202
$856$	1.94413e13	1.23763
$857$	−5.63216e12	−0.356666	−0.178333	−	0.983970i	$-0.557070\pi$
$857$	−5.63216e12	−0.356666	−0.178333	+	0.983970i	$0.557070\pi$
$858$	9.61718e11	0.0605836
$859$	2.28289e13	1.43059	0.715295	−	0.698822i	$-0.246292\pi$
$859$	2.28289e13	1.43059	0.715295	+	0.698822i	$0.246292\pi$
$860$	6.65814e12	0.415059
$861$	0	0
$862$	3.72401e12	0.229736
$863$	4.62918e12	0.284090	0.142045	−	0.989860i	$-0.454632\pi$
$863$	4.62918e12	0.284090	0.142045	+	0.989860i	$0.454632\pi$
$864$	−2.17966e12	−0.133069
$865$	−2.91386e13	−1.76968
$866$	8.67389e11	0.0524063
$867$	3.28503e12	0.197448
$868$	0	0
$869$	4.05470e12	0.241196
$870$	−1.04678e13	−0.619466
$871$	−8.56913e12	−0.504493
$872$	−5.76658e12	−0.337749
$873$	3.72440e12	0.217016
$874$	4.57162e12	0.265014
$875$	0	0
$876$	3.76268e12	0.215888
$877$	5.33611e12	0.304598	0.152299	−	0.988334i	$-0.451332\pi$
$877$	5.33611e12	0.304598	0.152299	+	0.988334i	$0.451332\pi$
$878$	−7.88294e12	−0.447675
$879$	−7.39369e12	−0.417745
$880$	−4.22074e12	−0.237256
$881$	−7.87890e12	−0.440630	−0.220315	−	0.975429i	$-0.570709\pi$
$881$	−7.87890e12	−0.440630	−0.220315	+	0.975429i	$0.570709\pi$
$882$	0	0
$883$	1.38973e13	0.769320	0.384660	−	0.923058i	$-0.374319\pi$
$883$	1.38973e13	0.769320	0.384660	+	0.923058i	$0.374319\pi$
$884$	1.63924e12	0.0902835
$885$	−2.51710e12	−0.137929
$886$	1.36560e13	0.744510
$887$	5.86607e12	0.318193	0.159097	−	0.987263i	$-0.449142\pi$
$887$	5.86607e12	0.318193	0.159097	+	0.987263i	$0.449142\pi$
$888$	9.53963e12	0.514841
$889$	0	0
$890$	1.86996e13	0.999026
$891$	9.09663e11	0.0483538
$892$	7.35232e11	0.0388851
$893$	3.30841e12	0.174096
$894$	2.04464e12	0.107053
$895$	6.62263e12	0.345006
$896$	0	0
$897$	−4.45871e12	−0.229955
$898$	−2.47103e12	−0.126805
$899$	1.73195e12	0.0884334
$900$	−4.78308e11	−0.0243006
$901$	2.19220e13	1.10820
$902$	2.74892e12	0.138271
$903$	0	0
$904$	−4.11761e13	−2.05063
$905$	1.46384e12	0.0725395
$906$	−1.48056e13	−0.730045
$907$	8.52250e12	0.418152	0.209076	−	0.977899i	$-0.432954\pi$
$907$	8.52250e12	0.418152	0.209076	+	0.977899i	$0.432954\pi$
$908$	−6.73277e12	−0.328706
$909$	−1.06473e13	−0.517254
$910$	0	0
$911$	1.63369e13	0.785843	0.392921	−	0.919572i	$-0.371464\pi$
$911$	1.63369e13	0.785843	0.392921	+	0.919572i	$0.371464\pi$
$912$	−1.52288e12	−0.0728934
$913$	5.83580e12	0.277960
$914$	2.35964e12	0.111838
$915$	−2.22256e13	−1.04823
$916$	9.97236e11	0.0468024
$917$	0	0
$918$	−2.67217e12	−0.124186
$919$	3.24712e13	1.50169	0.750843	−	0.660481i	$-0.229648\pi$
$919$	3.24712e13	1.50169	0.750843	+	0.660481i	$0.229648\pi$
$920$	3.39967e13	1.56456
$921$	−3.55647e12	−0.162873
$922$	1.44631e13	0.659134
$923$	1.13440e12	0.0514468
$924$	0	0
$925$	3.62456e12	0.162786
$926$	−3.21447e13	−1.43668
$927$	1.14885e13	0.510980
$928$	1.92459e13	0.851868
$929$	1.24571e13	0.548716	0.274358	−	0.961628i	$-0.411535\pi$
$929$	1.24571e13	0.548716	0.274358	+	0.961628i	$0.411535\pi$
$930$	−8.23339e11	−0.0360916
$931$	0	0
$932$	4.77843e12	0.207450
$933$	−6.19516e12	−0.267661
$934$	−1.15986e13	−0.498706
$935$	9.03167e12	0.386470
$936$	2.58042e12	0.109888
$937$	−9.29012e12	−0.393725	−0.196863	−	0.980431i	$-0.563075\pi$
$937$	−9.29012e12	−0.393725	−0.196863	+	0.980431i	$0.563075\pi$
$938$	0	0
$939$	2.17475e13	0.912883
$940$	6.60763e12	0.276039
$941$	3.24831e13	1.35053	0.675265	−	0.737575i	$-0.264029\pi$
$941$	3.24831e13	1.35053	0.675265	+	0.737575i	$0.264029\pi$
$942$	1.36557e13	0.565048
$943$	−1.27445e13	−0.524832
$944$	−2.65143e12	−0.108669
$945$	0	0
$946$	−8.80474e12	−0.357443
$947$	−4.16258e13	−1.68185	−0.840926	−	0.541151i	$-0.817989\pi$
$947$	−4.16258e13	−1.68185	−0.840926	+	0.541151i	$0.817989\pi$
$948$	2.92187e12	0.117496
$949$	−7.71265e12	−0.308678
$950$	−1.00525e12	−0.0400423
$951$	−1.23165e13	−0.488287
$952$	0	0
$953$	1.86479e13	0.732339	0.366169	−	0.930548i	$-0.380669\pi$
$953$	1.86479e13	0.732339	0.366169	+	0.930548i	$0.380669\pi$
$954$	9.26800e12	0.362258
$955$	−2.69950e13	−1.05019
$956$	1.19097e13	0.461148
$957$	−8.03213e12	−0.309547
$958$	3.37861e13	1.29596
$959$	0	0
$960$	−1.74325e13	−0.662428
$961$	−2.63034e13	−0.994848
$962$	−5.25167e12	−0.197702
$963$	−1.01233e13	−0.379320
$964$	1.91626e13	0.714674
$965$	2.00420e13	0.743991
$966$	0	0
$967$	−2.32990e13	−0.856875	−0.428437	−	0.903572i	$-0.640936\pi$
$967$	−2.32990e13	−0.856875	−0.428437	+	0.903572i	$0.640936\pi$
$968$	2.40835e13	0.881617
$969$	3.25870e12	0.118737
$970$	1.56333e13	0.566993
$971$	3.63628e13	1.31272	0.656358	−	0.754450i	$-0.272096\pi$
$971$	3.63628e13	1.31272	0.656358	+	0.754450i	$0.272096\pi$
$972$	6.55515e11	0.0235551
$973$	0	0
$974$	2.68839e13	0.957145
$975$	9.80425e11	0.0347451
$976$	−2.34118e13	−0.825866
$977$	5.18141e13	1.81938	0.909688	−	0.415291i	$-0.136320\pi$
$977$	5.18141e13	1.81938	0.909688	+	0.415291i	$0.136320\pi$
$978$	1.07131e12	0.0374447
$979$	1.43486e13	0.499214
$980$	0	0
$981$	3.00274e12	0.103516
$982$	−1.34516e13	−0.461608
$983$	2.54862e13	0.870592	0.435296	−	0.900287i	$-0.356644\pi$
$983$	2.54862e13	0.870592	0.435296	+	0.900287i	$0.356644\pi$
$984$	7.37571e12	0.250799
$985$	7.26121e12	0.245780
$986$	2.35947e13	0.795001
$987$	0	0
$988$	−8.45143e11	−0.0282178
$989$	4.08205e13	1.35673
$990$	3.81834e12	0.126333
$991$	3.92830e13	1.29382	0.646910	−	0.762567i	$-0.276061\pi$
$991$	3.92830e13	1.29382	0.646910	+	0.762567i	$0.276061\pi$
$992$	1.51378e12	0.0496318
$993$	2.13076e13	0.695447
$994$	0	0
$995$	2.93917e13	0.950649
$996$	4.20535e12	0.135405
$997$	−4.98389e13	−1.59750	−0.798748	−	0.601665i	$-0.794504\pi$
$997$	−4.98389e13	−1.59750	−0.798748	+	0.601665i	$0.794504\pi$
$998$	1.82340e13	0.581827
$999$	−4.96742e12	−0.157792

Twists

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

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

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