LMFDB - Embedded newform 64.24.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [64,24,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, 24, names="a")

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

chi := DirichletCharacter("64.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 64 = 2^{6} $
Weight:	$ k $	$=$	$ 24 $
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:	$214.530583901$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2 x^{5} - 376388081 x^{4} + 1624987949956 x^{3} + \cdots + 26\!\cdots\!25 $ x^6 - 2x^5 - 376388081x^4 + 1624987949956x^3 + 32369842380258997x^2 - 236529072927913245962*x + 267804601125256722828825
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{71}\cdot 3^{4}\cdot 5^{4} $
Twist minimal:	no (minimal twist has level 32)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-17982.9$ 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)

$f(q)$	$=$	$q-482133. q^{3} +1.37024e8 q^{5} -1.92818e9 q^{7} +1.38309e11 q^{9} +O(q^{10})$	$q-482133. q^{3} +1.37024e8 q^{5} -1.92818e9 q^{7} +1.38309e11 q^{9} -1.11828e10 q^{11} +4.97784e12 q^{13} -6.60637e13 q^{15} +1.59593e14 q^{17} -6.91449e14 q^{19} +9.29642e14 q^{21} +7.11706e15 q^{23} +6.85458e15 q^{25} -2.12940e16 q^{27} +1.00538e17 q^{29} +3.03339e16 q^{31} +5.39162e15 q^{33} -2.64207e17 q^{35} +1.55777e18 q^{37} -2.39998e18 q^{39} -5.17334e18 q^{41} +6.33945e18 q^{43} +1.89517e19 q^{45} +8.39743e18 q^{47} -2.36509e19 q^{49} -7.69450e19 q^{51} +9.68418e19 q^{53} -1.53231e18 q^{55} +3.33370e20 q^{57} +3.08157e20 q^{59} +1.66378e20 q^{61} -2.66686e20 q^{63} +6.82082e20 q^{65} -1.26836e21 q^{67} -3.43137e21 q^{69} -3.09619e21 q^{71} -2.48597e21 q^{73} -3.30482e21 q^{75} +2.15626e19 q^{77} +1.08565e21 q^{79} -2.75432e21 q^{81} -1.23354e22 q^{83} +2.18680e22 q^{85} -4.84728e22 q^{87} -4.40442e22 q^{89} -9.59820e21 q^{91} -1.46250e22 q^{93} -9.47449e22 q^{95} +9.25580e22 q^{97} -1.54669e21 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 483920 q^{3} + 6100380 q^{5} + 347289696 q^{7} + 260924449726 q^{9}+O(q^{10}) $ 6 * q + 483920 * q^3 + 6100380 * q^5 + 347289696 * q^7 + 260924449726 * q^9	$ 6 q + 483920 q^{3} + 6100380 q^{5} + 347289696 q^{7} + 260924449726 q^{9} + 926871857520 q^{11} + 3684897167820 q^{13} - 105662245358560 q^{15} + 71064722424780 q^{17} - 453921923982960 q^{19} + 17\!\cdots\!80 q^{21}+ \cdots + 39\!\cdots\!40 q^{99}+O(q^{100}) $ 6 * q + 483920 * q^3 + 6100380 * q^5 + 347289696 * q^7 + 260924449726 * q^9 + 926871857520 * q^11 + 3684897167820 * q^13 - 105662245358560 * q^15 + 71064722424780 * q^17 - 453921923982960 * q^19 + 1712900116737280 * q^21 + 7126581767144736 * q^23 + 21617163289317450 * q^25 + 41851914072529184 * q^27 + 90718382478351852 * q^29 - 53660517982277760 * q^31 + 607667723496123520 * q^33 - 843485446441350720 * q^35 - 1178800099078290660 * q^37 - 387144388087503200 * q^39 + 1672300630976121180 * q^41 + 9707130536958833904 * q^43 - 31072675924013630900 * q^45 + 12637324971625378368 * q^47 + 20589514456941037878 * q^49 - 56125446355277416800 * q^51 + 25955354185131109500 * q^53 - 79415390320029033120 * q^55 + 169187096172727794560 * q^57 + 407713345239006043440 * q^59 + 615884547554394402156 * q^61 + 578320926136902243296 * q^63 - 1095923787012414183240 * q^65 - 523768762996317716400 * q^67 - 596596128814415845632 * q^69 - 948379808687003287200 * q^71 - 4925435605783876580100 * q^73 + 11105120520135150430000 * q^75 - 1628144191735745368320 * q^77 + 6474134783625939495360 * q^79 + 23375719407022646959702 * q^81 + 12413209217367249862032 * q^83 + 5978612007137723165880 * q^85 - 17230630950338425832032 * q^87 + 7892765755425674057628 * q^89 + 117701223538009065704640 * q^91 - 65760567831273830333440 * q^93 - 112886120912929344409440 * q^95 - 12935113600510578486420 * q^97 + 397484583772859161352240 * q^99

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
$3$	−482133.	−1.57135	−0.785675	−	0.618640i	$-0.787684\pi$
$3$	−482133.	−1.57135	−0.785675	+	0.618640i	$0.787684\pi$
$4$	0	0
$5$	1.37024e8	1.25499	0.627496	−	0.778620i	$-0.284080\pi$
$5$	1.37024e8	1.25499	0.627496	+	0.778620i	$0.284080\pi$
$6$	0	0
$7$	−1.92818e9	−0.368571	−0.184286	−	0.982873i	$-0.558997\pi$
$7$	−1.92818e9	−0.368571	−0.184286	+	0.982873i	$0.558997\pi$
$8$	0	0
$9$	1.38309e11	1.46914
$10$	0	0
$11$	−1.11828e10	−0.0118178	−0.00590889	−	0.999983i	$-0.501881\pi$
$11$	−1.11828e10	−0.0118178	−0.00590889	+	0.999983i	$0.501881\pi$
$12$	0	0
$13$	4.97784e12	0.770358	0.385179	−	0.922842i	$-0.374140\pi$
$13$	4.97784e12	0.770358	0.385179	+	0.922842i	$0.374140\pi$
$14$	0	0
$15$	−6.60637e13	−1.97203
$16$	0	0
$17$	1.59593e14	1.12941	0.564704	−	0.825294i	$-0.308990\pi$
$17$	1.59593e14	1.12941	0.564704	+	0.825294i	$0.308990\pi$
$18$	0	0
$19$	−6.91449e14	−1.36174	−0.680869	−	0.732405i	$-0.738398\pi$
$19$	−6.91449e14	−1.36174	−0.680869	+	0.732405i	$0.738398\pi$
$20$	0	0
$21$	9.29642e14	0.579154
$22$	0	0
$23$	7.11706e15	1.55751	0.778754	−	0.627329i	$-0.215852\pi$
$23$	7.11706e15	1.55751	0.778754	+	0.627329i	$0.215852\pi$
$24$	0	0
$25$	6.85458e15	0.575003
$26$	0	0
$27$	−2.12940e16	−0.737182
$28$	0	0
$29$	1.00538e17	1.53022	0.765110	−	0.643900i	$-0.222685\pi$
$29$	1.00538e17	1.53022	0.765110	+	0.643900i	$0.222685\pi$
$30$	0	0
$31$	3.03339e16	0.214422	0.107211	−	0.994236i	$-0.465808\pi$
$31$	3.03339e16	0.214422	0.107211	+	0.994236i	$0.465808\pi$
$32$	0	0
$33$	5.39162e15	0.0185699
$34$	0	0
$35$	−2.64207e17	−0.462553
$36$	0	0
$37$	1.55777e18	1.43941	0.719703	−	0.694282i	$-0.244278\pi$
$37$	1.55777e18	1.43941	0.719703	+	0.694282i	$0.244278\pi$
$38$	0	0
$39$	−2.39998e18	−1.21050
$40$	0	0
$41$	−5.17334e18	−1.46810	−0.734052	−	0.679093i	$-0.762373\pi$
$41$	−5.17334e18	−1.46810	−0.734052	+	0.679093i	$0.762373\pi$
$42$	0	0
$43$	6.33945e18	1.04031	0.520157	−	0.854071i	$-0.325874\pi$
$43$	6.33945e18	1.04031	0.520157	+	0.854071i	$0.325874\pi$
$44$	0	0
$45$	1.89517e19	1.84376
$46$	0	0
$47$	8.39743e18	0.495474	0.247737	−	0.968827i	$-0.420313\pi$
$47$	8.39743e18	0.495474	0.247737	+	0.968827i	$0.420313\pi$
$48$	0	0
$49$	−2.36509e19	−0.864155
$50$	0	0
$51$	−7.69450e19	−1.77469
$52$	0	0
$53$	9.68418e19	1.43513	0.717564	−	0.696493i	$-0.245257\pi$
$53$	9.68418e19	1.43513	0.717564	+	0.696493i	$0.245257\pi$
$54$	0	0
$55$	−1.53231e18	−0.0148312
$56$	0	0
$57$	3.33370e20	2.13977
$58$	0	0
$59$	3.08157e20	1.33038	0.665188	−	0.746676i	$-0.268351\pi$
$59$	3.08157e20	1.33038	0.665188	+	0.746676i	$0.268351\pi$
$60$	0	0
$61$	1.66378e20	0.489558	0.244779	−	0.969579i	$-0.421285\pi$
$61$	1.66378e20	0.489558	0.244779	+	0.969579i	$0.421285\pi$
$62$	0	0
$63$	−2.66686e20	−0.541482
$64$	0	0
$65$	6.82082e20	0.966792
$66$	0	0
$67$	−1.26836e21	−1.26876	−0.634382	−	0.773020i	$-0.718745\pi$
$67$	−1.26836e21	−1.26876	−0.634382	+	0.773020i	$0.718745\pi$
$68$	0	0
$69$	−3.43137e21	−2.44739
$70$	0	0
$71$	−3.09619e21	−1.58985	−0.794925	−	0.606707i	$-0.792490\pi$
$71$	−3.09619e21	−1.58985	−0.794925	+	0.606707i	$0.792490\pi$
$72$	0	0
$73$	−2.48597e21	−0.927434	−0.463717	−	0.885983i	$-0.653485\pi$
$73$	−2.48597e21	−0.927434	−0.463717	+	0.885983i	$0.653485\pi$
$74$	0	0
$75$	−3.30482e21	−0.903531
$76$	0	0
$77$	2.15626e19	0.00435569
$78$	0	0
$79$	1.08565e21	0.163296	0.0816482	−	0.996661i	$-0.473982\pi$
$79$	1.08565e21	0.163296	0.0816482	+	0.996661i	$0.473982\pi$
$80$	0	0
$81$	−2.75432e21	−0.310769
$82$	0	0
$83$	−1.23354e22	−1.05137	−0.525686	−	0.850679i	$-0.676191\pi$
$83$	−1.23354e22	−1.05137	−0.525686	+	0.850679i	$0.676191\pi$
$84$	0	0
$85$	2.18680e22	1.41740
$86$	0	0
$87$	−4.84728e22	−2.40451
$88$	0	0
$89$	−4.40442e22	−1.68230	−0.841150	−	0.540801i	$-0.818121\pi$
$89$	−4.40442e22	−1.68230	−0.841150	+	0.540801i	$0.818121\pi$
$90$	0	0
$91$	−9.59820e21	−0.283932
$92$	0	0
$93$	−1.46250e22	−0.336932
$94$	0	0
$95$	−9.47449e22	−1.70897
$96$	0	0
$97$	9.25580e22	1.31383	0.656915	−	0.753965i	$-0.271861\pi$
$97$	9.25580e22	1.31383	0.656915	+	0.753965i	$0.271861\pi$
$98$	0	0
$99$	−1.54669e21	−0.0173620
$100$	0	0
$101$	2.05724e22	0.183480	0.0917402	−	0.995783i	$-0.470757\pi$
$101$	2.05724e22	0.183480	0.0917402	+	0.995783i	$0.470757\pi$
$102$	0	0
$103$	6.39127e22	0.454945	0.227473	−	0.973784i	$-0.426954\pi$
$103$	6.39127e22	0.454945	0.227473	+	0.973784i	$0.426954\pi$
$104$	0	0
$105$	1.27383e23	0.726833
$106$	0	0
$107$	−1.92353e23	−0.883456	−0.441728	−	0.897149i	$-0.645634\pi$
$107$	−1.92353e23	−0.883456	−0.441728	+	0.897149i	$0.645634\pi$
$108$	0	0
$109$	−2.71634e23	−1.00828	−0.504138	−	0.863623i	$-0.668190\pi$
$109$	−2.71634e23	−1.00828	−0.504138	+	0.863623i	$0.668190\pi$
$110$	0	0
$111$	−7.51053e23	−2.26181
$112$	0	0
$113$	4.59379e23	1.12660	0.563299	−	0.826253i	$-0.309532\pi$
$113$	4.59379e23	1.12660	0.563299	+	0.826253i	$0.309532\pi$
$114$	0	0
$115$	9.75206e23	1.95466
$116$	0	0
$117$	6.88482e23	1.13176
$118$	0	0
$119$	−3.07724e23	−0.416267
$120$	0	0
$121$	−8.95305e23	−0.999860
$122$	0	0
$123$	2.49424e24	2.30691
$124$	0	0
$125$	−6.94211e23	−0.533367
$126$	0	0
$127$	1.23893e24	0.793058	0.396529	−	0.918022i	$-0.370215\pi$
$127$	1.23893e24	0.793058	0.396529	+	0.918022i	$0.370215\pi$
$128$	0	0
$129$	−3.05646e24	−1.63470
$130$	0	0
$131$	2.48342e24	1.11284	0.556418	−	0.830903i	$-0.312176\pi$
$131$	2.48342e24	1.11284	0.556418	+	0.830903i	$0.312176\pi$
$132$	0	0
$133$	1.33324e24	0.501897
$134$	0	0
$135$	−2.91779e24	−0.925157
$136$	0	0
$137$	−2.38539e24	−0.638664	−0.319332	−	0.947643i	$-0.603458\pi$
$137$	−2.38539e24	−0.638664	−0.319332	+	0.947643i	$0.603458\pi$
$138$	0	0
$139$	6.59778e24	1.49530	0.747649	−	0.664094i	$-0.231182\pi$
$139$	6.59778e24	1.49530	0.747649	+	0.664094i	$0.231182\pi$
$140$	0	0
$141$	−4.04868e24	−0.778563
$142$	0	0
$143$	−5.56664e22	−0.00910392
$144$	0	0
$145$	1.37761e25	1.92041
$146$	0	0
$147$	1.14029e25	1.35789
$148$	0	0
$149$	3.86918e24	0.394437	0.197218	−	0.980360i	$-0.436809\pi$
$149$	3.86918e24	0.394437	0.197218	+	0.980360i	$0.436809\pi$
$150$	0	0
$151$	−7.81185e24	−0.683155	−0.341577	−	0.939854i	$-0.610961\pi$
$151$	−7.81185e24	−0.683155	−0.341577	+	0.939854i	$0.610961\pi$
$152$	0	0
$153$	2.20732e25	1.65926
$154$	0	0
$155$	4.15647e24	0.269098
$156$	0	0
$157$	6.12269e24	0.342055	0.171027	−	0.985266i	$-0.445291\pi$
$157$	6.12269e24	0.342055	0.171027	+	0.985266i	$0.445291\pi$
$158$	0	0
$159$	−4.66907e25	−2.25509
$160$	0	0
$161$	−1.37230e25	−0.574053
$162$	0	0
$163$	−1.09514e25	−0.397477	−0.198738	−	0.980053i	$-0.563684\pi$
$163$	−1.09514e25	−0.397477	−0.198738	+	0.980053i	$0.563684\pi$
$164$	0	0
$165$	7.38780e23	0.0233050
$166$	0	0
$167$	3.81724e25	1.04836	0.524179	−	0.851608i	$-0.324372\pi$
$167$	3.81724e25	1.04836	0.524179	+	0.851608i	$0.324372\pi$
$168$	0	0
$169$	−1.69750e25	−0.406549
$170$	0	0
$171$	−9.56339e25	−2.00058
$172$	0	0
$173$	2.97442e25	0.544343	0.272172	−	0.962249i	$-0.412258\pi$
$173$	2.97442e25	0.544343	0.272172	+	0.962249i	$0.412258\pi$
$174$	0	0
$175$	−1.32169e25	−0.211930
$176$	0	0
$177$	−1.48573e26	−2.09049
$178$	0	0
$179$	−2.32840e25	−0.287904	−0.143952	−	0.989585i	$-0.545981\pi$
$179$	−2.32840e25	−0.287904	−0.143952	+	0.989585i	$0.545981\pi$
$180$	0	0
$181$	−4.11564e24	−0.0447851	−0.0223925	−	0.999749i	$-0.507128\pi$
$181$	−4.11564e24	−0.0447851	−0.0223925	+	0.999749i	$0.507128\pi$
$182$	0	0
$183$	−8.02166e25	−0.769266
$184$	0	0
$185$	2.13451e26	1.80644
$186$	0	0
$187$	−1.78470e24	−0.0133471
$188$	0	0
$189$	4.10588e25	0.271704
$190$	0	0
$191$	1.45985e26	0.855906	0.427953	−	0.903801i	$-0.359235\pi$
$191$	1.45985e26	0.855906	0.427953	+	0.903801i	$0.359235\pi$
$192$	0	0
$193$	2.88936e25	0.150277	0.0751386	−	0.997173i	$-0.476060\pi$
$193$	2.88936e25	0.150277	0.0751386	+	0.997173i	$0.476060\pi$
$194$	0	0
$195$	−3.28855e26	−1.51917
$196$	0	0
$197$	1.53914e26	0.632289	0.316145	−	0.948711i	$-0.397612\pi$
$197$	1.53914e26	0.632289	0.316145	+	0.948711i	$0.397612\pi$
$198$	0	0
$199$	2.90017e26	1.06075	0.530375	−	0.847763i	$-0.322051\pi$
$199$	2.90017e26	1.06075	0.530375	+	0.847763i	$0.322051\pi$
$200$	0	0
$201$	6.11517e26	1.99367
$202$	0	0
$203$	−1.93856e26	−0.563994
$204$	0	0
$205$	−7.08871e26	−1.84246
$206$	0	0
$207$	9.84356e26	2.28820
$208$	0	0
$209$	7.73236e24	0.0160927
$210$	0	0
$211$	3.44005e26	0.641678	0.320839	−	0.947134i	$-0.396035\pi$
$211$	3.44005e26	0.641678	0.320839	+	0.947134i	$0.396035\pi$
$212$	0	0
$213$	1.49278e27	2.49821
$214$	0	0
$215$	8.68655e26	1.30558
$216$	0	0
$217$	−5.84894e25	−0.0790297
$218$	0	0
$219$	1.19857e27	1.45732
$220$	0	0
$221$	7.94428e26	0.870048
$222$	0	0
$223$	−1.05047e27	−1.03724	−0.518621	−	0.855005i	$-0.673554\pi$
$223$	−1.05047e27	−1.03724	−0.518621	+	0.855005i	$0.673554\pi$
$224$	0	0
$225$	9.48053e26	0.844760
$226$	0	0
$227$	−1.62638e27	−1.30895	−0.654476	−	0.756083i	$-0.727111\pi$
$227$	−1.62638e27	−1.30895	−0.654476	+	0.756083i	$0.727111\pi$
$228$	0	0
$229$	2.54526e27	1.85193	0.925965	−	0.377609i	$-0.123253\pi$
$229$	2.54526e27	1.85193	0.925965	+	0.377609i	$0.123253\pi$
$230$	0	0
$231$	−1.03960e25	−0.00684432
$232$	0	0
$233$	−1.01183e26	−0.0603272	−0.0301636	−	0.999545i	$-0.509603\pi$
$233$	−1.01183e26	−0.0603272	−0.0301636	+	0.999545i	$0.509603\pi$
$234$	0	0
$235$	1.15065e27	0.621816
$236$	0	0
$237$	−5.23426e26	−0.256596
$238$	0	0
$239$	−1.27089e26	−0.0565631	−0.0282816	−	0.999600i	$-0.509004\pi$
$239$	−1.27089e26	−0.0565631	−0.0282816	+	0.999600i	$0.509004\pi$
$240$	0	0
$241$	−3.81838e26	−0.154413	−0.0772063	−	0.997015i	$-0.524600\pi$
$241$	−3.81838e26	−0.154413	−0.0772063	+	0.997015i	$0.524600\pi$
$242$	0	0
$243$	3.33264e27	1.22551
$244$	0	0
$245$	−3.24073e27	−1.08451
$246$	0	0
$247$	−3.44192e27	−1.04903
$248$	0	0
$249$	5.94733e27	1.65207
$250$	0	0
$251$	−6.90748e27	−1.75014	−0.875068	−	0.484000i	$-0.839183\pi$
$251$	−6.90748e27	−1.75014	−0.875068	+	0.484000i	$0.839183\pi$
$252$	0	0
$253$	−7.95889e25	−0.0184063
$254$	0	0
$255$	−1.05433e28	−2.22723
$256$	0	0
$257$	5.16428e27	0.997191	0.498596	−	0.866835i	$-0.333849\pi$
$257$	5.16428e27	0.997191	0.498596	+	0.866835i	$0.333849\pi$
$258$	0	0
$259$	−3.00367e27	−0.530524
$260$	0	0
$261$	1.39054e28	2.24811
$262$	0	0
$263$	−3.84873e27	−0.569936	−0.284968	−	0.958537i	$-0.591983\pi$
$263$	−3.84873e27	−0.569936	−0.284968	+	0.958537i	$0.591983\pi$
$264$	0	0
$265$	1.32696e28	1.80107
$266$	0	0
$267$	2.12352e28	2.64348
$268$	0	0
$269$	7.95509e27	0.908853	0.454427	−	0.890784i	$-0.349844\pi$
$269$	7.95509e27	0.908853	0.454427	+	0.890784i	$0.349844\pi$
$270$	0	0
$271$	−8.71026e27	−0.913869	−0.456935	−	0.889500i	$-0.651053\pi$
$271$	−8.71026e27	−0.913869	−0.456935	+	0.889500i	$0.651053\pi$
$272$	0	0
$273$	4.62761e27	0.446156
$274$	0	0
$275$	−7.66536e25	−0.00679527
$276$	0	0
$277$	1.12887e28	0.920721	0.460361	−	0.887732i	$-0.347720\pi$
$277$	1.12887e28	0.920721	0.460361	+	0.887732i	$0.347720\pi$
$278$	0	0
$279$	4.19547e27	0.315016
$280$	0	0
$281$	−2.35031e27	−0.162556	−0.0812778	−	0.996691i	$-0.525900\pi$
$281$	−2.35031e27	−0.162556	−0.0812778	+	0.996691i	$0.525900\pi$
$282$	0	0
$283$	6.30983e27	0.402229	0.201114	−	0.979568i	$-0.435544\pi$
$283$	6.30983e27	0.402229	0.201114	+	0.979568i	$0.435544\pi$
$284$	0	0
$285$	4.56797e28	2.68539
$286$	0	0
$287$	9.97516e27	0.541101
$288$	0	0
$289$	5.50230e27	0.275562
$290$	0	0
$291$	−4.46253e28	−2.06449
$292$	0	0
$293$	−2.47568e28	−1.05856	−0.529282	−	0.848446i	$-0.677539\pi$
$293$	−2.47568e28	−1.05856	−0.529282	+	0.848446i	$0.677539\pi$
$294$	0	0
$295$	4.22249e28	1.66961
$296$	0	0
$297$	2.38128e26	0.00871186
$298$	0	0
$299$	3.54276e28	1.19984
$300$	0	0
$301$	−1.22236e28	−0.383429
$302$	0	0
$303$	−9.91866e27	−0.288312
$304$	0	0
$305$	2.27978e28	0.614391
$306$	0	0
$307$	6.03437e28	1.50848	0.754241	−	0.656597i	$-0.228005\pi$
$307$	6.03437e28	1.50848	0.754241	+	0.656597i	$0.228005\pi$
$308$	0	0
$309$	−3.08145e28	−0.714878
$310$	0	0
$311$	7.80203e28	1.68060	0.840298	−	0.542125i	$-0.182380\pi$
$311$	7.80203e28	1.68060	0.840298	+	0.542125i	$0.182380\pi$
$312$	0	0
$313$	3.19747e28	0.639803	0.319902	−	0.947451i	$-0.396350\pi$
$313$	3.19747e28	0.639803	0.319902	+	0.947451i	$0.396350\pi$
$314$	0	0
$315$	−3.65423e28	−0.679556
$316$	0	0
$317$	8.97518e27	0.155189	0.0775946	−	0.996985i	$-0.475276\pi$
$317$	8.97518e27	0.155189	0.0775946	+	0.996985i	$0.475276\pi$
$318$	0	0
$319$	−1.12430e27	−0.0180838
$320$	0	0
$321$	9.27397e28	1.38822
$322$	0	0
$323$	−1.10350e29	−1.53796
$324$	0	0
$325$	3.41210e28	0.442958
$326$	0	0
$327$	1.30964e29	1.58435
$328$	0	0
$329$	−1.61918e28	−0.182617
$330$	0	0
$331$	−7.59548e28	−0.798975	−0.399487	−	0.916739i	$-0.630812\pi$
$331$	−7.59548e28	−0.798975	−0.399487	+	0.916739i	$0.630812\pi$
$332$	0	0
$333$	2.15454e29	2.11469
$334$	0	0
$335$	−1.73795e29	−1.59229
$336$	0	0
$337$	5.31695e28	0.454903	0.227451	−	0.973789i	$-0.426961\pi$
$337$	5.31695e28	0.454903	0.227451	+	0.973789i	$0.426961\pi$
$338$	0	0
$339$	−2.21482e29	−1.77028
$340$	0	0
$341$	−3.39219e26	−0.00253399
$342$	0	0
$343$	9.83752e28	0.687074
$344$	0	0
$345$	−4.70179e29	−3.07145
$346$	0	0
$347$	2.79913e29	1.71094	0.855469	−	0.517854i	$-0.173269\pi$
$347$	2.79913e29	1.71094	0.855469	+	0.517854i	$0.173269\pi$
$348$	0	0
$349$	−2.34925e29	−1.34411	−0.672057	−	0.740499i	$-0.734589\pi$
$349$	−2.34925e29	−1.34411	−0.672057	+	0.740499i	$0.734589\pi$
$350$	0	0
$351$	−1.05998e29	−0.567894
$352$	0	0
$353$	1.57851e29	0.792205	0.396103	−	0.918206i	$-0.370362\pi$
$353$	1.57851e29	0.792205	0.396103	+	0.918206i	$0.370362\pi$
$354$	0	0
$355$	−4.24251e29	−1.99525
$356$	0	0
$357$	1.48364e29	0.654101
$358$	0	0
$359$	−4.20172e29	−1.73717	−0.868583	−	0.495544i	$-0.834969\pi$
$359$	−4.20172e29	−1.73717	−0.868583	+	0.495544i	$0.834969\pi$
$360$	0	0
$361$	2.20272e29	0.854330
$362$	0	0
$363$	4.31657e29	1.57113
$364$	0	0
$365$	−3.40637e29	−1.16392
$366$	0	0
$367$	−3.45845e29	−1.10974	−0.554871	−	0.831936i	$-0.687232\pi$
$367$	−3.45845e29	−1.10974	−0.554871	+	0.831936i	$0.687232\pi$
$368$	0	0
$369$	−7.15522e29	−2.15685
$370$	0	0
$371$	−1.86729e29	−0.528946
$372$	0	0
$373$	−4.70092e29	−1.25179	−0.625895	−	0.779907i	$-0.715266\pi$
$373$	−4.70092e29	−1.25179	−0.625895	+	0.779907i	$0.715266\pi$
$374$	0	0
$375$	3.34702e29	0.838106
$376$	0	0
$377$	5.00463e29	1.17882
$378$	0	0
$379$	7.13881e29	1.58225	0.791125	−	0.611655i	$-0.209496\pi$
$379$	7.13881e29	1.58225	0.791125	+	0.611655i	$0.209496\pi$
$380$	0	0
$381$	−5.97331e29	−1.24617
$382$	0	0
$383$	−2.93482e29	−0.576495	−0.288248	−	0.957556i	$-0.593073\pi$
$383$	−2.93482e29	−0.576495	−0.288248	+	0.957556i	$0.593073\pi$
$384$	0	0
$385$	2.95458e27	0.00546636
$386$	0	0
$387$	8.76806e29	1.52837
$388$	0	0
$389$	−5.81114e29	−0.954642	−0.477321	−	0.878729i	$-0.658392\pi$
$389$	−5.81114e29	−0.954642	−0.477321	+	0.878729i	$0.658392\pi$
$390$	0	0
$391$	1.13583e30	1.75906
$392$	0	0
$393$	−1.19734e30	−1.74865
$394$	0	0
$395$	1.48759e29	0.204936
$396$	0	0
$397$	6.24678e29	0.812017	0.406009	−	0.913869i	$-0.366920\pi$
$397$	6.24678e29	0.812017	0.406009	+	0.913869i	$0.366920\pi$
$398$	0	0
$399$	−6.42800e29	−0.788656
$400$	0	0
$401$	−1.34800e30	−1.56145	−0.780726	−	0.624874i	$-0.785150\pi$
$401$	−1.34800e30	−1.56145	−0.780726	+	0.624874i	$0.785150\pi$
$402$	0	0
$403$	1.50997e29	0.165182
$404$	0	0
$405$	−3.77408e29	−0.390012
$406$	0	0
$407$	−1.74203e28	−0.0170106
$408$	0	0
$409$	1.13048e30	1.04338	0.521691	−	0.853135i	$-0.325302\pi$
$409$	1.13048e30	1.04338	0.521691	+	0.853135i	$0.325302\pi$
$410$	0	0
$411$	1.15007e30	1.00356
$412$	0	0
$413$	−5.94184e29	−0.490338
$414$	0	0
$415$	−1.69025e30	−1.31946
$416$	0	0
$417$	−3.18101e30	−2.34964
$418$	0	0
$419$	4.04043e29	0.282466	0.141233	−	0.989976i	$-0.454893\pi$
$419$	4.04043e29	0.282466	0.141233	+	0.989976i	$0.454893\pi$
$420$	0	0
$421$	2.59101e30	1.71485	0.857423	−	0.514613i	$-0.172064\pi$
$421$	2.59101e30	1.71485	0.857423	+	0.514613i	$0.172064\pi$
$422$	0	0
$423$	1.16144e30	0.727920
$424$	0	0
$425$	1.09394e30	0.649413
$426$	0	0
$427$	−3.20808e29	−0.180437
$428$	0	0
$429$	2.68386e28	0.0143054
$430$	0	0
$431$	3.19912e30	1.61637	0.808187	−	0.588926i	$-0.200449\pi$
$431$	3.19912e30	1.61637	0.808187	+	0.588926i	$0.200449\pi$
$432$	0	0
$433$	4.05890e30	1.94445	0.972226	−	0.234043i	$-0.0751957\pi$
$433$	4.05890e30	1.94445	0.972226	+	0.234043i	$0.0751957\pi$
$434$	0	0
$435$	−6.64192e30	−3.01764
$436$	0	0
$437$	−4.92108e30	−2.12092
$438$	0	0
$439$	7.04853e29	0.288242	0.144121	−	0.989560i	$-0.453965\pi$
$439$	7.04853e29	0.288242	0.144121	+	0.989560i	$0.453965\pi$
$440$	0	0
$441$	−3.27114e30	−1.26956
$442$	0	0
$443$	−2.30793e30	−0.850316	−0.425158	−	0.905119i	$-0.639781\pi$
$443$	−2.30793e30	−0.850316	−0.425158	+	0.905119i	$0.639781\pi$
$444$	0	0
$445$	−6.03510e30	−2.11127
$446$	0	0
$447$	−1.86546e30	−0.619798
$448$	0	0
$449$	−1.20239e30	−0.379500	−0.189750	−	0.981832i	$-0.560768\pi$
$449$	−1.20239e30	−0.379500	−0.189750	+	0.981832i	$0.560768\pi$
$450$	0	0
$451$	5.78527e28	0.0173497
$452$	0	0
$453$	3.76635e30	1.07347
$454$	0	0
$455$	−1.31518e30	−0.356332
$456$	0	0
$457$	−3.44692e29	−0.0887962	−0.0443981	−	0.999014i	$-0.514137\pi$
$457$	−3.44692e29	−0.0887962	−0.0443981	+	0.999014i	$0.514137\pi$
$458$	0	0
$459$	−3.39838e30	−0.832579
$460$	0	0
$461$	−4.54108e30	−1.05827	−0.529137	−	0.848536i	$-0.677484\pi$
$461$	−4.54108e30	−1.05827	−0.529137	+	0.848536i	$0.677484\pi$
$462$	0	0
$463$	−4.40623e29	−0.0976980	−0.0488490	−	0.998806i	$-0.515555\pi$
$463$	−4.40623e29	−0.0976980	−0.0488490	+	0.998806i	$0.515555\pi$
$464$	0	0
$465$	−2.00397e30	−0.422846
$466$	0	0
$467$	−6.97174e28	−0.0140022	−0.00700111	−	0.999975i	$-0.502229\pi$
$467$	−6.97174e28	−0.0140022	−0.00700111	+	0.999975i	$0.502229\pi$
$468$	0	0
$469$	2.44562e30	0.467630
$470$	0	0
$471$	−2.95195e30	−0.537488
$472$	0	0
$473$	−7.08930e28	−0.0122942
$474$	0	0
$475$	−4.73959e30	−0.783004
$476$	0	0
$477$	1.33941e31	2.10840
$478$	0	0
$479$	1.15281e31	1.72942	0.864711	−	0.502270i	$-0.167502\pi$
$479$	1.15281e31	1.72942	0.864711	+	0.502270i	$0.167502\pi$
$480$	0	0
$481$	7.75433e30	1.10886
$482$	0	0
$483$	6.61632e30	0.902037
$484$	0	0
$485$	1.26826e31	1.64885
$486$	0	0
$487$	6.30565e29	0.0781892	0.0390946	−	0.999236i	$-0.487553\pi$
$487$	6.30565e29	0.0781892	0.0390946	+	0.999236i	$0.487553\pi$
$488$	0	0
$489$	5.28003e30	0.624575
$490$	0	0
$491$	−3.73472e30	−0.421523	−0.210762	−	0.977538i	$-0.567594\pi$
$491$	−3.73472e30	−0.421523	−0.210762	+	0.977538i	$0.567594\pi$
$492$	0	0
$493$	1.60452e31	1.72824
$494$	0	0
$495$	−2.11934e29	−0.0217891
$496$	0	0
$497$	5.97002e30	0.585973
$498$	0	0
$499$	1.94490e31	1.82281	0.911405	−	0.411510i	$-0.134999\pi$
$499$	1.94490e31	1.82281	0.911405	+	0.411510i	$0.134999\pi$
$500$	0	0
$501$	−1.84042e31	−1.64734
$502$	0	0
$503$	−3.16992e30	−0.271030	−0.135515	−	0.990775i	$-0.543269\pi$
$503$	−3.16992e30	−0.271030	−0.135515	+	0.990775i	$0.543269\pi$
$504$	0	0
$505$	2.81891e30	0.230266
$506$	0	0
$507$	8.18422e30	0.638830
$508$	0	0
$509$	1.40215e30	0.104602	0.0523009	−	0.998631i	$-0.483345\pi$
$509$	1.40215e30	0.104602	0.0523009	+	0.998631i	$0.483345\pi$
$510$	0	0
$511$	4.79341e30	0.341825
$512$	0	0
$513$	1.47237e31	1.00385
$514$	0	0
$515$	8.75756e30	0.570953
$516$	0	0
$517$	−9.39070e28	−0.00585540
$518$	0	0
$519$	−1.43407e31	−0.855353
$520$	0	0
$521$	−2.02349e30	−0.115469	−0.0577346	−	0.998332i	$-0.518388\pi$
$521$	−2.02349e30	−0.115469	−0.0577346	+	0.998332i	$0.518388\pi$
$522$	0	0
$523$	1.54046e31	0.841162	0.420581	−	0.907255i	$-0.361826\pi$
$523$	1.54046e31	0.841162	0.420581	+	0.907255i	$0.361826\pi$
$524$	0	0
$525$	6.37230e30	0.333016
$526$	0	0
$527$	4.84108e30	0.242170
$528$	0	0
$529$	2.97721e31	1.42583
$530$	0	0
$531$	4.26211e31	1.95451
$532$	0	0
$533$	−2.57521e31	−1.13097
$534$	0	0
$535$	−2.63569e31	−1.10873
$536$	0	0
$537$	1.12260e31	0.452398
$538$	0	0
$539$	2.64484e29	0.0102124
$540$	0	0
$541$	2.80348e31	1.03736	0.518679	−	0.854969i	$-0.326424\pi$
$541$	2.80348e31	1.03736	0.518679	+	0.854969i	$0.326424\pi$
$542$	0	0
$543$	1.98429e30	0.0703730
$544$	0	0
$545$	−3.72203e31	−1.26538
$546$	0	0
$547$	−5.69365e31	−1.85582	−0.927912	−	0.372799i	$-0.878398\pi$
$547$	−5.69365e31	−1.85582	−0.927912	+	0.372799i	$0.878398\pi$
$548$	0	0
$549$	2.30117e31	0.719228
$550$	0	0
$551$	−6.95169e31	−2.08376
$552$	0	0
$553$	−2.09333e30	−0.0601863
$554$	0	0
$555$	−1.02912e32	−2.83855
$556$	0	0
$557$	4.60452e31	1.21857	0.609283	−	0.792953i	$-0.291457\pi$
$557$	4.60452e31	1.21857	0.609283	+	0.792953i	$0.291457\pi$
$558$	0	0
$559$	3.15568e31	0.801414
$560$	0	0
$561$	8.60464e29	0.0209730
$562$	0	0
$563$	4.92698e31	1.15275	0.576374	−	0.817186i	$-0.304467\pi$
$563$	4.92698e31	1.15275	0.576374	+	0.817186i	$0.304467\pi$
$564$	0	0
$565$	6.29458e31	1.41387
$566$	0	0
$567$	5.31085e30	0.114540
$568$	0	0
$569$	1.16166e31	0.240597	0.120298	−	0.992738i	$-0.461615\pi$
$569$	1.16166e31	0.240597	0.120298	+	0.992738i	$0.461615\pi$
$570$	0	0
$571$	−5.41301e30	−0.107677	−0.0538386	−	0.998550i	$-0.517146\pi$
$571$	−5.41301e30	−0.107677	−0.0538386	+	0.998550i	$0.517146\pi$
$572$	0	0
$573$	−7.03845e31	−1.34493
$574$	0	0
$575$	4.87844e31	0.895573
$576$	0	0
$577$	−2.24619e31	−0.396209	−0.198105	−	0.980181i	$-0.563479\pi$
$577$	−2.24619e31	−0.396209	−0.198105	+	0.980181i	$0.563479\pi$
$578$	0	0
$579$	−1.39306e31	−0.236138
$580$	0	0
$581$	2.37850e31	0.387505
$582$	0	0
$583$	−1.08297e30	−0.0169600
$584$	0	0
$585$	9.43384e31	1.42035
$586$	0	0
$587$	1.13331e31	0.164063	0.0820314	−	0.996630i	$-0.473859\pi$
$587$	1.13331e31	0.164063	0.0820314	+	0.996630i	$0.473859\pi$
$588$	0	0
$589$	−2.09743e31	−0.291986
$590$	0	0
$591$	−7.42069e31	−0.993547
$592$	0	0
$593$	−2.04143e31	−0.262909	−0.131455	−	0.991322i	$-0.541965\pi$
$593$	−2.04143e31	−0.262909	−0.131455	+	0.991322i	$0.541965\pi$
$594$	0	0
$595$	−4.21656e31	−0.522412
$596$	0	0
$597$	−1.39827e32	−1.66681
$598$	0	0
$599$	6.65946e31	0.763889	0.381945	−	0.924185i	$-0.375255\pi$
$599$	6.65946e31	0.763889	0.381945	+	0.924185i	$0.375255\pi$
$600$	0	0
$601$	−8.90963e31	−0.983565	−0.491783	−	0.870718i	$-0.663655\pi$
$601$	−8.90963e31	−0.983565	−0.491783	+	0.870718i	$0.663655\pi$
$602$	0	0
$603$	−1.75426e32	−1.86399
$604$	0	0
$605$	−1.22678e32	−1.25482
$606$	0	0
$607$	1.10171e32	1.08491	0.542457	−	0.840083i	$-0.317494\pi$
$607$	1.10171e32	1.08491	0.542457	+	0.840083i	$0.317494\pi$
$608$	0	0
$609$	9.34645e31	0.886232
$610$	0	0
$611$	4.18011e31	0.381692
$612$	0	0
$613$	5.01871e31	0.441364	0.220682	−	0.975346i	$-0.429172\pi$
$613$	5.01871e31	0.441364	0.220682	+	0.975346i	$0.429172\pi$
$614$	0	0
$615$	3.41770e32	2.89515
$616$	0	0
$617$	−6.65909e31	−0.543420	−0.271710	−	0.962379i	$-0.587589\pi$
$617$	−6.65909e31	−0.543420	−0.271710	+	0.962379i	$0.587589\pi$
$618$	0	0
$619$	1.40432e32	1.10414	0.552068	−	0.833799i	$-0.313839\pi$
$619$	1.40432e32	1.10414	0.552068	+	0.833799i	$0.313839\pi$
$620$	0	0
$621$	−1.51551e32	−1.14817
$622$	0	0
$623$	8.49254e31	0.620047
$624$	0	0
$625$	−1.76836e32	−1.24437
$626$	0	0
$627$	−3.72803e30	−0.0252873
$628$	0	0
$629$	2.48609e32	1.62568
$630$	0	0
$631$	−1.63677e31	−0.103193	−0.0515963	−	0.998668i	$-0.516431\pi$
$631$	−1.63677e31	−0.103193	−0.0515963	+	0.998668i	$0.516431\pi$
$632$	0	0
$633$	−1.65856e32	−1.00830
$634$	0	0
$635$	1.69763e32	0.995281
$636$	0	0
$637$	−1.17730e32	−0.665709
$638$	0	0
$639$	−4.28232e32	−2.33571
$640$	0	0
$641$	−3.15839e32	−1.66187	−0.830937	−	0.556367i	$-0.812195\pi$
$641$	−3.15839e32	−1.66187	−0.830937	+	0.556367i	$0.812195\pi$
$642$	0	0
$643$	1.16414e32	0.590990	0.295495	−	0.955344i	$-0.404515\pi$
$643$	1.16414e32	0.590990	0.295495	+	0.955344i	$0.404515\pi$
$644$	0	0
$645$	−4.18808e32	−2.05153
$646$	0	0
$647$	−1.74026e32	−0.822650	−0.411325	−	0.911489i	$-0.634934\pi$
$647$	−1.74026e32	−0.822650	−0.411325	+	0.911489i	$0.634934\pi$
$648$	0	0
$649$	−3.44607e30	−0.0157221
$650$	0	0
$651$	2.81997e31	0.124183
$652$	0	0
$653$	7.97317e31	0.338945	0.169472	−	0.985535i	$-0.445794\pi$
$653$	7.97317e31	0.338945	0.169472	+	0.985535i	$0.445794\pi$
$654$	0	0
$655$	3.40288e32	1.39660
$656$	0	0
$657$	−3.43833e32	−1.36253
$658$	0	0
$659$	−3.78965e32	−1.45016	−0.725082	−	0.688663i	$-0.758198\pi$
$659$	−3.78965e32	−1.45016	−0.725082	+	0.688663i	$0.758198\pi$
$660$	0	0
$661$	−5.90571e30	−0.0218251	−0.0109125	−	0.999940i	$-0.503474\pi$
$661$	−5.90571e30	−0.0218251	−0.0109125	+	0.999940i	$0.503474\pi$
$662$	0	0
$663$	−3.83020e32	−1.36715
$664$	0	0
$665$	1.82686e32	0.629877
$666$	0	0
$667$	7.15535e32	2.38333
$668$	0	0
$669$	5.06469e32	1.62987
$670$	0	0
$671$	−1.86058e30	−0.00578549
$672$	0	0
$673$	2.31102e32	0.694434	0.347217	−	0.937785i	$-0.387127\pi$
$673$	2.31102e32	0.694434	0.347217	+	0.937785i	$0.387127\pi$
$674$	0	0
$675$	−1.45962e32	−0.423882
$676$	0	0
$677$	−5.19064e32	−1.45697	−0.728486	−	0.685060i	$-0.759776\pi$
$677$	−5.19064e32	−1.45697	−0.728486	+	0.685060i	$0.759776\pi$
$678$	0	0
$679$	−1.78469e32	−0.484240
$680$	0	0
$681$	7.84130e32	2.05682
$682$	0	0
$683$	−9.47861e31	−0.240385	−0.120192	−	0.992751i	$-0.538351\pi$
$683$	−9.47861e31	−0.240385	−0.120192	+	0.992751i	$0.538351\pi$
$684$	0	0
$685$	−3.26855e32	−0.801518
$686$	0	0
$687$	−1.22716e33	−2.91003
$688$	0	0
$689$	4.82063e32	1.10556
$690$	0	0
$691$	−4.65757e32	−1.03315	−0.516573	−	0.856243i	$-0.672792\pi$
$691$	−4.65757e32	−1.03315	−0.516573	+	0.856243i	$0.672792\pi$
$692$	0	0
$693$	2.98231e30	0.00639912
$694$	0	0
$695$	9.04053e32	1.87659
$696$	0	0
$697$	−8.25629e32	−1.65809
$698$	0	0
$699$	4.87836e31	0.0947951
$700$	0	0
$701$	3.98936e32	0.750146	0.375073	−	0.926995i	$-0.377618\pi$
$701$	3.98936e32	0.750146	0.375073	+	0.926995i	$0.377618\pi$
$702$	0	0
$703$	−1.07712e33	−1.96009
$704$	0	0
$705$	−5.54765e32	−0.977090
$706$	0	0
$707$	−3.96674e31	−0.0676256
$708$	0	0
$709$	−7.85157e32	−1.29576	−0.647880	−	0.761742i	$-0.724344\pi$
$709$	−7.85157e32	−1.29576	−0.647880	+	0.761742i	$0.724344\pi$
$710$	0	0
$711$	1.50155e32	0.239905
$712$	0	0
$713$	2.15888e32	0.333964
$714$	0	0
$715$	−7.62762e30	−0.0114253
$716$	0	0
$717$	6.12740e31	0.0888805
$718$	0	0
$719$	−2.17105e32	−0.304992	−0.152496	−	0.988304i	$-0.548731\pi$
$719$	−2.17105e32	−0.304992	−0.152496	+	0.988304i	$0.548731\pi$
$720$	0	0
$721$	−1.23236e32	−0.167680
$722$	0	0
$723$	1.84097e32	0.242636
$724$	0	0
$725$	6.89146e32	0.879881
$726$	0	0
$727$	6.30412e32	0.779792	0.389896	−	0.920859i	$-0.372511\pi$
$727$	6.30412e32	0.779792	0.389896	+	0.920859i	$0.372511\pi$
$728$	0	0
$729$	−1.34748e33	−1.61493
$730$	0	0
$731$	1.01173e33	1.17494
$732$	0	0
$733$	4.83137e32	0.543719	0.271860	−	0.962337i	$-0.412361\pi$
$733$	4.83137e32	0.543719	0.271860	+	0.962337i	$0.412361\pi$
$734$	0	0
$735$	1.56246e33	1.70414
$736$	0	0
$737$	1.41838e31	0.0149940
$738$	0	0
$739$	3.47318e32	0.355890	0.177945	−	0.984040i	$-0.443055\pi$
$739$	3.47318e32	0.355890	0.177945	+	0.984040i	$0.443055\pi$
$740$	0	0
$741$	1.65947e33	1.64839
$742$	0	0
$743$	1.19764e33	1.15334	0.576668	−	0.816978i	$-0.304353\pi$
$743$	1.19764e33	1.15334	0.576668	+	0.816978i	$0.304353\pi$
$744$	0	0
$745$	5.30170e32	0.495015
$746$	0	0
$747$	−1.70611e33	−1.54461
$748$	0	0
$749$	3.70892e32	0.325616
$750$	0	0
$751$	1.66045e33	1.41373	0.706863	−	0.707350i	$-0.250110\pi$
$751$	1.66045e33	1.41373	0.706863	+	0.707350i	$0.250110\pi$
$752$	0	0
$753$	3.33033e33	2.75007
$754$	0	0
$755$	−1.07041e33	−0.857353
$756$	0	0
$757$	−1.02358e33	−0.795276	−0.397638	−	0.917542i	$-0.630170\pi$
$757$	−1.02358e33	−0.795276	−0.397638	+	0.917542i	$0.630170\pi$
$758$	0	0
$759$	3.83725e31	0.0289227
$760$	0	0
$761$	1.48102e33	1.08302	0.541512	−	0.840693i	$-0.317852\pi$
$761$	1.48102e33	1.08302	0.541512	+	0.840693i	$0.317852\pi$
$762$	0	0
$763$	5.23761e32	0.371621
$764$	0	0
$765$	3.02455e33	2.08235
$766$	0	0
$767$	1.53396e33	1.02487
$768$	0	0
$769$	1.05398e33	0.683405	0.341703	−	0.939808i	$-0.388996\pi$
$769$	1.05398e33	0.683405	0.341703	+	0.939808i	$0.388996\pi$
$770$	0	0
$771$	−2.48987e33	−1.56694
$772$	0	0
$773$	−1.22665e33	−0.749302	−0.374651	−	0.927166i	$-0.622237\pi$
$773$	−1.22665e33	−0.749302	−0.374651	+	0.927166i	$0.622237\pi$
$774$	0	0
$775$	2.07926e32	0.123293
$776$	0	0
$777$	1.44817e33	0.833638
$778$	0	0
$779$	3.57710e33	1.99917
$780$	0	0
$781$	3.46242e31	0.0187885
$782$	0	0
$783$	−2.14086e33	−1.12805
$784$	0	0
$785$	8.38953e32	0.429276
$786$	0	0
$787$	3.68051e33	1.82894	0.914469	−	0.404656i	$-0.132609\pi$
$787$	3.68051e33	1.82894	0.914469	+	0.404656i	$0.132609\pi$
$788$	0	0
$789$	1.85560e33	0.895568
$790$	0	0
$791$	−8.85768e32	−0.415231
$792$	0	0
$793$	8.28205e32	0.377135
$794$	0	0
$795$	−6.39773e33	−2.83011
$796$	0	0
$797$	−2.74746e33	−1.18076	−0.590379	−	0.807126i	$-0.701022\pi$
$797$	−2.74746e33	−1.18076	−0.590379	+	0.807126i	$0.701022\pi$
$798$	0	0
$799$	1.34017e33	0.559592
$800$	0	0
$801$	−6.09173e33	−2.47153
$802$	0	0
$803$	2.78002e31	0.0109602
$804$	0	0
$805$	−1.88038e33	−0.720431
$806$	0	0
$807$	−3.83541e33	−1.42813
$808$	0	0
$809$	4.65342e33	1.68409	0.842043	−	0.539411i	$-0.181353\pi$
$809$	4.65342e33	1.68409	0.842043	+	0.539411i	$0.181353\pi$
$810$	0	0
$811$	−1.90593e33	−0.670452	−0.335226	−	0.942138i	$-0.608813\pi$
$811$	−1.90593e33	−0.670452	−0.335226	+	0.942138i	$0.608813\pi$
$812$	0	0
$813$	4.19951e33	1.43601
$814$	0	0
$815$	−1.50060e33	−0.498830
$816$	0	0
$817$	−4.38340e33	−1.41663
$818$	0	0
$819$	−1.32752e33	−0.417135
$820$	0	0
$821$	3.52358e33	1.07656	0.538280	−	0.842766i	$-0.319074\pi$
$821$	3.52358e33	1.07656	0.538280	+	0.842766i	$0.319074\pi$
$822$	0	0
$823$	6.68634e32	0.198651	0.0993254	−	0.995055i	$-0.468332\pi$
$823$	6.68634e32	0.198651	0.0993254	+	0.995055i	$0.468332\pi$
$824$	0	0
$825$	3.69573e31	0.0106777
$826$	0	0
$827$	−1.61167e33	−0.452859	−0.226429	−	0.974028i	$-0.572705\pi$
$827$	−1.61167e33	−0.452859	−0.226429	+	0.974028i	$0.572705\pi$
$828$	0	0
$829$	1.79490e33	0.490528	0.245264	−	0.969456i	$-0.421125\pi$
$829$	1.79490e33	0.490528	0.245264	+	0.969456i	$0.421125\pi$
$830$	0	0
$831$	−5.44268e33	−1.44677
$832$	0	0
$833$	−3.77451e33	−0.975984
$834$	0	0
$835$	5.23052e33	1.31568
$836$	0	0
$837$	−6.45932e32	−0.158068
$838$	0	0
$839$	−1.13694e33	−0.270693	−0.135346	−	0.990798i	$-0.543215\pi$
$839$	−1.13694e33	−0.270693	−0.135346	+	0.990798i	$0.543215\pi$
$840$	0	0
$841$	5.79119e33	1.34157
$842$	0	0
$843$	1.13316e33	0.255432
$844$	0	0
$845$	−2.32598e33	−0.510215
$846$	0	0
$847$	1.72631e33	0.368520
$848$	0	0
$849$	−3.04218e33	−0.632042
$850$	0	0
$851$	1.10867e34	2.24189
$852$	0	0
$853$	−6.94512e33	−1.36699	−0.683496	−	0.729954i	$-0.739541\pi$
$853$	−6.94512e33	−1.36699	−0.683496	+	0.729954i	$0.739541\pi$
$854$	0	0
$855$	−1.31041e34	−2.51071
$856$	0	0
$857$	−7.35117e33	−1.37112	−0.685562	−	0.728014i	$-0.740444\pi$
$857$	−7.35117e33	−1.37112	−0.685562	+	0.728014i	$0.740444\pi$
$858$	0	0
$859$	8.07773e32	0.146679	0.0733395	−	0.997307i	$-0.476634\pi$
$859$	8.07773e32	0.146679	0.0733395	+	0.997307i	$0.476634\pi$
$860$	0	0
$861$	−4.80936e33	−0.850259
$862$	0	0
$863$	9.25691e33	1.59346	0.796731	−	0.604334i	$-0.206561\pi$
$863$	9.25691e33	1.59346	0.796731	+	0.604334i	$0.206561\pi$
$864$	0	0
$865$	4.07567e33	0.683146
$866$	0	0
$867$	−2.65284e33	−0.433004
$868$	0	0
$869$	−1.21406e31	−0.00192980
$870$	0	0
$871$	−6.31367e33	−0.977402
$872$	0	0
$873$	1.28017e34	1.93020
$874$	0	0
$875$	1.33857e33	0.196584
$876$	0	0
$877$	6.91188e33	0.988782	0.494391	−	0.869240i	$-0.335391\pi$
$877$	6.91188e33	0.988782	0.494391	+	0.869240i	$0.335391\pi$
$878$	0	0
$879$	1.19361e34	1.66337
$880$	0	0
$881$	−1.56133e33	−0.211969	−0.105985	−	0.994368i	$-0.533799\pi$
$881$	−1.56133e33	−0.211969	−0.105985	+	0.994368i	$0.533799\pi$
$882$	0	0
$883$	1.71974e33	0.227465	0.113733	−	0.993511i	$-0.463719\pi$
$883$	1.71974e33	0.227465	0.113733	+	0.993511i	$0.463719\pi$
$884$	0	0
$885$	−2.03580e34	−2.62354
$886$	0	0
$887$	6.24701e33	0.784423	0.392212	−	0.919875i	$-0.371710\pi$
$887$	6.24701e33	0.784423	0.392212	+	0.919875i	$0.371710\pi$
$888$	0	0
$889$	−2.38889e33	−0.292298
$890$	0	0
$891$	3.08012e31	0.00367260
$892$	0	0
$893$	−5.80639e33	−0.674706
$894$	0	0
$895$	−3.19046e33	−0.361317
$896$	0	0
$897$	−1.70808e34	−1.88537
$898$	0	0
$899$	3.04971e33	0.328112
$900$	0	0
$901$	1.54553e34	1.62084
$902$	0	0
$903$	5.89342e33	0.602502
$904$	0	0
$905$	−5.63940e32	−0.0562049
$906$	0	0
$907$	3.90645e33	0.379576	0.189788	−	0.981825i	$-0.439220\pi$
$907$	3.90645e33	0.379576	0.189788	+	0.981825i	$0.439220\pi$
$908$	0	0
$909$	2.84536e33	0.269558
$910$	0	0
$911$	1.29406e34	1.19535	0.597673	−	0.801740i	$-0.296092\pi$
$911$	1.29406e34	1.19535	0.597673	+	0.801740i	$0.296092\pi$
$912$	0	0
$913$	1.37945e32	0.0124249
$914$	0	0
$915$	−1.09916e34	−0.965423
$916$	0	0
$917$	−4.78850e33	−0.410159
$918$	0	0
$919$	1.10840e34	0.925909	0.462954	−	0.886382i	$-0.346789\pi$
$919$	1.10840e34	0.925909	0.462954	+	0.886382i	$0.346789\pi$
$920$	0	0
$921$	−2.90937e34	−2.37035
$922$	0	0
$923$	−1.54123e34	−1.22475
$924$	0	0
$925$	1.06779e34	0.827664
$926$	0	0
$927$	8.83974e33	0.668378
$928$	0	0
$929$	−1.20238e34	−0.886871	−0.443436	−	0.896306i	$-0.646241\pi$
$929$	−1.20238e34	−0.886871	−0.443436	+	0.896306i	$0.646241\pi$
$930$	0	0
$931$	1.63533e34	1.17675
$932$	0	0
$933$	−3.76162e34	−2.64080
$934$	0	0
$935$	−2.44546e32	−0.0167505
$936$	0	0
$937$	1.79130e33	0.119719	0.0598596	−	0.998207i	$-0.480935\pi$
$937$	1.79130e33	0.119719	0.0598596	+	0.998207i	$0.480935\pi$
$938$	0	0
$939$	−1.54161e34	−1.00535
$940$	0	0
$941$	1.00098e34	0.637010	0.318505	−	0.947921i	$-0.396819\pi$
$941$	1.00098e34	0.637010	0.318505	+	0.947921i	$0.396819\pi$
$942$	0	0
$943$	−3.68190e34	−2.28659
$944$	0	0
$945$	5.62604e33	0.340986
$946$	0	0
$947$	−2.99345e34	−1.77071	−0.885353	−	0.464919i	$-0.846083\pi$
$947$	−2.99345e34	−1.77071	−0.885353	+	0.464919i	$0.846083\pi$
$948$	0	0
$949$	−1.23748e34	−0.714456
$950$	0	0
$951$	−4.32724e33	−0.243857
$952$	0	0
$953$	6.57345e32	0.0361597	0.0180799	−	0.999837i	$-0.494245\pi$
$953$	6.57345e32	0.0361597	0.0180799	+	0.999837i	$0.494245\pi$
$954$	0	0
$955$	2.00035e34	1.07415
$956$	0	0
$957$	5.42063e32	0.0284160
$958$	0	0
$959$	4.59947e33	0.235393
$960$	0	0
$961$	−1.90932e34	−0.954023
$962$	0	0
$963$	−2.66042e34	−1.29792
$964$	0	0
$965$	3.95911e33	0.188596
$966$	0	0
$967$	1.23180e34	0.572976	0.286488	−	0.958084i	$-0.407512\pi$
$967$	1.23180e34	0.572976	0.286488	+	0.958084i	$0.407512\pi$
$968$	0	0
$969$	5.32035e34	2.41667
$970$	0	0
$971$	−4.31839e34	−1.91558	−0.957792	−	0.287464i	$-0.907188\pi$
$971$	−4.31839e34	−1.91558	−0.957792	+	0.287464i	$0.907188\pi$
$972$	0	0
$973$	−1.27217e34	−0.551124
$974$	0	0
$975$	−1.64509e34	−0.696043
$976$	0	0
$977$	−1.99872e33	−0.0825970	−0.0412985	−	0.999147i	$-0.513149\pi$
$977$	−1.99872e33	−0.0825970	−0.0412985	+	0.999147i	$0.513149\pi$
$978$	0	0
$979$	4.92539e32	0.0198811
$980$	0	0
$981$	−3.75696e34	−1.48130
$982$	0	0
$983$	2.99251e34	1.15258	0.576290	−	0.817245i	$-0.304500\pi$
$983$	2.99251e34	1.15258	0.576290	+	0.817245i	$0.304500\pi$
$984$	0	0
$985$	2.10898e34	0.793517
$986$	0	0
$987$	7.80660e33	0.286956
$988$	0	0
$989$	4.51182e34	1.62030
$990$	0	0
$991$	8.28074e33	0.290551	0.145275	−	0.989391i	$-0.453593\pi$
$991$	8.28074e33	0.290551	0.145275	+	0.989391i	$0.453593\pi$
$992$	0	0
$993$	3.66203e34	1.25547
$994$	0	0
$995$	3.97392e34	1.33123
$996$	0	0
$997$	4.09834e34	1.34157	0.670785	−	0.741652i	$-0.265957\pi$
$997$	4.09834e34	1.34157	0.670785	+	0.741652i	$0.265957\pi$
$998$	0	0
$999$	−3.31712e34	−1.06110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	64.24.a.o.1.1		6
4.3	odd	2		64.24.a.m.1.6		6
8.3	odd	2		32.24.a.e.1.1	yes	6
8.5	even	2		32.24.a.c.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.24.a.c.1.6	✓	6	8.5	even	2
32.24.a.e.1.1	yes	6	8.3	odd	2
64.24.a.m.1.6		6	4.3	odd	2
64.24.a.o.1.1		6	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:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	64.a (trivial)

\(f(q)\)	\(=\)	\(q-482133. q^{3} +1.37024e8 q^{5} -1.92818e9 q^{7} +1.38309e11 q^{9} +O(q^{10})\)	\(q-482133. q^{3} +1.37024e8 q^{5} -1.92818e9 q^{7} +1.38309e11 q^{9} -1.11828e10 q^{11} +4.97784e12 q^{13} -6.60637e13 q^{15} +1.59593e14 q^{17} -6.91449e14 q^{19} +9.29642e14 q^{21} +7.11706e15 q^{23} +6.85458e15 q^{25} -2.12940e16 q^{27} +1.00538e17 q^{29} +3.03339e16 q^{31} +5.39162e15 q^{33} -2.64207e17 q^{35} +1.55777e18 q^{37} -2.39998e18 q^{39} -5.17334e18 q^{41} +6.33945e18 q^{43} +1.89517e19 q^{45} +8.39743e18 q^{47} -2.36509e19 q^{49} -7.69450e19 q^{51} +9.68418e19 q^{53} -1.53231e18 q^{55} +3.33370e20 q^{57} +3.08157e20 q^{59} +1.66378e20 q^{61} -2.66686e20 q^{63} +6.82082e20 q^{65} -1.26836e21 q^{67} -3.43137e21 q^{69} -3.09619e21 q^{71} -2.48597e21 q^{73} -3.30482e21 q^{75} +2.15626e19 q^{77} +1.08565e21 q^{79} -2.75432e21 q^{81} -1.23354e22 q^{83} +2.18680e22 q^{85} -4.84728e22 q^{87} -4.40442e22 q^{89} -9.59820e21 q^{91} -1.46250e22 q^{93} -9.47449e22 q^{95} +9.25580e22 q^{97} -1.54669e21 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 483920 q^{3} + 6100380 q^{5} + 347289696 q^{7} + 260924449726 q^{9}+O(q^{10}) \) 6 * q + 483920 * q^3 + 6100380 * q^5 + 347289696 * q^7 + 260924449726 * q^9	\( 6 q + 483920 q^{3} + 6100380 q^{5} + 347289696 q^{7} + 260924449726 q^{9} + 926871857520 q^{11} + 3684897167820 q^{13} - 105662245358560 q^{15} + 71064722424780 q^{17} - 453921923982960 q^{19} + 17\!\cdots\!80 q^{21}+ \cdots + 39\!\cdots\!40 q^{99}+O(q^{100}) \) 6 * q + 483920 * q^3 + 6100380 * q^5 + 347289696 * q^7 + 260924449726 * q^9 + 926871857520 * q^11 + 3684897167820 * q^13 - 105662245358560 * q^15 + 71064722424780 * q^17 - 453921923982960 * q^19 + 1712900116737280 * q^21 + 7126581767144736 * q^23 + 21617163289317450 * q^25 + 41851914072529184 * q^27 + 90718382478351852 * q^29 - 53660517982277760 * q^31 + 607667723496123520 * q^33 - 843485446441350720 * q^35 - 1178800099078290660 * q^37 - 387144388087503200 * q^39 + 1672300630976121180 * q^41 + 9707130536958833904 * q^43 - 31072675924013630900 * q^45 + 12637324971625378368 * q^47 + 20589514456941037878 * q^49 - 56125446355277416800 * q^51 + 25955354185131109500 * q^53 - 79415390320029033120 * q^55 + 169187096172727794560 * q^57 + 407713345239006043440 * q^59 + 615884547554394402156 * q^61 + 578320926136902243296 * q^63 - 1095923787012414183240 * q^65 - 523768762996317716400 * q^67 - 596596128814415845632 * q^69 - 948379808687003287200 * q^71 - 4925435605783876580100 * q^73 + 11105120520135150430000 * q^75 - 1628144191735745368320 * q^77 + 6474134783625939495360 * q^79 + 23375719407022646959702 * q^81 + 12413209217367249862032 * q^83 + 5978612007137723165880 * q^85 - 17230630950338425832032 * q^87 + 7892765755425674057628 * q^89 + 117701223538009065704640 * q^91 - 65760567831273830333440 * q^93 - 112886120912929344409440 * q^95 - 12935113600510578486420 * q^97 + 397484583772859161352240 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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