LMFDB - Embedded newform 9.36.a.a.1.1

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			1.1
Root			$741.587$ 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)

$f(q)$	$=$	$q-218549. q^{2} +1.34041e10 q^{4} +9.68425e11 q^{5} -5.65365e14 q^{7} +4.57985e15 q^{8} +O(q^{10})$	\(q-218549. q^{2} +1.34041e10 q^{4} +9.68425e11 q^{5} -5.65365e14 q^{7} +4.57985e15 q^{8} -2.11649e17 q^{10} +1.62372e18 q^{11} -2.52538e19 q^{13} +1.23560e20 q^{14} -1.46148e21 q^{16} -4.37227e21 q^{17} +1.72036e22 q^{19} +1.29808e22 q^{20} -3.54863e23 q^{22} +5.13356e23 q^{23} -1.97254e24 q^{25} +5.51920e24 q^{26} -7.57819e24 q^{28} +3.39397e25 q^{29} -9.89761e25 q^{31} +1.62044e26 q^{32} +9.55557e26 q^{34} -5.47514e26 q^{35} +4.58147e27 q^{37} -3.75982e27 q^{38} +4.43524e27 q^{40} +2.87989e28 q^{41} +6.85354e28 q^{43} +2.17644e28 q^{44} -1.12194e29 q^{46} +4.79363e26 q^{47} -5.91811e28 q^{49} +4.31096e29 q^{50} -3.38503e29 q^{52} -2.32896e30 q^{53} +1.57245e30 q^{55} -2.58929e30 q^{56} -7.41751e30 q^{58} -5.75836e30 q^{59} -2.67580e31 q^{61} +2.16312e31 q^{62} +1.48016e31 q^{64} -2.44564e31 q^{65} +7.66448e31 q^{67} -5.86062e31 q^{68} +1.19659e32 q^{70} +5.08152e31 q^{71} -2.74698e32 q^{73} -1.00128e33 q^{74} +2.30597e32 q^{76} -9.17994e32 q^{77} -2.13670e33 q^{79} -1.41534e33 q^{80} -6.29399e33 q^{82} +2.22116e33 q^{83} -4.23422e33 q^{85} -1.49784e34 q^{86} +7.43639e33 q^{88} -2.07592e34 q^{89} +1.42776e34 q^{91} +6.88105e33 q^{92} -1.04765e32 q^{94} +1.66604e34 q^{95} +1.55170e34 q^{97} +1.29340e34 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−218549.	−1.17903	−0.589515	−	0.807758i	$-0.700681\pi$
$2$	−218549.	−1.17903	−0.589515	+	0.807758i	$0.700681\pi$
$3$	0	0
$3$	0	0
$4$	1.34041e10	0.390109
$5$	9.68425e11	0.567664	0.283832	−	0.958874i	$-0.408394\pi$
$5$	9.68425e11	0.567664	0.283832	+	0.958874i	$0.408394\pi$
$6$	0	0
$7$	−5.65365e14	−0.918572	−0.459286	−	0.888288i	$-0.651895\pi$
$7$	−5.65365e14	−0.918572	−0.459286	+	0.888288i	$0.651895\pi$
$8$	4.57985e15	0.719079
$9$	0	0
$10$	−2.11649e17	−0.669292
$11$	1.62372e18	0.968588	0.484294	−	0.874905i	$-0.339077\pi$
$11$	1.62372e18	0.968588	0.484294	+	0.874905i	$0.339077\pi$
$12$	0	0
$13$	−2.52538e19	−0.809688	−0.404844	−	0.914386i	$-0.632674\pi$
$13$	−2.52538e19	−0.809688	−0.404844	+	0.914386i	$0.632674\pi$
$14$	1.23560e20	1.08302
$15$	0	0
$16$	−1.46148e21	−1.23792
$17$	−4.37227e21	−1.28189	−0.640946	−	0.767586i	$-0.721458\pi$
$17$	−4.37227e21	−1.28189	−0.640946	+	0.767586i	$0.721458\pi$
$18$	0	0
$19$	1.72036e22	0.720162	0.360081	−	0.932921i	$-0.382749\pi$
$19$	1.72036e22	0.720162	0.360081	+	0.932921i	$0.382749\pi$
$20$	1.29808e22	0.221451
$21$	0	0
$22$	−3.54863e23	−1.14199
$23$	5.13356e23	0.758895	0.379447	−	0.925213i	$-0.376114\pi$
$23$	5.13356e23	0.758895	0.379447	+	0.925213i	$0.376114\pi$
$24$	0	0
$25$	−1.97254e24	−0.677758
$26$	5.51920e24	0.954646
$27$	0	0
$28$	−7.57819e24	−0.358344
$29$	3.39397e25	0.868447	0.434224	−	0.900805i	$-0.357023\pi$
$29$	3.39397e25	0.868447	0.434224	+	0.900805i	$0.357023\pi$
$30$	0	0
$31$	−9.89761e25	−0.788317	−0.394158	−	0.919043i	$-0.628964\pi$
$31$	−9.89761e25	−0.788317	−0.394158	+	0.919043i	$0.628964\pi$
$32$	1.62044e26	0.740470
$33$	0	0
$34$	9.55557e26	1.51139
$35$	−5.47514e26	−0.521440
$36$	0	0
$37$	4.58147e27	1.64996	0.824982	−	0.565160i	$-0.191185\pi$
$37$	4.58147e27	1.64996	0.824982	+	0.565160i	$0.191185\pi$
$38$	−3.75982e27	−0.849092
$39$	0	0
$40$	4.43524e27	0.408195
$41$	2.87989e28	1.72052	0.860259	−	0.509858i	$-0.170302\pi$
$41$	2.87989e28	1.72052	0.860259	+	0.509858i	$0.170302\pi$
$42$	0	0
$43$	6.85354e28	1.77917	0.889583	−	0.456773i	$-0.150995\pi$
$43$	6.85354e28	1.77917	0.889583	+	0.456773i	$0.150995\pi$
$44$	2.17644e28	0.377855
$45$	0	0
$46$	−1.12194e29	−0.894759
$47$	4.79363e26	0.00262393	0.00131197	−	0.999999i	$-0.499582\pi$
$47$	4.79363e26	0.00262393	0.00131197	+	0.999999i	$0.499582\pi$
$48$	0	0
$49$	−5.91811e28	−0.156225
$50$	4.31096e29	0.799096
$51$	0	0
$52$	−3.38503e29	−0.315867
$53$	−2.32896e30	−1.55717	−0.778583	−	0.627541i	$-0.784061\pi$
$53$	−2.32896e30	−1.55717	−0.778583	+	0.627541i	$0.784061\pi$
$54$	0	0
$55$	1.57245e30	0.549832
$56$	−2.58929e30	−0.660526
$57$	0	0
$58$	−7.41751e30	−1.02392
$59$	−5.75836e30	−0.589371	−0.294685	−	0.955594i	$-0.595215\pi$
$59$	−5.75836e30	−0.589371	−0.294685	+	0.955594i	$0.595215\pi$
$60$	0	0
$61$	−2.67580e31	−1.52820	−0.764102	−	0.645095i	$-0.776818\pi$
$61$	−2.67580e31	−1.52820	−0.764102	+	0.645095i	$0.776818\pi$
$62$	2.16312e31	0.929448
$63$	0	0
$64$	1.48016e31	0.364889
$65$	−2.44564e31	−0.459630
$66$	0	0
$67$	7.66448e31	0.847566	0.423783	−	0.905764i	$-0.360702\pi$
$67$	7.66448e31	0.847566	0.423783	+	0.905764i	$0.360702\pi$
$68$	−5.86062e31	−0.500078
$69$	0	0
$70$	1.19659e32	0.614793
$71$	5.08152e31	0.203691	0.101846	−	0.994800i	$-0.467525\pi$
$71$	5.08152e31	0.203691	0.101846	+	0.994800i	$0.467525\pi$
$72$	0	0
$73$	−2.74698e32	−0.677181	−0.338590	−	0.940934i	$-0.609950\pi$
$73$	−2.74698e32	−0.677181	−0.338590	+	0.940934i	$0.609950\pi$
$74$	−1.00128e33	−1.94535
$75$	0	0
$76$	2.30597e32	0.280942
$77$	−9.17994e32	−0.889718
$78$	0	0
$79$	−2.13670e33	−1.32212	−0.661059	−	0.750334i	$-0.729893\pi$
$79$	−2.13670e33	−1.32212	−0.661059	+	0.750334i	$0.729893\pi$
$80$	−1.41534e33	−0.702724
$81$	0	0
$82$	−6.29399e33	−2.02854
$83$	2.22116e33	0.579046	0.289523	−	0.957171i	$-0.406503\pi$
$83$	2.22116e33	0.579046	0.289523	+	0.957171i	$0.406503\pi$
$84$	0	0
$85$	−4.23422e33	−0.727683
$86$	−1.49784e34	−2.09769
$87$	0	0
$88$	7.43639e33	0.696491
$89$	−2.07592e34	−1.59545	−0.797727	−	0.603018i	$-0.793965\pi$
$89$	−2.07592e34	−1.59545	−0.797727	+	0.603018i	$0.793965\pi$
$90$	0	0
$91$	1.42776e34	0.743757
$92$	6.88105e33	0.296052
$93$	0	0
$94$	−1.04765e32	−0.00309369
$95$	1.66604e34	0.408810
$96$	0	0
$97$	1.55170e34	0.264426	0.132213	−	0.991221i	$-0.457792\pi$
$97$	1.55170e34	0.264426	0.132213	+	0.991221i	$0.457792\pi$
$98$	1.29340e34	0.184194
$99$	0	0
$100$	−2.64400e34	−0.264400
$101$	1.03897e35	0.872929	0.436464	−	0.899722i	$-0.356230\pi$
$101$	1.03897e35	0.872929	0.436464	+	0.899722i	$0.356230\pi$
$102$	0	0
$103$	−1.94833e35	−1.16148	−0.580740	−	0.814089i	$-0.697237\pi$
$103$	−1.94833e35	−1.16148	−0.580740	+	0.814089i	$0.697237\pi$
$104$	−1.15659e35	−0.582229
$105$	0	0
$106$	5.08993e35	1.83594
$107$	3.61557e35	1.10652	0.553262	−	0.833007i	$-0.313383\pi$
$107$	3.61557e35	1.10652	0.553262	+	0.833007i	$0.313383\pi$
$108$	0	0
$109$	−7.33560e35	−1.62357	−0.811786	−	0.583954i	$-0.801505\pi$
$109$	−7.33560e35	−1.62357	−0.811786	+	0.583954i	$0.801505\pi$
$110$	−3.43658e35	−0.648268
$111$	0	0
$112$	8.26271e35	1.13712
$113$	5.95677e35	0.701678	0.350839	−	0.936436i	$-0.385896\pi$
$113$	5.95677e35	0.701678	0.350839	+	0.936436i	$0.385896\pi$
$114$	0	0
$115$	4.97147e35	0.430797
$116$	4.54930e35	0.338790
$117$	0	0
$118$	1.25849e36	0.694885
$119$	2.47193e36	1.17751
$120$	0	0
$121$	−1.73778e35	−0.0618372
$122$	5.84794e36	1.80180
$123$	0	0
$124$	−1.32668e36	−0.307530
$125$	−4.72874e36	−0.952402
$126$	0	0
$127$	1.88168e36	0.287065	0.143533	−	0.989646i	$-0.454154\pi$
$127$	1.88168e36	0.287065	0.143533	+	0.989646i	$0.454154\pi$
$128$	−8.80267e36	−1.17068
$129$	0	0
$130$	5.34493e36	0.541918
$131$	−6.22324e36	−0.551784	−0.275892	−	0.961189i	$-0.588973\pi$
$131$	−6.22324e36	−0.551784	−0.275892	+	0.961189i	$0.588973\pi$
$132$	0	0
$133$	−9.72629e36	−0.661521
$134$	−1.67507e37	−0.999305
$135$	0	0
$136$	−2.00244e37	−0.921781
$137$	−6.91179e36	−0.279886	−0.139943	−	0.990160i	$-0.544692\pi$
$137$	−6.91179e36	−0.279886	−0.139943	+	0.990160i	$0.544692\pi$
$138$	0	0
$139$	−4.10165e37	−1.28884	−0.644421	−	0.764671i	$-0.722901\pi$
$139$	−4.10165e37	−1.28884	−0.644421	+	0.764671i	$0.722901\pi$
$140$	−7.33891e36	−0.203419
$141$	0	0
$142$	−1.11056e37	−0.240158
$143$	−4.10051e37	−0.784254
$144$	0	0
$145$	3.28681e37	0.492986
$146$	6.00350e37	0.798416
$147$	0	0
$148$	6.14102e37	0.643666
$149$	−3.38483e37	−0.315339	−0.157670	−	0.987492i	$-0.550398\pi$
$149$	−3.38483e37	−0.315339	−0.157670	+	0.987492i	$0.550398\pi$
$150$	0	0
$151$	−4.14774e37	−0.305995	−0.152998	−	0.988227i	$-0.548893\pi$
$151$	−4.14774e37	−0.305995	−0.152998	+	0.988227i	$0.548893\pi$
$152$	7.87897e37	0.517853
$153$	0	0
$154$	2.00627e38	1.04900
$155$	−9.58510e37	−0.447499
$156$	0	0
$157$	2.79097e38	1.04115	0.520573	−	0.853817i	$-0.325718\pi$
$157$	2.79097e38	1.04115	0.520573	+	0.853817i	$0.325718\pi$
$158$	4.66975e38	1.55881
$159$	0	0
$160$	1.56927e38	0.420338
$161$	−2.90234e38	−0.697099
$162$	0	0
$163$	−9.06631e38	−1.75448	−0.877238	−	0.480056i	$-0.840616\pi$
$163$	−9.06631e38	−1.75448	−0.877238	+	0.480056i	$0.840616\pi$
$164$	3.86023e38	0.671190
$165$	0	0
$166$	−4.85433e38	−0.682712
$167$	2.20471e38	0.279134	0.139567	−	0.990213i	$-0.455429\pi$
$167$	2.20471e38	0.279134	0.139567	+	0.990213i	$0.455429\pi$
$168$	0	0
$169$	−3.35033e38	−0.344405
$170$	9.25386e38	0.857959
$171$	0	0
$172$	9.18652e38	0.694070
$173$	1.20919e39	0.825442	0.412721	−	0.910858i	$-0.364579\pi$
$173$	1.20919e39	0.825442	0.412721	+	0.910858i	$0.364579\pi$
$174$	0	0
$175$	1.11520e39	0.622570
$176$	−2.37304e39	−1.19904
$177$	0	0
$178$	4.53690e39	1.88109
$179$	−2.04025e39	−0.766930	−0.383465	−	0.923555i	$-0.625269\pi$
$179$	−2.04025e39	−0.766930	−0.383465	+	0.923555i	$0.625269\pi$
$180$	0	0
$181$	−4.15321e39	−1.28531	−0.642656	−	0.766155i	$-0.722168\pi$
$181$	−4.15321e39	−1.28531	−0.642656	+	0.766155i	$0.722168\pi$
$182$	−3.12036e39	−0.876911
$183$	0	0
$184$	2.35109e39	0.545705
$185$	4.43681e39	0.936624
$186$	0	0
$187$	−7.09935e39	−1.24162
$188$	6.42542e36	0.00102362
$189$	0	0
$190$	−3.64111e39	−0.481998
$191$	−6.52044e39	−0.787396	−0.393698	−	0.919240i	$-0.628804\pi$
$191$	−6.52044e39	−0.787396	−0.393698	+	0.919240i	$0.628804\pi$
$192$	0	0
$193$	−1.97397e39	−0.198649	−0.0993246	−	0.995055i	$-0.531668\pi$
$193$	−1.97397e39	−0.198649	−0.0993246	+	0.995055i	$0.531668\pi$
$194$	−3.39124e39	−0.311765
$195$	0	0
$196$	−7.93267e38	−0.0609450
$197$	−6.10473e39	−0.429050	−0.214525	−	0.976719i	$-0.568820\pi$
$197$	−6.10473e39	−0.429050	−0.214525	+	0.976719i	$0.568820\pi$
$198$	0	0
$199$	−8.83517e39	−0.520338	−0.260169	−	0.965563i	$-0.583778\pi$
$199$	−8.83517e39	−0.520338	−0.260169	+	0.965563i	$0.583778\pi$
$200$	−9.03392e39	−0.487361
$201$	0	0
$202$	−2.27066e40	−1.02921
$203$	−1.91883e40	−0.797732
$204$	0	0
$205$	2.78896e40	0.976675
$206$	4.25807e40	1.36942
$207$	0	0
$208$	3.69080e40	1.00233
$209$	2.79337e40	0.697540
$210$	0	0
$211$	7.88511e40	1.66673	0.833364	−	0.552724i	$-0.186412\pi$
$211$	7.88511e40	1.66673	0.833364	+	0.552724i	$0.186412\pi$
$212$	−3.12176e40	−0.607465
$213$	0	0
$214$	−7.90181e40	−1.30462
$215$	6.63714e40	1.00997
$216$	0	0
$217$	5.59576e40	0.724126
$218$	1.60319e41	1.91424
$219$	0	0
$220$	2.10772e40	0.214495
$221$	1.10416e41	1.03793
$222$	0	0
$223$	−2.84802e40	−0.228670	−0.114335	−	0.993442i	$-0.536474\pi$
$223$	−2.84802e40	−0.228670	−0.114335	+	0.993442i	$0.536474\pi$
$224$	−9.16138e40	−0.680175
$225$	0	0
$226$	−1.30185e41	−0.827299
$227$	−2.11879e41	−1.24634	−0.623168	−	0.782088i	$-0.714155\pi$
$227$	−2.11879e41	−1.24634	−0.623168	+	0.782088i	$0.714155\pi$
$228$	0	0
$229$	2.44651e40	0.123432	0.0617159	−	0.998094i	$-0.480343\pi$
$229$	2.44651e40	0.123432	0.0617159	+	0.998094i	$0.480343\pi$
$230$	−1.08651e41	−0.507922
$231$	0	0
$232$	1.55439e41	0.624482
$233$	−3.49375e41	−1.30186	−0.650929	−	0.759139i	$-0.725620\pi$
$233$	−3.49375e41	−1.30186	−0.650929	+	0.759139i	$0.725620\pi$
$234$	0	0
$235$	4.64228e38	0.00148951
$236$	−7.71854e40	−0.229919
$237$	0	0
$238$	−5.40239e41	−1.38832
$239$	3.32939e41	0.795063	0.397531	−	0.917589i	$-0.369867\pi$
$239$	3.32939e41	0.795063	0.397531	+	0.917589i	$0.369867\pi$
$240$	0	0
$241$	6.93771e40	0.143192	0.0715959	−	0.997434i	$-0.477191\pi$
$241$	6.93771e40	0.143192	0.0715959	+	0.997434i	$0.477191\pi$
$242$	3.79790e40	0.0729078
$243$	0	0
$244$	−3.58666e41	−0.596167
$245$	−5.73125e40	−0.0886835
$246$	0	0
$247$	−4.34455e41	−0.583106
$248$	−4.53296e41	−0.566862
$249$	0	0
$250$	1.03346e42	1.12291
$251$	−3.37146e40	−0.0341608	−0.0170804	−	0.999854i	$-0.505437\pi$
$251$	−3.37146e40	−0.0341608	−0.0170804	+	0.999854i	$0.505437\pi$
$252$	0	0
$253$	8.33546e41	0.735056
$254$	−4.11240e41	−0.338458
$255$	0	0
$256$	1.41524e42	1.01538
$257$	2.45764e41	0.164698	0.0823489	−	0.996604i	$-0.473758\pi$
$257$	2.45764e41	0.164698	0.0823489	+	0.996604i	$0.473758\pi$
$258$	0	0
$259$	−2.59020e42	−1.51561
$260$	−3.27815e41	−0.179306
$261$	0	0
$262$	1.36009e42	0.650569
$263$	1.00792e42	0.451026	0.225513	−	0.974240i	$-0.427594\pi$
$263$	1.00792e42	0.451026	0.225513	+	0.974240i	$0.427594\pi$
$264$	0	0
$265$	−2.25543e42	−0.883947
$266$	2.12567e42	0.779952
$267$	0	0
$268$	1.02735e42	0.330644
$269$	−3.53460e42	−1.06580	−0.532900	−	0.846178i	$-0.678898\pi$
$269$	−3.53460e42	−1.06580	−0.532900	+	0.846178i	$0.678898\pi$
$270$	0	0
$271$	2.05300e40	0.00543785	0.00271893	−	0.999996i	$-0.499135\pi$
$271$	2.05300e40	0.00543785	0.00271893	+	0.999996i	$0.499135\pi$
$272$	6.39000e42	1.58688
$273$	0	0
$274$	1.51057e42	0.329993
$275$	−3.20285e42	−0.656468
$276$	0	0
$277$	−3.99065e42	−0.720522	−0.360261	−	0.932851i	$-0.617312\pi$
$277$	−3.99065e42	−0.720522	−0.360261	+	0.932851i	$0.617312\pi$
$278$	8.96412e42	1.51958
$279$	0	0
$280$	−2.50753e42	−0.374956
$281$	6.62219e42	0.930338	0.465169	−	0.885222i	$-0.345994\pi$
$281$	6.62219e42	0.930338	0.465169	+	0.885222i	$0.345994\pi$
$282$	0	0
$283$	9.02584e42	1.12002	0.560009	−	0.828487i	$-0.310798\pi$
$283$	9.02584e42	1.12002	0.560009	+	0.828487i	$0.310798\pi$
$284$	6.81130e41	0.0794619
$285$	0	0
$286$	8.96163e42	0.924658
$287$	−1.62819e43	−1.58042
$288$	0	0
$289$	7.48323e42	0.643246
$290$	−7.18330e42	−0.581245
$291$	0	0
$292$	−3.68206e42	−0.264175
$293$	−1.83072e43	−1.23719	−0.618597	−	0.785708i	$-0.712299\pi$
$293$	−1.83072e43	−1.23719	−0.618597	+	0.785708i	$0.712299\pi$
$294$	0	0
$295$	−5.57654e42	−0.334564
$296$	2.09824e43	1.18645
$297$	0	0
$298$	7.39753e42	0.371794
$299$	−1.29642e43	−0.614468
$300$	0	0
$301$	−3.87475e43	−1.63429
$302$	9.06486e42	0.360778
$303$	0	0
$304$	−2.51427e43	−0.891506
$305$	−2.59131e43	−0.867506
$306$	0	0
$307$	−5.94182e43	−1.77418	−0.887091	−	0.461595i	$-0.847277\pi$
$307$	−5.94182e43	−1.77418	−0.887091	+	0.461595i	$0.847277\pi$
$308$	−1.23049e43	−0.347087
$309$	0	0
$310$	2.09482e43	0.527614
$311$	−9.43273e42	−0.224559	−0.112280	−	0.993677i	$-0.535815\pi$
$311$	−9.43273e42	−0.224559	−0.112280	+	0.993677i	$0.535815\pi$
$312$	0	0
$313$	5.95209e43	1.26661	0.633306	−	0.773902i	$-0.281697\pi$
$313$	5.95209e43	1.26661	0.633306	+	0.773902i	$0.281697\pi$
$314$	−6.09965e43	−1.22754
$315$	0	0
$316$	−2.86405e43	−0.515770
$317$	1.09193e44	1.86062	0.930311	−	0.366772i	$-0.119537\pi$
$317$	1.09193e44	1.86062	0.930311	+	0.366772i	$0.119537\pi$
$318$	0	0
$319$	5.51086e43	0.841168
$320$	1.43343e43	0.207134
$321$	0	0
$322$	6.34303e43	0.821901
$323$	−7.52186e43	−0.923169
$324$	0	0
$325$	4.98140e43	0.548773
$326$	1.98144e44	2.06858
$327$	0	0
$328$	1.31895e44	1.23719
$329$	−2.71015e41	−0.00241027
$330$	0	0
$331$	−6.64486e43	−0.531491	−0.265746	−	0.964043i	$-0.585618\pi$
$331$	−6.64486e43	−0.531491	−0.265746	+	0.964043i	$0.585618\pi$
$332$	2.97726e43	0.225891
$333$	0	0
$334$	−4.81837e43	−0.329107
$335$	7.42248e43	0.481132
$336$	0	0
$337$	−1.32087e44	−0.771504	−0.385752	−	0.922602i	$-0.626058\pi$
$337$	−1.32087e44	−0.771504	−0.385752	+	0.922602i	$0.626058\pi$
$338$	7.32211e43	0.406064
$339$	0	0
$340$	−5.67557e43	−0.283876
$341$	−1.60709e44	−0.763554
$342$	0	0
$343$	2.47630e44	1.06208
$344$	3.13882e44	1.27936
$345$	0	0
$346$	−2.64267e44	−0.973220
$347$	−1.51937e44	−0.531983	−0.265991	−	0.963975i	$-0.585699\pi$
$347$	−1.51937e44	−0.531983	−0.265991	+	0.963975i	$0.585699\pi$
$348$	0	0
$349$	−4.35219e44	−1.37804	−0.689022	−	0.724741i	$-0.741960\pi$
$349$	−4.35219e44	−1.37804	−0.689022	+	0.724741i	$0.741960\pi$
$350$	−2.43727e44	−0.734028
$351$	0	0
$352$	2.63113e44	0.717210
$353$	−3.37356e44	−0.875045	−0.437523	−	0.899207i	$-0.644144\pi$
$353$	−3.37356e44	−0.875045	−0.437523	+	0.899207i	$0.644144\pi$
$354$	0	0
$355$	4.92107e43	0.115628
$356$	−2.78257e44	−0.622402
$357$	0	0
$358$	4.45896e44	0.904233
$359$	−8.65151e44	−1.67086	−0.835428	−	0.549600i	$-0.814780\pi$
$359$	−8.65151e44	−1.67086	−0.835428	+	0.549600i	$0.814780\pi$
$360$	0	0
$361$	−2.74696e44	−0.481367
$362$	9.07681e44	1.51542
$363$	0	0
$364$	1.91378e44	0.290147
$365$	−2.66024e44	−0.384411
$366$	0	0
$367$	2.11463e44	0.277701	0.138851	−	0.990313i	$-0.455659\pi$
$367$	2.11463e44	0.277701	0.138851	+	0.990313i	$0.455659\pi$
$368$	−7.50261e44	−0.939454
$369$	0	0
$370$	−9.69661e44	−1.10431
$371$	1.31671e45	1.43037
$372$	0	0
$373$	−8.06525e44	−0.797468	−0.398734	−	0.917067i	$-0.630550\pi$
$373$	−8.06525e44	−0.797468	−0.398734	+	0.917067i	$0.630550\pi$
$374$	1.55156e45	1.46391
$375$	0	0
$376$	2.19541e42	0.00188681
$377$	−8.57107e44	−0.703172
$378$	0	0
$379$	1.62962e45	1.21871	0.609356	−	0.792897i	$-0.291428\pi$
$379$	1.62962e45	1.21871	0.609356	+	0.792897i	$0.291428\pi$
$380$	2.23316e44	0.159480
$381$	0	0
$382$	1.42504e45	0.928362
$383$	−3.08699e45	−1.92113	−0.960565	−	0.278055i	$-0.910310\pi$
$383$	−3.08699e45	−1.92113	−0.960565	+	0.278055i	$0.910310\pi$
$384$	0	0
$385$	−8.89009e44	−0.505060
$386$	4.31409e44	0.234213
$387$	0	0
$388$	2.07991e44	0.103155
$389$	2.76724e45	1.31199	0.655993	−	0.754767i	$-0.272250\pi$
$389$	2.76724e45	1.31199	0.655993	+	0.754767i	$0.272250\pi$
$390$	0	0
$391$	−2.24453e45	−0.972821
$392$	−2.71040e44	−0.112338
$393$	0	0
$394$	1.33418e45	0.505862
$395$	−2.06924e45	−0.750518
$396$	0	0
$397$	−3.58547e45	−1.19045	−0.595226	−	0.803558i	$-0.702938\pi$
$397$	−3.58547e45	−1.19045	−0.595226	+	0.803558i	$0.702938\pi$
$398$	1.93092e45	0.613494
$399$	0	0
$400$	2.88283e45	0.839013
$401$	4.26941e45	1.18944	0.594718	−	0.803934i	$-0.297264\pi$
$401$	4.26941e45	1.18944	0.594718	+	0.803934i	$0.297264\pi$
$402$	0	0
$403$	2.49952e45	0.638291
$404$	1.39264e45	0.340538
$405$	0	0
$406$	4.19360e45	0.940549
$407$	7.43902e45	1.59813
$408$	0	0
$409$	−8.56530e43	−0.0168883	−0.00844413	−	0.999964i	$-0.502688\pi$
$409$	−8.56530e43	−0.0168883	−0.00844413	+	0.999964i	$0.502688\pi$
$410$	−6.09526e45	−1.15153
$411$	0	0
$412$	−2.61156e45	−0.453104
$413$	3.25557e45	0.541379
$414$	0	0
$415$	2.15103e45	0.328704
$416$	−4.09221e45	−0.599550
$417$	0	0
$418$	−6.10490e45	−0.822420
$419$	−5.67787e45	−0.733567	−0.366783	−	0.930306i	$-0.619541\pi$
$419$	−5.67787e45	−0.733567	−0.366783	+	0.930306i	$0.619541\pi$
$420$	0	0
$421$	4.40748e45	0.523907	0.261953	−	0.965081i	$-0.415633\pi$
$421$	4.40748e45	0.523907	0.261953	+	0.965081i	$0.415633\pi$
$422$	−1.72329e46	−1.96512
$423$	0	0
$424$	−1.06663e46	−1.11973
$425$	8.62447e45	0.868812
$426$	0	0
$427$	1.51280e46	1.40377
$428$	4.84633e45	0.431666
$429$	0	0
$430$	−1.45054e46	−1.19078
$431$	−2.36863e46	−1.86700	−0.933500	−	0.358578i	$-0.883262\pi$
$431$	−2.36863e46	−1.86700	−0.933500	+	0.358578i	$0.883262\pi$
$432$	0	0
$433$	6.19663e45	0.450420	0.225210	−	0.974310i	$-0.427693\pi$
$433$	6.19663e45	0.450420	0.225210	+	0.974310i	$0.427693\pi$
$434$	−1.22295e46	−0.853765
$435$	0	0
$436$	−9.83268e45	−0.633371
$437$	8.83155e45	0.546527
$438$	0	0
$439$	−4.03275e45	−0.230394	−0.115197	−	0.993343i	$-0.536750\pi$
$439$	−4.03275e45	−0.230394	−0.115197	+	0.993343i	$0.536750\pi$
$440$	7.20159e45	0.395373
$441$	0	0
$442$	−2.41314e46	−1.22375
$443$	−9.72231e44	−0.0473919	−0.0236959	−	0.999719i	$-0.507543\pi$
$443$	−9.72231e44	−0.0473919	−0.0236959	+	0.999719i	$0.507543\pi$
$444$	0	0
$445$	−2.01037e46	−0.905681
$446$	6.22433e45	0.269608
$447$	0	0
$448$	−8.36833e45	−0.335177
$449$	3.45806e46	1.33205	0.666027	−	0.745928i	$-0.267994\pi$
$449$	3.45806e46	1.33205	0.666027	+	0.745928i	$0.267994\pi$
$450$	0	0
$451$	4.67614e46	1.66647
$452$	7.98448e45	0.273731
$453$	0	0
$454$	4.63060e46	1.46947
$455$	1.38268e46	0.422204
$456$	0	0
$457$	3.54182e46	1.00160	0.500799	−	0.865564i	$-0.333040\pi$
$457$	3.54182e46	1.00160	0.500799	+	0.865564i	$0.333040\pi$
$458$	−5.34684e45	−0.145530
$459$	0	0
$460$	6.66379e45	0.168058
$461$	−7.06935e45	−0.171638	−0.0858189	−	0.996311i	$-0.527351\pi$
$461$	−7.06935e45	−0.171638	−0.0858189	+	0.996311i	$0.527351\pi$
$462$	0	0
$463$	−6.22902e44	−0.0140201	−0.00701007	−	0.999975i	$-0.502231\pi$
$463$	−6.22902e44	−0.0140201	−0.00701007	+	0.999975i	$0.502231\pi$
$464$	−4.96023e46	−1.07507
$465$	0	0
$466$	7.63557e46	1.53493
$467$	6.28266e46	1.21646	0.608231	−	0.793760i	$-0.291880\pi$
$467$	6.28266e46	1.21646	0.608231	+	0.793760i	$0.291880\pi$
$468$	0	0
$469$	−4.33323e46	−0.778551
$470$	−1.01457e44	−0.00175618
$471$	0	0
$472$	−2.63724e46	−0.423804
$473$	1.11282e47	1.72328
$474$	0	0
$475$	−3.39346e46	−0.488095
$476$	3.31339e46	0.459358
$477$	0	0
$478$	−7.27636e46	−0.937402
$479$	−1.10146e47	−1.36804	−0.684020	−	0.729463i	$-0.739770\pi$
$479$	−1.10146e47	−1.36804	−0.684020	+	0.729463i	$0.739770\pi$
$480$	0	0
$481$	−1.15699e47	−1.33596
$482$	−1.51623e46	−0.168827
$483$	0	0
$484$	−2.32932e45	−0.0241233
$485$	1.50271e46	0.150105
$486$	0	0
$487$	8.13246e46	0.755901	0.377951	−	0.925826i	$-0.376629\pi$
$487$	8.13246e46	0.755901	0.377951	+	0.925826i	$0.376629\pi$
$488$	−1.22548e47	−1.09890
$489$	0	0
$490$	1.25256e46	0.104560
$491$	−1.83224e47	−1.47590	−0.737950	−	0.674855i	$-0.764206\pi$
$491$	−1.83224e47	−1.47590	−0.737950	+	0.674855i	$0.764206\pi$
$492$	0	0
$493$	−1.48394e47	−1.11326
$494$	9.49498e46	0.687499
$495$	0	0
$496$	1.44652e47	0.975876
$497$	−2.87291e46	−0.187105
$498$	0	0
$499$	9.12339e45	0.0553856	0.0276928	−	0.999616i	$-0.491184\pi$
$499$	9.12339e45	0.0553856	0.0276928	+	0.999616i	$0.491184\pi$
$500$	−6.33843e46	−0.371541
$501$	0	0
$502$	7.36830e45	0.0402766
$503$	1.87342e47	0.989001	0.494500	−	0.869177i	$-0.335351\pi$
$503$	1.87342e47	0.989001	0.494500	+	0.869177i	$0.335351\pi$
$504$	0	0
$505$	1.00616e47	0.495530
$506$	−1.82171e47	−0.866653
$507$	0	0
$508$	2.52221e46	0.111987
$509$	−1.22247e47	−0.524418	−0.262209	−	0.965011i	$-0.584451\pi$
$509$	−1.22247e47	−0.524418	−0.262209	+	0.965011i	$0.584451\pi$
$510$	0	0
$511$	1.55304e47	0.622039
$512$	−6.84151e45	−0.0264806
$513$	0	0
$514$	−5.37115e46	−0.194184
$515$	−1.88681e47	−0.659329
$516$	0	0
$517$	7.78352e44	0.00254151
$518$	5.66086e47	1.78695
$519$	0	0
$520$	−1.12007e47	−0.330510
$521$	6.28279e46	0.179264	0.0896318	−	0.995975i	$-0.471431\pi$
$521$	6.28279e46	0.179264	0.0896318	+	0.995975i	$0.471431\pi$
$522$	0	0
$523$	−2.46925e47	−0.658849	−0.329425	−	0.944182i	$-0.606855\pi$
$523$	−2.46925e47	−0.658849	−0.329425	+	0.944182i	$0.606855\pi$
$524$	−8.34167e46	−0.215256
$525$	0	0
$526$	−2.20281e47	−0.531773
$527$	4.32751e47	1.01054
$528$	0	0
$529$	−1.94053e47	−0.424079
$530$	4.92922e47	1.04220
$531$	0	0
$532$	−1.30372e47	−0.258065
$533$	−7.27282e47	−1.39308
$534$	0	0
$535$	3.50141e47	0.628133
$536$	3.51022e47	0.609467
$537$	0	0
$538$	7.72485e47	1.25661
$539$	−9.60935e46	−0.151318
$540$	0	0
$541$	1.20408e47	0.177706	0.0888529	−	0.996045i	$-0.471680\pi$
$541$	1.20408e47	0.177706	0.0888529	+	0.996045i	$0.471680\pi$
$542$	−4.48683e45	−0.00641139
$543$	0	0
$544$	−7.08499e47	−0.949202
$545$	−7.10398e47	−0.921643
$546$	0	0
$547$	8.44104e47	1.02711	0.513556	−	0.858056i	$-0.328328\pi$
$547$	8.44104e47	1.02711	0.513556	+	0.858056i	$0.328328\pi$
$548$	−9.26461e46	−0.109186
$549$	0	0
$550$	6.99980e47	0.773995
$551$	5.83884e47	0.625423
$552$	0	0
$553$	1.20802e48	1.21446
$554$	8.72153e47	0.849517
$555$	0	0
$556$	−5.49787e47	−0.502789
$557$	1.28303e48	1.13703	0.568514	−	0.822674i	$-0.307519\pi$
$557$	1.28303e48	1.13703	0.568514	+	0.822674i	$0.307519\pi$
$558$	0	0
$559$	−1.73078e48	−1.44057
$560$	8.00182e47	0.645503
$561$	0	0
$562$	−1.44727e48	−1.09690
$563$	−2.05838e48	−1.51227	−0.756133	−	0.654418i	$-0.772914\pi$
$563$	−2.05838e48	−1.51227	−0.756133	+	0.654418i	$0.772914\pi$
$564$	0	0
$565$	5.76868e47	0.398317
$566$	−1.97259e48	−1.32053
$567$	0	0
$568$	2.32726e47	0.146470
$569$	4.38677e47	0.267720	0.133860	−	0.991000i	$-0.457263\pi$
$569$	4.38677e47	0.267720	0.133860	+	0.991000i	$0.457263\pi$
$570$	0	0
$571$	−2.36363e48	−1.35658	−0.678292	−	0.734792i	$-0.737280\pi$
$571$	−2.36363e48	−1.35658	−0.678292	+	0.734792i	$0.737280\pi$
$572$	−5.49634e47	−0.305945
$573$	0	0
$574$	3.55840e48	1.86336
$575$	−1.01261e48	−0.514347
$576$	0	0
$577$	−1.45741e48	−0.696632	−0.348316	−	0.937377i	$-0.613246\pi$
$577$	−1.45741e48	−0.696632	−0.348316	+	0.937377i	$0.613246\pi$
$578$	−1.63546e48	−0.758406
$579$	0	0
$580$	4.40566e47	0.192318
$581$	−1.25577e48	−0.531896
$582$	0	0
$583$	−3.78159e48	−1.50825
$584$	−1.25807e48	−0.486946
$585$	0	0
$586$	4.00102e48	1.45869
$587$	2.31218e48	0.818190	0.409095	−	0.912492i	$-0.365844\pi$
$587$	2.31218e48	0.818190	0.409095	+	0.912492i	$0.365844\pi$
$588$	0	0
$589$	−1.70274e48	−0.567716
$590$	1.21875e48	0.394461
$591$	0	0
$592$	−6.69573e48	−2.04253
$593$	−4.31701e48	−1.27857	−0.639287	−	0.768968i	$-0.720770\pi$
$593$	−4.31701e48	−1.27857	−0.639287	+	0.768968i	$0.720770\pi$
$594$	0	0
$595$	2.39388e48	0.668429
$596$	−4.53705e47	−0.123017
$597$	0	0
$598$	2.83331e48	0.724476
$599$	2.66626e48	0.662114	0.331057	−	0.943611i	$-0.392595\pi$
$599$	2.66626e48	0.662114	0.331057	+	0.943611i	$0.392595\pi$
$600$	0	0
$601$	7.51112e48	1.75955	0.879775	−	0.475391i	$-0.157693\pi$
$601$	7.51112e48	1.75955	0.879775	+	0.475391i	$0.157693\pi$
$602$	8.46824e48	1.92688
$603$	0	0
$604$	−5.55966e47	−0.119372
$605$	−1.68291e47	−0.0351027
$606$	0	0
$607$	−4.81557e48	−0.948081	−0.474040	−	0.880503i	$-0.657205\pi$
$607$	−4.81557e48	−0.948081	−0.474040	+	0.880503i	$0.657205\pi$
$608$	2.78773e48	0.533258
$609$	0	0
$610$	5.66329e48	1.02281
$611$	−1.21057e46	−0.00212457
$612$	0	0
$613$	1.36361e48	0.226012	0.113006	−	0.993594i	$-0.463952\pi$
$613$	1.36361e48	0.226012	0.113006	+	0.993594i	$0.463952\pi$
$614$	1.29858e49	2.09181
$615$	0	0
$616$	−4.20428e48	−0.639777
$617$	−1.76559e48	−0.261156	−0.130578	−	0.991438i	$-0.541683\pi$
$617$	−1.76559e48	−0.261156	−0.130578	+	0.991438i	$0.541683\pi$
$618$	0	0
$619$	7.44879e48	1.04112	0.520559	−	0.853826i	$-0.325724\pi$
$619$	7.44879e48	1.04112	0.520559	+	0.853826i	$0.325724\pi$
$620$	−1.28479e48	−0.174573
$621$	0	0
$622$	2.06152e48	0.264762
$623$	1.17365e49	1.46554
$624$	0	0
$625$	1.16140e48	0.137114
$626$	−1.30083e49	−1.49337
$627$	0	0
$628$	3.74104e48	0.406161
$629$	−2.00314e49	−2.11507
$630$	0	0
$631$	4.61699e48	0.461153	0.230576	−	0.973054i	$-0.425939\pi$
$631$	4.61699e48	0.461153	0.230576	+	0.973054i	$0.425939\pi$
$632$	−9.78578e48	−0.950706
$633$	0	0
$634$	−2.38641e49	−2.19373
$635$	1.82227e48	0.162956
$636$	0	0
$637$	1.49455e48	0.126494
$638$	−1.20440e49	−0.991761
$639$	0	0
$640$	−8.52472e48	−0.664555
$641$	2.29073e49	1.73763	0.868816	−	0.495134i	$-0.164881\pi$
$641$	2.29073e49	1.73763	0.868816	+	0.495134i	$0.164881\pi$
$642$	0	0
$643$	−1.75961e49	−1.26394	−0.631969	−	0.774994i	$-0.717753\pi$
$643$	−1.75961e49	−1.26394	−0.631969	+	0.774994i	$0.717753\pi$
$644$	−3.89031e48	−0.271945
$645$	0	0
$646$	1.64390e49	1.08844
$647$	1.34530e49	0.866950	0.433475	−	0.901166i	$-0.357287\pi$
$647$	1.34530e49	0.866950	0.433475	+	0.901166i	$0.357287\pi$
$648$	0	0
$649$	−9.34996e48	−0.570857
$650$	−1.08868e49	−0.647019
$651$	0	0
$652$	−1.21525e49	−0.684438
$653$	1.55134e49	0.850601	0.425300	−	0.905052i	$-0.360168\pi$
$653$	1.55134e49	0.850601	0.425300	+	0.905052i	$0.360168\pi$
$654$	0	0
$655$	−6.02675e48	−0.313228
$656$	−4.20892e49	−2.12987
$657$	0	0
$658$	5.92302e46	0.00284178
$659$	1.67026e46	0.000780348 0	0.000390174	−	1.00000i	$-0.499876\pi$
$659$	1.67026e46	0.000780348 0	0.000390174		1.00000i	$0.499876\pi$
$660$	0	0
$661$	3.86727e49	1.71348	0.856740	−	0.515748i	$-0.172486\pi$
$661$	3.86727e49	1.71348	0.856740	+	0.515748i	$0.172486\pi$
$662$	1.45223e49	0.626644
$663$	0	0
$664$	1.01726e49	0.416380
$665$	−9.41918e48	−0.375521
$666$	0	0
$667$	1.74232e49	0.659060
$668$	2.95520e48	0.108893
$669$	0	0
$670$	−1.62218e49	−0.567269
$671$	−4.34475e49	−1.48020
$672$	0	0
$673$	1.92251e49	0.621734	0.310867	−	0.950453i	$-0.399381\pi$
$673$	1.92251e49	0.621734	0.310867	+	0.950453i	$0.399381\pi$
$674$	2.88676e49	0.909626
$675$	0	0
$676$	−4.49080e48	−0.134356
$677$	2.27583e49	0.663495	0.331747	−	0.943368i	$-0.392362\pi$
$677$	2.27583e49	0.663495	0.331747	+	0.943368i	$0.392362\pi$
$678$	0	0
$679$	−8.77279e48	−0.242894
$680$	−1.93921e49	−0.523261
$681$	0	0
$682$	3.51229e49	0.900253
$683$	7.47926e49	1.86851	0.934257	−	0.356599i	$-0.116064\pi$
$683$	7.47926e49	1.86851	0.934257	+	0.356599i	$0.116064\pi$
$684$	0	0
$685$	−6.69355e48	−0.158881
$686$	−5.41193e49	−1.25222
$687$	0	0
$688$	−1.00163e50	−2.20247
$689$	5.88151e49	1.26082
$690$	0	0
$691$	5.04033e49	1.02705	0.513527	−	0.858073i	$-0.328339\pi$
$691$	5.04033e49	1.02705	0.513527	+	0.858073i	$0.328339\pi$
$692$	1.62080e49	0.322013
$693$	0	0
$694$	3.32057e49	0.627223
$695$	−3.97214e49	−0.731628
$696$	0	0
$697$	−1.25917e50	−2.20552
$698$	9.51168e49	1.62475
$699$	0	0
$700$	1.49482e49	0.242870
$701$	−3.72125e48	−0.0589690	−0.0294845	−	0.999565i	$-0.509387\pi$
$701$	−3.72125e48	−0.0589690	−0.0294845	+	0.999565i	$0.509387\pi$
$702$	0	0
$703$	7.88175e49	1.18824
$704$	2.40337e49	0.353427
$705$	0	0
$706$	7.37288e49	1.03170
$707$	−5.87397e49	−0.801848
$708$	0	0
$709$	−5.15574e49	−0.669857	−0.334928	−	0.942244i	$-0.608712\pi$
$709$	−5.15574e49	−0.669857	−0.334928	+	0.942244i	$0.608712\pi$
$710$	−1.07550e49	−0.136329
$711$	0	0
$712$	−9.50738e49	−1.14726
$713$	−5.08100e49	−0.598249
$714$	0	0
$715$	−3.97103e49	−0.445193
$716$	−2.73477e49	−0.299187
$717$	0	0
$718$	1.89078e50	1.96999
$719$	3.36048e49	0.341700	0.170850	−	0.985297i	$-0.445349\pi$
$719$	3.36048e49	0.341700	0.170850	+	0.985297i	$0.445349\pi$
$720$	0	0
$721$	1.10152e50	1.06690
$722$	6.00346e49	0.567546
$723$	0	0
$724$	−5.56699e49	−0.501412
$725$	−6.69473e49	−0.588597
$726$	0	0
$727$	1.31541e50	1.10207	0.551033	−	0.834484i	$-0.314234\pi$
$727$	1.31541e50	1.10207	0.551033	+	0.834484i	$0.314234\pi$
$728$	6.53893e49	0.534820
$729$	0	0
$730$	5.81394e49	0.453232
$731$	−2.99655e50	−2.28070
$732$	0	0
$733$	−2.25359e50	−1.63514	−0.817570	−	0.575829i	$-0.804680\pi$
$733$	−2.25359e50	−1.63514	−0.817570	+	0.575829i	$0.804680\pi$
$734$	−4.62151e49	−0.327418
$735$	0	0
$736$	8.31861e49	0.561939
$737$	1.24450e50	0.820943
$738$	0	0
$739$	−1.93424e50	−1.21684	−0.608419	−	0.793616i	$-0.708196\pi$
$739$	−1.93424e50	−1.21684	−0.608419	+	0.793616i	$0.708196\pi$
$740$	5.94712e49	0.365386
$741$	0	0
$742$	−2.87767e50	−1.68645
$743$	−8.43115e49	−0.482595	−0.241297	−	0.970451i	$-0.577573\pi$
$743$	−8.43115e49	−0.482595	−0.241297	+	0.970451i	$0.577573\pi$
$744$	0	0
$745$	−3.27796e49	−0.179006
$746$	1.76266e50	0.940238
$747$	0	0
$748$	−9.51601e49	−0.484370
$749$	−2.04412e50	−1.01642
$750$	0	0
$751$	−2.50076e50	−1.18679	−0.593394	−	0.804912i	$-0.702212\pi$
$751$	−2.50076e50	−1.18679	−0.593394	+	0.804912i	$0.702212\pi$
$752$	−7.00581e47	−0.00324823
$753$	0	0
$754$	1.87320e50	0.829060
$755$	−4.01678e49	−0.173702
$756$	0	0
$757$	−8.14773e49	−0.336402	−0.168201	−	0.985753i	$-0.553796\pi$
$757$	−8.14773e49	−0.336402	−0.168201	+	0.985753i	$0.553796\pi$
$758$	−3.56153e50	−1.43690
$759$	0	0
$760$	7.63019e49	0.293966
$761$	3.09181e50	1.16408	0.582038	−	0.813161i	$-0.302255\pi$
$761$	3.09181e50	1.16408	0.582038	+	0.813161i	$0.302255\pi$
$762$	0	0
$763$	4.14729e50	1.49137
$764$	−8.74004e49	−0.307171
$765$	0	0
$766$	6.74660e50	2.26507
$767$	1.45420e50	0.477206
$768$	0	0
$769$	−9.48513e49	−0.297394	−0.148697	−	0.988883i	$-0.547508\pi$
$769$	−9.48513e49	−0.297394	−0.148697	+	0.988883i	$0.547508\pi$
$770$	1.94292e50	0.595481
$771$	0	0
$772$	−2.64592e49	−0.0774950
$773$	−1.05155e50	−0.301086	−0.150543	−	0.988603i	$-0.548102\pi$
$773$	−1.05155e50	−0.301086	−0.150543	+	0.988603i	$0.548102\pi$
$774$	0	0
$775$	1.95234e50	0.534288
$776$	7.10657e49	0.190143
$777$	0	0
$778$	−6.04779e50	−1.54687
$779$	4.95444e50	1.23905
$780$	0	0
$781$	8.25096e49	0.197293
$782$	4.90541e50	1.14698
$783$	0	0
$784$	8.64922e49	0.193395
$785$	2.70285e50	0.591021
$786$	0	0
$787$	−1.75648e50	−0.367354	−0.183677	−	0.982987i	$-0.558800\pi$
$787$	−1.75648e50	−0.367354	−0.183677	+	0.982987i	$0.558800\pi$
$788$	−8.18282e49	−0.167376
$789$	0	0
$790$	4.52230e50	0.884882
$791$	−3.36775e50	−0.644542
$792$	0	0
$793$	6.75741e50	1.23737
$794$	7.83602e50	1.40358
$795$	0	0
$796$	−1.18427e50	−0.202989
$797$	−5.53388e49	−0.0927917	−0.0463959	−	0.998923i	$-0.514774\pi$
$797$	−5.53388e49	−0.0927917	−0.0463959	+	0.998923i	$0.514774\pi$
$798$	0	0
$799$	−2.09591e48	−0.00336359
$800$	−3.19637e50	−0.501859
$801$	0	0
$802$	−9.33077e50	−1.40238
$803$	−4.46032e50	−0.655909
$804$	0	0
$805$	−2.81069e50	−0.395718
$806$	−5.46269e50	−0.752563
$807$	0	0
$808$	4.75832e50	0.627704
$809$	−4.98563e50	−0.643607	−0.321803	−	0.946807i	$-0.604289\pi$
$809$	−4.98563e50	−0.643607	−0.321803	+	0.946807i	$0.604289\pi$
$810$	0	0
$811$	−1.07303e51	−1.32662	−0.663309	−	0.748346i	$-0.730848\pi$
$811$	−1.07303e51	−1.32662	−0.663309	+	0.748346i	$0.730848\pi$
$812$	−2.57202e50	−0.311203
$813$	0	0
$814$	−1.62579e51	−1.88425
$815$	−8.78004e50	−0.995952
$816$	0	0
$817$	1.17905e51	1.28129
$818$	1.87194e49	0.0199117
$819$	0	0
$820$	3.73834e50	0.381010
$821$	2.21488e50	0.220976	0.110488	−	0.993877i	$-0.464759\pi$
$821$	2.21488e50	0.220976	0.110488	+	0.993877i	$0.464759\pi$
$822$	0	0
$823$	1.24351e51	1.18892	0.594459	−	0.804126i	$-0.297366\pi$
$823$	1.24351e51	1.18892	0.594459	+	0.804126i	$0.297366\pi$
$824$	−8.92306e50	−0.835195
$825$	0	0
$826$	−7.11504e50	−0.638302
$827$	−1.45573e49	−0.0127860	−0.00639299	−	0.999980i	$-0.502035\pi$
$827$	−1.45573e49	−0.0127860	−0.00639299	+	0.999980i	$0.502035\pi$
$828$	0	0
$829$	−9.35859e50	−0.787964	−0.393982	−	0.919118i	$-0.628903\pi$
$829$	−9.35859e50	−0.787964	−0.393982	+	0.919118i	$0.628903\pi$
$830$	−4.70106e50	−0.387551
$831$	0	0
$832$	−3.73797e50	−0.295446
$833$	2.58756e50	0.200264
$834$	0	0
$835$	2.13510e50	0.158454
$836$	3.74426e50	0.272117
$837$	0	0
$838$	1.24089e51	0.864897
$839$	7.95070e50	0.542714	0.271357	−	0.962479i	$-0.412528\pi$
$839$	7.95070e50	0.542714	0.271357	+	0.962479i	$0.412528\pi$
$840$	0	0
$841$	−3.75414e50	−0.245799
$842$	−9.63252e50	−0.617701
$843$	0	0
$844$	1.05692e51	0.650206
$845$	−3.24454e50	−0.195506
$846$	0	0
$847$	9.82478e49	0.0568019
$848$	3.40374e51	1.92765
$849$	0	0
$850$	−1.88487e51	−1.02435
$851$	2.35192e51	1.25215
$852$	0	0
$853$	−2.54840e50	−0.130214	−0.0651072	−	0.997878i	$-0.520739\pi$
$853$	−2.54840e50	−0.130214	−0.0651072	+	0.997878i	$0.520739\pi$
$854$	−3.30622e51	−1.65508
$855$	0	0
$856$	1.65588e51	0.795678
$857$	2.64469e51	1.24512	0.622558	−	0.782573i	$-0.286093\pi$
$857$	2.64469e51	1.24512	0.622558	+	0.782573i	$0.286093\pi$
$858$	0	0
$859$	−1.92463e51	−0.869894	−0.434947	−	0.900456i	$-0.643233\pi$
$859$	−1.92463e51	−0.869894	−0.434947	+	0.900456i	$0.643233\pi$
$860$	8.89646e50	0.393998
$861$	0	0
$862$	5.17661e51	2.20125
$863$	1.08280e51	0.451190	0.225595	−	0.974221i	$-0.427567\pi$
$863$	1.08280e51	0.451190	0.225595	+	0.974221i	$0.427567\pi$
$864$	0	0
$865$	1.17101e51	0.468573
$866$	−1.35427e51	−0.531058
$867$	0	0
$868$	7.50059e50	0.282488
$869$	−3.46941e51	−1.28059
$870$	0	0
$871$	−1.93557e51	−0.686264
$872$	−3.35959e51	−1.16748
$873$	0	0
$874$	−1.93013e51	−0.644371
$875$	2.67347e51	0.874850
$876$	0	0
$877$	1.72464e51	0.542258	0.271129	−	0.962543i	$-0.412603\pi$
$877$	1.72464e51	0.542258	0.271129	+	0.962543i	$0.412603\pi$
$878$	8.81354e50	0.271642
$879$	0	0
$880$	−2.29811e51	−0.680650
$881$	−8.76279e50	−0.254428	−0.127214	−	0.991875i	$-0.540603\pi$
$881$	−8.76279e50	−0.254428	−0.127214	+	0.991875i	$0.540603\pi$
$882$	0	0
$883$	−2.14016e51	−0.597221	−0.298610	−	0.954375i	$-0.596523\pi$
$883$	−2.14016e51	−0.597221	−0.298610	+	0.954375i	$0.596523\pi$
$884$	1.48003e51	0.404907
$885$	0	0
$886$	2.12480e50	0.0558764
$887$	3.78615e51	0.976189	0.488095	−	0.872791i	$-0.337692\pi$
$887$	3.78615e51	0.976189	0.488095	+	0.872791i	$0.337692\pi$
$888$	0	0
$889$	−1.06384e51	−0.263690
$890$	4.39365e51	1.06782
$891$	0	0
$892$	−3.81751e50	−0.0892061
$893$	8.24675e48	0.00188965
$894$	0	0
$895$	−1.97583e51	−0.435358
$896$	4.97672e51	1.07536
$897$	0	0
$898$	−7.55757e51	−1.57053
$899$	−3.35922e51	−0.684612
$900$	0	0
$901$	1.01829e52	1.99612
$902$	−1.02197e52	−1.96482
$903$	0	0
$904$	2.72811e51	0.504562
$905$	−4.02207e51	−0.729625
$906$	0	0
$907$	5.56638e51	0.971506	0.485753	−	0.874096i	$-0.338545\pi$
$907$	5.56638e51	0.971506	0.485753	+	0.874096i	$0.338545\pi$
$908$	−2.84004e51	−0.486208
$909$	0	0
$910$	−3.02184e51	−0.497790
$911$	4.53769e51	0.733268	0.366634	−	0.930365i	$-0.380510\pi$
$911$	4.53769e51	0.733268	0.366634	+	0.930365i	$0.380510\pi$
$912$	0	0
$913$	3.60654e51	0.560857
$914$	−7.74063e51	−1.18091
$915$	0	0
$916$	3.27932e50	0.0481519
$917$	3.51840e51	0.506853
$918$	0	0
$919$	−9.66145e50	−0.133974	−0.0669870	−	0.997754i	$-0.521339\pi$
$919$	−9.66145e50	−0.133974	−0.0669870	+	0.997754i	$0.521339\pi$
$920$	2.27686e51	0.309777
$921$	0	0
$922$	1.54500e51	0.202366
$923$	−1.28328e51	−0.164926
$924$	0	0
$925$	−9.03710e51	−1.11828
$926$	1.36135e50	0.0165302
$927$	0	0
$928$	5.49972e51	0.643059
$929$	−1.12588e52	−1.29187	−0.645935	−	0.763392i	$-0.723532\pi$
$929$	−1.12588e52	−1.29187	−0.645935	+	0.763392i	$0.723532\pi$
$930$	0	0
$931$	−1.01812e51	−0.112508
$932$	−4.68305e51	−0.507867
$933$	0	0
$934$	−1.37307e52	−1.43424
$935$	−6.87519e51	−0.704825
$936$	0	0
$937$	−9.93521e51	−0.981147	−0.490574	−	0.871400i	$-0.663213\pi$
$937$	−9.93521e51	−0.981147	−0.490574	+	0.871400i	$0.663213\pi$
$938$	9.47024e51	0.917934
$939$	0	0
$940$	6.22254e48	0.000581072 0
$941$	7.86741e51	0.721129	0.360565	−	0.932734i	$-0.382584\pi$
$941$	7.86741e51	0.721129	0.360565	+	0.932734i	$0.382584\pi$
$942$	0	0
$943$	1.47841e52	1.30569
$944$	8.41574e51	0.729596
$945$	0	0
$946$	−2.43206e52	−2.03180
$947$	−1.76717e52	−1.44928	−0.724641	−	0.689127i	$-0.757994\pi$
$947$	−1.76717e52	−1.44928	−0.724641	+	0.689127i	$0.757994\pi$
$948$	0	0
$949$	6.93715e51	0.548305
$950$	7.41639e51	0.575479
$951$	0	0
$952$	1.13211e52	0.846722
$953$	2.15077e52	1.57931	0.789656	−	0.613550i	$-0.210259\pi$
$953$	2.15077e52	1.57931	0.789656	+	0.613550i	$0.210259\pi$
$954$	0	0
$955$	−6.31456e51	−0.446976
$956$	4.46273e51	0.310162
$957$	0	0
$958$	2.40724e52	1.61296
$959$	3.90769e51	0.257095
$960$	0	0
$961$	−5.96747e51	−0.378557
$962$	2.52860e52	1.57513
$963$	0	0
$964$	9.29935e50	0.0558605
$965$	−1.91164e51	−0.112766
$966$	0	0
$967$	5.62647e51	0.320091	0.160045	−	0.987110i	$-0.448836\pi$
$967$	5.62647e51	0.320091	0.160045	+	0.987110i	$0.448836\pi$
$968$	−7.95875e50	−0.0444658
$969$	0	0
$970$	−3.28416e51	−0.176978
$971$	−3.42787e51	−0.181421	−0.0907104	−	0.995877i	$-0.528914\pi$
$971$	−3.42787e51	−0.181421	−0.0907104	+	0.995877i	$0.528914\pi$
$972$	0	0
$973$	2.31893e52	1.18389
$974$	−1.77734e52	−0.891230
$975$	0	0
$976$	3.91064e52	1.89180
$977$	−1.18458e52	−0.562872	−0.281436	−	0.959580i	$-0.590811\pi$
$977$	−1.18458e52	−0.562872	−0.281436	+	0.959580i	$0.590811\pi$
$978$	0	0
$979$	−3.37070e52	−1.54534
$980$	−7.68220e50	−0.0345963
$981$	0	0
$982$	4.00436e52	1.74013
$983$	−2.75159e52	−1.17462	−0.587311	−	0.809362i	$-0.699813\pi$
$983$	−2.75159e52	−1.17462	−0.587311	+	0.809362i	$0.699813\pi$
$984$	0	0
$985$	−5.91197e51	−0.243556
$986$	3.24314e52	1.31256
$987$	0	0
$988$	−5.82346e51	−0.227475
$989$	3.51830e52	1.35020
$990$	0	0
$991$	−3.30440e52	−1.22406	−0.612031	−	0.790834i	$-0.709647\pi$
$991$	−3.30440e52	−1.22406	−0.612031	+	0.790834i	$0.709647\pi$
$992$	−1.60384e52	−0.583725
$993$	0	0
$994$	6.27873e51	0.220602
$995$	−8.55620e51	−0.295377
$996$	0	0
$997$	−4.71253e52	−1.57068	−0.785342	−	0.619062i	$-0.787513\pi$
$997$	−4.71253e52	−1.57068	−0.785342	+	0.619062i	$0.787513\pi$
$998$	−1.99391e51	−0.0653012
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.36.a.a.1.2	✓	2	3.2	odd	2
9.36.a.a.1.1		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)

\(f(q)\)	\(=\)	\(q-218549. q^{2} +1.34041e10 q^{4} +9.68425e11 q^{5} -5.65365e14 q^{7} +4.57985e15 q^{8} +O(q^{10})\)	\(q-218549. q^{2} +1.34041e10 q^{4} +9.68425e11 q^{5} -5.65365e14 q^{7} +4.57985e15 q^{8} -2.11649e17 q^{10} +1.62372e18 q^{11} -2.52538e19 q^{13} +1.23560e20 q^{14} -1.46148e21 q^{16} -4.37227e21 q^{17} +1.72036e22 q^{19} +1.29808e22 q^{20} -3.54863e23 q^{22} +5.13356e23 q^{23} -1.97254e24 q^{25} +5.51920e24 q^{26} -7.57819e24 q^{28} +3.39397e25 q^{29} -9.89761e25 q^{31} +1.62044e26 q^{32} +9.55557e26 q^{34} -5.47514e26 q^{35} +4.58147e27 q^{37} -3.75982e27 q^{38} +4.43524e27 q^{40} +2.87989e28 q^{41} +6.85354e28 q^{43} +2.17644e28 q^{44} -1.12194e29 q^{46} +4.79363e26 q^{47} -5.91811e28 q^{49} +4.31096e29 q^{50} -3.38503e29 q^{52} -2.32896e30 q^{53} +1.57245e30 q^{55} -2.58929e30 q^{56} -7.41751e30 q^{58} -5.75836e30 q^{59} -2.67580e31 q^{61} +2.16312e31 q^{62} +1.48016e31 q^{64} -2.44564e31 q^{65} +7.66448e31 q^{67} -5.86062e31 q^{68} +1.19659e32 q^{70} +5.08152e31 q^{71} -2.74698e32 q^{73} -1.00128e33 q^{74} +2.30597e32 q^{76} -9.17994e32 q^{77} -2.13670e33 q^{79} -1.41534e33 q^{80} -6.29399e33 q^{82} +2.22116e33 q^{83} -4.23422e33 q^{85} -1.49784e34 q^{86} +7.43639e33 q^{88} -2.07592e34 q^{89} +1.42776e34 q^{91} +6.88105e33 q^{92} -1.04765e32 q^{94} +1.66604e34 q^{95} +1.55170e34 q^{97} +1.29340e34 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 60912 q^{2} + 57142939904 q^{4} + 1333779496740 q^{5} - 12\!\cdots\!44 q^{7}+ \cdots + 72\!\cdots\!24 q^{8}+O(q^{10}) \) 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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