LMFDB - Embedded newform 2009.2.a.n.1.3

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:	$1$
Dimension:	$5$
Coefficient field:	5.5.633117.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + 4x^{2} + 6x - 3 $ x^5 - x^4 - 6x^3 + 4x^2 + 6*x - 3
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			1.3
Root			$0.460315$ 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)

$f(q)$	$=$	$q-0.460315 q^{2} -0.539685 q^{3} -1.78811 q^{4} -4.10136 q^{5} +0.248425 q^{6} +1.74372 q^{8} -2.70874 q^{9} +O(q^{10})$	\(q-0.460315 q^{2} -0.539685 q^{3} -1.78811 q^{4} -4.10136 q^{5} +0.248425 q^{6} +1.74372 q^{8} -2.70874 q^{9} +1.88791 q^{10} +2.76768 q^{11} +0.965017 q^{12} +4.05697 q^{13} +2.21344 q^{15} +2.77356 q^{16} -5.22447 q^{17} +1.24687 q^{18} +0.109209 q^{19} +7.33368 q^{20} -1.27400 q^{22} +6.08681 q^{23} -0.941062 q^{24} +11.8211 q^{25} -1.86748 q^{26} +3.08092 q^{27} +2.25431 q^{29} -1.01888 q^{30} +1.18073 q^{31} -4.76415 q^{32} -1.49368 q^{33} +2.40490 q^{34} +4.84353 q^{36} -8.95429 q^{37} -0.0502704 q^{38} -2.18949 q^{39} -7.15163 q^{40} +1.00000 q^{41} -7.93974 q^{43} -4.94891 q^{44} +11.1095 q^{45} -2.80185 q^{46} +10.5714 q^{47} -1.49685 q^{48} -5.44143 q^{50} +2.81957 q^{51} -7.25431 q^{52} +6.23100 q^{53} -1.41819 q^{54} -11.3512 q^{55} -0.0589384 q^{57} -1.03769 q^{58} +9.43006 q^{59} -3.95788 q^{60} -6.89732 q^{61} -0.543506 q^{62} -3.35411 q^{64} -16.6391 q^{65} +0.687561 q^{66} -1.35699 q^{67} +9.34193 q^{68} -3.28496 q^{69} -7.90672 q^{71} -4.72329 q^{72} -9.88791 q^{73} +4.12179 q^{74} -6.37969 q^{75} -0.195277 q^{76} +1.00785 q^{78} -12.5668 q^{79} -11.3754 q^{80} +6.46349 q^{81} -0.460315 q^{82} +14.9633 q^{83} +21.4274 q^{85} +3.65478 q^{86} -1.21662 q^{87} +4.82606 q^{88} +0.852931 q^{89} -5.11387 q^{90} -10.8839 q^{92} -0.637221 q^{93} -4.86616 q^{94} -0.447904 q^{95} +2.57115 q^{96} -9.92806 q^{97} -7.49692 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9}+O(q^{10}) $ 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9	$ 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9} + 2 q^{11} + 2 q^{12} - 5 q^{13} - 5 q^{15} - q^{16} - 13 q^{17} + 21 q^{18} + 23 q^{20} + q^{22} + 2 q^{23} - 2 q^{24} + 22 q^{25} - 10 q^{27} - 5 q^{29} - 33 q^{30} - 17 q^{31} - 12 q^{32} - 3 q^{33} + 8 q^{34} + 15 q^{36} - 7 q^{37} + 3 q^{38} + 5 q^{39} - 7 q^{40} + 5 q^{41} + q^{43} - 47 q^{44} + 23 q^{45} - 24 q^{46} - 9 q^{47} + 19 q^{48} + 2 q^{50} + 5 q^{51} - 20 q^{52} + 5 q^{53} - 2 q^{54} - 33 q^{55} - 3 q^{57} - 27 q^{58} - 7 q^{59} - 16 q^{60} - 22 q^{61} + 28 q^{62} - 3 q^{64} - 31 q^{65} + 42 q^{66} - 3 q^{67} - 17 q^{68} + 22 q^{69} - 24 q^{71} - 12 q^{72} - 40 q^{73} - 5 q^{74} - 24 q^{75} + 19 q^{76} + 30 q^{78} - 42 q^{79} - 24 q^{80} + 9 q^{81} - q^{82} + 12 q^{83} - 23 q^{85} + 16 q^{86} + 32 q^{87} + 26 q^{88} - 8 q^{89} + 59 q^{90} + 12 q^{92} - 11 q^{93} + 23 q^{94} - 17 q^{95} + 17 q^{96} - 16 q^{97} - 45 q^{99}+O(q^{100}) $ 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9 + 2 * q^11 + 2 * q^12 - 5 * q^13 - 5 * q^15 - q^16 - 13 * q^17 + 21 * q^18 + 23 * q^20 + q^22 + 2 * q^23 - 2 * q^24 + 22 * q^25 - 10 * q^27 - 5 * q^29 - 33 * q^30 - 17 * q^31 - 12 * q^32 - 3 * q^33 + 8 * q^34 + 15 * q^36 - 7 * q^37 + 3 * q^38 + 5 * q^39 - 7 * q^40 + 5 * q^41 + q^43 - 47 * q^44 + 23 * q^45 - 24 * q^46 - 9 * q^47 + 19 * q^48 + 2 * q^50 + 5 * q^51 - 20 * q^52 + 5 * q^53 - 2 * q^54 - 33 * q^55 - 3 * q^57 - 27 * q^58 - 7 * q^59 - 16 * q^60 - 22 * q^61 + 28 * q^62 - 3 * q^64 - 31 * q^65 + 42 * q^66 - 3 * q^67 - 17 * q^68 + 22 * q^69 - 24 * q^71 - 12 * q^72 - 40 * q^73 - 5 * q^74 - 24 * q^75 + 19 * q^76 + 30 * q^78 - 42 * q^79 - 24 * q^80 + 9 * q^81 - q^82 + 12 * q^83 - 23 * q^85 + 16 * q^86 + 32 * q^87 + 26 * q^88 - 8 * q^89 + 59 * q^90 + 12 * q^92 - 11 * q^93 + 23 * q^94 - 17 * q^95 + 17 * q^96 - 16 * q^97 - 45 * 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 $

$2$	−0.460315	−0.325492	−0.162746	−	0.986668i	$-0.552035\pi$
$2$	−0.460315	−0.325492	−0.162746	+	0.986668i	$0.552035\pi$
$3$	−0.539685	−0.311588	−0.155794	−	0.987790i	$-0.549794\pi$
$3$	−0.539685	−0.311588	−0.155794	+	0.987790i	$0.549794\pi$
$4$	−1.78811	−0.894055
$5$	−4.10136	−1.83418	−0.917091	−	0.398678i	$-0.869469\pi$
$5$	−4.10136	−1.83418	−0.917091	+	0.398678i	$0.869469\pi$
$6$	0.248425	0.101419
$7$	0	0
$7$	0	0
$8$	1.74372	0.616499
$9$	−2.70874	−0.902913
$10$	1.88791	0.597011
$11$	2.76768	0.834486	0.417243	−	0.908795i	$-0.362996\pi$
$11$	2.76768	0.834486	0.417243	+	0.908795i	$0.362996\pi$
$12$	0.965017	0.278576
$13$	4.05697	1.12520	0.562600	−	0.826729i	$-0.309801\pi$
$13$	4.05697	1.12520	0.562600	+	0.826729i	$0.309801\pi$
$14$	0	0
$15$	2.21344	0.571508
$16$	2.77356	0.693390
$17$	−5.22447	−1.26712	−0.633560	−	0.773694i	$-0.718407\pi$
$17$	−5.22447	−1.26712	−0.633560	+	0.773694i	$0.718407\pi$
$18$	1.24687	0.293891
$19$	0.109209	0.0250542	0.0125271	−	0.999922i	$-0.496012\pi$
$19$	0.109209	0.0250542	0.0125271	+	0.999922i	$0.496012\pi$
$20$	7.33368	1.63986
$21$	0	0
$22$	−1.27400	−0.271618
$23$	6.08681	1.26919	0.634593	−	0.772846i	$-0.281168\pi$
$23$	6.08681	1.26919	0.634593	+	0.772846i	$0.281168\pi$
$24$	−0.941062	−0.192093
$25$	11.8211	2.36422
$26$	−1.86748	−0.366243
$27$	3.08092	0.592924
$28$	0	0
$29$	2.25431	0.418614	0.209307	−	0.977850i	$-0.432879\pi$
$29$	2.25431	0.418614	0.209307	+	0.977850i	$0.432879\pi$
$30$	−1.01888	−0.186021
$31$	1.18073	0.212065	0.106032	−	0.994363i	$-0.466185\pi$
$31$	1.18073	0.212065	0.106032	+	0.994363i	$0.466185\pi$
$32$	−4.76415	−0.842192
$33$	−1.49368	−0.260016
$34$	2.40490	0.412437
$35$	0	0
$36$	4.84353	0.807254
$37$	−8.95429	−1.47208	−0.736038	−	0.676940i	$-0.763305\pi$
$37$	−8.95429	−1.47208	−0.736038	+	0.676940i	$0.763305\pi$
$38$	−0.0502704	−0.00815494
$39$	−2.18949	−0.350598
$40$	−7.15163	−1.13077
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−7.93974	−1.21080	−0.605399	−	0.795922i	$-0.706987\pi$
$43$	−7.93974	−1.21080	−0.605399	+	0.795922i	$0.706987\pi$
$44$	−4.94891	−0.746077
$45$	11.1095	1.65611
$46$	−2.80185	−0.413110
$47$	10.5714	1.54199	0.770997	−	0.636839i	$-0.219758\pi$
$47$	10.5714	1.54199	0.770997	+	0.636839i	$0.219758\pi$
$48$	−1.49685	−0.216052
$49$	0	0
$50$	−5.44143	−0.769535
$51$	2.81957	0.394819
$52$	−7.25431	−1.00599
$53$	6.23100	0.855893	0.427947	−	0.903804i	$-0.359237\pi$
$53$	6.23100	0.855893	0.427947	+	0.903804i	$0.359237\pi$
$54$	−1.41819	−0.192992
$55$	−11.3512	−1.53060
$56$	0	0
$57$	−0.0589384	−0.00780658
$58$	−1.03769	−0.136255
$59$	9.43006	1.22769	0.613845	−	0.789427i	$-0.289622\pi$
$59$	9.43006	1.22769	0.613845	+	0.789427i	$0.289622\pi$
$60$	−3.95788	−0.510960
$61$	−6.89732	−0.883111	−0.441556	−	0.897234i	$-0.645573\pi$
$61$	−6.89732	−0.883111	−0.441556	+	0.897234i	$0.645573\pi$
$62$	−0.543506	−0.0690253
$63$	0	0
$64$	−3.35411	−0.419264
$65$	−16.6391	−2.06382
$66$	0.687561	0.0846329
$67$	−1.35699	−0.165782	−0.0828912	−	0.996559i	$-0.526415\pi$
$67$	−1.35699	−0.165782	−0.0828912	+	0.996559i	$0.526415\pi$
$68$	9.34193	1.13288
$69$	−3.28496	−0.395463
$70$	0	0
$71$	−7.90672	−0.938356	−0.469178	−	0.883104i	$-0.655450\pi$
$71$	−7.90672	−0.938356	−0.469178	+	0.883104i	$0.655450\pi$
$72$	−4.72329	−0.556645
$73$	−9.88791	−1.15729	−0.578646	−	0.815579i	$-0.696419\pi$
$73$	−9.88791	−1.15729	−0.578646	+	0.815579i	$0.696419\pi$
$74$	4.12179	0.479148
$75$	−6.37969	−0.736663
$76$	−0.195277	−0.0223999
$77$	0	0
$78$	1.00785	0.114117
$79$	−12.5668	−1.41388	−0.706939	−	0.707275i	$-0.749924\pi$
$79$	−12.5668	−1.41388	−0.706939	+	0.707275i	$0.749924\pi$
$80$	−11.3754	−1.27180
$81$	6.46349	0.718165
$82$	−0.460315	−0.0508332
$83$	14.9633	1.64244	0.821220	−	0.570611i	$-0.193294\pi$
$83$	14.9633	1.64244	0.821220	+	0.570611i	$0.193294\pi$
$84$	0	0
$85$	21.4274	2.32413
$86$	3.65478	0.394105
$87$	−1.21662	−0.130435
$88$	4.82606	0.514460
$89$	0.852931	0.0904105	0.0452053	−	0.998978i	$-0.485606\pi$
$89$	0.852931	0.0904105	0.0452053	+	0.998978i	$0.485606\pi$
$90$	−5.11387	−0.539049
$91$	0	0
$92$	−10.8839	−1.13472
$93$	−0.637221	−0.0660768
$94$	−4.86616	−0.501906
$95$	−0.447904	−0.0459540
$96$	2.57115	0.262416
$97$	−9.92806	−1.00804	−0.504021	−	0.863691i	$-0.668147\pi$
$97$	−9.92806	−1.00804	−0.504021	+	0.863691i	$0.668147\pi$
$98$	0	0
$99$	−7.49692	−0.753469
$100$	−21.1375	−2.11375
$101$	−11.2908	−1.12348	−0.561740	−	0.827314i	$-0.689868\pi$
$101$	−11.2908	−1.12348	−0.561740	+	0.827314i	$0.689868\pi$
$102$	−1.29789	−0.128510
$103$	10.8690	1.07096	0.535479	−	0.844549i	$-0.320131\pi$
$103$	10.8690	1.07096	0.535479	+	0.844549i	$0.320131\pi$
$104$	7.07423	0.693685
$105$	0	0
$106$	−2.86822	−0.278586
$107$	1.99215	0.192588	0.0962941	−	0.995353i	$-0.469301\pi$
$107$	1.99215	0.192588	0.0962941	+	0.995353i	$0.469301\pi$
$108$	−5.50903	−0.530107
$109$	−17.8607	−1.71074	−0.855371	−	0.518016i	$-0.826671\pi$
$109$	−17.8607	−1.71074	−0.855371	+	0.518016i	$0.826671\pi$
$110$	5.22514	0.498197
$111$	4.83250	0.458680
$112$	0	0
$113$	−16.2536	−1.52901	−0.764506	−	0.644616i	$-0.777017\pi$
$113$	−16.2536	−1.52901	−0.764506	+	0.644616i	$0.777017\pi$
$114$	0.0271302	0.00254098
$115$	−24.9642	−2.32792
$116$	−4.03095	−0.374264
$117$	−10.9893	−1.01596
$118$	−4.34079	−0.399602
$119$	0	0
$120$	3.85963	0.352334
$121$	−3.33996	−0.303633
$122$	3.17494	0.287445
$123$	−0.539685	−0.0486618
$124$	−2.11127	−0.189598
$125$	−27.9759	−2.50224
$126$	0	0
$127$	17.3566	1.54015	0.770073	−	0.637955i	$-0.220220\pi$
$127$	17.3566	1.54015	0.770073	+	0.637955i	$0.220220\pi$
$128$	11.0723	0.978658
$129$	4.28496	0.377270
$130$	7.65921	0.671757
$131$	0.803568	0.0702080	0.0351040	−	0.999384i	$-0.488824\pi$
$131$	0.803568	0.0702080	0.0351040	+	0.999384i	$0.488824\pi$
$132$	2.67086	0.232468
$133$	0	0
$134$	0.624641	0.0539608
$135$	−12.6360	−1.08753
$136$	−9.11002	−0.781178
$137$	−4.63907	−0.396343	−0.198171	−	0.980167i	$-0.563500\pi$
$137$	−4.63907	−0.396343	−0.198171	+	0.980167i	$0.563500\pi$
$138$	1.51212	0.128720
$139$	0.0641748	0.00544323	0.00272162	−	0.999996i	$-0.499134\pi$
$139$	0.0641748	0.00544323	0.00272162	+	0.999996i	$0.499134\pi$
$140$	0	0
$141$	−5.70522	−0.480466
$142$	3.63958	0.305427
$143$	11.2284	0.938964
$144$	−7.51285	−0.626071
$145$	−9.24572	−0.767815
$146$	4.55155	0.376689
$147$	0	0
$148$	16.0113	1.31612
$149$	14.2436	1.16688	0.583440	−	0.812156i	$-0.301706\pi$
$149$	14.2436	1.16688	0.583440	+	0.812156i	$0.301706\pi$
$150$	2.93666	0.239778
$151$	12.8350	1.04450	0.522249	−	0.852793i	$-0.325093\pi$
$151$	12.8350	1.04450	0.522249	+	0.852793i	$0.325093\pi$
$152$	0.190430	0.0154459
$153$	14.1517	1.14410
$154$	0	0
$155$	−4.84258	−0.388966
$156$	3.91504	0.313454
$157$	−14.3051	−1.14167	−0.570835	−	0.821064i	$-0.693381\pi$
$157$	−14.3051	−1.14167	−0.570835	+	0.821064i	$0.693381\pi$
$158$	5.78469	0.460205
$159$	−3.36278	−0.266686
$160$	19.5395	1.54473
$161$	0	0
$162$	−2.97524	−0.233757
$163$	5.60958	0.439376	0.219688	−	0.975570i	$-0.429496\pi$
$163$	5.60958	0.439376	0.219688	+	0.975570i	$0.429496\pi$
$164$	−1.78811	−0.139628
$165$	6.12610	0.476916
$166$	−6.88785	−0.534600
$167$	−4.49350	−0.347717	−0.173859	−	0.984771i	$-0.555624\pi$
$167$	−4.49350	−0.347717	−0.173859	+	0.984771i	$0.555624\pi$
$168$	0	0
$169$	3.45899	0.266076
$170$	−9.86335	−0.756484
$171$	−0.295818	−0.0226218
$172$	14.1971	1.08252
$173$	−14.2512	−1.08350	−0.541749	−	0.840541i	$-0.682238\pi$
$173$	−14.2512	−1.08350	−0.541749	+	0.840541i	$0.682238\pi$
$174$	0.560026	0.0424555
$175$	0	0
$176$	7.67632	0.578625
$177$	−5.08927	−0.382533
$178$	−0.392617	−0.0294279
$179$	5.78841	0.432646	0.216323	−	0.976322i	$-0.430594\pi$
$179$	5.78841	0.432646	0.216323	+	0.976322i	$0.430594\pi$
$180$	−19.8650	−1.48065
$181$	14.6662	1.09013	0.545065	−	0.838394i	$-0.316505\pi$
$181$	14.6662	1.09013	0.545065	+	0.838394i	$0.316505\pi$
$182$	0	0
$183$	3.72238	0.275166
$184$	10.6137	0.782452
$185$	36.7247	2.70006
$186$	0.293322	0.0215074
$187$	−14.4596	−1.05739
$188$	−18.9028	−1.37863
$189$	0	0
$190$	0.206177	0.0149576
$191$	8.41984	0.609238	0.304619	−	0.952474i	$-0.401471\pi$
$191$	8.41984	0.609238	0.304619	+	0.952474i	$0.401471\pi$
$192$	1.81016	0.130637
$193$	−8.76374	−0.630828	−0.315414	−	0.948954i	$-0.602143\pi$
$193$	−8.76374	−0.630828	−0.315414	+	0.948954i	$0.602143\pi$
$194$	4.57003	0.328109
$195$	8.97986	0.643061
$196$	0	0
$197$	−18.9953	−1.35336	−0.676680	−	0.736277i	$-0.736582\pi$
$197$	−18.9953	−1.35336	−0.676680	+	0.736277i	$0.736582\pi$
$198$	3.45094	0.245248
$199$	6.81886	0.483376	0.241688	−	0.970354i	$-0.422299\pi$
$199$	6.81886	0.483376	0.241688	+	0.970354i	$0.422299\pi$
$200$	20.6128	1.45754
$201$	0.732347	0.0516558
$202$	5.19734	0.365684
$203$	0	0
$204$	−5.04170	−0.352990
$205$	−4.10136	−0.286451
$206$	−5.00317	−0.348588
$207$	−16.4876	−1.14597
$208$	11.2522	0.780203
$209$	0.302255	0.0209074
$210$	0	0
$211$	5.02073	0.345641	0.172821	−	0.984953i	$-0.444712\pi$
$211$	5.02073	0.345641	0.172821	+	0.984953i	$0.444712\pi$
$212$	−11.1417	−0.765216
$213$	4.26714	0.292380
$214$	−0.917014	−0.0626858
$215$	32.5637	2.22083
$216$	5.37228	0.365537
$217$	0	0
$218$	8.22152	0.556832
$219$	5.33636	0.360598
$220$	20.2973	1.36844
$221$	−21.1955	−1.42576
$222$	−2.22447	−0.149297
$223$	−6.96231	−0.466231	−0.233115	−	0.972449i	$-0.574892\pi$
$223$	−6.96231	−0.466231	−0.233115	+	0.972449i	$0.574892\pi$
$224$	0	0
$225$	−32.0203	−2.13469
$226$	7.48178	0.497681
$227$	−10.1094	−0.670987	−0.335493	−	0.942043i	$-0.608903\pi$
$227$	−10.1094	−0.670987	−0.335493	+	0.942043i	$0.608903\pi$
$228$	0.105388	0.00697952
$229$	2.32356	0.153545	0.0767725	−	0.997049i	$-0.475538\pi$
$229$	2.32356	0.153545	0.0767725	+	0.997049i	$0.475538\pi$
$230$	11.4914	0.757718
$231$	0	0
$232$	3.93089	0.258075
$233$	17.5655	1.15075	0.575377	−	0.817888i	$-0.304855\pi$
$233$	17.5655	1.15075	0.575377	+	0.817888i	$0.304855\pi$
$234$	5.05852	0.330686
$235$	−43.3570	−2.82830
$236$	−16.8620	−1.09762
$237$	6.78213	0.440547
$238$	0	0
$239$	−23.0063	−1.48815	−0.744077	−	0.668093i	$-0.767111\pi$
$239$	−23.0063	−1.48815	−0.744077	+	0.668093i	$0.767111\pi$
$240$	6.13912	0.396278
$241$	12.6808	0.816839	0.408420	−	0.912794i	$-0.366080\pi$
$241$	12.6808	0.816839	0.408420	+	0.912794i	$0.366080\pi$
$242$	1.53743	0.0988298
$243$	−12.7310	−0.816695
$244$	12.3332	0.789550
$245$	0	0
$246$	0.248425	0.0158390
$247$	0.443057	0.0281910
$248$	2.05886	0.130738
$249$	−8.07550	−0.511764
$250$	12.8777	0.814457
$251$	18.5629	1.17168	0.585840	−	0.810427i	$-0.300765\pi$
$251$	18.5629	1.17168	0.585840	+	0.810427i	$0.300765\pi$
$252$	0	0
$253$	16.8463	1.05912
$254$	−7.98948	−0.501305
$255$	−11.5641	−0.724170
$256$	1.61150	0.100719
$257$	−18.1358	−1.13128	−0.565639	−	0.824653i	$-0.691370\pi$
$257$	−18.1358	−1.13128	−0.565639	+	0.824653i	$0.691370\pi$
$258$	−1.97243	−0.122798
$259$	0	0
$260$	29.7525	1.84517
$261$	−6.10633	−0.377972
$262$	−0.369894	−0.0228521
$263$	4.24808	0.261948	0.130974	−	0.991386i	$-0.458190\pi$
$263$	4.24808	0.261948	0.130974	+	0.991386i	$0.458190\pi$
$264$	−2.60456	−0.160299
$265$	−25.5555	−1.56986
$266$	0	0
$267$	−0.460315	−0.0281708
$268$	2.42644	0.148219
$269$	1.31427	0.0801326	0.0400663	−	0.999197i	$-0.487243\pi$
$269$	1.31427	0.0801326	0.0400663	+	0.999197i	$0.487243\pi$
$270$	5.81652	0.353982
$271$	7.91618	0.480874	0.240437	−	0.970665i	$-0.422709\pi$
$271$	7.91618	0.480874	0.240437	+	0.970665i	$0.422709\pi$
$272$	−14.4904	−0.878608
$273$	0	0
$274$	2.13543	0.129006
$275$	32.7171	1.97291
$276$	5.87387	0.353566
$277$	0.0684353	0.00411188	0.00205594	−	0.999998i	$-0.499346\pi$
$277$	0.0684353	0.00411188	0.00205594	+	0.999998i	$0.499346\pi$
$278$	−0.0295406	−0.00177173
$279$	−3.19828	−0.191476
$280$	0	0
$281$	8.33050	0.496956	0.248478	−	0.968638i	$-0.420070\pi$
$281$	8.33050	0.496956	0.248478	+	0.968638i	$0.420070\pi$
$282$	2.62619	0.156388
$283$	−3.09424	−0.183934	−0.0919668	−	0.995762i	$-0.529315\pi$
$283$	−3.09424	−0.183934	−0.0919668	+	0.995762i	$0.529315\pi$
$284$	14.1381	0.838942
$285$	0.241727	0.0143187
$286$	−5.16859	−0.305625
$287$	0	0
$288$	12.9049	0.760426
$289$	10.2951	0.605593
$290$	4.25594	0.249917
$291$	5.35803	0.314093
$292$	17.6807	1.03468
$293$	−4.47354	−0.261347	−0.130674	−	0.991425i	$-0.541714\pi$
$293$	−4.47354	−0.261347	−0.130674	+	0.991425i	$0.541714\pi$
$294$	0	0
$295$	−38.6760	−2.25181
$296$	−15.6138	−0.907533
$297$	8.52700	0.494787
$298$	−6.55653	−0.379809
$299$	24.6940	1.42809
$300$	11.4076	0.658617
$301$	0	0
$302$	−5.90813	−0.339975
$303$	6.09350	0.350063
$304$	0.302897	0.0173723
$305$	28.2884	1.61979
$306$	−6.51425	−0.372395
$307$	−25.8316	−1.47429	−0.737143	−	0.675737i	$-0.763825\pi$
$307$	−25.8316	−1.47429	−0.737143	+	0.675737i	$0.763825\pi$
$308$	0	0
$309$	−5.86586	−0.333697
$310$	2.22911	0.126605
$311$	−13.6802	−0.775735	−0.387867	−	0.921715i	$-0.626788\pi$
$311$	−13.6802	−0.775735	−0.387867	+	0.921715i	$0.626788\pi$
$312$	−3.81786	−0.216144
$313$	−24.0537	−1.35959	−0.679797	−	0.733400i	$-0.737932\pi$
$313$	−24.0537	−1.35959	−0.679797	+	0.733400i	$0.737932\pi$
$314$	6.58484	0.371604
$315$	0	0
$316$	22.4709	1.26408
$317$	3.80766	0.213859	0.106930	−	0.994267i	$-0.465898\pi$
$317$	3.80766	0.213859	0.106930	+	0.994267i	$0.465898\pi$
$318$	1.54794	0.0868039
$319$	6.23920	0.349328
$320$	13.7564	0.769006
$321$	−1.07513	−0.0600081
$322$	0	0
$323$	−0.570558	−0.0317467
$324$	−11.5574	−0.642080
$325$	47.9579	2.66023
$326$	−2.58217	−0.143013
$327$	9.63914	0.533046
$328$	1.74372	0.0962810
$329$	0	0
$330$	−2.81993	−0.155232
$331$	−21.1336	−1.16161	−0.580805	−	0.814043i	$-0.697262\pi$
$331$	−21.1336	−1.16161	−0.580805	+	0.814043i	$0.697262\pi$
$332$	−26.7561	−1.46843
$333$	24.2548	1.32916
$334$	2.06842	0.113179
$335$	5.56549	0.304075
$336$	0	0
$337$	−20.7801	−1.13197	−0.565983	−	0.824417i	$-0.691503\pi$
$337$	−20.7801	−1.13197	−0.565983	+	0.824417i	$0.691503\pi$
$338$	−1.59222	−0.0866055
$339$	8.77185	0.476421
$340$	−38.3146	−2.07790
$341$	3.26787	0.176965
$342$	0.136169	0.00736320
$343$	0	0
$344$	−13.8447	−0.746456
$345$	13.4728	0.725351
$346$	6.56003	0.352669
$347$	21.8355	1.17219	0.586096	−	0.810242i	$-0.300664\pi$
$347$	21.8355	1.17219	0.586096	+	0.810242i	$0.300664\pi$
$348$	2.17545	0.116616
$349$	6.23178	0.333579	0.166790	−	0.985992i	$-0.446660\pi$
$349$	6.23178	0.333579	0.166790	+	0.985992i	$0.446660\pi$
$350$	0	0
$351$	12.4992	0.667158
$352$	−13.1856	−0.702797
$353$	−28.5933	−1.52187	−0.760933	−	0.648830i	$-0.775258\pi$
$353$	−28.5933	−1.52187	−0.760933	+	0.648830i	$0.775258\pi$
$354$	2.34266	0.124511
$355$	32.4283	1.72112
$356$	−1.52514	−0.0808320
$357$	0	0
$358$	−2.66449	−0.140823
$359$	6.89008	0.363644	0.181822	−	0.983331i	$-0.441800\pi$
$359$	6.89008	0.363644	0.181822	+	0.983331i	$0.441800\pi$
$360$	19.3719	1.02099
$361$	−18.9881	−0.999372
$362$	−6.75107	−0.354828
$363$	1.80253	0.0946081
$364$	0	0
$365$	40.5539	2.12269
$366$	−1.71347	−0.0895644
$367$	−27.9358	−1.45824	−0.729119	−	0.684387i	$-0.760070\pi$
$367$	−27.9358	−1.45824	−0.729119	+	0.684387i	$0.760070\pi$
$368$	16.8821	0.880042
$369$	−2.70874	−0.141011
$370$	−16.9049	−0.878845
$371$	0	0
$372$	1.13942	0.0590763
$373$	6.20063	0.321057	0.160528	−	0.987031i	$-0.448680\pi$
$373$	6.20063	0.321057	0.160528	+	0.987031i	$0.448680\pi$
$374$	6.65599	0.344173
$375$	15.0982	0.779666
$376$	18.4335	0.950637
$377$	9.14565	0.471025
$378$	0	0
$379$	−18.4006	−0.945174	−0.472587	−	0.881284i	$-0.656680\pi$
$379$	−18.4006	−0.945174	−0.472587	+	0.881284i	$0.656680\pi$
$380$	0.800902	0.0410854
$381$	−9.36709	−0.479890
$382$	−3.87577	−0.198302
$383$	34.2322	1.74918	0.874591	−	0.484861i	$-0.161130\pi$
$383$	34.2322	1.74918	0.874591	+	0.484861i	$0.161130\pi$
$384$	−5.97554	−0.304938
$385$	0	0
$386$	4.03408	0.205329
$387$	21.5067	1.09325
$388$	17.7525	0.901245
$389$	−23.0399	−1.16817	−0.584085	−	0.811693i	$-0.698546\pi$
$389$	−23.0399	−1.16817	−0.584085	+	0.811693i	$0.698546\pi$
$390$	−4.13356	−0.209311
$391$	−31.8003	−1.60821
$392$	0	0
$393$	−0.433674	−0.0218760
$394$	8.74382	0.440507
$395$	51.5410	2.59331
$396$	13.4053	0.673643
$397$	−1.35123	−0.0678165	−0.0339082	−	0.999425i	$-0.510795\pi$
$397$	−1.35123	−0.0678165	−0.0339082	+	0.999425i	$0.510795\pi$
$398$	−3.13882	−0.157335
$399$	0	0
$400$	32.7866	1.63933
$401$	1.54256	0.0770319	0.0385160	−	0.999258i	$-0.487737\pi$
$401$	1.54256	0.0770319	0.0385160	+	0.999258i	$0.487737\pi$
$402$	−0.337110	−0.0168135
$403$	4.79017	0.238615
$404$	20.1893	1.00445
$405$	−26.5091	−1.31725
$406$	0	0
$407$	−24.7826	−1.22843
$408$	4.91655	0.243405
$409$	−4.34571	−0.214882	−0.107441	−	0.994211i	$-0.534266\pi$
$409$	−4.34571	−0.214882	−0.107441	+	0.994211i	$0.534266\pi$
$410$	1.88791	0.0932374
$411$	2.50364	0.123495
$412$	−19.4350	−0.957495
$413$	0	0
$414$	7.58947	0.373002
$415$	−61.3700	−3.01254
$416$	−19.3280	−0.947634
$417$	−0.0346342	−0.00169604
$418$	−0.139132	−0.00680518
$419$	−27.2835	−1.33288	−0.666442	−	0.745557i	$-0.732184\pi$
$419$	−27.2835	−1.33288	−0.666442	+	0.745557i	$0.732184\pi$
$420$	0	0
$421$	−16.6168	−0.809853	−0.404927	−	0.914349i	$-0.632703\pi$
$421$	−16.6168	−0.809853	−0.404927	+	0.914349i	$0.632703\pi$
$422$	−2.31111	−0.112503
$423$	−28.6351	−1.39229
$424$	10.8651	0.527657
$425$	−61.7591	−2.99576
$426$	−1.96423	−0.0951672
$427$	0	0
$428$	−3.56218	−0.172184
$429$	−6.05979	−0.292570
$430$	−14.9895	−0.722860
$431$	−9.36507	−0.451099	−0.225550	−	0.974232i	$-0.572418\pi$
$431$	−9.36507	−0.451099	−0.225550	+	0.974232i	$0.572418\pi$
$432$	8.54513	0.411128
$433$	3.87136	0.186046	0.0930228	−	0.995664i	$-0.470347\pi$
$433$	3.87136	0.186046	0.0930228	+	0.995664i	$0.470347\pi$
$434$	0	0
$435$	4.98978	0.239242
$436$	31.9368	1.52950
$437$	0.664733	0.0317985
$438$	−2.45641	−0.117372
$439$	−29.6011	−1.41279	−0.706393	−	0.707820i	$-0.749679\pi$
$439$	−29.6011	−1.41279	−0.706393	+	0.707820i	$0.749679\pi$
$440$	−19.7934	−0.943613
$441$	0	0
$442$	9.75660	0.464074
$443$	−0.570558	−0.0271080	−0.0135540	−	0.999908i	$-0.504315\pi$
$443$	−0.570558	−0.0271080	−0.0135540	+	0.999908i	$0.504315\pi$
$444$	−8.64104	−0.410086
$445$	−3.49817	−0.165829
$446$	3.20485	0.151754
$447$	−7.68705	−0.363585
$448$	0	0
$449$	18.8280	0.888551	0.444275	−	0.895890i	$-0.353461\pi$
$449$	18.8280	0.888551	0.444275	+	0.895890i	$0.353461\pi$
$450$	14.7394	0.694823
$451$	2.76768	0.130325
$452$	29.0633	1.36702
$453$	−6.92686	−0.325452
$454$	4.65352	0.218401
$455$	0	0
$456$	−0.102772	−0.00481275
$457$	22.2732	1.04190	0.520949	−	0.853588i	$-0.325578\pi$
$457$	22.2732	1.04190	0.520949	+	0.853588i	$0.325578\pi$
$458$	−1.06957	−0.0499776
$459$	−16.0962	−0.751306
$460$	44.6387	2.08129
$461$	−4.47354	−0.208354	−0.104177	−	0.994559i	$-0.533221\pi$
$461$	−4.47354	−0.208354	−0.104177	+	0.994559i	$0.533221\pi$
$462$	0	0
$463$	−3.62240	−0.168347	−0.0841736	−	0.996451i	$-0.526825\pi$
$463$	−3.62240	−0.168347	−0.0841736	+	0.996451i	$0.526825\pi$
$464$	6.25246	0.290263
$465$	2.61347	0.121197
$466$	−8.08565	−0.374561
$467$	1.54346	0.0714226	0.0357113	−	0.999362i	$-0.488630\pi$
$467$	1.54346	0.0714226	0.0357113	+	0.999362i	$0.488630\pi$
$468$	19.6500	0.908323
$469$	0	0
$470$	19.9578	0.920587
$471$	7.72025	0.355730
$472$	16.4434	0.756869
$473$	−21.9746	−1.01039
$474$	−3.12191	−0.143394
$475$	1.29097	0.0592338
$476$	0	0
$477$	−16.8781	−0.772797
$478$	10.5901	0.484382
$479$	14.5913	0.666693	0.333347	−	0.942804i	$-0.391822\pi$
$479$	14.5913	0.666693	0.333347	+	0.942804i	$0.391822\pi$
$480$	−10.5452	−0.481320
$481$	−36.3273	−1.65638
$482$	−5.83713	−0.265874
$483$	0	0
$484$	5.97221	0.271464
$485$	40.7185	1.84893
$486$	5.86027	0.265827
$487$	−1.52440	−0.0690771	−0.0345385	−	0.999403i	$-0.510996\pi$
$487$	−1.52440	−0.0690771	−0.0345385	+	0.999403i	$0.510996\pi$
$488$	−12.0270	−0.544437
$489$	−3.02741	−0.136904
$490$	0	0
$491$	−34.8827	−1.57424	−0.787118	−	0.616802i	$-0.788428\pi$
$491$	−34.8827	−1.57424	−0.787118	+	0.616802i	$0.788428\pi$
$492$	0.965017	0.0435063
$493$	−11.7776	−0.530435
$494$	−0.203945	−0.00917594
$495$	30.7475	1.38200
$496$	3.27482	0.147044
$497$	0	0
$498$	3.71727	0.166575
$499$	14.7766	0.661490	0.330745	−	0.943720i	$-0.392700\pi$
$499$	14.7766	0.661490	0.330745	+	0.943720i	$0.392700\pi$
$500$	50.0239	2.23714
$501$	2.42507	0.108344
$502$	−8.54478	−0.381372
$503$	−18.9590	−0.845338	−0.422669	−	0.906284i	$-0.638907\pi$
$503$	−18.9590	−0.845338	−0.422669	+	0.906284i	$0.638907\pi$
$504$	0	0
$505$	46.3078	2.06067
$506$	−7.75461	−0.344734
$507$	−1.86677	−0.0829060
$508$	−31.0355	−1.37698
$509$	17.0790	0.757011	0.378506	−	0.925599i	$-0.376438\pi$
$509$	17.0790	0.757011	0.378506	+	0.925599i	$0.376438\pi$
$510$	5.32311	0.235711
$511$	0	0
$512$	−22.8863	−1.01144
$513$	0.336464	0.0148552
$514$	8.34815	0.368221
$515$	−44.5778	−1.96433
$516$	−7.66198	−0.337300
$517$	29.2582	1.28677
$518$	0	0
$519$	7.69116	0.337604
$520$	−29.0139	−1.27234
$521$	−25.3095	−1.10883	−0.554415	−	0.832240i	$-0.687058\pi$
$521$	−25.3095	−1.10883	−0.554415	+	0.832240i	$0.687058\pi$
$522$	2.81083	0.123027
$523$	4.43499	0.193928	0.0969642	−	0.995288i	$-0.469087\pi$
$523$	4.43499	0.193928	0.0969642	+	0.995288i	$0.469087\pi$
$524$	−1.43687	−0.0627699
$525$	0	0
$526$	−1.95545	−0.0852617
$527$	−6.16867	−0.268712
$528$	−4.14280	−0.180292
$529$	14.0492	0.610835
$530$	11.7636	0.510978
$531$	−25.5436	−1.10850
$532$	0	0
$533$	4.05697	0.175727
$534$	0.211889	0.00916935
$535$	−8.17051	−0.353242
$536$	−2.36621	−0.102205
$537$	−3.12392	−0.134807
$538$	−0.604979	−0.0260825
$539$	0	0
$540$	22.5945	0.972313
$541$	−5.57149	−0.239537	−0.119769	−	0.992802i	$-0.538215\pi$
$541$	−5.57149	−0.239537	−0.119769	+	0.992802i	$0.538215\pi$
$542$	−3.64393	−0.156520
$543$	−7.91514	−0.339671
$544$	24.8902	1.06716
$545$	73.2529	3.13781
$546$	0	0
$547$	38.0432	1.62661	0.813304	−	0.581839i	$-0.197666\pi$
$547$	38.0432	1.62661	0.813304	+	0.581839i	$0.197666\pi$
$548$	8.29517	0.354352
$549$	18.6830	0.797373
$550$	−15.0601	−0.642167
$551$	0.246190	0.0104881
$552$	−5.72806	−0.243802
$553$	0	0
$554$	−0.0315018	−0.00133838
$555$	−19.8198	−0.841304
$556$	−0.114752	−0.00486655
$557$	−19.0835	−0.808594	−0.404297	−	0.914628i	$-0.632484\pi$
$557$	−19.0835	−0.808594	−0.404297	+	0.914628i	$0.632484\pi$
$558$	1.47222	0.0623239
$559$	−32.2113	−1.36239
$560$	0	0
$561$	7.80366	0.329471
$562$	−3.83465	−0.161755
$563$	19.1867	0.808621	0.404311	−	0.914622i	$-0.367511\pi$
$563$	19.1867	0.808621	0.404311	+	0.914622i	$0.367511\pi$
$564$	10.2016	0.429563
$565$	66.6619	2.80449
$566$	1.42432	0.0598688
$567$	0	0
$568$	−13.7871	−0.578495
$569$	29.3295	1.22956	0.614778	−	0.788700i	$-0.289246\pi$
$569$	29.3295	1.22956	0.614778	+	0.788700i	$0.289246\pi$
$570$	−0.111271	−0.00466061
$571$	−21.5864	−0.903362	−0.451681	−	0.892180i	$-0.649175\pi$
$571$	−21.5864	−0.903362	−0.451681	+	0.892180i	$0.649175\pi$
$572$	−20.0776	−0.839486
$573$	−4.54406	−0.189831
$574$	0	0
$575$	71.9529	3.00064
$576$	9.08541	0.378559
$577$	−5.28198	−0.219892	−0.109946	−	0.993938i	$-0.535068\pi$
$577$	−5.28198	−0.219892	−0.109946	+	0.993938i	$0.535068\pi$
$578$	−4.73898	−0.197115
$579$	4.72966	0.196558
$580$	16.5324	0.686469
$581$	0	0
$582$	−2.46638	−0.102235
$583$	17.2454	0.714231
$584$	−17.2418	−0.713470
$585$	45.0709	1.86345
$586$	2.05924	0.0850662
$587$	41.8869	1.72886	0.864428	−	0.502757i	$-0.167681\pi$
$587$	41.8869	1.72886	0.864428	+	0.502757i	$0.167681\pi$
$588$	0	0
$589$	0.128946	0.00531312
$590$	17.8031	0.732944
$591$	10.2515	0.421690
$592$	−24.8353	−1.02072
$593$	−25.8605	−1.06196	−0.530982	−	0.847383i	$-0.678177\pi$
$593$	−25.8605	−1.06196	−0.530982	+	0.847383i	$0.678177\pi$
$594$	−3.92510	−0.161049
$595$	0	0
$596$	−25.4691	−1.04325
$597$	−3.68004	−0.150614
$598$	−11.3670	−0.464831
$599$	−39.4470	−1.61176	−0.805881	−	0.592078i	$-0.798308\pi$
$599$	−39.4470	−1.61176	−0.805881	+	0.592078i	$0.798308\pi$
$600$	−11.1244	−0.454152
$601$	−40.0435	−1.63341	−0.816704	−	0.577056i	$-0.804201\pi$
$601$	−40.0435	−1.63341	−0.816704	+	0.577056i	$0.804201\pi$
$602$	0	0
$603$	3.67573	0.149687
$604$	−22.9504	−0.933838
$605$	13.6984	0.556918
$606$	−2.80493	−0.113942
$607$	10.7580	0.436653	0.218327	−	0.975876i	$-0.429940\pi$
$607$	10.7580	0.436653	0.218327	+	0.975876i	$0.429940\pi$
$608$	−0.520288	−0.0211004
$609$	0	0
$610$	−13.0215	−0.527227
$611$	42.8877	1.73505
$612$	−25.3049	−1.02289
$613$	16.7220	0.675393	0.337697	−	0.941255i	$-0.390352\pi$
$613$	16.7220	0.675393	0.337697	+	0.941255i	$0.390352\pi$
$614$	11.8906	0.479867
$615$	2.21344	0.0892546
$616$	0	0
$617$	−42.3381	−1.70447	−0.852234	−	0.523160i	$-0.824753\pi$
$617$	−42.3381	−1.70447	−0.852234	+	0.523160i	$0.824753\pi$
$618$	2.70014	0.108616
$619$	−32.0830	−1.28952	−0.644762	−	0.764384i	$-0.723043\pi$
$619$	−32.0830	−1.28952	−0.644762	+	0.764384i	$0.723043\pi$
$620$	8.65907	0.347757
$621$	18.7530	0.752531
$622$	6.29721	0.252495
$623$	0	0
$624$	−6.07267	−0.243101
$625$	55.6333	2.22533
$626$	11.0723	0.442536
$627$	−0.163123	−0.00651449
$628$	25.5791	1.02072
$629$	46.7814	1.86530
$630$	0	0
$631$	−44.9458	−1.78927	−0.894633	−	0.446802i	$-0.852563\pi$
$631$	−44.9458	−1.78927	−0.894633	+	0.446802i	$0.852563\pi$
$632$	−21.9130	−0.871654
$633$	−2.70961	−0.107698
$634$	−1.75272	−0.0696094
$635$	−71.1855	−2.82491
$636$	6.01302	0.238432
$637$	0	0
$638$	−2.87199	−0.113703
$639$	21.4173	0.847254
$640$	−45.4113	−1.79504
$641$	10.4353	0.412171	0.206085	−	0.978534i	$-0.433928\pi$
$641$	10.4353	0.412171	0.206085	+	0.978534i	$0.433928\pi$
$642$	0.494899	0.0195321
$643$	33.1360	1.30676	0.653378	−	0.757032i	$-0.273351\pi$
$643$	33.1360	1.30676	0.653378	+	0.757032i	$0.273351\pi$
$644$	0	0
$645$	−17.5742	−0.691981
$646$	0.262636	0.0103333
$647$	29.4094	1.15620	0.578101	−	0.815965i	$-0.303794\pi$
$647$	29.4094	1.15620	0.578101	+	0.815965i	$0.303794\pi$
$648$	11.2705	0.442748
$649$	26.0994	1.02449
$650$	−22.0757	−0.865881
$651$	0	0
$652$	−10.0306	−0.392827
$653$	−41.0121	−1.60493	−0.802464	−	0.596701i	$-0.796478\pi$
$653$	−41.0121	−1.60493	−0.802464	+	0.596701i	$0.796478\pi$
$654$	−4.43704	−0.173502
$655$	−3.29572	−0.128774
$656$	2.77356	0.108289
$657$	26.7838	1.04493
$658$	0	0
$659$	41.6194	1.62126	0.810631	−	0.585558i	$-0.199124\pi$
$659$	41.6194	1.62126	0.810631	+	0.585558i	$0.199124\pi$
$660$	−10.9541	−0.426389
$661$	43.0712	1.67527	0.837637	−	0.546227i	$-0.183936\pi$
$661$	43.0712	1.67527	0.837637	+	0.546227i	$0.183936\pi$
$662$	9.72812	0.378094
$663$	11.4389	0.444250
$664$	26.0919	1.01256
$665$	0	0
$666$	−11.1649	−0.432629
$667$	13.7215	0.531300
$668$	8.03487	0.310878
$669$	3.75746	0.145272
$670$	−2.56188	−0.0989739
$671$	−19.0896	−0.736944
$672$	0	0
$673$	44.0679	1.69869	0.849346	−	0.527837i	$-0.176997\pi$
$673$	44.0679	1.69869	0.849346	+	0.527837i	$0.176997\pi$
$674$	9.56540	0.368445
$675$	36.4200	1.40181
$676$	−6.18506	−0.237887
$677$	−5.02017	−0.192941	−0.0964704	−	0.995336i	$-0.530755\pi$
$677$	−5.02017	−0.192941	−0.0964704	+	0.995336i	$0.530755\pi$
$678$	−4.03781	−0.155071
$679$	0	0
$680$	37.3635	1.43282
$681$	5.45592	0.209071
$682$	−1.50425	−0.0576007
$683$	24.9476	0.954595	0.477297	−	0.878742i	$-0.341616\pi$
$683$	24.9476	0.954595	0.477297	+	0.878742i	$0.341616\pi$
$684$	0.528956	0.0202251
$685$	19.0265	0.726965
$686$	0	0
$687$	−1.25399	−0.0478427
$688$	−22.0213	−0.839556
$689$	25.2790	0.963052
$690$	−6.20172	−0.236096
$691$	−42.8508	−1.63012	−0.815061	−	0.579375i	$-0.803297\pi$
$691$	−42.8508	−1.63012	−0.815061	+	0.579375i	$0.803297\pi$
$692$	25.4827	0.968706
$693$	0	0
$694$	−10.0512	−0.381538
$695$	−0.263204	−0.00998389
$696$	−2.12144	−0.0804131
$697$	−5.22447	−0.197891
$698$	−2.86858	−0.108577
$699$	−9.47984	−0.358560
$700$	0	0
$701$	−46.3548	−1.75079	−0.875397	−	0.483404i	$-0.839400\pi$
$701$	−46.3548	−1.75079	−0.875397	+	0.483404i	$0.839400\pi$
$702$	−5.75357	−0.217154
$703$	−0.977887	−0.0368817
$704$	−9.28310	−0.349870
$705$	23.3991	0.881262
$706$	13.1619	0.495355
$707$	0	0
$708$	9.10017	0.342005
$709$	10.9521	0.411316	0.205658	−	0.978624i	$-0.434067\pi$
$709$	10.9521	0.411316	0.205658	+	0.978624i	$0.434067\pi$
$710$	−14.9272	−0.560208
$711$	34.0402	1.27661
$712$	1.48728	0.0557380
$713$	7.18686	0.269150
$714$	0	0
$715$	−46.0516	−1.72223
$716$	−10.3503	−0.386809
$717$	12.4162	0.463691
$718$	−3.17160	−0.118363
$719$	−7.62700	−0.284439	−0.142220	−	0.989835i	$-0.545424\pi$
$719$	−7.62700	−0.284439	−0.142220	+	0.989835i	$0.545424\pi$
$720$	30.8129	1.14833
$721$	0	0
$722$	8.74049	0.325287
$723$	−6.84362	−0.254517
$724$	−26.2248	−0.974637
$725$	26.6484	0.989698
$726$	−0.829729	−0.0307941
$727$	37.2537	1.38166	0.690832	−	0.723015i	$-0.257244\pi$
$727$	37.2537	1.38166	0.690832	+	0.723015i	$0.257244\pi$
$728$	0	0
$729$	−12.5197	−0.463693
$730$	−18.6675	−0.690916
$731$	41.4809	1.53423
$732$	−6.65603	−0.246014
$733$	−7.99745	−0.295393	−0.147696	−	0.989033i	$-0.547186\pi$
$733$	−7.99745	−0.295393	−0.147696	+	0.989033i	$0.547186\pi$
$734$	12.8593	0.474644
$735$	0	0
$736$	−28.9985	−1.06890
$737$	−3.75571	−0.138343
$738$	1.24687	0.0458980
$739$	19.7183	0.725350	0.362675	−	0.931916i	$-0.381864\pi$
$739$	19.7183	0.725350	0.362675	+	0.931916i	$0.381864\pi$
$740$	−65.6679	−2.41400
$741$	−0.239111	−0.00878397
$742$	0	0
$743$	31.1345	1.14221	0.571106	−	0.820876i	$-0.306514\pi$
$743$	31.1345	1.14221	0.571106	+	0.820876i	$0.306514\pi$
$744$	−1.11114	−0.0407363
$745$	−58.4180	−2.14027
$746$	−2.85424	−0.104501
$747$	−40.5318	−1.48298
$748$	25.8555	0.945369
$749$	0	0
$750$	−6.94990	−0.253775
$751$	−40.7231	−1.48601	−0.743004	−	0.669287i	$-0.766600\pi$
$751$	−40.7231	−1.48601	−0.743004	+	0.669287i	$0.766600\pi$
$752$	29.3203	1.06920
$753$	−10.0181	−0.365081
$754$	−4.20988	−0.153315
$755$	−52.6409	−1.91580
$756$	0	0
$757$	34.9086	1.26878	0.634388	−	0.773015i	$-0.281252\pi$
$757$	34.9086	1.26878	0.634388	+	0.773015i	$0.281252\pi$
$758$	8.47005	0.307646
$759$	−9.09171	−0.330008
$760$	−0.781021	−0.0283306
$761$	−4.76771	−0.172830	−0.0864148	−	0.996259i	$-0.527541\pi$
$761$	−4.76771	−0.172830	−0.0864148	+	0.996259i	$0.527541\pi$
$762$	4.31181	0.156200
$763$	0	0
$764$	−15.0556	−0.544693
$765$	−58.0413	−2.09849
$766$	−15.7576	−0.569344
$767$	38.2574	1.38140
$768$	−0.869704	−0.0313827
$769$	−51.9550	−1.87354	−0.936772	−	0.349941i	$-0.886202\pi$
$769$	−51.9550	−1.87354	−0.936772	+	0.349941i	$0.886202\pi$
$770$	0	0
$771$	9.78760	0.352492
$772$	15.6705	0.563995
$773$	−19.6577	−0.707038	−0.353519	−	0.935427i	$-0.615015\pi$
$773$	−19.6577	−0.707038	−0.353519	+	0.935427i	$0.615015\pi$
$774$	−9.89984	−0.355842
$775$	13.9575	0.501369
$776$	−17.3118	−0.621457
$777$	0	0
$778$	10.6056	0.380229
$779$	0.109209	0.00391281
$780$	−16.0570	−0.574932
$781$	−21.8833	−0.783045
$782$	14.6382	0.523459
$783$	6.94535	0.248207
$784$	0	0
$785$	58.6703	2.09403
$786$	0.199626	0.00712044
$787$	−16.1094	−0.574238	−0.287119	−	0.957895i	$-0.592698\pi$
$787$	−16.1094	−0.574238	−0.287119	+	0.957895i	$0.592698\pi$
$788$	33.9657	1.20998
$789$	−2.29263	−0.0816196
$790$	−23.7251	−0.844100
$791$	0	0
$792$	−13.0725	−0.464513
$793$	−27.9822	−0.993677
$794$	0.621992	0.0220737
$795$	13.7920	0.489150
$796$	−12.1929	−0.432165
$797$	−20.3109	−0.719447	−0.359724	−	0.933059i	$-0.617129\pi$
$797$	−20.3109	−0.719447	−0.359724	+	0.933059i	$0.617129\pi$
$798$	0	0
$799$	−55.2298	−1.95389
$800$	−56.3177	−1.99113
$801$	−2.31037	−0.0816329
$802$	−0.710064	−0.0250732
$803$	−27.3666	−0.965745
$804$	−1.30952	−0.0461831
$805$	0	0
$806$	−2.20499	−0.0776673
$807$	−0.709294	−0.0249683
$808$	−19.6881	−0.692625
$809$	3.62656	0.127503	0.0637515	−	0.997966i	$-0.479693\pi$
$809$	3.62656	0.127503	0.0637515	+	0.997966i	$0.479693\pi$
$810$	12.2025	0.428753
$811$	−10.2870	−0.361225	−0.180613	−	0.983554i	$-0.557808\pi$
$811$	−10.2870	−0.361225	−0.180613	+	0.983554i	$0.557808\pi$
$812$	0	0
$813$	−4.27225	−0.149834
$814$	11.4078	0.399843
$815$	−23.0069	−0.805896
$816$	7.82025	0.273763
$817$	−0.867089	−0.0303356
$818$	2.00039	0.0699422
$819$	0	0
$820$	7.33368	0.256103
$821$	6.42929	0.224384	0.112192	−	0.993687i	$-0.464213\pi$
$821$	6.42929	0.224384	0.112192	+	0.993687i	$0.464213\pi$
$822$	−1.15246	−0.0401967
$823$	4.04441	0.140979	0.0704896	−	0.997513i	$-0.477544\pi$
$823$	4.04441	0.140979	0.0704896	+	0.997513i	$0.477544\pi$
$824$	18.9526	0.660244
$825$	−17.6569	−0.614735
$826$	0	0
$827$	4.70225	0.163513	0.0817566	−	0.996652i	$-0.473947\pi$
$827$	4.70225	0.163513	0.0817566	+	0.996652i	$0.473947\pi$
$828$	29.4816	1.02456
$829$	6.74357	0.234214	0.117107	−	0.993119i	$-0.462638\pi$
$829$	6.74357	0.234214	0.117107	+	0.993119i	$0.462638\pi$
$830$	28.2495	0.980555
$831$	−0.0369335	−0.00128121
$832$	−13.6075	−0.471756
$833$	0	0
$834$	0.0159426	0.000552048 0
$835$	18.4294	0.637777
$836$	−0.540465	−0.0186924
$837$	3.63773	0.125738
$838$	12.5590	0.433842
$839$	−50.7412	−1.75178	−0.875890	−	0.482511i	$-0.839725\pi$
$839$	−50.7412	−1.75178	−0.875890	+	0.482511i	$0.839725\pi$
$840$	0	0
$841$	−23.9181	−0.824762
$842$	7.64895	0.263600
$843$	−4.49585	−0.154845
$844$	−8.97762	−0.309022
$845$	−14.1866	−0.488032
$846$	13.1812	0.453177
$847$	0	0
$848$	17.2820	0.593468
$849$	1.66992	0.0573114
$850$	28.4286	0.975093
$851$	−54.5030	−1.86834
$852$	−7.63013	−0.261404
$853$	−9.55166	−0.327042	−0.163521	−	0.986540i	$-0.552285\pi$
$853$	−9.55166	−0.327042	−0.163521	+	0.986540i	$0.552285\pi$
$854$	0	0
$855$	1.21326	0.0414925
$856$	3.47375	0.118730
$857$	25.8962	0.884598	0.442299	−	0.896868i	$-0.354163\pi$
$857$	25.8962	0.884598	0.442299	+	0.896868i	$0.354163\pi$
$858$	2.78941	0.0952289
$859$	41.3258	1.41002	0.705010	−	0.709198i	$-0.250943\pi$
$859$	41.3258	1.41002	0.705010	+	0.709198i	$0.250943\pi$
$860$	−58.2275	−1.98554
$861$	0	0
$862$	4.31088	0.146829
$863$	−1.76472	−0.0600719	−0.0300360	−	0.999549i	$-0.509562\pi$
$863$	−1.76472	−0.0600719	−0.0300360	+	0.999549i	$0.509562\pi$
$864$	−14.6780	−0.499356
$865$	58.4492	1.98733
$866$	−1.78204	−0.0605563
$867$	−5.55611	−0.188695
$868$	0	0
$869$	−34.7809	−1.17986
$870$	−2.29687	−0.0778711
$871$	−5.50526	−0.186539
$872$	−31.1440	−1.05467
$873$	26.8925	0.910175
$874$	−0.305986	−0.0103501
$875$	0	0
$876$	−9.54201	−0.322395
$877$	−37.4713	−1.26532	−0.632658	−	0.774432i	$-0.718036\pi$
$877$	−37.4713	−1.26532	−0.632658	+	0.774432i	$0.718036\pi$
$878$	13.6258	0.459850
$879$	2.41430	0.0814325
$880$	−31.4833	−1.06130
$881$	14.9319	0.503068	0.251534	−	0.967849i	$-0.419065\pi$
$881$	14.9319	0.503068	0.251534	+	0.967849i	$0.419065\pi$
$882$	0	0
$883$	35.3025	1.18802	0.594012	−	0.804456i	$-0.297543\pi$
$883$	35.3025	1.18802	0.594012	+	0.804456i	$0.297543\pi$
$884$	37.8999	1.27471
$885$	20.8729	0.701635
$886$	0.262636	0.00882343
$887$	6.34513	0.213049	0.106524	−	0.994310i	$-0.466028\pi$
$887$	6.34513	0.213049	0.106524	+	0.994310i	$0.466028\pi$
$888$	8.42654	0.282776
$889$	0	0
$890$	1.61026	0.0539761
$891$	17.8889	0.599299
$892$	12.4494	0.416836
$893$	1.15449	0.0386334
$894$	3.53846	0.118344
$895$	−23.7403	−0.793551
$896$	0	0
$897$	−13.3270	−0.444975
$898$	−8.66682	−0.289216
$899$	2.66172	0.0887734
$900$	57.2559	1.90853
$901$	−32.5537	−1.08452
$902$	−1.27400	−0.0424196
$903$	0	0
$904$	−28.3418	−0.942635
$905$	−60.1513	−1.99950
$906$	3.18853	0.105932
$907$	−21.6718	−0.719599	−0.359800	−	0.933030i	$-0.617155\pi$
$907$	−21.6718	−0.719599	−0.359800	+	0.933030i	$0.617155\pi$
$908$	18.0768	0.599899
$909$	30.5840	1.01441
$910$	0	0
$911$	−5.13876	−0.170255	−0.0851274	−	0.996370i	$-0.527130\pi$
$911$	−5.13876	−0.170255	−0.0851274	+	0.996370i	$0.527130\pi$
$912$	−0.163469	−0.00541301
$913$	41.4137	1.37059
$914$	−10.2527	−0.339129
$915$	−15.2668	−0.504705
$916$	−4.15478	−0.137278
$917$	0	0
$918$	7.40931	0.244544
$919$	−34.5055	−1.13823	−0.569116	−	0.822257i	$-0.692715\pi$
$919$	−34.5055	−1.13823	−0.569116	+	0.822257i	$0.692715\pi$
$920$	−43.5306	−1.43516
$921$	13.9409	0.459369
$922$	2.05924	0.0678173
$923$	−32.0773	−1.05584
$924$	0	0
$925$	−105.850	−3.48032
$926$	1.66744	0.0547956
$927$	−29.4414	−0.966982
$928$	−10.7399	−0.352553
$929$	5.42071	0.177848	0.0889238	−	0.996038i	$-0.471657\pi$
$929$	5.42071	0.177848	0.0889238	+	0.996038i	$0.471657\pi$
$930$	−1.20302	−0.0394485
$931$	0	0
$932$	−31.4090	−1.02884
$933$	7.38302	0.241709
$934$	−0.710475	−0.0232475
$935$	59.3042	1.93945
$936$	−19.1622	−0.626337
$937$	−46.9692	−1.53442	−0.767208	−	0.641398i	$-0.778355\pi$
$937$	−46.9692	−1.53442	−0.767208	+	0.641398i	$0.778355\pi$
$938$	0	0
$939$	12.9814	0.423633
$940$	77.5271	2.52865
$941$	−3.58221	−0.116777	−0.0583884	−	0.998294i	$-0.518596\pi$
$941$	−3.58221	−0.116777	−0.0583884	+	0.998294i	$0.518596\pi$
$942$	−3.55374	−0.115787
$943$	6.08681	0.198214
$944$	26.1548	0.851267
$945$	0	0
$946$	10.1152	0.328875
$947$	−35.5839	−1.15632	−0.578161	−	0.815923i	$-0.696229\pi$
$947$	−35.5839	−1.15632	−0.578161	+	0.815923i	$0.696229\pi$
$948$	−12.1272	−0.393873
$949$	−40.1150	−1.30219
$950$	−0.594253	−0.0192801
$951$	−2.05494	−0.0666359
$952$	0	0
$953$	−43.5164	−1.40963	−0.704817	−	0.709389i	$-0.748971\pi$
$953$	−43.5164	−1.40963	−0.704817	+	0.709389i	$0.748971\pi$
$954$	7.76926	0.251539
$955$	−34.5328	−1.11745
$956$	41.1378	1.33049
$957$	−3.36720	−0.108846
$958$	−6.71659	−0.217003
$959$	0	0
$960$	−7.42413	−0.239613
$961$	−29.6059	−0.955028
$962$	16.7220	0.539138
$963$	−5.39621	−0.173890
$964$	−22.6746	−0.730299
$965$	35.9432	1.15705
$966$	0	0
$967$	−22.2431	−0.715289	−0.357645	−	0.933858i	$-0.616420\pi$
$967$	−22.2431	−0.715289	−0.357645	+	0.933858i	$0.616420\pi$
$968$	−5.82396	−0.187189
$969$	0.307922	0.00989188
$970$	−18.7433	−0.601812
$971$	−10.0764	−0.323366	−0.161683	−	0.986843i	$-0.551692\pi$
$971$	−10.0764	−0.323366	−0.161683	+	0.986843i	$0.551692\pi$
$972$	22.7645	0.730171
$973$	0	0
$974$	0.701702	0.0224840
$975$	−25.8822	−0.828893
$976$	−19.1301	−0.612341
$977$	60.5914	1.93849	0.969245	−	0.246097i	$-0.0791481\pi$
$977$	60.5914	1.93849	0.969245	+	0.246097i	$0.0791481\pi$
$978$	1.39356	0.0445612
$979$	2.36064	0.0754463
$980$	0	0
$981$	48.3799	1.54465
$982$	16.0570	0.512401
$983$	−41.9563	−1.33820	−0.669100	−	0.743173i	$-0.733320\pi$
$983$	−41.9563	−1.33820	−0.669100	+	0.743173i	$0.733320\pi$
$984$	−0.941062	−0.0299999
$985$	77.9066	2.48231
$986$	5.42138	0.172652
$987$	0	0
$988$	−0.792234	−0.0252043
$989$	−48.3276	−1.53673
$990$	−14.1535	−0.449829
$991$	40.0186	1.27123	0.635616	−	0.772005i	$-0.280746\pi$
$991$	40.0186	1.27123	0.635616	+	0.772005i	$0.280746\pi$
$992$	−5.62517	−0.178599
$993$	11.4055	0.361943
$994$	0	0
$995$	−27.9666	−0.886599
$996$	14.4399	0.457545
$997$	−6.59339	−0.208815	−0.104407	−	0.994535i	$-0.533295\pi$
$997$	−6.59339	−0.208815	−0.104407	+	0.994535i	$0.533295\pi$
$998$	−6.80187	−0.215310
$999$	−27.5875	−0.872829

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.n.1.3		5
7.6	odd	2		287.2.a.e.1.3	✓	5
21.20	even	2		2583.2.a.r.1.3		5
28.27	even	2		4592.2.a.bb.1.3		5
35.34	odd	2		7175.2.a.n.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.e.1.3	✓	5	7.6	odd	2
2009.2.a.n.1.3		5	1.1	even	1	trivial
2583.2.a.r.1.3		5	21.20	even	2
4592.2.a.bb.1.3		5	28.27	even	2
7175.2.a.n.1.3		5	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)

\(f(q)\)	\(=\)	\(q-0.460315 q^{2} -0.539685 q^{3} -1.78811 q^{4} -4.10136 q^{5} +0.248425 q^{6} +1.74372 q^{8} -2.70874 q^{9} +O(q^{10})\)	\(q-0.460315 q^{2} -0.539685 q^{3} -1.78811 q^{4} -4.10136 q^{5} +0.248425 q^{6} +1.74372 q^{8} -2.70874 q^{9} +1.88791 q^{10} +2.76768 q^{11} +0.965017 q^{12} +4.05697 q^{13} +2.21344 q^{15} +2.77356 q^{16} -5.22447 q^{17} +1.24687 q^{18} +0.109209 q^{19} +7.33368 q^{20} -1.27400 q^{22} +6.08681 q^{23} -0.941062 q^{24} +11.8211 q^{25} -1.86748 q^{26} +3.08092 q^{27} +2.25431 q^{29} -1.01888 q^{30} +1.18073 q^{31} -4.76415 q^{32} -1.49368 q^{33} +2.40490 q^{34} +4.84353 q^{36} -8.95429 q^{37} -0.0502704 q^{38} -2.18949 q^{39} -7.15163 q^{40} +1.00000 q^{41} -7.93974 q^{43} -4.94891 q^{44} +11.1095 q^{45} -2.80185 q^{46} +10.5714 q^{47} -1.49685 q^{48} -5.44143 q^{50} +2.81957 q^{51} -7.25431 q^{52} +6.23100 q^{53} -1.41819 q^{54} -11.3512 q^{55} -0.0589384 q^{57} -1.03769 q^{58} +9.43006 q^{59} -3.95788 q^{60} -6.89732 q^{61} -0.543506 q^{62} -3.35411 q^{64} -16.6391 q^{65} +0.687561 q^{66} -1.35699 q^{67} +9.34193 q^{68} -3.28496 q^{69} -7.90672 q^{71} -4.72329 q^{72} -9.88791 q^{73} +4.12179 q^{74} -6.37969 q^{75} -0.195277 q^{76} +1.00785 q^{78} -12.5668 q^{79} -11.3754 q^{80} +6.46349 q^{81} -0.460315 q^{82} +14.9633 q^{83} +21.4274 q^{85} +3.65478 q^{86} -1.21662 q^{87} +4.82606 q^{88} +0.852931 q^{89} -5.11387 q^{90} -10.8839 q^{92} -0.637221 q^{93} -4.86616 q^{94} -0.447904 q^{95} +2.57115 q^{96} -9.92806 q^{97} -7.49692 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9}+O(q^{10}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9	\( 5 q - q^{2} - 4 q^{3} + 3 q^{4} + 5 q^{5} - 12 q^{6} - 3 q^{8} + q^{9} + 2 q^{11} + 2 q^{12} - 5 q^{13} - 5 q^{15} - q^{16} - 13 q^{17} + 21 q^{18} + 23 q^{20} + q^{22} + 2 q^{23} - 2 q^{24} + 22 q^{25} - 10 q^{27} - 5 q^{29} - 33 q^{30} - 17 q^{31} - 12 q^{32} - 3 q^{33} + 8 q^{34} + 15 q^{36} - 7 q^{37} + 3 q^{38} + 5 q^{39} - 7 q^{40} + 5 q^{41} + q^{43} - 47 q^{44} + 23 q^{45} - 24 q^{46} - 9 q^{47} + 19 q^{48} + 2 q^{50} + 5 q^{51} - 20 q^{52} + 5 q^{53} - 2 q^{54} - 33 q^{55} - 3 q^{57} - 27 q^{58} - 7 q^{59} - 16 q^{60} - 22 q^{61} + 28 q^{62} - 3 q^{64} - 31 q^{65} + 42 q^{66} - 3 q^{67} - 17 q^{68} + 22 q^{69} - 24 q^{71} - 12 q^{72} - 40 q^{73} - 5 q^{74} - 24 q^{75} + 19 q^{76} + 30 q^{78} - 42 q^{79} - 24 q^{80} + 9 q^{81} - q^{82} + 12 q^{83} - 23 q^{85} + 16 q^{86} + 32 q^{87} + 26 q^{88} - 8 q^{89} + 59 q^{90} + 12 q^{92} - 11 q^{93} + 23 q^{94} - 17 q^{95} + 17 q^{96} - 16 q^{97} - 45 q^{99}+O(q^{100}) \) 5 * q - q^2 - 4 * q^3 + 3 * q^4 + 5 * q^5 - 12 * q^6 - 3 * q^8 + q^9 + 2 * q^11 + 2 * q^12 - 5 * q^13 - 5 * q^15 - q^16 - 13 * q^17 + 21 * q^18 + 23 * q^20 + q^22 + 2 * q^23 - 2 * q^24 + 22 * q^25 - 10 * q^27 - 5 * q^29 - 33 * q^30 - 17 * q^31 - 12 * q^32 - 3 * q^33 + 8 * q^34 + 15 * q^36 - 7 * q^37 + 3 * q^38 + 5 * q^39 - 7 * q^40 + 5 * q^41 + q^43 - 47 * q^44 + 23 * q^45 - 24 * q^46 - 9 * q^47 + 19 * q^48 + 2 * q^50 + 5 * q^51 - 20 * q^52 + 5 * q^53 - 2 * q^54 - 33 * q^55 - 3 * q^57 - 27 * q^58 - 7 * q^59 - 16 * q^60 - 22 * q^61 + 28 * q^62 - 3 * q^64 - 31 * q^65 + 42 * q^66 - 3 * q^67 - 17 * q^68 + 22 * q^69 - 24 * q^71 - 12 * q^72 - 40 * q^73 - 5 * q^74 - 24 * q^75 + 19 * q^76 + 30 * q^78 - 42 * q^79 - 24 * q^80 + 9 * q^81 - q^82 + 12 * q^83 - 23 * q^85 + 16 * q^86 + 32 * q^87 + 26 * q^88 - 8 * q^89 + 59 * q^90 + 12 * q^92 - 11 * q^93 + 23 * q^94 - 17 * q^95 + 17 * q^96 - 16 * q^97 - 45 * q^99

Introduction

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