LMFDB - Embedded newform 126.14.a.q.1.2

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			1.2
Root			$251.737$ 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)

$f(q)$	$=$	$q+64.0000 q^{2} +4096.00 q^{4} +15323.1 q^{5} +117649. q^{7} +262144. q^{8} +O(q^{10})$	\(q+64.0000 q^{2} +4096.00 q^{4} +15323.1 q^{5} +117649. q^{7} +262144. q^{8} +980680. q^{10} +5.64640e6 q^{11} -2.06237e7 q^{13} +7.52954e6 q^{14} +1.67772e7 q^{16} -7.60354e7 q^{17} -3.33497e8 q^{19} +6.27635e7 q^{20} +3.61370e8 q^{22} -2.83209e8 q^{23} -9.85905e8 q^{25} -1.31992e9 q^{26} +4.81890e8 q^{28} -4.74314e8 q^{29} +4.90709e9 q^{31} +1.07374e9 q^{32} -4.86626e9 q^{34} +1.80275e9 q^{35} -2.20724e10 q^{37} -2.13438e10 q^{38} +4.01686e9 q^{40} +3.26777e10 q^{41} +1.07144e10 q^{43} +2.31277e10 q^{44} -1.81254e10 q^{46} -1.00347e11 q^{47} +1.38413e10 q^{49} -6.30979e10 q^{50} -8.44748e10 q^{52} -1.79847e11 q^{53} +8.65205e10 q^{55} +3.08410e10 q^{56} -3.03561e10 q^{58} +5.06252e11 q^{59} -1.45802e11 q^{61} +3.14053e11 q^{62} +6.87195e10 q^{64} -3.16020e11 q^{65} -2.84828e11 q^{67} -3.11441e11 q^{68} +1.15376e11 q^{70} -6.35097e11 q^{71} +6.84963e11 q^{73} -1.41263e12 q^{74} -1.36601e12 q^{76} +6.64294e11 q^{77} -3.93368e12 q^{79} +2.57079e11 q^{80} +2.09137e12 q^{82} +3.78847e12 q^{83} -1.16510e12 q^{85} +6.85720e11 q^{86} +1.48017e12 q^{88} +4.82036e12 q^{89} -2.42636e12 q^{91} -1.16002e12 q^{92} -6.42219e12 q^{94} -5.11022e12 q^{95} -4.74169e12 q^{97} +8.85842e11 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	15323.1	0.438573	0.219287	−	0.975660i	$-0.429627\pi$
$5$	15323.1	0.438573	0.219287	+	0.975660i	$0.429627\pi$
$6$	0	0
$7$	117649.	0.377964
$7$	117649.	0.377964
$8$	262144.	0.353553
$9$	0	0
$10$	980680.	0.310118
$11$	5.64640e6	0.960991	0.480496	−	0.876997i	$-0.340457\pi$
$11$	5.64640e6	0.960991	0.480496	+	0.876997i	$0.340457\pi$
$12$	0	0
$13$	−2.06237e7	−1.18505	−0.592523	−	0.805553i	$-0.701868\pi$
$13$	−2.06237e7	−1.18505	−0.592523	+	0.805553i	$0.701868\pi$
$14$	7.52954e6	0.267261
$15$	0	0
$16$	1.67772e7	0.250000
$17$	−7.60354e7	−0.764008	−0.382004	−	0.924161i	$-0.624766\pi$
$17$	−7.60354e7	−0.764008	−0.382004	+	0.924161i	$0.624766\pi$
$18$	0	0
$19$	−3.33497e8	−1.62627	−0.813137	−	0.582072i	$-0.802242\pi$
$19$	−3.33497e8	−1.62627	−0.813137	+	0.582072i	$0.802242\pi$
$20$	6.27635e7	0.219287
$21$	0	0
$22$	3.61370e8	0.679523
$23$	−2.83209e8	−0.398911	−0.199455	−	0.979907i	$-0.563917\pi$
$23$	−2.83209e8	−0.398911	−0.199455	+	0.979907i	$0.563917\pi$
$24$	0	0
$25$	−9.85905e8	−0.807653
$26$	−1.31992e9	−0.837955
$27$	0	0
$28$	4.81890e8	0.188982
$29$	−4.74314e8	−0.148074	−0.0740371	−	0.997255i	$-0.523588\pi$
$29$	−4.74314e8	−0.148074	−0.0740371	+	0.997255i	$0.523588\pi$
$30$	0	0
$31$	4.90709e9	0.993053	0.496527	−	0.868021i	$-0.334608\pi$
$31$	4.90709e9	0.993053	0.496527	+	0.868021i	$0.334608\pi$
$32$	1.07374e9	0.176777
$33$	0	0
$34$	−4.86626e9	−0.540235
$35$	1.80275e9	0.165765
$36$	0	0
$37$	−2.20724e10	−1.41429	−0.707145	−	0.707069i	$-0.750017\pi$
$37$	−2.20724e10	−1.41429	−0.707145	+	0.707069i	$0.750017\pi$
$38$	−2.13438e10	−1.14995
$39$	0	0
$40$	4.01686e9	0.155059
$41$	3.26777e10	1.07438	0.537188	−	0.843463i	$-0.319487\pi$
$41$	3.26777e10	1.07438	0.537188	+	0.843463i	$0.319487\pi$
$42$	0	0
$43$	1.07144e10	0.258477	0.129239	−	0.991614i	$-0.458747\pi$
$43$	1.07144e10	0.258477	0.129239	+	0.991614i	$0.458747\pi$
$44$	2.31277e10	0.480496
$45$	0	0
$46$	−1.81254e10	−0.282072
$47$	−1.00347e11	−1.35790	−0.678949	−	0.734185i	$-0.737564\pi$
$47$	−1.00347e11	−1.35790	−0.678949	+	0.734185i	$0.737564\pi$
$48$	0	0
$49$	1.38413e10	0.142857
$50$	−6.30979e10	−0.571097
$51$	0	0
$52$	−8.44748e10	−0.592523
$53$	−1.79847e11	−1.11458	−0.557289	−	0.830319i	$-0.688158\pi$
$53$	−1.79847e11	−1.11458	−0.557289	+	0.830319i	$0.688158\pi$
$54$	0	0
$55$	8.65205e10	0.421465
$56$	3.08410e10	0.133631
$57$	0	0
$58$	−3.03561e10	−0.104704
$59$	5.06252e11	1.56253	0.781266	−	0.624198i	$-0.214574\pi$
$59$	5.06252e11	1.56253	0.781266	+	0.624198i	$0.214574\pi$
$60$	0	0
$61$	−1.45802e11	−0.362342	−0.181171	−	0.983452i	$-0.557989\pi$
$61$	−1.45802e11	−0.362342	−0.181171	+	0.983452i	$0.557989\pi$
$62$	3.14053e11	0.702195
$63$	0	0
$64$	6.87195e10	0.125000
$65$	−3.16020e11	−0.519730
$66$	0	0
$67$	−2.84828e11	−0.384677	−0.192338	−	0.981329i	$-0.561607\pi$
$67$	−2.84828e11	−0.384677	−0.192338	+	0.981329i	$0.561607\pi$
$68$	−3.11441e11	−0.382004
$69$	0	0
$70$	1.15376e11	0.117214
$71$	−6.35097e11	−0.588384	−0.294192	−	0.955746i	$-0.595050\pi$
$71$	−6.35097e11	−0.588384	−0.294192	+	0.955746i	$0.595050\pi$
$72$	0	0
$73$	6.84963e11	0.529747	0.264874	−	0.964283i	$-0.414670\pi$
$73$	6.84963e11	0.529747	0.264874	+	0.964283i	$0.414670\pi$
$74$	−1.41263e12	−1.00005
$75$	0	0
$76$	−1.36601e12	−0.813137
$77$	6.64294e11	0.363221
$78$	0	0
$79$	−3.93368e12	−1.82064	−0.910318	−	0.413910i	$-0.864163\pi$
$79$	−3.93368e12	−1.82064	−0.910318	+	0.413910i	$0.864163\pi$
$80$	2.57079e11	0.109643
$81$	0	0
$82$	2.09137e12	0.759698
$83$	3.78847e12	1.27191	0.635955	−	0.771726i	$-0.280606\pi$
$83$	3.78847e12	1.27191	0.635955	+	0.771726i	$0.280606\pi$
$84$	0	0
$85$	−1.16510e12	−0.335073
$86$	6.85720e11	0.182771
$87$	0	0
$88$	1.48017e12	0.339762
$89$	4.82036e12	1.02812	0.514061	−	0.857754i	$-0.328141\pi$
$89$	4.82036e12	1.02812	0.514061	+	0.857754i	$0.328141\pi$
$90$	0	0
$91$	−2.42636e12	−0.447906
$92$	−1.16002e12	−0.199455
$93$	0	0
$94$	−6.42219e12	−0.960179
$95$	−5.11022e12	−0.713241
$96$	0	0
$97$	−4.74169e12	−0.577986	−0.288993	−	0.957331i	$-0.593320\pi$
$97$	−4.74169e12	−0.577986	−0.288993	+	0.957331i	$0.593320\pi$
$98$	8.85842e11	0.101015
$99$	0	0
$100$	−4.03827e12	−0.403827
$101$	−1.76920e13	−1.65839	−0.829196	−	0.558957i	$-0.811202\pi$
$101$	−1.76920e13	−1.65839	−0.829196	+	0.558957i	$0.811202\pi$
$102$	0	0
$103$	4.19037e12	0.345789	0.172894	−	0.984940i	$-0.444688\pi$
$103$	4.19037e12	0.345789	0.172894	+	0.984940i	$0.444688\pi$
$104$	−5.40639e12	−0.418977
$105$	0	0
$106$	−1.15102e13	−0.788125
$107$	1.65899e13	1.06869	0.534343	−	0.845268i	$-0.320559\pi$
$107$	1.65899e13	1.06869	0.534343	+	0.845268i	$0.320559\pi$
$108$	0	0
$109$	−2.58013e13	−1.47356	−0.736782	−	0.676131i	$-0.763655\pi$
$109$	−2.58013e13	−1.47356	−0.736782	+	0.676131i	$0.763655\pi$
$110$	5.53731e12	0.298021
$111$	0	0
$112$	1.97382e12	0.0944911
$113$	−4.07669e13	−1.84203	−0.921017	−	0.389522i	$-0.872640\pi$
$113$	−4.07669e13	−1.84203	−0.921017	+	0.389522i	$0.872640\pi$
$114$	0	0
$115$	−4.33964e12	−0.174952
$116$	−1.94279e12	−0.0740371
$117$	0	0
$118$	3.24002e13	1.10488
$119$	−8.94549e12	−0.288768
$120$	0	0
$121$	−2.64085e12	−0.0764959
$122$	−9.33130e12	−0.256214
$123$	0	0
$124$	2.00994e13	0.496527
$125$	−3.38121e13	−0.792788
$126$	0	0
$127$	6.87253e13	1.45343	0.726713	−	0.686942i	$-0.241047\pi$
$127$	6.87253e13	1.45343	0.726713	+	0.686942i	$0.241047\pi$
$128$	4.39805e12	0.0883883
$129$	0	0
$130$	−2.02253e13	−0.367505
$131$	−3.29512e13	−0.569650	−0.284825	−	0.958579i	$-0.591936\pi$
$131$	−3.29512e13	−0.569650	−0.284825	+	0.958579i	$0.591936\pi$
$132$	0	0
$133$	−3.92356e13	−0.614674
$134$	−1.82290e13	−0.272008
$135$	0	0
$136$	−1.99322e13	−0.270117
$137$	6.69463e13	0.865053	0.432526	−	0.901621i	$-0.357622\pi$
$137$	6.69463e13	0.865053	0.432526	+	0.901621i	$0.357622\pi$
$138$	0	0
$139$	3.43956e13	0.404489	0.202245	−	0.979335i	$-0.435176\pi$
$139$	3.43956e13	0.404489	0.202245	+	0.979335i	$0.435176\pi$
$140$	7.38406e12	0.0828826
$141$	0	0
$142$	−4.06462e13	−0.416050
$143$	−1.16450e14	−1.13882
$144$	0	0
$145$	−7.26797e12	−0.0649414
$146$	4.38376e13	0.374588
$147$	0	0
$148$	−9.04086e13	−0.707145
$149$	−1.78414e14	−1.33573	−0.667865	−	0.744283i	$-0.732792\pi$
$149$	−1.78414e14	−1.33573	−0.667865	+	0.744283i	$0.732792\pi$
$150$	0	0
$151$	1.60693e14	1.10318	0.551591	−	0.834115i	$-0.314021\pi$
$151$	1.60693e14	1.10318	0.551591	+	0.834115i	$0.314021\pi$
$152$	−8.74243e13	−0.574975
$153$	0	0
$154$	4.25148e13	0.256836
$155$	7.51919e13	0.435527
$156$	0	0
$157$	−4.19829e13	−0.223730	−0.111865	−	0.993723i	$-0.535682\pi$
$157$	−4.19829e13	−0.223730	−0.111865	+	0.993723i	$0.535682\pi$
$158$	−2.51756e14	−1.28738
$159$	0	0
$160$	1.64531e13	0.0775295
$161$	−3.33192e13	−0.150774
$162$	0	0
$163$	1.05367e14	0.440034	0.220017	−	0.975496i	$-0.429389\pi$
$163$	1.05367e14	0.440034	0.220017	+	0.975496i	$0.429389\pi$
$164$	1.33848e14	0.537188
$165$	0	0
$166$	2.42462e14	0.899377
$167$	−1.04806e14	−0.373876	−0.186938	−	0.982372i	$-0.559856\pi$
$167$	−1.04806e14	−0.373876	−0.186938	+	0.982372i	$0.559856\pi$
$168$	0	0
$169$	1.22463e14	0.404336
$170$	−7.45663e13	−0.236933
$171$	0	0
$172$	4.38861e13	0.129239
$173$	−4.34642e14	−1.23263	−0.616314	−	0.787501i	$-0.711375\pi$
$173$	−4.34642e14	−1.23263	−0.616314	+	0.787501i	$0.711375\pi$
$174$	0	0
$175$	−1.15991e14	−0.305264
$176$	9.47309e13	0.240248
$177$	0	0
$178$	3.08503e14	0.726992
$179$	−7.50597e14	−1.70554	−0.852771	−	0.522286i	$-0.825080\pi$
$179$	−7.50597e14	−1.70554	−0.852771	+	0.522286i	$0.825080\pi$
$180$	0	0
$181$	2.89595e14	0.612182	0.306091	−	0.952002i	$-0.400979\pi$
$181$	2.89595e14	0.612182	0.306091	+	0.952002i	$0.400979\pi$
$182$	−1.55287e14	−0.316717
$183$	0	0
$184$	−7.42415e13	−0.141036
$185$	−3.38218e14	−0.620270
$186$	0	0
$187$	−4.29326e14	−0.734205
$188$	−4.11020e14	−0.678949
$189$	0	0
$190$	−3.27054e14	−0.504337
$191$	−5.90213e14	−0.879613	−0.439807	−	0.898093i	$-0.644953\pi$
$191$	−5.90213e14	−0.879613	−0.439807	+	0.898093i	$0.644953\pi$
$192$	0	0
$193$	6.21104e14	0.865052	0.432526	−	0.901622i	$-0.357622\pi$
$193$	6.21104e14	0.865052	0.432526	+	0.901622i	$0.357622\pi$
$194$	−3.03468e14	−0.408698
$195$	0	0
$196$	5.66939e13	0.0714286
$197$	6.31232e13	0.0769411	0.0384706	−	0.999260i	$-0.487751\pi$
$197$	6.31232e13	0.0769411	0.0384706	+	0.999260i	$0.487751\pi$
$198$	0	0
$199$	2.34675e14	0.267868	0.133934	−	0.990990i	$-0.457239\pi$
$199$	2.34675e14	0.267868	0.133934	+	0.990990i	$0.457239\pi$
$200$	−2.58449e14	−0.285549
$201$	0	0
$202$	−1.13229e15	−1.17266
$203$	−5.58026e13	−0.0559668
$204$	0	0
$205$	5.00724e14	0.471192
$206$	2.68184e14	0.244510
$207$	0	0
$208$	−3.46009e14	−0.296262
$209$	−1.88306e15	−1.56284
$210$	0	0
$211$	−1.16936e15	−0.912246	−0.456123	−	0.889917i	$-0.650762\pi$
$211$	−1.16936e15	−0.912246	−0.456123	+	0.889917i	$0.650762\pi$
$212$	−7.36654e14	−0.557289
$213$	0	0
$214$	1.06176e15	0.755675
$215$	1.64178e14	0.113361
$216$	0	0
$217$	5.77314e14	0.375339
$218$	−1.65128e15	−1.04197
$219$	0	0
$220$	3.54388e14	0.210733
$221$	1.56813e15	0.905385
$222$	0	0
$223$	9.88233e13	0.0538118	0.0269059	−	0.999638i	$-0.491435\pi$
$223$	9.88233e13	0.0538118	0.0269059	+	0.999638i	$0.491435\pi$
$224$	1.26325e14	0.0668153
$225$	0	0
$226$	−2.60908e15	−1.30252
$227$	−3.53468e15	−1.71468	−0.857338	−	0.514754i	$-0.827883\pi$
$227$	−3.53468e15	−1.71468	−0.857338	+	0.514754i	$0.827883\pi$
$228$	0	0
$229$	−6.56673e14	−0.300897	−0.150449	−	0.988618i	$-0.548072\pi$
$229$	−6.56673e14	−0.300897	−0.150449	+	0.988618i	$0.548072\pi$
$230$	−2.77737e14	−0.123709
$231$	0	0
$232$	−1.24339e14	−0.0523521
$233$	−1.66753e15	−0.682747	−0.341373	−	0.939928i	$-0.610892\pi$
$233$	−1.66753e15	−0.682747	−0.341373	+	0.939928i	$0.610892\pi$
$234$	0	0
$235$	−1.53763e15	−0.595538
$236$	2.07361e15	0.781266
$237$	0	0
$238$	−5.72511e14	−0.204190
$239$	−2.76708e15	−0.960363	−0.480182	−	0.877169i	$-0.659429\pi$
$239$	−2.76708e15	−0.960363	−0.480182	+	0.877169i	$0.659429\pi$
$240$	0	0
$241$	−4.56799e15	−1.50181	−0.750903	−	0.660412i	$-0.770382\pi$
$241$	−4.56799e15	−1.50181	−0.750903	+	0.660412i	$0.770382\pi$
$242$	−1.69014e14	−0.0540908
$243$	0	0
$244$	−5.97203e14	−0.181171
$245$	2.12092e14	0.0626533
$246$	0	0
$247$	6.87796e15	1.92721
$248$	1.28636e15	0.351097
$249$	0	0
$250$	−2.16398e15	−0.560586
$251$	5.84990e15	1.47662	0.738311	−	0.674460i	$-0.235624\pi$
$251$	5.84990e15	1.47662	0.738311	+	0.674460i	$0.235624\pi$
$252$	0	0
$253$	−1.59911e15	−0.383350
$254$	4.39842e15	1.02773
$255$	0	0
$256$	2.81475e14	0.0625000
$257$	3.55727e15	0.770109	0.385054	−	0.922894i	$-0.374183\pi$
$257$	3.55727e15	0.770109	0.385054	+	0.922894i	$0.374183\pi$
$258$	0	0
$259$	−2.59680e15	−0.534551
$260$	−1.29442e15	−0.259865
$261$	0	0
$262$	−2.10888e15	−0.402804
$263$	−6.04279e15	−1.12597	−0.562983	−	0.826469i	$-0.690346\pi$
$263$	−6.04279e15	−1.12597	−0.562983	+	0.826469i	$0.690346\pi$
$264$	0	0
$265$	−2.75582e15	−0.488824
$266$	−2.51108e15	−0.434640
$267$	0	0
$268$	−1.16665e15	−0.192338
$269$	−5.22365e14	−0.0840591	−0.0420295	−	0.999116i	$-0.513382\pi$
$269$	−5.22365e14	−0.0840591	−0.0420295	+	0.999116i	$0.513382\pi$
$270$	0	0
$271$	9.42573e15	1.44549	0.722745	−	0.691115i	$-0.242880\pi$
$271$	9.42573e15	1.44549	0.722745	+	0.691115i	$0.242880\pi$
$272$	−1.27566e15	−0.191002
$273$	0	0
$274$	4.28456e15	0.611685
$275$	−5.56682e15	−0.776148
$276$	0	0
$277$	9.66957e15	1.28614	0.643071	−	0.765807i	$-0.277660\pi$
$277$	9.66957e15	1.28614	0.643071	+	0.765807i	$0.277660\pi$
$278$	2.20132e15	0.286017
$279$	0	0
$280$	4.72580e14	0.0586068
$281$	1.02639e16	1.24372	0.621858	−	0.783130i	$-0.286378\pi$
$281$	1.02639e16	1.24372	0.621858	+	0.783130i	$0.286378\pi$
$282$	0	0
$283$	5.83610e15	0.675322	0.337661	−	0.941268i	$-0.390364\pi$
$283$	5.83610e15	0.675322	0.337661	+	0.941268i	$0.390364\pi$
$284$	−2.60136e15	−0.294192
$285$	0	0
$286$	−7.45280e15	−0.805267
$287$	3.84449e15	0.406076
$288$	0	0
$289$	−4.12320e15	−0.416292
$290$	−4.65150e14	−0.0459205
$291$	0	0
$292$	2.80561e15	0.264874
$293$	1.13390e16	1.04697	0.523484	−	0.852035i	$-0.324632\pi$
$293$	1.13390e16	1.04697	0.523484	+	0.852035i	$0.324632\pi$
$294$	0	0
$295$	7.75737e15	0.685285
$296$	−5.78615e15	−0.500027
$297$	0	0
$298$	−1.14185e16	−0.944503
$299$	5.84082e15	0.472728
$300$	0	0
$301$	1.26054e15	0.0976952
$302$	1.02844e16	0.780067
$303$	0	0
$304$	−5.59516e15	−0.406569
$305$	−2.23413e15	−0.158913
$306$	0	0
$307$	7.53184e15	0.513454	0.256727	−	0.966484i	$-0.417356\pi$
$307$	7.53184e15	0.513454	0.256727	+	0.966484i	$0.417356\pi$
$308$	2.72095e15	0.181610
$309$	0	0
$310$	4.81228e15	0.307964
$311$	7.78207e15	0.487700	0.243850	−	0.969813i	$-0.421590\pi$
$311$	7.78207e15	0.487700	0.243850	+	0.969813i	$0.421590\pi$
$312$	0	0
$313$	2.34163e16	1.40761	0.703803	−	0.710395i	$-0.251484\pi$
$313$	2.34163e16	1.40761	0.703803	+	0.710395i	$0.251484\pi$
$314$	−2.68691e15	−0.158201
$315$	0	0
$316$	−1.61124e16	−0.910318
$317$	1.68957e16	0.935173	0.467586	−	0.883947i	$-0.345124\pi$
$317$	1.68957e16	0.935173	0.467586	+	0.883947i	$0.345124\pi$
$318$	0	0
$319$	−2.67817e15	−0.142298
$320$	1.05300e15	0.0548217
$321$	0	0
$322$	−2.13243e15	−0.106613
$323$	2.53576e16	1.24249
$324$	0	0
$325$	2.03330e16	0.957107
$326$	6.74350e15	0.311151
$327$	0	0
$328$	8.56625e15	0.379849
$329$	−1.18057e16	−0.513237
$330$	0	0
$331$	−5.55038e15	−0.231975	−0.115987	−	0.993251i	$-0.537003\pi$
$331$	−5.55038e15	−0.231975	−0.115987	+	0.993251i	$0.537003\pi$
$332$	1.55176e16	0.635955
$333$	0	0
$334$	−6.70755e15	−0.264370
$335$	−4.36445e15	−0.168709
$336$	0	0
$337$	2.39455e16	0.890489	0.445245	−	0.895409i	$-0.353117\pi$
$337$	2.39455e16	0.890489	0.445245	+	0.895409i	$0.353117\pi$
$338$	7.83766e15	0.285909
$339$	0	0
$340$	−4.77225e15	−0.167537
$341$	2.77074e16	0.954316
$342$	0	0
$343$	1.62841e15	0.0539949
$344$	2.80871e15	0.0913855
$345$	0	0
$346$	−2.78171e16	−0.871600
$347$	4.68235e16	1.43987	0.719933	−	0.694043i	$-0.244172\pi$
$347$	4.68235e16	1.43987	0.719933	+	0.694043i	$0.244172\pi$
$348$	0	0
$349$	−2.16760e16	−0.642117	−0.321059	−	0.947059i	$-0.604039\pi$
$349$	−2.16760e16	−0.642117	−0.321059	+	0.947059i	$0.604039\pi$
$350$	−7.42341e15	−0.215854
$351$	0	0
$352$	6.06278e15	0.169881
$353$	1.23689e16	0.340248	0.170124	−	0.985423i	$-0.445583\pi$
$353$	1.23689e16	0.340248	0.170124	+	0.985423i	$0.445583\pi$
$354$	0	0
$355$	−9.73167e15	−0.258049
$356$	1.97442e16	0.514061
$357$	0	0
$358$	−4.80382e16	−1.20600
$359$	1.62210e16	0.399912	0.199956	−	0.979805i	$-0.435920\pi$
$359$	1.62210e16	0.399912	0.199956	+	0.979805i	$0.435920\pi$
$360$	0	0
$361$	6.91675e16	1.64477
$362$	1.85341e16	0.432878
$363$	0	0
$364$	−9.93838e15	−0.223953
$365$	1.04958e16	0.232333
$366$	0	0
$367$	3.07981e16	0.657952	0.328976	−	0.944338i	$-0.393296\pi$
$367$	3.07981e16	0.657952	0.328976	+	0.944338i	$0.393296\pi$
$368$	−4.75145e15	−0.0997277
$369$	0	0
$370$	−2.16460e16	−0.438597
$371$	−2.11588e16	−0.421271
$372$	0	0
$373$	1.19635e16	0.230013	0.115006	−	0.993365i	$-0.463311\pi$
$373$	1.19635e16	0.230013	0.115006	+	0.993365i	$0.463311\pi$
$374$	−2.74769e16	−0.519161
$375$	0	0
$376$	−2.63053e16	−0.480090
$377$	9.78213e15	0.175475
$378$	0	0
$379$	1.31339e16	0.227635	0.113817	−	0.993502i	$-0.463692\pi$
$379$	1.31339e16	0.227635	0.113817	+	0.993502i	$0.463692\pi$
$380$	−2.09315e16	−0.356620
$381$	0	0
$382$	−3.77736e16	−0.621980
$383$	6.35584e16	1.02892	0.514459	−	0.857515i	$-0.327993\pi$
$383$	6.35584e16	1.02892	0.514459	+	0.857515i	$0.327993\pi$
$384$	0	0
$385$	1.01791e16	0.159299
$386$	3.97507e16	0.611684
$387$	0	0
$388$	−1.94220e16	−0.288993
$389$	−7.12809e16	−1.04304	−0.521519	−	0.853239i	$-0.674635\pi$
$389$	−7.12809e16	−1.04304	−0.521519	+	0.853239i	$0.674635\pi$
$390$	0	0
$391$	2.15339e16	0.304771
$392$	3.62841e15	0.0505076
$393$	0	0
$394$	4.03989e15	0.0544056
$395$	−6.02763e16	−0.798482
$396$	0	0
$397$	−4.92324e16	−0.631122	−0.315561	−	0.948905i	$-0.602193\pi$
$397$	−4.92324e16	−0.631122	−0.315561	+	0.948905i	$0.602193\pi$
$398$	1.50192e16	0.189411
$399$	0	0
$400$	−1.65407e16	−0.201913
$401$	−7.39682e16	−0.888396	−0.444198	−	0.895929i	$-0.646511\pi$
$401$	−7.39682e16	−0.888396	−0.444198	+	0.895929i	$0.646511\pi$
$402$	0	0
$403$	−1.01202e17	−1.17681
$404$	−7.24663e16	−0.829196
$405$	0	0
$406$	−3.57137e15	−0.0395745
$407$	−1.24630e17	−1.35912
$408$	0	0
$409$	9.56147e16	1.01000	0.505002	−	0.863118i	$-0.331492\pi$
$409$	9.56147e16	1.01000	0.505002	+	0.863118i	$0.331492\pi$
$410$	3.20463e16	0.333183
$411$	0	0
$412$	1.71638e16	0.172894
$413$	5.95601e16	0.590582
$414$	0	0
$415$	5.80512e16	0.557826
$416$	−2.21446e16	−0.209489
$417$	0	0
$418$	−1.20516e17	−1.10509
$419$	8.58774e15	0.0775332	0.0387666	−	0.999248i	$-0.487657\pi$
$419$	8.58774e15	0.0775332	0.0387666	+	0.999248i	$0.487657\pi$
$420$	0	0
$421$	−1.88315e17	−1.64835	−0.824176	−	0.566333i	$-0.808362\pi$
$421$	−1.88315e17	−1.64835	−0.824176	+	0.566333i	$0.808362\pi$
$422$	−7.48390e16	−0.645055
$423$	0	0
$424$	−4.71458e16	−0.394063
$425$	7.49637e16	0.617053
$426$	0	0
$427$	−1.71534e16	−0.136952
$428$	6.79523e16	0.534343
$429$	0	0
$430$	1.05074e16	0.0801584
$431$	−1.72198e17	−1.29397	−0.646986	−	0.762502i	$-0.723971\pi$
$431$	−1.72198e17	−1.29397	−0.646986	+	0.762502i	$0.723971\pi$
$432$	0	0
$433$	9.54958e16	0.696327	0.348163	−	0.937434i	$-0.386805\pi$
$433$	9.54958e16	0.696327	0.348163	+	0.937434i	$0.386805\pi$
$434$	3.69481e16	0.265405
$435$	0	0
$436$	−1.05682e17	−0.736782
$437$	9.44493e16	0.648738
$438$	0	0
$439$	6.10612e16	0.407142	0.203571	−	0.979060i	$-0.434745\pi$
$439$	6.10612e16	0.407142	0.203571	+	0.979060i	$0.434745\pi$
$440$	2.26808e16	0.149010
$441$	0	0
$442$	1.00361e17	0.640204
$443$	6.61674e16	0.415930	0.207965	−	0.978136i	$-0.433316\pi$
$443$	6.61674e16	0.415930	0.207965	+	0.978136i	$0.433316\pi$
$444$	0	0
$445$	7.38630e16	0.450907
$446$	6.32469e15	0.0380507
$447$	0	0
$448$	8.08478e15	0.0472456
$449$	−2.74356e17	−1.58021	−0.790103	−	0.612974i	$-0.789973\pi$
$449$	−2.74356e17	−1.58021	−0.790103	+	0.612974i	$0.789973\pi$
$450$	0	0
$451$	1.84511e17	1.03247
$452$	−1.66981e17	−0.921017
$453$	0	0
$454$	−2.26220e17	−1.21246
$455$	−3.71794e16	−0.196439
$456$	0	0
$457$	1.90076e17	0.976049	0.488025	−	0.872830i	$-0.337718\pi$
$457$	1.90076e17	0.976049	0.488025	+	0.872830i	$0.337718\pi$
$458$	−4.20271e16	−0.212767
$459$	0	0
$460$	−1.77752e16	−0.0874758
$461$	−1.01418e17	−0.492105	−0.246052	−	0.969257i	$-0.579134\pi$
$461$	−1.01418e17	−0.492105	−0.246052	+	0.969257i	$0.579134\pi$
$462$	0	0
$463$	2.03404e17	0.959582	0.479791	−	0.877383i	$-0.340712\pi$
$463$	2.03404e17	0.959582	0.479791	+	0.877383i	$0.340712\pi$
$464$	−7.95767e15	−0.0370185
$465$	0	0
$466$	−1.06722e17	−0.482775
$467$	−3.01383e17	−1.34449	−0.672247	−	0.740327i	$-0.734671\pi$
$467$	−3.01383e17	−1.34449	−0.672247	+	0.740327i	$0.734671\pi$
$468$	0	0
$469$	−3.35097e16	−0.145394
$470$	−9.84080e16	−0.421109
$471$	0	0
$472$	1.32711e17	0.552439
$473$	6.04977e16	0.248394
$474$	0	0
$475$	3.28797e17	1.31347
$476$	−3.66407e16	−0.144384
$477$	0	0
$478$	−1.77093e17	−0.679080
$479$	−1.96236e17	−0.742330	−0.371165	−	0.928567i	$-0.621042\pi$
$479$	−1.96236e17	−0.742330	−0.371165	+	0.928567i	$0.621042\pi$
$480$	0	0
$481$	4.55215e17	1.67600
$482$	−2.92351e17	−1.06194
$483$	0	0
$484$	−1.08169e16	−0.0382479
$485$	−7.26576e16	−0.253489
$486$	0	0
$487$	−3.59649e17	−1.22163	−0.610817	−	0.791772i	$-0.709159\pi$
$487$	−3.59649e17	−1.22163	−0.610817	+	0.791772i	$0.709159\pi$
$488$	−3.82210e16	−0.128107
$489$	0	0
$490$	1.35739e16	0.0443026
$491$	3.17998e17	1.02422	0.512112	−	0.858919i	$-0.328863\pi$
$491$	3.17998e17	1.02422	0.512112	+	0.858919i	$0.328863\pi$
$492$	0	0
$493$	3.60647e16	0.113130
$494$	4.40190e17	1.36274
$495$	0	0
$496$	8.23272e16	0.248263
$497$	−7.47185e16	−0.222388
$498$	0	0
$499$	−9.87909e16	−0.286460	−0.143230	−	0.989689i	$-0.545749\pi$
$499$	−9.87909e16	−0.286460	−0.143230	+	0.989689i	$0.545749\pi$
$500$	−1.38494e17	−0.396394
$501$	0	0
$502$	3.74394e17	1.04413
$503$	8.78308e16	0.241799	0.120900	−	0.992665i	$-0.461422\pi$
$503$	8.78308e16	0.241799	0.120900	+	0.992665i	$0.461422\pi$
$504$	0	0
$505$	−2.71096e17	−0.727327
$506$	−1.02343e17	−0.271069
$507$	0	0
$508$	2.81499e17	0.726713
$509$	−2.20677e17	−0.562459	−0.281230	−	0.959640i	$-0.590742\pi$
$509$	−2.20677e17	−0.562459	−0.281230	+	0.959640i	$0.590742\pi$
$510$	0	0
$511$	8.05852e16	0.200226
$512$	1.80144e16	0.0441942
$513$	0	0
$514$	2.27666e17	0.544549
$515$	6.42096e16	0.151654
$516$	0	0
$517$	−5.66598e17	−1.30493
$518$	−1.66195e17	−0.377985
$519$	0	0
$520$	−8.28427e16	−0.183752
$521$	−4.56008e16	−0.0998913	−0.0499456	−	0.998752i	$-0.515905\pi$
$521$	−4.56008e16	−0.0998913	−0.0499456	+	0.998752i	$0.515905\pi$
$522$	0	0
$523$	−2.09406e17	−0.447433	−0.223717	−	0.974654i	$-0.571819\pi$
$523$	−2.09406e17	−0.447433	−0.223717	+	0.974654i	$0.571819\pi$
$524$	−1.34968e17	−0.284825
$525$	0	0
$526$	−3.86739e17	−0.796178
$527$	−3.73112e17	−0.758700
$528$	0	0
$529$	−4.23829e17	−0.840870
$530$	−1.76372e17	−0.345651
$531$	0	0
$532$	−1.60709e17	−0.307337
$533$	−6.73936e17	−1.27319
$534$	0	0
$535$	2.54209e17	0.468697
$536$	−7.46659e16	−0.136004
$537$	0	0
$538$	−3.34314e16	−0.0594387
$539$	7.81535e16	0.137284
$540$	0	0
$541$	9.87980e17	1.69420	0.847102	−	0.531430i	$-0.178345\pi$
$541$	9.87980e17	1.69420	0.847102	+	0.531430i	$0.178345\pi$
$542$	6.03247e17	1.02212
$543$	0	0
$544$	−8.16424e16	−0.135059
$545$	−3.95356e17	−0.646265
$546$	0	0
$547$	7.20939e17	1.15075	0.575375	−	0.817890i	$-0.304856\pi$
$547$	7.20939e17	1.15075	0.575375	+	0.817890i	$0.304856\pi$
$548$	2.74212e17	0.432526
$549$	0	0
$550$	−3.56276e17	−0.548819
$551$	1.58183e17	0.240809
$552$	0	0
$553$	−4.62794e17	−0.688136
$554$	6.18852e17	0.909439
$555$	0	0
$556$	1.40885e17	0.202245
$557$	2.83144e17	0.401744	0.200872	−	0.979618i	$-0.435623\pi$
$557$	2.83144e17	0.401744	0.200872	+	0.979618i	$0.435623\pi$
$558$	0	0
$559$	−2.20971e17	−0.306308
$560$	3.02451e16	0.0414413
$561$	0	0
$562$	6.56889e17	0.879440
$563$	3.84715e17	0.509137	0.254568	−	0.967055i	$-0.418067\pi$
$563$	3.84715e17	0.509137	0.254568	+	0.967055i	$0.418067\pi$
$564$	0	0
$565$	−6.24676e17	−0.807867
$566$	3.73511e17	0.477525
$567$	0	0
$568$	−1.66487e17	−0.208025
$569$	7.59963e17	0.938778	0.469389	−	0.882991i	$-0.344474\pi$
$569$	7.59963e17	0.938778	0.469389	+	0.882991i	$0.344474\pi$
$570$	0	0
$571$	−9.82854e17	−1.18674	−0.593368	−	0.804931i	$-0.702202\pi$
$571$	−9.82854e17	−1.18674	−0.593368	+	0.804931i	$0.702202\pi$
$572$	−4.76979e17	−0.569410
$573$	0	0
$574$	2.46048e17	0.287139
$575$	2.79217e17	0.322182
$576$	0	0
$577$	1.77301e17	0.200018	0.100009	−	0.994987i	$-0.468113\pi$
$577$	1.77301e17	0.200018	0.100009	+	0.994987i	$0.468113\pi$
$578$	−2.63885e17	−0.294363
$579$	0	0
$580$	−2.97696e16	−0.0324707
$581$	4.45710e17	0.480737
$582$	0	0
$583$	−1.01549e18	−1.07110
$584$	1.79559e17	0.187294
$585$	0	0
$586$	7.25694e17	0.740319
$587$	1.61570e18	1.63009	0.815046	−	0.579396i	$-0.196711\pi$
$587$	1.61570e18	1.63009	0.815046	+	0.579396i	$0.196711\pi$
$588$	0	0
$589$	−1.63650e18	−1.61498
$590$	4.96471e17	0.484570
$591$	0	0
$592$	−3.70313e17	−0.353572
$593$	−7.90447e17	−0.746478	−0.373239	−	0.927735i	$-0.621753\pi$
$593$	−7.90447e17	−0.746478	−0.373239	+	0.927735i	$0.621753\pi$
$594$	0	0
$595$	−1.37073e17	−0.126646
$596$	−7.30784e17	−0.667865
$597$	0	0
$598$	3.73813e17	0.334269
$599$	1.53111e17	0.135435	0.0677175	−	0.997705i	$-0.478428\pi$
$599$	1.53111e17	0.135435	0.0677175	+	0.997705i	$0.478428\pi$
$600$	0	0
$601$	−1.08594e18	−0.939984	−0.469992	−	0.882671i	$-0.655743\pi$
$601$	−1.08594e18	−0.939984	−0.469992	+	0.882671i	$0.655743\pi$
$602$	8.06743e16	0.0690809
$603$	0	0
$604$	6.58199e17	0.551591
$605$	−4.04660e16	−0.0335490
$606$	0	0
$607$	−1.07256e18	−0.870356	−0.435178	−	0.900345i	$-0.643314\pi$
$607$	−1.07256e18	−0.870356	−0.435178	+	0.900345i	$0.643314\pi$
$608$	−3.58090e17	−0.287487
$609$	0	0
$610$	−1.42985e17	−0.112369
$611$	2.06953e18	1.60917
$612$	0	0
$613$	1.70702e18	1.29941	0.649706	−	0.760186i	$-0.274892\pi$
$613$	1.70702e18	1.29941	0.649706	+	0.760186i	$0.274892\pi$
$614$	4.82038e17	0.363067
$615$	0	0
$616$	1.74141e17	0.128418
$617$	1.38595e18	1.01133	0.505666	−	0.862730i	$-0.331247\pi$
$617$	1.38595e18	1.01133	0.505666	+	0.862730i	$0.331247\pi$
$618$	0	0
$619$	2.52441e18	1.80373	0.901864	−	0.432020i	$-0.142199\pi$
$619$	2.52441e18	1.80373	0.901864	+	0.432020i	$0.142199\pi$
$620$	3.07986e17	0.217763
$621$	0	0
$622$	4.98053e17	0.344856
$623$	5.67111e17	0.388594
$624$	0	0
$625$	6.85390e17	0.459958
$626$	1.49865e18	0.995327
$627$	0	0
$628$	−1.71962e17	−0.111865
$629$	1.67828e18	1.08053
$630$	0	0
$631$	−2.46593e18	−1.55521	−0.777606	−	0.628752i	$-0.783566\pi$
$631$	−2.46593e18	−1.55521	−0.777606	+	0.628752i	$0.783566\pi$
$632$	−1.03119e18	−0.643692
$633$	0	0
$634$	1.08133e18	0.661267
$635$	1.05309e18	0.637433
$636$	0	0
$637$	−2.85459e17	−0.169292
$638$	−1.71403e17	−0.100620
$639$	0	0
$640$	6.73918e16	0.0387648
$641$	2.57543e18	1.46647	0.733235	−	0.679976i	$-0.238010\pi$
$641$	2.57543e18	1.46647	0.733235	+	0.679976i	$0.238010\pi$
$642$	0	0
$643$	−3.10459e18	−1.73234	−0.866168	−	0.499752i	$-0.833424\pi$
$643$	−3.10459e18	−1.73234	−0.866168	+	0.499752i	$0.833424\pi$
$644$	−1.36476e17	−0.0753870
$645$	0	0
$646$	1.62289e18	0.878571
$647$	−1.76176e18	−0.944210	−0.472105	−	0.881542i	$-0.656506\pi$
$647$	−1.76176e18	−0.944210	−0.472105	+	0.881542i	$0.656506\pi$
$648$	0	0
$649$	2.85851e18	1.50158
$650$	1.30132e18	0.676777
$651$	0	0
$652$	4.31584e17	0.220017
$653$	−2.62459e18	−1.32472	−0.662362	−	0.749184i	$-0.730446\pi$
$653$	−2.62459e18	−1.32472	−0.662362	+	0.749184i	$0.730446\pi$
$654$	0	0
$655$	−5.04916e17	−0.249833
$656$	5.48240e17	0.268594
$657$	0	0
$658$	−7.55565e17	−0.362914
$659$	−3.32448e18	−1.58113	−0.790567	−	0.612376i	$-0.790214\pi$
$659$	−3.32448e18	−1.58113	−0.790567	+	0.612376i	$0.790214\pi$
$660$	0	0
$661$	−1.38824e18	−0.647374	−0.323687	−	0.946164i	$-0.604922\pi$
$661$	−1.38824e18	−0.647374	−0.323687	+	0.946164i	$0.604922\pi$
$662$	−3.55224e17	−0.164031
$663$	0	0
$664$	9.93126e17	0.449688
$665$	−6.01212e17	−0.269580
$666$	0	0
$667$	1.34330e17	0.0590683
$668$	−4.29283e17	−0.186938
$669$	0	0
$670$	−2.79325e17	−0.119295
$671$	−8.23254e17	−0.348207
$672$	0	0
$673$	−2.27577e18	−0.944127	−0.472064	−	0.881564i	$-0.656491\pi$
$673$	−2.27577e18	−0.944127	−0.472064	+	0.881564i	$0.656491\pi$
$674$	1.53251e18	0.629671
$675$	0	0
$676$	5.01610e17	0.202168
$677$	2.91265e18	1.16268	0.581342	−	0.813659i	$-0.302528\pi$
$677$	2.91265e18	1.16268	0.581342	+	0.813659i	$0.302528\pi$
$678$	0	0
$679$	−5.57856e17	−0.218458
$680$	−3.05424e17	−0.118466
$681$	0	0
$682$	1.77327e18	0.674803
$683$	1.16806e18	0.440282	0.220141	−	0.975468i	$-0.429348\pi$
$683$	1.16806e18	0.440282	0.220141	+	0.975468i	$0.429348\pi$
$684$	0	0
$685$	1.02583e18	0.379389
$686$	1.04218e17	0.0381802
$687$	0	0
$688$	1.79757e17	0.0646193
$689$	3.70912e18	1.32083
$690$	0	0
$691$	−4.44580e17	−0.155361	−0.0776807	−	0.996978i	$-0.524751\pi$
$691$	−4.44580e17	−0.155361	−0.0776807	+	0.996978i	$0.524751\pi$
$692$	−1.78029e18	−0.616314
$693$	0	0
$694$	2.99670e18	1.01814
$695$	5.27048e17	0.177398
$696$	0	0
$697$	−2.48466e18	−0.820831
$698$	−1.38727e18	−0.454046
$699$	0	0
$700$	−4.75098e17	−0.152632
$701$	−2.41325e18	−0.768131	−0.384066	−	0.923306i	$-0.625476\pi$
$701$	−2.41325e18	−0.768131	−0.384066	+	0.923306i	$0.625476\pi$
$702$	0	0
$703$	7.36109e18	2.30002
$704$	3.88018e17	0.120124
$705$	0	0
$706$	7.91611e17	0.240592
$707$	−2.08144e18	−0.626814
$708$	0	0
$709$	−1.83137e18	−0.541472	−0.270736	−	0.962654i	$-0.587267\pi$
$709$	−1.83137e18	−0.541472	−0.270736	+	0.962654i	$0.587267\pi$
$710$	−6.22827e17	−0.182468
$711$	0	0
$712$	1.26363e18	0.363496
$713$	−1.38973e18	−0.396140
$714$	0	0
$715$	−1.78438e18	−0.499456
$716$	−3.07445e18	−0.852771
$717$	0	0
$718$	1.03815e18	0.282780
$719$	−2.42480e18	−0.654543	−0.327272	−	0.944930i	$-0.606129\pi$
$719$	−2.42480e18	−0.654543	−0.327272	+	0.944930i	$0.606129\pi$
$720$	0	0
$721$	4.92993e17	0.130696
$722$	4.42672e18	1.16303
$723$	0	0
$724$	1.18618e18	0.306091
$725$	4.67629e17	0.119593
$726$	0	0
$727$	1.37931e16	0.00346489	0.00173245	−	0.999998i	$-0.499449\pi$
$727$	1.37931e16	0.00346489	0.00173245	+	0.999998i	$0.499449\pi$
$728$	−6.36056e17	−0.158359
$729$	0	0
$730$	6.71729e17	0.164284
$731$	−8.14672e17	−0.197478
$732$	0	0
$733$	6.09115e18	1.45052	0.725260	−	0.688475i	$-0.241720\pi$
$733$	6.09115e18	1.45052	0.725260	+	0.688475i	$0.241720\pi$
$734$	1.97108e18	0.465243
$735$	0	0
$736$	−3.04093e17	−0.0705181
$737$	−1.60825e18	−0.369671
$738$	0	0
$739$	−4.88425e18	−1.10309	−0.551543	−	0.834146i	$-0.685961\pi$
$739$	−4.88425e18	−1.10309	−0.551543	+	0.834146i	$0.685961\pi$
$740$	−1.38534e18	−0.310135
$741$	0	0
$742$	−1.35417e18	−0.297883
$743$	5.26174e18	1.14737	0.573683	−	0.819077i	$-0.305514\pi$
$743$	5.26174e18	1.14737	0.573683	+	0.819077i	$0.305514\pi$
$744$	0	0
$745$	−2.73386e18	−0.585815
$746$	7.65665e17	0.162643
$747$	0	0
$748$	−1.75852e18	−0.367102
$749$	1.95179e18	0.403925
$750$	0	0
$751$	3.23163e18	0.657297	0.328649	−	0.944452i	$-0.393407\pi$
$751$	3.23163e18	0.657297	0.328649	+	0.944452i	$0.393407\pi$
$752$	−1.68354e18	−0.339475
$753$	0	0
$754$	6.26057e17	0.124079
$755$	2.46232e18	0.483826
$756$	0	0
$757$	−3.43437e18	−0.663322	−0.331661	−	0.943399i	$-0.607609\pi$
$757$	−3.43437e18	−0.663322	−0.331661	+	0.943399i	$0.607609\pi$
$758$	8.40570e17	0.160962
$759$	0	0
$760$	−1.33961e18	−0.252169
$761$	−9.57445e18	−1.78696	−0.893478	−	0.449108i	$-0.851742\pi$
$761$	−9.57445e18	−1.78696	−0.893478	+	0.449108i	$0.851742\pi$
$762$	0	0
$763$	−3.03549e18	−0.556955
$764$	−2.41751e18	−0.439807
$765$	0	0
$766$	4.06774e18	0.727555
$767$	−1.04408e19	−1.85167
$768$	0	0
$769$	1.82074e18	0.317488	0.158744	−	0.987320i	$-0.449256\pi$
$769$	1.82074e18	0.317488	0.158744	+	0.987320i	$0.449256\pi$
$770$	6.51459e17	0.112641
$771$	0	0
$772$	2.54404e18	0.432526
$773$	5.16898e17	0.0871442	0.0435721	−	0.999050i	$-0.486126\pi$
$773$	5.16898e17	0.0871442	0.0435721	+	0.999050i	$0.486126\pi$
$774$	0	0
$775$	−4.83792e18	−0.802043
$776$	−1.24301e18	−0.204349
$777$	0	0
$778$	−4.56198e18	−0.737540
$779$	−1.08979e19	−1.74723
$780$	0	0
$781$	−3.58601e18	−0.565432
$782$	1.37817e18	0.215505
$783$	0	0
$784$	2.32218e17	0.0357143
$785$	−6.43309e17	−0.0981221
$786$	0	0
$787$	−6.24702e18	−0.937210	−0.468605	−	0.883408i	$-0.655243\pi$
$787$	−6.24702e18	−0.937210	−0.468605	+	0.883408i	$0.655243\pi$
$788$	2.58553e17	0.0384706
$789$	0	0
$790$	−3.85768e18	−0.564612
$791$	−4.79618e18	−0.696224
$792$	0	0
$793$	3.00697e18	0.429392
$794$	−3.15088e18	−0.446270
$795$	0	0
$796$	9.61227e17	0.133934
$797$	1.54181e18	0.213084	0.106542	−	0.994308i	$-0.466022\pi$
$797$	1.54181e18	0.213084	0.106542	+	0.994308i	$0.466022\pi$
$798$	0	0
$799$	7.62991e18	1.03744
$800$	−1.05861e18	−0.142774
$801$	0	0
$802$	−4.73396e18	−0.628191
$803$	3.86758e18	0.509082
$804$	0	0
$805$	−5.10554e17	−0.0661255
$806$	−6.47696e18	−0.832134
$807$	0	0
$808$	−4.63785e18	−0.586330
$809$	−8.74860e18	−1.09717	−0.548584	−	0.836095i	$-0.684833\pi$
$809$	−8.74860e18	−1.09717	−0.548584	+	0.836095i	$0.684833\pi$
$810$	0	0
$811$	−7.12118e18	−0.878853	−0.439426	−	0.898279i	$-0.644818\pi$
$811$	−7.12118e18	−0.878853	−0.439426	+	0.898279i	$0.644818\pi$
$812$	−2.28567e17	−0.0279834
$813$	0	0
$814$	−7.97630e18	−0.961043
$815$	1.61455e18	0.192987
$816$	0	0
$817$	−3.57322e18	−0.420355
$818$	6.11934e18	0.714181
$819$	0	0
$820$	2.05096e18	0.235596
$821$	−1.05361e18	−0.120074	−0.0600369	−	0.998196i	$-0.519122\pi$
$821$	−1.05361e18	−0.120074	−0.0600369	+	0.998196i	$0.519122\pi$
$822$	0	0
$823$	5.05517e18	0.567070	0.283535	−	0.958962i	$-0.408493\pi$
$823$	5.05517e18	0.567070	0.283535	+	0.958962i	$0.408493\pi$
$824$	1.09848e18	0.122255
$825$	0	0
$826$	3.81185e18	0.417604
$827$	−5.96414e18	−0.648279	−0.324140	−	0.946009i	$-0.605075\pi$
$827$	−5.96414e18	−0.648279	−0.324140	+	0.946009i	$0.605075\pi$
$828$	0	0
$829$	1.52872e19	1.63578	0.817888	−	0.575378i	$-0.195145\pi$
$829$	1.52872e19	1.63578	0.817888	+	0.575378i	$0.195145\pi$
$830$	3.71528e18	0.394443
$831$	0	0
$832$	−1.41725e18	−0.148131
$833$	−1.05243e18	−0.109144
$834$	0	0
$835$	−1.60595e18	−0.163972
$836$	−7.71301e18	−0.781418
$837$	0	0
$838$	5.49615e17	0.0548242
$839$	6.22909e18	0.616555	0.308277	−	0.951297i	$-0.400248\pi$
$839$	6.22909e18	0.616555	0.308277	+	0.951297i	$0.400248\pi$
$840$	0	0
$841$	−1.00357e19	−0.978074
$842$	−1.20521e19	−1.16556
$843$	0	0
$844$	−4.78970e18	−0.456123
$845$	1.87652e18	0.177331
$846$	0	0
$847$	−3.10693e17	−0.0289127
$848$	−3.01733e18	−0.278644
$849$	0	0
$850$	4.79767e18	0.436323
$851$	6.25110e18	0.564175
$852$	0	0
$853$	5.71797e18	0.508245	0.254122	−	0.967172i	$-0.418213\pi$
$853$	5.71797e18	0.508245	0.254122	+	0.967172i	$0.418213\pi$
$854$	−1.09782e18	−0.0968399
$855$	0	0
$856$	4.34895e18	0.377837
$857$	−6.17205e18	−0.532174	−0.266087	−	0.963949i	$-0.585731\pi$
$857$	−6.17205e18	−0.532174	−0.266087	+	0.963949i	$0.585731\pi$
$858$	0	0
$859$	−8.78472e18	−0.746058	−0.373029	−	0.927820i	$-0.621681\pi$
$859$	−8.78472e18	−0.746058	−0.373029	+	0.927820i	$0.621681\pi$
$860$	6.72472e17	0.0566806
$861$	0	0
$862$	−1.10206e19	−0.914976
$863$	−4.47461e17	−0.0368710	−0.0184355	−	0.999830i	$-0.505869\pi$
$863$	−4.47461e17	−0.0368710	−0.0184355	+	0.999830i	$0.505869\pi$
$864$	0	0
$865$	−6.66007e18	−0.540598
$866$	6.11173e18	0.492377
$867$	0	0
$868$	2.36468e18	0.187669
$869$	−2.22111e19	−1.74961
$870$	0	0
$871$	5.87421e18	0.455860
$872$	−6.76365e18	−0.520983
$873$	0	0
$874$	6.04476e18	0.458727
$875$	−3.97796e18	−0.299646
$876$	0	0
$877$	1.45440e19	1.07941	0.539706	−	0.841853i	$-0.318535\pi$
$877$	1.45440e19	1.07941	0.539706	+	0.841853i	$0.318535\pi$
$878$	3.90792e18	0.287893
$879$	0	0
$880$	1.45157e18	0.105366
$881$	1.41474e19	1.01937	0.509686	−	0.860361i	$-0.329762\pi$
$881$	1.41474e19	1.01937	0.509686	+	0.860361i	$0.329762\pi$
$882$	0	0
$883$	1.49661e19	1.06259	0.531294	−	0.847188i	$-0.321706\pi$
$883$	1.49661e19	1.06259	0.531294	+	0.847188i	$0.321706\pi$
$884$	6.42307e18	0.452692
$885$	0	0
$886$	4.23472e18	0.294107
$887$	1.72446e19	1.18891	0.594456	−	0.804128i	$-0.297367\pi$
$887$	1.72446e19	1.18891	0.594456	+	0.804128i	$0.297367\pi$
$888$	0	0
$889$	8.08547e18	0.549343
$890$	4.72723e18	0.318839
$891$	0	0
$892$	4.04780e17	0.0269059
$893$	3.34654e19	2.20832
$894$	0	0
$895$	−1.15015e19	−0.748005
$896$	5.17426e17	0.0334077
$897$	0	0
$898$	−1.75588e19	−1.11737
$899$	−2.32750e18	−0.147046
$900$	0	0
$901$	1.36747e19	0.851546
$902$	1.18087e19	0.730063
$903$	0	0
$904$	−1.06868e19	−0.651258
$905$	4.43750e18	0.268487
$906$	0	0
$907$	1.01372e19	0.604604	0.302302	−	0.953212i	$-0.402245\pi$
$907$	1.01372e19	0.604604	0.302302	+	0.953212i	$0.402245\pi$
$908$	−1.44781e19	−0.857338
$909$	0	0
$910$	−2.37948e18	−0.138904
$911$	1.52037e19	0.881213	0.440607	−	0.897700i	$-0.354763\pi$
$911$	1.52037e19	0.881213	0.440607	+	0.897700i	$0.354763\pi$
$912$	0	0
$913$	2.13912e19	1.22230
$914$	1.21649e19	0.690171
$915$	0	0
$916$	−2.68973e18	−0.150449
$917$	−3.87668e18	−0.215308
$918$	0	0
$919$	1.43546e19	0.786031	0.393016	−	0.919532i	$-0.371432\pi$
$919$	1.43546e19	0.786031	0.393016	+	0.919532i	$0.371432\pi$
$920$	−1.13761e18	−0.0618547
$921$	0	0
$922$	−6.49073e18	−0.347971
$923$	1.30981e19	0.697262
$924$	0	0
$925$	2.17613e19	1.14226
$926$	1.30178e19	0.678527
$927$	0	0
$928$	−5.09291e17	−0.0261761
$929$	−2.19653e19	−1.12108	−0.560538	−	0.828129i	$-0.689406\pi$
$929$	−2.19653e19	−1.12108	−0.560538	+	0.828129i	$0.689406\pi$
$930$	0	0
$931$	−4.61603e18	−0.232325
$932$	−6.83020e18	−0.341373
$933$	0	0
$934$	−1.92885e19	−0.950701
$935$	−6.57862e18	−0.322003
$936$	0	0
$937$	2.52512e19	1.21892	0.609459	−	0.792817i	$-0.291387\pi$
$937$	2.52512e19	1.21892	0.609459	+	0.792817i	$0.291387\pi$
$938$	−2.14462e18	−0.102809
$939$	0	0
$940$	−6.29812e18	−0.297769
$941$	2.36942e19	1.11252	0.556262	−	0.831007i	$-0.312235\pi$
$941$	2.36942e19	1.11252	0.556262	+	0.831007i	$0.312235\pi$
$942$	0	0
$943$	−9.25460e18	−0.428580
$944$	8.49351e18	0.390633
$945$	0	0
$946$	3.87185e18	0.175641
$947$	−3.37052e19	−1.51852	−0.759262	−	0.650785i	$-0.774440\pi$
$947$	−3.37052e19	−1.51852	−0.759262	+	0.650785i	$0.774440\pi$
$948$	0	0
$949$	−1.41265e19	−0.627775
$950$	2.10430e19	0.928761
$951$	0	0
$952$	−2.34501e18	−0.102095
$953$	1.71975e19	0.743640	0.371820	−	0.928305i	$-0.378734\pi$
$953$	1.71975e19	0.743640	0.371820	+	0.928305i	$0.378734\pi$
$954$	0	0
$955$	−9.04390e18	−0.385775
$956$	−1.13340e19	−0.480182
$957$	0	0
$958$	−1.25591e19	−0.524906
$959$	7.87616e18	0.326959
$960$	0	0
$961$	−3.38058e17	−0.0138449
$962$	2.91338e19	1.18511
$963$	0	0
$964$	−1.87105e19	−0.750903
$965$	9.51726e18	0.379389
$966$	0	0
$967$	−1.48904e17	−0.00585647	−0.00292823	−	0.999996i	$-0.500932\pi$
$967$	−1.48904e17	−0.00585647	−0.00292823	+	0.999996i	$0.500932\pi$
$968$	−6.92282e17	−0.0270454
$969$	0	0
$970$	−4.65008e18	−0.179244
$971$	−8.52756e18	−0.326512	−0.163256	−	0.986584i	$-0.552200\pi$
$971$	−8.52756e18	−0.326512	−0.163256	+	0.986584i	$0.552200\pi$
$972$	0	0
$973$	4.04661e18	0.152883
$974$	−2.30176e19	−0.863826
$975$	0	0
$976$	−2.44614e18	−0.0905854
$977$	2.32448e19	0.855088	0.427544	−	0.903994i	$-0.359379\pi$
$977$	2.32448e19	0.855088	0.427544	+	0.903994i	$0.359379\pi$
$978$	0	0
$979$	2.72177e19	0.988016
$980$	8.68728e17	0.0313267
$981$	0	0
$982$	2.03519e19	0.724235
$983$	4.88293e19	1.72617	0.863084	−	0.505060i	$-0.168530\pi$
$983$	4.88293e19	1.72617	0.863084	+	0.505060i	$0.168530\pi$
$984$	0	0
$985$	9.67245e17	0.0337443
$986$	2.30814e18	0.0799948
$987$	0	0
$988$	2.81721e19	0.963606
$989$	−3.03441e18	−0.103109
$990$	0	0
$991$	4.23573e19	1.42053	0.710263	−	0.703936i	$-0.248576\pi$
$991$	4.23573e19	1.42053	0.710263	+	0.703936i	$0.248576\pi$
$992$	5.26894e18	0.175549
$993$	0	0
$994$	−4.78198e18	−0.157252
$995$	3.59595e18	0.117480
$996$	0	0
$997$	−3.63545e19	−1.17230	−0.586151	−	0.810201i	$-0.699358\pi$
$997$	−3.63545e19	−1.17230	−0.586151	+	0.810201i	$0.699358\pi$
$998$	−6.32262e18	−0.202558
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.14.a.q.1.2	yes	3
3.2	odd	2		126.14.a.n.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.14.a.n.1.2	✓	3	3.2	odd	2
126.14.a.q.1.2	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)

\(f(q)\)	\(=\)	\(q+64.0000 q^{2} +4096.00 q^{4} +15323.1 q^{5} +117649. q^{7} +262144. q^{8} +O(q^{10})\)	\(q+64.0000 q^{2} +4096.00 q^{4} +15323.1 q^{5} +117649. q^{7} +262144. q^{8} +980680. q^{10} +5.64640e6 q^{11} -2.06237e7 q^{13} +7.52954e6 q^{14} +1.67772e7 q^{16} -7.60354e7 q^{17} -3.33497e8 q^{19} +6.27635e7 q^{20} +3.61370e8 q^{22} -2.83209e8 q^{23} -9.85905e8 q^{25} -1.31992e9 q^{26} +4.81890e8 q^{28} -4.74314e8 q^{29} +4.90709e9 q^{31} +1.07374e9 q^{32} -4.86626e9 q^{34} +1.80275e9 q^{35} -2.20724e10 q^{37} -2.13438e10 q^{38} +4.01686e9 q^{40} +3.26777e10 q^{41} +1.07144e10 q^{43} +2.31277e10 q^{44} -1.81254e10 q^{46} -1.00347e11 q^{47} +1.38413e10 q^{49} -6.30979e10 q^{50} -8.44748e10 q^{52} -1.79847e11 q^{53} +8.65205e10 q^{55} +3.08410e10 q^{56} -3.03561e10 q^{58} +5.06252e11 q^{59} -1.45802e11 q^{61} +3.14053e11 q^{62} +6.87195e10 q^{64} -3.16020e11 q^{65} -2.84828e11 q^{67} -3.11441e11 q^{68} +1.15376e11 q^{70} -6.35097e11 q^{71} +6.84963e11 q^{73} -1.41263e12 q^{74} -1.36601e12 q^{76} +6.64294e11 q^{77} -3.93368e12 q^{79} +2.57079e11 q^{80} +2.09137e12 q^{82} +3.78847e12 q^{83} -1.16510e12 q^{85} +6.85720e11 q^{86} +1.48017e12 q^{88} +4.82036e12 q^{89} -2.42636e12 q^{91} -1.16002e12 q^{92} -6.42219e12 q^{94} -5.11022e12 q^{95} -4.74169e12 q^{97} +8.85842e11 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 192 q^{2} + 12288 q^{4} + 28626 q^{5} + 352947 q^{7} + 786432 q^{8}+O(q^{10}) \) 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

Related objects

Downloads

Learn more