LMFDB - Embedded newform 16.10.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("16.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	16.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:	$8.24057337862$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 2)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+156.000 q^{3} +870.000 q^{5} +952.000 q^{7} +4653.00 q^{9} +O(q^{10})$

$q+156.000 q^{3} +870.000 q^{5} +952.000 q^{7} +4653.00 q^{9} +56148.0 q^{11} +178094. q^{13} +135720. q^{15} -247662. q^{17} -315380. q^{19} +148512. q^{21} -204504. q^{23} -1.19622e6 q^{25} -2.34468e6 q^{27} -3.84045e6 q^{29} +1.30941e6 q^{31} +8.75909e6 q^{33} +828240. q^{35} +4.30708e6 q^{37} +2.77827e7 q^{39} +1.51204e6 q^{41} -3.36706e7 q^{43} +4.04811e6 q^{45} +1.05811e7 q^{47} -3.94473e7 q^{49} -3.86353e7 q^{51} +1.66162e7 q^{53} +4.88488e7 q^{55} -4.91993e7 q^{57} -1.12235e8 q^{59} -3.31972e7 q^{61} +4.42966e6 q^{63} +1.54942e8 q^{65} +1.21372e8 q^{67} -3.19026e7 q^{69} +3.87173e8 q^{71} +2.55240e8 q^{73} -1.86611e8 q^{75} +5.34529e7 q^{77} -4.92102e8 q^{79} -4.57355e8 q^{81} +4.57420e8 q^{83} -2.15466e8 q^{85} -5.99110e8 q^{87} -3.18095e7 q^{89} +1.69545e8 q^{91} +2.04268e8 q^{93} -2.74381e8 q^{95} -6.73532e8 q^{97} +2.61257e8 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	156.000	1.11193	0.555967	−	0.831204i	$-0.312348\pi$
$3$	156.000	1.11193	0.555967	+	0.831204i	$0.312348\pi$
$4$	0	0
$5$	870.000	0.622521	0.311261	−	0.950325i	$-0.399249\pi$
$5$	870.000	0.622521	0.311261	+	0.950325i	$0.399249\pi$
$6$	0	0
$7$	952.000	0.149863	0.0749317	−	0.997189i	$-0.476126\pi$
$7$	952.000	0.149863	0.0749317	+	0.997189i	$0.476126\pi$
$8$	0	0
$9$	4653.00	0.236397
$10$	0	0
$11$	56148.0	1.15629	0.578146	−	0.815934i	$-0.303777\pi$
$11$	56148.0	1.15629	0.578146	+	0.815934i	$0.303777\pi$
$12$	0	0
$13$	178094.	1.72943	0.864717	−	0.502259i	$-0.167497\pi$
$13$	178094.	1.72943	0.864717	+	0.502259i	$0.167497\pi$
$14$	0	0
$15$	135720.	0.692203
$16$	0	0
$17$	−247662.	−0.719183	−0.359591	−	0.933110i	$-0.617084\pi$
$17$	−247662.	−0.719183	−0.359591	+	0.933110i	$0.617084\pi$
$18$	0	0
$19$	−315380.	−0.555192	−0.277596	−	0.960698i	$-0.589538\pi$
$19$	−315380.	−0.555192	−0.277596	+	0.960698i	$0.589538\pi$
$20$	0	0
$21$	148512.	0.166638
$22$	0	0
$23$	−204504.	−0.152380	−0.0761898	−	0.997093i	$-0.524275\pi$
$23$	−204504.	−0.152380	−0.0761898	+	0.997093i	$0.524275\pi$
$24$	0	0
$25$	−1.19622e6	−0.612467
$26$	0	0
$27$	−2.34468e6	−0.849076
$28$	0	0
$29$	−3.84045e6	−1.00830	−0.504152	−	0.863615i	$-0.668195\pi$
$29$	−3.84045e6	−1.00830	−0.504152	+	0.863615i	$0.668195\pi$
$30$	0	0
$31$	1.30941e6	0.254652	0.127326	−	0.991861i	$-0.459361\pi$
$31$	1.30941e6	0.254652	0.127326	+	0.991861i	$0.459361\pi$
$32$	0	0
$33$	8.75909e6	1.28572
$34$	0	0
$35$	828240.	0.0932932
$36$	0	0
$37$	4.30708e6	0.377811	0.188906	−	0.981995i	$-0.439506\pi$
$37$	4.30708e6	0.377811	0.188906	+	0.981995i	$0.439506\pi$
$38$	0	0
$39$	2.77827e7	1.92302
$40$	0	0
$41$	1.51204e6	0.0835673	0.0417837	−	0.999127i	$-0.486696\pi$
$41$	1.51204e6	0.0835673	0.0417837	+	0.999127i	$0.486696\pi$
$42$	0	0
$43$	−3.36706e7	−1.50191	−0.750953	−	0.660355i	$-0.770406\pi$
$43$	−3.36706e7	−1.50191	−0.750953	+	0.660355i	$0.770406\pi$
$44$	0	0
$45$	4.04811e6	0.147162
$46$	0	0
$47$	1.05811e7	0.316293	0.158146	−	0.987416i	$-0.449448\pi$
$47$	1.05811e7	0.316293	0.158146	+	0.987416i	$0.449448\pi$
$48$	0	0
$49$	−3.94473e7	−0.977541
$50$	0	0
$51$	−3.86353e7	−0.799684
$52$	0	0
$53$	1.66162e7	0.289262	0.144631	−	0.989486i	$-0.453801\pi$
$53$	1.66162e7	0.289262	0.144631	+	0.989486i	$0.453801\pi$
$54$	0	0
$55$	4.88488e7	0.719816
$56$	0	0
$57$	−4.91993e7	−0.617336
$58$	0	0
$59$	−1.12235e8	−1.20585	−0.602927	−	0.797796i	$-0.705999\pi$
$59$	−1.12235e8	−1.20585	−0.602927	+	0.797796i	$0.705999\pi$
$60$	0	0
$61$	−3.31972e7	−0.306985	−0.153493	−	0.988150i	$-0.549052\pi$
$61$	−3.31972e7	−0.306985	−0.153493	+	0.988150i	$0.549052\pi$
$62$	0	0
$63$	4.42966e6	0.0354273
$64$	0	0
$65$	1.54942e8	1.07661
$66$	0	0
$67$	1.21372e8	0.735839	0.367919	−	0.929858i	$-0.380070\pi$
$67$	1.21372e8	0.735839	0.367919	+	0.929858i	$0.380070\pi$
$68$	0	0
$69$	−3.19026e7	−0.169436
$70$	0	0
$71$	3.87173e8	1.80818	0.904091	−	0.427340i	$-0.140549\pi$
$71$	3.87173e8	1.80818	0.904091	+	0.427340i	$0.140549\pi$
$72$	0	0
$73$	2.55240e8	1.05195	0.525976	−	0.850499i	$-0.323700\pi$
$73$	2.55240e8	1.05195	0.525976	+	0.850499i	$0.323700\pi$
$74$	0	0
$75$	−1.86611e8	−0.681023
$76$	0	0
$77$	5.34529e7	0.173286
$78$	0	0
$79$	−4.92102e8	−1.42145	−0.710727	−	0.703467i	$-0.751634\pi$
$79$	−4.92102e8	−1.42145	−0.710727	+	0.703467i	$0.751634\pi$
$80$	0	0
$81$	−4.57355e8	−1.18051
$82$	0	0
$83$	4.57420e8	1.05795	0.528974	−	0.848638i	$-0.322577\pi$
$83$	4.57420e8	1.05795	0.528974	+	0.848638i	$0.322577\pi$
$84$	0	0
$85$	−2.15466e8	−0.447707
$86$	0	0
$87$	−5.99110e8	−1.12117
$88$	0	0
$89$	−3.18095e7	−0.0537405	−0.0268703	−	0.999639i	$-0.508554\pi$
$89$	−3.18095e7	−0.0537405	−0.0268703	+	0.999639i	$0.508554\pi$
$90$	0	0
$91$	1.69545e8	0.259179
$92$	0	0
$93$	2.04268e8	0.283156
$94$	0	0
$95$	−2.74381e8	−0.345619
$96$	0	0
$97$	−6.73532e8	−0.772477	−0.386238	−	0.922399i	$-0.626226\pi$
$97$	−6.73532e8	−0.772477	−0.386238	+	0.922399i	$0.626226\pi$
$98$	0	0
$99$	2.61257e8	0.273344
$100$	0	0
$101$	1.05772e9	1.01140	0.505701	−	0.862709i	$-0.331234\pi$
$101$	1.05772e9	1.01140	0.505701	+	0.862709i	$0.331234\pi$
$102$	0	0
$103$	−7.95866e8	−0.696743	−0.348371	−	0.937357i	$-0.613265\pi$
$103$	−7.95866e8	−0.696743	−0.348371	+	0.937357i	$0.613265\pi$
$104$	0	0
$105$	1.29205e8	0.103736
$106$	0	0
$107$	1.97413e9	1.45596	0.727981	−	0.685598i	$-0.240459\pi$
$107$	1.97413e9	1.45596	0.727981	+	0.685598i	$0.240459\pi$
$108$	0	0
$109$	−1.34465e9	−0.912408	−0.456204	−	0.889875i	$-0.650791\pi$
$109$	−1.34465e9	−0.912408	−0.456204	+	0.889875i	$0.650791\pi$
$110$	0	0
$111$	6.71904e8	0.420101
$112$	0	0
$113$	2.70680e9	1.56172	0.780861	−	0.624705i	$-0.214781\pi$
$113$	2.70680e9	1.56172	0.780861	+	0.624705i	$0.214781\pi$
$114$	0	0
$115$	−1.77918e8	−0.0948595
$116$	0	0
$117$	8.28671e8	0.408833
$118$	0	0
$119$	−2.35774e8	−0.107779
$120$	0	0
$121$	7.94650e8	0.337009
$122$	0	0
$123$	2.35879e8	0.0929213
$124$	0	0
$125$	−2.73993e9	−1.00380
$126$	0	0
$127$	−1.19960e9	−0.409185	−0.204593	−	0.978847i	$-0.565587\pi$
$127$	−1.19960e9	−0.409185	−0.204593	+	0.978847i	$0.565587\pi$
$128$	0	0
$129$	−5.25261e9	−1.67002
$130$	0	0
$131$	−2.78615e9	−0.826576	−0.413288	−	0.910600i	$-0.635620\pi$
$131$	−2.78615e9	−0.826576	−0.413288	+	0.910600i	$0.635620\pi$
$132$	0	0
$133$	−3.00242e8	−0.0832029
$134$	0	0
$135$	−2.03987e9	−0.528568
$136$	0	0
$137$	2.88233e9	0.699039	0.349519	−	0.936929i	$-0.386345\pi$
$137$	2.88233e9	0.699039	0.349519	+	0.936929i	$0.386345\pi$
$138$	0	0
$139$	−2.15641e9	−0.489965	−0.244982	−	0.969528i	$-0.578782\pi$
$139$	−2.15641e9	−0.489965	−0.244982	+	0.969528i	$0.578782\pi$
$140$	0	0
$141$	1.65065e9	0.351697
$142$	0	0
$143$	9.99962e9	1.99973
$144$	0	0
$145$	−3.34119e9	−0.627690
$146$	0	0
$147$	−6.15378e9	−1.08696
$148$	0	0
$149$	7.54548e9	1.25415	0.627074	−	0.778960i	$-0.284253\pi$
$149$	7.54548e9	1.25415	0.627074	+	0.778960i	$0.284253\pi$
$150$	0	0
$151$	4.31308e9	0.675136	0.337568	−	0.941301i	$-0.390396\pi$
$151$	4.31308e9	0.675136	0.337568	+	0.941301i	$0.390396\pi$
$152$	0	0
$153$	−1.15237e9	−0.170013
$154$	0	0
$155$	1.13918e9	0.158526
$156$	0	0
$157$	−4.23157e9	−0.555845	−0.277922	−	0.960604i	$-0.589646\pi$
$157$	−4.23157e9	−0.555845	−0.277922	+	0.960604i	$0.589646\pi$
$158$	0	0
$159$	2.59213e9	0.321640
$160$	0	0
$161$	−1.94688e8	−0.0228361
$162$	0	0
$163$	−8.28448e8	−0.0919223	−0.0459612	−	0.998943i	$-0.514635\pi$
$163$	−8.28448e8	−0.0919223	−0.0459612	+	0.998943i	$0.514635\pi$
$164$	0	0
$165$	7.62041e9	0.800388
$166$	0	0
$167$	2.85500e9	0.284041	0.142021	−	0.989864i	$-0.454640\pi$
$167$	2.85500e9	0.284041	0.142021	+	0.989864i	$0.454640\pi$
$168$	0	0
$169$	2.11130e10	1.99094
$170$	0	0
$171$	−1.46746e9	−0.131246
$172$	0	0
$173$	−1.76690e10	−1.49970	−0.749851	−	0.661607i	$-0.769875\pi$
$173$	−1.76690e10	−1.49970	−0.749851	+	0.661607i	$0.769875\pi$
$174$	0	0
$175$	−1.13881e9	−0.0917865
$176$	0	0
$177$	−1.75087e10	−1.34083
$178$	0	0
$179$	5.86732e8	0.0427170	0.0213585	−	0.999772i	$-0.493201\pi$
$179$	5.86732e8	0.0427170	0.0213585	+	0.999772i	$0.493201\pi$
$180$	0	0
$181$	−5.43396e9	−0.376325	−0.188162	−	0.982138i	$-0.560253\pi$
$181$	−5.43396e9	−0.376325	−0.188162	+	0.982138i	$0.560253\pi$
$182$	0	0
$183$	−5.17877e9	−0.341347
$184$	0	0
$185$	3.74716e9	0.235196
$186$	0	0
$187$	−1.39057e10	−0.831585
$188$	0	0
$189$	−2.23214e9	−0.127245
$190$	0	0
$191$	−3.23292e10	−1.75770	−0.878851	−	0.477096i	$-0.841689\pi$
$191$	−3.23292e10	−1.75770	−0.878851	+	0.477096i	$0.841689\pi$
$192$	0	0
$193$	−1.29399e10	−0.671311	−0.335655	−	0.941985i	$-0.608958\pi$
$193$	−1.29399e10	−0.671311	−0.335655	+	0.941985i	$0.608958\pi$
$194$	0	0
$195$	2.41709e10	1.19712
$196$	0	0
$197$	8.81090e9	0.416795	0.208397	−	0.978044i	$-0.433175\pi$
$197$	8.81090e9	0.416795	0.208397	+	0.978044i	$0.433175\pi$
$198$	0	0
$199$	2.48534e10	1.12343	0.561716	−	0.827330i	$-0.310141\pi$
$199$	2.48534e10	1.12343	0.561716	+	0.827330i	$0.310141\pi$
$200$	0	0
$201$	1.89341e10	0.818204
$202$	0	0
$203$	−3.65611e9	−0.151108
$204$	0	0
$205$	1.31548e9	0.0520224
$206$	0	0
$207$	−9.51557e8	−0.0360220
$208$	0	0
$209$	−1.77080e10	−0.641963
$210$	0	0
$211$	4.65163e10	1.61560	0.807801	−	0.589456i	$-0.200658\pi$
$211$	4.65163e10	1.61560	0.807801	+	0.589456i	$0.200658\pi$
$212$	0	0
$213$	6.03989e10	2.01058
$214$	0	0
$215$	−2.92934e10	−0.934969
$216$	0	0
$217$	1.24656e9	0.0381631
$218$	0	0
$219$	3.98175e10	1.16970
$220$	0	0
$221$	−4.41071e10	−1.24378
$222$	0	0
$223$	−4.66347e10	−1.26281	−0.631404	−	0.775454i	$-0.717521\pi$
$223$	−4.66347e10	−1.26281	−0.631404	+	0.775454i	$0.717521\pi$
$224$	0	0
$225$	−5.56603e9	−0.144785
$226$	0	0
$227$	−2.65867e10	−0.664582	−0.332291	−	0.943177i	$-0.607822\pi$
$227$	−2.65867e10	−0.664582	−0.332291	+	0.943177i	$0.607822\pi$
$228$	0	0
$229$	3.99907e10	0.960947	0.480474	−	0.877009i	$-0.340465\pi$
$229$	3.99907e10	0.960947	0.480474	+	0.877009i	$0.340465\pi$
$230$	0	0
$231$	8.33865e9	0.192682
$232$	0	0
$233$	6.53338e9	0.145223	0.0726116	−	0.997360i	$-0.476867\pi$
$233$	6.53338e9	0.145223	0.0726116	+	0.997360i	$0.476867\pi$
$234$	0	0
$235$	9.20553e9	0.196899
$236$	0	0
$237$	−7.67679e10	−1.58056
$238$	0	0
$239$	5.66773e10	1.12362	0.561809	−	0.827267i	$-0.310106\pi$
$239$	5.66773e10	1.12362	0.561809	+	0.827267i	$0.310106\pi$
$240$	0	0
$241$	4.61491e9	0.0881225	0.0440613	−	0.999029i	$-0.485970\pi$
$241$	4.61491e9	0.0881225	0.0440613	+	0.999029i	$0.485970\pi$
$242$	0	0
$243$	−2.51971e10	−0.463577
$244$	0	0
$245$	−3.43192e10	−0.608540
$246$	0	0
$247$	−5.61673e10	−0.960168
$248$	0	0
$249$	7.13576e10	1.17637
$250$	0	0
$251$	−6.80194e10	−1.08169	−0.540843	−	0.841124i	$-0.681895\pi$
$251$	−6.80194e10	−1.08169	−0.540843	+	0.841124i	$0.681895\pi$
$252$	0	0
$253$	−1.14825e10	−0.176195
$254$	0	0
$255$	−3.36127e10	−0.497820
$256$	0	0
$257$	−9.35958e10	−1.33831	−0.669156	−	0.743122i	$-0.733344\pi$
$257$	−9.35958e10	−1.33831	−0.669156	+	0.743122i	$0.733344\pi$
$258$	0	0
$259$	4.10034e9	0.0566201
$260$	0	0
$261$	−1.78696e10	−0.238360
$262$	0	0
$263$	9.40401e10	1.21203	0.606013	−	0.795454i	$-0.292768\pi$
$263$	9.40401e10	1.21203	0.606013	+	0.795454i	$0.292768\pi$
$264$	0	0
$265$	1.44561e10	0.180071
$266$	0	0
$267$	−4.96228e9	−0.0597559
$268$	0	0
$269$	1.22724e11	1.42904	0.714522	−	0.699613i	$-0.246644\pi$
$269$	1.22724e11	1.42904	0.714522	+	0.699613i	$0.246644\pi$
$270$	0	0
$271$	1.64257e11	1.84996	0.924982	−	0.380012i	$-0.124080\pi$
$271$	1.64257e11	1.84996	0.924982	+	0.380012i	$0.124080\pi$
$272$	0	0
$273$	2.64491e10	0.288190
$274$	0	0
$275$	−6.71656e10	−0.708190
$276$	0	0
$277$	6.50134e10	0.663505	0.331752	−	0.943367i	$-0.392360\pi$
$277$	6.50134e10	0.663505	0.331752	+	0.943367i	$0.392360\pi$
$278$	0	0
$279$	6.09268e9	0.0601990
$280$	0	0
$281$	5.20964e10	0.498459	0.249230	−	0.968444i	$-0.419823\pi$
$281$	5.20964e10	0.498459	0.249230	+	0.968444i	$0.419823\pi$
$282$	0	0
$283$	9.06992e10	0.840552	0.420276	−	0.907396i	$-0.361933\pi$
$283$	9.06992e10	0.840552	0.420276	+	0.907396i	$0.361933\pi$
$284$	0	0
$285$	−4.28034e10	−0.384305
$286$	0	0
$287$	1.43946e9	0.0125237
$288$	0	0
$289$	−5.72514e10	−0.482776
$290$	0	0
$291$	−1.05071e11	−0.858943
$292$	0	0
$293$	7.25569e10	0.575141	0.287571	−	0.957759i	$-0.407152\pi$
$293$	7.25569e10	0.575141	0.287571	+	0.957759i	$0.407152\pi$
$294$	0	0
$295$	−9.76445e10	−0.750670
$296$	0	0
$297$	−1.31649e11	−0.981779
$298$	0	0
$299$	−3.64209e10	−0.263530
$300$	0	0
$301$	−3.20544e10	−0.225081
$302$	0	0
$303$	1.65004e11	1.12461
$304$	0	0
$305$	−2.88816e10	−0.191105
$306$	0	0
$307$	−1.81977e11	−1.16921	−0.584607	−	0.811317i	$-0.698751\pi$
$307$	−1.81977e11	−1.16921	−0.584607	+	0.811317i	$0.698751\pi$
$308$	0	0
$309$	−1.24155e11	−0.774732
$310$	0	0
$311$	8.98295e10	0.544499	0.272250	−	0.962227i	$-0.412232\pi$
$311$	8.98295e10	0.544499	0.272250	+	0.962227i	$0.412232\pi$
$312$	0	0
$313$	5.51394e9	0.0324722	0.0162361	−	0.999868i	$-0.494832\pi$
$313$	5.51394e9	0.0324722	0.0162361	+	0.999868i	$0.494832\pi$
$314$	0	0
$315$	3.85380e9	0.0220542
$316$	0	0
$317$	−1.94806e10	−0.108351	−0.0541757	−	0.998531i	$-0.517253\pi$
$317$	−1.94806e10	−0.108351	−0.0541757	+	0.998531i	$0.517253\pi$
$318$	0	0
$319$	−2.15634e11	−1.16589
$320$	0	0
$321$	3.07965e11	1.61893
$322$	0	0
$323$	7.81076e10	0.399284
$324$	0	0
$325$	−2.13040e11	−1.05922
$326$	0	0
$327$	−2.09765e11	−1.01454
$328$	0	0
$329$	1.00732e10	0.0474007
$330$	0	0
$331$	1.06801e11	0.489046	0.244523	−	0.969644i	$-0.421369\pi$
$331$	1.06801e11	0.489046	0.244523	+	0.969644i	$0.421369\pi$
$332$	0	0
$333$	2.00408e10	0.0893134
$334$	0	0
$335$	1.05594e11	0.458075
$336$	0	0
$337$	−1.75776e11	−0.742380	−0.371190	−	0.928557i	$-0.621050\pi$
$337$	−1.75776e11	−0.742380	−0.371190	+	0.928557i	$0.621050\pi$
$338$	0	0
$339$	4.22261e11	1.73653
$340$	0	0
$341$	7.35206e10	0.294452
$342$	0	0
$343$	−7.59705e10	−0.296361
$344$	0	0
$345$	−2.77553e10	−0.105477
$346$	0	0
$347$	−8.33026e10	−0.308444	−0.154222	−	0.988036i	$-0.549287\pi$
$347$	−8.33026e10	−0.308444	−0.154222	+	0.988036i	$0.549287\pi$
$348$	0	0
$349$	3.21368e11	1.15955	0.579773	−	0.814778i	$-0.303141\pi$
$349$	3.21368e11	1.15955	0.579773	+	0.814778i	$0.303141\pi$
$350$	0	0
$351$	−4.17573e11	−1.46842
$352$	0	0
$353$	4.07688e11	1.39747	0.698735	−	0.715381i	$-0.253747\pi$
$353$	4.07688e11	1.39747	0.698735	+	0.715381i	$0.253747\pi$
$354$	0	0
$355$	3.36840e11	1.12563
$356$	0	0
$357$	−3.67808e10	−0.119843
$358$	0	0
$359$	5.60079e11	1.77961	0.889804	−	0.456343i	$-0.150841\pi$
$359$	5.60079e11	1.77961	0.889804	+	0.456343i	$0.150841\pi$
$360$	0	0
$361$	−2.23223e11	−0.691762
$362$	0	0
$363$	1.23965e11	0.374732
$364$	0	0
$365$	2.22059e11	0.654863
$366$	0	0
$367$	−3.76056e11	−1.08207	−0.541036	−	0.841000i	$-0.681968\pi$
$367$	−3.76056e11	−1.08207	−0.541036	+	0.841000i	$0.681968\pi$
$368$	0	0
$369$	7.03553e9	0.0197551
$370$	0	0
$371$	1.58186e10	0.0433497
$372$	0	0
$373$	−8.12245e10	−0.217269	−0.108634	−	0.994082i	$-0.534648\pi$
$373$	−8.12245e10	−0.217269	−0.108634	+	0.994082i	$0.534648\pi$
$374$	0	0
$375$	−4.27430e11	−1.11615
$376$	0	0
$377$	−6.83961e11	−1.74379
$378$	0	0
$379$	−2.02729e11	−0.504708	−0.252354	−	0.967635i	$-0.581205\pi$
$379$	−2.02729e11	−0.504708	−0.252354	+	0.967635i	$0.581205\pi$
$380$	0	0
$381$	−1.87138e11	−0.454987
$382$	0	0
$383$	4.76816e10	0.113229	0.0566143	−	0.998396i	$-0.481969\pi$
$383$	4.76816e10	0.113229	0.0566143	+	0.998396i	$0.481969\pi$
$384$	0	0
$385$	4.65040e10	0.107874
$386$	0	0
$387$	−1.56669e11	−0.355046
$388$	0	0
$389$	−1.89795e11	−0.420253	−0.210126	−	0.977674i	$-0.567388\pi$
$389$	−1.89795e11	−0.420253	−0.210126	+	0.977674i	$0.567388\pi$
$390$	0	0
$391$	5.06479e10	0.109589
$392$	0	0
$393$	−4.34639e11	−0.919098
$394$	0	0
$395$	−4.28129e11	−0.884886
$396$	0	0
$397$	4.00237e11	0.808649	0.404325	−	0.914616i	$-0.367507\pi$
$397$	4.00237e11	0.808649	0.404325	+	0.914616i	$0.367507\pi$
$398$	0	0
$399$	−4.68377e10	−0.0925162
$400$	0	0
$401$	8.76186e11	1.69218	0.846090	−	0.533040i	$-0.178951\pi$
$401$	8.76186e11	1.69218	0.846090	+	0.533040i	$0.178951\pi$
$402$	0	0
$403$	2.33198e11	0.440404
$404$	0	0
$405$	−3.97899e11	−0.734895
$406$	0	0
$407$	2.41834e11	0.436860
$408$	0	0
$409$	5.72300e11	1.01127	0.505637	−	0.862746i	$-0.331258\pi$
$409$	5.72300e11	1.01127	0.505637	+	0.862746i	$0.331258\pi$
$410$	0	0
$411$	4.49643e11	0.777285
$412$	0	0
$413$	−1.06848e11	−0.180713
$414$	0	0
$415$	3.97956e11	0.658595
$416$	0	0
$417$	−3.36400e11	−0.544809
$418$	0	0
$419$	−4.16693e11	−0.660469	−0.330235	−	0.943899i	$-0.607128\pi$
$419$	−4.16693e11	−0.660469	−0.330235	+	0.943899i	$0.607128\pi$
$420$	0	0
$421$	−1.19043e12	−1.84687	−0.923434	−	0.383757i	$-0.874630\pi$
$421$	−1.19043e12	−1.84687	−0.923434	+	0.383757i	$0.874630\pi$
$422$	0	0
$423$	4.92337e10	0.0747706
$424$	0	0
$425$	2.96259e11	0.440476
$426$	0	0
$427$	−3.16038e10	−0.0460059
$428$	0	0
$429$	1.55994e12	2.22357
$430$	0	0
$431$	4.36455e11	0.609245	0.304622	−	0.952473i	$-0.401470\pi$
$431$	4.36455e11	0.609245	0.304622	+	0.952473i	$0.401470\pi$
$432$	0	0
$433$	4.48430e11	0.613055	0.306527	−	0.951862i	$-0.400833\pi$
$433$	4.48430e11	0.613055	0.306527	+	0.951862i	$0.400833\pi$
$434$	0	0
$435$	−5.21226e11	−0.697950
$436$	0	0
$437$	6.44965e10	0.0845998
$438$	0	0
$439$	6.59703e11	0.847731	0.423866	−	0.905725i	$-0.360673\pi$
$439$	6.59703e11	0.847731	0.423866	+	0.905725i	$0.360673\pi$
$440$	0	0
$441$	−1.83548e11	−0.231088
$442$	0	0
$443$	−9.48507e11	−1.17010	−0.585051	−	0.810997i	$-0.698925\pi$
$443$	−9.48507e11	−1.17010	−0.585051	+	0.810997i	$0.698925\pi$
$444$	0	0
$445$	−2.76743e10	−0.0334546
$446$	0	0
$447$	1.17709e12	1.39453
$448$	0	0
$449$	−6.11763e11	−0.710354	−0.355177	−	0.934799i	$-0.615579\pi$
$449$	−6.11763e11	−0.710354	−0.355177	+	0.934799i	$0.615579\pi$
$450$	0	0
$451$	8.48981e10	0.0966282
$452$	0	0
$453$	6.72841e11	0.750707
$454$	0	0
$455$	1.47505e11	0.161345
$456$	0	0
$457$	−3.79033e11	−0.406494	−0.203247	−	0.979128i	$-0.565149\pi$
$457$	−3.79033e11	−0.406494	−0.203247	+	0.979128i	$0.565149\pi$
$458$	0	0
$459$	5.80688e11	0.610641
$460$	0	0
$461$	−8.90062e11	−0.917839	−0.458919	−	0.888478i	$-0.651763\pi$
$461$	−8.90062e11	−0.917839	−0.458919	+	0.888478i	$0.651763\pi$
$462$	0	0
$463$	−1.32852e12	−1.34355	−0.671776	−	0.740755i	$-0.734468\pi$
$463$	−1.32852e12	−1.34355	−0.671776	+	0.740755i	$0.734468\pi$
$464$	0	0
$465$	1.77713e11	0.176271
$466$	0	0
$467$	−1.65638e12	−1.61151	−0.805755	−	0.592249i	$-0.798240\pi$
$467$	−1.65638e12	−1.61151	−0.805755	+	0.592249i	$0.798240\pi$
$468$	0	0
$469$	1.15546e11	0.110275
$470$	0	0
$471$	−6.60125e11	−0.618062
$472$	0	0
$473$	−1.89054e12	−1.73664
$474$	0	0
$475$	3.77265e11	0.340037
$476$	0	0
$477$	7.73152e10	0.0683805
$478$	0	0
$479$	1.07973e12	0.937143	0.468571	−	0.883426i	$-0.344769\pi$
$479$	1.07973e12	0.937143	0.468571	+	0.883426i	$0.344769\pi$
$480$	0	0
$481$	7.67065e11	0.653400
$482$	0	0
$483$	−3.03713e10	−0.0253923
$484$	0	0
$485$	−5.85973e11	−0.480883
$486$	0	0
$487$	−1.60549e12	−1.29338	−0.646690	−	0.762753i	$-0.723847\pi$
$487$	−1.60549e12	−1.29338	−0.646690	+	0.762753i	$0.723847\pi$
$488$	0	0
$489$	−1.29238e11	−0.102212
$490$	0	0
$491$	−7.93629e11	−0.616242	−0.308121	−	0.951347i	$-0.599700\pi$
$491$	−7.93629e11	−0.616242	−0.308121	+	0.951347i	$0.599700\pi$
$492$	0	0
$493$	9.51134e11	0.725154
$494$	0	0
$495$	2.27293e11	0.170162
$496$	0	0
$497$	3.68588e11	0.270980
$498$	0	0
$499$	1.96951e12	1.42202	0.711010	−	0.703182i	$-0.248238\pi$
$499$	1.96951e12	1.42202	0.711010	+	0.703182i	$0.248238\pi$
$500$	0	0
$501$	4.45380e11	0.315835
$502$	0	0
$503$	5.42230e11	0.377683	0.188842	−	0.982008i	$-0.439527\pi$
$503$	5.42230e11	0.377683	0.188842	+	0.982008i	$0.439527\pi$
$504$	0	0
$505$	9.20216e11	0.629620
$506$	0	0
$507$	3.29362e12	2.21380
$508$	0	0
$509$	−1.69215e12	−1.11740	−0.558699	−	0.829370i	$-0.688699\pi$
$509$	−1.69215e12	−1.11740	−0.558699	+	0.829370i	$0.688699\pi$
$510$	0	0
$511$	2.42989e11	0.157649
$512$	0	0
$513$	7.39465e11	0.471400
$514$	0	0
$515$	−6.92403e11	−0.433737
$516$	0	0
$517$	5.94106e11	0.365727
$518$	0	0
$519$	−2.75637e12	−1.66757
$520$	0	0
$521$	2.97596e12	1.76953	0.884764	−	0.466040i	$-0.154320\pi$
$521$	2.97596e12	1.76953	0.884764	+	0.466040i	$0.154320\pi$
$522$	0	0
$523$	1.07989e12	0.631137	0.315568	−	0.948903i	$-0.397805\pi$
$523$	1.07989e12	0.631137	0.315568	+	0.948903i	$0.397805\pi$
$524$	0	0
$525$	−1.77654e11	−0.102060
$526$	0	0
$527$	−3.24291e11	−0.183141
$528$	0	0
$529$	−1.75933e12	−0.976780
$530$	0	0
$531$	−5.22230e11	−0.285060
$532$	0	0
$533$	2.69286e11	0.144524
$534$	0	0
$535$	1.71750e12	0.906367
$536$	0	0
$537$	9.15302e10	0.0474985
$538$	0	0
$539$	−2.21489e12	−1.13032
$540$	0	0
$541$	−2.02167e12	−1.01467	−0.507333	−	0.861750i	$-0.669369\pi$
$541$	−2.02167e12	−1.01467	−0.507333	+	0.861750i	$0.669369\pi$
$542$	0	0
$543$	−8.47697e11	−0.418448
$544$	0	0
$545$	−1.16984e12	−0.567994
$546$	0	0
$547$	2.62612e12	1.25421	0.627107	−	0.778933i	$-0.284239\pi$
$547$	2.62612e12	1.25421	0.627107	+	0.778933i	$0.284239\pi$
$548$	0	0
$549$	−1.54467e11	−0.0725703
$550$	0	0
$551$	1.21120e12	0.559802
$552$	0	0
$553$	−4.68481e11	−0.213024
$554$	0	0
$555$	5.84557e11	0.261522
$556$	0	0
$557$	3.48482e12	1.53402	0.767012	−	0.641633i	$-0.221743\pi$
$557$	3.48482e12	1.53402	0.767012	+	0.641633i	$0.221743\pi$
$558$	0	0
$559$	−5.99653e12	−2.59745
$560$	0	0
$561$	−2.16929e12	−0.924667
$562$	0	0
$563$	2.77091e12	1.16235	0.581173	−	0.813780i	$-0.302594\pi$
$563$	2.77091e12	1.16235	0.581173	+	0.813780i	$0.302594\pi$
$564$	0	0
$565$	2.35492e12	0.972205
$566$	0	0
$567$	−4.35402e11	−0.176916
$568$	0	0
$569$	−6.70382e11	−0.268113	−0.134056	−	0.990974i	$-0.542800\pi$
$569$	−6.70382e11	−0.268113	−0.134056	+	0.990974i	$0.542800\pi$
$570$	0	0
$571$	−2.67123e12	−1.05160	−0.525798	−	0.850609i	$-0.676233\pi$
$571$	−2.67123e12	−1.05160	−0.525798	+	0.850609i	$0.676233\pi$
$572$	0	0
$573$	−5.04336e12	−1.95445
$574$	0	0
$575$	2.44633e11	0.0933274
$576$	0	0
$577$	−6.59284e11	−0.247618	−0.123809	−	0.992306i	$-0.539511\pi$
$577$	−6.59284e11	−0.247618	−0.123809	+	0.992306i	$0.539511\pi$
$578$	0	0
$579$	−2.01863e12	−0.746453
$580$	0	0
$581$	4.35464e11	0.158548
$582$	0	0
$583$	9.32967e11	0.334471
$584$	0	0
$585$	7.20944e11	0.254507
$586$	0	0
$587$	−1.04947e12	−0.364835	−0.182418	−	0.983221i	$-0.558392\pi$
$587$	−1.04947e12	−0.364835	−0.182418	+	0.983221i	$0.558392\pi$
$588$	0	0
$589$	−4.12961e11	−0.141381
$590$	0	0
$591$	1.37450e12	0.463448
$592$	0	0
$593$	−1.31188e12	−0.435662	−0.217831	−	0.975987i	$-0.569898\pi$
$593$	−1.31188e12	−0.435662	−0.217831	+	0.975987i	$0.569898\pi$
$594$	0	0
$595$	−2.05124e11	−0.0670949
$596$	0	0
$597$	3.87713e12	1.24918
$598$	0	0
$599$	3.37603e12	1.07148	0.535742	−	0.844382i	$-0.320032\pi$
$599$	3.37603e12	1.07148	0.535742	+	0.844382i	$0.320032\pi$
$600$	0	0
$601$	2.63880e12	0.825034	0.412517	−	0.910950i	$-0.364650\pi$
$601$	2.63880e12	0.825034	0.412517	+	0.910950i	$0.364650\pi$
$602$	0	0
$603$	5.64745e11	0.173950
$604$	0	0
$605$	6.91346e11	0.209795
$606$	0	0
$607$	5.15939e12	1.54259	0.771293	−	0.636481i	$-0.219610\pi$
$607$	5.15939e12	1.54259	0.771293	+	0.636481i	$0.219610\pi$
$608$	0	0
$609$	−5.70353e11	−0.168022
$610$	0	0
$611$	1.88443e12	0.547008
$612$	0	0
$613$	−5.37354e11	−0.153705	−0.0768525	−	0.997042i	$-0.524487\pi$
$613$	−5.37354e11	−0.153705	−0.0768525	+	0.997042i	$0.524487\pi$
$614$	0	0
$615$	2.05214e11	0.0578455
$616$	0	0
$617$	4.63358e12	1.28716	0.643582	−	0.765378i	$-0.277448\pi$
$617$	4.63358e12	1.28716	0.643582	+	0.765378i	$0.277448\pi$
$618$	0	0
$619$	−3.06267e12	−0.838480	−0.419240	−	0.907876i	$-0.637703\pi$
$619$	−3.06267e12	−0.838480	−0.419240	+	0.907876i	$0.637703\pi$
$620$	0	0
$621$	4.79496e11	0.129382
$622$	0	0
$623$	−3.02827e10	−0.00805374
$624$	0	0
$625$	−4.73661e10	−0.0124167
$626$	0	0
$627$	−2.76244e12	−0.713821
$628$	0	0
$629$	−1.06670e12	−0.271715
$630$	0	0
$631$	5.46928e10	0.0137340	0.00686702	−	0.999976i	$-0.497814\pi$
$631$	5.46928e10	0.0137340	0.00686702	+	0.999976i	$0.497814\pi$
$632$	0	0
$633$	7.25654e12	1.79644
$634$	0	0
$635$	−1.04365e12	−0.254727
$636$	0	0
$637$	−7.02533e12	−1.69059
$638$	0	0
$639$	1.80151e12	0.427449
$640$	0	0
$641$	−4.78068e12	−1.11848	−0.559240	−	0.829006i	$-0.688907\pi$
$641$	−4.78068e12	−1.11848	−0.559240	+	0.829006i	$0.688907\pi$
$642$	0	0
$643$	−4.10484e12	−0.946994	−0.473497	−	0.880795i	$-0.657008\pi$
$643$	−4.10484e12	−0.946994	−0.473497	+	0.880795i	$0.657008\pi$
$644$	0	0
$645$	−4.56977e12	−1.03962
$646$	0	0
$647$	5.49263e12	1.23228	0.616142	−	0.787635i	$-0.288695\pi$
$647$	5.49263e12	1.23228	0.616142	+	0.787635i	$0.288695\pi$
$648$	0	0
$649$	−6.30178e12	−1.39432
$650$	0	0
$651$	1.94463e11	0.0424348
$652$	0	0
$653$	4.15994e12	0.895320	0.447660	−	0.894204i	$-0.352258\pi$
$653$	4.15994e12	0.895320	0.447660	+	0.894204i	$0.352258\pi$
$654$	0	0
$655$	−2.42395e12	−0.514561
$656$	0	0
$657$	1.18763e12	0.248678
$658$	0	0
$659$	−2.15295e12	−0.444681	−0.222341	−	0.974969i	$-0.571370\pi$
$659$	−2.15295e12	−0.444681	−0.222341	+	0.974969i	$0.571370\pi$
$660$	0	0
$661$	8.63978e12	1.76034	0.880169	−	0.474660i	$-0.157429\pi$
$661$	8.63978e12	1.76034	0.880169	+	0.474660i	$0.157429\pi$
$662$	0	0
$663$	−6.88071e12	−1.38300
$664$	0	0
$665$	−2.61210e11	−0.0517956
$666$	0	0
$667$	7.85387e11	0.153645
$668$	0	0
$669$	−7.27502e12	−1.40416
$670$	0	0
$671$	−1.86396e12	−0.354964
$672$	0	0
$673$	−2.90788e12	−0.546398	−0.273199	−	0.961957i	$-0.588082\pi$
$673$	−2.90788e12	−0.546398	−0.273199	+	0.961957i	$0.588082\pi$
$674$	0	0
$675$	2.80476e12	0.520031
$676$	0	0
$677$	4.26822e12	0.780904	0.390452	−	0.920623i	$-0.372319\pi$
$677$	4.26822e12	0.780904	0.390452	+	0.920623i	$0.372319\pi$
$678$	0	0
$679$	−6.41203e11	−0.115766
$680$	0	0
$681$	−4.14753e12	−0.738971
$682$	0	0
$683$	7.69165e11	0.135247	0.0676233	−	0.997711i	$-0.478458\pi$
$683$	7.69165e11	0.135247	0.0676233	+	0.997711i	$0.478458\pi$
$684$	0	0
$685$	2.50763e12	0.435166
$686$	0	0
$687$	6.23855e12	1.06851
$688$	0	0
$689$	2.95925e12	0.500259
$690$	0	0
$691$	−1.38648e12	−0.231347	−0.115673	−	0.993287i	$-0.536903\pi$
$691$	−1.38648e12	−0.231347	−0.115673	+	0.993287i	$0.536903\pi$
$692$	0	0
$693$	2.48716e11	0.0409642
$694$	0	0
$695$	−1.87608e12	−0.305014
$696$	0	0
$697$	−3.74475e11	−0.0601002
$698$	0	0
$699$	1.01921e12	0.161479
$700$	0	0
$701$	−5.51186e12	−0.862119	−0.431059	−	0.902324i	$-0.641860\pi$
$701$	−5.51186e12	−0.862119	−0.431059	+	0.902324i	$0.641860\pi$
$702$	0	0
$703$	−1.35837e12	−0.209758
$704$	0	0
$705$	1.43606e12	0.218939
$706$	0	0
$707$	1.00695e12	0.151572
$708$	0	0
$709$	2.43152e12	0.361385	0.180693	−	0.983540i	$-0.442166\pi$
$709$	2.43152e12	0.361385	0.180693	+	0.983540i	$0.442166\pi$
$710$	0	0
$711$	−2.28975e12	−0.336028
$712$	0	0
$713$	−2.67779e11	−0.0388038
$714$	0	0
$715$	8.69967e12	1.24487
$716$	0	0
$717$	8.84166e12	1.24939
$718$	0	0
$719$	2.70890e12	0.378018	0.189009	−	0.981975i	$-0.439472\pi$
$719$	2.70890e12	0.378018	0.189009	+	0.981975i	$0.439472\pi$
$720$	0	0
$721$	−7.57664e11	−0.104416
$722$	0	0
$723$	7.19927e11	0.0979864
$724$	0	0
$725$	4.59404e12	0.617553
$726$	0	0
$727$	−5.26647e11	−0.0699221	−0.0349611	−	0.999389i	$-0.511131\pi$
$727$	−5.26647e11	−0.0699221	−0.0349611	+	0.999389i	$0.511131\pi$
$728$	0	0
$729$	5.07138e12	0.665047
$730$	0	0
$731$	8.33893e12	1.08015
$732$	0	0
$733$	−2.78009e12	−0.355706	−0.177853	−	0.984057i	$-0.556915\pi$
$733$	−2.78009e12	−0.355706	−0.177853	+	0.984057i	$0.556915\pi$
$734$	0	0
$735$	−5.35379e12	−0.676656
$736$	0	0
$737$	6.81481e12	0.850844
$738$	0	0
$739$	2.36558e12	0.291768	0.145884	−	0.989302i	$-0.453397\pi$
$739$	2.36558e12	0.291768	0.145884	+	0.989302i	$0.453397\pi$
$740$	0	0
$741$	−8.76210e12	−1.06764
$742$	0	0
$743$	−1.31398e13	−1.58175	−0.790876	−	0.611977i	$-0.790375\pi$
$743$	−1.31398e13	−1.58175	−0.790876	+	0.611977i	$0.790375\pi$
$744$	0	0
$745$	6.56457e12	0.780733
$746$	0	0
$747$	2.12838e12	0.250095
$748$	0	0
$749$	1.87938e12	0.218195
$750$	0	0
$751$	7.29436e12	0.836773	0.418387	−	0.908269i	$-0.362596\pi$
$751$	7.29436e12	0.836773	0.418387	+	0.908269i	$0.362596\pi$
$752$	0	0
$753$	−1.06110e13	−1.20276
$754$	0	0
$755$	3.75238e12	0.420287
$756$	0	0
$757$	−1.63020e13	−1.80430	−0.902150	−	0.431423i	$-0.858012\pi$
$757$	−1.63020e13	−1.80430	−0.902150	+	0.431423i	$0.858012\pi$
$758$	0	0
$759$	−1.79127e12	−0.195917
$760$	0	0
$761$	−9.68945e12	−1.04729	−0.523646	−	0.851936i	$-0.675429\pi$
$761$	−9.68945e12	−1.04729	−0.523646	+	0.851936i	$0.675429\pi$
$762$	0	0
$763$	−1.28010e12	−0.136737
$764$	0	0
$765$	−1.00256e12	−0.105836
$766$	0	0
$767$	−1.99884e13	−2.08545
$768$	0	0
$769$	1.21329e13	1.25111	0.625554	−	0.780180i	$-0.284873\pi$
$769$	1.21329e13	1.25111	0.625554	+	0.780180i	$0.284873\pi$
$770$	0	0
$771$	−1.46009e13	−1.48811
$772$	0	0
$773$	−1.68647e13	−1.69891	−0.849454	−	0.527663i	$-0.823068\pi$
$773$	−1.68647e13	−1.69891	−0.849454	+	0.527663i	$0.823068\pi$
$774$	0	0
$775$	−1.56635e12	−0.155966
$776$	0	0
$777$	6.39653e11	0.0629578
$778$	0	0
$779$	−4.76868e11	−0.0463959
$780$	0	0
$781$	2.17390e13	2.09079
$782$	0	0
$783$	9.00463e12	0.856126
$784$	0	0
$785$	−3.68147e12	−0.346025
$786$	0	0
$787$	6.00116e12	0.557634	0.278817	−	0.960344i	$-0.410058\pi$
$787$	6.00116e12	0.557634	0.278817	+	0.960344i	$0.410058\pi$
$788$	0	0
$789$	1.46703e13	1.34769
$790$	0	0
$791$	2.57688e12	0.234045
$792$	0	0
$793$	−5.91223e12	−0.530911
$794$	0	0
$795$	2.25515e12	0.200228
$796$	0	0
$797$	−1.43155e13	−1.25674	−0.628368	−	0.777916i	$-0.716277\pi$
$797$	−1.43155e13	−1.25674	−0.628368	+	0.777916i	$0.716277\pi$
$798$	0	0
$799$	−2.62053e12	−0.227472
$800$	0	0
$801$	−1.48010e11	−0.0127041
$802$	0	0
$803$	1.43312e13	1.21636
$804$	0	0
$805$	−1.69378e11	−0.0142160
$806$	0	0
$807$	1.91450e13	1.58900
$808$	0	0
$809$	−1.09893e13	−0.901992	−0.450996	−	0.892526i	$-0.648931\pi$
$809$	−1.09893e13	−0.901992	−0.450996	+	0.892526i	$0.648931\pi$
$810$	0	0
$811$	−2.15444e13	−1.74880	−0.874399	−	0.485207i	$-0.838744\pi$
$811$	−2.15444e13	−1.74880	−0.874399	+	0.485207i	$0.838744\pi$
$812$	0	0
$813$	2.56242e13	2.05704
$814$	0	0
$815$	−7.20750e11	−0.0572236
$816$	0	0
$817$	1.06190e13	0.833846
$818$	0	0
$819$	7.88895e11	0.0612691
$820$	0	0
$821$	5.71748e12	0.439198	0.219599	−	0.975590i	$-0.429525\pi$
$821$	5.71748e12	0.439198	0.219599	+	0.975590i	$0.429525\pi$
$822$	0	0
$823$	1.00524e13	0.763787	0.381893	−	0.924206i	$-0.375272\pi$
$823$	1.00524e13	0.763787	0.381893	+	0.924206i	$0.375272\pi$
$824$	0	0
$825$	−1.04778e13	−0.787461
$826$	0	0
$827$	−2.29581e13	−1.70672	−0.853359	−	0.521324i	$-0.825438\pi$
$827$	−2.29581e13	−1.70672	−0.853359	+	0.521324i	$0.825438\pi$
$828$	0	0
$829$	−1.57277e13	−1.15657	−0.578283	−	0.815836i	$-0.696277\pi$
$829$	−1.57277e13	−1.15657	−0.578283	+	0.815836i	$0.696277\pi$
$830$	0	0
$831$	1.01421e13	0.737773
$832$	0	0
$833$	9.76960e12	0.703031
$834$	0	0
$835$	2.48385e12	0.176822
$836$	0	0
$837$	−3.07014e12	−0.216219
$838$	0	0
$839$	8.52168e12	0.593740	0.296870	−	0.954918i	$-0.404057\pi$
$839$	8.52168e12	0.593740	0.296870	+	0.954918i	$0.404057\pi$
$840$	0	0
$841$	2.41910e11	0.0166752
$842$	0	0
$843$	8.12705e12	0.554254
$844$	0	0
$845$	1.83683e13	1.23941
$846$	0	0
$847$	7.56507e11	0.0505054
$848$	0	0
$849$	1.41491e13	0.934638
$850$	0	0
$851$	−8.80815e11	−0.0575707
$852$	0	0
$853$	−1.83160e12	−0.118457	−0.0592285	−	0.998244i	$-0.518864\pi$
$853$	−1.83160e12	−0.118457	−0.0592285	+	0.998244i	$0.518864\pi$
$854$	0	0
$855$	−1.27669e12	−0.0817032
$856$	0	0
$857$	−6.20072e11	−0.0392671	−0.0196335	−	0.999807i	$-0.506250\pi$
$857$	−6.20072e11	−0.0392671	−0.0196335	+	0.999807i	$0.506250\pi$
$858$	0	0
$859$	5.71581e12	0.358186	0.179093	−	0.983832i	$-0.442684\pi$
$859$	5.71581e12	0.358186	0.179093	+	0.983832i	$0.442684\pi$
$860$	0	0
$861$	2.24556e11	0.0139255
$862$	0	0
$863$	−2.02596e13	−1.24332	−0.621658	−	0.783289i	$-0.713540\pi$
$863$	−2.02596e13	−1.24332	−0.621658	+	0.783289i	$0.713540\pi$
$864$	0	0
$865$	−1.53720e13	−0.933596
$866$	0	0
$867$	−8.93122e12	−0.536815
$868$	0	0
$869$	−2.76305e13	−1.64362
$870$	0	0
$871$	2.16157e13	1.27259
$872$	0	0
$873$	−3.13394e12	−0.182611
$874$	0	0
$875$	−2.60842e12	−0.150432
$876$	0	0
$877$	−9.14573e10	−0.00522059	−0.00261030	−	0.999997i	$-0.500831\pi$
$877$	−9.14573e10	−0.00522059	−0.00261030	+	0.999997i	$0.500831\pi$
$878$	0	0
$879$	1.13189e13	0.639519
$880$	0	0
$881$	1.73150e13	0.968347	0.484174	−	0.874972i	$-0.339120\pi$
$881$	1.73150e13	0.968347	0.484174	+	0.874972i	$0.339120\pi$
$882$	0	0
$883$	−1.38781e13	−0.768259	−0.384130	−	0.923279i	$-0.625498\pi$
$883$	−1.38781e13	−0.768259	−0.384130	+	0.923279i	$0.625498\pi$
$884$	0	0
$885$	−1.52325e13	−0.834695
$886$	0	0
$887$	−1.76586e13	−0.957853	−0.478926	−	0.877855i	$-0.658974\pi$
$887$	−1.76586e13	−0.957853	−0.478926	+	0.877855i	$0.658974\pi$
$888$	0	0
$889$	−1.14202e12	−0.0613219
$890$	0	0
$891$	−2.56796e13	−1.36502
$892$	0	0
$893$	−3.33706e12	−0.175603
$894$	0	0
$895$	5.10457e11	0.0265923
$896$	0	0
$897$	−5.68167e12	−0.293028
$898$	0	0
$899$	−5.02872e12	−0.256767
$900$	0	0
$901$	−4.11520e12	−0.208032
$902$	0	0
$903$	−5.00049e12	−0.250275
$904$	0	0
$905$	−4.72754e12	−0.234270
$906$	0	0
$907$	−1.23924e13	−0.608025	−0.304013	−	0.952668i	$-0.598327\pi$
$907$	−1.23924e13	−0.608025	−0.304013	+	0.952668i	$0.598327\pi$
$908$	0	0
$909$	4.92157e12	0.239092
$910$	0	0
$911$	1.38104e13	0.664313	0.332157	−	0.943224i	$-0.392224\pi$
$911$	1.38104e13	0.664313	0.332157	+	0.943224i	$0.392224\pi$
$912$	0	0
$913$	2.56832e13	1.22329
$914$	0	0
$915$	−4.50553e12	−0.212496
$916$	0	0
$917$	−2.65241e12	−0.123874
$918$	0	0
$919$	−8.56606e11	−0.0396152	−0.0198076	−	0.999804i	$-0.506305\pi$
$919$	−8.56606e11	−0.0396152	−0.0198076	+	0.999804i	$0.506305\pi$
$920$	0	0
$921$	−2.83884e13	−1.30009
$922$	0	0
$923$	6.89531e13	3.12713
$924$	0	0
$925$	−5.15223e12	−0.231397
$926$	0	0
$927$	−3.70316e12	−0.164708
$928$	0	0
$929$	1.29169e13	0.568968	0.284484	−	0.958681i	$-0.408178\pi$
$929$	1.29169e13	0.568968	0.284484	+	0.958681i	$0.408178\pi$
$930$	0	0
$931$	1.24409e13	0.542723
$932$	0	0
$933$	1.40134e13	0.605447
$934$	0	0
$935$	−1.20980e13	−0.517679
$936$	0	0
$937$	−3.67867e12	−0.155906	−0.0779530	−	0.996957i	$-0.524838\pi$
$937$	−3.67867e12	−0.155906	−0.0779530	+	0.996957i	$0.524838\pi$
$938$	0	0
$939$	8.60174e11	0.0361070
$940$	0	0
$941$	4.45145e13	1.85075	0.925376	−	0.379051i	$-0.123749\pi$
$941$	4.45145e13	1.85075	0.925376	+	0.379051i	$0.123749\pi$
$942$	0	0
$943$	−3.09219e11	−0.0127339
$944$	0	0
$945$	−1.94196e12	−0.0792130
$946$	0	0
$947$	1.99543e13	0.806236	0.403118	−	0.915148i	$-0.367926\pi$
$947$	1.99543e13	0.806236	0.403118	+	0.915148i	$0.367926\pi$
$948$	0	0
$949$	4.54567e13	1.81928
$950$	0	0
$951$	−3.03897e12	−0.120480
$952$	0	0
$953$	7.13202e12	0.280088	0.140044	−	0.990145i	$-0.455276\pi$
$953$	7.13202e12	0.280088	0.140044	+	0.990145i	$0.455276\pi$
$954$	0	0
$955$	−2.81264e13	−1.09421
$956$	0	0
$957$	−3.36388e13	−1.29639
$958$	0	0
$959$	2.74398e12	0.104760
$960$	0	0
$961$	−2.47251e13	−0.935152
$962$	0	0
$963$	9.18565e12	0.344185
$964$	0	0
$965$	−1.12577e13	−0.417905
$966$	0	0
$967$	−2.84176e12	−0.104512	−0.0522562	−	0.998634i	$-0.516641\pi$
$967$	−2.84176e12	−0.104512	−0.0522562	+	0.998634i	$0.516641\pi$
$968$	0	0
$969$	1.21848e13	0.443978
$970$	0	0
$971$	3.90309e13	1.40903	0.704517	−	0.709687i	$-0.251164\pi$
$971$	3.90309e13	1.40903	0.704517	+	0.709687i	$0.251164\pi$
$972$	0	0
$973$	−2.05290e12	−0.0734278
$974$	0	0
$975$	−3.32343e13	−1.17778
$976$	0	0
$977$	−2.17556e13	−0.763915	−0.381958	−	0.924180i	$-0.624750\pi$
$977$	−2.17556e13	−0.763915	−0.381958	+	0.924180i	$0.624750\pi$
$978$	0	0
$979$	−1.78604e12	−0.0621397
$980$	0	0
$981$	−6.25664e12	−0.215690
$982$	0	0
$983$	−4.64998e13	−1.58840	−0.794201	−	0.607655i	$-0.792110\pi$
$983$	−4.64998e13	−1.58840	−0.794201	+	0.607655i	$0.792110\pi$
$984$	0	0
$985$	7.66548e12	0.259464
$986$	0	0
$987$	1.57142e12	0.0527065
$988$	0	0
$989$	6.88577e12	0.228860
$990$	0	0
$991$	1.55209e13	0.511194	0.255597	−	0.966783i	$-0.417728\pi$
$991$	1.55209e13	0.511194	0.255597	+	0.966783i	$0.417728\pi$
$992$	0	0
$993$	1.66610e13	0.543786
$994$	0	0
$995$	2.16225e13	0.699361
$996$	0	0
$997$	−4.26334e13	−1.36654	−0.683268	−	0.730167i	$-0.739442\pi$
$997$	−4.26334e13	−1.36654	−0.683268	+	0.730167i	$0.739442\pi$
$998$	0	0
$999$	−1.00987e13	−0.320791

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.10.a.d.1.1		1
3.2	odd	2		144.10.a.d.1.1		1
4.3	odd	2		2.10.a.a.1.1	✓	1
5.2	odd	4		400.10.c.d.49.1		2
5.3	odd	4		400.10.c.d.49.2		2
5.4	even	2		400.10.a.b.1.1		1
8.3	odd	2		64.10.a.h.1.1		1
8.5	even	2		64.10.a.b.1.1		1
12.11	even	2		18.10.a.a.1.1		1
16.3	odd	4		256.10.b.g.129.1		2
16.5	even	4		256.10.b.e.129.1		2
16.11	odd	4		256.10.b.g.129.2		2
16.13	even	4		256.10.b.e.129.2		2
20.3	even	4		50.10.b.a.49.1		2
20.7	even	4		50.10.b.a.49.2		2
20.19	odd	2		50.10.a.c.1.1		1
28.3	even	6		98.10.c.b.79.1		2
28.11	odd	6		98.10.c.c.79.1		2
28.19	even	6		98.10.c.b.67.1		2
28.23	odd	6		98.10.c.c.67.1		2
28.27	even	2		98.10.a.c.1.1		1
36.7	odd	6		162.10.c.b.109.1		2
36.11	even	6		162.10.c.i.109.1		2
36.23	even	6		162.10.c.i.55.1		2
36.31	odd	6		162.10.c.b.55.1		2
44.43	even	2		242.10.a.a.1.1		1
52.51	odd	2		338.10.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.10.a.a.1.1	✓	1	4.3	odd	2
16.10.a.d.1.1		1	1.1	even	1	trivial
18.10.a.a.1.1		1	12.11	even	2
50.10.a.c.1.1		1	20.19	odd	2
50.10.b.a.49.1		2	20.3	even	4
50.10.b.a.49.2		2	20.7	even	4
64.10.a.b.1.1		1	8.5	even	2
64.10.a.h.1.1		1	8.3	odd	2
98.10.a.c.1.1		1	28.27	even	2
98.10.c.b.67.1		2	28.19	even	6
98.10.c.b.79.1		2	28.3	even	6
98.10.c.c.67.1		2	28.23	odd	6
98.10.c.c.79.1		2	28.11	odd	6
144.10.a.d.1.1		1	3.2	odd	2
162.10.c.b.55.1		2	36.31	odd	6
162.10.c.b.109.1		2	36.7	odd	6
162.10.c.i.55.1		2	36.23	even	6
162.10.c.i.109.1		2	36.11	even	6
242.10.a.a.1.1		1	44.43	even	2
256.10.b.e.129.1		2	16.5	even	4
256.10.b.e.129.2		2	16.13	even	4
256.10.b.g.129.1		2	16.3	odd	4
256.10.b.g.129.2		2	16.11	odd	4
338.10.a.a.1.1		1	52.51	odd	2
400.10.a.b.1.1		1	5.4	even	2
400.10.c.d.49.1		2	5.2	odd	4
400.10.c.d.49.2		2	5.3	odd	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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	16.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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