LMFDB - Embedded newform 2009.2.a.o.1.2

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			1.2
Root			$2.05073$ 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)

$f(q)$	$=$	$q-2.05073 q^{2} +1.62935 q^{3} +2.20548 q^{4} -4.18004 q^{5} -3.34135 q^{6} -0.421375 q^{8} -0.345215 q^{9} +O(q^{10})$	\(q-2.05073 q^{2} +1.62935 q^{3} +2.20548 q^{4} -4.18004 q^{5} -3.34135 q^{6} -0.421375 q^{8} -0.345215 q^{9} +8.57212 q^{10} -3.88169 q^{11} +3.59349 q^{12} -2.89984 q^{13} -6.81076 q^{15} -3.54683 q^{16} -2.83483 q^{17} +0.707942 q^{18} -5.96820 q^{19} -9.21898 q^{20} +7.96028 q^{22} +2.37065 q^{23} -0.686567 q^{24} +12.4728 q^{25} +5.94677 q^{26} -5.45053 q^{27} -5.37130 q^{29} +13.9670 q^{30} +3.48961 q^{31} +8.11632 q^{32} -6.32463 q^{33} +5.81345 q^{34} -0.761364 q^{36} +11.3705 q^{37} +12.2391 q^{38} -4.72486 q^{39} +1.76136 q^{40} -1.00000 q^{41} +5.56840 q^{43} -8.56097 q^{44} +1.44301 q^{45} -4.86155 q^{46} -1.09103 q^{47} -5.77903 q^{48} -25.5782 q^{50} -4.61893 q^{51} -6.39552 q^{52} -8.69245 q^{53} +11.1775 q^{54} +16.2256 q^{55} -9.72430 q^{57} +11.0151 q^{58} -1.15927 q^{59} -15.0210 q^{60} -13.9323 q^{61} -7.15624 q^{62} -9.55069 q^{64} +12.1214 q^{65} +12.9701 q^{66} +6.92134 q^{67} -6.25214 q^{68} +3.86262 q^{69} +7.31342 q^{71} +0.145465 q^{72} -0.0168592 q^{73} -23.3178 q^{74} +20.3225 q^{75} -13.1627 q^{76} +9.68938 q^{78} -0.301774 q^{79} +14.8259 q^{80} -7.84518 q^{81} +2.05073 q^{82} +4.90247 q^{83} +11.8497 q^{85} -11.4193 q^{86} -8.75173 q^{87} +1.63565 q^{88} +12.0332 q^{89} -2.95923 q^{90} +5.22841 q^{92} +5.68580 q^{93} +2.23740 q^{94} +24.9473 q^{95} +13.2243 q^{96} +15.3446 q^{97} +1.34002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.05073	−1.45008	−0.725041	−	0.688706i	$-0.758179\pi$
$2$	−2.05073	−1.45008	−0.725041	+	0.688706i	$0.758179\pi$
$3$	1.62935	0.940706	0.470353	−	0.882478i	$-0.344127\pi$
$3$	1.62935	0.940706	0.470353	+	0.882478i	$0.344127\pi$
$4$	2.20548	1.10274
$5$	−4.18004	−1.86937	−0.934686	−	0.355475i	$-0.884319\pi$
$5$	−4.18004	−1.86937	−0.934686	+	0.355475i	$0.884319\pi$
$6$	−3.34135	−1.36410
$7$	0	0
$7$	0	0
$8$	−0.421375	−0.148978
$9$	−0.345215	−0.115072
$10$	8.57212	2.71074
$11$	−3.88169	−1.17037	−0.585187	−	0.810899i	$-0.698979\pi$
$11$	−3.88169	−1.17037	−0.585187	+	0.810899i	$0.698979\pi$
$12$	3.59349	1.03735
$13$	−2.89984	−0.804271	−0.402135	−	0.915580i	$-0.631732\pi$
$13$	−2.89984	−0.804271	−0.402135	+	0.915580i	$0.631732\pi$
$14$	0	0
$15$	−6.81076	−1.75853
$16$	−3.54683	−0.886707
$17$	−2.83483	−0.687547	−0.343773	−	0.939053i	$-0.611705\pi$
$17$	−2.83483	−0.687547	−0.343773	+	0.939053i	$0.611705\pi$
$18$	0.707942	0.166863
$19$	−5.96820	−1.36920	−0.684600	−	0.728919i	$-0.740023\pi$
$19$	−5.96820	−1.36920	−0.684600	+	0.728919i	$0.740023\pi$
$20$	−9.21898	−2.06143
$21$	0	0
$22$	7.96028	1.69714
$23$	2.37065	0.494314	0.247157	−	0.968975i	$-0.420504\pi$
$23$	2.37065	0.494314	0.247157	+	0.968975i	$0.420504\pi$
$24$	−0.686567	−0.140145
$25$	12.4728	2.49455
$26$	5.94677	1.16626
$27$	−5.45053	−1.04895
$28$	0	0
$29$	−5.37130	−0.997426	−0.498713	−	0.866767i	$-0.666194\pi$
$29$	−5.37130	−0.997426	−0.498713	+	0.866767i	$0.666194\pi$
$30$	13.9670	2.55001
$31$	3.48961	0.626753	0.313376	−	0.949629i	$-0.398540\pi$
$31$	3.48961	0.626753	0.313376	+	0.949629i	$0.398540\pi$
$32$	8.11632	1.43478
$33$	−6.32463	−1.10098
$34$	5.81345	0.996999
$35$	0	0
$36$	−0.761364	−0.126894
$37$	11.3705	1.86930	0.934650	−	0.355569i	$-0.115713\pi$
$37$	11.3705	1.86930	0.934650	+	0.355569i	$0.115713\pi$
$38$	12.2391	1.98545
$39$	−4.72486	−0.756582
$40$	1.76136	0.278496
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	5.56840	0.849173	0.424586	−	0.905387i	$-0.360420\pi$
$43$	5.56840	0.849173	0.424586	+	0.905387i	$0.360420\pi$
$44$	−8.56097	−1.29062
$45$	1.44301	0.215112
$46$	−4.86155	−0.716797
$47$	−1.09103	−0.159143	−0.0795714	−	0.996829i	$-0.525355\pi$
$47$	−1.09103	−0.159143	−0.0795714	+	0.996829i	$0.525355\pi$
$48$	−5.77903	−0.834131
$49$	0	0
$50$	−25.5782	−3.61730
$51$	−4.61893	−0.646779
$52$	−6.39552	−0.886900
$53$	−8.69245	−1.19400	−0.597000	−	0.802242i	$-0.703641\pi$
$53$	−8.69245	−1.19400	−0.597000	+	0.802242i	$0.703641\pi$
$54$	11.1775	1.52107
$55$	16.2256	2.18786
$56$	0	0
$57$	−9.72430	−1.28801
$58$	11.0151	1.44635
$59$	−1.15927	−0.150924	−0.0754618	−	0.997149i	$-0.524043\pi$
$59$	−1.15927	−0.150924	−0.0754618	+	0.997149i	$0.524043\pi$
$60$	−15.0210	−1.93920
$61$	−13.9323	−1.78384	−0.891922	−	0.452188i	$-0.850643\pi$
$61$	−13.9323	−1.78384	−0.891922	+	0.452188i	$0.850643\pi$
$62$	−7.15624	−0.908843
$63$	0	0
$64$	−9.55069	−1.19384
$65$	12.1214	1.50348
$66$	12.9701	1.59651
$67$	6.92134	0.845576	0.422788	−	0.906229i	$-0.361051\pi$
$67$	6.92134	0.845576	0.422788	+	0.906229i	$0.361051\pi$
$68$	−6.25214	−0.758184
$69$	3.86262	0.465005
$70$	0	0
$71$	7.31342	0.867943	0.433972	−	0.900927i	$-0.357112\pi$
$71$	7.31342	0.867943	0.433972	+	0.900927i	$0.357112\pi$
$72$	0.145465	0.0171432
$73$	−0.0168592	−0.00197323	−0.000986613	−	1.00000i	$-0.500314\pi$
$73$	−0.0168592	−0.00197323	−0.000986613		1.00000i	$0.500314\pi$
$74$	−23.3178	−2.71064
$75$	20.3225	2.34664
$76$	−13.1627	−1.50987
$77$	0	0
$78$	9.68938	1.09711
$79$	−0.301774	−0.0339522	−0.0169761	−	0.999856i	$-0.505404\pi$
$79$	−0.301774	−0.0339522	−0.0169761	+	0.999856i	$0.505404\pi$
$80$	14.8259	1.65758
$81$	−7.84518	−0.871687
$82$	2.05073	0.226465
$83$	4.90247	0.538116	0.269058	−	0.963124i	$-0.413288\pi$
$83$	4.90247	0.538116	0.269058	+	0.963124i	$0.413288\pi$
$84$	0	0
$85$	11.8497	1.28528
$86$	−11.4193	−1.23137
$87$	−8.75173	−0.938284
$88$	1.63565	0.174360
$89$	12.0332	1.27552	0.637759	−	0.770236i	$-0.279862\pi$
$89$	12.0332	1.27552	0.637759	+	0.770236i	$0.279862\pi$
$90$	−2.95923	−0.311930
$91$	0	0
$92$	5.22841	0.545099
$93$	5.68580	0.589590
$94$	2.23740	0.230770
$95$	24.9473	2.55954
$96$	13.2243	1.34970
$97$	15.3446	1.55801	0.779003	−	0.627020i	$-0.215725\pi$
$97$	15.3446	1.55801	0.779003	+	0.627020i	$0.215725\pi$
$98$	0	0
$99$	1.34002	0.134677
$100$	27.5084	2.75084
$101$	−3.15297	−0.313732	−0.156866	−	0.987620i	$-0.550139\pi$
$101$	−3.15297	−0.313732	−0.156866	+	0.987620i	$0.550139\pi$
$102$	9.47215	0.937883
$103$	6.52355	0.642785	0.321392	−	0.946946i	$-0.395849\pi$
$103$	6.52355	0.642785	0.321392	+	0.946946i	$0.395849\pi$
$104$	1.22192	0.119819
$105$	0	0
$106$	17.8258	1.73140
$107$	−19.9116	−1.92493	−0.962465	−	0.271407i	$-0.912511\pi$
$107$	−19.9116	−1.92493	−0.962465	+	0.271407i	$0.912511\pi$
$108$	−12.0210	−1.15672
$109$	−14.0170	−1.34259	−0.671293	−	0.741192i	$-0.734261\pi$
$109$	−14.0170	−1.34259	−0.671293	+	0.741192i	$0.734261\pi$
$110$	−33.2743	−3.17258
$111$	18.5265	1.75846
$112$	0	0
$113$	9.35171	0.879734	0.439867	−	0.898063i	$-0.355025\pi$
$113$	9.35171	0.879734	0.439867	+	0.898063i	$0.355025\pi$
$114$	19.9419	1.86773
$115$	−9.90941	−0.924057
$116$	−11.8463	−1.09990
$117$	1.00107	0.0925488
$118$	2.37734	0.218851
$119$	0	0
$120$	2.86988	0.261983
$121$	4.06751	0.369774
$122$	28.5713	2.58672
$123$	−1.62935	−0.146914
$124$	7.69625	0.691144
$125$	−31.2364	−2.79387
$126$	0	0
$127$	3.18077	0.282247	0.141124	−	0.989992i	$-0.454928\pi$
$127$	3.18077	0.282247	0.141124	+	0.989992i	$0.454928\pi$
$128$	3.35321	0.296384
$129$	9.07288	0.798822
$130$	−24.8578	−2.18017
$131$	−0.812162	−0.0709589	−0.0354795	−	0.999370i	$-0.511296\pi$
$131$	−0.812162	−0.0709589	−0.0354795	+	0.999370i	$0.511296\pi$
$132$	−13.9488	−1.21409
$133$	0	0
$134$	−14.1938	−1.22615
$135$	22.7834	1.96089
$136$	1.19452	0.102430
$137$	−5.64719	−0.482472	−0.241236	−	0.970467i	$-0.577553\pi$
$137$	−5.64719	−0.482472	−0.241236	+	0.970467i	$0.577553\pi$
$138$	−7.92117	−0.674295
$139$	−0.622987	−0.0528411	−0.0264205	−	0.999651i	$-0.508411\pi$
$139$	−0.622987	−0.0528411	−0.0264205	+	0.999651i	$0.508411\pi$
$140$	0	0
$141$	−1.77767	−0.149707
$142$	−14.9978	−1.25859
$143$	11.2563	0.941297
$144$	1.22442	0.102035
$145$	22.4523	1.86456
$146$	0.0345737	0.00286134
$147$	0	0
$148$	25.0774	2.06135
$149$	10.4407	0.855335	0.427667	−	0.903936i	$-0.359335\pi$
$149$	10.4407	0.855335	0.427667	+	0.903936i	$0.359335\pi$
$150$	−41.6759	−3.40282
$151$	14.3432	1.16724	0.583618	−	0.812029i	$-0.301637\pi$
$151$	14.3432	1.16724	0.583618	+	0.812029i	$0.301637\pi$
$152$	2.51485	0.203981
$153$	0.978625	0.0791172
$154$	0	0
$155$	−14.5867	−1.17163
$156$	−10.4206	−0.834312
$157$	−2.94541	−0.235069	−0.117535	−	0.993069i	$-0.537499\pi$
$157$	−2.94541	−0.235069	−0.117535	+	0.993069i	$0.537499\pi$
$158$	0.618855	0.0492335
$159$	−14.1630	−1.12320
$160$	−33.9266	−2.68213
$161$	0	0
$162$	16.0883	1.26402
$163$	9.27654	0.726594	0.363297	−	0.931673i	$-0.381651\pi$
$163$	9.27654	0.726594	0.363297	+	0.931673i	$0.381651\pi$
$164$	−2.20548	−0.172219
$165$	26.4372	2.05814
$166$	−10.0536	−0.780312
$167$	−13.9285	−1.07782	−0.538909	−	0.842364i	$-0.681163\pi$
$167$	−13.9285	−1.07782	−0.538909	+	0.842364i	$0.681163\pi$
$168$	0	0
$169$	−4.59094	−0.353149
$170$	−24.3005	−1.86376
$171$	2.06031	0.157556
$172$	12.2810	0.936415
$173$	15.6097	1.18678	0.593390	−	0.804915i	$-0.297789\pi$
$173$	15.6097	1.18678	0.593390	+	0.804915i	$0.297789\pi$
$174$	17.9474	1.36059
$175$	0	0
$176$	13.7677	1.03778
$177$	−1.88885	−0.141975
$178$	−24.6768	−1.84961
$179$	−15.4337	−1.15357	−0.576786	−	0.816895i	$-0.695693\pi$
$179$	−15.4337	−1.15357	−0.576786	+	0.816895i	$0.695693\pi$
$180$	3.18253	0.237212
$181$	10.4360	0.775700	0.387850	−	0.921723i	$-0.373218\pi$
$181$	10.4360	0.775700	0.387850	+	0.921723i	$0.373218\pi$
$182$	0	0
$183$	−22.7006	−1.67807
$184$	−0.998931	−0.0736422
$185$	−47.5292	−3.49442
$186$	−11.6600	−0.854954
$187$	11.0039	0.804686
$188$	−2.40624	−0.175493
$189$	0	0
$190$	−51.1601	−3.71155
$191$	−20.5760	−1.48882	−0.744412	−	0.667720i	$-0.767270\pi$
$191$	−20.5760	−1.48882	−0.744412	+	0.667720i	$0.767270\pi$
$192$	−15.5614	−1.12305
$193$	−3.01664	−0.217143	−0.108571	−	0.994089i	$-0.534628\pi$
$193$	−3.01664	−0.217143	−0.108571	+	0.994089i	$0.534628\pi$
$194$	−31.4675	−2.25924
$195$	19.7501	1.41433
$196$	0	0
$197$	19.2009	1.36801	0.684004	−	0.729478i	$-0.260237\pi$
$197$	19.2009	1.36801	0.684004	+	0.729478i	$0.260237\pi$
$198$	−2.74801	−0.195293
$199$	14.0652	0.997056	0.498528	−	0.866874i	$-0.333874\pi$
$199$	14.0652	0.997056	0.498528	+	0.866874i	$0.333874\pi$
$200$	−5.25570	−0.371634
$201$	11.2773	0.795439
$202$	6.46588	0.454938
$203$	0	0
$204$	−10.1869	−0.713228
$205$	4.18004	0.291947
$206$	−13.3780	−0.932090
$207$	−0.818384	−0.0568816
$208$	10.2852	0.713152
$209$	23.1667	1.60247
$210$	0	0
$211$	2.81076	0.193500	0.0967502	−	0.995309i	$-0.469155\pi$
$211$	2.81076	0.193500	0.0967502	+	0.995309i	$0.469155\pi$
$212$	−19.1710	−1.31667
$213$	11.9161	0.816479
$214$	40.8333	2.79131
$215$	−23.2761	−1.58742
$216$	2.29672	0.156272
$217$	0	0
$218$	28.7450	1.94686
$219$	−0.0274696	−0.00185623
$220$	35.7852	2.41264
$221$	8.22054	0.552973
$222$	−37.9929	−2.54991
$223$	8.88504	0.594986	0.297493	−	0.954724i	$-0.403849\pi$
$223$	8.88504	0.594986	0.297493	+	0.954724i	$0.403849\pi$
$224$	0	0
$225$	−4.30578	−0.287052
$226$	−19.1778	−1.27569
$227$	−8.44837	−0.560738	−0.280369	−	0.959892i	$-0.590457\pi$
$227$	−8.44837	−0.560738	−0.280369	+	0.959892i	$0.590457\pi$
$228$	−21.4467	−1.42034
$229$	20.0603	1.32562	0.662811	−	0.748787i	$-0.269363\pi$
$229$	20.0603	1.32562	0.662811	+	0.748787i	$0.269363\pi$
$230$	20.3215	1.33996
$231$	0	0
$232$	2.26333	0.148595
$233$	−6.25521	−0.409793	−0.204896	−	0.978784i	$-0.565686\pi$
$233$	−6.25521	−0.409793	−0.204896	+	0.978784i	$0.565686\pi$
$234$	−2.05292	−0.134203
$235$	4.56055	0.297497
$236$	−2.55673	−0.166429
$237$	−0.491696	−0.0319391
$238$	0	0
$239$	0.782184	0.0505953	0.0252976	−	0.999680i	$-0.491947\pi$
$239$	0.782184	0.0505953	0.0252976	+	0.999680i	$0.491947\pi$
$240$	24.1566	1.55930
$241$	2.65015	0.170711	0.0853557	−	0.996351i	$-0.472797\pi$
$241$	2.65015	0.170711	0.0853557	+	0.996351i	$0.472797\pi$
$242$	−8.34135	−0.536202
$243$	3.56904	0.228954
$244$	−30.7273	−1.96711
$245$	0	0
$246$	3.34135	0.213037
$247$	17.3068	1.10121
$248$	−1.47043	−0.0933727
$249$	7.98784	0.506209
$250$	64.0573	4.05134
$251$	−0.504242	−0.0318275	−0.0159137	−	0.999873i	$-0.505066\pi$
$251$	−0.504242	−0.0318275	−0.0159137	+	0.999873i	$0.505066\pi$
$252$	0	0
$253$	−9.20212	−0.578533
$254$	−6.52288	−0.409282
$255$	19.3073	1.20907
$256$	12.2249	0.764055
$257$	6.56482	0.409503	0.204751	−	0.978814i	$-0.434361\pi$
$257$	6.56482	0.409503	0.204751	+	0.978814i	$0.434361\pi$
$258$	−18.6060	−1.15836
$259$	0	0
$260$	26.7336	1.65795
$261$	1.85426	0.114776
$262$	1.66552	0.102896
$263$	15.3587	0.947061	0.473530	−	0.880777i	$-0.342979\pi$
$263$	15.3587	0.947061	0.473530	+	0.880777i	$0.342979\pi$
$264$	2.66504	0.164022
$265$	36.3348	2.23203
$266$	0	0
$267$	19.6063	1.19989
$268$	15.2648	0.932449
$269$	27.4453	1.67337	0.836685	−	0.547684i	$-0.184490\pi$
$269$	27.4453	1.67337	0.836685	+	0.547684i	$0.184490\pi$
$270$	−46.7226	−2.84345
$271$	−3.53419	−0.214687	−0.107344	−	0.994222i	$-0.534234\pi$
$271$	−3.53419	−0.214687	−0.107344	+	0.994222i	$0.534234\pi$
$272$	10.0546	0.609652
$273$	0	0
$274$	11.5808	0.699623
$275$	−48.4154	−2.91956
$276$	8.51891	0.512778
$277$	7.50903	0.451174	0.225587	−	0.974223i	$-0.427570\pi$
$277$	7.50903	0.451174	0.225587	+	0.974223i	$0.427570\pi$
$278$	1.27758	0.0766239
$279$	−1.20467	−0.0721215
$280$	0	0
$281$	17.1221	1.02142	0.510710	−	0.859753i	$-0.329383\pi$
$281$	17.1221	1.02142	0.510710	+	0.859753i	$0.329383\pi$
$282$	3.64551	0.217087
$283$	20.3524	1.20982	0.604911	−	0.796293i	$-0.293209\pi$
$283$	20.3524	1.20982	0.604911	+	0.796293i	$0.293209\pi$
$284$	16.1296	0.957114
$285$	40.6480	2.40778
$286$	−23.0835	−1.36496
$287$	0	0
$288$	−2.80188	−0.165102
$289$	−8.96376	−0.527280
$290$	−46.0434	−2.70376
$291$	25.0017	1.46563
$292$	−0.0371827	−0.00217595
$293$	13.2704	0.775266	0.387633	−	0.921814i	$-0.373293\pi$
$293$	13.2704	0.775266	0.387633	+	0.921814i	$0.373293\pi$
$294$	0	0
$295$	4.84578	0.282132
$296$	−4.79124	−0.278485
$297$	21.1573	1.22767
$298$	−21.4110	−1.24031
$299$	−6.87450	−0.397563
$300$	44.8208	2.58773
$301$	0	0
$302$	−29.4140	−1.69259
$303$	−5.13730	−0.295130
$304$	21.1682	1.21408
$305$	58.2375	3.33467
$306$	−2.00689	−0.114726
$307$	−33.4148	−1.90708	−0.953541	−	0.301264i	$-0.902591\pi$
$307$	−33.4148	−1.90708	−0.953541	+	0.301264i	$0.902591\pi$
$308$	0	0
$309$	10.6292	0.604671
$310$	29.9134	1.69897
$311$	−20.4430	−1.15922	−0.579609	−	0.814895i	$-0.696795\pi$
$311$	−20.4430	−1.15922	−0.579609	+	0.814895i	$0.696795\pi$
$312$	1.99093	0.112714
$313$	−29.0675	−1.64299	−0.821495	−	0.570215i	$-0.806860\pi$
$313$	−29.0675	−1.64299	−0.821495	+	0.570215i	$0.806860\pi$
$314$	6.04023	0.340870
$315$	0	0
$316$	−0.665555	−0.0374404
$317$	−19.0482	−1.06985	−0.534927	−	0.844898i	$-0.679661\pi$
$317$	−19.0482	−1.06985	−0.534927	+	0.844898i	$0.679661\pi$
$318$	29.0445	1.62874
$319$	20.8497	1.16736
$320$	39.9223	2.23172
$321$	−32.4430	−1.81079
$322$	0	0
$323$	16.9188	0.941388
$324$	−17.3024	−0.961242
$325$	−36.1690	−2.00629
$326$	−19.0236	−1.05362
$327$	−22.8386	−1.26298
$328$	0.421375	0.0232665
$329$	0	0
$330$	−54.2155	−2.98447
$331$	−29.9361	−1.64544	−0.822719	−	0.568448i	$-0.807544\pi$
$331$	−29.9361	−1.64544	−0.822719	+	0.568448i	$0.807544\pi$
$332$	10.8123	0.593400
$333$	−3.92527	−0.215104
$334$	28.5635	1.56293
$335$	−28.9315	−1.58070
$336$	0	0
$337$	11.4207	0.622127	0.311064	−	0.950389i	$-0.399315\pi$
$337$	11.4207	0.622127	0.311064	+	0.950389i	$0.399315\pi$
$338$	9.41475	0.512095
$339$	15.2372	0.827572
$340$	26.1342	1.41733
$341$	−13.5456	−0.733535
$342$	−4.22514	−0.228469
$343$	0	0
$344$	−2.34638	−0.126508
$345$	−16.1459	−0.869267
$346$	−32.0111	−1.72093
$347$	−10.4317	−0.560001	−0.280000	−	0.960000i	$-0.590335\pi$
$347$	−10.4317	−0.560001	−0.280000	+	0.960000i	$0.590335\pi$
$348$	−19.3017	−1.03468
$349$	−18.7501	−1.00367	−0.501836	−	0.864963i	$-0.667342\pi$
$349$	−18.7501	−1.00367	−0.501836	+	0.864963i	$0.667342\pi$
$350$	0	0
$351$	15.8057	0.843644
$352$	−31.5050	−1.67922
$353$	21.0092	1.11821	0.559104	−	0.829098i	$-0.311145\pi$
$353$	21.0092	1.11821	0.559104	+	0.829098i	$0.311145\pi$
$354$	3.87351	0.205875
$355$	−30.5704	−1.62251
$356$	26.5390	1.40656
$357$	0	0
$358$	31.6504	1.67277
$359$	30.8388	1.62761	0.813805	−	0.581138i	$-0.197392\pi$
$359$	30.8388	1.62761	0.813805	+	0.581138i	$0.197392\pi$
$360$	−0.608050	−0.0320470
$361$	16.6194	0.874707
$362$	−21.4013	−1.12483
$363$	6.62741	0.347849
$364$	0	0
$365$	0.0704723	0.00368869
$366$	46.5526	2.43334
$367$	−27.6297	−1.44226	−0.721128	−	0.692802i	$-0.756376\pi$
$367$	−27.6297	−1.44226	−0.721128	+	0.692802i	$0.756376\pi$
$368$	−8.40828	−0.438312
$369$	0.345215	0.0179712
$370$	97.4694	5.06719
$371$	0	0
$372$	12.5399	0.650164
$373$	−8.11226	−0.420037	−0.210018	−	0.977697i	$-0.567352\pi$
$373$	−8.11226	−0.420037	−0.210018	+	0.977697i	$0.567352\pi$
$374$	−22.5660	−1.16686
$375$	−50.8951	−2.62821
$376$	0.459732	0.0237089
$377$	15.5759	0.802200
$378$	0	0
$379$	−17.8550	−0.917149	−0.458574	−	0.888656i	$-0.651640\pi$
$379$	−17.8550	−0.917149	−0.458574	+	0.888656i	$0.651640\pi$
$380$	55.0208	2.82251
$381$	5.18259	0.265512
$382$	42.1957	2.15892
$383$	14.5623	0.744097	0.372049	−	0.928213i	$-0.378655\pi$
$383$	14.5623	0.744097	0.372049	+	0.928213i	$0.378655\pi$
$384$	5.46355	0.278811
$385$	0	0
$386$	6.18631	0.314875
$387$	−1.92230	−0.0977158
$388$	33.8421	1.71807
$389$	22.4648	1.13901	0.569505	−	0.821988i	$-0.307135\pi$
$389$	22.4648	1.13901	0.569505	+	0.821988i	$0.307135\pi$
$390$	−40.5020	−2.05090
$391$	−6.72038	−0.339864
$392$	0	0
$393$	−1.32330	−0.0667515
$394$	−39.3758	−1.98372
$395$	1.26143	0.0634693
$396$	2.95538	0.148513
$397$	24.1841	1.21376	0.606882	−	0.794792i	$-0.292420\pi$
$397$	24.1841	1.21376	0.606882	+	0.794792i	$0.292420\pi$
$398$	−28.8439	−1.44581
$399$	0	0
$400$	−44.2387	−2.21194
$401$	−3.05614	−0.152617	−0.0763083	−	0.997084i	$-0.524313\pi$
$401$	−3.05614	−0.152617	−0.0763083	+	0.997084i	$0.524313\pi$
$402$	−23.1266	−1.15345
$403$	−10.1193	−0.504079
$404$	−6.95380	−0.345965
$405$	32.7932	1.62951
$406$	0	0
$407$	−44.1368	−2.18778
$408$	1.94630	0.0963562
$409$	−31.9557	−1.58011	−0.790054	−	0.613037i	$-0.789948\pi$
$409$	−31.9557	−1.58011	−0.790054	+	0.613037i	$0.789948\pi$
$410$	−8.57212	−0.423347
$411$	−9.20125	−0.453864
$412$	14.3875	0.708823
$413$	0	0
$414$	1.67828	0.0824830
$415$	−20.4925	−1.00594
$416$	−23.5360	−1.15395
$417$	−1.01507	−0.0497079
$418$	−47.5086	−2.32372
$419$	28.0474	1.37021	0.685103	−	0.728446i	$-0.259757\pi$
$419$	28.0474	1.37021	0.685103	+	0.728446i	$0.259757\pi$
$420$	0	0
$421$	−5.65162	−0.275443	−0.137722	−	0.990471i	$-0.543978\pi$
$421$	−5.65162	−0.275443	−0.137722	+	0.990471i	$0.543978\pi$
$422$	−5.76409	−0.280591
$423$	0.376640	0.0183128
$424$	3.66278	0.177880
$425$	−35.3581	−1.71512
$426$	−24.4367	−1.18396
$427$	0	0
$428$	−43.9146	−2.12269
$429$	18.3404	0.885484
$430$	47.7330	2.30189
$431$	−29.3226	−1.41242	−0.706209	−	0.708003i	$-0.749596\pi$
$431$	−29.3226	−1.41242	−0.706209	+	0.708003i	$0.749596\pi$
$432$	19.3321	0.930116
$433$	−16.3299	−0.784764	−0.392382	−	0.919802i	$-0.628349\pi$
$433$	−16.3299	−0.784764	−0.392382	+	0.919802i	$0.628349\pi$
$434$	0	0
$435$	36.5826	1.75400
$436$	−30.9142	−1.48052
$437$	−14.1485	−0.676815
$438$	0.0563327	0.00269168
$439$	9.63496	0.459852	0.229926	−	0.973208i	$-0.426152\pi$
$439$	9.63496	0.459852	0.229926	+	0.973208i	$0.426152\pi$
$440$	−6.83707	−0.325944
$441$	0	0
$442$	−16.8581	−0.801857
$443$	−15.1723	−0.720860	−0.360430	−	0.932786i	$-0.617370\pi$
$443$	−15.1723	−0.720860	−0.360430	+	0.932786i	$0.617370\pi$
$444$	40.8599	1.93912
$445$	−50.2993	−2.38442
$446$	−18.2208	−0.862779
$447$	17.0115	0.804619
$448$	0	0
$449$	12.8879	0.608217	0.304108	−	0.952637i	$-0.401642\pi$
$449$	12.8879	0.608217	0.304108	+	0.952637i	$0.401642\pi$
$450$	8.82998	0.416249
$451$	3.88169	0.182782
$452$	20.6250	0.970117
$453$	23.3701	1.09803
$454$	17.3253	0.813116
$455$	0	0
$456$	4.09757	0.191886
$457$	24.4732	1.14481	0.572405	−	0.819971i	$-0.306010\pi$
$457$	24.4732	1.14481	0.572405	+	0.819971i	$0.306010\pi$
$458$	−41.1382	−1.92226
$459$	15.4513	0.721205
$460$	−21.8550	−1.01899
$461$	−32.0535	−1.49288	−0.746441	−	0.665451i	$-0.768239\pi$
$461$	−32.0535	−1.49288	−0.746441	+	0.665451i	$0.768239\pi$
$462$	0	0
$463$	33.4444	1.55429	0.777147	−	0.629319i	$-0.216666\pi$
$463$	33.4444	1.55429	0.777147	+	0.629319i	$0.216666\pi$
$464$	19.0511	0.884424
$465$	−23.7669	−1.10216
$466$	12.8277	0.594233
$467$	−3.76189	−0.174080	−0.0870398	−	0.996205i	$-0.527741\pi$
$467$	−3.76189	−0.174080	−0.0870398	+	0.996205i	$0.527741\pi$
$468$	2.20783	0.102057
$469$	0	0
$470$	−9.35243	−0.431395
$471$	−4.79911	−0.221131
$472$	0.488485	0.0224843
$473$	−21.6148	−0.993849
$474$	1.00833	0.0463143
$475$	−74.4399	−3.41554
$476$	0	0
$477$	3.00076	0.137396
$478$	−1.60404	−0.0733673
$479$	31.5395	1.44108	0.720538	−	0.693416i	$-0.243895\pi$
$479$	31.5395	1.44108	0.720538	+	0.693416i	$0.243895\pi$
$480$	−55.2783	−2.52310
$481$	−32.9726	−1.50342
$482$	−5.43474	−0.247546
$483$	0	0
$484$	8.97080	0.407764
$485$	−64.1410	−2.91249
$486$	−7.31911	−0.332002
$487$	−18.6085	−0.843232	−0.421616	−	0.906775i	$-0.638537\pi$
$487$	−18.6085	−0.843232	−0.421616	+	0.906775i	$0.638537\pi$
$488$	5.87071	0.265754
$489$	15.1147	0.683512
$490$	0	0
$491$	−13.6354	−0.615356	−0.307678	−	0.951490i	$-0.599552\pi$
$491$	−13.6354	−0.615356	−0.307678	+	0.951490i	$0.599552\pi$
$492$	−3.59349	−0.162007
$493$	15.2267	0.685776
$494$	−35.4916	−1.59684
$495$	−5.60133	−0.251761
$496$	−12.3771	−0.555746
$497$	0	0
$498$	−16.3809	−0.734044
$499$	12.6869	0.567942	0.283971	−	0.958833i	$-0.408348\pi$
$499$	12.6869	0.567942	0.283971	+	0.958833i	$0.408348\pi$
$500$	−68.8912	−3.08091
$501$	−22.6944	−1.01391
$502$	1.03406	0.0461524
$503$	11.0219	0.491443	0.245722	−	0.969340i	$-0.420975\pi$
$503$	11.0219	0.491443	0.245722	+	0.969340i	$0.420975\pi$
$504$	0	0
$505$	13.1796	0.586482
$506$	18.8710	0.838920
$507$	−7.48024	−0.332209
$508$	7.01510	0.311245
$509$	40.4492	1.79288	0.896439	−	0.443167i	$-0.146145\pi$
$509$	40.4492	1.79288	0.896439	+	0.443167i	$0.146145\pi$
$510$	−39.5940	−1.75325
$511$	0	0
$512$	−31.7763	−1.40433
$513$	32.5299	1.43623
$514$	−13.4627	−0.593812
$515$	−27.2687	−1.20160
$516$	20.0100	0.880891
$517$	4.23503	0.186257
$518$	0	0
$519$	25.4336	1.11641
$520$	−5.10767	−0.223986
$521$	−7.16831	−0.314049	−0.157025	−	0.987595i	$-0.550190\pi$
$521$	−7.16831	−0.314049	−0.157025	+	0.987595i	$0.550190\pi$
$522$	−3.80257	−0.166434
$523$	−0.993219	−0.0434304	−0.0217152	−	0.999764i	$-0.506913\pi$
$523$	−0.993219	−0.0434304	−0.0217152	+	0.999764i	$0.506913\pi$
$524$	−1.79120	−0.0782491
$525$	0	0
$526$	−31.4966	−1.37332
$527$	−9.89245	−0.430922
$528$	22.4324	0.976244
$529$	−17.3800	−0.755653
$530$	−74.5127	−3.23662
$531$	0.400196	0.0173670
$532$	0	0
$533$	2.89984	0.125606
$534$	−40.2072	−1.73994
$535$	83.2314	3.59841
$536$	−2.91648	−0.125973
$537$	−25.1470	−1.08517
$538$	−56.2828	−2.42652
$539$	0	0
$540$	50.2483	2.16234
$541$	26.2669	1.12930	0.564651	−	0.825330i	$-0.309011\pi$
$541$	26.2669	1.12930	0.564651	+	0.825330i	$0.309011\pi$
$542$	7.24766	0.311314
$543$	17.0039	0.729706
$544$	−23.0084	−0.986475
$545$	58.5917	2.50979
$546$	0	0
$547$	−14.6661	−0.627078	−0.313539	−	0.949575i	$-0.601515\pi$
$547$	−14.6661	−0.627078	−0.313539	+	0.949575i	$0.601515\pi$
$548$	−12.4547	−0.532040
$549$	4.80963	0.205270
$550$	99.2866	4.23359
$551$	32.0570	1.36567
$552$	−1.62761	−0.0692757
$553$	0	0
$554$	−15.3990	−0.654239
$555$	−77.4417	−3.28722
$556$	−1.37398	−0.0582699
$557$	1.46736	0.0621740	0.0310870	−	0.999517i	$-0.490103\pi$
$557$	1.46736	0.0621740	0.0310870	+	0.999517i	$0.490103\pi$
$558$	2.47044	0.104582
$559$	−16.1475	−0.682965
$560$	0	0
$561$	17.9292	0.756973
$562$	−35.1128	−1.48114
$563$	−14.4783	−0.610187	−0.305094	−	0.952322i	$-0.598688\pi$
$563$	−14.4783	−0.610187	−0.305094	+	0.952322i	$0.598688\pi$
$564$	−3.92060	−0.165087
$565$	−39.0905	−1.64455
$566$	−41.7371	−1.75434
$567$	0	0
$568$	−3.08169	−0.129305
$569$	−14.0445	−0.588776	−0.294388	−	0.955686i	$-0.595116\pi$
$569$	−14.0445	−0.588776	−0.294388	+	0.955686i	$0.595116\pi$
$570$	−83.3578	−3.49148
$571$	6.09228	0.254954	0.127477	−	0.991842i	$-0.459312\pi$
$571$	6.09228	0.254954	0.127477	+	0.991842i	$0.459312\pi$
$572$	24.8254	1.03800
$573$	−33.5255	−1.40055
$574$	0	0
$575$	29.5685	1.23309
$576$	3.29704	0.137377
$577$	−40.3527	−1.67990	−0.839952	−	0.542661i	$-0.817417\pi$
$577$	−40.3527	−1.67990	−0.839952	+	0.542661i	$0.817417\pi$
$578$	18.3822	0.764599
$579$	−4.91517	−0.204268
$580$	49.5179	2.05612
$581$	0	0
$582$	−51.2717	−2.12528
$583$	33.7414	1.39742
$584$	0.00710406	0.000293968 0
$585$	−4.18451	−0.173008
$586$	−27.2140	−1.12420
$587$	−16.3902	−0.676494	−0.338247	−	0.941057i	$-0.609834\pi$
$587$	−16.3902	−0.676494	−0.338247	+	0.941057i	$0.609834\pi$
$588$	0	0
$589$	−20.8267	−0.858150
$590$	−9.93736	−0.409115
$591$	31.2850	1.28689
$592$	−40.3292	−1.65752
$593$	5.91021	0.242703	0.121352	−	0.992610i	$-0.461277\pi$
$593$	5.91021	0.242703	0.121352	+	0.992610i	$0.461277\pi$
$594$	−43.3877	−1.78022
$595$	0	0
$596$	23.0267	0.943210
$597$	22.9172	0.937937
$598$	14.0977	0.576498
$599$	39.1714	1.60050	0.800249	−	0.599668i	$-0.204701\pi$
$599$	39.1714	1.60050	0.800249	+	0.599668i	$0.204701\pi$
$600$	−8.56338	−0.349599
$601$	9.37092	0.382248	0.191124	−	0.981566i	$-0.438787\pi$
$601$	9.37092	0.382248	0.191124	+	0.981566i	$0.438787\pi$
$602$	0	0
$603$	−2.38935	−0.0973019
$604$	31.6336	1.28715
$605$	−17.0024	−0.691245
$606$	10.5352	0.427963
$607$	0.399377	0.0162102	0.00810511	−	0.999967i	$-0.497420\pi$
$607$	0.399377	0.0162102	0.00810511	+	0.999967i	$0.497420\pi$
$608$	−48.4398	−1.96450
$609$	0	0
$610$	−119.429	−4.83554
$611$	3.16381	0.127994
$612$	2.15833	0.0872455
$613$	−29.9191	−1.20842	−0.604211	−	0.796824i	$-0.706512\pi$
$613$	−29.9191	−1.20842	−0.604211	+	0.796824i	$0.706512\pi$
$614$	68.5245	2.76542
$615$	6.81076	0.274636
$616$	0	0
$617$	−25.4053	−1.02278	−0.511389	−	0.859350i	$-0.670869\pi$
$617$	−25.4053	−1.02278	−0.511389	+	0.859350i	$0.670869\pi$
$618$	−21.7975	−0.876823
$619$	40.0863	1.61121	0.805603	−	0.592456i	$-0.201842\pi$
$619$	40.0863	1.61121	0.805603	+	0.592456i	$0.201842\pi$
$620$	−32.1707	−1.29201
$621$	−12.9213	−0.518514
$622$	41.9231	1.68096
$623$	0	0
$624$	16.7582	0.670867
$625$	68.2058	2.72823
$626$	59.6094	2.38247
$627$	37.7467	1.50746
$628$	−6.49603	−0.259220
$629$	−32.2334	−1.28523
$630$	0	0
$631$	−31.6380	−1.25949	−0.629744	−	0.776803i	$-0.716840\pi$
$631$	−31.6380	−1.25949	−0.629744	+	0.776803i	$0.716840\pi$
$632$	0.127160	0.00505815
$633$	4.57971	0.182027
$634$	39.0627	1.55138
$635$	−13.2957	−0.527625
$636$	−31.2363	−1.23860
$637$	0	0
$638$	−42.7571	−1.69277
$639$	−2.52470	−0.0998757
$640$	−14.0165	−0.554053
$641$	7.23267	0.285673	0.142837	−	0.989746i	$-0.454378\pi$
$641$	7.23267	0.285673	0.142837	+	0.989746i	$0.454378\pi$
$642$	66.5317	2.62580
$643$	23.1605	0.913360	0.456680	−	0.889631i	$-0.349038\pi$
$643$	23.1605	0.913360	0.456680	+	0.889631i	$0.349038\pi$
$644$	0	0
$645$	−37.9250	−1.49330
$646$	−34.6959	−1.36509
$647$	−33.5485	−1.31893	−0.659463	−	0.751737i	$-0.729216\pi$
$647$	−33.5485	−1.31893	−0.659463	+	0.751737i	$0.729216\pi$
$648$	3.30576	0.129863
$649$	4.49991	0.176637
$650$	74.1726	2.90929
$651$	0	0
$652$	20.4592	0.801243
$653$	20.0321	0.783918	0.391959	−	0.919983i	$-0.371797\pi$
$653$	20.0321	0.783918	0.391959	+	0.919983i	$0.371797\pi$
$654$	46.8358	1.83142
$655$	3.39487	0.132649
$656$	3.54683	0.138480
$657$	0.00582007	0.000227062 0
$658$	0	0
$659$	−11.2992	−0.440153	−0.220076	−	0.975483i	$-0.570631\pi$
$659$	−11.2992	−0.440153	−0.220076	+	0.975483i	$0.570631\pi$
$660$	58.3067	2.26958
$661$	16.2302	0.631282	0.315641	−	0.948879i	$-0.397781\pi$
$661$	16.2302	0.631282	0.315641	+	0.948879i	$0.397781\pi$
$662$	61.3908	2.38602
$663$	13.3941	0.520186
$664$	−2.06578	−0.0801676
$665$	0	0
$666$	8.04966	0.311918
$667$	−12.7335	−0.493042
$668$	−30.7189	−1.18855
$669$	14.4769	0.559707
$670$	59.3306	2.29214
$671$	54.0808	2.08776
$672$	0	0
$673$	−29.9829	−1.15575	−0.577877	−	0.816124i	$-0.696119\pi$
$673$	−29.9829	−1.15575	−0.577877	+	0.816124i	$0.696119\pi$
$674$	−23.4208	−0.902135
$675$	−67.9831	−2.61667
$676$	−10.1252	−0.389431
$677$	4.16061	0.159905	0.0799526	−	0.996799i	$-0.474523\pi$
$677$	4.16061	0.159905	0.0799526	+	0.996799i	$0.474523\pi$
$678$	−31.2473	−1.20005
$679$	0	0
$680$	−4.99316	−0.191479
$681$	−13.7654	−0.527490
$682$	27.7783	1.06369
$683$	−21.8506	−0.836088	−0.418044	−	0.908427i	$-0.637284\pi$
$683$	−21.8506	−0.836088	−0.418044	+	0.908427i	$0.637284\pi$
$684$	4.54397	0.173743
$685$	23.6055	0.901919
$686$	0	0
$687$	32.6853	1.24702
$688$	−19.7502	−0.752967
$689$	25.2067	0.960298
$690$	33.1108	1.26051
$691$	−38.8471	−1.47782	−0.738908	−	0.673807i	$-0.764658\pi$
$691$	−38.8471	−1.47782	−0.738908	+	0.673807i	$0.764658\pi$
$692$	34.4267	1.30871
$693$	0	0
$694$	21.3925	0.812047
$695$	2.60411	0.0987796
$696$	3.68776	0.139784
$697$	2.83483	0.107377
$698$	38.4514	1.45541
$699$	−10.1919	−0.385494
$700$	0	0
$701$	27.1109	1.02396	0.511982	−	0.858996i	$-0.328911\pi$
$701$	27.1109	1.02396	0.511982	+	0.858996i	$0.328911\pi$
$702$	−32.4131	−1.22335
$703$	−67.8615	−2.55944
$704$	37.0728	1.39723
$705$	7.43073	0.279857
$706$	−43.0841	−1.62149
$707$	0	0
$708$	−4.16581	−0.156561
$709$	−30.8582	−1.15890	−0.579452	−	0.815006i	$-0.696733\pi$
$709$	−30.8582	−1.15890	−0.579452	+	0.815006i	$0.696733\pi$
$710$	62.6915	2.35277
$711$	0.104177	0.00390694
$712$	−5.07049	−0.190025
$713$	8.27264	0.309813
$714$	0	0
$715$	−47.0517	−1.75963
$716$	−34.0387	−1.27209
$717$	1.27445	0.0475953
$718$	−63.2420	−2.36017
$719$	−42.2796	−1.57676	−0.788382	−	0.615186i	$-0.789081\pi$
$719$	−42.2796	−1.57676	−0.788382	+	0.615186i	$0.789081\pi$
$720$	−5.11812	−0.190741
$721$	0	0
$722$	−34.0819	−1.26840
$723$	4.31803	0.160589
$724$	23.0163	0.855394
$725$	−66.9949	−2.48813
$726$	−13.5910	−0.504409
$727$	−5.41952	−0.200999	−0.100499	−	0.994937i	$-0.532044\pi$
$727$	−5.41952	−0.200999	−0.100499	+	0.994937i	$0.532044\pi$
$728$	0	0
$729$	29.3508	1.08707
$730$	−0.144519	−0.00534891
$731$	−15.7854	−0.583846
$732$	−50.0655	−1.85048
$733$	21.0545	0.777666	0.388833	−	0.921308i	$-0.372878\pi$
$733$	21.0545	0.777666	0.388833	+	0.921308i	$0.372878\pi$
$734$	56.6608	2.09139
$735$	0	0
$736$	19.2409	0.709231
$737$	−26.8665	−0.989640
$738$	−0.707942	−0.0260597
$739$	−17.8330	−0.655999	−0.328000	−	0.944678i	$-0.606374\pi$
$739$	−17.8330	−0.655999	−0.328000	+	0.944678i	$0.606374\pi$
$740$	−104.825	−3.85343
$741$	28.1989	1.03591
$742$	0	0
$743$	16.5883	0.608566	0.304283	−	0.952582i	$-0.401583\pi$
$743$	16.5883	0.608566	0.304283	+	0.952582i	$0.401583\pi$
$744$	−2.39585	−0.0878362
$745$	−43.6425	−1.59894
$746$	16.6360	0.609088
$747$	−1.69241	−0.0619219
$748$	24.2689	0.887358
$749$	0	0
$750$	104.372	3.81112
$751$	18.6754	0.681475	0.340738	−	0.940158i	$-0.389323\pi$
$751$	18.6754	0.681475	0.340738	+	0.940158i	$0.389323\pi$
$752$	3.86969	0.141113
$753$	−0.821587	−0.0299403
$754$	−31.9419	−1.16326
$755$	−59.9553	−2.18200
$756$	0	0
$757$	19.5129	0.709207	0.354604	−	0.935017i	$-0.384616\pi$
$757$	19.5129	0.709207	0.354604	+	0.935017i	$0.384616\pi$
$758$	36.6157	1.32994
$759$	−14.9935	−0.544229
$760$	−10.5122	−0.381317
$761$	34.9159	1.26570	0.632850	−	0.774275i	$-0.281885\pi$
$761$	34.9159	1.26570	0.632850	+	0.774275i	$0.281885\pi$
$762$	−10.6281	−0.385014
$763$	0	0
$764$	−45.3798	−1.64178
$765$	−4.09070	−0.147899
$766$	−29.8632	−1.07900
$767$	3.36168	0.121383
$768$	19.9186	0.718751
$769$	29.1970	1.05287	0.526436	−	0.850215i	$-0.323528\pi$
$769$	29.1970	1.05287	0.526436	+	0.850215i	$0.323528\pi$
$770$	0	0
$771$	10.6964	0.385222
$772$	−6.65314	−0.239452
$773$	1.20889	0.0434809	0.0217404	−	0.999764i	$-0.493079\pi$
$773$	1.20889	0.0434809	0.0217404	+	0.999764i	$0.493079\pi$
$774$	3.94210	0.141696
$775$	43.5251	1.56347
$776$	−6.46582	−0.232109
$777$	0	0
$778$	−46.0691	−1.65166
$779$	5.96820	0.213833
$780$	43.5584	1.55964
$781$	−28.3884	−1.01582
$782$	13.7817	0.492831
$783$	29.2764	1.04625
$784$	0	0
$785$	12.3119	0.439432
$786$	2.71372	0.0967952
$787$	−5.37827	−0.191715	−0.0958574	−	0.995395i	$-0.530559\pi$
$787$	−5.37827	−0.191715	−0.0958574	+	0.995395i	$0.530559\pi$
$788$	42.3471	1.50855
$789$	25.0248	0.890906
$790$	−2.58684	−0.0920357
$791$	0	0
$792$	−0.564650	−0.0200640
$793$	40.4013	1.43469
$794$	−49.5949	−1.76006
$795$	59.2021	2.09968
$796$	31.0205	1.09949
$797$	6.31630	0.223735	0.111867	−	0.993723i	$-0.464317\pi$
$797$	6.31630	0.223735	0.111867	+	0.993723i	$0.464317\pi$
$798$	0	0
$799$	3.09288	0.109418
$800$	101.233	3.57912
$801$	−4.15405	−0.146776
$802$	6.26731	0.221307
$803$	0.0654423	0.00230941
$804$	24.8718	0.877161
$805$	0	0
$806$	20.7519	0.730956
$807$	44.7181	1.57415
$808$	1.32858	0.0467394
$809$	36.9224	1.29812	0.649061	−	0.760737i	$-0.275162\pi$
$809$	36.9224	1.29812	0.649061	+	0.760737i	$0.275162\pi$
$810$	−67.2498	−2.36292
$811$	27.9336	0.980881	0.490440	−	0.871475i	$-0.336836\pi$
$811$	27.9336	0.980881	0.490440	+	0.871475i	$0.336836\pi$
$812$	0	0
$813$	−5.75844	−0.201957
$814$	90.5124	3.17246
$815$	−38.7763	−1.35827
$816$	16.3825	0.573504
$817$	−33.2333	−1.16269
$818$	65.5324	2.29129
$819$	0	0
$820$	9.21898	0.321941
$821$	−31.8187	−1.11048	−0.555241	−	0.831690i	$-0.687374\pi$
$821$	−31.8187	−1.11048	−0.555241	+	0.831690i	$0.687374\pi$
$822$	18.8692	0.658140
$823$	−22.2582	−0.775873	−0.387936	−	0.921686i	$-0.626812\pi$
$823$	−22.2582	−0.775873	−0.387936	+	0.921686i	$0.626812\pi$
$824$	−2.74886	−0.0957610
$825$	−78.8856	−2.74644
$826$	0	0
$827$	−18.1696	−0.631818	−0.315909	−	0.948790i	$-0.602309\pi$
$827$	−18.1696	−0.631818	−0.315909	+	0.948790i	$0.602309\pi$
$828$	−1.80493	−0.0627255
$829$	5.08080	0.176464	0.0882318	−	0.996100i	$-0.471878\pi$
$829$	5.08080	0.176464	0.0882318	+	0.996100i	$0.471878\pi$
$830$	42.0245	1.45869
$831$	12.2348	0.424422
$832$	27.6955	0.960167
$833$	0	0
$834$	2.08162	0.0720806
$835$	58.2216	2.01484
$836$	51.0936	1.76711
$837$	−19.0202	−0.657435
$838$	−57.5176	−1.98691
$839$	−17.1539	−0.592220	−0.296110	−	0.955154i	$-0.595690\pi$
$839$	−17.1539	−0.592220	−0.296110	+	0.955154i	$0.595690\pi$
$840$	0	0
$841$	−0.149125	−0.00514225
$842$	11.5899	0.399415
$843$	27.8980	0.960857
$844$	6.19905	0.213380
$845$	19.1903	0.660166
$846$	−0.772385	−0.0265551
$847$	0	0
$848$	30.8306	1.05873
$849$	33.1611	1.13809
$850$	72.5098	2.48706
$851$	26.9555	0.924022
$852$	26.2807	0.900363
$853$	33.0648	1.13212	0.566058	−	0.824365i	$-0.308468\pi$
$853$	33.0648	1.13212	0.566058	+	0.824365i	$0.308468\pi$
$854$	0	0
$855$	−8.61220	−0.294531
$856$	8.39025	0.286773
$857$	−28.8188	−0.984430	−0.492215	−	0.870474i	$-0.663813\pi$
$857$	−28.8188	−0.984430	−0.492215	+	0.870474i	$0.663813\pi$
$858$	−37.6112	−1.28402
$859$	−12.1956	−0.416109	−0.208054	−	0.978117i	$-0.566713\pi$
$859$	−12.1956	−0.416109	−0.208054	+	0.978117i	$0.566713\pi$
$860$	−51.3350	−1.75051
$861$	0	0
$862$	60.1325	2.04812
$863$	51.2533	1.74468	0.872341	−	0.488898i	$-0.162601\pi$
$863$	51.2533	1.74468	0.872341	+	0.488898i	$0.162601\pi$
$864$	−44.2382	−1.50502
$865$	−65.2490	−2.21853
$866$	33.4881	1.13797
$867$	−14.6051	−0.496015
$868$	0	0
$869$	1.17139	0.0397368
$870$	−75.0209	−2.54345
$871$	−20.0708	−0.680072
$872$	5.90641	0.200016
$873$	−5.29719	−0.179283
$874$	29.0147	0.981438
$875$	0	0
$876$	−0.0605836	−0.00204693
$877$	34.9693	1.18083	0.590415	−	0.807100i	$-0.298964\pi$
$877$	34.9693	1.18083	0.590415	+	0.807100i	$0.298964\pi$
$878$	−19.7587	−0.666823
$879$	21.6222	0.729298
$880$	−57.5495	−1.93999
$881$	−10.7634	−0.362629	−0.181315	−	0.983425i	$-0.558035\pi$
$881$	−10.7634	−0.362629	−0.181315	+	0.983425i	$0.558035\pi$
$882$	0	0
$883$	8.19089	0.275645	0.137823	−	0.990457i	$-0.455990\pi$
$883$	8.19089	0.275645	0.137823	+	0.990457i	$0.455990\pi$
$884$	18.1302	0.609785
$885$	7.89547	0.265403
$886$	31.1143	1.04531
$887$	8.15811	0.273922	0.136961	−	0.990576i	$-0.456266\pi$
$887$	8.15811	0.273922	0.136961	+	0.990576i	$0.456266\pi$
$888$	−7.80662	−0.261973
$889$	0	0
$890$	103.150	3.45760
$891$	30.4526	1.02020
$892$	19.5957	0.656114
$893$	6.51148	0.217898
$894$	−34.8860	−1.16676
$895$	64.5137	2.15646
$896$	0	0
$897$	−11.2010	−0.373990
$898$	−26.4295	−0.881964
$899$	−18.7438	−0.625139
$900$	−9.49630	−0.316543
$901$	24.6416	0.820930
$902$	−7.96028	−0.265048
$903$	0	0
$904$	−3.94057	−0.131061
$905$	−43.6228	−1.45007
$906$	−47.9258	−1.59223
$907$	49.8468	1.65514	0.827568	−	0.561366i	$-0.189724\pi$
$907$	49.8468	1.65514	0.827568	+	0.561366i	$0.189724\pi$
$908$	−18.6327	−0.618347
$909$	1.08845	0.0361017
$910$	0	0
$911$	28.3058	0.937814	0.468907	−	0.883248i	$-0.344648\pi$
$911$	28.3058	0.937814	0.468907	+	0.883248i	$0.344648\pi$
$912$	34.4904	1.14209
$913$	−19.0299	−0.629796
$914$	−50.1879	−1.66007
$915$	94.8893	3.13694
$916$	44.2425	1.46181
$917$	0	0
$918$	−31.6864	−1.04581
$919$	−17.9029	−0.590562	−0.295281	−	0.955410i	$-0.595413\pi$
$919$	−17.9029	−0.590562	−0.295281	+	0.955410i	$0.595413\pi$
$920$	4.17558	0.137665
$921$	−54.4444	−1.79400
$922$	65.7330	2.16480
$923$	−21.2077	−0.698061
$924$	0	0
$925$	141.822	4.66306
$926$	−68.5854	−2.25385
$927$	−2.25203	−0.0739663
$928$	−43.5952	−1.43108
$929$	1.87457	0.0615026	0.0307513	−	0.999527i	$-0.490210\pi$
$929$	1.87457	0.0615026	0.0307513	+	0.999527i	$0.490210\pi$
$930$	48.7394	1.59823
$931$	0	0
$932$	−13.7957	−0.451894
$933$	−33.3089	−1.09048
$934$	7.71461	0.252430
$935$	−45.9968	−1.50426
$936$	−0.421825	−0.0137878
$937$	−40.1232	−1.31077	−0.655385	−	0.755295i	$-0.727493\pi$
$937$	−40.1232	−1.31077	−0.655385	+	0.755295i	$0.727493\pi$
$938$	0	0
$939$	−47.3611	−1.54557
$940$	10.0582	0.328061
$941$	25.8994	0.844296	0.422148	−	0.906527i	$-0.361276\pi$
$941$	25.8994	0.844296	0.422148	+	0.906527i	$0.361276\pi$
$942$	9.84166	0.320658
$943$	−2.37065	−0.0771990
$944$	4.11172	0.133825
$945$	0	0
$946$	44.3260	1.44116
$947$	−30.0394	−0.976149	−0.488075	−	0.872802i	$-0.662301\pi$
$947$	−30.0394	−0.976149	−0.488075	+	0.872802i	$0.662301\pi$
$948$	−1.08442	−0.0352204
$949$	0.0488891	0.00158701
$950$	152.656	4.95281
$951$	−31.0362	−1.00642
$952$	0	0
$953$	26.0657	0.844351	0.422176	−	0.906514i	$-0.361267\pi$
$953$	26.0657	0.844351	0.422176	+	0.906514i	$0.361267\pi$
$954$	−6.15375	−0.199235
$955$	86.0084	2.78317
$956$	1.72509	0.0557933
$957$	33.9715	1.09814
$958$	−64.6788	−2.08968
$959$	0	0
$960$	65.0474	2.09940
$961$	−18.8226	−0.607181
$962$	67.6178	2.18009
$963$	6.87380	0.221505
$964$	5.84485	0.188250
$965$	12.6097	0.405921
$966$	0	0
$967$	18.8556	0.606355	0.303177	−	0.952934i	$-0.401953\pi$
$967$	18.8556	0.606355	0.303177	+	0.952934i	$0.401953\pi$
$968$	−1.71395	−0.0550883
$969$	27.5667	0.885570
$970$	131.536	4.22336
$971$	25.3185	0.812509	0.406254	−	0.913760i	$-0.366835\pi$
$971$	25.3185	0.812509	0.406254	+	0.913760i	$0.366835\pi$
$972$	7.87142	0.252476
$973$	0	0
$974$	38.1609	1.22276
$975$	−58.9319	−1.88733
$976$	49.4154	1.58175
$977$	2.44950	0.0783666	0.0391833	−	0.999232i	$-0.487524\pi$
$977$	2.44950	0.0783666	0.0391833	+	0.999232i	$0.487524\pi$
$978$	−30.9962	−0.991148
$979$	−46.7092	−1.49283
$980$	0	0
$981$	4.83889	0.154494
$982$	27.9624	0.892317
$983$	−19.4862	−0.621515	−0.310757	−	0.950489i	$-0.600583\pi$
$983$	−19.4862	−0.621515	−0.310757	+	0.950489i	$0.600583\pi$
$984$	0.686567	0.0218870
$985$	−80.2606	−2.55732
$986$	−31.2258	−0.994432
$987$	0	0
$988$	38.1698	1.21434
$989$	13.2007	0.419758
$990$	11.4868	0.365074
$991$	−1.00263	−0.0318497	−0.0159249	−	0.999873i	$-0.505069\pi$
$991$	−1.00263	−0.0318497	−0.0159249	+	0.999873i	$0.505069\pi$
$992$	28.3228	0.899250
$993$	−48.7765	−1.54787
$994$	0	0
$995$	−58.7932	−1.86387
$996$	17.6170	0.558216
$997$	14.2052	0.449882	0.224941	−	0.974372i	$-0.427781\pi$
$997$	14.2052	0.449882	0.224941	+	0.974372i	$0.427781\pi$
$998$	−26.0173	−0.823563
$999$	−61.9753	−1.96081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.o.1.2		6
7.6	odd	2		287.2.a.f.1.2	✓	6
21.20	even	2		2583.2.a.t.1.5		6
28.27	even	2		4592.2.a.bg.1.4		6
35.34	odd	2		7175.2.a.p.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.f.1.2	✓	6	7.6	odd	2
2009.2.a.o.1.2		6	1.1	even	1	trivial
2583.2.a.t.1.5		6	21.20	even	2
4592.2.a.bg.1.4		6	28.27	even	2
7175.2.a.p.1.5		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)

\(f(q)\)	\(=\)	\(q-2.05073 q^{2} +1.62935 q^{3} +2.20548 q^{4} -4.18004 q^{5} -3.34135 q^{6} -0.421375 q^{8} -0.345215 q^{9} +O(q^{10})\)	\(q-2.05073 q^{2} +1.62935 q^{3} +2.20548 q^{4} -4.18004 q^{5} -3.34135 q^{6} -0.421375 q^{8} -0.345215 q^{9} +8.57212 q^{10} -3.88169 q^{11} +3.59349 q^{12} -2.89984 q^{13} -6.81076 q^{15} -3.54683 q^{16} -2.83483 q^{17} +0.707942 q^{18} -5.96820 q^{19} -9.21898 q^{20} +7.96028 q^{22} +2.37065 q^{23} -0.686567 q^{24} +12.4728 q^{25} +5.94677 q^{26} -5.45053 q^{27} -5.37130 q^{29} +13.9670 q^{30} +3.48961 q^{31} +8.11632 q^{32} -6.32463 q^{33} +5.81345 q^{34} -0.761364 q^{36} +11.3705 q^{37} +12.2391 q^{38} -4.72486 q^{39} +1.76136 q^{40} -1.00000 q^{41} +5.56840 q^{43} -8.56097 q^{44} +1.44301 q^{45} -4.86155 q^{46} -1.09103 q^{47} -5.77903 q^{48} -25.5782 q^{50} -4.61893 q^{51} -6.39552 q^{52} -8.69245 q^{53} +11.1775 q^{54} +16.2256 q^{55} -9.72430 q^{57} +11.0151 q^{58} -1.15927 q^{59} -15.0210 q^{60} -13.9323 q^{61} -7.15624 q^{62} -9.55069 q^{64} +12.1214 q^{65} +12.9701 q^{66} +6.92134 q^{67} -6.25214 q^{68} +3.86262 q^{69} +7.31342 q^{71} +0.145465 q^{72} -0.0168592 q^{73} -23.3178 q^{74} +20.3225 q^{75} -13.1627 q^{76} +9.68938 q^{78} -0.301774 q^{79} +14.8259 q^{80} -7.84518 q^{81} +2.05073 q^{82} +4.90247 q^{83} +11.8497 q^{85} -11.4193 q^{86} -8.75173 q^{87} +1.63565 q^{88} +12.0332 q^{89} -2.95923 q^{90} +5.22841 q^{92} +5.68580 q^{93} +2.23740 q^{94} +24.9473 q^{95} +13.2243 q^{96} +15.3446 q^{97} +1.34002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 4 q^{3} + 9 q^{4} + q^{5} + 4 q^{6} + 3 q^{8} + 14 q^{9}+O(q^{10}) \) 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

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