LMFDB - Embedded newform 10.12.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,12,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, 12, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
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:	$7.68343180560$
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)

$f(q)$

$=$

\(q-32.0000 q^{2} +738.000 q^{3} +1024.00 q^{4} -3125.00 q^{5} -23616.0 q^{6} +25574.0 q^{7} -32768.0 q^{8} +367497. q^{9} +100000. q^{10} +769152. q^{11} +755712. q^{12} -918982. q^{13} -818368. q^{14} -2.30625e6 q^{15} +1.04858e6 q^{16} +1.03128e7 q^{17} -1.17599e7 q^{18} -5.52166e6 q^{19} -3.20000e6 q^{20} +1.88736e7 q^{21} -2.46129e7 q^{22} -3.99734e7 q^{23} -2.41828e7 q^{24} +9.76562e6 q^{25} +2.94074e7 q^{26} +1.40478e8 q^{27} +2.61878e7 q^{28} -1.52690e7 q^{29} +7.38000e7 q^{30} -2.41584e8 q^{31} -3.35544e7 q^{32} +5.67634e8 q^{33} -3.30009e8 q^{34} -7.99188e7 q^{35} +3.76317e8 q^{36} -2.57514e7 q^{37} +1.76693e8 q^{38} -6.78209e8 q^{39} +1.02400e8 q^{40} -1.21770e9 q^{41} -6.03956e8 q^{42} -6.83436e8 q^{43} +7.87612e8 q^{44} -1.14843e9 q^{45} +1.27915e9 q^{46} +1.53740e9 q^{47} +7.73849e8 q^{48} -1.32330e9 q^{49} -3.12500e8 q^{50} +7.61084e9 q^{51} -9.41038e8 q^{52} +3.57289e9 q^{53} -4.49531e9 q^{54} -2.40360e9 q^{55} -8.38009e8 q^{56} -4.07499e9 q^{57} +4.88608e8 q^{58} -1.06904e9 q^{59} -2.36160e9 q^{60} -2.09154e9 q^{61} +7.73068e9 q^{62} +9.39837e9 q^{63} +1.07374e9 q^{64} +2.87182e9 q^{65} -1.81643e10 q^{66} -1.46237e9 q^{67} +1.05603e10 q^{68} -2.95004e10 q^{69} +2.55740e9 q^{70} +9.66018e9 q^{71} -1.20421e10 q^{72} -5.60345e9 q^{73} +8.24046e8 q^{74} +7.20703e9 q^{75} -5.65418e9 q^{76} +1.96703e10 q^{77} +2.17027e10 q^{78} +5.02694e9 q^{79} -3.27680e9 q^{80} +3.85720e10 q^{81} +3.89664e10 q^{82} -3.84060e10 q^{83} +1.93266e10 q^{84} -3.22275e10 q^{85} +2.18700e10 q^{86} -1.12685e10 q^{87} -2.52036e10 q^{88} +3.55586e10 q^{89} +3.67497e10 q^{90} -2.35020e10 q^{91} -4.09328e10 q^{92} -1.78289e11 q^{93} -4.91966e10 q^{94} +1.72552e10 q^{95} -2.47632e10 q^{96} +1.05722e10 q^{97} +4.23455e10 q^{98} +2.82661e11 q^{99} +O(q^{100})\)

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−32.0000	−0.707107
$2$	−32.0000	−0.707107
$3$	738.000	1.75343	0.876717	−	0.481006i	$-0.159729\pi$
$3$	738.000	1.75343	0.876717	+	0.481006i	$0.159729\pi$
$4$	1024.00	0.500000
$5$	−3125.00	−0.447214
$5$	−3125.00	−0.447214
$6$	−23616.0	−1.23987
$7$	25574.0	0.575121	0.287561	−	0.957762i	$-0.407156\pi$
$7$	25574.0	0.575121	0.287561	+	0.957762i	$0.407156\pi$
$8$	−32768.0	−0.353553
$9$	367497.	2.07453
$10$	100000.	0.316228
$11$	769152.	1.43997	0.719983	−	0.693991i	$-0.244149\pi$
$11$	769152.	1.43997	0.719983	+	0.693991i	$0.244149\pi$
$12$	755712.	0.876717
$13$	−918982.	−0.686465	−0.343233	−	0.939250i	$-0.611522\pi$
$13$	−918982.	−0.686465	−0.343233	+	0.939250i	$0.611522\pi$
$14$	−818368.	−0.406672
$15$	−2.30625e6	−0.784160
$16$	1.04858e6	0.250000
$17$	1.03128e7	1.76160	0.880800	−	0.473489i	$-0.157005\pi$
$17$	1.03128e7	1.76160	0.880800	+	0.473489i	$0.157005\pi$
$18$	−1.17599e7	−1.46692
$19$	−5.52166e6	−0.511593	−0.255797	−	0.966731i	$-0.582338\pi$
$19$	−5.52166e6	−0.511593	−0.255797	+	0.966731i	$0.582338\pi$
$20$	−3.20000e6	−0.223607
$21$	1.88736e7	1.00844
$22$	−2.46129e7	−1.01821
$23$	−3.99734e7	−1.29500	−0.647498	−	0.762067i	$-0.724184\pi$
$23$	−3.99734e7	−1.29500	−0.647498	+	0.762067i	$0.724184\pi$
$24$	−2.41828e7	−0.619933
$25$	9.76562e6	0.200000
$26$	2.94074e7	0.485404
$27$	1.40478e8	1.88412
$28$	2.61878e7	0.287561
$29$	−1.52690e7	−0.138236	−0.0691181	−	0.997608i	$-0.522019\pi$
$29$	−1.52690e7	−0.138236	−0.0691181	+	0.997608i	$0.522019\pi$
$30$	7.38000e7	0.554485
$31$	−2.41584e8	−1.51558	−0.757789	−	0.652499i	$-0.773721\pi$
$31$	−2.41584e8	−1.51558	−0.757789	+	0.652499i	$0.773721\pi$
$32$	−3.35544e7	−0.176777
$33$	5.67634e8	2.52489
$34$	−3.30009e8	−1.24564
$35$	−7.99188e7	−0.257202
$36$	3.76317e8	1.03727
$37$	−2.57514e7	−0.0610509	−0.0305255	−	0.999534i	$-0.509718\pi$
$37$	−2.57514e7	−0.0610509	−0.0305255	+	0.999534i	$0.509718\pi$
$38$	1.76693e8	0.361751
$39$	−6.78209e8	−1.20367
$40$	1.02400e8	0.158114
$41$	−1.21770e9	−1.64146	−0.820728	−	0.571319i	$-0.806432\pi$
$41$	−1.21770e9	−1.64146	−0.820728	+	0.571319i	$0.806432\pi$
$42$	−6.03956e8	−0.713073
$43$	−6.83436e8	−0.708960	−0.354480	−	0.935064i	$-0.615342\pi$
$43$	−6.83436e8	−0.708960	−0.354480	+	0.935064i	$0.615342\pi$
$44$	7.87612e8	0.719983
$45$	−1.14843e9	−0.927759
$46$	1.27915e9	0.915700
$47$	1.53740e9	0.977794	0.488897	−	0.872342i	$-0.337399\pi$
$47$	1.53740e9	0.977794	0.488897	+	0.872342i	$0.337399\pi$
$48$	7.73849e8	0.438359
$49$	−1.32330e9	−0.669236
$50$	−3.12500e8	−0.141421
$51$	7.61084e9	3.08885
$52$	−9.41038e8	−0.343233
$53$	3.57289e9	1.17355	0.586776	−	0.809749i	$-0.300397\pi$
$53$	3.57289e9	1.17355	0.586776	+	0.809749i	$0.300397\pi$
$54$	−4.49531e9	−1.33227
$55$	−2.40360e9	−0.643973
$56$	−8.38009e8	−0.203336
$57$	−4.07499e9	−0.897045
$58$	4.88608e8	0.0977478
$59$	−1.06904e9	−0.194674	−0.0973369	−	0.995251i	$-0.531032\pi$
$59$	−1.06904e9	−0.194674	−0.0973369	+	0.995251i	$0.531032\pi$
$60$	−2.36160e9	−0.392080
$61$	−2.09154e9	−0.317067	−0.158534	−	0.987354i	$-0.550677\pi$
$61$	−2.09154e9	−0.317067	−0.158534	+	0.987354i	$0.550677\pi$
$62$	7.73068e9	1.07168
$63$	9.39837e9	1.19311
$64$	1.07374e9	0.125000
$65$	2.87182e9	0.306997
$66$	−1.81643e10	−1.78536
$67$	−1.46237e9	−0.132326	−0.0661631	−	0.997809i	$-0.521076\pi$
$67$	−1.46237e9	−0.132326	−0.0661631	+	0.997809i	$0.521076\pi$
$68$	1.05603e10	0.880800
$69$	−2.95004e10	−2.27069
$70$	2.55740e9	0.181869
$71$	9.66018e9	0.635425	0.317712	−	0.948187i	$-0.397085\pi$
$71$	9.66018e9	0.635425	0.317712	+	0.948187i	$0.397085\pi$
$72$	−1.20421e10	−0.733458
$73$	−5.60345e9	−0.316359	−0.158179	−	0.987410i	$-0.550562\pi$
$73$	−5.60345e9	−0.316359	−0.158179	+	0.987410i	$0.550562\pi$
$74$	8.24046e8	0.0431695
$75$	7.20703e9	0.350687
$76$	−5.65418e9	−0.255797
$77$	1.96703e10	0.828155
$78$	2.17027e10	0.851124
$79$	5.02694e9	0.183804	0.0919019	−	0.995768i	$-0.470705\pi$
$79$	5.02694e9	0.183804	0.0919019	+	0.995768i	$0.470705\pi$
$80$	−3.27680e9	−0.111803
$81$	3.85720e10	1.22915
$82$	3.89664e10	1.16068
$83$	−3.84060e10	−1.07021	−0.535105	−	0.844786i	$-0.679728\pi$
$83$	−3.84060e10	−1.07021	−0.535105	+	0.844786i	$0.679728\pi$
$84$	1.93266e10	0.504219
$85$	−3.22275e10	−0.787811
$86$	2.18700e10	0.501310
$87$	−1.12685e10	−0.242388
$88$	−2.52036e10	−0.509105
$89$	3.55586e10	0.674993	0.337497	−	0.941327i	$-0.390420\pi$
$89$	3.55586e10	0.674993	0.337497	+	0.941327i	$0.390420\pi$
$90$	3.67497e10	0.656024
$91$	−2.35020e10	−0.394801
$92$	−4.09328e10	−0.647498
$93$	−1.78289e11	−2.65747
$94$	−4.91966e10	−0.691405
$95$	1.72552e10	0.228791
$96$	−2.47632e10	−0.309966
$97$	1.05722e10	0.125003	0.0625017	−	0.998045i	$-0.480092\pi$
$97$	1.05722e10	0.125003	0.0625017	+	0.998045i	$0.480092\pi$
$98$	4.23455e10	0.473221
$99$	2.82661e11	2.98726
$100$	1.00000e10	0.100000
$101$	−8.84365e10	−0.837267	−0.418634	−	0.908155i	$-0.637491\pi$
$101$	−8.84365e10	−0.837267	−0.418634	+	0.908155i	$0.637491\pi$
$102$	−2.43547e11	−2.18415
$103$	1.73197e10	0.147210	0.0736048	−	0.997287i	$-0.476550\pi$
$103$	1.73197e10	0.147210	0.0736048	+	0.997287i	$0.476550\pi$
$104$	3.01132e10	0.242702
$105$	−5.89800e10	−0.450987
$106$	−1.14333e11	−0.829827
$107$	2.26284e11	1.55971	0.779855	−	0.625960i	$-0.215293\pi$
$107$	2.26284e11	1.55971	0.779855	+	0.625960i	$0.215293\pi$
$108$	1.43850e11	0.942060
$109$	−9.66241e10	−0.601506	−0.300753	−	0.953702i	$-0.597238\pi$
$109$	−9.66241e10	−0.601506	−0.300753	+	0.953702i	$0.597238\pi$
$110$	7.69152e10	0.455357
$111$	−1.90046e10	−0.107049
$112$	2.68163e10	0.143780
$113$	2.26933e11	1.15869	0.579345	−	0.815083i	$-0.303309\pi$
$113$	2.26933e11	1.15869	0.579345	+	0.815083i	$0.303309\pi$
$114$	1.30400e11	0.634307
$115$	1.24917e11	0.579140
$116$	−1.56355e10	−0.0691181
$117$	−3.37723e11	−1.42409
$118$	3.42092e10	0.137655
$119$	2.63739e11	1.01313
$120$	7.55712e10	0.277242
$121$	3.06283e11	1.07350
$122$	6.69291e10	0.224200
$123$	−8.98663e11	−2.87818
$124$	−2.47382e11	−0.757789
$125$	−3.05176e10	−0.0894427
$126$	−3.00748e11	−0.843654
$127$	9.72988e10	0.261329	0.130664	−	0.991427i	$-0.458289\pi$
$127$	9.72988e10	0.261329	0.130664	+	0.991427i	$0.458289\pi$
$128$	−3.43597e10	−0.0883883
$129$	−5.04376e11	−1.24311
$130$	−9.18982e10	−0.217079
$131$	3.04354e11	0.689267	0.344634	−	0.938737i	$-0.388003\pi$
$131$	3.04354e11	0.689267	0.344634	+	0.938737i	$0.388003\pi$
$132$	5.81257e11	1.26244
$133$	−1.41211e11	−0.294228
$134$	4.67958e10	0.0935687
$135$	−4.38995e11	−0.842604
$136$	−3.37930e11	−0.622820
$137$	6.91218e11	1.22364	0.611818	−	0.790999i	$-0.290439\pi$
$137$	6.91218e11	1.22364	0.611818	+	0.790999i	$0.290439\pi$
$138$	9.44012e11	1.60562
$139$	−5.76365e11	−0.942142	−0.471071	−	0.882095i	$-0.656133\pi$
$139$	−5.76365e11	−0.942142	−0.471071	+	0.882095i	$0.656133\pi$
$140$	−8.18368e10	−0.128601
$141$	1.13460e12	1.71450
$142$	−3.09126e11	−0.449313
$143$	−7.06837e11	−0.988487
$144$	3.85349e11	0.518633
$145$	4.77157e10	0.0618211
$146$	1.79310e11	0.223699
$147$	−9.76593e11	−1.17346
$148$	−2.63695e10	−0.0305255
$149$	−1.68636e12	−1.88117	−0.940583	−	0.339565i	$-0.889720\pi$
$149$	−1.68636e12	−1.88117	−0.940583	+	0.339565i	$0.889720\pi$
$150$	−2.30625e11	−0.247973
$151$	−9.63792e10	−0.0999103	−0.0499551	−	0.998751i	$-0.515908\pi$
$151$	−9.63792e10	−0.0999103	−0.0499551	+	0.998751i	$0.515908\pi$
$152$	1.80934e11	0.180876
$153$	3.78992e12	3.65449
$154$	−6.29449e11	−0.585594
$155$	7.54949e11	0.677787
$156$	−6.94486e11	−0.601836
$157$	1.46946e12	1.22945	0.614725	−	0.788741i	$-0.289267\pi$
$157$	1.46946e12	1.22945	0.614725	+	0.788741i	$0.289267\pi$
$158$	−1.60862e11	−0.129969
$159$	2.63679e12	2.05775
$160$	1.04858e11	0.0790569
$161$	−1.02228e12	−0.744779
$162$	−1.23430e12	−0.869140
$163$	7.35409e11	0.500607	0.250304	−	0.968167i	$-0.419470\pi$
$163$	7.35409e11	0.500607	0.250304	+	0.968167i	$0.419470\pi$
$164$	−1.24692e12	−0.820728
$165$	−1.77386e12	−1.12916
$166$	1.22899e12	0.756753
$167$	−2.76551e12	−1.64753	−0.823767	−	0.566929i	$-0.808131\pi$
$167$	−2.76551e12	−1.64753	−0.823767	+	0.566929i	$0.808131\pi$
$168$	−6.18451e11	−0.356536
$169$	−9.47632e11	−0.528765
$170$	1.03128e12	0.557067
$171$	−2.02919e12	−1.06132
$172$	−6.99839e11	−0.354480
$173$	−5.19253e11	−0.254757	−0.127378	−	0.991854i	$-0.540656\pi$
$173$	−5.19253e11	−0.254757	−0.127378	+	0.991854i	$0.540656\pi$
$174$	3.60593e11	0.171394
$175$	2.49746e11	0.115024
$176$	8.06514e11	0.359992
$177$	−7.88951e11	−0.341348
$178$	−1.13787e12	−0.477292
$179$	−1.34822e12	−0.548365	−0.274183	−	0.961678i	$-0.588407\pi$
$179$	−1.34822e12	−0.548365	−0.274183	+	0.961678i	$0.588407\pi$
$180$	−1.17599e12	−0.463879
$181$	2.23738e12	0.856067	0.428033	−	0.903763i	$-0.359207\pi$
$181$	2.23738e12	0.856067	0.428033	+	0.903763i	$0.359207\pi$
$182$	7.52065e11	0.279166
$183$	−1.54355e12	−0.555956
$184$	1.30985e12	0.457850
$185$	8.04733e10	0.0273028
$186$	5.70524e12	1.87911
$187$	7.93211e12	2.53664
$188$	1.57429e12	0.488897
$189$	3.59259e12	1.08360
$190$	−5.52166e11	−0.161780
$191$	−6.30421e12	−1.79452	−0.897258	−	0.441507i	$-0.854444\pi$
$191$	−6.30421e12	−1.79452	−0.897258	+	0.441507i	$0.854444\pi$
$192$	7.92421e11	0.219179
$193$	−4.20897e12	−1.13139	−0.565693	−	0.824616i	$-0.691391\pi$
$193$	−4.20897e12	−1.13139	−0.565693	+	0.824616i	$0.691391\pi$
$194$	−3.38311e11	−0.0883908
$195$	2.11940e12	0.538298
$196$	−1.35506e12	−0.334618
$197$	1.26338e12	0.303368	0.151684	−	0.988429i	$-0.451530\pi$
$197$	1.26338e12	0.303368	0.151684	+	0.988429i	$0.451530\pi$
$198$	−9.04515e12	−2.11231
$199$	4.57100e12	1.03829	0.519145	−	0.854686i	$-0.326250\pi$
$199$	4.57100e12	1.03829	0.519145	+	0.854686i	$0.326250\pi$
$200$	−3.20000e11	−0.0707107
$201$	−1.07923e12	−0.232025
$202$	2.82997e12	0.592037
$203$	−3.90490e11	−0.0795026
$204$	7.79350e12	1.54442
$205$	3.80531e12	0.734081
$206$	−5.54231e11	−0.104093
$207$	−1.46901e13	−2.68651
$208$	−9.63622e11	−0.171616
$209$	−4.24700e12	−0.736677
$210$	1.88736e12	0.318896
$211$	1.84263e12	0.303309	0.151655	−	0.988434i	$-0.451540\pi$
$211$	1.84263e12	0.303309	0.151655	+	0.988434i	$0.451540\pi$
$212$	3.65864e12	0.586776
$213$	7.12921e12	1.11418
$214$	−7.24110e12	−1.10288
$215$	2.13574e12	0.317056
$216$	−4.60319e12	−0.666137
$217$	−6.17826e12	−0.871642
$218$	3.09197e12	0.425329
$219$	−4.13534e12	−0.554714
$220$	−2.46129e12	−0.321986
$221$	−9.47727e12	−1.20928
$222$	6.08146e11	0.0756949
$223$	5.98599e12	0.726875	0.363437	−	0.931619i	$-0.381603\pi$
$223$	5.98599e12	0.726875	0.363437	+	0.931619i	$0.381603\pi$
$224$	−8.58121e11	−0.101668
$225$	3.58884e12	0.414906
$226$	−7.26187e12	−0.819317
$227$	4.69750e12	0.517278	0.258639	−	0.965974i	$-0.416726\pi$
$227$	4.69750e12	0.517278	0.258639	+	0.965974i	$0.416726\pi$
$228$	−4.17278e12	−0.448523
$229$	1.02879e13	1.07952	0.539759	−	0.841820i	$-0.318515\pi$
$229$	1.02879e13	1.07952	0.539759	+	0.841820i	$0.318515\pi$
$230$	−3.99734e12	−0.409514
$231$	1.45167e13	1.45212
$232$	5.00335e11	0.0488739
$233$	3.58800e12	0.342290	0.171145	−	0.985246i	$-0.445253\pi$
$233$	3.58800e12	0.342290	0.171145	+	0.985246i	$0.445253\pi$
$234$	1.08071e13	1.00699
$235$	−4.80436e12	−0.437283
$236$	−1.09470e12	−0.0973369
$237$	3.70988e12	0.322288
$238$	−8.43966e12	−0.716394
$239$	1.12937e13	0.936800	0.468400	−	0.883517i	$-0.344831\pi$
$239$	1.12937e13	0.936800	0.468400	+	0.883517i	$0.344831\pi$
$240$	−2.41828e12	−0.196040
$241$	−5.85420e12	−0.463846	−0.231923	−	0.972734i	$-0.574502\pi$
$241$	−5.85420e12	−0.463846	−0.231923	+	0.972734i	$0.574502\pi$
$242$	−9.80106e12	−0.759082
$243$	3.58082e12	0.271112
$244$	−2.14173e12	−0.158534
$245$	4.13530e12	0.299291
$246$	2.87572e13	2.03518
$247$	5.07431e12	0.351191
$248$	7.91622e12	0.535838
$249$	−2.83436e13	−1.87654
$250$	9.76562e11	0.0632456
$251$	1.36866e13	0.867145	0.433572	−	0.901119i	$-0.357253\pi$
$251$	1.36866e13	0.867145	0.433572	+	0.901119i	$0.357253\pi$
$252$	9.62393e12	0.596554
$253$	−3.07456e13	−1.86475
$254$	−3.11356e12	−0.184787
$255$	−2.37839e13	−1.38138
$256$	1.09951e12	0.0625000
$257$	−1.47897e13	−0.822860	−0.411430	−	0.911441i	$-0.634971\pi$
$257$	−1.47897e13	−0.822860	−0.411430	+	0.911441i	$0.634971\pi$
$258$	1.61400e13	0.879014
$259$	−6.58567e11	−0.0351117
$260$	2.94074e12	0.153498
$261$	−5.61132e12	−0.286775
$262$	−9.73934e12	−0.487385
$263$	3.33643e13	1.63503	0.817514	−	0.575909i	$-0.195352\pi$
$263$	3.33643e13	1.63503	0.817514	+	0.575909i	$0.195352\pi$
$264$	−1.86002e13	−0.892682
$265$	−1.11653e13	−0.524829
$266$	4.51875e12	0.208051
$267$	2.62422e13	1.18356
$268$	−1.49747e12	−0.0661631
$269$	−3.44100e11	−0.0148952	−0.00744762	−	0.999972i	$-0.502371\pi$
$269$	−3.44100e11	−0.0148952	−0.00744762	+	0.999972i	$0.502371\pi$
$270$	1.40478e13	0.595811
$271$	−1.57978e13	−0.656546	−0.328273	−	0.944583i	$-0.606467\pi$
$271$	−1.57978e13	−0.656546	−0.328273	+	0.944583i	$0.606467\pi$
$272$	1.08137e13	0.440400
$273$	−1.73445e13	−0.692257
$274$	−2.21190e13	−0.865241
$275$	7.51125e12	0.287993
$276$	−3.02084e13	−1.13534
$277$	1.76707e13	0.651051	0.325525	−	0.945533i	$-0.394459\pi$
$277$	1.76707e13	0.651051	0.325525	+	0.945533i	$0.394459\pi$
$278$	1.84437e13	0.666195
$279$	−8.87813e13	−3.14412
$280$	2.61878e12	0.0909347
$281$	1.06554e13	0.362816	0.181408	−	0.983408i	$-0.441935\pi$
$281$	1.06554e13	0.362816	0.181408	+	0.983408i	$0.441935\pi$
$282$	−3.63071e13	−1.21233
$283$	5.42001e13	1.77490	0.887451	−	0.460902i	$-0.152474\pi$
$283$	5.42001e13	1.77490	0.887451	+	0.460902i	$0.152474\pi$
$284$	9.89202e12	0.317712
$285$	1.27343e13	0.401171
$286$	2.26188e13	0.698966
$287$	−3.11415e13	−0.944036
$288$	−1.23312e13	−0.366729
$289$	7.20818e13	2.10323
$290$	−1.52690e12	−0.0437141
$291$	7.80231e12	0.219185
$292$	−5.73793e12	−0.158179
$293$	−7.08232e12	−0.191604	−0.0958018	−	0.995400i	$-0.530542\pi$
$293$	−7.08232e12	−0.191604	−0.0958018	+	0.995400i	$0.530542\pi$
$294$	3.12510e13	0.829762
$295$	3.34075e12	0.0870608
$296$	8.43823e11	0.0215848
$297$	1.08049e14	2.71307
$298$	5.39637e13	1.33018
$299$	3.67349e13	0.888969
$300$	7.38000e12	0.175343
$301$	−1.74782e13	−0.407738
$302$	3.08413e12	0.0706472
$303$	−6.52662e13	−1.46809
$304$	−5.78988e12	−0.127898
$305$	6.53605e12	0.141797
$306$	−1.21277e14	−2.58412
$307$	−5.83026e13	−1.22019	−0.610095	−	0.792329i	$-0.708869\pi$
$307$	−5.83026e13	−1.22019	−0.610095	+	0.792329i	$0.708869\pi$
$308$	2.01424e13	0.414078
$309$	1.27820e13	0.258122
$310$	−2.41584e13	−0.479268
$311$	4.47811e13	0.872796	0.436398	−	0.899754i	$-0.356254\pi$
$311$	4.47811e13	0.872796	0.436398	+	0.899754i	$0.356254\pi$
$312$	2.22235e13	0.425562
$313$	−9.71664e13	−1.82819	−0.914097	−	0.405495i	$-0.867099\pi$
$313$	−9.71664e13	−1.82819	−0.914097	+	0.405495i	$0.867099\pi$
$314$	−4.70229e13	−0.869353
$315$	−2.93699e13	−0.533574
$316$	5.14758e12	0.0919019
$317$	−5.38908e13	−0.945560	−0.472780	−	0.881181i	$-0.656749\pi$
$317$	−5.38908e13	−0.945560	−0.472780	+	0.881181i	$0.656749\pi$
$318$	−8.43774e13	−1.45505
$319$	−1.17442e13	−0.199056
$320$	−3.35544e12	−0.0559017
$321$	1.66998e14	2.73485
$322$	3.27130e13	0.526639
$323$	−5.69437e13	−0.901223
$324$	3.94977e13	0.614574
$325$	−8.97443e12	−0.137293
$326$	−2.35331e13	−0.353983
$327$	−7.13086e13	−1.05470
$328$	3.99016e13	0.580342
$329$	3.93173e13	0.562350
$330$	5.67634e13	0.798439
$331$	3.08291e13	0.426488	0.213244	−	0.976999i	$-0.431597\pi$
$331$	3.08291e13	0.426488	0.213244	+	0.976999i	$0.431597\pi$
$332$	−3.93277e13	−0.535105
$333$	−9.46358e12	−0.126652
$334$	8.84962e13	1.16498
$335$	4.56990e12	0.0591780
$336$	1.97904e13	0.252109
$337$	−1.38550e13	−0.173638	−0.0868188	−	0.996224i	$-0.527670\pi$
$337$	−1.38550e13	−0.173638	−0.0868188	+	0.996224i	$0.527670\pi$
$338$	3.03242e13	0.373894
$339$	1.67477e14	2.03169
$340$	−3.30009e13	−0.393906
$341$	−1.85815e14	−2.18238
$342$	6.49342e13	0.750464
$343$	−8.44102e13	−0.960013
$344$	2.23948e13	0.250655
$345$	9.21887e13	1.01548
$346$	1.66161e13	0.180140
$347$	−6.14870e13	−0.656101	−0.328051	−	0.944660i	$-0.606392\pi$
$347$	−6.14870e13	−0.656101	−0.328051	+	0.944660i	$0.606392\pi$
$348$	−1.15390e13	−0.121194
$349$	−9.31373e13	−0.962905	−0.481453	−	0.876472i	$-0.659891\pi$
$349$	−9.31373e13	−0.962905	−0.481453	+	0.876472i	$0.659891\pi$
$350$	−7.99187e12	−0.0813344
$351$	−1.29097e14	−1.29338
$352$	−2.58085e13	−0.254553
$353$	1.04175e14	1.01158	0.505791	−	0.862656i	$-0.331201\pi$
$353$	1.04175e14	1.01158	0.505791	+	0.862656i	$0.331201\pi$
$354$	2.52464e13	0.241369
$355$	−3.01881e13	−0.284171
$356$	3.64120e13	0.337497
$357$	1.94640e14	1.77646
$358$	4.31431e13	0.387753
$359$	8.83142e13	0.781647	0.390824	−	0.920466i	$-0.372190\pi$
$359$	8.83142e13	0.781647	0.390824	+	0.920466i	$0.372190\pi$
$360$	3.76317e13	0.328012
$361$	−8.60015e13	−0.738272
$362$	−7.15962e13	−0.605331
$363$	2.26037e14	1.88232
$364$	−2.40661e13	−0.197400
$365$	1.75108e13	0.141480
$366$	4.93937e13	0.393120
$367$	1.28309e14	1.00599	0.502996	−	0.864289i	$-0.332231\pi$
$367$	1.28309e14	1.00599	0.502996	+	0.864289i	$0.332231\pi$
$368$	−4.19152e13	−0.323749
$369$	−4.47501e14	−3.40525
$370$	−2.57514e12	−0.0193060
$371$	9.13731e13	0.674935
$372$	−1.82568e14	−1.32873
$373$	1.08177e14	0.775773	0.387886	−	0.921707i	$-0.373205\pi$
$373$	1.08177e14	0.775773	0.387886	+	0.921707i	$0.373205\pi$
$374$	−2.53827e14	−1.79368
$375$	−2.25220e13	−0.156832
$376$	−5.03774e13	−0.345702
$377$	1.40319e13	0.0948944
$378$	−1.14963e14	−0.766219
$379$	2.49029e14	1.63582	0.817908	−	0.575348i	$-0.195134\pi$
$379$	2.49029e14	1.63582	0.817908	+	0.575348i	$0.195134\pi$
$380$	1.76693e13	0.114396
$381$	7.18065e13	0.458223
$382$	2.01735e14	1.26891
$383$	−2.99433e14	−1.85655	−0.928275	−	0.371894i	$-0.878709\pi$
$383$	−2.99433e14	−1.85655	−0.928275	+	0.371894i	$0.878709\pi$
$384$	−2.53575e13	−0.154983
$385$	−6.14697e13	−0.370362
$386$	1.34687e14	0.800011
$387$	−2.51161e14	−1.47076
$388$	1.08260e13	0.0625017
$389$	3.05298e13	0.173780	0.0868902	−	0.996218i	$-0.472307\pi$
$389$	3.05298e13	0.173780	0.0868902	+	0.996218i	$0.472307\pi$
$390$	−6.78209e13	−0.380634
$391$	−4.12238e14	−2.28126
$392$	4.33618e13	0.236610
$393$	2.24614e14	1.20858
$394$	−4.04281e13	−0.214513
$395$	−1.57092e13	−0.0821995
$396$	2.89445e14	1.49363
$397$	3.46957e14	1.76575	0.882873	−	0.469611i	$-0.155606\pi$
$397$	3.46957e14	1.76575	0.882873	+	0.469611i	$0.155606\pi$
$398$	−1.46272e14	−0.734182
$399$	−1.04214e14	−0.515910
$400$	1.02400e13	0.0500000
$401$	2.73373e14	1.31662	0.658312	−	0.752746i	$-0.271271\pi$
$401$	2.73373e14	1.31662	0.658312	+	0.752746i	$0.271271\pi$
$402$	3.45353e13	0.164067
$403$	2.22011e14	1.04039
$404$	−9.05590e13	−0.418634
$405$	−1.20537e14	−0.549692
$406$	1.24957e13	0.0562168
$407$	−1.98068e13	−0.0879113
$408$	−2.49392e14	−1.09207
$409$	−1.59143e14	−0.687558	−0.343779	−	0.939050i	$-0.611707\pi$
$409$	−1.59143e14	−0.687558	−0.343779	+	0.939050i	$0.611707\pi$
$410$	−1.21770e14	−0.519074
$411$	5.10119e14	2.14556
$412$	1.77354e13	0.0736048
$413$	−2.73396e13	−0.111961
$414$	4.70084e14	1.89965
$415$	1.20019e14	0.478613
$416$	3.08359e13	0.121351
$417$	−4.25358e14	−1.65198
$418$	1.35904e14	0.520909
$419$	−1.01759e14	−0.384941	−0.192471	−	0.981303i	$-0.561650\pi$
$419$	−1.01759e14	−0.384941	−0.192471	+	0.981303i	$0.561650\pi$
$420$	−6.03956e13	−0.225493
$421$	−1.40104e14	−0.516295	−0.258148	−	0.966105i	$-0.583112\pi$
$421$	−1.40104e14	−0.516295	−0.258148	+	0.966105i	$0.583112\pi$
$422$	−5.89643e13	−0.214472
$423$	5.64988e14	2.02846
$424$	−1.17077e14	−0.414913
$425$	1.00711e14	0.352320
$426$	−2.28135e14	−0.787841
$427$	−5.34889e13	−0.182352
$428$	2.31715e14	0.779855
$429$	−5.21646e14	−1.73325
$430$	−6.83436e13	−0.224193
$431$	−3.17454e13	−0.102815	−0.0514074	−	0.998678i	$-0.516371\pi$
$431$	−3.17454e13	−0.102815	−0.0514074	+	0.998678i	$0.516371\pi$
$432$	1.47302e14	0.471030
$433$	−2.29493e14	−0.724579	−0.362290	−	0.932066i	$-0.618005\pi$
$433$	−2.29493e14	−0.724579	−0.362290	+	0.932066i	$0.618005\pi$
$434$	1.97704e14	0.616344
$435$	3.52142e13	0.108399
$436$	−9.89431e13	−0.300753
$437$	2.20720e14	0.662511
$438$	1.32331e14	0.392242
$439$	5.56662e14	1.62943	0.814717	−	0.579859i	$-0.196892\pi$
$439$	5.56662e14	1.62943	0.814717	+	0.579859i	$0.196892\pi$
$440$	7.87612e13	0.227679
$441$	−4.86308e14	−1.38835
$442$	3.03273e14	0.855088
$443$	1.23574e14	0.344118	0.172059	−	0.985087i	$-0.444958\pi$
$443$	1.23574e14	0.344118	0.172059	+	0.985087i	$0.444958\pi$
$444$	−1.94607e13	−0.0535244
$445$	−1.11121e14	−0.301866
$446$	−1.91552e14	−0.513978
$447$	−1.24454e15	−3.29850
$448$	2.74599e13	0.0718902
$449$	−5.65613e14	−1.46273	−0.731365	−	0.681986i	$-0.761117\pi$
$449$	−5.65613e14	−1.46273	−0.731365	+	0.681986i	$0.761117\pi$
$450$	−1.14843e14	−0.293383
$451$	−9.36596e14	−2.36364
$452$	2.32380e14	0.579345
$453$	−7.11279e13	−0.175186
$454$	−1.50320e14	−0.365771
$455$	7.34439e13	0.176560
$456$	1.33529e14	0.317153
$457$	2.42787e13	0.0569752	0.0284876	−	0.999594i	$-0.490931\pi$
$457$	2.42787e13	0.0569752	0.0284876	+	0.999594i	$0.490931\pi$
$458$	−3.29211e14	−0.763334
$459$	1.44872e15	3.31907
$460$	1.27915e14	0.289570
$461$	5.72909e14	1.28154	0.640768	−	0.767735i	$-0.278616\pi$
$461$	5.72909e14	1.28154	0.640768	+	0.767735i	$0.278616\pi$
$462$	−4.64534e14	−1.02680
$463$	−1.72526e14	−0.376841	−0.188421	−	0.982088i	$-0.560337\pi$
$463$	−1.72526e14	−0.376841	−0.188421	+	0.982088i	$0.560337\pi$
$464$	−1.60107e13	−0.0345591
$465$	5.57153e14	1.18846
$466$	−1.14816e14	−0.242036
$467$	3.75877e14	0.783075	0.391537	−	0.920162i	$-0.371943\pi$
$467$	3.75877e14	0.783075	0.391537	+	0.920162i	$0.371943\pi$
$468$	−3.45828e14	−0.712047
$469$	−3.73986e13	−0.0761036
$470$	1.53740e14	0.309206
$471$	1.08447e15	2.15576
$472$	3.50303e13	0.0688276
$473$	−5.25666e14	−1.02088
$474$	−1.18716e14	−0.227892
$475$	−5.39225e13	−0.102319
$476$	2.70069e14	0.506567
$477$	1.31303e15	2.43457
$478$	−3.61398e14	−0.662418
$479$	−8.04779e13	−0.145825	−0.0729124	−	0.997338i	$-0.523229\pi$
$479$	−8.04779e13	−0.145825	−0.0729124	+	0.997338i	$0.523229\pi$
$480$	7.73849e13	0.138621
$481$	2.36651e13	0.0419093
$482$	1.87335e14	0.327989
$483$	−7.54443e14	−1.30592
$484$	3.13634e14	0.536752
$485$	−3.30382e13	−0.0559033
$486$	−1.14586e14	−0.191705
$487$	7.07883e14	1.17099	0.585494	−	0.810677i	$-0.300901\pi$
$487$	7.07883e14	1.17099	0.585494	+	0.810677i	$0.300901\pi$
$488$	6.85354e13	0.112100
$489$	5.42732e14	0.877782
$490$	−1.32330e14	−0.211631
$491$	4.39301e14	0.694726	0.347363	−	0.937731i	$-0.387077\pi$
$491$	4.39301e14	0.694726	0.347363	+	0.937731i	$0.387077\pi$
$492$	−9.20231e14	−1.43909
$493$	−1.57466e14	−0.243517
$494$	−1.62378e14	−0.248330
$495$	−8.83316e14	−1.33594
$496$	−2.53319e14	−0.378895
$497$	2.47049e14	0.365446
$498$	9.06995e14	1.32692
$499$	−9.86713e14	−1.42770	−0.713851	−	0.700297i	$-0.753051\pi$
$499$	−9.86713e14	−1.42770	−0.713851	+	0.700297i	$0.753051\pi$
$500$	−3.12500e13	−0.0447214
$501$	−2.04094e15	−2.88884
$502$	−4.37973e14	−0.613164
$503$	−6.20085e14	−0.858672	−0.429336	−	0.903145i	$-0.641252\pi$
$503$	−6.20085e14	−0.858672	−0.429336	+	0.903145i	$0.641252\pi$
$504$	−3.07966e14	−0.421827
$505$	2.76364e14	0.374437
$506$	9.83860e14	1.31858
$507$	−6.99353e14	−0.927155
$508$	9.96340e13	0.130664
$509$	1.24095e15	1.60993	0.804966	−	0.593321i	$-0.202183\pi$
$509$	1.24095e15	1.60993	0.804966	+	0.593321i	$0.202183\pi$
$510$	7.61084e14	0.976780
$511$	−1.43303e14	−0.181945
$512$	−3.51844e13	−0.0441942
$513$	−7.75673e14	−0.963903
$514$	4.73269e14	0.581850
$515$	−5.41241e13	−0.0658342
$516$	−5.16481e14	−0.621557
$517$	1.18249e15	1.40799
$518$	2.10742e13	0.0248277
$519$	−3.83209e14	−0.446699
$520$	−9.41038e13	−0.108540
$521$	1.51842e15	1.73295	0.866473	−	0.499224i	$-0.166382\pi$
$521$	1.51842e15	1.73295	0.866473	+	0.499224i	$0.166382\pi$
$522$	1.79562e14	0.202781
$523$	5.59189e14	0.624884	0.312442	−	0.949937i	$-0.398853\pi$
$523$	5.59189e14	0.624884	0.312442	+	0.949937i	$0.398853\pi$
$524$	3.11659e14	0.344634
$525$	1.84313e14	0.201687
$526$	−1.06766e15	−1.15614
$527$	−2.49140e15	−2.66984
$528$	5.95208e14	0.631222
$529$	6.45065e14	0.677013
$530$	3.57289e14	0.371110
$531$	−3.92869e14	−0.403857
$532$	−1.44600e14	−0.147114
$533$	1.11904e15	1.12680
$534$	−8.39752e14	−0.836901
$535$	−7.07139e14	−0.697524
$536$	4.79189e13	0.0467844
$537$	−9.94988e14	−0.961522
$538$	1.10112e13	0.0105325
$539$	−1.01782e15	−0.963677
$540$	−4.49531e14	−0.421302
$541$	−1.49107e15	−1.38329	−0.691643	−	0.722240i	$-0.743113\pi$
$541$	−1.49107e15	−1.38329	−0.691643	+	0.722240i	$0.743113\pi$
$542$	5.05529e14	0.464248
$543$	1.65119e15	1.50106
$544$	−3.46040e14	−0.311410
$545$	3.01950e14	0.269002
$546$	5.55024e14	0.489500
$547$	1.60550e15	1.40178	0.700889	−	0.713270i	$-0.252787\pi$
$547$	1.60550e15	1.40178	0.700889	+	0.713270i	$0.252787\pi$
$548$	7.07808e14	0.611818
$549$	−7.68633e14	−0.657765
$550$	−2.40360e14	−0.203642
$551$	8.43103e13	0.0707207
$552$	9.66669e14	0.802810
$553$	1.28559e14	0.105709
$554$	−5.65462e14	−0.460362
$555$	5.93893e13	0.0478737
$556$	−5.90198e14	−0.471071
$557$	−1.11199e15	−0.878816	−0.439408	−	0.898288i	$-0.644812\pi$
$557$	−1.11199e15	−0.878816	−0.439408	+	0.898288i	$0.644812\pi$
$558$	2.84100e15	2.22323
$559$	6.28066e14	0.486676
$560$	−8.38009e13	−0.0643005
$561$	5.85389e15	4.44784
$562$	−3.40974e14	−0.256550
$563$	2.80669e14	0.209121	0.104561	−	0.994519i	$-0.466656\pi$
$563$	2.80669e14	0.209121	0.104561	+	0.994519i	$0.466656\pi$
$564$	1.16183e15	0.857249
$565$	−7.09167e14	−0.518182
$566$	−1.73440e15	−1.25505
$567$	9.86440e14	0.706910
$568$	−3.16545e14	−0.224657
$569$	−2.23674e15	−1.57216	−0.786082	−	0.618122i	$-0.787894\pi$
$569$	−2.23674e15	−1.57216	−0.786082	+	0.618122i	$0.787894\pi$
$570$	−4.07499e14	−0.283671
$571$	1.37303e15	0.946633	0.473317	−	0.880892i	$-0.343057\pi$
$571$	1.37303e15	0.946633	0.473317	+	0.880892i	$0.343057\pi$
$572$	−7.23801e14	−0.494244
$573$	−4.65251e15	−3.14656
$574$	9.96527e14	0.667534
$575$	−3.90365e14	−0.258999
$576$	3.94597e14	0.259316
$577$	7.05140e14	0.458996	0.229498	−	0.973309i	$-0.426292\pi$
$577$	7.05140e14	0.458996	0.229498	+	0.973309i	$0.426292\pi$
$578$	−2.30662e15	−1.48721
$579$	−3.10622e15	−1.98381
$580$	4.88608e13	0.0309106
$581$	−9.82194e14	−0.615501
$582$	−2.49674e14	−0.154987
$583$	2.74810e15	1.68988
$584$	1.83614e14	0.111850
$585$	1.05538e15	0.636874
$586$	2.26634e14	0.135484
$587$	−8.88812e14	−0.526381	−0.263191	−	0.964744i	$-0.584775\pi$
$587$	−8.88812e14	−0.526381	−0.263191	+	0.964744i	$0.584775\pi$
$588$	−1.00003e15	−0.586730
$589$	1.33394e15	0.775360
$590$	−1.06904e14	−0.0615613
$591$	9.32374e14	0.531936
$592$	−2.70023e13	−0.0152627
$593$	−1.09724e15	−0.614471	−0.307235	−	0.951634i	$-0.599404\pi$
$593$	−1.09724e15	−0.614471	−0.307235	+	0.951634i	$0.599404\pi$
$594$	−3.45757e15	−1.91843
$595$	−8.24186e14	−0.453087
$596$	−1.72684e15	−0.940583
$597$	3.37339e15	1.82057
$598$	−1.17552e15	−0.628596
$599$	2.28533e15	1.21088	0.605442	−	0.795890i	$-0.292997\pi$
$599$	2.28533e15	1.21088	0.605442	+	0.795890i	$0.292997\pi$
$600$	−2.36160e14	−0.123987
$601$	−1.90568e15	−0.991383	−0.495692	−	0.868499i	$-0.665085\pi$
$601$	−1.90568e15	−0.991383	−0.495692	+	0.868499i	$0.665085\pi$
$602$	5.59302e14	0.288314
$603$	−5.37416e14	−0.274515
$604$	−9.86923e13	−0.0499551
$605$	−9.57135e14	−0.480085
$606$	2.08852e15	1.03810
$607$	1.10407e13	0.00543826	0.00271913	−	0.999996i	$-0.499134\pi$
$607$	1.10407e13	0.00543826	0.00271913	+	0.999996i	$0.499134\pi$
$608$	1.85276e14	0.0904378
$609$	−2.88181e14	−0.139403
$610$	−2.09154e14	−0.100265
$611$	−1.41284e15	−0.671222
$612$	3.88088e15	1.82725
$613$	3.09426e15	1.44386	0.721929	−	0.691967i	$-0.243256\pi$
$613$	3.09426e15	1.44386	0.721929	+	0.691967i	$0.243256\pi$
$614$	1.86568e15	0.862804
$615$	2.80832e15	1.28716
$616$	−6.44556e14	−0.292797
$617$	−1.89971e15	−0.855300	−0.427650	−	0.903944i	$-0.640658\pi$
$617$	−1.89971e15	−0.855300	−0.427650	+	0.903944i	$0.640658\pi$
$618$	−4.09023e14	−0.182520
$619$	2.71829e14	0.120226	0.0601129	−	0.998192i	$-0.480854\pi$
$619$	2.71829e14	0.120226	0.0601129	+	0.998192i	$0.480854\pi$
$620$	7.73068e14	0.338894
$621$	−5.61540e15	−2.43993
$622$	−1.43300e15	−0.617160
$623$	9.09375e14	0.388203
$624$	−7.11153e14	−0.300918
$625$	9.53674e13	0.0400000
$626$	3.10933e15	1.29273
$627$	−3.13428e15	−1.29172
$628$	1.50473e15	0.614725
$629$	−2.65569e14	−0.107547
$630$	9.39837e14	0.377294
$631$	7.79292e14	0.310127	0.155063	−	0.987905i	$-0.450442\pi$
$631$	7.79292e14	0.310127	0.155063	+	0.987905i	$0.450442\pi$
$632$	−1.64723e14	−0.0649844
$633$	1.35986e15	0.531833
$634$	1.72451e15	0.668612
$635$	−3.04059e14	−0.116870
$636$	2.70008e15	1.02887
$637$	1.21609e15	0.459407
$638$	3.75814e14	0.140754
$639$	3.55009e15	1.31821
$640$	1.07374e14	0.0395285
$641$	9.89428e14	0.361131	0.180566	−	0.983563i	$-0.442207\pi$
$641$	9.89428e14	0.361131	0.180566	+	0.983563i	$0.442207\pi$
$642$	−5.34393e15	−1.93383
$643$	−1.16638e15	−0.418485	−0.209242	−	0.977864i	$-0.567100\pi$
$643$	−1.16638e15	−0.418485	−0.209242	+	0.977864i	$0.567100\pi$
$644$	−1.04682e15	−0.372390
$645$	1.57617e15	0.555938
$646$	1.82220e15	0.637261
$647$	9.70993e14	0.336699	0.168350	−	0.985727i	$-0.446156\pi$
$647$	9.70993e14	0.336699	0.168350	+	0.985727i	$0.446156\pi$
$648$	−1.26393e15	−0.434570
$649$	−8.22254e14	−0.280324
$650$	2.87182e14	0.0970808
$651$	−4.55956e15	−1.52837
$652$	7.53059e14	0.250304
$653$	3.95021e15	1.30196	0.650981	−	0.759094i	$-0.274358\pi$
$653$	3.95021e15	1.30196	0.650981	+	0.759094i	$0.274358\pi$
$654$	2.28188e15	0.745786
$655$	−9.51108e14	−0.308250
$656$	−1.27685e15	−0.410364
$657$	−2.05925e15	−0.656296
$658$	−1.25816e15	−0.397642
$659$	2.99308e15	0.938100	0.469050	−	0.883172i	$-0.344596\pi$
$659$	2.99308e15	0.938100	0.469050	+	0.883172i	$0.344596\pi$
$660$	−1.81643e15	−0.564582
$661$	−5.38432e15	−1.65967	−0.829837	−	0.558006i	$-0.811567\pi$
$661$	−5.38432e15	−1.65967	−0.829837	+	0.558006i	$0.811567\pi$
$662$	−9.86530e14	−0.301572
$663$	−6.99423e15	−2.12039
$664$	1.25849e15	0.378376
$665$	4.41284e14	0.131583
$666$	3.02835e14	0.0895565
$667$	6.10355e14	0.179015
$668$	−2.83188e15	−0.823767
$669$	4.41766e15	1.27453
$670$	−1.46237e14	−0.0418452
$671$	−1.60871e15	−0.456566
$672$	−6.33293e14	−0.178268
$673$	−5.89845e15	−1.64685	−0.823427	−	0.567422i	$-0.807941\pi$
$673$	−5.89845e15	−1.64685	−0.823427	+	0.567422i	$0.807941\pi$
$674$	4.43362e14	0.122780
$675$	1.37186e15	0.376824
$676$	−9.70376e14	−0.264383
$677$	−2.00406e15	−0.541594	−0.270797	−	0.962636i	$-0.587287\pi$
$677$	−2.00406e15	−0.541594	−0.270797	+	0.962636i	$0.587287\pi$
$678$	−5.35926e15	−1.43662
$679$	2.70374e14	0.0718922
$680$	1.05603e15	0.278533
$681$	3.46675e15	0.907013
$682$	5.94607e15	1.54318
$683$	1.22063e15	0.314247	0.157123	−	0.987579i	$-0.449778\pi$
$683$	1.22063e15	0.314247	0.157123	+	0.987579i	$0.449778\pi$
$684$	−2.07789e15	−0.530658
$685$	−2.16006e15	−0.547227
$686$	2.70113e15	0.678832
$687$	7.59244e15	1.89286
$688$	−7.16635e14	−0.177240
$689$	−3.28342e15	−0.805603
$690$	−2.95004e15	−0.718055
$691$	6.48436e15	1.56581	0.782903	−	0.622144i	$-0.213738\pi$
$691$	6.48436e15	1.56581	0.782903	+	0.622144i	$0.213738\pi$
$692$	−5.31715e14	−0.127378
$693$	7.22877e15	1.71803
$694$	1.96758e15	0.463934
$695$	1.80114e15	0.421339
$696$	3.69247e14	0.0856971
$697$	−1.25579e16	−2.89159
$698$	2.98039e15	0.680877
$699$	2.64794e15	0.600184
$700$	2.55740e14	0.0575121
$701$	5.88302e15	1.31266	0.656329	−	0.754475i	$-0.272108\pi$
$701$	5.88302e15	1.31266	0.656329	+	0.754475i	$0.272108\pi$
$702$	4.13110e15	0.914560
$703$	1.42191e14	0.0312332
$704$	8.25871e14	0.179996
$705$	−3.54562e15	−0.766746
$706$	−3.33359e15	−0.715297
$707$	−2.26168e15	−0.481530
$708$	−8.07886e14	−0.170674
$709$	−5.42392e15	−1.13700	−0.568498	−	0.822684i	$-0.692475\pi$
$709$	−5.42392e15	−1.13700	−0.568498	+	0.822684i	$0.692475\pi$
$710$	9.66018e14	0.200939
$711$	1.84738e15	0.381307
$712$	−1.16518e15	−0.238646
$713$	9.65693e15	1.96267
$714$	−6.22847e15	−1.25615
$715$	2.20887e15	0.442065
$716$	−1.38058e15	−0.274183
$717$	8.33473e15	1.64262
$718$	−2.82605e15	−0.552708
$719$	−2.51534e15	−0.488188	−0.244094	−	0.969752i	$-0.578491\pi$
$719$	−2.51534e15	−0.488188	−0.244094	+	0.969752i	$0.578491\pi$
$720$	−1.20421e15	−0.231940
$721$	4.42935e14	0.0846634
$722$	2.75205e15	0.522037
$723$	−4.32040e15	−0.813324
$724$	2.29108e15	0.428033
$725$	−1.49111e14	−0.0276472
$726$	−7.23318e15	−1.33100
$727$	9.61573e15	1.75607	0.878037	−	0.478592i	$-0.158853\pi$
$727$	9.61573e15	1.75607	0.878037	+	0.478592i	$0.158853\pi$
$728$	7.70115e14	0.139583
$729$	−4.19027e15	−0.753772
$730$	−5.60345e14	−0.100041
$731$	−7.04814e15	−1.24890
$732$	−1.58060e15	−0.277978
$733$	−6.79402e15	−1.18592	−0.592959	−	0.805233i	$-0.702040\pi$
$733$	−6.79402e15	−1.18592	−0.592959	+	0.805233i	$0.702040\pi$
$734$	−4.10589e15	−0.711343
$735$	3.05185e15	0.524787
$736$	1.34129e15	0.228925
$737$	−1.12478e15	−0.190545
$738$	1.43200e16	2.40788
$739$	−3.11194e15	−0.519382	−0.259691	−	0.965692i	$-0.583621\pi$
$739$	−3.11194e15	−0.519382	−0.259691	+	0.965692i	$0.583621\pi$
$740$	8.24046e13	0.0136514
$741$	3.74484e15	0.615790
$742$	−2.92394e15	−0.477251
$743$	2.87948e15	0.466525	0.233262	−	0.972414i	$-0.425060\pi$
$743$	2.87948e15	0.466525	0.233262	+	0.972414i	$0.425060\pi$
$744$	5.84217e15	0.939557
$745$	5.26989e15	0.841283
$746$	−3.46165e15	−0.548554
$747$	−1.41141e16	−2.22018
$748$	8.12248e15	1.26832
$749$	5.78700e15	0.897022
$750$	7.20703e14	0.110897
$751$	−4.18093e15	−0.638636	−0.319318	−	0.947648i	$-0.603454\pi$
$751$	−4.18093e15	−0.638636	−0.319318	+	0.947648i	$0.603454\pi$
$752$	1.61208e15	0.244448
$753$	1.01007e16	1.52048
$754$	−4.49022e14	−0.0671005
$755$	3.01185e14	0.0446812
$756$	3.67881e15	0.541799
$757$	−9.69613e13	−0.0141766	−0.00708828	−	0.999975i	$-0.502256\pi$
$757$	−9.69613e13	−0.0141766	−0.00708828	+	0.999975i	$0.502256\pi$
$758$	−7.96894e15	−1.15670
$759$	−2.26903e16	−3.26972
$760$	−5.65418e14	−0.0808900
$761$	6.02237e15	0.855366	0.427683	−	0.903929i	$-0.359330\pi$
$761$	6.02237e15	0.855366	0.427683	+	0.903929i	$0.359330\pi$
$762$	−2.29781e15	−0.324012
$763$	−2.47107e15	−0.345939
$764$	−6.45551e15	−0.897258
$765$	−1.18435e16	−1.63434
$766$	9.58186e15	1.31278
$767$	9.82428e14	0.133637
$768$	8.11440e14	0.109590
$769$	−1.18406e16	−1.58773	−0.793866	−	0.608092i	$-0.791935\pi$
$769$	−1.18406e16	−1.58773	−0.793866	+	0.608092i	$0.791935\pi$
$770$	1.96703e15	0.261886
$771$	−1.09148e16	−1.44283
$772$	−4.30999e15	−0.565693
$773$	−3.87913e15	−0.505530	−0.252765	−	0.967528i	$-0.581340\pi$
$773$	−3.87913e15	−0.505530	−0.252765	+	0.967528i	$0.581340\pi$
$774$	8.03714e15	1.03998
$775$	−2.35922e15	−0.303116
$776$	−3.46431e14	−0.0441954
$777$	−4.86023e14	−0.0615660
$778$	−9.76952e14	−0.122881
$779$	6.72373e15	0.839758
$780$	2.17027e15	0.269149
$781$	7.43015e15	0.914991
$782$	1.31916e16	1.61310
$783$	−2.14496e15	−0.260454
$784$	−1.38758e15	−0.167309
$785$	−4.59208e15	−0.549827
$786$	−7.18764e15	−0.854598
$787$	9.91706e15	1.17091	0.585453	−	0.810707i	$-0.300917\pi$
$787$	9.91706e15	1.17091	0.585453	+	0.810707i	$0.300917\pi$
$788$	1.29370e15	0.151684
$789$	2.46228e16	2.86691
$790$	5.02694e14	0.0581239
$791$	5.80360e15	0.666387
$792$	−9.26224e15	−1.05615
$793$	1.92208e15	0.217655
$794$	−1.11026e16	−1.24857
$795$	−8.23998e15	−0.920252
$796$	4.68070e15	0.519145
$797$	1.24267e16	1.36879	0.684394	−	0.729112i	$-0.260067\pi$
$797$	1.24267e16	1.36879	0.684394	+	0.729112i	$0.260067\pi$
$798$	3.33484e15	0.364803
$799$	1.58548e16	1.72248
$800$	−3.27680e14	−0.0353553
$801$	1.30677e16	1.40029
$802$	−8.74793e15	−0.930993
$803$	−4.30990e15	−0.455546
$804$	−1.10513e15	−0.116013
$805$	3.19463e15	0.333075
$806$	−7.10436e15	−0.735668
$807$	−2.53946e14	−0.0261178
$808$	2.89789e15	0.296019
$809$	1.44691e16	1.46800	0.734000	−	0.679149i	$-0.237651\pi$
$809$	1.44691e16	1.46800	0.734000	+	0.679149i	$0.237651\pi$
$810$	3.85720e15	0.388691
$811$	4.81262e15	0.481689	0.240844	−	0.970564i	$-0.422576\pi$
$811$	4.81262e15	0.481689	0.240844	+	0.970564i	$0.422576\pi$
$812$	−3.99861e14	−0.0397513
$813$	−1.16588e16	−1.15121
$814$	6.33817e14	0.0621627
$815$	−2.29815e15	−0.223878
$816$	7.98055e15	0.772212
$817$	3.77370e15	0.362699
$818$	5.09258e15	0.486177
$819$	−8.63693e15	−0.819027
$820$	3.89664e15	0.367041
$821$	−1.99742e16	−1.86888	−0.934439	−	0.356123i	$-0.884099\pi$
$821$	−1.99742e16	−1.86888	−0.934439	+	0.356123i	$0.884099\pi$
$822$	−1.63238e16	−1.51714
$823$	−1.10902e16	−1.02385	−0.511927	−	0.859029i	$-0.671068\pi$
$823$	−1.10902e16	−1.02385	−0.511927	+	0.859029i	$0.671068\pi$
$824$	−5.67533e14	−0.0520465
$825$	5.54330e15	0.504977
$826$	8.74867e14	0.0791684
$827$	9.09463e15	0.817532	0.408766	−	0.912639i	$-0.365959\pi$
$827$	9.09463e15	0.817532	0.408766	+	0.912639i	$0.365959\pi$
$828$	−1.50427e16	−1.34325
$829$	−1.00720e16	−0.893438	−0.446719	−	0.894674i	$-0.647408\pi$
$829$	−1.00720e16	−0.893438	−0.446719	+	0.894674i	$0.647408\pi$
$830$	−3.84060e15	−0.338430
$831$	1.30410e16	1.14157
$832$	−9.86749e14	−0.0858082
$833$	−1.36469e16	−1.17893
$834$	1.36114e16	1.16813
$835$	8.64221e15	0.736799
$836$	−4.34892e15	−0.368339
$837$	−3.39373e16	−2.85553
$838$	3.25628e15	0.272195
$839$	−1.68675e16	−1.40075	−0.700373	−	0.713777i	$-0.746983\pi$
$839$	−1.68675e16	−1.40075	−0.700373	+	0.713777i	$0.746983\pi$
$840$	1.93266e15	0.159448
$841$	−1.19674e16	−0.980891
$842$	4.48332e15	0.365076
$843$	7.86371e15	0.636174
$844$	1.88686e15	0.151655
$845$	2.96135e15	0.236471
$846$	−1.80796e16	−1.43434
$847$	7.83288e15	0.617395
$848$	3.74645e15	0.293388
$849$	3.99996e16	3.11217
$850$	−3.22275e15	−0.249128
$851$	1.02937e15	0.0790606
$852$	7.30031e15	0.557088
$853$	8.50662e15	0.644967	0.322483	−	0.946575i	$-0.395482\pi$
$853$	8.50662e15	0.644967	0.322483	+	0.946575i	$0.395482\pi$
$854$	1.71165e15	0.128942
$855$	6.34123e15	0.474635
$856$	−7.41489e15	−0.551441
$857$	−2.25172e16	−1.66387	−0.831937	−	0.554870i	$-0.812768\pi$
$857$	−2.25172e16	−1.66387	−0.831937	+	0.554870i	$0.812768\pi$
$858$	1.66927e16	1.22559
$859$	−1.53158e16	−1.11732	−0.558660	−	0.829397i	$-0.688684\pi$
$859$	−1.53158e16	−1.11732	−0.558660	+	0.829397i	$0.688684\pi$
$860$	2.18700e15	0.158528
$861$	−2.29824e16	−1.65531
$862$	1.01585e15	0.0727010
$863$	−5.26510e15	−0.374410	−0.187205	−	0.982321i	$-0.559943\pi$
$863$	−5.26510e15	−0.374410	−0.187205	+	0.982321i	$0.559943\pi$
$864$	−4.71367e15	−0.333068
$865$	1.62267e15	0.113931
$866$	7.34377e15	0.512355
$867$	5.31964e16	3.68788
$868$	−6.32654e15	−0.435821
$869$	3.86648e15	0.264671
$870$	−1.12685e15	−0.0766499
$871$	1.34389e15	0.0908373
$872$	3.16618e15	0.212664
$873$	3.88526e15	0.259324
$874$	−7.06303e15	−0.468466
$875$	−7.80457e14	−0.0514404
$876$	−4.23459e15	−0.277357
$877$	−2.62728e16	−1.71005	−0.855025	−	0.518587i	$-0.826458\pi$
$877$	−2.62728e16	−1.71005	−0.855025	+	0.518587i	$0.826458\pi$
$878$	−1.78132e16	−1.15218
$879$	−5.22675e15	−0.335964
$880$	−2.52036e15	−0.160993
$881$	−5.98661e15	−0.380026	−0.190013	−	0.981782i	$-0.560853\pi$
$881$	−5.98661e15	−0.380026	−0.190013	+	0.981782i	$0.560853\pi$
$882$	1.55618e16	0.981712
$883$	1.34655e16	0.844187	0.422094	−	0.906552i	$-0.361295\pi$
$883$	1.34655e16	0.844187	0.422094	+	0.906552i	$0.361295\pi$
$884$	−9.70473e15	−0.604639
$885$	2.46547e15	0.152655
$886$	−3.95438e15	−0.243328
$887$	−2.64087e16	−1.61498	−0.807490	−	0.589882i	$-0.799174\pi$
$887$	−2.64087e16	−1.61498	−0.807490	+	0.589882i	$0.799174\pi$
$888$	6.22742e14	0.0378474
$889$	2.48832e15	0.150296
$890$	3.55586e15	0.213452
$891$	2.96677e16	1.76993
$892$	6.12966e15	0.363437
$893$	−8.48897e15	−0.500233
$894$	3.98252e16	2.33239
$895$	4.21320e15	0.245236
$896$	−8.78716e14	−0.0508340
$897$	2.71103e16	1.55875
$898$	1.80996e16	1.03431
$899$	3.68875e15	0.209508
$900$	3.67497e15	0.207453
$901$	3.68465e16	2.06733
$902$	2.99711e16	1.67135
$903$	−1.28989e16	−0.714941
$904$	−7.43615e15	−0.409659
$905$	−6.99181e15	−0.382845
$906$	2.27609e15	0.123875
$907$	−2.68100e16	−1.45030	−0.725148	−	0.688593i	$-0.758229\pi$
$907$	−2.68100e16	−1.45030	−0.725148	+	0.688593i	$0.758229\pi$
$908$	4.81024e15	0.258639
$909$	−3.25002e16	−1.73694
$910$	−2.35020e15	−0.124847
$911$	−9.34548e15	−0.493458	−0.246729	−	0.969084i	$-0.579356\pi$
$911$	−9.34548e15	−0.493458	−0.246729	+	0.969084i	$0.579356\pi$
$912$	−4.27293e15	−0.224261
$913$	−2.95400e16	−1.54107
$914$	−7.76917e14	−0.0402875
$915$	4.82360e15	0.248631
$916$	1.05348e16	0.539759
$917$	7.78356e15	0.396412
$918$	−4.63592e16	−2.34693
$919$	1.29542e16	0.651892	0.325946	−	0.945388i	$-0.394317\pi$
$919$	1.29542e16	0.651892	0.325946	+	0.945388i	$0.394317\pi$
$920$	−4.09328e15	−0.204757
$921$	−4.30273e16	−2.13952
$922$	−1.83331e16	−0.906183
$923$	−8.87753e15	−0.436197
$924$	1.48651e16	0.726058
$925$	−2.51479e14	−0.0122102
$926$	5.52082e15	0.266467
$927$	6.36495e15	0.305391
$928$	5.12343e14	0.0244369
$929$	3.86830e16	1.83415	0.917073	−	0.398720i	$-0.130546\pi$
$929$	3.86830e16	1.83415	0.917073	+	0.398720i	$0.130546\pi$
$930$	−1.78289e16	−0.840365
$931$	7.30680e15	0.342376
$932$	3.67411e15	0.171145
$933$	3.30485e16	1.53039
$934$	−1.20281e16	−0.553717
$935$	−2.47878e16	−1.13442
$936$	1.10665e16	0.503493
$937$	−2.80469e15	−0.126858	−0.0634290	−	0.997986i	$-0.520204\pi$
$937$	−2.80469e15	−0.126858	−0.0634290	+	0.997986i	$0.520204\pi$
$938$	1.19676e15	0.0538134
$939$	−7.17088e16	−3.20562
$940$	−4.91966e15	−0.218641
$941$	3.03866e16	1.34258	0.671288	−	0.741197i	$-0.265741\pi$
$941$	3.03866e16	1.34258	0.671288	+	0.741197i	$0.265741\pi$
$942$	−3.47029e16	−1.52435
$943$	4.86756e16	2.12568
$944$	−1.12097e15	−0.0486684
$945$	−1.12269e16	−0.484600
$946$	1.68213e16	0.721870
$947$	1.12019e16	0.477931	0.238965	−	0.971028i	$-0.423192\pi$
$947$	1.12019e16	0.477931	0.238965	+	0.971028i	$0.423192\pi$
$948$	3.79892e15	0.161144
$949$	5.14947e15	0.217169
$950$	1.72552e15	0.0723502
$951$	−3.97714e16	−1.65798
$952$	−8.64221e15	−0.358197
$953$	5.77274e15	0.237887	0.118944	−	0.992901i	$-0.462049\pi$
$953$	5.77274e15	0.237887	0.118944	+	0.992901i	$0.462049\pi$
$954$	−4.20169e16	−1.72150
$955$	1.97007e16	0.802532
$956$	1.15647e16	0.468400
$957$	−8.66721e15	−0.349031
$958$	2.57529e15	0.103114
$959$	1.76772e16	0.703739
$960$	−2.47632e15	−0.0980199
$961$	3.29542e16	1.29698
$962$	−7.57284e14	−0.0296344
$963$	8.31588e16	3.23567
$964$	−5.99470e15	−0.231923
$965$	1.31530e16	0.505971
$966$	2.41422e16	0.923426
$967$	−7.07033e14	−0.0268902	−0.0134451	−	0.999910i	$-0.504280\pi$
$967$	−7.07033e14	−0.0268902	−0.0134451	+	0.999910i	$0.504280\pi$
$968$	−1.00363e16	−0.379541
$969$	−4.20245e16	−1.58023
$970$	1.05722e15	0.0395296
$971$	−3.68438e16	−1.36980	−0.684902	−	0.728636i	$-0.740155\pi$
$971$	−3.68438e16	−1.36980	−0.684902	+	0.728636i	$0.740155\pi$
$972$	3.66676e15	0.135556
$973$	−1.47400e16	−0.541846
$974$	−2.26523e16	−0.828013
$975$	−6.62313e15	−0.240734
$976$	−2.19313e15	−0.0792668
$977$	−1.66132e16	−0.597082	−0.298541	−	0.954397i	$-0.596500\pi$
$977$	−1.66132e16	−0.597082	−0.298541	+	0.954397i	$0.596500\pi$
$978$	−1.73674e16	−0.620685
$979$	2.73500e16	0.971968
$980$	4.23455e15	0.149646
$981$	−3.55091e16	−1.24784
$982$	−1.40576e16	−0.491246
$983$	1.46153e16	0.507884	0.253942	−	0.967219i	$-0.418273\pi$
$983$	1.46153e16	0.507884	0.253942	+	0.967219i	$0.418273\pi$
$984$	2.94474e16	1.01759
$985$	−3.94806e15	−0.135670
$986$	5.03892e15	0.172192
$987$	2.90162e16	0.986044
$988$	5.19609e15	0.175596
$989$	2.73193e16	0.918099
$990$	2.82661e16	0.944653
$991$	−1.64205e16	−0.545736	−0.272868	−	0.962052i	$-0.587972\pi$
$991$	−1.64205e16	−0.545736	−0.272868	+	0.962052i	$0.587972\pi$
$992$	8.10621e15	0.267919
$993$	2.27519e16	0.747818
$994$	−7.90558e15	−0.258410
$995$	−1.42844e16	−0.464338
$996$	−2.90238e16	−0.938272
$997$	−1.68193e16	−0.540734	−0.270367	−	0.962757i	$-0.587145\pi$
$997$	−1.68193e16	−0.540734	−0.270367	+	0.962757i	$0.587145\pi$
$998$	3.15748e16	1.00954
$999$	−3.61752e15	−0.115027

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.12.a.b.1.1	✓	1
3.2	odd	2		90.12.a.k.1.1		1
4.3	odd	2		80.12.a.a.1.1		1
5.2	odd	4		50.12.b.a.49.1		2
5.3	odd	4		50.12.b.a.49.2		2
5.4	even	2		50.12.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.12.a.b.1.1	✓	1	1.1	even	1	trivial
50.12.a.c.1.1		1	5.4	even	2
50.12.b.a.49.1		2	5.2	odd	4
50.12.b.a.49.2		2	5.3	odd	4
80.12.a.a.1.1		1	4.3	odd	2
90.12.a.k.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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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