LMFDB - Embedded newform 126.14.a.q.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,14,Mod(1,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, 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("126.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	126.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:	$135.110970479$
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} - 166540x + 26034700 $ x^3 - x^2 - 166540*x + 26034700
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{4}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$219.795$ of defining polynomial
Character	$\chi$	$=$	126.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+64.0000 q^{2} +4096.00 q^{4} -23421.3 q^{5} +117649. q^{7} +262144. q^{8} +O(q^{10})$	\(q+64.0000 q^{2} +4096.00 q^{4} -23421.3 q^{5} +117649. q^{7} +262144. q^{8} -1.49897e6 q^{10} -2.00858e6 q^{11} -1.97988e7 q^{13} +7.52954e6 q^{14} +1.67772e7 q^{16} +1.64768e8 q^{17} +2.66170e8 q^{19} -9.59338e7 q^{20} -1.28549e8 q^{22} -5.52686e8 q^{23} -6.72144e8 q^{25} -1.26713e9 q^{26} +4.81890e8 q^{28} -1.20173e9 q^{29} -3.58457e9 q^{31} +1.07374e9 q^{32} +1.05451e10 q^{34} -2.75550e9 q^{35} +1.69919e10 q^{37} +1.70349e10 q^{38} -6.13976e9 q^{40} -3.89401e10 q^{41} +2.98933e10 q^{43} -8.22715e9 q^{44} -3.53719e10 q^{46} +7.47652e8 q^{47} +1.38413e10 q^{49} -4.30172e10 q^{50} -8.10960e10 q^{52} +1.17642e11 q^{53} +4.70436e10 q^{55} +3.08410e10 q^{56} -7.69104e10 q^{58} -4.13305e11 q^{59} -4.43254e11 q^{61} -2.29412e11 q^{62} +6.87195e10 q^{64} +4.63715e11 q^{65} -5.10733e11 q^{67} +6.74888e11 q^{68} -1.76352e11 q^{70} -1.65509e12 q^{71} -2.30371e12 q^{73} +1.08748e12 q^{74} +1.09023e12 q^{76} -2.36307e11 q^{77} +3.84641e12 q^{79} -3.92945e11 q^{80} -2.49217e12 q^{82} +1.32415e12 q^{83} -3.85908e12 q^{85} +1.91317e12 q^{86} -5.26537e11 q^{88} +4.64662e12 q^{89} -2.32931e12 q^{91} -2.26380e12 q^{92} +4.78498e10 q^{94} -6.23406e12 q^{95} -2.81833e12 q^{97} +8.85842e11 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 192 q^{2} + 12288 q^{4} + 28626 q^{5} + 352947 q^{7} + 786432 q^{8}+O(q^{10}) $ 3 * q + 192 * q^2 + 12288 * q^4 + 28626 * q^5 + 352947 * q^7 + 786432 * q^8	\( 3 q + 192 q^{2} + 12288 q^{4} + 28626 q^{5} + 352947 q^{7} + 786432 q^{8} + 1832064 q^{10} - 6749178 q^{11} - 20854146 q^{13} + 22588608 q^{14} + 50331648 q^{16} - 100425522 q^{17} + 12403932 q^{19} + 117252096 q^{20} - 431947392 q^{22} - 1036880814 q^{23} - 1530084579 q^{25} - 1334665344 q^{26} + 1445670912 q^{28} - 6435734376 q^{29} - 7714124292 q^{31} + 3221225472 q^{32} - 6427233408 q^{34} + 3367820274 q^{35} - 4624801554 q^{37} + 793851648 q^{38} + 7504134144 q^{40} - 46350517542 q^{41} + 51758123748 q^{43} - 27644633088 q^{44} - 66360372096 q^{46} - 21038057028 q^{47} + 41523861603 q^{49} - 97925413056 q^{50} - 85418582016 q^{52} - 128680526676 q^{53} - 247890301164 q^{55} + 92522938368 q^{56} - 411887000064 q^{58} - 24358384620 q^{59} - 545351650806 q^{61} - 493703954688 q^{62} + 206158430208 q^{64} + 866329895316 q^{65} + 615866153748 q^{67} - 411342938112 q^{68} + 215540497536 q^{70} - 605458102410 q^{71} - 445510372998 q^{73} - 295987299456 q^{74} + 50806505472 q^{76} - 794034042522 q^{77} - 4236900439512 q^{79} + 480264585216 q^{80} - 2966433122688 q^{82} + 4730128213344 q^{83} - 11970847755036 q^{85} + 3312519919872 q^{86} - 1769256517632 q^{88} + 8837998962402 q^{89} - 2453469422754 q^{91} - 4247063814144 q^{92} - 1346435649792 q^{94} - 8416214321784 q^{95} - 19638839012358 q^{97} + 2657527142592 q^{98}+O(q^{100}) \) 3 * q + 192 * q^2 + 12288 * q^4 + 28626 * q^5 + 352947 * q^7 + 786432 * q^8 + 1832064 * q^10 - 6749178 * q^11 - 20854146 * q^13 + 22588608 * q^14 + 50331648 * q^16 - 100425522 * q^17 + 12403932 * q^19 + 117252096 * q^20 - 431947392 * q^22 - 1036880814 * q^23 - 1530084579 * q^25 - 1334665344 * q^26 + 1445670912 * q^28 - 6435734376 * q^29 - 7714124292 * q^31 + 3221225472 * q^32 - 6427233408 * q^34 + 3367820274 * q^35 - 4624801554 * q^37 + 793851648 * q^38 + 7504134144 * q^40 - 46350517542 * q^41 + 51758123748 * q^43 - 27644633088 * q^44 - 66360372096 * q^46 - 21038057028 * q^47 + 41523861603 * q^49 - 97925413056 * q^50 - 85418582016 * q^52 - 128680526676 * q^53 - 247890301164 * q^55 + 92522938368 * q^56 - 411887000064 * q^58 - 24358384620 * q^59 - 545351650806 * q^61 - 493703954688 * q^62 + 206158430208 * q^64 + 866329895316 * q^65 + 615866153748 * q^67 - 411342938112 * q^68 + 215540497536 * q^70 - 605458102410 * q^71 - 445510372998 * q^73 - 295987299456 * q^74 + 50806505472 * q^76 - 794034042522 * q^77 - 4236900439512 * q^79 + 480264585216 * q^80 - 2966433122688 * q^82 + 4730128213344 * q^83 - 11970847755036 * q^85 + 3312519919872 * q^86 - 1769256517632 * q^88 + 8837998962402 * q^89 - 2453469422754 * q^91 - 4247063814144 * q^92 - 1346435649792 * q^94 - 8416214321784 * q^95 - 19638839012358 * q^97 + 2657527142592 * q^98

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 $

$2$	64.0000	0.707107
$2$	64.0000	0.707107
$3$	0	0
$3$	0	0
$4$	4096.00	0.500000
$5$	−23421.3	−0.670358	−0.335179	−	0.942155i	$-0.608797\pi$
$5$	−23421.3	−0.670358	−0.335179	+	0.942155i	$0.608797\pi$
$6$	0	0
$7$	117649.	0.377964
$7$	117649.	0.377964
$8$	262144.	0.353553
$9$	0	0
$10$	−1.49897e6	−0.474014
$11$	−2.00858e6	−0.341851	−0.170925	−	0.985284i	$-0.554676\pi$
$11$	−2.00858e6	−0.341851	−0.170925	+	0.985284i	$0.554676\pi$
$12$	0	0
$13$	−1.97988e7	−1.13765	−0.568824	−	0.822459i	$-0.692601\pi$
$13$	−1.97988e7	−1.13765	−0.568824	+	0.822459i	$0.692601\pi$
$14$	7.52954e6	0.267261
$15$	0	0
$16$	1.67772e7	0.250000
$17$	1.64768e8	1.65559	0.827797	−	0.561028i	$-0.189594\pi$
$17$	1.64768e8	1.65559	0.827797	+	0.561028i	$0.189594\pi$
$18$	0	0
$19$	2.66170e8	1.29796	0.648979	−	0.760806i	$-0.275196\pi$
$19$	2.66170e8	1.29796	0.648979	+	0.760806i	$0.275196\pi$
$20$	−9.59338e7	−0.335179
$21$	0	0
$22$	−1.28549e8	−0.241725
$23$	−5.52686e8	−0.778480	−0.389240	−	0.921136i	$-0.627262\pi$
$23$	−5.52686e8	−0.778480	−0.389240	+	0.921136i	$0.627262\pi$
$24$	0	0
$25$	−6.72144e8	−0.550621
$26$	−1.26713e9	−0.804438
$27$	0	0
$28$	4.81890e8	0.188982
$29$	−1.20173e9	−0.375162	−0.187581	−	0.982249i	$-0.560065\pi$
$29$	−1.20173e9	−0.375162	−0.187581	+	0.982249i	$0.560065\pi$
$30$	0	0
$31$	−3.58457e9	−0.725414	−0.362707	−	0.931903i	$-0.618147\pi$
$31$	−3.58457e9	−0.725414	−0.362707	+	0.931903i	$0.618147\pi$
$32$	1.07374e9	0.176777
$33$	0	0
$34$	1.05451e10	1.17068
$35$	−2.75550e9	−0.253371
$36$	0	0
$37$	1.69919e10	1.08876	0.544379	−	0.838839i	$-0.316765\pi$
$37$	1.69919e10	1.08876	0.544379	+	0.838839i	$0.316765\pi$
$38$	1.70349e10	0.917795
$39$	0	0
$40$	−6.13976e9	−0.237007
$41$	−3.89401e10	−1.28027	−0.640135	−	0.768262i	$-0.721122\pi$
$41$	−3.89401e10	−1.28027	−0.640135	+	0.768262i	$0.721122\pi$
$42$	0	0
$43$	2.98933e10	0.721155	0.360577	−	0.932729i	$-0.382580\pi$
$43$	2.98933e10	0.721155	0.360577	+	0.932729i	$0.382580\pi$
$44$	−8.22715e9	−0.170925
$45$	0	0
$46$	−3.53719e10	−0.550468
$47$	7.47652e8	0.0101173	0.00505864	−	0.999987i	$-0.498390\pi$
$47$	7.47652e8	0.0101173	0.00505864	+	0.999987i	$0.498390\pi$
$48$	0	0
$49$	1.38413e10	0.142857
$50$	−4.30172e10	−0.389348
$51$	0	0
$52$	−8.10960e10	−0.568824
$53$	1.17642e11	0.729072	0.364536	−	0.931189i	$-0.381228\pi$
$53$	1.17642e11	0.729072	0.364536	+	0.931189i	$0.381228\pi$
$54$	0	0
$55$	4.70436e10	0.229162
$56$	3.08410e10	0.133631
$57$	0	0
$58$	−7.69104e10	−0.265279
$59$	−4.13305e11	−1.27565	−0.637826	−	0.770180i	$-0.720166\pi$
$59$	−4.13305e11	−1.27565	−0.637826	+	0.770180i	$0.720166\pi$
$60$	0	0
$61$	−4.43254e11	−1.10156	−0.550781	−	0.834650i	$-0.685670\pi$
$61$	−4.43254e11	−1.10156	−0.550781	+	0.834650i	$0.685670\pi$
$62$	−2.29412e11	−0.512945
$63$	0	0
$64$	6.87195e10	0.125000
$65$	4.63715e11	0.762631
$66$	0	0
$67$	−5.10733e11	−0.689775	−0.344887	−	0.938644i	$-0.612083\pi$
$67$	−5.10733e11	−0.689775	−0.344887	+	0.938644i	$0.612083\pi$
$68$	6.74888e11	0.827797
$69$	0	0
$70$	−1.76352e11	−0.179161
$71$	−1.65509e12	−1.53335	−0.766676	−	0.642034i	$-0.778091\pi$
$71$	−1.65509e12	−1.53335	−0.766676	+	0.642034i	$0.778091\pi$
$72$	0	0
$73$	−2.30371e12	−1.78168	−0.890838	−	0.454321i	$-0.849882\pi$
$73$	−2.30371e12	−1.78168	−0.890838	+	0.454321i	$0.849882\pi$
$74$	1.08748e12	0.769868
$75$	0	0
$76$	1.09023e12	0.648979
$77$	−2.36307e11	−0.129208
$78$	0	0
$79$	3.84641e12	1.78024	0.890121	−	0.455724i	$-0.150619\pi$
$79$	3.84641e12	1.78024	0.890121	+	0.455724i	$0.150619\pi$
$80$	−3.92945e11	−0.167589
$81$	0	0
$82$	−2.49217e12	−0.905288
$83$	1.32415e12	0.444560	0.222280	−	0.974983i	$-0.428650\pi$
$83$	1.32415e12	0.444560	0.222280	+	0.974983i	$0.428650\pi$
$84$	0	0
$85$	−3.85908e12	−1.10984
$86$	1.91317e12	0.509933
$87$	0	0
$88$	−5.26537e11	−0.120863
$89$	4.64662e12	0.991066	0.495533	−	0.868589i	$-0.334973\pi$
$89$	4.64662e12	0.991066	0.495533	+	0.868589i	$0.334973\pi$
$90$	0	0
$91$	−2.32931e12	−0.429990
$92$	−2.26380e12	−0.389240
$93$	0	0
$94$	4.78498e10	0.00715400
$95$	−6.23406e12	−0.870097
$96$	0	0
$97$	−2.81833e12	−0.343538	−0.171769	−	0.985137i	$-0.554948\pi$
$97$	−2.81833e12	−0.343538	−0.171769	+	0.985137i	$0.554948\pi$
$98$	8.85842e11	0.101015
$99$	0	0
$100$	−2.75310e12	−0.275310
$101$	2.48736e12	0.233157	0.116579	−	0.993181i	$-0.462807\pi$
$101$	2.48736e12	0.233157	0.116579	+	0.993181i	$0.462807\pi$
$102$	0	0
$103$	−6.14235e12	−0.506865	−0.253433	−	0.967353i	$-0.581560\pi$
$103$	−6.14235e12	−0.506865	−0.253433	+	0.967353i	$0.581560\pi$
$104$	−5.19014e12	−0.402219
$105$	0	0
$106$	7.52911e12	0.515532
$107$	−2.15493e13	−1.38816	−0.694078	−	0.719900i	$-0.744188\pi$
$107$	−2.15493e13	−1.38816	−0.694078	+	0.719900i	$0.744188\pi$
$108$	0	0
$109$	−7.57392e12	−0.432562	−0.216281	−	0.976331i	$-0.569393\pi$
$109$	−7.57392e12	−0.432562	−0.216281	+	0.976331i	$0.569393\pi$
$110$	3.01079e12	0.162042
$111$	0	0
$112$	1.97382e12	0.0944911
$113$	−2.92039e13	−1.31957	−0.659784	−	0.751456i	$-0.729352\pi$
$113$	−2.92039e13	−1.31957	−0.659784	+	0.751456i	$0.729352\pi$
$114$	0	0
$115$	1.29446e13	0.521860
$116$	−4.92227e12	−0.187581
$117$	0	0
$118$	−2.64515e13	−0.902023
$119$	1.93847e13	0.625756
$120$	0	0
$121$	−3.04883e13	−0.883138
$122$	−2.83683e13	−0.778922
$123$	0	0
$124$	−1.46824e13	−0.362707
$125$	4.43330e13	1.03947
$126$	0	0
$127$	−5.37141e13	−1.13596	−0.567981	−	0.823042i	$-0.692275\pi$
$127$	−5.37141e13	−1.13596	−0.567981	+	0.823042i	$0.692275\pi$
$128$	4.39805e12	0.0883883
$129$	0	0
$130$	2.96778e13	0.539261
$131$	−5.22851e13	−0.903887	−0.451944	−	0.892046i	$-0.649269\pi$
$131$	−5.22851e13	−0.903887	−0.451944	+	0.892046i	$0.649269\pi$
$132$	0	0
$133$	3.13146e13	0.490582
$134$	−3.26869e13	−0.487744
$135$	0	0
$136$	4.31928e13	0.585341
$137$	−1.09484e14	−1.41470	−0.707352	−	0.706861i	$-0.750111\pi$
$137$	−1.09484e14	−1.41470	−0.707352	+	0.706861i	$0.750111\pi$
$138$	0	0
$139$	1.12145e14	1.31881	0.659407	−	0.751786i	$-0.270807\pi$
$139$	1.12145e14	1.31881	0.659407	+	0.751786i	$0.270807\pi$
$140$	−1.12865e13	−0.126686
$141$	0	0
$142$	−1.05926e14	−1.08424
$143$	3.97675e13	0.388906
$144$	0	0
$145$	2.81460e13	0.251492
$146$	−1.47437e14	−1.25984
$147$	0	0
$148$	6.95989e13	0.544379
$149$	−1.29443e14	−0.969099	−0.484550	−	0.874764i	$-0.661016\pi$
$149$	−1.29443e14	−0.969099	−0.484550	+	0.874764i	$0.661016\pi$
$150$	0	0
$151$	7.39145e13	0.507434	0.253717	−	0.967279i	$-0.418347\pi$
$151$	7.39145e13	0.507434	0.253717	+	0.967279i	$0.418347\pi$
$152$	6.97749e13	0.458898
$153$	0	0
$154$	−1.51237e13	−0.0913635
$155$	8.39553e13	0.486287
$156$	0	0
$157$	9.27114e12	0.0494067	0.0247033	−	0.999695i	$-0.492136\pi$
$157$	9.27114e12	0.0494067	0.0247033	+	0.999695i	$0.492136\pi$
$158$	2.46170e14	1.25882
$159$	0	0
$160$	−2.51485e13	−0.118504
$161$	−6.50229e13	−0.294238
$162$	0	0
$163$	2.62042e14	1.09434	0.547168	−	0.837023i	$-0.315706\pi$
$163$	2.62042e14	1.09434	0.547168	+	0.837023i	$0.315706\pi$
$164$	−1.59499e14	−0.640135
$165$	0	0
$166$	8.47457e13	0.314351
$167$	−4.63843e14	−1.65468	−0.827340	−	0.561701i	$-0.810147\pi$
$167$	−4.63843e14	−1.65468	−0.827340	+	0.561701i	$0.810147\pi$
$168$	0	0
$169$	8.91185e13	0.294242
$170$	−2.46981e14	−0.784776
$171$	0	0
$172$	1.22443e14	0.360577
$173$	−3.76226e14	−1.06696	−0.533481	−	0.845812i	$-0.679117\pi$
$173$	−3.76226e14	−1.06696	−0.533481	+	0.845812i	$0.679117\pi$
$174$	0	0
$175$	−7.90771e13	−0.208115
$176$	−3.36984e13	−0.0854627
$177$	0	0
$178$	2.97384e14	0.700789
$179$	−3.55960e14	−0.808829	−0.404414	−	0.914576i	$-0.632525\pi$
$179$	−3.55960e14	−0.808829	−0.404414	+	0.914576i	$0.632525\pi$
$180$	0	0
$181$	5.67232e14	1.19909	0.599543	−	0.800343i	$-0.295349\pi$
$181$	5.67232e14	1.19909	0.599543	+	0.800343i	$0.295349\pi$
$182$	−1.49076e14	−0.304049
$183$	0	0
$184$	−1.44883e14	−0.275234
$185$	−3.97974e14	−0.729857
$186$	0	0
$187$	−3.30949e14	−0.565966
$188$	3.06238e12	0.00505864
$189$	0	0
$190$	−3.98980e14	−0.615251
$191$	−7.86451e14	−1.17207	−0.586037	−	0.810284i	$-0.699313\pi$
$191$	−7.86451e14	−1.17207	−0.586037	+	0.810284i	$0.699313\pi$
$192$	0	0
$193$	−1.11357e15	−1.55094	−0.775471	−	0.631383i	$-0.782488\pi$
$193$	−1.11357e15	−1.55094	−0.775471	+	0.631383i	$0.782488\pi$
$194$	−1.80373e14	−0.242918
$195$	0	0
$196$	5.66939e13	0.0714286
$197$	−5.38581e14	−0.656479	−0.328240	−	0.944595i	$-0.606455\pi$
$197$	−5.38581e14	−0.656479	−0.328240	+	0.944595i	$0.606455\pi$
$198$	0	0
$199$	−5.97703e14	−0.682246	−0.341123	−	0.940019i	$-0.610807\pi$
$199$	−5.97703e14	−0.682246	−0.341123	+	0.940019i	$0.610807\pi$
$200$	−1.76199e14	−0.194674
$201$	0	0
$202$	1.59191e14	0.164867
$203$	−1.41382e14	−0.141798
$204$	0	0
$205$	9.12029e14	0.858239
$206$	−3.93110e14	−0.358408
$207$	0	0
$208$	−3.32169e14	−0.284412
$209$	−5.34624e14	−0.443708
$210$	0	0
$211$	1.33378e15	1.04052	0.520258	−	0.854009i	$-0.325836\pi$
$211$	1.33378e15	1.04052	0.520258	+	0.854009i	$0.325836\pi$
$212$	4.81863e14	0.364536
$213$	0	0
$214$	−1.37915e15	−0.981574
$215$	−7.00140e14	−0.483432
$216$	0	0
$217$	−4.21721e14	−0.274181
$218$	−4.84731e14	−0.305868
$219$	0	0
$220$	1.92691e14	0.114581
$221$	−3.26221e15	−1.88348
$222$	0	0
$223$	1.22712e15	0.668197	0.334098	−	0.942538i	$-0.391568\pi$
$223$	1.22712e15	0.668197	0.334098	+	0.942538i	$0.391568\pi$
$224$	1.26325e14	0.0668153
$225$	0	0
$226$	−1.86905e15	−0.933075
$227$	−2.74136e14	−0.132984	−0.0664919	−	0.997787i	$-0.521181\pi$
$227$	−2.74136e14	−0.132984	−0.0664919	+	0.997787i	$0.521181\pi$
$228$	0	0
$229$	−1.96759e15	−0.901577	−0.450789	−	0.892631i	$-0.648857\pi$
$229$	−1.96759e15	−0.901577	−0.450789	+	0.892631i	$0.648857\pi$
$230$	8.28457e14	0.369011
$231$	0	0
$232$	−3.15025e14	−0.132640
$233$	1.14535e15	0.468949	0.234475	−	0.972122i	$-0.424663\pi$
$233$	1.14535e15	0.468949	0.234475	+	0.972122i	$0.424663\pi$
$234$	0	0
$235$	−1.75110e13	−0.00678219
$236$	−1.69290e15	−0.637826
$237$	0	0
$238$	1.24062e15	0.442476
$239$	−2.35401e14	−0.0817000	−0.0408500	−	0.999165i	$-0.513007\pi$
$239$	−2.35401e14	−0.0817000	−0.0408500	+	0.999165i	$0.513007\pi$
$240$	0	0
$241$	3.22527e15	1.06037	0.530183	−	0.847883i	$-0.322123\pi$
$241$	3.22527e15	1.06037	0.530183	+	0.847883i	$0.322123\pi$
$242$	−1.95125e15	−0.624473
$243$	0	0
$244$	−1.81557e15	−0.550781
$245$	−3.24181e14	−0.0957654
$246$	0	0
$247$	−5.26986e15	−1.47662
$248$	−9.39673e14	−0.256472
$249$	0	0
$250$	2.83731e15	0.735017
$251$	2.16102e15	0.545480	0.272740	−	0.962088i	$-0.412070\pi$
$251$	2.16102e15	0.545480	0.272740	+	0.962088i	$0.412070\pi$
$252$	0	0
$253$	1.11011e15	0.266124
$254$	−3.43770e15	−0.803246
$255$	0	0
$256$	2.81475e14	0.0625000
$257$	6.98514e15	1.51220	0.756101	−	0.654455i	$-0.227102\pi$
$257$	6.98514e15	1.51220	0.756101	+	0.654455i	$0.227102\pi$
$258$	0	0
$259$	1.99908e15	0.411512
$260$	1.89938e15	0.381315
$261$	0	0
$262$	−3.34624e15	−0.639145
$263$	6.19339e15	1.15403	0.577014	−	0.816734i	$-0.304218\pi$
$263$	6.19339e15	1.15403	0.577014	+	0.816734i	$0.304218\pi$
$264$	0	0
$265$	−2.75534e15	−0.488739
$266$	2.00414e15	0.346894
$267$	0	0
$268$	−2.09196e15	−0.344887
$269$	−7.26589e15	−1.16923	−0.584614	−	0.811312i	$-0.698754\pi$
$269$	−7.26589e15	−1.16923	−0.584614	+	0.811312i	$0.698754\pi$
$270$	0	0
$271$	1.98290e15	0.304089	0.152045	−	0.988374i	$-0.451414\pi$
$271$	1.98290e15	0.304089	0.152045	+	0.988374i	$0.451414\pi$
$272$	2.76434e15	0.413899
$273$	0	0
$274$	−7.00696e15	−1.00035
$275$	1.35006e15	0.188230
$276$	0	0
$277$	−8.25652e15	−1.09819	−0.549097	−	0.835759i	$-0.685028\pi$
$277$	−8.25652e15	−1.09819	−0.549097	+	0.835759i	$0.685028\pi$
$278$	7.17728e15	0.932542
$279$	0	0
$280$	−7.22337e14	−0.0895803
$281$	−5.69232e15	−0.689760	−0.344880	−	0.938647i	$-0.612080\pi$
$281$	−5.69232e15	−0.689760	−0.344880	+	0.938647i	$0.612080\pi$
$282$	0	0
$283$	9.46280e15	1.09498	0.547492	−	0.836811i	$-0.315583\pi$
$283$	9.46280e15	1.09498	0.547492	+	0.836811i	$0.315583\pi$
$284$	−6.77924e15	−0.766676
$285$	0	0
$286$	2.54512e15	0.274998
$287$	−4.58126e15	−0.483897
$288$	0	0
$289$	1.72438e16	1.74099
$290$	1.80134e15	0.177832
$291$	0	0
$292$	−9.43599e15	−0.890838
$293$	−2.67607e15	−0.247091	−0.123546	−	0.992339i	$-0.539427\pi$
$293$	−2.67607e15	−0.247091	−0.123546	+	0.992339i	$0.539427\pi$
$294$	0	0
$295$	9.68015e15	0.855144
$296$	4.45433e15	0.384934
$297$	0	0
$298$	−8.28436e15	−0.685257
$299$	1.09425e16	0.885635
$300$	0	0
$301$	3.51691e15	0.272571
$302$	4.73053e15	0.358810
$303$	0	0
$304$	4.46559e15	0.324490
$305$	1.03816e16	0.738441
$306$	0	0
$307$	1.60788e16	1.09611	0.548056	−	0.836442i	$-0.315368\pi$
$307$	1.60788e16	1.09611	0.548056	+	0.836442i	$0.315368\pi$
$308$	−9.67915e14	−0.0646038
$309$	0	0
$310$	5.37314e15	0.343857
$311$	1.77367e16	1.11155	0.555777	−	0.831331i	$-0.312421\pi$
$311$	1.77367e16	1.11155	0.555777	+	0.831331i	$0.312421\pi$
$312$	0	0
$313$	2.56422e15	0.154140	0.0770702	−	0.997026i	$-0.475443\pi$
$313$	2.56422e15	0.154140	0.0770702	+	0.997026i	$0.475443\pi$
$314$	5.93353e14	0.0349358
$315$	0	0
$316$	1.57549e16	0.890121
$317$	−8.06035e15	−0.446138	−0.223069	−	0.974803i	$-0.571607\pi$
$317$	−8.06035e15	−0.446138	−0.223069	+	0.974803i	$0.571607\pi$
$318$	0	0
$319$	2.41376e15	0.128249
$320$	−1.60950e15	−0.0837947
$321$	0	0
$322$	−4.16147e15	−0.208057
$323$	4.38562e16	2.14889
$324$	0	0
$325$	1.33077e16	0.626412
$326$	1.67707e16	0.773813
$327$	0	0
$328$	−1.02079e16	−0.452644
$329$	8.79606e13	0.00382397
$330$	0	0
$331$	7.42526e15	0.310334	0.155167	−	0.987888i	$-0.450408\pi$
$331$	7.42526e15	0.310334	0.155167	+	0.987888i	$0.450408\pi$
$332$	5.42372e15	0.222280
$333$	0	0
$334$	−2.96860e16	−1.17004
$335$	1.19620e16	0.462396
$336$	0	0
$337$	5.15280e15	0.191623	0.0958117	−	0.995399i	$-0.469455\pi$
$337$	5.15280e15	0.191623	0.0958117	+	0.995399i	$0.469455\pi$
$338$	5.70359e15	0.208060
$339$	0	0
$340$	−1.58068e16	−0.554920
$341$	7.19989e15	0.247983
$342$	0	0
$343$	1.62841e15	0.0539949
$344$	7.83634e15	0.254967
$345$	0	0
$346$	−2.40785e16	−0.754457
$347$	−1.14126e16	−0.350948	−0.175474	−	0.984484i	$-0.556146\pi$
$347$	−1.14126e16	−0.350948	−0.175474	+	0.984484i	$0.556146\pi$
$348$	0	0
$349$	3.03033e16	0.897688	0.448844	−	0.893610i	$-0.351836\pi$
$349$	3.03033e16	0.897688	0.448844	+	0.893610i	$0.351836\pi$
$350$	−5.06093e15	−0.147160
$351$	0	0
$352$	−2.15670e15	−0.0604313
$353$	5.32565e16	1.46500	0.732498	−	0.680769i	$-0.238354\pi$
$353$	5.32565e16	1.46500	0.732498	+	0.680769i	$0.238354\pi$
$354$	0	0
$355$	3.87644e16	1.02789
$356$	1.90326e16	0.495533
$357$	0	0
$358$	−2.27814e16	−0.571928
$359$	−3.01077e16	−0.742273	−0.371136	−	0.928578i	$-0.621032\pi$
$359$	−3.01077e16	−0.742273	−0.371136	+	0.928578i	$0.621032\pi$
$360$	0	0
$361$	2.87935e16	0.684697
$362$	3.63029e16	0.847882
$363$	0	0
$364$	−9.54086e15	−0.214995
$365$	5.39559e16	1.19436
$366$	0	0
$367$	−6.91288e15	−0.147683	−0.0738414	−	0.997270i	$-0.523526\pi$
$367$	−6.91288e15	−0.147683	−0.0738414	+	0.997270i	$0.523526\pi$
$368$	−9.27253e15	−0.194620
$369$	0	0
$370$	−2.54703e16	−0.516087
$371$	1.38405e16	0.275563
$372$	0	0
$373$	−3.54397e16	−0.681369	−0.340685	−	0.940178i	$-0.610659\pi$
$373$	−3.54397e16	−0.681369	−0.340685	+	0.940178i	$0.610659\pi$
$374$	−2.11807e16	−0.400199
$375$	0	0
$376$	1.95993e14	0.00357700
$377$	2.37928e16	0.426802
$378$	0	0
$379$	−4.71180e16	−0.816642	−0.408321	−	0.912838i	$-0.633886\pi$
$379$	−4.71180e16	−0.816642	−0.408321	+	0.912838i	$0.633886\pi$
$380$	−2.55347e16	−0.435048
$381$	0	0
$382$	−5.03329e16	−0.828781
$383$	5.09740e16	0.825196	0.412598	−	0.910913i	$-0.364622\pi$
$383$	5.09740e16	0.825196	0.412598	+	0.910913i	$0.364622\pi$
$384$	0	0
$385$	5.53464e15	0.0866152
$386$	−7.12686e16	−1.09668
$387$	0	0
$388$	−1.15439e16	−0.171769
$389$	−1.03907e17	−1.52045	−0.760227	−	0.649657i	$-0.774912\pi$
$389$	−1.03907e17	−1.52045	−0.760227	+	0.649657i	$0.774912\pi$
$390$	0	0
$391$	−9.10647e16	−1.28885
$392$	3.62841e15	0.0505076
$393$	0	0
$394$	−3.44692e16	−0.464201
$395$	−9.00880e16	−1.19340
$396$	0	0
$397$	3.79770e16	0.486835	0.243418	−	0.969922i	$-0.421731\pi$
$397$	3.79770e16	0.486835	0.243418	+	0.969922i	$0.421731\pi$
$398$	−3.82530e16	−0.482420
$399$	0	0
$400$	−1.12767e16	−0.137655
$401$	7.93205e16	0.952680	0.476340	−	0.879261i	$-0.341963\pi$
$401$	7.93205e16	0.952680	0.476340	+	0.879261i	$0.341963\pi$
$402$	0	0
$403$	7.09702e16	0.825265
$404$	1.01882e16	0.116579
$405$	0	0
$406$	−9.04844e15	−0.100266
$407$	−3.41297e16	−0.372193
$408$	0	0
$409$	1.57534e17	1.66407	0.832037	−	0.554720i	$-0.187175\pi$
$409$	1.57534e17	1.66407	0.832037	+	0.554720i	$0.187175\pi$
$410$	5.83698e16	0.606867
$411$	0	0
$412$	−2.51591e16	−0.253433
$413$	−4.86249e16	−0.482151
$414$	0	0
$415$	−3.10134e16	−0.298014
$416$	−2.12588e16	−0.201110
$417$	0	0
$418$	−3.42159e16	−0.313749
$419$	3.31594e16	0.299375	0.149688	−	0.988733i	$-0.452173\pi$
$419$	3.31594e16	0.299375	0.149688	+	0.988733i	$0.452173\pi$
$420$	0	0
$421$	−3.51710e16	−0.307858	−0.153929	−	0.988082i	$-0.549193\pi$
$421$	−3.51710e16	−0.307858	−0.153929	+	0.988082i	$0.549193\pi$
$422$	8.53620e16	0.735756
$423$	0	0
$424$	3.08392e16	0.257766
$425$	−1.10748e17	−0.911604
$426$	0	0
$427$	−5.21484e16	−0.416352
$428$	−8.82659e16	−0.694078
$429$	0	0
$430$	−4.48090e16	−0.341838
$431$	1.01407e17	0.762022	0.381011	−	0.924571i	$-0.375576\pi$
$431$	1.01407e17	0.762022	0.381011	+	0.924571i	$0.375576\pi$
$432$	0	0
$433$	1.15896e17	0.845079	0.422539	−	0.906345i	$-0.361139\pi$
$433$	1.15896e17	0.845079	0.422539	+	0.906345i	$0.361139\pi$
$434$	−2.69901e16	−0.193875
$435$	0	0
$436$	−3.10228e16	−0.216281
$437$	−1.47108e17	−1.01043
$438$	0	0
$439$	1.64181e17	1.09472	0.547361	−	0.836897i	$-0.315632\pi$
$439$	1.64181e17	1.09472	0.547361	+	0.836897i	$0.315632\pi$
$440$	1.23322e16	0.0810211
$441$	0	0
$442$	−2.08781e17	−1.33182
$443$	−2.35260e17	−1.47885	−0.739425	−	0.673239i	$-0.764903\pi$
$443$	−2.35260e17	−1.47885	−0.739425	+	0.673239i	$0.764903\pi$
$444$	0	0
$445$	−1.08830e17	−0.664368
$446$	7.85355e16	0.472486
$447$	0	0
$448$	8.08478e15	0.0472456
$449$	−3.05604e16	−0.176018	−0.0880092	−	0.996120i	$-0.528050\pi$
$449$	−3.05604e16	−0.176018	−0.0880092	+	0.996120i	$0.528050\pi$
$450$	0	0
$451$	7.82143e16	0.437662
$452$	−1.19619e17	−0.659784
$453$	0	0
$454$	−1.75447e16	−0.0940337
$455$	5.45556e16	0.288247
$456$	0	0
$457$	3.57247e17	1.83448	0.917239	−	0.398336i	$-0.130412\pi$
$457$	3.57247e17	1.83448	0.917239	+	0.398336i	$0.130412\pi$
$458$	−1.25925e17	−0.637512
$459$	0	0
$460$	5.30212e16	0.260930
$461$	−1.87244e17	−0.908555	−0.454278	−	0.890860i	$-0.650103\pi$
$461$	−1.87244e17	−0.908555	−0.454278	+	0.890860i	$0.650103\pi$
$462$	0	0
$463$	2.11042e17	0.995618	0.497809	−	0.867287i	$-0.334138\pi$
$463$	2.11042e17	0.995618	0.497809	+	0.867287i	$0.334138\pi$
$464$	−2.01616e16	−0.0937904
$465$	0	0
$466$	7.33026e16	0.331597
$467$	−1.79539e17	−0.800936	−0.400468	−	0.916311i	$-0.631153\pi$
$467$	−1.79539e17	−0.800936	−0.400468	+	0.916311i	$0.631153\pi$
$468$	0	0
$469$	−6.00872e16	−0.260710
$470$	−1.12070e15	−0.00479574
$471$	0	0
$472$	−1.08345e17	−0.451011
$473$	−6.00430e16	−0.246527
$474$	0	0
$475$	−1.78905e17	−0.714683
$476$	7.93999e16	0.312878
$477$	0	0
$478$	−1.50657e16	−0.0577707
$479$	1.29090e17	0.488326	0.244163	−	0.969734i	$-0.421487\pi$
$479$	1.29090e17	0.488326	0.244163	+	0.969734i	$0.421487\pi$
$480$	0	0
$481$	−3.36420e17	−1.23862
$482$	2.06418e17	0.749792
$483$	0	0
$484$	−1.24880e17	−0.441569
$485$	6.60089e16	0.230293
$486$	0	0
$487$	4.13467e17	1.40444	0.702218	−	0.711962i	$-0.252193\pi$
$487$	4.13467e17	1.40444	0.702218	+	0.711962i	$0.252193\pi$
$488$	−1.16196e17	−0.389461
$489$	0	0
$490$	−2.07476e16	−0.0677164
$491$	−2.50225e17	−0.805938	−0.402969	−	0.915214i	$-0.632022\pi$
$491$	−2.50225e17	−0.805938	−0.402969	+	0.915214i	$0.632022\pi$
$492$	0	0
$493$	−1.98005e17	−0.621115
$494$	−3.37271e17	−1.04413
$495$	0	0
$496$	−6.01391e16	−0.181353
$497$	−1.94719e17	−0.579553
$498$	0	0
$499$	5.88602e17	1.70674	0.853372	−	0.521303i	$-0.174554\pi$
$499$	5.88602e17	1.70674	0.853372	+	0.521303i	$0.174554\pi$
$500$	1.81588e17	0.519735
$501$	0	0
$502$	1.38305e17	0.385713
$503$	−3.98673e17	−1.09755	−0.548776	−	0.835970i	$-0.684906\pi$
$503$	−3.98673e17	−1.09755	−0.548776	+	0.835970i	$0.684906\pi$
$504$	0	0
$505$	−5.82572e16	−0.156299
$506$	7.10473e16	0.188178
$507$	0	0
$508$	−2.20013e17	−0.567981
$509$	−3.09802e17	−0.789622	−0.394811	−	0.918762i	$-0.629190\pi$
$509$	−3.09802e17	−0.789622	−0.394811	+	0.918762i	$0.629190\pi$
$510$	0	0
$511$	−2.71029e17	−0.673410
$512$	1.80144e16	0.0441942
$513$	0	0
$514$	4.47049e17	1.06929
$515$	1.43862e17	0.339781
$516$	0	0
$517$	−1.50172e15	−0.00345860
$518$	1.27941e17	0.290983
$519$	0	0
$520$	1.21560e17	0.269631
$521$	1.78663e17	0.391371	0.195685	−	0.980667i	$-0.437307\pi$
$521$	1.78663e17	0.391371	0.195685	+	0.980667i	$0.437307\pi$
$522$	0	0
$523$	2.92415e17	0.624796	0.312398	−	0.949951i	$-0.398868\pi$
$523$	2.92415e17	0.624796	0.312398	+	0.949951i	$0.398868\pi$
$524$	−2.14160e17	−0.451944
$525$	0	0
$526$	3.96377e17	0.816021
$527$	−5.90621e17	−1.20099
$528$	0	0
$529$	−1.98575e17	−0.393970
$530$	−1.76342e17	−0.345591
$531$	0	0
$532$	1.28265e17	0.245291
$533$	7.70968e17	1.45650
$534$	0	0
$535$	5.04713e17	0.930561
$536$	−1.33885e17	−0.243872
$537$	0	0
$538$	−4.65017e17	−0.826769
$539$	−2.78013e16	−0.0488358
$540$	0	0
$541$	−3.65456e17	−0.626690	−0.313345	−	0.949639i	$-0.601450\pi$
$541$	−3.65456e17	−0.626690	−0.313345	+	0.949639i	$0.601450\pi$
$542$	1.26906e17	0.215024
$543$	0	0
$544$	1.76918e17	0.292670
$545$	1.77391e17	0.289971
$546$	0	0
$547$	−1.14536e18	−1.82820	−0.914102	−	0.405485i	$-0.867103\pi$
$547$	−1.14536e18	−1.82820	−0.914102	+	0.405485i	$0.867103\pi$
$548$	−4.48445e17	−0.707352
$549$	0	0
$550$	8.64036e16	0.133099
$551$	−3.19863e17	−0.486944
$552$	0	0
$553$	4.52526e17	0.672869
$554$	−5.28418e17	−0.776540
$555$	0	0
$556$	4.59346e17	0.659407
$557$	6.71259e17	0.952426	0.476213	−	0.879330i	$-0.342009\pi$
$557$	6.71259e17	0.952426	0.476213	+	0.879330i	$0.342009\pi$
$558$	0	0
$559$	−5.91852e17	−0.820420
$560$	−4.62296e16	−0.0633428
$561$	0	0
$562$	−3.64309e17	−0.487734
$563$	4.33941e17	0.574283	0.287141	−	0.957888i	$-0.407295\pi$
$563$	4.33941e17	0.574283	0.287141	+	0.957888i	$0.407295\pi$
$564$	0	0
$565$	6.83995e17	0.884582
$566$	6.05619e17	0.774271
$567$	0	0
$568$	−4.33871e17	−0.542122
$569$	1.21356e18	1.49910	0.749551	−	0.661947i	$-0.230270\pi$
$569$	1.21356e18	1.49910	0.749551	+	0.661947i	$0.230270\pi$
$570$	0	0
$571$	−1.47028e18	−1.77527	−0.887636	−	0.460545i	$-0.847654\pi$
$571$	−1.47028e18	−1.77527	−0.887636	+	0.460545i	$0.847654\pi$
$572$	1.62888e17	0.194453
$573$	0	0
$574$	−2.93201e17	−0.342167
$575$	3.71484e17	0.428647
$576$	0	0
$577$	9.78596e17	1.10398	0.551989	−	0.833851i	$-0.313869\pi$
$577$	9.78596e17	1.10398	0.551989	+	0.833851i	$0.313869\pi$
$578$	1.10360e18	1.23107
$579$	0	0
$580$	1.15286e17	0.125746
$581$	1.55785e17	0.168028
$582$	0	0
$583$	−2.36294e17	−0.249234
$584$	−6.03903e17	−0.629918
$585$	0	0
$586$	−1.71268e17	−0.174720
$587$	−7.72132e17	−0.779012	−0.389506	−	0.921024i	$-0.627354\pi$
$587$	−7.72132e17	−0.779012	−0.389506	+	0.921024i	$0.627354\pi$
$588$	0	0
$589$	−9.54105e17	−0.941557
$590$	6.19530e17	0.604678
$591$	0	0
$592$	2.85077e17	0.272190
$593$	2.18752e17	0.206584	0.103292	−	0.994651i	$-0.467062\pi$
$593$	2.18752e17	0.206584	0.103292	+	0.994651i	$0.467062\pi$
$594$	0	0
$595$	−4.54017e17	−0.419480
$596$	−5.30199e17	−0.484550
$597$	0	0
$598$	7.00322e17	0.626239
$599$	1.50673e18	1.33279	0.666396	−	0.745598i	$-0.267836\pi$
$599$	1.50673e18	1.33279	0.666396	+	0.745598i	$0.267836\pi$
$600$	0	0
$601$	−5.67536e17	−0.491258	−0.245629	−	0.969364i	$-0.578994\pi$
$601$	−5.67536e17	−0.491258	−0.245629	+	0.969364i	$0.578994\pi$
$602$	2.25082e17	0.192737
$603$	0	0
$604$	3.02754e17	0.253717
$605$	7.14077e17	0.592018
$606$	0	0
$607$	−1.07479e18	−0.872162	−0.436081	−	0.899907i	$-0.643634\pi$
$607$	−1.07479e18	−0.872162	−0.436081	+	0.899907i	$0.643634\pi$
$608$	2.85798e17	0.229449
$609$	0	0
$610$	6.64423e17	0.522157
$611$	−1.48026e16	−0.0115099
$612$	0	0
$613$	−2.38151e18	−1.81284	−0.906421	−	0.422375i	$-0.861196\pi$
$613$	−2.38151e18	−1.81284	−0.906421	+	0.422375i	$0.861196\pi$
$614$	1.02904e18	0.775068
$615$	0	0
$616$	−6.19466e16	−0.0456818
$617$	−1.95877e18	−1.42932	−0.714662	−	0.699470i	$-0.753419\pi$
$617$	−1.95877e18	−1.42932	−0.714662	+	0.699470i	$0.753419\pi$
$618$	0	0
$619$	−4.04759e17	−0.289206	−0.144603	−	0.989490i	$-0.546190\pi$
$619$	−4.04759e17	−0.289206	−0.144603	+	0.989490i	$0.546190\pi$
$620$	3.43881e17	0.243143
$621$	0	0
$622$	1.13515e18	0.785988
$623$	5.46671e17	0.374588
$624$	0	0
$625$	−2.17850e17	−0.146196
$626$	1.64110e17	0.108994
$627$	0	0
$628$	3.79746e16	0.0247033
$629$	2.79972e18	1.80254
$630$	0	0
$631$	8.71701e17	0.549764	0.274882	−	0.961478i	$-0.411361\pi$
$631$	8.71701e17	0.549764	0.274882	+	0.961478i	$0.411361\pi$
$632$	1.00831e18	0.629411
$633$	0	0
$634$	−5.15863e17	−0.315467
$635$	1.25805e18	0.761501
$636$	0	0
$637$	−2.74041e17	−0.162521
$638$	1.54481e17	0.0906860
$639$	0	0
$640$	−1.03008e17	−0.0592518
$641$	−1.69840e18	−0.967081	−0.483541	−	0.875322i	$-0.660649\pi$
$641$	−1.69840e18	−0.967081	−0.483541	+	0.875322i	$0.660649\pi$
$642$	0	0
$643$	−5.45846e17	−0.304578	−0.152289	−	0.988336i	$-0.548665\pi$
$643$	−5.45846e17	−0.304578	−0.152289	+	0.988336i	$0.548665\pi$
$644$	−2.66334e17	−0.147119
$645$	0	0
$646$	2.80680e18	1.51950
$647$	2.01243e18	1.07855	0.539277	−	0.842128i	$-0.318698\pi$
$647$	2.01243e18	1.07855	0.539277	+	0.842128i	$0.318698\pi$
$648$	0	0
$649$	8.30156e17	0.436083
$650$	8.51691e17	0.442940
$651$	0	0
$652$	1.07332e18	0.547168
$653$	9.20122e17	0.464419	0.232209	−	0.972666i	$-0.425405\pi$
$653$	9.20122e17	0.464419	0.232209	+	0.972666i	$0.425405\pi$
$654$	0	0
$655$	1.22459e18	0.605928
$656$	−6.53306e17	−0.320068
$657$	0	0
$658$	5.62948e15	0.00270396
$659$	2.27269e18	1.08090	0.540448	−	0.841377i	$-0.318255\pi$
$659$	2.27269e18	1.08090	0.540448	+	0.841377i	$0.318255\pi$
$660$	0	0
$661$	3.69043e18	1.72094	0.860472	−	0.509497i	$-0.170169\pi$
$661$	3.69043e18	1.72094	0.860472	+	0.509497i	$0.170169\pi$
$662$	4.75217e17	0.219439
$663$	0	0
$664$	3.47118e17	0.157176
$665$	−7.33431e17	−0.328866
$666$	0	0
$667$	6.64176e17	0.292056
$668$	−1.89990e18	−0.827340
$669$	0	0
$670$	7.65570e17	0.326963
$671$	8.90312e17	0.376570
$672$	0	0
$673$	−3.12858e18	−1.29792	−0.648962	−	0.760821i	$-0.724797\pi$
$673$	−3.12858e18	−1.29792	−0.648962	+	0.760821i	$0.724797\pi$
$674$	3.29779e17	0.135498
$675$	0	0
$676$	3.65030e17	0.147121
$677$	−4.47234e18	−1.78529	−0.892644	−	0.450763i	$-0.851152\pi$
$677$	−4.47234e18	−1.78529	−0.892644	+	0.450763i	$0.851152\pi$
$678$	0	0
$679$	−3.31573e17	−0.129845
$680$	−1.01163e18	−0.392388
$681$	0	0
$682$	4.60793e17	0.175351
$683$	−1.57013e18	−0.591837	−0.295918	−	0.955213i	$-0.595626\pi$
$683$	−1.57013e18	−0.591837	−0.295918	+	0.955213i	$0.595626\pi$
$684$	0	0
$685$	2.56425e18	0.948358
$686$	1.04218e17	0.0381802
$687$	0	0
$688$	5.01526e17	0.180289
$689$	−2.32918e18	−0.829427
$690$	0	0
$691$	−2.67383e18	−0.934386	−0.467193	−	0.884155i	$-0.654735\pi$
$691$	−2.67383e18	−0.934386	−0.467193	+	0.884155i	$0.654735\pi$
$692$	−1.54102e18	−0.533481
$693$	0	0
$694$	−7.30405e17	−0.248158
$695$	−2.62658e18	−0.884077
$696$	0	0
$697$	−6.41607e18	−2.11961
$698$	1.93941e18	0.634761
$699$	0	0
$700$	−3.23900e17	−0.104058
$701$	3.07765e18	0.979606	0.489803	−	0.871833i	$-0.337069\pi$
$701$	3.07765e18	0.979606	0.489803	+	0.871833i	$0.337069\pi$
$702$	0	0
$703$	4.52274e18	1.41316
$704$	−1.38029e17	−0.0427314
$705$	0	0
$706$	3.40841e18	1.03591
$707$	2.92635e17	0.0881252
$708$	0	0
$709$	6.83405e17	0.202059	0.101029	−	0.994883i	$-0.467786\pi$
$709$	6.83405e17	0.202059	0.101029	+	0.994883i	$0.467786\pi$
$710$	2.48092e18	0.726831
$711$	0	0
$712$	1.21808e18	0.350395
$713$	1.98114e18	0.564720
$714$	0	0
$715$	−9.31409e17	−0.260706
$716$	−1.45801e18	−0.404414
$717$	0	0
$718$	−1.92689e18	−0.524866
$719$	−1.34506e18	−0.363081	−0.181541	−	0.983383i	$-0.558108\pi$
$719$	−1.34506e18	−0.363081	−0.181541	+	0.983383i	$0.558108\pi$
$720$	0	0
$721$	−7.22641e17	−0.191577
$722$	1.84279e18	0.484154
$723$	0	0
$724$	2.32338e18	0.599543
$725$	8.07733e17	0.206572
$726$	0	0
$727$	−5.81055e18	−1.45963	−0.729816	−	0.683644i	$-0.760394\pi$
$727$	−5.81055e18	−1.45963	−0.729816	+	0.683644i	$0.760394\pi$
$728$	−6.10615e17	−0.152025
$729$	0	0
$730$	3.45318e18	0.844540
$731$	4.92544e18	1.19394
$732$	0	0
$733$	2.44434e17	0.0582084	0.0291042	−	0.999576i	$-0.490735\pi$
$733$	2.44434e17	0.0582084	0.0291042	+	0.999576i	$0.490735\pi$
$734$	−4.42425e17	−0.104427
$735$	0	0
$736$	−5.93442e17	−0.137617
$737$	1.02585e18	0.235800
$738$	0	0
$739$	3.45173e18	0.779557	0.389779	−	0.920909i	$-0.372551\pi$
$739$	3.45173e18	0.779557	0.389779	+	0.920909i	$0.372551\pi$
$740$	−1.63010e18	−0.364929
$741$	0	0
$742$	8.85792e17	0.194853
$743$	−7.48952e18	−1.63315	−0.816576	−	0.577238i	$-0.804131\pi$
$743$	−7.48952e18	−1.63315	−0.816576	+	0.577238i	$0.804131\pi$
$744$	0	0
$745$	3.03173e18	0.649643
$746$	−2.26814e18	−0.481801
$747$	0	0
$748$	−1.35557e18	−0.282983
$749$	−2.53525e18	−0.524674
$750$	0	0
$751$	−7.07612e18	−1.43925	−0.719624	−	0.694364i	$-0.755686\pi$
$751$	−7.07612e18	−1.43925	−0.719624	+	0.694364i	$0.755686\pi$
$752$	1.25435e16	0.00252932
$753$	0	0
$754$	1.52274e18	0.301794
$755$	−1.73118e18	−0.340162
$756$	0	0
$757$	−2.71915e18	−0.525182	−0.262591	−	0.964907i	$-0.584577\pi$
$757$	−2.71915e18	−0.525182	−0.262591	+	0.964907i	$0.584577\pi$
$758$	−3.01555e18	−0.577453
$759$	0	0
$760$	−1.63422e18	−0.307626
$761$	3.75390e18	0.700620	0.350310	−	0.936634i	$-0.386076\pi$
$761$	3.75390e18	0.700620	0.350310	+	0.936634i	$0.386076\pi$
$762$	0	0
$763$	−8.91064e17	−0.163493
$764$	−3.22130e18	−0.586037
$765$	0	0
$766$	3.26234e18	0.583501
$767$	8.18295e18	1.45124
$768$	0	0
$769$	−2.01020e18	−0.350525	−0.175262	−	0.984522i	$-0.556077\pi$
$769$	−2.01020e18	−0.350525	−0.175262	+	0.984522i	$0.556077\pi$
$770$	3.54217e17	0.0612462
$771$	0	0
$772$	−4.56119e18	−0.775471
$773$	−1.12666e19	−1.89945	−0.949723	−	0.313091i	$-0.898636\pi$
$773$	−1.12666e19	−1.89945	−0.949723	+	0.313091i	$0.898636\pi$
$774$	0	0
$775$	2.40935e18	0.399428
$776$	−7.38807e17	−0.121459
$777$	0	0
$778$	−6.65006e18	−1.07512
$779$	−1.03647e19	−1.66174
$780$	0	0
$781$	3.32438e18	0.524178
$782$	−5.82814e18	−0.911352
$783$	0	0
$784$	2.32218e17	0.0357143
$785$	−2.17143e17	−0.0331201
$786$	0	0
$787$	1.05482e18	0.158249	0.0791247	−	0.996865i	$-0.474787\pi$
$787$	1.05482e18	0.158249	0.0791247	+	0.996865i	$0.474787\pi$
$788$	−2.20603e18	−0.328240
$789$	0	0
$790$	−5.76563e18	−0.843861
$791$	−3.43581e18	−0.498750
$792$	0	0
$793$	8.77592e18	1.25319
$794$	2.43053e18	0.344244
$795$	0	0
$796$	−2.44819e18	−0.341123
$797$	−5.41811e18	−0.748805	−0.374403	−	0.927266i	$-0.622152\pi$
$797$	−5.41811e18	−0.748805	−0.374403	+	0.927266i	$0.622152\pi$
$798$	0	0
$799$	1.23189e17	0.0167501
$800$	−7.21709e17	−0.0973369
$801$	0	0
$802$	5.07651e18	0.673647
$803$	4.62718e18	0.609068
$804$	0	0
$805$	1.52292e18	0.197244
$806$	4.54210e18	0.583551
$807$	0	0
$808$	6.52046e17	0.0824336
$809$	−3.40592e18	−0.427139	−0.213569	−	0.976928i	$-0.568509\pi$
$809$	−3.40592e18	−0.427139	−0.213569	+	0.976928i	$0.568509\pi$
$810$	0	0
$811$	−6.56822e18	−0.810611	−0.405305	−	0.914181i	$-0.632835\pi$
$811$	−6.56822e18	−0.810611	−0.405305	+	0.914181i	$0.632835\pi$
$812$	−5.79100e17	−0.0708989
$813$	0	0
$814$	−2.18430e18	−0.263180
$815$	−6.13736e18	−0.733597
$816$	0	0
$817$	7.95669e18	0.936029
$818$	1.00822e19	1.17668
$819$	0	0
$820$	3.73567e18	0.429120
$821$	−1.24012e19	−1.41330	−0.706648	−	0.707566i	$-0.749793\pi$
$821$	−1.24012e19	−1.41330	−0.706648	+	0.707566i	$0.749793\pi$
$822$	0	0
$823$	−1.25113e19	−1.40347	−0.701735	−	0.712438i	$-0.747591\pi$
$823$	−1.25113e19	−1.40347	−0.701735	+	0.712438i	$0.747591\pi$
$824$	−1.61018e18	−0.179204
$825$	0	0
$826$	−3.11199e18	−0.340933
$827$	−9.25974e18	−1.00650	−0.503249	−	0.864142i	$-0.667862\pi$
$827$	−9.25974e18	−1.00650	−0.503249	+	0.864142i	$0.667862\pi$
$828$	0	0
$829$	−1.47271e19	−1.57585	−0.787923	−	0.615773i	$-0.788844\pi$
$829$	−1.47271e19	−1.57585	−0.787923	+	0.615773i	$0.788844\pi$
$830$	−1.98486e18	−0.210728
$831$	0	0
$832$	−1.36057e18	−0.142206
$833$	2.28060e18	0.236513
$834$	0	0
$835$	1.08638e19	1.10923
$836$	−2.18982e18	−0.221854
$837$	0	0
$838$	2.12220e18	0.211690
$839$	7.00176e18	0.693034	0.346517	−	0.938044i	$-0.387364\pi$
$839$	7.00176e18	0.693034	0.346517	+	0.938044i	$0.387364\pi$
$840$	0	0
$841$	−8.81648e18	−0.859254
$842$	−2.25094e18	−0.217689
$843$	0	0
$844$	5.46317e18	0.520258
$845$	−2.08728e18	−0.197247
$846$	0	0
$847$	−3.58692e18	−0.333795
$848$	1.97371e18	0.182268
$849$	0	0
$850$	−7.08785e18	−0.644602
$851$	−9.39119e18	−0.847576
$852$	0	0
$853$	9.37798e18	0.833567	0.416784	−	0.909006i	$-0.363157\pi$
$853$	9.37798e18	0.833567	0.416784	+	0.909006i	$0.363157\pi$
$854$	−3.33750e18	−0.294405
$855$	0	0
$856$	−5.64902e18	−0.490787
$857$	1.22211e18	0.105375	0.0526874	−	0.998611i	$-0.483221\pi$
$857$	1.22211e18	0.105375	0.0526874	+	0.998611i	$0.483221\pi$
$858$	0	0
$859$	−1.39678e19	−1.18624	−0.593122	−	0.805113i	$-0.702105\pi$
$859$	−1.39678e19	−1.18624	−0.593122	+	0.805113i	$0.702105\pi$
$860$	−2.86777e18	−0.241716
$861$	0	0
$862$	6.49007e18	0.538831
$863$	1.18210e19	0.974056	0.487028	−	0.873386i	$-0.338081\pi$
$863$	1.18210e19	0.974056	0.487028	+	0.873386i	$0.338081\pi$
$864$	0	0
$865$	8.81172e18	0.715247
$866$	7.41734e18	0.597561
$867$	0	0
$868$	−1.72737e18	−0.137090
$869$	−7.72582e18	−0.608578
$870$	0	0
$871$	1.01119e19	0.784721
$872$	−1.98546e18	−0.152934
$873$	0	0
$874$	−9.41494e18	−0.714485
$875$	5.21573e18	0.392883
$876$	0	0
$877$	1.65808e19	1.23057	0.615286	−	0.788304i	$-0.289040\pi$
$877$	1.65808e19	1.23057	0.615286	+	0.788304i	$0.289040\pi$
$878$	1.05076e19	0.774085
$879$	0	0
$880$	7.89261e17	0.0572906
$881$	2.75257e19	1.98333	0.991664	−	0.128850i	$-0.0411287\pi$
$881$	2.75257e19	1.98333	0.991664	+	0.128850i	$0.0411287\pi$
$882$	0	0
$883$	1.62598e19	1.15444	0.577218	−	0.816590i	$-0.304138\pi$
$883$	1.62598e19	1.15444	0.577218	+	0.816590i	$0.304138\pi$
$884$	−1.33620e19	−0.941741
$885$	0	0
$886$	−1.50567e19	−1.04571
$887$	4.75597e18	0.327895	0.163948	−	0.986469i	$-0.447577\pi$
$887$	4.75597e18	0.327895	0.163948	+	0.986469i	$0.447577\pi$
$888$	0	0
$889$	−6.31940e18	−0.429353
$890$	−6.96513e18	−0.469779
$891$	0	0
$892$	5.02627e18	0.334098
$893$	1.99003e17	0.0131318
$894$	0	0
$895$	8.33706e18	0.542205
$896$	5.17426e17	0.0334077
$897$	0	0
$898$	−1.95587e18	−0.124464
$899$	4.30767e18	0.272147
$900$	0	0
$901$	1.93836e19	1.20705
$902$	5.00571e18	0.309474
$903$	0	0
$904$	−7.65564e18	−0.466537
$905$	−1.32853e19	−0.803817
$906$	0	0
$907$	3.02495e17	0.0180414	0.00902070	−	0.999959i	$-0.497129\pi$
$907$	3.02495e17	0.0180414	0.00902070	+	0.999959i	$0.497129\pi$
$908$	−1.12286e18	−0.0664919
$909$	0	0
$910$	3.49156e18	0.203822
$911$	−1.67132e19	−0.968704	−0.484352	−	0.874873i	$-0.660945\pi$
$911$	−1.67132e19	−0.968704	−0.484352	+	0.874873i	$0.660945\pi$
$912$	0	0
$913$	−2.65966e18	−0.151973
$914$	2.28638e19	1.29717
$915$	0	0
$916$	−8.05923e18	−0.450789
$917$	−6.15129e18	−0.341637
$918$	0	0
$919$	8.42253e18	0.461202	0.230601	−	0.973048i	$-0.425931\pi$
$919$	8.42253e18	0.461202	0.230601	+	0.973048i	$0.425931\pi$
$920$	3.39336e18	0.184505
$921$	0	0
$922$	−1.19836e19	−0.642446
$923$	3.27688e19	1.74441
$924$	0	0
$925$	−1.14210e19	−0.599493
$926$	1.35067e19	0.704008
$927$	0	0
$928$	−1.29034e18	−0.0663198
$929$	1.25875e19	0.642446	0.321223	−	0.947004i	$-0.395906\pi$
$929$	1.25875e19	0.642446	0.321223	+	0.947004i	$0.395906\pi$
$930$	0	0
$931$	3.68414e18	0.185423
$932$	4.69136e18	0.234475
$933$	0	0
$934$	−1.14905e19	−0.566348
$935$	7.75127e18	0.379400
$936$	0	0
$937$	5.23382e18	0.252646	0.126323	−	0.991989i	$-0.459682\pi$
$937$	5.23382e18	0.252646	0.126323	+	0.991989i	$0.459682\pi$
$938$	−3.84558e18	−0.184350
$939$	0	0
$940$	−7.17251e16	−0.00339110
$941$	3.31505e19	1.55653	0.778264	−	0.627937i	$-0.216100\pi$
$941$	3.31505e19	1.55653	0.778264	+	0.627937i	$0.216100\pi$
$942$	0	0
$943$	2.15216e19	0.996665
$944$	−6.93411e18	−0.318913
$945$	0	0
$946$	−3.84275e18	−0.174321
$947$	2.27873e19	1.02664	0.513321	−	0.858197i	$-0.328415\pi$
$947$	2.27873e19	1.02664	0.513321	+	0.858197i	$0.328415\pi$
$948$	0	0
$949$	4.56107e19	2.02692
$950$	−1.14499e19	−0.505357
$951$	0	0
$952$	5.08160e18	0.221238
$953$	1.50640e19	0.651383	0.325692	−	0.945476i	$-0.394403\pi$
$953$	1.50640e19	0.651383	0.325692	+	0.945476i	$0.394403\pi$
$954$	0	0
$955$	1.84197e19	0.785709
$956$	−9.64203e17	−0.0408500
$957$	0	0
$958$	8.26173e18	0.345299
$959$	−1.28806e19	−0.534708
$960$	0	0
$961$	−1.15684e19	−0.473775
$962$	−2.15309e19	−0.875839
$963$	0	0
$964$	1.32107e19	0.530183
$965$	2.60813e19	1.03969
$966$	0	0
$967$	1.08669e19	0.427399	0.213699	−	0.976899i	$-0.431449\pi$
$967$	1.08669e19	0.427399	0.213699	+	0.976899i	$0.431449\pi$
$968$	−7.99233e18	−0.312236
$969$	0	0
$970$	4.22457e18	0.162842
$971$	−4.92269e19	−1.88485	−0.942426	−	0.334415i	$-0.891461\pi$
$971$	−4.92269e19	−1.88485	−0.942426	+	0.334415i	$0.891461\pi$
$972$	0	0
$973$	1.31937e19	0.498465
$974$	2.64619e19	0.993087
$975$	0	0
$976$	−7.43658e18	−0.275391
$977$	4.65195e19	1.71128	0.855639	−	0.517573i	$-0.173164\pi$
$977$	4.65195e19	1.71128	0.855639	+	0.517573i	$0.173164\pi$
$978$	0	0
$979$	−9.33312e18	−0.338797
$980$	−1.32785e18	−0.0478827
$981$	0	0
$982$	−1.60144e19	−0.569884
$983$	−1.05496e17	−0.00372941	−0.00186470	−	0.999998i	$-0.500594\pi$
$983$	−1.05496e17	−0.00372941	−0.00186470	+	0.999998i	$0.500594\pi$
$984$	0	0
$985$	1.26143e19	0.440076
$986$	−1.26724e19	−0.439195
$987$	0	0
$988$	−2.15853e19	−0.738310
$989$	−1.65216e19	−0.561404
$990$	0	0
$991$	9.41331e18	0.315692	0.157846	−	0.987464i	$-0.449545\pi$
$991$	9.41331e18	0.315692	0.157846	+	0.987464i	$0.449545\pi$
$992$	−3.84890e18	−0.128236
$993$	0	0
$994$	−1.24620e19	−0.409806
$995$	1.39990e19	0.457349
$996$	0	0
$997$	−3.35430e18	−0.108164	−0.0540821	−	0.998536i	$-0.517223\pi$
$997$	−3.35430e18	−0.108164	−0.0540821	+	0.998536i	$0.517223\pi$
$998$	3.76705e19	1.20685
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.14.a.q.1.1	yes	3
3.2	odd	2		126.14.a.n.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.14.a.n.1.3	✓	3	3.2	odd	2
126.14.a.q.1.1	yes	3	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	126.a (trivial)

\(f(q)\)	\(=\)	\(q+64.0000 q^{2} +4096.00 q^{4} -23421.3 q^{5} +117649. q^{7} +262144. q^{8} +O(q^{10})\)	\(q+64.0000 q^{2} +4096.00 q^{4} -23421.3 q^{5} +117649. q^{7} +262144. q^{8} -1.49897e6 q^{10} -2.00858e6 q^{11} -1.97988e7 q^{13} +7.52954e6 q^{14} +1.67772e7 q^{16} +1.64768e8 q^{17} +2.66170e8 q^{19} -9.59338e7 q^{20} -1.28549e8 q^{22} -5.52686e8 q^{23} -6.72144e8 q^{25} -1.26713e9 q^{26} +4.81890e8 q^{28} -1.20173e9 q^{29} -3.58457e9 q^{31} +1.07374e9 q^{32} +1.05451e10 q^{34} -2.75550e9 q^{35} +1.69919e10 q^{37} +1.70349e10 q^{38} -6.13976e9 q^{40} -3.89401e10 q^{41} +2.98933e10 q^{43} -8.22715e9 q^{44} -3.53719e10 q^{46} +7.47652e8 q^{47} +1.38413e10 q^{49} -4.30172e10 q^{50} -8.10960e10 q^{52} +1.17642e11 q^{53} +4.70436e10 q^{55} +3.08410e10 q^{56} -7.69104e10 q^{58} -4.13305e11 q^{59} -4.43254e11 q^{61} -2.29412e11 q^{62} +6.87195e10 q^{64} +4.63715e11 q^{65} -5.10733e11 q^{67} +6.74888e11 q^{68} -1.76352e11 q^{70} -1.65509e12 q^{71} -2.30371e12 q^{73} +1.08748e12 q^{74} +1.09023e12 q^{76} -2.36307e11 q^{77} +3.84641e12 q^{79} -3.92945e11 q^{80} -2.49217e12 q^{82} +1.32415e12 q^{83} -3.85908e12 q^{85} +1.91317e12 q^{86} -5.26537e11 q^{88} +4.64662e12 q^{89} -2.32931e12 q^{91} -2.26380e12 q^{92} +4.78498e10 q^{94} -6.23406e12 q^{95} -2.81833e12 q^{97} +8.85842e11 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 192 q^{2} + 12288 q^{4} + 28626 q^{5} + 352947 q^{7} + 786432 q^{8}+O(q^{10}) \) 3 * q + 192 * q^2 + 12288 * q^4 + 28626 * q^5 + 352947 * q^7 + 786432 * q^8	\( 3 q + 192 q^{2} + 12288 q^{4} + 28626 q^{5} + 352947 q^{7} + 786432 q^{8} + 1832064 q^{10} - 6749178 q^{11} - 20854146 q^{13} + 22588608 q^{14} + 50331648 q^{16} - 100425522 q^{17} + 12403932 q^{19} + 117252096 q^{20} - 431947392 q^{22} - 1036880814 q^{23} - 1530084579 q^{25} - 1334665344 q^{26} + 1445670912 q^{28} - 6435734376 q^{29} - 7714124292 q^{31} + 3221225472 q^{32} - 6427233408 q^{34} + 3367820274 q^{35} - 4624801554 q^{37} + 793851648 q^{38} + 7504134144 q^{40} - 46350517542 q^{41} + 51758123748 q^{43} - 27644633088 q^{44} - 66360372096 q^{46} - 21038057028 q^{47} + 41523861603 q^{49} - 97925413056 q^{50} - 85418582016 q^{52} - 128680526676 q^{53} - 247890301164 q^{55} + 92522938368 q^{56} - 411887000064 q^{58} - 24358384620 q^{59} - 545351650806 q^{61} - 493703954688 q^{62} + 206158430208 q^{64} + 866329895316 q^{65} + 615866153748 q^{67} - 411342938112 q^{68} + 215540497536 q^{70} - 605458102410 q^{71} - 445510372998 q^{73} - 295987299456 q^{74} + 50806505472 q^{76} - 794034042522 q^{77} - 4236900439512 q^{79} + 480264585216 q^{80} - 2966433122688 q^{82} + 4730128213344 q^{83} - 11970847755036 q^{85} + 3312519919872 q^{86} - 1769256517632 q^{88} + 8837998962402 q^{89} - 2453469422754 q^{91} - 4247063814144 q^{92} - 1346435649792 q^{94} - 8416214321784 q^{95} - 19638839012358 q^{97} + 2657527142592 q^{98}+O(q^{100}) \) 3 * q + 192 * q^2 + 12288 * q^4 + 28626 * q^5 + 352947 * q^7 + 786432 * q^8 + 1832064 * q^10 - 6749178 * q^11 - 20854146 * q^13 + 22588608 * q^14 + 50331648 * q^16 - 100425522 * q^17 + 12403932 * q^19 + 117252096 * q^20 - 431947392 * q^22 - 1036880814 * q^23 - 1530084579 * q^25 - 1334665344 * q^26 + 1445670912 * q^28 - 6435734376 * q^29 - 7714124292 * q^31 + 3221225472 * q^32 - 6427233408 * q^34 + 3367820274 * q^35 - 4624801554 * q^37 + 793851648 * q^38 + 7504134144 * q^40 - 46350517542 * q^41 + 51758123748 * q^43 - 27644633088 * q^44 - 66360372096 * q^46 - 21038057028 * q^47 + 41523861603 * q^49 - 97925413056 * q^50 - 85418582016 * q^52 - 128680526676 * q^53 - 247890301164 * q^55 + 92522938368 * q^56 - 411887000064 * q^58 - 24358384620 * q^59 - 545351650806 * q^61 - 493703954688 * q^62 + 206158430208 * q^64 + 866329895316 * q^65 + 615866153748 * q^67 - 411342938112 * q^68 + 215540497536 * q^70 - 605458102410 * q^71 - 445510372998 * q^73 - 295987299456 * q^74 + 50806505472 * q^76 - 794034042522 * q^77 - 4236900439512 * q^79 + 480264585216 * q^80 - 2966433122688 * q^82 + 4730128213344 * q^83 - 11970847755036 * q^85 + 3312519919872 * q^86 - 1769256517632 * q^88 + 8837998962402 * q^89 - 2453469422754 * q^91 - 4247063814144 * q^92 - 1346435649792 * q^94 - 8416214321784 * q^95 - 19638839012358 * q^97 + 2657527142592 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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