LMFDB - Embedded newform 64.20.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,20,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, 20, names="a")

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

chi := DirichletCharacter("64.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 20 $
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:	$146.442685796$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$

$=$

$q+50652.0 q^{3} +2.37741e6 q^{5} +1.69175e7 q^{7} +1.40336e9 q^{9} +O(q^{10})$

$q+50652.0 q^{3} +2.37741e6 q^{5} +1.69175e7 q^{7} +1.40336e9 q^{9} -1.62121e7 q^{11} -5.04216e10 q^{13} +1.20421e11 q^{15} +2.25070e11 q^{17} -1.71028e12 q^{19} +8.56907e11 q^{21} -1.40365e13 q^{23} -1.34214e13 q^{25} +1.22123e13 q^{27} -1.13784e12 q^{29} +1.04627e14 q^{31} -8.21176e11 q^{33} +4.02199e13 q^{35} +1.69392e14 q^{37} -2.55396e15 q^{39} -3.30998e15 q^{41} +1.12791e15 q^{43} +3.33637e15 q^{45} -3.49869e15 q^{47} -1.11127e16 q^{49} +1.14003e16 q^{51} -2.99563e16 q^{53} -3.85428e13 q^{55} -8.66290e16 q^{57} +5.83914e16 q^{59} -2.33737e16 q^{61} +2.37415e16 q^{63} -1.19873e17 q^{65} -2.05103e17 q^{67} -7.10979e17 q^{69} +1.77902e17 q^{71} +2.99854e17 q^{73} -6.79821e17 q^{75} -2.74269e14 q^{77} +9.22271e16 q^{79} -1.01250e18 q^{81} +1.20854e18 q^{83} +5.35084e17 q^{85} -5.76336e16 q^{87} +4.37120e18 q^{89} -8.53010e17 q^{91} +5.29956e18 q^{93} -4.06603e18 q^{95} -6.35013e17 q^{97} -2.27515e16 q^{99} +O(q^{100})$

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
$3$	50652.0	1.48575	0.742873	−	0.669432i	$-0.233463\pi$
$3$	50652.0	1.48575	0.742873	+	0.669432i	$0.233463\pi$
$4$	0	0
$5$	2.37741e6	0.544364	0.272182	−	0.962246i	$-0.412255\pi$
$5$	2.37741e6	0.544364	0.272182	+	0.962246i	$0.412255\pi$
$6$	0	0
$7$	1.69175e7	0.158455	0.0792275	−	0.996857i	$-0.474755\pi$
$7$	1.69175e7	0.158455	0.0792275	+	0.996857i	$0.474755\pi$
$8$	0	0
$9$	1.40336e9	1.20744
$10$	0	0
$11$	−1.62121e7	−0.00207305	−0.00103652	−	0.999999i	$-0.500330\pi$
$11$	−1.62121e7	−0.00207305	−0.00103652	+	0.999999i	$0.500330\pi$
$12$	0	0
$13$	−5.04216e10	−1.31873	−0.659364	−	0.751824i	$-0.729174\pi$
$13$	−5.04216e10	−1.31873	−0.659364	+	0.751824i	$0.729174\pi$
$14$	0	0
$15$	1.20421e11	0.808786
$16$	0	0
$17$	2.25070e11	0.460313	0.230156	−	0.973154i	$-0.426076\pi$
$17$	2.25070e11	0.460313	0.230156	+	0.973154i	$0.426076\pi$
$18$	0	0
$19$	−1.71028e12	−1.21593	−0.607964	−	0.793965i	$-0.708013\pi$
$19$	−1.71028e12	−1.21593	−0.607964	+	0.793965i	$0.708013\pi$
$20$	0	0
$21$	8.56907e11	0.235424
$22$	0	0
$23$	−1.40365e13	−1.62497	−0.812485	−	0.582982i	$-0.801886\pi$
$23$	−1.40365e13	−1.62497	−0.812485	+	0.582982i	$0.801886\pi$
$24$	0	0
$25$	−1.34214e13	−0.703668
$26$	0	0
$27$	1.22123e13	0.308207
$28$	0	0
$29$	−1.13784e12	−0.0145646	−0.00728230	−	0.999973i	$-0.502318\pi$
$29$	−1.13784e12	−0.0145646	−0.00728230	+	0.999973i	$0.502318\pi$
$30$	0	0
$31$	1.04627e14	0.710734	0.355367	−	0.934727i	$-0.384356\pi$
$31$	1.04627e14	0.710734	0.355367	+	0.934727i	$0.384356\pi$
$32$	0	0
$33$	−8.21176e11	−0.00308002
$34$	0	0
$35$	4.02199e13	0.0862571
$36$	0	0
$37$	1.69392e14	0.214278	0.107139	−	0.994244i	$-0.465831\pi$
$37$	1.69392e14	0.214278	0.107139	+	0.994244i	$0.465831\pi$
$38$	0	0
$39$	−2.55396e15	−1.95929
$40$	0	0
$41$	−3.30998e15	−1.57899	−0.789495	−	0.613757i	$-0.789657\pi$
$41$	−3.30998e15	−1.57899	−0.789495	+	0.613757i	$0.789657\pi$
$42$	0	0
$43$	1.12791e15	0.342236	0.171118	−	0.985251i	$-0.445262\pi$
$43$	1.12791e15	0.342236	0.171118	+	0.985251i	$0.445262\pi$
$44$	0	0
$45$	3.33637e15	0.657288
$46$	0	0
$47$	−3.49869e15	−0.456012	−0.228006	−	0.973660i	$-0.573221\pi$
$47$	−3.49869e15	−0.456012	−0.228006	+	0.973660i	$0.573221\pi$
$48$	0	0
$49$	−1.11127e16	−0.974892
$50$	0	0
$51$	1.14003e16	0.683908
$52$	0	0
$53$	−2.99563e16	−1.24700	−0.623501	−	0.781822i	$-0.714290\pi$
$53$	−2.99563e16	−1.24700	−0.623501	+	0.781822i	$0.714290\pi$
$54$	0	0
$55$	−3.85428e13	−0.00112849
$56$	0	0
$57$	−8.66290e16	−1.80656
$58$	0	0
$59$	5.83914e16	0.877515	0.438758	−	0.898605i	$-0.355419\pi$
$59$	5.83914e16	0.877515	0.438758	+	0.898605i	$0.355419\pi$
$60$	0	0
$61$	−2.33737e16	−0.255914	−0.127957	−	0.991780i	$-0.540842\pi$
$61$	−2.33737e16	−0.255914	−0.127957	+	0.991780i	$0.540842\pi$
$62$	0	0
$63$	2.37415e16	0.191325
$64$	0	0
$65$	−1.19873e17	−0.717867
$66$	0	0
$67$	−2.05103e17	−0.921002	−0.460501	−	0.887659i	$-0.652330\pi$
$67$	−2.05103e17	−0.921002	−0.460501	+	0.887659i	$0.652330\pi$
$68$	0	0
$69$	−7.10979e17	−2.41429
$70$	0	0
$71$	1.77902e17	0.460498	0.230249	−	0.973132i	$-0.426046\pi$
$71$	1.77902e17	0.460498	0.230249	+	0.973132i	$0.426046\pi$
$72$	0	0
$73$	2.99854e17	0.596132	0.298066	−	0.954545i	$-0.403658\pi$
$73$	2.99854e17	0.596132	0.298066	+	0.954545i	$0.403658\pi$
$74$	0	0
$75$	−6.79821e17	−1.04547
$76$	0	0
$77$	−2.74269e14	−0.000328485 0
$78$	0	0
$79$	9.22271e16	0.0865767	0.0432884	−	0.999063i	$-0.486217\pi$
$79$	9.22271e16	0.0865767	0.0432884	+	0.999063i	$0.486217\pi$
$80$	0	0
$81$	−1.01250e18	−0.749525
$82$	0	0
$83$	1.20854e18	0.709611	0.354805	−	0.934940i	$-0.384547\pi$
$83$	1.20854e18	0.709611	0.354805	+	0.934940i	$0.384547\pi$
$84$	0	0
$85$	5.35084e17	0.250578
$86$	0	0
$87$	−5.76336e16	−0.0216393
$88$	0	0
$89$	4.37120e18	1.32250	0.661250	−	0.750166i	$-0.270026\pi$
$89$	4.37120e18	1.32250	0.661250	+	0.750166i	$0.270026\pi$
$90$	0	0
$91$	−8.53010e17	−0.208959
$92$	0	0
$93$	5.29956e18	1.05597
$94$	0	0
$95$	−4.06603e18	−0.661907
$96$	0	0
$97$	−6.35013e17	−0.0848108	−0.0424054	−	0.999100i	$-0.513502\pi$
$97$	−6.35013e17	−0.0848108	−0.0424054	+	0.999100i	$0.513502\pi$
$98$	0	0
$99$	−2.27515e16	−0.00250308
$100$	0	0
$101$	1.42252e19	1.29421	0.647105	−	0.762401i	$-0.275979\pi$
$101$	1.42252e19	1.29421	0.647105	+	0.762401i	$0.275979\pi$
$102$	0	0
$103$	−4.90729e18	−0.370586	−0.185293	−	0.982683i	$-0.559323\pi$
$103$	−4.90729e18	−0.370586	−0.185293	+	0.982683i	$0.559323\pi$
$104$	0	0
$105$	2.03722e18	0.128156
$106$	0	0
$107$	2.64625e19	1.39151	0.695753	−	0.718281i	$-0.255071\pi$
$107$	2.64625e19	1.39151	0.695753	+	0.718281i	$0.255071\pi$
$108$	0	0
$109$	1.84178e19	0.812242	0.406121	−	0.913819i	$-0.366881\pi$
$109$	1.84178e19	0.812242	0.406121	+	0.913819i	$0.366881\pi$
$110$	0	0
$111$	8.58006e18	0.318363
$112$	0	0
$113$	2.57421e19	0.806118	0.403059	−	0.915174i	$-0.367947\pi$
$113$	2.57421e19	0.806118	0.403059	+	0.915174i	$0.367947\pi$
$114$	0	0
$115$	−3.33706e19	−0.884575
$116$	0	0
$117$	−7.07599e19	−1.59229
$118$	0	0
$119$	3.80763e18	0.0729389
$120$	0	0
$121$	−6.11588e19	−0.999996
$122$	0	0
$123$	−1.67657e20	−2.34598
$124$	0	0
$125$	−7.72537e19	−0.927415
$126$	0	0
$127$	−8.80720e19	−0.909290	−0.454645	−	0.890673i	$-0.650234\pi$
$127$	−8.80720e19	−0.909290	−0.454645	+	0.890673i	$0.650234\pi$
$128$	0	0
$129$	5.71311e19	0.508476
$130$	0	0
$131$	7.19289e19	0.553129	0.276564	−	0.960995i	$-0.410804\pi$
$131$	7.19289e19	0.553129	0.276564	+	0.960995i	$0.410804\pi$
$132$	0	0
$133$	−2.89337e19	−0.192670
$134$	0	0
$135$	2.90337e19	0.167776
$136$	0	0
$137$	−2.95426e20	−1.48458	−0.742290	−	0.670079i	$-0.766260\pi$
$137$	−2.95426e20	−1.48458	−0.742290	+	0.670079i	$0.766260\pi$
$138$	0	0
$139$	1.38478e20	0.606375	0.303187	−	0.952931i	$-0.401949\pi$
$139$	1.38478e20	0.606375	0.303187	+	0.952931i	$0.401949\pi$
$140$	0	0
$141$	−1.77216e20	−0.677518
$142$	0	0
$143$	8.17441e17	0.00273378
$144$	0	0
$145$	−2.70510e18	−0.00792843
$146$	0	0
$147$	−5.62880e20	−1.44844
$148$	0	0
$149$	2.66021e20	0.602070	0.301035	−	0.953613i	$-0.402668\pi$
$149$	2.66021e20	0.602070	0.301035	+	0.953613i	$0.402668\pi$
$150$	0	0
$151$	−5.75578e20	−1.14769	−0.573844	−	0.818965i	$-0.694548\pi$
$151$	−5.75578e20	−1.14769	−0.573844	+	0.818965i	$0.694548\pi$
$152$	0	0
$153$	3.15855e20	0.555801
$154$	0	0
$155$	2.48741e20	0.386898
$156$	0	0
$157$	1.07238e21	1.47673	0.738363	−	0.674403i	$-0.235599\pi$
$157$	1.07238e21	1.47673	0.738363	+	0.674403i	$0.235599\pi$
$158$	0	0
$159$	−1.51735e21	−1.85273
$160$	0	0
$161$	−2.37464e20	−0.257485
$162$	0	0
$163$	−5.80765e20	−0.560039	−0.280019	−	0.959994i	$-0.590341\pi$
$163$	−5.80765e20	−0.560039	−0.280019	+	0.959994i	$0.590341\pi$
$164$	0	0
$165$	−1.95227e18	−0.00167665
$166$	0	0
$167$	−2.43392e20	−0.186423	−0.0932117	−	0.995646i	$-0.529713\pi$
$167$	−2.43392e20	−0.186423	−0.0932117	+	0.995646i	$0.529713\pi$
$168$	0	0
$169$	1.08042e21	0.739041
$170$	0	0
$171$	−2.40014e21	−1.46816
$172$	0	0
$173$	1.19350e21	0.653711	0.326855	−	0.945074i	$-0.394011\pi$
$173$	1.19350e21	0.653711	0.326855	+	0.945074i	$0.394011\pi$
$174$	0	0
$175$	−2.27057e20	−0.111500
$176$	0	0
$177$	2.95764e21	1.30377
$178$	0	0
$179$	−4.14664e21	−1.64283	−0.821415	−	0.570331i	$-0.806815\pi$
$179$	−4.14664e21	−1.64283	−0.821415	+	0.570331i	$0.806815\pi$
$180$	0	0
$181$	−3.32364e21	−1.18486	−0.592430	−	0.805622i	$-0.701831\pi$
$181$	−3.32364e21	−1.18486	−0.592430	+	0.805622i	$0.701831\pi$
$182$	0	0
$183$	−1.18392e21	−0.380223
$184$	0	0
$185$	4.02715e20	0.116645
$186$	0	0
$187$	−3.64886e18	−0.000954250 0
$188$	0	0
$189$	2.06602e20	0.0488369
$190$	0	0
$191$	−6.19380e21	−1.32477	−0.662384	−	0.749164i	$-0.730455\pi$
$191$	−6.19380e21	−1.32477	−0.662384	+	0.749164i	$0.730455\pi$
$192$	0	0
$193$	−5.20697e21	−1.00877	−0.504383	−	0.863480i	$-0.668280\pi$
$193$	−5.20697e21	−1.00877	−0.504383	+	0.863480i	$0.668280\pi$
$194$	0	0
$195$	−6.07180e21	−1.06657
$196$	0	0
$197$	−2.42384e21	−0.386433	−0.193216	−	0.981156i	$-0.561892\pi$
$197$	−2.42384e21	−0.386433	−0.193216	+	0.981156i	$0.561892\pi$
$198$	0	0
$199$	1.05907e21	0.153399	0.0766993	−	0.997054i	$-0.475562\pi$
$199$	1.05907e21	0.153399	0.0766993	+	0.997054i	$0.475562\pi$
$200$	0	0
$201$	−1.03889e22	−1.36837
$202$	0	0
$203$	−1.92494e19	−0.00230783
$204$	0	0
$205$	−7.86919e21	−0.859545
$206$	0	0
$207$	−1.96984e22	−1.96206
$208$	0	0
$209$	2.77272e19	0.00252067
$210$	0	0
$211$	−1.32424e22	−1.09972	−0.549861	−	0.835256i	$-0.685319\pi$
$211$	−1.32424e22	−1.09972	−0.549861	+	0.835256i	$0.685319\pi$
$212$	0	0
$213$	9.01111e21	0.684183
$214$	0	0
$215$	2.68151e21	0.186301
$216$	0	0
$217$	1.77003e21	0.112619
$218$	0	0
$219$	1.51882e22	0.885701
$220$	0	0
$221$	−1.13484e22	−0.607027
$222$	0	0
$223$	−2.00921e22	−0.986575	−0.493287	−	0.869866i	$-0.664205\pi$
$223$	−2.00921e22	−0.986575	−0.493287	+	0.869866i	$0.664205\pi$
$224$	0	0
$225$	−1.88351e22	−0.849639
$226$	0	0
$227$	−2.03494e22	−0.843929	−0.421965	−	0.906612i	$-0.638659\pi$
$227$	−2.03494e22	−0.843929	−0.421965	+	0.906612i	$0.638659\pi$
$228$	0	0
$229$	3.99900e22	1.52586	0.762930	−	0.646481i	$-0.223760\pi$
$229$	3.99900e22	1.52586	0.762930	+	0.646481i	$0.223760\pi$
$230$	0	0
$231$	−1.38923e19	−0.000488045 0
$232$	0	0
$233$	2.42170e22	0.783862	0.391931	−	0.919995i	$-0.371807\pi$
$233$	2.42170e22	0.783862	0.391931	+	0.919995i	$0.371807\pi$
$234$	0	0
$235$	−8.31783e21	−0.248236
$236$	0	0
$237$	4.67149e21	0.128631
$238$	0	0
$239$	−2.62411e22	−0.667116	−0.333558	−	0.942730i	$-0.608249\pi$
$239$	−2.62411e22	−0.667116	−0.333558	+	0.942730i	$0.608249\pi$
$240$	0	0
$241$	7.36445e22	1.72973	0.864865	−	0.502004i	$-0.167404\pi$
$241$	7.36445e22	1.72973	0.864865	+	0.502004i	$0.167404\pi$
$242$	0	0
$243$	−6.54789e22	−1.42181
$244$	0	0
$245$	−2.64194e22	−0.530696
$246$	0	0
$247$	8.62350e22	1.60348
$248$	0	0
$249$	6.12151e22	1.05430
$250$	0	0
$251$	7.29309e22	1.16416	0.582078	−	0.813133i	$-0.302240\pi$
$251$	7.29309e22	1.16416	0.582078	+	0.813133i	$0.302240\pi$
$252$	0	0
$253$	2.27562e20	0.00336864
$254$	0	0
$255$	2.71031e22	0.372295
$256$	0	0
$257$	−6.38120e22	−0.813838	−0.406919	−	0.913464i	$-0.633397\pi$
$257$	−6.38120e22	−0.813838	−0.406919	+	0.913464i	$0.633397\pi$
$258$	0	0
$259$	2.86570e21	0.0339534
$260$	0	0
$261$	−1.59680e21	−0.0175859
$262$	0	0
$263$	1.35820e23	1.39118	0.695590	−	0.718439i	$-0.255143\pi$
$263$	1.35820e23	1.39118	0.695590	+	0.718439i	$0.255143\pi$
$264$	0	0
$265$	−7.12184e22	−0.678823
$266$	0	0
$267$	2.21410e23	1.96490
$268$	0	0
$269$	1.33672e23	1.10508	0.552540	−	0.833486i	$-0.313659\pi$
$269$	1.33672e23	1.10508	0.552540	+	0.833486i	$0.313659\pi$
$270$	0	0
$271$	−2.00548e23	−1.54529	−0.772643	−	0.634840i	$-0.781066\pi$
$271$	−2.00548e23	−1.54529	−0.772643	+	0.634840i	$0.781066\pi$
$272$	0	0
$273$	−4.32067e22	−0.310460
$274$	0	0
$275$	2.17589e20	0.00145874
$276$	0	0
$277$	−2.00223e23	−1.25301	−0.626507	−	0.779416i	$-0.715516\pi$
$277$	−2.00223e23	−1.25301	−0.626507	+	0.779416i	$0.715516\pi$
$278$	0	0
$279$	1.46830e23	0.858170
$280$	0	0
$281$	−1.19239e23	−0.651194	−0.325597	−	0.945509i	$-0.605565\pi$
$281$	−1.19239e23	−0.651194	−0.325597	+	0.945509i	$0.605565\pi$
$282$	0	0
$283$	−3.46108e21	−0.0176702	−0.00883509	−	0.999961i	$-0.502812\pi$
$283$	−3.46108e21	−0.0176702	−0.00883509	+	0.999961i	$0.502812\pi$
$284$	0	0
$285$	−2.05953e23	−0.983425
$286$	0	0
$287$	−5.59968e22	−0.250199
$288$	0	0
$289$	−1.88416e23	−0.788112
$290$	0	0
$291$	−3.21647e22	−0.126007
$292$	0	0
$293$	2.13236e23	0.782739	0.391370	−	0.920234i	$-0.372001\pi$
$293$	2.13236e23	0.782739	0.391370	+	0.920234i	$0.372001\pi$
$294$	0	0
$295$	1.38820e23	0.477687
$296$	0	0
$297$	−1.97987e20	−0.000638927 0
$298$	0	0
$299$	7.07745e23	2.14289
$300$	0	0
$301$	1.90815e22	0.0542290
$302$	0	0
$303$	7.20534e23	1.92287
$304$	0	0
$305$	−5.55688e22	−0.139310
$306$	0	0
$307$	1.91887e23	0.452097	0.226048	−	0.974116i	$-0.427419\pi$
$307$	1.91887e23	0.452097	0.226048	+	0.974116i	$0.427419\pi$
$308$	0	0
$309$	−2.48564e23	−0.550596
$310$	0	0
$311$	1.54522e23	0.321933	0.160967	−	0.986960i	$-0.448539\pi$
$311$	1.54522e23	0.321933	0.160967	+	0.986960i	$0.448539\pi$
$312$	0	0
$313$	2.87408e23	0.563413	0.281707	−	0.959501i	$-0.409100\pi$
$313$	2.87408e23	0.563413	0.281707	+	0.959501i	$0.409100\pi$
$314$	0	0
$315$	5.64432e22	0.104150
$316$	0	0
$317$	−2.63533e22	−0.0457901	−0.0228950	−	0.999738i	$-0.507288\pi$
$317$	−2.63533e22	−0.0457901	−0.0228950	+	0.999738i	$0.507288\pi$
$318$	0	0
$319$	1.84467e19	3.01931e−5 0
$320$	0	0
$321$	1.34038e24	2.06743
$322$	0	0
$323$	−3.84933e23	−0.559707
$324$	0	0
$325$	6.76729e23	0.927946
$326$	0	0
$327$	9.32897e23	1.20679
$328$	0	0
$329$	−5.91893e22	−0.0722574
$330$	0	0
$331$	−1.05338e24	−1.21400	−0.606998	−	0.794703i	$-0.707626\pi$
$331$	−1.05338e24	−1.21400	−0.606998	+	0.794703i	$0.707626\pi$
$332$	0	0
$333$	2.37719e23	0.258728
$334$	0	0
$335$	−4.87613e23	−0.501360
$336$	0	0
$337$	6.76160e23	0.657000	0.328500	−	0.944504i	$-0.393457\pi$
$337$	6.76160e23	0.657000	0.328500	+	0.944504i	$0.393457\pi$
$338$	0	0
$339$	1.30389e24	1.19769
$340$	0	0
$341$	−1.69622e21	−0.00147338
$342$	0	0
$343$	−3.80841e23	−0.312932
$344$	0	0
$345$	−1.69029e24	−1.31425
$346$	0	0
$347$	1.06325e24	0.782535	0.391268	−	0.920277i	$-0.372037\pi$
$347$	1.06325e24	0.782535	0.391268	+	0.920277i	$0.372037\pi$
$348$	0	0
$349$	7.14667e23	0.498037	0.249019	−	0.968499i	$-0.419892\pi$
$349$	7.14667e23	0.498037	0.249019	+	0.968499i	$0.419892\pi$
$350$	0	0
$351$	−6.15764e23	−0.406440
$352$	0	0
$353$	−5.07321e23	−0.317266	−0.158633	−	0.987338i	$-0.550709\pi$
$353$	−5.07321e23	−0.317266	−0.158633	+	0.987338i	$0.550709\pi$
$354$	0	0
$355$	4.22947e23	0.250678
$356$	0	0
$357$	1.92864e23	0.108369
$358$	0	0
$359$	−3.32006e24	−1.76909	−0.884544	−	0.466458i	$-0.845530\pi$
$359$	−3.32006e24	−1.76909	−0.884544	+	0.466458i	$0.845530\pi$
$360$	0	0
$361$	9.46633e23	0.478479
$362$	0	0
$363$	−3.09782e24	−1.48574
$364$	0	0
$365$	7.12875e23	0.324512
$366$	0	0
$367$	2.24430e24	0.969958	0.484979	−	0.874526i	$-0.338827\pi$
$367$	2.24430e24	0.969958	0.484979	+	0.874526i	$0.338827\pi$
$368$	0	0
$369$	−4.64511e24	−1.90654
$370$	0	0
$371$	−5.06787e23	−0.197594
$372$	0	0
$373$	−5.10606e24	−1.89170	−0.945850	−	0.324603i	$-0.894769\pi$
$373$	−5.10606e24	−1.89170	−0.945850	+	0.324603i	$0.894769\pi$
$374$	0	0
$375$	−3.91305e24	−1.37790
$376$	0	0
$377$	5.73715e22	0.0192067
$378$	0	0
$379$	−4.28975e24	−1.36571	−0.682857	−	0.730552i	$-0.739263\pi$
$379$	−4.28975e24	−1.36571	−0.682857	+	0.730552i	$0.739263\pi$
$380$	0	0
$381$	−4.46102e24	−1.35098
$382$	0	0
$383$	1.86803e24	0.538264	0.269132	−	0.963103i	$-0.413263\pi$
$383$	1.86803e24	0.538264	0.269132	+	0.963103i	$0.413263\pi$
$384$	0	0
$385$	−6.52050e20	−0.000178815 0
$386$	0	0
$387$	1.58287e24	0.413230
$388$	0	0
$389$	6.47448e24	1.60947	0.804737	−	0.593632i	$-0.202306\pi$
$389$	6.47448e24	1.60947	0.804737	+	0.593632i	$0.202306\pi$
$390$	0	0
$391$	−3.15920e24	−0.747995
$392$	0	0
$393$	3.64334e24	0.821809
$394$	0	0
$395$	2.19262e23	0.0471292
$396$	0	0
$397$	−1.22760e24	−0.251505	−0.125752	−	0.992062i	$-0.540134\pi$
$397$	−1.22760e24	−0.251505	−0.125752	+	0.992062i	$0.540134\pi$
$398$	0	0
$399$	−1.46555e24	−0.286258
$400$	0	0
$401$	−5.17895e23	−0.0964651	−0.0482326	−	0.998836i	$-0.515359\pi$
$401$	−5.17895e23	−0.0964651	−0.0482326	+	0.998836i	$0.515359\pi$
$402$	0	0
$403$	−5.27546e24	−0.937264
$404$	0	0
$405$	−2.40712e24	−0.408014
$406$	0	0
$407$	−2.74621e21	−0.000444208 0
$408$	0	0
$409$	2.81877e24	0.435199	0.217599	−	0.976038i	$-0.430177\pi$
$409$	2.81877e24	0.435199	0.217599	+	0.976038i	$0.430177\pi$
$410$	0	0
$411$	−1.49639e25	−2.20571
$412$	0	0
$413$	9.87839e23	0.139047
$414$	0	0
$415$	2.87320e24	0.386286
$416$	0	0
$417$	7.01420e24	0.900919
$418$	0	0
$419$	8.65571e24	1.06235	0.531177	−	0.847261i	$-0.321750\pi$
$419$	8.65571e24	1.06235	0.531177	+	0.847261i	$0.321750\pi$
$420$	0	0
$421$	5.21652e24	0.611929	0.305964	−	0.952043i	$-0.401021\pi$
$421$	5.21652e24	0.611929	0.305964	+	0.952043i	$0.401021\pi$
$422$	0	0
$423$	−4.90994e24	−0.550608
$424$	0	0
$425$	−3.02076e24	−0.323908
$426$	0	0
$427$	−3.95425e23	−0.0405508
$428$	0	0
$429$	4.14050e22	0.00406171
$430$	0	0
$431$	−1.04364e25	−0.979526	−0.489763	−	0.871856i	$-0.662917\pi$
$431$	−1.04364e25	−0.979526	−0.489763	+	0.871856i	$0.662917\pi$
$432$	0	0
$433$	1.45110e25	1.30335	0.651675	−	0.758499i	$-0.274067\pi$
$433$	1.45110e25	1.30335	0.651675	+	0.758499i	$0.274067\pi$
$434$	0	0
$435$	−1.37019e23	−0.0117796
$436$	0	0
$437$	2.40064e25	1.97585
$438$	0	0
$439$	−1.79857e25	−1.41747	−0.708735	−	0.705474i	$-0.750734\pi$
$439$	−1.79857e25	−1.41747	−0.708735	+	0.705474i	$0.750734\pi$
$440$	0	0
$441$	−1.55951e25	−1.17713
$442$	0	0
$443$	8.73685e24	0.631712	0.315856	−	0.948807i	$-0.397708\pi$
$443$	8.73685e24	0.631712	0.315856	+	0.948807i	$0.397708\pi$
$444$	0	0
$445$	1.03921e25	0.719921
$446$	0	0
$447$	1.34745e25	0.894523
$448$	0	0
$449$	−1.60576e25	−1.02174	−0.510870	−	0.859658i	$-0.670677\pi$
$449$	−1.60576e25	−1.02174	−0.510870	+	0.859658i	$0.670677\pi$
$450$	0	0
$451$	5.36618e22	0.00327332
$452$	0	0
$453$	−2.91542e25	−1.70517
$454$	0	0
$455$	−2.02795e24	−0.113750
$456$	0	0
$457$	−2.67587e24	−0.143966	−0.0719831	−	0.997406i	$-0.522933\pi$
$457$	−2.67587e24	−0.143966	−0.0719831	+	0.997406i	$0.522933\pi$
$458$	0	0
$459$	2.74863e24	0.141871
$460$	0	0
$461$	−6.96807e24	−0.345107	−0.172553	−	0.985000i	$-0.555202\pi$
$461$	−6.96807e24	−0.345107	−0.172553	+	0.985000i	$0.555202\pi$
$462$	0	0
$463$	2.49843e25	1.18754	0.593770	−	0.804635i	$-0.297639\pi$
$463$	2.49843e25	1.18754	0.593770	+	0.804635i	$0.297639\pi$
$464$	0	0
$465$	1.25992e25	0.574832
$466$	0	0
$467$	1.94531e25	0.852075	0.426037	−	0.904706i	$-0.359909\pi$
$467$	1.94531e25	0.852075	0.426037	+	0.904706i	$0.359909\pi$
$468$	0	0
$469$	−3.46983e24	−0.145937
$470$	0	0
$471$	5.43180e25	2.19404
$472$	0	0
$473$	−1.82859e22	−0.000709471 0
$474$	0	0
$475$	2.29543e25	0.855610
$476$	0	0
$477$	−4.20396e25	−1.50568
$478$	0	0
$479$	−3.34153e25	−1.15016	−0.575080	−	0.818097i	$-0.695029\pi$
$479$	−3.34153e25	−1.15016	−0.575080	+	0.818097i	$0.695029\pi$
$480$	0	0
$481$	−8.54103e24	−0.282574
$482$	0	0
$483$	−1.20280e25	−0.382557
$484$	0	0
$485$	−1.50969e24	−0.0461679
$486$	0	0
$487$	4.86181e25	1.42979	0.714896	−	0.699231i	$-0.246474\pi$
$487$	4.86181e25	1.42979	0.714896	+	0.699231i	$0.246474\pi$
$488$	0	0
$489$	−2.94169e25	−0.832075
$490$	0	0
$491$	9.86730e24	0.268488	0.134244	−	0.990948i	$-0.457139\pi$
$491$	9.86730e24	0.268488	0.134244	+	0.990948i	$0.457139\pi$
$492$	0	0
$493$	−2.56093e23	−0.00670427
$494$	0	0
$495$	−5.40896e22	−0.00136259
$496$	0	0
$497$	3.00967e24	0.0729681
$498$	0	0
$499$	−3.54150e25	−0.826481	−0.413240	−	0.910622i	$-0.635603\pi$
$499$	−3.54150e25	−0.826481	−0.413240	+	0.910622i	$0.635603\pi$
$500$	0	0
$501$	−1.23283e25	−0.276978
$502$	0	0
$503$	−1.47204e25	−0.318436	−0.159218	−	0.987243i	$-0.550897\pi$
$503$	−1.47204e25	−0.318436	−0.159218	+	0.987243i	$0.550897\pi$
$504$	0	0
$505$	3.38191e25	0.704521
$506$	0	0
$507$	5.47254e25	1.09803
$508$	0	0
$509$	4.88290e25	0.943754	0.471877	−	0.881664i	$-0.343577\pi$
$509$	4.88290e25	0.943754	0.471877	+	0.881664i	$0.343577\pi$
$510$	0	0
$511$	5.07279e24	0.0944601
$512$	0	0
$513$	−2.08864e25	−0.374757
$514$	0	0
$515$	−1.16667e25	−0.201733
$516$	0	0
$517$	5.67212e22	0.000945334 0
$518$	0	0
$519$	6.04533e25	0.971248
$520$	0	0
$521$	7.14445e25	1.10665	0.553325	−	0.832965i	$-0.313359\pi$
$521$	7.14445e25	1.10665	0.553325	+	0.832965i	$0.313359\pi$
$522$	0	0
$523$	8.99895e25	1.34408	0.672041	−	0.740514i	$-0.265418\pi$
$523$	8.99895e25	1.34408	0.672041	+	0.740514i	$0.265418\pi$
$524$	0	0
$525$	−1.15009e25	−0.165660
$526$	0	0
$527$	2.35484e25	0.327160
$528$	0	0
$529$	1.22409e26	1.64053
$530$	0	0
$531$	8.19444e25	1.05955
$532$	0	0
$533$	1.66895e26	2.08226
$534$	0	0
$535$	6.29123e25	0.757486
$536$	0	0
$537$	−2.10036e26	−2.44083
$538$	0	0
$539$	1.80160e23	0.00202100
$540$	0	0
$541$	9.33602e25	1.01109	0.505543	−	0.862802i	$-0.331292\pi$
$541$	9.33602e25	1.01109	0.505543	+	0.862802i	$0.331292\pi$
$542$	0	0
$543$	−1.68349e26	−1.76040
$544$	0	0
$545$	4.37866e25	0.442155
$546$	0	0
$547$	−2.74670e25	−0.267875	−0.133938	−	0.990990i	$-0.542762\pi$
$547$	−2.74670e25	−0.267875	−0.133938	+	0.990990i	$0.542762\pi$
$548$	0	0
$549$	−3.28018e25	−0.309001
$550$	0	0
$551$	1.94602e24	0.0177095
$552$	0	0
$553$	1.56026e24	0.0137185
$554$	0	0
$555$	2.03983e25	0.173305
$556$	0	0
$557$	−1.42589e26	−1.17074	−0.585370	−	0.810766i	$-0.699051\pi$
$557$	−1.42589e26	−1.17074	−0.585370	+	0.810766i	$0.699051\pi$
$558$	0	0
$559$	−5.68712e25	−0.451316
$560$	0	0
$561$	−1.84822e23	−0.00141777
$562$	0	0
$563$	−1.72252e26	−1.27742	−0.638712	−	0.769446i	$-0.720533\pi$
$563$	−1.72252e26	−1.27742	−0.638712	+	0.769446i	$0.720533\pi$
$564$	0	0
$565$	6.11995e25	0.438821
$566$	0	0
$567$	−1.71290e25	−0.118766
$568$	0	0
$569$	5.24893e25	0.351969	0.175984	−	0.984393i	$-0.443689\pi$
$569$	5.24893e25	0.351969	0.175984	+	0.984393i	$0.443689\pi$
$570$	0	0
$571$	−3.21674e24	−0.0208628	−0.0104314	−	0.999946i	$-0.503320\pi$
$571$	−3.21674e24	−0.0208628	−0.0104314	+	0.999946i	$0.503320\pi$
$572$	0	0
$573$	−3.13728e26	−1.96827
$574$	0	0
$575$	1.88390e26	1.14344
$576$	0	0
$577$	1.17453e26	0.689752	0.344876	−	0.938648i	$-0.387921\pi$
$577$	1.17453e26	0.689752	0.344876	+	0.938648i	$0.387921\pi$
$578$	0	0
$579$	−2.63744e26	−1.49877
$580$	0	0
$581$	2.04456e25	0.112441
$582$	0	0
$583$	4.85655e23	0.00258509
$584$	0	0
$585$	−1.68225e26	−0.866783
$586$	0	0
$587$	1.86886e24	0.00932213	0.00466107	−	0.999989i	$-0.498516\pi$
$587$	1.86886e24	0.00932213	0.00466107	+	0.999989i	$0.498516\pi$
$588$	0	0
$589$	−1.78941e26	−0.864201
$590$	0	0
$591$	−1.22772e26	−0.574141
$592$	0	0
$593$	−1.50165e26	−0.680063	−0.340032	−	0.940414i	$-0.610438\pi$
$593$	−1.50165e26	−0.680063	−0.340032	+	0.940414i	$0.610438\pi$
$594$	0	0
$595$	9.05231e24	0.0397053
$596$	0	0
$597$	5.36441e25	0.227911
$598$	0	0
$599$	−1.65804e26	−0.682403	−0.341201	−	0.939990i	$-0.610834\pi$
$599$	−1.65804e26	−0.682403	−0.341201	+	0.939990i	$0.610834\pi$
$600$	0	0
$601$	−2.54795e26	−1.01598	−0.507989	−	0.861364i	$-0.669611\pi$
$601$	−2.54795e26	−1.01598	−0.507989	+	0.861364i	$0.669611\pi$
$602$	0	0
$603$	−2.87833e26	−1.11206
$604$	0	0
$605$	−1.45400e26	−0.544361
$606$	0	0
$607$	−3.14191e26	−1.13999	−0.569996	−	0.821648i	$-0.693055\pi$
$607$	−3.14191e26	−1.13999	−0.569996	+	0.821648i	$0.693055\pi$
$608$	0	0
$609$	−9.75020e23	−0.00342885
$610$	0	0
$611$	1.76410e26	0.601355
$612$	0	0
$613$	3.91478e26	1.29370	0.646848	−	0.762619i	$-0.276087\pi$
$613$	3.91478e26	1.29370	0.646848	+	0.762619i	$0.276087\pi$
$614$	0	0
$615$	−3.98590e26	−1.27707
$616$	0	0
$617$	4.86066e26	1.51003	0.755016	−	0.655706i	$-0.227629\pi$
$617$	4.86066e26	1.51003	0.755016	+	0.655706i	$0.227629\pi$
$618$	0	0
$619$	−4.51098e26	−1.35897	−0.679485	−	0.733689i	$-0.737797\pi$
$619$	−4.51098e26	−1.35897	−0.679485	+	0.733689i	$0.737797\pi$
$620$	0	0
$621$	−1.71418e26	−0.500827
$622$	0	0
$623$	7.39500e25	0.209557
$624$	0	0
$625$	7.23294e25	0.198817
$626$	0	0
$627$	1.40444e24	0.00374508
$628$	0	0
$629$	3.81251e25	0.0986349
$630$	0	0
$631$	−2.03805e26	−0.511607	−0.255803	−	0.966729i	$-0.582340\pi$
$631$	−2.03805e26	−0.511607	−0.255803	+	0.966729i	$0.582340\pi$
$632$	0	0
$633$	−6.70753e26	−1.63391
$634$	0	0
$635$	−2.09383e26	−0.494985
$636$	0	0
$637$	5.60320e26	1.28562
$638$	0	0
$639$	2.49662e26	0.556024
$640$	0	0
$641$	5.77927e26	1.24946	0.624729	−	0.780842i	$-0.285209\pi$
$641$	5.77927e26	1.24946	0.624729	+	0.780842i	$0.285209\pi$
$642$	0	0
$643$	7.72049e26	1.62047	0.810235	−	0.586106i	$-0.199340\pi$
$643$	7.72049e26	1.62047	0.810235	+	0.586106i	$0.199340\pi$
$644$	0	0
$645$	1.35824e26	0.276796
$646$	0	0
$647$	1.39226e24	0.00275504	0.00137752	−	0.999999i	$-0.499562\pi$
$647$	1.39226e24	0.00275504	0.00137752	+	0.999999i	$0.499562\pi$
$648$	0	0
$649$	−9.46648e23	−0.00181913
$650$	0	0
$651$	8.96556e25	0.167324
$652$	0	0
$653$	6.19470e26	1.12291	0.561455	−	0.827507i	$-0.310242\pi$
$653$	6.19470e26	1.12291	0.561455	+	0.827507i	$0.310242\pi$
$654$	0	0
$655$	1.71004e26	0.301103
$656$	0	0
$657$	4.20804e26	0.719795
$658$	0	0
$659$	−7.96627e25	−0.132386	−0.0661932	−	0.997807i	$-0.521085\pi$
$659$	−7.96627e25	−0.132386	−0.0661932	+	0.997807i	$0.521085\pi$
$660$	0	0
$661$	1.85436e26	0.299420	0.149710	−	0.988730i	$-0.452166\pi$
$661$	1.85436e26	0.299420	0.149710	+	0.988730i	$0.452166\pi$
$662$	0	0
$663$	−5.74819e26	−0.901888
$664$	0	0
$665$	−6.87873e25	−0.104882
$666$	0	0
$667$	1.59713e25	0.0236670
$668$	0	0
$669$	−1.01771e27	−1.46580
$670$	0	0
$671$	3.78937e23	0.000530521 0
$672$	0	0
$673$	5.91532e26	0.805073	0.402536	−	0.915404i	$-0.368129\pi$
$673$	5.91532e26	0.805073	0.402536	+	0.915404i	$0.368129\pi$
$674$	0	0
$675$	−1.63906e26	−0.216875
$676$	0	0
$677$	2.97418e26	0.382626	0.191313	−	0.981529i	$-0.438725\pi$
$677$	2.97418e26	0.382626	0.191313	+	0.981529i	$0.438725\pi$
$678$	0	0
$679$	−1.07429e25	−0.0134387
$680$	0	0
$681$	−1.03074e27	−1.25387
$682$	0	0
$683$	−1.25943e27	−1.48997	−0.744983	−	0.667084i	$-0.767542\pi$
$683$	−1.25943e27	−1.48997	−0.744983	+	0.667084i	$0.767542\pi$
$684$	0	0
$685$	−7.02349e26	−0.808151
$686$	0	0
$687$	2.02558e27	2.26704
$688$	0	0
$689$	1.51044e27	1.64446
$690$	0	0
$691$	3.19965e25	0.0338891	0.0169446	−	0.999856i	$-0.494606\pi$
$691$	3.19965e25	0.0338891	0.0169446	+	0.999856i	$0.494606\pi$
$692$	0	0
$693$	−3.84899e23	−0.000396626 0
$694$	0	0
$695$	3.29220e26	0.330088
$696$	0	0
$697$	−7.44979e26	−0.726829
$698$	0	0
$699$	1.22664e27	1.16462
$700$	0	0
$701$	−2.06463e27	−1.90775	−0.953874	−	0.300208i	$-0.902944\pi$
$701$	−2.06463e27	−1.90775	−0.953874	+	0.300208i	$0.902944\pi$
$702$	0	0
$703$	−2.89708e26	−0.260546
$704$	0	0
$705$	−4.21315e26	−0.368816
$706$	0	0
$707$	2.40655e26	0.205074
$708$	0	0
$709$	1.44096e27	1.19539	0.597697	−	0.801722i	$-0.296082\pi$
$709$	1.44096e27	1.19539	0.597697	+	0.801722i	$0.296082\pi$
$710$	0	0
$711$	1.29428e26	0.104536
$712$	0	0
$713$	−1.46860e27	−1.15492
$714$	0	0
$715$	1.94339e24	0.00148817
$716$	0	0
$717$	−1.32916e27	−0.991165
$718$	0	0
$719$	1.26393e27	0.917907	0.458953	−	0.888460i	$-0.348224\pi$
$719$	1.26393e27	0.917907	0.458953	+	0.888460i	$0.348224\pi$
$720$	0	0
$721$	−8.30194e25	−0.0587211
$722$	0	0
$723$	3.73024e27	2.56994
$724$	0	0
$725$	1.52714e25	0.0102486
$726$	0	0
$727$	−5.54468e26	−0.362493	−0.181246	−	0.983438i	$-0.558013\pi$
$727$	−5.54468e26	−0.362493	−0.181246	+	0.983438i	$0.558013\pi$
$728$	0	0
$729$	−2.13985e27	−1.36293
$730$	0	0
$731$	2.53860e26	0.157536
$732$	0	0
$733$	−8.06563e26	−0.487698	−0.243849	−	0.969813i	$-0.578410\pi$
$733$	−8.06563e26	−0.487698	−0.243849	+	0.969813i	$0.578410\pi$
$734$	0	0
$735$	−1.33820e27	−0.788479
$736$	0	0
$737$	3.32514e24	0.00190928
$738$	0	0
$739$	6.63850e26	0.371490	0.185745	−	0.982598i	$-0.440530\pi$
$739$	6.63850e26	0.371490	0.185745	+	0.982598i	$0.440530\pi$
$740$	0	0
$741$	4.36798e27	2.38236
$742$	0	0
$743$	3.64095e27	1.93562	0.967811	−	0.251677i	$-0.0809820\pi$
$743$	3.64095e27	1.93562	0.967811	+	0.251677i	$0.0809820\pi$
$744$	0	0
$745$	6.32441e26	0.327745
$746$	0	0
$747$	1.69603e27	0.856814
$748$	0	0
$749$	4.47681e26	0.220491
$750$	0	0
$751$	1.55458e27	0.746505	0.373253	−	0.927730i	$-0.378242\pi$
$751$	1.55458e27	0.746505	0.373253	+	0.927730i	$0.378242\pi$
$752$	0	0
$753$	3.69410e27	1.72964
$754$	0	0
$755$	−1.36839e27	−0.624759
$756$	0	0
$757$	−1.33406e27	−0.593970	−0.296985	−	0.954882i	$-0.595981\pi$
$757$	−1.33406e27	−0.593970	−0.296985	+	0.954882i	$0.595981\pi$
$758$	0	0
$759$	1.15265e25	0.00500494
$760$	0	0
$761$	−6.89829e25	−0.0292137	−0.0146069	−	0.999893i	$-0.504650\pi$
$761$	−6.89829e25	−0.0292137	−0.0146069	+	0.999893i	$0.504650\pi$
$762$	0	0
$763$	3.11584e26	0.128704
$764$	0	0
$765$	7.50917e26	0.302558
$766$	0	0
$767$	−2.94419e27	−1.15720
$768$	0	0
$769$	−8.09673e26	−0.310463	−0.155231	−	0.987878i	$-0.549612\pi$
$769$	−8.09673e26	−0.310463	−0.155231	+	0.987878i	$0.549612\pi$
$770$	0	0
$771$	−3.23221e27	−1.20916
$772$	0	0
$773$	−1.00924e27	−0.368374	−0.184187	−	0.982891i	$-0.558965\pi$
$773$	−1.00924e27	−0.368374	−0.184187	+	0.982891i	$0.558965\pi$
$774$	0	0
$775$	−1.40424e27	−0.500121
$776$	0	0
$777$	1.45154e26	0.0504461
$778$	0	0
$779$	5.66100e27	1.91994
$780$	0	0
$781$	−2.88417e24	−0.000954633 0
$782$	0	0
$783$	−1.38956e25	−0.00448890
$784$	0	0
$785$	2.54948e27	0.803876
$786$	0	0
$787$	−4.88307e27	−1.50291	−0.751456	−	0.659784i	$-0.770648\pi$
$787$	−4.88307e27	−1.50291	−0.751456	+	0.659784i	$0.770648\pi$
$788$	0	0
$789$	6.87955e27	2.06694
$790$	0	0
$791$	4.35493e26	0.127733
$792$	0	0
$793$	1.17854e27	0.337480
$794$	0	0
$795$	−3.60735e27	−1.00856
$796$	0	0
$797$	−1.18346e27	−0.323072	−0.161536	−	0.986867i	$-0.551645\pi$
$797$	−1.18346e27	−0.323072	−0.161536	+	0.986867i	$0.551645\pi$
$798$	0	0
$799$	−7.87451e26	−0.209908
$800$	0	0
$801$	6.13438e27	1.59684
$802$	0	0
$803$	−4.86126e24	−0.00123581
$804$	0	0
$805$	−5.64549e26	−0.140165
$806$	0	0
$807$	6.77075e27	1.64187
$808$	0	0
$809$	−5.08495e27	−1.20441	−0.602207	−	0.798340i	$-0.705712\pi$
$809$	−5.08495e27	−1.20441	−0.602207	+	0.798340i	$0.705712\pi$
$810$	0	0
$811$	−2.72133e25	−0.00629627	−0.00314813	−	0.999995i	$-0.501002\pi$
$811$	−2.72133e25	−0.00629627	−0.00314813	+	0.999995i	$0.501002\pi$
$812$	0	0
$813$	−1.01581e28	−2.29590
$814$	0	0
$815$	−1.38072e27	−0.304865
$816$	0	0
$817$	−1.92905e27	−0.416134
$818$	0	0
$819$	−1.19708e27	−0.252306
$820$	0	0
$821$	5.16381e26	0.106343	0.0531716	−	0.998585i	$-0.483067\pi$
$821$	5.16381e26	0.106343	0.0531716	+	0.998585i	$0.483067\pi$
$822$	0	0
$823$	1.97624e27	0.397687	0.198843	−	0.980031i	$-0.436282\pi$
$823$	1.97624e27	0.397687	0.198843	+	0.980031i	$0.436282\pi$
$824$	0	0
$825$	1.10213e25	0.00216731
$826$	0	0
$827$	−1.16795e27	−0.224450	−0.112225	−	0.993683i	$-0.535798\pi$
$827$	−1.16795e27	−0.224450	−0.112225	+	0.993683i	$0.535798\pi$
$828$	0	0
$829$	−4.20809e27	−0.790345	−0.395173	−	0.918607i	$-0.629315\pi$
$829$	−4.20809e27	−0.790345	−0.395173	+	0.918607i	$0.629315\pi$
$830$	0	0
$831$	−1.01417e28	−1.86166
$832$	0	0
$833$	−2.50113e27	−0.448755
$834$	0	0
$835$	−5.78644e26	−0.101482
$836$	0	0
$837$	1.27774e27	0.219053
$838$	0	0
$839$	−8.49254e27	−1.42331	−0.711654	−	0.702530i	$-0.752053\pi$
$839$	−8.49254e27	−1.42331	−0.711654	+	0.702530i	$0.752053\pi$
$840$	0	0
$841$	−6.10197e27	−0.999788
$842$	0	0
$843$	−6.03972e27	−0.967508
$844$	0	0
$845$	2.56860e27	0.402307
$846$	0	0
$847$	−1.03466e27	−0.158454
$848$	0	0
$849$	−1.75311e26	−0.0262534
$850$	0	0
$851$	−2.37768e27	−0.348195
$852$	0	0
$853$	9.33345e27	1.33668	0.668338	−	0.743857i	$-0.267006\pi$
$853$	9.33345e27	1.33668	0.668338	+	0.743857i	$0.267006\pi$
$854$	0	0
$855$	−5.70612e27	−0.799214
$856$	0	0
$857$	−1.11037e28	−1.52108	−0.760539	−	0.649292i	$-0.775065\pi$
$857$	−1.11037e28	−1.52108	−0.760539	+	0.649292i	$0.775065\pi$
$858$	0	0
$859$	1.11478e28	1.49367	0.746834	−	0.665011i	$-0.231573\pi$
$859$	1.11478e28	1.49367	0.746834	+	0.665011i	$0.231573\pi$
$860$	0	0
$861$	−2.83635e27	−0.371732
$862$	0	0
$863$	−1.15445e28	−1.48004	−0.740021	−	0.672583i	$-0.765185\pi$
$863$	−1.15445e28	−1.48004	−0.740021	+	0.672583i	$0.765185\pi$
$864$	0	0
$865$	2.83745e27	0.355856
$866$	0	0
$867$	−9.54364e27	−1.17093
$868$	0	0
$869$	−1.49520e24	−0.000179478 0
$870$	0	0
$871$	1.03416e28	1.21455
$872$	0	0
$873$	−8.91154e26	−0.102404
$874$	0	0
$875$	−1.30694e27	−0.146954
$876$	0	0
$877$	−1.55912e28	−1.71547	−0.857734	−	0.514094i	$-0.828128\pi$
$877$	−1.55912e28	−1.71547	−0.857734	+	0.514094i	$0.828128\pi$
$878$	0	0
$879$	1.08008e28	1.16295
$880$	0	0
$881$	3.35920e26	0.0353969	0.0176985	−	0.999843i	$-0.494366\pi$
$881$	3.35920e26	0.0353969	0.0176985	+	0.999843i	$0.494366\pi$
$882$	0	0
$883$	−1.34374e26	−0.0138576	−0.00692882	−	0.999976i	$-0.502206\pi$
$883$	−1.34374e26	−0.0138576	−0.00692882	+	0.999976i	$0.502206\pi$
$884$	0	0
$885$	7.03153e27	0.709722
$886$	0	0
$887$	−9.23887e27	−0.912735	−0.456367	−	0.889791i	$-0.650850\pi$
$887$	−9.23887e27	−0.912735	−0.456367	+	0.889791i	$0.650850\pi$
$888$	0	0
$889$	−1.48996e27	−0.144082
$890$	0	0
$891$	1.64147e25	0.00155380
$892$	0	0
$893$	5.98374e27	0.554478
$894$	0	0
$895$	−9.85826e27	−0.894296
$896$	0	0
$897$	3.58487e28	3.18379
$898$	0	0
$899$	−1.19048e26	−0.0103516
$900$	0	0
$901$	−6.74227e27	−0.574011
$902$	0	0
$903$	9.66517e26	0.0805705
$904$	0	0
$905$	−7.90165e27	−0.644995
$906$	0	0
$907$	−1.80585e28	−1.44349	−0.721743	−	0.692161i	$-0.756659\pi$
$907$	−1.80585e28	−1.44349	−0.721743	+	0.692161i	$0.756659\pi$
$908$	0	0
$909$	1.99631e28	1.56268
$910$	0	0
$911$	1.99304e28	1.52789	0.763943	−	0.645283i	$-0.223261\pi$
$911$	1.99304e28	1.52789	0.763943	+	0.645283i	$0.223261\pi$
$912$	0	0
$913$	−1.95930e25	−0.00147106
$914$	0	0
$915$	−2.81467e27	−0.206980
$916$	0	0
$917$	1.21686e27	0.0876460
$918$	0	0
$919$	−1.04320e28	−0.735984	−0.367992	−	0.929829i	$-0.619955\pi$
$919$	−1.04320e28	−0.735984	−0.367992	+	0.929829i	$0.619955\pi$
$920$	0	0
$921$	9.71946e27	0.671701
$922$	0	0
$923$	−8.97012e27	−0.607271
$924$	0	0
$925$	−2.27348e27	−0.150781
$926$	0	0
$927$	−6.88672e27	−0.447461
$928$	0	0
$929$	−5.17736e27	−0.329578	−0.164789	−	0.986329i	$-0.552694\pi$
$929$	−5.17736e27	−0.329578	−0.164789	+	0.986329i	$0.552694\pi$
$930$	0	0
$931$	1.90058e28	1.18540
$932$	0	0
$933$	7.82683e27	0.478311
$934$	0	0
$935$	−8.67484e24	−0.000519459 0
$936$	0	0
$937$	9.33202e27	0.547582	0.273791	−	0.961789i	$-0.411722\pi$
$937$	9.33202e27	0.547582	0.273791	+	0.961789i	$0.411722\pi$
$938$	0	0
$939$	1.45578e28	0.837089
$940$	0	0
$941$	−4.50115e27	−0.253642	−0.126821	−	0.991926i	$-0.540477\pi$
$941$	−4.50115e27	−0.253642	−0.126821	+	0.991926i	$0.540477\pi$
$942$	0	0
$943$	4.64607e28	2.56581
$944$	0	0
$945$	4.91178e26	0.0265850
$946$	0	0
$947$	1.76126e28	0.934324	0.467162	−	0.884172i	$-0.345276\pi$
$947$	1.76126e28	0.934324	0.467162	+	0.884172i	$0.345276\pi$
$948$	0	0
$949$	−1.51191e28	−0.786135
$950$	0	0
$951$	−1.33485e27	−0.0680325
$952$	0	0
$953$	5.93730e27	0.296624	0.148312	−	0.988941i	$-0.452616\pi$
$953$	5.93730e27	0.296624	0.148312	+	0.988941i	$0.452616\pi$
$954$	0	0
$955$	−1.47252e28	−0.721155
$956$	0	0
$957$	9.34363e23	4.48593e−5 0
$958$	0	0
$959$	−4.99789e27	−0.235239
$960$	0	0
$961$	−1.07239e28	−0.494857
$962$	0	0
$963$	3.71365e28	1.68016
$964$	0	0
$965$	−1.23791e28	−0.549136
$966$	0	0
$967$	2.58489e28	1.12432	0.562160	−	0.827028i	$-0.309970\pi$
$967$	2.58489e28	1.12432	0.562160	+	0.827028i	$0.309970\pi$
$968$	0	0
$969$	−1.94976e28	−0.831583
$970$	0	0
$971$	2.05732e28	0.860438	0.430219	−	0.902725i	$-0.358436\pi$
$971$	2.05732e28	0.860438	0.430219	+	0.902725i	$0.358436\pi$
$972$	0	0
$973$	2.34271e27	0.0960831
$974$	0	0
$975$	3.42777e28	1.37869
$976$	0	0
$977$	−2.34524e28	−0.925099	−0.462550	−	0.886593i	$-0.653065\pi$
$977$	−2.34524e28	−0.925099	−0.462550	+	0.886593i	$0.653065\pi$
$978$	0	0
$979$	−7.08664e25	−0.00274160
$980$	0	0
$981$	2.58468e28	0.980736
$982$	0	0
$983$	−4.25526e28	−1.58368	−0.791840	−	0.610729i	$-0.790877\pi$
$983$	−4.25526e28	−1.58368	−0.791840	+	0.610729i	$0.790877\pi$
$984$	0	0
$985$	−5.76245e27	−0.210360
$986$	0	0
$987$	−2.99806e27	−0.107356
$988$	0	0
$989$	−1.58320e28	−0.556123
$990$	0	0
$991$	−5.21472e28	−1.79693	−0.898466	−	0.439044i	$-0.855317\pi$
$991$	−5.21472e28	−1.79693	−0.898466	+	0.439044i	$0.855317\pi$
$992$	0	0
$993$	−5.33556e28	−1.80369
$994$	0	0
$995$	2.51785e27	0.0835046
$996$	0	0
$997$	1.61541e27	0.0525629	0.0262815	−	0.999655i	$-0.491633\pi$
$997$	1.61541e27	0.0525629	0.0262815	+	0.999655i	$0.491633\pi$
$998$	0	0
$999$	2.06867e27	0.0660419

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.20.a.h.1.1		1
4.3	odd	2		64.20.a.b.1.1		1
8.3	odd	2		1.20.a.a.1.1	✓	1
8.5	even	2		16.20.a.a.1.1		1
24.11	even	2		9.20.a.a.1.1		1
40.3	even	4		25.20.b.a.24.1		2
40.19	odd	2		25.20.a.a.1.1		1
40.27	even	4		25.20.b.a.24.2		2
56.27	even	2		49.20.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.20.a.a.1.1	✓	1	8.3	odd	2
9.20.a.a.1.1		1	24.11	even	2
16.20.a.a.1.1		1	8.5	even	2
25.20.a.a.1.1		1	40.19	odd	2
25.20.b.a.24.1		2	40.3	even	4
25.20.b.a.24.2		2	40.27	even	4
49.20.a.b.1.1		1	56.27	even	2
64.20.a.b.1.1		1	4.3	odd	2
64.20.a.h.1.1		1	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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