LMFDB - Embedded newform 9.36.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,36,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 36, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 36);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 36 $
Character orbit:	$[\chi]$	$=$	9.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:	$69.8356175703$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{2196841}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 549210 $ x^2 - x - 549210
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{4}\cdot 3\cdot 7 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-740.587$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+279461. q^{2} +4.37389e10 q^{4} +3.65354e11 q^{5} -6.36148e14 q^{7} +2.62111e15 q^{8} +O(q^{10})$	\(q+279461. q^{2} +4.37389e10 q^{4} +3.65354e11 q^{5} -6.36148e14 q^{7} +2.62111e15 q^{8} +1.02102e17 q^{10} -1.49276e17 q^{11} +5.52590e19 q^{13} -1.77779e20 q^{14} -7.70358e20 q^{16} -1.81211e21 q^{17} -3.32454e22 q^{19} +1.59802e22 q^{20} -4.17169e22 q^{22} -1.00717e24 q^{23} -2.77690e24 q^{25} +1.54428e25 q^{26} -2.78244e25 q^{28} +4.49573e25 q^{29} -2.23850e25 q^{31} -3.05346e26 q^{32} -5.06414e26 q^{34} -2.32419e26 q^{35} -2.91588e27 q^{37} -9.29079e27 q^{38} +9.57633e26 q^{40} +4.18186e27 q^{41} -5.84123e28 q^{43} -6.52916e27 q^{44} -2.81465e29 q^{46} +5.23894e28 q^{47} +2.58653e28 q^{49} -7.76036e29 q^{50} +2.41697e30 q^{52} +2.64063e30 q^{53} -5.45386e28 q^{55} -1.66741e30 q^{56} +1.25638e31 q^{58} -2.44829e30 q^{59} -1.37521e31 q^{61} -6.25575e30 q^{62} -5.88631e31 q^{64} +2.01891e31 q^{65} -6.70306e31 q^{67} -7.92595e31 q^{68} -6.49522e31 q^{70} -4.91498e32 q^{71} +1.37337e32 q^{73} -8.14875e32 q^{74} -1.45411e33 q^{76} +9.49616e31 q^{77} +1.07453e33 q^{79} -2.81454e32 q^{80} +1.16867e33 q^{82} +3.27927e33 q^{83} -6.62061e32 q^{85} -1.63240e34 q^{86} -3.91268e32 q^{88} -3.27218e33 q^{89} -3.51529e34 q^{91} -4.40526e34 q^{92} +1.46408e34 q^{94} -1.21463e34 q^{95} -1.46799e34 q^{97} +7.22835e33 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 60912 q^{2} + 57142939904 q^{4} + 1333779496740 q^{5} - 12\!\cdots\!44 q^{7}+ \cdots + 72\!\cdots\!24 q^{8}+O(q^{10}) $ 2 * q + 60912 * q^2 + 57142939904 * q^4 + 1333779496740 * q^5 - 1201512782952944 * q^7 + 7200956480385024 * q^8	$ 2 q + 60912 q^{2} + 57142939904 q^{4} + 1333779496740 q^{5} - 12\!\cdots\!44 q^{7}+ \cdots + 20\!\cdots\!08 q^{98}+O(q^{100}) $ 2 * q + 60912 * q^2 + 57142939904 * q^4 + 1333779496740 * q^5 - 1201512782952944 * q^7 + 7200956480385024 * q^8 - 109546268366103840 * q^10 + 1474443852221320632 * q^11 + 30005213658205678828 * q^13 - 54218555116626208896 * q^14 - 2231841205794746859520 * q^16 - 6184381389914139549732 * q^17 - 16041801819745886283464 * q^19 + 28961016325243993797120 * q^20 - 396579699860875428206016 * q^22 - 493815500335770240457872 * q^23 - 4749434950612517913953650 * q^25 + 20961946321168144205905056 * q^26 - 35402577540025316459804672 * q^28 + 78897034119133299270862548 * q^29 - 121361162005932759518102048 * q^31 - 143302306271809670376062976 * q^32 + 449143657751740113402393888 * q^34 - 779933046239496469635406560 * q^35 + 1665586101311009800179225916 * q^37 - 13050613787750726714918949312 * q^38 + 5392874139550798797233971200 * q^40 + 32980805501198249253748474188 * q^41 + 10123013327213364172045565320 * q^43 + 15235271860221308020423891968 * q^44 - 393659059100782290327277976448 * q^46 + 52868797790119241441973340320 * q^47 - 33315801381283359525177211950 * q^49 - 344939599216803384993788031600 * q^50 + 2078463386549395848792119629312 * q^52 + 311667073507824309034483504068 * q^53 + 1517912603348115987616960289520 * q^55 - 4256698060894361051133439672320 * q^56 + 5146318056193673657686145949024 * q^58 - 8206652402409843531446945489064 * q^59 - 40510115780163122120323644143540 * q^61 + 15375406801958157810336643623168 * q^62 - 44061412872652964817027532324864 * q^64 - 4267286913056298521798082678120 * q^65 + 9614178644969763076047165071512 * q^67 - 137865760810106900938814269960704 * q^68 + 54706539117989427731737467528960 * q^70 - 440682364431613985484841574021424 * q^71 - 137360814802453541976117247925708 * q^73 - 1816151331037101511972964229252576 * q^74 - 1223517123700955304313856844145664 * q^76 - 823032801538075311095559373941312 * q^77 - 1062176452444830588280514345530880 * q^79 - 1696790522509490100466806063759360 * q^80 - 5125322741804470577254960235914848 * q^82 + 5500428376968501051342971557654344 * q^83 - 4896281708923407655277594784149640 * q^85 - 31302341732489137882852872722637888 * q^86 + 7045123450598581655224211356532736 * q^88 - 24031331951145259183892358374185236 * q^89 - 20875281935852853469733451535930528 * q^91 - 37171500488799640786609596619278336 * q^92 + 14536054971850529082624931738946304 * q^94 + 4514020436462465865986658897865200 * q^95 + 837150039420646979154473176256452 * q^97 + 20162335337791628242056365171146608 * 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 $

$2$	279461.	1.50764	0.753818	−	0.657083i	$-0.228210\pi$
$2$	279461.	1.50764	0.753818	+	0.657083i	$0.228210\pi$
$3$	0	0
$3$	0	0
$4$	4.37389e10	1.27297
$5$	3.65354e11	0.214160	0.107080	−	0.994250i	$-0.465850\pi$
$5$	3.65354e11	0.214160	0.107080	+	0.994250i	$0.465850\pi$
$6$	0	0
$7$	−6.36148e14	−1.03358	−0.516788	−	0.856113i	$-0.672872\pi$
$7$	−6.36148e14	−1.03358	−0.516788	+	0.856113i	$0.672872\pi$
$8$	2.62111e15	0.411538
$9$	0	0
$10$	1.02102e17	0.322876
$11$	−1.49276e17	−0.0890467	−0.0445234	−	0.999008i	$-0.514177\pi$
$11$	−1.49276e17	−0.0890467	−0.0445234	+	0.999008i	$0.514177\pi$
$12$	0	0
$13$	5.52590e19	1.77172	0.885858	−	0.463956i	$-0.153570\pi$
$13$	5.52590e19	1.77172	0.885858	+	0.463956i	$0.153570\pi$
$14$	−1.77779e20	−1.55826
$15$	0	0
$16$	−7.70358e20	−0.652519
$17$	−1.81211e21	−0.531285	−0.265643	−	0.964072i	$-0.585584\pi$
$17$	−1.81211e21	−0.531285	−0.265643	+	0.964072i	$0.585584\pi$
$18$	0	0
$19$	−3.32454e22	−1.39169	−0.695846	−	0.718191i	$-0.744970\pi$
$19$	−3.32454e22	−1.39169	−0.695846	+	0.718191i	$0.744970\pi$
$20$	1.59802e22	0.272620
$21$	0	0
$22$	−4.17169e22	−0.134250
$23$	−1.00717e24	−1.48890	−0.744451	−	0.667677i	$-0.767289\pi$
$23$	−1.00717e24	−1.48890	−0.744451	+	0.667677i	$0.767289\pi$
$24$	0	0
$25$	−2.77690e24	−0.954135
$26$	1.54428e25	2.67111
$27$	0	0
$28$	−2.78244e25	−1.31571
$29$	4.49573e25	1.15036	0.575182	−	0.818026i	$-0.304931\pi$
$29$	4.49573e25	1.15036	0.575182	+	0.818026i	$0.304931\pi$
$30$	0	0
$31$	−2.23850e25	−0.178291	−0.0891453	−	0.996019i	$-0.528414\pi$
$31$	−2.23850e25	−0.178291	−0.0891453	+	0.996019i	$0.528414\pi$
$32$	−3.05346e26	−1.39530
$33$	0	0
$34$	−5.06414e26	−0.800985
$35$	−2.32419e26	−0.221351
$36$	0	0
$37$	−2.91588e27	−1.05012	−0.525060	−	0.851065i	$-0.675957\pi$
$37$	−2.91588e27	−1.05012	−0.525060	+	0.851065i	$0.675957\pi$
$38$	−9.29079e27	−2.09817
$39$	0	0
$40$	9.57633e26	0.0881352
$41$	4.18186e27	0.249834	0.124917	−	0.992167i	$-0.460134\pi$
$41$	4.18186e27	0.249834	0.124917	+	0.992167i	$0.460134\pi$
$42$	0	0
$43$	−5.84123e28	−1.51638	−0.758188	−	0.652037i	$-0.773915\pi$
$43$	−5.84123e28	−1.51638	−0.758188	+	0.652037i	$0.773915\pi$
$44$	−6.52916e27	−0.113354
$45$	0	0
$46$	−2.81465e29	−2.24472
$47$	5.23894e28	0.286768	0.143384	−	0.989667i	$-0.454202\pi$
$47$	5.23894e28	0.286768	0.143384	+	0.989667i	$0.454202\pi$
$48$	0	0
$49$	2.58653e28	0.0682788
$50$	−7.76036e29	−1.43849
$51$	0	0
$52$	2.41697e30	2.25534
$53$	2.64063e30	1.76555	0.882775	−	0.469796i	$-0.155673\pi$
$53$	2.64063e30	1.76555	0.882775	+	0.469796i	$0.155673\pi$
$54$	0	0
$55$	−5.45386e28	−0.0190703
$56$	−1.66741e30	−0.425356
$57$	0	0
$58$	1.25638e31	1.73433
$59$	−2.44829e30	−0.250584	−0.125292	−	0.992120i	$-0.539987\pi$
$59$	−2.44829e30	−0.250584	−0.125292	+	0.992120i	$0.539987\pi$
$60$	0	0
$61$	−1.37521e31	−0.785412	−0.392706	−	0.919664i	$-0.628461\pi$
$61$	−1.37521e31	−0.785412	−0.392706	+	0.919664i	$0.628461\pi$
$62$	−6.25575e30	−0.268797
$63$	0	0
$64$	−5.88631e31	−1.45109
$65$	2.01891e31	0.379432
$66$	0	0
$67$	−6.70306e31	−0.741249	−0.370625	−	0.928783i	$-0.620856\pi$
$67$	−6.70306e31	−0.741249	−0.370625	+	0.928783i	$0.620856\pi$
$68$	−7.92595e31	−0.676310
$69$	0	0
$70$	−6.49522e31	−0.333717
$71$	−4.91498e32	−1.97015	−0.985077	−	0.172113i	$-0.944941\pi$
$71$	−4.91498e32	−1.97015	−0.985077	+	0.172113i	$0.944941\pi$
$72$	0	0
$73$	1.37337e32	0.338561	0.169280	−	0.985568i	$-0.445856\pi$
$73$	1.37337e32	0.338561	0.169280	+	0.985568i	$0.445856\pi$
$74$	−8.14875e32	−1.58320
$75$	0	0
$76$	−1.45411e33	−1.77158
$77$	9.49616e31	0.0920365
$78$	0	0
$79$	1.07453e33	0.664879	0.332440	−	0.943125i	$-0.392128\pi$
$79$	1.07453e33	0.664879	0.332440	+	0.943125i	$0.392128\pi$
$80$	−2.81454e32	−0.139744
$81$	0	0
$82$	1.16867e33	0.376659
$83$	3.27927e33	0.854890	0.427445	−	0.904041i	$-0.359414\pi$
$83$	3.27927e33	0.854890	0.427445	+	0.904041i	$0.359414\pi$
$84$	0	0
$85$	−6.62061e32	−0.113780
$86$	−1.63240e34	−2.28614
$87$	0	0
$88$	−3.91268e32	−0.0366461
$89$	−3.27218e33	−0.251485	−0.125743	−	0.992063i	$-0.540131\pi$
$89$	−3.27218e33	−0.251485	−0.125743	+	0.992063i	$0.540131\pi$
$90$	0	0
$91$	−3.51529e34	−1.83120
$92$	−4.40526e34	−1.89533
$93$	0	0
$94$	1.46408e34	0.432343
$95$	−1.21463e34	−0.298045
$96$	0	0
$97$	−1.46799e34	−0.250160	−0.125080	−	0.992147i	$-0.539919\pi$
$97$	−1.46799e34	−0.250160	−0.125080	+	0.992147i	$0.539919\pi$
$98$	7.22835e33	0.102940
$99$	0	0
$100$	−1.21458e35	−1.21458
$101$	2.12591e35	1.78617	0.893083	−	0.449893i	$-0.148538\pi$
$101$	2.12591e35	1.78617	0.893083	+	0.449893i	$0.148538\pi$
$102$	0	0
$103$	−5.17494e34	−0.308499	−0.154250	−	0.988032i	$-0.549296\pi$
$103$	−5.17494e34	−0.308499	−0.154250	+	0.988032i	$0.549296\pi$
$104$	1.44840e35	0.729129
$105$	0	0
$106$	7.37954e35	2.66181
$107$	−1.53325e35	−0.469242	−0.234621	−	0.972087i	$-0.575385\pi$
$107$	−1.53325e35	−0.469242	−0.234621	+	0.972087i	$0.575385\pi$
$108$	0	0
$109$	4.10693e35	0.908979	0.454489	−	0.890752i	$-0.349822\pi$
$109$	4.10693e35	0.908979	0.454489	+	0.890752i	$0.349822\pi$
$110$	−1.52414e34	−0.0287511
$111$	0	0
$112$	4.90062e35	0.674428
$113$	1.00388e36	1.18253	0.591263	−	0.806479i	$-0.298629\pi$
$113$	1.00388e36	1.18253	0.591263	+	0.806479i	$0.298629\pi$
$114$	0	0
$115$	−3.67974e35	−0.318864
$116$	1.96638e36	1.46438
$117$	0	0
$118$	−6.84203e35	−0.377790
$119$	1.15277e36	0.549124
$120$	0	0
$121$	−2.78796e36	−0.992071
$122$	−3.84318e36	−1.18412
$123$	0	0
$124$	−9.79097e35	−0.226958
$125$	−2.07787e36	−0.418498
$126$	0	0
$127$	−4.93177e36	−0.752381	−0.376191	−	0.926542i	$-0.622766\pi$
$127$	−4.93177e36	−0.752381	−0.376191	+	0.926542i	$0.622766\pi$
$128$	−5.95834e36	−0.792412
$129$	0	0
$130$	5.64208e36	0.572045
$131$	1.37663e37	1.22059	0.610294	−	0.792175i	$-0.291051\pi$
$131$	1.37663e37	1.22059	0.610294	+	0.792175i	$0.291051\pi$
$132$	0	0
$133$	2.11490e37	1.43842
$134$	−1.87325e37	−1.11753
$135$	0	0
$136$	−4.74973e36	−0.218644
$137$	−1.40102e37	−0.567328	−0.283664	−	0.958924i	$-0.591550\pi$
$137$	−1.40102e37	−0.567328	−0.283664	+	0.958924i	$0.591550\pi$
$138$	0	0
$139$	4.03059e37	1.26651	0.633256	−	0.773942i	$-0.281718\pi$
$139$	4.03059e37	1.26651	0.633256	+	0.773942i	$0.281718\pi$
$140$	−1.01658e37	−0.281773
$141$	0	0
$142$	−1.37355e38	−2.97028
$143$	−8.24884e36	−0.157766
$144$	0	0
$145$	1.64253e37	0.246362
$146$	3.83803e37	0.510427
$147$	0	0
$148$	−1.27537e38	−1.33677
$149$	−1.09713e38	−1.02211	−0.511054	−	0.859548i	$-0.670745\pi$
$149$	−1.09713e38	−1.02211	−0.511054	+	0.859548i	$0.670745\pi$
$150$	0	0
$151$	1.08195e38	0.798199	0.399099	−	0.916908i	$-0.369323\pi$
$151$	1.08195e38	0.798199	0.399099	+	0.916908i	$0.369323\pi$
$152$	−8.71396e37	−0.572734
$153$	0	0
$154$	2.65381e37	0.138758
$155$	−8.17847e36	−0.0381828
$156$	0	0
$157$	3.80493e38	1.41939	0.709697	−	0.704507i	$-0.248832\pi$
$157$	3.80493e38	1.41939	0.709697	+	0.704507i	$0.248832\pi$
$158$	3.00288e38	1.00240
$159$	0	0
$160$	−1.11559e38	−0.298818
$161$	6.40710e38	1.53889
$162$	0	0
$163$	−5.15630e38	−0.997826	−0.498913	−	0.866652i	$-0.666267\pi$
$163$	−5.15630e38	−0.997826	−0.498913	+	0.866652i	$0.666267\pi$
$164$	1.82910e38	0.318031
$165$	0	0
$166$	9.16428e38	1.28886
$167$	2.92786e38	0.370691	0.185346	−	0.982673i	$-0.440660\pi$
$167$	2.92786e38	0.370691	0.185346	+	0.982673i	$0.440660\pi$
$168$	0	0
$169$	2.08077e39	2.13898
$170$	−1.85020e38	−0.171539
$171$	0	0
$172$	−2.55489e39	−1.93030
$173$	2.25696e39	1.54070	0.770349	−	0.637623i	$-0.220082\pi$
$173$	2.25696e39	1.54070	0.770349	+	0.637623i	$0.220082\pi$
$174$	0	0
$175$	1.76652e39	0.986171
$176$	1.14996e38	0.0581047
$177$	0	0
$178$	−9.14448e38	−0.379148
$179$	−3.55925e39	−1.33792	−0.668961	−	0.743298i	$-0.733261\pi$
$179$	−3.55925e39	−1.33792	−0.668961	+	0.743298i	$0.733261\pi$
$180$	0	0
$181$	−4.44114e39	−1.37442	−0.687211	−	0.726458i	$-0.741165\pi$
$181$	−4.44114e39	−1.37442	−0.687211	+	0.726458i	$0.741165\pi$
$182$	−9.82387e39	−2.76079
$183$	0	0
$184$	−2.63990e39	−0.612740
$185$	−1.06533e39	−0.224894
$186$	0	0
$187$	2.70504e38	0.0473092
$188$	2.29146e39	0.365047
$189$	0	0
$190$	−3.39443e39	−0.449344
$191$	8.19302e39	0.989373	0.494686	−	0.869072i	$-0.335283\pi$
$191$	8.19302e39	0.989373	0.494686	+	0.869072i	$0.335283\pi$
$192$	0	0
$193$	3.38085e39	0.340230	0.170115	−	0.985424i	$-0.445586\pi$
$193$	3.38085e39	0.340230	0.170115	+	0.985424i	$0.445586\pi$
$194$	−4.10246e39	−0.377150
$195$	0	0
$196$	1.13132e39	0.0869168
$197$	1.27322e40	0.894836	0.447418	−	0.894325i	$-0.352344\pi$
$197$	1.27322e40	0.894836	0.447418	+	0.894325i	$0.352344\pi$
$198$	0	0
$199$	−7.27758e39	−0.428606	−0.214303	−	0.976767i	$-0.568748\pi$
$199$	−7.27758e39	−0.428606	−0.214303	+	0.976767i	$0.568748\pi$
$200$	−7.27855e39	−0.392663
$201$	0	0
$202$	5.94111e40	2.69289
$203$	−2.85995e40	−1.18899
$204$	0	0
$205$	1.52786e39	0.0535046
$206$	−1.44620e40	−0.465105
$207$	0	0
$208$	−4.25692e40	−1.15608
$209$	4.96273e39	0.123926
$210$	0	0
$211$	−2.76616e40	−0.584701	−0.292351	−	0.956311i	$-0.594437\pi$
$211$	−2.76616e40	−0.584701	−0.292351	+	0.956311i	$0.594437\pi$
$212$	1.15498e41	2.24749
$213$	0	0
$214$	−4.28484e40	−0.707446
$215$	−2.13412e40	−0.324747
$216$	0	0
$217$	1.42402e40	0.184277
$218$	1.14773e41	1.37041
$219$	0	0
$220$	−2.38546e39	−0.0242759
$221$	−1.00135e41	−0.941287
$222$	0	0
$223$	3.35919e40	0.269712	0.134856	−	0.990865i	$-0.456943\pi$
$223$	3.35919e40	0.269712	0.134856	+	0.990865i	$0.456943\pi$
$224$	1.94245e41	1.44215
$225$	0	0
$226$	2.80547e41	1.78282
$227$	−1.89749e41	−1.11616	−0.558081	−	0.829787i	$-0.688462\pi$
$227$	−1.89749e41	−1.11616	−0.558081	+	0.829787i	$0.688462\pi$
$228$	0	0
$229$	−1.77014e41	−0.893071	−0.446536	−	0.894766i	$-0.647342\pi$
$229$	−1.77014e41	−0.893071	−0.446536	+	0.894766i	$0.647342\pi$
$230$	−1.02835e41	−0.480731
$231$	0	0
$232$	1.17838e41	0.473419
$233$	1.57002e40	0.0585026	0.0292513	−	0.999572i	$-0.490688\pi$
$233$	1.57002e40	0.0585026	0.0292513	+	0.999572i	$0.490688\pi$
$234$	0	0
$235$	1.91407e40	0.0614144
$236$	−1.07086e41	−0.318986
$237$	0	0
$238$	3.22154e41	0.827879
$239$	2.98699e41	0.713297	0.356648	−	0.934239i	$-0.383919\pi$
$239$	2.98699e41	0.713297	0.356648	+	0.934239i	$0.383919\pi$
$240$	0	0
$241$	−6.82984e40	−0.140965	−0.0704827	−	0.997513i	$-0.522454\pi$
$241$	−6.82984e40	−0.140965	−0.0704827	+	0.997513i	$0.522454\pi$
$242$	−7.79127e41	−1.49568
$243$	0	0
$244$	−6.01502e41	−0.999805
$245$	9.45000e39	0.0146226
$246$	0	0
$247$	−1.83710e42	−2.46568
$248$	−5.86736e40	−0.0733734
$249$	0	0
$250$	−5.80685e41	−0.630944
$251$	8.56382e40	0.0867715	0.0433858	−	0.999058i	$-0.486186\pi$
$251$	8.56382e40	0.0867715	0.0433858	+	0.999058i	$0.486186\pi$
$252$	0	0
$253$	1.50347e41	0.132582
$254$	−1.37824e42	−1.13432
$255$	0	0
$256$	3.57394e41	0.256417
$257$	−1.59187e42	−1.06679	−0.533393	−	0.845868i	$-0.679083\pi$
$257$	−1.59187e42	−1.06679	−0.533393	+	0.845868i	$0.679083\pi$
$258$	0	0
$259$	1.85493e42	1.08538
$260$	8.83049e41	0.483005
$261$	0	0
$262$	3.84715e42	1.84020
$263$	1.67624e42	0.750085	0.375043	−	0.927008i	$-0.377628\pi$
$263$	1.67624e42	0.750085	0.375043	+	0.927008i	$0.377628\pi$
$264$	0	0
$265$	9.64766e41	0.378111
$266$	5.91032e42	2.16861
$267$	0	0
$268$	−2.93184e42	−0.943587
$269$	8.26329e41	0.249166	0.124583	−	0.992209i	$-0.460241\pi$
$269$	8.26329e41	0.249166	0.124583	+	0.992209i	$0.460241\pi$
$270$	0	0
$271$	5.20129e42	1.37768	0.688840	−	0.724914i	$-0.258120\pi$
$271$	5.20129e42	1.37768	0.688840	+	0.724914i	$0.258120\pi$
$272$	1.39597e42	0.346674
$273$	0	0
$274$	−3.91531e42	−0.855325
$275$	4.14524e41	0.0849626
$276$	0	0
$277$	−8.57159e41	−0.154762	−0.0773812	−	0.997002i	$-0.524656\pi$
$277$	−8.57159e41	−0.154762	−0.0773812	+	0.997002i	$0.524656\pi$
$278$	1.12639e43	1.90944
$279$	0	0
$280$	−6.09196e41	−0.0910944
$281$	−7.78049e42	−1.09307	−0.546533	−	0.837438i	$-0.684053\pi$
$281$	−7.78049e42	−1.09307	−0.546533	+	0.837438i	$0.684053\pi$
$282$	0	0
$283$	−5.95094e41	−0.0738454	−0.0369227	−	0.999318i	$-0.511756\pi$
$283$	−5.95094e41	−0.0738454	−0.0369227	+	0.999318i	$0.511756\pi$
$284$	−2.14976e43	−2.50795
$285$	0	0
$286$	−2.30523e42	−0.237853
$287$	−2.66028e42	−0.258222
$288$	0	0
$289$	−8.34982e42	−0.717736
$290$	4.59025e42	0.371425
$291$	0	0
$292$	6.00696e42	0.430977
$293$	1.97041e43	1.33160	0.665800	−	0.746130i	$-0.268090\pi$
$293$	1.97041e43	1.33160	0.665800	+	0.746130i	$0.268090\pi$
$294$	0	0
$295$	−8.94495e41	−0.0536652
$296$	−7.64283e42	−0.432165
$297$	0	0
$298$	−3.06605e43	−1.54097
$299$	−5.56553e43	−2.63791
$300$	0	0
$301$	3.71589e43	1.56729
$302$	3.02363e43	1.20339
$303$	0	0
$304$	2.56108e43	0.908105
$305$	−5.02439e42	−0.168204
$306$	0	0
$307$	−3.56177e43	−1.06352	−0.531759	−	0.846896i	$-0.678469\pi$
$307$	−3.56177e43	−1.06352	−0.531759	+	0.846896i	$0.678469\pi$
$308$	4.15351e42	0.117160
$309$	0	0
$310$	−2.28557e42	−0.0575658
$311$	−3.70185e43	−0.881276	−0.440638	−	0.897685i	$-0.645248\pi$
$311$	−3.70185e43	−0.881276	−0.440638	+	0.897685i	$0.645248\pi$
$312$	0	0
$313$	−4.19837e43	−0.893419	−0.446709	−	0.894679i	$-0.647404\pi$
$313$	−4.19837e43	−0.893419	−0.446709	+	0.894679i	$0.647404\pi$
$314$	1.06333e44	2.13993
$315$	0	0
$316$	4.69986e43	0.846371
$317$	−3.62720e43	−0.618066	−0.309033	−	0.951051i	$-0.600005\pi$
$317$	−3.62720e43	−0.618066	−0.309033	+	0.951051i	$0.600005\pi$
$318$	0	0
$319$	−6.71104e42	−0.102436
$320$	−2.15059e43	−0.310765
$321$	0	0
$322$	1.79054e44	2.32009
$323$	6.02441e43	0.739385
$324$	0	0
$325$	−1.53449e44	−1.69046
$326$	−1.44099e44	−1.50436
$327$	0	0
$328$	1.09611e43	0.102816
$329$	−3.33274e43	−0.296397
$330$	0	0
$331$	−1.52756e44	−1.22182	−0.610911	−	0.791700i	$-0.709197\pi$
$331$	−1.52756e44	−1.22182	−0.610911	+	0.791700i	$0.709197\pi$
$332$	1.43432e44	1.08825
$333$	0	0
$334$	8.18224e43	0.558868
$335$	−2.44899e43	−0.158746
$336$	0	0
$337$	−1.48437e44	−0.867002	−0.433501	−	0.901153i	$-0.642722\pi$
$337$	−1.48437e44	−0.867002	−0.433501	+	0.901153i	$0.642722\pi$
$338$	5.81495e44	3.22481
$339$	0	0
$340$	−2.89578e43	−0.144839
$341$	3.34155e42	0.0158762
$342$	0	0
$343$	2.24531e44	0.963004
$344$	−1.53105e44	−0.624046
$345$	0	0
$346$	6.30734e44	2.32281
$347$	−4.00770e44	−1.40323	−0.701616	−	0.712555i	$-0.747538\pi$
$347$	−4.00770e44	−1.40323	−0.701616	+	0.712555i	$0.747538\pi$
$348$	0	0
$349$	9.71517e43	0.307614	0.153807	−	0.988101i	$-0.450847\pi$
$349$	9.71517e43	0.307614	0.153807	+	0.988101i	$0.450847\pi$
$350$	4.93674e44	1.48679
$351$	0	0
$352$	4.55808e43	0.124247
$353$	−5.81527e44	−1.50839	−0.754193	−	0.656653i	$-0.771972\pi$
$353$	−5.81527e44	−1.50839	−0.754193	+	0.656653i	$0.771972\pi$
$354$	0	0
$355$	−1.79571e44	−0.421929
$356$	−1.43122e44	−0.320133
$357$	0	0
$358$	−9.94673e44	−2.01710
$359$	3.64874e43	0.0704676	0.0352338	−	0.999379i	$-0.488782\pi$
$359$	3.64874e43	0.0704676	0.0352338	+	0.999379i	$0.488782\pi$
$360$	0	0
$361$	5.34595e44	0.936805
$362$	−1.24113e45	−2.07213
$363$	0	0
$364$	−1.53755e45	−2.33107
$365$	5.01766e43	0.0725063
$366$	0	0
$367$	6.94503e44	0.912049	0.456025	−	0.889967i	$-0.349273\pi$
$367$	6.94503e44	0.912049	0.456025	+	0.889967i	$0.349273\pi$
$368$	7.75883e44	0.971537
$369$	0	0
$370$	−2.97718e44	−0.339059
$371$	−1.67983e45	−1.82483
$372$	0	0
$373$	−1.97985e45	−1.95762	−0.978808	−	0.204781i	$-0.934352\pi$
$373$	−1.97985e45	−1.95762	−0.978808	+	0.204781i	$0.934352\pi$
$374$	7.55954e43	0.0713251
$375$	0	0
$376$	1.37318e44	0.118016
$377$	2.48429e45	2.03812
$378$	0	0
$379$	1.79049e45	1.33902	0.669508	−	0.742805i	$-0.266505\pi$
$379$	1.79049e45	1.33902	0.669508	+	0.742805i	$0.266505\pi$
$380$	−5.31267e44	−0.379402
$381$	0	0
$382$	2.28963e45	1.49162
$383$	1.49796e45	0.932225	0.466113	−	0.884725i	$-0.345654\pi$
$383$	1.49796e45	0.932225	0.466113	+	0.884725i	$0.345654\pi$
$384$	0	0
$385$	3.46946e43	0.0197106
$386$	9.44816e44	0.512943
$387$	0	0
$388$	−6.42082e44	−0.318446
$389$	−1.77359e45	−0.840882	−0.420441	−	0.907320i	$-0.638125\pi$
$389$	−1.77359e45	−0.840882	−0.420441	+	0.907320i	$0.638125\pi$
$390$	0	0
$391$	1.82510e45	0.791032
$392$	6.77957e43	0.0280993
$393$	0	0
$394$	3.55815e45	1.34909
$395$	3.92583e44	0.142391
$396$	0	0
$397$	−2.45730e44	−0.0815876	−0.0407938	−	0.999168i	$-0.512989\pi$
$397$	−2.45730e44	−0.0815876	−0.0407938	+	0.999168i	$0.512989\pi$
$398$	−2.03380e45	−0.646182
$399$	0	0
$400$	2.13921e45	0.622591
$401$	3.47243e45	0.967401	0.483701	−	0.875234i	$-0.339292\pi$
$401$	3.47243e45	0.967401	0.483701	+	0.875234i	$0.339292\pi$
$402$	0	0
$403$	−1.23698e45	−0.315880
$404$	9.29851e45	2.27373
$405$	0	0
$406$	−7.99245e45	−1.79256
$407$	4.35271e44	0.0935098
$408$	0	0
$409$	−5.60182e45	−1.10451	−0.552257	−	0.833674i	$-0.686233\pi$
$409$	−5.60182e45	−1.10451	−0.552257	+	0.833674i	$0.686233\pi$
$410$	4.26978e44	0.0806655
$411$	0	0
$412$	−2.26346e45	−0.392710
$413$	1.55748e45	0.258998
$414$	0	0
$415$	1.19809e45	0.183084
$416$	−1.68731e46	−2.47208
$417$	0	0
$418$	1.38689e45	0.186835
$419$	−1.30103e46	−1.68090	−0.840449	−	0.541891i	$-0.817709\pi$
$419$	−1.30103e46	−1.68090	−0.840449	+	0.541891i	$0.817709\pi$
$420$	0	0
$421$	−3.23759e45	−0.384844	−0.192422	−	0.981312i	$-0.561634\pi$
$421$	−3.23759e45	−0.384844	−0.192422	+	0.981312i	$0.561634\pi$
$422$	−7.73034e45	−0.881517
$423$	0	0
$424$	6.92138e45	0.726591
$425$	5.03204e45	0.506918
$426$	0	0
$427$	8.74838e45	0.811783
$428$	−6.70626e45	−0.597330
$429$	0	0
$430$	−5.96404e45	−0.489601
$431$	7.33523e45	0.578178	0.289089	−	0.957302i	$-0.406648\pi$
$431$	7.33523e45	0.578178	0.289089	+	0.957302i	$0.406648\pi$
$432$	0	0
$433$	−3.13432e44	−0.0227827	−0.0113913	−	0.999935i	$-0.503626\pi$
$433$	−3.13432e44	−0.0227827	−0.0113913	+	0.999935i	$0.503626\pi$
$434$	3.97958e45	0.277823
$435$	0	0
$436$	1.79633e46	1.15710
$437$	3.34838e46	2.07209
$438$	0	0
$439$	−4.96227e45	−0.283499	−0.141749	−	0.989903i	$-0.545273\pi$
$439$	−4.96227e45	−0.283499	−0.141749	+	0.989903i	$0.545273\pi$
$440$	−1.42952e44	−0.00784815
$441$	0	0
$442$	−2.79839e46	−1.41912
$443$	−3.90477e46	−1.90340	−0.951701	−	0.307026i	$-0.900666\pi$
$443$	−3.90477e46	−1.90340	−0.951701	+	0.307026i	$0.900666\pi$
$444$	0	0
$445$	−1.19551e45	−0.0538581
$446$	9.38765e45	0.406627
$447$	0	0
$448$	3.74456e46	1.49981
$449$	−9.78942e45	−0.377091	−0.188545	−	0.982064i	$-0.560377\pi$
$449$	−9.78942e45	−0.377091	−0.188545	+	0.982064i	$0.560377\pi$
$450$	0	0
$451$	−6.24251e44	−0.0222469
$452$	4.39088e46	1.50532
$453$	0	0
$454$	−5.30275e46	−1.68277
$455$	−1.28433e46	−0.392171
$456$	0	0
$457$	−7.87990e45	−0.222837	−0.111419	−	0.993774i	$-0.535539\pi$
$457$	−7.87990e45	−0.222837	−0.111419	+	0.993774i	$0.535539\pi$
$458$	−4.94685e46	−1.34643
$459$	0	0
$460$	−1.60948e46	−0.405904
$461$	6.50894e46	1.58032	0.790158	−	0.612903i	$-0.209998\pi$
$461$	6.50894e46	1.58032	0.790158	+	0.612903i	$0.209998\pi$
$462$	0	0
$463$	4.77272e46	1.07423	0.537117	−	0.843508i	$-0.319513\pi$
$463$	4.77272e46	1.07423	0.537117	+	0.843508i	$0.319513\pi$
$464$	−3.46332e46	−0.750634
$465$	0	0
$466$	4.38759e45	0.0882008
$467$	3.34554e46	0.647769	0.323885	−	0.946097i	$-0.395011\pi$
$467$	3.34554e46	0.647769	0.323885	+	0.946097i	$0.395011\pi$
$468$	0	0
$469$	4.26414e46	0.766137
$470$	5.34909e45	0.0925906
$471$	0	0
$472$	−6.41724e45	−0.103125
$473$	8.71956e45	0.135028
$474$	0	0
$475$	9.23190e46	1.32786
$476$	5.04208e46	0.699017
$477$	0	0
$478$	8.34748e46	1.07539
$479$	9.78794e46	1.21568	0.607841	−	0.794059i	$-0.292036\pi$
$479$	9.78794e46	1.21568	0.607841	+	0.794059i	$0.292036\pi$
$480$	0	0
$481$	−1.61129e47	−1.86052
$482$	−1.90868e46	−0.212525
$483$	0	0
$484$	−1.21942e47	−1.26288
$485$	−5.36336e45	−0.0535743
$486$	0	0
$487$	1.03689e47	0.963777	0.481889	−	0.876232i	$-0.339951\pi$
$487$	1.03689e47	0.963777	0.481889	+	0.876232i	$0.339951\pi$
$488$	−3.60458e46	−0.323227
$489$	0	0
$490$	2.64091e45	0.0220456
$491$	−1.30638e46	−0.105231	−0.0526155	−	0.998615i	$-0.516756\pi$
$491$	−1.30638e46	−0.105231	−0.0526155	+	0.998615i	$0.516756\pi$
$492$	0	0
$493$	−8.14674e46	−0.611171
$494$	−5.13400e47	−3.71735
$495$	0	0
$496$	1.72445e46	0.116338
$497$	3.12665e47	2.03630
$498$	0	0
$499$	1.66085e46	0.100826	0.0504129	−	0.998728i	$-0.483946\pi$
$499$	1.66085e46	0.100826	0.0504129	+	0.998728i	$0.483946\pi$
$500$	−9.08838e46	−0.532735
$501$	0	0
$502$	2.39326e46	0.130820
$503$	−2.15922e47	−1.13987	−0.569937	−	0.821689i	$-0.693032\pi$
$503$	−2.15922e47	−1.13987	−0.569937	+	0.821689i	$0.693032\pi$
$504$	0	0
$505$	7.76712e46	0.382526
$506$	4.20160e46	0.199885
$507$	0	0
$508$	−2.15710e47	−0.957758
$509$	−3.50805e47	−1.50489	−0.752444	−	0.658656i	$-0.771125\pi$
$509$	−3.50805e47	−1.50489	−0.752444	+	0.658656i	$0.771125\pi$
$510$	0	0
$511$	−8.73665e46	−0.349928
$512$	3.04605e47	1.17900
$513$	0	0
$514$	−4.44865e47	−1.60832
$515$	−1.89069e46	−0.0660683
$516$	0	0
$517$	−7.82048e45	−0.0255358
$518$	5.18381e47	1.63636
$519$	0	0
$520$	5.29178e46	0.156151
$521$	−4.99886e47	−1.42630	−0.713149	−	0.701012i	$-0.752732\pi$
$521$	−4.99886e47	−1.42630	−0.713149	+	0.701012i	$0.752732\pi$
$522$	0	0
$523$	−2.90357e46	−0.0774733	−0.0387367	−	0.999249i	$-0.512333\pi$
$523$	−2.90357e46	−0.0774733	−0.0387367	+	0.999249i	$0.512333\pi$
$524$	6.02122e47	1.55377
$525$	0	0
$526$	4.68444e47	1.13086
$527$	4.05641e46	0.0947231
$528$	0	0
$529$	5.56807e47	1.21683
$530$	2.69615e47	0.570054
$531$	0	0
$532$	9.25032e47	1.83106
$533$	2.31085e47	0.442635
$534$	0	0
$535$	−5.60179e46	−0.100493
$536$	−1.75694e47	−0.305052
$537$	0	0
$538$	2.30927e47	0.375651
$539$	−3.86107e45	−0.00608001
$540$	0	0
$541$	−7.56060e47	−1.11585	−0.557923	−	0.829893i	$-0.688402\pi$
$541$	−7.56060e47	−1.11585	−0.557923	+	0.829893i	$0.688402\pi$
$542$	1.45356e48	2.07704
$543$	0	0
$544$	5.53320e47	0.741302
$545$	1.50048e47	0.194667
$546$	0	0
$547$	−5.49459e47	−0.668586	−0.334293	−	0.942469i	$-0.608497\pi$
$547$	−5.49459e47	−0.668586	−0.334293	+	0.942469i	$0.608497\pi$
$548$	−6.12790e47	−0.722191
$549$	0	0
$550$	1.15844e47	0.128093
$551$	−1.49462e48	−1.60095
$552$	0	0
$553$	−6.83557e47	−0.687203
$554$	−2.39543e47	−0.233325
$555$	0	0
$556$	1.76293e48	1.61223
$557$	−1.06798e48	−0.946449	−0.473225	−	0.880942i	$-0.656910\pi$
$557$	−1.06798e48	−0.946449	−0.473225	+	0.880942i	$0.656910\pi$
$558$	0	0
$559$	−3.22781e48	−2.68659
$560$	1.79046e47	0.144436
$561$	0	0
$562$	−2.17435e48	−1.64795
$563$	2.95577e47	0.217157	0.108578	−	0.994088i	$-0.465370\pi$
$563$	2.95577e47	0.217157	0.108578	+	0.994088i	$0.465370\pi$
$564$	0	0
$565$	3.66773e47	0.253250
$566$	−1.66306e47	−0.111332
$567$	0	0
$568$	−1.28827e48	−0.810794
$569$	−1.55924e47	−0.0951587	−0.0475794	−	0.998867i	$-0.515151\pi$
$569$	−1.55924e47	−0.0951587	−0.0475794	+	0.998867i	$0.515151\pi$
$570$	0	0
$571$	2.44889e48	1.40552	0.702761	−	0.711426i	$-0.251950\pi$
$571$	2.44889e48	1.40552	0.702761	+	0.711426i	$0.251950\pi$
$572$	−3.60795e47	−0.200831
$573$	0	0
$574$	−7.43445e47	−0.389306
$575$	2.79681e48	1.42061
$576$	0	0
$577$	2.16685e48	1.03575	0.517873	−	0.855458i	$-0.326724\pi$
$577$	2.16685e48	1.03575	0.517873	+	0.855458i	$0.326724\pi$
$578$	−2.33345e48	−1.08209
$579$	0	0
$580$	7.18426e47	0.313612
$581$	−2.08610e48	−0.883594
$582$	0	0
$583$	−3.94183e47	−0.157216
$584$	3.59974e47	0.139331
$585$	0	0
$586$	5.50654e48	2.00757
$587$	−3.51258e47	−0.124296	−0.0621482	−	0.998067i	$-0.519795\pi$
$587$	−3.51258e47	−0.124296	−0.0621482	+	0.998067i	$0.519795\pi$
$588$	0	0
$589$	7.44199e47	0.248125
$590$	−2.49977e47	−0.0809076
$591$	0	0
$592$	2.24627e48	0.685224
$593$	−3.58906e47	−0.106298	−0.0531489	−	0.998587i	$-0.516926\pi$
$593$	−3.58906e47	−0.106298	−0.0531489	+	0.998587i	$0.516926\pi$
$594$	0	0
$595$	4.21169e47	0.117601
$596$	−4.79871e48	−1.30111
$597$	0	0
$598$	−1.55535e49	−3.97702
$599$	2.08154e48	0.516911	0.258456	−	0.966023i	$-0.416786\pi$
$599$	2.08154e48	0.516911	0.258456	+	0.966023i	$0.416786\pi$
$600$	0	0
$601$	−1.00213e48	−0.234758	−0.117379	−	0.993087i	$-0.537449\pi$
$601$	−1.00213e48	−0.234758	−0.117379	+	0.993087i	$0.537449\pi$
$602$	1.03845e49	2.36290
$603$	0	0
$604$	4.73233e48	1.01608
$605$	−1.01859e48	−0.212462
$606$	0	0
$607$	−4.36540e48	−0.859453	−0.429726	−	0.902959i	$-0.641390\pi$
$607$	−4.36540e48	−0.859453	−0.429726	+	0.902959i	$0.641390\pi$
$608$	1.01513e49	1.94183
$609$	0	0
$610$	−1.40412e48	−0.253591
$611$	2.89499e48	0.508072
$612$	0	0
$613$	9.45680e48	1.56742	0.783711	−	0.621126i	$-0.213324\pi$
$613$	9.45680e48	1.56742	0.783711	+	0.621126i	$0.213324\pi$
$614$	−9.95378e48	−1.60340
$615$	0	0
$616$	2.48905e47	0.0378765
$617$	6.32292e47	0.0935249	0.0467625	−	0.998906i	$-0.485110\pi$
$617$	6.32292e47	0.0935249	0.0467625	+	0.998906i	$0.485110\pi$
$618$	0	0
$619$	2.65684e48	0.371346	0.185673	−	0.982612i	$-0.440553\pi$
$619$	2.65684e48	0.371346	0.185673	+	0.982612i	$0.440553\pi$
$620$	−3.57717e47	−0.0486055
$621$	0	0
$622$	−1.03452e49	−1.32864
$623$	2.08159e48	0.259929
$624$	0	0
$625$	7.32268e48	0.864510
$626$	−1.17328e49	−1.34695
$627$	0	0
$628$	1.66423e49	1.80684
$629$	5.28389e48	0.557914
$630$	0	0
$631$	2.52797e47	0.0252498	0.0126249	−	0.999920i	$-0.495981\pi$
$631$	2.52797e47	0.0252498	0.0126249	+	0.999920i	$0.495981\pi$
$632$	2.81645e48	0.273623
$633$	0	0
$634$	−1.01366e49	−0.931819
$635$	−1.80184e48	−0.161130
$636$	0	0
$637$	1.42929e48	0.120971
$638$	−1.87548e48	−0.154436
$639$	0	0
$640$	−2.17691e48	−0.169703
$641$	−1.43723e49	−1.09021	−0.545105	−	0.838368i	$-0.683510\pi$
$641$	−1.43723e49	−1.09021	−0.545105	+	0.838368i	$0.683510\pi$
$642$	0	0
$643$	−3.98874e48	−0.286513	−0.143256	−	0.989686i	$-0.545757\pi$
$643$	−3.98874e48	−0.286513	−0.143256	+	0.989686i	$0.545757\pi$
$644$	2.80239e49	1.95896
$645$	0	0
$646$	1.68359e49	1.11472
$647$	2.33006e49	1.50156	0.750781	−	0.660552i	$-0.229678\pi$
$647$	2.33006e49	1.50156	0.750781	+	0.660552i	$0.229678\pi$
$648$	0	0
$649$	3.65471e47	0.0223137
$650$	−4.28830e49	−2.54860
$651$	0	0
$652$	−2.25531e49	−1.27020
$653$	−1.17028e49	−0.641666	−0.320833	−	0.947136i	$-0.603963\pi$
$653$	−1.17028e49	−0.641666	−0.320833	+	0.947136i	$0.603963\pi$
$654$	0	0
$655$	5.02957e48	0.261402
$656$	−3.22153e48	−0.163021
$657$	0	0
$658$	−9.31372e48	−0.446859
$659$	1.32090e49	0.617128	0.308564	−	0.951204i	$-0.400152\pi$
$659$	1.32090e49	0.617128	0.308564	+	0.951204i	$0.400152\pi$
$660$	0	0
$661$	−3.80316e49	−1.68508	−0.842538	−	0.538637i	$-0.818940\pi$
$661$	−3.80316e49	−1.68508	−0.842538	+	0.538637i	$0.818940\pi$
$662$	−4.26893e49	−1.84206
$663$	0	0
$664$	8.59531e48	0.351820
$665$	7.72686e48	0.308052
$666$	0	0
$667$	−4.52797e49	−1.71278
$668$	1.28061e49	0.471879
$669$	0	0
$670$	−6.84399e48	−0.239332
$671$	2.05286e48	0.0699383
$672$	0	0
$673$	1.15552e49	0.373692	0.186846	−	0.982389i	$-0.440173\pi$
$673$	1.15552e49	0.373692	0.186846	+	0.982389i	$0.440173\pi$
$674$	−4.14825e49	−1.30712
$675$	0	0
$676$	9.10106e49	2.72286
$677$	−5.18340e48	−0.151117	−0.0755585	−	0.997141i	$-0.524074\pi$
$677$	−5.18340e48	−0.151117	−0.0755585	+	0.997141i	$0.524074\pi$
$678$	0	0
$679$	9.33858e48	0.258559
$680$	−1.73533e48	−0.0468249
$681$	0	0
$682$	9.33834e47	0.0239355
$683$	−4.66690e49	−1.16591	−0.582957	−	0.812503i	$-0.698104\pi$
$683$	−4.66690e49	−1.16591	−0.582957	+	0.812503i	$0.698104\pi$
$684$	0	0
$685$	−5.11868e48	−0.121499
$686$	6.27476e49	1.45186
$687$	0	0
$688$	4.49984e49	0.989463
$689$	1.45919e50	3.12805
$690$	0	0
$691$	5.17806e49	1.05512	0.527559	−	0.849519i	$-0.323107\pi$
$691$	5.17806e49	1.05512	0.527559	+	0.849519i	$0.323107\pi$
$692$	9.87170e49	1.96126
$693$	0	0
$694$	−1.12000e50	−2.11557
$695$	1.47259e49	0.271237
$696$	0	0
$697$	−7.57797e48	−0.132733
$698$	2.71501e49	0.463770
$699$	0	0
$700$	7.72655e49	1.25537
$701$	−1.34782e49	−0.213582	−0.106791	−	0.994281i	$-0.534058\pi$
$701$	−1.34782e49	−0.213582	−0.106791	+	0.994281i	$0.534058\pi$
$702$	0	0
$703$	9.69394e49	1.46144
$704$	8.78684e48	0.129214
$705$	0	0
$706$	−1.62514e50	−2.27410
$707$	−1.35240e50	−1.84614
$708$	0	0
$709$	5.95415e49	0.773589	0.386795	−	0.922166i	$-0.373582\pi$
$709$	5.95415e49	0.773589	0.386795	+	0.922166i	$0.373582\pi$
$710$	−5.01831e49	−0.636116
$711$	0	0
$712$	−8.57674e48	−0.103496
$713$	2.25456e49	0.265457
$714$	0	0
$715$	−3.01375e48	−0.0337871
$716$	−1.55678e50	−1.70313
$717$	0	0
$718$	1.01968e49	0.106240
$719$	−9.50970e49	−0.966966	−0.483483	−	0.875354i	$-0.660629\pi$
$719$	−9.50970e49	−0.966966	−0.483483	+	0.875354i	$0.660629\pi$
$720$	0	0
$721$	3.29203e49	0.318857
$722$	1.49399e50	1.41236
$723$	0	0
$724$	−1.94251e50	−1.74960
$725$	−1.24842e50	−1.09760
$726$	0	0
$727$	−7.28338e49	−0.610212	−0.305106	−	0.952318i	$-0.598692\pi$
$727$	−7.28338e49	−0.610212	−0.305106	+	0.952318i	$0.598692\pi$
$728$	−9.21395e49	−0.753610
$729$	0	0
$730$	1.40224e49	0.109313
$731$	1.05849e50	0.805628
$732$	0	0
$733$	−2.38824e50	−1.73284	−0.866421	−	0.499314i	$-0.833585\pi$
$733$	−2.38824e50	−1.73284	−0.866421	+	0.499314i	$0.833585\pi$
$734$	1.94087e50	1.37504
$735$	0	0
$736$	3.07536e50	2.07747
$737$	1.00061e49	0.0660058
$738$	0	0
$739$	2.40229e50	1.51129	0.755646	−	0.654980i	$-0.227323\pi$
$739$	2.40229e50	1.51129	0.755646	+	0.654980i	$0.227323\pi$
$740$	−4.65963e49	−0.286283
$741$	0	0
$742$	−4.69448e50	−2.75118
$743$	3.09674e49	0.177256	0.0886279	−	0.996065i	$-0.471752\pi$
$743$	3.09674e49	0.177256	0.0886279	+	0.996065i	$0.471752\pi$
$744$	0	0
$745$	−4.00840e49	−0.218895
$746$	−5.53291e50	−2.95137
$747$	0	0
$748$	1.18315e49	0.0602232
$749$	9.75373e49	0.484997
$750$	0	0
$751$	4.66674e49	0.221470	0.110735	−	0.993850i	$-0.464680\pi$
$751$	4.66674e49	0.221470	0.110735	+	0.993850i	$0.464680\pi$
$752$	−4.03586e49	−0.187122
$753$	0	0
$754$	6.94264e50	3.07274
$755$	3.95296e49	0.170943
$756$	0	0
$757$	−1.36549e50	−0.563780	−0.281890	−	0.959447i	$-0.590961\pi$
$757$	−1.36549e50	−0.563780	−0.281890	+	0.959447i	$0.590961\pi$
$758$	5.00373e50	2.01875
$759$	0	0
$760$	−3.18368e49	−0.122657
$761$	−2.28332e48	−0.00859677	−0.00429839	−	0.999991i	$-0.501368\pi$
$761$	−2.28332e48	−0.00859677	−0.00429839	+	0.999991i	$0.501368\pi$
$762$	0	0
$763$	−2.61262e50	−0.939498
$764$	3.58353e50	1.25944
$765$	0	0
$766$	4.18621e50	1.40546
$767$	−1.35290e50	−0.443964
$768$	0	0
$769$	−5.95370e49	−0.186671	−0.0933354	−	0.995635i	$-0.529753\pi$
$769$	−5.95370e49	−0.186671	−0.0933354	+	0.995635i	$0.529753\pi$
$770$	9.69580e48	0.0297164
$771$	0	0
$772$	1.47874e50	0.433102
$773$	−3.53372e50	−1.01179	−0.505895	−	0.862595i	$-0.668838\pi$
$773$	−3.53372e50	−1.01179	−0.505895	+	0.862595i	$0.668838\pi$
$774$	0	0
$775$	6.21610e49	0.170113
$776$	−3.84776e49	−0.102950
$777$	0	0
$778$	−4.95650e50	−1.26774
$779$	−1.39027e50	−0.347692
$780$	0	0
$781$	7.33688e49	0.175436
$782$	5.10046e50	1.19259
$783$	0	0
$784$	−1.99255e49	−0.0445532
$785$	1.39015e50	0.303978
$786$	0	0
$787$	−2.59047e50	−0.541777	−0.270888	−	0.962611i	$-0.587317\pi$
$787$	−2.59047e50	−0.541777	−0.270888	+	0.962611i	$0.587317\pi$
$788$	5.56891e50	1.13910
$789$	0	0
$790$	1.09712e50	0.214674
$791$	−6.38619e50	−1.22223
$792$	0	0
$793$	−7.59928e50	−1.39153
$794$	−6.86720e49	−0.123004
$795$	0	0
$796$	−3.18313e50	−0.545602
$797$	2.98933e49	0.0501249	0.0250624	−	0.999686i	$-0.492022\pi$
$797$	2.98933e49	0.0501249	0.0250624	+	0.999686i	$0.492022\pi$
$798$	0	0
$799$	−9.49353e49	−0.152356
$800$	8.47915e50	1.33130
$801$	0	0
$802$	9.70409e50	1.45849
$803$	−2.05011e49	−0.0301477
$804$	0	0
$805$	2.34086e50	0.329570
$806$	−3.45687e50	−0.476233
$807$	0	0
$808$	5.57225e50	0.735075
$809$	5.81772e50	0.751023	0.375512	−	0.926818i	$-0.377467\pi$
$809$	5.81772e50	0.751023	0.375512	+	0.926818i	$0.377467\pi$
$810$	0	0
$811$	−2.08851e50	−0.258209	−0.129104	−	0.991631i	$-0.541210\pi$
$811$	−2.08851e50	−0.258209	−0.129104	+	0.991631i	$0.541210\pi$
$812$	−1.25091e51	−1.51355
$813$	0	0
$814$	1.21641e50	0.140979
$815$	−1.88388e50	−0.213695
$816$	0	0
$817$	1.94194e51	2.11033
$818$	−1.56549e51	−1.66521
$819$	0	0
$820$	6.68269e49	0.0681097
$821$	−4.12142e50	−0.411189	−0.205595	−	0.978637i	$-0.565913\pi$
$821$	−4.12142e50	−0.411189	−0.205595	+	0.978637i	$0.565913\pi$
$822$	0	0
$823$	−1.26215e50	−0.120674	−0.0603371	−	0.998178i	$-0.519218\pi$
$823$	−1.26215e50	−0.120674	−0.0603371	+	0.998178i	$0.519218\pi$
$824$	−1.35641e50	−0.126959
$825$	0	0
$826$	4.35254e50	0.390474
$827$	1.65632e51	1.45478	0.727390	−	0.686224i	$-0.240733\pi$
$827$	1.65632e51	1.45478	0.727390	+	0.686224i	$0.240733\pi$
$828$	0	0
$829$	−1.04352e51	−0.878607	−0.439303	−	0.898339i	$-0.644775\pi$
$829$	−1.04352e51	−0.878607	−0.439303	+	0.898339i	$0.644775\pi$
$830$	3.34821e50	0.276024
$831$	0	0
$832$	−3.25271e51	−2.57091
$833$	−4.68707e49	−0.0362755
$834$	0	0
$835$	1.06971e50	0.0793874
$836$	2.17064e50	0.157753
$837$	0	0
$838$	−3.63587e51	−2.53418
$839$	−2.81406e51	−1.92088	−0.960438	−	0.278493i	$-0.910165\pi$
$839$	−2.81406e51	−1.92088	−0.960438	+	0.278493i	$0.910165\pi$
$840$	0	0
$841$	4.93839e50	0.323337
$842$	−9.04780e50	−0.580205
$843$	0	0
$844$	−1.20989e51	−0.744307
$845$	7.60218e50	0.458085
$846$	0	0
$847$	1.77355e51	1.02538
$848$	−2.03423e51	−1.15205
$849$	0	0
$850$	1.40626e51	0.764248
$851$	2.93679e51	1.56353
$852$	0	0
$853$	2.01221e51	1.02817	0.514085	−	0.857739i	$-0.328131\pi$
$853$	2.01221e51	1.02817	0.514085	+	0.857739i	$0.328131\pi$
$854$	2.44483e51	1.22387
$855$	0	0
$856$	−4.01881e50	−0.193111
$857$	2.58977e50	0.121926	0.0609630	−	0.998140i	$-0.480583\pi$
$857$	2.58977e50	0.121926	0.0609630	+	0.998140i	$0.480583\pi$
$858$	0	0
$859$	−3.01104e50	−0.136093	−0.0680465	−	0.997682i	$-0.521677\pi$
$859$	−3.01104e50	−0.136093	−0.0680465	+	0.997682i	$0.521677\pi$
$860$	−9.33440e50	−0.413393
$861$	0	0
$862$	2.04991e51	0.871682
$863$	3.72938e51	1.55399	0.776995	−	0.629507i	$-0.216743\pi$
$863$	3.72938e51	1.55399	0.776995	+	0.629507i	$0.216743\pi$
$864$	0	0
$865$	8.24591e50	0.329956
$866$	−8.75921e49	−0.0343480
$867$	0	0
$868$	6.22850e50	0.234579
$869$	−1.60401e50	−0.0592053
$870$	0	0
$871$	−3.70404e51	−1.31328
$872$	1.07647e51	0.374079
$873$	0	0
$874$	9.35742e51	3.12396
$875$	1.32183e51	0.432550
$876$	0	0
$877$	1.47614e51	0.464124	0.232062	−	0.972701i	$-0.425453\pi$
$877$	1.47614e51	0.464124	0.232062	+	0.972701i	$0.425453\pi$
$878$	−1.38676e51	−0.427413
$879$	0	0
$880$	4.20143e49	0.0124437
$881$	−5.35936e50	−0.155609	−0.0778045	−	0.996969i	$-0.524791\pi$
$881$	−5.35936e50	−0.155609	−0.0778045	+	0.996969i	$0.524791\pi$
$882$	0	0
$883$	2.24200e51	0.625638	0.312819	−	0.949813i	$-0.398727\pi$
$883$	2.24200e51	0.625638	0.312819	+	0.949813i	$0.398727\pi$
$884$	−4.37980e51	−1.19823
$885$	0	0
$886$	−1.09123e52	−2.86964
$887$	7.00150e51	1.80521	0.902605	−	0.430470i	$-0.141652\pi$
$887$	7.00150e51	1.80521	0.902605	+	0.430470i	$0.141652\pi$
$888$	0	0
$889$	3.13734e51	0.777643
$890$	−3.34097e50	−0.0811985
$891$	0	0
$892$	1.46927e51	0.343335
$893$	−1.74171e51	−0.399093
$894$	0	0
$895$	−1.30039e51	−0.286530
$896$	3.79038e51	0.819017
$897$	0	0
$898$	−2.73576e51	−0.568516
$899$	−1.00637e51	−0.205099
$900$	0	0
$901$	−4.78511e51	−0.938011
$902$	−1.74454e50	−0.0335403
$903$	0	0
$904$	2.63129e51	0.486655
$905$	−1.62259e51	−0.294347
$906$	0	0
$907$	−1.01982e52	−1.77990	−0.889951	−	0.456057i	$-0.849261\pi$
$907$	−1.01982e52	−1.77990	−0.889951	+	0.456057i	$0.849261\pi$
$908$	−8.29941e51	−1.42084
$909$	0	0
$910$	−3.58919e51	−0.591252
$911$	1.62989e51	0.263382	0.131691	−	0.991291i	$-0.457959\pi$
$911$	1.62989e51	0.263382	0.131691	+	0.991291i	$0.457959\pi$
$912$	0	0
$913$	−4.89516e50	−0.0761252
$914$	−2.20213e51	−0.335957
$915$	0	0
$916$	−7.74238e51	−1.13685
$917$	−8.75740e51	−1.26157
$918$	0	0
$919$	7.87901e51	1.09257	0.546286	−	0.837599i	$-0.316041\pi$
$919$	7.87901e51	1.09257	0.546286	+	0.837599i	$0.316041\pi$
$920$	−9.64500e50	−0.131225
$921$	0	0
$922$	1.81900e52	2.38254
$923$	−2.71597e52	−3.49056
$924$	0	0
$925$	8.09710e51	1.00196
$926$	1.33379e52	1.61955
$927$	0	0
$928$	−1.37275e52	−1.60510
$929$	4.74316e51	0.544243	0.272122	−	0.962263i	$-0.412275\pi$
$929$	4.74316e51	0.544243	0.272122	+	0.962263i	$0.412275\pi$
$930$	0	0
$931$	−8.59901e50	−0.0950230
$932$	6.86708e50	0.0744721
$933$	0	0
$934$	9.34948e51	0.976601
$935$	9.88298e49	0.0101318
$936$	0	0
$937$	−1.00541e52	−0.992888	−0.496444	−	0.868069i	$-0.665361\pi$
$937$	−1.00541e52	−0.992888	−0.496444	+	0.868069i	$0.665361\pi$
$938$	1.19166e52	1.15506
$939$	0	0
$940$	8.37193e50	0.0781786
$941$	6.43294e51	0.589646	0.294823	−	0.955552i	$-0.404739\pi$
$941$	6.43294e51	0.589646	0.294823	+	0.955552i	$0.404739\pi$
$942$	0	0
$943$	−4.21185e51	−0.371979
$944$	1.88606e51	0.163511
$945$	0	0
$946$	2.43678e51	0.203574
$947$	8.46249e51	0.694023	0.347011	−	0.937861i	$-0.387197\pi$
$947$	8.46249e51	0.694023	0.347011	+	0.937861i	$0.387197\pi$
$948$	0	0
$949$	7.58909e51	0.599834
$950$	2.57996e52	2.00193
$951$	0	0
$952$	3.02153e51	0.225985
$953$	2.50917e51	0.184248	0.0921242	−	0.995748i	$-0.470634\pi$
$953$	2.50917e51	0.184248	0.0921242	+	0.995748i	$0.470634\pi$
$954$	0	0
$955$	2.99335e51	0.211884
$956$	1.30648e52	0.908005
$957$	0	0
$958$	2.73535e52	1.83281
$959$	8.91255e51	0.586376
$960$	0	0
$961$	−1.52627e52	−0.968212
$962$	−4.50292e52	−2.80498
$963$	0	0
$964$	−2.98730e51	−0.179445
$965$	1.23521e51	0.0728638
$966$	0	0
$967$	3.67568e50	0.0209110	0.0104555	−	0.999945i	$-0.496672\pi$
$967$	3.67568e50	0.0209110	0.0104555	+	0.999945i	$0.496672\pi$
$968$	−7.30754e51	−0.408275
$969$	0	0
$970$	−1.49885e51	−0.0807706
$971$	−2.67841e52	−1.41756	−0.708778	−	0.705431i	$-0.750753\pi$
$971$	−2.67841e52	−1.41756	−0.708778	+	0.705431i	$0.750753\pi$
$972$	0	0
$973$	−2.56405e52	−1.30904
$974$	2.89771e52	1.45303
$975$	0	0
$976$	1.05941e52	0.512496
$977$	−1.70901e52	−0.812062	−0.406031	−	0.913859i	$-0.633088\pi$
$977$	−1.70901e52	−0.812062	−0.406031	+	0.913859i	$0.633088\pi$
$978$	0	0
$979$	4.88458e50	0.0223939
$980$	4.13332e50	0.0186141
$981$	0	0
$982$	−3.65083e51	−0.158650
$983$	−2.12016e50	−0.00905069	−0.00452535	−	0.999990i	$-0.501440\pi$
$983$	−2.12016e50	−0.00905069	−0.00452535	+	0.999990i	$0.501440\pi$
$984$	0	0
$985$	4.65175e51	0.191638
$986$	−2.27670e52	−0.921424
$987$	0	0
$988$	−8.03529e52	−3.13874
$989$	5.88312e52	2.25773
$990$	0	0
$991$	6.93693e50	0.0256968	0.0128484	−	0.999917i	$-0.495910\pi$
$991$	6.93693e50	0.0256968	0.0128484	+	0.999917i	$0.495910\pi$
$992$	6.83518e51	0.248769
$993$	0	0
$994$	8.73778e52	3.07001
$995$	−2.65889e51	−0.0917904
$996$	0	0
$997$	2.96189e52	0.987196	0.493598	−	0.869690i	$-0.335681\pi$
$997$	2.96189e52	0.987196	0.493598	+	0.869690i	$0.335681\pi$
$998$	4.64144e51	0.152009
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.36.a.a.1.2		2
3.2	odd	2		3.36.a.a.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.36.a.a.1.1	✓	2	3.2	odd	2
9.36.a.a.1.2		2	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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 36 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+279461. q^{2} +4.37389e10 q^{4} +3.65354e11 q^{5} -6.36148e14 q^{7} +2.62111e15 q^{8} +O(q^{10})\)	\(q+279461. q^{2} +4.37389e10 q^{4} +3.65354e11 q^{5} -6.36148e14 q^{7} +2.62111e15 q^{8} +1.02102e17 q^{10} -1.49276e17 q^{11} +5.52590e19 q^{13} -1.77779e20 q^{14} -7.70358e20 q^{16} -1.81211e21 q^{17} -3.32454e22 q^{19} +1.59802e22 q^{20} -4.17169e22 q^{22} -1.00717e24 q^{23} -2.77690e24 q^{25} +1.54428e25 q^{26} -2.78244e25 q^{28} +4.49573e25 q^{29} -2.23850e25 q^{31} -3.05346e26 q^{32} -5.06414e26 q^{34} -2.32419e26 q^{35} -2.91588e27 q^{37} -9.29079e27 q^{38} +9.57633e26 q^{40} +4.18186e27 q^{41} -5.84123e28 q^{43} -6.52916e27 q^{44} -2.81465e29 q^{46} +5.23894e28 q^{47} +2.58653e28 q^{49} -7.76036e29 q^{50} +2.41697e30 q^{52} +2.64063e30 q^{53} -5.45386e28 q^{55} -1.66741e30 q^{56} +1.25638e31 q^{58} -2.44829e30 q^{59} -1.37521e31 q^{61} -6.25575e30 q^{62} -5.88631e31 q^{64} +2.01891e31 q^{65} -6.70306e31 q^{67} -7.92595e31 q^{68} -6.49522e31 q^{70} -4.91498e32 q^{71} +1.37337e32 q^{73} -8.14875e32 q^{74} -1.45411e33 q^{76} +9.49616e31 q^{77} +1.07453e33 q^{79} -2.81454e32 q^{80} +1.16867e33 q^{82} +3.27927e33 q^{83} -6.62061e32 q^{85} -1.63240e34 q^{86} -3.91268e32 q^{88} -3.27218e33 q^{89} -3.51529e34 q^{91} -4.40526e34 q^{92} +1.46408e34 q^{94} -1.21463e34 q^{95} -1.46799e34 q^{97} +7.22835e33 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 60912 q^{2} + 57142939904 q^{4} + 1333779496740 q^{5} - 12\!\cdots\!44 q^{7}+ \cdots + 72\!\cdots\!24 q^{8}+O(q^{10}) \) 2 * q + 60912 * q^2 + 57142939904 * q^4 + 1333779496740 * q^5 - 1201512782952944 * q^7 + 7200956480385024 * q^8	\( 2 q + 60912 q^{2} + 57142939904 q^{4} + 1333779496740 q^{5} - 12\!\cdots\!44 q^{7}+ \cdots + 20\!\cdots\!08 q^{98}+O(q^{100}) \) 2 * q + 60912 * q^2 + 57142939904 * q^4 + 1333779496740 * q^5 - 1201512782952944 * q^7 + 7200956480385024 * q^8 - 109546268366103840 * q^10 + 1474443852221320632 * q^11 + 30005213658205678828 * q^13 - 54218555116626208896 * q^14 - 2231841205794746859520 * q^16 - 6184381389914139549732 * q^17 - 16041801819745886283464 * q^19 + 28961016325243993797120 * q^20 - 396579699860875428206016 * q^22 - 493815500335770240457872 * q^23 - 4749434950612517913953650 * q^25 + 20961946321168144205905056 * q^26 - 35402577540025316459804672 * q^28 + 78897034119133299270862548 * q^29 - 121361162005932759518102048 * q^31 - 143302306271809670376062976 * q^32 + 449143657751740113402393888 * q^34 - 779933046239496469635406560 * q^35 + 1665586101311009800179225916 * q^37 - 13050613787750726714918949312 * q^38 + 5392874139550798797233971200 * q^40 + 32980805501198249253748474188 * q^41 + 10123013327213364172045565320 * q^43 + 15235271860221308020423891968 * q^44 - 393659059100782290327277976448 * q^46 + 52868797790119241441973340320 * q^47 - 33315801381283359525177211950 * q^49 - 344939599216803384993788031600 * q^50 + 2078463386549395848792119629312 * q^52 + 311667073507824309034483504068 * q^53 + 1517912603348115987616960289520 * q^55 - 4256698060894361051133439672320 * q^56 + 5146318056193673657686145949024 * q^58 - 8206652402409843531446945489064 * q^59 - 40510115780163122120323644143540 * q^61 + 15375406801958157810336643623168 * q^62 - 44061412872652964817027532324864 * q^64 - 4267286913056298521798082678120 * q^65 + 9614178644969763076047165071512 * q^67 - 137865760810106900938814269960704 * q^68 + 54706539117989427731737467528960 * q^70 - 440682364431613985484841574021424 * q^71 - 137360814802453541976117247925708 * q^73 - 1816151331037101511972964229252576 * q^74 - 1223517123700955304313856844145664 * q^76 - 823032801538075311095559373941312 * q^77 - 1062176452444830588280514345530880 * q^79 - 1696790522509490100466806063759360 * q^80 - 5125322741804470577254960235914848 * q^82 + 5500428376968501051342971557654344 * q^83 - 4896281708923407655277594784149640 * q^85 - 31302341732489137882852872722637888 * q^86 + 7045123450598581655224211356532736 * q^88 - 24031331951145259183892358374185236 * q^89 - 20875281935852853469733451535930528 * q^91 - 37171500488799640786609596619278336 * q^92 + 14536054971850529082624931738946304 * q^94 + 4514020436462465865986658897865200 * q^95 + 837150039420646979154473176256452 * q^97 + 20162335337791628242056365171146608 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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