LMFDB - Embedded newform 2299.2.a.y.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2299,2,Mod(1,2299)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2299.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2299, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2299 = 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2299.a (trivial)

Newform invariants

comment:select newform

sage:traces = [20,1,4,21,18,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	yes
Analytic conductor:	$18.3576074247$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} - 30 x^{18} + 28 x^{17} + 374 x^{16} - 321 x^{15} - 2521 x^{14} + 1965 x^{13} + \cdots + 80 $ x^20 - x^19 - 30x^18 + 28x^17 + 374x^16 - 321x^15 - 2521x^14 + 1965x^13 + 10017x^12 - 7030x^11 - 23999x^10 + 15056x^9 + 34039x^8 - 18683x^7 - 26866x^6 + 11940x^5 + 10535x^4 - 2840x^3 - 1880x^2 + 120x + 80
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 209)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$0.240189$ of defining polynomial
Character	$\chi$	$=$	2299.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.240189 q^{2} +2.97370 q^{3} -1.94231 q^{4} +3.63017 q^{5} +0.714249 q^{6} -3.43180 q^{7} -0.946898 q^{8} +5.84289 q^{9} +0.871926 q^{10} -5.77585 q^{12} +4.97039 q^{13} -0.824280 q^{14} +10.7950 q^{15} +3.65718 q^{16} +1.72267 q^{17} +1.40340 q^{18} -1.00000 q^{19} -7.05092 q^{20} -10.2052 q^{21} +3.59285 q^{23} -2.81579 q^{24} +8.17816 q^{25} +1.19383 q^{26} +8.45391 q^{27} +6.66562 q^{28} -0.308840 q^{29} +2.59285 q^{30} -4.91113 q^{31} +2.77221 q^{32} +0.413765 q^{34} -12.4580 q^{35} -11.3487 q^{36} -4.59065 q^{37} -0.240189 q^{38} +14.7805 q^{39} -3.43740 q^{40} +5.77995 q^{41} -2.45116 q^{42} -8.61391 q^{43} +21.2107 q^{45} +0.862961 q^{46} +7.87037 q^{47} +10.8754 q^{48} +4.77727 q^{49} +1.96430 q^{50} +5.12270 q^{51} -9.65404 q^{52} -2.42159 q^{53} +2.03053 q^{54} +3.24957 q^{56} -2.97370 q^{57} -0.0741798 q^{58} -3.31161 q^{59} -20.9673 q^{60} -2.56732 q^{61} -1.17960 q^{62} -20.0517 q^{63} -6.64852 q^{64} +18.0434 q^{65} +3.26451 q^{67} -3.34595 q^{68} +10.6841 q^{69} -2.99228 q^{70} -3.71792 q^{71} -5.53262 q^{72} +10.7657 q^{73} -1.10262 q^{74} +24.3194 q^{75} +1.94231 q^{76} +3.55010 q^{78} +10.7108 q^{79} +13.2762 q^{80} +7.61072 q^{81} +1.38828 q^{82} +6.50944 q^{83} +19.8216 q^{84} +6.25358 q^{85} -2.06896 q^{86} -0.918398 q^{87} +3.00520 q^{89} +5.09457 q^{90} -17.0574 q^{91} -6.97842 q^{92} -14.6042 q^{93} +1.89037 q^{94} -3.63017 q^{95} +8.24372 q^{96} +4.97012 q^{97} +1.14745 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 4 q^{3} + 21 q^{4} + 18 q^{5} - 10 q^{6} - 2 q^{7} + 3 q^{8} + 32 q^{9} + 11 q^{10} + 10 q^{12} + q^{13} + 25 q^{14} + 28 q^{15} + 27 q^{16} + 2 q^{17} + 4 q^{18} - 20 q^{19} + 47 q^{20}+ \cdots + 45 q^{98}+O(q^{100}) $ 20 * q + q^2 + 4 * q^3 + 21 * q^4 + 18 * q^5 - 10 * q^6 - 2 * q^7 + 3 * q^8 + 32 * q^9 + 11 * q^10 + 10 * q^12 + q^13 + 25 * q^14 + 28 * q^15 + 27 * q^16 + 2 * q^17 + 4 * q^18 - 20 * q^19 + 47 * q^20 + 11 * q^21 + 8 * q^23 - 36 * q^24 + 36 * q^25 + 8 * q^26 - 2 * q^27 + 28 * q^28 + 17 * q^29 - 10 * q^30 - 9 * q^31 + 2 * q^32 - 19 * q^34 - 20 * q^35 + 17 * q^36 + 29 * q^37 - q^38 + 3 * q^39 + 29 * q^40 + 4 * q^41 - 16 * q^42 + 12 * q^43 + 65 * q^45 - 36 * q^46 + 10 * q^47 + 42 * q^48 + 34 * q^49 + 25 * q^50 - 10 * q^51 - 13 * q^52 + 50 * q^53 - 26 * q^54 + 37 * q^56 - 4 * q^57 + 4 * q^58 + 46 * q^59 - 7 * q^60 + 22 * q^61 - 5 * q^62 - 69 * q^63 + 47 * q^64 + 13 * q^65 + 26 * q^67 - 5 * q^68 + 65 * q^69 + 26 * q^70 + 38 * q^71 + 104 * q^72 - 3 * q^73 - 10 * q^74 + 13 * q^75 - 21 * q^76 - 45 * q^78 + 14 * q^79 + 31 * q^80 + 76 * q^81 - 10 * q^82 + 14 * q^83 - 5 * q^84 + 9 * q^85 + 15 * q^86 + 21 * q^87 + 48 * q^89 - 28 * q^90 + 24 * q^91 + q^92 + 42 * q^93 + 79 * q^94 - 18 * q^95 - 21 * q^96 - 5 * q^97 + 45 * q^98

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 $

$2$	0.240189	0.169839	0.0849195	−	0.996388i	$-0.472937\pi$
$2$	0.240189	0.169839	0.0849195	+	0.996388i	$0.472937\pi$
$3$	2.97370	1.71687	0.858433	−	0.512925i	$-0.171438\pi$
$3$	2.97370	1.71687	0.858433	+	0.512925i	$0.171438\pi$
$4$	−1.94231	−0.971155
$5$	3.63017	1.62346	0.811732	−	0.584031i	$-0.198525\pi$
$5$	3.63017	1.62346	0.811732	+	0.584031i	$0.198525\pi$
$6$	0.714249	0.291591
$7$	−3.43180	−1.29710	−0.648550	−	0.761172i	$-0.724624\pi$
$7$	−3.43180	−1.29710	−0.648550	+	0.761172i	$0.724624\pi$
$8$	−0.946898	−0.334779
$9$	5.84289	1.94763
$10$	0.871926	0.275727
$11$	0	0
$11$	0	0
$12$	−5.77585	−1.66734
$13$	4.97039	1.37854	0.689269	−	0.724505i	$-0.257932\pi$
$13$	4.97039	1.37854	0.689269	+	0.724505i	$0.257932\pi$
$14$	−0.824280	−0.220298
$15$	10.7950	2.78727
$16$	3.65718	0.914296
$17$	1.72267	0.417808	0.208904	−	0.977936i	$-0.433010\pi$
$17$	1.72267	0.417808	0.208904	+	0.977936i	$0.433010\pi$
$18$	1.40340	0.330784
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−7.05092	−1.57663
$21$	−10.2052	−2.22695
$22$	0	0
$23$	3.59285	0.749161	0.374580	−	0.927194i	$-0.377787\pi$
$23$	3.59285	0.749161	0.374580	+	0.927194i	$0.377787\pi$
$24$	−2.81579	−0.574771
$25$	8.17816	1.63563
$26$	1.19383	0.234130
$27$	8.45391	1.62696
$28$	6.66562	1.25968
$29$	−0.308840	−0.0573501	−0.0286751	−	0.999589i	$-0.509129\pi$
$29$	−0.308840	−0.0573501	−0.0286751	+	0.999589i	$0.509129\pi$
$30$	2.59285	0.473387
$31$	−4.91113	−0.882064	−0.441032	−	0.897491i	$-0.645388\pi$
$31$	−4.91113	−0.882064	−0.441032	+	0.897491i	$0.645388\pi$
$32$	2.77221	0.490062
$33$	0	0
$34$	0.413765	0.0709601
$35$	−12.4580	−2.10579
$36$	−11.3487	−1.89145
$37$	−4.59065	−0.754698	−0.377349	−	0.926071i	$-0.623164\pi$
$37$	−4.59065	−0.754698	−0.377349	+	0.926071i	$0.623164\pi$
$38$	−0.240189	−0.0389637
$39$	14.7805	2.36677
$40$	−3.43740	−0.543501
$41$	5.77995	0.902677	0.451338	−	0.892353i	$-0.350947\pi$
$41$	5.77995	0.902677	0.451338	+	0.892353i	$0.350947\pi$
$42$	−2.45116	−0.378222
$43$	−8.61391	−1.31361	−0.656805	−	0.754061i	$-0.728092\pi$
$43$	−8.61391	−1.31361	−0.656805	+	0.754061i	$0.728092\pi$
$44$	0	0
$45$	21.2107	3.16191
$46$	0.862961	0.127237
$47$	7.87037	1.14801	0.574005	−	0.818851i	$-0.305389\pi$
$47$	7.87037	1.14801	0.574005	+	0.818851i	$0.305389\pi$
$48$	10.8754	1.56972
$49$	4.77727	0.682467
$50$	1.96430	0.277794
$51$	5.12270	0.717321
$52$	−9.65404	−1.33877
$53$	−2.42159	−0.332631	−0.166315	−	0.986073i	$-0.553187\pi$
$53$	−2.42159	−0.332631	−0.166315	+	0.986073i	$0.553187\pi$
$54$	2.03053	0.276321
$55$	0	0
$56$	3.24957	0.434242
$57$	−2.97370	−0.393876
$58$	−0.0741798	−0.00974029
$59$	−3.31161	−0.431135	−0.215568	−	0.976489i	$-0.569160\pi$
$59$	−3.31161	−0.431135	−0.215568	+	0.976489i	$0.569160\pi$
$60$	−20.9673	−2.70687
$61$	−2.56732	−0.328712	−0.164356	−	0.986401i	$-0.552555\pi$
$61$	−2.56732	−0.328712	−0.164356	+	0.986401i	$0.552555\pi$
$62$	−1.17960	−0.149809
$63$	−20.0517	−2.52627
$64$	−6.64852	−0.831065
$65$	18.0434	2.23801
$66$	0	0
$67$	3.26451	0.398823	0.199411	−	0.979916i	$-0.436097\pi$
$67$	3.26451	0.398823	0.199411	+	0.979916i	$0.436097\pi$
$68$	−3.34595	−0.405756
$69$	10.6841	1.28621
$70$	−2.99228	−0.357646
$71$	−3.71792	−0.441236	−0.220618	−	0.975360i	$-0.570807\pi$
$71$	−3.71792	−0.441236	−0.220618	+	0.975360i	$0.570807\pi$
$72$	−5.53262	−0.652026
$73$	10.7657	1.26003	0.630014	−	0.776584i	$-0.283049\pi$
$73$	10.7657	1.26003	0.630014	+	0.776584i	$0.283049\pi$
$74$	−1.10262	−0.128177
$75$	24.3194	2.80816
$76$	1.94231	0.222798
$77$	0	0
$78$	3.55010	0.401969
$79$	10.7108	1.20506	0.602529	−	0.798097i	$-0.294160\pi$
$79$	10.7108	1.20506	0.602529	+	0.798097i	$0.294160\pi$
$80$	13.2762	1.48433
$81$	7.61072	0.845635
$82$	1.38828	0.153310
$83$	6.50944	0.714504	0.357252	−	0.934008i	$-0.383714\pi$
$83$	6.50944	0.714504	0.357252	+	0.934008i	$0.383714\pi$
$84$	19.8216	2.16271
$85$	6.25358	0.678296
$86$	−2.06896	−0.223102
$87$	−0.918398	−0.0984626
$88$	0	0
$89$	3.00520	0.318550	0.159275	−	0.987234i	$-0.449084\pi$
$89$	3.00520	0.318550	0.159275	+	0.987234i	$0.449084\pi$
$90$	5.09457	0.537015
$91$	−17.0574	−1.78810
$92$	−6.97842	−0.727551
$93$	−14.6042	−1.51439
$94$	1.89037	0.194977
$95$	−3.63017	−0.372448
$96$	8.24372	0.841371
$97$	4.97012	0.504639	0.252320	−	0.967644i	$-0.418807\pi$
$97$	4.97012	0.504639	0.252320	+	0.967644i	$0.418807\pi$
$98$	1.14745	0.115910
$99$	0	0
$100$	−15.8845	−1.58845
$101$	−0.271898	−0.0270549	−0.0135274	−	0.999909i	$-0.504306\pi$
$101$	−0.271898	−0.0270549	−0.0135274	+	0.999909i	$0.504306\pi$
$102$	1.23041	0.121829
$103$	14.1811	1.39730	0.698652	−	0.715462i	$-0.253784\pi$
$103$	14.1811	1.39730	0.698652	+	0.715462i	$0.253784\pi$
$104$	−4.70645	−0.461506
$105$	−37.0465	−3.61537
$106$	−0.581638	−0.0564937
$107$	10.8716	1.05099	0.525497	−	0.850795i	$-0.323879\pi$
$107$	10.8716	1.05099	0.525497	+	0.850795i	$0.323879\pi$
$108$	−16.4201	−1.58003
$109$	4.70206	0.450376	0.225188	−	0.974315i	$-0.427700\pi$
$109$	4.70206	0.450376	0.225188	+	0.974315i	$0.427700\pi$
$110$	0	0
$111$	−13.6512	−1.29572
$112$	−12.5507	−1.18593
$113$	−19.4296	−1.82779	−0.913894	−	0.405954i	$-0.866939\pi$
$113$	−19.4296	−1.82779	−0.913894	+	0.405954i	$0.866939\pi$
$114$	−0.714249	−0.0668955
$115$	13.0427	1.21623
$116$	0.599863	0.0556959
$117$	29.0415	2.68488
$118$	−0.795412	−0.0732236
$119$	−5.91185	−0.541939
$120$	−10.2218	−0.933119
$121$	0	0
$122$	−0.616642	−0.0558281
$123$	17.1878	1.54978
$124$	9.53893	0.856621
$125$	11.5373	1.03193
$126$	−4.81618	−0.429059
$127$	11.3068	1.00332	0.501659	−	0.865066i	$-0.332723\pi$
$127$	11.3068	1.00332	0.501659	+	0.865066i	$0.332723\pi$
$128$	−7.14132	−0.631209
$129$	−25.6152	−2.25529
$130$	4.33381	0.380101
$131$	−18.9828	−1.65854	−0.829270	−	0.558849i	$-0.811243\pi$
$131$	−18.9828	−1.65854	−0.829270	+	0.558849i	$0.811243\pi$
$132$	0	0
$133$	3.43180	0.297575
$134$	0.784097	0.0677357
$135$	30.6892	2.64130
$136$	−1.63119	−0.139873
$137$	−3.89700	−0.332943	−0.166472	−	0.986046i	$-0.553237\pi$
$137$	−3.89700	−0.332943	−0.166472	+	0.986046i	$0.553237\pi$
$138$	2.56619	0.218448
$139$	−11.5200	−0.977116	−0.488558	−	0.872532i	$-0.662477\pi$
$139$	−11.5200	−0.977116	−0.488558	+	0.872532i	$0.662477\pi$
$140$	24.1974	2.04505
$141$	23.4041	1.97098
$142$	−0.893002	−0.0749391
$143$	0	0
$144$	21.3685	1.78071
$145$	−1.12114	−0.0931058
$146$	2.58580	0.214002
$147$	14.2062	1.17171
$148$	8.91646	0.732929
$149$	−1.41055	−0.115557	−0.0577785	−	0.998329i	$-0.518402\pi$
$149$	−1.41055	−0.115557	−0.0577785	+	0.998329i	$0.518402\pi$
$150$	5.84124	0.476935
$151$	−18.9562	−1.54263	−0.771317	−	0.636451i	$-0.780402\pi$
$151$	−18.9562	−1.54263	−0.771317	+	0.636451i	$0.780402\pi$
$152$	0.946898	0.0768036
$153$	10.0654	0.813736
$154$	0	0
$155$	−17.8282	−1.43200
$156$	−28.7082	−2.29850
$157$	−2.29137	−0.182871	−0.0914355	−	0.995811i	$-0.529146\pi$
$157$	−2.29137	−0.182871	−0.0914355	+	0.995811i	$0.529146\pi$
$158$	2.57261	0.204666
$159$	−7.20108	−0.571083
$160$	10.0636	0.795598
$161$	−12.3299	−0.971736
$162$	1.82801	0.143622
$163$	−9.98909	−0.782406	−0.391203	−	0.920304i	$-0.627941\pi$
$163$	−9.98909	−0.782406	−0.391203	+	0.920304i	$0.627941\pi$
$164$	−11.2265	−0.876639
$165$	0	0
$166$	1.56349	0.121351
$167$	−23.7396	−1.83703	−0.918513	−	0.395391i	$-0.870609\pi$
$167$	−23.7396	−1.83703	−0.918513	+	0.395391i	$0.870609\pi$
$168$	9.66324	0.745535
$169$	11.7048	0.900368
$170$	1.50204	0.115201
$171$	−5.84289	−0.446817
$172$	16.7309	1.27572
$173$	−0.404563	−0.0307583	−0.0153792	−	0.999882i	$-0.504896\pi$
$173$	−0.404563	−0.0307583	−0.0153792	+	0.999882i	$0.504896\pi$
$174$	−0.220589	−0.0167228
$175$	−28.0658	−2.12158
$176$	0	0
$177$	−9.84774	−0.740202
$178$	0.721814	0.0541022
$179$	−6.29255	−0.470327	−0.235164	−	0.971956i	$-0.575563\pi$
$179$	−6.29255	−0.470327	−0.235164	+	0.971956i	$0.575563\pi$
$180$	−41.1978	−3.07070
$181$	−18.1010	−1.34544	−0.672719	−	0.739898i	$-0.734874\pi$
$181$	−18.1010	−1.34544	−0.672719	+	0.739898i	$0.734874\pi$
$182$	−4.09699	−0.303689
$183$	−7.63445	−0.564355
$184$	−3.40206	−0.250803
$185$	−16.6649	−1.22522
$186$	−3.50777	−0.257202
$187$	0	0
$188$	−15.2867	−1.11490
$189$	−29.0122	−2.11032
$190$	−0.871926	−0.0632562
$191$	−25.4096	−1.83857	−0.919286	−	0.393591i	$-0.871233\pi$
$191$	−25.4096	−1.83857	−0.919286	+	0.393591i	$0.871233\pi$
$192$	−19.7707	−1.42683
$193$	−7.46941	−0.537660	−0.268830	−	0.963188i	$-0.586637\pi$
$193$	−7.46941	−0.537660	−0.268830	+	0.963188i	$0.586637\pi$
$194$	1.19377	0.0857074
$195$	53.6556	3.84236
$196$	−9.27894	−0.662781
$197$	4.21937	0.300617	0.150309	−	0.988639i	$-0.451973\pi$
$197$	4.21937	0.300617	0.150309	+	0.988639i	$0.451973\pi$
$198$	0	0
$199$	26.5503	1.88210	0.941051	−	0.338264i	$-0.109840\pi$
$199$	26.5503	1.88210	0.941051	+	0.338264i	$0.109840\pi$
$200$	−7.74388	−0.547575
$201$	9.70766	0.684725
$202$	−0.0653068	−0.00459497
$203$	1.05988	0.0743889
$204$	−9.94986	−0.696630
$205$	20.9822	1.46546
$206$	3.40614	0.237317
$207$	20.9926	1.45909
$208$	18.1776	1.26039
$209$	0	0
$210$	−8.89814	−0.614030
$211$	12.4040	0.853923	0.426962	−	0.904270i	$-0.359584\pi$
$211$	12.4040	0.853923	0.426962	+	0.904270i	$0.359584\pi$
$212$	4.70347	0.323036
$213$	−11.0560	−0.757543
$214$	2.61123	0.178500
$215$	−31.2700	−2.13260
$216$	−8.00499	−0.544670
$217$	16.8540	1.14413
$218$	1.12938	0.0764913
$219$	32.0139	2.16330
$220$	0	0
$221$	8.56233	0.575965
$222$	−3.27887	−0.220063
$223$	−3.83310	−0.256683	−0.128342	−	0.991730i	$-0.540965\pi$
$223$	−3.83310	−0.256683	−0.128342	+	0.991730i	$0.540965\pi$
$224$	−9.51368	−0.635659
$225$	47.7841	3.18561
$226$	−4.66678	−0.310430
$227$	−6.90872	−0.458548	−0.229274	−	0.973362i	$-0.573635\pi$
$227$	−6.90872	−0.458548	−0.229274	+	0.973362i	$0.573635\pi$
$228$	5.77585	0.382515
$229$	15.0112	0.991966	0.495983	−	0.868332i	$-0.334808\pi$
$229$	15.0112	0.991966	0.495983	+	0.868332i	$0.334808\pi$
$230$	3.13270	0.206564
$231$	0	0
$232$	0.292440	0.0191996
$233$	−14.2940	−0.936433	−0.468217	−	0.883614i	$-0.655103\pi$
$233$	−14.2940	−0.936433	−0.468217	+	0.883614i	$0.655103\pi$
$234$	6.97543	0.455998
$235$	28.5708	1.86375
$236$	6.43218	0.418699
$237$	31.8507	2.06892
$238$	−1.41996	−0.0920423
$239$	−18.4968	−1.19646	−0.598230	−	0.801324i	$-0.704129\pi$
$239$	−18.4968	−1.19646	−0.598230	+	0.801324i	$0.704129\pi$
$240$	39.4795	2.54839
$241$	−19.9707	−1.28642	−0.643212	−	0.765688i	$-0.722399\pi$
$241$	−19.9707	−1.28642	−0.643212	+	0.765688i	$0.722399\pi$
$242$	0	0
$243$	−2.72974	−0.175113
$244$	4.98654	0.319230
$245$	17.3423	1.10796
$246$	4.12832	0.263212
$247$	−4.97039	−0.316258
$248$	4.65033	0.295297
$249$	19.3571	1.22671
$250$	2.77112	0.175261
$251$	−6.86515	−0.433324	−0.216662	−	0.976247i	$-0.569517\pi$
$251$	−6.86515	−0.433324	−0.216662	+	0.976247i	$0.569517\pi$
$252$	38.9465	2.45340
$253$	0	0
$254$	2.71577	0.170402
$255$	18.5963	1.16454
$256$	11.5818	0.723861
$257$	6.67199	0.416187	0.208094	−	0.978109i	$-0.433274\pi$
$257$	6.67199	0.416187	0.208094	+	0.978109i	$0.433274\pi$
$258$	−6.15248	−0.383037
$259$	15.7542	0.978919
$260$	−35.0458	−2.17345
$261$	−1.80452	−0.111697
$262$	−4.55946	−0.281685
$263$	15.1344	0.933226	0.466613	−	0.884462i	$-0.345474\pi$
$263$	15.1344	0.933226	0.466613	+	0.884462i	$0.345474\pi$
$264$	0	0
$265$	−8.79079	−0.540014
$266$	0.824280	0.0505398
$267$	8.93655	0.546908
$268$	−6.34068	−0.387319
$269$	−9.31696	−0.568065	−0.284032	−	0.958815i	$-0.591672\pi$
$269$	−9.31696	−0.568065	−0.284032	+	0.958815i	$0.591672\pi$
$270$	7.37119	0.448596
$271$	−19.0275	−1.15584	−0.577920	−	0.816093i	$-0.696136\pi$
$271$	−19.0275	−1.15584	−0.577920	+	0.816093i	$0.696136\pi$
$272$	6.30011	0.382000
$273$	−50.7236	−3.06993
$274$	−0.936016	−0.0565468
$275$	0	0
$276$	−20.7517	−1.24911
$277$	14.9645	0.899130	0.449565	−	0.893248i	$-0.351579\pi$
$277$	14.9645	0.899130	0.449565	+	0.893248i	$0.351579\pi$
$278$	−2.76698	−0.165952
$279$	−28.6952	−1.71794
$280$	11.7965	0.704975
$281$	22.1559	1.32171	0.660855	−	0.750514i	$-0.270194\pi$
$281$	22.1559	1.32171	0.660855	+	0.750514i	$0.270194\pi$
$282$	5.62140	0.334749
$283$	−21.8076	−1.29633	−0.648163	−	0.761501i	$-0.724463\pi$
$283$	−21.8076	−1.29633	−0.648163	+	0.761501i	$0.724463\pi$
$284$	7.22135	0.428508
$285$	−10.7950	−0.639443
$286$	0	0
$287$	−19.8357	−1.17086
$288$	16.1977	0.954460
$289$	−14.0324	−0.825436
$290$	−0.269286	−0.0158130
$291$	14.7796	0.866398
$292$	−20.9103	−1.22368
$293$	10.5735	0.617710	0.308855	−	0.951109i	$-0.400054\pi$
$293$	10.5735	0.617710	0.308855	+	0.951109i	$0.400054\pi$
$294$	3.41216	0.199001
$295$	−12.0217	−0.699932
$296$	4.34688	0.252657
$297$	0	0
$298$	−0.338799	−0.0196261
$299$	17.8579	1.03275
$300$	−47.2358	−2.72716
$301$	29.5613	1.70388
$302$	−4.55307	−0.261999
$303$	−0.808544	−0.0464496
$304$	−3.65718	−0.209754
$305$	−9.31983	−0.533652
$306$	2.41758	0.138204
$307$	−20.5341	−1.17194	−0.585970	−	0.810332i	$-0.699287\pi$
$307$	−20.5341	−1.17194	−0.585970	+	0.810332i	$0.699287\pi$
$308$	0	0
$309$	42.1703	2.39898
$310$	−4.28214	−0.243209
$311$	−27.7476	−1.57342	−0.786710	−	0.617323i	$-0.788217\pi$
$311$	−27.7476	−1.57342	−0.786710	+	0.617323i	$0.788217\pi$
$312$	−13.9956	−0.792344
$313$	−4.89129	−0.276472	−0.138236	−	0.990399i	$-0.544143\pi$
$313$	−4.89129	−0.276472	−0.138236	+	0.990399i	$0.544143\pi$
$314$	−0.550360	−0.0310586
$315$	−72.7910	−4.10131
$316$	−20.8037	−1.17030
$317$	8.97725	0.504212	0.252106	−	0.967700i	$-0.418877\pi$
$317$	8.97725	0.504212	0.252106	+	0.967700i	$0.418877\pi$
$318$	−1.72962	−0.0969921
$319$	0	0
$320$	−24.1353	−1.34920
$321$	32.3288	1.80442
$322$	−2.96151	−0.165039
$323$	−1.72267	−0.0958518
$324$	−14.7824	−0.821242
$325$	40.6487	2.25478
$326$	−2.39927	−0.132883
$327$	13.9825	0.773235
$328$	−5.47302	−0.302197
$329$	−27.0095	−1.48908
$330$	0	0
$331$	−19.6144	−1.07810	−0.539051	−	0.842273i	$-0.681217\pi$
$331$	−19.6144	−1.07810	−0.539051	+	0.842273i	$0.681217\pi$
$332$	−12.6433	−0.693894
$333$	−26.8227	−1.46987
$334$	−5.70198	−0.311999
$335$	11.8507	0.647474
$336$	−37.3221	−2.03609
$337$	10.7310	0.584554	0.292277	−	0.956334i	$-0.405587\pi$
$337$	10.7310	0.584554	0.292277	+	0.956334i	$0.405587\pi$
$338$	2.81136	0.152918
$339$	−57.7779	−3.13807
$340$	−12.1464	−0.658730
$341$	0	0
$342$	−1.40340	−0.0758870
$343$	7.62797	0.411872
$344$	8.15650	0.439769
$345$	38.7850	2.08811
$346$	−0.0971714	−0.00522396
$347$	−21.3287	−1.14499	−0.572493	−	0.819910i	$-0.694024\pi$
$347$	−21.3287	−1.14499	−0.572493	+	0.819910i	$0.694024\pi$
$348$	1.78381	0.0956224
$349$	10.5088	0.562524	0.281262	−	0.959631i	$-0.409247\pi$
$349$	10.5088	0.562524	0.281262	+	0.959631i	$0.409247\pi$
$350$	−6.74109	−0.360327
$351$	42.0192	2.24282
$352$	0	0
$353$	2.14407	0.114117	0.0570585	−	0.998371i	$-0.481828\pi$
$353$	2.14407	0.114117	0.0570585	+	0.998371i	$0.481828\pi$
$354$	−2.36532	−0.125715
$355$	−13.4967	−0.716330
$356$	−5.83702	−0.309361
$357$	−17.5801	−0.930437
$358$	−1.51140	−0.0798799
$359$	−1.09058	−0.0575587	−0.0287794	−	0.999586i	$-0.509162\pi$
$359$	−1.09058	−0.0575587	−0.0287794	+	0.999586i	$0.509162\pi$
$360$	−20.0844	−1.05854
$361$	1.00000	0.0526316
$362$	−4.34766	−0.228508
$363$	0	0
$364$	33.1308	1.73652
$365$	39.0813	2.04561
$366$	−1.83371	−0.0958495
$367$	4.62671	0.241512	0.120756	−	0.992682i	$-0.461468\pi$
$367$	4.62671	0.241512	0.120756	+	0.992682i	$0.461468\pi$
$368$	13.1397	0.684955
$369$	33.7716	1.75808
$370$	−4.00271	−0.208091
$371$	8.31041	0.431455
$372$	28.3659	1.47070
$373$	−23.9884	−1.24207	−0.621036	−	0.783782i	$-0.713288\pi$
$373$	−23.9884	−1.24207	−0.621036	+	0.783782i	$0.713288\pi$
$374$	0	0
$375$	34.3084	1.77168
$376$	−7.45243	−0.384330
$377$	−1.53506	−0.0790594
$378$	−6.96839	−0.358415
$379$	17.2638	0.886780	0.443390	−	0.896329i	$-0.353776\pi$
$379$	17.2638	0.886780	0.443390	+	0.896329i	$0.353776\pi$
$380$	7.05092	0.361705
$381$	33.6231	1.72256
$382$	−6.10309	−0.312261
$383$	−26.6417	−1.36133	−0.680664	−	0.732596i	$-0.738309\pi$
$383$	−26.6417	−1.36133	−0.680664	+	0.732596i	$0.738309\pi$
$384$	−21.2361	−1.08370
$385$	0	0
$386$	−1.79407	−0.0913156
$387$	−50.3302	−2.55843
$388$	−9.65351	−0.490083
$389$	19.8483	1.00635	0.503175	−	0.864184i	$-0.332165\pi$
$389$	19.8483	1.00635	0.503175	+	0.864184i	$0.332165\pi$
$390$	12.8875	0.652582
$391$	6.18928	0.313005
$392$	−4.52359	−0.228476
$393$	−56.4493	−2.84749
$394$	1.01344	0.0510565
$395$	38.8820	1.95637
$396$	0	0
$397$	6.95940	0.349282	0.174641	−	0.984632i	$-0.444123\pi$
$397$	6.95940	0.349282	0.174641	+	0.984632i	$0.444123\pi$
$398$	6.37708	0.319654
$399$	10.2052	0.510897
$400$	29.9090	1.49545
$401$	2.64600	0.132135	0.0660675	−	0.997815i	$-0.478955\pi$
$401$	2.64600	0.132135	0.0660675	+	0.997815i	$0.478955\pi$
$402$	2.33167	0.116293
$403$	−24.4102	−1.21596
$404$	0.528110	0.0262745
$405$	27.6282	1.37286
$406$	0.254571	0.0126341
$407$	0	0
$408$	−4.85067	−0.240144
$409$	28.1956	1.39418	0.697091	−	0.716982i	$-0.254477\pi$
$409$	28.1956	1.39418	0.697091	+	0.716982i	$0.254477\pi$
$410$	5.03969	0.248893
$411$	−11.5885	−0.571620
$412$	−27.5441	−1.35700
$413$	11.3648	0.559225
$414$	5.04219	0.247810
$415$	23.6304	1.15997
$416$	13.7790	0.675569
$417$	−34.2571	−1.67758
$418$	0	0
$419$	−16.7829	−0.819897	−0.409948	−	0.912109i	$-0.634453\pi$
$419$	−16.7829	−0.819897	−0.409948	+	0.912109i	$0.634453\pi$
$420$	71.9557	3.51108
$421$	−19.1258	−0.932134	−0.466067	−	0.884749i	$-0.654330\pi$
$421$	−19.1258	−0.932134	−0.466067	+	0.884749i	$0.654330\pi$
$422$	2.97929	0.145029
$423$	45.9857	2.23590
$424$	2.29300	0.111358
$425$	14.0882	0.683380
$426$	−2.65552	−0.128660
$427$	8.81055	0.426372
$428$	−21.1160	−1.02068
$429$	0	0
$430$	−7.51070	−0.362198
$431$	11.8864	0.572546	0.286273	−	0.958148i	$-0.407584\pi$
$431$	11.8864	0.572546	0.286273	+	0.958148i	$0.407584\pi$
$432$	30.9175	1.48752
$433$	10.6232	0.510520	0.255260	−	0.966872i	$-0.417839\pi$
$433$	10.6232	0.510520	0.255260	+	0.966872i	$0.417839\pi$
$434$	4.04814	0.194317
$435$	−3.33394	−0.159850
$436$	−9.13286	−0.437384
$437$	−3.59285	−0.171869
$438$	7.68938	0.367413
$439$	9.64647	0.460401	0.230200	−	0.973143i	$-0.426062\pi$
$439$	9.64647	0.460401	0.230200	+	0.973143i	$0.426062\pi$
$440$	0	0
$441$	27.9131	1.32919
$442$	2.05657	0.0978212
$443$	−4.24791	−0.201824	−0.100912	−	0.994895i	$-0.532176\pi$
$443$	−4.24791	−0.201824	−0.100912	+	0.994895i	$0.532176\pi$
$444$	26.5149	1.25834
$445$	10.9094	0.517154
$446$	−0.920666	−0.0435948
$447$	−4.19456	−0.198396
$448$	22.8164	1.07797
$449$	34.2906	1.61827	0.809137	−	0.587620i	$-0.199935\pi$
$449$	34.2906	1.61827	0.809137	+	0.587620i	$0.199935\pi$
$450$	11.4772	0.541040
$451$	0	0
$452$	37.7384	1.77506
$453$	−56.3701	−2.64850
$454$	−1.65940	−0.0778793
$455$	−61.9213	−2.90292
$456$	2.81579	0.131861
$457$	3.59698	0.168259	0.0841297	−	0.996455i	$-0.473189\pi$
$457$	3.59698	0.168259	0.0841297	+	0.996455i	$0.473189\pi$
$458$	3.60551	0.168474
$459$	14.5633	0.679755
$460$	−25.3329	−1.18115
$461$	21.9653	1.02302	0.511512	−	0.859276i	$-0.329085\pi$
$461$	21.9653	1.02302	0.511512	+	0.859276i	$0.329085\pi$
$462$	0	0
$463$	−20.4818	−0.951869	−0.475935	−	0.879481i	$-0.657890\pi$
$463$	−20.4818	−0.951869	−0.475935	+	0.879481i	$0.657890\pi$
$464$	−1.12948	−0.0524350
$465$	−53.0158	−2.45855
$466$	−3.43326	−0.159043
$467$	29.2181	1.35205	0.676026	−	0.736878i	$-0.263701\pi$
$467$	29.2181	1.35205	0.676026	+	0.736878i	$0.263701\pi$
$468$	−56.4075	−2.60744
$469$	−11.2031	−0.517313
$470$	6.86238	0.316538
$471$	−6.81384	−0.313965
$472$	3.13576	0.144335
$473$	0	0
$474$	7.65017	0.351384
$475$	−8.17816	−0.375240
$476$	11.4827	0.526306
$477$	−14.1491	−0.647842
$478$	−4.44273	−0.203206
$479$	5.70128	0.260498	0.130249	−	0.991481i	$-0.458422\pi$
$479$	5.70128	0.260498	0.130249	+	0.991481i	$0.458422\pi$
$480$	29.9261	1.36593
$481$	−22.8173	−1.04038
$482$	−4.79673	−0.218485
$483$	−36.6656	−1.66834
$484$	0	0
$485$	18.0424	0.819263
$486$	−0.655653	−0.0297410
$487$	−11.3528	−0.514442	−0.257221	−	0.966353i	$-0.582807\pi$
$487$	−11.3528	−0.514442	−0.257221	+	0.966353i	$0.582807\pi$
$488$	2.43099	0.110046
$489$	−29.7046	−1.34329
$490$	4.16543	0.188175
$491$	−8.17015	−0.368714	−0.184357	−	0.982859i	$-0.559020\pi$
$491$	−8.17015	−0.368714	−0.184357	+	0.982859i	$0.559020\pi$
$492$	−33.3841	−1.50507
$493$	−0.532029	−0.0239614
$494$	−1.19383	−0.0537130
$495$	0	0
$496$	−17.9609	−0.806468
$497$	12.7592	0.572327
$498$	4.64936	0.208343
$499$	−2.00327	−0.0896787	−0.0448393	−	0.998994i	$-0.514278\pi$
$499$	−2.00327	−0.0896787	−0.0448393	+	0.998994i	$0.514278\pi$
$500$	−22.4090	−1.00216
$501$	−70.5945	−3.15393
$502$	−1.64893	−0.0735954
$503$	−15.2246	−0.678832	−0.339416	−	0.940636i	$-0.610229\pi$
$503$	−15.2246	−0.678832	−0.339416	+	0.940636i	$0.610229\pi$
$504$	18.9869	0.845742
$505$	−0.987037	−0.0439226
$506$	0	0
$507$	34.8065	1.54581
$508$	−21.9613	−0.974376
$509$	31.9971	1.41824	0.709122	−	0.705086i	$-0.249091\pi$
$509$	31.9971	1.41824	0.709122	+	0.705086i	$0.249091\pi$
$510$	4.46661	0.197785
$511$	−36.9457	−1.63438
$512$	17.0644	0.754149
$513$	−8.45391	−0.373249
$514$	1.60254	0.0706848
$515$	51.4798	2.26847
$516$	49.7526	2.19024
$517$	0	0
$518$	3.78398	0.166259
$519$	−1.20305	−0.0528080
$520$	−17.0852	−0.749237
$521$	−14.6982	−0.643939	−0.321969	−	0.946750i	$-0.604345\pi$
$521$	−14.6982	−0.643939	−0.321969	+	0.946750i	$0.604345\pi$
$522$	−0.433425	−0.0189705
$523$	32.0653	1.40212	0.701059	−	0.713104i	$-0.252711\pi$
$523$	32.0653	1.40212	0.701059	+	0.713104i	$0.252711\pi$
$524$	36.8706	1.61070
$525$	−83.4594	−3.64247
$526$	3.63511	0.158498
$527$	−8.46024	−0.368534
$528$	0	0
$529$	−10.0914	−0.438758
$530$	−2.11145	−0.0917154
$531$	−19.3494	−0.839692
$532$	−6.66562	−0.288991
$533$	28.7286	1.24437
$534$	2.14646	0.0928863
$535$	39.4657	1.70625
$536$	−3.09115	−0.133517
$537$	−18.7122	−0.807489
$538$	−2.23783	−0.0964796
$539$	0	0
$540$	−59.6078	−2.56511
$541$	24.8298	1.06752	0.533759	−	0.845637i	$-0.320779\pi$
$541$	24.8298	1.06752	0.533759	+	0.845637i	$0.320779\pi$
$542$	−4.57020	−0.196307
$543$	−53.8270	−2.30994
$544$	4.77559	0.204752
$545$	17.0693	0.731168
$546$	−12.1832	−0.521394
$547$	43.4659	1.85847	0.929234	−	0.369491i	$-0.120468\pi$
$547$	43.4659	1.85847	0.929234	+	0.369491i	$0.120468\pi$
$548$	7.56919	0.323340
$549$	−15.0006	−0.640210
$550$	0	0
$551$	0.308840	0.0131570
$552$	−10.1167	−0.430596
$553$	−36.7573	−1.56308
$554$	3.59430	0.152707
$555$	−49.5563	−2.10355
$556$	22.3755	0.948931
$557$	−23.8835	−1.01198	−0.505989	−	0.862540i	$-0.668872\pi$
$557$	−23.8835	−1.01198	−0.505989	+	0.862540i	$0.668872\pi$
$558$	−6.89225	−0.291772
$559$	−42.8145	−1.81086
$560$	−45.5614	−1.92532
$561$	0	0
$562$	5.32159	0.224478
$563$	−27.4955	−1.15880	−0.579399	−	0.815044i	$-0.696713\pi$
$563$	−27.4955	−1.15880	−0.579399	+	0.815044i	$0.696713\pi$
$564$	−45.4580	−1.91413
$565$	−70.5330	−2.96734
$566$	−5.23794	−0.220167
$567$	−26.1185	−1.09687
$568$	3.52049	0.147716
$569$	−41.2077	−1.72752	−0.863758	−	0.503906i	$-0.831896\pi$
$569$	−41.2077	−1.72752	−0.863758	+	0.503906i	$0.831896\pi$
$570$	−2.59285	−0.108602
$571$	41.3615	1.73093	0.865463	−	0.500973i	$-0.167024\pi$
$571$	41.3615	1.73093	0.865463	+	0.500973i	$0.167024\pi$
$572$	0	0
$573$	−75.5604	−3.15658
$574$	−4.76430	−0.198858
$575$	29.3829	1.22535
$576$	−38.8466	−1.61861
$577$	24.6836	1.02759	0.513796	−	0.857912i	$-0.328239\pi$
$577$	24.6836	1.02759	0.513796	+	0.857912i	$0.328239\pi$
$578$	−3.37043	−0.140191
$579$	−22.2118	−0.923091
$580$	2.17761	0.0904202
$581$	−22.3391	−0.926783
$582$	3.54990	0.147148
$583$	0	0
$584$	−10.1940	−0.421831
$585$	105.426	4.35881
$586$	2.53963	0.104911
$587$	−31.1927	−1.28746	−0.643731	−	0.765252i	$-0.722614\pi$
$587$	−31.1927	−1.28746	−0.643731	+	0.765252i	$0.722614\pi$
$588$	−27.5928	−1.13791
$589$	4.91113	0.202359
$590$	−2.88748	−0.118876
$591$	12.5471	0.516120
$592$	−16.7889	−0.690018
$593$	42.4308	1.74243	0.871213	−	0.490906i	$-0.163334\pi$
$593$	42.4308	1.74243	0.871213	+	0.490906i	$0.163334\pi$
$594$	0	0
$595$	−21.4611	−0.879818
$596$	2.73973	0.112224
$597$	78.9527	3.23132
$598$	4.28925	0.175401
$599$	22.8996	0.935651	0.467826	−	0.883821i	$-0.345038\pi$
$599$	22.8996	0.935651	0.467826	+	0.883821i	$0.345038\pi$
$600$	−23.0280	−0.940114
$601$	−34.4330	−1.40455	−0.702276	−	0.711905i	$-0.747833\pi$
$601$	−34.4330	−1.40455	−0.702276	+	0.711905i	$0.747833\pi$
$602$	7.10028	0.289386
$603$	19.0742	0.776760
$604$	36.8188	1.49814
$605$	0	0
$606$	−0.194203	−0.00788895
$607$	−18.2757	−0.741790	−0.370895	−	0.928675i	$-0.620949\pi$
$607$	−18.2757	−0.741790	−0.370895	+	0.928675i	$0.620949\pi$
$608$	−2.77221	−0.112428
$609$	3.15176	0.127716
$610$	−2.23852	−0.0906349
$611$	39.1188	1.58258
$612$	−19.5500	−0.790264
$613$	29.8748	1.20663	0.603316	−	0.797502i	$-0.293846\pi$
$613$	29.8748	1.20663	0.603316	+	0.797502i	$0.293846\pi$
$614$	−4.93205	−0.199041
$615$	62.3949	2.51600
$616$	0	0
$617$	−25.6808	−1.03387	−0.516936	−	0.856024i	$-0.672927\pi$
$617$	−25.6808	−1.03387	−0.516936	+	0.856024i	$0.672927\pi$
$618$	10.1288	0.407441
$619$	6.98676	0.280821	0.140411	−	0.990093i	$-0.455158\pi$
$619$	6.98676	0.280821	0.140411	+	0.990093i	$0.455158\pi$
$620$	34.6280	1.39069
$621$	30.3736	1.21885
$622$	−6.66465	−0.267228
$623$	−10.3132	−0.413191
$624$	54.0548	2.16393
$625$	0.991511	0.0396604
$626$	−1.17483	−0.0469557
$627$	0	0
$628$	4.45054	0.177596
$629$	−7.90816	−0.315319
$630$	−17.4836	−0.696562
$631$	−32.1719	−1.28074	−0.640372	−	0.768065i	$-0.721220\pi$
$631$	−32.1719	−1.28074	−0.640372	+	0.768065i	$0.721220\pi$
$632$	−10.1420	−0.403428
$633$	36.8856	1.46607
$634$	2.15623	0.0856349
$635$	41.0457	1.62885
$636$	13.9867	0.554610
$637$	23.7449	0.940807
$638$	0	0
$639$	−21.7234	−0.859365
$640$	−25.9242	−1.02474
$641$	−19.8122	−0.782535	−0.391267	−	0.920277i	$-0.627963\pi$
$641$	−19.8122	−0.782535	−0.391267	+	0.920277i	$0.627963\pi$
$642$	7.76501	0.306460
$643$	−20.8075	−0.820568	−0.410284	−	0.911958i	$-0.634570\pi$
$643$	−20.8075	−0.820568	−0.410284	+	0.911958i	$0.634570\pi$
$644$	23.9486	0.943706
$645$	−92.9876	−3.66138
$646$	−0.413765	−0.0162794
$647$	6.56353	0.258039	0.129020	−	0.991642i	$-0.458817\pi$
$647$	6.56353	0.258039	0.129020	+	0.991642i	$0.458817\pi$
$648$	−7.20657	−0.283101
$649$	0	0
$650$	9.76334	0.382950
$651$	50.1188	1.96431
$652$	19.4019	0.759837
$653$	33.4534	1.30913	0.654565	−	0.756005i	$-0.272852\pi$
$653$	33.4534	1.30913	0.654565	+	0.756005i	$0.272852\pi$
$654$	3.35844	0.131325
$655$	−68.9110	−2.69258
$656$	21.1384	0.825314
$657$	62.9028	2.45407
$658$	−6.48738	−0.252905
$659$	−42.8961	−1.67100	−0.835498	−	0.549494i	$-0.814821\pi$
$659$	−42.8961	−1.67100	−0.835498	+	0.549494i	$0.814821\pi$
$660$	0	0
$661$	8.63980	0.336049	0.168025	−	0.985783i	$-0.446261\pi$
$661$	8.63980	0.336049	0.168025	+	0.985783i	$0.446261\pi$
$662$	−4.71114	−0.183104
$663$	25.4618	0.988854
$664$	−6.16377	−0.239201
$665$	12.4580	0.483102
$666$	−6.44250	−0.249642
$667$	−1.10962	−0.0429645
$668$	46.1097	1.78404
$669$	−11.3985	−0.440691
$670$	2.84641	0.109966
$671$	0	0
$672$	−28.2908	−1.09134
$673$	−16.3368	−0.629737	−0.314868	−	0.949135i	$-0.601960\pi$
$673$	−16.3368	−0.629737	−0.314868	+	0.949135i	$0.601960\pi$
$674$	2.57746	0.0992801
$675$	69.1374	2.66110
$676$	−22.7343	−0.874397
$677$	−36.7155	−1.41109	−0.705545	−	0.708665i	$-0.749298\pi$
$677$	−36.7155	−1.41109	−0.705545	+	0.708665i	$0.749298\pi$
$678$	−13.8776	−0.532966
$679$	−17.0565	−0.654567
$680$	−5.92150	−0.227079
$681$	−20.5445	−0.787265
$682$	0	0
$683$	−1.53856	−0.0588715	−0.0294357	−	0.999567i	$-0.509371\pi$
$683$	−1.53856	−0.0588715	−0.0294357	+	0.999567i	$0.509371\pi$
$684$	11.3487	0.433929
$685$	−14.1468	−0.540521
$686$	1.83215	0.0699519
$687$	44.6387	1.70307
$688$	−31.5027	−1.20103
$689$	−12.0362	−0.458544
$690$	9.31571	0.354643
$691$	33.0915	1.25886	0.629429	−	0.777058i	$-0.283289\pi$
$691$	33.0915	1.25886	0.629429	+	0.777058i	$0.283289\pi$
$692$	0.785786	0.0298711
$693$	0	0
$694$	−5.12291	−0.194463
$695$	−41.8197	−1.58631
$696$	0.869629	0.0329632
$697$	9.95693	0.377146
$698$	2.52410	0.0955385
$699$	−42.5062	−1.60773
$700$	54.5125	2.06038
$701$	20.2466	0.764703	0.382352	−	0.924017i	$-0.375114\pi$
$701$	20.2466	0.764703	0.382352	+	0.924017i	$0.375114\pi$
$702$	10.0925	0.380918
$703$	4.59065	0.173140
$704$	0	0
$705$	84.9610	3.19982
$706$	0.514980	0.0193815
$707$	0.933101	0.0350929
$708$	19.1274	0.718850
$709$	−33.2528	−1.24883	−0.624417	−	0.781091i	$-0.714663\pi$
$709$	−33.2528	−1.24883	−0.624417	+	0.781091i	$0.714663\pi$
$710$	−3.24175	−0.121661
$711$	62.5820	2.34701
$712$	−2.84561	−0.106644
$713$	−17.6449	−0.660808
$714$	−4.22254	−0.158024
$715$	0	0
$716$	12.2221	0.456760
$717$	−55.0040	−2.05416
$718$	−0.261945	−0.00977572
$719$	15.0721	0.562095	0.281047	−	0.959694i	$-0.409318\pi$
$719$	15.0721	0.562095	0.281047	+	0.959694i	$0.409318\pi$
$720$	77.5715	2.89092
$721$	−48.6667	−1.81244
$722$	0.240189	0.00893889
$723$	−59.3868	−2.20862
$724$	35.1578	1.30663
$725$	−2.52574	−0.0938037
$726$	0	0
$727$	13.6674	0.506897	0.253448	−	0.967349i	$-0.418435\pi$
$727$	13.6674	0.506897	0.253448	+	0.967349i	$0.418435\pi$
$728$	16.1516	0.598619
$729$	−30.9496	−1.14628
$730$	9.38689	0.347424
$731$	−14.8389	−0.548837
$732$	14.8285	0.548076
$733$	15.7494	0.581716	0.290858	−	0.956766i	$-0.406059\pi$
$733$	15.7494	0.581716	0.290858	+	0.956766i	$0.406059\pi$
$734$	1.11128	0.0410182
$735$	51.5709	1.90222
$736$	9.96013	0.367135
$737$	0	0
$738$	8.11156	0.298591
$739$	19.6813	0.723990	0.361995	−	0.932180i	$-0.382096\pi$
$739$	19.6813	0.723990	0.361995	+	0.932180i	$0.382096\pi$
$740$	32.3683	1.18988
$741$	−14.7805	−0.542973
$742$	1.99607	0.0732779
$743$	1.84817	0.0678027	0.0339014	−	0.999425i	$-0.489207\pi$
$743$	1.84817	0.0678027	0.0339014	+	0.999425i	$0.489207\pi$
$744$	13.8287	0.506985
$745$	−5.12055	−0.187603
$746$	−5.76174	−0.210952
$747$	38.0340	1.39159
$748$	0	0
$749$	−37.3091	−1.36324
$750$	8.24049	0.300900
$751$	−16.0299	−0.584940	−0.292470	−	0.956275i	$-0.594477\pi$
$751$	−16.0299	−0.584940	−0.292470	+	0.956275i	$0.594477\pi$
$752$	28.7834	1.04962
$753$	−20.4149	−0.743960
$754$	−0.368703	−0.0134274
$755$	−68.8143	−2.50441
$756$	56.3506	2.04945
$757$	−35.0946	−1.27553	−0.637767	−	0.770230i	$-0.720142\pi$
$757$	−35.0946	−1.27553	−0.637767	+	0.770230i	$0.720142\pi$
$758$	4.14656	0.150610
$759$	0	0
$760$	3.43740	0.124688
$761$	−3.05654	−0.110800	−0.0553998	−	0.998464i	$-0.517643\pi$
$761$	−3.05654	−0.110800	−0.0553998	+	0.998464i	$0.517643\pi$
$762$	8.07588	0.292558
$763$	−16.1365	−0.584182
$764$	49.3532	1.78554
$765$	36.5390	1.32107
$766$	−6.39904	−0.231207
$767$	−16.4600	−0.594337
$768$	34.4407	1.24277
$769$	13.1419	0.473908	0.236954	−	0.971521i	$-0.423851\pi$
$769$	13.1419	0.473908	0.236954	+	0.971521i	$0.423851\pi$
$770$	0	0
$771$	19.8405	0.714538
$772$	14.5079	0.522151
$773$	54.9244	1.97549	0.987747	−	0.156064i	$-0.0498807\pi$
$773$	54.9244	1.97549	0.987747	+	0.156064i	$0.0498807\pi$
$774$	−12.0887	−0.434521
$775$	−40.1640	−1.44273
$776$	−4.70620	−0.168943
$777$	46.8483	1.68067
$778$	4.76735	0.170918
$779$	−5.77995	−0.207088
$780$	−104.216	−3.73152
$781$	0	0
$782$	1.48659	0.0531605
$783$	−2.61091	−0.0933061
$784$	17.4714	0.623977
$785$	−8.31806	−0.296884
$786$	−13.5585	−0.483615
$787$	−16.6210	−0.592476	−0.296238	−	0.955114i	$-0.595732\pi$
$787$	−16.6210	−0.592476	−0.296238	+	0.955114i	$0.595732\pi$
$788$	−8.19531	−0.291946
$789$	45.0051	1.60222
$790$	9.33902	0.332267
$791$	66.6787	2.37082
$792$	0	0
$793$	−12.7606	−0.453142
$794$	1.67157	0.0593218
$795$	−26.1412	−0.927131
$796$	−51.5689	−1.82781
$797$	−20.4679	−0.725010	−0.362505	−	0.931982i	$-0.618078\pi$
$797$	−20.4679	−0.725010	−0.362505	+	0.931982i	$0.618078\pi$
$798$	2.45116	0.0867702
$799$	13.5580	0.479648
$800$	22.6716	0.801561
$801$	17.5590	0.620418
$802$	0.635539	0.0224417
$803$	0	0
$804$	−18.8553	−0.664974
$805$	−44.7598	−1.57758
$806$	−5.86306	−0.206517
$807$	−27.7058	−0.975292
$808$	0.257460	0.00905740
$809$	6.61853	0.232695	0.116348	−	0.993209i	$-0.462881\pi$
$809$	6.61853	0.232695	0.116348	+	0.993209i	$0.462881\pi$
$810$	6.63598	0.233165
$811$	10.5181	0.369339	0.184670	−	0.982801i	$-0.440878\pi$
$811$	10.5181	0.369339	0.184670	+	0.982801i	$0.440878\pi$
$812$	−2.05861	−0.0722431
$813$	−56.5822	−1.98442
$814$	0	0
$815$	−36.2621	−1.27021
$816$	18.7346	0.655844
$817$	8.61391	0.301363
$818$	6.77226	0.236787
$819$	−99.6646	−3.48256
$820$	−40.7540	−1.42319
$821$	6.43861	0.224709	0.112355	−	0.993668i	$-0.464161\pi$
$821$	6.43861	0.224709	0.112355	+	0.993668i	$0.464161\pi$
$822$	−2.78343	−0.0970833
$823$	47.3409	1.65020	0.825100	−	0.564987i	$-0.191119\pi$
$823$	47.3409	1.65020	0.825100	+	0.564987i	$0.191119\pi$
$824$	−13.4280	−0.467788
$825$	0	0
$826$	2.72970	0.0949783
$827$	4.22212	0.146818	0.0734088	−	0.997302i	$-0.476612\pi$
$827$	4.22212	0.146818	0.0734088	+	0.997302i	$0.476612\pi$
$828$	−40.7742	−1.41700
$829$	−9.02949	−0.313607	−0.156804	−	0.987630i	$-0.550119\pi$
$829$	−9.02949	−0.313607	−0.156804	+	0.987630i	$0.550119\pi$
$830$	5.67575	0.197008
$831$	44.4999	1.54369
$832$	−33.0457	−1.14565
$833$	8.22965	0.285140
$834$	−8.22816	−0.284918
$835$	−86.1789	−2.98234
$836$	0	0
$837$	−41.5182	−1.43508
$838$	−4.03105	−0.139250
$839$	42.8767	1.48027	0.740135	−	0.672459i	$-0.234762\pi$
$839$	42.8767	1.48027	0.740135	+	0.672459i	$0.234762\pi$
$840$	35.0792	1.21035
$841$	−28.9046	−0.996711
$842$	−4.59380	−0.158313
$843$	65.8849	2.26920
$844$	−24.0923	−0.829292
$845$	42.4904	1.46171
$846$	11.0452	0.379743
$847$	0	0
$848$	−8.85620	−0.304123
$849$	−64.8492	−2.22562
$850$	3.38384	0.116065
$851$	−16.4935	−0.565390
$852$	21.4741	0.735692
$853$	44.2253	1.51424	0.757122	−	0.653273i	$-0.226605\pi$
$853$	44.2253	1.51424	0.757122	+	0.653273i	$0.226605\pi$
$854$	2.11619	0.0724146
$855$	−21.2107	−0.725391
$856$	−10.2943	−0.351851
$857$	51.4914	1.75891	0.879456	−	0.475980i	$-0.157907\pi$
$857$	51.4914	1.75891	0.879456	+	0.475980i	$0.157907\pi$
$858$	0	0
$859$	−29.3415	−1.00112	−0.500559	−	0.865702i	$-0.666872\pi$
$859$	−29.3415	−1.00112	−0.500559	+	0.865702i	$0.666872\pi$
$860$	60.7360	2.07108
$861$	−58.9853	−2.01021
$862$	2.85497	0.0972406
$863$	−15.3482	−0.522460	−0.261230	−	0.965277i	$-0.584128\pi$
$863$	−15.3482	−0.522460	−0.261230	+	0.965277i	$0.584128\pi$
$864$	23.4360	0.797309
$865$	−1.46863	−0.0499350
$866$	2.55158	0.0867061
$867$	−41.7282	−1.41716
$868$	−32.7357	−1.11112
$869$	0	0
$870$	−0.800775	−0.0271488
$871$	16.2259	0.549793
$872$	−4.45237	−0.150776
$873$	29.0399	0.982851
$874$	−0.862961	−0.0291901
$875$	−39.5937	−1.33851
$876$	−62.1809	−2.10090
$877$	−37.1658	−1.25500	−0.627499	−	0.778617i	$-0.715921\pi$
$877$	−37.1658	−1.25500	−0.627499	+	0.778617i	$0.715921\pi$
$878$	2.31697	0.0781940
$879$	31.4424	1.06053
$880$	0	0
$881$	−28.2259	−0.950954	−0.475477	−	0.879728i	$-0.657724\pi$
$881$	−28.2259	−0.950954	−0.475477	+	0.879728i	$0.657724\pi$
$882$	6.70440	0.225749
$883$	21.5975	0.726815	0.363407	−	0.931630i	$-0.381613\pi$
$883$	21.5975	0.726815	0.363407	+	0.931630i	$0.381613\pi$
$884$	−16.6307	−0.559351
$885$	−35.7490	−1.20169
$886$	−1.02030	−0.0342776
$887$	−2.22420	−0.0746813	−0.0373406	−	0.999303i	$-0.511889\pi$
$887$	−2.22420	−0.0746813	−0.0373406	+	0.999303i	$0.511889\pi$
$888$	12.9263	0.433779
$889$	−38.8027	−1.30140
$890$	2.62031	0.0878330
$891$	0	0
$892$	7.44506	0.249279
$893$	−7.87037	−0.263372
$894$	−1.00749	−0.0336954
$895$	−22.8430	−0.763559
$896$	24.5076	0.818741
$897$	53.1039	1.77309
$898$	8.23622	0.274846
$899$	1.51675	0.0505865
$900$	−92.8115	−3.09372
$901$	−4.17159	−0.138976
$902$	0	0
$903$	87.9063	2.92534
$904$	18.3979	0.611905
$905$	−65.7098	−2.18427
$906$	−13.5395	−0.449818
$907$	38.3223	1.27247	0.636236	−	0.771494i	$-0.280490\pi$
$907$	38.3223	1.27247	0.636236	+	0.771494i	$0.280490\pi$
$908$	13.4189	0.445321
$909$	−1.58867	−0.0526929
$910$	−14.8728	−0.493028
$911$	53.4070	1.76945	0.884726	−	0.466112i	$-0.154345\pi$
$911$	53.4070	1.76945	0.884726	+	0.466112i	$0.154345\pi$
$912$	−10.8754	−0.360120
$913$	0	0
$914$	0.863953	0.0285770
$915$	−27.7144	−0.916209
$916$	−29.1563	−0.963352
$917$	65.1454	2.15129
$918$	3.49793	0.115449
$919$	−0.0601538	−0.00198429	−0.000992145	−	1.00000i	$-0.500316\pi$
$919$	−0.0601538	−0.00198429	−0.000992145		1.00000i	$0.500316\pi$
$920$	−12.3501	−0.407170
$921$	−61.0621	−2.01207
$922$	5.27581	0.173749
$923$	−18.4795	−0.608261
$924$	0	0
$925$	−37.5431	−1.23441
$926$	−4.91949	−0.161665
$927$	82.8586	2.72143
$928$	−0.856169	−0.0281051
$929$	45.5718	1.49516	0.747581	−	0.664170i	$-0.231215\pi$
$929$	45.5718	1.49516	0.747581	+	0.664170i	$0.231215\pi$
$930$	−12.7338	−0.417558
$931$	−4.77727	−0.156569
$932$	27.7634	0.909422
$933$	−82.5129	−2.70135
$934$	7.01785	0.229631
$935$	0	0
$936$	−27.4993	−0.898843
$937$	−30.8138	−1.00664	−0.503321	−	0.864099i	$-0.667889\pi$
$937$	−30.8138	−1.00664	−0.503321	+	0.864099i	$0.667889\pi$
$938$	−2.69087	−0.0878599
$939$	−14.5452	−0.474666
$940$	−55.4933	−1.80999
$941$	−16.5597	−0.539829	−0.269915	−	0.962884i	$-0.586996\pi$
$941$	−16.5597	−0.539829	−0.269915	+	0.962884i	$0.586996\pi$
$942$	−1.63661	−0.0533235
$943$	20.7665	0.676250
$944$	−12.1112	−0.394185
$945$	−105.319	−3.42603
$946$	0	0
$947$	26.1615	0.850136	0.425068	−	0.905161i	$-0.360250\pi$
$947$	26.1615	0.850136	0.425068	+	0.905161i	$0.360250\pi$
$948$	−61.8639	−2.00924
$949$	53.5097	1.73700
$950$	−1.96430	−0.0637303
$951$	26.6956	0.865665
$952$	5.59792	0.181430
$953$	10.1025	0.327252	0.163626	−	0.986522i	$-0.447681\pi$
$953$	10.1025	0.327252	0.163626	+	0.986522i	$0.447681\pi$
$954$	−3.39845	−0.110029
$955$	−92.2411	−2.98485
$956$	35.9266	1.16195
$957$	0	0
$958$	1.36938	0.0442427
$959$	13.3737	0.431861
$960$	−71.7711	−2.31640
$961$	−6.88084	−0.221963
$962$	−5.48046	−0.176697
$963$	63.5214	2.04695
$964$	38.7892	1.24932
$965$	−27.1153	−0.872871
$966$	−8.80665	−0.283349
$967$	15.2328	0.489855	0.244927	−	0.969541i	$-0.421236\pi$
$967$	15.2328	0.489855	0.244927	+	0.969541i	$0.421236\pi$
$968$	0	0
$969$	−5.12270	−0.164565
$970$	4.33358	0.139143
$971$	−12.4024	−0.398012	−0.199006	−	0.979998i	$-0.563771\pi$
$971$	−12.4024	−0.398012	−0.199006	+	0.979998i	$0.563771\pi$
$972$	5.30201	0.170062
$973$	39.5345	1.26742
$974$	−2.72680	−0.0873723
$975$	120.877	3.87116
$976$	−9.38918	−0.300540
$977$	−0.244589	−0.00782509	−0.00391255	−	0.999992i	$-0.501245\pi$
$977$	−0.244589	−0.00782509	−0.00391255	+	0.999992i	$0.501245\pi$
$978$	−7.13470	−0.228142
$979$	0	0
$980$	−33.6842	−1.07600
$981$	27.4736	0.877165
$982$	−1.96238	−0.0626220
$983$	18.7400	0.597712	0.298856	−	0.954298i	$-0.403395\pi$
$983$	18.7400	0.597712	0.298856	+	0.954298i	$0.403395\pi$
$984$	−16.2751	−0.518832
$985$	15.3170	0.488041
$986$	−0.127787	−0.00406957
$987$	−80.3183	−2.55656
$988$	9.65404	0.307136
$989$	−30.9485	−0.984104
$990$	0	0
$991$	5.45323	0.173228	0.0866138	−	0.996242i	$-0.472395\pi$
$991$	5.45323	0.173228	0.0866138	+	0.996242i	$0.472395\pi$
$992$	−13.6147	−0.432266
$993$	−58.3272	−1.85096
$994$	3.06461	0.0972034
$995$	96.3823	3.05552
$996$	−37.5975	−1.19132
$997$	0.725474	0.0229760	0.0114880	−	0.999934i	$-0.496343\pi$
$997$	0.725474	0.0229760	0.0114880	+	0.999934i	$0.496343\pi$
$998$	−0.481163	−0.0152309
$999$	−38.8089	−1.22786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2299.2.a.y.1.11		20
11.7	odd	10		209.2.f.c.115.5	yes	40
11.8	odd	10		209.2.f.c.20.5	✓	40
11.10	odd	2		2299.2.a.x.1.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.f.c.20.5	✓	40	11.8	odd	10
209.2.f.c.115.5	yes	40	11.7	odd	10
2299.2.a.x.1.10		20	11.10	odd	2
2299.2.a.y.1.11		20	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:	\( N \)	\(=\)	\( 2299 = 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2299.a (trivial)

\(f(q)\)	\(=\)	\(q+0.240189 q^{2} +2.97370 q^{3} -1.94231 q^{4} +3.63017 q^{5} +0.714249 q^{6} -3.43180 q^{7} -0.946898 q^{8} +5.84289 q^{9} +0.871926 q^{10} -5.77585 q^{12} +4.97039 q^{13} -0.824280 q^{14} +10.7950 q^{15} +3.65718 q^{16} +1.72267 q^{17} +1.40340 q^{18} -1.00000 q^{19} -7.05092 q^{20} -10.2052 q^{21} +3.59285 q^{23} -2.81579 q^{24} +8.17816 q^{25} +1.19383 q^{26} +8.45391 q^{27} +6.66562 q^{28} -0.308840 q^{29} +2.59285 q^{30} -4.91113 q^{31} +2.77221 q^{32} +0.413765 q^{34} -12.4580 q^{35} -11.3487 q^{36} -4.59065 q^{37} -0.240189 q^{38} +14.7805 q^{39} -3.43740 q^{40} +5.77995 q^{41} -2.45116 q^{42} -8.61391 q^{43} +21.2107 q^{45} +0.862961 q^{46} +7.87037 q^{47} +10.8754 q^{48} +4.77727 q^{49} +1.96430 q^{50} +5.12270 q^{51} -9.65404 q^{52} -2.42159 q^{53} +2.03053 q^{54} +3.24957 q^{56} -2.97370 q^{57} -0.0741798 q^{58} -3.31161 q^{59} -20.9673 q^{60} -2.56732 q^{61} -1.17960 q^{62} -20.0517 q^{63} -6.64852 q^{64} +18.0434 q^{65} +3.26451 q^{67} -3.34595 q^{68} +10.6841 q^{69} -2.99228 q^{70} -3.71792 q^{71} -5.53262 q^{72} +10.7657 q^{73} -1.10262 q^{74} +24.3194 q^{75} +1.94231 q^{76} +3.55010 q^{78} +10.7108 q^{79} +13.2762 q^{80} +7.61072 q^{81} +1.38828 q^{82} +6.50944 q^{83} +19.8216 q^{84} +6.25358 q^{85} -2.06896 q^{86} -0.918398 q^{87} +3.00520 q^{89} +5.09457 q^{90} -17.0574 q^{91} -6.97842 q^{92} -14.6042 q^{93} +1.89037 q^{94} -3.63017 q^{95} +8.24372 q^{96} +4.97012 q^{97} +1.14745 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 4 q^{3} + 21 q^{4} + 18 q^{5} - 10 q^{6} - 2 q^{7} + 3 q^{8} + 32 q^{9} + 11 q^{10} + 10 q^{12} + q^{13} + 25 q^{14} + 28 q^{15} + 27 q^{16} + 2 q^{17} + 4 q^{18} - 20 q^{19} + 47 q^{20}+ \cdots + 45 q^{98}+O(q^{100}) \) 20 * q + q^2 + 4 * q^3 + 21 * q^4 + 18 * q^5 - 10 * q^6 - 2 * q^7 + 3 * q^8 + 32 * q^9 + 11 * q^10 + 10 * q^12 + q^13 + 25 * q^14 + 28 * q^15 + 27 * q^16 + 2 * q^17 + 4 * q^18 - 20 * q^19 + 47 * q^20 + 11 * q^21 + 8 * q^23 - 36 * q^24 + 36 * q^25 + 8 * q^26 - 2 * q^27 + 28 * q^28 + 17 * q^29 - 10 * q^30 - 9 * q^31 + 2 * q^32 - 19 * q^34 - 20 * q^35 + 17 * q^36 + 29 * q^37 - q^38 + 3 * q^39 + 29 * q^40 + 4 * q^41 - 16 * q^42 + 12 * q^43 + 65 * q^45 - 36 * q^46 + 10 * q^47 + 42 * q^48 + 34 * q^49 + 25 * q^50 - 10 * q^51 - 13 * q^52 + 50 * q^53 - 26 * q^54 + 37 * q^56 - 4 * q^57 + 4 * q^58 + 46 * q^59 - 7 * q^60 + 22 * q^61 - 5 * q^62 - 69 * q^63 + 47 * q^64 + 13 * q^65 + 26 * q^67 - 5 * q^68 + 65 * q^69 + 26 * q^70 + 38 * q^71 + 104 * q^72 - 3 * q^73 - 10 * q^74 + 13 * q^75 - 21 * q^76 - 45 * q^78 + 14 * q^79 + 31 * q^80 + 76 * q^81 - 10 * q^82 + 14 * q^83 - 5 * q^84 + 9 * q^85 + 15 * q^86 + 21 * q^87 + 48 * q^89 - 28 * q^90 + 24 * q^91 + q^92 + 42 * q^93 + 79 * q^94 - 18 * q^95 - 21 * q^96 - 5 * q^97 + 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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