LMFDB - Embedded newform 147.10.a.b.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 21)
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)

$f(q)$

$=$

$q-24.0000 q^{2} -81.0000 q^{3} +64.0000 q^{4} +144.000 q^{5} +1944.00 q^{6} +10752.0 q^{8} +6561.00 q^{9} +O(q^{10})$

\(q-24.0000 q^{2} -81.0000 q^{3} +64.0000 q^{4} +144.000 q^{5} +1944.00 q^{6} +10752.0 q^{8} +6561.00 q^{9} -3456.00 q^{10} -15030.0 q^{11} -5184.00 q^{12} +151486. q^{13} -11664.0 q^{15} -290816. q^{16} +350448. q^{17} -157464. q^{18} +691108. q^{19} +9216.00 q^{20} +360720. q^{22} +892458. q^{23} -870912. q^{24} -1.93239e6 q^{25} -3.63566e6 q^{26} -531441. q^{27} +1.64852e6 q^{29} +279936. q^{30} +3.73430e6 q^{31} +1.47456e6 q^{32} +1.21743e6 q^{33} -8.41075e6 q^{34} +419904. q^{36} -1.14719e7 q^{37} -1.65866e7 q^{38} -1.22704e7 q^{39} +1.54829e6 q^{40} -1.39857e7 q^{41} +1.67945e7 q^{43} -961920. q^{44} +944784. q^{45} -2.14190e7 q^{46} +1.40121e7 q^{47} +2.35561e7 q^{48} +4.63773e7 q^{50} -2.83863e7 q^{51} +9.69510e6 q^{52} -9.74399e7 q^{53} +1.27546e7 q^{54} -2.16432e6 q^{55} -5.59797e7 q^{57} -3.95644e7 q^{58} -1.10798e8 q^{59} -746496. q^{60} +9.38167e7 q^{61} -8.96231e7 q^{62} +1.13508e8 q^{64} +2.18140e7 q^{65} -2.92183e7 q^{66} -1.22446e8 q^{67} +2.24287e7 q^{68} -7.22891e7 q^{69} +2.06197e8 q^{71} +7.05439e7 q^{72} -2.50338e8 q^{73} +2.75326e8 q^{74} +1.56524e8 q^{75} +4.42309e7 q^{76} +2.94489e8 q^{78} -3.83149e7 q^{79} -4.18775e7 q^{80} +4.30467e7 q^{81} +3.35657e8 q^{82} +5.14087e8 q^{83} +5.04645e7 q^{85} -4.03069e8 q^{86} -1.33530e8 q^{87} -1.61603e8 q^{88} +1.06129e9 q^{89} -2.26748e7 q^{90} +5.71173e7 q^{92} -3.02478e8 q^{93} -3.36289e8 q^{94} +9.95196e7 q^{95} -1.19439e8 q^{96} +7.38416e7 q^{97} -9.86118e7 q^{99} +O(q^{100})\)

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 $

$2$	−24.0000	−1.06066	−0.530330	−	0.847791i	$-0.677932\pi$
$2$	−24.0000	−1.06066	−0.530330	+	0.847791i	$0.677932\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	64.0000	0.125000
$5$	144.000	0.103038	0.0515190	−	0.998672i	$-0.483594\pi$
$5$	144.000	0.103038	0.0515190	+	0.998672i	$0.483594\pi$
$6$	1944.00	0.612372
$7$	0	0
$7$	0	0
$8$	10752.0	0.928078
$9$	6561.00	0.333333
$10$	−3456.00	−0.109288
$11$	−15030.0	−0.309522	−0.154761	−	0.987952i	$-0.549461\pi$
$11$	−15030.0	−0.309522	−0.154761	+	0.987952i	$0.549461\pi$
$12$	−5184.00	−0.0721688
$13$	151486.	1.47105	0.735525	−	0.677498i	$-0.236936\pi$
$13$	151486.	1.47105	0.735525	+	0.677498i	$0.236936\pi$
$14$	0	0
$15$	−11664.0	−0.0594890
$16$	−290816.	−1.10938
$17$	350448.	1.01766	0.508831	−	0.860867i	$-0.330078\pi$
$17$	350448.	1.01766	0.508831	+	0.860867i	$0.330078\pi$
$18$	−157464.	−0.353553
$19$	691108.	1.21662	0.608310	−	0.793700i	$-0.291848\pi$
$19$	691108.	1.21662	0.608310	+	0.793700i	$0.291848\pi$
$20$	9216.00	0.0128798
$21$	0	0
$22$	360720.	0.328298
$23$	892458.	0.664986	0.332493	−	0.943106i	$-0.392110\pi$
$23$	892458.	0.664986	0.332493	+	0.943106i	$0.392110\pi$
$24$	−870912.	−0.535826
$25$	−1.93239e6	−0.989383
$26$	−3.63566e6	−1.56028
$27$	−531441.	−0.192450
$28$	0	0
$29$	1.64852e6	0.432815	0.216408	−	0.976303i	$-0.430566\pi$
$29$	1.64852e6	0.432815	0.216408	+	0.976303i	$0.430566\pi$
$30$	279936.	0.0630976
$31$	3.73430e6	0.726242	0.363121	−	0.931742i	$-0.381711\pi$
$31$	3.73430e6	0.726242	0.363121	+	0.931742i	$0.381711\pi$
$32$	1.47456e6	0.248592
$33$	1.21743e6	0.178703
$34$	−8.41075e6	−1.07939
$35$	0	0
$36$	419904.	0.0416667
$37$	−1.14719e7	−1.00630	−0.503150	−	0.864199i	$-0.667826\pi$
$37$	−1.14719e7	−1.00630	−0.503150	+	0.864199i	$0.667826\pi$
$38$	−1.65866e7	−1.29042
$39$	−1.22704e7	−0.849311
$40$	1.54829e6	0.0956273
$41$	−1.39857e7	−0.772961	−0.386481	−	0.922298i	$-0.626309\pi$
$41$	−1.39857e7	−0.772961	−0.386481	+	0.922298i	$0.626309\pi$
$42$	0	0
$43$	1.67945e7	0.749134	0.374567	−	0.927200i	$-0.377791\pi$
$43$	1.67945e7	0.749134	0.374567	+	0.927200i	$0.377791\pi$
$44$	−961920.	−0.0386903
$45$	944784.	0.0343460
$46$	−2.14190e7	−0.705324
$47$	1.40121e7	0.418853	0.209426	−	0.977824i	$-0.432840\pi$
$47$	1.40121e7	0.418853	0.209426	+	0.977824i	$0.432840\pi$
$48$	2.35561e7	0.640498
$49$	0	0
$50$	4.63773e7	1.04940
$51$	−2.83863e7	−0.587547
$52$	9.69510e6	0.183881
$53$	−9.74399e7	−1.69627	−0.848136	−	0.529779i	$-0.822275\pi$
$53$	−9.74399e7	−1.69627	−0.848136	+	0.529779i	$0.822275\pi$
$54$	1.27546e7	0.204124
$55$	−2.16432e6	−0.0318926
$56$	0	0
$57$	−5.59797e7	−0.702416
$58$	−3.95644e7	−0.459070
$59$	−1.10798e8	−1.19042	−0.595208	−	0.803571i	$-0.702931\pi$
$59$	−1.10798e8	−1.19042	−0.595208	+	0.803571i	$0.702931\pi$
$60$	−746496.	−0.00743613
$61$	9.38167e7	0.867553	0.433776	−	0.901021i	$-0.357181\pi$
$61$	9.38167e7	0.867553	0.433776	+	0.901021i	$0.357181\pi$
$62$	−8.96231e7	−0.770296
$63$	0	0
$64$	1.13508e8	0.845703
$65$	2.18140e7	0.151574
$66$	−2.92183e7	−0.189543
$67$	−1.22446e8	−0.742352	−0.371176	−	0.928563i	$-0.621045\pi$
$67$	−1.22446e8	−0.742352	−0.371176	+	0.928563i	$0.621045\pi$
$68$	2.24287e7	0.127208
$69$	−7.22891e7	−0.383930
$70$	0	0
$71$	2.06197e8	0.962987	0.481494	−	0.876450i	$-0.340094\pi$
$71$	2.06197e8	0.962987	0.481494	+	0.876450i	$0.340094\pi$
$72$	7.05439e7	0.309359
$73$	−2.50338e8	−1.03175	−0.515873	−	0.856665i	$-0.672533\pi$
$73$	−2.50338e8	−1.03175	−0.515873	+	0.856665i	$0.672533\pi$
$74$	2.75326e8	1.06734
$75$	1.56524e8	0.571221
$76$	4.42309e7	0.152077
$77$	0	0
$78$	2.94489e8	0.900830
$79$	−3.83149e7	−0.110674	−0.0553370	−	0.998468i	$-0.517623\pi$
$79$	−3.83149e7	−0.110674	−0.0553370	+	0.998468i	$0.517623\pi$
$80$	−4.18775e7	−0.114308
$81$	4.30467e7	0.111111
$82$	3.35657e8	0.819849
$83$	5.14087e8	1.18901	0.594504	−	0.804092i	$-0.297348\pi$
$83$	5.14087e8	1.18901	0.594504	+	0.804092i	$0.297348\pi$
$84$	0	0
$85$	5.04645e7	0.104858
$86$	−4.03069e8	−0.794577
$87$	−1.33530e8	−0.249886
$88$	−1.61603e8	−0.287261
$89$	1.06129e9	1.79300	0.896502	−	0.443041i	$-0.146100\pi$
$89$	1.06129e9	1.79300	0.896502	+	0.443041i	$0.146100\pi$
$90$	−2.26748e7	−0.0364294
$91$	0	0
$92$	5.71173e7	0.0831233
$93$	−3.02478e8	−0.419296
$94$	−3.36289e8	−0.444260
$95$	9.95196e7	0.125358
$96$	−1.19439e8	−0.143525
$97$	7.38416e7	0.0846892	0.0423446	−	0.999103i	$-0.486517\pi$
$97$	7.38416e7	0.0846892	0.0423446	+	0.999103i	$0.486517\pi$
$98$	0	0
$99$	−9.86118e7	−0.103174
$100$	−1.23673e8	−0.123673
$101$	7.95314e8	0.760488	0.380244	−	0.924886i	$-0.375840\pi$
$101$	7.95314e8	0.760488	0.380244	+	0.924886i	$0.375840\pi$
$102$	6.81271e8	0.623188
$103$	−1.74058e9	−1.52380	−0.761899	−	0.647696i	$-0.775733\pi$
$103$	−1.74058e9	−1.52380	−0.761899	+	0.647696i	$0.775733\pi$
$104$	1.62878e9	1.36525
$105$	0	0
$106$	2.33856e9	1.79917
$107$	4.59742e8	0.339068	0.169534	−	0.985524i	$-0.445774\pi$
$107$	4.59742e8	0.339068	0.169534	+	0.985524i	$0.445774\pi$
$108$	−3.40122e7	−0.0240563
$109$	2.23071e9	1.51365	0.756823	−	0.653620i	$-0.226751\pi$
$109$	2.23071e9	1.51365	0.756823	+	0.653620i	$0.226751\pi$
$110$	5.19437e7	0.0338272
$111$	9.29224e8	0.580988
$112$	0	0
$113$	1.50615e9	0.868989	0.434494	−	0.900675i	$-0.356927\pi$
$113$	1.50615e9	0.868989	0.434494	+	0.900675i	$0.356927\pi$
$114$	1.34351e9	0.745024
$115$	1.28514e8	0.0685188
$116$	1.05505e8	0.0541019
$117$	9.93900e8	0.490350
$118$	2.65916e9	1.26263
$119$	0	0
$120$	−1.25411e8	−0.0552104
$121$	−2.13205e9	−0.904196
$122$	−2.25160e9	−0.920178
$123$	1.13284e9	0.446269
$124$	2.38995e8	0.0907802
$125$	−5.59514e8	−0.204982
$126$	0	0
$127$	3.48105e9	1.18739	0.593695	−	0.804690i	$-0.297668\pi$
$127$	3.48105e9	1.18739	0.593695	+	0.804690i	$0.297668\pi$
$128$	−3.47918e9	−1.14560
$129$	−1.36036e9	−0.432513
$130$	−5.23536e8	−0.160769
$131$	1.03115e9	0.305916	0.152958	−	0.988233i	$-0.451120\pi$
$131$	1.03115e9	0.305916	0.152958	+	0.988233i	$0.451120\pi$
$132$	7.79155e7	0.0223378
$133$	0	0
$134$	2.93871e9	0.787383
$135$	−7.65275e7	−0.0198297
$136$	3.76802e9	0.944469
$137$	7.78537e9	1.88815	0.944075	−	0.329730i	$-0.106958\pi$
$137$	7.78537e9	1.88815	0.944075	+	0.329730i	$0.106958\pi$
$138$	1.73494e9	0.407219
$139$	−1.25602e9	−0.285384	−0.142692	−	0.989767i	$-0.545576\pi$
$139$	−1.25602e9	−0.285384	−0.142692	+	0.989767i	$0.545576\pi$
$140$	0	0
$141$	−1.13498e9	−0.241825
$142$	−4.94874e9	−1.02140
$143$	−2.27683e9	−0.455323
$144$	−1.90804e9	−0.369792
$145$	2.37387e8	0.0445964
$146$	6.00810e9	1.09433
$147$	0	0
$148$	−7.34202e8	−0.125788
$149$	9.70766e9	1.61353	0.806764	−	0.590874i	$-0.201217\pi$
$149$	9.70766e9	1.61353	0.806764	+	0.590874i	$0.201217\pi$
$150$	−3.75656e9	−0.605871
$151$	−1.23865e10	−1.93889	−0.969445	−	0.245310i	$-0.921110\pi$
$151$	−1.23865e10	−1.93889	−0.969445	+	0.245310i	$0.921110\pi$
$152$	7.43079e9	1.12912
$153$	2.29929e9	0.339221
$154$	0	0
$155$	5.37739e8	0.0748305
$156$	−7.85303e8	−0.106164
$157$	−7.44207e8	−0.0977564	−0.0488782	−	0.998805i	$-0.515565\pi$
$157$	−7.44207e8	−0.0977564	−0.0488782	+	0.998805i	$0.515565\pi$
$158$	9.19556e8	0.117387
$159$	7.89263e9	0.979343
$160$	2.12337e8	0.0256144
$161$	0	0
$162$	−1.03312e9	−0.117851
$163$	−5.11701e9	−0.567770	−0.283885	−	0.958858i	$-0.591623\pi$
$163$	−5.11701e9	−0.567770	−0.283885	+	0.958858i	$0.591623\pi$
$164$	−8.95086e8	−0.0966201
$165$	1.75310e8	0.0184132
$166$	−1.23381e10	−1.26113
$167$	−1.54561e10	−1.53772	−0.768858	−	0.639419i	$-0.779175\pi$
$167$	−1.54561e10	−1.53772	−0.768858	+	0.639419i	$0.779175\pi$
$168$	0	0
$169$	1.23435e10	1.16399
$170$	−1.21115e9	−0.111219
$171$	4.53436e9	0.405540
$172$	1.07485e9	0.0936418
$173$	1.21248e10	1.02912	0.514559	−	0.857455i	$-0.327956\pi$
$173$	1.21248e10	1.02912	0.514559	+	0.857455i	$0.327956\pi$
$174$	3.20472e9	0.265044
$175$	0	0
$176$	4.37096e9	0.343376
$177$	8.97466e9	0.687287
$178$	−2.54711e10	−1.90177
$179$	−4.20407e9	−0.306077	−0.153039	−	0.988220i	$-0.548906\pi$
$179$	−4.20407e9	−0.306077	−0.153039	+	0.988220i	$0.548906\pi$
$180$	6.04662e7	0.00429325
$181$	−7.40381e9	−0.512745	−0.256373	−	0.966578i	$-0.582527\pi$
$181$	−7.40381e9	−0.512745	−0.256373	+	0.966578i	$0.582527\pi$
$182$	0	0
$183$	−7.59915e9	−0.500882
$184$	9.59571e9	0.617159
$185$	−1.65195e9	−0.103687
$186$	7.25947e9	0.444730
$187$	−5.26723e9	−0.314989
$188$	8.96771e8	0.0523566
$189$	0	0
$190$	−2.38847e9	−0.132962
$191$	−2.09740e10	−1.14033	−0.570166	−	0.821529i	$-0.693121\pi$
$191$	−2.09740e10	−1.14033	−0.570166	+	0.821529i	$0.693121\pi$
$192$	−9.19418e9	−0.488267
$193$	−3.08559e10	−1.60077	−0.800387	−	0.599484i	$-0.795372\pi$
$193$	−3.08559e10	−1.60077	−0.800387	+	0.599484i	$0.795372\pi$
$194$	−1.77220e9	−0.0898265
$195$	−1.76693e9	−0.0875113
$196$	0	0
$197$	−7.61328e9	−0.360142	−0.180071	−	0.983654i	$-0.557633\pi$
$197$	−7.61328e9	−0.360142	−0.180071	+	0.983654i	$0.557633\pi$
$198$	2.36668e9	0.109433
$199$	3.86586e10	1.74746	0.873729	−	0.486413i	$-0.161695\pi$
$199$	3.86586e10	1.74746	0.873729	+	0.486413i	$0.161695\pi$
$200$	−2.07770e10	−0.918224
$201$	9.91816e9	0.428597
$202$	−1.90875e10	−0.806619
$203$	0	0
$204$	−1.81672e9	−0.0734434
$205$	−2.01394e9	−0.0796444
$206$	4.17740e10	1.61623
$207$	5.85542e9	0.221662
$208$	−4.40546e10	−1.63195
$209$	−1.03874e10	−0.376571
$210$	0	0
$211$	−4.77331e10	−1.65786	−0.828931	−	0.559351i	$-0.811050\pi$
$211$	−4.77331e10	−1.65786	−0.828931	+	0.559351i	$0.811050\pi$
$212$	−6.23615e9	−0.212034
$213$	−1.67020e10	−0.555981
$214$	−1.10338e10	−0.359636
$215$	2.41841e9	0.0771893
$216$	−5.71405e9	−0.178609
$217$	0	0
$218$	−5.35371e10	−1.60546
$219$	2.02773e10	0.595679
$220$	−1.38516e8	−0.00398657
$221$	5.30880e10	1.49703
$222$	−2.23014e10	−0.616231
$223$	1.00554e9	0.0272286	0.0136143	−	0.999907i	$-0.495666\pi$
$223$	1.00554e9	0.0272286	0.0136143	+	0.999907i	$0.495666\pi$
$224$	0	0
$225$	−1.26784e10	−0.329794
$226$	−3.61475e10	−0.921702
$227$	3.73860e10	0.934528	0.467264	−	0.884118i	$-0.345240\pi$
$227$	3.73860e10	0.934528	0.467264	+	0.884118i	$0.345240\pi$
$228$	−3.58270e9	−0.0878019
$229$	−6.91078e10	−1.66061	−0.830305	−	0.557309i	$-0.811834\pi$
$229$	−6.91078e10	−1.66061	−0.830305	+	0.557309i	$0.811834\pi$
$230$	−3.08433e9	−0.0726752
$231$	0	0
$232$	1.77249e10	0.401686
$233$	8.31632e10	1.84854	0.924271	−	0.381737i	$-0.124674\pi$
$233$	8.31632e10	1.84854	0.924271	+	0.381737i	$0.124674\pi$
$234$	−2.38536e10	−0.520095
$235$	2.01774e9	0.0431578
$236$	−7.09109e9	−0.148802
$237$	3.10350e9	0.0638976
$238$	0	0
$239$	1.29881e10	0.257487	0.128743	−	0.991678i	$-0.458906\pi$
$239$	1.29881e10	0.257487	0.128743	+	0.991678i	$0.458906\pi$
$240$	3.39208e9	0.0659956
$241$	3.29469e10	0.629127	0.314563	−	0.949236i	$-0.398142\pi$
$241$	3.29469e10	0.629127	0.314563	+	0.949236i	$0.398142\pi$
$242$	5.11691e10	0.959045
$243$	−3.48678e9	−0.0641500
$244$	6.00427e9	0.108444
$245$	0	0
$246$	−2.71882e10	−0.473340
$247$	1.04693e11	1.78971
$248$	4.01512e10	0.674009
$249$	−4.16410e10	−0.686475
$250$	1.34283e10	0.217416
$251$	3.15564e10	0.501829	0.250914	−	0.968009i	$-0.419269\pi$
$251$	3.15564e10	0.501829	0.250914	+	0.968009i	$0.419269\pi$
$252$	0	0
$253$	−1.34136e10	−0.205828
$254$	−8.35452e10	−1.25942
$255$	−4.08763e9	−0.0605397
$256$	2.53839e10	0.369385
$257$	−7.71626e10	−1.10334	−0.551668	−	0.834064i	$-0.686009\pi$
$257$	−7.71626e10	−1.10334	−0.551668	+	0.834064i	$0.686009\pi$
$258$	3.26486e10	0.458749
$259$	0	0
$260$	1.39609e9	0.0189468
$261$	1.08159e10	0.144272
$262$	−2.47477e10	−0.324473
$263$	8.68605e9	0.111949	0.0559746	−	0.998432i	$-0.482173\pi$
$263$	8.68605e9	0.111949	0.0559746	+	0.998432i	$0.482173\pi$
$264$	1.30898e10	0.165850
$265$	−1.40313e10	−0.174780
$266$	0	0
$267$	−8.59649e10	−1.03519
$268$	−7.83657e9	−0.0927939
$269$	9.27474e10	1.07998	0.539991	−	0.841671i	$-0.318428\pi$
$269$	9.27474e10	1.07998	0.539991	+	0.841671i	$0.318428\pi$
$270$	1.83666e9	0.0210325
$271$	8.85724e10	0.997554	0.498777	−	0.866730i	$-0.333783\pi$
$271$	8.85724e10	0.997554	0.498777	+	0.866730i	$0.333783\pi$
$272$	−1.01916e11	−1.12897
$273$	0	0
$274$	−1.86849e11	−2.00269
$275$	2.90438e10	0.306236
$276$	−4.62650e9	−0.0479912
$277$	1.00100e11	1.02159	0.510796	−	0.859702i	$-0.329351\pi$
$277$	1.00100e11	1.02159	0.510796	+	0.859702i	$0.329351\pi$
$278$	3.01444e10	0.302695
$279$	2.45007e10	0.242081
$280$	0	0
$281$	5.75978e10	0.551096	0.275548	−	0.961287i	$-0.411141\pi$
$281$	5.75978e10	0.551096	0.275548	+	0.961287i	$0.411141\pi$
$282$	2.72394e10	0.256494
$283$	−6.04278e10	−0.560013	−0.280006	−	0.959998i	$-0.590337\pi$
$283$	−6.04278e10	−0.560013	−0.280006	+	0.959998i	$0.590337\pi$
$284$	1.31966e10	0.120373
$285$	−8.06108e9	−0.0723755
$286$	5.46440e10	0.482943
$287$	0	0
$288$	9.67459e9	0.0828641
$289$	4.22592e9	0.0356354
$290$	−5.69728e9	−0.0473017
$291$	−5.98117e9	−0.0488953
$292$	−1.60216e10	−0.128968
$293$	−1.32347e11	−1.04908	−0.524542	−	0.851385i	$-0.675763\pi$
$293$	−1.32347e11	−1.04908	−0.524542	+	0.851385i	$0.675763\pi$
$294$	0	0
$295$	−1.59550e10	−0.122658
$296$	−1.23346e11	−0.933925
$297$	7.98756e9	0.0595676
$298$	−2.32984e11	−1.71141
$299$	1.35195e11	0.978228
$300$	1.00175e10	0.0714026
$301$	0	0
$302$	2.97277e11	2.05650
$303$	−6.44204e10	−0.439068
$304$	−2.00985e11	−1.34969
$305$	1.35096e10	0.0893909
$306$	−5.51829e10	−0.359798
$307$	1.87229e11	1.20296	0.601479	−	0.798888i	$-0.294578\pi$
$307$	1.87229e11	1.20296	0.601479	+	0.798888i	$0.294578\pi$
$308$	0	0
$309$	1.40987e11	0.879765
$310$	−1.29057e10	−0.0793697
$311$	1.93013e11	1.16994	0.584972	−	0.811054i	$-0.301106\pi$
$311$	1.93013e11	1.16994	0.584972	+	0.811054i	$0.301106\pi$
$312$	−1.31931e11	−0.788227
$313$	1.18735e11	0.699245	0.349623	−	0.936891i	$-0.386310\pi$
$313$	1.18735e11	0.699245	0.349623	+	0.936891i	$0.386310\pi$
$314$	1.78610e10	0.103686
$315$	0	0
$316$	−2.45215e9	−0.0138342
$317$	−6.29568e10	−0.350168	−0.175084	−	0.984554i	$-0.556020\pi$
$317$	−6.29568e10	−0.350168	−0.175084	+	0.984554i	$0.556020\pi$
$318$	−1.89423e11	−1.03875
$319$	−2.47772e10	−0.133966
$320$	1.63452e10	0.0871396
$321$	−3.72391e10	−0.195761
$322$	0	0
$323$	2.42197e11	1.23811
$324$	2.75499e9	0.0138889
$325$	−2.92730e11	−1.45543
$326$	1.22808e11	0.602211
$327$	−1.80688e11	−0.873903
$328$	−1.50375e11	−0.717368
$329$	0	0
$330$	−4.20744e9	−0.0195301
$331$	2.29973e11	1.05305	0.526526	−	0.850159i	$-0.323494\pi$
$331$	2.29973e11	1.05305	0.526526	+	0.850159i	$0.323494\pi$
$332$	3.29016e10	0.148626
$333$	−7.52671e10	−0.335433
$334$	3.70947e11	1.63099
$335$	−1.76323e10	−0.0764904
$336$	0	0
$337$	3.42956e11	1.44845	0.724227	−	0.689562i	$-0.242197\pi$
$337$	3.42956e11	1.44845	0.724227	+	0.689562i	$0.242197\pi$
$338$	−2.96244e11	−1.23460
$339$	−1.21998e11	−0.501711
$340$	3.22973e9	0.0131072
$341$	−5.61265e10	−0.224788
$342$	−1.08825e11	−0.430140
$343$	0	0
$344$	1.80575e11	0.695255
$345$	−1.04096e10	−0.0395594
$346$	−2.90994e11	−1.09154
$347$	−7.98041e10	−0.295490	−0.147745	−	0.989026i	$-0.547201\pi$
$347$	−7.98041e10	−0.295490	−0.147745	+	0.989026i	$0.547201\pi$
$348$	−8.54592e9	−0.0312358
$349$	2.47686e11	0.893689	0.446844	−	0.894612i	$-0.352548\pi$
$349$	2.47686e11	0.893689	0.446844	+	0.894612i	$0.352548\pi$
$350$	0	0
$351$	−8.05059e10	−0.283104
$352$	−2.21626e10	−0.0769448
$353$	5.62222e11	1.92718	0.963589	−	0.267388i	$-0.0861606\pi$
$353$	5.62222e11	1.92718	0.963589	+	0.267388i	$0.0861606\pi$
$354$	−2.15392e11	−0.728978
$355$	2.96924e10	0.0992243
$356$	6.79229e10	0.224125
$357$	0	0
$358$	1.00898e11	0.324644
$359$	−5.77810e11	−1.83595	−0.917973	−	0.396644i	$-0.870175\pi$
$359$	−5.77810e11	−1.83595	−0.917973	+	0.396644i	$0.870175\pi$
$360$	1.01583e10	0.0318758
$361$	1.54943e11	0.480163
$362$	1.77691e11	0.543848
$363$	1.72696e11	0.522038
$364$	0	0
$365$	−3.60486e10	−0.106309
$366$	1.82380e11	0.531265
$367$	−6.60152e10	−0.189953	−0.0949766	−	0.995480i	$-0.530278\pi$
$367$	−6.60152e10	−0.189953	−0.0949766	+	0.995480i	$0.530278\pi$
$368$	−2.59541e11	−0.737719
$369$	−9.17603e10	−0.257654
$370$	3.96469e10	0.109977
$371$	0	0
$372$	−1.93586e10	−0.0524120
$373$	1.63118e11	0.436327	0.218164	−	0.975912i	$-0.429993\pi$
$373$	1.63118e11	0.436327	0.218164	+	0.975912i	$0.429993\pi$
$374$	1.26414e11	0.334096
$375$	4.53206e10	0.118346
$376$	1.50658e11	0.388728
$377$	2.49727e11	0.636693
$378$	0	0
$379$	−6.77491e11	−1.68666	−0.843329	−	0.537398i	$-0.819407\pi$
$379$	−6.77491e11	−1.68666	−0.843329	+	0.537398i	$0.819407\pi$
$380$	6.36925e9	0.0156698
$381$	−2.81965e11	−0.685540
$382$	5.03377e11	1.20951
$383$	2.77893e11	0.659908	0.329954	−	0.943997i	$-0.392967\pi$
$383$	2.77893e11	0.659908	0.329954	+	0.943997i	$0.392967\pi$
$384$	2.81813e11	0.661410
$385$	0	0
$386$	7.40541e11	1.69788
$387$	1.10189e11	0.249711
$388$	4.72586e9	0.0105862
$389$	8.55002e11	1.89319	0.946594	−	0.322428i	$-0.104499\pi$
$389$	8.55002e11	1.89319	0.946594	+	0.322428i	$0.104499\pi$
$390$	4.24064e10	0.0928198
$391$	3.12760e11	0.676731
$392$	0	0
$393$	−8.35234e10	−0.176621
$394$	1.82719e11	0.381988
$395$	−5.51734e9	−0.0114036
$396$	−6.31116e9	−0.0128968
$397$	1.31207e11	0.265093	0.132546	−	0.991177i	$-0.457685\pi$
$397$	1.31207e11	0.265093	0.132546	+	0.991177i	$0.457685\pi$
$398$	−9.27805e11	−1.85346
$399$	0	0
$400$	5.61970e11	1.09760
$401$	−1.33922e11	−0.258644	−0.129322	−	0.991603i	$-0.541280\pi$
$401$	−1.33922e11	−0.258644	−0.129322	+	0.991603i	$0.541280\pi$
$402$	−2.38036e11	−0.454596
$403$	5.65694e11	1.06834
$404$	5.09001e10	0.0950610
$405$	6.19873e9	0.0114487
$406$	0	0
$407$	1.72423e11	0.311472
$408$	−3.05209e11	−0.545289
$409$	4.18109e10	0.0738814	0.0369407	−	0.999317i	$-0.488239\pi$
$409$	4.18109e10	0.0738814	0.0369407	+	0.999317i	$0.488239\pi$
$410$	4.83347e10	0.0844756
$411$	−6.30615e11	−1.09012
$412$	−1.11397e11	−0.190475
$413$	0	0
$414$	−1.40530e11	−0.235108
$415$	7.40285e10	0.122513
$416$	2.23375e11	0.365692
$417$	1.01737e11	0.164766
$418$	2.49296e11	0.399414
$419$	6.75773e11	1.07112	0.535559	−	0.844498i	$-0.320101\pi$
$419$	6.75773e11	1.07112	0.535559	+	0.844498i	$0.320101\pi$
$420$	0	0
$421$	−7.93483e11	−1.23103	−0.615514	−	0.788126i	$-0.711052\pi$
$421$	−7.93483e11	−1.23103	−0.615514	+	0.788126i	$0.711052\pi$
$422$	1.14559e12	1.75843
$423$	9.19331e10	0.139618
$424$	−1.04767e12	−1.57427
$425$	−6.77202e11	−1.00686
$426$	4.00848e11	0.589707
$427$	0	0
$428$	2.94235e10	0.0423836
$429$	1.84424e11	0.262881
$430$	−5.80419e10	−0.0818716
$431$	1.31339e12	1.83336	0.916679	−	0.399624i	$-0.130859\pi$
$431$	1.31339e12	1.83336	0.916679	+	0.399624i	$0.130859\pi$
$432$	1.54552e11	0.213499
$433$	1.28557e12	1.75752	0.878762	−	0.477261i	$-0.158370\pi$
$433$	1.28557e12	1.75752	0.878762	+	0.477261i	$0.158370\pi$
$434$	0	0
$435$	−1.92283e10	−0.0257478
$436$	1.42766e11	0.189206
$437$	6.16785e11	0.809035
$438$	−4.86656e11	−0.631813
$439$	−1.04495e12	−1.34278	−0.671388	−	0.741106i	$-0.734302\pi$
$439$	−1.04495e12	−1.34278	−0.671388	+	0.741106i	$0.734302\pi$
$440$	−2.32708e10	−0.0295988
$441$	0	0
$442$	−1.27411e12	−1.58784
$443$	−6.00509e11	−0.740803	−0.370402	−	0.928872i	$-0.620780\pi$
$443$	−6.00509e11	−0.740803	−0.370402	+	0.928872i	$0.620780\pi$
$444$	5.94703e10	0.0726235
$445$	1.52826e11	0.184747
$446$	−2.41329e10	−0.0288803
$447$	−7.86321e11	−0.931571
$448$	0	0
$449$	−7.94091e11	−0.922066	−0.461033	−	0.887383i	$-0.652521\pi$
$449$	−7.94091e11	−0.922066	−0.461033	+	0.887383i	$0.652521\pi$
$450$	3.04282e11	0.349800
$451$	2.10205e11	0.239249
$452$	9.63934e10	0.108624
$453$	1.00331e12	1.11942
$454$	−8.97264e11	−0.991217
$455$	0	0
$456$	−6.01894e11	−0.651896
$457$	−1.71970e11	−0.184429	−0.0922144	−	0.995739i	$-0.529395\pi$
$457$	−1.71970e11	−0.184429	−0.0922144	+	0.995739i	$0.529395\pi$
$458$	1.65859e12	1.76134
$459$	−1.86242e11	−0.195849
$460$	8.22489e9	0.00856485
$461$	−1.15474e12	−1.19078	−0.595390	−	0.803437i	$-0.703003\pi$
$461$	−1.15474e12	−1.19078	−0.595390	+	0.803437i	$0.703003\pi$
$462$	0	0
$463$	8.13368e11	0.822570	0.411285	−	0.911507i	$-0.365080\pi$
$463$	8.13368e11	0.822570	0.411285	+	0.911507i	$0.365080\pi$
$464$	−4.79415e11	−0.480155
$465$	−4.35568e10	−0.0432034
$466$	−1.99592e12	−1.96068
$467$	−6.47702e11	−0.630157	−0.315079	−	0.949066i	$-0.602031\pi$
$467$	−6.47702e11	−0.630157	−0.315079	+	0.949066i	$0.602031\pi$
$468$	6.36096e10	0.0612937
$469$	0	0
$470$	−4.84257e10	−0.0457757
$471$	6.02808e10	0.0564397
$472$	−1.19130e12	−1.10480
$473$	−2.52422e11	−0.231874
$474$	−7.44841e10	−0.0677736
$475$	−1.33549e12	−1.20370
$476$	0	0
$477$	−6.39303e11	−0.565424
$478$	−3.11714e11	−0.273106
$479$	−9.20693e11	−0.799107	−0.399554	−	0.916710i	$-0.630835\pi$
$479$	−9.20693e11	−0.799107	−0.399554	+	0.916710i	$0.630835\pi$
$480$	−1.71993e10	−0.0147885
$481$	−1.73783e12	−1.48032
$482$	−7.90726e11	−0.667290
$483$	0	0
$484$	−1.36451e11	−0.113024
$485$	1.06332e10	0.00872621
$486$	8.36828e10	0.0680414
$487$	−2.88038e11	−0.232044	−0.116022	−	0.993247i	$-0.537014\pi$
$487$	−2.88038e11	−0.232044	−0.116022	+	0.993247i	$0.537014\pi$
$488$	1.00872e12	0.805156
$489$	4.14478e11	0.327802
$490$	0	0
$491$	−8.43206e11	−0.654737	−0.327368	−	0.944897i	$-0.606162\pi$
$491$	−8.43206e11	−0.654737	−0.327368	+	0.944897i	$0.606162\pi$
$492$	7.25020e10	0.0557837
$493$	5.77720e11	0.440460
$494$	−2.51264e12	−1.89827
$495$	−1.42001e10	−0.0106309
$496$	−1.08599e12	−0.805674
$497$	0	0
$498$	9.99385e11	0.728116
$499$	4.65323e11	0.335972	0.167986	−	0.985789i	$-0.446274\pi$
$499$	4.65323e11	0.335972	0.167986	+	0.985789i	$0.446274\pi$
$500$	−3.58089e10	−0.0256228
$501$	1.25195e12	0.887801
$502$	−7.57354e11	−0.532270
$503$	2.57883e11	0.179625	0.0898127	−	0.995959i	$-0.471373\pi$
$503$	2.57883e11	0.179625	0.0898127	+	0.995959i	$0.471373\pi$
$504$	0	0
$505$	1.14525e11	0.0783592
$506$	3.21927e11	0.218314
$507$	−9.99824e11	−0.672029
$508$	2.22787e11	0.148424
$509$	9.31227e11	0.614930	0.307465	−	0.951559i	$-0.400519\pi$
$509$	9.31227e11	0.614930	0.307465	+	0.951559i	$0.400519\pi$
$510$	9.81030e10	0.0642121
$511$	0	0
$512$	1.17212e12	0.753804
$513$	−3.67283e11	−0.234139
$514$	1.85190e12	1.17027
$515$	−2.50644e11	−0.157009
$516$	−8.70628e10	−0.0540641
$517$	−2.10601e11	−0.129644
$518$	0	0
$519$	−9.82105e11	−0.594162
$520$	2.34544e11	0.140672
$521$	4.14171e11	0.246269	0.123135	−	0.992390i	$-0.460705\pi$
$521$	4.14171e11	0.246269	0.123135	+	0.992390i	$0.460705\pi$
$522$	−2.59582e11	−0.153023
$523$	−2.26745e12	−1.32519	−0.662597	−	0.748976i	$-0.730546\pi$
$523$	−2.26745e12	−1.32519	−0.662597	+	0.748976i	$0.730546\pi$
$524$	6.59938e10	0.0382395
$525$	0	0
$526$	−2.08465e11	−0.118740
$527$	1.30868e12	0.739068
$528$	−3.54048e11	−0.198248
$529$	−1.00467e12	−0.557794
$530$	3.36752e11	0.185383
$531$	−7.26948e11	−0.396806
$532$	0	0
$533$	−2.11864e12	−1.13706
$534$	2.06316e12	1.09799
$535$	6.62029e10	0.0349369
$536$	−1.31654e12	−0.688960
$537$	3.40529e11	0.176714
$538$	−2.22594e12	−1.14549
$539$	0	0
$540$	−4.89776e9	−0.00247871
$541$	−2.83447e12	−1.42260	−0.711302	−	0.702886i	$-0.751894\pi$
$541$	−2.83447e12	−1.42260	−0.711302	+	0.702886i	$0.751894\pi$
$542$	−2.12574e12	−1.05807
$543$	5.99709e11	0.296034
$544$	5.16757e11	0.252983
$545$	3.21222e11	0.155963
$546$	0	0
$547$	1.47431e11	0.0704118	0.0352059	−	0.999380i	$-0.488791\pi$
$547$	1.47431e11	0.0704118	0.0352059	+	0.999380i	$0.488791\pi$
$548$	4.98264e11	0.236019
$549$	6.15531e11	0.289184
$550$	−6.97051e11	−0.324812
$551$	1.13930e12	0.526572
$552$	−7.77252e11	−0.356317
$553$	0	0
$554$	−2.40241e12	−1.08356
$555$	1.33808e11	0.0598638
$556$	−8.03851e10	−0.0356730
$557$	2.60191e12	1.14537	0.572683	−	0.819777i	$-0.305903\pi$
$557$	2.60191e12	1.14537	0.572683	+	0.819777i	$0.305903\pi$
$558$	−5.88017e11	−0.256765
$559$	2.54414e12	1.10201
$560$	0	0
$561$	4.26646e11	0.181859
$562$	−1.38235e12	−0.584526
$563$	−3.00613e11	−0.126101	−0.0630506	−	0.998010i	$-0.520083\pi$
$563$	−3.00613e11	−0.126101	−0.0630506	+	0.998010i	$0.520083\pi$
$564$	−7.26385e10	−0.0302281
$565$	2.16885e11	0.0895389
$566$	1.45027e12	0.593983
$567$	0	0
$568$	2.21703e12	0.893727
$569$	−1.89695e11	−0.0758666	−0.0379333	−	0.999280i	$-0.512077\pi$
$569$	−1.89695e11	−0.0758666	−0.0379333	+	0.999280i	$0.512077\pi$
$570$	1.93466e11	0.0767658
$571$	−1.24139e11	−0.0488705	−0.0244353	−	0.999701i	$-0.507779\pi$
$571$	−1.24139e11	−0.0488705	−0.0244353	+	0.999701i	$0.507779\pi$
$572$	−1.45717e11	−0.0569153
$573$	1.69890e12	0.658371
$574$	0	0
$575$	−1.72458e12	−0.657926
$576$	7.44728e11	0.281901
$577$	5.07002e12	1.90423	0.952113	−	0.305746i	$-0.0989058\pi$
$577$	5.07002e12	1.90423	0.952113	+	0.305746i	$0.0989058\pi$
$578$	−1.01422e11	−0.0377970
$579$	2.49933e12	0.924207
$580$	1.51927e10	0.00557455
$581$	0	0
$582$	1.43548e11	0.0518613
$583$	1.46452e12	0.525034
$584$	−2.69163e12	−0.957541
$585$	1.43122e11	0.0505247
$586$	3.17633e12	1.11272
$587$	2.82481e12	0.982015	0.491007	−	0.871155i	$-0.336629\pi$
$587$	2.82481e12	0.982015	0.491007	+	0.871155i	$0.336629\pi$
$588$	0	0
$589$	2.58080e12	0.883560
$590$	3.82919e11	0.130099
$591$	6.16676e11	0.207928
$592$	3.33621e12	1.11636
$593$	−6.31379e11	−0.209674	−0.104837	−	0.994489i	$-0.533432\pi$
$593$	−6.31379e11	−0.209674	−0.104837	+	0.994489i	$0.533432\pi$
$594$	−1.91701e11	−0.0631810
$595$	0	0
$596$	6.21291e11	0.201691
$597$	−3.13134e12	−1.00890
$598$	−3.24468e12	−1.03757
$599$	4.11496e12	1.30601	0.653003	−	0.757355i	$-0.273509\pi$
$599$	4.11496e12	1.30601	0.653003	+	0.757355i	$0.273509\pi$
$600$	1.68294e12	0.530137
$601$	2.84834e12	0.890548	0.445274	−	0.895394i	$-0.353106\pi$
$601$	2.84834e12	0.890548	0.445274	+	0.895394i	$0.353106\pi$
$602$	0	0
$603$	−8.03371e11	−0.247451
$604$	−7.92737e11	−0.242361
$605$	−3.07015e11	−0.0931666
$606$	1.54609e12	0.465702
$607$	−2.53150e12	−0.756884	−0.378442	−	0.925625i	$-0.623540\pi$
$607$	−2.53150e12	−0.756884	−0.378442	+	0.925625i	$0.623540\pi$
$608$	1.01908e12	0.302442
$609$	0	0
$610$	−3.24230e11	−0.0948134
$611$	2.12263e12	0.616153
$612$	1.47155e11	0.0424026
$613$	1.99373e12	0.570288	0.285144	−	0.958485i	$-0.407959\pi$
$613$	1.99373e12	0.570288	0.285144	+	0.958485i	$0.407959\pi$
$614$	−4.49350e12	−1.27593
$615$	1.63129e11	0.0459827
$616$	0	0
$617$	5.74672e12	1.59638	0.798191	−	0.602404i	$-0.205790\pi$
$617$	5.74672e12	1.59638	0.798191	+	0.602404i	$0.205790\pi$
$618$	−3.38369e12	−0.933132
$619$	−1.48335e12	−0.406102	−0.203051	−	0.979168i	$-0.565086\pi$
$619$	−1.48335e12	−0.406102	−0.203051	+	0.979168i	$0.565086\pi$
$620$	3.44153e10	0.00935381
$621$	−4.74289e11	−0.127977
$622$	−4.63231e12	−1.24091
$623$	0	0
$624$	3.56842e12	0.942204
$625$	3.69363e12	0.968262
$626$	−2.84964e12	−0.741661
$627$	8.41376e11	0.217413
$628$	−4.76293e10	−0.0122196
$629$	−4.02031e12	−1.02407
$630$	0	0
$631$	5.00163e11	0.125597	0.0627986	−	0.998026i	$-0.479997\pi$
$631$	5.00163e11	0.125597	0.0627986	+	0.998026i	$0.479997\pi$
$632$	−4.11961e11	−0.102714
$633$	3.86638e12	0.957167
$634$	1.51096e12	0.371409
$635$	5.01271e11	0.122346
$636$	5.05128e11	0.122418
$637$	0	0
$638$	5.94653e11	0.142092
$639$	1.35286e12	0.320996
$640$	−5.01001e11	−0.118040
$641$	−5.74052e11	−0.134304	−0.0671522	−	0.997743i	$-0.521391\pi$
$641$	−5.74052e11	−0.134304	−0.0671522	+	0.997743i	$0.521391\pi$
$642$	8.93739e11	0.207636
$643$	5.76391e12	1.32974	0.664871	−	0.746958i	$-0.268486\pi$
$643$	5.76391e12	1.32974	0.664871	+	0.746958i	$0.268486\pi$
$644$	0	0
$645$	−1.95891e11	−0.0445653
$646$	−5.81274e12	−1.31321
$647$	−2.87360e12	−0.644699	−0.322349	−	0.946621i	$-0.604473\pi$
$647$	−2.87360e12	−0.644699	−0.322349	+	0.946621i	$0.604473\pi$
$648$	4.62838e11	0.103120
$649$	1.66530e12	0.368461
$650$	7.02552e12	1.54372
$651$	0	0
$652$	−3.27489e11	−0.0709712
$653$	5.20689e12	1.12065	0.560324	−	0.828274i	$-0.310677\pi$
$653$	5.20689e12	1.12065	0.560324	+	0.828274i	$0.310677\pi$
$654$	4.33650e12	0.926915
$655$	1.48486e11	0.0315210
$656$	4.06727e12	0.857504
$657$	−1.64246e12	−0.343916
$658$	0	0
$659$	−1.47330e12	−0.304304	−0.152152	−	0.988357i	$-0.548620\pi$
$659$	−1.47330e12	−0.304304	−0.152152	+	0.988357i	$0.548620\pi$
$660$	1.12198e10	0.00230165
$661$	6.67120e12	1.35924	0.679622	−	0.733562i	$-0.262144\pi$
$661$	6.67120e12	1.35924	0.679622	+	0.733562i	$0.262144\pi$
$662$	−5.51934e12	−1.11693
$663$	−4.30013e12	−0.864311
$664$	5.52746e12	1.10349
$665$	0	0
$666$	1.80641e12	0.355781
$667$	1.47123e12	0.287816
$668$	−9.89191e11	−0.192215
$669$	−8.14485e10	−0.0157205
$670$	4.23175e11	0.0811303
$671$	−1.41006e12	−0.268527
$672$	0	0
$673$	5.90443e12	1.10946	0.554728	−	0.832032i	$-0.312822\pi$
$673$	5.90443e12	1.10946	0.554728	+	0.832032i	$0.312822\pi$
$674$	−8.23096e12	−1.53632
$675$	1.02695e12	0.190407
$676$	7.89985e11	0.145498
$677$	1.06454e12	0.194765	0.0973826	−	0.995247i	$-0.468953\pi$
$677$	1.06454e12	0.194765	0.0973826	+	0.995247i	$0.468953\pi$
$678$	2.92795e12	0.532145
$679$	0	0
$680$	5.42594e11	0.0973162
$681$	−3.02826e12	−0.539550
$682$	1.34704e12	0.238424
$683$	−7.62358e12	−1.34050	−0.670248	−	0.742137i	$-0.733812\pi$
$683$	−7.62358e12	−1.34050	−0.670248	+	0.742137i	$0.733812\pi$
$684$	2.90199e11	0.0506925
$685$	1.12109e12	0.194551
$686$	0	0
$687$	5.59774e12	0.958754
$688$	−4.88412e12	−0.831071
$689$	−1.47608e13	−2.49530
$690$	2.49831e11	0.0419590
$691$	1.05786e13	1.76514	0.882568	−	0.470184i	$-0.155813\pi$
$691$	1.05786e13	1.76514	0.882568	+	0.470184i	$0.155813\pi$
$692$	7.75984e11	0.128640
$693$	0	0
$694$	1.91530e12	0.313414
$695$	−1.80866e11	−0.0294054
$696$	−1.43571e12	−0.231914
$697$	−4.90127e12	−0.786613
$698$	−5.94445e12	−0.947900
$699$	−6.73622e12	−1.06726
$700$	0	0
$701$	−1.91667e11	−0.0299789	−0.0149895	−	0.999888i	$-0.504771\pi$
$701$	−1.91667e11	−0.0299789	−0.0149895	+	0.999888i	$0.504771\pi$
$702$	1.93214e12	0.300277
$703$	−7.92832e12	−1.22428
$704$	−1.70603e12	−0.261764
$705$	−1.63437e11	−0.0249171
$706$	−1.34933e13	−2.04408
$707$	0	0
$708$	5.74378e11	0.0859109
$709$	2.95570e12	0.439291	0.219645	−	0.975580i	$-0.429510\pi$
$709$	2.95570e12	0.439291	0.219645	+	0.975580i	$0.429510\pi$
$710$	−7.12618e11	−0.105243
$711$	−2.51384e11	−0.0368913
$712$	1.14110e13	1.66405
$713$	3.33270e12	0.482941
$714$	0	0
$715$	−3.27864e11	−0.0469155
$716$	−2.69060e11	−0.0382596
$717$	−1.05204e12	−0.148660
$718$	1.38674e13	1.94731
$719$	−1.65393e12	−0.230800	−0.115400	−	0.993319i	$-0.536815\pi$
$719$	−1.65393e12	−0.230800	−0.115400	+	0.993319i	$0.536815\pi$
$720$	−2.74758e11	−0.0381026
$721$	0	0
$722$	−3.71862e12	−0.509289
$723$	−2.66870e12	−0.363227
$724$	−4.73844e11	−0.0640932
$725$	−3.18558e12	−0.428220
$726$	−4.14470e12	−0.553705
$727$	−8.68882e11	−0.115360	−0.0576801	−	0.998335i	$-0.518370\pi$
$727$	−8.68882e11	−0.115360	−0.0576801	+	0.998335i	$0.518370\pi$
$728$	0	0
$729$	2.82430e11	0.0370370
$730$	8.65167e11	0.112758
$731$	5.88561e12	0.762365
$732$	−4.86346e11	−0.0626102
$733$	4.73579e12	0.605933	0.302967	−	0.953001i	$-0.402023\pi$
$733$	4.73579e12	0.605933	0.302967	+	0.953001i	$0.402023\pi$
$734$	1.58436e12	0.201476
$735$	0	0
$736$	1.31598e12	0.165310
$737$	1.84037e12	0.229774
$738$	2.20225e12	0.273283
$739$	2.33245e12	0.287682	0.143841	−	0.989601i	$-0.454055\pi$
$739$	2.33245e12	0.287682	0.143841	+	0.989601i	$0.454055\pi$
$740$	−1.05725e11	−0.0129609
$741$	−8.48015e12	−1.03329
$742$	0	0
$743$	−9.34556e12	−1.12501	−0.562504	−	0.826794i	$-0.690162\pi$
$743$	−9.34556e12	−1.12501	−0.562504	+	0.826794i	$0.690162\pi$
$744$	−3.25224e12	−0.389139
$745$	1.39790e12	0.166255
$746$	−3.91483e12	−0.462795
$747$	3.37292e12	0.396336
$748$	−3.37103e11	−0.0393736
$749$	0	0
$750$	−1.08770e12	−0.125525
$751$	4.69328e12	0.538390	0.269195	−	0.963086i	$-0.413242\pi$
$751$	4.69328e12	0.538390	0.269195	+	0.963086i	$0.413242\pi$
$752$	−4.07493e12	−0.464665
$753$	−2.55607e12	−0.289731
$754$	−5.99346e12	−0.675315
$755$	−1.78366e12	−0.199779
$756$	0	0
$757$	−2.23676e11	−0.0247565	−0.0123782	−	0.999923i	$-0.503940\pi$
$757$	−2.23676e11	−0.0247565	−0.0123782	+	0.999923i	$0.503940\pi$
$758$	1.62598e13	1.78897
$759$	1.08651e12	0.118835
$760$	1.07003e12	0.116342
$761$	−1.10727e12	−0.119680	−0.0598400	−	0.998208i	$-0.519059\pi$
$761$	−1.10727e12	−0.119680	−0.0598400	+	0.998208i	$0.519059\pi$
$762$	6.76716e12	0.727125
$763$	0	0
$764$	−1.34234e12	−0.142542
$765$	3.31098e11	0.0349526
$766$	−6.66943e12	−0.699938
$767$	−1.67844e13	−1.75116
$768$	−2.05610e12	−0.213264
$769$	−5.81971e12	−0.600113	−0.300056	−	0.953921i	$-0.597006\pi$
$769$	−5.81971e12	−0.600113	−0.300056	+	0.953921i	$0.597006\pi$
$770$	0	0
$771$	6.25017e12	0.637012
$772$	−1.97478e12	−0.200097
$773$	2.63702e12	0.265647	0.132824	−	0.991140i	$-0.457596\pi$
$773$	2.63702e12	0.265647	0.132824	+	0.991140i	$0.457596\pi$
$774$	−2.64453e12	−0.264859
$775$	−7.21611e12	−0.718531
$776$	7.93945e11	0.0785982
$777$	0	0
$778$	−2.05200e13	−2.00803
$779$	−9.66565e12	−0.940399
$780$	−1.13084e11	−0.0109389
$781$	−3.09915e12	−0.298066
$782$	−7.50624e12	−0.717781
$783$	−8.76090e11	−0.0832954
$784$	0	0
$785$	−1.07166e11	−0.0100726
$786$	2.00456e12	0.187334
$787$	1.62527e13	1.51022	0.755110	−	0.655598i	$-0.227583\pi$
$787$	1.62527e13	1.51022	0.755110	+	0.655598i	$0.227583\pi$
$788$	−4.87250e11	−0.0450178
$789$	−7.03570e11	−0.0646339
$790$	1.32416e11	0.0120954
$791$	0	0
$792$	−1.06027e12	−0.0957536
$793$	1.42119e13	1.27621
$794$	−3.14896e12	−0.281174
$795$	1.13654e12	0.100910
$796$	2.47415e12	0.218432
$797$	−6.84678e12	−0.601069	−0.300534	−	0.953771i	$-0.597165\pi$
$797$	−6.84678e12	−0.601069	−0.300534	+	0.953771i	$0.597165\pi$
$798$	0	0
$799$	4.91050e12	0.426250
$800$	−2.84942e12	−0.245953
$801$	6.96316e12	0.597668
$802$	3.21413e12	0.274333
$803$	3.76257e12	0.319349
$804$	6.34762e11	0.0535746
$805$	0	0
$806$	−1.35766e13	−1.13314
$807$	−7.51254e12	−0.623528
$808$	8.55122e12	0.705792
$809$	2.16337e13	1.77567	0.887836	−	0.460160i	$-0.152208\pi$
$809$	2.16337e13	1.77567	0.887836	+	0.460160i	$0.152208\pi$
$810$	−1.48769e11	−0.0121431
$811$	4.03349e12	0.327406	0.163703	−	0.986510i	$-0.447656\pi$
$811$	4.03349e12	0.327406	0.163703	+	0.986510i	$0.447656\pi$
$812$	0	0
$813$	−7.17436e12	−0.575938
$814$	−4.13814e12	−0.330366
$815$	−7.36850e11	−0.0585019
$816$	8.25519e12	0.651810
$817$	1.16068e13	0.911411
$818$	−1.00346e12	−0.0783631
$819$	0	0
$820$	−1.28892e11	−0.00995555
$821$	2.52495e12	0.193959	0.0969793	−	0.995286i	$-0.469082\pi$
$821$	2.52495e12	0.193959	0.0969793	+	0.995286i	$0.469082\pi$
$822$	1.51348e13	1.15625
$823$	−3.39851e12	−0.258220	−0.129110	−	0.991630i	$-0.541212\pi$
$823$	−3.39851e12	−0.258220	−0.129110	+	0.991630i	$0.541212\pi$
$824$	−1.87148e13	−1.41420
$825$	−2.35255e12	−0.176806
$826$	0	0
$827$	−1.57141e13	−1.16820	−0.584098	−	0.811683i	$-0.698552\pi$
$827$	−1.57141e13	−1.16820	−0.584098	+	0.811683i	$0.698552\pi$
$828$	3.74747e11	0.0277078
$829$	−1.22738e12	−0.0902578	−0.0451289	−	0.998981i	$-0.514370\pi$
$829$	−1.22738e12	−0.0902578	−0.0451289	+	0.998981i	$0.514370\pi$
$830$	−1.77668e12	−0.129945
$831$	−8.10814e12	−0.589816
$832$	1.71949e13	1.24407
$833$	0	0
$834$	−2.44170e12	−0.174761
$835$	−2.22568e12	−0.158443
$836$	−6.64791e11	−0.0470713
$837$	−1.98456e12	−0.139765
$838$	−1.62185e13	−1.13609
$839$	−1.35297e12	−0.0942671	−0.0471335	−	0.998889i	$-0.515009\pi$
$839$	−1.35297e12	−0.0942671	−0.0471335	+	0.998889i	$0.515009\pi$
$840$	0	0
$841$	−1.17895e13	−0.812671
$842$	1.90436e13	1.30570
$843$	−4.66542e12	−0.318175
$844$	−3.05492e12	−0.207233
$845$	1.77747e12	0.119935
$846$	−2.20639e12	−0.148087
$847$	0	0
$848$	2.83371e13	1.88180
$849$	4.89465e12	0.323324
$850$	1.62528e13	1.06793
$851$	−1.02382e13	−0.669176
$852$	−1.06893e12	−0.0694976
$853$	−3.62402e12	−0.234380	−0.117190	−	0.993110i	$-0.537389\pi$
$853$	−3.62402e12	−0.234380	−0.117190	+	0.993110i	$0.537389\pi$
$854$	0	0
$855$	6.52948e11	0.0417860
$856$	4.94315e12	0.314682
$857$	5.75207e11	0.0364259	0.0182130	−	0.999834i	$-0.494202\pi$
$857$	5.75207e11	0.0364259	0.0182130	+	0.999834i	$0.494202\pi$
$858$	−4.42617e12	−0.278827
$859$	−1.59420e13	−0.999015	−0.499508	−	0.866309i	$-0.666486\pi$
$859$	−1.59420e13	−0.999015	−0.499508	+	0.866309i	$0.666486\pi$
$860$	1.54778e11	0.00964866
$861$	0	0
$862$	−3.15215e13	−1.94457
$863$	−3.66004e12	−0.224614	−0.112307	−	0.993674i	$-0.535824\pi$
$863$	−3.66004e12	−0.224614	−0.112307	+	0.993674i	$0.535824\pi$
$864$	−7.83642e11	−0.0478416
$865$	1.74596e12	0.106038
$866$	−3.08537e13	−1.86414
$867$	−3.42300e11	−0.0205741
$868$	0	0
$869$	5.75872e11	0.0342560
$870$	4.61480e11	0.0273096
$871$	−1.85489e13	−1.09204
$872$	2.39846e13	1.40478
$873$	4.84475e11	0.0282297
$874$	−1.48028e13	−0.858111
$875$	0	0
$876$	1.29775e12	0.0744599
$877$	−1.87410e13	−1.06978	−0.534890	−	0.844922i	$-0.679647\pi$
$877$	−1.87410e13	−1.06978	−0.534890	+	0.844922i	$0.679647\pi$
$878$	2.50787e13	1.42423
$879$	1.07201e13	0.605689
$880$	6.29419e11	0.0353808
$881$	−2.13381e13	−1.19334	−0.596669	−	0.802488i	$-0.703509\pi$
$881$	−2.13381e13	−1.19334	−0.596669	+	0.802488i	$0.703509\pi$
$882$	0	0
$883$	8.04505e12	0.445354	0.222677	−	0.974892i	$-0.428520\pi$
$883$	8.04505e12	0.445354	0.222677	+	0.974892i	$0.428520\pi$
$884$	3.39763e12	0.187129
$885$	1.29235e12	0.0708167
$886$	1.44122e13	0.785741
$887$	1.87667e13	1.01796	0.508980	−	0.860778i	$-0.330023\pi$
$887$	1.87667e13	1.01796	0.508980	+	0.860778i	$0.330023\pi$
$888$	9.99102e12	0.539202
$889$	0	0
$890$	−3.66784e12	−0.195954
$891$	−6.46992e11	−0.0343914
$892$	6.43544e10	0.00340358
$893$	9.68384e12	0.509584
$894$	1.88717e13	0.988080
$895$	−6.05385e11	−0.0315376
$896$	0	0
$897$	−1.09508e13	−0.564780
$898$	1.90582e13	0.977998
$899$	6.15605e12	0.314329
$900$	−8.11418e11	−0.0412243
$901$	−3.41476e13	−1.72623
$902$	−5.04493e12	−0.253762
$903$	0	0
$904$	1.61941e13	0.806489
$905$	−1.06615e12	−0.0528323
$906$	−2.40794e13	−1.18732
$907$	−2.94035e13	−1.44267	−0.721334	−	0.692587i	$-0.756471\pi$
$907$	−2.94035e13	−1.44267	−0.721334	+	0.692587i	$0.756471\pi$
$908$	2.39270e12	0.116816
$909$	5.21806e12	0.253496
$910$	0	0
$911$	−2.78849e13	−1.34133	−0.670667	−	0.741759i	$-0.733992\pi$
$911$	−2.78849e13	−1.34133	−0.670667	+	0.741759i	$0.733992\pi$
$912$	1.62798e13	0.779242
$913$	−7.72673e12	−0.368025
$914$	4.12727e12	0.195616
$915$	−1.09428e12	−0.0516099
$916$	−4.42290e12	−0.207576
$917$	0	0
$918$	4.46982e12	0.207729
$919$	−1.16191e13	−0.537346	−0.268673	−	0.963231i	$-0.586585\pi$
$919$	−1.16191e13	−0.537346	−0.268673	+	0.963231i	$0.586585\pi$
$920$	1.38178e12	0.0635908
$921$	−1.51656e13	−0.694528
$922$	2.77139e13	1.26301
$923$	3.12360e13	1.41660
$924$	0	0
$925$	2.21682e13	0.995617
$926$	−1.95208e13	−0.872467
$927$	−1.14200e13	−0.507933
$928$	2.43084e12	0.107595
$929$	3.01934e13	1.32997	0.664983	−	0.746858i	$-0.268439\pi$
$929$	3.01934e13	1.32997	0.664983	+	0.746858i	$0.268439\pi$
$930$	1.04536e12	0.0458241
$931$	0	0
$932$	5.32244e12	0.231068
$933$	−1.56341e13	−0.675467
$934$	1.55448e13	0.668383
$935$	−7.58482e11	−0.0324558
$936$	1.06864e13	0.455083
$937$	−7.46208e12	−0.316251	−0.158125	−	0.987419i	$-0.550545\pi$
$937$	−7.46208e12	−0.316251	−0.158125	+	0.987419i	$0.550545\pi$
$938$	0	0
$939$	−9.61754e12	−0.403709
$940$	1.29135e11	0.00539472
$941$	−1.73402e13	−0.720945	−0.360472	−	0.932770i	$-0.617384\pi$
$941$	−1.73402e13	−0.720945	−0.360472	+	0.932770i	$0.617384\pi$
$942$	−1.44674e12	−0.0598633
$943$	−1.24817e13	−0.514008
$944$	3.22219e13	1.32062
$945$	0	0
$946$	6.05812e12	0.245939
$947$	−1.04752e13	−0.423241	−0.211621	−	0.977352i	$-0.567874\pi$
$947$	−1.04752e13	−0.423241	−0.211621	+	0.977352i	$0.567874\pi$
$948$	1.98624e11	0.00798720
$949$	−3.79226e13	−1.51775
$950$	3.20517e13	1.27672
$951$	5.09950e12	0.202169
$952$	0	0
$953$	3.91536e13	1.53764	0.768818	−	0.639468i	$-0.220845\pi$
$953$	3.91536e13	1.53764	0.768818	+	0.639468i	$0.220845\pi$
$954$	1.53433e13	0.599723
$955$	−3.02026e12	−0.117498
$956$	8.31239e11	0.0321859
$957$	2.00696e12	0.0773453
$958$	2.20966e13	0.847581
$959$	0	0
$960$	−1.32396e12	−0.0503101
$961$	−1.24947e13	−0.472573
$962$	4.17080e13	1.57011
$963$	3.01637e12	0.113023
$964$	2.10860e12	0.0786409
$965$	−4.44324e12	−0.164941
$966$	0	0
$967$	5.06632e13	1.86326	0.931631	−	0.363407i	$-0.118386\pi$
$967$	5.06632e13	1.86326	0.931631	+	0.363407i	$0.118386\pi$
$968$	−2.29238e13	−0.839164
$969$	−1.96180e13	−0.714821
$970$	−2.55196e11	−0.00925554
$971$	5.45881e13	1.97066	0.985329	−	0.170666i	$-0.0545919\pi$
$971$	5.45881e13	1.97066	0.985329	+	0.170666i	$0.0545919\pi$
$972$	−2.23154e11	−0.00801875
$973$	0	0
$974$	6.91292e12	0.246119
$975$	2.37111e13	0.840294
$976$	−2.72834e13	−0.962441
$977$	−1.24014e13	−0.435458	−0.217729	−	0.976009i	$-0.569865\pi$
$977$	−1.24014e13	−0.435458	−0.217729	+	0.976009i	$0.569865\pi$
$978$	−9.94747e12	−0.347687
$979$	−1.59513e13	−0.554974
$980$	0	0
$981$	1.46357e13	0.504548
$982$	2.02369e13	0.694453
$983$	−5.11447e13	−1.74707	−0.873533	−	0.486764i	$-0.838177\pi$
$983$	−5.11447e13	−1.74707	−0.873533	+	0.486764i	$0.838177\pi$
$984$	1.21803e13	0.414173
$985$	−1.09631e12	−0.0371083
$986$	−1.38653e13	−0.467178
$987$	0	0
$988$	6.70036e12	0.223713
$989$	1.49884e13	0.498164
$990$	3.40802e11	0.0112757
$991$	2.59995e13	0.856316	0.428158	−	0.903704i	$-0.359163\pi$
$991$	2.59995e13	0.856316	0.428158	+	0.903704i	$0.359163\pi$
$992$	5.50644e12	0.180538
$993$	−1.86278e13	−0.607980
$994$	0	0
$995$	5.56683e12	0.180055
$996$	−2.66503e12	−0.0858093
$997$	−1.43157e13	−0.458865	−0.229432	−	0.973325i	$-0.573687\pi$
$997$	−1.43157e13	−0.458865	−0.229432	+	0.973325i	$0.573687\pi$
$998$	−1.11678e13	−0.356352
$999$	6.09664e12	0.193663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.10.a.b.1.1		1
7.6	odd	2		21.10.a.a.1.1	✓	1
21.20	even	2		63.10.a.a.1.1		1
28.27	even	2		336.10.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.10.a.a.1.1	✓	1	7.6	odd	2
63.10.a.a.1.1		1	21.20	even	2
147.10.a.b.1.1		1	1.1	even	1	trivial
336.10.a.d.1.1		1	28.27	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

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