LMFDB - Embedded newform 2499.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2499,2,Mod(1,2499)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2499, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2499.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2499 = 3 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2499.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:	$19.9546154651$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.1383597.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 14x^{2} + 7x - 15 $ x^5 - 2x^4 - 7x^3 + 14x^2 + 7x - 15
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 357)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.49001$ of defining polynomial
Character	$\chi$	$=$	2499.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49001 q^{2} +1.00000 q^{3} +4.20014 q^{4} +2.33064 q^{5} -2.49001 q^{6} -5.47838 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.49001 q^{2} +1.00000 q^{3} +4.20014 q^{4} +2.33064 q^{5} -2.49001 q^{6} -5.47838 q^{8} +1.00000 q^{9} -5.80332 q^{10} -5.14774 q^{11} +4.20014 q^{12} +0.596965 q^{13} +2.33064 q^{15} +5.24092 q^{16} -1.00000 q^{17} -2.49001 q^{18} -1.89304 q^{19} +9.78904 q^{20} +12.8179 q^{22} -4.15937 q^{23} -5.47838 q^{24} +0.431901 q^{25} -1.48645 q^{26} +1.00000 q^{27} -2.90140 q^{29} -5.80332 q^{30} +6.44107 q^{31} -2.09319 q^{32} -5.14774 q^{33} +2.49001 q^{34} +4.20014 q^{36} -9.40385 q^{37} +4.71370 q^{38} +0.596965 q^{39} -12.7682 q^{40} +2.09319 q^{41} +11.3362 q^{43} -21.6212 q^{44} +2.33064 q^{45} +10.3569 q^{46} -4.38305 q^{47} +5.24092 q^{48} -1.07544 q^{50} -1.00000 q^{51} +2.50734 q^{52} -10.9311 q^{53} -2.49001 q^{54} -11.9975 q^{55} -1.89304 q^{57} +7.22450 q^{58} -3.21206 q^{59} +9.78904 q^{60} -10.5832 q^{61} -16.0383 q^{62} -5.26979 q^{64} +1.39131 q^{65} +12.8179 q^{66} -14.7690 q^{67} -4.20014 q^{68} -4.15937 q^{69} -6.91028 q^{71} -5.47838 q^{72} -0.434038 q^{73} +23.4157 q^{74} +0.431901 q^{75} -7.95106 q^{76} -1.48645 q^{78} -6.15965 q^{79} +12.2147 q^{80} +1.00000 q^{81} -5.21206 q^{82} +5.17802 q^{83} -2.33064 q^{85} -28.2274 q^{86} -2.90140 q^{87} +28.2012 q^{88} -0.394683 q^{89} -5.80332 q^{90} -17.4699 q^{92} +6.44107 q^{93} +10.9138 q^{94} -4.41201 q^{95} -2.09319 q^{96} +17.4653 q^{97} -5.14774 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} + 5 q^{3} + 8 q^{4} - q^{5} - 2 q^{6} + 5 q^{9}+O(q^{10}) $ 5 * q - 2 * q^2 + 5 * q^3 + 8 * q^4 - q^5 - 2 * q^6 + 5 * q^9	$ 5 q - 2 q^{2} + 5 q^{3} + 8 q^{4} - q^{5} - 2 q^{6} + 5 q^{9} - 13 q^{10} - 11 q^{11} + 8 q^{12} - 7 q^{13} - q^{15} - 2 q^{16} - 5 q^{17} - 2 q^{18} - 9 q^{19} - 12 q^{20} + 5 q^{22} - 23 q^{23} + 14 q^{25} - 18 q^{26} + 5 q^{27} - 18 q^{29} - 13 q^{30} - 9 q^{31} + 3 q^{32} - 11 q^{33} + 2 q^{34} + 8 q^{36} - 7 q^{39} - 31 q^{40} - 3 q^{41} + 12 q^{43} - 33 q^{44} - q^{45} + 13 q^{46} - 11 q^{47} - 2 q^{48} + 24 q^{50} - 5 q^{51} - 5 q^{52} - 3 q^{53} - 2 q^{54} + 10 q^{55} - 9 q^{57} - 34 q^{58} + 14 q^{59} - 12 q^{60} - 29 q^{61} + 5 q^{62} - 8 q^{65} + 5 q^{66} + 16 q^{67} - 8 q^{68} - 23 q^{69} - 19 q^{71} - 11 q^{73} + 45 q^{74} + 14 q^{75} - 9 q^{76} - 18 q^{78} + q^{79} + 5 q^{80} + 5 q^{81} + 4 q^{82} - 5 q^{83} + q^{85} - 3 q^{86} - 18 q^{87} + 37 q^{88} - 8 q^{89} - 13 q^{90} - 48 q^{92} - 9 q^{93} + 18 q^{94} - 21 q^{95} + 3 q^{96} - 19 q^{97} - 11 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 + 5 * q^3 + 8 * q^4 - q^5 - 2 * q^6 + 5 * q^9 - 13 * q^10 - 11 * q^11 + 8 * q^12 - 7 * q^13 - q^15 - 2 * q^16 - 5 * q^17 - 2 * q^18 - 9 * q^19 - 12 * q^20 + 5 * q^22 - 23 * q^23 + 14 * q^25 - 18 * q^26 + 5 * q^27 - 18 * q^29 - 13 * q^30 - 9 * q^31 + 3 * q^32 - 11 * q^33 + 2 * q^34 + 8 * q^36 - 7 * q^39 - 31 * q^40 - 3 * q^41 + 12 * q^43 - 33 * q^44 - q^45 + 13 * q^46 - 11 * q^47 - 2 * q^48 + 24 * q^50 - 5 * q^51 - 5 * q^52 - 3 * q^53 - 2 * q^54 + 10 * q^55 - 9 * q^57 - 34 * q^58 + 14 * q^59 - 12 * q^60 - 29 * q^61 + 5 * q^62 - 8 * q^65 + 5 * q^66 + 16 * q^67 - 8 * q^68 - 23 * q^69 - 19 * q^71 - 11 * q^73 + 45 * q^74 + 14 * q^75 - 9 * q^76 - 18 * q^78 + q^79 + 5 * q^80 + 5 * q^81 + 4 * q^82 - 5 * q^83 + q^85 - 3 * q^86 - 18 * q^87 + 37 * q^88 - 8 * q^89 - 13 * q^90 - 48 * q^92 - 9 * q^93 + 18 * q^94 - 21 * q^95 + 3 * q^96 - 19 * q^97 - 11 * 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 $

$2$	−2.49001	−1.76070	−0.880351	−	0.474323i	$-0.842693\pi$
$2$	−2.49001	−1.76070	−0.880351	+	0.474323i	$0.842693\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.20014	2.10007
$5$	2.33064	1.04230	0.521148	−	0.853466i	$-0.325504\pi$
$5$	2.33064	1.04230	0.521148	+	0.853466i	$0.325504\pi$
$6$	−2.49001	−1.01654
$7$	0	0
$7$	0	0
$8$	−5.47838	−1.93690
$9$	1.00000	0.333333
$10$	−5.80332	−1.83517
$11$	−5.14774	−1.55210	−0.776050	−	0.630671i	$-0.782780\pi$
$11$	−5.14774	−1.55210	−0.776050	+	0.630671i	$0.782780\pi$
$12$	4.20014	1.21248
$13$	0.596965	0.165568	0.0827841	−	0.996568i	$-0.473619\pi$
$13$	0.596965	0.165568	0.0827841	+	0.996568i	$0.473619\pi$
$14$	0	0
$15$	2.33064	0.601770
$16$	5.24092	1.31023
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.49001	−0.586901
$19$	−1.89304	−0.434294	−0.217147	−	0.976139i	$-0.569675\pi$
$19$	−1.89304	−0.434294	−0.217147	+	0.976139i	$0.569675\pi$
$20$	9.78904	2.18890
$21$	0	0
$22$	12.8179	2.73279
$23$	−4.15937	−0.867288	−0.433644	−	0.901084i	$-0.642772\pi$
$23$	−4.15937	−0.867288	−0.433644	+	0.901084i	$0.642772\pi$
$24$	−5.47838	−1.11827
$25$	0.431901	0.0863802
$26$	−1.48645	−0.291516
$27$	1.00000	0.192450
$28$	0	0
$29$	−2.90140	−0.538776	−0.269388	−	0.963032i	$-0.586821\pi$
$29$	−2.90140	−0.538776	−0.269388	+	0.963032i	$0.586821\pi$
$30$	−5.80332	−1.05954
$31$	6.44107	1.15685	0.578425	−	0.815736i	$-0.303668\pi$
$31$	6.44107	1.15685	0.578425	+	0.815736i	$0.303668\pi$
$32$	−2.09319	−0.370027
$33$	−5.14774	−0.896106
$34$	2.49001	0.427033
$35$	0	0
$36$	4.20014	0.700024
$37$	−9.40385	−1.54598	−0.772992	−	0.634416i	$-0.781241\pi$
$37$	−9.40385	−1.54598	−0.772992	+	0.634416i	$0.781241\pi$
$38$	4.71370	0.764663
$39$	0.596965	0.0955908
$40$	−12.7682	−2.01882
$41$	2.09319	0.326901	0.163451	−	0.986552i	$-0.447738\pi$
$41$	2.09319	0.326901	0.163451	+	0.986552i	$0.447738\pi$
$42$	0	0
$43$	11.3362	1.72876	0.864381	−	0.502838i	$-0.167711\pi$
$43$	11.3362	1.72876	0.864381	+	0.502838i	$0.167711\pi$
$44$	−21.6212	−3.25952
$45$	2.33064	0.347432
$46$	10.3569	1.52704
$47$	−4.38305	−0.639334	−0.319667	−	0.947530i	$-0.603571\pi$
$47$	−4.38305	−0.639334	−0.319667	+	0.947530i	$0.603571\pi$
$48$	5.24092	0.756462
$49$	0	0
$50$	−1.07544	−0.152090
$51$	−1.00000	−0.140028
$52$	2.50734	0.347705
$53$	−10.9311	−1.50150	−0.750749	−	0.660587i	$-0.770307\pi$
$53$	−10.9311	−1.50150	−0.750749	+	0.660587i	$0.770307\pi$
$54$	−2.49001	−0.338847
$55$	−11.9975	−1.61775
$56$	0	0
$57$	−1.89304	−0.250740
$58$	7.22450	0.948624
$59$	−3.21206	−0.418174	−0.209087	−	0.977897i	$-0.567049\pi$
$59$	−3.21206	−0.418174	−0.209087	+	0.977897i	$0.567049\pi$
$60$	9.78904	1.26376
$61$	−10.5832	−1.35504	−0.677520	−	0.735505i	$-0.736945\pi$
$61$	−10.5832	−1.35504	−0.677520	+	0.735505i	$0.736945\pi$
$62$	−16.0383	−2.03687
$63$	0	0
$64$	−5.26979	−0.658724
$65$	1.39131	0.172571
$66$	12.8179	1.57778
$67$	−14.7690	−1.80432	−0.902158	−	0.431406i	$-0.858018\pi$
$67$	−14.7690	−1.80432	−0.902158	+	0.431406i	$0.858018\pi$
$68$	−4.20014	−0.509342
$69$	−4.15937	−0.500729
$70$	0	0
$71$	−6.91028	−0.820099	−0.410050	−	0.912063i	$-0.634489\pi$
$71$	−6.91028	−0.820099	−0.410050	+	0.912063i	$0.634489\pi$
$72$	−5.47838	−0.645633
$73$	−0.434038	−0.0508003	−0.0254002	−	0.999677i	$-0.508086\pi$
$73$	−0.434038	−0.0508003	−0.0254002	+	0.999677i	$0.508086\pi$
$74$	23.4157	2.72202
$75$	0.431901	0.0498716
$76$	−7.95106	−0.912049
$77$	0	0
$78$	−1.48645	−0.168307
$79$	−6.15965	−0.693015	−0.346507	−	0.938047i	$-0.612632\pi$
$79$	−6.15965	−0.693015	−0.346507	+	0.938047i	$0.612632\pi$
$80$	12.2147	1.36565
$81$	1.00000	0.111111
$82$	−5.21206	−0.575576
$83$	5.17802	0.568362	0.284181	−	0.958771i	$-0.408278\pi$
$83$	5.17802	0.568362	0.284181	+	0.958771i	$0.408278\pi$
$84$	0	0
$85$	−2.33064	−0.252794
$86$	−28.2274	−3.04383
$87$	−2.90140	−0.311062
$88$	28.2012	3.00626
$89$	−0.394683	−0.0418363	−0.0209182	−	0.999781i	$-0.506659\pi$
$89$	−0.394683	−0.0418363	−0.0209182	+	0.999781i	$0.506659\pi$
$90$	−5.80332	−0.611724
$91$	0	0
$92$	−17.4699	−1.82137
$93$	6.44107	0.667908
$94$	10.9138	1.12568
$95$	−4.41201	−0.452663
$96$	−2.09319	−0.213635
$97$	17.4653	1.77334	0.886668	−	0.462407i	$-0.153014\pi$
$97$	17.4653	1.77334	0.886668	+	0.462407i	$0.153014\pi$
$98$	0	0
$99$	−5.14774	−0.517367
$100$	1.81405	0.181405
$101$	−15.1623	−1.50871	−0.754353	−	0.656468i	$-0.772049\pi$
$101$	−15.1623	−1.50871	−0.754353	+	0.656468i	$0.772049\pi$
$102$	2.49001	0.246548
$103$	13.7806	1.35784	0.678921	−	0.734211i	$-0.262448\pi$
$103$	13.7806	1.35784	0.678921	+	0.734211i	$0.262448\pi$
$104$	−3.27040	−0.320689
$105$	0	0
$106$	27.2185	2.64369
$107$	−0.881414	−0.0852095	−0.0426048	−	0.999092i	$-0.513566\pi$
$107$	−0.881414	−0.0852095	−0.0426048	+	0.999092i	$0.513566\pi$
$108$	4.20014	0.404159
$109$	13.8871	1.33014	0.665072	−	0.746779i	$-0.268401\pi$
$109$	13.8871	1.33014	0.665072	+	0.746779i	$0.268401\pi$
$110$	29.8740	2.84837
$111$	−9.40385	−0.892574
$112$	0	0
$113$	−16.4092	−1.54365	−0.771823	−	0.635838i	$-0.780655\pi$
$113$	−16.4092	−1.54365	−0.771823	+	0.635838i	$0.780655\pi$
$114$	4.71370	0.441478
$115$	−9.69400	−0.903970
$116$	−12.1863	−1.13147
$117$	0.596965	0.0551894
$118$	7.99805	0.736280
$119$	0	0
$120$	−12.7682	−1.16557
$121$	15.4992	1.40902
$122$	26.3523	2.38582
$123$	2.09319	0.188736
$124$	27.0534	2.42947
$125$	−10.6466	−0.952262
$126$	0	0
$127$	5.62184	0.498858	0.249429	−	0.968393i	$-0.419757\pi$
$127$	5.62184	0.498858	0.249429	+	0.968393i	$0.419757\pi$
$128$	17.3082	1.52984
$129$	11.3362	0.998101
$130$	−3.46438	−0.303846
$131$	−8.44374	−0.737733	−0.368866	−	0.929482i	$-0.620254\pi$
$131$	−8.44374	−0.737733	−0.368866	+	0.929482i	$0.620254\pi$
$132$	−21.6212	−1.88189
$133$	0	0
$134$	36.7749	3.17686
$135$	2.33064	0.200590
$136$	5.47838	0.469767
$137$	−0.871731	−0.0744770	−0.0372385	−	0.999306i	$-0.511856\pi$
$137$	−0.871731	−0.0744770	−0.0372385	+	0.999306i	$0.511856\pi$
$138$	10.3569	0.881634
$139$	12.3738	1.04954	0.524768	−	0.851245i	$-0.324152\pi$
$139$	12.3738	1.04954	0.524768	+	0.851245i	$0.324152\pi$
$140$	0	0
$141$	−4.38305	−0.369120
$142$	17.2067	1.44395
$143$	−3.07302	−0.256978
$144$	5.24092	0.436744
$145$	−6.76212	−0.561564
$146$	1.08076	0.0894442
$147$	0	0
$148$	−39.4975	−3.24668
$149$	−5.12268	−0.419666	−0.209833	−	0.977737i	$-0.567292\pi$
$149$	−5.12268	−0.419666	−0.209833	+	0.977737i	$0.567292\pi$
$150$	−1.07544	−0.0878091
$151$	−3.73715	−0.304125	−0.152062	−	0.988371i	$-0.548591\pi$
$151$	−3.73715	−0.304125	−0.152062	+	0.988371i	$0.548591\pi$
$152$	10.3708	0.841184
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	15.0118	1.20578
$156$	2.50734	0.200748
$157$	3.61723	0.288686	0.144343	−	0.989528i	$-0.453893\pi$
$157$	3.61723	0.288686	0.144343	+	0.989528i	$0.453893\pi$
$158$	15.3376	1.22019
$159$	−10.9311	−0.866891
$160$	−4.87848	−0.385677
$161$	0	0
$162$	−2.49001	−0.195634
$163$	−5.73928	−0.449535	−0.224768	−	0.974412i	$-0.572162\pi$
$163$	−5.73928	−0.449535	−0.224768	+	0.974412i	$0.572162\pi$
$164$	8.79169	0.686516
$165$	−11.9975	−0.934007
$166$	−12.8933	−1.00072
$167$	25.0743	1.94031	0.970154	−	0.242490i	$-0.0779641\pi$
$167$	25.0743	1.94031	0.970154	+	0.242490i	$0.0779641\pi$
$168$	0	0
$169$	−12.6436	−0.972587
$170$	5.80332	0.445095
$171$	−1.89304	−0.144765
$172$	47.6139	3.63052
$173$	−16.5331	−1.25699	−0.628495	−	0.777814i	$-0.716329\pi$
$173$	−16.5331	−1.25699	−0.628495	+	0.777814i	$0.716329\pi$
$174$	7.22450	0.547688
$175$	0	0
$176$	−26.9789	−2.03361
$177$	−3.21206	−0.241433
$178$	0.982765	0.0736613
$179$	4.57024	0.341596	0.170798	−	0.985306i	$-0.445366\pi$
$179$	4.57024	0.341596	0.170798	+	0.985306i	$0.445366\pi$
$180$	9.78904	0.729632
$181$	−23.3136	−1.73289	−0.866444	−	0.499275i	$-0.833600\pi$
$181$	−23.3136	−1.73289	−0.866444	+	0.499275i	$0.833600\pi$
$182$	0	0
$183$	−10.5832	−0.782332
$184$	22.7866	1.67985
$185$	−21.9170	−1.61137
$186$	−16.0383	−1.17599
$187$	5.14774	0.376440
$188$	−18.4095	−1.34265
$189$	0	0
$190$	10.9859	0.797005
$191$	18.2638	1.32152	0.660760	−	0.750597i	$-0.270234\pi$
$191$	18.2638	1.32152	0.660760	+	0.750597i	$0.270234\pi$
$192$	−5.26979	−0.380314
$193$	−0.0899108	−0.00647192	−0.00323596	−	0.999995i	$-0.501030\pi$
$193$	−0.0899108	−0.00647192	−0.00323596	+	0.999995i	$0.501030\pi$
$194$	−43.4888	−3.12232
$195$	1.39131	0.0996339
$196$	0	0
$197$	4.49561	0.320299	0.160150	−	0.987093i	$-0.448802\pi$
$197$	4.49561	0.320299	0.160150	+	0.987093i	$0.448802\pi$
$198$	12.8179	0.910929
$199$	14.3258	1.01553	0.507763	−	0.861497i	$-0.330473\pi$
$199$	14.3258	1.01553	0.507763	+	0.861497i	$0.330473\pi$
$200$	−2.36612	−0.167310
$201$	−14.7690	−1.04172
$202$	37.7543	2.65638
$203$	0	0
$204$	−4.20014	−0.294069
$205$	4.87848	0.340728
$206$	−34.3138	−2.39076
$207$	−4.15937	−0.289096
$208$	3.12865	0.216933
$209$	9.74489	0.674068
$210$	0	0
$211$	17.5551	1.20854	0.604270	−	0.796780i	$-0.293465\pi$
$211$	17.5551	1.20854	0.604270	+	0.796780i	$0.293465\pi$
$212$	−45.9121	−3.15326
$213$	−6.91028	−0.473485
$214$	2.19473	0.150029
$215$	26.4208	1.80188
$216$	−5.47838	−0.372756
$217$	0	0
$218$	−34.5790	−2.34199
$219$	−0.434038	−0.0293296
$220$	−50.3914	−3.39739
$221$	−0.596965	−0.0401562
$222$	23.4157	1.57156
$223$	−24.8716	−1.66553	−0.832764	−	0.553628i	$-0.813243\pi$
$223$	−24.8716	−1.66553	−0.832764	+	0.553628i	$0.813243\pi$
$224$	0	0
$225$	0.431901	0.0287934
$226$	40.8590	2.71790
$227$	8.32737	0.552707	0.276353	−	0.961056i	$-0.410874\pi$
$227$	8.32737	0.552707	0.276353	+	0.961056i	$0.410874\pi$
$228$	−7.95106	−0.526572
$229$	−17.0257	−1.12509	−0.562544	−	0.826767i	$-0.690177\pi$
$229$	−17.0257	−1.12509	−0.562544	+	0.826767i	$0.690177\pi$
$230$	24.1381	1.59162
$231$	0	0
$232$	15.8949	1.04355
$233$	−15.3997	−1.00887	−0.504433	−	0.863451i	$-0.668299\pi$
$233$	−15.3997	−1.00887	−0.504433	+	0.863451i	$0.668299\pi$
$234$	−1.48645	−0.0971721
$235$	−10.2153	−0.666375
$236$	−13.4911	−0.878196
$237$	−6.15965	−0.400112
$238$	0	0
$239$	12.0954	0.782388	0.391194	−	0.920308i	$-0.372062\pi$
$239$	12.0954	0.782388	0.391194	+	0.920308i	$0.372062\pi$
$240$	12.2147	0.788457
$241$	−14.7946	−0.953007	−0.476503	−	0.879173i	$-0.658096\pi$
$241$	−14.7946	−0.953007	−0.476503	+	0.879173i	$0.658096\pi$
$242$	−38.5931	−2.48086
$243$	1.00000	0.0641500
$244$	−44.4510	−2.84568
$245$	0	0
$246$	−5.21206	−0.332309
$247$	−1.13008	−0.0719053
$248$	−35.2866	−2.24070
$249$	5.17802	0.328144
$250$	26.5102	1.67665
$251$	11.4881	0.725121	0.362560	−	0.931960i	$-0.381903\pi$
$251$	11.4881	0.725121	0.362560	+	0.931960i	$0.381903\pi$
$252$	0	0
$253$	21.4113	1.34612
$254$	−13.9984	−0.878340
$255$	−2.33064	−0.145951
$256$	−32.5580	−2.03487
$257$	−7.85522	−0.489995	−0.244997	−	0.969524i	$-0.578787\pi$
$257$	−7.85522	−0.489995	−0.244997	+	0.969524i	$0.578787\pi$
$258$	−28.2274	−1.75736
$259$	0	0
$260$	5.84371	0.362412
$261$	−2.90140	−0.179592
$262$	21.0250	1.29893
$263$	15.6574	0.965477	0.482738	−	0.875765i	$-0.339642\pi$
$263$	15.6574	0.965477	0.482738	+	0.875765i	$0.339642\pi$
$264$	28.2012	1.73567
$265$	−25.4764	−1.56501
$266$	0	0
$267$	−0.394683	−0.0241542
$268$	−62.0318	−3.78919
$269$	−28.7669	−1.75395	−0.876975	−	0.480536i	$-0.840442\pi$
$269$	−28.7669	−1.75395	−0.876975	+	0.480536i	$0.840442\pi$
$270$	−5.80332	−0.353179
$271$	4.86925	0.295786	0.147893	−	0.989003i	$-0.452751\pi$
$271$	4.86925	0.295786	0.147893	+	0.989003i	$0.452751\pi$
$272$	−5.24092	−0.317778
$273$	0	0
$274$	2.17062	0.131132
$275$	−2.22331	−0.134071
$276$	−17.4699	−1.05157
$277$	19.2587	1.15714	0.578572	−	0.815631i	$-0.303610\pi$
$277$	19.2587	1.15714	0.578572	+	0.815631i	$0.303610\pi$
$278$	−30.8110	−1.84792
$279$	6.44107	0.385617
$280$	0	0
$281$	14.6294	0.872716	0.436358	−	0.899773i	$-0.356268\pi$
$281$	14.6294	0.872716	0.436358	+	0.899773i	$0.356268\pi$
$282$	10.9138	0.649910
$283$	−11.9803	−0.712155	−0.356078	−	0.934456i	$-0.615886\pi$
$283$	−11.9803	−0.712155	−0.356078	+	0.934456i	$0.615886\pi$
$284$	−29.0242	−1.72227
$285$	−4.41201	−0.261345
$286$	7.65184	0.452463
$287$	0	0
$288$	−2.09319	−0.123342
$289$	1.00000	0.0588235
$290$	16.8377	0.988746
$291$	17.4653	1.02384
$292$	−1.82302	−0.106684
$293$	7.08802	0.414087	0.207043	−	0.978332i	$-0.433616\pi$
$293$	7.08802	0.414087	0.207043	+	0.978332i	$0.433616\pi$
$294$	0	0
$295$	−7.48616	−0.435861
$296$	51.5179	2.99441
$297$	−5.14774	−0.298702
$298$	12.7555	0.738907
$299$	−2.48299	−0.143595
$300$	1.81405	0.104734
$301$	0	0
$302$	9.30553	0.535473
$303$	−15.1623	−0.871052
$304$	−9.92130	−0.569026
$305$	−24.6657	−1.41235
$306$	2.49001	0.142344
$307$	−30.7472	−1.75484	−0.877418	−	0.479726i	$-0.840736\pi$
$307$	−30.7472	−1.75484	−0.877418	+	0.479726i	$0.840736\pi$
$308$	0	0
$309$	13.7806	0.783951
$310$	−37.3796	−2.12302
$311$	−32.8830	−1.86463	−0.932313	−	0.361652i	$-0.882213\pi$
$311$	−32.8830	−1.86463	−0.932313	+	0.361652i	$0.882213\pi$
$312$	−3.27040	−0.185150
$313$	2.35409	0.133061	0.0665306	−	0.997784i	$-0.478807\pi$
$313$	2.35409	0.133061	0.0665306	+	0.997784i	$0.478807\pi$
$314$	−9.00694	−0.508291
$315$	0	0
$316$	−25.8714	−1.45538
$317$	30.5798	1.71753	0.858765	−	0.512370i	$-0.171232\pi$
$317$	30.5798	1.71753	0.858765	+	0.512370i	$0.171232\pi$
$318$	27.2185	1.52634
$319$	14.9356	0.836234
$320$	−12.2820	−0.686585
$321$	−0.881414	−0.0491957
$322$	0	0
$323$	1.89304	0.105332
$324$	4.20014	0.233341
$325$	0.257830	0.0143018
$326$	14.2909	0.791498
$327$	13.8871	0.767959
$328$	−11.4673	−0.633175
$329$	0	0
$330$	29.8740	1.64451
$331$	−4.00756	−0.220275	−0.110138	−	0.993916i	$-0.535129\pi$
$331$	−4.00756	−0.220275	−0.110138	+	0.993916i	$0.535129\pi$
$332$	21.7485	1.19360
$333$	−9.40385	−0.515328
$334$	−62.4352	−3.41630
$335$	−34.4212	−1.88063
$336$	0	0
$337$	−23.1664	−1.26195	−0.630977	−	0.775801i	$-0.717346\pi$
$337$	−23.1664	−1.26195	−0.630977	+	0.775801i	$0.717346\pi$
$338$	31.4828	1.71244
$339$	−16.4092	−0.891224
$340$	−9.78904	−0.530885
$341$	−33.1569	−1.79555
$342$	4.71370	0.254888
$343$	0	0
$344$	−62.1043	−3.34844
$345$	−9.69400	−0.521907
$346$	41.1676	2.21318
$347$	−5.91250	−0.317399	−0.158700	−	0.987327i	$-0.550730\pi$
$347$	−5.91250	−0.317399	−0.158700	+	0.987327i	$0.550730\pi$
$348$	−12.1863	−0.653253
$349$	−26.4483	−1.41575	−0.707874	−	0.706339i	$-0.750345\pi$
$349$	−26.4483	−1.41575	−0.707874	+	0.706339i	$0.750345\pi$
$350$	0	0
$351$	0.596965	0.0318636
$352$	10.7752	0.574319
$353$	4.33083	0.230507	0.115254	−	0.993336i	$-0.463232\pi$
$353$	4.33083	0.230507	0.115254	+	0.993336i	$0.463232\pi$
$354$	7.99805	0.425092
$355$	−16.1054	−0.854786
$356$	−1.65773	−0.0878593
$357$	0	0
$358$	−11.3799	−0.601448
$359$	1.39743	0.0737535	0.0368768	−	0.999320i	$-0.488259\pi$
$359$	1.39743	0.0737535	0.0368768	+	0.999320i	$0.488259\pi$
$360$	−12.7682	−0.672941
$361$	−15.4164	−0.811389
$362$	58.0511	3.05110
$363$	15.4992	0.813496
$364$	0	0
$365$	−1.01159	−0.0529489
$366$	26.3523	1.37745
$367$	1.65967	0.0866339	0.0433169	−	0.999061i	$-0.486207\pi$
$367$	1.65967	0.0866339	0.0433169	+	0.999061i	$0.486207\pi$
$368$	−21.7989	−1.13635
$369$	2.09319	0.108967
$370$	54.5736	2.83715
$371$	0	0
$372$	27.0534	1.40265
$373$	1.84010	0.0952770	0.0476385	−	0.998865i	$-0.484830\pi$
$373$	1.84010	0.0952770	0.0476385	+	0.998865i	$0.484830\pi$
$374$	−12.8179	−0.662798
$375$	−10.6466	−0.549789
$376$	24.0120	1.23833
$377$	−1.73203	−0.0892041
$378$	0	0
$379$	−4.60612	−0.236600	−0.118300	−	0.992978i	$-0.537745\pi$
$379$	−4.60612	−0.236600	−0.118300	+	0.992978i	$0.537745\pi$
$380$	−18.5311	−0.950625
$381$	5.62184	0.288016
$382$	−45.4769	−2.32680
$383$	11.3713	0.581049	0.290524	−	0.956868i	$-0.406170\pi$
$383$	11.3713	0.581049	0.290524	+	0.956868i	$0.406170\pi$
$384$	17.3082	0.883255
$385$	0	0
$386$	0.223879	0.0113951
$387$	11.3362	0.576254
$388$	73.3569	3.72413
$389$	3.25360	0.164964	0.0824821	−	0.996593i	$-0.473715\pi$
$389$	3.25360	0.164964	0.0824821	+	0.996593i	$0.473715\pi$
$390$	−3.46438	−0.175426
$391$	4.15937	0.210348
$392$	0	0
$393$	−8.44374	−0.425930
$394$	−11.1941	−0.563952
$395$	−14.3559	−0.722326
$396$	−21.6212	−1.08651
$397$	−0.132962	−0.00667320	−0.00333660	−	0.999994i	$-0.501062\pi$
$397$	−0.132962	−0.00667320	−0.00333660	+	0.999994i	$0.501062\pi$
$398$	−35.6713	−1.78804
$399$	0	0
$400$	2.26356	0.113178
$401$	−10.1833	−0.508532	−0.254266	−	0.967134i	$-0.581834\pi$
$401$	−10.1833	−0.508532	−0.254266	+	0.967134i	$0.581834\pi$
$402$	36.7749	1.83416
$403$	3.84509	0.191538
$404$	−63.6839	−3.16839
$405$	2.33064	0.115811
$406$	0	0
$407$	48.4085	2.39952
$408$	5.47838	0.271220
$409$	14.0633	0.695387	0.347694	−	0.937608i	$-0.386965\pi$
$409$	14.0633	0.695387	0.347694	+	0.937608i	$0.386965\pi$
$410$	−12.1475	−0.599920
$411$	−0.871731	−0.0429993
$412$	57.8805	2.85157
$413$	0	0
$414$	10.3569	0.509012
$415$	12.0681	0.592401
$416$	−1.24956	−0.0612647
$417$	12.3738	0.605950
$418$	−24.2649	−1.18683
$419$	−26.5734	−1.29820	−0.649098	−	0.760704i	$-0.724854\pi$
$419$	−26.5734	−1.29820	−0.649098	+	0.760704i	$0.724854\pi$
$420$	0	0
$421$	−11.0420	−0.538155	−0.269077	−	0.963119i	$-0.586719\pi$
$421$	−11.0420	−0.538155	−0.269077	+	0.963119i	$0.586719\pi$
$422$	−43.7122	−2.12788
$423$	−4.38305	−0.213111
$424$	59.8846	2.90825
$425$	−0.431901	−0.0209503
$426$	17.2067	0.833665
$427$	0	0
$428$	−3.70207	−0.178946
$429$	−3.07302	−0.148367
$430$	−65.7879	−3.17258
$431$	−6.41568	−0.309032	−0.154516	−	0.987990i	$-0.549382\pi$
$431$	−6.41568	−0.309032	−0.154516	+	0.987990i	$0.549382\pi$
$432$	5.24092	0.252154
$433$	20.9787	1.00817	0.504086	−	0.863654i	$-0.331830\pi$
$433$	20.9787	1.00817	0.504086	+	0.863654i	$0.331830\pi$
$434$	0	0
$435$	−6.76212	−0.324219
$436$	58.3279	2.79340
$437$	7.87386	0.376658
$438$	1.08076	0.0516406
$439$	7.13534	0.340551	0.170276	−	0.985396i	$-0.445534\pi$
$439$	7.13534	0.340551	0.170276	+	0.985396i	$0.445534\pi$
$440$	65.7271	3.13341
$441$	0	0
$442$	1.48645	0.0707031
$443$	23.8498	1.13314	0.566569	−	0.824014i	$-0.308270\pi$
$443$	23.8498	1.13314	0.566569	+	0.824014i	$0.308270\pi$
$444$	−39.4975	−1.87447
$445$	−0.919866	−0.0436058
$446$	61.9306	2.93250
$447$	−5.12268	−0.242294
$448$	0	0
$449$	31.7250	1.49720	0.748598	−	0.663025i	$-0.230727\pi$
$449$	31.7250	1.49720	0.748598	+	0.663025i	$0.230727\pi$
$450$	−1.07544	−0.0506966
$451$	−10.7752	−0.507383
$452$	−68.9209	−3.24177
$453$	−3.73715	−0.175587
$454$	−20.7352	−0.973152
$455$	0	0
$456$	10.3708	0.485658
$457$	27.7215	1.29676	0.648379	−	0.761317i	$-0.275447\pi$
$457$	27.7215	1.29676	0.648379	+	0.761317i	$0.275447\pi$
$458$	42.3941	1.98095
$459$	−1.00000	−0.0466760
$460$	−40.7162	−1.89840
$461$	22.6069	1.05291	0.526453	−	0.850204i	$-0.323522\pi$
$461$	22.6069	1.05291	0.526453	+	0.850204i	$0.323522\pi$
$462$	0	0
$463$	7.23081	0.336044	0.168022	−	0.985783i	$-0.446262\pi$
$463$	7.23081	0.336044	0.168022	+	0.985783i	$0.446262\pi$
$464$	−15.2060	−0.705921
$465$	15.0118	0.696157
$466$	38.3453	1.77631
$467$	30.8947	1.42964	0.714818	−	0.699311i	$-0.246510\pi$
$467$	30.8947	1.42964	0.714818	+	0.699311i	$0.246510\pi$
$468$	2.50734	0.115902
$469$	0	0
$470$	25.4363	1.17329
$471$	3.61723	0.166673
$472$	17.5969	0.809962
$473$	−58.3560	−2.68321
$474$	15.3376	0.704478
$475$	−0.817607	−0.0375144
$476$	0	0
$477$	−10.9311	−0.500500
$478$	−30.1177	−1.37755
$479$	21.8112	0.996577	0.498289	−	0.867011i	$-0.333962\pi$
$479$	21.8112	0.996577	0.498289	+	0.867011i	$0.333962\pi$
$480$	−4.87848	−0.222671
$481$	−5.61377	−0.255966
$482$	36.8388	1.67796
$483$	0	0
$484$	65.0988	2.95904
$485$	40.7055	1.84834
$486$	−2.49001	−0.112949
$487$	4.55823	0.206553	0.103277	−	0.994653i	$-0.467067\pi$
$487$	4.55823	0.206553	0.103277	+	0.994653i	$0.467067\pi$
$488$	57.9788	2.62458
$489$	−5.73928	−0.259539
$490$	0	0
$491$	−1.59981	−0.0721983	−0.0360992	−	0.999348i	$-0.511493\pi$
$491$	−1.59981	−0.0721983	−0.0360992	+	0.999348i	$0.511493\pi$
$492$	8.79169	0.396360
$493$	2.90140	0.130672
$494$	2.81391	0.126604
$495$	−11.9975	−0.539249
$496$	33.7571	1.51574
$497$	0	0
$498$	−12.8933	−0.577764
$499$	−25.1531	−1.12601	−0.563003	−	0.826455i	$-0.690354\pi$
$499$	−25.1531	−1.12601	−0.563003	+	0.826455i	$0.690354\pi$
$500$	−44.7173	−1.99982
$501$	25.0743	1.12024
$502$	−28.6054	−1.27672
$503$	−17.2499	−0.769135	−0.384568	−	0.923097i	$-0.625649\pi$
$503$	−17.2499	−0.769135	−0.384568	+	0.923097i	$0.625649\pi$
$504$	0	0
$505$	−35.3380	−1.57252
$506$	−53.3144	−2.37011
$507$	−12.6436	−0.561523
$508$	23.6125	1.04764
$509$	15.5206	0.687939	0.343969	−	0.938981i	$-0.388228\pi$
$509$	15.5206	0.687939	0.343969	+	0.938981i	$0.388228\pi$
$510$	5.80332	0.256976
$511$	0	0
$512$	46.4533	2.05296
$513$	−1.89304	−0.0835799
$514$	19.5596	0.862735
$515$	32.1177	1.41527
$516$	47.6139	2.09608
$517$	22.5628	0.992311
$518$	0	0
$519$	−16.5331	−0.725723
$520$	−7.62213	−0.334253
$521$	−25.4897	−1.11672	−0.558361	−	0.829598i	$-0.688570\pi$
$521$	−25.4897	−1.11672	−0.558361	+	0.829598i	$0.688570\pi$
$522$	7.22450	0.316208
$523$	−9.02877	−0.394801	−0.197400	−	0.980323i	$-0.563250\pi$
$523$	−9.02877	−0.394801	−0.197400	+	0.980323i	$0.563250\pi$
$524$	−35.4649	−1.54929
$525$	0	0
$526$	−38.9871	−1.69992
$527$	−6.44107	−0.280577
$528$	−26.9789	−1.17411
$529$	−5.69968	−0.247812
$530$	63.4366	2.75551
$531$	−3.21206	−0.139391
$532$	0	0
$533$	1.24956	0.0541244
$534$	0.982765	0.0425284
$535$	−2.05426	−0.0888135
$536$	80.9100	3.49478
$537$	4.57024	0.197220
$538$	71.6299	3.08818
$539$	0	0
$540$	9.78904	0.421253
$541$	−34.3990	−1.47893	−0.739464	−	0.673196i	$-0.764921\pi$
$541$	−34.3990	−1.47893	−0.739464	+	0.673196i	$0.764921\pi$
$542$	−12.1245	−0.520791
$543$	−23.3136	−1.00048
$544$	2.09319	0.0897447
$545$	32.3659	1.38640
$546$	0	0
$547$	−24.1154	−1.03110	−0.515551	−	0.856859i	$-0.672413\pi$
$547$	−24.1154	−1.03110	−0.515551	+	0.856859i	$0.672413\pi$
$548$	−3.66140	−0.156407
$549$	−10.5832	−0.451680
$550$	5.53606	0.236059
$551$	5.49247	0.233987
$552$	22.7866	0.969861
$553$	0	0
$554$	−47.9544	−2.03739
$555$	−21.9170	−0.930326
$556$	51.9719	2.20410
$557$	18.3993	0.779605	0.389803	−	0.920898i	$-0.372543\pi$
$557$	18.3993	0.779605	0.389803	+	0.920898i	$0.372543\pi$
$558$	−16.0383	−0.678956
$559$	6.76734	0.286228
$560$	0	0
$561$	5.14774	0.217338
$562$	−36.4273	−1.53659
$563$	13.6735	0.576271	0.288136	−	0.957590i	$-0.406965\pi$
$563$	13.6735	0.576271	0.288136	+	0.957590i	$0.406965\pi$
$564$	−18.4095	−0.775178
$565$	−38.2439	−1.60893
$566$	29.8311	1.25389
$567$	0	0
$568$	37.8571	1.58845
$569$	−23.5955	−0.989177	−0.494588	−	0.869127i	$-0.664681\pi$
$569$	−23.5955	−0.989177	−0.494588	+	0.869127i	$0.664681\pi$
$570$	10.9859	0.460151
$571$	−5.71608	−0.239211	−0.119605	−	0.992822i	$-0.538163\pi$
$571$	−5.71608	−0.239211	−0.119605	+	0.992822i	$0.538163\pi$
$572$	−12.9071	−0.539673
$573$	18.2638	0.762980
$574$	0	0
$575$	−1.79643	−0.0749164
$576$	−5.26979	−0.219575
$577$	25.2430	1.05088	0.525440	−	0.850830i	$-0.323901\pi$
$577$	25.2430	1.05088	0.525440	+	0.850830i	$0.323901\pi$
$578$	−2.49001	−0.103571
$579$	−0.0899108	−0.00373656
$580$	−28.4019	−1.17932
$581$	0	0
$582$	−43.4888	−1.80267
$583$	56.2703	2.33048
$584$	2.37782	0.0983951
$585$	1.39131	0.0575237
$586$	−17.6492	−0.729083
$587$	−10.1988	−0.420950	−0.210475	−	0.977599i	$-0.567501\pi$
$587$	−10.1988	−0.420950	−0.210475	+	0.977599i	$0.567501\pi$
$588$	0	0
$589$	−12.1932	−0.502413
$590$	18.6406	0.767422
$591$	4.49561	0.184925
$592$	−49.2849	−2.02560
$593$	3.24533	0.133270	0.0666349	−	0.997777i	$-0.478774\pi$
$593$	3.24533	0.133270	0.0666349	+	0.997777i	$0.478774\pi$
$594$	12.8179	0.525925
$595$	0	0
$596$	−21.5160	−0.881329
$597$	14.3258	0.586314
$598$	6.18268	0.252828
$599$	−21.1408	−0.863790	−0.431895	−	0.901924i	$-0.642155\pi$
$599$	−21.1408	−0.863790	−0.431895	+	0.901924i	$0.642155\pi$
$600$	−2.36612	−0.0965963
$601$	−8.77314	−0.357864	−0.178932	−	0.983861i	$-0.557264\pi$
$601$	−8.77314	−0.357864	−0.178932	+	0.983861i	$0.557264\pi$
$602$	0	0
$603$	−14.7690	−0.601439
$604$	−15.6966	−0.638684
$605$	36.1231	1.46861
$606$	37.7543	1.53366
$607$	20.4797	0.831245	0.415623	−	0.909537i	$-0.363564\pi$
$607$	20.4797	0.831245	0.415623	+	0.909537i	$0.363564\pi$
$608$	3.96250	0.160701
$609$	0	0
$610$	61.4177	2.48673
$611$	−2.61653	−0.105853
$612$	−4.20014	−0.169781
$613$	30.0882	1.21525	0.607626	−	0.794223i	$-0.292122\pi$
$613$	30.0882	1.21525	0.607626	+	0.794223i	$0.292122\pi$
$614$	76.5609	3.08974
$615$	4.87848	0.196719
$616$	0	0
$617$	37.8597	1.52417	0.762086	−	0.647476i	$-0.224175\pi$
$617$	37.8597	1.52417	0.762086	+	0.647476i	$0.224175\pi$
$618$	−34.3138	−1.38030
$619$	11.0834	0.445480	0.222740	−	0.974878i	$-0.428500\pi$
$619$	11.0834	0.445480	0.222740	+	0.974878i	$0.428500\pi$
$620$	63.0519	2.53222
$621$	−4.15937	−0.166910
$622$	81.8791	3.28305
$623$	0	0
$624$	3.12865	0.125246
$625$	−26.9730	−1.07892
$626$	−5.86172	−0.234281
$627$	9.74489	0.389173
$628$	15.1929	0.606262
$629$	9.40385	0.374956
$630$	0	0
$631$	−23.5684	−0.938243	−0.469122	−	0.883134i	$-0.655429\pi$
$631$	−23.5684	−0.938243	−0.469122	+	0.883134i	$0.655429\pi$
$632$	33.7449	1.34230
$633$	17.5551	0.697751
$634$	−76.1439	−3.02406
$635$	13.1025	0.519957
$636$	−45.9121	−1.82053
$637$	0	0
$638$	−37.1898	−1.47236
$639$	−6.91028	−0.273366
$640$	40.3392	1.59455
$641$	24.8881	0.983020	0.491510	−	0.870872i	$-0.336445\pi$
$641$	24.8881	0.983020	0.491510	+	0.870872i	$0.336445\pi$
$642$	2.19473	0.0866191
$643$	−21.5679	−0.850557	−0.425278	−	0.905063i	$-0.639824\pi$
$643$	−21.5679	−0.850557	−0.425278	+	0.905063i	$0.639824\pi$
$644$	0	0
$645$	26.4208	1.04032
$646$	−4.71370	−0.185458
$647$	22.2146	0.873348	0.436674	−	0.899620i	$-0.356156\pi$
$647$	22.2146	0.873348	0.436674	+	0.899620i	$0.356156\pi$
$648$	−5.47838	−0.215211
$649$	16.5348	0.649049
$650$	−0.641998	−0.0251812
$651$	0	0
$652$	−24.1058	−0.944057
$653$	−22.5442	−0.882224	−0.441112	−	0.897452i	$-0.645416\pi$
$653$	−22.5442	−0.882224	−0.441112	+	0.897452i	$0.645416\pi$
$654$	−34.5790	−1.35215
$655$	−19.6793	−0.768936
$656$	10.9702	0.428316
$657$	−0.434038	−0.0169334
$658$	0	0
$659$	−38.3546	−1.49408	−0.747041	−	0.664778i	$-0.768526\pi$
$659$	−38.3546	−1.49408	−0.747041	+	0.664778i	$0.768526\pi$
$660$	−50.3914	−1.96148
$661$	−28.2755	−1.09979	−0.549895	−	0.835234i	$-0.685332\pi$
$661$	−28.2755	−1.09979	−0.549895	+	0.835234i	$0.685332\pi$
$662$	9.97886	0.387839
$663$	−0.596965	−0.0231842
$664$	−28.3672	−1.10086
$665$	0	0
$666$	23.4157	0.907339
$667$	12.0680	0.467274
$668$	105.316	4.07479
$669$	−24.8716	−0.961593
$670$	85.7091	3.31123
$671$	54.4795	2.10316
$672$	0	0
$673$	21.8417	0.841937	0.420969	−	0.907075i	$-0.361690\pi$
$673$	21.8417	0.841937	0.420969	+	0.907075i	$0.361690\pi$
$674$	57.6846	2.22193
$675$	0.431901	0.0166239
$676$	−53.1051	−2.04250
$677$	−6.00000	−0.230599	−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000	−0.230599	−0.115299	+	0.993331i	$0.536783\pi$
$678$	40.8590	1.56918
$679$	0	0
$680$	12.7682	0.489636
$681$	8.32737	0.319105
$682$	82.5610	3.16142
$683$	13.6129	0.520884	0.260442	−	0.965490i	$-0.416132\pi$
$683$	13.6129	0.520884	0.260442	+	0.965490i	$0.416132\pi$
$684$	−7.95106	−0.304016
$685$	−2.03169	−0.0776271
$686$	0	0
$687$	−17.0257	−0.649570
$688$	59.4124	2.26508
$689$	−6.52547	−0.248600
$690$	24.1381	0.918923
$691$	21.8801	0.832357	0.416178	−	0.909283i	$-0.363369\pi$
$691$	21.8801	0.832357	0.416178	+	0.909283i	$0.363369\pi$
$692$	−69.4415	−2.63977
$693$	0	0
$694$	14.7222	0.558846
$695$	28.8390	1.09393
$696$	15.8949	0.602496
$697$	−2.09319	−0.0792852
$698$	65.8566	2.49271
$699$	−15.3997	−0.582469
$700$	0	0
$701$	−23.2153	−0.876829	−0.438414	−	0.898773i	$-0.644460\pi$
$701$	−23.2153	−0.876829	−0.438414	+	0.898773i	$0.644460\pi$
$702$	−1.48645	−0.0561023
$703$	17.8019	0.671412
$704$	27.1275	1.02241
$705$	−10.2153	−0.384732
$706$	−10.7838	−0.405854
$707$	0	0
$708$	−13.4911	−0.507027
$709$	2.57424	0.0966775	0.0483387	−	0.998831i	$-0.484607\pi$
$709$	2.57424	0.0966775	0.0483387	+	0.998831i	$0.484607\pi$
$710$	40.1026	1.50502
$711$	−6.15965	−0.231005
$712$	2.16222	0.0810328
$713$	−26.7908	−1.00332
$714$	0	0
$715$	−7.16211	−0.267848
$716$	19.1957	0.717375
$717$	12.0954	0.451712
$718$	−3.47961	−0.129858
$719$	−18.8277	−0.702156	−0.351078	−	0.936346i	$-0.614185\pi$
$719$	−18.8277	−0.702156	−0.351078	+	0.936346i	$0.614185\pi$
$720$	12.2147	0.455216
$721$	0	0
$722$	38.3869	1.42861
$723$	−14.7946	−0.550219
$724$	−97.9205	−3.63919
$725$	−1.25312	−0.0465395
$726$	−38.5931	−1.43232
$727$	16.5235	0.612823	0.306411	−	0.951899i	$-0.400872\pi$
$727$	16.5235	0.612823	0.306411	+	0.951899i	$0.400872\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.51886	0.0932273
$731$	−11.3362	−0.419286
$732$	−44.4510	−1.64295
$733$	16.0732	0.593678	0.296839	−	0.954928i	$-0.404068\pi$
$733$	16.0732	0.593678	0.296839	+	0.954928i	$0.404068\pi$
$734$	−4.13258	−0.152536
$735$	0	0
$736$	8.70634	0.320920
$737$	76.0267	2.80048
$738$	−5.21206	−0.191859
$739$	−6.34693	−0.233476	−0.116738	−	0.993163i	$-0.537244\pi$
$739$	−6.34693	−0.233476	−0.116738	+	0.993163i	$0.537244\pi$
$740$	−92.0547	−3.38400
$741$	−1.13008	−0.0415145
$742$	0	0
$743$	8.14793	0.298918	0.149459	−	0.988768i	$-0.452247\pi$
$743$	8.14793	0.298918	0.149459	+	0.988768i	$0.452247\pi$
$744$	−35.2866	−1.29367
$745$	−11.9391	−0.437416
$746$	−4.58188	−0.167754
$747$	5.17802	0.189454
$748$	21.6212	0.790550
$749$	0	0
$750$	26.5102	0.968014
$751$	37.1529	1.35573	0.677864	−	0.735187i	$-0.262906\pi$
$751$	37.1529	1.35573	0.677864	+	0.735187i	$0.262906\pi$
$752$	−22.9712	−0.837675
$753$	11.4881	0.418649
$754$	4.31277	0.157062
$755$	−8.70996	−0.316988
$756$	0	0
$757$	9.61543	0.349479	0.174739	−	0.984615i	$-0.444092\pi$
$757$	9.61543	0.349479	0.174739	+	0.984615i	$0.444092\pi$
$758$	11.4693	0.416583
$759$	21.4113	0.777181
$760$	24.1707	0.876762
$761$	0.158420	0.00574271	0.00287136	−	0.999996i	$-0.499086\pi$
$761$	0.158420	0.00574271	0.00287136	+	0.999996i	$0.499086\pi$
$762$	−13.9984	−0.507110
$763$	0	0
$764$	76.7104	2.77529
$765$	−2.33064	−0.0842646
$766$	−28.3147	−1.02305
$767$	−1.91749	−0.0692364
$768$	−32.5580	−1.17484
$769$	−25.6975	−0.926674	−0.463337	−	0.886182i	$-0.653348\pi$
$769$	−25.6975	−0.926674	−0.463337	+	0.886182i	$0.653348\pi$
$770$	0	0
$771$	−7.85522	−0.282899
$772$	−0.377638	−0.0135915
$773$	31.4991	1.13294	0.566472	−	0.824081i	$-0.308308\pi$
$773$	31.4991	1.13294	0.566472	+	0.824081i	$0.308308\pi$
$774$	−28.2274	−1.01461
$775$	2.78190	0.0999289
$776$	−95.6817	−3.43477
$777$	0	0
$778$	−8.10150	−0.290453
$779$	−3.96250	−0.141971
$780$	5.84371	0.209238
$781$	35.5723	1.27288
$782$	−10.3569	−0.370360
$783$	−2.90140	−0.103687
$784$	0	0
$785$	8.43048	0.300897
$786$	21.0250	0.749936
$787$	−35.2712	−1.25728	−0.628642	−	0.777695i	$-0.716389\pi$
$787$	−35.2712	−1.25728	−0.628642	+	0.777695i	$0.716389\pi$
$788$	18.8822	0.672652
$789$	15.6574	0.557418
$790$	35.7464	1.27180
$791$	0	0
$792$	28.2012	1.00209
$793$	−6.31779	−0.224351
$794$	0.331078	0.0117495
$795$	−25.4764	−0.903556
$796$	60.1703	2.13268
$797$	−2.97165	−0.105261	−0.0526306	−	0.998614i	$-0.516761\pi$
$797$	−2.97165	−0.105261	−0.0526306	+	0.998614i	$0.516761\pi$
$798$	0	0
$799$	4.38305	0.155061
$800$	−0.904050	−0.0319630
$801$	−0.394683	−0.0139454
$802$	25.3566	0.895374
$803$	2.23431	0.0788472
$804$	−62.0318	−2.18769
$805$	0	0
$806$	−9.57431	−0.337241
$807$	−28.7669	−1.01264
$808$	83.0649	2.92221
$809$	46.1154	1.62133	0.810665	−	0.585510i	$-0.199106\pi$
$809$	46.1154	1.62133	0.810665	+	0.585510i	$0.199106\pi$
$810$	−5.80332	−0.203908
$811$	28.0004	0.983227	0.491614	−	0.870813i	$-0.336407\pi$
$811$	28.0004	0.983227	0.491614	+	0.870813i	$0.336407\pi$
$812$	0	0
$813$	4.86925	0.170772
$814$	−120.538	−4.22484
$815$	−13.3762	−0.468549
$816$	−5.24092	−0.183469
$817$	−21.4600	−0.750791
$818$	−35.0178	−1.22437
$819$	0	0
$820$	20.4903	0.715553
$821$	14.1398	0.493483	0.246741	−	0.969081i	$-0.420640\pi$
$821$	14.1398	0.493483	0.246741	+	0.969081i	$0.420640\pi$
$822$	2.17062	0.0757090
$823$	−33.7286	−1.17570	−0.587852	−	0.808968i	$-0.700026\pi$
$823$	−33.7286	−1.17570	−0.587852	+	0.808968i	$0.700026\pi$
$824$	−75.4953	−2.63000
$825$	−2.22331	−0.0774058
$826$	0	0
$827$	−43.8428	−1.52456	−0.762282	−	0.647245i	$-0.775921\pi$
$827$	−43.8428	−1.52456	−0.762282	+	0.647245i	$0.775921\pi$
$828$	−17.4699	−0.607122
$829$	−30.8288	−1.07073	−0.535365	−	0.844621i	$-0.679826\pi$
$829$	−30.8288	−1.07073	−0.535365	+	0.844621i	$0.679826\pi$
$830$	−30.0498	−1.04304
$831$	19.2587	0.668078
$832$	−3.14588	−0.109064
$833$	0	0
$834$	−30.8110	−1.06690
$835$	58.4393	2.02237
$836$	40.9299	1.41559
$837$	6.44107	0.222636
$838$	66.1681	2.28574
$839$	0.689347	0.0237989	0.0118995	−	0.999929i	$-0.496212\pi$
$839$	0.689347	0.0237989	0.0118995	+	0.999929i	$0.496212\pi$
$840$	0	0
$841$	−20.5819	−0.709721
$842$	27.4947	0.947531
$843$	14.6294	0.503863
$844$	73.7338	2.53802
$845$	−29.4678	−1.01372
$846$	10.9138	0.375226
$847$	0	0
$848$	−57.2889	−1.96731
$849$	−11.9803	−0.411163
$850$	1.07544	0.0368872
$851$	39.1140	1.34081
$852$	−29.0242	−0.994352
$853$	8.18346	0.280196	0.140098	−	0.990138i	$-0.455258\pi$
$853$	8.18346	0.280196	0.140098	+	0.990138i	$0.455258\pi$
$854$	0	0
$855$	−4.41201	−0.150888
$856$	4.82872	0.165042
$857$	−51.0210	−1.74285	−0.871423	−	0.490533i	$-0.836802\pi$
$857$	−51.0210	−1.74285	−0.871423	+	0.490533i	$0.836802\pi$
$858$	7.65184	0.261229
$859$	−19.5477	−0.666960	−0.333480	−	0.942757i	$-0.608223\pi$
$859$	−19.5477	−0.666960	−0.333480	+	0.942757i	$0.608223\pi$
$860$	110.971	3.78408
$861$	0	0
$862$	15.9751	0.544114
$863$	−0.855775	−0.0291309	−0.0145655	−	0.999894i	$-0.504636\pi$
$863$	−0.855775	−0.0291309	−0.0145655	+	0.999894i	$0.504636\pi$
$864$	−2.09319	−0.0712117
$865$	−38.5328	−1.31015
$866$	−52.2371	−1.77509
$867$	1.00000	0.0339618
$868$	0	0
$869$	31.7082	1.07563
$870$	16.8377	0.570853
$871$	−8.81655	−0.298737
$872$	−76.0789	−2.57636
$873$	17.4653	0.591112
$874$	−19.6060	−0.663182
$875$	0	0
$876$	−1.82302	−0.0615942
$877$	−10.0215	−0.338403	−0.169201	−	0.985581i	$-0.554119\pi$
$877$	−10.0215	−0.338403	−0.169201	+	0.985581i	$0.554119\pi$
$878$	−17.7671	−0.599609
$879$	7.08802	0.239073
$880$	−62.8782	−2.11962
$881$	−32.1954	−1.08469	−0.542345	−	0.840156i	$-0.682463\pi$
$881$	−32.1954	−1.08469	−0.542345	+	0.840156i	$0.682463\pi$
$882$	0	0
$883$	19.5142	0.656706	0.328353	−	0.944555i	$-0.393506\pi$
$883$	19.5142	0.656706	0.328353	+	0.944555i	$0.393506\pi$
$884$	−2.50734	−0.0843309
$885$	−7.48616	−0.251645
$886$	−59.3863	−1.99512
$887$	−0.283933	−0.00953355	−0.00476678	−	0.999989i	$-0.501517\pi$
$887$	−0.283933	−0.00953355	−0.00476678	+	0.999989i	$0.501517\pi$
$888$	51.5179	1.72883
$889$	0	0
$890$	2.29047	0.0767769
$891$	−5.14774	−0.172456
$892$	−104.465	−3.49773
$893$	8.29731	0.277659
$894$	12.7555	0.426608
$895$	10.6516	0.356044
$896$	0	0
$897$	−2.48299	−0.0829048
$898$	−78.9955	−2.63612
$899$	−18.6881	−0.623283
$900$	1.81405	0.0604682
$901$	10.9311	0.364167
$902$	26.8303	0.893351
$903$	0	0
$904$	89.8957	2.98989
$905$	−54.3357	−1.80618
$906$	9.30553	0.309156
$907$	13.7107	0.455256	0.227628	−	0.973748i	$-0.426903\pi$
$907$	13.7107	0.455256	0.227628	+	0.973748i	$0.426903\pi$
$908$	34.9761	1.16072
$909$	−15.1623	−0.502902
$910$	0	0
$911$	−24.6522	−0.816762	−0.408381	−	0.912811i	$-0.633907\pi$
$911$	−24.6522	−0.816762	−0.408381	+	0.912811i	$0.633907\pi$
$912$	−9.92130	−0.328527
$913$	−26.6551	−0.882155
$914$	−69.0269	−2.28321
$915$	−24.6657	−0.815422
$916$	−71.5103	−2.36277
$917$	0	0
$918$	2.49001	0.0821825
$919$	−5.64476	−0.186203	−0.0931017	−	0.995657i	$-0.529678\pi$
$919$	−5.64476	−0.186203	−0.0931017	+	0.995657i	$0.529678\pi$
$920$	53.1074	1.75090
$921$	−30.7472	−1.01316
$922$	−56.2913	−1.85385
$923$	−4.12519	−0.135782
$924$	0	0
$925$	−4.06153	−0.133542
$926$	−18.0048	−0.591674
$927$	13.7806	0.452614
$928$	6.07317	0.199362
$929$	−29.4644	−0.966696	−0.483348	−	0.875428i	$-0.660579\pi$
$929$	−29.4644	−0.966696	−0.483348	+	0.875428i	$0.660579\pi$
$930$	−37.3796	−1.22573
$931$	0	0
$932$	−64.6809	−2.11869
$933$	−32.8830	−1.07654
$934$	−76.9280	−2.51716
$935$	11.9975	0.392361
$936$	−3.27040	−0.106896
$937$	−0.947116	−0.0309409	−0.0154705	−	0.999880i	$-0.504925\pi$
$937$	−0.947116	−0.0309409	−0.0154705	+	0.999880i	$0.504925\pi$
$938$	0	0
$939$	2.35409	0.0768230
$940$	−42.9059	−1.39944
$941$	5.55752	0.181170	0.0905850	−	0.995889i	$-0.471126\pi$
$941$	5.55752	0.181170	0.0905850	+	0.995889i	$0.471126\pi$
$942$	−9.00694	−0.293462
$943$	−8.70634	−0.283517
$944$	−16.8342	−0.547905
$945$	0	0
$946$	145.307	4.72434
$947$	30.2236	0.982135	0.491068	−	0.871121i	$-0.336607\pi$
$947$	30.2236	0.982135	0.491068	+	0.871121i	$0.336607\pi$
$948$	−25.8714	−0.840264
$949$	−0.259105	−0.00841092
$950$	2.03585	0.0660517
$951$	30.5798	0.991616
$952$	0	0
$953$	47.8740	1.55079	0.775395	−	0.631476i	$-0.217551\pi$
$953$	47.8740	1.55079	0.775395	+	0.631476i	$0.217551\pi$
$954$	27.2185	0.881231
$955$	42.5663	1.37741
$956$	50.8025	1.64307
$957$	14.9356	0.482800
$958$	−54.3100	−1.75468
$959$	0	0
$960$	−12.2820	−0.396400
$961$	10.4874	0.338302
$962$	13.9783	0.450679
$963$	−0.881414	−0.0284032
$964$	−62.1396	−2.00138
$965$	−0.209550	−0.00674565
$966$	0	0
$967$	−32.5941	−1.04816	−0.524078	−	0.851671i	$-0.675590\pi$
$967$	−32.5941	−1.04816	−0.524078	+	0.851671i	$0.675590\pi$
$968$	−84.9104	−2.72912
$969$	1.89304	0.0608133
$970$	−101.357	−3.25438
$971$	60.5552	1.94331	0.971654	−	0.236408i	$-0.0759701\pi$
$971$	60.5552	1.94331	0.971654	+	0.236408i	$0.0759701\pi$
$972$	4.20014	0.134720
$973$	0	0
$974$	−11.3500	−0.363679
$975$	0.257830	0.00825715
$976$	−55.4657	−1.77541
$977$	−2.22708	−0.0712505	−0.0356253	−	0.999365i	$-0.511342\pi$
$977$	−2.22708	−0.0712505	−0.0356253	+	0.999365i	$0.511342\pi$
$978$	14.2909	0.456972
$979$	2.03172	0.0649342
$980$	0	0
$981$	13.8871	0.443381
$982$	3.98354	0.127120
$983$	32.8917	1.04908	0.524541	−	0.851385i	$-0.324237\pi$
$983$	32.8917	1.04908	0.524541	+	0.851385i	$0.324237\pi$
$984$	−11.4673	−0.365564
$985$	10.4777	0.333847
$986$	−7.22450	−0.230075
$987$	0	0
$988$	−4.74650	−0.151006
$989$	−47.1516	−1.49933
$990$	29.8740	0.949457
$991$	−39.3179	−1.24897	−0.624487	−	0.781035i	$-0.714692\pi$
$991$	−39.3179	−1.24897	−0.624487	+	0.781035i	$0.714692\pi$
$992$	−13.4824	−0.428066
$993$	−4.00756	−0.127176
$994$	0	0
$995$	33.3882	1.05848
$996$	21.7485	0.689126
$997$	38.6376	1.22366	0.611832	−	0.790988i	$-0.290433\pi$
$997$	38.6376	1.22366	0.611832	+	0.790988i	$0.290433\pi$
$998$	62.6314	1.98256
$999$	−9.40385	−0.297525

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2499.2.a.bb.1.1		5
3.2	odd	2		7497.2.a.bw.1.5		5
7.3	odd	6		357.2.i.f.205.5	✓	10
7.5	odd	6		357.2.i.f.256.5	yes	10
7.6	odd	2		2499.2.a.ba.1.1		5
21.5	even	6		1071.2.i.g.613.1		10
21.17	even	6		1071.2.i.g.919.1		10
21.20	even	2		7497.2.a.bv.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.i.f.205.5	✓	10	7.3	odd	6
357.2.i.f.256.5	yes	10	7.5	odd	6
1071.2.i.g.613.1		10	21.5	even	6
1071.2.i.g.919.1		10	21.17	even	6
2499.2.a.ba.1.1		5	7.6	odd	2
2499.2.a.bb.1.1		5	1.1	even	1	trivial
7497.2.a.bv.1.5		5	21.20	even	2
7497.2.a.bw.1.5		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2499 = 3 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2499.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49001 q^{2} +1.00000 q^{3} +4.20014 q^{4} +2.33064 q^{5} -2.49001 q^{6} -5.47838 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.49001 q^{2} +1.00000 q^{3} +4.20014 q^{4} +2.33064 q^{5} -2.49001 q^{6} -5.47838 q^{8} +1.00000 q^{9} -5.80332 q^{10} -5.14774 q^{11} +4.20014 q^{12} +0.596965 q^{13} +2.33064 q^{15} +5.24092 q^{16} -1.00000 q^{17} -2.49001 q^{18} -1.89304 q^{19} +9.78904 q^{20} +12.8179 q^{22} -4.15937 q^{23} -5.47838 q^{24} +0.431901 q^{25} -1.48645 q^{26} +1.00000 q^{27} -2.90140 q^{29} -5.80332 q^{30} +6.44107 q^{31} -2.09319 q^{32} -5.14774 q^{33} +2.49001 q^{34} +4.20014 q^{36} -9.40385 q^{37} +4.71370 q^{38} +0.596965 q^{39} -12.7682 q^{40} +2.09319 q^{41} +11.3362 q^{43} -21.6212 q^{44} +2.33064 q^{45} +10.3569 q^{46} -4.38305 q^{47} +5.24092 q^{48} -1.07544 q^{50} -1.00000 q^{51} +2.50734 q^{52} -10.9311 q^{53} -2.49001 q^{54} -11.9975 q^{55} -1.89304 q^{57} +7.22450 q^{58} -3.21206 q^{59} +9.78904 q^{60} -10.5832 q^{61} -16.0383 q^{62} -5.26979 q^{64} +1.39131 q^{65} +12.8179 q^{66} -14.7690 q^{67} -4.20014 q^{68} -4.15937 q^{69} -6.91028 q^{71} -5.47838 q^{72} -0.434038 q^{73} +23.4157 q^{74} +0.431901 q^{75} -7.95106 q^{76} -1.48645 q^{78} -6.15965 q^{79} +12.2147 q^{80} +1.00000 q^{81} -5.21206 q^{82} +5.17802 q^{83} -2.33064 q^{85} -28.2274 q^{86} -2.90140 q^{87} +28.2012 q^{88} -0.394683 q^{89} -5.80332 q^{90} -17.4699 q^{92} +6.44107 q^{93} +10.9138 q^{94} -4.41201 q^{95} -2.09319 q^{96} +17.4653 q^{97} -5.14774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} + 5 q^{3} + 8 q^{4} - q^{5} - 2 q^{6} + 5 q^{9}+O(q^{10}) \) 5 * q - 2 * q^2 + 5 * q^3 + 8 * q^4 - q^5 - 2 * q^6 + 5 * q^9	\( 5 q - 2 q^{2} + 5 q^{3} + 8 q^{4} - q^{5} - 2 q^{6} + 5 q^{9} - 13 q^{10} - 11 q^{11} + 8 q^{12} - 7 q^{13} - q^{15} - 2 q^{16} - 5 q^{17} - 2 q^{18} - 9 q^{19} - 12 q^{20} + 5 q^{22} - 23 q^{23} + 14 q^{25} - 18 q^{26} + 5 q^{27} - 18 q^{29} - 13 q^{30} - 9 q^{31} + 3 q^{32} - 11 q^{33} + 2 q^{34} + 8 q^{36} - 7 q^{39} - 31 q^{40} - 3 q^{41} + 12 q^{43} - 33 q^{44} - q^{45} + 13 q^{46} - 11 q^{47} - 2 q^{48} + 24 q^{50} - 5 q^{51} - 5 q^{52} - 3 q^{53} - 2 q^{54} + 10 q^{55} - 9 q^{57} - 34 q^{58} + 14 q^{59} - 12 q^{60} - 29 q^{61} + 5 q^{62} - 8 q^{65} + 5 q^{66} + 16 q^{67} - 8 q^{68} - 23 q^{69} - 19 q^{71} - 11 q^{73} + 45 q^{74} + 14 q^{75} - 9 q^{76} - 18 q^{78} + q^{79} + 5 q^{80} + 5 q^{81} + 4 q^{82} - 5 q^{83} + q^{85} - 3 q^{86} - 18 q^{87} + 37 q^{88} - 8 q^{89} - 13 q^{90} - 48 q^{92} - 9 q^{93} + 18 q^{94} - 21 q^{95} + 3 q^{96} - 19 q^{97} - 11 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 + 5 * q^3 + 8 * q^4 - q^5 - 2 * q^6 + 5 * q^9 - 13 * q^10 - 11 * q^11 + 8 * q^12 - 7 * q^13 - q^15 - 2 * q^16 - 5 * q^17 - 2 * q^18 - 9 * q^19 - 12 * q^20 + 5 * q^22 - 23 * q^23 + 14 * q^25 - 18 * q^26 + 5 * q^27 - 18 * q^29 - 13 * q^30 - 9 * q^31 + 3 * q^32 - 11 * q^33 + 2 * q^34 + 8 * q^36 - 7 * q^39 - 31 * q^40 - 3 * q^41 + 12 * q^43 - 33 * q^44 - q^45 + 13 * q^46 - 11 * q^47 - 2 * q^48 + 24 * q^50 - 5 * q^51 - 5 * q^52 - 3 * q^53 - 2 * q^54 + 10 * q^55 - 9 * q^57 - 34 * q^58 + 14 * q^59 - 12 * q^60 - 29 * q^61 + 5 * q^62 - 8 * q^65 + 5 * q^66 + 16 * q^67 - 8 * q^68 - 23 * q^69 - 19 * q^71 - 11 * q^73 + 45 * q^74 + 14 * q^75 - 9 * q^76 - 18 * q^78 + q^79 + 5 * q^80 + 5 * q^81 + 4 * q^82 - 5 * q^83 + q^85 - 3 * q^86 - 18 * q^87 + 37 * q^88 - 8 * q^89 - 13 * q^90 - 48 * q^92 - 9 * q^93 + 18 * q^94 - 21 * q^95 + 3 * q^96 - 19 * q^97 - 11 * q^99

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