LMFDB - Embedded newform 6026.2.a.m.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [6026,2,Mod(1,6026)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6026, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("6026.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment:select newform

sage:traces = [41,41,4,41,9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6026.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -1.56181 q^{3} +1.00000 q^{4} +1.51273 q^{5} -1.56181 q^{6} +2.72551 q^{7} +1.00000 q^{8} -0.560757 q^{9} +1.51273 q^{10} -1.08693 q^{11} -1.56181 q^{12} -3.25138 q^{13} +2.72551 q^{14} -2.36260 q^{15} +1.00000 q^{16} -6.54570 q^{17} -0.560757 q^{18} +7.89936 q^{19} +1.51273 q^{20} -4.25672 q^{21} -1.08693 q^{22} +1.00000 q^{23} -1.56181 q^{24} -2.71164 q^{25} -3.25138 q^{26} +5.56122 q^{27} +2.72551 q^{28} -4.02445 q^{29} -2.36260 q^{30} +5.65283 q^{31} +1.00000 q^{32} +1.69758 q^{33} -6.54570 q^{34} +4.12297 q^{35} -0.560757 q^{36} -5.71628 q^{37} +7.89936 q^{38} +5.07803 q^{39} +1.51273 q^{40} +8.21663 q^{41} -4.25672 q^{42} +10.6057 q^{43} -1.08693 q^{44} -0.848275 q^{45} +1.00000 q^{46} -12.0232 q^{47} -1.56181 q^{48} +0.428399 q^{49} -2.71164 q^{50} +10.2231 q^{51} -3.25138 q^{52} +10.9686 q^{53} +5.56122 q^{54} -1.64424 q^{55} +2.72551 q^{56} -12.3373 q^{57} -4.02445 q^{58} +8.07821 q^{59} -2.36260 q^{60} +5.67453 q^{61} +5.65283 q^{62} -1.52835 q^{63} +1.00000 q^{64} -4.91847 q^{65} +1.69758 q^{66} +13.2548 q^{67} -6.54570 q^{68} -1.56181 q^{69} +4.12297 q^{70} -1.75710 q^{71} -0.560757 q^{72} +4.47561 q^{73} -5.71628 q^{74} +4.23506 q^{75} +7.89936 q^{76} -2.96244 q^{77} +5.07803 q^{78} +15.1732 q^{79} +1.51273 q^{80} -7.00328 q^{81} +8.21663 q^{82} -11.1953 q^{83} -4.25672 q^{84} -9.90190 q^{85} +10.6057 q^{86} +6.28542 q^{87} -1.08693 q^{88} +12.0812 q^{89} -0.848275 q^{90} -8.86167 q^{91} +1.00000 q^{92} -8.82863 q^{93} -12.0232 q^{94} +11.9496 q^{95} -1.56181 q^{96} +6.02816 q^{97} +0.428399 q^{98} +0.609505 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19}+ \cdots - 10 q^{99}+O(q^{100}) $ 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.56181	−0.901710	−0.450855	−	0.892597i	$-0.648881\pi$
$3$	−1.56181	−0.901710	−0.450855	+	0.892597i	$0.648881\pi$
$4$	1.00000	0.500000
$5$	1.51273	0.676515	0.338257	−	0.941054i	$-0.390163\pi$
$5$	1.51273	0.676515	0.338257	+	0.941054i	$0.390163\pi$
$6$	−1.56181	−0.637605
$7$	2.72551	1.03015	0.515073	−	0.857146i	$-0.327765\pi$
$7$	2.72551	1.03015	0.515073	+	0.857146i	$0.327765\pi$
$8$	1.00000	0.353553
$9$	−0.560757	−0.186919
$10$	1.51273	0.478368
$11$	−1.08693	−0.327723	−0.163861	−	0.986483i	$-0.552395\pi$
$11$	−1.08693	−0.327723	−0.163861	+	0.986483i	$0.552395\pi$
$12$	−1.56181	−0.450855
$13$	−3.25138	−0.901771	−0.450885	−	0.892582i	$-0.648892\pi$
$13$	−3.25138	−0.901771	−0.450885	+	0.892582i	$0.648892\pi$
$14$	2.72551	0.728423
$15$	−2.36260	−0.610020
$16$	1.00000	0.250000
$17$	−6.54570	−1.58757	−0.793783	−	0.608201i	$-0.791891\pi$
$17$	−6.54570	−1.58757	−0.793783	+	0.608201i	$0.791891\pi$
$18$	−0.560757	−0.132172
$19$	7.89936	1.81224	0.906119	−	0.423023i	$-0.139031\pi$
$19$	7.89936	1.81224	0.906119	+	0.423023i	$0.139031\pi$
$20$	1.51273	0.338257
$21$	−4.25672	−0.928893
$22$	−1.08693	−0.231735
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.56181	−0.318803
$25$	−2.71164	−0.542328
$26$	−3.25138	−0.637648
$27$	5.56122	1.07026
$28$	2.72551	0.515073
$29$	−4.02445	−0.747321	−0.373661	−	0.927565i	$-0.621898\pi$
$29$	−4.02445	−0.747321	−0.373661	+	0.927565i	$0.621898\pi$
$30$	−2.36260	−0.431349
$31$	5.65283	1.01528	0.507639	−	0.861570i	$-0.330518\pi$
$31$	5.65283	1.01528	0.507639	+	0.861570i	$0.330518\pi$
$32$	1.00000	0.176777
$33$	1.69758	0.295511
$34$	−6.54570	−1.12258
$35$	4.12297	0.696909
$36$	−0.560757	−0.0934594
$37$	−5.71628	−0.939751	−0.469875	−	0.882733i	$-0.655701\pi$
$37$	−5.71628	−0.939751	−0.469875	+	0.882733i	$0.655701\pi$
$38$	7.89936	1.28145
$39$	5.07803	0.813136
$40$	1.51273	0.239184
$41$	8.21663	1.28322	0.641611	−	0.767030i	$-0.278266\pi$
$41$	8.21663	1.28322	0.641611	+	0.767030i	$0.278266\pi$
$42$	−4.25672	−0.656826
$43$	10.6057	1.61736	0.808680	−	0.588248i	$-0.200182\pi$
$43$	10.6057	1.61736	0.808680	+	0.588248i	$0.200182\pi$
$44$	−1.08693	−0.163861
$45$	−0.848275	−0.126453
$46$	1.00000	0.147442
$47$	−12.0232	−1.75376	−0.876880	−	0.480709i	$-0.840379\pi$
$47$	−12.0232	−1.75376	−0.876880	+	0.480709i	$0.840379\pi$
$48$	−1.56181	−0.225428
$49$	0.428399	0.0611999
$50$	−2.71164	−0.383484
$51$	10.2231	1.43152
$52$	−3.25138	−0.450885
$53$	10.9686	1.50665	0.753327	−	0.657646i	$-0.228448\pi$
$53$	10.9686	1.50665	0.753327	+	0.657646i	$0.228448\pi$
$54$	5.56122	0.756786
$55$	−1.64424	−0.221709
$56$	2.72551	0.364211
$57$	−12.3373	−1.63411
$58$	−4.02445	−0.528436
$59$	8.07821	1.05169	0.525847	−	0.850579i	$-0.323748\pi$
$59$	8.07821	1.05169	0.525847	+	0.850579i	$0.323748\pi$
$60$	−2.36260	−0.305010
$61$	5.67453	0.726550	0.363275	−	0.931682i	$-0.381659\pi$
$61$	5.67453	0.726550	0.363275	+	0.931682i	$0.381659\pi$
$62$	5.65283	0.717910
$63$	−1.52835	−0.192554
$64$	1.00000	0.125000
$65$	−4.91847	−0.610061
$66$	1.69758	0.208958
$67$	13.2548	1.61933	0.809664	−	0.586893i	$-0.199649\pi$
$67$	13.2548	1.61933	0.809664	+	0.586893i	$0.199649\pi$
$68$	−6.54570	−0.793783
$69$	−1.56181	−0.188020
$70$	4.12297	0.492789
$71$	−1.75710	−0.208529	−0.104265	−	0.994550i	$-0.533249\pi$
$71$	−1.75710	−0.208529	−0.104265	+	0.994550i	$0.533249\pi$
$72$	−0.560757	−0.0660858
$73$	4.47561	0.523830	0.261915	−	0.965091i	$-0.415646\pi$
$73$	4.47561	0.523830	0.261915	+	0.965091i	$0.415646\pi$
$74$	−5.71628	−0.664504
$75$	4.23506	0.489022
$76$	7.89936	0.906119
$77$	−2.96244	−0.337602
$78$	5.07803	0.574974
$79$	15.1732	1.70712	0.853558	−	0.520998i	$-0.174440\pi$
$79$	15.1732	1.70712	0.853558	+	0.520998i	$0.174440\pi$
$80$	1.51273	0.169129
$81$	−7.00328	−0.778143
$82$	8.21663	0.907375
$83$	−11.1953	−1.22885	−0.614423	−	0.788977i	$-0.710611\pi$
$83$	−11.1953	−1.22885	−0.614423	+	0.788977i	$0.710611\pi$
$84$	−4.25672	−0.464446
$85$	−9.90190	−1.07401
$86$	10.6057	1.14365
$87$	6.28542	0.673867
$88$	−1.08693	−0.115867
$89$	12.0812	1.28060	0.640300	−	0.768125i	$-0.278810\pi$
$89$	12.0812	1.28060	0.640300	+	0.768125i	$0.278810\pi$
$90$	−0.848275	−0.0894160
$91$	−8.86167	−0.928955
$92$	1.00000	0.104257
$93$	−8.82863	−0.915487
$94$	−12.0232	−1.24010
$95$	11.9496	1.22601
$96$	−1.56181	−0.159401
$97$	6.02816	0.612067	0.306034	−	0.952021i	$-0.400998\pi$
$97$	6.02816	0.612067	0.306034	+	0.952021i	$0.400998\pi$
$98$	0.428399	0.0432749
$99$	0.609505	0.0612575
$100$	−2.71164	−0.271164
$101$	11.1625	1.11071	0.555356	−	0.831613i	$-0.312582\pi$
$101$	11.1625	1.11071	0.555356	+	0.831613i	$0.312582\pi$
$102$	10.2231	1.01224
$103$	5.38566	0.530665	0.265333	−	0.964157i	$-0.414518\pi$
$103$	5.38566	0.530665	0.265333	+	0.964157i	$0.414518\pi$
$104$	−3.25138	−0.318824
$105$	−6.43928	−0.628410
$106$	10.9686	1.06537
$107$	5.56524	0.538012	0.269006	−	0.963139i	$-0.413305\pi$
$107$	5.56524	0.538012	0.269006	+	0.963139i	$0.413305\pi$
$108$	5.56122	0.535128
$109$	18.0035	1.72443	0.862213	−	0.506545i	$-0.169078\pi$
$109$	18.0035	1.72443	0.862213	+	0.506545i	$0.169078\pi$
$110$	−1.64424	−0.156772
$111$	8.92773	0.847383
$112$	2.72551	0.257536
$113$	−10.3281	−0.971590	−0.485795	−	0.874073i	$-0.661470\pi$
$113$	−10.3281	−0.971590	−0.485795	+	0.874073i	$0.661470\pi$
$114$	−12.3373	−1.15549
$115$	1.51273	0.141063
$116$	−4.02445	−0.373661
$117$	1.82323	0.168558
$118$	8.07821	0.743660
$119$	−17.8404	−1.63542
$120$	−2.36260	−0.215675
$121$	−9.81858	−0.892598
$122$	5.67453	0.513748
$123$	−12.8328	−1.15709
$124$	5.65283	0.507639
$125$	−11.6657	−1.04341
$126$	−1.52835	−0.136156
$127$	−1.13819	−0.100998	−0.0504988	−	0.998724i	$-0.516081\pi$
$127$	−1.13819	−0.100998	−0.0504988	+	0.998724i	$0.516081\pi$
$128$	1.00000	0.0883883
$129$	−16.5641	−1.45839
$130$	−4.91847	−0.431378
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	1.69758	0.147755
$133$	21.5298	1.86687
$134$	13.2548	1.14504
$135$	8.41264	0.724045
$136$	−6.54570	−0.561289
$137$	−6.46391	−0.552249	−0.276124	−	0.961122i	$-0.589050\pi$
$137$	−6.46391	−0.552249	−0.276124	+	0.961122i	$0.589050\pi$
$138$	−1.56181	−0.132950
$139$	−12.6275	−1.07105	−0.535524	−	0.844520i	$-0.679886\pi$
$139$	−12.6275	−1.07105	−0.535524	+	0.844520i	$0.679886\pi$
$140$	4.12297	0.348454
$141$	18.7779	1.58138
$142$	−1.75710	−0.147453
$143$	3.53403	0.295531
$144$	−0.560757	−0.0467297
$145$	−6.08792	−0.505574
$146$	4.47561	0.370404
$147$	−0.669077	−0.0551846
$148$	−5.71628	−0.469875
$149$	2.41085	0.197504	0.0987522	−	0.995112i	$-0.468515\pi$
$149$	2.41085	0.197504	0.0987522	+	0.995112i	$0.468515\pi$
$150$	4.23506	0.345791
$151$	−13.2218	−1.07597	−0.537986	−	0.842954i	$-0.680815\pi$
$151$	−13.2218	−1.07597	−0.537986	+	0.842954i	$0.680815\pi$
$152$	7.89936	0.640723
$153$	3.67054	0.296746
$154$	−2.96244	−0.238721
$155$	8.55122	0.686851
$156$	5.07803	0.406568
$157$	−23.1492	−1.84751	−0.923753	−	0.382990i	$-0.874894\pi$
$157$	−23.1492	−1.84751	−0.923753	+	0.382990i	$0.874894\pi$
$158$	15.1732	1.20711
$159$	−17.1309	−1.35856
$160$	1.51273	0.119592
$161$	2.72551	0.214800
$162$	−7.00328	−0.550230
$163$	18.9577	1.48488	0.742442	−	0.669911i	$-0.233668\pi$
$163$	18.9577	1.48488	0.742442	+	0.669911i	$0.233668\pi$
$164$	8.21663	0.641611
$165$	2.56799	0.199917
$166$	−11.1953	−0.868925
$167$	13.0447	1.00943	0.504715	−	0.863286i	$-0.331598\pi$
$167$	13.0447	1.00943	0.504715	+	0.863286i	$0.331598\pi$
$168$	−4.25672	−0.328413
$169$	−2.42852	−0.186809
$170$	−9.90190	−0.759441
$171$	−4.42962	−0.338741
$172$	10.6057	0.808680
$173$	−1.61076	−0.122464	−0.0612320	−	0.998124i	$-0.519503\pi$
$173$	−1.61076	−0.122464	−0.0612320	+	0.998124i	$0.519503\pi$
$174$	6.28542	0.476496
$175$	−7.39059	−0.558676
$176$	−1.08693	−0.0819306
$177$	−12.6166	−0.948323
$178$	12.0812	0.905521
$179$	−10.9706	−0.819978	−0.409989	−	0.912091i	$-0.634467\pi$
$179$	−10.9706	−0.819978	−0.409989	+	0.912091i	$0.634467\pi$
$180$	−0.848275	−0.0632267
$181$	2.15287	0.160022	0.0800108	−	0.996794i	$-0.474505\pi$
$181$	2.15287	0.160022	0.0800108	+	0.996794i	$0.474505\pi$
$182$	−8.86167	−0.656870
$183$	−8.86253	−0.655137
$184$	1.00000	0.0737210
$185$	−8.64721	−0.635755
$186$	−8.82863	−0.647347
$187$	7.11474	0.520281
$188$	−12.0232	−0.876880
$189$	15.1571	1.10252
$190$	11.9496	0.866917
$191$	11.4780	0.830522	0.415261	−	0.909702i	$-0.363690\pi$
$191$	11.4780	0.830522	0.415261	+	0.909702i	$0.363690\pi$
$192$	−1.56181	−0.112714
$193$	14.9276	1.07451	0.537256	−	0.843419i	$-0.319461\pi$
$193$	14.9276	1.07451	0.537256	+	0.843419i	$0.319461\pi$
$194$	6.02816	0.432797
$195$	7.68171	0.550098
$196$	0.428399	0.0306000
$197$	−23.4357	−1.66973	−0.834863	−	0.550458i	$-0.814453\pi$
$197$	−23.4357	−1.66973	−0.834863	+	0.550458i	$0.814453\pi$
$198$	0.609505	0.0433156
$199$	−14.3032	−1.01392	−0.506962	−	0.861968i	$-0.669232\pi$
$199$	−14.3032	−1.01392	−0.506962	+	0.861968i	$0.669232\pi$
$200$	−2.71164	−0.191742
$201$	−20.7014	−1.46017
$202$	11.1625	0.785392
$203$	−10.9687	−0.769850
$204$	10.2231	0.715762
$205$	12.4296	0.868119
$206$	5.38566	0.375237
$207$	−0.560757	−0.0389753
$208$	−3.25138	−0.225443
$209$	−8.58608	−0.593911
$210$	−6.43928	−0.444353
$211$	20.1435	1.38674	0.693368	−	0.720584i	$-0.256126\pi$
$211$	20.1435	1.38674	0.693368	+	0.720584i	$0.256126\pi$
$212$	10.9686	0.753327
$213$	2.74425	0.188033
$214$	5.56524	0.380432
$215$	16.0437	1.09417
$216$	5.56122	0.378393
$217$	15.4068	1.04588
$218$	18.0035	1.21935
$219$	−6.99004	−0.472343
$220$	−1.64424	−0.110855
$221$	21.2826	1.43162
$222$	8.92773	0.599190
$223$	−14.8615	−0.995200	−0.497600	−	0.867406i	$-0.665785\pi$
$223$	−14.8615	−0.995200	−0.497600	+	0.867406i	$0.665785\pi$
$224$	2.72551	0.182106
$225$	1.52057	0.101371
$226$	−10.3281	−0.687018
$227$	−3.92557	−0.260549	−0.130275	−	0.991478i	$-0.541586\pi$
$227$	−3.92557	−0.260549	−0.130275	+	0.991478i	$0.541586\pi$
$228$	−12.3373	−0.817057
$229$	20.5271	1.35647	0.678233	−	0.734847i	$-0.262746\pi$
$229$	20.5271	1.35647	0.678233	+	0.734847i	$0.262746\pi$
$230$	1.51273	0.0997467
$231$	4.62677	0.304419
$232$	−4.02445	−0.264218
$233$	−29.5168	−1.93371	−0.966854	−	0.255330i	$-0.917816\pi$
$233$	−29.5168	−1.93371	−0.966854	+	0.255330i	$0.917816\pi$
$234$	1.82323	0.119188
$235$	−18.1879	−1.18644
$236$	8.07821	0.525847
$237$	−23.6976	−1.53932
$238$	−17.8404	−1.15642
$239$	15.8106	1.02270	0.511351	−	0.859372i	$-0.329145\pi$
$239$	15.8106	1.02270	0.511351	+	0.859372i	$0.329145\pi$
$240$	−2.36260	−0.152505
$241$	17.8829	1.15194	0.575971	−	0.817470i	$-0.304624\pi$
$241$	17.8829	1.15194	0.575971	+	0.817470i	$0.304624\pi$
$242$	−9.81858	−0.631162
$243$	−5.74587	−0.368598
$244$	5.67453	0.363275
$245$	0.648054	0.0414026
$246$	−12.8328	−0.818189
$247$	−25.6838	−1.63422
$248$	5.65283	0.358955
$249$	17.4849	1.10806
$250$	−11.6657	−0.737801
$251$	−3.89626	−0.245930	−0.122965	−	0.992411i	$-0.539240\pi$
$251$	−3.89626	−0.245930	−0.122965	+	0.992411i	$0.539240\pi$
$252$	−1.52835	−0.0962768
$253$	−1.08693	−0.0683349
$254$	−1.13819	−0.0714161
$255$	15.4649	0.968447
$256$	1.00000	0.0625000
$257$	2.54566	0.158794	0.0793969	−	0.996843i	$-0.474701\pi$
$257$	2.54566	0.158794	0.0793969	+	0.996843i	$0.474701\pi$
$258$	−16.5641	−1.03124
$259$	−15.5798	−0.968080
$260$	−4.91847	−0.305031
$261$	2.25674	0.139688
$262$	1.00000	0.0617802
$263$	2.59768	0.160180	0.0800899	−	0.996788i	$-0.474479\pi$
$263$	2.59768	0.160180	0.0800899	+	0.996788i	$0.474479\pi$
$264$	1.69758	0.104479
$265$	16.5926	1.01927
$266$	21.5298	1.32008
$267$	−18.8685	−1.15473
$268$	13.2548	0.809664
$269$	3.84494	0.234430	0.117215	−	0.993107i	$-0.462603\pi$
$269$	3.84494	0.234430	0.117215	+	0.993107i	$0.462603\pi$
$270$	8.41264	0.511977
$271$	19.5477	1.18744	0.593720	−	0.804671i	$-0.297659\pi$
$271$	19.5477	1.18744	0.593720	+	0.804671i	$0.297659\pi$
$272$	−6.54570	−0.396891
$273$	13.8402	0.837648
$274$	−6.46391	−0.390499
$275$	2.94737	0.177733
$276$	−1.56181	−0.0940098
$277$	7.78713	0.467883	0.233942	−	0.972251i	$-0.424838\pi$
$277$	7.78713	0.467883	0.233942	+	0.972251i	$0.424838\pi$
$278$	−12.6275	−0.757345
$279$	−3.16986	−0.189775
$280$	4.12297	0.246394
$281$	−7.12347	−0.424951	−0.212475	−	0.977166i	$-0.568152\pi$
$281$	−7.12347	−0.424951	−0.212475	+	0.977166i	$0.568152\pi$
$282$	18.7779	1.11821
$283$	−13.2971	−0.790433	−0.395216	−	0.918588i	$-0.629330\pi$
$283$	−13.2971	−0.790433	−0.395216	+	0.918588i	$0.629330\pi$
$284$	−1.75710	−0.104265
$285$	−18.6630	−1.10550
$286$	3.53403	0.208972
$287$	22.3945	1.32191
$288$	−0.560757	−0.0330429
$289$	25.8462	1.52037
$290$	−6.08792	−0.357495
$291$	−9.41483	−0.551907
$292$	4.47561	0.261915
$293$	33.6550	1.96614	0.983072	−	0.183220i	$-0.0586521\pi$
$293$	33.6550	1.96614	0.983072	+	0.183220i	$0.0586521\pi$
$294$	−0.669077	−0.0390214
$295$	12.2202	0.711487
$296$	−5.71628	−0.332252
$297$	−6.04467	−0.350747
$298$	2.41085	0.139657
$299$	−3.25138	−0.188032
$300$	4.23506	0.244511
$301$	28.9061	1.66612
$302$	−13.2218	−0.760827
$303$	−17.4337	−1.00154
$304$	7.89936	0.453060
$305$	8.58406	0.491522
$306$	3.67054	0.209831
$307$	11.9374	0.681305	0.340653	−	0.940189i	$-0.389352\pi$
$307$	11.9374	0.681305	0.340653	+	0.940189i	$0.389352\pi$
$308$	−2.96244	−0.168801
$309$	−8.41137	−0.478506
$310$	8.55122	0.485677
$311$	30.3911	1.72332	0.861659	−	0.507487i	$-0.169425\pi$
$311$	30.3911	1.72332	0.861659	+	0.507487i	$0.169425\pi$
$312$	5.07803	0.287487
$313$	26.0508	1.47248	0.736239	−	0.676722i	$-0.236600\pi$
$313$	26.0508	1.47248	0.736239	+	0.676722i	$0.236600\pi$
$314$	−23.1492	−1.30638
$315$	−2.31198	−0.130265
$316$	15.1732	0.853558
$317$	3.62877	0.203812	0.101906	−	0.994794i	$-0.467506\pi$
$317$	3.62877	0.203812	0.101906	+	0.994794i	$0.467506\pi$
$318$	−17.1309	−0.960650
$319$	4.37430	0.244914
$320$	1.51273	0.0845644
$321$	−8.69183	−0.485131
$322$	2.72551	0.151887
$323$	−51.7069	−2.87705
$324$	−7.00328	−0.389071
$325$	8.81657	0.489055
$326$	18.9577	1.04997
$327$	−28.1181	−1.55493
$328$	8.21663	0.453687
$329$	−32.7693	−1.80663
$330$	2.56799	0.141363
$331$	−3.86538	−0.212460	−0.106230	−	0.994342i	$-0.533878\pi$
$331$	−3.86538	−0.212460	−0.106230	+	0.994342i	$0.533878\pi$
$332$	−11.1953	−0.614423
$333$	3.20544	0.175657
$334$	13.0447	0.713774
$335$	20.0509	1.09550
$336$	−4.25672	−0.232223
$337$	−20.4027	−1.11141	−0.555703	−	0.831381i	$-0.687551\pi$
$337$	−20.4027	−1.11141	−0.555703	+	0.831381i	$0.687551\pi$
$338$	−2.42852	−0.132094
$339$	16.1306	0.876092
$340$	−9.90190	−0.537006
$341$	−6.14425	−0.332730
$342$	−4.42962	−0.239526
$343$	−17.9110	−0.967101
$344$	10.6057	0.571823
$345$	−2.36260	−0.127198
$346$	−1.61076	−0.0865952
$347$	−24.3575	−1.30758	−0.653789	−	0.756676i	$-0.726822\pi$
$347$	−24.3575	−1.30758	−0.653789	+	0.756676i	$0.726822\pi$
$348$	6.28542	0.336934
$349$	−31.6986	−1.69679	−0.848394	−	0.529366i	$-0.822430\pi$
$349$	−31.6986	−1.69679	−0.848394	+	0.529366i	$0.822430\pi$
$350$	−7.39059	−0.395044
$351$	−18.0816	−0.965126
$352$	−1.08693	−0.0579337
$353$	−22.3874	−1.19156	−0.595782	−	0.803146i	$-0.703158\pi$
$353$	−22.3874	−1.19156	−0.595782	+	0.803146i	$0.703158\pi$
$354$	−12.6166	−0.670566
$355$	−2.65802	−0.141073
$356$	12.0812	0.640300
$357$	27.8632	1.47468
$358$	−10.9706	−0.579812
$359$	1.91933	0.101298	0.0506492	−	0.998717i	$-0.483871\pi$
$359$	1.91933	0.101298	0.0506492	+	0.998717i	$0.483871\pi$
$360$	−0.848275	−0.0447080
$361$	43.3999	2.28421
$362$	2.15287	0.113152
$363$	15.3347	0.804865
$364$	−8.86167	−0.464478
$365$	6.77040	0.354379
$366$	−8.86253	−0.463252
$367$	25.7720	1.34529	0.672643	−	0.739967i	$-0.265159\pi$
$367$	25.7720	1.34529	0.672643	+	0.739967i	$0.265159\pi$
$368$	1.00000	0.0521286
$369$	−4.60753	−0.239858
$370$	−8.64721	−0.449547
$371$	29.8950	1.55207
$372$	−8.82863	−0.457743
$373$	12.6845	0.656777	0.328388	−	0.944543i	$-0.393495\pi$
$373$	12.6845	0.656777	0.328388	+	0.944543i	$0.393495\pi$
$374$	7.11474	0.367894
$375$	18.2195	0.940851
$376$	−12.0232	−0.620048
$377$	13.0850	0.673913
$378$	15.1571	0.779600
$379$	32.3547	1.66195	0.830975	−	0.556309i	$-0.187783\pi$
$379$	32.3547	1.66195	0.830975	+	0.556309i	$0.187783\pi$
$380$	11.9496	0.613003
$381$	1.77763	0.0910706
$382$	11.4780	0.587268
$383$	−9.13968	−0.467016	−0.233508	−	0.972355i	$-0.575020\pi$
$383$	−9.13968	−0.467016	−0.233508	+	0.972355i	$0.575020\pi$
$384$	−1.56181	−0.0797007
$385$	−4.48139	−0.228393
$386$	14.9276	0.759795
$387$	−5.94724	−0.302315
$388$	6.02816	0.306034
$389$	11.3707	0.576516	0.288258	−	0.957553i	$-0.406924\pi$
$389$	11.3707	0.576516	0.288258	+	0.957553i	$0.406924\pi$
$390$	7.68171	0.388978
$391$	−6.54570	−0.331030
$392$	0.428399	0.0216374
$393$	−1.56181	−0.0787828
$394$	−23.4357	−1.18067
$395$	22.9530	1.15489
$396$	0.609505	0.0306288
$397$	13.0132	0.653116	0.326558	−	0.945177i	$-0.394111\pi$
$397$	13.0132	0.653116	0.326558	+	0.945177i	$0.394111\pi$
$398$	−14.3032	−0.716953
$399$	−33.6254	−1.68337
$400$	−2.71164	−0.135582
$401$	−24.4429	−1.22062	−0.610311	−	0.792162i	$-0.708955\pi$
$401$	−24.4429	−1.22062	−0.610311	+	0.792162i	$0.708955\pi$
$402$	−20.7014	−1.03249
$403$	−18.3795	−0.915548
$404$	11.1625	0.555356
$405$	−10.5941	−0.526425
$406$	−10.9687	−0.544366
$407$	6.21321	0.307977
$408$	10.2231	0.506120
$409$	−11.7592	−0.581455	−0.290727	−	0.956806i	$-0.593897\pi$
$409$	−11.7592	−0.581455	−0.290727	+	0.956806i	$0.593897\pi$
$410$	12.4296	0.613853
$411$	10.0954	0.497968
$412$	5.38566	0.265333
$413$	22.0172	1.08340
$414$	−0.560757	−0.0275597
$415$	−16.9355	−0.831333
$416$	−3.25138	−0.159412
$417$	19.7217	0.965774
$418$	−8.58608	−0.419959
$419$	17.5087	0.855356	0.427678	−	0.903931i	$-0.359332\pi$
$419$	17.5087	0.855356	0.427678	+	0.903931i	$0.359332\pi$
$420$	−6.43928	−0.314205
$421$	−14.4704	−0.705245	−0.352623	−	0.935766i	$-0.614710\pi$
$421$	−14.4704	−0.705245	−0.352623	+	0.935766i	$0.614710\pi$
$422$	20.1435	0.980570
$423$	6.74207	0.327811
$424$	10.9686	0.532683
$425$	17.7496	0.860981
$426$	2.74425	0.132960
$427$	15.4660	0.748452
$428$	5.56524	0.269006
$429$	−5.51948	−0.266483
$430$	16.0437	0.773694
$431$	0.00182411	8.78642e−5 0	4.39321e−5	−	1.00000i	$-0.499986\pi$
$431$	0.00182411	8.78642e−5 0	4.39321e−5		1.00000i	$0.499986\pi$
$432$	5.56122	0.267564
$433$	23.2150	1.11564	0.557820	−	0.829962i	$-0.311638\pi$
$433$	23.2150	1.11564	0.557820	+	0.829962i	$0.311638\pi$
$434$	15.4068	0.739552
$435$	9.50816	0.455881
$436$	18.0035	0.862213
$437$	7.89936	0.377878
$438$	−6.99004	−0.333997
$439$	15.3362	0.731956	0.365978	−	0.930624i	$-0.380735\pi$
$439$	15.3362	0.731956	0.365978	+	0.930624i	$0.380735\pi$
$440$	−1.64424	−0.0783860
$441$	−0.240228	−0.0114394
$442$	21.2826	1.01231
$443$	−24.5279	−1.16535	−0.582677	−	0.812704i	$-0.697995\pi$
$443$	−24.5279	−1.16535	−0.582677	+	0.812704i	$0.697995\pi$
$444$	8.92773	0.423691
$445$	18.2756	0.866345
$446$	−14.8615	−0.703713
$447$	−3.76528	−0.178092
$448$	2.72551	0.128768
$449$	35.2692	1.66446	0.832228	−	0.554433i	$-0.187065\pi$
$449$	35.2692	1.66446	0.832228	+	0.554433i	$0.187065\pi$
$450$	1.52057	0.0716803
$451$	−8.93092	−0.420541
$452$	−10.3281	−0.485795
$453$	20.6499	0.970215
$454$	−3.92557	−0.184236
$455$	−13.4053	−0.628452
$456$	−12.3373	−0.577746
$457$	37.3570	1.74749	0.873744	−	0.486386i	$-0.161685\pi$
$457$	37.3570	1.74749	0.873744	+	0.486386i	$0.161685\pi$
$458$	20.5271	0.959167
$459$	−36.4021	−1.69910
$460$	1.51273	0.0705315
$461$	−10.2337	−0.476629	−0.238315	−	0.971188i	$-0.576595\pi$
$461$	−10.2337	−0.476629	−0.238315	+	0.971188i	$0.576595\pi$
$462$	4.62677	0.215257
$463$	−31.0320	−1.44218	−0.721089	−	0.692843i	$-0.756358\pi$
$463$	−31.0320	−1.44218	−0.721089	+	0.692843i	$0.756358\pi$
$464$	−4.02445	−0.186830
$465$	−13.3554	−0.619340
$466$	−29.5168	−1.36734
$467$	28.9904	1.34152	0.670758	−	0.741677i	$-0.265969\pi$
$467$	28.9904	1.34152	0.670758	+	0.741677i	$0.265969\pi$
$468$	1.82323	0.0842790
$469$	36.1260	1.66814
$470$	−18.1879	−0.838943
$471$	36.1546	1.66591
$472$	8.07821	0.371830
$473$	−11.5277	−0.530046
$474$	−23.6976	−1.08847
$475$	−21.4202	−0.982827
$476$	−17.8404	−0.817712
$477$	−6.15072	−0.281622
$478$	15.8106	0.723160
$479$	20.6800	0.944894	0.472447	−	0.881359i	$-0.343371\pi$
$479$	20.6800	0.944894	0.472447	+	0.881359i	$0.343371\pi$
$480$	−2.36260	−0.107837
$481$	18.5858	0.847440
$482$	17.8829	0.814546
$483$	−4.25672	−0.193688
$484$	−9.81858	−0.446299
$485$	9.11901	0.414073
$486$	−5.74587	−0.260638
$487$	−16.5595	−0.750381	−0.375190	−	0.926948i	$-0.622423\pi$
$487$	−16.5595	−0.750381	−0.375190	+	0.926948i	$0.622423\pi$
$488$	5.67453	0.256874
$489$	−29.6083	−1.33893
$490$	0.648054	0.0292761
$491$	−15.7102	−0.708992	−0.354496	−	0.935057i	$-0.615348\pi$
$491$	−15.7102	−0.708992	−0.354496	+	0.935057i	$0.615348\pi$
$492$	−12.8328	−0.578547
$493$	26.3428	1.18642
$494$	−25.6838	−1.15557
$495$	0.922018	0.0414416
$496$	5.65283	0.253820
$497$	−4.78899	−0.214816
$498$	17.4849	0.783519
$499$	−43.5807	−1.95094	−0.975470	−	0.220133i	$-0.929351\pi$
$499$	−43.5807	−1.95094	−0.975470	+	0.220133i	$0.929351\pi$
$500$	−11.6657	−0.521704
$501$	−20.3733	−0.910213
$502$	−3.89626	−0.173899
$503$	13.2458	0.590603	0.295301	−	0.955404i	$-0.404580\pi$
$503$	13.2458	0.590603	0.295301	+	0.955404i	$0.404580\pi$
$504$	−1.52835	−0.0680780
$505$	16.8859	0.751414
$506$	−1.08693	−0.0483201
$507$	3.79289	0.168448
$508$	−1.13819	−0.0504988
$509$	−1.41738	−0.0628243	−0.0314121	−	0.999507i	$-0.510000\pi$
$509$	−1.41738	−0.0628243	−0.0314121	+	0.999507i	$0.510000\pi$
$510$	15.4649	0.684796
$511$	12.1983	0.539621
$512$	1.00000	0.0441942
$513$	43.9301	1.93956
$514$	2.54566	0.112284
$515$	8.14707	0.359003
$516$	−16.5641	−0.729195
$517$	13.0684	0.574747
$518$	−15.5798	−0.684536
$519$	2.51570	0.110427
$520$	−4.91847	−0.215689
$521$	21.3336	0.934642	0.467321	−	0.884088i	$-0.345219\pi$
$521$	21.3336	0.934642	0.467321	+	0.884088i	$0.345219\pi$
$522$	2.25674	0.0987746
$523$	−15.4468	−0.675441	−0.337720	−	0.941246i	$-0.609656\pi$
$523$	−15.4468	−0.675441	−0.337720	+	0.941246i	$0.609656\pi$
$524$	1.00000	0.0436852
$525$	11.5427	0.503764
$526$	2.59768	0.113264
$527$	−37.0017	−1.61182
$528$	1.69758	0.0738777
$529$	1.00000	0.0434783
$530$	16.5926	0.720735
$531$	−4.52991	−0.196581
$532$	21.5298	0.933435
$533$	−26.7154	−1.15717
$534$	−18.8685	−0.816518
$535$	8.41872	0.363973
$536$	13.2548	0.572519
$537$	17.1339	0.739382
$538$	3.84494	0.165767
$539$	−0.465641	−0.0200566
$540$	8.41264	0.362022
$541$	−29.0401	−1.24853	−0.624266	−	0.781212i	$-0.714602\pi$
$541$	−29.0401	−1.24853	−0.624266	+	0.781212i	$0.714602\pi$
$542$	19.5477	0.839647
$543$	−3.36237	−0.144293
$544$	−6.54570	−0.280645
$545$	27.2346	1.16660
$546$	13.8402	0.592307
$547$	−6.02558	−0.257635	−0.128818	−	0.991668i	$-0.541118\pi$
$547$	−6.02558	−0.257635	−0.128818	+	0.991668i	$0.541118\pi$
$548$	−6.46391	−0.276124
$549$	−3.18203	−0.135806
$550$	2.94737	0.125676
$551$	−31.7906	−1.35432
$552$	−1.56181	−0.0664750
$553$	41.3546	1.75858
$554$	7.78713	0.330843
$555$	13.5053	0.573267
$556$	−12.6275	−0.535524
$557$	36.2804	1.53725	0.768626	−	0.639699i	$-0.220941\pi$
$557$	36.2804	1.53725	0.768626	+	0.639699i	$0.220941\pi$
$558$	−3.16986	−0.134191
$559$	−34.4833	−1.45849
$560$	4.12297	0.174227
$561$	−11.1119	−0.469143
$562$	−7.12347	−0.300485
$563$	−42.2236	−1.77951	−0.889757	−	0.456435i	$-0.849126\pi$
$563$	−42.2236	−1.77951	−0.889757	+	0.456435i	$0.849126\pi$
$564$	18.7779	0.790692
$565$	−15.6237	−0.657295
$566$	−13.2971	−0.558920
$567$	−19.0875	−0.801600
$568$	−1.75710	−0.0737263
$569$	−39.2330	−1.64473	−0.822365	−	0.568960i	$-0.807346\pi$
$569$	−39.2330	−1.64473	−0.822365	+	0.568960i	$0.807346\pi$
$570$	−18.6630	−0.781708
$571$	2.40972	0.100843	0.0504217	−	0.998728i	$-0.483943\pi$
$571$	2.40972	0.100843	0.0504217	+	0.998728i	$0.483943\pi$
$572$	3.53403	0.147765
$573$	−17.9265	−0.748891
$574$	22.3945	0.934728
$575$	−2.71164	−0.113083
$576$	−0.560757	−0.0233649
$577$	−7.43139	−0.309373	−0.154686	−	0.987964i	$-0.549437\pi$
$577$	−7.43139	−0.309373	−0.154686	+	0.987964i	$0.549437\pi$
$578$	25.8462	1.07506
$579$	−23.3141	−0.968899
$580$	−6.08792	−0.252787
$581$	−30.5129	−1.26589
$582$	−9.41483	−0.390257
$583$	−11.9221	−0.493764
$584$	4.47561	0.185202
$585$	2.75806	0.114032
$586$	33.6550	1.39027
$587$	8.13279	0.335676	0.167838	−	0.985815i	$-0.446321\pi$
$587$	8.13279	0.335676	0.167838	+	0.985815i	$0.446321\pi$
$588$	−0.669077	−0.0275923
$589$	44.6538	1.83993
$590$	12.2202	0.503097
$591$	36.6021	1.50561
$592$	−5.71628	−0.234938
$593$	−22.0230	−0.904374	−0.452187	−	0.891923i	$-0.649356\pi$
$593$	−22.0230	−0.904374	−0.452187	+	0.891923i	$0.649356\pi$
$594$	−6.04467	−0.248016
$595$	−26.9877	−1.10639
$596$	2.41085	0.0987522
$597$	22.3388	0.914266
$598$	−3.25138	−0.132959
$599$	10.9285	0.446526	0.223263	−	0.974758i	$-0.428329\pi$
$599$	10.9285	0.446526	0.223263	+	0.974758i	$0.428329\pi$
$600$	4.23506	0.172896
$601$	−41.1819	−1.67984	−0.839922	−	0.542707i	$-0.817400\pi$
$601$	−41.1819	−1.67984	−0.839922	+	0.542707i	$0.817400\pi$
$602$	28.9061	1.17812
$603$	−7.43270	−0.302683
$604$	−13.2218	−0.537986
$605$	−14.8529	−0.603856
$606$	−17.4337	−0.708196
$607$	−24.2073	−0.982544	−0.491272	−	0.871006i	$-0.663468\pi$
$607$	−24.2073	−0.982544	−0.491272	+	0.871006i	$0.663468\pi$
$608$	7.89936	0.320361
$609$	17.1310	0.694181
$610$	8.58406	0.347558
$611$	39.0919	1.58149
$612$	3.67054	0.148373
$613$	28.9450	1.16908	0.584538	−	0.811366i	$-0.301276\pi$
$613$	28.9450	1.16908	0.584538	+	0.811366i	$0.301276\pi$
$614$	11.9374	0.481756
$615$	−19.4126	−0.782791
$616$	−2.96244	−0.119360
$617$	34.8958	1.40485	0.702426	−	0.711757i	$-0.252100\pi$
$617$	34.8958	1.40485	0.702426	+	0.711757i	$0.252100\pi$
$618$	−8.41137	−0.338355
$619$	−6.87238	−0.276224	−0.138112	−	0.990417i	$-0.544103\pi$
$619$	−6.87238	−0.276224	−0.138112	+	0.990417i	$0.544103\pi$
$620$	8.55122	0.343425
$621$	5.56122	0.223164
$622$	30.3911	1.21857
$623$	32.9273	1.31921
$624$	5.07803	0.203284
$625$	−4.08883	−0.163553
$626$	26.0508	1.04120
$627$	13.4098	0.535536
$628$	−23.1492	−0.923753
$629$	37.4171	1.49192
$630$	−2.31198	−0.0921115
$631$	−9.21077	−0.366675	−0.183337	−	0.983050i	$-0.558690\pi$
$631$	−9.21077	−0.366675	−0.183337	+	0.983050i	$0.558690\pi$
$632$	15.1732	0.603556
$633$	−31.4603	−1.25043
$634$	3.62877	0.144117
$635$	−1.72177	−0.0683264
$636$	−17.1309	−0.679282
$637$	−1.39289	−0.0551883
$638$	4.37430	0.173180
$639$	0.985306	0.0389781
$640$	1.51273	0.0597960
$641$	15.4426	0.609946	0.304973	−	0.952361i	$-0.401353\pi$
$641$	15.4426	0.609946	0.304973	+	0.952361i	$0.401353\pi$
$642$	−8.69183	−0.343039
$643$	−25.2905	−0.997360	−0.498680	−	0.866786i	$-0.666182\pi$
$643$	−25.2905	−0.997360	−0.498680	+	0.866786i	$0.666182\pi$
$644$	2.72551	0.107400
$645$	−25.0571	−0.986623
$646$	−51.7069	−2.03438
$647$	−3.05479	−0.120096	−0.0600480	−	0.998195i	$-0.519125\pi$
$647$	−3.05479	−0.120096	−0.0600480	+	0.998195i	$0.519125\pi$
$648$	−7.00328	−0.275115
$649$	−8.78048	−0.344664
$650$	8.81657	0.345814
$651$	−24.0625	−0.943085
$652$	18.9577	0.742442
$653$	−1.47574	−0.0577500	−0.0288750	−	0.999583i	$-0.509192\pi$
$653$	−1.47574	−0.0577500	−0.0288750	+	0.999583i	$0.509192\pi$
$654$	−28.1181	−1.09950
$655$	1.51273	0.0591074
$656$	8.21663	0.320805
$657$	−2.50973	−0.0979137
$658$	−32.7693	−1.27748
$659$	9.09470	0.354279	0.177140	−	0.984186i	$-0.443316\pi$
$659$	9.09470	0.354279	0.177140	+	0.984186i	$0.443316\pi$
$660$	2.56799	0.0999587
$661$	−30.2407	−1.17623	−0.588113	−	0.808779i	$-0.700129\pi$
$661$	−30.2407	−1.17623	−0.588113	+	0.808779i	$0.700129\pi$
$662$	−3.86538	−0.150232
$663$	−33.2393	−1.29091
$664$	−11.1953	−0.434463
$665$	32.5688	1.26296
$666$	3.20544	0.124208
$667$	−4.02445	−0.155827
$668$	13.0447	0.504715
$669$	23.2108	0.897382
$670$	20.0509	0.774635
$671$	−6.16784	−0.238107
$672$	−4.25672	−0.164207
$673$	−26.5414	−1.02309	−0.511547	−	0.859255i	$-0.670928\pi$
$673$	−26.5414	−1.02309	−0.511547	+	0.859255i	$0.670928\pi$
$674$	−20.4027	−0.785882
$675$	−15.0800	−0.580430
$676$	−2.42852	−0.0934047
$677$	−21.8123	−0.838314	−0.419157	−	0.907914i	$-0.637674\pi$
$677$	−21.8123	−0.838314	−0.419157	+	0.907914i	$0.637674\pi$
$678$	16.1306	0.619491
$679$	16.4298	0.630519
$680$	−9.90190	−0.379721
$681$	6.13099	0.234940
$682$	−6.14425	−0.235275
$683$	16.8991	0.646625	0.323313	−	0.946292i	$-0.395203\pi$
$683$	16.8991	0.646625	0.323313	+	0.946292i	$0.395203\pi$
$684$	−4.42962	−0.169371
$685$	−9.77817	−0.373604
$686$	−17.9110	−0.683844
$687$	−32.0593	−1.22314
$688$	10.6057	0.404340
$689$	−35.6631	−1.35866
$690$	−2.36260	−0.0899426
$691$	−37.9433	−1.44343	−0.721716	−	0.692189i	$-0.756646\pi$
$691$	−37.9433	−1.44343	−0.721716	+	0.692189i	$0.756646\pi$
$692$	−1.61076	−0.0612320
$693$	1.66121	0.0631042
$694$	−24.3575	−0.924598
$695$	−19.1020	−0.724580
$696$	6.28542	0.238248
$697$	−53.7836	−2.03720
$698$	−31.6986	−1.19981
$699$	46.0995	1.74364
$700$	−7.39059	−0.279338
$701$	−52.5182	−1.98358	−0.991792	−	0.127858i	$-0.959190\pi$
$701$	−52.5182	−1.98358	−0.991792	+	0.127858i	$0.959190\pi$
$702$	−18.0816	−0.682447
$703$	−45.1550	−1.70305
$704$	−1.08693	−0.0409653
$705$	28.4059	1.06983
$706$	−22.3874	−0.842563
$707$	30.4236	1.14420
$708$	−12.6166	−0.474162
$709$	36.1311	1.35693	0.678466	−	0.734632i	$-0.262645\pi$
$709$	36.1311	1.35693	0.678466	+	0.734632i	$0.262645\pi$
$710$	−2.65802	−0.0997539
$711$	−8.50846	−0.319092
$712$	12.0812	0.452761
$713$	5.65283	0.211700
$714$	27.8632	1.04275
$715$	5.34605	0.199931
$716$	−10.9706	−0.409989
$717$	−24.6931	−0.922181
$718$	1.91933	0.0716289
$719$	−14.8378	−0.553356	−0.276678	−	0.960963i	$-0.589234\pi$
$719$	−14.8378	−0.553356	−0.276678	+	0.960963i	$0.589234\pi$
$720$	−0.848275	−0.0316133
$721$	14.6787	0.546662
$722$	43.3999	1.61518
$723$	−27.9297	−1.03872
$724$	2.15287	0.0800108
$725$	10.9128	0.405293
$726$	15.3347	0.569125
$727$	18.7814	0.696564	0.348282	−	0.937390i	$-0.386765\pi$
$727$	18.7814	0.696564	0.348282	+	0.937390i	$0.386765\pi$
$728$	−8.86167	−0.328435
$729$	29.9838	1.11051
$730$	6.77040	0.250584
$731$	−69.4220	−2.56767
$732$	−8.86253	−0.327569
$733$	4.43884	0.163952	0.0819761	−	0.996634i	$-0.473877\pi$
$733$	4.43884	0.163952	0.0819761	+	0.996634i	$0.473877\pi$
$734$	25.7720	0.951261
$735$	−1.01214	−0.0373332
$736$	1.00000	0.0368605
$737$	−14.4071	−0.530691
$738$	−4.60753	−0.169605
$739$	6.63646	0.244126	0.122063	−	0.992522i	$-0.461049\pi$
$739$	6.63646	0.244126	0.122063	+	0.992522i	$0.461049\pi$
$740$	−8.64721	−0.317878
$741$	40.1132	1.47360
$742$	29.8950	1.09748
$743$	7.80530	0.286349	0.143174	−	0.989697i	$-0.454269\pi$
$743$	7.80530	0.286349	0.143174	+	0.989697i	$0.454269\pi$
$744$	−8.82863	−0.323673
$745$	3.64697	0.133615
$746$	12.6845	0.464411
$747$	6.27785	0.229694
$748$	7.11474	0.260141
$749$	15.1681	0.554230
$750$	18.2195	0.665282
$751$	7.88850	0.287855	0.143928	−	0.989588i	$-0.454027\pi$
$751$	7.88850	0.287855	0.143928	+	0.989588i	$0.454027\pi$
$752$	−12.0232	−0.438440
$753$	6.08521	0.221757
$754$	13.0850	0.476528
$755$	−20.0010	−0.727911
$756$	15.1571	0.551260
$757$	−34.2950	−1.24647	−0.623236	−	0.782034i	$-0.714182\pi$
$757$	−34.2950	−1.24647	−0.623236	+	0.782034i	$0.714182\pi$
$758$	32.3547	1.17518
$759$	1.69758	0.0616182
$760$	11.9496	0.433459
$761$	−34.0557	−1.23452	−0.617260	−	0.786760i	$-0.711757\pi$
$761$	−34.0557	−1.23452	−0.617260	+	0.786760i	$0.711757\pi$
$762$	1.77763	0.0643967
$763$	49.0688	1.77641
$764$	11.4780	0.415261
$765$	5.55255	0.200753
$766$	−9.13968	−0.330230
$767$	−26.2654	−0.948387
$768$	−1.56181	−0.0563569
$769$	9.28676	0.334889	0.167445	−	0.985881i	$-0.446448\pi$
$769$	9.28676	0.334889	0.167445	+	0.985881i	$0.446448\pi$
$770$	−4.48139	−0.161498
$771$	−3.97583	−0.143186
$772$	14.9276	0.537256
$773$	10.1820	0.366223	0.183111	−	0.983092i	$-0.441383\pi$
$773$	10.1820	0.366223	0.183111	+	0.983092i	$0.441383\pi$
$774$	−5.94724	−0.213769
$775$	−15.3284	−0.550613
$776$	6.02816	0.216399
$777$	24.3326	0.872928
$778$	11.3707	0.407658
$779$	64.9061	2.32550
$780$	7.68171	0.275049
$781$	1.90985	0.0683398
$782$	−6.54570	−0.234074
$783$	−22.3808	−0.799826
$784$	0.428399	0.0153000
$785$	−35.0185	−1.24986
$786$	−1.56181	−0.0557078
$787$	−35.1319	−1.25232	−0.626159	−	0.779695i	$-0.715374\pi$
$787$	−35.1319	−1.25232	−0.626159	+	0.779695i	$0.715374\pi$
$788$	−23.4357	−0.834863
$789$	−4.05708	−0.144436
$790$	22.9530	0.816630
$791$	−28.1494	−1.00088
$792$	0.609505	0.0216578
$793$	−18.4501	−0.655181
$794$	13.0132	0.461823
$795$	−25.9144	−0.919089
$796$	−14.3032	−0.506962
$797$	9.67701	0.342777	0.171389	−	0.985203i	$-0.445175\pi$
$797$	9.67701	0.342777	0.171389	+	0.985203i	$0.445175\pi$
$798$	−33.6254	−1.19033
$799$	78.7001	2.78421
$800$	−2.71164	−0.0958709
$801$	−6.77459	−0.239368
$802$	−24.4429	−0.863109
$803$	−4.86468	−0.171671
$804$	−20.7014	−0.730083
$805$	4.12297	0.145316
$806$	−18.3795	−0.647390
$807$	−6.00506	−0.211388
$808$	11.1625	0.392696
$809$	−31.1101	−1.09377	−0.546887	−	0.837206i	$-0.684187\pi$
$809$	−31.1101	−1.09377	−0.546887	+	0.837206i	$0.684187\pi$
$810$	−10.5941	−0.372239
$811$	8.20981	0.288285	0.144143	−	0.989557i	$-0.453958\pi$
$811$	8.20981	0.288285	0.144143	+	0.989557i	$0.453958\pi$
$812$	−10.9687	−0.384925
$813$	−30.5298	−1.07073
$814$	6.21321	0.217773
$815$	28.6780	1.00455
$816$	10.2231	0.357881
$817$	83.7786	2.93104
$818$	−11.7592	−0.411151
$819$	4.96924	0.173639
$820$	12.4296	0.434059
$821$	−4.74624	−0.165645	−0.0828224	−	0.996564i	$-0.526393\pi$
$821$	−4.74624	−0.165645	−0.0828224	+	0.996564i	$0.526393\pi$
$822$	10.0954	0.352117
$823$	−44.9693	−1.56753	−0.783765	−	0.621058i	$-0.786703\pi$
$823$	−44.9693	−1.56753	−0.783765	+	0.621058i	$0.786703\pi$
$824$	5.38566	0.187618
$825$	−4.60322	−0.160264
$826$	22.0172	0.766078
$827$	45.1189	1.56894	0.784469	−	0.620168i	$-0.212935\pi$
$827$	45.1189	1.56894	0.784469	+	0.620168i	$0.212935\pi$
$828$	−0.560757	−0.0194876
$829$	−33.8643	−1.17616	−0.588078	−	0.808804i	$-0.700115\pi$
$829$	−33.8643	−1.17616	−0.588078	+	0.808804i	$0.700115\pi$
$830$	−16.9355	−0.587841
$831$	−12.1620	−0.421895
$832$	−3.25138	−0.112721
$833$	−2.80417	−0.0971589
$834$	19.7217	0.682906
$835$	19.7332	0.682894
$836$	−8.58608	−0.296956
$837$	31.4366	1.08661
$838$	17.5087	0.604828
$839$	−34.6650	−1.19677	−0.598384	−	0.801209i	$-0.704190\pi$
$839$	−34.6650	−1.19677	−0.598384	+	0.801209i	$0.704190\pi$
$840$	−6.43928	−0.222176
$841$	−12.8038	−0.441511
$842$	−14.4704	−0.498684
$843$	11.1255	0.383182
$844$	20.1435	0.693368
$845$	−3.67371	−0.126379
$846$	6.74207	0.231797
$847$	−26.7606	−0.919506
$848$	10.9686	0.376663
$849$	20.7676	0.712741
$850$	17.7496	0.608805
$851$	−5.71628	−0.195952
$852$	2.74425	0.0940166
$853$	−53.5648	−1.83402	−0.917012	−	0.398860i	$-0.869406\pi$
$853$	−53.5648	−1.83402	−0.917012	+	0.398860i	$0.869406\pi$
$854$	15.4660	0.529235
$855$	−6.70083	−0.229164
$856$	5.56524	0.190216
$857$	13.0609	0.446151	0.223076	−	0.974801i	$-0.428390\pi$
$857$	13.0609	0.446151	0.223076	+	0.974801i	$0.428390\pi$
$858$	−5.51948	−0.188432
$859$	−8.65611	−0.295342	−0.147671	−	0.989037i	$-0.547178\pi$
$859$	−8.65611	−0.295342	−0.147671	+	0.989037i	$0.547178\pi$
$860$	16.0437	0.547084
$861$	−34.9759	−1.19198
$862$	0.00182411	6.21294e−5 0
$863$	16.0251	0.545502	0.272751	−	0.962085i	$-0.412067\pi$
$863$	16.0251	0.545502	0.272751	+	0.962085i	$0.412067\pi$
$864$	5.56122	0.189196
$865$	−2.43666	−0.0828488
$866$	23.2150	0.788877
$867$	−40.3668	−1.37093
$868$	15.4068	0.522942
$869$	−16.4922	−0.559460
$870$	9.50816	0.322357
$871$	−43.0963	−1.46026
$872$	18.0035	0.609677
$873$	−3.38033	−0.114407
$874$	7.89936	0.267200
$875$	−31.7948	−1.07486
$876$	−6.99004	−0.236171
$877$	−12.2416	−0.413369	−0.206684	−	0.978408i	$-0.566267\pi$
$877$	−12.2416	−0.413369	−0.206684	+	0.978408i	$0.566267\pi$
$878$	15.3362	0.517571
$879$	−52.5626	−1.77289
$880$	−1.64424	−0.0554273
$881$	12.0892	0.407295	0.203647	−	0.979044i	$-0.434720\pi$
$881$	12.0892	0.407295	0.203647	+	0.979044i	$0.434720\pi$
$882$	−0.240228	−0.00808889
$883$	31.5017	1.06012	0.530058	−	0.847961i	$-0.322170\pi$
$883$	31.5017	1.06012	0.530058	+	0.847961i	$0.322170\pi$
$884$	21.2826	0.715810
$885$	−19.0856	−0.641555
$886$	−24.5279	−0.824029
$887$	−30.6375	−1.02871	−0.514354	−	0.857578i	$-0.671968\pi$
$887$	−30.6375	−1.02871	−0.514354	+	0.857578i	$0.671968\pi$
$888$	8.92773	0.299595
$889$	−3.10214	−0.104042
$890$	18.2756	0.612599
$891$	7.61210	0.255015
$892$	−14.8615	−0.497600
$893$	−94.9754	−3.17823
$894$	−3.76528	−0.125930
$895$	−16.5955	−0.554727
$896$	2.72551	0.0910529
$897$	5.07803	0.169551
$898$	35.2692	1.17695
$899$	−22.7495	−0.758739
$900$	1.52057	0.0506856
$901$	−71.7972	−2.39191
$902$	−8.93092	−0.297367
$903$	−45.1457	−1.50235
$904$	−10.3281	−0.343509
$905$	3.25672	0.108257
$906$	20.6499	0.686046
$907$	34.8927	1.15859	0.579296	−	0.815117i	$-0.303327\pi$
$907$	34.8927	1.15859	0.579296	+	0.815117i	$0.303327\pi$
$908$	−3.92557	−0.130275
$909$	−6.25946	−0.207613
$910$	−13.4053	−0.444383
$911$	32.4180	1.07406	0.537028	−	0.843564i	$-0.319547\pi$
$911$	32.4180	1.07406	0.537028	+	0.843564i	$0.319547\pi$
$912$	−12.3373	−0.408528
$913$	12.1686	0.402721
$914$	37.3570	1.23566
$915$	−13.4066	−0.443210
$916$	20.5271	0.678233
$917$	2.72551	0.0900042
$918$	−36.4021	−1.20145
$919$	35.8162	1.18147	0.590734	−	0.806866i	$-0.298838\pi$
$919$	35.8162	1.18147	0.590734	+	0.806866i	$0.298838\pi$
$920$	1.51273	0.0498733
$921$	−18.6440	−0.614340
$922$	−10.2337	−0.337028
$923$	5.71300	0.188046
$924$	4.62677	0.152210
$925$	15.5005	0.509653
$926$	−31.0320	−1.01977
$927$	−3.02005	−0.0991913
$928$	−4.02445	−0.132109
$929$	−0.851646	−0.0279416	−0.0139708	−	0.999902i	$-0.504447\pi$
$929$	−0.851646	−0.0279416	−0.0139708	+	0.999902i	$0.504447\pi$
$930$	−13.3554	−0.437940
$931$	3.38408	0.110909
$932$	−29.5168	−0.966854
$933$	−47.4650	−1.55393
$934$	28.9904	0.948595
$935$	10.7627	0.351978
$936$	1.82323	0.0595942
$937$	43.1395	1.40931	0.704653	−	0.709552i	$-0.251103\pi$
$937$	43.1395	1.40931	0.704653	+	0.709552i	$0.251103\pi$
$938$	36.1260	1.17956
$939$	−40.6863	−1.32775
$940$	−18.1879	−0.593222
$941$	−23.5991	−0.769309	−0.384655	−	0.923061i	$-0.625679\pi$
$941$	−23.5991	−0.769309	−0.384655	+	0.923061i	$0.625679\pi$
$942$	36.1546	1.17798
$943$	8.21663	0.267570
$944$	8.07821	0.262923
$945$	22.9287	0.745871
$946$	−11.5277	−0.374799
$947$	−13.2680	−0.431152	−0.215576	−	0.976487i	$-0.569163\pi$
$947$	−13.2680	−0.431152	−0.215576	+	0.976487i	$0.569163\pi$
$948$	−23.6976	−0.769662
$949$	−14.5519	−0.472375
$950$	−21.4202	−0.694964
$951$	−5.66744	−0.183779
$952$	−17.8404	−0.578210
$953$	18.6019	0.602573	0.301287	−	0.953534i	$-0.402584\pi$
$953$	18.6019	0.602573	0.301287	+	0.953534i	$0.402584\pi$
$954$	−6.15072	−0.199137
$955$	17.3632	0.561861
$956$	15.8106	0.511351
$957$	−6.83182	−0.220841
$958$	20.6800	0.668141
$959$	−17.6174	−0.568897
$960$	−2.36260	−0.0762525
$961$	0.954489	0.0307900
$962$	18.5858	0.599230
$963$	−3.12074	−0.100565
$964$	17.8829	0.575971
$965$	22.5815	0.726924
$966$	−4.25672	−0.136958
$967$	−1.23516	−0.0397200	−0.0198600	−	0.999803i	$-0.506322\pi$
$967$	−1.23516	−0.0397200	−0.0198600	+	0.999803i	$0.506322\pi$
$968$	−9.81858	−0.315581
$969$	80.7562	2.59426
$970$	9.11901	0.292794
$971$	−24.9619	−0.801065	−0.400533	−	0.916283i	$-0.631175\pi$
$971$	−24.9619	−0.801065	−0.400533	+	0.916283i	$0.631175\pi$
$972$	−5.74587	−0.184299
$973$	−34.4163	−1.10333
$974$	−16.5595	−0.530599
$975$	−13.7698	−0.440986
$976$	5.67453	0.181637
$977$	48.8232	1.56199	0.780996	−	0.624536i	$-0.214712\pi$
$977$	48.8232	1.56199	0.780996	+	0.624536i	$0.214712\pi$
$978$	−29.6083	−0.946769
$979$	−13.1314	−0.419682
$980$	0.648054	0.0207013
$981$	−10.0956	−0.322328
$982$	−15.7102	−0.501333
$983$	−7.01059	−0.223603	−0.111802	−	0.993731i	$-0.535662\pi$
$983$	−7.01059	−0.223603	−0.111802	+	0.993731i	$0.535662\pi$
$984$	−12.8328	−0.409095
$985$	−35.4520	−1.12959
$986$	26.3428	0.838927
$987$	51.1793	1.62906
$988$	−25.6838	−0.817112
$989$	10.6057	0.337243
$990$	0.922018	0.0293036
$991$	8.68939	0.276028	0.138014	−	0.990430i	$-0.455928\pi$
$991$	8.68939	0.276028	0.138014	+	0.990430i	$0.455928\pi$
$992$	5.65283	0.179478
$993$	6.03697	0.191578
$994$	−4.78899	−0.151898
$995$	−21.6369	−0.685935
$996$	17.4849	0.554031
$997$	17.1932	0.544514	0.272257	−	0.962225i	$-0.412230\pi$
$997$	17.1932	0.544514	0.272257	+	0.962225i	$0.412230\pi$
$998$	−43.5807	−1.37952
$999$	−31.7895	−1.00577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.11	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.11	✓	41	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.56181 q^{3} +1.00000 q^{4} +1.51273 q^{5} -1.56181 q^{6} +2.72551 q^{7} +1.00000 q^{8} -0.560757 q^{9} +1.51273 q^{10} -1.08693 q^{11} -1.56181 q^{12} -3.25138 q^{13} +2.72551 q^{14} -2.36260 q^{15} +1.00000 q^{16} -6.54570 q^{17} -0.560757 q^{18} +7.89936 q^{19} +1.51273 q^{20} -4.25672 q^{21} -1.08693 q^{22} +1.00000 q^{23} -1.56181 q^{24} -2.71164 q^{25} -3.25138 q^{26} +5.56122 q^{27} +2.72551 q^{28} -4.02445 q^{29} -2.36260 q^{30} +5.65283 q^{31} +1.00000 q^{32} +1.69758 q^{33} -6.54570 q^{34} +4.12297 q^{35} -0.560757 q^{36} -5.71628 q^{37} +7.89936 q^{38} +5.07803 q^{39} +1.51273 q^{40} +8.21663 q^{41} -4.25672 q^{42} +10.6057 q^{43} -1.08693 q^{44} -0.848275 q^{45} +1.00000 q^{46} -12.0232 q^{47} -1.56181 q^{48} +0.428399 q^{49} -2.71164 q^{50} +10.2231 q^{51} -3.25138 q^{52} +10.9686 q^{53} +5.56122 q^{54} -1.64424 q^{55} +2.72551 q^{56} -12.3373 q^{57} -4.02445 q^{58} +8.07821 q^{59} -2.36260 q^{60} +5.67453 q^{61} +5.65283 q^{62} -1.52835 q^{63} +1.00000 q^{64} -4.91847 q^{65} +1.69758 q^{66} +13.2548 q^{67} -6.54570 q^{68} -1.56181 q^{69} +4.12297 q^{70} -1.75710 q^{71} -0.560757 q^{72} +4.47561 q^{73} -5.71628 q^{74} +4.23506 q^{75} +7.89936 q^{76} -2.96244 q^{77} +5.07803 q^{78} +15.1732 q^{79} +1.51273 q^{80} -7.00328 q^{81} +8.21663 q^{82} -11.1953 q^{83} -4.25672 q^{84} -9.90190 q^{85} +10.6057 q^{86} +6.28542 q^{87} -1.08693 q^{88} +12.0812 q^{89} -0.848275 q^{90} -8.86167 q^{91} +1.00000 q^{92} -8.82863 q^{93} -12.0232 q^{94} +11.9496 q^{95} -1.56181 q^{96} +6.02816 q^{97} +0.428399 q^{98} +0.609505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19}+ \cdots - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more