LMFDB - Embedded newform 64.14.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,14,Mod(1,64)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(64, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("64.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	64.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:	$68.6277945292$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2195x - 37995 $ x^3 - x^2 - 2195*x - 37995
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	no (minimal twist has level 32)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-29.9193$ of defining polynomial
Character	$\chi$	$=$	64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1141.42 q^{3} -48826.1 q^{5} -397601. q^{7} -291488. q^{9} +7.39162e6 q^{11} +3.11510e7 q^{13} +5.57310e7 q^{15} +1.86044e7 q^{17} +2.63490e7 q^{19} +4.53829e8 q^{21} -5.66755e8 q^{23} +1.16328e9 q^{25} +2.15250e9 q^{27} -4.67895e9 q^{29} +6.11292e9 q^{31} -8.43693e9 q^{33} +1.94133e10 q^{35} +6.38303e9 q^{37} -3.55563e10 q^{39} -2.34979e9 q^{41} +4.94124e10 q^{43} +1.42322e10 q^{45} -7.78323e10 q^{47} +6.11977e10 q^{49} -2.12354e10 q^{51} -4.23613e10 q^{53} -3.60904e11 q^{55} -3.00752e10 q^{57} +4.87180e11 q^{59} -6.08935e11 q^{61} +1.15896e11 q^{63} -1.52098e12 q^{65} -8.91737e11 q^{67} +6.46905e11 q^{69} +3.71573e11 q^{71} +1.15284e12 q^{73} -1.32779e12 q^{75} -2.93892e12 q^{77} +3.28048e12 q^{79} -1.99217e12 q^{81} +4.48598e12 q^{83} -9.08380e11 q^{85} +5.34064e12 q^{87} -2.70738e12 q^{89} -1.23857e13 q^{91} -6.97739e12 q^{93} -1.28652e12 q^{95} -1.46940e13 q^{97} -2.15457e12 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 520 q^{3} - 11594 q^{5} - 96304 q^{7} - 196793 q^{9} + 1923816 q^{11} + 11211006 q^{13} + 10944368 q^{15} - 16892538 q^{17} + 74665048 q^{19} + 115146880 q^{21} - 486642576 q^{23} + 442696461 q^{25}+ \cdots + 2082116453576 q^{99}+O(q^{100}) $ 3 * q - 520 * q^3 - 11594 * q^5 - 96304 * q^7 - 196793 * q^9 + 1923816 * q^11 + 11211006 * q^13 + 10944368 * q^15 - 16892538 * q^17 + 74665048 * q^19 + 115146880 * q^21 - 486642576 * q^23 + 442696461 * q^25 + 3111524144 * q^27 - 1747468946 * q^29 - 6471356864 * q^31 - 2901436352 * q^33 + 32905782432 * q^35 + 1189828278 * q^37 - 73495249232 * q^39 - 12181275970 * q^41 + 151151885096 * q^43 - 19024866434 * q^45 - 273552663072 * q^47 - 26716022709 * q^49 + 361685604336 * q^51 - 151381970362 * q^53 - 594621149104 * q^55 - 253183022656 * q^57 + 534333367560 * q^59 - 598414222482 * q^61 - 138475736176 * q^63 - 1313304118564 * q^65 - 703511405320 * q^67 - 1246094112384 * q^69 + 1867178467152 * q^71 - 2138161799730 * q^73 - 3649896495992 * q^75 - 4774654840448 * q^77 + 6521880375328 * q^79 - 6029061199109 * q^81 - 5725896739752 * q^83 - 8753386407828 * q^85 + 9313876797488 * q^87 - 11930629520834 * q^89 - 10949018828768 * q^91 - 15654956180992 * q^93 + 3955366679088 * q^95 - 23076828823050 * q^97 + 2082116453576 * q^99

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
$3$	−1141.42	−0.903975	−0.451988	−	0.892024i	$-0.649285\pi$
$3$	−1141.42	−0.903975	−0.451988	+	0.892024i	$0.649285\pi$
$4$	0	0
$5$	−48826.1	−1.39748	−0.698742	−	0.715374i	$-0.746256\pi$
$5$	−48826.1	−1.39748	−0.698742	+	0.715374i	$0.746256\pi$
$6$	0	0
$7$	−397601.	−1.27735	−0.638676	−	0.769476i	$-0.720517\pi$
$7$	−397601.	−1.27735	−0.638676	+	0.769476i	$0.720517\pi$
$8$	0	0
$9$	−291488.	−0.182829
$10$	0	0
$11$	7.39162e6	1.25802	0.629009	−	0.777398i	$-0.283461\pi$
$11$	7.39162e6	1.25802	0.629009	+	0.777398i	$0.283461\pi$
$12$	0	0
$13$	3.11510e7	1.78995	0.894974	−	0.446118i	$-0.147194\pi$
$13$	3.11510e7	1.78995	0.894974	+	0.446118i	$0.147194\pi$
$14$	0	0
$15$	5.57310e7	1.26329
$16$	0	0
$17$	1.86044e7	0.186938	0.0934690	−	0.995622i	$-0.470204\pi$
$17$	1.86044e7	0.186938	0.0934690	+	0.995622i	$0.470204\pi$
$18$	0	0
$19$	2.63490e7	0.128489	0.0642444	−	0.997934i	$-0.479536\pi$
$19$	2.63490e7	0.128489	0.0642444	+	0.997934i	$0.479536\pi$
$20$	0	0
$21$	4.53829e8	1.15469
$22$	0	0
$23$	−5.66755e8	−0.798297	−0.399149	−	0.916886i	$-0.630694\pi$
$23$	−5.66755e8	−0.798297	−0.399149	+	0.916886i	$0.630694\pi$
$24$	0	0
$25$	1.16328e9	0.952962
$26$	0	0
$27$	2.15250e9	1.06925
$28$	0	0
$29$	−4.67895e9	−1.46070	−0.730351	−	0.683072i	$-0.760644\pi$
$29$	−4.67895e9	−1.46070	−0.730351	+	0.683072i	$0.760644\pi$
$30$	0	0
$31$	6.11292e9	1.23708	0.618540	−	0.785753i	$-0.287725\pi$
$31$	6.11292e9	1.23708	0.618540	+	0.785753i	$0.287725\pi$
$32$	0	0
$33$	−8.43693e9	−1.13722
$34$	0	0
$35$	1.94133e10	1.78508
$36$	0	0
$37$	6.38303e9	0.408993	0.204496	−	0.978867i	$-0.434444\pi$
$37$	6.38303e9	0.408993	0.204496	+	0.978867i	$0.434444\pi$
$38$	0	0
$39$	−3.55563e10	−1.61807
$40$	0	0
$41$	−2.34979e9	−0.0772562	−0.0386281	−	0.999254i	$-0.512299\pi$
$41$	−2.34979e9	−0.0772562	−0.0386281	+	0.999254i	$0.512299\pi$
$42$	0	0
$43$	4.94124e10	1.19204	0.596020	−	0.802970i	$-0.296748\pi$
$43$	4.94124e10	1.19204	0.596020	+	0.802970i	$0.296748\pi$
$44$	0	0
$45$	1.42322e10	0.255501
$46$	0	0
$47$	−7.78323e10	−1.05323	−0.526616	−	0.850104i	$-0.676539\pi$
$47$	−7.78323e10	−1.05323	−0.526616	+	0.850104i	$0.676539\pi$
$48$	0	0
$49$	6.11977e10	0.631627
$50$	0	0
$51$	−2.12354e10	−0.168987
$52$	0	0
$53$	−4.23613e10	−0.262528	−0.131264	−	0.991347i	$-0.541904\pi$
$53$	−4.23613e10	−0.262528	−0.131264	+	0.991347i	$0.541904\pi$
$54$	0	0
$55$	−3.60904e11	−1.75806
$56$	0	0
$57$	−3.00752e10	−0.116151
$58$	0	0
$59$	4.87180e11	1.50367	0.751833	−	0.659354i	$-0.229170\pi$
$59$	4.87180e11	1.50367	0.751833	+	0.659354i	$0.229170\pi$
$60$	0	0
$61$	−6.08935e11	−1.51331	−0.756653	−	0.653816i	$-0.773167\pi$
$61$	−6.08935e11	−1.51331	−0.756653	+	0.653816i	$0.773167\pi$
$62$	0	0
$63$	1.15896e11	0.233537
$64$	0	0
$65$	−1.52098e12	−2.50142
$66$	0	0
$67$	−8.91737e11	−1.20434	−0.602172	−	0.798366i	$-0.705698\pi$
$67$	−8.91737e11	−1.20434	−0.602172	+	0.798366i	$0.705698\pi$
$68$	0	0
$69$	6.46905e11	0.721641
$70$	0	0
$71$	3.71573e11	0.344242	0.172121	−	0.985076i	$-0.444938\pi$
$71$	3.71573e11	0.344242	0.172121	+	0.985076i	$0.444938\pi$
$72$	0	0
$73$	1.15284e12	0.891602	0.445801	−	0.895132i	$-0.352919\pi$
$73$	1.15284e12	0.891602	0.445801	+	0.895132i	$0.352919\pi$
$74$	0	0
$75$	−1.32779e12	−0.861454
$76$	0	0
$77$	−2.93892e12	−1.60693
$78$	0	0
$79$	3.28048e12	1.51831	0.759156	−	0.650909i	$-0.225612\pi$
$79$	3.28048e12	1.51831	0.759156	+	0.650909i	$0.225612\pi$
$80$	0	0
$81$	−1.99217e12	−0.783745
$82$	0	0
$83$	4.48598e12	1.50609	0.753043	−	0.657971i	$-0.228585\pi$
$83$	4.48598e12	1.50609	0.753043	+	0.657971i	$0.228585\pi$
$84$	0	0
$85$	−9.08380e11	−0.261243
$86$	0	0
$87$	5.34064e12	1.32044
$88$	0	0
$89$	−2.70738e12	−0.577451	−0.288725	−	0.957412i	$-0.593231\pi$
$89$	−2.70738e12	−0.577451	−0.288725	+	0.957412i	$0.593231\pi$
$90$	0	0
$91$	−1.23857e13	−2.28639
$92$	0	0
$93$	−6.97739e12	−1.11829
$94$	0	0
$95$	−1.28652e12	−0.179561
$96$	0	0
$97$	−1.46940e13	−1.79112	−0.895559	−	0.444943i	$-0.853224\pi$
$97$	−1.46940e13	−1.79112	−0.895559	+	0.444943i	$0.853224\pi$
$98$	0	0
$99$	−2.15457e12	−0.230002
$100$	0	0
$101$	−1.25399e13	−1.17545	−0.587725	−	0.809061i	$-0.699976\pi$
$101$	−1.25399e13	−1.17545	−0.587725	+	0.809061i	$0.699976\pi$
$102$	0	0
$103$	−2.01648e13	−1.66399	−0.831996	−	0.554781i	$-0.812802\pi$
$103$	−2.01648e13	−1.66399	−0.831996	+	0.554781i	$0.812802\pi$
$104$	0	0
$105$	−2.21587e13	−1.61367
$106$	0	0
$107$	1.09182e13	0.703326	0.351663	−	0.936127i	$-0.385616\pi$
$107$	1.09182e13	0.703326	0.351663	+	0.936127i	$0.385616\pi$
$108$	0	0
$109$	−5.40622e12	−0.308760	−0.154380	−	0.988012i	$-0.549338\pi$
$109$	−5.40622e12	−0.308760	−0.154380	+	0.988012i	$0.549338\pi$
$110$	0	0
$111$	−7.28571e12	−0.369719
$112$	0	0
$113$	2.46345e13	1.11310	0.556549	−	0.830815i	$-0.312125\pi$
$113$	2.46345e13	1.11310	0.556549	+	0.830815i	$0.312125\pi$
$114$	0	0
$115$	2.76724e13	1.11561
$116$	0	0
$117$	−9.08016e12	−0.327254
$118$	0	0
$119$	−7.39713e12	−0.238786
$120$	0	0
$121$	2.01133e13	0.582612
$122$	0	0
$123$	2.68209e12	0.0698377
$124$	0	0
$125$	2.80359e12	0.0657353
$126$	0	0
$127$	1.21465e13	0.256877	0.128439	−	0.991717i	$-0.459003\pi$
$127$	1.21465e13	0.256877	0.128439	+	0.991717i	$0.459003\pi$
$128$	0	0
$129$	−5.64002e13	−1.07757
$130$	0	0
$131$	5.48079e13	0.947501	0.473751	−	0.880659i	$-0.342900\pi$
$131$	5.48079e13	0.947501	0.473751	+	0.880659i	$0.342900\pi$
$132$	0	0
$133$	−1.04764e13	−0.164125
$134$	0	0
$135$	−1.05098e14	−1.49426
$136$	0	0
$137$	−8.95353e13	−1.15694	−0.578470	−	0.815704i	$-0.696350\pi$
$137$	−8.95353e13	−1.15694	−0.578470	+	0.815704i	$0.696350\pi$
$138$	0	0
$139$	3.33958e11	0.00392731	0.00196366	−	0.999998i	$-0.499375\pi$
$139$	3.33958e11	0.00392731	0.00196366	+	0.999998i	$0.499375\pi$
$140$	0	0
$141$	8.88392e13	0.952095
$142$	0	0
$143$	2.30256e14	2.25179
$144$	0	0
$145$	2.28455e14	2.04131
$146$	0	0
$147$	−6.98521e13	−0.570975
$148$	0	0
$149$	−9.98890e13	−0.747837	−0.373918	−	0.927462i	$-0.621986\pi$
$149$	−9.98890e13	−0.747837	−0.373918	+	0.927462i	$0.621986\pi$
$150$	0	0
$151$	4.97037e13	0.341223	0.170612	−	0.985338i	$-0.445426\pi$
$151$	4.97037e13	0.341223	0.170612	+	0.985338i	$0.445426\pi$
$152$	0	0
$153$	−5.42297e12	−0.0341777
$154$	0	0
$155$	−2.98470e14	−1.72880
$156$	0	0
$157$	2.17725e14	1.16027	0.580136	−	0.814520i	$-0.302999\pi$
$157$	2.17725e14	1.16027	0.580136	+	0.814520i	$0.302999\pi$
$158$	0	0
$159$	4.83519e13	0.237319
$160$	0	0
$161$	2.25343e14	1.01971
$162$	0	0
$163$	−4.19264e13	−0.175093	−0.0875463	−	0.996160i	$-0.527903\pi$
$163$	−4.19264e13	−0.175093	−0.0875463	+	0.996160i	$0.527903\pi$
$164$	0	0
$165$	4.11942e14	1.58924
$166$	0	0
$167$	−3.24031e13	−0.115593	−0.0577963	−	0.998328i	$-0.518407\pi$
$167$	−3.24031e13	−0.115593	−0.0577963	+	0.998328i	$0.518407\pi$
$168$	0	0
$169$	6.67511e14	2.20391
$170$	0	0
$171$	−7.68042e12	−0.0234915
$172$	0	0
$173$	−1.22717e14	−0.348019	−0.174010	−	0.984744i	$-0.555672\pi$
$173$	−1.22717e14	−0.348019	−0.174010	+	0.984744i	$0.555672\pi$
$174$	0	0
$175$	−4.62523e14	−1.21727
$176$	0	0
$177$	−5.56076e14	−1.35928
$178$	0	0
$179$	−2.25282e14	−0.511896	−0.255948	−	0.966691i	$-0.582388\pi$
$179$	−2.25282e14	−0.511896	−0.255948	+	0.966691i	$0.582388\pi$
$180$	0	0
$181$	7.59426e14	1.60537	0.802684	−	0.596405i	$-0.203405\pi$
$181$	7.59426e14	1.60537	0.802684	+	0.596405i	$0.203405\pi$
$182$	0	0
$183$	6.95049e14	1.36799
$184$	0	0
$185$	−3.11658e14	−0.571561
$186$	0	0
$187$	1.37517e14	0.235172
$188$	0	0
$189$	−8.55836e14	−1.36581
$190$	0	0
$191$	−6.34686e14	−0.945894	−0.472947	−	0.881091i	$-0.656810\pi$
$191$	−6.34686e14	−0.945894	−0.472947	+	0.881091i	$0.656810\pi$
$192$	0	0
$193$	2.31525e14	0.322460	0.161230	−	0.986917i	$-0.448454\pi$
$193$	2.31525e14	0.322460	0.161230	+	0.986917i	$0.448454\pi$
$194$	0	0
$195$	1.73608e15	2.26122
$196$	0	0
$197$	−1.16985e14	−0.142593	−0.0712967	−	0.997455i	$-0.522714\pi$
$197$	−1.16985e14	−0.142593	−0.0712967	+	0.997455i	$0.522714\pi$
$198$	0	0
$199$	−5.38208e13	−0.0614335	−0.0307167	−	0.999528i	$-0.509779\pi$
$199$	−5.38208e13	−0.0614335	−0.0307167	+	0.999528i	$0.509779\pi$
$200$	0	0
$201$	1.01784e15	1.08870
$202$	0	0
$203$	1.86036e15	1.86583
$204$	0	0
$205$	1.14731e14	0.107964
$206$	0	0
$207$	1.65203e14	0.145952
$208$	0	0
$209$	1.94762e14	0.161641
$210$	0	0
$211$	−1.51952e15	−1.18542	−0.592708	−	0.805417i	$-0.701941\pi$
$211$	−1.51952e15	−1.18542	−0.592708	+	0.805417i	$0.701941\pi$
$212$	0	0
$213$	−4.24119e14	−0.311187
$214$	0	0
$215$	−2.41261e15	−1.66586
$216$	0	0
$217$	−2.43050e15	−1.58019
$218$	0	0
$219$	−1.31587e15	−0.805986
$220$	0	0
$221$	5.79546e14	0.334609
$222$	0	0
$223$	3.24769e14	0.176845	0.0884225	−	0.996083i	$-0.471817\pi$
$223$	3.24769e14	0.176845	0.0884225	+	0.996083i	$0.471817\pi$
$224$	0	0
$225$	−3.39084e14	−0.174229
$226$	0	0
$227$	−3.38576e15	−1.64243	−0.821217	−	0.570616i	$-0.806705\pi$
$227$	−3.38576e15	−1.64243	−0.821217	+	0.570616i	$0.806705\pi$
$228$	0	0
$229$	−7.60944e14	−0.348676	−0.174338	−	0.984686i	$-0.555779\pi$
$229$	−7.60944e14	−0.348676	−0.174338	+	0.984686i	$0.555779\pi$
$230$	0	0
$231$	3.35453e15	1.45263
$232$	0	0
$233$	−2.28099e15	−0.933922	−0.466961	−	0.884278i	$-0.654651\pi$
$233$	−2.28099e15	−0.933922	−0.466961	+	0.884278i	$0.654651\pi$
$234$	0	0
$235$	3.80025e15	1.47187
$236$	0	0
$237$	−3.74440e15	−1.37252
$238$	0	0
$239$	−2.56633e14	−0.0890691	−0.0445345	−	0.999008i	$-0.514180\pi$
$239$	−2.56633e14	−0.0890691	−0.0445345	+	0.999008i	$0.514180\pi$
$240$	0	0
$241$	−6.60353e14	−0.217103	−0.108551	−	0.994091i	$-0.534621\pi$
$241$	−6.60353e14	−0.217103	−0.108551	+	0.994091i	$0.534621\pi$
$242$	0	0
$243$	−1.15788e15	−0.360762
$244$	0	0
$245$	−2.98804e15	−0.882688
$246$	0	0
$247$	8.20797e14	0.229988
$248$	0	0
$249$	−5.12038e15	−1.36147
$250$	0	0
$251$	−6.89089e15	−1.73939	−0.869693	−	0.493593i	$-0.835683\pi$
$251$	−6.89089e15	−1.73939	−0.869693	+	0.493593i	$0.835683\pi$
$252$	0	0
$253$	−4.18924e15	−1.00427
$254$	0	0
$255$	1.03684e15	0.236157
$256$	0	0
$257$	1.27624e15	0.276292	0.138146	−	0.990412i	$-0.455886\pi$
$257$	1.27624e15	0.276292	0.138146	+	0.990412i	$0.455886\pi$
$258$	0	0
$259$	−2.53790e15	−0.522428
$260$	0	0
$261$	1.36386e15	0.267059
$262$	0	0
$263$	6.94528e15	1.29413	0.647065	−	0.762435i	$-0.275996\pi$
$263$	6.94528e15	1.29413	0.647065	+	0.762435i	$0.275996\pi$
$264$	0	0
$265$	2.06834e15	0.366879
$266$	0	0
$267$	3.09026e15	0.522001
$268$	0	0
$269$	6.17240e15	0.993263	0.496631	−	0.867962i	$-0.334570\pi$
$269$	6.17240e15	0.993263	0.496631	+	0.867962i	$0.334570\pi$
$270$	0	0
$271$	−4.69860e15	−0.720557	−0.360278	−	0.932845i	$-0.617318\pi$
$271$	−4.69860e15	−0.720557	−0.360278	+	0.932845i	$0.617318\pi$
$272$	0	0
$273$	1.41372e16	2.06684
$274$	0	0
$275$	8.59855e15	1.19884
$276$	0	0
$277$	6.48219e15	0.862190	0.431095	−	0.902306i	$-0.358127\pi$
$277$	6.48219e15	0.862190	0.431095	+	0.902306i	$0.358127\pi$
$278$	0	0
$279$	−1.78185e15	−0.226174
$280$	0	0
$281$	−1.49215e16	−1.80809	−0.904046	−	0.427434i	$-0.859417\pi$
$281$	−1.49215e16	−1.80809	−0.904046	+	0.427434i	$0.859417\pi$
$282$	0	0
$283$	7.36188e15	0.851877	0.425938	−	0.904752i	$-0.359944\pi$
$283$	7.36188e15	0.851877	0.425938	+	0.904752i	$0.359944\pi$
$284$	0	0
$285$	1.46845e15	0.162319
$286$	0	0
$287$	9.34278e14	0.0986833
$288$	0	0
$289$	−9.55845e15	−0.965054
$290$	0	0
$291$	1.67720e16	1.61913
$292$	0	0
$293$	3.82149e15	0.352853	0.176426	−	0.984314i	$-0.443546\pi$
$293$	3.82149e15	0.352853	0.176426	+	0.984314i	$0.443546\pi$
$294$	0	0
$295$	−2.37871e16	−2.10135
$296$	0	0
$297$	1.59105e16	1.34513
$298$	0	0
$299$	−1.76550e16	−1.42891
$300$	0	0
$301$	−1.96464e16	−1.52265
$302$	0	0
$303$	1.43132e16	1.06258
$304$	0	0
$305$	2.97319e16	2.11482
$306$	0	0
$307$	−9.89899e14	−0.0674825	−0.0337413	−	0.999431i	$-0.510742\pi$
$307$	−9.89899e14	−0.0674825	−0.0337413	+	0.999431i	$0.510742\pi$
$308$	0	0
$309$	2.30164e16	1.50421
$310$	0	0
$311$	−7.48376e15	−0.469005	−0.234502	−	0.972116i	$-0.575346\pi$
$311$	−7.48376e15	−0.469005	−0.234502	+	0.972116i	$0.575346\pi$
$312$	0	0
$313$	−7.09529e15	−0.426512	−0.213256	−	0.976996i	$-0.568407\pi$
$313$	−7.09529e15	−0.426512	−0.213256	+	0.976996i	$0.568407\pi$
$314$	0	0
$315$	−5.65875e15	−0.326364
$316$	0	0
$317$	−6.34435e15	−0.351158	−0.175579	−	0.984465i	$-0.556180\pi$
$317$	−6.34435e15	−0.351158	−0.175579	+	0.984465i	$0.556180\pi$
$318$	0	0
$319$	−3.45851e16	−1.83759
$320$	0	0
$321$	−1.24622e16	−0.635789
$322$	0	0
$323$	4.90207e14	0.0240194
$324$	0	0
$325$	3.62375e16	1.70575
$326$	0	0
$327$	6.17076e15	0.279112
$328$	0	0
$329$	3.09462e16	1.34535
$330$	0	0
$331$	3.85743e15	0.161219	0.0806095	−	0.996746i	$-0.474313\pi$
$331$	3.85743e15	0.161219	0.0806095	+	0.996746i	$0.474313\pi$
$332$	0	0
$333$	−1.86058e15	−0.0747758
$334$	0	0
$335$	4.35400e16	1.68305
$336$	0	0
$337$	1.94508e16	0.723341	0.361670	−	0.932306i	$-0.382207\pi$
$337$	1.94508e16	0.723341	0.361670	+	0.932306i	$0.382207\pi$
$338$	0	0
$339$	−2.81182e16	−1.00621
$340$	0	0
$341$	4.51844e16	1.55627
$342$	0	0
$343$	1.41909e16	0.470542
$344$	0	0
$345$	−3.15858e16	−1.00848
$346$	0	0
$347$	9.93018e15	0.305363	0.152681	−	0.988275i	$-0.451209\pi$
$347$	9.93018e15	0.305363	0.152681	+	0.988275i	$0.451209\pi$
$348$	0	0
$349$	−3.03149e16	−0.898031	−0.449015	−	0.893524i	$-0.648225\pi$
$349$	−3.03149e16	−0.898031	−0.449015	+	0.893524i	$0.648225\pi$
$350$	0	0
$351$	6.70525e16	1.91390
$352$	0	0
$353$	3.61841e16	0.995364	0.497682	−	0.867360i	$-0.334185\pi$
$353$	3.61841e16	0.995364	0.497682	+	0.867360i	$0.334185\pi$
$354$	0	0
$355$	−1.81424e16	−0.481073
$356$	0	0
$357$	8.44322e15	0.215856
$358$	0	0
$359$	6.56753e15	0.161915	0.0809577	−	0.996718i	$-0.474202\pi$
$359$	6.56753e15	0.161915	0.0809577	+	0.996718i	$0.474202\pi$
$360$	0	0
$361$	−4.13587e16	−0.983491
$362$	0	0
$363$	−2.29577e16	−0.526666
$364$	0	0
$365$	−5.62888e16	−1.24600
$366$	0	0
$367$	−8.23736e15	−0.175978	−0.0879891	−	0.996121i	$-0.528044\pi$
$367$	−8.23736e15	−0.175978	−0.0879891	+	0.996121i	$0.528044\pi$
$368$	0	0
$369$	6.84936e14	0.0141247
$370$	0	0
$371$	1.68429e16	0.335341
$372$	0	0
$373$	−8.50635e16	−1.63545	−0.817723	−	0.575612i	$-0.804764\pi$
$373$	−8.50635e16	−1.63545	−0.817723	+	0.575612i	$0.804764\pi$
$374$	0	0
$375$	−3.20006e15	−0.0594231
$376$	0	0
$377$	−1.45754e17	−2.61458
$378$	0	0
$379$	6.89885e16	1.19570	0.597849	−	0.801609i	$-0.296022\pi$
$379$	6.89885e16	1.19570	0.597849	+	0.801609i	$0.296022\pi$
$380$	0	0
$381$	−1.38642e16	−0.232211
$382$	0	0
$383$	−1.19107e17	−1.92816	−0.964081	−	0.265607i	$-0.914428\pi$
$383$	−1.19107e17	−1.92816	−0.964081	+	0.265607i	$0.914428\pi$
$384$	0	0
$385$	1.43496e17	2.24566
$386$	0	0
$387$	−1.44031e16	−0.217939
$388$	0	0
$389$	−1.67660e16	−0.245334	−0.122667	−	0.992448i	$-0.539145\pi$
$389$	−1.67660e16	−0.245334	−0.122667	+	0.992448i	$0.539145\pi$
$390$	0	0
$391$	−1.05441e16	−0.149232
$392$	0	0
$393$	−6.25587e16	−0.856517
$394$	0	0
$395$	−1.60173e17	−2.12182
$396$	0	0
$397$	6.25740e16	0.802150	0.401075	−	0.916045i	$-0.368637\pi$
$397$	6.25740e16	0.802150	0.401075	+	0.916045i	$0.368637\pi$
$398$	0	0
$399$	1.19579e16	0.148365
$400$	0	0
$401$	−7.19337e16	−0.863961	−0.431981	−	0.901883i	$-0.642185\pi$
$401$	−7.19337e16	−0.863961	−0.431981	+	0.901883i	$0.642185\pi$
$402$	0	0
$403$	1.90424e17	2.21431
$404$	0	0
$405$	9.72700e16	1.09527
$406$	0	0
$407$	4.71809e16	0.514521
$408$	0	0
$409$	−8.31503e16	−0.878340	−0.439170	−	0.898404i	$-0.644727\pi$
$409$	−8.31503e16	−0.878340	−0.439170	+	0.898404i	$0.644727\pi$
$410$	0	0
$411$	1.02197e17	1.04584
$412$	0	0
$413$	−1.93703e17	−1.92071
$414$	0	0
$415$	−2.19033e17	−2.10473
$416$	0	0
$417$	−3.81186e14	−0.00355019
$418$	0	0
$419$	−9.60024e16	−0.866744	−0.433372	−	0.901215i	$-0.642676\pi$
$419$	−9.60024e16	−0.866744	−0.433372	+	0.901215i	$0.642676\pi$
$420$	0	0
$421$	9.89742e16	0.866340	0.433170	−	0.901312i	$-0.357395\pi$
$421$	9.89742e16	0.866340	0.433170	+	0.901312i	$0.357395\pi$
$422$	0	0
$423$	2.26872e16	0.192561
$424$	0	0
$425$	2.16422e16	0.178145
$426$	0	0
$427$	2.42113e17	1.93302
$428$	0	0
$429$	−2.62819e17	−2.03556
$430$	0	0
$431$	1.11296e16	0.0836333	0.0418166	−	0.999125i	$-0.486685\pi$
$431$	1.11296e16	0.0836333	0.0418166	+	0.999125i	$0.486685\pi$
$432$	0	0
$433$	1.35934e17	0.991192	0.495596	−	0.868553i	$-0.334950\pi$
$433$	1.35934e17	0.991192	0.495596	+	0.868553i	$0.334950\pi$
$434$	0	0
$435$	−2.60763e17	−1.84529
$436$	0	0
$437$	−1.49334e16	−0.102572
$438$	0	0
$439$	−1.79614e17	−1.19762	−0.598812	−	0.800890i	$-0.704360\pi$
$439$	−1.79614e17	−1.19762	−0.598812	+	0.800890i	$0.704360\pi$
$440$	0	0
$441$	−1.78384e16	−0.115480
$442$	0	0
$443$	−7.21646e16	−0.453628	−0.226814	−	0.973938i	$-0.572831\pi$
$443$	−7.21646e16	−0.453628	−0.226814	+	0.973938i	$0.572831\pi$
$444$	0	0
$445$	1.32191e17	0.806978
$446$	0	0
$447$	1.14015e17	0.676026
$448$	0	0
$449$	−1.39777e17	−0.805073	−0.402536	−	0.915404i	$-0.631871\pi$
$449$	−1.39777e17	−0.805073	−0.402536	+	0.915404i	$0.631871\pi$
$450$	0	0
$451$	−1.73687e16	−0.0971898
$452$	0	0
$453$	−5.67327e16	−0.308457
$454$	0	0
$455$	6.04744e17	3.19520
$456$	0	0
$457$	−2.75884e17	−1.41668	−0.708340	−	0.705871i	$-0.750556\pi$
$457$	−2.75884e17	−1.41668	−0.708340	+	0.705871i	$0.750556\pi$
$458$	0	0
$459$	4.00459e16	0.199883
$460$	0	0
$461$	2.06356e16	0.100129	0.0500646	−	0.998746i	$-0.484057\pi$
$461$	2.06356e16	0.100129	0.0500646	+	0.998746i	$0.484057\pi$
$462$	0	0
$463$	3.21265e17	1.51561	0.757804	−	0.652483i	$-0.226272\pi$
$463$	3.21265e17	1.51561	0.757804	+	0.652483i	$0.226272\pi$
$464$	0	0
$465$	3.40679e17	1.56279
$466$	0	0
$467$	7.30554e16	0.325906	0.162953	−	0.986634i	$-0.447898\pi$
$467$	7.30554e16	0.325906	0.162953	+	0.986634i	$0.447898\pi$
$468$	0	0
$469$	3.54556e17	1.53837
$470$	0	0
$471$	−2.48515e17	−1.04886
$472$	0	0
$473$	3.65238e17	1.49961
$474$	0	0
$475$	3.06513e16	0.122445
$476$	0	0
$477$	1.23478e16	0.0479978
$478$	0	0
$479$	6.31390e16	0.238846	0.119423	−	0.992843i	$-0.461896\pi$
$479$	6.31390e16	0.238846	0.119423	+	0.992843i	$0.461896\pi$
$480$	0	0
$481$	1.98838e17	0.732076
$482$	0	0
$483$	−2.57210e17	−0.921789
$484$	0	0
$485$	7.17451e17	2.50306
$486$	0	0
$487$	−4.40097e17	−1.49489	−0.747446	−	0.664322i	$-0.768720\pi$
$487$	−4.40097e17	−1.49489	−0.747446	+	0.664322i	$0.768720\pi$
$488$	0	0
$489$	4.78555e16	0.158279
$490$	0	0
$491$	−3.06075e17	−0.985820	−0.492910	−	0.870080i	$-0.664067\pi$
$491$	−3.06075e17	−0.985820	−0.492910	+	0.870080i	$0.664067\pi$
$492$	0	0
$493$	−8.70491e16	−0.273061
$494$	0	0
$495$	1.05199e17	0.321425
$496$	0	0
$497$	−1.47738e17	−0.439718
$498$	0	0
$499$	−6.69462e14	−0.00194121	−0.000970605	−	1.00000i	$-0.500309\pi$
$499$	−6.69462e14	−0.00194121	−0.000970605		1.00000i	$0.500309\pi$
$500$	0	0
$501$	3.69855e16	0.104493
$502$	0	0
$503$	8.04728e15	0.0221543	0.0110771	−	0.999939i	$-0.496474\pi$
$503$	8.04728e15	0.0221543	0.0110771	+	0.999939i	$0.496474\pi$
$504$	0	0
$505$	6.12273e17	1.64267
$506$	0	0
$507$	−7.61908e17	−1.99228
$508$	0	0
$509$	−3.96340e17	−1.01019	−0.505094	−	0.863064i	$-0.668542\pi$
$509$	−3.96340e17	−1.01019	−0.505094	+	0.863064i	$0.668542\pi$
$510$	0	0
$511$	−4.58371e17	−1.13889
$512$	0	0
$513$	5.67161e16	0.137386
$514$	0	0
$515$	9.84567e17	2.32540
$516$	0	0
$517$	−5.75307e17	−1.32498
$518$	0	0
$519$	1.40071e17	0.314601
$520$	0	0
$521$	−5.02031e17	−1.09973	−0.549864	−	0.835254i	$-0.685320\pi$
$521$	−5.02031e17	−1.09973	−0.549864	+	0.835254i	$0.685320\pi$
$522$	0	0
$523$	5.45377e17	1.16530	0.582648	−	0.812725i	$-0.302017\pi$
$523$	5.45377e17	1.16530	0.582648	+	0.812725i	$0.302017\pi$
$524$	0	0
$525$	5.27932e17	1.10038
$526$	0	0
$527$	1.13727e17	0.231257
$528$	0	0
$529$	−1.82825e17	−0.362721
$530$	0	0
$531$	−1.42007e17	−0.274914
$532$	0	0
$533$	−7.31983e16	−0.138285
$534$	0	0
$535$	−5.33093e17	−0.982887
$536$	0	0
$537$	2.57141e17	0.462741
$538$	0	0
$539$	4.52350e17	0.794598
$540$	0	0
$541$	5.75931e17	0.987617	0.493808	−	0.869571i	$-0.335604\pi$
$541$	5.75931e17	0.987617	0.493808	+	0.869571i	$0.335604\pi$
$542$	0	0
$543$	−8.66822e17	−1.45121
$544$	0	0
$545$	2.63965e17	0.431488
$546$	0	0
$547$	8.13450e17	1.29841	0.649207	−	0.760611i	$-0.275101\pi$
$547$	8.13450e17	1.29841	0.649207	+	0.760611i	$0.275101\pi$
$548$	0	0
$549$	1.77497e17	0.276676
$550$	0	0
$551$	−1.23286e17	−0.187684
$552$	0	0
$553$	−1.30432e18	−1.93942
$554$	0	0
$555$	3.55733e17	0.516677
$556$	0	0
$557$	−1.53990e17	−0.218491	−0.109245	−	0.994015i	$-0.534843\pi$
$557$	−1.53990e17	−0.218491	−0.109245	+	0.994015i	$0.534843\pi$
$558$	0	0
$559$	1.53925e18	2.13369
$560$	0	0
$561$	−1.56964e17	−0.212589
$562$	0	0
$563$	−4.03985e17	−0.534640	−0.267320	−	0.963608i	$-0.586138\pi$
$563$	−4.03985e17	−0.534640	−0.267320	+	0.963608i	$0.586138\pi$
$564$	0	0
$565$	−1.20280e18	−1.55554
$566$	0	0
$567$	7.92091e17	1.00112
$568$	0	0
$569$	2.69575e17	0.333004	0.166502	−	0.986041i	$-0.446753\pi$
$569$	2.69575e17	0.333004	0.166502	+	0.986041i	$0.446753\pi$
$570$	0	0
$571$	−1.00094e18	−1.20857	−0.604287	−	0.796767i	$-0.706542\pi$
$571$	−1.00094e18	−1.20857	−0.604287	+	0.796767i	$0.706542\pi$
$572$	0	0
$573$	7.24442e17	0.855064
$574$	0	0
$575$	−6.59297e17	−0.760747
$576$	0	0
$577$	9.66416e17	1.09024	0.545119	−	0.838359i	$-0.316484\pi$
$577$	9.66416e17	1.09024	0.545119	+	0.838359i	$0.316484\pi$
$578$	0	0
$579$	−2.64267e17	−0.291495
$580$	0	0
$581$	−1.78363e18	−1.92380
$582$	0	0
$583$	−3.13119e17	−0.330266
$584$	0	0
$585$	4.43349e17	0.457333
$586$	0	0
$587$	−4.82465e17	−0.486764	−0.243382	−	0.969931i	$-0.578257\pi$
$587$	−4.82465e17	−0.486764	−0.243382	+	0.969931i	$0.578257\pi$
$588$	0	0
$589$	1.61069e17	0.158951
$590$	0	0
$591$	1.33529e17	0.128901
$592$	0	0
$593$	−1.90725e18	−1.80116	−0.900581	−	0.434688i	$-0.856859\pi$
$593$	−1.90725e18	−1.80116	−0.900581	+	0.434688i	$0.856859\pi$
$594$	0	0
$595$	3.61173e17	0.333699
$596$	0	0
$597$	6.14320e16	0.0555343
$598$	0	0
$599$	4.30062e17	0.380414	0.190207	−	0.981744i	$-0.439084\pi$
$599$	4.30062e17	0.380414	0.190207	+	0.981744i	$0.439084\pi$
$600$	0	0
$601$	−7.59740e17	−0.657629	−0.328815	−	0.944394i	$-0.606649\pi$
$601$	−7.59740e17	−0.657629	−0.328815	+	0.944394i	$0.606649\pi$
$602$	0	0
$603$	2.59931e17	0.220189
$604$	0	0
$605$	−9.82055e17	−0.814191
$606$	0	0
$607$	9.12616e17	0.740563	0.370281	−	0.928920i	$-0.379261\pi$
$607$	9.12616e17	0.740563	0.370281	+	0.928920i	$0.379261\pi$
$608$	0	0
$609$	−2.12345e18	−1.68666
$610$	0	0
$611$	−2.42455e18	−1.88523
$612$	0	0
$613$	−8.78930e17	−0.669054	−0.334527	−	0.942386i	$-0.608577\pi$
$613$	−8.78930e17	−0.669054	−0.334527	+	0.942386i	$0.608577\pi$
$614$	0	0
$615$	−1.30956e17	−0.0975971
$616$	0	0
$617$	6.43399e17	0.469490	0.234745	−	0.972057i	$-0.424574\pi$
$617$	6.43399e17	0.469490	0.234745	+	0.972057i	$0.424574\pi$
$618$	0	0
$619$	−4.54790e16	−0.0324954	−0.0162477	−	0.999868i	$-0.505172\pi$
$619$	−4.54790e16	−0.0324954	−0.0162477	+	0.999868i	$0.505172\pi$
$620$	0	0
$621$	−1.21994e18	−0.853578
$622$	0	0
$623$	1.07646e18	0.737607
$624$	0	0
$625$	−1.55691e18	−1.04483
$626$	0	0
$627$	−2.22304e17	−0.146120
$628$	0	0
$629$	1.18752e17	0.0764563
$630$	0	0
$631$	−6.14133e17	−0.387322	−0.193661	−	0.981069i	$-0.562036\pi$
$631$	−6.14133e17	−0.387322	−0.193661	+	0.981069i	$0.562036\pi$
$632$	0	0
$633$	1.73441e18	1.07159
$634$	0	0
$635$	−5.93064e17	−0.358982
$636$	0	0
$637$	1.90637e18	1.13058
$638$	0	0
$639$	−1.08309e17	−0.0629375
$640$	0	0
$641$	−7.00097e17	−0.398640	−0.199320	−	0.979934i	$-0.563873\pi$
$641$	−7.00097e17	−0.398640	−0.199320	+	0.979934i	$0.563873\pi$
$642$	0	0
$643$	−1.85864e18	−1.03711	−0.518555	−	0.855044i	$-0.673530\pi$
$643$	−1.85864e18	−1.03711	−0.518555	+	0.855044i	$0.673530\pi$
$644$	0	0
$645$	2.75380e18	1.50589
$646$	0	0
$647$	1.15411e17	0.0618540	0.0309270	−	0.999522i	$-0.490154\pi$
$647$	1.15411e17	0.0618540	0.0309270	+	0.999522i	$0.490154\pi$
$648$	0	0
$649$	3.60105e18	1.89164
$650$	0	0
$651$	2.77422e18	1.42845
$652$	0	0
$653$	1.45570e18	0.734746	0.367373	−	0.930074i	$-0.380257\pi$
$653$	1.45570e18	0.734746	0.367373	+	0.930074i	$0.380257\pi$
$654$	0	0
$655$	−2.67606e18	−1.32412
$656$	0	0
$657$	−3.36040e17	−0.163011
$658$	0	0
$659$	1.85743e18	0.883402	0.441701	−	0.897162i	$-0.354375\pi$
$659$	1.85743e18	0.883402	0.441701	+	0.897162i	$0.354375\pi$
$660$	0	0
$661$	−1.76561e18	−0.823349	−0.411675	−	0.911331i	$-0.635056\pi$
$661$	−1.76561e18	−0.823349	−0.411675	+	0.911331i	$0.635056\pi$
$662$	0	0
$663$	−6.61504e17	−0.302479
$664$	0	0
$665$	5.11521e17	0.229362
$666$	0	0
$667$	2.65182e18	1.16607
$668$	0	0
$669$	−3.70697e17	−0.159864
$670$	0	0
$671$	−4.50102e18	−1.90377
$672$	0	0
$673$	1.71305e18	0.710676	0.355338	−	0.934738i	$-0.384366\pi$
$673$	1.71305e18	0.710676	0.355338	+	0.934738i	$0.384366\pi$
$674$	0	0
$675$	2.50397e18	1.01895
$676$	0	0
$677$	−3.04430e18	−1.21524	−0.607619	−	0.794229i	$-0.707875\pi$
$677$	−3.04430e18	−1.21524	−0.607619	+	0.794229i	$0.707875\pi$
$678$	0	0
$679$	5.84236e18	2.28789
$680$	0	0
$681$	3.86457e18	1.48472
$682$	0	0
$683$	6.84479e17	0.258004	0.129002	−	0.991644i	$-0.458823\pi$
$683$	6.84479e17	0.258004	0.129002	+	0.991644i	$0.458823\pi$
$684$	0	0
$685$	4.37166e18	1.61680
$686$	0	0
$687$	8.68555e17	0.315194
$688$	0	0
$689$	−1.31960e18	−0.469912
$690$	0	0
$691$	−1.52154e18	−0.531712	−0.265856	−	0.964013i	$-0.585655\pi$
$691$	−1.52154e18	−0.531712	−0.265856	+	0.964013i	$0.585655\pi$
$692$	0	0
$693$	8.56660e17	0.293794
$694$	0	0
$695$	−1.63059e16	−0.00548836
$696$	0	0
$697$	−4.37164e16	−0.0144421
$698$	0	0
$699$	2.60357e18	0.844243
$700$	0	0
$701$	2.38685e18	0.759727	0.379864	−	0.925042i	$-0.375971\pi$
$701$	2.38685e18	0.759727	0.379864	+	0.925042i	$0.375971\pi$
$702$	0	0
$703$	1.68186e17	0.0525510
$704$	0	0
$705$	−4.33767e18	−1.33054
$706$	0	0
$707$	4.98587e18	1.50146
$708$	0	0
$709$	2.62202e18	0.775238	0.387619	−	0.921820i	$-0.373298\pi$
$709$	2.62202e18	0.775238	0.387619	+	0.921820i	$0.373298\pi$
$710$	0	0
$711$	−9.56221e17	−0.277591
$712$	0	0
$713$	−3.46453e18	−0.987557
$714$	0	0
$715$	−1.12425e19	−3.14684
$716$	0	0
$717$	2.92926e17	0.0805162
$718$	0	0
$719$	−3.47031e18	−0.936765	−0.468383	−	0.883526i	$-0.655163\pi$
$719$	−3.47031e18	−0.936765	−0.468383	+	0.883526i	$0.655163\pi$
$720$	0	0
$721$	8.01754e18	2.12550
$722$	0	0
$723$	7.53739e17	0.196255
$724$	0	0
$725$	−5.44295e18	−1.39199
$726$	0	0
$727$	−2.70856e18	−0.680402	−0.340201	−	0.940353i	$-0.610495\pi$
$727$	−2.70856e18	−0.680402	−0.340201	+	0.940353i	$0.610495\pi$
$728$	0	0
$729$	4.49779e18	1.10986
$730$	0	0
$731$	9.19288e17	0.222838
$732$	0	0
$733$	7.55062e18	1.79807	0.899035	−	0.437877i	$-0.144269\pi$
$733$	7.55062e18	1.79807	0.899035	+	0.437877i	$0.144269\pi$
$734$	0	0
$735$	3.41061e18	0.797928
$736$	0	0
$737$	−6.59138e18	−1.51509
$738$	0	0
$739$	−8.36772e18	−1.88981	−0.944905	−	0.327345i	$-0.893846\pi$
$739$	−8.36772e18	−1.88981	−0.944905	+	0.327345i	$0.893846\pi$
$740$	0	0
$741$	−9.36872e17	−0.207904
$742$	0	0
$743$	−7.67222e18	−1.67299	−0.836496	−	0.547974i	$-0.815399\pi$
$743$	−7.67222e18	−1.67299	−0.836496	+	0.547974i	$0.815399\pi$
$744$	0	0
$745$	4.87719e18	1.04509
$746$	0	0
$747$	−1.30761e18	−0.275356
$748$	0	0
$749$	−4.34109e18	−0.898395
$750$	0	0
$751$	7.27779e18	1.48027	0.740134	−	0.672460i	$-0.234762\pi$
$751$	7.27779e18	1.48027	0.740134	+	0.672460i	$0.234762\pi$
$752$	0	0
$753$	7.86538e18	1.57236
$754$	0	0
$755$	−2.42684e18	−0.476854
$756$	0	0
$757$	3.87838e18	0.749077	0.374539	−	0.927211i	$-0.377801\pi$
$757$	3.87838e18	0.749077	0.374539	+	0.927211i	$0.377801\pi$
$758$	0	0
$759$	4.78167e18	0.907838
$760$	0	0
$761$	−4.20319e18	−0.784474	−0.392237	−	0.919864i	$-0.628299\pi$
$761$	−4.20319e18	−0.784474	−0.392237	+	0.919864i	$0.628299\pi$
$762$	0	0
$763$	2.14952e18	0.394395
$764$	0	0
$765$	2.64782e17	0.0477628
$766$	0	0
$767$	1.51762e19	2.69148
$768$	0	0
$769$	−1.05786e18	−0.184462	−0.0922309	−	0.995738i	$-0.529400\pi$
$769$	−1.05786e18	−0.184462	−0.0922309	+	0.995738i	$0.529400\pi$
$770$	0	0
$771$	−1.45673e18	−0.249761
$772$	0	0
$773$	−3.99865e18	−0.674135	−0.337067	−	0.941480i	$-0.609435\pi$
$773$	−3.99865e18	−0.674135	−0.337067	+	0.941480i	$0.609435\pi$
$774$	0	0
$775$	7.11106e18	1.17889
$776$	0	0
$777$	2.89681e18	0.472262
$778$	0	0
$779$	−6.19145e16	−0.00992656
$780$	0	0
$781$	2.74652e18	0.433063
$782$	0	0
$783$	−1.00714e19	−1.56185
$784$	0	0
$785$	−1.06306e19	−1.62146
$786$	0	0
$787$	3.70765e18	0.556242	0.278121	−	0.960546i	$-0.410288\pi$
$787$	3.70765e18	0.556242	0.278121	+	0.960546i	$0.410288\pi$
$788$	0	0
$789$	−7.92747e18	−1.16986
$790$	0	0
$791$	−9.79470e18	−1.42182
$792$	0	0
$793$	−1.89689e19	−2.70874
$794$	0	0
$795$	−2.36084e18	−0.331650
$796$	0	0
$797$	−9.34891e18	−1.29206	−0.646029	−	0.763313i	$-0.723571\pi$
$797$	−9.34891e18	−1.29206	−0.646029	+	0.763313i	$0.723571\pi$
$798$	0	0
$799$	−1.44802e18	−0.196889
$800$	0	0
$801$	7.89171e17	0.105575
$802$	0	0
$803$	8.52137e18	1.12165
$804$	0	0
$805$	−1.10026e19	−1.42502
$806$	0	0
$807$	−7.04529e18	−0.897885
$808$	0	0
$809$	7.08823e17	0.0888940	0.0444470	−	0.999012i	$-0.485847\pi$
$809$	7.08823e17	0.0888940	0.0444470	+	0.999012i	$0.485847\pi$
$810$	0	0
$811$	3.89604e17	0.0480826	0.0240413	−	0.999711i	$-0.492347\pi$
$811$	3.89604e17	0.0480826	0.0240413	+	0.999711i	$0.492347\pi$
$812$	0	0
$813$	5.36307e18	0.651365
$814$	0	0
$815$	2.04710e18	0.244689
$816$	0	0
$817$	1.30197e18	0.153164
$818$	0	0
$819$	3.61028e18	0.418019
$820$	0	0
$821$	7.16237e18	0.816256	0.408128	−	0.912925i	$-0.366182\pi$
$821$	7.16237e18	0.816256	0.408128	+	0.912925i	$0.366182\pi$
$822$	0	0
$823$	1.18202e19	1.32595	0.662975	−	0.748642i	$-0.269294\pi$
$823$	1.18202e19	1.32595	0.662975	+	0.748642i	$0.269294\pi$
$824$	0	0
$825$	−9.81454e18	−1.08373
$826$	0	0
$827$	2.55631e18	0.277862	0.138931	−	0.990302i	$-0.455633\pi$
$827$	2.55631e18	0.277862	0.138931	+	0.990302i	$0.455633\pi$
$828$	0	0
$829$	8.49442e17	0.0908928	0.0454464	−	0.998967i	$-0.485529\pi$
$829$	8.49442e17	0.0908928	0.0454464	+	0.998967i	$0.485529\pi$
$830$	0	0
$831$	−7.39889e18	−0.779399
$832$	0	0
$833$	1.13855e18	0.118075
$834$	0	0
$835$	1.58212e18	0.161539
$836$	0	0
$837$	1.31580e19	1.32274
$838$	0	0
$839$	−3.04116e18	−0.301014	−0.150507	−	0.988609i	$-0.548091\pi$
$839$	−3.04116e18	−0.301014	−0.150507	+	0.988609i	$0.548091\pi$
$840$	0	0
$841$	1.16320e19	1.13365
$842$	0	0
$843$	1.70316e19	1.63447
$844$	0	0
$845$	−3.25919e19	−3.07993
$846$	0	0
$847$	−7.99709e18	−0.744200
$848$	0	0
$849$	−8.40298e18	−0.770075
$850$	0	0
$851$	−3.61762e18	−0.326498
$852$	0	0
$853$	−8.23955e18	−0.732377	−0.366188	−	0.930541i	$-0.619337\pi$
$853$	−8.23955e18	−0.732377	−0.366188	+	0.930541i	$0.619337\pi$
$854$	0	0
$855$	3.75005e17	0.0328289
$856$	0	0
$857$	1.38781e19	1.19662	0.598309	−	0.801266i	$-0.295840\pi$
$857$	1.38781e19	1.19662	0.598309	+	0.801266i	$0.295840\pi$
$858$	0	0
$859$	−2.04003e19	−1.73253	−0.866265	−	0.499585i	$-0.833486\pi$
$859$	−2.04003e19	−1.73253	−0.866265	+	0.499585i	$0.833486\pi$
$860$	0	0
$861$	−1.06640e18	−0.0892073
$862$	0	0
$863$	1.01018e18	0.0832393	0.0416196	−	0.999134i	$-0.486748\pi$
$863$	1.01018e18	0.0832393	0.0416196	+	0.999134i	$0.486748\pi$
$864$	0	0
$865$	5.99177e18	0.486352
$866$	0	0
$867$	1.09102e19	0.872385
$868$	0	0
$869$	2.42481e19	1.91007
$870$	0	0
$871$	−2.77785e19	−2.15571
$872$	0	0
$873$	4.28313e18	0.327468
$874$	0	0
$875$	−1.11471e18	−0.0839671
$876$	0	0
$877$	−6.40587e18	−0.475424	−0.237712	−	0.971336i	$-0.576397\pi$
$877$	−6.40587e18	−0.475424	−0.237712	+	0.971336i	$0.576397\pi$
$878$	0	0
$879$	−4.36192e18	−0.318970
$880$	0	0
$881$	−2.13343e19	−1.53722	−0.768609	−	0.639719i	$-0.779051\pi$
$881$	−2.13343e19	−1.53722	−0.768609	+	0.639719i	$0.779051\pi$
$882$	0	0
$883$	1.52275e19	1.08115	0.540574	−	0.841296i	$-0.318207\pi$
$883$	1.52275e19	1.08115	0.540574	+	0.841296i	$0.318207\pi$
$884$	0	0
$885$	2.71510e19	1.89957
$886$	0	0
$887$	1.15760e19	0.798095	0.399048	−	0.916930i	$-0.369341\pi$
$887$	1.15760e19	0.798095	0.399048	+	0.916930i	$0.369341\pi$
$888$	0	0
$889$	−4.82945e18	−0.328123
$890$	0	0
$891$	−1.47254e19	−0.985966
$892$	0	0
$893$	−2.05080e18	−0.135328
$894$	0	0
$895$	1.09996e19	0.715366
$896$	0	0
$897$	2.01517e19	1.29170
$898$	0	0
$899$	−2.86021e19	−1.80701
$900$	0	0
$901$	−7.88107e17	−0.0490765
$902$	0	0
$903$	2.24248e19	1.37644
$904$	0	0
$905$	−3.70798e19	−2.24348
$906$	0	0
$907$	4.61304e18	0.275132	0.137566	−	0.990493i	$-0.456072\pi$
$907$	4.61304e18	0.275132	0.137566	+	0.990493i	$0.456072\pi$
$908$	0	0
$909$	3.65523e18	0.214906
$910$	0	0
$911$	−1.15962e19	−0.672116	−0.336058	−	0.941841i	$-0.609094\pi$
$911$	−1.15962e19	−0.672116	−0.336058	+	0.941841i	$0.609094\pi$
$912$	0	0
$913$	3.31587e19	1.89469
$914$	0	0
$915$	−3.39365e19	−1.91175
$916$	0	0
$917$	−2.17917e19	−1.21029
$918$	0	0
$919$	3.37058e19	1.84567	0.922836	−	0.385194i	$-0.125866\pi$
$919$	3.37058e19	1.84567	0.922836	+	0.385194i	$0.125866\pi$
$920$	0	0
$921$	1.12989e18	0.0610025
$922$	0	0
$923$	1.15749e19	0.616176
$924$	0	0
$925$	7.42527e18	0.389755
$926$	0	0
$927$	5.87780e18	0.304226
$928$	0	0
$929$	1.85962e19	0.949121	0.474561	−	0.880223i	$-0.342607\pi$
$929$	1.85962e19	0.949121	0.474561	+	0.880223i	$0.342607\pi$
$930$	0	0
$931$	1.61250e18	0.0811569
$932$	0	0
$933$	8.54209e18	0.423969
$934$	0	0
$935$	−6.71440e18	−0.328649
$936$	0	0
$937$	−1.98036e19	−0.955956	−0.477978	−	0.878372i	$-0.658630\pi$
$937$	−1.98036e19	−0.955956	−0.477978	+	0.878372i	$0.658630\pi$
$938$	0	0
$939$	8.09869e18	0.385557
$940$	0	0
$941$	−4.72442e18	−0.221828	−0.110914	−	0.993830i	$-0.535378\pi$
$941$	−4.72442e18	−0.221828	−0.110914	+	0.993830i	$0.535378\pi$
$942$	0	0
$943$	1.33175e18	0.0616734
$944$	0	0
$945$	4.17871e19	1.90869
$946$	0	0
$947$	6.80052e18	0.306385	0.153192	−	0.988196i	$-0.451045\pi$
$947$	6.80052e18	0.306385	0.153192	+	0.988196i	$0.451045\pi$
$948$	0	0
$949$	3.59122e19	1.59592
$950$	0	0
$951$	7.24156e18	0.317438
$952$	0	0
$953$	2.79658e19	1.20927	0.604636	−	0.796502i	$-0.293319\pi$
$953$	2.79658e19	1.20927	0.604636	+	0.796502i	$0.293319\pi$
$954$	0	0
$955$	3.09893e19	1.32187
$956$	0	0
$957$	3.94760e19	1.66114
$958$	0	0
$959$	3.55993e19	1.47782
$960$	0	0
$961$	1.29502e19	0.530366
$962$	0	0
$963$	−3.18253e18	−0.128588
$964$	0	0
$965$	−1.13045e19	−0.450632
$966$	0	0
$967$	1.17480e19	0.462053	0.231026	−	0.972948i	$-0.425792\pi$
$967$	1.17480e19	0.462053	0.231026	+	0.972948i	$0.425792\pi$
$968$	0	0
$969$	−5.59531e17	−0.0217130
$970$	0	0
$971$	2.00922e19	0.769313	0.384656	−	0.923060i	$-0.374320\pi$
$971$	2.00922e19	0.769313	0.384656	+	0.923060i	$0.374320\pi$
$972$	0	0
$973$	−1.32782e17	−0.00501656
$974$	0	0
$975$	−4.13621e19	−1.54196
$976$	0	0
$977$	2.46828e18	0.0907986	0.0453993	−	0.998969i	$-0.485544\pi$
$977$	2.46828e18	0.0907986	0.0453993	+	0.998969i	$0.485544\pi$
$978$	0	0
$979$	−2.00120e19	−0.726444
$980$	0	0
$981$	1.57585e18	0.0564503
$982$	0	0
$983$	−4.47351e19	−1.58143	−0.790716	−	0.612183i	$-0.790292\pi$
$983$	−4.47351e19	−1.58143	−0.790716	+	0.612183i	$0.790292\pi$
$984$	0	0
$985$	5.71192e18	0.199272
$986$	0	0
$987$	−3.53226e19	−1.21616
$988$	0	0
$989$	−2.80047e19	−0.951602
$990$	0	0
$991$	−3.50615e18	−0.117585	−0.0587924	−	0.998270i	$-0.518725\pi$
$991$	−3.50615e18	−0.117585	−0.0587924	+	0.998270i	$0.518725\pi$
$992$	0	0
$993$	−4.40294e18	−0.145738
$994$	0	0
$995$	2.62786e18	0.0858523
$996$	0	0
$997$	5.04474e19	1.62675	0.813373	−	0.581742i	$-0.197629\pi$
$997$	5.04474e19	1.62675	0.813373	+	0.581742i	$0.197629\pi$
$998$	0	0
$999$	1.37395e19	0.437315

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.14.a.m.1.1		3
4.3	odd	2		64.14.a.n.1.3		3
8.3	odd	2		32.14.a.c.1.1	✓	3
8.5	even	2		32.14.a.d.1.3	yes	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.14.a.c.1.1	✓	3	8.3	odd	2
32.14.a.d.1.3	yes	3	8.5	even	2
64.14.a.m.1.1		3	1.1	even	1	trivial
64.14.a.n.1.3		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)

\(f(q)\)	\(=\)	\(q-1141.42 q^{3} -48826.1 q^{5} -397601. q^{7} -291488. q^{9} +7.39162e6 q^{11} +3.11510e7 q^{13} +5.57310e7 q^{15} +1.86044e7 q^{17} +2.63490e7 q^{19} +4.53829e8 q^{21} -5.66755e8 q^{23} +1.16328e9 q^{25} +2.15250e9 q^{27} -4.67895e9 q^{29} +6.11292e9 q^{31} -8.43693e9 q^{33} +1.94133e10 q^{35} +6.38303e9 q^{37} -3.55563e10 q^{39} -2.34979e9 q^{41} +4.94124e10 q^{43} +1.42322e10 q^{45} -7.78323e10 q^{47} +6.11977e10 q^{49} -2.12354e10 q^{51} -4.23613e10 q^{53} -3.60904e11 q^{55} -3.00752e10 q^{57} +4.87180e11 q^{59} -6.08935e11 q^{61} +1.15896e11 q^{63} -1.52098e12 q^{65} -8.91737e11 q^{67} +6.46905e11 q^{69} +3.71573e11 q^{71} +1.15284e12 q^{73} -1.32779e12 q^{75} -2.93892e12 q^{77} +3.28048e12 q^{79} -1.99217e12 q^{81} +4.48598e12 q^{83} -9.08380e11 q^{85} +5.34064e12 q^{87} -2.70738e12 q^{89} -1.23857e13 q^{91} -6.97739e12 q^{93} -1.28652e12 q^{95} -1.46940e13 q^{97} -2.15457e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 520 q^{3} - 11594 q^{5} - 96304 q^{7} - 196793 q^{9} + 1923816 q^{11} + 11211006 q^{13} + 10944368 q^{15} - 16892538 q^{17} + 74665048 q^{19} + 115146880 q^{21} - 486642576 q^{23} + 442696461 q^{25}+ \cdots + 2082116453576 q^{99}+O(q^{100}) \) 3 * q - 520 * q^3 - 11594 * q^5 - 96304 * q^7 - 196793 * q^9 + 1923816 * q^11 + 11211006 * q^13 + 10944368 * q^15 - 16892538 * q^17 + 74665048 * q^19 + 115146880 * q^21 - 486642576 * q^23 + 442696461 * q^25 + 3111524144 * q^27 - 1747468946 * q^29 - 6471356864 * q^31 - 2901436352 * q^33 + 32905782432 * q^35 + 1189828278 * q^37 - 73495249232 * q^39 - 12181275970 * q^41 + 151151885096 * q^43 - 19024866434 * q^45 - 273552663072 * q^47 - 26716022709 * q^49 + 361685604336 * q^51 - 151381970362 * q^53 - 594621149104 * q^55 - 253183022656 * q^57 + 534333367560 * q^59 - 598414222482 * q^61 - 138475736176 * q^63 - 1313304118564 * q^65 - 703511405320 * q^67 - 1246094112384 * q^69 + 1867178467152 * q^71 - 2138161799730 * q^73 - 3649896495992 * q^75 - 4774654840448 * q^77 + 6521880375328 * q^79 - 6029061199109 * q^81 - 5725896739752 * q^83 - 8753386407828 * q^85 + 9313876797488 * q^87 - 11930629520834 * q^89 - 10949018828768 * q^91 - 15654956180992 * q^93 + 3955366679088 * q^95 - 23076828823050 * q^97 + 2082116453576 * q^99

Introduction

L-functions

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