LMFDB - Embedded newform 2009.2.a.o.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2009,2,Mod(1,2009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2009, 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("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2009 = 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2009.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:	$16.0419457661$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.185257757.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 10x^{4} + 10x^{3} + 23x^{2} - 24x + 5 $ x^6 - x^5 - 10x^4 + 10x^3 + 23x^2 - 24x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 287)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.46179$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.46179 q^{2} +2.61045 q^{3} +4.06039 q^{4} -2.85638 q^{5} +6.42638 q^{6} +5.07224 q^{8} +3.81447 q^{9} +O(q^{10})$	\(q+2.46179 q^{2} +2.61045 q^{3} +4.06039 q^{4} -2.85638 q^{5} +6.42638 q^{6} +5.07224 q^{8} +3.81447 q^{9} -7.03179 q^{10} +3.40285 q^{11} +10.5995 q^{12} +2.37205 q^{13} -7.45644 q^{15} +4.36599 q^{16} -5.67084 q^{17} +9.39040 q^{18} +7.43823 q^{19} -11.5980 q^{20} +8.37710 q^{22} +1.38955 q^{23} +13.2408 q^{24} +3.15889 q^{25} +5.83948 q^{26} +2.12613 q^{27} -5.08246 q^{29} -18.3562 q^{30} +10.4853 q^{31} +0.603648 q^{32} +8.88299 q^{33} -13.9604 q^{34} +15.4882 q^{36} -0.480267 q^{37} +18.3113 q^{38} +6.19213 q^{39} -14.4882 q^{40} -1.00000 q^{41} -4.77388 q^{43} +13.8169 q^{44} -10.8956 q^{45} +3.42077 q^{46} -1.26945 q^{47} +11.3972 q^{48} +7.77650 q^{50} -14.8035 q^{51} +9.63145 q^{52} -2.05358 q^{53} +5.23407 q^{54} -9.71983 q^{55} +19.4171 q^{57} -12.5119 q^{58} -13.8270 q^{59} -30.2760 q^{60} +8.73445 q^{61} +25.8126 q^{62} -7.24592 q^{64} -6.77547 q^{65} +21.8680 q^{66} +3.63547 q^{67} -23.0258 q^{68} +3.62735 q^{69} -10.2527 q^{71} +19.3479 q^{72} -16.3264 q^{73} -1.18231 q^{74} +8.24612 q^{75} +30.2021 q^{76} +15.2437 q^{78} -1.82053 q^{79} -12.4709 q^{80} -5.89324 q^{81} -2.46179 q^{82} -16.3735 q^{83} +16.1981 q^{85} -11.7523 q^{86} -13.2675 q^{87} +17.2601 q^{88} -9.48112 q^{89} -26.8225 q^{90} +5.64210 q^{92} +27.3714 q^{93} -3.12511 q^{94} -21.2464 q^{95} +1.57579 q^{96} -2.62406 q^{97} +12.9801 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9}+O(q^{10}) $ 6 * q - q^2 + 4 * q^3 + 9 * q^4 + q^5 + 4 * q^6 + 3 * q^8 + 14 * q^9	$ 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9} - 10 q^{10} + 6 q^{11} - 9 q^{12} - 7 q^{13} - 13 q^{15} + 7 q^{16} - 7 q^{17} - 5 q^{18} - 2 q^{19} - 11 q^{20} + 15 q^{22} + 20 q^{23} + 36 q^{24} + 29 q^{25} + 43 q^{26} - 2 q^{27} - 9 q^{29} + 13 q^{30} + 27 q^{31} - 10 q^{32} - 17 q^{33} - 6 q^{34} + 29 q^{36} + 19 q^{37} + 23 q^{38} + q^{39} - 23 q^{40} - 6 q^{41} + 19 q^{43} + 21 q^{44} + 35 q^{45} - 8 q^{46} + 19 q^{47} + 9 q^{48} - 58 q^{50} - 19 q^{51} + 5 q^{53} + 37 q^{54} - 3 q^{55} + 37 q^{57} + 13 q^{58} + 7 q^{59} - 110 q^{60} + 12 q^{61} - 37 q^{64} - 13 q^{65} + 54 q^{66} + 27 q^{67} - 31 q^{68} - 16 q^{69} - 6 q^{71} + 5 q^{72} - 52 q^{73} - 14 q^{74} + 46 q^{75} - 13 q^{76} - 45 q^{78} + 26 q^{80} - 22 q^{81} + q^{82} - 12 q^{83} + 25 q^{85} - 10 q^{86} - 42 q^{87} - 2 q^{88} + 38 q^{89} - 93 q^{90} + 45 q^{92} + 33 q^{93} + 8 q^{94} + q^{95} + 12 q^{96} - 8 q^{97} + q^{99}+O(q^{100}) $ 6 * q - q^2 + 4 * q^3 + 9 * q^4 + q^5 + 4 * q^6 + 3 * q^8 + 14 * q^9 - 10 * q^10 + 6 * q^11 - 9 * q^12 - 7 * q^13 - 13 * q^15 + 7 * q^16 - 7 * q^17 - 5 * q^18 - 2 * q^19 - 11 * q^20 + 15 * q^22 + 20 * q^23 + 36 * q^24 + 29 * q^25 + 43 * q^26 - 2 * q^27 - 9 * q^29 + 13 * q^30 + 27 * q^31 - 10 * q^32 - 17 * q^33 - 6 * q^34 + 29 * q^36 + 19 * q^37 + 23 * q^38 + q^39 - 23 * q^40 - 6 * q^41 + 19 * q^43 + 21 * q^44 + 35 * q^45 - 8 * q^46 + 19 * q^47 + 9 * q^48 - 58 * q^50 - 19 * q^51 + 5 * q^53 + 37 * q^54 - 3 * q^55 + 37 * q^57 + 13 * q^58 + 7 * q^59 - 110 * q^60 + 12 * q^61 - 37 * q^64 - 13 * q^65 + 54 * q^66 + 27 * q^67 - 31 * q^68 - 16 * q^69 - 6 * q^71 + 5 * q^72 - 52 * q^73 - 14 * q^74 + 46 * q^75 - 13 * q^76 - 45 * q^78 + 26 * q^80 - 22 * q^81 + q^82 - 12 * q^83 + 25 * q^85 - 10 * q^86 - 42 * q^87 - 2 * q^88 + 38 * q^89 - 93 * q^90 + 45 * q^92 + 33 * q^93 + 8 * q^94 + q^95 + 12 * q^96 - 8 * q^97 + 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 $

$2$	2.46179	1.74075	0.870373	−	0.492393i	$-0.163878\pi$
$2$	2.46179	1.74075	0.870373	+	0.492393i	$0.163878\pi$
$3$	2.61045	1.50715	0.753573	−	0.657364i	$-0.228329\pi$
$3$	2.61045	1.50715	0.753573	+	0.657364i	$0.228329\pi$
$4$	4.06039	2.03020
$5$	−2.85638	−1.27741	−0.638705	−	0.769452i	$-0.720530\pi$
$5$	−2.85638	−1.27741	−0.638705	+	0.769452i	$0.720530\pi$
$6$	6.42638	2.62356
$7$	0	0
$7$	0	0
$8$	5.07224	1.79331
$9$	3.81447	1.27149
$10$	−7.03179	−2.22365
$11$	3.40285	1.02600	0.512999	−	0.858389i	$-0.328534\pi$
$11$	3.40285	1.02600	0.512999	+	0.858389i	$0.328534\pi$
$12$	10.5995	3.05980
$13$	2.37205	0.657889	0.328944	−	0.944349i	$-0.393307\pi$
$13$	2.37205	0.657889	0.328944	+	0.944349i	$0.393307\pi$
$14$	0	0
$15$	−7.45644	−1.92524
$16$	4.36599	1.09150
$17$	−5.67084	−1.37538	−0.687691	−	0.726004i	$-0.741376\pi$
$17$	−5.67084	−1.37538	−0.687691	+	0.726004i	$0.741376\pi$
$18$	9.39040	2.21334
$19$	7.43823	1.70645	0.853223	−	0.521546i	$-0.174645\pi$
$19$	7.43823	1.70645	0.853223	+	0.521546i	$0.174645\pi$
$20$	−11.5980	−2.59339
$21$	0	0
$22$	8.37710	1.78600
$23$	1.38955	0.289740	0.144870	−	0.989451i	$-0.453724\pi$
$23$	1.38955	0.289740	0.144870	+	0.989451i	$0.453724\pi$
$24$	13.2408	2.70278
$25$	3.15889	0.631777
$26$	5.83948	1.14522
$27$	2.12613	0.409174
$28$	0	0
$29$	−5.08246	−0.943789	−0.471894	−	0.881655i	$-0.656430\pi$
$29$	−5.08246	−0.943789	−0.471894	+	0.881655i	$0.656430\pi$
$30$	−18.3562	−3.35136
$31$	10.4853	1.88322	0.941609	−	0.336709i	$-0.109314\pi$
$31$	10.4853	1.88322	0.941609	+	0.336709i	$0.109314\pi$
$32$	0.603648	0.106711
$33$	8.88299	1.54633
$34$	−13.9604	−2.39419
$35$	0	0
$36$	15.4882	2.58137
$37$	−0.480267	−0.0789554	−0.0394777	−	0.999220i	$-0.512569\pi$
$37$	−0.480267	−0.0789554	−0.0394777	+	0.999220i	$0.512569\pi$
$38$	18.3113	2.97049
$39$	6.19213	0.991534
$40$	−14.4882	−2.29079
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	−4.77388	−0.728011	−0.364005	−	0.931397i	$-0.618591\pi$
$43$	−4.77388	−0.728011	−0.364005	+	0.931397i	$0.618591\pi$
$44$	13.8169	2.08298
$45$	−10.8956	−1.62421
$46$	3.42077	0.504364
$47$	−1.26945	−0.185168	−0.0925840	−	0.995705i	$-0.529513\pi$
$47$	−1.26945	−0.185168	−0.0925840	+	0.995705i	$0.529513\pi$
$48$	11.3972	1.64505
$49$	0	0
$50$	7.77650	1.09976
$51$	−14.8035	−2.07290
$52$	9.63145	1.33564
$53$	−2.05358	−0.282082	−0.141041	−	0.990004i	$-0.545045\pi$
$53$	−2.05358	−0.282082	−0.141041	+	0.990004i	$0.545045\pi$
$54$	5.23407	0.712267
$55$	−9.71983	−1.31062
$56$	0	0
$57$	19.4171	2.57186
$58$	−12.5119	−1.64290
$59$	−13.8270	−1.80012	−0.900061	−	0.435764i	$-0.856478\pi$
$59$	−13.8270	−1.80012	−0.900061	+	0.435764i	$0.856478\pi$
$60$	−30.2760	−3.90862
$61$	8.73445	1.11833	0.559166	−	0.829056i	$-0.311121\pi$
$61$	8.73445	1.11833	0.559166	+	0.829056i	$0.311121\pi$
$62$	25.8126	3.27820
$63$	0	0
$64$	−7.24592	−0.905740
$65$	−6.77547	−0.840394
$66$	21.8680	2.69177
$67$	3.63547	0.444143	0.222072	−	0.975030i	$-0.428718\pi$
$67$	3.63547	0.444143	0.222072	+	0.975030i	$0.428718\pi$
$68$	−23.0258	−2.79229
$69$	3.62735	0.436681
$70$	0	0
$71$	−10.2527	−1.21677	−0.608385	−	0.793642i	$-0.708183\pi$
$71$	−10.2527	−1.21677	−0.608385	+	0.793642i	$0.708183\pi$
$72$	19.3479	2.28017
$73$	−16.3264	−1.91086	−0.955432	−	0.295212i	$-0.904610\pi$
$73$	−16.3264	−1.91086	−0.955432	+	0.295212i	$0.904610\pi$
$74$	−1.18231	−0.137441
$75$	8.24612	0.952180
$76$	30.2021	3.46442
$77$	0	0
$78$	15.2437	1.72601
$79$	−1.82053	−0.204826	−0.102413	−	0.994742i	$-0.532656\pi$
$79$	−1.82053	−0.204826	−0.102413	+	0.994742i	$0.532656\pi$
$80$	−12.4709	−1.39429
$81$	−5.89324	−0.654805
$82$	−2.46179	−0.271859
$83$	−16.3735	−1.79722	−0.898611	−	0.438746i	$-0.855423\pi$
$83$	−16.3735	−1.79722	−0.898611	+	0.438746i	$0.855423\pi$
$84$	0	0
$85$	16.1981	1.75693
$86$	−11.7523	−1.26728
$87$	−13.2675	−1.42243
$88$	17.2601	1.83993
$89$	−9.48112	−1.00500	−0.502498	−	0.864578i	$-0.667586\pi$
$89$	−9.48112	−1.00500	−0.502498	+	0.864578i	$0.667586\pi$
$90$	−26.8225	−2.82734
$91$	0	0
$92$	5.64210	0.588230
$93$	27.3714	2.83828
$94$	−3.12511	−0.322330
$95$	−21.2464	−2.17983
$96$	1.57579	0.160829
$97$	−2.62406	−0.266433	−0.133217	−	0.991087i	$-0.542531\pi$
$97$	−2.62406	−0.266433	−0.133217	+	0.991087i	$0.542531\pi$
$98$	0	0
$99$	12.9801	1.30455
$100$	12.8263	1.28263
$101$	−1.17737	−0.117152	−0.0585762	−	0.998283i	$-0.518656\pi$
$101$	−1.17737	−0.117152	−0.0585762	+	0.998283i	$0.518656\pi$
$102$	−36.4430	−3.60839
$103$	7.98233	0.786522	0.393261	−	0.919427i	$-0.371347\pi$
$103$	7.98233	0.786522	0.393261	+	0.919427i	$0.371347\pi$
$104$	12.0316	1.17980
$105$	0	0
$106$	−5.05549	−0.491032
$107$	9.38756	0.907529	0.453765	−	0.891122i	$-0.350081\pi$
$107$	9.38756	0.907529	0.453765	+	0.891122i	$0.350081\pi$
$108$	8.63291	0.830702
$109$	3.41399	0.327001	0.163500	−	0.986543i	$-0.447722\pi$
$109$	3.41399	0.327001	0.163500	+	0.986543i	$0.447722\pi$
$110$	−23.9281	−2.28146
$111$	−1.25371	−0.118997
$112$	0	0
$113$	−5.20398	−0.489549	−0.244775	−	0.969580i	$-0.578714\pi$
$113$	−5.20398	−0.489549	−0.244775	+	0.969580i	$0.578714\pi$
$114$	47.8009	4.47696
$115$	−3.96907	−0.370117
$116$	−20.6368	−1.91608
$117$	9.04811	0.836498
$118$	−34.0391	−3.13355
$119$	0	0
$120$	−37.8208	−3.45255
$121$	0.579408	0.0526734
$122$	21.5024	1.94673
$123$	−2.61045	−0.235377
$124$	42.5745	3.82330
$125$	5.25891	0.470372
$126$	0	0
$127$	17.8345	1.58256	0.791279	−	0.611456i	$-0.209416\pi$
$127$	17.8345	1.58256	0.791279	+	0.611456i	$0.209416\pi$
$128$	−19.0452	−1.68337
$129$	−12.4620	−1.09722
$130$	−16.6798	−1.46291
$131$	4.66478	0.407564	0.203782	−	0.979016i	$-0.434677\pi$
$131$	4.66478	0.407564	0.203782	+	0.979016i	$0.434677\pi$
$132$	36.0684	3.13935
$133$	0	0
$134$	8.94975	0.773140
$135$	−6.07302	−0.522683
$136$	−28.7639	−2.46648
$137$	22.0331	1.88241	0.941206	−	0.337832i	$-0.109694\pi$
$137$	22.0331	1.88241	0.941206	+	0.337832i	$0.109694\pi$
$138$	8.92975	0.760151
$139$	8.62376	0.731458	0.365729	−	0.930721i	$-0.380820\pi$
$139$	8.62376	0.731458	0.365729	+	0.930721i	$0.380820\pi$
$140$	0	0
$141$	−3.31383	−0.279075
$142$	−25.2399	−2.11809
$143$	8.07174	0.674993
$144$	16.6539	1.38783
$145$	14.5174	1.20561
$146$	−40.1922	−3.32633
$147$	0	0
$148$	−1.95007	−0.160295
$149$	17.1752	1.40705	0.703524	−	0.710671i	$-0.251609\pi$
$149$	17.1752	1.40705	0.703524	+	0.710671i	$0.251609\pi$
$150$	20.3002	1.65750
$151$	−4.61367	−0.375455	−0.187728	−	0.982221i	$-0.560112\pi$
$151$	−4.61367	−0.375455	−0.187728	+	0.982221i	$0.560112\pi$
$152$	37.7285	3.06018
$153$	−21.6312	−1.74878
$154$	0	0
$155$	−29.9500	−2.40564
$156$	25.1425	2.01301
$157$	−1.84988	−0.147636	−0.0738181	−	0.997272i	$-0.523518\pi$
$157$	−1.84988	−0.147636	−0.0738181	+	0.997272i	$0.523518\pi$
$158$	−4.48176	−0.356550
$159$	−5.36079	−0.425138
$160$	−1.72425	−0.136314
$161$	0	0
$162$	−14.5079	−1.13985
$163$	−17.4226	−1.36465	−0.682323	−	0.731051i	$-0.739030\pi$
$163$	−17.4226	−1.36465	−0.682323	+	0.731051i	$0.739030\pi$
$164$	−4.06039	−0.317063
$165$	−25.3732	−1.97530
$166$	−40.3080	−3.12851
$167$	−0.938868	−0.0726518	−0.0363259	−	0.999340i	$-0.511565\pi$
$167$	−0.938868	−0.0726518	−0.0363259	+	0.999340i	$0.511565\pi$
$168$	0	0
$169$	−7.37337	−0.567182
$170$	39.8762	3.05836
$171$	28.3729	2.16973
$172$	−19.3838	−1.47800
$173$	9.83106	0.747441	0.373721	−	0.927541i	$-0.378082\pi$
$173$	9.83106	0.747441	0.373721	+	0.927541i	$0.378082\pi$
$174$	−32.6618	−2.47608
$175$	0	0
$176$	14.8568	1.11987
$177$	−36.0947	−2.71305
$178$	−23.3405	−1.74944
$179$	−6.83268	−0.510698	−0.255349	−	0.966849i	$-0.582190\pi$
$179$	−6.83268	−0.510698	−0.255349	+	0.966849i	$0.582190\pi$
$180$	−44.2402	−3.29747
$181$	16.2089	1.20480	0.602399	−	0.798195i	$-0.294212\pi$
$181$	16.2089	1.20480	0.602399	+	0.798195i	$0.294212\pi$
$182$	0	0
$183$	22.8009	1.68549
$184$	7.04811	0.519594
$185$	1.37182	0.100858
$186$	67.3826	4.94073
$187$	−19.2970	−1.41114
$188$	−5.15445	−0.375927
$189$	0	0
$190$	−52.3040	−3.79453
$191$	20.9134	1.51324	0.756621	−	0.653854i	$-0.226849\pi$
$191$	20.9134	1.51324	0.756621	+	0.653854i	$0.226849\pi$
$192$	−18.9151	−1.36508
$193$	6.82862	0.491535	0.245767	−	0.969329i	$-0.420960\pi$
$193$	6.82862	0.491535	0.245767	+	0.969329i	$0.420960\pi$
$194$	−6.45988	−0.463793
$195$	−17.6871	−1.26660
$196$	0	0
$197$	−13.6463	−0.972262	−0.486131	−	0.873886i	$-0.661592\pi$
$197$	−13.6463	−0.972262	−0.486131	+	0.873886i	$0.661592\pi$
$198$	31.9542	2.27088
$199$	−19.0820	−1.35269	−0.676345	−	0.736585i	$-0.736437\pi$
$199$	−19.0820	−1.35269	−0.676345	+	0.736585i	$0.736437\pi$
$200$	16.0226	1.13297
$201$	9.49022	0.669389
$202$	−2.89843	−0.203932
$203$	0	0
$204$	−60.1079	−4.20839
$205$	2.85638	0.199498
$206$	19.6508	1.36914
$207$	5.30038	0.368402
$208$	10.3563	0.718083
$209$	25.3112	1.75081
$210$	0	0
$211$	3.45644	0.237951	0.118975	−	0.992897i	$-0.462039\pi$
$211$	3.45644	0.237951	0.118975	+	0.992897i	$0.462039\pi$
$212$	−8.33835	−0.572681
$213$	−26.7642	−1.83385
$214$	23.1102	1.57978
$215$	13.6360	0.929968
$216$	10.7842	0.733774
$217$	0	0
$218$	8.40450	0.569225
$219$	−42.6194	−2.87995
$220$	−39.4663	−2.66082
$221$	−13.4515	−0.904848
$222$	−3.08638	−0.207144
$223$	1.57387	0.105394	0.0526970	−	0.998611i	$-0.483218\pi$
$223$	1.57387	0.105394	0.0526970	+	0.998611i	$0.483218\pi$
$224$	0	0
$225$	12.0495	0.803298
$226$	−12.8111	−0.852181
$227$	11.6785	0.775127	0.387563	−	0.921843i	$-0.373317\pi$
$227$	11.6785	0.775127	0.387563	+	0.921843i	$0.373317\pi$
$228$	78.8412	5.22138
$229$	14.8793	0.983254	0.491627	−	0.870806i	$-0.336402\pi$
$229$	14.8793	0.983254	0.491627	+	0.870806i	$0.336402\pi$
$230$	−9.77100	−0.644280
$231$	0	0
$232$	−25.7794	−1.69250
$233$	−17.0750	−1.11862	−0.559311	−	0.828958i	$-0.688934\pi$
$233$	−17.0750	−1.11862	−0.559311	+	0.828958i	$0.688934\pi$
$234$	22.2745	1.45613
$235$	3.62602	0.236535
$236$	−56.1430	−3.65460
$237$	−4.75241	−0.308702
$238$	0	0
$239$	8.61866	0.557494	0.278747	−	0.960364i	$-0.410081\pi$
$239$	8.61866	0.557494	0.278747	+	0.960364i	$0.410081\pi$
$240$	−32.5547	−2.10140
$241$	−7.66476	−0.493731	−0.246865	−	0.969050i	$-0.579401\pi$
$241$	−7.66476	−0.493731	−0.246865	+	0.969050i	$0.579401\pi$
$242$	1.42638	0.0916910
$243$	−21.7624	−1.39606
$244$	35.4653	2.27043
$245$	0	0
$246$	−6.42638	−0.409731
$247$	17.6439	1.12265
$248$	53.1840	3.37719
$249$	−42.7422	−2.70868
$250$	12.9463	0.818797
$251$	4.02583	0.254108	0.127054	−	0.991896i	$-0.459448\pi$
$251$	4.02583	0.254108	0.127054	+	0.991896i	$0.459448\pi$
$252$	0	0
$253$	4.72842	0.297273
$254$	43.9048	2.75483
$255$	42.2843	2.64794
$256$	−32.3934	−2.02459
$257$	18.5931	1.15981	0.579904	−	0.814685i	$-0.303090\pi$
$257$	18.5931	1.15981	0.579904	+	0.814685i	$0.303090\pi$
$258$	−30.6788	−1.90998
$259$	0	0
$260$	−27.5111	−1.70616
$261$	−19.3869	−1.20002
$262$	11.4837	0.709465
$263$	14.4186	0.889086	0.444543	−	0.895758i	$-0.353366\pi$
$263$	14.4186	0.889086	0.444543	+	0.895758i	$0.353366\pi$
$264$	45.0566	2.77304
$265$	5.86581	0.360334
$266$	0	0
$267$	−24.7500	−1.51468
$268$	14.7614	0.901697
$269$	4.17487	0.254546	0.127273	−	0.991868i	$-0.459378\pi$
$269$	4.17487	0.254546	0.127273	+	0.991868i	$0.459378\pi$
$270$	−14.9505	−0.909857
$271$	−28.1837	−1.71204	−0.856018	−	0.516947i	$-0.827069\pi$
$271$	−28.1837	−1.71204	−0.856018	+	0.516947i	$0.827069\pi$
$272$	−24.7588	−1.50122
$273$	0	0
$274$	54.2407	3.27680
$275$	10.7492	0.648203
$276$	14.7284	0.886548
$277$	−0.474918	−0.0285351	−0.0142675	−	0.999898i	$-0.504542\pi$
$277$	−0.474918	−0.0285351	−0.0142675	+	0.999898i	$0.504542\pi$
$278$	21.2299	1.27328
$279$	39.9959	2.39449
$280$	0	0
$281$	1.61285	0.0962143	0.0481072	−	0.998842i	$-0.484681\pi$
$281$	1.61285	0.0962143	0.0481072	+	0.998842i	$0.484681\pi$
$282$	−8.15795	−0.485799
$283$	6.48893	0.385727	0.192863	−	0.981226i	$-0.438223\pi$
$283$	6.48893	0.385727	0.192863	+	0.981226i	$0.438223\pi$
$284$	−41.6299	−2.47028
$285$	−55.4627	−3.28533
$286$	19.8709	1.17499
$287$	0	0
$288$	2.30260	0.135682
$289$	15.1585	0.891674
$290$	35.7388	2.09865
$291$	−6.85000	−0.401554
$292$	−66.2917	−3.87943
$293$	−8.26774	−0.483006	−0.241503	−	0.970400i	$-0.577640\pi$
$293$	−8.26774	−0.483006	−0.241503	+	0.970400i	$0.577640\pi$
$294$	0	0
$295$	39.4951	2.29949
$296$	−2.43603	−0.141591
$297$	7.23490	0.419812
$298$	42.2817	2.44931
$299$	3.29608	0.190617
$300$	33.4825	1.93311
$301$	0	0
$302$	−11.3579	−0.653572
$303$	−3.07346	−0.176566
$304$	32.4752	1.86258
$305$	−24.9489	−1.42857
$306$	−53.2515	−3.04419
$307$	−14.3308	−0.817900	−0.408950	−	0.912557i	$-0.634105\pi$
$307$	−14.3308	−0.817900	−0.408950	+	0.912557i	$0.634105\pi$
$308$	0	0
$309$	20.8375	1.18540
$310$	−73.7305	−4.18761
$311$	5.01224	0.284218	0.142109	−	0.989851i	$-0.454612\pi$
$311$	5.01224	0.284218	0.142109	+	0.989851i	$0.454612\pi$
$312$	31.4080	1.77813
$313$	−16.8781	−0.954009	−0.477004	−	0.878901i	$-0.658277\pi$
$313$	−16.8781	−0.954009	−0.477004	+	0.878901i	$0.658277\pi$
$314$	−4.55400	−0.256997
$315$	0	0
$316$	−7.39207	−0.415836
$317$	5.89618	0.331163	0.165581	−	0.986196i	$-0.447050\pi$
$317$	5.89618	0.331163	0.165581	+	0.986196i	$0.447050\pi$
$318$	−13.1971	−0.740057
$319$	−17.2949	−0.968326
$320$	20.6971	1.15700
$321$	24.5058	1.36778
$322$	0	0
$323$	−42.1810	−2.34701
$324$	−23.9289	−1.32938
$325$	7.49304	0.415639
$326$	−42.8908	−2.37550
$327$	8.91205	0.492838
$328$	−5.07224	−0.280068
$329$	0	0
$330$	−62.4633	−3.43849
$331$	18.6161	1.02323	0.511616	−	0.859214i	$-0.329047\pi$
$331$	18.6161	1.02323	0.511616	+	0.859214i	$0.329047\pi$
$332$	−66.4827	−3.64871
$333$	−1.83196	−0.100391
$334$	−2.31129	−0.126468
$335$	−10.3843	−0.567353
$336$	0	0
$337$	20.9163	1.13938	0.569692	−	0.821859i	$-0.307063\pi$
$337$	20.9163	1.13938	0.569692	+	0.821859i	$0.307063\pi$
$338$	−18.1517	−0.987320
$339$	−13.5847	−0.737822
$340$	65.7705	3.56690
$341$	35.6800	1.93218
$342$	69.8479	3.77694
$343$	0	0
$344$	−24.2143	−1.30555
$345$	−10.3611	−0.557821
$346$	24.2020	1.30111
$347$	−4.56558	−0.245093	−0.122546	−	0.992463i	$-0.539106\pi$
$347$	−4.56558	−0.245093	−0.122546	+	0.992463i	$0.539106\pi$
$348$	−53.8713	−2.88781
$349$	−0.142070	−0.00760484	−0.00380242	−	0.999993i	$-0.501210\pi$
$349$	−0.142070	−0.00760484	−0.00380242	+	0.999993i	$0.501210\pi$
$350$	0	0
$351$	5.04329	0.269191
$352$	2.05413	0.109485
$353$	−3.22239	−0.171511	−0.0857553	−	0.996316i	$-0.527330\pi$
$353$	−3.22239	−0.171511	−0.0857553	+	0.996316i	$0.527330\pi$
$354$	−88.8575	−4.72272
$355$	29.2856	1.55432
$356$	−38.4971	−2.04034
$357$	0	0
$358$	−16.8206	−0.888996
$359$	2.84694	0.150256	0.0751278	−	0.997174i	$-0.476064\pi$
$359$	2.84694	0.150256	0.0751278	+	0.997174i	$0.476064\pi$
$360$	−55.2649	−2.91271
$361$	36.3272	1.91196
$362$	39.9028	2.09725
$363$	1.51252	0.0793865
$364$	0	0
$365$	46.6344	2.44096
$366$	56.1309	2.93401
$367$	−11.9792	−0.625307	−0.312653	−	0.949867i	$-0.601218\pi$
$367$	−11.9792	−0.625307	−0.312653	+	0.949867i	$0.601218\pi$
$368$	6.06674	0.316251
$369$	−3.81447	−0.198573
$370$	3.37713	0.175569
$371$	0	0
$372$	111.139	5.76227
$373$	−0.330232	−0.0170988	−0.00854938	−	0.999963i	$-0.502721\pi$
$373$	−0.330232	−0.0170988	−0.00854938	+	0.999963i	$0.502721\pi$
$374$	−47.5052	−2.45644
$375$	13.7282	0.708919
$376$	−6.43894	−0.332063
$377$	−12.0559	−0.620908
$378$	0	0
$379$	7.10938	0.365184	0.182592	−	0.983189i	$-0.441551\pi$
$379$	7.10938	0.365184	0.182592	+	0.983189i	$0.441551\pi$
$380$	−86.2686	−4.42548
$381$	46.5562	2.38515
$382$	51.4844	2.63417
$383$	−2.41188	−0.123242	−0.0616208	−	0.998100i	$-0.519627\pi$
$383$	−2.41188	−0.123242	−0.0616208	+	0.998100i	$0.519627\pi$
$384$	−49.7166	−2.53709
$385$	0	0
$386$	16.8106	0.855637
$387$	−18.2098	−0.925657
$388$	−10.6547	−0.540912
$389$	2.59149	0.131394	0.0656970	−	0.997840i	$-0.479073\pi$
$389$	2.59149	0.131394	0.0656970	+	0.997840i	$0.479073\pi$
$390$	−43.5417	−2.20482
$391$	−7.87990	−0.398504
$392$	0	0
$393$	12.1772	0.614258
$394$	−33.5944	−1.69246
$395$	5.20012	0.261647
$396$	52.7041	2.64848
$397$	26.2214	1.31602	0.658008	−	0.753011i	$-0.271399\pi$
$397$	26.2214	1.31602	0.658008	+	0.753011i	$0.271399\pi$
$398$	−46.9759	−2.35469
$399$	0	0
$400$	13.7917	0.689583
$401$	39.6001	1.97753	0.988766	−	0.149470i	$-0.0477566\pi$
$401$	39.6001	1.97753	0.988766	+	0.149470i	$0.0477566\pi$
$402$	23.3629	1.16524
$403$	24.8717	1.23895
$404$	−4.78057	−0.237842
$405$	16.8333	0.836454
$406$	0	0
$407$	−1.63428	−0.0810081
$408$	−75.0868	−3.71735
$409$	−1.68956	−0.0835433	−0.0417717	−	0.999127i	$-0.513300\pi$
$409$	−1.68956	−0.0835433	−0.0417717	+	0.999127i	$0.513300\pi$
$410$	7.03179	0.347275
$411$	57.5163	2.83707
$412$	32.4114	1.59679
$413$	0	0
$414$	13.0484	0.641294
$415$	46.7688	2.29579
$416$	1.43188	0.0702039
$417$	22.5119	1.10241
$418$	62.3107	3.04772
$419$	−24.1404	−1.17933	−0.589667	−	0.807647i	$-0.700741\pi$
$419$	−24.1404	−1.17933	−0.589667	+	0.807647i	$0.700741\pi$
$420$	0	0
$421$	−17.4853	−0.852181	−0.426090	−	0.904681i	$-0.640109\pi$
$421$	−17.4853	−0.852181	−0.426090	+	0.904681i	$0.640109\pi$
$422$	8.50901	0.414212
$423$	−4.84227	−0.235439
$424$	−10.4163	−0.505859
$425$	−17.9135	−0.868935
$426$	−65.8877	−3.19227
$427$	0	0
$428$	38.1171	1.84246
$429$	21.0709	1.01731
$430$	33.5689	1.61884
$431$	8.05967	0.388220	0.194110	−	0.980980i	$-0.437818\pi$
$431$	8.05967	0.388220	0.194110	+	0.980980i	$0.437818\pi$
$432$	9.28265	0.446612
$433$	30.8858	1.48428	0.742139	−	0.670246i	$-0.233811\pi$
$433$	30.8858	1.48428	0.742139	+	0.670246i	$0.233811\pi$
$434$	0	0
$435$	37.8970	1.81702
$436$	13.8621	0.663875
$437$	10.3358	0.494427
$438$	−104.920	−5.01326
$439$	27.6588	1.32008	0.660041	−	0.751229i	$-0.270539\pi$
$439$	27.6588	1.32008	0.660041	+	0.751229i	$0.270539\pi$
$440$	−49.3013	−2.35035
$441$	0	0
$442$	−33.1148	−1.57511
$443$	−25.0286	−1.18915	−0.594573	−	0.804042i	$-0.702679\pi$
$443$	−25.0286	−1.18915	−0.594573	+	0.804042i	$0.702679\pi$
$444$	−5.09057	−0.241588
$445$	27.0817	1.28379
$446$	3.87452	0.183464
$447$	44.8351	2.12063
$448$	0	0
$449$	−3.97316	−0.187505	−0.0937525	−	0.995596i	$-0.529886\pi$
$449$	−3.97316	−0.187505	−0.0937525	+	0.995596i	$0.529886\pi$
$450$	29.6632	1.39834
$451$	−3.40285	−0.160234
$452$	−21.1302	−0.993880
$453$	−12.0438	−0.565866
$454$	28.7499	1.34930
$455$	0	0
$456$	98.4884	4.61214
$457$	−10.6995	−0.500500	−0.250250	−	0.968181i	$-0.580513\pi$
$457$	−10.6995	−0.500500	−0.250250	+	0.968181i	$0.580513\pi$
$458$	36.6297	1.71160
$459$	−12.0569	−0.562770
$460$	−16.1160	−0.751411
$461$	29.3144	1.36531	0.682655	−	0.730741i	$-0.260825\pi$
$461$	29.3144	1.36531	0.682655	+	0.730741i	$0.260825\pi$
$462$	0	0
$463$	−9.92635	−0.461316	−0.230658	−	0.973035i	$-0.574088\pi$
$463$	−9.92635	−0.461316	−0.230658	+	0.973035i	$0.574088\pi$
$464$	−22.1899	−1.03014
$465$	−78.1831	−3.62565
$466$	−42.0351	−1.94724
$467$	41.4382	1.91753	0.958765	−	0.284198i	$-0.0917274\pi$
$467$	41.4382	1.91753	0.958765	+	0.284198i	$0.0917274\pi$
$468$	36.7389	1.69825
$469$	0	0
$470$	8.92649	0.411748
$471$	−4.82901	−0.222509
$472$	−70.1338	−3.22817
$473$	−16.2448	−0.746938
$474$	−11.6994	−0.537372
$475$	23.4965	1.07809
$476$	0	0
$477$	−7.83333	−0.358664
$478$	21.2173	0.970456
$479$	−37.4347	−1.71043	−0.855217	−	0.518271i	$-0.826576\pi$
$479$	−37.4347	−1.71043	−0.855217	+	0.518271i	$0.826576\pi$
$480$	−4.50106	−0.205445
$481$	−1.13922	−0.0519439
$482$	−18.8690	−0.859459
$483$	0	0
$484$	2.35262	0.106937
$485$	7.49532	0.340345
$486$	−53.5744	−2.43018
$487$	−22.1844	−1.00527	−0.502636	−	0.864498i	$-0.667636\pi$
$487$	−22.1844	−1.00527	−0.502636	+	0.864498i	$0.667636\pi$
$488$	44.3032	2.00551
$489$	−45.4810	−2.05672
$490$	0	0
$491$	−10.2159	−0.461036	−0.230518	−	0.973068i	$-0.574042\pi$
$491$	−10.2159	−0.461036	−0.230518	+	0.973068i	$0.574042\pi$
$492$	−10.5995	−0.477861
$493$	28.8218	1.29807
$494$	43.4354	1.95425
$495$	−37.0760	−1.66644
$496$	45.7787	2.05553
$497$	0	0
$498$	−105.222	−4.71512
$499$	−12.3186	−0.551454	−0.275727	−	0.961236i	$-0.588919\pi$
$499$	−12.3186	−0.551454	−0.275727	+	0.961236i	$0.588919\pi$
$500$	21.3532	0.954946
$501$	−2.45087	−0.109497
$502$	9.91073	0.442337
$503$	−28.1361	−1.25452	−0.627262	−	0.778808i	$-0.715825\pi$
$503$	−28.1361	−1.25452	−0.627262	+	0.778808i	$0.715825\pi$
$504$	0	0
$505$	3.36300	0.149652
$506$	11.6404	0.517477
$507$	−19.2478	−0.854827
$508$	72.4151	3.21290
$509$	6.97469	0.309148	0.154574	−	0.987981i	$-0.450600\pi$
$509$	6.97469	0.309148	0.154574	+	0.987981i	$0.450600\pi$
$510$	104.095	4.60940
$511$	0	0
$512$	−41.6551	−1.84091
$513$	15.8146	0.698233
$514$	45.7723	2.01893
$515$	−22.8005	−1.00471
$516$	−50.6006	−2.22757
$517$	−4.31974	−0.189982
$518$	0	0
$519$	25.6635	1.12650
$520$	−34.3668	−1.50708
$521$	25.7377	1.12759	0.563795	−	0.825915i	$-0.309341\pi$
$521$	25.7377	1.12759	0.563795	+	0.825915i	$0.309341\pi$
$522$	−47.7263	−2.08892
$523$	−38.1487	−1.66812	−0.834062	−	0.551670i	$-0.813991\pi$
$523$	−38.1487	−1.66812	−0.834062	+	0.551670i	$0.813991\pi$
$524$	18.9408	0.827434
$525$	0	0
$526$	35.4954	1.54767
$527$	−59.4606	−2.59014
$528$	38.7830	1.68781
$529$	−21.0692	−0.916050
$530$	14.4404	0.627250
$531$	−52.7426	−2.28884
$532$	0	0
$533$	−2.37205	−0.102745
$534$	−60.9293	−2.63667
$535$	−26.8144	−1.15929
$536$	18.4400	0.796485
$537$	−17.8364	−0.769697
$538$	10.2776	0.443100
$539$	0	0
$540$	−24.6588	−1.06115
$541$	4.88511	0.210027	0.105014	−	0.994471i	$-0.466511\pi$
$541$	4.88511	0.210027	0.105014	+	0.994471i	$0.466511\pi$
$542$	−69.3821	−2.98022
$543$	42.3126	1.81581
$544$	−3.42319	−0.146768
$545$	−9.75163	−0.417714
$546$	0	0
$547$	−0.560447	−0.0239630	−0.0119815	−	0.999928i	$-0.503814\pi$
$547$	−0.560447	−0.0239630	−0.0119815	+	0.999928i	$0.503814\pi$
$548$	89.4629	3.82167
$549$	33.3173	1.42195
$550$	26.4623	1.12836
$551$	−37.8045	−1.61052
$552$	18.3988	0.783104
$553$	0	0
$554$	−1.16915	−0.0496723
$555$	3.58108	0.152008
$556$	35.0158	1.48500
$557$	32.9926	1.39794	0.698970	−	0.715151i	$-0.253642\pi$
$557$	32.9926	1.39794	0.698970	+	0.715151i	$0.253642\pi$
$558$	98.4613	4.16820
$559$	−11.3239	−0.478950
$560$	0	0
$561$	−50.3740	−2.12679
$562$	3.97048	0.167485
$563$	−1.13497	−0.0478332	−0.0239166	−	0.999714i	$-0.507614\pi$
$563$	−1.13497	−0.0478332	−0.0239166	+	0.999714i	$0.507614\pi$
$564$	−13.4555	−0.566577
$565$	14.8645	0.625355
$566$	15.9744	0.671452
$567$	0	0
$568$	−52.0041	−2.18204
$569$	15.0804	0.632204	0.316102	−	0.948725i	$-0.397626\pi$
$569$	15.0804	0.632204	0.316102	+	0.948725i	$0.397626\pi$
$570$	−136.537	−5.71892
$571$	−6.70238	−0.280486	−0.140243	−	0.990117i	$-0.544788\pi$
$571$	−6.70238	−0.280486	−0.140243	+	0.990117i	$0.544788\pi$
$572$	32.7744	1.37037
$573$	54.5935	2.28068
$574$	0	0
$575$	4.38942	0.183051
$576$	−27.6393	−1.15164
$577$	−9.85763	−0.410379	−0.205189	−	0.978722i	$-0.565781\pi$
$577$	−9.85763	−0.410379	−0.205189	+	0.978722i	$0.565781\pi$
$578$	37.3169	1.55218
$579$	17.8258	0.740815
$580$	58.9464	2.44761
$581$	0	0
$582$	−16.8632	−0.699003
$583$	−6.98805	−0.289415
$584$	−82.8115	−3.42677
$585$	−25.8448	−1.06855
$586$	−20.3534	−0.840791
$587$	−22.2985	−0.920358	−0.460179	−	0.887826i	$-0.652215\pi$
$587$	−22.2985	−0.920358	−0.460179	+	0.887826i	$0.652215\pi$
$588$	0	0
$589$	77.9921	3.21361
$590$	97.2285	4.00283
$591$	−35.6232	−1.46534
$592$	−2.09684	−0.0861796
$593$	11.5318	0.473554	0.236777	−	0.971564i	$-0.423909\pi$
$593$	11.5318	0.473554	0.236777	+	0.971564i	$0.423909\pi$
$594$	17.8108	0.730785
$595$	0	0
$596$	69.7381	2.85658
$597$	−49.8128	−2.03870
$598$	8.11423	0.331816
$599$	26.9923	1.10287	0.551437	−	0.834216i	$-0.314080\pi$
$599$	26.9923	1.10287	0.551437	+	0.834216i	$0.314080\pi$
$600$	41.8263	1.70755
$601$	4.87493	0.198853	0.0994264	−	0.995045i	$-0.468299\pi$
$601$	4.87493	0.198853	0.0994264	+	0.995045i	$0.468299\pi$
$602$	0	0
$603$	13.8674	0.564723
$604$	−18.7333	−0.762248
$605$	−1.65501	−0.0672856
$606$	−7.56620	−0.307356
$607$	18.7786	0.762199	0.381100	−	0.924534i	$-0.375545\pi$
$607$	18.7786	0.762199	0.381100	+	0.924534i	$0.375545\pi$
$608$	4.49007	0.182096
$609$	0	0
$610$	−61.4188	−2.48677
$611$	−3.01120	−0.121820
$612$	−87.8313	−3.55037
$613$	−1.49331	−0.0603143	−0.0301572	−	0.999545i	$-0.509601\pi$
$613$	−1.49331	−0.0603143	−0.0301572	+	0.999545i	$0.509601\pi$
$614$	−35.2793	−1.42376
$615$	7.45644	0.300673
$616$	0	0
$617$	2.97935	0.119944	0.0599721	−	0.998200i	$-0.480899\pi$
$617$	2.97935	0.119944	0.0599721	+	0.998200i	$0.480899\pi$
$618$	51.2975	2.06349
$619$	34.0942	1.37036	0.685181	−	0.728373i	$-0.259723\pi$
$619$	34.0942	1.37036	0.685181	+	0.728373i	$0.259723\pi$
$620$	−121.609	−4.88392
$621$	2.95435	0.118554
$622$	12.3391	0.494751
$623$	0	0
$624$	27.0348	1.08226
$625$	−30.8159	−1.23263
$626$	−41.5504	−1.66069
$627$	66.0737	2.63873
$628$	−7.51122	−0.299730
$629$	2.72352	0.108594
$630$	0	0
$631$	−9.51903	−0.378947	−0.189473	−	0.981886i	$-0.560678\pi$
$631$	−9.51903	−0.378947	−0.189473	+	0.981886i	$0.560678\pi$
$632$	−9.23417	−0.367316
$633$	9.02287	0.358627
$634$	14.5151	0.576470
$635$	−50.9421	−2.02158
$636$	−21.7669	−0.863113
$637$	0	0
$638$	−42.5762	−1.68561
$639$	−39.1086	−1.54711
$640$	54.4003	2.15036
$641$	−10.8843	−0.429905	−0.214953	−	0.976625i	$-0.568960\pi$
$641$	−10.8843	−0.429905	−0.214953	+	0.976625i	$0.568960\pi$
$642$	60.3280	2.38096
$643$	25.9468	1.02324	0.511621	−	0.859211i	$-0.329045\pi$
$643$	25.9468	1.02324	0.511621	+	0.859211i	$0.329045\pi$
$644$	0	0
$645$	35.5962	1.40160
$646$	−103.841	−4.08556
$647$	−38.7905	−1.52501	−0.762505	−	0.646982i	$-0.776031\pi$
$647$	−38.7905	−1.52501	−0.762505	+	0.646982i	$0.776031\pi$
$648$	−29.8919	−1.17427
$649$	−47.0512	−1.84692
$650$	18.4463	0.723522
$651$	0	0
$652$	−70.7427	−2.77050
$653$	−25.3413	−0.991683	−0.495841	−	0.868413i	$-0.665140\pi$
$653$	−25.3413	−0.991683	−0.495841	+	0.868413i	$0.665140\pi$
$654$	21.9396	0.857905
$655$	−13.3244	−0.520626
$656$	−4.36599	−0.170463
$657$	−62.2766	−2.42964
$658$	0	0
$659$	−44.5034	−1.73361	−0.866803	−	0.498650i	$-0.833829\pi$
$659$	−44.5034	−1.73361	−0.866803	+	0.498650i	$0.833829\pi$
$660$	−103.025	−4.01024
$661$	20.9677	0.815549	0.407775	−	0.913083i	$-0.366305\pi$
$661$	20.9677	0.815549	0.407775	+	0.913083i	$0.366305\pi$
$662$	45.8288	1.78119
$663$	−35.1146	−1.36374
$664$	−83.0502	−3.22297
$665$	0	0
$666$	−4.50990	−0.174755
$667$	−7.06231	−0.273454
$668$	−3.81217	−0.147497
$669$	4.10851	0.158844
$670$	−25.5638	−0.987618
$671$	29.7221	1.14741
$672$	0	0
$673$	8.06605	0.310923	0.155462	−	0.987842i	$-0.450313\pi$
$673$	8.06605	0.310923	0.155462	+	0.987842i	$0.450313\pi$
$674$	51.4914	1.98338
$675$	6.71620	0.258507
$676$	−29.9388	−1.15149
$677$	−17.5655	−0.675097	−0.337548	−	0.941308i	$-0.609598\pi$
$677$	−17.5655	−0.675097	−0.337548	+	0.941308i	$0.609598\pi$
$678$	−33.4427	−1.28436
$679$	0	0
$680$	82.1605	3.15071
$681$	30.4861	1.16823
$682$	87.8364	3.36343
$683$	46.6469	1.78490	0.892448	−	0.451150i	$-0.148986\pi$
$683$	46.6469	1.78490	0.892448	+	0.451150i	$0.148986\pi$
$684$	115.205	4.40497
$685$	−62.9348	−2.40461
$686$	0	0
$687$	38.8418	1.48191
$688$	−20.8427	−0.794621
$689$	−4.87121	−0.185578
$690$	−25.5067	−0.971025
$691$	9.52681	0.362417	0.181208	−	0.983445i	$-0.441999\pi$
$691$	9.52681	0.362417	0.181208	+	0.983445i	$0.441999\pi$
$692$	39.9179	1.51745
$693$	0	0
$694$	−11.2395	−0.426645
$695$	−24.6327	−0.934372
$696$	−67.2960	−2.55085
$697$	5.67084	0.214799
$698$	−0.349746	−0.0132381
$699$	−44.5736	−1.68593
$700$	0	0
$701$	26.2484	0.991388	0.495694	−	0.868497i	$-0.334914\pi$
$701$	26.2484	0.991388	0.495694	+	0.868497i	$0.334914\pi$
$702$	12.4155	0.468593
$703$	−3.57233	−0.134733
$704$	−24.6568	−0.929288
$705$	9.46556	0.356494
$706$	−7.93283	−0.298556
$707$	0	0
$708$	−146.559	−5.50801
$709$	−10.6790	−0.401057	−0.200529	−	0.979688i	$-0.564266\pi$
$709$	−10.6790	−0.401057	−0.200529	+	0.979688i	$0.564266\pi$
$710$	72.0948	2.70567
$711$	−6.94436	−0.260434
$712$	−48.0905	−1.80227
$713$	14.5698	0.545644
$714$	0	0
$715$	−23.0559	−0.862243
$716$	−27.7433	−1.03682
$717$	22.4986	0.840226
$718$	7.00855	0.261557
$719$	3.49013	0.130160	0.0650799	−	0.997880i	$-0.479270\pi$
$719$	3.49013	0.130160	0.0650799	+	0.997880i	$0.479270\pi$
$720$	−47.5699	−1.77282
$721$	0	0
$722$	89.4298	3.32823
$723$	−20.0085	−0.744124
$724$	65.8144	2.44597
$725$	−16.0549	−0.596264
$726$	3.72349	0.138192
$727$	−0.0175720	−0.000651711 0	−0.000325855	−	1.00000i	$-0.500104\pi$
$727$	−0.0175720	−0.000651711 0	−0.000325855		1.00000i	$0.500104\pi$
$728$	0	0
$729$	−39.1301	−1.44926
$730$	114.804	4.24908
$731$	27.0720	1.00129
$732$	92.5805	3.42187
$733$	−24.6286	−0.909680	−0.454840	−	0.890573i	$-0.650304\pi$
$733$	−24.6286	−0.909680	−0.454840	+	0.890573i	$0.650304\pi$
$734$	−29.4901	−1.08850
$735$	0	0
$736$	0.838797	0.0309185
$737$	12.3710	0.455690
$738$	−9.39040	−0.345665
$739$	47.9656	1.76444	0.882222	−	0.470833i	$-0.156047\pi$
$739$	47.9656	1.76444	0.882222	+	0.470833i	$0.156047\pi$
$740$	5.57014	0.204762
$741$	46.0585	1.69200
$742$	0	0
$743$	−38.6117	−1.41652	−0.708262	−	0.705949i	$-0.750521\pi$
$743$	−38.6117	−1.41652	−0.708262	+	0.705949i	$0.750521\pi$
$744$	138.834	5.08992
$745$	−49.0589	−1.79738
$746$	−0.812960	−0.0297646
$747$	−62.4561	−2.28515
$748$	−78.3535	−2.86489
$749$	0	0
$750$	33.7958	1.23405
$751$	−24.0774	−0.878595	−0.439298	−	0.898342i	$-0.644773\pi$
$751$	−24.0774	−0.878595	−0.439298	+	0.898342i	$0.644773\pi$
$752$	−5.54239	−0.202110
$753$	10.5092	0.382978
$754$	−29.6789	−1.08084
$755$	13.1784	0.479610
$756$	0	0
$757$	−40.2965	−1.46460	−0.732301	−	0.680982i	$-0.761553\pi$
$757$	−40.2965	−1.46460	−0.732301	+	0.680982i	$0.761553\pi$
$758$	17.5018	0.635693
$759$	12.3433	0.448034
$760$	−107.767	−3.90911
$761$	−19.1533	−0.694306	−0.347153	−	0.937809i	$-0.612852\pi$
$761$	−19.1533	−0.694306	−0.347153	+	0.937809i	$0.612852\pi$
$762$	114.611	4.15193
$763$	0	0
$764$	84.9166	3.07218
$765$	61.7870	2.23391
$766$	−5.93754	−0.214532
$767$	−32.7984	−1.18428
$768$	−84.5614	−3.05135
$769$	4.09187	0.147556	0.0737782	−	0.997275i	$-0.476494\pi$
$769$	4.09187	0.147556	0.0737782	+	0.997275i	$0.476494\pi$
$770$	0	0
$771$	48.5365	1.74800
$772$	27.7269	0.997912
$773$	49.4712	1.77936	0.889678	−	0.456588i	$-0.150929\pi$
$773$	49.4712	1.77936	0.889678	+	0.456588i	$0.150929\pi$
$774$	−44.8287	−1.61133
$775$	33.1219	1.18977
$776$	−13.3099	−0.477797
$777$	0	0
$778$	6.37970	0.228723
$779$	−7.43823	−0.266502
$780$	−71.8163	−2.57144
$781$	−34.8884	−1.24841
$782$	−19.3986	−0.693694
$783$	−10.8060	−0.386173
$784$	0	0
$785$	5.28394	0.188592
$786$	29.9776	1.06927
$787$	22.0679	0.786636	0.393318	−	0.919402i	$-0.371327\pi$
$787$	22.0679	0.786636	0.393318	+	0.919402i	$0.371327\pi$
$788$	−55.4095	−1.97388
$789$	37.6390	1.33998
$790$	12.8016	0.455460
$791$	0	0
$792$	65.8380	2.33945
$793$	20.7186	0.735738
$794$	64.5515	2.29085
$795$	15.3124	0.543076
$796$	−77.4805	−2.74622
$797$	−27.9105	−0.988642	−0.494321	−	0.869279i	$-0.664583\pi$
$797$	−27.9105	−0.988642	−0.494321	+	0.869279i	$0.664583\pi$
$798$	0	0
$799$	7.19884	0.254677
$800$	1.90686	0.0674175
$801$	−36.1654	−1.27784
$802$	97.4869	3.44238
$803$	−55.5564	−1.96054
$804$	38.5340	1.35899
$805$	0	0
$806$	61.2288	2.15669
$807$	10.8983	0.383638
$808$	−5.97189	−0.210090
$809$	13.2817	0.466958	0.233479	−	0.972362i	$-0.424989\pi$
$809$	13.2817	0.466958	0.233479	+	0.972362i	$0.424989\pi$
$810$	41.4400	1.45605
$811$	46.0527	1.61713	0.808564	−	0.588408i	$-0.200245\pi$
$811$	46.0527	1.61713	0.808564	+	0.588408i	$0.200245\pi$
$812$	0	0
$813$	−73.5721	−2.58029
$814$	−4.02324	−0.141015
$815$	49.7656	1.74321
$816$	−64.6318	−2.26256
$817$	−35.5092	−1.24231
$818$	−4.15933	−0.145428
$819$	0	0
$820$	11.5980	0.405020
$821$	39.3192	1.37225	0.686125	−	0.727483i	$-0.259310\pi$
$821$	39.3192	1.37225	0.686125	+	0.727483i	$0.259310\pi$
$822$	141.593	4.93862
$823$	−25.1697	−0.877360	−0.438680	−	0.898643i	$-0.644554\pi$
$823$	−25.1697	−0.877360	−0.438680	+	0.898643i	$0.644554\pi$
$824$	40.4883	1.41048
$825$	28.0603	0.976936
$826$	0	0
$827$	18.2674	0.635220	0.317610	−	0.948221i	$-0.397120\pi$
$827$	18.2674	0.635220	0.317610	+	0.948221i	$0.397120\pi$
$828$	21.5216	0.747928
$829$	33.9029	1.17750	0.588748	−	0.808316i	$-0.299621\pi$
$829$	33.9029	1.17750	0.588748	+	0.808316i	$0.299621\pi$
$830$	115.135	3.99639
$831$	−1.23975	−0.0430065
$832$	−17.1877	−0.595876
$833$	0	0
$834$	55.4195	1.91902
$835$	2.68176	0.0928062
$836$	102.773	3.55449
$837$	22.2931	0.770563
$838$	−59.4284	−2.05292
$839$	43.2539	1.49329	0.746646	−	0.665222i	$-0.231663\pi$
$839$	43.2539	1.49329	0.746646	+	0.665222i	$0.231663\pi$
$840$	0	0
$841$	−3.16862	−0.109263
$842$	−43.0450	−1.48343
$843$	4.21026	0.145009
$844$	14.0345	0.483087
$845$	21.0611	0.724525
$846$	−11.9206	−0.409839
$847$	0	0
$848$	−8.96592	−0.307891
$849$	16.9391	0.581347
$850$	−44.0993	−1.51259
$851$	−0.667353	−0.0228766
$852$	−108.673	−3.72308
$853$	−36.7107	−1.25695	−0.628475	−	0.777830i	$-0.716321\pi$
$853$	−36.7107	−1.25695	−0.628475	+	0.777830i	$0.716321\pi$
$854$	0	0
$855$	−81.0436	−2.77163
$856$	47.6159	1.62748
$857$	−30.7957	−1.05196	−0.525981	−	0.850497i	$-0.676302\pi$
$857$	−30.7957	−1.05196	−0.525981	+	0.850497i	$0.676302\pi$
$858$	51.8721	1.77088
$859$	38.5139	1.31408	0.657039	−	0.753857i	$-0.271809\pi$
$859$	38.5139	1.31408	0.657039	+	0.753857i	$0.271809\pi$
$860$	55.3675	1.88802
$861$	0	0
$862$	19.8412	0.675793
$863$	24.3529	0.828982	0.414491	−	0.910053i	$-0.363960\pi$
$863$	24.3529	0.828982	0.414491	+	0.910053i	$0.363960\pi$
$864$	1.28343	0.0436633
$865$	−28.0812	−0.954789
$866$	76.0343	2.58375
$867$	39.5705	1.34388
$868$	0	0
$869$	−6.19500	−0.210151
$870$	93.2944	3.16298
$871$	8.62352	0.292197
$872$	17.3166	0.586413
$873$	−10.0094	−0.338767
$874$	25.4444	0.860671
$875$	0	0
$876$	−173.051	−5.84686
$877$	−45.3557	−1.53155	−0.765777	−	0.643107i	$-0.777645\pi$
$877$	−45.3557	−1.53155	−0.765777	+	0.643107i	$0.777645\pi$
$878$	68.0900	2.29793
$879$	−21.5825	−0.727961
$880$	−42.4367	−1.43054
$881$	0.182718	0.00615592	0.00307796	−	0.999995i	$-0.499020\pi$
$881$	0.182718	0.00615592	0.00307796	+	0.999995i	$0.499020\pi$
$882$	0	0
$883$	−30.0189	−1.01022	−0.505108	−	0.863056i	$-0.668547\pi$
$883$	−30.0189	−1.01022	−0.505108	+	0.863056i	$0.668547\pi$
$884$	−54.6185	−1.83702
$885$	103.100	3.46567
$886$	−61.6151	−2.07000
$887$	16.8496	0.565756	0.282878	−	0.959156i	$-0.408711\pi$
$887$	16.8496	0.565756	0.282878	+	0.959156i	$0.408711\pi$
$888$	−6.35914	−0.213399
$889$	0	0
$890$	66.6692	2.23476
$891$	−20.0538	−0.671829
$892$	6.39051	0.213970
$893$	−9.44244	−0.315979
$894$	110.374	3.69147
$895$	19.5167	0.652371
$896$	0	0
$897$	8.60425	0.287288
$898$	−9.78107	−0.326399
$899$	−53.2911	−1.77736
$900$	48.9255	1.63085
$901$	11.6456	0.387970
$902$	−8.37710	−0.278927
$903$	0	0
$904$	−26.3958	−0.877912
$905$	−46.2987	−1.53902
$906$	−29.6492	−0.985029
$907$	23.5503	0.781974	0.390987	−	0.920396i	$-0.372134\pi$
$907$	23.5503	0.781974	0.390987	+	0.920396i	$0.372134\pi$
$908$	47.4191	1.57366
$909$	−4.49103	−0.148958
$910$	0	0
$911$	−21.1002	−0.699082	−0.349541	−	0.936921i	$-0.613662\pi$
$911$	−21.1002	−0.699082	−0.349541	+	0.936921i	$0.613662\pi$
$912$	84.7750	2.80718
$913$	−55.7165	−1.84395
$914$	−26.3398	−0.871243
$915$	−65.1279	−2.15306
$916$	60.4159	1.99620
$917$	0	0
$918$	−29.6816	−0.979639
$919$	−16.3527	−0.539426	−0.269713	−	0.962941i	$-0.586929\pi$
$919$	−16.3527	−0.539426	−0.269713	+	0.962941i	$0.586929\pi$
$920$	−20.1321	−0.663734
$921$	−37.4098	−1.23270
$922$	72.1659	2.37666
$923$	−24.3199	−0.800500
$924$	0	0
$925$	−1.51711	−0.0498822
$926$	−24.4365	−0.803035
$927$	30.4483	1.00005
$928$	−3.06802	−0.100713
$929$	42.0266	1.37885	0.689424	−	0.724358i	$-0.257864\pi$
$929$	42.0266	1.37885	0.689424	+	0.724358i	$0.257864\pi$
$930$	−192.470	−6.31134
$931$	0	0
$932$	−69.3313	−2.27102
$933$	13.0842	0.428358
$934$	102.012	3.33793
$935$	55.1196	1.80260
$936$	45.8942	1.50010
$937$	−20.4719	−0.668786	−0.334393	−	0.942434i	$-0.608531\pi$
$937$	−20.4719	−0.668786	−0.334393	+	0.942434i	$0.608531\pi$
$938$	0	0
$939$	−44.0596	−1.43783
$940$	14.7231	0.480213
$941$	−5.23475	−0.170648	−0.0853240	−	0.996353i	$-0.527193\pi$
$941$	−5.23475	−0.170648	−0.0853240	+	0.996353i	$0.527193\pi$
$942$	−11.8880	−0.387332
$943$	−1.38955	−0.0452499
$944$	−60.3685	−1.96483
$945$	0	0
$946$	−39.9913	−1.30023
$947$	41.6425	1.35320	0.676599	−	0.736352i	$-0.263453\pi$
$947$	41.6425	1.35320	0.676599	+	0.736352i	$0.263453\pi$
$948$	−19.2966	−0.626726
$949$	−38.7271	−1.25714
$950$	57.8434	1.87669
$951$	15.3917	0.499110
$952$	0	0
$953$	8.22874	0.266555	0.133277	−	0.991079i	$-0.457450\pi$
$953$	8.22874	0.266555	0.133277	+	0.991079i	$0.457450\pi$
$954$	−19.2840	−0.624342
$955$	−59.7366	−1.93303
$956$	34.9951	1.13182
$957$	−45.1474	−1.45941
$958$	−92.1561	−2.97743
$959$	0	0
$960$	54.0288	1.74377
$961$	78.9417	2.54651
$962$	−2.80451	−0.0904210
$963$	35.8085	1.15391
$964$	−31.1219	−1.00237
$965$	−19.5051	−0.627892
$966$	0	0
$967$	−43.4940	−1.39867	−0.699336	−	0.714793i	$-0.746521\pi$
$967$	−43.4940	−1.39867	−0.699336	+	0.714793i	$0.746521\pi$
$968$	2.93889	0.0944596
$969$	−110.112	−3.53729
$970$	18.4519	0.592454
$971$	−31.9031	−1.02382	−0.511909	−	0.859039i	$-0.671062\pi$
$971$	−31.9031	−1.02382	−0.511909	+	0.859039i	$0.671062\pi$
$972$	−88.3639	−2.83427
$973$	0	0
$974$	−54.6132	−1.74992
$975$	19.5602	0.626429
$976$	38.1345	1.22066
$977$	−36.0972	−1.15485	−0.577425	−	0.816444i	$-0.695942\pi$
$977$	−36.0972	−1.15485	−0.577425	+	0.816444i	$0.695942\pi$
$978$	−111.964	−3.58023
$979$	−32.2629	−1.03113
$980$	0	0
$981$	13.0225	0.415778
$982$	−25.1493	−0.802546
$983$	−4.69064	−0.149608	−0.0748040	−	0.997198i	$-0.523833\pi$
$983$	−4.69064	−0.149608	−0.0748040	+	0.997198i	$0.523833\pi$
$984$	−13.2408	−0.422103
$985$	38.9791	1.24198
$986$	70.9532	2.25961
$987$	0	0
$988$	71.6409	2.27920
$989$	−6.63353	−0.210934
$990$	−91.2731	−2.90085
$991$	38.7213	1.23002	0.615011	−	0.788519i	$-0.289152\pi$
$991$	38.7213	1.23002	0.615011	+	0.788519i	$0.289152\pi$
$992$	6.32944	0.200960
$993$	48.5964	1.54216
$994$	0	0
$995$	54.5055	1.72794
$996$	−173.550	−5.49914
$997$	7.43745	0.235546	0.117773	−	0.993041i	$-0.462424\pi$
$997$	7.43745	0.235546	0.117773	+	0.993041i	$0.462424\pi$
$998$	−30.3256	−0.959941
$999$	−1.02111	−0.0323065

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.o.1.6		6
7.6	odd	2		287.2.a.f.1.6	✓	6
21.20	even	2		2583.2.a.t.1.1		6
28.27	even	2		4592.2.a.bg.1.5		6
35.34	odd	2		7175.2.a.p.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.f.1.6	✓	6	7.6	odd	2
2009.2.a.o.1.6		6	1.1	even	1	trivial
2583.2.a.t.1.1		6	21.20	even	2
4592.2.a.bg.1.5		6	28.27	even	2
7175.2.a.p.1.1		6	35.34	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:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2009.a (trivial)

\(f(q)\)	\(=\)	\(q+2.46179 q^{2} +2.61045 q^{3} +4.06039 q^{4} -2.85638 q^{5} +6.42638 q^{6} +5.07224 q^{8} +3.81447 q^{9} +O(q^{10})\)	\(q+2.46179 q^{2} +2.61045 q^{3} +4.06039 q^{4} -2.85638 q^{5} +6.42638 q^{6} +5.07224 q^{8} +3.81447 q^{9} -7.03179 q^{10} +3.40285 q^{11} +10.5995 q^{12} +2.37205 q^{13} -7.45644 q^{15} +4.36599 q^{16} -5.67084 q^{17} +9.39040 q^{18} +7.43823 q^{19} -11.5980 q^{20} +8.37710 q^{22} +1.38955 q^{23} +13.2408 q^{24} +3.15889 q^{25} +5.83948 q^{26} +2.12613 q^{27} -5.08246 q^{29} -18.3562 q^{30} +10.4853 q^{31} +0.603648 q^{32} +8.88299 q^{33} -13.9604 q^{34} +15.4882 q^{36} -0.480267 q^{37} +18.3113 q^{38} +6.19213 q^{39} -14.4882 q^{40} -1.00000 q^{41} -4.77388 q^{43} +13.8169 q^{44} -10.8956 q^{45} +3.42077 q^{46} -1.26945 q^{47} +11.3972 q^{48} +7.77650 q^{50} -14.8035 q^{51} +9.63145 q^{52} -2.05358 q^{53} +5.23407 q^{54} -9.71983 q^{55} +19.4171 q^{57} -12.5119 q^{58} -13.8270 q^{59} -30.2760 q^{60} +8.73445 q^{61} +25.8126 q^{62} -7.24592 q^{64} -6.77547 q^{65} +21.8680 q^{66} +3.63547 q^{67} -23.0258 q^{68} +3.62735 q^{69} -10.2527 q^{71} +19.3479 q^{72} -16.3264 q^{73} -1.18231 q^{74} +8.24612 q^{75} +30.2021 q^{76} +15.2437 q^{78} -1.82053 q^{79} -12.4709 q^{80} -5.89324 q^{81} -2.46179 q^{82} -16.3735 q^{83} +16.1981 q^{85} -11.7523 q^{86} -13.2675 q^{87} +17.2601 q^{88} -9.48112 q^{89} -26.8225 q^{90} +5.64210 q^{92} +27.3714 q^{93} -3.12511 q^{94} -21.2464 q^{95} +1.57579 q^{96} -2.62406 q^{97} +12.9801 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9}+O(q^{10}) \) 6 * q - q^2 + 4 * q^3 + 9 * q^4 + q^5 + 4 * q^6 + 3 * q^8 + 14 * q^9	\( 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9} - 10 q^{10} + 6 q^{11} - 9 q^{12} - 7 q^{13} - 13 q^{15} + 7 q^{16} - 7 q^{17} - 5 q^{18} - 2 q^{19} - 11 q^{20} + 15 q^{22} + 20 q^{23} + 36 q^{24} + 29 q^{25} + 43 q^{26} - 2 q^{27} - 9 q^{29} + 13 q^{30} + 27 q^{31} - 10 q^{32} - 17 q^{33} - 6 q^{34} + 29 q^{36} + 19 q^{37} + 23 q^{38} + q^{39} - 23 q^{40} - 6 q^{41} + 19 q^{43} + 21 q^{44} + 35 q^{45} - 8 q^{46} + 19 q^{47} + 9 q^{48} - 58 q^{50} - 19 q^{51} + 5 q^{53} + 37 q^{54} - 3 q^{55} + 37 q^{57} + 13 q^{58} + 7 q^{59} - 110 q^{60} + 12 q^{61} - 37 q^{64} - 13 q^{65} + 54 q^{66} + 27 q^{67} - 31 q^{68} - 16 q^{69} - 6 q^{71} + 5 q^{72} - 52 q^{73} - 14 q^{74} + 46 q^{75} - 13 q^{76} - 45 q^{78} + 26 q^{80} - 22 q^{81} + q^{82} - 12 q^{83} + 25 q^{85} - 10 q^{86} - 42 q^{87} - 2 q^{88} + 38 q^{89} - 93 q^{90} + 45 q^{92} + 33 q^{93} + 8 q^{94} + q^{95} + 12 q^{96} - 8 q^{97} + q^{99}+O(q^{100}) \) 6 * q - q^2 + 4 * q^3 + 9 * q^4 + q^5 + 4 * q^6 + 3 * q^8 + 14 * q^9 - 10 * q^10 + 6 * q^11 - 9 * q^12 - 7 * q^13 - 13 * q^15 + 7 * q^16 - 7 * q^17 - 5 * q^18 - 2 * q^19 - 11 * q^20 + 15 * q^22 + 20 * q^23 + 36 * q^24 + 29 * q^25 + 43 * q^26 - 2 * q^27 - 9 * q^29 + 13 * q^30 + 27 * q^31 - 10 * q^32 - 17 * q^33 - 6 * q^34 + 29 * q^36 + 19 * q^37 + 23 * q^38 + q^39 - 23 * q^40 - 6 * q^41 + 19 * q^43 + 21 * q^44 + 35 * q^45 - 8 * q^46 + 19 * q^47 + 9 * q^48 - 58 * q^50 - 19 * q^51 + 5 * q^53 + 37 * q^54 - 3 * q^55 + 37 * q^57 + 13 * q^58 + 7 * q^59 - 110 * q^60 + 12 * q^61 - 37 * q^64 - 13 * q^65 + 54 * q^66 + 27 * q^67 - 31 * q^68 - 16 * q^69 - 6 * q^71 + 5 * q^72 - 52 * q^73 - 14 * q^74 + 46 * q^75 - 13 * q^76 - 45 * q^78 + 26 * q^80 - 22 * q^81 + q^82 - 12 * q^83 + 25 * q^85 - 10 * q^86 - 42 * q^87 - 2 * q^88 + 38 * q^89 - 93 * q^90 + 45 * q^92 + 33 * q^93 + 8 * q^94 + q^95 + 12 * q^96 - 8 * q^97 + q^99

Introduction

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