LMFDB - Embedded newform 9.34.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,34,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, 34, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 34 $
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:	$62.0845459929$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 589050 $ x^2 - x - 589050
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$767.996$ 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)

$f(q)$	$=$	$q-49679.4 q^{2} -6.12189e9 q^{4} -2.04307e10 q^{5} -1.22168e14 q^{7} +7.30875e14 q^{8} +O(q^{10})$	\(q-49679.4 q^{2} -6.12189e9 q^{4} -2.04307e10 q^{5} -1.22168e14 q^{7} +7.30875e14 q^{8} +1.01499e15 q^{10} -2.15763e17 q^{11} -1.07762e18 q^{13} +6.06926e18 q^{14} +1.62772e19 q^{16} -2.54532e20 q^{17} -1.22020e21 q^{19} +1.25075e20 q^{20} +1.07190e22 q^{22} +5.11280e21 q^{23} -1.15998e23 q^{25} +5.35354e22 q^{26} +7.47901e23 q^{28} +1.64733e23 q^{29} -6.75706e24 q^{31} -7.08681e24 q^{32} +1.26450e25 q^{34} +2.49599e24 q^{35} -7.46520e25 q^{37} +6.06190e25 q^{38} -1.49323e25 q^{40} -4.96453e26 q^{41} -1.99347e26 q^{43} +1.32088e27 q^{44} -2.54001e26 q^{46} -2.16452e27 q^{47} +7.19411e27 q^{49} +5.76271e27 q^{50} +6.59706e27 q^{52} +3.60439e28 q^{53} +4.40819e27 q^{55} -8.92898e28 q^{56} -8.18385e27 q^{58} +1.87520e29 q^{59} +4.18340e27 q^{61} +3.35687e29 q^{62} +2.12249e29 q^{64} +2.20165e28 q^{65} +4.85975e29 q^{67} +1.55822e30 q^{68} -1.23999e29 q^{70} +3.42819e30 q^{71} +7.01467e30 q^{73} +3.70867e30 q^{74} +7.46995e30 q^{76} +2.63594e31 q^{77} -2.95630e30 q^{79} -3.32554e29 q^{80} +2.46635e31 q^{82} +1.23020e31 q^{83} +5.20028e30 q^{85} +9.90343e30 q^{86} -1.57696e32 q^{88} -7.05623e31 q^{89} +1.31651e32 q^{91} -3.13000e31 q^{92} +1.07532e32 q^{94} +2.49297e31 q^{95} -7.71791e32 q^{97} -3.57399e32 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 121680 q^{2} + 14652233984 q^{4} + 181061536500 q^{5} - 67153080066800 q^{7} + 28\!\cdots\!40 q^{8}+O(q^{10}) $ 2 * q + 121680 * q^2 + 14652233984 * q^4 + 181061536500 * q^5 - 67153080066800 * q^7 + 2818750585098240 * q^8	$ 2 q + 121680 q^{2} + 14652233984 q^{4} + 181061536500 q^{5} - 67153080066800 q^{7} + 28\!\cdots\!40 q^{8}+ \cdots - 11\!\cdots\!40 q^{98}+O(q^{100}) $ 2 * q + 121680 * q^2 + 14652233984 * q^4 + 181061536500 * q^5 - 67153080066800 * q^7 + 2818750585098240 * q^8 + 35542592216532000 * q^10 - 133871815441914264 * q^11 - 2981610478259443940 * q^13 + 15496641262468340352 * q^14 + 195605979111894351872 * q^16 + 79361149261175525340 * q^17 - 1360696443041697171800 * q^19 + 4310900037459183168000 * q^20 + 24751741840613395122240 * q^22 - 26163854053674631579440 * q^23 - 191814088084783724781250 * q^25 - 272731683634642092710304 * q^26 + 1890794991723644827125760 * q^28 + 1674519971630399929109700 * q^29 - 6238301225723632337095616 * q^31 + 5708163006744585940500480 * q^32 + 69860790536166916073075808 * q^34 + 13581143663546216842308000 * q^35 - 104802741516758180098173620 * q^37 + 36544090911856460663722560 * q^38 + 405758480738092701742080000 * q^40 - 277566613022002182732188244 * q^41 + 1567661189367072113768291800 * q^43 + 3022085914387766085808346112 * q^44 - 5613550634763385681470869376 * q^46 - 5421061461431251260476972640 * q^47 + 2489799365888888933444851314 * q^49 - 7229107516344249428363250000 * q^50 - 32956722688372988680703091200 * q^52 + 26867414785542903092975171220 * q^53 + 20908570805489145209222682000 * q^55 + 25575237795171758759822131200 * q^56 + 250532370716581201796821222560 * q^58 + 305786409635298433026663995400 * q^59 - 5745893983413264859067362436 * q^61 + 424581887479352364037004290560 * q^62 + 864365322360380859973709594624 * q^64 - 361623311364964256200313721000 * q^65 + 1598906337224495341750209565960 * q^67 + 8494558579722382470601861086720 * q^68 + 1775546165763388432770973344000 * q^70 + 2669761937956104715736810084976 * q^71 + 946314321191998870965166536340 * q^73 - 1457936998080019494211346192928 * q^74 + 4551314657470802548563162035200 * q^76 + 30864620292716415864215760033600 * q^77 - 8535199972765636469730106191200 * q^79 + 35800819471604723635001769984000 * q^80 + 62171822095602398237444019107040 * q^82 - 29072605803747945444403983322920 * q^83 + 72477213859794605306963311287000 * q^85 + 312696885737578501917214826406336 * q^86 + 13282372192867492753038509752320 * q^88 - 132719467655604316264938597726900 * q^89 + 26902102147452358410548887211744 * q^91 - 681044992402323869436382557788160 * q^92 - 450506433888867898835049561530112 * q^94 - 3378716387067841884487537110000 * q^95 - 367787330930535727150839877856060 * q^97 - 1163527978168280943548587223169840 * 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 $

$2$	−49679.4	−0.536021	−0.268010	−	0.963416i	$-0.586366\pi$
$2$	−49679.4	−0.536021	−0.268010	+	0.963416i	$0.586366\pi$
$3$	0	0
$3$	0	0
$4$	−6.12189e9	−0.712682
$5$	−2.04307e10	−0.0598796	−0.0299398	−	0.999552i	$-0.509532\pi$
$5$	−2.04307e10	−0.0598796	−0.0299398	+	0.999552i	$0.509532\pi$
$6$	0	0
$7$	−1.22168e14	−1.38944	−0.694722	−	0.719278i	$-0.744473\pi$
$7$	−1.22168e14	−1.38944	−0.694722	+	0.719278i	$0.744473\pi$
$8$	7.30875e14	0.918033
$9$	0	0
$10$	1.01499e15	0.0320967
$11$	−2.15763e17	−1.41578	−0.707892	−	0.706321i	$-0.750354\pi$
$11$	−2.15763e17	−1.41578	−0.707892	+	0.706321i	$0.750354\pi$
$12$	0	0
$13$	−1.07762e18	−0.449158	−0.224579	−	0.974456i	$-0.572101\pi$
$13$	−1.07762e18	−0.449158	−0.224579	+	0.974456i	$0.572101\pi$
$14$	6.06926e18	0.744771
$15$	0	0
$16$	1.62772e19	0.220597
$17$	−2.54532e20	−1.26863	−0.634316	−	0.773074i	$-0.718718\pi$
$17$	−2.54532e20	−1.26863	−0.634316	+	0.773074i	$0.718718\pi$
$18$	0	0
$19$	−1.22020e21	−0.970505	−0.485252	−	0.874374i	$-0.661272\pi$
$19$	−1.22020e21	−0.970505	−0.485252	+	0.874374i	$0.661272\pi$
$20$	1.25075e20	0.0426751
$21$	0	0
$22$	1.07190e22	0.758890
$23$	5.11280e21	0.173840	0.0869199	−	0.996215i	$-0.472298\pi$
$23$	5.11280e21	0.173840	0.0869199	+	0.996215i	$0.472298\pi$
$24$	0	0
$25$	−1.15998e23	−0.996414
$26$	5.35354e22	0.240758
$27$	0	0
$28$	7.47901e23	0.990231
$29$	1.64733e23	0.122240	0.0611201	−	0.998130i	$-0.480533\pi$
$29$	1.64733e23	0.122240	0.0611201	+	0.998130i	$0.480533\pi$
$30$	0	0
$31$	−6.75706e24	−1.66836	−0.834181	−	0.551491i	$-0.814059\pi$
$31$	−6.75706e24	−1.66836	−0.834181	+	0.551491i	$0.814059\pi$
$32$	−7.08681e24	−1.03628
$33$	0	0
$34$	1.26450e25	0.680013
$35$	2.49599e24	0.0831994
$36$	0	0
$37$	−7.46520e25	−0.994748	−0.497374	−	0.867536i	$-0.665702\pi$
$37$	−7.46520e25	−0.994748	−0.497374	+	0.867536i	$0.665702\pi$
$38$	6.06190e25	0.520211
$39$	0	0
$40$	−1.49323e25	−0.0549715
$41$	−4.96453e26	−1.21603	−0.608016	−	0.793925i	$-0.708034\pi$
$41$	−4.96453e26	−1.21603	−0.608016	+	0.793925i	$0.708034\pi$
$42$	0	0
$43$	−1.99347e26	−0.222525	−0.111263	−	0.993791i	$-0.535489\pi$
$43$	−1.99347e26	−0.222525	−0.111263	+	0.993791i	$0.535489\pi$
$44$	1.32088e27	1.00900
$45$	0	0
$46$	−2.54001e26	−0.0931818
$47$	−2.16452e27	−0.556862	−0.278431	−	0.960456i	$-0.589814\pi$
$47$	−2.16452e27	−0.556862	−0.278431	+	0.960456i	$0.589814\pi$
$48$	0	0
$49$	7.19411e27	0.930555
$50$	5.76271e27	0.534099
$51$	0	0
$52$	6.59706e27	0.320107
$53$	3.60439e28	1.27726	0.638631	−	0.769513i	$-0.279501\pi$
$53$	3.60439e28	1.27726	0.638631	+	0.769513i	$0.279501\pi$
$54$	0	0
$55$	4.40819e27	0.0847766
$56$	−8.92898e28	−1.27556
$57$	0	0
$58$	−8.18385e27	−0.0655233
$59$	1.87520e29	1.13237	0.566186	−	0.824278i	$-0.308418\pi$
$59$	1.87520e29	1.13237	0.566186	+	0.824278i	$0.308418\pi$
$60$	0	0
$61$	4.18340e27	0.0145743	0.00728715	−	0.999973i	$-0.497680\pi$
$61$	4.18340e27	0.0145743	0.00728715	+	0.999973i	$0.497680\pi$
$62$	3.35687e29	0.894276
$63$	0	0
$64$	2.12249e29	0.334870
$65$	2.20165e28	0.0268954
$66$	0	0
$67$	4.85975e29	0.360064	0.180032	−	0.983661i	$-0.442380\pi$
$67$	4.85975e29	0.360064	0.180032	+	0.983661i	$0.442380\pi$
$68$	1.55822e30	0.904130
$69$	0	0
$70$	−1.23999e29	−0.0445966
$71$	3.42819e30	0.975667	0.487834	−	0.872937i	$-0.337787\pi$
$71$	3.42819e30	0.975667	0.487834	+	0.872937i	$0.337787\pi$
$72$	0	0
$73$	7.01467e30	1.26235	0.631175	−	0.775640i	$-0.282573\pi$
$73$	7.01467e30	1.26235	0.631175	+	0.775640i	$0.282573\pi$
$74$	3.70867e30	0.533206
$75$	0	0
$76$	7.46995e30	0.691661
$77$	2.63594e31	1.96715
$78$	0	0
$79$	−2.95630e30	−0.144511	−0.0722555	−	0.997386i	$-0.523020\pi$
$79$	−2.95630e30	−0.144511	−0.0722555	+	0.997386i	$0.523020\pi$
$80$	−3.32554e29	−0.0132092
$81$	0	0
$82$	2.46635e31	0.651818
$83$	1.23020e31	0.266187	0.133094	−	0.991103i	$-0.457509\pi$
$83$	1.23020e31	0.266187	0.133094	+	0.991103i	$0.457509\pi$
$84$	0	0
$85$	5.20028e30	0.0759652
$86$	9.90343e30	0.119278
$87$	0	0
$88$	−1.57696e32	−1.29974
$89$	−7.05623e31	−0.482656	−0.241328	−	0.970444i	$-0.577583\pi$
$89$	−7.05623e31	−0.482656	−0.241328	+	0.970444i	$0.577583\pi$
$90$	0	0
$91$	1.31651e32	0.624080
$92$	−3.13000e31	−0.123892
$93$	0	0
$94$	1.07532e32	0.298490
$95$	2.49297e31	0.0581135
$96$	0	0
$97$	−7.71791e32	−1.27575	−0.637875	−	0.770140i	$-0.720187\pi$
$97$	−7.71791e32	−1.27575	−0.637875	+	0.770140i	$0.720187\pi$
$98$	−3.57399e32	−0.498797
$99$	0	0
$100$	7.10126e32	0.710126
$101$	−1.88601e33	−1.60045	−0.800224	−	0.599701i	$-0.795286\pi$
$101$	−1.88601e33	−1.60045	−0.800224	+	0.599701i	$0.795286\pi$
$102$	0	0
$103$	−4.05317e32	−0.248874	−0.124437	−	0.992227i	$-0.539713\pi$
$103$	−4.05317e32	−0.248874	−0.124437	+	0.992227i	$0.539713\pi$
$104$	−7.87604e32	−0.412342
$105$	0	0
$106$	−1.79064e33	−0.684640
$107$	1.13905e33	0.373003	0.186501	−	0.982455i	$-0.440285\pi$
$107$	1.13905e33	0.373003	0.186501	+	0.982455i	$0.440285\pi$
$108$	0	0
$109$	5.47789e32	0.132153	0.0660764	−	0.997815i	$-0.478952\pi$
$109$	5.47789e32	0.132153	0.0660764	+	0.997815i	$0.478952\pi$
$110$	−2.18997e32	−0.0454421
$111$	0	0
$112$	−1.98855e33	−0.306507
$113$	−7.05689e33	−0.939332	−0.469666	−	0.882844i	$-0.655626\pi$
$113$	−7.05689e33	−0.939332	−0.469666	+	0.882844i	$0.655626\pi$
$114$	0	0
$115$	−1.04458e32	−0.0104095
$116$	−1.00848e33	−0.0871183
$117$	0	0
$118$	−9.31588e33	−0.606975
$119$	3.10958e34	1.76269
$120$	0	0
$121$	2.33284e34	1.00444
$122$	−2.07829e32	−0.00781213
$123$	0	0
$124$	4.13660e34	1.18901
$125$	4.74838e33	0.119545
$126$	0	0
$127$	−1.88228e34	−0.364689	−0.182344	−	0.983235i	$-0.558369\pi$
$127$	−1.88228e34	−0.364689	−0.182344	+	0.983235i	$0.558369\pi$
$128$	5.03308e34	0.856780
$129$	0	0
$130$	−1.09377e33	−0.0144165
$131$	1.26378e35	1.46790	0.733949	−	0.679204i	$-0.237675\pi$
$131$	1.26378e35	1.46790	0.733949	+	0.679204i	$0.237675\pi$
$132$	0	0
$133$	1.49070e35	1.34846
$134$	−2.41430e34	−0.193002
$135$	0	0
$136$	−1.86031e35	−1.16465
$137$	−2.95759e35	−1.64077	−0.820387	−	0.571809i	$-0.806242\pi$
$137$	−2.95759e35	−1.64077	−0.820387	+	0.571809i	$0.806242\pi$
$138$	0	0
$139$	−8.22498e34	−0.359245	−0.179622	−	0.983736i	$-0.557488\pi$
$139$	−8.22498e34	−0.359245	−0.179622	+	0.983736i	$0.557488\pi$
$140$	−1.52802e34	−0.0592947
$141$	0	0
$142$	−1.70310e35	−0.522978
$143$	2.32510e35	0.635911
$144$	0	0
$145$	−3.36562e33	−0.00731970
$146$	−3.48485e35	−0.676646
$147$	0	0
$148$	4.57011e35	0.708939
$149$	−5.29045e35	−0.734378	−0.367189	−	0.930146i	$-0.619680\pi$
$149$	−5.29045e35	−0.734378	−0.367189	+	0.930146i	$0.619680\pi$
$150$	0	0
$151$	−5.18728e35	−0.577856	−0.288928	−	0.957351i	$-0.593299\pi$
$151$	−5.18728e35	−0.577856	−0.288928	+	0.957351i	$0.593299\pi$
$152$	−8.91816e35	−0.890955
$153$	0	0
$154$	−1.30952e36	−1.05444
$155$	1.38052e35	0.0999009
$156$	0	0
$157$	1.31075e36	0.767669	0.383835	−	0.923402i	$-0.374603\pi$
$157$	1.31075e36	0.767669	0.383835	+	0.923402i	$0.374603\pi$
$158$	1.46867e35	0.0774609
$159$	0	0
$160$	1.44789e35	0.0620519
$161$	−6.24622e35	−0.241541
$162$	0	0
$163$	1.61518e36	0.509478	0.254739	−	0.967010i	$-0.418010\pi$
$163$	1.61518e36	0.509478	0.254739	+	0.967010i	$0.418010\pi$
$164$	3.03923e36	0.866643
$165$	0	0
$166$	−6.11157e35	−0.142682
$167$	6.45682e35	0.136520	0.0682601	−	0.997668i	$-0.478255\pi$
$167$	6.45682e35	0.136520	0.0682601	+	0.997668i	$0.478255\pi$
$168$	0	0
$169$	−4.59487e36	−0.798257
$170$	−2.58347e35	−0.0407189
$171$	0	0
$172$	1.22038e36	0.158590
$173$	6.58049e36	0.777137	0.388569	−	0.921420i	$-0.372970\pi$
$173$	6.58049e36	0.777137	0.388569	+	0.921420i	$0.372970\pi$
$174$	0	0
$175$	1.41713e37	1.38446
$176$	−3.51200e36	−0.312317
$177$	0	0
$178$	3.50549e36	0.258714
$179$	2.08823e37	1.40508	0.702542	−	0.711642i	$-0.252048\pi$
$179$	2.08823e37	1.40508	0.702542	+	0.711642i	$0.252048\pi$
$180$	0	0
$181$	−2.42658e37	−1.35925	−0.679624	−	0.733561i	$-0.737857\pi$
$181$	−2.42658e37	−1.35925	−0.679624	+	0.733561i	$0.737857\pi$
$182$	−6.54034e36	−0.334520
$183$	0	0
$184$	3.73682e36	0.159591
$185$	1.52520e36	0.0595652
$186$	0	0
$187$	5.49185e37	1.79611
$188$	1.32510e37	0.396865
$189$	0	0
$190$	−1.23849e36	−0.0311500
$191$	−4.06968e37	−0.938664	−0.469332	−	0.883022i	$-0.655505\pi$
$191$	−4.06968e37	−0.938664	−0.469332	+	0.883022i	$0.655505\pi$
$192$	0	0
$193$	−5.23242e37	−1.01627	−0.508133	−	0.861279i	$-0.669664\pi$
$193$	−5.23242e37	−1.01627	−0.508133	+	0.861279i	$0.669664\pi$
$194$	3.83421e37	0.683829
$195$	0	0
$196$	−4.40416e37	−0.663189
$197$	−1.35006e38	−1.86922	−0.934611	−	0.355672i	$-0.884252\pi$
$197$	−1.35006e38	−1.86922	−0.934611	+	0.355672i	$0.884252\pi$
$198$	0	0
$199$	−9.91562e37	−1.16210	−0.581051	−	0.813867i	$-0.697358\pi$
$199$	−9.91562e37	−1.16210	−0.581051	+	0.813867i	$0.697358\pi$
$200$	−8.47800e37	−0.914741
$201$	0	0
$202$	9.36960e37	0.857874
$203$	−2.01252e37	−0.169846
$204$	0	0
$205$	1.01429e37	0.0728155
$206$	2.01359e37	0.133402
$207$	0	0
$208$	−1.75406e37	−0.0990828
$209$	2.63274e38	1.37403
$210$	0	0
$211$	−2.07128e38	−0.923802	−0.461901	−	0.886931i	$-0.652832\pi$
$211$	−2.07128e38	−0.923802	−0.461901	+	0.886931i	$0.652832\pi$
$212$	−2.20657e38	−0.910282
$213$	0	0
$214$	−5.65876e37	−0.199937
$215$	4.07280e36	0.0133247
$216$	0	0
$217$	8.25499e38	2.31809
$218$	−2.72139e37	−0.0708367
$219$	0	0
$220$	−2.69865e37	−0.0604187
$221$	2.74288e38	0.569816
$222$	0	0
$223$	−4.51334e38	−0.808106	−0.404053	−	0.914736i	$-0.632399\pi$
$223$	−4.51334e38	−0.808106	−0.404053	+	0.914736i	$0.632399\pi$
$224$	8.65784e38	1.43985
$225$	0	0
$226$	3.50582e38	0.503501
$227$	2.43217e38	0.324764	0.162382	−	0.986728i	$-0.448082\pi$
$227$	2.43217e38	0.324764	0.162382	+	0.986728i	$0.448082\pi$
$228$	0	0
$229$	3.41418e38	0.394458	0.197229	−	0.980357i	$-0.436806\pi$
$229$	3.41418e38	0.394458	0.197229	+	0.980357i	$0.436806\pi$
$230$	5.18943e36	0.00557969
$231$	0	0
$232$	1.20399e38	0.112221
$233$	6.99608e37	0.0607410	0.0303705	−	0.999539i	$-0.490331\pi$
$233$	6.99608e37	0.0607410	0.0303705	+	0.999539i	$0.490331\pi$
$234$	0	0
$235$	4.42228e37	0.0333447
$236$	−1.14798e39	−0.807020
$237$	0	0
$238$	−1.54482e39	−0.944840
$239$	1.63523e39	0.933282	0.466641	−	0.884447i	$-0.345464\pi$
$239$	1.63523e39	0.933282	0.466641	+	0.884447i	$0.345464\pi$
$240$	0	0
$241$	−3.64560e38	−0.181338	−0.0906689	−	0.995881i	$-0.528900\pi$
$241$	−3.64560e38	−0.181338	−0.0906689	+	0.995881i	$0.528900\pi$
$242$	−1.15894e39	−0.538403
$243$	0	0
$244$	−2.56103e37	−0.0103868
$245$	−1.46981e38	−0.0557213
$246$	0	0
$247$	1.31491e39	0.435910
$248$	−4.93857e39	−1.53161
$249$	0	0
$250$	−2.35897e38	−0.0640784
$251$	−1.94693e39	−0.495147	−0.247573	−	0.968869i	$-0.579633\pi$
$251$	−1.94693e39	−0.495147	−0.247573	+	0.968869i	$0.579633\pi$
$252$	0	0
$253$	−1.10315e39	−0.246120
$254$	9.35105e38	0.195481
$255$	0	0
$256$	−4.32361e39	−0.794122
$257$	5.64464e39	0.972164	0.486082	−	0.873913i	$-0.338426\pi$
$257$	5.64464e39	0.972164	0.486082	+	0.873913i	$0.338426\pi$
$258$	0	0
$259$	9.12012e39	1.38215
$260$	−1.34783e38	−0.0191679
$261$	0	0
$262$	−6.27840e39	−0.786824
$263$	−9.75930e39	−1.14855	−0.574274	−	0.818663i	$-0.694715\pi$
$263$	−9.75930e39	−1.14855	−0.574274	+	0.818663i	$0.694715\pi$
$264$	0	0
$265$	−7.36404e38	−0.0764820
$266$	−7.40572e39	−0.722804
$267$	0	0
$268$	−2.97508e39	−0.256611
$269$	1.08142e40	0.877168	0.438584	−	0.898690i	$-0.355480\pi$
$269$	1.08142e40	0.877168	0.438584	+	0.898690i	$0.355480\pi$
$270$	0	0
$271$	−6.19121e39	−0.444408	−0.222204	−	0.975000i	$-0.571325\pi$
$271$	−6.19121e39	−0.444408	−0.222204	+	0.975000i	$0.571325\pi$
$272$	−4.14306e39	−0.279856
$273$	0	0
$274$	1.46931e40	0.879489
$275$	2.50280e40	1.41071
$276$	0	0
$277$	−5.15662e39	−0.257898	−0.128949	−	0.991651i	$-0.541160\pi$
$277$	−5.15662e39	−0.257898	−0.128949	+	0.991651i	$0.541160\pi$
$278$	4.08612e39	0.192563
$279$	0	0
$280$	1.82426e39	0.0763798
$281$	1.28386e40	0.506832	0.253416	−	0.967357i	$-0.418446\pi$
$281$	1.28386e40	0.506832	0.253416	+	0.967357i	$0.418446\pi$
$282$	0	0
$283$	3.83806e40	1.34783	0.673915	−	0.738809i	$-0.264611\pi$
$283$	3.83806e40	1.34783	0.673915	+	0.738809i	$0.264611\pi$
$284$	−2.09870e40	−0.695340
$285$	0	0
$286$	−1.15510e40	−0.340862
$287$	6.06509e40	1.68961
$288$	0	0
$289$	2.45321e40	0.609426
$290$	1.67202e38	0.00392351
$291$	0	0
$292$	−4.29430e40	−0.899654
$293$	−1.90344e40	−0.376897	−0.188449	−	0.982083i	$-0.560346\pi$
$293$	−1.90344e40	−0.376897	−0.188449	+	0.982083i	$0.560346\pi$
$294$	0	0
$295$	−3.83117e39	−0.0678060
$296$	−5.45613e40	−0.913212
$297$	0	0
$298$	2.62827e40	0.393642
$299$	−5.50964e39	−0.0780816
$300$	0	0
$301$	2.43538e40	0.309186
$302$	2.57701e40	0.309743
$303$	0	0
$304$	−1.98614e40	−0.214090
$305$	−8.54701e37	−0.000872703 0
$306$	0	0
$307$	−1.48955e41	−1.36544	−0.682718	−	0.730682i	$-0.739202\pi$
$307$	−1.48955e41	−1.36544	−0.682718	+	0.730682i	$0.739202\pi$
$308$	−1.61369e41	−1.40195
$309$	0	0
$310$	−6.85834e39	−0.0535489
$311$	7.37928e39	0.0546345	0.0273173	−	0.999627i	$-0.491304\pi$
$311$	7.37928e39	0.0546345	0.0273173	+	0.999627i	$0.491304\pi$
$312$	0	0
$313$	−2.63324e40	−0.175391	−0.0876957	−	0.996147i	$-0.527950\pi$
$313$	−2.63324e40	−0.175391	−0.0876957	+	0.996147i	$0.527950\pi$
$314$	−6.51171e40	−0.411487
$315$	0	0
$316$	1.80981e40	0.102990
$317$	−1.79226e41	−0.968109	−0.484054	−	0.875038i	$-0.660836\pi$
$317$	−1.79226e41	−0.968109	−0.484054	+	0.875038i	$0.660836\pi$
$318$	0	0
$319$	−3.55433e40	−0.173066
$320$	−4.33641e39	−0.0200519
$321$	0	0
$322$	3.10309e40	0.129471
$323$	3.10581e41	1.23121
$324$	0	0
$325$	1.25001e41	0.447548
$326$	−8.02413e40	−0.273091
$327$	0	0
$328$	−3.62845e41	−1.11636
$329$	2.64436e41	0.773728
$330$	0	0
$331$	6.16181e41	1.63135	0.815674	−	0.578512i	$-0.196366\pi$
$331$	6.16181e41	1.63135	0.815674	+	0.578512i	$0.196366\pi$
$332$	−7.53115e40	−0.189707
$333$	0	0
$334$	−3.20771e40	−0.0731777
$335$	−9.92883e39	−0.0215605
$336$	0	0
$337$	4.51357e41	0.888437	0.444218	−	0.895919i	$-0.353481\pi$
$337$	4.51357e41	0.888437	0.444218	+	0.895919i	$0.353481\pi$
$338$	2.28271e41	0.427882
$339$	0	0
$340$	−3.18355e40	−0.0541390
$341$	1.45792e42	2.36204
$342$	0	0
$343$	6.55899e40	0.0964903
$344$	−1.45697e41	−0.204286
$345$	0	0
$346$	−3.26915e41	−0.416562
$347$	−8.17900e41	−0.993720	−0.496860	−	0.867831i	$-0.665514\pi$
$347$	−8.17900e41	−0.993720	−0.496860	+	0.867831i	$0.665514\pi$
$348$	0	0
$349$	−1.22969e42	−1.35886	−0.679432	−	0.733739i	$-0.737774\pi$
$349$	−1.22969e42	−1.35886	−0.679432	+	0.733739i	$0.737774\pi$
$350$	−7.04021e41	−0.742101
$351$	0	0
$352$	1.52907e42	1.46715
$353$	−1.62570e41	−0.148853	−0.0744266	−	0.997226i	$-0.523713\pi$
$353$	−1.62570e41	−0.148853	−0.0744266	+	0.997226i	$0.523713\pi$
$354$	0	0
$355$	−7.00404e40	−0.0584226
$356$	4.31974e41	0.343980
$357$	0	0
$358$	−1.03742e42	−0.753155
$359$	−3.64036e41	−0.252398	−0.126199	−	0.992005i	$-0.540278\pi$
$359$	−3.64036e41	−0.252398	−0.126199	+	0.992005i	$0.540278\pi$
$360$	0	0
$361$	−9.18755e40	−0.0581207
$362$	1.20551e42	0.728585
$363$	0	0
$364$	−8.05951e41	−0.444771
$365$	−1.43315e41	−0.0755891
$366$	0	0
$367$	1.35581e42	0.653442	0.326721	−	0.945121i	$-0.394056\pi$
$367$	1.35581e42	0.653442	0.326721	+	0.945121i	$0.394056\pi$
$368$	8.32218e40	0.0383485
$369$	0	0
$370$	−7.57709e40	−0.0319282
$371$	−4.40343e42	−1.77469
$372$	0	0
$373$	1.93457e42	0.713493	0.356746	−	0.934201i	$-0.383886\pi$
$373$	1.93457e42	0.713493	0.356746	+	0.934201i	$0.383886\pi$
$374$	−2.72832e42	−0.962752
$375$	0	0
$376$	−1.58200e42	−0.511218
$377$	−1.77519e41	−0.0549052
$378$	0	0
$379$	−5.45789e42	−1.54696	−0.773478	−	0.633823i	$-0.781485\pi$
$379$	−5.45789e42	−1.54696	−0.773478	+	0.633823i	$0.781485\pi$
$380$	−1.52617e41	−0.0414164
$381$	0	0
$382$	2.02180e42	0.503143
$383$	5.06942e42	1.20831	0.604155	−	0.796867i	$-0.293511\pi$
$383$	5.06942e42	1.20831	0.604155	+	0.796867i	$0.293511\pi$
$384$	0	0
$385$	−5.38542e41	−0.117792
$386$	2.59944e42	0.544740
$387$	0	0
$388$	4.72482e42	0.909204
$389$	−7.51028e42	−1.38512	−0.692560	−	0.721360i	$-0.743517\pi$
$389$	−7.51028e42	−1.38512	−0.692560	+	0.721360i	$0.743517\pi$
$390$	0	0
$391$	−1.30137e42	−0.220539
$392$	5.25800e42	0.854280
$393$	0	0
$394$	6.70703e42	1.00194
$395$	6.03993e40	0.00865327
$396$	0	0
$397$	−1.26926e43	−1.67304	−0.836519	−	0.547938i	$-0.815413\pi$
$397$	−1.26926e43	−1.67304	−0.836519	+	0.547938i	$0.815413\pi$
$398$	4.92603e42	0.622911
$399$	0	0
$400$	−1.88812e42	−0.219806
$401$	−5.29553e42	−0.591598	−0.295799	−	0.955250i	$-0.595586\pi$
$401$	−5.29553e42	−0.591598	−0.295799	+	0.955250i	$0.595586\pi$
$402$	0	0
$403$	7.28153e42	0.749358
$404$	1.15459e43	1.14061
$405$	0	0
$406$	9.99807e41	0.0910410
$407$	1.61071e43	1.40835
$408$	0	0
$409$	1.80907e43	1.45888	0.729442	−	0.684042i	$-0.239780\pi$
$409$	1.80907e43	1.45888	0.729442	+	0.684042i	$0.239780\pi$
$410$	−5.03894e41	−0.0390306
$411$	0	0
$412$	2.48130e42	0.177368
$413$	−2.29090e43	−1.57337
$414$	0	0
$415$	−2.51339e41	−0.0159392
$416$	7.63687e42	0.465453
$417$	0	0
$418$	−1.30793e43	−0.736506
$419$	−9.59306e42	−0.519309	−0.259654	−	0.965702i	$-0.583609\pi$
$419$	−9.59306e42	−0.519309	−0.259654	+	0.965702i	$0.583609\pi$
$420$	0	0
$421$	−1.95406e43	−0.977875	−0.488938	−	0.872319i	$-0.662615\pi$
$421$	−1.95406e43	−0.977875	−0.488938	+	0.872319i	$0.662615\pi$
$422$	1.02900e43	0.495177
$423$	0	0
$424$	2.63436e43	1.17257
$425$	2.95252e43	1.26408
$426$	0	0
$427$	−5.11080e41	−0.0202502
$428$	−6.97316e42	−0.265832
$429$	0	0
$430$	−2.02334e41	−0.00714233
$431$	−4.01382e43	−1.36359	−0.681794	−	0.731544i	$-0.738800\pi$
$431$	−4.01382e43	−1.36359	−0.681794	+	0.731544i	$0.738800\pi$
$432$	0	0
$433$	−1.24146e43	−0.390735	−0.195367	−	0.980730i	$-0.562590\pi$
$433$	−1.24146e43	−0.390735	−0.195367	+	0.980730i	$0.562590\pi$
$434$	−4.10103e43	−1.24255
$435$	0	0
$436$	−3.35350e42	−0.0941829
$437$	−6.23865e42	−0.168712
$438$	0	0
$439$	−6.07044e43	−1.52249	−0.761247	−	0.648462i	$-0.775413\pi$
$439$	−6.07044e43	−1.52249	−0.761247	+	0.648462i	$0.775413\pi$
$440$	3.22184e42	0.0778278
$441$	0	0
$442$	−1.36265e43	−0.305433
$443$	−6.61294e43	−1.42802	−0.714009	−	0.700137i	$-0.753122\pi$
$443$	−6.61294e43	−1.42802	−0.714009	+	0.700137i	$0.753122\pi$
$444$	0	0
$445$	1.44164e42	0.0289013
$446$	2.24220e43	0.433162
$447$	0	0
$448$	−2.59301e43	−0.465283
$449$	1.54504e43	0.267225	0.133612	−	0.991034i	$-0.457342\pi$
$449$	1.54504e43	0.267225	0.133612	+	0.991034i	$0.457342\pi$
$450$	0	0
$451$	1.07116e44	1.72164
$452$	4.32015e43	0.669444
$453$	0	0
$454$	−1.20829e43	−0.174080
$455$	−2.68972e42	−0.0373697
$456$	0	0
$457$	7.12331e43	0.920586	0.460293	−	0.887767i	$-0.347744\pi$
$457$	7.12331e43	0.920586	0.460293	+	0.887767i	$0.347744\pi$
$458$	−1.69615e43	−0.211438
$459$	0	0
$460$	6.39482e41	0.00741864
$461$	1.34004e44	1.49986	0.749932	−	0.661515i	$-0.230086\pi$
$461$	1.34004e44	1.49986	0.749932	+	0.661515i	$0.230086\pi$
$462$	0	0
$463$	−5.53073e43	−0.576363	−0.288182	−	0.957576i	$-0.593051\pi$
$463$	−5.53073e43	−0.576363	−0.288182	+	0.957576i	$0.593051\pi$
$464$	2.68139e42	0.0269658
$465$	0	0
$466$	−3.47561e42	−0.0325584
$467$	3.51798e43	0.318101	0.159050	−	0.987270i	$-0.449157\pi$
$467$	3.51798e43	0.318101	0.159050	+	0.987270i	$0.449157\pi$
$468$	0	0
$469$	−5.93707e43	−0.500288
$470$	−2.19696e42	−0.0178734
$471$	0	0
$472$	1.37054e44	1.03955
$473$	4.30116e43	0.315048
$474$	0	0
$475$	1.41541e44	0.967025
$476$	−1.90365e44	−1.25624
$477$	0	0
$478$	−8.12372e43	−0.500258
$479$	2.90520e44	1.72838	0.864192	−	0.503162i	$-0.167830\pi$
$479$	2.90520e44	1.72838	0.864192	+	0.503162i	$0.167830\pi$
$480$	0	0
$481$	8.04464e43	0.446799
$482$	1.81112e43	0.0972008
$483$	0	0
$484$	−1.42814e44	−0.715849
$485$	1.57683e43	0.0763915
$486$	0	0
$487$	−1.45706e44	−0.659551	−0.329776	−	0.944059i	$-0.606973\pi$
$487$	−1.45706e44	−0.659551	−0.329776	+	0.944059i	$0.606973\pi$
$488$	3.05755e42	0.0133797
$489$	0	0
$490$	7.30194e42	0.0298678
$491$	−1.43984e44	−0.569469	−0.284735	−	0.958606i	$-0.591905\pi$
$491$	−1.43984e44	−0.569469	−0.284735	+	0.958606i	$0.591905\pi$
$492$	0	0
$493$	−4.19299e43	−0.155078
$494$	−6.53241e43	−0.233657
$495$	0	0
$496$	−1.09986e44	−0.368035
$497$	−4.18816e44	−1.35564
$498$	0	0
$499$	1.76176e44	0.533687	0.266843	−	0.963740i	$-0.414019\pi$
$499$	1.76176e44	0.533687	0.266843	+	0.963740i	$0.414019\pi$
$500$	−2.90690e43	−0.0851972
$501$	0	0
$502$	9.67224e43	0.265409
$503$	2.43829e44	0.647460	0.323730	−	0.946149i	$-0.395063\pi$
$503$	2.43829e44	0.647460	0.323730	+	0.946149i	$0.395063\pi$
$504$	0	0
$505$	3.85326e43	0.0958343
$506$	5.48039e43	0.131925
$507$	0	0
$508$	1.15231e44	0.259907
$509$	−3.49786e44	−0.763763	−0.381882	−	0.924211i	$-0.624724\pi$
$509$	−3.49786e44	−0.763763	−0.381882	+	0.924211i	$0.624724\pi$
$510$	0	0
$511$	−8.56970e44	−1.75396
$512$	−2.17544e44	−0.431114
$513$	0	0
$514$	−2.80422e44	−0.521100
$515$	8.28092e42	0.0149025
$516$	0	0
$517$	4.67023e44	0.788396
$518$	−4.53082e44	−0.740860
$519$	0	0
$520$	1.60913e43	0.0246909
$521$	3.31981e44	0.493505	0.246752	−	0.969079i	$-0.420637\pi$
$521$	3.31981e44	0.493505	0.246752	+	0.969079i	$0.420637\pi$
$522$	0	0
$523$	1.02645e45	1.43238	0.716190	−	0.697905i	$-0.245884\pi$
$523$	1.02645e45	1.43238	0.716190	+	0.697905i	$0.245884\pi$
$524$	−7.73674e44	−1.04614
$525$	0	0
$526$	4.84837e44	0.615645
$527$	1.71989e45	2.11654
$528$	0	0
$529$	−8.38864e44	−0.969780
$530$	3.65842e43	0.0409960
$531$	0	0
$532$	−9.12591e44	−0.961024
$533$	5.34987e44	0.546191
$534$	0	0
$535$	−2.32717e43	−0.0223353
$536$	3.55187e44	0.330550
$537$	0	0
$538$	−5.37245e44	−0.470180
$539$	−1.55222e45	−1.31746
$540$	0	0
$541$	4.08746e44	0.326361	0.163180	−	0.986596i	$-0.447825\pi$
$541$	4.08746e44	0.326361	0.163180	+	0.986596i	$0.447825\pi$
$542$	3.07576e44	0.238212
$543$	0	0
$544$	1.80382e45	1.31465
$545$	−1.11917e43	−0.00791326
$546$	0	0
$547$	7.54748e44	0.502355	0.251178	−	0.967941i	$-0.419182\pi$
$547$	7.54748e44	0.502355	0.251178	+	0.967941i	$0.419182\pi$
$548$	1.81060e45	1.16935
$549$	0	0
$550$	−1.24338e45	−0.756169
$551$	−2.01008e44	−0.118635
$552$	0	0
$553$	3.61166e44	0.200790
$554$	2.56178e44	0.138239
$555$	0	0
$556$	5.03524e44	0.256027
$557$	3.77046e45	1.86116	0.930581	−	0.366087i	$-0.119303\pi$
$557$	3.77046e45	1.86116	0.930581	+	0.366087i	$0.119303\pi$
$558$	0	0
$559$	2.14819e44	0.0999491
$560$	4.06276e43	0.0183535
$561$	0	0
$562$	−6.37816e44	−0.271673
$563$	−1.99523e45	−0.825284	−0.412642	−	0.910893i	$-0.635394\pi$
$563$	−1.99523e45	−0.825284	−0.412642	+	0.910893i	$0.635394\pi$
$564$	0	0
$565$	1.44177e44	0.0562468
$566$	−1.90672e45	−0.722465
$567$	0	0
$568$	2.50558e45	0.895695
$569$	−2.38895e45	−0.829574	−0.414787	−	0.909919i	$-0.636144\pi$
$569$	−2.38895e45	−0.829574	−0.414787	+	0.909919i	$0.636144\pi$
$570$	0	0
$571$	9.25875e44	0.303429	0.151714	−	0.988424i	$-0.451521\pi$
$571$	9.25875e44	0.303429	0.151714	+	0.988424i	$0.451521\pi$
$572$	−1.42340e45	−0.453202
$573$	0	0
$574$	−3.01310e45	−0.905665
$575$	−5.93074e44	−0.173217
$576$	0	0
$577$	−3.73598e45	−1.03040	−0.515198	−	0.857071i	$-0.672281\pi$
$577$	−3.73598e45	−1.03040	−0.515198	+	0.857071i	$0.672281\pi$
$578$	−1.21874e45	−0.326665
$579$	0	0
$580$	2.06040e43	0.00521661
$581$	−1.50292e45	−0.369853
$582$	0	0
$583$	−7.77694e45	−1.80833
$584$	5.12684e45	1.15888
$585$	0	0
$586$	9.45617e44	0.202025
$587$	−6.35230e45	−1.31948	−0.659739	−	0.751495i	$-0.729333\pi$
$587$	−6.35230e45	−1.31948	−0.659739	+	0.751495i	$0.729333\pi$
$588$	0	0
$589$	8.24499e45	1.61915
$590$	1.90330e44	0.0363454
$591$	0	0
$592$	−1.21512e45	−0.219438
$593$	−7.20521e45	−1.26545	−0.632724	−	0.774378i	$-0.718063\pi$
$593$	−7.20521e45	−1.26545	−0.632724	+	0.774378i	$0.718063\pi$
$594$	0	0
$595$	−6.35310e44	−0.105549
$596$	3.23876e45	0.523377
$597$	0	0
$598$	2.73716e44	0.0418534
$599$	6.37291e45	0.947971	0.473985	−	0.880533i	$-0.342815\pi$
$599$	6.37291e45	0.947971	0.473985	+	0.880533i	$0.342815\pi$
$600$	0	0
$601$	−8.13523e45	−1.14536	−0.572679	−	0.819780i	$-0.694096\pi$
$601$	−8.13523e45	−1.14536	−0.572679	+	0.819780i	$0.694096\pi$
$602$	−1.20989e45	−0.165730
$603$	0	0
$604$	3.17559e45	0.411827
$605$	−4.76616e44	−0.0601458
$606$	0	0
$607$	8.31211e45	0.993339	0.496670	−	0.867940i	$-0.334556\pi$
$607$	8.31211e45	0.993339	0.496670	+	0.867940i	$0.334556\pi$
$608$	8.64734e45	1.00571
$609$	0	0
$610$	4.24610e42	0.000467787 0
$611$	2.33253e45	0.250119
$612$	0	0
$613$	−2.99559e44	−0.0304358	−0.0152179	−	0.999884i	$-0.504844\pi$
$613$	−2.99559e44	−0.0304358	−0.0152179	+	0.999884i	$0.504844\pi$
$614$	7.40000e45	0.731903
$615$	0	0
$616$	1.92654e46	1.80591
$617$	−9.03503e45	−0.824564	−0.412282	−	0.911056i	$-0.635268\pi$
$617$	−9.03503e45	−0.824564	−0.412282	+	0.911056i	$0.635268\pi$
$618$	0	0
$619$	−1.15706e46	−1.00106	−0.500528	−	0.865720i	$-0.666861\pi$
$619$	−1.15706e46	−1.00106	−0.500528	+	0.865720i	$0.666861\pi$
$620$	−8.45138e44	−0.0711975
$621$	0	0
$622$	−3.66598e44	−0.0292853
$623$	8.62048e45	0.670623
$624$	0	0
$625$	1.34069e46	0.989256
$626$	1.30818e45	0.0940135
$627$	0	0
$628$	−8.02424e45	−0.547104
$629$	1.90013e46	1.26197
$630$	0	0
$631$	−1.43742e46	−0.905939	−0.452970	−	0.891526i	$-0.649635\pi$
$631$	−1.43742e46	−0.905939	−0.452970	+	0.891526i	$0.649635\pi$
$632$	−2.16068e45	−0.132666
$633$	0	0
$634$	8.90387e45	0.518927
$635$	3.84563e44	0.0218374
$636$	0	0
$637$	−7.75250e45	−0.417966
$638$	1.76577e45	0.0927668
$639$	0	0
$640$	−1.02830e45	−0.0513037
$641$	−1.34213e46	−0.652586	−0.326293	−	0.945269i	$-0.605800\pi$
$641$	−1.34213e46	−0.652586	−0.326293	+	0.945269i	$0.605800\pi$
$642$	0	0
$643$	3.48572e46	1.60995	0.804973	−	0.593312i	$-0.202180\pi$
$643$	3.48572e46	1.60995	0.804973	+	0.593312i	$0.202180\pi$
$644$	3.82387e45	0.172142
$645$	0	0
$646$	−1.54295e46	−0.659956
$647$	−3.47978e46	−1.45088	−0.725440	−	0.688285i	$-0.758364\pi$
$647$	−3.47978e46	−1.45088	−0.725440	+	0.688285i	$0.758364\pi$
$648$	0	0
$649$	−4.04598e46	−1.60319
$650$	−6.21000e45	−0.239895
$651$	0	0
$652$	−9.88796e45	−0.363096
$653$	−1.19815e46	−0.428986	−0.214493	−	0.976726i	$-0.568810\pi$
$653$	−1.19815e46	−0.428986	−0.214493	+	0.976726i	$0.568810\pi$
$654$	0	0
$655$	−2.58200e45	−0.0878972
$656$	−8.08085e45	−0.268252
$657$	0	0
$658$	−1.31370e46	−0.414735
$659$	2.00047e46	0.615918	0.307959	−	0.951400i	$-0.400354\pi$
$659$	2.00047e46	0.615918	0.307959	+	0.951400i	$0.400354\pi$
$660$	0	0
$661$	3.80588e46	1.11463	0.557316	−	0.830301i	$-0.311831\pi$
$661$	3.80588e46	1.11463	0.557316	+	0.830301i	$0.311831\pi$
$662$	−3.06115e46	−0.874437
$663$	0	0
$664$	8.99123e45	0.244369
$665$	−3.04561e45	−0.0807454
$666$	0	0
$667$	8.42247e44	0.0212502
$668$	−3.95279e45	−0.0972954
$669$	0	0
$670$	4.93259e44	0.0115569
$671$	−9.02622e44	−0.0206341
$672$	0	0
$673$	−5.38328e46	−1.17165	−0.585825	−	0.810437i	$-0.699230\pi$
$673$	−5.38328e46	−1.17165	−0.585825	+	0.810437i	$0.699230\pi$
$674$	−2.24231e46	−0.476221
$675$	0	0
$676$	2.81293e46	0.568903
$677$	9.38585e46	1.85251	0.926255	−	0.376898i	$-0.123009\pi$
$677$	9.38585e46	1.85251	0.926255	+	0.376898i	$0.123009\pi$
$678$	0	0
$679$	9.42884e46	1.77258
$680$	3.80076e45	0.0697386
$681$	0	0
$682$	−7.24288e46	−1.26610
$683$	−1.22152e46	−0.208430	−0.104215	−	0.994555i	$-0.533233\pi$
$683$	−1.22152e46	−0.208430	−0.104215	+	0.994555i	$0.533233\pi$
$684$	0	0
$685$	6.04258e45	0.0982489
$686$	−3.25847e45	−0.0517208
$687$	0	0
$688$	−3.24480e45	−0.0490883
$689$	−3.88416e46	−0.573693
$690$	0	0
$691$	−1.01396e47	−1.42768	−0.713841	−	0.700308i	$-0.753046\pi$
$691$	−1.01396e47	−1.42768	−0.713841	+	0.700308i	$0.753046\pi$
$692$	−4.02850e46	−0.553851
$693$	0	0
$694$	4.06328e46	0.532655
$695$	1.68042e45	0.0215115
$696$	0	0
$697$	1.26363e47	1.54270
$698$	6.10903e46	0.728379
$699$	0	0
$700$	−8.67549e46	−0.986681
$701$	1.07227e47	1.19112	0.595560	−	0.803311i	$-0.296930\pi$
$701$	1.07227e47	1.19112	0.595560	+	0.803311i	$0.296930\pi$
$702$	0	0
$703$	9.10906e46	0.965408
$704$	−4.57954e46	−0.474103
$705$	0	0
$706$	8.07639e45	0.0797884
$707$	2.30411e47	2.22373
$708$	0	0
$709$	−3.54939e45	−0.0326957	−0.0163478	−	0.999866i	$-0.505204\pi$
$709$	−3.54939e45	−0.0326957	−0.0163478	+	0.999866i	$0.505204\pi$
$710$	3.47957e45	0.0313157
$711$	0	0
$712$	−5.15722e46	−0.443094
$713$	−3.45475e46	−0.290028
$714$	0	0
$715$	−4.75035e45	−0.0380781
$716$	−1.27839e47	−1.00138
$717$	0	0
$718$	1.80851e46	0.135290
$719$	−6.94896e46	−0.508035	−0.254017	−	0.967200i	$-0.581752\pi$
$719$	−6.94896e46	−0.508035	−0.254017	+	0.967200i	$0.581752\pi$
$720$	0	0
$721$	4.95169e46	0.345797
$722$	4.56432e45	0.0311539
$723$	0	0
$724$	1.48553e47	0.968711
$725$	−1.91087e46	−0.121802
$726$	0	0
$727$	−1.73359e47	−1.05592	−0.527958	−	0.849270i	$-0.677042\pi$
$727$	−1.73359e47	−1.05592	−0.527958	+	0.849270i	$0.677042\pi$
$728$	9.62203e46	0.572926
$729$	0	0
$730$	7.11980e45	0.0405173
$731$	5.07401e46	0.282303
$732$	0	0
$733$	4.59301e46	0.244277	0.122138	−	0.992513i	$-0.461025\pi$
$733$	4.59301e46	0.244277	0.122138	+	0.992513i	$0.461025\pi$
$734$	−6.73556e46	−0.350259
$735$	0	0
$736$	−3.62334e46	−0.180146
$737$	−1.04855e47	−0.509773
$738$	0	0
$739$	−3.24514e47	−1.50869	−0.754346	−	0.656477i	$-0.772046\pi$
$739$	−3.24514e47	−1.50869	−0.754346	+	0.656477i	$0.772046\pi$
$740$	−9.33708e45	−0.0424510
$741$	0	0
$742$	2.18760e47	0.951268
$743$	−3.63726e47	−1.54689	−0.773443	−	0.633866i	$-0.781467\pi$
$743$	−3.63726e47	−1.54689	−0.773443	+	0.633866i	$0.781467\pi$
$744$	0	0
$745$	1.08088e46	0.0439743
$746$	−9.61085e46	−0.382447
$747$	0	0
$748$	−3.36205e47	−1.28005
$749$	−1.39156e47	−0.518267
$750$	0	0
$751$	2.28361e47	0.813885	0.406943	−	0.913454i	$-0.366595\pi$
$751$	2.28361e47	0.813885	0.406943	+	0.913454i	$0.366595\pi$
$752$	−3.52323e46	−0.122842
$753$	0	0
$754$	8.81906e45	0.0294303
$755$	1.05980e46	0.0346018
$756$	0	0
$757$	−1.23646e47	−0.386453	−0.193226	−	0.981154i	$-0.561895\pi$
$757$	−1.23646e47	−0.386453	−0.193226	+	0.981154i	$0.561895\pi$
$758$	2.71145e47	0.829201
$759$	0	0
$760$	1.82205e46	0.0533501
$761$	1.65073e47	0.472966	0.236483	−	0.971636i	$-0.424005\pi$
$761$	1.65073e47	0.472966	0.236483	+	0.971636i	$0.424005\pi$
$762$	0	0
$763$	−6.69225e46	−0.183619
$764$	2.49141e47	0.668968
$765$	0	0
$766$	−2.51846e47	−0.647679
$767$	−2.02075e47	−0.508614
$768$	0	0
$769$	−2.15810e47	−0.520339	−0.260170	−	0.965563i	$-0.583778\pi$
$769$	−2.15810e47	−0.520339	−0.260170	+	0.965563i	$0.583778\pi$
$770$	2.67544e46	0.0631392
$771$	0	0
$772$	3.20323e47	0.724274
$773$	−5.97126e46	−0.132161	−0.0660806	−	0.997814i	$-0.521049\pi$
$773$	−5.97126e46	−0.132161	−0.0660806	+	0.997814i	$0.521049\pi$
$774$	0	0
$775$	7.83805e47	1.66238
$776$	−5.64083e47	−1.17118
$777$	0	0
$778$	3.73106e47	0.742453
$779$	6.05774e47	1.18016
$780$	0	0
$781$	−7.39675e47	−1.38133
$782$	6.46514e46	0.118213
$783$	0	0
$784$	1.17100e47	0.205277
$785$	−2.67795e46	−0.0459677
$786$	0	0
$787$	2.40999e47	0.396673	0.198336	−	0.980134i	$-0.436446\pi$
$787$	2.40999e47	0.396673	0.198336	+	0.980134i	$0.436446\pi$
$788$	8.26493e47	1.33216
$789$	0	0
$790$	−3.00060e45	−0.00463833
$791$	8.62128e47	1.30515
$792$	0	0
$793$	−4.50811e45	−0.00654616
$794$	6.30559e47	0.896783
$795$	0	0
$796$	6.07023e47	0.828209
$797$	−5.30320e47	−0.708722	−0.354361	−	0.935109i	$-0.615302\pi$
$797$	−5.30320e47	−0.708722	−0.354361	+	0.935109i	$0.615302\pi$
$798$	0	0
$799$	5.50941e47	0.706452
$800$	8.22055e47	1.03256
$801$	0	0
$802$	2.63079e47	0.317109
$803$	−1.51350e48	−1.78722
$804$	0	0
$805$	1.27615e46	0.0144634
$806$	−3.61742e47	−0.401672
$807$	0	0
$808$	−1.37844e48	−1.46926
$809$	−6.52623e47	−0.681572	−0.340786	−	0.940141i	$-0.610693\pi$
$809$	−6.52623e47	−0.681572	−0.340786	+	0.940141i	$0.610693\pi$
$810$	0	0
$811$	−4.54256e47	−0.455466	−0.227733	−	0.973724i	$-0.573131\pi$
$811$	−4.54256e47	−0.455466	−0.227733	+	0.973724i	$0.573131\pi$
$812$	1.23204e47	0.121046
$813$	0	0
$814$	−8.00193e47	−0.754904
$815$	−3.29994e46	−0.0305074
$816$	0	0
$817$	2.43243e47	0.215962
$818$	−8.98736e47	−0.781993
$819$	0	0
$820$	−6.20938e46	−0.0518943
$821$	3.88660e47	0.318352	0.159176	−	0.987250i	$-0.449116\pi$
$821$	3.88660e47	0.318352	0.159176	+	0.987250i	$0.449116\pi$
$822$	0	0
$823$	−2.16262e48	−1.70170	−0.850849	−	0.525410i	$-0.823912\pi$
$823$	−2.16262e48	−1.70170	−0.850849	+	0.525410i	$0.823912\pi$
$824$	−2.96236e47	−0.228475
$825$	0	0
$826$	1.13811e48	0.843358
$827$	5.70292e47	0.414244	0.207122	−	0.978315i	$-0.433590\pi$
$827$	5.70292e47	0.414244	0.207122	+	0.978315i	$0.433590\pi$
$828$	0	0
$829$	1.81254e48	1.26514	0.632569	−	0.774504i	$-0.282001\pi$
$829$	1.81254e48	1.26514	0.632569	+	0.774504i	$0.282001\pi$
$830$	1.24864e46	0.00854375
$831$	0	0
$832$	−2.28723e47	−0.150410
$833$	−1.83113e48	−1.18053
$834$	0	0
$835$	−1.31918e46	−0.00817478
$836$	−1.61174e48	−0.979242
$837$	0	0
$838$	4.76578e47	0.278360
$839$	1.88483e47	0.107945	0.0539723	−	0.998542i	$-0.482812\pi$
$839$	1.88483e47	0.107945	0.0539723	+	0.998542i	$0.482812\pi$
$840$	0	0
$841$	−1.78894e48	−0.985057
$842$	9.70766e47	0.524162
$843$	0	0
$844$	1.26802e48	0.658377
$845$	9.38766e46	0.0477993
$846$	0	0
$847$	−2.84999e48	−1.39562
$848$	5.86693e47	0.281760
$849$	0	0
$850$	−1.46680e48	−0.677575
$851$	−3.81681e47	−0.172927
$852$	0	0
$853$	3.65000e48	1.59087	0.795434	−	0.606040i	$-0.207243\pi$
$853$	3.65000e48	1.59087	0.795434	+	0.606040i	$0.207243\pi$
$854$	2.53901e46	0.0108545
$855$	0	0
$856$	8.32507e47	0.342429
$857$	1.58574e48	0.639807	0.319903	−	0.947450i	$-0.396350\pi$
$857$	1.58574e48	0.639807	0.319903	+	0.947450i	$0.396350\pi$
$858$	0	0
$859$	2.88906e48	1.12168	0.560840	−	0.827924i	$-0.310478\pi$
$859$	2.88906e48	1.12168	0.560840	+	0.827924i	$0.310478\pi$
$860$	−2.49332e46	−0.00949629
$861$	0	0
$862$	1.99404e48	0.730912
$863$	−3.38580e46	−0.0121754	−0.00608770	−	0.999981i	$-0.501938\pi$
$863$	−3.38580e46	−0.0121754	−0.00608770	+	0.999981i	$0.501938\pi$
$864$	0	0
$865$	−1.34444e47	−0.0465347
$866$	6.16750e47	0.209442
$867$	0	0
$868$	−5.05361e48	−1.65206
$869$	6.37858e47	0.204596
$870$	0	0
$871$	−5.23695e47	−0.161726
$872$	4.00366e47	0.121321
$873$	0	0
$874$	3.09933e47	0.0904334
$875$	−5.80101e47	−0.166100
$876$	0	0
$877$	−4.24252e48	−1.16985	−0.584925	−	0.811087i	$-0.698876\pi$
$877$	−4.24252e48	−1.16985	−0.584925	+	0.811087i	$0.698876\pi$
$878$	3.01576e48	0.816089
$879$	0	0
$880$	7.17528e46	0.0187014
$881$	2.17405e48	0.556119	0.278059	−	0.960564i	$-0.410309\pi$
$881$	2.17405e48	0.556119	0.278059	+	0.960564i	$0.410309\pi$
$882$	0	0
$883$	4.77705e48	1.17708	0.588542	−	0.808466i	$-0.299702\pi$
$883$	4.77705e48	1.17708	0.588542	+	0.808466i	$0.299702\pi$
$884$	−1.67916e48	−0.406098
$885$	0	0
$886$	3.28527e48	0.765447
$887$	5.12275e48	1.17156	0.585779	−	0.810471i	$-0.300789\pi$
$887$	5.12275e48	1.17156	0.585779	+	0.810471i	$0.300789\pi$
$888$	0	0
$889$	2.29955e48	0.506714
$890$	−7.16199e46	−0.0154917
$891$	0	0
$892$	2.76302e48	0.575922
$893$	2.64116e48	0.540437
$894$	0	0
$895$	−4.26640e47	−0.0841359
$896$	−6.14883e48	−1.19045
$897$	0	0
$898$	−7.67570e47	−0.143238
$899$	−1.11311e48	−0.203941
$900$	0	0
$901$	−9.17434e48	−1.62038
$902$	−5.32147e48	−0.922834
$903$	0	0
$904$	−5.15770e48	−0.862338
$905$	4.95769e47	0.0813912
$906$	0	0
$907$	7.71888e48	1.22190	0.610948	−	0.791671i	$-0.290789\pi$
$907$	7.71888e48	1.22190	0.610948	+	0.791671i	$0.290789\pi$
$908$	−1.48895e48	−0.231453
$909$	0	0
$910$	1.33624e47	0.0200309
$911$	1.06274e49	1.56450	0.782250	−	0.622964i	$-0.214072\pi$
$911$	1.06274e49	1.56450	0.782250	+	0.622964i	$0.214072\pi$
$912$	0	0
$913$	−2.65432e48	−0.376864
$914$	−3.53882e48	−0.493454
$915$	0	0
$916$	−2.09012e48	−0.281123
$917$	−1.54394e49	−2.03956
$918$	0	0
$919$	8.89051e48	1.13298	0.566488	−	0.824070i	$-0.308302\pi$
$919$	8.89051e48	1.13298	0.566488	+	0.824070i	$0.308302\pi$
$920$	−7.63460e46	−0.00955624
$921$	0	0
$922$	−6.65723e48	−0.803959
$923$	−3.69428e48	−0.438229
$924$	0	0
$925$	8.65948e48	0.991182
$926$	2.74764e48	0.308943
$927$	0	0
$928$	−1.16743e48	−0.126675
$929$	7.35883e48	0.784422	0.392211	−	0.919875i	$-0.371710\pi$
$929$	7.35883e48	0.784422	0.392211	+	0.919875i	$0.371710\pi$
$930$	0	0
$931$	−8.77828e48	−0.903108
$932$	−4.28292e47	−0.0432890
$933$	0	0
$934$	−1.74771e48	−0.170509
$935$	−1.12203e48	−0.107550
$936$	0	0
$937$	−7.92924e48	−0.733717	−0.366858	−	0.930277i	$-0.619567\pi$
$937$	−7.92924e48	−0.733717	−0.366858	+	0.930277i	$0.619567\pi$
$938$	2.94950e48	0.268165
$939$	0	0
$940$	−2.70727e47	−0.0237641
$941$	−1.44230e49	−1.24402	−0.622008	−	0.783011i	$-0.713683\pi$
$941$	−1.44230e49	−1.24402	−0.622008	+	0.783011i	$0.713683\pi$
$942$	0	0
$943$	−2.53827e48	−0.211395
$944$	3.05229e48	0.249797
$945$	0	0
$946$	−2.13679e48	−0.168872
$947$	−9.83625e48	−0.763932	−0.381966	−	0.924176i	$-0.624753\pi$
$947$	−9.83625e48	−0.763932	−0.381966	+	0.924176i	$0.624753\pi$
$948$	0	0
$949$	−7.55913e48	−0.566995
$950$	−7.03168e48	−0.518346
$951$	0	0
$952$	2.27271e49	1.61821
$953$	8.19274e48	0.573319	0.286660	−	0.958033i	$-0.407455\pi$
$953$	8.19274e48	0.573319	0.286660	+	0.958033i	$0.407455\pi$
$954$	0	0
$955$	8.31467e47	0.0562068
$956$	−1.00107e49	−0.665133
$957$	0	0
$958$	−1.44329e49	−0.926450
$959$	3.61324e49	2.27976
$960$	0	0
$961$	2.92544e49	1.78343
$962$	−3.99653e48	−0.239494
$963$	0	0
$964$	2.23180e48	0.129236
$965$	1.06902e48	0.0608536
$966$	0	0
$967$	−1.65015e49	−0.907791	−0.453895	−	0.891055i	$-0.649966\pi$
$967$	−1.65015e49	−0.907791	−0.453895	+	0.891055i	$0.649966\pi$
$968$	1.70501e49	0.922113
$969$	0	0
$970$	−7.83358e47	−0.0409474
$971$	3.28602e49	1.68870	0.844352	−	0.535789i	$-0.179986\pi$
$971$	3.28602e49	1.68870	0.844352	+	0.535789i	$0.179986\pi$
$972$	0	0
$973$	1.00483e49	0.499151
$974$	7.23857e48	0.353533
$975$	0	0
$976$	6.80939e46	0.00321504
$977$	−1.17177e49	−0.543977	−0.271989	−	0.962300i	$-0.587681\pi$
$977$	−1.17177e49	−0.543977	−0.271989	+	0.962300i	$0.587681\pi$
$978$	0	0
$979$	1.52247e49	0.683336
$980$	8.99802e47	0.0397115
$981$	0	0
$982$	7.15306e48	0.305247
$983$	−3.61572e49	−1.51726	−0.758632	−	0.651519i	$-0.774132\pi$
$983$	−3.61572e49	−1.51726	−0.758632	+	0.651519i	$0.774132\pi$
$984$	0	0
$985$	2.75828e48	0.111928
$986$	2.08305e48	0.0831249
$987$	0	0
$988$	−8.04975e48	−0.310665
$989$	−1.01922e48	−0.0386838
$990$	0	0
$991$	2.27623e49	0.835603	0.417802	−	0.908538i	$-0.362801\pi$
$991$	2.27623e49	0.835603	0.417802	+	0.908538i	$0.362801\pi$
$992$	4.78860e49	1.72889
$993$	0	0
$994$	2.08065e49	0.726649
$995$	2.02584e48	0.0695863
$996$	0	0
$997$	−5.01160e49	−1.66535	−0.832676	−	0.553761i	$-0.813192\pi$
$997$	−5.01160e49	−1.66535	−0.832676	+	0.553761i	$0.813192\pi$
$998$	−8.75230e48	−0.286067
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.34.a.b.1.1		2
3.2	odd	2		1.34.a.a.1.2	✓	2
12.11	even	2		16.34.a.b.1.2		2
15.2	even	4		25.34.b.a.24.3		4
15.8	even	4		25.34.b.a.24.2		4
15.14	odd	2		25.34.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.34.a.a.1.2	✓	2	3.2	odd	2
9.34.a.b.1.1		2	1.1	even	1	trivial
16.34.a.b.1.2		2	12.11	even	2
25.34.a.a.1.1		2	15.14	odd	2
25.34.b.a.24.2		4	15.8	even	4
25.34.b.a.24.3		4	15.2	even	4

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:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-49679.4 q^{2} -6.12189e9 q^{4} -2.04307e10 q^{5} -1.22168e14 q^{7} +7.30875e14 q^{8} +O(q^{10})\)	\(q-49679.4 q^{2} -6.12189e9 q^{4} -2.04307e10 q^{5} -1.22168e14 q^{7} +7.30875e14 q^{8} +1.01499e15 q^{10} -2.15763e17 q^{11} -1.07762e18 q^{13} +6.06926e18 q^{14} +1.62772e19 q^{16} -2.54532e20 q^{17} -1.22020e21 q^{19} +1.25075e20 q^{20} +1.07190e22 q^{22} +5.11280e21 q^{23} -1.15998e23 q^{25} +5.35354e22 q^{26} +7.47901e23 q^{28} +1.64733e23 q^{29} -6.75706e24 q^{31} -7.08681e24 q^{32} +1.26450e25 q^{34} +2.49599e24 q^{35} -7.46520e25 q^{37} +6.06190e25 q^{38} -1.49323e25 q^{40} -4.96453e26 q^{41} -1.99347e26 q^{43} +1.32088e27 q^{44} -2.54001e26 q^{46} -2.16452e27 q^{47} +7.19411e27 q^{49} +5.76271e27 q^{50} +6.59706e27 q^{52} +3.60439e28 q^{53} +4.40819e27 q^{55} -8.92898e28 q^{56} -8.18385e27 q^{58} +1.87520e29 q^{59} +4.18340e27 q^{61} +3.35687e29 q^{62} +2.12249e29 q^{64} +2.20165e28 q^{65} +4.85975e29 q^{67} +1.55822e30 q^{68} -1.23999e29 q^{70} +3.42819e30 q^{71} +7.01467e30 q^{73} +3.70867e30 q^{74} +7.46995e30 q^{76} +2.63594e31 q^{77} -2.95630e30 q^{79} -3.32554e29 q^{80} +2.46635e31 q^{82} +1.23020e31 q^{83} +5.20028e30 q^{85} +9.90343e30 q^{86} -1.57696e32 q^{88} -7.05623e31 q^{89} +1.31651e32 q^{91} -3.13000e31 q^{92} +1.07532e32 q^{94} +2.49297e31 q^{95} -7.71791e32 q^{97} -3.57399e32 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 121680 q^{2} + 14652233984 q^{4} + 181061536500 q^{5} - 67153080066800 q^{7} + 28\!\cdots\!40 q^{8}+O(q^{10}) \) 2 * q + 121680 * q^2 + 14652233984 * q^4 + 181061536500 * q^5 - 67153080066800 * q^7 + 2818750585098240 * q^8	\( 2 q + 121680 q^{2} + 14652233984 q^{4} + 181061536500 q^{5} - 67153080066800 q^{7} + 28\!\cdots\!40 q^{8}+ \cdots - 11\!\cdots\!40 q^{98}+O(q^{100}) \) 2 * q + 121680 * q^2 + 14652233984 * q^4 + 181061536500 * q^5 - 67153080066800 * q^7 + 2818750585098240 * q^8 + 35542592216532000 * q^10 - 133871815441914264 * q^11 - 2981610478259443940 * q^13 + 15496641262468340352 * q^14 + 195605979111894351872 * q^16 + 79361149261175525340 * q^17 - 1360696443041697171800 * q^19 + 4310900037459183168000 * q^20 + 24751741840613395122240 * q^22 - 26163854053674631579440 * q^23 - 191814088084783724781250 * q^25 - 272731683634642092710304 * q^26 + 1890794991723644827125760 * q^28 + 1674519971630399929109700 * q^29 - 6238301225723632337095616 * q^31 + 5708163006744585940500480 * q^32 + 69860790536166916073075808 * q^34 + 13581143663546216842308000 * q^35 - 104802741516758180098173620 * q^37 + 36544090911856460663722560 * q^38 + 405758480738092701742080000 * q^40 - 277566613022002182732188244 * q^41 + 1567661189367072113768291800 * q^43 + 3022085914387766085808346112 * q^44 - 5613550634763385681470869376 * q^46 - 5421061461431251260476972640 * q^47 + 2489799365888888933444851314 * q^49 - 7229107516344249428363250000 * q^50 - 32956722688372988680703091200 * q^52 + 26867414785542903092975171220 * q^53 + 20908570805489145209222682000 * q^55 + 25575237795171758759822131200 * q^56 + 250532370716581201796821222560 * q^58 + 305786409635298433026663995400 * q^59 - 5745893983413264859067362436 * q^61 + 424581887479352364037004290560 * q^62 + 864365322360380859973709594624 * q^64 - 361623311364964256200313721000 * q^65 + 1598906337224495341750209565960 * q^67 + 8494558579722382470601861086720 * q^68 + 1775546165763388432770973344000 * q^70 + 2669761937956104715736810084976 * q^71 + 946314321191998870965166536340 * q^73 - 1457936998080019494211346192928 * q^74 + 4551314657470802548563162035200 * q^76 + 30864620292716415864215760033600 * q^77 - 8535199972765636469730106191200 * q^79 + 35800819471604723635001769984000 * q^80 + 62171822095602398237444019107040 * q^82 - 29072605803747945444403983322920 * q^83 + 72477213859794605306963311287000 * q^85 + 312696885737578501917214826406336 * q^86 + 13282372192867492753038509752320 * q^88 - 132719467655604316264938597726900 * q^89 + 26902102147452358410548887211744 * q^91 - 681044992402323869436382557788160 * q^92 - 450506433888867898835049561530112 * q^94 - 3378716387067841884487537110000 * q^95 - 367787330930535727150839877856060 * q^97 - 1163527978168280943548587223169840 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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