LMFDB - Embedded newform 119.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [119,2,Mod(1,119)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(119, 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("119.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	119.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:	$0.950219784053$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.453749.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 10x^{2} + x - 3 $ x^5 - 2x^4 - 5x^3 + 10*x^2 + x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.609440$ of defining polynomial
Character	$\chi$	$=$	119.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.49227 q^{2} -2.82084 q^{3} +4.21140 q^{4} +2.51889 q^{5} -7.03030 q^{6} -1.00000 q^{7} +5.51141 q^{8} +4.95716 q^{9} +6.27775 q^{10} -5.25717 q^{11} -11.8797 q^{12} -4.20342 q^{13} -2.49227 q^{14} -7.10539 q^{15} +5.31311 q^{16} +1.00000 q^{17} +12.3546 q^{18} +0.781120 q^{19} +10.6081 q^{20} +2.82084 q^{21} -13.1023 q^{22} +2.42281 q^{23} -15.5468 q^{24} +1.34480 q^{25} -10.4760 q^{26} -5.52084 q^{27} -4.21140 q^{28} +3.42230 q^{29} -17.7085 q^{30} +6.94170 q^{31} +2.21888 q^{32} +14.8296 q^{33} +2.49227 q^{34} -2.51889 q^{35} +20.8766 q^{36} -7.02282 q^{37} +1.94676 q^{38} +11.8572 q^{39} +13.8826 q^{40} +1.83631 q^{41} +7.03030 q^{42} +8.63974 q^{43} -22.1400 q^{44} +12.4865 q^{45} +6.03829 q^{46} -1.34285 q^{47} -14.9875 q^{48} +1.00000 q^{49} +3.35160 q^{50} -2.82084 q^{51} -17.7023 q^{52} -1.95716 q^{53} -13.7594 q^{54} -13.2422 q^{55} -5.51141 q^{56} -2.20342 q^{57} +8.52928 q^{58} +2.43776 q^{59} -29.9237 q^{60} +6.16369 q^{61} +17.3006 q^{62} -4.95716 q^{63} -5.09618 q^{64} -10.5879 q^{65} +36.9595 q^{66} +1.53435 q^{67} +4.21140 q^{68} -6.83436 q^{69} -6.27775 q^{70} -1.65664 q^{71} +27.3209 q^{72} -14.3197 q^{73} -17.5028 q^{74} -3.79346 q^{75} +3.28961 q^{76} +5.25717 q^{77} +29.5513 q^{78} +12.6262 q^{79} +13.3831 q^{80} +0.701939 q^{81} +4.57657 q^{82} -11.8451 q^{83} +11.8797 q^{84} +2.51889 q^{85} +21.5326 q^{86} -9.65376 q^{87} -28.9744 q^{88} +4.49202 q^{89} +31.1198 q^{90} +4.20342 q^{91} +10.2034 q^{92} -19.5814 q^{93} -3.34674 q^{94} +1.96755 q^{95} -6.25911 q^{96} +12.9267 q^{97} +2.49227 q^{98} -26.0606 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - q^{6} - 5 q^{7} + 6 q^{8} + 11 q^{9} + 4 q^{10} - 2 q^{11} - 22 q^{12} + 2 q^{13} - 2 q^{14} + 8 q^{15} + 4 q^{16} + 5 q^{17} - 18 q^{18} + 6 q^{19} - 19 q^{20} + 2 q^{21}+ \cdots - 62 q^{99}+O(q^{100}) $ 5 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - q^6 - 5 * q^7 + 6 * q^8 + 11 * q^9 + 4 * q^10 - 2 * q^11 - 22 * q^12 + 2 * q^13 - 2 * q^14 + 8 * q^15 + 4 * q^16 + 5 * q^17 - 18 * q^18 + 6 * q^19 - 19 * q^20 + 2 * q^21 + 6 * q^22 - 10 * q^23 + 2 * q^24 + 21 * q^25 - 26 * q^26 - 26 * q^27 - 10 * q^28 - 8 * q^29 - 51 * q^30 + 9 * q^32 + 6 * q^33 + 2 * q^34 + 39 * q^36 + 8 * q^37 + 14 * q^38 + 14 * q^39 + 5 * q^40 + 18 * q^41 + q^42 + 8 * q^43 - 14 * q^44 + 8 * q^46 - 10 * q^47 - 27 * q^48 + 5 * q^49 + 27 * q^50 - 2 * q^51 + 4 * q^52 + 4 * q^53 + 5 * q^54 - 24 * q^55 - 6 * q^56 + 12 * q^57 + 12 * q^58 + 8 * q^59 - 7 * q^60 + 22 * q^61 + 16 * q^62 - 11 * q^63 - 16 * q^64 - 30 * q^65 + 68 * q^66 + 16 * q^67 + 10 * q^68 - 32 * q^69 - 4 * q^70 - 2 * q^71 + 9 * q^72 + 10 * q^73 - 40 * q^74 - 14 * q^75 + 24 * q^76 + 2 * q^77 + 30 * q^78 + 18 * q^79 - 4 * q^80 + 25 * q^81 - 31 * q^82 - 12 * q^83 + 22 * q^84 + 23 * q^86 - 26 * q^87 - 46 * q^88 + 20 * q^89 + 97 * q^90 - 2 * q^91 + 28 * q^92 - 28 * q^93 - 42 * q^94 - 22 * q^95 - 18 * q^96 + 12 * q^97 + 2 * q^98 - 62 * q^99

Coefficient data

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

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

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

$2$	2.49227	1.76230	0.881150	−	0.472837i	$-0.156770\pi$
$2$	2.49227	1.76230	0.881150	+	0.472837i	$0.156770\pi$
$3$	−2.82084	−1.62861	−0.814307	−	0.580434i	$-0.802883\pi$
$3$	−2.82084	−1.62861	−0.814307	+	0.580434i	$0.802883\pi$
$4$	4.21140	2.10570
$5$	2.51889	1.12648	0.563241	−	0.826293i	$-0.309554\pi$
$5$	2.51889	1.12648	0.563241	+	0.826293i	$0.309554\pi$
$6$	−7.03030	−2.87011
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	5.51141	1.94858
$9$	4.95716	1.65239
$10$	6.27775	1.98520
$11$	−5.25717	−1.58510	−0.792548	−	0.609810i	$-0.791246\pi$
$11$	−5.25717	−1.58510	−0.792548	+	0.609810i	$0.791246\pi$
$12$	−11.8797	−3.42938
$13$	−4.20342	−1.16582	−0.582909	−	0.812537i	$-0.698086\pi$
$13$	−4.20342	−1.16582	−0.582909	+	0.812537i	$0.698086\pi$
$14$	−2.49227	−0.666087
$15$	−7.10539	−1.83460
$16$	5.31311	1.32828
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	12.3546	2.91200
$19$	0.781120	0.179201	0.0896006	−	0.995978i	$-0.471441\pi$
$19$	0.781120	0.179201	0.0896006	+	0.995978i	$0.471441\pi$
$20$	10.6081	2.37203
$21$	2.82084	0.615559
$22$	−13.1023	−2.79341
$23$	2.42281	0.505190	0.252595	−	0.967572i	$-0.418716\pi$
$23$	2.42281	0.505190	0.252595	+	0.967572i	$0.418716\pi$
$24$	−15.5468	−3.17348
$25$	1.34480	0.268960
$26$	−10.4760	−2.05452
$27$	−5.52084	−1.06249
$28$	−4.21140	−0.795880
$29$	3.42230	0.635505	0.317752	−	0.948174i	$-0.397072\pi$
$29$	3.42230	0.635505	0.317752	+	0.948174i	$0.397072\pi$
$30$	−17.7085	−3.23312
$31$	6.94170	1.24677	0.623383	−	0.781917i	$-0.285758\pi$
$31$	6.94170	1.24677	0.623383	+	0.781917i	$0.285758\pi$
$32$	2.21888	0.392246
$33$	14.8296	2.58151
$34$	2.49227	0.427421
$35$	−2.51889	−0.425770
$36$	20.8766	3.47943
$37$	−7.02282	−1.15455	−0.577273	−	0.816552i	$-0.695883\pi$
$37$	−7.02282	−1.15455	−0.577273	+	0.816552i	$0.695883\pi$
$38$	1.94676	0.315806
$39$	11.8572	1.89867
$40$	13.8826	2.19504
$41$	1.83631	0.286783	0.143391	−	0.989666i	$-0.454199\pi$
$41$	1.83631	0.286783	0.143391	+	0.989666i	$0.454199\pi$
$42$	7.03030	1.08480
$43$	8.63974	1.31755	0.658774	−	0.752341i	$-0.271075\pi$
$43$	8.63974	1.31755	0.658774	+	0.752341i	$0.271075\pi$
$44$	−22.1400	−3.33774
$45$	12.4865	1.86138
$46$	6.03829	0.890297
$47$	−1.34285	−0.195875	−0.0979374	−	0.995193i	$-0.531225\pi$
$47$	−1.34285	−0.195875	−0.0979374	+	0.995193i	$0.531225\pi$
$48$	−14.9875	−2.16325
$49$	1.00000	0.142857
$50$	3.35160	0.473987
$51$	−2.82084	−0.394997
$52$	−17.7023	−2.45487
$53$	−1.95716	−0.268836	−0.134418	−	0.990925i	$-0.542917\pi$
$53$	−1.95716	−0.268836	−0.134418	+	0.990925i	$0.542917\pi$
$54$	−13.7594	−1.87242
$55$	−13.2422	−1.78558
$56$	−5.51141	−0.736493
$57$	−2.20342	−0.291850
$58$	8.52928	1.11995
$59$	2.43776	0.317369	0.158685	−	0.987329i	$-0.449275\pi$
$59$	2.43776	0.317369	0.158685	+	0.987329i	$0.449275\pi$
$60$	−29.9237	−3.86313
$61$	6.16369	0.789180	0.394590	−	0.918857i	$-0.370887\pi$
$61$	6.16369	0.789180	0.394590	+	0.918857i	$0.370887\pi$
$62$	17.3006	2.19717
$63$	−4.95716	−0.624543
$64$	−5.09618	−0.637022
$65$	−10.5879	−1.31327
$66$	36.9595	4.54939
$67$	1.53435	0.187451	0.0937254	−	0.995598i	$-0.470122\pi$
$67$	1.53435	0.187451	0.0937254	+	0.995598i	$0.470122\pi$
$68$	4.21140	0.510708
$69$	−6.83436	−0.822760
$70$	−6.27775	−0.750334
$71$	−1.65664	−0.196607	−0.0983035	−	0.995156i	$-0.531342\pi$
$71$	−1.65664	−0.196607	−0.0983035	+	0.995156i	$0.531342\pi$
$72$	27.3209	3.21980
$73$	−14.3197	−1.67600	−0.837998	−	0.545674i	$-0.816274\pi$
$73$	−14.3197	−1.67600	−0.837998	+	0.545674i	$0.816274\pi$
$74$	−17.5028	−2.03465
$75$	−3.79346	−0.438031
$76$	3.28961	0.377344
$77$	5.25717	0.599110
$78$	29.5513	3.34602
$79$	12.6262	1.42056	0.710281	−	0.703919i	$-0.248568\pi$
$79$	12.6262	1.42056	0.710281	+	0.703919i	$0.248568\pi$
$80$	13.3831	1.49628
$81$	0.701939	0.0779932
$82$	4.57657	0.505397
$83$	−11.8451	−1.30017	−0.650085	−	0.759862i	$-0.725267\pi$
$83$	−11.8451	−1.30017	−0.650085	+	0.759862i	$0.725267\pi$
$84$	11.8797	1.29618
$85$	2.51889	0.273212
$86$	21.5326	2.32191
$87$	−9.65376	−1.03499
$88$	−28.9744	−3.08868
$89$	4.49202	0.476153	0.238076	−	0.971246i	$-0.423483\pi$
$89$	4.49202	0.476153	0.238076	+	0.971246i	$0.423483\pi$
$90$	31.1198	3.28031
$91$	4.20342	0.440638
$92$	10.2034	1.06378
$93$	−19.5814	−2.03050
$94$	−3.34674	−0.345190
$95$	1.96755	0.201867
$96$	−6.25911	−0.638818
$97$	12.9267	1.31251	0.656256	−	0.754538i	$-0.272139\pi$
$97$	12.9267	1.31251	0.656256	+	0.754538i	$0.272139\pi$
$98$	2.49227	0.251757
$99$	−26.0606	−2.61919
$100$	5.66349	0.566349
$101$	−1.82279	−0.181374	−0.0906872	−	0.995879i	$-0.528906\pi$
$101$	−1.82279	−0.181374	−0.0906872	+	0.995879i	$0.528906\pi$
$102$	−7.03030	−0.696103
$103$	1.40734	0.138670	0.0693349	−	0.997593i	$-0.477912\pi$
$103$	1.40734	0.138670	0.0693349	+	0.997593i	$0.477912\pi$
$104$	−23.1668	−2.27169
$105$	7.10539	0.693415
$106$	−4.87776	−0.473770
$107$	−16.0074	−1.54749	−0.773745	−	0.633497i	$-0.781619\pi$
$107$	−16.0074	−1.54749	−0.773745	+	0.633497i	$0.781619\pi$
$108$	−23.2505	−2.23728
$109$	16.5143	1.58179	0.790893	−	0.611954i	$-0.209616\pi$
$109$	16.5143	1.58179	0.790893	+	0.611954i	$0.209616\pi$
$110$	−33.0032	−3.14673
$111$	19.8103	1.88031
$112$	−5.31311	−0.502042
$113$	−1.61548	−0.151971	−0.0759857	−	0.997109i	$-0.524210\pi$
$113$	−1.61548	−0.151971	−0.0759857	+	0.997109i	$0.524210\pi$
$114$	−5.49151	−0.514327
$115$	6.10278	0.569087
$116$	14.4127	1.33818
$117$	−20.8370	−1.92638
$118$	6.07555	0.559300
$119$	−1.00000	−0.0916698
$120$	−39.1607	−3.57487
$121$	16.6378	1.51253
$122$	15.3616	1.39077
$123$	−5.17993	−0.467059
$124$	29.2343	2.62532
$125$	−9.20705	−0.823503
$126$	−12.3546	−1.10063
$127$	11.4177	1.01316	0.506580	−	0.862193i	$-0.330909\pi$
$127$	11.4177	1.01316	0.506580	+	0.862193i	$0.330909\pi$
$128$	−17.1388	−1.51487
$129$	−24.3714	−2.14578
$130$	−26.3880	−2.31438
$131$	−9.96907	−0.871002	−0.435501	−	0.900188i	$-0.643429\pi$
$131$	−9.96907	−0.871002	−0.435501	+	0.900188i	$0.643429\pi$
$132$	62.4536	5.43589
$133$	−0.781120	−0.0677317
$134$	3.82401	0.330345
$135$	−13.9064	−1.19687
$136$	5.51141	0.472600
$137$	−19.3454	−1.65279	−0.826395	−	0.563091i	$-0.809612\pi$
$137$	−19.3454	−1.65279	−0.826395	+	0.563091i	$0.809612\pi$
$138$	−17.0331	−1.44995
$139$	−6.31075	−0.535271	−0.267636	−	0.963520i	$-0.586242\pi$
$139$	−6.31075	−0.535271	−0.267636	+	0.963520i	$0.586242\pi$
$140$	−10.6081	−0.896544
$141$	3.78797	0.319005
$142$	−4.12879	−0.346480
$143$	22.0981	1.84793
$144$	26.3379	2.19483
$145$	8.62038	0.715884
$146$	−35.6886	−2.95361
$147$	−2.82084	−0.232659
$148$	−29.5759	−2.43113
$149$	7.73465	0.633647	0.316824	−	0.948484i	$-0.397384\pi$
$149$	7.73465	0.633647	0.316824	+	0.948484i	$0.397384\pi$
$150$	−9.45433	−0.771943
$151$	13.4088	1.09119	0.545596	−	0.838049i	$-0.316303\pi$
$151$	13.4088	1.09119	0.545596	+	0.838049i	$0.316303\pi$
$152$	4.30507	0.349188
$153$	4.95716	0.400762
$154$	13.1023	1.05581
$155$	17.4854	1.40446
$156$	49.9354	3.99803
$157$	−12.3806	−0.988082	−0.494041	−	0.869439i	$-0.664481\pi$
$157$	−12.3806	−0.988082	−0.494041	+	0.869439i	$0.664481\pi$
$158$	31.4679	2.50346
$159$	5.52084	0.437831
$160$	5.58911	0.441858
$161$	−2.42281	−0.190944
$162$	1.74942	0.137447
$163$	10.7487	0.841901	0.420951	−	0.907084i	$-0.361697\pi$
$163$	10.7487	0.841901	0.420951	+	0.907084i	$0.361697\pi$
$164$	7.73343	0.603879
$165$	37.3542	2.90802
$166$	−29.5212	−2.29129
$167$	−10.4586	−0.809314	−0.404657	−	0.914469i	$-0.632609\pi$
$167$	−10.4586	−0.809314	−0.404657	+	0.914469i	$0.632609\pi$
$168$	15.5468	1.19946
$169$	4.66872	0.359132
$170$	6.27775	0.481481
$171$	3.87214	0.296110
$172$	36.3854	2.77436
$173$	3.83241	0.291373	0.145686	−	0.989331i	$-0.453461\pi$
$173$	3.83241	0.291373	0.145686	+	0.989331i	$0.453461\pi$
$174$	−24.0598	−1.82397
$175$	−1.34480	−0.101657
$176$	−27.9319	−2.10545
$177$	−6.87654	−0.516872
$178$	11.1953	0.839124
$179$	−17.5918	−1.31488	−0.657438	−	0.753509i	$-0.728360\pi$
$179$	−17.5918	−1.31488	−0.657438	+	0.753509i	$0.728360\pi$
$180$	52.5858	3.91951
$181$	−16.9212	−1.25774	−0.628870	−	0.777510i	$-0.716482\pi$
$181$	−16.9212	−1.25774	−0.628870	+	0.777510i	$0.716482\pi$
$182$	10.4760	0.776536
$183$	−17.3868	−1.28527
$184$	13.3531	0.984403
$185$	−17.6897	−1.30057
$186$	−48.8022	−3.57835
$187$	−5.25717	−0.384442
$188$	−5.65529	−0.412454
$189$	5.52084	0.401582
$190$	4.90367	0.355750
$191$	−4.97998	−0.360339	−0.180169	−	0.983636i	$-0.557665\pi$
$191$	−4.97998	−0.360339	−0.180169	+	0.983636i	$0.557665\pi$
$192$	14.3755	1.03746
$193$	18.1725	1.30808	0.654042	−	0.756458i	$-0.273072\pi$
$193$	18.1725	1.30808	0.654042	+	0.756458i	$0.273072\pi$
$194$	32.2169	2.31304
$195$	29.8669	2.13881
$196$	4.21140	0.300815
$197$	4.33864	0.309116	0.154558	−	0.987984i	$-0.450605\pi$
$197$	4.33864	0.309116	0.154558	+	0.987984i	$0.450605\pi$
$198$	−64.9500	−4.61580
$199$	−16.8964	−1.19775	−0.598877	−	0.800841i	$-0.704386\pi$
$199$	−16.8964	−1.19775	−0.598877	+	0.800841i	$0.704386\pi$
$200$	7.41173	0.524089
$201$	−4.32816	−0.305285
$202$	−4.54288	−0.319636
$203$	−3.42230	−0.240198
$204$	−11.8797	−0.831746
$205$	4.62545	0.323055
$206$	3.50748	0.244378
$207$	12.0102	0.834769
$208$	−22.3332	−1.54853
$209$	−4.10648	−0.284051
$210$	17.7085	1.22201
$211$	−23.7938	−1.63803	−0.819017	−	0.573770i	$-0.805480\pi$
$211$	−23.7938	−1.63803	−0.819017	+	0.573770i	$0.805480\pi$
$212$	−8.24238	−0.566089
$213$	4.67312	0.320197
$214$	−39.8946	−2.72714
$215$	21.7625	1.48419
$216$	−30.4276	−2.07034
$217$	−6.94170	−0.471233
$218$	41.1582	2.78758
$219$	40.3937	2.72955
$220$	−55.7683	−3.75990
$221$	−4.20342	−0.282752
$222$	49.3726	3.31367
$223$	−1.14333	−0.0765629	−0.0382814	−	0.999267i	$-0.512188\pi$
$223$	−1.14333	−0.0765629	−0.0382814	+	0.999267i	$0.512188\pi$
$224$	−2.21888	−0.148255
$225$	6.66637	0.444425
$226$	−4.02621	−0.267819
$227$	13.4560	0.893108	0.446554	−	0.894757i	$-0.352651\pi$
$227$	13.4560	0.893108	0.446554	+	0.894757i	$0.352651\pi$
$228$	−9.27948	−0.614549
$229$	−5.86006	−0.387243	−0.193622	−	0.981076i	$-0.562023\pi$
$229$	−5.86006	−0.387243	−0.193622	+	0.981076i	$0.562023\pi$
$230$	15.2098	1.00290
$231$	−14.8296	−0.975719
$232$	18.8617	1.23833
$233$	2.41891	0.158468	0.0792341	−	0.996856i	$-0.474753\pi$
$233$	2.41891	0.158468	0.0792341	+	0.996856i	$0.474753\pi$
$234$	−51.9314	−3.39486
$235$	−3.38249	−0.220649
$236$	10.2664	0.668285
$237$	−35.6166	−2.31355
$238$	−2.49227	−0.161550
$239$	−8.20587	−0.530794	−0.265397	−	0.964139i	$-0.585503\pi$
$239$	−8.20587	−0.530794	−0.265397	+	0.964139i	$0.585503\pi$
$240$	−37.7517	−2.43686
$241$	26.1567	1.68490	0.842450	−	0.538775i	$-0.181113\pi$
$241$	26.1567	1.68490	0.842450	+	0.538775i	$0.181113\pi$
$242$	41.4659	2.66553
$243$	14.5824	0.935464
$244$	25.9578	1.66178
$245$	2.51889	0.160926
$246$	−12.9098	−0.823098
$247$	−3.28337	−0.208916
$248$	38.2585	2.42942
$249$	33.4132	2.11747
$250$	−22.9464	−1.45126
$251$	7.98792	0.504193	0.252097	−	0.967702i	$-0.418880\pi$
$251$	7.98792	0.504193	0.252097	+	0.967702i	$0.418880\pi$
$252$	−20.8766	−1.31510
$253$	−12.7371	−0.800774
$254$	28.4561	1.78549
$255$	−7.10539	−0.444957
$256$	−32.5222	−2.03263
$257$	9.29833	0.580014	0.290007	−	0.957025i	$-0.406342\pi$
$257$	9.29833	0.580014	0.290007	+	0.957025i	$0.406342\pi$
$258$	−60.7400	−3.78150
$259$	7.02282	0.436377
$260$	−44.5901	−2.76536
$261$	16.9649	1.05010
$262$	−24.8456	−1.53497
$263$	3.59317	0.221564	0.110782	−	0.993845i	$-0.464664\pi$
$263$	3.59317	0.221564	0.110782	+	0.993845i	$0.464664\pi$
$264$	81.7323	5.03027
$265$	−4.92986	−0.302839
$266$	−1.94676	−0.119364
$267$	−12.6713	−0.775470
$268$	6.46177	0.394715
$269$	6.51331	0.397124	0.198562	−	0.980088i	$-0.436373\pi$
$269$	6.51331	0.397124	0.198562	+	0.980088i	$0.436373\pi$
$270$	−34.6584	−2.10924
$271$	1.29935	0.0789296	0.0394648	−	0.999221i	$-0.487435\pi$
$271$	1.29935	0.0789296	0.0394648	+	0.999221i	$0.487435\pi$
$272$	5.31311	0.322155
$273$	−11.8572	−0.717629
$274$	−48.2140	−2.91271
$275$	−7.06982	−0.426326
$276$	−28.7822	−1.73249
$277$	−12.0668	−0.725026	−0.362513	−	0.931979i	$-0.618081\pi$
$277$	−12.0668	−0.725026	−0.362513	+	0.931979i	$0.618081\pi$
$278$	−15.7281	−0.943308
$279$	34.4111	2.06014
$280$	−13.8826	−0.829646
$281$	1.77411	0.105834	0.0529172	−	0.998599i	$-0.483148\pi$
$281$	1.77411	0.105834	0.0529172	+	0.998599i	$0.483148\pi$
$282$	9.44064	0.562182
$283$	10.8859	0.647101	0.323550	−	0.946211i	$-0.395124\pi$
$283$	10.8859	0.647101	0.323550	+	0.946211i	$0.395124\pi$
$284$	−6.97678	−0.413996
$285$	−5.55016	−0.328763
$286$	55.0743	3.25661
$287$	−1.83631	−0.108394
$288$	10.9993	0.648142
$289$	1.00000	0.0588235
$290$	21.4843	1.26160
$291$	−36.4643	−2.13758
$292$	−60.3061	−3.52915
$293$	23.7828	1.38940	0.694702	−	0.719298i	$-0.255536\pi$
$293$	23.7828	1.38940	0.694702	+	0.719298i	$0.255536\pi$
$294$	−7.03030	−0.410015
$295$	6.14044	0.357511
$296$	−38.7057	−2.24972
$297$	29.0239	1.68414
$298$	19.2768	1.11668
$299$	−10.1841	−0.588960
$300$	−15.9758	−0.922364
$301$	−8.63974	−0.497986
$302$	33.4183	1.92301
$303$	5.14181	0.295389
$304$	4.15018	0.238029
$305$	15.5257	0.888996
$306$	12.3546	0.706264
$307$	17.4011	0.993134	0.496567	−	0.867999i	$-0.334594\pi$
$307$	17.4011	0.993134	0.496567	+	0.867999i	$0.334594\pi$
$308$	22.1400	1.26155
$309$	−3.96990	−0.225840
$310$	43.5782	2.47508
$311$	−14.1485	−0.802288	−0.401144	−	0.916015i	$-0.631387\pi$
$311$	−14.1485	−0.802288	−0.401144	+	0.916015i	$0.631387\pi$
$312$	65.3498	3.69970
$313$	4.04918	0.228873	0.114437	−	0.993431i	$-0.463494\pi$
$313$	4.04918	0.228873	0.114437	+	0.993431i	$0.463494\pi$
$314$	−30.8558	−1.74130
$315$	−12.4865	−0.703536
$316$	53.1741	2.99128
$317$	−32.6583	−1.83427	−0.917136	−	0.398575i	$-0.869505\pi$
$317$	−32.6583	−1.83427	−0.917136	+	0.398575i	$0.869505\pi$
$318$	13.7594	0.771589
$319$	−17.9916	−1.00734
$320$	−12.8367	−0.717594
$321$	45.1543	2.52026
$322$	−6.03829	−0.336501
$323$	0.781120	0.0434627
$324$	2.95615	0.164230
$325$	−5.65275	−0.313558
$326$	26.7886	1.48368
$327$	−46.5843	−2.57612
$328$	10.1206	0.558819
$329$	1.34285	0.0740338
$330$	93.0967	5.12481
$331$	14.3272	0.787496	0.393748	−	0.919219i	$-0.371178\pi$
$331$	14.3272	0.787496	0.393748	+	0.919219i	$0.371178\pi$
$332$	−49.8845	−2.73777
$333$	−34.8132	−1.90775
$334$	−26.0657	−1.42625
$335$	3.86486	0.211160
$336$	14.9875	0.817633
$337$	21.9938	1.19808	0.599038	−	0.800720i	$-0.295550\pi$
$337$	21.9938	1.19808	0.599038	+	0.800720i	$0.295550\pi$
$338$	11.6357	0.632899
$339$	4.55701	0.247503
$340$	10.6081	0.575303
$341$	−36.4936	−1.97624
$342$	9.65040	0.521834
$343$	−1.00000	−0.0539949
$344$	47.6172	2.56735
$345$	−17.2150	−0.926824
$346$	9.55140	0.513486
$347$	−18.2108	−0.977606	−0.488803	−	0.872394i	$-0.662566\pi$
$347$	−18.2108	−0.977606	−0.488803	+	0.872394i	$0.662566\pi$
$348$	−40.6559	−2.17938
$349$	13.6621	0.731313	0.365657	−	0.930750i	$-0.380844\pi$
$349$	13.6621	0.731313	0.365657	+	0.930750i	$0.380844\pi$
$350$	−3.35160	−0.179150
$351$	23.2064	1.23866
$352$	−11.6650	−0.621748
$353$	−7.82913	−0.416703	−0.208351	−	0.978054i	$-0.566810\pi$
$353$	−7.82913	−0.416703	−0.208351	+	0.978054i	$0.566810\pi$
$354$	−17.1382	−0.910884
$355$	−4.17289	−0.221474
$356$	18.9177	1.00264
$357$	2.82084	0.149295
$358$	−43.8436	−2.31720
$359$	36.9947	1.95251	0.976253	−	0.216634i	$-0.0695079\pi$
$359$	36.9947	1.95251	0.976253	+	0.216634i	$0.0695079\pi$
$360$	68.8184	3.62705
$361$	−18.3899	−0.967887
$362$	−42.1721	−2.21652
$363$	−46.9326	−2.46332
$364$	17.7023	0.927852
$365$	−36.0698	−1.88798
$366$	−43.3326	−2.26503
$367$	−31.6345	−1.65131	−0.825654	−	0.564177i	$-0.809194\pi$
$367$	−31.6345	−1.65131	−0.825654	+	0.564177i	$0.809194\pi$
$368$	12.8726	0.671033
$369$	9.10286	0.473876
$370$	−44.0875	−2.29200
$371$	1.95716	0.101611
$372$	−82.4653	−4.27563
$373$	−28.3894	−1.46995	−0.734974	−	0.678095i	$-0.762806\pi$
$373$	−28.3894	−1.46995	−0.734974	+	0.678095i	$0.762806\pi$
$374$	−13.1023	−0.677502
$375$	25.9716	1.34117
$376$	−7.40100	−0.381678
$377$	−14.3853	−0.740883
$378$	13.7594	0.707707
$379$	−21.6022	−1.10963	−0.554814	−	0.831974i	$-0.687211\pi$
$379$	−21.6022	−1.10963	−0.554814	+	0.831974i	$0.687211\pi$
$380$	8.28616	0.425071
$381$	−32.2077	−1.65005
$382$	−12.4115	−0.635025
$383$	17.4402	0.891153	0.445577	−	0.895244i	$-0.352999\pi$
$383$	17.4402	0.891153	0.445577	+	0.895244i	$0.352999\pi$
$384$	48.3459	2.46714
$385$	13.2422	0.674886
$386$	45.2907	2.30524
$387$	42.8286	2.17710
$388$	54.4397	2.76376
$389$	30.6552	1.55428	0.777141	−	0.629326i	$-0.216669\pi$
$389$	30.6552	1.55428	0.777141	+	0.629326i	$0.216669\pi$
$390$	74.4364	3.76923
$391$	2.42281	0.122527
$392$	5.51141	0.278368
$393$	28.1212	1.41853
$394$	10.8131	0.544754
$395$	31.8040	1.60024
$396$	−109.752	−5.51523
$397$	11.0023	0.552189	0.276095	−	0.961130i	$-0.410960\pi$
$397$	11.0023	0.552189	0.276095	+	0.961130i	$0.410960\pi$
$398$	−42.1104	−2.11080
$399$	2.20342	0.110309
$400$	7.14506	0.357253
$401$	3.98115	0.198809	0.0994046	−	0.995047i	$-0.468306\pi$
$401$	3.98115	0.198809	0.0994046	+	0.995047i	$0.468306\pi$
$402$	−10.7869	−0.538004
$403$	−29.1788	−1.45350
$404$	−7.67651	−0.381920
$405$	1.76811	0.0878579
$406$	−8.52928	−0.423301
$407$	36.9201	1.83006
$408$	−15.5468	−0.769683
$409$	21.0687	1.04178	0.520890	−	0.853624i	$-0.325600\pi$
$409$	21.0687	1.04178	0.520890	+	0.853624i	$0.325600\pi$
$410$	11.5279	0.569321
$411$	54.5704	2.69176
$412$	5.92690	0.291997
$413$	−2.43776	−0.119954
$414$	29.9327	1.47111
$415$	−29.8365	−1.46462
$416$	−9.32688	−0.457288
$417$	17.8016	0.871750
$418$	−10.2344	−0.500583
$419$	15.8730	0.775446	0.387723	−	0.921776i	$-0.373262\pi$
$419$	15.8730	0.775446	0.387723	+	0.921776i	$0.373262\pi$
$420$	29.9237	1.46013
$421$	12.7787	0.622794	0.311397	−	0.950280i	$-0.399203\pi$
$421$	12.7787	0.622794	0.311397	+	0.950280i	$0.399203\pi$
$422$	−59.3006	−2.88671
$423$	−6.65672	−0.323661
$424$	−10.7867	−0.523849
$425$	1.34480	0.0652323
$426$	11.6467	0.564283
$427$	−6.16369	−0.298282
$428$	−67.4135	−3.25855
$429$	−62.3352	−3.00957
$430$	54.2381	2.61559
$431$	−39.1793	−1.88720	−0.943601	−	0.331084i	$-0.892586\pi$
$431$	−39.1793	−1.88720	−0.943601	+	0.331084i	$0.892586\pi$
$432$	−29.3328	−1.41128
$433$	−16.2650	−0.781648	−0.390824	−	0.920465i	$-0.627810\pi$
$433$	−16.2650	−0.781648	−0.390824	+	0.920465i	$0.627810\pi$
$434$	−17.3006	−0.830454
$435$	−24.3168	−1.16590
$436$	69.5485	3.33077
$437$	1.89250	0.0905307
$438$	100.672	4.81029
$439$	−1.97235	−0.0941354	−0.0470677	−	0.998892i	$-0.514988\pi$
$439$	−1.97235	−0.0941354	−0.0470677	+	0.998892i	$0.514988\pi$
$440$	−72.9833	−3.47934
$441$	4.95716	0.236055
$442$	−10.4760	−0.498295
$443$	34.1280	1.62147	0.810734	−	0.585414i	$-0.199068\pi$
$443$	34.1280	1.62147	0.810734	+	0.585414i	$0.199068\pi$
$444$	83.4291	3.95937
$445$	11.3149	0.536377
$446$	−2.84948	−0.134927
$447$	−21.8182	−1.03197
$448$	5.09618	0.240772
$449$	−6.09912	−0.287835	−0.143918	−	0.989590i	$-0.545970\pi$
$449$	−6.09912	−0.287835	−0.143918	+	0.989590i	$0.545970\pi$
$450$	16.6144	0.783210
$451$	−9.65376	−0.454578
$452$	−6.80343	−0.320007
$453$	−37.8241	−1.77713
$454$	33.5360	1.57392
$455$	10.5879	0.496370
$456$	−12.1439	−0.568692
$457$	−14.9650	−0.700034	−0.350017	−	0.936743i	$-0.613824\pi$
$457$	−14.9650	−0.700034	−0.350017	+	0.936743i	$0.613824\pi$
$458$	−14.6048	−0.682439
$459$	−5.52084	−0.257691
$460$	25.7013	1.19833
$461$	−25.9096	−1.20673	−0.603365	−	0.797465i	$-0.706174\pi$
$461$	−25.9096	−1.20673	−0.603365	+	0.797465i	$0.706174\pi$
$462$	−36.9595	−1.71951
$463$	19.7323	0.917037	0.458518	−	0.888685i	$-0.348380\pi$
$463$	19.7323	0.917037	0.458518	+	0.888685i	$0.348380\pi$
$464$	18.1830	0.844127
$465$	−49.3234	−2.28732
$466$	6.02858	0.279269
$467$	−10.7158	−0.495868	−0.247934	−	0.968777i	$-0.579752\pi$
$467$	−10.7158	−0.495868	−0.247934	+	0.968777i	$0.579752\pi$
$468$	−87.7530	−4.05639
$469$	−1.53435	−0.0708497
$470$	−8.43008	−0.388850
$471$	34.9238	1.60920
$472$	13.4355	0.618419
$473$	−45.4205	−2.08844
$474$	−88.7661	−4.07716
$475$	1.05045	0.0481979
$476$	−4.21140	−0.193029
$477$	−9.70194	−0.444221
$478$	−20.4512	−0.935418
$479$	6.99221	0.319482	0.159741	−	0.987159i	$-0.448934\pi$
$479$	6.99221	0.319482	0.159741	+	0.987159i	$0.448934\pi$
$480$	−15.7660	−0.719616
$481$	29.5199	1.34599
$482$	65.1895	2.96930
$483$	6.83436	0.310974
$484$	70.0685	3.18493
$485$	32.5610	1.47852
$486$	36.3434	1.64857
$487$	11.2113	0.508032	0.254016	−	0.967200i	$-0.418248\pi$
$487$	11.2113	0.508032	0.254016	+	0.967200i	$0.418248\pi$
$488$	33.9707	1.53778
$489$	−30.3203	−1.37113
$490$	6.27775	0.283600
$491$	26.1467	1.17999	0.589993	−	0.807408i	$-0.299130\pi$
$491$	26.1467	1.17999	0.589993	+	0.807408i	$0.299130\pi$
$492$	−21.8148	−0.983486
$493$	3.42230	0.154133
$494$	−8.18305	−0.368173
$495$	−65.6437	−2.95047
$496$	36.8820	1.65605
$497$	1.65664	0.0743105
$498$	83.2746	3.73163
$499$	−0.887794	−0.0397431	−0.0198716	−	0.999803i	$-0.506326\pi$
$499$	−0.887794	−0.0397431	−0.0198716	+	0.999803i	$0.506326\pi$
$500$	−38.7746	−1.73405
$501$	29.5022	1.31806
$502$	19.9080	0.888540
$503$	23.2662	1.03739	0.518694	−	0.854960i	$-0.326418\pi$
$503$	23.2662	1.03739	0.518694	+	0.854960i	$0.326418\pi$
$504$	−27.3209	−1.21697
$505$	−4.59141	−0.204315
$506$	−31.7443	−1.41120
$507$	−13.1697	−0.584888
$508$	48.0847	2.13341
$509$	−1.45906	−0.0646718	−0.0323359	−	0.999477i	$-0.510295\pi$
$509$	−1.45906	−0.0646718	−0.0323359	+	0.999477i	$0.510295\pi$
$510$	−17.7085	−0.784147
$511$	14.3197	0.633467
$512$	−46.7763	−2.06724
$513$	−4.31244	−0.190399
$514$	23.1739	1.02216
$515$	3.54494	0.156209
$516$	−102.638	−4.51837
$517$	7.05959	0.310480
$518$	17.5028	0.769027
$519$	−10.8106	−0.474534
$520$	−58.3545	−2.55901
$521$	−42.0865	−1.84384	−0.921921	−	0.387377i	$-0.873381\pi$
$521$	−42.0865	−1.84384	−0.921921	+	0.387377i	$0.873381\pi$
$522$	42.2810	1.85059
$523$	17.2674	0.755051	0.377525	−	0.925999i	$-0.376775\pi$
$523$	17.2674	0.755051	0.377525	+	0.925999i	$0.376775\pi$
$524$	−41.9838	−1.83407
$525$	3.79346	0.165560
$526$	8.95513	0.390462
$527$	6.94170	0.302385
$528$	78.7915	3.42896
$529$	−17.1300	−0.744783
$530$	−12.2865	−0.533693
$531$	12.0844	0.524417
$532$	−3.28961	−0.142623
$533$	−7.71876	−0.334337
$534$	−31.5802	−1.36661
$535$	−40.3208	−1.74322
$536$	8.45644	0.365263
$537$	49.6238	2.14143
$538$	16.2329	0.699851
$539$	−5.25717	−0.226442
$540$	−58.5653	−2.52025
$541$	−24.7411	−1.06370	−0.531851	−	0.846838i	$-0.678503\pi$
$541$	−24.7411	−1.06370	−0.531851	+	0.846838i	$0.678503\pi$
$542$	3.23832	0.139098
$543$	47.7320	2.04837
$544$	2.21888	0.0951337
$545$	41.5978	1.78185
$546$	−29.5513	−1.26468
$547$	4.66104	0.199292	0.0996459	−	0.995023i	$-0.468229\pi$
$547$	4.66104	0.199292	0.0996459	+	0.995023i	$0.468229\pi$
$548$	−81.4713	−3.48028
$549$	30.5544	1.30403
$550$	−17.6199	−0.751315
$551$	2.67323	0.113883
$552$	−37.6670	−1.60321
$553$	−12.6262	−0.536922
$554$	−30.0738	−1.27771
$555$	49.8999	2.11813
$556$	−26.5771	−1.12712
$557$	−13.1120	−0.555573	−0.277787	−	0.960643i	$-0.589601\pi$
$557$	−13.1120	−0.555573	−0.277787	+	0.960643i	$0.589601\pi$
$558$	85.7617	3.63058
$559$	−36.3164	−1.53602
$560$	−13.3831	−0.565541
$561$	14.8296	0.626108
$562$	4.42155	0.186512
$563$	−27.6650	−1.16594	−0.582971	−	0.812493i	$-0.698110\pi$
$563$	−27.6650	−1.16594	−0.582971	+	0.812493i	$0.698110\pi$
$564$	15.9527	0.671729
$565$	−4.06921	−0.171193
$566$	27.1306	1.14039
$567$	−0.701939	−0.0294787
$568$	−9.13042	−0.383104
$569$	10.8911	0.456578	0.228289	−	0.973593i	$-0.426687\pi$
$569$	10.8911	0.456578	0.228289	+	0.973593i	$0.426687\pi$
$570$	−13.8325	−0.579379
$571$	40.3446	1.68837	0.844184	−	0.536053i	$-0.180085\pi$
$571$	40.3446	1.68837	0.844184	+	0.536053i	$0.180085\pi$
$572$	93.0639	3.89120
$573$	14.0477	0.586853
$574$	−4.57657	−0.191022
$575$	3.25819	0.135876
$576$	−25.2626	−1.05261
$577$	30.0190	1.24971	0.624855	−	0.780741i	$-0.285158\pi$
$577$	30.0190	1.24971	0.624855	+	0.780741i	$0.285158\pi$
$578$	2.49227	0.103665
$579$	−51.2618	−2.13037
$580$	36.3039	1.50744
$581$	11.8451	0.491418
$582$	−90.8789	−3.76705
$583$	10.2891	0.426131
$584$	−78.9218	−3.26581
$585$	−52.4861	−2.17003
$586$	59.2730	2.44855
$587$	38.3982	1.58486	0.792432	−	0.609960i	$-0.208815\pi$
$587$	38.3982	1.58486	0.792432	+	0.609960i	$0.208815\pi$
$588$	−11.8797	−0.489911
$589$	5.42230	0.223422
$590$	15.3036	0.630041
$591$	−12.2386	−0.503430
$592$	−37.3130	−1.53356
$593$	5.71631	0.234741	0.117370	−	0.993088i	$-0.462554\pi$
$593$	5.71631	0.234741	0.117370	+	0.993088i	$0.462554\pi$
$594$	72.3355	2.96796
$595$	−2.51889	−0.103264
$596$	32.5737	1.33427
$597$	47.6621	1.95068
$598$	−25.3814	−1.03792
$599$	−29.9765	−1.22481	−0.612404	−	0.790545i	$-0.709798\pi$
$599$	−29.9765	−1.22481	−0.612404	+	0.790545i	$0.709798\pi$
$600$	−20.9073	−0.853539
$601$	28.2586	1.15269	0.576346	−	0.817206i	$-0.304478\pi$
$601$	28.2586	1.15269	0.576346	+	0.817206i	$0.304478\pi$
$602$	−21.5326	−0.877601
$603$	7.60602	0.309741
$604$	56.4698	2.29772
$605$	41.9087	1.70383
$606$	12.8148	0.520564
$607$	−43.1772	−1.75251	−0.876253	−	0.481851i	$-0.839965\pi$
$607$	−43.1772	−1.75251	−0.876253	+	0.481851i	$0.839965\pi$
$608$	1.73321	0.0702910
$609$	9.65376	0.391190
$610$	38.6941	1.56668
$611$	5.64456	0.228355
$612$	20.8766	0.843886
$613$	−12.1412	−0.490380	−0.245190	−	0.969475i	$-0.578850\pi$
$613$	−12.1412	−0.490380	−0.245190	+	0.969475i	$0.578850\pi$
$614$	43.3682	1.75020
$615$	−13.0477	−0.526133
$616$	28.9744	1.16741
$617$	23.0826	0.929270	0.464635	−	0.885502i	$-0.346185\pi$
$617$	23.0826	0.929270	0.464635	+	0.885502i	$0.346185\pi$
$618$	−9.89405	−0.397997
$619$	7.86057	0.315943	0.157972	−	0.987444i	$-0.449505\pi$
$619$	7.86057	0.315943	0.157972	+	0.987444i	$0.449505\pi$
$620$	73.6379	2.95737
$621$	−13.3759	−0.536757
$622$	−35.2619	−1.41387
$623$	−4.49202	−0.179969
$624$	62.9985	2.52196
$625$	−29.9155	−1.19662
$626$	10.0917	0.403344
$627$	11.5837	0.462610
$628$	−52.1398	−2.08061
$629$	−7.02282	−0.280018
$630$	−31.1198	−1.23984
$631$	35.8212	1.42602	0.713010	−	0.701154i	$-0.247331\pi$
$631$	35.8212	1.42602	0.713010	+	0.701154i	$0.247331\pi$
$632$	69.5883	2.76807
$633$	67.1186	2.66773
$634$	−81.3932	−3.23254
$635$	28.7600	1.14131
$636$	23.2505	0.921941
$637$	−4.20342	−0.166545
$638$	−44.8399	−1.77523
$639$	−8.21222	−0.324871
$640$	−43.1707	−1.70647
$641$	−5.24743	−0.207261	−0.103631	−	0.994616i	$-0.533046\pi$
$641$	−5.24743	−0.207261	−0.103631	+	0.994616i	$0.533046\pi$
$642$	112.537	4.44146
$643$	32.1828	1.26917	0.634583	−	0.772855i	$-0.281172\pi$
$643$	32.1828	1.26917	0.634583	+	0.772855i	$0.281172\pi$
$644$	−10.2034	−0.402071
$645$	−61.3887	−2.41718
$646$	1.94676	0.0765943
$647$	−16.6171	−0.653286	−0.326643	−	0.945148i	$-0.605917\pi$
$647$	−16.6171	−0.653286	−0.326643	+	0.945148i	$0.605917\pi$
$648$	3.86867	0.151976
$649$	−12.8157	−0.503061
$650$	−14.0882	−0.552583
$651$	19.5814	0.767457
$652$	45.2670	1.77279
$653$	0.159913	0.00625786	0.00312893	−	0.999995i	$-0.499004\pi$
$653$	0.159913	0.00625786	0.00312893	+	0.999995i	$0.499004\pi$
$654$	−116.101	−4.53990
$655$	−25.1110	−0.981167
$656$	9.75650	0.380927
$657$	−70.9851	−2.76939
$658$	3.34674	0.130470
$659$	32.4256	1.26312	0.631561	−	0.775326i	$-0.282414\pi$
$659$	32.4256	1.26312	0.631561	+	0.775326i	$0.282414\pi$
$660$	157.314	6.12343
$661$	−31.9068	−1.24103	−0.620516	−	0.784194i	$-0.713077\pi$
$661$	−31.9068	−1.24103	−0.620516	+	0.784194i	$0.713077\pi$
$662$	35.7073	1.38780
$663$	11.8572	0.460495
$664$	−65.2832	−2.53348
$665$	−1.96755	−0.0762985
$666$	−86.7640	−3.36203
$667$	8.29157	0.321051
$668$	−44.0455	−1.70417
$669$	3.22515	0.124691
$670$	9.63226	0.372127
$671$	−32.4036	−1.25093
$672$	6.25911	0.241451
$673$	31.4641	1.21285	0.606425	−	0.795141i	$-0.292603\pi$
$673$	31.4641	1.21285	0.606425	+	0.795141i	$0.292603\pi$
$674$	54.8144	2.11137
$675$	−7.42441	−0.285766
$676$	19.6619	0.756225
$677$	24.6433	0.947120	0.473560	−	0.880762i	$-0.342969\pi$
$677$	24.6433	0.947120	0.473560	+	0.880762i	$0.342969\pi$
$678$	11.3573	0.436175
$679$	−12.9267	−0.496083
$680$	13.8826	0.532375
$681$	−37.9573	−1.45453
$682$	−90.9520	−3.48273
$683$	−24.5793	−0.940502	−0.470251	−	0.882533i	$-0.655837\pi$
$683$	−24.5793	−0.940502	−0.470251	+	0.882533i	$0.655837\pi$
$684$	16.3071	0.623518
$685$	−48.7289	−1.86184
$686$	−2.49227	−0.0951553
$687$	16.5303	0.630670
$688$	45.9039	1.75007
$689$	8.22675	0.313414
$690$	−42.9044	−1.63334
$691$	30.5847	1.16350	0.581749	−	0.813368i	$-0.302368\pi$
$691$	30.5847	1.16350	0.581749	+	0.813368i	$0.302368\pi$
$692$	16.1398	0.613544
$693$	26.0606	0.989960
$694$	−45.3862	−1.72283
$695$	−15.8961	−0.602973
$696$	−53.2059	−2.01676
$697$	1.83631	0.0695550
$698$	34.0495	1.28879
$699$	−6.82337	−0.258084
$700$	−5.66349	−0.214060
$701$	−39.8182	−1.50391	−0.751956	−	0.659213i	$-0.770889\pi$
$701$	−39.8182	−1.50391	−0.751956	+	0.659213i	$0.770889\pi$
$702$	57.8365	2.18290
$703$	−5.48567	−0.206896
$704$	26.7915	1.00974
$705$	9.54148	0.359353
$706$	−19.5123	−0.734355
$707$	1.82279	0.0685531
$708$	−28.9599	−1.08838
$709$	−1.22040	−0.0458331	−0.0229166	−	0.999737i	$-0.507295\pi$
$709$	−1.22040	−0.0458331	−0.0229166	+	0.999737i	$0.507295\pi$
$710$	−10.4000	−0.390304
$711$	62.5902	2.34732
$712$	24.7574	0.927821
$713$	16.8184	0.629854
$714$	7.03030	0.263102
$715$	55.6625	2.08166
$716$	−74.0863	−2.76874
$717$	23.1475	0.864459
$718$	92.2007	3.44090
$719$	−14.9740	−0.558435	−0.279218	−	0.960228i	$-0.590075\pi$
$719$	−14.9740	−0.558435	−0.279218	+	0.960228i	$0.590075\pi$
$720$	66.3423	2.47243
$721$	−1.40734	−0.0524122
$722$	−45.8325	−1.70571
$723$	−73.7839	−2.74405
$724$	−71.2619	−2.64843
$725$	4.60230	0.170925
$726$	−116.969	−4.34111
$727$	−24.6970	−0.915959	−0.457980	−	0.888963i	$-0.651427\pi$
$727$	−24.6970	−0.915959	−0.457980	+	0.888963i	$0.651427\pi$
$728$	23.1668	0.858617
$729$	−43.2406	−1.60150
$730$	−89.8955	−3.32718
$731$	8.63974	0.319552
$732$	−73.2229	−2.70640
$733$	−5.36434	−0.198136	−0.0990682	−	0.995081i	$-0.531586\pi$
$733$	−5.36434	−0.198136	−0.0990682	+	0.995081i	$0.531586\pi$
$734$	−78.8417	−2.91010
$735$	−7.10539	−0.262086
$736$	5.37592	0.198159
$737$	−8.06634	−0.297127
$738$	22.6868	0.835111
$739$	20.4094	0.750772	0.375386	−	0.926869i	$-0.377510\pi$
$739$	20.4094	0.750772	0.375386	+	0.926869i	$0.377510\pi$
$740$	−74.4985	−2.73862
$741$	9.26188	0.340244
$742$	4.87776	0.179068
$743$	−16.9780	−0.622861	−0.311431	−	0.950269i	$-0.600808\pi$
$743$	−16.9780	−0.622861	−0.311431	+	0.950269i	$0.600808\pi$
$744$	−107.921	−3.95659
$745$	19.4827	0.713791
$746$	−70.7541	−2.59049
$747$	−58.7180	−2.14838
$748$	−22.1400	−0.809520
$749$	16.0074	0.584896
$750$	64.7283	2.36354
$751$	−8.99611	−0.328273	−0.164136	−	0.986438i	$-0.552484\pi$
$751$	−8.99611	−0.328273	−0.164136	+	0.986438i	$0.552484\pi$
$752$	−7.13472	−0.260176
$753$	−22.5327	−0.821136
$754$	−35.8521	−1.30566
$755$	33.7752	1.22921
$756$	23.2505	0.845611
$757$	8.75655	0.318262	0.159131	−	0.987257i	$-0.449131\pi$
$757$	8.75655	0.318262	0.159131	+	0.987257i	$0.449131\pi$
$758$	−53.8384	−1.95550
$759$	35.9294	1.30415
$760$	10.8440	0.393353
$761$	−51.5596	−1.86903	−0.934517	−	0.355920i	$-0.884168\pi$
$761$	−51.5596	−1.86903	−0.934517	+	0.355920i	$0.884168\pi$
$762$	−80.2701	−2.90788
$763$	−16.5143	−0.597859
$764$	−20.9727	−0.758766
$765$	12.4865	0.451451
$766$	43.4657	1.57048
$767$	−10.2469	−0.369995
$768$	91.7399	3.31038
$769$	1.84214	0.0664292	0.0332146	−	0.999448i	$-0.489426\pi$
$769$	1.84214	0.0664292	0.0332146	+	0.999448i	$0.489426\pi$
$770$	33.0032	1.18935
$771$	−26.2291	−0.944619
$772$	76.5317	2.75444
$773$	54.9320	1.97577	0.987884	−	0.155196i	$-0.0496007\pi$
$773$	54.9320	1.97577	0.987884	+	0.155196i	$0.0496007\pi$
$774$	106.740	3.83670
$775$	9.33518	0.335329
$776$	71.2446	2.55753
$777$	−19.8103	−0.710690
$778$	76.4011	2.73911
$779$	1.43438	0.0513918
$780$	125.782	4.50370
$781$	8.70923	0.311641
$782$	6.03829	0.215929
$783$	−18.8939	−0.675214
$784$	5.31311	0.189754
$785$	−31.1854	−1.11306
$786$	70.0856	2.49987
$787$	−5.34624	−0.190573	−0.0952865	−	0.995450i	$-0.530377\pi$
$787$	−5.34624	−0.190573	−0.0952865	+	0.995450i	$0.530377\pi$
$788$	18.2718	0.650905
$789$	−10.1358	−0.360842
$790$	79.2642	2.82009
$791$	1.61548	0.0574398
$792$	−143.631	−5.10369
$793$	−25.9086	−0.920041
$794$	27.4207	0.973123
$795$	13.9064	0.493208
$796$	−71.1575	−2.52211
$797$	47.0419	1.66631	0.833156	−	0.553039i	$-0.186532\pi$
$797$	47.0419	1.66631	0.833156	+	0.553039i	$0.186532\pi$
$798$	5.49151	0.194397
$799$	−1.34285	−0.0475066
$800$	2.98394	0.105498
$801$	22.2676	0.786788
$802$	9.92210	0.350362
$803$	75.2811	2.65661
$804$	−18.2276	−0.642839
$805$	−6.10278	−0.215095
$806$	−72.7215	−2.56151
$807$	−18.3730	−0.646761
$808$	−10.0461	−0.353422
$809$	27.2918	0.959527	0.479763	−	0.877398i	$-0.340722\pi$
$809$	27.2918	0.959527	0.479763	+	0.877398i	$0.340722\pi$
$810$	4.40659	0.154832
$811$	−31.6841	−1.11258	−0.556289	−	0.830989i	$-0.687775\pi$
$811$	−31.6841	−1.11258	−0.556289	+	0.830989i	$0.687775\pi$
$812$	−14.4127	−0.505786
$813$	−3.66525	−0.128546
$814$	92.0149	3.22512
$815$	27.0747	0.948386
$816$	−14.9875	−0.524666
$817$	6.74867	0.236106
$818$	52.5089	1.83593
$819$	20.8370	0.728104
$820$	19.4796	0.680258
$821$	13.2126	0.461124	0.230562	−	0.973058i	$-0.425943\pi$
$821$	13.2126	0.461124	0.230562	+	0.973058i	$0.425943\pi$
$822$	136.004	4.74369
$823$	8.52446	0.297144	0.148572	−	0.988902i	$-0.452532\pi$
$823$	8.52446	0.297144	0.148572	+	0.988902i	$0.452532\pi$
$824$	7.75645	0.270209
$825$	19.9429	0.694322
$826$	−6.07555	−0.211396
$827$	2.47994	0.0862360	0.0431180	−	0.999070i	$-0.486271\pi$
$827$	2.47994	0.0862360	0.0431180	+	0.999070i	$0.486271\pi$
$828$	50.5799	1.75777
$829$	47.4995	1.64972	0.824862	−	0.565333i	$-0.191252\pi$
$829$	47.4995	1.64972	0.824862	+	0.565333i	$0.191252\pi$
$830$	−74.3606	−2.58109
$831$	34.0387	1.18079
$832$	21.4214	0.742652
$833$	1.00000	0.0346479
$834$	44.3665	1.53629
$835$	−26.3441	−0.911676
$836$	−17.2940	−0.598127
$837$	−38.3240	−1.32467
$838$	39.5598	1.36657
$839$	−32.9427	−1.13731	−0.568653	−	0.822577i	$-0.692535\pi$
$839$	−32.9427	−1.13731	−0.568653	+	0.822577i	$0.692535\pi$
$840$	39.1607	1.35117
$841$	−17.2879	−0.596134
$842$	31.8479	1.09755
$843$	−5.00448	−0.172363
$844$	−100.205	−3.44921
$845$	11.7600	0.404556
$846$	−16.5903	−0.570388
$847$	−16.6378	−0.571681
$848$	−10.3986	−0.357089
$849$	−30.7075	−1.05388
$850$	3.35160	0.114959
$851$	−17.0149	−0.583265
$852$	19.6804	0.674239
$853$	47.5645	1.62858	0.814288	−	0.580460i	$-0.197127\pi$
$853$	47.5645	1.62858	0.814288	+	0.580460i	$0.197127\pi$
$854$	−15.3616	−0.525663
$855$	9.75348	0.333562
$856$	−88.2232	−3.01541
$857$	−34.0918	−1.16455	−0.582277	−	0.812991i	$-0.697838\pi$
$857$	−34.0918	−1.16455	−0.582277	+	0.812991i	$0.697838\pi$
$858$	−155.356	−5.30377
$859$	13.1715	0.449405	0.224703	−	0.974427i	$-0.427859\pi$
$859$	13.1715	0.449405	0.224703	+	0.974427i	$0.427859\pi$
$860$	91.6508	3.12527
$861$	5.17993	0.176532
$862$	−97.6455	−3.32582
$863$	−5.24872	−0.178668	−0.0893342	−	0.996002i	$-0.528474\pi$
$863$	−5.24872	−0.178668	−0.0893342	+	0.996002i	$0.528474\pi$
$864$	−12.2501	−0.416756
$865$	9.65342	0.328226
$866$	−40.5368	−1.37750
$867$	−2.82084	−0.0958009
$868$	−29.2343	−0.992276
$869$	−66.3782	−2.25172
$870$	−60.6039	−2.05466
$871$	−6.44952	−0.218534
$872$	91.0173	3.08223
$873$	64.0799	2.16878
$874$	4.71663	0.159542
$875$	9.20705	0.311255
$876$	170.114	5.74762
$877$	45.7500	1.54487	0.772434	−	0.635096i	$-0.219039\pi$
$877$	45.7500	1.54487	0.772434	+	0.635096i	$0.219039\pi$
$878$	−4.91564	−0.165895
$879$	−67.0874	−2.26280
$880$	−70.3574	−2.37175
$881$	0.719858	0.0242526	0.0121263	−	0.999926i	$-0.496140\pi$
$881$	0.719858	0.0242526	0.0121263	+	0.999926i	$0.496140\pi$
$882$	12.3546	0.416000
$883$	−36.3191	−1.22224	−0.611118	−	0.791539i	$-0.709280\pi$
$883$	−36.3191	−1.22224	−0.611118	+	0.791539i	$0.709280\pi$
$884$	−17.7023	−0.595392
$885$	−17.3212	−0.582247
$886$	85.0561	2.85751
$887$	−12.7805	−0.429126	−0.214563	−	0.976710i	$-0.568833\pi$
$887$	−12.7805	−0.429126	−0.214563	+	0.976710i	$0.568833\pi$
$888$	109.183	3.66393
$889$	−11.4177	−0.382939
$890$	28.1997	0.945258
$891$	−3.69021	−0.123627
$892$	−4.81501	−0.161219
$893$	−1.04893	−0.0351010
$894$	−54.3769	−1.81864
$895$	−44.3119	−1.48118
$896$	17.1388	0.572567
$897$	28.7277	0.959189
$898$	−15.2006	−0.507252
$899$	23.7565	0.792325
$900$	28.0748	0.935826
$901$	−1.95716	−0.0652024
$902$	−24.0598	−0.801103
$903$	24.3714	0.811028
$904$	−8.90357	−0.296128
$905$	−42.6225	−1.41682
$906$	−94.2678	−3.13184
$907$	27.1387	0.901126	0.450563	−	0.892745i	$-0.351223\pi$
$907$	27.1387	0.901126	0.450563	+	0.892745i	$0.351223\pi$
$908$	56.6688	1.88062
$909$	−9.03586	−0.299701
$910$	26.3880	0.874753
$911$	34.9889	1.15923	0.579616	−	0.814890i	$-0.303202\pi$
$911$	34.9889	1.15923	0.579616	+	0.814890i	$0.303202\pi$
$912$	−11.7070	−0.387658
$913$	62.2717	2.06089
$914$	−37.2969	−1.23367
$915$	−43.7954	−1.44783
$916$	−24.6791	−0.815419
$917$	9.96907	0.329208
$918$	−13.7594	−0.454128
$919$	−19.0980	−0.629984	−0.314992	−	0.949094i	$-0.602002\pi$
$919$	−19.0980	−0.629984	−0.314992	+	0.949094i	$0.602002\pi$
$920$	33.6349	1.10891
$921$	−49.0858	−1.61743
$922$	−64.5737	−2.12662
$923$	6.96355	0.229208
$924$	−62.4536	−2.05457
$925$	−9.44428	−0.310526
$926$	49.1781	1.61609
$927$	6.97643	0.229136
$928$	7.59367	0.249274
$929$	38.5323	1.26420	0.632102	−	0.774885i	$-0.282193\pi$
$929$	38.5323	1.26420	0.632102	+	0.774885i	$0.282193\pi$
$930$	−122.927	−4.03094
$931$	0.781120	0.0256002
$932$	10.1870	0.333687
$933$	39.9107	1.30662
$934$	−26.7067	−0.873869
$935$	−13.2422	−0.433067
$936$	−114.841	−3.75371
$937$	40.9170	1.33670	0.668350	−	0.743847i	$-0.267001\pi$
$937$	40.9170	1.33670	0.668350	+	0.743847i	$0.267001\pi$
$938$	−3.82401	−0.124858
$939$	−11.4221	−0.372747
$940$	−14.2450	−0.464622
$941$	14.9176	0.486298	0.243149	−	0.969989i	$-0.421820\pi$
$941$	14.9176	0.486298	0.243149	+	0.969989i	$0.421820\pi$
$942$	87.0395	2.83590
$943$	4.44901	0.144880
$944$	12.9521	0.421555
$945$	13.9064	0.452374
$946$	−113.200	−3.68046
$947$	−54.3712	−1.76683	−0.883413	−	0.468595i	$-0.844760\pi$
$947$	−54.3712	−1.76683	−0.883413	+	0.468595i	$0.844760\pi$
$948$	−149.996	−4.87164
$949$	60.1917	1.95391
$950$	2.61800	0.0849391
$951$	92.1239	2.98732
$952$	−5.51141	−0.178626
$953$	−33.1263	−1.07306	−0.536532	−	0.843880i	$-0.680266\pi$
$953$	−33.1263	−1.07306	−0.536532	+	0.843880i	$0.680266\pi$
$954$	−24.1798	−0.782851
$955$	−12.5440	−0.405915
$956$	−34.5582	−1.11769
$957$	50.7514	1.64056
$958$	17.4265	0.563024
$959$	19.3454	0.624696
$960$	36.2103	1.16868
$961$	17.1871	0.554424
$962$	73.5714	2.37204
$963$	−79.3510	−2.55705
$964$	110.156	3.54790
$965$	45.7745	1.47353
$966$	17.0331	0.548030
$967$	−54.0452	−1.73798	−0.868988	−	0.494834i	$-0.835229\pi$
$967$	−54.0452	−1.73798	−0.868988	+	0.494834i	$0.835229\pi$
$968$	91.6977	2.94728
$969$	−2.20342	−0.0707840
$970$	81.1508	2.60560
$971$	−40.0719	−1.28597	−0.642984	−	0.765880i	$-0.722304\pi$
$971$	−40.0719	−1.28597	−0.642984	+	0.765880i	$0.722304\pi$
$972$	61.4126	1.96981
$973$	6.31075	0.202313
$974$	27.9415	0.895305
$975$	15.9455	0.510665
$976$	32.7484	1.04825
$977$	37.2405	1.19143	0.595715	−	0.803196i	$-0.296869\pi$
$977$	37.2405	1.19143	0.595715	+	0.803196i	$0.296869\pi$
$978$	−75.5664	−2.41635
$979$	−23.6153	−0.754748
$980$	10.6081	0.338862
$981$	81.8641	2.61372
$982$	65.1647	2.07949
$983$	12.0729	0.385067	0.192534	−	0.981290i	$-0.438330\pi$
$983$	12.0729	0.385067	0.192534	+	0.981290i	$0.438330\pi$
$984$	−28.5487	−0.910100
$985$	10.9286	0.348213
$986$	8.52928	0.271628
$987$	−3.78797	−0.120572
$988$	−13.8276	−0.439915
$989$	20.9324	0.665612
$990$	−163.602	−5.19961
$991$	−6.66778	−0.211809	−0.105905	−	0.994376i	$-0.533774\pi$
$991$	−6.66778	−0.211809	−0.105905	+	0.994376i	$0.533774\pi$
$992$	15.4028	0.489039
$993$	−40.4149	−1.28253
$994$	4.12879	0.130957
$995$	−42.5601	−1.34925
$996$	140.716	4.45877
$997$	13.2321	0.419064	0.209532	−	0.977802i	$-0.432806\pi$
$997$	13.2321	0.419064	0.209532	+	0.977802i	$0.432806\pi$
$998$	−2.21262	−0.0700393
$999$	38.7719	1.22669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.2.a.b.1.5	✓	5
3.2	odd	2		1071.2.a.m.1.1		5
4.3	odd	2		1904.2.a.t.1.4		5
5.4	even	2		2975.2.a.m.1.1		5
7.2	even	3		833.2.e.i.18.1		10
7.3	odd	6		833.2.e.h.324.1		10
7.4	even	3		833.2.e.i.324.1		10
7.5	odd	6		833.2.e.h.18.1		10
7.6	odd	2		833.2.a.g.1.5		5
8.3	odd	2		7616.2.a.bq.1.2		5
8.5	even	2		7616.2.a.bt.1.4		5
17.16	even	2		2023.2.a.j.1.5		5
21.20	even	2		7497.2.a.br.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.a.b.1.5	✓	5	1.1	even	1	trivial
833.2.a.g.1.5		5	7.6	odd	2
833.2.e.h.18.1		10	7.5	odd	6
833.2.e.h.324.1		10	7.3	odd	6
833.2.e.i.18.1		10	7.2	even	3
833.2.e.i.324.1		10	7.4	even	3
1071.2.a.m.1.1		5	3.2	odd	2
1904.2.a.t.1.4		5	4.3	odd	2
2023.2.a.j.1.5		5	17.16	even	2
2975.2.a.m.1.1		5	5.4	even	2
7497.2.a.br.1.1		5	21.20	even	2
7616.2.a.bq.1.2		5	8.3	odd	2
7616.2.a.bt.1.4		5	8.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	119.a (trivial)

\(f(q)\)	\(=\)	\(q+2.49227 q^{2} -2.82084 q^{3} +4.21140 q^{4} +2.51889 q^{5} -7.03030 q^{6} -1.00000 q^{7} +5.51141 q^{8} +4.95716 q^{9} +6.27775 q^{10} -5.25717 q^{11} -11.8797 q^{12} -4.20342 q^{13} -2.49227 q^{14} -7.10539 q^{15} +5.31311 q^{16} +1.00000 q^{17} +12.3546 q^{18} +0.781120 q^{19} +10.6081 q^{20} +2.82084 q^{21} -13.1023 q^{22} +2.42281 q^{23} -15.5468 q^{24} +1.34480 q^{25} -10.4760 q^{26} -5.52084 q^{27} -4.21140 q^{28} +3.42230 q^{29} -17.7085 q^{30} +6.94170 q^{31} +2.21888 q^{32} +14.8296 q^{33} +2.49227 q^{34} -2.51889 q^{35} +20.8766 q^{36} -7.02282 q^{37} +1.94676 q^{38} +11.8572 q^{39} +13.8826 q^{40} +1.83631 q^{41} +7.03030 q^{42} +8.63974 q^{43} -22.1400 q^{44} +12.4865 q^{45} +6.03829 q^{46} -1.34285 q^{47} -14.9875 q^{48} +1.00000 q^{49} +3.35160 q^{50} -2.82084 q^{51} -17.7023 q^{52} -1.95716 q^{53} -13.7594 q^{54} -13.2422 q^{55} -5.51141 q^{56} -2.20342 q^{57} +8.52928 q^{58} +2.43776 q^{59} -29.9237 q^{60} +6.16369 q^{61} +17.3006 q^{62} -4.95716 q^{63} -5.09618 q^{64} -10.5879 q^{65} +36.9595 q^{66} +1.53435 q^{67} +4.21140 q^{68} -6.83436 q^{69} -6.27775 q^{70} -1.65664 q^{71} +27.3209 q^{72} -14.3197 q^{73} -17.5028 q^{74} -3.79346 q^{75} +3.28961 q^{76} +5.25717 q^{77} +29.5513 q^{78} +12.6262 q^{79} +13.3831 q^{80} +0.701939 q^{81} +4.57657 q^{82} -11.8451 q^{83} +11.8797 q^{84} +2.51889 q^{85} +21.5326 q^{86} -9.65376 q^{87} -28.9744 q^{88} +4.49202 q^{89} +31.1198 q^{90} +4.20342 q^{91} +10.2034 q^{92} -19.5814 q^{93} -3.34674 q^{94} +1.96755 q^{95} -6.25911 q^{96} +12.9267 q^{97} +2.49227 q^{98} -26.0606 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - q^{6} - 5 q^{7} + 6 q^{8} + 11 q^{9} + 4 q^{10} - 2 q^{11} - 22 q^{12} + 2 q^{13} - 2 q^{14} + 8 q^{15} + 4 q^{16} + 5 q^{17} - 18 q^{18} + 6 q^{19} - 19 q^{20} + 2 q^{21}+ \cdots - 62 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - q^6 - 5 * q^7 + 6 * q^8 + 11 * q^9 + 4 * q^10 - 2 * q^11 - 22 * q^12 + 2 * q^13 - 2 * q^14 + 8 * q^15 + 4 * q^16 + 5 * q^17 - 18 * q^18 + 6 * q^19 - 19 * q^20 + 2 * q^21 + 6 * q^22 - 10 * q^23 + 2 * q^24 + 21 * q^25 - 26 * q^26 - 26 * q^27 - 10 * q^28 - 8 * q^29 - 51 * q^30 + 9 * q^32 + 6 * q^33 + 2 * q^34 + 39 * q^36 + 8 * q^37 + 14 * q^38 + 14 * q^39 + 5 * q^40 + 18 * q^41 + q^42 + 8 * q^43 - 14 * q^44 + 8 * q^46 - 10 * q^47 - 27 * q^48 + 5 * q^49 + 27 * q^50 - 2 * q^51 + 4 * q^52 + 4 * q^53 + 5 * q^54 - 24 * q^55 - 6 * q^56 + 12 * q^57 + 12 * q^58 + 8 * q^59 - 7 * q^60 + 22 * q^61 + 16 * q^62 - 11 * q^63 - 16 * q^64 - 30 * q^65 + 68 * q^66 + 16 * q^67 + 10 * q^68 - 32 * q^69 - 4 * q^70 - 2 * q^71 + 9 * q^72 + 10 * q^73 - 40 * q^74 - 14 * q^75 + 24 * q^76 + 2 * q^77 + 30 * q^78 + 18 * q^79 - 4 * q^80 + 25 * q^81 - 31 * q^82 - 12 * q^83 + 22 * q^84 + 23 * q^86 - 26 * q^87 - 46 * q^88 + 20 * q^89 + 97 * q^90 - 2 * q^91 + 28 * q^92 - 28 * q^93 - 42 * q^94 - 22 * q^95 - 18 * q^96 + 12 * q^97 + 2 * q^98 - 62 * q^99

Introduction

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