LMFDB - Embedded newform 10.10.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
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:	$5.15035836164$
Analytic rank:	$1$
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)

$f(q)$

$=$

$q-16.0000 q^{2} +46.0000 q^{3} +256.000 q^{4} -625.000 q^{5} -736.000 q^{6} -10318.0 q^{7} -4096.00 q^{8} -17567.0 q^{9} +O(q^{10})$

\(q-16.0000 q^{2} +46.0000 q^{3} +256.000 q^{4} -625.000 q^{5} -736.000 q^{6} -10318.0 q^{7} -4096.00 q^{8} -17567.0 q^{9} +10000.0 q^{10} -5568.00 q^{11} +11776.0 q^{12} +45986.0 q^{13} +165088. q^{14} -28750.0 q^{15} +65536.0 q^{16} -381318. q^{17} +281072. q^{18} +610460. q^{19} -160000. q^{20} -474628. q^{21} +89088.0 q^{22} -1.44791e6 q^{23} -188416. q^{24} +390625. q^{25} -735776. q^{26} -1.71350e6 q^{27} -2.64141e6 q^{28} +5.38551e6 q^{29} +460000. q^{30} +3.05385e6 q^{31} -1.04858e6 q^{32} -256128. q^{33} +6.10109e6 q^{34} +6.44875e6 q^{35} -4.49715e6 q^{36} +1.28894e7 q^{37} -9.76736e6 q^{38} +2.11536e6 q^{39} +2.56000e6 q^{40} -3.37866e7 q^{41} +7.59405e6 q^{42} -3.68862e7 q^{43} -1.42541e6 q^{44} +1.09794e7 q^{45} +2.31666e7 q^{46} -4.41638e7 q^{47} +3.01466e6 q^{48} +6.61075e7 q^{49} -6.25000e6 q^{50} -1.75406e7 q^{51} +1.17724e7 q^{52} +2.97463e7 q^{53} +2.74160e7 q^{54} +3.48000e6 q^{55} +4.22625e7 q^{56} +2.80812e7 q^{57} -8.61682e7 q^{58} -6.55754e7 q^{59} -7.36000e6 q^{60} +4.01832e7 q^{61} -4.88616e7 q^{62} +1.81256e8 q^{63} +1.67772e7 q^{64} -2.87412e7 q^{65} +4.09805e6 q^{66} -1.15706e8 q^{67} -9.76174e7 q^{68} -6.66040e7 q^{69} -1.03180e8 q^{70} -2.31682e8 q^{71} +7.19544e7 q^{72} +3.58692e8 q^{73} -2.06231e8 q^{74} +1.79688e7 q^{75} +1.56278e8 q^{76} +5.74506e7 q^{77} -3.38457e7 q^{78} -4.86017e8 q^{79} -4.09600e7 q^{80} +2.66950e8 q^{81} +5.40586e8 q^{82} +2.51169e8 q^{83} -1.21505e8 q^{84} +2.38324e8 q^{85} +5.90180e8 q^{86} +2.47733e8 q^{87} +2.28065e7 q^{88} -5.26039e8 q^{89} -1.75670e8 q^{90} -4.74484e8 q^{91} -3.70666e8 q^{92} +1.40477e8 q^{93} +7.06621e8 q^{94} -3.81538e8 q^{95} -4.82345e7 q^{96} -1.07598e9 q^{97} -1.05772e9 q^{98} +9.78131e7 q^{99} +O(q^{100})\)

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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	46.0000	0.327878	0.163939	−	0.986470i	$-0.447580\pi$
$3$	46.0000	0.327878	0.163939	+	0.986470i	$0.447580\pi$
$4$	256.000	0.500000
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	−736.000	−0.231845
$7$	−10318.0	−1.62426	−0.812128	−	0.583480i	$-0.801691\pi$
$7$	−10318.0	−1.62426	−0.812128	+	0.583480i	$0.801691\pi$
$8$	−4096.00	−0.353553
$9$	−17567.0	−0.892496
$10$	10000.0	0.316228
$11$	−5568.00	−0.114665	−0.0573327	−	0.998355i	$-0.518260\pi$
$11$	−5568.00	−0.114665	−0.0573327	+	0.998355i	$0.518260\pi$
$12$	11776.0	0.163939
$13$	45986.0	0.446561	0.223280	−	0.974754i	$-0.428323\pi$
$13$	45986.0	0.446561	0.223280	+	0.974754i	$0.428323\pi$
$14$	165088.	1.14852
$15$	−28750.0	−0.146631
$16$	65536.0	0.250000
$17$	−381318.	−1.10730	−0.553652	−	0.832748i	$-0.686766\pi$
$17$	−381318.	−1.10730	−0.553652	+	0.832748i	$0.686766\pi$
$18$	281072.	0.631090
$19$	610460.	1.07465	0.537324	−	0.843376i	$-0.319435\pi$
$19$	610460.	1.07465	0.537324	+	0.843376i	$0.319435\pi$
$20$	−160000.	−0.223607
$21$	−474628.	−0.532558
$22$	89088.0	0.0810806
$23$	−1.44791e6	−1.07887	−0.539433	−	0.842029i	$-0.681361\pi$
$23$	−1.44791e6	−1.07887	−0.539433	+	0.842029i	$0.681361\pi$
$24$	−188416.	−0.115922
$25$	390625.	0.200000
$26$	−735776.	−0.315766
$27$	−1.71350e6	−0.620508
$28$	−2.64141e6	−0.812128
$29$	5.38551e6	1.41396	0.706978	−	0.707236i	$-0.250058\pi$
$29$	5.38551e6	1.41396	0.706978	+	0.707236i	$0.250058\pi$
$30$	460000.	0.103684
$31$	3.05385e6	0.593910	0.296955	−	0.954892i	$-0.404029\pi$
$31$	3.05385e6	0.593910	0.296955	+	0.954892i	$0.404029\pi$
$32$	−1.04858e6	−0.176777
$33$	−256128.	−0.0375962
$34$	6.10109e6	0.782983
$35$	6.44875e6	0.726389
$36$	−4.49715e6	−0.446248
$37$	1.28894e7	1.13065	0.565323	−	0.824870i	$-0.308752\pi$
$37$	1.28894e7	1.13065	0.565323	+	0.824870i	$0.308752\pi$
$38$	−9.76736e6	−0.759890
$39$	2.11536e6	0.146417
$40$	2.56000e6	0.158114
$41$	−3.37866e7	−1.86731	−0.933657	−	0.358168i	$-0.883401\pi$
$41$	−3.37866e7	−1.86731	−0.933657	+	0.358168i	$0.883401\pi$
$42$	7.59405e6	0.376575
$43$	−3.68862e7	−1.64534	−0.822671	−	0.568518i	$-0.807517\pi$
$43$	−3.68862e7	−1.64534	−0.822671	+	0.568518i	$0.807517\pi$
$44$	−1.42541e6	−0.0573327
$45$	1.09794e7	0.399136
$46$	2.31666e7	0.762873
$47$	−4.41638e7	−1.32016	−0.660079	−	0.751196i	$-0.729477\pi$
$47$	−4.41638e7	−1.32016	−0.660079	+	0.751196i	$0.729477\pi$
$48$	3.01466e6	0.0819695
$49$	6.61075e7	1.63821
$50$	−6.25000e6	−0.141421
$51$	−1.75406e7	−0.363061
$52$	1.17724e7	0.223280
$53$	2.97463e7	0.517835	0.258917	−	0.965899i	$-0.416634\pi$
$53$	2.97463e7	0.517835	0.258917	+	0.965899i	$0.416634\pi$
$54$	2.74160e7	0.438765
$55$	3.48000e6	0.0512799
$56$	4.22625e7	0.574261
$57$	2.80812e7	0.352353
$58$	−8.61682e7	−0.999818
$59$	−6.55754e7	−0.704542	−0.352271	−	0.935898i	$-0.614590\pi$
$59$	−6.55754e7	−0.704542	−0.352271	+	0.935898i	$0.614590\pi$
$60$	−7.36000e6	−0.0733157
$61$	4.01832e7	0.371587	0.185793	−	0.982589i	$-0.440514\pi$
$61$	4.01832e7	0.371587	0.185793	+	0.982589i	$0.440514\pi$
$62$	−4.88616e7	−0.419958
$63$	1.81256e8	1.44964
$64$	1.67772e7	0.125000
$65$	−2.87412e7	−0.199708
$66$	4.09805e6	0.0265846
$67$	−1.15706e8	−0.701487	−0.350744	−	0.936471i	$-0.614071\pi$
$67$	−1.15706e8	−0.701487	−0.350744	+	0.936471i	$0.614071\pi$
$68$	−9.76174e7	−0.553652
$69$	−6.66040e7	−0.353736
$70$	−1.03180e8	−0.513635
$71$	−2.31682e8	−1.08200	−0.541002	−	0.841021i	$-0.681955\pi$
$71$	−2.31682e8	−1.08200	−0.541002	+	0.841021i	$0.681955\pi$
$72$	7.19544e7	0.315545
$73$	3.58692e8	1.47832	0.739160	−	0.673529i	$-0.235223\pi$
$73$	3.58692e8	1.47832	0.739160	+	0.673529i	$0.235223\pi$
$74$	−2.06231e8	−0.799487
$75$	1.79688e7	0.0655756
$76$	1.56278e8	0.537324
$77$	5.74506e7	0.186246
$78$	−3.38457e7	−0.103533
$79$	−4.86017e8	−1.40388	−0.701939	−	0.712237i	$-0.747682\pi$
$79$	−4.86017e8	−1.40388	−0.701939	+	0.712237i	$0.747682\pi$
$80$	−4.09600e7	−0.111803
$81$	2.66950e8	0.689045
$82$	5.40586e8	1.32039
$83$	2.51169e8	0.580917	0.290459	−	0.956888i	$-0.406192\pi$
$83$	2.51169e8	0.580917	0.290459	+	0.956888i	$0.406192\pi$
$84$	−1.21505e8	−0.266279
$85$	2.38324e8	0.495202
$86$	5.90180e8	1.16343
$87$	2.47733e8	0.463605
$88$	2.28065e7	0.0405403
$89$	−5.26039e8	−0.888716	−0.444358	−	0.895849i	$-0.646568\pi$
$89$	−5.26039e8	−0.888716	−0.444358	+	0.895849i	$0.646568\pi$
$90$	−1.75670e8	−0.282232
$91$	−4.74484e8	−0.725329
$92$	−3.70666e8	−0.539433
$93$	1.40477e8	0.194730
$94$	7.06621e8	0.933493
$95$	−3.81538e8	−0.480597
$96$	−4.82345e7	−0.0579612
$97$	−1.07598e9	−1.23405	−0.617024	−	0.786944i	$-0.711662\pi$
$97$	−1.07598e9	−1.23405	−0.617024	+	0.786944i	$0.711662\pi$
$98$	−1.05772e9	−1.15839
$99$	9.78131e7	0.102338
$100$	1.00000e8	0.100000
$101$	−6.63828e8	−0.634760	−0.317380	−	0.948298i	$-0.602803\pi$
$101$	−6.63828e8	−0.634760	−0.317380	+	0.948298i	$0.602803\pi$
$102$	2.80650e8	0.256723
$103$	5.86835e8	0.513746	0.256873	−	0.966445i	$-0.417308\pi$
$103$	5.86835e8	0.513746	0.256873	+	0.966445i	$0.417308\pi$
$104$	−1.88359e8	−0.157883
$105$	2.96642e8	0.238167
$106$	−4.75940e8	−0.366164
$107$	8.58643e8	0.633265	0.316633	−	0.948548i	$-0.397448\pi$
$107$	8.58643e8	0.633265	0.316633	+	0.948548i	$0.397448\pi$
$108$	−4.38656e8	−0.310254
$109$	2.41003e9	1.63532	0.817660	−	0.575702i	$-0.195271\pi$
$109$	2.41003e9	1.63532	0.817660	+	0.575702i	$0.195271\pi$
$110$	−5.56800e7	−0.0362604
$111$	5.92914e8	0.370714
$112$	−6.76200e8	−0.406064
$113$	−7.85949e8	−0.453462	−0.226731	−	0.973957i	$-0.572804\pi$
$113$	−7.85949e8	−0.453462	−0.226731	+	0.973957i	$0.572804\pi$
$114$	−4.49299e8	−0.249151
$115$	9.04946e8	0.482484
$116$	1.37869e9	0.706978
$117$	−8.07836e8	−0.398554
$118$	1.04921e9	0.498186
$119$	3.93444e9	1.79855
$120$	1.17760e8	0.0518421
$121$	−2.32695e9	−0.986852
$122$	−6.42931e8	−0.262752
$123$	−1.55418e9	−0.612251
$124$	7.81786e8	0.296955
$125$	−2.44141e8	−0.0894427
$126$	−2.90010e9	−1.02505
$127$	−1.33021e9	−0.453735	−0.226868	−	0.973926i	$-0.572848\pi$
$127$	−1.33021e9	−0.453735	−0.226868	+	0.973926i	$0.572848\pi$
$128$	−2.68435e8	−0.0883883
$129$	−1.69677e9	−0.539471
$130$	4.59860e8	0.141215
$131$	3.16854e9	0.940022	0.470011	−	0.882661i	$-0.344250\pi$
$131$	3.16854e9	0.940022	0.470011	+	0.882661i	$0.344250\pi$
$132$	−6.55688e7	−0.0187981
$133$	−6.29873e9	−1.74550
$134$	1.85130e9	0.496026
$135$	1.07094e9	0.277499
$136$	1.56188e9	0.391491
$137$	4.33448e9	1.05122	0.525611	−	0.850725i	$-0.323837\pi$
$137$	4.33448e9	1.05122	0.525611	+	0.850725i	$0.323837\pi$
$138$	1.06566e9	0.250129
$139$	−7.74223e9	−1.75914	−0.879568	−	0.475774i	$-0.842168\pi$
$139$	−7.74223e9	−1.75914	−0.879568	+	0.475774i	$0.842168\pi$
$140$	1.65088e9	0.363195
$141$	−2.03153e9	−0.432851
$142$	3.70691e9	0.765093
$143$	−2.56050e8	−0.0512050
$144$	−1.15127e9	−0.223124
$145$	−3.36594e9	−0.632340
$146$	−5.73907e9	−1.04533
$147$	3.04095e9	0.537132
$148$	3.29970e9	0.565323
$149$	3.71367e9	0.617256	0.308628	−	0.951183i	$-0.400130\pi$
$149$	3.71367e9	0.617256	0.308628	+	0.951183i	$0.400130\pi$
$150$	−2.87500e8	−0.0463689
$151$	5.80652e9	0.908908	0.454454	−	0.890770i	$-0.349834\pi$
$151$	5.80652e9	0.908908	0.454454	+	0.890770i	$0.349834\pi$
$152$	−2.50044e9	−0.379945
$153$	6.69861e9	0.988265
$154$	−9.19210e8	−0.131696
$155$	−1.90866e9	−0.265604
$156$	5.41531e8	0.0732087
$157$	−4.94193e9	−0.649154	−0.324577	−	0.945859i	$-0.605222\pi$
$157$	−4.94193e9	−0.649154	−0.324577	+	0.945859i	$0.605222\pi$
$158$	7.77627e9	0.992692
$159$	1.36833e9	0.169787
$160$	6.55360e8	0.0790569
$161$	1.49396e10	1.75235
$162$	−4.27120e9	−0.487229
$163$	−1.80144e8	−0.0199883	−0.00999415	−	0.999950i	$-0.503181\pi$
$163$	−1.80144e8	−0.0199883	−0.00999415	+	0.999950i	$0.503181\pi$
$164$	−8.64937e9	−0.933657
$165$	1.60080e8	0.0168135
$166$	−4.01870e9	−0.410771
$167$	4.51616e9	0.449309	0.224655	−	0.974438i	$-0.427875\pi$
$167$	4.51616e9	0.449309	0.224655	+	0.974438i	$0.427875\pi$
$168$	1.94408e9	0.188288
$169$	−8.48979e9	−0.800583
$170$	−3.81318e9	−0.350161
$171$	−1.07240e10	−0.959119
$172$	−9.44288e9	−0.822671
$173$	−2.34640e9	−0.199157	−0.0995784	−	0.995030i	$-0.531749\pi$
$173$	−2.34640e9	−0.199157	−0.0995784	+	0.995030i	$0.531749\pi$
$174$	−3.96374e9	−0.327818
$175$	−4.03047e9	−0.324851
$176$	−3.64904e8	−0.0286663
$177$	−3.01647e9	−0.231004
$178$	8.41663e9	0.628417
$179$	−1.06237e10	−0.773461	−0.386731	−	0.922193i	$-0.626396\pi$
$179$	−1.06237e10	−0.773461	−0.386731	+	0.922193i	$0.626396\pi$
$180$	2.81072e9	0.199568
$181$	8.91608e9	0.617476	0.308738	−	0.951147i	$-0.400093\pi$
$181$	8.91608e9	0.617476	0.308738	+	0.951147i	$0.400093\pi$
$182$	7.59174e9	0.512885
$183$	1.84843e9	0.121835
$184$	5.93066e9	0.381437
$185$	−8.05590e9	−0.505640
$186$	−2.24764e9	−0.137695
$187$	2.12318e9	0.126969
$188$	−1.13059e10	−0.660079
$189$	1.76799e10	1.00786
$190$	6.10460e9	0.339833
$191$	−9.95469e8	−0.0541225	−0.0270612	−	0.999634i	$-0.508615\pi$
$191$	−9.95469e8	−0.0541225	−0.0270612	+	0.999634i	$0.508615\pi$
$192$	7.71752e8	0.0409847
$193$	2.51853e10	1.30659	0.653295	−	0.757103i	$-0.273386\pi$
$193$	2.51853e10	1.30659	0.653295	+	0.757103i	$0.273386\pi$
$194$	1.72157e10	0.872604
$195$	−1.32210e9	−0.0654799
$196$	1.69235e10	0.819103
$197$	−2.25774e9	−0.106801	−0.0534005	−	0.998573i	$-0.517006\pi$
$197$	−2.25774e9	−0.106801	−0.0534005	+	0.998573i	$0.517006\pi$
$198$	−1.56501e9	−0.0723641
$199$	−4.30919e9	−0.194786	−0.0973928	−	0.995246i	$-0.531050\pi$
$199$	−4.30919e9	−0.194786	−0.0973928	+	0.995246i	$0.531050\pi$
$200$	−1.60000e9	−0.0707107
$201$	−5.32248e9	−0.230002
$202$	1.06213e10	0.448843
$203$	−5.55677e10	−2.29663
$204$	−4.49040e9	−0.181530
$205$	2.11166e10	0.835088
$206$	−9.38935e9	−0.363273
$207$	2.54355e10	0.962884
$208$	3.01374e9	0.111640
$209$	−3.39904e9	−0.123225
$210$	−4.74628e9	−0.168409
$211$	−3.40832e10	−1.18378	−0.591888	−	0.806020i	$-0.701617\pi$
$211$	−3.40832e10	−1.18378	−0.591888	+	0.806020i	$0.701617\pi$
$212$	7.61504e9	0.258917
$213$	−1.06574e10	−0.354765
$214$	−1.37383e10	−0.447786
$215$	2.30539e10	0.735819
$216$	7.01850e9	0.219383
$217$	−3.15096e10	−0.964661
$218$	−3.85604e10	−1.15635
$219$	1.64998e10	0.484709
$220$	8.90880e8	0.0256399
$221$	−1.75353e10	−0.494479
$222$	−9.48663e9	−0.262134
$223$	1.84783e10	0.500369	0.250184	−	0.968198i	$-0.419509\pi$
$223$	1.84783e10	0.500369	0.250184	+	0.968198i	$0.419509\pi$
$224$	1.08192e10	0.287131
$225$	−6.86211e9	−0.178499
$226$	1.25752e10	0.320646
$227$	−1.47458e10	−0.368598	−0.184299	−	0.982870i	$-0.559001\pi$
$227$	−1.47458e10	−0.368598	−0.184299	+	0.982870i	$0.559001\pi$
$228$	7.18878e9	0.176177
$229$	6.19124e10	1.48771	0.743855	−	0.668341i	$-0.232995\pi$
$229$	6.19124e10	1.48771	0.743855	+	0.668341i	$0.232995\pi$
$230$	−1.44791e10	−0.341167
$231$	2.64273e9	0.0610659
$232$	−2.20590e10	−0.499909
$233$	2.93095e10	0.651488	0.325744	−	0.945458i	$-0.394385\pi$
$233$	2.93095e10	0.651488	0.325744	+	0.945458i	$0.394385\pi$
$234$	1.29254e10	0.281820
$235$	2.76024e10	0.590393
$236$	−1.67873e10	−0.352271
$237$	−2.23568e10	−0.460301
$238$	−6.29510e10	−1.27176
$239$	7.51562e9	0.148996	0.0744979	−	0.997221i	$-0.476265\pi$
$239$	7.51562e9	0.148996	0.0744979	+	0.997221i	$0.476265\pi$
$240$	−1.88416e9	−0.0366579
$241$	1.54331e10	0.294697	0.147349	−	0.989085i	$-0.452926\pi$
$241$	1.54331e10	0.294697	0.147349	+	0.989085i	$0.452926\pi$
$242$	3.72311e10	0.697810
$243$	4.60065e10	0.846430
$244$	1.02869e10	0.185793
$245$	−4.13172e10	−0.732628
$246$	2.48670e10	0.432927
$247$	2.80726e10	0.479895
$248$	−1.25086e10	−0.209979
$249$	1.15538e10	0.190470
$250$	3.90625e9	0.0632456
$251$	−8.53077e9	−0.135661	−0.0678307	−	0.997697i	$-0.521608\pi$
$251$	−8.53077e9	−0.135661	−0.0678307	+	0.997697i	$0.521608\pi$
$252$	4.64016e10	0.724821
$253$	8.06199e9	0.123709
$254$	2.12833e10	0.320839
$255$	1.09629e10	0.162366
$256$	4.29497e9	0.0625000
$257$	−2.26760e10	−0.324240	−0.162120	−	0.986771i	$-0.551833\pi$
$257$	−2.26760e10	−0.324240	−0.162120	+	0.986771i	$0.551833\pi$
$258$	2.71483e10	0.381464
$259$	−1.32993e11	−1.83646
$260$	−7.35776e9	−0.0998540
$261$	−9.46073e10	−1.26195
$262$	−5.06966e10	−0.664696
$263$	5.46655e10	0.704551	0.352275	−	0.935896i	$-0.385408\pi$
$263$	5.46655e10	0.704551	0.352275	+	0.935896i	$0.385408\pi$
$264$	1.04910e9	0.0132923
$265$	−1.85914e10	−0.231583
$266$	1.00780e11	1.23426
$267$	−2.41978e10	−0.291390
$268$	−2.96208e10	−0.350744
$269$	−4.91761e10	−0.572623	−0.286311	−	0.958137i	$-0.592429\pi$
$269$	−4.91761e10	−0.572623	−0.286311	+	0.958137i	$0.592429\pi$
$270$	−1.71350e10	−0.196222
$271$	1.47503e11	1.66127	0.830633	−	0.556821i	$-0.187979\pi$
$271$	1.47503e11	1.66127	0.830633	+	0.556821i	$0.187979\pi$
$272$	−2.49901e10	−0.276826
$273$	−2.18262e10	−0.237819
$274$	−6.93517e10	−0.743327
$275$	−2.17500e9	−0.0229331
$276$	−1.70506e10	−0.176868
$277$	−1.35893e11	−1.38688	−0.693439	−	0.720515i	$-0.743905\pi$
$277$	−1.35893e11	−1.38688	−0.693439	+	0.720515i	$0.743905\pi$
$278$	1.23876e11	1.24390
$279$	−5.36470e10	−0.530062
$280$	−2.64141e10	−0.256817
$281$	−1.12160e11	−1.07315	−0.536573	−	0.843854i	$-0.680282\pi$
$281$	−1.12160e11	−1.07315	−0.536573	+	0.843854i	$0.680282\pi$
$282$	3.25046e10	0.306072
$283$	−4.83922e10	−0.448473	−0.224237	−	0.974535i	$-0.571989\pi$
$283$	−4.83922e10	−0.448473	−0.224237	+	0.974535i	$0.571989\pi$
$284$	−5.93105e10	−0.541002
$285$	−1.75507e10	−0.157577
$286$	4.09680e9	0.0362074
$287$	3.48610e11	3.03300
$288$	1.84203e10	0.157773
$289$	2.68155e10	0.226124
$290$	5.38551e10	0.447132
$291$	−4.94951e10	−0.404617
$292$	9.18251e10	0.739160
$293$	1.96104e11	1.55447	0.777236	−	0.629209i	$-0.216621\pi$
$293$	1.96104e11	1.55447	0.777236	+	0.629209i	$0.216621\pi$
$294$	−4.86551e10	−0.379809
$295$	4.09846e10	0.315081
$296$	−5.27952e10	−0.399743
$297$	9.54077e9	0.0711507
$298$	−5.94187e10	−0.436466
$299$	−6.65838e10	−0.481779
$300$	4.60000e9	0.0327878
$301$	3.80592e11	2.67246
$302$	−9.29044e10	−0.642695
$303$	−3.05361e10	−0.208124
$304$	4.00071e10	0.268662
$305$	−2.51145e10	−0.166179
$306$	−1.07178e11	−0.698809
$307$	5.05542e9	0.0324814	0.0162407	−	0.999868i	$-0.494830\pi$
$307$	5.05542e9	0.0324814	0.0162407	+	0.999868i	$0.494830\pi$
$308$	1.47074e10	0.0931229
$309$	2.69944e10	0.168446
$310$	3.05385e10	0.187811
$311$	−1.88662e11	−1.14357	−0.571783	−	0.820405i	$-0.693748\pi$
$311$	−1.88662e11	−1.14357	−0.571783	+	0.820405i	$0.693748\pi$
$312$	−8.66450e9	−0.0517664
$313$	−9.28080e10	−0.546557	−0.273279	−	0.961935i	$-0.588108\pi$
$313$	−9.28080e10	−0.546557	−0.273279	+	0.961935i	$0.588108\pi$
$314$	7.90708e10	0.459021
$315$	−1.13285e11	−0.648299
$316$	−1.24420e11	−0.701939
$317$	−1.90705e11	−1.06071	−0.530354	−	0.847776i	$-0.677941\pi$
$317$	−1.90705e11	−1.06071	−0.530354	+	0.847776i	$0.677941\pi$
$318$	−2.18933e10	−0.120057
$319$	−2.99865e10	−0.162132
$320$	−1.04858e10	−0.0559017
$321$	3.94976e10	0.207634
$322$	−2.39033e11	−1.23910
$323$	−2.32779e11	−1.18996
$324$	6.83393e10	0.344523
$325$	1.79633e10	0.0893122
$326$	2.88231e9	0.0141339
$327$	1.10861e11	0.536185
$328$	1.38390e11	0.660195
$329$	4.55682e11	2.14427
$330$	−2.56128e9	−0.0118890
$331$	1.24343e11	0.569373	0.284686	−	0.958621i	$-0.408111\pi$
$331$	1.24343e11	0.569373	0.284686	+	0.958621i	$0.408111\pi$
$332$	6.42992e10	0.290459
$333$	−2.26429e11	−1.00910
$334$	−7.22586e10	−0.317710
$335$	7.23163e10	0.313715
$336$	−3.11052e10	−0.133139
$337$	−3.33152e11	−1.40705	−0.703523	−	0.710673i	$-0.748391\pi$
$337$	−3.33152e11	−1.40705	−0.703523	+	0.710673i	$0.748391\pi$
$338$	1.35837e11	0.566098
$339$	−3.61537e10	−0.148680
$340$	6.10109e10	0.247601
$341$	−1.70038e10	−0.0681008
$342$	1.71583e11	0.678199
$343$	−2.65729e11	−1.03661
$344$	1.51086e11	0.581716
$345$	4.16275e10	0.158196
$346$	3.75424e10	0.140825
$347$	1.61683e11	0.598662	0.299331	−	0.954149i	$-0.403237\pi$
$347$	1.61683e11	0.598662	0.299331	+	0.954149i	$0.403237\pi$
$348$	6.34198e10	0.231802
$349$	2.20719e11	0.796388	0.398194	−	0.917301i	$-0.369637\pi$
$349$	2.20719e11	0.796388	0.398194	+	0.917301i	$0.369637\pi$
$350$	6.44875e10	0.229704
$351$	−7.87970e10	−0.277094
$352$	5.83847e9	0.0202702
$353$	−7.98456e10	−0.273694	−0.136847	−	0.990592i	$-0.543697\pi$
$353$	−7.98456e10	−0.273694	−0.136847	+	0.990592i	$0.543697\pi$
$354$	4.82635e10	0.163344
$355$	1.44801e11	0.483887
$356$	−1.34666e11	−0.444358
$357$	1.80984e11	0.589703
$358$	1.69980e11	0.546920
$359$	−2.53605e10	−0.0805810	−0.0402905	−	0.999188i	$-0.512828\pi$
$359$	−2.53605e10	−0.0805810	−0.0402905	+	0.999188i	$0.512828\pi$
$360$	−4.49715e10	−0.141116
$361$	4.99737e10	0.154867
$362$	−1.42657e11	−0.436622
$363$	−1.07039e11	−0.323567
$364$	−1.21468e11	−0.362664
$365$	−2.24182e11	−0.661125
$366$	−2.95748e10	−0.0861504
$367$	−2.95956e11	−0.851590	−0.425795	−	0.904820i	$-0.640006\pi$
$367$	−2.95956e11	−0.851590	−0.425795	+	0.904820i	$0.640006\pi$
$368$	−9.48905e10	−0.269716
$369$	5.93530e11	1.66657
$370$	1.28894e11	0.357541
$371$	−3.06922e11	−0.841096
$372$	3.59622e10	0.0973649
$373$	3.29080e11	0.880260	0.440130	−	0.897934i	$-0.354932\pi$
$373$	3.29080e11	0.880260	0.440130	+	0.897934i	$0.354932\pi$
$374$	−3.39709e10	−0.0897810
$375$	−1.12305e10	−0.0293263
$376$	1.80895e11	0.466746
$377$	2.47658e11	0.631417
$378$	−2.82878e11	−0.712667
$379$	−7.29572e11	−1.81632	−0.908159	−	0.418626i	$-0.862512\pi$
$379$	−7.29572e11	−1.81632	−0.908159	+	0.418626i	$0.862512\pi$
$380$	−9.76736e10	−0.240298
$381$	−6.11895e10	−0.148770
$382$	1.59275e10	0.0382704
$383$	5.46931e10	0.129879	0.0649394	−	0.997889i	$-0.479315\pi$
$383$	5.46931e10	0.129879	0.0649394	+	0.997889i	$0.479315\pi$
$384$	−1.23480e10	−0.0289806
$385$	−3.59066e10	−0.0832917
$386$	−4.02965e11	−0.923899
$387$	6.47980e11	1.46846
$388$	−2.75451e11	−0.617024
$389$	−8.37798e11	−1.85509	−0.927547	−	0.373706i	$-0.878087\pi$
$389$	−8.37798e11	−1.85509	−0.927547	+	0.373706i	$0.878087\pi$
$390$	2.11536e10	0.0463013
$391$	5.52116e11	1.19463
$392$	−2.70776e11	−0.579193
$393$	1.45753e11	0.308212
$394$	3.61238e10	0.0755197
$395$	3.03761e11	0.627834
$396$	2.50401e10	0.0511692
$397$	−1.26117e11	−0.254809	−0.127405	−	0.991851i	$-0.540665\pi$
$397$	−1.26117e11	−0.254809	−0.127405	+	0.991851i	$0.540665\pi$
$398$	6.89471e10	0.137734
$399$	−2.89741e11	−0.572312
$400$	2.56000e10	0.0500000
$401$	−1.65707e11	−0.320031	−0.160016	−	0.987114i	$-0.551154\pi$
$401$	−1.65707e11	−0.320031	−0.160016	+	0.987114i	$0.551154\pi$
$402$	8.51597e10	0.162636
$403$	1.40434e11	0.265217
$404$	−1.69940e11	−0.317380
$405$	−1.66844e11	−0.308150
$406$	8.89083e11	1.62396
$407$	−7.17684e10	−0.129646
$408$	7.18464e10	0.128361
$409$	2.32261e11	0.410413	0.205207	−	0.978719i	$-0.434213\pi$
$409$	2.32261e11	0.410413	0.205207	+	0.978719i	$0.434213\pi$
$410$	−3.37866e11	−0.590497
$411$	1.99386e11	0.344673
$412$	1.50230e11	0.256873
$413$	6.76607e11	1.14436
$414$	−4.06968e11	−0.680862
$415$	−1.56981e11	−0.259794
$416$	−4.82198e10	−0.0789415
$417$	−3.56142e11	−0.576782
$418$	5.43847e10	0.0871331
$419$	7.82753e11	1.24069	0.620343	−	0.784331i	$-0.286993\pi$
$419$	7.82753e11	1.24069	0.620343	+	0.784331i	$0.286993\pi$
$420$	7.59405e10	0.119083
$421$	2.17217e11	0.336996	0.168498	−	0.985702i	$-0.446108\pi$
$421$	2.17217e11	0.336996	0.168498	+	0.985702i	$0.446108\pi$
$422$	5.45331e11	0.837056
$423$	7.75825e11	1.17824
$424$	−1.21841e11	−0.183082
$425$	−1.48952e11	−0.221461
$426$	1.70518e11	0.250857
$427$	−4.14610e11	−0.603552
$428$	2.19813e11	0.316633
$429$	−1.17783e10	−0.0167890
$430$	−3.68862e11	−0.520303
$431$	−5.67022e11	−0.791502	−0.395751	−	0.918358i	$-0.629516\pi$
$431$	−5.67022e11	−0.791502	−0.395751	+	0.918358i	$0.629516\pi$
$432$	−1.12296e11	−0.155127
$433$	5.02627e10	0.0687148	0.0343574	−	0.999410i	$-0.489062\pi$
$433$	5.02627e10	0.0687148	0.0343574	+	0.999410i	$0.489062\pi$
$434$	5.04154e11	0.682118
$435$	−1.54833e11	−0.207330
$436$	6.16967e11	0.817660
$437$	−8.83894e11	−1.15940
$438$	−2.63997e11	−0.342741
$439$	−8.61417e11	−1.10694	−0.553469	−	0.832870i	$-0.686696\pi$
$439$	−8.61417e11	−1.10694	−0.553469	+	0.832870i	$0.686696\pi$
$440$	−1.42541e10	−0.0181302
$441$	−1.16131e12	−1.46209
$442$	2.80565e11	0.349649
$443$	3.82256e10	0.0471561	0.0235781	−	0.999722i	$-0.492494\pi$
$443$	3.82256e10	0.0471561	0.0235781	+	0.999722i	$0.492494\pi$
$444$	1.51786e11	0.185357
$445$	3.28774e11	0.397446
$446$	−2.95653e11	−0.353814
$447$	1.70829e11	0.202385
$448$	−1.73107e11	−0.203032
$449$	−1.60804e12	−1.86719	−0.933594	−	0.358332i	$-0.883346\pi$
$449$	−1.60804e12	−1.86719	−0.933594	+	0.358332i	$0.883346\pi$
$450$	1.09794e11	0.126218
$451$	1.88124e11	0.214116
$452$	−2.01203e11	−0.226731
$453$	2.67100e11	0.298011
$454$	2.35933e11	0.260638
$455$	2.96552e11	0.324377
$456$	−1.15020e11	−0.124576
$457$	−5.06545e11	−0.543244	−0.271622	−	0.962404i	$-0.587560\pi$
$457$	−5.06545e11	−0.543244	−0.271622	+	0.962404i	$0.587560\pi$
$458$	−9.90599e11	−1.05197
$459$	6.53388e11	0.687091
$460$	2.31666e11	0.241242
$461$	1.90359e11	0.196299	0.0981495	−	0.995172i	$-0.468708\pi$
$461$	1.90359e11	0.196299	0.0981495	+	0.995172i	$0.468708\pi$
$462$	−4.22837e10	−0.0431801
$463$	−5.01410e11	−0.507082	−0.253541	−	0.967325i	$-0.581595\pi$
$463$	−5.01410e11	−0.507082	−0.253541	+	0.967325i	$0.581595\pi$
$464$	3.52945e11	0.353489
$465$	−8.77982e10	−0.0870858
$466$	−4.68951e11	−0.460671
$467$	1.90958e12	1.85785	0.928926	−	0.370265i	$-0.120733\pi$
$467$	1.90958e12	1.85785	0.928926	+	0.370265i	$0.120733\pi$
$468$	−2.06806e11	−0.199277
$469$	1.19386e12	1.13939
$470$	−4.41638e11	−0.417471
$471$	−2.27329e11	−0.212843
$472$	2.68597e11	0.249093
$473$	2.05383e11	0.188664
$474$	3.57709e11	0.325482
$475$	2.38461e11	0.214929
$476$	1.00722e12	0.899273
$477$	−5.22553e11	−0.462165
$478$	−1.20250e11	−0.105356
$479$	1.64266e12	1.42573	0.712864	−	0.701302i	$-0.247398\pi$
$479$	1.64266e12	1.42573	0.712864	+	0.701302i	$0.247398\pi$
$480$	3.01466e10	0.0259210
$481$	5.92734e11	0.504902
$482$	−2.46929e11	−0.208382
$483$	6.87221e11	0.574558
$484$	−5.95698e11	−0.493426
$485$	6.72488e11	0.551883
$486$	−7.36105e11	−0.598517
$487$	−1.09565e12	−0.882659	−0.441329	−	0.897345i	$-0.645493\pi$
$487$	−1.09565e12	−0.882659	−0.441329	+	0.897345i	$0.645493\pi$
$488$	−1.64590e11	−0.131376
$489$	−8.28663e9	−0.00655372
$490$	6.61075e11	0.518046
$491$	3.55730e11	0.276219	0.138110	−	0.990417i	$-0.455897\pi$
$491$	3.55730e11	0.276219	0.138110	+	0.990417i	$0.455897\pi$
$492$	−3.97871e11	−0.306126
$493$	−2.05359e12	−1.56568
$494$	−4.49162e11	−0.339337
$495$	−6.11332e10	−0.0457671
$496$	2.00137e11	0.148477
$497$	2.39049e12	1.75745
$498$	−1.84860e11	−0.134683
$499$	4.00601e11	0.289241	0.144620	−	0.989487i	$-0.453804\pi$
$499$	4.00601e11	0.289241	0.144620	+	0.989487i	$0.453804\pi$
$500$	−6.25000e10	−0.0447214
$501$	2.07743e11	0.147319
$502$	1.36492e11	0.0959271
$503$	−1.73792e12	−1.21052	−0.605261	−	0.796027i	$-0.706931\pi$
$503$	−1.73792e12	−1.21052	−0.605261	+	0.796027i	$0.706931\pi$
$504$	−7.42426e11	−0.512526
$505$	4.14893e11	0.283873
$506$	−1.28992e11	−0.0874751
$507$	−3.90530e11	−0.262494
$508$	−3.40533e11	−0.226868
$509$	4.73007e11	0.312347	0.156174	−	0.987730i	$-0.450084\pi$
$509$	4.73007e11	0.312347	0.156174	+	0.987730i	$0.450084\pi$
$510$	−1.75406e11	−0.114810
$511$	−3.70098e12	−2.40117
$512$	−6.87195e10	−0.0441942
$513$	−1.04602e12	−0.666827
$514$	3.62816e11	0.229272
$515$	−3.66772e11	−0.229754
$516$	−4.34372e11	−0.269736
$517$	2.45904e11	0.151376
$518$	2.12789e12	1.29857
$519$	−1.07935e11	−0.0652991
$520$	1.17724e11	0.0706075
$521$	1.09352e12	0.650214	0.325107	−	0.945677i	$-0.394600\pi$
$521$	1.09352e12	0.650214	0.325107	+	0.945677i	$0.394600\pi$
$522$	1.51372e12	0.892333
$523$	9.50535e11	0.555534	0.277767	−	0.960648i	$-0.410406\pi$
$523$	9.50535e11	0.555534	0.277767	+	0.960648i	$0.410406\pi$
$524$	8.11146e11	0.470011
$525$	−1.85402e11	−0.106512
$526$	−8.74648e11	−0.498193
$527$	−1.16449e12	−0.657639
$528$	−1.67856e10	−0.00939906
$529$	2.95302e11	0.163952
$530$	2.97463e11	0.163754
$531$	1.15196e12	0.628801
$532$	−1.61247e12	−0.872751
$533$	−1.55371e12	−0.833869
$534$	3.87165e11	0.206044
$535$	−5.36652e11	−0.283205
$536$	4.73932e11	0.248013
$537$	−4.88692e11	−0.253601
$538$	7.86817e11	0.404906
$539$	−3.68087e11	−0.187845
$540$	2.74160e11	0.138750
$541$	−5.24515e10	−0.0263251	−0.0131625	−	0.999913i	$-0.504190\pi$
$541$	−5.24515e10	−0.0263251	−0.0131625	+	0.999913i	$0.504190\pi$
$542$	−2.36005e12	−1.17469
$543$	4.10140e11	0.202457
$544$	3.99841e11	0.195746
$545$	−1.50627e12	−0.731337
$546$	3.49220e11	0.168164
$547$	−2.41313e12	−1.15249	−0.576245	−	0.817277i	$-0.695483\pi$
$547$	−2.41313e12	−1.15249	−0.576245	+	0.817277i	$0.695483\pi$
$548$	1.10963e12	0.525611
$549$	−7.05898e11	−0.331640
$550$	3.48000e10	0.0162161
$551$	3.28764e12	1.51950
$552$	2.72810e11	0.125065
$553$	5.01472e12	2.28026
$554$	2.17429e12	0.980671
$555$	−3.70571e11	−0.165788
$556$	−1.98201e12	−0.879568
$557$	4.13701e12	1.82112	0.910560	−	0.413376i	$-0.135651\pi$
$557$	4.13701e12	1.82112	0.910560	+	0.413376i	$0.135651\pi$
$558$	8.58352e11	0.374810
$559$	−1.69625e12	−0.734745
$560$	4.22625e11	0.181597
$561$	9.76662e10	0.0416305
$562$	1.79456e12	0.758830
$563$	−1.88257e12	−0.789702	−0.394851	−	0.918745i	$-0.629204\pi$
$563$	−1.88257e12	−0.789702	−0.394851	+	0.918745i	$0.629204\pi$
$564$	−5.20073e11	−0.216425
$565$	4.91218e11	0.202795
$566$	7.74275e11	0.317118
$567$	−2.75439e12	−1.11919
$568$	9.48968e11	0.382546
$569$	−2.81240e12	−1.12479	−0.562396	−	0.826868i	$-0.690120\pi$
$569$	−2.81240e12	−1.12479	−0.562396	+	0.826868i	$0.690120\pi$
$570$	2.80812e11	0.111424
$571$	4.78186e12	1.88250	0.941248	−	0.337715i	$-0.109654\pi$
$571$	4.78186e12	1.88250	0.941248	+	0.337715i	$0.109654\pi$
$572$	−6.55488e10	−0.0256025
$573$	−4.57916e10	−0.0177456
$574$	−5.57777e12	−2.14465
$575$	−5.65591e11	−0.215773
$576$	−2.94725e11	−0.111562
$577$	3.85796e12	1.44899	0.724497	−	0.689278i	$-0.242072\pi$
$577$	3.85796e12	1.44899	0.724497	+	0.689278i	$0.242072\pi$
$578$	−4.29049e11	−0.159894
$579$	1.15852e12	0.428402
$580$	−8.61682e11	−0.316170
$581$	−2.59156e12	−0.943558
$582$	7.91922e11	0.286107
$583$	−1.65627e11	−0.0593777
$584$	−1.46920e12	−0.522665
$585$	5.04898e11	0.178239
$586$	−3.13767e12	−1.09918
$587$	−8.50973e11	−0.295831	−0.147916	−	0.989000i	$-0.547256\pi$
$587$	−8.50973e11	−0.295831	−0.147916	+	0.989000i	$0.547256\pi$
$588$	7.78482e11	0.268566
$589$	1.86425e12	0.638243
$590$	−6.55754e11	−0.222796
$591$	−1.03856e11	−0.0350177
$592$	8.44722e11	0.282661
$593$	−3.74270e12	−1.24291	−0.621454	−	0.783450i	$-0.713458\pi$
$593$	−3.74270e12	−1.24291	−0.621454	+	0.783450i	$0.713458\pi$
$594$	−1.52652e11	−0.0503112
$595$	−2.45902e12	−0.804334
$596$	9.50699e11	0.308628
$597$	−1.98223e11	−0.0638659
$598$	1.06534e12	0.340669
$599$	−3.17943e12	−1.00909	−0.504544	−	0.863386i	$-0.668339\pi$
$599$	−3.17943e12	−1.00909	−0.504544	+	0.863386i	$0.668339\pi$
$600$	−7.36000e10	−0.0231845
$601$	1.11865e12	0.349750	0.174875	−	0.984591i	$-0.444048\pi$
$601$	1.11865e12	0.349750	0.174875	+	0.984591i	$0.444048\pi$
$602$	−6.08947e12	−1.88971
$603$	2.03261e12	0.626075
$604$	1.48647e12	0.454454
$605$	1.45434e12	0.441334
$606$	4.88578e11	0.147166
$607$	2.97775e12	0.890306	0.445153	−	0.895454i	$-0.353149\pi$
$607$	2.97775e12	0.890306	0.445153	+	0.895454i	$0.353149\pi$
$608$	−6.40114e11	−0.189973
$609$	−2.55611e12	−0.753013
$610$	4.01832e11	0.117506
$611$	−2.03092e12	−0.589531
$612$	1.71485e12	0.494133
$613$	−9.38863e11	−0.268553	−0.134277	−	0.990944i	$-0.542871\pi$
$613$	−9.38863e11	−0.268553	−0.134277	+	0.990944i	$0.542871\pi$
$614$	−8.08867e10	−0.0229678
$615$	9.71365e11	0.273807
$616$	−2.35318e11	−0.0658478
$617$	−5.17370e11	−0.143720	−0.0718601	−	0.997415i	$-0.522894\pi$
$617$	−5.17370e11	−0.143720	−0.0718601	+	0.997415i	$0.522894\pi$
$618$	−4.31910e11	−0.119109
$619$	4.35233e12	1.19155	0.595777	−	0.803150i	$-0.296844\pi$
$619$	4.35233e12	1.19155	0.595777	+	0.803150i	$0.296844\pi$
$620$	−4.88616e11	−0.132802
$621$	2.48100e12	0.669445
$622$	3.01858e12	0.808624
$623$	5.42767e12	1.44350
$624$	1.38632e11	0.0366044
$625$	1.52588e11	0.0400000
$626$	1.48493e12	0.386474
$627$	−1.56356e11	−0.0404027
$628$	−1.26513e12	−0.324577
$629$	−4.91498e12	−1.25197
$630$	1.81256e12	0.458417
$631$	−2.88599e12	−0.724708	−0.362354	−	0.932041i	$-0.618027\pi$
$631$	−2.88599e12	−0.724708	−0.362354	+	0.932041i	$0.618027\pi$
$632$	1.99073e12	0.496346
$633$	−1.56783e12	−0.388134
$634$	3.05128e12	0.750033
$635$	8.31379e11	0.202916
$636$	3.50292e11	0.0848933
$637$	3.04002e12	0.731558
$638$	4.79784e11	0.114644
$639$	4.06995e12	0.965685
$640$	1.67772e11	0.0395285
$641$	−2.31205e12	−0.540924	−0.270462	−	0.962731i	$-0.587176\pi$
$641$	−2.31205e12	−0.540924	−0.270462	+	0.962731i	$0.587176\pi$
$642$	−6.31961e11	−0.146819
$643$	−8.90549e11	−0.205451	−0.102726	−	0.994710i	$-0.532756\pi$
$643$	−8.90549e11	−0.205451	−0.102726	+	0.994710i	$0.532756\pi$
$644$	3.82453e12	0.876177
$645$	1.06048e12	0.241259
$646$	3.72447e12	0.841430
$647$	−1.96637e12	−0.441159	−0.220580	−	0.975369i	$-0.570795\pi$
$647$	−1.96637e12	−0.441159	−0.220580	+	0.975369i	$0.570795\pi$
$648$	−1.09343e12	−0.243614
$649$	3.65124e11	0.0807865
$650$	−2.87412e11	−0.0631532
$651$	−1.44944e12	−0.316291
$652$	−4.61169e10	−0.00999415
$653$	−2.12169e12	−0.456638	−0.228319	−	0.973586i	$-0.573323\pi$
$653$	−2.12169e12	−0.456638	−0.228319	+	0.973586i	$0.573323\pi$
$654$	−1.77378e12	−0.379140
$655$	−1.98034e12	−0.420391
$656$	−2.21424e12	−0.466829
$657$	−6.30114e12	−1.31940
$658$	−7.29091e12	−1.51623
$659$	4.04493e12	0.835462	0.417731	−	0.908571i	$-0.362826\pi$
$659$	4.04493e12	0.835462	0.417731	+	0.908571i	$0.362826\pi$
$660$	4.09805e10	0.00840677
$661$	−3.66237e12	−0.746200	−0.373100	−	0.927791i	$-0.621705\pi$
$661$	−3.66237e12	−0.746200	−0.373100	+	0.927791i	$0.621705\pi$
$662$	−1.98949e12	−0.402607
$663$	−8.06623e11	−0.162129
$664$	−1.02879e12	−0.205385
$665$	3.93670e12	0.780612
$666$	3.62286e12	0.713539
$667$	−7.79776e12	−1.52547
$668$	1.15614e12	0.224655
$669$	8.50002e11	0.164060
$670$	−1.15706e12	−0.221830
$671$	−2.23740e11	−0.0426081
$672$	4.97684e11	0.0941438
$673$	6.67203e11	0.125369	0.0626845	−	0.998033i	$-0.480034\pi$
$673$	6.67203e11	0.125369	0.0626845	+	0.998033i	$0.480034\pi$
$674$	5.33043e12	0.994931
$675$	−6.69336e11	−0.124102
$676$	−2.17339e12	−0.400292
$677$	−5.83451e12	−1.06747	−0.533735	−	0.845652i	$-0.679212\pi$
$677$	−5.83451e12	−1.06747	−0.533735	+	0.845652i	$0.679212\pi$
$678$	5.78458e11	0.105133
$679$	1.11020e13	2.00441
$680$	−9.76174e11	−0.175080
$681$	−6.78308e11	−0.120855
$682$	2.72062e11	0.0481546
$683$	−1.19899e12	−0.210824	−0.105412	−	0.994429i	$-0.533616\pi$
$683$	−1.19899e12	−0.210824	−0.105412	+	0.994429i	$0.533616\pi$
$684$	−2.74533e12	−0.479559
$685$	−2.70905e12	−0.470121
$686$	4.25166e12	0.732994
$687$	2.84797e12	0.487787
$688$	−2.41738e12	−0.411336
$689$	1.36791e12	0.231245
$690$	−6.66040e11	−0.111861
$691$	−1.02896e13	−1.71691	−0.858455	−	0.512889i	$-0.828575\pi$
$691$	−1.02896e13	−1.71691	−0.858455	+	0.512889i	$0.828575\pi$
$692$	−6.00679e11	−0.0995784
$693$	−1.00924e12	−0.166224
$694$	−2.58693e12	−0.423318
$695$	4.83889e12	0.786709
$696$	−1.01472e12	−0.163909
$697$	1.28834e13	2.06769
$698$	−3.53150e12	−0.563131
$699$	1.34824e12	0.213608
$700$	−1.03180e12	−0.162426
$701$	2.82990e12	0.442630	0.221315	−	0.975202i	$-0.428965\pi$
$701$	2.82990e12	0.442630	0.221315	+	0.975202i	$0.428965\pi$
$702$	1.26075e12	0.195935
$703$	7.86849e12	1.21505
$704$	−9.34155e10	−0.0143332
$705$	1.26971e12	0.193577
$706$	1.27753e12	0.193531
$707$	6.84938e12	1.03101
$708$	−7.72216e11	−0.115502
$709$	−4.94478e12	−0.734917	−0.367459	−	0.930040i	$-0.619772\pi$
$709$	−4.94478e12	−0.734917	−0.367459	+	0.930040i	$0.619772\pi$
$710$	−2.31682e12	−0.342160
$711$	8.53786e12	1.25296
$712$	2.15466e12	0.314209
$713$	−4.42172e12	−0.640749
$714$	−2.89575e12	−0.416983
$715$	1.60031e11	0.0228996
$716$	−2.71968e12	−0.386731
$717$	3.45718e11	0.0488524
$718$	4.05768e11	0.0569793
$719$	−5.73384e12	−0.800139	−0.400070	−	0.916485i	$-0.631014\pi$
$719$	−5.73384e12	−0.800139	−0.400070	+	0.916485i	$0.631014\pi$
$720$	7.19544e11	0.0997841
$721$	−6.05496e12	−0.834454
$722$	−7.99579e11	−0.109508
$723$	7.09922e11	0.0966247
$724$	2.28252e12	0.308738
$725$	2.10371e12	0.282791
$726$	1.71263e12	0.228796
$727$	−1.15318e13	−1.53106	−0.765530	−	0.643400i	$-0.777523\pi$
$727$	−1.15318e13	−1.53106	−0.765530	+	0.643400i	$0.777523\pi$
$728$	1.94348e12	0.256442
$729$	−3.13808e12	−0.411519
$730$	3.58692e12	0.467486
$731$	1.40654e13	1.82190
$732$	4.73197e11	0.0609176
$733$	9.98900e12	1.27807	0.639034	−	0.769178i	$-0.279334\pi$
$733$	9.98900e12	1.27807	0.639034	+	0.769178i	$0.279334\pi$
$734$	4.73530e12	0.602165
$735$	−1.90059e12	−0.240213
$736$	1.51825e12	0.190718
$737$	6.44252e11	0.0804363
$738$	−9.49647e12	−1.17844
$739$	−9.79393e12	−1.20797	−0.603986	−	0.796995i	$-0.706422\pi$
$739$	−9.79393e12	−1.20797	−0.603986	+	0.796995i	$0.706422\pi$
$740$	−2.06231e12	−0.252820
$741$	1.29134e12	0.157347
$742$	4.91075e12	0.594744
$743$	1.50756e13	1.81478	0.907389	−	0.420291i	$-0.138072\pi$
$743$	1.50756e13	1.81478	0.907389	+	0.420291i	$0.138072\pi$
$744$	−5.75395e11	−0.0688474
$745$	−2.32104e12	−0.276045
$746$	−5.26527e12	−0.622438
$747$	−4.41228e12	−0.518467
$748$	5.43534e11	0.0634847
$749$	−8.85948e12	−1.02858
$750$	1.79688e11	0.0207368
$751$	−1.32862e13	−1.52413	−0.762066	−	0.647499i	$-0.775815\pi$
$751$	−1.32862e13	−1.52413	−0.762066	+	0.647499i	$0.775815\pi$
$752$	−2.89432e12	−0.330040
$753$	−3.92415e11	−0.0444804
$754$	−3.96253e12	−0.446479
$755$	−3.62908e12	−0.406476
$756$	4.52605e12	0.503932
$757$	6.92698e12	0.766677	0.383338	−	0.923608i	$-0.374774\pi$
$757$	6.92698e12	0.766677	0.383338	+	0.923608i	$0.374774\pi$
$758$	1.16732e13	1.28433
$759$	3.70851e11	0.0405613
$760$	1.56278e12	0.169917
$761$	1.10058e12	0.118957	0.0594786	−	0.998230i	$-0.481056\pi$
$761$	1.10058e12	0.118957	0.0594786	+	0.998230i	$0.481056\pi$
$762$	9.79032e11	0.105196
$763$	−2.48667e13	−2.65618
$764$	−2.54840e11	−0.0270612
$765$	−4.18663e12	−0.441966
$766$	−8.75090e11	−0.0918382
$767$	−3.01555e12	−0.314621
$768$	1.97568e11	0.0204924
$769$	2.68920e12	0.277303	0.138652	−	0.990341i	$-0.455723\pi$
$769$	2.68920e12	0.277303	0.138652	+	0.990341i	$0.455723\pi$
$770$	5.74506e11	0.0588961
$771$	−1.04309e12	−0.106311
$772$	6.44744e12	0.653295
$773$	1.44167e13	1.45230	0.726151	−	0.687535i	$-0.241307\pi$
$773$	1.44167e13	1.45230	0.726151	+	0.687535i	$0.241307\pi$
$774$	−1.03677e13	−1.03836
$775$	1.19291e12	0.118782
$776$	4.40722e12	0.436302
$777$	−6.11769e12	−0.602134
$778$	1.34048e13	1.31175
$779$	−2.06254e13	−2.00670
$780$	−3.38457e11	−0.0327399
$781$	1.29000e12	0.124068
$782$	−8.83385e12	−0.844733
$783$	−9.22807e12	−0.877370
$784$	4.33242e12	0.409551
$785$	3.08870e12	0.290311
$786$	−2.33204e12	−0.217939
$787$	9.29043e12	0.863276	0.431638	−	0.902047i	$-0.357936\pi$
$787$	9.29043e12	0.863276	0.431638	+	0.902047i	$0.357936\pi$
$788$	−5.77981e11	−0.0534005
$789$	2.51461e12	0.231007
$790$	−4.86017e12	−0.443945
$791$	8.10942e12	0.736539
$792$	−4.00642e11	−0.0361821
$793$	1.84786e12	0.165936
$794$	2.01787e12	0.180177
$795$	−8.55205e11	−0.0759308
$796$	−1.10315e12	−0.0973928
$797$	2.10631e13	1.84910	0.924550	−	0.381061i	$-0.124441\pi$
$797$	2.10631e13	1.84910	0.924550	+	0.381061i	$0.124441\pi$
$798$	4.63586e12	0.404685
$799$	1.68405e13	1.46182
$800$	−4.09600e11	−0.0353553
$801$	9.24093e12	0.793176
$802$	2.65132e12	0.226296
$803$	−1.99720e12	−0.169512
$804$	−1.36256e12	−0.115001
$805$	−9.33724e12	−0.783677
$806$	−2.24695e12	−0.187537
$807$	−2.26210e12	−0.187750
$808$	2.71904e12	0.224422
$809$	2.05162e13	1.68395	0.841975	−	0.539516i	$-0.181393\pi$
$809$	2.05162e13	1.68395	0.841975	+	0.539516i	$0.181393\pi$
$810$	2.66950e12	0.217895
$811$	1.27620e13	1.03592	0.517958	−	0.855406i	$-0.326692\pi$
$811$	1.27620e13	1.03592	0.517958	+	0.855406i	$0.326692\pi$
$812$	−1.42253e13	−1.14831
$813$	6.78514e12	0.544692
$814$	1.14829e12	0.0916734
$815$	1.12590e11	0.00893904
$816$	−1.14954e12	−0.0907652
$817$	−2.25176e13	−1.76816
$818$	−3.71617e12	−0.290206
$819$	8.33525e12	0.647353
$820$	5.40586e12	0.417544
$821$	−9.37494e12	−0.720152	−0.360076	−	0.932923i	$-0.617249\pi$
$821$	−9.37494e12	−0.720152	−0.360076	+	0.932923i	$0.617249\pi$
$822$	−3.19018e12	−0.243720
$823$	6.38047e12	0.484790	0.242395	−	0.970178i	$-0.422067\pi$
$823$	6.38047e12	0.484790	0.242395	+	0.970178i	$0.422067\pi$
$824$	−2.40367e12	−0.181637
$825$	−1.00050e11	−0.00751925
$826$	−1.08257e13	−0.809182
$827$	−6.81794e12	−0.506849	−0.253425	−	0.967355i	$-0.581557\pi$
$827$	−6.81794e12	−0.506849	−0.253425	+	0.967355i	$0.581557\pi$
$828$	6.51149e12	0.481442
$829$	3.25233e12	0.239166	0.119583	−	0.992824i	$-0.461844\pi$
$829$	3.25233e12	0.239166	0.119583	+	0.992824i	$0.461844\pi$
$830$	2.51169e12	0.183702
$831$	−6.25108e12	−0.454727
$832$	7.71517e11	0.0558201
$833$	−2.52080e13	−1.81399
$834$	5.69828e12	0.407846
$835$	−2.82260e12	−0.200937
$836$	−8.70155e11	−0.0616124
$837$	−5.23278e12	−0.368525
$838$	−1.25241e13	−0.877297
$839$	−9.68433e12	−0.674747	−0.337373	−	0.941371i	$-0.609538\pi$
$839$	−9.68433e12	−0.674747	−0.337373	+	0.941371i	$0.609538\pi$
$840$	−1.21505e12	−0.0842047
$841$	1.44966e13	0.999271
$842$	−3.47548e12	−0.238292
$843$	−5.15936e12	−0.351861
$844$	−8.72530e12	−0.591888
$845$	5.30612e12	0.358032
$846$	−1.24132e13	−0.833139
$847$	2.40094e13	1.60290
$848$	1.94945e12	0.129459
$849$	−2.22604e12	−0.147044
$850$	2.38324e12	0.156597
$851$	−1.86628e13	−1.21981
$852$	−2.72828e12	−0.177383
$853$	−2.07651e13	−1.34296	−0.671479	−	0.741024i	$-0.734341\pi$
$853$	−2.07651e13	−1.34296	−0.671479	+	0.741024i	$0.734341\pi$
$854$	6.63376e12	0.426776
$855$	6.70247e12	0.428931
$856$	−3.51700e12	−0.223893
$857$	9.58593e12	0.607045	0.303522	−	0.952824i	$-0.401837\pi$
$857$	9.58593e12	0.607045	0.303522	+	0.952824i	$0.401837\pi$
$858$	1.88453e11	0.0118716
$859$	−6.74764e12	−0.422846	−0.211423	−	0.977395i	$-0.567810\pi$
$859$	−6.74764e12	−0.422846	−0.211423	+	0.977395i	$0.567810\pi$
$860$	5.90180e12	0.367910
$861$	1.60361e13	0.994452
$862$	9.07234e12	0.559676
$863$	−6.14103e12	−0.376871	−0.188435	−	0.982086i	$-0.560342\pi$
$863$	−6.14103e12	−0.376871	−0.188435	+	0.982086i	$0.560342\pi$
$864$	1.79673e12	0.109691
$865$	1.46650e12	0.0890656
$866$	−8.04203e11	−0.0485887
$867$	1.23351e12	0.0741410
$868$	−8.06647e12	−0.482330
$869$	2.70614e12	0.160976
$870$	2.47733e12	0.146605
$871$	−5.32086e12	−0.313257
$872$	−9.87147e12	−0.578173
$873$	1.89018e13	1.10138
$874$	1.41423e13	0.819820
$875$	2.51904e12	0.145278
$876$	4.22396e12	0.242354
$877$	−2.56598e13	−1.46472	−0.732359	−	0.680918i	$-0.761581\pi$
$877$	−2.56598e13	−1.46472	−0.732359	+	0.680918i	$0.761581\pi$
$878$	1.37827e13	0.782723
$879$	9.02080e12	0.509677
$880$	2.28065e11	0.0128200
$881$	−4.59727e12	−0.257104	−0.128552	−	0.991703i	$-0.541033\pi$
$881$	−4.59727e12	−0.257104	−0.128552	+	0.991703i	$0.541033\pi$
$882$	1.85810e13	1.03386
$883$	−1.57594e13	−0.872404	−0.436202	−	0.899849i	$-0.643677\pi$
$883$	−1.57594e13	−0.872404	−0.436202	+	0.899849i	$0.643677\pi$
$884$	−4.48903e12	−0.247239
$885$	1.88529e12	0.103308
$886$	−6.11610e11	−0.0333444
$887$	2.39701e13	1.30021	0.650106	−	0.759843i	$-0.274724\pi$
$887$	2.39701e13	1.30021	0.650106	+	0.759843i	$0.274724\pi$
$888$	−2.42858e12	−0.131067
$889$	1.37251e13	0.736982
$890$	−5.26039e12	−0.281037
$891$	−1.48638e12	−0.0790096
$892$	4.73045e12	0.250184
$893$	−2.69602e13	−1.41870
$894$	−2.73326e12	−0.143107
$895$	6.63983e12	0.345902
$896$	2.76972e12	0.143565
$897$	−3.06285e12	−0.157965
$898$	2.57286e13	1.32030
$899$	1.64466e13	0.839762
$900$	−1.75670e12	−0.0892496
$901$	−1.13428e13	−0.573401
$902$	−3.00998e12	−0.151403
$903$	1.75072e13	0.876239
$904$	3.21925e12	0.160323
$905$	−5.57255e12	−0.276144
$906$	−4.27360e12	−0.210726
$907$	2.21205e13	1.08533	0.542666	−	0.839949i	$-0.317415\pi$
$907$	2.21205e13	1.08533	0.542666	+	0.839949i	$0.317415\pi$
$908$	−3.77493e12	−0.184299
$909$	1.16615e13	0.566521
$910$	−4.74484e12	−0.229369
$911$	−1.80354e13	−0.867547	−0.433773	−	0.901022i	$-0.642818\pi$
$911$	−1.80354e13	−0.867547	−0.433773	+	0.901022i	$0.642818\pi$
$912$	1.84033e12	0.0880883
$913$	−1.39851e12	−0.0666111
$914$	8.10472e12	0.384132
$915$	−1.15527e12	−0.0544863
$916$	1.58496e13	0.743855
$917$	−3.26930e13	−1.52684
$918$	−1.04542e13	−0.485847
$919$	−2.93522e13	−1.35744	−0.678720	−	0.734397i	$-0.737465\pi$
$919$	−2.93522e13	−1.35744	−0.678720	+	0.734397i	$0.737465\pi$
$920$	−3.70666e12	−0.170584
$921$	2.32549e11	0.0106499
$922$	−3.04574e12	−0.138804
$923$	−1.06541e13	−0.483181
$924$	6.76539e11	0.0305329
$925$	5.03494e12	0.226129
$926$	8.02256e12	0.358561
$927$	−1.03089e13	−0.458516
$928$	−5.64712e12	−0.249954
$929$	−2.11839e13	−0.933114	−0.466557	−	0.884491i	$-0.654506\pi$
$929$	−2.11839e13	−0.933114	−0.466557	+	0.884491i	$0.654506\pi$
$930$	1.40477e12	0.0615790
$931$	4.03560e13	1.76049
$932$	7.50322e12	0.325744
$933$	−8.67843e12	−0.374950
$934$	−3.05532e13	−1.31370
$935$	−1.32699e12	−0.0567825
$936$	3.30890e12	0.140910
$937$	−1.90740e13	−0.808376	−0.404188	−	0.914676i	$-0.632446\pi$
$937$	−1.90740e13	−0.808376	−0.404188	+	0.914676i	$0.632446\pi$
$938$	−1.91017e13	−0.805674
$939$	−4.26917e12	−0.179204
$940$	7.06621e12	0.295196
$941$	−1.05187e12	−0.0437331	−0.0218666	−	0.999761i	$-0.506961\pi$
$941$	−1.05187e12	−0.0437331	−0.0218666	+	0.999761i	$0.506961\pi$
$942$	3.63726e12	0.150503
$943$	4.89201e13	2.01458
$944$	−4.29755e12	−0.176135
$945$	−1.10499e13	−0.450730
$946$	−3.28612e12	−0.133405
$947$	3.41112e13	1.37823	0.689116	−	0.724651i	$-0.257999\pi$
$947$	3.41112e13	1.37823	0.689116	+	0.724651i	$0.257999\pi$
$948$	−5.72334e12	−0.230150
$949$	1.64948e13	0.660160
$950$	−3.81538e12	−0.151978
$951$	−8.77243e12	−0.347783
$952$	−1.61155e13	−0.635882
$953$	5.00063e13	1.96384	0.981921	−	0.189293i	$-0.0606195\pi$
$953$	5.00063e13	1.96384	0.981921	+	0.189293i	$0.0606195\pi$
$954$	8.36084e12	0.326800
$955$	6.22168e11	0.0242043
$956$	1.92400e12	0.0744979
$957$	−1.37938e12	−0.0531594
$958$	−2.62825e13	−1.00814
$959$	−4.47232e13	−1.70745
$960$	−4.82345e11	−0.0183289
$961$	−1.71136e13	−0.647271
$962$	−9.48374e12	−0.357019
$963$	−1.50838e13	−0.565187
$964$	3.95087e12	0.147349
$965$	−1.57408e13	−0.584325
$966$	−1.09955e13	−0.406274
$967$	−4.55647e13	−1.67575	−0.837875	−	0.545862i	$-0.816202\pi$
$967$	−4.55647e13	−1.67575	−0.837875	+	0.545862i	$0.816202\pi$
$968$	9.53117e12	0.348905
$969$	−1.07079e13	−0.390162
$970$	−1.07598e13	−0.390240
$971$	4.18316e13	1.51014	0.755071	−	0.655643i	$-0.227602\pi$
$971$	4.18316e13	1.51014	0.755071	+	0.655643i	$0.227602\pi$
$972$	1.17777e13	0.423215
$973$	7.98843e13	2.85729
$974$	1.75304e13	0.624134
$975$	8.26311e11	0.0292835
$976$	2.63345e12	0.0928967
$977$	−3.90186e12	−0.137008	−0.0685041	−	0.997651i	$-0.521823\pi$
$977$	−3.90186e12	−0.137008	−0.0685041	+	0.997651i	$0.521823\pi$
$978$	1.32586e11	0.00463418
$979$	2.92899e12	0.101905
$980$	−1.05772e13	−0.366314
$981$	−4.23369e13	−1.45952
$982$	−5.69168e12	−0.195317
$983$	−5.23200e12	−0.178721	−0.0893607	−	0.995999i	$-0.528482\pi$
$983$	−5.23200e12	−0.178721	−0.0893607	+	0.995999i	$0.528482\pi$
$984$	6.36594e12	0.216463
$985$	1.41109e12	0.0477629
$986$	3.28575e13	1.10710
$987$	2.09614e13	0.703060
$988$	7.18659e12	0.239948
$989$	5.34081e13	1.77510
$990$	9.78131e11	0.0323622
$991$	3.67753e12	0.121122	0.0605612	−	0.998164i	$-0.480711\pi$
$991$	3.67753e12	0.121122	0.0605612	+	0.998164i	$0.480711\pi$
$992$	−3.20220e12	−0.104989
$993$	5.71979e12	0.186685
$994$	−3.82479e13	−1.24271
$995$	2.69325e12	0.0871108
$996$	2.95776e12	0.0952350
$997$	2.43599e13	0.780815	0.390407	−	0.920642i	$-0.372334\pi$
$997$	2.43599e13	0.780815	0.390407	+	0.920642i	$0.372334\pi$
$998$	−6.40961e12	−0.204524
$999$	−2.20861e13	−0.701574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.10.a.b.1.1	✓	1
3.2	odd	2		90.10.a.h.1.1		1
4.3	odd	2		80.10.a.b.1.1		1
5.2	odd	4		50.10.b.b.49.1		2
5.3	odd	4		50.10.b.b.49.2		2
5.4	even	2		50.10.a.d.1.1		1
8.3	odd	2		320.10.a.f.1.1		1
8.5	even	2		320.10.a.e.1.1		1
20.3	even	4		400.10.c.i.49.1		2
20.7	even	4		400.10.c.i.49.2		2
20.19	odd	2		400.10.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.10.a.b.1.1	✓	1	1.1	even	1	trivial
50.10.a.d.1.1		1	5.4	even	2
50.10.b.b.49.1		2	5.2	odd	4
50.10.b.b.49.2		2	5.3	odd	4
80.10.a.b.1.1		1	4.3	odd	2
90.10.a.h.1.1		1	3.2	odd	2
320.10.a.e.1.1		1	8.5	even	2
320.10.a.f.1.1		1	8.3	odd	2
400.10.a.h.1.1		1	20.19	odd	2
400.10.c.i.49.1		2	20.3	even	4
400.10.c.i.49.2		2	20.7	even	4

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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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