LMFDB - Embedded newform 9.10.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,10,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, 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("9.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	9.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:	$4.63532252547$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+36.0000 q^{2} +784.000 q^{4} +1314.00 q^{5} -4480.00 q^{7} +9792.00 q^{8} +O(q^{10})$

\(q+36.0000 q^{2} +784.000 q^{4} +1314.00 q^{5} -4480.00 q^{7} +9792.00 q^{8} +47304.0 q^{10} -1476.00 q^{11} -151522. q^{13} -161280. q^{14} -48896.0 q^{16} -108162. q^{17} +593084. q^{19} +1.03018e6 q^{20} -53136.0 q^{22} +969480. q^{23} -226529. q^{25} -5.45479e6 q^{26} -3.51232e6 q^{28} +6.64252e6 q^{29} +7.07060e6 q^{31} -6.77376e6 q^{32} -3.89383e6 q^{34} -5.88672e6 q^{35} -7.47241e6 q^{37} +2.13510e7 q^{38} +1.28667e7 q^{40} +4.35015e6 q^{41} -4.35872e6 q^{43} -1.15718e6 q^{44} +3.49013e7 q^{46} -2.83092e7 q^{47} -2.02832e7 q^{49} -8.15504e6 q^{50} -1.18793e8 q^{52} -1.61117e7 q^{53} -1.93946e6 q^{55} -4.38682e7 q^{56} +2.39131e8 q^{58} +8.60760e7 q^{59} +3.22139e7 q^{61} +2.54542e8 q^{62} -2.18821e8 q^{64} -1.99100e8 q^{65} +9.95315e7 q^{67} -8.47990e7 q^{68} -2.11922e8 q^{70} +4.41705e7 q^{71} -2.35606e7 q^{73} -2.69007e8 q^{74} +4.64978e8 q^{76} +6.61248e6 q^{77} -4.01755e8 q^{79} -6.42493e7 q^{80} +1.56605e8 q^{82} +7.44529e8 q^{83} -1.42125e8 q^{85} -1.56914e8 q^{86} -1.44530e7 q^{88} -7.69871e8 q^{89} +6.78819e8 q^{91} +7.60072e8 q^{92} -1.01913e9 q^{94} +7.79312e8 q^{95} +9.07131e8 q^{97} -7.30195e8 q^{98} +O(q^{100})\)

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 $

$2$	36.0000	1.59099	0.795495	−	0.605960i	$-0.207211\pi$
$2$	36.0000	1.59099	0.795495	+	0.605960i	$0.207211\pi$
$3$	0	0
$3$	0	0
$4$	784.000	1.53125
$5$	1314.00	0.940222	0.470111	−	0.882607i	$-0.344214\pi$
$5$	1314.00	0.940222	0.470111	+	0.882607i	$0.344214\pi$
$6$	0	0
$7$	−4480.00	−0.705240	−0.352620	−	0.935767i	$-0.614709\pi$
$7$	−4480.00	−0.705240	−0.352620	+	0.935767i	$0.614709\pi$
$8$	9792.00	0.845214
$9$	0	0
$10$	47304.0	1.49588
$11$	−1476.00	−0.0303962	−0.0151981	−	0.999885i	$-0.504838\pi$
$11$	−1476.00	−0.0303962	−0.0151981	+	0.999885i	$0.504838\pi$
$12$	0	0
$13$	−151522.	−1.47140	−0.735700	−	0.677308i	$-0.763147\pi$
$13$	−151522.	−1.47140	−0.735700	+	0.677308i	$0.763147\pi$
$14$	−161280.	−1.12203
$15$	0	0
$16$	−48896.0	−0.186523
$17$	−108162.	−0.314090	−0.157045	−	0.987591i	$-0.550197\pi$
$17$	−108162.	−0.314090	−0.157045	+	0.987591i	$0.550197\pi$
$18$	0	0
$19$	593084.	1.04406	0.522029	−	0.852927i	$-0.325175\pi$
$19$	593084.	1.04406	0.522029	+	0.852927i	$0.325175\pi$
$20$	1.03018e6	1.43971
$21$	0	0
$22$	−53136.0	−0.0483601
$23$	969480.	0.722376	0.361188	−	0.932493i	$-0.382371\pi$
$23$	969480.	0.722376	0.361188	+	0.932493i	$0.382371\pi$
$24$	0	0
$25$	−226529.	−0.115983
$26$	−5.45479e6	−2.34098
$27$	0	0
$28$	−3.51232e6	−1.07990
$29$	6.64252e6	1.74398	0.871991	−	0.489522i	$-0.162829\pi$
$29$	6.64252e6	1.74398	0.871991	+	0.489522i	$0.162829\pi$
$30$	0	0
$31$	7.07060e6	1.37508	0.687541	−	0.726145i	$-0.258690\pi$
$31$	7.07060e6	1.37508	0.687541	+	0.726145i	$0.258690\pi$
$32$	−6.77376e6	−1.14197
$33$	0	0
$34$	−3.89383e6	−0.499715
$35$	−5.88672e6	−0.663082
$36$	0	0
$37$	−7.47241e6	−0.655470	−0.327735	−	0.944770i	$-0.606285\pi$
$37$	−7.47241e6	−0.655470	−0.327735	+	0.944770i	$0.606285\pi$
$38$	2.13510e7	1.66109
$39$	0	0
$40$	1.28667e7	0.794688
$41$	4.35015e6	0.240423	0.120212	−	0.992748i	$-0.461643\pi$
$41$	4.35015e6	0.240423	0.120212	+	0.992748i	$0.461643\pi$
$42$	0	0
$43$	−4.35872e6	−0.194424	−0.0972121	−	0.995264i	$-0.530993\pi$
$43$	−4.35872e6	−0.194424	−0.0972121	+	0.995264i	$0.530993\pi$
$44$	−1.15718e6	−0.0465442
$45$	0	0
$46$	3.49013e7	1.14929
$47$	−2.83092e7	−0.846229	−0.423115	−	0.906076i	$-0.639063\pi$
$47$	−2.83092e7	−0.846229	−0.423115	+	0.906076i	$0.639063\pi$
$48$	0	0
$49$	−2.02832e7	−0.502637
$50$	−8.15504e6	−0.184528
$51$	0	0
$52$	−1.18793e8	−2.25308
$53$	−1.61117e7	−0.280479	−0.140239	−	0.990118i	$-0.544787\pi$
$53$	−1.61117e7	−0.280479	−0.140239	+	0.990118i	$0.544787\pi$
$54$	0	0
$55$	−1.93946e6	−0.0285792
$56$	−4.38682e7	−0.596078
$57$	0	0
$58$	2.39131e8	2.77466
$59$	8.60760e7	0.924800	0.462400	−	0.886671i	$-0.346988\pi$
$59$	8.60760e7	0.924800	0.462400	+	0.886671i	$0.346988\pi$
$60$	0	0
$61$	3.22139e7	0.297892	0.148946	−	0.988845i	$-0.452412\pi$
$61$	3.22139e7	0.297892	0.148946	+	0.988845i	$0.452412\pi$
$62$	2.54542e8	2.18774
$63$	0	0
$64$	−2.18821e8	−1.63034
$65$	−1.99100e8	−1.38344
$66$	0	0
$67$	9.95315e7	0.603426	0.301713	−	0.953399i	$-0.402442\pi$
$67$	9.95315e7	0.603426	0.301713	+	0.953399i	$0.402442\pi$
$68$	−8.47990e7	−0.480951
$69$	0	0
$70$	−2.11922e8	−1.05496
$71$	4.41705e7	0.206286	0.103143	−	0.994667i	$-0.467110\pi$
$71$	4.41705e7	0.206286	0.103143	+	0.994667i	$0.467110\pi$
$72$	0	0
$73$	−2.35606e7	−0.0971033	−0.0485517	−	0.998821i	$-0.515461\pi$
$73$	−2.35606e7	−0.0971033	−0.0485517	+	0.998821i	$0.515461\pi$
$74$	−2.69007e8	−1.04285
$75$	0	0
$76$	4.64978e8	1.59872
$77$	6.61248e6	0.0214366
$78$	0	0
$79$	−4.01755e8	−1.16048	−0.580242	−	0.814444i	$-0.697042\pi$
$79$	−4.01755e8	−1.16048	−0.580242	+	0.814444i	$0.697042\pi$
$80$	−6.42493e7	−0.175373
$81$	0	0
$82$	1.56605e8	0.382511
$83$	7.44529e8	1.72199	0.860994	−	0.508615i	$-0.169842\pi$
$83$	7.44529e8	1.72199	0.860994	+	0.508615i	$0.169842\pi$
$84$	0	0
$85$	−1.42125e8	−0.295315
$86$	−1.56914e8	−0.309327
$87$	0	0
$88$	−1.44530e7	−0.0256913
$89$	−7.69871e8	−1.30066	−0.650329	−	0.759653i	$-0.725369\pi$
$89$	−7.69871e8	−1.30066	−0.650329	+	0.759653i	$0.725369\pi$
$90$	0	0
$91$	6.78819e8	1.03769
$92$	7.60072e8	1.10614
$93$	0	0
$94$	−1.01913e9	−1.34634
$95$	7.79312e8	0.981647
$96$	0	0
$97$	9.07131e8	1.04039	0.520196	−	0.854047i	$-0.325859\pi$
$97$	9.07131e8	1.04039	0.520196	+	0.854047i	$0.325859\pi$
$98$	−7.30195e8	−0.799690
$99$	0	0
$100$	−1.77599e8	−0.177599
$101$	4.21902e8	0.403427	0.201714	−	0.979445i	$-0.435349\pi$
$101$	4.21902e8	0.403427	0.201714	+	0.979445i	$0.435349\pi$
$102$	0	0
$103$	5.79043e8	0.506924	0.253462	−	0.967345i	$-0.418431\pi$
$103$	5.79043e8	0.506924	0.253462	+	0.967345i	$0.418431\pi$
$104$	−1.48370e9	−1.24365
$105$	0	0
$106$	−5.80022e8	−0.446239
$107$	−1.39714e9	−1.03042	−0.515208	−	0.857065i	$-0.672285\pi$
$107$	−1.39714e9	−1.03042	−0.515208	+	0.857065i	$0.672285\pi$
$108$	0	0
$109$	−2.68530e9	−1.82211	−0.911054	−	0.412286i	$-0.864730\pi$
$109$	−2.68530e9	−1.82211	−0.911054	+	0.412286i	$0.864730\pi$
$110$	−6.98207e7	−0.0454692
$111$	0	0
$112$	2.19054e8	0.131544
$113$	−4.54749e8	−0.262373	−0.131186	−	0.991358i	$-0.541879\pi$
$113$	−4.54749e8	−0.262373	−0.131186	+	0.991358i	$0.541879\pi$
$114$	0	0
$115$	1.27390e9	0.679194
$116$	5.20774e9	2.67047
$117$	0	0
$118$	3.09873e9	1.47135
$119$	4.84566e8	0.221509
$120$	0	0
$121$	−2.35577e9	−0.999076
$122$	1.15970e9	0.473944
$123$	0	0
$124$	5.54335e9	2.10559
$125$	−2.86407e9	−1.04927
$126$	0	0
$127$	−8.38650e7	−0.0286064	−0.0143032	−	0.999898i	$-0.504553\pi$
$127$	−8.38650e7	−0.0286064	−0.0143032	+	0.999898i	$0.504553\pi$
$128$	−4.40938e9	−1.45189
$129$	0	0
$130$	−7.16760e9	−2.20104
$131$	3.73601e9	1.10838	0.554188	−	0.832391i	$-0.313029\pi$
$131$	3.73601e9	1.10838	0.554188	+	0.832391i	$0.313029\pi$
$132$	0	0
$133$	−2.65702e9	−0.736312
$134$	3.58313e9	0.960044
$135$	0	0
$136$	−1.05912e9	−0.265473
$137$	−6.43598e9	−1.56089	−0.780444	−	0.625225i	$-0.785007\pi$
$137$	−6.43598e9	−1.56089	−0.780444	+	0.625225i	$0.785007\pi$
$138$	0	0
$139$	1.81833e9	0.413148	0.206574	−	0.978431i	$-0.433769\pi$
$139$	1.81833e9	0.413148	0.206574	+	0.978431i	$0.433769\pi$
$140$	−4.61519e9	−1.01534
$141$	0	0
$142$	1.59014e9	0.328199
$143$	2.23646e8	0.0447250
$144$	0	0
$145$	8.72827e9	1.63973
$146$	−8.48183e8	−0.154490
$147$	0	0
$148$	−5.85837e9	−1.00369
$149$	8.30199e9	1.37989	0.689944	−	0.723863i	$-0.257635\pi$
$149$	8.30199e9	1.37989	0.689944	+	0.723863i	$0.257635\pi$
$150$	0	0
$151$	3.84057e9	0.601173	0.300587	−	0.953755i	$-0.402818\pi$
$151$	3.84057e9	0.601173	0.300587	+	0.953755i	$0.402818\pi$
$152$	5.80748e9	0.882453
$153$	0	0
$154$	2.38049e8	0.0341054
$155$	9.29077e9	1.29288
$156$	0	0
$157$	−2.17912e9	−0.286242	−0.143121	−	0.989705i	$-0.545714\pi$
$157$	−2.17912e9	−0.286242	−0.143121	+	0.989705i	$0.545714\pi$
$158$	−1.44632e10	−1.84632
$159$	0	0
$160$	−8.90072e9	−1.07371
$161$	−4.34327e9	−0.509449
$162$	0	0
$163$	−1.54147e10	−1.71038	−0.855188	−	0.518317i	$-0.826559\pi$
$163$	−1.54147e10	−1.71038	−0.855188	+	0.518317i	$0.826559\pi$
$164$	3.41052e9	0.368148
$165$	0	0
$166$	2.68030e10	2.73967
$167$	5.65506e9	0.562617	0.281309	−	0.959617i	$-0.409232\pi$
$167$	5.65506e9	0.562617	0.281309	+	0.959617i	$0.409232\pi$
$168$	0	0
$169$	1.23544e10	1.16502
$170$	−5.11650e9	−0.469843
$171$	0	0
$172$	−3.41723e9	−0.297712
$173$	−7.69892e7	−0.00653465	−0.00326733	−	0.999995i	$-0.501040\pi$
$173$	−7.69892e7	−0.00653465	−0.00326733	+	0.999995i	$0.501040\pi$
$174$	0	0
$175$	1.01485e9	0.0817957
$176$	7.21705e7	0.00566960
$177$	0	0
$178$	−2.77154e10	−2.06933
$179$	−2.32247e10	−1.69087	−0.845436	−	0.534077i	$-0.820659\pi$
$179$	−2.32247e10	−1.69087	−0.845436	+	0.534077i	$0.820659\pi$
$180$	0	0
$181$	−1.23532e10	−0.855513	−0.427756	−	0.903894i	$-0.640696\pi$
$181$	−1.23532e10	−0.855513	−0.427756	+	0.903894i	$0.640696\pi$
$182$	2.44375e10	1.65095
$183$	0	0
$184$	9.49315e9	0.610562
$185$	−9.81875e9	−0.616287
$186$	0	0
$187$	1.59647e8	0.00954715
$188$	−2.21945e10	−1.29579
$189$	0	0
$190$	2.80552e10	1.56179
$191$	4.20433e9	0.228584	0.114292	−	0.993447i	$-0.463540\pi$
$191$	4.20433e9	0.228584	0.114292	+	0.993447i	$0.463540\pi$
$192$	0	0
$193$	−4.38611e9	−0.227547	−0.113774	−	0.993507i	$-0.536294\pi$
$193$	−4.38611e9	−0.227547	−0.113774	+	0.993507i	$0.536294\pi$
$194$	3.26567e10	1.65525
$195$	0	0
$196$	−1.59020e10	−0.769663
$197$	3.36694e10	1.59271	0.796356	−	0.604828i	$-0.206758\pi$
$197$	3.36694e10	1.59271	0.796356	+	0.604828i	$0.206758\pi$
$198$	0	0
$199$	1.02732e10	0.464374	0.232187	−	0.972671i	$-0.425412\pi$
$199$	1.02732e10	0.464374	0.232187	+	0.972671i	$0.425412\pi$
$200$	−2.21817e9	−0.0980303
$201$	0	0
$202$	1.51885e10	0.641849
$203$	−2.97585e10	−1.22993
$204$	0	0
$205$	5.71610e9	0.226051
$206$	2.08455e10	0.806512
$207$	0	0
$208$	7.40882e9	0.274450
$209$	−8.75392e8	−0.0317354
$210$	0	0
$211$	7.96696e9	0.276708	0.138354	−	0.990383i	$-0.455819\pi$
$211$	7.96696e9	0.276708	0.138354	+	0.990383i	$0.455819\pi$
$212$	−1.26316e10	−0.429483
$213$	0	0
$214$	−5.02970e10	−1.63938
$215$	−5.72735e9	−0.182802
$216$	0	0
$217$	−3.16763e10	−0.969763
$218$	−9.66710e10	−2.89896
$219$	0	0
$220$	−1.52054e9	−0.0437619
$221$	1.63889e10	0.462152
$222$	0	0
$223$	6.96581e9	0.188625	0.0943126	−	0.995543i	$-0.469935\pi$
$223$	6.96581e9	0.188625	0.0943126	+	0.995543i	$0.469935\pi$
$224$	3.03464e10	0.805363
$225$	0	0
$226$	−1.63709e10	−0.417432
$227$	−3.35697e10	−0.839133	−0.419567	−	0.907725i	$-0.637818\pi$
$227$	−3.35697e10	−0.839133	−0.419567	+	0.907725i	$0.637818\pi$
$228$	0	0
$229$	2.93198e10	0.704534	0.352267	−	0.935900i	$-0.385411\pi$
$229$	2.93198e10	0.704534	0.352267	+	0.935900i	$0.385411\pi$
$230$	4.58603e10	1.08059
$231$	0	0
$232$	6.50436e10	1.47404
$233$	8.20079e10	1.82286	0.911431	−	0.411453i	$-0.134978\pi$
$233$	8.20079e10	1.82286	0.911431	+	0.411453i	$0.134978\pi$
$234$	0	0
$235$	−3.71984e10	−0.795643
$236$	6.74836e10	1.41610
$237$	0	0
$238$	1.74444e10	0.352419
$239$	−6.26609e10	−1.24224	−0.621121	−	0.783715i	$-0.713323\pi$
$239$	−6.26609e10	−1.24224	−0.621121	+	0.783715i	$0.713323\pi$
$240$	0	0
$241$	7.75548e10	1.48092	0.740460	−	0.672100i	$-0.234608\pi$
$241$	7.75548e10	1.48092	0.740460	+	0.672100i	$0.234608\pi$
$242$	−8.48077e10	−1.58952
$243$	0	0
$244$	2.52557e10	0.456148
$245$	−2.66521e10	−0.472590
$246$	0	0
$247$	−8.98653e10	−1.53623
$248$	6.92353e10	1.16224
$249$	0	0
$250$	−1.03106e11	−1.66938
$251$	5.81901e10	0.925374	0.462687	−	0.886522i	$-0.346885\pi$
$251$	5.81901e10	0.925374	0.462687	+	0.886522i	$0.346885\pi$
$252$	0	0
$253$	−1.43095e9	−0.0219575
$254$	−3.01914e9	−0.0455126
$255$	0	0
$256$	−4.67014e10	−0.679595
$257$	7.41485e9	0.106024	0.0530119	−	0.998594i	$-0.483118\pi$
$257$	7.41485e9	0.106024	0.0530119	+	0.998594i	$0.483118\pi$
$258$	0	0
$259$	3.34764e10	0.462264
$260$	−1.56094e11	−2.11840
$261$	0	0
$262$	1.34496e11	1.76342
$263$	1.05271e11	1.35677	0.678387	−	0.734705i	$-0.262679\pi$
$263$	1.05271e11	1.35677	0.678387	+	0.734705i	$0.262679\pi$
$264$	0	0
$265$	−2.11708e10	−0.263712
$266$	−9.56526e10	−1.17147
$267$	0	0
$268$	7.80327e10	0.923995
$269$	−4.67239e10	−0.544069	−0.272034	−	0.962288i	$-0.587696\pi$
$269$	−4.67239e10	−0.544069	−0.272034	+	0.962288i	$0.587696\pi$
$270$	0	0
$271$	2.86868e10	0.323087	0.161544	−	0.986866i	$-0.448353\pi$
$271$	2.86868e10	0.323087	0.161544	+	0.986866i	$0.448353\pi$
$272$	5.28869e9	0.0585852
$273$	0	0
$274$	−2.31695e11	−2.48336
$275$	3.34357e8	0.00352544
$276$	0	0
$277$	8.50676e10	0.868171	0.434085	−	0.900872i	$-0.357072\pi$
$277$	8.50676e10	0.868171	0.434085	+	0.900872i	$0.357072\pi$
$278$	6.54598e10	0.657314
$279$	0	0
$280$	−5.76428e10	−0.560446
$281$	7.87257e8	0.00753248	0.00376624	−	0.999993i	$-0.498801\pi$
$281$	7.87257e8	0.00753248	0.00376624	+	0.999993i	$0.498801\pi$
$282$	0	0
$283$	2.48961e10	0.230724	0.115362	−	0.993324i	$-0.463197\pi$
$283$	2.48961e10	0.230724	0.115362	+	0.993324i	$0.463197\pi$
$284$	3.46297e10	0.315875
$285$	0	0
$286$	8.05127e9	0.0711570
$287$	−1.94887e10	−0.169556
$288$	0	0
$289$	−1.06889e11	−0.901347
$290$	3.14218e11	2.60879
$291$	0	0
$292$	−1.84715e10	−0.148689
$293$	−1.57074e11	−1.24509	−0.622543	−	0.782586i	$-0.713900\pi$
$293$	−1.57074e11	−1.24509	−0.622543	+	0.782586i	$0.713900\pi$
$294$	0	0
$295$	1.13104e11	0.869517
$296$	−7.31698e10	−0.554012
$297$	0	0
$298$	2.98871e11	2.19539
$299$	−1.46898e11	−1.06290
$300$	0	0
$301$	1.95270e10	0.137116
$302$	1.38261e11	0.956461
$303$	0	0
$304$	−2.89994e10	−0.194741
$305$	4.23291e10	0.280085
$306$	0	0
$307$	−2.45737e11	−1.57887	−0.789437	−	0.613831i	$-0.789628\pi$
$307$	−2.45737e11	−1.57887	−0.789437	+	0.613831i	$0.789628\pi$
$308$	5.18418e9	0.0328248
$309$	0	0
$310$	3.34468e11	2.05696
$311$	1.61050e11	0.976201	0.488101	−	0.872787i	$-0.337690\pi$
$311$	1.61050e11	0.976201	0.488101	+	0.872787i	$0.337690\pi$
$312$	0	0
$313$	−2.44646e11	−1.44075	−0.720374	−	0.693586i	$-0.756030\pi$
$313$	−2.44646e11	−1.44075	−0.720374	+	0.693586i	$0.756030\pi$
$314$	−7.84484e10	−0.455408
$315$	0	0
$316$	−3.14976e11	−1.77699
$317$	−1.12832e11	−0.627575	−0.313787	−	0.949493i	$-0.601598\pi$
$317$	−1.12832e11	−0.627575	−0.313787	+	0.949493i	$0.601598\pi$
$318$	0	0
$319$	−9.80436e9	−0.0530104
$320$	−2.87530e11	−1.53288
$321$	0	0
$322$	−1.56358e11	−0.810528
$323$	−6.41492e10	−0.327929
$324$	0	0
$325$	3.43241e10	0.170657
$326$	−5.54930e11	−2.72119
$327$	0	0
$328$	4.25967e10	0.203209
$329$	1.26825e11	0.596794
$330$	0	0
$331$	2.87348e11	1.31578	0.657889	−	0.753115i	$-0.271450\pi$
$331$	2.87348e11	1.31578	0.657889	+	0.753115i	$0.271450\pi$
$332$	5.83711e11	2.63679
$333$	0	0
$334$	2.03582e11	0.895119
$335$	1.30784e11	0.567354
$336$	0	0
$337$	−2.52635e10	−0.106699	−0.0533494	−	0.998576i	$-0.516990\pi$
$337$	−2.52635e10	−0.106699	−0.0533494	+	0.998576i	$0.516990\pi$
$338$	4.44759e11	1.85353
$339$	0	0
$340$	−1.11426e11	−0.452200
$341$	−1.04362e10	−0.0417973
$342$	0	0
$343$	2.71653e11	1.05972
$344$	−4.26805e10	−0.164330
$345$	0	0
$346$	−2.77161e9	−0.0103966
$347$	−9.04803e10	−0.335020	−0.167510	−	0.985870i	$-0.553573\pi$
$347$	−9.04803e10	−0.335020	−0.167510	+	0.985870i	$0.553573\pi$
$348$	0	0
$349$	−1.53822e10	−0.0555016	−0.0277508	−	0.999615i	$-0.508834\pi$
$349$	−1.53822e10	−0.0555016	−0.0277508	+	0.999615i	$0.508834\pi$
$350$	3.65346e10	0.130136
$351$	0	0
$352$	9.99807e9	0.0347116
$353$	1.46875e11	0.503457	0.251728	−	0.967798i	$-0.419001\pi$
$353$	1.46875e11	0.503457	0.251728	+	0.967798i	$0.419001\pi$
$354$	0	0
$355$	5.80400e10	0.193955
$356$	−6.03579e11	−1.99163
$357$	0	0
$358$	−8.36088e11	−2.69016
$359$	4.42246e11	1.40520	0.702602	−	0.711583i	$-0.252021\pi$
$359$	4.42246e11	1.40520	0.702602	+	0.711583i	$0.252021\pi$
$360$	0	0
$361$	2.90609e10	0.0900590
$362$	−4.44716e11	−1.36111
$363$	0	0
$364$	5.32194e11	1.58896
$365$	−3.09587e10	−0.0912987
$366$	0	0
$367$	1.48110e11	0.426175	0.213088	−	0.977033i	$-0.431648\pi$
$367$	1.48110e11	0.426175	0.213088	+	0.977033i	$0.431648\pi$
$368$	−4.74037e10	−0.134740
$369$	0	0
$370$	−3.53475e11	−0.980507
$371$	7.21805e10	0.197805
$372$	0	0
$373$	7.63489e10	0.204227	0.102114	−	0.994773i	$-0.467440\pi$
$373$	7.63489e10	0.204227	0.102114	+	0.994773i	$0.467440\pi$
$374$	5.74730e9	0.0151894
$375$	0	0
$376$	−2.77204e11	−0.715244
$377$	−1.00649e12	−2.56609
$378$	0	0
$379$	−2.70192e11	−0.672660	−0.336330	−	0.941744i	$-0.609186\pi$
$379$	−2.70192e11	−0.672660	−0.336330	+	0.941744i	$0.609186\pi$
$380$	6.10981e11	1.50315
$381$	0	0
$382$	1.51356e11	0.363676
$383$	6.61033e11	1.56974	0.784872	−	0.619658i	$-0.212729\pi$
$383$	6.61033e11	1.56974	0.784872	+	0.619658i	$0.212729\pi$
$384$	0	0
$385$	8.68880e9	0.0201552
$386$	−1.57900e11	−0.362026
$387$	0	0
$388$	7.11191e11	1.59310
$389$	3.09861e11	0.686109	0.343054	−	0.939316i	$-0.388538\pi$
$389$	3.09861e11	0.686109	0.343054	+	0.939316i	$0.388538\pi$
$390$	0	0
$391$	−1.04861e11	−0.226891
$392$	−1.98613e11	−0.424835
$393$	0	0
$394$	1.21210e12	2.53399
$395$	−5.27906e11	−1.09111
$396$	0	0
$397$	−6.50589e11	−1.31447	−0.657233	−	0.753688i	$-0.728273\pi$
$397$	−6.50589e11	−1.31447	−0.657233	+	0.753688i	$0.728273\pi$
$398$	3.69836e11	0.738814
$399$	0	0
$400$	1.10764e10	0.0216335
$401$	−2.76701e10	−0.0534393	−0.0267196	−	0.999643i	$-0.508506\pi$
$401$	−2.76701e10	−0.0534393	−0.0267196	+	0.999643i	$0.508506\pi$
$402$	0	0
$403$	−1.07135e12	−2.02330
$404$	3.30771e11	0.617748
$405$	0	0
$406$	−1.07131e12	−1.95680
$407$	1.10293e10	0.0199238
$408$	0	0
$409$	2.08505e11	0.368436	0.184218	−	0.982885i	$-0.441025\pi$
$409$	2.08505e11	0.368436	0.184218	+	0.982885i	$0.441025\pi$
$410$	2.05779e11	0.359646
$411$	0	0
$412$	4.53969e11	0.776228
$413$	−3.85620e11	−0.652206
$414$	0	0
$415$	9.78311e11	1.61905
$416$	1.02637e12	1.68029
$417$	0	0
$418$	−3.15141e10	−0.0504907
$419$	−4.50465e11	−0.714000	−0.357000	−	0.934104i	$-0.616200\pi$
$419$	−4.50465e11	−0.714000	−0.357000	+	0.934104i	$0.616200\pi$
$420$	0	0
$421$	8.60883e11	1.33559	0.667797	−	0.744343i	$-0.267237\pi$
$421$	8.60883e11	1.33559	0.667797	+	0.744343i	$0.267237\pi$
$422$	2.86810e11	0.440239
$423$	0	0
$424$	−1.57766e11	−0.237065
$425$	2.45018e10	0.0364291
$426$	0	0
$427$	−1.44318e11	−0.210086
$428$	−1.09536e12	−1.57782
$429$	0	0
$430$	−2.06185e11	−0.290836
$431$	3.02405e10	0.0422125	0.0211063	−	0.999777i	$-0.493281\pi$
$431$	3.02405e10	0.0422125	0.0211063	+	0.999777i	$0.493281\pi$
$432$	0	0
$433$	1.03636e12	1.41682	0.708410	−	0.705802i	$-0.249413\pi$
$433$	1.03636e12	1.41682	0.708410	+	0.705802i	$0.249413\pi$
$434$	−1.14035e12	−1.54288
$435$	0	0
$436$	−2.10528e12	−2.79010
$437$	5.74983e11	0.754204
$438$	0	0
$439$	−5.90670e11	−0.759022	−0.379511	−	0.925187i	$-0.623908\pi$
$439$	−5.90670e11	−0.759022	−0.379511	+	0.925187i	$0.623908\pi$
$440$	−1.89912e10	−0.0241555
$441$	0	0
$442$	5.90001e11	0.735280
$443$	−1.27097e12	−1.56790	−0.783948	−	0.620827i	$-0.786797\pi$
$443$	−1.27097e12	−1.56790	−0.783948	+	0.620827i	$0.786797\pi$
$444$	0	0
$445$	−1.01161e12	−1.22291
$446$	2.50769e11	0.300101
$447$	0	0
$448$	9.80316e11	1.14978
$449$	9.34644e11	1.08527	0.542635	−	0.839969i	$-0.317427\pi$
$449$	9.34644e11	1.08527	0.542635	+	0.839969i	$0.317427\pi$
$450$	0	0
$451$	−6.42082e9	−0.00730796
$452$	−3.56523e11	−0.401758
$453$	0	0
$454$	−1.20851e12	−1.33505
$455$	8.91968e11	0.975658
$456$	0	0
$457$	−4.52481e11	−0.485263	−0.242632	−	0.970119i	$-0.578011\pi$
$457$	−4.52481e11	−0.485263	−0.242632	+	0.970119i	$0.578011\pi$
$458$	1.05551e12	1.12091
$459$	0	0
$460$	9.98735e11	1.04002
$461$	8.56467e11	0.883195	0.441597	−	0.897213i	$-0.354412\pi$
$461$	8.56467e11	0.883195	0.441597	+	0.897213i	$0.354412\pi$
$462$	0	0
$463$	9.21380e11	0.931803	0.465902	−	0.884836i	$-0.345730\pi$
$463$	9.21380e11	0.931803	0.465902	+	0.884836i	$0.345730\pi$
$464$	−3.24793e11	−0.325294
$465$	0	0
$466$	2.95228e12	2.90016
$467$	−8.65382e10	−0.0841941	−0.0420971	−	0.999114i	$-0.513404\pi$
$467$	−8.65382e10	−0.0841941	−0.0420971	+	0.999114i	$0.513404\pi$
$468$	0	0
$469$	−4.45901e11	−0.425560
$470$	−1.33914e12	−1.26586
$471$	0	0
$472$	8.42856e11	0.781654
$473$	6.43346e9	0.00590976
$474$	0	0
$475$	−1.34351e11	−0.121093
$476$	3.79900e11	0.339186
$477$	0	0
$478$	−2.25579e12	−1.97640
$479$	−7.63707e11	−0.662852	−0.331426	−	0.943481i	$-0.607530\pi$
$479$	−7.63707e11	−0.662852	−0.331426	+	0.943481i	$0.607530\pi$
$480$	0	0
$481$	1.13223e12	0.964458
$482$	2.79197e12	2.35613
$483$	0	0
$484$	−1.84692e12	−1.52984
$485$	1.19197e12	0.978200
$486$	0	0
$487$	−5.25531e11	−0.423368	−0.211684	−	0.977338i	$-0.567895\pi$
$487$	−5.25531e11	−0.423368	−0.211684	+	0.977338i	$0.567895\pi$
$488$	3.15439e11	0.251783
$489$	0	0
$490$	−9.59477e11	−0.751886
$491$	−2.37265e12	−1.84233	−0.921163	−	0.389177i	$-0.872759\pi$
$491$	−2.37265e12	−1.84233	−0.921163	+	0.389177i	$0.872759\pi$
$492$	0	0
$493$	−7.18468e11	−0.547768
$494$	−3.23515e12	−2.44412
$495$	0	0
$496$	−3.45724e11	−0.256485
$497$	−1.97884e11	−0.145481
$498$	0	0
$499$	−1.33387e11	−0.0963080	−0.0481540	−	0.998840i	$-0.515334\pi$
$499$	−1.33387e11	−0.0963080	−0.0481540	+	0.998840i	$0.515334\pi$
$500$	−2.24543e12	−1.60670
$501$	0	0
$502$	2.09484e12	1.47226
$503$	6.58632e11	0.458762	0.229381	−	0.973337i	$-0.426330\pi$
$503$	6.58632e11	0.458762	0.229381	+	0.973337i	$0.426330\pi$
$504$	0	0
$505$	5.54379e11	0.379311
$506$	−5.15143e10	−0.0349342
$507$	0	0
$508$	−6.57501e10	−0.0438036
$509$	1.01965e12	0.673322	0.336661	−	0.941626i	$-0.390702\pi$
$509$	1.01965e12	0.673322	0.336661	+	0.941626i	$0.390702\pi$
$510$	0	0
$511$	1.05552e11	0.0684811
$512$	5.76350e11	0.370656
$513$	0	0
$514$	2.66935e11	0.168683
$515$	7.60862e11	0.476621
$516$	0	0
$517$	4.17845e10	0.0257221
$518$	1.20515e12	0.735457
$519$	0	0
$520$	−1.94959e12	−1.16930
$521$	5.57535e11	0.331514	0.165757	−	0.986167i	$-0.446993\pi$
$521$	5.57535e11	0.331514	0.165757	+	0.986167i	$0.446993\pi$
$522$	0	0
$523$	2.12050e12	1.23931	0.619657	−	0.784873i	$-0.287272\pi$
$523$	2.12050e12	1.23931	0.619657	+	0.784873i	$0.287272\pi$
$524$	2.92903e12	1.69720
$525$	0	0
$526$	3.78975e12	2.15861
$527$	−7.64770e11	−0.431900
$528$	0	0
$529$	−8.61261e11	−0.478172
$530$	−7.62148e11	−0.419564
$531$	0	0
$532$	−2.08310e12	−1.12748
$533$	−6.59143e11	−0.353759
$534$	0	0
$535$	−1.83584e12	−0.968820
$536$	9.74612e11	0.510024
$537$	0	0
$538$	−1.68206e12	−0.865608
$539$	2.99380e10	0.0152782
$540$	0	0
$541$	1.92746e12	0.967379	0.483690	−	0.875240i	$-0.339296\pi$
$541$	1.92746e12	0.967379	0.483690	+	0.875240i	$0.339296\pi$
$542$	1.03272e12	0.514029
$543$	0	0
$544$	7.32663e11	0.358682
$545$	−3.52849e12	−1.71319
$546$	0	0
$547$	−2.32751e12	−1.11160	−0.555799	−	0.831317i	$-0.687588\pi$
$547$	−2.32751e12	−1.11160	−0.555799	+	0.831317i	$0.687588\pi$
$548$	−5.04581e12	−2.39011
$549$	0	0
$550$	1.20368e10	0.00560894
$551$	3.93957e12	1.82082
$552$	0	0
$553$	1.79986e12	0.818419
$554$	3.06243e12	1.38125
$555$	0	0
$556$	1.42557e12	0.632633
$557$	−4.94739e11	−0.217785	−0.108892	−	0.994054i	$-0.534730\pi$
$557$	−4.94739e11	−0.217785	−0.108892	+	0.994054i	$0.534730\pi$
$558$	0	0
$559$	6.60441e11	0.286076
$560$	2.87837e11	0.123680
$561$	0	0
$562$	2.83413e10	0.0119841
$563$	−1.14083e12	−0.478557	−0.239279	−	0.970951i	$-0.576911\pi$
$563$	−1.14083e12	−0.478557	−0.239279	+	0.970951i	$0.576911\pi$
$564$	0	0
$565$	−5.97540e11	−0.246688
$566$	8.96260e11	0.367079
$567$	0	0
$568$	4.32517e11	0.174356
$569$	1.64398e10	0.00657495	0.00328747	−	0.999995i	$-0.498954\pi$
$569$	1.64398e10	0.00657495	0.00328747	+	0.999995i	$0.498954\pi$
$570$	0	0
$571$	−3.67652e12	−1.44735	−0.723676	−	0.690139i	$-0.757549\pi$
$571$	−3.67652e12	−1.44735	−0.723676	+	0.690139i	$0.757549\pi$
$572$	1.75339e11	0.0684851
$573$	0	0
$574$	−7.01592e11	−0.269762
$575$	−2.19615e11	−0.0837833
$576$	0	0
$577$	−2.29045e12	−0.860260	−0.430130	−	0.902767i	$-0.641532\pi$
$577$	−2.29045e12	−0.860260	−0.430130	+	0.902767i	$0.641532\pi$
$578$	−3.84800e12	−1.43403
$579$	0	0
$580$	6.84297e12	2.51084
$581$	−3.33549e12	−1.21441
$582$	0	0
$583$	2.37809e10	0.00852549
$584$	−2.30706e11	−0.0820730
$585$	0	0
$586$	−5.65465e12	−1.98092
$587$	−4.68750e12	−1.62956	−0.814780	−	0.579771i	$-0.803142\pi$
$587$	−4.68750e12	−1.62956	−0.814780	+	0.579771i	$0.803142\pi$
$588$	0	0
$589$	4.19346e12	1.43567
$590$	4.07174e12	1.38339
$591$	0	0
$592$	3.65371e11	0.122261
$593$	2.33770e12	0.776323	0.388162	−	0.921591i	$-0.373110\pi$
$593$	2.33770e12	0.776323	0.388162	+	0.921591i	$0.373110\pi$
$594$	0	0
$595$	6.36719e11	0.208268
$596$	6.50876e12	2.11295
$597$	0	0
$598$	−5.28831e12	−1.69107
$599$	4.66995e12	1.48215	0.741075	−	0.671423i	$-0.234316\pi$
$599$	4.66995e12	1.48215	0.741075	+	0.671423i	$0.234316\pi$
$600$	0	0
$601$	−3.96517e12	−1.23973	−0.619864	−	0.784709i	$-0.712812\pi$
$601$	−3.96517e12	−1.23973	−0.619864	+	0.784709i	$0.712812\pi$
$602$	7.02974e11	0.218150
$603$	0	0
$604$	3.01101e12	0.920546
$605$	−3.09548e12	−0.939353
$606$	0	0
$607$	6.24743e12	1.86790	0.933948	−	0.357409i	$-0.116340\pi$
$607$	6.24743e12	1.86790	0.933948	+	0.357409i	$0.116340\pi$
$608$	−4.01741e12	−1.19228
$609$	0	0
$610$	1.52385e12	0.445612
$611$	4.28947e12	1.24514
$612$	0	0
$613$	−3.73193e12	−1.06748	−0.533742	−	0.845647i	$-0.679215\pi$
$613$	−3.73193e12	−1.06748	−0.533742	+	0.845647i	$0.679215\pi$
$614$	−8.84653e12	−2.51197
$615$	0	0
$616$	6.47494e10	0.0181185
$617$	6.05181e12	1.68113	0.840567	−	0.541708i	$-0.182222\pi$
$617$	6.05181e12	1.68113	0.840567	+	0.541708i	$0.182222\pi$
$618$	0	0
$619$	4.69849e12	1.28632	0.643162	−	0.765730i	$-0.277622\pi$
$619$	4.69849e12	1.28632	0.643162	+	0.765730i	$0.277622\pi$
$620$	7.28396e12	1.97973
$621$	0	0
$622$	5.79780e12	1.55313
$623$	3.44902e12	0.917275
$624$	0	0
$625$	−3.32094e12	−0.870565
$626$	−8.80724e12	−2.29222
$627$	0	0
$628$	−1.70843e12	−0.438308
$629$	8.08231e11	0.205877
$630$	0	0
$631$	2.16875e12	0.544600	0.272300	−	0.962212i	$-0.412216\pi$
$631$	2.16875e12	0.544600	0.272300	+	0.962212i	$0.412216\pi$
$632$	−3.93398e12	−0.980857
$633$	0	0
$634$	−4.06195e12	−0.998466
$635$	−1.10199e11	−0.0268964
$636$	0	0
$637$	3.07335e12	0.739580
$638$	−3.52957e11	−0.0843391
$639$	0	0
$640$	−5.79392e12	−1.36509
$641$	−3.56446e12	−0.833936	−0.416968	−	0.908921i	$-0.636907\pi$
$641$	−3.56446e12	−0.833936	−0.416968	+	0.908921i	$0.636907\pi$
$642$	0	0
$643$	−5.37917e12	−1.24098	−0.620491	−	0.784213i	$-0.713067\pi$
$643$	−5.37917e12	−1.24098	−0.620491	+	0.784213i	$0.713067\pi$
$644$	−3.40512e12	−0.780093
$645$	0	0
$646$	−2.30937e12	−0.521732
$647$	−6.01827e12	−1.35021	−0.675107	−	0.737720i	$-0.735903\pi$
$647$	−6.01827e12	−1.35021	−0.675107	+	0.737720i	$0.735903\pi$
$648$	0	0
$649$	−1.27048e11	−0.0281104
$650$	1.23567e12	0.271514
$651$	0	0
$652$	−1.20852e13	−2.61901
$653$	3.68383e11	0.0792849	0.0396424	−	0.999214i	$-0.487378\pi$
$653$	3.68383e11	0.0792849	0.0396424	+	0.999214i	$0.487378\pi$
$654$	0	0
$655$	4.90912e12	1.04212
$656$	−2.12705e11	−0.0448446
$657$	0	0
$658$	4.56572e12	0.949494
$659$	5.24810e12	1.08397	0.541985	−	0.840388i	$-0.317673\pi$
$659$	5.24810e12	1.08397	0.541985	+	0.840388i	$0.317673\pi$
$660$	0	0
$661$	1.55039e11	0.0315888	0.0157944	−	0.999875i	$-0.494972\pi$
$661$	1.55039e11	0.0315888	0.0157944	+	0.999875i	$0.494972\pi$
$662$	1.03445e13	2.09339
$663$	0	0
$664$	7.29043e12	1.45545
$665$	−3.49132e12	−0.692297
$666$	0	0
$667$	6.43979e12	1.25981
$668$	4.43357e12	0.861508
$669$	0	0
$670$	4.70824e12	0.902655
$671$	−4.75477e10	−0.00905479
$672$	0	0
$673$	5.89588e11	0.110785	0.0553925	−	0.998465i	$-0.482359\pi$
$673$	5.89588e11	0.110785	0.0553925	+	0.998465i	$0.482359\pi$
$674$	−9.09487e11	−0.169757
$675$	0	0
$676$	9.68586e12	1.78393
$677$	−3.32980e12	−0.609214	−0.304607	−	0.952478i	$-0.598525\pi$
$677$	−3.32980e12	−0.609214	−0.304607	+	0.952478i	$0.598525\pi$
$678$	0	0
$679$	−4.06395e12	−0.733726
$680$	−1.39169e12	−0.249604
$681$	0	0
$682$	−3.75703e11	−0.0664991
$683$	−2.28928e12	−0.402536	−0.201268	−	0.979536i	$-0.564506\pi$
$683$	−2.28928e12	−0.402536	−0.201268	+	0.979536i	$0.564506\pi$
$684$	0	0
$685$	−8.45687e12	−1.46758
$686$	9.77951e12	1.68600
$687$	0	0
$688$	2.13124e11	0.0362647
$689$	2.44128e12	0.412697
$690$	0	0
$691$	−9.46129e12	−1.57870	−0.789349	−	0.613945i	$-0.789582\pi$
$691$	−9.46129e12	−1.57870	−0.789349	+	0.613945i	$0.789582\pi$
$692$	−6.03596e10	−0.0100062
$693$	0	0
$694$	−3.25729e12	−0.533014
$695$	2.38928e12	0.388451
$696$	0	0
$697$	−4.70521e11	−0.0755147
$698$	−5.53761e11	−0.0883024
$699$	0	0
$700$	7.95642e11	0.125250
$701$	−8.22209e12	−1.28603	−0.643015	−	0.765854i	$-0.722317\pi$
$701$	−8.22209e12	−1.28603	−0.643015	+	0.765854i	$0.722317\pi$
$702$	0	0
$703$	−4.43177e12	−0.684349
$704$	3.22979e11	0.0495562
$705$	0	0
$706$	5.28751e12	0.800995
$707$	−1.89012e12	−0.284513
$708$	0	0
$709$	7.61957e12	1.13246	0.566230	−	0.824247i	$-0.308401\pi$
$709$	7.61957e12	1.13246	0.566230	+	0.824247i	$0.308401\pi$
$710$	2.08944e12	0.308580
$711$	0	0
$712$	−7.53858e12	−1.09933
$713$	6.85481e12	0.993327
$714$	0	0
$715$	2.93871e11	0.0420514
$716$	−1.82081e13	−2.58915
$717$	0	0
$718$	1.59209e13	2.23567
$719$	−7.94823e12	−1.10915	−0.554575	−	0.832134i	$-0.687119\pi$
$719$	−7.94823e12	−1.10915	−0.554575	+	0.832134i	$0.687119\pi$
$720$	0	0
$721$	−2.59411e12	−0.357503
$722$	1.04619e12	0.143283
$723$	0	0
$724$	−9.68492e12	−1.31000
$725$	−1.50472e12	−0.202272
$726$	0	0
$727$	−5.75787e12	−0.764464	−0.382232	−	0.924066i	$-0.624844\pi$
$727$	−5.75787e12	−0.764464	−0.382232	+	0.924066i	$0.624844\pi$
$728$	6.64699e12	0.877069
$729$	0	0
$730$	−1.11451e12	−0.145255
$731$	4.71447e11	0.0610668
$732$	0	0
$733$	1.07808e13	1.37938	0.689690	−	0.724105i	$-0.257747\pi$
$733$	1.07808e13	1.37938	0.689690	+	0.724105i	$0.257747\pi$
$734$	5.33198e12	0.678041
$735$	0	0
$736$	−6.56702e12	−0.824933
$737$	−1.46908e11	−0.0183418
$738$	0	0
$739$	7.37756e12	0.909940	0.454970	−	0.890507i	$-0.349650\pi$
$739$	7.37756e12	0.909940	0.454970	+	0.890507i	$0.349650\pi$
$740$	−7.69790e12	−0.943690
$741$	0	0
$742$	2.59850e12	0.314706
$743$	1.02899e13	1.23869	0.619346	−	0.785118i	$-0.287398\pi$
$743$	1.02899e13	1.23869	0.619346	+	0.785118i	$0.287398\pi$
$744$	0	0
$745$	1.09088e13	1.29740
$746$	2.74856e12	0.324923
$747$	0	0
$748$	1.25163e11	0.0146191
$749$	6.25918e12	0.726690
$750$	0	0
$751$	−7.56555e12	−0.867882	−0.433941	−	0.900941i	$-0.642877\pi$
$751$	−7.56555e12	−0.867882	−0.433941	+	0.900941i	$0.642877\pi$
$752$	1.38421e12	0.157842
$753$	0	0
$754$	−3.62336e13	−4.08263
$755$	5.04651e12	0.565236
$756$	0	0
$757$	−6.88713e12	−0.762267	−0.381133	−	0.924520i	$-0.624466\pi$
$757$	−6.88713e12	−0.762267	−0.381133	+	0.924520i	$0.624466\pi$
$758$	−9.72690e12	−1.07020
$759$	0	0
$760$	7.63103e12	0.829701
$761$	−4.30641e12	−0.465462	−0.232731	−	0.972541i	$-0.574766\pi$
$761$	−4.30641e12	−0.465462	−0.232731	+	0.972541i	$0.574766\pi$
$762$	0	0
$763$	1.20302e13	1.28502
$764$	3.29619e12	0.350020
$765$	0	0
$766$	2.37972e13	2.49745
$767$	−1.30424e13	−1.36075
$768$	0	0
$769$	2.16296e12	0.223039	0.111519	−	0.993762i	$-0.464428\pi$
$769$	2.16296e12	0.223039	0.111519	+	0.993762i	$0.464428\pi$
$770$	3.12797e11	0.0320667
$771$	0	0
$772$	−3.43871e12	−0.348432
$773$	8.15447e12	0.821463	0.410731	−	0.911756i	$-0.365273\pi$
$773$	8.15447e12	0.821463	0.410731	+	0.911756i	$0.365273\pi$
$774$	0	0
$775$	−1.60170e12	−0.159486
$776$	8.88263e12	0.879354
$777$	0	0
$778$	1.11550e13	1.09159
$779$	2.58000e12	0.251016
$780$	0	0
$781$	−6.51956e10	−0.00627031
$782$	−3.77499e12	−0.360982
$783$	0	0
$784$	9.91768e11	0.0937535
$785$	−2.86337e12	−0.269131
$786$	0	0
$787$	−2.25199e12	−0.209257	−0.104629	−	0.994511i	$-0.533365\pi$
$787$	−2.25199e12	−0.209257	−0.104629	+	0.994511i	$0.533365\pi$
$788$	2.63968e13	2.43884
$789$	0	0
$790$	−1.90046e13	−1.73595
$791$	2.03727e12	0.185036
$792$	0	0
$793$	−4.88112e12	−0.438319
$794$	−2.34212e13	−2.09130
$795$	0	0
$796$	8.05420e12	0.711072
$797$	1.16128e13	1.01947	0.509737	−	0.860331i	$-0.329743\pi$
$797$	1.16128e13	1.01947	0.509737	+	0.860331i	$0.329743\pi$
$798$	0	0
$799$	3.06198e12	0.265792
$800$	1.53445e12	0.132449
$801$	0	0
$802$	−9.96122e11	−0.0850214
$803$	3.47755e10	0.00295157
$804$	0	0
$805$	−5.70706e12	−0.478995
$806$	−3.85687e13	−3.21904
$807$	0	0
$808$	4.13126e12	0.340982
$809$	−2.31768e12	−0.190233	−0.0951165	−	0.995466i	$-0.530322\pi$
$809$	−2.31768e12	−0.190233	−0.0951165	+	0.995466i	$0.530322\pi$
$810$	0	0
$811$	−9.18815e12	−0.745821	−0.372910	−	0.927867i	$-0.621640\pi$
$811$	−9.18815e12	−0.745821	−0.372910	+	0.927867i	$0.621640\pi$
$812$	−2.33307e13	−1.88332
$813$	0	0
$814$	3.97054e11	0.0316986
$815$	−2.02550e13	−1.60813
$816$	0	0
$817$	−2.58508e12	−0.202990
$818$	7.50620e12	0.586179
$819$	0	0
$820$	4.48142e12	0.346141
$821$	1.92679e13	1.48010	0.740048	−	0.672554i	$-0.234803\pi$
$821$	1.92679e13	1.48010	0.740048	+	0.672554i	$0.234803\pi$
$822$	0	0
$823$	−1.04990e13	−0.797713	−0.398857	−	0.917013i	$-0.630593\pi$
$823$	−1.04990e13	−0.797713	−0.398857	+	0.917013i	$0.630593\pi$
$824$	5.66999e12	0.428459
$825$	0	0
$826$	−1.38823e13	−1.03765
$827$	8.10053e12	0.602197	0.301098	−	0.953593i	$-0.402647\pi$
$827$	8.10053e12	0.602197	0.301098	+	0.953593i	$0.402647\pi$
$828$	0	0
$829$	−1.52452e13	−1.12108	−0.560542	−	0.828126i	$-0.689407\pi$
$829$	−1.52452e13	−1.12108	−0.560542	+	0.828126i	$0.689407\pi$
$830$	3.52192e13	2.57589
$831$	0	0
$832$	3.31561e13	2.39888
$833$	2.19387e12	0.157873
$834$	0	0
$835$	7.43075e12	0.528985
$836$	−6.86307e11	−0.0485949
$837$	0	0
$838$	−1.62168e13	−1.13597
$839$	−2.72258e13	−1.89694	−0.948468	−	0.316874i	$-0.897367\pi$
$839$	−2.72258e13	−1.89694	−0.948468	+	0.316874i	$0.897367\pi$
$840$	0	0
$841$	2.96160e13	2.04147
$842$	3.09918e13	2.12492
$843$	0	0
$844$	6.24609e12	0.423709
$845$	1.62337e13	1.09537
$846$	0	0
$847$	1.05538e13	0.704588
$848$	7.87798e11	0.0523159
$849$	0	0
$850$	8.82066e11	0.0579583
$851$	−7.24435e12	−0.473496
$852$	0	0
$853$	5.38234e12	0.348097	0.174048	−	0.984737i	$-0.444315\pi$
$853$	5.38234e12	0.348097	0.174048	+	0.984737i	$0.444315\pi$
$854$	−5.19546e12	−0.334244
$855$	0	0
$856$	−1.36808e13	−0.870922
$857$	−2.13114e12	−0.134958	−0.0674791	−	0.997721i	$-0.521496\pi$
$857$	−2.13114e12	−0.134958	−0.0674791	+	0.997721i	$0.521496\pi$
$858$	0	0
$859$	1.07650e13	0.674598	0.337299	−	0.941398i	$-0.390487\pi$
$859$	1.07650e13	0.674598	0.337299	+	0.941398i	$0.390487\pi$
$860$	−4.49024e12	−0.279916
$861$	0	0
$862$	1.08866e12	0.0671597
$863$	−2.36698e13	−1.45260	−0.726299	−	0.687379i	$-0.758761\pi$
$863$	−2.36698e13	−1.45260	−0.726299	+	0.687379i	$0.758761\pi$
$864$	0	0
$865$	−1.01164e11	−0.00614402
$866$	3.73089e13	2.25415
$867$	0	0
$868$	−2.48342e13	−1.48495
$869$	5.92990e11	0.0352743
$870$	0	0
$871$	−1.50812e13	−0.887880
$872$	−2.62945e13	−1.54007
$873$	0	0
$874$	2.06994e13	1.19993
$875$	1.28310e13	0.739988
$876$	0	0
$877$	−9.91806e12	−0.566146	−0.283073	−	0.959098i	$-0.591354\pi$
$877$	−9.91806e12	−0.566146	−0.283073	+	0.959098i	$0.591354\pi$
$878$	−2.12641e13	−1.20760
$879$	0	0
$880$	9.48320e10	0.00533069
$881$	−1.28992e13	−0.721391	−0.360696	−	0.932684i	$-0.617461\pi$
$881$	−1.28992e13	−0.721391	−0.360696	+	0.932684i	$0.617461\pi$
$882$	0	0
$883$	1.00956e13	0.558866	0.279433	−	0.960165i	$-0.409854\pi$
$883$	1.00956e13	0.558866	0.279433	+	0.960165i	$0.409854\pi$
$884$	1.28489e13	0.707671
$885$	0	0
$886$	−4.57548e13	−2.49451
$887$	2.22403e12	0.120638	0.0603190	−	0.998179i	$-0.480788\pi$
$887$	2.22403e12	0.120638	0.0603190	+	0.998179i	$0.480788\pi$
$888$	0	0
$889$	3.75715e11	0.0201744
$890$	−3.64180e13	−1.94563
$891$	0	0
$892$	5.46119e12	0.288832
$893$	−1.67898e13	−0.883513
$894$	0	0
$895$	−3.05172e13	−1.58979
$896$	1.97540e13	1.02393
$897$	0	0
$898$	3.36472e13	1.72665
$899$	4.69666e13	2.39812
$900$	0	0
$901$	1.74267e12	0.0880957
$902$	−2.31150e11	−0.0116269
$903$	0	0
$904$	−4.45290e12	−0.221761
$905$	−1.62321e13	−0.804372
$906$	0	0
$907$	−6.35542e12	−0.311825	−0.155913	−	0.987771i	$-0.549832\pi$
$907$	−6.35542e12	−0.311825	−0.155913	+	0.987771i	$0.549832\pi$
$908$	−2.63186e13	−1.28492
$909$	0	0
$910$	3.21108e13	1.55226
$911$	1.91432e13	0.920837	0.460418	−	0.887702i	$-0.347699\pi$
$911$	1.91432e13	0.920837	0.460418	+	0.887702i	$0.347699\pi$
$912$	0	0
$913$	−1.09892e12	−0.0523419
$914$	−1.62893e13	−0.772049
$915$	0	0
$916$	2.29867e13	1.07882
$917$	−1.67373e13	−0.781671
$918$	0	0
$919$	2.86053e13	1.32290	0.661449	−	0.749991i	$-0.269942\pi$
$919$	2.86053e13	1.32290	0.661449	+	0.749991i	$0.269942\pi$
$920$	1.24740e13	0.574064
$921$	0	0
$922$	3.08328e13	1.40515
$923$	−6.69280e12	−0.303529
$924$	0	0
$925$	1.69272e12	0.0760233
$926$	3.31697e13	1.48249
$927$	0	0
$928$	−4.49948e13	−1.99158
$929$	1.18899e13	0.523728	0.261864	−	0.965105i	$-0.415663\pi$
$929$	1.18899e13	0.523728	0.261864	+	0.965105i	$0.415663\pi$
$930$	0	0
$931$	−1.20296e13	−0.524782
$932$	6.42942e13	2.79126
$933$	0	0
$934$	−3.11537e12	−0.133952
$935$	2.09776e11	0.00897644
$936$	0	0
$937$	−3.45871e13	−1.46584	−0.732920	−	0.680315i	$-0.761843\pi$
$937$	−3.45871e13	−1.46584	−0.732920	+	0.680315i	$0.761843\pi$
$938$	−1.60524e13	−0.677061
$939$	0	0
$940$	−2.91635e13	−1.21833
$941$	−2.59742e13	−1.07991	−0.539956	−	0.841693i	$-0.681559\pi$
$941$	−2.59742e13	−1.07991	−0.539956	+	0.841693i	$0.681559\pi$
$942$	0	0
$943$	4.21738e12	0.173676
$944$	−4.20877e12	−0.172497
$945$	0	0
$946$	2.31605e11	0.00940237
$947$	−2.43739e13	−0.984804	−0.492402	−	0.870368i	$-0.663881\pi$
$947$	−2.43739e13	−0.984804	−0.492402	+	0.870368i	$0.663881\pi$
$948$	0	0
$949$	3.56995e12	0.142878
$950$	−4.83663e12	−0.192658
$951$	0	0
$952$	4.74487e12	0.187222
$953$	2.34891e13	0.922461	0.461230	−	0.887280i	$-0.347408\pi$
$953$	2.34891e13	0.922461	0.461230	+	0.887280i	$0.347408\pi$
$954$	0	0
$955$	5.52449e12	0.214920
$956$	−4.91262e13	−1.90218
$957$	0	0
$958$	−2.74934e13	−1.05459
$959$	2.88332e13	1.10080
$960$	0	0
$961$	2.35538e13	0.890851
$962$	4.07604e13	1.53444
$963$	0	0
$964$	6.08029e13	2.26766
$965$	−5.76335e12	−0.213945
$966$	0	0
$967$	4.68639e12	0.172353	0.0861766	−	0.996280i	$-0.472535\pi$
$967$	4.68639e12	0.172353	0.0861766	+	0.996280i	$0.472535\pi$
$968$	−2.30677e13	−0.844433
$969$	0	0
$970$	4.29109e13	1.55631
$971$	4.63936e13	1.67483	0.837416	−	0.546566i	$-0.184065\pi$
$971$	4.63936e13	1.67483	0.837416	+	0.546566i	$0.184065\pi$
$972$	0	0
$973$	−8.14611e12	−0.291368
$974$	−1.89191e13	−0.673574
$975$	0	0
$976$	−1.57513e12	−0.0555639
$977$	−2.53890e13	−0.891496	−0.445748	−	0.895159i	$-0.647062\pi$
$977$	−2.53890e13	−0.891496	−0.445748	+	0.895159i	$0.647062\pi$
$978$	0	0
$979$	1.13633e12	0.0395350
$980$	−2.08953e13	−0.723654
$981$	0	0
$982$	−8.54153e13	−2.93112
$983$	8.90780e12	0.304284	0.152142	−	0.988359i	$-0.451383\pi$
$983$	8.90780e12	0.304284	0.152142	+	0.988359i	$0.451383\pi$
$984$	0	0
$985$	4.42416e13	1.49750
$986$	−2.58649e13	−0.871493
$987$	0	0
$988$	−7.04544e13	−2.35235
$989$	−4.22569e12	−0.140448
$990$	0	0
$991$	3.90840e13	1.28727	0.643633	−	0.765335i	$-0.277427\pi$
$991$	3.90840e13	1.28727	0.643633	+	0.765335i	$0.277427\pi$
$992$	−4.78945e13	−1.57030
$993$	0	0
$994$	−7.12382e12	−0.231459
$995$	1.34990e13	0.436614
$996$	0	0
$997$	−1.94045e12	−0.0621975	−0.0310988	−	0.999516i	$-0.509901\pi$
$997$	−1.94045e12	−0.0621975	−0.0310988	+	0.999516i	$0.509901\pi$
$998$	−4.80195e12	−0.153225
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.10.a.c.1.1		1
3.2	odd	2		3.10.a.a.1.1	✓	1
4.3	odd	2		144.10.a.l.1.1		1
5.2	odd	4		225.10.b.a.199.2		2
5.3	odd	4		225.10.b.a.199.1		2
5.4	even	2		225.10.a.a.1.1		1
9.2	odd	6		81.10.c.e.28.1		2
9.4	even	3		81.10.c.a.55.1		2
9.5	odd	6		81.10.c.e.55.1		2
9.7	even	3		81.10.c.a.28.1		2
12.11	even	2		48.10.a.e.1.1		1
15.2	even	4		75.10.b.a.49.1		2
15.8	even	4		75.10.b.a.49.2		2
15.14	odd	2		75.10.a.d.1.1		1
21.20	even	2		147.10.a.a.1.1		1
24.5	odd	2		192.10.a.m.1.1		1
24.11	even	2		192.10.a.f.1.1		1
33.32	even	2		363.10.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.10.a.a.1.1	✓	1	3.2	odd	2
9.10.a.c.1.1		1	1.1	even	1	trivial
48.10.a.e.1.1		1	12.11	even	2
75.10.a.d.1.1		1	15.14	odd	2
75.10.b.a.49.1		2	15.2	even	4
75.10.b.a.49.2		2	15.8	even	4
81.10.c.a.28.1		2	9.7	even	3
81.10.c.a.55.1		2	9.4	even	3
81.10.c.e.28.1		2	9.2	odd	6
81.10.c.e.55.1		2	9.5	odd	6
144.10.a.l.1.1		1	4.3	odd	2
147.10.a.a.1.1		1	21.20	even	2
192.10.a.f.1.1		1	24.11	even	2
192.10.a.m.1.1		1	24.5	odd	2
225.10.a.a.1.1		1	5.4	even	2
225.10.b.a.199.1		2	5.3	odd	4
225.10.b.a.199.2		2	5.2	odd	4
363.10.a.b.1.1		1	33.32	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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