LMFDB - Embedded newform 10.16.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,16,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	10.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:	$14.2693505100$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-128.000 q^{2} -918.000 q^{3} +16384.0 q^{4} -78125.0 q^{5} +117504. q^{6} -953554. q^{7} -2.09715e6 q^{8} -1.35062e7 q^{9} +O(q^{10})$

\(q-128.000 q^{2} -918.000 q^{3} +16384.0 q^{4} -78125.0 q^{5} +117504. q^{6} -953554. q^{7} -2.09715e6 q^{8} -1.35062e7 q^{9} +1.00000e7 q^{10} +1.77832e7 q^{11} -1.50405e7 q^{12} +1.40533e8 q^{13} +1.22055e8 q^{14} +7.17188e7 q^{15} +2.68435e8 q^{16} +2.99887e9 q^{17} +1.72879e9 q^{18} +3.25585e9 q^{19} -1.28000e9 q^{20} +8.75363e8 q^{21} -2.27625e9 q^{22} +6.77481e9 q^{23} +1.92519e9 q^{24} +6.10352e9 q^{25} -1.79883e10 q^{26} +2.55710e10 q^{27} -1.56230e10 q^{28} -7.34032e9 q^{29} -9.18000e9 q^{30} -1.15428e11 q^{31} -3.43597e10 q^{32} -1.63250e10 q^{33} -3.83855e11 q^{34} +7.44964e10 q^{35} -2.21285e11 q^{36} +1.50301e11 q^{37} -4.16749e11 q^{38} -1.29010e11 q^{39} +1.63840e11 q^{40} +1.84160e12 q^{41} -1.12046e11 q^{42} +1.51002e12 q^{43} +2.91360e11 q^{44} +1.05517e12 q^{45} -8.67176e11 q^{46} +6.09375e12 q^{47} -2.46424e11 q^{48} -3.83830e12 q^{49} -7.81250e11 q^{50} -2.75296e12 q^{51} +2.30250e12 q^{52} -8.26741e12 q^{53} -3.27308e12 q^{54} -1.38932e12 q^{55} +1.99975e12 q^{56} -2.98887e12 q^{57} +9.39561e11 q^{58} -2.35169e13 q^{59} +1.17504e12 q^{60} -3.13537e12 q^{61} +1.47748e13 q^{62} +1.28789e13 q^{63} +4.39805e12 q^{64} -1.09792e13 q^{65} +2.08960e12 q^{66} -3.60310e13 q^{67} +4.91335e13 q^{68} -6.21928e12 q^{69} -9.53554e12 q^{70} +5.21697e13 q^{71} +2.83245e13 q^{72} +6.99771e13 q^{73} -1.92385e13 q^{74} -5.60303e12 q^{75} +5.33439e13 q^{76} -1.69573e13 q^{77} +1.65132e13 q^{78} -1.35318e14 q^{79} -2.09715e13 q^{80} +1.70325e14 q^{81} -2.35725e14 q^{82} +4.27456e14 q^{83} +1.43419e13 q^{84} -2.34287e14 q^{85} -1.93282e14 q^{86} +6.73842e12 q^{87} -3.72941e13 q^{88} -4.46582e14 q^{89} -1.35062e14 q^{90} -1.34006e14 q^{91} +1.10999e14 q^{92} +1.05963e14 q^{93} -7.80000e14 q^{94} -2.54363e14 q^{95} +3.15422e13 q^{96} +1.81247e14 q^{97} +4.91302e14 q^{98} -2.40184e14 q^{99} +O(q^{100})\)

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 $

$2$	−128.000	−0.707107
$2$	−128.000	−0.707107
$3$	−918.000	−0.242345	−0.121172	−	0.992631i	$-0.538665\pi$
$3$	−918.000	−0.242345	−0.121172	+	0.992631i	$0.538665\pi$
$4$	16384.0	0.500000
$5$	−78125.0	−0.447214
$5$	−78125.0	−0.447214
$6$	117504.	0.171363
$7$	−953554.	−0.437633	−0.218816	−	0.975766i	$-0.570220\pi$
$7$	−953554.	−0.437633	−0.218816	+	0.975766i	$0.570220\pi$
$8$	−2.09715e6	−0.353553
$9$	−1.35062e7	−0.941269
$10$	1.00000e7	0.316228
$11$	1.77832e7	0.275147	0.137574	−	0.990492i	$-0.456070\pi$
$11$	1.77832e7	0.275147	0.137574	+	0.990492i	$0.456070\pi$
$12$	−1.50405e7	−0.121172
$13$	1.40533e8	0.621161	0.310580	−	0.950547i	$-0.399477\pi$
$13$	1.40533e8	0.621161	0.310580	+	0.950547i	$0.399477\pi$
$14$	1.22055e8	0.309453
$15$	7.17188e7	0.108380
$16$	2.68435e8	0.250000
$17$	2.99887e9	1.77252	0.886259	−	0.463189i	$-0.153295\pi$
$17$	2.99887e9	1.77252	0.886259	+	0.463189i	$0.153295\pi$
$18$	1.72879e9	0.665578
$19$	3.25585e9	0.835627	0.417814	−	0.908533i	$-0.362796\pi$
$19$	3.25585e9	0.835627	0.417814	+	0.908533i	$0.362796\pi$
$20$	−1.28000e9	−0.223607
$21$	8.75363e8	0.106058
$22$	−2.27625e9	−0.194559
$23$	6.77481e9	0.414895	0.207448	−	0.978246i	$-0.433484\pi$
$23$	6.77481e9	0.414895	0.207448	+	0.978246i	$0.433484\pi$
$24$	1.92519e9	0.0856817
$25$	6.10352e9	0.200000
$26$	−1.79883e10	−0.439227
$27$	2.55710e10	0.470456
$28$	−1.56230e10	−0.218816
$29$	−7.34032e9	−0.0790188	−0.0395094	−	0.999219i	$-0.512579\pi$
$29$	−7.34032e9	−0.0790188	−0.0395094	+	0.999219i	$0.512579\pi$
$30$	−9.18000e9	−0.0766361
$31$	−1.15428e11	−0.753529	−0.376765	−	0.926309i	$-0.622963\pi$
$31$	−1.15428e11	−0.753529	−0.376765	+	0.926309i	$0.622963\pi$
$32$	−3.43597e10	−0.176777
$33$	−1.63250e10	−0.0666805
$34$	−3.83855e11	−1.25336
$35$	7.44964e10	0.195715
$36$	−2.21285e11	−0.470635
$37$	1.50301e11	0.260285	0.130142	−	0.991495i	$-0.458457\pi$
$37$	1.50301e11	0.260285	0.130142	+	0.991495i	$0.458457\pi$
$38$	−4.16749e11	−0.590878
$39$	−1.29010e11	−0.150535
$40$	1.63840e11	0.158114
$41$	1.84160e12	1.47678	0.738392	−	0.674371i	$-0.235585\pi$
$41$	1.84160e12	1.47678	0.738392	+	0.674371i	$0.235585\pi$
$42$	−1.12046e11	−0.0749943
$43$	1.51002e12	0.847167	0.423583	−	0.905857i	$-0.360772\pi$
$43$	1.51002e12	0.847167	0.423583	+	0.905857i	$0.360772\pi$
$44$	2.91360e11	0.137574
$45$	1.05517e12	0.420948
$46$	−8.67176e11	−0.293375
$47$	6.09375e12	1.75449	0.877245	−	0.480043i	$-0.159379\pi$
$47$	6.09375e12	1.75449	0.877245	+	0.480043i	$0.159379\pi$
$48$	−2.46424e11	−0.0605861
$49$	−3.83830e12	−0.808477
$50$	−7.81250e11	−0.141421
$51$	−2.75296e12	−0.429560
$52$	2.30250e12	0.310580
$53$	−8.26741e12	−0.966720	−0.483360	−	0.875422i	$-0.660584\pi$
$53$	−8.26741e12	−0.966720	−0.483360	+	0.875422i	$0.660584\pi$
$54$	−3.27308e12	−0.332663
$55$	−1.38932e12	−0.123050
$56$	1.99975e12	0.154727
$57$	−2.98887e12	−0.202510
$58$	9.39561e11	0.0558747
$59$	−2.35169e13	−1.23024	−0.615120	−	0.788434i	$-0.710892\pi$
$59$	−2.35169e13	−1.23024	−0.615120	+	0.788434i	$0.710892\pi$
$60$	1.17504e12	0.0541899
$61$	−3.13537e12	−0.127736	−0.0638682	−	0.997958i	$-0.520344\pi$
$61$	−3.13537e12	−0.127736	−0.0638682	+	0.997958i	$0.520344\pi$
$62$	1.47748e13	0.532826
$63$	1.28789e13	0.411930
$64$	4.39805e12	0.125000
$65$	−1.09792e13	−0.277792
$66$	2.08960e12	0.0471502
$67$	−3.60310e13	−0.726298	−0.363149	−	0.931731i	$-0.618298\pi$
$67$	−3.60310e13	−0.726298	−0.363149	+	0.931731i	$0.618298\pi$
$68$	4.91335e13	0.886259
$69$	−6.21928e12	−0.100548
$70$	−9.53554e12	−0.138392
$71$	5.21697e13	0.680740	0.340370	−	0.940292i	$-0.389448\pi$
$71$	5.21697e13	0.680740	0.340370	+	0.940292i	$0.389448\pi$
$72$	2.83245e13	0.332789
$73$	6.99771e13	0.741370	0.370685	−	0.928759i	$-0.379123\pi$
$73$	6.99771e13	0.741370	0.370685	+	0.928759i	$0.379123\pi$
$74$	−1.92385e13	−0.184049
$75$	−5.60303e12	−0.0484689
$76$	5.33439e13	0.417814
$77$	−1.69573e13	−0.120414
$78$	1.65132e13	0.106444
$79$	−1.35318e14	−0.792778	−0.396389	−	0.918083i	$-0.629737\pi$
$79$	−1.35318e14	−0.792778	−0.396389	+	0.918083i	$0.629737\pi$
$80$	−2.09715e13	−0.111803
$81$	1.70325e14	0.827257
$82$	−2.35725e14	−1.04424
$83$	4.27456e14	1.72904	0.864522	−	0.502596i	$-0.167621\pi$
$83$	4.27456e14	1.72904	0.864522	+	0.502596i	$0.167621\pi$
$84$	1.43419e13	0.0530290
$85$	−2.34287e14	−0.792694
$86$	−1.93282e14	−0.599037
$87$	6.73842e12	0.0191498
$88$	−3.72941e13	−0.0972793
$89$	−4.46582e14	−1.07023	−0.535113	−	0.844780i	$-0.679731\pi$
$89$	−4.46582e14	−1.07023	−0.535113	+	0.844780i	$0.679731\pi$
$90$	−1.35062e14	−0.297655
$91$	−1.34006e14	−0.271841
$92$	1.10999e14	0.207448
$93$	1.05963e14	0.182614
$94$	−7.80000e14	−1.24061
$95$	−2.54363e14	−0.373704
$96$	3.15422e13	0.0428409
$97$	1.81247e14	0.227763	0.113882	−	0.993494i	$-0.463672\pi$
$97$	1.81247e14	0.227763	0.113882	+	0.993494i	$0.463672\pi$
$98$	4.91302e14	0.571680
$99$	−2.40184e14	−0.258988
$100$	1.00000e14	0.100000
$101$	1.59292e15	1.47837	0.739184	−	0.673504i	$-0.235212\pi$
$101$	1.59292e15	1.47837	0.739184	+	0.673504i	$0.235212\pi$
$102$	3.52379e14	0.303745
$103$	1.37238e15	1.09950	0.549750	−	0.835329i	$-0.314723\pi$
$103$	1.37238e15	1.09950	0.549750	+	0.835329i	$0.314723\pi$
$104$	−2.94720e14	−0.219614
$105$	−6.83877e13	−0.0474306
$106$	1.05823e15	0.683574
$107$	2.22197e15	1.33770	0.668851	−	0.743397i	$-0.266787\pi$
$107$	2.22197e15	1.33770	0.668851	+	0.743397i	$0.266787\pi$
$108$	4.18955e14	0.235228
$109$	−3.67848e15	−1.92739	−0.963694	−	0.267007i	$-0.913965\pi$
$109$	−3.67848e15	−1.92739	−0.963694	+	0.267007i	$0.913965\pi$
$110$	1.77832e14	0.0870093
$111$	−1.37976e14	−0.0630786
$112$	−2.55968e14	−0.109408
$113$	−4.86923e14	−0.194703	−0.0973513	−	0.995250i	$-0.531037\pi$
$113$	−4.86923e14	−0.194703	−0.0973513	+	0.995250i	$0.531037\pi$
$114$	3.82576e14	0.143196
$115$	−5.29282e14	−0.185547
$116$	−1.20264e14	−0.0395094
$117$	−1.89807e15	−0.584680
$118$	3.01016e15	0.869911
$119$	−2.85959e15	−0.775713
$120$	−1.50405e14	−0.0383180
$121$	−3.86100e15	−0.924294
$122$	4.01327e14	0.0903233
$123$	−1.69059e15	−0.357891
$124$	−1.89118e15	−0.376765
$125$	−4.76837e14	−0.0894427
$126$	−1.64850e15	−0.291279
$127$	1.64122e15	0.273300	0.136650	−	0.990619i	$-0.456366\pi$
$127$	1.64122e15	0.273300	0.136650	+	0.990619i	$0.456366\pi$
$128$	−5.62950e14	−0.0883883
$129$	−1.38620e15	−0.205306
$130$	1.40533e15	0.196428
$131$	9.75949e15	1.28793	0.643965	−	0.765055i	$-0.277288\pi$
$131$	9.75949e15	1.28793	0.643965	+	0.765055i	$0.277288\pi$
$132$	−2.67469e14	−0.0333402
$133$	−3.10463e15	−0.365698
$134$	4.61197e15	0.513571
$135$	−1.99773e15	−0.210394
$136$	−6.28909e15	−0.626680
$137$	−1.17615e15	−0.110933	−0.0554664	−	0.998461i	$-0.517665\pi$
$137$	−1.17615e15	−0.110933	−0.0554664	+	0.998461i	$0.517665\pi$
$138$	7.96068e14	0.0710979
$139$	2.34504e16	1.98399	0.991996	−	0.126267i	$-0.0402996\pi$
$139$	2.34504e16	1.98399	0.991996	+	0.126267i	$0.0402996\pi$
$140$	1.22055e15	0.0978577
$141$	−5.59406e15	−0.425191
$142$	−6.67773e15	−0.481356
$143$	2.49914e15	0.170911
$144$	−3.62554e15	−0.235317
$145$	5.73463e14	0.0353383
$146$	−8.95707e15	−0.524227
$147$	3.52356e15	0.195930
$148$	2.46253e15	0.130142
$149$	3.02392e16	1.51940	0.759702	−	0.650271i	$-0.225345\pi$
$149$	3.02392e16	1.51940	0.759702	+	0.650271i	$0.225345\pi$
$150$	7.17188e14	0.0342727
$151$	2.83905e16	1.29076	0.645380	−	0.763862i	$-0.276699\pi$
$151$	2.83905e16	1.29076	0.645380	+	0.763862i	$0.276699\pi$
$152$	−6.82802e15	−0.295439
$153$	−4.05033e16	−1.66842
$154$	2.17053e15	0.0851453
$155$	9.01784e15	0.336988
$156$	−2.11369e15	−0.0752675
$157$	−3.08752e16	−1.04800	−0.524002	−	0.851717i	$-0.675561\pi$
$157$	−3.08752e16	−1.04800	−0.524002	+	0.851717i	$0.675561\pi$
$158$	1.73207e16	0.560578
$159$	7.58948e15	0.234279
$160$	2.68435e15	0.0790569
$161$	−6.46015e15	−0.181572
$162$	−2.18016e16	−0.584959
$163$	−5.91704e16	−1.51599	−0.757996	−	0.652259i	$-0.773822\pi$
$163$	−5.91704e16	−1.51599	−0.757996	+	0.652259i	$0.773822\pi$
$164$	3.01728e16	0.738392
$165$	1.27539e15	0.0298204
$166$	−5.47144e16	−1.22262
$167$	4.19097e16	0.895243	0.447622	−	0.894223i	$-0.352271\pi$
$167$	4.19097e16	0.895243	0.447622	+	0.894223i	$0.352271\pi$
$168$	−1.83577e15	−0.0374972
$169$	−3.14363e16	−0.614159
$170$	2.99887e16	0.560520
$171$	−4.39741e16	−0.786550
$172$	2.47401e16	0.423583
$173$	−6.80559e16	−1.11563	−0.557815	−	0.829965i	$-0.688360\pi$
$173$	−6.80559e16	−1.11563	−0.557815	+	0.829965i	$0.688360\pi$
$174$	−8.62517e14	−0.0135409
$175$	−5.82003e15	−0.0875266
$176$	4.77365e15	0.0687869
$177$	2.15885e16	0.298142
$178$	5.71624e16	0.756765
$179$	1.10140e17	1.39813	0.699065	−	0.715058i	$-0.253600\pi$
$179$	1.10140e17	1.39813	0.699065	+	0.715058i	$0.253600\pi$
$180$	1.72879e16	0.210474
$181$	1.87053e15	0.0218462	0.0109231	−	0.999940i	$-0.496523\pi$
$181$	1.87053e15	0.0218462	0.0109231	+	0.999940i	$0.496523\pi$
$182$	1.71528e16	0.192220
$183$	2.87827e15	0.0309562
$184$	−1.42078e16	−0.146688
$185$	−1.17423e16	−0.116403
$186$	−1.35633e16	−0.129127
$187$	5.33296e16	0.487704
$188$	9.98400e16	0.877245
$189$	−2.43833e16	−0.205887
$190$	3.25585e16	0.264249
$191$	1.85883e17	1.45041	0.725204	−	0.688534i	$-0.241745\pi$
$191$	1.85883e17	1.45041	0.725204	+	0.688534i	$0.241745\pi$
$192$	−4.03741e15	−0.0302931
$193$	−1.28077e17	−0.924254	−0.462127	−	0.886814i	$-0.652914\pi$
$193$	−1.28077e17	−0.924254	−0.462127	+	0.886814i	$0.652914\pi$
$194$	−2.31997e16	−0.161053
$195$	1.00789e16	0.0673213
$196$	−6.28866e16	−0.404239
$197$	1.14450e17	0.708140	0.354070	−	0.935219i	$-0.384798\pi$
$197$	1.14450e17	0.708140	0.354070	+	0.935219i	$0.384798\pi$
$198$	3.07435e16	0.183132
$199$	−2.29969e17	−1.31908	−0.659540	−	0.751669i	$-0.729249\pi$
$199$	−2.29969e17	−1.31908	−0.659540	+	0.751669i	$0.729249\pi$
$200$	−1.28000e16	−0.0707107
$201$	3.30764e16	0.176014
$202$	−2.03893e17	−1.04536
$203$	6.99939e15	0.0345812
$204$	−4.51046e16	−0.214780
$205$	−1.43875e17	−0.660438
$206$	−1.75665e17	−0.777463
$207$	−9.15019e16	−0.390528
$208$	3.77241e16	0.155290
$209$	5.78996e16	0.229921
$210$	8.75363e15	0.0335385
$211$	1.84151e17	0.680855	0.340427	−	0.940271i	$-0.389428\pi$
$211$	1.84151e17	0.680855	0.340427	+	0.940271i	$0.389428\pi$
$212$	−1.35453e17	−0.483360
$213$	−4.78918e16	−0.164974
$214$	−2.84412e17	−0.945898
$215$	−1.17970e17	−0.378864
$216$	−5.36262e16	−0.166331
$217$	1.10067e17	0.329769
$218$	4.70845e17	1.36287
$219$	−6.42390e16	−0.179667
$220$	−2.27625e16	−0.0615248
$221$	4.21441e17	1.10102
$222$	1.76610e16	0.0446033
$223$	4.17711e17	1.01998	0.509988	−	0.860182i	$-0.329650\pi$
$223$	4.17711e17	1.01998	0.509988	+	0.860182i	$0.329650\pi$
$224$	3.27639e16	0.0773633
$225$	−8.24352e16	−0.188254
$226$	6.23261e16	0.137675
$227$	−2.08871e17	−0.446358	−0.223179	−	0.974777i	$-0.571643\pi$
$227$	−2.08871e17	−0.446358	−0.223179	+	0.974777i	$0.571643\pi$
$228$	−4.89697e16	−0.101255
$229$	7.31152e16	0.146299	0.0731496	−	0.997321i	$-0.476695\pi$
$229$	7.31152e16	0.146299	0.0731496	+	0.997321i	$0.476695\pi$
$230$	6.77481e16	0.131201
$231$	1.55668e16	0.0291816
$232$	1.53938e16	0.0279373
$233$	4.67231e17	0.821036	0.410518	−	0.911852i	$-0.365348\pi$
$233$	4.67231e17	0.821036	0.410518	+	0.911852i	$0.365348\pi$
$234$	2.42953e17	0.413431
$235$	−4.76074e17	−0.784632
$236$	−3.85301e17	−0.615120
$237$	1.24222e17	0.192125
$238$	3.66027e17	0.548512
$239$	−8.83271e17	−1.28266	−0.641328	−	0.767267i	$-0.721616\pi$
$239$	−8.83271e17	−1.28266	−0.641328	+	0.767267i	$0.721616\pi$
$240$	1.92519e16	0.0270949
$241$	4.55014e17	0.620722	0.310361	−	0.950619i	$-0.399550\pi$
$241$	4.55014e17	0.620722	0.310361	+	0.950619i	$0.399550\pi$
$242$	4.94209e17	0.653574
$243$	−5.23274e17	−0.670937
$244$	−5.13699e16	−0.0638682
$245$	2.99867e17	0.361562
$246$	2.16396e17	0.253067
$247$	4.57556e17	0.519059
$248$	2.42071e17	0.266413
$249$	−3.92405e17	−0.419024
$250$	6.10352e16	0.0632456
$251$	−9.59950e17	−0.965374	−0.482687	−	0.875793i	$-0.660339\pi$
$251$	−9.59950e17	−0.965374	−0.482687	+	0.875793i	$0.660339\pi$
$252$	2.11007e17	0.205965
$253$	1.20478e17	0.114157
$254$	−2.10077e17	−0.193252
$255$	2.15075e17	0.192105
$256$	7.20576e16	0.0625000
$257$	−9.58487e17	−0.807398	−0.403699	−	0.914892i	$-0.632276\pi$
$257$	−9.58487e17	−0.807398	−0.403699	+	0.914892i	$0.632276\pi$
$258$	1.77433e17	0.145173
$259$	−1.43320e17	−0.113909
$260$	−1.79883e17	−0.138896
$261$	9.91397e16	0.0743779
$262$	−1.24921e18	−0.910704
$263$	−2.62316e18	−1.85847	−0.929236	−	0.369487i	$-0.879533\pi$
$263$	−2.62316e18	−1.85847	−0.929236	+	0.369487i	$0.879533\pi$
$264$	3.42360e16	0.0235751
$265$	6.45892e17	0.432330
$266$	3.97393e17	0.258588
$267$	4.09962e17	0.259364
$268$	−5.90332e17	−0.363149
$269$	4.64128e17	0.277649	0.138824	−	0.990317i	$-0.455668\pi$
$269$	4.64128e17	0.277649	0.138824	+	0.990317i	$0.455668\pi$
$270$	2.55710e17	0.148771
$271$	3.27935e17	0.185574	0.0927871	−	0.995686i	$-0.470422\pi$
$271$	3.27935e17	0.185574	0.0927871	+	0.995686i	$0.470422\pi$
$272$	8.05003e17	0.443130
$273$	1.23018e17	0.0658791
$274$	1.50548e17	0.0784413
$275$	1.08540e17	0.0550295
$276$	−1.01897e17	−0.0502738
$277$	2.34150e18	1.12434	0.562169	−	0.827023i	$-0.309967\pi$
$277$	2.34150e18	1.12434	0.562169	+	0.827023i	$0.309967\pi$
$278$	−3.00166e18	−1.40289
$279$	1.55900e18	0.709274
$280$	−1.56230e17	−0.0691958
$281$	−1.87773e18	−0.809722	−0.404861	−	0.914378i	$-0.632680\pi$
$281$	−1.87773e18	−0.809722	−0.404861	+	0.914378i	$0.632680\pi$
$282$	7.16040e17	0.300655
$283$	2.84513e18	1.16333	0.581666	−	0.813427i	$-0.302401\pi$
$283$	2.84513e18	1.16333	0.581666	+	0.813427i	$0.302401\pi$
$284$	8.54749e17	0.340370
$285$	2.33506e17	0.0905651
$286$	−3.19889e17	−0.120852
$287$	−1.75607e18	−0.646290
$288$	4.64069e17	0.166394
$289$	6.13080e18	2.14182
$290$	−7.34032e16	−0.0249879
$291$	−1.66385e17	−0.0551972
$292$	1.14651e18	0.370685
$293$	5.35043e17	0.168609	0.0843047	−	0.996440i	$-0.473133\pi$
$293$	5.35043e17	0.168609	0.0843047	+	0.996440i	$0.473133\pi$
$294$	−4.51015e17	−0.138544
$295$	1.83726e18	0.550180
$296$	−3.15204e17	−0.0920246
$297$	4.54735e17	0.129445
$298$	−3.87062e18	−1.07438
$299$	9.52087e17	0.257717
$300$	−9.18000e16	−0.0242345
$301$	−1.43988e18	−0.370748
$302$	−3.63398e18	−0.912705
$303$	−1.46230e18	−0.358274
$304$	8.73986e17	0.208907
$305$	2.44951e17	0.0571255
$306$	5.18442e18	1.17975
$307$	−5.09810e18	−1.13206	−0.566031	−	0.824384i	$-0.691522\pi$
$307$	−5.09810e18	−1.13206	−0.566031	+	0.824384i	$0.691522\pi$
$308$	−2.77828e17	−0.0602068
$309$	−1.25984e18	−0.266458
$310$	−1.15428e18	−0.238287
$311$	−7.82502e18	−1.57682	−0.788411	−	0.615149i	$-0.789096\pi$
$311$	−7.82502e18	−1.57682	−0.788411	+	0.615149i	$0.789096\pi$
$312$	2.70553e17	0.0532222
$313$	−2.86136e18	−0.549528	−0.274764	−	0.961512i	$-0.588600\pi$
$313$	−2.86136e18	−0.549528	−0.274764	+	0.961512i	$0.588600\pi$
$314$	3.95203e18	0.741050
$315$	−1.00616e18	−0.184221
$316$	−2.21704e18	−0.396389
$317$	−7.45321e18	−1.30137	−0.650683	−	0.759350i	$-0.725517\pi$
$317$	−7.45321e18	−1.30137	−0.650683	+	0.759350i	$0.725517\pi$
$318$	−9.71454e17	−0.165660
$319$	−1.30535e17	−0.0217418
$320$	−3.43597e17	−0.0559017
$321$	−2.03976e18	−0.324185
$322$	8.26899e17	0.128391
$323$	9.76388e18	1.48117
$324$	2.79060e18	0.413628
$325$	8.57747e17	0.124232
$326$	7.57381e18	1.07197
$327$	3.37684e18	0.467092
$328$	−3.86212e18	−0.522122
$329$	−5.81072e18	−0.767822
$330$	−1.63250e17	−0.0210862
$331$	5.88563e18	0.743162	0.371581	−	0.928401i	$-0.378816\pi$
$331$	5.88563e18	0.743162	0.371581	+	0.928401i	$0.378816\pi$
$332$	7.00344e18	0.864522
$333$	−2.02999e18	−0.244998
$334$	−5.36444e18	−0.633033
$335$	2.81492e18	0.324811
$336$	2.34978e17	0.0265145
$337$	2.23642e18	0.246791	0.123395	−	0.992358i	$-0.460622\pi$
$337$	2.23642e18	0.246791	0.123395	+	0.992358i	$0.460622\pi$
$338$	4.02384e18	0.434276
$339$	4.46995e17	0.0471851
$340$	−3.83855e18	−0.396347
$341$	−2.05269e18	−0.207332
$342$	5.62869e18	0.556175
$343$	8.18708e18	0.791449
$344$	−3.16674e18	−0.299519
$345$	4.85881e17	0.0449663
$346$	8.71116e18	0.788869
$347$	1.58037e18	0.140052	0.0700258	−	0.997545i	$-0.477692\pi$
$347$	1.58037e18	0.140052	0.0700258	+	0.997545i	$0.477692\pi$
$348$	1.10402e17	0.00957488
$349$	−6.74552e18	−0.572565	−0.286282	−	0.958145i	$-0.592420\pi$
$349$	−6.74552e18	−0.572565	−0.286282	+	0.958145i	$0.592420\pi$
$350$	7.44964e17	0.0618906
$351$	3.59357e18	0.292229
$352$	−6.11027e17	−0.0486397
$353$	1.34977e19	1.05184	0.525920	−	0.850534i	$-0.323721\pi$
$353$	1.34977e19	1.05184	0.525920	+	0.850534i	$0.323721\pi$
$354$	−2.76333e18	−0.210818
$355$	−4.07576e18	−0.304436
$356$	−7.31679e18	−0.535113
$357$	2.62510e18	0.187990
$358$	−1.40979e19	−0.988628
$359$	−1.46040e19	−1.00291	−0.501457	−	0.865183i	$-0.667202\pi$
$359$	−1.46040e19	−1.00291	−0.501457	+	0.865183i	$0.667202\pi$
$360$	−2.21285e18	−0.148828
$361$	−4.58055e18	−0.301727
$362$	−2.39428e17	−0.0154476
$363$	3.54440e18	0.223998
$364$	−2.19556e18	−0.135920
$365$	−5.46696e18	−0.331551
$366$	−3.68418e17	−0.0218894
$367$	1.78654e19	1.03996	0.519980	−	0.854179i	$-0.325939\pi$
$367$	1.78654e19	1.03996	0.519980	+	0.854179i	$0.325939\pi$
$368$	1.81860e18	0.103724
$369$	−2.48730e19	−1.39005
$370$	1.50301e18	0.0823093
$371$	7.88342e18	0.423068
$372$	1.73610e18	0.0913068
$373$	6.15035e18	0.317018	0.158509	−	0.987358i	$-0.449331\pi$
$373$	6.15035e18	0.317018	0.158509	+	0.987358i	$0.449331\pi$
$374$	−6.82619e18	−0.344859
$375$	4.37737e17	0.0216760
$376$	−1.27795e19	−0.620306
$377$	−1.03156e18	−0.0490834
$378$	3.12106e18	0.145584
$379$	1.25656e19	0.574633	0.287316	−	0.957836i	$-0.407237\pi$
$379$	1.25656e19	0.574633	0.287316	+	0.957836i	$0.407237\pi$
$380$	−4.16749e18	−0.186852
$381$	−1.50664e18	−0.0662328
$382$	−2.37931e19	−1.02559
$383$	1.22018e19	0.515742	0.257871	−	0.966179i	$-0.416979\pi$
$383$	1.22018e19	0.515742	0.257871	+	0.966179i	$0.416979\pi$
$384$	5.16788e17	0.0214204
$385$	1.32479e18	0.0538506
$386$	1.63939e19	0.653546
$387$	−2.03946e19	−0.797412
$388$	2.96956e18	0.113882
$389$	−1.33006e19	−0.500321	−0.250161	−	0.968204i	$-0.580483\pi$
$389$	−1.33006e19	−0.500321	−0.250161	+	0.968204i	$0.580483\pi$
$390$	−1.29010e18	−0.0476033
$391$	2.03168e19	0.735410
$392$	8.04949e18	0.285840
$393$	−8.95921e18	−0.312123
$394$	−1.46496e19	−0.500730
$395$	1.05717e19	0.354541
$396$	−3.93517e18	−0.129494
$397$	−2.74241e18	−0.0885532	−0.0442766	−	0.999019i	$-0.514098\pi$
$397$	−2.74241e18	−0.0885532	−0.0442766	+	0.999019i	$0.514098\pi$
$398$	2.94360e19	0.932731
$399$	2.85005e18	0.0886249
$400$	1.63840e18	0.0500000
$401$	−3.40188e18	−0.101891	−0.0509455	−	0.998701i	$-0.516223\pi$
$401$	−3.40188e18	−0.101891	−0.0509455	+	0.998701i	$0.516223\pi$
$402$	−4.23378e18	−0.124461
$403$	−1.62215e19	−0.468063
$404$	2.60983e19	0.739184
$405$	−1.33066e19	−0.369960
$406$	−8.95922e17	−0.0244526
$407$	2.67284e18	0.0716167
$408$	5.77338e18	0.151872
$409$	4.83971e19	1.24996	0.624978	−	0.780642i	$-0.285108\pi$
$409$	4.83971e19	1.24996	0.624978	+	0.780642i	$0.285108\pi$
$410$	1.84160e19	0.467000
$411$	1.07971e18	0.0268839
$412$	2.24851e19	0.549750
$413$	2.24246e19	0.538393
$414$	1.17122e19	0.276145
$415$	−3.33950e19	−0.773252
$416$	−4.82869e18	−0.109807
$417$	−2.15275e19	−0.480810
$418$	−7.41115e18	−0.162579
$419$	7.81533e19	1.68400	0.842000	−	0.539478i	$-0.181378\pi$
$419$	7.81533e19	1.68400	0.842000	+	0.539478i	$0.181378\pi$
$420$	−1.12046e18	−0.0237153
$421$	1.47668e19	0.307023	0.153511	−	0.988147i	$-0.450942\pi$
$421$	1.47668e19	0.307023	0.153511	+	0.988147i	$0.450942\pi$
$422$	−2.35713e19	−0.481437
$423$	−8.23033e19	−1.65145
$424$	1.73380e19	0.341787
$425$	1.83037e19	0.354504
$426$	6.13015e18	0.116654
$427$	2.98974e18	0.0559017
$428$	3.64047e19	0.668851
$429$	−2.29421e18	−0.0414193
$430$	1.51002e19	0.267898
$431$	−8.96929e19	−1.56379	−0.781896	−	0.623409i	$-0.785747\pi$
$431$	−8.96929e19	−1.56379	−0.781896	+	0.623409i	$0.785747\pi$
$432$	6.86416e18	0.117614
$433$	−1.13182e20	−1.90598	−0.952988	−	0.303007i	$-0.902009\pi$
$433$	−1.13182e20	−1.90598	−0.952988	+	0.303007i	$0.902009\pi$
$434$	−1.40886e19	−0.233182
$435$	−5.26439e17	−0.00856404
$436$	−6.02682e19	−0.963694
$437$	2.20578e19	0.346698
$438$	8.22259e18	0.127044
$439$	−5.19380e19	−0.788863	−0.394431	−	0.918925i	$-0.629058\pi$
$439$	−5.19380e19	−0.788863	−0.394431	+	0.918925i	$0.629058\pi$
$440$	2.91360e18	0.0435046
$441$	5.18407e19	0.760995
$442$	−5.39445e19	−0.778538
$443$	−3.90249e19	−0.553750	−0.276875	−	0.960906i	$-0.589299\pi$
$443$	−3.90249e19	−0.553750	−0.276875	+	0.960906i	$0.589299\pi$
$444$	−2.26060e18	−0.0315393
$445$	3.48892e19	0.478620
$446$	−5.34671e19	−0.721232
$447$	−2.77596e19	−0.368220
$448$	−4.19377e18	−0.0547041
$449$	2.33062e19	0.298967	0.149484	−	0.988764i	$-0.452239\pi$
$449$	2.33062e19	0.298967	0.149484	+	0.988764i	$0.452239\pi$
$450$	1.05517e19	0.133116
$451$	3.27497e19	0.406334
$452$	−7.97774e18	−0.0973513
$453$	−2.60625e19	−0.312809
$454$	2.67354e19	0.315623
$455$	1.04692e19	0.121571
$456$	6.26812e18	0.0715980
$457$	1.39663e20	1.56931	0.784655	−	0.619933i	$-0.212840\pi$
$457$	1.39663e20	1.56931	0.784655	+	0.619933i	$0.212840\pi$
$458$	−9.35875e18	−0.103449
$459$	7.66840e19	0.833892
$460$	−8.67176e18	−0.0927734
$461$	7.29158e19	0.767476	0.383738	−	0.923442i	$-0.374637\pi$
$461$	7.29158e19	0.767476	0.383738	+	0.923442i	$0.374637\pi$
$462$	−1.99255e18	−0.0206345
$463$	−8.27075e18	−0.0842728	−0.0421364	−	0.999112i	$-0.513416\pi$
$463$	−8.27075e18	−0.0842728	−0.0421364	+	0.999112i	$0.513416\pi$
$464$	−1.97040e18	−0.0197547
$465$	−8.27838e18	−0.0816673
$466$	−5.98056e19	−0.580560
$467$	1.00791e19	0.0962824	0.0481412	−	0.998841i	$-0.484670\pi$
$467$	1.00791e19	0.0962824	0.0481412	+	0.998841i	$0.484670\pi$
$468$	−3.10980e19	−0.292340
$469$	3.43575e19	0.317852
$470$	6.09375e19	0.554818
$471$	2.83434e19	0.253978
$472$	4.93185e19	0.434955
$473$	2.68530e19	0.233096
$474$	−1.59004e19	−0.135853
$475$	1.98721e19	0.167125
$476$	−4.68514e19	−0.387856
$477$	1.11661e20	0.909943
$478$	1.13059e20	0.906974
$479$	−2.74663e19	−0.216912	−0.108456	−	0.994101i	$-0.534591\pi$
$479$	−2.74663e19	−0.216912	−0.108456	+	0.994101i	$0.534591\pi$
$480$	−2.46424e18	−0.0191590
$481$	2.11223e19	0.161679
$482$	−5.82418e19	−0.438917
$483$	5.93042e18	0.0440029
$484$	−6.32587e19	−0.462147
$485$	−1.41600e19	−0.101859
$486$	6.69790e19	0.474424
$487$	−1.98772e20	−1.38640	−0.693198	−	0.720747i	$-0.743799\pi$
$487$	−1.98772e20	−1.38640	−0.693198	+	0.720747i	$0.743799\pi$
$488$	6.57535e18	0.0451617
$489$	5.43184e19	0.367393
$490$	−3.83830e19	−0.255663
$491$	1.45614e19	0.0955198	0.0477599	−	0.998859i	$-0.484792\pi$
$491$	1.45614e19	0.0955198	0.0477599	+	0.998859i	$0.484792\pi$
$492$	−2.76987e19	−0.178945
$493$	−2.20127e19	−0.140062
$494$	−5.85671e19	−0.367030
$495$	1.87643e19	0.115823
$496$	−3.09851e19	−0.188382
$497$	−4.97467e19	−0.297914
$498$	5.02278e19	0.296295
$499$	−1.07372e20	−0.623932	−0.311966	−	0.950093i	$-0.600988\pi$
$499$	−1.07372e20	−0.623932	−0.311966	+	0.950093i	$0.600988\pi$
$500$	−7.81250e18	−0.0447214
$501$	−3.84731e19	−0.216957
$502$	1.22874e20	0.682623
$503$	−6.30371e19	−0.345014	−0.172507	−	0.985008i	$-0.555187\pi$
$503$	−6.30371e19	−0.345014	−0.172507	+	0.985008i	$0.555187\pi$
$504$	−2.70090e19	−0.145639
$505$	−1.24446e20	−0.661146
$506$	−1.54212e19	−0.0807215
$507$	2.88585e19	0.148838
$508$	2.68898e19	0.136650
$509$	−3.12584e20	−1.56525	−0.782624	−	0.622494i	$-0.786119\pi$
$509$	−3.12584e20	−1.56525	−0.782624	+	0.622494i	$0.786119\pi$
$510$	−2.75296e19	−0.135839
$511$	−6.67270e19	−0.324448
$512$	−9.22337e18	−0.0441942
$513$	8.32553e19	0.393126
$514$	1.22686e20	0.570917
$515$	−1.07217e20	−0.491711
$516$	−2.27114e19	−0.102653
$517$	1.08367e20	0.482743
$518$	1.83450e19	0.0805460
$519$	6.24753e19	0.270367
$520$	2.30250e19	0.0982142
$521$	−1.18550e20	−0.498449	−0.249224	−	0.968446i	$-0.580176\pi$
$521$	−1.18550e20	−0.498449	−0.249224	+	0.968446i	$0.580176\pi$
$522$	−1.26899e19	−0.0525931
$523$	3.27493e20	1.33795	0.668975	−	0.743285i	$-0.266733\pi$
$523$	3.27493e20	1.33795	0.668975	+	0.743285i	$0.266733\pi$
$524$	1.59899e20	0.643965
$525$	5.34279e18	0.0212116
$526$	3.35764e20	1.31414
$527$	−3.46155e20	−1.33564
$528$	−4.38221e18	−0.0166701
$529$	−2.20737e20	−0.827862
$530$	−8.26741e19	−0.305704
$531$	3.17623e20	1.15799
$532$	−5.08663e19	−0.182849
$533$	2.58807e20	0.917321
$534$	−5.24751e19	−0.183398
$535$	−1.73591e20	−0.598238
$536$	7.55625e19	0.256785
$537$	−1.01109e20	−0.338829
$538$	−5.94084e19	−0.196327
$539$	−6.82573e19	−0.222451
$540$	−3.27308e19	−0.105197
$541$	−1.74748e18	−0.00553902	−0.00276951	−	0.999996i	$-0.500882\pi$
$541$	−1.74748e18	−0.00553902	−0.00276951	+	0.999996i	$0.500882\pi$
$542$	−4.19756e19	−0.131221
$543$	−1.71715e18	−0.00529431
$544$	−1.03040e20	−0.313340
$545$	2.87381e20	0.861955
$546$	−1.57463e19	−0.0465835
$547$	5.08896e20	1.48499	0.742495	−	0.669851i	$-0.233642\pi$
$547$	5.08896e20	1.48499	0.742495	+	0.669851i	$0.233642\pi$
$548$	−1.92701e19	−0.0554664
$549$	4.23469e19	0.120234
$550$	−1.38932e19	−0.0389117
$551$	−2.38990e19	−0.0660302
$552$	1.30428e19	0.0355489
$553$	1.29033e20	0.346946
$554$	−2.99712e20	−0.795027
$555$	1.07794e19	0.0282096
$556$	3.84212e20	0.991996
$557$	−1.86800e20	−0.475842	−0.237921	−	0.971284i	$-0.576466\pi$
$557$	−1.86800e20	−0.475842	−0.237921	+	0.971284i	$0.576466\pi$
$558$	−1.99552e20	−0.501532
$559$	2.12208e20	0.526227
$560$	1.99975e19	0.0489288
$561$	−4.89566e19	−0.118192
$562$	2.40350e20	0.572560
$563$	6.50191e20	1.52837	0.764185	−	0.644998i	$-0.223142\pi$
$563$	6.50191e20	1.52837	0.764185	+	0.644998i	$0.223142\pi$
$564$	−9.16531e19	−0.212595
$565$	3.80408e19	0.0870736
$566$	−3.64177e20	−0.822600
$567$	−1.62414e20	−0.362035
$568$	−1.09408e20	−0.240678
$569$	−2.25474e20	−0.489501	−0.244751	−	0.969586i	$-0.578706\pi$
$569$	−2.25474e20	−0.489501	−0.244751	+	0.969586i	$0.578706\pi$
$570$	−2.98887e19	−0.0640392
$571$	−2.96425e20	−0.626823	−0.313411	−	0.949617i	$-0.601472\pi$
$571$	−2.96425e20	−0.626823	−0.313411	+	0.949617i	$0.601472\pi$
$572$	4.09459e19	0.0854554
$573$	−1.70641e20	−0.351498
$574$	2.24777e20	0.456996
$575$	4.13502e19	0.0829791
$576$	−5.94008e19	−0.117659
$577$	3.14895e20	0.615669	0.307834	−	0.951440i	$-0.400396\pi$
$577$	3.14895e20	0.615669	0.307834	+	0.951440i	$0.400396\pi$
$578$	−7.84743e20	−1.51450
$579$	1.17575e20	0.223988
$580$	9.39561e18	0.0176691
$581$	−4.07603e20	−0.756686
$582$	2.12973e19	0.0390303
$583$	−1.47021e20	−0.265991
$584$	−1.46753e20	−0.262114
$585$	1.48287e20	0.261477
$586$	−6.84855e19	−0.119225
$587$	9.02661e19	0.155145	0.0775727	−	0.996987i	$-0.475283\pi$
$587$	9.02661e19	0.155145	0.0775727	+	0.996987i	$0.475283\pi$
$588$	5.77299e19	0.0979651
$589$	−3.75818e20	−0.629670
$590$	−2.35169e20	−0.389036
$591$	−1.05065e20	−0.171614
$592$	4.03461e19	0.0650712
$593$	−7.79096e20	−1.24074	−0.620370	−	0.784309i	$-0.713018\pi$
$593$	−7.79096e20	−1.24074	−0.620370	+	0.784309i	$0.713018\pi$
$594$	−5.82060e19	−0.0915313
$595$	2.23405e20	0.346909
$596$	4.95439e20	0.759702
$597$	2.11112e20	0.319672
$598$	−1.21867e20	−0.182233
$599$	5.67360e20	0.837834	0.418917	−	0.908025i	$-0.362410\pi$
$599$	5.67360e20	0.837834	0.418917	+	0.908025i	$0.362410\pi$
$600$	1.17504e19	0.0171363
$601$	−1.16608e21	−1.67947	−0.839733	−	0.542999i	$-0.817289\pi$
$601$	−1.16608e21	−1.67947	−0.839733	+	0.542999i	$0.817289\pi$
$602$	1.84305e20	0.262158
$603$	4.86641e20	0.683642
$604$	4.65150e20	0.645380
$605$	3.01641e20	0.413357
$606$	1.87174e20	0.253338
$607$	−1.25651e21	−1.67978	−0.839889	−	0.542758i	$-0.817380\pi$
$607$	−1.25651e21	−1.67978	−0.839889	+	0.542758i	$0.817380\pi$
$608$	−1.11870e20	−0.147719
$609$	−6.42544e18	−0.00838057
$610$	−3.13537e19	−0.0403938
$611$	8.56375e20	1.08982
$612$	−6.63606e20	−0.834209
$613$	−6.82643e20	−0.847696	−0.423848	−	0.905733i	$-0.639321\pi$
$613$	−6.82643e20	−0.847696	−0.423848	+	0.905733i	$0.639321\pi$
$614$	6.52556e20	0.800489
$615$	1.32078e20	0.160054
$616$	3.55620e19	0.0425726
$617$	8.18292e20	0.967764	0.483882	−	0.875133i	$-0.339226\pi$
$617$	8.18292e20	0.967764	0.483882	+	0.875133i	$0.339226\pi$
$618$	1.61260e20	0.188414
$619$	1.56583e21	1.80745	0.903723	−	0.428119i	$-0.140823\pi$
$619$	1.56583e21	1.80745	0.903723	+	0.428119i	$0.140823\pi$
$620$	1.47748e20	0.168494
$621$	1.73239e20	0.195190
$622$	1.00160e21	1.11498
$623$	4.25840e20	0.468366
$624$	−3.46307e19	−0.0376337
$625$	3.72529e19	0.0400000
$626$	3.66254e20	0.388575
$627$	−5.31518e19	−0.0557201
$628$	−5.05860e20	−0.524002
$629$	4.50733e20	0.461360
$630$	1.28789e20	0.130264
$631$	−1.35170e21	−1.35101	−0.675506	−	0.737355i	$-0.736075\pi$
$631$	−1.35170e21	−1.35101	−0.675506	+	0.737355i	$0.736075\pi$
$632$	2.83782e20	0.280289
$633$	−1.69050e20	−0.165001
$634$	9.54011e20	0.920204
$635$	−1.28221e20	−0.122223
$636$	1.24346e20	0.117140
$637$	−5.39409e20	−0.502195
$638$	1.67084e19	0.0153738
$639$	−7.04614e20	−0.640759
$640$	4.39805e19	0.0395285
$641$	1.68209e21	1.49422	0.747111	−	0.664699i	$-0.231440\pi$
$641$	1.68209e21	1.49422	0.747111	+	0.664699i	$0.231440\pi$
$642$	2.61090e20	0.229233
$643$	−4.44180e20	−0.385458	−0.192729	−	0.981252i	$-0.561734\pi$
$643$	−4.44180e20	−0.385458	−0.192729	+	0.981252i	$0.561734\pi$
$644$	−1.05843e20	−0.0907859
$645$	1.08297e20	0.0918157
$646$	−1.24978e21	−1.04734
$647$	−1.61572e21	−1.33840	−0.669198	−	0.743084i	$-0.733362\pi$
$647$	−1.61572e21	−1.33840	−0.669198	+	0.743084i	$0.733362\pi$
$648$	−3.57197e20	−0.292479
$649$	−4.18206e20	−0.338497
$650$	−1.09792e20	−0.0878454
$651$	−1.01042e20	−0.0799178
$652$	−9.69447e20	−0.757996
$653$	−6.08831e20	−0.470596	−0.235298	−	0.971923i	$-0.575607\pi$
$653$	−6.08831e20	−0.470596	−0.235298	+	0.971923i	$0.575607\pi$
$654$	−4.32236e20	−0.330284
$655$	−7.62460e20	−0.575980
$656$	4.94352e20	0.369196
$657$	−9.45124e20	−0.697828
$658$	7.43772e20	0.542932
$659$	1.57653e21	1.13779	0.568893	−	0.822412i	$-0.307372\pi$
$659$	1.57653e21	1.13779	0.568893	+	0.822412i	$0.307372\pi$
$660$	2.08960e19	0.0149102
$661$	−1.06777e21	−0.753301	−0.376650	−	0.926355i	$-0.622924\pi$
$661$	−1.06777e21	−0.753301	−0.376650	+	0.926355i	$0.622924\pi$
$662$	−7.53361e20	−0.525495
$663$	−3.86883e20	−0.266826
$664$	−8.96441e20	−0.611309
$665$	2.42549e20	0.163545
$666$	2.59839e20	0.173240
$667$	−4.97293e19	−0.0327845
$668$	6.86649e20	0.447622
$669$	−3.83459e20	−0.247186
$670$	−3.60310e20	−0.229676
$671$	−5.57570e19	−0.0351464
$672$	−3.00772e19	−0.0187486
$673$	1.36637e21	0.842281	0.421140	−	0.906995i	$-0.361630\pi$
$673$	1.36637e21	0.842281	0.421140	+	0.906995i	$0.361630\pi$
$674$	−2.86262e20	−0.174507
$675$	1.56073e20	0.0940912
$676$	−5.15052e20	−0.307080
$677$	2.90704e21	1.71410	0.857049	−	0.515235i	$-0.172295\pi$
$677$	2.90704e21	1.71410	0.857049	+	0.515235i	$0.172295\pi$
$678$	−5.72154e19	−0.0333649
$679$	−1.72829e20	−0.0996767
$680$	4.91335e20	0.280260
$681$	1.91743e20	0.108172
$682$	2.62744e20	0.146606
$683$	7.40733e20	0.408796	0.204398	−	0.978888i	$-0.434476\pi$
$683$	7.40733e20	0.408796	0.204398	+	0.978888i	$0.434476\pi$
$684$	−7.20472e20	−0.393275
$685$	9.18870e19	0.0496106
$686$	−1.04795e21	−0.559639
$687$	−6.71198e19	−0.0354548
$688$	4.05342e20	0.211792
$689$	−1.16185e21	−0.600489
$690$	−6.21928e19	−0.0317959
$691$	5.35533e20	0.270832	0.135416	−	0.990789i	$-0.456763\pi$
$691$	5.35533e20	0.270832	0.135416	+	0.990789i	$0.456763\pi$
$692$	−1.11503e21	−0.557815
$693$	2.29028e20	0.113342
$694$	−2.02288e20	−0.0990315
$695$	−1.83207e21	−0.887268
$696$	−1.41315e19	−0.00677046
$697$	5.52273e21	2.61763
$698$	8.63426e20	0.404864
$699$	−4.28918e20	−0.198974
$700$	−9.53554e19	−0.0437633
$701$	3.32394e21	1.50927	0.754637	−	0.656142i	$-0.227813\pi$
$701$	3.32394e21	1.50927	0.754637	+	0.656142i	$0.227813\pi$
$702$	−4.59977e20	−0.206637
$703$	4.89358e20	0.217501
$704$	7.82115e19	0.0343934
$705$	4.37036e20	0.190151
$706$	−1.72771e21	−0.743763
$707$	−1.51893e21	−0.646982
$708$	3.53706e20	0.149071
$709$	−2.00277e21	−0.835189	−0.417595	−	0.908633i	$-0.637127\pi$
$709$	−2.00277e21	−0.835189	−0.417595	+	0.908633i	$0.637127\pi$
$710$	5.21697e20	0.215269
$711$	1.82763e21	0.746217
$712$	9.36550e20	0.378382
$713$	−7.82006e20	−0.312636
$714$	−3.36013e20	−0.132929
$715$	−1.95245e20	−0.0764337
$716$	1.80454e21	0.699065
$717$	8.10843e20	0.310844
$718$	1.86931e21	0.709167
$719$	−4.22930e21	−1.58782	−0.793911	−	0.608033i	$-0.791959\pi$
$719$	−4.22930e21	−1.58782	−0.793911	+	0.608033i	$0.791959\pi$
$720$	2.83245e20	0.105237
$721$	−1.30864e21	−0.481177
$722$	5.86311e20	0.213353
$723$	−4.17703e20	−0.150429
$724$	3.06468e19	0.0109231
$725$	−4.48018e19	−0.0158038
$726$	−4.53684e20	−0.158390
$727$	−1.04718e21	−0.361838	−0.180919	−	0.983498i	$-0.557907\pi$
$727$	−1.04718e21	−0.361838	−0.180919	+	0.983498i	$0.557907\pi$
$728$	2.81031e20	0.0961101
$729$	−1.96361e21	−0.664659
$730$	6.99771e20	0.234442
$731$	4.52835e21	1.50162
$732$	4.71576e19	0.0154781
$733$	−6.14856e19	−0.0199753	−0.00998766	−	0.999950i	$-0.503179\pi$
$733$	−6.14856e19	−0.0199753	−0.00998766	+	0.999950i	$0.503179\pi$
$734$	−2.28677e21	−0.735363
$735$	−2.75278e20	−0.0876226
$736$	−2.32781e20	−0.0733438
$737$	−6.40747e20	−0.199839
$738$	3.18375e21	0.982915
$739$	4.00685e21	1.22453	0.612265	−	0.790652i	$-0.290258\pi$
$739$	4.00685e21	1.22453	0.612265	+	0.790652i	$0.290258\pi$
$740$	−1.92385e20	−0.0582015
$741$	−4.20036e20	−0.125791
$742$	−1.00908e21	−0.299155
$743$	−4.55846e21	−1.33783	−0.668916	−	0.743338i	$-0.733241\pi$
$743$	−4.55846e21	−1.33783	−0.668916	+	0.743338i	$0.733241\pi$
$744$	−2.22221e20	−0.0645637
$745$	−2.36244e21	−0.679499
$746$	−7.87244e20	−0.224165
$747$	−5.77330e21	−1.62750
$748$	8.73752e20	0.243852
$749$	−2.11876e21	−0.585422
$750$	−5.60303e19	−0.0153272
$751$	−3.38681e21	−0.917258	−0.458629	−	0.888628i	$-0.651659\pi$
$751$	−3.38681e21	−0.917258	−0.458629	+	0.888628i	$0.651659\pi$
$752$	1.63578e21	0.438622
$753$	8.81234e20	0.233953
$754$	1.32040e20	0.0347072
$755$	−2.21801e21	−0.577246
$756$	−3.99496e20	−0.102944
$757$	6.56517e21	1.67505	0.837524	−	0.546401i	$-0.184003\pi$
$757$	6.56517e21	1.67505	0.837524	+	0.546401i	$0.184003\pi$
$758$	−1.60840e21	−0.406327
$759$	−1.10599e20	−0.0276654
$760$	5.33439e20	0.132124
$761$	−1.48142e21	−0.363324	−0.181662	−	0.983361i	$-0.558148\pi$
$761$	−1.48142e21	−0.363324	−0.181662	+	0.983361i	$0.558148\pi$
$762$	1.92850e20	0.0468336
$763$	3.50763e21	0.843489
$764$	3.04551e21	0.725204
$765$	3.16432e21	0.746139
$766$	−1.56183e21	−0.364684
$767$	−3.30491e21	−0.764177
$768$	−6.61489e19	−0.0151465
$769$	−1.98526e21	−0.450162	−0.225081	−	0.974340i	$-0.572265\pi$
$769$	−1.98526e21	−0.450162	−0.225081	+	0.974340i	$0.572265\pi$
$770$	−1.69573e20	−0.0380781
$771$	8.79891e20	0.195669
$772$	−2.09841e21	−0.462127
$773$	−5.63698e21	−1.22942	−0.614710	−	0.788753i	$-0.710727\pi$
$773$	−5.63698e21	−1.22942	−0.614710	+	0.788753i	$0.710727\pi$
$774$	2.61051e21	0.563855
$775$	−7.04519e20	−0.150706
$776$	−3.80103e20	−0.0805265
$777$	1.31568e20	0.0276053
$778$	1.70248e21	0.353780
$779$	5.99599e21	1.23404
$780$	1.65132e20	0.0336606
$781$	9.27747e20	0.187304
$782$	−2.60055e21	−0.520013
$783$	−1.87699e20	−0.0371748
$784$	−1.03033e21	−0.202119
$785$	2.41213e21	0.468681
$786$	1.14678e21	0.220704
$787$	2.51295e21	0.479041	0.239521	−	0.970891i	$-0.423010\pi$
$787$	2.51295e21	0.479041	0.239521	+	0.970891i	$0.423010\pi$
$788$	1.87515e21	0.354070
$789$	2.40806e21	0.450390
$790$	−1.35318e21	−0.250698
$791$	4.64307e20	0.0852082
$792$	5.03701e20	0.0915660
$793$	−4.40624e20	−0.0793449
$794$	3.51029e20	0.0626166
$795$	−5.92929e20	−0.104773
$796$	−3.76781e21	−0.659540
$797$	−3.92010e21	−0.679766	−0.339883	−	0.940468i	$-0.610387\pi$
$797$	−3.92010e21	−0.679766	−0.339883	+	0.940468i	$0.610387\pi$
$798$	−3.64807e20	−0.0626673
$799$	1.82744e22	3.10987
$800$	−2.09715e20	−0.0353553
$801$	6.03161e21	1.00737
$802$	4.35440e20	0.0720478
$803$	1.24442e21	0.203986
$804$	5.41924e20	0.0880072
$805$	5.04699e20	0.0812014
$806$	2.07636e21	0.330970
$807$	−4.26070e20	−0.0672867
$808$	−3.34059e21	−0.522682
$809$	−3.88505e21	−0.602257	−0.301129	−	0.953584i	$-0.597363\pi$
$809$	−3.88505e21	−0.602257	−0.301129	+	0.953584i	$0.597363\pi$
$810$	1.70325e21	0.261602
$811$	−4.70714e21	−0.716310	−0.358155	−	0.933662i	$-0.616594\pi$
$811$	−4.70714e21	−0.716310	−0.358155	+	0.933662i	$0.616594\pi$
$812$	1.14678e20	0.0172906
$813$	−3.01044e20	−0.0449729
$814$	−3.42123e20	−0.0506407
$815$	4.62268e21	0.677973
$816$	−7.38993e20	−0.107390
$817$	4.91640e21	0.707916
$818$	−6.19483e21	−0.883853
$819$	1.80991e21	0.255875
$820$	−2.35725e21	−0.330219
$821$	−4.61086e21	−0.640041	−0.320021	−	0.947411i	$-0.603690\pi$
$821$	−4.61086e21	−0.640041	−0.320021	+	0.947411i	$0.603690\pi$
$822$	−1.38203e20	−0.0190098
$823$	4.54021e21	0.618838	0.309419	−	0.950926i	$-0.399865\pi$
$823$	4.54021e21	0.618838	0.309419	+	0.950926i	$0.399865\pi$
$824$	−2.87809e21	−0.388732
$825$	−9.96399e19	−0.0133361
$826$	−2.87035e21	−0.380702
$827$	−8.33406e21	−1.09538	−0.547690	−	0.836681i	$-0.684493\pi$
$827$	−8.33406e21	−1.09538	−0.547690	+	0.836681i	$0.684493\pi$
$828$	−1.49917e21	−0.195264
$829$	−6.21441e21	−0.802123	−0.401061	−	0.916051i	$-0.631359\pi$
$829$	−6.21441e21	−0.802123	−0.401061	+	0.916051i	$0.631359\pi$
$830$	4.27456e21	0.546772
$831$	−2.14950e21	−0.272477
$832$	6.18072e20	0.0776451
$833$	−1.15106e22	−1.43304
$834$	2.75552e21	0.339984
$835$	−3.27420e21	−0.400365
$836$	9.48627e20	0.114960
$837$	−2.95162e21	−0.354502
$838$	−1.00036e22	−1.19077
$839$	5.99543e20	0.0707304	0.0353652	−	0.999374i	$-0.488741\pi$
$839$	5.99543e20	0.0707304	0.0353652	+	0.999374i	$0.488741\pi$
$840$	1.43419e20	0.0167692
$841$	−8.57531e21	−0.993756
$842$	−1.89015e21	−0.217098
$843$	1.72376e21	0.196232
$844$	3.01712e21	0.340427
$845$	2.45596e21	0.274660
$846$	1.05348e22	1.16775
$847$	3.68168e21	0.404501
$848$	−2.21927e21	−0.241680
$849$	−2.61183e21	−0.281927
$850$	−2.34287e21	−0.250672
$851$	1.01826e21	0.107991
$852$	−7.84660e20	−0.0824868
$853$	−5.35432e21	−0.557938	−0.278969	−	0.960300i	$-0.589993\pi$
$853$	−5.35432e21	−0.557938	−0.278969	+	0.960300i	$0.589993\pi$
$854$	−3.82687e20	−0.0395285
$855$	3.43548e21	0.351756
$856$	−4.65980e21	−0.472949
$857$	9.25366e21	0.931016	0.465508	−	0.885044i	$-0.345872\pi$
$857$	9.25366e21	0.931016	0.465508	+	0.885044i	$0.345872\pi$
$858$	2.93659e20	0.0292879
$859$	−1.83196e21	−0.181120	−0.0905600	−	0.995891i	$-0.528866\pi$
$859$	−1.83196e21	−0.181120	−0.0905600	+	0.995891i	$0.528866\pi$
$860$	−1.93282e21	−0.189432
$861$	1.61207e21	0.156625
$862$	1.14807e22	1.10577
$863$	3.51203e21	0.335334	0.167667	−	0.985844i	$-0.446377\pi$
$863$	3.51203e21	0.335334	0.167667	+	0.985844i	$0.446377\pi$
$864$	−8.78612e20	−0.0831657
$865$	5.31687e21	0.498925
$866$	1.44873e22	1.34773
$867$	−5.62808e21	−0.519059
$868$	1.80334e21	0.164885
$869$	−2.40639e21	−0.218131
$870$	6.73842e19	0.00605569
$871$	−5.06355e21	−0.451148
$872$	7.71433e21	0.681435
$873$	−2.44796e21	−0.214387
$874$	−2.82340e21	−0.245152
$875$	4.54690e20	0.0391431
$876$	−1.05249e21	−0.0898334
$877$	1.19989e22	1.01542	0.507710	−	0.861528i	$-0.330492\pi$
$877$	1.19989e22	1.01542	0.507710	+	0.861528i	$0.330492\pi$
$878$	6.64807e21	0.557810
$879$	−4.91170e20	−0.0408616
$880$	−3.72941e20	−0.0307624
$881$	−7.70134e21	−0.629864	−0.314932	−	0.949114i	$-0.601982\pi$
$881$	−7.70134e21	−0.629864	−0.314932	+	0.949114i	$0.601982\pi$
$882$	−6.63561e21	−0.538105
$883$	1.74096e22	1.39986	0.699929	−	0.714212i	$-0.253215\pi$
$883$	1.74096e22	1.39986	0.699929	+	0.714212i	$0.253215\pi$
$884$	6.90489e21	0.550510
$885$	−1.68660e21	−0.133333
$886$	4.99518e21	0.391560
$887$	−9.86355e21	−0.766666	−0.383333	−	0.923610i	$-0.625224\pi$
$887$	−9.86355e21	−0.766666	−0.383333	+	0.923610i	$0.625224\pi$
$888$	2.89357e20	0.0223017
$889$	−1.56499e21	−0.119605
$890$	−4.46582e21	−0.338435
$891$	3.02893e21	0.227618
$892$	6.84378e21	0.509988
$893$	1.98404e22	1.46610
$894$	3.55323e21	0.260371
$895$	−8.60470e21	−0.625263
$896$	5.36803e20	0.0386817
$897$	−8.74016e20	−0.0624563
$898$	−2.98319e21	−0.211402
$899$	8.47282e20	0.0595429
$900$	−1.35062e21	−0.0941269
$901$	−2.47929e22	−1.71353
$902$	−4.19196e21	−0.287321
$903$	1.32181e21	0.0898488
$904$	1.02115e21	0.0688377
$905$	−1.46135e20	−0.00976992
$906$	3.33599e21	0.221189
$907$	2.23495e21	0.146965	0.0734825	−	0.997297i	$-0.476589\pi$
$907$	2.23495e21	0.146965	0.0734825	+	0.997297i	$0.476589\pi$
$908$	−3.42214e21	−0.223179
$909$	−2.15142e22	−1.39154
$910$	−1.34006e21	−0.0859635
$911$	2.93366e22	1.86647	0.933237	−	0.359260i	$-0.116971\pi$
$911$	2.93366e22	1.86647	0.933237	+	0.359260i	$0.116971\pi$
$912$	−8.02319e20	−0.0506274
$913$	7.60155e21	0.475742
$914$	−1.78768e22	−1.10967
$915$	−2.24865e20	−0.0138441
$916$	1.19792e21	0.0731496
$917$	−9.30620e21	−0.563641
$918$	−9.81556e21	−0.589651
$919$	−3.75300e21	−0.223621	−0.111810	−	0.993730i	$-0.535665\pi$
$919$	−3.75300e21	−0.223621	−0.111810	+	0.993730i	$0.535665\pi$
$920$	1.10999e21	0.0656007
$921$	4.68005e21	0.274349
$922$	−9.33322e21	−0.542687
$923$	7.33159e21	0.422849
$924$	2.55046e20	0.0145908
$925$	9.17364e20	0.0520570
$926$	1.05866e21	0.0595899
$927$	−1.85356e22	−1.03492
$928$	2.52212e20	0.0139687
$929$	−9.10883e21	−0.500432	−0.250216	−	0.968190i	$-0.580502\pi$
$929$	−9.10883e21	−0.500432	−0.250216	+	0.968190i	$0.580502\pi$
$930$	1.05963e21	0.0577475
$931$	−1.24969e22	−0.675586
$932$	7.65511e21	0.410518
$933$	7.18337e21	0.382134
$934$	−1.29013e21	−0.0680819
$935$	−4.16638e21	−0.218108
$936$	3.98054e21	0.206715
$937$	5.95960e21	0.307023	0.153511	−	0.988147i	$-0.450942\pi$
$937$	5.95960e21	0.307023	0.153511	+	0.988147i	$0.450942\pi$
$938$	−4.39776e21	−0.224755
$939$	2.62673e21	0.133175
$940$	−7.80000e21	−0.392316
$941$	2.84336e22	1.41876	0.709382	−	0.704824i	$-0.248974\pi$
$941$	2.84336e22	1.41876	0.709382	+	0.704824i	$0.248974\pi$
$942$	−3.62796e21	−0.179589
$943$	1.24765e22	0.612711
$944$	−6.31277e21	−0.307560
$945$	1.90495e21	0.0920755
$946$	−3.43718e21	−0.164824
$947$	−2.37984e22	−1.13220	−0.566100	−	0.824337i	$-0.691548\pi$
$947$	−2.37984e22	−1.13220	−0.566100	+	0.824337i	$0.691548\pi$
$948$	2.03525e21	0.0960627
$949$	9.83412e21	0.460510
$950$	−2.54363e21	−0.118176
$951$	6.84205e21	0.315379
$952$	5.99698e21	0.274256
$953$	2.82670e22	1.28258	0.641289	−	0.767300i	$-0.278400\pi$
$953$	2.82670e22	1.28258	0.641289	+	0.767300i	$0.278400\pi$
$954$	−1.42926e22	−0.643427
$955$	−1.45221e22	−0.648642
$956$	−1.44715e22	−0.641328
$957$	1.19831e20	0.00526901
$958$	3.51569e21	0.153380
$959$	1.12153e21	0.0485478
$960$	3.15422e20	0.0135475
$961$	−1.01415e22	−0.432194
$962$	−2.70365e21	−0.114324
$963$	−3.00103e22	−1.25914
$964$	7.45495e21	0.310361
$965$	1.00060e22	0.413339
$966$	−7.59093e20	−0.0311148
$967$	2.76539e22	1.12475	0.562377	−	0.826881i	$-0.309887\pi$
$967$	2.76539e22	1.12475	0.562377	+	0.826881i	$0.309887\pi$
$968$	8.09711e21	0.326787
$969$	−8.96324e21	−0.358952
$970$	1.81247e21	0.0720251
$971$	−2.65287e22	−1.04610	−0.523048	−	0.852303i	$-0.675205\pi$
$971$	−2.65287e22	−1.04610	−0.523048	+	0.852303i	$0.675205\pi$
$972$	−8.57332e21	−0.335469
$973$	−2.23613e22	−0.868260
$974$	2.54428e22	0.980330
$975$	−7.87412e20	−0.0301070
$976$	−8.41644e20	−0.0319341
$977$	2.77737e22	1.04574	0.522871	−	0.852412i	$-0.324861\pi$
$977$	2.77737e22	1.04574	0.522871	+	0.852412i	$0.324861\pi$
$978$	−6.95275e21	−0.259786
$979$	−7.94166e21	−0.294470
$980$	4.91302e21	0.180781
$981$	4.96822e22	1.81419
$982$	−1.86387e21	−0.0675427
$983$	3.52259e22	1.26681	0.633403	−	0.773822i	$-0.281657\pi$
$983$	3.52259e22	1.26681	0.633403	+	0.773822i	$0.281657\pi$
$984$	3.54543e21	0.126533
$985$	−8.94140e21	−0.316690
$986$	2.81762e21	0.0990389
$987$	5.33424e21	0.186078
$988$	7.49659e21	0.259530
$989$	1.02301e22	0.351485
$990$	−2.40184e21	−0.0818991
$991$	−3.75141e21	−0.126953	−0.0634763	−	0.997983i	$-0.520219\pi$
$991$	−3.75141e21	−0.126953	−0.0634763	+	0.997983i	$0.520219\pi$
$992$	3.96609e21	0.133206
$993$	−5.40301e21	−0.180101
$994$	6.36757e21	0.210657
$995$	1.79663e22	0.589911
$996$	−6.42916e21	−0.209512
$997$	2.77450e22	0.897368	0.448684	−	0.893691i	$-0.351893\pi$
$997$	2.77450e22	0.897368	0.448684	+	0.893691i	$0.351893\pi$
$998$	1.37436e22	0.441187
$999$	3.84334e21	0.122453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.16.a.b.1.1	✓	1
3.2	odd	2		90.16.a.h.1.1		1
4.3	odd	2		80.16.a.a.1.1		1
5.2	odd	4		50.16.b.c.49.1		2
5.3	odd	4		50.16.b.c.49.2		2
5.4	even	2		50.16.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.16.a.b.1.1	✓	1	1.1	even	1	trivial
50.16.a.c.1.1		1	5.4	even	2
50.16.b.c.49.1		2	5.2	odd	4
50.16.b.c.49.2		2	5.3	odd	4
80.16.a.a.1.1		1	4.3	odd	2
90.16.a.h.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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