LMFDB - Embedded newform 2009.2.a.r.1.7

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:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 3 x^{16} - 25 x^{15} + 77 x^{14} + 247 x^{13} - 790 x^{12} - 1231 x^{11} + 4173 x^{10} + \cdots - 464 $ x^17 - 3x^16 - 25x^15 + 77x^14 + 247x^13 - 790x^12 - 1231x^11 + 4173x^10 + 3251x^9 - 12183x^8 - 4259x^7 + 19567x^6 + 2029x^5 - 16136x^4 + 299x^3 + 5775x^2 - 312x - 464
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			1.7
Root			$-0.902479$ 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)

$f(q)$	$=$	$q-0.902479 q^{2} +3.32518 q^{3} -1.18553 q^{4} +0.938362 q^{5} -3.00091 q^{6} +2.87488 q^{8} +8.05685 q^{9} +O(q^{10})$	\(q-0.902479 q^{2} +3.32518 q^{3} -1.18553 q^{4} +0.938362 q^{5} -3.00091 q^{6} +2.87488 q^{8} +8.05685 q^{9} -0.846852 q^{10} +5.46037 q^{11} -3.94211 q^{12} +2.52551 q^{13} +3.12023 q^{15} -0.223453 q^{16} -6.71133 q^{17} -7.27114 q^{18} -0.857408 q^{19} -1.11246 q^{20} -4.92787 q^{22} +4.76683 q^{23} +9.55949 q^{24} -4.11948 q^{25} -2.27922 q^{26} +16.8150 q^{27} +3.28519 q^{29} -2.81594 q^{30} -0.119237 q^{31} -5.54809 q^{32} +18.1567 q^{33} +6.05684 q^{34} -9.55165 q^{36} -3.81897 q^{37} +0.773793 q^{38} +8.39777 q^{39} +2.69767 q^{40} -1.00000 q^{41} +1.64508 q^{43} -6.47344 q^{44} +7.56024 q^{45} -4.30197 q^{46} -4.73681 q^{47} -0.743022 q^{48} +3.71774 q^{50} -22.3164 q^{51} -2.99407 q^{52} +2.24391 q^{53} -15.1752 q^{54} +5.12380 q^{55} -2.85104 q^{57} -2.96482 q^{58} -4.44654 q^{59} -3.69913 q^{60} -11.9605 q^{61} +0.107609 q^{62} +5.45394 q^{64} +2.36984 q^{65} -16.3861 q^{66} -11.7311 q^{67} +7.95649 q^{68} +15.8506 q^{69} +9.78432 q^{71} +23.1624 q^{72} +3.71532 q^{73} +3.44654 q^{74} -13.6980 q^{75} +1.01648 q^{76} -7.57881 q^{78} -2.81292 q^{79} -0.209680 q^{80} +31.7423 q^{81} +0.902479 q^{82} -3.41464 q^{83} -6.29766 q^{85} -1.48465 q^{86} +10.9239 q^{87} +15.6979 q^{88} +14.2417 q^{89} -6.82296 q^{90} -5.65123 q^{92} -0.396486 q^{93} +4.27487 q^{94} -0.804559 q^{95} -18.4484 q^{96} +8.40546 q^{97} +43.9934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 3 q^{2} - q^{3} + 25 q^{4} + q^{5} - 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) $ 17 * q + 3 * q^2 - q^3 + 25 * q^4 + q^5 - 2 * q^6 + 9 * q^8 + 26 * q^9	$ 17 q + 3 q^{2} - q^{3} + 25 q^{4} + q^{5} - 2 q^{6} + 9 q^{8} + 26 q^{9} + 2 q^{10} + 15 q^{11} - 4 q^{12} + 5 q^{13} + 24 q^{15} + 33 q^{16} - 4 q^{17} + 10 q^{18} - 5 q^{19} + 26 q^{20} + 16 q^{22} + 12 q^{23} - 16 q^{24} + 24 q^{25} - 31 q^{26} + 11 q^{27} + 14 q^{29} - 33 q^{30} + 3 q^{31} + 16 q^{32} - 4 q^{33} + 24 q^{34} + 57 q^{36} + 24 q^{37} + 45 q^{39} - 36 q^{40} - 17 q^{41} + 14 q^{43} - 9 q^{44} + 21 q^{45} + 44 q^{46} - 19 q^{47} + 60 q^{48} - 4 q^{50} + 2 q^{51} + 25 q^{52} + 4 q^{53} - 68 q^{54} - 9 q^{55} - 12 q^{57} - q^{58} + 27 q^{59} + 66 q^{60} + q^{61} + 23 q^{62} + 75 q^{64} + 22 q^{65} + 16 q^{66} + 49 q^{67} - 45 q^{68} - 12 q^{69} + 40 q^{71} - 23 q^{72} + 14 q^{73} + 33 q^{74} - 27 q^{75} + 9 q^{76} - 12 q^{78} + 61 q^{79} + 82 q^{80} + 53 q^{81} - 3 q^{82} + 18 q^{83} - 13 q^{85} - 4 q^{86} + 17 q^{87} + 74 q^{88} - 18 q^{89} + 20 q^{90} + 28 q^{92} - 36 q^{93} + 5 q^{94} + 20 q^{95} - 148 q^{96} - 26 q^{97} + 38 q^{99}+O(q^{100}) $ 17 * q + 3 * q^2 - q^3 + 25 * q^4 + q^5 - 2 * q^6 + 9 * q^8 + 26 * q^9 + 2 * q^10 + 15 * q^11 - 4 * q^12 + 5 * q^13 + 24 * q^15 + 33 * q^16 - 4 * q^17 + 10 * q^18 - 5 * q^19 + 26 * q^20 + 16 * q^22 + 12 * q^23 - 16 * q^24 + 24 * q^25 - 31 * q^26 + 11 * q^27 + 14 * q^29 - 33 * q^30 + 3 * q^31 + 16 * q^32 - 4 * q^33 + 24 * q^34 + 57 * q^36 + 24 * q^37 + 45 * q^39 - 36 * q^40 - 17 * q^41 + 14 * q^43 - 9 * q^44 + 21 * q^45 + 44 * q^46 - 19 * q^47 + 60 * q^48 - 4 * q^50 + 2 * q^51 + 25 * q^52 + 4 * q^53 - 68 * q^54 - 9 * q^55 - 12 * q^57 - q^58 + 27 * q^59 + 66 * q^60 + q^61 + 23 * q^62 + 75 * q^64 + 22 * q^65 + 16 * q^66 + 49 * q^67 - 45 * q^68 - 12 * q^69 + 40 * q^71 - 23 * q^72 + 14 * q^73 + 33 * q^74 - 27 * q^75 + 9 * q^76 - 12 * q^78 + 61 * q^79 + 82 * q^80 + 53 * q^81 - 3 * q^82 + 18 * q^83 - 13 * q^85 - 4 * q^86 + 17 * q^87 + 74 * q^88 - 18 * q^89 + 20 * q^90 + 28 * q^92 - 36 * q^93 + 5 * q^94 + 20 * q^95 - 148 * q^96 - 26 * q^97 + 38 * 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 $

$2$	−0.902479	−0.638149	−0.319075	−	0.947730i	$-0.603372\pi$
$2$	−0.902479	−0.638149	−0.319075	+	0.947730i	$0.603372\pi$
$3$	3.32518	1.91980	0.959898	−	0.280349i	$-0.0904503\pi$
$3$	3.32518	1.91980	0.959898	+	0.280349i	$0.0904503\pi$
$4$	−1.18553	−0.592766
$5$	0.938362	0.419648	0.209824	−	0.977739i	$-0.432711\pi$
$5$	0.938362	0.419648	0.209824	+	0.977739i	$0.432711\pi$
$6$	−3.00091	−1.22512
$7$	0	0
$7$	0	0
$8$	2.87488	1.01642
$9$	8.05685	2.68562
$10$	−0.846852	−0.267798
$11$	5.46037	1.64636	0.823181	−	0.567779i	$-0.192197\pi$
$11$	5.46037	1.64636	0.823181	+	0.567779i	$0.192197\pi$
$12$	−3.94211	−1.13799
$13$	2.52551	0.700449	0.350225	−	0.936666i	$-0.386105\pi$
$13$	2.52551	0.700449	0.350225	+	0.936666i	$0.386105\pi$
$14$	0	0
$15$	3.12023	0.805639
$16$	−0.223453	−0.0558632
$17$	−6.71133	−1.62774	−0.813868	−	0.581049i	$-0.802642\pi$
$17$	−6.71133	−1.62774	−0.813868	+	0.581049i	$0.802642\pi$
$18$	−7.27114	−1.71382
$19$	−0.857408	−0.196703	−0.0983514	−	0.995152i	$-0.531357\pi$
$19$	−0.857408	−0.196703	−0.0983514	+	0.995152i	$0.531357\pi$
$20$	−1.11246	−0.248753
$21$	0	0
$22$	−4.92787	−1.05062
$23$	4.76683	0.993953	0.496977	−	0.867764i	$-0.334443\pi$
$23$	4.76683	0.993953	0.496977	+	0.867764i	$0.334443\pi$
$24$	9.55949	1.95132
$25$	−4.11948	−0.823895
$26$	−2.27922	−0.446991
$27$	16.8150	3.23604
$28$	0	0
$29$	3.28519	0.610045	0.305023	−	0.952345i	$-0.401336\pi$
$29$	3.28519	0.610045	0.305023	+	0.952345i	$0.401336\pi$
$30$	−2.81594	−0.514118
$31$	−0.119237	−0.0214157	−0.0107078	−	0.999943i	$-0.503408\pi$
$31$	−0.119237	−0.0214157	−0.0107078	+	0.999943i	$0.503408\pi$
$32$	−5.54809	−0.980773
$33$	18.1567	3.16068
$34$	6.05684	1.03874
$35$	0	0
$36$	−9.55165	−1.59194
$37$	−3.81897	−0.627835	−0.313917	−	0.949450i	$-0.601642\pi$
$37$	−3.81897	−0.627835	−0.313917	+	0.949450i	$0.601642\pi$
$38$	0.773793	0.125526
$39$	8.39777	1.34472
$40$	2.69767	0.426540
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	1.64508	0.250873	0.125436	−	0.992102i	$-0.459967\pi$
$43$	1.64508	0.250873	0.125436	+	0.992102i	$0.459967\pi$
$44$	−6.47344	−0.975907
$45$	7.56024	1.12701
$46$	−4.30197	−0.634290
$47$	−4.73681	−0.690935	−0.345468	−	0.938431i	$-0.612280\pi$
$47$	−4.73681	−0.690935	−0.345468	+	0.938431i	$0.612280\pi$
$48$	−0.743022	−0.107246
$49$	0	0
$50$	3.71774	0.525768
$51$	−22.3164	−3.12492
$52$	−2.99407	−0.415202
$53$	2.24391	0.308224	0.154112	−	0.988053i	$-0.450748\pi$
$53$	2.24391	0.308224	0.154112	+	0.988053i	$0.450748\pi$
$54$	−15.1752	−2.06508
$55$	5.12380	0.690893
$56$	0	0
$57$	−2.85104	−0.377629
$58$	−2.96482	−0.389300
$59$	−4.44654	−0.578890	−0.289445	−	0.957195i	$-0.593471\pi$
$59$	−4.44654	−0.578890	−0.289445	+	0.957195i	$0.593471\pi$
$60$	−3.69913	−0.477555
$61$	−11.9605	−1.53138	−0.765690	−	0.643210i	$-0.777602\pi$
$61$	−11.9605	−1.53138	−0.765690	+	0.643210i	$0.777602\pi$
$62$	0.107609	0.0136664
$63$	0	0
$64$	5.45394	0.681743
$65$	2.36984	0.293942
$66$	−16.3861	−2.01699
$67$	−11.7311	−1.43318	−0.716591	−	0.697493i	$-0.754299\pi$
$67$	−11.7311	−1.43318	−0.716591	+	0.697493i	$0.754299\pi$
$68$	7.95649	0.964867
$69$	15.8506	1.90819
$70$	0	0
$71$	9.78432	1.16119	0.580593	−	0.814194i	$-0.302821\pi$
$71$	9.78432	1.16119	0.580593	+	0.814194i	$0.302821\pi$
$72$	23.1624	2.72972
$73$	3.71532	0.434845	0.217422	−	0.976078i	$-0.430235\pi$
$73$	3.71532	0.434845	0.217422	+	0.976078i	$0.430235\pi$
$74$	3.44654	0.400652
$75$	−13.6980	−1.58171
$76$	1.01648	0.116599
$77$	0	0
$78$	−7.57881	−0.858132
$79$	−2.81292	−0.316478	−0.158239	−	0.987401i	$-0.550582\pi$
$79$	−2.81292	−0.316478	−0.158239	+	0.987401i	$0.550582\pi$
$80$	−0.209680	−0.0234429
$81$	31.7423	3.52692
$82$	0.902479	0.0996622
$83$	−3.41464	−0.374805	−0.187403	−	0.982283i	$-0.560007\pi$
$83$	−3.41464	−0.374805	−0.187403	+	0.982283i	$0.560007\pi$
$84$	0	0
$85$	−6.29766	−0.683077
$86$	−1.48465	−0.160094
$87$	10.9239	1.17116
$88$	15.6979	1.67340
$89$	14.2417	1.50962	0.754808	−	0.655946i	$-0.227730\pi$
$89$	14.2417	1.50962	0.754808	+	0.655946i	$0.227730\pi$
$90$	−6.82296	−0.719203
$91$	0	0
$92$	−5.65123	−0.589181
$93$	−0.396486	−0.0411137
$94$	4.27487	0.440920
$95$	−0.804559	−0.0825460
$96$	−18.4484	−1.88288
$97$	8.40546	0.853446	0.426723	−	0.904382i	$-0.359668\pi$
$97$	8.40546	0.853446	0.426723	+	0.904382i	$0.359668\pi$
$98$	0	0
$99$	43.9934	4.42150
$100$	4.88377	0.488377
$101$	6.27309	0.624196	0.312098	−	0.950050i	$-0.398968\pi$
$101$	6.27309	0.624196	0.312098	+	0.950050i	$0.398968\pi$
$102$	20.1401	1.99417
$103$	−8.74565	−0.861735	−0.430867	−	0.902415i	$-0.641792\pi$
$103$	−8.74565	−0.861735	−0.430867	+	0.902415i	$0.641792\pi$
$104$	7.26051	0.711952
$105$	0	0
$106$	−2.02508	−0.196693
$107$	−10.5229	−1.01729	−0.508643	−	0.860978i	$-0.669853\pi$
$107$	−10.5229	−1.01729	−0.508643	+	0.860978i	$0.669853\pi$
$108$	−19.9347	−1.91821
$109$	−3.24852	−0.311152	−0.155576	−	0.987824i	$-0.549723\pi$
$109$	−3.24852	−0.311152	−0.155576	+	0.987824i	$0.549723\pi$
$110$	−4.62412	−0.440893
$111$	−12.6988	−1.20531
$112$	0	0
$113$	4.20493	0.395566	0.197783	−	0.980246i	$-0.436626\pi$
$113$	4.20493	0.395566	0.197783	+	0.980246i	$0.436626\pi$
$114$	2.57300	0.240984
$115$	4.47301	0.417111
$116$	−3.89470	−0.361614
$117$	20.3476	1.88114
$118$	4.01291	0.369418
$119$	0	0
$120$	8.97026	0.818869
$121$	18.8156	1.71051
$122$	10.7941	0.977248
$123$	−3.32518	−0.299822
$124$	0.141360	0.0126945
$125$	−8.55737	−0.765394
$126$	0	0
$127$	6.36861	0.565123	0.282561	−	0.959249i	$-0.408816\pi$
$127$	6.36861	0.565123	0.282561	+	0.959249i	$0.408816\pi$
$128$	6.17411	0.545720
$129$	5.47020	0.481624
$130$	−2.13873	−0.187579
$131$	−6.50705	−0.568524	−0.284262	−	0.958747i	$-0.591749\pi$
$131$	−6.50705	−0.568524	−0.284262	+	0.958747i	$0.591749\pi$
$132$	−21.5254	−1.87354
$133$	0	0
$134$	10.5871	0.914584
$135$	15.7785	1.35800
$136$	−19.2942	−1.65447
$137$	13.2635	1.13318	0.566588	−	0.824001i	$-0.308263\pi$
$137$	13.2635	1.13318	0.566588	+	0.824001i	$0.308263\pi$
$138$	−14.3048	−1.21771
$139$	−5.17790	−0.439184	−0.219592	−	0.975592i	$-0.570473\pi$
$139$	−5.17790	−0.439184	−0.219592	+	0.975592i	$0.570473\pi$
$140$	0	0
$141$	−15.7508	−1.32645
$142$	−8.83015	−0.741010
$143$	13.7902	1.15319
$144$	−1.80033	−0.150027
$145$	3.08270	0.256004
$146$	−3.35299	−0.277496
$147$	0	0
$148$	4.52751	0.372159
$149$	3.67578	0.301132	0.150566	−	0.988600i	$-0.451890\pi$
$149$	3.67578	0.301132	0.150566	+	0.988600i	$0.451890\pi$
$150$	12.3622	1.00937
$151$	14.2667	1.16101	0.580505	−	0.814257i	$-0.302855\pi$
$151$	14.2667	1.16101	0.580505	+	0.814257i	$0.302855\pi$
$152$	−2.46494	−0.199933
$153$	−54.0722	−4.37148
$154$	0	0
$155$	−0.111888	−0.00898705
$156$	−9.95582	−0.797104
$157$	−9.04941	−0.722222	−0.361111	−	0.932523i	$-0.617602\pi$
$157$	−9.04941	−0.722222	−0.361111	+	0.932523i	$0.617602\pi$
$158$	2.53860	0.201960
$159$	7.46140	0.591727
$160$	−5.20612	−0.411580
$161$	0	0
$162$	−28.6468	−2.25070
$163$	−8.89264	−0.696525	−0.348263	−	0.937397i	$-0.613228\pi$
$163$	−8.89264	−0.696525	−0.348263	+	0.937397i	$0.613228\pi$
$164$	1.18553	0.0925744
$165$	17.0376	1.32637
$166$	3.08164	0.239182
$167$	−7.46298	−0.577503	−0.288751	−	0.957404i	$-0.593240\pi$
$167$	−7.46298	−0.577503	−0.288751	+	0.957404i	$0.593240\pi$
$168$	0	0
$169$	−6.62182	−0.509371
$170$	5.68350	0.435905
$171$	−6.90801	−0.528269
$172$	−1.95030	−0.148709
$173$	15.0207	1.14200	0.571001	−	0.820949i	$-0.306555\pi$
$173$	15.0207	1.14200	0.571001	+	0.820949i	$0.306555\pi$
$174$	−9.85857	−0.747377
$175$	0	0
$176$	−1.22013	−0.0919711
$177$	−14.7856	−1.11135
$178$	−12.8528	−0.963360
$179$	−17.9193	−1.33935	−0.669677	−	0.742653i	$-0.733567\pi$
$179$	−17.9193	−1.33935	−0.669677	+	0.742653i	$0.733567\pi$
$180$	−8.96290	−0.668055
$181$	24.9578	1.85510	0.927548	−	0.373705i	$-0.121913\pi$
$181$	24.9578	1.85510	0.927548	+	0.373705i	$0.121913\pi$
$182$	0	0
$183$	−39.7707	−2.93994
$184$	13.7041	1.01028
$185$	−3.58358	−0.263470
$186$	0.357821	0.0262367
$187$	−36.6463	−2.67984
$188$	5.61564	0.409563
$189$	0	0
$190$	0.726098	0.0526767
$191$	16.3014	1.17952	0.589762	−	0.807577i	$-0.299221\pi$
$191$	16.3014	1.17952	0.589762	+	0.807577i	$0.299221\pi$
$192$	18.1354	1.30881
$193$	−9.74950	−0.701784	−0.350892	−	0.936416i	$-0.614122\pi$
$193$	−9.74950	−0.701784	−0.350892	+	0.936416i	$0.614122\pi$
$194$	−7.58576	−0.544626
$195$	7.88015	0.564309
$196$	0	0
$197$	−24.4370	−1.74106	−0.870531	−	0.492114i	$-0.836224\pi$
$197$	−24.4370	−1.74106	−0.870531	+	0.492114i	$0.836224\pi$
$198$	−39.7031	−2.82158
$199$	4.93046	0.349511	0.174756	−	0.984612i	$-0.444086\pi$
$199$	4.93046	0.349511	0.174756	+	0.984612i	$0.444086\pi$
$200$	−11.8430	−0.837425
$201$	−39.0081	−2.75142
$202$	−5.66133	−0.398330
$203$	0	0
$204$	26.4568	1.85235
$205$	−0.938362	−0.0655380
$206$	7.89277	0.549915
$207$	38.4057	2.66938
$208$	−0.564331	−0.0391293
$209$	−4.68176	−0.323844
$210$	0	0
$211$	27.1561	1.86950	0.934751	−	0.355303i	$-0.115622\pi$
$211$	27.1561	1.86950	0.934751	+	0.355303i	$0.115622\pi$
$212$	−2.66022	−0.182705
$213$	32.5347	2.22924
$214$	9.49668	0.649180
$215$	1.54368	0.105278
$216$	48.3409	3.28918
$217$	0	0
$218$	2.93172	0.198561
$219$	12.3541	0.834813
$220$	−6.07442	−0.409538
$221$	−16.9495	−1.14015
$222$	11.4604	0.769171
$223$	8.74237	0.585432	0.292716	−	0.956199i	$-0.405441\pi$
$223$	8.74237	0.585432	0.292716	+	0.956199i	$0.405441\pi$
$224$	0	0
$225$	−33.1900	−2.21267
$226$	−3.79486	−0.252430
$227$	−14.6898	−0.975000	−0.487500	−	0.873123i	$-0.662091\pi$
$227$	−14.6898	−0.975000	−0.487500	+	0.873123i	$0.662091\pi$
$228$	3.38000	0.223846
$229$	5.30412	0.350506	0.175253	−	0.984523i	$-0.443926\pi$
$229$	5.30412	0.350506	0.175253	+	0.984523i	$0.443926\pi$
$230$	−4.03680	−0.266179
$231$	0	0
$232$	9.44453	0.620064
$233$	−4.42564	−0.289933	−0.144967	−	0.989437i	$-0.546307\pi$
$233$	−4.42564	−0.289933	−0.144967	+	0.989437i	$0.546307\pi$
$234$	−18.3633	−1.20045
$235$	−4.44484	−0.289950
$236$	5.27151	0.343146
$237$	−9.35347	−0.607573
$238$	0	0
$239$	−0.685835	−0.0443630	−0.0221815	−	0.999754i	$-0.507061\pi$
$239$	−0.685835	−0.0443630	−0.0221815	+	0.999754i	$0.507061\pi$
$240$	−0.697223	−0.0450056
$241$	−8.86786	−0.571229	−0.285614	−	0.958345i	$-0.592198\pi$
$241$	−8.86786	−0.571229	−0.285614	+	0.958345i	$0.592198\pi$
$242$	−16.9807	−1.09156
$243$	55.1041	3.53493
$244$	14.1795	0.907749
$245$	0	0
$246$	3.00091	0.191331
$247$	−2.16539	−0.137780
$248$	−0.342793	−0.0217674
$249$	−11.3543	−0.719550
$250$	7.72285	0.488436
$251$	−3.42941	−0.216463	−0.108231	−	0.994126i	$-0.534519\pi$
$251$	−3.42941	−0.216463	−0.108231	+	0.994126i	$0.534519\pi$
$252$	0	0
$253$	26.0287	1.63641
$254$	−5.74754	−0.360633
$255$	−20.9409	−1.31137
$256$	−16.4799	−1.02999
$257$	−15.2304	−0.950048	−0.475024	−	0.879973i	$-0.657561\pi$
$257$	−15.2304	−0.950048	−0.475024	+	0.879973i	$0.657561\pi$
$258$	−4.93674	−0.307348
$259$	0	0
$260$	−2.80952	−0.174239
$261$	26.4683	1.63835
$262$	5.87248	0.362803
$263$	−12.2741	−0.756852	−0.378426	−	0.925632i	$-0.623535\pi$
$263$	−12.2741	−0.756852	−0.378426	+	0.925632i	$0.623535\pi$
$264$	52.1983	3.21258
$265$	2.10560	0.129346
$266$	0	0
$267$	47.3562	2.89815
$268$	13.9076	0.849541
$269$	−12.8300	−0.782258	−0.391129	−	0.920336i	$-0.627915\pi$
$269$	−12.8300	−0.782258	−0.391129	+	0.920336i	$0.627915\pi$
$270$	−14.2398	−0.866606
$271$	−17.9718	−1.09171	−0.545854	−	0.837881i	$-0.683795\pi$
$271$	−17.9718	−1.09171	−0.545854	+	0.837881i	$0.683795\pi$
$272$	1.49967	0.0909306
$273$	0	0
$274$	−11.9700	−0.723135
$275$	−22.4939	−1.35643
$276$	−18.7914	−1.13111
$277$	−0.834736	−0.0501544	−0.0250772	−	0.999686i	$-0.507983\pi$
$277$	−0.834736	−0.0501544	−0.0250772	+	0.999686i	$0.507983\pi$
$278$	4.67295	0.280265
$279$	−0.960678	−0.0575143
$280$	0	0
$281$	5.96703	0.355963	0.177982	−	0.984034i	$-0.443043\pi$
$281$	5.96703	0.355963	0.177982	+	0.984034i	$0.443043\pi$
$282$	14.2147	0.846476
$283$	−18.4158	−1.09470	−0.547352	−	0.836902i	$-0.684364\pi$
$283$	−18.4158	−1.09470	−0.547352	+	0.836902i	$0.684364\pi$
$284$	−11.5996	−0.688311
$285$	−2.67531	−0.158472
$286$	−12.4454	−0.735909
$287$	0	0
$288$	−44.7001	−2.63398
$289$	28.0420	1.64953
$290$	−2.78207	−0.163369
$291$	27.9497	1.63844
$292$	−4.40462	−0.257761
$293$	18.3646	1.07287	0.536435	−	0.843941i	$-0.319771\pi$
$293$	18.3646	1.07287	0.536435	+	0.843941i	$0.319771\pi$
$294$	0	0
$295$	−4.17246	−0.242930
$296$	−10.9791	−0.638145
$297$	91.8158	5.32770
$298$	−3.31732	−0.192167
$299$	12.0387	0.696214
$300$	16.2394	0.937584
$301$	0	0
$302$	−12.8754	−0.740897
$303$	20.8592	1.19833
$304$	0.191590	0.0109885
$305$	−11.2232	−0.642640
$306$	48.7990	2.78965
$307$	−16.8758	−0.963153	−0.481577	−	0.876404i	$-0.659936\pi$
$307$	−16.8758	−0.963153	−0.481577	+	0.876404i	$0.659936\pi$
$308$	0	0
$309$	−29.0809	−1.65436
$310$	0.100976	0.00573508
$311$	−10.4537	−0.592775	−0.296387	−	0.955068i	$-0.595782\pi$
$311$	−10.4537	−0.592775	−0.296387	+	0.955068i	$0.595782\pi$
$312$	24.1425	1.36680
$313$	6.26929	0.354361	0.177180	−	0.984178i	$-0.443302\pi$
$313$	6.26929	0.354361	0.177180	+	0.984178i	$0.443302\pi$
$314$	8.16691	0.460885
$315$	0	0
$316$	3.33480	0.187597
$317$	−26.1750	−1.47013	−0.735066	−	0.677995i	$-0.762849\pi$
$317$	−26.1750	−1.47013	−0.735066	+	0.677995i	$0.762849\pi$
$318$	−6.73376	−0.377610
$319$	17.9384	1.00436
$320$	5.11777	0.286092
$321$	−34.9905	−1.95298
$322$	0	0
$323$	5.75435	0.320181
$324$	−37.6315	−2.09064
$325$	−10.4038	−0.577097
$326$	8.02542	0.444487
$327$	−10.8019	−0.597349
$328$	−2.87488	−0.158738
$329$	0	0
$330$	−15.3761	−0.846424
$331$	7.35150	0.404075	0.202037	−	0.979378i	$-0.435244\pi$
$331$	7.35150	0.404075	0.202037	+	0.979378i	$0.435244\pi$
$332$	4.04816	0.222172
$333$	−30.7689	−1.68612
$334$	6.73518	0.368533
$335$	−11.0080	−0.601432
$336$	0	0
$337$	−1.58075	−0.0861092	−0.0430546	−	0.999073i	$-0.513709\pi$
$337$	−1.58075	−0.0861092	−0.0430546	+	0.999073i	$0.513709\pi$
$338$	5.97606	0.325055
$339$	13.9822	0.759407
$340$	7.46607	0.404904
$341$	−0.651080	−0.0352580
$342$	6.23433	0.337114
$343$	0	0
$344$	4.72940	0.254992
$345$	14.8736	0.800767
$346$	−13.5559	−0.728768
$347$	21.8834	1.17476	0.587382	−	0.809310i	$-0.300159\pi$
$347$	21.8834	1.17476	0.587382	+	0.809310i	$0.300159\pi$
$348$	−12.9506	−0.694225
$349$	−5.31231	−0.284362	−0.142181	−	0.989841i	$-0.545411\pi$
$349$	−5.31231	−0.284362	−0.142181	+	0.989841i	$0.545411\pi$
$350$	0	0
$351$	42.4663	2.26668
$352$	−30.2946	−1.61471
$353$	−25.5285	−1.35874	−0.679371	−	0.733795i	$-0.737747\pi$
$353$	−25.5285	−1.35874	−0.679371	+	0.733795i	$0.737747\pi$
$354$	13.3437	0.709207
$355$	9.18124	0.487289
$356$	−16.8840	−0.894848
$357$	0	0
$358$	16.1718	0.854708
$359$	20.2278	1.06758	0.533792	−	0.845616i	$-0.320766\pi$
$359$	20.2278	1.06758	0.533792	+	0.845616i	$0.320766\pi$
$360$	21.7348	1.14552
$361$	−18.2649	−0.961308
$362$	−22.5239	−1.18383
$363$	62.5653	3.28383
$364$	0	0
$365$	3.48631	0.182482
$366$	35.8922	1.87612
$367$	32.6414	1.70387	0.851934	−	0.523649i	$-0.175430\pi$
$367$	32.6414	1.70387	0.851934	+	0.523649i	$0.175430\pi$
$368$	−1.06516	−0.0555254
$369$	−8.05685	−0.419423
$370$	3.23410	0.168133
$371$	0	0
$372$	0.470047	0.0243708
$373$	−8.84603	−0.458030	−0.229015	−	0.973423i	$-0.573550\pi$
$373$	−8.84603	−0.458030	−0.229015	+	0.973423i	$0.573550\pi$
$374$	33.0725	1.71014
$375$	−28.4548	−1.46940
$376$	−13.6177	−0.702282
$377$	8.29678	0.427306
$378$	0	0
$379$	10.5565	0.542252	0.271126	−	0.962544i	$-0.412604\pi$
$379$	10.5565	0.542252	0.271126	+	0.962544i	$0.412604\pi$
$380$	0.953830	0.0489304
$381$	21.1768	1.08492
$382$	−14.7116	−0.752713
$383$	−24.8543	−1.27000	−0.634998	−	0.772514i	$-0.718999\pi$
$383$	−24.8543	−1.27000	−0.634998	+	0.772514i	$0.718999\pi$
$384$	20.5301	1.04767
$385$	0	0
$386$	8.79872	0.447843
$387$	13.2542	0.673747
$388$	−9.96494	−0.505893
$389$	7.24246	0.367207	0.183604	−	0.983000i	$-0.441224\pi$
$389$	7.24246	0.367207	0.183604	+	0.983000i	$0.441224\pi$
$390$	−7.11167	−0.360113
$391$	−31.9918	−1.61789
$392$	0	0
$393$	−21.6372	−1.09145
$394$	22.0538	1.11106
$395$	−2.63953	−0.132809
$396$	−52.1555	−2.62091
$397$	34.7019	1.74164	0.870819	−	0.491603i	$-0.163589\pi$
$397$	34.7019	1.74164	0.870819	+	0.491603i	$0.163589\pi$
$398$	−4.44964	−0.223040
$399$	0	0
$400$	0.920509	0.0460254
$401$	18.7650	0.937080	0.468540	−	0.883442i	$-0.344780\pi$
$401$	18.7650	0.937080	0.468540	+	0.883442i	$0.344780\pi$
$402$	35.2040	1.75582
$403$	−0.301135	−0.0150006
$404$	−7.43694	−0.370002
$405$	29.7858	1.48007
$406$	0	0
$407$	−20.8530	−1.03364
$408$	−64.1569	−3.17624
$409$	−29.6476	−1.46598	−0.732989	−	0.680241i	$-0.761875\pi$
$409$	−29.6476	−1.46598	−0.732989	+	0.680241i	$0.761875\pi$
$410$	0.846852	0.0418230
$411$	44.1035	2.17547
$412$	10.3682	0.510807
$413$	0	0
$414$	−34.6603	−1.70346
$415$	−3.20417	−0.157286
$416$	−14.0117	−0.686982
$417$	−17.2175	−0.843144
$418$	4.22519	0.206661
$419$	8.62323	0.421273	0.210636	−	0.977564i	$-0.432446\pi$
$419$	8.62323	0.421273	0.210636	+	0.977564i	$0.432446\pi$
$420$	0	0
$421$	11.6599	0.568267	0.284134	−	0.958785i	$-0.408294\pi$
$421$	11.6599	0.568267	0.284134	+	0.958785i	$0.408294\pi$
$422$	−24.5078	−1.19302
$423$	−38.1638	−1.85559
$424$	6.45095	0.313286
$425$	27.6472	1.34108
$426$	−29.3619	−1.42259
$427$	0	0
$428$	12.4752	0.603012
$429$	45.8549	2.21390
$430$	−1.39314	−0.0671832
$431$	−28.5212	−1.37382	−0.686910	−	0.726743i	$-0.741033\pi$
$431$	−28.5212	−1.37382	−0.686910	+	0.726743i	$0.741033\pi$
$432$	−3.75735	−0.180776
$433$	6.13071	0.294623	0.147312	−	0.989090i	$-0.452938\pi$
$433$	6.13071	0.294623	0.147312	+	0.989090i	$0.452938\pi$
$434$	0	0
$435$	10.2506	0.491476
$436$	3.85123	0.184440
$437$	−4.08712	−0.195514
$438$	−11.1493	−0.532735
$439$	−23.3280	−1.11338	−0.556692	−	0.830719i	$-0.687930\pi$
$439$	−23.3280	−1.11338	−0.556692	+	0.830719i	$0.687930\pi$
$440$	14.7303	0.702239
$441$	0	0
$442$	15.2966	0.727584
$443$	−22.2285	−1.05611	−0.528053	−	0.849211i	$-0.677078\pi$
$443$	−22.2285	−1.05611	−0.528053	+	0.849211i	$0.677078\pi$
$444$	15.0548	0.714469
$445$	13.3639	0.633507
$446$	−7.88981	−0.373593
$447$	12.2227	0.578112
$448$	0	0
$449$	−11.6146	−0.548126	−0.274063	−	0.961712i	$-0.588368\pi$
$449$	−11.6146	−0.548126	−0.274063	+	0.961712i	$0.588368\pi$
$450$	29.9533	1.41201
$451$	−5.46037	−0.257119
$452$	−4.98507	−0.234478
$453$	47.4395	2.22890
$454$	13.2573	0.622195
$455$	0	0
$456$	−8.19639	−0.383831
$457$	−3.42393	−0.160165	−0.0800823	−	0.996788i	$-0.525518\pi$
$457$	−3.42393	−0.160165	−0.0800823	+	0.996788i	$0.525518\pi$
$458$	−4.78685	−0.223675
$459$	−112.851	−5.26742
$460$	−5.30290	−0.247249
$461$	−9.15435	−0.426360	−0.213180	−	0.977013i	$-0.568382\pi$
$461$	−9.15435	−0.426360	−0.213180	+	0.977013i	$0.568382\pi$
$462$	0	0
$463$	4.14841	0.192793	0.0963965	−	0.995343i	$-0.469268\pi$
$463$	4.14841	0.192793	0.0963965	+	0.995343i	$0.469268\pi$
$464$	−0.734086	−0.0340791
$465$	−0.372048	−0.0172533
$466$	3.99405	0.185021
$467$	3.34964	0.155003	0.0775014	−	0.996992i	$-0.475306\pi$
$467$	3.34964	0.155003	0.0775014	+	0.996992i	$0.475306\pi$
$468$	−24.1227	−1.11507
$469$	0	0
$470$	4.01138	0.185031
$471$	−30.0910	−1.38652
$472$	−12.7832	−0.588396
$473$	8.98275	0.413027
$474$	8.44131	0.387722
$475$	3.53207	0.162063
$476$	0	0
$477$	18.0788	0.827772
$478$	0.618952	0.0283102
$479$	2.03920	0.0931733	0.0465866	−	0.998914i	$-0.485166\pi$
$479$	2.03920	0.0931733	0.0465866	+	0.998914i	$0.485166\pi$
$480$	−17.3113	−0.790149
$481$	−9.64483	−0.439766
$482$	8.00306	0.364529
$483$	0	0
$484$	−22.3065	−1.01393
$485$	7.88737	0.358147
$486$	−49.7303	−2.25581
$487$	26.9204	1.21988	0.609941	−	0.792447i	$-0.291193\pi$
$487$	26.9204	1.21988	0.609941	+	0.792447i	$0.291193\pi$
$488$	−34.3848	−1.55653
$489$	−29.5697	−1.33719
$490$	0	0
$491$	−29.1260	−1.31444	−0.657218	−	0.753700i	$-0.728267\pi$
$491$	−29.1260	−1.31444	−0.657218	+	0.753700i	$0.728267\pi$
$492$	3.94211	0.177724
$493$	−22.0480	−0.992993
$494$	1.95422	0.0879244
$495$	41.2817	1.85547
$496$	0.0266439	0.00119635
$497$	0	0
$498$	10.2470	0.459180
$499$	−19.9991	−0.895283	−0.447642	−	0.894213i	$-0.647736\pi$
$499$	−19.9991	−0.895283	−0.447642	+	0.894213i	$0.647736\pi$
$500$	10.1450	0.453700
$501$	−24.8158	−1.10869
$502$	3.09497	0.138135
$503$	−41.5151	−1.85107	−0.925534	−	0.378663i	$-0.876384\pi$
$503$	−41.5151	−1.85107	−0.925534	+	0.378663i	$0.876384\pi$
$504$	0	0
$505$	5.88643	0.261943
$506$	−23.4903	−1.04427
$507$	−22.0188	−0.977888
$508$	−7.55019	−0.334985
$509$	−29.0128	−1.28597	−0.642985	−	0.765879i	$-0.722304\pi$
$509$	−29.0128	−1.28597	−0.642985	+	0.765879i	$0.722304\pi$
$510$	18.8987	0.836848
$511$	0	0
$512$	2.52453	0.111570
$513$	−14.4173	−0.636539
$514$	13.7451	0.606272
$515$	−8.20659	−0.361625
$516$	−6.48509	−0.285490
$517$	−25.8647	−1.13753
$518$	0	0
$519$	49.9466	2.19241
$520$	6.81299	0.298769
$521$	−11.3478	−0.497155	−0.248578	−	0.968612i	$-0.579963\pi$
$521$	−11.3478	−0.497155	−0.248578	+	0.968612i	$0.579963\pi$
$522$	−23.8871	−1.04551
$523$	25.2211	1.10284	0.551420	−	0.834227i	$-0.314086\pi$
$523$	25.2211	1.10284	0.551420	+	0.834227i	$0.314086\pi$
$524$	7.71432	0.337002
$525$	0	0
$526$	11.0771	0.482984
$527$	0.800242	0.0348591
$528$	−4.05717	−0.176566
$529$	−0.277306	−0.0120568
$530$	−1.90026	−0.0825418
$531$	−35.8251	−1.55468
$532$	0	0
$533$	−2.52551	−0.109392
$534$	−42.7380	−1.84945
$535$	−9.87427	−0.426902
$536$	−33.7255	−1.45672
$537$	−59.5851	−2.57129
$538$	11.5788	0.499197
$539$	0	0
$540$	−18.7059	−0.804975
$541$	−35.2542	−1.51570	−0.757848	−	0.652431i	$-0.773749\pi$
$541$	−35.2542	−1.51570	−0.757848	+	0.652431i	$0.773749\pi$
$542$	16.2191	0.696672
$543$	82.9891	3.56140
$544$	37.2351	1.59644
$545$	−3.04829	−0.130574
$546$	0	0
$547$	31.7557	1.35778	0.678889	−	0.734241i	$-0.262462\pi$
$547$	31.7557	1.35778	0.678889	+	0.734241i	$0.262462\pi$
$548$	−15.7243	−0.671708
$549$	−96.3636	−4.11270
$550$	20.3002	0.865605
$551$	−2.81675	−0.119998
$552$	45.5685	1.93952
$553$	0	0
$554$	0.753332	0.0320060
$555$	−11.9161	−0.505808
$556$	6.13857	0.260333
$557$	34.4676	1.46044	0.730219	−	0.683213i	$-0.239418\pi$
$557$	34.4676	1.46044	0.730219	+	0.683213i	$0.239418\pi$
$558$	0.866992	0.0367027
$559$	4.15466	0.175723
$560$	0	0
$561$	−121.856	−5.14476
$562$	−5.38512	−0.227158
$563$	−12.2696	−0.517103	−0.258552	−	0.965997i	$-0.583245\pi$
$563$	−12.2696	−0.517103	−0.258552	+	0.965997i	$0.583245\pi$
$564$	18.6730	0.786277
$565$	3.94574	0.165999
$566$	16.6199	0.698584
$567$	0	0
$568$	28.1287	1.18025
$569$	−13.4078	−0.562083	−0.281041	−	0.959696i	$-0.590680\pi$
$569$	−13.4078	−0.562083	−0.281041	+	0.959696i	$0.590680\pi$
$570$	2.41441	0.101128
$571$	10.4275	0.436376	0.218188	−	0.975907i	$-0.429985\pi$
$571$	10.4275	0.436376	0.218188	+	0.975907i	$0.429985\pi$
$572$	−16.3487	−0.683573
$573$	54.2050	2.26445
$574$	0	0
$575$	−19.6369	−0.818914
$576$	43.9416	1.83090
$577$	−1.40263	−0.0583921	−0.0291960	−	0.999574i	$-0.509295\pi$
$577$	−1.40263	−0.0583921	−0.0291960	+	0.999574i	$0.509295\pi$
$578$	−25.3073	−1.05264
$579$	−32.4189	−1.34728
$580$	−3.65464	−0.151751
$581$	0	0
$582$	−25.2240	−1.04557
$583$	12.2525	0.507449
$584$	10.6811	0.441986
$585$	19.0934	0.789416
$586$	−16.5737	−0.684651
$587$	−40.2338	−1.66063	−0.830313	−	0.557298i	$-0.811838\pi$
$587$	−40.2338	−1.66063	−0.830313	+	0.557298i	$0.811838\pi$
$588$	0	0
$589$	0.102235	0.00421253
$590$	3.76556	0.155026
$591$	−81.2574	−3.34248
$592$	0.853360	0.0350729
$593$	−15.2417	−0.625903	−0.312952	−	0.949769i	$-0.601318\pi$
$593$	−15.2417	−0.625903	−0.312952	+	0.949769i	$0.601318\pi$
$594$	−82.8619	−3.39986
$595$	0	0
$596$	−4.35776	−0.178501
$597$	16.3947	0.670990
$598$	−10.8646	−0.444288
$599$	−2.71702	−0.111014	−0.0555071	−	0.998458i	$-0.517678\pi$
$599$	−2.71702	−0.111014	−0.0555071	+	0.998458i	$0.517678\pi$
$600$	−39.3801	−1.60769
$601$	−22.9588	−0.936511	−0.468255	−	0.883593i	$-0.655117\pi$
$601$	−22.9588	−0.936511	−0.468255	+	0.883593i	$0.655117\pi$
$602$	0	0
$603$	−94.5158	−3.84898
$604$	−16.9136	−0.688206
$605$	17.6558	0.717812
$606$	−18.8250	−0.764712
$607$	44.2606	1.79648	0.898241	−	0.439502i	$-0.144845\pi$
$607$	44.2606	1.79648	0.898241	+	0.439502i	$0.144845\pi$
$608$	4.75698	0.192921
$609$	0	0
$610$	10.1287	0.410100
$611$	−11.9628	−0.483965
$612$	64.1043	2.59126
$613$	21.0919	0.851894	0.425947	−	0.904748i	$-0.359941\pi$
$613$	21.0919	0.851894	0.425947	+	0.904748i	$0.359941\pi$
$614$	15.2301	0.614635
$615$	−3.12023	−0.125820
$616$	0	0
$617$	−22.5480	−0.907750	−0.453875	−	0.891065i	$-0.649959\pi$
$617$	−22.5480	−0.907750	−0.453875	+	0.891065i	$0.649959\pi$
$618$	26.2449	1.05573
$619$	33.7969	1.35841	0.679205	−	0.733948i	$-0.262325\pi$
$619$	33.7969	1.35841	0.679205	+	0.733948i	$0.262325\pi$
$620$	0.132647	0.00532721
$621$	80.1541	3.21647
$622$	9.43424	0.378279
$623$	0	0
$624$	−1.87651	−0.0751203
$625$	12.5675	0.502699
$626$	−5.65790	−0.226135
$627$	−15.5677	−0.621715
$628$	10.7284	0.428108
$629$	25.6304	1.02195
$630$	0	0
$631$	34.1027	1.35761	0.678803	−	0.734321i	$-0.262499\pi$
$631$	34.1027	1.35761	0.678803	+	0.734321i	$0.262499\pi$
$632$	−8.08679	−0.321675
$633$	90.2990	3.58906
$634$	23.6224	0.938164
$635$	5.97606	0.237153
$636$	−8.84572	−0.350756
$637$	0	0
$638$	−16.1890	−0.640929
$639$	78.8308	3.11850
$640$	5.79355	0.229010
$641$	11.0824	0.437728	0.218864	−	0.975755i	$-0.429765\pi$
$641$	11.0824	0.437728	0.218864	+	0.975755i	$0.429765\pi$
$642$	31.5782	1.24629
$643$	−33.9767	−1.33991	−0.669954	−	0.742402i	$-0.733686\pi$
$643$	−33.9767	−1.33991	−0.669954	+	0.742402i	$0.733686\pi$
$644$	0	0
$645$	5.13302	0.202113
$646$	−5.19318	−0.204323
$647$	−7.89261	−0.310291	−0.155145	−	0.987892i	$-0.549585\pi$
$647$	−7.89261	−0.310291	−0.155145	+	0.987892i	$0.549585\pi$
$648$	91.2551	3.58484
$649$	−24.2797	−0.953062
$650$	9.38918	0.368274
$651$	0	0
$652$	10.5425	0.412876
$653$	34.3369	1.34370	0.671852	−	0.740685i	$-0.265499\pi$
$653$	34.3369	1.34370	0.671852	+	0.740685i	$0.265499\pi$
$654$	9.74853	0.381198
$655$	−6.10597	−0.238580
$656$	0.223453	0.00872437
$657$	29.9337	1.16783
$658$	0	0
$659$	−23.9977	−0.934819	−0.467409	−	0.884041i	$-0.654813\pi$
$659$	−23.9977	−0.934819	−0.467409	+	0.884041i	$0.654813\pi$
$660$	−20.1986	−0.786229
$661$	9.55555	0.371668	0.185834	−	0.982581i	$-0.440501\pi$
$661$	9.55555	0.371668	0.185834	+	0.982581i	$0.440501\pi$
$662$	−6.63457	−0.257860
$663$	−56.3602	−2.18885
$664$	−9.81667	−0.380961
$665$	0	0
$666$	27.7683	1.07600
$667$	15.6600	0.606357
$668$	8.84759	0.342324
$669$	29.0700	1.12391
$670$	9.93451	0.383804
$671$	−65.3085	−2.52120
$672$	0	0
$673$	3.20764	0.123645	0.0618227	−	0.998087i	$-0.480309\pi$
$673$	3.20764	0.123645	0.0618227	+	0.998087i	$0.480309\pi$
$674$	1.42660	0.0549505
$675$	−69.2688	−2.66616
$676$	7.85038	0.301938
$677$	−1.62436	−0.0624293	−0.0312147	−	0.999513i	$-0.509938\pi$
$677$	−1.62436	−0.0624293	−0.0312147	+	0.999513i	$0.509938\pi$
$678$	−12.6186	−0.484615
$679$	0	0
$680$	−18.1050	−0.694294
$681$	−48.8465	−1.87180
$682$	0.587586	0.0224998
$683$	37.7267	1.44357	0.721786	−	0.692117i	$-0.243322\pi$
$683$	37.7267	1.44357	0.721786	+	0.692117i	$0.243322\pi$
$684$	8.18966	0.313140
$685$	12.4459	0.475535
$686$	0	0
$687$	17.6372	0.672900
$688$	−0.367598	−0.0140145
$689$	5.66699	0.215895
$690$	−13.4231	−0.511009
$691$	−38.9512	−1.48177	−0.740886	−	0.671631i	$-0.765594\pi$
$691$	−38.9512	−1.48177	−0.740886	+	0.671631i	$0.765594\pi$
$692$	−17.8075	−0.676940
$693$	0	0
$694$	−19.7493	−0.749674
$695$	−4.85875	−0.184303
$696$	31.4048	1.19040
$697$	6.71133	0.254210
$698$	4.79425	0.181465
$699$	−14.7161	−0.556613
$700$	0	0
$701$	−8.29770	−0.313400	−0.156700	−	0.987646i	$-0.550086\pi$
$701$	−8.29770	−0.313400	−0.156700	+	0.987646i	$0.550086\pi$
$702$	−38.3249	−1.44648
$703$	3.27442	0.123497
$704$	29.7805	1.12240
$705$	−14.7799	−0.556644
$706$	23.0389	0.867081
$707$	0	0
$708$	17.5287	0.658770
$709$	21.9274	0.823502	0.411751	−	0.911296i	$-0.364917\pi$
$709$	21.9274	0.823502	0.411751	+	0.911296i	$0.364917\pi$
$710$	−8.28588	−0.310963
$711$	−22.6633	−0.849939
$712$	40.9431	1.53441
$713$	−0.568385	−0.0212862
$714$	0	0
$715$	12.9402	0.483935
$716$	21.2439	0.793923
$717$	−2.28053	−0.0851679
$718$	−18.2552	−0.681278
$719$	12.1598	0.453485	0.226742	−	0.973955i	$-0.427192\pi$
$719$	12.1598	0.453485	0.226742	+	0.973955i	$0.427192\pi$
$720$	−1.68936	−0.0629586
$721$	0	0
$722$	16.4836	0.613458
$723$	−29.4873	−1.09664
$724$	−29.5882	−1.09964
$725$	−13.5333	−0.502614
$726$	−56.4639	−2.09557
$727$	−5.65386	−0.209690	−0.104845	−	0.994489i	$-0.533435\pi$
$727$	−5.65386	−0.209690	−0.104845	+	0.994489i	$0.533435\pi$
$728$	0	0
$729$	88.0044	3.25942
$730$	−3.14632	−0.116451
$731$	−11.0407	−0.408354
$732$	47.1494	1.74269
$733$	24.3253	0.898475	0.449238	−	0.893412i	$-0.351696\pi$
$733$	24.3253	0.898475	0.449238	+	0.893412i	$0.351696\pi$
$734$	−29.4582	−1.08732
$735$	0	0
$736$	−26.4468	−0.974843
$737$	−64.0561	−2.35954
$738$	7.27114	0.267654
$739$	−38.7324	−1.42480	−0.712398	−	0.701776i	$-0.752391\pi$
$739$	−38.7324	−1.42480	−0.712398	+	0.701776i	$0.752391\pi$
$740$	4.24844	0.156176
$741$	−7.20032	−0.264510
$742$	0	0
$743$	−5.26170	−0.193033	−0.0965165	−	0.995331i	$-0.530770\pi$
$743$	−5.26170	−0.193033	−0.0965165	+	0.995331i	$0.530770\pi$
$744$	−1.13985	−0.0417889
$745$	3.44921	0.126369
$746$	7.98336	0.292291
$747$	−27.5112	−1.00658
$748$	43.4454	1.58852
$749$	0	0
$750$	25.6799	0.937697
$751$	52.3230	1.90929	0.954646	−	0.297743i	$-0.0962340\pi$
$751$	52.3230	1.90929	0.954646	+	0.297743i	$0.0962340\pi$
$752$	1.05845	0.0385978
$753$	−11.4034	−0.415564
$754$	−7.48767	−0.272685
$755$	13.3873	0.487215
$756$	0	0
$757$	21.9399	0.797421	0.398710	−	0.917077i	$-0.369458\pi$
$757$	21.9399	0.797421	0.398710	+	0.917077i	$0.369458\pi$
$758$	−9.52704	−0.346038
$759$	86.5501	3.14157
$760$	−2.31301	−0.0839016
$761$	9.81830	0.355913	0.177957	−	0.984038i	$-0.443051\pi$
$761$	9.81830	0.355913	0.177957	+	0.984038i	$0.443051\pi$
$762$	−19.1116	−0.692341
$763$	0	0
$764$	−19.3258	−0.699182
$765$	−50.7393	−1.83448
$766$	22.4305	0.810447
$767$	−11.2297	−0.405483
$768$	−54.7987	−1.97738
$769$	−3.37717	−0.121784	−0.0608920	−	0.998144i	$-0.519395\pi$
$769$	−3.37717	−0.121784	−0.0608920	+	0.998144i	$0.519395\pi$
$770$	0	0
$771$	−50.6440	−1.82390
$772$	11.5583	0.415994
$773$	38.3502	1.37936	0.689681	−	0.724114i	$-0.257751\pi$
$773$	38.3502	1.37936	0.689681	+	0.724114i	$0.257751\pi$
$774$	−11.9616	−0.429951
$775$	0.491196	0.0176443
$776$	24.1647	0.867461
$777$	0	0
$778$	−6.53617	−0.234333
$779$	0.857408	0.0307198
$780$	−9.34216	−0.334503
$781$	53.4260	1.91173
$782$	28.8719	1.03246
$783$	55.2404	1.97413
$784$	0	0
$785$	−8.49162	−0.303079
$786$	19.5271	0.696508
$787$	17.2611	0.615291	0.307645	−	0.951501i	$-0.400459\pi$
$787$	17.2611	0.615291	0.307645	+	0.951501i	$0.400459\pi$
$788$	28.9708	1.03204
$789$	−40.8136	−1.45300
$790$	2.38213	0.0847522
$791$	0	0
$792$	126.475	4.49411
$793$	−30.2062	−1.07265
$794$	−31.3177	−1.11143
$795$	7.00149	0.248317
$796$	−5.84521	−0.207178
$797$	−19.8669	−0.703722	−0.351861	−	0.936052i	$-0.614451\pi$
$797$	−19.8669	−0.703722	−0.351861	+	0.936052i	$0.614451\pi$
$798$	0	0
$799$	31.7903	1.12466
$800$	22.8552	0.808054
$801$	114.743	4.05425
$802$	−16.9350	−0.597997
$803$	20.2870	0.715912
$804$	46.2453	1.63095
$805$	0	0
$806$	0.271768	0.00957262
$807$	−42.6621	−1.50178
$808$	18.0344	0.634446
$809$	−30.8800	−1.08568	−0.542842	−	0.839835i	$-0.682652\pi$
$809$	−30.8800	−1.08568	−0.542842	+	0.839835i	$0.682652\pi$
$810$	−26.8810	−0.944503
$811$	−22.6923	−0.796834	−0.398417	−	0.917204i	$-0.630440\pi$
$811$	−22.6923	−0.796834	−0.398417	+	0.917204i	$0.630440\pi$
$812$	0	0
$813$	−59.7594	−2.09586
$814$	18.8194	0.659619
$815$	−8.34452	−0.292296
$816$	4.98666	0.174568
$817$	−1.41051	−0.0493474
$818$	26.7563	0.935512
$819$	0	0
$820$	1.11246	0.0388487
$821$	30.3921	1.06069	0.530345	−	0.847782i	$-0.322062\pi$
$821$	30.3921	1.06069	0.530345	+	0.847782i	$0.322062\pi$
$822$	−39.8025	−1.38827
$823$	−51.0855	−1.78073	−0.890364	−	0.455249i	$-0.849550\pi$
$823$	−51.0855	−1.78073	−0.890364	+	0.455249i	$0.849550\pi$
$824$	−25.1427	−0.875886
$825$	−74.7962	−2.60407
$826$	0	0
$827$	−53.5924	−1.86359	−0.931794	−	0.362987i	$-0.881757\pi$
$827$	−53.5924	−1.86359	−0.931794	+	0.362987i	$0.881757\pi$
$828$	−45.5311	−1.58232
$829$	4.38093	0.152156	0.0760780	−	0.997102i	$-0.475760\pi$
$829$	4.38093	0.152156	0.0760780	+	0.997102i	$0.475760\pi$
$830$	2.89169	0.100372
$831$	−2.77565	−0.0962863
$832$	13.7740	0.477526
$833$	0	0
$834$	15.5384	0.538051
$835$	−7.00297	−0.242348
$836$	5.55038	0.191964
$837$	−2.00497	−0.0693020
$838$	−7.78229	−0.268835
$839$	5.15856	0.178093	0.0890466	−	0.996027i	$-0.471618\pi$
$839$	5.15856	0.178093	0.0890466	+	0.996027i	$0.471618\pi$
$840$	0	0
$841$	−18.2075	−0.627845
$842$	−10.5228	−0.362639
$843$	19.8415	0.683376
$844$	−32.1944	−1.10818
$845$	−6.21367	−0.213757
$846$	34.4420	1.18414
$847$	0	0
$848$	−0.501407	−0.0172184
$849$	−61.2358	−2.10161
$850$	−24.9510	−0.855812
$851$	−18.2044	−0.624039
$852$	−38.5709	−1.32142
$853$	−16.7568	−0.573744	−0.286872	−	0.957969i	$-0.592615\pi$
$853$	−16.7568	−0.573744	−0.286872	+	0.957969i	$0.592615\pi$
$854$	0	0
$855$	−6.48221	−0.221687
$856$	−30.2520	−1.03399
$857$	32.2109	1.10030	0.550152	−	0.835064i	$-0.314570\pi$
$857$	32.2109	1.10030	0.550152	+	0.835064i	$0.314570\pi$
$858$	−41.3831	−1.41280
$859$	25.0365	0.854234	0.427117	−	0.904196i	$-0.359529\pi$
$859$	25.0365	0.854234	0.427117	+	0.904196i	$0.359529\pi$
$860$	−1.83008	−0.0624053
$861$	0	0
$862$	25.7398	0.876702
$863$	5.24286	0.178469	0.0892346	−	0.996011i	$-0.471558\pi$
$863$	5.24286	0.178469	0.0892346	+	0.996011i	$0.471558\pi$
$864$	−93.2909	−3.17382
$865$	14.0948	0.479239
$866$	−5.53284	−0.188013
$867$	93.2447	3.16676
$868$	0	0
$869$	−15.3596	−0.521037
$870$	−9.25091	−0.313635
$871$	−29.6270	−1.00387
$872$	−9.33910	−0.316262
$873$	67.7216	2.29203
$874$	3.68854	0.124767
$875$	0	0
$876$	−14.6462	−0.494849
$877$	49.7732	1.68072	0.840361	−	0.542028i	$-0.182343\pi$
$877$	49.7732	1.68072	0.840361	+	0.542028i	$0.182343\pi$
$878$	21.0530	0.710505
$879$	61.0656	2.05969
$880$	−1.14493	−0.0385955
$881$	−4.99315	−0.168223	−0.0841117	−	0.996456i	$-0.526805\pi$
$881$	−4.99315	−0.168223	−0.0841117	+	0.996456i	$0.526805\pi$
$882$	0	0
$883$	−44.6535	−1.50271	−0.751354	−	0.659899i	$-0.770599\pi$
$883$	−44.6535	−1.50271	−0.751354	+	0.659899i	$0.770599\pi$
$884$	20.0942	0.675840
$885$	−13.8742	−0.466376
$886$	20.0607	0.673954
$887$	−36.4120	−1.22259	−0.611297	−	0.791401i	$-0.709352\pi$
$887$	−36.4120	−1.22259	−0.611297	+	0.791401i	$0.709352\pi$
$888$	−36.5074	−1.22511
$889$	0	0
$890$	−12.0606	−0.404272
$891$	173.325	5.80659
$892$	−10.3644	−0.347024
$893$	4.06138	0.135909
$894$	−11.0307	−0.368922
$895$	−16.8148	−0.562057
$896$	0	0
$897$	40.0308	1.33659
$898$	10.4819	0.349786
$899$	−0.391718	−0.0130645
$900$	39.3478	1.31159
$901$	−15.0596	−0.501708
$902$	4.92787	0.164080
$903$	0	0
$904$	12.0886	0.402062
$905$	23.4194	0.778487
$906$	−42.8131	−1.42237
$907$	−2.20992	−0.0733791	−0.0366896	−	0.999327i	$-0.511681\pi$
$907$	−2.20992	−0.0733791	−0.0366896	+	0.999327i	$0.511681\pi$
$908$	17.4153	0.577946
$909$	50.5413	1.67635
$910$	0	0
$911$	46.7251	1.54807	0.774035	−	0.633142i	$-0.218235\pi$
$911$	46.7251	1.54807	0.774035	+	0.633142i	$0.218235\pi$
$912$	0.637073	0.0210956
$913$	−18.6452	−0.617066
$914$	3.09002	0.102209
$915$	−37.3193	−1.23374
$916$	−6.28820	−0.207768
$917$	0	0
$918$	101.845	3.36140
$919$	24.9123	0.821780	0.410890	−	0.911685i	$-0.365218\pi$
$919$	24.9123	0.821780	0.410890	+	0.911685i	$0.365218\pi$
$920$	12.8594	0.423961
$921$	−56.1152	−1.84906
$922$	8.26161	0.272082
$923$	24.7104	0.813352
$924$	0	0
$925$	15.7322	0.517270
$926$	−3.74385	−0.123031
$927$	−70.4624	−2.31429
$928$	−18.2266	−0.598316
$929$	1.10615	0.0362915	0.0181458	−	0.999835i	$-0.494224\pi$
$929$	1.10615	0.0362915	0.0181458	+	0.999835i	$0.494224\pi$
$930$	0.335765	0.0110102
$931$	0	0
$932$	5.24673	0.171862
$933$	−34.7605	−1.13801
$934$	−3.02298	−0.0989149
$935$	−34.3875	−1.12459
$936$	58.4969	1.91203
$937$	4.28847	0.140098	0.0700491	−	0.997544i	$-0.477684\pi$
$937$	4.28847	0.140098	0.0700491	+	0.997544i	$0.477684\pi$
$938$	0	0
$939$	20.8465	0.680301
$940$	5.26950	0.171872
$941$	20.9465	0.682836	0.341418	−	0.939912i	$-0.389093\pi$
$941$	20.9465	0.682836	0.341418	+	0.939912i	$0.389093\pi$
$942$	27.1565	0.884806
$943$	−4.76683	−0.155229
$944$	0.993591	0.0323386
$945$	0	0
$946$	−8.10674	−0.263573
$947$	7.51231	0.244117	0.122059	−	0.992523i	$-0.461050\pi$
$947$	7.51231	0.244117	0.122059	+	0.992523i	$0.461050\pi$
$948$	11.0888	0.360149
$949$	9.38305	0.304587
$950$	−3.18762	−0.103420
$951$	−87.0366	−2.82236
$952$	0	0
$953$	−30.4377	−0.985974	−0.492987	−	0.870037i	$-0.664095\pi$
$953$	−30.4377	−0.985974	−0.492987	+	0.870037i	$0.664095\pi$
$954$	−16.3157	−0.528242
$955$	15.2966	0.494985
$956$	0.813079	0.0262969
$957$	59.6484	1.92816
$958$	−1.84033	−0.0594585
$959$	0	0
$960$	17.0175	0.549238
$961$	−30.9858	−0.999541
$962$	8.70426	0.280637
$963$	−84.7813	−2.73204
$964$	10.5131	0.338605
$965$	−9.14856	−0.294503
$966$	0	0
$967$	43.8093	1.40881	0.704405	−	0.709798i	$-0.251214\pi$
$967$	43.8093	1.40881	0.704405	+	0.709798i	$0.251214\pi$
$968$	54.0925	1.73860
$969$	19.1343	0.614681
$970$	−7.11818	−0.228551
$971$	−7.16246	−0.229854	−0.114927	−	0.993374i	$-0.536663\pi$
$971$	−7.16246	−0.229854	−0.114927	+	0.993374i	$0.536663\pi$
$972$	−65.3276	−2.09538
$973$	0	0
$974$	−24.2951	−0.778467
$975$	−34.5944	−1.10791
$976$	2.67260	0.0855477
$977$	42.0266	1.34455	0.672276	−	0.740301i	$-0.265317\pi$
$977$	42.0266	1.34455	0.672276	+	0.740301i	$0.265317\pi$
$978$	26.6860	0.853325
$979$	77.7648	2.48537
$980$	0	0
$981$	−26.1729	−0.835635
$982$	26.2856	0.838806
$983$	−13.2127	−0.421421	−0.210710	−	0.977549i	$-0.567578\pi$
$983$	−13.2127	−0.421421	−0.210710	+	0.977549i	$0.567578\pi$
$984$	−9.55949	−0.304745
$985$	−22.9307	−0.730633
$986$	19.8979	0.633678
$987$	0	0
$988$	2.56714	0.0816715
$989$	7.84183	0.249356
$990$	−37.2559	−1.18407
$991$	26.6369	0.846150	0.423075	−	0.906095i	$-0.360951\pi$
$991$	26.6369	0.846150	0.423075	+	0.906095i	$0.360951\pi$
$992$	0.661540	0.0210039
$993$	24.4451	0.775741
$994$	0	0
$995$	4.62656	0.146672
$996$	13.4609	0.426525
$997$	−55.5759	−1.76011	−0.880054	−	0.474874i	$-0.842494\pi$
$997$	−55.5759	−1.76011	−0.880054	+	0.474874i	$0.842494\pi$
$998$	18.0488	0.571324
$999$	−64.2158	−2.03170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.r.1.7		17
7.3	odd	6		287.2.e.d.247.11	yes	34
7.5	odd	6		287.2.e.d.165.11	✓	34
7.6	odd	2		2009.2.a.s.1.7		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.11	✓	34	7.5	odd	6
287.2.e.d.247.11	yes	34	7.3	odd	6
2009.2.a.r.1.7		17	1.1	even	1	trivial
2009.2.a.s.1.7		17	7.6	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)

\(f(q)\)	\(=\)	\(q-0.902479 q^{2} +3.32518 q^{3} -1.18553 q^{4} +0.938362 q^{5} -3.00091 q^{6} +2.87488 q^{8} +8.05685 q^{9} +O(q^{10})\)	\(q-0.902479 q^{2} +3.32518 q^{3} -1.18553 q^{4} +0.938362 q^{5} -3.00091 q^{6} +2.87488 q^{8} +8.05685 q^{9} -0.846852 q^{10} +5.46037 q^{11} -3.94211 q^{12} +2.52551 q^{13} +3.12023 q^{15} -0.223453 q^{16} -6.71133 q^{17} -7.27114 q^{18} -0.857408 q^{19} -1.11246 q^{20} -4.92787 q^{22} +4.76683 q^{23} +9.55949 q^{24} -4.11948 q^{25} -2.27922 q^{26} +16.8150 q^{27} +3.28519 q^{29} -2.81594 q^{30} -0.119237 q^{31} -5.54809 q^{32} +18.1567 q^{33} +6.05684 q^{34} -9.55165 q^{36} -3.81897 q^{37} +0.773793 q^{38} +8.39777 q^{39} +2.69767 q^{40} -1.00000 q^{41} +1.64508 q^{43} -6.47344 q^{44} +7.56024 q^{45} -4.30197 q^{46} -4.73681 q^{47} -0.743022 q^{48} +3.71774 q^{50} -22.3164 q^{51} -2.99407 q^{52} +2.24391 q^{53} -15.1752 q^{54} +5.12380 q^{55} -2.85104 q^{57} -2.96482 q^{58} -4.44654 q^{59} -3.69913 q^{60} -11.9605 q^{61} +0.107609 q^{62} +5.45394 q^{64} +2.36984 q^{65} -16.3861 q^{66} -11.7311 q^{67} +7.95649 q^{68} +15.8506 q^{69} +9.78432 q^{71} +23.1624 q^{72} +3.71532 q^{73} +3.44654 q^{74} -13.6980 q^{75} +1.01648 q^{76} -7.57881 q^{78} -2.81292 q^{79} -0.209680 q^{80} +31.7423 q^{81} +0.902479 q^{82} -3.41464 q^{83} -6.29766 q^{85} -1.48465 q^{86} +10.9239 q^{87} +15.6979 q^{88} +14.2417 q^{89} -6.82296 q^{90} -5.65123 q^{92} -0.396486 q^{93} +4.27487 q^{94} -0.804559 q^{95} -18.4484 q^{96} +8.40546 q^{97} +43.9934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 3 q^{2} - q^{3} + 25 q^{4} + q^{5} - 2 q^{6} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 17 * q + 3 * q^2 - q^3 + 25 * q^4 + q^5 - 2 * q^6 + 9 * q^8 + 26 * q^9	\( 17 q + 3 q^{2} - q^{3} + 25 q^{4} + q^{5} - 2 q^{6} + 9 q^{8} + 26 q^{9} + 2 q^{10} + 15 q^{11} - 4 q^{12} + 5 q^{13} + 24 q^{15} + 33 q^{16} - 4 q^{17} + 10 q^{18} - 5 q^{19} + 26 q^{20} + 16 q^{22} + 12 q^{23} - 16 q^{24} + 24 q^{25} - 31 q^{26} + 11 q^{27} + 14 q^{29} - 33 q^{30} + 3 q^{31} + 16 q^{32} - 4 q^{33} + 24 q^{34} + 57 q^{36} + 24 q^{37} + 45 q^{39} - 36 q^{40} - 17 q^{41} + 14 q^{43} - 9 q^{44} + 21 q^{45} + 44 q^{46} - 19 q^{47} + 60 q^{48} - 4 q^{50} + 2 q^{51} + 25 q^{52} + 4 q^{53} - 68 q^{54} - 9 q^{55} - 12 q^{57} - q^{58} + 27 q^{59} + 66 q^{60} + q^{61} + 23 q^{62} + 75 q^{64} + 22 q^{65} + 16 q^{66} + 49 q^{67} - 45 q^{68} - 12 q^{69} + 40 q^{71} - 23 q^{72} + 14 q^{73} + 33 q^{74} - 27 q^{75} + 9 q^{76} - 12 q^{78} + 61 q^{79} + 82 q^{80} + 53 q^{81} - 3 q^{82} + 18 q^{83} - 13 q^{85} - 4 q^{86} + 17 q^{87} + 74 q^{88} - 18 q^{89} + 20 q^{90} + 28 q^{92} - 36 q^{93} + 5 q^{94} + 20 q^{95} - 148 q^{96} - 26 q^{97} + 38 q^{99}+O(q^{100}) \) 17 * q + 3 * q^2 - q^3 + 25 * q^4 + q^5 - 2 * q^6 + 9 * q^8 + 26 * q^9 + 2 * q^10 + 15 * q^11 - 4 * q^12 + 5 * q^13 + 24 * q^15 + 33 * q^16 - 4 * q^17 + 10 * q^18 - 5 * q^19 + 26 * q^20 + 16 * q^22 + 12 * q^23 - 16 * q^24 + 24 * q^25 - 31 * q^26 + 11 * q^27 + 14 * q^29 - 33 * q^30 + 3 * q^31 + 16 * q^32 - 4 * q^33 + 24 * q^34 + 57 * q^36 + 24 * q^37 + 45 * q^39 - 36 * q^40 - 17 * q^41 + 14 * q^43 - 9 * q^44 + 21 * q^45 + 44 * q^46 - 19 * q^47 + 60 * q^48 - 4 * q^50 + 2 * q^51 + 25 * q^52 + 4 * q^53 - 68 * q^54 - 9 * q^55 - 12 * q^57 - q^58 + 27 * q^59 + 66 * q^60 + q^61 + 23 * q^62 + 75 * q^64 + 22 * q^65 + 16 * q^66 + 49 * q^67 - 45 * q^68 - 12 * q^69 + 40 * q^71 - 23 * q^72 + 14 * q^73 + 33 * q^74 - 27 * q^75 + 9 * q^76 - 12 * q^78 + 61 * q^79 + 82 * q^80 + 53 * q^81 - 3 * q^82 + 18 * q^83 - 13 * q^85 - 4 * q^86 + 17 * q^87 + 74 * q^88 - 18 * q^89 + 20 * q^90 + 28 * q^92 - 36 * q^93 + 5 * q^94 + 20 * q^95 - 148 * q^96 - 26 * q^97 + 38 * q^99

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