LMFDB - Embedded newform 931.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, 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("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.5744.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} - 2x + 1 $ x^4 - 5x^2 - 2x + 1
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			1.1
Root			$-1.92022$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.92022 q^{2} +1.52077 q^{3} +1.68725 q^{4} -2.00692 q^{5} -2.92022 q^{6} +0.600553 q^{8} -0.687248 q^{9} +O(q^{10})$	\(q-1.92022 q^{2} +1.52077 q^{3} +1.68725 q^{4} -2.00692 q^{5} -2.92022 q^{6} +0.600553 q^{8} -0.687248 q^{9} +3.85372 q^{10} -0.645701 q^{11} +2.56592 q^{12} -0.232973 q^{13} -3.05207 q^{15} -4.52769 q^{16} +5.71912 q^{17} +1.31967 q^{18} -1.00000 q^{19} -3.38617 q^{20} +1.23989 q^{22} +4.21494 q^{23} +0.913304 q^{24} -0.972286 q^{25} +0.447359 q^{26} -5.60747 q^{27} +3.65262 q^{29} +5.86064 q^{30} +1.75375 q^{31} +7.49306 q^{32} -0.981965 q^{33} -10.9820 q^{34} -1.15956 q^{36} +3.06650 q^{37} +1.92022 q^{38} -0.354299 q^{39} -1.20526 q^{40} +6.88559 q^{41} +3.13184 q^{43} -1.08946 q^{44} +1.37925 q^{45} -8.09361 q^{46} +12.5133 q^{47} -6.88559 q^{48} +1.86700 q^{50} +8.69748 q^{51} -0.393083 q^{52} -0.719116 q^{53} +10.7676 q^{54} +1.29587 q^{55} -1.52077 q^{57} -7.01383 q^{58} -3.78086 q^{59} -5.14959 q^{60} +3.12493 q^{61} -3.36758 q^{62} -5.33295 q^{64} +0.467557 q^{65} +1.88559 q^{66} +3.07702 q^{67} +9.64957 q^{68} +6.40997 q^{69} -6.14844 q^{71} -0.412729 q^{72} -3.95485 q^{73} -5.88835 q^{74} -1.47863 q^{75} -1.68725 q^{76} +0.680332 q^{78} -14.1872 q^{79} +9.08670 q^{80} -6.46595 q^{81} -13.2219 q^{82} +15.6761 q^{83} -11.4778 q^{85} -6.01383 q^{86} +5.55480 q^{87} -0.387778 q^{88} +8.41604 q^{89} -2.64846 q^{90} +7.11165 q^{92} +2.66705 q^{93} -24.0282 q^{94} +2.00692 q^{95} +11.3952 q^{96} +15.7044 q^{97} +0.443757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^8 + 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{8} + 2 q^{9} + 10 q^{10} - 6 q^{11} + 6 q^{12} + 2 q^{13} + 4 q^{15} + 2 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} - 14 q^{22} - 8 q^{23} + 12 q^{24} + 20 q^{25} + 16 q^{26} - 10 q^{27} + 2 q^{29} + 2 q^{30} + 2 q^{32} + 18 q^{33} - 22 q^{34} - 20 q^{36} + 10 q^{37} + 2 q^{39} + 22 q^{40} + 12 q^{41} + 4 q^{43} - 14 q^{44} + 8 q^{45} - 8 q^{46} + 16 q^{47} - 12 q^{48} + 12 q^{50} - 10 q^{51} + 28 q^{52} + 12 q^{53} + 4 q^{54} - 8 q^{55} - 2 q^{57} + 4 q^{58} + 14 q^{59} - 2 q^{60} + 20 q^{61} - 20 q^{62} - 20 q^{64} + 10 q^{65} - 8 q^{66} + 2 q^{67} - 24 q^{68} + 14 q^{69} - 2 q^{71} - 8 q^{72} - 16 q^{73} - 26 q^{74} + 36 q^{75} - 2 q^{76} + 14 q^{78} - 8 q^{79} + 28 q^{80} - 20 q^{81} - 12 q^{82} + 20 q^{83} - 14 q^{85} + 8 q^{86} - 20 q^{87} - 2 q^{88} + 16 q^{89} - 32 q^{90} + 26 q^{92} + 12 q^{93} + 10 q^{94} - 8 q^{95} - 12 q^{96} + 2 q^{97} + 8 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^8 + 2 * q^9 + 10 * q^10 - 6 * q^11 + 6 * q^12 + 2 * q^13 + 4 * q^15 + 2 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 - 14 * q^22 - 8 * q^23 + 12 * q^24 + 20 * q^25 + 16 * q^26 - 10 * q^27 + 2 * q^29 + 2 * q^30 + 2 * q^32 + 18 * q^33 - 22 * q^34 - 20 * q^36 + 10 * q^37 + 2 * q^39 + 22 * q^40 + 12 * q^41 + 4 * q^43 - 14 * q^44 + 8 * q^45 - 8 * q^46 + 16 * q^47 - 12 * q^48 + 12 * q^50 - 10 * q^51 + 28 * q^52 + 12 * q^53 + 4 * q^54 - 8 * q^55 - 2 * q^57 + 4 * q^58 + 14 * q^59 - 2 * q^60 + 20 * q^61 - 20 * q^62 - 20 * q^64 + 10 * q^65 - 8 * q^66 + 2 * q^67 - 24 * q^68 + 14 * q^69 - 2 * q^71 - 8 * q^72 - 16 * q^73 - 26 * q^74 + 36 * q^75 - 2 * q^76 + 14 * q^78 - 8 * q^79 + 28 * q^80 - 20 * q^81 - 12 * q^82 + 20 * q^83 - 14 * q^85 + 8 * q^86 - 20 * q^87 - 2 * q^88 + 16 * q^89 - 32 * q^90 + 26 * q^92 + 12 * q^93 + 10 * q^94 - 8 * q^95 - 12 * q^96 + 2 * q^97 + 8 * q^99

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 $

$2$	−1.92022	−1.35780	−0.678901	−	0.734230i	$-0.737543\pi$
$2$	−1.92022	−1.35780	−0.678901	+	0.734230i	$0.737543\pi$
$3$	1.52077	0.878019	0.439009	−	0.898482i	$-0.355329\pi$
$3$	1.52077	0.878019	0.439009	+	0.898482i	$0.355329\pi$
$4$	1.68725	0.843624
$5$	−2.00692	−0.897520	−0.448760	−	0.893652i	$-0.648134\pi$
$5$	−2.00692	−0.897520	−0.448760	+	0.893652i	$0.648134\pi$
$6$	−2.92022	−1.19218
$7$	0	0
$7$	0	0
$8$	0.600553	0.212327
$9$	−0.687248	−0.229083
$10$	3.85372	1.21865
$11$	−0.645701	−0.194686	−0.0973431	−	0.995251i	$-0.531034\pi$
$11$	−0.645701	−0.194686	−0.0973431	+	0.995251i	$0.531034\pi$
$12$	2.56592	0.740718
$13$	−0.232973	−0.0646150	−0.0323075	−	0.999478i	$-0.510286\pi$
$13$	−0.232973	−0.0646150	−0.0323075	+	0.999478i	$0.510286\pi$
$14$	0	0
$15$	−3.05207	−0.788040
$16$	−4.52769	−1.13192
$17$	5.71912	1.38709	0.693545	−	0.720414i	$-0.256048\pi$
$17$	5.71912	1.38709	0.693545	+	0.720414i	$0.256048\pi$
$18$	1.31967	0.311049
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.38617	−0.757170
$21$	0	0
$22$	1.23989	0.264345
$23$	4.21494	0.878875	0.439438	−	0.898273i	$-0.355178\pi$
$23$	4.21494	0.878875	0.439438	+	0.898273i	$0.355178\pi$
$24$	0.913304	0.186427
$25$	−0.972286	−0.194457
$26$	0.447359	0.0877343
$27$	−5.60747	−1.07916
$28$	0	0
$29$	3.65262	0.678274	0.339137	−	0.940737i	$-0.389865\pi$
$29$	3.65262	0.678274	0.339137	+	0.940737i	$0.389865\pi$
$30$	5.86064	1.07000
$31$	1.75375	0.314982	0.157491	−	0.987520i	$-0.449659\pi$
$31$	1.75375	0.314982	0.157491	+	0.987520i	$0.449659\pi$
$32$	7.49306	1.32460
$33$	−0.981965	−0.170938
$34$	−10.9820	−1.88339
$35$	0	0
$36$	−1.15956	−0.193260
$37$	3.06650	0.504129	0.252065	−	0.967710i	$-0.418890\pi$
$37$	3.06650	0.504129	0.252065	+	0.967710i	$0.418890\pi$
$38$	1.92022	0.311501
$39$	−0.354299	−0.0567332
$40$	−1.20526	−0.190568
$41$	6.88559	1.07535	0.537674	−	0.843153i	$-0.319303\pi$
$41$	6.88559	1.07535	0.537674	+	0.843153i	$0.319303\pi$
$42$	0	0
$43$	3.13184	0.477602	0.238801	−	0.971069i	$-0.423246\pi$
$43$	3.13184	0.477602	0.238801	+	0.971069i	$0.423246\pi$
$44$	−1.08946	−0.164242
$45$	1.37925	0.205606
$46$	−8.09361	−1.19334
$47$	12.5133	1.82525	0.912623	−	0.408802i	$-0.134053\pi$
$47$	12.5133	1.82525	0.912623	+	0.408802i	$0.134053\pi$
$48$	−6.88559	−0.993849
$49$	0	0
$50$	1.86700	0.264034
$51$	8.69748	1.21789
$52$	−0.393083	−0.0545108
$53$	−0.719116	−0.0987781	−0.0493891	−	0.998780i	$-0.515727\pi$
$53$	−0.719116	−0.0987781	−0.0493891	+	0.998780i	$0.515727\pi$
$54$	10.7676	1.46528
$55$	1.29587	0.174735
$56$	0	0
$57$	−1.52077	−0.201431
$58$	−7.01383	−0.920961
$59$	−3.78086	−0.492226	−0.246113	−	0.969241i	$-0.579153\pi$
$59$	−3.78086	−0.492226	−0.246113	+	0.969241i	$0.579153\pi$
$60$	−5.14959	−0.664809
$61$	3.12493	0.400106	0.200053	−	0.979785i	$-0.435889\pi$
$61$	3.12493	0.400106	0.200053	+	0.979785i	$0.435889\pi$
$62$	−3.36758	−0.427683
$63$	0	0
$64$	−5.33295	−0.666619
$65$	0.467557	0.0579933
$66$	1.88559	0.232100
$67$	3.07702	0.375917	0.187959	−	0.982177i	$-0.439813\pi$
$67$	3.07702	0.375917	0.187959	+	0.982177i	$0.439813\pi$
$68$	9.64957	1.17018
$69$	6.40997	0.771669
$70$	0	0
$71$	−6.14844	−0.729686	−0.364843	−	0.931069i	$-0.618877\pi$
$71$	−6.14844	−0.729686	−0.364843	+	0.931069i	$0.618877\pi$
$72$	−0.412729	−0.0486405
$73$	−3.95485	−0.462880	−0.231440	−	0.972849i	$-0.574344\pi$
$73$	−3.95485	−0.462880	−0.231440	+	0.972849i	$0.574344\pi$
$74$	−5.88835	−0.684507
$75$	−1.47863	−0.170737
$76$	−1.68725	−0.193541
$77$	0	0
$78$	0.680332	0.0770324
$79$	−14.1872	−1.59619	−0.798094	−	0.602533i	$-0.794158\pi$
$79$	−14.1872	−1.59619	−0.798094	+	0.602533i	$0.794158\pi$
$80$	9.08670	1.01592
$81$	−6.46595	−0.718438
$82$	−13.2219	−1.46011
$83$	15.6761	1.72068	0.860339	−	0.509722i	$-0.170252\pi$
$83$	15.6761	1.72068	0.860339	+	0.509722i	$0.170252\pi$
$84$	0	0
$85$	−11.4778	−1.24494
$86$	−6.01383	−0.648488
$87$	5.55480	0.595538
$88$	−0.387778	−0.0413372
$89$	8.41604	0.892099	0.446049	−	0.895008i	$-0.352831\pi$
$89$	8.41604	0.892099	0.446049	+	0.895008i	$0.352831\pi$
$90$	−2.64846	−0.279173
$91$	0	0
$92$	7.11165	0.741440
$93$	2.66705	0.276560
$94$	−24.0282	−2.47832
$95$	2.00692	0.205905
$96$	11.3952	1.16302
$97$	15.7044	1.59454	0.797270	−	0.603623i	$-0.206277\pi$
$97$	15.7044	1.59454	0.797270	+	0.603623i	$0.206277\pi$
$98$	0	0
$99$	0.443757	0.0445993
$100$	−1.64049	−0.164049
$101$	18.0900	1.80002	0.900012	−	0.435866i	$-0.143558\pi$
$101$	18.0900	1.80002	0.900012	+	0.435866i	$0.143558\pi$
$102$	−16.7011	−1.65365
$103$	−4.02351	−0.396448	−0.198224	−	0.980157i	$-0.563517\pi$
$103$	−4.02351	−0.396448	−0.198224	+	0.980157i	$0.563517\pi$
$104$	−0.139912	−0.0137195
$105$	0	0
$106$	1.38086	0.134121
$107$	15.4133	1.49006	0.745029	−	0.667032i	$-0.232436\pi$
$107$	15.4133	1.49006	0.745029	+	0.667032i	$0.232436\pi$
$108$	−9.46119	−0.910404
$109$	13.4133	1.28476	0.642380	−	0.766387i	$-0.277947\pi$
$109$	13.4133	1.28476	0.642380	+	0.766387i	$0.277947\pi$
$110$	−2.48835	−0.237255
$111$	4.66345	0.442635
$112$	0	0
$113$	−14.8022	−1.39247	−0.696237	−	0.717812i	$-0.745144\pi$
$113$	−14.8022	−1.39247	−0.696237	+	0.717812i	$0.745144\pi$
$114$	2.92022	0.273504
$115$	−8.45903	−0.788809
$116$	6.16287	0.572208
$117$	0.160110	0.0148022
$118$	7.26009	0.668345
$119$	0	0
$120$	−1.83293	−0.167322
$121$	−10.5831	−0.962097
$122$	−6.00055	−0.543264
$123$	10.4714	0.944176
$124$	2.95900	0.265726
$125$	11.9859	1.07205
$126$	0	0
$127$	17.9639	1.59404	0.797021	−	0.603952i	$-0.206408\pi$
$127$	17.9639	1.59404	0.797021	+	0.603952i	$0.206408\pi$
$128$	−4.74568	−0.419463
$129$	4.76283	0.419343
$130$	−0.897812	−0.0787433
$131$	10.2183	0.892773	0.446386	−	0.894840i	$-0.352711\pi$
$131$	10.2183	0.892773	0.446386	+	0.894840i	$0.352711\pi$
$132$	−1.65682	−0.144208
$133$	0	0
$134$	−5.90855	−0.510421
$135$	11.2537	0.968566
$136$	3.43463	0.294517
$137$	−2.79889	−0.239126	−0.119563	−	0.992827i	$-0.538149\pi$
$137$	−2.79889	−0.239126	−0.119563	+	0.992827i	$0.538149\pi$
$138$	−12.3086	−1.04777
$139$	16.2440	1.37780	0.688901	−	0.724856i	$-0.258094\pi$
$139$	16.2440	1.37780	0.688901	+	0.724856i	$0.258094\pi$
$140$	0	0
$141$	19.0298	1.60260
$142$	11.8064	0.990768
$143$	0.150431	0.0125797
$144$	3.11165	0.259304
$145$	−7.33050	−0.608765
$146$	7.59419	0.628499
$147$	0	0
$148$	5.17394	0.425295
$149$	−23.8055	−1.95022	−0.975112	−	0.221712i	$-0.928836\pi$
$149$	−23.8055	−1.95022	−0.975112	+	0.221712i	$0.928836\pi$
$150$	2.83929	0.231827
$151$	13.0836	1.06473	0.532366	−	0.846514i	$-0.321303\pi$
$151$	13.0836	1.06473	0.532366	+	0.846514i	$0.321303\pi$
$152$	−0.600553	−0.0487112
$153$	−3.93045	−0.317758
$154$	0	0
$155$	−3.51962	−0.282703
$156$	−0.597790	−0.0478615
$157$	−15.5734	−1.24289	−0.621446	−	0.783457i	$-0.713454\pi$
$157$	−15.5734	−1.24289	−0.621446	+	0.783457i	$0.713454\pi$
$158$	27.2426	2.16731
$159$	−1.09361	−0.0867291
$160$	−15.0379	−1.18885
$161$	0	0
$162$	12.4160	0.975496
$163$	5.26285	0.412218	0.206109	−	0.978529i	$-0.433920\pi$
$163$	5.26285	0.412218	0.206109	+	0.978529i	$0.433920\pi$
$164$	11.6177	0.907190
$165$	1.97072	0.153421
$166$	−30.1016	−2.33634
$167$	−17.3853	−1.34531	−0.672657	−	0.739955i	$-0.734847\pi$
$167$	−17.3853	−1.34531	−0.672657	+	0.739955i	$0.734847\pi$
$168$	0	0
$169$	−12.9457	−0.995825
$170$	22.0399	1.69038
$171$	0.687248	0.0525552
$172$	5.28420	0.402916
$173$	−5.63819	−0.428663	−0.214332	−	0.976761i	$-0.568757\pi$
$173$	−5.63819	−0.428663	−0.214332	+	0.976761i	$0.568757\pi$
$174$	−10.6665	−0.808622
$175$	0	0
$176$	2.92354	0.220370
$177$	−5.74983	−0.432184
$178$	−16.1607	−1.21129
$179$	−11.1795	−0.835593	−0.417796	−	0.908541i	$-0.637197\pi$
$179$	−11.1795	−0.835593	−0.417796	+	0.908541i	$0.637197\pi$
$180$	2.32714	0.173455
$181$	9.64409	0.716840	0.358420	−	0.933561i	$-0.383316\pi$
$181$	9.64409	0.716840	0.358420	+	0.933561i	$0.383316\pi$
$182$	0	0
$183$	4.75231	0.351301
$184$	2.53129	0.186609
$185$	−6.15421	−0.452466
$186$	−5.12133	−0.375514
$187$	−3.69284	−0.270047
$188$	21.1130	1.53982
$189$	0	0
$190$	−3.85372	−0.279578
$191$	0.298871	0.0216255	0.0108128	−	0.999942i	$-0.496558\pi$
$191$	0.298871	0.0216255	0.0108128	+	0.999942i	$0.496558\pi$
$192$	−8.11021	−0.585304
$193$	−13.4100	−0.965270	−0.482635	−	0.875821i	$-0.660320\pi$
$193$	−13.4100	−0.965270	−0.482635	+	0.875821i	$0.660320\pi$
$194$	−30.1559	−2.16507
$195$	0.711048	0.0509192
$196$	0	0
$197$	9.80636	0.698674	0.349337	−	0.936997i	$-0.386407\pi$
$197$	9.80636	0.698674	0.349337	+	0.936997i	$0.386407\pi$
$198$	−0.852112	−0.0605569
$199$	−14.9515	−1.05989	−0.529943	−	0.848033i	$-0.677787\pi$
$199$	−14.9515	−1.05989	−0.529943	+	0.848033i	$0.677787\pi$
$200$	−0.583909	−0.0412886
$201$	4.67944	0.330063
$202$	−34.7368	−2.44407
$203$	0	0
$204$	14.6748	1.02744
$205$	−13.8188	−0.965147
$206$	7.72603	0.538298
$207$	−2.89671	−0.201335
$208$	1.05483	0.0731392
$209$	0.645701	0.0446641
$210$	0	0
$211$	−6.50966	−0.448143	−0.224072	−	0.974573i	$-0.571935\pi$
$211$	−6.50966	−0.448143	−0.224072	+	0.974573i	$0.571935\pi$
$212$	−1.21333	−0.0833316
$213$	−9.35038	−0.640678
$214$	−29.5969	−2.02320
$215$	−6.28535	−0.428657
$216$	−3.36758	−0.229135
$217$	0	0
$218$	−25.7565	−1.74445
$219$	−6.01443	−0.406418
$220$	2.18645	0.147411
$221$	−1.33240	−0.0896268
$222$	−8.95485	−0.601010
$223$	−5.10113	−0.341597	−0.170798	−	0.985306i	$-0.554635\pi$
$223$	−5.10113	−0.341597	−0.170798	+	0.985306i	$0.554635\pi$
$224$	0	0
$225$	0.668202	0.0445468
$226$	28.4235	1.89070
$227$	−2.70500	−0.179537	−0.0897684	−	0.995963i	$-0.528613\pi$
$227$	−2.70500	−0.179537	−0.0897684	+	0.995963i	$0.528613\pi$
$228$	−2.56592	−0.169932
$229$	2.55624	0.168921	0.0844606	−	0.996427i	$-0.473083\pi$
$229$	2.55624	0.168921	0.0844606	+	0.996427i	$0.473083\pi$
$230$	16.2432	1.07105
$231$	0	0
$232$	2.19359	0.144016
$233$	−23.5692	−1.54407	−0.772034	−	0.635581i	$-0.780761\pi$
$233$	−23.5692	−1.54407	−0.772034	+	0.635581i	$0.780761\pi$
$234$	−0.307447	−0.0200984
$235$	−25.1131	−1.63820
$236$	−6.37925	−0.415254
$237$	−21.5756	−1.40148
$238$	0	0
$239$	19.7767	1.27925	0.639623	−	0.768689i	$-0.279091\pi$
$239$	19.7767	1.27925	0.639623	+	0.768689i	$0.279091\pi$
$240$	13.8188	0.892000
$241$	9.14568	0.589125	0.294562	−	0.955632i	$-0.404826\pi$
$241$	9.14568	0.589125	0.294562	+	0.955632i	$0.404826\pi$
$242$	20.3218	1.30634
$243$	6.98917	0.448355
$244$	5.27253	0.337539
$245$	0	0
$246$	−20.1074	−1.28200
$247$	0.232973	0.0148237
$248$	1.05322	0.0668793
$249$	23.8398	1.51079
$250$	−23.0155	−1.45563
$251$	−8.53737	−0.538874	−0.269437	−	0.963018i	$-0.586838\pi$
$251$	−8.53737	−0.538874	−0.269437	+	0.963018i	$0.586838\pi$
$252$	0	0
$253$	−2.72159	−0.171105
$254$	−34.4947	−2.16439
$255$	−17.4551	−1.09308
$256$	19.7786	1.23617
$257$	−0.529129	−0.0330061	−0.0165031	−	0.999864i	$-0.505253\pi$
$257$	−0.529129	−0.0330061	−0.0165031	+	0.999864i	$0.505253\pi$
$258$	−9.14568	−0.569385
$259$	0	0
$260$	0.788884	0.0489245
$261$	−2.51025	−0.155381
$262$	−19.6213	−1.21221
$263$	−19.4235	−1.19771	−0.598853	−	0.800859i	$-0.704376\pi$
$263$	−19.4235	−1.19771	−0.598853	+	0.800859i	$0.704376\pi$
$264$	−0.589722	−0.0362949
$265$	1.44321	0.0886554
$266$	0	0
$267$	12.7989	0.783280
$268$	5.19169	0.317133
$269$	25.3323	1.54454	0.772270	−	0.635294i	$-0.219121\pi$
$269$	25.3323	1.54454	0.772270	+	0.635294i	$0.219121\pi$
$270$	−21.6096	−1.31512
$271$	−8.39164	−0.509756	−0.254878	−	0.966973i	$-0.582035\pi$
$271$	−8.39164	−0.509756	−0.254878	+	0.966973i	$0.582035\pi$
$272$	−25.8944	−1.57008
$273$	0	0
$274$	5.37450	0.324685
$275$	0.627806	0.0378582
$276$	10.8152	0.650999
$277$	−6.32575	−0.380077	−0.190039	−	0.981777i	$-0.560861\pi$
$277$	−6.32575	−0.380077	−0.190039	+	0.981777i	$0.560861\pi$
$278$	−31.1922	−1.87078
$279$	−1.20526	−0.0721570
$280$	0	0
$281$	−16.6210	−0.991527	−0.495763	−	0.868458i	$-0.665112\pi$
$281$	−16.6210	−0.991527	−0.495763	+	0.868458i	$0.665112\pi$
$282$	−36.5415	−2.17601
$283$	−23.8495	−1.41771	−0.708853	−	0.705356i	$-0.750787\pi$
$283$	−23.8495	−1.41771	−0.708853	+	0.705356i	$0.750787\pi$
$284$	−10.3739	−0.615580
$285$	3.05207	0.180789
$286$	−0.288860	−0.0170807
$287$	0	0
$288$	−5.14959	−0.303443
$289$	15.7083	0.924017
$290$	14.0762	0.826582
$291$	23.8828	1.40004
$292$	−6.67282	−0.390497
$293$	2.00305	0.117019	0.0585097	−	0.998287i	$-0.481365\pi$
$293$	2.00305	0.117019	0.0585097	+	0.998287i	$0.481365\pi$
$294$	0	0
$295$	7.58787	0.441783
$296$	1.84159	0.107040
$297$	3.62075	0.210097
$298$	45.7119	2.64802
$299$	−0.981965	−0.0567885
$300$	−2.49481	−0.144038
$301$	0	0
$302$	−25.1235	−1.44569
$303$	27.5108	1.58045
$304$	4.52769	0.259681
$305$	−6.27147	−0.359103
$306$	7.54734	0.431452
$307$	−7.55379	−0.431118	−0.215559	−	0.976491i	$-0.569157\pi$
$307$	−7.55379	−0.431118	−0.215559	+	0.976491i	$0.569157\pi$
$308$	0	0
$309$	−6.11885	−0.348089
$310$	6.75845	0.383854
$311$	14.1352	0.801531	0.400766	−	0.916181i	$-0.368744\pi$
$311$	14.1352	0.801531	0.400766	+	0.916181i	$0.368744\pi$
$312$	−0.212775	−0.0120460
$313$	−28.2914	−1.59912	−0.799561	−	0.600585i	$-0.794934\pi$
$313$	−28.2914	−1.59912	−0.799561	+	0.600585i	$0.794934\pi$
$314$	29.9043	1.68760
$315$	0	0
$316$	−23.9374	−1.34658
$317$	23.9013	1.34243	0.671215	−	0.741262i	$-0.265773\pi$
$317$	23.9013	1.34243	0.671215	+	0.741262i	$0.265773\pi$
$318$	2.09998	0.117761
$319$	−2.35850	−0.132051
$320$	10.7028	0.598304
$321$	23.4401	1.30830
$322$	0	0
$323$	−5.71912	−0.318220
$324$	−10.9097	−0.606092
$325$	0.226516	0.0125649
$326$	−10.1058	−0.559710
$327$	20.3986	1.12804
$328$	4.13516	0.228326
$329$	0	0
$330$	−3.78422	−0.208315
$331$	−4.23381	−0.232711	−0.116356	−	0.993208i	$-0.537121\pi$
$331$	−4.23381	−0.232711	−0.116356	+	0.993208i	$0.537121\pi$
$332$	26.4495	1.45161
$333$	−2.10745	−0.115487
$334$	33.3836	1.82667
$335$	−6.17531	−0.337393
$336$	0	0
$337$	−12.4792	−0.679784	−0.339892	−	0.940464i	$-0.610391\pi$
$337$	−12.4792	−0.679784	−0.339892	+	0.940464i	$0.610391\pi$
$338$	24.8586	1.35213
$339$	−22.5108	−1.22262
$340$	−19.3659	−1.05026
$341$	−1.13240	−0.0613227
$342$	−1.31967	−0.0713595
$343$	0	0
$344$	1.88084	0.101408
$345$	−12.8643	−0.692589
$346$	10.8266	0.582040
$347$	−34.2362	−1.83790	−0.918949	−	0.394377i	$-0.870960\pi$
$347$	−34.2362	−1.83790	−0.918949	+	0.394377i	$0.870960\pi$
$348$	9.37233	0.502410
$349$	−2.57805	−0.138000	−0.0690000	−	0.997617i	$-0.521981\pi$
$349$	−2.57805	−0.138000	−0.0690000	+	0.997617i	$0.521981\pi$
$350$	0	0
$351$	1.30639	0.0697298
$352$	−4.83828	−0.257881
$353$	−3.24044	−0.172471	−0.0862356	−	0.996275i	$-0.527484\pi$
$353$	−3.24044	−0.172471	−0.0862356	+	0.996275i	$0.527484\pi$
$354$	11.0409	0.586820
$355$	12.3394	0.654908
$356$	14.2000	0.752596
$357$	0	0
$358$	21.4670	1.13457
$359$	11.3254	0.597734	0.298867	−	0.954295i	$-0.403391\pi$
$359$	11.3254	0.597734	0.298867	+	0.954295i	$0.403391\pi$
$360$	0.828312	0.0436559
$361$	1.00000	0.0526316
$362$	−18.5188	−0.973326
$363$	−16.0945	−0.844740
$364$	0	0
$365$	7.93706	0.415445
$366$	−9.12548	−0.476996
$367$	−20.2579	−1.05745	−0.528726	−	0.848792i	$-0.677330\pi$
$367$	−20.2579	−1.05745	−0.528726	+	0.848792i	$0.677330\pi$
$368$	−19.0839	−0.994819
$369$	−4.73211	−0.246344
$370$	11.8174	0.614359
$371$	0	0
$372$	4.49998	0.233313
$373$	33.9822	1.75953	0.879765	−	0.475408i	$-0.157700\pi$
$373$	33.9822	1.75953	0.879765	+	0.475408i	$0.157700\pi$
$374$	7.09107	0.366670
$375$	18.2278	0.941280
$376$	7.51487	0.387550
$377$	−0.850960	−0.0438267
$378$	0	0
$379$	−20.2122	−1.03823	−0.519115	−	0.854704i	$-0.673738\pi$
$379$	−20.2122	−1.03823	−0.519115	+	0.854704i	$0.673738\pi$
$380$	3.38617	0.173707
$381$	27.3191	1.39960
$382$	−0.573898	−0.0293632
$383$	32.4978	1.66056	0.830279	−	0.557348i	$-0.188181\pi$
$383$	32.4978	1.66056	0.830279	+	0.557348i	$0.188181\pi$
$384$	−7.21710	−0.368296
$385$	0	0
$386$	25.7501	1.31065
$387$	−2.15235	−0.109410
$388$	26.4972	1.34519
$389$	−6.65953	−0.337652	−0.168826	−	0.985646i	$-0.553998\pi$
$389$	−6.65953	−0.337652	−0.168826	+	0.985646i	$0.553998\pi$
$390$	−1.36537	−0.0691381
$391$	24.1057	1.21908
$392$	0	0
$393$	15.5396	0.783872
$394$	−18.8304	−0.948661
$395$	28.4726	1.43261
$396$	0.748728	0.0376250
$397$	27.3950	1.37491	0.687457	−	0.726225i	$-0.258727\pi$
$397$	27.3950	1.37491	0.687457	+	0.726225i	$0.258727\pi$
$398$	28.7103	1.43911
$399$	0	0
$400$	4.40221	0.220111
$401$	11.5291	0.575737	0.287869	−	0.957670i	$-0.407053\pi$
$401$	11.5291	0.575737	0.287869	+	0.957670i	$0.407053\pi$
$402$	−8.98557	−0.448159
$403$	−0.408575	−0.0203526
$404$	30.5223	1.51854
$405$	12.9766	0.644813
$406$	0	0
$407$	−1.98004	−0.0981470
$408$	5.22329	0.258592
$409$	−39.7423	−1.96513	−0.982565	−	0.185920i	$-0.940474\pi$
$409$	−39.7423	−1.96513	−0.982565	+	0.185920i	$0.940474\pi$
$410$	26.5352	1.31048
$411$	−4.25648	−0.209957
$412$	−6.78866	−0.334453
$413$	0	0
$414$	5.56232	0.273373
$415$	−31.4607	−1.54434
$416$	−1.74568	−0.0855889
$417$	24.7035	1.20974
$418$	−1.23989	−0.0606450
$419$	−22.8335	−1.11549	−0.557744	−	0.830013i	$-0.688333\pi$
$419$	−22.8335	−1.11549	−0.557744	+	0.830013i	$0.688333\pi$
$420$	0	0
$421$	18.8016	0.916334	0.458167	−	0.888866i	$-0.348506\pi$
$421$	18.8016	0.916334	0.458167	+	0.888866i	$0.348506\pi$
$422$	12.5000	0.608489
$423$	−8.59971	−0.418132
$424$	−0.431867	−0.0209733
$425$	−5.56062	−0.269730
$426$	17.9548	0.869913
$427$	0	0
$428$	26.0060	1.25705
$429$	0.228771	0.0110452
$430$	12.0693	0.582031
$431$	26.7224	1.28717	0.643587	−	0.765373i	$-0.277445\pi$
$431$	26.7224	1.28717	0.643587	+	0.765373i	$0.277445\pi$
$432$	25.3889	1.22152
$433$	20.7393	0.996668	0.498334	−	0.866985i	$-0.333945\pi$
$433$	20.7393	0.996668	0.498334	+	0.866985i	$0.333945\pi$
$434$	0	0
$435$	−11.1480	−0.534507
$436$	22.6315	1.08385
$437$	−4.21494	−0.201628
$438$	11.5490	0.551834
$439$	28.9789	1.38309	0.691544	−	0.722334i	$-0.256931\pi$
$439$	28.9789	1.38309	0.691544	+	0.722334i	$0.256931\pi$
$440$	0.778237	0.0371010
$441$	0	0
$442$	2.55850	0.121695
$443$	−9.13936	−0.434224	−0.217112	−	0.976147i	$-0.569664\pi$
$443$	−9.13936	−0.434224	−0.217112	+	0.976147i	$0.569664\pi$
$444$	7.86840	0.373418
$445$	−16.8903	−0.800677
$446$	9.79529	0.463821
$447$	−36.2028	−1.71233
$448$	0	0
$449$	7.36398	0.347528	0.173764	−	0.984787i	$-0.444407\pi$
$449$	7.36398	0.347528	0.173764	+	0.984787i	$0.444407\pi$
$450$	−1.28310	−0.0604857
$451$	−4.44604	−0.209356
$452$	−24.9750	−1.17473
$453$	19.8973	0.934855
$454$	5.19419	0.243775
$455$	0	0
$456$	−0.913304	−0.0427694
$457$	−18.8052	−0.879671	−0.439835	−	0.898078i	$-0.644963\pi$
$457$	−18.8052	−0.879671	−0.439835	+	0.898078i	$0.644963\pi$
$458$	−4.90855	−0.229362
$459$	−32.0698	−1.49689
$460$	−14.2725	−0.665458
$461$	−6.42512	−0.299248	−0.149624	−	0.988743i	$-0.547806\pi$
$461$	−6.42512	−0.299248	−0.149624	+	0.988743i	$0.547806\pi$
$462$	0	0
$463$	2.03434	0.0945439	0.0472720	−	0.998882i	$-0.484947\pi$
$463$	2.03434	0.0945439	0.0472720	+	0.998882i	$0.484947\pi$
$464$	−16.5379	−0.767754
$465$	−5.35255	−0.248218
$466$	45.2580	2.09654
$467$	−11.0506	−0.511362	−0.255681	−	0.966761i	$-0.582300\pi$
$467$	−11.0506	−0.511362	−0.255681	+	0.966761i	$0.582300\pi$
$468$	0.270145	0.0124875
$469$	0	0
$470$	48.2226	2.22434
$471$	−23.6836	−1.09128
$472$	−2.27061	−0.104513
$473$	−2.02224	−0.0929825
$474$	41.4298	1.90294
$475$	0.972286	0.0446115
$476$	0	0
$477$	0.494211	0.0226284
$478$	−37.9756	−1.73696
$479$	−17.0714	−0.780011	−0.390006	−	0.920813i	$-0.627527\pi$
$479$	−17.0714	−0.780011	−0.390006	+	0.920813i	$0.627527\pi$
$480$	−22.8693	−1.04384
$481$	−0.714410	−0.0325743
$482$	−17.5617	−0.799914
$483$	0	0
$484$	−17.8563	−0.811648
$485$	−31.5174	−1.43113
$486$	−13.4207	−0.608778
$487$	5.59220	0.253407	0.126703	−	0.991941i	$-0.459560\pi$
$487$	5.59220	0.253407	0.126703	+	0.991941i	$0.459560\pi$
$488$	1.87668	0.0849535
$489$	8.00360	0.361935
$490$	0	0
$491$	30.2011	1.36295	0.681477	−	0.731839i	$-0.261338\pi$
$491$	30.2011	1.36295	0.681477	+	0.731839i	$0.261338\pi$
$492$	17.6679	0.796530
$493$	20.8897	0.940827
$494$	−0.447359	−0.0201276
$495$	−0.890583	−0.0400287
$496$	−7.94042	−0.356535
$497$	0	0
$498$	−45.7778	−2.05135
$499$	−0.903338	−0.0404390	−0.0202195	−	0.999796i	$-0.506436\pi$
$499$	−0.903338	−0.0404390	−0.0202195	+	0.999796i	$0.506436\pi$
$500$	20.2232	0.904407
$501$	−26.4391	−1.18121
$502$	16.3936	0.731684
$503$	0.668202	0.0297937	0.0148968	−	0.999889i	$-0.495258\pi$
$503$	0.668202	0.0297937	0.0148968	+	0.999889i	$0.495258\pi$
$504$	0	0
$505$	−36.3051	−1.61556
$506$	5.22606	0.232327
$507$	−19.6875	−0.874353
$508$	30.3096	1.34477
$509$	−7.41600	−0.328708	−0.164354	−	0.986401i	$-0.552554\pi$
$509$	−7.41600	−0.328708	−0.164354	+	0.986401i	$0.552554\pi$
$510$	33.5177	1.48419
$511$	0	0
$512$	−28.4880	−1.25900
$513$	5.60747	0.247576
$514$	1.01604	0.0448158
$515$	8.07485	0.355821
$516$	8.03607	0.353768
$517$	−8.07983	−0.355350
$518$	0	0
$519$	−8.57440	−0.376374
$520$	0.280792	0.0123136
$521$	39.6778	1.73832	0.869159	−	0.494533i	$-0.164661\pi$
$521$	39.6778	1.73832	0.869159	+	0.494533i	$0.164661\pi$
$522$	4.82024	0.210976
$523$	31.7681	1.38912	0.694562	−	0.719433i	$-0.255598\pi$
$523$	31.7681	1.38912	0.694562	+	0.719433i	$0.255598\pi$
$524$	17.2407	0.753165
$525$	0	0
$526$	37.2974	1.62625
$527$	10.0299	0.436908
$528$	4.44604	0.193489
$529$	−5.23430	−0.227578
$530$	−2.77127	−0.120376
$531$	2.59839	0.112760
$532$	0	0
$533$	−1.60415	−0.0694836
$534$	−24.5767	−1.06354
$535$	−30.9332	−1.33736
$536$	1.84791	0.0798176
$537$	−17.0014	−0.733666
$538$	−48.6437	−2.09718
$539$	0	0
$540$	18.9878	0.817106
$541$	34.2022	1.47047	0.735233	−	0.677815i	$-0.237073\pi$
$541$	34.2022	1.47047	0.735233	+	0.677815i	$0.237073\pi$
$542$	16.1138	0.692147
$543$	14.6665	0.629399
$544$	42.8537	1.83734
$545$	−26.9193	−1.15310
$546$	0	0
$547$	−8.74798	−0.374037	−0.187018	−	0.982356i	$-0.559882\pi$
$547$	−8.74798	−0.374037	−0.187018	+	0.982356i	$0.559882\pi$
$548$	−4.72243	−0.201732
$549$	−2.14760	−0.0916574
$550$	−1.20553	−0.0514038
$551$	−3.65262	−0.155607
$552$	3.84952	0.163847
$553$	0	0
$554$	12.1468	0.516069
$555$	−9.35915	−0.397274
$556$	27.4077	1.16235
$557$	24.2097	1.02580	0.512899	−	0.858449i	$-0.328571\pi$
$557$	24.2097	1.02580	0.512899	+	0.858449i	$0.328571\pi$
$558$	2.31436	0.0979748
$559$	−0.729634	−0.0308602
$560$	0	0
$561$	−5.61597	−0.237107
$562$	31.9160	1.34630
$563$	−23.5382	−0.992017	−0.496009	−	0.868318i	$-0.665202\pi$
$563$	−23.5382	−0.992017	−0.496009	+	0.868318i	$0.665202\pi$
$564$	32.1080	1.35199
$565$	29.7068	1.24977
$566$	45.7963	1.92496
$567$	0	0
$568$	−3.69246	−0.154932
$569$	40.8720	1.71344	0.856721	−	0.515780i	$-0.172498\pi$
$569$	40.8720	1.71344	0.856721	+	0.515780i	$0.172498\pi$
$570$	−5.86064	−0.245475
$571$	−8.95010	−0.374550	−0.187275	−	0.982308i	$-0.559966\pi$
$571$	−8.95010	−0.374550	−0.187275	+	0.982308i	$0.559966\pi$
$572$	0.253814	0.0106125
$573$	0.454515	0.0189876
$574$	0	0
$575$	−4.09813	−0.170904
$576$	3.66506	0.152711
$577$	10.9327	0.455133	0.227566	−	0.973763i	$-0.426923\pi$
$577$	10.9327	0.455133	0.227566	+	0.973763i	$0.426923\pi$
$578$	−30.1634	−1.25463
$579$	−20.3935	−0.847526
$580$	−12.3684	−0.513569
$581$	0	0
$582$	−45.8603	−1.90097
$583$	0.464334	0.0192307
$584$	−2.37510	−0.0982822
$585$	−0.321328	−0.0132853
$586$	−3.84630	−0.158889
$587$	−37.5213	−1.54867	−0.774335	−	0.632775i	$-0.781916\pi$
$587$	−37.5213	−1.54867	−0.774335	+	0.632775i	$0.781916\pi$
$588$	0	0
$589$	−1.75375	−0.0722618
$590$	−14.5704	−0.599853
$591$	14.9133	0.613449
$592$	−13.8842	−0.570635
$593$	12.1249	0.497909	0.248955	−	0.968515i	$-0.419913\pi$
$593$	12.1249	0.497909	0.248955	+	0.968515i	$0.419913\pi$
$594$	−6.95264	−0.285270
$595$	0	0
$596$	−40.1658	−1.64526
$597$	−22.7379	−0.930600
$598$	1.88559	0.0771075
$599$	21.8083	0.891061	0.445531	−	0.895267i	$-0.353015\pi$
$599$	21.8083	0.891061	0.445531	+	0.895267i	$0.353015\pi$
$600$	−0.887993	−0.0362522
$601$	−18.1878	−0.741895	−0.370947	−	0.928654i	$-0.620967\pi$
$601$	−18.1878	−0.741895	−0.370947	+	0.928654i	$0.620967\pi$
$602$	0	0
$603$	−2.11467	−0.0861162
$604$	22.0754	0.898234
$605$	21.2393	0.863502
$606$	−52.8268	−2.14594
$607$	−27.4341	−1.11351	−0.556757	−	0.830675i	$-0.687955\pi$
$607$	−27.4341	−1.11351	−0.556757	+	0.830675i	$0.687955\pi$
$608$	−7.49306	−0.303884
$609$	0	0
$610$	12.0426	0.487591
$611$	−2.91525	−0.117938
$612$	−6.63165	−0.268068
$613$	24.8456	1.00350	0.501752	−	0.865011i	$-0.332689\pi$
$613$	24.8456	1.00350	0.501752	+	0.865011i	$0.332689\pi$
$614$	14.5049	0.585372
$615$	−21.0153	−0.847418
$616$	0	0
$617$	22.9991	0.925909	0.462955	−	0.886382i	$-0.346789\pi$
$617$	22.9991	0.925909	0.462955	+	0.886382i	$0.346789\pi$
$618$	11.7495	0.472636
$619$	−1.64294	−0.0660353	−0.0330176	−	0.999455i	$-0.510512\pi$
$619$	−1.64294	−0.0660353	−0.0330176	+	0.999455i	$0.510512\pi$
$620$	−5.93848	−0.238495
$621$	−23.6351	−0.948445
$622$	−27.1426	−1.08832
$623$	0	0
$624$	1.60415	0.0642176
$625$	−19.1932	−0.767729
$626$	54.3256	2.17129
$627$	0.981965	0.0392159
$628$	−26.2762	−1.04853
$629$	17.5377	0.699272
$630$	0	0
$631$	−5.63823	−0.224455	−0.112227	−	0.993683i	$-0.535798\pi$
$631$	−5.63823	−0.224455	−0.112227	+	0.993683i	$0.535798\pi$
$632$	−8.52017	−0.338914
$633$	−9.89971	−0.393478
$634$	−45.8958	−1.82275
$635$	−36.0521	−1.43068
$636$	−1.84520	−0.0731667
$637$	0	0
$638$	4.52884	0.179299
$639$	4.22550	0.167158
$640$	9.52418	0.376476
$641$	34.9878	1.38194	0.690968	−	0.722885i	$-0.257185\pi$
$641$	34.9878	1.38194	0.690968	+	0.722885i	$0.257185\pi$
$642$	−45.0102	−1.77641
$643$	−9.93598	−0.391837	−0.195918	−	0.980620i	$-0.562769\pi$
$643$	−9.93598	−0.391837	−0.195918	+	0.980620i	$0.562769\pi$
$644$	0	0
$645$	−9.55859	−0.376369
$646$	10.9820	0.432080
$647$	−0.220703	−0.00867674	−0.00433837	−	0.999991i	$-0.501381\pi$
$647$	−0.220703	−0.00867674	−0.00433837	+	0.999991i	$0.501381\pi$
$648$	−3.88314	−0.152544
$649$	2.44131	0.0958297
$650$	−0.434961	−0.0170606
$651$	0	0
$652$	8.87973	0.347757
$653$	26.3684	1.03188	0.515938	−	0.856626i	$-0.327444\pi$
$653$	26.3684	1.03188	0.515938	+	0.856626i	$0.327444\pi$
$654$	−39.1697	−1.53166
$655$	−20.5072	−0.801282
$656$	−31.1758	−1.21721
$657$	2.71796	0.106038
$658$	0	0
$659$	−19.0242	−0.741079	−0.370540	−	0.928817i	$-0.620827\pi$
$659$	−19.0242	−0.741079	−0.370540	+	0.928817i	$0.620827\pi$
$660$	3.32510	0.129429
$661$	33.1950	1.29114	0.645568	−	0.763703i	$-0.276621\pi$
$661$	33.1950	1.29114	0.645568	+	0.763703i	$0.276621\pi$
$662$	8.12985	0.315976
$663$	−2.02628	−0.0786940
$664$	9.41434	0.365347
$665$	0	0
$666$	4.04676	0.156809
$667$	15.3956	0.596118
$668$	−29.3333	−1.13494
$669$	−7.75766	−0.299928
$670$	11.8580	0.458113
$671$	−2.01777	−0.0778952
$672$	0	0
$673$	−31.3013	−1.20658	−0.603289	−	0.797523i	$-0.706143\pi$
$673$	−31.3013	−1.20658	−0.603289	+	0.797523i	$0.706143\pi$
$674$	23.9628	0.923012
$675$	5.45206	0.209850
$676$	−21.8426	−0.840102
$677$	−12.0271	−0.462240	−0.231120	−	0.972925i	$-0.574239\pi$
$677$	−12.0271	−0.462240	−0.231120	+	0.972925i	$0.574239\pi$
$678$	43.2257	1.66007
$679$	0	0
$680$	−6.89301	−0.264335
$681$	−4.11369	−0.157637
$682$	2.17445	0.0832640
$683$	−7.00387	−0.267995	−0.133998	−	0.990982i	$-0.542781\pi$
$683$	−7.00387	−0.267995	−0.133998	+	0.990982i	$0.542781\pi$
$684$	1.15956	0.0443368
$685$	5.61715	0.214620
$686$	0	0
$687$	3.88747	0.148316
$688$	−14.1800	−0.540608
$689$	0.167534	0.00638255
$690$	24.7022	0.940398
$691$	38.5256	1.46558	0.732792	−	0.680453i	$-0.238217\pi$
$691$	38.5256	1.46558	0.732792	+	0.680453i	$0.238217\pi$
$692$	−9.51302	−0.361631
$693$	0	0
$694$	65.7411	2.49550
$695$	−32.6004	−1.23661
$696$	3.33595	0.126449
$697$	39.3795	1.49160
$698$	4.95043	0.187377
$699$	−35.8434	−1.35572
$700$	0	0
$701$	−32.9668	−1.24514	−0.622569	−	0.782565i	$-0.713911\pi$
$701$	−32.9668	−1.24514	−0.622569	+	0.782565i	$0.713911\pi$
$702$	−2.50855	−0.0946792
$703$	−3.06650	−0.115655
$704$	3.44349	0.129782
$705$	−38.1913	−1.43837
$706$	6.22236	0.234182
$707$	0	0
$708$	−9.70139	−0.364601
$709$	32.2564	1.21142	0.605708	−	0.795687i	$-0.292890\pi$
$709$	32.2564	1.21142	0.605708	+	0.795687i	$0.292890\pi$
$710$	−23.6944	−0.889234
$711$	9.75014	0.365659
$712$	5.05428	0.189417
$713$	7.39193	0.276830
$714$	0	0
$715$	−0.301902	−0.0112905
$716$	−18.8625	−0.704926
$717$	30.0758	1.12320
$718$	−21.7473	−0.811603
$719$	−37.9595	−1.41565	−0.707825	−	0.706387i	$-0.750324\pi$
$719$	−37.9595	−1.41565	−0.707825	+	0.706387i	$0.750324\pi$
$720$	−6.24482	−0.232731
$721$	0	0
$722$	−1.92022	−0.0714632
$723$	13.9085	0.517263
$724$	16.2720	0.604743
$725$	−3.55139	−0.131895
$726$	30.9049	1.14699
$727$	5.40908	0.200612	0.100306	−	0.994957i	$-0.468018\pi$
$727$	5.40908	0.200612	0.100306	+	0.994957i	$0.468018\pi$
$728$	0	0
$729$	30.0268	1.11210
$730$	−15.2409	−0.564091
$731$	17.9114	0.662476
$732$	8.01832	0.296366
$733$	−40.3312	−1.48967	−0.744833	−	0.667251i	$-0.767471\pi$
$733$	−40.3312	−1.48967	−0.744833	+	0.667251i	$0.767471\pi$
$734$	38.8996	1.43581
$735$	0	0
$736$	31.5828	1.16416
$737$	−1.98683	−0.0731860
$738$	9.08670	0.334486
$739$	−17.8947	−0.658268	−0.329134	−	0.944283i	$-0.606757\pi$
$739$	−17.8947	−0.658268	−0.329134	+	0.944283i	$0.606757\pi$
$740$	−10.3837	−0.381711
$741$	0.354299	0.0130155
$742$	0	0
$743$	−0.0581426	−0.00213305	−0.00106652	−	0.999999i	$-0.500339\pi$
$743$	−0.0581426	−0.00213305	−0.00106652	+	0.999999i	$0.500339\pi$
$744$	1.60170	0.0587213
$745$	47.7757	1.75037
$746$	−65.2533	−2.38909
$747$	−10.7734	−0.394178
$748$	−6.23074	−0.227818
$749$	0	0
$750$	−35.0014	−1.27807
$751$	−46.2886	−1.68909	−0.844547	−	0.535482i	$-0.820130\pi$
$751$	−46.2886	−1.68909	−0.844547	+	0.535482i	$0.820130\pi$
$752$	−56.6561	−2.06604
$753$	−12.9834	−0.473142
$754$	1.63403	0.0595079
$755$	−26.2578	−0.955619
$756$	0	0
$757$	28.3733	1.03125	0.515623	−	0.856815i	$-0.327560\pi$
$757$	28.3733	1.03125	0.515623	+	0.856815i	$0.327560\pi$
$758$	38.8118	1.40971
$759$	−4.13892	−0.150233
$760$	1.20526	0.0437193
$761$	−39.2965	−1.42450	−0.712249	−	0.701927i	$-0.752323\pi$
$761$	−39.2965	−1.42450	−0.712249	+	0.701927i	$0.752323\pi$
$762$	−52.4586	−1.90038
$763$	0	0
$764$	0.504270	0.0182438
$765$	7.88809	0.285194
$766$	−62.4029	−2.25471
$767$	0.880837	0.0318052
$768$	30.0788	1.08538
$769$	41.1096	1.48245	0.741225	−	0.671256i	$-0.234245\pi$
$769$	41.1096	1.48245	0.741225	+	0.671256i	$0.234245\pi$
$770$	0	0
$771$	−0.804685	−0.0289800
$772$	−22.6259	−0.814325
$773$	44.3906	1.59662	0.798309	−	0.602248i	$-0.205728\pi$
$773$	44.3906	1.59662	0.798309	+	0.602248i	$0.205728\pi$
$774$	4.13300	0.148557
$775$	−1.70514	−0.0612505
$776$	9.43132	0.338564
$777$	0	0
$778$	12.7878	0.458464
$779$	−6.88559	−0.246702
$780$	1.19971	0.0429567
$781$	3.97006	0.142060
$782$	−46.2883	−1.65527
$783$	−20.4819	−0.731965
$784$	0	0
$785$	31.2545	1.11552
$786$	−29.8396	−1.06434
$787$	39.4575	1.40651	0.703254	−	0.710939i	$-0.251730\pi$
$787$	39.4575	1.40651	0.703254	+	0.710939i	$0.251730\pi$
$788$	16.5458	0.589419
$789$	−29.5388	−1.05161
$790$	−54.6736	−1.94520
$791$	0	0
$792$	0.266499	0.00946965
$793$	−0.728023	−0.0258528
$794$	−52.6044	−1.86686
$795$	2.19479	0.0778411
$796$	−25.2270	−0.894146
$797$	−23.3858	−0.828369	−0.414184	−	0.910193i	$-0.635933\pi$
$797$	−23.3858	−0.828369	−0.414184	+	0.910193i	$0.635933\pi$
$798$	0	0
$799$	71.5648	2.53178
$800$	−7.28540	−0.257578
$801$	−5.78391	−0.204364
$802$	−22.1385	−0.781737
$803$	2.55365	0.0901164
$804$	7.89538	0.278449
$805$	0	0
$806$	0.784554	0.0276347
$807$	38.5248	1.35614
$808$	10.8640	0.382194
$809$	−12.5745	−0.442094	−0.221047	−	0.975263i	$-0.570947\pi$
$809$	−12.5745	−0.442094	−0.221047	+	0.975263i	$0.570947\pi$
$810$	−24.9180	−0.875528
$811$	7.91138	0.277806	0.138903	−	0.990306i	$-0.455642\pi$
$811$	7.91138	0.277806	0.138903	+	0.990306i	$0.455642\pi$
$812$	0	0
$813$	−12.7618	−0.447575
$814$	3.80212	0.133264
$815$	−10.5621	−0.369974
$816$	−39.3795	−1.37856
$817$	−3.13184	−0.109569
$818$	76.3140	2.66826
$819$	0	0
$820$	−23.3158	−0.814221
$821$	31.2830	1.09178	0.545892	−	0.837855i	$-0.316191\pi$
$821$	31.2830	1.09178	0.545892	+	0.837855i	$0.316191\pi$
$822$	8.17339	0.285080
$823$	−6.04702	−0.210786	−0.105393	−	0.994431i	$-0.533610\pi$
$823$	−6.04702	−0.210786	−0.105393	+	0.994431i	$0.533610\pi$
$824$	−2.41633	−0.0841769
$825$	0.954751	0.0332402
$826$	0	0
$827$	−30.6559	−1.06601	−0.533005	−	0.846112i	$-0.678937\pi$
$827$	−30.6559	−1.06601	−0.533005	+	0.846112i	$0.678937\pi$
$828$	−4.88747	−0.169851
$829$	−42.1300	−1.46324	−0.731618	−	0.681715i	$-0.761235\pi$
$829$	−42.1300	−1.46324	−0.731618	+	0.681715i	$0.761235\pi$
$830$	60.4115	2.09691
$831$	−9.62003	−0.333715
$832$	1.24243	0.0430736
$833$	0	0
$834$	−47.4362	−1.64258
$835$	34.8908	1.20745
$836$	1.08946	0.0376797
$837$	−9.83408	−0.339915
$838$	43.8453	1.51461
$839$	−14.4798	−0.499897	−0.249949	−	0.968259i	$-0.580414\pi$
$839$	−14.4798	−0.499897	−0.249949	+	0.968259i	$0.580414\pi$
$840$	0	0
$841$	−15.6584	−0.539944
$842$	−36.1032	−1.24420
$843$	−25.2768	−0.870579
$844$	−10.9834	−0.378064
$845$	25.9810	0.893773
$846$	16.5133	0.567741
$847$	0	0
$848$	3.25593	0.111809
$849$	−36.2697	−1.24477
$850$	10.6776	0.366239
$851$	12.9251	0.443067
$852$	−15.7764	−0.540491
$853$	−31.7188	−1.08603	−0.543016	−	0.839722i	$-0.682718\pi$
$853$	−31.7188	−1.08603	−0.543016	+	0.839722i	$0.682718\pi$
$854$	0	0
$855$	−1.37925	−0.0471693
$856$	9.25648	0.316380
$857$	−33.3132	−1.13796	−0.568978	−	0.822353i	$-0.692661\pi$
$857$	−33.3132	−1.13796	−0.568978	+	0.822353i	$0.692661\pi$
$858$	−0.439291	−0.0149972
$859$	5.57339	0.190162	0.0950808	−	0.995470i	$-0.469689\pi$
$859$	5.57339	0.190162	0.0950808	+	0.995470i	$0.469689\pi$
$860$	−10.6049	−0.361626
$861$	0	0
$862$	−51.3130	−1.74773
$863$	−30.8841	−1.05131	−0.525654	−	0.850699i	$-0.676179\pi$
$863$	−30.8841	−1.05131	−0.525654	+	0.850699i	$0.676179\pi$
$864$	−42.0171	−1.42945
$865$	11.3154	0.384734
$866$	−39.8241	−1.35328
$867$	23.8887	0.811304
$868$	0	0
$869$	9.16071	0.310756
$870$	21.4067	0.725754
$871$	−0.716861	−0.0242899
$872$	8.05538	0.272790
$873$	−10.7928	−0.365282
$874$	8.09361	0.273771
$875$	0	0
$876$	−10.1478	−0.342864
$877$	8.83319	0.298276	0.149138	−	0.988816i	$-0.452350\pi$
$877$	8.83319	0.298276	0.149138	+	0.988816i	$0.452350\pi$
$878$	−55.6459	−1.87796
$879$	3.04619	0.102745
$880$	−5.86729	−0.197786
$881$	36.3004	1.22299	0.611496	−	0.791247i	$-0.290568\pi$
$881$	36.3004	1.22299	0.611496	+	0.791247i	$0.290568\pi$
$882$	0	0
$883$	39.9694	1.34508	0.672539	−	0.740062i	$-0.265204\pi$
$883$	39.9694	1.34508	0.672539	+	0.740062i	$0.265204\pi$
$884$	−2.24809	−0.0756113
$885$	11.5394	0.387894
$886$	17.5496	0.589590
$887$	3.13202	0.105163	0.0525814	−	0.998617i	$-0.483255\pi$
$887$	3.13202	0.105163	0.0525814	+	0.998617i	$0.483255\pi$
$888$	2.80065	0.0939835
$889$	0	0
$890$	32.4331	1.08716
$891$	4.17507	0.139870
$892$	−8.60687	−0.288179
$893$	−12.5133	−0.418740
$894$	69.5174	2.32501
$895$	22.4363	0.749961
$896$	0	0
$897$	−1.49335	−0.0498614
$898$	−14.1405	−0.471873
$899$	6.40576	0.213644
$900$	1.12742	0.0375807
$901$	−4.11271	−0.137014
$902$	8.53737	0.284263
$903$	0	0
$904$	−8.88950	−0.295661
$905$	−19.3549	−0.643378
$906$	−38.2071	−1.26935
$907$	10.5535	0.350424	0.175212	−	0.984531i	$-0.443939\pi$
$907$	10.5535	0.350424	0.175212	+	0.984531i	$0.443939\pi$
$908$	−4.56400	−0.151462
$909$	−12.4323	−0.412354
$910$	0	0
$911$	−20.6476	−0.684087	−0.342043	−	0.939684i	$-0.611119\pi$
$911$	−20.6476	−0.684087	−0.342043	+	0.939684i	$0.611119\pi$
$912$	6.88559	0.228005
$913$	−10.1221	−0.334993
$914$	36.1102	1.19442
$915$	−9.53748	−0.315299
$916$	4.31302	0.142506
$917$	0	0
$918$	61.5810	2.03248
$919$	29.5158	0.973638	0.486819	−	0.873503i	$-0.338157\pi$
$919$	29.5158	0.973638	0.486819	+	0.873503i	$0.338157\pi$
$920$	−5.08009	−0.167486
$921$	−11.4876	−0.378530
$922$	12.3377	0.406319
$923$	1.43242	0.0471486
$924$	0	0
$925$	−2.98151	−0.0980316
$926$	−3.90639	−0.128372
$927$	2.76515	0.0908195
$928$	27.3693	0.898441
$929$	−1.17531	−0.0385608	−0.0192804	−	0.999814i	$-0.506138\pi$
$929$	−1.17531	−0.0385608	−0.0192804	+	0.999814i	$0.506138\pi$
$930$	10.2781	0.337031
$931$	0	0
$932$	−39.7671	−1.30261
$933$	21.4964	0.703760
$934$	21.2196	0.694328
$935$	7.41122	0.242373
$936$	0.0961545	0.00314291
$937$	6.87262	0.224519	0.112259	−	0.993679i	$-0.464191\pi$
$937$	6.87262	0.224519	0.112259	+	0.993679i	$0.464191\pi$
$938$	0	0
$939$	−43.0247	−1.40406
$940$	−42.3720	−1.38202
$941$	−28.0438	−0.914202	−0.457101	−	0.889415i	$-0.651112\pi$
$941$	−28.0438	−0.914202	−0.457101	+	0.889415i	$0.651112\pi$
$942$	45.4777	1.48174
$943$	29.0223	0.945097
$944$	17.1186	0.557162
$945$	0	0
$946$	3.88314	0.126252
$947$	−9.09378	−0.295508	−0.147754	−	0.989024i	$-0.547204\pi$
$947$	−9.09378	−0.295508	−0.147754	+	0.989024i	$0.547204\pi$
$948$	−36.4033	−1.18232
$949$	0.921372	0.0299090
$950$	−1.86700	−0.0605736
$951$	36.3485	1.17868
$952$	0	0
$953$	7.70805	0.249688	0.124844	−	0.992176i	$-0.460157\pi$
$953$	7.70805	0.249688	0.124844	+	0.992176i	$0.460157\pi$
$954$	−0.948994	−0.0307248
$955$	−0.599809	−0.0194094
$956$	33.3681	1.07920
$957$	−3.58674	−0.115943
$958$	32.7808	1.05910
$959$	0	0
$960$	16.2765	0.525322
$961$	−27.9244	−0.900786
$962$	1.37183	0.0442294
$963$	−10.5927	−0.341347
$964$	15.4310	0.497000
$965$	26.9127	0.866350
$966$	0	0
$967$	−16.2862	−0.523729	−0.261864	−	0.965105i	$-0.584337\pi$
$967$	−16.2862	−0.523729	−0.261864	+	0.965105i	$0.584337\pi$
$968$	−6.35569	−0.204280
$969$	−8.69748	−0.279403
$970$	60.5204	1.94319
$971$	15.2756	0.490218	0.245109	−	0.969496i	$-0.421176\pi$
$971$	15.2756	0.490218	0.245109	+	0.969496i	$0.421176\pi$
$972$	11.7925	0.378243
$973$	0	0
$974$	−10.7383	−0.344076
$975$	0.344480	0.0110322
$976$	−14.1487	−0.452889
$977$	51.3383	1.64246	0.821229	−	0.570598i	$-0.193289\pi$
$977$	51.3383	1.64246	0.821229	+	0.570598i	$0.193289\pi$
$978$	−15.3687	−0.491436
$979$	−5.43425	−0.173679
$980$	0	0
$981$	−9.21825	−0.294316
$982$	−57.9927	−1.85062
$983$	26.2107	0.835993	0.417996	−	0.908449i	$-0.362732\pi$
$983$	26.2107	0.835993	0.417996	+	0.908449i	$0.362732\pi$
$984$	6.28864	0.200475
$985$	−19.6806	−0.627075
$986$	−40.1129	−1.27746
$987$	0	0
$988$	0.393083	0.0125056
$989$	13.2005	0.419752
$990$	1.71012	0.0543511
$991$	27.9607	0.888201	0.444101	−	0.895977i	$-0.353523\pi$
$991$	27.9607	0.888201	0.444101	+	0.895977i	$0.353523\pi$
$992$	13.1409	0.417225
$993$	−6.43867	−0.204325
$994$	0	0
$995$	30.0065	0.951270
$996$	40.2237	1.27454
$997$	26.4041	0.836226	0.418113	−	0.908395i	$-0.362692\pi$
$997$	26.4041	0.836226	0.418113	+	0.908395i	$0.362692\pi$
$998$	1.73461	0.0549081
$999$	−17.1953	−0.544035

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.m.1.1	yes	4
3.2	odd	2		8379.2.a.bu.1.4		4
7.2	even	3		931.2.f.n.704.4		8
7.3	odd	6		931.2.f.o.324.4		8
7.4	even	3		931.2.f.n.324.4		8
7.5	odd	6		931.2.f.o.704.4		8
7.6	odd	2		931.2.a.l.1.1	✓	4
21.20	even	2		8379.2.a.bv.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.l.1.1	✓	4	7.6	odd	2
931.2.a.m.1.1	yes	4	1.1	even	1	trivial
931.2.f.n.324.4		8	7.4	even	3
931.2.f.n.704.4		8	7.2	even	3
931.2.f.o.324.4		8	7.3	odd	6
931.2.f.o.704.4		8	7.5	odd	6
8379.2.a.bu.1.4		4	3.2	odd	2
8379.2.a.bv.1.4		4	21.20	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q-1.92022 q^{2} +1.52077 q^{3} +1.68725 q^{4} -2.00692 q^{5} -2.92022 q^{6} +0.600553 q^{8} -0.687248 q^{9} +O(q^{10})\)	\(q-1.92022 q^{2} +1.52077 q^{3} +1.68725 q^{4} -2.00692 q^{5} -2.92022 q^{6} +0.600553 q^{8} -0.687248 q^{9} +3.85372 q^{10} -0.645701 q^{11} +2.56592 q^{12} -0.232973 q^{13} -3.05207 q^{15} -4.52769 q^{16} +5.71912 q^{17} +1.31967 q^{18} -1.00000 q^{19} -3.38617 q^{20} +1.23989 q^{22} +4.21494 q^{23} +0.913304 q^{24} -0.972286 q^{25} +0.447359 q^{26} -5.60747 q^{27} +3.65262 q^{29} +5.86064 q^{30} +1.75375 q^{31} +7.49306 q^{32} -0.981965 q^{33} -10.9820 q^{34} -1.15956 q^{36} +3.06650 q^{37} +1.92022 q^{38} -0.354299 q^{39} -1.20526 q^{40} +6.88559 q^{41} +3.13184 q^{43} -1.08946 q^{44} +1.37925 q^{45} -8.09361 q^{46} +12.5133 q^{47} -6.88559 q^{48} +1.86700 q^{50} +8.69748 q^{51} -0.393083 q^{52} -0.719116 q^{53} +10.7676 q^{54} +1.29587 q^{55} -1.52077 q^{57} -7.01383 q^{58} -3.78086 q^{59} -5.14959 q^{60} +3.12493 q^{61} -3.36758 q^{62} -5.33295 q^{64} +0.467557 q^{65} +1.88559 q^{66} +3.07702 q^{67} +9.64957 q^{68} +6.40997 q^{69} -6.14844 q^{71} -0.412729 q^{72} -3.95485 q^{73} -5.88835 q^{74} -1.47863 q^{75} -1.68725 q^{76} +0.680332 q^{78} -14.1872 q^{79} +9.08670 q^{80} -6.46595 q^{81} -13.2219 q^{82} +15.6761 q^{83} -11.4778 q^{85} -6.01383 q^{86} +5.55480 q^{87} -0.387778 q^{88} +8.41604 q^{89} -2.64846 q^{90} +7.11165 q^{92} +2.66705 q^{93} -24.0282 q^{94} +2.00692 q^{95} +11.3952 q^{96} +15.7044 q^{97} +0.443757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^8 + 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} + 8 q^{5} - 4 q^{6} + 6 q^{8} + 2 q^{9} + 10 q^{10} - 6 q^{11} + 6 q^{12} + 2 q^{13} + 4 q^{15} + 2 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} - 14 q^{22} - 8 q^{23} + 12 q^{24} + 20 q^{25} + 16 q^{26} - 10 q^{27} + 2 q^{29} + 2 q^{30} + 2 q^{32} + 18 q^{33} - 22 q^{34} - 20 q^{36} + 10 q^{37} + 2 q^{39} + 22 q^{40} + 12 q^{41} + 4 q^{43} - 14 q^{44} + 8 q^{45} - 8 q^{46} + 16 q^{47} - 12 q^{48} + 12 q^{50} - 10 q^{51} + 28 q^{52} + 12 q^{53} + 4 q^{54} - 8 q^{55} - 2 q^{57} + 4 q^{58} + 14 q^{59} - 2 q^{60} + 20 q^{61} - 20 q^{62} - 20 q^{64} + 10 q^{65} - 8 q^{66} + 2 q^{67} - 24 q^{68} + 14 q^{69} - 2 q^{71} - 8 q^{72} - 16 q^{73} - 26 q^{74} + 36 q^{75} - 2 q^{76} + 14 q^{78} - 8 q^{79} + 28 q^{80} - 20 q^{81} - 12 q^{82} + 20 q^{83} - 14 q^{85} + 8 q^{86} - 20 q^{87} - 2 q^{88} + 16 q^{89} - 32 q^{90} + 26 q^{92} + 12 q^{93} + 10 q^{94} - 8 q^{95} - 12 q^{96} + 2 q^{97} + 8 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 - 4 * q^6 + 6 * q^8 + 2 * q^9 + 10 * q^10 - 6 * q^11 + 6 * q^12 + 2 * q^13 + 4 * q^15 + 2 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 - 14 * q^22 - 8 * q^23 + 12 * q^24 + 20 * q^25 + 16 * q^26 - 10 * q^27 + 2 * q^29 + 2 * q^30 + 2 * q^32 + 18 * q^33 - 22 * q^34 - 20 * q^36 + 10 * q^37 + 2 * q^39 + 22 * q^40 + 12 * q^41 + 4 * q^43 - 14 * q^44 + 8 * q^45 - 8 * q^46 + 16 * q^47 - 12 * q^48 + 12 * q^50 - 10 * q^51 + 28 * q^52 + 12 * q^53 + 4 * q^54 - 8 * q^55 - 2 * q^57 + 4 * q^58 + 14 * q^59 - 2 * q^60 + 20 * q^61 - 20 * q^62 - 20 * q^64 + 10 * q^65 - 8 * q^66 + 2 * q^67 - 24 * q^68 + 14 * q^69 - 2 * q^71 - 8 * q^72 - 16 * q^73 - 26 * q^74 + 36 * q^75 - 2 * q^76 + 14 * q^78 - 8 * q^79 + 28 * q^80 - 20 * q^81 - 12 * q^82 + 20 * q^83 - 14 * q^85 + 8 * q^86 - 20 * q^87 - 2 * q^88 + 16 * q^89 - 32 * q^90 + 26 * q^92 + 12 * q^93 + 10 * q^94 - 8 * q^95 - 12 * q^96 + 2 * q^97 + 8 * q^99

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