LMFDB - Embedded newform 2299.2.a.n.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2299,2,Mod(1,2299)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$18.3576074247$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.246832.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 6x^{2} + 7x - 2 $ x^5 - 2x^4 - 5x^3 + 6x^2 + 7x - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			1.3
Root			$-1.15351$ 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)

$f(q)$	$=$	$q-0.484093 q^{2} +2.26452 q^{3} -1.76565 q^{4} +0.637602 q^{5} -1.09624 q^{6} -2.66942 q^{7} +1.82293 q^{8} +2.12805 q^{9} +O(q^{10})$	\(q-0.484093 q^{2} +2.26452 q^{3} -1.76565 q^{4} +0.637602 q^{5} -1.09624 q^{6} -2.66942 q^{7} +1.82293 q^{8} +2.12805 q^{9} -0.308658 q^{10} -3.99836 q^{12} +1.20725 q^{13} +1.29225 q^{14} +1.44386 q^{15} +2.64884 q^{16} -0.222022 q^{17} -1.03017 q^{18} +1.00000 q^{19} -1.12578 q^{20} -6.04495 q^{21} -9.48717 q^{23} +4.12805 q^{24} -4.59346 q^{25} -0.584420 q^{26} -1.97454 q^{27} +4.71327 q^{28} -4.94518 q^{29} -0.698963 q^{30} -3.05563 q^{31} -4.92814 q^{32} +0.107479 q^{34} -1.70203 q^{35} -3.75740 q^{36} +7.18015 q^{37} -0.484093 q^{38} +2.73384 q^{39} +1.16230 q^{40} +6.92650 q^{41} +2.92632 q^{42} -1.53538 q^{43} +1.35685 q^{45} +4.59267 q^{46} +5.94581 q^{47} +5.99836 q^{48} +0.125785 q^{49} +2.22366 q^{50} -0.502774 q^{51} -2.13158 q^{52} -9.63879 q^{53} +0.955862 q^{54} -4.86615 q^{56} +2.26452 q^{57} +2.39392 q^{58} +2.65817 q^{59} -2.54936 q^{60} +0.809792 q^{61} +1.47921 q^{62} -5.68066 q^{63} -2.91201 q^{64} +0.769744 q^{65} -2.22447 q^{67} +0.392015 q^{68} -21.4839 q^{69} +0.823938 q^{70} +2.58912 q^{71} +3.87928 q^{72} -16.6108 q^{73} -3.47586 q^{74} -10.4020 q^{75} -1.76565 q^{76} -1.32343 q^{78} -5.69298 q^{79} +1.68891 q^{80} -10.8556 q^{81} -3.35307 q^{82} +2.93784 q^{83} +10.6733 q^{84} -0.141562 q^{85} +0.743267 q^{86} -11.1985 q^{87} -5.54136 q^{89} -0.656841 q^{90} -3.22265 q^{91} +16.7511 q^{92} -6.91954 q^{93} -2.87832 q^{94} +0.637602 q^{95} -11.1599 q^{96} +13.7728 q^{97} -0.0608914 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + q^3 + 6 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 - 6 * q^8 + 4 * q^9	$ 5 q - 2 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} - 6 q^{8} + 4 q^{9} - 12 q^{10} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 3 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} + 5 q^{19} - 8 q^{20} - 10 q^{21} + 3 q^{23} + 14 q^{24} + 6 q^{25} - 6 q^{26} - 11 q^{27} + 10 q^{28} - 10 q^{29} - 6 q^{30} + 11 q^{31} - 14 q^{32} - 4 q^{34} + 8 q^{35} - 26 q^{36} + q^{37} - 2 q^{38} - 2 q^{39} + 16 q^{40} - 2 q^{41} - 16 q^{42} - 20 q^{43} - 28 q^{45} + 4 q^{46} - 20 q^{47} + 4 q^{48} + 3 q^{49} + 32 q^{50} - 24 q^{51} - 6 q^{52} - 14 q^{53} - 16 q^{54} - 38 q^{56} + q^{57} - 6 q^{58} + 3 q^{59} - 40 q^{60} + 10 q^{61} + 6 q^{62} - 24 q^{63} + 9 q^{67} - 24 q^{68} - 5 q^{69} + 50 q^{70} + 23 q^{71} + 12 q^{72} - 8 q^{74} - 18 q^{75} + 6 q^{76} - 22 q^{78} - 44 q^{79} - 18 q^{80} + q^{81} - 30 q^{82} + 14 q^{83} - 14 q^{84} + 12 q^{85} + 52 q^{86} - 28 q^{87} - 27 q^{89} - 26 q^{90} + 24 q^{91} + 58 q^{92} - 27 q^{93} + 8 q^{94} - 5 q^{95} - 50 q^{96} + 15 q^{97} + 10 q^{98}+O(q^{100}) $ 5 * q - 2 * q^2 + q^3 + 6 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 - 6 * q^8 + 4 * q^9 - 12 * q^10 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 3 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 + 5 * q^19 - 8 * q^20 - 10 * q^21 + 3 * q^23 + 14 * q^24 + 6 * q^25 - 6 * q^26 - 11 * q^27 + 10 * q^28 - 10 * q^29 - 6 * q^30 + 11 * q^31 - 14 * q^32 - 4 * q^34 + 8 * q^35 - 26 * q^36 + q^37 - 2 * q^38 - 2 * q^39 + 16 * q^40 - 2 * q^41 - 16 * q^42 - 20 * q^43 - 28 * q^45 + 4 * q^46 - 20 * q^47 + 4 * q^48 + 3 * q^49 + 32 * q^50 - 24 * q^51 - 6 * q^52 - 14 * q^53 - 16 * q^54 - 38 * q^56 + q^57 - 6 * q^58 + 3 * q^59 - 40 * q^60 + 10 * q^61 + 6 * q^62 - 24 * q^63 + 9 * q^67 - 24 * q^68 - 5 * q^69 + 50 * q^70 + 23 * q^71 + 12 * q^72 - 8 * q^74 - 18 * q^75 + 6 * q^76 - 22 * q^78 - 44 * q^79 - 18 * q^80 + q^81 - 30 * q^82 + 14 * q^83 - 14 * q^84 + 12 * q^85 + 52 * q^86 - 28 * q^87 - 27 * q^89 - 26 * q^90 + 24 * q^91 + 58 * q^92 - 27 * q^93 + 8 * q^94 - 5 * q^95 - 50 * q^96 + 15 * q^97 + 10 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.484093	−0.342305	−0.171153	−	0.985245i	$-0.554749\pi$
$2$	−0.484093	−0.342305	−0.171153	+	0.985245i	$0.554749\pi$
$3$	2.26452	1.30742	0.653711	−	0.756745i	$-0.273211\pi$
$3$	2.26452	1.30742	0.653711	+	0.756745i	$0.273211\pi$
$4$	−1.76565	−0.882827
$5$	0.637602	0.285144	0.142572	−	0.989784i	$-0.454463\pi$
$5$	0.637602	0.285144	0.142572	+	0.989784i	$0.454463\pi$
$6$	−1.09624	−0.447537
$7$	−2.66942	−1.00894	−0.504472	−	0.863428i	$-0.668313\pi$
$7$	−2.66942	−1.00894	−0.504472	+	0.863428i	$0.668313\pi$
$8$	1.82293	0.644502
$9$	2.12805	0.709351
$10$	−0.308658	−0.0976064
$11$	0	0
$11$	0	0
$12$	−3.99836	−1.15423
$13$	1.20725	0.334831	0.167415	−	0.985886i	$-0.446458\pi$
$13$	1.20725	0.334831	0.167415	+	0.985886i	$0.446458\pi$
$14$	1.29225	0.345367
$15$	1.44386	0.372804
$16$	2.64884	0.662211
$17$	−0.222022	−0.0538483	−0.0269242	−	0.999637i	$-0.508571\pi$
$17$	−0.222022	−0.0538483	−0.0269242	+	0.999637i	$0.508571\pi$
$18$	−1.03017	−0.242814
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.12578	−0.251733
$21$	−6.04495	−1.31912
$22$	0	0
$23$	−9.48717	−1.97821	−0.989106	−	0.147206i	$-0.952972\pi$
$23$	−9.48717	−1.97821	−0.989106	+	0.147206i	$0.952972\pi$
$24$	4.12805	0.842635
$25$	−4.59346	−0.918693
$26$	−0.584420	−0.114614
$27$	−1.97454	−0.380001
$28$	4.71327	0.890724
$29$	−4.94518	−0.918297	−0.459148	−	0.888360i	$-0.651845\pi$
$29$	−4.94518	−0.918297	−0.459148	+	0.888360i	$0.651845\pi$
$30$	−0.698963	−0.127613
$31$	−3.05563	−0.548808	−0.274404	−	0.961615i	$-0.588480\pi$
$31$	−3.05563	−0.548808	−0.274404	+	0.961615i	$0.588480\pi$
$32$	−4.92814	−0.871180
$33$	0	0
$34$	0.107479	0.0184326
$35$	−1.70203	−0.287695
$36$	−3.75740	−0.626234
$37$	7.18015	1.18041	0.590205	−	0.807254i	$-0.299047\pi$
$37$	7.18015	1.18041	0.590205	+	0.807254i	$0.299047\pi$
$38$	−0.484093	−0.0785302
$39$	2.73384	0.437765
$40$	1.16230	0.183776
$41$	6.92650	1.08174	0.540869	−	0.841107i	$-0.318096\pi$
$41$	6.92650	1.08174	0.540869	+	0.841107i	$0.318096\pi$
$42$	2.92632	0.451540
$43$	−1.53538	−0.234144	−0.117072	−	0.993123i	$-0.537351\pi$
$43$	−1.53538	−0.234144	−0.117072	+	0.993123i	$0.537351\pi$
$44$	0	0
$45$	1.35685	0.202267
$46$	4.59267	0.677152
$47$	5.94581	0.867285	0.433642	−	0.901085i	$-0.357228\pi$
$47$	5.94581	0.867285	0.433642	+	0.901085i	$0.357228\pi$
$48$	5.99836	0.865789
$49$	0.125785	0.0179692
$50$	2.22366	0.314473
$51$	−0.502774	−0.0704024
$52$	−2.13158	−0.295598
$53$	−9.63879	−1.32399	−0.661995	−	0.749509i	$-0.730290\pi$
$53$	−9.63879	−1.32399	−0.661995	+	0.749509i	$0.730290\pi$
$54$	0.955862	0.130076
$55$	0	0
$56$	−4.86615	−0.650266
$57$	2.26452	0.299943
$58$	2.39392	0.314338
$59$	2.65817	0.346065	0.173032	−	0.984916i	$-0.444643\pi$
$59$	2.65817	0.346065	0.173032	+	0.984916i	$0.444643\pi$
$60$	−2.54936	−0.329121
$61$	0.809792	0.103683	0.0518416	−	0.998655i	$-0.483491\pi$
$61$	0.809792	0.103683	0.0518416	+	0.998655i	$0.483491\pi$
$62$	1.47921	0.187860
$63$	−5.68066	−0.715696
$64$	−2.91201	−0.364001
$65$	0.769744	0.0954750
$66$	0	0
$67$	−2.22447	−0.271763	−0.135881	−	0.990725i	$-0.543387\pi$
$67$	−2.22447	−0.271763	−0.135881	+	0.990725i	$0.543387\pi$
$68$	0.392015	0.0475387
$69$	−21.4839	−2.58636
$70$	0.823938	0.0984794
$71$	2.58912	0.307272	0.153636	−	0.988127i	$-0.450902\pi$
$71$	2.58912	0.307272	0.153636	+	0.988127i	$0.450902\pi$
$72$	3.87928	0.457178
$73$	−16.6108	−1.94414	−0.972071	−	0.234687i	$-0.924594\pi$
$73$	−16.6108	−1.94414	−0.972071	+	0.234687i	$0.924594\pi$
$74$	−3.47586	−0.404060
$75$	−10.4020	−1.20112
$76$	−1.76565	−0.202534
$77$	0	0
$78$	−1.32343	−0.149849
$79$	−5.69298	−0.640510	−0.320255	−	0.947331i	$-0.603769\pi$
$79$	−5.69298	−0.640510	−0.320255	+	0.947331i	$0.603769\pi$
$80$	1.68891	0.188826
$81$	−10.8556	−1.20617
$82$	−3.35307	−0.370284
$83$	2.93784	0.322470	0.161235	−	0.986916i	$-0.448452\pi$
$83$	2.93784	0.322470	0.161235	+	0.986916i	$0.448452\pi$
$84$	10.6733	1.16455
$85$	−0.141562	−0.0153545
$86$	0.743267	0.0801486
$87$	−11.1985	−1.20060
$88$	0	0
$89$	−5.54136	−0.587383	−0.293692	−	0.955900i	$-0.594884\pi$
$89$	−5.54136	−0.587383	−0.293692	+	0.955900i	$0.594884\pi$
$90$	−0.656841	−0.0692372
$91$	−3.22265	−0.337826
$92$	16.7511	1.74642
$93$	−6.91954	−0.717523
$94$	−2.87832	−0.296876
$95$	0.637602	0.0654166
$96$	−11.1599	−1.13900
$97$	13.7728	1.39842	0.699209	−	0.714917i	$-0.253536\pi$
$97$	13.7728	1.39842	0.699209	+	0.714917i	$0.253536\pi$
$98$	−0.0608914	−0.00615096
$99$	0	0
$100$	8.11047	0.811047
$101$	−12.0308	−1.19711	−0.598555	−	0.801082i	$-0.704258\pi$
$101$	−12.0308	−1.19711	−0.598555	+	0.801082i	$0.704258\pi$
$102$	0.243389	0.0240991
$103$	8.53068	0.840553	0.420276	−	0.907396i	$-0.361933\pi$
$103$	8.53068	0.840553	0.420276	+	0.907396i	$0.361933\pi$
$104$	2.20073	0.215799
$105$	−3.85427	−0.376138
$106$	4.66607	0.453208
$107$	−1.64585	−0.159110	−0.0795552	−	0.996830i	$-0.525350\pi$
$107$	−1.64585	−0.159110	−0.0795552	+	0.996830i	$0.525350\pi$
$108$	3.48636	0.335475
$109$	−16.8065	−1.60977	−0.804886	−	0.593430i	$-0.797774\pi$
$109$	−16.8065	−1.60977	−0.804886	+	0.593430i	$0.797774\pi$
$110$	0	0
$111$	16.2596	1.54329
$112$	−7.07087	−0.668134
$113$	−11.2947	−1.06252	−0.531258	−	0.847210i	$-0.678280\pi$
$113$	−11.2947	−1.06252	−0.531258	+	0.847210i	$0.678280\pi$
$114$	−1.09624	−0.102672
$115$	−6.04904	−0.564076
$116$	8.73148	0.810697
$117$	2.56909	0.237512
$118$	−1.28680	−0.118460
$119$	0.592670	0.0543300
$120$	2.63205	0.240273
$121$	0	0
$122$	−0.392015	−0.0354913
$123$	15.6852	1.41429
$124$	5.39519	0.484502
$125$	−6.11681	−0.547104
$126$	2.74997	0.244986
$127$	−18.5894	−1.64954	−0.824771	−	0.565467i	$-0.808696\pi$
$127$	−18.5894	−1.64954	−0.824771	+	0.565467i	$0.808696\pi$
$128$	11.2660	0.995779
$129$	−3.47690	−0.306124
$130$	−0.372628	−0.0326816
$131$	3.09098	0.270060	0.135030	−	0.990842i	$-0.456887\pi$
$131$	3.09098	0.270060	0.135030	+	0.990842i	$0.456887\pi$
$132$	0	0
$133$	−2.66942	−0.231468
$134$	1.07685	0.0930257
$135$	−1.25897	−0.108355
$136$	−0.404730	−0.0347053
$137$	−8.67619	−0.741257	−0.370629	−	0.928781i	$-0.620858\pi$
$137$	−8.67619	−0.741257	−0.370629	+	0.928781i	$0.620858\pi$
$138$	10.4002	0.885323
$139$	−14.5426	−1.23348	−0.616742	−	0.787166i	$-0.711548\pi$
$139$	−14.5426	−1.23348	−0.616742	+	0.787166i	$0.711548\pi$
$140$	3.00519	0.253985
$141$	13.4644	1.13391
$142$	−1.25338	−0.105181
$143$	0	0
$144$	5.63688	0.469740
$145$	−3.15306	−0.261847
$146$	8.04115	0.665490
$147$	0.284842	0.0234933
$148$	−12.6777	−1.04210
$149$	18.4716	1.51325	0.756625	−	0.653849i	$-0.226847\pi$
$149$	18.4716	1.51325	0.756625	+	0.653849i	$0.226847\pi$
$150$	5.03553	0.411149
$151$	0.913992	0.0743796	0.0371898	−	0.999308i	$-0.488159\pi$
$151$	0.913992	0.0743796	0.0371898	+	0.999308i	$0.488159\pi$
$152$	1.82293	0.147859
$153$	−0.472475	−0.0381973
$154$	0	0
$155$	−1.94828	−0.156489
$156$	−4.82702	−0.386471
$157$	−2.39421	−0.191079	−0.0955395	−	0.995426i	$-0.530458\pi$
$157$	−2.39421	−0.191079	−0.0955395	+	0.995426i	$0.530458\pi$
$158$	2.75593	0.219250
$159$	−21.8272	−1.73101
$160$	−3.14219	−0.248412
$161$	25.3252	1.99591
$162$	5.25509	0.412879
$163$	14.1986	1.11212	0.556061	−	0.831141i	$-0.312312\pi$
$163$	14.1986	1.11212	0.556061	+	0.831141i	$0.312312\pi$
$164$	−12.2298	−0.954987
$165$	0	0
$166$	−1.42219	−0.110383
$167$	−9.25056	−0.715830	−0.357915	−	0.933754i	$-0.616512\pi$
$167$	−9.25056	−0.715830	−0.357915	+	0.933754i	$0.616512\pi$
$168$	−11.0195	−0.850172
$169$	−11.5426	−0.887888
$170$	0.0685290	0.00525594
$171$	2.12805	0.162736
$172$	2.71095	0.206708
$173$	−5.39376	−0.410080	−0.205040	−	0.978754i	$-0.565732\pi$
$173$	−5.39376	−0.410080	−0.205040	+	0.978754i	$0.565732\pi$
$174$	5.42109	0.410972
$175$	12.2619	0.926910
$176$	0	0
$177$	6.01949	0.452453
$178$	2.68253	0.201064
$179$	1.30720	0.0977048	0.0488524	−	0.998806i	$-0.484444\pi$
$179$	1.30720	0.0977048	0.0488524	+	0.998806i	$0.484444\pi$
$180$	−2.39573	−0.178567
$181$	−10.7624	−0.799961	−0.399980	−	0.916524i	$-0.630983\pi$
$181$	−10.7624	−0.799961	−0.399980	+	0.916524i	$0.630983\pi$
$182$	1.56006	0.115639
$183$	1.83379	0.135558
$184$	−17.2944	−1.27496
$185$	4.57808	0.336587
$186$	3.34970	0.245612
$187$	0	0
$188$	−10.4982	−0.765663
$189$	5.27088	0.383400
$190$	−0.308658	−0.0223924
$191$	15.3041	1.10737	0.553684	−	0.832727i	$-0.313222\pi$
$191$	15.3041	1.10737	0.553684	+	0.832727i	$0.313222\pi$
$192$	−6.59431	−0.475903
$193$	18.3032	1.31749	0.658747	−	0.752364i	$-0.271087\pi$
$193$	18.3032	1.31749	0.658747	+	0.752364i	$0.271087\pi$
$194$	−6.66732	−0.478686
$195$	1.74310	0.124826
$196$	−0.222092	−0.0158637
$197$	0.576171	0.0410505	0.0205252	−	0.999789i	$-0.493466\pi$
$197$	0.576171	0.0410505	0.0205252	+	0.999789i	$0.493466\pi$
$198$	0	0
$199$	−10.1678	−0.720778	−0.360389	−	0.932802i	$-0.617356\pi$
$199$	−10.1678	−0.720778	−0.360389	+	0.932802i	$0.617356\pi$
$200$	−8.37354	−0.592099
$201$	−5.03736	−0.355308
$202$	5.82402	0.409777
$203$	13.2007	0.926510
$204$	0.887725	0.0621532
$205$	4.41635	0.308451
$206$	−4.12964	−0.287726
$207$	−20.1892	−1.40325
$208$	3.19781	0.221728
$209$	0	0
$210$	1.86582	0.128754
$211$	7.25837	0.499687	0.249843	−	0.968286i	$-0.419621\pi$
$211$	7.25837	0.499687	0.249843	+	0.968286i	$0.419621\pi$
$212$	17.0188	1.16885
$213$	5.86312	0.401734
$214$	0.796745	0.0544643
$215$	−0.978963	−0.0667647
$216$	−3.59945	−0.244911
$217$	8.15675	0.553716
$218$	8.13591	0.551033
$219$	−37.6154	−2.54181
$220$	0	0
$221$	−0.268036	−0.0180301
$222$	−7.87115	−0.528277
$223$	16.2772	1.09000	0.545000	−	0.838436i	$-0.316529\pi$
$223$	16.2772	1.09000	0.545000	+	0.838436i	$0.316529\pi$
$224$	13.1553	0.878972
$225$	−9.77513	−0.651675
$226$	5.46768	0.363705
$227$	20.9260	1.38890	0.694452	−	0.719539i	$-0.255647\pi$
$227$	20.9260	1.38890	0.694452	+	0.719539i	$0.255647\pi$
$228$	−3.99836	−0.264798
$229$	−10.8083	−0.714234	−0.357117	−	0.934060i	$-0.616240\pi$
$229$	−10.8083	−0.714234	−0.357117	+	0.934060i	$0.616240\pi$
$230$	2.92830	0.193086
$231$	0	0
$232$	−9.01469	−0.591844
$233$	25.4173	1.66514	0.832570	−	0.553919i	$-0.186868\pi$
$233$	25.4173	1.66514	0.832570	+	0.553919i	$0.186868\pi$
$234$	−1.24368	−0.0813017
$235$	3.79106	0.247301
$236$	−4.69342	−0.305515
$237$	−12.8919	−0.837417
$238$	−0.286907	−0.0185974
$239$	−0.352238	−0.0227844	−0.0113922	−	0.999935i	$-0.503626\pi$
$239$	−0.352238	−0.0227844	−0.0113922	+	0.999935i	$0.503626\pi$
$240$	3.82457	0.246875
$241$	15.6832	1.01024	0.505122	−	0.863048i	$-0.331448\pi$
$241$	15.6832	1.01024	0.505122	+	0.863048i	$0.331448\pi$
$242$	0	0
$243$	−18.6590	−1.19697
$244$	−1.42981	−0.0915344
$245$	0.0802004	0.00512382
$246$	−7.59309	−0.484118
$247$	1.20725	0.0768154
$248$	−5.57019	−0.353707
$249$	6.65281	0.421605
$250$	2.96110	0.187277
$251$	1.16332	0.0734282	0.0367141	−	0.999326i	$-0.488311\pi$
$251$	1.16332	0.0734282	0.0367141	+	0.999326i	$0.488311\pi$
$252$	10.0301	0.631836
$253$	0	0
$254$	8.99899	0.564647
$255$	−0.320570	−0.0200748
$256$	0.370256	0.0231410
$257$	−15.0510	−0.938857	−0.469428	−	0.882971i	$-0.655540\pi$
$257$	−15.0510	−0.938857	−0.469428	+	0.882971i	$0.655540\pi$
$258$	1.68314	0.104788
$259$	−19.1668	−1.19097
$260$	−1.35910	−0.0842879
$261$	−10.5236	−0.651394
$262$	−1.49632	−0.0924429
$263$	20.6609	1.27400	0.637002	−	0.770862i	$-0.280174\pi$
$263$	20.6609	1.27400	0.637002	+	0.770862i	$0.280174\pi$
$264$	0	0
$265$	−6.14571	−0.377528
$266$	1.29225	0.0792326
$267$	−12.5485	−0.767958
$268$	3.92765	0.239919
$269$	−2.82662	−0.172342	−0.0861711	−	0.996280i	$-0.527463\pi$
$269$	−2.82662	−0.172342	−0.0861711	+	0.996280i	$0.527463\pi$
$270$	0.609459	0.0370905
$271$	−23.5970	−1.43341	−0.716707	−	0.697375i	$-0.754351\pi$
$271$	−23.5970	−1.43341	−0.716707	+	0.697375i	$0.754351\pi$
$272$	−0.588102	−0.0356589
$273$	−7.29776	−0.441680
$274$	4.20008	0.253736
$275$	0	0
$276$	37.9331	2.28331
$277$	18.7773	1.12822	0.564110	−	0.825700i	$-0.309219\pi$
$277$	18.7773	1.12822	0.564110	+	0.825700i	$0.309219\pi$
$278$	7.03994	0.422228
$279$	−6.50254	−0.389297
$280$	−3.10267	−0.185420
$281$	−27.2632	−1.62639	−0.813194	−	0.581993i	$-0.802273\pi$
$281$	−27.2632	−1.62639	−0.813194	+	0.581993i	$0.802273\pi$
$282$	−6.51802	−0.388142
$283$	27.2601	1.62044	0.810221	−	0.586124i	$-0.199347\pi$
$283$	27.2601	1.62044	0.810221	+	0.586124i	$0.199347\pi$
$284$	−4.57149	−0.271268
$285$	1.44386	0.0855270
$286$	0	0
$287$	−18.4897	−1.09141
$288$	−10.4873	−0.617972
$289$	−16.9507	−0.997100
$290$	1.52637	0.0896316
$291$	31.1888	1.82832
$292$	29.3289	1.71634
$293$	−30.9996	−1.81101	−0.905507	−	0.424332i	$-0.860509\pi$
$293$	−30.9996	−1.81101	−0.905507	+	0.424332i	$0.860509\pi$
$294$	−0.137890	−0.00804189
$295$	1.69486	0.0986784
$296$	13.0889	0.760776
$297$	0	0
$298$	−8.94195	−0.517993
$299$	−11.4534	−0.662366
$300$	18.3663	1.06038
$301$	4.09858	0.236238
$302$	−0.442457	−0.0254605
$303$	−27.2440	−1.56513
$304$	2.64884	0.151922
$305$	0.516325	0.0295647
$306$	0.228722	0.0130751
$307$	18.2495	1.04156	0.520778	−	0.853692i	$-0.325642\pi$
$307$	18.2495	1.04156	0.520778	+	0.853692i	$0.325642\pi$
$308$	0	0
$309$	19.3179	1.09896
$310$	0.943146	0.0535671
$311$	30.8931	1.75179	0.875894	−	0.482503i	$-0.160272\pi$
$311$	30.8931	1.75179	0.875894	+	0.482503i	$0.160272\pi$
$312$	4.98359	0.282140
$313$	28.7973	1.62772	0.813859	−	0.581062i	$-0.197363\pi$
$313$	28.7973	1.62772	0.813859	+	0.581062i	$0.197363\pi$
$314$	1.15902	0.0654073
$315$	−3.62200	−0.204076
$316$	10.0518	0.565460
$317$	5.96040	0.334769	0.167385	−	0.985892i	$-0.446468\pi$
$317$	5.96040	0.334769	0.167385	+	0.985892i	$0.446468\pi$
$318$	10.5664	0.592534
$319$	0	0
$320$	−1.85670	−0.103793
$321$	−3.72706	−0.208024
$322$	−12.2597	−0.683209
$323$	−0.222022	−0.0123536
$324$	19.1671	1.06484
$325$	−5.54545	−0.307606
$326$	−6.87345	−0.380685
$327$	−38.0587	−2.10465
$328$	12.6265	0.697181
$329$	−15.8718	−0.875043
$330$	0	0
$331$	33.4010	1.83589	0.917944	−	0.396711i	$-0.129849\pi$
$331$	33.4010	1.83589	0.917944	+	0.396711i	$0.129849\pi$
$332$	−5.18722	−0.284686
$333$	15.2797	0.837325
$334$	4.47813	0.245032
$335$	−1.41833	−0.0774915
$336$	−16.0121	−0.873533
$337$	−24.9988	−1.36177	−0.680885	−	0.732390i	$-0.738405\pi$
$337$	−24.9988	−1.36177	−0.680885	+	0.732390i	$0.738405\pi$
$338$	5.58766	0.303929
$339$	−25.5771	−1.38916
$340$	0.249949	0.0135554
$341$	0	0
$342$	−1.03017	−0.0557055
$343$	18.3501	0.990815
$344$	−2.79889	−0.150906
$345$	−13.6982	−0.737485
$346$	2.61108	0.140372
$347$	8.35577	0.448561	0.224281	−	0.974525i	$-0.427997\pi$
$347$	8.35577	0.448561	0.224281	+	0.974525i	$0.427997\pi$
$348$	19.7726	1.05992
$349$	28.3911	1.51974	0.759871	−	0.650074i	$-0.225262\pi$
$349$	28.3911	1.51974	0.759871	+	0.650074i	$0.225262\pi$
$350$	−5.93588	−0.317286
$351$	−2.38377	−0.127236
$352$	0	0
$353$	−12.4082	−0.660423	−0.330212	−	0.943907i	$-0.607120\pi$
$353$	−12.4082	−0.660423	−0.330212	+	0.943907i	$0.607120\pi$
$354$	−2.91399	−0.154877
$355$	1.65083	0.0876169
$356$	9.78413	0.518558
$357$	1.34211	0.0710322
$358$	−0.632806	−0.0334448
$359$	−12.1134	−0.639319	−0.319659	−	0.947533i	$-0.603568\pi$
$359$	−12.1134	−0.639319	−0.319659	+	0.947533i	$0.603568\pi$
$360$	2.47344	0.130362
$361$	1.00000	0.0526316
$362$	5.20999	0.273831
$363$	0	0
$364$	5.69009	0.298242
$365$	−10.5911	−0.554361
$366$	−0.887725	−0.0464021
$367$	−4.06064	−0.211964	−0.105982	−	0.994368i	$-0.533799\pi$
$367$	−4.06064	−0.211964	−0.105982	+	0.994368i	$0.533799\pi$
$368$	−25.1300	−1.30999
$369$	14.7399	0.767331
$370$	−2.21621	−0.115216
$371$	25.7299	1.33583
$372$	12.2175	0.633449
$373$	−35.4898	−1.83759	−0.918796	−	0.394732i	$-0.870837\pi$
$373$	−35.4898	−1.83759	−0.918796	+	0.394732i	$0.870837\pi$
$374$	0	0
$375$	−13.8516	−0.715296
$376$	10.8388	0.558967
$377$	−5.97006	−0.307474
$378$	−2.55159	−0.131240
$379$	13.5584	0.696449	0.348224	−	0.937411i	$-0.386785\pi$
$379$	13.5584	0.696449	0.348224	+	0.937411i	$0.386785\pi$
$380$	−1.12578	−0.0577515
$381$	−42.0961	−2.15665
$382$	−7.40862	−0.379058
$383$	−23.8326	−1.21779	−0.608894	−	0.793251i	$-0.708387\pi$
$383$	−23.8326	−1.21779	−0.608894	+	0.793251i	$0.708387\pi$
$384$	25.5120	1.30190
$385$	0	0
$386$	−8.86045	−0.450985
$387$	−3.26737	−0.166090
$388$	−24.3180	−1.23456
$389$	−12.7567	−0.646789	−0.323395	−	0.946264i	$-0.604824\pi$
$389$	−12.7567	−0.646789	−0.323395	+	0.946264i	$0.604824\pi$
$390$	−0.843823	−0.0427286
$391$	2.10636	0.106523
$392$	0.229296	0.0115812
$393$	6.99958	0.353082
$394$	−0.278920	−0.0140518
$395$	−3.62986	−0.182638
$396$	0	0
$397$	−30.3169	−1.52156	−0.760780	−	0.649009i	$-0.775184\pi$
$397$	−30.3169	−1.52156	−0.760780	+	0.649009i	$0.775184\pi$
$398$	4.92217	0.246726
$399$	−6.04495	−0.302626
$400$	−12.1674	−0.608368
$401$	32.6370	1.62982	0.814908	−	0.579591i	$-0.196788\pi$
$401$	32.6370	1.62982	0.814908	+	0.579591i	$0.196788\pi$
$402$	2.43855	0.121624
$403$	−3.68891	−0.183758
$404$	21.2422	1.05684
$405$	−6.92152	−0.343933
$406$	−6.39038	−0.317149
$407$	0	0
$408$	−0.916520	−0.0453745
$409$	23.1587	1.14512	0.572562	−	0.819862i	$-0.305950\pi$
$409$	23.1587	1.14512	0.572562	+	0.819862i	$0.305950\pi$
$410$	−2.13792	−0.105584
$411$	−19.6474	−0.969135
$412$	−15.0622	−0.742063
$413$	−7.09578	−0.349160
$414$	9.77344	0.480338
$415$	1.87318	0.0919506
$416$	−5.94949	−0.291698
$417$	−32.9319	−1.61268
$418$	0	0
$419$	−14.2213	−0.694755	−0.347377	−	0.937725i	$-0.612928\pi$
$419$	−14.2213	−0.694755	−0.347377	+	0.937725i	$0.612928\pi$
$420$	6.80531	0.332065
$421$	15.9605	0.777866	0.388933	−	0.921266i	$-0.372844\pi$
$421$	15.9605	0.777866	0.388933	+	0.921266i	$0.372844\pi$
$422$	−3.51373	−0.171045
$423$	12.6530	0.615209
$424$	−17.5708	−0.853313
$425$	1.01985	0.0494701
$426$	−2.83829	−0.137516
$427$	−2.16167	−0.104611
$428$	2.90600	0.140467
$429$	0	0
$430$	0.473909	0.0228539
$431$	−24.5100	−1.18061	−0.590304	−	0.807181i	$-0.700992\pi$
$431$	−24.5100	−1.18061	−0.590304	+	0.807181i	$0.700992\pi$
$432$	−5.23026	−0.251641
$433$	−19.1839	−0.921921	−0.460961	−	0.887421i	$-0.652495\pi$
$433$	−19.1839	−0.921921	−0.460961	+	0.887421i	$0.652495\pi$
$434$	−3.94862	−0.189540
$435$	−7.14016	−0.342344
$436$	29.6745	1.42115
$437$	−9.48717	−0.453833
$438$	18.2093	0.870076
$439$	−13.7961	−0.658450	−0.329225	−	0.944251i	$-0.606788\pi$
$439$	−13.7961	−0.658450	−0.329225	+	0.944251i	$0.606788\pi$
$440$	0	0
$441$	0.267676	0.0127465
$442$	0.129754	0.00617178
$443$	14.1259	0.671140	0.335570	−	0.942015i	$-0.391071\pi$
$443$	14.1259	0.671140	0.335570	+	0.942015i	$0.391071\pi$
$444$	−28.7088	−1.36246
$445$	−3.53318	−0.167489
$446$	−7.87967	−0.373113
$447$	41.8292	1.97846
$448$	7.77337	0.367257
$449$	−21.0016	−0.991129	−0.495565	−	0.868571i	$-0.665039\pi$
$449$	−21.0016	−0.991129	−0.495565	+	0.868571i	$0.665039\pi$
$450$	4.73207	0.223072
$451$	0	0
$452$	19.9425	0.938018
$453$	2.06975	0.0972455
$454$	−10.1301	−0.475429
$455$	−2.05477	−0.0963290
$456$	4.12805	0.193314
$457$	22.4621	1.05073	0.525367	−	0.850876i	$-0.323928\pi$
$457$	22.4621	1.05073	0.525367	+	0.850876i	$0.323928\pi$
$458$	5.23223	0.244486
$459$	0.438393	0.0204624
$460$	10.6805	0.497981
$461$	31.1213	1.44946	0.724732	−	0.689031i	$-0.241964\pi$
$461$	31.1213	1.44946	0.724732	+	0.689031i	$0.241964\pi$
$462$	0	0
$463$	31.6932	1.47291	0.736455	−	0.676487i	$-0.236498\pi$
$463$	31.6932	1.47291	0.736455	+	0.676487i	$0.236498\pi$
$464$	−13.0990	−0.608106
$465$	−4.41191	−0.204597
$466$	−12.3043	−0.569986
$467$	−1.75474	−0.0811995	−0.0405997	−	0.999175i	$-0.512927\pi$
$467$	−1.75474	−0.0811995	−0.0405997	+	0.999175i	$0.512927\pi$
$468$	−4.53612	−0.209682
$469$	5.93804	0.274193
$470$	−1.83522	−0.0846525
$471$	−5.42174	−0.249821
$472$	4.84566	0.223039
$473$	0	0
$474$	6.24086	0.286652
$475$	−4.59346	−0.210763
$476$	−1.04645	−0.0479640
$477$	−20.5118	−0.939173
$478$	0.170516	0.00779922
$479$	11.1294	0.508515	0.254257	−	0.967137i	$-0.418169\pi$
$479$	11.1294	0.508515	0.254257	+	0.967137i	$0.418169\pi$
$480$	−7.11555	−0.324779
$481$	8.66823	0.395237
$482$	−7.59212	−0.345812
$483$	57.3495	2.60949
$484$	0	0
$485$	8.78158	0.398751
$486$	9.03268	0.409731
$487$	3.27007	0.148181	0.0740905	−	0.997252i	$-0.476395\pi$
$487$	3.27007	0.148181	0.0740905	+	0.997252i	$0.476395\pi$
$488$	1.47619	0.0668240
$489$	32.1531	1.45401
$490$	−0.0388244	−0.00175391
$491$	−29.2686	−1.32087	−0.660437	−	0.750882i	$-0.729629\pi$
$491$	−29.2686	−1.32087	−0.660437	+	0.750882i	$0.729629\pi$
$492$	−27.6946	−1.24857
$493$	1.09794	0.0494487
$494$	−0.584420	−0.0262943
$495$	0	0
$496$	−8.09389	−0.363426
$497$	−6.91145	−0.310021
$498$	−3.22058	−0.144317
$499$	−1.04828	−0.0469275	−0.0234638	−	0.999725i	$-0.507469\pi$
$499$	−1.04828	−0.0469275	−0.0234638	+	0.999725i	$0.507469\pi$
$500$	10.8002	0.482998
$501$	−20.9481	−0.935891
$502$	−0.563155	−0.0251348
$503$	−28.4724	−1.26952	−0.634761	−	0.772709i	$-0.718901\pi$
$503$	−28.4724	−1.26952	−0.634761	+	0.772709i	$0.718901\pi$
$504$	−10.3554	−0.461267
$505$	−7.67086	−0.341349
$506$	0	0
$507$	−26.1383	−1.16084
$508$	32.8224	1.45626
$509$	39.6801	1.75879	0.879396	−	0.476091i	$-0.157947\pi$
$509$	39.6801	1.75879	0.879396	+	0.476091i	$0.157947\pi$
$510$	0.155185	0.00687173
$511$	44.3410	1.96153
$512$	−22.7112	−1.00370
$513$	−1.97454	−0.0871782
$514$	7.28609	0.321376
$515$	5.43918	0.239679
$516$	6.13901	0.270255
$517$	0	0
$518$	9.27852	0.407675
$519$	−12.2143	−0.536147
$520$	1.40319	0.0615338
$521$	−15.3168	−0.671043	−0.335522	−	0.942033i	$-0.608913\pi$
$521$	−15.3168	−0.671043	−0.335522	+	0.942033i	$0.608913\pi$
$522$	5.09440	0.222976
$523$	4.17850	0.182713	0.0913566	−	0.995818i	$-0.470880\pi$
$523$	4.17850	0.182713	0.0913566	+	0.995818i	$0.470880\pi$
$524$	−5.45760	−0.238416
$525$	27.7672	1.21186
$526$	−10.0018	−0.436098
$527$	0.678418	0.0295524
$528$	0	0
$529$	67.0064	2.91332
$530$	2.97509	0.129230
$531$	5.65674	0.245481
$532$	4.71327	0.204346
$533$	8.36201	0.362199
$534$	6.07465	0.262876
$535$	−1.04940	−0.0453694
$536$	−4.05505	−0.175151
$537$	2.96018	0.127741
$538$	1.36835	0.0589937
$539$	0	0
$540$	2.22291	0.0956588
$541$	14.6201	0.628565	0.314283	−	0.949329i	$-0.398236\pi$
$541$	14.6201	0.628565	0.314283	+	0.949329i	$0.398236\pi$
$542$	11.4231	0.490665
$543$	−24.3716	−1.04589
$544$	1.09416	0.0469116
$545$	−10.7159	−0.459017
$546$	3.53279	0.151189
$547$	34.7220	1.48461	0.742303	−	0.670064i	$-0.233733\pi$
$547$	34.7220	1.48461	0.742303	+	0.670064i	$0.233733\pi$
$548$	15.3192	0.654402
$549$	1.72328	0.0735478
$550$	0	0
$551$	−4.94518	−0.210672
$552$	−39.1635	−1.66691
$553$	15.1969	0.646240
$554$	−9.08997	−0.386196
$555$	10.3672	0.440061
$556$	25.6771	1.08895
$557$	7.07603	0.299821	0.149910	−	0.988700i	$-0.452101\pi$
$557$	7.07603	0.299821	0.149910	+	0.988700i	$0.452101\pi$
$558$	3.14783	0.133258
$559$	−1.85359	−0.0783985
$560$	−4.50840	−0.190515
$561$	0	0
$562$	13.1979	0.556721
$563$	32.5712	1.37271	0.686357	−	0.727265i	$-0.259209\pi$
$563$	32.5712	1.37271	0.686357	+	0.727265i	$0.259209\pi$
$564$	−23.7735	−1.00104
$565$	−7.20152	−0.302970
$566$	−13.1964	−0.554686
$567$	28.9780	1.21696
$568$	4.71978	0.198037
$569$	−32.6457	−1.36858	−0.684290	−	0.729210i	$-0.739888\pi$
$569$	−32.6457	−1.36858	−0.684290	+	0.729210i	$0.739888\pi$
$570$	−0.698963	−0.0292763
$571$	35.8059	1.49843	0.749216	−	0.662326i	$-0.230431\pi$
$571$	35.8059	1.49843	0.749216	+	0.662326i	$0.230431\pi$
$572$	0	0
$573$	34.6565	1.44780
$574$	8.95073	0.373596
$575$	43.5790	1.81737
$576$	−6.19691	−0.258205
$577$	15.7218	0.654509	0.327254	−	0.944936i	$-0.393877\pi$
$577$	15.7218	0.654509	0.327254	+	0.944936i	$0.393877\pi$
$578$	8.20571	0.341313
$579$	41.4480	1.72252
$580$	5.56721	0.231166
$581$	−7.84233	−0.325355
$582$	−15.0983	−0.625844
$583$	0	0
$584$	−30.2802	−1.25300
$585$	1.63806	0.0677253
$586$	15.0067	0.619919
$587$	24.4810	1.01044	0.505220	−	0.862991i	$-0.331412\pi$
$587$	24.4810	1.01044	0.505220	+	0.862991i	$0.331412\pi$
$588$	−0.502932	−0.0207406
$589$	−3.05563	−0.125905
$590$	−0.820468	−0.0337781
$591$	1.30475	0.0536703
$592$	19.0191	0.781680
$593$	21.2995	0.874666	0.437333	−	0.899300i	$-0.355923\pi$
$593$	21.2995	0.874666	0.437333	+	0.899300i	$0.355923\pi$
$594$	0	0
$595$	0.377887	0.0154919
$596$	−32.6144	−1.33594
$597$	−23.0253	−0.942361
$598$	5.54450	0.226731
$599$	−8.90839	−0.363987	−0.181994	−	0.983300i	$-0.558255\pi$
$599$	−8.90839	−0.363987	−0.181994	+	0.983300i	$0.558255\pi$
$600$	−18.9621	−0.774123
$601$	8.36794	0.341335	0.170668	−	0.985329i	$-0.445408\pi$
$601$	8.36794	0.341335	0.170668	+	0.985329i	$0.445408\pi$
$602$	−1.98409	−0.0808655
$603$	−4.73379	−0.192775
$604$	−1.61379	−0.0656643
$605$	0	0
$606$	13.1886	0.535751
$607$	−43.2321	−1.75474	−0.877368	−	0.479819i	$-0.840702\pi$
$607$	−43.2321	−1.75474	−0.877368	+	0.479819i	$0.840702\pi$
$608$	−4.92814	−0.199862
$609$	29.8933	1.21134
$610$	−0.249949	−0.0101201
$611$	7.17807	0.290394
$612$	0.834228	0.0337216
$613$	12.4893	0.504438	0.252219	−	0.967670i	$-0.418840\pi$
$613$	12.4893	0.504438	0.252219	+	0.967670i	$0.418840\pi$
$614$	−8.83447	−0.356530
$615$	10.0009	0.403276
$616$	0	0
$617$	−18.4079	−0.741073	−0.370536	−	0.928818i	$-0.620826\pi$
$617$	−18.4079	−0.741073	−0.370536	+	0.928818i	$0.620826\pi$
$618$	−9.35165	−0.376179
$619$	−7.30900	−0.293773	−0.146887	−	0.989153i	$-0.546925\pi$
$619$	−7.30900	−0.293773	−0.146887	+	0.989153i	$0.546925\pi$
$620$	3.43998	0.138153
$621$	18.7328	0.751722
$622$	−14.9551	−0.599646
$623$	14.7922	0.592637
$624$	7.24151	0.289893
$625$	19.0672	0.762689
$626$	−13.9406	−0.557177
$627$	0	0
$628$	4.22735	0.168690
$629$	−1.59415	−0.0635631
$630$	1.75338	0.0698564
$631$	−11.8397	−0.471329	−0.235665	−	0.971834i	$-0.575727\pi$
$631$	−11.8397	−0.471329	−0.235665	+	0.971834i	$0.575727\pi$
$632$	−10.3779	−0.412810
$633$	16.4367	0.653301
$634$	−2.88538	−0.114593
$635$	−11.8526	−0.470357
$636$	38.5393	1.52818
$637$	0.151853	0.00601664
$638$	0	0
$639$	5.50979	0.217964
$640$	7.18320	0.283941
$641$	−36.5974	−1.44551	−0.722756	−	0.691104i	$-0.757125\pi$
$641$	−36.5974	−1.44551	−0.722756	+	0.691104i	$0.757125\pi$
$642$	1.80424	0.0712078
$643$	−14.0452	−0.553888	−0.276944	−	0.960886i	$-0.589322\pi$
$643$	−14.0452	−0.553888	−0.276944	+	0.960886i	$0.589322\pi$
$644$	−44.7156	−1.76204
$645$	−2.21688	−0.0872896
$646$	0.107479	0.00422872
$647$	−43.5266	−1.71121	−0.855604	−	0.517631i	$-0.826814\pi$
$647$	−43.5266	−1.71121	−0.855604	+	0.517631i	$0.826814\pi$
$648$	−19.7889	−0.777380
$649$	0	0
$650$	2.68451	0.105295
$651$	18.4711	0.723941
$652$	−25.0699	−0.981812
$653$	44.0328	1.72314	0.861568	−	0.507642i	$-0.169483\pi$
$653$	44.0328	1.72314	0.861568	+	0.507642i	$0.169483\pi$
$654$	18.4239	0.720433
$655$	1.97081	0.0770060
$656$	18.3472	0.716338
$657$	−35.3486	−1.37908
$658$	7.68344	0.299532
$659$	3.86784	0.150670	0.0753349	−	0.997158i	$-0.475997\pi$
$659$	3.86784	0.150670	0.0753349	+	0.997158i	$0.475997\pi$
$660$	0	0
$661$	7.96999	0.309997	0.154998	−	0.987915i	$-0.450463\pi$
$661$	7.96999	0.309997	0.154998	+	0.987915i	$0.450463\pi$
$662$	−16.1692	−0.628434
$663$	−0.606973	−0.0235729
$664$	5.35547	0.207833
$665$	−1.70203	−0.0660017
$666$	−7.39681	−0.286621
$667$	46.9158	1.81659
$668$	16.3333	0.631954
$669$	36.8600	1.42509
$670$	0.686602	0.0265258
$671$	0	0
$672$	29.7903	1.14919
$673$	−21.7872	−0.839835	−0.419917	−	0.907562i	$-0.637941\pi$
$673$	−21.7872	−0.839835	−0.419917	+	0.907562i	$0.637941\pi$
$674$	12.1017	0.466141
$675$	9.06999	0.349104
$676$	20.3802	0.783852
$677$	−33.2004	−1.27599	−0.637997	−	0.770039i	$-0.720237\pi$
$677$	−33.2004	−1.27599	−0.637997	+	0.770039i	$0.720237\pi$
$678$	12.3817	0.475515
$679$	−36.7654	−1.41093
$680$	−0.258057	−0.00989602
$681$	47.3873	1.81588
$682$	0	0
$683$	−34.9595	−1.33769	−0.668843	−	0.743403i	$-0.733210\pi$
$683$	−34.9595	−1.33769	−0.668843	+	0.743403i	$0.733210\pi$
$684$	−3.75740	−0.143668
$685$	−5.53196	−0.211365
$686$	−8.88317	−0.339161
$687$	−24.4757	−0.933805
$688$	−4.06699	−0.155052
$689$	−11.6364	−0.443312
$690$	6.63118	0.252445
$691$	−30.4626	−1.15885	−0.579426	−	0.815025i	$-0.696723\pi$
$691$	−30.4626	−1.15885	−0.579426	+	0.815025i	$0.696723\pi$
$692$	9.52351	0.362030
$693$	0	0
$694$	−4.04497	−0.153545
$695$	−9.27236	−0.351721
$696$	−20.4140	−0.773789
$697$	−1.53784	−0.0582497
$698$	−13.7439	−0.520215
$699$	57.5579	2.17704
$700$	−21.6502	−0.818301
$701$	−10.3329	−0.390269	−0.195135	−	0.980776i	$-0.562514\pi$
$701$	−10.3329	−0.390269	−0.195135	+	0.980776i	$0.562514\pi$
$702$	1.15396	0.0435535
$703$	7.18015	0.270805
$704$	0	0
$705$	8.58493	0.323327
$706$	6.00673	0.226066
$707$	32.1152	1.20782
$708$	−10.6283	−0.399437
$709$	−45.4499	−1.70691	−0.853454	−	0.521169i	$-0.825496\pi$
$709$	−45.4499	−1.70691	−0.853454	+	0.521169i	$0.825496\pi$
$710$	−0.799154	−0.0299917
$711$	−12.1150	−0.454347
$712$	−10.1015	−0.378570
$713$	28.9893	1.08566
$714$	−0.649707	−0.0243147
$715$	0	0
$716$	−2.30806	−0.0862564
$717$	−0.797651	−0.0297888
$718$	5.86399	0.218842
$719$	−7.51239	−0.280165	−0.140082	−	0.990140i	$-0.544737\pi$
$719$	−7.51239	−0.280165	−0.140082	+	0.990140i	$0.544737\pi$
$720$	3.59408	0.133944
$721$	−22.7719	−0.848071
$722$	−0.484093	−0.0180161
$723$	35.5149	1.32081
$724$	19.0026	0.706227
$725$	22.7155	0.843632
$726$	0	0
$727$	4.79898	0.177984	0.0889922	−	0.996032i	$-0.471635\pi$
$727$	4.79898	0.177984	0.0889922	+	0.996032i	$0.471635\pi$
$728$	−5.87465	−0.217729
$729$	−9.68700	−0.358778
$730$	5.12705	0.189761
$731$	0.340889	0.0126082
$732$	−3.23784	−0.119674
$733$	8.55077	0.315830	0.157915	−	0.987453i	$-0.449523\pi$
$733$	8.55077	0.315830	0.157915	+	0.987453i	$0.449523\pi$
$734$	1.96572	0.0725562
$735$	0.181616	0.00669899
$736$	46.7541	1.72338
$737$	0	0
$738$	−7.13550	−0.262661
$739$	−38.8820	−1.43030	−0.715149	−	0.698972i	$-0.753641\pi$
$739$	−38.8820	−1.43030	−0.715149	+	0.698972i	$0.753641\pi$
$740$	−8.08330	−0.297148
$741$	2.73384	0.100430
$742$	−12.4557	−0.457262
$743$	−28.4350	−1.04318	−0.521589	−	0.853197i	$-0.674660\pi$
$743$	−28.4350	−1.04318	−0.521589	+	0.853197i	$0.674660\pi$
$744$	−12.6138	−0.462445
$745$	11.7775	0.431494
$746$	17.1804	0.629018
$747$	6.25189	0.228745
$748$	0	0
$749$	4.39346	0.160534
$750$	6.70548	0.244849
$751$	18.2732	0.666799	0.333400	−	0.942786i	$-0.391804\pi$
$751$	18.2732	0.666799	0.333400	+	0.942786i	$0.391804\pi$
$752$	15.7495	0.574326
$753$	2.63436	0.0960015
$754$	2.89006	0.105250
$755$	0.582763	0.0212089
$756$	−9.30655	−0.338476
$757$	1.10637	0.0402117	0.0201058	−	0.999798i	$-0.493600\pi$
$757$	1.10637	0.0402117	0.0201058	+	0.999798i	$0.493600\pi$
$758$	−6.56352	−0.238398
$759$	0	0
$760$	1.16230	0.0421611
$761$	−1.10110	−0.0399147	−0.0199573	−	0.999801i	$-0.506353\pi$
$761$	−1.10110	−0.0399147	−0.0199573	+	0.999801i	$0.506353\pi$
$762$	20.3784	0.738231
$763$	44.8636	1.62417
$764$	−27.0218	−0.977615
$765$	−0.301251	−0.0108918
$766$	11.5372	0.416855
$767$	3.20908	0.115873
$768$	0.838451	0.0302550
$769$	−30.2914	−1.09234	−0.546169	−	0.837675i	$-0.683914\pi$
$769$	−30.2914	−1.09234	−0.546169	+	0.837675i	$0.683914\pi$
$770$	0	0
$771$	−34.0833	−1.22748
$772$	−32.3171	−1.16312
$773$	−43.9677	−1.58141	−0.790704	−	0.612199i	$-0.790285\pi$
$773$	−43.9677	−1.58141	−0.790704	+	0.612199i	$0.790285\pi$
$774$	1.58171	0.0568535
$775$	14.0359	0.504186
$776$	25.1068	0.901283
$777$	−43.4036	−1.55710
$778$	6.17542	0.221399
$779$	6.92650	0.248168
$780$	−3.07771	−0.110200
$781$	0	0
$782$	−1.01967	−0.0364635
$783$	9.76447	0.348954
$784$	0.333183	0.0118994
$785$	−1.52655	−0.0544851
$786$	−3.38845	−0.120862
$787$	37.8350	1.34867	0.674337	−	0.738424i	$-0.264430\pi$
$787$	37.8350	1.34867	0.674337	+	0.738424i	$0.264430\pi$
$788$	−1.01732	−0.0362405
$789$	46.7870	1.66566
$790$	1.75719	0.0625179
$791$	30.1502	1.07202
$792$	0	0
$793$	0.977621	0.0347163
$794$	14.6762	0.520838
$795$	−13.9171	−0.493588
$796$	17.9529	0.636323
$797$	11.2902	0.399918	0.199959	−	0.979804i	$-0.435919\pi$
$797$	11.2902	0.399918	0.199959	+	0.979804i	$0.435919\pi$
$798$	2.92632	0.103590
$799$	−1.32010	−0.0467018
$800$	22.6372	0.800347
$801$	−11.7923	−0.416661
$802$	−15.7993	−0.557894
$803$	0	0
$804$	8.89424	0.313676
$805$	16.1474	0.569121
$806$	1.78577	0.0629012
$807$	−6.40095	−0.225324
$808$	−21.9313	−0.771539
$809$	−17.8104	−0.626180	−0.313090	−	0.949723i	$-0.601364\pi$
$809$	−17.8104	−0.626180	−0.313090	+	0.949723i	$0.601364\pi$
$810$	3.35066	0.117730
$811$	−28.1638	−0.988965	−0.494482	−	0.869188i	$-0.664642\pi$
$811$	−28.1638	−0.988965	−0.494482	+	0.869188i	$0.664642\pi$
$812$	−23.3079	−0.817949
$813$	−53.4358	−1.87408
$814$	0	0
$815$	9.05307	0.317115
$816$	−1.33177	−0.0466213
$817$	−1.53538	−0.0537162
$818$	−11.2110	−0.391982
$819$	−6.85797	−0.239637
$820$	−7.79774	−0.272309
$821$	44.2644	1.54484	0.772418	−	0.635114i	$-0.219047\pi$
$821$	44.2644	1.54484	0.772418	+	0.635114i	$0.219047\pi$
$822$	9.51117	0.331740
$823$	−22.4258	−0.781716	−0.390858	−	0.920451i	$-0.627822\pi$
$823$	−22.4258	−0.781716	−0.390858	+	0.920451i	$0.627822\pi$
$824$	15.5508	0.541738
$825$	0	0
$826$	3.43501	0.119519
$827$	−19.7303	−0.686090	−0.343045	−	0.939319i	$-0.611458\pi$
$827$	−19.7303	−0.686090	−0.343045	+	0.939319i	$0.611458\pi$
$828$	35.6471	1.23882
$829$	5.70836	0.198259	0.0991297	−	0.995075i	$-0.468394\pi$
$829$	5.70836	0.198259	0.0991297	+	0.995075i	$0.468394\pi$
$830$	−0.906791	−0.0314752
$831$	42.5216	1.47506
$832$	−3.51552	−0.121879
$833$	−0.0279270	−0.000967612 0
$834$	15.9421	0.552030
$835$	−5.89817	−0.204115
$836$	0	0
$837$	6.03348	0.208547
$838$	6.88441	0.237818
$839$	−0.0666011	−0.00229932	−0.00114966	−	0.999999i	$-0.500366\pi$
$839$	−0.0666011	−0.00229932	−0.00114966	+	0.999999i	$0.500366\pi$
$840$	−7.02605	−0.242422
$841$	−4.54521	−0.156731
$842$	−7.72635	−0.266268
$843$	−61.7381	−2.12637
$844$	−12.8158	−0.441137
$845$	−7.35955	−0.253176
$846$	−6.12522	−0.210589
$847$	0	0
$848$	−25.5316	−0.876760
$849$	61.7310	2.11860
$850$	−0.493703	−0.0169339
$851$	−68.1193	−2.33510
$852$	−10.3522	−0.354662
$853$	14.8615	0.508848	0.254424	−	0.967093i	$-0.418114\pi$
$853$	14.8615	0.508848	0.254424	+	0.967093i	$0.418114\pi$
$854$	1.04645	0.0358088
$855$	1.35685	0.0464033
$856$	−3.00026	−0.102547
$857$	−12.5169	−0.427569	−0.213785	−	0.976881i	$-0.568579\pi$
$857$	−12.5169	−0.427569	−0.213785	+	0.976881i	$0.568579\pi$
$858$	0	0
$859$	−21.2738	−0.725854	−0.362927	−	0.931818i	$-0.618223\pi$
$859$	−21.2738	−0.725854	−0.362927	+	0.931818i	$0.618223\pi$
$860$	1.72851	0.0589417
$861$	−41.8703	−1.42694
$862$	11.8651	0.404128
$863$	−34.4402	−1.17236	−0.586179	−	0.810181i	$-0.699369\pi$
$863$	−34.4402	−1.17236	−0.586179	+	0.810181i	$0.699369\pi$
$864$	9.73082	0.331049
$865$	−3.43907	−0.116932
$866$	9.28680	0.315578
$867$	−38.3852	−1.30363
$868$	−14.4020	−0.488836
$869$	0	0
$870$	3.45650	0.117186
$871$	−2.68549	−0.0909944
$872$	−30.6370	−1.03750
$873$	29.3093	0.991969
$874$	4.59267	0.155349
$875$	16.3283	0.551998
$876$	66.4158	2.24398
$877$	0.910260	0.0307373	0.0153687	−	0.999882i	$-0.495108\pi$
$877$	0.910260	0.0307373	0.0153687	+	0.999882i	$0.495108\pi$
$878$	6.67857	0.225391
$879$	−70.1991	−2.36776
$880$	0	0
$881$	33.7502	1.13707	0.568537	−	0.822658i	$-0.307510\pi$
$881$	33.7502	1.13707	0.568537	+	0.822658i	$0.307510\pi$
$882$	−0.129580	−0.00436319
$883$	39.8800	1.34207	0.671035	−	0.741426i	$-0.265850\pi$
$883$	39.8800	1.34207	0.671035	+	0.741426i	$0.265850\pi$
$884$	0.473259	0.0159174
$885$	3.83804	0.129014
$886$	−6.83822	−0.229735
$887$	16.1868	0.543500	0.271750	−	0.962368i	$-0.412398\pi$
$887$	16.1868	0.543500	0.271750	+	0.962368i	$0.412398\pi$
$888$	29.6400	0.994655
$889$	49.6228	1.66430
$890$	1.71039	0.0573324
$891$	0	0
$892$	−28.7399	−0.962282
$893$	5.94581	0.198969
$894$	−20.2492	−0.677236
$895$	0.833474	0.0278599
$896$	−30.0735	−1.00469
$897$	−25.9364	−0.865991
$898$	10.1667	0.339269
$899$	15.1106	0.503968
$900$	17.2595	0.575317
$901$	2.14003	0.0712946
$902$	0	0
$903$	9.28131	0.308863
$904$	−20.5894	−0.684793
$905$	−6.86211	−0.228104
$906$	−1.00195	−0.0332876
$907$	−14.3005	−0.474839	−0.237419	−	0.971407i	$-0.576302\pi$
$907$	−14.3005	−0.474839	−0.237419	+	0.971407i	$0.576302\pi$
$908$	−36.9480	−1.22616
$909$	−25.6022	−0.849171
$910$	0.994698	0.0329739
$911$	−8.50108	−0.281653	−0.140827	−	0.990034i	$-0.544976\pi$
$911$	−8.50108	−0.281653	−0.140827	+	0.990034i	$0.544976\pi$
$912$	5.99836	0.198626
$913$	0	0
$914$	−10.8738	−0.359672
$915$	1.16923	0.0386535
$916$	19.0838	0.630545
$917$	−8.25111	−0.272476
$918$	−0.212223	−0.00700439
$919$	26.0156	0.858177	0.429088	−	0.903263i	$-0.358835\pi$
$919$	26.0156	0.858177	0.429088	+	0.903263i	$0.358835\pi$
$920$	−11.0269	−0.363548
$921$	41.3265	1.36175
$922$	−15.0656	−0.496159
$923$	3.12571	0.102884
$924$	0	0
$925$	−32.9818	−1.08443
$926$	−15.3425	−0.504185
$927$	18.1537	0.596247
$928$	24.3705	0.800001
$929$	5.99773	0.196779	0.0983896	−	0.995148i	$-0.468631\pi$
$929$	5.99773	0.196779	0.0983896	+	0.995148i	$0.468631\pi$
$930$	2.13577	0.0700348
$931$	0.125785	0.00412242
$932$	−44.8781	−1.47003
$933$	69.9581	2.29033
$934$	0.849454	0.0277950
$935$	0	0
$936$	4.68326	0.153077
$937$	50.5847	1.65253	0.826265	−	0.563282i	$-0.190461\pi$
$937$	50.5847	1.65253	0.826265	+	0.563282i	$0.190461\pi$
$938$	−2.87456	−0.0938578
$939$	65.2120	2.12811
$940$	−6.69370	−0.218324
$941$	21.8640	0.712747	0.356373	−	0.934344i	$-0.384013\pi$
$941$	21.8640	0.712747	0.356373	+	0.934344i	$0.384013\pi$
$942$	2.62463	0.0855149
$943$	−65.7129	−2.13991
$944$	7.04109	0.229168
$945$	3.36072	0.109324
$946$	0	0
$947$	−33.1722	−1.07795	−0.538976	−	0.842321i	$-0.681188\pi$
$947$	−33.1722	−1.07795	−0.538976	+	0.842321i	$0.681188\pi$
$948$	22.7626	0.739295
$949$	−20.0533	−0.650958
$950$	2.22366	0.0721451
$951$	13.4974	0.437685
$952$	1.08039	0.0350157
$953$	−22.4494	−0.727209	−0.363604	−	0.931553i	$-0.618454\pi$
$953$	−22.4494	−0.727209	−0.363604	+	0.931553i	$0.618454\pi$
$954$	9.92963	0.321484
$955$	9.75794	0.315760
$956$	0.621931	0.0201147
$957$	0	0
$958$	−5.38765	−0.174067
$959$	23.1604	0.747887
$960$	−4.20454	−0.135701
$961$	−21.6631	−0.698810
$962$	−4.19623	−0.135292
$963$	−3.50246	−0.112865
$964$	−27.6911	−0.891870
$965$	11.6702	0.375676
$966$	−27.7625	−0.893242
$967$	0.790013	0.0254051	0.0127026	−	0.999919i	$-0.495957\pi$
$967$	0.790013	0.0254051	0.0127026	+	0.999919i	$0.495957\pi$
$968$	0	0
$969$	−0.502774	−0.0161514
$970$	−4.25110	−0.136495
$971$	51.6970	1.65904	0.829518	−	0.558479i	$-0.188615\pi$
$971$	51.6970	1.65904	0.829518	+	0.558479i	$0.188615\pi$
$972$	32.9453	1.05672
$973$	38.8201	1.24452
$974$	−1.58302	−0.0507231
$975$	−12.5578	−0.402171
$976$	2.14501	0.0686602
$977$	21.4536	0.686360	0.343180	−	0.939270i	$-0.388496\pi$
$977$	21.4536	0.686360	0.343180	+	0.939270i	$0.388496\pi$
$978$	−15.5651	−0.497716
$979$	0	0
$980$	−0.141606	−0.00452345
$981$	−35.7651	−1.14189
$982$	14.1687	0.452142
$983$	−42.9916	−1.37122	−0.685610	−	0.727969i	$-0.740464\pi$
$983$	−42.9916	−1.37122	−0.685610	+	0.727969i	$0.740464\pi$
$984$	28.5929	0.911510
$985$	0.367368	0.0117053
$986$	−0.531505	−0.0169266
$987$	−35.9421	−1.14405
$988$	−2.13158	−0.0678147
$989$	14.5664	0.463186
$990$	0	0
$991$	57.7319	1.83392	0.916958	−	0.398985i	$-0.130637\pi$
$991$	57.7319	1.83392	0.916958	+	0.398985i	$0.130637\pi$
$992$	15.0586	0.478110
$993$	75.6373	2.40028
$994$	3.34578	0.106122
$995$	−6.48303	−0.205526
$996$	−11.7466	−0.372204
$997$	30.3487	0.961152	0.480576	−	0.876953i	$-0.340428\pi$
$997$	30.3487	0.961152	0.480576	+	0.876953i	$0.340428\pi$
$998$	0.507466	0.0160635
$999$	−14.1775	−0.448557

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2299.2.a.n.1.3		5
11.10	odd	2		209.2.a.c.1.3	✓	5
33.32	even	2		1881.2.a.k.1.3		5
44.43	even	2		3344.2.a.t.1.1		5
55.54	odd	2		5225.2.a.h.1.3		5
209.208	even	2		3971.2.a.h.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.a.c.1.3	✓	5	11.10	odd	2
1881.2.a.k.1.3		5	33.32	even	2
2299.2.a.n.1.3		5	1.1	even	1	trivial
3344.2.a.t.1.1		5	44.43	even	2
3971.2.a.h.1.3		5	209.208	even	2
5225.2.a.h.1.3		5	55.54	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-0.484093 q^{2} +2.26452 q^{3} -1.76565 q^{4} +0.637602 q^{5} -1.09624 q^{6} -2.66942 q^{7} +1.82293 q^{8} +2.12805 q^{9} +O(q^{10})\)	\(q-0.484093 q^{2} +2.26452 q^{3} -1.76565 q^{4} +0.637602 q^{5} -1.09624 q^{6} -2.66942 q^{7} +1.82293 q^{8} +2.12805 q^{9} -0.308658 q^{10} -3.99836 q^{12} +1.20725 q^{13} +1.29225 q^{14} +1.44386 q^{15} +2.64884 q^{16} -0.222022 q^{17} -1.03017 q^{18} +1.00000 q^{19} -1.12578 q^{20} -6.04495 q^{21} -9.48717 q^{23} +4.12805 q^{24} -4.59346 q^{25} -0.584420 q^{26} -1.97454 q^{27} +4.71327 q^{28} -4.94518 q^{29} -0.698963 q^{30} -3.05563 q^{31} -4.92814 q^{32} +0.107479 q^{34} -1.70203 q^{35} -3.75740 q^{36} +7.18015 q^{37} -0.484093 q^{38} +2.73384 q^{39} +1.16230 q^{40} +6.92650 q^{41} +2.92632 q^{42} -1.53538 q^{43} +1.35685 q^{45} +4.59267 q^{46} +5.94581 q^{47} +5.99836 q^{48} +0.125785 q^{49} +2.22366 q^{50} -0.502774 q^{51} -2.13158 q^{52} -9.63879 q^{53} +0.955862 q^{54} -4.86615 q^{56} +2.26452 q^{57} +2.39392 q^{58} +2.65817 q^{59} -2.54936 q^{60} +0.809792 q^{61} +1.47921 q^{62} -5.68066 q^{63} -2.91201 q^{64} +0.769744 q^{65} -2.22447 q^{67} +0.392015 q^{68} -21.4839 q^{69} +0.823938 q^{70} +2.58912 q^{71} +3.87928 q^{72} -16.6108 q^{73} -3.47586 q^{74} -10.4020 q^{75} -1.76565 q^{76} -1.32343 q^{78} -5.69298 q^{79} +1.68891 q^{80} -10.8556 q^{81} -3.35307 q^{82} +2.93784 q^{83} +10.6733 q^{84} -0.141562 q^{85} +0.743267 q^{86} -11.1985 q^{87} -5.54136 q^{89} -0.656841 q^{90} -3.22265 q^{91} +16.7511 q^{92} -6.91954 q^{93} -2.87832 q^{94} +0.637602 q^{95} -11.1599 q^{96} +13.7728 q^{97} -0.0608914 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + q^3 + 6 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 - 6 * q^8 + 4 * q^9	\( 5 q - 2 q^{2} + q^{3} + 6 q^{4} - 5 q^{5} + 2 q^{6} - 6 q^{7} - 6 q^{8} + 4 q^{9} - 12 q^{10} + 6 q^{12} - 4 q^{13} - 14 q^{14} + 3 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} + 5 q^{19} - 8 q^{20} - 10 q^{21} + 3 q^{23} + 14 q^{24} + 6 q^{25} - 6 q^{26} - 11 q^{27} + 10 q^{28} - 10 q^{29} - 6 q^{30} + 11 q^{31} - 14 q^{32} - 4 q^{34} + 8 q^{35} - 26 q^{36} + q^{37} - 2 q^{38} - 2 q^{39} + 16 q^{40} - 2 q^{41} - 16 q^{42} - 20 q^{43} - 28 q^{45} + 4 q^{46} - 20 q^{47} + 4 q^{48} + 3 q^{49} + 32 q^{50} - 24 q^{51} - 6 q^{52} - 14 q^{53} - 16 q^{54} - 38 q^{56} + q^{57} - 6 q^{58} + 3 q^{59} - 40 q^{60} + 10 q^{61} + 6 q^{62} - 24 q^{63} + 9 q^{67} - 24 q^{68} - 5 q^{69} + 50 q^{70} + 23 q^{71} + 12 q^{72} - 8 q^{74} - 18 q^{75} + 6 q^{76} - 22 q^{78} - 44 q^{79} - 18 q^{80} + q^{81} - 30 q^{82} + 14 q^{83} - 14 q^{84} + 12 q^{85} + 52 q^{86} - 28 q^{87} - 27 q^{89} - 26 q^{90} + 24 q^{91} + 58 q^{92} - 27 q^{93} + 8 q^{94} - 5 q^{95} - 50 q^{96} + 15 q^{97} + 10 q^{98}+O(q^{100}) \) 5 * q - 2 * q^2 + q^3 + 6 * q^4 - 5 * q^5 + 2 * q^6 - 6 * q^7 - 6 * q^8 + 4 * q^9 - 12 * q^10 + 6 * q^12 - 4 * q^13 - 14 * q^14 + 3 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 + 5 * q^19 - 8 * q^20 - 10 * q^21 + 3 * q^23 + 14 * q^24 + 6 * q^25 - 6 * q^26 - 11 * q^27 + 10 * q^28 - 10 * q^29 - 6 * q^30 + 11 * q^31 - 14 * q^32 - 4 * q^34 + 8 * q^35 - 26 * q^36 + q^37 - 2 * q^38 - 2 * q^39 + 16 * q^40 - 2 * q^41 - 16 * q^42 - 20 * q^43 - 28 * q^45 + 4 * q^46 - 20 * q^47 + 4 * q^48 + 3 * q^49 + 32 * q^50 - 24 * q^51 - 6 * q^52 - 14 * q^53 - 16 * q^54 - 38 * q^56 + q^57 - 6 * q^58 + 3 * q^59 - 40 * q^60 + 10 * q^61 + 6 * q^62 - 24 * q^63 + 9 * q^67 - 24 * q^68 - 5 * q^69 + 50 * q^70 + 23 * q^71 + 12 * q^72 - 8 * q^74 - 18 * q^75 + 6 * q^76 - 22 * q^78 - 44 * q^79 - 18 * q^80 + q^81 - 30 * q^82 + 14 * q^83 - 14 * q^84 + 12 * q^85 + 52 * q^86 - 28 * q^87 - 27 * q^89 - 26 * q^90 + 24 * q^91 + 58 * q^92 - 27 * q^93 + 8 * q^94 - 5 * q^95 - 50 * q^96 + 15 * q^97 + 10 * q^98

Introduction

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